diff --git a/.coveragerc b/.coveragerc index dff79e56d..0ba728323 100644 --- a/.coveragerc +++ b/.coveragerc @@ -1,4 +1,5 @@ [report] +omit = *tests*, setup.py exclude_lines = pragma: no cover def __repr__ diff --git a/.travis.yml b/.travis.yml index 65d3c9578..3193bd0c7 100644 --- a/.travis.yml +++ b/.travis.yml @@ -13,7 +13,7 @@ install: - python setup.py install script: - - pytest -W ignore::UserWarning --durations=5 --cov=./ -d --tx 3*popen//python=python3.6 --pyargs tests + - pytest -W ignore::UserWarning --durations=5 --cov=./gpflow -d --tx 3*popen//python=python3.6 --pyargs ./tests - codecov --token=2ae2a756-f39c-467c-bd9c-4bdb3dc439c8 cache: diff --git a/doc/source/notebooks/multiclass.ipynb b/doc/source/notebooks/multiclass.ipynb index c700a536b..622969118 100644 --- a/doc/source/notebooks/multiclass.ipynb +++ b/doc/source/notebooks/multiclass.ipynb @@ -21,7 +21,7 @@ "import tensorflow as tf\n", "import matplotlib\n", "import numpy as np\n", - "import matplotlib.pyplot as plt \n", + "import matplotlib.pyplot as plt\n", "plt.style.use('ggplot')\n", "%matplotlib inline" ] @@ -74,6 +74,14 @@ "execution_count": 4, "metadata": {}, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Conditional: Inducing Feature - Kernel\n", + "base conditional\n" + ] + }, { "data": { "text/html": [ @@ -120,10 +128,10 @@ " Parameter\n", " None\n", " +ve\n", - " True\n", + " False\n", " ()\n", " True\n", - " 1.0\n", + " 0.01\n", " \n", " \n", " SVGP/kern/kernels/0/variance\n", @@ -140,10 +148,10 @@ " Parameter\n", " None\n", " +ve\n", - " False\n", + " True\n", " ()\n", " True\n", - " 0.01\n", + " 1.0\n", " \n", " \n", " SVGP/likelihood/invlink/epsilon\n", @@ -156,24 +164,24 @@ " 0.001\n", " \n", " \n", - " SVGP/q_mu\n", + " SVGP/q_sqrt\n", " Parameter\n", " None\n", - " (none)\n", + " +ve\n", " True\n", " (20, 3)\n", " True\n", - " [[0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, ...\n", + " [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, ...\n", " \n", " \n", - " SVGP/q_sqrt\n", + " SVGP/q_mu\n", " Parameter\n", " None\n", - " +ve\n", + " (none)\n", " True\n", " (20, 3)\n", " True\n", - " [[1.0, 1.0, 1.0], [1.0, 1.0, 1.0], [1.0, 1.0, ...\n", + " [[0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, ...\n", " \n", " \n", "\n", @@ -267,10 +275,6 @@ " a3.set_xticks([])\n", " a3.set_yticks([])\n", " \n", - " \n", - " a3.set_xticks([])\n", - " a3.set_yticks([])\n", - " \n", " for i in range(m.likelihood.num_classes):\n", " x = m.X.read_value()[m.Y.read_value().flatten()==i]\n", " points, = a3.plot(x, x*0, '.')\n", @@ -290,6 +294,16 @@ "execution_count": 7, "metadata": {}, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Conditional: Inducing Feature - Kernel\n", + "base conditional\n", + "Conditional: Inducing Feature - Kernel\n", + "base conditional\n" + ] + }, { "data": { "image/png": "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\n", @@ -680,7 +694,7 @@ " Parameter\n", " None\n", " +ve\n", - " True\n", + " False\n", " ()\n", " True\n", " 0.1076942498850328\n", @@ -878,6 +892,16 @@ "execution_count": 16, "metadata": {}, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Conditional: Inducing Feature - Kernel\n", + "base conditional\n", + "Conditional: Inducing Feature - Kernel\n", + "base conditional\n" + ] + }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAzEAAAGnCAYAAACHNtn3AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAIABJREFUeJzs3Xd03Nl93/33nUHvnQBIAuxlyS3cIu2uilXWkVwkWbbDWFEcx08iPec8iR0/x04cJ/GJc2yn2EkeOe0kcmI7diRHUCR7JSuyiler9fZdLpfLNiRI9F4HvQzmd58/vhhgAAwaUYghP689ewjM/Ob3u/Ob3wzud+79fq/z3iMiIiIiIpIuQne7ASIiIiIiIpuhIEZERERERNKKghgREREREUkrCmJERERERCStKIgREREREZG0oiBGRERERETSioIYERERERFJKwpiREREREQkrSiIERERERGRtJJxl47r79JxRURERERkb3PrbXC3ghi6urru1qFFRERERGQPqq2t3dB2mk4mIiIiIiJpRUGMiIiIiIikFQUxIiIiIiKSVhTEiIiIiIhIWlEQIyIiIiIiaUVBjIiIiIiIpBUFMSIiIiIiklYUxIiIiIiISFpRECMiIiIiImlFQYyIiIiIiKQVBTEiIiIiIpJWFMSIiIiIiEhaURAjIiIiIiJpRUGMiIiIiIikFQUxIiIiIiKSVhTEiIiIiIhIWlEQIyIiIiIiaUVBjIiIiIiIpJXwr/3ar92N4/7a2NjY3TjuEkMDc3S0zDI2Gqe/Zw7nIDdv7bhuaGCOxqvT9HbHyMxyS7ZP7G+1/Wz0/s20Z7Mi/VM83zxKyDkq8jPXva19ZJbv3IryZuc4hdnhhfvX2+dmjp+4/ctXBvnO7ShXeicXjvWtxih/9HY/s3HPsfKcDT3H5ed5vfO+1mO3sv/NHHerbdoMfzuCf/V7EArD8MDCz66sYs1tE/cvvy3VNqs9NtW+fXcH/urFVbfbynP03R0EL3wbLr8B+YXbtv87bVPwjYZV27L8fAUvfIvgq3+I72rDX3gZ/+J38G+8ADevLHn8eud5rfbs1PnfzPHv9Lh38vjlz3krz32jx/e3I/j/00Bw6Q1cQeGq77mdeD1SvleT2rJbr3fiWiY2i6s/lrJta7V5+fum5fYMkXemGRmZY2Qofkef9ck2+pm22f0F3/8W/it/gI8OEXrgkU3v506Pu9HP860+z80ef6dE+qf4/Bu9PHt9CA8cK89Zt1+S6HMs79ss73Nspn+TvO+tPGZgcm7VftJafbW3uyc2dcyttHenFRYWAvzz9bZz3vudb81Kvqur624cd8HQwByvPD9OEF+8LRSGpz5QQFlFxqqPefl74/hgfvsQPPVB2z55f6n2s5n7N9qezYr0T/Grf9HGXNyTEXb8+ofrAFa9LRb3JF8dGSH4zWfqOVWZu+Y+k+9f7/inKnOJ9E/xT77bylyw9FgfP1nGV68PLdz2/7yrmo8cL1nzOS4/z2fO5XL14tSq532tx6badqP738i+NmK79pPgb0cI/u0/hbk5u4Cdg3gcMjII/eJv4I6eSr3t/P3AktvcT30G/79+d8k27uiplI9Nue9YDPDWjozMFdtt6Tkm9p2QkUnol35zy/u/4zb99j+G+FzKtiw/X3z4Y/DnX1l9h/OPB9Y8z2u2Z4fO/0asd33sxONXXhdu8d/MzT33jR7f344Q/Jt/AnMxuyEUtvfdsvfc4v5i4O+sTeu10f3UZ/B//PnFtoQzCP2Df7Hjr3fwwrfwf/SfFn53P/13cfvrU56/lG3+4n9d8r5p/5l/x+XW4iXH2OxnfbKUx0zxmbZRi9fZ7NI7PvoThH/iZza8n83a8GfuNj3PzR5/p0T6p/jH32klnvRR/+Ony/izm8Or9kuW9zkyQ47feKaO1ugM//n1ng3vZ7X2bLRPlOoxoRA4HPFgZT9pvb6aAzI3eMyttHc31NbWgj2lNd2308kG++aWBAwAQWC3r/UYH6TePnl/qfazmfs32p7NutI7yVzcEwBzgedK7+Saty0Pb+OB7WO9fW7m+Inb48HSbeMBvNK+dLTu5bb1R++Wn+ee9tia532tx6badqP738i+NmK79pPgb1y2PzI+gCA+32kKID5n96227fz9K2678NKKbVZ7bMp9J64y71Nut6XnuPwKntue/d9xm+JJb/BlbVl+vnjr5bV3OLfK67HB57eT539Tx99ku7fy+JXXRdK/m2zDRo9v28UWb1jlPbe4vztv07ptvPDSirbsxuvtL7y04vfVzl/KNi9733R3xFhus5/1S9qzwc+0DT/fhetsmfXe01u04c/cbXqemz3+TrnSO7kkgAHrO6zVL1ne50hss7yPsd5+VmvPVh4TDyAWpO4nrddX85s45lbau5fct0FMeVUGofDS20Ihu32tx7hQ6u0X9udS72fD92+iPZt1dl8eGWFHyEFGyHF2X96aty0PgcMh28d6+9zM8RO3h5ddieEQPHWwcMltT9ct/T2V5ee5+mDmmud9rcem2naj+9/IvjZiu/aT4E4+aN/0h0L2dWVGpv0czrD7Vtt2/v4Vtz32nhXbrPbYlPt281eZcym329JzdMuu4Izt2f8dtymc9AZf1pbl54tHn157hxmrvB4bfH47ef43dfxNtnsrj0/5nBP/brINGz2+bZc0PWOV99xOvB6p36tL27Ibr7d77D0rfl/t/KVs87L3Tc2BldNdNvtZv6Q9G/xM2/DzTexvufXe01u04c/cbXqemz3+Tjm7L4/wso/6pw4WrtkvWd7nSGyzvI+x3n5Wa89WHhMO2chQqn7Sen01x8aPuZX27iX37XQysKk6g31zZGY7YjOe8qqMdYefhwbm6GieBQcHDmWtmBI22De36n42ev9m2rNZkf4prvROcnZf3sKQ4Vq3FWaHaRqaBuCDR4pTDjOmevxmjp+4/XtNIwxPz1Gak7FwrG81Rnm5bYyn6wrXnUqWsPw8r3fe13rsVva/meNutU2b4W9H8DcuL/yRSfy82nSY5fcvvy3VNqs9NtW+KSiC8dFVt9vKc6SgCN96G+fAPfWhuzKVLLlNwcvPrdqW5ecreOFb9m1p3VGYnIDRKOBxxaVLHr/eeV6rPTt1/jdz/Ds97p08fvlz3spz3+jx/e0I/pXn8B5CT3/Iblvj/bKdr0fK92pSW3br9U5cy+6x9xB6/0dStm2tNi9/37TcnqGnPUZhaYiszNAdfdYn2+hn2mb357vaofkGPPr0jk4lW37cjX6eb/V5bvb4OyXSP8VXrw4yNDXHDx4r4SPHS9btlyT6HLC0b7O8z7GZ/k3yvrfyGGDVftJafbWxmfimjrmV9u60jU4nu6+DGBERERER2TuUEyMiIiIiIvckBTEiIiIiIpJWFMSIiIiIiEhaURAjIiIiIiJpRUGMiIiIiIikFQUxIiIiIiKSVhTEiIiIiIhIWlEQIyIiIiIiaUVBjIiIiIiIpBUFMSIiIiIiklYUxIiIiIiISFpRECMiIiIiImlFQYyIiIiIiKQVBTEiIiIiIpJWFMSIiIiIiEhaURAjIiIiIiJpRUGMiIiIiIikFee9vxvHvSsHFRERERGRPc+tt0HGbrQihXUbJiIiIiIikoqmk4mIiIiISFpRECMiIiIiImlFQYyIiIiIiKQVBTEiIiIiIpJWFMSIiIiIiEhaURAjIiIiIiJpRUGMiIiIiIikFQUxIiIiIiKSVhTEiIiIiIhIWlEQIyIiIiIiaUVBjIiIiIiIpBUFMSIiIiIiklYUxIiIiIiISFpRECMiIiIiImlFQYyIiIiIiKQVBTEiIiIiIpJWFMSIiIiIiEhaURAjIiIiIiJpRUGMiIiIiIikFQUxIiIiIiKSVjK2Yyfnz5//PeBHgb6GhoazG3iI347jioiIiIjIPcett8G2BDHAHwD/EfjDjT6gq6trmw4tIiIiIiL3gtra2g1tty3TyRoaGl4AhrZjXyIiIiIiImvZrpGYdZ0/f/6zwGcBGhoaqKio2K1Dr+n3/9OtHd3/Ux+GU6eO7egxdlokEuGfvzJI2+juzQIsz4Gv/d/v3bXj3Y96IxH4lb+NZneKiMid2vcnL9/V43/8v77I4PRdbcI94aW/n359Luf99nRgzp8/fwj4s43mxNyr08me+/MoEyNrb3P8YTh1qmR3GrRBn/hCZMv7KArBjz0EP3Hm1B09/itXI/zh26nve6oG/tGH7my/AvHf+CVovbn+hg8/Rfjv/crON0juOfFvfAVefx4G+2BmageP5KCgEGoPw8c+TfiUPhdEdlP8t38Vbl5a9f7w735tx9uQqr+QDTR8Wp8HmxGJRPjcdfv5v3xy75y7+elk6+bEKIjZJZFIlMYU7/n8YvjQR+9OQJMqcHl2j30A/KvnIrzSvfS2vdbGvSj+z34OulpT3OMI/+6zu94eERG5d8UjEfi3/3DJbTsRzCwPXtQfuDcpiNnjLr0Zpe320ts+9td2J5j59BcjjM+/7CdK4Ld/JD0+BP7BNyLcjC7+/guPwQf1LeyC+Gc+vvJGjayIiMguWj7yv13BzE99IUJijFfBy71tV4OY8+fP/zHwAaAC6AX+WUNDw39f4yH3fRCT7Otfii75fSeDmeTRl3T+EEh+Hv/6MTh1nwYzqQKX3RjKFxERWUvyjICt/l1K/M0PA19N476LbMyuj8RskoKYFN54OUpPu/283XkzkUiEX75gP6dz8JIs+TnBvfO81pNqPrICFxER2WuSp5nd6d+pRADzUAX8+kfuj7/z9zsFMWkseWRmO0ZlvheJ8Ll7LIBJlvz84N58jpBi1OUXf0tJzSIisucl/n5tNpBJBDD384yL+5GCmDT3zT+JMjdrP28lkPkPL0b47nx+973auU/4yS9EiM3//DcfufMqaXtJ/PXn4Hc/t3hDcSnhf/M/7l6DRERE7sBmA5lEHuwz9fBz703/v+eycQpi7gEvfDfKyKD9fCeBzL04hWwj7oW8n/gv/QyMDC/eoFEXERFJY/Ev/j5870/gg58k/Nd/dt3tE3/L0/XvuNw5BTH3iK9/OQoBEIKP/dXNBTL38wdA8hSzdEoEXD5lTLkuIiJyr9joaMz93H8RBTH3lESOTHE5vP+ZjQUy+gAwP/aFyMJ69Hu5JPOS4CU7l/B//NLda4yIiMgOWS+QUf9FNhrEhHa+KbJVialkiall69EHwKI//fSphfPwuQupF/i8m+Kf+fhiAPPkM4R/92sKYERE5N71wU8C8zmfq3iqZrcaI+lMIzFpJDEis1Z+jAKY1SWv9Hs3p5itWNn4M79A+F0fuittERER2W2rjcaoDyOgkZh7UiJ4Wb44ZkLizf8Lj+1ak9LKT5yxURkHxLHz9b3I7o3MxF9/zj64EwHML/6WjbwogBERkftIIniJJ/0NjkTUh5HN0UhMmkksiJlfDB/66OKITKKUclEI/uhT+gZjI3aritnyMslK1hcRkfvd8tEYjcJIgkZi7lFPPG2By8TI0tsTa8EogNm4Zz99in89/43PJ74Q2fZ8mXgkYh/S8wFM+He/pgBGREQE4Bd/C7C/lV+5qgBGNk8jMWkqOT9G315sXfKioLC1c7k850WBi4iIyEqJ0Zgf/4AFNOrHCKjE8n3h61+KMjs3yx8ypDf+NvnpP44wGtjP2UDDJs7rioR9LVApIiKyqngkwq996UXeOfZe9WNkwUaDmIydb4rslO/Tw/vD+/ib677MslGJ6Xif+EKEmfl/HVaqeTUKXkRERDYvfOoU7xwJIBa7202RNKQgJk1FIhEa5+BdTJObUX23m3PPSXwj9In5xTJXm7K3ZJFKBS8iIiIb9h9ejEDI8dUX/gnxJ/U3VDZH08nSVHKneiPrx8jW/PgXIsSTfv/q8xp5ERER2YpEXybxN1U5pALKibmnpRoVUCCzO3763/8Fo6U14BzMzfHs33rwbjdJREQk7SQWoH7206cWp2Vr8WdBJZbvWZ/+YurFoI4/bP+uthCmbE38Mx8n/pmP8weXf4evRn6HhyodZGYulGb+/dd3b9FMERGRdPeHby/+vDCbIWlNNZH1aCQmjUQiEX75gv2cqorHd78RZWp85UKYcufiP//XYWrcfglnEv4vX1mxzfL1ZVRhRUREZHXfi0T43IVV8kxPPEz4H/z6XWqZ7AWqTnYPWiuAAXjmR0r4+peiTIxAJBLl1CkFMncq/tu/CjcvLfy+1jzd5CIAyf/+68fglHJlRERElvjchTXuTPrbK7IWjcSkic0saKn8mDsX/8ZX4E//x8Lvd5JkuHzhTNDojIiICCyux7ba38X4Zz4OmdmE//OXd7llsldoJOYekvzN/kZ87K/ZiMzXvxRVILNBy9d62UqFlJ977yl+7r328/LRmWfq7X4REZH7UWJB6VW5MMRmiEciqvwpa9JIzB6X6Pz+zUfgJ85s7s2sEZmNSV7rZafKOybnMyVoupmIiNxPNjqrJPF3WSWX708qsXwPSLzZH6qAX//InXV2Fcis7m4tVPmr34rwzsDS2xTQiIjIvSwxjWyjf+8UyNy/FMSkuUQAUxSCP/rUnXduI5EojfM5cgpkTPwzHyfCKZre/XOQlwXh7HUfU1wOVQfY9mIJf+d/R+ifWXqbAhoREbnXbCa3FyD++nNWcln5MfcdBTFpKnna0YkS+O0f2Z7O7P02IvPGy1F62pfdmHytew+hnVsmKbfAqsVtxqe/GGF82dtxO68BERGR3bbe8hBriX/mE4CHqhrCv/lft79xsicpiElDyeuN7EQ1q0Qgc/zh7R9RuNvWWuTzwPf/Cw/FXrZfHn6K8N/7lW09dvJo12as9Tr8/usR/rRx5e2qciYiIuni578WoXXMfr7Tv1+7kbcqe4uCmDSSHLxkAw072FFN7uyn86jMaoHD8Yfg1OmSFdXGqD9B+J/+m91rYAprBVrLLR/JWb6gZoKCGhER2Yu284vZ+C//bRjqBxTI3A92NYg5f/78R4HfAcLAf2toaPhX6zzkvg9ilndKd3Pa0PIAIF2CmUtvRmm7vfL25PbH/9+/AeOji3f+2M8Q/pGf2IXWbc3mRnMm+G9zYynv+bHj8LPvUmAjIiJ3R3L/pr4Q/v3Ht+dv0pJ13J58hvDf/vlt2a/sPbsWxJw/fz4M3AR+EOgA3gA+1dDQcG2Nh913Qcxe/Cb9m38SZW525e11R+Hhx/dGYJNq9KK8Gp7+gaTA5Zd+BkaGl2xzr31T88J3o4wMrnavJwg83tv/MWL8GSOMJG2hYgEiIrJTlvdxtlqUaC1LKovuwBRxuft2M4h5Cvi1hoaGj8z//isADQ0N/3KNh91TQcxXrkb40tsws/6mPFUD/+hDe68zmTIRfqtCcPzBtfNvNjoCcfxhOP5Hvwx93atvtItlkveS1c5hqvd24rZEwJP4L06cOeYYYoLXQvB/nYMP3ofnUu7M1/80wsAM9AFFQCaOzHgmYR8mRAg3/18IK6aR+D3xcyoev+Jnj8dn+IXf8/FAweKDQpCRAZlZkJUNGZmQnw/Z85vca7mAIrslEonwry7B8Nza2/3CY7v3t2NJMJOs/gT85N+5L/sDGxH/7/8eLr4EM1NLbt9LX/7uZhDzk8BHGxoa/s787z8NvLuhoeHvLdvus8BnARoaGh6bnU0xBHAXvOf/ewHcuudpbcurXnkPMzP8izf+OffiWygCtJ/5h8SKDluPIRSyc5g4j8vP51rnd/m5CwIyB27wg1d/a/2G/MvfY58+pDYsErnFhRdhdgZixAjF5zuUy16f5b+LrOcu5VZuiq5rkW3mVv8SYtelwWfQnhaP87N/f+/0p7KysmADQUzGzjfFNDQ0fB74/PyvfmBgYK3Nd82zP/3Azu38s3snqt1OZ+b/3zmVwHs3tOVeuY7SQUVFCR/5sbvdChEREdlr9lJ/an4kZl3bsVBGJ3Aw6fcD87eJiIiIiIhsu+0YiXkDOH7+/PnDWPDyU8Bf34b9ioiIiIiIrLBdJZZ/GPgcVmL59xoaGn5znYdo8qKIiIiIiKSyZxe7FBERERERuSPbkRMjIiIiIiKyaxTEiIiIiIhIWlEQIyIiIiIiaUVBjIiIiIiIpBUFMSIiIiIiklYUxIiIiIiISFpRECMiIiIiImlFQYyIiIiIiKQVBTEiIiIiIpJWFMSIiIiIiEhaURAjIiIiIiJpRUGMiIiIiIikFQUxIiIiIiKSVhTEiIiIiIhIWlEQIyIiIiIiaUVBjIiIiIiIpBUFMSIiIiIiklYUxIiIiIiISFpRECMiIiIiImlFQYyIiIiIiKSVjLt0XH+XjisiIiIiInubW2+DuxXE0NXVdbcOvURFRQUDAwN3uxmShnTtyJ3StSN3SteO3CldO3Kndvvaqa2t3dB2mk4mIiIiIiJpRUGMiIiIiIikFQUxIiIiIiKSVhTEiIiIiIhIWlEQIyIiIiIiaUVBjIiIiIiIpBUFMSIiIiIiklYUxIiIiIiISFpRECMiIiIiImlFQYyIiGwbf/3S3W6CiIjcBxTEiIjItvCD/ZCZiR8ZvttNERGRe5yCGBER2R6jUdyxB6C/+263RERE7nEKYkREZHtV1eB7u+52K0RE5B6mIEZERLbMT09BVjYArqgUxqJ47+9yq0RE5F6lIEZEUvLRobvdBEknPR1Qe3DhV3/gCP77f46Px+9io0RE5F6lIEZEVvBTk6oyJZvjwTlnP46N4NpuQVklvrcj9eadrfjO1t1soYiI3EMUxIgIAD5I+sa8rwt38JBNEQL8YB9+Znpj+9nDU4h8R/PdbsI9yQcBuPmfO5phbAR34izu9MPQtso5n52Bqck9fb2IiMjepSBGRPBjI/DOm/jhQbsh8LD/EHS3W3ATHYLOViuhu9Z+Jsbg2tv42xF8dHDnG74JvvU2jI4sDdZke3R3QM1Bu35y8nC1dQC4zEyIz63YfCFwqT8Kbbd3s6UiInKPUBAjcp/zE2PQ34N75N0w2Ltwe2JqEC234NBx3JGTEI/h25pW31lnG+7MOdzRUxCP429dx0+OLx6rpRHf0bJr37777g584zWC3m7IzYUTZ6CjZVeOfV+ZncFl58BgH65i39L7QuGVeTFd7VBbh8vMgrm5Fff7iTF8n6qbiYjI6hTEiNzH/OQE9HRagAJw4PCSIMVn5+Knp3DhMACuqhbKK/G3rq/cV9ttqDu88Lsrr8IdO20dVrBv6QuKoLIGWhrxTTfwU5M7+OyAqQn8gUPQeAXicVxGJsytHBmQrfOD/VBWufKOqhp8+7IpZbPTFvQAvqgY//Jf4CPvLAa3fT0wMbHDLRYRkXSmIEbkPuWDANpu26jJPJeTi58cw2dl2e8TY7ic3CWPc/mFNnWouXFxX2OjkJGJy8lbeaD8Qvz4KAz2QWkFLjsbd/gE1B3F37q2M08OmyIXzM3B9Uvw6NP46CDBa89DKKSKWVvgJ8ZtNG0+APXRISgugeEBXFnFiu1deSWMDi8+fj5Q8f09+OabuKwcXN0R/MHDNuqXfKwgwDffxL/1snJnRERkCQUxIverng44dHzl7dm5MDGOH+iF8kpwbkUH0uUXQEkZvrONYGoCf/EViM3iW2/h+5au1u5qDuAjl/EFhXDlAj4xnaurDYZT5834sRF8662U960n6O6waWvvvAHf/hN88y3c6DDuxIPgQgTlVZpStkkWcDRa4Do+CvtqYWQI39JowWk8DsunkSUUl8HkOH4uZr/3dED1ARiN4g6fwBWXQt1RXNMNfHSAeONVfHaOHfP2dTh4GE49BFo8U0REkiiIEblfzcysGGUBcDhcZTX0dePKKqG2HpaVwvVXLuBKyyEjA//8N3Hv/gFc/TFc/THIyFxZBSwIoKsD9/C7oKDIgozudvzsLH5oYGXbejrv6CkFY6Pw5l8S1By0/R48CplhKK+yKXGPPo27/GbKZHNZw9gI7vBx+39fLS4zC1d9AHfouI3kjUZxJWVLHuK9x1++AN3tUFW7eA1NT1llsqKShW2dc7gHH8edfRxuR3DBHBw9iSsowmVk4vIKYErTy0REZFHGVndw/vz5g8AfAvsAD3y+oaHhd7a6XxHZOh+LQRDgsrM39ThXWg6l5fZzdjZ+dmZxn3MxmJ7Cj4/iZ2YgvwBGhqyjCriyCnzI4dtu4+qO4ns6oKQEZmft/pIygp4OfG8nVNUQtDYSTpqG5Hu7oKoG7qS62aXX8D/4Y/DsFyGcSejDP0xw5S1ob4YjJwllZBAEwcKUskSuj6zORuSqVr+/rxsqq1fe0XQDTpyFjmZwIQtkEwZ6l0xjBLuuXGamBcJAqLxqyZRFERGRZNsxEjMH/GJDQ8MDwJPA3z1//vwD27BfEdmqjhbobFlxs4/HIbSJt39xGT4xOtLbDQ89ge/ugKYIofd9BLKy8TevLAQ7rqQcSsoIXn3egojhIXxpJfHvfp34pddt/ZnqAxCbhVvXF/MkvIexqE1hux1ZbO8andng8gWC7nb85Dh+eopQRzPgoXKfdZyzsghGojbt7cYVqDlI4APrXEtKfnJicbHT0ahN+VrNxBguaVQFwHe32+hXdjbUH4Oedhuh62zFF5VAihFA/+rztkhmxT6IBwtrFC0or8L392z1qYmIyD1iy0FMQ0NDd0NDw1vzP48B14H9W92viGwHD4lSycm626D24Mqthwdh2bQgmE/ODjkbJYnN4LKy8e1N+PpjNhWopByOn4HONlsjpr8HPzEONQdx1ftxT7wX19EMczGYGCdUVkno3FO42nrIySV462U7UNttqDtKcPMKvqcLP19JzPd22v5SPcOWRvzbrxF89Y+gpJzg4mtQVYvzAX5oAFdUCv3d8M6bcPAQLjsH19lmeRySWm8X1B8luHnZRlFW4YOAhVUuE7dFhwC3ML3MZWRAXj5BfgH+1nVcdAhq6/BdbQt5T35yHDKz8H1dNpWx7ojlTLFYCMAVlVg+joiICNucE3P+/PlDwDngte3cr4hs3kIHs7zSpgQli83ZGh3LRYdsKlkKbn66mB8awE+M43LzCSUtHOmcg7oj+KxsvAc6WnA+wB05BThcxT5CJ8/iKmvwszM2dejwcUv87mzD93ZZHkVnq+VP5OYSvPM6vr8H98DDMLD4LXwQ7i6nAAAgAElEQVRilMYHcRgasP+ramGoH25esXbsr7Ok88E+CDyuYp/lVszF8HNzBLAQJN0vVpQ6XoPLKwAXwk9NrF4ZrLMVDtQvva2/B1dzYOm+HnoCd+1tePw9EArbtTI1CSXl1qbeLsuXml9MdWGNon01yxL6UwTkIiJyX9pyTkzC+fPnC4CvAL/Q0NCw4uuy8+fPfxb4LEBDQwMVFStLcd4NGRkZe6Ytkl72+rUTa7lFxkPncNk5xG5eIzOprbHhviW/r3f7gooKpkcGCa69Rc6HPkow0EcoL5dQXj7BxBhzzY34rEwIZsn+oU8SH+wnPtALMxNkPPI48fZmgplp5ppvkXPmIYKhKMHR48QH+vBN18k4ehI/OkKspARmZqG3k6yKSrJPnyV2a47Migri/T3MhSCrvJyJL/8Bc7m5hGsOEHvnDTKOniL0oR/B9XQQKimFoiIyauuI3b5OZmUlsctvkPuBjzLt4zAzRXiol6wHHt6J07+mVNfOzIWXyX7s6R097uSbf0neuSfW3S5xHcSGKsmoO0ys6QZZDzyycruhPjJrahd+n+tqJ3TmYUJFxSu2na49AF2tZL/rfQSDfXD8JOGySuIDfcxeu0RWQT6x8nJy5s9LkBHCz0wT5GQtXJNxAgh5wqnWo7lP7PXPHdm7dO3Indqr1862BDHnz5/PxAKYLzQ0NHw11TYNDQ2fBz4//6sfGEhRkeguqKioYK+0RdLLXr92fF8vrqAExsbxoyPQ14sLhS3Zf3wCl6LtPjqS8vaF+72HrBwoq2Jyagbyi/GXL0JJueWyVFbb2i/l+wgNDOCbb+Fr9sOr34eebtzxB/B5cfx3vs74aBSXV4g/dhr6+3BnHiVUdYD489/GPfgYjI/im24w1dqE238EolHcwAC+pRk/PoF/4bv2LX3VfsjOgxMPEZscI/TkBwme/QKhffvtm/62ZvzkJHR3wV98g/F9B3DFFQSvP0+oth4uvYXbX7eTL8UKy68dHx2C8Qloa7ERkB3ggzh+ZoaJ7m5cZubq20WHwIegpQnm5nDjE/isPLh2GVdVs2R/jC69XnxHmy2cmuraCmVAWRXjw8P4lqaF7XzgLZfq5edxlTWMJ++vrQWcSzpGCH/7Ji64f0dk9vrnjuxdunbkTu32tVNbW7v+RmzDdLLz58874L8D1xsaGv7dVvcnIpvjO1vxYyMr70jOhTlwaHFtlO42qEmRD7ORxQSHB/GhMJQmfSOTX2iVxoIAxkYIPfxuXGx2sRld7bj3/RUYG8FffBXefBl+8mdhdhZ37DQu8o4VGRiNEn/h21BagU+0p60J/8hTtqL7fNGAYGoC39cFtyMQHbY8id5OqD8K2Tn47jaYmrL1RaKDuIIiiMXh4mtw+AT+ygUYHoCxMYLhYatUtsp6NbtmsA8eeGRn10IZ7MedOWfrtKxleBBKy/Hd7QtTCF1J2ZIFKwHoaIX9hxZ+9UGwIn/Gjw5bBbt5rqTc8l9ykxZF7WrDnXkU99h7UswWcxZ8JV2bfmrSikqIiMh9bTtyYt4D/DTwofPnz789//8Pb8N+RWQdvrPVOoS9S9dVWViocp7LyIRE/kc8sGTr5QZ6V1+wMGF0GBePWxll723hyokx3MHDuCMncdXzuRDzJYz93Nx8ed04ruagrRFSWUMoOwdXWW0VqE4/DF3t+G//KVy5ANEBW1vkhW9BfiF891k48SC++Sbx7g5b1f3AYVtrJCPT2pxfgOvpJHTiLP7KW1BSih/sg/m8H/feZ6DxGuyvt9sys+DISXj2fxL099ginUmd7e3i52LrBod+cgJy8hbzQHbK5LgVYNhAHpDvaoP2Zvx8mWt/4WWoqcN3ti1uNF8SeUGq/JihAWiK2DkIZ1h57u4OuxYSYjFbdyYctiA0uSrZwUMwM2PXJhYUMT1lgawCGRGR+9qWp5M1NDS8iLItRXad72iBvAILKDKz8d0diwnVYyO4wyeWPiAvf9UKXwCMj1plqI0cu7PVApL99SkXzGT/IXx7E7Q34T/wQ7jWW1B/DBebtc5nQQHuoSfwVy5YsPHQE/B/vgxzs3D6Idt3QTH0d0FGhgUpJx/Ef//PITcHujts7ZfyKrj+NlTV4kvKwAfQ3gJHT+HffgP30U9aB3hqAgqLoL0JYjP4+qOEH3uaeGwOBnvwBcX4F75J6NTDsL8OF1p7/Rg/0GulgNdz44pVe9tfv/o23e2La6Y4G3lY7/h3JBFMrfFpHYyPLpTkdu//CPT3EPR244pLYGYKpsYtIPErR12IzaYuFnHklK0Zc+CwvW7za/P4/h4LUpPtq7XXr/6otSEjE7JzYHwMn5GJH43i8gtthK6wCD8zRejQ8Y2fgsF+q7QnIiJpb1urk4nI7vAdzZBfiJtfJNIVFsHkuOUpJG83MW5rdgCu+oAFPlkrF770Y6OwgY6zj89ZJzQ2izt6CpeTayWOb16dr4Y2LxzGRy7jS0pwt65ZB3pijCCvwKaOTU8vTCMKve+vwOU3oboWnni/LYoZHbZ1Xo49ALMz+Gtv4zzQchNu34Q3X7SRpulJ6O+zIGWwDz88BOMjVumqs9nKP1dW4195Do4/AI8+DcXl+BtXCcZHcQ8+CpOTuLojUFphnfj2ZnxzI36oP/U56OlcKA285rlquw2HT9iI0WrbzMUsSEvYX79QWni3+eab0HobHn4Ct/8QLiNzfvRsEsKZMDIMB49CW5NNTTxwaPGxsdmFUa8l++xogXAIyiphuB9/+zr+wGGrLucc/sZly6ea50LhpYtiAuTm44f68JPjuKkJOHwcV3cE9+jTMD5G8Nr3N/b8Zmbw19++gzMjIiJ7kYIYkXQUi60shXz4ODQ32mhLIjm8pwMKi/G3rtsUs+F+fPnSCiN+ZgZ6OnDz336vqa8Hn19oZZHBigR4bGrWrWv40ahtd/MqFJdYvkxZJX6w31Z2//Lv40eGCVoa8bn5MDyAn5iA8grILyR07LSt/r6vFldbZ2vZ5OTBhZcIutoWA4J9tdaZHu6Hx5606XTFpXDjMvzgJ/CXXodTDxO89cpCu0Mf+lFcexPuxBlcQQH+7dfh0uu4o6fxF1/FZWVbABEKW+nn1YKYwf7FhT9X4UeGITMbl5dvv682paytCQ4eWfjVZWZBLLb+67DWsdfLbcovxC9bb8WCX4fLK8AND9o0LrDFJ6sPQEGhldXOzra1fmZnl04l62hdMdrk+7ogN9+mj5XOT2OrPoi7HYG6IzaSNTO9eK2upno/rqQcNxqFo6ftdao5CD0dhM4+CvE5gjUCxQVdbbi6o3bNiohI2lMQI5Jm/FC/fbO9jAuFrUPYdAOqauYTrR2uoAh37LSNtJRW4toW1wrxQRyaInDs9PrHnZmGjEzrTCYWxGy7DfVHcRkZuBNnYWwUf/Ui1B+xBScH+uc7n6fwr78AJ89YFbOuVmi+gW9rskT742dxpx+GgiKIBzZ9qKsNzj1lSfi9HfDN/w04yM6yEZncPHvcgcM2tanumI3wXHsbhgcI7a/HZ2YSvPOGBV2xGevA347gs3Jt8c6MTAvu4gFMjMPMtK0f03gNv7/eRrySz8HUJEyM4uqPrVx7J/mc9nYtTu2rOZAymd6mZXlcaHs/hv1qIxOJnJuKfQs5Jgs62xbzWebmbBoXQF83bl+tTTMcGbJr6tDxldPAWPo8/OgwfnbWpm7N5+C4A4dwFVW4k2cXp51V1UDH2mvXOOcs6Dp+ZiFwcrl5ts4MwIOPWy7VuvxdHekSEZHtpSBGJN2MRHHFpSnvcjUHoKTMksTbm5d+y19WQejkWdhXa1OivLecjZNnN5ZU3tsFielrztkITkbmks6r21+HO3MOl5OHG+zFl5bjYzEcHvp6oKLa2pSbh88vxMdjUL3fqp7NzhK8+B2YnrARltEovPECVFTZN/azs5Ync+QkRAdhYsw61nH7hp8XvwWz0zA0CPEAn1cAtyL4d96E7Gz85bcs0KqsgXdet457djY0N8KBept2d/Q0vP59Sx+5fAE/0Ld0mlx3O768yo7bP59sPtSPjydN42u6AfM5Lj7yjiWmJyerJ7TdtpXplyspv+NqaT46ZCMVy2+fHLcRLeYXklw+WDMXsymAczHIysL39xC8/Rp+sG9xQdDqA/i2Jlw4vGQxSz82uiSo8TPT0N+LKyqGwpKlx4nHrYhCWxO+o8XaGg4vXXS0pGzJ8/cTY7icPKvgliwcxsfjhAqLrRrdWuclNmvXajjFdDUREUlLCmJE9iDvPf76pY1tOzlunc957uBh+2F59ajE/cWl+Ikxq+J19NSGk8j9YN+SdUJob4K6I/ate6qOYSwGt67jb7xD8MaLljBfVmHrtzzylFULK6+2qWehkCX/l1XYiEh8zjqbkSsW/JRWWY5MEINLb0BBiY3EVFZDWzNkzVdfKyyGkIPBXvzzf2Z5HJkZVma55gD0dds2hUUWCEUuw7l3w2vfh55OGB20AOvaRXxvJz4zC//id63SmvcWMI0M2e1drfY8hwehpdHO0dycTSMLz6/Hk5NrI0ksnebl43Eb8UiRR+JKy61tdyI6CPv2r6y0trzyXFLM6uNxy1PqareE/dp6KwxRWIx7/D3Q0Ww5LIeOLZbpTuJvXVu4LvxcDJpvWqGC+VLNOCu/7L23Cmn1x2xEpGKf/Vt31K6l5Oc/MrR4gK523MmzsLyM+P5DS9qT8hpM6GyFXV4LSEREdpaCGJG9aGjARh5WkUgs90FgIy7LEuv9UP/StVySHxuP28hARmbKb+1XNTVp070APz0JObn2rX5nG/T3LNk0iMXw09NWKvnGFVvTJb8A39dNMDxACA8PPmY5LPE53NQE/qEnbLu+rvk8mxOWl+JC8P4ftBGb42dgZtamlBUUQ0Y29LRb1auyKqugVXMA8vKgrxeqD0B0GJ+VjY/P4fPy4bmvQ0mFBULe4+JzVjnryGlobbYk9ur9kJ2Lm57E+4Dg9ResI4yzoKqnE5pvEUyM2zS9nDzLRepMyg2Zr8gGQFXtkjVg5m5HbFrWTqjZv3L6WhDYKESShaCqs8XaPDNt08iCgGBqCj8yjAuFcYeOWzL97Ru2RsuynBvf3oSfmbbSyLcjcPLBxAGgq80S6i++ir/4ykIujguHcfPXjwuFwPulQcj8IXxPh40cNl6DmoNLSjy7jAxIFLKorLEpiqvxfjFYX69Kn4iIpAUFMSJ70WgUag7YVJ0kfngQX1xqlaTA8lmOnoYTZ6Hx6uKGw4M2LefWNau01dyIH43a6MCNy7jTD+Fq9lt+SOutjXfqhgdstKSjFTdfncoHcUtkT7Sxv8cS6yfGISff8ndKyqx6VTgDYjGCtibLXfE2IuG9t7yGcBiysnCPPAlXL1qgUlwMb71q06GaG20UITPbvpnvbIGJCaugNTdrla4efx+MjdvoQrTfqrGFM+Dt1/HPfhHe/QEY6rMgY3jAApucPHjzecupeeARGyXqbLMS1g89AVcuENy8bM+rudFGWI6cxH/lDwgi79g56W6z9XAyMix3JicXbl7BT0/h8gsWcjj8XMxylcJrjIBlZi4s7rlZKSt8LZ8uWFVjeT+D/RCPw9QUPvBQUGg5Kv1duBNnrCBEb5cFMyfOQEkpwatLc25caSW+pRE6WnAnH1w6NTEWI3TyLK6sEldaiSsoTt3ouiNLRmNgPrdofAxXVGKv7+T4YonnhOwc/PSkjTjOztpo2eTE0v3MT5VLfu70da95DkVEZO9TECOyR7mqGhhYOsJBdAgXcrjaOoLmm1C+z5LqMzKg/qgFJbFZ/MwU3LoOh07gDh+3aluzM9ZRPP2wdUpLym3az8EjMDFmpZITAU9LI0HSlKZgahIysy1YGei19VmYn/Z2K4K/+tb84pfN+LERuPAyjA3D9LgFFsMDFkyMj8JgL7zzhnW0Z60yGi2NcO0dKK2EiXH85dftwMWlEMqAsVELNGoOQmamHT8rx0ZN6o9YmeK2Jhv5+doXoWofxGYhIwtOPIjzAXzsp+z48Tnb5+FjNlr1tf8FrTehvAamxi0Pp78bhgZsdKHxmk2z6u6wfw8cshGXiRFrQ/0xgkuv44vLF6uzdbZAcSl+asKqstnZsn9ab5ORWBdmNbV1G05AT5TQ9tOTtqZKyo2WJcHk5kNPpwWcAN1tdl1V1RIM9eOKyxcLQuTm4W9cASD02NMwOboQRAftzfiiYhgawB07bQHx9UurB8WlZfihgRU3u4xMyMqxYg5gUwKbbsDhE5ZjU1ZlQevBIzbymFBz0KbBhUME3R3429dXTnnrbLWpZ4lj7fSioiIisisUxIjsRWv1s6JD+P2HoKdzSZlll5Nn37C/8C0oKbdSwklrkLiKfbgjJ1d04lwohKuqwR06vhjwhEJw4zL+doSgvRnefBF/+LiNXhw8jCstx3d3ELz5kgUiWTkE/+d/E4yP2lS3wV7rUD9wznIpCootET8335Lpn/mErfMyNQUnzkDTTSsRXX3ARlaKyq3jOjlupZpPnLZk/8kxO150AI6etOlmI1FLnp+agJwceOrDcPgk5OXDWy/DlTdtQc3vfxM+/CM2fenBc5CZhTv3pOXS5BZYjkZOvgU6Jx6E/Hy4ehE/3G/t7uqwUYv8fBtZOnTCjtl224K0gR7IzbUgrqAYf+Uibv8hGI1ajkpFtU2HysxctyKZC4VXBh6r6e20EZXeLti3324LuRVrBi3RdtvOdXY2vqMFX1RqwUp0CAZ6cA88stiWohIoLbcE+1AYt+/gYuL/hZdw+QX4cAbB89+0oK+oFPq78aOLOSx+chwKCnEl5ZanlOo51xyAgiJbc6h8H+Tk2WhVd7tNEQyFLICNzS6Mxjjn8F2tBL0dUFWDy82HktKlI5gpptLtRctHXVcTTIzZ6y0icp9TECOyx/iZaZsuBZCTa9+wL+M6W2z9juW3FxbjDh0nVLt+ErOPxWzUZXmOQ2+XVZsqLLY8hclxfE4uobERXP1xCOIEV9+y4KK7zUY4iothoA/aWmzF9XPvXizje/OqTRE7fBJXWgbl+wiVVVjydlY27tGn4PAJ3KFjuOlJy9fp74YHHrbO6+CATS0bHoS5uOWXlFbaN+4ZYZsaligv/eM/A3/2v+DV71kQUH8MxscsgGprgpEovrsdNzhgox2z03CgDmanLCDparGCBIeO23SwqUkb0UlElR4YG7NAp/kGzExaQDA+ankfHvzLf4Fvb4H6I1aauKgE+rpwhUVWsjmpYtya3DqBCFbKmPlAiSCpzHH1AcvbIZG4v9iJ99OT4EK47Cw710Wl0HoLV1uHv34Jd/CorQeT3JSqGssFAlx+AaF3vd9GcKanIPAwPgLv/wihkxb8+XAGfnwEPzlmO4jHbUrfek+5qASOncb1dEAsZqODXe0QubSYyF93FBqv2X0tjYDDVe7HzUzD7AyuqtauH+YLLSQ/91vX7PmXVey5QMC//erKggzLt/GeuebGpYUPRETuUwpiRPaank5LLAfrjHZbkraPDtkUpYFeS8R2KysyBV3tVvI3MTWs9dbS8r9J/NW37L6mG/imG/i5GD46aEHU0AAUleGycwidfBCHw5dV4PH4m1dx01P4/m4IhQl1d0B+ETzxHojHbOHKvh549GlouQ0HD1sydV+XjU74wIKksTHcRz6Jv/AyHDtla7icOGMjIkHcig5MTNg38YUlcO5JyMywBTBLy2yUJjMLDp+wYCQ2a1PJDh6yTn1mlpVmHh+FS6/b/UUlMD1tneupCfv2+8RZ62RPjFpH23toa7Tn0H4brl+y6W7tTVZF7cQDllfRGLH2FZfBbAwOHiaUkYmvPYgfjxKqrbOpXrFZgmtvE9yO2OjURkv87q+3vJy1DPRZoLSMy86x0SlYWZmsvQVXdwQyMmGgl1BOLpRVEkxO4IcHcetV8SoqwTc3EqqqsX2EQ4SOnrYy2mCjLdOTFtzk5uNnZ3CFRTAyjO+05Pu1FuR0oRDu2GkbFTx0HFdz0K6XcHi+olumjTIeOm6V5k49hAviVjVuer7wgHMEY6Nw8/JCoQXf2QY1dXY++ntWXefnbvBBHLesSltKTTfIPHEGQqF1A1wRkXudghiROzAZ28EOhF+c/rJk6leiZO30JC6/MHXeRNMN3LknSUwN48BhSBQBSD7E3ByMjeLCIcuLOXQcf/lNgmuXrFrXsdOEDtRDfA4/MY6fnca33MJ3tEB2Lr64zNZfGY0SXLmAK68ilJsPOBtFqthnuS77aqC0FLe/HuoOWXBx7AGC1ltQVIwrsxwYwIKOpptWlay0Av/yc1a9rP6ojYr0d0M0aqWjTz5kuTYHj8Dt6/DJv2EBQnYelFYS+ls/j3vyA/DDf9WCnvxCW9CzpdEKDXS12/kcHrCgYnrazmdvp91346pVYpsYt2ppdUdt5Kkpgn/xO7Z9Vwvsq7VAKToI46MEYyPQ1U7o3FP4zlaCrg6bijYyBH3d+LwC/NWLxDeQWO4ys2z9ltUukyUlm+cgvPLj3DfftPLIfV2W5/TWK/iZKQtuZ2fwVTVQW2e5Ly9+20bEilKvQZRYR8aVV0JOjs12O3PORt4q9y2M1Cy0PTsbCosscAmFbUrZ8CA+K9uCiOkpKzSRaGuK4M5PTkBurk0tHOyzKW9TSSOTo1FCFfvsHBeVQeBtRCMWg8aruAfOWaGFIICpCVx+gS2OevTU/JS36OovwG7q67HAODvHvkRIwff32DTRrGzLy2pvWXOXfmZ6oaCHiMi9SEGMyCZ1j83yTs/KKV7bZvmX1EmVqnxLo32bDNaZiS2WYQ7GRm3aVsbi2jAuHLZpYaNL8xD8tYtw4oGFfbtQCD86gisuwR0+sRg85eQRtNyEjla48JKNBDXdsKCisgYee4/lHOTkEPR02AKH01PwAz9sa41UVBEqLIGaOtzUNO5Tn4W3XrFO//Gztrjl0ZPW6R3staBsYgwKC216WFW1jaycOWeBQ1Y27tzTVhmttAI6m+Gx90F02HJbzjxC+Id/0r69H+yDrCwryzwXs2lp5VUWpLTcWiwGADaSMzFhU6sys+zb+pJiey1chlV+y8qB6JB1OC+8BHmF1nkei1puT1UttN6GuQBXUkYwPACRt+15FRTBI+8mFMRx2dl4sOpg636b7lYftehosc4swNQkfr789cJrPBezkaPagxbseY+rqiZ09jFc/TFcVQ2hgmIbJZmagNo6QuWpy3LHv/M1fGn5wsiQqzloU9BKyvCVluvju5eWdQ5VVuNGhi1Zf38dDA/gzj6KmxrHDw/YuW9ttDVkbl2Ht19bOWqYyPPJzbXrovqAjcwxH8QlcmNqDsBQn+XyhDPsGi4pW9xP6y3LzUqcVedw+w/tndGY6Ulcbt58cNK84m4/PQUTYxZAMl8IIT63crtxK7rgmxttemf9UZietIIfyxYL1UiOiKQ7BTEimxCLe0Zn4tSXZDMytfq35Bvhp6fwbcvKynq/Mqm/tt7W24jPwVB/ylwYAC6+YosTLuP21S4pKevjcRgZtkUna23Kkh8bsWpUeQVLOpJBZTW89JyNciQWO5y1JHoXn7NE+6kJguf+zJL/O1otoT7yDuAIPfo0xAMoKIDpKdxAj3WG43Hc2Ah0d1iVtPIqm5o0MwWFJTYlKS/fpqTNzFgHdl8t4KG2Dn/xVSgqtjyQikoLHnLzlpYSPnkWbl61ilpnzlk56tkZGOq1XJmeLlvT5Ot/bG0ci9rUt95OqKi2NWiysq1YQDgM0xP2+8NPzC+YWWxTzUIhmJmAi69YbsjVC8SvX7IpefmFNopQXoXvaCaYi+FrDhIMDRBkZtkioGup3r+Q27Lw+sViNroRm11c56egEDey7Bv3iTGCnDzbtu021B21UYiE3i7c/jr7pr6nE5ebb/kkyceaniSIXIbxEfzrf2mjAcnX1vQUoaxsXFaWjdTcumbTHhPqj1vxhXCG5XdNjOPLq/CRy1bCOR63stWHT8DD77JgI/n4kxO29sztiAXZya9vr0279B0t+IkxOFCPb7qBe/BxuHUNX1iMjw7ZFwCh0JLgHrCAIWntnr3AOWejXNNTC7f58VFoa8ItX1coK3shh8ZHh2zEbXzUArjDx3H76+aLdtTaaGs4Y3GKaUuj5RUN7a28IBGRzVAQI7IJNwenOFGeQ01hFp0jqad9bFhXG8xOL51G099tIxxJXChkFbhGo1BWYWuOJBQU4UejBLOzEA4vLui3XM3BhfK1/volm06T2DceejvtW976o9bJaWuyMrqvfd9GRDIzrcJYELf1UaLD+OgwtDfbqMi5Jy3oeM8zuHgcLr4ET7x38TkM9FlgMjMNg/3z7R62gGR0GF9YbLkdhcWWRF5VA5XVFjzEZu1c9XXBUx+Ct17GV++3KUyFxXjnbJ2Ww8dtYc15oSoL3vyt6zad7Qd+CC6+auWaM8L2rf5Y1HJaag5asDQ2ZkHJeBRGR6xy2mjUgonCEhvRab5pbXr4cRvtGRq0oKjxqt1/6iH48u/ZVLXSChgdss55UyM89w18Xyfx4UELqjqaCean+wStt1e8bC43z0a2kjXfwE+M4ZNe6+UV5/zUJJRX4a6/bdPFDp9YUqErMbrjh/ptVOzAoaXBB/MLTfZ2AR735A/gcnLwIUdw8yrB/DXrg8Cujbk5W2Pm8En89UsEzY342Kyt3xIEVnL67OPQ2Yrr64bScuI97bjyKguew2Frn/e27tBcDH/rGkyOW37MyQchOmhlvEsrCLrbYWoSl1dghRi62y1YHB+DsRH8oePQetvKkLc12XTA5ec2MxOC+N4bkUgUMAD7kmMkamv0zPNBgO9stVLqF16092lsFnf01OpfcACupMyCm/pjuEPH7ZwuD3xFRNKIghiRDeoanaW6IHNb1pnwQWCjBodOLP32eWJiaZCS2L6sAldVjVv2lnWV1RYUvPGX8MT7Vj2eyy+0KUexGAz1L1Qv897jp6cJwuKx9b8AACAASURBVFkEw/Pf5na24iurreMbm7UOfyI3JL8ABzaKkpdvIxOZWYSycmzK0gt/js/Ng3iAq6zBD/YRtN3C+8BGnjKybFRlNArBHKHag7ipSZgYJ+juWEg2JxTG4Qk9+QGbslVQAhXVuOr9Vkp3YhxXWGKjLZ1tMDmBe+L99q3/vKC9Gcoq8V1t9m381AQce8DWngm8TSHrbLVk/7OPWiBWUWmJ4HmFts7NoRM2mjI5BqVVNoVnYgx+9FM2kpOfb6MMtyM23ay7A268Y0FNRiZcfsumpOUVWNuKSuCbX7Xk9AOH4d0fwH/3WeIXX8V//5sWjK589Rd/6myDmoO4jExcYophqulmna12//76hevVj43i33zR8qG62vGZWTA1NZ9Q3mzV0OanV/m+bsjMxtUfs+T/mjobuQhlWJGGl/4Cn51j1dtq62zaUk+nTTE79ZCNeOXk4S9fsLLfw0OEEiNaJ87iHn0aXn/Rgs/auoWEfw4dxzdex3/vGwQjUajZv/icauvwb76EG+zFN14jecjSHXsAN399Mj6Kiw7aqFrrLYLo0Orv2bOP2UjQXbAQSC57/Zxzlvtz8wpUVS8ptOB7OojdvAqV1YQOn8BVH7D3aYriDiIiq3mzc3Etr77xGNHpldNT04GCGJENmI0HjM3GKc9bnJJSnp/F0NQdvvHbm2y9lYwMwC1JcE7Fzc4snQqUxM9Og3OEsrJT3r/g8HGCF79t5YOZ/6b9xmX88ACur9O+kZ+bg3NP4Xo6iTdFLNiqO2IjKF0d8K4PwKmH8KEQ9PfYN+clZQST4xZ8lVTa4pDlVfDO6wSDfZCZYwnXzTdtNCgchptXoLgM39MJ+/bjb1+zUahQCF9YaOenotpGimanCL3rvRYIjI/iikstp8E5QpXVFjDtr7NqWbPTxKen8NFB6GrDPfwE7ukPW65EZ+viyM7MDOAsACkqsZGYfTU26vHMxy3QedcHoL/LgrOMTKiosBLPZZW48agl6598EHo77HF5+Zabc8AWD2Vm2tajyS+wwKzlph1/ZtqCx95O+POv2Gtz5S3oaMG//erK1628Ej/QawtIBnEbxerpxGdmEbQ1ETz/TYKZGXx2Dn5q0oKVqUlr58yMbR/EbTTr0aetGl3bLVxOrk0nCwI7XzPTlvMDMBrFlVfaMXNy7Ro8eMRm6/X3WPwwGrVE+axsXEYmPhy2RVELi+dLHdfgHnwMqg/YIqlgowXOESootGplr3zP8pZmpi24GurHX7uIf/rDhMoqYXYWPzRgo3b9PZb3U1Vra83sr7NyyTnzC3yeOGvXTfV+XM1BQvtqcR/7lFXSm01dujhUXGqjN3dD6y0L3oYGLJhL4vbX406ctbWfAD8atbyh/EKyTj2YNI2waMPry6SUkbHuZ4+I3HtCzvJ7x2bijM3GKclZvwT+XqQgRmQVw1NzNA5OcXNgitboDCfKl66Gvq8wm4GJO+wAzM0tztGvP7o4GpPiC+OFUZtV7md40Dpw63ChMKG6o4Tq5tcpmRi3KUdHTuBb7PiuqhYuvUZw8wo8/21cXr59C19WAeWVuM5WXFcb7uBhS7qfmbEE4sZr8Ph7IYjB40/jDh6yqV8XX4XJMUvcz8m1UYr99ZCVRah8H/7ICSuBPDFh395PjMHUNBw8gisumU/edpaU7pxNH8orwB84bKNA5VVWNeyhJ+w5nT4Hf/I/bapbRTVuNIrr7yZUXIZ7/0dtJOVAvSWaz05bHs3HPgXP/k+4+Cruh37SOrYV+2xBzSAOFVVWCS2/CJ75UauwNfn/s/deT5KeWXrf7/3Su3JZ3nWZrq72jTbwGIyf5ZC7K0o0QYaCoQhdSBeK0KWuV9eK0B8gUSGJwSVFrkjtrB2DAQYYAD0AutG+u7z3lVnpfeb36uLJqupqAzNuB7N1IioaqErz2czzvOcxRU1rikU4+wIEw3Jls65cuUZOCTQEIzDzUM9v75QGafwMlXd/JOrZhRcl+q9V1IzPPtQ5t/ZAF2Fa2rEbq9iVeczQKPbT69iJs9DVg711XS5z/oAsoz+9jp26i2nvUBDq0Kjc2OYewcQZrLW4e7tYj+9w9X5tERttxfgD2FAY994NgTrAzj/CjE42rx8HE22RYYMxmN4BZbjsV2uHwEVyR05wy3M6f7WqXO4qZZkNAG6pIJOIfU0LFvv+j7HJHczr38HZz6QZGsXOPsAuzmKuvYETi4k+VcyDcY4EfBpjdC8tHLrxmbmH2Ei0mSfznGrreErr81urcgmbSz/fEa5Z9sYH0B7HxFqP/N509x1k4vxS9SyHw+M6ruP6va5K3SUe9pEu1VlJVxjvCH7+k35H6xjEHNdxPaNmkyUqdZeJeIhTnSEm4qFfC40MmmGSPYcCauM4EvPuJQ5WvY9U04XK1mpy1HqiTM8ATmf357/vY6GHNpVU6nwmhdM7qAnB4IjS5F/7tsIroxFsoy475EwKvvF9SO5gi3ltS6OBGZ+UhsQfxH78c7mYpfewgyOiPJ27jHPpJRgeE5AZPaVAQ7+ySZxKReJkj6OpSCQGlZI0Er2Dsmnu7pNw2+MRtWZzFZNLS+sRa8XpG8RpAkLT1g4nxuTINH0XJs4e6IHMwLCavvPXRIOKd8PV13HWl+GFVzHnr+L0DgiQxFr1mHodzlyS0D8SxfkH/1SOWJmkRPzRFoGbzh5NMsbPaCqzMC1NzO6GHmfQpGZrTU19tEUToJn7asbDMfjeP4a1BdyVBez2OvbRnUOqUSoBjYYASDEPMw8wa0vw6rf1Kb6xLE2JYwRMm1M709oOG8uilTke7J//WxkpdHRq8gFQq2HSe3DxmrY9uYuJRPXezYnMQXX1Yjt7BOIamtK5q4vYYgEn1oppNLDFPMbvx9ZquH/576VJyWVEp2uCNO5/qnNdq0O9jjN2Wi5yuSxOdx+2UcdurogW99KbAp8L07KsDkcEgJZmjgZ8IqCOkaObXV/B9gxgwmFRKZ8Tbmn6h7Fbq8/822+8Bk4cMd14VrmpBMS7oNHArsxLC/M46LL2M3N3PquMx/PFc4uO67iO63euFvY+X5u7lasykyixmRNdeTVTZSDmYzFd5mz3M3qOr1Adg5jjOq7HylrLg50ifTE/vTH/5z6+K+JjJ/8lpzH5rFa0HyszOCpu/hPuUMChC9XOxlN/t66rxvWLVJPCBoi2U8xj9y2avT4cr1cAY3MVU6tLI7K7Jf3K1/8BnngX1udXjsX0HRgcxURbYXEG09OPGRmHMxels7Bgb34gbYXXh713Q5kkNz6QTiIcEYhyG6LTFApw7WtqbBPbHDgxlYqY/kHs/PRhYGO8GzKpZ4PK9jgmEMRurMntam5KNLR67aBZM+US5vv/BKoVnGgLDI5oyrB/bLr7RHGq1wS0/AGBvOSOXNBirTIQ6OgU1aylVVMdtyaXrUZd+9Woywzhxa/D1D2BlfZOpcUXC/DTv5YofvaBbJgzAkX27g3sjQ9Eo7rzMbZWw4yewjl/RcculZBWafICZmEKM3YG+gYxIxOY3iGcsVOH10d6T9qWSAx3YUr7WKtgxiZhcQa7vaHclnBIIHNnAy6+KO3N+vLTJhMtbTjBkCyWw2GcoVHYWMH90X+GWkXap4/fxc48FOXw5BmB0fZO3GgrNpMS5a1U1Pbms5BK4E7fx1gXc/IM7tqSjufZy7oOinmM4+Bite+xVszV155y9gNER+wZwM48AANmeV4TsloVm9x5ZrNv4t1QazxlQ/7bKBMMydzjs0DI3CPM5HkB8HgPpZ/+zQE9D1AW1OeFZB7XcR3X711lKw3Ws1Xq7rM/P5bTFWYSJUI+h1OdIfJVmZhYLPOpCpd6IqTLv2PGJl+yjkHMcR1Xsxqu5d52kVPxIFH/c1y+nqj2kPdLCeJsNq0m+BllXv/2kVXlpx5ffcxSd782V6F36Iu9eaOB8Xpxd7cELlJJ6OiksTSrbBRrJexv65DjWKWiRj7WhvN45kZyBzw+TC6Nm9gSGIm1wuoSzqvfxARDam59fpwXXsauL2F3NqSZcYzslyfOqFG3FtJNwfvcA011rr2B3VqTEYA/gDGOHJWa2gfTHj+kjz15DD1eTTqqZTwDJ0RrmrkvsLGyAL2DmFBYk4fWdrl8Lc/hXH5Z+0WTNjU4AmOntV0jJ3UsJi8oQLR3oOmGdkoOaYWsJg2tHbC9CYuzmsBE2mQ6sL4oqty+5iQSxa3VRD07dQ68fgGzpVlpbqbuSuM0NqnHvvs3uLc/wp2f0r61xgUMsylZBw+NgjWa5Pm8h8AURM/q6Rfw3G7qexxHuUBt7bhrS5h6DRNtazqN+WWXXMpj93Yxz5rw+fwyJjBG046hEVl7l0uY3gHM+BmYOIPx+XGCYYi1aNL20bvQ04879xAKeczoSUzfEObii5q8DY7q3G6uQjh2eM1trWNbOjDW4kyeh1AEUynrmD9ZXX2YTOogS4axSYy1mnQ9ngv05HXTHofd33xmjJ2fevqXPQPPBSHWWumLmtoYE4niHT2prKNmmUAAarVnhoV+oerofO6U6nexbHJHIPu4jusrUvlKg0e7RR7sFH/pqemzajNX5dWhKIupp6cxdddSbbic6gzR+oTepd6weIxhoDVAovjV1sQdg5jj+ntb1lpmk6WDn7cXMgS8hqV0hblkmeQXvLm/6EeSzWU15ejue+bfnwIoALtbz308IGAT+BxBP/riJ96NO30PFqYFNlralBWzPActLdJOeDy4U/eUX/KLnykfJrkN+Rzu/Ztaqfd4ZbPs84vuc/qS6FvBoETeE0072FwG09GlqUMuqwYuGAaMRPFdPaLFWOC1b0F6D9M/jOfEuPQ6GytyJmuLi5LVc+hUdQTsPX4C2jtFnYp3YwtawWfstHJGWlrh0W04cRK7uiCaVKOulPSdTeVuLM3i3v4Yu7Yk2+nzV2B3C+dr38PxB+TeNTQmLUshC+//RPSysdMCF+sLogqOngZjBUj6huHCNWl/2jvUlKd2pbWZmxK4OX9VVLNiUVk56yu4mRTOxDloNGBnHfvTv9QxaGkVregnf4F54WVMrAXj9eiY9g5p21GeDOvLCqFcWYCeQWmU/EFsLqPE990t/XdbB6zMY154WfSmwVFwG5pSwNEQysERbDDUnMqVMJ+8j+kekMlBKondWMWJteGcPKOJTy6jffB65JI39wgzPCbqV/8QbK5igyHcB7dwf/5jGJuUA1piWzqaJmAygZDOdUsbVKWzcQPBA50NyJLaLkxhB4axxYKCPMNRTdd2No9Qp+zCtIwBABwjXc6vscF4suzmqs7t47/LZWU9Xq0+12WOzkPnMVvMyxShvR2781jGzYlxTQmffM9Pr3+uhbRpbde09Xe43F/87PD4ZNPSkD2jbCF/DHCO63emirUGj3aK7JXrnOkKc7IjyL3tXw+QsdaSrzT4waM9njWIWUyVGWt/WutSqbtsF2qMdXx+3/BVqGMQc1x/b2sqUWKkLchEXJqXkfYAk51hJuIhTsaDJIpfbMIy2OJnJfPsL1VAq/1zj6CQVTbD/u+t/UxB8RFBPzxb1P9FK70nGs/KgtyyHq9MGk5dwH10R/oIY+DiNczr31bja60CM5O7Co3MZdSAzj2CljaMz4etNxR+CZiBYdzNNaw/QOPeJ2oeB07A5gqcvaLpAw526p5oWeevYj5+D/P9f3JIEYt3Q6Us7UtLG+bMC6I7Pav6Bg9XuGOtsDyPufTiwWq8CQSwHkcA8h/+c7myBUKYs5el2Rk/rUlUsaBm+8SYphHtcWXelIrSkHT3K3PG54XWNszZyzonF18UDW5pWjbLXX1Qr8o0wG3A9bdhbVHN/Mc/lw7J7xe9LBAQRfCH/0nHupTX9KtahU/eo7GxCjtb+uk/AfNKtsfnF/j64C3cuUfYlQXcxA4szWrCtbMpN7hgSFkp3X3YSknAcXkOu7bU1Cb5sdWKJhGuK5exckk6rMKhBSf3b0rLRTPt3m3oeLmucnG2VnXuLlyDRl3TH2txH0j74nT1wV4S294pIDw4otdNJbBryzrO1oUrr2FcF1PMY6fvaTtcC0PNx+833N19ArjzU9j3f3IEZDlf+x7GdQ/0X6ZvEJPZg2gMN7GFLRex0/cFNvfDLvuHdT72rZ5/E1UsQN8wNpUUsA9FYG9HNMnHzT0eK5tKHtUkbW/gHTiB6R3Cbm8e6JqM1wfWPXIc7PyUJpGba19g435z4O1XLVvIaTK6unDY/D1Pn7i5oqnnb3J78lns2uLnNqLWdZV1dFx/78pay0yixHa+xumuEMOtAgwBr8OZrhB3t4u4vyKQWclUSBSrnIwH2chVSD/hlOrap+9qjzEs7JXpifgOgE/Q61CsfXUpZccg5rh+r8paywfLWXY/xzVsM1elM+zD59GX4bM+UHqjvgMh3GdVxO+hWH02lcOm92AvocC+J4PoMnvPp5FUytgPfypL2eeUzWchEpV24olU9yOPq1VxK2Xsg0+Vs+I7XIGxlTI4Hpx2TTusAVuvY1wr2tDYJLgNGlP3oKsPp1LB+e4fN6cqQZyxSdn5rimTBZp2sL94BzNyEpPLYSbOKTsktQceA20dOBevQbkoTUhqFy6+iKnXtMpOM5jvzCX9tzGYJyxoHy8TDEFnD3Z9WY20MZpqRWIHDYeJtmKGxjQZ2VrDXLiq191vdNvjmImzmPHTOO2dmIsv4YSjCliMd4sOt7WGxSqTpFjAtHZg/pv/Ed7+a+laBsdh7JQa7FIJrr7RFP33qvEOhaRJSiXxv/iGKFbGQEeHwkeHRgR8oq0yVlhbhp/+paZhPQN6jZZ2AbyTZzRJef07mFpVX1b5jOh9hRzu7CPsez9SAOReQmYAi7PYcAxz5gXs8pzc5SIxTck217DtcYHtahW3XsUGwwI81YqE5ZWyLJdBmgxjDgCXrYjOYDZXYeKsro+FaV1DlbImLhjsB2/p+rv/KY0//1Pch3cgGsN6vJjOHlH9unoxIxPYYBg3l8W4DTXpbR3az1RCmjKPV9fdi29qioXuf/fdH2J6BjCPf4U7Hpk8rC3hfvKBNCaRGPvf5Mbn17VT+/z7/cuUvfMxttGQhXVb0zEuvSfqYhOcGGMO3Psen67YSll6oH0t2OPV2aPFiMVDJzZGToqSSDMks7tPQPWZ2UNPlNd3hIb4d102sS16JMDOpkBMrabMp5Y2hbQ++Zyt9WdrCn+d22WtJsSdvbIqX54/AmZspayg4OSOsqNa2o7ql47r9762clWmdkuMtgcYaQs8pd30eRzOdYd5sFNkLlk+YIKsfcZCaLXxdH8xtVuiLxbgUl+UegPWsofP385X6Yr4+PlSlkJTB5Or1NkuVLm3XeBkPMgHy1nSpTqDLX5WMxXyla8mkDkGMcf1e1XL6QpX+qMUqo3n0sHKdZd8tUFX5DDzZSNbZaDl6Ep/a9BL9gve2AMt/md/CKWTh4Lxp/62p4TzphZjv2yjAQvT0gv4/NjFGdyHt7H+J0bDu9tKtd/bEf1m7uHTqevry7i/eEdi+a5ezOmLmK5e6SvaOpRT0d4B6yvSMgyNNRshK33J7ibm9e/AozsS4w+PikZWyCo4EiT+b49jvH5svY59eAszeUF2sD6fphpTd2VtvLGKabqKEQzJUKD/hPJekrvPbti+QJnWdvD5sIltzEtf1y9jLdibH0KsTfve1QtjpzEdXU9pj556vVAYXnhJj9/VJMSGIwdNofPSm8qrWVuCl9+UxbXfp2O0MAUXX4J7N+DSixAOSy9TkRiffFZBjr2D8PAO5PMyIViZly11Lg3tXTA+KbpZKqFJQWpHf4vEYO6hgM/2hlr1aAvmje/C/LQodYvTmNe+JdA6cRr71l9AvYpz9hKmfwgaLu7qkoDk6gJ2YQpTLOg1L16D+7dxWtuwLe2yce4/gRkewy7N0Zi+J8qOMbC1jjl5RuGZ9Rq2UsYJRaRFGT+N8QWkHdrZhI6m3mXyPDazB1dfw/QP41x+BTt7H7s4i52fOpj4OO1xOau1yn7YtMeld9mvQFCmBemkhPtuA3vzA03HWtsPQCyA7RuEX7yLufyyHjv38Dkr6eZz6VdfqvYNOZK7B9Q8QNMqr+/IQ/cXOez+5GR9Wfd3s+xeQtRKmsDHcZQh1JzmGsej3Je1RYXSPkd798wa+B2zWs6mjwTXAloAWJnXNVAsHvmTdRuyZw+EsOnkL68P2n+95M6zp+SLM3JYDIYw46cFzh/dbm6Di73+Du79m/ocmjgry/pnAK7j+v2s6ytZtnJVznSH8XkcfjKfeeYCqdcxXOiJcDJ+yAQp1Z++Zq213Nks8OHK0SyrtUyFSt3lTJecxSbiQeb3Dg1C0uUGXgOnu0Isp9WX3N0qkirVKdZcFlMVrvVH2cxVMc3pTND31YQDX82tPq7jek6V65aQz2GkPUi63Him6H4uWWYiftRWsFR3CfueFvO3BjxPjWmfVbGAh/xzpjGfVQcrs82y1sLMfWysTSup7XHM6Ck1/Lln8NbXl2BgBNPShjl5FqoV3A/fxr3+Du7yrHQB9YaCCs+KkmU6OgVa2uKQSmLaOyXi7u5TE3z6oubQBgVgdjW3w+ORwPj6283myshed3sDPB5svEsr/NYKBGyuaYW3VBDNy3UxV1/DtLbhzj5UoxlrkQbi11Cmu1+2yOmkJgr5rKY5e7ui74B0KZ8x1Tnyeo7noFGkpx+Tz+GcvaxjAmoWO7pw/EF483uaMOxuC0QUsqInVcqyU/b79DqJLQVnVsqaJMRaRGH7+U8k6i8WZH6wNKMpRzEn4b/PqynM5joEg5j+ExAKYm/9ArbXYWVOU45KWdS91SWFoN75GBPvkeYlEtWq4NoSTJ6HD3+q1zv7gih7Ayeaf1+EeKeuq0JOFLmNZQGMYABufAD1mnREgyM612dfwH3rL2XMEI4erD7a5DZ4vFjrQqxNVJ/EDpSaVMH1ZdyHt8Hrw7z4hp4XDGFnHwok+QO4hTzuh28faUzdckkAqbVd1/raEiwvYFs7oLMPe/sjHe+dTezuFmZ9GQZHcEZOYbp6sI4Hpu4e0dPQHsdGIjJj+DWVTSVx5x4JzOxXOKLp5ZOPrdd1DXu92PVlbKPeDMNtVmZPnxePlenogszeIfAaHgev/1DLVC6Cxzm0035OGcej6/DXUPZxGuKXeV7zmMgK3oHObtyV+UP6q8crm2mQfq2pZ7JrizLTGJnQfeNvuuz9KpXeEz3vMWBn93Yh1nqE1mp8fugbxl1bxE7fw8ZaZULynGnRZ9Vx6OhXuzayVcAQ9Hmw1rKUKvPKYJTF1JenN6ZLdaZ2i/ztbIqQzxD0GO5s6b5quJZbmwXONoFSue5yoi1AT9TH9ZUs1YaLzzFs5Wvkqw2qDctWrkKloR6nWnfxOnBjI0/Q63B9JcuJtiC/QTngb7SOQcxx/d7UerZKf+xwdXO8I8huocZsssRcssxcssy97cKXErT1xvxsf8FAy76Yr/lB9vxaeoaLCC1th/ausw+wg6OYRg0Ta8W6Lu7SLCzPyj622WBZ11VjWC6ridyvcglz8Rrm5Texu9uatFy4JkrO45qSzm7cxRlRSIJhqNXUJOTSCrg89wJmZAIsmK1VeOlNBQ9urWH9QUwgiBMIiI5Tr0FyV1SP+UfYTBq3XsfubAiU+Zvi63RKk6WObuzsfelvxk5DsaAJUpNKdqS+ZDaPGRoVnaxJ3zPdfWpuMimFJG6vC7x9mdfs6JKeZbRp+xxtEUgKRTQBOnMJT0eXXMuqFWWttLRpkhLvxJw6D6cvyTY4l4XXv4Nn/KxWvtviAi22AX2DkE0JDO1sKfzSWmlFHtwS9c7rkY7jla8LaLoN7MIMTFyAtRWIRvW4zi41doMjasgcDyS2aXz0LjaTwiS2RDVrUohsk1Zl63Vtl/HgXn8Hm96TnXKsDTsygcnnpIOJd2l/wtHmMeqUScDutiyWrcWduY/FwX3rB5BJY0IhiMYw45M4V17BhCICXMYIjPzr/xV3a12C+2oZNxjGnDgp0HTpJVhd1DZaC59eh2uvCmj3D4tSOHISs7OJOXla27W5hvv2X+Gm9zQV6unHbm/IormrV9bS+dzBvWfa4piCNEk2lfxMiuYXKdt0oqNalS5uHyR092G31nEf3sJW9dliiwXpjjbXNDEMhZVR1H/icJ+f0WVY14XRSZ1rOAghPaipu1hf4NCt7bPK4z0K6n6ZfS4XsfdufOnnuSsLuH/2f+p/1haVHbW5hl2aw3T3C5SuLWEvvoRdXcD2DWCn7wtY1+oyTVlfUkjuyMSBucUvtQ+5DMRaBCiDYVHG6nXRgh+bjB1UvQarS7oGK2WFzfYNQT6r1woEDw0knveeK/Pw8PYvvc3H9dsr9xm5THulOpu5Kme6Q5xoC7CcrlCqu7QEvc+1P36SKWIwB1OblXSZct1yrjtM3YX1XJUba3l+PJdiKlHE5zGMdwSx1vKnd3apuZb2kI/5vTLvLGQYaQ9QrrsEPA6nOoPc2Sqy0bRibgBb+RqvDbewlK7g9RgmO0NfWZcyz5/8yZ/8Xbzvn+Ryuc9/1G+hwuEwxeJnf8Ac11ejNrJVBlqPApR42Ec87KMj7KUj7KUn6sfneRq775XqxMO+p34PkKs0CPkcvE/ksTx57QS9DuvZKp1NmppNJSEUOrBHBa1+DLT49VoprayaSFT6h1wa+oYwG8uY8dNKGU+JKmNeeBkD2N1NTWX2dqFcxIxNHlCj7O6W6FvtcdkSl4o4V14VNaOj86j7WSEnAXwgBAG/mstc5iBTxLS04hYLsL2BibTgdPdiCznclQVRY176uhprj0eThvFTajZTSa2ippJw+VW5YtWaGS2xGM6Fa1plz6YwrU1tzPKcAi4HThw5vrZchHrtqUydzysTPmpcYIyRg1d7/NlNyBd5zfZO0esAE43p3+Zq9/7v8fpELTnzgnQbJ8/itLSpgbYW29MP927CmUs40MaGbgAAIABJREFUD25Qv/CiGvjdTU1hqmXI5+Bf/Q/ws7+GYknC/511iPfAzAMZI7iuGvrFGQiEBGpyGT3/+/8M8+mHCvS8+4kmZquLcpjrHdRrOB5lzkzd1bmpVXXtVcqYQk5f0AZNgYp5HbN4N9y7iV1bhvNXcIJhTfkqJYj34N79WADOIzc4uzwH81OYcFjg4NJLAtGxVpwzl5or3QrTpGdAtLyxSbl3pZLQOww33hcYaeuAB59iW9sx/UNqaGOteIbGsMvz4Pdhwi3YxKbygzw+ASrrwtaG3NA6uxV4uTij8xZrw4QjWmk3Hkx7XCv6rguOg5vPCmR/wands8rOPtT9nN6T69vcIygXFBi7uYozOKp7u7MbluYw5y4f7L/p6dckcV/Uv7UOnT0Yn59QMEgxsQPRmI5VtEUW4FhM4JByajfXoF/vj7VPTXGe2l6/H7Ox9rmP+8xaX5Gu6QscN/vojiYrxoj22dkjYX6thukbhP5h7KO7oq8mdyEcEXWwUNC5e3RHz3EcXXvRFpx4F8YfwM5PYU6M/1K7YJfnMRUtRpiePi3uzD2QxfoTiyrWWp2bSEzuc9k9qNWx5QJm4jyszGOHxjDry889rnZtSTq4SFQ0w8DTjlJHHu+6Op+/RPjycb/zq5VrFcOQqTRIFuv4PQ4Na9nM1fB5HAZbA/g8hjvbBU53hfF7HAxQqLqsZqokS3WCHoe5vTJbuRqlunvQd/i9hmSxTrJYYzVbpT2ofqXasLw0GCMW9OJ34N/fTTLSGmCiM8Sj3RJej6HeEANlO19jJV3hbHeElUyF8z3ahu6wl5lkiYYVa6TWcIkFPBgD3WEf6UqD7qgPz2dkzv22r51YLAbwP3/e444nMcf1e1E7+RpdkafT7L9I7RZqdD4HwACMNFdWvkgdMQPI7B1Z9U8Ua7zQpw8XOY8dPs8ao6lIKqkv72JBYKW1Qw2013eg67CzD3C31jHB8AHdxBZyUCocNOl2a13uSwCF3AEQsJmUpji1mmx0/cqYIBxVQ53Yhv4hrQze/BDb0ib7WdeFtSVMNo0ZmcAszykfxDEYrxfP+BmJXV0XAkE1ZlN3oD2O090HjRqmb1gr0oltgaX97evowmaeQZXb3T5iL/u7VKaj6+nfDZyQAP/ORzA8pibjxLjAKOC5/IqoZqsLeEYnIJuR2D+f1b/W6vk3P5AmplbRanyxIIBUqzXdrLrBBfPP/luByO5eNXHxbsyDT7Hnr+KEwnD1NXj/LQFJ19X1FIqq+bVWU6COTszEWRg5KT7/7H3pbXY2BHSTO7g/+1vcP/+3ypwZGZdQv6MTE2vBViq4Nz+AlUWcq69B/4iuoUd3IN6F88o3dVzyWUx7XJbRAAZspEUTnum7Mo04d1kJ8pUyzN3X9Xn9HYHcWCvc/gXuO38NXb0Y15XZwplLMiZYW4CP3sN58x8oy+fa68rsGZ2ASAQ3GNJUxx/AtsVl7hCJYVraBXgaDQmyHQ+2o1uAY3H2QFPzS1U2jSnmRUV0HMzkeQGRsUlMZw+2Usb09OE+uoNt7cDe/1SasEhUlsKPazJKatwB6kuzsjYPR2Vc8f5P1PRvrUuTdu8mbqMhABqJaZ+f49hlqxVNvuanMIuzWPeLZ149+wVdae0+R8xu11dg4IQ+jz54C06ewZk8r8/B5VkBzXIJc/kV+Phd7Php6VTWFqFvAPuLd7SIM35Gtt7VCqZUOHyDji65ED75vp9Dq3NXFnT9njwDoZBc/GItmAvXDheLSkXld4H0ZEOjAtOtcS1GfPeP5Zo3ex/bO4hZW3z+cdhc1dSt6TRod7ewGyu4D27jPoeWZ5fnsEtP22kf12+uphMlZhMlfjybJuAx9ER8THaGyFcarGaqdIS8dD7Wf7QFvCSaDI542MfNjTxDrX5W0hWSpTpnu8MEfQ75Zlhlqeayna+RqzSYSZboivg40x0mFvBQrDVIFGv0xfwsp6t8/1QbFddlJV1hI1sl5vOwkq5wb7tIqW6puzC1WyDkdfhwNUet4TKVKOMxDvN7ZQZifmJ+Lw93ilzoiZCrumzmql8q7+53qY5BzHH9XtRnTVI+r9LlOu2h5wMgYwwGcVE/r9pCXvZK9WeK+faKdTrDPrFCEtuHCfSAaTQw5bKa/WiLBNudvZDaPTI9ML2DWplcmpGQemFaq8nry5jhx1Yem8DF5jIHNC2by0gjcOcjqJYx45OiH2VSYF3cQg4bCkMxD44H29GlBrj/BCzP4Xq8MhcwDrZ/GFPIyz3N29QSDY0pmK+jCxuMQGILz6WXAKuGPRDATt0T8AqFsPtubR5HdKon60lNwO94GWOgpQPzB/8Vpt5Qw1UuQS6DjTWnSROnobWD6r2bsLkse+uWDlFSTl/Usbj9UdNCOKz/D0UljA8E1FxvrMLiI5zWdgGgU+cEdCIx7Klz8O6PYOKMqGR7u81JTw2nf1gC7loF99FdzKmzgMW2dQi41GtyWQuGdb621uVsdfkVWBKQsPPT+rcJrMwr31BY5j/657jRVpi5p+d094kuBrp+E08ESbZ3wuo8NGp6H8fRZPDiizjf+SNIp+DTD+C//u+kMajV5DwVDIums7mKXZrF6R2Qc5VxBBaa14tZX9aEKZ8RFe1Hf46bSooadP2n2HJRoa/dfQILa0uYl95UbtDWmqYBJ09LT/Xktn/BsvW6Vsw7unAXp7EL07A4i1ur6d7eU8ir3VzFJLdFM8tloOFiHeeAfmYrFek89qteB59fCwvrS5jJC3pe/xD20+tw+gK8/xNN/kCUvdQutml+cLB968s69qOnNPkNR0Sv+xXctKy1sJd4rpjdFnK6dho17OoidmkO+oZxHEfnd2MVhsZwP/45duouTt8gnLoAP/hTAWPk5Ga+8X0du601TXXj3Vhf4ABcmPb4obvZ/nvvbMDDW8/f9tmHso9/5RtNkwOje+pJELKxouMGuk5W5jGDI5hcCto68LS0wYmTmqQuz2GrVaxjngJQ7s0PsdmMtn3ukai6m6vY9k6MY2QMsr9tj1MbN1Zha+Wp/Tuu30zt076qDcu3xls53RUmXa6zlavS3+JnsjNEslinI+RlLVPh/eUsYJlNlrm1kefWZp6RtgDb+Srnu8P4HEO+0qA96CXk01TkP9zd5U/v7DCbLFCuu5yKh6g3XKZ3RQN7dzHLbJNGtpWr4gAb2Qrze0Xqrku5YemP+bjQE2a0Pci7i1m8HnhtKMbcXplspUGl4RL1O1igZi1Bn4dksUZr0INB9stfxToGMcf1layZROnAnnA6UaIt+LQo/9dZ4x1B5vaeoWd5Rp3uDPFop/Tc6AVjwM0/Nh1J7kpsPjR6BIiYhWmFKD5WtlzEaevA+S//Fc74aVkgt3UcOoXRpJXtA5/EziEI2lzDTJyVqDmfhVIBe+sjgaGPf64gxJZWAaLBEUy1IpGxkVjXJHdwuno0fcmkJET2eA+mJSabUt5FNAaRCAQi+mKO6jWt4xHIOfsCpq0Tk2p+Ce8lMKcvqqn6ipdpacE+uou5dA0zeR67vaHV/PQe7o33oVzCGRoheOVVTRw2VkQjaVohU63KzSyfgUirGnF/AEoF2TVj5YgUjtF46y9FDTt1AdqagGZlURk52TQsL8DgsKY4mQxurSJ6TPcA3HgfG4oK/KSS4PHpmukdFD3pyqswfkbX1uY6XHkFpu/B4CjO2KSA/eRFzOwDzKvf0ir4HQVpmlAY4t0HOpv9OsIjz+ew9YZc1foGcSbPy80p1irA9bXv4vz3/xNOek/mEC1tmJEJ6OoR6G5rF21t7iH24S1dg/MCCu7tj+RctjgNZ69g8lno6sX+1b+H4VHw+rFLc7Kgvv0LcAxuYhv70bsCooktreR7/QKTrov70c8ObKS/SLmrCxKGR2KyVy4UdK+On4Y7H2FqFWX2LMxAeyc2EsV092E3VrFzD3Vvuw1NZ9cWYWBExzCTwmnrUODop9dlLd500jKRmDQZrivDha11bDatfYr34N69AXc+0bQmmxaNqWn2YKsVGT5EYp+ZXfW5lU5Kp1UuPfUnm89if/ZDWF2Ubfn2OsRioslGY7KdjsYwnaKu2un7NB7d0Xl88w+U6fT6d3BGT2EGRiCXw958H3PpZV2TpcJhs987gLWudF2Ls7jzU9jZR9hw9JnTGOs2FKoaDGk7fH7929YB0RZdUyDNkNcL/UO4tz5SdlQ2gxk4oWlyawcATlefglaDIdmbN1zpd/ZfZ3MNfF5MKIQ7+1AmGf3DB6GztMdFtavXsbmMpi/794+1mP5hqJaPgz1/CzWTKPFgu8hoRwC/x2ElXaajuei5nK5wdytPulxjfq9MyOcQ8Bou9UV5/USMVKmOsTDZGeLWZpFctUGu2mA5XSZRqLFTqPHeYpZ8rUFLwOHOVonx9iCfrud4ZzHDZr7KTrFG1O+wmq5SrjVwLUQCXj5cyeB1ZCQQ8hrWsjW8HshVapTrLqZJ9WgJeFlMlSlUXYIeh91incGYn0rdZStXoyfiZStfI3TsTnZcx/XbK2M4sCec7AzRG3tOEOKvqTyOwecYys+wQXzWY4fJs+DEDn5XrDUOLAyHWwOsPE4t3ZP9asIrLYfdFw76/U9bAS8vaGXaOQRtJhw9+rhcRlbAj5VdnofhMT0+n4Wx07j3b6lxLeS14h/vghsf4mYzsrvNpOSM9vF72L0drNerL/u2DjkuFfKAkRPP1jo2FMF09cHEOQxgIhHc1SU5VPUPYeYewckzElYHQ2rMQUL8cBQwet9fk0vS30mdPAtuHeYeYdu75HAW78F+8nNsIIBz6WXo7if07T8S175/SA5lHZ1qnosFHdfdLUgnYOK8LJyjLaKR+QLw4TsS7//iHU00PB45vZUKcrabvof7yQey6H3hFTXir30T7t5sgpJVZdL82f+hicuHb4uO1jSKwB/AGTihpnh4HKbvarvDEU3QEttqpAIBmLyAfXQbN5MSCGvvwHnlG5A9zDACoG/oQFxuyyVsMacJTqMBJ88crP7bclMT0jckoDQygTl9QaGYiW1paXIZWJrD6eyRqL1eh4efwtCo6EC5NO7GKvQP42DVtAb8srhO7TUzZSzmzT8QwIu0wM3rmMuvaNU8mxFFr5AVJQ0ruuXKwhd23rIP72DOX4GHt6UJijQ/C3x+vWexII1Qcgfn7GVMrYbbqGMf3caOnRKd6vwV3Ftqeg/0D4ltPN19OteNBqa1A5DVtU3uwIWr8PF7oqp6vdipu7iphKaxiW249BJ2/iF2+r5AVUpOe2ysYK68JvC3vf6ZQY42l8XOPFBjvTyH+/G7uOk9Aa5aTYG+iZ0mWEodvJZdX1H+y/AYfPQeZmgMp3dQIH7mIXZrVU6IrisAEWuBezcw3/ljPGcuSbMVjsgwYfahrumVxcNAyfEzUC7KHMHxYHa3BXZHTmKsCy++rmnU7AOFVS7OHgruN9cAo8lypdQ0BDkprVJbHPvgFu6DW7CygFsuYpdmsUsz2HufaOoYiYr+FmueZ8dg2+O6X7NpbCGvqVF7J+5eAlsuYto6FXC7tQapBM4f/gvt19a67Lb7h7DLs5qet7TBxgpuLq1FDpqW3NGY9GfH9RuphmtJFGsMtwVwXeXLrWaqfLCcJeh1iPoc1rI1XhlqYbwjyPWVHLmyegSPMdzbKTLUFmAlXSFfFVDJVxpMJUrsFmsUa3WylTpBr8NyukpP2IPHMTzYKXK6M0S5ZumN+FjPVgn6DPN7Fc51h4n4DJmyy3BbiHPdYU60BRlq8fPJWoG1bJWuiJeJeJCZZLnZT7gUag2+Pd7GVq7KbKJMte7iOIb/eD9JX8z7hVxYfxfrWNh/LHT7ylWqVCfgdZ5pifxlK1tpYJDY7fOqLehhbq98kC8TDocpFAo82i1RqDZoe4yS5t/doNbZR77SIBrwsJSuMNoMvvI6ht3tJPGeppi4ZwDj83Nnq0DQ6xBObUugH44cUHJAXGgGhp/Kl3i8bL0O+RymrUMrspmUqCjVCqajU/z71SWceJeoHMvzym/p6VfjGGvDeAz25Fl472/h2tc0ofH6xUFv7ZDD1uqiGqlaFXP2hWbTvQeXX4aP34V4L7alVdQHg5qk17+DE+9WExIIaBIB0tCEIpiWVjVbKwuio1j7Kwmr/y7KBEM6P6OT0g3lszJ46BvApJJw4iRmd5vI0AmKuZyOQe+gJjDZtEDNzpZAC0gLUqtphTubEj0tEgHb1C919WA/fg9KZR2zahX2khIiAzheuHhNUzW/X2L/hRk1/rFWOH9FgavD43K1KhUFRqIt0D+obcqmdM4qJUzvEOSyOKekbbHZNPb6283MowlpXnIZKGRk2bu5Kj1OIYddXQQM7u4GjutKV1Sv4QyPqZFraZcZwMTZo8fU48UMDMPWBk7foK7rnj7YXJdm4aU3MY26dAyNuswOHnyK+dYfYcol0ZcqZbnAtbQKsAXDON39AhS5tCyk+4a0GFAsQKWCGT2FXZgW2EjvwekLmCb1zQSPWrQ/Xq7rwr0beK6+ru3zekTPrFXh+tvYRk3HONaKGTutxrylDfu//S/wzT/EqZYV9hoMCSz4A5jNNQGrbIZw3wDFR/cxXT244SimSX/D58d4PZj2TpzhMenxOnuwn36IsRbjujgnxg/ygZzTF9VkpxK6j7v7BB78AnyPL4TYuYe6H8MRUdhOntE2tnUos2XqtiaG/qDopBEJ7421okLGu3Wdjp6C6fuYMxcxIAOFlQXMxZdkIlLI6Zr88G3pttZXICTtn82lpQ3y+iTaL5dgZREcD2ag6VAXDMuFsFTEhsKYYkHBn/Ge5rZsYFNJzJkXZJqwsaLrtVbV9d2oY0Ym5FhXr4PbwK1V9TrGaJJSLOhYX3sDs7WOc+GqgN3mKsbrwxpRKE0uK3pmd5+c0/YS8OLX4Ob70mINj8PiDPb0Bbh1HXPpJez9mzB4Qp/DHV3Yh7exhRxmabZJwVzUsSpkD64RUs0g1SdNB7bWsY/uHmiy4Ljf+ayqNexTwvZP1vNEfB5eHIjyyVqejrDo4r1RP5lync18jTdHWsiUGyzuVSjVG/S1+FjPVNnK15iMB1nPVXm4W+LrIzFSJZdbGzmy5TqtAS/L6SrRoEN/1E9LwMNarkap2sBiyFUbpEp1OkI+Kq6l4YIxloW9CuvZGv0tPk60B6m7lvVslUt9UQIeh618lVjAS9Tv4cMVvVfNBa/H8O3xdizw8+Usp+Ihag2XVKlBpW450RYk4n9+H3Qs7D+u4/o1VaJYI/4ZGpYvU9v5Kr3RL6alMcYQ83vINgVwlXqDe9tFJuIhQj45kx0+GHqifoo1l0K1gbVQdy0Pdw4/BKzbULMUjrCdr3I6vcjezp5WaSslfWntPzaVhGD4iNPZs8quzmuV0XXVGPYNyDFo4ISoXfU65uKL+gK1Lrz2TUylonR6DM7ll9UEfnpdFJYf/ic5Y0WiMDSK/eR95b6U8mo23IaSqQMhaNRx/AE1lW4Dk9jW9ODeTTla7bvzpJKHwvi9xBGRvPF4MKMTCpLbtzT+KlYhp31oKITPeeEV5fisLGDLRaqP7mrSFghp5Rlkxby1rrDJq6/JRvnyy3KsOnNJq7bGwIlJTc5eeFkOZRurEAmrEauWlfFy8UWdG48jetfQqHQt174m8HP1NYEGtw7danJsV7/oWoGAXOHalbPC0BhYi/Pdf4yJd2Ha2sXhn58Sde7a67C1ijl9SY1vclfGEcntw8whi2g55RIszWFjrbKUHlQQrC3kYOY+7Av/HytrrbJlalXpdzwOZmgcm0rIBW7fEMFtQK2iqUesFaerB3oHMFdfFVXqwjWczl4oFMCAu7MlQHPvhjJs/uLfYVebwu70nuiOiW3c/WDXW7+AkZO4H71L48O3n3nabWJbwaKnzuNuren67x/GXZ6D1QVZgDsenO//U213Oqmm+/4NzLU3cAaGoV7X62yuSpxfzGNbWvW4oRHqC9Oy7+4bwkzdEfWtPS63Lq9PIv/98gcwTSc5G4vhTt3FuHXM4IgoorEW6Ugen+yOn5GZwv4+rcxLx2cc7Nwj3MQu7u7m4Xv4fPDyN/XZUC7i3v5I2USLM9L2eH24/+FfC2iVC7AyB7Uq7toyxhfAjJ/GiXfqfXw+7J/9X/rs6+mDyy/B0gzu5rquAccjq+zNVTXmE2dhdQ73vR9JH9hoaPpkDGZ3E3v+GqZaFYhensW59oYa/6a1uBkeh33N0tqi7lmAZEILM/FuuP4O9sorWrgZPAFXXoONFU0NW9qwhTzu1qqysioV7I0PMIGgaHnnr+IEggLXrot9/y0YGJGGae6RAM6tj+D174o219Yh8LS1Jn3XPt3zyquwuykjhnwGN//YInDf4BELbeu60vcEg81r//nGAselstbyzmLm4Lt9v/aKNdpDXlYyVfZNTb0OhHzKZ/E48OFylny1wemuEF7H4Vx3hFylwdxeiXM9EVzX4ncgU3bpCHs52REkXWrQcC3/5GwHfsfhzlYBn8chFvBQt5Aq19jO1eiO+OiJ+dnKVljLlAl5PfzLS110RbyMtAXoifq5s5mn5rq8NZdmZrdIoeYSD3l4fylLoeayla+SrTQYbAlQrjU43RmiLehwcyNPulRnpD3AeDx0xJjgq1THIOa4vpL1y9hLft5rFaqfT2MabA2wnq2SLtWZ3ilwoSeMz2PoifqxWLbz1SPc+dH2AGuZKtv5KoupCgMtftZSBbpCHrZn5iUARQm77S1hSCXkLPTYdtlykVpi99DN67NqdQnz8tfVQBQKcpZanKaR3MUmdzGVEmZgWBxsf7Ap7D2JxR5Q1MzJs/riTCe1+tuoAVY0lYvX1Ni6rlZOT56F4XFsMAQtmh6YYFirpo5HTffACZwj6eFNqoo/oCbyeefF+dUnbX8XZUYmFEC4uyVANjiihmtwRCL/nQ18Y5OYMy9oMnP6kgIrewcUQpnLynK1d1D0npGTOg/1uvRGW2uiziR35SD2+nc0cWltV/N34UXY2Yazl0Vre3BLjf3L35DbV/8gTD8QB9/jV/PV3Y9ZnZeJw9kXRAW7/RF4vDoPA0MCKNmM+PgjJ+Vu1mi6p119A26+rwMwNokzPI4ZOQWFvI7B6IT2dWEa52vfk93sygJ2Y1mC92oVc/qi3MkeK7u5BvOP5N5ULWO31nD6hkW9q5Rxzr4gzUmpgNnegJ1traLvZ3P4g5ilOTV6pSJMXmjSlx7AT/9CQOHUWczYKYH2YFj6mpZW3GQz3LDeED1ocw33R/8f5tobUMjJQSqfxc5P4S5M4/78x9J1VSvKD1qYwUyck2lBJoUNxzSJSO/p3h4/LZA1egrT0i7aXHIHG47iTt9XCCjAucuyUN7e0ESn0dA0whhouJqybSzL+exJ17yZB5jLr2K6e8G12PkpaO+UDuWT93CrFTBGdtQg0JVNC+RVyjq2/oAmCW0d2M4emL2Hff8nuIW8tDQ+P040pmvvxz+QOP29H8LkReyn18XMnzwPjhG4OX8VW62qKV+chu11Gj/8z5q8RFsFHmo16fle+gacPAdv/QBzYhz74Jbc/gJBbVcxj/nDfwnbm7iba9i//X+VXfWf/o00V3/zZzrGWGxHN+6dj2DiLHbm/iFlLhiGdBoa9ccCVa3MDuandA0/vA0trZo0bixrkeDdH2IuXBVAvv0RjJ/G9Ooz2qaTkM9gAn4dl85eAaCHn8qRrVTEnDqnSVYmhekfwr3/qfY1uY2t1Wg0Gk39V1yUXdeKLnfjA7j7yYFJw34+DTQXxqbuyKyhLa5796uaYvhbrJ1CjVcGo2w2AyIBpnZLBDwOo+1BKnWXgNchU6oz0BJgrCNIvtJgLiEnsc6wj8VUma6wl2rDZbgtQLnmkizWSJUbtAW99ER9FKt1ppMVeqI+phJFZvfKtAa9vDnayjfHWumO+vF7IOB12MhXaQ162M1XWUpXSJcb/OHpDqZ2i2QrDXpbAiyny0wnytzbKpEs1jCO4VujLTxKlFnNVXlxIMxCqowHQzTg4eP1Ahu5Kh5j2CvWcQy8MhRjvCPI2udk3P2u1jGIOa7jatb11RyVL6B5iQU8PNotEfI5zCbLTCdKLOyVGWwJUKq5JN7+sRo85GjyyXqOs91hTnWGaA16yW3t0DrYT6biYrzeg4RdgOHJEZZXD92QrNuApTnuhgePhGPZfS77Y+WmkhCJKbQulcTOP5LF8bf+CD76GXZhSray/kCzQW1qKfwhiUg71QAZn08UsEAQTkxAewfsbEhY293XzLMZBBzYXJE2IrOHiT1GP1lfVgih62q1fd8Kej+NG9S0D41+qXP0VSnTnDCwvSnbXARKnVe+gRkcpb66IM3H0KhoNxPnoF7H6eiCC1dEB3t4R/z4l96EB7fhjW/LhSuTgO4e5bh0dGmCYd2DyQsr8+DziiZ07rKAYiqhhsjnh1e/Davzor75/YCBzWWcr30Px3Fw/EHl2tQ1TTGvfROTz4uWhc6hXZzB3r+JaW3HnDqH09MHgRBuYkurwn2DmIkzR1aBndZ2zHf/CwiFsYkd7PqSmsQmcHEf3m5qDZo/cw8VOnjyrMwpBk7AzANsZy92cRYCAdxoC8a6OBeuaZJVqzbDQL+Je+9T3P/nf8ctFjV9TOzg/ud/o2suEBSYKzXzPIbHtAr+8c9lquC6mhjEu7Btcexf/DtpbMZOCYBde0OZTXc+kWFDtQIvfU1mHb39us73G+KlOXjp67CxpMc16aDG5z+a/t7ShptNw+x9OXFtb2C+/n3lL9Wqcg5cnsc3/pjZR2sHtq0D5+RZzBOifDv3EE6MYXw+nJGJ5vta2VrX69iWduxPfgBeL6bRwLquaE65jEIl33+raXPeI8C7vY59568wf/gvMBdexP7iHTmM1WsCm1urzcnIEjadEr0xEMQGm9PGeA/25gc4vQO6RqItmL4hLEbUxt0tUUk9HrnrxdrgxvsSyH/te9K2J+0CAAAgAElEQVTvjUxgd7YU/Lu5hmnr0PTq4jVd4/ms6HAvvCTQPDSCLeaw4ShOuahJTnJXQOLdH+Kur2Dv3hB9slrDfe9HNHY2cJfncG+8L6Dj80Eoos/IfFY253c/gWAQ962/wq1VYGcLz9ikFiAwuNffkSHF3RsQCOgz0hjRyWbvH2RMudP3obNb+TfdA9Ir7ht4/ODfwrlL0Nqm7WjUpXPz+qCzB/dnP3xaP7i5BifPHnV1bGn7lRzn/j5UruJSaVgmO0OsZioUaxLfD7QG2CvVCHgM7SEvm/kqAy1+Hu4U2CnWKDdcynWXpVSZD1eyLKbLvLuYYS1b5Vtjbfzft3bIletcGYiwmCrzzmIWrwOxoIdc1fLzpQw+A/lKg/94L8lmpkK61KA77MV14c5mkbfm07x5ooWGtfzZ/QT3twqsZMos7pV4byFDulTjteEoM8kSuUqD66t5oj5Dudrg7naJbMVScRu8PtxCe9DDcKto7Vf6IyymK3ywlOVnixnaf8PmSL+pOtbEHHNEv1Jlrf2V7JQfr7VMhfaQl6DXIVGs0R3xs1uo0xH+7LHqWla+8Kf6Oog5sk3OVhp4jaEr7GH77j0SQ2foCPt4uFvCAOd7DrUtgfQuO5kS9fZOOmMh5vbKjAUbGNfFm0uz09pDPLmmFe+ZBzBxjmLdUqwpGMtWKlqdxh4JgrR3b0ifsjCtlPp7n8jtKRTBlAqY0Ul9EYdC8OHbmKuv4oQimFpVK+ALMxKper1avT93Rau8O1uYgRGcK69iojFsKonz2rc1Eejo1MrtXkKWzY6D+/5bkNjG1KriapcKmJEJaUU2lkWD8XgUyPl4AOfvWZlIVA1VewfGPLZelE0R8HqphGNyhpp7CJdfwewlcNdXMKUijDVXdbN7mMQuvPk9ieCtFa1lZFIc+4Ycvg4E7wBXX9e52VzD+eY/EgVl+CSOAVspyXK5UsFceVXgZ3VRrkqVCiYUwjbqmgyVSxBtE4BwG9iZ+1DKY5MJwGLOXNJ+7e1IU9M3CB+/h2ntEO3MOEpXr1Wl50nvQTqF3dvRCvqLb6iZczwKBN2f2rTF9dPRdfT6cDzw6BZOe6e2u3cIZu5jRielH4tEtUo/90hN8f2b8I//lZ4zeVEOfOOTOL0D2GJRx8Hr14Szb0jalZ0NUS3XlsA4Aua5DObcZUwmhblwVXkuC1OAwZm8IJqXcXC8fuyJk5i5KbmPtcWxdz6Gy6/iJLc1XaiURSPrHz4SUmvDUWlGFmc0ZUsnNGk6fwWwmobmc5hIjMjwCMViEVsuYQzSSZwYx7gNics7OrVNvYNNTVxA93TTKtqUy9Kk9A5gaxW4/6nCa6fvSSiez2Km7sLUHWy8B6zF3vlE2pKeQTwTZ7VvmT018w9vY89dhke3Md/4h/DwFs4//KfY7WbW0O6WtG6ui2ltl3HCo9uih+1sCLjMPZKl+INPNTE7eUa0PmOl8cpnNe2olqEjrnumWMAZHIHdbWkByyXRs+Jd+llZkGW9I0BvJs9jajXsyEntay6ta9e6Ou75nOiMH/xUgKFnCFNVJhLLc9BwNWXrbdI6J89Lx7e9Ca1t+gxN7uB8/fvYn/9I2zB1F9sax3P+KszP6J7e2oByQc5ie7uYUBj78I62Y+a+dEqBoOjDxQJOV6+0Xbc/kiX7H/8LTV8KTU2d25DpRqWsqVFn99HPoXBEmsT2zuN+5zl1f6dAwOtQrDUY7wjxYKdIpQ4TnUHubRW4uVFguC3IdKLEXkmRDF1hL4OtAf7sfpJEoU7Y73CuJ0KiWGM5VWGyM8jd7RL5aoNq3VKuu8wmy3SEvUzEQ1TrLl7HoT3sJRbw4DWG+VSZZKmO12MYaAmynimzlKnSGfZSqFn6oj5m98pEfB5WMlV8HsPVgSjTiTJYUd1aQ15CXphKlkmXGvRGPLjW0Nfixxg5qrnW4lrwOQZrDH9wso26qwnQ8+pYE3Ncx/VrqESxfiCs/1WqWGtQaVjaggIsyWKd7qgP+xxfZDt9D1vIs1uoEQ97GWkPHrnhT7QFWM5UYHuTkckxTlSS/GQuTSzgwXHMkYyZmM+QL1ZoiYk7C+Aktg/sXEPtccrVOvbhbRgao4Y5mNQAEqNefBEwByuvdm0JWloltHbt/8/emwXZdV73fr9v77PPPHaf0/PcaHQ3ZhAECU4SKVHUYNmWLYuxEzt2ORXfqlt1nTzmJVV+zUueEt/Eubl2rGu7DNuSNVgDKYriPGAeu4FGo+fhdJ8+87yHLw/roEGKlKJr8cpijFWFQgFo7LOns/f6f+s/oF/5njgVBcPoq+fQ/cMYk9OS1fKj78LsMahV0f6A8NYNhRoY7uQjsJ9toueviki1I+T25iUHRN+ZQzdq0oQOjMjnb60LNahchEefRvf0S+MWT90XQtv2+1af//9eKp78IC1ueAJ3e+P+KmonsV53AKk680kMyyf2t8m0TNN2t6FRRz37a7LC/87LHXG+hBmSy8pk614j6LowfhAvuyl/9/r3BSgku0RfMzKOfvk7QnHzmVDaQ9+dx/M6QuzZE+KCN3EQb3EOFQiKAD2WhK0VyTSav4b2+YSepJQAstEpvNdfvH/8j31KXMjGplBjU3g3LqI0ApANU8Tn+6vEP532oupVmSLUKuhURu6zakmmiYC3tS4g75Ofk9ybX/1tDNdGxZJ4V89BOiPBlvUaBAPSHJfyQtO58i762nnRQCzOyVSmVkVrLXQo1wWfKROM/A46nkJNzorWpVGHVgsdDMLd2+hiAe2zRF9T3JPtWlYnfFYJSFlf3j8uXS6Kq1wgKC5+2+uSzTN1GG95Ad1oSEBnYQ/dP3z/hGyvQ98Q6shD90X4sYSIw9O9AurqFfS7r+BdPYeybYz+YQlWtdsSwFmvw8NP4L31kjjMVSvo6xelwZ6clanZS98SStT6kjhmrS/D8gLK9eQeLObh61+FIw/LMyscwdtclSb79nXRAqW6Jfvqzpxsp1aWiYs/BMcflkmt5RcDkUBApml9w9Lw9w6KKUP/EAxPYoxOCXBfW+pofeKymFMuCJBo1IWWVSmJwYhlQSCI5w/irS7C3g5q7IDcPxurYrMdCIrbWyAgC0DROOxtS7bMnTlxSkumYXNNDFAME8OxZWHGtcVKOZUWu3zTlGybakXc/25fE4eo3j4BtfGEaAgX50Vbs7sDSmEcOg6PfUqmdVvrAkqOnUbnd9GmD/AE3L3+khzb4IgsIrTbEmRbyMtU7D2ZMvre8xx+quPcv+bytACMya4glqFYLbWwDIOW47Bdsdkot7E9jwPdQfpjfuJ+k4btsVeXrJf+mJ9YwCDsNzCUwjIMDqZD/F/nd/j9kxkeGYpxLVvn/EYNvwloeG21TDrip9hyyFZsXl0uY5mip9lr2GxX2mSrLQotj0OZAFeydcKWQSrkYzjhZzoToti0AcWvTHdRaDgc6gkR8vuwDMXtXJvnJhIUmg6WadIX9eNpcU7dKMs0KVd3aHuapu1xfadB+IHF8oN6UP/lq9h09oHHz1NL+RaTXUEAmo5HwOzoT37Sc97yo7fX2ana9EY/vAkfTQZYztdR8SSFSpNjfRESQR/HeiNsVYRvqi+8gZfPMTKcoel4XN6q0h+1QHv7K7PDZpO19CRMHESFI6yV2gwnAqRCvg6lTIsVZ6shGQhLt0WHU8iJG87wOCrdg3HoIaGUrSzA4i28WkWasdKe5M/s7cikRSOaisFRANyOMxjXLkI8hXHiUaFeLM6j6zVxpgqGRYBcKsiLPhLB6x3q0IMsDKeN4bMwjp4Setq9evAiRZkmZqZPsnP2Ojk+jiP0okRKQE8khsplUcMT0mAlu1GhsKwM9/RJg/T4M7LC3T8kzc3IpDRweznI7WD8yvPSSHYskXW1LK5KuR3RYsUT6Fe+L/bH4ahMdq6cE/B585Jsa3gc7syhRiagfwRWF1GxJMapx2Vis3RrnxoDYGjvfYYMogUaR68u4jbqooMJR9+vaetY2WIYPz1Rvd0WEXthT5rV7DocOSXNbD4nzmbP/hpqaQF16gnMdK+AbZ8FdkumTd0ZaZR7h4RONntC9AVaSyO4dleMNSan5TwrJTbBP/gGum9YJg8amXjYLVntb9TkOpSLQjGrlcX+enlBqD+X3obhCbTnoBfn0OGQrJ6DNOGX30bXqxiTM0LFGhpD1apCjSuLIxc/+DagYWtVGuJmQ9zCDOO+fbPpk6nBAcnb0dWyaN+OnYZKEePEI2KrrBHL78V59NYqynGkaT7/Ot71i6jDJ6GrW7RDNy5CIAwXXhMg8+I38Sol2cdESswhonHZz3ZTxOmHH4KFObmv0r2wsy1Tpp0Nacy31sEKyn35m78n4KVRg8WbMDYJjzwtU7SbFyV3qpzH+OyX5R7PbuD94Btw/RJ84rPoGxegXpfj7EpLto/nwTf+Wu6rH3wLFm8JLfalb4thyq3r8vxKJEWjlNuRXBbTQN+6LmG/00flurkOxJOonkGMg7MC0L77d+jlBbydrFjNb2+iHvsUeuEGGCbed/9eDDNaLdGwNRroS++IQ1xmAJ79dXkO5naEdry7ifrkZ8H15NmaSHaCbk2h/sYS6L/696AVxhd+CxWNii19qSD3qOWHjVX5PuY7Orl7ld0UYDU4KlS0B/WBWuzoUlaKLXqjfkI+g+8tFIj4LSwTon6D3qifzVKLgbifK9kartY8MRrj+k6D5490U255bJTa1NsubVemHEcyYV5dEnH9c1Mp2q5HueWRifg41hMR05+m5MaEfAZN2+X2XgOlIeb3YWuN7brk6i7D8QBRy+DN1QqZsMVSQfa1J2Lxl5d3GUkGWC21yddt5nfrDMb9JEIWzx1Islu3UYDteLiupum4XN2u8+hQhEcGo2yW22yWWh9wZvu41AMQ86D+1dXdfJOx1H2aykqxxWhS/hwLmJRb7+cZ6+116BtksQaT3cGfuN2o38TTUGxrijb0xfx0hXykIxYNx5NGKRyFjRWi3d00HQ9DKZx7GWb3rDLzOUik9p3IPC3Wj5mIRa5Yl/XqcERWyk8/KSvG1TI6kUKdeAS1uQq9QyIADUfg9/6dOIt9828kLyYQhjd+gI5K8rpSoFwXZfnRVgBeeUEalloZ48zTncyaoNDS7Ba6ZwDmr4rINJlE37gkFIgXvy7UlcERdCQuL2LYX2DX2xuyqvqgMHv6RPxbKsh0pH8I7+YlaQxB+P8HDqG60ijXQd+dF0evUhHOPAOZfsyTZ+DYI3DlHXj4CVQiKU1Rsy7bu/AGbK2hHnsGXBfv+gVpiJRkBRmf/U3RGzz6jACY449Ijo/2ZKVYuxK42juI26yL/W13D7rZwNtalenM8UfRt8XOWXueCMSLe3jzV0TXsnBT7oNgSJzufuN3Yfn2+86FsvzSQGb6hNr2IaXnrqC1h9E7KI1avQKBIEYwhHbaIpQeHpPpxNAY1Mq4F94Q17N2G/pHUMEganBMAj/v3paV/lxWhOCvvyC21cqATI+s0B86IROB9SVxJ1u4ITSmslgye3u7Qkk7eUb0LsoQelTvgKTPBwJiptBq4r36ffjhd0GDujOHd+MS7gtfx/unszAwivGJz6HDEQE9niOUrtnjQgeNRAUgBMPohTm83W2ZcPx49Q0K5Wt9WZrsC2+K+UNhD903IvqP9WUJ4QxFZNKX6QOnLceggI1ltFJiZ92VEf1atSjN/sEj8Oyvyvl49QWZClUKMiUxfQIMxqeEPpZdl/uyVhV9yzuviHX40m2wm0LHKhfhhX+UZ8vUEQFDPku2GY6BduXPu9uAxkh0iWPZwpzcA3dvwegB9Iv/CLubcg87LaEgprpRkTiEghAOo1pNAYDZTQnWXLuLOnhUAOfgiCzupHuFvhsIyH3/xKehUkaNTQmI7xkQC/RaBQ6fEMpfNIbxxedloeb2DQGe1QrG6afkvnryM9BsoIt59NxV9OAIRnZTNCtPfkoc/NK9GN09Mu2pVcTBbmtNFs7eflmerT0Doktq1EXj4jjo1SWZZFaK4k63viTT83JRvjPFPQGBxT1UILjvyPag7leuZnMr1yBgKCKWwbVsDb+p6IlapEIm66U2Ycsg5jf5/p0iqYBBy/bY6kxoukI+cnWxQvabBnsNm/GUn1u5Bk+MxXlsJMbxvgjdQZO2C0+MxCk0XCxTcWW7SlfYJFdvE/YZXNupE/ebZKIWYb9JreVSarj0Rf08ORZjqdgmHjCJB30c7