diff --git a/docs/source/notebooks/index.md b/docs/source/notebooks/index.md index 32c431568..afd4c5ff3 100644 --- a/docs/source/notebooks/index.md +++ b/docs/source/notebooks/index.md @@ -9,6 +9,7 @@ Here you will find a collection of examples and how-to guides for using PyMC-Mar mmm/mmm_example mmm/mmm_budget_allocation_example +mmm/mmm_allocation_assessment mmm/mmm_lift_test mmm/mmm_counterfactuals mmm/mmm_tvp_example diff --git a/docs/source/notebooks/mmm/mmm_allocation_assessment.ipynb b/docs/source/notebooks/mmm/mmm_allocation_assessment.ipynb new file mode 100644 index 000000000..305f4dfd6 --- /dev/null +++ b/docs/source/notebooks/mmm/mmm_allocation_assessment.ipynb @@ -0,0 +1,1351 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "(mmm_allocation_assessment)=\n", + "# Budget Allocation Risk Assessment with PyMC-Marketing\n", + "\n", + "This notebook is centered around evaluating the risks tied to different budget allocations across various marketing channels. You'll discover how to create an optimal budget allocation that aligns with your specific risk tolerance. This knowledge will empower you to make well-informed decisions regarding your budget distribution.\n", + "\n", + "## Prerequisite Knowledge\n", + "The notebook assumes the reader has knowledge of the essential functionalities of PyMC-Marketing. If one is unfamiliar, the [\"MMM Example Notebook\"](https://www.pymc-marketing.io/en/stable/notebooks/mmm/mmm_example.html) serves as an excellent starting point, offering a comprehensive introduction to media mix models in this context.\n", + "\n", + "## Expected Outcomes \n", + "Upon completion of this notebook, readers will acquire a comprehensive understanding of how to evaluate the risks associated with various budget allocations and how to develop an optimal budget allocation based on specified risk tolerance criteria.\n", + "\n", + "## Preliminary Setup \n", + "Consistent with previous notebooks in the PyMC-Marketing series, this document relies on a specific set of libraries. Below are the necessary imports required for executing the code snippets presented hereafter." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import warnings\n", + "\n", + "import arviz as az\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "\n", + "from pymc_marketing.mmm import MMM\n", + "\n", + "warnings.filterwarnings(\"ignore\")\n", + "\n", + "az.style.use(\"arviz-darkgrid\")\n", + "plt.rcParams[\"figure.figsize\"] = [12, 7]\n", + "plt.rcParams[\"figure.dpi\"] = 