From 7608ee0751dd9f1194c5372b7b246712083200ff Mon Sep 17 00:00:00 2001 From: Amanda Kube Date: Tue, 15 Aug 2023 14:29:36 -0500 Subject: [PATCH] edits to ch11 --- ...b => Probability_1_RulesDefinitions.ipynb} | 105 +++-- textbook/11/1/img/complement.png | Bin 86814 -> 77136 bytes textbook/11/1/img/conditionalprobability.png | Bin 133000 -> 115901 bytes textbook/11/1/img/intersection.png | Bin 127590 -> 112964 bytes textbook/11/1/img/union.png | Bin 128424 -> 121075 bytes ...=> Probability_2_SimulationSolution.ipynb} | 75 +++- textbook/11/3/Math_vs_Computation.ipynb | 234 ---------- .../3/Probability_3_MathVsComputation.ipynb | 233 ++++++++++ .../4/Birthday_Pb_Relaxed_Assumptions.ipynb | 417 ----------------- ...lity_4_BirthdayPb_RelaxedAssumptions.ipynb | 420 ++++++++++++++++++ textbook/11/4/US_births_2000-2014_SSA.csv | 1 + textbook/11/Probability.ipynb | 290 ------------ textbook/11/Probability_Intro.ipynb | 294 ++++++++++++ 13 files changed, 1050 insertions(+), 1019 deletions(-) rename textbook/11/1/{Rules_Definitions.ipynb => Probability_1_RulesDefinitions.ipynb} (72%) rename textbook/11/2/{Simulation_Solution.ipynb => Probability_2_SimulationSolution.ipynb} (79%) delete mode 100644 textbook/11/3/Math_vs_Computation.ipynb create mode 100644 textbook/11/3/Probability_3_MathVsComputation.ipynb delete mode 100644 textbook/11/4/Birthday_Pb_Relaxed_Assumptions.ipynb create mode 100644 textbook/11/4/Probability_4_BirthdayPb_RelaxedAssumptions.ipynb create mode 100755 textbook/11/4/US_births_2000-2014_SSA.csv delete mode 100644 textbook/11/Probability.ipynb create mode 100644 textbook/11/Probability_Intro.ipynb diff --git a/textbook/11/1/Rules_Definitions.ipynb b/textbook/11/1/Probability_1_RulesDefinitions.ipynb similarity index 72% rename from textbook/11/1/Rules_Definitions.ipynb rename to textbook/11/1/Probability_1_RulesDefinitions.ipynb index faf12717..3d3bd6dd 100644 --- a/textbook/11/1/Rules_Definitions.ipynb +++ b/textbook/11/1/Probability_1_RulesDefinitions.ipynb @@ -4,9 +4,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Probability: Definitions and Rules \n", + "# Probability: Definitions and Rules \n", "\n", - "The intention here is not to have a comprehensive introduction to probability, but just to provide a reminder of the basic definitions and rules. Every statistics textbook has a chapter on probability that is more complete than this section. We encourage the readers who have not encounter the concept of probability to find a good introductory chapter, and we offer a suggestion/reference at the end of this section.\n", + "The intention here is not to have a comprehensive introduction to probability, but just to provide a reminder of the basic definitions and rules. Every statistics textbook has a chapter on probability that is more complete than this section. We encourage the readers who have not encountered the concept of probability to find a good introductory chapter, and we offer a suggestion/reference at the end of this section.\n", "\n", "We start with some basic definitions illustrated on three examples:\n", "\n", @@ -26,52 +26,60 @@ "3. Having at least two people sharing birthdays.\n", "\n", "**Mutually exclusive events**: Events $A$ and $B$ are mutually exclusive (or disjoint) if they have no outcomes in common. Examples:\n", - "1. A is as above and B is rolling a 3.\n", - "2. A is as above and B is the event that the number of boys is between 60 and 70. \n", - "3. A is as above and B is the event that there is a birthday to celebrate for every day in March." + "1. A is as above (rolling an even number) and B is rolling a 3.\n", + "2. A is as above (less than half of the babies are boys) and B is the event that the number of boys is between 60 and 70. \n", + "3. A is as above (t least two people share birthdays) and B is the event that there is a birthday to celebrate for every day in the month of March.\n", + "\n", + "\n", + "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "**Complement of an event**: The complement of an event $A$ is the event that $A$ does not occur, denoted by $A^C$. For the events $A$ defined above:\n", - "1. $A^C$ is rolling an odd number: $A^C=\\{1,3,5\\}$ \n", - "2. $A^C$ is the event that more than half of the babies are boys, or the set of integers from 50 to 100.\n", - "3. $A^C$ is the event when there are no shared birthdays.\n", "\n", - "" + "**Complement of an event**: The complement of an event $A$ is the event that $A$ does not occur, denoted by $A^C$. \n", + "\n", + "\n", + "\n", + "For the events $A$ defined above:\n", + "1. $A$ is as above (rolling an even number): $A^C$ is rolling an odd number: $A^C=\\{1,3,5\\}$ \n", + "2. $A$ is as above (less than half of the babies are boys): $A^C$ is the event that more than half of the babies are boys, or the set of integers from 50 to 100.\n", + "3. $A$ is as above (t least two people share birthdays): $A^C$ is the event when there are no shared birthdays.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "**Compound events**: Events built from combinations of other events.\n", + "\n", + "**Compound events**: Events built from combinations of other events; for example, union and intersection.\n", "\n", "**Union:** ($A$ or $B$) = ($A\\cup B$): set of all outcomes in $A$, or in $B$, or in both.\n", "\n", - "" + "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ + "\n", "**Intersection:** ($A$ and $B$) = ($A\\cap B$): set of all outcomes that are in $A$ and in $B$.\n", "\n", - "" + "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Definition of Probability\n", + "### Definition of Probability\n", "\n", "Probabilities describe how likely events are and so probability models consist of:\n", "- A list of possible outcomes (sample space)\n", - "- An assignment of probabilities $P$\n", + "- An assignment of probabilities $P$ for each possible outcome\n", "\n", "The **frequentist interpretation of the probability** of an event $A$, $\\mbox{P}(A)$, is the long run relative frequency of the event $A$. Suppose you are interested in the probability of \"Heads\" when tossing a coin. In this frequentist interpretation, probability is given by the limit of the relative frequency of \"Heads\" when tossing the coin repeatedly. Note that while you can imagine repeating the coin toss for a large number of times (and some people have done it!), there are other events where the intutition behind frequentists probabilities are not as evident. For example, what is the probability that it will rain next Sunday? This where the **Bayesian interpretation** of probability - based on a subjective degree of belief - is more natural. In the Bayesian world, two people could have different viewpoints and assign different probabilities. \n", "\n", @@ -82,42 +90,41 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Basic Probability Rules\n", - "- $0 \\le \\mbox{P}(A) \\le 1$, for any event $A$\n", + "### Basic Probability Rules\n", "\n", - "- $\\mbox{P}(S) = 1$\n", + "Given a sample space S and events $A, B \\subseteq S$, we have:\n", "\n", - "- **Equally likely outcomes**:\n", - "$P(A)=\\frac{\\mbox{ Number of outcomes in A}}{\\mbox{ Total number of outcomes}}$\n", + "- $0 \\le \\mbox{P}(A) \\le 1$\n", + "\n", + "- $\\mbox{P}(S) = 1$\n", "\n", - "- $\\mbox{P}(E^C) = 1 - \\mbox{P}(E)$ for any event $E$\n", + "- $\\mbox{P}(A^C) = 1 - \\mbox{P}(A)$\n", "\n", "- $\\mbox{P}(A \\cup B) = \\mbox{P}(A) +\n", "\\mbox{P}(B) - \\mbox{P}(A \\cap B)$\n", "\n", + "- **Equally likely outcomes**:\n", + "$$P(A)=\\frac{\\mbox{ Number of outcomes in A}}{\\mbox{ Total number of outcomes}}$$\n", "\n", - "\n", - "\n", - "\n" + "The last rule refers to situations where all outcomes of an experiment are equally likely (for example, roll a fair die).\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Conditional Probability\n", - "\n", - "If $\\mbox{P}(A) \\ne 0$, the conditional probability of event $B$\n", - "given $A$ has occurred, denoted by $\\mbox{P}(B|A)$, is defined by,\n", - "$ \\mbox{P}(B|A) = \\frac{\\mbox{P}(A \\mbox{ and } B)}{\\mbox{P}(A)}$\n", + "### Conditional Probability\n", + "If $\\mbox{P}(B) \\ne 0$, the conditional probability of event $A$\n", + "given $B$ has occurred, denoted by $\\mbox{P}(A|B)$, is defined by,\n", + "$$ \\mbox{P}(A|B) = \\frac{\\mbox{P}(A \\mbox{ and } B)}{\\mbox{P}(B)}$$\n", "\n", "\n", "\n", "Example:\n", "- Select one subject at random in US;\n", - "- B is the event that the subject read a book last week;\n", - "- A is the event that the subject is a college student;\n", - "- Consider P(B|A) versus P(B): the fraction of college students who read a book last week is likely different than the fraction of US population who did that.\n", + "- A is the event that the subject read a book last week;\n", + "- B is the event that the subject is a college student;\n", + "- Consider P(A|B) versus P(A): the fraction of college students who read a book last week is likely different than the fraction of US population who did that.\n", "\n", "**Multiplication rule**: $\\mbox{P}(A \\mbox{ and } B) = \\mbox{P}(A|B) \\mbox{P}(B)$. Note that this follows directly from the definition of conditional probability." ] @@ -126,21 +133,19 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Independence\n", + "### Independence\n", "\n", "Events $A$ and $B$ are called independent if $\\mbox{P}(A|B) =\n", "\\mbox{P}(A)$ (or equivalently, $\\mbox{P}(B|A) = \\mbox{P}(B)$)\n", "\n", "Equivalent condition for **independence**: \n", - "$\\mbox{P}(A \\mbox{ and } B) = \\mbox{P}(A) \\mbox{P}(B)$\n", + "$$\\mbox{P}(A \\mbox{ and } B) = \\mbox{P}(A) \\mbox{P}(B)$$\n", "\n", "### The Bayes Theorem\n", "\n", "The following property follows directly from the definition of conditional independence and the multiplication rule:\n", "\n", - "\\begin{eqnarray}\n", - "\\mbox{P}(A|B) & = & \\frac{\\mbox{P}(B|A) \\mbox{P}(A)}{\\mbox{P}(B)} \\nonumber\n", - "\\end{eqnarray}\n", + "$$\\mbox{P}(A|B) = \\frac{\\mbox{P}(B|A) \\mbox{P}(A)}{\\mbox{P}(B)}$$\n", "\n", "This is one of the most important rules in statistics and data science because it describes statistical learning, and provides a way to update a belief (probability) given additional evidence (data)." ] @@ -149,33 +154,23 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## The solution to the birthday problem\n", + "### The solution to the birthday problem\n", "\n", "We will use the **equally likely outcomes** formula from the Basic Probability Rules above. Note that, for $n$ random subjects, the total number of outcomes (number of possible combination of birthdays) is \n", - "\n", "$$365^n.$$\n", "\n", "The number of outcomes that lead to a set of distinct birthdays is\n", - "\n", "$$365\\times364\\times ...\\times (365-n+1)$$\n", - "\n", "and the intuition comes from the way we can count the total number of distinct birthdays as follows:\n", "- suppose you look at people sequentially;\n", - "- first person can have any of the 365 birthdays without leading to mathched birthdays;\n", + "- first person can have any of the 365 birthdays without leading to matched birthdays;\n", "- the second can have any of birthdays except the one of the first person: so 364 possibilities;\n", "- the $n$-th person can have any of birthdays except any of the (n-1) different birthdays of the other people: so (365-n+1) possibilities.\n", "\n", - "So the probability of having $n$ distinct birtdays is:\n", - "\n", - "$$\n", - "\\frac{365\\times364\\times ...\\times (365-n+1)}{365^n}\n", - "$$\n", - "\n", + "So the probability of having $n$ distinct birthdays is:\n", + "$$\\frac{365\\times364\\times ...\\times (365-n+1)}{365^n}$$\n", "The complement of this event is the event of interest (at least two people share birthdays) and so the probability of interest is:\n", - "\n", - "$$\n", - "P_n ~=~ 1-\\frac{365\\times364\\times ...\\times (365-n+1)}{365^n}\n", - "$$\n", + "$$P_n ~=~ 1-\\frac{365\\times364\\times ...\\times (365-n+1)}{365^n}$$\n", "\n", "**Reference.**\n", "\n", @@ -185,7 +180,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3 (ipykernel)", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -199,9 +194,9 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.10.6" + "version": "3.8.8" } }, "nbformat": 4, - "nbformat_minor": 4 + "nbformat_minor": 2 } diff --git a/textbook/11/1/img/complement.png b/textbook/11/1/img/complement.png index 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"outputs": [], "source": [ - "import numpy as np" + "import numpy as np\n", + "import pandas as pd\n", + "\n", + "%matplotlib inline\n", + "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "# A simulation-based solution\n", + "# A simulation-based solution\n", "\n", - "Simulations are used to imitate real-world scenarios. They can have many roles, ranging from obtaining insight into a physical system to testing and training of models and algorithms. In this chapter, we will use simulations to estimate probabilities. We will explore other applications later, such as gaining insight into probability distributions.\n", + "We have introduced the concept of simulation in Section 5.3 (we simulated the output of rolling a six-sided die). Simulations are used to imitate real-world scenarios. They can have many roles, ranging from obtaining insight into a physical system to testing and training of models and algorithms. In this chapter, we will use simulations to estimate probabilities. We will explore other applications later, such as gaining insight into probability distributions.\n", "\n", "Here we use the computer to run/execute our simulations and we will develop code that will allow us to do that. There are several steps in designing and executing a simulation:\n", "- Conceptualize what to simulate;\n", @@ -31,7 +35,7 @@ "- Simulations will give us only an estimate/approximation of the probability we are interested in; the more repetitions, the better the approximation.\n", "- The number of repetitions is important and strategies for selecting them will be discussed in more detail later in the chapter.\n", "\n", - "## Conceptualize and simulate one instance\n", + "### Conceptualize and simulate one instance\n", "\n", "In the birthday problem described at the beginning of this chapter (30 people at a party), the only information that is needed for deciding on matching birthdays is the set of birthdates. The simulation we will construct will focus on that - we just need a function that generates 30 random birthdays. It turns out we have already seen a function in `numpy` that can do that: `random.choice`.\n", "\n", @@ -46,9 +50,9 @@ { "data": { "text/plain": [ - "array([ 48, 240, 100, 295, 177, 359, 107, 96, 255, 100, 126, 217, 271,\n", - " 224, 209, 172, 71, 361, 319, 73, 346, 73, 208, 166, 305, 75,\n", - " 197, 114, 126, 178])" + "array([353, 265, 326, 356, 124, 329, 122, 304, 144, 176, 268, 93, 117,\n", + " 178, 215, 112, 76, 120, 231, 139, 142, 227, 110, 295, 159, 210,\n", + " 77, 6, 159, 42])" ] }, "execution_count": 2, @@ -78,9 +82,9 @@ { "data": { "text/plain": [ - "array([ 48, 71, 73, 73, 75, 96, 100, 100, 107, 114, 126, 126, 166,\n", - " 172, 177, 178, 197, 208, 209, 217, 224, 240, 255, 271, 295, 305,\n", - " 319, 346, 359, 361])" + "array([ 6, 42, 76, 77, 93, 110, 112, 117, 120, 122, 124, 139, 142,\n", + " 144, 159, 159, 176, 178, 210, 215, 227, 231, 265, 268, 295, 304,\n", + " 326, 329, 353, 356])" ] }, "execution_count": 3, @@ -176,7 +180,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Repeated simulations and summary\n", + "### Repeated simulations and summary\n", "\n", "We now create a function that will simulate **nrep** repetitions of the \n", "birthday setting for **n** subjects. The function returns an array that has **nrep** entries, each showing the count (frequency) of the most frequent birthday in one simulation." @@ -207,7 +211,7 @@ { "data": { "text/plain": [ - "array([1., 2., 2., 2., 2., 2., 1., 1., 1., 1.])" + "array([1., 2., 1., 1., 1., 2., 1., 2., 2., 2.])" ] }, "execution_count": 8, @@ -227,11 +231,9 @@ "\n", "We are ready now to estimate the probability that at least two people share a birthday in a group of n random subjects. In a similar fashion to the coin toss example where the probability of heads was given by the long run frequency (number of heads / number of tosses), the estimated probability is \n", "\n", - "$$\n", - "\\frac{\\mbox{number of repetitions with shared birthdays}}{\\mbox{nrep}}\n", - "$$\n", + "$$\\frac{\\mbox{number of repetitions with shared birthdays}}{\\mbox{nrep}}$$\n", "\n", - "As mentioned above, the number of repetitions affects both accuracy (better accuracy for more repetitions) and computational time. Section ?? provides more details on this issue. In the cell code below we use 1000 repetitions." + "As mentioned above, the number of repetitions affects both accuracy (better accuracy for more repetitions) and computational time. Chapter 12 provides more details on this issue. In the cell code below we use 1000 repetitions." ] }, { @@ -242,7 +244,7 @@ { "data": { "text/plain": [ - "0.488" + "0.486" ] }, "execution_count": 9, @@ -260,9 +262,36 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Note that the result we obtain is close but not equal to the probability we calculated at the beginning of this chapter (0.5073). Increasing the number of repetitions will lead to an estimate that is closer to the exact probability.