gniNw0G436057FeamN1fHQcrXG1h6PhK0fSmIYiEjC5vF3j2k6dmbRMlLYqNlezDT59IIlWmvXSTzbZ+WWuByDmQf2rqlJT+Kb3/NC9zmTg3spwX9Riu/JjD/t6jaYVRsWSBMr5D2xTry7uh/qN+9us2RYHox/y4btbeKEwBAUIjaeCjCYDbBdqApS214V2gSYd9bNbsz+4jVxWrE7rFRHiKoVx5CGMeBIjGIbCHl44Cvms0GyqFRHHhkLivtTbL3qL0UnY3ZTwPv99YKbLBbhzXRqw4QnRdWwsi83u6qLQbfayMHFQGrt3XkP5/KgTjwgAm5wVClW9Kpqe91ajJtt7UDKJKRf3J1Pq3nSiMw1TSok1MkigYziKqpZF+/Dwk9LoLi8I1SnT30m6d8TxqlmXhtQwYXIW/eYPZcX88jn5PLstFsvZDbHk9Vy5ruvLKMtCBSPoDs3KW1sSEHL2z9GmTyZ3e1n0Wz9CHX1Y9jHdKw3T2hLYDurEGdGTjE0JoMhuSpPbaIhtcyrzwaTxTD/61RfQm6sSoHjuNbzXXsS7eh69viRhimvLIsAfPwjVskwb+oYEcFRLcn+vL6NOPY46/iiUixLWGgjIVOvkY6h2Sxr5dI+AA8+VJv33/xjQqKMPQ60m2qFzr3cmIXWYOiLH2qiL2L1UhIII15XnwYFDAuZ2tsVsAS2r/y9+Q67HxTdRj38K2g2Zsh0+Ia5uIA3m2l30i98UIffbr0ClM0Up5VF7Oxhf/gPRfDTqOBuraMsvjoAgIZd0rvfqomS4jE3JlEhr9JV3MAIB2FrFS3ZhzB5H9fThvfYiWhloZYp5gOvJIsvCDTh+Gj00CpUKrC3DxDREY0I/e/RpdE+fTK2UIWL2Yl4A3DuviN4FRA/WO9AxMzDlOdPdK05gO5vQ1SvHNHdFQOChkzA0IXSrz39ZhP1occ+78KZQFy+/A5MHpeHP5+Qc5nZkoaS4Jy5gdltogrevCxi/fF5MT4JhoQleOy/H3W7Ivk/MyHW2/PL73i6MHRAQ127JlNvnEwrgyh04fkaAVK0K7Tbe9jreC98QIHTwsFDL9nZBadTGMvQNSB7Sl35XvmuthmRoFfJQq8l0DMQAZG9HroHnyRRQKaFGDozIvZ/LYhw7LfdiuYi3dBtvbxdVKYEyBSQ26xJwWsiLW51hiOuaP4h3L2D4QXE332Q+12AmHWImE+bydo3RRIDXV8p0hXwYSrFXt3G14vHRGNW2y/mtGqOpALOZIJe3ZAHw5k6dqe4gB9MhNis2Ly2WCZqKatvj5btl0mEf37xVoCto4GqPtuuJpbIBtqewPTAMxbOTSVyt2Sq3abseu3WXVNhkPBXi8maNgZiPluuxUmjhaYPhhJ/bew1eW6mQCBpE/CbH+sLMpMOsl21Wi02ubtdIBk2GEgFClsF0d5D1sk0mYhH0GYwlAvgNiFg+BuIfT5r3RwJinn/++f/4/PPP7zz//PMfsjz0oB7UR1M/L6e31nbZqtiMJO5PYZYLLcbfM5X5QGBYo86yE2C11GJyrFdelD9ejiMvzXYLqhWOTg2gwmF0oy55D4vzQkuoVVGba6jpY+h6lUC7weD2AsPVLVaSo6jZ4/ub7A5b5Go2paZD/D1BnF1+Ta7hdAINb6IrZdnP4h7aMOQFuDgnK+Y3L8kxJZLohTmhV+SyQoNJ94o98s4m3u42ulrEe+MHsrKc6EJFYhiHH5JtNxtiFeq6soK4tgSjk6jdLRE8Tx2CO/PS1A6NoiNR2Zf9k9q5dg+oZO+vngF0KCLJ4UsLqJHJ97sKdUqZpjh0dZodwzBkGhOKYByYRR0+KYGGPf3StExMQzACnouRTAl1zHNlevHqCyIYbjSkae0dgAtvyMr14KgkrccTYm/bbmEMjwsQmZgWEXSmT+hJyti3Q1ZdaVnt391G9Q2K8Dm/Kzvv86EbdWkMRyZQmyvQauDNXRYaZHZTUtRX74BjyzShXEJNHcJ46jMy1avXZdW9UkRZfoxkF+qJZ6F3UAJbgyEBZPcUbXYb7t4Sh7jVRdmXaFwsdDdWJHSzuIdKpWUymO6D9SVU7yC6XgbDJ1kptYrQnIIhuPquaGlcDdqRPJ21ZXA90YFtrgmQatYF9DcakpHTbsDpJ8WtrTsjoYv+AMb4tDStfj/q0HF0PIEancQ8eFS+J70DsL0u52dkQv7vzDEoF7CX70hz22wAQg1zL72Nfu37aCuA9+YPcf/+z2VyGo2JecHQGBx9GH74bdxv/624B6IFsJx7Fbp7UM99STRWuSyqVhEtzM6GgL0Xvwn5PHruErwpVDm9OC/6qU9+TsDAGy/B5CGZ6G2uwdKiTHgaDUgPiKnHoePyLCwX4OHHhf5WKQn4GxyVyYg/IM/UwVGhlVWr6JU7MllOpUWbEk/et8MeGhVd1fQxcfQbGEYdOin308iEOPb99b8Xuu36sky1FudgdVmmPJpO4KcjepZWS6bG/UPy3Tn/Oqwt4732fdGd+Xxy/bszYgTw938u35FkF0YoIpOSm5dl/8Idqt9eVhYWrl+UjJfFW5JJ09svmpf3WM2rZhO6M52FCVeuQbkozmVay32Y7hVAphTKbuOtLEIoKotWjz4ttNB7ttlDY3LcA8M4K3c/oofXx7tajkfT9hiK+9HAermFTynWym1MQxEPmEynQ/gMRd12CVsmqZBJtmIzlgzgeIrhhCw05mo2yaAPn6E42hNiNBVgvCuEoTRPjcV44U4RT2vqjofjwWqxza3dBkd6o9RtF6U1tuexnG8Q8Bmc7I9wLVsnakFvJMDl7Sqrpaa4iqFIhy0sQxP2GSwXmkT9BoYSS2jLMIkFTGbSIRJ+H2+sVjiUCZGrt+kJW0QDBmulNqDpCvuIh0wWCy0SQR9blQ9ZNP0Y1Ec1ifkL4HMf0bYe1IP60Nqu2vT/BD3K/1eVWy7r5TYzmfcnbduexm9++Ndgt2Yzd2uVzOgQAzE/21Ubz9PvA1PatvctU9neEABg+aVBXZwTDvj4QYK5LWqLd+SlMzwuvPCtNdT0EaJBP+2uXhzv/U1+T9Ribre+r8HR7RbpqJ/8nbvyEkv3Spr66l10pYxCobvSsh9D4xJYODwhL/y+QYxGXUT5mX7Y3ZLGJhAAp41KdIsu4+ARoTEYBioQEIch00LHk/Ly1kimx9qyUBVaTby9rHDrS0UBOBsrkkmxtCCr09H4vgj5Qd0vNTEtlKxOjor6KXbTKhx535+NZJes6NaqqOmjkOjG29lG9fRj/s4fCae/UUcdOIThs2Qq19WDSvdgnnlaQgnPvy7g13VlShaLQ08f+q2X4egpSQzXHrzzCqpZR3VlMGaOYR46CdG4aCo2RaPh7W5JuF6qW4BYshtvfQXv7/4cfeENdDSOSqVRE9MYJ89Ido5lobWHPve6NNyHTwoFTXtCkwFUd484OqX7BJivL8mq9OYqamwKrl9AR+NopfC+/zURos9fRZdL6Ny2AKBGHa0MWLiJPnRCbMj7h8Hvx3zyWQF+a0tC53RdCQutluHhJ+W+LRbEYtdxZcLZPyzOblur0vSm0jJZWLoluqRgZ2LzyvcglcZ46rNiP33xLZl+Oo7oy9aX4eHHBVTNX5UJE0gTv7Uu++C6GIhWw5icgb5hnI1l1NY6eB7elXNw4jFxTnviWRQadeoJcXz74vPSKPsssUBeXxYg/NgzknR/5JQAtEoFle5DzRyTCVOyG93dIyYfU0dEbN7TD2+8KJOZ7VVYXpRA3EK+MykYEpCc2xEAYjvgOdKIg1DWuntk0jA0CiiZ0Ny9JQCid1AoX+PTAnivnpOptGnB8dPy3Lk3QfMH5FcwKJ9pdCYQCgHNW2tCqwuHZQp4/LRcv3Sv/L/slgBd25brNzAk/767LQ3/0m2wbcnQKRclrHRrXUT9xx9BmT4BY33D8LW/EKfAt16CIyflezx9VICzbUuuzvKi6MJWFmUCurywP6lUY1OywHBPr+Lz4TVqqGQXKhyFAzOyIGFZ6HxO3j2ri6KH8fnQd+YlCNO1YWtFrqdji0lIVRa4lOWXd4FSGJHY/sLXP7d0YU9omh/jultoohSMpYSFcGWrjqc11ZbDZrnNkZ4wntbEgz4abQ/H9UgEfeJGX7HRaAI+g/VSi2LLBQU+U7FabNMd8nG0N8TcToMb2QY3durkGw6WYbBZsdmqtIhYJl+cTjGYEIv7rXKbN9cqbJZblFoOw/EAIctkvCuA42k+M5nk1ZUKxabDVq3NUrHNY6MJlCHC/uVim5nuICvFBlG/ScCEpVKTWtuj0HRZyrdoe5rzGzV8JlTaHif6o4wmA7Qcj4Zts1po/MtelH9mfSQg5uzZs68CH+TZPKgH9RFWte0Sfc9U4metYtMhW20znX4/gNmqtOntOJ05nmZhr8HCXoNK2+Xd9QqgmY0L9Wy12CLqN7kb6uHOwipzO3V5oWws77+UtWOj7gGielWCAQdHUYZB/4ExNo2IrEYrJVkb94L9tMdUJszC3vsfIt0d6+Z90LS5iucPgKEwDnTCDvuH8FxHXl7D4+i/+Q9wYEacp7p6pLG0bZQ/IBajPf2oSgltmHiba9xrJnQggDr5qKRbG0aH1oa8CD0XtbGCTvfgtRtoQ+GhILeLnr8qWShf/G0JNBwcQ8USGJPT8kI/eFhWnJuNDzTi/9pL+Xyywv7PKX9QePLrSyL8j8YkALLjUmWkuqFalnunf1iax94BdN8AenEe5dCeBsIAACAASURBVNiy0lyrCtUsuyWNnGHA4rykjIM4y40fRDdqQt26t++xuIDYZDf6e1+DG1fQQ+8BYcEQ3L4m1KrdLDTrqMj966/8Abz8njSZE9Oyot9ZOVeFvf0gPwDv7VdhH/RoaWYbDfkZ10Ftr0ko4s42RiqN6h1EHZiBWh1KeVk9f/tlPJ8Pdf2CnKd6RaYytao09Z4nzWyl3LEPLsD6iixCHJgRy+Zzr4o5wPamNLq9Q0IvSnQJrSneJef5+kWZ4mhPzv3GCmrsoDTMxYI02e0m6pFPYLTasLeLTnTDpbdllb53SBrq7U2YmMGz2/J/V+6gZo7gZrfRezuisbh1DVUtwtgBAUVdPXiLNwWwbq7C0DhqbFJyfeauyhRuax2eeg7DH0AdeUi0bU5bwCuIycLCDZmg2J2phWmJHmRkHBJp0Q15Lvh9oi/aWpcJSaNjSJBICh1q7ooE5wbDcr86MpFmckYAomvLzw+OoIfHBZQADI3Iz/ssePOHch3tltDe1pYglZFz/uYPZXJ1+ITsg9ZguwIoO3QtdrPQasi0JhCSZ7M/KMAz3Qc3rgjoXL4tILarW6aOX/tPkuHyxLPw8rfgj/9n1PaG3Ns3r8Jr3xeTiMlpQEvQqufKd8NQQrEzTclssiwR36fScryGgX7nFZg6LN+FVmeqFozIxOrkGRgaxfCLW5qamhUK6e0bcu4MA574jADNC29CMiMTpmgM/Td/Jt+rwVGhJIKA+3oN3z3d2M9ThVxHp/TxrLrtYruaZOj+1LvhuHxqMsncboP+mMU3bxW4vFVjLBFgKBngb6/nSARMtKc52hfGbyjmdupYpsFE0s92tU0q6KPS9kiFfKyVWmxVbGq2S2/YZDHfYCodoNJ0UIbBr8wk+dtre4RMU3xCXI9MxGKiK0jT0aBgLBWg2vZ4ajRGvukS9BkMJQIMxgKkIxarxSYxy6AnYjGbDlJseayV2nhas111adseAZ9iqjtEvuEwGLNYK4mIP+QzWMw3CVsmn59K8dLdMsOJn6z3/WWuB5qYB/VLW+8Nd/x5tpGvO0x1hz7wb6WmS8v1uJVrsFxoMZEKMtUd4tRAlGTQR7q4DQPDLOw1mUoHiQVMpga7OOBrcqA7xPm1Eq7niZtU/6CsQiL0K7Y3UO+xQzU2lqG7F6OjecBuywvw3r8rGROvZ4si4PVcvPNvMhT3cyffSWN2XdTtm3SNj5Gr2/LyXLxFY3UFYilxAOofxBiZFD56cU9ErJaFSnbh7W6jMn3C9w+G4caFTmaLD1WvoeIpvGJBKC7+gKy4OY6sOB+SnAy2NiDTD+t34cSjchyHTgjFCWSVcey+OxU8oJL9F6l0j+ijJmdh/ooAxHBEmmgQYO040sREIjI9m5xBDYxKw94zICAKMOIJiCXwshsdi9wonuMISLl5WRzKNHIf3KvJGfSta+C00YaCZAJe/R5eU3IE9NJtdKMmzWGmVxzs3mOtrbsyQiMKhkSIHU9BpYzh88PRU+hL7wDgXXobAgHMwydkhXtzDfqH0Z6L/sZfCSiYu4p+6ZuibQiGxXVtfRnl92GcfkqA+bHT4iL11GchlUH1DWMcOIReXsCwLKEuFYui89pYliaw1aGE5bJCKUr3igbEc9C7WWmw+4bEondgREDYbke8fupxAYBDY+il2wIW1paEmpXph1s3MCamRTsxPiUuUtl19Lf+WvJLtCfOU4VdmXRMHJSJQ7OBSqakiU2mhAZ44JBQ+NZXZJLw6guiv+m4l9GoSzZPsyHTP38As28QIlHJnDp8XCZaq3eF1hWOiM4o3QvNpgDRgAWZATl+AwEUtSqE4wIKTp6RYysV4NxrQCckcnsdolH5Gc+VQMxUt+hfdrdkuuV5gELdviGOYH1DskDy7mtyXk1TaLyRuFzjzRV5dt28KGBk4iDq8ENCdZy7AmUJjmRzVfZp8SYcekimMLYNg8NyX+/tiN30yh35fXhcqGdtWxwcDSX31/nXUac/gRkIoUNhARKlPTmmdJ/oc1ptaNTwvvs1vLdfkQUkPPmcvmExX6mV4Ufflen3kZNorWWx4eRjAnD2dkVnVKsKHWzpNrRaGF1piCbkWtht9OaaTMq310QvtLEiz/u1JaGTnXkaCrvo730N79Y10cP0Dd0HL70D77Nh/s+uH6Ncf9xqtdjGMhT9MT9eR4OSifhoOR6HesKsFNsczoS4sFnl3c0yEcvAMhSbFZtK2+Wd9QoLew3ObUrkwm7doWGLTbPjaRytuZ5tMBDzEQ+YdEf8JAImV7YbNByH00MRVoptjvQG6Yn5OTUQJVux+bWZLkDxlSMZBuJ+Grbm0aEo8YBJ29VYpmK31sZQmsM9Ib4xl+cL091c3q7RFw8yEPfTHTY5t1FlKO5jtjdCqenw6FCUXzmY4p21KnVbsmkSAYOQT7FWauH3GYwlA4T8H8/r+vN71f6M9fzzz/8R8EcAZ8+eJZ1O/6I++qeWz+f7pdmXB3W/PK25UdyDYJDpHhGD77oV0unYz7yNbKWFqR0eGbm/Anx5o0TQZ1Ju2jhWiL5MnMORD1LUdpwKyXKZalc/A2Gbga7w/r/ZhR186S76PZd3d1IcT6YI+NI0bl/DUKCqRfxnnsJeuImvuxulFI0rb5OafYp0OoH2POy+fgD86TR2KYeVTpNOw+LVGzjDk6QWLrJatznslthsmfgbO/iqJXwzh0n5fFwzQmht4qgYzXKb3qMj9Cbj4GmUAW6qC7q6CT3xqf39rv/gW4Se+QKN3S18QyO0VhfxGaBGxjEDAax0msLFN4j+4b9DOQ61s39O9L/5I7y+PqyeHlrpHux6GdNuYh59CIVLM50hmO7GSqdxi3n08Ci+nveHrTmrdzGOnhC++IMCPprnjl0vY/X14SXiqGCI9sW30ZUCwdkjANQnDqAKO/iCfrzHPomzvoQvHsd/4ila77wiQCcQxDAMfF/6bZqvv4QanSD4u/+G2j98FR8evic/DZ5LK5XCu3uL6OknRAuTTlPfWMK7/A5Obofwp7+A53ro29eF39/VjVcNYITDuPldvPUl4p/9dXHAs9vY26uoWaEuepUS/jNP0fjRd7GSCaypWerrSxgL1zGGR1HmBFY6Dek0jY0l/JEQevoQ9VtX8RJJ/I89TeuNH5D4t/8T7VvXUbjoUBDfI0+ionGcYEDAVaVMqK+PasAiMDiENTRG/aVvE0omcU+dof7dfyD+h/8D9Ze+TePNlzF7BzAyPdh7O3iNGv6pQ7j5HNbkLM7qIlo7WJMHcXO7UMrjmD5cAwhHCRVz6FaT8Og4rnZx3nwR2zTxH5jBuXkBw/ITwsPp7sbbXKW1sSQapngKamV8x05h9A3S+tH38Y1OEFIa86FHqL/wDZx4EqNawZ8+jmq3cH74LcxMH77jp3A3l3BnDuNvVLBOPIx9Zw7z4TPUdzbwHZjFe/MHhH/1eZTpo7VyG6dWwvfQ49Q21jDcNqp/AGd3B5p1/BMHsTuBjDRqGBq8jQLhL36Fyl/9GZ5lYbYbGMPj+IZGaa3dxRwYQQUDGJEEXrWEEYvhtloYmV4Cjz9D5S/+d/ypNL5QCGdwBCe3i+/UGQlQtZuoZBfR04/h5vdovvUjArNHaLk2dmGXwOgEupTHO3wC+8JbeJ6L4XlY60uYTht39S6tRg01fw2jK43nuViNKrZp4fNsvGpRAkSjCeyeHlR+D2P+Cl67TaB7mvCv/9eU//R/IfTUp2kv3UHbbUzt4m2uYHalCVaL2Llt3ICFOX5IJkeOgxkM0BoZw1lZwD80jgqHUFYAe2cD38i4ZM+0W9i3rmP4LFQsjlkrYx6cJdB5BtQiEewXv45/9hhuOELoiWewb1yCSh3f5DTKMKnfuIjR249ZzmP2D+Hmd2j5/fh6B2h8/asETj+B2ZXBXbiJ9fDjuOUi7toSvstvEXnu1+W95fORmThAe+4qVlfXvq3/z1perYI3MIhu1OU7+TGrasvBqhlMdEdYzteFpdEy+G9Pj7JSaDDWF2SrAfFEnOCejc8fIBiJMOYPMdYV5tpmhZvbFRzP5n98eopXFvd4drqHtuPxF++uMpgI0jZDHB6OcCdXBa24uVOmJxGmaWscBX/8zCz/dCNL0XEJhQxCIYiGKhQ8i95UjFOT/cwV15nsDjOQjnB+rchjB5JEw2VeuZPjbtnD8CuSkRCnJvupscdkdwTLZ/Dy7Ry9KYNyw+bXjvTSIsulPBwd72ertUM6qWnYHtofZrHqslFsctoX4uHxXmKJKOmfMo35Ze2Vf2Eg5uzZs38G/FnnjzqXy/2iPvqnVjqd5pdlXx7U/VovtxgL+3DtGq/ezDOdDlEutciZH7QBzNVtcjWHkaSfsCUUrWy1TcvRjCQD5HIyqq/bLl7DIZ0MkKs3OJIJoRtlch9CBS1m8xRUm7nlLQ73hNndre2L/nU0BVcukIxGGRtJ8+atdQ762/jWV1GOJ2FsuRzaH4K565DpQ1cqFCtldnfb4ho0MAI7m+ilRVSliurcg/F2maU7i1R2i+yGkiRXF+jp7uXi8g6j6TCbm2VxrhqIMtIdwtUVcAssZvOE/C3JKTj3uljtmga199zbnmlRe/s1tDLRtZo4PAUjkmHwic+hVpbxGjVK2sCbv4EemaTdaEOhgMrlcPf2oNFE5fNg+NA3r6KmjtLc20PFcuiFmyLy/7Hvk85uo8JxqH08Obf/JeqjeO7oznUBoCa6D299leqE/J3nanR2C8MKSqBp24EbVzBiKTAsSPfjvfp91OOfwqg38doOqitOLZ/HC4XRtouxvoKulNHjszB3mcZL3xHtTiSGd+UijIyhZo7R3smK7ffEDPgDopUpl1GNBtrVsLeLXSrLqvCtazLh2F7HMy3U8iLK9KN7B2H5LkaqB8+0YPUuamJW7HA7x6m7+/Be/p6sVvcOQSlP6+LbgMHu976BmjoMOztifRuMouevy2RwbQldqVBZWgTDR2NrExWM4vUNU33tJYyjp3AXbtL4u79EDYyg6w2cu7dFB3biUXjxmzR3d8Dvx95cE9pZvYrts+C3/hD+4S/E5Wx3BwxFY+QA3L1F8ztfk2DZag26emg326Kx6e6h/vdflVX8ShlCMejtgxuXO+LyNqrRRIfCtHa3qV94B3XqcbxikYD2aCW7aL32IurTvyqTAY0YNSwvoJ58lvr1SxiJbtyXvw+f+KwsbtRr6GCERkEseL2VZVmVv/i2OH0dPiHi/FAYxg/iRKIypfD74bf/e3FNa7cpvfhNoUr5Q7iZXtxQDPulf4J0Bi+RAl9Apg3RuExlRiYgHKN19RKEI7TuzNHyB5Dgz2nczTXUsdMyHYjEaH3nH1EHZtCDYzS3N+HKu/A7/4b6P35VJjjlEnzuy/CNv8J7/AytgVFUq4U2LejpR7dbuCuLYBi0owmIJ7ALoiEBhWtaUCyiE124tQqk0jT7x2j+P38K/SNU9nKS3XL0EdqNGpw4A+dfp765geoZROdzqOwW6vFPi85ldxud6IJiEafZFGpk3xA027SKBYxPfBbvL/83yOdQZ54WlzUP1MY6VKqid7l+CTxNa30F9cwXabz1irj4XX0LBsYwijm88YOSeRMIYkzO4i3egkaDltaQ7qWR6JYATc+j2WhK0OduFt55jdrEDMoKodaWKVpBCYu98La499GZlm9voPo/XLeo567Id/bepD2bhWx239zj41JXtmr4fQoV8ZhbL6DQzG/VePO2ImKZOJ4mbrq8Mr9FPGCS9Nn47Dr1WovbjTpO26VQq5EJW5y7m+WRvjC7ewU8DX7lUqs3cJsG13INmp7GcTyWclUmUyEm4hZDyQAXFjcoVhrM5xrMZkLU2y7dQQPLaRHULt+7tsJsyiLldyiWSgyGPf7h0hq/faSbfDnMcrHGbqXO56ZSzK1mSRiau1s5emIWTw0FqNkury+3uLG6g8+z+dH8Fk69woXlEoMJP0d6wlxd3ePLh7t4rDfCn767jmkolJ3Ab4d/4rn7RffKAwMDP9PPPaCTPahfymrYHhG/STxgMtkV5M3VCgOxDxf1FxoO0+kguZrDrVyDuZ06tisA5r0loZF+Wo6H3/zpo9PB+i6vtxOMpwLo/C7MXxVRMQg3v1lHuw6GYTAbaLF84bJQezJ9+9tQkRjUq/ICmJwlE7bI1R0RWVqWAJnrF/ZzytdKLXStwrivxY7200r1oDJ9mAdm6B/uo2CEmXSLTI0LbULvbMHeLurJ50Tk6bfwTFNoav4AWAGh9awvSfJ4NC6/D42KrmD0gACzYBhVKYr7zuRM56TuYTz+afTKgtjjglA6PKG56LVlCV/s0OP0xqpw5n+sHqRE/wJraAwqJaEIgYj7sxuivSrmMR56DNWVxjv3qhg2KCV0rkLHcc9uiZU2wENPoJo1EXQHQxitBngeOruB3l7H21ju5Hj4RGsVS6IMUxLCb18XHYSnZR+UAbkd3Lu35d8OHhFdWKZfGtTBMXSpgOrqBbuNm90U3n3fMN7ld/b1MdrzJEzStiGWFN1Luy33eiAA+R203UL5xSpXN+tyfPeMN/qHhYJ24sz+KTN6B6GQwyuXJGTR5xOHMb8l9KfHPwPXzstnJERvxPxVoVGGoyL8fvdVoVnu7ogGJhiGdzvNe08/NJuodI/Ym9+dFwAWTQjoMX1CTVKgMv3ieDV9RL6fhZzsT1cPtJt4d27KhORewn29ho7EUH3D0tzfuCwmHIU8xBJy3op78I3/JK5o/cMoNHp5Afelb8tzYXNNdCY9g3BnXihkU4flvF58SwCV6Yfzb8r9tZeVRtpxxKXt0ENynk4/JRqU/C7sbQuFLN0nlLt6Tc4TGh5+SuhqqYwEjQZDIvDP9EGtjJqcRh19SEwghsfkfHdl4JXvCtgrF0VUv7UuWqpbN4SKZ1lyXSYOYnzpd+HIw2LRHAyJ2UKmV+iMPQPiZHf4IaG1WX7RL60vi/lFT7/obIIR0Rh5Gu7MiSbqwuvoc68h4OsQymdJ2GggKFqaY6eEjuYPiKvaV/4A7s7jLc4JWD14RK6JRizxH34C5blouw1PPSfUt1QaVS7IPZ7dgMeeRs1dQdfrGOGo7OPOJnq9YwTQ1Q25XdF93b4hmrhaBe0PoG9elOd1IoX+wTchEsUrinRZ+SwBTx36J6uLQmP8kNLb63Jfd/KglFKip/t5tTW/4Noot7mwWWUg5me91KI/ZlFouvzmoS7SYYuAz2C3ZtMV8pEISu/hNxXLxRabZZum7XJjp85ALMBew8VnKBSKuu0RtgyCPgPXg7ndOoWmy82dOouFFsmgj96Yj3zLxVSKxb0mM5kQE8kAlmHQcjWPDcd4d6OKYRgc641wsj+Kz1Ts1R2mukL820f7aLhwtD+MzzCY7Q6yUmxRbrtE/LINQymifsm0+f2TGRbyLX7zUDdjSYt/uJnnUE+QYsMhFjBJR0zu5Jtc2a4R8xscygR/Yn/1y14flcXy3wBvAdPPP//8+vPPP//ffRTbfVAPCiDgM0iGTOq2+xN/RinFSDLAdDrEwXSIocT7Acy9ZlopeSi911b5wyrsU0yng4Q27gromD0uLj+dl4DeWMXNbqDrNcz8rrjrhMLy8n/fBwN7Oxj9QyRDPgpzN9F9g/v7ogZGUIkU5fk57i5v087vQf8QB3WZmfFecTWqV+kKKIb8NsoTEb9uNsV202mjqiX03dso14NLb8HTnwfXwRgYlpW2TD/6yjkJtgwERY9Q3MOYPS4WouEo3uW3wfMke6OwJ5kQSkmjFI1LY1nMSXCbKUJV1TMgzWizjq5V7ieHv7fuzO1nnzyoj7h+jJuuDFNsVxduoB0bI5GCWBJ97bysrm+uygq65UcffRh9+V0RrjuO/P/TT+2vrBp+P8apJ2SFvlxETc5gTB9BpXvR6X4BI8cfhp1tVDQuO2AY6K11cTvTWjJnUmmM6cOS4bK1ipo5dt+a+e68aE/SPdKYvfuKuOD96DuoR5/GOHwS1Wqg63W8N3+Ifv0FiKUkHHBqFpbuiCg/GEI99xvStN65Kc1pPIm+el4+FyDRhXbaYJiigcn03Rc9Tx8RTY1pigi8b1DE+jPHUL19UK/DU5+Rxtm2xaq8f7DjPDgNV8+JNbACPvub8IWviOlGoy65OjcuoocnwPCJlkUjwGh4EpbmYeYoxFPo6xfkfKMEhBTyAojKJfT0MdGkRWMCFna2RUvz1/8nengMrr4Ls0dhbVGacNPE+9pXRQ+V7Bbw1DckTnLVCirdgxqb2k+kR3my0v7wk2LmYVkygTl0UgDAzcsi4E92yzFYlrhy3b4Bj35C9CPjU6L32V6XBvzWVeRgtYCDaBzV0y/bsG1xsQuG5T6ORFFf+j2ZvimF6h9CdfUIcOnu/P7IJwQcX3pb9iESFcCV3RCXs3QvmBZedlP0QukeeR4HghDwC4icnBXtkuvIPtktcXIsFwQgLc6L/igoAa1q7IBoX8JR0WOFIhiTM2J3DOCz8MamUOEoRjyF8bkvy3ewfxhjbweefFbMALbWxSVtdQmV6d3/zupYAhZuiqnGw0/AnTm066HrVXQgiGq14MhD6LVFPM8ToOEPolcWJS9qJysaoURKzkWpAB5w6zpgyN/5fHIPvfYCvv6hfT2MGhqH9RWhf2ot4Ovefm1vCLgCiQZIdqEHhsXljo7j2ccsPHNut84jQ1HWS222Km0G4wFcT+P3GQwnAqyWmmyUW+zUHD41kSDfdHA9cLXHTs1ms2JzsDtEwDT4r452s11ts5hvEvEbNGwXp7NwGrF8JEMmQ/EAPlMx1R1kPBWiJ+KjP+ZnMOGn1vbw+wxSIZN83eHJsTh/cDKDRkKyAYbiATJhkytbNRwPEgFTAFHUIuT3kQn7eHQohqfBNBSOq9motPGZivlck56Ij/lcg2JLc3owQqXtEfWbXNyska+71G2PnapNKmTRcsSJ7eNYH5U72e+cPXu2/+zZs9bZs2eHzp49+39/FNt9UA8KxDks6DNkivEzlGl8cMqyXGwxlgx8INzyw0rvbEKmj571eegbRPXIWFP1iWuQV6ugygX8Dz2GPvcqamKamA8qbRf1Y5+tt9fl5QqStF2toNaX0fXq/s+oWIK1rlEeGwyzkRqVl2WmV6yfB4bh6nkYGEEFwqhGHbKbxAMmhUAMAkF0qUBiaorC5UvSKNyzv7y334EgKpESqpdporbXZYUyGkO/9UNZ8Ww0ZbUtloT8LirRJduIxGD+Crz7CviC8rK78AbGmafvH6SnwXMlv+C9x744L/vt/+mA8UF9dKVCYbyRcdhYkfOf6UWNHcSYOYYam0KHo0IbuXYOdfoJ1Pg03rpkR6jgB80vGBqDgB+9cFNW7dO98PYPZXoXTdyf0qU7FLBGbT/zQleK6Gvn8fqHpRHevG8McA/sqGe+IFPOchHtegJ6xw/KpBJQ/SMofxAdDGF84nOooVFUs4luNdFbaxJime4YBxiGAPa1JaHFROIilEaybNROFjU5I7bUUUk218sLAuyuXZCpRaYXffkdMTU48Rh6e1MmAdfOS9O2sylN4dIdmTDYLQEzGmmGK0WMRz4hP9uoS6Ps2EIhvXMTHv0k1MtwcFaAZT4H/WMics/0ScN971gcW6YxaHj9RbG1XbotYbKf/y0J5ozG4G//owDRclkmHdWyGHJsrogZQDEP3b14f/1/iEnB0m2YPoou5WW/JqbFWGH+ikyJCnk5b42mNN+FnARQhsPw3JcEJAZDkinj2nKcqS6Zaswcg5OPy/loNWWyVy5BKCzPgbFJOc71u7L/pbxMpLObGJEojB3A215HV8vivFcuiW39k5/BeO43oCuN+syX4MCsNP61CowdlOnzwIjcw6UO+Pv8bwmgWlmUKZXjyNRn5ID8jGEJKI50Jmr9QzLRGxgR4FTckym6z5KQ3lBYQoJBnCDXlmBwBF7+Npx6Qs5hqSAZTntZPNOH8vkF1HT3oHa3xamskINoHO/e92H0ANy4jMpl5bpkN6DVEttly0LVyqhnflUcBZfviF11KS9C/lpFrqlpCti6MycZQyDnRGux0u/OoAs56j/4lkxr703IEyn0jUuyD8GQZJstLQhIXbq9/y4EUPmc7N/6cudL/HM8qP4Fqt526Y1KLkyx6XJ1q0oyaJLuuIDW2x7llkup5ZCO+Gm7mnpb/v54v2S6lFsOIcvg+nYNA8mKeXutwt18k6BlkK1KUOVmuc3hTJBHBiKkQhYaOD0YI2gZxP0my8UWT43GGUoEaLuasGVSaLiM/Rh7ZLwrhAdc2qzRF/PjNw0eGoiSCvn2T79S0B+zWMg36Qr5SIctZjIh/D6D+VyDM0NRvnwkQ7npslt32KnaFBo2TdtjsBOCOdkVYq34Qar+x6Ee0Mke1M9U/1xaUMvx/rNdxlqOh/UeMLCYbzLR8XPXWlO3XS5uVtFas1uz6Q5b7/v/tut9YJttV/b/6nZ9f1s/sWpVaWjGDqCCP8YRnZxBv/ESenyK9tXzcOgkemeL/qBiu6GR5VgpvbMJ8aRMP2pVuHOTyLGTbPZPS6hgZ1VrtdhiOBHAZzdwfBa63ZKVLjpgy3H2gYC2LLyFOTKJMLuLy+KoUy7Sk4qwG+yShuLuvDR/P9aUKn8ANTIhnO54ElbuygQplpBE7WoZInG0z4c2lKzgF/eEjhGOQSopDcHUYaGQdCyTVSiMMXNMqEudMFC9tCAOWJHoTz/XD+qfX6bv/mrpvTr0EOrCm0LlmZiW6VwpL3kwhT2Ix6UpT3aDMjAOzEC5tE8z+UBlN1GTs6ipQ6iBYYzxg9J8ZnpFVxWV6ZuKJVDLt2XbuaykyPuDQjlcuAlnPgk7W2jHQTcb6FwWlezGSPfJvqAEKB8+9YFppjINjLEDAjiW78CJ0+hrFwSghaXxZW1ZHPQCQWlgt9YxDp+QbJnlBbwr74hrYE8/+so7uFfPoV/+J7zFWwJaxqfEUnhzDS69jRo7ANl1GjJi1QAAIABJREFUeP1FoVhOHBSqV/+w0HeaDaGcLd0Ra9vBYZmo5LLynTWNzneqCp//Crzxgkwp5q/C4YdltXx9EY49Aq98R445HJXm3PLL9hs1aYr3dgVAvPUj6OrFP3scFYnKMyHTL0Az3QfVsjhZPffrEvoYigrYGDsgoZKOAxtrQgt87UWZbjg26sln5bMy/eIe1mpAd69QxAZGpCmOxiWw02dJvsyZpzuZJI40244jWpjrF1CnHhOwm0oLKDt0QqhU2xuyX6ZP0uZvXBDHrZljQoFqt1CjB8Sdce4q3tJtKOZQz/wK6sQjAmxHJ8UVr1SQXJ3shiyo3J0Xp8WJabknwmFUtSKUNZB7wh+E+csCuGpVsYNOdsm+NxsykfI8mdLYHYpbYQ81dRjd+TntDwioCUdkQafVAn8Q455demEPtbUKx8+g7twEn4n2WaKbqVVQn/4iemMVHY6gv/aXQueqlOT+0mDcA73DowIksht42S2UacrkfGRcADZarg/Iud7ekCncmaflOV4rg9Lw9a+iZ04IwFq6jX37Bl6jivf1r+L+h/9VgFQnQ8ZLdKPffQX6hySAM5ZEr96VdwWI8UR3RjRvHxb6/Etc2WobQym6QyamgqClePFukXLLJRXyka22GYr7KTQckn6DFxeLWAYs5JuUWi5jCT99MaGDp0ImmxWbWtslZJk8O5Hg1eUyPREfYb9JxG8SC/rYa7psVmxOD0XRwEgiwIXNKqWWS9BUxIM+3lmtMNEVRGvNcqnFga4P9iZnhmMMxC0W9ho0bJdS02Gj3KJpa3aqNtrTWKZBpeWQ7vRChlIc6Ary7GSCbM3mZlZoYyMJi8muIMMJP3fyDbLVNn1Ri6l0iOHkx3Ox0fyTP/mTf4nP/ZNK5ZcjLCkcDlOv1/+ld+OXvuZzDeq2R/JDRo7Zapta2yXq/6DI785ek4bj7X+5fpZaLbYYTgYwlML1NPmGQyZiEbFMVoptdmo2s5kwi4UWLddjKP7+L9/LSyUG4n58hmKvbnNzp0HD9kApxlMB/D7B7rs1m3LLJfae7Bnt2BIc2W7vT2DeV5tr6GoJwx8g1DtAO9MvL5BMP3vFKt2pqLzcmg2o11AT0+hIDBZuoPoGiff20LQ9dswoqYCibQbI2QYD2UUoFcjXHbqKW6jZEyjTFCF0tYS3s4XObQsVx3UxTj/J3sULdPVlRJdQ3KOAn+7hAXmRdmX2s16050raebJLwOidm5AWAawq7EoTYsqLVvX0CY3E+3/Ze68nye4rz+/zu/em91mZVVm+qquqq71Dw4MESA4NxtBM7Ix2Z6VVaBUKvSn0qMfRH6EIPUgPCsXOhJa7O4azXHIIEiAAwjRco321KW8zK72/7qeHk1XdDTTohsMhdvpENImuysqszmvynPN1oGbmUb6PMXUE/dYrsqEdGoGpWUGExqeF3hAIoqIxeb3yvvCrR8fvf/g9rk/Vb+S+EwyJWDiRPPySsiy078soXdoV2++pOdEmXHkPIxIVSo/jovpdVCojfP6dNciNCsXnwSrtyeNBGsdkGhVPCp2mXkGNTsggFQiKrXEqg3IdVCwhW2vHhso+5rEzgua0G2L1GwofbrX15qo0bIGAIH8769L89vvoWgWVHYJIDH9jGX3nugzS3Q7q974poZ+lXciPYHRa6NKuoDC9nuQTWRYqk5OmNT8ig1ytIq5MX/mm0JCOnRYdzI3Lon1wHaEjxZLytU5TrucvfF3OcdeW9d8f/pkMMMkBannmKaEl5YbFvKBvS7htcVu24p4L9uD3qldEQ5MfEQRkdgGadYyFgW4inRU05vRF+PAtsTzudqAwRjg3TK+0h5qZl4betgU5cXroZEb+rbubQjHqtuHYWXjj78VmenZOBrWtVblvLZxABYIo00Q99aJoWmIJGSy0i4onhPp18QWhKOVGUKcuoLptVDAsFK3dLVQyA4UxoQcODQvaM3NU3rsT51G725K3c+uKDFSJ9CCDanB/CYVlYO62JTensi8oQzCMkUiKWD4aF/rq8pLcc3xPzl2lhFI2PgVjE+jSnqDmtbIgX8u35LUDQVheQn3t2zIYlktw/Kzk4Mwfl3MODeWimFfkhqFSRM0dl9ycehVSGdTxs0J5S2XQ1z+Uvx8sa2oVKG6jRkYFQer3ZBmUl4wcwwoInfcH/xHGpuHGR6jFMxhzi+j330IfPSXnZ6cl59zcCbj0Ovr1H6DTQ3JuKiUI/eaqWHBPzMhjHVvsmlduy7/V9+V4XH4XAiYUJrBSGbxrH8nQ9KU/hL/6f+HYaTmP3vwRDI9hzC7gv/5D+fyKxmS4VZJ7ozJDQhve3pBrxLYfjeD+jtStUpds1OJmqUsiZGL7MJEKcWWnTc/VuD5EAwaXd9p8uNMmG7U4Nxan1Xe5UezS7nsczUeJBEyu7XX41vEh3lxtUOt55KIB4kGD15br1G2fbx/Lcnm3jeNphqIBIpZJuesymwmTCZu0bM1kKsgr9+p8YSaJ42luFLsMxwOs1foMRwOMfIYuJRcNMBQNkIsF8DS0bR9LKXbbNumwRbXnMpoIsduyyUUtTEORCJnstRzGk0G2Gg7fPjGEZRpkIxaZSABHi/Z4NBGibUtgZ9j6bFzjt90rJxIJgP/9Fz3uMRLzuH6pMpUSd69HIDKNvkej/2m9StfxCVu/uve4pzWWobi21+Fasc3cYDsRNBW39jucGo6KTiZsUvkEylPuOJwtxFip9AahTw7xoMnTkwmm0yFCloHn60FYpWTFPIQybayCgv7oNFd22zT7B6JiD710DTcW51Zyhptjp7nRBM/Xkr+RSDIcVuxFhoQ2U9yRVHLDQK3chlBYOMjAcDxALmpxqx/iTqXHfGUZHQmjDFOQkmplIIRFKCGJFOxuoqbnUSfOyyCztSZN1t62fFBG42jbhv0i6tQTD7+h2+uyQQahGSWz6LvXYXcTXZhEPfEcxpHFgQjaQrkeSvuy1Qb8Xk+2utkcLJ6UsDzPk41zuYQaum+prManpMlJZn7l4/64frVS4Yg00Z/8ejIt1BJAT89Br41qN1HPfVnODa2loT/IlPE9dK+H/tmPDp9Duy567R5aP4BqprJQr8oAsnhavjZ/HFbuoDeWRcAfDsPYJHp/734yeCQi9MnZBXj9h0LpmT9+/7UiUbh3C/XC11COjbrwnKSdN2oyJBsm+p3XZHi6KNtndeoJ1MqSPG8kJgP6yBhUyugbl+8PY7eu4N+9iY4l0Gt34eaVQXbNmDhn5QsiYA9F4E//R/BdGQ5vXhV92ciY0CUzebghdE00kmT/4+/B7CLqG38MhoUKR1CLp9Gv/z1gyAC4eFq244YhoviJGRk0Vu6IlmRnQxCgr34btXgKFBhj07KEOH0RFYnIFt1zZUgYnaDzxiv4Gyv4Vz+QLX6vLQPL4jmwgqhGXXQ95aKgJa99X1Cee7cEkWi3BA059xRU9sW4ZHpecmIaddTsUYz8CLTb6GgCcsOCtM6fkAXFfhHtI/cbDcbpJ2DqCMbEDEzOCi1qfBquvScI3fQRdK+D0esKHWx0UoaM5dvSeB/cJ4MPNHAHGTN//G8EXTl+VpA4KyDW4J0W6rmvSCaQ0xdEuddF3/gYFYmhNHDxBdTrP5AA1ZkFQbT/5/9NELlWQxzEnnlJjvfRU0KtO/Mk7G6gTVOQnIlZdLMmg/LMvOQF+Q9cE4Gg0Lwe/L0dG5WQsE+mjgilbvoI7G4J8rG5MghKvS0oyNGT6DdfEc3Mneuws46uVWXQK+0ILe/Fl2F7HfXiy/L3nU0ZbGcWZZiJDpZntYoMY9mcDMCj4zJ0F/egVsW5fEloxr0e/O2/E90XyMD3xa9DJIr30TtQrwmFMplBv/Vj9Ord+zS1g/tMNj/QcP1u181il5Yty8qeKz3JlWKHlxfSnBiOsN9xGIkFqPcc/tXpHIZShEyTjuNjGIpKx2Gr0WcsEWS72ScXtxhNBJhIB1mpdrlT6ZEIGqzV+3x1LsNEKsRUMshu22YmHeTKboeFXBSNJhmyyEYs9jsuN0tdWrZLOmwymggSCfzyTm+5qEUsaBA0FEop6j2Ps4UoV3bbrFSFFmYaiq4rep6RuIVSilPDUWxPU+q4oCEaMBmJB7hd7hL7FV7/d6keIzGPkZhfWF3Hx/Y00+kwy5Xep+hbla5oVT759XuVHnPZMEHLoNxxH0I8fl5Vui5B08BUsNN0JejJUCzt9xhPBokFTSxDEQ+aLO13iQUNdpo2la7Lrf0uYcug3HX5aKdNPhYgaBpkBum8pbbDRqPP0VyERMgkETJZr9uH39eVEsrzuK3SnBqJUmo7bDVtYjsrFPOz7LkBFmkwMlFg1O9wrWPSHiBU4WaFbTNBdvmq8MZTadjbkRTnkTFU6P7GKmQZxCtbRNZvEx0bk5Tx0UmMnQ1a6WFiIQv2tvGvXxYXnERSshomj+C3GuhLb1DpuWQjFmpsCu7eoj19jHAihtlqQL93f4NeLsn2F/Dv3ZI065kF1FAew/dRI+NQK8vQsnBCnJ3whfMNYiOaSIDrYIxNQSIpjUIiJT83QHwe1y9fv7H7Tq2MSj/8/qtYXDammSGUYYjdcXVfBlWAYEgEw522DDvZPKpWgZPn0DevoMYmhQ9fGJcttWOjG3XZ9q7eFlrN5qqkwTcbsgW3ezA1j2rW5bxLZeDmx0JhzI9ICJ9tC80lmZZA1kHppSvQ72E+8ZwEQ548j778jjT4+TGhdO5uoUfGUb6LyhdQswtitHHrKuroKVQ0hr53W5Lk97bEbncQ5qnv3EBFYoIcnX1SjAgsS4b7YFCuj8lZQR16XWnA00OCCI1NwdGT8PxX4JXvCbJ15gnYWIOF4yLKrlXAVCjXhWYddeZJ2ZjfvSkIj2MLtWp7Q4aL3S2xNz9+VhrRqIjbVa0iQ0+rKSGkEzPouzeFlrazKQhHp038xa/RW1+RxrMwLl8vbg3QkiuyIa9WpPEOhkXLMTkL3RZGYQJtGGKV62u48IzogVxHmtbMEMap83K8dzahXka99AfoD96U+9DZJ9HXL4Nl3b8XKCXaj9EJ9EfvoJ55CdXvQiCEeull0fQ1qjC7gBFLyePDEXRuROhrvhbBfioDI+PC9W/VIZbEXDx1/zwpl8C0xPBh4YSgaeGouKvFE7Ls6XXknJs/jlq9g3rmS9DriRnJyhLmxefRWyvy/ihQvS54vqCCqczgGE1IaObwmJyvK3cFbeu0oTIINHZdVHaA8Nl9CR1VSobcRh3jyFGoV/Avv4tKpjFOnENvrYre6ehpOScKExI4unYPNXcM88iiXF+hKMaJsxhnLqK//104/wzG9Dz6vTdRR0/Cf/krGYp3N2SgHqBXzB0XjdL5ZwVtP1gseL4MzL5GVUuC6PQ68N7rYjZR2pXHba6hwmGh17VqEAhhvvQyOhqD6x/JYB1LiJFLICTnveschiP/LtZuy6ZlCz292LLpOZo31up4nman5dB3NDf3O9zd7zGdDtO0fc4UoiRDJj9baxCxFBcnElzbbZOPB4mHTHqOTyERAq24WeowmggyFAlS7jp8eS7NSrVHuesxkQyRCIm4/sJojFv7XT7ebfP1hQwKqHVdCokgmYhFJGDQ7Itm5xfVXsshE7EImIqlco+juQieLzofrSEdsRiKyNDSd33ms2GqPY+haAClFOmIyZW9NtPpEB3Xx9fw7GSCruuLDvcz6jES87g+t7XZ6DOZChIwFUo9WnNyQP06qLbtEQ0YKKVIhkya9mc7iz2qdpo2Hcfnmck4i7kILdvn5HCE2YxYC94odqh1HWYyIT7cbrMwFGFhKMJkKnT43/lYgGP5KEcGSM5O08b2NMfz0UPxf8gycHyNr7U4j7WbrKQmmM6EUEoxkQpxLBdhr28QjwRYjHoYcaEOBPPDLAY6KGBltwahiDRNU0ekaVi7h75zHeXrTyETurJPqFEl8+TTqPHpQw1Mqt+gEUqgCuPoSBQ1PoVx/mnUyDh6dwvvxmVUt4O6+Bwx7dLSJsruoyJRJjIRNuu2CFVDIfS9W/j9Pnq/KLQ0EKQpN4LKjw3Sq6dkMxkMw8JJlBVAe65QXeJJobVc/0C2pmNTMD6DUgZqdFLEt481L79TpX0fffld9PKSaJ9SGYy0UED8Gx+JmH5g/a1mFyCexMiNiKPY3VvobhuvWpYNc2UfdeF5mDwiz9esCeoxuyDD08iYDC/5AkzMYpimICgby2BaYiscT6K31yU5PBiEJ78oQ/LOxv1fulyE2aP4e+IWppQSkfp+Sdz4RsbELW/1rqCVE7PSUKeHpOHqtKXBbVYxT5zDeOll6LbQP/5b/Dd+JEL3a++LfiyZRs0soK+8J+f28m2IJdDdjlAkp+aEilMrQzwtCOrCCXj7VdmU5wsyyBTGRCv0zEtw9T0Z7OwuKANdKYo2KJESutO9JRFff+vPBF2olsQpDCXfHxoRZHW4IFSpTBYKEwNr3jRoJcjJ0VMi0N7fG+Qx7Qlyms4AhhyfvS3o9WVo0Fr+HDsn13SnhY+WLbsZFE1bNC4Ncb0qX48l8He2JF9EDV73xkfyuLEpVL2KSqUxBq5vSinU0VOgfWmkx2fgxmWhFZ4fDEj9HmpmAVbvCnIWT4obmUIG0OGCUMGCIbj6nlCp2i3U2ScfOrdVKCS6mE77MKTRmJwVp7y545jPvITKjch5ub0uixrTRB0/I8NDv4/u9+R4zMzLcd9aE3v67XWh2AWCov/zPKEtpoaEbljbFwe2VFaO+c46frcjEsjx6fumFVpDp4leu4u/uSrW21ZAFkTxJHz5D+H2VSjvYbz4DTl/N9dQU3Poqx+gMznYWMZ3bLx3XhPEr98XJ71+D/36D2B2XoaQRFpe//wzQn3zfQiE5D0JhuS1546LfvHah7C5QnB2QX62si8I3+ptQdmjUckM6nUFsRucm/72Oka+gHr+9wAtlM63XpXrptMSy/Olq4dsBn3vltwrVu6g1+4emnz8tkprjTPQv3Ztj426TaXrcGWvQ7njMp0OstdymEqFMA3FSCLIQjbCUDTA6UIUpeDaXoe/W6ry3FSCas/j8k6bm+UeR4fCrFR6xIImpwtRAibEAyYXx+LU+g6psMVPV+rsNITCZRkK2/M5lgvxf7y7w1bDJjBYqPY9jWUqhqIixJ9IBhn9JS2OsxGL8WSI4XiQ0XiA9VqfvuszHLOYSAo17I3VBnfKIgE4MDHaa9msVntEAyZPjMZ5b6uF9jQhS/q0R8kBPg/1eIj5Ryj9QDP/X0Npfd/Naz4b5m7lPoWl1feIBUwmU0E26vdvWBt1+6Gcll+GVFbvuey3HZIhk67ro+FwMzCeDBIwDQylcH2NaSheX23SsT2+OJNko96n1hNo1vNF8L+Yi7DXEpHwdsM+fJ5P1pFMmHtbVfTeFvVgAisYfPiC1j4zCUP0QKUd4QgDZjYPtQr1vsv6VgnyI0yFXNa9QTZFViwTfa2lSTx4uk5LNCqx+KdtiesVSGdFm/PmK/JBu7EizkTT87B0BX37OvrGxxQunGOv1hVxaDCI0ajiGwbKdTEWTsjj331NeOsby3iX3oBYDAWoZm3AJd+Rxmp0Am5exh9siUlnUcoQ6sLQCJx5EiMaf1gzUdp9tG7ocf326pMue9trcOIcaoC66Ls3oDCGcf4Zcaq6fe2wsVCJlOgOQDbK03Oo0Un48d9Kw2/bqFBIHOzOPY2RHUbvbeHfuCzZJZurgBJdhWOjxqdkK9zvSVMzPo12bdT0AmpqDpUdFqpRQQZgvbMptrGuK25hb72C3tnA++AtabCnjoBt4y8vSRM+Og6ee+hcpmsVoeLc/BicvlCOKiVpNGcWxInvxa9LVk1hEpXKoi+9if/K38r2uVaR4aK2L5qGY2ekod8buIOFQiIa3y9CcUuaxLljsnR44gWMfAG9fAvOPo36yh+i4il0LC6LgvQgc6TZEKF8KIJRKaEWTqK++A0xC/jeX4JlyNDS78nxqZYhlhQtQqclAmrbBnz4+D0ZyFCDx+6jp+fFAvrYGUGKnnhBaGuJJIRCqPNPi2Pi/p4MkH/374ViNjktFLVeD04/KZv4c09hnDiLSqVlE+9LphWxOMbpi6hOC12romaPyrF+4PzTAyqTcf5pGRim5sRkYG8TojGMo6ekia9XUfmCDIOdtqCA49NiD752T/4eT6BmFjAesGbXvgeGIblUW2sPn/Nf+84hYqMyOfk3FcYP6bBKKfnacEFst/OjqHR2sOwJo04/gRoZx/z9PxU91ez8oTOYceFZVKcjQ5bjQDiCf/V9cUZ77w306KSgSu2WNO9r98TQZHpePgO+9S/R6ysyJGeGYH+AegRD6Ds3ZHi88Az+6z/Ad/rwwVsyZHz0ljjRTcxArYJuVOV6OMjyyeRFv9TvyRB1YFtuKLTriFW454oGaXx2gIT28R1HNDO3r8sxyAzJkDp/QvRZGyti+33uaZg+gn7vZ/K8sTh+OIb+8ffENLu2j7+zgQ5H0EdPw/a6aN4MU5De2QW5hxR3ZJg5+DPIWvvHqrVan+Vqj1ulLm+sN7gwGmMmHWS/LeYFO00HpaDvaTIhkyOZADeKXS6MRnljtUkuZtL3fPY7Nnf2u+SjFtsNm2NDIX680sDxNUHTxPU0mYhFz/NJRSzOFKLcLffYbtgs5iIkwyYfbrdQClLhABfH4pweibIwFKbec/G0ZrvhYChIh02UUuRjv5xuuJCQhXIuGgCl8H2YTodo9n1ODEcOhyRTKfIxi62GTchUbDdsnEFvOpsNE7IMJtMhFDy0gP681eMh5jdcWmvWlm38z/FJ8WB9MhhSKUm2PdCK7LRsRhNC2Tq4QFp9CWB6sMYSQbYbNrXuwzbJD2ps9loOV/babNR6FJs2C0OPFgx2HJ9UyAQ0GkU0YNAdeJ6nwhZvbTRZzMl2pdJx2Wz0BzaEj950WMUt/HoV1wqymRhj6hMZM2wPaCUADwx0AP7A/ll5Pn1MQpU9HMflzse3uLNZ5m4wx55rwdpd9Po9sT7dXBUXnk+Uf/NjdL2K3t6QRvHIogwjhXGhcJSLEIzAN76Dmj8uYlDfk43awgnY2ZQm9OBYWZZwxT0xNaDVkMFqZEyatNIu5MS96XAjfPcmOhKXzBsQOkssIR/6kc9O831cvyNl24fUDpXNoeZPHKKAavIIOp6Ae7fQ8SS6XgVAN+uouaNCH+p1hdIzsCb233kVFk9jZIZE73T0lAw/kag0Jd6AhnRkEd0caDEME7W3Jef4nZv4+7uoySMouwfPfll0FRrZgH//u+KytrEiIZSpIWjVMY6ewjiyiC7twuV3MZ75sqAc1gPXcEX0WCoQlKY+GkffuCzi7fFpOHURfekN0dvkRmBrFePUeRku8qPSsKUy8MTzqJNPwLUPUXs7cPI8JFKi7YonUVrDV78jjenOhjS063eFmqkUxlNfRHmebLGvvo9KpjHnjgtC4dkymHge/tAIulGTDJRIVNAL25EBMpZAf/AmjE2hV++IHsnxRBuXSIoIPBxBjYzjLC+hP74kls5//9eSL1PcFrODY6dh8QxsromLVSwpFsqzRyVY9NhJee8OtBMf/Ewa92wO44RkYalIDLY3hTI3syADCEh2TXEblc0fDhUwGGB2NgT5CIZQX/v24T1SnX9G6HUgAvgB9VQphRoeRYUG5+rUEdSZixgLJ2VIyubl/HIGepOt9ft5U5OzMjCs3kGv3sEYnxbKpO+LyL0wfj+76KD6XbmPTR0RGtnUnJwjsQR0O+iV2/K4QBBV3BXL5AEqoSemJQzUdeR8+fBtoVRtr6F//D38n70iyEu5hL75sVwHAEPDGHu7oDV6Z0ME/bvbch9dOIH+6B1BeXa34cYVWQpk84CCtRU48yT63Z+ijp+WwbhRlQEokRaELDciy6e3XxXzBseGs0/Dz16RAXF+gMJMzchga1p4u1vyveFR+TzptEWz88O/wjx5QZYapiWGF898CdZu42+u4v3n78KP/hr+m/8J4+JzcryrZUHoKiVZrBXGZVk5OGaCms7IdTP4g/PLxST8utX3NIu5CLOZEPWey07L4Wapx0uzaSIBg3uVHpZhiIO5hvW6y1QqxNVSh+F4gFrX58Zeh5btEw6YHM1HqXcdNIpqx6XnyqDQc4VCHg2YfLDdpu9oshGTrusRDxm8vlLnWC5My/Z5aiJBIRnEVIoT+ShvrjWYSYf51vGsXAc/J+7hF9W50Rh9zycTsWR42+9iGYpzozFiQYNS2+VGsUPbFmtouO80+2/O5Vmv28xmwoc6ms9jPR5iHijH9n8tK+F+32e/6KK1plHzmJgO0qj9avSp39Var/cfQlQAptIhNhv3T/pPXoSbDZvJTwwC8ZBJuePw7mbr8D3uOB7vbj6Ql6IgFjDxfNHXHKAon6xU2GSrYXM0F2ExF+FGsUup7XC33OXNtQZRy+DAoXkyHcJU6pEDTL3nsnPtBkSizC1M8dOlEosjj6BHOe4h3euTtdqBtGcyZBqs1fpox2Yhplk4e4yFqM9CPkbNBn/mKIyMD5xyTnzqeXzHRu9uoo6fJTA+SX99FTUzGHRqFeF8GwZqYhozk8M4eV5SocenUJ4nmR1ozHYDd5BQrpsN2fTNzKMTacko2FyFVhM/MyQWuLEETM3Jh++B801xW7boxR0Zbpweqt0SDjeIBWplXza6j+uftpRxiPJpuy90mM96aCyO8jxYPIU6sEEGsSOePwHVMrq8J6GV77+Jv3oHCuMYDwh6lVKoyVmMI0fFQW9oBJUryD2guCPPk82Jo5VSqJFR0XokkkJF813RThS3RQTtOtLoLJ6CtbuivVpewt9elwDWJ14QncMAfUE/TGXVrQY6nhB3peK2UJ7mjsmw0G6iXnoZ9Qd/IguEvW3ZvOeGRaMylIehHKrdkmZ64QRqalaauNKuBBleeQ/dbmJsrqBmFlDnnpJtuGOjt9YxnvsK7O/KMGUF4MI+C8qrAAAgAElEQVSzYmpw75YMjKmMNHurS/D+m4L4rC+LXW4oIt+/+AXRz4Si6Ld/gr59Hf/mxyjTQB05Jk1vflTyegoTmOms5LYcHJe5k2KXnkjK+1DagV4b49QTApRsrgraOnUEbE829N2OILWFcUG9eh0Ym0YNj+JvrEgSfCYrupeDyhckY+TA9WpkDDK5ASUreD/bJ3r/HnoQiCunqiE6oIOqD9wODx6bSN3/79EJoabtbsqA0W3ft52PREXsP7Mgf2YXpPlfvycW3M4DQvuDmpiBVgP/7g0ZShMpWLmDml2Qe2kmg//Oa+h6Be3YqDlBMv3Srjy+ui+/T60CmZw4uSUzEqpqmBjzJwTxWjx5eP6qiWnJCTt2ShDRW1dFt+Q4sLcLZ5/CvPiCDIPxmDzfvVtw/Iz8foOMIF2tyHs9PC7nS6+DGpsQ9GVmAeZPirYnFhct0cxRoT4UdzG+9a9leZVMQySKmRmYRGgNT70otLNOCxo1vJ+9In83AzJYfe8voNUSClurAV/9FmYkKiL/UEToguvLguxMSDYVM59ezh2U36gJivUPrOVKjzvl7uGfWyXRafhas9dyWK/3uVHqkAqZbNb7KMTwZyQWoNy2MZWm6/hkwhaJoGIhF2an7hA0BK1o2x6FmMXpkRhz2TCFZIixRJCxRAATzZW9Do6v+elKg3hQ3L6mM2H6riAiWw2boahFJhrkSCZ8SF3PxwNcL3aYy4aJBAwC5q8/vBxULhpAa6h2XaZTIY7no/Rcn3wsQK3nsZiLcGokwuVdMTeYTIXYqEtfpZRiOh3kXqWLp/UjTZs+D/V4iBmU3fdp1n0q+/eHD8/T1CoutbJLueTSaj56MKlXXCJRRbno0uv5WAH1yc/az21pLXqXT1bEEvTjwQpZBrWu+5mOZNtNm1TYYHNAO9tq2ANERXQ21a6LqzWZaIAL43Fqvc8eBI8PR4iHTEKWwdxQmIAJjq/5vbk0i/kIW025UONB85EDTKntsL9TohbJotJZzI17BNJpuhtrn3rsz6u2kSLuNfHcAf1sb1tgdESfoJTB0QQs7Q9sZY+eOuRza98X7vDKHbj0BpgB1Pg0EyGf7fSEaBWadXS1hIrGUf2+WOIeVKuJERk0DOv30EoxEVFsxSWcTN/6GHXstDSTlZLQyE5dEBH33Ztw7Ax+qyW/VyIF2Zxwxu/eQN+4jL57TQaVYAS1eOr+sJoviG3owVDzuP7pamhYaCUgTcQDFJxH1sExnDsGGyvo0i76AL3LDaMWTmKMTcMzX0aNjGHMHP3spxoaUFoSSdG8DD4DVTAEI6MyqIxNwsJJdLkojenOJsbF58W0YmtdGrFWQ3QQz7wo108wJIPS17+D2loRxEZrVCAgiIdj47/9KnpoGL23jfJ91OxRyBVQuWH89RW4cRnj6ReFzw+CLuRGpAlV6n5S/ei0BPwVd4QWpLXkbZy8gDF/HBWNYZx7GnX2qYH+ZAiVSKJOXpDBbIBm+fUaZIdRvR7qxZdRc8fke9UKPPk86umXhELU60A2j7+9IVv4mQWMTlOGhvV7ElY7M48am8I4+5TQ8xwHdfKcNOrvv4E1MYMKRcRAYWoWGmX4wlelAf3obRHtDw3LgGsGZFidWZChsd+V8yQYkp+PJ0QfNC9Cee37qFYDNTaNOv2kuJ8d1M4GLJwSU4deT9zxEikRfc/M8SvXyfOHiO8jzy/LEsOF2aOCav2cUuEIhwNNtSRI0aC072GkMjLg9/tohdz/Tl8Q7SJgDI1IgKtSYs5QmEB94avivFevivNaqwEXnhUE4/qHkMpivvBVyXaZmReN1daauP3dvSnI5rEzsgiqlgQpNAzRrzRrqGj0/vt64TmMREo0WXtb4uS3vSEo3M6GDAqGCeefltfo9wSVWb4Ft68KchoIod9+Df3qfxa0sNsSWuPGqlhNb6zgNZuCKCXlPOMLX5N/z5kn4T/8PzJw+77k5JT2BM27fUM0THduCuK1synPMTQslL2xSXEl9P2fjyp8fOnwePy65fkax9eHutdM2OTt9SZ/fbPMX14pEbEUy+Ueq9U+s9kIG/U+1a5HLGTiaaj1pWeJWAbvbja5utfF8TRjyQAKCdbuuZq+J1SsnYZNNmximQaljk2p4zISs1gYipCNWBwfjnK+EOVepctsJkghHmIoZtHzYDEXJhy432LnogHOFGJMph5eAv9DazoTYiIlGt4HB5GgKcL+atfj4ngc29Xstx36D2iaF3NRyh2XjVqPtc8pGvPPfohp1h1s26fd9MnmLeJJg3rVw7Z9ahWPVNokPWQxlLdw7U9Pqs2Gh+uA3ZfvhUIGzbpHOGrQ7Xy+JxnH87GMR9+UptMhVqq9hwaciWSQ97dbTD8iNGmnaTOXCQOKG6UuIDeM68UOnq/5cKfNaDzA8AO80GzE+lRQ5kG45XbDYXwwnBTbDoYyOJ6XD4V7lR4dW957z9e0PmH/vNWw6bs++W4Hy0hTrrXY9wOcGgoefg9kiH1QvK5rZUhnadki9tspdYmnU4R7EhSYj5rs2MJv1Z4nHw7jU5hKBHyl9v1/i+60xWpzek4+ePMFVKMKjoNV3MJLZmWzvrcF+yX08Ch6/pggIEjiOUMjhA2fVruD3t1CpYcIjY7h+FqyO/o9VDIt+ppOWxxlHBs9NiUW0I0qfPCmWNzCQCewL3ag8Thk8qj8COrEuYfeP2Wakhr+D4DBH9dvplQsfminjNaHA/JnVmECdrZk0JicFQrU0hWxH44lUM06TM9h9DoYnzjugDiCPbjpDgRkO2wFIBhA37slouxIDF2rYBw5hjE2KcMDyNDi+8Lpv3tTqGTpIXQ0gXr7NUGJFk5K8xyOiqtUu43/F/+nhAbCgHaTQ22vS0M9e1SGtwEiwOpASzAoff0jccbKjQwGmSoYCuP0kxhHT6DGp/BvfixW4ltrqMIkRiQizz32GUPh2l0J/XRsCUK8cgnj6AlphAf6AHXyPOrc04JUxZMYp86joglBIFaWML7yTYyZeXHs1Qgy4tqCGqHxXvs++tYVcQgbnRJNSa8ndLLdTaGPDY9jPPMlyeZ56gsQjkmznRvFDwTQl14Xi91qWYIZtS8UtbNPou2evO7WBsYA5dC3rqDHp8VIYXxK7LK3BqL1fk8CRNfv3Rc5Li/Jsc+NPOJN+vn1qSDh31TNLoqF9UENLOZVZjAozp9CLZwQK2tjsHzSYJx7Sqh4jSo6EBQHvcK4oFh2TwbMaByGx9CdFmp8Shry8SkZOFAD04fBUuDIomjFUlkoTItxwKXXBQX0XGg18ey+iPsjcfTZp+T4BEOYX/kj1Ne/I7bmTh88LWGz0Ti4jlDWtC/3+G/+mVwPlinXWbMpWqxgCP/735X7+c6mUL9cVxCfSkXopK5kF+G6gvY7thgFzCzI+eh78vlXK6N3N/A/+Nn9oOPrH8L8cfS7P4V285F5Mf5P/k7+3/dlI5rOyKLi16y7lR7jiSAdRz7TL221+fIRsT0fTQQ5PxYnFTb5+kKaH9yucmWvxZ1yl91mnw+3W8RDBmHL5F65w1Q6xHK1y0q1RzRoEbAMhmMWC0NhkmGD4XiQa6UOhmHQ6nuYhsFsJkwsaLJa7VG3Xc4UYnzvVpWAoTgyFCFoKW4UuxzPhdkdGAiIydF9jW0saB72J7+JSoUsal2XsWRAND+IydJMOsTbG01GE0Hms2Harv8pg6VG36Npe4ynQow9Qi/8eajHQ0zDodXwyeQsHNsnGFRYASjtuAzlLYGIgU7bx3HuDzFaayr7LoGAIhozSKVNWg2PVMbEdTXhiKLX/XwPMau1/uFAUu26hzcOECiy2HYYSwS4Vepwe7/LbtPm2l6b//v9InfLMqis1/r8dKVGrefiAZmwyVDU4s5+h8s7LWxXc3VPAqJKHZdYwHjIOWy/8zCHtjawFdbowya61HIImgrTENH/dsMW8aHW3N7vUuu5LO0L7PwXl0torZlIhXBdxXDaori8QTk1wlDY5FjK4FaxTaXssL/noot7QqMAqFXwU1lWqj3SAZPbOy2OjIXR7SZB3UTduk1zbE62uVtrQjsIhiAcYdh0KbYdtNboalmaxqk5cXbZ2ZAPteNnJdRND/5tK7fR4SgkkhhoDAz58ABxl4pEKTgNdta24cyTImpFHEv9D9+F0xfxHQd/5TY6YKHsnrg6mQYqV0BXy8JF7/eEAlOrQCqL8cQL6CsfyDa5si/BbZ8odf6Z39Rp9rj+oaW1NDUP0HE+q1QoLJawgHFkEfMLXxNHp+l5sZktjMvgbJoPDysHNTQsw/lBTczC+rJYAk/NyTmzcAI9PCZuVQeVSEnuy9Sc0IOSqft0RAXsbqBOnMPIj0rwYTgqDefSVbj4vKTM37yMXynhD+hcvmXJQDRIHNfalwGg3xfR8eodEU/3eyISnzyCf+l10ZbkRkTjkx5CzSyI1fJbP0ZfeE7ySsJRCeU8uN4erLEpuUYtS6hwxd1Dsw8VjsiGeuGEbP9DEXF3s3uSjYLGr5TQnivLgNyI2CJPzYn4PhgSilWrKUPL8JiIyJeuyvvVqIvGqdWU+0s0jq7so9EyoCaSshkPWPDDvxIaUjCEeuI5Ccn99n8r1u+7W0LfO/sU1MtiqV6vynm0vS5aunxBmvZuW6impnl/caE1endLfoeh/P1h4HeglGmKZqs1yClyHLkPDw2j5hYxH3E/O/zZzVX4/T+Bjy/hX3lf3vNoAn96DnXynAy2uWHJbDlwJfN8Qbj2i2KIEhmcO0rJYHDnujzPE8+Jq5/WEg67vS6hl4unUHtbMhTMHgVXsstUdR/ji18XVOyP/lQ0jrMLgvh4vqAnIxOo7XU5x5QhtEV8uaZSGSjuSuhquwmzC4Sf/qIMUe2G0CZbdbjwPLzzqnw9EhGkcnNVPouC4UFwc0cMAPZ2ZNm1tSbvRTAEG6tiNmFacp4ELLRjo/s99MptvJ/+AP2D/4g+fhaVHkLv7/3Kx3Rpv4vj+RgKtpo2G3WbSxtNZtIh/tPNCn90LEOl4/KfbpTZadlc2e1Q6ThMJCRostFz8dAkghZ3yz0s06TVd2n1fW6Xu+y3baZSIe6Wu/gaFrIRru62ZYYLmeSjFp6v2W46NPset0odkkGTv79To9F3iQVNGn2PewNHsHjIQmvJatlpOowmHhbtW4ai0nV/I45g+ZhFqeMQDZh0HI+JlCxjlVI8NREnM7BbnkmF+HinzV6zz7sbTZb2hWI2lw1zLBfBe0wn+3yW6/pEovI2NOo+jZqHY2tCEcXmmk217NLt+LSaHp22T7/vU6u4VPc9kmkTw4BASFGrekzMBqnse8STJq2mj1J8rgX+/uAiBBHd36v0HnKxGI4FWK31eW+rxd/crHBps8VsJsyfnM5yq9Tl1eUa14ptGn2PVl+Gkb6nqXY9bpa6uJ7m5n6bakcgzp7rs1rr03M89lo21/fuc10/q4otm1rPpdr1mEmHWK70iAdN0iGT68UOmYjFRCrEYi6C1oLabDZsGnst4mmLhNXGIYFf3ueSl8IdnWGiss9GxyY/YlFrWw98cEsC8LGhCDHPpGEMhrr9Pca8GsWiaE1+fK+Odvr3efwjo1DcZiGu+O4bS/IBF4sLzWDgbEOnhRoZG3D8k+h+F9/T8uEbT8oWy+6jsnm8rXX8OzfE9SeRQPf7qOo+5EbQ/T7jS++w3nKliXrt+5LEfP0j9LGz4pITTwoP2/cABakM2rJEoF0tS5Pa74qLUDz1O9WgPK7PqNKuHK9fpj4DQNNv/UTsZW0bPSyOdnp56aFhRhq0+1kByjBkKM/fbwyVFUBtr90f/kGoS6XdwwZJnXniAWqkRmXykqU0lEe1GqB9QRuPnsI8+xTGM18S4bjryAY6HEFtb2C89DL6Z6/g376Org70DGOT0vyHIqB9yTbp9wX5PBB2P/i7RaKoXEHcqPZ3JXxxdAL1QCDnQ29fOHLo/gYI1XJ0QkwIAgEZJA6+ly+IfkH76NIuamZBsmUGCwdA0Cmthbrz5IuofkeGm90tufcMHNpwPTh2Sq7b/SJ6+RZ6Z12Qlu0N9Os/hEZdGs32IPE9nUVlR0AZkgESjghy4jqSW/X2T8S6OZ3Hv31dKKvjUxgPnkuTR9Bvvyq6EoCRCVmuuLaYR5x7+tEn1D9hqbEpQR/kb/K/w6NyTjyqQiGh0mof0woIzSwSldyeSBT+5i9lCHU9WF8B18VfX0ZXy7CyhL+3JVTBsSl575sN/Ls3od8XUwvLxJiYRX39j4V6Vq8AWtDPeAK9t4WuV1G+J3TkQaOvlBLa2NI1eY07NyXXa2cDY2oOY3QC/9oHosfqtGGoIIP9zIIc69FxGaIicUhnRNh//llBXrbXIBCC9buAL+duNCEZSpYl13k2J4PY9pogM/UqvPwvBPm8/K44A/7b/1UyZyZn0OvL6KFhKO7i31sSp0BTTDeMfk8yex6kKP4StV7vEwsa/Gy9yezATSsdNtlt2XQdD9+Hj3c7FOJBfF/j+3Btr03b9khFTLJRi2LbJRe2aPZdUmGTbMTkTrmHaWgaPZf5bJjtZo9sNMBuy6bt+lwvdbBMRSEeQCs4MRzjD45mWK31KbZdUGIylI8FsX1NMmRSbDs8OxGXIfSwbdCfouTPZEK8t9l6iHny69YnGRFhyzikjD2IAC3kInzzeJaOC03b40gmzGQqxEgswG6jT6Tyqw+Xvwv1z36IAQ4RE9OAbtfHMCEQUIRCkBkSS9lK0aXd8tjfdUllTLJ5C8tSQj3r+1iWwrIM4gmDbtvHdTSptEmj+vkU+Nd7LsmBXqXRcym1baZTIa4XO2it2WvZaDQ3ix2qHYe5bJBaz+PZyQS+VizmI/i+put4nC3E2GsJktPou+SiEkK333EJmnC91MX3NSeGo+SiARbzUS7vtIkHBd5dHXA1nYFt4IO/24fbbXLRAEdzYWo9l3LH4Vg+TKPvsdWwKQwoZ6W2Q63n8vuLGe6UunR3iwQmJ1F7WwSGsmw3eswXUtzetYlaLnMjYVZqXQKmpt+T82O5rZlMBante3RCHqPJkAxYI2PEZmbp9R1cTxMNGjR29mB8RuyUl2+jN9egXCSSz7ETy4PvY2uD9f22UGdSWXHKqVdRSpHrltkPp+SDt1I+FPGq4VHZmk0dQdt9saxNpqSxMRR66QqRwhi9aBLvb/6dpGpbIcl3abfQS1fRwZAEAS6clJ/d25GtXSYnjefMgnxwF3dQyV+83X9c/8T1a9D6HjIw0aAbVdSxM7CxjJqeQ22soI4sohMp9Ptv4P/0B/j3bj70c1pryTUZnUS16uiV26LxajXA86R5ebDCUdFSvfBVWF8WSqXdxwgMLFkPntcw0fduwvAoxkGQ6pFFVL2G7vUEGSjuyqB16wrqi19H722JYP/uTUEPy0U5z5MZycvY34PJWQzLEmTjE9bgygqIiN51pSH8FUulMkLTGpt62ALYEjqcCkclxDKRkuPVHSxo9rblMeEQxhe+hmGADoRkIApF0KEQxpPPY37zX2HkRyASkxyfC88K0jU8ipqYwXjhqxhnnpJ+/eLzov8YGcNQSA7LlUvo/Cj+Wz+RxrkwIY2oErtmfe19VLsJR0+gRh7WuqlQCHXh2cNlhsqPoEo7qInZX/l9+q3WyJggcYOhUsUSDw2fD9XwGNy6en+4HBpGjU9jjIzJ+37yAv5PfwDturyv/+J/gPffRO9uoes1GWwMA2VagqhXinIdZPNyfDM5KG4LpbG0J/ktm6KfIZGSe//SNQkbnZ6T59U+/vWPIJ0RxA+F3loXqvBAdKsNAxaOS/BmtShoTyAgSOGf/Fv5vQ70WaEI1ui4BHbOHRfK3d6moCzZYVlgHTsrj51dENeyXlc+m4LBgXlEQnLKBgsurr6PYRiCjL79GuxsoFbv4peLMvjkC3LNKiUUz1AIut1Pvf3addBXP3jkoWnbHtmIRcAQKvpYIki167KYj3Kz2CUZMnltuc5IIsB+xyUZsmj3XSJBk7FkkI26QzpsUmq7dF2f0yMR7lZ6DMcstDYoxIO0Xbhb7mOhcX3pf7q2h2XA1d0OhXiAkXhgYFDkslrtYQBDUYtvHs9SiAcJWQZnR2NEgiYb9f6nXU4fKEMpRuKBwyXxb6uiAZOZdIiJZIBrAyp/MmzR3NoaOON9/uqf/RBjBQwaNY/KvoOvZWLWvsJ1NOWiDCCRqFjyBQIK05TJt1p2qVVcXFcTDBmHfUQobOAM+I7KUHyecJi1Wp/WgDMpEKgMAMvVHkPRAJsDD/Qru22afZ87+z06tsd+x2Gl2ufEcIRyx+W9rRaNntxEtIYf3qkxkQqSCJq8u9Gk0nUIB0xQMJ2KsFrpMZ8NH4r8xcYwStBUlNruoXXzel3obcW2w0g8yL1KT/Lc0DT7LsWWg+NpPtxus1bvM5kKobU+zI1p2b44miUiXG07IpqNJfGCGqcfIGAbYCjCMQur79Ba3Sc0U6DV9Nlp9olaYDdgKG/Rq9Y4PZpkpSpBk0a/S3MoS6ZYYtRvc5ukIDG7W4NsiSnWosN8w17j2m5brLg70G53xTHJNPnRvTo6HMW//hHpWISaEUF3O6AHAYUKaW6SGYxgEHpddK0m+RRao29dFYtUyyIbUuwPz0K9DKcuSOPXacLF58W2c2YeFY2hhobl4C8vHSZ766WrcPEFSS1/XL/71Wwc0pl+qRoZUMYOKmCh93ZkQD4IRZ2YRd+7hQqFMJ79MuqLXxcK0Zs/wi8XZZt6+zpMzqLqFfkdChOo2QUJ1SwXBVGslQ9fRndbYsX6/e+KvWx+BDU195Bbn7b7gwBGE+Xfp+Mq05SwyVsfS3NVK4tweeGkDC3poYFlblxcxp78AvruDWlip46IvmNzDYZGJKz1k9qheEIG95/j7vYLKxqTpg9kqw+y0W/URMPCYGg59YQ4we1tCyoTDh+K6PXSNVRhXKyKsznwPEFqQdwCAwHCF57BeOkbcq1PzAiyddCAjIyj+j2h+eQLMlTVKuhAUKhP2+uDDJB5cZnSGuO5L4k25uR5VKcthgWfqAfzrFQ6e2ib/LtcKpmWZv4BvY76DO2OsiwZ5A8soFOZ+1RCrTHOXBTtWa0C1gA5y+ShLvoZ4nExVAiFUE4f9d//L3D1fQmeDUfkWB7U2l2MY2eEQlwtg2PL+zszL8c0NyKmGGvLQu8qTEAshj7zJOzvyLA8dQS/XoFaBRWO4r/zmpzDRaEWo7VcP+MzcOEZsWLeXMNv1IUi9sLvDXQ+KaEeDo0I4r+zIefwEy/IMLO8JIhMJCav+8QL6P/yHyQLL5EAx5FQzxdflqyYVhP/2odw8yMJxKxX4MolCEfF/KPbhl4Xv/eJQWZ9GaKxwyXJgRZ2vSaf46vVPs9PJ9ls2Nwb5NQFDNhtOwxFDAKWks9ArVmpdVmp2diuj6UUIUsRtkyW9rsUW31eXWmItweKSMCg3HEYT1gs5iP0fdhv22hP4wOFeIAzI1Gy0SDH8hEqXZdoQHFqJMpe2+GJsTixoEkqZLDbtA+Rj1Q4QKXr/lwWybnRR1BVf80KWwYdR4a9/c59XcyjaiYTom1rLIPD9xLXu88c+ZzVP/shpl61yeYM7L5PveIRTxl02iLsN0yoVRxaTQ/H8ckVTEpFl07bo9/zSWctIhEDu69xXTlhel2fcsnDNKHfE6pap/VoNKbb8T/ze/9Y1bY/+/Vsz2el2qPec4kGDFaqPcodh6t7HeJBk72Ww2qtT6nt8N5mg2LbIR8LohRUei7VroOrNfWey0q1z2q1z9J+l9v73cHP21S6HnfLffY7DhHLIBIwiAcMtho2P1muEzIVWw2b4ViAWNCk3BWdTKvv4Wt9uLnoOB7X99oMxy0qXY+9totSwjV9d6NFyFJMpUNsldssLa0xkQwSsQzRw8QsKj50tjbxR8bYatlMWxbv7TXJpkyK8TE6q9vMx2xuFTX9gEd9tUwoXiCVMfG1j1EpYazcwtlYxdvboR+J07MCxGIRUtv36ITihxbRB3Cv1mDFIpjVEv1SCR2Pk7B86s0O68EMZwJtttyAcLjrVVS3jX39I4H0GbiZVfdFd9DtCP/Y7jKUibN8d0MGHMtCv/sqObdNmaC4TZ17Sigrt65i1CpQ2Ucv30Y7otHxV26LoHliBpXKoDdXMQsTqML4P/LZ+Lh+I3Xy/CMbz88qFYk+vA0dmZDtLEhOyda6DLhzxw4zZtq2Lzayz7wkuRDb62KLXC5hFwYWycUd/Gsfovo2zB5FtRropWsAolWpVSQk8pt/Jg5e9ZqEPw4CVHWvC6t3MM5cREVjEuRoPhCueucGfPXbMsB4Lio1JD/baqBOXcC/8j4qPyqIwsayhEVeeEayPtaXIZk6bFI/9Z7kC5K98ovc3X7e+zo6eZiXwurd+18fnxIr4noF/dYrGCfPoxZPSS5UrYzKjwn10/NgfBpjZkFoWuksxsi4UNWWrsLiaVQ6i1/clXuKaYIyUaeeAMBvNyVvptMWTc78cXRxBz8aFyRqdBLaTYxwRIYr30NlcoJCqUHT/2CY7X8FpY6e/OUf++yXHv2NsUnRiERisgDo9/Ff/TvUky/IsLi3KYGSKNEZjk7KkimehDMXxe0tPYT2fbylq2jTRG+toU5ewHj5T0SnNjEDyQzatsWOuVGHI0dRyhS0PRrH2NtCfftfo0bGIBpDFXfQSgnKP3dMMoGGC0LLnDyCXruL+cf/Her2DXn+elnOmUQCPEeQvEoJvvgyDBfkMbsbgvL8f/+X0A77ffn8CQTl2uh2JXdod1Myjir7ItRfuS1Lr5tX5P2wHaFInzgvlORT50V/s70Bc4ui/xmU1lo+HMemYGeDjXqf/7xU5dJmk6btslbtc2mzyXKlx3QqyM1SmzfXGtwodRmOWSQiAeJBg0sbLQrxAB3bp2m7BExDegoL3tlskgqBYZhMp4LkoyFmM2Fc3+PCeIL9rkciaOJozXgqxA7oZcEAACAASURBVFbLodHzODkSIxu1WKn2iFgGzb7H2dEYlqE4mY/RHZgAdRx9mMMCkAyZVLsu2w37kQHbv+kaTwYH1s4Byh2XyVSQzcajIyqCpvRdH223cX2xVg4a+tDQ6PNW5p//+Z//U7zunzebzX+K1/1U7W66rC93aNQ96jUPz4Vo3KTdcvE8RWlPhhZDiR42kTJZX+6LoD9u4Gt9uLy0LOi0fEbGLar7LihFImnSbok+xhpYD/d7Po2qh2WBbWvCkd/eLPnda2UK8SCxRwjKKl2XmXSY11cbtB2Hf3+twnajz3eOD1FIBPF8mEmHKLZFKP8vz+S5vtfBQDEcCxAwFHsth/FkiETQoNx1uVvuEbQUrZ7L5d0uuYjBaq1H2BKXkFwsgGkqVio2xZaN52u6rk/H8biy1yEdshiJB9hrS9JuOmxR73vsNm12mw6GofjKXJp40GC35XCz1CEcEPOAo7koV2+tMWn2udW1ODmWoN/UZNpCPbm+06KmwgxrC9Or40dl21ir+0wHqwRNnxUnjtltkC4ViRVShBMRVm6vMTU/TfrIPJ1Om3dXKtyr9JkMuhRDeTy/j1EYx+t06GmTRCqB0+3SqDXJ5rOY3TaXdruci3tkU3Hu7dbxDJPp/WX2pk+Svfw66hvfIVvIc+f2Ojlz4AaztS6N2MT/z9579laWnfl+v7V2OjkzZ7JYrNRZ6iC1RmqNJtyZ66uLgXEB49pv/M6Av4PhT+AvYRg2bNhjDCZofEfSKEudq7q6Aos5HJInx5338ovFYlV1tcJIak33dP+BApqnD3k2z9ncez3ref6//5Keid/8EJYukeo3sbtNNle+RMHvY6IgCBj5MamXX8eSoE7rcLxHe/k6mVJJjzAMejpT4kSTzuSr39BG4VtvIa88q3eTA/+J/IYv9PtRJpNhPB7/+if+BvqtKHHd9qMFfb+rR56m5/RuXKP+5M4x8JODAbWshWNb2pAuhE77Pj2iyTSmJbBqVd1xqE3q3IqFFRgNtAHYMBG+i7z+vEZ+Z/P6/HJHese329aLntUrCCEI2x2igwPMy1cvxtLU3ZsYz7+iR9VeeEUXK76rF1lKoW69hXjxK8jpOT2mMzmDbJ1pChfoUMQk1gjdUuXp96RYeiLj5LdSr609ZlKi3vu5JoUZhn7PFtcgnUVWJvSi9uabEMcYX/tT4LyIGPT0YtRJ6c7Q+eiOqE3p4rPXwXaHBPmy/l2GPb1z73uon30P/DFsPItcXNUI6fsfaNP40iVkuarzc6bn9fib7+lx0ijU4Yfv/hRx40ufW+rgL/P+CdPS8Iovf02jjE1Lf6aDPlSq2lt0cghrG4h+DxZXEEJqUEoQ6PO3VEF98C58+J4uVLM55LNf1qN6pYr+DLbvasrcsy9r2tt4jDrcQVm23gxQMSJKUOI8XLRxovOGUmk9Mre/hXzjL5G16YvPXklDX/t37kM2T/5rf4I3s4jYfaA9WPV93Y0BDRVQSufYjIeP/n37P2s/TOhrwMTEtA7eHPXPs45Kejv8wT19LTFMuKwJgyJX0D/3YBth2hpsMDWnARWLq/p1jw9gcoaR4bC5e8rUdI2OF/HB2RiJYqnk8Hf3exRSklGo2O54rFfTmFLHHg38mCBKQMHzszn+v80uPT/i6kSay7U0XqinMS7VshQdgyBKkIZgteRwOooopkyiROFHisYwZDJn0fdjlisaXWxKyfEgwI8V1ycz3DwZkyj4xmqR/a5/3v2IsAyBKfT0yEolxUTW4s2j0QU19RM9d4UGBVQzFn0vpuAYF18/1G7H4+yc7rrZcimmTEqOQbvZYbmSoo3zK0EDv8971m+ifD4P8D//uud97jsxlQmLOBYEPqTSglYjpN0IOT2OyBUkuZwk8BKiSDDqxwwHCbYtOdgJOKuHJIkubHJ5Sf0wpFwzcUeKx1DclCom7jjBc8/BAaGiMmGSyf1hDdNRovDCmJ2O99T/U0rRHke8czxkr+PxzrHLtzdKtN2IpqtN+Yslm58eDKhmTKZzNn0vImMLDEN7YBrjkKxtaoSygJ4fMZk1KdiSN+tjJjIG/+0LUxRTJu+dDNntuHTGAcf9gNOhT86WtN2Yl+dymEIyX3CIleKwH7B3vhOy3/OJYsV/2e6xXHJ4YTbHTsfDEIKCY9IYxWQtwXE/ZK/rMQpi3NkVBkcnxAM97mcQMW2EkMpwdhYxnR5h14pM2RaHJwH12Kd5UKeerjHnH9HvKuxSEfeggQoDoiAkNC02G0Pe2m3jFWpMlLJ8kJnnGbvFpJMlZ9i0D/p4RoV7+y57VoWl5jaiXGV+Y4V2o42II5KDbY4aPVYXJ/Uc9umxnotOZ5FCkCbGXbqsUamzi4gkwfd8bhlV/FINMexB/YCsLbnevMf+wRmnc1fASbFYsDkYhHBWZzQY8uHMDTp9l2ZlAXHpqjZJd5pw6YrOihGCpHmqF1GgC5x/yZjSF/pM6cLf0m3pBfRDlarasPyYHu70XWhqVo+ELaySSgvccaJHzEpVaJz7VbbvIQplPeZxeoRYe2SUV0mivSOtMy5CCxcfZY30ZZWxXdH5R/UDku27OhMFdG7IwS7qeJ+kcar9BLubiGvPI04O9e/Vamj/QTaPmFvW40K+p/0xv6TDKH4fM+ELK/Dh+3qka2lN7253WhcjfHLtysVT5Ve/9XT+yeyiJl/lC7rQ+Gg9YRhgp1A7m7oD0zzTpMOzuvbHFCtIKTQQRAjUcICyHEQY6h37TPYi30mUz0fwBj1dWF19/tcjuj+nEs+8pMM6Vzag3UA++zJKSoTv65HfMIJEobwxyZs/Rh3sIF94Bd75iT7/v//3GhLw4mvnReOTEA5RnUT+2V9pnH27qYvW2QX9eTVPdBdl+bLGn0exHv8qFGFyVgMofvJdxB//h0e+JcuGiRnUWz/SuOyv/jHML+H+5Luwt6U3FeIYVq/qLqxhwe13dfeoMqHPw+de0V6h1hny0lVd4BSK8OH7cP8OfO3P9UiaQB+PP9bG4nYDfvCP8J//B8TGDeT6Ne0Dqk2Dk0IdfySLzRtDKs0HpyOulwx6bkDKFOQtiWUafGezwwszad46GlLLmISxximPQ8XQj9hte9im5L2TEf/r+w2GYcRM3mYia3E6DBkECZNZXajcmMqw1fHI25Ldvh5Rq2VMiild3IyihDdWiqxX0xeB3evVFJbUI2QAjgGvLuoNz6Wyw/d3elyqpFgtpwgTRSltUDjPsPvacp4/tFbKDrvdJzNfBn6sCY7o6341Y1HLmNxpjDk6abNN4WM3tj8L+txfsU6OPHJFgZQJpinx3IR2K2B1wyEKFUIqBv0Ez40Y9BWjYUTrLGA8Sqgf+rROI1SiaDYipITT45CzkxDD0DkjcawXCrqQiRmPYnL5851Fpei24ydNtr8HfXD68dXy5jn+715zzNnwSXzqfs/nbBRw+3TE5ck0pgH3WroLs9V0+eedLvcaLu1xyGbLZWMixVbbZ7cTMJO3GQYxB/2AtYrDdE7jBZ+ZSGMZ+kI0X7TY6fj85GCAZUjGoaLrxfzkYETeFIDibsMjbUl+sNdnqaiNctttj1snIxSakNYZR9xtjCmnDI4HAcc9n4msxckwZCpnEiYJfT9mt+vx5uGQggm/uD9kojZFxT+4INFV3Q61QoV8SbBzOKCUKZMSBi8vZZkbHHOwohdE81cvkS4XGccKY3mZ47e32WpJDo593DDhq2aX51YnKTmSpXKKTm0BMbfIfNGhRUg3HHJwfMJ+J8A4d0idvfMe66bL5v0j9ideZGl1nsPNXT0PPbtIkslfEFyW7Ih934DlS8iZefxYcW/ziGt7b3MwTNjJzWqa0so6YvkSG6+8AFHEqUgjM5rE86AxptEZcf3Lz3JJDDlLnS9Yp+f1zauufTv6JLmNePlreiY7ij6zc7Jf6NdockYvfD9GFyGW54oTDdS4UCarFzSDHolpIx+aU8/q53klf4SoH6BmFyCKkNmcXuw8HtS6eT7i8tHZeGA4iMmmYu0LWbuizfl72xfBm8IwEOvXUCuXdedi80NYu4pA6O7F/Q80shh0d6lUOR/x2tSdRSf1u713v0LCtHSg7OyixjrXD1C5gj7O5OlxDfEwaPSx7yeOUUlCEvg64PBxzS/rzlK3iZRS+2Rq09rsnS/qHXjQOVV33kdMzCBvvIi88SKiUEIuXbr4m9a0rUi/Z/Cb0+0+x5Ir63qcEU3mEzde0l0REoRtI7/+54hRn2TYR737c90lGfQQr34DkckgmqeIKNLBlL73JCgjSTSm+MN3Yfse6hc/1B2fdBb5H/873f24dwuVKyKfeQkm50je+xls3YWJaeRHz+tcQWd9hQFy7Qpy9QrmwrIOOJ1dRGWziJe+Cl/5FtR3NWzirK59OJ4L2Sxcfx5aTZ1XdD66Sa8FlqG7oEs6JoDv/LW+Jrz6Bmzc0O/Rzj1NJLRsfe67I10U7W7psefA1565YpnDns/pMETNLfHgwSFepHhhLseNyTS3Tl0edDyqaZOxn1DLGrx9PGQYxNQHEcMwYbMxxg0THEMwkTFZLqa4feayWk4xm7e4PpUlUYq9rsdEzua5mRzfWC6dU0sV4zDhudkcU1m9WbNYcjClYCJjIYTgzy+XkULwoO0xnbepnXc4MpbBN1aKGFJHPCieDAd/nA72ScuUgjB+FD0h0NdupRR7XR8hwI8S3jwaslJ2qGY0qODh5fv3gXv+19DnvoiZmskACeMx9Dqxps4qiWlKgkDRaYYoleC6ilQW/LEiTgS5vKTXSVAK7t5ycceJ3uU3oVg2cEcJUsKg98iDIqXEMAXJeWEz6CUUywbNM93p+H0UM4c93dF46Md4XNtt3bEwpXiqG3On4XL7dEw1a1F2DK7W0ozCGMMQzBZt3jwa8YvDPsMgwRCCOw2X9jig7YaYUgc8JYniR7t97jU8frDX54OGiyEgY0ssIUnbeg4zVoqiI/FiRcYS9MMEN4SsDaeDgKu1ND87HLJe1e3c9WqKjC3puSHf2+nR92Na44jLtTRSCnK2gWMK3q+PKDgG31wtMA4SJnMW212TD3ojrl8ug5AcvbVLUp0CFEM3otmIuVJKKFVNpucsrPo2RmEey7ER69fo9gRXahFt2+F0HHFfFHg90yBRMFtwyPpD5qpZVjOKL89lee9kRLFs4g3a5PNZwm6br88ktBtjNj2T5HiPzr17jBbWOTBmuH02ZuNLzxGMdZ6Nd7DHL2rX2Ns7ZdDpQiZDsXlIb2YN/6TOfaPMjdEBIl9g/doqU+srvH88IFlcR7h6R2vaCAmkRdvMsVqyme3sszxTQZZrMDXHRi3N/ZYOwqRchWEPOXNOJEoSPZ8//HSMe36hT0Y6JHOEajU0Ocl2LszogEbOnhcYR4OA2YLNZNbS15XKBOqdn8KLrzHYPiZXkNhmjJfo2W8hBKxfRxzuodIZlDQQL39Dj7SAJpjNLeElDiNnQpOMzpUkisBXpDJSG58BOk3txfmIpDtGzsxr30PoazDF3JLOLnGeJAMJIXSmzfBfhnf9nbV2FdFuPJWNoZIYWo2P9egopfTC8Bc/0B2txySkgVGe0MnzD+7AzBwqjjRyN1dAzCygOm1dyF15BvHMi49eY3JGexge18nhU4XUF/o1mpgh+c7/rXN1mqeIv/hPOmdp7Sp02ohv/DsdHnr5uu6UjQaok0PUOz9FRYHGfB/u6qL6/geo8YhkZxP1T3+DOtjRpL75FQ2paJzo0UKA3S3UyoYuZtwx8sXX4Hif5O77H+v9Ed5Ye+W+/Lr+em6R9B/9GWJuWf/d1KY1uCOOoFDV5LA40oVMpaY7QtUJDYX5/t/rkbJUWhdHG89qaI1tQ+ccF33lOe292r6vNyx+8UO4fEMTCQtFlO/q8TXTROXy1O/c1X8DtSmOBiH1QcD7jYBBkLBSdhgFCZstn9mCzWLeZjrv8OODAa2RBirdrOu1xGzeJu+YXJ/K4IYJo1BxdTLNawsF6sOAMNExDaMgYbfj8+2NMhMZi+Y4ZK5gEyZgG3AyCPjqYo6bp2Oenc4yDhJK6UcesdNhwFTOemrc8nHC2FTWopr51/GVzRccDvu6A7NYdFAKbp2OeND2mMiaoDQAoOPG2IZkMmcxl7N4fdLgXsv9zHpiPvdFjOfGtM4UxbKBQhHFuoNy7wOXwFP0+4rRQFe1gadIVIJpwcS0qeEi7ZAwgjhQtJoB7iih14kYDROCQKESRbsZ0m1H9Du6W9Np65tzHCvSGQ0V8L2E44OQwP/tT6QwVozChOVyiq73pIH/bBgSJorLE2kmshZHA5/6QBc6my2XubzNfi9goeiw1ws4GYYsFR0645CDnjan9f2EG1MZ2m7E/abHW8cj3CCmNQ7571+aZK2S5l7TBRLCMOZew2W24DCRNjjsezSGIX4UM5u3MaRkuejw7HQaP1Z6DtVLuNsc8+bxiJOBz/9zu81XF/McD0Iaw5B3T8bM5vXFJ1FQzVgslhzuN13m8hbv10dcm8pQyzq8upDne5ttEmWQShmcDEPE3BJp4dFveFCbIqMM1ksjnIYOxktuvUV6aZZLi3nu77lsvbeFkxYYnTPmViaZm7CZtEZ489dxhscYPpoYdrgLJ4dIKZnOWbx9NKTXaPFHz8xTMOHHqsY3gx0Okhl++FaL09oyXxId5qtpyvsfkuw+gEadg17I1fe+Q6mcZyYNRzdv05u5xEwly34v5G69z425okZ5SokQgkznjI1aisPjpr5xNE7ANFiaKtKtzjPa3Sa1ewf58Ea2sIJ1buzrHR7qndy5ZQDUoK/Nq6DRq5/R8Ksv9C9Qv6M7FdNzelHyUHPLmjZUP8CPElKmpJw29XVFAUIg80WU6yKlINPaZWwWNI6V86Jh7Qqi00IYBjKX12NqH7wN5Qqq2cAtzGJcvUHn/a2LDZxuK6ZcMfSYTL5AEkc6lTz95Fy5GvYhm8eNFT/c7TM8On4SQ/4xEtkc4pkv/d7fwl8lYRhw6Sq0Ti8oYwBs3XvU/XxMSik4OUTNLukgw/3tp55j1Cb1qNjkDOLFr8Cd9zXVLZVBlSq6ULvyLEIaeqzo4bEUSppc9fC1kvi3wnN/3iVe/5bGKKfTqJu/QOw/0IViJqt9XdLQnbDTY+Sf/5X2yxzvw/wycu0qYjwiSWKUk4bLN0je+jFq60Pkn3wbMT2HCkI42tW0tOJ5GOu9W3D1Wdj8QL9OFOpuabECuSLyI4WoShLUaIQ4H02+OHbL0j6cdEZ7UwwDsXYF+e3/Btav6dGuJNGFTOMUYaehcQxrG0jD1CNhS+v6vHn/59Dtam/Mted1R+oct8z6deh1NGwindEF0p2bOpdmPID9HTYPe/TRC/7ttselssOP9/sYhsF+Y4glBY1RwGo5xUvzBRxTMI5izkYh75+M8MKY1jig4Ejmiw6VtKWDnhUooYuORAFKT6dIKcjaBrZpECv4ymIBIQTrtRTjULHT9RmH2oPTHIdI8YjwlShFaxxddGB+mUpp8wkfyh9SlqHDvgHSluSg51MfhBx0ffZ7urvUdEOmsibhud8h3TnBm1zg6kSKzePuv8px/6763BcxpYqNkNqcv7TikC9IVKIN+pnsOVJZQjorsGzBaAgoGA30STAcxiRRzHAY4w6h2w0Z9hMmZwwaxyGHe7qwsR1Bbdqi247xxglBoIMze52YVEpychRSmzQZD3/7Imaz5bJeTfHm4ZBxEOM9Vlm33JCBF7NQsJjI2kxkLN4+HtIch+Rsg7eOhiwUbVrjCC9M2KhluHU24s0jHVY5nbWYyFnca4zouBH/6XqFvhdRydi8PJ/nQdtjpZzCEFB0TGzLoJASvHcy5G5Dj15NZk0KKZOUKQiThGrGxJIGA093rYQUTGZtwkhhGJI7DZc3D4fs93zeOxmzXLIJY8XJMODaZJqjvk/ONshaku/v9EmURiLWBwFXaikGo4DV+SLLpRR7XZ8wVFjr6zqfIlsg9APaoxBm5hHL63rhNejjKsX8lA3jMYctvcv0sPVqmopDV7IymWF06z3UzKLeVatMoiKd3Pv8TJalrNAzqLFBOACjWuXZ4TZW2eRF94zc/DydZodxIUt9bKKKVVIbVxEbNzD3HmCd7HPZ9DirNzgxppg2HRZNk+6tHbqyxkCWUMf7qA/eIX35Kv7+DpgWatSH0Qjml7k0meP43hbt7NTFCI3a3UTtbDJ3ssXPmwnNQCArE6jmKereLb2TDZpE4z/tnfpC/8Z0XjwIw3hi3EkIoTM18kXY39EF7rmSoz0dJgg6B+JwVyNdBz29c/vwZ9gOzC3qUS7Ox9Qu30CUqnT6gsqUQyZvUbBcmic+o0GMkxaIc09HbmGS4b29i+9/QqfH+LUZtoMUr0+ZHHm/JeDgDyBh2YjnXtHI58DXaOXq5NM5OqBH4176CqLdQFgmzC+hdjafeIoxvwSvfEMnutuOzurJFmB2AbF9H/H6n/zS90I8Th/bvKM9PF/oXyRZrmE8/wrGq28gVjZIQI/mnhzpjub+1qPcoFwe5lZQ+SJy7QpieV1nHp0cad/U5oeIag3x/Gsa1FIoIWbPaXTuCLG2oZHWV5/Tf0+x9jaImQXdKfVc5Nf//KljVPc/AMfWr/dLpAl450hpy9ZhnN/6tt4MWN2ATAbVboACMbuESjkaXLG8rnHQhTJBtsg7L/wF7uZ9aJ3qTo1AgzVqU/C//E/al3O4q703cQTZPP7kHO29PU6Ls3S9iEEQURq1qGZM1i/NsXD/F0zbMe2xxhQfb+9zOgzJmoIwUTw3k2WlorPhNibSeFHCO8cDiilNJd1s+tSyFinD4KW5HAslh0sVhysTGRaKzgX6uO3qwmQyazGft8jYkj9aLvDD3T6LJZv6IEApxb2my+VaGj9KsP7A2S6/jTZbLktlPcUymbOZzJhstT1KjknaluycZ+/NWhE7g4R4MOR69rOZafi5L2Juvt0iiqB0js6NI111pzKwedfXobpZiCKB5WhfZblq0u/FTMwY5HIGhZLFeJRg2Yp2I2ZiWnJyFCENGI8Sohh67ZjxKEFKwXicUD8IkUJ3Y0+PQ6SE/e2AOPr43e/kfLbxobqt6OK/O27EW0dDqhkTKQRuPybnGHx4Hkw5CmIaowiFYrsT0HFDalmNJfz54QCJPukvVVMMvIi+H3G/NUYoaLshbhDz9dUi//FKlQ/OPA57Hn99t40hBXGc8N2tLu8ejyindVLsTw+HQIIfKl5fzJO2JKWUiRtplN8PdgcsFFKsVVMEkWKmYOGHihtTWU6HAR+eDdjt+qyc74goFC/PZRkGCbfPxjiGwaVKmrsNl9NhQGsUstlwqWUN3q+PeWYqw1TeYdYwGVuSqZxFECmG/YghIWknYn/fZzzukivlOZPnu7y5AmrQ56gf8EolRi5McXJ8RnC+u9HsjrAci6kJi46cJLp3G7wxqljWBJb9LQBkpwnlml6UIVieczgeu1TKcLl3SoiDP73KOIxYWp7kza0OV6bzOtxMWsiVdeJsAbc7olaZox2H5G2XYlFSik4pGT1Up034/B9pA7BpIZbXdXL64R4im9X8/p99n42NZeIrN7jXdNnaPyO2HR60x9zzJC/aI+4e91D9LtiOzow538UWtqPDD7/Qv11NzjwJblCJHi97TCJXgMUVbRDf3WSpd8De7hEqmyc+OUamUpouNreEYyUXwbCPf//jZnFhOwx6IdlUcrHQNuYXqAy3SRLIPgY7MRKfGPOJxb7yPdTWXfxMngctj+tXF3WyveJXZjL8a0uk0jow8Xt/hxr2n6K/KaVQ92/D4soT3gaRyUG5qgvFh48JgcxkHhWdr72hAxmPdmF+6Tcq5i7yc36LYM8v9Ehi/drFGC/eWPu88iV9Y5+eh04bWa0hHh/jOzvWXpKpWZ0rs3oFWZvUnbnDXagfoV7+BlSnL3xKSik9ChjHj67RSsHKuvarPCbV72gz/vpvjpcGNGJ/eg7yJQ198cYa8DHooU4PUT/6Jw3R6DQRwyHBK29w77DNC/NldpI0Y+ccQjC/or1cw7721/zZX+nHkgRMk0OjwOb9A5YWJ+j//KfsNgYkwwGDd99mImujogiRL3B/9wzLEAwaLdLFPNlRh76fXNBQz0YhlbTF397rctgPyFiSvGOxVk4RxAm2hNeXCyyXbCSCpVKK9VqaUtrENgR+lNA4z5ybKzgMg4SVsgbcbNTSxInifsvlQdtjJm9jSh3/MP8rQiz/tSUQ3DkbM5OzWavo3L6VssNSOcVs3map5OjQ1PPnSyE56PtcirtPbEB9lvS5L2JqUykmJjUS+WgvIJMVOLZECoGU2t/mpCTptEGvmWBZujApVw3iKCEKod8LcVISaQiyOclpXRcsw0GM6ybsbLr0ujHZnGR6ziKXM+h3I1qNiMZZhGkL8kWDYkUyGMQXMIDH1W3H9DqPKmXPU4zOM2ZOhwFSQHMc8f3bPTCgLEwao5DNpssPdnq4YcxhP2DQiAkT2O96JAmkpOSfd3uYQntL9nvBRTDkqwt54kSRc0x+sj/gfsulkDI4G4V0vZjloo2fJBwPAmxD8P7JmKGfsFF1aAwjUpb+eVN5HXqZtw0O+xG2IbgykWK77bHb9bk+mSFBYUiYzBrUBxEvTWdYq6XY73rYUjIKEvw4Ya5oM5PXZI2MJfnOZodgqChh0RzFrFYchBDs9zymU+BGMX6oyNqSw57P4LjObnaCuwcek/mQ+lmHfqaiM1cMk63UBGtRCzptnl2bxBCSt7p6UdA6OMIvTTJXdMi1HhDkpxgFtg6IOz3SFW4UQa/NUBRRKmGtHHOpt4d9vINv2KSHJ4yKi3ywO+RF85TTyMQJPcSlK6wd32ErPcXCbI399CyhlaO6VOT6TJbN3TpJp6WPc/ND8rbL4LijR1TcEaJUQQ26kCQkjROSH/wDpNJIw2BqcZ6NWpp5r8VWvc/Csze49twVKuMWwewSeyS3xwAAIABJREFU8rkvn9Op1BMLoKH/2dyZ+UK/mUQ290S+jFjd0GNKW3dR56NlcaIDgM+SSdyJNVJrlwkq04jAY3DYQqbh3fI6SadFZnGG8ehXd5LjSBEe1UmtLD563cVVxNkx+eKjYuWg53P/zs7FiJg6q6O27kLjhHj5MvdFieuTad3tbJ6wsjh1sbv4aZVx6aoGHAT+E/4jNR7q4NCVdUTq4djco3uAKFUgk0Nt39PFTqD9MKp+SLJ9DznooYoVMKwnQil/mdT9D3RIafqTR7/+W5dwUpAtoD54G6XOC3PH0cS35XMPydpVWL5EsnlbFyPjEXJ5XY9fpTMXn4OQErG8jipX4Xt/gygUUTv3UTv3da7Kyrq+vzwsPH0P4/INcF3dYX/47+wUsbT2yw/6V/0+2Twi8DTC/E//SudKfPMv9QgZ6PE1KQivvsC9KM2NAojGEdemMuxlphlbGU1eazW0uX/jWfju3+qcpBe+wu1uTDYJSfXOeOaFqxx4gvcenGId7/LVjUmmj+5y98Ex1uWrdM6adOqnzNqKtfkJ+jh0Bi7ltMHJMOKwF/Ana0UcQ1LLmuRsHcfwrUslVisO+72Q7bbL39xtY5uCasZko6ZhN0ulJwleVyfSXKqmSJl6SXxtMsPlmu7arFfTlFK6gxkrhfkp7sQslWyWyg658+DwVxbyF9SxtCX1OJ0hKDgGJydNtlSGuYL9qe1i/yb63Bcxtm1QLFtYjmA8gsBXuG6Ck5aUKgbpLEQBeG6ENBVBAIN+TKFoYpqSfi/WII+cNvo7KUGvnRBHilRKMDFl4HswHoecHgfcvTVGKR1yGYUKpaBYMmi3dB5Nq6G9M49LKUUcKYb9+IJwViwb+K4iiGJ6fsx6NU0WySCOaUYh/+V+lyRR/O8ftNhsu5wOQ67VUiznUgRhTN+PEQK8OKHnRgz8iM3mmJ4fabRxok1tphSMwoi/v9fmf3uvQb3nk7YkbpgQJgrTkGQiSa8X8c87PTYmMoxDaLh6LK3vRWy3Q+aKNgM/oZYxiRNF30vYanu8NJtjt+tzpZrCCxOGITim4F5rTL0fcDqK+PcbZU6G2viXJPDtK2X++m6b22djqhmD0SgmZwmmHQtbSt48GjAaJExlYxaKNolK8GPF7TOXVt9ndapIoBKOhpIk0cm81A/plqZJFfI47hBUQtaxuVw0aI1jTgcBHV9Ry9ko38fqn7H4whLNtiSyM3qHbHGN7MF96n4W0xJkx2faPH1WZ/lbf8xefpb01Q3S6zWSuwfkX/0mXwkOyFVL1I9aGIc7iHIFSwqGZpnSn37z4hzY2jvlwBM6sC6bQ65skDm4Sd+32TbKBGdnhIf7iPNxHfnqN5DPv6KpZfkCqt3AMgSXV6ZJWYYOxhQCmcqQKPXUfPzpMOB+62ly1Bf6ty1RqWkiWDaP2tuiPgyYzpmYlg7nTZpn2OUy3coS202XRrvPjakMe82hhgX8GnXaMaWURyxMmmcR7jjRnZZiRY9ZAUnjhOHeHmY+j39yXryk0jp8c36ZrY7e+Lig8KxuYJeKF/Pgn2bJZ76kscrH+6hWQxeLzTMdFvpYQCYT01CdvPhSVGrap3T3JsH929pv9OXXEbatw06bpzoU03Of6Np8VA+zpUQq/cn9kp8zyRsvQCoDnkfy9k/gaB+xdAmAXnlad86W13XO1/42LJzno1QnniLWqX5Xjwm++BUdirpyGbFyWXtOpNQFwvGB7rack+jE4ooubhZWEcvrCCkufI6/lWwHZdnIchV8D7l8GXH/A33cU3OEQcydwzY32g80BnrtKkQxV40Re1YVN0y0B6hQ1EX7OUHwjmeRCl3Kxw9Q/R7/eOAjvQFBBPO43N5tIHpdGq0+/3AYcmKV6UcGpzj8/J37mLaBF8NaOsY2BSlLcPvMZbpgMldw+NJ8jigRvFMf8fWVIiuVFDemsighuD6ZZbH0WIdTCNrnXYqHXz8/8ztmRH0KZBny1xLRlkoOwyBm57BFujaBI0B9UcR8dpXNmQz7Ee5IUa6aKASGqbsvlZpFuWqSzUuCAFIpUwM8Yjg+DBj0YmwHgiCh04wI/BgpBAsrJqalODuNGXQTcgXBoJtQPwywHcH9DwOcjCAIFAI4OQ4xDRgN9CZLqxExGsbcPBlxMgjodxOGw5jalEGnGdM6ixj0YhSKD/ddirZkOI7xXMWVuTRvH4+YnbK4ms1wyXGwAm1QywiLehwwHCXsdjx6fsjAjzkaBlgG7LQ9crbgeBhgS8Hf3e+Ss01OBxHDIMZPEiIFS0WHF2cyJEhmcxar5TTEGm3Y8UJSlmAyY3FjOkPGMsjbkjAWzBYspjO6LRskerZ0o+ZQciykYQCK5ZLDUsmh7SYXbd/Dns8o0ECAnGNw88xluWjz/HSGH+8M2D31ySuTXGJxbSJNZxxhx4qXZwwetHxSlkFvHBJ7LqtzZe43Rlh2QtFyaPia4EEUceaj2fDTc3oWGJhwBM+uT/OP7+3ixoqJrKUXCaUKhikpVW36nZgw1DejbH9IN50nnZG6UCiWEYAxHpKfnqKfrdBIF5mKW4ROnnHk8Ny05O6dE1Quz9rSNHcOxlhp9G5rv8tb3/0JRSPhTn5JmzmdFKc+7A089q99nVmvTQhseQYqlYb6IXgf8bO0mwj0Ykj1OjrVuzbNUgY2m66+6TyWVt7zYvLOZxO5+IV+d4l8AeIIN0wYtxPCUOGkoHM8YrpSZXPfZ+mFZ1h+8BZWFBIqfSuxHfHUSNlD9bsxuRx0RxajQUx1wrh4rigUdaL9zn12PIOVosmKGlI38qjljYscm54XkbXlE0Qgcb7Yr2V09/lTrfkVONzRC9M40sXZ4qoe45Py4rojcoWnQmaF46DWrhCf1jXZ6mgPtb8ND+7CpXNIwN4W+J7G9X5EqnECE1OfKGL68yphWshrz+tNgPVrF49vt70LYhQbN1D7W5ootnUXdettVBzrzufxvg7H7DR1t6P85LihkAYc7iLmVwClTffno2ZiYhpWL8PuJqp+qB/7XRalz78C77+pu4W5vCaqzS8hTJOesHkwfUUXMJWavh95HqxcAtPkan+P/df/Shc2idJZUFFIuzhF20hTONll+5mvg2Vhf/gud+xpUvUt7FEPxiO+15Z0EsHWcQd/NERkM/xXL8yyZ1f46f4YS8C3ggPe3uuSNg3CRPHGSonOKGQUJvS8CD9SnA0jZvMW5bTuPHxc9+S1xTy28bstgZXvoY73f6ef8YeWEAKl4MWyzv+a7J9wWpy5mOz5rOlzX8Q0G/55HgzkipIkTkgi8EYJw36MbUlyRUkYJLjjhMqExdScRRAkpNIG6YxACnHetdHFwtF+iDQMpISpOYvZeQfDFPR7Ca2zkCBIsCxBsWSSKLBtSRwpimWBbUm63ZCxF2F6AtsQ3Nkdc+IH3D32UWmwbMF4lFAqG/gDRfsoZn/PZ2MxRdeNaI1Dbu6OeXtvyETJIo41BjDwEswsrBZS1LI2UaIDnJqjENuUSEOyUkpz+bx9Wk6ZvDSXQ5AQJjCZtck7kumCzd2GhyEUR/2QjhtTy1qsVTNMZExSY8nGRIa+r9vrfqJ4cSbNMIhpHEUsFjUx57++XuEfNrsoHcFEJbGZdGwcQzIKYvxQZ778X7db5BzJbten4BjcOXMZBQkzhRQv5fMUSyajQsxU2uT922NemsrRabbJzS8QJIrFks3hWUjBGHMvSFE/jJm12wwzeV6rSLpezIf95JHJOVeA8VATZqRkebrMqnRxahMaCnCwpT0w0iAV90mtrzLYOcG/e4fkxitYp9uodlMvGh58qBcU7oiF6TJ3egmLaUku7mK891P8xWtk28dkZ+Y4nruOIQVRCLJ3SrT5IVuHTbxE8MLXX2X7uMX9syEPMjPIB7e5nINnVzOMnGmeeefv2HNqjG++RzS5gPLGqPu39U2ycYKyHSiUdDBbu6H9D8M+y+uLHA0CCKMLklGiFEKAIcRnYnf7C31CmprFP24ShjAzZxN4kLJieu2Y9SkHw7Jgfgluv405PUsYJ2RzBv1ujOfqRbSKIlQSMxzE9LsRo51jipdnKZbNJxdac8sI2yHO5olaDeLsFJ3iJSanMxw3H+Hij/sBUymbbjv66NFSzVi03acf/zRJmKbeBUNT1ERJ09zotnQH7KMI5I9+/8EO6W/+hd6hX17XeOT1a5qItfcAllZ1Rs65P+8J9bsXRu4v9IdR3jEYnI/limJZU/dWNERGvPEXCM/Vn3uposlmS5eg1/5Y9PZFbpdhPJUfJKSmjJEr/M4BxdJ2NP3saA/xxl/C7XcRqSxHuSl6ieRa2UScHGj0c21Kd4iQkMmBO6a6fYuzxATLgvXrqEKFHbIstPeYmJmk1NxnOz3NT+MyZ4HBlis4FSm+l14hkgankU3fDTCjgMmsxf/5fgOnvo+VsnBM+Keuhed6XKmluDKRZhQmGIZkrmDzpbks31gpECtF3jH5P241mcvbLJd/Ox9LxjIYBfrzG/jxRZaKGg11h/is/pkB4KgkucDmp0zBQ9dC0Yhp9fXG/WdRn82j/j1qcipNZdKiXLUolQ2W11M4aYNURhBHijgWdBoJM/MmU7Mm+aKJUFAompRrBu4QZpdMRsOExdU0liUxDIEQMaEPzdOQ8SghDBS2Dbm8QS4rcMcKKcEdJSRJQqsRUT8MieKY0IP333M5uB1w+iBkKm8RxgnNdsjOqcdbN8fc2XP5/vt9RBp26j6eG7N95HFrZ8SXc3mEI7gTjlnOplgs2nTHIbFK+LAx5rDvU0yZdMYht06GeCFEMXhhwq3TAY4h+MXxkChJWC7b1IcRc3mLhIS+F7PXCdiQabpeTNUw+fKlLKWUDk2azNhULZvXFnJs1NK8upDjxkSalhszk7GIjARbSSayNsMQoiShNQ4JooRC2sBOBF03Zr2SpuPHTOUsiimTlZKDHyUYQvKttSJOYJJzDErSJFuUPGh5RDmFk5c8uO2TsnyUaSFHQ8TWHSLP48ZymXvNMUMvohcnVOImqdwkBdsgThQnjweAViZRP/s+akqne3/1q8/xbDZi894u4tI1RPMMOT1Hym0SZKuo2SV6W6eUJhw6c5fYvHmHreaYB0kWN1dCBXoh9mpVEHz3+5RWqvjlOSpxg/7sc6QyKYbDEZ1WxPXlNFH9mB/Pv0L9qMFXViucugnrWYXlDlnrH3Jz9nl9nO0G6c236GaXmZ9b4V75Bg1rBhQkSYK6d0vTi9oNbbQ8q+vd4O37cPkGsdA8+cehEbsdn+WSw0LR5rD36fYZfKFPTqM4g/C8i4DYUjHGUzZhoBgNE3IFQ8/zX32elYnsxYz5xLRFkkC7GXL29hZ7b9U5fK9OZnBMuzcmiJ82kwvDYHcQszUSXHr2KoFwkAJmCzaNgf673O/6LBQdhv34ccvIE7Kk+PTnHZSqqMeKlYe4aAAqtafgChfPC3ywPpJTMTUHp0fagJ3KIFIZvdCNnwxRftiF+UKfkAxD+xXLVe1LiSLCWPsnlkoOux0PDnYQlqUXkpatuyuZHGo0QGRyiNlF7XlSivfqo4vFM+gdf+zzhfjCqgYDfIxEvvCEz+23Vm0KdbiLNE1IFFvFRZxGneWsRAS+Ppf2tvVIXOrcBxN4MDNH7Ud/Tas8S7R6lXdOXD4cKuxum6XFKRgP6NXP6IoUA2mTD0cMhYNlmSSjEf9enpAJRkxOlng/yrFz2uPmzik/70mGQ5cFGfCjpEpGJlw2XZYNj3fvHnK5luJmfcQ4THjQ8jgZaG9vnChm8jZSCFS3reEZ/wJN56yLdcHJMGA6Z6HqB3pDYO0KYmEFFUcXxcGnWoe7F1ld836Lg9Sjbl8Sg2l+NkfKPvdFTDpjoBKoThrkiyaZrEG5KhmNFcWKQaEsMC2BkzIpVSziSJErSEwbet2YTFaQyRhMzVm0GhHN04gbLzgY0iBfkniu7r6kUhIh9CZcsWrijhMaJyGFSYOlSymUgjiEUU+BAe5Y4WSg2Yjw4gRpSYo5yZRhMF0wqDoGbl8hgZJjEsfw9tmIhh9QzhmUbQOJYCQjZAJiJKiPQxYKNnsdn/mcyU7H5/s7PRQJjXHI9Yk0Z6OEB22PvG2yWEpx+3RMyhRcqqSwhOT52Qx/tlBiK/JZTaW4Xs2gSNjp+FyupVAemBWIxjpBNmcbpGyT6bzNYjqNm1IUDQM3Shj6EaaU5B2D9jjGkgIjJ/hKraipJH5MnCgmMwaNcUzOMakPfPKRyetrOUYdXeT0k4ScIzkaB8xkLBoiYkaleNDymDV8btqz5Md99qMUcaJ56pY7JLbTTE7lUcMxx0ae1ZvfpTPWxYbIZKE2hTg7Qu1s0v6bv8M7G1JMWWynp/in/RFJpwnlCVCKOIiw5ufh3i06t24xm3e4dHmR9ZeeZTs7Q3IeHrm3fQSBj1xaQ7kjRr0u1kSVjNclkylzsrOPefAAWd9n+v3vcqUAe2OoDwNiBcFwRD1Tpep1kC99FaKI1OEdSmmP9EKVFyZCTvtthkYRcU6OUlGI6jT1/HWpokPyVi8zGksGvZjJcMBh6tHOX5QoLENiGZLwi07M51JRqDTqPJvCikYAiPoB9tw0dgpGw4TQTzSBqX6AFILHT5VMVlLub2MszJNfmebyV+fozs0QrS/SGYaMz0cXUmmJO044GQT0avN4qfzFqFixYtDtxNQyFvtdHy9KSJuSBGiMP35sbKXscLf56V5QiEoNuq1HRcbpsaZCAaIyoUeKPk4HO4/8FA9/Viarg2mbp4hzCAKgAxUfz5jpdxGF8u/z1/hCj2tmXgeHlqq6E3K8z+HdTWZbu6S7DdyDfZLFNZiaQ73/pqaYAWJm/ol8Jnd/nw/MCa5NpjkePBZYfbR3Me4rhHiC+PdJSAgJCyuovQe0SzNkDh9Qu7qux9UKJU1Iq9ag30OEHvLGi/Dia5wNfPbmn2Wh5PBPJzG9CHbnbjDZ3oNf/JDESXPHmaYhU8x6LaZ7h/TsHC2ryNDJ8zZ6bHRtfMbVgsTvdslHHhu2T0omBEog4ph07DNuNMkaiqOxwhCCiazNRi3DXs9jKmdxqZLiP1ytkH04Ft1uwGO5Sb+JDCmeph6OR/pze6iDXZ0F9GlXFMLkLKrVQIzHiFQG1W1dZHt9VvW5L2Lml7LEkSKdNggDPUaTyhikbEm7EaESPdqZyetQSiEg9BWGlES+vqCEgR7x8t0Y00w4PUpQwMy8SRhAtSZx3YRMVmKaMOzHmOeIv61Dj91Nj24nxnIUMiUIZYJjCRwJoUzo9CKyUlK1bU5aEXOLFsVpiYWgcxwTmDHZguDkwCf04K3uiNBTvLaQ46/vd7jneaR8Ay+IedD0+dZakb/d7NIaR/T8hNmcSdEx2Uhn+dpinoGfsFS2Oen7/OxgSMEx6foxXS9iIuPwi/0BV2bTfHk2xyhM+H/vdknZgq2WT8qQXJtOIdEEjONhwJdms0zlLM6GEf/ja9MsFFPEccIwiJkp2LTciLSSBJbiQcvFTCtyiYEp9Ajb0SDCi2L+7FKJXi+mrUL2PZ+4q+haEQVHEkTw0myWzY7Hcs0iCA1GzZgpW/Ja1odclre3zlhUMf3Io+dG5CeqZHKSuTji0IXbSYGTm5ogEyO4ObYQi2v4U8vsiDwPGg3ePZP84t4QYtg87SNSadKHtyleWQTD5HgQ8PLm99mtrUAYIoplrskBdzKzNI5PGQYxrVSJZNDnwB2xay7xYK9J6FmceRlYmiY+OmDeUdxbe43iwT3OxiGXyw5x85SOmaZfnCbrnxPJvDEYAvHGX+K0T/CihGvPrLAbZZHL68jX3kBOz2O88Zea/e+OEZkMYn6FOFIYpsD2x3i2JuSMw5iU9bm/LHzuNRzEuGZMvjJFdljXDyYJYCANyeTMQ2O+gnNiVtaSDM93j8PjOj1RYX9fEYUJZ6OQrC25OpGhQ0yioNONMGyhA4ddvaHhmII4VhiGQEoBCnKOZBTGrFdT9DsxZ0nAOPz4bosQgsvVNDdPRhdBdZ9KGQZ3ToacdIZ67OZxVSZQrbMnHvrYLsxDZbJPBWcKy4ZQZ1yo0+MLLO8X+mSk3289yiiyOcTiKtH0As6lK6hhn1X3hK0ReiFpfmSU0nZQvk9jFHLQdXl2sfKEV0N122D+ks/+k9L6VeTKZShWOBtHTLcPEJYDtSkajS7tVBnhpBGLK6ggRN18EyFNtkWBH6WX+WFTgIppZKpMOApv5AKKH08/TzdVYI88sTBYtCLsJOKtKIcXRnwnnGTF8MkOW7zcvUsx8fCcHEm5yh+7WyjHYcWJKMmYjS8/x0zY59vuHUq9EzYmdG7MWiXNlYkMOceg48bMF5xzcM3v4b62v/1EtpIKQw3OcT/dGyeq34V8UWOUO7rTK4WAToukUMUyxUUA5mdNn/vVSuPUJVEQho9uePm8gTQ1OazbjpmZtTClxiAvrDhYjqRYEkzMWORKkoNdnyiBIFBIw6DbDonChDgWhCF4nsCyzycghKRYMjFMQagUURtOjkJsB8ZjjbU1QomdgfZQez/dQUKzHtHxIvqe4v9n7816JMnSM73nHNvN9yX2PTMyszIra+2dTbCbwyGbGEkjaQSUJEAQBEg/QJf6D7oSoBsBEiQNpAtBgEBqyKF6msOlh13dXXtW7pFr7B6+b+a229GFRUVm1sJeWN1dxc73KtPDw8PM/bjZ953vXXZ7ER92fYwUtAy8IGM4VGw5DpHIeCFxOAkiHrRDri44PB6G9NOY/UnEamhx7XjGfMHAT1IWCxoHk4SLjVy382q1iBCKpqMzixWGltus3mjPWC+bnEwjHEPjcsU6Kyz+66/MUyhKwqnim2sl4gg0yFNiKzYFU+PWsc/rqy6zOKPpGry2XEQBFUvjG6sl0kRx0bGp6DoXFvJQqS1p8wfrFVxTYkrJfjenk9zqzZhMMiZhiqcUs1gxCBJIYRgn7AQzsrKPTKHvC95+qNheaaKHglnHY3ywQ8upc6HhcKvtU3QSBocDrr5+me7+IerGu9x/cMh46nN08y4nP3qfYRazNXjEN8U+m1af9sxiOvVJem0sGWNO2jidB/Qim8p3/5DqzZ8wKOXjWk0I1rdWeO/tW5yXERO3xPWDEVc36rz06jKv2j2KpZCun9BIPPYe7XP91e8RFqvcq2ziJiHL999hcdYDy6U1SxDN+dxVbPcBYu0c0jRZ1iOOIg3reBdr2KJ7J7fc5NS2VQiR7/im6VnoXbGsYaQaXpzTTw5GEWvlZ3ervsj5G8/xq4MXZ7iGzAXnpzqONFE05nQMQ1KqaGSZ4kDbor9zjPt4n/uPPf7uwy4PTgKKqw2cgsZokuJFKQvFfF1tVCy6Sczjk4DrOx53DwKmw5SNsolraHR6MaVyfmuq1DRm04xVM7+AhqnCMSSa9uw1+2k4huTFeZeb7VnulPRFxNoWeveY8d7BJ6cr9SYMesApj711kIdgfux5Z89fXv/0nfm1c/n0Zjr+hEnAc/x6oLIUkSSYr38LtfeQ5OAxYmH5GYttVjdR+4/ojH0uVp9taFXrALwpYv3TP/tfFcSp5uZEK7KwugiTIWo8pJtIvP4AP8441AqQZnyw2+NeL+D/6xncm7/IigWGSllOptQGRxTvXUOMhvylexGrUuNYK7EVdRkZBa5TZYGALFVURYwjEq6lJabDCdf6CatWRsHWkYHPQWywXLZ56YVVlKYxPDik1fN44cbfMDk+oRJ5NFyd8qcZ0uw/hrXN/FqW/OK6OaVUvpudxHno6Ec4OYBXvpFPeb7I6D4xglALq6jeCQVTMk0Uk3HK+WWLw3H0M17ki4nf+iam2w6xHYEQkCS5vbLUQEqJ7UoMQ1Bf0AkCRZaBpglMQxD4UCpLpJCkUtEOIixTUqrmDmelio4moVITjAYJliWp1g0sG9IsLwaSCAoFgWaApkmmXoaZwGickWagSQg8GIQJ9ZJO09ZYrepouqQ1iimvCFpezPqiyXicF/EbsU1jVcdNdJZ1i4NHEdvYdOMQESu8MCWZZYThaYEiNGxd0BukaAWFkLk5wcN+xGvLLr1ZHn75B+crOKZOGZ1mzeCDHZ+mazBXMNmqO2ia5IWqzSBJ6O6mRFlGxdJQSvH2vSl1oXF53eVwErFUNrjYdGi6Jvd6IfMFnTnH4N09jw3bYqfn07ANpC14eBhytVBgQTOYTjPMgmA6S1mzTTyZMpskuLqg7uh8uDsDG67KEcbcAnU54XCYMnMdDF0yiUEYGZsbS8wwefDO+yy17pF5I0I/w/cjgtoCmWbSKS1w9atXeS+Y4y29xNerGU0Rc8NapLq2hrtY4tHDPg8q63mq+Z0PsS5skw6niCuvstTdpVVayMfvhRLd4w4Xpgdcn7p4BYf5Zhn9I7//zW1W1ZANy+PxjUPeKb5EwbF53Zxyw1xkwe8j6nOUjh/k52DaNBcadEYzmAyJGwtkaYronpCNhrC2xcXXzrErl3I71ZUnmRwqSXL+tlIgQPdHVColdJEHeSnyZmcaplxreayUzWdpDc/xWwOV5ZNp1s6h3vtxLuIlvwYWy3mhYNuSQkEjaaxQvbrFdHTMK0ab9avrvH3TQ5QzxiphTnvSGBctjTDOiCLFcJowClO2aza9o4SVoklrEuc2sYDUBJohaB8nnLQS+kRsVC0WmgZHnc/Wa2lS8PJigb1RSPczqGe/Cdzr+fmmgDhtDMVnOEk15/N8kP2HUKkjXnztF96JF5YFvneWtfMcvwE8ugfnLiEMgwuvvcjdxoWcFna0x832jJ2uz71ewI2pYH18lBfap2h29zmJ9Weu379uDIKExvIC/Af/OcNCg3GUsd7aYeXeO5jFMh9QY+0//I+xX/8mhWqJ1+IW3zh+l2VHcs/XSFbO4QUJE7fKT4wlfnCUsFLOzXvIMqbSZDXoYWUxqZA4Kma9IKgWDfYq66wc3qFJwEKjSFpp8i3ZRZOCORnROezAbIK4/CpjRG8ZAAAgAElEQVSDic98OGCePJgSciF+4fBBnsOUJnmw6+IqnBz+jLP+JNpeTLN/8EktUnxqtmBZuWnOFxAqy56JTxDjARTLzFnQjvIMP1PXcmfWLyF+65sYqQksW2Kagsko5Xg/Jk1zTneWCaQmODmKyVKFrgu6JzGWK9F1SRwrimWBkmAEEqMCSys6L7zkoOuC0SDlyisFdD3X1XjjDN2QrKzrREmGacDaukmcgmUL0gSm07zhDyZwkgaYLtimTmlRMJ5kWCZ0jhIiL+O4naJJGB1nCKCXROip4KAV0rR0Hj0OKLoapiZJEsG25eIsCdIAOoOYPzxXIc0yXpx32Co7BEP41/cGuJrkfMPiouVSdw0sTRB5cLVhcbftEyrF1y6UmIwzWmHEw2MfKaAoNKqpzsubLmRAAHosGKuUmm4w7CW8WHCxLYlKYKGo81LV4dEgYqtocTiLqGo6D/cC+irmtSWX5mJuvdydJczilEuWQzGV7Bz5rK+ZRFJxPIzww5SCKfnehRr/717CWGlMj+/x9fOLnK8W0AoKaSas2xP6YcrFxSJVS+Nk94DJSZvLVZ87RwmuBu/sDahaEjMRrKguqaWza8/zDg0qWsILDYtSPMLRJZNEEHkerGzRFTZ1POJUA8Nk/iff5+jwhNm9HchSNlaa9KTDcjphVMhDwyBPMadU4dKdvyDoD9m+0OTW3oz+e3cJMygVLLLWIfMqYL+5xdqFDdxGncHdHXZUmUfVDR689T6EPvLKK4hTusJq1eRay2MUPLXzdLgLK5tMx7kwm14HrdrA0gW7w5C5Qt5YHYwjHF1i6/KLu5v9HL8SZGkeehp6inJFy9dTrUHqlNE+Jv4cDVPqczqNOZ3RUGEtLxNtXIBIMGfrLM6bnJuziePsGaF5E4OjIKItY17ddCkUNRpzeh7+KwX9fkz3JM6pZVJgWoLROKbs5Gt7rmAyDFKSRNE9iRn0Ega9hDh6djpzqekQp4p7X4DMo5NpRNXWudPxuXEyY3FjCbm4+qm0N1Ft5A5kG9sIx+X6icedjv8LmxYE517M3Raf41cPt5CHD5PTcp0kyM0WtLzhl0KwWLY4msQkmcLUBBebDhebDkFjicd9Hz+F0WDM9Xdu4FXnmLi/uQna7jBk/bSw/dHhjL5RYvvVF5Ff+RbiyqvMmxlqOuHNgynt/pj6bMAH9jr/8+r32L3yO1iOjVWp8nZhk7+rXOCrYkgS+PS8mEhKJprNit9l5NaoOhopGq5K2Hz8HmPd5VU35u2Fl3ACj8E04sVyRjqZsNR+yIWwy1hB3DogXdlAdFq5M9vJ0dmU62gcsFy2UHdvoD4KFLUsiH6xTbn5gsH97oyqniF04+w6ppRCtQ5yq+xa45dqjn4tOHh8psECIIoQ25cR3/9/yJ4y+5Dxl9PE57e+iak3LBpzOr6vWF4zOH/JQso8gHJlw8AwBaYpcIsyzzQQ0JzXaSzo2I5knGYUDY1onBEZMB6luAVJtZ7ny6QJvPiag+dlpGnGJEg4acdECoqu5CAICQX0RylxlhIL8NKYWCYUhI5hgJnBzrWY/jhm5sGxF3AoA2ZhRqlgkLiKqZkSZxlppiiPddQEJmaM4QuCaYajCdIIGrGJsARGKLl3EvLd5QokkmXbYC8KuFS3mNdNEl/x5t6Epq3zSrNE14v4m1tTvrNR5krFYXveRhqwOWdx88inquuEM4VblCyvG2SB4IWGw50TH10Kttdsqg0dy5EowJ9mNJSBPpZ8tVlgFKdYlqRY0Fh1bOYNk3dv+NzaDVioGViZYKNqExsKt6zRHsV0BykrVYOmbmDFggEJSil+ryr54bstPNHALLgIBf3umFeWXaZ2mWQ8pjk84nZgUjclHafOysuXoV5jkhTot0Oy4jLdacQkzfhdfcTiUpPi5gZXsiFq5waydcTS9gIMQh5mLsLQGfSGWAXJtR/kHvv1V15hmOk8shpsrs+R3r/NipliuQ5GOKPlzqH2H6H8GSJNSYMAnARjnLA6eYA7bbM97fBwnMAP/pTK5gZmo4khBe8eeez1PM5XTS6lA+JMoU7pJskpzaZY0uidzPjx+/e58+Fd7t3YoZ8IhK6TJurMjaRU0QinigsNh7qjEyYZpibYqlk8/oKnoD/H54c0ydfNZJyRWRmcbuIAiO3LTMcpxVOa1yhIiCKFZeU/13WBZQtcpdHxYnwvxTQlVcegUtERUjAe5pQ0b5JiOzkl7I8uVzmZxAR+RqmsE/oZc7bO/iiiMa/TPo7PgjYnJCw6TyY6KlGMBimNeZ1aQ6daz3Nn+t1n6SJLJZPVssWNkxmz+DeXhTAMUuYKBlfmXYIk4yAyWas77P0MB8AgySiZGpeaNofjiBvH4597Y+FPb/fYf+4w+OvB3CJ0cv3Y0Thmadz6xBSl6Rr4ccYtrc5W3D97vOoYvPjNV/nR+w94fNDmpa9eZabZRMlvhsp7OArZ6fkcT2Lu9Xz2R/kEFCBb2USdfwF1/jKzdos1PebuXpetis6txGYsDBrZDHf7Ai88fge3XiNqLHIymbFWNugLi3esVb4V7jIyy9wXZSJpMVWSeX/AsNCgOhtRGRwQ6iaLx3fx222ubjQpdfa5GHWYv3yJSsHmOLE52j9mrmih3n2TTDfIbl3LT6LTgpV1KFcRo8EvRSMDqNg646MWbF3IH3hwh+zu9ZziWZ+Dyy8jxmPUZPx5vPWfP+LoLD7hIwjdQCyukrQHWLZETUYwHv6GDvAfht/6JmZuwUYIQXNeZ9jPKFU0dF2SZbk2Jk1zSkVoZZgVcWqfnDc2ti1RVs7bNmzBStFkrKX4swxdFximZOqlDIKUlVWTJMmYeCmP78XEEiKlkANBtSLQJNTXNFZWNHRNkCS55XFvkKB8UJHCG0F3mnBExPcqDSazhP4sZBanJKkiCPLJkidSBn5CwdAItIyaNGjYBsM0Yj7ViWcZW1gk04zBJKE40llY0nl1rUCcwj89X2Eyy7DKglKi88pcgVTCpYbD5aZLlsKgl3Bh3eEn9yd8balITemYxXw5CSFQKIqmxnrFoiY1CkXt9Gd5Bg9A4CkubNnM+hl1S8ctSCZRQpoo4okikSmvrRVIZ4Ktps1a3aRQlJyrWhzEEfeCgLJhMGl7VIOY0SDlz9/cZ8VRNBuCuKjR1iJiJ0NOA5aMjGkGUQZWo0k8nbDfGzFnKV5fKtIdjtgrVelqCYPHt3m8u8vG5hJLxztc2x8g17ZgPEC1DnhhpcYo0yimPh1R4OYw5UE/QMQBBTlm+Nq/z8i3WJ0es7y6AP/7/8jD1/85axXBig1JFNM5bucmAu+9yUNRZuer/x6/+9IGR/UKGzu3CIoFNqZtJrHOpLkMjXn00CfOFN9yZmxoAVq5gkoTLjDhgbuMpST7RxEzL+XBKOBVMeGPvnmJdGGN8y9eoF1aPFv7KgzBNNF0gcpgvphPYR4NQrZq1jPuZOq5LuYfNZRS3N31+fChx87BjOEwZbXyMScflX+3W5OI250ZmswpuB8h0RSWEgTDnKpYKOXXA00XCHJnxixThIHCDzOKFY26a6A7Av/0miAFTMcZVlGgANOS6IbEqOaZG4NeXoiEQUYSQrWhndGshMhpbo4rPxHc5hiSqwsuj35DTfnAT6jaT7j6VUdnq27R9pKfmcW0OwzZqFoIIThXt7m6VObR4Imm4rMMDPZGIRebDrfaX0yayz82CCnPrL/VZISsfrob3HbDZj/UkLMpSilOHh8QHexx+4M7fOfFVerraxyMQi408qb1N2FQcavj893NMtsNm7Kl8ccXa+yeWqg/nmbc6cc8GkX0yovE0xHfurjI/32gWKnYOK7FO/seYmWTH+rLHAiXl9cbaMUKH3YivHIDl5Qjq0GmaWzEPb4j2vzBuRpGGJAkGY/cOd421/jmXE7tfj3rMtnfZ+nkPu3dA2rBiMIHb6JpsFdaoapnsLwOf/Z/wV/9K7x338IO8vdXSAkXr8K9mz/3fezpsFilFK9WgDhGPbqHOjmEmQdrW4hKNW8IFpZQ7eNfxUfxD4IaD3M3uY/+H+fGEgBifpF4GuEWJHTbZ5qZLxt+65uYp7G4YiCloFzVSBJotxLmFgy8aUZvGnM0jHIXsiBjMk5JDUW1qLO0YrK1bbOwaOJaksOjCMeVuAVJexRxdBSzddFGGRITiaEJ5tclB7MYL1YUDY0wgywS3IkCVtd0LFPHiiRJptCLEKoUb5YQAw1hEE1gpjJGXoo7ljRSnYahM4oTfDvl5U0HqSRjlaKbMG8Z6AXJu76HJzMiW2GYkn4vpbGgQSrZP44QAoqOxopmEO5llBOJURScKzislnNx7egowZukRElGNgGVQTDN0K0nXuOGJfH9lJWywUbtSUL0wW5IEGYM+gmzWX6hsByBFWk0hc7OJMB2JeNJyrGM6LZiXtxyqFQ0Co7EH2ZkQ8HlLYcrcw6GhG80Q17acKhpQ26PJ+xHiv90y+aeKlA0dQpGjKFbaFHAtdaMxe0NCg9v0qyV+XcscsFVzOIMy0+wOyM+1BcxUsg6IaLfIa3PsXxhi+rohNvWAmmhzPzhHYIUcGC52iTs96k6Ov1RgFVyieYrVLwD0rVXEMd5hkOQ6lSsBOG4XCrBeDzjZi/i4dorrLbu8OLFFaRpUusdIAuw/urvsNjUMIwyN+e+w8niVeq2RufWPsPbe4AClXF87xEzu4CmaZgJJMWMO8c+F6o2hq4IvIy1qsXeMCTqK2ZhAgI43oOlNSAvEPunvvqa/CjVV9F0daTIOcHP8Y8LYZKdcvJ97p74zNcMXj5X4MKKw/q8Rbn6KQJZYBSmNDCQhWcfP/Fittcc1udNTrwYTXuWelapaRw8jqg1NA6GIZv1/LrgOhIvyDVYCkWprNHE4MbujG4acxLHzMKMgjA4OYrpncSEgWJzyWJv8GzQnFKK8Sgl9BXqU4q/haJB5zewlttefGZsEKUZhhS4hkbwc9LDPq6HWSyZHJ9q1f7tw9EnirNxkJyZKSwUTfaGz6cxv1YM+59ZFB6MQr61VsqpwLfucc3T2byyzZXXLmMWXNYqFo4h2ekFrFQM3j6c/Nx/dnLqIvoPwcEopO7qGKcOaeMwpe7op6HU8KDnM41T/mJnxB++ss7jmeQnd1vcDU0MTVI2JLMUHFPjhrNCSVP8m67ELhaQbgFz5iF1jY7TxC/VeW12gCNSlh+9z4Wkw+ZonygVNPWENEv5Z8sanungf/gBg0Qw1V1KrUesJkMKL7/K8fx5lk7uwVt/C5Uq1Jrs7x6x8uga6n/678nq8wgpUcsbqL/7Acq2Uf4M9eHbZ+ec7T8k/ZP/k+ytH5LFMdy9jrp7nSwKUe/+iAUZQvcEtbaJWNnInUFPDmE+15uJ5XWYTfIw7C8SOq1n1+HpPf+MEleqkh3v85nBW18CPG9iPgO1hkavnVCpacSVDNfTGZ+kxJEiTRXNeYPjacxy2aRcza2UVaY4v+jgiQypCdyiRhQryjVJkoHZABKBUVE4QjBX1skqEEYpYZIyzhICPSVDMNUSnLrGiYzpT2JEnO9mjvsxS8ogTBMalo7QAJHnsoRJhtIFm66Dq+msOzaEkPgZVWlwpVrAjgXVWKOW6VxJCmxgQQAPvQChQV3oXL/l4fehT0LF1fHaCbVQo2kb6Lqk6OYptg8eB6wWDO7c8/H6GQJFdEplKtQl01FG6INGfgOeDBNCX2E7kijIaM7pDPsJw15KoSR5aakAkWB13cSVkoqmE0QZeychycExzcmIR35IEGcUE4njSR4ceFQKNpFyKfsZr6c+A2OBm48DZonO8TikMulyZDv0jjzWjYi1sM90PKXVGbBlZ3TNMj+99hBHOXzV7PK6kVFA8kJ5Rhak/MRY5kLQYnGxwaWS5H5k0XIbJK0DhEpZKoBmVLg07LJYqhLeuctUsxFxSG17EddK6RXPox7dR3zl20AePveaPsFe3+Di+hxGYw71/k8YRxlL3UcMdZfBgw7ha3+AOHqMM7/EnV6RV+bm2S/XiApVVLdNNJ0yLs9xGOnM6zrdNOF4kheT00dtipsLSE2QThWTdkq9rnP7XpDrYT7apQLWF00O2xEPBwHnajaTUUq/kyJngjhRjMPfHA3nOX412On5XGjYXGg4LBgmjZp+dnPTdPFME+LPMizn9HaRKeZcg7b/6cVSpaAz87Iz8T+AW5SMJimTQkoUKTpRwtYpPWW9avEoCBFDCJXCMATHnZhglHFp0WFO6lxYcVjZMFg7Z3DSismUolLR8bxnm4DJKMNxJG5BMOh/cs02XYP+Zxz3rwpelOI8ZVu+P4qeEdG6hnZmTf1x9GYxdUd/5rEkybAzwcBPGPkxWzWL48mTxixTiv1RhC4FyyWDkpW/fpx+eQuVLxNUpwWnU5idrk97+mzTPI0yGq7BwvIcSxe32VyonCXBf4SGa3Cp6bBWtnjQD7nf/9maroGfcL/n86Pdn7/p+TTcbPu8tlT4xOOGFNzv+xiaZDBLWKkY7M8Uk8GISr2MISVLJZNm0aRQNHlzp0UxDanUK6y6gvdUAy0NaWsuEQa6gEXlsTxtM6dF3Khd4Iqb4qHxFdHnak1jfaHKoqtxIRsxwaAtC5xzUvZ9WNcjqjJjs6wjMpVbwJdr8O1/mhfvpUpOJ3v/x/kJtPZRugnDfq5lGQ7ITo5QOzdRh3tgmCipo/7X/4Hsr/6cLAzgJ3+NihNEYy5vXo4PcmOGheXc8etpV8Dzl8luvPvMe6bufPgP+iz+IfjIlv0ZpFnuTDrso8p1ypUig/74GeH/lw3Pm5jPgGVLLr9sE2cKoQlqNY1CWeJWJG5BI8nUR7psAOoNjU4n5m7X55CQv7s3Jo5TpBCcW7K525pRKOqcv2QhLOidZJQcjdpMoxcpRmZCP4hhJNifRUzCBMMQlIRkHCfEZCSaYkaKnyq8KEN5UMFgT4XsiZDMVBSVpGnrOEuCMExZSkymZKhEUUdjHGf07ATH0YiiDE0JXDSGuwlNQ6ftJaShYHFdo+TrfOOlAp2jFDWD8SCh3tQoWRrtKMXJJKEPxbpA10Cfaey2wtMRriBL89TuYS+m14k4PoypNzUCP2M8SvG8lF4nxS4IKjWNxTmDtWWDZdegaEnmE4MwgyTNaKmU3e6MZqxj2wIzkvTChJeKfbKywbwcIFyNuFHkm/oh1aTFv9iu8N4dj4cDk++VJ2SBz1dWqujTIe8bi/izhLi5SSwtap7k6nzAA63GitdhXJ4jNiWtB8cMsHi7FXEwCtEMnReqGmbscxCA5thEb/0AmwnV4w8oJn2U22T0wXXU1kXu/vUPaQ0mlK0ZcXMLfzAlvnOTWWQQbX2FgtQ4eLiPWD8PpQrHt+6yNOtSX1rHP7fG4Z0eF+I99JokdBSmISl7PYYPrpMUl9lxlrhUsyg1Goz6HqWCzutLLmVLo26O6XsOtiOpNXSW6yYf7s1QUhEFyTMXLk3L9VtpqoiCnA7UmNepNjRSDyb9JG84+wnHJxGH7ec7u19mPOgHzGsGo6cKfSEE00lGsaQRRxlH+9HZZ97rxTiu5GgcUcx0yjUNKXIq0+32jFvtGSfT6GwSYjsCJZ4UzaHK2O0GnKvb3D70kdaT6cIoSHHKEjuVZKU8ZDO1FGZRMhmnGIbAtCRCCCpVg8UVA2+SEQUZ2cdq/zRVFEqS2Uxh2QJ/9slJR8GQTD+lKf9V5SQcjKMzgTTkTcZHgZ4CwUJBP5uqfBzdWXJmtvERBt2IMFBcaNi8fehxoeHgPaX1udvxeWHOyV9fCNYrFqYmvhDmBv8YMRo8tZaa8/QfPKQ+/yQ8OM7Ume5pFCRnFsA1RydMMyr2p088Acq2ztdWChyMIo4nn33N7XgxwyChaGk4xi+f+dGaRtRsjQf9PPX+aZQsjaNxxL2ez7tHE35vo8RfPxxz5YVNPM3KA6fHIfWCju24jPyMpZUmC1rK1aTHUSyoL8wTKgO3WsSIZzgCrpW3MITA1wyMlXUCq8Sr++8xdSpshz2Ozr3GrNdj0TshLNfJ7t1CpSmyUqM5V2P9z/4XuHgFkgQWVwhvfYhZLoImIPDBsEhvvIdqHeYZKecu5Y3Lj/4SdfM9cNxc3zK3iKg3Ed/5Y/iP/gu4dyuf5k6HqJNj1GiQWywbJsItQvjsFFhubEO3k1O2II83cAu/Oa3Mp4TjnmHUx5NlVuZMuqFCacanP+9LgOdNzN8Dy5Y86AV5Wr0h2Zizzy5Gj053rCG/kd/tBfSSlGXT4MUFl4CUnz6aMctSHk8DDjsxF5dt3j2Z0s4SVKKwkbTMmDhOmCUZ3SSh4Wr0ooRaphHEKVoZBjIjMcG1JANijtKQW2KCSAURCYuWxdhMkEhqrk449WntxlhILD3fHQmniuNRTBOdTcfGsSS2rmNbOuWyxqW6Q/9RynxBx/MVw35Kw9V568ceBUei6YLJKKPXTTBtwbxuYAjJi685rNQsirbEcSSanbH/MCSJFJqh8H3F+jmL6USh63D7us+onyAl9DsJpp3n4JQqGqYpqRsGt+8GlOqSVy67lHSJPpPUMGhpBbxWyP0gwFmSeCKlKjTanRGrnVsEoUZjbYXB8nk8t4I5PiKb9uhNI7Q332Tp8jK7+x4du0nPrtMo1CgaFiIyaEvBtaGHkcC4skhv4DHFxEh8/tnkNrXjBzDs80DlO1TNCxdYLehYswk/bryIe/wIdJN9ZTP82jfp9z2uPeixpMX4TomH+hJXv71J+tabzBZfwBAJ1XkbO5WEkxmD3X3UrfdhNkWcv4Q5t0Kt4tDrtels/R76wR0W+rc5eeenyK7PibBISnUslSLOX6JQX2UyPGajanH7foCKI6ShU65KBr2E6SRF2BDZGWGkmO22UMvPik4DM6WW6XRaMWms8GcZQgiubDqM9YyOiumoGFzoewnp853dLyW6sxhbl5hCggDfz9CNvKjOA1Dh3VserSCko2LaWczETmlNIqZRimtIpBScq9nc6fnULB1bl7y2VORez2d3ECI1cabb6HgxnVnCZs0mGGXoMYwG+fpRSnE0jlgtm5TqGpGnkA44umSrabJz6OMWny3yimUNxxFMJylGJnjnYIJSijjOGA0SBt0k53kDMy/7BNVqtWJx+LEC7WQa8fbh9HN/r+M0Q5fP7nI+fThrFZOD03yGjx/np/H3lVIoFILcRlrXxJlZwck01yqtVqyzJgnA0ASZyovm3hfIbvofA2ZeysxLyU6pi6JUoX/uJRquQW8WU3N0VsomBUNy71Qov3yawzUO8+/URzTDp7VR94587h/nTWfB1Hl1scD7xx6zT5nYHU8igiRj67QeWT2d3vwyuHbs8fW1EqMg5frJjHtdn/1RyFsHE9rTGE3mjI+1qs3DQUjbi/jrA5+6pbFVy/Uz0zCjHyQUNKg3qhgLC/xF32TdVKxYKUqDf76o+PZmlakwGUuT1c4jvp21+NukhiqV+BtrnYdHA9565xa97/858yWb7a0lriyX+dBcQN+7D0tr1H76bzhZfoGsXIMkhIPH7G++zNrqInTaefxBvw1v/TA/wSRB7dzMHbtWNuDDt8l8Dyq1nHJ25zpkGSKcwbkXwC0g1rchDFDHe89oZeD0+3iaoSUKRShXYO9BHlbrFvPNyc6vXyvzkfblaRrqRxrYjxC9/y6GcSryj/Ka4cuI503M34Ohn1C284VQqmgUn7qZKsXZjeL6icdSyeDyisNklmFLyavNIp0gYn5Ro3WU0PUj3tkfc7cVUDN1jLKgFcSsLei0/JjYyigYEmlC4kE8p3gwDbADjX4WEVRT7BWNup0LsZekTShSNCTKylgoGQhdYdmQjcdM2xnEgpKmU3d0NB1MBHZBIhwoSo2CBZoC15DUyzrLDRNnplFbAOlB0dYIIkUwSmnMaQiRsf8oZDpJGXcTSlVJEmf4szzXZjZNGexn9Icp0SDDD/IFliTgOJLhIKWxYDAcZBTLkjSFJModD6UUeNMUQwmiKMOwJd5EsbpkEmUZa7bkUr3GdtUnlIrjScx5c8S+NUfFG9KWNrFh45qSoNtFn1/gh1GVc1WL45nO/YVXqO0e0jctWhOdl6oLIGH73jsURMh2OuBAOSxWHUrn1/hJp89PWzqbep/xSLF9foXJ8TELy/Pc9C2yUZ6vUvTHnFMTVvZu8CCxKF19ma/U4MAtoU1nGJnEPNnDb67hiITCpS1K032Mzi7K9ygfX6N47z5HvqJ33MGu14mlg5e5bKzYXCgmdGOTR4uXWNhcJWwuEyzPM8yqDKwiNJd4dBTSj2Mqrs5J28MxJaOHj2B1C9OUFIqSXjuhEyZ8Y61If5ZQNnzG02eLw7WqhSYEa1sm1YZOkii8aYoQgqWSyYWGw4WGw1LJxCqJZ3cgn+NLgSRTdKYxi4Vc/1epabSPYoqlXAyfpIprhx6Nos7RLGa9aHGx6XB5zmXgJ4RhetbwSAFj8olsqhS2lNRTg5fPudQdnb1hxN2uT5BknK/baJrA8zK0imCpafC4FfLhoxkL0qCcabS9mM05m2tdj9W6SRIKDOuTu8qmKREyn844SnI0jNnrhBwfxKxtmmdOaaGv8PWUfv+T9DFNiDN61dBP8OOMuYLxuRtY7HQDtmpPpjC9WUzDfUIPs/TcPCNNFAePnxQRszgvIlc/Fjw7HWdU6xaaIXjQCfid9RK32z6PBgGagMtzLiVL42QaMf/UBEeI3KXtZPq8ifm8oJTCnynmlwwmo6fWqJZ/vr2npmgN12CpZFJ6KojxcBzysB8QJhl7w5APjp/oKfwgQyLYOwlZLhl0ZjF/tF3j+/eHZE8V0oNZzE7Xf4aeaJ7SQKOfMY251sptu0+m+bo7GIZUbZ00U7SnEd9aK+LFKVfmbP7kdp9xmPL2/oSBH+Nokg+OptQcnYqlcX+Q/64AHg98NCEoFAxuHw7401t9HNPgd1+Y42SaUDThbi+h6vX49nqBpYrNW3Ke4+MefXWKyPwAACAASURBVLOE7rikVpGrUYvf367zUkmx+cZ/Bt/7F+jv/5jL7R3Wo35uaawUl//J77BzPOYgtkE3IIqREjCt/DmDDrz6jdyt7OKL8HgHjvZg8wK4Rfjb74NpoQpFiHzE+UuIzYvIah2RJIi1rdNA0l2Y5lS9bNhHFSu5I9qf/h+oaT5tEW6BbDRAdduI+aVfbEH9klDvvZln4TyNvQew/rFMm5MDWFgBIDk+RG5fIjvYJQw1BlONaP/o13K8nzeeNzGfgfY05l/d6TOLU4Z+wuE43+US5DfVjxrcO50ZQZJxMo0ZBwkTLUH3BLW6TmhktAYxRyOfedfkx3enLLo6ZkEwJGM8Sbh23yfVYazFLFkGJwcJ+5rPg2FAVEnpzGJsTXAynPL9/Q5+lBLJjHXXRlbAFBqDIKXpGISpIg6mZIUqkYgxNYFdhGgKrq4jkKwUTOpTHc9PCU4DNftHuVB2flHHdiWLZRsvzsfkugFSz93SkjgXe8eR4uJVG2+acvdGiB+kBLOc9mXakt4gxiJ3XAvCjL0HueOI76XMzemoLGPmKWxbYBgyNwjIMqJQsVgxiWJFv5vvqNYrOpkBXiJAZZx/scoVIi7NOXSnMVbdQvczusKlYOYTgmQ0pJeZHO8OcRKT9YLgQDrsJiXWG2ukqSSuKdRoj/NWh/GjfTxvxn+yKmmNNar+CeeSLvuZRbyyBd/4DtJ1wJ9RuP5TLoweczuyeKWYcLO0TtEf8m/P/z5TaTMMU+6/9R4rL2xjrDTx20PKk5BO5DLcOWRU3gLThhdeZvb+NfojneYff4e5ic8Plr5OqAzG9w8or1bIjg9Qms75y8t8zYiZJoq1K2ukIx/dsJj6FvvHGnZBsFA3GdeW+fB2iwtrFntjecbXjSJFtakRjDLcTENUBHvTvDkf9p7QxHZ2A7TiE5pPqZwHYU0nKfOFZwXRQgik5Pk05ksEpRQ32zMuzTlMhinlak7RMi1BGCj2DyJ2hwErhklkKLaXbabjJ41q0ZRMJoriqevY/X7A11aLnExi4vCJ3XEcK8quxkuLLgsF46zAytK8WPezjO05F6MoWJgzaM4Z1BsGVkXiupJMQaGk0ZjX2WxY7LSDT5yLbggKRUkGuGlODyuVNTRdUqxoTEYZ5apGf5iwOwg/0Zycq1s8GgTM4pQTL2azZrNUNGl9jkX+40HASsVEPrUb2vcTGu4nqRuFRCPUnxSd+6OIcZh+wlAjiRWmKSmWJLNphqlJXl8u8M21Mk+7Lo/DlIr9pFmacw3a05j1ivVc5P8LIk4zfrw3+URTMOyl1OoamibOJjF/H4qmxsppU/pR3s+LCy5vH0yJTmllmVKEQYZm5DR0P0k57sZcb824f6ph+9/e7/Cg73O7M+OdI4+1ikWcKoanVLU8TDKnjH4WHg8DdgcBF5s2hib513f7/Mtrbb62WuTmiYcfZzwahuz0An5wf8S3Vou8fzTl0SBECJiEMTu9kGZB55WlInc7+cRGCMFS0cTU4KEn2RumNF3JUQD7o5AuFg2RoFs6c/N1YrvIa02DtnCoLc5jhD5f0YY0yhbfsGfQPoLxINe13L4GSmFVymjjAbSPYTzAeO/HvDDdp5J63I4dTEPPG5ZiGUwHWkcQR3lQZfsYbl3Ld2C8MVRquQXx138Padlw5TXU7gPYuUHW2of5JdRP/xbhz6BzjBp2yd77Mdx8H3H+BdA15NWvok6O8nDa+hz4M1RrP598AFQbZA/voh7cQR3u/pKr8O9BfQ4O987ycVQSg6Z9wgyELNfDqJnHOCqQtTuMH5+gFy1qhRjr3Obnf2y/BvzWNzHZU3zFWZyy0/XZ6foIFBmwXbeJUsWf3e1zqzXjTsfjrx6OWCmb7HRndGcx31wrc7HpcOLFzJKMyrzG3+2P+S9fn+MHO0Pe6ww5aAUUAx2zJvnL3RGdWchBGBCMUpQLfqx4pz9jZqaslEyWqgZaCkcyopIauEKgAsGRiii5GqW6RprljYJVgkpm0NVjrNSka4JDhpAQzxRa6KFSaC4KOlpM4IPlSqoljUZd4E/B9/ORuGVLVJYvjFiBrqA5bzDspug6zKZZnvBqSnxPUSoLBp2MclUw7GUsNAx84OQwYWHJoFDSSBLFwW6Macnc/UqXOK5kfsmgXJUUi5KDxzFCwrAXo6Uin9CkGdNRiq4rHnZMTqIYvVphSwu5dmuEaVm0RzPqneuYeoVH4yneOEXrHNM8OWQt0TlntJm3dUzdp7Tucq4445WVMjvHQ2ZhDMvrnGgFtsoG5f2HdPs9GqnP0tIC54J9bnfhpNfmRkdjcfsch5svY25tM9d+yMSpEJXq+CfHfKue8Uop5fxihRe/9jJfWS5ydyao6lNcv4Ump1TdmLKb0vddEmEQlpcwKiVkGlPZf48rjSaiucW41qRw7y24fxvZmEOWitgbWwRGk71WwNzAw7Bs7M0i0yShJHRKlsbleZdlB969f4RVKDMOU2ZxSm+c0EkStpdtfC+jmo3oG2WMIhhFQbWuk9qKl7ZdOh8TPRdLufZBj8UzrjcFQ0NzeT6N+YJjNEgI/Iwwybh+MuPKnIsUuX2xEIIkURSKGt44pe8lLNkmcQRGAc7VbVrTOLcBzxSzRLFaNrnb9fnJ/gRNCJoFg/1eSFXTqc/ljbHvZTgFyULRfKYIV8DKpsEoTGi6Omtlk4Xik4J+tWLy5v6EqwvuGe2pXNFRAZ9w8SqVNbxpxkxm6BrseSEHk5B7PZ+un4dk6kZuHV6uSDofy46RIqdYPegHXGrm+pGi9dkC+18U3VmMrgmqtv6zn5xAsaDhqYzuMKI1iejOYhaLJg3X4HrL4639CfdaPrFU3D6ZsDcMKZpPLO3LP+PYq45+ppnwopTsuWX6z4273YBvrhW50/HPmuEwyNDNp3KUTp87CVMsXTIJ00+I9T/COEz54eMxk0FK0ZCsVS0UuQnA/ihiOk2x3PyzvbTisjcOuVyyCVPFi/MuX10p8JcPRpxMIxaKBprI13HHi5kvGBiaJFFgafJTw1GjNON22+e7WxUe9nLtS83ReHHO5VbbJ0xzI5cfPZ7QGoccT2KWyiZKKNYqFrau4ycq37ydJNRsjVRl2LrgYBzx3vGM9iSmamn8N5dNLpkRTRsqOswVdIxCkWo0YSUccDwMiK98hX8yu8d4/SL1YYvNKxf5/QWJPR3A4R5oOmrrIkKKnAJWKMHWRZhNYTpBSQGVGiWVcLl3j/V7P81P9MFteHwX6k14fC/XsNz6APod+K/+Wxj08qlZfQ51/R3UwSOEYaIOHpMNB3DrGsp2Ed/6LmgS8Y3vIJwiKo5Q5SqyWAJvitq+nG8Yrm6ijvZgdQOxcQF1+Bj14A4MujAd5U1P9PluIKhgBraDuHAFHu3kDczup0xhnkK69wjZaCJ6R5T3P0A+uEGaKrJR/zN/54uMz6WJeeONN/74jTfeuPvGG2/cf+ONN/67z+M1f11IWwdn/97/4AYXinCx6XA4ifi9zRKHk4i6q6MJwXbTYb1q887hlD+52SNMFV9fLbE3DHhrf8J23aY/S/iX1zpoUvGj/SmOGfFSTSc0YeBGTNspG7bJjZHHQRhRKkt2ph5RovjjixWaDZMF3SJGsaG5UFBIpdBiixo6nkipuAZKg3JZY1ZJqI4MsggWfY3qkotRE4RZhqXDguuT6Tp6AaxIpxhrGECjJknjjCAQCC1P3j7YjYnDlNk0gQS2tiWTMUxGKYWKxLQlo6HCtGA6TqnWNGaeQmj5ZKVYgnE/RfngOLBzy2c8TGkdxqgspd400HRBqawRR7nwdtBLKVZ0Bv2EUT93xLJLCscQKFexdxhRMUa4VZPzCxY3W1Ochstyr41tN7lz95APC2sYtsZ5V2IkGR1tkThzWXbHDGcJjfSA6smIng/6/vsEymLD///Ze88fy+70zu9z8rnn5lg5dXd1IjuQHJKazFEcW94V4F0Q0hp646AXtv8Nv/cLGzDW8AowsLLckAyP5FlLM9IkkUMOU7MDO1TOdXM+Ofz84tQ02TMcaaShuBqZX6DRVbfuPbdunfR7nucbunTkHLcK15nBYdobsBGUWCi6NDsBmVGHSjQkri0wd2mVE73KbWOOUX+EqM+heRInE/A2HiJn8lj9Fly+jti4j9SYp5bVcNpdwvoMu5d+jYut9+n2J0itI6pLFrYt4fsySRRiv/UObakM86tUlYiousCkMY8t5ZDOrA/zRRk1K6GNWsx7j9nUa1zIGbhGQhDHjAYx00lMdmGO460+48ji7c0Ju8c+WibVJ5w6IWpZwrM9NsOE43bA0Zk2oOdE1D6mQwxg5RSiUDzVzZ7JabSd6LNpzD9xCAHtQcjOwOPajIWmSAR+gq6fOQaOYvJFme40QvHSqV3GOpvQKPKTQvW1/TH9UUijrHE8DujYIecqJmEgWM2bFLPKU8fHj7uAgnQCFEcCRZF41PWYy6eZJ+9s2dzZdxidFcc5XcEJYmZyGl3nw6JjPq+x/TNE6WpOkBUK0lTmylJKd1QVib2Bh+1HFIoyDV3naPTT05j1qskzDeuT/HMDaZe9a0csFoynHv9ZVLWipDJIIpZqOqNpzMk44MaMxfmKQcFQsHQZU5PpjyIejhzWKhaPex6VTEp/u9e0n9r2aBSh/Ng0YfDTVLr1Woat3s/u0n+GD5Gm1utIksTFWoaNs7/bdJKQ/4j7nqpLjOyIo3Gacn8yCZjLp/vndJKK4Te6Dq/vj7GDmOWiznxO56QTslIyqGRUJCRaE5+OHT2V0VQpqniSYE7W+M6jETVL41I1g6UqXJ/NUs9ptKYBhyOfrb73xCRirWywM/jp/fz93TFfXM4zDmJOpyFZXaFganx+Oc/bRxN6bsTuwMWNYiIhcMOYbzzo052GeFFCNaOQUWVm8xpenPDtrSEXqhkyqsLEj7hcN2nkdWRJUFtcoKPmmNdi7my3sP2Y1UqGqhLztlRDz5icny1SV2OmO9v8Rm6aTl6yebhwNf2FJeDd1xClKlx5Li1KjEzKkcxkUz76cADP3EgnN4YJ996B0yO4fCNd1O9swM7jNFKgNgOvfQvp3KWUfqYosP0IkS1CFMKwC4fbcP4SUuQjmVZqnazpSI3Z9P3efZ1kfwuqDaTWMcIew/4W8rPPIe1twsIKkhCwto50/jJSrsiPP8xP6mp+IbSbUDuzUL50DTY+AFl+2jXtDEmSEO9tMkoKFOZyoBnw8leoJzbdaUDMzzaY+KeMX7iIefXVVxXgfwb+E+Aq8Huvvvrq1V90u58WWl56QAnPASubHvhAz40QQsIJEv5qa8BaWUeT0/PmxqzF3ZZNexKiKzKPuy4DN+R4EpCc8Umb0xBVFlQM+K8+36DpTigrOi0vZNKJsWIFTZI5nXgUDZklw+DhxGVjaLM99cgKFdmCQqKSURMUScaVYi4VTGQFFnMai5ZOOJbQVBnPjTDViJNhhN0ZkJMVkCCXjZidH2PmJHrdiLAPuaJE6yRGUqBYVtE00PXUUtV1Bb12RMaCYTvNRVIUqNZUTAMQ0OtEdJohYSAY9CJcB7IFsKeCKErIaalYOAwFM/OpwfJkIhgNI473A3LFdBLTaUZIkiAJReo2dNZJlCSZuVmDDjEDN2bSC5CTJpv32riHPX6wneBqBooCc4GKkcmRyILlbIXBfpMXXjqHHwgWawZl3aPa3YHZKoassbf4OYzhBg1ylNUYP5GQi2VOfJmVoMes26PVn2KqMnVNIA96vH1ks1wzsCQZJ5F456/fpZevsGbB4dSkqBcIjQLS+hVoHnE49Nh45x4Tq8QfDmu81wlYXFugFwD7WyBJyDNzZE8/IOwM8ZauMi3lGTttIuFiRBqn2gz72ctIekRkCB7vjsgc75IEEf5Mg999rsZO20cxJB6eujhxzL0NG1mT+cqvXebR1CMyBJGecOr6VDMqYZxwv+WwbEnMFnWqhsZPDJwpGArjj8kZyBcVFP9DVydFllKb27Ly2TTmnzCGXoQTJlypp4v15nGIPU3I5j+8YUmSxNCOWDtvksSCj2YGyIrEwdBnoaAjhRK6KbFUNPj8Up6jkc9oGHH+gommSYz6McNe9FQ+y7myycOOy2Qco2fhe7tDDkc+t7emrM+aLOcMRn7MTt/jYOjxuYUcWz3vifMZQKGkUpY0NnvuU/86UchhO+Dt7pS5gsJ72zajQUQ1o3J5McMPHk/YGHj4gaBSUWm2n6Zmdezw585p+ftgo+dyqWb+1ONtO2TmJ5zG7GlMIa8QC0HF0qhkVCxdIWekU60oEUQJrBgG84bO9UKWO5tDVA9CVXDvwOX1gwk7AxchoNMK2D7wKCbp/nUd8cShzVRlvCg1GlBk6R/ls/9zwtiPEUJQOJummapM1VLZOnHJF59eOmkZ2DrxnpxnkJ5XDzoueV1hvZrB0hQsXUGRJBo5ndtNm3omLVb6bsTXL5Z4fOQjWwJTfXr71xayPHJcVkoGp60QL0izv45GPm8dTsgbMrO5VLc48eMn79+ZRvxgb8RWzyNOBLePUhZJwVSxg4RGTsUNE5wg4d3jKXN5nfY0ZBokXK6brBQNLtZNYgTTMOFC1aRkaXix4AtLOXb7Hn035HzZ5O3jKVVLpWRqmKpEwdT4y40+QsjE+SIYGZypw5wlcaoW+NHU4JlLi3ByCItrqBkLbWYGxkMkSUbKWNCYg2E/pYW9/1Y6Wcnl0nC6Sj0tXh7eAZK08BkO4d67UGlAEsMXXoHQTxcy+QLsPEq3GUUIe5IWTEKk1LPdx8jrV5Ff/HJaHCkqYm87FcnrRiru102kYgluvIQ4o4gle1sQi3T6EQSIQhlp+yEiDEh++J10B9ZnSbYfIXL5VI/zSSGJU8vks/3N5eup1ucnIFwHHt1FvPE9pGGfpNdBmplFap1QvHSZ9jim2/nlbEZ+EpOYl4CtW7du7dy6dSsA/hj4nU9gu58K7Fhi4gZM9vbR5xb58Q187MW4UXpiT4PUjrZlR6wUDR52XC5WTR51Hd47mdKahgjgD99tcTgOeGE+y8iNePNgQt2ADV8jQwwqjOSYSIF93yM2ItrJkFM7Yj6v86jn0I8SRCCIzZjv7I1wcAlzCbmMipIHKwmpRhqtcYgdJRxLPqiCUeDRsmLypsqFqYSiJzg+eJGgl8kyZwbEAsplmWxWQQZW1kwkBCIBhESlpqLrqXYtW1AwDJl8XsLzYjrtENdLGyCuA/UZmdEoxg8E+byCjIx65mBWrp25HtkC3xWohoRppNcU3xE4kzjl4fsJswsah/sBmibwHEHgJxTzKlZO5lfWszx32SJpJ1xaXUYul5i7PMe5xQqBlWE5LyFFRxxHC/TjOkuFKVric7I5Ripl4PiYSi3H9sw6lj2iqLqMhI5AUAjGuHoJzY2wtQw5pigyTI+O8byA5y/MIi4+yzirExx2yOYUAkewonpotodRK3JwcoIq2wRWgba1jnR8QNuaZeP2Ma5U5BXNR1VVppKWXogb84jaHIQhSatJjgkzz8whnR5yXFnmV7I+g26HgmaTG3iEBzu49TlkGXLDHoXFi2SDDkmlgaJIzBQ1blQtHnY9tpsOmiLjkjAOEmbKKi838hxMfPaHAc8v5LjSsPhcPqKjWFiaTKAkZIXCB22H2TNaz2z+43UBmwOXnCpzOn3awUSS0uI3CD5bEP1TxMiLWarq+H7CaBCj69KTrn0cC2QZpl6MrqROV6os8dHKtpxRGUURUzthtWzw+v6Y1bJBLavRaUdUaipJkgqcf1z+xMnZFEYI3j+1sXSZ5jTkTtPm5lyWVjtgKsVYZ4HAFTnNc/rrnRHtacjQTa+HW2ecflWVMCWZ1bzxxFxivZqhUdDw/ITVgsmjocdACskVFAbdmIypMJfVSEQa3rdaMWlOgiefPRGC3pnW8aPQ5H+4PS3ATt/jQiXz03x00kVx4SP0MiEE3lluFsCwH9GcRiyX9NT1KBFsnblj7p34LC7rlKsqjaJBJpR53HGYtzSWSzrvHTv4UUKzGyIZIGLYfODQPA7w3HRRu1jUn6Sunysb7P4tmon/v0MIwf7QY7X8dDFaszQCX+B9ZPK1N/B41PU4V0knb16UPClC5Biss6+dMKFmpXbacgI5S6Flf3j8iRjmsxqbH5mSOWGaMZRSxXS0jMzllQzLmkEcC7b6Lt/ZGXM89nltf8R3d4Z4YYKhyIzc9Fi62rAAwe7Apz31udqwOByljYnDUYAsCaIk4UrDYq6QhmtWMmnG3f4o5HAU8uJCnryucDTyUYkZOCF/tTPhxcUspirT9yKiJMEJBTld5mgcMJvXkCWJek5FUSTyGjxfkfkqHYqNGlfPzbJSzUKSsJ1fpEAEngf5ItL8chrSuH41LSiGvbTYmF1EqjRgcTUtTIYdyJdgNII3vweeky40PCed2PzZH0NjAbotuP0jkOSU0tU8gof3YDJKv372BchYqbwgjJC+8GvIy+cg8Em+8e8RP/wOYjRAPL6H6LWRlteQFBWeeR62HiB8B/H2awhZBkkm8V3E/dvpvX7rAXSaiH4n1csc7qb7e/sR4vRDJtBTx5//Dzs3JVn+2GtPcrgLrsv4K79LfnqAc/8xlh5DbRZp0GVinKO6XPgHved/bHwSRcwCcPiR74/OHvulQHVlmf0PNjhVcvSckBM35X/bQcx7x1OKpsKjjk/D0pgvaHxra4ClytihIEwER2Of2ayGGyXM5TRWixrbfQ9dkWmOPRRN5a93RlwtwJgQw5HpKD4rlknoRxQsk4ZpcL9jMxi7JEFAhODdUwc9K7ieTQhknWxGYl3PoUgRSQYiA7IzMucWTWwjYYRPVWQ5p3tYjSJZWaGWsdkeybh2hnASIKmwtKozHiYoiuD0KHgiIhQIFCVtcKg6BG6CrApyJQV7AkGQkESpQ5+qwNFBQhgkiBhm5lSKZRUzIyMkCAMZSUhY2XQiE/kCSYLajMr5KwZRLNE6iZiOYxw7QdMlMjmV1mlIqaKQ1xSmckwtq6ONO6iGyvB4zLLhoscS3XGEtVLg6INjliKfpgGqHNLrSRSA434MJ/tk+9vshzpjs0SlVmYQJHylMEAU5giHG8wbdep2hK/qBLpKKRugYCHVFwiMDLmlJabFGeLxmMjxuKI7vLfrIFkZmvoK247GryyX+KC4SpQrcq/pc2eS46uXDK5bfdb1IbEnqDmH3MmvsWTEHO4fEyUKci4D5SpCVQnHI+RiEc0ZIdZvwLRHOTzl8hLkbJeKBtW8RKUqEfV7qIvLFIoK8zmdiZ0wW9c4skPWLxrUpLQb99X1Ij/am1A2NZ6dsdgbeAgh6G47FKplGlmNB30XS5I5HQdPLa5+EmM/JqsrNO2Qj2PEFMsK9iTB9z8rZP4pYexFZDU51bxMYkQCupGadAAM+zGFksLWsUc9q5IrpK5fIzd+ErDYngaMkphypFKraIQJJCKlmGVyMuJsO7mCTGgIOiLkeOoz9mO+tTUko0l0JiEIwd1jh3gXFms6i2Wd7b7Hvu1z59BmrqDzb67XkWWJ9arJD7bHjAcRgzONVqWu4nmp4Yd/Nj3/oOMQSIL1nEmpoOIECZt9lx8zKTp2xFxe48D1GY8iKlWV/+f9AWM/4gd7Y/pO9FOWwwsFg+NxwGQU/70njHYQpwwX7ee7rY6HCcWSwsCN2B/6fG9jxINjm9NxQK8bcnDkYyoSjw5dPF/w5vGUx12XyTBkqWxihQoPWja/spSnklWpkjrCJclZXk5BRbXAsdOTVpYkSqbCw45D342oZTU2ui47fe/J1OszpNgZ+E+0Uh+F7yWs1A2Ox2kxGMQJf3S3mzYDRVr87A08loo6bhDjTGIm47QJGNkJxyOPth2ydZgyMBJSa3AhBLtbPl+4kGfzI/tjf+BzOvb5s4c9zlUMZCktkvSCxOaxS9FUeHYmQ8eO+MpKgS+tFNgZeGz2XH54OKZqqdQsjZqlMXQDZnJpoeWEH1p/b3Q9KpbG/tBjp+eiSTL1nM7Aj4njGFWW+Opqgbyhkgh47zTVkV2umZw/K9hfmMtTz2mUTIV3T6Y8P5flQsVkGibkdZmhG/MbDRiZBbT2EbWsSimTTht3pglNq8EN7xjWLoE9QUgSYmY+ddOysunE5NxFqM8gFDUV6U/OQhoVNRXqhxHMLabUkcAHKw+Om9LHdCP9uSzD7CLIZ69pnUK/lz7+zPOIN7+LSOJ0ynJ6mHZskxhcF/Y3YdSHpXOIN7+PaJ2kFLUv/jqMhimNbdgHw0QaDeCLvwpxhOh3AZCiMDUYKJYRj+6mtDIri9h88IRiJsIQsfUgnZq4zid3QN99C3HjJSQzg1KrEelZtI33oTFLvHwRHAdd/+WUyP8cqsNPBq+++uofAH8AcOvWLWq12qf11n8rvrPZRXYcfqgtYA985DhP9DcHtGOFl5aKJLLMfFnixFNYLBkcOzbPLdcIk4QoSnj3cETOVFBkmfV6iTcOhiiyQtEyyMsTWnoJQ1EIrDofbHQ5XzI4nUYsGllebMS4iYSq5LnT7VIoWLxQhIvzc3zvpM+X5i2MyOOL9Tm+efcQ09SZEQZ5K0OkxNzruvzmlTne2TolGeo8WyviJUMUq4QRjlhoKJRtmLsxR/vxHo2MxWSkoBsCw5C5er3Ie28N0LSYKBTIkonrOFSrCucvF1EVuPvekIylEnpS6kilyCAidF1BljWsBsSJzuJKniAY0W1NyZg6ztinNmMwGoZYOQVVU9A1i+3HE+bmM2QypI4uicT8YobOqcuVZ8t02h6VWo4wiQl7PoI8tZmAjQO4UVHxuglfemGOPcfjwd1jXihW0aWI9sjmouXxlbkB3xuVcRyH7s1XeGmxyv137hKff4GVhQqnP/wu6ysrvKufo5QFb+hQqsicaHnscZNaVWaUyTAw5/CmLmbGZPXaNVo/2mC+7pCT88Rr62y2evx2rUhT6CB5GLkIv1Pi+ZpLoXNM3DrGu/wC3aVEjQAAIABJREFUq77DM3qFv/E0vni8yeDLX0eRNOYe/4Dwy1/n5Nt/wY7I83nniNKli5y3FfZXnuOG/RilWKYfJJQmfdSXP0e0v0VmZg6zUqFWz4PwqUsOvu0zl5GoN2roQsJ1IhZmDeKHLl+4NEMjZ7LdtXE8eOa8wXGmSjsJyZgaZiZP1uep89FTXVRDpZRJpzMnJ2OeP1/gnWBApqhSKGXRVZlOPKFazSFJErUadNseVkbFyn54WZlOQjKW+lT6+2cAVVX/0a+BzdMxFxZ0ajWTfntErqjT7/o0Zk1MXWFhETKWgnkkKOYzzM7lcKYT+lHI+mKZztTHUxKeXytxpZ5nFEZ8+VKOw5bD+VKWlXM62z2HUInpCpnZusFlS+PP3jzhdifmd55bJWdqfOONY4ayRN4xyK1ZXCjn0KsqmiKhKTIty2OpmCFf1NBzPk4Q8/ycxcSPuNf3eW4xw+nY5+ZiGUtXGI9COkMfO/F49kKRyUlAQbb43HqBja5NVjaoWVnqswkVTcOr+5y6KqWyxYWqwY+OfJ5bbeBHCT/aH/zUfhgyISu0tPHyMbSwn4Wj4xEvrs/8zJ934gm1Wh4hBEki6AwmjByBJRtUE0FpBjK+hD2AqYBBmKBPJeRIoVKz0AoKz62V2Nu0KS5lUIYud7ZHPBxAKZejeRxz82aNumwgyaCqMl1lzLCbcOPsM/74o56OPU7HHi9fLBIngt2+QxIJrszm//4H2j9DNMMx8zMfdqabY4/Zgkmn6bGwaGJOfCIheNgc8y+vLzJbMBg7Ee1OTD/R6cQmJycOTs5gaa3Bds9mAYmTjQHLJZPIF0yIsSyFN/dCZosWiS7QywWuLYYcBxqNnEE3DBChwlcX87RCnefON/iLhy0+t9RAYsoH3Qn/9Zcv8r++ccAEg3KlwpcuWXx/q0vX9nk0lqhaCi+t1LjTP+F47LNQKnJ+PkfXDijmE1YzqabGAbaGPqah0HGhnJFpuwm/fbVOO9LJmCaHnQkvLZWp5DRe2x1QzOl87dIsr52MWasXiWKIpj6/9uwyb+0PeHapytAOeHYxw7N5nWk7Qp1d5+ryDA+bE3rjgHGuzm9/cQ33f/k+VqNBLAlkU0dRZJJyGX9tnfj0CI720HK5VLzePiFev0Jw9120Uon4eEQcB8jZCkm/hZBkMl/8NcIPbqPVZ3AfvY+kG8j2GHN5hdhzCB7dR4gE9eIzSO++hlIsE3eaGI0Z4skA8/OvkIyGeK/9FdF0iLpyDuuLX8N/53Ui3yH/r38f4XnIhSJBEhEd7RHtPEQullEXlrGuPYcfpw0c47mXSVwb/+3X0Z65iQgjoge3UUUdUakQ3X4DZW4BOWOhvvxlAKKth2hLyz91bMbtU+RyDUnTCIcdtL/jPhK1TrAlifjC51gt6iTJKvYH36P23/4B0fZjDvQ1qtX9v/N+9Gncs/4h+CSKmGNg6SPfL5499hRu3br1b4F/e/at6Ha7n8Bb/+J48+ERJV+nO7Yp6ZDxp0yHE9YLeW4/GrE8VyFIYNSdIIagxCqPT/r8ly/M8LDj8B3bpTuFS9UMh70R62WVrh1x73jAnJLwm6s53tgf85dbY0wEUuAhCQk9snnW7iFX87w5VIjjhP/mRp7Tx9v0T1RqMiSnPcTyEqFjY/pthr7Jc/Mam9MBBwf71OfX2NjvIgY91EaRRhk2HyZUrDYlK0Y4DjI52g/2GQUOV27W2bzvIauC+WWF997uMDOvMuwL2qcxhwdjNA1MS2UynuA6CfmCwPcFQRCjaTLFssT+tsDKgz0OcR1BoSw4OQ453HVRVBgPXVRNwp76ZHPguQmOHbL92EPRJA73x1QbKpaVjqxjLyGIE0YjG8MAkTg4gc+DNx6TvXYJ+2iApRpsHRgQuWimR9/XqHhNdkOVZTHh2BnxfVVn2ciy0z1i1SpwTo6w334d47jNI2MO2j22gllWHvaoxy5rxQn74y5t8wWKuTZbDwdUvvyrlGNBZ7+PH0xoBxa/dQ7enPZ5Ky6gKBJvH4143j9i49xNxg877FvwJWmfneEia+oR/85e5l/lS2w83GGeHHG+iH16wv9x7hmsd+9wL8rwq+fqPH73HlEg42RU4myVcaGCfbCLPU04vLxO5+49GpkCiu0hV2bYf7xL1QAFlzc3RnjjhCEhjzdH3FzIcnc3JG8o9Ichi0ODqpHw/QdHvLJapChLvL0z4IWCC7LNwWCK4sKm59PQZe7vnjCbT/nZJvCg6aYGF+OArC7T7QbMZGM2TsZMxiMuVE1kP2TjcEpRS3OIJFni9CTtnP9Yu2iYMmEzoVj+1PolvxSo1Wr8Y14DwzhhOvSZ6DrD4ZBOJ8TMaggS2i0HTZOp1FXefexghBLWPOxu22QLMnv7Du++6fJBy+WVl/JMApvDTioYPlcwcJouHwxtrkgZmi2H2Ifr5SzC9XnryGW/N2WupuFMhnRPE/JRxLe6Q64ZWdp9m3jisaoYjIIYCYkLVZPTUwc/THMmekMfyQFdElhJwJ+8O+DzS3n+5J0u62ed38E0hFGMG0ckkkA3BI83O+RKCn3X4+2/afGFi3n6PQ87DqgkBve7Q16YzzHthLy/2+LlpTxVNea7H+xzbSb75G/XOXXIV008J0kpIz8HDkc+BUOh2/14i2YnjPGmIfebU8yMxGQcMxQhF+ctDiY+swWFZhJyZcXiaMdnoMRkMzFaT0YO4MKixqAX8oM7+6yXaiBPODiyiTI+zW2PnKqiZ0BpRsytWYwHMX4saNk2cRdarc5TjQQNmNUSbm8fs1o2qcopZbSrfma/HMQJziSgq6VUr2kQc6dpc71hETsgqSoK8P3dESMv5j+7VGJ7MGQmq3H7YEpoQqEg89ifAhJ/fnuXMEnZCGZG4vHQpY5GuabQkKDpuhTzMp0o5J2tCWs5jaN2H2lqMGk5rM7oyHGCEga8tzUlS8zGUZu9kYfhwWjQp6xFxJ7DH725zW9cKDNjJJhIrGZijsYj/vC1NntDn1zGpD8Y8vWLZe4fjJjP6xx37bNA2hA/iFCE4GZd4y83h4QCAs/hf7vXZL6gUdQk1MTn/tGEoga/vmryqOOixgGdYUCYJCQJdHp9clLI3abNWtngUi3DD5syX5lu8qByg4tHj5j6RR4etHjxuXUm4xHid/4LRp1TEllD2j6zK+6cplbFCysgEvzBIKWJDfpQm4fZU/zN+1CoQGOeuHOShlRORrjdNhRKRHfehlIVsbJOXChhD4bg++DZcPkGoWpALo9kZRH72wQnxzDs4fzJ/w6GBYEH558hOjnEH08QnRboJsHD+8hXbxJ/808hDtPfybNTOlomx7TVQlpYQ/zwO8hL5xGTEcnGAyTdTG2cmycga8i5PKJaRzx+gPz5V5B6PQDEcIT0E/cIYU9S++j93dSkwPV+6jlPPV8Iku/+BSyuMe4NibwI8YO/Ilw4T/eP/x3+xecZSmOECTt3HlNYqP7Mbf1j37N+EvPz8z/X8z6J+dHbwPqrr7669uqrr+rA7wJ/9gls91NBTkqQDBPbD8l2T1hYmmVs5NnFIkLhTsslp8u0j9vsH3XJdw6RxkOkfpu7pzZenNCwFLb7Lp1JyL2WQ0aXKZkqF7Kw051yfNplLq+jRh6FYoZiRkctW0TFGe73NdRxiysLBd7ZbFO7uE42dpnVYzZbI9bzFpPWIZ+rqHyeNs9cXcUcHzG1ZphX+7xsRSRyjlyoMFP0mK8IJqMp+WxEtytIwgA1cgnVPG6zz3AQkzlzBavWFeJISievOcjmZAJfoGgSniOQZQlJkUiSdIHq2QlhCI1ZhfEgAgSSnGpcRv2IJIJiWSYMBVGcEMcCTVdYvWCSJCndNY5TDrjvCexpgusIRv10MqTIKd1lOkno3O5iqBGZwRFmPOb6woDpWJCfKyD1u1xwN7HlgIrkYtkez8Rdvti5w2iqULJqdKwq+6OQ7faIydoVlIKJNR6zlKh4ExulbvL+jo2cM9GP73MUFrFnVmhWF8nXKjTtMT1LR9E87vRj+rkSo9hglKtRn80Tuy75u7d5aTFCl7Pc0c5z7vTbfJcrrPld7p46eEmB1RL0ug6fM3yiCVQSi/PC4/9qGUynLofZGcauTySf8akDmYYV82DrBOnKdRRVJmo1ee94wulBi9y1m1iaQtFQubKcoSg0FkjYanU4nQRM/BBbinl46hCJBHUicX8/FVZfVrpsGXU0XUL1oZRXOQ1CMihPHKJ+jDgRHAw9xl70xCY2YylI8YchapWMSt+N6HWjJ+LhYlnFyimUqyrlqoqVTS27P8Oni52BT13XCAJBGAouXDZon0bsJx6TcYxmpDe4IEgwNQVFkYkj0DQZEtjt+pxb1HEHghlL5Xjkg0g42Am4csmi1lC5vWWnDne+TxiLJ6n3v3q5SEPTeOd4iuPE7Lse51UDzYB6WeXyiknvNCJOoJRJBehWNg3bBFguGXSdkFxRRvZlXl7MMxrFrJRM9kc+AsEwjFmo6ziThOurWQwUplGClkiYpoIqybx/6lC3VCQbyAjKOZWtvsf6kkkuUmhOA+aLOs1JSHymPwGIgjOdykeGh3+bCD6ME5wweSqX5SdxMg7JJgqNOZVCUSGfV1BNmb6T2h6bqszlWoa9oc/xMKRph0w7CVcvW2iGzOlxlF6PJxJ6VcUOEwpFmeEwpi40yjmZdhBimhIn04DdoUfXCVgp6Zgm3N93aE4+1F+EoWDUj/H8Dylzpirjhn/3yZrE4gml758j9gY+qx8JKD0aBXxxucD2sU+xpOCEaVETJwI3igmS9Fw6GAVUMjovLeR4dOwSqIIvr+QpmArPNCwqpkJWl+nbIcMgZKvvMTzTK7lOwsW1DINhTJQI9k59/npzSGIJFEOiH0SMpmluUE5X6LsRFVOFHOwf+VxrWIyDhJEfczLxQYLFgsHrBxMGTsTYi3m2btGdBhwMfTZ7HifjgLYdcr/lcDoNaE8Chn5E1VLw4jRi4oX5LK/tj1FVwXxeZa6gc7fl0pxGvLSYZ7fvsd33CBJYLeksF3VuzmWxgwQBrFVMBBILBQOh6kjPpZQmyXO5XLN4oSxhnGmGpGwOVi4gdU4RhpnqRZYvIN94CanXQTp/FalYQsoXka5cT3Uys0sp/92wUmH96iUon00L4hiWzqUdNT2TOo/pBjy+B/UZuP5SShGr1OFwJw3ENC34m29BtQHnL6evKVeR6nW49gLiO3+emgYoCmLrIcnhDhztIV26Ds4EbAeGPUS+gPjON586rkSnCecuI771f8P2BpQqcHoIKxeQVy8ir65D8xjRPn36dUmC8Jx0AnW0j7S6nn6mThPqs08/9+Qg1drsbiJ2N0m+/Y3UsU0zCDYe0/rWG0yiNA9H/u1XmchVlO4x1UqRvvTL2Wj8hYuYW7duRcB/D/wl8DB96NYHv+h2PzVI8FcnIRdkD9NQeXOnw74DL86aIEEQxjQHNlM3wDUsusU5nsmE/I9/vcW7e30aWZ2tQYCiSDTtkKIuY2ky0yBk04atwx6SJLFcMtA0lXnJo2AqTLyQHw5i9MGYWEp4ZTkLzoST0x7P1yXsccjve/fZ22syW9IoZ3XymoSIIi4rU65GfdYsCO0OlXqejCkzPhqwWpky+2yNfujQUDsYqmCYCK7frKLYYyp1hcU1g2JZpdbQqVouxYqCLKfFh4TEyppBpa4QHR+TDXqU5BH5aEC5Igg8qDY0KlWVKISZeQU9oyDLgnJNJY5BElAuqRhmGgI2HQtkRaZUkRCJzGiYEHiC6TjGc2N0U8L3EqYdm4UVHWQBbsg4v8DUVTATj8CLMOQApzPBz1Qw7/6IcDygmDGILBOrukLLlbly9ENm5yp8perTebTHhc/d4HJRoTxs4UgFltZrVAhY1AIYD2k2E4Z+SDaXxb72eRRJokWGqZ/w/LDJ1YzBuD3iZkOhgMOkKrPY7nNcazBwFGhuU2tusLe/Q68yS963uWgKksp5BjmTXl+iVKpSkgoovR10u4OX9DmXBOx5RTJxQMGQuD1R2Pxgm7Dbo1esUtcSNEXByEpMG5dg4x6+mUUy0ptrUVVQFZmgM2R5NU/NynFOdek5MS8u5JnIMVeqFmEg6Dshmy2XnJ4Wo7m8Qj5WkY30+o8i8KdPc+I/aDv8h43hUwnTkIqDT84E0pKUisR1XSLwPny9pn1GHfs04YTxU5qG+KzIFDFIkkBVJaIQOn7EMxWLdhAR+Ak7+x6GkMnmZcbDVNcCMBxFoAsWSiblqkKvE9N3QpSewvJ5HUWRqGc1zjUMuqMQibQrHcaC+ZxOQVVYzBsEbsJ3t0a0whDDV/naC0VyeZk4kiiYCitZnf6ZlbKZkZ+4HYahYL6g8+6xzVrZ5GrDIrHhQtHk2oyFHkE1UokCQbGi4joJcZTmwYxGMQt5DSdMWCkbnCQhs7Ma+57PWt5krqTRHkdcms1gJBIjL2KpqD9JLu+MQvIZ5YnDk0gEUSL47s7oZ/79dwY+F6sfTzv7cVEgSK+t7x/bDAcxxYqCM41pD0IyYerW+PgseX2+opGdypTzGoe7PisXDF4/GvNw3yZyBNuHUzYPXSxdIhvKoAuSSHCxlGFn6nOyH7CY02lYGsEYLF2hqmpoksS7G1Pa7RDPTegkAcet8InZQVlWf8ro4OMwHqVaxn+uEPAkoNSPEvSzCZahyDhRwsEwOHMYUxn7Mf/TGycM3Ih6VgVZYHcTagWF3jBka9ejN4qYy+sMvJhSRuOFao53elMuVk36YUhGgJfEbA1c5ARGbsRiTke3ZK7PZblUszg/azAYReQNhZGX5vx4cUJWU/CNBCNQMHwJEcPr+xPCKM28y2gyN+ayzBU03jycECeQELM3cMjpCs/WMzSyGrYfocpQNhRkGXb6PrN5jYql4kYxBUPFTyCIBbqSXlckCb67M+ZqPUMlo9C2IwQSr5wrcjL2KRoqN2ezFIwPgxd3HYVzZROKZeaTKeZP0IwlSYKFZXAcJN1ACgOkxhzSv/w9pNBH2BNEt4nYfJDmvtRm4OI16LcgCJG/9tvpY1/9euoCNhml+hlZBnuaami6LTjcQ/qt/zwtZI730rDIP/8/01+iWIZeK9W4dFtIqxeQXn4FyZ6mndjJEG68mIr0v/0N+Be/hzg5Sp3SbrycFlZIYJiId15DqCqJ66TTFwmYWUxTxlUVBCR/8aeIg22EqkBjPnVF2/gAMeqT3HsPDrYRu5uw+SA1OgCozSB6LST1abdDMRqmmiBZQvguPL4LuQK2WUduzDLz7CL6XB3bVWifhmDlyF5YRmudkjd+OXVxn4iS59atW//h1q1bF2/dunX+1q1b/8Mnsc1PC66RRbVM6pZELmehRjGxorB51Gc+mWIRM5t4yLrO1hiO7ZD3pyqHUo6rJYlkMuFfzcZ8zZiQJAJZkbjWsFhSQnroSALWMgmj3pBri0Xu7HaIbAdt3Ccf9uioEstGxMl+k0alxOWqwe7EpT7uoswtwqP7VJcXaQ4d9HPriNe+jXt6wk1lQD4QHPRl8ihYikwlH2CoglqpyHxB43TcYxxrUM7hHnZRVcFqeYxMmtEiRkOGmycsrenkCgqeIzCzEt1OhDLpk12qEeZq6DM1jJk6c2afYllhPIzRTchYEkKkTmfTqWBhWaPaUDGzCvlyKiiOY4Hvx9Qa6dRnYUVjaVVDUSRKVYVcXuWZGyZRKDAGRxw/GnD0aMR6qYexmMHt2+jVPJM4h1krkJseMm2N6T/765THbYZTm+Vsgrd7hzirIxbPc3X4AOXxfaprL/LmXsy47dD2JfKJz6IFM6bNfljjXD2HUZmlbcesFkISV8ZQZMIkoZLIhP6Ay5UQWxSxhwGr8QbZTptjz2XqWOQvXOBo7iINw8fNWBif/1UuXCrR7OXoC53L3pSjzCzaXB3zymWWsgpNOcv+IMAeHpMp65yMVa7MzVEY9iHOsD8as6r5eAmctIfcDTO8Rw0jX2Axq+JHCXEkaJ2EdAYBRhSglS0GcgZjPKCR05gGMTN5jTgDs7qOGoInR7w1SJAl6PUiGhWNnhtxuWbSjSIKksLxOC1O3j2e8syMxc25LJoi8UHbITpbJMtIzGa1J2nQgS2eykv4DJ8+DkcBOwOPx12XIEq488hlVk8zKuxJQqmi0OqHlEoK7kRw82KWzVOPk5OQYkbB9xKSWKAbMq1OgBvCzIyGqqZ5GNW6yoxrML+koWkynptwchLyxo7NC7UcM7JOXVXpdiNKIl2wTEYxF6wM7TDkim4x0UIGXsTAi7HDhMasRrf59PSvVFEpVRQmo4j9ls+srqHrEsN+xI2LFnf3bcxQptOLCXzBaTfk6lKGg4lPVpZRJQkswQ8eTFivGNhBzDnL5HAQEsUiXT+UNVwnoVxSyaESR4KJHzP2Qq7UMxx1AlZnDZrTIDVEsBO2eh4vL+VpTT9+gd+aBEw/xp2v54T86GhCzwkJXEGiJrjthKOJT7sfMnZi6jmV7ROP946nyBKIWLB/7HPxnEk+KxMJwYMDl+urFrIskxgCPacwW9PYcn2WF3RORxHuRKDlJeZVDbMmMZ7EnPZDKqZKQVc5aHnInsRzFywGcoSnJKiKTLYks3vkEUeCfidC8HMsZES6FvykMZ38x7dqd8KYzEfsjfeGPmtlg+k45vycwVY/jVNYKRn03JjrjSxIEnaYMPZjEOnivumGXJvN8vrOmN0jjx8djmlOAu63HExFJqPLdEYhiQY4MrtTn9mMxkrZZEE1uD92yOoy0VkGVz2r03NC8rrCatng+myWja6HF8U86LpUair1qorqg5FILJdMzpUNyhmVu02HelYno8lkTZmDUcQ3Hw/IqPBH97pkNOi7MTlDJUpgqWBgKRKrJZOKqSIh89xcGvapK2l+lKnKtKYBkiRwooTjSYgbJfzWhRIdO+Rx10MCuk5EOaMSxAlzOZ22HaApElJtBvHwTmp3/BOQV9fhaBeRxCmNjLS4kVYuIL30ChzsIi2tIX/p16FYTIuKy9ege4KoNdIwS81IrYbbTTAzaSHTOoH33kjpZuUK4i/+FIolGPYRl6/TlWbToqZYTCvZ4wOQQLRPEe+/iWicTT3yRdh+DNls+v93vwm3fwi//9/BdJhOZN57E2lxJXVOMy3EN/49BB6SYcLX/lNw7DTPZf0K0tIaIggQrgutE6RqHS5cQb75MlIuj7S6fmbdXHqS/yIVy2lR9hGI1gkMe+nzl84hei2IE7ByxDMraOUikgyR0Jhb1KnPqqgq6YR3YYVqtfTJnkyfEn457Qg+QQz9mJym0O5O+cBWkSOfpYLG1lgwtl0qcshr3ZiZQpa8BmMnZNeTWJkpkXMmyMUCF4b71IMBL9JDTKe89+b7qPaIGSmgNxzjnJ4yHDsYuobthvyms0Exo+JbJdqFCtdFn8hz+fpqhnNLddoDm7I7hH6bSjHDyf/7TdZaGyw8fotRb0BhaZHlGZ3i3lvcnAWzKPPMop46Y8wvIytg9NpcrZpEIsFAQXWH2Idtkvvvk915O7XwHHVJNB2zucNMLSaxHfJGQn1GI7Q98vXcmUtPRHVGw1AFQQjZfOpGpRkyhikznUYkCZiWjKbJVOsKgS+Ry6sUihqBn9LEIE3gVlWZfEnG8wAEu5sBBdVDyhfxTttk9ZAQk3BgU0lakLHwqivkkyFOZob5nW+zd7vLrAEdDHh4B5EITDXD2ChA+xTl3DrzczmQHe5kV7g67iDFEe3dxyiNGTLDAfHCHNfWc8wkClXhoaiCo90W2f0mi8kBk1FM82EbvSxjiSYPZi/zYvch14PHyGqe2kKFQ6PGSu+Q65dW2HUkqlqEWq2QZIvoqsSNF2YZjIcovSalvk1csdgSGezTFv9iAURGYxxLLOQEeycxomKR9acw8RkdO1AoU8tqXFGmrF6/xN7QZzKKmV/W2Lnf4cq1KtlEZT6vEZZrVJwuf/aoz825HM1BQLGiMJsxkFojrMIcG22P1jhgtq4RTAXvNx0KBYVEwO2DKd/fG6OrEpdrGW7OpLSAK/UM91oOQqQp6Of/P/be7EmS9Lry+32+u8e+ZESulVlb19JdvaHZaOzgMgKHY6L0II6epBeZ3vQ8z9TfoQeZyWQymUwa2UgGgQNyBiDRWBoN9FZ7VWblHhl7hIdH+O7+6cGrC2w2QJASRyRFXLM0y8jMiMhYPPyee+45p27x8HFAEGTkGWi/hnnRDEHyGwvm/2DlRSnXmhbXWxaPTwNKawKRi8JBzFEIfMksTbm2abFaZkTLHLEANy0Y0YWbYZcESSz5+MJnra2w4ZhEUeG4tPRyFk7Cefg8tO8iwDNSthp6kR8VKJwPE9wkoVQvVgiFEByeh7xZKdO1NW5esfj24xnvbJdZiCKrRgpQF4UF8qflr3IWboZugHueE8eS8TDBthTqUuPEj7jSMWlVVHQBTycBR35EkkuMVMHPJKYqqJRUZAS9WUzm5zyeBCxlykePfXZqBZvZaKtYmQoBZFLQX8RYuiBMi8ZRNwSeX1jcNm0NN/x8k/10EtAq6Yz9hNPnjyNNi9W6ZZxTNlSeTALyGI5GMfM4Y62uc7/nkwhIkHSrOoZQGAwSHjz0McqCOJAoS5gsU8ZKyug4QcuAGLZNi8OzCEcX5Kmg42hEKRy5ESduyDxKWYiM2TzFX6RkaU4S5jTaGoqicKNtMw0S5mHKWzsVni0jBr2ESu3XDyN+VWDn37R+FVAJ/JzF/P9bEDMZpp8L6j11Y3aeB01muUQRRQPdm8cYpsIsyLA0QZJLvDCjU9F5e6tMkkmCJEcXCutbBm6WUS+pdNs6u3WT/ZOAtjD46lqVZ9OIqtAQEZydR6zynI2qwf5hRF1XmcYpa2WNT52+/aR4XpaxZLyKefd4wbvHi2JYVTZoOzqrOEXVFIyqwrplcLFMcJ/3NoYqGHrF5T96fYt3dsqUDI1pkHGrbfH+2YplnBIkEl0V3Bv4zOI6tpslAAAgAElEQVSMMJX86YHLlabF9w7naIrgS5eq/Ce3W3zrep2PL1a8vl7ibn9Fw9K42rT5+YXP/VHAKx2bG2v2C4e3MzfmpTWbd3Z+YRwhbr1arJD9srp2s7BZdkqf+bFiWSh/8J8VP+9sIErVYuVr6zK8/qUCpFTriME53HkDGi1AFJoV24ZqrXAli6KC8VF1qNZYZTZG7BL0hrB7HZAFU/Ll34PhRQGMTp/BV/8jmI7h8kuwcIuVszAoGJ/z4wIUdTdh1EN+939Hfvgj+OgnhVvadIIcDYowzEYTNnaKlbnNHeTJPtz7GfnJAXI84EVWlygyXkS7iwj/SuCvqhZZNA8+KhzNdAOEQJ4fF5fvfQgvv1Hk23gFk5xPR6TlNpouCHxJlhV9m/qPeHtC/eM//uO/j/v9Y8/z/j7u93P1ncdTvCjhbJXTMhSOfQm5xPA9/nk7p+oO6Rs1HqxULENjW66Yaw7N5ZhPPIU39lo8HIUcai3evtZmsEr5YGng5grtToPxbEUrWbDebnAtGTNLBXq1yu8nRxy4KRt720TTGd35Oa277yJlzsFKUj0+pLPTgs4uk3KNjdkparPFkVpnLxwW1KJpwc1XaccLauEcxTRROpto3gjvfIZlSiqpR+6GqMs5taaC+fJtSDOiwYx8PKb9xZdRPvohlgwYqlts2lOGnk26DGlsVYsGNRdU/TNmc7DbNcpVjYuzhO09DctSuThNCqF+SSPPYTxMqTU0cophhWUp+CswbUG1rmGXBNNhhmUXCeFxDCU8wkxnMhG8UX2IMHRi6ZDNz1Cv3sE8+oT5NCdRLRRDh9UKt/sWU02hmaWoocvS2Cbe22R92WN1+2uU9t9Dq3VY5TmWopKEAfH5lOr2OmkeMZc1nOEZtmFxr3SF9d4HRMo6XQaEfo7euELPnWOmYxY33+JaMqaUpGwkI7yNDe7OLF6SA8bUSBJBe71GsH+GuHKN0J3RrRgocsXDhYJoNFjMUyb+jG7Npl6vkgx9mrnHx7OAL10t0Zie0mpaPIsNGmtb7JUlB4nCdupiGhbm9jYTP8WWCsFKEi6HNDbXEVlhmXmSCOrLCdeubJDlUJIq4yzlUsegvJoRNivkI5gYKZomUBLYaBoESU5/GVNDo1ZViQOJmapEfs6KjLWSgRulrOKctZrOqJ9iNQX9UYwXZWy3TZJYYpiCPIOVl2Nav5iP6IbAW+Qv8jB+U+A4Dr7/d2Oh+eGFT8lQqVkaRq6wvWZiWgrDiwTDEPQWMVe3LPL4eYCkgPE8o1NTmYUZiZIzmiaczSKqVRVTV6npKqYtOD+OyaUkCODWlk3D1HAUhUhI2pqOqiisdTWEKBoVW1dYr+qcH8cMlZRt02CV5FzethmvEhSh0LB1FssMXRZriG6QYgmF5aIAXb1lzJplYJVEsY6VFo1kra6i5QrjNOWoF7Ozo+FkKlIHP8rRcoFqCmZpRkmq6EIwGCR02zqX6xYf93y6qk6tomE7CrNximMKelFMuJA0lUJsfbaIOZ5HqIpg7Cbc3CwCDKdBSsvRibOcj/srZkHK/aHPNy7XaNiF/eyjs4CFlxIFkt22SZDlPBmE3GpbHJzF7JRNoijjWRjRNnVubtoMBgmns5iVl7Na5nzhzRKGohBFkoskoRQWIcS1skpqwW63yv35nHKksgxy3nilTKrl9M9jFmnGqRvzcsdhHKaUDJVWU2M2zyiZCu48o1xRmAYZa8+DN3t+jBkonLsxjiOo2sXrKeFzmRPLRRGUGkfyb308R2GhgczzgvX7y+W5GZ6XUSoXeWP/TysKM9xphlP69YAsDHKS+LOPY+IX1tO9UcST84BN2yAOJR8fBWx1dCbP1x+DNCfJoWKq3FyzeTQKCLycN3YdkhhOvYhZP6VkqVxfc/joYMUXbjigweA85WbH5jiLkC68su0wW6WEaYYtVC5kzE7VJAdudx0+7vtM/RQ3SBmuEv7Tl1t0Snph1TwN+Y9vNHj/vFhPi9KMJJS06xqzMONHJx7/7FqN7z6doSqCt/fa3Ou5aALOFwnLOOPRcMV21WQZZ/hJRrus4SewUzPIcpgHKZfqFl/dq3IyjxDAbt0iy6Fqq0SpZK9pYemCOM2JkiJz5tPcqWmQIoG1kv6Z95OwHH5ViXob0d188fcrL3vxnhGGWQTWHe2DoqJ88ZtwdoiyuQNrG0W+zKWrcPgUqg147S04OSoyYpK40Lt0t2AxL8TxJ8/wlSq10w/wWtexr14qNCfPniD+xR/Bz96Ft78BP/8RvPP1Ikjv5+8W1s9vfhme3INbr4E7Q1y9VWhxOhtgOYjN3cLOOVgWYOdovwBJW5fAX8LxQbGG1upCtf4ckO0iBj2YDJHzGSKJyDW9AG5ZgjALYCiTGM6OiwDtN95BZCny/AR5dlyszJWrKC/dZqlWMSenZJ1LmPd+RPzqV7AdleUiQ1EFWSKp1tXPHet/tf4uz1l/k6pUKgD/7a/7u3/yXYXMczRVpU2EbhlEQifWTL5iudwLDbSVS5hDVUl4S0y52dDI0oTdoE/TkOwdf8wVM6KVLvjO4ZL9WYxUVK4ZMa14yTU95JrmU5IRd8/nvHp9k+sONDttNjZavPThdxhP5nT6+3DnLXjwEfNFSOfaHvngAmEY6IspMQrhaIThexDGxQGwtg7vfR8t8tGCFaJSQyYJ4n/578jrbaQAO3PpOi7VmzsopglP7iHqTaIgQl9N0f7P/wFKZZKLC1reAQop7VbOWltyehxh2ypa5CLKFQgDvGmIO0sx1ZQohHpL48oNi0ZTYzJMKJUV1ro6qiYwdUEYimJ9o62gaQpSShpNDaeisJjnaGpGugrI7RpzV1DWVkzTOpV33sLSBJ5ep1RW8bISpU6VmpwzzxvYIqRd8skCh3lgMK99AdYsbEflfO23yJ8+wMk89GqXm/GUxWJFbpk0d/YYn/pcVDapCMHTqU7pyh55MMd0ruOEF4TDiOZ2m0RZ4tQq+HGGMe2TpBk2KyY3v8JC0XDjiPqzAw7ql+lbLW7MjxiENklZ4RV5xpHaobcI+eYbXVI3pGtLvmW67LbL1K/cRjk/oLZ/F6NRZ969gtzcQ9u4zslRgJ0E4FSI+j1KzTJJu6DVu7rGUT+iHp9jb6+xWuZ4ccbAT9kq6Wxd3WV90WewSlCFoKIXAZUqAidW6WxrjCYJUZpjagqKFNxecximKXouCMc53bKOq6Y01zQiT5JLiYLg8ThAiOJD71rHpmRptG2Nd49cjJJg0Evw3Iws/ex0U3zaEf2m/s5rHqTUUhV3mZI/d0D6tAxLIUgkmi1wdJXVMkPTBKaloFUkhqKyUTN4adtht2MhF4LzZwnKCgYXCdNximkKPJFz87LFws1YuEW2TJJJyIsgSttRyVQomSo7tslP7nsohkTT4ek4ZBilxFmhc1kuU7QQhtMEoQoUBZIkZ+ImrOK0CMH1JVlSsBijQUJnXceyBZWqRuTllFBZailVoRMjuV61CLQc4gKwbVR13DAlWUrWujobZRMSwdWqRWLm7J8HPOr77F9EhB70VwmbGzpXL1kcziN6Xsx2RedkHlIzPyt2zaXkZB5xvWyTScmlmsnPz5dkuaRuqeyUDDodnZcuWSwXGQfHIatFRhIV4HFny8BdZmSACOHgWcTIjGlbOp2Wim9l9C4SkkSCBNfN2Ns0EZtwNk1p1lX+r/cuMGPBPMhwdIVJlPDBfEVd6mytWVyyTd478hAaHK8iNF1QLWkcnUasrevMpxlBktMbRzw9DehKnZMkQo9hvsg5WxTC75P5553KslR+DmT8dezMdJy+YFiCVbGaKCWf0dQkcY7np/y05zEdpb/0drzFr2dppJT0zxM8LyNN//oPnE+DXv/y55IXZZQNlaWXcdaPmQQZrbaOXVHoVjR+eOJRtVQ6ZYPjWcT15+GWjq5SNRTSRHI4jHnwdIXlC0IhqeoaTl2Ql4o8pe9/4qE14KUti3aqYZUUTAtECraiMslimoqGXAmaUuMnJx66Kvjeocte16ChFsDzwSjgd6/UcDSF9x4uiTLJ0TzCylSiFJKVJEslt2ybf/NwRgbs1kzqts5GWcXUBL9zpcYqSsiFIEhzrrQspITjecK/+toWUsKddYc3t8q8vlHiwcAnk5J3LlWYhyl/eKvJ6TzG0gSmqqArgrqt8cZmmY2KwYWXMFqlL8Dy36ZEqfyiqc4zyXScFcfEp793SrB7rWjgPbdwLAOUzR2UjR2UehPR2UQEK/j4fTCNAhz8y/8KglWR97K+VbArr75VaFSqNWqTx7jdlxGWDaUq8qd/AZeuIn7+Q2itwcc/K9gXTYdbrxeAZrUo1t42dhDVOiJJUK7cAM8tgi276/DkEVSq8OXfhR/+KeLyDYS/gusvF5qc46fw7GGxIhb4kKawdx3ZWSf/2bvw7f8ZylUYDZCP75GPBwjTRp6fwJd+G9E/LzZxQr+4fhhAcw3Z2STNVLJqC2NQaHKEUD53rvh1AOYfcv2TBzG3Vj22oymLDK7lLnuWpBvPmKUqD2cpA7vOWuxxqVNjP9Y4CwT/tXnOX2jbXG5ZjPojNqan1ElQlwtsMi7pAXfKOef9MW95z5jbbVbjKSKK+OZreyjlEpwfUc18lp1dyoqk5s8gWHFuNinLCD2LWbkRtt9nd3HOcW2bIy9lT3ow6sGNV4spglCQDz5APr0P7XXy939QHJTDC4hjePIQ8dGPC3GYacNqiYxDksEMq6zDnS+gtDqE19+me7ON7g5pnH1IVF1nrZGxHLpEkcATVdRKiY42xVoOuJQf0F7TmQwTNrZ1Ohs6TlnFtBQuXTFpdzR6ZzGNJqiqJIkllZqCoggWbo6uKxhqTnQ2pFtasdaGHbPH1sttosEU7+NH1C7uoq3tMHnvR4jNSxiGYBWrJFGCSEOqZx+hBHN8Zw3KFTQR0Vku6YcWuR8S3v4KWuCirXVYlzFhlDL1QtaWfcpJyOTsnJopOctM7PkQrbrE7G4RWzZtETPJYcuCg8oWnf6I9PIrmMScRha/fWeX6WrOvxd77DZsAin5xKuxJOXDoxEilQyihGt1C0tXidwltWTEU22HS5evwnyCXWmhb7/Mzc0qH909oKnOGRsaVzaq5GUdvz+nublNLzNYrXJm4xR/ISl1FU7ckL31OuWKghulXG+YeF5efLhLSdkv1g2sVCG7mPMkrNBaUymVNMIoI5MSsyIopyqfnPh8bbfKfhqy2dLp1g2ajsaxGxWhhIOwyMwo6S+Ev5amEKY5t6441BKde4c+OQWoRfy/Xzv5Tf3NauDFVG2F2Je4swJgAMRREUYbljJurBeTO2+R02ipjCYJmlQ4nEQ8mQQkac7Tk5BOVy1E4iYklZy5n2GXVVbzDG+eM5uk5FnOo9OA6SjBXRb3l+US0xaggGkqXGlaPPFCShIEAjdNOTgL2FJNUGA/CJE6PJ0H+HpGvJT0vIjzfsJ795eUFYUVOWM/BVVyPol52g/5aH9Jb5oQGRmbawYlXSU3QIaCNVtnRkIDlXmQkegS4cMrlx0MRSAUUAW8erlE09DRXYWXrpj4pKihQBOCPz9xcXSFVzoOp27CvUFA0/kFiNmqGpwvYiJfcnAR0rJUtmsmr647HM8j5tOMZlsjiHKEECyUDDsTVEOV9/tLNloqk1GKu8qoJSpXLlk8C0KiFRxkPn9xtOQ0DzlOIp72fJ4MQnRb8u6JR6esIQx4chKTxBmDUUquS8yy4E/vu9yqOtQtFXeUYiQqr22V8OOMdq5z/9BHVyFMJG6c8ngeEM4zNnSDmczYqBlM8wQUQVPReDYL6S9jet5fL/L/9Bg/efarbZkVpWBi3dkvwEmlqpLEeaHFyiXnpwn7o5CttsHZ5PO3lWeSs8P4136mTMcphiOYkzIbF/f36SrWXy3PzYiinDCSL26358WUMxVFwDzPWK9qRFHOUT/i8o6Jt8holwqnPk2Bbll/ERjZUnU8kTAap/TNlGpDQwaw0zJ4fBqyt2HRmyZcyg28JMV2FN68UWa7ZTAOMjplndTI8dOc0JXcumwxiBKaqkac5vzu1RrbNYsgyXg48jl3IxxDYVs1GWUJsZ8zXCZsl0w2yzqjaUq0zHHzFHeVkmSSRErO5gEXXoqlq/zJ/ozeMmWvZhHnkifjgMtNEz/OmYcpaS6ZBilf2a3yeBxg6Qp3uiV6XkzLKViVSzWTJANbEzwcBrQdDT/JSfNi+OVGKRVDRXluAvM3AaN/tRZuxtaujud+9rrCNGH3GtKdIpzPr6WJVgduv47QDZQ/+JeQpYjFDHHrtcKRrH8OsxGpu0TbWIetPdQ8RvnxnxFNF0V3nCbglEhvv4mrtJg/G+Ie9Jm/+i3cpYrrSmZ/9K+IljHCspCnh0hNJXdnRaimzOHJfTB0sEoob36pEPy//wOkvyrO13vXUP7Ff17oeFQVefikYHPOjl4YTNDukv/4e2DZSJnBwUPk2josXTh8gjw7In98r+j5FFFogKZDxHSELFWI7Sbm/R8jmp3iOZ1nWMMDVK1470spkZPh3/q1+YdQ/+RBTPvyLi2REKDy3TOfWZKxU7eoVmy+UY85Vlt00wUbyYLSWoc8DjmeBvxWeML5POIosxhi8ngSEFtl4izjG/WUe/Mcw/dYKBazWhd36fNfGD2U02eUpj288ZTt2zfYimesm5KTS68iTJvH9ctcDkdYFvi3vob20++hZAkZAqVURtz/EDZ3ETdegekYUakWdn0f/ZT80UcQh6hf/32s+RnB2APbgVoLhn3EZAi718ifPsRs2PgzH5FncOMOYrmgImeYIma2gEY6wL1/REN1qe/UiUJI0RDHj+jkPTRTxQmGhL58LuTN6W7qLyh6b5Fx/ZbFycMFyrBHpVoI+8Mgx3MzyhWV7fIMWa5TVVcoyxnqYkI1GeFnFo6ZUtsss5lcMI5KxLnB0ssR/gJz1mNav0l052tsN2wmZoVYKbG91eHJUUB9LWeRmUSqg6XnlLIp2ZXblFOHXqSg+uc4/RHdvTaxo3K1Y5H58MmojTzx0LtNQqfDGzWNOPRRpU5zzUF5/JR9e51Eb/Pv/v09vrzTJc4NduSSO+aMxUzh2ktN8if3eChbXDEmDMUG42FCd/SEyatvENd2SXt9EuGg1auUvvw27UVEVO9wuH6DuDfl6ktrTA2HZLvNnmUzXKQoSrFrbzsKXVvQi4uwQNNSyDOoWSqL53adYnuPSpQwm44Jwhy5ynj7Cy1OBgnfe+bSbejMFil+IrHqCiM/wYwUbjRtMqdoOGqGWqwD2ILzUcxmRadla0xWMTmSMMjRDUEuwWkJ3nqpTD+IC2Gso7ywXH5R/3gHPf+gazLJ2OgaXFozOJ3EKM+bqvk0wykL1OeXAz/HMgWLWc75KKIXx9y8YdHd0PjBcEF3XUfkArOtcHvXZrOkk1oZaxs6aSDxVylxnHNwGtJbxohMcjIN+bODOf/HoykNS6NZ0xi5Cb1pjFVV6fVS1CqwhMN+TKOl0qzq2Jrg5ppN1VZZL5lc27ExcpXLGwajYcoqSqEs+chbMvMkGgInLRweX7vtMPMySqbK4SxkGaZIKZn1U1QDnEzFNhRaik6pohCFWTFsl7BeMfjugQuiSEmvl3VECbZMg49OVwTjHFUo3B2sGPsJbUtjmWcv7IQdXSVMc2bLlM6GxnCYsVExOPdiwrBguXrTmP3johF/PA5YzSFT4dkkQosV4ijHMzKqusL3n7jkoaRkKkyilG9eqaGpCusVjVmcM1Zjvnq5SpZLSlLl+paOlsMffHmTRZji+hmnfsSV3EJPYallNKSGTCWTRYISQVbPWSQ5/YuERZbjLTIqhsq2Y/JwEjCfpfSXCZuGSU/GDCcxSSbx44xl/Ium8eHQx1/l2KWiZTAMQRxLJqOElSeJol+tebOd4jrhX7JlrjU0gueDGc2RKJbg7ZcqjJfZC6vtT2vhFs55k9GnGVSS2ThlPi2+xsOU6TghTSQLNcOsKGSZ5HQU8bPz1QtL+L9cUhZB7ELIF6zQ/CzFsgXDIKFaUrmzV+LRWUCU5IziFFsoHM4iDKXQEzybRlyqmdztLzmdxSiqwiJMmAYJQ78QsD+bRHhRxu9eq5JFkr4WEwfP7a3nkrqlEegZi1XGfS8g9iRGWfBoHPLla1W8ICMIczolg27ZoFPSee90SZhKHh6GfPlWmfsznziSmIlCLiViJTiYhXhKxvUNCz1V2KwYvNp1+Ph8Uax3SdAVQfTcOvya5dAVBnFesC//00cjNqsGw2XCYJlwvWXTKRkMvJgsl3TKBbvy5laZKMv5uLdiraxjqAqX6ib9ZaER8/2cUzdiu2oQ+Dn+8le/T/4qSPm00kSymGeEfs7wImY++cVr7zo7TCfyc1bDAKLRgk/ehy9+o2AaLl8nP3pSgItgVdgpewtWokLlG18tAEerSyWf4r32e7jrd5gPItxLb+F/eJ9Ky6Ae9aitl2hWMmqqR62p0irHJFJnFthIzYDOFtz9oNiW6Z3AclFYPa888jAoVtXCoPg/pmPEpWvIo6fFZcuBex8gFQU5GZKfHhYuGm9/E2YTcn8JqxXS95F//h149bdASqSqQv+cMDeYde8Qj2bwha+w6k2xx4cI24Fv/D6ZBHonZMeHjI5c5OMHOBUFeXGGFP844cA/zv/677AuJgtk/5zfKsWEqkESxUwHY46XOYeTACFhPZrimBpJFLHnwPpwnwujieK5rCUeh6nDK0aIN5/zO4tHNI8eoFZqOIbOx7KOOeqxZUrEbMSjb/9bWj/8Dv3GNht/8j/invcxVgsS00JGPsJyUEplzHqFaOoVtOJkyM75Qy4/+3kR6JLGUG0gqjVkc62gRh0Hfvg9KBUpw5bXJ+qP4Wu/B2++U6D1OEJmKW5g0jj+KblTAQSy34O9a/Cdf4357ENKH/47Zh88oqqvqNzYpdnR8A7OCQYzqrioX/gStZ0m/mBOvaXizSLSuNBZNFoanltMJCs1jYa+pNEUCApnsvEgwXYULEdQtjIuNZaslDLVJz/A1DKmD85ZM2YMD1zm5T2qi1OMFPTRA0pGQiZ1MqNEpaYwcwVmOGOm53iKwSqpEGsOL8sTls0mkyd9ps+OeHSU4c0z7LUq1/VDTtQu0cY2+ysdvVvh/PGAcr3O684MvRxQEjr9lcTXW4wygzvhhLsbNyjPJ9x1yywSl/rNXTaVEfWqzfcf5ZzM6jxzFxycTWjbGuNFwLQ34aJ3wdOfPkUv13g2h64xZhHbVGyTzMpodiwUIVBWkmCesS5jzEYFU1U4XkVUSyq4UKqJAjRkoI16OJ019ichj0YBE5kQJZCHv5iOZs119FgSL1wsI0dVBZtlgy/ulNnrWhwPIywVvvNkhidTxiTcPV3RX0S02hqDi5RqpnK6iElMSbSQ7NRMlEgw11MGvYSXNi2O51HhHCMEV5sWx7OIVJHE0Wenpoap/P86W+Lvo7JMskoz2o5OvaIRBr9oAsIgo+cm1HON+TRl0IsJgpzRNOLYi/nmK1X2uhaqUbjNzZYp7x0u0bxiSnfhppyeJzw5D9jbNvG8jEmcUC/rKDGUMo1vvFnjtXKJd6oVPugt2bB0PhwsORcxZ8MQNJjNU6otlTc2HP7tU5fFRYYMBUZZoJcF93yf01lEEOWcj1PKhmCR5JwuYt5slym14WQYsX8aM5tmlMoqZ6MIS1OYeSkEsD8OuMhjgrlkPE25GEXUbQWzJRj1U1S1sH2XliTs5XheRuhLPjxd8mQa0qyqhBNJs6qhKlAzNSq5ghIL7s98Aj9nPChCLIfLGAXYrJpotmCxyPjhsUd/nIAF00XKy7sWj3o+zCDTcjqOhhoKTgYJ06jQ/7gLSSlQ0WOFnwyX3HYctjZ0vnG5yvceLLAaAlNXcMoqhqqgxwI3kbTbGt99MMKLM8aDGHeUcXXTQkhIHHDKCtWqwulxwuVtk28fznjorbDKCk4qSBeFu+HTNCBY5pxPYg4XK5ZJyp1tmzwRjLyEVZTzdFQIiaWUPJtFRGH2Qutm2oL+eUIaS27cMRn2fnnI56eV59Boacwmv2Bk6i0NRRX005jNsk6eQL2psH8cEEcZyXN76jiSNNc0fK+47Lk51Yb63M1OKxwz3RxNF0gBW2WD01WE62W81DQ5mccvHsdqWYDeMMiLVca4+P7jh0vmSUaQZRwOQqqmyoMTnwM35P6Zz8HjkFKsYEaC0XmKpQkOexGzacr+QURqSF6pO/TDhLGX4M0zEkuy3tCQQLIsTBxCmTMLEu4uVvh5Rs1USaXkZBXxkmKjOYJ7Q5+rDQtDFYRGjpOphGlxbGeK5LJlsCUNYrPIqPnDm01MQ2Hp57irjEWWYtUFm4aBripUDJWTecRgldIsFcOoNC8YqE3D5O1mmbeuldiuGdiawn/zziZrFZ0nk5CXuw41U8WLUqqWSrOkEf2lVb3TeYSmKJQtlW9dq7NeMdAUwW7dZLtqUIsKJsnUFOJQYpq/fJqV5zlH+9ELcNI/T+ifF4AliiS1usrmJQNNV6i3tBevfWPdRlnNEaVKIWrPP3uOEVduoNiF9ka99Rpi76VCLxJFxRpYrYFUNcT+A7j9OpQrsPcS9d6H1G7tUvcOaVRSaneuoW1dKjZgPvwxsncC936OaLTBnVHZqFFJh0xPFySrCJKoMBH4+u9DLmFzp2BX/tf/Hi5dhkefwE++h4zDYsA3n8JLL8NFAXrkZIhUFHj4cQGGpiO4egO++2+QqwWcHsBigVKpI15+E2pNmI0Jb32Z1rpDEmW4yhpLrYV17QqYFuL4gKC8gXZplxwF5eXXmC419P4RHD0tnsN/hPVPXtgfLn2OZksqJZulu2TTVolcF90x+e3bW3wy9Fkj4JGvUc0C3hzcox57yGaLt0/ex7j9GheLgKRUQYY+l1slppkCrTW+GJ9z197GXSz5L70PEPUG09GUydoeytYureEx5uiMe5U9WtUSZaDVNeAAACAASURBVBLu21u8PLiPtd4lsao49/4CDAPDnaIkEWw99yA/PSz80P/kfysEYZJivKQbyP4ZPPyYsLaFdXK/ELBpWrFidvKMYJXhKAHx27+P5Y9ZJTpmPEc9fgrrO6jkGI5OZlcx7v0YddRj3I9oNAXVtlOESdWbeA8OqN+6xPLREUrkY3cKiz77uTsRQDqeUXUyIruB7ajw4AOcvU2Ssx5pv0/7lR3OLgStZ+9iXL5cZD54K9JKizgG6a8wSzZDL8HKUvI8J0kFrbP3mG68wXzpI7Y6XDOXPJlWqMgJreUpDS3m8TkoSobasjCcJjExF27G9loDz1thlR3srXXm94/ovnSJ+PATtFu3aYklru+zMiv444zr23Ue9jzCUhnplKjmM8qJ5ORsxrxcpRwmJOEKVcKmlmMlCvdLXa6xohLMsecTLjrXCM4TepFFo1ZmZ/oBdzdewc8kK81hPugT+Q5JHuBaFpamoKoCM1doVzXu9QI2KgaTVcyD/hwhq7y2V2IRZdxZdziZRaQriVVVKJuF/kFRHeaBR8l2qHUc+tOYVk3HMVRmy5SLVQIKNGwNicS2FYbjlJubNv4qJwxyNjtGkfSsq5hCYbpM2e6Y+GlOu1aIS9Nc0naKjKC1sk5/lTCaJ+QaL3JmNL1wufqNuL+ovwuR5HSSMsoTdsoWnpsS6Tk2Cv3zhJWXgwNXd2yiMEcIsEsq3z9e8Du3arRqBsfziK2aAXOB56ekTbjZspmTEkcSQxarOcpcoT9MuLbtICnEz3GcU7U0pJSkiWQ2SzlaxDQaGg004lxixCovX7F5FkeUULBihcE4QdPgOIp5rVPCSVXG45TWjsrdhU87NSivg7vI6ZR0Hvsh6lxlr2sw9xPuT1e0bZ29skUoc+JMMopSfqtbYW1D42QaEY0kdy6XcJUcNRDEkUSRgv3zkGquoW3kLBc5202Dp8MQR1GJo5yW1LncMWmbOofnEU1bYylyRCrwvIxySeW98yVfXK8gdUCBs2FETVUxbIXxKiksaGOFB08i6rbgTItZEzp6oCBqsFgWmjGVwrRgJGOsWBCVJA1NJ1xlDOcpKZKXqja+JgnynINnEc0NleOzCNfPUeKMMJJoHXhzu8LgIiUo5aihwFtI5lmCq2V0cwOBYBKktCyV/Wchp1lMSagoCKqpwvkyYV0z2O8XoaXX2iYPTgOsXOHIDykbGts1A9fLaNZ08lwyHWWYlkDTFVINwkVOrfFZ/VCaSoYXKU65yAAqV1VUjReueVJKhrOEfj/hSttC1QThSjILUzIPfC/HdhT8VU6jpREGOaomSBP5QrgfhXlhGmIJ/KhgcQ5HESd+RKeks/Ay5lnCTt3i+Czi0UFIs1KwCAKBaQlGFylPvYCqqfLkNKRd0ovhjA7X6hb+UJI1ct7aLbN/EuErObcaNqdBRG8WY+kKh6uQyJMEcU5N1RjNE772SoVxlLL0MjIXzuKITsvg9rrDaJIy8BLOlwmHXogeC3arJktytqo652HM/iRiu6Zj2wqLWY5hCaqOyuQ0ZbdrMkxSEIJbazZHo4gskAhD0rB0Ai3HW+ac+hHbtkkvjLnettmfxgwWAZ/0V9iJhmJIWg2d/VnEyEtYq+jc2Sjh6CrLKMNQBRfLhOEq4VvXG7hhEcbZcjTeP1uySnN+90qNnhdzpWl/5vWfz4ph5nSe0m0YhEHxGPLnWjqZyxd9wmSUoumCTlfHdlSSRFIqKywXOc01ldEgRdUEmi5IU/mZLLJQK2PVbBAK2dIn0y1UVSAHPWKnieb8IsNJNFqItXXE+hakKdKwiZ4cYFbMQt+SF5bEysUpnDyDUhm59ApNsKohk6QQ6Tc70O6ibOwg211YzBGzMbYpWawUdFNB6WzA+KLou+xSEWy5WsL25UIKcPM1+PinRa7MdAj7j4o+bX0b/vw7RTCnUypsmr//7eI6hlmAMNspBtm1Oqy8ov8bD4gUB3Ori3H6CLus43euY7aqJL0LrHmPwFnDFw7ZMqRztUmuW4SDMVZ/H26/9tdqY/6hCvv/yYOYjU9+wH5ksBqPuWRL7lx8jNRNhtKiupzwwNcYZAbfrMVUdUHounyy/QbmoEctnPNe+QpvJ+d8Ilr8YfCE5sYa780Evzf4Gd1kwaS2gSYzXh/cI2+uM0skzUad0WROa3CIpquY1Sp+KjmYx/hRwuu7TXj2BMc9K2hHRYHJCNY3wZ0XVOj+Q5gMwZ3BjTvFG1lVCv/xD38ClkWklTEsBdE7KcRo+w8KwDI7Q3vrS4SrFPPkHquRT2lyWPitTwbwxjsoaYAZuYhLVxC+T3z7bcx5H2erDZ6LaLQJ5z7Wso/ZLGMRojRbn3t+w9GcVLVwqjrKYkrkrvD6HmGlS4xFKlXkakmUKNQefJ9FbKNdvky6CmDhslh/mcSqQZ4xyWzq0YTYaqLWa4wiC0fG2Ne6xHYFrxexWB6yn1ZY29tjsCih6Rp5pUnZydAXRzQuegS33qQ97TE0VPJUo7t8zMWqxmjrMm83Ax71U0YyJ17NWCsbGN1tnvkJlxswFlVeEyMOxTZ2GtDyXQQmX7VP8V+5RrvSRVVsSnFMUlPox2tU0lPqHYsTu0GnrmOWVdLhlHlrjbe2KnTqBuo45IESs65IdnebrJV0umWDT/ZX3Lxis7+I8KYZkzzlWp5ib1aREfgyZ61kIDTBeB4TBTlrdYP5NKVUUch0iwSddkunt4jplnSqtsbhIiRfwSu1ElZZwY8lr2+WeHAeUNIU1uo6y0WOXRWFtawGdU1jOEu4umkzSRJajo4bZlwsIo7diN2WSeBJNpoGplQwbYVnsxBdEdi6Shj8BsR8Wr/shPBpgOin30eh/JX21XkmOZvGWI6CESt4bs7Otsmj/YB4KfGznGvXbIJFhr/MSFLJ3aWPE6q8cavYHz8dRCSTnPk4I9Il+Qpu7tgspznnMuKSabJ/HnJ1w0ZUoV3TGYcJ7irjattmmKVouYKf50zdjEZZQ4Y5g2FG3VRRFUGlrrLZNNBRyGcgyoJ5nLFe0ZELQbmk0GlofHwe4MkMLRNM3IyzIGa0SrjTLDFcxZQVjdEyJYxyLjsW02nKuZugzRU6us4iTpiSskJSW+icLhO213V6boxqCpolldNpwlZVx0sluS5RQjgdxGx0dIxYJcpyNCC2JO2SznCWchKG7JYtpCoZuAlbDZ35KuPxechWyShcqlZgWwqn54VF7uNBhGMJIh+GWkI2gVZZw3IEaQ65I8lmEjdL8ZKMRM+pGhqvr5VYhjm6oxAtJT0/5ngVghT4i4ydpklgSnrLhEkak6QSW1VxagqzZcZymZFlgrJSAIvEg7eulsg9wVgmqJ4gVkArCyqRxqqUoUiIYkmppGEGCqsoYzhKKQmFbslkmMR8MvQxBBiqSqems5hn1Jsa01FKva3xgyceQkDNVtE0QRgUTeZykaNq4C9znLKCbhSDGU0XzCcZi0XGxSLGcRSqusZ4kFIrK/T7CUkkcRyVJJY4JQXVFCzCIvtm5qfIHPJYkkuo1lWiUNJbxMyClEvbFuuqia0qBOTcHwa8tuHw8FmIaQrqzwHQYpGRpXA2D0kRxCXJy