100\n", + "\n", + "%load_ext autoreload\n", + "%autoreload 2\n", + "%config InlineBackend.figure_format = \"retina\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The expectation is that a model has already been trained using the functionalities provided in prior versions of the PyMC-Marketing library. Thus, the data generation and training processes will be replicated in a different notebook. Those unfamiliar with these procedures are advised to refer to the [\"MMM Example Notebook.\"](https://www.pymc-marketing.io/en/stable/notebooks/mmm/mmm_example.html)\n", + "\n", + "## Loading a Pre-Trained Model\n", + "To utilize a saved model, load it into a new instance of the MMM class using the load method below." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "mmm = MMM.load(\"model.nc\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Formulating the Budget Allocation Challenge \n", + "As in earlier notebooks, it is essential to delineate the budget allocation challenge. Specifically, we must define the duration of our budget allocation and the permissible expenditure per time unit. Our model utilizes weekly data; therefore, we will maintain the same temporal granularity.\n", + "\n", + "In this example, we aim to distribute a budget across two channels over the course of eight weeks, with a weekly budget of 3 Million. Consequently, the total budget available for allocation amounts to 24 Million." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Total budget to allocate: 24M\n" + ] + } + ], + "source": [ + "num_periods = (\n", + " 8 # Number of time periods to allocate the budget (weeks for this example)\n", + ")\n", + "time_unit_budget = 3 # Imagine is 3K or 3M (per week in this case)\n", + "\n", + "# Define your channels\n", + "channels = [\"x1\", \"x2\"]\n", + "\n", + "print(f\"Total budget to allocate: {num_periods * time_unit_budget}M\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Based on our intuition, we were thinking of distributing this million into 2.5 Million for Google ($x2$) and 0.5 Million for Facebook ($x1$). Using this allocation, we can compute the response distribution and plot it." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sampling: [y]\n" + ] + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "a58498aa55c64debbcd5635b53e2d050", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "Output()" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "
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fv3+xPz/Hjx8fZ5xxRixbtqxY/fLy8uKxxx6L0047rdjBrh/bsmVL/Oc//4lf/epX8fbbb2/3OEX55z//GWeffXbSYNfWnn322fj9739f6vXsCMr7Xrds2bI499xz449//GOxgl1bW758efzpT3+Kc889t0T3zKI8/PDD8Yc//KHCg12rV6+OQYMGxRVXXFHs+25hUr0HJ7Jw4cI45ZRTUgp2/dg333wTp556apm8XqnIycmJp556Kvr375/yLLGp2rJlS/z+97+Pm266qVjfGXJycuL666+Pl19+uVTrmTt3bpx88skpBbt+bHtfo02bNsUdd9wR559/frGCXYWN8/zzz0ffvn1LNA4AAEAywl0AAECZSOVBdceOHYs15l133RU33HBDiYIrP7Zu3bq4/vrr469//WvStuvXr49BgwZFdnZ2qZy7tD333HNx7733bnf/p59+OuESdVubNWtWnHDCCTFt2rTtPufW1qxZE1dddVU8+uijpTbmO++8E5deeul2v2cmTpwYTz/9dNJ2b7/9dqnWXVzjxo2L0047rdgBkUSefvrpuPTSS5POgFVS++23X7Rp0yZhm1GjRqU83syZMwssN1WY/v37F7rM12233Za0b7p68MEH47333qvoMgq1cOHCOPfcc7d7Kd7Zs2fHmWeeGWvWrEmpfW5ublx11VVx7733llqwbsWKFXHBBRcU672YzD//+c/4/e9/v901/utf/4rXX3+91OrZEZT3vW7u3LnRr1+/mDRp0nafc2uTJk2Kk08+udiBxURGjRoVDz74YKmNt73mz58f/fr1i3//+98VXUq+pUuXxplnnhlfffXVdve/6aabSrmq4vnqq6/ioosuKtVfCLjhhhvyZwktrry8vLjtttti4cKFpVLLwoUL48wzzyzWEsg/VtzXaOPGjXHOOeek9P0uVfPnz4/TTjst3n///VIbEwAA4MeEuwAAgFK3Zs2alGZKOeKII1Iec/jw4TFs2LCSlFWk+++/P+mDyBdffDHmzZtXJucvDY8//niJx3jsscdiypQpSdstW7YsLrzwwjILut1///0Jl+krjjFjxpR4FqO//OUvSWdCqciH6tOmTYurr766TGbZmjBhQtxyyy2lPu7Wiloi8QcfffRRzJkzJ6Wxks0mUq1atTjhhBO22f/VV1+Vycxx5WHVqlXx1FNPVXQZRXrxxRdLPPPNN998E3fddVdKbe+6665iz/6Siry8vPjtb38bkydPLpXxRo0aVeJZie67775SqWVHUZ73uhUrVsT5559fqiGsHyxYsCAuvPDCUgmrr1q1Kv7whz+UvKgSWrlyZQwYMCDtviv997//LXHwefz48RU+K9O0adPiscceK7XxijuL2dbWrFlTavW8//77sXjx4hKNkeprlJeXF9dcc01KnwHFlZOTE5dddll8/fXXpT42AACAcBcAAFCqNmzYEDfccEOsXr06Ybu99947unTpktKY06ZNS3kppapVq0abNm1i3333jY4dO0bNmjWT9snLy4vf/e53sWTJkiLbvPbaaymdv1GjRtGxY8fo2rVrdOzYMXbdddeUaihtDRo0iL322iv22GOPqFWrVkp9cnNz44Ybbkg6i8ygQYNSnq2hZs2a0b59+9h7772jSZMmKfWJiPjtb38bc+fOTbl9qqpVqxZt27aNzp07R926dVPqk52dnTAosnDhwvjkk0+SjlOlSpXYddddY5999okuXbpEu3btolmzZlG58vb/03zNmjVx6aWXpjybR1ZWVuy9997RuXPnaNSoUUp9nn/++TKfHahv376RkZGRsE0qD6Jzc3OTBjUPP/zwaNiw4Tb7X3311aTjR0TUrl072rdvH127do3OnTtHmzZtol69ein1LStvvPFGSuG+GjVqRNu2bWPfffeNffbZJ3bbbbeU3welKSMjI9q1axf77LNP7LLLLin3e+GFF5LOTjZ27NiUg24/1NGlS5fo0KFDZGZmJu2Tk5MTv/nNb2L9+vUpnaM4atSoEe3bt49OnTqlfN/4+uuvyySksKMoy3vd9ddfn/JMQvXr149OnTrFvvvuGy1atEipz4wZM4o1i1hRVq9eHWvXri3xOCX129/+tljBrsqVK0eLFi2ic+fOsddee0WLFi2iSpUqZVjh/9eyZctif/4899xz232+KlWqxC677BLt2rWLzp07R7du3WKfffaJdu3aFev+MXz48KTfr7dXvXr1Yq+99op27dql/DqMGjWq1GbT3VpZvUbDhg1L+X5fo0aN6NChQ3Tp0iXatm0bVatWTdpn1apVMWjQoFJZThQAAODHkv+LBAAAYCtbLzmSk5MTK1asiM8++yzGjBmT9Lfva9SoEbfddlvK57vnnnsiNzc3YZtmzZrF5ZdfHn369CnwUHzLli3x5ptvxp/+9KeEM/9s2LAhhgwZEn/84x8LPT579uyE5//FL34RV155ZbRq1WqbY3l5ebFw4cL46quvYsqUKTF58uT49NNPS225sB9r165d/O53v4v