\n", - "\n", - "## On the assumptions used in simulations\n", + "Note that the result we obtain is close but not equal to the probability we calculated at the beginning of this chapter (0.5073). Increasing the number of repetitions will lead to an estimate that is closer to the exact probability. Also, rerunning the above cell will lead to a (slightly) different result:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.514" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "n=23\n", + "nrep=1000\n", + "sum(birthday_sim(n,nrep)>=2)/nrep" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### On the assumptions used in simulations\n", "\n", "It is important to consider whether the assumptions made in the simulations are the same or different than the ones we made in the mathematical derivation. The answer is yes (same assumptions) because: (i) the `birthdays` array has 365 elements (so we implicitly assume the year has 365 days); and (ii) birthdates are independent and equally likely (because the `numpy` `random.choice` function is designed to sample elements this way when only sample size is provided). \n", "\n", @@ -272,7 +301,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3 (ipykernel)", + "display_name": "Python 3", "language": "python", "name": "python3" }, @@ -286,9 +315,9 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.10.6" + "version": "3.8.8" } }, "nbformat": 4, - "nbformat_minor": 4 + "nbformat_minor": 2 } diff --git a/textbook/11/3/Math_vs_Computation.ipynb b/textbook/11/3/Math_vs_Computation.ipynb deleted file mode 100644 index 9be5c053..00000000 --- a/textbook/11/3/Math_vs_Computation.ipynb +++ /dev/null @@ -1,234 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "tags": [ - "remove-cell" - ] - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "import pandas as pd\n", - "\n", - "import matplotlib.pyplot as plots\n", - "\n", - "plots.style.use('fivethirtyeight')\n", - "\n", - "from collections import Counter\n", - "\n", - "birthdays=np.arange(1,366,1)\n", - "\n", - "def birthday_sim(n,nrep):\n", - " '''Estimate birthday matching probabilities using nrep simulations'''\n", - " outcomes = np.array([])\n", - " for i in np.arange(nrep):\n", - " outcomes = np.append(outcomes, \n", - " Counter(np.random.choice(birthdays,n)).most_common(1)[0][1])\n", - " return outcomes" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Mathematical derivation versus computational estimation\n", - "\n", - "We illustrated in the previous sections how to approach a simple problem using either mathematics or simulations (a computational solution).\n", - "There are many examples of scientitfic problems where advances have been made using either computational or mathematical solutions or both. For example, in meteorology (**expand here**):\n", - "- Mathematical models of precipitation levels\n", - "- Simulations of local weather patterns\n", - "\n", - "The debate of the merits of these two approaches is beyond the scope of this textbook (but it can lead to a stimulating classroom discussion), but we would like to note that there are problems where analytical derivations are preferred and problems where computational solutions are optimal. For example, when calculating the probability of winning a lottery where the number of combinations is very large (for example, hundreds of millions), a mathematical derivation works better because the estimation of very rare events require an enormous number of repetitions. Below we show a generalization of the birthday problem where the code is almost identical to what we introduced above, while a mathematical derivation is a lot more difficult.\n", - "\n", - "## The triplets problem\n", - "\n", - "Given a number of people, $n$, what is the probability that at least three share a birthday? Assumptions are the same as before:\n", - "\n", - "a. 365 days in a year.\n", - "\n", - "b. All days are equally likely.\n", - "\n", - "c. Subjects have independent birthdays.\n", - "\n", - "The exact formula for this probability is a lot more complicated than the one for the classical birthday problem (see reference below). Recall that we solved the birthday problem by focusing on the complement of the event of interest. The complement in the context of the triplets problem is as complicated as the event itself.\n", - "\n", - "The next cell constructs a data frame with the estimated probabilities for $n$ ranging from 40 to 120; the range was selected to illustrate how probabilities are different than in the previous section.\n", - "\n", - "Note that the only difference in the code is when we count the number of repetitions where the most frequent birthday count is larger or equal to 3." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "

" - ], - "text/plain": [ - " Number of people Triplet Probability\n", - "76 116 0.789\n", - "77 117 0.797\n", - "78 118 0.807\n", - "79 119 0.844\n", - "80 120 0.824" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "nrep=1000\n", - "number_people=np.arange(40,121,1)\n", - "probs3= np.array([])\n", - "for i in number_people: probs3= np.append(probs3,sum(birthday_sim(i,nrep)>=3)/nrep)\n", - "\n", - "Birthday3_df=pd.DataFrame(\n", - " {\"Number of people\":number_people,\n", - " \"Triplet Probability\":probs3})\n", - "\n", - "Birthday3_df.tail(5)" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": { - "scrolled": true - }, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "Birthday3_df.plot.scatter(\"Number of people\",\"Triplet Probability\");" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "If you want to obtain a smoother curve (reflecting a more accurate estimation of probabilities) you need to increase the number of simulations. Play with the code and see how the number of simulations affects the smoothness of the function!\n", - "\n", - "Note that for triplets, the number of people that yields a probability closest to 0.5 is 87." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "0.4915" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "n=87\n", - "nrep=10000\n", - "sum(birthday_sim(n,nrep)>=3)/nrep" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Reference for the triplets problem:\n", - "\n", - "DasGupta A (2005) The matching, birthday and the strong birthday problem: a contemporary review. Journal of Statistical Planning and Inference, Volume 130, Issues 1–2, 377-389." - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "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": "3.10.6" - } - }, - "nbformat": 4, - "nbformat_minor": 4 -} diff --git a/textbook/11/3/Probability_3_MathVsComputation.ipynb b/textbook/11/3/Probability_3_MathVsComputation.ipynb new file mode 100644 index 00000000..adc97ed7 --- /dev/null +++ b/textbook/11/3/Probability_3_MathVsComputation.ipynb @@ -0,0 +1,233 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [ + "remove-cell" + ] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "\n", + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from collections import Counter\n", + "\n", + "birthdays=np.arange(1,366,1)\n", + "def birthday_sim(n,nrep):\n", + " '''Estimate birthday matching probabilities using nrep simulations'''\n", + " outcomes = np.array([])\n", + " for i in np.arange(nrep):\n", + " outcomes = np.append(outcomes, \n", + " Counter(np.random.choice(birthdays,n)).most_common(1)[0][1])\n", + " return outcomes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Mathematical derivation versus computational estimation\n", + "\n", + "We illustrated in the previous sections how to approach a simple problem using either mathematics or simulations (a computational solution).\n", + "There are many examples of scientitfic problems where advances have been made using either computational or mathematical solutions or both. For example, both approaches are used in meteorology where mathematical models are used for precipitation levels, and simulations are run to predict local weather patterns.\n", + "\n", + "The debate of the merits of these two approaches is beyond the scope of this textbook (and it can lead to a stimulating classroom discussion), but we would like to note that there are problems where analytical derivations are preferred and problems where computational solutions are optimal. For example, when calculating the probability of winning a lottery where the number of combinations is very large (for example, hundreds of millions), a mathematical derivation works better because the estimation of very rare events require an enormous number of repetitions. Below we show a generalization of the birthday problem where the code is almost identical to what we introduced above, while a mathematical derivation is a lot more difficult.\n", + "\n", + "#### The triplets problem\n", + "\n", + "Given a number of people, $n$, what is the probability that at least three share a birthday? Assumptions are the same as before:\n", + "\n", + "a. 365 days in a year.\n", + "\n", + "b. All days are equally likely.\n", + "\n", + "c. Subjects have independent birthdays.\n", + "\n", + "The exact formula for this probability is a lot more complicated than the one for the classical birthday problem (see reference below). Recall that we solved the birthday problem by focusing on the complement of the event of interest. The complement in the context of the triplets problem is as complicated as the event itself.\n", + "\n", + "\n", + "The next cell constructs a data frame with the estimated probabilities for $n$ ranging from 40 to 120; the range was selected to illustrate how probabilities are different than in the previous section.\n", + "\n", + "Note that the only difference in the code is when we count the number of repetitions where the most frequent birthday count is larger or equal to 3.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " Number of people Triplet Probability\n", + "76 116 0.779\n", + "77 117 0.812\n", + "78 118 0.847\n", + "79 119 0.821\n", + "80 120 0.823" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "nrep=1000\n", + "number_people=np.arange(40,121,1)\n", + "probs3= np.array([])\n", + "for i in number_people: probs3= np.append(probs3,sum(birthday_sim(i,nrep)>=3)/nrep)\n", + "\n", + "Birthday3_df=pd.DataFrame(\n", + " {\"Number of people\":number_people,\n", + " \"Triplet Probability\":probs3})\n", + "\n", + "Birthday3_df.tail(5)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "Birthday3_df.plot.scatter(\"Number of people\",\"Triplet Probability\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "If you want to obtain a smoother curve (reflecting a more accurate estimation of probabilities) you need to increase the number of simulations. Play with the code and see how the number of simulations affects the smoothness of the function!\n", + "\n", + "Note that for triplets, the number of people that yields a probability closest to 0.5 is 87." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.4891" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "n=87\n", + "nrep=10000\n", + "sum(birthday_sim(n,nrep)>=3)/nrep" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Reference for the triplets problem:**\n", + "\n", + "DasGupta A (2005) The matching, birthday and the strong birthday problem: a contemporary review. Journal of Statistical Planning and Inference, Volume 130, Issues 1–2, 377-389." + ] + } + ], + "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": "3.8.8" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/textbook/11/4/Birthday_Pb_Relaxed_Assumptions.ipynb b/textbook/11/4/Birthday_Pb_Relaxed_Assumptions.ipynb deleted file mode 100644 index 9b8cca09..00000000 --- a/textbook/11/4/Birthday_Pb_Relaxed_Assumptions.ipynb +++ /dev/null @@ -1,417 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "tags": [ - "remove-cell" - ] - }, - "outputs": [], - "source": [ - "from collections import Counter\n", - "\n", - "import numpy as np\n", - "import pandas as pd\n", - "\n", - "import matplotlib.pyplot as plots\n", - "\n", - "plots.style.use('fivethirtyeight')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# The birthday problem: relaxed assumptions\n", - "\n", - "There are two assumptions we used in the last few sections while investigating the birthday problem - equally likely birthdates and ignoring February 29 as a possible birth date. While relaxing these can complicate the mathematical calculation, the simulations can be easily modified to account for more complicated scenarios.\n", - "\n", - "We use below a dataset from FiveThirtyEight that contains the number of daily births in US between 2000 and 2014 to estimate the odds of each day of the year to be a birthday:\n", - "\n", - "https://github.com/fivethirtyeight/data/tree/master/births\n", - "\n", - "Note that in the following dataset, the variable for day of week is coded 1 for Monday and 7 for Sunday. Also note that there are four leap years in this dataset - finding the correct probability for being born in a leap year is beyond the scope of this section." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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5479 rows × 5 columns

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" - ], - "text/plain": [ - " year month date_of_month day_of_week births\n", - "0 2000 1 1 6 9083\n", - "1 2000 1 2 7 8006\n", - "2 2000 1 3 1 11363\n", - "3 2000 1 4 2 13032\n", - "4 2000 1 5 3 12558\n", - "... ... ... ... ... ...\n", - "5474 2014 12 27 6 8656\n", - "5475 2014 12 28 7 7724\n", - "5476 2014 12 29 1 12811\n", - "5477 2014 12 30 2 13634\n", - "5478 2014 12 31 3 11990\n", - "\n", - "[5479 rows x 5 columns]" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "birth_data = pd.read_csv(\n", - " \"https://raw.githubusercontent.com\"\n", - " \"/fivethirtyeight/data/18a5be518548601fdc77176481da105573ef704f/births/US_births_2000-2014_SSA.csv\",\n", - ")\n", - "\n", - "birth_data" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This is an interesting dataset and we encourage you to use it to answer questions like: what is the least frequent day of the week for giving birth?\n", - "\n", - "The `pandas` library has commands that allow you to group rows by unique values in a column. We used it before and we will use it below. You will learn more about it in Section ???." - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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births
monthdate_of_month
11116030
2144083
3170115
4171663
5166682
\n", - "
" - ], - "text/plain": [ - " births\n", - "month date_of_month \n", - "1 1 116030\n", - " 2 144083\n", - " 3 170115\n", - " 4 171663\n", - " 5 166682" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "counts_df=birth_data.groupby(['month','date_of_month']).sum()[['births']]\n", - "counts_df.head(5)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We see that there were 116,030 births on January 1st, 144,083 (much larger! why?) on January 2nd etc. A histogram of the counts in the above data frame:" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "counts_df.hist(\"births\",bins = np.arange(116000, 195000, 2000));" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Note that some days of the year are outliers in number of births. Can you guess which?\n", - "\n", - "We will use these counts to estimate the probability that a given date is a birthday for a random US subject." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [], - "source": [ - "bday_probs=counts_df.births/sum(counts_df.births)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "These probabilities are added to the simulation when using the `random.choice` function. Look at the function below and compare it to the `birthday_sim` function introduced in Section ???." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [], - "source": [ - "# adding February 29 - the number of possible birthdays is now 366\n", - "birthdays2=np.arange(1,367,1)\n", - "\n", - "def birthday_sim2(n,nrep,pr):\n", - " '''Estimate birthday matching probabilities using nrep simulations.\n", - " The 366 possible birthdays are weighted by given probabilities'''\n", - " outcomes = np.array([])\n", - " for i in np.arange(nrep):\n", - " outcomes = np.append(outcomes,\n", - " Counter(np.random.choice(birthdays2,n,p=pr)).most_common(1)[0][1])\n", - " return outcomes" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We calculate below the probability for the case $n=23$ using these relaxed assumptions. Before running the cell or reading its output, do you think the probabililty will be higher or lower? " - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "0.51041" - ] - }, - "execution_count": 7, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "n=23\n", - "nrep=100000\n", - "sum(birthday_sim2(n,nrep,bday_probs)>1)/nrep" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**Note**: more accurate simulation experiments do not always lead to different results - but we do not know that before performing them!\n", - "\n", - "We will continue to investigate the issue of analytical and computation approaches throughout this textbook.\n" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "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": "3.10.6" - } - }, - "nbformat": 4, - "nbformat_minor": 4 -} diff --git a/textbook/11/4/Probability_4_BirthdayPb_RelaxedAssumptions.ipynb b/textbook/11/4/Probability_4_BirthdayPb_RelaxedAssumptions.ipynb new file mode 100644 index 00000000..df2903bf --- /dev/null +++ b/textbook/11/4/Probability_4_BirthdayPb_RelaxedAssumptions.ipynb @@ -0,0 +1,420 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [ + "remove-cell" + ] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "\n", + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from collections import Counter" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# The birthday problem: relaxed assumptions\n", + "\n", + "There are two assumptions we used in the last few sections while investigating the birthday problem - equally likely birthdates and ignoring February 29 as a possible birth date. While relaxing these can complicate the mathematical calculation, the simulations can be easily modified to account for more complicated scenarios.\n", + "\n", + "We use below a dataset from FiveThirtyEight that contains the number of daily births in US between 2000 and 2014 to estimate the odds of each day of the year to be a birthday:\n", + "\n", + "https://github.com/fivethirtyeight/data/tree/master/births\n", + "\n", + "Note that in the following dataset, the variable for day of week is coded 1 for Monday and 7 for Sunday. Also note that there are four leap years in this dataset - finding the correct probability for being born in a leap year is beyond the scope of this section." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " year month date_of_month day_of_week births\n", + "0 2000 1 1 6 9083\n", + "1 2000 1 2 7 8006\n", + "2 2000 1 3 1 11363\n", + "3 2000 1 4 2 13032\n", + "4 2000 1 5 3 12558\n", + "... ... ... ... ... ...\n", + "5474 2014 12 27 6 8656\n", + "5475 2014 12 28 7 7724\n", + "5476 2014 12 29 1 12811\n", + "5477 2014 12 30 2 13634\n", + "5478 2014 12 31 3 11990\n", + "\n", + "[5479 rows x 5 columns]" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "birth_data = pd.read_csv(\"US_births_2000-2014_SSA.csv\")\n", + "birth_data" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is an interesting dataset and we encourage you to use it to answer questions like: what is the least frequent day of the week for giving birth?\n", + "\n", + "The `pandas` library has commands that allow you to group rows by unique values in a column. We introduced it in Chapter 7." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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\n", + "