22HB6MVWqLQrRnUDMG9o4BenqCjcLwMmecpwVxi6gqpI3ltt0S0lLiTFKetECo51Ugjrwh0BcaTlGApqXc1BnHCm80yF/MUuySIopymNBgGMXEIlYrgZqdEEOdcblscTEO8KCfOcu6d+9RMjekgYxAUgnmpwTwsHCsf9X3Q4P2ZR1sa9IOYZ4uQMz+kqRqUHIVEKsz8iJIm2ClZ7HRNwhQmQUK3auDOMho1jUmQUDYU9poW9wY+37pWp2JqNGyNe4c+x9OIjbrBKx2Hh2cBtbJKu6SzcFP65zG1ugoJjLOUJJQvQEy5otI/T8gycOfF+UBRBaN+zHJROMWZVpFFVa1pxHGxfl64ZxWrZXEsX6woQmG7HMcSvWyzOBwSG9Xi94NzZmqXOPzs3wNFXkvg45c3sbZaqEdPinyXnauw/wDx2ttFT6Xr8OguMoqQdqkANscHRQjmO99Enh/Bd/81dDYRYYBAYlcMpuUrWA9/jHLz1ecWzeOCcfHmcOUmot6A2Rg2d+GHf1q4puUZCLXo8z55vwA9tWYh1le1gqVRtcLKediHZgvxxW8g732APHgIGztE9S2s0TNIEqKtG+Rmidkko37wLsoX3mElKvgPDyjduILtqOSKjv70Q4Irb5JkClbll4f2/qpz1n/I+o072d+wMsMi2Nzjel1nU/pYW7scKVXWFxd8e1Hmm+aUDSOnPT7lpbNPWJpVzOWMV0YPMMtlyqMTfpZUSeYuV+WC7WDM1/0DupHLqVHna+sqX1Un0OpwNpiyvbvF2sldTG/G8Stf54ISWyLkld7HDBcxl2tGAUTSBEYXxZ7magm//c/hra8XKD7L4OarcHJQsDCjiwLk6AY8ewyGAZ0NKuUcb1WwQvz8XTJvSeTnmCKGn/8IqWmFq0aaFPRmmsGnb9LFApIU2TtBJhFm7zG5ZjGdC+K7d3E/fEi1JqB/hqprCG/2OeGlzHMQgqzeQZtewGKOo4bYVYstc4zaatFMelTshNkwYd65jZksCEcLRLlKS4xprg4pz46RE59qHDLOHXxdcG5eQvHmrLcVmujEK4kuUq7PJySqzZ/1A67ofaRTJ5QJz0SJWn/AuHybcLmgfHmTWwcfMXz8IfutKwSoNAKPn34yYDhYEvgZ45XJy1/Y4f9m771+JUvyO79PxPHp7fX3ljdtprvH9tAOd8nFaiVBIrSQBK32QYAgQH+SngVIAvQgAZQjuUsNd3aWHJI97auru0zX9Sb9ycyTx0aEHqLZ3JGWpAhwhdHOBlAo1K2b5t7MOBnf39dFZkO4cVhvXB4ftjlf1TjghPv9iiRdU/iK2puP6QqPlVFs3evQi18RJz2UERRHb/M08/nN+23iQFNkGWPhsVfzKZUtGpyGHYbXlxStDsfTzPZxjDc4QvCHx0vivCItNd/bi/Bcyb1hyPm8QH/Vc7DV8MjqkK9hMS3R2sYmbjU9lqUiTRV+JEi/0n8HnsRRknbdRtFmlaIVujQjh1fXOWEkaXUdnp9mfP+wyfuXCZmsCKTgYpJ9/RoPai6eI9lp+JzFJSeL/Ov2+KYveW1YY7z5V0tNtLZT/H+77ET54rT8+vWcTaxk7y9bi7mCSBO6EiEMUU1QbgxFoanV5Nf9Kj/9acLTZxmnVwX5SPHuY9u7UGlDfKWYjitaHYf+jsvrRxGXpwW51HyjU+fE5DSMR+FXXOgSR9rAADYCVRj2fI+iprhQOdTgl19rUqU25rbuO3QbDu2G5EE/oig1rbZk6Lr0PJeraclEFXx5nvMyy9lv+QwLj63QY7/r4CLo1zx8I9AePNmsKZSm5bqc3eScTEvudQKGfY+DQ4/lUpOcGWorhwf3Q9bzipfHGY4Q1F3J09OUstB4kWQ51bx7r8XZScWtKOD4quTwgcf20OV6UfH8KuM0y6l1BV3lcjLN+Ox0w27DRWeC987WfLBcM6XiwU5AvjSUmWY4dHm+yIhViW7AylS0E5sEZVmbgmtpJUi1uotxDI26YOj67JmA9z9LEAb2jI8XCqJA0nZc7nsh/+CX2jzbpLyKU2quiy8lKoBQSZ4+y9iNXJqlS68ruP0oQPmKuKgoSkN/S9LLPRJjME3D7TLAb9nD9bgoCZXAMbBpKYZ9F98IJqrCRIYjQt7dr3NxXoGtT+GLccqHNwnGwPPZhlouUcJwMraSvz/3w8ULxXqpSNY/O7zwPIHnG16d5eQYeo6HkLB/5NHtezTakjTXbFaKeFZxcZPz+WlKrSFoOZKwhGfHKaebjLAu+JMv1hSl4qoqqLUchq7H/VsBV9OCMBR8q9fgv/3xhAeHIcOux+lFjq4gCATSE1ysS5pC0Cokk6wg0ZrM08S65J99kNAZSHY2Hi8vU3bdgAMVEDgObx/VUCn84auYVVzSb3lIXyASwa++2WQ6KvniJGO74fIy2bBYVTQDh9CXSAGeEUTaoREKSg+uKRg4tiAbJVgWit1WwF7TYz3RdH2PduXSbEj2hh4pFV+eZVxcFDyZbshDzWReUkmDqTR+DVrGoRm6PO5GfHy14dOrJb4Et5KspaIZSN7YDnljq0YrdHhrt87FsuD7B00GdTuk6kYuy696vq5XBVIIHCNIYs0nxxt8QGVgtOHqrMQAVxclArhcFgzqHlWlQcDouqJWl3T7Ltt77tdG/3iuafckq2VFsrZR22CLGGt1B4wgzwyOA/NZRTz/i2tjEFqpmhDCxoIDJkshjPB8Qb0pf0bG+PXq9CnXKd4mhmYT3v4evPdjK886fWn7XvZuwXqBurqAZ5/AYgJHd6Hbx7z3Y/j0fTa/8tvwp/8MU29aVsZoBoyZLRxMnlsGpdWx0c7f+3XE1g6m04cvPrX395XPhd6WBTy/89//hW9GG+j04bf/cwt0shTetj4YtvYxzz+D+RRG16TdI8LzpzYS+vZDll/e4FQ5VaWYpTXEasnoywUtuaLd9VgtFY31BVG/waYKCNp/SWfPz/n6hWdifvy7P6LhS+IK2u06fziG11enPJBrRkGbX7v5mNf/43/I8z/7CL17m+NVxfeuP+KuTFA7hzz88qc8793lUXrFvXIGL54ycBQsZky9FgduQff4U8hzRoRsF0vodOm2Ij653tC8c4fh6gbWK478gvzqkl67boHIMoayBDR843u2IOni2Oon7z6C8bX1srz8Al57C558YCcHixn0txC1Olljm/D2PrpSLJwdejcfWu2jF5CN5ng6p9IOgUrsRp6Obcb58XO7uaQDw13kn/yQVvwlURmTdg7RzS6hW0KaYpYL21QshX38V89t6+zNJbkTofOCML7CDHZwfvd/RK5mlI0Bae5Q/+D3iH76B0xb90kae2T7r4MfwtmXFE5EFMDG7RBEAu/iGZ2gRPdvsxZtWrNTdKNDtVjTchXy/IR555Cddx4gR1OWwzpZEoHTRudTTBrjhgXLuWA7vaD17bco5jl+2Ge3ZrheO2RNQWOzZHfYont7i86gzdnpmHSt0G6bezs1Xl0v+Za4IBYhI/8W3a0ep1Ofes/F9SF8+YKGU3BSDCDMaWx3KYzL49qGkjqffH7Mr37/Po7yOE8LTq5y7u76eF4XL/AIkCgXwsJhr+cx7Ph08fBqIC5ndO9uobRkVBUEhUO/Y+URRaUZLyuCQtqeHiVotBwaDcnL4wy/IalhG9oncUUNyXhVUHcdRmXFw0FElii+nOfc3gpIjGIxVuzvBBRK8+w843Av4IurjJtVyb1hyMmioOE71H07iasjebnK6DU8ysz2Qfx5v0aWaoLQ+meMMYyvy68mrX99p8O/aatWq/H8esEkKWk4kmSt2dpxiecKIWA1V0hXEEUCx/lZNiZNFdORNWT3pEuewO6BzzpWXI4KrmYVxoVmzUGU8Pi1GutCEUUOIZLFTHEyyRAJ3HsY0um5zBNFz/eoKkMmNGVp+HyVMqgcPlyl/ObDFotVxfOrlIOGh1G2v63wberRG90ajYbDzThnu2lNvJ26Szqz09XxtCByJKOsIvQFdcfh+SJDZxD6gmoFyVqTBbaAbb/hkW4Mom5456jBn0zXnFc5R1VAv+uwkpqoIRGhoNl3WSeKTaUJMsF4XlHv2t+pTASNLYdsZag2IJvQqMPVlxVaaHwfSgnfOKpzcVMiNxAXmi3fJ1OapnA4ned0lc9NUUFpWAqFU0j2PZd4YWh1JPFUIzVcjyoeH0YsForzacGiqPC0Q1JpitJQCRiULk+LhMeHNcrIYIzgV+43uYhLAl/wjcc1PrpO6Ls+nhCESIZbAb4jOI8L0lygK81uO6DmOCzmFSYCx5XkCdzaD/jhFzHvHtSZpxpPC67XBV1cmgOXfGlISo1Th7ZySTNDrCuSQCHm4HmSGSWjRUk7lBQziXYVl6uCm7SkSA0vZimeEZwtCvp1F12CL0F5hmbosloozkc5m7ahoa0nMqxJzm5yLpYFV9cVg30rO+5HHmWg+fQ8pRe4CA2rRFEa6A0lq8zw1r06+RriqeJmXlDrORzVA764zDg9yxkVik7H4dtHDbLETt5fbjJmF5q9XZ/pVYlqGebLCp3bdMU8N3x0leAFgm3pIyPJe9drispwtxdyPVUYYVBd6OFR+ppkqbl3ELLSCp1CLjSfXm+440S4keDsJmdf+JyXNjZ7VJZkytAKJDXH5TcetvjgLOHNvRqla8s0v7wp+PajOq4WKG1oSJdUa7wAslhzPi7ZbvgIY5jdKPKWZppVDGoex1nGrFJ0pcOvP27z+fOMmpDUXYepqagbh7AmKXMwroGNQyE1A9dn2PN4Z7fOP30Z8+5BAwVsBz6NuuCz5ynTQvH2Xh3fkbycZcRZRb1yuLcdEhSSB7dDWoHtR1rPFKa0TElZQKfrEtYcRpOKu9sh07HC8wSdnktZ2DRDIWzQjxB2aHPvUcjFSUmtLqk3HarSoJU9z7e7ttupKAxpoplNFMOdv4huzlKNFwjK6RzTaBOMj+HwDnlmqDcdpIT1Uv0MmBZRjcxvE5JaZiPbWO/KdGRTzSoFvkeyrJhVbZpdD17/JmSJjWb+3q9TrDMW/deI9Bp5dWyBijbwe/8zQbdGrJpEMv+qDPPYxjwHofW67B7aofM/+q/hR78Ln71vVTdVCf/Jf2mZmN4A6g2otGVg7jyALz6BO4/sD/Hyc/v1yQ1J4dHwSzi4C9u7TNM6O90c8+kHiHaH63UTL1sQPLiHXM1QbkiYThD1BiqvaB4O/trPrJ9HJuYXHsRM/uD3GZ4/5aPhG7xaVnxv9SWvlWM+6j/iV50pJku5qxZcT2LOS4dv3R3ijq9oB5KLVclm/y73rj7jaW2PmqmYEXD81t9hZ3bKbJXS7zQsJZhn9t+LK/BDnEaDi0QhanV2JidQZOQHDxAXxzTu3IbrS5ts4bgwGcEP/j7cXMLxMwssPvgTOLhty5wcCUrDfATtgTX+BxHceUR2MyM4+ZRZ4z79rkbkqdVgakWR5GSFQ2v6AmE0XJzZJtqXTy3aTzcQBCAlbi1EOA6kCX6nRnj70GaTOw7cXNgpQVUhjEFPbqxvZjbGXc0oVwlBMoGnH8K7P8ANXJKbJcGz95ilNdLtB9RrBuIp1NtkUQ/n+gQlfUqnTrA8x202mK99zHCfUtbIN+B5hluXP6TwWqwul3TyS6q912g26mwlL+j1dnC9EJWm7OTHbAlD+423OJ+UlPWQtecQDFo0hcANU4rSY+/yGY3dBq07j6kCh3laoeYJ3W6Ho4MG2XjFJBd0hWKlQkRvh6pKqScZ082Y5mbDerLixutRb/mkEZzEDnUvQCVTZqbGy9EEPxqQS8N7rxLe3W8gtUOv7zNOStQCthsuk6Jiq+nhCcHVosAxgnq+pHd7yCpWjLKSrYbH1aJgmlekleY6LtiLfLZ3va9p9NCTfHGWcrQT0G97zKuKg76VwqxyTbExVAr2Wy6rXLMpNK8Sa27VGmrSoZKGMjMcDUP8ULAdeXx8nNDxXYJQMqx7nC8LmsLhaGjT+mpGUqs5zNKKXuQipaAobOTqxUmJ78N6ren03L9ml/6bs7SyYL9Wq/HF8Yw00YQ49AaujeVd2Imh70v8QJBt9M+AvKoyXJ+X3LoX8HKVcacZItuAgOdnGXpjOCkLHjYjIk9ynZYIV3C5rHh9N0QIiR/A9XWJZwS9gUe95TCOK0IkXgueXRS4ChxHkFWQZIoHnYjPTzK0gEcHEWFNUjgKqQTX04p0oykWmulYEQwExRJ2+i6qsuWny0ShI7jxStxc8GKaoZaGsCHY3fXJ55pxVuEEBiLY7gZs7XjEsWJclZzFBa+1IjDWE9GJHNrSo11zuLooOOgHPI9TGkqiPLh76GMKQ1EzmJlhvNHICLakS7xSCAciV5IVBkJBQzusG5pNrGg0JAutUCmUBmQp8LRkua5whKRyNXID842ddg9DjzLXJJ5muikpBZRrw1IptoOAVt2hblxWWpGUiqZ2wRe0XI9xWfK4VUMBOoFBz+PzZYq3kFQLwzQrUImNqZ5WFTsNj4UW7LYkv/6gyYefbTgahlylBVuOSxxXzFeKXssjnUK1siCy0XO4XBa0S5duX/JklHLoBVQapIFVqfntb3R5Ns4oSkNcKpzI8Gpd0JcOrpDcLEsWWclJnKE30G467NZ9SgEi15S57fU7Pc+ZbxR16WBWhnilCAOJ48HLs5yjVsAGzdPLjHRpaLYkBYawkhhtcCp4NSsoCsPNpOS1OxEnLwraXclqqZhNFCYF7RnStKJEgGPo+x6UguNlSsvxwIPpteJmXLLb9xjrisgIbqYlZWo48wpWWcm3+w0mi4q4UGy04sF2RLfyuLPl8/54zevDiGoFca6gDt3QYbasaIYuT6YJd0xI23UpBcw3FTd5yWDX4+5uSD/zSI2m8MExgptZSRJovnlYJ4sNm0pjFPzKoyYFhnGsiJSk1Jqdus8XScZsVdLuO+zJgPNlyVpVCMfw/DTn7Vs1PhltEEoQFZLTZUbTdblalXgNQSN0cJTk7YM6n51s6NcCMqX4L74zZK8TkCtNpW18PkAjctjxAy5uCu62A5Yo7vVCHg4i0kJjKjCFwGhoNKXd247ioOsxn2rSROMH4mvAcjDwSdaa2aii3pDUGw7CgTwz+L7tK5nc2FCg3tDGKGutaXVc4oUiiARSCnz/q1S8wHqppmPF9q5nB6dYEFPkhiCfU0Zt9HKJqnfxA4Hr2j/GGOZThf+VrPH505RG0yGsVrYgUzqwfxtOXiJqDcRgi+LpU4qde3SyC5INBONjEqcDQuL0u6yat+g/+V3iwWOizRje/4mNOf67/x4yTci/eEbw8L5NgV3GVqI2uoIig/NT64H57CPrfXnz2zCfgetYBU4QwuQa3MAOlAdbVqUzm1jpmdHW73znj9QReQAAIABJREFUEWxWZL0jwqMdaHa4XjUZboEYXZAT0usK1q+ukJ5LmE5hMaXl59ZmsJjZM9dqhtNu/aWfXf8WxPzs+rkBMfHNhJPKZ5BO8e89YjmeoVyf7WrF1skTamFA7cXHfD58xE4252ZT8ZZY8LJ7m4vS5Y1qRqEMR76imcUcVEva0wte+Fv0yKlnS2h2qDYJy/4BvcePrKfly+dsN3zeq9p442vmR68xvrrhbjlDXJxYyZjnQ76xpq3b923jbKsDowtQlXVLD3astrLM7eZJ1zbiL9tYBD+bMIlusxXG1hvTtznh1Oo48YRF4y7t1bE1lv3Wb8PpCzsJyDN7+2VsC6UaLUtl/of/GP7P/xU++8C21D5/YuMNT76E3sBSpcfPLQD78hliNSc4/tSyRo0m4q3vwnpJVtui/fxfUOaaRqDYFB75/mO8w3362Tml30QvV2TGw6mF7C8/Jfa2CKslWriEpORpQW27izc+QyzHyDsPqNrbiHxDV6+JQ4fu9hYrHHpnX3CV+dTHpzjbhzSLG4b1BrNMUbSH6Ok5e6NTZL3Hnd/6Ps+urM73h8dL9qqc4uSEOM6pPM1mu8381Q3du3fQNRf//AU6dNlvtDkXEaMsIWgNqdIL9vZvsb/rESK5nAvcfMWjaMMm7NFoO/g5VCn0erb4rOW7XC5yRCZoRg6jdUl8pdnb9siUZrVe0+3ZfpjpRKECQ7Y2vL4fMay7PH2ZsqgUN0lJoQwro7hYFvZDP7CtyRfLgoN2wM2ipNN1GCUVjwchX4xzOl2XtFRsCoMSsF/zWeeabsulzAwJGkcIbvUDvohT2qE1cp/GBY4rGNRdytyw1/V5crGxfggpiHNFu+ayjCvG1xWdvsOEitm0Yn87+Ne2v8tCYwxfRw//f71WS8VmZfswfF9yflLS7jrUajVeni5gI+jvOISeNZdXlbHMi4FW12E2rmi1bZvyn0fLhpGg0IZpXuEoOE8KXo1y7rVC0sJwvSoYdDzGccnCVLyYZOz3PHbaFhg4oWCdWgDSbDtMqope4HAZF7yaFAw9h3Wm2Q58BocuxcZwflFQbjSdfYf9dojrSY7PC4QrqEWCrYbP8WlOf89FuAJdKeIbTbPtkqwV2oOny4zffNRmPlHUXEm/6TCnYnFtuHcrJE01qmW4mVa8uVVnt+tzMs7Bh63Qw80dkqoiimwsuh9Idg98ZlcVXgCbuWZqKsQAqqm9XC43GrWGRl2g12Da0JIO48z+/J2uh8oUyoe9uo8r4fgs5923mlwvSsIaqLHkssyZZgV7YYA08PaDOucmp4PLyaRACDgbFaiWZjpTBK5gvCqI2pJe3cOvoDtw8XOHsC0RBjp1l6Zw2Wv7fHK+IYk1BIb5WpEvFXmouVjmtByHfsvjNM6o11y2OzUcoQg3krN5jmcEZVMTblycumSZV9yKfMKO4VqVDLs2ve7pdUrbdfh8lrLjezS6kkWq6IYuk7Lk4qagFbkspgrpGUwKEZIrStaZTfM6JKQZul+xqz6bTIMwyFKSCQ0Lyf07Af2GR5FpVnOF04ZqBcfnuWXj8pJHtyIuFyWNUjILK5xCcGsYcLks2EysH6j0DT3HZVqv6IcuKJvQeHFT4XoQ55rVDHZDhzNRsB35pMqm31FCWmiWE41f2uCEfKPwtcRTkgJIwop+EKBL+HKSEW9sn0qn8igLzXVWcRD6nJ+XlFKzMhoPQelYA//5uqC58jg89EHAeFUSRIKDWsC7D5vUA4du5HI5LnnjdkToSxaV4uEw5OObDYf9gLkq6UmP3Ida4LDeVEzjiiATDPc9noxT8kxzuxaSxprBnsMHVxsGDQ9lNM9ucsLCQQhDaeAiKzGOoV25fOdug+/fazJdVYyTnHIueHO3hTCKZsdlkSnev0x42I9wpCB0JYU2BJWk5Ts4RlD45uuySpEKcl8zviwZ9F3OXpV0Bw5xWVHDpdESzMcVeWbT5KKavW6FkWS9UuSZoaoMrbZNmgtrEt+XXJwU1BqWGas3BDcXFdt71kNTldDq/MWQyxjDcq4oSo3j8PWAJ8vsdb6KV4g8RbcHaOFQb1i2TylDvFB4rg0WSFaK0VVJGAoaZokxkIdd3OUY4XrEC42/1WcRG7pBgpzesNkIone/y7j2kKRzi9qnP0I9/ibRu98nLx2CIkZcnUFZWE/NfILXbrBeC4KjPZtW5gVwfgLtHuL+Y6u0OX0J/9E/tn+fvIT7r8NqCbv7cPIKVGkVLt/6Zfjgjy3QynLo9SGO4fwVpt4iDzr2fLRcMk88enLK8SvD2tRZxljfztE9OrWS+t0jjOvAckHV6BOvJAJN2P3LJWU/ryDmF94TM20O+PWbD/mtRko+nZPg8d3Jp7y1OeXj4WsMWiGqUuy3PL7FlHtnn/C8c4uPt97gl5wZtdPPSdpDjoKKqQkgDKm98SZXYZet7Y6VZX3yZ5yZGkdnn1gd5OFdWC0INgv+/V7GPTXj3naLb/gZot22YOHhY9soi7Celh/+b7bkUhhYrSyYqZRlNxotaHctcu9t2Td8lsGTDwkXZ+zOP0K892MrM3vjHQuQ3v4O7nCAPz6x+sr+0Go+88yGB9RbFigJbU8D3/0VywqdfQm7Bzb7/F/8U0t/Pn8Cdx/C+Zfo60vkN75rb1Nm8OA1e7uuDQTgj/4AjCF69hPSBPqMic4+RUUNjmoj6r4iuRgR1aD+2l2y3hG1dgitNmE5Z0mb8OFD9nsZWvokzUOGk08pDl6nlY9wdYEzu6Z2Zxd395D5qwntxYJzdxf6A7QbcHD9HpOVz6J9m4u0Q6JSnJtLau88ogya5JlmvxnwZ+dr+o7D4OaE++/c4s7yBY2DHb6z26BsSu6+c5tkNKfbq1He2maVS1pX53x7t8MbQcxr+212eh5HQci3HzbRUURnFhO39hirkrqS3GlF3HgluTD888+WZErz+uM6Zc1QDx2yUtHuCvIEilJTjwzx0k7ra13BZq7xG7bocDZSDNoe9/YC3tyrUWQabeDxIGKW2oPVn322puVIqso2VkvXRnAKKchdTT9yORgG1HFICsUsrdhQEZ8pK2upuRTK8HKW0fAdBi2PPDCgDW3l8MUi5XJuddN3eyGfjja0QpdlbrXPk5uKwbZDUJcIxL/2Ysz1SrNa/M0L1v621nRUEUR2EjifVkzHJelG8fJ0jVdIbu35XCf29VwtNf2hR5EbHNdOIOtNSbxQdvo4qmi0rUzqdFTgCEgzjZ9ItpTL9aTkZJPzzcM6S1dBCYFwKErN1bLkOit4Pk358fGSeKpoHTicLwtezFJu4opv3Kuja4AU+EogNawWmpqR+Epybgr6eDTbkvN5zsGOz01eEm0c6r4kS2GtK4qFoVv3aXdd2h1JIQy5p+lJl17k0o0cNimENRcpJf5G8OnNhg4u87GiVZOY0mBKyISmygxvNeq02w7GF6RCU29bWUqyUqxXivFVxWZjEAruhSEZtvxPCcOLIqNekzTqktGyJHE1KrVk9d62ByUUheLsPOfJNKXrufQbLv0dh2oFKM2MAm3gZZKymil+eLGkiA3xpuJVmvPBeEOiFfXCpa0dZkmJqcHA89DaxgmvppqNW/FqldH3PTSGuiNYJhV6DVv7LvFSMx9VXBYFc6diz4R4hxKDZWrGq4Ks1FSl4WRWcqsZ8SrLCBcOEy9HOJrFoqIxcLiRit980ObT5YZ5UtFyJeuFpiNcbu0FXK5K5nnJplexXfcoF+BrgZCGvuezGwVsPEMtcAhcSYlhVpQERlKvHNJlhVzD1agk32jKGcRFxXsfbpjNS1axolaXFKUhdTXx0hAvKtrK5cNXCR1XMq1K/u7dNvuNgI8+25CuK9Jc4ewI9oYeYSjppz7Hec7VMuf5q5SSCoQNLtiUFZcTRX0iyTeadFFRZpqlqchGmm5TID1YTirqmct0pFgXFc+ThCzTvLkdkRlN6Rq60mNQ89g79Fg5Noq7Fjoo3/BZnnK/HtKsOew3fda6ol+5tLYd6jhMRMW8VDzeiyAUZGvN9bxkrRXttmQTa945qtNzXO72I/aaAR+PElwBndBlOiqZv6xwcpglJd2+w2dPE4pE0dIO45uS+bqiHTgEpWAdK/7ewx5bA5eoJtChlcj9p+90SVxFr+mxmthhlhvB9UTRDAVpqDnwfV5OM/alh9gIbkYFQQ7z84oH/YiXlxmttkOc2veFvY5WCGDoeihteHmRkYWa83VJtYZOz+HmoqI7dL8ObviXVxBYA388/9mvJ2uF1oYglNxclmQbq8aaT4t/ZbXYZFQRRJJm02Fyo6hKY0tT1VcN9FJaP0xgDepCCIpcs5gpBlsuQtjjTrI29Icu8cJ6feZrl3W0jVmvSf0uRhuuNx26OzU4fgHv/gaNmmZc9HD1hqgTcuY/pOkV8PwJ7RbE0QG8/jZ8+5cxf/bPod3BCXx0nttEtGbHFm0+eA2mNxjpwvkrq3750e/Z89HBHRunnOdWeVPm0OlaX8wf/xDKyjIyO3tWgRPPoCxJv//vEj2+D8uYm53vsf3d+2SvzjFBwL3hku5OwO5Qs33gEw671gLw5EPMR3/G7IPnrD56aksy/3+4fuGZmKP/6b9BdvtQFtw6/oB3snOu2/v0RifcSq6Ryzkvtx5xv5rhLsY0dEFRab47cAnTNYtFgoumsVlAd8BGetRqEZdJxUBneKqENGFifIZFbNMv7j6wNGGyRtablvE4ewXdPjielWatVvCP/it4/4/h3uvWcD+5sSi+0YD+ttVCrpfwnV9FHNy27a2Og/j7//CrYIBL6O/Ad38Nzo+tIW3/tk0gKwpQmno1g8szS6Ue3rEg6OLE0ps/+Afwh/8H1JtWAN8b2GlBEFqglGewdxuGu3azTcdwfY7xAysxqyprOnv4Bowu7e2EA7MR7stPSdw24Z1D0rjAGfRBaeTnH9ARC9amTtJ/gNtuU0VtuuqGePdN4sTHCz30JqUsNQZDOznBDLZZyS5hJ8QZnRP3HhMYh3k8haspqVun11vTDly4vuJ6/xvkRcKg1ePi5ef07t/mn3x+g9c/5Do3vD9bk641v1bd8Hnm8lr2kvBwl8tYkcUZ10VJd3ebmw+/pPnNh9zpRXxyWRGtZiwLh1vfuUsri7nym7Q9l+u4YHfLZzmvSFSL9Voh5oL7D0OexxlOIRhon6tlyeEgYLqyBsgqtpG2jx/WmF5csdXf4TxRaMcwqPsUQpPFoBLrPzlWOfHc8GAnpCYdhg2XV3GOVwi8QJCh2Y0sxV/5BiOgHlmpTFO63NoKbRlaAX4oGGeKIHVohg6tusPCWNP2x9cbOpHDo0GNRVahJbxcZOQzg5NDGmga0mGjFZerEs8ReIVkuG0ndM8nKQ8HIdO1LZH715ValqUaIW05n/hrLtKbUuE5f3vPo6oMm7XCcaw3CQxpopiMKgpXUpMa1xFspCaohE1hcgWbROO6XxlWczu9LHJDd+ByfVays+/xYpxSFQZHSxrGQecQbypWqaYXuWSp4WyVc9T1qIUuvpF0hpJHwxrrlSJbaYqGpu5ImoHLXs3ns/mGrYY9dNfrEqclucgLdCz4o3xpJ/7K2P9vOIymJXVPcvcwxGhYF4plaXCNIBCCB69HfPE8Y6UVw5aV95ydlqxyxWHPIzYV26HPRW5jau9thZyMCvZ7HpvUsForVGYvh7e2AyrfcDLJ2W64PFtnNLRDslQ4jkOmFEaC0xeo0nof4kpx98hjkinSsSZtK8rM8HyVMfA8tuo2EcvzJaeXBa+SHLcQHPZ9FnnJybpETQWZVsR5xV4jYJKU1EKHe/2QzzYbkkwTVpILN6duJLXMpbfncTrN2en6uAvBeZoz6LvMl4p2y0Mo6HouZgh6DWdxQb2U7N/3+fTLDbKCdsMjziq8UpJSMf6KLf3J2Zrb23WKuGS75qGWhmmtpCNddCS4WhaMVMl200O4MCpKaoX1z0klCApJ5Lm4oWG5ViRGM9qUtDYeUsLLIsVzJL3QZVqV6MJw0AvwKoG7BO0b9mshrjGcrwuGXY8eHiNT8sZhyLNJRid0mIwV0jHkARTa8HA/ZDKvKDQUleJFnOHOXYKGpCoM65nmYMfj9LQiF1BqjfEkTe1wPa6YzEp8BGUCjZpkb+AynVnwP8lLKmHIXcV6ZKAUaMemWImGAS1YZ4qNo5gEJe5Ssg4Ve7nPJFGs5hWNrsNEVTgGboqK0aIkCiWJUpTG8CrL6FUezS2HRazwtGQsK97p1HiyTDlf57SaDi3hstX3OR0X1D1JLjSR5+CGgioGtYRRVrBd83l2meHmDl4BWaFZtyvUTPBlnnK7E/L+NKEX+wz7DqvcUG8KRknFTVXSKVzqgWQeazq+i4qgXCrqPYdO4GMkpAuDcTWvlgU1JG3hk2JwteHeXsCLT3IKqS0jNFNsVoa7twIuL0u6A8k4VhwOA9ZLzXRUMdh2GV1WeNLK1JqBy93DEFlCrS6ZXFf0hzYSOlkr6k0HzxPkmcYA8UwRBALzlfs+CGzXkOvZQtNVrNjd92m2HC4vKoJAUFV8de2ETaJJVpqtXQ+lDMtFRboxaG3QWhBEAu34BFKROXWkBLC+m97ADj2m44p21yadhV95bFazjHZT09hqE288ystr8tY22WhCd/oUtXPE/Coj3O5xvWzQvLONvjxHTaaUXo3ILZGDAenxBcHWVxHOe4dw+pJXxwbRHdBwMkSzbeX3VQmLuZWIHd61PpxXzwFp5WVlac9Tnme/x/XteTHb2PPUfGa/7/lT22uzu0dS36Fh1oyaD0mPLxm+c4urVyltd0Owv8em8qkKReU3iPwK8/IZkwe/gYgilv0HZFXA0Tu7f+Xn2c8rE/MLD2L8xYTq6C5kCeHjN/GM5iboMhh2kf0hpswZVw5bP/g7kKxxlgvGxmPr9DPwPE6CPreLGRzdpTa95OyNX6N//ClFsmFpXPomA1Uxa27Rv3fHvmGfPYHtfTsSuDy1ueDLJWzvWkZlnYDvI5SyjEujaYHF4Cvg8vhtawq7OrWG+u/8KkYKS1VORzZLPE0sG/ONb1tZ2ru/ZpH8zSV87wfwO/+DZVduLm0+er1hN0y9YUeUVQUvPrNsz/au9ceUpWViXnsb0hRGV4gf/Dvwpz+yz60sLeCZ3sD1BTx43RrRnn2VwvHsCfwH/xn8+PfBswct/5vfJjmf0o1yNgdv0MquWR2+gycVW+oCffiA+HxOUj+gMD5et0U1GtNKzlh17hGNX5B1jmgEJbQ6LOcKf6eH52qCps/syXOE36bbCyhaEeWdO6SjOTf47AYhfqvO+nrJ/p0+apOw9re51ZHsEHN39Irnywi1d8ihmeH1unz85Jqh2dAVKWlWsdQBWT3gQT8iHc15Gns4hwNyBwaeZp5rtvp1jm9yDkm4WUqSmseDYchJkeNVEkfDRijuDENWpSKUAlPATz5Z0x5K8tSws+URxGOSRpe8UCQbw61hwCyrcAJwKsFY25hMPbcHyru3Qtax5nKT0/E8msYhKw0HuwGLSUW3ZaM0PVfSEg6TtKLXclgVmlvtgLKEmie5XpR86/U6SsGqqtgOfHrCZVUoVqViu+mz1/JZrxW9loPJBb6U3KgCWUhuspJW4BAoSbPlEmcVQghaoUusK/SS/0fHxN/GylL9FYCQX3dT/FXrn7yMud8L/8qs/L/JGl2VdHq2Pyes2f6WTsdBCImo+wxatutlZ8vjfFywM7DxT2Vuze1Rzfpi1rFidF3hhwJjBLWWw0/P1xwYn/qORC8galj/1rJTUc4Eq4Vi78hncWkYRC6tgUO8VHxxlpEVmmHgc7sXMk4qTGmjnK/zAt+R3KoFxEqzG/qo3GACzdm8oCUcmi2HwHGImgJXSpKJprnjEF8r8ppmUHNpRC6N0ALT948TQiGZp5pVpKhVAhOCqgTbbY+zUUln6JCNDc1dyTipqDsOWamZXmk6u5KXRcbLWcZB26Pr2xK+R52IWl1y/Lzgm9+r8dllzpbvsnAq8spw0PRpdyTTLw2q0kQNwcoY8kITSYGSUCYQNATLtUILAblh2PARUvDiJLeJfspK7/xI0nYdTCZIQk1cVdzdDjg9Kcg8xQqFv3bwfYGbwqUuqRtJmhtCKflwmrAtPRq5S4ZBeYYolDRrDjc3BboQ/Ol0iZBwvx4hPcmFyHlUr5GsNFoKluuKuuvwZrtFvyaYziqMD0PHx9GSB/cCRnGJDjSbjSaqO3w5y5mpkoMqwoskzQOHzbViU2iOs5xzJ6dpHGrKwQ0E801JK3IxBbAjqMcO67XmsO0zSSvKEpaqxN04pKWh6btkgSZPDcOay2xaES81xtGsNhotBKEjuLwqCZvwk/kKlcGWDrm143G0HXA8yQlc2Or7ZCvNe+mSB35ElDpMVYneQD90idcVRkt6LUmRCdalwRWSaa3gthuBlkQNhxUV8YUmLTVOKpm5FXWsWf71XgRGEmwEL5cZs7ykEbhIJbjROZ6SOLngtcOQONHUfIfTZc53d5ssZUVdOYTaYeIVzBYVYdMhm2qEByYS9IVHb+gyHVU82A755EXKa3dDCmPIJobtXY/TL0syqcgCTbEAtw4zocgE+AYajsfTqw2RdNgOfdqBw2Rccp2VvFrk/PIbTSoFSakRK4kwgoetkI+uE9ZraJYOedOwGmlebjL2jU/Dd1GRoRgBgaaZeZyscroNlxqSoBQE0qZX1kPJ89OcKBLI8itwoI2deyrDfFrRaDpoA0IYBIL1yg4Uw0AAgk1i2eTxdYlSBikMi6kirDlsNpqtHY/jlzlCgOPYa6MxsL3n4XiCeKFodx1abcky1lyc5kQ1B8+1ARFKGW4uK3p9hyQxpKmmLGC4GxH026Qb/VVogC3gtlJcZQHTQlFvWfVBvS6ZzxSuI6nLhFHZZ3j+x8zdLfzxGXKzIqHBZCGR27uEek0xniNUiWoN2Ln8Y+bdx4TXz3Cl4qb5mGqdElULdH+bpAxhs2J1OiXREXI1xes04Tu/YgfUgy0b2/zWd2E1t6FG0oH52J6nggg2S3uueuNbVp2ztQtP3re+mFaH8pu/wWxUoBYxZriLuxxjvnjCRrQI19fMpobmbpPW2Qfk4xkyWRHXj6j1AsY3mnXuc9SJCYfdv/Lz7OcVxPzCy8mE59sD+/4dePUF3H+NfuQwUQ58/wecdm9x62AIv/PfWTYj8K0B695jyukE995D29MCoEr65ZKP6rfYf/N1y2y8/V2K7/wGXp7A9j4ijCyoALj3mgUcxoDvQXdo37hHd+DWPcx6ae97MfsK8JzA3cc2rkMp2zDb6WFGV/DD/x22dmwc83s/suNLKexmOHtlQcXuod0Af/oji+T/6A+tOezuIzsh8AILkr71S3B9btma4ba9r+GO/f1sH0CzC9dn0Ghh3v+jr/w4OfSG8Cc/gk/ft99vsM/r4sTK09pdiCe2qClJiMqYq5Ggk7yyj/3JTxGNBjTbUG+yMXV2bv6UfpiQ+D3qoaG51URLl6vgPt1WSV649H7wbWSysBHOMqEZKJhcUv3+/8LtPqhqwtooruYhT55PMXcecD+5YpIFbMefsbff4r1Pxux2O7wdzRhdzwmdOq2DI7aP6igl+XDV4SfLgD2v4HD2BHnwmPDVFcVOx+p0s4pAp2h8uj3H+lNEm2wy4fPxhm/sCm5OMtir0Soknb5D7FQ8mW14OKixSWzfweOjkFejjM9mKYG74bVbNdw6/OjJio4vSNHc245YzhXzaUm21OgNVE3DnUZEsTaEPUG6trR9p+8QlJLS10wnFXtNnxfTlGbbIY01ndTjoO1DHXwBz88zepHLTV5yMilIJhrPCJ6dpjRags3IdhboOjQ9l6HwOJlkHJ9kDEMXE8DHWUK6tpO1qrLN0GYDT9cbjucZl8uC/ZbdA46U6P8XcrLJqMLov5nsLN1oav9S8ar+K25/HufclQEXy+Jv9Bh/2cpzjVZQa9gpojEGpQyu7yB9WI0KityQ54b4RmH+b7agPy/5U5UhSWx7+fmrAi80/PBlzEC6ZNLgTAXDPQchDZmClnKZpSVSQjxW+K4gTzSuB7O44uNkTS2TNBsSIaCoDLIQXOQZH11teH2rRlZqhIayNEjHkr2PZY0ocugFLnFR8Xv/F3vv1StZl5/3/dZaO1cOJ6eOb/ebJw9nSApDypZpwpZhyxe6MeA7fwN/Gn8AX8q+MGDKsEyBIodp4jtv7HT6nD65ctWOK/hi9QxNSzOCAAMegNpAoxun0BVOVe29/ut5nt/z1RxS//8XU835okIk0JWSTEm6/YDreUPuDFkqESVsyQCR+cbtojF8dVNh2pZOW4JwTGeGuC1YNJpuo/jWBxkPBiltKzlwMRe3Db2eJJaCn55v6IYBg07Al9OS3ZHfXb2ZNIzbAbV2pEFAsit4sBtzoRv+i3d7qFhwEMceYtCHSWXoppJiaRgGEatcUwtLt6PIrGSyrqmE5d37GWjQCgLh2IpDWAgaZ1mWlkMidqOARltumoahDlCVoN8NCBpJGiiMg5U2dJuAsKNY3Vp+dLuh3w7Bwk6R8Mf3+mR9qEvNVhBy3VSMVAQri6gk96MEkSqOdyKWC4MU0HGKk3FAxwU87CXcUxlBKvhHu10iJagr+CrPOQwi4rlAd2GZG2ZNwx9tDUitxLYcYSnpEbCQNUVtyZYSLRy51mymjm6i6AhFqwrJtSWILKayiGtBnRt++HpFhcVGjmEWkAYBz9c5by4qlqVmLgwDpaiMo0ZzeefR+pmQqEDy/K7gZqOJQ8lkptHS27wCLSECZ6CsNaYS6EQjNThl2csiohYUa8Om1Fw0DVHgMxzzXLNNQKMMXQLmrxzzdYOQgu0kJLZeaZMhOCWIAoGtoG4ceWOwxrKTRrw3TnERDJXih3dLzic1SaN4c1dhHdxrp8RrQVE61AIaZfnqIvcQi6uC6aJmLTTLwBDuOq4nhuRCkhq4XjQMCsXsdcNlU7O1HaBl1LEBAAAgAElEQVSkoCcDvvU7GWEgybYD9rOYRAg+3mrT6knmNw2V1fzB97ucXzVETlBXhkEnoB8pWm3Bk25K2XXIRFBsDIkTjFTAy4salQvMBIbtgJOHMb1+wMV5zXxqYAV6CrdXDbM7zcVpTbExCOEw2lHklu3dtxaykacqRpEfZvwAYbh+UxOnXqGZTw0qFLQ6PpMynTQsZgbdWHTts4AA1dthZHsnYHKriRNJU1s2K0f8tktzOddgodNVOCGIIkEcS4rcsphrjPH5raZ2b9UYTz9TgQfdVIVlfqfZLP1QngzbDJINrz9bsm9e8XLwPbbtG3pqyezB97HjA1S3hzA10fUrFnmE2RQMd2Ouw/v03rvP+nqFEmBrTfvpA9bPz7l6sWaneUXWCSjCHr3FS+7qPqQt5PQW+T/8j8gPvgkffhMTt7gZfOwVl+k1/LP/3ueXl3O/LnT4jen9Yx83aBqYTTHjA1Y//Bs6LCEIUPNbtrslS9OmVimmrknskk4G4mvfIdpMue69xyhZkf/vfwLdAXKzovv48P+T697/H8c/eCWmfXyP4l//iSc+HN6DQJGtp5zpiDE119kWu9XcL/7LHO4/YbauGIyHPF9ZHt7bQ9x/7BfeRUFW51zogOP3HpFmKdfLkqmIOVleINtdxHgbLs/9QPH6uZ/Iz15Akvlh4aPveMtZufHDy+6hx+jt7AESfu8fI5584K1b7a4fbgYjaPe8kqJr+PY/gvEWRKn3TH7rd+HNa68CpW1oZX6Kz9d+KHLWKzJC+Od1+pWnaFy9/rvszdF9/wW6OIOf/tBLnFHsh52dfT+YfP4z790cb3s72d6xV2CK3P9u+wOPgT55BJ/8mGDUp3PzJQIH8zvK+x+TrG+pVEZrf8gsPqR79mPE/gnzq5JsmLIsIo55zm3RpZ+UrJaOY/maYnSPSrWIbl8z2Aq5WyYED05o3txwZC9JmppIpGwaT9ShM2YyyZFJFzkY83xWckBJce+YyTKkvV5jKove2+XDZMZPdcAoafPgZIvg2SfIzhYT2eHJ/RafTBussTSzHIujU234slFstyNeXC24NiHx1Rnr0R7lBvbGIZ/dlOwNY2a64WQYU68sRWjphIqfvcrppzmLQvNec0na7jNZWm4XFcm4w24vYn8rYrbR9AcB97YTxq2QqrSsC8Pj44SvzissjlEvZJJr9NIhnODgMOJm2kDhd9WshXJlmeWGw07MZ2cl7x7F/PQq52En4UJ4hPLrskItBeNeyI/nOXEgORxGVFjkQrCShr1BzN++2vCgkzDTDaHxu26fLwuGYUivq5iVht1ORDvyi/tYCS5uGna3ot/4Pf0lfeY/xHZWFvZX6kuciH9Ljam0ZVUZ0lByuW7YiiJuVw07/d/8XP59R755S+mJ/K6hVFDmltnEMN4KOL2r6IcJde37fGaThs624oefbTgZhzS1J/9cnddoDcXGsmjXlNrRCLB3DuHAFQ7efo0XNCShYH5niI1ESBi4kHgE841vRj8cxQQrSSx84eA6tdzlmqKyvLiredJNyZzkYl7zwYMUlQpeTCoSAee24WE7YTLT7B+GtCLFVzcl39xtoTdwKwz9QGFzwfH9CGMEXyxyNnPL0TghsDDXlrK0DPsBHQLiULCzHZMvDMvCt3rf1jWDOsB1/EJ7rozHDFeKwIIRApMIhqHik1cFva6iE0saDdO1piMCJnnDQSui21E0a4fUglYn4NWs4gcfdJneGSrl6IUBB62IF9OKUhmCUBIqhVOQF4a8cIRCcB3WmBImlbfPdcKArgoRjaSwmhmaLRFRWMdWJ8KEDlOC7DoiI2lHilgKRlHI0mhSFFstybKxTCpNu5Fo59gbRJRLEBFMC02wkuwMI5a55qgVkQtLNwwZxBGffb4iLyy7JwFbWUQUSGZlQyQV33rc4mxR89lFwdE4olx7a1XQEuhccOoKNqXla60W1grqxrElY07rgpYOWGlDgGBmG9pNSNcFTJqGuJEsjKatFE56K2PlLIOuIpUBp3lJxwU0xiFqx9Jq387eEegNnK5LBnXIwVZMUEnqrqWcOuqNY2ccIAqJDQ22FnRbHrW83hhiFFUBRltiKciVZVEZOqEkjw33uwm3K4MuHL0soKsCtncCaARXukZXjsejjMldQ6UsmZJU1rKzHzFZ+sLWqBEkRqEb6IsAHQtcATdNzfE4oZw65pEmKhXzQvOgl7Ki4UE/5bsPOpwtK65qzV4rZDmz9PqS01cNX3svpVrBbhjz9HHKujC8vqtZ5QYqQR04zkztC0KNxADvjFJ0z2EVPD3MODsvEaWgSAyblQdSTGqfr3t6mNFElud3JaKCREoKbVkvDJVzBLkkjRTLmaExlscPOmyufL4lUJL2ABKpSFJFlPgA/t5hRLstKXLj83kKVgtLXVmmdw0gsY0vGg0iTypbLQxp5jeLZCBIUuFJhZEkbQmuLxq29wPqAqJEcnFa0+4omgZvc9ICoQT52vDgnYTV3HrlJhWslpasLVjPHaOdkLPTGqUEcSKY3miaxjF4S7iMIv+4CN+9VVd+A6nbD5jdGRwCqXzW8NnnFUkiqAoHRU60NWadbTMrUoLLl6helybpkzcRaTtCjw4YXv6IdbhFllqGH7/D6vQa1kt0kFA9+Ta9q5+zuZ6ztm2anQfI979OurqibBSj944wRYluIPnax774Ml/jypLlF69RaUKS4E/oQvp14tE9P8gcPYCf/w1MbpiZHiJNCeoNi5UiOtzFbgqig13y19fUq4Kl6DP66B4zO2R/D0RvQN47wpQ1YbeNPDhi+dUb7GgHpQv6Oylucodod37tde23VYn5Bz/EqM9+Qt00oBTyn/5zPxQYw1olLF3AIDCk1cZbrkZbECfE7RZ3P/5bqm//gK1miRhvI9s93HAEk1v27Bp2jwiF5WqlQdeMd8aeIqYb/wHtD6GpkQfHuPG+Vy/uP0bUFepr3/Gqz+P34KtPvbx4e+Uff2sPoRvE5BoOT7yKFKdwcOytZFrD4/f99qlUflgp/AdP/v5/ijMaLi+8na2pAOHzNvtH/rWHkR9oktQrPU0NozGcvYLFDM5fQNqB7/2BL9l8+aUP908nf2dH297zw870xj/2Wyua+C//OfzF/+ltbospCBCruVd+Kh9gyzv7dDYXbA4/oHf7C8Roi+r4fdLiml5cUUR9RmKKrWvylaFIxrj5lFFPM78u6YwSVrc5nXcfcvF8g3jwDsmoA86wEgM6D3Y4u6hJhyPEzWeIbMxMCfK14kivMEKSz2rq9QLR2aU3iCC/o3V4yOUS+uvXuGRIqByrnafcq055Kbrcvb6jGyruxxOWZQfTjXg0Svk4WKOWU3YfPmV/nHCyF/Pjsw29OCBMBLWGOBAcpBE/vco5va4Y7iqKyxXx9pClGjKqp2wtLjiNtikd9DIFWvBmVvNg5+8adq31i6eNtGwHIS+WJUiHFQ7milwaEiGJrGChDJlQZC1FmTtMYrmpNQdZyJ/+YsVuGPPOUcL5umay1ozLkDtn6A0VOnc82fOwgFwbWkKhU0flLLuDiE1laGrHNx62QTt2RMQs0pTGcdiN2NSWcRbinCNQgou7mu1+iFS/3sZVvaXP/PssYdY5/uJsxTgMCUKP+jTGeRTo3IdI08wPUM+nJcvKEAcS0zg6iWK28Yvp/5Bjszbka29fyDeGV89qxtvebpGkPudyc9ngrCOMJHVs6QYJm3XldxorS762BEO4fdPQTRWfflbw5sz78vPaMp1b2l1BaiWNMkwmlu1OyGZpaY0E5xODzP3CP4sVrUSBAONglht2s4BCOyrtqFewVo6dfsBF0XBxVvPOMOX7H3Q4m9bEPcF2J+LTm5wol7xsKr79oE0oBeuJYYWl0wpYLy3vHWbka0sVWkwNHaWIEwmx42evC9ptRWEs/bakXSv2dyN204heWyIKwcpYZmuDbSwvmoqHcUToFEtleNBO+dHtmsNBxN4o4mbZcO/IY4FNZemGkqyrWE8sK2sQKagc8spxOAiRTtIkjsY4Wkiuq4Z2KolKicocV+uGJIE3jSaoBHeqoa0D8kpT5RALwTqwXJqGURliHGy3YnTpqAvHomy4qTUnNvF5KiQ3dcOtaXg3SSkctDKFtY5QC9KOpIq8ba6Zg1WC40HIzUTz3ocpLR1gE0vxtgTW1ZJvPs34q9mKSoK0gmEWQC1Y5ZregeSN1TzdSmlqOJ/XHPUjQqVYTTV/fbtGrARH7ZjVymCcRbYFceSLUb95r8MKS1ALJquGwSgkAnplyE4/xhYOhS/UbCLoqwjpfMalJwNKa6hw/HW1ZjsIkKWnh5XWkNSK8X5IywbkG4MLYF36wb5bB1gNprTMakPQKNYbw/WtJu0L9EawMJomd7R1SGcHZgtNkijKwLIQmso6+kGAiwWBkEzvNDsDnzvqjyTFEqrEclGW9F3ovwuhYDRWGCQ6dOiNo24sF7KkkbATxCSpZFFqBpFCF5aZNewScl5WtBqFVY5gLaGAvXHM3aphvx1zNqvYagW8mFX04oC7K00SSB4fZdzNal8iXFacXtRMpKaeOvLEsNeNeP9Byt1ccxXV7KqQs2XNd7Y72MDx4rKgWsLjRzGfXOdEocQuJMu8Yao023HEz14VFLnFKceOTNiKFa8WFcfthHJhcbUjVYpCGB52O1hTs8kdSRcS43Mrxw9ilISLs5q6dF4FfmuDnU0M7a4kTiTrhQ/Ex4lkcqtJM8n1habTlUxuDVs7Ad2+YnprEBIWMz/IZlmAQLCYa8JIYB2EgfBF9BeGo5OQLBOsF5bBKOTFlxXDrYA48UuQl19WhIHFOsdyaglCSZZ5GEAYyV8hlJNEUb2tFtisvJIcRv411hXUhWW4FXBz1RCGPnPz6GnM9M2acDxiPjU8fCdmdmdYZnu02gqna3LZYXO3RrQyinREs32f3uY1ZjIhf/UGe/KYjWkR37uHPHtG9PVv8ubZip6+pcuSbLvLdTMiufgS++TrJJmCT3+MaHUQaUZReGRy8tGH3gEzu/MZ6D/6Z955U5dwfoo7fkg5OMTcThC9LqiAupEQxb5Y++AJYjNjHuywO7a01uckB/vMvrogXE/I7l4QSMtN3iEc9uD6DYNxRH56STzuIbPWr73O/bYOMf/g7WTxt3/fS3VHD7B/9We4xQzihJNRm6sPf5/Rw4eIk4eQpl7FMJbWBx/z+cPf4VgWnsp19QYA+dG3PZErzfwi/ed/S5JE1HEb+fRDP2BY6wPxukE8fg832oGz5/DRN/zCv9sHwB0/hD/5F75o8r/+7zyyY73yJLDxDvzgj70VbrwDn/0E6Zz/8H/vD3xWxhhEHPvbVwu4ucQ9/9KTNpIY9Uf/DbzzobeRtTKfk3n41Cs69x57SEB/6KXMVy98mCx/i29OEviX/8JbxNKWz+gsZ17ijFKv0Ozs+2Ht3Y/9/Z6+wP3J/+LRgXHsyWfagJCI7/8hHJ6QPn5EtLvNuo5xf/MXxDpnGe3S3Zyx3WvYzCoGcsFEbHPvwNLOr0hjjYxCVitBuLcHD9/nuh5gnn1OlCnEckGrEzDRA7b7NeHS0JiIZWXofOMd+tNfsLh4xaOs4FXd4e5K0OiU9miHiRZYY5k3oHPLXtTgKnjVPaYY7fvenJ093pEbAuPIJpccfOvrxFsDvufm/OX5mmJ4iO4dUml/gf/ioiSLJIkS9GLFIFVc3jTInt+B+ycf9zjoJgwTw24T8mJa0ntyQv7wXR4edBiFIf/m1ZrzNxUy8Jap9fKXlBZHp6VYLgyj7YDtXkhx43C3gpOHIbKC67sG3cDSas7nFYtA0xtKLp5pNjNDPIS0IxADy2ZjMQ6O04jn65KyMCwLQxpI0kBSNIbltcE62Ky0R433YwZ9RewkQQyfXhVc6Aa7hv12xGHX+6aMdfzsOufZpCTpCiZ3/45G5beHbhyruS+BNOY3W8pezSoy43cRVQCTW81mZWl1JAcnEWXhaTa/PPY6EZ9cb+i+xXFGsWC1/rdpZlX56wlndeXoDwP6Q9+F0x34C3+np7DG2+mqyqINTERDvfGvQQTQOIvW3k9/fW24XVueXxRcTwyl8kWgd3XDs8uCyZ3lk0mOWUn6qcA5S6cn+eq2xlWOaUvTybwVRTrfj3YbNBwMA+JdjzA9HIaQQNFo/uqrNc3UMu4FrIXl5kKzKBqGb4tJL1437PcibADvbmcM45BkoDi/aMgiQScSfHK3YVVrSuuIlCBuCeracb5qqErH/VGCraHWgk5b0Q0Dbi4bri80xjj6jaLSlnvHCcXEsr6GVWDolIrX05LjKqaTB/zkFxs6ieLnNwUPehHzG8uXk4paGebCsFpbOi0FHcGwo9hoR1M5DoYRD/cSdnohdeH4/EcV4x3FMA25mpW8mFc83Up4+DBmz0Zoa6gKxygL2e+FCAGZFAjlT22DtiQIQPQdRsOQgG5HsS1CjLCoQHCvSZE9QeBge6S4ampCqZhWmpnWfP1+i1Zfkq815QLagUQaMAmsAsd6pdElZBFc3Gl2tiI+q3PIYNiTLBcNsRQsK4feWKT055ZqDZezmp9crHlpS572EwYmwDWQHAqyVDFfaNYby3Yn4vayoSn9Trw2jpPdkOu0oVaGsPED24WoWQnDSAW4lgULzgpWoVcwZAMHNuJyUZNYicghxJPMqg1UgYcHVNqwT0RXKJrcEaSwDAyB8UHvWa5BwuIGr7ytBbIWBCHU2hc1BlawUpp2S2FDh9qCfOLzSGLk/CJVOtwC1o3hYlmyFUfcDhoWuSYWgrPbBukgMILVW1x81AREwIPHIeXa0pLS466NoGMk1wtNvxd6le9Kk3UFNnSMMkVmFaerkpZWTBde7TC1NzVICbd3DbOZ48vbksuzmsY53m0njNOIp4OE4UhRLv157b6KybYVe1HMy2XJo2GKXgqWwjDYiZiWhvlGcyoKlJCMVIiNHT0XYJ2jp0M2RnM5axiIkMVCE4QSUQm0sIyjiP3DFGsFQQpt4fN67b5iMdPcXmuSRFJWju29kLSlKAtHq63oD0Nmd5owliSZoKp9v1e+tgy2JMuZ9pl1DfOp73fxAX/HZm3o9LyFGgSTG0O5sayWmtuLhrJwLOaWVkdRFI7b64YnHyREseDF5w1h5O1ltzeGmwvDe19P6fQk1nl4SqcrqSrLemkJIkHTOPLcIoTj6rwmUJBvDHECceY/b9M7zda2V28cUFT++UWR7zJL90eMHoyZbGJcrXn4tQHBesZrHhFtppja8uLTNeGTJ9TZGLlaUn/1JetPv6QKO7z4oqLfasibmGUeEndSGiOx3/oBajVh/otXvpD83mPs0SOCr30XtXsAFnj0Li6O4T/5p/DiS5hPEI8/gK99l2WyT9KO/MZc/x7h06csew/o5mcQxehnX3ArDzixz7h+Pic8POLupqHTdiS/+HNwDpXPWJ/dEe1uY8uaVi+gWDXMbe83Xlt/W49/8EpMPL2mqGu/cJ/dIsoCeXCCyFocTk4R9x55FcRYH1g/egAXp8Tf/X1Giytkf4hbLbzSsFnj9o68qiAVLBf0nj6lLTRRu4VTEn78Q3jnA0QQ+EzMj/4C8fQjxHAHbi4Qj96DXh9xe41LMuQ3vgevn+OyzFPA0gy295CzO2/ZujyHOMHt7sPzzxB7R1BXiLLEvfO+z8g4C9uHiP4A0WojD44RgxE4g3BAkiGEQH7vD3Dtrre3vfORt6DdXnnZU0o/fCWJH6Y2K//vbh8u32KatfbqjNY+iPb8M28jKwrfbXN94e1xP/1Ln6t5+oH/PS1m8P0/hDevCc6/hM2Kee8R6vgeYSyIrk8R/RHz9IDOz/8P1idfp3vQJ/7pv2Z1+HWqGrJBhuv0KCZrpKnZVxdUuUE9fAe3KchNjFUB9u4WMx6RRoq6E/HzRcrvHobc2xF8th4RWsNBa0Mz7tMPAoq7KVedDnalMIsJ43abaLDLm7NrAhxj5ly/eMWmCuhtD4lHXe7uNGLVEG+3mS0c4yzly2XBYmVoOUWQQV46skBxMk744jKn3Qp4upeipOT6aoqzEXv7Hb6aVoz7AeeThnasKJUhXEps30ItyKTEGJ/BkMLL5BdXDSeHCXrtOFtX6AZsFybnmk+anHIBgfXB2HrteLYs+e7TFrcXmotS89FOi8/vCtZzy147QjcOEQvebGr20pDj7Ziz6xrZCJaV5vZSs1k5+tsBoyxkkIa8vKpYW43MHHlpeVGWHAQRN2WNVIK/PF9zrx9TakcYCmTuO0t+mV/JN4bF3JC1FIu5IYj8z5vKkfwGNeZqWTO/1pS1bw4fjPyuoZQeWVzmluXcspKGtlAoLXi5LjlIYtJM0W8HPH9Tsj34uzZoax2/+HHJeEf9O/tm/p+2tWJjCENvyxgMAy7OKia3DYuZY/cg4F+9WfJuKyOJE66rNYV1REjiRDC/NtwfxcznBgVscsPtsmYpDLFTxEikdBQTsAICJykax+mqIgSMgsQqdOQHo9XScH8/JkgFeWFpGqjXsK41Wych2zLiLm94upcxWWtORhGvrhoeHyX87KucJJBsD0KeLUse91IWM8OdbriqavajiPfGGafTii9vKoISPj7JmCiNWwv+/HLBvSym3wsoCkO3pUilZPcgZDYx9HqKTj+gLCyVscwqw74KeXgQ89NNzv1OwiowyFzQChUy8++dSWH6UvP9r3fI1xZrBXdGc9yPvK2rFfLwMOX1siRufNmnMoJuL+D0smaQBPx8UaAE3N1YbooGVQrcQHBTNuiWI6wV+/sh04XFOAcVDNOQzCrSruC6bOi1FdczzSAMWIQN3TrEjX3YGgtzoXm31eJZXiILH5qO9yQPRjGn65pVabmfxEwaw9448jvIieF8UeGWku9+lDFfOurI0o0C7m3HBKlk9caxNUzI84bSObrtgJZSSAHPXpUQw8tNxbAfcGgSqggej3ywfL10PN+U7LqIrJas15aqtCxsgwwlbARmgQd+bAxLq+mYgElQU7Usi0KjtaMKDROrGYuI2jkO0gjjILGSDZYsE9zWhswKtsYBc6spCz+4Z5HyhDthyaxEaFgHmsEo5MMnCS9vKih9V1KJIxWSa1sTJ546Z2ug5YhLyVebioM0JiyBWnBb17QjSbOCjTW8VhXHMqFyXombFQ22hvNOgdnAUAaEQrLQmsJY9FrQMgEihP6uZLI0qEogW9DRithKbk3Dw+2E8U7A6W1DKwqwAei1I0XSSE/+ms40ubMsVhoRCvLK+PsZKWY3hlgKFteO26phqy+ZziwauLYNH/VTXk8b3lw3bHUU51XFX92sOK9rfveog84FAvjekzZ/8WxNL1KUlaMIDMoJNsIyaIekic/FVAqa3LLdCjCNIGpbNktDK5OoAEzjWK8st9cNUSKJIo8g3t0PPT1MCXYOIi7OatpdyWAU4Byslj4Ps5xZqtqSpIre0KOPf3kOrCtLWXr122ivOPcHkjD0A44K/cDX6Snqyt+nUtDpBr/K3kzvDCePIw8JcIJe35fo6reZl8mtf5x2J0A3nuY4vWtoGkeZO9pdQVNDEApG45DrNw3rleHkUYKUjsXMYlY5uYnZ2Q8xBiaLgKqC/XjCXdFic7uh1oImbCGKFf1ggSYkjBRiPOa26PD4uOK2aFMvC7KWotcySF2yLAKq0RHBzTlVbw9uLohigTo6RsURy7mhN4q8ne16BnXFldlD7R2QbA1xp8/g/BVu54CiCVjfrJjER1gUcjxmcNgn1zEVMWb3HptScdK+g/kU8c3fpXf7KfLVF5jxPrOT7zB7fkNFSNMaeXVm/ppF65idR32k/PXX1t9WJeYf/BCT6IYq6/gBYjHHxYn3Be4d4X7yQ3AWd3vliyXDCPlP/itoKrpXr3wAf7zjm+q7feSDJ4i1L7fkxWcgFeoHf0TU7/tvahB5WpezYC0yCBDf/D5ivUTEieebj7Zxf/mnuPUcESeIKEY8eAexe4i4/wj2TxA/+aEfdu6uEdt7iPAtyez4IerdjxHrFewdIedTn9WZz3wWJ/CNtML450sU415+hTg48SrLzgFieuvbawdDn3f5wX/uVZPRDnz8bfj8516V+v4fwk//2mdvnn8BVeHvX0qvTC2mfkBZzb2Kc++RxzYv534AGm97QALCD11R7K12r74kGA5Q7RaLBYzyU9zWDkQJtjemNpL6zSW9P/2fCe7dYz54jNls6L//gPzshvVdQX+/Sz1f0xw+xpY1ReHYHWm6ccUy2CLa8w3Lopb0xJqkgckmZpUlNDokyC+ZBD2ynkDfVhwc95jfrlBBwuupI0exMB1M1kK0euQ7e5Suw/vdNS/XKbMLyzit6XfanC48xabdUTwapGxvB1zeNixrw147pJ8FfHadczTyC4E0kNy9fkPQ2+bzvOTmqkbHjq4KcImlZUNmVUPgBLWFsJGMtgOft9gJCUPJpGhIEsmz1xXJAA7ShG5fcXdXE6GgEITODzYrYzjai3ixqni1qtiuA4ZZyGSuuZo1fO2oRb+vOH/L7R9ZT4+5WzQkseQnL3K2dxRCCx+pGkVcrmou85qrm5qjnYS9JOSmrjnZTji/btC1Y9QNOOknfH6X00sCmpnzzshEIAWsl5Y4lejGsVxYxtshdelA/HpL2eWqZjnR5BuLSgQPjpK/d3tZGH50umaYKm7mDYMo4M2y4YPDjDeTmq1+iBSCq3nNVi/81UA1m/i+i3ztfoX7fHNa0+0ritwSRj5j4pxj+vZ9KNaGqnJcXdXka0eaCRal5ayoiGsJrYA3VwWDHcVVrcnPLKuVZbU2TJKGCMXukeTm1lAvHV9/L+V60zBsK6bThk1lCAOJGjrKEjpBwKJuCLRgtKMoSq/+9EeS29zQ1ooydNxOG3aOI/bjiB9OVwx0SNN3rBcNf3u6AS0oa41CsTsKuF40yEBwfd3QCMNsrfloN+N8XROFgunMk5nGQcjplWbQUty4mmoCjx8nlOs96uQAACAASURBVLkjGSgCA5FTFLljtbTcfxxTV46m8Tu1TeiRq7YDroRKO0YuoEwtW62I959mnF5WqIWg6jjePc5QQjBdN7w7TMmt5ctFwQ8e9Dg9q5gsLKxhimGlDc8XFd1KsbcfUODYXFi6XUU3C1gYzXSl6TSKJZaOktSRIItgXlrf0VNoOonitmxwkYNCsCw1u1lMvA5QMSxMg9GCc1EQ1gqxBmccYxWyqRyXZc2TUcpq48lZnX1FkPvBszKWwlrWE0u7LRlFIXlhebmq+NZJhisELnIsJ5qn93rM65LQCmrARJYvn5d0k4DbpuHr9zPOrxsyJ6kDx3NR0tz4EtR0S3ESJOS5pTQOCeTCcrgfczGtsYmjqQWhBe0scSS4k5ruJiAXlq00otKWyEmcdQTAT3XObhTgNMSRoJ9GzGlYCsOuijAGFoWhjUILmClNhqKuIezAtDGkQkLbsry2hKFES8dgO+Cmrmk2jkQHXMqa/XZCahR3uWYvjVhLi1xKXN9ynlccDBOqxnDalKShYqwi2kIxdQ2ikogIrHEcqZSp1rRNCNYyE4b7/ZRNrgl2BMuF5aUu6ZqARw8iLuaaXl9yTcNuHKOUYHFnsANH0Vhip8i1oR8p5qWhEwTUsWW98Cjzw0HIcZSSdn1m494g4bO1h1N8eVnycJSirGAiGrZHIfW1X6BfLRr/GLewP4x5sp+wurFEA4FygqvbmmnZMCDk0YOUvf2IUTdgJAJuVjVFY0kTRa0tu/0A3Sju5iWDliJKFFlL4iwsZr5YcnvXq7BNA2EAi4XGAdNbAwi2dv0iP0kFVWFZzt1bgAu8837CZz8ryXNvIStzy95xxHLqh9/FzKICqGuHNaCto9hY+oOAMJD0+pLNypK1/d/TiaaVKWYzTbHxFXngUIGkLh3OeSMJwOxO0xsqzl5VSAnzO28/3j8ImNwaBiM/4Mxnhvm0oa7AaK8yXZ41BLbibh4wGIasVtq/XgH1pqJJe2xmJdsjRxO0SDNBGEIzPqJalIjRDqPDFms1pFoUbArJdidnePZX3J7nNA8/RoQBW+tn2L0jZjcVO1yx7t4nbXkgQRj67E/+2Veo9z4mePOM+eAdenKJfPwe7uqcef8d8uOPWE1rgk4L6TSRq+nENbVqUTQhG9cmTBTjs7+k2hg6j/Y9yWy8zSoP6Lc1RROQFhOuzRZpS7F+M6P79JggywjCX2/p/o9DzN8/fmuGmM7+IYVQuC9/4elZ7R7i4MQ3r27tIPZP/OK8rv3Pk9T/eed9RLePuDhDKIW899jf4WyKfPQU98mPfEg+ShDLme9x0dpnSI4fwOW5V03WK58h6Q1wjc/PyK1d5Dd/F3H8ANHz2DsRhB7NGgRgLfbsBTiLPLyPuzj1+Zr9I0S3j/vFjxEffhPGO7i/+TNodZDf+B5itYS//Ffw8XcQKkBEMe7mCnl44rto/q//DYIA8fF3EKuFV1mWC8Q3vgd/9i99m+x4x2dcnnzkCWWbtW+i3T+G3WM/qLQ70B14FcdZUJG30XW63sJ2d+07Z1odxM4+LBdgteeeBwE8eEJULHAqoFwWVDdzNkGfbl8i4oT1XUH76lPko6cYApZLEHVFr22YvZ5TDI9Z2zZpgi8a0xE73YJqcMButsD0e9Qbx7CrULMNlQk5Gm7oPdimelNwvCNoyZDXtUPmNfldTRhrjndSrqsavY5pteBiZRDKsCNi4mbFG5XStynXSjPudUgW15yVKb1YESnB4V6MFILbuUYJQWMgEZLj3Zi/Ot+QRZJCO8qbFe3dPpNSsxdE1KHjcT/h5bzmpBOz1oZJY3g8iLmc1dQLR11a3NvyyJum4WZR895OxmriKBKD3jiUFQySkLQNWRjw7ffb3OW+jdsIx8ppqqUPR2aJ4nRVc7+TMNloROXpQKOBYlprfrHJ0QW0QsnvfNBhvvR2q2lu+NOzBf/4cZ/Lq4beIKCuHLu9kL+93PCfvdfn3jDhbqLpBIp5rdFLyALFwVHEcmEpC0e76y1ZIChLw3DkrT1l4Sk46v+Vn3HO8eysQtfQI+DKaB7tJr8ikq0qw19/saExvoNiURtUIymN70m4XjWsJ4bBIGBpNEEpSTL5FtPpkFJQ5JbeIGC9Mly8btjaDdisLJ23g816ZcHBJ5ON71aYae7mFgLfaP6mqbmfxsSRJM5iopVmMdeUN75MrjMKMBvLMA2xErpJwHRu0JlFrhXGWso7QSMs68DQjkKq2hEHEonATqDuOqwQyFwSjaEsJWkgUBYuZhVhI7nraD453zAKQtJY+XJBCZ/OC8JI0NqEJAPHfG55WZT0XcBHD1K+eFOxdpYPx220tjzZy5htGsJa8ejdiGEn4HReM7k23NuLSFsKXXoYg9aOdiT57EVBNISicuxuhUQpvpeip9isLM+nFVsmYlUaXpQVv/e4zcuzioPdkNNXNcY5xAgOuhFKC06LmixXnN81YGG3E/HyuqIoDWSCj08yELCZWd45jnj2SnMYhXzRFNwfJTgreOEK/nDco5WFLBpNrxsyKhRZKJneNEwDzZ6LSXuSeuWYBQazgNhKQiuIXUAyltgStlohdQV7rZDdJGKYhFgnCLbhOm94ME6YrL2l8E1V894gI0slZWC5mWiePk74alpil2AiqFfgQjjoJVyeNgQdQZkqJlcVSUdw09TMNppxGjJdajpS8WgrQ+SWTzY5R2lEWVtWxtDLAn6n0+HZtKTtJN2tgM3SghOUGP60WPKknfL+Xszs1qKsIN6SzGrDWIQYvHpsBewkEdPKoISgLRSbxqCQKOtD/7WDa1dDIyD3CkOKIEURhJ4/05YBE9fQVwFN5ZheGpZKUxkHqUdfN8JhC9hphWSJomm8IpS8tedlleSCglEa0SkDbnXDQhqEhVRKDo9DVCFYbwzdVLHVDWkq0NZiNSjncIHDSLA1HO2FLDeG27qhE0ikBiUU86oh6ymMgJ5S1GuLFrAwGjaCSVizF8RoIUik5GQ75HajkX3BDz7okZSK63XN7dTQUQKdOoz1fv6Bi/jd73YQJazuDJ/dFIyCkMPtgLu5xjlB4hS7QYjcSEztaJYw22iEE7SMYrgVMhoqkkDSKIueQ1GBqhU2gm5HUk6g3YlYrWsiKTk8iagKx92tRgjHeCckSX22pd39O6pjsfFdW91+QFVYRtshwsFmY31+Jve3rxeW5cJgtAcBOOfAQRgLHA7d+Psoc8fOQYgzPuu4tReRtSSTO01VwHymEdI/bvQ2eP/gnRjrhIcHCPGrImelBJuVxQmHrnyOpzdQTCeGVlsQxQFFoVnOvWpbl37gSt9SK1UgUAo2pSTQJf3dlGLjz1lRBJdvDLtHKblO6CQVmyZCJC26B0Mmt4aO2tA/6uGcYLU09HbbqHaK0Q65tcMXqyMOjxRhO+bydYMs1wTjEetZSbK/jQp8f87rVxXXn99gemMOHnWpkz6t6pb56zmtruT2xZxieEL2+Z9TakV3t01tAtZ1jByMiO4ds/j0lEX/IcsywAQpZdCmfvWa1vIMsb3P6unvkX/xgjVdSpHRdTMaDTIKiCPoHo1/41r5Pw4xf//4rRlifvnGuLOXuK//DnKz8tQv3SDvPUakmV+QNzXi4VO4foM4vIcQwn/J5xNv8aorRNqCpsZZ63HBf/zfwt/8G0R/iBiMfejdWcRm7QP3/RGiqRHjHT+grBe/oqSJNPt7z9M9+9SrGPMp7uI1hBEiThH3HuNOn3s16KNvIaSEnX2fl5nc4FYLRFUi7j1GDMfw5EPEq6+8SnJz6cP19x4jlcLVJWIwQvSHoGuEMTjdIMMQl2Rekdna9ZmXsvDNslr7waTM3yKel94eFkUeDCAUZJnHLFdvA/1Zyw9u4x3Eh99CWAP3n4AK4OS+t8kVBbFdk4z7JMsr0tkp4tmnxCfHLNYSMRiSZAp9/ob86D3ScZ+tXoNSjuUcDnYaWmHD4N1j1pMSkaWQtIn/1/+JbGeH61WOnRTYpEs07tG9/Dl2/IAtd8V5tUswuya6eU0SJsikQ7LbYn41ZW+45XsYSmjFAcvGsDsKkHcr3pCx0wq5fxLzxWVJUmgKm1Aoy+PtlNu8oPqbT+nutDmbObJMkgrF9jDi5zcbRlXIJ7dT9qII2Uvpp4q9YcSXL3M+fNjmetJA5Rj1Q8aDELvyF4fF0jAahdzVmnlj2BEheWk53IkxBTw8TDh71qBGYOZwcpjwclKyaAxPDzPOb2reO8jYjiNm84YnhxnLtSYwgnJjSTqSD560mKwabhaaTWGIWoodG7A7Dnm2qsikxAr461drfv9hjySWfPWm4PeedFhZQ9sGXJU17VCx1QkZ9UJe3VWYhSMdC7RxJEJ6LGYgmNxojIbBluL/Zu/NfuXK7iy9bw9njjnixp0vxyQzKSmVmqrK7qpu2C64DdiA4YeGAb/4X/RTo2zDblc10GWrBqmUmpKZnO/lHWIeznzO3n7YlFRCSdWygW4UbG2AuCQjGDcYDMbZv73W+tbyrmU8dUH9MjeOtKR/NcjkmeF6VhN0oUotk6HHel8zHCqKreXloqQsDW0Jf/j1Dl9cFTzphbSJZZ+1LDct0rd8/+cpJ30fHUiyXYswgrJwJ6K/GGLCyD236bHHfmcQwvUOBIHDQP/gXcr6ruXxQUidtpjQkknLyFfc7Bq+eZFQBS3pHJbzkttdzb0TxftZg0gFO1pkK5nlJbO8pi4t0yAgFoJV0CDXLmo21AF3RUWZG/pas0sb8tq1g1eppWhaHpyF+LVFZoLZtsZImHZ8vJ7go5MIzyrq1pA3FtkRqI1gFHps/Ro/U6S5YbFv+OY0ZpG2bOqG8YcOkb7WXO+dxz/uKYQVPDwM6Q8UN5ua7z3ocFc0VKXhfBJQYlluGqaRx7MnMXluuS1rfvpVDp4l3Rr2teH+RUCeGipluBj4vJ3VSA3PX5ccdn0a37DMWi43FQe+x65pGESaH68yPruIma1qdhuDHwhIBJ1Ssdg2qAQSPG6airVp6BvN1z+JWeUNvpDcLlv+4LOYz68yDqaK9Y3lza7ACFC+IA4Uy6zhrqw5xMNUTsVwmx1JljXEjYcaWoJKMQl8Tj+WDAOP7balFZDSslWGddkQtZJOqJhdt0wPNX+9TvmvPxvy7q5yw/2iYV8aKs/QD10HULZrifuSL65zRNxys6kZhpp0Y5lvas7HPoO+IvYlry9rHp+FXG5K3mwr/uX9ATvb8JNZjl9IpCfoJq5MddrziGLFiedx6vtke8gbQz/y2LUt1IKi0zLGJ49aVCUIhaCtoZGWlWgYWo/QVySe4K6qqGTrrI3CYlrLwGosMOz7lLnBJhYL+FYSotmUNVoKdk3LuOdx2PVZVS23aUVXuab1QawYnyluFg0dK9nW7uAkkYqoq6ALygpXZuprmhoOhh773FJnhjjS3OYVQ+nRvS+4vq2xocWXmtp3m+JR4BEbybo0qJ3goOvzelVQHVjywnAe++wr62xYUtBUhiUtZWv57DBmtTJUtCSR5jj2oQfH0uf5oiAaw/4azqea+bLF9yQSSahBGUl/oNhvDb2OJrUtm63FSyS+kJQDw0XHx3iWxU1D41l8ochNQ6wlCElYwr5oiUvNNm1QRmA77jPfs/DZd2IWC4ORLb5yVDFj4f07VwB5ej9ku27YbQ39gcbzBdneoY2HI4+ko9h8wOYvZy1+IEFaqsJS5E5hCSNBHLssYNNAnAi0L1gvXX4vzwxta0i6HlVpSPdOya5Kg7VORd4sDcORwhrIPqgU+50ljCEvYHFTO/JZCIcnPnfXLVEiubtu0eoXUVtLllq0dkq67wui0KkdWEORO9WpbS3rVUOWQV+nEHVoW0c1E7sNxovIMkt3INmXIUG9JRp3MMYymXrsm4DmZz9x0KB6zkTOQfmsFjVZpTl8OmH9dkkgDcEoIW9DumZN4fdZbwTvrxrSXUOHHbFN8Y+mlCUUrcfB4wnLLKCUCWs9ZXwxQNYZi/gxQbujk0DPrii7B9w9n+MHivnWp+OXWOkx7VfotmR++G12q4qsd4ExlsZqOvMvObz8S2b+BVE/ZvDoCF1niPDX952/aa/8H2v9foj5Hdcvh5jeAPHF567HZbtC/EJZAad+7LdOqcn2iP7oVw+wXTnFpchcW31ZwE9/6HIr1rqNvdJOtREC5nfYxS3i/kcuGL7fIA4+NKXevnf2sNUcMZ7+8lvYNy9geoyYniAGY8cPv7lEPPsWXL6CIkNoD3nvkXu+nuf+jOd9eByLWC1ckEwIxOjAKU91hYg7Lh8Djkw2PXH3Sbru9iBEPPrYDVWHJ25wiRPHLP9AcmN8AH/wz+GH33dDTRi5vE8YOajAeOqyMWkKT77mcNLHp07p+du/dN7N0QQ5cUE3MRi71+3oA4baGMS3/ggWd4jv/jHF8y8dkaMzoPZC1vKQdG+Jmw3Dj88QyxnbTcv08RhRptjdjq0a48/eEH30ALlasDh5Sr4PGU4jwnpLjeZHO8VpmLJp+oTsEUXDwnaI+l3GXY9DsUUOBkz6Hut1y+FhxGbrulpEWeH3QioND45CvnxX4lcN8djDGzvbkb15jT55yv7uNaLj/KcXRwFSCfYby1eLHC/fMjqZEkeKe4OQq31FtjGISHA88rm8K+krj03V0utJ0rlrpU6t4aijeXgSoRRUKczTmlAKFrMGCfgTSb2ybFRNz9e01l1kAqMorWHqe7xsCjZLw0lfIzaSN6bk/r0AX0msZ3k9K0kKjwOlOR762K7gZl8R+PDifcVHRyEnsc+/fb/lfi9ANlApy1B7PL8p6DSKo4mmyi3ztEH7gjBSGAN+K6hKd1Hs9CRZ2lIWzm7wdluxb1ravRtaBIIokayXDVLAkoamteidoDAWqeH7l3v2K0NbW2QlOb6nGUQeL7YFcSHJpeHxQYTJLFooxNDy7qpiMtYs1g3NztnXitzSGyjq0lnb8r0hiAS3790Ff7trWM4absqKfWaYKM1MNs4nP5Xk2nD9ATHaQfF2W3HoB9zMS+KO4gdXGZ2uQBWSeCK4yiu6lUeeG8JW0xqDP5RkC4O0IAPwteRVk2OMxbeSvW3RASQTF55+XRRMA80qtSDhdl8jjaCKDBM8Xu8L/uUnQ95va2QJoa95OAh4Nc+RSI4GPre7ilrB8ZmPlILNvqUrNTKATz6K+fxFjt8KHjwIeHldIkNB1VoGniZSkpf7ggTFg8OQvDbMFjUyF3R6Ck8IisKQloZR38NvBePQp99RrHYtvY5iXRuOpOf6QLRlck8zXzV876zL7W3Nl0XOZ2cJ//urDWtRk6D5q+s9g0hB4LJGA6WpE/eeshKyqOVyVTFUmn3TMl/X7uBhGvA/v91wPwl41I9487YgKBUrVfMkiAkSSaQkS1MTG5friHxJHHnYsaWuLNOpozfJgcsrXXRDrlYV447HbNfQhq48dtxRPN8VfDfp8GZZ0QaWb0xiMmN4f9WwLRseT0Nyz9BgsakLGw8SRdyRHOgIAstFEmAzuC1rKmEYBx6VscyzhsOuJs8Nl37N9x5EzFJD0JOUmeHIC/CHknzvykkrCb2J4mQUIDzBumjRviT0BFlrXBFu2SKkZRJ61LVxFkklsdIpD1ZBIQwicAjbrW5Zlw0DoViblqH0UIeOqvZWFnQrTXsBdWK4W9R0UCyDmmntExzAwjSUtaFfaRrtUOzUkrumxjRgIqgLg61BdARBKblsctqVIMGhn+NG8lVRUFaWxHMFiYGVpLS8WVbEHUkoFF1fM5Y+md/wZlfRjzwILCqTtAeGZVHzWMZcViVBqailQSKZRIpsY1hpw5NxRJ0b6r1DZB91PTablnfziveLymGcW0X/yFGzcmX5xpOI7V3L4NhjEClqAya07ArDmeejpbMsjnqKV9uKr51ErN4a2ljweBSiYqhjixAw7is8q/B6gosTR00TBRS1RSPwI8FHH4W8ftfQ9S3HZz77nbOQKW1pWwEWbq9q4kTRtuIDyVHStoK2hdltjTUOJGGNO2y6fd/gBziKWOk+K3p9xe1NS6cDTSsc3rkBJQXTI4/FXUuZG8rSdWfVtRt0w1iipGR+5wACUSzZbVu6A81wrMj2LsvjSjahbiy7jaE/EoSRZPvB1laVltGBxteQpo70F0VumBofeNy8d5j4X3TbXF9VhJFAYPBljdUBx2c+Yr3EdPrkaUtTQ1lZIlHy8NMhpoUwFFTrHXZ2x74OCI7GdO8dcvvzGZ2oZrENUXGAjgPS1+8ZPjmjbBRdsWXFAV62ZLkPeHCYcXZs6UcNd0UfrOX0wifdWcYnMV/+aMPRsyN2L67YmR6jT06xuy22btG9LsPtS+72HeZVl+7+ik/m/yuz6TcZ9Qx722WhjxHCYMsadXKKfPMFfb9gVg7pb78i7CdU8ZjoePKPFj3/Ux1i/n9PJ/vFkoMRLG6x1sDwt8hq7165YP/fX6f34OoNYjxFPHyKePgUygJxdO5yL2cPENn+V/dvG7A4NefkwtmyfrE+euYsZhcP3RAC2JtL6PQQnd4v7yaSDsLz3MDV7WMtECeuVPD6HfbLnzor3MGRUzsePHVKx4ufucec3yIOTxAXDyH5FVJPDMa/9iYWx+dwcIS9fY84uUD4ISjp7HD9IUyO3A9wFrOqhCx1XTevniP/8F84THS2hzABLZ2aVObIP/kvYbtGjA9gNMHef+ysZ0nHPb4xiMXdL7HSFBn8sz/F/C//E4PbH1M9+Q5BL2CiNkSxYnIouZwHGD9mWr1iGxwj0w2sFoATeaq7O8STr0NdUWctWMH0RJOtcjb9Bxytfs67YExUrQhFTTW6h54OOJHviRLFLtdEsWsjfvowomkFXgXdvkAkJekcdqrl377YcG+q+bIK6O83DEPNYHvHS3vA0Zkm756j13OMdU3pbeNaxbe65Z72eZ2VHHV+FSwXHpT7lmnikWLxfcFx5HM1r+lOJXUNqoT92nB7XZPuDIOeYjFrODnz6Q0kBstu1bAwzj99OvF5cBqwXLScjjzSpaPN9DzFZtugreb4TBMGgsWm4t2mZF0YFnnN0YFCFlAqy5ODiLo1KE/Q9ySTiaYsDWVq+Oxhwqu3FWYPs2XN2cij6bT8+Msca+Fg7DHf1FzfVlRly3LmFI7+0DVeSwnz24b+WJOnBq+QrL2aSjrC2PyuptNV+LF0OZqZIey7ZvPzQUC38BhPNUmjuGwqdpXh7abgsO9OmLsogsAVtGW0PPFjlBSsbmpuqRkeaHp9BwYIQmcv6/YUrYEvf1ISJ4LBSHJXNLxelCxnLY96IeenPmIJM9uwEg0Rkpu6hD3MbirKNeRZy7pbEU9g7GnkVvAyTlnsW0ZakZoGiSASTnmZhB6qEHha0FgLHkhleXY/RkjQCIYHPm/nBRZLrS1lZTGFJdsaTpMA0Qj+i2/1ORsF1Bk8f13QBAZvIljuKvLAMDzwyOuWwECtLP2BC9a/XVWEfUHQEexSw/PLgkFPkilLF83DfoDILWMUQeB6TmwD445mu265u6uJA8noQDvP+r5mNW9phGVR11SVJe5J7t41PB6GpKnlrO+zWbcYD2Qs+Nks59v3ElosNoA4Evybn2748SYjb1oaa3jaifjmk5gXm4JCtXx+l9EGBlp4uytYlw1nfZ/pscfdomZdtWQZEEG/VUx6mh8+T6k8Qy1aDoVPlkKuDOu84bTj00pLqCSRkDSqcUNgXzI+8jhIfB50PFToLCtVbREKbGDpt4oDq/n8Vc53kg5v3zb0Q8UdNfeOXDfGTtRka0sRGnQrGXc0gyP5wX5qEaWkCOA08Xh8GGByNzzcTyIGfQWVUzc++1aCF0gGjSKt3Gf6/TDgcTfEi+HB1OfA0wy6Cq9xRbdX1zXJWIAWDAcC1YNECFKv5VkcMxUB9dKSaE03kbShRVtIUGjfdRW92hfcVTWyEYx8D41EBoLbTsUo8PiKnCdexCuTk29bllnD3mvc/61CU6qW66uavd9SGcutrTmMNXIA26xBhwLTgX3Ssm8MHaUQFbxc55yVIXEkEIEr7lwbQywk13lJXTtbaXesMSHoCvrGY101rIwruO0WmscHEVd1Sb0CHYNnJcdR6ChgmeKjk4C2gmVZc7Ov0Z7kO35MZAWhlegR+EbyYlWyU61Tn7qaP/pGh0/uRzwchQhfYBvY5A1eIAi7DvX7flsyQKNiiAPFQV8TdzVRoXk0DHn5umJvDPf7PklXkqvWqUWnmvNBQG5bmgpmVUPoKVoPtBXcv+fTHUl+8oMcpQVFBvudRQj3mRZ3nNK13dTUNTx4HOAHgjgRhLGgqSxN5Q6T4sQRvD7+NKap3F4m8CX3HoUIYLep2awbuj3oDjyMMWgNnnLX4Cy19CeC9dqAcEBTLEjpci51Y7AGysxw/3FA07g48vymZjBSDCcO4X505rnBS4DADT+DscTikMzZ3qC0ZDSR+J6jv61mNW9elJjWIqSzIN/d1gxGDhRwvQyJTMp2VjilzQj6A0nbOONMkRmSoP3lHinuKGS247r/daLAkOeCn/wwQ4Q+u5s9qhOjtWCfCqLQUt3OMK++YmVHKG15O4sY2ju4u6bd58gkxg8EXiB496qiqlo2q5ZO0LJZNDRZQZAEJB2FGR3RtWuyWnO56qD6XTQ1x5OafHRBW9Ss8oCN6fHt//yIeDLkYec94id/g8kyVBxxkOxRhycwPmDwoz+jup3/lt3xP+31eyXm702X1rQI3IDxD9Zq6axgo4Nf+20hFSxnv1QzhBDYPHOWrNHEbaIPDuHmyuVbuj1Y3CE/fA/x92gQQrifC+05BSN1r5GYHv+DpyOOz93XuOMC+EWOaBo3tBydOjvZh+cjfN+pSUEIz38C2kOcnDuVJfnt5UaAC9zfvUcMJ9jFHXgeRDHi7tqVfN5cOvvbcOKec3/oLHan99zXbO8wzE+/7ixob55Db4gYjLA//qHLzxydwd/8O/jeP0e8fO7Uo80K8eybiNY4MTL3fwAAIABJREFUOEBviBAW/s2/Rv2r/xERJzSv3xIejdjLAcf+gmXdpcgF2+TMZXu0ItpdofZLxOw9m7pDkC7R4z5vrxpGkw5tK9jcZlxnit7okGY/42L3grvRN3j27T53m5Z+L8K7ecngtMe+icj2LXlmSDNL0DU0WclOWcrW52tHEbulpcgt27blwM9JWsnOWE4PRnz/bkfX89Ey5+rWEA483rwveXIR4hUV12vDf/XtAz5/l5NIRS9RzNY1t7uGZeM2B/1YMegr2i3MdUOhLW1oGQiPtrZEiQtGdvuKm3XN5qZFT2F+21IGlqHnMRgoQu2IUenOYXb/5l3K3b4ikYpp7NHra9oSPp9lfOdeF9savrorGMcar5SIxHI48nm7KdmVhrH0eHoe8WdfbXiShBxOfJ5/VaCMQA0tj7ohf/k8pe9rBolGt4Kup7gxFVtjSEJJKlpuZiX7tcE2giCUXG0qPn2c0O9ppl2f9b7hLq2ZDlze5vm1K3oTOczWNUEj8bRgvWlopaO4nR/6dCPNj15lNJlh31jKtSUIXJ4kLRtCJWmaD6fMUvByXhEMBDfXFa+KgqIwzFYl1+8bUmOYjDSrumW1rNnkLYeJx8HII91bNpsW5UneXRZkc4s+EngrwaI0mNywiy2UhnRmWXgV/drDG0o2aYsuBD4SEBQY+qHPm3mJ30rq0GAqwbqpedKP+XyR8vG9iPfzCp0I4q1kTcux7yFwONQkkuy3ln3VkG4s+6ahn2i+rHNsLlg3DfUWCiwfTQOq2vJuX3N05HGXN1xEAVVgiH1FUEpe3Zb4teBmV/H1JxFtYeknmlQbFnXD380ykkiyW1juDQJMYPE/NGrHyhVxXu5qjmKforK8XVacRQFmAEPpiHJVY7g3CNhWLdvG0A0Vi7rhYS/ir29Sno5CGgkvFgWeLzju+QStoitdD0+rcQWBtWE2b1ChA0zGiWKza9FKcLep6ceaA18TdyQ/f1MwMR7zskHUgoVqOJYB2ofjoWafGZ4cRsxmDR0t0b4mFS1PT0N2lSUMJIkQaKOpqpZ365oukquywa8UXSF5tSx5Ese0DbTaUedGB4qrtOJu1bCY13w0DchylydYVA1nJwEH2uN225LJlk+fjanbktW84fVNwakO6UUCL5LUjaXEcu8o4PO3GQcHmmoFnUAwmzsb3SY0fOM8YVZWGCUIhGBTt4yk5q5omAaavbbUqev9sUBnKjkbuFC3n0iCRHJ44pFvDGVh6YQSoSSB7zaVflcwzDxmokGGFhpB01gO8WlayyUVZ3HAvSAi8CRv0pyoVTAAXQjq1lBUBqTgZBBQ7FpaYUlzQ50YVCUIlCBtDJ6wBErx0i9oC0ispsFw0NO8LAqe+jGeFpwcey7HUwh2qsbUAt1x9//WxzGzm4bjiY+RFqwl9w2PJyHreUtpDX6hOBn6zBc1/Y7HyVizN5bNpqEjFNvacnHhsdsaelqhhXDv4dzgt+7vv5i1dGPJ26Zgd2MZTzzGQ4+k57puPCSLRcvx2OP1ZUk/kGy9lnCrKLFMhoqH9yMW+4arRcnJIOAkDBhMFDe3Dd2+5IurgrCRnB0HDPuKShnKDXgdSbcbIq1hMatQwuU4Ts49FreNs3YFDjmstWC7cha7PP1V/kQplyNJEsXb1zVh5P69D448d3jyYYDACjcsCAeAiBIJRmCFpa0E6c6pL1LBYKSZHHnECWzWLVEkKQpL01ry9MPtUw8/lKSp4eBAk2eWzbJFa0G3p8iLlnTrSl19H5rWMp56rBYNTeVsaEEgUQqijmS/M2xXLUpLOn1Jtsc9t7BDvd1z+97iew0qSSgygxdItuuW83FONB1QlRbdpOx3DfONR8crqIiwAgrj0yw3DI67GKkxLUy6NfvXN5w+islLxfquoG4lZ8eW7tc+IlV9RLdLGApurxuEEOw2jh4YthkmiEiKGYWMnePD+iT5nCyDW++c0ngcnHfo3/0E2ekhux1qndC1a6pdQT7bUs/XFMGQiZiz8w/AWoZDKF9fEZ6f0E5P8ZLod9or/8dYv7eT/Y7r1/5hygImRwj/N5Td+b7LsGj9D29bL2Aw+pWKkadweg8RhG4AmJ7AfoddzRDLOXT7v7Jw/ZYl+kPYb385rPyj6+QCcfYAMTr45fDyGx/TD2B04Aas/ydru3aUs6vXiPtPEO9eIs4fONUkT93r5nm//Cqefh35tW87FWW3QXzyGTLdYadHMLtF/Df/vcNRf/ePoSpRX/8OSIVY3DoS2WYNx2fw9hVgsYMx/F9/7gbJ8wcIqShyg5WS+NkTsjfXbLaCwfkQz5eM1IrbtQ9hSNZG+KMu7WpL8/hT1HBAvUkx6xVZMmY0VDSrHRsT8FC8h0qz/uQZxULgVxvCbszdBuJORHQ8pqktni9Yr1oePR3w7tUVR7ph1/b53qcJL16WPDoPma1qKuPC8h8HG670AW8WFX8525MIRd2Judhv+NsNfG1kGW3f8+5lTTQdkCiPUAtevyu5fxqyy1vezyvIJV87ifiLV1tWly0fPwtJa8ObK3fSOBxqIi3p9CSmcZVFb74q8RS8LWsOlMeDo5BVUTNMPNKd67UwyvLVZcE2NdjGoKVEact08OG0etdwMvTI95ZrW0EleDAK2RWG08OAv75MGUQaiaUuLG/Kim8OO/zw9d5B/XqCy1lNkVre39YQWh6fh/R7mjiS1IUlxzDMPPq+JpaKXdtyvak5GnnkxhIr9UsqWSAlq2XD9aIhGUqev8/ZFobDkUedwuOnIdoTZG3LZmXxQ0ffmTUVqbQ0taEMLeOO4vXrmuGhIJvD6anPtjZOeXhfEiM5jDX3zgL+/K92Tv1I3UmmCC2zZcNs7+hjnYFkt3Mh/l6suNvWtKJlh8VvYRRolnVL3Eo6QnNTNMSNQEyhV2nKyuL3BHItEUDsKfyO4E1d0PddVkh4kOYGGQoa32KNQ05vKwMFnI58tktDYw0ngY83FIwHPoEQvHpfoJTLvJRYvnU/ptSWh52A+aoh9Ru+O+yxSBuOBz5fbHIW+5ZeqxCAqiXb1JG7rHWWjWgguS5r3swq7p2EvFoWKCG4Nwz4d++2PPFizs98LtMSvZboRLAsGp6/qxiPPdK25ac3OX9w0OH5vuCTsfNjayUJeoJXy5JRRxNphbGCQaB4PivYyxbtCfxG0OlrAi3ptZqfbwqexBGrlcuRvJlVCAuihWVbg7A8nIZMZcBPNxn/6tMJfRS73PL5i4yOUWy1a34fdj2EJ0giRWDgZt1Q9wzFUqCss98lEWRDg5e4QPbRocftdcs8bbERBBV88xsdZkVFLhqeHIZstoZvPIuIewpTWvq+ZJVaVmlD2rSMhUbWksKADS2dWjEeaF5WJWItmJxJhr0OP3q7Jk8tpm+Ra/d+WXdaPhrGiK4hnVtu2grdSjpaImrYziHpCOKppCc0bWzJd4ZBpLnOa8JIuAFCWRrg3j2PfGtIPEkjISwV3gA6oeJlWnCc+KxyFy4PteLoSPNuVfEnj3us9w1VZfB64ClFp6vwAjgNQ35g91x4TtE4TwIePA7411drPj2IeV7lYGBc+RgjaLVhcC6pdoLugSRbGhfnrGtGwqeJDSPjoQcCsxNc2oIkVHRKD2vh6TjB0aMNm3WL30jKssVXmttOxYUNEVKw2RpiJVipFt0RpLuWbqgJa3cgskkbpC/oxxJTCyZ9jfUEqhXEVtFay62seDKNUL5gtW85PvAIpWSrWyZdD2Gc+7pRhne7mvtTH8+XHASaH7zOGHQ0uhZ4yhUZlyEMrOb2pibsCJJYgBFMRx63Wc180fC18wilBenWcHTi8cO3KUOlmSQeJ+cu67RIa0aJYl21fOdrB6RpTlHAxYMApGV+axDSIIQr5pW4fEueu5JgP3AFqZu1QyfXlXMDrJYNvb6mP9Is5w1BqNhtDd2e5Ft/mPD6RcXBkUIpRVm6fIrvK1ZLh1H2fNdlFYbOyLFaOJWjLI2jGG4MH38aojXkmWUyVdSFpTNw1jKLIelopHLQGe1BVVgmx4p85waqurJcPApY3LYUubOv6Q8ll/2hoqkNVQVgaRvLdmWIeiETbiiSQ9ZL10+237d4ITQyYqw3hOMuy59d8mYzRCAI/ZbNXnFyETC/bRnKBSC4+NqYbJXDfkvn/pRN0yWlS2l8EBLZ7RElzjo3v21pW7h9X9PpKdoW4o6kM/CY//SadeeM1RJklVMZn1kaM5FzbupD/F7EoGsYzX5MMTyjFCEyDBm1t/Do68SHfdqba5QE+Y1vo1c32PfvSWLwmh2X/kd0HpzgBb9hf/th/X6I+fX1T3KIEd3+bx5gcAPAbxxgwGU/3nzlNvublbv/LyxpReGa66sSVgvEgycI7L9XAfnF8/ld1i8hA7/Lff8RDvhvXZ0eXL0GL0CUBey3yG/9EfZnfwff/RP48d84StnkwNnoFjPk06871PJoisj3H7pxfOzrL5GHJ3B4iux0HV56NHFqy73HiMUd9u0LKHLsyy+wQiBPLyDuOATz2QOEFBTLlGQQUIVD5GZB4AvGD8cUWUM1WxDbjKo0HHx0QH67olAdjp5OuHzbslvVtISUTUFb+zTNlqjJic8OwQrmVUCy37DdScJswWxZ8/jTCduNK9Q6OPLoBDXR/IYX0uN4PKHeW8RIUOSG6cDjdlszHWqWRvHOdnm3qvjmNOHiKOBqVfHt0w5eJ6K92vL4GMzknBcbV0z29ElEU8Cmaog9yXVZUmwM047HT4qMOFJgBGnZYlPwpCRPLbO8JkwFN1c1cSI5PncnUdd1g4frhSmMQRpBL1Rke8su/HDCOXenhdXeeaOz2lGB0szgCcXrq5I7UXM+Cvjpbcb9wwghLVfLihEeTyYRX6Y5f/s84+LIZ28bbl83TKeum8BId4G5d+jxfFOw3LUYDYNYM1s3VLnl6eOQKnOB30pbGmnZb1uePYrBHY6Sp4Zt1vB//nzPJ4cxP5vnLFYNhTFcLUu6WvK8LhhZTSENs+uatGM4GnkMIo+7dYUSkl5XY0tIZ4arTcUo8ihzy060FIVhrD1WTUueG26zmmplUS2IWnI00azrFrGGCM3etvSUh2wl+dZwW1R4I8nLWck9ESBc1QhnkY/JJHsapJYsvBqjLe1a4CWC/dyijMVi2YuWGggiSZvDpBega0VtWxZRxbo0BLmAGmQu6B9I9mvL4FTTFZq6hcuqotco3m9q0tLg+ZKvPQtZrd3FMm0Mm9wwz2qkFI5GNRS8mZdMhppJ4PHRYcjWbxn5HmdDH68vOEkCvroqeHQW8s2jhLRp+evbnbNYeYphrHlxmzNVLn+UbQxnRwGNZ/j+qz1xqyhC40oKW9BC8MlhxM/e55wfOCz2ZKAZJx6Jpzgce8wXDcexxw9fpRx1fBbrhr7WXPR87nkRN2WNzgXtwFIrSzdQPC9zpqHHSeKzrhpeZyX9xiOrDAMU/VBzOPW5MiXromF83yOtLToV3LQVBx2Pra0JW8WybugYhVSSg4FmpioeHYR8NIn4sy83eBK2i5bJRJMo6drgQ/jkYcTzWUHcKoyFldfw6b2EBMXrVxWbwmBSw+mF5seXOZPAZ9RTBF3ooWgbSOsWr5QcHWruNobhOELtKn40z/gf/uiAcme4peZs5LOvW9RGcV2WxIni1A+QvjtckD4sVMt3jhJm+4aO0vhS8Gpf0uxgeOhRLgxZbfnWg4RRrLm9axBIolgQKcm8bsmF4dmDiG6t8QeCYg5gmDz00Frwv11vGONx1Av4SZ2jreVREvN+U7PwKzxPctwLSPctgw+dNP/dp0P+4nLLp/2EvW0pCosCTh4EXN7VPDwIKFOHM24rZ607VprLtmLc89imltpvOT0J2c9bVGBJhUHsIQgVadOSCEWlwGsl27Ll6f0Y0QqiWrJKG/7osw7v5zWBFmSZRVroBIr7FwGbhSEONdu55f4jH1sIGu3KJIOBYHHb0ok0988Dxn3Nj19nPLuI+eptQaQlpbFkS8PpPZ+bogEr0Ai0FXQCxfdXe05GAaNQ01aWF4uSShj6gWBuWoyBoJB4seDkxOPv3mZ0fMXJMGC1aKkrS2+qeHVX0is0nXuS47HPZtmyLQxpbRgGmuEo5u3LPaORy56UuSWK3Wu031lHyss/FKgGrrDS8wWbdYM1gtGBAzRcvq44vSfZrODo1CfbORXH992g0jbQtgalpIO2fFBXqtKSdBWDkUIrRVN+wDl7guFEE8WSIBBkHwL/QSApCnjwUcDNpdvcX72pqErjqIeVZTDUzG5c7ibpSooUxoceRepokgLLdu0KjpMOeFrgeQI/UKyWLQJB0hFUpav4mx579C5G3L6vSRKJxXUUDYeaXQpmn2KDiNurkrTy6fQk69TnwWDB5TyiMxC0jcDsdqyqHkGxYLH3qaMRWaVZrxpMa3nwJGZ2U384nBMEocsh1bXDVreNJfAVaSbY7Sz9aYItciK/5d6zEWWrefe6wusEHJxFrN+nHD0ZURiPzQYGvdYpLss5G9slmr9GdLr0o5r21QviP/1TssWe9v7HrF4tmE6Fi1X8lvX7IebX1z/JIeb/7RKe51SQgSN7icGvVBbR7TmS2OGJ64D5/l8gPvnm7zx0/FNYQkoXqtfKac1Vge0N4PY96qNn2OtLkCDufeRyOh9/6syuZY48u+9eGyHcbVXp8jW9gXvwMHLI5bZxuaLBCHH+EBYz7OgA6QcuO+QH2P4QsVogohg1HlHHQ2rj4XVD1KBHEHkUb65oR8ckJ2NWC8NJ+5r8bg3njzE4f6vfjxjvXtB2LGJn2NYl/ZMzdm8W6OkUUTdoNlTeiP75iMwTdO6u2c1T/HrDV+82vL+refDZx7zLMqaxRxJJbm5roqGkqzQ5hrqA81HAIm94NI7IK8O9YcjWtjSpYZVZjBeS+RGmhttNgwoFSgo6oeLk0OfzLzN8Kfn5uuAo8jAhVHvLzms4SHykL/GVw1jKPeyMYeArHnzkThjfXVc8exTjeWD2cDzR1DUsdy2Elknf4/37ikgoAqn4xrOI/+Nui2xhNFEsN5Z/9mnCj25SRtrjyWnED69SWm2RtaPXbJqWbVYz6HlsNw2xp9mlhsOuRmuJFZbuRLK9s+xyS0cJMmN4dBxwua6gdpjgt1nJRHt8cZsTRxIt4KubkuGh4t3biuWda+v+0cuM0ChUZBARjrrleZx3fFJrWeQ1t+ua2EiqBr5z3kE3kuW+xiJ40A3dae5VTawV5cYSaGgiw0h5pHnLfm1pKsv7siLftMTKo7EGhbMrFUuD8S01Bq8rEa0g8dxgmaWWF35G1Cj6tc+2aTmNffaVwZYCKwyVtTw68DG5wJaw0BVNbWiMOwXvR5pMtDw9c/0wtrLUrWHWNnih5EIHyECiteBnpLTGMvE8egcS3wgKoFYG3XNhfrOHh8OQv8z2PPIDMt1wdVWjY8FJ10cjmdc1p0OfMm8J0fQ7gnxnUT7k0pIkilfrEipIBpI+HkoKLo4Dns8L7g9DvloWhFKwXLS0ChIj+cZZhy/SnB/fZZxFARf9gEejkG5H8vKu5OPjCGrBF9uCsCs4HQWke/f693oK7Uk2ZcvPZzmxUIRWcN4L2HcM50nAetOwLlsOhx7P9wX/7bMRA6n58TKlH7lT2chKkolGZIJxR/HoIOTNvmQ00mRNy3zesKJlmdZEpRtwPjkN2C0tVWDwpSAUmshK4qmgquFs5NOUMNCa//TjHptrw+OLiHJvSfqKW7+mUzokudKCy2XJH3+9xw9eZGznDckIuh1BUQvqFYxGHnEjObinuds1/NHHXdLMcFvWfHqR8PA85OevcrLGMFsWPO6F6FowGClUINgXLUmsSJeGd8uSj4Yho67i9rZhbyzfuBeTh4ajyA2hRd2SF5ZuTxClkp9WGYeJj4/AZLBetegETsY+b7cutzQ4UAgjuIgCNjQcRB53tw29e5JEaC66HrvMEFWK734z5m5TM7KaMjSsTM1now4365qerxAI1n7Dt05j+tZjZ1uWVy2ffZIgFVQWlBD8PHfqTMeTyFISJxJdS9CCZxcRr3cV3/4k4eamQiuJtILwSFBlDkTQSMObpiTqSDqe4vvNjlPpM619UC7voJXkJq3p9SR+JTk/9/hyUaCNpC88fA33Lzxeva84G3t0B4rZbUN3ovjqpmQaaCbHHqt9zftZQ/+DApIkknVtCEPo+ordxvBVk3O/GyADwaPjiL96m9LvKsatx8uiYH3VspctJ57Pl1lJZyLwWqeGTU81P3qTke8M58c+XaXIUod2f3VV0hsoZCWYnnrU1pKvLUWnpV6CLyRxFLBZ58QdzWbV0hsopsc+nueyL/ce+SxmjrrY7SqSrrMb16WlP5JgHUo+CFwzgpAWa1xnizWC43Ofw2OP2+sGrZ1dLem6PppuT5FlluMTh1TOsxblQRQrko5CCEv6CwWltihlsdYhlHfblrq2LGcNAmcbGx9o1gtDkkhub2q6XcX9xyF5bjCtOwAzjWE1dzjruANhqJHSEsWaIMAN0iPF2UWEFILVomU4kew27tSsrCzjqcIYd7hnDFBVkG65K3sgJHGi2O9bAlETDBKyRc6+ivDqHQ++c8D+i3fUw2OklJyceZSFpSxbytziB4Lt2tLtSXpDxavnJX7ocrJVaWmMU6WmFzHZ3jD0d+xzDxmF7Dc18vol6uCQkZ3T7DN2+oDgYEB6vWJjB8iyoHfzOaKuKY1m9OkjslXBMKmQH39K8eULbpojzuI5ZnyMN/ztB+e/H2J+ff1/aoj5961fqDtCaTg4QgTBf9Dv9x9ktY0L2O/WECXY7/854g/+uSvpfPUcqgr1n/xnEMaI5QyWd4j7T/7Bw4iTCzfM/OLXnu/6ZIT4teGPpIPYrh2lbLt2A878BnH2AJvtUZcvyA+eICQkw5AwdkF4b3PL2g7xfEHdCtTBlI7KqLsTpIQglESRcqfd6ZbufkH98CmH2zfUkzOqxnJYXvHKHNINXWswnkT0BtxVAVsv4XgyIBpFKOXTZBWZMNw/jnh7WRH3Xc5jWxrGvmZZNXwyifjb25SPTkN8I+l6itvbmvey4sl5RLo0XN5U6AiGfc1i1vDofoSSgtu7innd0lGSUCsqbRhpV9J3taj41sOE+bxGpRITWcIh5DvoRor9zrBvGhrl0KP373tcftmQ1wa/a9lsLbU19Iym11WkvZb705B1VfN2VbHatoRSoLqCu6yBEk5in3Ag+fkio1qBsRZZOKHxex93Wc5bVC446ns8OUvY7g1eKLha1/iVYNjTZK3rE9jeWqrMsNsb8sCw+qJlJhriRvPxecjtVYv0JGOhefokJJWGOJZcXtc8ONH87W1Kv3QWOjKBDS1mbxnmHmndIo1kFGpW2wYjLItFS3sHgw/+82rt6Dk6gNuichfrAvaZIQ4EZWkZSo8sMw5NWVo8q1hnrqldCsl1WjG4UExrTRNYsJImt6yrlouOR24dUWxDy75quf2/2XuTH8my7Mzvd4c32rPR3czNh/CYI3Koqswsljh0t8gF0QuptdCid9L/p4W2WkgQhJYEEWBTRbLJqqzKOUaf3W02e9MdtLjOKhLsIpsNQihBeTYBBMzNHeb+3rvnnO/7faKhh2LVGCyeWdOSNopb33JRhy3RRMXoSLDxDhGDcoL1zmK1Z6AUa2U5OUq52DXEIhixc6Epuop6I5jvDIN9ifGwlI7beUsmJUUsOZu3xFrSrTVqINg1AXBRtpaDOOZq12IkdFvJurHUsef8rOFff9yjrzT1nedu1WIFRLVASM/bu4Y//qDP//TVnI/HGd9+W1N6y/Te2bM0hkRIjtIYo4PB93Zm+PnVjukwRkuJlZ7VhUP3glFYtiGVfG4t71c1qhVY6fnx84LvzgOqe9tY2hr0vsA2nkk3xjeeq5uWS9+SGcXcWw46oUl73EkY9yM0gkEa8X5TM18aLleGdXO/FWoFw0KTScnljaHbV7xrGw7jmGkvYjxR7BbBrN32HM0dvHyWsryzzFeGJAr5E48eJ1wvWuZLw5UJmU228qSporCKcut4sJ9CLej3FLcLy8Mi5q61PJ6krLzh8X5Ks/G8Wtf86HHOq0VNs3bM5pY8EfzoWU618WSFohdHfPWuoptLqsRiViHbKIslFZbtGj77YYdX84rd1rLaWB50Ex4/TFjeOJrGMRCaQazxmScjZDg9PgzBjrdvDU8/SPjgqMNsaaAEk3vUVvLhRymT/ZjtznNxYRBWUGaW8VDjFpK4I/jluuTTk4LrpuXxJGNtLUtv6LuA5z6caJbXljNV8yBNucPwgycZHak4tgmv2xK3kDw4jfluXSGU5+g44WmW8mZdMU0irsoGUYJKBP1BzGEecbkxvNvWnI4SrjF0veS7Xc2P9rtksUDknqrxDApJbyC5PXfcmZaxi1jfOurU8WQv43Aas5k53m9qEq9weYBmdFKFjwWTJGI4Vry9aImsoKcl371teH6Y0QpPtXOcPI2xFZzPWya9CDuDz693JJEgjgVl42m2HreETkfhGiiOJI/GKcNEE0fw7CCnVI6kFUgrMDvBwaFmtrLYgSO+U6h9x0jHnC1rJsOIL15VfHyasds4yh1IbbDGoyPJk+cpbRuySg5PY4SQbNaW/jDIxJoaOl2FVILBXkTTeJJM8eh5gmnh4ZMEKSWbleXFDxJmN+4eUBr8jG0bAoK9CxLsTqGIY0nWEezWnm5PU+8svaFkOApERgjNgrM+5F+58H+mDUHHzoHzgm5PY53l3ZuW4UihlCDJAnhgvbJYG5qggyPJZu2JI8H0OKLcwcFhgMfUladTSPYPNOXOMbsNxLJuXwV/Tic0L4tby/GjiLtrgzeWSDhutynDPYVtCcCX1vP4scBv1uhBF9N6NucLOnLHJh6jNGzXjuWypalAa8dyHpDTaSa5vWlJszBond8GyWy1cySJYLX0KOlRUpC7NTcLRWKWlNGI5+lryv4TvflJAAAgAElEQVQpaeKot5bb84qom5Fubzj+eJ/LZc7YvKUZP0HVO/JHE1aXO842Azww7mzxSU5SJKjh8DceAb9vYv5u/f+qifnb9Zvkar/tJTpFQEKvV9AfITYhSRbAn70NZLbRfoASfPmz4NPJOv/Iu95XVeGlBO9/1eCIKELsjQO3/OI9DEbB7H9wdC9dm2KTgiyXbFaOLJf43RbpDXrQpzdQLGct9dszBs+mtC4KCdPR/XToYMDt1xfU0z0O6y39Dx/SWEVh5qx9j1ZF9AYKF3kuz1re3rU8O0kYJJpy65lOYr573zDtCr4ra57upTQ2mIgtnlGm6eSKSAp+8b5k2ovwqSBtAvf/3azFZ54iVgjnma0tp0VCWgguZobTSYxSgs3W8e6u5oePMn462/BZp+AKQ89pzmzDOIrwG8HjRwk288yuHAdjzduLBipPchDQkqs7yyiLmVmDF452I1lULVMdDinT05h1a7lctxhg4wzbref5KKVdefJIMYo0m5Xl9172eH/dUK5cIGVpaEpPlsHdzFBvHZud5YMnGTfLBraCpvFcbRsGE810GIJbm5XDVgKLx6wcdDyilExzzXJuWCwtRSRZGsO7s4beWHL+rmWzNJw1BtlIIiFRDlQl0MBiA91ekBRIIUilwEjPcu1Y2pbeSOEqQbnzbGtLkUqO9iNq4+/NqGDwbKQjGyh2C0slHS9fJmxuHbGQtG146MwqQ+IF7dIjpKQtYbUyxEKgDbhWEnuBVUHC8KhIOY8b5A6GKmVRhb8V1UqubM3xMOagH6N2kt5Ek40l65VjvTbs+ZhWhI1ANlQIA9vGMenGHPgYUs+laRj0NXe25Q9/0OOnX20xpSUvJf3DiKHQDHJFU8BIaRINUSNZe8PDPKWMPGMRcZgnXLuWM9PyRwddtsazvnUIoO44ukPFEI1PPMpJyGG9s8zqlttzQx05fCv4Fy8LMqWY9CPa1BNnkk9PClInSbVkWToOiggEvD1vePoopdmBl2C85911zXQc00Hyf59vEKnA4Smtg57HrwXdqeSDcc5s2fL2uuHRUUrRlyGrpdBYAZNU4yJ4Mc6YO0NcStKpwDewqi2ZUvQSzUFPk7YakQtuyhYy6DhFZyx52Q/koPXCMZlqXA2m9mxXBqxgu3W4yFNkiiQJRufZTcsvypIfDjrEhcBs4LifsJq1tN7jHPSGmvPbhkiFsMBnL1K+ua34yZMu382qEBbYwl/Mt4gKei7ifWl4chCTSsmb84Zt5OgPFUkj+OJ9hU4ELpVMdcR3Vw0dr3Bdz59er4Ln4Mbzgyc5xycxArA1lFFANKuu53CcoKXAZp6HRynzW8vkIOJkGoZvK2sg9nSMwlvYn0Sk9z6yyUTTbD3pWPHl64rfe9LhbN3QLRRl63i/bPjvPtnnu1lFFivGg4g3q5p3Vy3Ww5OjjLr1TDoRF6UhaiX7Q8Xq2nGT1yxugwxxGGmOjmJwYRO4do5uV1HEGlEIfjDNeTBM+OV8h8PTiRTvqoaL1vDDbkqcCUY6YtFYkn1B0gY/CKXHNRLTemIpmbeG54cZdekD+bG1dAeKuvSkQ8nyxjLqSnbScncWslCeHeZcbFrWK0uyJ3jQT3hz12JKWMWGrJH4RqAGgh8d5pxftSzqlrL29F2QZA4SzWSseX1bs1dEZLVCKUnZWKq1J0UyGkQkSjLaj7gqW2IkuRJoq1i2hmgteLWuyYRAm7BFMU2Al1RV8JvEsaLcBQntYKipK4+KggdFKcALjh/GpKmkP9R88bOSoweKcuNJEsFwT/Pq65rpkQYkWodFxeFxxOzOsFqGZ/P0JEZqwWAo2Ww806OY1oQGom4c3grcPWJfRYK9fY13AhUJ0jSY6rMcdCTZ7Rz7B6Gxurk0mBb6A0mSaIq+wBq4vjBkueLwJGKzCpK5poGmguG+5uq8pSw9g6GkaaCugv/H2CBvk0KQdyS7nWe7dAwniqaCKBZ4J9iRoWOF1pIkVSGU02ri9R3eC1ZNTtJNaO7mxOM9FmWCdwGCsVp6ul2BNQqtg0y6rkAApg0b9yyF1SI8Zxbz8BluV47Ka5J2jYgjtnLAYW/LyF6zutnSDI85+Xifq2/XnLqvaGXGaP4lF+UQO19iBgfUViGdJT2dcvt2Q1FI9vYk9uoa//IHRLH6jce039Ym5nvE8vf1T6vpCWK9DBxDwJc75JOXyKcf/Po1zz76exS3f6jE4cm9s+83IP6evIAvfx7gAdzjqVdzil5YdePvX3f5HqYnFD0FixlT84aye8Cyyu4RkjbcyGpPVTqenygW796RH4+pbEwcwWZWk+x1efE45e15w+Wrln4kSVvIIonzIeszzSRHz/Igm9mEhOLHxylxDm+vWopU0emGoL00lpx2E85ua2a3hjQT+MIxNJoYwRe3FYNI0e9Jrt4aZA6rpeGvzjf89GrDMNH86fWGvY7mdm04EBFfbUpe7qd8+7ri5Dim21c0WzgaxLyvWqSAz89KhpnGWUdbBirVVltsH/7D3RYTB2pM3IM/ebNC4Pnp+QbhIYsVN6LhSrcY5xnvR6jc0xjH/KZlqmI+Pg5G7G6m2Y8jPv+qYuENYhCyYf63Xy5pNp5WO+obR6IFDw8S7A5cDTtr2ZSGOJJgJUmk6KWC+bbl7ZWhbODxg5jVyrIpHdUFGBxzY3mzregpRbk1KA9eem7PPTqBhbPQCLqRZFU7WutZbwzZLuKjhxnLdUio74w1lXGIKCSR161jJltyr6iNY3HTsjWGSMK1snQKzW3TkDrNurY44fAWslawawzLrSFVsO635CjWzmA6jtgLVC24WTY8I+M6qzEuIKSHZUSrHcMkwteClbU03lFtLd2O4rKt6XpFGTua3FEWDms8LvNkHcHxKKJWjgxJN9YIIfmdUZf/5edzkJ5Ca3a153Cg8YVnpCL6HcmrVYVpBJXx5K1mFGs+HmYs7yxJBJO9iOf7GevYMRCKqAB68KOjgkhJ8khRKc+sbSkbx27n+Em/y4O9mHLh+XTc4dtVRX+geHfTME3/1vBGBNzx0f32dIBiZVtenmakiWRTWv78/SYgWReOP/3lht990uHTww6JFpz2YlKneHmUhcAIYLkxFKlgOoz5s+82JFnIK9kzmlJZfnCckSQCextkg9+cV9xYg4nDIX7XGlIU00Izmxtcz+NaUAU8i1NM63nwKEHr4D8cjDTjbhxM8NbT7SryKGSa9IfhIBDFgoFWPHuQslt6urliXTUs7xyDVNN2PfPIcDqOyfuSqBCY0qGloIgVH05yJpOY+dKTtJKpitkmhhcHHc6WDRvj+PBJxuMi5XLdcHgQk2eK85uGgyzgbR9NY25aw8paRi7id4cFeSxZKcvXs4rlwtLpSnq5wmvYGY+yYWKdFGGrNNzXjPZ+7QftpoHKFQnxq3twVTpeHKdc3xo+/aCDXcOT05gvLyouq4bGeZ7vpfz+ScH5uuXZXooHbjYtv/+wS5M6ysRy2I0YDTSLlWXqIz4vt/xsvWOXW4wI3rHHaYaWktudxXjPh5Ocm53h44MOk27Mf/vhCFN7Yid5Eef8V08GkMJUReSJYF8nDAvFd4uKsnF0neTtVc1XbytGA42UgqcnKadHMVjB+9sG74LXqpdrxNDjGlgIwzJy3LyyjETMfk+RdgXWeeqVYzqIub2zvD+v8Q6QntncYUoghuNeFOAc3jNpEx7FCb6W+MwFSZZtGYiI3a1jf6wZFYqLC4O1Dj2UDAuFjuCrb0vybrjHxIni+DjGO0/ck+w7jVuFv8X4PsNntw3SrM3KY21oaJoavvuqpq4sWkkiTQjeHCqUDo/Y3dayP1HcXDiM9Wy3jov3LdZ5pg8SpIL+UDM+0CwXluOHMZNpxNGDmCyXdDqSs3ctURT8MklyTztTCmOhbmzAJDtABBy7aTwffpJx/DCmbQMZrehKFneWq7OG8TTi4dMEawW7naHcQBxL9seaolC/yo85PEnodsN12bQOJQXdnmC3DXK2/ihgpotC4xwUPRWudaDoScYHEUqHY8/dUrJeQ5JAnAimx2EL7pzndhWx2GiUBp1KyiZiLfocHGqEFOgoNHJ7k4g4CffCLA9gFyEhy0NmXF0LpApYZ2eh6MpwWvcw2I+RRY9cbNlcb3h9nVG7hOz6W97+u58TdxTxoIdMU26K56gkJpnuM3i0Tzf3yLbmbpMz7jYw2IO7G7JHU5L3X/4nn9l+m+r7Tcz/y93l/9dLKAWzW0SahRyat98i7kM2f/Wa9Ddj+n5jLWZ4+I9S24SQ+JsrePAoSPIg4KJnt1S6IOsIytIT70Jopj97A84RPX7C7M4yGGna1nNzaQItKxJEkaT7+IiTSZ94b8hmbREXb2hHhzQ15LlgUER0u5IoUizuLDeLhtI5on3JZun44dN9vr1bsp45tjtLGVuud4ZChAyJOvFgPSdHCXfzlvXcMRlHxFoQF4JXtw3aQWU8w1iTCIWJPX0Uny9KDqKIpCc4LhLezmqEFehW8MmLjOtzS6eQXFy1/M7HBUKI0KhYy7tZw8fjjHLruK4M5+9b9jqahbI86CR0O4pWeAZG8/lqhy4ktXHkseZH0w6jVFO2jk8OC/7ycotcSH74JEO2km3jOL9pmY40qyqYwv/whz3e39bcrQwvBhkHoxjlYbO17FrH1bylozSdgaKcecrEokpwO4hVIKn1upLSOsRW0DmF9TxkZnjjKVsPVqJEIIItfMMw1VDDauOoGk9nqqjn4DW821QcFpq69uQR+AiKWFGvHRczS28E2znsH0oGSnG2tMQeSERA6K5bZtYyIaF1Hp1JNrVluzPQhu3O/2Hm7DUJ0ofpoBDghKc2nrLxaC/oes3XdscojtEN2IGnO1LcXhk6QlNZh1Kw6liKjuJQJ5TGoYQAKyjGkss3Bhd5trHFR3BmGw7rhOl+hKkhzyR325DXsMks//azPZrY8X++XrHnYjpSIRO43Bh++CTji+9q5nXL+1WN8bARhqFRjIYRzgmaNkAF9gYRw1RSG+hEktRK9vKIqnQkTnJWh8bkP8x2PIxSVmvLs9OUi7uWQV/xwWFGKRzr2hEXErv1CC8YdjVaC37xpuK0F7Itzs5bhqcRj4Yp311XbJXj0SDh/a7lYt3QKSS+FDwYxSxqy14UcbszyEhwUER8eVGx3jhGfY1S8PZdwy620IJZe8oGHg4S3p7XVK3nwWnCzaLl1oSgz3GqKZWjnnls5Vlmhp88KohqQeXD12adQGUzFrQK2v+qdBweRLxbNrgtHB5FXM5aJsMY03qW1pF7hdSw34kYdTW/+HnJwUGENfDxy5yDjma99KyFY7KvOX/bkicKEnizCLkhs7uW017CedSQWcnvf3jAk7FE2YC97Q0UuhZc7lqiVnDZNBwNIi6Wlu2dhS78m98Z8t26pn7rGT6WvJzkRK3g7aLhcBSTR4rzumZWG6yFhbVMi4hES+JYsl7aX9EBi1iyl2m8IUBWSk9VhcT1NBO8uW7IBvDzmxJhIOtJ/s2LEQ7B+brhetsyLiK+uqtYNRbj4F897PFkmLKqHOvG8smDnMfTlFGu+Z+/mfNu2zLuaHIp+YNHBV7CXqK5blue7qX8+cWGx8OU/Z7m7tYgNByNE44PYgaD4CM57aa8zHMwnsFIceZbPn3S4ekoI7KCq22DSASpFuwd6YCoP2tpHOznEcudpT8W3N451sbxwTjDlx6jHN1E4Qg+orK29DLNRx9lbLaWOZZIw+3ckJaSOvcMEsnRXsJiaZl7QyoFqRN47dksPKePYj6/KnkySNluHdUqBFSe1xU9H8I4/U4QZ5KFMdhG0BUKHYXwy2YDG2nx3nM0TZgcxEghsFZhbUueK3Yby3bj2NuPWM4Nwz3J5blht/WM9jWrpSWKwnak25e8fdXw4FGMdZ7ZreXx84QokkwOg/cxyyWreUD7VztHp6vo9hVRHGABVeWYTCP2JhE3l8EnFsWCcmPp9oK5fTm3jMYaQdiEjCaaszfB0O9MkKIWhWZvEoUwyLFmu3ZMjzWLOwuE5mow0igtuHwfqIRKhuaoaRzl1vPgccLdtaM/lNSVR+sgH4bw+eW5pFMoNiuLjiTGhGvNNB7rgqzrxccZ1oUNatt6thuLQ+CFxsqQbSatpRVxGKLOw7Q1TRXOhmZ3f6K4vTTEiWe1CMGcUSQwDhCeage9gaSuHWmhGO1pri4cUbsh6aXo8R7loqLqjDn47Alb1WOgt9TFAfb9W+SzDxmZc2ZNj47fMOh6ZpuIWuZMkgVrNaT36s8QL36AOn3y985ef7t+Wzcx3zcx3zcx//RazhDPP8IbA5vl3/Wy/OdW3oVvf/l3Mnq8978GIMzvEJv1r6lvs1vYrokOxpQ78LMb6A1QbQnWIqbH9+8RjIhpKsPB4/7m2ulKdhtPOuzcv71Bblfo0RAh7jnz+5reQLOYGfJUUW88j09TepHm3W1DLiNuViV+63k4SejpiNparkqDaT0ygr0kot9RvJ83sAM38vgSWqCsLe9val5OM7SVnD5JaGOP3gi+2O7opIonk5R5Y4nmksXCcvow4vrO8oOTnC9fVeyU4/BeoqiF4BdXJb/zrMOrtxVawXEnIU4kc2WpcDw/zPj8dcnvPS9oNp5BTzHoKT476pIZhTKCL+5K9oqIT6cdbq5aNqVlsB9BLRA9x2LpiLwIYZRrw93CsDKWvtV8/DxjsbUMM831zJBrTWQVSsHBRCNTUBt4c9mAF6RdRVVarBNMHmrK0jObGy6ahkGiWc1CUOG8bWk3sDEWlwt2c0fjPF2naRPP8tZSdBV6BEWkyLqSxa3BOYlwgtZ4SmNZtS3bypP4kLoe9QTtImxwbk2L2YRU8Y6VeBk02SqFzzcbtA+HeethuKfZtIaRi/giKknupW1GBYznXqLZGkfHazKCLOVWGN7PGlKhiJVCujARHO5rysbx5GEMd5K5NbTC0UkUzdZykbQcxTFz1VIbT7bTfGNLVCW5nLcMOoqt8UgvMDo8sJ0JhK/l0tLvas58w/zO8eEw50En5kYbMiGC0XQBMobxMCaWgrfvDVpA2wiyjmCcRMyM5eFRipDwelaTJJJvZhU7a3ixl1KrYJ5fbSw//qCLbWC1tUzHEQ+GCe9nDY8nKcuFpTaWq3nL0TCm2njObcO/fN7ji5uSdWM5ymJ+uSzpZYqxjviDlz2mezF3t4ZSWJYzy+PDhFQrvnld8WZX85MHBdvWcbVoeLmX8Xbe8qO9DmdrwzhT9AvN9brlwSjmfN4yN4YPD3N6UnG1blFG0kaOjpdkhaK0nnYFo67i2aOM+a0JzYIWlLtAPSq3jiiSVCtP6S2JkOys4+FJwuu3NXtjTVU5NmtPaiXLuWW5tBwcxPTuJUnWgI4ETWQ5vzA8OEoQ2nNzZRlnmpUIuSYbLC72dKTmYFAgdcvsJhz4tmvHrrZ8c1lT5JLHJxn1rccmnoOJJpaKm7khtQKXeCZpQqcjqXY+XAMdST9XNDPo7isO05iTvYRE/1qo4ZxnswqG7yiSrOaWwVAFhO+NoegqhnuafldzPIk57if88mbHv/1sn8ttywfjnF9c7/hokpPFihf7GZ8edpBC8GpeMelE/OXFlt857nCxaqmt592qJo8ll+uWo37MXqZ5u2z44xcDHk4SvrioiHPBqg5SxzRSHHZjXm0rXh7kSBEm/W+WNTscWkE/k+wfRNQ1ZJnkR9MCrQSdjiRrFH+2XPNHL/pcLw3rnaObCa5mDcejGLoeawTrjWU/0VSVpVx5nrxI8R1oFuAN3CwtH7/M6BSad+cNrfHshEM2El0K2qHjRKccnsS8XtTErafaemalY9rTRAeC8+uWmTM8miTkSjEaBZTwunLIRODxiDI0rAdJRCs9hVZcnhlAMBgGyePZ3PD0JKFtYG+ikSQslxWnTxPmM8ujpwlCweWZoehpoljQHQSS2PggZrinubkMwbRpLjg4igMIIRLkuaJTBGN7kHuFbcTNpaHoKaJYIKVgtbA4D8ORJo7Dds8Yz944Yr20OMLmYzGzHBzGNE1QCOw2jiQN1413oanZrDyHJxFppihLh1KCTqHYbhwHJxHVNtx/O11NlAgWd5bhfsTJoxihwpYmywVKS56+SMgyRWsCTKDbD81K03jyjiLrSK7OG/ojTbersPe5N+l98LGQ/v6McU9Ti2BbKnQaYU3wAj38cECcCjYrR9uE+/2jZ/H9UECTdySrpaHcQtEXlBtPb6gZjwPoYDn35J0gc37xUcbJw5T5SnD0ss9mIxFKYN6/J330gIOjmKaC3Kwo0z3cdsvytkZ2CkrRob284qIc0ckcW9/BxD3iV3+NmB4TC4NVEfIf8Gv/tjYx38vJvq9/evnQYPD2W/hHuvf/1BJJAnWD++aX+FdfB1jA538Rvt3ZGzh5FDoSCKGbzuKbBvn1X+Ocp8eSrS9wVxe/amAgTE1PHoZ19tX7lsvzljgN6MamcdxctczvDL3qAn10yN6+ZrMOU0epQgPV6yuqyjMYBHTkYKT54cucq23L8wcJtfaUW0eTWLqZphNJWu3Zbhyv35Z882WNNoLhJKInNLetYbe1NNYxtxZXhZTin/9ix82i4Vo19I2GOBigp2lEogRNbsi94mZuMc4TG0EeCe5kS116ZrahJ0KC9U1t6GjNcF+x8Ibff1YwjSKuNg17ecQoj4gPoDCKs2VDW3miCAYjRVt7zMYxv7MkA4nIwa49O2mplgJvHH99u2NpHI+nCWlfEA8FvVTz5n1DgWJmDIkRuBgoPbmC9a3h869Lzq5a9rsxaaTYbQzWe6qdZeI1qQS3hq5QLCuLUFC38FbVfNfs0AgumoauVkxEhMxAVxLh4Z0peb+rccaTRYJUa1rn8JmnXFuuOzU2AxzMk4Z1bbirLN7Cza4laxSzZU2jwjbEtpD1NK8WFZ8mXdbehQRyIN0pjmVCXXge+IQoEvgwCKQfaTbWESWCbq5YRkE6VrSSqnFEFt67GoTEecFf322xeM6vDXEumRSag0FMew1xIXk4SNjvaqSX/NenQ3ZY1ktLRytM6rncGLx29FDMloZUS45UTIzk8DgY2D876lArx+mjmOXG0s8VuVLcnhn+8He7RF7y+astUsPTo5jXy4rzecPqwpKmEhkJfv5qx1eXJS+PM+qNw0SeT0YF/+PnM8Y9xXYTfl9Z9OvHyqSI0TL4sgD2xpq/er3jtBca76IDLQ4pYFYanIZcBjqYqODJSUAuv1/WbCNDUSucdjQbKDLJ0SDmj076VOsgmbu5MkRWcqg1X9+V/MtPCz77OGe2Mzw8jlkvHUp7aOFhL8Y1hBR469mzmrOo4Y8+6oWmNIUsU2xWjuPTGKXDoThJBct5mCRbC71CMT2NuF0agJA30Rr2s4jawfGDmKMHMVEsmE4iZm3L9Cimrhy7jaM/ULhaMB1H7HUjpt2EXc+GrCAvqaKQTh8vFehgct5uLEIGQ/bMtVzctDxMYi4qw5NBzHVrmOYRO+kpipC9sRdrlsoxPYy4vTJ47xl3Ii5WDQiIMkGsxK/luX+rOoVitK+x1jO7DX/PQobf6emThP7w78cPPB6k/PRsQ6okm8Yy6URcb1vudi1Va5FC8JOjDg8HCbX1/OGjHv/rN0sQjq/vSpwLpvuTXsx//8mEbRNyfv79qw27+2fBMIv4q4sNH08yIin45U3Jsrasavurn6NsLS/3Uzbe8bpp6OaaYaLD9zWOzcrS7Sk+/izng9OMP7teI2JPPhBMBwk28vz0YkPaUwwKRRJL+lPFpnZ0h5IOOgwIfpQhPXz4KKNtgmSqSBQ/PO1w1IshdyyEYWw0B0ean3+9Q1pPjMS0kAzAWsknDzt8sdzxcByz2jg0AiHg6qwl7wpE5lnvLBerhoGRXNwZ0lreZ6CEBmByGPH0Scoo0Ww3YUvw3Zc1N9cV0+OI1cLSLSTXFy3nb1uefRi8kf2hIssUcRSkgp7gIx2ONUmqWM7D5yrvh4txIv8OabXTVWQdgfOexcyE/JgsgAvmd4b5nWExM4CnbS3bjWV/EnF7ZXl6n++1P4lYrywnj+IQdHkQkWSCKJZEkaBzLwsbjjQIkDI0Mt2uRkUCISVJKigKxcFRTK8fMNHdbogmePg0ZXYdTPRSBdyytRZn4cnzJEgHW8flu5Y4VQgf5HjLmeXx85i8kDx8FrNZesqtRwp48Chh+iBBSdhuDP1RuG+sV+Fe/TelNCzmwTs1mSpWC8/4MKKpg1StKqGtHYu55ebKgQjyN2NguTDcXDUICV/+rKQsHbdXlmzUwbWWxV1L0ZMgwDuPePyM4eIrclWTjPpUusuR+Y5qa3j+YcrEvOVWTNnKHs3FFWX9m/0wv831/Sbm+03MP72UgvUS6gqxN/lne1t/+ABur5DPPwqysu4Af/EOUZeIg+OAY765hPUC8fAZYjzFv/4aqpLaJ/RYMouP6PR/rb+v6/uH/toxHGt2a8tmFTj4SRqCBQVgZzNMMWK3dXSKkC6c5pK2CTKJvUlYT+92AckYKcnKSprbBtt1XM8NMZIXJxmb2iEa+PHzDq++almVLcfjmCp1VFuHryCNJJ1aM840F+eGqvBsvSWuJN2OZH8Y8e6rYIhdriwff5DRQ/Pvz9eBnGMNTQXPX6b8769WPNyP+fJVTZ4Lzlct1c6hM7hetjw8SBgUEZutY2YMH0wy2tpT4TF42pWln+jA1BeCVjiuGsNHxxlvFk0IB9t4ukPJu5saieKDUcZl2fBfvuzx5XWFbSBRkqqF86ZmYQyfPcy5mhmQcHgcc3vt8LFjkEREArq54l1Sk68V86Ll8sIilGBbOzbe8aXbMUATIegWipGL2bUOJaCLZls7lqIldjJs7QroC0XZeDZ3DhlJ4jjw/zd1oCWtdo7MSsqOp7EO0YoQiNgIdEdQtR6fgG4lO2eZt4ZxL2K7dORO0VeapTdkIjzgXQqxF+znMW3jeO0qFt5ykEYUcXU882kAACAASURBVMROGlrv2VpH7CUvH2dsFo6DowyVWAYThdpJxMCzP45IN5LhVLM2hqrxTHsxlfd811QMjGbdOt5VFc9th+XQIoxn1FNcbQz9VPP6vGazNjydZgz2NH9+taFIFcd5OIxRC67rlqM4wkjPrLR8+rRDch+I+H7W8OAo4ZtFzeOTGLOFYUdjjGeUa4Zp0Km/XVVkCJwQfHaa8/m3Ncu1IRpDbSFx4d88l9Q2wB9EFeRGX1/XvJhm7E80f3m542QvZtFYfu+kS6ElN9ctGkFlPS8PMxaVZds4Xs1rjvOEVWVDCOzSUfQkyyqkoF8tWlZ3jg+eZczmhm3jef4gJdKK81XY5C3Khus7y0dHGd99XWOtY1M6lJeoVhBPJM3W82iSUDrPg2GMt55OoVgvbQihM0GSul4FL8hwXxI7xd2mxShPvfGkuUQ7wdFEM8oj2sazWTua2tMqRyYDrj6KBW/vGvbziINBRJJIklTy+rrmxVHG5XlLlVvcFrp9TTfVrJdQbYMn8S4yjHNNR2gudw2HSczX7ys+OE5pu9CJFWlH8PAwYbf0fPo8R8owwNmsQwO11414taixEYyjiDiR6Og/HgEQJtmSNPvH558PBgn/w89u+d2Tgutty4eTnIMibFT+5N0a6z3z0uKc59+9WtJYR6wE68rz6VGHsnV8O6v5bz4Y8m7Z8OVtyU+OC1zr+XpWUVWGySAiUoJEK4SA416CFFC2Hi3Befj6ruLTww7LyvB6XrPfiRjHEYejmK/uKgrCNgHC65eNZbG0vFrWbI3jbtdyXjWcjhM+Osq5Om95dJDw6vyePtY6jk8ivjtrGHU1bR38atcXlidPU7pdxV5P8+au4c61HLQJ2064H0Q9AUvJrrKkeyHIN5YK4zxHvYjGOHQriaIAD7i6MBjt2dx4enuS1dyTFxJlgk8zyxXD/RA6eXNlGPUVQgqSJGSYDQcZae4DrnesWN/LpcYHMZ2uoq7CFuLu2tBUYTj34HFC3pE4G5rZN9/WpFlolH71nK1CKKa1AWTa7Qc/ys1FixD3ssd+yIGJY0Fbe9581/DwaRgs4D2jcZCrQsi+K+6bFSnF/fUWCGE3lwbvCZk1NgRaWhOuud3a4b0n72j6w5BHY1qPbcPwcTQOctbVPPiCBiPF/M4Qx4rD0xjTwvWlYbuxmNaT3w8zm9qzN9GUu0Aik0pS7kKT4WzwxgghODiKyDJFXcNgFAAfV+ctRVfx+HnC3a0N6Ggr8A6MdVy8N+gYnAkY6M3WIwh0QaFCc/PRJxnLuaOpHA+fplyetcRJkOOZtEdfrVlWKUenMaVL8PM5FTl9vUVsltjhmKpR7G+/4abuc2DfoR89Ie6mXF86zPU1+z9+9g9Gf/y2bmK+b2K+b2L+ySWSFP/nf4L4+LNfe1T+Od5XqZBGdfEO0R8hogj/i78MoIA4RkQx/vO/QDz7KKCZAY5O0fNLzN4x9dklhSxZX65Idrcwn7G92bC6XHPQ2aA7GeOj7F5DGxMn4WGc2HVgxvscJQVpJtltHUUvTJ4G92vwtg1JxXc3AUGZ6Yz3NxtODzPq1hFFAtlIHh+FQMG29mhgPNYBn+slVeWovCOPFMeTmP1+xLvzmjJyTKOYO29YbC3b0uMjT7enSDJJLwokmi9mJZ896XAxMxQDwa0JG50vbkt+p99h3IlxsWN+a5ETKKzmw4cZb9c11coy21jGowhqOBhG/NnVhrGPsAKKTHFdtozyiKtNy+225dEg5ScPOvzptxsuNy1HhzGZEdCF11WDrEKKdFQLkljSbj3DkaKH5ra0VK1DdgU3K0MhJZlUqCFs7+DOt/z+SYfq3j+TVopdbalNyFGpU4cpBUWkyL1k2zrWxnIkYjIlaaznnW84yhJq5VlgiI3ix8cdXt829DPFqjXc2ZptYdnNPLvYUNiItbAMxpp+HrHeWLwCXUsWypApxdpaqr5DG5iohCRWuNqBhEY48khSScfp85jtbZgKl41j1ImYHkWs1o5uocIEOom4aw1zaxEZ7NuIa2d4NEp4v26JpOCwl/CDvZzdyrDXjTnftqROsn+sSGSYJMZOYpzjjz8ecFk3fHLSYVLEdPsRTsPTQQoWausxHc9hEfF21XA0iImNYNiP+OKiZLincHPB3jiikyvebxsO8oj10vHsScJfvdtxPIj59qomTQRHgwSZC5bOsMOx9Zbt3LFqHH/wsuAvv93RixTSCf7g4z6xEHz5vma8p/n59Y63y5o8kmDgfN6Q5YLDQUxde17fNlTK89m0w+zGkmnFl7uKTyYdHh0lXG8b7raGl+OM82UdMkwiqG4dR6fhGv7FtyWyy73GH/Z6kqp1HIw0f/1FydmqRmbQ3nq+rWu0gGeHGbIQrCtDufM8GidcRS3TJKaTKSIkJJ6TvYTZjaE/1FQ7R9ZRVKXDWhhPNZ1ukMEgYDyMuF433NaGIlHMSsPCWlYzS6rkrw5jnVxhs5AFJIRgqyxiLXAuGKOFhNeXNdoJyDzPBjk/+3bHv/hhl/Eg5s4KfNVw07Z8fNxhdmG5qRr2M8X+MGZ743j8NMUJ6OeaReU47MZ4Fya9Te1YrxyjPY1pA8532zrmpaEvdACj/DPVd7OKcR7xcj/cWwEiJWmd58V+xijXFInifN1y3Iu52rT85KTAODgdJHxxW/LpYcFPzzaA4F896vPtVc1JEXM8idkZz11puNq0SASesLB/vp/xZlHzZlkz6UTsdSJiFabUn0w7YAMToisVr9c1037MqjLhZ/SwH2n2Ys2//KCHE54PipzztuHRMOVu0/LVu4aDKJjY52vL5bzlsm0p+qGBOH0QB1yuJcjAFpb53NDWAUf/wUnKqBdxft5yd90yLDTKSbbaYX3IQSkiydm1oZhI1tZz4ww/Ps1ZrhyjVHPUTxiPIoa90BwsZpa0I1EqoHmt8zx8khLFgsszgxSeupYkqWNvopndhmGes57BKDzHq9Ih73/9o3HwxQxHms0qyLB3m4Ad7tyb5v+m4kSwXlqa2tPrq0DBqy3VzhPFkt7g1+cEIe+9MNtA6BsfaNZLR2/w62tLqzBEhDAwuL4MW4ZeP+TbFD1JnASvzXgaYW2gi3W6gv1JCKC8uzH3jZekbfyv3u9van4Xgi7zQtIaj7Ow21nq0iJV8Dk+eZliDOwd6ECHu78H1JWj3FniSPwKN61UkM9ZC2kaGp+28czuLMORIi8UOM/djaE3VEyPQ4Nj25DJZl3YZDVV+Aydd1gTCG1t49HaEycBUa2UZ7mwPHgUMrXaTYXKM/YnEdsd1LMl0aBLmU3Yfznh4s/fwHjKeuU5ke8wo2Pick50cow7e8uaLrlsiEe933gt/7Y2Md/Lyb6v/6wSH36CiP/5825EXkCc4ud3eOdgfIi4eAuAD2LcAIz/m9cLgRjuk3/+f6GOT6kPn+EPTzHHT7nLH9H78BGDlyeU+RhurvBffY5ut9SV+/U3vb5AHhwxmcaBiNJ6FjNLUwdjI3Bv8Av6VyGCnCORCtUT6FrweJSihGCnLYuZ4dlJyrffVRwcRRw/SHkyyPDa8/W2onSwqxwWWG4togejTsT+KGKSaYhg2Ggm3Yi+jXi9q/nipuS2ajnwCa92NbmXfLNo6DrJC5nxIEpY0FLXjrhU7I8015uWx4cJl2ctsyvDu1XDf3Hc4Wbb8P+w914/kmX5nd/nnHuuDe8y0mdVlm8z3dNjejhDkbsUidWK0INcayE96G0Bve+b/hQBehXQWECQIK0EaEXs0qwWu8PRDNtXdZfJSp8RGf7Gtefo4WRmVbWbJqc5bEL1BRJVFZURefPa3/n9vkYLw4dHMT/oVkikZjjNefJZxulphl4YboUhnzxJWI08pJRUtGSj4jGelpzFOWUIf3yzhc5gdU2x1vJIMs2kzIgXBjzDKC7ot1yqQpLNNboN2gcVQ8OTZK7mwycJuQMN43KiMhamxHgQ+JKu64LRqELgInEKQWAk5AJp4MjJeMWJGJCxve7jlRJZCD54uqTbckFDpaLwjWSpDZWaZNsELFWBWwp6HZdHRwleE051ZnnayqUmXCIl2JYBbddF5xBTIIRgUhYUgMkFoefw0emS7W3XTr4qWDpJN6BWdXgYxxQaTuY5GsPrWyHdsc/qjkOtbhc2nhIUpWG97fLLv1pScRXrfY9CGLrXFD+8XqdZVWRzQyGsO9JG1ee//b0+biaYYjls//mrbU50zr3tiHbd5bWViD/dm1ltV+QSVhy2A5+VpuJkknNtw6OB4u2bNbLSMBjltNqKIHBo1RWzM8016fM4SfnlwZwPTxYIBKaAyaFmPjZ0G4rZSFOTtrgRVc1sXjAaF9xc8XFcweNxSq/icrsbkbqaD58uQcHeIuXByRIloe45JBci3VrDQbo2JyJyHe4PEm51A07nOVtewEGeUZU2w+ISzRWHONEkM/DWYBCXbPV9ejUPt25D/jaFzyIuKUeG371b5/7TJdNhwSQ2dK87IGBVuISBw621kMNJhnTstf55epUf2OJJCLsoEQKKzNBoOWyEPoErkUvBaqDY8nzywE5zs0zT6SlaVcVoXhBVJOmFU1Knr6i37OP4YJpxezOgdA131iN0CT++XePBUcJoWND1XAbznGv1gOOnGaNZjsghi+3Gdldd/ECyXvf4dJjQr7pXTZnLfdxoOnaqVBqMMWw3fFar3779/483a6zVfVznxQ7vWs3jcJpRasP+JOM/vdfm3x8suNsLOZrlBErwP38w5D+62eDxKOF2J+BuL+BoliEvNIu3ehGfnSesVly2Gz4/2a5xsxNwu2uNZZQUGAM3OpaSuFJ1udMN8Rz5LMQxM9zsB3x2nnCyyFmpuLy+WuHhOCUKbDX/5naVo0XOqnH55+8PGXvWRUu5kk/2E7IM+qHLz25UcZXA79oQ4MwxfHIc8+HeksNFRn/DpdFStGuSxaJkOisJaoAQVCuSGzsBk1nJZ0nCmucxGGje3Im4u1bh7npIVhpOsoLrbZ/1FY/lUl+4XVm74WRptUGtjsIPJepin/uBoLeq6K56RDVFvNAUhUFrY62Bk0tth/0zXRpWNz2WsSaqSoYDmzBfFgbpCBzHLs6eh5R2EQ7PaIZnRwX9dRfXEy8+b4Hxecnalkt3RV11/5expsjtdRRVbZZXvLDva7YU9Ya95jsr9hl9ibIwFDnUmw6dng3SdBxBt6dIE43rvVjmLi90sWEomU0tjUwg6PYd8sxQqTk0W5Jm2yGq2NfOz0rOjnKSpSasiKvFmrygX7qupZp6vqDVcUAImh3F0ycZ6xuWoj4aFKxt+fQ3XAbHBYPTnNlY099QNNsejYai3XHZuuYhhCCeCTZ2XJpNB993qDUUs3HBZFQgpQQjcCT4oV0AKQ/291KkFEhhF2/SEQynHrLbpTZ6yLyMqGZnpL0dzhYRZV7iiZwoEFRvbH7zC/s7hJeTmJeTmL8RRKX6t/fZ1TrsP4bxAHHttp3X5jkc7SPuvgGHe4i2FfgbY+DsBHH9Fl6vTVnYEfh0XLK66V3cWCTzucDtNnF6K6jREaO5pNYO7EJpOrpyRRPCTmK0MTx9nLOx7XE+KHE96z8fx5r+uuJ4P+fmnTZltuR4mKMTUNo63Dw9yri+GbD3KKO36VKNHLLM0HAVnbbi7Rs1IiUZZQWD/cJaYqZwQm7FwUtNJCRJYTinuCoygrpkNiqIZ5qlp1mvukwSgx9Iuq7i5KxkpW/DHddXfYyCYZ5zez3kX3825R/crvH+SYyjJWdlzrrwSGewserz6Sjh9dsB44VmZy2gXnU4TjNWlGs1R67Dm/eqjI4KchcePU354Y2IPIXFpMAVkmlZUhcuNUdiUsHNmwGp0hye5syykv6KItCS02lOLgUr6zZtWqYS15E0A4c4MwS+QLngJQ5l1TBdFNRzh6c6YQ0fDWQVSwVrhQrZskVlbgxdXIrc0Iwcu9jShkFZEFUlYikRCk5VTr10aIeK82lOIg01abUrjaoNX8MxDIsSpSWRJykWECqHxFir4zKFzZ6HO1Xsn2e0Ky5FYOhEiuGJpreh2G75PDm1HOZe3WNSlrzaq3Dg5Vxv1alFJedZSbvpIs4FqgKdhkLWBdnSsNP3OZrnTIqS43FGr2snJ2vKJ0s1R3nKbiegGShaoUupDZkwDKclNeGw0nJZrXqUxnC943N4lnFa5oTa4XovJF5YLZZbwMOnKdtrPrHQtOqK1brL8XmGZySxKbkuQlqBouFb+9BKTdILXP7qYczd7YC9s5xhVuI5kmla0ggUS2FwYoEWmo8HCXFh2O77vL5qqUKjWUnFk2y2fZapplm3RcqjUcJG5BHrknFScr0VsD9O6fgueHB+XuAby8VfGttomE80Sa6pdCxFNNIOI0oWuWY+1yxMjpHQrntUOpJe6PFwkKLaguU5VEJLk9pa8fGUpEgM9ZoDuUBrW9gkS21pYso60rnPUa6kY+8bRQ4bLR/HgWbbpVp3CF2Hw0GGUwi6fUvXGg5zokhymmU0tUuz5bCY2s8/XeTsdkI6VUvX8QOJKWEwK6l5krXVBr4siKoOy1STVTVbzYD2RfFaqzskicbzJBt1j9C1NJtLLcF0XNJo2m656wnm05IglNT8i9/xG1DFvim6kfuCRuoSvpIczjKO5xmvrER4SvLjzRr9qoevJD8/mLPd8DFC8HicMc81b6xWmaQFu7WAybJkTslgYd3Dfu/6i0njT8Ypdd8aCDxPkale5GAIIa6CFRs1RV5qjuY5mw0fKQQxBXfXrDmAFIKjNIVSUCQG5QiSuQ0KjiqSOCjZbvlkSxjrglrgcP9wSVSRbDcCKkoiEkGEw07bmir86n6C1xd8tpfS8AWNqkujrfjgMKbfcbnRD5iLgm7VIzaaXx0teH01YrPhE4SSxdwG/0ZVyfC0YDbVBJG1UFYKXM8K4xttO7moN21BXq1UqLdKDp/kNNuSwak1Ami1FculRkhwlH1mJolNlJdSMJ/aqYbn2fM8CJ4J7y+RLjUGQxhZCtd8pml2FL5vxflRxX5vPC+vWBCXx2Y+02htr6uo4uAoQRhJisIwn5SkqaHWuLAuv1gwjIYlrm/1afLC9vx5CCHs9ANIEo0fWMrXYmppoY22whhDntvIhcm5pttXeJ5gPrOLnzTRKGVDNutNh2RRcrCXk6UahKBWdzg5LFjd9FjMNWUBRWFptEJArWazZkbDkkbLYTGzmS9R1eHh/QzPh96qXdw6EtLU0Oy4nB7lBKFgZc1jPi3prtjcnHRpg6Jd306QDp5kbOx46MkMv1kjTQ1pYqg3JW6+wK1HPHyQcufNBoyHtNwZ5/QQwuCt9sgOjpiXFYLpIUFVIWsvJzEv8RLfDm7chUodoRRiZR0O90C5lnLmupg8x8yn8OADWN9CNNsARBWHlTX36oF9iWbHYTy0C4Lw1i7Z2QSTxLD/CDavf+HHN5rW+/34MKfdcahUHfQFx38xsxaOxhjqgWJZamZJySwsaEcuiWd4dD9htas4GFnuupS2I7YRXjiJKcluPyRwJGsNGy43TUuOlxl95TFDE1dKNIZN6aMqgum0ZIlBVuHu9ZBe36WiBf/yYMSj84QwEPwfn41ZpCULUbBW9UkLw//64Jzfe6XOJ6cpAbag8TPJcmnY2HFpNRW/d6/G//bLCU3PPtA/Oo253grIfUNR2BujNgap4D/+YYvfuVXl472U0JUUuSDsSfyaZPWaot91iTxbpPzFkxmjMudmN+DpWU7kSQKlqK2DM5cUKXz/VZ/YFCzSksATyFgyXJT4pWS16iOMYFZq6kYxI0d6cDYtyEvNMCkwM5jllicdVSR1V3EyKJjKkgLDQOWcxwUTP6fXd/EKyVxoHj7ICB0Hk8As0xgHkkIz8gqmqaYtFas1xTjJ0aVNfC4Cze+90uTcLXgaZ0xMjl9K9og5ynI+LRPOsxwMTEVJpSLIIsNbtyrWMCEsyUrD9nrEbiWiUVP0XJeRKNhoepwsCg4HGd2mYrPhc6cb8mSU0m4p/uhGEyUE9ZbVLHSqNqQzKTTLXHO7G3KyyHlrPeTPDqesux7XWgEg+Hiw5GmS0nYUkStwI8PRPOMgTSGH5qbDIMs5Glrjh1pd0W97RFXBYGHdp7LMIB04LXK6Ky5FbChDw8ePE4w0rCuPpqPYrHrszzMWy5JWReEWDr9/vc7v7tSQEj4ZLGkEDhLYbYe4qWCpSoan9pi6UhLVBI8OE1YuCvlkah/Mi4GmESg+zpfEi5K9owy1lEgXEqF5tRtyuszZX6T0qoprawFv3IuQM4dJqfnBaxFHT3NSR6OV4W49pNNwODIZJjLkC0O8KFlpu3QilyzR1BqK6dg2MsAWR+Fz1JRq3VrJziYapezExfO44vdXPYfpPMcPnhXTN9YCPjtMAOuMlSwNBmsB+2VothVv3Iw4d0pbwA0KZpOSk2XOvVWb1xRVbVPA8yVZ+iXq/AsY86xbri7MCYwxV5343xYavsO1ZnAlEr9Er+Lyn9xt8zs7dW53Q36yVeVgau81xkCjobizFtIOFT/baXCjHbzw/v1JSqisJfjXQQhr2gLQr3r8aONZY263FXIyfzbx/93rDV5dj/j9O3Vm84JAwNa6x4rnkWIYLApcT7AWukwSuzhfr1r3rWZboTxBteFwEKdMhaZXUZwe5nSkS7Nhwyo/OoxZ73nMY40fCspMUHqGs0VOt2LPx2WsGZ9b45lGy+H8rGA0KPED++xrtOy5JKUNdZyOS4y2VCeAas266nVXFenS5o8EEXx2P2F4WjAZ6istCkC9YZsWcQxCwvCswPPs4jfPXzxnKjWH5cL+e3ReUGs+d43U7NTDGMNyaV64fgA6XYeDJxnN9ovP7TCStLqK3uqLCxTXE3RXFGVhODksaHW/ntYeRhcaFrAi2KvPkbS7iiBy8HxxMeGxkyMpDUrZKZOUgiB08COHZsuh2Va0Woruikuz7XC8n7GYWdOC2cUiqSzh7LTEUYJb93wMUGs6SAmzScnubZfbr4ZkKRf3F0mzY6lqzY6iveLS6to65OQwZ3ReUKk59FZdTo/sPdlRAoGhNDYHb2PLY2VVMSsivHTCw09Smi2HeGHIN24T/eAHZBu3CR6/jwp8xMk+Y1pMRItytvjaffhdxctFzEt8JyGktCGYl7j9KmxdLDY2r8N7P4fJCHH7NYT/4kNMCOuGcinqv3yt2VGWvw74W+ssHzyGJEG4X3zY+YEVLvqBvHrghxWJ60kWc0O96TAcpExGBRttl6Au6BmPipD4VZhObcfFNYLRMqfesGPpZGlv8lobPv14iRAQ+BBUBPdqIddrAW5FU5UOt/ohbeGCC+1QUc0krb7kbJHz54+n/Lsncwph+EG7RjK1YtKdms/9WYI20AgkbirQc/jgLObWZsB2PcBFsN72KFxNEtvtiXzF7ZWA+ydLHo9T7vZCNkKPQZyjS1jfdPnF+3N6kSJNNZttn2rkUOk7vHY7YqvrUw9t1/lpmpHXDGi4Hvq8uh2xDAyd1CUzmiwtmMbWoSWXhkeDjNCXLNISCQxFRl07VFqC5UyzVCUpmp7rIh0H7RhWhEuv4qKFoRso4oVhJww4W2RMRI4WBlUB0bCBZWQwLgrOhwVzv+Tt7YjEsfqkvTwlDAV/8L06s6RgmheUoSFalUxVyWmZsbntMS0KttcD9BK+dy3i/STmSZJifI2bSzZbLm9tVGhtKVo9xf4yo1pT/KM3G4yTkm5L8Sd7E2qBZJIWvH+yIMglUVXgaMH13YD8wgBA+fac25+mtEKHP9htsjdJeXurysEso1pzkNJqAG51Qh4Mlxhgu+Hz8SLhTjPk/eMlgZS8sRohEezHGTqDtDD82ZMZN1Z9KrFDjCYVhk/PEyrCmiS4nrVpTQsIHcGRTMmF4d9/OEMou+A+G+fMRMl62ydYl2xedzkd5JwcFBhXs3ec0ukodtsBriORQqCk4E43ZG+ScXctQgiBH0ric3tN3d9LeLUX8icfz2gYxXKi+WxvSS1wGA0tX7+sGlZrHodxxtLVNDoKSug3FA9HCRXj8KO7VfIESm1Yq3k0Q4dUa+6fJAzzgseHKX/0/SZrXZfAk1xv+1Q8WwhlF9PNS4SR5PzMTvO+CnYxYHAcK9g15lmllCaallJM1TMOjufbVPjQsZ3neKFpth3iuSZPDPFCMxoWV4UfgHNBE9EYEHAyy2j7yqbHf2568vyy4PlCM8/NF0T79abDdGyd0r7ud/y2sVrzqPm/Xn9T8Rz+yet28r5adTlb5lSqDoO4YKXqUvEcPh0mV1+eI68Wv1+HyyyRSzy/mKoH6gWHM8Au5GP4ye0aO2sB7cBjEBd8f63CJ4OEak2il4It38eU8ODD1OpR9jPQgA/tpst65KFdzXhWUBSarTWfax2fnu/Sabm0HIf/Z29G1XM4XeSsVz2mhyXDU7uoanWsOH00LDEG7n4vpCisLqVaU7S7Vr9VazgXduDP9nEY2fysas1BeXZyMx8bpLCWwGEkOB8UDE6scBysUP/mHd861PUUo/OSZKmpXyzcL1EUtslVlubq/y/hB1aXMhqUlm71OQSRc6Wl+TJ81evNtuLaLe+F4/hl8IMvX9hXa3aqFUaWDtfuunT7iniu7aTaiCsb8zCSVKp2OuT51oFtNCwQEvJcE1YkSlka29lxzmxqmQDbuz5lYfNkwDA4Kbn7eoDj2OmY58F8ViIdS2vrr9vjV687JLHN6NH6wo2va6c5rifIMkOr6/DpxylJJvE8rqbkfiC4v1+hLA2NlsLzJdWagzHQ2ajiSMP0eEKmFZ5T0NxuMa+sf+0+/K7i5SLmJf5eQCj36kYmpES89TuIjZ2v/H4rQnyxq6mUzTbRpb0xzLo3v9YiOowsxSRe2IdZENobmCltINZ0nON6km7TY2c1wL8Qcq7jMSpySg1bHZ/Dk5zjRW7D8nLN6XF+waW1biYHT3IQgjB1uL0R8nCY0W86YfJy7AAAIABJREFUeFqQlZrbmyEfPlwShpK3d+r8YKdKVEreqlQRJdQTBycEbQQ/3qjye9t1js5zFmnJw2FKJjT/cKPBas1jEZVc2/SZLUtGk5LzYXHFixehoBEqGlphNMRzTSVzeHqSXjnXlAUcPU351WHMnWsBp8ucZay5v7/kxzcraF/zdJix2vFoonhjq0IgJLt9j3hZMB1pzsuCuVMwSktq25JfPl1wMs6pVAUzSqotyTgsGKmS2TinX/pEjkRFgszRxKVm4hZ4WhIgeThN2Qo9houUaaYpW1YUyxwOkyXdQKEcwR92mlQaDtdlwPuHCXd2A4wPC6cgE4bPHmTgQJhKOm1F4EhaVUUQSH6ZLFgKTRHDx8uYJLSLp2tVn7wOsdSsrHj4VYc/er3JMrcC3T9+q0UTj+/vVqiimKmSe72Q37nWJnEM6y07fXl9PeLPPpmw2vIopSYvDVmh+cXBgn98u81ZnKMNhK5DVhrSQuM5li60P0l5ZSXio9Mlu+2AyLNmAE5k+OjJkjQxyAR+f6XOh4OYKg6tQCEDgYoEXc/lp9s1xBIenKc8PcowxnCUpdyuhkS+wyeDJR9PlygF1zyf8bjgwSLhtSAkr2tWIg8nkIiaQSvNwdOCbk2xUnlWTB5OUp4OUv7s8YS81BxnGY/OlkxnJVHbdnenuuDoPGc1Umxt+0Se5GSaIWJBrjS+K6l4DjtNn6qvEMLwlwczGlLhVyWDYcHr1yyF6GCacr3lY4whLTWdQLHh+ez2fTxH4Ag4GuSsdFykEOw0ffxAvtD8uES9+dUF1iX8QOK6lhLiuvKKt38+KKjXXYxjF1WXePNGRFTYgq7ZsiYilYaDuBD/tjr23Jucl4yHBaNhjj8V/OKjEZ11hXZgtesxPi+uFjGOYzM4XF9YyguWqlO5EOvPp6VN//7cfbEsrQjZ876bJcHlvq8HillakhQa/2K6sFH3uNkJrr6+yQLmm6AdKoZx/sJrra6DnzqMlgWFNhhX45WSak1wNMgpSxuGePdayILSTuimJdWG5GiWsVZzOcwzfFcSOA6h57CXpojAcDzMuNa05+bkXFP4mq3I568+ivnenRBH2WM6GVnnrHZX0ekpTo5yguDLj1t/3b2KCvg8wkjiKsnGNQ/XkxzuZbR76upzKxdULK0tXTJe2ClNu6tYxlaPUxTmOS2NJrigjlWq8gvXS7Pt4Id2qvFl2N79m2lsL7Uy3wTL+EW65OU2SiFY37IsiaP9nKjqsLnjXeXg1JoOg9OcdtclqtqpTqVqs5HaXTu57q54eL5gMi6tlfJQ47uCg70MqWw+zHymWdtykVJSv3BwSzNotR3Oz6zz6WRUUm/YiUulJqnVFc2OS7enmE40vb5idV2BEXR7HgZo16028pP3l3z6UYrnSQpcqmFJHJfkuV3UVmoOfiBItu5RvPdLwm6dFeeMLOpS60Z/o/3/d43f6I71zjvv/JfvvPPOB++8845+5513fvhtbdRLvMS3hee7kEVhA9umk5JK1YbNiSD82veHkbyanoAtEqoNy0W9tOW8fF1rw+qGSzoypKWlbSRxyWrkgjY8HWe2Y2RgPilpdxyiyH5GntibjDAC5UlKaRg9LTCB5QD7mc1ccaTtXH+vW6G54pAq2Fzx2F0JQNsu3b1bEdstn8FBgSPgbj8kTQyPzxOSwnbIJtOS3W2fc53x/uMF/9cHExq+ww/vVvl0P2EyKWl2FFvrHrmjeXpkOf2r6y7jpe06jYYFK7g2/X1pkFJyfJzTrrjUPQcRCG5shPihZHJWErmK80XBbivk7KTgYJFwNs9ZZJr1FR9fK0IleZTlrFQV05MCF4fVjk/UkiQLw2bTp1Z1CLqSZaY5FhnVwqYu61wgfbjmBmRNQ1lae8pe5LPV91m6lprhBIJoQ7J/nvHG9Qo/XKujM9gbpxSFISgc3Jkknpecy4J76xEbgYsCBkVmHWwWmsh3yFxNKjXVqsNwWdCvKpJCk5UQOjbtvHYR5LZSc/lnv7OOQfCnnw7phy5JplE5dLoum9KnU3F4dSsizjX//IMhf3TTcv2nSUndv+Tzw94kZbPuUfWss5SStgh/PE75yVaNu9sh+RzSoOTj05jr6z43tkL+8b0WrZrD8lzzYJpwXthO4uA8Z63v0agJPjiI+bePZzSNS70pudUNSXLDvUZA0RLsDzLOZwX9usus0IyTkju9gGWuyVPDHBvSt1bz+L8/mvB4mPB//mLMrx7EdAuXvvC45ge0taJf8UiCkr1JxoenMVrBRuRhLmxLZSxYGMP2rsf+YUYuNNsNH7cUTEVOB487lYhKRaIxNBzFo+OUs0VOM7DFzeA457Qs2K4E1Jt24VtWDJOR1dz0nit6lQtF+ex+cdnhbfd+faEUVayOYHPHhlkuLpooeWo7tzfbAR+dLa++X0pJVJEsZuVVevmj4yWdwKPTcxifW6vXZ2MVwea2T3874tNxwk7LJ4wka5vPBPm1hl30VKrPmjjlRQq4pYx9eVe73rSuWn9f8GScstP89o1lnsdK1eVsUbzwmpTWNavfdPl4vqAf+iQLzXrT5+mZtR5GW/qjDG2IcndFAVbP8P5pTOBKBm7BVuiTG82m63M6zRmflizGJcNhwc2Wz5rn8+Q4YXvTw/MthcloaypzOU3zLhYN7l/Dk6FSlVdZaMq12TC1uvPCQv2SfVCWlpqWX5xDn4ed4j2bWPmhJF3qF56Nz++7y4XRl+GrbL2/TaTJFzVfYWQnHUVhODu2kQLXbnqUpbjKP2p3HXRpmIwKgtCh0VAvfo6wtcbKmku7a/UrxkBYlQhhr7vhmaWC5rnNWppNS85O8qt9v77tIQScnRSsbtp7kuNYXc/u7YAgcsiWhlLbe4dyBWEkuPtaSH21ipMt8TyHds9BuVBfr7IVDanW7CTpElIKlqUPu3c5H2nCfEK15uD5380Gxq/Db7rV7wP/GfCn38K2vMRLfKuoPTfuLkvDeFhQqT0bzQaRLSDAdmgGp8/cUJ5HpSaZT8uLz7SuIK4nWF2PvuC6AoaiBCewFqz7eznLpcZLJe3Q4cl5Rrwo8QNJu+eijRUzeqUgVZrTScb3ViMeDXNSDHVXMjzL2VzzmIuSPNPEY01QSj45WNIIBFHFYavjsyxLzgb2oXt3LeTTecI/+WmXxdzwJFvycD8hVJIn4xS3EExmJVu1gIqveH0jIh5pFlnJVt/l0X6CI20Xd3c95IP5go2+ZwMwV2DD95g6Jb0Vl8IYTAHH+xkny5z/4G6NDwYLehdd+DtrIaOhFd6XoSF3DaESdFyPjutSC2B/uSTNDcNKjtGGo9McowxeJDAu/OhuhdIzdFzrauYsBKZiqPkOhdQ0fJe1tk9WGO4fL/lgEpNS0mkq2h1JreKwP80IYkG3oyiNQYew4rp0HIUX2m50LVD0VhSfiiX7OuHJScLDYYKYCFbaHmFTMjfW1nq3HrAINPcqEZ2Wy91uwDzTHEwzvr8WoYG00Bcp2A7dquLTJymeFuh5ybws2R+l9H0PXWqK1GqlhBDc7ob8dKdG6NqHfq/islazlUroShYX6c8A3Ujx8Dyh6jvUfYeDaUYlcNhtBRzPcw7TjGZoj8VGz2eeaxpKcTTJqEgrTP7FgxjtwE9vNNjoe1RnDgtRIoTAqUAfxS9PF2w2PN5bLJgsC2o9SVpo0rRkktjrwziG2RTubPuUPtQCS/+7XQvoNBXNDYduxb3QlNlF8W475PV+xHrdY6Xq2ryJ3E4wRMUQSoGjBIVjCIXD4dOMR58mxLOSdHZRlAh4updzreez1vD41dMFW32f+cwGxxFBo+5wtJ8TuyW9uovjCBzvRerVYqYJQ1vwf9nU4tdBCK7uL34g2HuYXnSfbQPiWtPnvZPF1UQmjCRpap2iKlWbQi611Tc02+rZV0fR6iikI7jdq7Dp+tSbXywIhRBUapLxeXFlqnb55/hCXPxlUEqwsf3tTDD+tlHxbDL8r5uMfRuIXMkie5FWFlUkji9Qyqa/x0tNrZBkY8PTSYoRF6nxrsOysC52mdIcnudQwCIreftGjVbb4eZOyJCC672QG9d8xuOS1S2X6axESEOsNRtdu1hbzK0ua33LI0sNs2nJZFSyvumymFo9Flycf1+zazzfUrsuIYSdjnT7itnU6jouQykP9zL0xbOz9hw9TCmrH1EXAbDng4KisFqX4BvmCP22IQSYL1mnB6GljE9G5ZWrGYgrIwL7Xhu26fk2H6z+ueuoVre1hhDWoWw6Kdi54bN93SeqWB1MtS6JIkmtLq9ybYanBY2mZBkbooq1hQ4Dm/fzebS7Cj8UiIvNWt1wOT7IKUuYFRUiM6fVdRDYaVK15jBZOMwnBfWmnQidHVttja532GwnyDAinqQUw+G3uKd/u/iNzrR33333o3ffffeTb2tjXuIlvk1c0iT0Rcp0Z8X66WMuOjKB5cMOzwqMNldCwc8vZHzfFhrGXDw4hV3YLOPiir5xidOjgvUtD+XD0VFOq2O7W7NJSbuhCKoC35eEFYFyBe2usp73SEbTgvGyoB0qpA9IgdGG44McrSEelSxjgx/aEK3QOOhCME4KfE+ytu7ycD8B4JP9Jb2OS1YYOhUHB8nPbtdpGcXeQcYsKRmKHKcimIwL1loetzZDPjtMqIcuMjQ8Okz56HHMw5OE82FBrmxHCQ3FErLS/t5KSxo1h6M4w6kKvIogXkCj4jCc5Hx8FEMO3TWHhnFZypIfbFT5cBFjxoCxQXVCQVt6CGXor7isKA+nhCkZ791POZM5w9iwFAbhwaQoaUuXSDnUIkG8KNnq+Yil4E495Md3a/ilw0fnCW+tVUEY/I6lHD0apdxa9/nlfMHeLKUZOhzrlNE4ZxaW9FyPYWm4sRXgNyXpEpaNklQYbjZCbq75PBplvL1do9GVGAWOlFxvBdzqhLx3EvMHuw0+PbfHw3UF/VWP6bDk0eOUN7YadGsKpSW9hs1JKAuuHo71C9HzJbaf6zpv1LwrKg1AJ3LpRooPT2O6kUIKeDpJ6XVcftytUnMd9ibp1fff24qIi4J0ZjiZ5fybvRmvrAX0PMX5smC3E5AITXLRmTcGOlWPdtvlVifk7WtV+qsu/arHa5sRzdxlf5IynhRU64o7dwLGE01aGF7pRFxvhLTaDq2WYrsZICUMznL244SPjpeczDNWKi6/PFqwUbcFmqkbPpzEdrEU2KJ1nBZsdHziuc2GcKaSpdB4vuHxYUItlLQ7LrHUdByXRJeUuWEcF9SltRfevOZddZlrDQc3EMwzfTXlAktPmV/87uIrqC9fhUbTBgWOhwVhZLOl3ItpHEDVd3ilF/Hx2ZL5heai1XEYDS8LZXtfyL6E0vY8XCm+sogPQklYsd32otAIYR2h/FBeCby/DF9FO/quYaPucbf39RP0bwvbTZ+nk+yF17QxDOOCe72IcW6d3Vwl6ew4GGM4HxVMJwWhdjgZZQx0zidnS25uBrSkwpGCZqAIK5Ja5OAImMysw9YiyOk5HkFD8uHDJVsNn9mkZBlrm3lyIbqvNWxY6mRsFw9CcqVhWcz0N8r6eZ6l0GhbrcVoYJ3MWh27eK7WHbuA/pxwvlp/1tir1m2oZJra56z87q1fgIsMlvyLuphLNDsOrmdtiVsd9QXzASntAiUI5BdqBEfZvB2A0cBOT1sdax/dbNl78myiyXPDMrZ28kVm2N51OXiaX3Uazs8KVta/upmwfd23bm1LzXxasJhrmm3Jxo4PGJJYI6StSYQAvxFikpTzgXVnM9gMm6IUTCYapKJzc4XZUlFMJ3+j/fp3jW8vqfDX4J133vmnwD8FePfdd+l2u7+tH/21UEp9Z7blJb59KCdjMcu5+4oVERtjGJ6lGA3rN3zufzjl9t36VUHQ7cJomOJ6kmrt2c2k3TKcnSRU6y7NG5LJKGcx01y/scLgJKXbDUAnnBcZ65sBh0ODavn0Qp/5rLA20dpntRdSlQoXad8DFOmSNI4JepLFcYbnVXj9XoSrJPNRThgJut2Acblg92aX0cfn+F7Azp2A+Kzg/mDGrdtN2nGGk6fkRcThIuG//tlN3j+asQgMb7XqbGxWiBcFol4hKB2OFgkfzDK+v9XFcz2aDcWTc8m13RbzyRhVdWj5gpHO+Zmu8tks5qe3O+jjhM3tCmcmx/V8ajXDat0nyUsenGsezCQ3brZ4/yRlpxPRylx6rzgMgowHeyO6FZ+F9Hit3UIiWCkdxtOc5YbEXUhu1uvca9U4iRKMEuhFiago6qVHbSVgx6ny5+djwjVFfKrxQpe4o1C5oKs8xp2Yn+x2OctSup5gvan4kwcxb7/RR0pBcpYxPhJ8cqhRwqEfuHw2ifnptQ7TYUF9zaeSSf67t/r8j3/+hBvNiHpDchwUbAUuf/H+kF0Vsr5eYa3b4pOTGf/o9T6TZUG3W7PH9LTklWt9houMo2nCq6s1hBC0XxW8udIgizVrsoW/nXPvVWvvvVwWhOE3uyX3ei/+uwtsFCXvHc54c6fL+SJjvMzpNqu8cnedf/HhCeteldW6Pef+/f2M9VWf9VbEPcel0lAUE83hNKElFBubPp/tzTg/czBhyGt3QuLS0GxV4BjWfUFY9WgKRbpMmAvNmUkpQ5cf3e7xZ78641avSbPlEYQOZycJBTndbo24XLD3aM4r231cKZA1yfEsZVzEbK/1OZMJK67PrMz5+HzOZiPgaKy4c71D4EfcuA29fkBRm3B+kPL4gSD2XP747XWmkwwKyRvXQ/7qswn9io8KDSsrAb1ei73RktevNckutAvNpk8uBXfWKggDwmR0ej5nxwkIrq7Rvw56K8/+3mgkGGO393n0V+D+6RwTuPSqPmGQMxpm9NZcbu40ODlaUq9ZGtHzKEvD6VHG7q3+1y5IANqtgo/fn3Dv9TazafGFbXiJb4ZuOafRinAdycPBgkVe8tO7XZQUvCenyLHBkQ6h59H0FHGgGR4m/OiVFsWnc1abAZV6gXQk00HGT263cB2JLhJ6fZ8tDX/yb4558/UWp+OMu9fqZI8n7GwrdnsVO32PCxrNFzljRbZk602fwWlKs2kbdt1uiCmTrzzWl/VOvVaymBe0WtC5mPT0erCMC/JMU2965LlGipx25ytoezq5uj5Gw5RXXndxv8RO+7uE1dUvf73Z0Ow9XrB7q/aV7223DeeDlJ1rAZORzZGq1Z/VCKZMQEOjaYgiTbdbufq/SpRzdBBjjGFt3T6H774aIISgVk3Ze7QgCHz6ax6bW19tcwxg9JLjwyUnBzlv/XiVk6OE3Vs1GtfO+Pm+i6tcvvf9Fp98OKXT26K2f4DfWWH3Vg2j4ew0YX1D8fN/Maa2s0opzqj2+5RKsdr96uiM72qtLH6dreI777zzL4EvO/T//bvvvvu/XHzPvwL+2bvvvvvzb/hzzeHh4V9nO//W0O12GQwGf9eb8RK/RYzPrR1vs21tY4vcfIGrOx2X1m3luXvypW99mhiMNuzs9jjcH5Is7fdmqWa5sNOaslqSGbi7FtkumjZMxyWLhYYGbDY8G5oXa+bzEgzE1RJ3JAgCh7hacqsT8unDBCeydKJZVlJog1MIHoyX3GlH9FcU/9O/HnC3H1BbUVyr+/zvfzHirdeqbHd9PtiLmeYFa4HHzpqPkILRMOdU51QWDoOy4NWdkMf3MxothyTTnM1y2p6iu2opNw/PE0uDebhg5mruBCErqy5pVvKLhwte24xo1BUfP1myt0g40QX/1etdnp6n+BNLh/vR71b5H/70hB+2I/7VaEa/9Gh7LkOTkRSa2tjhgzDmtgrpBB7djsNpXNAPFO89idlTKT9wK9AX1IcORzpns6J4b5Cw0lLshAGLRckoK5AVQbHUvHo35OhhwaDMcRqCtZrLr05iGji80Qz55XHMRs9jdgBzY4XUMoOHIuGVRsj1asjHo5iHccpW3WO75ZNrw/E04/gg57/5/R5SwK+OF7y5VuXBcMmtju0Q/8nDMX+w2wQgKzX3Bwk7Tf/KjenyvvP8e74NaGP45GzJvZWIaVKwN8y4XveZUjJNCkpjQwAPRinh0qG9rugJl6MyJZooxhR870bI43HG3iRF5ZCfGoaq4OZqwGJhyIKSH63UeDpL6XseQlrB+GfjhNM059XVCDcV3LoVXDUHxuOcYVZQSgNzQUVIisLy4De2PYwxPDpLWeaa682AT0+WRFKSGs1BlmMm8IOdCp0VxeS8RFYgzjU1HP7yvTlLz/CjnSpHecZmZNPpJ/OCw7OM3Nd872aVZqD4ZLDkzkUY4oOh1acIBDc7AePzgnrTur5NRgVGQ7Pzm/X5Lu81ra/4nMswyprvMI9LhllxpfWYjKwzWaNlp7l5ppmONbfv9Rl+Q/rH+SBHa0Gn9+uNCV7iy6GN4d/tz2kEDlsN/yprBmCelpyMcm6sBgzjnNnIUhUNhifDDFUV6Mzwy8cL3rpVoekpIuFcTea0NpweFWileZJl3KuEX8g7+TLMJiV+IK50DJfmDmVhDRq+6rx9vt55+ihjbdP9ghblfFDQ7ipGw4Jm+6vPm+evl/Gw+I2vlb8PGA2Lq2t5Oi6tLfPF1GN8XlxkNBnCUL5AvwMYnuYsFvoF04RLPHqQkGewec39Uj3R84gXmrIwPH2S0u3ac80PJMvHB0y9HkVuWN+y5ivzacmGe8K5WmN712bZeL7V+Ra5sU6jlRHnywCvUaXe/Opj+NuuldfX1+FriZEWv/ase/fdd//w29igl3iJ7xKqdYf5TFOrO8Tzgs9nd34Z3zxeWOEyxrBY6IsAMIPABlbdf3+JkFCpOngVh49GMY5j6SLj85JrNz3+31/EyMIwOC3Q2lwEdxl6qx6ziWCUlrTacBkp5QlBomzY4c2tkJ9/MKfrK5LUkMWaxwcptzsBj05T+o5hkWmurwesVFzmU5szEyHJPM1kbDMLBIJsYagIQdtxeO/TmM22j1KCSEqKsSHLNJ9+lNC8Lul4iqgiWet5zAcJo7QgG2sGhzlns4LHKsWf5zwYLPnJVpWlMSRFie8J9k9SolDyl4dzdusBR8uSP1xvMhUF80XJWuxxnhc8EEv+i40u9w+XrESSD6cxt8OItuNy7abHyUc5+yJjbe7T3lRkDwzHNSuaDV2HoCLZ6Xv82w8X+HWBLx0agct7ZYxxoYvHKCl5e6PKzx/P2BsV1JTL+LEVbzebik7VYbwsWXU9Ctfw2XLJfpbyH95ocH+4RBt4vR/RjhT9enGlSbnWDNgbp/Qil9N5/gV3JM+RvNaPeDxK2J+mKCkYlHNG4yXtbzh5+aaQQlxtVz1QXO8JHh+kvHo9YpKUvLISUmr70JUTweODhGrLQaWScVrgNOEv9ub8aLPK4TQjrEju3PD4y4cxtVzyq2zG7VrIuS7QKRRK4wmJ1taGez4oqVYkrYaL1uBcXEaDLGcyKKlIRa9jE7fDiuXmH+9neIGk67kM45yPRwu80iFRmlsrIdlnhj2dXhXzACeLnJvtgOVC44WSVktSaUmcU4HrWsF8s61Yak2hDM1AUWqD81xBZozdXwbblCgKrpyT6k1rR/qbIs/s7/lVuNkJ+OA05mY74DTJX6ANNloOZWE4H5RIaTn9necSzr8JrG7ji05RL/HNIYXgRxvVq+vqeVR9h1Mv52CasVH3OJvkxLGm13dZT21Wy/1BzBs3IjrapRkpZhc0LK0Nw9MC34dmx2Nd+IzPiy/8jM+jLA1lYb4wpQtCm3L/TQ91vSm/VExfqVkqIny1tTFwYbFcXonf//+AS3dT6QjqTYfDvQwvEOSZ1bRMRpa2Wa1/8Zpv9xTNDl86Qd267vP0UfprFzDAlVan01VkmcZRgum4wDGwsuqyv2fpj2sbLmlHUWZruHsDPvhli1pdsbImqTdsXMTwLOckadFInlI0vnoK9V3Gd3v29xIv8bcE1xVXFqjfFFFF2hCqnkutLjk9XqI8yHJIE4NyJetbPpvXPPLYEEWSR0/SC7cgyaePU+bNAkdJVtcVrrKpu4uZIapYTnKlJojnhoavGC1ywqrks4OUYVyQFpoy12S54ftrFVZWXSZpyQ9eq1LxFK+vhKgM3rhd4ewkJyk1raYteoS0PvhaG5te7EmSrLQst9KgXGg0Je2ewikE86SgVpccPs6phZbnv9pzkRKk0jz5OGW759GIFG/eq/DGboXWmiIMHavB2M8Y7ueknmFZKzl6ktHxFJ4juN4L+NluHe3Dw2XCdujTbbkcxzlJpjkZaRpG0ZSKzpridFFwpxLy5q2Im6sBu72At39cZV5o1toeTilwNNw/S1g4BZ3cYZ5ohmc5O6s+WzLghzer9LTL0ShnIwyZmAJHC+ZegdqCTddDLiUbqy63OgHNUDHOC252Qq63A/7B9Qav9i0lcb3mcR4/KzaaoeW559owSQtGy4Kq+8WH0bVWwL1exK1OyN1+lVud8NcG8v1N0AwU46XdvorngAuzWUEjcJgkBU/GKdeaPp2mIvAkomnotVxqq5KO67JSdQmU/P/Yu7MeObI0ze//c2w335fYgzuZzMrKWrqq1D3dUA8w6JmBgJEGkCAQupR0MR9BgDAfQbe60FcQb0a6EKDRDNQXkgbqVu+VmVWZzCSZ3GPxCF9tt3N0YR4eEYzgzkwyyPMDCqhkLG4R4e5mx877Pi8Xux6PJinCEZy/6jBRioa2uNoLSHJFN7DYmhVkWZW+ha4uyiOtaDQlk1HJaL9qEN4dFXi2ZGPdpd2pkn1crwrImM0UnV6V0GMpQTbUJJR485O1F1Yxp4+jnCRWuPM4WSEEaar5R3/QwG9Ibu8nLDv2sYbcTy+GePMm4zv7KRc7h4sEpaEXVn1wg92CXv/wb3bQ7PymavVqtsTzfLYU8PvdmFxp7Kce07IFvSWbRst6qTv0T2u2rcWQTuP1nbaAOXC561NzJL/bjoh0tYCBKqkriRV3hymfrVS7iNFMMR2X7A9NNad0AAAgAElEQVQKxvsl/RUbxLP7mw4c7bucDEtaR4ZCloVeXBi3u9YLn28HnrX48Lyq5+O0NLKj5Hwm0sek0bIYj6oF3mxSRSKH84TATs+h3rRwnNP/nkKIZ5aA2rZg88Krpe15fnVzwvMl0pKs9zI6fYfeksPuTl6lqHVsuisBm52IJFYMdrLq5uk8Sr3dtRjuK7LConHKwusseNOI5f/8xo0bD4A/Bv63Gzdu/Nu3c1iG8cPSuioVK8vqDspsWr74i47o9Bw8v5oy3O3bZKlanBSkrJpzm47NKKlSgrQF+9OCCz2fYj61uNO3GQ2q4V/jYYkfSoSQxLGCGfztlzO2ipT1hsNnGwG//XJGHmtUCbtbOXJ+DhJCsHne4ZsHKdIW7DzJcV3BoCzYbHrYviBPNM2Wxd1vM4JQcmXFYzCrtr9X6i6PJhnffZPx6H7GlQses1gzmpT4TlVCV1iaWw9S6qVFUQr8ULCXFlzte/yfd0d8Ny/NkbKapDzYK4gTRSngziglKTWhDwma/WmBEIJfrdf5aS1EtDSfrPrcfZJw5VMPpw5LlstEFDyKM64GPpcveJxzAuxAcG8npdGy8ZQkLRUXmx4PxxmhL/n8k5BkBn/0aZ0HaY7jS0Z2yV9/PaUIFRuByy+vBFg5hCH0ag5SwLkLLiudKr+/FzrYUuJYkl+vV1t0nn34VimF4E8vHq9b3mi6jNOSKCv5Yivi56vvLnN/ue6wc2S+xWcbAbe2EtYaLk+mOYXSOFb183y6FPAPDyIcX3ClHxA6EkFVQtPybLqhw/fTFFtJtrKcC4HHIMq52vN5PM1RStPpWbSXLFQscCzBl1sRhQZ0NWMiaEomoqRuWWwXOV/di9kucx6nGbtU5V67OwVZqnAc0IngpxdrrDdcxqMSWResNh1CKfnqYcSwyPjtk4ikqK6g9uMC3xZ4Qjx36F2hFLuPC/Z3q+jiT5cCPCXJIk1/2XnlJv6XEdZfXMYlhODz5XCRanYa+wXD/Ix3qx3Y/GQ5JCs1v9uO+HaQ8CjJ+O39GSvznVkhqrv3a5suti1OLb86CIrZHxSLCfNa60VYxHBQVCXJR0wnito8Ra9qPn/zi9Hekr34ni+S5xrrR4hHfh9IWUUnx5FC6er1HR4pDbOd17/58To3G5bWbISAbs8iIUQnEcurDkmkjyWnbqct2vUqPW06PrwBNx0fpDG+eojJ++KN9gFv3rz5b4B/85aOxTB+FEFYDatqti32dkssq6oxjub1qi/7JrS0EvD44Yg0KYmnmpUNZ7ENH9Ykjx6XWI5ACPh6J2K17rDacLj/JKMINJ2GzY6VV6kpmULKalrvdCzJc8XVDZ/QsnikUqZjhdOEmudSW5b4ueDLbyOuna8aKzsNh3ickqaKpctVROf+tJqsrEsoM41lg21Xd+B2t3P8psAPJL4vuPO7BIuSz9dCnjyoLv7LGvxkw2c6UXw5iOgt2awuudwbply/FvDXfxdx9aeCbuywO80ILMFOkfPtNwV1SxIphd+CK9Jnf1ryl08i/milxld3Yh7tpLQCm37X5l6UseI7xI2Ivu8Q5zmryw61JcnuXsG5JY9BUtBt2wx2ClwftrYyeoFNWYJsw0+CgP/n3oR/cb7DPVK8UGDnsFx3Wa67PLyX8ZN2QK1h8fd3ZpzvesxiRaMpqEmLetOi0bK5NYhZqjnsxwVXuv6xxctRT98xB7jS9fn33w3JCo1/yk7Mj+loKZQQgk7NZmuUYwnIDyLGA4nWsOw63ItSPqtXC68LbY/vhymF0izXHLTWPNnOaLYsrERQzGDmK+qhRaSqxLytMmO5ZrNV5HQDm28GEb3Mod2r+lBCIRnkBde9gLyl6fSqmnshYCQL7m2nRHcUl695BC1BMi4pC9hWOZ8uBdyWCQ93MoSAP78z4c+utPjrO1N6dZtZoggcwZo8GTs8zUpCxyLKS0Qi6K9V087TRLG/W+B4gvAlkpx+aJYU/GT5bA6bMw79ZqPOF1sR/ZrFUs3hcSHJvaeGLjuHiZaziToW411vSPYG1Tkpiaop8ZNRdV6ynWrGiAZGeyWa6qJaKf1Wdg2PelFoxIFaw2LrUc7GubMRz/02WJYgS/WpceWNH/m9pJr/BI4nmfhd/N0t8u55Wu2qtHBt06UsNYO0SY8t7N4qW48LukslQSBR5fx6aOYSThK8xtkL/zib+0eG8QY8X5KlVQN+b+kwSrK/ZDPaf/kdmSSu4pT3dkuyTB2rL262LdKJJmhKHkUZPe3QatskE03dsRirgjxXBEHVF2DJar6DZQkaLcnj+zl1z6a/7OBlkkGUMduBC+ddEq3wgyou8uCO+lrDwfck29OcJC7ZyjKWbJskUtSkpFCKx9s56+erhJvZpBp6eX8n5avvEzxPM5oobn2fUCrFp1d9aoEky2Cc5KwHDjuDAhFoPFvQadikecl0AJaGL++kfLObkKMoUo3fF6S5ptW0KaTmfM+jjQV1yaVPXS6t+bQCm8GkuuNYLyz+q0/7PNkuWF9zWNt00JFA1MFRsnrDtTUt12I/zqsG7rpLmAn2s4KHexlrXYdRUmLbkr97MiNXYAlYrjmEHcl4VDIZl+SJplW3CdqS2NVstNwTd8tftx3in1xqMslebVfvhyDE8enwl9Z8Hm6nOJZYDHP0A4nnCxxLslKrYpKh2nXK53Ghgqo04no/RArBxrJLx7L55lHMJ+sB00IxnpfWRXk1t+dqz+dvHs14OE75D/fH5KXGyiW/ul5j93FBq2MtBi+2uzYXzvtcXvP52U9D7mylNLqSaKrZGxVVBK0UXOsFXFny2QhdfrNZx7Ul52oehdD4tlw0Wx/8HUulub2X8O0gYb3h8GCUsRTYix0Nz5d0+jZ+TWKZs6DxlthS8Mu1GlLA17sxd6Iq7e9pgmqH5SCCe/HvUjAdV/N8hKzKf8tSL84t03FVwnQwN6jelO+0XNBxq5Kys3oX/3U029Yz5y39mPygGvLc7dtV3LXtkEQFSaxYXneJZ4osVdz6KqHelCy3M65cr3YBb3+dsPU4p9W1aLQtdrIWznj7Xf9Ir8W8fRsG1c5JHCvQx/PznyWaKWp1h2bbIggPB1BB9fVKVReDvaaNrQRlUjXqPt7NqbUE2LD9qKBWl6SJYjqZ75pozd5OiZTVDs5ov+DSVZ9oppGWJpwPwSpkSWhbi0m8UgiEDReWPf72y4j9R1WG/GRcTXpPRpoHT1IeTjP29wrqDYuOcOgu2fzB9RArsigtzVaZU6tZ6BLWmy7NlmQ4U8xQ2Cns7ZXoCP72H2aEnsV+ltNuW5zbcPgXm120AqcpYSq4etHHl5JoqihTRadj06hZfNILuLebMs0KokKxFDq0u9WE8ThQXLsQkKWgGpqlwMF2BRc7Prf3E86vuhQzwZ1xyqeXAjxlMdgq2JmV/KPLTYZJwe+2Zwjg1xs1JllVk35txcfzJE/GGf2w6vvAAdcSi2bvo3/35ZpDlL96wbclJf/y0+4rf93bdqHtcf/IbBiA9ZbL7d0E70hp0ni/5NqmzygteTjOeDBN+Xor4tE4oygPfx+BK5nGJUttF98XrPYdHo4zrvQ87kcpZa7Zy3KWPIfzbZ+fLYcENYuOZdO2ba6vBgghWN1wkFIwGVWL6ANpofjLJ1MarqTh2QzKnKkoOdc8jJWtNSQPBjnnWx7dwKbhWXy+WmO14dDGodG2UFrzxVbE7f2Ecy2XX67VqrTAUmOfsqu2M8sXQ1kN423phQ7X+wF/cqlJcUqv/tFBzEclscL1xKL0bDgoTuyyHL3hYlmCeuPdXlBvXjCvn3fB8wVJXD2HOj0bxxHsTaq/hR9Ui9uvv0hAay5e9ZHnLyIe3ePcJRfLEthWlcJ499u0Cifobb7LH+e1mUWMYVDdmU2Taot461E1sXi0f/zsUxaayahkuFdUOxz16g5bq+MsTiRVqVoVp7yyZLM/LViqOQhgkpbEdcVgXJDFmtVNB8uWrJ1zqTcsVKl5cDfDsgXLaw6jYUFZgutKhIDWxuHJ6rsHKevzuuWDEjY3FLQKi7txwmrLZTYpqTUk3b5D0JDkhWL7cc7tBzG9ZbsqJapXsYt04PMNHzVS7JVFNdBrWvJkO6NMYXtQoDLYGudMpyW39xP6lyxkKhhEBbNC0WpbzHYVo1lBvWlx/VyAnQnsXDJLSn5+ucbWvZyvHsTsRiVfb8W06hbnll2C0CINNZu96g22LDXjtMRKxWKL/tN+wO93Yi6ve7hJ1dT4+Sch06xkrWMzzUq0hl9v1Fmuu4SBZHuYMUoKHEvS7lrsDQpqrqTVsfFsSZSpRYjjKClp+9XftBPY/GL1MOf/VQTvwawE15KLYaQHVpYcrgchvpLszXtmtAbPkWxPq0SbzzZDVl2XP73YJC0V8Xzbptm2cDLBOKliV7eHOd8NYnajgm8nCXYuWOk6xPN6/SXp8uUo4lzLYzot6cyjOw8meRe54qtBxD88maG0ZifL+WW7xl5e4maSS+sel9b9Yxd6caSQIZBX08sPGph7oUNZVNPDvx0kXO8HXOsFi13KQZTj55JG6+TfZZapY5G5hvFjsOYljU+ng0VTNS/zrErEphNFs109b9NULQZavk8+pl2Y98nT1QONloUlNMO9qnfKFzG94e9Zm1dfCNeDIkcKQX/VYjorUUqwsuawuu6izmhIw7s/2xrGu3DKZouUgtGwBDTt7mHEqtaa3a2caKYI5tGt3aXDEoGwVsUVlmWV0pSl1Y7O6rrHdFCdqNxA8t3DhKs1n3GkCJpVOlMQVnfdhICgJrHtqmZ6adWphl1OSvYHOUIIHu3m/P13M/a3c+JYk6WC4V7JcFDNkxCi+u+fXA1wOoLeksPWo4LdJzmqgFGuuLLkkeeara2M8bBgsJMzmpU06za1hk3Pdfn2XoIfCtbPuzwZFkxbJZ/0fZweLCub85seSz2Hq92Abs3i4VZKkFeJNmWq6acOy02nmpFRaK6ue8SAlQuWujbRpKQRCopMM5iVzOySbx7HfD2O+KTnc3c/4fthynrdOZYS71iS5bqDtuGPLtcY7Rf4nuRC06dVsxjGBZ8th6w3vfnfxSKJ1KIBXKHxAklvpfrbebbgl52Qe0lKlJfsRgX98MONCxVCsL7hstqq+rL2BwXhfCEwSkuu9nz2kmo+iiUFv1yrM4wLHo5Ttp/kLC/b3H2YsR0VLNVc/vGlFkrBZtPl9l7CSt1dvKx8SyAtwSQtsZ+68JpNSu7GKRdCjwu+x188mBLWqhpuL6xS9Bq+TadmUx5ZiI1nJZ2uTTyPOj9oYI4jhR9KkkJhySpc4KjdqKAdnB5NrF+7cNAwXo7rzs8JT/F8eawfZjIuqTfl4kYYsJjpAdUC5+n5IoZxlONollYdbFnSzx9Rnr9GY1rNZBwPS6axhR9CrWaTpRpdaqKpYjZ5PxfIL8MsYoyPkzhZNlZvSjo9m6UVh/GwugNdLWAKuvOY02elBDVbVaSsEILJWFFvVp+r5zM5nuylBIXEdQVXNzzuD1N2tgum83KwVseizKs0J9cVaK1ptKqhaEIIfvFpyB9erbO87HBtKWT5XNU34nqC7pLFk4c5sgAs+MVqjWFc4LhVUEAUKayWxnUFd75JWe+6PJhWmfR7uyWP91KurHm4ruDaFY+atvkPX0yYzRS7k4Llps3FSx5JDNt29bv4jz9rUuaQuxqGgm7HRoRQCyx+9qtqYFu7a0NLsNJycW14+DhjO85ZDVw6HZtu3UEG1cV1Xio6gcO3eykrdZeLHY9ixona417okJea0oZHccZv786YuQWlU0UYH1UoRS906IUOaVLyuzsJP7nkV82w80WfKyQ/X6/xaJyzNcs+qHkaTa+KVH6a60n8ZrUz5fmSO/sJv96oEeeK/fj45/9yrUZRwHeDGJ0JbB8G+zl1V6KV5uerIaFrLZLZBNWiYivL+fV6jaEscAPBbFrFyg52cr54FPHzzRo6B9sShKUgLTTTekFDWdSORH3a9mEU+tY053zLxXZgNKx2RId7RTWLJZTc3ku43DkZU5onerEDZBg/trAuq93upzTbh8l1ZVENH3Q9iR9IskSRJtUuzEHJkGE8TxwpfFdRq0vKu98Rr1/n3LUGpDF7OwWeL8i7a3iDB2Sp5vI1H2lVKXm9lSr++ywy7+zGRymsyRMv2offZxRFNfywLMEPBA/v5fSWX5xYJqRY7O60jsxmsNwq8ji3NCt9F9cTXO74JGNNZJeLeTVCClKlWDvnEk0Vk5EizzVhTRBNFY4jafg2o6jAsgWhIxmnB0loFkWusaYCqwuTkWLVd9jOcvJMM5sqxpGi23RYu+SyecHDnknuxSmPsxRHSaZjxb7OubuTsrwh+XIr4c9/P6TISojgL29N+fxCwFrDoVdz8HxJkiiyBC6uedSFxa27Catdh29/n7L1KGNrO6ecau4+TLnc89kXBWtLDnGm2N3Kaa1YfH4+5Hzdw/Us/vRCg0+XAgKnmnacxOrU3/uljo8UgutrAddWAv6gV+epyik2mx5/9WBK27LxJ4KvbsdoqYlGmtF+yd39lEtHLniv9nz+cONsDvt6ltWGy9Y0P/VjF+cJZKXSpIWmH7oMk5K9qODJLOfbQcKDUUqUKxrKYmnFZhYrprpEl9Xi4tGDnNF+yfVawK97df7892O8umTrcY50oK1tHjzO+P33MfcmKbvk3NlPudLzF+luiaVoujaXGz79msNK6PJgXtoG1Y2Fybhc3HAYDxUguHDFWyyUm22L/bigc8puy939hI5tE4TmVGe8Gy+6MaJ1Fanc7h6/YRPNFGHNQojq/3u+eQ4bzxZHijAAvvmC5ufXyFJdzYZJGzT9pJon47joNAVRVXxMpyVhXRCEltmJMYyzxPUkeXp45RvNFEurDtP5IKtmq9qlCMNXyH2f7+4cjXkVEvbKgstLAbVGFZc5GSnWeg4PZml1kTYqyUrF341maKp66SxTWBbEkcbzDx8/m2oaLcm5lsfDUUqtXpWceb4gizXCrb52Oqju5D2eZOznOfVcErYEX4wihoMCFWl+9yjmwSQjLTR3dxPujTM00Ft1+I9Wa9zdzVhZdln1XXp9m40jF/2zacmjSUatLahj4SWwfbegyKrJxNISPJ5kbLRcSlfTcGzGosRKJN8UCS3t8MvzddYaVe+OG4oTDatrm4dN3U9bqjlIIeYJW5Jioknyw1SwwKl+182Gxcqqi9eX1NoWnb5NrS4Z75Xk8fGVz9NlSB8yz5akpeabQcy1XrWDdanj4dqC5brN+YZLN7T53U7MOClJS7ja9YmykqGsFtKOD0NRsKNzsobCLQX/9rdDvtiLCErJTJa4dcHFdY/zPa9KGOv6WFQNqV4g2Z7lXFr32RnmfPcwodWyKJRGqerCbjKqEnb+l9/u4aaSoCZOxCgDPJlkrDWOP19u7yV4VrXgN4x3SQieOQdof7ek0z+93BGqHZvtx/mxIa6GAeB6VW/VbFpWz4+VDdi4gHAc2l2bNNH0f7KGtfMQgEbbYpI4i5tC9YZkvF/dzPXewnyhd+FsHrVhvGVpXGXyH5xmbEewfs5FvsKFbaN5PHFGa03DspAltDtV+tZsWs0AqNcs4oP0KwHf7Mb8k0st7o9SPB+yRC9SzqRVlZeVpUbIwzt7qw2XQVaV00RRVXpQpNXgvnrT4sqay5NJwShQnFvyyCZVgtTjvZxJp+AP1kKuLfv86mchcia41PZYb7r06y6lpbmy4vOLazW01EyfKO7dTrG04Pv7CTtPcixbkIyq+M9BXNJdE8RxiW0JkrikzBXbuzkPHuXcehiTTBR/P5hxKXDptg97T7ZnBZvNZy9YXsQPJJ9d8Pnd3WQxIG5rO8N2qwhfP5BM0pJOUD1mpBTLyw6WJV56oNtZJYU4FrV8VM2VhI61mEZecy06fhXbGk0VoWOx7Dps9j1+uhJiOYKygF+t1rgXpQyikrWGy7VewPXlkN+cr3F50+Pn10IeZhl7cc4v63Uuhj539lPysgpRsGzBdFLyOMlYnieDTaySS12fDI0jBYO9Koq53pA4nkCPoLkqcd2Tf69H44y1I8+fUlUJZcs1h5qqykBP8zIphIbxNlRpZCej1yejchGtf5TtimMDLDcvvP77o/HhOph5l8ZVyazwfET9cBBzqzMvWdTV9YRlCcrOMv5kqwpKmQ8IzrOz+174YZ/BDeMlxFF1VxgO8/sXXuG1XZWhHX7BaL/k4gWfS6v+YtLvyrpDbZ5ktt5wubUbM5IFbV2lZeVKE800Ya0q8Wq05CKOc7xf4jUOT3adwGYYF2itcWyJF1hkcbWF7PmSW49Srpx3uLbk8miaUzqabu7wJM5Y7npstD0utDweTDKmeUktt6jVLRqexU8v1PjNZo2v78U82M355Wchjis413MZZSVlF7ptG1dLLFtSZBrXl/ihRalgOy/Y2S95QMr1Cx7tpsUfX6rTqlvUtU2nb5GlijxT5Chqb5gQJS1J2JEURVWqtq8KNnoeav637IY2O7OqtOrxJGO96c5jKD/st8BLHY9v95JTP7bZ9LjQPt5DstH0eDjJF8/7ItU4853AekMSKouo0FzvB1xc9lCHlV8IBKt1l51ZztWej5tYpGFJkWt+uhzwD99HhDWBV4dvHlZDRXuhw71RyrmWx6U1jyfTjAttj8fjrHrNCPhiEnG9HxA9Iz5nlh+myuWl4ovtiJ8sBdRcyTiqbhqcZpopmp5plDZ+eJYlTqQ/RbMSITi1TKzesI4t2J9OMTMM4EgP7gvOY+vn4fH96ms8H09FzCbVMO5m+/QF9lnxYZ/BDeN55ueFJFKLrfr6U7sptivIs1dveEsThWWLE0EABxUDlhCQC2a7it1ZTs2uLqYOFlDNjoU7j3227fmEZ1G9aR1dZF3p+WwX+aLEJqxLth5nFJbCQ9LBpa1ddKnZSXP+2a9aNEKLwJG0OhbdnkM0UXTOS+5+l9Ga12WHNUmrYeM3JW6tmqUShNWE9yLTJKlib1Tw2acBiVtyccPHcSU7Vsb3ecKtOOZPflnn5+063cBB1wWetNjEo96UNJo2s6lid784Ni/kTVzu+GzlBf0VB2ELNlsuD8cZhdKnzoL5GFhSIAWL4ZUv4liCYr5zo+ahFEeFrmQ4DwsIwpNNx8t1h5+v1rATyZVzPnXP5sE05ZudGEsL/u+HE36/FXO+61FzJIXSxLmi4R02ORe5RthV+MJv5zsqP7ke8KI/ndaar3Zifr4SYknBaL9kX+TcHaanfv6TaTUzyDB+TFpr9ncLtK7ON4bxJnp9a5HU+CwiCCGJgfmuYGwxm6pFOp7na6LB5Ac/1h+CWcQYH7UkVrhHek5s5/huSu0ZyTLPUqtLZpOy2kWZn6C8oLrYazQtpuPqe63UHKK9kt2sINQWuJpoWpLNNGFDImWV336QzOQ4glbHohPY7Cfl4tin+4oyBSesjn2j5VLUNXe3E+rCor/s0F+26TkO+8OCaayYFSXdoLpotO2q3Mh1bD79mb/o/ymV5nGcsR8XrC45TObHXZYQuyWNUhK2JMIWTKKCrVl19z50BVGm+OfXOjSDqv8kqAsEVbldp3e8ybpKnDqZKPU6Di7A9+OCtm8ROhZJofh+mHKh7XGx7fF/fT95a493Vlzp+nz3jN2Y5xkPS7y6oOlZjJOCB+OMlbqDfkZ52sHzPJ5UCTm2LegGNp+fD1m2XM61XH6zXsPKJFFYpYvd2j3syTkQTRWtlsXfPJrx+XxBIqXAloK81GSpYrBTLaR2ZvliIfLVTsxnS9VQTaU0WoHvnpyXA/OBtJpFKZ1h/NCCUDLcKxjslDQ7lolLNt6K8GWfR36AjqPqnN/ssxYMqpui+wPCrVv47eCHPdAfiFnEGB+tWl2ys1U892RS1ZO+/Pd0PcneoFzsaMD8jnVUzYtJU8XebkE+1Xg1wa82aqz4LvdmKXGiWAoctqKTiVKNloWUgl5gM4hyBjsFZanp9m0+Ox9wd5hRb0jSmeb+foaXWmwcqaPevODSVg6/uxOxvuTwaHL4GEWpcSxx7PdwZz8lLhRN32KcleS5piiqmGZlQeRpNlsutwYxUgnONVw+WQ+4N8oJnOriFap+lUdRzsV5KMBkWoIL06xEuWA5L07veRUbTZe/fTxjpV797FqD0hpLCjxbcr7lvhfDKH9MUhwsAF5+MW67gvGspO7Z9Gs2O1FBnCuWeg7p7PAFIeXhoj8IJdNxNXD0oERmOi5JYk2eKzxP0gocNpsuF7s+d4cpLd9CHvn7Nz2LaVpyrunyq/UaR1sFzrc97o9SZhPFfI4lw6RKJbu9l3Cu5S0GXI72ykXa00rd4fHkSN0bcHeYcrH9cS1mjXfLDySWLegv2yd6YAzjB7d2Du7fBkCENex4gr7zDWQp4upnSOtszkj7uM7mhnGE40r6yydfuH7wZtn8mxec58yTsej0LBptC2lVZVrtrsWm43FvlCKVID3lYnO0X1AU1WwTrTS2zWLRIYTAklBqyDPNRs1luescS1XLSs3mksOtOOFqL1zMkCwKje/Jw5CBuVJrslJTd6uhn8m8YV4GcL5VHes0VfRDh1pPMslL7k5TdqOcX63Xj32vXGlcSzIZF9wZJ+zFBZO0pBCKTzfC1/01n6rhWfxm4/jj20d+D0/PkvlYXOl6fLd3elnV0/qhQyRKEkexUq9S4LSu1vKWJdBHnioH85EOzGaKRqv6fWepQinIUk2aaEBXuzgCXEvyi0s1vPT4DYRwnmomhEAKwdY0Z2Xe/G9LQaEOwwGKolo8PZ5k1F1r0d9SFBppsSgXbfv2Io78QFZqPNuc/owfV8OUjxnviBAC1s+jH35fhRDRgPULiJX1d31ob8S8ixsftdPmRxwkfhwQUqBesqcAnr+z4HqyasYblXg1QVCr+l4kgoawGST5qX0bqmQxgDON9KKWepKW/H4nZqXm8N1uTBwr7sfpYq5yeYIAAB2LSURBVAGzPc14Mkl5MM5Ybbj8+nxVnhM6kllWMhkVuLXjx7s9zVmqOezMcs61PGwpaPUlnie5P8o43/bwbcHfPZkxTkvu72cIKWh5Fn+4WWeYHF4wTtIS1xLEkeLuXsofXKyz2fRYa7is1N0fJNb4aLP25a5/onn9YySEwLUEaVE9r6O8et5M0pMNnZ3AZpwqhHNYbjXNShrz8IWjiWdiHlihlGawnZNEit2tEqUU41FJs23NE3JgOlJMxmqRFjabVDHiw73DAZtFAdaRJuZJVtL0D280pNMqwrzelAyHBYJqN2a5ftjbMh5Wj7sXF/TmpWZNz1r08jwYpWw0TNqTYRgfF1FvglZY2QzVXkZ4Z//caBYxhvEC1cC9N5tm63iCLD3yPXR1Aej5kv3dHAS06xaEMBuqRaoWVHe0bVfgOFUUoirg2/2EW4OYaVZyve9zf5wRjTRLG5J0F5rt6qX9t49nfLkdc3eYsFPm7A1LBlHORtPlwThje1qw2fIWfQ8A+0mBawk6vs1eXHCh7XFnK1skoIySEkcK/vH5Jo1Csu54nF91GaUlV7oBjycZtwYxX+/GjJKC9cBhFin8hvzRZ7HYUhwrV/qYXep4fLkd8fVuzCAquN73T5RZPUtcKNYa1YJgc8nh7tZhj43tVE30GljdcGh1LR7czen2qsWHUpp6w0JpzXRSlZvtbhcE89lAGphOSlR5MkjgaaFlMcmqnZonk5y00HzSO6zlzjKF41bfdy8u6PjVgmntyODPWa6om1QywzA+QmLzEjy8+64P460xixjDOIVlHZarVCU0x3dHntXcfBqtq8jk6KmAAF9I7j9MwRbskvMkzVF5lSJ2d7u6SPQDyd6goN6oopa3BjkPJxlXuz7XegFrDRchBM3Sotm2+MtHEZ9e9NmLC24NYlbrLudaHudbHp+uhFzrBPzF/SnTeeJaWlbzQFYbLvd3M9JCkZWah+OMX63XGEQ5lhRoNF9uRxSl4q8eTlmVDulMMbVLPjnvM07LxQ5IN7C53PG53g/oOQ7TiWZX51zpfpylXO8LIQS/Wq9zvR9wruU9d8dQP9UI9sfnGovPb9cdppFapPY1mhaNloXjCBpNi72dAi84jJSdjEoaLYu1TRetNdNxSX/ZxnGrhDytqjLI7ScFrbZFy7PZj3LUU5m0SaxY67rszHvGoqIkdOSx5vyjgRoHP/MBRwrujdLFbBrDMIyP0oWruLvfkyZvdnP2fWAWMYZxikZLMn1GdrpWmgffn2y+P81wULC3W1YLmPn1VDQtKUtNQ1gMZMFUlVxseXx+LmTN87i+EfJ338+4N0zwfEGWVr0wjycZ4zznYtM71jczGZX0mg45miRXXFz1+Go7oulVM1+ARTxt6Es+b4R8cWfGYD9DHbkhPdtT/PbxDM+C6/3g2AVgy7cYJiU/Xamx5rms9TxaHRtFVXL0ZJqz1nCJ8pInuzmD3YLhYB7F2xb4ttkReR8JwbFdvwPOPAnsWcK2ZDpRi5PgQQmXtARbec7KmstoXv6oVHUjQAjB2qZLu3u8D63btykLTbMtUQqcRHD/ScbX3ycs+4cLjnimjk0t39MFHQ6/V55pnOfM07jU8Xg8yRZDTw3DMD5GwvMJuzWie1vv+lDemFnEGMYpxLyZ+YDtCIZ7BcO9gof3slMv/J6WJgrLEfSWbCy7KrlJE8XOk4J6y6LdsfnlWo1PNnxm83I12xGshy71ts3eoGA0LdhNcr7ejZECLnZ92p7Nk0nVOzPYKXBcQViTfNL3UWj+4sEUWwpmmeJC20MeuVCtNSzOr3vVjBjlkKWK+ztVw7cbwL2tlE/6x5vt80zhOHIRhZuliu9nKbcGMYMoJ84VjhTc3U94Msm50HSZ2CW7FPiB4Pth+tE21L/vNpseD8YnS8o2Wx5Lz9mxEAiaHYs4UsymJVJWr5mtaUbuzJ9rdclsevxGgHxGpHFv2SaaaaYTRbtnEbQkdlNABrNpWc2sOXK2+v1OxOWufyw5cDIuF/02px6zEPzRZuOZHzcMw/hYiKVVQKN3nrzrQ3kjZhFjGM/gHUkpqzct2l2bdtem1rBwbEF6SlP0gaps5rC0xQ8k3SWbKFI021WT/AEhD2OcGy2LybjkQtdlK8p5tJ1zcdljre6wXHPIUk2rZRFNSwY7JZ2ehR8cfq9uYLPRdOnXHMp5tLCGE7sgK56LaAhaXZtHk5T//W+HbI8L1hveiWCB2VSxp3JW6i5b+xnbacE4KVBKsRcV/MWDCVFe0q85rAcufmBxpetzruXy1U5MyzN3vt9XgSMXzf5H2VI8dxFzruVyf5TS7tqUBbQ61fN8lJRc6fnszHL8QDKbHN89eRYhqujZKgTgyA5gx676Xx7mtOYDXc+1PL7aifmkH4CodkaLXB9LBMzLamFtGIZhnE70liHL0Hs77/pQXpu5ujCMZwhrkv3d4tgiIc+qeS9BKBgPM8QzbvyO9o/PigGoNySDnfLYAuY0UsJq4LLbLJgNFfdFRs+2eTTJWZUOtbpFbWKxb+Xs7+doDRfaHjuznJ+v1ng8ydma5vTDw5f305VcohDcnib80ystnH7AeFiSa0U0VdzeTxf9K6FjcXc34fK6z5NJxu8fRvzBpRBBNVjyTy/6i5I1qMrn2vOGbs+W/HT57UYoG+8Hzz4cItlsH3+edwObb3ZjlmoOy2vHF0JK65cqK+wENntRVY4Y1iRh7TBNzD/yvGq0LMYjRVlqOr3D43g0qcobDcMwjNO5viSrbeJu30U7LqLReteH9MrMToxhPIcQVbrSgemk2l0JatYzZ8lkqcKyxIlZMUIIpuNykfJ1VHCk9KbVsVAzINesrzr0LWde3mOzNat6cS6tVY391f987o1Svh+mhE61C7LecPlmN+HhvFQosKtI5epnKJlS8qv1Gt/OJ7mrUtPrOKgcSqUWgxF7ocXOtGCSKcpC0286jJKSpZpTxe6alKczz7NPzgl6HcO4oOU/+/mQlYo/vz16qe/V8W1cSzBKikUp5DQruTWIuTWIFyESliXIc7XouTn6WGYOjGEYxrOFNUk8U4jzl6HefNeH81rMu7xhPEezYy3msxxVDcQ8vZxsOlHPrM1fP+ecmgrleZI8nc/eEAIEfNoKSZyqFyCOFQ3LwrJhEB0PFRBCcK0XEDiSL7cikkJRas1PlgNqjuRc02Wj6fJoHqc7i0piFCt1l344n2Y+P6TlNYd6bPHtoFrcfDtIWKnbTLOSsLTwXqI0yDhbNpsuD8YvNwjzqCrs4XDGy05UlRwC9EKb3aeep7f3Un69XufJS8Q6f7Mbs9ZwSQvN7b2q/2qUlFw5ksp3IAjkIlLcMAzDeHXPS6t8n5l3fsN4DikPJ5TPpuXx+n5xMmq5LDXWc2ahuM8pJTv6nQ56A5TWrKzbbD/OiWaKK2s+O7Pi1D6Ghmfx2XLAk0nGg1HKg1HK/a2Ue48yRnsl8VgxHBQ8yXM+mTfpH+yopPM46SCQFDk0XIsvtmY0schsTcOW1RT054gjhX/K8FDj/fa6qXErdZft6eFC5WgrVS902I8PFzhpoXAtQTuwGT2nlwxga5rRrzl4tmS57nC1Vy1cNpruqcdaa1hn9gRsGIZhvD5zxWEYLxDUJNFMkaUazz98yTSaNtPJ8cXEZFi+9l3hsCaZTqoLPCkF3X7VW2JZklpNMhqWTCeK632fr3fjYw34O7Ocfljt8pxreZxr+Wy2PDYbHiqEds/GbwgGecHF/vEZIVc7PveP3IlvtCR+LhkmJeNI8e1WzNZOwf00wZWCumsR5SWBc/znTGN1rH/I+Hic9nw46s5+yqVONR265kim2ekLmVJp9qLiuaEChmEYxtvh+vJMz4sxVxyG8QJ+IEkixdP3em1bUhZPDcHk9bdlPV+SpadHN9uOoNWy8HzB/qBk0/e4NTicmj5MisX8i3ujlPNtl9CSxIVio+nyYJRScy32ioKWfzzPYzpVfLoRcGsQw/z4H0cZ14OAhpKsNF0+uxQwyRUPxhmrdYeH44x10zj9wViqOWxNX1zm9TQpBKXSPBhlbDaPPx+6QVVSdrALc/C62Gx5i16tp32zO08dewOjpFj0zBiGYRjPFtYkcWQWMYbxQbMdcSKFKQht0uxw0VHkGvs5w/ZeRqN1vAdHUJWUqRKkJXBdSbdv41kCTwkeT1Jubyfc30v5bq9q5J+kJa4lCUvJ1CpoeBaTrGQYl7SDkxd3ZaGpBxZNz2J7muOFEiEEnY5N7Gh+faHBo0lGP3SwJNwfpUy2SzO88gPS9m3GLyjzOs2Ftsu9UbWL9/TivRc67EUFt/eTxS7MAUG163LUQRmZ9YbRyNuznGWzk2MYhvHBM4sYw3gJB9PIjwprFtmRbdjJuKTeeLOXlOMIikIvSsWW6w7b05yi1Me+96MsYxKXfPkgxikEPelwse3RCSyu9g4GSx7e/RYwH3p5+FhPJhlf78bcG6XMspKVust+UvDtMGa95oCATCmavkUx/8Je6FDGYNUEk/HhRW80KwlM0/+ZJhCMjzTqvwzHqpLN7GcsPHKl8Sx5YoFzuetzZ79a/GituTWISQv91srITI+MYRjGh89cdRjGaxJC4LjiWD3p27h4anUsRvvVAqE530Wp1eViETVOS+quxecXavx6ucbdQUKzZpGnmtCxCB2LLFU4bvX5aaGqu9sC1hsu94Ypt/cShIDr/YBzTZdhUvLNbkySl9wfpWgFjx5mNOZx0EWpKUpNYEvars0vztcock05nxWSJcf7hYyz52rPZy8uXjmpLFeaC23v1I9d6fondmGgGqZZas3WNON3OzHnWx7nn/E9DMMwjB+O653dvhhz1WEYb8DzBXGkyFKF676du7+WVSWiaaWZjErioSLP9OJN5skkW0TMdnoOa57L+SWXaHr4JjSbKuqNqnTs20HC1a7PuZbHIMr5YjuiE9is1F201ggh2Gi6fNIPcKTgXNPl//t2xr29lIudaldnEBcgBGs1ZzE4s921GO69egmS8f662PEJbMnvd44HRzzPL1ZrzywB8+2TuzAHNpoulhR8thy+tZkueflyx2wYhmFUwprkJd/u3ztmEWMYb+DgAm02VdQab6+ZuNW12N0p8ANJ0Ja0uzbx7OSdkiLXtNsW431FrXGYbnZgYz4jRogqVUxp+GdXWotZHdFULWKjJ2lJw7dZt32uX/bZT0p2BlWE7p+cb2BLmIwVrXlvkBCCsCaJpmYh8yHphQ6Xu8eDI34IddeiH7693hWlNV/tRFzt+i/+ZMMwDGPhrCaLns2jNoz3hOs9O1HsTUgpWFpxFiVhB7an+bG+gemkarAfj8oq3SzRRDNFMJ/XEjoW7eAwjexy18exJC3fZj8uyDON60l2ZjkPRilNZdFoSi6t+PzZz5rc38tIC4UUAq2rWSDiyF33IJRMJ4qgbt5KPiSuJVGal96NeR98sRXx0+XQ9MMYhmF8JMyVh2G8gSAUFLn+Qe9iuJZcDLc8GqUM1UWmkALPr3ZEWh2L3a38hcez3nR5PMnISs2X2xFKazZ9D8cVi4GcYd3ip+cCvrgXMc1KbC1OTV9bXnPwnjPE0zibLnU87g5frT/mXfndTsS1XvDMgAHDMAzjw2OuPAzjDQghCOtysfPxQ1hvODyeZDieoMiO3xmPZppG02Jl3WZnq8CyBecuvdz8lvNtj8fTjMt1DyeROI4grB0vifMDi0sNj795NKOF9cbpa8bZ4dmS7Az0mNwbpmw03OcO2zQMwzA+POZd3zDec44lyZVmUBR0rcNSMq01ZVHNphFC4DiCNFUvXU4T2oK2slEKun37mbs3Qc3iN0t1pBSmVOcjs1qvFtDvs7RUNJ8a4GoYhmF8+MwixjDOiKRQ+PbhIiKaKoLw8L/7Kza7Tw7nfCil2dstntl4v/WwYGXDoVZ/fiBBEEpG+8WZbfwzXl/rNYdgGoZhGMYPzVyVGMYb8gNJdEpy2NtUKk7U++/tFvSXD3dmXE8iLYgjxWi/YLRf0ulaJMnJkiCtNdkr9PIsrTg/aMmc8f5q+xZ78asNwfyxxLl6a/HMhmEYxtli3v0N4w35wQ8/KMq3BRfaHq5/+FhPJ4VBtWsSz0pqDYtOz0ZIQa1+Mnp5MlLUai//8j+tod/4OKzUXban+bs+jFM9HGdsNF6uB8wwDMP4sJhFjGG8BUJU5Vs/lIsdH0tWc1kOhms6pywsmm0LaQnsI2Vnnn8yBjrP1bHPMYznseT7Gbes0c8ctGkYhmF82MwixjDegmbbYjz8kXoHNEzGJeEps1mkFFi2YLhXMNwr2B8UTCcl9YZkOq6ObzopsSxB8Ao7McbHbanmsD17P3djDMMwjI+TuYoxjLdAymoY5I9BaU0cKeqN0xvyG02Ldtem3bXp9OzFQMtsHs+cpRp0tUNjGC+j/R42+L+PO0OGYRjGj8dcxRjGW+L5kiQ+3htT5Joif7sXW0msse1qx+VlCAFaaepNyfaT3DToGx+ER5OcNdMPYxiG8dF6o3D9Gzdu/A/AfwZkwHfAf3Pz5s3h2zgwwzhrwppkf3AYRZznmvGwxJLQ7p18qalSVwli/Zd/GSaxotGSDAcvf1e80bIYj0paHRvf1wShJI1/2CACw/ihRXnJRtMsYgzDMD5Wb3pL9t8Bn9+8efPnwDfAf//mh2QYZ5tWmjyrFjC9pWcvUMajEi+Qr9RLM5sqGk2bjQsvf/FmWQI1X7M02xZxpPDNbozxinqhw47pizEMwzDeE2+0E3Pz5s3/48h//r/Af/lmh2MYZ1urbTHYKZBSHC5gRFW/f2Lava52b6KZYjIuaTSfP3RyPCxptqrPka+YyCQllKXGsgRprE7dGTKM5+kGNrcGMUs158WfbBiGYRg/sLd5JfPfAv/zsz5448aNfwX8K4CbN2/S7/ff4kO/Ptu235tjMc6WZz13PC+j1T7cKWm3FJNxTqfnLf5Na40uU/p9H/owHuVorY993VFFodBlxtKK/1rH2u1qBjvV4+kyqR7XeGfO6vvOTjGh32+868NgkhZsWDX6neBdH8qP7qw+d4x3zzx3jNf1vj53xIsSXm7cuPHvgdVTPvSvb968+b/OP+dfA78B/oubN2++TBezfvTo0ase6w+i3++zu7v7rg/DOINe5bkzHBTHdj+mkxLPEzjuYVnXbFKiNCd2ZIpCMxwU9Jbtk7s5r2B/UNDp2SeOxfjxndX3nVuDmGu9d79wuDWIudL1kW/wejirzupzx3j3zHPHeF0/9nNnfX0d4IVv8C+8krl58+Y/fd7Hb9y48V8D/ynwZy+5gDGMj87TL4wi0ycikmuNql/l6CIjTRWzsXrjBQyAbQtmkxLXRCsbr6nt2+zFBd3g3S+CP8YFjGEYhnHoja5mbty48Z8A/x3wL2/evBm9nUMyjA+P4wqy9MWJYEEoqTUku9s50awkiRTdpTdfwADziOWC0Ay5NF7TUs1hEJnmfsMwDOPde9Ormf8RaAD/7saNG39348aN/+ktHJNhfHBqdUk0rRYxaaJwvWcvShxX0u3baAWtztu74y2EYGXt3d9BN4w3sRcX1N3nh2AYhmEYH743TSe7+rYOxDA+ZEKIRUlZPHtxOpiUglrj7V+ohXVz8WecXaXSPB5n/HQlfNeHYhiGYbxjpq7EMH4kgiqVzDDOsqZnMUyKd/LYX+/GfLr07oMFDMMwjHfP1JYYxo+k3rQYD0vEK854MYz3yXLN4bdbETtOjkBQKP2jLCweTzJW6g6Wef0YhmEYmJ0Yw/jR2I5gf1DSaJmXnXF2CSH4+WqNa72Aqz2fjabLw3H2Ul+7M3u9UICkUEyzkl5oBm0ahmEYFXM1ZRg/otUNB2nuJBsfkIZnMc3KF37evVHKzixnGL9aKZrWmm92Y652zYBWwzAM45BZxBjGj8gPzEvO+PBIUTXdP8ssKylKzWfLIQ/H2Sv1hv12K+Kz5fCtxIwbhmEYHw5zRWUYhmG8kYttj++H6TM/fnc/5fJ8J+VKz+e7vWd/7lG/24641guwze6lYRiG8RSziDEMwzDeiGNJ8mfsxHw7SBYLGADfljiWYJI+vwTt20HCRtMlcMxpyjAMwzjJnB0MwzCMN+ZZgrRQx/5tEOX4jjixELnQ9rj3nJ2bh+OMlm/R9E2ApmEYhnE6s4gxDMMw3tiFp0rKhknBMCnZbHqnfv7Fjsc3u/GJf5+kJWmhWKqZJDLDMAzj2cwixjAMw3hjQggOCsrGacnOLOfKcxLFaq7Fct3h9l6y+DelNXeHx8vPDMMwDOM0ZhFjGIZhvBUtz+LhOOPxJONa78UDMNu+Tcu3Fjs4X+/E/GQp/KEP0zAMw/gAmEWMYRiG8VasNlzGacH1/osXMAd6oYNvC/7q4ZSVhmuSyAzDMIyXYromDcMwjLfmdXZSVuouvdAxCxjDMAzjpZmdGMMwDOOdMwsYwzAM41WYRYxhGIZhGIZhGGeKWcQYhmEYhmEYhnGmmEWMYRiGYRiGYRhnilnEGIZhGIZhGIZxpphFjGEYhmEYhmEYZ8r/397dhFhVh3Ec/04KtcgSdBNpEKSRSWDZC7QJbKERuiieNISiyZAwCi0waiG1qYSihUXZi9lCeWoRAxluUoLQ6NVFBiFmNRUoJm6kF2FanEtM0zBzuuD/nNP9fuAP3nv/MD/kx5n7nHPuHYcYSZIkSZ3iECNJkiSpUxxiJEmSJHWKQ4wkSZKkTnGIkSRJktQpQ2NjY0383EZ+qCRJkqTWG5puQ1NXYobasiLi86YzuLq57I6r32V3XP0uu+Pqd9kdV7+roe5My9vJJEmSJHWKQ4wkSZKkTnGIgVebDqDOsjvql91Rv+yO+mV31K9WdqepD/ZLkiRJUl+8EiNJkiSpU2Y2HaCUiFgOvAjMAF7LzGcmvH4+sBO4DjgJ3JWZx0rnVPvU6M5G4H7gLHACuC8zvy8eVK0zXXfG7bsDeBe4PjM/KxhRLVWnOxERwBaqP1twKDPvLhpSrVTjd9ZlwFvA7N6ezZm5p3hQtUpEvAHcDhzPzMWTvD5E1avbgDPAvZn5RdmU/zQQV2IiYgawDVgBLALWRMSiCduGgVOZeQXwAvBs2ZRqo5rd+RJYmpnXUL0Rfa5sSrVRze4QEbOAh4FPyiZUW9XpTkQsAB4Hbs7Mq4FHigdV69Q87jwJZGYuAVYDL5VNqZbaASyf4vUVwILeegB4uUCmKQ3EEAPcABzJzKOZ+QewG1g1Yc8qqjMTUL0RXdabOjXYpu1OZu7LzDO9hweBeYUzqp3qHHcAnqY6afJbyXBqtTrdWQdsy8xTAJl5vHBGtVOd7owBF/X+fTHwc8F8aqnM/Aj4dYotq4CdmTmWmQeB2RFxSZl0kxuUIeZS4Mdxj0d7z026JzPPAqeBOUXSqc3qdGe8YeCDc5pIXTFtdyLiWmB+Zr5fMphar85xZyGwMCI+joiDvVuIpDrd2QKsjYhRYA/wUJlo6rj/+n7onBuUIUY65yJiLbAU2Np0FrVfRJwHPA9sajqLOmkm1W0dtwBrgO0RMbvRROqKNcCOzJxH9fmGt3vHI6lTBqW0PwHzxz2e13tu0j0RMZPqEuvJIunUZnW6Q0TcCjwBrMzM3wtlU7tN151ZwGJgf0QcA24CRiJiabGEaqs6x51RYCQz/8zM74BvqYYaDbY63RkGEiAzDwAXAHOLpFOX1Xo/VNKgfDvZp8CCiLic6j98NTDxW1xGgHuAA8CdwIeZ6R/R0bTdiYglwCvAcu9L1zhTdiczTzPujUNE7Ace9dvJRL3fWe9RnVF/MyLmUt1edrRoSrVRne78ACwDdkTEVVRDzImiKdVFI8CGiNgN3Aiczsxfmgw0EFdiep9x2QDsBb6pnsqvI+KpiFjZ2/Y6MCcijgAbgc3NpFWb1OzOVuBC4J2I+CoiRhqKqxap2R3pX2p2Zy9wMiIOA/uAxzLTuwcGXM3ubALWRcQhYBfVV+V60nbARcQuqhP5V0bEaEQMR8T6iFjf27KH6kTJEWA78GBDUf82NDZmbyVJkiR1x0BciZEkSZL0/+EQI0mSJKlTHGIkSZIkdYpDjCRJkqROcYiRJEmS1CkOMZIkSZI6xSFGkiRJUqc4xEiSJEnqlL8AxH+SEMq0dpAAAAAASUVORK5CYII=\n", @@ -1061,6 +1085,13 @@ "_ = plt.hist(np.vstack(samples['SGPMC/kern/kernels/0/lengthscales']).flatten(), 50, density=True)\n", "plt.xlabel('lengthscale');" ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/doc/source/notebooks/multioutput.ipynb b/doc/source/notebooks/multioutput.ipynb new file mode 100644 index 000000000..8321a5e84 --- /dev/null +++ b/doc/source/notebooks/multioutput.ipynb @@ -0,0 +1,1133 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Multi Output GPs in GPflow" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$\n", + "\\newcommand{\\GP}{\\mathcal{GP}}\n", + "\\newcommand{\\NN}{\\mathcal{N}}\n", + "\\newcommand{\\LL}{\\mathcal{L}}\n", + "\\newcommand{\\RR}{\\mathbb{R}}\n", + "\\newcommand{\\EE}{\\mathbb{E}}\n", + "\\newcommand{\\valpha}{\\boldsymbol\\alpha}\n", + "\\newcommand{\\vf}{\\mathbf{f}}\n", + "\\newcommand{\\vF}{\\mathbf{F}}\n", + "\\newcommand{\\vg}{\\mathbf{g}}\n", + "\\newcommand{\\vW}{\\mathbf{W}}\n", + "\\newcommand{\\vI}{\\mathbf{I}}\n", + "\\newcommand{\\vZ}{\\mathbf{Z}}\n", + "\\newcommand{\\vu}{\\mathbf{u}}\n", + "\\newcommand{\\vU}{\\mathbf{U}}\n", + "\\newcommand{\\vX}{\\mathbf{X}}\n", + "\\newcommand{\\vY}{\\mathbf{Y}}\n", + "\\newcommand{\\identity}{\\mathbb{I}}\n", + "$\n", + "- $X \\in \\mathbb{R}^{N \\times D}$ the input\n", + "- $Y \\in \\RR^{N \\times P}$ the output\n", + "- $k_{1..L}$, $L$ kernels on $\\RR^{N \\times D}$\n", + "- $g_{1..L}$, $L$ independent $\\GP$s with $g_l \\sim \\GP(0,k_l)$\n", + "- $f_{1..P}$, $P$ correlated $\\GP$s with $\\vf = \\vW \\vg$ " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Multi Output Kernels class diagram\n", + "![new_multioutput_gp_kernels.png](./new_multioutput_gp_kernels.png)\n", + "\n", + "\n", + "\n", + "\n", + "### Multi Output Features class diagram\n", + "\n", + "![new_multioutput_gp_features.png](./new_multioutput_gp_features.