9998/f9m5TZs2xauvvhqDBw9OOnvO3Llz47XXXotjjjmm0ONvv/12SkvONG7cOK699tro06dPgdDOF198EXfffXe8++67Cftv2rQpHnzwwbjnnnuSnisVGRkZcckll8Tpp58eO+20U0T87307YsSIGDx4cNKZud59993o27dvoce++eabhH0zMzPjuuuui1/96ldRu3btbY5v3Lgxvvnmm/jiiy/i/fffj8mTJ6c8y8hTTz2VdFaZGjVqxMCBA6N///7bBOw+/fTTuO++++K///1vwjHuvffeOOyww8rswXv9+vXjyCOPjFdeeaXINiNHjozLL7+80OUUfzBp0qRYunRpwnOdcsophe5Pdo136NAhbrzxxujSpUuhgbzly5fH7NmzY+rUqTF58uSYOnVquQUukr0Hs7Ky4uabb44DDzyw0IfTq1evjq+//jqmTZsWkydPjilTpsTKlStLvc4aNWrEr3/96zj55JMLXAtffPFFDB48OKWl74YOHRo9evQo9NjmzZtTCsu0bds2fv3rX8ehhx5a4PNp06ZNMWbMmLj77rsTflYuW7Ysnnrqqbj44ouTnisVderUiUGDBkXfvn2jRo0aEfG/pYCHDRsWQ4YMSRoSeOedd6Jbt24F9vXr1y+6d++ev/3dd9/Fb37zm4TjHHTQQXHBBRckbFMRYcDClPW9bvLkyfHWW28lraNfv35xzjnnRPv27QvsX7RoUQwdOjT+/ve/J3z9nn322TjrrLNSDoSlqmXLltGtW7do2LBhbNiwIRYvXhxffvnldi97l8yECRNi/PjxKbVt06ZNXHDBBdG7d+9tQtZr1qyJqVOnxqhRo+K1115Lem8uruOPPz6uuOKKaN68ef6+SZMmxQ033BCLFi1K2DfZ95YfVK5cOfbee+/Yf//9o3PnzrHHHntEkyZNEt4/lyxZEm+++WY88sgjCb9Dr1q1KsaOHRv9+/dPqZZUtGrVKn7/+9/HgQcemH9vW7p0afzxj39MGoJau3ZtfPzxx3HAAQeUWj1l+RqtWrUqpaXY991337j88sujR48eBV63tWvXxj//+c/485//nPD+/vnnn8fo0aPj+OOPT3ouAACAVAl3AQAAxXbWWWdtd99atWrFkCFDtnkQWpRJkyYlXQKrffv28fTTT0f9+vW3OValSpU44ogjolu3bnHqqacmDHC8+OKLccUVV0Tjxo23ObZixYoi+zVr1izuu+++ImdgqlSpUmRlZUVWVlb06tUrIv63fNG4cePinXfeSfh3K46OHTvGM888s02AKCMjI4477rjo2LFjnHrqqUlDG8OHDy/ygfeQIUOS1tGkSZP4xz/+UeDB3A86dOgQjz/+eFxzzTVJZ1h65ZVX4uKLL47ddtst6TkTqVq1ajz88MNxyCGHFNhfrVq1OO2006JKlSpx0003JRwj0cxcy5cvT9j3nHPOidNPP73I45mZmdGhQ4fo0KFDfoDsiy++iP/85z+Fvqd/sGrVqqRLldaqVSueeeaZ6NSpU6HHO3XqFEOHDo2rr746YbBq9uzZMW7cuOjTp0/C85XEySefnLCG+fPnx4cffrhNiOXHks3u1bJly+jZs2ehxxJd4xH/W3pz1113LfJ4gwYNokGDBtGtW7e44IILYtOmTfHOO+/EmDFjks5KVlLJ3oN//OMfEz58r1OnTuyzzz6xzz77xNlnnx1btmyJyZMnx5gxYwoNJG6PatWqxV//+tfYf//9tznWoUOHeOKJJ+LXv/510lni3n333fj2228LDdK+/PLLScMrBxxwQDzyyCNRvXr1bY5lZGRE3759o1u3bnHyySfH999/X+Q4w4YNi4EDB0a1atUSni+Z2rVrxzPPPBN77rlngf01atSISy+9NDZu3Jg0jPDpp59us6958+YFPoNTCYw2bty40Ncn3ZTHve7Pf/5z0jpuvfXWIsOiu+yyS9x4442x2267JVzaNicnJ5588smk96BUtW3bNm688cYiX8evv/661ANTEZFSYCYi4oQTTohbbrmlyM/E2rVrxyGHHBKHHHJILFu2LB544IFSCxVffPHFceWVV26zv2fPnjF06NA4/vjjY8uWLUX2X7JkSSxdujR23nnnItvstttu8fbbbxf6PTKRJk2axP/93//FYYcdFn369Ek4G9YHH3xQauGudu3axd/+9rdtQnY777xz3H///XHmmWfGhx9+mHCMTz75pNTCXWX9Gj355JNJlxT/1a9+FXfeeWeh77tatWrF2Wefnf9vikTX0mOPPSbcBQAAlCrLMgIAAOWme/fu8a9//SsOPPDAlPskWg4v4n/BqT/96U8JQzAR/1tu5pprrknYZsuWLUX+1n+iJbKqV69e7KX16tWrF/37948HH3ywWP2KUrly5bjjjjsSBjHatGkTgwYNSjrW1KlTCw26LF68OKZPn560/0033VRosOvHtd5yyy1JH37m5uamPBNIImedddY2wa4f69evX/5sOUWZO3dukbOvJFs+LdWlwn6sQ4cOcdVVV8WAAQOKbPPOO+8knRnqN7/5TZHBrh9Urlw5brzxxqQhlQkTJiQ8XlI9evQoNLDzY4nCW+vWrYtx48Yl7N+/f/8iZ/4q7dcxIyMjDj/88Lj33ntLHFBMprRrr1KlSvTs2TNuu+22ImfJKq4zzzwzYXCoSpUqcdttt0WdOnUSjpOXlxdvvPFGoceS3S9q1KgRd999d6HBrh9r3rx50lm5Vq1aFR999FHCNqn4zW9+s02w68cSBUN/UFazMaWj8rjXLV26NOlSl0cffXSRwa4fO+2006Jjx44J26QyQ1gq9tprr3j22WcTXme77bZbwvfb9pg3b17SAFBExGGHHRZ33HFHymHXxo0bx+23354w0JuqvfbaK6644ooij+++++4pBRsTzQAb8b+gbHGDXT/WpEmTpL/8MHXq1O0e/8eqVKkSd999d5FLVFepUiX+7//+L+k4pfX5Ux6vUbJ7RJMmTeK2225LGijs2LFjnHbaaQnbfPnllynPwgoAAJAK4S4AAKBMVapUKX7xi1/EU089FcOHD4/WrVsXq3+yJVb23nvv6NChQ0pj/XiJqqK8/fbbhe7fZZddiuwze/bsePjhh2PTpk0p1VEWevTokdLPoW/fvvnLEiZSWGghlSWJdt111zjiiCOStqtdu3acfPLJSdslWy4wmapVq8bAgQMTtsnIyIg2bdokbJObm1tkkKpZs2YJ+z799NMpPfgurmSvR7Vq1YpcSnJr9evXj3bt2iVsU5qzzBXlpJNOSnh87NixRV5n48aNSzjbSbVq1eKEE04o8niiazwi4uabb046Q1ZFSVb7nXfeGQsXLiynarZVqVKllGZ8bNCgQRx77LFJ2xX2+bRx48akgZzevXunvKxgSe4XqapXr17Sz8EmTZokDS+vWbOmRHXsSMrjXpfKfac4Mycley8tWLAgvv7665THK0z16tXjvvvuSxqOLAupXAfVqlWLm2++OeGyumXpwgsvTHruVN5Xq1evLtZ5N27cGG+99VY88MADceWVV0bfvn3j0EMPjf333z/22muvaN++/Tb/JQuNJlv6PFW9evVK+ndO5WdSWp8/Zf0aLViwIOkSxr/61a8iMzMz6TkiUrtHlMf3JgAA4OfDsowAAECZysvLi/feey9233336Nq1a7GWJ1u0aFEsWLAgYZuPP/445SUeU1HUso0HHHBAfPHFF0X2e/DBB2Po0KHRuXPnaNOmTTRv3jxatmwZLVu2jF133TXpTDEl9cNyj8lkZGREz54949VXX03Ybtq0adG7d+8C+1IJKB166KEp1RHxv6DFww8/nLDN1KlTIy8vb7sfCHft2jUaNmyYtF0qgY81a9YUOltMhw4domHDhkUu4fbdd9/FaaedFllZWdGpU6do0aJFtGjRIv+90axZs+36+33wwQcJj+fk5ETXrl2LPW5Rli1bFqtWrUopMLG9TjzxxPjzn/8cOTk5hR5ftWpVjB8/Pn7xi19sc2zUqFEJx04W7DnwwAPjmWeeKfL466+/Hm+99Vbsscce0bZt2wKvY6tWrYqc/aQ8JJsN8aOPPorevXvnhwd+qL1FixbRunXraNCgQZnW165du6QBtB8ceuih8dxzzyVsM23atG32ffLJJ7Fhw4aE/V555ZWES38WV6JlflPRu3fvlJZ1bNiwYcJlQ4sbONmRlce9Ltlna0QkDQ0X1zfffFOiGf6OO+64aNmyZSlWlLpEyxb/4NBDD035M6C0ZWZmpvS+SeW7QqrX2tdffx0PP/xwvPHGG7F+/fqU+qQqJycn1q9fn3TG0WSOPvropG1S+W5UGp8/5fEapXJdP/bYY/HYY48lbZeqkt4jAAAAfky4CwAAKHMrVqyIIUOGxOuvvx6PP/54ykvWLF26tIwr21ZRAZ3TTjsthg8fXmToJOJ/y8K999578d577xXYX7ly5dh1112jc+fO0b179+jVq1eJlu0pTHECbu3atUv6wPu7777bZt+yZcuSjr3HHnukXEfbtm2jcuXKkZubW2SbTZs2RXZ2dtSrVy/lcX8s2XJYP0jlIenmzZsL3V+pUqU444wz4s9//nPC/gsWLCg0rFizZs3o0KFD7LPPPtGzZ8/o0aNHSiHIVF6P0vb999+XabirQYMGcfjhh8fYsWOLbDNy5Mhtwl1Lly6NSZMmJRw72QxJBx10ULRu3TrhzB6bN2+OTz75pNAwQ5MmTaJTp07RrVu3OOSQQ2L33XdPeL7S1LZt2+jZs2fCn0FeXl588cUXhYZUGzRoEB07doyuXbvGgQceGJ07dy7V+lKdXTEiks4gF1H453RF3C9KOpNbaX0+bdmypUR17EjK416XTt89UnXMMceUUiXFN3fu3KRtUpnlqKzsvvvuKd1TU/kekOxay8vLi/vuuy+eeOKJMr0uV61aVeJwVyrLc5bGzyQV5fEa7Yj3CAAAgB+zLCMAAFBuPv/88xg4cGCRy9ttLdFMJWVl5cqVhe5v0aJFXH311ds1Zm5ubnzzzTcxcuTI+N3vfheHHHJIDBw4MOkSYsWRymwGP0i2xFdERHZ29jb7UnlIVZwZgDIzMwudCWt7zluUJk2apNQuldlzEjn33HNj77333q6+69ati6lTp8awYcPi/PPPj4MOOigGDx6c8GH/unXrks5SVBbK45o85ZRTEh5/9913t3lP/Pvf/074gLl58+ZJZ7eqWrVq3H777ds9y96SJUti/Pjxcdddd8Wxxx4bv/rVr+Lll19OGF4sTTfffPN2z8C1fPnyeOedd+KBBx6I/v37x5FHHhlPP/10qS01W5zPp1T+Dps3b95mKbCKuF+U9JxNmzZNqV1JP59+SsrjXrcjvpf22muvUqqk+FKpPSsrqxwqKVyq11lxZpYtyg033BCPPfZYmQcuE/2iQapS+bmU12dPebxGO+J1DQAA8GPCXQAAQLHNnDkz/78PP/wwRowYEQMGDEjpocsXX3wRf/zjH1M6T2EPXctaogdmAwYMiFtuuSWlQFIiubm58c4778Tpp58ef/rTn0o01g+KE0ipWbNm0jaFBfC2DlMUprgzSaTSPpXzFiXV16py5ZL987h69eoxdOjQQpcLLK7s7Ox48skn45hjjikyALhq1aoSn2d7lMYD5WR69uwZLVq0SFjD1kvrjRw5MuGYJ598ckpLX3bt2jWeeOKJUlne7IsvvojrrrsuBgwYkHKgtSRat24dzzzzTMqzQSUyd+7cuOOOO+Kkk04qlRniMjMzU25bo0aNlF6rrX+m6Xa/SEWtWrVSalfSz6efkvK411XE52tJ3ku1atWKOnXqlGI1xZNKCLSk35tKItVzb+/yzz945ZVX4qWXXirRGOUplZ9LeX32lMdrtKNd1wAAAFvzf4cAAIASqV27dnTu3DluuOGG+Mc//pHSkm0vvvhiTJw4MWm7dJyt5P/+7/9i7Nixcfnll0fz5s1LPN4TTzwRQ4cOLfE4xZnFad26dUnbFBY6SOXh2/r161OuI9X2JXkonOqDydJ4gLnTTjvFAw88EH//+9/juOOOK/GSSStXrowLL7yw0CWvqlatWqKx01mlSpWif//+Cdu8/PLL+X+eOXNmoUsN/qBq1apxwgknpHz+bt26xb///e+47bbbtns2th97//3346qrrirxOKlo27ZtjBgxIu67777o2bNnid/XM2fOjIEDBxa5JGmqNm7cmHLb9evXR15eXtJ2W39G7YjXRHl+Pv1UlMe9bkd7L1VksCsitdmUShLSLqnyus7uvffepG122mmnuPjii+OFF16IyZMnx2effVbgFyZmzpxZbktYpvL3La/PnvJ4jXa06xoAAGBr/lUDAACUmr322ivuueeeuOCCC5K2veOOO2LUqFEJH9SksqRS375946677ipWnSXVuHHjuOyyy+Kyyy6Lb7/9Nj744IP4/PPPY/bs2fHtt9/GkiVLirUU28MPPxwnnHDCdi+pFhEJl/DbWirLxNStW3ebfanUV5wlFDdu3JjSA9+S/FwqQrdu3aJbt26xadOmmD59enz44Yfx1VdfxezZs2Pu3LnFmj1izZo1cf/998f9999fYH/dunWjcuXKCd9nzZo1izfffHO7/x4V6cQTT4whQ4YUOevFp59+Gl9//XXstttuSWft6t27dzRu3LhY58/MzIyTTz45Tj755Fi+fHm8//778cknn8Ts2bPjm2++iQULFhRrRo4JEybE22+/HYccckix6tgeVapUiWOPPTaOPfbYWL16dXzwwQcxbdq0/NrnzZtXrIDMF198ESNGjIhTTz11u2sqzudTKp8hVatW3Sb0mcr94tJLL41f//rXKddC+imPe10q76XXX3894QyD5alKlSoVev5Ufl4LFy4sh0oqzvTp02PBggUJ2zRo0CBeeOGFpO+b4obkSU0q79M77rgjTjzxxHKoBgAAoPiEuwAAgFLVq1evOO6442L06NEJ23355ZcxatSo6Nu3b5FtUpkZa8aMGcUtsVS1atUqWrVqVWBfTk5OLFq0KGbPnh0ff/xxjBo1KuFDv3Xr1sWbb75ZogdKM2fOjJ49e6bUdtasWUnbNGrUaJt9qQRkEs2gtLUvv/wyaQguIyOj0IfvO4KMjIz8oNePrVmzJubOnRuzZs2KSZMmxZgxYxIuazV+/PjYsGFDgeXIqlWrFk2aNIlFixYV2W/hwoWxfPnyHS4cF/G/999hhx0Wr732WpFtRo4cGVdeeWX8+9//TjjWySefXKJaGjRoEL/4xS8KLLmZl5cXS5cujTlz5sSMGTNi7Nix8fHHHycc55VXXimXcNeP1alTJ3r37h29e/cusP/777+POXPmxOeffx5vvPFGvPvuuwnHeeWVV0oU7iru50IyDRs23GbfjnC/oOTK417XvHnz+PDDDxP2mzFjRtqEuypay5Ytk/683n///TjzzDPLqaLyl+zvHxFx3nnnpfSe+akH4SpKqvcI4S4AACBdmdcdAAAodVdddVVKSyo+8sgjsWXLliKPt2jRIurVq5dwjC+//DKlB7ipKM5sW4lUq1YtWrZsGYceemhceeWVMWrUqGjTpk3CPh999FGJzjlhwoSU2m3atCnee++9pO0KW46uS5cuSfsVZ6aoN954I2mbfffdNypVqpTymDuC2rVrx5577pk/69yjjz6asP3GjRsLDaV06tQp6bnGjBmz3XX+WGldG8WRLJQ1evTomDhxYixZsqTINllZWXHggQeWdmlRqVKlaNKkSXTv3j3OOeeceP755+O4445L2Kek13hpatiwYXTp0iVOP/30eOKJJ+Kiiy5K2P7jjz9OaanEosyaNSthEPHHUvksK+zzqVOnTkk/K/773/+mNJtTKirimiiJVD5HS/Ial5fyuNeV52drxI73XtraXnvtlbTNW2+9lfJnwI5o2bJlSdu0b98+aZvp06cXa3Y6UpfKdf3aa68Va1bORHb06xoAAEg/wl0AAECpy8rKihNOOCFpu2+//TbpA9JUghn33HNPyrUVZvny5XH33XfHH//4xxKNU5TatWtHr169Erb57rvvSnSO9957L6XZcUaOHBnZ2dlJ2+2zzz7b7DvooIOS9pszZ05Koa01a9bEiBEjkrZL5Zw7ugMPPDBpiLGwh72p/GweffTRWL169faWFps2bYq///3vFTLjyoEHHhhZWVlFHl+4cGHcfvvtCcfo379/wqVfS9MxxxyT8HhJr/GylKz2nJyclD43ipKXlxfPPPNM0nYrVqxIOhNbxP9Cn1urU6dOoUGdH8vJyYk///nPScdPZP78+XHTTTfF448/XqJxyluNGjWStinJa1xe0uVe99prryWdrS+ZCRMmxMknn7zDz9SUyoyEOTk5ceutt+4QAcLtkcp9NpUlmR966KHSKIdCtG/fPnbeeeeEbZYtWxZPPfVUic4za9as/F/sAAAAKE3CXQAAQJk4//zzo2rV5CvBP/roowkf9h1//PFJx5gwYULcfvvtCWcBK8z06dPjtttui969e8fQoUNj3bp1Rba9++6745prrolJkyZt18PJmTNnJjxe3Nq3lpubG7/97W9jzZo1RbaZM2dO3HvvvUnH6tKlS6FL+e2yyy7RuXPnpP1vueWWhA+r8/Ly4pZbbomlS5cmHKdy5cpx+OGHJz1fOjjuuOPioYceSrj8ZlEWLFiQ9MHw5s2bt9l39NFHR2ZmZsJ+y5Yti4suuqjYoY0FCxbEo48+GkcccUTceuutFTLjSuXKleOkk05K2Gb27NlFHqtatWqxllcaN25cnHPOOTF69OjYsGFDyv1+UNbXeCKffvppnHLKKfH8889vV5gvWe0RJa9/+PDh8f777xd5PDc3N26++eakAYhKlSrFYYcdVuixVO4Xzz77bAwbNixpu61re//99+P666+PPn36xPPPP59wKdV0VKdOnaRtpk6dmvAekg7K417Xpk2bpLP85OXlxWWXXVbsmUNXr14dI0aMiBNOOCEuuOCCmDZtWrH6p6MWLVpE165dk7Z744034qabbkr52lm5cmXcdNNN8cEHH5S0xDKXyvX10ksvJTz+0EMPpTwzHcVXqVKl+OUvf5m03QMPPBCvvPJKscbOycmJN998My677LI4/vjj4z//+Y+ZuwAAgFKX/EkLAADAdmjRokUce+yxMXLkyITtvvrqqxg7dmz84he/KPR4r169ol27dkkfoD7zzDPx4YcfxsCBA6NXr15Rq1atbdosW7Yspk+fHh9//HG89tpr8e2336b891m/fn2MGjUqRo0aFfXq1YsePXrEAQccEHvssUe0adMmateuXWi/2bNnx6OPPhoTJ05MOH6y2QRSMWPGjDj11FPjd7/7Xey///75y3Bt2rQpXnvttRg8eHBKS5IlmqXpsssuiwsuuCBh/8WLF8f//d//xbXXXhtHHXVUZGRk5B+bOXNm3H333fHOO+8kreOYY46J3XbbLWm7dDB//vwYMmRIDBkyJNq2bRs9e/aM7t27x2677RYtW7YsNOiYk5MTEydOjDvuuCNpcKaw90f9+vXjxBNPjH/84x8J+06ZMiWOPfbYGDhwYBxzzDGFjrV27dr49NNPY9q0afHWW2/F1KlT02KGlRNPPDEefvjhQsNtyRx66KHFuq62bNkSEydOjIkTJ0ZmZmZ07do1evbsGXvvvXe0adMmGjduXGi/5cuXxwsvvBAPP/xwwvFL4xovSl5eXnz88cfx8ccfx2233RadO3eOAw44IPbdd99o06ZNNG3atNBl+dasWROjRo1KOvthtWrVCg3BFEdOTk5ceOGFccUVV0T//v0LfGbOmjUr7rrrrnj33XeTjnPQQQdF69atCz12wgknxEMPPRTLly9POMZdd90VEyZMiHPOOSd69uxZaEhy4cKFMW3atJg6dWq89tprsXjx4qS1pbNq1arFzjvvnDBUm52dHaeeemqcdNJJ0apVq6hevXqB45mZmYXOdFXeyuNeN3DgwLjyyisT9l+2bFmceOKJccYZZ8SJJ54Yu++++zZtcnJyYtasWTFt2