" + ], + "text/plain": [ + " births\n", + "month date_of_month \n", + "1 1 116030\n", + " 2 144083\n", + " 3 170115\n", + " 4 171663\n", + " 5 166682" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "counts_df=birth_data.groupby(['month','date_of_month']).sum()[['births']]\n", + "counts_df.head(5)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "scrolled": true + }, + "source": [ + "We see that there were 116,030 births on January 1st, 144,083 (much larger! why?) on January 2nd etc. A histogram of the counts in the above data frame:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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kr6ELeemnDHCN0/voziU/ZaDtYfrfwyQBnjiw7aGB5UcH1h/lsfP4TJ8Pouim//yTqjq7v51RVVN/AH40S30zTRk6ipmef7rZnnPK4Gt9hCOvbyPwfuD5wN5+hkEJMMA1RlX1PbrTA5cONO+nCyfovvXk2Hkc+uIkT+jPiz8LuB/4FPBHSY4FSPKLSZ4y10HoRuov6c9br6GbXe6zIzz/OUnO6M99/wEwyqT+/zdV22z6451eVTcBbwVOAJ46wrG1ShjgGrf30p0XnnIVXWjeCryA4SPVmdxPF7T/Dryxqn4MfJBu5rjb+4/o/QNDZt+sqgPA24Cb6L7/8Paqum6E578F2EY31e0DwCdH2Gc7cOfAm5gzWQN8JMldwBeBv6tpn2rR6uZshJLUKEfgktQoA1ySGmWAS1KjDHBJapQBLkmNMsAlqVEGuCQ16v8BxXhP7wfv1rcAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.hist(counts_df.births,bins = np.arange(116000, 195000, 2000))\n", + "plt.xticks(ticks=[130000,150000,170000,190000], labels=[\"130K\",\"150K\",\"170K\",\"190K\"])\n", + "plt.xlabel(\"Number of births\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that some days of the year are outliers in number of births. Can you guess which?\n", + "\n", + "We will use these counts to estimate the probability that a given date is a birthday for a random US subject." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "bday_probs=counts_df.births/sum(counts_df.births)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "These probabilities are added to the simulation when using the `random.choice` function. Look at the function below and compare it to the `birthday_sim` function introduced in Section 11.2." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "# adding February 29 - the number of possible birthdays is now 366\n", + "birthdays2=np.arange(1,367,1)\n", + "\n", + "def birthday_sim2(n,nrep,pr):\n", + " '''Estimate birthday matching probabilities using nrep simulations.\n", + " The 366 possible birthdays are weighted by given probabilities'''\n", + " outcomes = np.array([])\n", + " for i in np.arange(nrep):\n", + " outcomes = np.append(outcomes,\n", + " Counter(np.random.choice(birthdays2,n,p=pr)).most_common(1)[0][1])\n", + " return outcomes" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We calculate below the probability for the case $n=23$ using these relaxed assumptions. Before running the cell or reading its output, do you think the probabililty will be higher or lower? " + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.50538" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "n=23\n", + "nrep=100000\n", + "sum(birthday_sim2(n,nrep,bday_probs)>1)/nrep" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Note**: more accurate simulation experiments do not always lead to different results - but we do not know that before performing them!\n", + "\n", + "We will continue to investigate the issue of analytical and computation approaches throughout this textbook.\n" + ] + } + ], + "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": "3.8.8" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/textbook/11/4/US_births_2000-2014_SSA.csv b/textbook/11/4/US_births_2000-2014_SSA.csv new file mode 100755 index 00000000..e3ac5128 --- /dev/null +++ b/textbook/11/4/US_births_2000-2014_SSA.csv @@ -0,0 +1 @@ +year,month,date_of_month,day_of_week,births 2000,1,1,6,9083 2000,1,2,7,8006 2000,1,3,1,11363 2000,1,4,2,13032 2000,1,5,3,12558 2000,1,6,4,12466 2000,1,7,5,12516 2000,1,8,6,8934 2000,1,9,7,7949 2000,1,10,1,11668 2000,1,11,2,12611 2000,1,12,3,12398 2000,1,13,4,11815 2000,1,14,5,12180 2000,1,15,6,8525 2000,1,16,7,7657 2000,1,17,1,10824 2000,1,18,2,12350 2000,1,19,3,12405 2000,1,20,4,12506 2000,1,21,5,11953 2000,1,22,6,8855 2000,1,23,7,7856 2000,1,24,1,11449 2000,1,25,2,12593 2000,1,26,3,12143 2000,1,27,4,12408 2000,1,28,5,11934 2000,1,29,6,8805 2000,1,30,7,7764 2000,1,31,1,11133 2000,2,1,2,12614 2000,2,2,3,12465 2000,2,3,4,12062 2000,2,4,5,12035 2000,2,5,6,8624 2000,2,6,7,7862 2000,2,7,1,11630 2000,2,8,2,12879 2000,2,9,3,12315 2000,2,10,4,12612 2000,2,11,5,12411 2000,2,12,6,8836 2000,2,13,7,7933 2000,2,14,1,12152 2000,2,15,2,13017 2000,2,16,3,12504 2000,2,17,4,12520 2000,2,18,5,12406 2000,2,19,6,8861 2000,2,20,7,7943 2000,2,21,1,10610 2000,2,22,2,12664 2000,2,23,3,12252 2000,2,24,4,12423 2000,2,25,5,12204 2000,2,26,6,9026 2000,2,27,7,7836 2000,2,28,1,11455 2000,2,29,2,11895 2000,3,1,3,12672 2000,3,2,4,12524 2000,3,3,5,12390 2000,3,4,6,9054 2000,3,5,7,7734 2000,3,6,1,11375 2000,3,7,2,12420 2000,3,8,3,12338 2000,3,9,4,12615 2000,3,10,5,12152 2000,3,11,6,8822 2000,3,12,7,7937 2000,3,13,1,11157 2000,3,14,2,12773 2000,3,15,3,12428 2000,3,16,4,12431 2000,3,17,5,12385 2000,3,18,6,8677 2000,3,19,7,7782 2000,3,20,1,11595 2000,3,21,2,12689 2000,3,22,3,12272 2000,3,23,4,12396 2000,3,24,5,12327 2000,3,25,6,9155 2000,3,26,7,7815 2000,3,27,1,11291 2000,3,28,2,12650 2000,3,29,3,12077 2000,3,30,4,12071 2000,3,31,5,11820 2000,4,1,6,8388 2000,4,2,7,7540 2000,4,3,1,11397 2000,4,4,2,12797 2000,4,5,3,12209 2000,4,6,4,12192 2000,4,7,5,12213 2000,4,8,6,8743 2000,4,9,7,7759 2000,4,10,1,11333 2000,4,11,2,12850 2000,4,12,3,12545 2000,4,13,4,11907 2000,4,14,5,12053 2000,4,15,6,8887 2000,4,16,7,7859 2000,4,17,1,11322 2000,4,18,2,12783 2000,4,19,3,12562 2000,4,20,4,12301 2000,4,21,5,11257 2000,4,22,6,8367 2000,4,23,7,7483 2000,4,24,1,11309 2000,4,25,2,12488 2000,4,26,3,12245 2000,4,27,4,12235 2000,4,28,5,11989 2000,4,29,6,8703 2000,4,30,7,7641 2000,5,1,1,11621 2000,5,2,2,12934 2000,5,3,3,12259 2000,5,4,4,12434 2000,5,5,5,12539 2000,5,6,6,8814 2000,5,7,7,7797 2000,5,8,1,11604 2000,5,9,2,12744 2000,5,10,3,12607 2000,5,11,4,12442 2000,5,12,5,12132 2000,5,13,6,8747 2000,5,14,7,7617 2000,5,15,1,11587 2000,5,16,2,12898 2000,5,17,3,12729 2000,5,18,4,12580 2000,5,19,5,12174 2000,5,20,6,8673 2000,5,21,7,7887 2000,5,22,1,11582 2000,5,23,2,13097 2000,5,24,3,12669 2000,5,25,4,13026 2000,5,26,5,12726 2000,5,27,6,8991 2000,5,28,7,7873 2000,5,29,1,8272 2000,5,30,2,11954 2000,5,31,3,12941 2000,6,1,4,13363 2000,6,2,5,12695 2000,6,3,6,8940 2000,6,4,7,7983 2000,6,5,1,11647 2000,6,6,2,12765 2000,6,7,3,12474 2000,6,8,4,12751 2000,6,9,5,12504 2000,6,10,6,9134 2000,6,11,7,8116 2000,6,12,1,11848 2000,6,13,2,12683 2000,6,14,3,12849 2000,6,15,4,12798 2000,6,16,5,12727 2000,6,17,6,9143 2000,6,18,7,8162 2000,6,19,1,11649 2000,6,20,2,13017 2000,6,21,3,12729 2000,6,22,4,12809 2000,6,23,5,12603 2000,6,24,6,9094 2000,6,25,7,8178 2000,6,26,1,12164 2000,6,27,2,13354 2000,6,28,3,13033 2000,6,29,4,13462 2000,6,30,5,13225 2000,7,1,6,9376 2000,7,2,7,8100 2000,7,3,1,11345 2000,7,4,2,9550 2000,7,5,3,12346 2000,7,6,4,13853 2000,7,7,5,13658 2000,7,8,6,9631 2000,7,9,7,8586 2000,7,10,1,12420 2000,7,11,2,13584 2000,7,12,3,12827 2000,7,13,4,12980 2000,7,14,5,13230 2000,7,15,6,9627 2000,7,16,7,8423 2000,7,17,1,12053 2000,7,18,2,13663 2000,7,19,3,13001 2000,7,20,4,13173 2000,7,21,5,13027 2000,7,22,6,9463 2000,7,23,7,8166 2000,7,24,1,12128 2000,7,25,2,13176 2000,7,26,3,12931 2000,7,27,4,13155 2000,7,28,5,12890 2000,7,29,6,9465 2000,7,30,7,8444 2000,7,31,1,11860 2000,8,1,2,13356 2000,8,2,3,12835 2000,8,3,4,13092 2000,8,4,5,12940 2000,8,5,6,9398 2000,8,6,7,8350 2000,8,7,1,11864 2000,8,8,2,13693 2000,8,9,3,13170 2000,8,10,4,12953 2000,8,11,5,12729 2000,8,12,6,9305 2000,8,13,7,8313 2000,8,14,1,11927 2000,8,15,2,13374 2000,8,16,3,13174 2000,8,17,4,13099 2000,8,18,5,13124 2000,8,19,6,9276 2000,8,20,7,8346 2000,8,21,1,12003 2000,8,22,2,13406 2000,8,23,3,12929 2000,8,24,4,13021 2000,8,25,5,12926 2000,8,26,6,9341 2000,8,27,7,8240 2000,8,28,1,12074 2000,8,29,2,13237 2000,8,30,3,13111 2000,8,31,4,13287 2000,9,1,5,13145 2000,9,2,6,9265 2000,9,3,7,8248 2000,9,4,1,8603 2000,9,5,2,12200 2000,9,6,3,13917 2000,9,7,4,13512 2000,9,8,5,13487 2000,9,9,6,9860 2000,9,10,7,8552 2000,9,11,1,12405 2000,9,12,2,13649 2000,9,13,3,13299 2000,9,14,4,13739 2000,9,15,5,13552 2000,9,16,6,9780 2000,9,17,7,8683 2000,9,18,1,12554 2000,9,19,2,13850 2000,9,20,3,13775 2000,9,21,4,13350 2000,9,22,5,13189 2000,9,23,6,9494 2000,9,24,7,8539 2000,9,25,1,12432 2000,9,26,2,13540 2000,9,27,3,13467 2000,9,28,4,13515 2000,9,29,5,13045 2000,9,30,6,9335 2000,10,1,7,8453 2000,10,2,1,12223 2000,10,3,2,13245 2000,10,4,3,13154 2000,10,5,4,13288 2000,10,6,5,12774 2000,10,7,6,9131 2000,10,8,7,8119 2000,10,9,1,11343 2000,10,10,2,13124 2000,10,11,3,12907 2000,10,12,4,13038 2000,10,13,5,11723 2000,10,14,6,9163 2000,10,15,7,8156 2000,10,16,1,12001 2000,10,17,2,13106 2000,10,18,3,12816 2000,10,19,4,12502 2000,10,20,5,12471 2000,10,21,6,8956 2000,10,22,7,7938 2000,10,23,1,11810 2000,10,24,2,12995 2000,10,25,3,12780 2000,10,26,4,12787 2000,10,27,5,12333 2000,10,28,6,8978 2000,10,29,7,8124 2000,10,30,1,11558 2000,10,31,2,11372 2000,11,1,3,12927 2000,11,2,4,13066 2000,11,3,5,12630 2000,11,4,6,9084 2000,11,5,7,8078 2000,11,6,1,11862 2000,11,7,2,12822 2000,11,8,3,12829 2000,11,9,4,12778 2000,11,10,5,12554 2000,11,11,6,9318 2000,11,12,7,8070 2000,11,13,1,11480 2000,11,14,2,13153 2000,11,15,3,12953 2000,11,16,4,13061 2000,11,17,5,12888 2000,11,18,6,9137 2000,11,19,7,8077 2000,11,20,1,12974 2000,11,21,2,13991 2000,11,22,3,12420 2000,11,23,4,8144 2000,11,24,5,9805 2000,11,25,6,8537 2000,11,26,7,7950 2000,11,27,1,12175 2000,11,28,2,13799 2000,11,29,3,13114 2000,11,30,4,12818 2000,12,1,5,12545 2000,12,2,6,8914 2000,12,3,7,7930 2000,12,4,1,11501 2000,12,5,2,12997 2000,12,6,3,12697 2000,12,7,4,12820 2000,12,8,5,12548 2000,12,9,6,8853 2000,12,10,7,8022 2000,12,11,1,11811 2000,12,12,2,13627 2000,12,13,3,12567 2000,12,14,4,12640 2000,12,15,5,12656 2000,12,16,6,9184 2000,12,17,7,8026 2000,12,18,1,12590 2000,12,19,2,13829 2000,12,20,3,13762 2000,12,21,4,13524 2000,12,22,5,12248 2000,12,23,6,8484 2000,12,24,7,6971 2000,12,25,1,6719 2000,12,26,2,10395 2000,12,27,3,13252 2000,12,28,4,13900 2000,12,29,5,13607 2000,12,30,6,9405 2000,12,31,7,7892 2001,1,1,1,7663 2001,1,2,2,10635 2001,1,3,3,12449 2001,1,4,4,12678 2001,1,5,5,12647 2001,1,6,6,9180 2001,1,7,7,7883 2001,1,8,1,11447 2001,1,9,2,12386 2001,1,10,3,12455 2001,1,11,4,12433 2001,1,12,5,12735 2001,1,13,6,8836 2001,1,14,7,7818 2001,1,15,1,10926 2001,1,16,2,12327 2001,1,17,3,12344 2001,1,18,4,12648 2001,1,19,5,12339 2001,1,20,6,8771 2001,1,21,7,7850 2001,1,22,1,11444 2001,1,23,2,12446 2001,1,24,3,12244 2001,1,25,4,12570 2001,1,26,5,12191 2001,1,27,6,8795 2001,1,28,7,7761 2001,1,29,1,11513 2001,1,30,2,12488 2001,1,31,3,12477 2001,2,1,4,12477 2001,2,2,5,12470 2001,2,3,6,8650 2001,2,4,7,7716 2001,2,5,1,11825 2001,2,6,2,12536 2001,2,7,3,12343 2001,2,8,4,12390 2001,2,9,5,12343 2001,2,10,6,8791 2001,2,11,7,7563 2001,2,12,1,11670 2001,2,13,2,12267 2001,2,14,3,13191 2001,2,15,4,12632 2001,2,16,5,12355 2001,2,17,6,8609 2001,2,18,7,7555 2001,2,19,1,10522 2001,2,20,2,12373 2001,2,21,3,12492 2001,2,22,4,12482 2001,2,23,5,12242 2001,2,24,6,8656 2001,2,25,7,7794 2001,2,26,1,11332 2001,2,27,2,12334 2001,2,28,3,12209 2001,3,1,4,12530 2001,3,2,5,12383 2001,3,3,6,8935 2001,3,4,7,7799 2001,3,5,1,11411 2001,3,6,2,12339 2001,3,7,3,12351 2001,3,8,4,12440 2001,3,9,5,12461 2001,3,10,6,8807 2001,3,11,7,7697 2001,3,12,1,11595 2001,3,13,2,12534 2001,3,14,3,12578 2001,3,15,4,12525 2001,3,16,5,12460 2001,3,17,6,9006 2001,3,18,7,7526 2001,3,19,1,11352 2001,3,20,2,12868 2001,3,21,3,12690 2001,3,22,4,12472 2001,3,23,5,12432 2001,3,24,6,8830 2001,3,25,7,7800 2001,3,26,1,11290 2001,3,27,2,12570 2001,3,28,3,12469 2001,3,29,4,12366 2001,3,30,5,12059 2001,3,31,6,8770 2001,4,1,7,7212 2001,4,2,1,11673 2001,4,3,2,12864 2001,4,4,3,12655 2001,4,5,4,12438 2001,4,6,5,12407 2001,4,7,6,8755 2001,4,8,7,7718 2001,4,9,1,11617 2001,4,10,2,13031 2001,4,11,3,12912 2001,4,12,4,12733 2001,4,13,5,10881 2001,4,14,6,8262 2001,4,15,7,7230 2001,4,16,1,11220 2001,4,17,2,12867 2001,4,18,3,12381 2001,4,19,4,12257 2001,4,20,5,12296 2001,4,21,6,8849 2001,4,22,7,7758 2001,4,23,1,11672 2001,4,24,2,12981 2001,4,25,3,12728 2001,4,26,4,12560 2001,4,27,5,12335 2001,4,28,6,8574 2001,4,29,7,7602 2001,4,30,1,11416 2001,5,1,2,13037 2001,5,2,3,12542 2001,5,3,4,12596 2001,5,4,5,12276 2001,5,5,6,8795 2001,5,6,7,8001 2001,5,7,1,11635 2001,5,8,2,13032 2001,5,9,3,12477 2001,5,10,4,12632 2001,5,11,5,12296 2001,5,12,6,8692 2001,5,13,7,7479 2001,5,14,1,11577 2001,5,15,2,13124 2001,5,16,3,12625 2001,5,17,4,12630 2001,5,18,5,12313 2001,5,19,6,8803 2001,5,20,7,7732 2001,5,21,1,11680 2001,5,22,2,13047 2001,5,23,3,12936 2001,5,24,4,13179 2001,5,25,5,12722 2001,5,26,6,8911 2001,5,27,7,7529 2001,5,28,1,7993 2001,5,29,2,12013 2001,5,30,3,13334 2001,5,31,4,13051 2001,6,1,5,12677 2001,6,2,6,8920 2001,6,3,7,7887 2001,6,4,1,11500 2001,6,5,2,12683 2001,6,6,3,12804 2001,6,7,4,12566 2001,6,8,5,12451 2001,6,9,6,8756 2001,6,10,7,7674 2001,6,11,1,11776 2001,6,12,2,13218 2001,6,13,3,12342 2001,6,14,4,12655 2001,6,15,5,12394 2001,6,16,6,8780 2001,6,17,7,7722 2001,6,18,1,11756 2001,6,19,2,12785 2001,6,20,3,12704 2001,6,21,4,12615 2001,6,22,5,12299 2001,6,23,6,8452 2001,6,24,7,7639 2001,6,25,1,11575 2001,6,26,2,12939 2001,6,27,3,12809 2001,6,28,4,13059 2001,6,29,5,12922 2001,6,30,6,9247 2001,7,1,7,8145 2001,7,2,1,12390 2001,7,3,2,13364 2001,7,4,3,9608 2001,7,5,4,12531 2001,7,6,5,13151 2001,7,7,6,9544 2001,7,8,7,8249 2001,7,9,1,12036 2001,7,10,2,13614 2001,7,11,3,13026 2001,7,12,4,13188 2001,7,13,5,12187 2001,7,14,6,9269 2001,7,15,7,8047 2001,7,16,1,12383 2001,7,17,2,13657 2001,7,18,3,13241 2001,7,19,4,13293 2001,7,20,5,12950 2001,7,21,6,9410 2001,7,22,7,8116 2001,7,23,1,12099 2001,7,24,2,13532 2001,7,25,3,12988 2001,7,26,4,13022 2001,7,27,5,12677 2001,7,28,6,9102 2001,7,29,7,7892 2001,7,30,1,12150 2001,7,31,2,13218 2001,8,1,3,12960 2001,8,2,4,13097 2001,8,3,5,12859 2001,8,4,6,9143 2001,8,5,7,8062 2001,8,6,1,12008 2001,8,7,2,13488 2001,8,8,3,13185 2001,8,9,4,13339 2001,8,10,5,13094 2001,8,11,6,9275 2001,8,12,7,8261 2001,8,13,1,11682 2001,8,14,2,13325 2001,8,15,3,13332 2001,8,16,4,13372 2001,8,17,5,13102 2001,8,18,6,9294 2001,8,19,7,7945 2001,8,20,1,12313 2001,8,21,2,13590 2001,8,22,3,13146 2001,8,23,4,13158 2001,8,24,5,12996 2001,8,25,6,9229 2001,8,26,7,8115 2001,8,27,1,12080 2001,8,28,2,13792 2001,8,29,3,13160 2001,8,30,4,13520 2001,8,31,5,13461 2001,9,1,6,9248 2001,9,2,7,8239 2001,9,3,1,8115 2001,9,4,2,12501 2001,9,5,3,14055 2001,9,6,4,13925 2001,9,7,5,13721 2001,9,8,6,9344 2001,9,9,7,8347 2001,9,10,1,12459 2001,9,11,2,13590 2001,9,12,3,13149 2001,9,13,4,13186 2001,9,14,5,13444 2001,9,15,6,9662 2001,9,16,7,8319 2001,9,17,1,12664 2001,9,18,2,13526 2001,9,19,3,13575 2001,9,20,4,13750 2001,9,21,5,13341 2001,9,22,6,9607 2001,9,23,7,8495 2001,9,24,1,12564 2001,9,25,2,14063 2001,9,26,3,13441 2001,9,27,4,13199 2001,9,28,5,13174 2001,9,29,6,9243 2001,9,30,7,8042 2001,10,1,1,12425 2001,10,2,2,13523 2001,10,3,3,13056 2001,10,4,4,13182 2001,10,5,5,12851 2001,10,6,6,8872 2001,10,7,7,7744 2001,10,8,1,11531 2001,10,9,2,12886 2001,10,10,3,12858 2001,10,11,4,12568 2001,10,12,5,12676 2001,10,13,6,8659 2001,10,14,7,7753 2001,10,15,1,11649 2001,10,16,2,12770 2001,10,17,3,12599 2001,10,18,4,12579 2001,10,19,5,12359 2001,10,20,6,8747 2001,10,21,7,7506 2001,10,22,1,11705 2001,10,23,2,12896 2001,10,24,3,12676 2001,10,25,4,12516 2001,10,26,5,12296 2001,10,27,6,8458 2001,10,28,7,7676 2001,10,29,1,11389 2001,10,30,2,12534 2001,10,31,3,10913 2001,11,1,4,12879 2001,11,2,5,12374 2001,11,3,6,8572 2001,11,4,7,7533 2001,11,5,1,11668 2001,11,6,2,12662 2001,11,7,3,12419 2001,11,8,4,12519 2001,11,9,5,12416 2001,11,10,6,8665 2001,11,11,7,7599 2001,11,12,1,11670 2001,11,13,2,12382 2001,11,14,3,12602 2001,11,15,4,12936 2001,11,16,5,12979 2001,11,17,6,8774 2001,11,18,7,7495 2001,11,19,1,12709 2001,11,20,2,13603 2001,11,21,3,12167 2001,11,22,4,7513 2001,11,23,5,9594 2001,11,24,6,8100 2001,11,25,7,7456 2001,11,26,1,11732 2001,11,27,2,13249 2001,11,28,3,12516 2001,11,29,4,12474 2001,11,30,5,12019 2001,12,1,6,8255 2001,12,2,7,7385 2001,12,3,1,11548 2001,12,4,2,12605 2001,12,5,3,12609 2001,12,6,4,12188 2001,12,7,5,11693 2001,12,8,6,8372 2001,12,9,7,7498 2001,12,10,1,11655 2001,12,11,2,12798 2001,12,12,3,12884 2001,12,13,4,12230 2001,12,14,5,12405 2001,12,15,6,8615 2001,12,16,7,7432 2001,12,17,1,12392 2001,12,18,2,13657 2001,12,19,3,13404 2001,12,20,4,13871 2001,12,21,5,13530 2001,12,22,6,9062 2001,12,23,7,7245 2001,12,24,1,7626 2001,12,25,2,6603 2001,12,26,3,11040 2001,12,27,4,14151 2001,12,28,5,14235 2001,12,29,6,9563 2001,12,30,7,7840 2001,12,31,1,10272 2002,1,1,2,7927 2002,1,2,3,10723 2002,1,3,4,12465 2002,1,4,5,12671 2002,1,5,6,8902 2002,1,6,7,7647 2002,1,7,1,11548 2002,1,8,2,12515 2002,1,9,3,11654 2002,1,10,4,12596 2002,1,11,5,12276 2002,1,12,6,8591 2002,1,13,7,7471 2002,1,14,1,11530 2002,1,15,2,12369 2002,1,16,3,11996 2002,1,17,4,12412 2002,1,18,5,12251 2002,1,19,6,8434 2002,1,20,7,7462 2002,1,21,1,10921 2002,1,22,2,12361 2002,1,23,3,12252 2002,1,24,4,12549 2002,1,25,5,12069 2002,1,26,6,8530 2002,1,27,7,7510 2002,1,28,1,11354 2002,1,29,2,12215 2002,1,30,3,12146 2002,1,31,4,12125 2002,2,1,5,12130 2002,2,2,6,9021 2002,2,3,7,7442 2002,2,4,1,11412 2002,2,5,2,12488 2002,2,6,3,12210 2002,2,7,4,12418 2002,2,8,5,12444 2002,2,9,6,8706 2002,2,10,7,7569 2002,2,11,1,11547 2002,2,12,2,12779 2002,2,13,3,12069 2002,2,14,4,13062 2002,2,15,5,12548 2002,2,16,6,8710 2002,2,17,7,7484 2002,2,18,1,10907 2002,2,19,2,12262 2002,2,20,3,12817 2002,2,21,4,12384 2002,2,22,5,12667 2002,2,23,6,8639 2002,2,24,7,7488 2002,2,25,1,11547 2002,2,26,2,12487 2002,2,27,3,12303 2002,2,28,4,12370 2002,3,1,5,12388 2002,3,2,6,8507 2002,3,3,7,7624 2002,3,4,1,11661 2002,3,5,2,12678 2002,3,6,3,12372 2002,3,7,4,12525 2002,3,8,5,12244 2002,3,9,6,8606 2002,3,10,7,7633 2002,3,11,1,11197 2002,3,12,2,12667 2002,3,13,3,12031 2002,3,14,4,12583 2002,3,15,5,12472 2002,3,16,6,8696 2002,3,17,7,7680 2002,3,18,1,11621 2002,3,19,2,12674 2002,3,20,3,12577 2002,3,21,4,12502 2002,3,22,5,12252 2002,3,23,6,8569 2002,3,24,7,7419 