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Shape of Kuu and Kuf and the underlying conditional code depends on Mof and Mok classes used\n", + "\n", + "| Feature | Kernel | Kuu | Kuf | conditional | note |\n", + "|------------------------|-------------------------------|---------------|---------------|---------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|\n", + "| InducingPoints | Mok | MxPxMxP | MxPxNxP | fully_correlated_conditional | This is the default. Will be very inefficient for certain kernels. In this case q_mu and q_sqrt are 1 x MP and 1 x MP x MP |\n", + "| SharedIndependentMof | SharedIndependentMok | M x M | M x N | base_conditional | These two classes are in a sense redundant as we can achieve the same behaviour using the single output Kernel and InducingFeature classes. They are added for illustrative purposes. But thanks to the conditinal dispatch the most efficient code path will be used |\n", + "| SeparateIndependentMof | SharedIndependentMok | P x M x M | P x M x N | P x base_conditional | We loop P times over the base_conditional |\n", + "| SharedIndependentMof | SeparateIndependentMok | P x M x M | P x M x N | P x base_conditional | We loop P times over the base_conditional |\n", + "| SeparateIndependentMof | SeparateIndependentMok | P x M x M | P x M x N | P x base_conditional | We loop P times over the base_conditional |\n", + "| SharedIndependentMof | SeparateMixedKernel | L x M x M | M x L x N x P | independent_interdomain_conditional | inducing outputs live in g-space |\n", + "| SeparateIndependentMof | SeparateMixedKernel | L x M x M | M x L x N x P | independent_interdomain_conditional | very similar as above |\n", + "| MixedKernelSharedMof | SeparateMixedKernel | L x M x M | L x M x N | base_conditinal | this is the most efficient implementation for MixedKernels. The inducing outputs live in g-space. Here we use the output of the base conditional and project the mean and covariance with the mixing matrix W. |" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Notes:\n", + "- MixedKernelSeparateMof is not implemented but can easily added to the framework" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import gpflow as gpf\n", + "\n", + "import gpflow.multioutput.kernels as mk\n", + "import gpflow.multioutput.features as mf" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "X = np.random.rand(100)[:, None] * 10 - 5\n", + "G = np.hstack((0.5 * np.sin(3 * X) + X, 3.0 * np.cos(X) - X))\n", + "Ptrue = np.array([[0.5, -0.3, 1.5], [-0.4, 0.43, 0.0]])\n", + "Y = np.matmul(G, Ptrue)\n", + "Y += np.random.randn(*Y.shape) * [0.2, 0.2, 0.2]\n", + "\n", + "D = 1\n", + "M = 20\n", + "L = 2\n", + "P = 3\n", + "MAXITER = gpf.test_util.notebook_niter(int(15e1), 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "pX = np.linspace(-6, 6, 100)[:, None]\n", + "def plot_model(m):\n", + " pY, pYv = m.predict_y(pX)\n", + " if pY.ndim == 3:\n", + " pY = pY[:, 0, :]\n", + " plt.plot(m.X.value, m.Y.value, 'x')\n", + " plt.gca().set_prop_cycle(None)\n", + " plt.plot(pX, pY)\n", + " for i in range(pY.shape[1]):\n", + " top = pY[:, i] + 2.0 * pYv[:, i] ** 0.5\n", + " bot = pY[:, i] - 2.0 * pYv[:, i] ** 0.5\n", + " plt.fill_between(pX[:, 0], top, bot, alpha=0.3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Shared Independent MOK & Shared Independent Features (SLOW CODE)\n", + "\n", + "We will use the same kernel to model each of the output dimensions.\n", + "We will use the same inducing inputs in each of the approximations." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "q_mu = np.zeros((M, P)).reshape(M * P, 1)\n", + "q_sqrt = np.eye(M * P).reshape(1, M * P, M * P)\n", + "\n", + "kernel = mk.SharedIndependentMok(gpf.kernels.RBF(D) + gpf.kernels.Linear(D), P)\n", + "feature = gpf.features.InducingPoints(X[:M,...].copy())" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "scrolled": false + }, + "outputs": [], + "source": [ + "m = gpf.models.SVGP(X, Y, kernel, gpf.likelihoods.Gaussian(), feature, q_mu=q_mu, q_sqrt=q_sqrt)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "INFO:tensorflow:Optimization terminated with:\n", + " Message: b'STOP: TOTAL NO. of ITERATIONS EXCEEDS LIMIT'\n", + " Objective function value: 50.005441\n", + " Number of iterations: 1501\n", + " Number of functions evaluations: 1581\n" + ] + } + ], + "source": [ + "opt = gpf.train.ScipyOptimizer()\n", + "opt.minimize(m, disp=True, maxiter=MAXITER)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Conditional: InducingPoints -- Mok\n", + "Kuu: InducingPoints - Mok\n", + "Kuf: InducingPoints - Mok\n", + "base conditional\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_model(m)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [], + "source": [ + "def vimshow(K):\n", + " vmax = np.abs(K).max()\n", + " plt.imshow(K, cmap='RdBu_r', vmin=-vmax, vmax=vmax)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "K = (kernel.compute_K_symm(pX))\n", + "K_trans = np.transpose(K, [1, 0, 3, 2])\n", + "vimshow(np.reshape(K_trans, [100 * 3, 100*3]))\n", + "plt.colorbar();\n", + "plt.title(\"Kff\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "All the outputs are uncorrelated, and the same kernel is used for each output. However, during the `conditional` calculations we do not assume this particular block-diagonal structure. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Shared Independent MOK & Shared Independent Features\n", + "\n", + "We will use the same kernel to model each of the output dimensions.\n", + "We will use the same inducing inputs in each of the approximations." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "kernel = mk.SharedIndependentMok(gpf.kernels.RBF(1) + gpf.kernels.Linear(1), P)\n", + "feature = mf.SharedIndependentMof(gpf.features.InducingPoints(X[:M,...].copy()))" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Conditional: SharedIndependentMof - SharedIndepedentMok\n", + "False False\n", + "Kuu: SharedIndependentMof - SharedIndependentMok\n", + "Kuf: SharedIndependentMof - SharedIndependentMok\n", + "base conditional\n" + ] + } + ], + "source": [ + "m = gpf.models.SVGP(X, Y, kernel, gpf.likelihoods.Gaussian(), feat=feature)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "INFO:tensorflow:Optimization terminated with:\n", + " Message: b'STOP: TOTAL NO. of ITERATIONS EXCEEDS LIMIT'\n", + " Objective function value: 49.912192\n", + " Number of iterations: 1501\n", + " Number of functions evaluations: 1605\n" + ] + } + ], + "source": [ + "opt = gpf.train.ScipyOptimizer()\n", + "opt.minimize(m, disp=True, maxiter=MAXITER)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Conditional: SharedIndependentMof - SharedIndepedentMok\n", + "False False\n", + "Kuu: SharedIndependentMof - SharedIndependentMok\n", + "Kuf: SharedIndependentMof - SharedIndependentMok\n", + "base conditional\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_model(m)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Again, same kernel used for each output dimension and the outputs are uncorrelated. In the `conditional`, however, we explicitly use the block-diagonal structure." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Separate Independent MOK & Shared Independent Features (SLOW CODE)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "q_mu = np.zeros((M, P)).reshape(M * P, 1)\n", + "q_sqrt = np.eye(M * P).reshape(1, M * P, M * P)\n", + "\n", + "kern_list = [gpf.kernels.RBF(D) + gpf.kernels.Linear(1) for _ in range(P)]\n", + "kernel = mk.SeparateIndependentMok(kern_list)\n", + "feature = gpf.features.InducingPoints(X[:M,...].copy())" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Conditional: InducingPoints -- Mok\n", + "Kuu: InducingPoints - Mok\n", + "Kuf: InducingPoints - Mok\n", + "base conditional\n" + ] + } + ], + "source": [ + "m = gpf.models.SVGP(X, Y, kernel, gpf.likelihoods.Gaussian(), feature, q_mu=q_mu, q_sqrt=q_sqrt)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "INFO:tensorflow:Optimization terminated with:\n", + " Message: b'STOP: TOTAL NO. of ITERATIONS EXCEEDS LIMIT'\n", + " Objective function value: 49.540682\n", + " Number of iterations: 1501\n", + " Number of functions evaluations: 1578\n" + ] + } + ], + "source": [ + "opt = gpf.train.ScipyOptimizer()\n", + "opt.minimize(m, disp=True, maxiter=MAXITER)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_model(m)" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "K = (kernel.compute_K_symm(pX))\n", + "K_trans = np.transpose(K, [1, 0, 3, 2])\n", + "vimshow(np.reshape(K_trans, [100 * 3, 100*3]));\n", + "plt.colorbar();\n", + "plt.title(\"Kff\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "All the outputs are uncorrelated, *but a different kernel* is used for each output. However, during the `conditional` calculations we do not assume this particular block-diagonal structure. " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Separate Independent MOK & Shared Independent Features" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "kern_list = [gpf.kernels.RBF(D) + gpf.kernels.Linear(1) for _ in range(P)]\n", + "kernel = mk.SeparateIndependentMok(kern_list)\n", + "feature = mf.SharedIndependentMof(gpf.features.InducingPoints(X[:M,...].copy()))" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Conditional\n", + "object, SharedIndependentMof, SeparateIndependentMok, object\n", + "object, SeparateIndependentMof, SharedIndependentMok, object\n", + "object, SeparateIndependentMof, SeparateIndependentMok, object\n", + "base conditional\n" + ] + } + ], + "source": [ + "m = gpf.models.SVGP(X, Y, kernel, gpf.likelihoods.Gaussian(), feat=feature)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "INFO:tensorflow:Optimization terminated with:\n", + " Message: b'STOP: TOTAL NO. of ITERATIONS EXCEEDS LIMIT'\n", + " Objective function value: 55.116299\n", + " Number of iterations: 1501\n", + " Number of functions evaluations: 1799\n" + ] + } + ], + "source": [ + "opt = gpf.train.ScipyOptimizer()\n", + "opt.minimize(m, disp=True, maxiter=MAXITER)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Conditional\n", + "object, SharedIndependentMof, SeparateIndependentMok, object\n", + "object, SeparateIndependentMof, SharedIndependentMok, object\n", + "object, SeparateIndependentMof, SeparateIndependentMok, object\n", + "base conditional\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_model(m)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-55.11629898369668" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "m.compute_log_likelihood()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Separate Independent Kernel & Separate Independent Features" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [], + "source": [ + "kern_list = [gpf.kernels.RBF(D) + gpf.kernels.Linear(1) for _ in range(P)]\n", + "kernel = mk.SeparateIndependentMok(kern_list)\n", + "feature_list = [gpf.features.InducingPoints(X[np.random.permutation(len(X))[:M],...].copy()) for _ in range(P)]\n", + "feature = mf.SeparateIndependentMof(feature_list)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Conditional\n", + "object, SharedIndependentMof, SeparateIndependentMok, object\n", + "object, SeparateIndependentMof, SharedIndependentMok, object\n", + "object, SeparateIndependentMof, SeparateIndependentMok, object\n", + "base conditional\n" + ] + } + ], + "source": [ + "m = gpf.models.SVGP(X, Y, kernel, gpf.likelihoods.Gaussian(), feat=feature)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "INFO:tensorflow:Optimization terminated with:\n", + " Message: b'CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH'\n", + " Objective function value: 67.682607\n", + " Number of iterations: 1350\n", + " Number of functions evaluations: 1444\n" + ] + } + ], + "source": [ + "opt = gpf.train.ScipyOptimizer()\n", + "opt.minimize(m, disp=True, maxiter=MAXITER)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Conditional\n", + "object, SharedIndependentMof, SeparateIndependentMok, object\n", + "object, SeparateIndependentMof, SharedIndependentMok, object\n", + "object, SeparateIndependentMof, SeparateIndependentMok, object\n", + "base conditional\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_model(m)" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Conditional\n", + "object, SharedIndependentMof, SeparateIndependentMok, object\n", + "object, SeparateIndependentMof, SharedIndependentMok, object\n", + "object, SeparateIndependentMof, SeparateIndependentMok, object\n", + "base conditional\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for i in range(len(m.feature.feat_list)):\n", + " q_mu_unwhitenede, q_var_unwhitened = m.predict_f(m.feature.feat_list[i].Z.value)\n", + " plt.plot(m.feature.feat_list[i].Z.value, q_mu_unwhitenede[:, [i]], \"o\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This plot shows that we use different inducing *inputs* in each output dimension." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Mixed Kernel\n", + "\n", + "## 1. Mixed Kernel & Correlated features (SLOW)\n", + "\n", + "Remember: $f(x) = W g(x)$, where $g(x) \\in \\mathbb{R}^L$, $f(x) \\in \\mathbb{R}^P$ and $W \\in \\mathbb{R}^{P \\times L}$.\n", + "In this scenario we ignore the fact that observations are produced by mixing uncorrelated latent GPs. We directly model the correlated observations. This means that we place our inducing outputs in the $f$ space and end up with the following (large) correlation matrices.\n", + "\n", + "- $ K_{uu} = M \\times P \\times M \\times P $\n", + "- $ K_{uf} = M \\times P \\times N \\times P $\n", + "\n", + "We'll have to use `fully_correlated_conditional` or `base_conditional` depending on the `full_cov`/`full_output_cov` args." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [], + "source": [ + "q_mu = np.zeros((M, P)).reshape(M * P, 1)\n", + "q_sqrt = np.eye(M * P).reshape(1, M * P, M * P)\n", + "\n", + "kern_list = [gpf.kernels.RBF(D) + gpf.kernels.Linear(D) for _ in range(L)]\n", + "kernel = mk.SeparateMixedMok(kern_list, W=np.random.randn(P, L))\n", + "feature = gpf.features.InducingPoints(X[:M,...].copy())" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Conditional: InducingPoints -- Mok\n", + "Kuu: InducingPoints - Mok\n", + "Kuf: InducingPoints - Mok\n", + "base conditional\n" + ] + } + ], + "source": [ + "m = gpf.models.SVGP(X, Y, kernel, gpf.likelihoods.Gaussian(), feat=feature, q_mu=q_mu, q_sqrt=q_sqrt)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "INFO:tensorflow:Optimization terminated with:\n", + " Message: b'STOP: TOTAL NO. of ITERATIONS EXCEEDS LIMIT'\n", + " Objective function value: 13.443127\n", + " Number of iterations: 1501\n", + " Number of functions evaluations: 1623\n" + ] + } + ], + "source": [ + "opt = gpf.train.ScipyOptimizer()\n", + "opt.minimize(m, disp=True, maxiter=MAXITER);" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Conditional: InducingPoints -- Mok\n", + "Kuu: InducingPoints - Mok\n", + "Kuf: InducingPoints - Mok\n", + "base conditional\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_model(m)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "vimshow(m.kern.W.value.T)\n", + "plt.colorbar()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2. Mixed Kernel & Uncorrelated features (BETTER)\n", + "\n", + "Remember: $f(x) = W g(x)$, where $g(x) \\in \\mathbb{R}^L$, $f(x) \\in \\mathbb{R}^P$ and $W \\in \\mathbb{R}^{P \\times L}$.\n", + "We assume that the outputs of $g$ are uncorrelated, and by *mixing* them with $W$ they become correlated.\n", + "In this scenario we assume that are inducing outputs live in the $g$ (i.e. $\\mathbb{R}^L$) space.\n", + "\n", + "\n", + "- $ K_{uu} = L \\times M \\times M $\n", + "- $ K_{uf} = M \\times L \\times N \\times P $\n", + "\n", + "We'll use `independent_latents_conditional`" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [], + "source": [ + "q_mu = np.zeros((M, L))\n", + "q_sqrt = np.repeat(np.eye(M)[None, ...], L, axis=0) * 1.0\n", + "\n", + "kern_list = [gpf.kernels.RBF(D) + gpf.kernels.Linear(D) for _ in range(L)]\n", + "kernel = mk.SeparateMixedMok(kern_list, W=Ptrue.T)\n", + "feature = mf.SharedIndependentMof(gpf.features.InducingPoints(X[:M,...].copy()))" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Conditional: (SharedIndependentMof, SeparateIndepedentMof) - SeparateMixedMok\n", + "independent_interdomain_conditional\n" + ] + } + ], + "source": [ + "m = gpf.models.SVGP(X, Y, kernel, gpf.likelihoods.Gaussian(), feat=feature, q_mu=q_mu, q_sqrt=q_sqrt)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "INFO:tensorflow:Optimization terminated with:\n", + " Message: b'STOP: TOTAL NO. of ITERATIONS EXCEEDS LIMIT'\n", + " Objective function value: 15.373198\n", + " Number of iterations: 1501\n", + " Number of functions evaluations: 1691\n" + ] + } + ], + "source": [ + "opt = gpf.train.ScipyOptimizer()\n", + "opt.minimize(m, disp=True, maxiter=MAXITER)" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Conditional: (SharedIndependentMof, SeparateIndepedentMof) - SeparateMixedMok\n", + "independent_interdomain_conditional\n" + ] + }, + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAD8CAYAAAB0IB+mAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAIABJREFUeJzsnXd8HNW5v5+ZLeq9F6tLlm1ZtnDB2HIFDDaEktDikIC5oSQ4hBBuzb3JvbnJL8kFEggmgAl2EggkQIAQisEFF7lJtuUiyZKsuuq972rbzO+PI60kbMAY25Ll8/DZj7QzszNnVvh7znzPe95X0XUdiUQikUx+1PFugEQikUguDFLwJRKJ5BJBCr5EIpFcIkjBl0gkkksEKfgSiURyiSAFXyKRSC4RpOBLJBLJJYIUfIlEIrlEkIIvkUgklwjG8W7AaMLDw/WkpKTxboZEIpFcVBw6dKhd1/WIzztuQgl+UlISBw8eHO9mSCQSyUWFoii1Z3KctHQkEonkEkEKvkQikVwiSMGXSCSSSwQp+BKJRHKJIAVfIpFILhGk4EskEsklghR8iUQiuUSQgi+RSCSXCFLwJRKJZBxxuB3U99VfkGudE8FXFGWjoiitiqIUjdoWqijKFkVRTg79DDkX15JIJJLJgKZrWHotHGg6QKu19YJc81yN8P8AXPuJbf8GbNN1PR3YNvReIpFILml0XadloIUDTQeo6qnCrbsv2LXPSS4dXdd3KYqS9InNNwLLhn7/I7AD+NdzcT2JRCK5GOmx91DRXUGfo29crn8+k6dF6breNPR7MxB1Hq8lkUgkExar00pVTxXttvZxbccFyZap67quKIp+un2KotwH3AeQkJBwIZojkUgkFwSH20F1TzXNA83onFYCLyjnU/BbFEWJ0XW9SVGUGOC0sxK6rm8ANgDMnTt3/L8RiUQi+ZK4NTf1/fVYei0X1KP/PM6n4L8D3AX8cujn38/jtSQSiWTc0XWdFmsLVT1VONyO8W7OKZwTwVcU5VXEBG24oij1wE8QQv+aoij/BNQCt52La0kkEslEZLwnZM+EcxWl8/VP2XXluTi/RCKRTFScbieVPZU0DzSPd1M+lwlV4lAikUguJpr6m6jsqcSluca7KWeEFHyJRCL5gtjddko7S+ka7BrvpnwhZC4diUQi+QK0DLRQ0FxwzsS+zdrGhmMb2FK75Zyc77OQI3yJRCI5AzRd42TXSZoGmj7/4DOg09bJ5prNHGg+gEExsChu0Tk572chBV8ikUg+h0HXIMUdxeckAqfN2saW2i3kN+ejoJAbl8vX0r7GisQV56Cln40UfIlEIvkMeh29FLUV4dC+XFx9fV892y3bOdR6CFVRWRi7kKsSryLUO5RAc+A5au1nIwVfIpFIPoV2WzslHSVounZWn9d0jdLOUrZbtlPWVYbZYGZZ/DJWJKwgyCvoHLf285GCL5FIJKehqb+J8q7ys8qBM+AcYH/TfvY07KHN1kaQOYgbUm9gUewifE2+56G1Z4YUfIlEIvkEll4LVT1VX+gzmq5R1lnGgeYDHGs7hlNzkhKUwurk1cyOnI1RHX+5Hf8WSCQSyQSiqqcKS6/ljI7VdZ26vjoOtRzicOthuu3d+Bp9WRCzgNy4XGL9Y89za78YUvAlEokEId6V3ZXU9392fVld12kaaOJw62EOtxymzdaGQTEwLWwaX0v/GjPCZ2BSTReo1V8MKfgSieSSR9M1fpX/K8J8wsgIyfBsL+8qx9Jr4arEq2iztnGw5SCHWw7TbG1GQSE9JJ2rEq9iVsQs/Ex+43gHZ4YUfIlEcknj1JwUtxcT5hPGpqJNrM1ai6XXgqqofFTzEfNi5vHEwSeo6a0BIC04jdvib2NW5KwLFk55rpCCL5FILik2Fm0kKyyL+THzsTqtFHcUU9haiKXXwtqstWwq2kRSYBJFHUUYFSM76nYQ5h2GWTWzZtoa5kTNGe9bOGtkLh2JRHJJkRWWxaM7H+W9qvc42HKQwtZCNhVtos3WRrutHT+TH0UdRaio6OhMCZjCoGuQ+2fdf1GLPcgRvkQiucQobC1kVfIqfrb/Z+TG5ZLXkMfiuMUUtBSwt3EvAClBKTT0N+DSXNT11XFt0rVjvP2LFTnCl0gklwRuzU11TzUGxcA7le8wLWwam2s2E+odygc1H9A52IlBMeClepERkoGma7h1N/Oi55HXkEd5V/k5b5NJNZEUmMTM8Jnn/NynQ47wJRLJpGXYr08JTuFk10nsbjsaGomBiRQ0F+Bt8MbSZyHCJ4Ls8Gymh0/nZNdJNtdsxqSauDntZjRdY0HMAs+E7rkY6fub/InzjyPSNxKDajgHd3pmSMGXSCSTlumh0/nBjh9w14y7yAjJoLyrnBeOvYBbd2NUjAy6B0kOTKbV2sr08OkA5DXkkRGSgaXXQnxAvEfgh6N3zlbwDYqBCN8IYvxixiWPDkjBl0gkk5Q+Rx+KonDXjLvYVLSJ3LhcdtfvJsI3grq+OlRUcuNyOdJ6hJVJKznUcohjbcc8o/jyrvIxo/rh1xfBqBoJ8Q4h0ieSMJ8wVGV8XXQp+BKJZNLROdhJcXsxbt1NRkgGuXG5bK7ZzBT/KdT11WFUjHw7+9vMCJtBTmQOm4o2kR2RzX0z72N6+HRURSUnMgdTtomqnqozFnofow/+Jn/8zf6EeIcQYApAUZTzfLdnjhR8iUQyqWi1tlLaWepJaVzeVc7u+t1E+UZR119HnH8cN6fdzNTQqQDkROYQc3kMTf1NrJ25dsy55kXPA8CluXBqTlyaC5fmQkdH13UURcGkmjCpJswG87iP4D8PKfgSiWTS8NShp/Ax+XhG5OVd5Ww4ugFvkzct1haPhaMoiic1wpkkODOqxgmR7fLLMrG7I4lEIjlD2m3t+Jp82VS0yRNCWdBcgFN30mPv4RuZ3+D2qbezNmst9X31zIyYOeGyWZ5vLv4uSyKRXPL02Hso6SghPSTdkx5hUewiDjYfRNM1bsu4jQWxCwDICs/iG9O+cVEkOzvXSMGXSCQXNVanlaL2Io9nnxGSwaLYRXxY+yEAN6beyOL4xQCoisqMsBmXpNjDZLJ03M7xboFEIrnAuDQXRe1FOLWRf//lXeV8XPcxIFayJgQmePalB6ePWwz8RGDyCH77SeisHu9WSCSSC0hZZxlWl9XzvryrnA3HNuDQHMyLmsf92fd7PP1Y/1hi/GPGsbXjzySydHRoKwV7L0TNBHXy9GUSieRU6nrraLO1jdl2pPUILs1FSlAKX5/2dUyqibVZa2kZaCEtOG2cWjpxmESCP0RvIzgGIPYyMHmPd2skEsl5oHuw+5Qi4522TgpbCwnxDuHemfd6ygxOC53GndPunPAx8heCyfkNDPaAZS/Yuse7JRKJ5BzjcDso6ShBR/dss7vsPH/8edy6mweyH8Df7O/Zlx6Sjq/JdzyaOuGYnIIP4LJD3QHoaRjvlkgkknOEruuc6DyBQ3N4tmm6xssnXhYrZWesJcovyrMvwieCaL/o8WjqhGTyWTqj0TVoPgb2PoiYChMop4VEIvniWPosdA12ed5vrd1K00ATR9qOcHPazUwLm+YpPL46efWkKFpyLpm8I/zRdFVDwyEZuimRXMR0D3ZT01MzZpvD7SC/OZ/M0EyWT1nuyXCZEJhAZlgmJoNpfBo7QZncI/zRDLRB7V6ImwNe/p9/vEQimTAMugZP8e0tvRa2WrYS7RdNXW8d71e/T15DHmuz1rJsyjJCvUPHscUTk8kxwrd1w7HXhG//WTitYNkHfS0Xpl0SieRL49bcFLUXjfHte+w9vHD8BfxN/nwv53ssjl/M5prN5MblMjtiNqlBqePY4onL5BD80ndhz5PwzkNQ8g44bZ9+rOaCxsNioZauf/pxEolkQlDWVUa/s9/z3uF2sOHYBqwuK/fPup/mgWbyGvK4Nula8hrysLqsF7Rs4JfFrem093/OYPUcMTksnZw7xc8Dz8HRV+DEOzDtBsi4Boxep/9MR4UI34yZBdLnk0gmJLW9tbRaWz3v3ZqbjUUbqeur49szv82Ac2BMVaol8Uv48Z4f8/jSx5kfM38cW/75OFwa9V1W6rps+JoNhPt/iladQyaH4APE5sDyH4mRe9EbQvjL3oesr0LKCjCc5lYH2qAmD+IuA+9LN7+GRDIRqe2tpbpnJF2Kpmu8UvoKxR3F3JZxG9kR2Wyt3eoR+zDvMJbGLyXKN4qijqIJKfi6rtNlddLYbaO1bxBNG9phvjBPJIp+nm0NRVFqgD7ADbh0XZ/7acfOnTtXP3jw4NldqKUYui0j71tPwLG/QFsZ+EfDrDtgyuWnD81UVIjIhJDEs7u2RCI5p1R1V2Hps4zZ9nbF22yzbGN18mpWJa8as8/L4MXc6Lme1bUTCV3X6bY6ae2z09ZnZ9DpPuWYIF8T85LOfpJZUZRDn6Wtw1yoEf5yXdfbL9C1BJHT4Mr/hsZCOPKK8PjD0uGyb0L4J2JzdQ1aS8DaAdEzpcUjkXwGG4s2khWWRU5UDlanFZvLRkFzAWVdZdyacSuqouJt8MbP5IeP0ecL1XR1aS4quytpGmjybNN1nXcq32GbZRuL4xZzbdK1Yz6jKiozwmdMGLHXNJ0+u4seq5Muq4MuqwOXe2LMF04eS+d0KIqwa2JmQfVOOP46bPkxJFwBs9eAX8TY4/tboLZXHO8TMj5tlkgmIKNFPsY3hod3PMxVCVeh6RoJgQkeH320BQNCjP1N/gR5BYmXOei0sfEuzUVDfwN1fXW4NJdnu1tz82rpqxxoPkBuXC63ZNxySgeSHpxOoDnwS9/jczsryY4PYmFquGfb3sp2jtX38MDSkagfXddxuDUcLvGyOd0MOjVsDjd9dic2h3vCxoNcCEunGugCdOB5Xdc3fGL/fcB9AAkJCXNqa2vP7kKftHROh3NQTOiW/kO0JvM6mH7TaZKsKRCWBmGpcnWuRALkN+XzyI5HuCfrHlKCU9hu2c5bFW8xL3oeJzpOeHz0M8FsMONv8ueD6g9IDExkauhUBpwDuDSXZ5XsVYlXYXfb+UPRHyjqKGJV8ipWJa06ReyTApNICko65Rq6rmN3adhdGk63eLk1HU0DTRfR/LrnJ4DOYUs3P3/vBP92bSYz44M4UtfF/20u45GrM8iMCcSt6Tjd2nkZrV8oS+dCCH6crusNiqJEAluA7+m6vut0x55TD/+zGGiHo3+B2jzwDhb+fvIS4eWPxicEorPBLBMvSS5dbC4bZZ1l5Dfns6loE7lxueQ15DEtbBoFzQVcm3Qt16Vc94XP+2rpqxxuPcy9M+8lIySD8q5yXjj+ApdFXsacqDm8cuIVOgc7uW3qbeTG5Z7y+Ri/GKaGTsWt6fTanPTYnPQOOhmwu7E5XWgafFDURHK4H5nRI08Af9pXgw7cdUWSZ1tpcy/V7QMkh/vx3M4qlk2NYEdZGw8sTRnz2fPFpBH8MRdTlP8G+nVdf/x0+y+Y4A/TfhIO/1GEaIamwGV3iZw7o1GNYj4gKP7s2iWRXMT0Ofp4rOAx4gPiyQjJ4L2q99hcs5nEgETq+uqI8I2gzdaGl8GLAFMAMf4xhHqHEuMXg6Io9Nn7uDrp6tOeu7yrnBeOvQAKLItfxo76HeiaTnpoOkXtRUT4RLBm2prT5rH3NYQQYUpl455qooO8mRo1IsrD4r0qK4bS5l6e21nlEe7S5l6e3HoSg6rwvRVpnm3PfFzJ3KQQ7roiibePNPDusSauz47hptlx5+27Hc2kEHxFUfwAVdf1vqHftwA/1XV98+mOv+CCD2LCtnavmNi1dULiQpi1BvzCxx7nHwVRWWA0n137JJKLjB57D8fbj1PSUcKmok2smLKCzTXin65Dc6CgEOkbiUE10DzQDDoEeQcx4BjwrIr1NniTGpxKclAyyUHJxPnH4Wv09VgzZZ1lPHf0OVy6CwUFRVHQdZ1lU5Zxfcr1mA3i35um6fTbXfQOOjFp4YSaElAU5bSCPvo94Nm2bGoEH5e2cuW0SDYXN6OgcHlyKAeqO9HRufuKJEwGlT/srWF5ZuQFGeEP2F3UdVlp73dwzYxorkgNO6vzTBTBTwHeGnprBF7Rdf3nn3b8lxJ8twscfWDvB0e/SLdg7xWCfia4BsUq3dJ/ACpMvxEyrx8R+JJ3xOh/9jfAf2iyt3oXNByG3IfPrs0SyQSla7CL4+3HPYXBXy97nV0NwolVUEgJSqF5oJl7Zt5DRkgGLx0ood94BIv1OItiF7G7YTcZAZfTNtCPy2ihxTqSzsSkmggyB2FQDXQOdo6pRzs7Yjark1cT7RfNoNPNgN1N76CTfrsLXVeI9kkkzGtsmcLRgr6jrI1vL07C38uEpdNKc88grb12Ktr66be7OFOMqoLZqGJzugnxMZEZE4jTrTHodDM3KRQ/sxE/LwO+ZiNmg4rZqGIyKKhDHZmm6ziG5hAGnW76Bl30DNlObX12WvvstPYN0mUdufd7Fyfzo+umf/E/FhNE8L8oX0rwT4emwWC3CLccaBMraz+P/lY48meRS98vAnK+CfHzRNjmnidh0cMwdRX0t8Hf7oFb/yD8f4lkkmB1WjnUcgi37satuXm78m121O3ArJpxaA6PZz96gvVEvZvffTjI3DnbOdj5EXNDV3Lw0Aq+e403De6PxZOAYqDF2kKvo5e6vjrqutux6z2oisK00CzKOk+go5Ci3MmStES0UdLkpXoT45OMvyn4lPb22pz8Ob+WQ7XdeBtVHG7N81mTQcHHZKBv0EVCmC+N3TaWpEdgNqp8VNyCW9cxqgorZ0RxsqWfmvYB5iWHMuh0c7SuB03X8fMyAMoX6jA+iwBvI5EBXkQGeBMb7M2UEF+mxwWycvrZ5+2faHH444Oqgm+oeIWng8shQi/7mkUnwGk6O/9IyP2BsIgO/QHyfg0xs2HO3ULs9zwp9lVsha+9IMVeMqlwak6Otx/HrbtxuB28WPQiJR0lzAyfSVV3FSsSVpDXkEd6SDoZIRmeyJxp8QZuXFzH27V7mGK+ioK2PSyfm4SvTwrG3gheKvkz18R9nRjfOTjslVh69+FviMdqt3JZ0BpmhSbjZa+moOcV+n2OoOliEaQBA+HecYR5xXhKFFodLspb+jnR1Etpcx8N3SJ3lqqAw62hKgqrZ0azMDWMQksXrx9q4La58aycHk1pcy/rP65A18FkVFg1LZqtJ1r4uLSNB5eL0Mvhp4WSpl4UVJZNFfbOD69OJynMnz67E6vdzYDDhdXh9oRnOtwjboKigJfRgNmo4m1UCfQxEehtItDbiJfp1FW1Qb4XZg3B5Bb8T2I0Q/AU8XI5oK9J1MAdPE0pxKgZcO0vofxDEb///qPC5klZAcVvwoyvAoqYNwhOuOC3IpGcazRdo7i9GJvLhtVp5fljz1PdU02SeSknuw5yb7awbzrbknn+yEYWBX+Hf1l+JQODOq8e3cf7DX8kw3AXh4sSyMpIZH/3y/h4306sbwrLo2/nw4ZXyQyaT2lPPsujb6d9sIEkey77j6Zj7dE4VpPOgllrULzq8VZ9CDZHEmwOx+ZQOFbfy8nWPsqa+6jttKLrYDaoxAR7Yzao3DInjiXpEVS09bP+4wq2nRD5dz4qafGIPUBmdCAZkQGUNPXy8FXpZEYHkhkdwPqPK8iv7uRbVySxbGqEZ9IW8Pw+LUakX/ExGyBgfP5GX5ZLS/BHYzSLVAohicL376kXr1F+IqoBMldD4hVQ+BIU/U2EboYkQ/kHwiJKXAhpV4o5g6ajYqGX9PUlFyGV3ZV027uxOq08Xfg0TQNN3D3jbkpb2qk5vgZ3aipB0UFkh+ays8RF5/Qmqpq8OFbfzRvHDnN53EMcKAnl+uwIdpQZuGrOg/Q5yzEo6cT6ppAZNJ8jnTuYHbqMWN8UYn1TALD2aBwoN3BFhoHZYQsZsHpRVgv1XVYsHWW09IlMkgZVITXCj+tnxpAZHUhKhB9bT7SQPGck7DIzOpB1y9N491iTR6hHWyUmo8rM+CBumRvPrPhgDKpCZKAX/t4mypv7ONnax46yNq7PjmHriRYUFK7PjmFHWRuZ0QEXJETzfHLpCv5ovPwhMlOkXOhrgq4aMeE7jE8IpF4JDYVgMIsKWqpRTNpa9onjS/4Oud+H1+8Wvr5EchHx9OGn8TJ6kRyUzAvHX6B5oJnrUq6jc7CTNdkruSxM47mPHPR0efNKvoWvZS3lvePNvOaoY0dZG6tnfp33jzd7olrSIvzYsBu+kj2LPRYrbmMTJ/pUor0e5FBbPRaDi84eP7yMKp0DLryMKvvK3ewrH8nAEu5vZkqIL7np4aRF+pMU5ofJMHatzKqsmE/eCgD1XTZuzolj24kWrp4WxbKpkfh6GTAZVJZmRJxyfHZ8MHsr21n3SiHPfCMHu1Pj47JWdE1nVnwQmdEBp0T/XIxIwR+NqkJQnHgNdAhhH2gT+zoqYcmjEJoqkrKVbwYUEb5Z+DIk5ULek/CVp6WvL7mosDqt+Bh9+P3x3xMfEE9FdwXXJF7Ddst21matJcAcwJ05mdQ3VfHcriquz47h6unRDDjcvHusidVZ0TR225gZF8iWkhZezKv2RJ/89WD90FW8gJVUAAY1HosygFl10jdoIDbIm5QIf7qtDooae1mRGcHNs+OFdfIF8DYZsHQO8Pvd1axfk8OyqZEeEY8I9BqTMuF0HKvvYf2aHBamhvPczkpe+NZcz/b7lqSSEuFHoaWbYF8TvYPOkUyXFxGTO0rnXDDYA+0VMNA6dntLMex+XBRb8Q0Ha7vw9bNvG0rLkCbTMkgmPJqucbjlMP3Ofl4qeYn85nzSg9NpGmhibdZaroi5gkjvVP5+uInfbq/whD5emxXFu0ebCPM309A9CIACRAd5kxDqS0yQN8G+ZkJ8TZzo345Ji2T7EV+WTo1gV3k7X7l8gLKuEtK8vsL7x5s95109Mxq3pn/qyH00XiaVEF8zwb4mQv3M+JqNZ5wP50t/b5ruCbXsHXTSa3NidZyaBfNMmWzZMi9evIMgfg7YukSqZVvXyD7FAH6RojPwDoIT74LZT+TosfeJJGy1e6SnL5mwVHZX8nbF29jddvKb84nzj+Nk90nmRc2jw9aBl5bA6wUNHjsjNcKfph4bbxxqAKDH5iIrLpCKln7uW5JCdvypYZMzuBkAfXBkBeuVSbO5MmkRANahJ4VP+u2jMRoUAryNItJlKOLldE8ApxP1hanhnzu6/6KoqkKQr2lMdI3TrTFgd9E36KLf7sLqcDFgF1E8EwUp+GeKTwgkLIDeJhG1s/NXkLwU6vaL7JuWfcLXL3xJHJ95HeRvgF2PSU9fMqEYznyZEpxCQ38DAeYA/n7i7/gYfege7GZe1DwOthwkxW8elo5BqtsHyJkSRGlTL7/fXU23zUmIr4moQG+mxQRw3cxYTzqD0wk+iMVRw5OhoydAh7d/JTuGHeVtzEkMYW5iKD5mFW+TWNjk52XAyzjxSxaaDCrBvmaCfceuxne6hzJqOtyezJqDTvdQcrcL2yFIwf+iBMaA5obLvyNKKmbfJsTdNwxK3wMUkabB3g+VW2Hpv0DsZePdaonEQ1ZYFj/c+UPunnE3UwKm8EH1B4BIkiayX5Zyc+L9vGv5M2GmFHISMnlhVxW1nR1EBXrxw9wMQOf5XdWe0EUR3igmM1VVxKB7GcUK1JLGXl7YXc1Pb5zBvKRQVmVF86O3i/inRcls3FPNs3deRm5aOPuqOlj3SiHr1+QwM/7cjsjHE5NBxWRQCfQ+fay9ruu4tQtjrUsP/8tQ+j68dT+kXQUVW0QnULkdGobuYdqNMPvroJpEuKbv2Xt0Esm5YGPRRqaHTaeyu5L1hesJ8gqiob+BSJ9IEoMSKWguYGXcN1gVu5bynkK2lzVzpDwSk0FlYWoY+6s6Tskz42VSiQjwItjHjJ+XAT+zEVUdmb/6NF99w64q7luSct799ksB6eFfCDJXw/z7YfdjYsI27jIRttl8DNwOKH1XTN5OmQf1BWLFbkDUeLdacgmTFZbFD3b8gLtm3EVyUDLH24+jorIobhEf1Wzh6tg17Gl5lyles9lTHMjBGjdZsQGsXZRMkI/wzd891sQNs2K5eno00UHeBHobP7Oq1Rfx1c+H3y4ZQQr+l6F6FxzaCEv+BQpeAK8AsQp36b+K6J79z8CeX8Pl34XkxaLcYtQMsdJXIrkADPv182Pms7FoIyW1PmQFLud3R36HWxdRJRo6b5/8gGsj/pmVcUsJJYent7ShOVxkxQbx0JXpqEOZKXeWtfHNBQm8e6yJO+ZPYWr0Rbrk9BJFCv7ZUr1rZJFV8hIh6K/cDjl3ClEH4evv/CUU/B7ay8WkLzq47BCeJrNtSs47WWFZPLrzUR5f+jjpwek8U/gIDqcLDELsDRhxDqRh8qvh/WNtKLZm/nEMjHoIavAxrs261SP2G3ZX8bs7L2NxegSrZsZ4/HY5Ir94kB7+2ZL3pLBwRi+yqt4F9YcgY+VIbv6+JtjxS5GsTTXCkn8WHUJ/K2z7H5ltU3LeyW/K59Gdj7I4bjEf1X7EoNsO6CgY0Nwmlod/l+mRsbxXVENRRTz+XgY0Hb67LJXM6ED8vY3sr+xgfkqo9NsnKDI98njTbYHWEyIf/7afQX8TWDtFDp+p14mIntBk+M5ekbNHIjmP/M/e/+GNk2+QFpRGRU8FAPa2FUwPn0qz6RVm8CO2HdcI9TPTOeDwVHuKC/FhalTAmElYycTjTAVf/bwDJGdJcILIo6+aIC5HjPADY4SdU/wmuO1if32ByNwpkZwn3q16l801m1kSt2RI7BX0rmX4hh+goklDaXyIbcc10iP9sTvdnsRh7x5rZFpMoBT7SYQU/POJb6jw7WfeIgqp9DaO7FNU0SnYusSiLcfA+LVTMmnZUruFn+//Od+a/i1Ku0oB0N0m0kJT+VbaP+M2NdLU4YeiQFVbP99Zlkp2fBBGVWVbaSt7K9s/5wqSiwkp+OcbL3+xEjdqhhB5AJ8wYfXs/BU0HgGnFWr3CctHIjkLNhZtJL8pf8y2HXU7ePH4i6zNWktxRzGt1lYSjFeTZvwm5W2N7D0eg619EeGh7aCD0aBS3T7Aszsq2fCtOTz/zTkcqz/eWQAfAAAgAElEQVSDKnGSiwYZpXMhMHqJBVm6BhGZIifPsJ2z92mImwMGEyQtgpm3inTLx/8mPhuaLKN4JJ/L6Gic+THz2VW/i3/f/e+szVpLv6OfnfU7mR+5mJlBS/BR/TAOzOdgbReJYb6090Xxw5WpWDqtvHawnodWpHkmZ2UEzuRCCv6FYO96OLkFrv4ZpCwVOXYKX4akJWDZAzW7hddv2Qed1VD0JqCLqJ47/jzerZd8CUbHwQ+T35RPUUcR92Tdc86uMz9mPo8vfZxHdz7KTWk38Xr566zNWotZNfPyiZeJ90tkeuAKVAwcLA/kYG07iWG+1HZYuT47hlA/Mxv31PDQijRePmBhQWqYFPtJiLR0LgRVO2Dlz2DR9yAmGxY+BLGzhae/4sdg8gbNIVItF74kfqLA1zaKkM296+HlW8b7LiRnwfDIe2/jXur76nnz5Js8vONhfIw+lHeV09TfRL+j/5xca37MfG5Mu5FNxZuYFjqNMO8wNhzbgJ8xgIyAhWw+uZ+PjwSwpaSdWfFBtPfZWZASyodFzfzig1LWr8nhkZVTWb8mh3WvFEr/fhIiBf9CcOcbsHDdyPuIDFjwIAy0gOaCa34BRh9GiqprEJYiEoxv/zl89J+QsuyCN3tSkPekWB8BoOvgdkHlTrH9ApAVnsX353yfH+74IU8dforHCh7j7hl3E+MXQ2N/I2VdZRxsOUh+Uz61vbVsOLrhFC8+vymfjUUbP/daH1R9wBvlbzAvah4FLQU8cegJrE4nccZl7Gn9O1rvPAotA8QEeVPS1Mt12TGcaOpjccbYkfzC1HDWr8mR/v0kRFo640X2rcK3f2edyLHjso3d33wc3v2BqLO74Dsw/77xaefFhq6L8pS2bnD0Q12+mBxf8i+ijOVw4ZrEhRCdJTpaL38w+4sU2N7BIt0jfPriujNcHd080Ex5Vzlh3mHkxuWyuWYz1yZdi6VXLMrLCMkAYGvtVlRFRdM1EgITeHjHw9yZeSdeRi9mhs/0ePOfhs1l462Tb/F04dOszVrLicpIAoyV9Dk6CTWkUtT3IYFd36OyzZ+UcD+q2geYHhPAh8UtPHvnZSxMDfcsohrt3UtLZ/IhBX88mXETFL8NJW+JYiooEBgLPUOrdHvqwC9CiNe+Z8DeA1f+RFbS+iSDvaIUpbUDDv1RTHQPp7eIuwwqtsLHP4NpN4ji8yiQsBDcTvGy90LJOxCWCtHZIiVGQJSIqnrldljzVyH6o9NpfILRXv2Lx18k2DuYDlsHll4LCYEJ7KjbQWpQKjvrdzIncg4f1nzIzek3c3n05aiKylsVb3Fz2s1Yei3MCp/Fs8ee5fLoy3mx6EXWZK7haNvRMfMATs3Js0eeJcYvhii/KEo6SlibtZYB5wB7B/6PAZeVEGMSHa5KzJ330tgeQmSAFy29gyxICWV/Vecpk7NS4Cc/cqXteFK9SwhKaCq0l0LyMlFQxeQH/c0jx8XOgY5yWPSwGJmGTwW/sHFr9rijaWDrhP4W8XLZxfaSd8Sq5ZK3xXcVNUOsaD76F0AX9pnBLJLbDXcIw0IPsOdJ8TmA2r1Qnw8534Kjr8K8b8PBFz81FUZ+Uz7rtq/ju7O+i9lg5jeHfgMKzImYw76mfehD/30SBQVFUZgaMpXa3lpmhM2goKWAqSFTKesqY17UPE50nmBt1loyQzNRFRVVUXG6nZR1lbGpaBNrs9aSEZJBQXMBL5W8hKoYSPW6ktL+PIwdd9LTmUxIgI2uPh8WpIRyoqmPu65I5OUDFpkLZ5IgUytMdD6ZfK1iO7xxN4SmQeMhCIyD3oaR41NWwOWjbB2fEAhLn7zC/0k7RdNEuunaPZB2NWjOscePFvtpN0DxW2Kk3lMHPqFDpSl1QBEL4lSjWPiGAs1HIfsO8I+CfU+LAjeqARY/KjqGY6+J1dELHoRrfn7aJ6yNRRup76vnjfI3mBs9l+Ptx3G4HGiIakZeBi80XWNFwgp8jb5UdldS3FGMW3cT7BVMt73bc65o32iarc2kBqVS2VNJbmwut2fe7tn/aumrNPQ1cEPaDRwod3HU9kci/cKo66vDoBhI915FuXU7xubv0dEdQmigFXvUE6Ro91NUGcl/XJfJvYtTPQW+pehf/MjUChOdhsNjR4tpK+DWl4Q1ETVTiH14xsjxtXmw/znhQYMQsPp82PsMbPnxyCh3stBVDX/5BhS9JRan7XkK3roP2k+eKvZulxDoI68Ia+zIn8Vitp46sd82tKDNLwJQhPWjayKxXfNR8d0d/qMoR+kcFLUMEhYKsW8pFsVtZnwVCv8E+34HfS2nNHdG2Az+Xvl34v3jKWguwKyaPWIf7RvNLxf/kgdmPcCehj3YXDbKu8sxqSauTboWl+ZiZeJKzKoZb4M3zdZmFBQqeyoJ9w4nrzGP7ZbtAGy3bCe/OZ/GgUY2HNuA4m3B7tSp6xP3Ot3nqxTVuTE0f5+O7hACvAx09vqywP/7BAY38x/XZfLsjir2VrbLydlLEDnCn2hU74LXvgVRWVCTB0m5ooKWyUesxFWNEH+5COUMjB2xL0Bk6gxPg8WPgFfQyOTjmfAlJyjPGfZ+0emd3ApbfwzoQ5ZXuZiQjc6CzOvBYRWdoK0bOipAdyPCmnQxEeuyDY3sO0UnYPSCjGuhfLMYwSflwvx7hfBbO0VnYdk7ti0+IaI9UxbAwgeF+A/bPglXQMRU8BMj46ruKh4reIy8xjyMihGX7gLAqBgxqkbuzb6XjJAM3qt6j801mzGpJh6Y9QAZIRlst2z3ePhuzU1NTw3HOo6hoKCjoyCeKMJ9wmmztZEWnIbD7cDSZ/E0VddU0E04Gr+FPyl09isYVLgiJYzYYB8+LG7m2TvnjJmglVkuJw+y4tXFyLDNs/hR2P0EzL0bjr8BWbcIiyJ5mRA5yx484habI1bmFr0htsXPgYIXoaNSlFc0+4HJVyzsMphEh6EoQ59HnEPXRVGW174Fqx8fWQX8/qNw3ROicPvBFyEmR+T9N5jFuWr3fLkOweUQkTR7noTgRAhJEqNrEBPUCVeIRWktRWJb0mKw7Bcjfo8froiOLes2mLoKtv1UPB14BYqnoLB08bQUN0fYMjO+KkbuHZVDH1fFPEDTEfHdaC7xfTv6RecAULcX8k2idvGih8VnOyqF95+8lN827aDd2ceR5gJ8MWAdEnuABTELyInKYVPRJlYlr2JPwx6ywrKo6qnCz+Tnic65Oe1mNF0jMSiRzTWbyY3NJcgriK7BLvY27cWgGGiztWFQDFR11xJoCibSJ5JWWysAgc6lNDdlgG6icxBM/if5/sLryIwOJCHMl5ty4jxROHKC9tJFjvAnEsOj7IbD4mfCFWIhVl2BEJeOSjFpu/sJIWqAR/iHJyNhZBQ6PDF5OoYnK0cfU/qe8KszrxM2xuhzjB7dDlsde56Cpf8McXNHOgF1uFNRR7xuXYdDf4DwdDFCdzmE5dJYOCKcw+fuqBzx4qffJCZcP2nhDN+3ahhbY6D0PfF9+UWMWGPdNWKEXr1LPBlUbIHcH0DktLH3FT9ffLddNUOroHOh4RBEzxSVzIZTY8TNFekvTn4EtXk4E67gj/FTec7yAcFuFy1GIybFhFN3EmUKpNvZz78s+BFdg128WPQi61esZ37MfE+O+seWPkZWeBbttnZaBlp4p/IdVEVlS+0W1matxdJrYW/jXtpsbcT6xdLr6CU76EryKpswBB0CdHQ0XAMJOBvuxeVW8Yr9K3NDV7P2sqtICvclLVJWpZrsyEnbyURvI7SWiBDCYYFKWAQVHwkRGiZ8qgjpXPQwxMz67HO2FIv49OzbhcAPnzckSawBiMqCGTd/focwLNhRM8ZGvHRUwvQbxHmHjxl9vfwXhIWSdYuwWMJSRUfmFwHdtRCSLMR39EheUUblIxKZH5nxVci+beh+/k9YUnX5QrzLN0PqCpGy4o5XIXXZyFPULZuGOs9fi7mSqBkw2C2eCvY+LZ4shs8N4pz71os2uOwc9A+iTndyw6CTuqQF/M9AOQd9vDABTiDLN47igXq+FjiNKaYASM49oxQLvY5eWgZa2FW/i2cKXyDIFEK7o54p/lPosncR751Nad9eT/GSCPs3sLS5cdtSUQxWvGNeQ+u6EsWexs9uyuKWObKc5qWAFPzJhsshwgM/+tGIZ7/zV8ICUVQxih4WR4NZCGhgHATFg1+kGKV6+Qt/W1XFZ8q3wPG/ijmBxkIhfK1Fwv5oKRaRMfHzYO5dUPgK1B2A+LkjYhg1YyR8cbhNu58Q7Vj8qHg/+qmg9L1Ro+eD4vyKCrPuEBOsFdtG7mEY1SgKxdt7xejdP0pYMMNPEapBpKfobRQ2Tv5zI5Phe9fD1v+Gq/577Ernz5qbqPwY3lgL028UOY0WfX/sU07eb8Dkg3OgDQWoNJsp9DLz8/BQ8TdQFK4ZdPN/be38KTqF3xn6WT/7YeYHZ3wh+0vTNe5+9yEKO3cS4TUFq9ZJqCEDi62QIEM8Tg18+1dTU5cCgL9/B3rM7whUp/CNxP9HeXMfeZUdMgLnEkEK/mQk70lhi/TUw9afAApkfU0IUeNhPDZHbI4YrfY0gvM85Nk3+oBrUIx2o2eB2RfqDw5ZPUWiHQkLxDzArK+LTkdzCV/8xD+gs0p0Sm4npwi8d7A4t1+E6ASGO5Y9TwprpmqHuK5qggXfhfznxefu+POIFXa2E8+fDJWt3CFCZZf9m5hjAE+Ipq6aKAwIQbV1szY2iliniw5VYZFmpMDg5vHWduYP2sm/fC1FfgHcs//PX6icZX5TPuu2rSNIv4wm5xEiDdm0sY9k74UEG+OprVpIbccgACZzDz5J63H3XI536AGWhf6QJ77yNTk5ewkhBX8yk/ekKJ8YdxnY+4QYTr9JiG1zERiMYoSt67DnNzDzdvCPEBEnLpuwRbShsMSaXUJk+1vAN1yIclSWOFfsZdBeJsIY/aNGwhlh6IkCMSnstA1FyZwpQ/MOKKIz6KkbiqQxi3aP9tGbjgh/PWkR9DWDtQty1ogR/rDAF/1NWEBfNprosyKV5twlRvxbf4Ir9UqU0vfox8XVU+Lw1nX+Ud+Ej6ZhAgq8zDwaFcHjbZ3Mj5or7KBbXoRpX/ncJjy3sxKDbwV/qPgZ3874CQM9iTx98EVMke8RpS6ky1VDT/XduJ2B+JgM2NVaApL+QH/d11masIBDLQfxjX+Fp1b8eox9JJncSMG/VNjxKxGeGRAjJjdbioWtEpoivPBPm7wd9uyn3yQmSGNmizDQqCxoOT52ZB0zW9g4UTNFB+B2jI12CU0RxyUuguodQsvj54lJz+k3Cnuppx6Ovy4mTsveF08hNbtFW4YnWXO+KeYQhtul6yLqaNtPheeeuvwCfrFj2bjrv8g69CrzVq/nqLuX2O2/4pveAzQajYQqBhIGbfy6tY0It+gQSwMi2KsOck9Pn4guuuJBESYalnbaxXKaptPeb+c/3y4ir+11bpx2OVcmLeLV49vZ3/8UjrYr0e1xuGxTAJ3MeJ2Hlszn1wXPUd0QRpx3Fm19Dl68ey5G36pznn5ZMrGRYZmXCsuGInOG0w2EJEPHSRHdMizKp6OjckTshzsFo7eYjE1aLHLOlG+GxT8cOUfNbjGynvFVcVzUjJEIm9wfjByj6EKcU5ePePhup7CfSt4eObYuX3RSA23imiVvi8noa38pYuZ9QsV8Q1iaGGWPo+Bn2e08GhXBPxudHGg7RmGATiMmslzwx+ZW/jcyihXxsTzT2sYSm53MvjYyAVDEfEVLsfi+6vN57oQX2WmJLMxKpcfm5Kmt5Vgdbpxujez4ILaXLeWNPMg7XkyzXow2sA7dFYKmg6rA6rl2AoLrqWqfTrNlIZlhvhQ39nJzTtyQXx8uR/eS0yJH+JONYR96zlo4uBGu+7XIwe92iJfmGrLNddEpRGYK66bpiJjgnP1N0F3C/6/cBtf8TNg4H/14JEZ+xY9EZM3ocMbPi9KZfsPYUNCSd0QY5/E3RIhkZ+XIxO8ErfC1o24H/77730kzh3Ck30KQ0Zf/vfw/6T+0icesZawcsNEQOoVne10jK6JhZAHXrDsg8zqOFx9n25FKsqamkmro4FnDGl47VM9tc+NZOT2al/ZVs/NkxynXz4oLpKK1n4zIAIJ9TRTWdXPPoiRe2m9haUYEbxc2eNImSC4t5Aj/UuSTk44pS8e+/yTxc8d+9vaXT/Wvj/8NSv8h0jlnfU1sHw5rvPVPYvQ69x4xgo/KEp2Cro28QpKEP6+o4mnE6C1WvRrM8Oa9sOYvn5uJciLg1tz4Gn25IuYKtli2YFKNuBSVDxrz2Oes4wlDPPNDg2DK5SI8NHomtJwQ9k2/SMWgH/kzfT2dTKvbyWDMKlLLf8vrYd9hc1sda2YG8vaxJo7UdXOy5dSCKMsywrlzQRIflTTz2sF65iWFsG55Gs/vqvJE4kyPDeDXH51kRmyQjMyRnJbzPsJXFOVa4CnAAPxe1/VfftqxcoT/JTkf6RHOV8qFiZLK4Qwp6yxjZ/1Onjv6HE7NibfBm5kRMyloLuD+7PtZl7NOFFZ5/VviSWU49/6eJ3GnrkQpfQdFcwE6Dq9wDC4rLwat4xeNs7kszInVpVDaI8ZfCmA0KCSE+lLZNoCqgNmoctW0KHaWt3Hv4hTMRpE2Izt+rLjLyJxLkwkxaasoigEoB64G6oEC4Ou6rpec7ngp+JKJSLutnTdPvskLx15g0D3I0vilhHqH8nbF21yfcj15DXmieHjlXtGJTVkAHRVoXRbe2H2EdFc5MWYb0XXv4zAHYbL3oCvwvnsBz7u/wnEtmUijjXS9mjqvqVisKlcmeXOgyUVWXBD7qzqJCvSipdfOQyvSeGTl1PH+SiQTjIli6cwHKnRdrxpq1F+AG4HTCr5EMtGwu+2UdZZxsuskBsVAtG8008Om81LJSzwy5xE0NG5Ku4lHdz7KkuBHWK1NZ6HRTE9AOmXdARw3w7s1Chu8f0tr+AL2tSj8wXUNKw2H+KZhC9cb9lNpTCXc0cjbkQ8S43yHIv9knq6ZxV0ZTm6ZH81uYwvdlfm05jwgC4xLvhTnW/DjgLpR7+uBy8/zNSWSc4KmaxS3F+NwO2gcaGTQPci6Geso7SzlF4t/wbIpyzzHPr70cd4rP8CDfz7Mv63KJMzPi9LmQeqrivmt17PcN/ggFQ1xNOrhJCnN2PziUAY1Go0JpLgqUVRY0fsWxujpLKp7hpz4GzAP6nAyjTssT7Fn9k+pj/Dn1rnxMoe95KwZ90lbRVHuA+4DSEhIGOfWSCQjVHZX0uvoZV/TPo61HeOmtJuID4hncfxiEgMTPcc9t7OS7PgUHp47mziljv/6ezFpEX6cbO1nXQxc37WeereCP1amh8KTyXX0tbWxzTaPG1x76AyfR1DnMWJox2j5B7rZj+Xtr0JiLrai92hOvZHrjQWQPA2iIjw57KXgS74o57sASgMwOntT/NA2D7qub9B1fa6u63MjIiLOc3MkkjOjZaCFhv4GWq2t/K38b2SEZLB8ynKCvIJICBg7MJkZG8Q9mwr4xQcnSAn3Jy3Cj5KmPgyKwm/qM+lxmwCIj46kpBN+0n4lzzRnstJ0lI6k6wnuLYWZt2DEDeFTURxD6TBq8/AJjSO57m0RzjrYDbX7WOjfygO5iZ9sskTyuZzvEX4BkK4oSjJC6O8A1pzna0okX4o+Rx9lXWV8WP0hB5oPYFSN3DntTkyqiX5HP5uKN7GrIItFaWHcMS8BVVW4YXYsrx2s5++FDdjdIhBi0KXh72Wgb9DlibH/fV4V1OzmKe/16F99gbDQeDiZI9Y0DK8+9ouEgVYRztpWKorZdNWOZB398EcQlgI3Py/KNcKEjnCSTBzO6whf13UXsA74EDgBvKbrevFnf0oiGT+sTivH246j6RrVvdW02dpYkbCCEO8QBpwD/CjvR2SFZbEoNYz/914pP3u3hAH7SMGTYbE3qgqxwd70290khPqwcno0FW39nGjq4+tx7axzPkSh93yxKO6KB2HOPSIbadLiEbEfzk9k7xHlFWt2izKM3bWiItiWH0Nr6VA46N1iFXTek+PwrUkuFs67h6/r+vvA++f7OhLJl2Fj0UZqempICU4hKTCJ/U37Ke4oJtwnnI9qPsJsMPOx5WMeX/o4+SdCCPAxcOvceP56sJ5DtV1UtAkbRlGGCoj5mmjsHmRaTACVrQMctnTxl/w6nr3zMhamriR8dAFxtQSOvAxf/ytUbRfZSCs+EgI+vIANRmr0qkaRZqLwZZForuko5D4Ceb+esAvXJBMDWcRcMu48t7OSvZXtY7btrWznuZ2VF6wNmaGZfFD9Ac8ceYY9DXv4S+lfUFHpc/SRE5XDmyff5Lapt5Hgm41BVXhscxkJob4khfl6xD7C34yvyUC4v5n2fgeJoT789o4cXrx7Lpv21PCd5SmeidYxBcSHC9qnrYD0ldB4SAh4xLQhsVdGtVQR6TE6ToqEeTW7RfK8vF/D9UOjeznKl3wKUvAl5xVN0+kddNLYbaOyrZ+y5j6KGno4WtdNUUMPJY29hPmZ+e7Lh9lc1MSg083eodFvdnzQeW/fxqKN7KrfhVERhcZ1TecvZX/BrbsxGUysTl5NaWcplwXeyp+KX+WtEztJjwzggaUp/GZLOTUdVs+5uq1OrsuOoXfQRUq4H7WdNn7xwQkWp0fw4t1zcWtjr70wNVysiM19eGTF8bD4py6HvkaYupoxNQNUA8y8DQY6xH4U4fPHzBKF3v/6TTEXIJGchnEPy5RMLtyaTrfVQZfVQUe/g367C12HD4qaSA73IzM6EBDvDaqCW9NZlRXDtxcn84O/HiUxzJeGbhv/eu1UpoT4YnW48DWfv/9NkwOT+ddd/8rarLXE+8ejqioMCXN2eDbbLNv4j7m/oLYhlkOlYWzUf8qaxP/i1X0Ghux6VmRGUNNupap9gLcON/DE7bMJ9zPzT38sIK+ig72V7WdeODz34ZG8QrmPiKpmBi9w20V66pbjoqC9aoCgBFHSEsRI37JfFGvx8ge3S5SQlBO5klFIwZ9EiHjwC59bxeHSaO+309Znp3PAgVs7NV1Hcrgfv91WwU05saycHs3Jlj6ONfSyLCPc0xk43RqlzX0sSAml0NJNt9VJZnQgr1f8CbM7keszllDV1s93lqWdth7sF0HTNRr6GzCoBtZmrWXj8Y043eDQbaioGFQDh1oKmeZ1G9sLA1mVFcADl6/kt3lePF1qRXN7oSqwKiuaneXtPLA0hXeONlLZ2k9FSx//fcDCi3fPA/jiMfPDo/yGw5B4BdTugyt/LIrTJCyAgy9CUJIoYDPtBlE6UneLVNNdNdDfKiqB7X4cbv3jWX0/ksmJFPxJRHZ80JhVmHtHTQyea/rtLjr67bywq4qYIG+mRgd6hBugun2AVVkxlDb3UtXWz4KUcHLTwnjtYD0HazqxdNpQFdhR3k5MbBnvlPri0qYwPSaA/VWd5GS0sbn+BFfHfZW8Kh+8Yn/Dx++08uAV1/LX4x/zdNGPeXzp42fV9q7BLiq6KxgYKv+YGJCIUTUy4OoBTWVlzP0E+cMblX+gyPomfn5J2ByRbD3RgsMaA4gonIevSiczOpDpsYFs2FXNs9+4jP1VHfx2ewUPrUgb49d/IYZH5MlLIA+4Yt2I5aPrQvT3rh+pK1CxVYz47X1w5M8iFXPlVlE9LDr7rL4jyeRE5sOfZAyL/J2XJ/DyAQvr1+SwIHmkwpKigKIon3GGU3G6NdZvryA1wo+UCH86Bxw4XBqlzb0cqO6k0NLNA0tFMe1nPq5E0zWuz46ltsNKoaUbk0Fh0KV9zlUEwb4KirGPAfMevJ3T6O2ZQma8jqW3CnPcK/gQjUNt5IYpDzAteA6xAcF0uKp5v/av/NPMe8YU/hj9FOB0O2mztdFqbaXb3u055s2DbRy2/Y4eZzuB5mCsDhvW+m+S6JtN42AJCVPKqKqLB+tMBp0aBhVSI/yxdFpZtzyNuUmhZMUFcay+m38cbeTD4pYx3/15Ww3rtMHhl2D7T0V2ztBUMaJvKRL7ExbCoodEeGfsbOHzS3tn0jJRkqdJLiB2l5u0CH9WZUXz2+0V3JwTh92psb20dcxxqgpGVcWoKhhUBaNB/A6iQwBwunWcbg2HS7wKLV08v6uSdcvTyIwOpLS5l/UfVzA/KZQHlqbwux2VJIX5YXe50XT422GxoDomyJv0SH/iQ3yxu9y8f7yZqEAvGtxbifFJpaklGqemo3q1YA4oweVKxNofhtZ7DQ5AUXRK61VCA1IYbM/FHf4RqmakpqOXk7UWYuO2s7Xxr0Toy7m/6SFS/HJYnbYUPy8zvz3yBKl+OXx0ooa0GI2rEq8CoLyrnOruWpID09nb/xyD7gHSfa5m6ZQlHG2qoSD6VSobFBZPWUBP72wGe7oBIfY/uCrDc/8v7K4mZ0oI/l7in9GHxS0ekV+QGnZ+c96YfMBphbSV4o9m8hYVzNpKRRSPZS8EREP2bXD4T7BvPdz2p3PfDslFhRzhX+T87uMK4kN9iQnypsfqpLS5l2c+riQxzJf6LhsPLE3xTJR+Fp+cVAUobe4dY80883ElOjpXTYtiS0kz6AqzE4Kp77LR0G0DIMDb+P/bO+/ouqor/3/Ofe9JT733Xm01F9mWbXDFBlzABCchBH5JxqGETOAHGTKZtF8ma80kk0kISWYgIcEYmARISChmKMY4YBtj4oaLiiVZtmT13tur5/fHUTPulmW181lLS3733XfvPpL1Pfvus8/ehPl6cqq5h7XZkXw2N3boWk/tOsW6nEjezq8nPLyKButm7LV3kRuTyJG6cizRzyMMB8nWFZRUBuDpSqKjPWKg5bkAXFh8ahA++Zh9ikkLzKKi/2Ps7bNYl3QbR+vKqbe8gMnkwmQYzPa+m70n6/EIf5vrI9cyN2QpVd0neavyRXxJo1MUYnaDo5wAACAASURBVBYWUj3XcOjoQlKjJBUNJoTnabwtXrS0hWEINTkmhXpT2drHN1amMDsukMwof0oauobWR8Zr/YTy3fDyVyDrNtU9LPMz6rvLruL6UXOGu4nNvAXCZgzP6popw4Soh3+5aMG/NJ7adZLMKH8iA6zsKGrgNztPsi4nkrqOfg5WtCGRPLgydeDcU+cU/XcK6mjqspGXFDzksT75wUlSw31Ij/CjscvGwYo2vrEyhZmR/rjdklcPV/NuYcPIJEEMATGBXjR02rg+NYSPT7UgEKzKCGdnSdPQvQezct7Or+eB5cl8dLKeg/WH8Yx+kRTfBZzu/xinCzydmdgshXgZwfTJRkzuQJwuEKZu3I4gXP2xuPtjcfdHInFh9jlFkv8M1mRFU90ieOvE+1hC30dIC47WpZiCPsTZkYtnYD5ZwbkUte3H6RIIk400v7ksCL0JL7Mv2z4xUVxtIABDCNwDU4xbMlQWobi+k9/vPsWTd+eyNG0C1X0q3w0vfkE1ka/6uxJ3T3/Y/gOV3RO/GK5/WJ3rF6Xi+obOyJ5KaMGforjckq1HavjOK/lDGS+Dbe/C/Txo6bazYU40ZsOgrddOVWsvbb0OQn09kUgMIbBaTPQ7XBTXdyIQXJcSgsVk8EFJI24JSaHeVLX2IZGkR/jRY3NR296Hc0T2jRCwLjuSpFAfntt7+owY/qcnnIdXpbIwOYQ3jtSSFe1PUpSTH37wW1KC4qjvL6Og828YGBjCA6fsH7qHhQDsshsDM27sGG4f3EYvQgyvB7jtIbj6IzG7IkA4cJubcPRF4BG8F8PkwMALl7sPXP4IS+eg9cR7z2BV1N3UtwmOnTYorTEYHF6EvyddfU7mJwYRGWDF5ZZ8Zm4MMyL8KGvqnpgdpd7/Mez+GSy4D1JXqW5bex5XvYed/ZC+FuZ9RZ3bXqkyfpY+Or42a64aWvCnIB29DgprO+i1u4ZEflFyMEerOvDyMGjtcZxxvqfZINDbgs9AHrsQasKwOd30O1z02F3YL7CYOpgnH+BlpsfmQkqJ2WQwJy6AQ5XtmA1BXmLw0FPCYFjI28NMXUcfDyxPoaiuk8LaTh5YnsKWgi1E+0RjNVspbSvl98d+j8PtQEo5MBkZzI+YT35zPnHW2ZR0HiLUI54W50l8SaHTWU+AcymdHjsQhhOTLQmHC4RnPcLoB3H+/8vS5YWzNx63LRR3XzJmRyoOhwcutwpvxAZ6sTQtlBNN3RysaGNRcjD3LlGTWHSgF2kRvlhME9QrHszbn3+PStlccB/8/Unl6Tvt8OHP1Y7dwATVUL2hAHK/Ajf9u+pJXPCKuk5Qkl7UnaToRdsphNstOdXcw1O7ykgMUXH2VTMjOHi6jb+fagWgz+EiwMtCn93F7XOjuT41FC+L6aIZOa8druat/HpAhWc8TAZL0kLZc6IZBMyI8KWorotwPw+6+l3cOjuKt/Pr2Tg3hv89WocEsqIDCPbx4NGbZhDq6znUbxVgaVrYUPgjxieGH338IzZlb6LP0YfdZUciCfAIoM+l8t8XRi1kYdRCnjqyhTifJKr7SgmyRNFqP0mCxzoanY0gzdibl2EJ3Eea9U5KqwUBMTtprZ8FnuUIj3ZwhOB2+OKyReK2hSGdwTC4GmDuJtDbQWKsJ9Lpx+LkcObEBVFc38n/HqtjUXIwn5xupzq7j425MfhbLWPxa706fLpxfdJSFd5Z+ijEzFPe/fLvwu6fqqJr7adBmOHoi2pxt/BV9RRgmOHOF8Z7NJoxRgv+BKff4SK/poOOXgeJIT78dudJVmWEs+dEM629wx59eoQP3745Y2hxNC7Y+6KLtcX1nfytuBEPk4FLunG5wSUlVosJBoqAnWruYVFyMH8/1UpGlN9QDH52XCC58UHUtPexLD0Mk3HhieWJw0/gafJkU/YmNh/brDx7JIGegbTb2lmTuIa0oDQqOytZnbCaOeGZHGg4QLRPNLU9tczwn095z/vYLTDX58skRSez93QSZeJPpMfeia/chKcFau29WH1rcfuUY3Ik0NtqxexdjiXwAMJwI90WnM034hdk4r7FD2ISpqGfxeB6x6LkEJq7bXzvtQLSI3wndqORwU1ag3n6Scvgrj+r4/GLoeYQROXAzA1Q9NrAh9zK8//keSX0ZqsS+5EN5TVTEi34E5iOPgfHqtuxOVTYJdDbg0BvC28crQPU5h8pJTMi/Siq62J7UT03ZUbywPJkypt7Lij4g2mVAsH/XZXC/vJWPj7VgpTw5oCXe6SqnbzEYP7h+kQsJoMPTzRzc1YEX12SdFnlDnodvXiZvdicv5mbEm/C7rbjki4MDPpd/axJXMOemj2kB6Vzx4w7qOioIL85n7yIPA40HGBd0jr21u4l0pJBVHAo31+ynh57DzdlB/FagZni5koWpyXxcbGgp1vQZ27A05mA3XIab98IHNZjCDywNV2HNXQv5pD3CWRY7AFOt/Ty/XUZrJ8dNeTR+3tZJn5nqXOFYJKWDYt33EI49JzaiJW1EUreBqeNofoRbqcq2OYTrmZ4ncEzpdGCP8EYTO9LDfOloLYDtxuO13Ww43gjx+u6MJsEkf6e1HfaEAIeGcgL315Uz+tHasmMDmBNdhR+VjOeZgMPs4F5ICNjsHSvyy0prO1gfU4UN2ZGkBsfxGfnxfLivkqe2nmS+QlBHKlq5xsrUrlnaRJHKtsprO3k9rnRbCto4EhV+yWLoMvtorClkJTAFNYmreUvpX8BwMDAjZu1iWtZnbCa66Kv4/FDj+Np8mRz/mYemvsQm/M3863532Jz/mbuy7mPzfmb+VrugyQHJA9df2HUAnocPfQ6eylue44++Q7hzg3UV13H7JyPKWArJmmmp3ITyb6zOVWZgn/CHwkPP46/160EelsI8fHghpnhGJ96Srnk+jcTmcq9sPMncPNPwCcMPHzg8B+G3xcmKH0HIrLUQm7kLDB7jJ+9mjFFC/4E4qldJzEZ8I9//IR7lyYxM9Kf/z1awxvH6pASsmP8WZISyh/3VTIz0o/TLb0IARH+Vv5lzUxumx1Dfm0HqeG+F73Xw6vTz3i992QzL+yr5Pl78s4oy2D1MPjtzlNDG4g+P7/5sjYUlbSV0OPooaqriq0ntw4dTw1KJSskix2VO1iTuIbb024nxjeGZwuf5bHlj1HQUsBjyx8jLyqPmcEzh14XtBScsZvWYrIQaAqk6KSTXeWH+Xzm1/nX5f84YL8HCTNqON3WwNrUJbx5rI5bZy1hd5WZyEQXeUnBl/HbmaSMDPkc/ZNaoDUsaua3eIK9Bxw2VaQNwNapcvcbCvTO3CmIztKZIAyK/RPvnyQh2IsTjT1EBnhS3tyLIWBVRjh9dhdHqjp4YHkyWTEBtPXY+bc3i3jy7txRe6Ln2zj0+92nuH9Z8hVtKKrrrqOkrYR2Wzs/O/Az7C47SFgZv5I9NXv4waIfEOYVNqoiaJdi//WpIfx256mhkgdfX5GMy83ES60ca/b8Sgl5byskXAf+MfD+v0NnNQgDklbAwvtVSufe/1Y7c5OXj7fVmktAp2VOEgaFCuDrf/yEm7MieP1wLfaB4ulmQ/CFBXFsPVJLbnwgC5ODuSkzkoQQHzzMxrXZzXkF9Dn7OFh/EJvLxn8d/i+qu6qxGBbuybmHrJAs7C47/7r3X4e8+LFiZAG5TxeUm/ThmiulpwVqD6vqmi4HHHhaZfsYZkhfB+UfqJTOhOshMkeVW9ZcfZx21Zi+r13tig7PuOJLacGfJOw92cw9zx3kK4sT8LWa+fXfTuBwDf9OLIYAAYuTQ/jGylSyYgKGardMVKSUHGk6Qoetg7+W/pVd1buYHzGfxdGLyQzJZE7YHHw9fEdd4vhSGLeSBxMdWxdUH1Rpm1LCrp9B3WH1XspqyLtXefqtp1SKZ1CS3p07Wuy90NcGfa3qu71n+D1roCqFfYXoPPxJwnUpoXxlcQJP7T7FwqSgM8TeEOAY2P6ZFe3PgsTgsxYWJyJVXVV02Do4WH+QXdW7WBm3ko1pGzEJEzmhOfh6KI8xLypvTL17OHfYZkosxo4WTz8V1qk5BP0dEJmtBN+wqIweR69qtnL9I6qTVke1qsPjFznelk8eHH3Q2zLw1aom13FGC/44U9bYzfzEYBZWtbGvvO2c51hMgvY+x4QX+y0FW0gJSEEIQVNvEy+VvES0TzS+Fl8MYZATmkOA59i3LdRcImZPlbb5yfNQ9DrM/ZLaiGV4q+yewAQIjFPnHv0ThKRA4hJVitknVHXZ0gu7w7gcwwLf06wmzQmGFvxxpLy5h4rmHo7XdXDw9LDYz4z05URjNy43XJcSQkKIN+8WNnDr7OYJ7ZlmhmTyzQ++yVeyvsI75e8A0G5rJzEgkbTANAKtgeNsoeYsDBP0d8Lan4NXoAozFL6qxL6jCt76Z1hwjxL7jwaao/e1QctJVX//c8+Or/3jidutYvCDAt/fwRn9hycgWvDHiZ++fRxfqxkpJb/+Wxku92DlSSvF9d1YTIJb50TxbmEDD96Qyq2zoyf8JqBI70g2ZW/id0d/h91tx9PkyT0597A8djlRvlHjbZ7mfAx66IVbVfesrI1Q9h4suBdOvKeKsIWkwZy7lein3gil29ROXpddhYX8osA7RD01TGXsPUrce5tVmMbtHG+LLgst+ONAdVsvvlYzv915En8vC063xGSAxTBYnBJK05FaVZZ3QRx3LIgbyiqZiIuMWwq2kB2STWZIJpVdlXibvXG4VcmHFbEryA3PJS0obZyt1FyU8t3w1jfhs8+Ah7faiPXRr2DxQ1C9X00ErWVq8bbwVZXRk3CdKsrW3QgnP1Be/+w7VYE2Tz/15eGjSjecawfvnl9BTO6ZJR3Kd0+sMJGjXy2yDnrxEyAOPxq04F8DRmaK1LT3UVzXhZSSQG8LNe39BHtb6LW7ePCGVDr6HGzZNNz8+oHlKTxx19wJ691nh2TzrV3f4r6c+4j0jeS3R3+LRDI3fC4f1X7Ebam3YQid3THhGblBy+1SWSOgRHzBvWoH7t5fq6wdUJ5t7WE1MTQUqsnh+kdU3Pqs2LVQu3fNVjB5gskCJg+1APzyl2H9L9XaQPV+2PogbHx6oKCbiWuK2w32LpUm2d+hQlcTMA4/GnRa5jVgMPXyvmVJzIoJpLi+cyj9MsjbQluvg1tmRfHoTTOGmoBPJraWbeWn+3+Kn4cfdT11LI5azF0Zd2Fz2vjxvh+Pea69ZozoblKZOk6bEvVd/6lCOMHJquqm26UarThtELsAUlaqCWCQhkI1YWRuOP89BieL1BtVGOn6R4avIQwl+oZFTRKGBUzmEa/NI45bBs41q3IRg58dREqV6+52qi+nXXnrzn4VprF3w5GX1FrF5Y5hJE67upajB1zO4fsJQ9lmmFV7Sg9f9X3wyUenZU4drksJ5f5lSfz6b2VDpXcdLolJCHrtTm6ZFcWHJ5q5a2H8pBP8DlsHgZ6B5ITm8HHdx4RaQ7kr4y7CvMPICskiyBp0VjkEzSTBNwy8lqo+ufufVgI6c+OwMBe8Am0V6tzTe1RmT+wC5a27nXDgGVjyTSh648JCmnqjChNlbTzzHOlGlXB1wJmtHi6dc917/9Pqe959Z9pTtV9VFF36reEnlw8fUw3hQU0a/R3QVQtd9dDdoCbFvhbobYP+NmXrpSIMJfTeIeAXofoZZG+8woFeGlrwrwF1HX3Mig0cKjMMYBICswkeuiGN9bOiuWth/KTbAep0OzneepzClkL21e3DarLS5+yjvKOc62OuB65Nrr1mDDFZVGij9jCs/pHK3onIUkKIUCJdug1i5yvxr9qnvkCFb46+CGYvKPgLJK+EsJkqHl74GkTNhcLX4cT24YViDx/15HCpHvXFGMwuGnxyaChU6wRCqDWIkcIelqHEfPfPITB+IHwl1ALt9v8HHZUDlUYHECbwCVGCHZo2vHbh4QMWbxW2MsxqopTuAW/fpcJE9h61+a2vTf08WsvVU9MYowV/jKlp7+Px7SWYDMHhyvah40E+ZjKjAlibE0VSqA9JoT4TOlZ/Lk60neBY0zE252/GjZuvZn8Vk2HimYJnyArJ0kI/Vaj5BO54XsX3u+qVOCFUls6sO4YXeK9/BOqOwfGtEDlbea0dNWpR1+1Wwn5i+/B1Kz+CStS1ynao74f/oGr8dNYMLPz6g9UfrAED/w5Qr00DFT0v9vQQkaXsGhk2mn2navS+++cQt0jZIVHeuTUAuurUZrNBWiuUmLvdkL4GonPV+oN3yNVbZxhlSOdS0YI/hlS19lJS34XJELx8sBpQbQPTwn0oru/G38tCSthwnZLJtAO0vqeeht4GDjccxul2sjhqMRkhGUT5RDEnbI4O40wlRmbM+EWqOP7GzerfPU3Donp6r1p4HfTWMzfA/AEhlhIO/xFK3oLEpSr0U7FHeb0NBUo8O6pUeqejVx2zdZ4/RGK2qho/wgzH/qxE3ydMTUY9Derp4eCz6vo9jYBQYSNrgOoJ4LIpr7t85/A1u2rVpCIM9Z4wqYkldZUaz4rvnDmxTEK04I8RZY3dVDSrWhmnmrqHjs9LCKSototbciL52/FG9p6c2JupBhlMv8yLyqPD1kFpWynHmo5xqPEQIV4hbEzbiNVsJSUwBbNh1mI/lRk5AThtyutvP63EfjB0MtLrj8iCxiKo2D08GSSvgKX/pK5x7OXhGP6sO868l6MfbB1qc1h/h5oE+jvVMXsP2LrVQm5LmXoqGKxP01iohBtUDRsAr2D1ufAsVSaicp9ayDXMKm5vsqjQjtmqPPnSbWpyO9f6wiRFC/5Vxu2WFNV1Ut+h8nV3lzZx6HQ74X6eJIZ4s7+8jTvz4viP23P4+FTLpAnhDKZf/vuSf8cQBsdbjvNswbO4pZt/nPOPWM1WZgbNxGzo/1LTCrMnBCUoYb7jfyAiW21I8g5RQtpUos4bKf4jJwNQE8DgRDD4/iAWq/ryjbiwHSMnjcHrD24Qs1g/tRD7C+X5mz2HhX3vr9X6AkIVi4vIGm4WE5R4btsmIfqv8ypid7rJr+mgrccOwPvFjby4v5KcmABWzQxj854K7lwQx/bCBjbMjr6qIRy3dOMcsevPbJivav57QUsBm7I28S+7/4UlMUv4oOoDnNJJRnAGif6JxPjG6NIJ05mRXr9vuPoel6fSFPf8AjY8AVGzlcccEKti4mU7VFhn2beV2H76qeBSaSg8e9IYzPyJyIas24evFzHg3dcXDAt7RJaaBPo7h481FUPRVsh7AJCqTPT2H8Da/1T1hwbTKaVUC7Fuhxqbo1+FpCboBi0t+FeJ9l47+TUd2BxupJS8XVDPa4drmBMXyIoZoWz+sILvrJ3BXXkJbJgTfVUycmwuG429jbT1t9Fh68AlXUPvGcLAz8OPAI8Agq3BBHgGIEbRrzQtMI1v7/42GcEZbKvYhiEMTMLEqvhVeJm9zmg7qNEMYfaAFd89+3hkjspSWfT14Z22qavUpFBzCGLmDeTJ29R3R//wa/eIuP7ITV9D4j0ig6jsvbPvHZ4J2Z9Vwm22qrIRwUnQWKLsMXupJ5NPN3YPSlAL2MFJFx+326XCT4ObuHqbLy9lc4zQG6+ukMHds4uTQ6hs7aWssZvn9laAlBiGwa7SJhYmBXNdSgjvFTXwhQVx3L0wYaji5WhqsjvcDqq6qqjuqsYt3UPHd5zeQbx/POlBw+0LS9tKqeys5JaUW4j0jiTSJxKr2XpZ92vtb6WopYjtFdt5rew1TMKES7pYk7iGW1NuZW74XPw8/C57HBrNFeF2KfF32eHj36jGIbHz1fGqffDWo6ox++p/VZPHW4/ChidV9y7zwE7fa42UqtBad5PKAvr0Dl698WpiMys2gG+88AkPr0ojNsib4vpODpS3Yne5cUtYmx1JZpQfv9tdzr+smXGG2MOVZ+Q09jbyxOEnaOhtYF7EPCo7K4n3jwegrL2Md8rfYX3yetzSTbx/PM8WPMum7E30O/up6KygorOCYGsw0b7RbC3bSk5ozhkLrCObkthddmq6a6jsrKSkrYTtFdvxMnvR5+wjKySLPTV7WB67XIu95tpimFR8HR+44ftnvle0Fb740rBnHpSosndqPoGM9dfa0mGEUGEsryAIS1frHJ010FmnFo6vlRnaw798frOzjHA/Txo6+/ntzlOsmBHGe0UNmA1Br92Fh9ngxswIdpY0nVPsrwQpJeWd5VR2VlLaVsrTx54GATfF38S209twup0IBJHekdT01JDgn0BTbxNfzf4qM4JnnPOaJ9tP8kzBM/xg4Q9YEruEQw2H+OFHP+SHi39ItG80LX0tQ08Q75a/y776fTT1NbEgYgHHW4+zIWUD4d7h3JNzz6jGptFMW1wOaK9UYZ+Y3Cu+jG5xeJV5atdJcqIDSAj15q1jdfz3+2Ukh3rT1uegqrUPAKvFYH1OFIW1nRTXd/GFBSobZ7Ri73K7KG4t5qXil4ZCNh/VfMTLJS/jZjikMxhqGYmfhx8ZwRnkReaRFpR21kJuaVspzxY8S7RvNJVdldyXc99QSGgwHJQbnssTR56gqa+J1fGruS31Nsrby9lSuIVfLP+FTsHUaMaZcQ/pCCF+BNwHNA0c+p6U8u2xut9Y4nJLogO9eOCFQ3xtWTIzI/1ZlxM5tJkK1BPbqpnhvJ1fj0Ry18J4thXUc9uc6FEtzLqlm/zmfNpt7cT7x/NM/jPE+sVS2laKSZiG+i0k+iVS0VXBgogFFLUUkRuRy/76/UT5RJHfnM/++v0EeQaRF5XHwsiFhHmHAZAelM6SmCVsq9imrjfA4FNEgEcA755+F6fbyS3Jt3Bz4s2UtZVhd9v5xfJf6A1WGs0kYsw8/AHB75ZSPnapn5loHn6/w0V1Wx817X04nG6K6zt5apcK4WwvrMc+0H/WEDA/MYj95W1YTIKffXYWt+fGsvdk86iycaSUFLUU0dSn5swjjUd4vuh5nG4nUT5R1PXUDYm0S7qYETSDkrYSbk+9nRvibxjy3r+U+SX6nH3sq9tHcWsxEkmINYRZYbOI9Y3l1ROvkhmSyYGGAxgY3JhwI+9XvY9LunBLNwYGd2XcxcKohZS2lfI/Rf/D48sf10Kv0UwQxt3Dn6y43ZKmbhs17X20dtvPeG9mpD/Xp4bw5rG6oWOLkoL5pLKd/eVtxAd7kRsfxO25sYBamL3c+jgjd7SWtpXS1NdESWsJ751+j5K2EhL9EwnwDOBo01FMwsSGlA28U/EOhtvgZMdJlkQv4b3T7xHrF0t6UDqbsjdR2VnJ6oTVzIuYR1t/GwfqD/BhzYd8UPUBAN5mbxp6GxAI3Lh59/S7AHiaPFkWu4zkgGReOP4CJa0lHGs+xm9W/UaLvUYzCRlrwX9QCPFl4CDwqJTy3F26xxkpJe29Duo6+mns6sfpOvupR0rJq4dr2F7YMHTs9rnRpIT5cqS6HQ8MWnvs3LEg7ozPXW42TlVXFU8fe5rvLfwefh5+HG85zlPHnsIt3eRF5jEvYp4K6/jG0tzfTGNvI4/kPoKP2YePaj8iwieC1YmrKW4pZmbwTNKD0s9I0wyyBnFT4k3cmHAjWwq2UNBcQKBnINVd1QR6BtJmU78iAxXrH7xGRnAGBxoOcEvyLVrsNZpJyqhCOkKIHUDkOd76PvB3oBkVZf43IEpK+dVzXON+4H6A+Pj4eadPj32J0EG6+h00dPZT32Gj33H+1KgTjV384ePT1Hb0E+lvJSPKjzA/T944WotA8J11M0kK8eGdgjreLWy4ohDOoGcP8MCOBxAIZoXO4lDjISSSrJAs/D38yW/OZ1P2JmaHzabd1s6P/37+BiMut4sOewctfS009DacsRN3kLdOvcW2im0siFxAflM+CNWacGf1TlxuFybDxKzQWRyoP8D65PV8VPORbmii0UwwJlSWjhAiEXhTSpl9ofOuRQy/z+6ivrOfhs5+uvsv3IC4vrOfVz6p5nBlO1aLwfL0MD6bG4sxsGP1fz6uwN/Lwn9/ce7QLtYr3VC1v24/39r1LX6y5CfsqNzBKydeGXovKySL052nmRU2i0WRi1iTtIZIn0iEEGfkzV8It3TT0tdCfU89rf2tSORQjH9JzBJ2nN6BIQy+NvtrpAelq0Xb/Kfxt/jT2NfIrcm38pOlPxmyU4u+RjNxGPcYvhAiSko5GOy+HSgYq3tdjH6Hi8ZOGw1d/XT0Xnx7c3uvnTeO1rKnrBmLyeC2OdHclBGBp2U4i8Xbw8R/35VLgNeZu/audENVXlQeN8TfwD/t+ieyQ8+cF0taS/j6nK8zL2Ie2aHZeJo8z/jcpQivIQzCvMMI8w7D4XLw3un3eK7wOe7NuZeUwBQ67Z180vDJ0PmLoxbjdDt5Ov9pbk2+lT01e9hft5+8qDweW/6Yzs7RaCYhYxnD/5kQYg4qpFMBfG0M73UWfXYXTV02mrr7aeu5tBoWvXYn2wrr2VHUiEtKVqSHs35W1FmiHhfsTWq4L6ZR5td/mpywHF4ve50D9QcAtZja6+xFIgm2BjM3fO5VKYhmMVmo763nVyt+RV5UHr2OXrJDsznaeJTStlKui76OI41H+FPxn/jd6t+RF5V3lmevxV6jmXxMmY1XTpeb9j4HrT12Wrrt9NguHK4ZicPlZmdJE2/l19Ftc7IwKZjPzIkhzM/zjPO8PUxkRPkT5ONxRTZeiOa+Zl498SpPHn7yjM1Ug6mWy2KW8eTqJ6/6fc/HyGyhQS41fKTRaK4t4x7SudaUNXVTPbDj9VKRUnKoso1XDtXQ1G0jI8qPz+XGkhBydiPx+BBvUsKuvlcP8PSxp6ntruWd8nfwMHngcDtwSRcGBndn3E2XvYsnDj8xFFK5FpxL1LVnr9FMbqaM4F8uFc09/PlgFScau4kJ9OKRVWlkxwScdZ63h4nMaH8Cva++Vw/wTP4zNPc1s7VsK6HeoTT0NCCRGBiYDTNHm47yo+t+spUzgwAADotJREFUxMzgmTpurtFoRsW0E/yOPgevfFLN3pMt+FnNfGlRAktTQ89Z72YsvfpBInwi2Jy/mYyQDI41H0MgVGmGmXexMn4l/7zrn1mXtE571xqNZtRMG8F3utz8rbiR/z1Wi8MlWZMVyfqcKLw8zu467+VhInOMYvWDbCnYQkpACv4e/mxI2cCLxS8OFT9bFLWIRxc8isWw6IwYjUZz1ZgWgl9Q08FLBypp6LQxKzaAL8yPI8L/3E1AogKtzIjww2y6eu0Bz0VmSCbf/OCbfCnzS+ys3jkk9tE+0RS3FnO44fCQV6/FXqPRXA2mtOA3dPbz8sEqjlZ3EOHvycOr0sg5R5wewGQSZET6Exlwed2grpRQayibsjfx1NGncAy0bJsRNIP6nnrun3W/3tyk0WiuOlNS8HvtTt48VsffihsxG4LP5cayOiP8vF67n9VMTmwA3h7X5sfR2t9KdbdqTzhS7H+y9Ce097fzrV3f4t6ce3UoR6PRXFWmlOA73W4+PNHMG0dr6e53cn1qKLfPjTlr49RIogO9mBnpN+omJZeK3WWnuKWYXkcvzxU+B0BuRC6lraW09rWyKHrRUNxe57trNJqryZQQfCklH5U18/vdp2jotJEW7ssXVsWReI58+kEMQ5U7jg70uqZ2FrUUYXfbeabgGXocPdwx4w6Wxy5HSsm3d39b72TVaDRjxpQQ/D8fqOLf3jxOZICVB1emMjs2YKiY2bnwtBjMjgvE33ptutdvKdhCVVcVc8Pm4u/pz6GGQ5S2lRLmFYbNaSPJP4k4/zidkaPRaMaUKSH4G+ZEU9/ZT0ak/0Vz5gO9LeTEBuBpPjsdc6yo6qrizZNv8ubJN/nizC/yUvFLCAStfa1khmQS66capmjPXqPRjCVjm3t4jfD2MLMmO/KiYh8dqDpSXUuxB1gZtxJQ9emfK3wOm8uGRHJb6m3cnnb7BZ9GNBqN5moxJQT/YggBMyL9yIz2v2aLs4M4XA48TZ7cN+s+XNKFHOg6viByAQ/MfgAv87VbQ9BoNNObKS/4JpNgdlwgccHe1/zebummoKWAPmcfVV1VQ1UwDWFQ0FxAVVfVNbdJo9FMX6a04Ht5mMhLDCbU1/PiJ19l3NLN8ZbjdNg6ONJ4hNfLXgcgNywXD0OVbHj4g4fZX7f/mtum0WimJ1NW8IN8LCxIDMbH89qvSzvdTo41HaOprwm7y86fS/4MwA1xN7ApZxM/XvJjTMJEbnguBS3j1ghMo9FMM6ZEls6nudBmKrvLTp+zj35nP4ZQJYgthgVvi/dV6SZlc9k41nSMHkcPbunm+aLn6XZ0sy5pHWuT1hLlE8WM4BkEegbqzVUajeaaMqUEXwhIC/cjPmQ4Xu9yu2iztdHc10xLX8tQKYNPYwgDfw9//D39CbGGEOB57po7F6Kpt4kT7Sewu+wAvF72OseajrExbSMr41biY/EhNTAV0CmYGo3m2jNlBN9sqMXZwXi9zWWjpruG2u5anO6Ltzt0Szfttnbabe1UdlbiafIkzCuMUK9Q/D39L+j9d9m7ONl+knZbO6B21L5b8S4fVH3A8tjlrIhdgSEMMoIzMBnXNiVUo9FoBpkygp8c6othCGwuGxUdFTT0NuCW7ot/8DzYXDaqu6up7q7GJEx8WPMh2SHZzIuch4fhgUu6+M/9/4nD7eBz6Z8b+tzx1uO8dfItTnedZkHkAjambUQIQWpgKr4evldjqBqNRnNFTBnBd+Gkor1qqArlVb22dBHqFcp/7P8PNmVvIj0ondK2UvbU7AEBs8JmkR6Uzh+K/sDBhoO4pZubE29mfdJ6TrSfoKO/gxVxK66qTRqNRnO5TBnBL+8op7a7dsyunx6UzqbsTTxb8CxLYpbwfuX7rE9eT6xfLFvyt5AcmEx+cz6gdtbeknwLpW2lPFf4HL9c8csxs0uj0WgulSkj+NeC9KB0lsQsYVvFNhZELGB7xXaWxS3DbJjJb85HIFgWu4wD9QfwNHnyUc1HPL7icRZGLRxv0zUajUYL/vmQUmJ32bG5bNjddlXHvrWYD6o+IMQawqGGQyDgnfJ3ADAwEAhmhc3Cy+zFtopt3JdzH4uiF43zSDQajUYx7QXf5rJR0lpCdVc1dT111PfW02Xvos/Zd961AJvLhkAgpMDAwI0bk2HiluRbeDr/aQSC+2fdz19K/sKiqEU6/VKj0UwIpqXg2112DjUc4mjTUUraSnC6nQgEoV6hRPpEkhaYhrfZG6vZitVsxWJYKG4tJtYvlpzQHAI9A6norODJI0+CBIthGUq3NDBYm7SWh+Y+xMLIhbo3rUajmTBMK8HvtHfyYfWHfFjzIT2OHkKsISyJWcKs0Fkk+CfgYfI472fPFYc3CRMO6eCm+JuYGz6XXx76JQ/NfYgvZ30ZUJurdFMTjUYzUZgWgm9z2niv8j3er3wfh9tBdmg2N8TdQGpg6hXXoj/UcAiTMLEuZR07q3by+fTP8+SqJ8+qjaN31Go0monClBZ8t3Szr24fb556k057J7nhuaxLWkeET8SorlvRWUFBcwG/WPELlsUuY3/d/qHQja6No9FoJipTVvDre+p5qfglTnWcIsk/iXtz7iUpIOmKr+dt9ibMO4wwrzBOdZzilyt+OeS569CNRqOZDEw5wXe5Xbx3+j3erXgXD5MHd8+8m4VRC68odGM2zER6RxLhE4Gfh9/Q8XN58Tp0o9FoJjpTSvBrumv4Y9Efqe6uJjc8l8+mfxZ/D//Lvo7VbCXOL45I70hd7Eyj0UwZpoTgO91O/lr6V14ueRlvszf35tzL7LDZl30dD5MHyQHJRHhH6MbiGo1myjElBP/1std5qfgl5obP5Y70Oy67KqUhDGL9Yon3i8dsTIkfiUaj0ZzFlFC3z6R+BofbQZRP1GV/1s/Dj4zgDLwt177JuUaj0VxLpoTgmw0z8yLmXVa1TIEgwT+BBP8EHb7RaDTTgikh+JeLp8mTzJDMK2pjqNFoNJOVaSf4QdYgMoMzsZgs422KRqPRXFOmleAn+CeQ6J+oQzgajWZacv7O3JeAEOLzQohCIYRbCDH/U+99VwhRJoQoEULcPDozR4chDLJCskgKSNJir9Fopi2j9fALgI3A70YeFEJkAncCWUA0sEMIkS6ldI3yfpeN1WwlOyRbNxDXaDTTnlEJvpTyOHAur/k24E9SShtQLoQoA/KAj0dzv8sl0DOQrJAsHa/XaDQaRhnSuQAxQNWI19UDx85CCHG/EOKgEOJgU1PTVTMgyieKWWGztNhrNBrNABf18IUQO4DIc7z1fSnl1tEaIKX8PfB7gPnz58vRXk8gSAlMIdYvdrSX0mg0minFRQVfSrn6Cq5bA8SNeB07cGxMsRgWskKyCLQGjvWtNBqNZtIxViGdN4A7hRCeQogkIA3YP0b3AsDX4ktuRK4We41GozkPo03LvF0IUQ0sBt4SQrwLIKUsBF4GioBtwDfGOkMn2jcaL7PXWN5Co9FoJjWjzdJ5DXjtPO/9GPjxaK6v0Wg0mqvHWIV0NBqNRjPB0IKv0Wg00wQt+BqNRjNN0IKv0Wg00wQt+BqNRjNN0IKv0Wg00wQt+BqNRjNN0IKv0Wg00wQh5ajrlV01hBBNwOkr/Hgo0HwVzRlP9FgmJlNlLFNlHKDHMkiClDLsYidNKMEfDUKIg1LK+Rc/c+KjxzIxmSpjmSrjAD2Wy0WHdDQajWaaoAVfo9FopglTSfB/P94GXEX0WCYmU2UsU2UcoMdyWUyZGL5Go9FoLsxU8vA1Go1GcwGmnOALIR4SQhQLIQqFED8bb3tGixDiUSGEFEKEjrctV4oQ4ucDv5NjQojXhBCTqi2ZEGKNEKJECFEmhPjOeNtzpQgh4oQQHwghigb+Ph4eb5tGgxDCJIQ4LIR4c7xtGQ1CiEAhxF8H/kaOCyEWj9W9ppTgCyFWArcBs6WUWcBj42zSqBBCxAE3AZXjbcsoeQ/IllLOAkqB746zPZeMEMIEPAmsBTKBLwohMsfXqivGCTwqpcwEFgHfmMRjAXgYOD7eRlwFfg1sk1LOBGYzhmOaUoIPfB34qZTSBiClbBxne0bLL4FvA5N6oUVKuV1K6Rx4+XdUU/vJQh5QJqU8JaW0A39CORWTDillnZTyk4F/d6GEJWZ8rboyhBCxwHpg83jbMhqEEAHAMuAZACmlXUrZPlb3m2qCnw4sFULsE0LsEkIsGG+DrhQhxG1AjZTy6HjbcpX5KvDOeBtxGcQAVSNeVzNJRXIkQohEYC6wb3wtuWJ+hXKG3ONtyChJApqAZwfCU5uFED5jdbNR9bQdD4QQO4DIc7z1fdR4glGPqwuAl4UQyXKCpiJdZCzfQ4VzJgUXGouUcuvAOd9HhRVeuJa2ac5ECOELvAI8IqXsHG97LhchxC1Ao5TykBBixXjbM0rMQC7wkJRynxDi18B3gP83VjebVEgpV5/vPSHE14FXBwR+vxDCjapP0XSt7LsczjcWIUQOauY/KoQAFQL5RAiRJ6Wsv4YmXjIX+r0ACCH+AbgFWDVRJ+DzUAPEjXgdO3BsUiKEsKDE/gUp5avjbc8Vcj2wQQixDrAC/kKIP0op/88423UlVAPVUsrBJ62/ogR/TJhqIZ3XgZUAQoh0wINJWFhJSpkvpQyXUiZKKRNR/ylyJ6rYXwwhxBrU4/cGKWXveNtzmRwA0oQQSUIID+BO4I1xtumKEMp7eAY4LqV8fLztuVKklN+VUsYO/G3cCbw/ScWegb/pKiHEjIFDq4CisbrfpPPwL8IWYIsQogCwA1+ZZN7kVOUJwBN4b+CJ5e9SygfG16RLQ0rpFEI8CLwLmIAtUsrCcTbrSrke+BKQL4Q4MnDse1LKt8fRJg08BLww4FCcAjaN1Y30TluNRqOZJky1kI5Go9FozoMWfI1Go5kmaMHXaDSaaYIWfI1Go5kmaMHXaDSaaYIWfI1Go5kmaMHXaDSaaYIWfI1Go5km/H/nb2O+FJEcXQAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_model(m)" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.imshow(m.kern.W.value.T)\n", + "plt.colorbar()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3. Mixed Kernel & Uncorrelated features (OPTIMAL)\n", + "\n", + "Remember: $f(x) = W g(x)$, where $g(x) \\in \\mathbb{R}^L$, $f(x) \\in \\mathbb{R}^P$ and $W \\in \\mathbb{R}^{P \\times L}$.