Modelling_Assignment_2.ipynb

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    "<h1> FIT5197 Assignment 2 Semester 1, 2020 </h1>\n",
    "    \n",
    "<h2> <span style=\"color:green\"> Do </span> & <span style=\"color:red\">Don't</span> </h2>\n",
    "\n",
    "1. <span style=\"color:green\">Some of these policies are similar to your assignment 1; however, please read carefully as there are some differences between this assignment and the first assignment.</span>\n",
    "\n",
    "3. <span style=\"color:green\">These questions are meant for you to solve independently, we encourage students to figure out the questions themselves as it would be good for their understandings of the topics; however, please feel free to consult your tutors if needed. Plagiarism (either from using online sources or copying the answers from your classmates) will be penalised accordingly.</span>\n",
    "\n",
    "5. <span style=\"color:green\">Requests for special consideration or extension must be submitted at least 2 days BEFORE THE DEADLINE. The due date is on Sunday, so the latest day you can ask for extension is on Friday (the last official working day of the week for the teaching team). Please follow Monash guidelines to request for extensions (medical certificates, doctor or GP letter, etc). Emergencies are to be adjusted individually.</span>\n",
    "\n",
    "8. <span style=\"color:green\">Please show all working when answering questions, you will not get full marks for a question if you don't comply.</span>\n",
    "\n",
    "11. <span style=\"color:green\">Assignments need to be submitted in PDF and ipynb file format. Failure to comply will result in 20% penalty on each missing file. </span>\n",
    "\n",
    "12. <span style=\"color:green\">Filename format for submitting the assignment should be “Assignment2_StudentId.pdf” and \"Assignment2_StudentId.ipynb\". Files with the wrong format incurs 20% penalty each.</span>\n",
    "\n",
    "13. <span style=\"color:green\">This assignment has 10 marks for presentation, this includes presenting your explanation in **Markdown**, writing and commenting on code efficiently, creating good plots with clear labels on the axis, etc.</span>\n",
    "\n",
    "14. <span style=\"color:green\">Only answers with correct methodology will be considered for consequential marks. Meaning if you attempt the question and your answer is incorrect, but your methodology is correct, you will still receive partial marks for subsequent questions. However, answers with incorrect methodology (misunderstanding the questions) will generate no marks for subsequent questions.</span>\n",
    "\n",
    "15. <span style=\"color:green\">Challenge questions are for students aiming to get a HD for the assignment. We don't advise for students to spend time on these questions before finishing all the other parts in the assignment. This assignment is designed in a way that students can get up to 80 (HD) without attempting the challenge questions.</span>\n",
    "\n",
    "10. <span style=\"color:red\">Please don’t send emails to tutors asking for suggestions, we have Moodle and consultations for that. When writing your inquiries on Moodle please try to be clear in your problem and not revealing your working to others as this might be counted as plagiarism on your part. A good format for inquiry topic would be e.g. “Assignment 2 – Tutorial 10 (your tutorial slot) – Question about median\"</span>\n",
    "\n",
    "2. <span style=\"color:red\">Handwritten answers incur a penalty of 10% on your assignment, you have Markdown, please learn how to use it as it will be an useful skill for you going through the degree as well as in real life situation.</span>\n",
    "\n",
    "3. This assignment will contribute towards 20% of your total score.\n",
    "\n",
    "7. Late submission is 5% per day, after 10 days you will be given no marks. Late submission is calculated as follows: If you get 70% on this assignment and you are late for 2 days (you submit on Tuesday), your score is now 70% -10% (2x5% per day) = 60%. This is done to ensure that the teaching team can release your result as soon as possible so that you can review on your mistakes and have a better study experience.\n",
    "\n",
    "9. Assignments shall be marked completely in two weeks’ time according to Monash Policies. If there are any changes to the marking time, we will duly inform you. Solutions will not be released for this assignment; you can come to the tutorial and ask for explanation about how to solve the questions after scores are released."