2002,3,25,1,11507 2002,3,26,2,12840 2002,3,27,3,12568 2002,3,28,4,12454 2002,3,29,5,11449 2002,3,30,6,8270 2002,3,31,7,7083 2002,4,1,1,10264 2002,4,2,2,12884 2002,4,3,3,12372 2002,4,4,4,12262 2002,4,5,5,12006 2002,4,6,6,8301 2002,4,7,7,7109 2002,4,8,1,11706 2002,4,9,2,12741 2002,4,10,3,12418 2002,4,11,4,12236 2002,4,12,5,12272 2002,4,13,6,8448 2002,4,14,7,7578 2002,4,15,1,11412 2002,4,16,2,12847 2002,4,17,3,12575 2002,4,18,4,12490 2002,4,19,5,12297 2002,4,20,6,8224 2002,4,21,7,7298 2002,4,22,1,11576 2002,4,23,2,12457 2002,4,24,3,12297 2002,4,25,4,12469 2002,4,26,5,11917 2002,4,27,6,8243 2002,4,28,7,7502 2002,4,29,1,11422 2002,4,30,2,12666 2002,5,1,3,12297 2002,5,2,4,12405 2002,5,3,5,12130 2002,5,4,6,8215 2002,5,5,7,7447 2002,5,6,1,11362 2002,5,7,2,12505 2002,5,8,3,12334 2002,5,9,4,12219 2002,5,10,5,12329 2002,5,11,6,8329 2002,5,12,7,7487 2002,5,13,1,11404 2002,5,14,2,12909 2002,5,15,3,12705 2002,5,16,4,12609 2002,5,17,5,12218 2002,5,18,6,8528 2002,5,19,7,7470 2002,5,20,1,11788 2002,5,21,2,12916 2002,5,22,3,12670 2002,5,23,4,13123 2002,5,24,5,12775 2002,5,25,6,8515 2002,5,26,7,7282 2002,5,27,1,7765 2002,5,28,2,12148 2002,5,29,3,13436 2002,5,30,4,12963 2002,5,31,5,12568 2002,6,1,6,8547 2002,6,2,7,7662 2002,6,3,1,11433 2002,6,4,2,12616 2002,6,5,3,12663 2002,6,6,4,12745 2002,6,7,5,12280 2002,6,8,6,8524 2002,6,9,7,7485 2002,6,10,1,11863 2002,6,11,2,12713 2002,6,12,3,12758 2002,6,13,4,12457 2002,6,14,5,12562 2002,6,15,6,8708 2002,6,16,7,7685 2002,6,17,1,11738 2002,6,18,2,13139 2002,6,19,3,12598 2002,6,20,4,12847 2002,6,21,5,12377 2002,6,22,6,8676 2002,6,23,7,7661 2002,6,24,1,11972 2002,6,25,2,13425 2002,6,26,3,13167 2002,6,27,4,13310 2002,6,28,5,12996 2002,6,29,6,8994 2002,6,30,7,7831 2002,7,1,1,12584 2002,7,2,2,14187 2002,7,3,3,13626 2002,7,4,4,9481 2002,7,5,5,11326 2002,7,6,6,8816 2002,7,7,7,8080 2002,7,8,1,12253 2002,7,9,2,13814 2002,7,10,3,13264 2002,7,11,4,13215 2002,7,12,5,12760 2002,7,13,6,8896 2002,7,14,7,7884 2002,7,15,1,12370 2002,7,16,2,13606 2002,7,17,3,13396 2002,7,18,4,13395 2002,7,19,5,12900 2002,7,20,6,8799 2002,7,21,7,7954 2002,7,22,1,12194 2002,7,23,2,13630 2002,7,24,3,13231 2002,7,25,4,13345 2002,7,26,5,12914 2002,7,27,6,9073 2002,7,28,7,7915 2002,7,29,1,12148 2002,7,30,2,13593 2002,7,31,3,13311 2002,8,1,4,13267 2002,8,2,5,13127 2002,8,3,6,8963 2002,8,4,7,7833 2002,8,5,1,12191 2002,8,6,2,13407 2002,8,7,3,13035 2002,8,8,4,13420 2002,8,9,5,12893 2002,8,10,6,9078 2002,8,11,7,7970 2002,8,12,1,12311 2002,8,13,2,13603 2002,8,14,3,13302 2002,8,15,4,13551 2002,8,16,5,13132 2002,8,17,6,9298 2002,8,18,7,7925 2002,8,19,1,12299 2002,8,20,2,13820 2002,8,21,3,13356 2002,8,22,4,13232 2002,8,23,5,13133 2002,8,24,6,9086 2002,8,25,7,7961 2002,8,26,1,12182 2002,8,27,2,13788 2002,8,28,3,13398 2002,8,29,4,13426 2002,8,30,5,13300 2002,8,31,6,9122 2002,9,1,7,7947 2002,9,2,1,8297 2002,9,3,2,12613 2002,9,4,3,13969 2002,9,5,4,14021 2002,9,6,5,13680 2002,9,7,6,9354 2002,9,8,7,8077 2002,9,9,1,12875 2002,9,10,2,13940 2002,9,11,3,12655 2002,9,12,4,14247 2002,9,13,5,13028 2002,9,14,6,9388 2002,9,15,7,8433 2002,9,16,1,12793 2002,9,17,2,14241 2002,9,18,3,13953 2002,9,19,4,13899 2002,9,20,5,13721 2002,9,21,6,9613 2002,9,22,7,8222 2002,9,23,1,12795 2002,9,24,2,14205 2002,9,25,3,13518 2002,9,26,4,13469 2002,9,27,5,13298 2002,9,28,6,9250 2002,9,29,7,7968 2002,9,30,1,12232 2002,10,1,2,13625 2002,10,2,3,13512 2002,10,3,4,13044 2002,10,4,5,12814 2002,10,5,6,8922 2002,10,6,7,7801 2002,10,7,1,11970 2002,10,8,2,13066 2002,10,9,3,12658 2002,10,10,4,12684 2002,10,11,5,12467 2002,10,12,6,8451 2002,10,13,7,7416 2002,10,14,1,11559 2002,10,15,2,12788 2002,10,16,3,12642 2002,10,17,4,12507 2002,10,18,5,12197 2002,10,19,6,8534 2002,10,20,7,7405 2002,10,21,1,11690 2002,10,22,2,13214 2002,10,23,3,12656 2002,10,24,4,12679 2002,10,25,5,12523 2002,10,26,6,8414 2002,10,27,7,7690 2002,10,28,1,11853 2002,10,29,2,12833 2002,10,30,3,12274 2002,10,31,4,10850 2002,11,1,5,12591 2002,11,2,6,8561 2002,11,3,7,7502 2002,11,4,1,11761 2002,11,5,2,12906 2002,11,6,3,12602 2002,11,7,4,12653 2002,11,8,5,12472 2002,11,9,6,8615 2002,11,10,7,7691 2002,11,11,1,11509 2002,11,12,2,12725 2002,11,13,3,12097 2002,11,14,4,12485 2002,11,15,5,12273 2002,11,16,6,8295 2002,11,17,7,7353 2002,11,18,1,11790 2002,11,19,2,12716 2002,11,20,3,12574 2002,11,21,4,12716 2002,11,22,5,12978 2002,11,23,6,8581 2002,11,24,7,7650 2002,11,25,1,12470 2002,11,26,2,13377 2002,11,27,3,11544 2002,11,28,4,7392 2002,11,29,5,9341 2002,11,30,6,8159 2002,12,1,7,7402 2002,12,2,1,11929 2002,12,3,2,13314 2002,12,4,3,12684 2002,12,5,4,12596 2002,12,6,5,11775 2002,12,7,6,8513 2002,12,8,7,7339 2002,12,9,1,11547 2002,12,10,2,12867 2002,12,11,3,12632 2002,12,12,4,12850 2002,12,13,5,11600 2002,12,14,6,8420 2002,12,15,7,7516 2002,12,16,1,12344 2002,12,17,2,13454 2002,12,18,3,13580 2002,12,19,4,13665 2002,12,20,5,14015 2002,12,21,6,9092 2002,12,22,7,7607 2002,12,23,1,11396 2002,12,24,2,9131 2002,12,25,3,6774 2002,12,26,4,11242 2002,12,27,5,13650 2002,12,28,6,9114 2002,12,29,7,8035 2002,12,30,1,13158 2002,12,31,2,12582 2003,1,1,3,7908 2003,1,2,4,11124 2003,1,3,5,12252 2003,1,4,6,8519 2003,1,5,7,7495 2003,1,6,1,11364 2003,1,7,2,12657 2003,1,8,3,12167 2003,1,9,4,12081 2003,1,10,5,12517 2003,1,11,6,8471 2003,1,12,7,7297 2003,1,13,1,11197 2003,1,14,2,12918 2003,1,15,3,12140 2003,1,16,4,12136 2003,1,17,5,12110 2003,1,18,6,8431 2003,1,19,7,7498 2003,1,20,1,11045 2003,1,21,2,12288 2003,1,22,3,12097 2003,1,23,4,12185 2003,1,24,5,12107 2003,1,25,6,8379 2003,1,26,7,7389 2003,1,27,1,11418 2003,1,28,2,12595 2003,1,29,3,12100 2003,1,30,4,12289 2003,1,31,5,11989 2003,2,1,6,8667 2003,2,2,7,7685 2003,2,3,1,11498 2003,2,4,2,12566 2003,2,5,3,12011 2003,2,6,4,12352 2003,2,7,5,12381 2003,2,8,6,8573 2003,2,9,7,7482 2003,2,10,1,11996 2003,2,11,2,12961 2003,2,12,3,12595 2003,2,13,4,12340 2003,2,14,5,13051 2003,2,15,6,8850 2003,2,16,7,7669 2003,2,17,1,10707 2003,2,18,2,12637 2003,2,19,3,12626 2003,2,20,4,12545 2003,2,21,5,12689 2003,2,22,6,8883 2003,2,23,7,7723 2003,2,24,1,11874 2003,2,25,2,12882 2003,2,26,3,12356 2003,2,27,4,12657 2003,2,28,5,12533 2003,3,1,6,8587 2003,3,2,7,7545 2003,3,3,1,12774 2003,3,4,2,12871 2003,3,5,3,12483 2003,3,6,4,12604 2003,3,7,5,12503 2003,3,8,6,8649 2003,3,9,7,7387 2003,3,10,1,11671 2003,3,11,2,12935 2003,3,12,3,12520 2003,3,13,4,12333 2003,3,14,5,12770 2003,3,15,6,8601 2003,3,16,7,7472 2003,3,17,1,11990 2003,3,18,2,12960 2003,3,19,3,12587 2003,3,20,4,12755 2003,3,21,5,12653 2003,3,22,6,8488 2003,3,23,7,7420 2003,3,24,1,11654 2003,3,25,2,13054 2003,3,26,3,12549 2003,3,27,4,12601 2003,3,28,5,12493 2003,3,29,6,8691 2003,3,30,7,7493 2003,3,31,1,11481 2003,4,1,2,12000 2003,4,2,3,12994 2003,4,3,4,12599 2003,4,4,5,12669 2003,4,5,6,8440 2003,4,6,7,7265 2003,4,7,1,11750 2003,4,8,2,13020 2003,4,9,3,12397 2003,4,10,4,12689 2003,4,11,5,12397 2003,4,12,6,8517 2003,4,13,7,7234 2003,4,14,1,11800 2003,4,15,2,13055 2003,4,16,3,12947 2003,4,17,4,12926 2003,4,18,5,11680 2003,4,19,6,8155 2003,4,20,7,7155 2003,4,21,1,11465 2003,4,22,2,12696 2003,4,23,3,12616 2003,4,24,4,12530 2003,4,25,5,12255 2003,4,26,6,8343 2003,4,27,7,7453 2003,4,28,1,11666 2003,4,29,2,12672 2003,4,30,3,12306 2003,5,1,4,12727 2003,5,2,5,12549 2003,5,3,6,8488 2003,5,4,7,7551 2003,5,5,1,12001 2003,5,6,2,13165 2003,5,7,3,12667 2003,5,8,4,12902 2003,5,9,5,12710 2003,5,10,6,8706 2003,5,11,7,7576 2003,5,12,1,12118 2003,5,13,2,12685 2003,5,14,3,12833 2003,5,15,4,13074 2003,5,16,5,12840 2003,5,17,6,8687 2003,5,18,7,7606 2003,5,19,1,12035 2003,5,20,2,13239 2003,5,21,3,13380 2003,5,22,4,13393 2003,5,23,5,13176 2003,5,24,6,8769 2003,5,25,7,7690 2003,5,26,1,7933 2003,5,27,2,12390 2003,5,28,3,13854 2003,5,29,4,13497 2003,5,30,5,13224 2003,5,31,6,8850 2003,6,1,7,7650 2003,6,2,1,12041 2003,6,3,2,13090 2003,6,4,3,12853 2003,6,5,4,12850 2003,6,6,5,12869 2003,6,7,6,8670 2003,6,8,7,7606 2003,6,9,1,11917 2003,6,10,2,13326 2003,6,11,3,13154 2003,6,12,4,13092 2003,6,13,5,12013 2003,6,14,6,8696 2003,6,15,7,7680 2003,6,16,1,12388 2003,6,17,2,13443 2003,6,18,3,13082 2003,6,19,4,12975 2003,6,20,5,12693 2003,6,21,6,8734 2003,6,22,7,7742 2003,6,23,1,12236 2003,6,24,2,13578 2003,6,25,3,13468 2003,6,26,4,13330 2003,6,27,5,12862 2003,6,28,6,8862 2003,6,29,7,7723 2003,6,30,1,12261 2003,7,1,2,13930 2003,7,2,3,13823 2003,7,3,4,13487 2003,7,4,5,9504 2003,7,5,6,8269 2003,7,6,7,7871 2003,7,7,1,12630 2003,7,8,2,13906 2003,7,9,3,13508 2003,7,10,4,13600 2003,7,11,5,13096 2003,7,12,6,8908 2003,7,13,7,7946 2003,7,14,1,12281 2003,7,15,2,13711 2003,7,16,3,13480 2003,7,17,4,13729 2003,7,18,5,13225 2003,7,19,6,8926 2003,7,20,7,8058 2003,7,21,1,12419 2003,7,22,2,13775 2003,7,23,3,13539 2003,7,24,4,13569 2003,7,25,5,12977 2003,7,26,6,8978 2003,7,27,7,7830 2003,7,28,1,12434 2003,7,29,2,13825 2003,7,30,3,13557 2003,7,31,4,13445 2003,8,1,5,13242 2003,8,2,6,8882 2003,8,3,7,7838 2003,8,4,1,12233 2003,8,5,2,13735 2003,8,6,3,13363 2003,8,7,4,13539 2003,8,8,5,13352 2003,8,9,6,9226 2003,8,10,7,7954 2003,8,11,1,12282 2003,8,12,2,13995 2003,8,13,3,13202 2003,8,14,4,13391 2003,8,15,5,13206 2003,8,16,6,9316 2003,8,17,7,8181 2003,8,18,1,12437 2003,8,19,2,13831 2003,8,20,3,13464 2003,8,21,4,13528 2003,8,22,5,13478 2003,8,23,6,9240 2003,8,24,7,7936 2003,8,25,1,12631 2003,8,26,2,14008 2003,8,27,3,13854 2003,8,28,4,14099 2003,8,29,5,13769 2003,8,30,6,9344 2003,8,31,7,7865 2003,9,1,1,8164 2003,9,2,2,12684 2003,9,3,3,14427 2003,9,4,4,14161 2003,9,5,5,13897 2003,9,6,6,9400 2003,9,7,7,8188 2003,9,8,1,12701 2003,9,9,2,13869 2003,9,10,3,14180 2003,9,11,4,13196 2003,9,12,5,13848 2003,9,13,6,9574 2003,9,14,7,8500 2003,9,15,1,13068 2003,9,16,2,14399 2003,9,17,3,14018 2003,9,18,4,14066 2003,9,19,5,13560 2003,9,20,6,9688 2003,9,21,7,8500 2003,9,22,1,12987 2003,9,23,2,14376 2003,9,24,3,13841 2003,9,25,4,13865 2003,9,26,5,13846 2003,9,27,6,9177 2003,9,28,7,8206 2003,9,29,1,12522 2003,9,30,2,13413 2003,10,1,3,13398 2003,10,2,4,13638 2003,10,3,5,13284 2003,10,4,6,8983 2003,10,5,7,7744 2003,10,6,1,12104 2003,10,7,2,13523 2003,10,8,3,13509 2003,10,9,4,13285 2003,10,10,5,13306 2003,10,11,6,8721 2003,10,12,7,7816 2003,10,13,1,11455 2003,10,14,2,13274 2003,10,15,3,12949 2003,10,16,4,12711 2003,10,17,5,12676 2003,10,18,6,8564 2003,10,19,7,7561 2003,10,20,1,12073 2003,10,21,2,13300 2003,10,22,3,13054 2003,10,23,4,12817 2003,10,24,5,12566 2003,10,25,6,8568 2003,10,26,7,7818 2003,10,27,1,11956 2003,10,28,2,13426 2003,10,29,3,12950 2003,10,30,4,12600 2003,10,31,5,11005 2003,11,1,6,8491 2003,11,2,7,7716 2003,11,3,1,12443 2003,11,4,2,13374 2003,11,5,3,12998 2003,11,6,4,12801 2003,11,7,5,12535 2003,11,8,6,8719 2003,11,9,7,7481 2003,11,10,1,12117 2003,11,11,2,13166 2003,11,12,3,12680 2003,11,13,4,12438 2003,11,14,5,12433 2003,11,15,6,8309 2003,11,16,7,7486 2003,11,17,1,12006 2003,11,18,2,13330 2003,11,19,3,12879 2003,11,20,4,12988 2003,11,21,5,13036 2003,11,22,6,8623 2003,11,23,7,7383 2003,11,24,1,13035 2003,11,25,2,13732 2003,11,26,3,12069 2003,11,27,4,7340 2003,11,28,5,9407 2003,11,29,6,8043 2003,11,30,7,7330 2003,12,1,1,12213 2003,12,2,2,13454 2003,12,3,3,13199 2003,12,4,4,12631 2003,12,5,5,12180 2003,12,6,6,8247 2003,12,7,7,7383 2003,12,8,1,11708 2003,12,9,2,13001 2003,12,10,3,12739 2003,12,11,4,12502 2003,12,12,5,12484 2003,12,13,6,8303 2003,12,14,7,7462 2003,12,15,1,12319 2003,12,16,2,13649 2003,12,17,3,13454 2003,12,18,4,13865 2003,12,19,5,13693 2003,12,20,6,8953 2003,12,21,7,7657 2003,12,22,1,13249 2003,12,23,2,12939 2003,12,24,3,9272 2003,12,25,4,6744 2003,12,26,5,10431 2003,12,27,6,8785 2003,12,28,7,7763 2003,12,29,1,13125 2003,12,30,2,14700 2003,12,31,3,12540 2004,1,1,4,8205 2004,1,2,5,10586 2004,1,3,6,8337 2004,1,4,7,7359 2004,1,5,1,11489 2004,1,6,2,12755 2004,1,7,3,12716 2004,1,8,4,12781 2004,1,9,5,12469 2004,1,10,6,8337 2004,1,11,7,7316 2004,1,12,1,11813 2004,1,13,2,12639 2004,1,14,3,12965 2004,1,15,4,12837 2004,1,16,5,12424 2004,1,17,6,8442 2004,1,18,7,7512 2004,1,19,1,11152 2004,1,20,2,12810 2004,1,21,3,12753 2004,1,22,4,12675 2004,1,23,5,12643 2004,1,24,6,8632 2004,1,25,7,7556 2004,1,26,1,11611 2004,1,27,2,12892 2004,1,28,3,12373 2004,1,29,4,12313 2004,1,30,5,12375 2004,1,31,6,8310 2004,2,1,7,7270 2004,2,2,1,11686 2004,2,3,2,13211 2004,2,4,3,12580 2004,2,5,4,12572 2004,2,6,5,12371 2004,2,7,6,8533 2004,2,8,7,7440 2004,2,9,1,11654 2004,2,10,2,13139 2004,2,11,3,12966 2004,2,12,4,12957 2004,2,13,5,11749 2004,2,14,6,8944 2004,2,15,7,7603 2004,2,16,1,11280 2004,2,17,2,12790 2004,2,18,3,12954 2004,2,19,4,12709 2004,2,20,5,12720 2004,2,21,6,8481 2004,2,22,7,7552 2004,2,23,1,11565 2004,2,24,2,13009 2004,2,25,3,12800 2004,2,26,4,12621 2004,2,27,5,12403 2004,2,28,6,8488 2004,2,29,7,7301 2004,3,1,1,12017 2004,3,2,2,12943 2004,3,3,3,12696 2004,3,4,4,12611 2004,3,5,5,12407 2004,3,6,6,8532 2004,3,7,7,7304 2004,3,8,1,11816 2004,3,9,2,12988 2004,3,10,3,12777 2004,3,11,4,12797 2004,3,12,5,12519 2004,3,13,6,8398 2004,3,14,7,7401 2004,3,15,1,11903 2004,3,16,2,12873 2004,3,17,3,12979 2004,3,18,4,12710 2004,3,19,5,12480 2004,3,20,6,8329 2004,3,21,7,7548 2004,3,22,1,11842 2004,3,23,2,12978 2004,3,24,3,12765 2004,3,25,4,12835 2004,3,26,5,12372 2004,3,27,6,8602 2004,3,28,7,7549 2004,3,29,1,11788 2004,3,30,2,13078 2004,3,31,3,12542 2004,4,1,4,12138 2004,4,2,5,12776 2004,4,3,6,8479 2004,4,4,7,7559 2004,4,5,1,12013 2004,4,6,2,13122 2004,4,7,3,12929 2004,4,8,4,12836 2004,4,9,5,11695 2004,4,10,6,8148 2004,4,11,7,6969 2004,4,12,1,11751 2004,4,13,2,12613 2004,4,14,3,12732 2004,4,15,4,12785 2004,4,16,5,12482 2004,4,17,6,8584 2004,4,18,7,7447 2004,4,19,1,11792 2004,4,20,2,13128 2004,4,21,3,12787 2004,4,22,4,12866 2004,4,23,5,12442 2004,4,24,6,8595 2004,4,25,7,7507 2004,4,26,1,12020 2004,4,27,2,13147 2004,4,28,3,12756 2004,4,29,4,12617 2004,4,30,5,12364 2004,5,1,6,8259 2004,5,2,7,7433 2004,5,3,1,11839 2004,5,4,2,12824 2004,5,5,3,12852 2004,5,6,4,12707 2004,5,7,5,12582 2004,5,8,6,8599 2004,5,9,7,7380 2004,5,10,1,12243 2004,5,11,2,13229 2004,5,12,3,12989 2004,5,13,4,12373 2004,5,14,5,12688 2004,5,15,6,8498 2004,5,16,7,7614 2004,5,17,1,12172 2004,5,18,2,13294 2004,5,19,3,12576 2004,5,20,4,13036 2004,5,21,5,12625 2004,5,22,6,8614 2004,5,23,7,7628 2004,5,24,1,12341 2004,5,25,2,13451 2004,5,26,3,12891 2004,5,27,4,13470 2004,5,28,5,12941 2004,5,29,6,8720 2004,5,30,7,7511 2004,5,31,1,7869 2004,6,1,2,12440 2004,6,2,3,13785 2004,6,3,4,13644 2004,6,4,5,13059 2004,6,5,6,8706 2004,6,6,7,7451 2004,6,7,1,12173 2004,6,8,2,13339 2004,6,9,3,12806 2004,6,10,4,13141 2004,6,11,5,12691 2004,6,12,6,8581 2004,6,13,7,7649 2004,6,14,1,12200 2004,6,15,2,13317 2004,6,16,3,13141 2004,6,17,4,13165 2004,6,18,5,12785 2004,6,19,6,8492 2004,6,20,7,7629 2004,6,21,1,12093 2004,6,22,2,13237 2004,6,23,3,13096 2004,6,24,4,13267 2004,6,25,5,13074 2004,6,26,6,8786 2004,6,27,7,7715 2004,6,28,1,12383 2004,6,29,2,13587 2004,6,30,3,13444 2004,7,1,4,13887 2004,7,2,5,13271 2004,7,3,6,8900 2004,7,4,7,7820 2004,7,5,1,8978 2004,7,6,2,13221 2004,7,7,3,14496 2004,7,8,4,14056 2004,7,9,5,13874 2004,7,10,6,9040 2004,7,11,7,7862 2004,7,12,1,12621 2004,7,13,2,13214 2004,7,14,3,13610 2004,7,15,4,13601 2004,7,16,5,13411 2004,7,17,6,9067 2004,7,18,7,7797 2004,7,19,1,12286 2004,7,20,2,13804 2004,7,21,3,13370 2004,7,22,4,13574 2004,7,23,5,12974 2004,7,24,6,9046 2004,7,25,7,7549 2004,7,26,1,12266 2004,7,27,2,13454 2004,7,28,3,13258 2004,7,29,4,13281 2004,7,30,5,12934 2004,7,31,6,8858 2004,8,1,7,7837 2004,8,2,1,12428 2004,8,3,2,13249 2004,8,4,3,13498 2004,8,5,4,13234 2004,8,6,5,12935 2004,8,7,6,8860 2004,8,8,7,7773 2004,8,9,1,12310 2004,8,10,2,13571 2004,8,11,3,13405 2004,8,12,4,13448 2004,8,13,5,12275 2004,8,14,6,8884 2004,8,15,7,7885 2004,8,16,1,12328 2004,8,17,2,13551 2004,8,18,3,13274 2004,8,19,4,13088 2004,8,20,5,13228 2004,8,21,6,8944 2004,8,22,7,7950 2004,8,23,1,12285 2004,8,24,2,13556 2004,8,25,3,13116 2004,8,26,4,13196 2004,8,27,5,12971 2004,8,28,6,9049 2004,8,29,7,7783 2004,8,30,1,12342 2004,8,31,2,13582 2004,9,1,3,13418 2004,9,2,4,13539 2004,9,3,5,13245 2004,9,4,6,8881 2004,9,5,7,7875 2004,9,6,1,8281 2004,9,7,2,12884 2004,9,8,3,14492 2004,9,9,4,14526 2004,9,10,5,14081 2004,9,11,6,9253 2004,9,12,7,8281 2004,9,13,1,12644 2004,9,14,2,14172 2004,9,15,3,13641 2004,9,16,4,13432 2004,9,17,5,13577 2004,9,18,6,9387 2004,9,19,7,8251 2004,9,20,1,12963 2004,9,21,2,13932 2004,9,22,3,13749 2004,9,23,4,13969 2004,9,24,5,13722 2004,9,25,6,9142 2004,9,26,7,8143 2004,9,27,1,12674 2004,9,28,2,13882 2004,9,29,3,13416 2004,9,30,4,13443 2004,10,1,5,13256 2004,10,2,6,8886 2004,10,3,7,7719 2004,10,4,1,12591 2004,10,5,2,13707 2004,10,6,3,13317 2004,10,7,4,13383 2004,10,8,5,13122 2004,10,9,6,8716 2004,10,10,7,7709 2004,10,11,1,11758 2004,10,12,2,13405 2004,10,13,3,13069 2004,10,14,4,13259 2004,10,15,5,13111 2004,10,16,6,8802 2004,10,17,7,7661 2004,10,18,1,12252 2004,10,19,2,13271 2004,10,20,3,12967 2004,10,21,4,12959 2004,10,22,5,12887 2004,10,23,6,8627 2004,10,24,7,7699 2004,10,25,1,12341 2004,10,26,2,13464 2004,10,27,3,13178 2004,10,28,4,13287 2004,10,29,5,12473 2004,10,30,6,8616 2004,10,31,7,7556 2004,11,1,1,12173 2004,11,2,2,13212 2004,11,3,3,13004 2004,11,4,4,13075 2004,11,5,5,12900 2004,11,6,6,8789 2004,11,7,7,7734 2004,11,8,1,12420 2004,11,9,2,13351 2004,11,10,3,13017 2004,11,11,4,12976 2004,11,12,5,12783 2004,11,13,6,8626 2004,11,14,7,7503 2004,11,15,1,12293 2004,11,16,2,13528 2004,11,17,3,13124 2004,11,18,4,13348 2004,11,19,5,13063 2004,11,20,6,8694 2004,11,21,7,7742 2004,11,22,1,13463 2004,11,23,2,14238 2004,11,24,3,12430 2004,11,25,4,7614 2004,11,26,5,9370 2004,11,27,6,8118 2004,11,28,7,7540 2004,11,29,1,12315 2004,11,30,2,13916 2004,12,1,3,13385 2004,12,2,4,12989 2004,12,3,5,12604 2004,12,4,6,8616 2004,12,5,7,7606 2004,12,6,1,12054 2004,12,7,2,13372 2004,12,8,3,13179 2004,12,9,4,12872 2004,12,10,5,12719 2004,12,11,6,8550 2004,12,12,7,7649 2004,12,13,1,11809 2004,12,14,2,13360 2004,12,15,3,13380 2004,12,16,4,13418 2004,12,17,5,13090 2004,12,18,6,8623 2004,12,19,7,7552 2004,12,20,1,13587 2004,12,21,2,14390 2004,12,22,3,13006 2004,12,23,4,11043 2004,12,24,5,7813 2004,12,25,6,6259 2004,12,26,7,7087 2004,12,27,1,12276 2004,12,28,2,13965 2004,12,29,3,13642 2004,12,30,4,13314 2004,12,31,5,10130 2005,1,1,6,7317 2005,1,2,7,6871 2005,1,3,1,11153 2005,1,4,2,12644 2005,1,5,3,12671 2005,1,6,4,12733 2005,1,7,5,12581 2005,1,8,6,8376 2005,1,9,7,7169 2005,1,10,1,11803 2005,1,11,2,12949 2005,1,12,3,12842 2005,1,13,4,12357 2005,1,14,5,12562 2005,1,15,6,8502 2005,1,16,7,7192 2005,1,17,1,11059 2005,1,18,2,12677 2005,1,19,3,12726 2005,1,20,4,12847 2005,1,21,5,12579 2005,1,22,6,8255 2005,1,23,7,7376 2005,1,24,1,11716 2005,1,25,2,13295 2005,1,26,3,12733 2005,1,27,4,12680 2005,1,28,5,12578 2005,1,29,6,8303 