\n", + "We assume that the outputs of $g$ are uncorrelated, and by *mixing* them with $W$ they become correlated.\n", + "With this setup we perform the optimal routine to calculate the conditional. Namely, calculate the conditional of the uncorrelated latent $g$ and afterwards project the mean and variance using the mixing matrix: $\\mu_f = W \\mu_g$ and $\\Sigma_f = W~\\Sigma_g W^\\top$\n", + "\n", + "\n", + "- $ K_{uu} = L \\times M \\times M $\n", + "- $ K_{uf} = L \\times M \\times N $\n", + "\n", + "We'll use `base_conditional`" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [], + "source": [ + "q_mu = np.zeros((M, L))\n", + "q_sqrt = np.repeat(np.eye(M)[None, ...], L, axis=0) * 1.0\n", + "\n", + "kern_list = [gpf.kernels.RBF(D) + gpf.kernels.Linear(D) for _ in range(L)]\n", + "kernel = mk.SeparateMixedMok(kern_list, W=np.random.randn(P, L))\n", + "feature = mf.MixedKernelSharedMof(gpf.features.InducingPoints(X[:M,...].copy()))" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "conditional: MixedKernelSharedMof, SeparateMixedMok\n", + "Conditional\n", + "object, SharedIndependentMof, SeparateIndependentMok, object\n", + "object, SeparateIndependentMof, SharedIndependentMok, object\n", + "object, SeparateIndependentMof, SeparateIndependentMok, object\n", + "Kuu: MixedKernelSharedMof, SeparateMixedMok\n", + "Kuf: MixedKernelSharedMof, SeparateMixedMok\n", + "base conditional\n" + ] + } + ], + "source": [ + "m = gpf.models.SVGP(X, Y, kernel, gpf.likelihoods.Gaussian(), feat=feature, q_mu=q_mu, q_sqrt=q_sqrt)" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "INFO:tensorflow:Optimization terminated with:\n", + " Message: b'STOP: TOTAL NO. of ITERATIONS EXCEEDS LIMIT'\n", + " Objective function value: 14.089764\n", + " Number of iterations: 1501\n", + " Number of functions evaluations: 1628\n" + ] + } + ], + "source": [ + "opt = gpf.train.ScipyOptimizer()\n", + "opt.minimize(m, disp=True, maxiter=MAXITER)" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "conditional: MixedKernelSharedMof, SeparateMixedMok\n", + "Conditional\n", + "object, SharedIndependentMof, SeparateIndependentMok, object\n", + "object, SeparateIndependentMof, SharedIndependentMok, object\n", + "object, SeparateIndependentMof, SeparateIndependentMok, object\n", + "Kuu: MixedKernelSharedMof, SeparateMixedMok\n", + "Kuf: MixedKernelSharedMof, SeparateMixedMok\n", + "base conditional\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_model(m)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.5" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/doc/source/notebooks/new_multioutput_gp_features.png b/doc/source/notebooks/new_multioutput_gp_features.png new file mode 100644 index 000000000..c522da9af Binary files /dev/null and b/doc/source/notebooks/new_multioutput_gp_features.png differ diff --git a/doc/source/notebooks/new_multioutput_gp_kernels.png b/doc/source/notebooks/new_multioutput_gp_kernels.png new file mode 100644 index 000000000..ced2b5cc2 Binary files /dev/null and b/doc/source/notebooks/new_multioutput_gp_kernels.png differ diff --git a/gpflow/__init__.py b/gpflow/__init__.py index d85918c01..dad9d0f8d 100644 --- a/gpflow/__init__.py +++ b/gpflow/__init__.py @@ -51,5 +51,8 @@ from .params import DataHolder from .params import Minibatch from .params import Parameterized + from .saver import Saver from .saver import SaverContext + +from . import multioutput \ No newline at end of file diff --git a/gpflow/conditionals.py b/gpflow/conditionals.py index 32e3739c1..61734c5f5 100644 --- a/gpflow/conditionals.py +++ b/gpflow/conditionals.py @@ -17,13 +17,66 @@ from . import settings, mean_functions from .decors import name_scope -from .features import InducingPoints +from .dispatch import conditional, sample_conditional from .expectations import expectation +from .features import Kuu, Kuf, InducingPoints, InducingFeature +from .kernels import Kernel, Combination from .probability_distributions import Gaussian -@name_scope() -def conditional(Xnew, X, kern, f, *, full_cov=False, q_sqrt=None, white=False): +logger = settings.logger() + + +# ---------------------------------------------------------------------------- +############################### CONDITIONAL ################################## +# ---------------------------------------------------------------------------- + +@conditional.register(object, InducingFeature, Kernel, object) +@name_scope("conditional") +def _conditional(Xnew, feat, kern, f, *, full_cov=False, full_output_cov=False, q_sqrt=None, white=False): + """ + Single-output GP conditional. + + The covariance matrices used to calculate the conditional have the following shape: + - Kuu: M x M + - Kuf: M x N + - Kff: N or N x N + + Further reference + ----------------- + - See `gpflow.conditionals._conditional` (below) for a detailed explanation of + conditional in the single-output case. + - See the multiouput notebook for more information about the multiouput framework. + + Parameters + ---------- + :param Xnew: data matrix, size N x D. + :param f: data matrix, M x R + :param full_cov: return the covariance between the datapoints + :param full_output_cov: return the covariance between the outputs. + Note: as we are using a single-output kernel with repetitions these covariances will be zero. + :param q_sqrt: matrix of standard-deviations or Cholesky matrices, + size M x R or R x M x M. + :param white: boolean of whether to use the whitened representation + :return: + - mean: N x R + - variance: N x R, R x N x N, N x R x R or N x R x N x R + Please see `gpflow.conditional._expand_independent_outputs` for more information + about the shape of the variance, depending on `full_cov` and `full_output_cov`. + """ + logger.debug("Conditional: Inducing Feature - Kernel") + Kmm = Kuu(feat, kern, jitter=settings.numerics.jitter_level) # M x M + Kmn = Kuf(feat, kern, Xnew) # M x N + Knn = kern.K(Xnew) if full_cov else kern.Kdiag(Xnew) + + fmean, fvar = base_conditional(Kmn, Kmm, Knn, f, full_cov=full_cov, + q_sqrt=q_sqrt, white=white) # N x R, R x N x N or N x R + return fmean, _expand_independent_outputs(fvar, full_cov, full_output_cov) + + +@conditional.register(object, object, Kernel, object) +@name_scope("conditional") +def _conditional(Xnew, X, kern, f, *, full_cov=False, q_sqrt=None, white=False): """ Given f, representing the GP at the points X, produce the mean and (co-)variance of the GP at the points Xnew. @@ -42,21 +95,23 @@ def conditional(Xnew, X, kern, f, *, full_cov=False, q_sqrt=None, white=False): The method can either return the diagonals of the covariance matrix for each output (default) or the full covariance matrix (full_cov=True). - We assume K independent GPs, represented by the columns of f (and the - last dimension of q_sqrt). + We assume R independent GPs, represented by the columns of f (and the + first dimension of q_sqrt). - :param Xnew: data matrix, size N x D. + :param Xnew: data matrix, size N x D. Evaluate the GP at these new points :param X: data points, size M x D. :param kern: GPflow kernel. - :param f: data matrix, M x K, representing the function values at X, + :param f: data matrix, M x R, representing the function values at X, for K functions. :param q_sqrt: matrix of standard-deviations or Cholesky matrices, - size M x K or K x M x M. + size M x R or R x M x M. :param white: boolean of whether to use the whitened representation as described above. - - :return: two element tuple with conditional mean and variance. + :return: + - mean: N x R + - variance: N x R (full_cov = False), R x N x N (full_cov = True) """ + logger.debug("Conditional: Kernel") num_data = tf.shape(X)[0] # M Kmm = kern.K(X) + tf.eye(num_data, dtype=settings.float_type) * settings.numerics.jitter_level Kmn = kern.K(X, Xnew) @@ -64,24 +119,70 @@ def conditional(Xnew, X, kern, f, *, full_cov=False, q_sqrt=None, white=False): Knn = kern.K(Xnew) else: Knn = kern.Kdiag(Xnew) - return base_conditional(Kmn, Kmm, Knn, f, full_cov=full_cov, q_sqrt=q_sqrt, white=white) + mean, var = base_conditional(Kmn, Kmm, Knn, f, full_cov=full_cov, q_sqrt=q_sqrt, white=white) + return mean, var # N x R, N x R or R x N x N -@name_scope() -def feature_conditional(Xnew, feat, kern, f, *, full_cov=False, q_sqrt=None, white=False): - Kmm = feat.Kuu(kern, jitter=settings.numerics.jitter_level) - Kmn = feat.Kuf(kern, Xnew) - if full_cov: - Knn = kern.K(Xnew) - else: - Knn = kern.Kdiag(Xnew) - return base_conditional(Kmn, Kmm, Knn, f, full_cov=full_cov, q_sqrt=q_sqrt, white=white) +# ---------------------------------------------------------------------------- +############################ SAMPLE CONDITIONAL ############################## +# ---------------------------------------------------------------------------- + + +@sample_conditional.register(object, InducingFeature, Kernel, object) +@name_scope("sample_conditional") +def _sample_conditional(Xnew, feat, kern, f, *, full_output_cov=False, q_sqrt=None, white=False): + """ + `sample_conditional` will return a sample from the conditinoal distribution. + In most cases this means calculating the conditional mean m and variance v and then + returning m + sqrt(v) * eps, with eps ~ N(0, 1). + However, for some combinations of Mok and Mof more efficient sampling routines exists. + The dispatcher will make sure that we use the most efficent one. + + :return: N x P (full_output_cov = False) or N x P x P (full_output_cov = True) + """ + logger.debug("sample conditional: InducingFeature Kernel") + mean, var = conditional(Xnew, feat, kern, f, full_cov=False, full_output_cov=full_output_cov, + q_sqrt=q_sqrt, white=white) # N x P, N x P (x P) + cov_structure = "full" if full_output_cov else "diag" + return _sample_mvn(mean, var, cov_structure) + + +@sample_conditional.register(object, object, Kernel, object) +@name_scope("sample_conditional") +def _sample_conditional(Xnew, X, kern, f, *, q_sqrt=None, white=False): + logger.debug("sample conditional: Kernel") + mean, var = conditional(Xnew, X, kern, f, q_sqrt=q_sqrt, white=white, full_cov=False) # N x P, N x P + return _sample_mvn(mean, var, "diag") # N x P + + +# ---------------------------------------------------------------------------- +############################# CONDITIONAL MATHS ############################## +# ---------------------------------------------------------------------------- @name_scope() def base_conditional(Kmn, Kmm, Knn, f, *, full_cov=False, q_sqrt=None, white=False): + """ + Given a g1 and g2, and distribution p and q such that + p(g2) = N(g2;0,Kmm) + p(g1) = N(g1;0,Knn) + p(g1|g2) = N(g1;0,Knm) + And + q(g2) = N(g2;f,q_sqrt*q_sqrt^T) + This method computes the mean and (co)variance of + q(g1) = \int q(g2) p(g1|g2) + :param Kmn: M x N + :param Kmm: M x M + :param Knn: N x N or N + :param f: M x R + :param full_cov: bool + :param q_sqrt: None or R x M x M (lower triangular) + :param white: bool + :return: N x R or R x N x N + """ + logger.debug("base conditional") # compute kernel stuff - num_func = tf.shape(f)[1] # K + num_func = tf.shape(f)[1] # R Lm = tf.cholesky(Kmm) # Compute the projection matrix A @@ -90,11 +191,10 @@ def base_conditional(Kmn, Kmm, Knn, f, *, full_cov=False, q_sqrt=None, white=Fal # compute the covariance due to the conditioning if full_cov: fvar = Knn - tf.matmul(A, A, transpose_a=True) - shape = tf.stack([num_func, 1, 1]) + fvar = tf.tile(fvar[None, :, :], [num_func, 1, 1]) # R x N x N else: fvar = Knn - tf.reduce_sum(tf.square(A), 0) - shape = tf.stack([num_func, 1]) - fvar = tf.tile(tf.expand_dims(fvar, 0), shape) # K x N x N or K x N + fvar = tf.tile(fvar[None, :], [num_func, 1]) # R x N # another backsubstitution in the unwhitened case if not white: @@ -105,26 +205,32 @@ def base_conditional(Kmn, Kmm, Knn, f, *, full_cov=False, q_sqrt=None, white=Fal if q_sqrt is not None: if q_sqrt.get_shape().ndims == 2: - LTA = A * tf.expand_dims(tf.transpose(q_sqrt), 2) # K x M x N + LTA = A * tf.expand_dims(tf.transpose(q_sqrt), 2) # R x M x N elif q_sqrt.get_shape().ndims == 3: - L = tf.matrix_band_part(q_sqrt, -1, 0) # K x M x M + L = tf.matrix_band_part(q_sqrt, -1, 0) # R x M x M A_tiled = tf.tile(tf.expand_dims(A, 0), tf.stack([num_func, 1, 1])) - LTA = tf.matmul(L, A_tiled, transpose_a=True) # K x M x N + LTA = tf.matmul(L, A_tiled, transpose_a=True) # R x M x N else: # pragma: no cover raise ValueError("Bad dimension for q_sqrt: %s" % str(q_sqrt.get_shape().ndims)) if full_cov: - fvar = fvar + tf.matmul(LTA, LTA, transpose_a=True) # K x N x N + fvar = fvar + tf.matmul(LTA, LTA, transpose_a=True) # R x N x N else: - fvar = fvar + tf.reduce_sum(tf.square(LTA), 1) # K x N - fvar = tf.transpose(fvar) # N x K or N x N x K + fvar = fvar + tf.reduce_sum(tf.square(LTA), 1) # R x N - return fmean, fvar + if not full_cov: + fvar = tf.transpose(fvar) # N x R + return fmean, fvar # N x R, R x N x N or N x R + + +# ---------------------------------------------------------------------------- +############################ UNCERTAIN CONDITIONAL ########################### +# ---------------------------------------------------------------------------- @name_scope() def uncertain_conditional(Xnew_mu, Xnew_var, feat, kern, q_mu, q_sqrt, *, - mean_function=None, full_cov_output=False, full_cov=False, white=False): + mean_function=None, full_output_cov=False, full_cov=False, white=False): """ Calculates the conditional for uncertain inputs Xnew, p(Xnew) = N(Xnew_mu, Xnew_var). See ``conditional`` documentation for further reference. @@ -135,16 +241,16 @@ def uncertain_conditional(Xnew_mu, Xnew_var, feat, kern, q_mu, q_sqrt, *, :param kern: gpflow kernel or ekernel object. :param q_mu: mean inducing points, size M x Dout :param q_sqrt: cholesky of the covariance matrix of the inducing points, size Dout x M x M - :param full_cov_output: boolean wheter to compute covariance between output dimension. + :param full_output_cov: boolean wheter to compute covariance between output dimension. Influences the shape of return value ``fvar``. Default is False :param white: boolean whether to use whitened representation. Default is False. :return fmean, fvar: mean and covariance of the conditional, size ``fmean`` is N x Dout, - size ``fvar`` depends on ``full_cov_output``: if True ``f_var`` is N x Dout x Dout, + size ``fvar`` depends on ``full_output_cov``: if True ``f_var`` is N x Dout x Dout, if False then ``f_var`` is N x Dout """ - # TODO: Tensorflow 1.4 doesn't support broadcasting in``tf.matmul`` and + # TODO(VD): Tensorflow 1.7 doesn't support broadcasting in``tf.matmul`` and # ``tf.matrix_triangular_solve``. This is reported in issue 216. # As a temporary workaround, we are using ``tf.einsum`` for the matrix # multiplications and tiling in the triangular solves. @@ -154,7 +260,7 @@ def uncertain_conditional(Xnew_mu, Xnew_var, feat, kern, q_mu, q_sqrt, *, raise NotImplementedError if full_cov: - # TODO: ``full_cov`` True would return a ``fvar`` of shape N x N x D x D, + # TODO(VD): ``full_cov`` True would return a ``fvar`` of shape N x N x D x D, # encoding the covariance between input datapoints as well. # This is not implemented as this feature is only used for plotting purposes. raise NotImplementedError @@ -167,7 +273,7 @@ def uncertain_conditional(Xnew_mu, Xnew_var, feat, kern, q_mu, q_sqrt, *, q_sqrt_r = tf.matrix_band_part(q_sqrt, -1, 0) # D x M x M - eKuf = tf.transpose(expectation(pXnew, (kern, feat))) # M x N (psi1) + eKuf = tf.transpose(expectation(pXnew, (kern, feat))) # M x N (psi1) Kuu = feat.Kuu(kern, jitter=settings.numerics.jitter_level) # M x M Luu = tf.cholesky(Kuu) # M x M @@ -180,10 +286,10 @@ def uncertain_conditional(Xnew_mu, Xnew_var, feat, kern, q_mu, q_sqrt, *, fmean = tf.matmul(Li_eKuf, q_mu, transpose_a=True) eKff = expectation(pXnew, kern) # N (psi0) - eKuffu = expectation(pXnew, (kern, feat), (kern, feat)) # N x M x M (psi2) + eKuffu = expectation(pXnew, (kern, feat), (kern, feat)) # N x M x M (psi2) Luu_tiled = tf.tile(Luu[None, :, :], [num_data, 1, 1]) # remove this line, once issue 216 is fixed - Li_eKuffu_Lit = tf.matrix_triangular_solve(Luu_tiled, tf.matrix_transpose(eKuffu), lower=True) - Li_eKuffu_Lit = tf.matrix_triangular_solve(Luu_tiled, tf.matrix_transpose(Li_eKuffu_Lit), lower=True) # N x M x M + Li_eKuffu = tf.matrix_triangular_solve(Luu_tiled, eKuffu, lower=True) + Li_eKuffu_Lit = tf.matrix_triangular_solve(Luu_tiled, tf.matrix_transpose(Li_eKuffu), lower=True) # N x M x M cov = tf.matmul(q_sqrt_r, q_sqrt_r, transpose_b=True) # D x M x M if mean_function is None or isinstance(mean_function, mean_functions.Zero): @@ -194,32 +300,86 @@ def uncertain_conditional(Xnew_mu, Xnew_var, feat, kern, q_mu, q_sqrt, *, # Calculate: m(x) m(x)^T + m(x) \mu(x)^T + \mu(x) m(x)^T, # where m(x) is the mean_function and \mu(x) is fmean - e_mean_mean = expectation(pXnew, mean_function, mean_function) # N x D x D + e_mean_mean = expectation(pXnew, mean_function, mean_function) # N x D x D Lit_q_mu = tf.matrix_triangular_solve(Luu, q_mu, adjoint=True) - e_mean_Kuf = expectation(pXnew, mean_function, (kern, feat)) # N x D x M + e_mean_Kuf = expectation(pXnew, mean_function, (kern, feat)) # N x D x M # einsum isn't able to infer the rank of e_mean_Kuf, hence we explicitly set the rank of the tensor: e_mean_Kuf = tf.reshape(e_mean_Kuf, [num_data, num_func, num_ind]) - e_fmean_mean = tf.einsum("nqm,mz->nqz", e_mean_Kuf, Lit_q_mu) # N x D x D + e_fmean_mean = tf.einsum("nqm,mz->nqz", e_mean_Kuf, Lit_q_mu) # N x D x D e_related_to_mean = e_fmean_mean + tf.matrix_transpose(e_fmean_mean) + e_mean_mean - - if full_cov_output: + if full_output_cov: fvar = ( - tf.matrix_diag(tf.tile((eKff - tf.trace(Li_eKuffu_Lit))[:, None], [1, num_func])) + - tf.matrix_diag(tf.einsum("nij,dji->nd", Li_eKuffu_Lit, cov)) + - # tf.matrix_diag(tf.trace(tf.matmul(Li_eKuffu_Lit, cov))) + - tf.einsum("ig,nij,jh->ngh", q_mu, Li_eKuffu_Lit, q_mu) - - # tf.matmul(q_mu, tf.matmul(Li_eKuffu_Lit, q_mu), transpose_a=True) - - fmean[:, :, None] * fmean[:, None, :] + - e_related_to_mean + tf.matrix_diag(tf.tile((eKff - tf.trace(Li_eKuffu_Lit))[:, None], [1, num_func])) + + tf.matrix_diag(tf.einsum("nij,dji->nd", Li_eKuffu_Lit, cov)) + + # tf.matrix_diag(tf.trace(tf.matmul(Li_eKuffu_Lit, cov))) + + tf.einsum("ig,nij,jh->ngh", q_mu, Li_eKuffu_Lit, q_mu) - + # tf.matmul(q_mu, tf.matmul(Li_eKuffu_Lit, q_mu), transpose_a=True) - + fmean[:, :, None] * fmean[:, None, :] + + e_related_to_mean ) else: fvar = ( - (eKff - tf.trace(Li_eKuffu_Lit))[:, None] + - tf.einsum("nij,dji->nd", Li_eKuffu_Lit, cov) + - tf.einsum("ig,nij,jg->ng", q_mu, Li_eKuffu_Lit, q_mu) - - fmean ** 2 + - tf.matrix_diag_part(e_related_to_mean) + (eKff - tf.trace(Li_eKuffu_Lit))[:, None] + + tf.einsum("nij,dji->nd", Li_eKuffu_Lit, cov) + + tf.einsum("ig,nij,jg->ng", q_mu, Li_eKuffu_Lit, q_mu) - + fmean ** 2 + + tf.matrix_diag_part(e_related_to_mean) ) return fmean, fvar + + +# --------------------------------------------------------------- +########################## HELPERS ############################## +# --------------------------------------------------------------- + +def _sample_mvn(mean, cov, cov_structure): + """ + Returns a sample from a D-dimensional Multivariate Normal distribution + :param mean: N x D + :param cov: N x D or N x D x D + :param cov_structure: "diag" or "full" + - "diag": cov holds the diagonal elements of the covariance matrix + - "full": cov holds the full covariance matrix (without jitter) + :return: sample from the MVN of shape N x D + """ + eps = tf.random_normal(tf.shape(mean), dtype=settings.float_type) # N x P + if cov_structure == "diag": + sample = mean + tf.sqrt(cov) * eps # N x P + elif cov_structure == "full": + cov = cov + (tf.eye(tf.shape(mean)[1], dtype=settings.float_type) * settings.numerics.jitter_level)[None, ...] # N x P x P + chol = tf.cholesky(cov) # N x P x P + return mean + (tf.matmul(chol, eps[..., None])[..., 0]) # N x P + else: + raise NotImplementedError # pragma: no cover + + return sample # N x P + +def _expand_independent_outputs(fvar, full_cov, full_output_cov): + """ + Reshapes fvar to the correct shape, specified by `full_cov` and `full_output_cov`. + + :param fvar: has shape N x P (full_cov = False) or P x N x N (full_cov = True). + :return: + 1. full_cov: True and full_output_cov: True + fvar N x P x N x P + 2. full_cov: True and full_output_cov: False + fvar P x N x N + 3. full_cov: False and full_output_cov: True + fvar N x P x P + 4. full_cov: False and full_output_cov: False + fvar N x P + """ + if full_cov and full_output_cov: + fvar = tf.matrix_diag(tf.transpose(fvar)) # N x N x P x P + fvar = tf.transpose(fvar, [0, 2, 1, 3]) # N x P x N x P + if not full_cov and full_output_cov: + fvar = tf.matrix_diag(fvar) # N x P x P + if full_cov and not full_output_cov: + pass # P x N x N + if not full_cov and not full_output_cov: + pass # N x P + + return fvar + diff --git a/gpflow/dispatch.py b/gpflow/dispatch.py new file mode 100644 index 000000000..6241983da --- /dev/null +++ b/gpflow/dispatch.py @@ -0,0 +1,10 @@ +from multipledispatch import dispatch, Dispatcher +from functools import partial + +# By default multipledispatch uses a global namespace in multipledispatch.core.global_namespace +# We define our own GPflow namespace to avoid any conflict which may arise +gpflow_md_namespace = dict() +dispatch = partial(dispatch, namespace=gpflow_md_namespace) + +conditional = Dispatcher('conditional') +sample_conditional = Dispatcher('sample_conditional') \ No newline at end of file diff --git a/gpflow/expectations.py b/gpflow/expectations.py index 2f18cdb0d..5603a7483 100644 --- a/gpflow/expectations.py +++ b/gpflow/expectations.py @@ -25,13 +25,10 @@ from .quadrature import mvnquad from .probability_distributions import Gaussian, DiagonalGaussian, MarkovGaussian -from multipledispatch import dispatch -from functools import partial +from .dispatch import dispatch -# By default multipledispatch uses a global namespace in multipledispatch.core.global_namespace -# We define our own GPflow namespace to avoid any conflict which may arise -gpflow_md_namespace = dict() -dispatch = partial(dispatch, namespace=gpflow_md_namespace) + +logger = settings.logger() # Sections: @@ -113,8 +110,8 @@ def _quadrature_expectation(p, obj1, feature1, obj2, feature2, num_gauss_hermite """ num_gauss_hermite_points = 100 if num_gauss_hermite_points is None else num_gauss_hermite_points - warnings.warn("Quadrature is used to calculate the expectation. This means that " - "an analytical implementations is not available for the given combination.") + logger.warn("Quadrature is used to calculate the expectation. This means that " + "an analytical implementations is not available for the given combination.") if obj2 is None: eval_func = lambda x: get_eval_func(obj1, feature1)(x) @@ -155,8 +152,8 @@ def _quadrature_expectation(p, obj1, feature1, obj2, feature2, num_gauss_hermite """ num_gauss_hermite_points = 40 if num_gauss_hermite_points is None else num_gauss_hermite_points - warnings.warn("Quadrature is used to calculate the expectation. This means that " - "an analytical implementations is not available for the given combination.") + logger.warn("Quadrature is used to calculate the expectation. This means that " + "an analytical implementations is not available for the given combination.") if obj2 is None: eval_func = lambda x: get_eval_func(obj1, feature1)(x) diff --git a/gpflow/features.py b/gpflow/features.py index 75d3cfe53..27f2c3f17 100644 --- a/gpflow/features.py +++ b/gpflow/features.py @@ -13,13 +13,18 @@ # limitations under the License. from abc import abstractmethod -from functools import singledispatch +import warnings import numpy as np import tensorflow as tf -from . import conditionals, transforms, kernels, decors, settings +from . import transforms, kernels, settings +from .decors import params_as_tensors, params_as_tensors_for from .params import Parameter, Parameterized +from .dispatch import dispatch + + +logger = settings.logger() class InducingFeature(Parameterized): @@ -35,23 +40,32 @@ def __len__(self) -> int: """ raise NotImplementedError() - @abstractmethod def Kuu(self, kern, jitter=0.0): """ Calculates the covariance matrix between features for kernel `kern`. + + Return shape M x M + M = len(feat) """ - raise NotImplementedError() + warnings.warn('Please replace feature.Kuu(kernel) with Kuu(feature, kernel)', + DeprecationWarning) + return Kuu(self, kern, jitter=jitter) - @abstractmethod def Kuf(self, kern, Xnew): """ Calculates the covariance matrix with function values at new points `Xnew` for kernel `kern`. + + Return shape M x N + M = len(feat) + N = len(Xnew) """ - raise NotImplementedError() + warnings.warn('Please replace feature.Kuf(kernel, Xnew) with Kuf(feature, kernel, Xnew)', + DeprecationWarning) + return Kuf(self, kern, Xnew) -class InducingPoints(InducingFeature): +class InducingPointsBase(InducingFeature): """ Real-space inducing points """ @@ -66,19 +80,25 @@ def __init__(self, Z): def __len__(self): return self.Z.shape[0] - @decors.params_as_tensors - def Kuu(self, kern, jitter=0.0): - Kzz = kern.K(self.Z) - Kzz += jitter * tf.eye(len(self), dtype=settings.dtypes.float_type) - return Kzz - @decors.params_as_tensors - def Kuf(self, kern, Xnew): - Kzx = kern.K(self.Z, Xnew) - return Kzx +class InducingPoints(InducingPointsBase): + pass +@dispatch(InducingPoints, kernels.Kernel) +def Kuu(feat, kern, *, jitter=0.0): + with params_as_tensors_for(feat): + Kzz = kern.K(feat.Z) + Kzz += jitter * tf.eye(len(feat), dtype=settings.dtypes.float_type) + return Kzz -class Multiscale(InducingPoints): +@dispatch(InducingPoints, kernels.Kernel, object) +def Kuf(feat, kern, Xnew): + with params_as_tensors_for(feat): + Kzx = kern.K(feat.Z, Xnew) + return Kzx + + +class Multiscale(InducingPointsBase): """ Multi-scale inducing features Originally proposed in @@ -101,69 +121,39 @@ def __init__(self, Z, scales): if self.Z.shape != scales.shape: raise ValueError("Input locations `Z` and `scales` must have the same shape.") # pragma: no cover - def _cust_square_dist(self, A, B, sc): + @staticmethod + def _cust_square_dist(A, B, sc): """ Custom version of _square_dist that allows sc to provide per-datapoint length scales. sc: N x M x D. """ return tf.reduce_sum(tf.square((tf.expand_dims(A, 1) - tf.expand_dims(B, 0)) / sc), 2) - @decors.params_as_tensors - def Kuf(self, kern, Xnew): - if isinstance(kern, kernels.RBF): - with decors.params_as_tensors_for(kern): - Xnew, _ = kern._slice(Xnew, None) - Zmu, Zlen = kern._slice(self.Z, self.scales) - idlengthscales = kern.lengthscales + Zlen - d = self._cust_square_dist(Xnew, Zmu, idlengthscales) - Kuf = tf.transpose(kern.variance * tf.exp(-d / 2) * - tf.reshape(tf.reduce_prod(kern.lengthscales / idlengthscales, 1), - (1, -1))) - return Kuf - else: - raise NotImplementedError( - "Multiscale features not implemented for `%s`." % str(type(kern))) - - @decors.params_as_tensors - def Kuu(self, kern, jitter=0.0): - if isinstance(kern, kernels.RBF): - with decors.params_as_tensors_for(kern): - Zmu, Zlen = kern._slice(self.Z, self.scales) - idlengthscales2 = tf.square(kern.lengthscales + Zlen) - sc = tf.sqrt( - tf.expand_dims(idlengthscales2, 0) + tf.expand_dims(idlengthscales2, 1) - tf.square( - kern.lengthscales)) - d = self._cust_square_dist(Zmu, Zmu, sc) - Kzz = kern.variance * tf.exp(-d / 2) * tf.reduce_prod(kern.lengthscales / sc, 2) - Kzz += jitter * tf.eye(len(self), dtype=settings.float_type) - return Kzz - else: - raise NotImplementedError( - "Multiscale features not implemented for `%s`." % str(type(kern))) - - -@singledispatch -def conditional(feat, kern, Xnew, f, *, full_cov=False, q_sqrt=None, white=False): - """ - Note the changed function signature compared to conditionals.conditional() - to allow for single dispatch on the first argument. - """ - raise NotImplementedError("No implementation for {} found".format(type(feat).__name__)) - -@conditional.register(InducingPoints) -@conditional.register(Multiscale) -def default_feature_conditional(feat, kern, Xnew, f, *, full_cov=False, q_sqrt=None, white=False): - """ - Uses the same code path as conditionals.conditional(), except Kuu/Kuf - matrices are constructed using the feature. - To use this with features defined in external modules, register your - feature class using - >>> gpflow.features.conditional.register(YourFeatureClass, - ... gpflow.features.default_feature_conditional) - """ - return conditionals.feature_conditional(Xnew, feat, kern, f, full_cov=full_cov, q_sqrt=q_sqrt, - white=white) +@dispatch(Multiscale, kernels.RBF, object) +def Kuf(feat, kern, Xnew): + with params_as_tensors_for(feat, kern): + Xnew, _ = kern._slice(Xnew, None) + Zmu, Zlen = kern._slice(feat.Z, feat.scales) + idlengthscales = kern.lengthscales + Zlen + d = feat._cust_square_dist(Xnew, Zmu, idlengthscales) + Kuf = tf.transpose(kern.variance * tf.exp(-d / 2) * + tf.reshape(tf.reduce_prod(kern.lengthscales / idlengthscales, 1), + (1, -1))) + return Kuf + +@dispatch(Multiscale, kernels.RBF) +def Kuu(feat, kern, *, jitter=0.0): + with params_as_tensors_for(feat, kern): + Zmu, Zlen = kern._slice(feat.Z, feat.scales) + idlengthscales2 = tf.square(kern.lengthscales + Zlen) + sc = tf.sqrt( + tf.expand_dims(idlengthscales2, 0) + tf.expand_dims(idlengthscales2, 1) - tf.square( + kern.lengthscales)) + d = feat._cust_square_dist(Zmu, Zmu, sc) + Kzz = kern.variance * tf.exp(-d / 2) * tf.reduce_prod(kern.lengthscales / sc, 2) + Kzz += jitter * tf.eye(len(feat), dtype=settings.float_type) + return Kzz def inducingpoint_wrapper(feat, Z): diff --git a/gpflow/gpflowrc b/gpflow/gpflowrc index 7a48aa567..0f53c0b59 100644 --- a/gpflow/gpflowrc +++ b/gpflow/gpflowrc @@ -4,8 +4,6 @@ level = WARNING [verbosity] tf_compile_verb = False -hmc_verb = True -optimisation_verb = False [dtypes] float_type = float64 diff --git a/gpflow/kullback_leiblers.py b/gpflow/kullback_leiblers.py index 5865a02dc..486957122 100644 --- a/gpflow/kullback_leiblers.py +++ b/gpflow/kullback_leiblers.py @@ -35,7 +35,7 @@ def gauss_kl(q_mu, q_sqrt, K=None): q_mu is a matrix (M x L), each column contains a mean. - q_sqrt can be a 3D tensor (L xM x M), each matrix within is a lower + q_sqrt can be a 3D tensor (L x M x M), each matrix within is a lower triangular square-root matrix of the covariance of q. q_sqrt can be a matrix (M x L), each column represents the diagonal of a square-root matrix of the covariance of q. @@ -70,7 +70,7 @@ def gauss_kl(q_mu, q_sqrt, K=None): mahalanobis = tf.reduce_sum(tf.square(alpha)) # Constant term: - B * M - constant = tf.cast(-tf.size(q_mu, out_type=tf.int64), dtype=settings.float_type) + constant = - tf.cast(tf.size(q_mu, out_type=tf.int64), dtype=settings.float_type) # Log-determinant of the covariance of q(x): logdet_qcov = tf.reduce_sum(tf.log(tf.square(Lq_diag))) @@ -101,4 +101,4 @@ def gauss_kl(q_mu, q_sqrt, K=None): scale = 1.0 if batch else tf.cast(B, settings.float_type) twoKL += scale * sum_log_sqdiag_Lp - return 0.5 * twoKL \ No newline at end of file + return 0.5 * twoKL diff --git a/gpflow/logdensities.py b/gpflow/logdensities.py index 922849e15..1305738d7 100644 --- a/gpflow/logdensities.py +++ b/gpflow/logdensities.py @@ -21,8 +21,11 @@ from . import settings +logger = settings.logger() + + def gaussian(x, mu, var): - return -0.5 * (np.log(2 * np.pi) + tf.log(var) + tf.square(mu-x)/var) + return -0.5 * (np.log(2 * np.pi) + tf.log(var) + tf.square(mu-x) / var) def lognormal(x, mu, var): @@ -86,11 +89,11 @@ def multivariate_normal(x, mu, L): x[n] ~ N(mu, LL^T) or x ~ N(mu[n], LL^T) or x[n] ~ N(mu[n], LL^T) """ if x.shape.ndims is None: - warnings.warn('Shape of x must be 2D at computation.') + logger.warn('Shape of x must be 2D at computation.') elif x.shape.ndims != 2: raise ValueError('Shape of x must be 2D.') if mu.shape.ndims is None: - warnings.warn('Shape of mu may be unknown or not 2D.') + logger.warn('Shape of mu may be unknown or not 2D.') elif mu.shape.ndims != 2: raise ValueError('Shape of mu must be 2D.') diff --git a/gpflow/models/gpr.py b/gpflow/models/gpr.py index 045149201..5a90a9748 100644 --- a/gpflow/models/gpr.py +++ b/gpflow/models/gpr.py @@ -17,6 +17,7 @@ from .. import likelihoods from .. import settings +from ..conditionals import base_conditional from ..params import DataHolder from ..decors import params_as_tensors from ..decors import name_scope @@ -78,17 +79,10 @@ def _build_predict(self, Xnew, full_cov=False): where F* are points on the GP at Xnew, Y are noisy observations at X. """ - Kx = self.kern.K(self.X, Xnew) - K = self.kern.K(self.X) + tf.eye(tf.shape(self.X)[0], dtype=settings.float_type) * self.likelihood.variance - L = tf.cholesky(K) - A = tf.matrix_triangular_solve(L, Kx, lower=True) - V = tf.matrix_triangular_solve(L, self.Y - self.mean_function(self.X)) - fmean = tf.matmul(A, V, transpose_a=True) + self.mean_function(Xnew) - if full_cov: - fvar = self.kern.K(Xnew) - tf.matmul(A, A, transpose_a=True) - shape = tf.stack([1, 1, tf.shape(self.Y)[1]]) - fvar = tf.tile(tf.expand_dims(fvar, 2), shape) - else: - fvar = self.kern.Kdiag(Xnew) - tf.reduce_sum(tf.square(A), 0) - fvar = tf.tile(tf.reshape(fvar, (-1, 1)), [1, tf.shape(self.Y)[1]]) - return fmean, fvar + y = self.Y - self.mean_function(self.X) + Kmn = self.kern.K(self.X, Xnew) + Kmm_sigma = self.kern.K(self.X) + tf.eye(tf.shape(self.X)[0], dtype=settings.float_type) * self.likelihood.variance + Knn = self.kern.K(Xnew) if full_cov else self.kern.Kdiag(Xnew) + f_mean, f_var = base_conditional(Kmn, Kmm_sigma, Knn, y, full_cov=full_cov, white=False) # N x P, N x P or P x N x N + return f_mean + self.mean_function(Xnew), f_var + diff --git a/gpflow/models/model.py b/gpflow/models/model.py index 721ad55f5..2768d4ab8 100755 --- a/gpflow/models/model.py +++ b/gpflow/models/model.py @@ -161,11 +161,11 @@ def predict_f_samples(self, Xnew, num_samples): Produce samples from the posterior latent function(s) at the points Xnew. """ - mu, var = self._build_predict(Xnew, full_cov=True) + mu, var = self._build_predict(Xnew, full_cov=True) # N x P, # P x N x N jitter = tf.eye(tf.shape(mu)[0], dtype=settings.float_type) * settings.numerics.jitter_level samples = [] for i in range(self.num_latent): - L = tf.cholesky(var[:, :, i] + jitter) + L = tf.cholesky(var[i, :, :] + jitter) shape = tf.stack([tf.shape(L)[0], num_samples]) V = tf.random_normal(shape, dtype=settings.float_type) samples.append(mu[:, i:i + 1] + tf.matmul(L, V)) diff --git a/gpflow/models/sgpmc.py b/gpflow/models/sgpmc.py index da2b6b85f..0867f317d 100644 --- a/gpflow/models/sgpmc.py +++ b/gpflow/models/sgpmc.py @@ -17,7 +17,8 @@ import tensorflow as tf from ..models.model import GPModel -from ..features import inducingpoint_wrapper, conditional +from ..conditionals import conditional +from ..features import inducingpoint_wrapper from ..params import Parameter, DataHolder from ..priors import Gaussian from ..decors import params_as_tensors @@ -85,7 +86,7 @@ def _build_likelihood(self): return tf.reduce_sum(self.likelihood.variational_expectations(fmean, fvar, self.Y)) @params_as_tensors - def _build_predict(self, Xnew, full_cov=False): + def _build_predict(self, Xnew, full_cov=False, full_output_cov=False): """ Xnew is a data matrix, point at which we want to predict @@ -96,6 +97,6 @@ def _build_predict(self, Xnew, full_cov=False): where F* are points on the GP at Xnew, F=LV are points on the GP at Z, """ - mu, var = conditional(self.feature, self.kern, Xnew, self.V, full_cov=full_cov, q_sqrt=None, - white=True) + mu, var = conditional(Xnew, self.feature, self.kern, self.V, full_cov=full_cov, q_sqrt=None, + white=True, full_output_cov=full_output_cov) return mu + self.mean_function(Xnew), var diff --git a/gpflow/models/sgpr.py b/gpflow/models/sgpr.py index 329df3c3e..ba8aa266d 100644 --- a/gpflow/models/sgpr.py +++ b/gpflow/models/sgpr.py @@ -183,13 +183,11 @@ def _build_predict(self, Xnew, full_cov=False): if full_cov: var = self.kern.K(Xnew) + tf.matmul(tmp2, tmp2, transpose_a=True) \ - tf.matmul(tmp1, tmp1, transpose_a=True) - shape = tf.stack([1, 1, tf.shape(self.Y)[1]]) - var = tf.tile(tf.expand_dims(var, 2), shape) + var = tf.tile(var[None, ...], [self.num_latent, 1, 1]) # P x N x N else: var = self.kern.Kdiag(Xnew) + tf.reduce_sum(tf.square(tmp2), 0) \ - tf.reduce_sum(tf.square(tmp1), 0) - shape = tf.stack([1, tf.shape(self.Y)[1]]) - var = tf.tile(tf.expand_dims(var, 1), shape) + var = tf.tile(var[:, None], [1, self.num_latent]) return mean + self.mean_function(Xnew), var @@ -315,11 +313,11 @@ def _build_predict(self, Xnew, full_cov=False): if full_cov: var = self.kern.K(Xnew) - tf.matmul(w, w, transpose_a=True) \ + tf.matmul(intermediateA, intermediateA, transpose_a=True) - var = tf.tile(tf.expand_dims(var, 2), tf.stack([1, 1, tf.shape(self.Y)[1]])) + var = tf.tile(var[None, ...], [self.num_latent, 1, 1]) # P x N x N else: var = self.kern.Kdiag(Xnew) - tf.reduce_sum(tf.square(w), 0) \ + tf.reduce_sum(tf.square(intermediateA), 0) # size Xnew, - var = tf.tile(tf.expand_dims(var, 1), tf.stack([1, tf.shape(self.Y)[1]])) + var = tf.tile(var[:, None], [1, self.num_latent]) return mean, var diff --git a/gpflow/models/svgp.py b/gpflow/models/svgp.py index ea22b96ef..6e2b3ef2d 100644 --- a/gpflow/models/svgp.py +++ b/gpflow/models/svgp.py @@ -13,21 +13,18 @@ # limitations under the License. -import tensorflow as tf import numpy as np +import tensorflow as tf +from .. import kullback_leiblers, features from .. import settings from .. import transforms -from .. import conditionals -from .. import kullback_leiblers, features - -from ..params import Parameter -from ..params import Minibatch -from ..params import DataHolder - +from ..conditionals import conditional, Kuu from ..decors import params_as_tensors - from ..models.model import GPModel +from ..params import DataHolder +from ..params import Minibatch +from ..params import Parameter class SVGP(GPModel): @@ -45,6 +42,7 @@ class SVGP(GPModel): } """ + def __init__(self, X, Y, kern, likelihood, feat=None, mean_function=None, num_latent=None, @@ -53,10 +51,12 @@ def __init__(self, X, Y, kern, likelihood, feat=None, minibatch_size=None, Z=None, num_data=None, + q_mu=None, + q_sqrt=None, **kwargs): """ - X is a data matrix, size N x D - - Y is a data matrix, size N x R + - Y is a data matrix, size N x P - kern, likelihood, mean_function are appropriate GPflow objects - Z is a matrix of pseudo inputs, size M x D - num_latent is the number of latent process to use, default to @@ -85,21 +85,64 @@ def __init__(self, X, Y, kern, likelihood, feat=None, # init variational parameters num_inducing = len(self.feature) - self.q_mu = Parameter(np.zeros((num_inducing, self.num_latent), dtype=settings.float_type)) - if self.q_diag: - self.q_sqrt = Parameter(np.ones((num_inducing, self.num_latent), dtype=settings.float_type), - transforms.positive) + self._init_variational_parameters(num_inducing, q_mu, q_sqrt, q_diag) + + def _init_variational_parameters(self, num_inducing, q_mu, q_sqrt, q_diag): + """ + Constructs the mean and cholesky of the covariance of the variational Gaussian posterior. + If a user passes values for `q_mu` and `q_sqrt` the routine checks if they have consistent + and correct shapes. If a user does not specify any values for `q_mu` and `q_sqrt`, the routine + initializes them, their shape depends on `num_inducing` and `q_diag`. + + Note: most often the comments refer to the number of observations (=output dimensions) with P, + number of latent GPs with L, and number of inducing points M. Typically P equals L, + but when certain multioutput kernels are used, this can change. + + Parameters + ---------- + :param num_inducing: int + Number of inducing variables, typically refered to as M. + :param q_mu: np.array or None + Mean of the variational Gaussian posterior. If None the function will initialise + the mean with zeros. If not None, the shape of `q_mu` is checked. + :param q_sqrt: np.array or None + Cholesky of the covariance of the variational Gaussian posterior. + If None the function will initialise `q_sqrt` with identity matrix. + If not None, the shape of `q_sqrt` is checked, depending on `q_diag`. + :param q_diag: bool + Used to check if `q_mu` and `q_sqrt` have the correct shape or to + construct them with the correct shape. If `q_diag` is true, + `q_sqrt` is two dimensional and only holds the square root of the + covariance diagonal elements. If False, `q_sqrt` is three dimensional. + """ + q_mu = np.zeros((num_inducing, self.num_latent)) if q_mu is None else q_mu + self.q_mu = Parameter(q_mu, dtype=settings.float_type) # M x P + + if q_sqrt is None: + if self.q_diag: + self.q_sqrt = Parameter(np.ones((num_inducing, self.num_latent), dtype=settings.float_type), + transform=transforms.positive) # M x P + else: + q_sqrt = np.array([np.eye(num_inducing, dtype=settings.float_type) for _ in range(self.num_latent)]) + self.q_sqrt = Parameter(q_sqrt, transform=transforms.LowerTriangular(num_inducing, self.num_latent)) # P x M x M else: - q_sqrt = np.array([np.eye(num_inducing, dtype=settings.float_type) - for _ in range(self.num_latent)]) - self.q_sqrt = Parameter(q_sqrt, transform=transforms.LowerTriangular(num_inducing, self.num_latent)) + if q_diag: + assert q_sqrt.ndim == 2 + self.num_latent = q_sqrt.shape[1] + self.q_sqrt = Parameter(q_sqrt, transform=transforms.positive) # M x L/P + else: + assert q_sqrt.ndim == 3 + self.num_latent = q_sqrt.shape[0] + num_inducing = q_sqrt.shape[1] + self.q_sqrt = Parameter(q_sqrt, transform=transforms.LowerTriangular(num_inducing, self.num_latent)) # L/P x M x M @params_as_tensors def build_prior_KL(self): if self.whiten: K = None else: - K = self.feature.Kuu(self.kern, jitter=settings.numerics.jitter_level) + K = Kuu(self.feature, self.kern, jitter=settings.numerics.jitter_level) # (P x) x M x M + return kullback_leiblers.gauss_kl(self.q_mu, self.q_sqrt, K) @params_as_tensors @@ -112,7 +155,7 @@ def _build_likelihood(self): KL = self.build_prior_KL() # Get conditionals - fmean, fvar = self._build_predict(self.X, full_cov=False) + fmean, fvar = self._build_predict(self.X, full_cov=False, full_output_cov=False) # Get variational expectations. var_exp = self.likelihood.variational_expectations(fmean, fvar, self.Y) @@ -123,7 +166,7 @@ def _build_likelihood(self): return tf.reduce_sum(var_exp) * scale - KL @params_as_tensors - def _build_predict(self, Xnew, full_cov=False): - mu, var = features.conditional(self.feature, self.kern, Xnew, self.q_mu, - q_sqrt=self.q_sqrt, full_cov=full_cov, white=self.whiten) + def _build_predict(self, Xnew, full_cov=False, full_output_cov=False): + mu, var = conditional(Xnew, self.feature, self.kern, self.q_mu, q_sqrt=self.q_sqrt, full_cov=full_cov, + white=self.whiten, full_output_cov=full_output_cov) return mu + self.mean_function(Xnew), var diff --git a/gpflow/multioutput/__init__.py b/gpflow/multioutput/__init__.py new file mode 100644 index 000000000..4167dea71 --- /dev/null +++ b/gpflow/multioutput/__init__.py @@ -0,0 +1,27 @@ +# Copyright 2018 GPflow authors +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +# flake8: noqa + +from .kernels import Mok +from .kernels import SharedIndependentMok +from .kernels import SeparateIndependentMok +from .kernels import SeparateMixedMok + +from .features import Mof +from .features import SharedIndependentMof +from .features import SeparateIndependentMof +from .features import MixedKernelSharedMof + +from . import conditionals \ No newline at end of file diff --git a/gpflow/multioutput/conditionals.py b/gpflow/multioutput/conditionals.py new file mode 100644 index 000000000..88d2bbc9f --- /dev/null +++ b/gpflow/multioutput/conditionals.py @@ -0,0 +1,454 @@ +# Copyright 2018 GPflow authors +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +import tensorflow as tf + +from .features import SeparateIndependentMof, SharedIndependentMof, MixedKernelSharedMof +from .features import Kuu, Kuf +from .kernels import Mok, SharedIndependentMok, SeparateIndependentMok, SeparateMixedMok +from .. import settings +from ..conditionals import base_conditional, _expand_independent_outputs, _sample_mvn +from ..decors import name_scope, params_as_tensors_for +from ..dispatch import conditional, sample_conditional +from ..features import InducingPoints +from ..kernels import Combination + + +logger = settings.logger() + + +# ----------- +# Conditional +# ----------- + +@conditional.register(object, SharedIndependentMof, SharedIndependentMok, object) +@name_scope("conditional") +def _conditional(Xnew, feat, kern, f, *, full_cov=False, full_output_cov=False, q_sqrt=None, white=False): + """ + Multioutput conditional for an independent kernel and shared inducing features. + Same behaviour as conditional with non-multioutput kernels. + + The covariance matrices used to calculate the conditional have the following shape: + - Kuu: M x M + - Kuf: M x N + - Kff: N or N x N + + Further reference + ----------------- + - See `gpflow.conditionals._conditional` for a detailed explanation of + conditional in the single-output case. + - See the multiouput notebook for more information about the multiouput framework. + + Parameters + ---------- + :param Xnew: data matrix, size N x D. + :param f: data matrix, M x P + :param full_cov: return the covariance between the datapoints + :param full_output_cov: return the covariance between the outputs. + Note: as we are using a independent kernel these covariances will be zero. + :param q_sqrt: matrix of standard-deviations or Cholesky matrices, + size M x P or P x M x M. + :param white: boolean of whether to use the whitened representation + :return: + - mean: N x P + - variance: N x P, P x N x N, N x P x P or N x P x N x P + Please see `gpflow.conditional._expand_independent_outputs` for more information + about the shape of the variance, depending on `full_cov` and `full_output_cov`. + """ + logger.debug("Conditional: SharedIndependentMof - SharedIndepedentMok") + + + Kmm = Kuu(feat, kern, jitter=settings.numerics.jitter_level) # M x M + Kmn = Kuf(feat, kern, Xnew) # M x N + if full_cov: + Knn = kern.K(Xnew, full_output_cov=False)[0, ...] # N x N + else: + Knn = kern.Kdiag(Xnew, full_output_cov=False)[..., 0] # N + + fmean, fvar = base_conditional(Kmn, Kmm, Knn, f, full_cov=full_cov, q_sqrt=q_sqrt, white=white) # N x P, P x N x N or N x P + return fmean, _expand_independent_outputs(fvar, full_cov, full_output_cov) + + +@conditional.register(object, SeparateIndependentMof, SeparateIndependentMok, object) +@conditional.register(object, SharedIndependentMof, SeparateIndependentMok, object) +@conditional.register(object, SeparateIndependentMof, SharedIndependentMok, object) +@name_scope("conditional") +def _conditional(Xnew, feat, kern, f, *, full_cov=False, full_output_cov=False, q_sqrt=None, white=False): + """ + Multi-output GP with independent GP priors. + Number of latent processes equals the number of outputs (L = P). + + The covariance matrices used to calculate the conditional have the following shape: + - Kuu: P x M x M + - Kuf: P x M x N + - Kff: P x N or P x N x N + + Further reference + ----------------- + - See `gpflow.conditionals._conditional` for a detailed explanation of + conditional in the single-output case. + - See the multiouput notebook for more information about the multiouput framework. + - See above for the parameters and the return value. + """ + + logger.debug("conditional: object, SharedIndependentMof, SeparateIndependentMok, object") + # Following are: P x M x M - P x M x N - P x N(x N) + Kmms = Kuu(feat, kern, jitter=settings.numerics.jitter_level) # P x M x M + Kmns = Kuf(feat, kern, Xnew) # P x M x N + kern_list = kern.kernels if isinstance(kern, Combination) else [kern.kern] * len(feat.feat_list) + Knns = tf.stack([k.K(Xnew) if full_cov else k.Kdiag(Xnew) for k in kern_list], axis=0) + fs = tf.transpose(f)[:, :, None] # P x M x 1 + # P x 1 x M x M or P x M x 1 + q_sqrts = tf.transpose(q_sqrt)[:, :, None] if q_sqrt.shape.ndims == 2 else q_sqrt[:, None, :, :] + + def single_gp_conditional(t): + Kmm, Kmn, Knn, f, q_sqrt = t + return base_conditional(Kmn, Kmm, Knn, f, full_cov=full_cov, q_sqrt=q_sqrt, white=white) + + rmu, rvar = tf.map_fn(single_gp_conditional, + (Kmms, Kmns, Knns, fs, q_sqrts), + (settings.float_type, settings.float_type)) # P x N x 1, P x 1 x N x N or P x N x 1 + + fmu = tf.matrix_transpose(rmu[:, :, 0]) # N x P + + if full_cov: + fvar = rvar[:, 0, :, :] # P x N x N + else: + fvar = tf.transpose(rvar[..., 0]) # N x P + + return fmu, _expand_independent_outputs(fvar, full_cov, full_output_cov) + + +@conditional.register(object, (SharedIndependentMof, SeparateIndependentMof), SeparateMixedMok, object) +@name_scope("conditional") +def _conditional(Xnew, feat, kern, f, *, full_cov=False, full_output_cov=False, q_sqrt=None, white=False): + """ + Interdomain conditional with independent latents. + In this case the number of latent GPs (L) will be different than the number of outputs (P) + + The covariance matrices used to calculate the conditional have the following shape: + - Kuu: L x M x M + - Kuf: M x L x N x P + - Kff: N x P x N x P, N x P x P, N x P + + Further reference + ----------------- + - See `gpflow.conditionals._conditional` for a detailed explanation of + conditional in the single-output case. + - See the multiouput notebook for more information about the multiouput framework. + - See above for the parameters and the return value. + """ + + logger.debug("Conditional: (SharedIndependentMof, SeparateIndepedentMof) - SeparateMixedMok") + Kmm = Kuu(feat, kern, jitter=settings.numerics.jitter_level) # L x M x M + Kmn = Kuf(feat, kern, Xnew) # M x L x N x P + Knn = kern.K(Xnew, full_output_cov=full_output_cov) if full_cov \ + else kern.Kdiag(Xnew, full_output_cov=full_output_cov) # N x P(x N)x P or N x P(x P) + + return independent_interdomain_conditional(Kmn, Kmm, Knn, f, full_cov=full_cov, full_output_cov=full_output_cov, + q_sqrt=q_sqrt, white=white) + + +@conditional.register(object, InducingPoints, Mok, object) +@name_scope("conditional") +def _conditional(Xnew, feat, kern, f, *, full_cov=False, full_output_cov=False, q_sqrt=None, white=False): + """ + Multi-output GP with fully correlated inducing variables. + The inducing variables are shaped in the same way as evaluations of K, to allow a default + inducing point scheme for multi-output kernels. + + The covariance matrices used to calculate the conditional have the following shape: + - Kuu: M x L x M x L + - Kuf: M x L x N x P + - Kff: N x P x N x P, N x P x P, N x P + + Further reference + ----------------- + - See `gpflow.conditionals._conditional` for a detailed explanation of + conditional in the single-output case. + - See the multiouput notebook for more information about the multiouput framework. + + Parameters + ---------- + :param f: variational mean, ML x 1 + :param q_sqrt: standard-deviations or cholesky, ML x 1 or 1 x ML x ML + """ + logger.debug("Conditional: InducingPoints -- Mok") + Kmm = Kuu(feat, kern, jitter=settings.numerics.jitter_level) # M x L x M x L + Kmn = Kuf(feat, kern, Xnew) # M x L x N x P + Knn = kern.K(Xnew, full_output_cov=full_output_cov) if full_cov \ + else kern.Kdiag(Xnew, full_output_cov=full_output_cov) # N x P(x