rSYNGlSvPXWWztcMDAVF154YdLvBhERL7zwQkydOjXOP//86N27d+y0004Fjm/YsCGmTZsWr7zySowePTrWrVsXxx57bFmVXWqaN2+etM0777wTV199dVx99dXRtGnT/P1z5syJBx54oFSX+qRwZ599dvztb39LeA1u3rw5fvOb38Srr74aZ5xxRuy7776FLjX/7bffxrRp0+LDDz+M1157rdSW/AUAACiKcBcAAFBmLrzwwhg9enTS315/5JFHok+fPoWGDypVqhS///3v4+yzz04aNpkxY0ZcddVVUbly5WjZsmX+UncrV67M/680rFy5MsaOHRtjx47N39ewYcOoW7du1KpVKzIzM2PDhg2xcOHCpCGDHySbJSRVs2bNirPPPjsaNGgQzZs3jy1btsScOXNSno2lRYsWceSRRxZ5vFevXtG9e/eYPHlywnGWLFkSgwYNipo1a8auu+4amZmZsXjx4pQDEtWqVYvLL788pbbp5ssvv4wvv/wyfxm6H0IVtWrVilq1akWlSpVi9erVMW/evJRmiMrIyIh27doVeuzXv/51/Oc//0n6UHHZsmVx5513xp133hlNmjSJxo0bR0ZGRqxatSpWrlwZy5cvT8tZJpo0aRK9evWK8ePHF7vvySefvN3n3bhxY37Q6wd16tSJBg0aRK1ataJmzZqxefPmWLZsWSxcuDClIFxpXePJ5OTkxIcffhgffvhh/r6aNWtGo0aN8mvPzc2N77//PhYsWJDSjFx77rlnoZ/PxbV+/foYPHhw3HfffdGqVauoVatWLFmypFjL0p133nlFHqtRo0Zce+21cf311ycd57333ov33nsvqlatGi1btoy6devG5s2bIzs7O5YvX572M1htj06dOiVdNnfWrFlxxx13FHosKysrpWV3y0NZ3+t+8YtfxLPPPptwtrmI/wXKhg0bFsOGDYu6detGs2bNokaNGrF27drIzs6O77//PnJycor1d9sR9erVK3r37p3S++Orr76K6667LipXrhwtWrSIevXqRV5eXqxcuTIWLVq0Q/68Dj744JTajR49OsaMGRNNmzaNnXfeOb777ruYN29eGVfHD5o2bRoXXnhhDBkyJGnbV199NV599dXIzMyMli1bRu3atWPTpk2xcuXKWLFiRcLZfgEAAMqCcBcAAFBmdttttzjqqKMKhKAKM3PmzBg/fnwcccQRhR7ff//946KLLopHHnkkpfPm5uYWa1au0vD999/H999/v119q1WrFn369CnVepYvX55ysOwHlSpVijvuuKPQGQp+7J577omTTz45paDWunXr4vPPPy9WHRERt99+e7Rq1arY/dJRTk7Odi3X+IPDDjtsm9lNflC/fv2455574oILLkh52bwlS5bEkiVLtrue8nbKKacUO9yVlZWV8sP2VK1evXq7ljz8QSpLBpaVdevWxdy5c7e7f2nXvmnTpmIvZxfxv5ncevbsmbBNv379YuLEiTFq1KiUxty8eXPC5T1/So444oi0CWeVlrK81919991xwgknxHfffZfSuNnZ2cVeAven5I477oiTTjop5s+fn1L73NzcmDNnTsyZM6eMKyt7LVq0iP333z9pGDDif7NELliwoNDvBVWrVo369evHsmXLyqJMIuKiiy6K999/P+kvKfxg48aN8eWXX5ZxVQAAAMlVrugCAACAn7aLL744pRlf/vKXvyQ8fsUVV8Rpp51WWmWllSuuuCLq169fojEuu+yyEtcxcODA6N69e9J2TZo0ib/+9a9Rp06dEp+zMJdffnn86le/KpOxdzQ1a9aMq6++OmGbgw46KAYPHlzo0o8/BQcffHA0a9asWH1OPPHEqFw5ff6XR69eveKwww6r6DK2yx577FGiWdAiIvr371/iZSlbtWoVv/3tb1Nqe/vtt8fhhx9eovP9FB177LHRqFGjii6jRMr7Xjds2LBo2LBhic/5c1C/fv146qmnUlqi8KfommuuKfF9+De/+U2Ry85SOqpWrRp/+ctf0mKJWQAAgOJIn//TCQAA/CR16NAhDj300KTtZsyYERMmTCjyeKVKleLmm2+OO++8M2rWrFmKFRY8R3k76aSTEi4zlqp+/frFDTfcsN39zzjjjKQhoh/r0KFDvPTSS7HXXntt9zm3VrNmzbjnnntK5eH9T0HNmjXjgQceiJYtWyZte/zxx8c//vGPlNruaCpXrhwnnnhiyu2rVKkSJ510UhlWVDydO3eOwYMHV3QZ26VVq1bx4IMPRkZGRonGadKkSTz55JPRuHHj7a7jmWeeidq1a6fUPiMjIx566KEYNGhQ0tmZtldF3C9Kqnr16nHPPfdElSpVKrqU7Vbe97r27dvHyy+/HAceeOB2nzOZHfG9VJQWLVrEyy+/HL/85S8rupRyt9dee8Uf/vCH7e5/5plnlsr3QZKrU6dODB8+PAYMGFBm199P6bo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