2005,1,30,7,7402 2005,1,31,1,11530 2005,2,1,2,13263 2005,2,2,3,12966 2005,2,3,4,12638 2005,2,4,5,12671 2005,2,5,6,8539 2005,2,6,7,7432 2005,2,7,1,11867 2005,2,8,2,12927 2005,2,9,3,12469 2005,2,10,4,12865 2005,2,11,5,12517 2005,2,12,6,8462 2005,2,13,7,7395 2005,2,14,1,12386 2005,2,15,2,13378 2005,2,16,3,13029 2005,2,17,4,12718 2005,2,18,5,12589 2005,2,19,6,8318 2005,2,20,7,7342 2005,2,21,1,11087 2005,2,22,2,12699 2005,2,23,3,12685 2005,2,24,4,12733 2005,2,25,5,12495 2005,2,26,6,8293 2005,2,27,7,7449 2005,2,28,1,11678 2005,3,1,2,13042 2005,3,2,3,12765 2005,3,3,4,13018 2005,3,4,5,12772 2005,3,5,6,8499 2005,3,6,7,7382 2005,3,7,1,11801 2005,3,8,2,12969 2005,3,9,3,12700 2005,3,10,4,12920 2005,3,11,5,12777 2005,3,12,6,8511 2005,3,13,7,7239 2005,3,14,1,12086 2005,3,15,2,13144 2005,3,16,3,12718 2005,3,17,4,13118 2005,3,18,5,12690 2005,3,19,6,8557 2005,3,20,7,7454 2005,3,21,1,12108 2005,3,22,2,13386 2005,3,23,3,12910 2005,3,24,4,12912 2005,3,25,5,12111 2005,3,26,6,7980 2005,3,27,7,6923 2005,3,28,1,11820 2005,3,29,2,13028 2005,3,30,3,12947 2005,3,31,4,12834 2005,4,1,5,11760 2005,4,2,6,8574 2005,4,3,7,7065 2005,4,4,1,12457 2005,4,5,2,13274 2005,4,6,3,13200 2005,4,7,4,12996 2005,4,8,5,12747 2005,4,9,6,8355 2005,4,10,7,7443 2005,4,11,1,12143 2005,4,12,2,13146 2005,4,13,3,12452 2005,4,14,4,12976 2005,4,15,5,13063 2005,4,16,6,8291 2005,4,17,7,7214 2005,4,18,1,12023 2005,4,19,2,13197 2005,4,20,3,13120 2005,4,21,4,12978 2005,4,22,5,12543 2005,4,23,6,8244 2005,4,24,7,7267 2005,4,25,1,12002 2005,4,26,2,13157 2005,4,27,3,12929 2005,4,28,4,12822 2005,4,29,5,12342 2005,4,30,6,8280 2005,5,1,7,7230 2005,5,2,1,11980 2005,5,3,2,13079 2005,5,4,3,12841 2005,5,5,4,14357 2005,5,6,5,12496 2005,5,7,6,8204 2005,5,8,7,7349 2005,5,9,1,12155 2005,5,10,2,13299 2005,5,11,3,12762 2005,5,12,4,13251 2005,5,13,5,11803 2005,5,14,6,8610 2005,5,15,7,7515 2005,5,16,1,12307 2005,5,17,2,13659 2005,5,18,3,13378 2005,5,19,4,13114 2005,5,20,5,13007 2005,5,21,6,8490 2005,5,22,7,7386 2005,5,23,1,12445 2005,5,24,2,13740 2005,5,25,3,13793 2005,5,26,4,13654 2005,5,27,5,13378 2005,5,28,6,8688 2005,5,29,7,7270 2005,5,30,1,7886 2005,5,31,2,12610 2005,6,1,3,14054 2005,6,2,4,13666 2005,6,3,5,13483 2005,6,4,6,8686 2005,6,5,7,7791 2005,6,6,1,12363 2005,6,7,2,13481 2005,6,8,3,13138 2005,6,9,4,13422 2005,6,10,5,13230 2005,6,11,6,8621 2005,6,12,7,7487 2005,6,13,1,11843 2005,6,14,2,13815 2005,6,15,3,13261 2005,6,16,4,13033 2005,6,17,5,12821 2005,6,18,6,8573 2005,6,19,7,7522 2005,6,20,1,12332 2005,6,21,2,13439 2005,6,22,3,13342 2005,6,23,4,13458 2005,6,24,5,13032 2005,6,25,6,8737 2005,6,26,7,7603 2005,6,27,1,12488 2005,6,28,2,13813 2005,6,29,3,14039 2005,6,30,4,14003 2005,7,1,5,13759 2005,7,2,6,8862 2005,7,3,7,7668 2005,7,4,1,7733 2005,7,5,2,12847 2005,7,6,3,14562 2005,7,7,4,14627 2005,7,8,5,14136 2005,7,9,6,9189 2005,7,10,7,7829 2005,7,11,1,12626 2005,7,12,2,13884 2005,7,13,3,13431 2005,7,14,4,14038 2005,7,15,5,13685 2005,7,16,6,9036 2005,7,17,7,7793 2005,7,18,1,12698 2005,7,19,2,13791 2005,7,20,3,13603 2005,7,21,4,13870 2005,7,22,5,13390 2005,7,23,6,8916 2005,7,24,7,7762 2005,7,25,1,12651 2005,7,26,2,13671 2005,7,27,3,13528 2005,7,28,4,13621 2005,7,29,5,13260 2005,7,30,6,8987 2005,7,31,7,7743 2005,8,1,1,12415 2005,8,2,2,13730 2005,8,3,3,13350 2005,8,4,4,13511 2005,8,5,5,13413 2005,8,6,6,8820 2005,8,7,7,7662 2005,8,8,1,12553 2005,8,9,2,13893 2005,8,10,3,13593 2005,8,11,4,14011 2005,8,12,5,13610 2005,8,13,6,9049 2005,8,14,7,7867 2005,8,15,1,12740 2005,8,16,2,13998 2005,8,17,3,13801 2005,8,18,4,14009 2005,8,19,5,13365 2005,8,20,6,9118 2005,8,21,7,7776 2005,8,22,1,12487 2005,8,23,2,13739 2005,8,24,3,13569 2005,8,25,4,13824 2005,8,26,5,13327 2005,8,27,6,8952 2005,8,28,7,7743 2005,8,29,1,12711 2005,8,30,2,13933 2005,8,31,3,13898 2005,9,1,4,14160 2005,9,2,5,13904 2005,9,3,6,9128 2005,9,4,7,7931 2005,9,5,1,8116 2005,9,6,2,13124 2005,9,7,3,14744 2005,9,8,4,14740 2005,9,9,5,14505 2005,9,10,6,9565 2005,9,11,7,8041 2005,9,12,1,13189 2005,9,13,2,13951 2005,9,14,3,14160 2005,9,15,4,14263 2005,9,16,5,14189 2005,9,17,6,9459 2005,9,18,7,8262 2005,9,19,1,13460 2005,9,20,2,14590 2005,9,21,3,14203 2005,9,22,4,13973 2005,9,23,5,13776 2005,9,24,6,9207 2005,9,25,7,8028 2005,9,26,1,12952 2005,9,27,2,13955 2005,9,28,3,13785 2005,9,29,4,13540 2005,9,30,5,13454 2005,10,1,6,8820 2005,10,2,7,7841 2005,10,3,1,12816 2005,10,4,2,13449 2005,10,5,3,13488 2005,10,6,4,13552 2005,10,7,5,13056 2005,10,8,6,8846 2005,10,9,7,7508 2005,10,10,1,12298 2005,10,11,2,13256 2005,10,12,3,13191 2005,10,13,4,12922 2005,10,14,5,13087 2005,10,15,6,8733 2005,10,16,7,7432 2005,10,17,1,12230 2005,10,18,2,13442 2005,10,19,3,12932 2005,10,20,4,13267 2005,10,21,5,12828 2005,10,22,6,8568 2005,10,23,7,7371 2005,10,24,1,12012 2005,10,25,2,13351 2005,10,26,3,12798 2005,10,27,4,13273 2005,10,28,5,12619 2005,10,29,6,8509 2005,10,30,7,7459 2005,10,31,1,10207 2005,11,1,2,13682 2005,11,2,3,13275 2005,11,3,4,13284 2005,11,4,5,12928 2005,11,5,6,8675 2005,11,6,7,7565 2005,11,7,1,12176 2005,11,8,2,13678 2005,11,9,3,13208 2005,11,10,4,13227 2005,11,11,5,12584 2005,11,12,6,8333 2005,11,13,7,7420 2005,11,14,1,12164 2005,11,15,2,13549 2005,11,16,3,13113 2005,11,17,4,13280 2005,11,18,5,13153 2005,11,19,6,8481 2005,11,20,7,7594 2005,11,21,1,13399 2005,11,22,2,14175 2005,11,23,3,12202 2005,11,24,4,7267 2005,11,25,5,9090 2005,11,26,6,7848 2005,11,27,7,7197 2005,11,28,1,12716 2005,11,29,2,13743 2005,11,30,3,13176 2005,12,1,4,13210 2005,12,2,5,12599 2005,12,3,6,8241 2005,12,4,7,7297 2005,12,5,1,12106 2005,12,6,2,13249 2005,12,7,3,13017 2005,12,8,4,13048 2005,12,9,5,12391 2005,12,10,6,8401 2005,12,11,7,7368 2005,12,12,1,12494 2005,12,13,2,13323 2005,12,14,3,13768 2005,12,15,4,13586 2005,12,16,5,13320 2005,12,17,6,8701 2005,12,18,7,7617 2005,12,19,1,13410 2005,12,20,2,14659 2005,12,21,3,14159 2005,12,22,4,12877 2005,12,23,5,10642 2005,12,24,6,7256 2005,12,25,7,6224 2005,12,26,1,8505 2005,12,27,2,13056 2005,12,28,3,14381 2005,12,29,4,13972 2005,12,30,5,13208 2005,12,31,6,8635 2006,1,1,7,7137 2006,1,2,1,8198 2006,1,3,2,11992 2006,1,4,3,12966 2006,1,5,4,13117 2006,1,6,5,13071 2006,1,7,6,8546 2006,1,8,7,7409 2006,1,9,1,11809 2006,1,10,2,12992 2006,1,11,3,12844 2006,1,12,4,13309 2006,1,13,5,11994 2006,1,14,6,8628 2006,1,15,7,7312 2006,1,16,1,11477 2006,1,17,2,13018 2006,1,18,3,13079 2006,1,19,4,13125 2006,1,20,5,13040 2006,1,21,6,8408 2006,1,22,7,7442 2006,1,23,1,12102 2006,1,24,2,12983 2006,1,25,3,12911 2006,1,26,4,13044 2006,1,27,5,12917 2006,1,28,6,8439 2006,1,29,7,7572 2006,1,30,1,12150 2006,1,31,2,12945 2006,2,1,3,12960 2006,2,2,4,13231 2006,2,3,5,13089 2006,2,4,6,8647 2006,2,5,7,7506 2006,2,6,1,12302 2006,2,7,2,13555 2006,2,8,3,13057 2006,2,9,4,13232 2006,2,10,5,13298 2006,2,11,6,8702 2006,2,12,7,7404 2006,2,13,1,11955 2006,2,14,2,13886 2006,2,15,3,13424 2006,2,16,4,13303 2006,2,17,5,13218 2006,2,18,6,8738 2006,2,19,7,7577 2006,2,20,1,11466 2006,2,21,2,13172 2006,2,22,3,13341 2006,2,23,4,13280 2006,2,24,5,12832 2006,2,25,6,8557 2006,2,26,7,7400 2006,2,27,1,12080 2006,2,28,2,13223 2006,3,1,3,13422 2006,3,2,4,13210 2006,3,3,5,13212 2006,3,4,6,8682 2006,3,5,7,7440 2006,3,6,1,12361 2006,3,7,2,13248 2006,3,8,3,13427 2006,3,9,4,13305 2006,3,10,5,13162 2006,3,11,6,8602 2006,3,12,7,7558 2006,3,13,1,11742 2006,3,14,2,13358 2006,3,15,3,13183 2006,3,16,4,13125 2006,3,17,5,13003 2006,3,18,6,8757 2006,3,19,7,7355 2006,3,20,1,12335 2006,3,21,2,13378 2006,3,22,3,13027 2006,3,23,4,13042 2006,3,24,5,12874 2006,3,25,6,8381 2006,3,26,7,7403 2006,3,27,1,12095 2006,3,28,2,13246 2006,3,29,3,13114 2006,3,30,4,13067 2006,3,31,5,12406 2006,4,1,6,8268 2006,4,2,7,7271 2006,4,3,1,12398 2006,4,4,2,13287 2006,4,5,3,13348 2006,4,6,4,13069 2006,4,7,5,12922 2006,4,8,6,8333 2006,4,9,7,7314 2006,4,10,1,12233 2006,4,11,2,13504 2006,4,12,3,13120 2006,4,13,4,12853 2006,4,14,5,12139 2006,4,15,6,8227 2006,4,16,7,7030 2006,4,17,1,11897 2006,4,18,2,13415 2006,4,19,3,12979 2006,4,20,4,13157 2006,4,21,5,12776 2006,4,22,6,8397 2006,4,23,7,7141 2006,4,24,1,12164 2006,4,25,2,13238 2006,4,26,3,13011 2006,4,27,4,13120 2006,4,28,5,12562 2006,4,29,6,8287 2006,4,30,7,7127 2006,5,1,1,12248 2006,5,2,2,13242 2006,5,3,3,13059 2006,5,4,4,12941 2006,5,5,5,12983 2006,5,6,6,8297 2006,5,7,7,7343 2006,5,8,1,12355 2006,5,9,2,13100 2006,5,10,3,13079 2006,5,11,4,12921 2006,5,12,5,12685 2006,5,13,6,8260 2006,5,14,7,7288 2006,5,15,1,12476 2006,5,16,2,13630 2006,5,17,3,13444 2006,5,18,4,13274 2006,5,19,5,12731 2006,5,20,6,8624 2006,5,21,7,7473 2006,5,22,1,12775 2006,5,23,2,13827 2006,5,24,3,13544 2006,5,25,4,14074 2006,5,26,5,13355 2006,5,27,6,8883 2006,5,28,7,7651 2006,5,29,1,8099 2006,5,30,2,13051 2006,5,31,3,14189 2006,6,1,4,14257 2006,6,2,5,13772 2006,6,3,6,8878 2006,6,4,7,7834 2006,6,5,1,13004 2006,6,6,2,11661 2006,6,7,3,13693 2006,6,8,4,14137 2006,6,9,5,13203 2006,6,10,6,8619 2006,6,11,7,7653 2006,6,12,1,12652 2006,6,13,2,13378 2006,6,14,3,13800 2006,6,15,4,13765 2006,6,16,5,13461 2006,6,17,6,8892 2006,6,18,7,7902 2006,6,19,1,12869 2006,6,20,2,14021 2006,6,21,3,13586 2006,6,22,4,13722 2006,6,23,5,13136 2006,6,24,6,8740 2006,6,25,7,7727 2006,6,26,1,12660 2006,6,27,2,14119 2006,6,28,3,14246 2006,6,29,4,14218 2006,6,30,5,14010 2006,7,1,6,9285 2006,7,2,7,7817 2006,7,3,1,11867 2006,7,4,2,9083 2006,7,5,3,13124 2006,7,6,4,15007 2006,7,7,5,14580 2006,7,8,6,9526 2006,7,9,7,8088 2006,7,10,1,13306 2006,7,11,2,14413 2006,7,12,3,13919 2006,7,13,4,13926 2006,7,14,5,14174 2006,7,15,6,9477 2006,7,16,7,8150 2006,7,17,1,13454 2006,7,18,2,14456 2006,7,19,3,14019 2006,7,20,4,14239 2006,7,21,5,14195 2006,7,22,6,9219 2006,7,23,7,8156 2006,7,24,1,13075 2006,7,25,2,14387 2006,7,26,3,14093 2006,7,27,4,14270 2006,7,28,5,13912 2006,7,29,6,9332 2006,7,30,7,8105 2006,7,31,1,12791 2006,8,1,2,14537 2006,8,2,3,14114 2006,8,3,4,14093 2006,8,4,5,13899 2006,8,5,6,9441 2006,8,6,7,7881 2006,8,7,1,13112 2006,8,8,2,14507 2006,8,9,3,14277 2006,8,10,4,14331 2006,8,11,5,13975 2006,8,12,6,9401 2006,8,13,7,7979 2006,8,14,1,13313 2006,8,15,2,14570 2006,8,16,3,14330 2006,8,17,4,14355 2006,8,18,5,13864 2006,8,19,6,9509 2006,8,20,7,8217 2006,8,21,1,13236 2006,8,22,2,14433 2006,8,23,3,14360 2006,8,24,4,14109 2006,8,25,5,13921 2006,8,26,6,9313 2006,8,27,7,8144 2006,8,28,1,13433 2006,8,29,2,14688 2006,8,30,3,14466 2006,8,31,4,14391 2006,9,1,5,14458 2006,9,2,6,9426 2006,9,3,7,8162 2006,9,4,1,8298 2006,9,5,2,13654 2006,9,6,3,15391 2006,9,7,4,15454 2006,9,8,5,15018 2006,9,9,6,9759 2006,9,10,7,8407 2006,9,11,1,12868 2006,9,12,2,15078 2006,9,13,3,14769 2006,9,14,4,15099 2006,9,15,5,14762 2006,9,16,6,9648 2006,9,17,7,8701 2006,9,18,1,13958 2006,9,19,2,15205 2006,9,20,3,14850 2006,9,21,4,14965 2006,9,22,5,14708 2006,9,23,6,9815 2006,9,24,7,8371 2006,9,25,1,13740 2006,9,26,2,14912 2006,9,27,3,14465 2006,9,28,4,14281 2006,9,29,5,13828 2006,9,30,6,9154 2006,10,1,7,8263 2006,10,2,1,13109 2006,10,3,2,14550 2006,10,4,3,14214 2006,10,5,4,14212 2006,10,6,5,13829 2006,10,7,6,9015 2006,10,8,7,7940 2006,10,9,1,12796 2006,10,10,2,14480 2006,10,11,3,14086 2006,10,12,4,13985 2006,10,13,5,12628 2006,10,14,6,8804 2006,10,15,7,7757 2006,10,16,1,12873 2006,10,17,2,14304 2006,10,18,3,13877 2006,10,19,4,13648 2006,10,20,5,13327 2006,10,21,6,8803 2006,10,22,7,7805 2006,10,23,1,12836 2006,10,24,2,14153 2006,10,25,3,13751 2006,10,26,4,13974 2006,10,27,5,13374 2006,10,28,6,8789 2006,10,29,7,7974 2006,10,30,1,12465 2006,10,31,2,12064 2006,11,1,3,13969 2006,11,2,4,13920 2006,11,3,5,13589 2006,11,4,6,8787 2006,11,5,7,7957 2006,11,6,1,12893 2006,11,7,2,13779 2006,11,8,3,13798 2006,11,9,4,13783 2006,11,10,5,13571 2006,11,11,6,8807 2006,11,12,7,7650 2006,11,13,1,12546 2006,11,14,2,14229 2006,11,15,3,13881 2006,11,16,4,14073 2006,11,17,5,14158 2006,11,18,6,8844 2006,11,19,7,7577 2006,11,20,1,14053 2006,11,21,2,14835 2006,11,22,3,13181 2006,11,23,4,7521 2006,11,24,5,9640 2006,11,25,6,8217 2006,11,26,7,7585 2006,11,27,1,13150 2006,11,28,2,14575 2006,11,29,3,13997 2006,11,30,4,13411 2006,12,1,5,13451 2006,12,2,6,8740 2006,12,3,7,7607 2006,12,4,1,12498 2006,12,5,2,13859 2006,12,6,3,13840 2006,12,7,4,13619 2006,12,8,5,12945 2006,12,9,6,8769 2006,12,10,7,7520 2006,12,11,1,12803 2006,12,12,2,14301 2006,12,13,3,13794 2006,12,14,4,13993 2006,12,15,5,13489 2006,12,16,6,9012 2006,12,17,7,7741 2006,12,18,1,13597 2006,12,19,2,14900 2006,12,20,3,14900 2006,12,21,4,14452 2006,12,22,5,12998 2006,12,23,6,8318 2006,12,24,7,6708 2006,12,25,1,6409 2006,12,26,2,11087 2006,12,27,3,14795 2006,12,28,4,14997 2006,12,29,5,14402 2006,12,30,6,9498 2006,12,31,7,7569 2007,1,1,1,7322 2007,1,2,2,11807 2007,1,3,3,13687 2007,1,4,4,13564 2007,1,5,5,13960 2007,1,6,6,8865 2007,1,7,7,7580 2007,1,8,1,12315 2007,1,9,2,13237 2007,1,10,3,13264 2007,1,11,4,13517 2007,1,12,5,13400 2007,1,13,6,8670 2007,1,14,7,7653 2007,1,15,1,11820 2007,1,16,2,12825 2007,1,17,3,13244 2007,1,18,4,13495 2007,1,19,5,12921 2007,1,20,6,8600 2007,1,21,7,7563 2007,1,22,1,12454 2007,1,23,2,13418 2007,1,24,3,13320 2007,1,25,4,13448 2007,1,26,5,13110 2007,1,27,6,8633 2007,1,28,7,7633 2007,1,29,1,12402 2007,1,30,2,13486 2007,1,31,3,13308 2007,2,1,4,13557 2007,2,2,5,13305 2007,2,3,6,8821 2007,2,4,7,7628 2007,2,5,1,12369 2007,2,6,2,13495 2007,2,7,3,13466 2007,2,8,4,13451 2007,2,9,5,13419 2007,2,10,6,8732 2007,2,11,7,7833 2007,2,12,1,12792 2007,2,13,2,13437 2007,2,14,3,13647 2007,2,15,4,13642 2007,2,16,5,13517 2007,2,17,6,8940 2007,2,18,7,7791 2007,2,19,1,11752 2007,2,20,2,13466 2007,2,21,3,13470 2007,2,22,4,13748 2007,2,23,5,13347 2007,2,24,6,8732 2007,2,25,7,7725 2007,2,26,1,12578 2007,2,27,2,13591 2007,2,28,3,13366 2007,3,1,4,13572 2007,3,2,5,13244 2007,3,3,6,8739 2007,3,4,7,7566 2007,3,5,1,12480 2007,3,6,2,13551 2007,3,7,3,13520 2007,3,8,4,13751 2007,3,9,5,13508 2007,3,10,6,8729 2007,3,11,7,7390 2007,3,12,1,12524 2007,3,13,2,13147 2007,3,14,3,13311 2007,3,15,4,13471 2007,3,16,5,13286 2007,3,17,6,8791 2007,3,18,7,7681 2007,3,19,1,12366 2007,3,20,2,13844 2007,3,21,3,13710 2007,3,22,4,13388 2007,3,23,5,13464 2007,3,24,6,8762 2007,3,25,7,7785 2007,3,26,1,12462 2007,3,27,2,13664 2007,3,28,3,13420 2007,3,29,4,13171 2007,3,30,5,13138 2007,3,31,6,8453 2007,4,1,7,7372 2007,4,2,1,12450 2007,4,3,2,13504 2007,4,4,3,13729 2007,4,5,4,13360 2007,4,6,5,12308 2007,4,7,6,8253 2007,4,8,7,6903 2007,4,9,1,12120 2007,4,10,2,13564 2007,4,11,3,13430 2007,4,12,4,13609 2007,4,13,5,12168 2007,4,14,6,8237 2007,4,15,7,7225 2007,4,16,1,12502 2007,4,17,2,13604 2007,4,18,3,13386 2007,4,19,4,13358 2007,4,20,5,13000 2007,4,21,6,8302 2007,4,22,7,7590 2007,4,23,1,12431 2007,4,24,2,13519 2007,4,25,3,13368 2007,4,26,4,13001 2007,4,27,5,12795 2007,4,28,6,8302 2007,4,29,7,7409 2007,4,30,1,12182 2007,5,1,2,13902 2007,5,2,3,13325 2007,5,3,4,13155 2007,5,4,5,12773 2007,5,5,6,8374 2007,5,6,7,7476 2007,5,7,1,12250 2007,5,8,2,13267 2007,5,9,3,13111 2007,5,10,4,13504 2007,5,11,5,13070 2007,5,12,6,8489 2007,5,13,7,7260 2007,5,14,1,12552 2007,5,15,2,13995 2007,5,16,3,13723 2007,5,17,4,13408 2007,5,18,5,12782 2007,5,19,6,8560 2007,5,20,7,7577 2007,5,21,1,12816 2007,5,22,2,14143 2007,5,23,3,13906 2007,5,24,4,14010 2007,5,25,5,13670 2007,5,26,6,8764 2007,5,27,7,7607 2007,5,28,1,7917 2007,5,29,2,13291 2007,5,30,3,14569 2007,5,31,4,14245 2007,6,1,5,13714 2007,6,2,6,8977 2007,6,3,7,7813 2007,6,4,1,12711 2007,6,5,2,13848 2007,6,6,3,13703 2007,6,7,4,13674 2007,6,8,5,13595 2007,6,9,6,8810 2007,6,10,7,7596 2007,6,11,1,12826 2007,6,12,2,13969 2007,6,13,3,13534 2007,6,14,4,14139 2007,6,15,5,13563 2007,6,16,6,8967 2007,6,17,7,7837 2007,6,18,1,13178 2007,6,19,2,14017 2007,6,20,3,13904 2007,6,21,4,13837 2007,6,22,5,13697 2007,6,23,6,9105 2007,6,24,7,7710 2007,6,25,1,12972 2007,6,26,2,14395 2007,6,27,3,14318 2007,6,28,4,14224 2007,6,29,5,13837 2007,6,30,6,9016 2007,7,1,7,7937 2007,7,2,1,13794 2007,7,3,2,14814 2007,7,4,3,9746 2007,7,5,4,13367 2007,7,6,5,14143 2007,7,7,6,10499 2007,7,8,7,8322 2007,7,9,1,13473 2007,7,10,2,14927 2007,7,11,3,14594 2007,7,12,4,14115 2007,7,13,5,13228 2007,7,14,6,9327 2007,7,15,7,7983 2007,7,16,1,13483 2007,7,17,2,14828 2007,7,18,3,14349 2007,7,19,4,14169 2007,7,20,5,14070 2007,7,21,6,9356 2007,7,22,7,7963 2007,7,23,1,13293 2007,7,24,2,14783 2007,7,25,3,14510 2007,7,26,4,14212 2007,7,27,5,14354 2007,7,28,6,9258 2007,7,29,7,8116 2007,7,30,1,13439 2007,7,31,2,14409 2007,8,1,3,14627 2007,8,2,4,14241 2007,8,3,5,13961 2007,8,4,6,9083 2007,8,5,7,8160 2007,8,6,1,13318 2007,8,7,2,14670 2007,8,8,3,14477 2007,8,9,4,14314 2007,8,10,5,13836 2007,8,11,6,9200 2007,8,12,7,7945 2007,8,13,1,13199 2007,8,14,2,14695 2007,8,15,3,14629 2007,8,16,4,14674 2007,8,17,5,14136 2007,8,18,6,9332 2007,8,19,7,8115 2007,8,20,1,13496 2007,8,21,2,14541 2007,8,22,3,14344 2007,8,23,4,14447 2007,8,24,5,14162 2007,8,25,6,9234 2007,8,26,7,8025 2007,8,27,1,13187 2007,8,28,2,14959 2007,8,29,3,14517 2007,8,30,4,14668 2007,8,31,5,14163 2007,9,1,6,9465 2007,9,2,7,7957 2007,9,3,1,8397 2007,9,4,2,13600 2007,9,5,3,15440 2007,9,6,4,15010 2007,9,7,5,14818 2007,9,8,6,9745 2007,9,9,7,8389 2007,9,10,1,13844 2007,9,11,2,14063 2007,9,12,3,14960 2007,9,13,4,14525 2007,9,14,5,14603 2007,9,15,6,9807 2007,9,16,7,8283 2007,9,17,1,13798 2007,9,18,2,15194 2007,9,19,3,14783 2007,9,20,4,15139 2007,9,21,5,14473 2007,9,22,6,9604 2007,9,23,7,8512 2007,9,24,1,13534 2007,9,25,2,14788 2007,9,26,3,14417 2007,9,27,4,14519 2007,9,28,5,13926 2007,9,29,6,9198 2007,9,30,7,7983 2007,10,1,1,13244 2007,10,2,2,14231 2007,10,3,3,14021 2007,10,4,4,13756 2007,10,5,5,13649 2007,10,6,6,8901 2007,10,7,7,7858 2007,10,8,1,12582 2007,10,9,2,14033 2007,10,10,3,14086 2007,10,11,4,13580 2007,10,12,5,13400 2007,10,13,6,8756 2007,10,14,7,7579 2007,10,15,1,12987 2007,10,16,2,14039 2007,10,17,3,13783 2007,10,18,4,13581 2007,10,19,5,13437 2007,10,20,6,8607 2007,10,21,7,7723 2007,10,22,1,12730 2007,10,23,2,13681 2007,10,24,3,13771 2007,10,25,4,13874 2007,10,26,5,13223 2007,10,27,6,8806 2007,10,28,7,7560 2007,10,29,1,12648 2007,10,30,2,13389 2007,10,31,3,11757 2007,11,1,4,13926 2007,11,2,5,13803 2007,11,3,6,8837 2007,11,4,7,7975 2007,11,5,1,13023 2007,11,6,2,14159 2007,11,7,3,13905 2007,11,8,4,13734 2007,11,9,5,13542 2007,11,10,6,8755 2007,11,11,7,7920 2007,11,12,1,12746 2007,11,13,2,13640 2007,11,14,3,13850 2007,11,15,4,14432 2007,11,16,5,14156 2007,11,17,6,9123 2007,11,18,7,7898 2007,11,19,1,13944 2007,11,20,2,14808 2007,11,21,3,13230 2007,11,22,4,7567 2007,11,23,5,9598 2007,11,24,6,8380 2007,11,25,7,7668 2007,11,26,1,13192 2007,11,27,2,14707 2007,11,28,3,14030 2007,11,29,4,13821 2007,11,30,5,12966 2007,12,1,6,8761 2007,12,2,7,7676 2007,12,3,1,12581 2007,12,4,2,13878 2007,12,5,3,13695 2007,12,6,4,13514 2007,12,7,5,13168 2007,12,8,6,8676 