N)x P or N x P(x P) + + M, L, N, K = [tf.shape(Kmn)[i] for i in range(Kmn.shape.ndims)] + Kmm = tf.reshape(Kmm, (M * L, M * L)) + + if full_cov == full_output_cov: + Kmn = tf.reshape(Kmn, (M * L, N * K)) + Knn = tf.reshape(Knn, (N * K, N * K)) if full_cov else tf.reshape(Knn, (N * K,)) + fmean, fvar = base_conditional(Kmn, Kmm, Knn, f, full_cov=full_cov, q_sqrt=q_sqrt, white=white) # NK x 1, 1 x NK(x NK) + fmean = tf.reshape(fmean, (N, K)) + fvar = tf.reshape(fvar, (N, K, N, K) if full_cov else (N, K)) + else: + Kmn = tf.reshape(Kmn, (M * L, N, K)) + fmean, fvar = fully_correlated_conditional(Kmn, Kmm, Knn, f, full_cov=full_cov, + full_output_cov=full_output_cov, q_sqrt=q_sqrt, white=white) + return fmean, fvar + + +@conditional.register(object, MixedKernelSharedMof, SeparateMixedMok, object) +@name_scope("conditional") +def _conditional(Xnew, feat, kern, f, *, full_cov=False, full_output_cov=False, q_sqrt=None, white=False): + """ + Most efficient routine to project L independent latent gps through a mixing matrix W. + The mixing matrix is a member of the `SeparateMixedMok` and has shape P x L. + + The covariance matrices used to calculate the conditional have the following shape: + - Kuu: L x M x M + - Kuf: L x M x N + - Kff: L x N or L x N x N + + Further reference + ----------------- + - See `gpflow.conditionals._conditional` for a detailed explanation of + conditional in the single-output case. + - See the multiouput notebook for more information about the multiouput framework. + + """ + logger.debug("conditional: MixedKernelSharedMof, SeparateMixedMok") + independent_cond = conditional.dispatch(object, SeparateIndependentMof, SeparateIndependentMok, object) + gmu, gvar = independent_cond(Xnew, feat, kern, f, full_cov=full_cov, q_sqrt=q_sqrt, + full_output_cov=False, white=white) # N x L, L x N x N or N x L + + gmu = tf.matrix_transpose(gmu) # L x N + if not full_cov: + gvar = tf.matrix_transpose(gvar) # L x N (x N) + + Wgmu = tf.tensordot(gmu, kern.W, [[0], [1]]) # N x P + + if full_output_cov: + Wt_expanded = tf.matrix_transpose(kern.W)[:, None, :] # L x 1 x P + if full_cov: + Wt_expanded = tf.expand_dims(Wt_expanded, axis=-1) # L x 1 x P x 1 + + gvarW = tf.expand_dims(gvar, axis=2) * Wt_expanded # L x N x P (x N) + WgvarW = tf.tensordot(gvarW, kern.W, [[0], [1]]) # N x P (x N) x P + else: + if not full_cov: + WgvarW = tf.tensordot(gvar, kern.W ** 2, [[0], [1]]) # N x P + else: + WgvarW = tf.tensordot(kern.W ** 2, gvar, [[1], [0]]) # P x N (x N) + + return Wgmu, WgvarW + + +# ------------------ +# Sample conditional +# ------------------ + +@sample_conditional.register(object, MixedKernelSharedMof, SeparateMixedMok, object) +@name_scope("sample_conditional") +def _sample_conditional(Xnew, feat, kern, f, *, full_output_cov=False, q_sqrt=None, white=False): + """ + `sample_conditional` will return a sample from the conditinoal distribution. + In most cases this means calculating the conditional mean m and variance v and then + returning m + sqrt(v) * eps, with eps ~ N(0, 1). + However, for some combinations of Mok and Mof more efficient sampling routines exists. + The dispatcher will make sure that we use the most efficent one. + + :return: N x P (full_output_cov = False) or N x P x P (full_output_cov = True) + """ + logger.debug("sample conditional: MixedKernelSharedMof, SeparateMixedMok") + independent_cond = conditional.dispatch(object, SeparateIndependentMof, SeparateIndependentMok, object) + g_mu, g_var = independent_cond(Xnew, feat, kern, f, white=white, q_sqrt=q_sqrt, + full_output_cov=False, full_cov=False) # N x L, N x L + g_sample = _sample_mvn(g_mu, g_var, "diag") # N x L + with params_as_tensors_for(kern): + f_sample = tf.einsum("pl,nl->np", kern.W, g_sample) + return f_sample + + +# ----------------- +# Conditional maths +# ----------------- + +def independent_interdomain_conditional(Kmn, Kmm, Knn, f, *, full_cov=False, full_output_cov=False, + q_sqrt=None, white=False): + """ + The inducing outputs live in the g-space (R^L). + Interdomain conditional calculation. + + :param Kmn: M x L x N x P + :param Kmm: L x M x M + :param Knn: N x P or N x N or P x N x N or N x P x N x P + :param f: data matrix, M x L + :param q_sqrt: L x M x M or M x L + :param full_cov: calculate covariance between inputs + :param full_output_cov: calculate covariance between outputs + :param white: use whitened representation + :return: + - mean: N x P + - variance: N x P, N x P x P, P x N x N, N x P x N x P + """ + logger.debug("independent_interdomain_conditional") + M, L, N, P = [tf.shape(Kmn)[i] for i in range(Kmn.shape.ndims)] + + Lm = tf.cholesky(Kmm) # L x M x M + + # Compute the projection matrix A + Kmn = tf.reshape(tf.transpose(Kmn, (1, 0, 2, 3)), (L, M, N * P)) + A = tf.matrix_triangular_solve(Lm, Kmn, lower=True) # L x M x M * L x M x NP -> L x M x NP + Ar = tf.reshape(A, (L, M, N, P)) + + # compute the covariance due to the conditioning + if full_cov and full_output_cov: + fvar = Knn - tf.tensordot(Ar, Ar, [[0, 1], [0, 1]]) # N x P x N x P + elif full_cov and not full_output_cov: + At = tf.reshape(tf.transpose(Ar), (P, N, M * L)) # P x N x ML + fvar = Knn - tf.matmul(At, At, transpose_b=True) # P x N x N + elif not full_cov and full_output_cov: + At = tf.reshape(tf.transpose(Ar, [2, 3, 1, 0]), (N, P, M * L)) # N x P x ML + fvar = Knn - tf.matmul(At, At, transpose_b=True) # N x P x P + elif not full_cov and not full_output_cov: + fvar = Knn - tf.reshape(tf.reduce_sum(tf.square(A), [0, 1]), (N, P)) # Knn: N x P + + # another backsubstitution in the unwhitened case + if not white: + A = tf.matrix_triangular_solve(Lm, Ar) # L x M x M * L x M x NP -> L x M x NP + Ar = tf.reshape(A, (L, M, N, P)) + + fmean = tf.tensordot(Ar, f, [[1, 0], [0, 1]]) # N x P + + if q_sqrt is not None: + if q_sqrt.shape.ndims == 3: + Lf = tf.matrix_band_part(q_sqrt, -1, 0) # L x M x M + LTA = tf.matmul(Lf, A, transpose_a=True) # L x M x M * L x M x NP -> L x M x NP + else: # q_sqrt M x L + LTA = (A * tf.transpose(q_sqrt)[..., None]) # L x M x NP + + if full_cov and full_output_cov: + LTAr = tf.reshape(LTA, (L * M, N * P)) + fvar = fvar + tf.reshape(tf.matmul(LTAr, LTAr, transpose_a=True), (N, P, N, P)) + elif full_cov and not full_output_cov: + LTAr = tf.transpose(tf.reshape(LTA, (L * M, N, P)), [2, 0, 1]) # P x LM x N + fvar = fvar + tf.matmul(LTAr, LTAr, transpose_a=True) # P x N x N + elif not full_cov and full_output_cov: + LTAr = tf.transpose(tf.reshape(LTA, (L * M, N, P)), [1, 0, 2]) # N x LM x P + fvar = fvar + tf.matmul(LTAr, LTAr, transpose_a=True) # N x P x P + elif not full_cov and not full_output_cov: + fvar = fvar + tf.reshape(tf.reduce_sum(tf.square(LTA), (0, 1)), (N, P)) + return fmean, fvar + + +def fully_correlated_conditional(Kmn, Kmm, Knn, f, *, full_cov=False, full_output_cov=False, q_sqrt=None, white=False): + """ + This function handles conditioning of multi-output GPs in the case where the conditioning + points are all fully correlated, in both the prior and posterior. + :param Kmn: LM x N x P + :param Kmm: LM x LM + :param Knn: N x P or N x P x N x P + :param f: data matrix, LM x 1 + :param q_sqrt: 1 x LM x LM or 1 x ML + :param full_cov: calculate covariance between inputs + :param full_output_cov: calculate covariance between outputs + :param white: use whitened representation + :return: + - mean: N x P + - variance: N x P, N x P x P, P x N x N, N x P x N x P + """ + m, v = fully_correlated_conditional_repeat(Kmn, Kmm, Knn, f, full_cov=full_cov, + full_output_cov=full_output_cov, q_sqrt=q_sqrt, white=white) + return m[0, ...], v[0, ...] + + +def fully_correlated_conditional_repeat(Kmn, Kmm, Knn, f, *, full_cov=False, full_output_cov=False, q_sqrt=None, + white=False): + """ + This function handles conditioning of multi-output GPs in the case where the conditioning + points are all fully correlated, in both the prior and posterior. + + Note: This conditional can handle 'repetitions' R, given in `f` and `q_sqrt`. + + :param Kmn: LM x N x P + :param Kmm: LM x LM + :param Knn: N x P or N x P x N x P + :param f: data matrix, LM x R + :param q_sqrt: R x LM x LM or R x ML + :param full_cov: calculate covariance between inputs + :param full_output_cov: calculate covariance between outputs + :param white: use whitened representation + :return: + - mean: R x N x P + - variance: R x N x P, R x N x P x P, R x P x N x N, R x N x P x N x P + """ + logger.debug("fully correlated conditional") + R = tf.shape(f)[1] + M, N, K = [tf.shape(Kmn)[i] for i in range(Kmn.shape.ndims)] + Lm = tf.cholesky(Kmm) + + # Compute the projection matrix A + # Lm: M x M Kmn: M x NK + Kmn = tf.reshape(Kmn, (M, N * K)) # M x NK + A = tf.matrix_triangular_solve(Lm, Kmn, lower=True) # M x NK + Ar = tf.reshape(A, (M, N, K)) + + # compute the covariance due to the conditioning + if full_cov and full_output_cov: + # fvar = Knn - tf.matmul(Ar, Ar, transpose_a=True) # NK x NK, then reshape? + fvar = Knn - tf.tensordot(Ar, Ar, [[0], [0]]) # N x K x N x K + elif full_cov and not full_output_cov: + At = tf.transpose(Ar) # K x N x M + fvar = Knn - tf.matmul(At, At, transpose_b=True) # K x N x N + elif not full_cov and full_output_cov: + # This transpose is annoying + At = tf.transpose(Ar, [1, 0, 2]) # N x M x K + # fvar = Knn - tf.einsum('mnk,mnl->nkl', Ar, Ar) + fvar = Knn - tf.matmul(At, At, transpose_a=True) # N x K x K + elif not full_cov and not full_output_cov: + # Knn: N x K + fvar = Knn - tf.reshape(tf.reduce_sum(tf.square(A), [0, 1]), (N, K)) # Can also do this with a matmul + + # another backsubstitution in the unwhitened case + if not white: + # A = tf.matrix_triangular_solve(tf.matrix_transpose(Lm), A, lower=False) # M x NK + raise NotImplementedError("Need to verify this.") # pragma: no cover + + # f: M x R + fmean = tf.matmul(f, A, transpose_a=True) # R x M * M x NK -> R x NK + fmean = tf.reshape(fmean, (R, N, K)) # R x N x K + + if q_sqrt is not None: + Lf = tf.matrix_band_part(q_sqrt, -1, 0) # R x M x M + if q_sqrt.get_shape().ndims == 3: + A_tiled = tf.tile(A[None, :, :], tf.stack([R, 1, 1])) # R x M x NK + LTA = tf.matmul(Lf, A_tiled, transpose_a=True) # R x M x NK + elif q_sqrt.get_shape().ndims == 2: # pragma: no cover + raise NotImplementedError("Does not support diagonal q_sqrt yet...") + else: # pragma: no cover + raise ValueError("Bad dimension for q_sqrt: %s" % + str(q_sqrt.get_shape().ndims)) + + if full_cov and full_output_cov: + addvar = tf.matmul(LTA, LTA, transpose_a=True) # R x NK x NK + fvar = fvar[None, :, :, :, :] + tf.reshape(addvar, (R, N, K, N, K)) + elif full_cov and not full_output_cov: + LTAr = tf.transpose(tf.reshape(LTA, [R, M, N, K]), [0, 3, 1, 2]) # R x K x M x N + addvar = tf.matmul(LTAr, LTAr, transpose_a=True) # R x K x N x N + fvar = fvar[None, ...] + addvar # R x K x N x N + elif not full_cov and full_output_cov: + LTAr = tf.transpose(tf.reshape(LTA, (R, M, N, K)), [0, 2, 3, 1]) # R x N x K x M + fvar = fvar[None, ...] + tf.matmul(LTAr, LTAr, transpose_b=True) # R x N x K x K + elif not full_cov and not full_output_cov: + addvar = tf.reshape(tf.reduce_sum(tf.square(LTA), axis=1), (R, N, K)) # R x N x K + fvar = fvar[None, ...] + addvar # R x N x K + return fmean, fvar diff --git a/gpflow/multioutput/features.py b/gpflow/multioutput/features.py new file mode 100644 index 000000000..104495960 --- /dev/null +++ b/gpflow/multioutput/features.py @@ -0,0 +1,183 @@ +# Copyright 2018 GPflow authors +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +import tensorflow as tf + +from .. import settings +from ..dispatch import dispatch +from ..features import InducingPoints, InducingFeature, Kuu, Kuf +from ..decors import params_as_tensors_for +from ..params import ParamList +from .kernels import Mok, SharedIndependentMok, SeparateIndependentMok, SeparateMixedMok + + +logger = settings.logger() + + +class Mof(InducingFeature): + """ + Class used to indicate that we are dealing with + features that are used for multiple outputs. + """ + pass + + +class SharedIndependentMof(Mof): + """ + Same feature is used for each output. + """ + def __init__(self, feat): + Mof.__init__(self) + self.feat = feat + + def __len__(self): + return len(self.feat) + + +class SeparateIndependentMof(Mof): + """ + A different feature is used for each output. + Note: each feature should have the same number of points, M. + """ + def __init__(self, feat_list): + Mof.__init__(self) + self.feat_list = ParamList(feat_list) + + def __len__(self): + return len(self.feat_list[0]) + + +class MixedKernelSharedMof(SharedIndependentMof): + """ + This Mof is used in combination with the `SeparateMixedMok`. + Using this feature with the `SeparateMixedMok` leads to the most efficient code. + """ + pass + + +# --- +# Kuf +# --- + +def debug_kuf(feat, kern): + msg = "Dispatch to Kuf(feat: {}, kern: {})" + logger.debug(msg.format( + feat.__class__.__name__, + kern.__class__.__name__)) + +@dispatch(InducingPoints, Mok, object) +def Kuf(feat, kern, Xnew): + debug_kuf(feat, kern) + return kern.K(feat.Z, Xnew, full_output_cov=True) # M x P x N x P + + +@dispatch(SharedIndependentMof, SharedIndependentMok, object) +def Kuf(feat, kern, Xnew): + debug_kuf(feat, kern) + return Kuf(feat.feat, kern.kern, Xnew) # M x N + + +@dispatch(SeparateIndependentMof, SharedIndependentMok, object) +def Kuf(feat, kern, Xnew): + debug_kuf(feat, kern) + return tf.stack([Kuf(f, kern.kern, Xnew) for f in feat.feat_list], axis=0) # L x M x N + + +@dispatch(SharedIndependentMof, SeparateIndependentMok, object) +def Kuf(feat, kern, Xnew): + debug_kuf(feat, kern) + return tf.stack([Kuf(feat.feat, k, Xnew) for k in kern.kernels], axis=0) # L x M x N + + +@dispatch(SeparateIndependentMof, SeparateIndependentMok, object) +def Kuf(feat, kern, Xnew): + debug_kuf(feat, kern) + return tf.stack([Kuf(f, k, Xnew) for f, k in zip(feat.feat_list, kern.kernels)], axis=0) # L x M x N + + +@dispatch((SeparateIndependentMof, SharedIndependentMof), SeparateMixedMok, object) +def Kuf(feat, kern, Xnew): + debug_kuf(feat, kern) + kuf_impl = Kuf.dispatch(type(feat), SeparateIndependentMok, object) + K = tf.transpose(kuf_impl(feat, kern, Xnew), [1, 0, 2]) # M x L x N + with params_as_tensors_for(kern): + return K[:, :, :, None] * tf.transpose(kern.W)[None, :, None, :] # M x L x N x P + + +@dispatch(MixedKernelSharedMof, SeparateMixedMok, object) +def Kuf(feat, kern, Xnew): + debug_kuf(feat, kern) + return tf.stack([Kuf(feat.feat, k, Xnew) for k in kern.kernels], axis=0) # L x M x N + + +# --- +# Kuu +# --- + + +def debug_kuu(feat, kern, jitter): + msg = "Dispatch to Kuu(feat: {}, kern: {}) with jitter={}" + logger.debug(msg.format( + feat.__class__.__name__, + kern.__class__.__name__, + jitter)) + + +@dispatch(InducingPoints, Mok) +def Kuu(feat, kern, *, jitter=0.0): + debug_kuu(feat, kern, jitter) + Kmm = kern.K(feat.Z, full_output_cov=True) # M x P x M x P + M = tf.shape(Kmm)[0] * tf.shape(Kmm)[1] + jittermat = jitter * tf.reshape(tf.eye(M, dtype=settings.float_type), tf.shape(Kmm)) + return Kmm + jittermat + + +@dispatch(SharedIndependentMof, SharedIndependentMok) +def Kuu(feat, kern, *, jitter=0.0): + debug_kuu(feat, kern, jitter) + Kmm = Kuu(feat.feat, kern.kern) # M x M + jittermat = tf.eye(len(feat), dtype=settings.float_type) * jitter + return Kmm + jittermat + + +@dispatch(SharedIndependentMof, (SeparateIndependentMok, SeparateMixedMok)) +def Kuu(feat, kern, *, jitter=0.0): + debug_kuu(feat, kern, jitter) + Kmm = tf.stack([Kuu(feat.feat, k) for k in kern.kernels], axis=0) # L x M x M + jittermat = tf.eye(len(feat), dtype=settings.float_type)[None, :, :] * jitter + return Kmm + jittermat + + +@dispatch(SeparateIndependentMof, SharedIndependentMok) +def Kuu(feat, kern, *, jitter): + debug_kuu(feat, kern, jitter) + Kmm = tf.stack([Kuu(f, kern.kern) for f in feat.feat_list], axis=0) # L x M x M + jittermat = tf.eye(len(feat), dtype=settings.float_type)[None, :, :] * jitter + return Kmm + jittermat + + +@dispatch(SeparateIndependentMof, (SeparateIndependentMok, SeparateMixedMok)) +def Kuu(feat, kern, *, jitter=0.0): + debug_kuu(feat, kern, jitter) + Kmm = tf.stack([Kuu(f, k) for f, k in zip(feat.feat_list, kern.kernels)], axis=0) # L x M x M + jittermat = tf.eye(len(feat), dtype=settings.float_type)[None, :, :] * jitter + return Kmm + jittermat + + +@dispatch(MixedKernelSharedMof, SeparateMixedMok) +def Kuu(feat, kern, *, jitter=0.0): + debug_kuu(feat, kern, jitter) + Kmm = tf.stack([Kuu(feat.feat, k) for k in kern.kernels], axis=0) # L x M x M + jittermat = tf.eye(len(feat), dtype=settings.float_type)[None, :, :] * jitter + return Kmm + jittermat diff --git a/gpflow/multioutput/kernels.py b/gpflow/multioutput/kernels.py new file mode 100644 index 000000000..42580d3b4 --- /dev/null +++ b/gpflow/multioutput/kernels.py @@ -0,0 +1,152 @@ +# Copyright 2018 GPflow authors +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + + +import tensorflow as tf + +from .. import kernels +from .. import settings +from ..decors import params_as_tensors, autoflow +from ..kernels import Kernel, Combination +from ..params import Parameter + + +class Mok(Kernel): + """ + Multi Output Kernel class. + This kernel can represent correlation between outputs of different datapoints. + Therefore, subclasses of Mok should implement `K` which returns: + - N x P x N x P if full_output_cov = True + - P x N x N if full_output_cov = False + and `Kdiag` returns: + - N x P x P if full_output_cov = True + - N x P if full_output_cov = False + + The `full_output_cov` argument holds whether the kernel should calculate + the covariance between the outputs. In case there is no correlation but + `full_output_cov` is set to True the covariance matrix will be filled with zeros + until the appropriate size is reached. + """ + + def K(self, X, X2=None, full_output_cov=True): + """ + Returns the correlation of f(X1) and f(X2), where f(.) can be multi-dimensional. + :param X: data matrix, N1 x D + :param X2: data matrix, N2 x D + :param full_output_cov: calculate correlation between outputs. + :return: cov[f(X1), f(X2)] with shape + - N1 x P x N2 x P if `full_output_cov` = True + - P x N1 x N2 if `full_output_cov` = False + """ + raise NotImplemented # pragma: no cover + + def Kdiag(self, X, full_output_cov=True): + """ + Returns the correlation of f(X) and f(X), where f(.) can be multi-dimensional. + :param X: data matrix, N x D + :param full_output_cov: calculate correlation between outputs. + :return: var[f(X)] with shape + - N x P x N x P if `full_output_cov` = True + - N x P if `full_output_cov` = False + """ + raise NotImplemented # pragma: no cover + +class SharedIndependentMok(Mok): + """ + - Shared: we use the same kernel for each latent GP + - Independent: Latents are uncorrelated a priori. + + Note: this class is created only for testing and comparison purposes. + Use `gpflow.kernels` instead for more efficient code. + """ + def __init__(self, kern: Kernel, output_dimensionality, name=None): + Mok.__init__(self, kern.input_dim, name) + self.kern = kern + self.P = output_dimensionality + + def K(self, X, X2=None, full_output_cov=True): + K = self.kern.K(X, X2) # N x N2 + if full_output_cov: + Ks = tf.tile(K[..., None], [1, 1, self.P]) # N x N2 x P + return tf.transpose(tf.matrix_diag(Ks), [0, 2, 1, 3]) # N x P x N2 x P + else: + return tf.tile(K[None, ...], [self.P, 1, 1]) # P x N x N2 + + def Kdiag(self, X, full_output_cov=True): + K = self.kern.Kdiag(X) # N + Ks = tf.tile(K[:, None], [1, self.P]) # N x P + return tf.matrix_diag(Ks) if full_output_cov else Ks # N x P x P or N x P + + +class SeparateIndependentMok(Mok, Combination): + """ + - Separate: we use different kernel for each output latent + - Independent: Latents are uncorrelated a priori. + """ + def __init__(self, kernels, name=None): + Combination.__init__(self, kernels, name) + + def K(self, X, X2=None, full_output_cov=True): + if full_output_cov: + Kxxs = tf.stack([k.K(X, X2) for k in self.kernels], axis=2) # N x N2 x P + return tf.transpose(tf.matrix_diag(Kxxs), [0, 2, 1, 3]) # N x P x N2 x P + else: + return tf.stack([k.K(X, X2) for k in self.kernels], axis=0) # P x N x N2 + + def Kdiag(self, X, full_output_cov=False): + stacked = tf.stack([k.Kdiag(X) for k in self.kernels], axis=1) # N x P + return tf.matrix_diag(stacked) if full_output_cov else stacked # N x P x P or N x P + + +class SeparateMixedMok(Mok, Combination): + """ + Linear mixing of the latent GPs to form the output + """ + + def __init__(self, kernels, W, name=None): + Combination.__init__(self, kernels, name) + self.W = Parameter(W) # P x L + + @params_as_tensors + def Kgg(self, X, X2): + return tf.stack([k.K(X, X2) for k in self.kernels], axis=0) # L x N x N2 + + @autoflow((settings.float_type, [None, None]), + (settings.float_type, [None, None])) + def compute_Kgg(self, X, X2): + return self.Kgg(X, X2) + + @params_as_tensors + def K(self, X, X2=None, full_output_cov=True): + Kxx = self.Kgg(X, X2) # L x N x N2 + KxxW = Kxx[None, :, :, :] * self.W[:, :, None, None] # P x L x N x N2 + if full_output_cov: + # return tf.einsum('lnm,kl,ql->nkmq', Kxx, self.W, self.W) + WKxxW = tf.tensordot(self.W, KxxW, [[1], [1]]) # P x P x N x N2 + return tf.transpose(WKxxW, [2, 0, 3, 1]) # N x P x N2 x P + else: + # return tf.einsum('lnm,kl,kl->knm', Kxx, self.W, self.W) + return tf.reduce_sum(self.W[:, :, None, None] * KxxW, [1]) # P x N x N2 + + @params_as_tensors + def Kdiag(self, X, full_output_cov=True): + K = tf.stack([k.Kdiag(X) for k in self.kernels], axis=1) # N x L + if full_output_cov: + # Can currently not use einsum due to unknown shape from `tf.stack()` + # return tf.einsum('nl,lk,lq->nkq', K, self.W, self.W) # N x P x P + Wt = tf.transpose(self.W) # L x P + return tf.reduce_sum(K[:, :, None, None] * Wt[None, :, :, None] * Wt[None, :, None, :], axis=1) # N x P x P + else: + # return tf.einsum('nl,lk,lk->nkq', K, self.W, self.W) # N x P + return tf.matmul(K, self.W ** 2.0, transpose_b=True) # N x L * L x P -> N x P diff --git a/gpflow/session_manager.py b/gpflow/session_manager.py index 4f7fc1f68..97194373f 100644 --- a/gpflow/session_manager.py +++ b/gpflow/session_manager.py @@ -21,6 +21,9 @@ from . import settings +logger = settings.logger() + + class _DefaultSessionKeeper: session = None @@ -33,8 +36,7 @@ def __init__(self, output_file_name=None, output_directory=None, self.each_time = each_time self.local_run_metadata = None if self.each_time: - warnings.warn("Outputting a trace for each run. " - "May result in large disk usage.") + logger.warn("Outputting a trace for each run. May result in large disk usage.") super(TracerSession, self).__init__(**kwargs) self.counter = 0 diff --git a/gpflow/test_util.py b/gpflow/test_util.py index 87b036f2d..c7033c046 100644 --- a/gpflow/test_util.py +++ b/gpflow/test_util.py @@ -13,10 +13,15 @@ # limitations under the License. +# pragma: no cover +# pylint: skip-file + + import functools import contextlib import tensorflow as tf import pytest +import os @pytest.fixture @@ -107,3 +112,13 @@ def test_context(self, graph=None): graph = self.test_graph if graph is None else graph with graph.as_default(), self.test_session(graph=graph) as session: yield session + +def is_continuous_integration(): + ci = os.environ.get('CI') + return (ci == 'true') or (ci == '1') + +def notebook_niter(n, test_n=1): + return test_n if is_continuous_integration() else n + +def notebook_range(n, test_n=1): + return range(notebook_niter(n, test_n)) diff --git a/tests/test_config.py b/tests/test_config.py index 5deb37ae3..882f59cac 100644 --- a/tests/test_config.py +++ b/tests/test_config.py @@ -116,23 +116,23 @@ def testDeprecated(self): _ = s.np_int def testMutability(self): - orig = gpflow.settings.verbosity.hmc_verb - gpflow.settings.verbosity.hmc_verb = False - self.assertEqual(gpflow.settings.verbosity.hmc_verb, False) - gpflow.settings.verbosity.hmc_verb = True - self.assertEqual(gpflow.settings.verbosity.hmc_verb, True) - gpflow.settings.verbosity.hmc_verb = orig + orig = gpflow.settings.verbosity.tf_compile_verb + gpflow.settings.verbosity.tf_compile_verb = False + self.assertEqual(gpflow.settings.verbosity.tf_compile_verb, False) + gpflow.settings.verbosity.tf_compile_verb = True + self.assertEqual(gpflow.settings.verbosity.tf_compile_verb, True) + gpflow.settings.verbosity.tf_compile_verb = orig def testContextManager(self): - orig = gpflow.settings.verbosity.hmc_verb - gpflow.settings.verbosity.hmc_verb = True + orig = gpflow.settings.verbosity.tf_compile_verb + gpflow.settings.verbosity.tf_compile_verb = True config = gpflow.settings.get_settings() - config.verbosity.hmc_verb = False - self.assertEqual(gpflow.settings.verbosity.hmc_verb, True) + config.verbosity.tf_compile_verb = False + self.assertEqual(gpflow.settings.verbosity.tf_compile_verb, True) with gpflow.settings.temp_settings(config): - self.assertEqual(gpflow.settings.verbosity.hmc_verb, False) - self.assertEqual(gpflow.settings.verbosity.hmc_verb, True) - gpflow.settings.verbosity.hmc_verb = orig + self.assertEqual(gpflow.settings.verbosity.tf_compile_verb, False) + self.assertEqual(gpflow.settings.verbosity.tf_compile_verb, True) + gpflow.settings.verbosity.tf_compile_verb = orig def test_logging(): def level_name(log): diff --git a/tests/test_coregion.py b/tests/test_coregion.py index e6280bfe6..5d3b730e0 100644 --- a/tests/test_coregion.py +++ b/tests/test_coregion.py @@ -154,7 +154,7 @@ def test_predicts(self): self.assertTrue(np.allclose(pred_ydensity0, pred_ydensity_c0, atol=1e-2)) pred_ydensity1 = self.vgp1.predict_density(self.Xtest, Ytest) pred_ydensity_c1 = self.cvgp.predict_density(X_augumented1, Y_augumented1) - assert_allclose(pred_ydensity1, pred_ydensity_c1, atol=1e-2) + np.testing.assert_allclose(pred_ydensity1, pred_ydensity_c1, atol=1e-2) # just check predict_f_samples(self) works self.cvgp.predict_f_samples(X_augumented0, 1) diff --git a/tests/test_hmc.py b/tests/test_hmc.py index fb76bab68..77f36f06e 100644 --- a/tests/test_hmc.py +++ b/tests/test_hmc.py @@ -175,7 +175,7 @@ def test_multiple_runs(self): with self.test_context(): m = self.model() hmc = gpflow.train.HMC() - for n in range(1, 5): + for n in range(1, 3): samples = hmc.sample(m, num_samples=n, lmax=10, epsilon=0.05) self.check_last_variables_state(m, samples) diff --git a/tests/test_method_equivalence.py b/tests/test_method_equivalence.py index 7109fcf11..88ee10b05 100644 --- a/tests/test_method_equivalence.py +++ b/tests/test_method_equivalence.py @@ -102,7 +102,7 @@ def test_all(self): assert_allclose(variances, variances[0], 1e-5) assert_allclose(lengthscales, lengthscales.mean(), 1e-4) mu0, var0 = models[0].predict_y(self.Xtest) - for m in models[1:]: + for i, m in enumerate(models[1:]): mu, var = m.predict_y(self.Xtest) assert_allclose(mu, mu0, 1e-3) assert_allclose(var, var0, 1e-4) diff --git a/tests/test_multioutput.py b/tests/test_multioutput.py new file mode 100644 index 000000000..4760b4885 --- /dev/null +++ b/tests/test_multioutput.py @@ -0,0 +1,484 @@ +import gpflow +import numpy as np +import pytest +import scipy +import tensorflow as tf + +import gpflow.multioutput.features as mf +import gpflow.multioutput.kernels as mk + +from gpflow.features import InducingPoints +from gpflow.kernels import RBF +from gpflow.likelihoods import Gaussian +from gpflow.models import SVGP +from gpflow.test_util import session_tf +from gpflow.training import ScipyOptimizer +from gpflow.conditionals import _sample_mvn, sample_conditional + +float_type = gpflow.settings.float_type +np.random.seed(1) + +# ------------------------------------------ +# Helpers +# ------------------------------------------ + +def predict(sess, model, Xnew, full_cov, full_output_cov): + m, v = model._build_predict(Xnew, full_cov=full_cov, full_output_cov=full_output_cov) + return sess.run([m, v]) + + +def predict_all(sess, models, Xnew, full_cov, full_output_cov): + """ + Returns the mean and variance of f(Xnew) for each model in `models`. + """ + ms, vs = [], [] + for model in models: + m, v = predict(sess, model, Xnew, full_cov, full_output_cov) + ms.append(m) + vs.append(v) + return ms, vs + + +def assert_all_array_elements_almost_equal(arr, decimal): + """ + Check if consecutive elements of `arr` are almost equal. + """ + for i in range(len(arr) - 1): + np.testing.assert_almost_equal(arr[i], arr[i+1], decimal=decimal) + + +def check_equality_predictions(sess, models, decimal=4): + """ + Executes a couple of checks to compare the equality of predictions + of different models. The models should be configured with the same + training data (X, Y). The following checks are done: + - check if log_likelihood is (almost) equal for all models + - check if predicted mean is (almost) equal + - check if predicted variance is (almost) equal. + All possible variances over the inputs and outputs are calculated + and equality is checked. + - check if variances within model are consistent. Parts of the covariance + matrices should overlap, and this is tested. + """ + + log_likelihoods = [m.compute_log_likelihood() for m in models] + + # Check equality of log likelihood + assert_all_array_elements_almost_equal(log_likelihoods, decimal=5) + + # Predict: full_cov = True and full_output_cov = True + means_tt, vars_tt = predict_all(sess, models, Data.Xs, full_cov=True, full_output_cov=True) + # Predict: full_cov = True and full_output_cov = False + means_tf, vars_tf = predict_all(sess, models, Data.Xs, full_cov=True, full_output_cov=False) + # Predict: full_cov = False and full_output_cov = True + means_ft, vars_ft = predict_all(sess, models, Data.Xs, full_cov=False, full_output_cov=True) + # Predict: full_cov = False and full_output_cov = False + means_ff, vars_ff = predict_all(sess, models, Data.Xs, full_cov=False, full_output_cov=False) + + # check equality of all the means + all_means = means_tt + means_tf + means_ft + means_ff + assert_all_array_elements_almost_equal(all_means, decimal=decimal) + + # check equality of all the variances within a category + # (e.g. full_cov=True and full_output_cov=False) + all_vars = [vars_tt, vars_tf, vars_ft, vars_ff] + _ = [assert_all_array_elements_almost_equal(var, decimal=decimal) for var in all_vars] + + # Here we check that the variance in different categories are equal + # after transforming to the right shape. + var_tt = vars_tt[0] # N x P x N x P + var_tf = vars_tf[0] # P x N x c + var_ft = vars_ft[0] # N x P x P + var_ff = vars_ff[0] # N x P + + np.testing.assert_almost_equal(np.diagonal(var_tt, axis1=1, axis2=3), + np.transpose(var_tf, [1, 2, 0]), decimal=decimal) + np.testing.assert_almost_equal(np.diagonal(var_tt, axis1=0, axis2=2), + np.transpose(var_ft, [1, 2, 0]), decimal=decimal) + np.testing.assert_almost_equal(np.diagonal(np.diagonal(var_tt, axis1=0, axis2=2)), + var_ff, decimal=decimal) + + +def expand_cov(q_sqrt, W): + """ + :param G: cholesky of covariance matrices, L x M x M + :param W: mixing matrix (square), L x L + :return: cholesky of 1 x LM x LM covariance matrix + """ + q_cov = np.matmul(q_sqrt, q_sqrt.transpose(0, 2, 1)) # L x M x M + q_cov_expanded = scipy.linalg.block_diag(*q_cov) # LM x LM + q_sqrt_expanded = np.linalg.cholesky(q_cov_expanded) # LM x LM + return q_sqrt_expanded[None, ...] + + +def create_q_sqrt(M, L): + """ returns an array of L lower triangular matrices of size M x M """ + return np.array([np.tril(np.random.randn(M, M)) for _ in range(L)]) # L x M x M + + +# ------------------------------------------ +# Data classes: storing constants +# ------------------------------------------ + +class Data: + N, Ntest = 20, 5 + D = 1 # input dimension + M = 3 # inducing points + L = 2 # latent gps + P = 3 # output dimension + MAXITER = int(15e2) + + X = np.random.rand(N)[:, None] * 10 - 5 + G = np.hstack((0.5 * np.sin(3 * X) + X, 3.0 * np.cos(X) - X)) + Ptrue = np.array([[0.5, -0.3, 1.5], [-0.4, 0.43, 0.0]]) # L x P + Y = np.matmul(G, Ptrue) + Y += np.random.randn(*Y.shape) * [0.2, 0.2, 0.2] + Xs = np.linspace(-6, 6, Ntest)[:, None] + + +class DataMixedKernelWithEye(Data): + """ Note in this class L == P """ + M, L = 4, 3 + W = np.eye(L) + + G = np.hstack([0.5 * np.sin(3 * Data.X) + Data.X, + 3.0 * np.cos(Data.X) - Data.X, + 1.0 + Data.X]) # N x P + + mu_data = np.random.randn(M, L) # M x L + sqrt_data = create_q_sqrt(M, L) # L x M x M + + mu_data_full = (mu_data @ W).reshape(-1, 1) # ML x 1 + sqrt_data_full = expand_cov(sqrt_data, W) # 1 x LM x LM + + Y = np.matmul(G, W) + Y += np.random.randn(*Y.shape) * np.ones((L,)) * 0.2 + + +class DataMixedKernel(Data): + M = 5 + L = 2 + P = 3 + W = np.random.randn(P, L) + G = np.hstack([0.5 * np.sin(3 * Data.X) + Data.X, + 3.0 * np.cos(Data.X) - Data.X]) # N x L + + mu_data = np.random.randn(M, L) # M x L + sqrt_data = create_q_sqrt(M, L) # L x M x M + + Y = np.matmul(G, W.T) + Y += np.random.randn(*Y.shape) * np.ones((P,)) * 0.1 + +# ------------------------------------------ +# Test sample conditional +# ------------------------------------------ + + +@pytest.mark.parametrize("cov_structure", ["full", "diag"]) +def test_sample_mvn(session_tf, cov_structure): + """ + Draws 10,000 samples from a distribution + with known mean and covariance. The test checks + if the mean and covariance of the samples is + close to the true mean and covariance. + """ + + N, D = 10000, 2 + means = tf.ones((N, D), dtype=float_type) + if cov_structure == "full": + covs = tf.eye(D, batch_shape=[N], dtype=float_type) + elif cov_structure == "diag": + covs = tf.ones((N, D), dtype=float_type) + + samples = _sample_mvn(means, covs, cov_structure) + value = session_tf.run(samples) + samples_mean = np.mean(value, axis=0) + samples_cov = np.cov(value, rowvar=False) + np.testing.assert_array_almost_equal(samples_mean, [1., 1.], decimal=1) + np.testing.assert_array_almost_equal(samples_cov, [[1., 0.], [0., 1.]], decimal=1) + + +def _create_placeholder_dict(values): + return {name: tf.placeholder(float_type, shape=arr.shape) for name, arr in values.items()} + +def _create_feed_dict(placeholders_dict, value_dict): + return {placeholder: value_dict[name] for name, placeholder in placeholders_dict.items()} + + +@pytest.mark.parametrize("whiten", [True, False]) +def test_sample_conditional(session_tf, whiten): + q_mu = np.random.randn(Data.M , Data.P) # M x P + q_sqrt = np.array([np.tril(np.random.randn(Data.M, Data.M)) for _ in range(Data.P)]) # P x M x M + Z = Data.X[:Data.M, ...] # M x D + Xs = np.ones((int(10e5), Data.D), dtype=float_type) + + feature = InducingPoints(Z.copy()) + kernel = RBF(Data.D) + + values = {"Z": Z, "Xnew": Xs, "q_mu": q_mu, "q_sqrt": q_sqrt} + placeholders = _create_placeholder_dict(values) + feed_dict = _create_feed_dict(placeholders, values) + + # Path 1 + sample = sample_conditional(placeholders["Xnew"], placeholders["Z"], kernel, + placeholders["q_mu"], q_sqrt=placeholders["q_sqrt"], white=whiten) + value = session_tf.run(sample, feed_dict=feed_dict) + + # Path 2 + sample2 = sample_conditional(placeholders["Xnew"], feature, kernel, + placeholders["q_mu"], q_sqrt=placeholders["q_sqrt"], white=whiten) + value2 = session_tf.run(sample2, feed_dict=feed_dict) + + # check if mean and covariance of samples are similar + np.testing.assert_array_almost_equal(np.mean(value, axis=0), + np.mean(value2, axis=0), decimal=1) + np.testing.assert_array_almost_equal(np.cov(value, rowvar=False), + np.cov(value2, rowvar=False), decimal=1) + + +def test_sample_conditional_mixedkernel(session_tf): + q_mu = np.random.randn(Data.M , Data.L) # M x L + q_sqrt = np.array([np.tril(np.random.randn(Data.M, Data.M)) for _ in range(Data.L)]) # L x M x M + Z = Data.X[:Data.M,...] # M x D + N = int(10e5) + Xs = np.ones((N, Data.D), dtype=float_type) + + + values = {"Xnew": Xs, "q_mu": q_mu, "q_sqrt": q_sqrt} + placeholders = _create_placeholder_dict(values) + feed_dict = _create_feed_dict(placeholders, values) + + # Path 1: mixed kernel: most efficient route + W = np.random.randn(Data.P, Data.L) + mixed_kernel = mk.SeparateMixedMok([RBF(Data.D) for _ in range(Data.L)], W) + mixed_feature = mf.MixedKernelSharedMof(InducingPoints(Z.copy())) + + sample = sample_conditional(placeholders["Xnew"], mixed_feature, mixed_kernel, + placeholders["q_mu"], q_sqrt=placeholders["q_sqrt"], white=True) + value = session_tf.run(sample, feed_dict=feed_dict) + + + # Path 2: independent kernels, mixed later + separate_kernel = mk.SeparateIndependentMok([RBF(Data.D) for _ in range(Data.L)]) + shared_feature = mf.SharedIndependentMof(InducingPoints(Z.copy())) + sample2 = sample_conditional(placeholders["Xnew"], shared_feature, separate_kernel, + placeholders["q_mu"], q_sqrt=placeholders["q_sqrt"], white=True) + value2 = session_tf.run(sample2, feed_dict=feed_dict) + value2 = np.matmul(value2, W.T) + # check if mean and covariance of samples are similar + np.testing.assert_array_almost_equal(np.mean(value, axis=0), + np.mean(value2, axis=0), decimal=1) + np.testing.assert_array_almost_equal(np.cov(value, rowvar=False), + np.cov(value2, rowvar=False), decimal=1) + +# ------------------------------------------ +# Test Mixed Mok Kgg +# ------------------------------------------ + +def test_MixedMok_Kgg(session_tf): + data = DataMixedKernel + kern_list = [RBF(data.D) for _ in range(data.L)] + kern = mk.SeparateMixedMok(kern_list, W=data.W) + + Kgg = kern.compute_Kgg(Data.X, Data.X) # L x N x N + Kff = kern.compute_K(Data.X, Data.X) # N x P x N x P + + # Kff = W @ Kgg @ W^T + Kff_infered = np.einsum("lnm,pl,ql->npmq", Kgg, data.W, data.W) + + np.testing.assert_array_almost_equal(Kff, Kff_infered, decimal=5) + + +# ------------------------------------------ +# Integration tests +# ------------------------------------------ + + +def test_shared_independent_mok(session_tf): + """ + In this test we use the same kernel and the same inducing features + for each of the outputs. The outputs are considered to be uncorrelated. + This is how GPflow handled multiple outputs before the multioutput framework was added. + We compare three models here: + 1) an ineffient one, where we use a SharedIndepedentMok with InducingPoints. + This combination will uses a Kff of size N x P x N x P, Kfu if size N x P x M x P + which is extremely inefficient as most of the elements are zero. + 2) efficient: SharedIndependentMok and SharedIndependentMof + This combinations uses the most efficient form of matrices + 3) the old way, efficient way: using Kernel and InducingPoints + Model 2) and 3) follow more or less the same code path. + """ + # Model 1 + q_mu_1 = np.random.randn(Data.M * Data.P, 1) # MP x 1 + q_sqrt_1 = np.tril(np.random.randn(Data.M * Data.P, Data.M * Data.P))[None, ...] # 1 x MP x MP + kernel_1 = mk.SharedIndependentMok(RBF(Data.D, variance=0.5, lengthscales=1.2), Data.P) + feature_1 = InducingPoints(Data.X[:Data.M,...].copy()) + m1 = SVGP(Data.X, Data.Y, kernel_1, Gaussian(), feature_1, q_mu=q_mu_1, q_sqrt=q_sqrt_1) + m1.set_trainable(False) + m1.q_sqrt.set_trainable(True) + gpflow.training.ScipyOptimizer().minimize(m1, maxiter=Data.MAXITER) + + # Model 2 + q_mu_2 = np.reshape(q_mu_1, [Data.M, Data.P]) # M x P + q_sqrt_2 = np.array([np.tril(np.random.randn(Data.M, Data.M)) for _ in range(Data.P)]) # P x M x M + kernel_2 = RBF(Data.D, variance=0.5, lengthscales=1.2) + feature_2 = InducingPoints(Data.X[:Data.M, ...].copy()) + m2 = SVGP(Data.X, Data.Y, kernel_2, Gaussian(), feature_2, q_mu=q_mu_2, q_sqrt=q_sqrt_2) + m2.set_trainable(False) + m2.q_sqrt.set_trainable(True) + gpflow.training.ScipyOptimizer().minimize(m2, maxiter=Data.MAXITER) + + # Model 3 + q_mu_3 = np.reshape(q_mu_1, [Data.M, Data.P]) # M x P + q_sqrt_3 = np.array([np.tril(np.random.randn(Data.M, Data.M)) for _ in range(Data.P)]) # P x M x M + kernel_3 = mk.SharedIndependentMok(RBF(Data.D, variance=0.5, lengthscales=1.2), Data.P) + feature_3 = mf.SharedIndependentMof(InducingPoints(Data.X[:Data.M, ...].copy())) + m3 = SVGP(Data.X, Data.Y, kernel_3, Gaussian(), feature_3, q_mu=q_mu_3, q_sqrt=q_sqrt_3) + m3.set_trainable(False) + m3.q_sqrt.set_trainable(True) + gpflow.training.ScipyOptimizer().minimize(m3, maxiter=Data.MAXITER) + + check_equality_predictions(session_tf, [m1, m2, m3]) + + + +def test_separate_independent_mok(session_tf): + """ + We use different independent kernels for each of the output dimensions. + We can achieve this in two ways: + 1) efficient: SeparateIndependentMok with Shared/SeparateIndependentMof + 2) inefficient: SeparateIndependentMok with InducingPoints + However, both methods should return the same conditional, + and after optimization return the same log likelihood. + """ + # Model 1 (INefficient) + q_mu_1 = np.random.randn(Data.M * Data.P, 1) + q_sqrt_1 = np.tril(np.random.randn(Data.M * Data.P, Data.M * Data.P))[None, ...] # 1 x MP x MP + kern_list_1 = [RBF(Data.D, variance=0.5, lengthscales=1.2) for _ in range(Data.P)] + kernel_1 = mk.SeparateIndependentMok(kern_list_1) + feature_1 = InducingPoints(Data.X[:Data.M,...].copy()) + m1 = SVGP(Data.X, Data.Y, kernel_1, Gaussian(), feature_1, q_mu=q_mu_1, q_sqrt=q_sqrt_1) + m1.set_trainable(False) + m1.q_sqrt.set_trainable(True) + m1.q_mu.set_trainable(True) + gpflow.training.ScipyOptimizer().minimize(m1, maxiter=Data.MAXITER) + + # Model 2 (efficient) + q_mu_2 = np.random.randn(Data.M, Data.P) + q_sqrt_2 = np.array([np.tril(np.random.randn(Data.M, Data.M)) for _ in range(Data.P)]) # P x M x M + kern_list_2 = [RBF(Data.D, variance=0.5, lengthscales=1.2) for _ in range(Data.P)] + kernel_2 = mk.SeparateIndependentMok(kern_list_2) + feature_2 = mf.SharedIndependentMof(InducingPoints(Data.X[:Data.M, ...].copy())) + m2 = SVGP(Data.X, Data.Y, kernel_2, Gaussian(), feature_2, q_mu=q_mu_2, q_sqrt=q_sqrt_2) + m2.set_trainable(False) + m2.q_sqrt.set_trainable(True) + m2.q_mu.set_trainable(True) + gpflow.training.ScipyOptimizer().minimize(m2, maxiter=Data.MAXITER) + + check_equality_predictions(session_tf, [m1, m2]) + + +def test_separate_independent_mof(session_tf): + """ + Same test as above but we use different (i.e. separate) inducing features + for each of the output dimensions. + """ + np.random.seed(0) + + # Model 1 (INefficient) + q_mu_1 = np.random.randn(Data.M * Data.P, 1) + q_sqrt_1 = np.tril(np.random.randn(Data.M * Data.P, Data.M * Data.P))[None, ...] # 1 x MP x MP + kernel_1 = mk.SharedIndependentMok(RBF(Data.D, variance=0.5, lengthscales=1.2), Data.P) + feature_1 = InducingPoints(Data.X[:Data.M,...].copy()) + m1 = SVGP(Data.X, Data.Y, kernel_1, Gaussian(), feature_1, q_mu=q_mu_1, q_sqrt=q_sqrt_1) + m1.set_trainable(False) + m1.q_sqrt.set_trainable(True) + m1.q_mu.set_trainable(True) + gpflow.training.ScipyOptimizer().minimize(m1, maxiter=Data.MAXITER) + + # Model 2 (efficient) + q_mu_2 = np.random.randn(Data.M, Data.P) + q_sqrt_2 = np.array([np.tril(np.random.randn(Data.M, Data.M)) for _ in range(Data.P)]) # P x M x M + kernel_2 = mk.SharedIndependentMok(RBF(Data.D, variance=0.5, lengthscales=1.2), Data.P) + feat_list_2 = [InducingPoints(Data.X[:Data.M, ...].copy()) for _ in range(Data.P)] + feature_2 = mf.SeparateIndependentMof(feat_list_2) + m2 = SVGP(Data.X, Data.Y, kernel_2, Gaussian(), feature_2, q_mu=q_mu_2, q_sqrt=q_sqrt_2) + m2.set_trainable(False) + m2.q_sqrt.set_trainable(True) + m2.q_mu.set_trainable(True) + gpflow.training.ScipyOptimizer().minimize(m2, maxiter=Data.MAXITER) + + # Model 3 (Inefficient): an idenitical feature is used P times, + # and treated as a separate feature. + q_mu_3 = np.random.randn(Data.M, Data.P) + q_sqrt_3 = np.array([np.tril(np.random.randn(Data.M, Data.M)) for _ in range(Data.P)]) # P x M x M + kern_list = [RBF(Data.D, variance=0.5, lengthscales=1.2) for _ in range(Data.P)] + kernel_3 = mk.SeparateIndependentMok(kern_list) + feat_list_3 = [InducingPoints(Data.X[:Data.M, ...].copy()) for _ in range(Data.P)] + feature_3 = mf.SeparateIndependentMof(feat_list_3) + m3 = SVGP(Data.X, Data.Y, kernel_3, Gaussian(), feature_3, q_mu=q_mu_3, q_sqrt=q_sqrt_3) + m3.set_trainable(False) + m3.q_sqrt.set_trainable(True) + m3.q_mu.set_trainable(True) + gpflow.training.ScipyOptimizer().minimize(m3, maxiter=Data.MAXITER) + + check_equality_predictions(session_tf, [m1, m2, m3]) + + +def test_mixed_mok_with_Id_vs_independent_mok(session_tf): + data = DataMixedKernelWithEye + # Independent model + k1 = mk.SharedIndependentMok(RBF(data.D, variance=0.5, lengthscales=1.2), data.L) + f1 = InducingPoints(data.X[:data.M, ...].copy()) + m1 = SVGP(data.X, data.Y, k1, Gaussian(), f1, + q_mu=data.mu_data_full, q_sqrt=data.sqrt_data_full) + m1.set_trainable(False) + m1.q_sqrt.set_trainable(True) + gpflow.training.ScipyOptimizer().minimize(m1, maxiter=data.MAXITER) + + # Mixed Model + kern_list = [RBF(data.D, variance=0.5, lengthscales=1.2) for _ in range(data.L)] + k2 = mk.SeparateMixedMok(kern_list, data.W) + f2 = InducingPoints(data.X[:data.M, ...].copy()) + m2 = SVGP(data.X, data.Y, k2, Gaussian(), f2, + q_mu=data.mu_data_full, q_sqrt=data.sqrt_data_full) + m2.set_trainable(False) + m2.q_sqrt.set_trainable(True) + gpflow.training.ScipyOptimizer().minimize(m2, maxiter=data.MAXITER) + + check_equality_predictions(session_tf, [m1, m2]) + + +def test_compare_mixed_kernel(session_tf): + data = DataMixedKernel + + kern_list = [RBF(data.D) for _ in range(data.L)] + k1 = mk.SeparateMixedMok(kern_list, W=data.W) + f1 = mf.SharedIndependentMof(InducingPoints(data.X[:data.M,...].copy())) + m1 = SVGP(data.X, data.Y, k1, Gaussian(), feat=f1, q_mu=data.mu_data, q_sqrt=data.sqrt_data) + + kern_list = [RBF(data.D) for _ in range(data.L)] + k2 = mk.SeparateMixedMok(kern_list, W=data.W) + f2 = mf.MixedKernelSharedMof(InducingPoints(data.X[:data.M,...].copy())) + m2 = SVGP(data.X, data.Y, k2, Gaussian(), feat=f2, q_mu=data.mu_data, q_sqrt=data.sqrt_data) + + check_equality_predictions(session_tf, [m1, m2]) + + +def test_multioutput_with_diag_q_sqrt(session_tf): + data = DataMixedKernel + + q_sqrt_diag = np.ones((data.M, data.L)) * 2 + q_sqrt = np.repeat(np.eye(data.M)[None, ...], data.L, axis=0) * 2 # L x M x M + + kern_list = [RBF(data.D) for _ in range(data.L)] + k1 = mk.SeparateMixedMok(kern_list, W=data.W) + f1 = mf.SharedIndependentMof(InducingPoints(data.X[:data.M,...].copy())) + m1 = SVGP(data.X, data.Y, k1, Gaussian(), feat=f1, q_mu=data.mu_data, q_sqrt=q_sqrt_diag, q_diag=True) + + kern_list = [RBF(data.D) for _ in range(data.L)] + k2 = mk.SeparateMixedMok(kern_list, W=data.W) + f2 = mf.SharedIndependentMof(InducingPoints(data.X[:data.M,...].copy())) + m2 = SVGP(data.X, data.Y, k2, Gaussian(), feat=f2, q_mu=data.mu_data, q_sqrt=q_sqrt, q_diag=False) + + check_equality_predictions(session_tf, [m1, m2]) diff --git a/tests/test_multioutput_features.py b/tests/test_multioutput_features.py new file mode 100644 index 000000000..da304b7b6 --- /dev/null +++ b/tests/test_multioutput_features.py @@ -0,0 +1,97 @@ +import gpflow +import gpflow.multioutput.features as mf +import gpflow.multioutput.kernels as mk +import numpy as np +import pytest +import tensorflow as tf +from gpflow.features import InducingPoints +from gpflow.kernels import RBF +from gpflow.likelihoods import Gaussian +from gpflow.models import SVGP +from gpflow.test_util import session_tf + + +float_type = gpflow.settings.float_type +np.random.seed(1) + + +class Datum: + D = 1 + L = 2 + P = 3 + M = 10 + N = 100 + W = np.random.randn(P, L) + X = np.random.randn(N)[:, None] + Xnew = np.random.randn(N)[:, None] + + +def make_kernel(): + return gpflow.kernels.RBF(Datum.D) + + +def make_kernels(num): + return [make_kernel() for _ in range(num)] + + +def make_ip(): + x = np.random.permutation(Datum.X) + return gpflow.features.InducingPoints(x[:Datum.M, ...]) + + +def make_ips(num): + return [make_ip() for _ in range(num)] + + +class Mofs: + def shared_independent(self): + return mf.SharedIndependentMof(make_ip()) + + def separate_independent(self, num=Datum.P): + return mf.SeparateIndependentMof(make_ips(num)) + + def features(self): + return [self.shared_independent, self.separate_independent] + + def mixed_shared(self): + return mf.MixedKernelSharedMof(make_ip()) + + +class Moks: + def shared_independent(self): + return mk.SharedIndependentMok(make_kernel(), Datum.P) + + def separate_independent(self, num=Datum.L): + return mk.SeparateIndependentMok(make_kernels(num)) + + def separate_mixed(self, num=Datum.L): + return mk.SeparateMixedMok(make_kernels(num), Datum.W) + + def kernels(self): + return [self.shared_independent, self.separate_independent, self.separate_mixed] + + +@pytest.mark.parametrize('feature', Mofs().features()) +@pytest.mark.parametrize('kernel', Moks().kernels()) +def test_kuu(session_tf, feature, kernel): + Kuu = mf.Kuu(feature(), kernel(), jitter=1e-9) + session_tf.run(tf.cholesky(Kuu)) + + +@pytest.mark.parametrize('feature', Mofs().features()) +@pytest.mark.parametrize('kernel', Moks().kernels()) +def test_kuf(session_tf, feature, kernel): + Kuf = mf.Kuf(feature(), kernel(), Datum.Xnew) + session_tf.run(Kuf) + + +@pytest.mark.parametrize('fun', [mf.Kuu, mf.Kuf]) +def test_mixed_shared(session_tf, fun): + f = Mofs().mixed_shared() + k = Moks().separate_mixed() + if fun is mf.Kuu: + t = tf.cholesky(fun(f, k, jitter=1e-9)) + else: + t = fun(f, k, Datum.Xnew) + print(t.shape) + session_tf.run(t) diff --git a/tests/test_notebooks.py b/tests/test_notebooks.py index d4980d138..06abd73d6 100644 --- a/tests/test_notebooks.py +++ b/tests/test_notebooks.py @@ -38,7 +38,8 @@ "models.ipynb", "multiclass.ipynb", "classification.ipynb", - "monitor-tensorboard.ipynb" + "multioutput.ipynb", + "monitor-tensorboard.ipynb", # Blacklist: # "FITCvsVFE.ipynb", # "svi.ipynb", diff --git a/tests/test_predict.py b/tests/test_predict.py index 707e0b90a..06f5516d2 100644 --- a/tests/test_predict.py +++ b/tests/test_predict.py @@ -85,7 +85,7 @@ class TestFullCov(GPflowTestCase): rng = np.random.RandomState(0) num_samples = 5 samples_shape = (num_samples, Ntest, output_dim) - covar_shape = (Ntest, Ntest, output_dim) + covar_shape = (output_dim, Ntest, Ntest) X = rng.randn(N, input_dim) Y = rng.randn(N, output_dim) Z = rng.randn(M, input_dim) @@ -107,12 +107,13 @@ def test_cov(self): self.assertTrue(covar.shape == self.covar_shape) self.assertTrue(var.shape == (self.Ntest, self.output_dim)) for i in range(self.output_dim): - self.assertTrue(np.allclose(var[:, i], np.diag(covar[:, :, i]))) + self.assertTrue(np.allclose(var[:, i], np.diag(covar[i, :, :]))) def test_samples(self): with self.test_context(): m = self.prepare() samples = m.predict_f_samples(self.Xtest, self.num_samples) + print(samples.shape) self.assertTrue(samples.shape == self.samples_shape) diff --git a/tests/test_uncertain_conditional.py b/tests/test_uncertain_conditional.py index 5290c4e1b..8e3ee6adf 100644 --- a/tests/test_uncertain_conditional.py +++ b/tests/test_uncertain_conditional.py @@ -23,8 +23,8 @@ import gpflow from gpflow import settings +from gpflow.conditionals import conditional from gpflow.conditionals import uncertain_conditional -from gpflow.conditionals import feature_conditional from gpflow.quadrature import mvnquad from gpflow.test_util import session_context @@ -35,7 +35,7 @@ def uncertain_predict_f_moment_matching(self, Xmu, Xcov): return uncertain_conditional( Xmu, Xcov, self.feature, self.kern, self.q_mu, self.q_sqrt, mean_function=self.mean_function, white=self.whiten, - full_cov_output=self.full_cov_output) + full_output_cov=self.full_output_cov) def uncertain_predict_f_monte_carlo(self, Xmu, Xchol, mc_iter=int(1e6)): rng = np.random.RandomState(0) @@ -135,15 +135,15 @@ def tensors(cls, white, mean_name): } def mean_fn(X): - mean, _ = feature_conditional(X, feat, kern, q_mu, q_sqrt=q_sqrt, white=white) + mean, _ = conditional(X, feat, kern, q_mu, q_sqrt=q_sqrt, white=white) return mean + effective_mean(X) def var_fn(X): - _, var = feature_conditional(X, feat, kern, q_mu, q_sqrt=q_sqrt, white=white) + _, var = conditional(X, feat, kern, q_mu, q_sqrt=q_sqrt, white=white) return var def mean_sq_fn(X): - mean, _ = feature_conditional(X, feat, kern, q_mu, q_sqrt=q_sqrt, white=white) + mean, _ = conditional(X, feat, kern, q_mu, q_sqrt=q_sqrt, white=white) return (mean + effective_mean(X)) ** 2 Collection = namedtuple('QuadratureCollection', @@ -176,7 +176,7 @@ def test_no_uncertainty(white, mean): model = MomentMatchingSVGP( Data.X, Data.Y, k, gpflow.likelihoods.Gaussian(), mean_function=m, Z=Data.X.copy(), whiten=white) - model.full_cov_output = False + model.full_output_cov = False gpflow.train.AdamOptimizer().minimize(model, maxiter=50) mean1, var1 = model.predict_f(Data.Xnew_mu) @@ -198,7 +198,7 @@ def test_monte_carlo_1_din(white, mean): model = MomentMatchingSVGP( DataMC1.X, DataMC1.Y, k, gpflow.likelihoods.Gaussian(), Z=DataMC1.X.copy(), whiten=white) - model.full_cov_output = True + model.full_output_cov = True gpflow.train.AdamOptimizer().minimize(model, maxiter=50) pred_mm = model.uncertain_predict_f_moment_matching( @@ -222,7 +222,7 @@ def test_monte_carlo_2_din(white, mean): model = MomentMatchingSVGP( DataMC2.X, DataMC2.Y, k, gpflow.likelihoods.Gaussian(), mean_function=m, Z=DataMC2.X.copy(), whiten=white) - model.full_cov_output = True + model.full_output_cov = True gpflow.train.AdamOptimizer().minimize(model) pred_mm = model.uncertain_predict_f_moment_matching( @@ -251,7 +251,7 @@ def test_quadrature(white, mean): d.Xmu, d.Xvar, d.feat, d.kern, d.q_mu, d.q_sqrt, mean_function=d.mean_function, - full_cov_output=False, + full_output_cov=False, white=white) mean_quad, var_quad, mean_sq_quad = session.run(