2007,12,9,7,7603 2007,12,10,1,12759 2007,12,11,2,13962 2007,12,12,3,13906 2007,12,13,4,13418 2007,12,14,5,13267 2007,12,15,6,8654 2007,12,16,7,7636 2007,12,17,1,13455 2007,12,18,2,14983 2007,12,19,3,14941 2007,12,20,4,15214 2007,12,21,5,14808 2007,12,22,6,9194 2007,12,23,7,7398 2007,12,24,1,7727 2007,12,25,2,6624 2007,12,26,3,12306 2007,12,27,4,15590 2007,12,28,5,15555 2007,12,29,6,9961 2007,12,30,7,8191 2007,12,31,1,11102 2008,1,1,2,8014 2008,1,2,3,11729 2008,1,3,4,13691 2008,1,4,5,13799 2008,1,5,6,9113 2008,1,6,7,7610 2008,1,7,1,12335 2008,1,8,2,13336 2008,1,9,3,13022 2008,1,10,4,13617 2008,1,11,5,13412 2008,1,12,6,8712 2008,1,13,7,7407 2008,1,14,1,12566 2008,1,15,2,13344 2008,1,16,3,13183 2008,1,17,4,13332 2008,1,18,5,13473 2008,1,19,6,8480 2008,1,20,7,7481 2008,1,21,1,11883 2008,1,22,2,13297 2008,1,23,3,13458 2008,1,24,4,13485 2008,1,25,5,13305 2008,1,26,6,8717 2008,1,27,7,7643 2008,1,28,1,12592 2008,1,29,2,13412 2008,1,30,3,13233 2008,1,31,4,13187 2008,2,1,5,13191 2008,2,2,6,8646 2008,2,3,7,7616 2008,2,4,1,12592 2008,2,5,2,13447 2008,2,6,3,13338 2008,2,7,4,13636 2008,2,8,5,13582 2008,2,9,6,8862 2008,2,10,7,7637 2008,2,11,1,12578 2008,2,12,2,13867 2008,2,13,3,13125 2008,2,14,4,14207 2008,2,15,5,13696 2008,2,16,6,8780 2008,2,17,7,7646 2008,2,18,1,12032 2008,2,19,2,13548 2008,2,20,3,13418 2008,2,21,4,13507 2008,2,22,5,13183 2008,2,23,6,8973 2008,2,24,7,7505 2008,2,25,1,12621 2008,2,26,2,13500 2008,2,27,3,13316 2008,2,28,4,13674 2008,2,29,5,11631 2008,3,1,6,8832 2008,3,2,7,7535 2008,3,3,1,12621 2008,3,4,2,13622 2008,3,5,3,13160 2008,3,6,4,13279 2008,3,7,5,13104 2008,3,8,6,8409 2008,3,9,7,7216 2008,3,10,1,12648 2008,3,11,2,13571 2008,3,12,3,13353 2008,3,13,4,13037 2008,3,14,5,13321 2008,3,15,6,8806 2008,3,16,7,7626 2008,3,17,1,13006 2008,3,18,2,13766 2008,3,19,3,13356 2008,3,20,4,13614 2008,3,21,5,12606 2008,3,22,6,8477 2008,3,23,7,7174 2008,3,24,1,12352 2008,3,25,2,13572 2008,3,26,3,13116 2008,3,27,4,13224 2008,3,28,5,12886 2008,3,29,6,8616 2008,3,30,7,7368 2008,3,31,1,12211 2008,4,1,2,12771 2008,4,2,3,13491 2008,4,3,4,13340 2008,4,4,5,13405 2008,4,5,6,8600 2008,4,6,7,7606 2008,4,7,1,12312 2008,4,8,2,13526 2008,4,9,3,13009 2008,4,10,4,13236 2008,4,11,5,13053 2008,4,12,6,8531 2008,4,13,7,7384 2008,4,14,1,12386 2008,4,15,2,13274 2008,4,16,3,13120 2008,4,17,4,13164 2008,4,18,5,13090 2008,4,19,6,8695 2008,4,20,7,7504 2008,4,21,1,12376 2008,4,22,2,13428 2008,4,23,3,13284 2008,4,24,4,13317 2008,4,25,5,12851 2008,4,26,6,8304 2008,4,27,7,7439 2008,4,28,1,12325 2008,4,29,2,13313 2008,4,30,3,13210 2008,5,1,4,13520 2008,5,2,5,12872 2008,5,3,6,8329 2008,5,4,7,7135 2008,5,5,1,12480 2008,5,6,2,13416 2008,5,7,3,13059 2008,5,8,4,13387 2008,5,9,5,12934 2008,5,10,6,8554 2008,5,11,7,7293 2008,5,12,1,12613 2008,5,13,2,13238 2008,5,14,3,13405 2008,5,15,4,13521 2008,5,16,5,13062 2008,5,17,6,8246 2008,5,18,7,7573 2008,5,19,1,12614 2008,5,20,2,13912 2008,5,21,3,13853 2008,5,22,4,13732 2008,5,23,5,13342 2008,5,24,6,8529 2008,5,25,7,7441 2008,5,26,1,7948 2008,5,27,2,13181 2008,5,28,3,14397 2008,5,29,4,13783 2008,5,30,5,13602 2008,5,31,6,8864 2008,6,1,7,7651 2008,6,2,1,12590 2008,6,3,2,13459 2008,6,4,3,13597 2008,6,5,4,13438 2008,6,6,5,13159 2008,6,7,6,8708 2008,6,8,7,7727 2008,6,9,1,12450 2008,6,10,2,13789 2008,6,11,3,13609 2008,6,12,4,13796 2008,6,13,5,12394 2008,6,14,6,8603 2008,6,15,7,7779 2008,6,16,1,12732 2008,6,17,2,13756 2008,6,18,3,13638 2008,6,19,4,13452 2008,6,20,5,13403 2008,6,21,6,8857 2008,6,22,7,7651 2008,6,23,1,12794 2008,6,24,2,13983 2008,6,25,3,13728 2008,6,26,4,13547 2008,6,27,5,13411 2008,6,28,6,8991 2008,6,29,7,7840 2008,6,30,1,12898 2008,7,1,2,14350 2008,7,2,3,14189 2008,7,3,4,14182 2008,7,4,5,9449 2008,7,5,6,8061 2008,7,6,7,7725 2008,7,7,1,13340 2008,7,8,2,14771 2008,7,9,3,14098 2008,7,10,4,13952 2008,7,11,5,13697 2008,7,12,6,9084 2008,7,13,7,7885 2008,7,14,1,12881 2008,7,15,2,14221 2008,7,16,3,14016 2008,7,17,4,13987 2008,7,18,5,13542 2008,7,19,6,8978 2008,7,20,7,7999 2008,7,21,1,13053 2008,7,22,2,14241 2008,7,23,3,13994 2008,7,24,4,13622 2008,7,25,5,13417 2008,7,26,6,8898 2008,7,27,7,7940 2008,7,28,1,13054 2008,7,29,2,14259 2008,7,30,3,13883 2008,7,31,4,13939 2008,8,1,5,13684 2008,8,2,6,9018 2008,8,3,7,7911 2008,8,4,1,13155 2008,8,5,2,13981 2008,8,6,3,13800 2008,8,7,4,13859 2008,8,8,5,15374 2008,8,9,6,9233 2008,8,10,7,7951 2008,8,11,1,13186 2008,8,12,2,14336 2008,8,13,3,13933 2008,8,14,4,14248 2008,8,15,5,13890 2008,8,16,6,9180 2008,8,17,7,7848 2008,8,18,1,13404 2008,8,19,2,14348 2008,8,20,3,14083 2008,8,21,4,14010 2008,8,22,5,13923 2008,8,23,6,8997 2008,8,24,7,8008 2008,8,25,1,13051 2008,8,26,2,14260 2008,8,27,3,14213 2008,8,28,4,14718 2008,8,29,5,14260 2008,8,30,6,9182 2008,8,31,7,8002 2008,9,1,1,8105 2008,9,2,2,13488 2008,9,3,3,14657 2008,9,4,4,14980 2008,9,5,5,14475 2008,9,6,6,9450 2008,9,7,7,8209 2008,9,8,1,13437 2008,9,9,2,14567 2008,9,10,3,14474 2008,9,11,4,13391 2008,9,12,5,14312 2008,9,13,6,9552 2008,9,14,7,8405 2008,9,15,1,13775 2008,9,16,2,14736 2008,9,17,3,14316 2008,9,18,4,14512 2008,9,19,5,14151 2008,9,20,6,9227 2008,9,21,7,8183 2008,9,22,1,13246 2008,9,23,2,14464 2008,9,24,3,14016 2008,9,25,4,14176 2008,9,26,5,13705 2008,9,27,6,9168 2008,9,28,7,7892 2008,9,29,1,12819 2008,9,30,2,13737 2008,10,1,3,13761 2008,10,2,4,13742 2008,10,3,5,13189 2008,10,4,6,8788 2008,10,5,7,7609 2008,10,6,1,12557 2008,10,7,2,13728 2008,10,8,3,13499 2008,10,9,4,13301 2008,10,10,5,13264 2008,10,11,6,8624 2008,10,12,7,7590 2008,10,13,1,11616 2008,10,14,2,13396 2008,10,15,3,13299 2008,10,16,4,13163 2008,10,17,5,12957 2008,10,18,6,8373 2008,10,19,7,7205 2008,10,20,1,12384 2008,10,21,2,13478 2008,10,22,3,13256 2008,10,23,4,13239 2008,10,24,5,12872 2008,10,25,6,8409 2008,10,26,7,7318 2008,10,27,1,12358 2008,10,28,2,13528 2008,10,29,3,12954 2008,10,30,4,12950 2008,10,31,5,11013 2008,11,1,6,8395 2008,11,2,7,7807 2008,11,3,1,12887 2008,11,4,2,13244 2008,11,5,3,13041 2008,11,6,4,13153 2008,11,7,5,13203 2008,11,8,6,8538 2008,11,9,7,7305 2008,11,10,1,12333 2008,11,11,2,13323 2008,11,12,3,12852 2008,11,13,4,12541 2008,11,14,5,12824 2008,11,15,6,8377 2008,11,16,7,7225 2008,11,17,1,12251 2008,11,18,2,13202 2008,11,19,3,12874 2008,11,20,4,13436 2008,11,21,5,13189 2008,11,22,6,8449 2008,11,23,7,7301 2008,11,24,1,13493 2008,11,25,2,13929 2008,11,26,3,12242 2008,11,27,4,7126 2008,11,28,5,9247 2008,11,29,6,7803 2008,11,30,7,7315 2008,12,1,1,13029 2008,12,2,2,14138 2008,12,3,3,13317 2008,12,4,4,13250 2008,12,5,5,12734 2008,12,6,6,8422 2008,12,7,7,7282 2008,12,8,1,12322 2008,12,9,2,13112 2008,12,10,3,13113 2008,12,11,4,12851 2008,12,12,5,12903 2008,12,13,6,8436 2008,12,14,7,7380 2008,12,15,1,12377 2008,12,16,2,13900 2008,12,17,3,13814 2008,12,18,4,14324 2008,12,19,5,14007 2008,12,20,6,8665 2008,12,21,7,7635 2008,12,22,1,13831 2008,12,23,2,13374 2008,12,24,3,9235 2008,12,25,4,6471 2008,12,26,5,10890 2008,12,27,6,8728 2008,12,28,7,7677 2008,12,29,1,13951 2008,12,30,2,15645 2008,12,31,3,12906 2009,1,1,4,8145 2009,1,2,5,10995 2009,1,3,6,8338 2009,1,4,7,7283 2009,1,5,1,12125 2009,1,6,2,13222 2009,1,7,3,13119 2009,1,8,4,13019 2009,1,9,5,12647 2009,1,10,6,8233 2009,1,11,7,7122 2009,1,12,1,12178 2009,1,13,2,12597 2009,1,14,3,13013 2009,1,15,4,12800 2009,1,16,5,12542 2009,1,17,6,8175 2009,1,18,7,7151 2009,1,19,1,11353 2009,1,20,2,12935 2009,1,21,3,12822 2009,1,22,4,13125 2009,1,23,5,12995 2009,1,24,6,8357 2009,1,25,7,7261 2009,1,26,1,12156 2009,1,27,2,13107 2009,1,28,3,12703 2009,1,29,4,12729 2009,1,30,5,12527 2009,1,31,6,8201 2009,2,1,7,7255 2009,2,2,1,12525 2009,2,3,2,13330 2009,2,4,3,12894 2009,2,5,4,12817 2009,2,6,5,12517 2009,2,7,6,8451 2009,2,8,7,7462 2009,2,9,1,12484 2009,2,10,2,13612 2009,2,11,3,13219 2009,2,12,4,13635 2009,2,13,5,11832 2009,2,14,6,8550 2009,2,15,7,7434 2009,2,16,1,11731 2009,2,17,2,13151 2009,2,18,3,13324 2009,2,19,4,13171 2009,2,20,5,12995 2009,2,21,6,8628 2009,2,22,7,7286 2009,2,23,1,12363 2009,2,24,2,13110 2009,2,25,3,13084 2009,2,26,4,13134 2009,2,27,5,12732 2009,2,28,6,8396 2009,3,1,7,7342 2009,3,2,1,12276 2009,3,3,2,13265 2009,3,4,3,12903 2009,3,5,4,13176 2009,3,6,5,13081 2009,3,7,6,8556 2009,3,8,7,7314 2009,3,9,1,12400 2009,3,10,2,13568 2009,3,11,3,12999 2009,3,12,4,13134 2009,3,13,5,12087 2009,3,14,6,8396 2009,3,15,7,7130 2009,3,16,1,12264 2009,3,17,2,13542 2009,3,18,3,12987 2009,3,19,4,12706 2009,3,20,5,12927 2009,3,21,6,8286 2009,3,22,7,7168 2009,3,23,1,12056 2009,3,24,2,13309 2009,3,25,3,13027 2009,3,26,4,12785 2009,3,27,5,12692 2009,3,28,6,8381 2009,3,29,7,7348 2009,3,30,1,12330 2009,3,31,2,13136 2009,4,1,3,12247 2009,4,2,4,13233 2009,4,3,5,13078 2009,4,4,6,8389 2009,4,5,7,7238 2009,4,6,1,12200 2009,4,7,2,13589 2009,4,8,3,13177 2009,4,9,4,13278 2009,4,10,5,12007 2009,4,11,6,7906 2009,4,12,7,6864 2009,4,13,1,11617 2009,4,14,2,13415 2009,4,15,3,12804 2009,4,16,4,13095 2009,4,17,5,12481 2009,4,18,6,8364 2009,4,19,7,7309 2009,4,20,1,12252 2009,4,21,2,13273 2009,4,22,3,12958 2009,4,23,4,12872 2009,4,24,5,12231 2009,4,25,6,8191 2009,4,26,7,7198 2009,4,27,1,12199 2009,4,28,2,13243 2009,4,29,3,12701 2009,4,30,4,12413 2009,5,1,5,12930 2009,5,2,6,8169 2009,5,3,7,7220 2009,5,4,1,12126 2009,5,5,2,13358 2009,5,6,3,12686 2009,5,7,4,13088 2009,5,8,5,12738 2009,5,9,6,8180 2009,5,10,7,7339 2009,5,11,1,12410 2009,5,12,2,13415 2009,5,13,3,12920 2009,5,14,4,13033 2009,5,15,5,12874 2009,5,16,6,8327 2009,5,17,7,7256 2009,5,18,1,12467 2009,5,19,2,13543 2009,5,20,3,13694 2009,5,21,4,13569 2009,5,22,5,13314 2009,5,23,6,8618 2009,5,24,7,7481 2009,5,25,1,8058 2009,5,26,2,13239 2009,5,27,3,14350 2009,5,28,4,14057 2009,5,29,5,13290 2009,5,30,6,8602 2009,5,31,7,7480 2009,6,1,1,12541 2009,6,2,2,13408 2009,6,3,3,13080 2009,6,4,4,13036 2009,6,5,5,12648 2009,6,6,6,8428 2009,6,7,7,7221 2009,6,8,1,12472 2009,6,9,2,13368 2009,6,10,3,13248 2009,6,11,4,13079 2009,6,12,5,12780 2009,6,13,6,8376 2009,6,14,7,7380 2009,6,15,1,12465 2009,6,16,2,13542 2009,6,17,3,13440 2009,6,18,4,13611 2009,6,19,5,12846 2009,6,20,6,8603 2009,6,21,7,7559 2009,6,22,1,12396 2009,6,23,2,13700 2009,6,24,3,13268 2009,6,25,4,13362 2009,6,26,5,12981 2009,6,27,6,8474 2009,6,28,7,7471 2009,6,29,1,12776 2009,6,30,2,14061 2009,7,1,3,14311 2009,7,2,4,13931 2009,7,3,5,10630 2009,7,4,6,7978 2009,7,5,7,7333 2009,7,6,1,12415 2009,7,7,2,14208 2009,7,8,3,14252 2009,7,9,4,13566 2009,7,10,5,13276 2009,7,11,6,8769 2009,7,12,7,7627 2009,7,13,1,12570 2009,7,14,2,14086 2009,7,15,3,13939 2009,7,16,4,14012 2009,7,17,5,13258 2009,7,18,6,8626 2009,7,19,7,7536 2009,7,20,1,12612 2009,7,21,2,13974 2009,7,22,3,13657 2009,7,23,4,13880 2009,7,24,5,13132 2009,7,25,6,8887 2009,7,26,7,7716 2009,7,27,1,12684 2009,7,28,2,14163 2009,7,29,3,13619 2009,7,30,4,13537 2009,7,31,5,13307 2009,8,1,6,8684 2009,8,2,7,7492 2009,8,3,1,12642 2009,8,4,2,13937 2009,8,5,3,13510 2009,8,6,4,13377 2009,8,7,5,13122 2009,8,8,6,8830 2009,8,9,7,7683 2009,8,10,1,12759 2009,8,11,2,14021 2009,8,12,3,13764 2009,8,13,4,13391 2009,8,14,5,13398 2009,8,15,6,8566 2009,8,16,7,7750 2009,8,17,1,13104 2009,8,18,2,14226 2009,8,19,3,13634 2009,8,20,4,13994 2009,8,21,5,13291 2009,8,22,6,8952 2009,8,23,7,7650 2009,8,24,1,12664 2009,8,25,2,13928 2009,8,26,3,13770 2009,8,27,4,13861 2009,8,28,5,13530 2009,8,29,6,8805 2009,8,30,7,7702 2009,8,31,1,12758 2009,9,1,2,14107 2009,9,2,3,13659 2009,9,3,4,13900 2009,9,4,5,13622 2009,9,5,6,8959 2009,9,6,7,7587 2009,9,7,1,7947 2009,9,8,2,13555 2009,9,9,3,16081 2009,9,10,4,14887 2009,9,11,5,13032 2009,9,12,6,9264 2009,9,13,7,7871 2009,9,14,1,13393 2009,9,15,2,14558 2009,9,16,3,14130 2009,9,17,4,14095 2009,9,18,5,13951 2009,9,19,6,9032 2009,9,20,7,8014 2009,9,21,1,13415 2009,9,22,2,14318 2009,9,23,3,13973 2009,9,24,4,14048 2009,9,25,5,13449 2009,9,26,6,9013 2009,9,27,7,7817 2009,9,28,1,12723 2009,9,29,2,13829 2009,9,30,3,13465 2009,10,1,4,13628 2009,10,2,5,13264 2009,10,3,6,8548 2009,10,4,7,7443 2009,10,5,1,12559 2009,10,6,2,13674 2009,10,7,3,13078 2009,10,8,4,13174 2009,10,9,5,12706 2009,10,10,6,8577 2009,10,11,7,7268 2009,10,12,1,12105 2009,10,13,2,12941 2009,10,14,3,12882 2009,10,15,4,13115 2009,10,16,5,12605 2009,10,17,6,8155 2009,10,18,7,7356 2009,10,19,1,12056 2009,10,20,2,13142 2009,10,21,3,12924 2009,10,22,4,12935 2009,10,23,5,12621 2009,10,24,6,8353 2009,10,25,7,7120 2009,10,26,1,12238 2009,10,27,2,13230 2009,10,28,3,13043 2009,10,29,4,12683 2009,10,30,5,11978 2009,10,31,6,7658 2009,11,1,7,7519 2009,11,2,1,12212 2009,11,3,2,13205 2009,11,4,3,12743 2009,11,5,4,12805 2009,11,6,5,12314 2009,11,7,6,8044 2009,11,8,7,7260 2009,11,9,1,11874 2009,11,10,2,13287 2009,11,11,3,12889 2009,11,12,4,12751 2009,11,13,5,11739 2009,11,14,6,8281 2009,11,15,7,7232 2009,11,16,1,11940 2009,11,17,2,12950 2009,11,18,3,12866 2009,11,19,4,12822 2009,11,20,5,13002 2009,11,21,6,8335 2009,11,22,7,7230 2009,11,23,1,13125 2009,11,24,2,13907 2009,11,25,3,11986 2009,11,26,4,6864 2009,11,27,5,8750 2009,11,28,6,7604 2009,11,29,7,7169 2009,11,30,1,12542 2009,12,1,2,13900 2009,12,2,3,13267 2009,12,3,4,12952 2009,12,4,5,12131 2009,12,5,6,7855 2009,12,6,7,7103 2009,12,7,1,11732 2009,12,8,2,12823 2009,12,9,3,12497 2009,12,10,4,12299 2009,12,11,5,11834 2009,12,12,6,8082 2009,12,13,7,7027 2009,12,14,1,12254 2009,12,15,2,13347 2009,12,16,3,12961 2009,12,17,4,13425 2009,12,18,5,13478 2009,12,19,6,8436 2009,12,20,7,7225 2009,12,21,1,13512 2009,12,22,2,14102 2009,12,23,3,11819 2009,12,24,4,8441 2009,12,25,5,6160 2009,12,26,6,7172 2009,12,27,7,7480 2009,12,28,1,13354 2009,12,29,2,14600 2009,12,30,3,13829 2009,12,31,4,11667 2010,1,1,5,7871 2010,1,2,6,6990 2010,1,3,7,6988 2010,1,4,1,11844 2010,1,5,2,12995 2010,1,6,3,12520 2010,1,7,4,12541 2010,1,8,5,12183 2010,1,9,6,7809 2010,1,10,7,6963 2010,1,11,1,11892 2010,1,12,2,12921 2010,1,13,3,12307 2010,1,14,4,12543 2010,1,15,5,12278 2010,1,16,6,8032 2010,1,17,7,7131 2010,1,18,1,11220 2010,1,19,2,12510 2010,1,20,3,12514 2010,1,21,4,12762 2010,1,22,5,12364 2010,1,23,6,7996 2010,1,24,7,7014 2010,1,25,1,11623 2010,1,26,2,12821 2010,1,27,3,12441 2010,1,28,4,12342 2010,1,29,5,11838 2010,1,30,6,8035 2010,1,31,7,6832 2010,2,1,1,11445 2010,2,2,2,12831 2010,2,3,3,12453 2010,2,4,4,12369 2010,2,5,5,12362 2010,2,6,6,7948 2010,2,7,7,6893 2010,2,8,1,11912 2010,2,9,2,12747 2010,2,10,3,12535 2010,2,11,4,12389 2010,2,12,5,12281 2010,2,13,6,7947 2010,2,14,7,7167 2010,2,15,1,11156 2010,2,16,2,12363 2010,2,17,3,12734 2010,2,18,4,12764 2010,2,19,5,12401 2010,2,20,6,8201 2010,2,21,7,7211 2010,2,22,1,11996 2010,2,23,2,12628 2010,2,24,3,12438 2010,2,25,4,12449 2010,2,26,5,12046 2010,2,27,6,7832 2010,2,28,7,6895 2010,3,1,1,11984 2010,3,2,2,12868 2010,3,3,3,12525 2010,3,4,4,12549 2010,3,5,5,12272 2010,3,6,6,7832 2010,3,7,7,6887 2010,3,8,1,11514 2010,3,9,2,12839 2010,3,10,3,12740 2010,3,11,4,12481 2010,3,12,5,12347 2010,3,13,6,7893 2010,3,14,7,6808 2010,3,15,1,11548 2010,3,16,2,12700 2010,3,17,3,12781 2010,3,18,4,12054 2010,3,19,5,12119 2010,3,20,6,8005 2010,3,21,7,6992 2010,3,22,1,11657 2010,3,23,2,12752 2010,3,24,3,12473 2010,3,25,4,12591 2010,3,26,5,12088 2010,3,27,6,7995 2010,3,28,7,6922 2010,3,29,1,11745 2010,3,30,2,12868 2010,3,31,3,12619 2010,4,1,4,11994 2010,4,2,5,11666 2010,4,3,6,7854 2010,4,4,7,6721 2010,4,5,1,11571 2010,4,6,2,12888 2010,4,7,3,12228 2010,4,8,4,12312 2010,4,9,5,11988 2010,4,10,6,7844 2010,4,11,7,6907 2010,4,12,1,11964 2010,4,13,2,12549 2010,4,14,3,12708 2010,4,15,4,12614 2010,4,16,5,12136 2010,4,17,6,7878 2010,4,18,7,6978 2010,4,19,1,11845 2010,4,20,2,13010 2010,4,21,3,12594 2010,4,22,4,12485 2010,4,23,5,12095 2010,4,24,6,7964 2010,4,25,7,6965 2010,4,26,1,12034 2010,4,27,2,12619 2010,4,28,3,12500 2010,4,29,4,12374 2010,4,30,5,11852 2010,5,1,6,7911 2010,5,2,7,6922 2010,5,3,1,11995 2010,5,4,2,12770 2010,5,5,3,12801 2010,5,6,4,12410 2010,5,7,5,11914 2010,5,8,6,7877 2010,5,9,7,6823 2010,5,10,1,12286 2010,5,11,2,12845 2010,5,12,3,12637 2010,5,13,4,12246 2010,5,14,5,12337 2010,5,15,6,7963 2010,5,16,7,7022 2010,5,17,1,11953 2010,5,18,2,12854 2010,5,19,3,12411 2010,5,20,4,12559 2010,5,21,5,12302 2010,5,22,6,8093 2010,5,23,7,7094 2010,5,24,1,11893 2010,5,25,2,13421 2010,5,26,3,12972 2010,5,27,4,13115 2010,5,28,5,12519 2010,5,29,6,8159 2010,5,30,7,7111 2010,5,31,1,7436 2010,6,1,2,12591 2010,6,2,3,13812 2010,6,3,4,13150 2010,6,4,5,12640 2010,6,5,6,8260 2010,6,6,7,7374 2010,6,7,1,11924 2010,6,8,2,12874 2010,6,9,3,12419 2010,6,10,4,12824 2010,6,11,5,11965 2010,6,12,6,8011 2010,6,13,7,6963 2010,6,14,1,11929 2010,6,15,2,12805 2010,6,16,3,12654 2010,6,17,4,12836 2010,6,18,5,12331 2010,6,19,6,8085 2010,6,20,7,7164 2010,6,21,1,11922 2010,6,22,2,12838 2010,6,23,3,12878 2010,6,24,4,12671 2010,6,25,5,12552 2010,6,26,6,8294 2010,6,27,7,7234 2010,6,28,1,12157 2010,6,29,2,13042 2010,6,30,3,12767 2010,7,1,4,13181 2010,7,2,5,12486 2010,7,3,6,7932 2010,7,4,7,7279 2010,7,5,1,8444 2010,7,6,2,12772 2010,7,7,3,13940 2010,7,8,4,13421 2010,7,9,5,12843 2010,7,10,6,8485 2010,7,11,7,7382 2010,7,12,1,12408 2010,7,13,2,12697 2010,7,14,3,13031 2010,7,15,4,13118 2010,7,16,5,12888 2010,7,17,6,8370 2010,7,18,7,7352 2010,7,19,1,11865 2010,7,20,2,13291 2010,7,21,3,13158 2010,7,22,4,12939 2010,7,23,5,12542 2010,7,24,6,8396 2010,7,25,7,7392 2010,7,26,1,12262 2010,7,27,2,13264 2010,7,28,3,12877 2010,7,29,4,12952 2010,7,30,5,12320 2010,7,31,6,8361 2010,8,1,7,7370 2010,8,2,1,12092 2010,8,3,2,13136 2010,8,4,3,12911 2010,8,5,4,12929 2010,8,6,5,12556 2010,8,7,6,8516 2010,8,8,7,7361 2010,8,9,1,12923 2010,8,10,2,13514 2010,8,11,3,13084 2010,8,12,4,13365 2010,8,13,5,12092 2010,8,14,6,8445 2010,8,15,7,7352 2010,8,16,1,12409 2010,8,17,2,13286 2010,8,18,3,13102 2010,8,19,4,12964 2010,8,20,5,12910 2010,8,21,6,8404 2010,8,22,7,7461 2010,8,23,1,12195 2010,8,24,2,13226 2010,8,25,3,13328 2010,8,26,4,13008 2010,8,27,5,12966 2010,8,28,6,8553 2010,8,29,7,7496 2010,8,30,1,12246 2010,8,31,2,13527 2010,9,1,3,13409 2010,9,2,4,13420 2010,9,3,5,13047 2010,9,4,6,8414 2010,9,5,7,7586 2010,9,6,1,7815 2010,9,7,2,13033 2010,9,8,3,14239 2010,9,9,4,14135 2010,9,10,5,13641 2010,9,11,6,8775 2010,9,12,7,7749 2010,9,13,1,12559 2010,9,14,2,13949 2010,9,15,3,13893 2010,9,16,4,13964 2010,9,17,5,13605 2010,9,18,6,8979 2010,9,19,7,7899 2010,9,20,1,12992 2010,9,21,2,13919 2010,9,22,3,13640 2010,9,23,4,13717 2010,9,24,5,13280 2010,9,25,6,8780 2010,9,26,7,7543 2010,9,27,1,12652 2010,9,28,2,13208 2010,9,29,3,13080 2010,9,30,4,12965 2010,10,1,5,13141 2010,10,2,6,8412 2010,10,3,7,7380 2010,10,4,1,12326 2010,10,5,2,13146 2010,10,6,3,12691 2010,10,7,4,12889 2010,10,8,5,12536 2010,10,9,6,8194 2010,10,10,7,8490 2010,10,11,1,12134 2010,10,12,2,12913 2010,10,13,3,12358 2010,10,14,4,12668 2010,10,15,5,12507 2010,10,16,6,8081 2010,10,17,7,7181 2010,10,18,1,11888 2010,10,19,2,12693 2010,10,20,3,12838 2010,10,21,4,12747 2010,10,22,5,12235 2010,10,23,6,8033 2010,10,24,7,7242 2010,10,25,1,12190 2010,10,26,2,13176 2010,10,27,3,12700 2010,10,28,4,12408 2010,10,29,5,11679 2010,10,30,6,7996 2010,10,31,7,6895 2010,11,1,1,12044 2010,11,2,2,13035 2010,11,3,3,12608 2010,11,4,4,12821 2010,11,5,5,12495 2010,11,6,6,8126 2010,11,7,7,7251 2010,11,8,1,12023 2010,11,9,2,12889 2010,11,10,3,12671 2010,11,11,4,12773 2010,11,12,5,12090 2010,11,13,6,8115 2010,11,14,7,7120 2010,11,15,1,12163 2010,11,16,2,13205 2010,11,17,3,12710 2010,11,18,4,13025 2010,11,19,5,12634 2010,11,20,6,8511 2010,11,21,7,7285 2010,11,22,1,13195 2010,11,23,2,13762 2010,11,24,3,11964 2010,11,25,4,7162 2010,11,26,5,8689 2010,11,27,6,7526 2010,11,28,7,7217 2010,11,29,1,12430 2010,11,30,2,13445 2010,12,1,3,13107 2010,12,2,4,12982 2010,12,3,5,12288 2010,12,4,6,7881 2010,12,5,7,7122 2010,12,6,1,11749 2010,12,7,2,12833 2010,12,8,3,12462 2010,12,9,4,12364 2010,12,10,5,12351 2010,12,11,6,8142 2010,12,12,7,7134 2010,12,13,1,11721 2010,12,14,2,12981 2010,12,15,3,12962 2010,12,16,4,12975 2010,12,17,5,12829 2010,12,18,6,8470 2010,12,19,7,7257 2010,12,20,1,13280 2010,12,21,2,14255 2010,12,22,3,13029 2010,12,23,4,11237 2010,12,24,5,7532 2010,12,25,6,6159 2010,12,26,7,6796 2010,12,27,1,12231 2010,12,28,2,13654 2010,12,29,3,13441 2010,12,30,4,13272 2010,12,31,5,9751 2011,1,1,6,7254 2011,1,2,7,6540 2011,1,3,1,11143 2011,1,4,2,12599 2011,1,5,3,11933 2011,1,6,4,12143 2011,1,7,5,12044 2011,1,8,6,7840 2011,1,9,7,6933 2011,1,10,1,11093 2011,1,11,2,13222 2011,1,12,3,11950 2011,1,13,4,11813 2011,1,14,5,12114 2011,1,15,6,7810 2011,1,16,7,7046 2011,1,17,1,10969 2011,1,18,2,12298 2011,1,19,3,12271 2011,1,20,4,12382 2011,1,21,5,12035 2011,1,22,6,7895 2011,1,23,7,7005 2011,1,24,1,11616 2011,1,25,2,12692 2011,1,26,3,12174 2011,1,27,4,12026 2011,1,28,5,11814 2011,1,29,6,7808 2011,1,30,7,6888 2011,1,31,1,11495 2011,2,1,2,12498 2011,2,2,3,11954 2011,2,3,4,11917 2011,2,4,5,11962 2011,2,5,6,8070 2011,2,6,7,7109 2011,2,7,1,11873 2011,2,8,2,12764 2011,2,9,3,11880 2011,2,10,4,12078 2011,2,11,5,12029 2011,2,12,6,8086 2011,2,13,7,6853 2011,2,14,1,12111 2011,2,15,2,12863 2011,2,16,3,12396 2011,2,17,4,12399 2011,2,18,5,12328 2011,2,19,6,7969 2011,2,20,7,7056 2011,2,21,1,10757 2011,2,22,2,12601 2011,2,23,3,12232 2011,2,24,4,12129 2011,2,25,5,11945 2011,2,26,6,7919 2011,2,27,7,6989 2011,2,28,1,11160 2011,3,1,2,12530 2011,3,2,3,12149 2011,3,3,4,12172 2011,3,4,5,11842 2011,3,5,6,7825 2011,3,6,7,6950 2011,3,7,1,11490 2011,3,8,2,12254 2011,3,9,3,12119 2011,3,10,4,11921 2011,3,11,5,11989 2011,3,12,6,7897 2011,3,13,7,6557 2011,3,14,1,11275 2011,3,15,2,12191 2011,3,16,3,11880 2011,3,17,4,12192 2011,3,18,5,11682 2011,3,19,6,7786 2011,3,20,7,7024 2011,3,21,1,11794 2011,3,22,2,12462 2011,3,23,3,12050 2011,3,24,4,12062 2011,3,25,5,11854 2011,3,26,6,7658 2011,3,27,7,6871 2011,3,28,1,11489 2011,3,29,2,12279 2011,3,30,3,12022 2011,3,31,4,12173 2011,4,1,5,11264 2011,4,2,6,8102 2011,4,3,7,7028 2011,4,4,1,11772 2011,4,5,2,12387 2011,4,6,3,11858 2011,4,7,4,12330 2011,4,8,5,11904 2011,4,9,6,7840 2011,4,10,7,6861 2011,4,11,1,11711 2011,4,12,2,12320 2011,4,13,3,11671 2011,4,14,4,12349 2011,4,15,5,11964 2011,4,16,6,7683 2011,4,17,7,6939 2011,4,18,1,11681 2011,4,19,2,12564 2011,4,20,3,12216 2011,4,21,4,12276 2011,4,22,5,11113 2011,4,23,6,7524 2011,4,24,7,6570 2011,4,25,1,11427 2011,4,26,2,12563 2011,4,27,3,12007 2011,4,28,4,12180 2011,4,29,5,11456 2011,4,30,6,7665 2011,5,1,7,6926 2011,5,2,1,11595 2011,5,3,2,12299 2011,5,4,3,11984 2011,5,5,4,12055 2011,5,6,5,11824 2011,5,7,6,7919 2011,5,8,7,6972 2011,5,9,1,11511 2011,5,10,2,12578 2011,5,11,3,12464 2011,5,12,4,12203 2011,5,13,5,11125 2011,5,14,6,7854 2011,5,15,7,7061 2011,5,16,1,11899 2011,5,17,2,12819 2011,5,18,3,12387 2011,5,19,4,12222 2011,5,20,5,12011 2011,5,21,6,7934 2011,5,22,7,7257 2011,5,23,1,11896 2011,5,24,2,12851 2011,5,25,3,12715 2011,5,26,4,12822 2011,5,27,5,12379 2011,5,28,6,8276 2011,5,29,7,7145 2011,5,30,1,7492 2011,5,31,2,12192 2011,6,1,3,13446 2011,6,2,4,13258 2011,6,3,5,12680 2011,6,4,6,8398 2011,6,5,7,7261 2011,6,6,1,11934 2011,6,7,2,12629 2011,6,8,3,12660 2011,6,9,4,12471 2011,6,10,5,12279 2011,6,11,6,8091 2011,6,12,7,7314 2011,6,13,1,11744 2011,6,14,2,12841 2011,6,15,3,12681 2011,6,16,4,12990 2011,6,17,5,12463 2011,6,18,6,8498 2011,6,19,7,7344 2011,6,20,1,12045 2011,6,21,2,13143 2011,6,22,3,13017 2011,6,23,4,12681 2011,6,24,5,12504 2011,6,25,6,8351 2011,6,26,7,7140 2011,6,27,1,12344 2011,6,28,2,13234 2011,6,29,3,13002 2011,6,30,4,13194 2011,7,1,5,13392 2011,7,2,6,8510 2011,7,3,7,7489 2011,7,4,1,7541 2011,7,5,2,12751 2011,7,6,3,13950 2011,7,7,4,14200 2011,7,8,5,13363 2011,7,9,6,8845 2011,7,10,7,7635 2011,7,11,1,12617 2011,7,12,2,13392 2011,7,13,3,12900 2011,7,14,4,13278 2011,7,15,5,13097 2011,7,16,6,8534 2011,7,17,7,7637 2011,7,18,1,12414 2011,7,19,2,13156 2011,7,20,3,13219 2011,7,21,4,13262 2011,7,22,5,12777 2011,7,23,6,8671 2011,7,24,7,7351 2011,7,25,1,12126 2011,7,26,2,13270 2011,7,27,3,13023 2011,7,28,4,13152 2011,7,29,5,12501 2011,7,30,6,8338 2011,7,31,7,7450 2011,8,1,1,12546 2011,8,2,2,13491 2011,8,3,3,13164 2011,8,4,4,13031 2011,8,5,5,12848 2011,8,6,6,8567 2011,8,7,7,7605 2011,8,8,1,12505 2011,8,9,2,13360 2011,8,10,3,13160 2011,8,11,4,13092 2011,8,12,5,12978 2011,8,13,6,8448 2011,8,14,7,7470 2011,8,15,1,12756 2011,8,16,2,13576 2011,8,17,3,13267 2011,8,18,4,13150 2011,8,19,5,12900 2011,8,20,6,8572 2011,8,21,7,7493 2011,8,22,1,12286 2011,8,23,2,13422 2011,8,24,3,12986 2011,8,25,4,13046 2011,8,26,5,12910 2011,8,27,6,8700 2011,8,28,7,7633 2011,8,29,1,12281 2011,8,30,2,13561 2011,8,31,3,13390 2011,9,1,4,13723 2011,9,2,5,13224 2011,9,3,6,8588 2011,9,4,7,7399 2011,9,5,1,7770 2011,9,6,2,12892 2011,9,7,3,14234 2011,9,8,4,13544 2011,9,9,5,13537 2011,9,10,6,9115 2011,9,11,7,7501 2011,9,12,1,12770 2011,9,13,2,13205 2011,9,14,3,13590 2011,9,15,4,13583 2011,9,16,5,13322 2011,9,17,6,8792 2011,9,18,7,7724 2011,9,19,1,12818 2011,9,20,2,13648 2011,9,21,3,13138 2011,9,22,4,13157 2011,9,23,5,13062 2011,9,24,6,8496 2011,9,25,7,7609 2011,9,26,1,12719 2011,9,27,2,13455 2011,9,28,3,12815 2011,9,29,4,12813 2011,9,30,5,12419 2011,10,1,6,8506 2011,10,2,7,7419 2011,10,3,1,12310 2011,10,4,2,12924 2011,10,5,3,12748 2011,10,6,4,12744 2011,10,7,5,12195 2011,10,8,6,8206 2011,10,9,7,7160 2011,10,10,1,11839 2011,10,11,2,12865 2011,10,12,3,12581 2011,10,13,4,12201 2011,10,14,5,12065 2011,10,15,6,8043 2011,10,16,7,7145 2011,10,17,1,11803 2011,10,18,2,12819 2011,10,19,3,12605 2011,10,20,4,12536 2011,10,21,5,11936 2011,10,22,6,7899 2011,10,23,7,7104 2011,10,24,1,11773 2011,10,25,2,12672 2011,10,26,3,12085 2011,10,27,4,12390 2011,10,28,5,12049 2011,10,29,6,7812 2011,10,30,7,6870 2011,10,31,1,9828 2011,11,1,2,13632 2011,11,2,3,12657 2011,11,3,4,12310 2011,11,4,5,11965 2011,11,5,6,8045 2011,11,6,7,7236 2011,11,7,1,11574 2011,11,8,2,12300 2011,11,9,3,11990 2011,11,10,4,11978 2011,11,11,5,14392 2011,11,12,6,8087 2011,11,13,7,6877 2011,11,14,1,11590 2011,11,15,2,12676 2011,11,16,3,12433 2011,11,17,4,12461 2011,11,18,5,12424 2011,11,19,6,8042 2011,11,20,7,7218 2011,11,21,1,12929 2011,11,22,2,13415 2011,11,23,3,11775 2011,11,24,4,6894 2011,11,25,5,8618 2011,11,26,6,7512 2011,11,27,7,6879 2011,11,28,1,12410 2011,11,29,2,13204 2011,11,30,3,12584 2011,12,1,4,12716 2011,12,2,5,11853 2011,12,3,6,7895 2011,12,4,7,6957 2011,12,5,1,11622 2011,12,6,2,12477 2011,12,7,3,12119 2011,12,8,4,12024 2011,12,9,5,11565 2011,12,10,6,7658 2011,12,11,7,6832 2011,12,12,1,12087 2011,12,13,2,12592 2011,12,14,3,12632 2011,12,15,4,12506 2011,12,16,5,12211 2011,12,17,6,7941 2011,12,18,7,6876 2011,12,19,1,12708 2011,12,20,2,13640 2011,12,21,3,13227 2011,12,22,4,12215 2011,12,23,5,10017 2011,12,24,6,6688 2011,12,25,7,5728 2011,12,26,1,8039 2011,12,27,2,12475 2011,12,28,3,13478 2011,12,29,4,12985 2011,12,30,5,12434 2011,12,31,6,8035 2012,1,1,7,6629 2012,1,2,1,7821 2012,1,3,2,11324 2012,1,4,3,12075 2012,1,5,4,12171 2012,1,6,5,11920 2012,1,7,6,7783 2012,1,8,7,6887 2012,1,9,1,11248 2012,1,10,2,11939 2012,1,11,3,11860 2012,1,12,4,12391 2012,1,13,5,11380 2012,1,14,6,7901 2012,1,15,7,6899 2012,1,16,1,10707 2012,1,17,2,12175 2012,1,18,3,11981 2012,1,19,4,11997 2012,1,20,5,11914 2012,1,21,6,7948 2012,1,22,7,6816 2012,1,23,1,11464 2012,1,24,2,12356 2012,1,25,3,11692 2012,1,26,4,12003 2012,1,27,5,11648 2012,1,28,6,7827 2012,1,29,7,6733 2012,1,30,1,11253 2012,1,31,2,11919 2012,2,1,3,11916 2012,2,2,4,12135 2012,2,3,5,11826 2012,2,4,6,7833 2012,2,5,7,6733 2012,2,6,1,11229 2012,2,7,2,12310 2012,2,8,3,11946 2012,2,9,4,11862 2012,2,10,5,11981 2012,2,11,6,7895 2012,2,12,7,7012 2012,2,13,1,11023 2012,2,14,2,12708 2012,2,15,3,12250 2012,2,16,4,12376 2012,2,17,5,11985 2012,2,18,6,7818 2012,2,19,7,6905 2012,2,20,1,10837 2012,2,21,2,12125 2012,2,22,3,12436 2012,2,23,4,12045 2012,2,24,5,11802 2012,2,25,6,7842 2012,2,26,7,6707 2012,2,27,1,11475 2012,2,28,2,12208 2012,2,29,3,11042 2012,3,1,4,12519 2012,3,2,5,11789 2012,3,3,6,8010 2012,3,4,7,7021 2012,3,5,1,11391 2012,3,6,2,12076 2012,3,7,3,11972 2012,3,8,4,11985 2012,3,9,5,11817 2012,3,10,6,7691 2012,3,11,7,6497 2012,3,12,1,11571 2012,3,13,2,11779 2012,3,14,3,11797 2012,3,15,4,11783 2012,3,16,5,11608 2012,3,17,6,8066 2012,3,18,7,6918 2012,3,19,1,11578 2012,3,20,2,12338 2012,3,21,3,12056 2012,3,22,4,11925 2012,3,23,5,11816 2012,3,24,6,7893 2012,3,25,7,6915 2012,3,26,1,11474 2012,3,27,2,12245 2012,3,28,3,12035 2012,3,29,4,11864 2012,3,30,5,11834 2012,3,31,6,7860 2012,4,1,7,6909 2012,4,2,1,11647 2012,4,3,2,12273 2012,4,4,3,12307 2012,4,5,4,11986 2012,4,6,5,10955 2012,4,7,6,7384 2012,4,8,7,6545 2012,4,9,1,11237 2012,4,10,2,12179 2012,4,11,3,11635 2012,4,12,4,12050 2012,4,13,5,10910 2012,4,14,6,7699 2012,4,15,7,6951 2012,4,16,1,11536 2012,4,17,2,12240 2012,4,18,3,11850 2012,4,19,4,11583 2012,4,20,5,11608 2012,4,21,6,7757 2012,4,22,7,6843 2012,4,23,1,11297 2012,4,24,2,12191 2012,4,25,3,11765 2012,4,26,4,11871 2012,4,27,5,11226 2012,4,28,6,7590 2012,4,29,7,6713 2012,4,30,1,11381 2012,5,1,2,12470 2012,5,2,3,12095 2012,5,3,4,11804 2012,5,4,5,11488 2012,5,5,6,7634 2012,5,6,7,6868 2012,5,7,1,11424 2012,5,8,2,12158 2012,5,9,3,11749 2012,5,10,4,11825 2012,5,11,5,11683 2012,5,12,6,7751 2012,5,13,7,6909 2012,5,14,1,11763 2012,5,15,2,12565 2012,5,16,3,12199 2012,5,17,4,12048 2012,5,18,5,11771 2012,5,19,6,7914 2012,5,20,7,7202 2012,5,21,1,11919 2012,5,22,2,12601 2012,5,23,3,12649 2012,5,24,4,12414 2012,5,25,5,12350 2012,5,26,6,7921 2012,5,27,7,7015 2012,5,28,1,7532 2012,5,29,2,12307 2012,5,30,3,13194 2012,5,31,4,12686 2012,6,1,5,12623 2012,6,2,6,8040 2012,6,3,7,7075 2012,6,4,1,12011 2012,6,5,2,12424 2012,6,6,3,12410 2012,6,7,4,12305 2012,6,8,5,12145 2012,6,9,6,8293 2012,6,10,7,7131 2012,6,11,1,11700 2012,6,12,2,12892 2012,6,13,3,11999 2012,6,14,4,12626 2012,6,15,5,12278 2012,6,16,6,8213 2012,6,17,7,7316 2012,6,18,1,12028 2012,6,19,2,12767 2012,6,20,3,12674 2012,6,21,4,12713 2012,6,22,5,12370 2012,6,23,6,8141 2012,6,24,7,7246 2012,6,25,1,12091 2012,6,26,2,12950 2012,6,27,3,12545 2012,6,28,4,12994 2012,6,29,5,12462 2012,6,30,6,8323 2012,7,1,7,7550 2012,7,2,1,12837 2012,7,3,2,13752 2012,7,4,3,9296 2012,7,5,4,12618 2012,7,6,5,12804 2012,7,7,6,8952 2012,7,8,7,7541 2012,7,9,1,12333 2012,7,10,2,13527 2012,7,11,3,13024 2012,7,12,4,12787 2012,7,13,5,12109 2012,7,14,6,8657 2012,7,15,7,7559 2012,7,16,1,12380 2012,7,17,2,13318 2012,7,18,3,12865 2012,7,19,4,12798 2012,7,20,5,12503 2012,7,21,6,8611 2012,7,22,7,7531 2012,7,23,1,12553 2012,7,24,2,13390 2012,7,25,3,13045 2012,7,26,4,13056 2012,7,27,5,12785 2012,7,28,6,8493 2012,7,29,7,7550 2012,7,30,1,12061 2012,7,31,2,13187 2012,8,1,3,12976 2012,8,2,4,13006 2012,8,3,5,12743 2012,8,4,6,8786 2012,8,5,7,7693 2012,8,6,1,12671 2012,8,7,2,13316 2012,8,8,3,13204 2012,8,9,4,13179 2012,8,10,5,12898 2012,8,11,6,8602 2012,8,12,7,7630 2012,8,13,1,12126 2012,8,14,2,13788 2012,8,15,3,13391 2012,8,16,4,13361 2012,8,17,5,12913 2012,8,18,6,8678 2012,8,19,7,7678 2012,8,20,1,12580 2012,8,21,2,13239 2012,8,22,3,12973 2012,8,23,4,12889 2012,8,24,5,13114 2012,8,25,6,8653 2012,8,26,7,7629 2012,8,27,1,12533 2012,8,28,2,13674 2012,8,29,3,12968 2012,8,30,4,13323 2012,8,31,5,13287 2012,9,1,6,8967 2012,9,2,7,7817 2012,9,3,1,8030 2012,9,4,2,12941 2012,9,5,3,13991 2012,9,6,4,13709 2012,9,7,5,13841 2012,9,8,6,8987 2012,9,9,7,7930 2012,9,10,1,12853 2012,9,11,2,12543 2012,9,12,3,13653 2012,9,13,4,13396 2012,9,14,5,13529 2012,9,15,6,9094 2012,9,16,7,7867 2012,9,17,1,12960 2012,9,18,2,13628 2012,9,19,3,13490 2012,9,20,4,13524 2012,9,21,5,13174 2012,9,22,6,8899 2012,9,23,7,8007 2012,9,24,1,12748 2012,9,25,2,13533 2012,9,26,3,13100 2012,9,27,4,13159 2012,9,28,5,12661 2012,9,29,6,8695 2012,9,30,7,7607 2012,10,1,1,12537 2012,10,2,2,13293 2012,10,3,3,12900 2012,10,4,4,12785 2012,10,5,5,12521 2012,10,6,6,8333 2012,10,7,7,7367 2012,10,8,1,11711 2012,10,9,2,12692 2012,10,10,3,12597 2012,10,11,4,13705 2012,10,12,5,12349 2012,10,13,6,8153 2012,10,14,7,7408 2012,10,15,1,12347 2012,10,16,2,12888 2012,10,17,3,12752 2012,10,18,4,12604 2012,10,19,5,12367 2012,10,20,6,8365 2012,10,21,7,7279 2012,10,22,1,12260 2012,10,23,2,12923 2012,10,24,3,12610 2012,10,25,4,12769 2012,10,26,5,11989 2012,10,27,6,8127 2012,10,28,7,7362 2012,10,29,1,11957 2012,10,30,2,12011 2012,10,31,3,11012 2012,11,1,4,13042 2012,11,2,5,12692 2012,11,3,6,8224 2012,11,4,7,7436 2012,11,5,1,11885 2012,11,6,2,12690 2012,11,7,3,12536 2012,11,8,4,12386 2012,11,9,5,12374 2012,11,10,6,8172 2012,11,11,7,7219 2012,11,12,1,12036 2012,11,13,2,12364 2012,11,14,3,12728 2012,11,15,4,12812 2012,11,16,5,12555 2012,11,17,6,8503 2012,11,18,7,7390 2012,11,19,1,12916 2012,11,20,2,13427 2012,11,21,3,12083 2012,11,22,4,7267 2012,11,23,5,9171 2012,11,24,6,7651 2012,11,25,7,7191 2012,11,26,1,12403 2012,11,27,2,13296 2012,11,28,3,12614 2012,11,29,4,12503 2012,11,30,5,11740 2012,12,1,6,8248 2012,12,2,7,7204 2012,12,3,1,11833 2012,12,4,2,12566 2012,12,5,3,12313 2012,12,6,4,12084 2012,12,7,5,11733 2012,12,8,6,7995 2012,12,9,7,7003 2012,12,10,1,11529 2012,12,11,2,12234 2012,12,12,3,14667 2012,12,13,4,11893 2012,12,14,5,11872 2012,12,15,6,7913 2012,12,16,7,7146 2012,12,17,1,11979 2012,12,18,2,13305 2012,12,19,3,12849 2012,12,20,4,13109 2012,12,21,5,13186 2012,12,22,6,8396 2012,12,23,7,6845 2012,12,24,1,7614 2012,12,25,2,6325 2012,12,26,3,11362 2012,12,27,4,14126 2012,12,28,5,13888 2012,12,29,6,9030 2012,12,30,7,7545 2012,12,31,1,10634 2013,1,1,2,7537 2013,1,2,3,10887 2013,1,3,4,12616 2013,1,4,5,12431 2013,1,5,6,8332 2013,1,6,7,7271 2013,1,7,1,11463 2013,1,8,2,12040 2013,1,9,3,11598 2013,1,10,4,11887 2013,1,11,5,12082 2013,1,12,6,8140 2013,1,13,7,7092 2013,1,14,1,11401 2013,1,15,2,11953 2013,1,16,3,11678 2013,1,17,4,12113 2013,1,18,5,11846 2013,1,19,6,7708 2013,1,20,7,7001 2013,1,21,1,10777 2013,1,22,2,11835 2013,1,23,3,11917 2013,1,24,4,12016 2013,1,25,5,11638 2013,1,26,6,8047 2013,1,27,7,6916 2013,1,28,1,11520 2013,1,29,2,12168 2013,1,30,3,11752 2013,1,31,4,11690 2013,2,1,5,11995 2013,2,2,6,7881 2013,2,3,7,6876 2013,2,4,1,11237 2013,2,5,2,12114 2013,2,6,3,11617 2013,2,7,4,12025 2013,2,8,5,11959 2013,2,9,6,7776 2013,2,10,7,6735 2013,2,11,1,11460 2013,2,12,2,12243 2013,2,13,3,11648 2013,2,14,4,12422 2013,2,15,5,11914 2013,2,16,6,7902 2013,2,17,7,7044 2013,2,18,1,10863 2013,2,19,2,12137 2013,2,20,3,11941 2013,2,21,4,11899 2013,2,22,5,11778 2013,2,23,6,7866 2013,2,24,7,6914 2013,2,25,1,11358 2013,2,26,2,11982 2013,2,27,3,11695 2013,2,28,4,11601 2013,3,1,5,12075 2013,3,2,6,7836 2013,3,3,7,7098 2013,3,4,1,11667 2013,3,5,2,12172 2013,3,6,3,11800 2013,3,7,4,11918 2013,3,8,5,11787 2013,3,9,6,7946 2013,3,10,7,6610 2013,3,11,1,11591 2013,3,12,2,12102 2013,3,13,3,11937 2013,3,14,4,11831 2013,3,15,5,11811 2013,3,16,6,7906 2013,3,17,7,7134 2013,3,18,1,11825 2013,3,19,2,12070 2013,3,20,3,12024 2013,3,21,4,12096 2013,3,22,5,11949 2013,3,23,6,7876 2013,3,24,7,6956 2013,3,25,1,11619 2013,3,26,2,12199 2013,3,27,3,12204 2013,3,28,4,12006 2013,3,29,5,10986 2013,3,30,6,7863 2013,3,31,7,6735 2013,4,1,1,10440 2013,4,2,2,12389 2013,4,3,3,12081 2013,4,4,4,12019 2013,4,5,5,11858 2013,4,6,6,7789 2013,4,7,7,6796 2013,4,8,1,11423 2013,4,9,2,12074 2013,4,10,3,11759 2013,4,11,4,11765 2013,4,12,5,11494 2013,4,13,6,7643 2013,4,14,7,6898 2013,4,15,1,11318 2013,4,16,2,12168 2013,4,17,3,11765 2013,4,18,4,11665 2013,4,19,5,11511 2013,4,20,6,7718 2013,4,21,7,6722 2013,4,22,1,11410 2013,4,23,2,11956 2013,4,24,3,11537 2013,4,25,4,11620 2013,4,26,5,11442 2013,4,27,6,7651 2013,4,28,7,6852 2013,4,29,1,11259 2013,4,30,2,11825 2013,5,1,3,11948 2013,5,2,4,11787 2013,5,3,5,11805 2013,5,4,6,7714 2013,5,5,7,6609 2013,5,6,1,11316 2013,5,7,2,12275 2013,5,8,3,11867 2013,5,9,4,11628 2013,5,10,5,11813 2013,5,11,6,7727 2013,5,12,7,7060 2013,5,13,1,11289 2013,5,14,2,12345 2013,5,15,3,12184 2013,5,16,4,12145 2013,5,17,5,11945 2013,5,18,6,7764 2013,5,19,7,7049 2013,5,20,1,11968 2013,5,21,2,12685 2013,5,22,3,12366 2013,5,23,4,12523 2013,5,24,5,12265 2013,5,25,6,8156 2013,5,26,7,6880 2013,5,27,1,7351 2013,5,28,2,12462 2013,5,29,3,13062 2013,5,30,4,12798 2013,5,31,5,12082 2013,6,1,6,8320 2013,6,2,7,7015 2013,6,3,1,11718 2013,6,4,2,12315 2013,6,5,3,12343 2013,6,6,4,11935 2013,6,7,5,12203 2013,6,8,6,8184 2013,6,9,7,7306 2013,6,10,1,11852 2013,6,11,2,12304 2013,6,12,3,11924 2013,6,13,4,12096 2013,6,14,5,12046 2013,6,15,6,8235 2013,6,16,7,7267 2013,6,17,1,12166 2013,6,18,2,12754 2013,6,19,3,12217 2013,6,20,4,12417 2013,6,21,5,12175 2013,6,22,6,8301 2013,6,23,7,7435 2013,6,24,1,12033 2013,6,25,2,12819 2013,6,26,3,12526 2013,6,27,4,12733 2013,6,28,5,12585 2013,6,29,6,8325 2013,6,30,7,7319 2013,7,1,1,12558 2013,7,2,2,13437 2013,7,3,3,13247 2013,7,4,4,8883 2013,7,5,5,11318 2013,7,6,6,8420 2013,7,7,7,7454 2013,7,8,1,12493 2013,7,9,2,13408 2013,7,10,3,12915 2013,7,11,4,12806 2013,7,12,5,12535 2013,7,13,6,8485 2013,7,14,7,7536 2013,7,15,1,12506 2013,7,16,2,13083 2013,7,17,3,12912 2013,7,18,4,12824 2013,7,19,5,12528 2013,7,20,6,8389 2013,7,21,7,7564 2013,7,22,1,12544 2013,7,23,2,13316 2013,7,24,3,12804 2013,7,25,4,12860 2013,7,26,5,12249 2013,7,27,6,8328 2013,7,28,7,7492 2013,7,29,1,12096 2013,7,30,2,12880 2013,7,31,3,12625 2013,8,1,4,12971 2013,8,2,5,12561 2013,8,3,6,8539 2013,8,4,7,7600 2013,8,5,1,12434 2013,8,6,2,13055 2013,8,7,3,13109 2013,8,8,4,13207 2013,8,9,5,12756 2013,8,10,6,8777 2013,8,11,7,7797 2013,8,12,1,12391 2013,8,13,2,12975 2013,8,14,3,13049 2013,8,15,4,13101 2013,8,16,5,12702 2013,8,17,6,8747 2013,8,18,7,7612 2013,8,19,1,12426 2013,8,20,2,13051 2013,8,21,3,12903 2013,8,22,4,12873 2013,8,23,5,12805 2013,8,24,6,8801 2013,8,25,7,7638 2013,8,26,1,12293 2013,8,27,2,13131 2013,8,28,3,13129 2013,8,29,4,12873 2013,8,30,5,12814 2013,8,31,6,8759 2013,9,1,7,7620 2013,9,2,1,7896 2013,9,3,2,12910 2013,9,4,3,13680 2013,9,5,4,13337 2013,9,6,5,12876 2013,9,7,6,8800 2013,9,8,7,7737 2013,9,9,1,12653 2013,9,10,2,13440 2013,9,11,3,12074 2013,9,12,4,13460 2013,9,13,5,12669 2013,9,14,6,8795 2013,9,15,7,7865 2013,9,16,1,12842 2013,9,17,2,13542 2013,9,18,3,13242 2013,9,19,4,13333 2013,9,20,5,13040 2013,9,21,6,8863 2013,9,22,7,7817 2013,9,23,1,12715 2013,9,24,2,13173 2013,9,25,3,13042 2013,9,26,4,13044 2013,9,27,5,12774 2013,9,28,6,8704 2013,9,29,7,7618 2013,9,30,1,12115 2013,10,1,2,13195 2013,10,2,3,12614 2013,10,3,4,12880 2013,10,4,5,12493 2013,10,5,6,8593 2013,10,6,7,7471 2013,10,7,1,11877 2013,10,8,2,12765 2013,10,9,3,12393 2013,10,10,4,12804 2013,10,11,5,12192 2013,10,12,6,8223 2013,10,13,7,7172 2013,10,14,1,11736 2013,10,15,2,12582 2013,10,16,3,12227 2013,10,17,4,12220 2013,10,18,5,12169 2013,10,19,6,7995 2013,10,20,7,7121 2013,10,21,1,11687 2013,10,22,2,12462 2013,10,23,3,12223 2013,10,24,4,12320 2013,10,25,5,12210 2013,10,26,6,8077 2013,10,27,7,7139 2013,10,28,1,12199 2013,10,29,2,12519 2013,10,30,3,11752 2013,10,31,4,10975 2013,11,1,5,12653 2013,11,2,6,8407 2013,11,3,7,7368 2013,11,4,1,12164 2013,11,5,2,12785 2013,11,6,3,12113 2013,11,7,4,12566 2013,11,8,5,12026 2013,11,9,6,8092 2013,11,10,7,7258 2013,11,11,1,11418 2013,11,12,2,13669 2013,11,13,3,12130 2013,11,14,4,12206 2013,11,15,5,12339 2013,11,16,6,8305 2013,11,17,7,7348 2013,11,18,1,12154 2013,11,19,2,12413 2013,11,20,3,12503 2013,11,21,4,12499 2013,11,22,5,12459 2013,11,23,6,8239 2013,11,24,7,7362 2013,11,25,1,12658 2013,11,26,2,13211 2013,11,27,3,11782 2013,11,28,4,7175 2013,11,29,5,9077 2013,11,30,6,7778 2013,12,1,7,7449 2013,12,2,1,12512 2013,12,3,2,13352 2013,12,4,3,12947 2013,12,5,4,12437 2013,12,6,5,11861 2013,12,7,6,8068 2013,12,8,7,7226 2013,12,9,1,11824 2013,12,10,2,12597 2013,12,11,3,12413 2013,12,12,4,12485 2013,12,13,5,11484 2013,12,14,6,8163 2013,12,15,7,7305 2013,12,16,1,12316 2013,12,17,2,13252 2013,12,18,3,13132 2013,12,19,4,13320 2013,12,20,5,13248 2013,12,21,6,8836 2013,12,22,7,7535 2013,12,23,1,12140 2013,12,24,2,9194 2013,12,25,3,6620 2013,12,26,4,11375 2013,12,27,5,13588 2013,12,28,6,9203 2013,12,29,7,7896 2013,12,30,1,13096 2013,12,31,2,12525 2014,1,1,3,8018 2014,1,2,4,11171 2014,1,3,5,12317 2014,1,4,6,8199 2014,1,5,7,7174 2014,1,6,1,11400 2014,1,7,2,12310 2014,1,8,3,11829 2014,1,9,4,11827 2014,1,10,5,11989 2014,1,11,6,8292 2014,1,12,7,7298 2014,1,13,1,11714 2014,1,14,2,12598 2014,1,15,3,11785 2014,1,16,4,11822 2014,1,17,5,11932 2014,1,18,6,8143 2014,1,19,7,6924 2014,1,20,1,11024 2014,1,21,2,12177 2014,1,22,3,11936 2014,1,23,4,12162 2014,1,24,5,11840 2014,1,25,6,8190 2014,1,26,7,7424 2014,1,27,1,11561 2014,1,28,2,12031 2014,1,29,3,11381 2014,1,30,4,11651 2014,1,31,5,11843 2014,2,1,6,8206 2014,2,2,7,7265 2014,2,3,1,11825 2014,2,4,2,12519 2014,2,5,3,11914 2014,2,6,4,11807 2014,2,7,5,12246 2014,2,8,6,8129 2014,2,9,7,7060 2014,2,10,1,11886 2014,2,11,2,12311 2014,2,12,3,12154 2014,2,13,4,11384 2014,2,14,5,12494 2014,2,15,6,8391 2014,2,16,7,7259 2014,2,17,1,11144 2014,2,18,2,12331 2014,2,19,3,11932 2014,2,20,4,12142 2014,2,21,5,11988 2014,2,22,6,8049 2014,2,23,7,7092 2014,2,24,1,11621 2014,2,25,2,12291 2014,2,26,3,11932 2014,2,27,4,11856 2014,2,28,5,11671 2014,3,1,6,8186 2014,3,2,7,7267 2014,3,3,1,11793 2014,3,4,2,12065 2014,3,5,3,12129 2014,3,6,4,12069 2014,3,7,5,12035 2014,3,8,6,8140 2014,3,9,7,6789 2014,3,10,1,11620 2014,3,11,2,12084 2014,3,12,3,11819 2014,3,13,4,11623 2014,3,14,5,11841 2014,3,15,6,8080 2014,3,16,7,6973 2014,3,17,1,11936 2014,3,18,2,12231 2014,3,19,3,11953 2014,3,20,4,12266 2014,3,21,5,11987 2014,3,22,6,8109 2014,3,23,7,7147 2014,3,24,1,11542 2014,3,25,2,12342 2014,3,26,3,11809 2014,3,27,4,11823 2014,3,28,5,11730 2014,3,29,6,8153 2014,3,30,7,7215 2014,3,31,1,11511 2014,4,1,2,11710 2014,4,2,3,12003 2014,4,3,4,11984 2014,4,4,5,12319 2014,4,5,6,7926 2014,4,6,7,7127 2014,4,7,1,11508 2014,4,8,2,12187 2014,4,9,3,11875 2014,4,10,4,12026 2014,4,11,5,12018 2014,4,12,6,7980 2014,4,13,7,7181 2014,4,14,1,11912 2014,4,15,2,12274 2014,4,16,3,11858 2014,4,17,4,12070 2014,4,18,5,11132 2014,4,19,6,7641 2014,4,20,7,6877 2014,4,21,1,11664 2014,4,22,2,12528 2014,4,23,3,12014 2014,4,24,4,12178 2014,4,25,5,11811 2014,4,26,6,7949 2014,4,27,7,7184 2014,4,28,1,11681 2014,4,29,2,12121 2014,4,30,3,11591 2014,5,1,4,12412 2014,5,2,5,12011 2014,5,3,6,8015 2014,5,4,7,7171 2014,5,5,1,11788 2014,5,6,2,12487 2014,5,7,3,12127 2014,5,8,4,12166 2014,5,9,5,11949 2014,5,10,6,8100 2014,5,11,7,7145 2014,5,12,1,11671 2014,5,13,2,12057 2014,5,14,3,12234 2014,5,15,4,12387 2014,5,16,5,12065 2014,5,17,6,8051 2014,5,18,7,7200 2014,5,19,1,11925 2014,5,20,2,12854 2014,5,21,3,12545 2014,5,22,4,12634 2014,5,23,5,12631 2014,5,24,6,8456 2014,5,25,7,7393 2014,5,26,1,7657 2014,5,27,2,12490 2014,5,28,3,13411 2014,5,29,4,12753 2014,5,30,5,12257 2014,5,31,6,8462 2014,6,1,7,7474 2014,6,2,1,11885 2014,6,3,2,12246 2014,6,4,3,12320 2014,6,5,4,12256 2014,6,6,5,11965 2014,6,7,6,8164 2014,6,8,7,7359 2014,6,9,1,11886 2014,6,10,2,12513 2014,6,11,3,12090 2014,6,12,4,12442 2014,6,13,5,11651 2014,6,14,6,8199 2014,6,15,7,7375 2014,6,16,1,12068 2014,6,17,2,12555 2014,6,18,3,12524 2014,6,19,4,12217 2014,6,20,5,12532 2014,6,21,6,8299 2014,6,22,7,7414 2014,6,23,1,11939 2014,6,24,2,12704 2014,6,25,3,12499 2014,6,26,4,12621 2014,6,27,5,12236 2014,6,28,6,8441 2014,6,29,7,7563 2014,6,30,1,12243 2014,7,1,2,13575 2014,7,2,3,13183 2014,7,3,4,13043 2014,7,4,5,9278 2014,7,5,6,7778 2014,7,6,7,7568 2014,7,7,1,13038 2014,7,8,2,13500 2014,7,9,3,12577 2014,7,10,4,13146 2014,7,11,5,12699 2014,7,12,6,8650 2014,7,13,7,7626 2014,7,14,1,12394 2014,7,15,2,13207 2014,7,16,3,12881 2014,7,17,4,12817 2014,7,18,5,12439 2014,7,19,6,8720 2014,7,20,7,7567 2014,7,21,1,12497 2014,7,22,2,13239 2014,7,23,3,12692 2014,7,24,4,12929 2014,7,25,5,12662 2014,7,26,6,8740 2014,7,27,7,7822 2014,7,28,1,12532 2014,7,29,2,13252 2014,7,30,3,12752 2014,7,31,4,12673 2014,8,1,5,12782 2014,8,2,6,8814 2014,8,3,7,7679 2014,8,4,1,12511 2014,8,5,2,13415 2014,8,6,3,12900 2014,8,7,4,13152 2014,8,8,5,12887 2014,8,9,6,8958 2014,8,10,7,7832 2014,8,11,1,12589 2014,8,12,2,13413 2014,8,13,3,12817 2014,8,14,4,13031 2014,8,15,5,13048 2014,8,16,6,8885 2014,8,17,7,7783 2014,8,18,1,12582 2014,8,19,2,13198 2014,8,20,3,13167 2014,8,21,4,13153 2014,8,22,5,12891 2014,8,23,6,8912 2014,8,24,7,7630 2014,8,25,1,12346 2014,8,26,2,13278 2014,8,27,3,13113 2014,8,28,4,13418 2014,8,29,5,13099 2014,8,30,6,8899 2014,8,31,7,7884 2014,9,1,1,8043 2014,9,2,2,13071 2014,9,3,3,13863 2014,9,4,4,13556 2014,9,5,5,13457 2014,9,6,6,8806 2014,9,7,7,7770 2014,9,8,1,12743 2014,9,9,2,13629 2014,9,10,3,13230 2014,9,11,4,12104 2014,9,12,5,13415 2014,9,13,6,8903 2014,9,14,7,8109 2014,9,15,1,13018 2014,9,16,2,13661 2014,9,17,3,13341 2014,9,18,4,13451 2014,9,19,5,13129 2014,9,20,6,9202 2014,9,21,7,8002 2014,9,22,1,12713 2014,9,23,2,13149 2014,9,24,3,13033 2014,9,25,4,12908 2014,9,26,5,12478 2014,9,27,6,8797 2014,9,28,7,7639 2014,9,29,1,12318 2014,9,30,2,12959 2014,10,1,3,13082 2014,10,2,4,12841 2014,10,3,5,12539 2014,10,4,6,8425 2014,10,5,7,7484 2014,10,6,1,11893 2014,10,7,2,12860 2014,10,8,3,12363 2014,10,9,4,12130 2014,10,10,5,12155 2014,10,11,6,8262 2014,10,12,7,7283 2014,10,13,1,11241 2014,10,14,2,12658 2014,10,15,3,12405 2014,10,16,4,12506 2014,10,17,5,12087 2014,10,18,6,8305 2014,10,19,7,7279 2014,10,20,1,11744 2014,10,21,2,12565 2014,10,22,3,12282 2014,10,23,4,12162 2014,10,24,5,12119 2014,10,25,6,8256 2014,10,26,7,7576 2014,10,27,1,12007 2014,10,28,2,12831 2014,10,29,3,12102 2014,10,30,4,12192 2014,10,31,5,10837 2014,11,1,6,8367 2014,11,2,7,7736 2014,11,3,1,12309 2014,11,4,2,12748 2014,11,5,3,12461 2014,11,6,4,12489 2014,11,7,5,12422 2014,11,8,6,8268 2014,11,9,7,7479 2014,11,10,1,11898 2014,11,11,2,12794 2014,11,12,3,12244 2014,11,13,4,12103 2014,11,14,5,12234 2014,11,15,6,8305 2014,11,16,7,7219 2014,11,17,1,11784 2014,11,18,2,12822 2014,11,19,3,12100 2014,11,20,4,12541 2014,11,21,5,12638 2014,11,22,6,8647 2014,11,23,7,7497 2014,11,24,1,12791 2014,11,25,2,13349 2014,11,26,3,11747 2014,11,27,4,7351 2014,11,28,5,9049 2014,11,29,6,8035 2014,11,30,7,7228 2014,12,1,1,12584 2014,12,2,2,13083 2014,12,3,3,12427 2014,12,4,4,12384 2014,12,5,5,11964 2014,12,6,6,8280 2014,12,7,7,7196 2014,12,8,1,11773 2014,12,9,2,12419 2014,12,10,3,12203 2014,12,11,4,12042 2014,12,12,5,12001 2014,12,13,6,8596 2014,12,14,7,7291 2014,12,15,1,12013 2014,12,16,2,12748 2014,12,17,3,12684 2014,12,18,4,12816 2014,12,19,5,12714 2014,12,20,6,8465 2014,12,21,7,7382 2014,12,22,1,12799 2014,12,23,2,12604 2014,12,24,3,9308 2014,12,25,4,6749 2014,12,26,5,10386 2014,12,27,6,8656 2014,12,28,7,7724 2014,12,29,1,12811 2014,12,30,2,13634 2014,12,31,3,11990 \ No newline at end of file diff --git a/textbook/11/Probability.ipynb b/textbook/11/Probability.ipynb deleted file mode 100644 index 810bb643..00000000 --- a/textbook/11/Probability.ipynb +++ /dev/null @@ -1,290 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "tags": [ - "remove-cell" - ] - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "import pandas as pd\n", - "\n", - "import matplotlib.pyplot as plots\n", - "\n", - "plots.style.use('fivethirtyeight')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Probability: Mathematical/Theoretical and Computational Approaches\n", - "\n", - "*Dan L. Nicolae* \n", - "\n", - "We will see throughout this textbook that some problems can be solved either mathematically, or computationally (using simulations), or through a combination of analytical and computational approaches. Each approach has its strengths and, in this chapter, we use the calculation or estimation of probabilities to highlight some of them.\n", - "\n", - "We illustrate the concepts we want to introduce with a classic probability problem called **the birthday problem**. Suppose you and a friend go to a party where there are 30 people (all unknown to both of you) and your friend wants to bet you that there are two people at that party who share their birthday. Would you be willing to take that bet? \n", - "\n", - "Your willingness to take the bet should be related to the chance of winning the bet. What do you think it is more likely to happen: finding a pair with shared birthdays or having 30 distinct birthdays? \n", - "\n", - "We will answer this question using the language of probability; we will calculate the probability of the event that at least two people share the birthdays in a group of 30 people. Next section will introduce the rules we need for deriving this probability. In the following section, we will also show how to estimate them using simulations.\n", - "\n", - "Let's start with a simpler problem: what is the probability that two people share their birthday. Can you justify the following result?\n", - "\n", - "$$P(\\mbox{two random people have the same birthday}) ~=~ \\frac{1}{365}$$\n", - "\n", - "Think about the assumptions you implicitly or explicitly made in your justification. \n", - "\n", - "We will show in the next section that, given a number of people, **n** (with $2\\leq n\\leq 365$), the probability, $P_n$, that at least two share a birthday is given by:\n", - "\n", - "$$P_n ~=~ 1-\\frac{365\\times364\\times ...\\times (365-n+1)}{365^n}$$\n", - "\n", - "which can also be written as\n", - "\n", - "$$P_n ~=~ 1-\\frac{365}{365}\\times\\frac{364}{365}\\times\\frac{363}{365}\\times ...\\times \\frac{(365-n+1)}{365}$$\n", - "\n", - "The asssumptions used to obtain the above formula for $P_n$ are:\n", - "\n", - "a. 365 days in a year;\n", - "\n", - "b. All days are equally likely to be a birthday;\n", - "\n", - "c. Subjects' birthdays are independent of each other (for example, no twins in the room).\n", - "\n", - "The function below calculates these probabilities. Note that, for computational reasons, we implement the second formula for $P_n$: consider how large is $365^n$ for n= 30 or 50." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "# a function that calculates the probability for 1\n", - "\n", - "\n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - " \n", - "
Number of peopleProbability
020.0027
130.0082
240.0164
350.0271
460.0405
570.0562
680.0743
\n", - "" - ], - "text/plain": [ - " Number of people Probability\n", - "0 2 0.0027\n", - "1 3 0.0082\n", - "2 4 0.0164\n", - "3 5 0.0271\n", - "4 6 0.0405\n", - "5 7 0.0562\n", - "6 8 0.0743" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Construct a data frame with the probabilities for a range of n's\n", - "number_people=np.arange(2,61,1)\n", - "b_probs= np.array([]) # an empty array\n", - "for i in number_people: b_probs= np.append(b_probs,birthday_prob(i))\n", - "\n", - "Birthday_df=pd.DataFrame(\n", - " {\"Number of people\":number_people,\n", - " \"Probability\":b_probs})\n", - "Birthday_df.head(7)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We construct below a line graph of these probabilities that shows the trend. " - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "Birthday_df.plot.scatter(\"Number of people\",\"Probability\");" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Are the above probabilities surprising? Can you provide an intuition for them? Note that the number of people that yields the probability closest to a fair bet is 23." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "0.5073" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "birthday_prob(23)" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "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": "3.10.6" - } - }, - "nbformat": 4, - "nbformat_minor": 4 -} diff --git a/textbook/11/Probability_Intro.ipynb b/textbook/11/Probability_Intro.ipynb new file mode 100644 index 00000000..7ec177a2 --- /dev/null +++ b/textbook/11/Probability_Intro.ipynb @@ -0,0 +1,294 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "tags": [ + "remove-cell" + ] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import pandas as pd\n", + "\n", + "%matplotlib inline\n", + "import matplotlib.pyplot as plt\n", + "plt.style.use('fivethirtyeight')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Probability: Mathematical/Theoretical and Computational Approaches\n", + "\n", + "*Dan L. Nicolae* \n", + "\n", + "We will illustrate throughout this textbook how some problems can be solved either mathematically, or computationally (using simulations), or through a combination of mathematical/analytical and computational approaches. Each approach has its strengths and, in this chapter, we use the calculation versus estimation of probabilities to highlight some of them.\n", + "\n", + "We illustrate the concepts we want to introduce with a classic probability exercise called **the birthday problem**. Suppose you and a friend go to a party where there are 30 people (all unknown to both of you) and your friend wants to bet you that there are two people at that party who share their birthday. Would you be willing to take that bet? \n", + "\n", + "Your willingness to take the bet should be related to the chance of winning the bet. What do you think it is more likely to happen: finding a pair with shared birthdays or having 30 distinct birthdays? \n", + "\n", + "We will answer this question using the language of probability; we will calculate the probability of the event that at least two people share birthdays in a group of 30 people. In the following sections, we will introduce the rules we need for deriving this probability and then show how to estimate them using simulations.\n", + "\n", + "Let's start with a simpler problem: what is the probability that two people share their birthday. Can you justify the following result?\n", + "\n", + "$$P(\\mbox{two random people have the same birthday}) ~=~ \\frac{1}{365}$$\n", + "\n", + "Think about the assumptions you implicitly or explicitly made in your justification. \n", + "\n", + "We will show in the next section that, given a number of people, **n** (with $2\\leq n\\leq 365$), the probability, $P_n$, that at least two share a birthday is given by:\n", + "\n", + "$$P_n ~=~ 1-\\frac{365\\times364\\times ...\\times (365-n+1)}{365^n}$$\n", + "\n", + "which can also be written as\n", + "\n", + "$$P_n ~=~ 1-\\frac{365}{365}\\times\\frac{364}{365}\\times\\frac{363}{365}\\times ...\\times \\frac{(365-n+1)}{365}$$\n", + "\n", + "The asssumptions used to obtain the above formula for $P_n$ are:\n", + "\n", + "a. 365 days in a year;\n", + "\n", + "b. All days are equally likely to be a birthday;\n", + "\n", + "c. Subjects' birthdays are independent of each other (for example, no twins in the room).\n", + "\n", + "The function below calculates these probabilities. Note that, for computational reasons, we implement the second formula for $P_n$: consider how large $365^n$ is for n= 30 or 50." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "# a function that calculates the probability for 1\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
Number of peopleProbability
020.0027
130.0082
240.0164
350.0271
460.0405
570.0562
680.0743
\n", + "" + ], + "text/plain": [ + " Number of people Probability\n", + "0 2 0.0027\n", + "1 3 0.0082\n", + "2 4 0.0164\n", + "3 5 0.0271\n", + "4 6 0.0405\n", + "5 7 0.0562\n", + "6 8 0.0743" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Construct a data frame with the probabilities for a range of n's\n", + "number_people=np.arange(2,61,1)\n", + "b_probs= np.array([]) # an empty array\n", + "\n", + "for i in number_people: \n", + " b_probs= np.append(b_probs,birthday_prob(i))\n", + "\n", + "Birthday_df=pd.DataFrame(\n", + " {\"Number of people\":number_people,\n", + " \"Probability\":b_probs})\n", + "Birthday_df.head(7)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We construct below a line graph of these probabilities that shows the trend. " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Birthday_df.plot.scatter(\"Number of people\",\"Probability\");" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Are the above probabilities surprising? Can you provide an intuition for them? Note that the number of people that yields the probability closest to a fair bet is 23." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.5073" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "birthday_prob(23)" + ] + } + ], + "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": "3.8.8" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}