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   "source": [
    "<h2>Question 1 - Probabilities (10 Marks)</h2>\n",
    "\n",
    "A box contains $n$ pairs of shoes ($2n$ shoes in total). If $2r$ (with the assumption that $2r \\leq n$) shoes are selected at random, find the probability for the following scenarios:"
   ]
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   "cell_type": "markdown",
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   "source": [
    "<h3> Question 1a. (2 Marks)</h3>\n",
    "\n",
    "$A_0$ = ‘No matching pair’ "
   ]
  },
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   "source": [
    "**ANSWER:**\n",
    "\n",
    "**Number of ways of selecting 2r shoes from 2n shoes:**\n",
    "\n",
    "$$\\text{Total probability} = \\binom{2n}{2r}$$ \n",
    "\n",
    "**Number of ways of selecting r pairs i.e 2r shoes from n pairs:** = $$\\binom{n}{2r}$$\n",
    "\n",
    "**Number of ways of selecting separate shoes from these r pairs i.e 2r shoes** = $$2^{2r}$$\n",
    "\n",
    "$$\\text{P(No matching pair)}= \\frac{\\binom{n}{2r}2^{2r}}{\\binom{2n}{2r}}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Question 1b. (3 Marks)  </h3>\n",
    "\n",
    "$A_1$ = ‘only one matching pair’"
   ]
  },
  {
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   "source": [
    "**ANSWER:**\n",
    "\n",
    "**Number of ways of selecting 2r shoes from 2n shoes:**\n",
    "\n",
    "$$\\text{Total probability} = \\binom{2n}{2r}$$ \n",
    "\n",
    "**Number of ways of selecting 1 pair from n pairs:** = $$\\binom{n}{1}$$ \n",
    "\n",
    "**Now,**\\\n",
    "We need to select **(r - 1)** pairs from **(n - 1)** pairs.\n",
    "Thus, \\\n",
    "**Number of ways of selecting (r - 1) pairs from **(n - 1)** pairs =  $$\\binom{n - 1}{2r - 2}$$\n",
    "**Now,**\\\n",
    "**Number of ways of selecting separate shoes from these (r -1) pairs i.e (2r - 2) shoes** = $$2^{2r - 2}$$\n",
    "\n",
    "$$\\text{P(Only one matching pair)}= \\frac{n\\binom{n - 1}{2r - 2}2^{2r - 2}}{\\binom{2n}{2r}}$$"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "<h3> Question 1c. (2 Marks)</h3>\n",
    "\n",
    "$A_2$ = ‘exactly two matching pairs’"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**ANSWER:**\n",
    "\n",
    "**Number of ways of selecting 2r shoes from 2n shoes:**\n",
    "\n",
    "$$\\text{Total probability} = \\binom{2n}{2r}$$ \n",
    "\n",
    "**Number of ways of selecting 2 pairs from n pairs:** = $$\\binom{n}{2}$$\n",
    "\n",
    "**Now,**\\\n",
    "We need to select **(r - 2)** pairs from **(n - 2)** pairs.\n",
    "Thus, \\\n",
    "**Number of ways of selecting (2r - 4) pairs from (n - 2)** pairs =  $$\\binom{n - 2}{2r - 4}$$\n",
    "**Now,**\\\n",
    "**Number of ways of selecting separate shoes from these (r -2) pairs i.e 2r - 4** = $$2^{2r - 4}$$\n",
    "\n",
    "$$\\text{P(Exactly two pairs)}= \\frac{\\binom{n}{2}\\binom{n - 2}{2r - 4}2^{2r - 4}}{\\binom{2n}{2r}}$$"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "<h3> Question 1d. (3 Marks)</h3>\n",
    "\n",
    "$A_r$ = ‘exactly r matching pairs’"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**ANSWER:**\n",
    "\n",
    "**Number of ways of selecting 2r shoes from 2n shoes:**\n",
    "\n",
    "$$\\text{Total probability} = \\binom{2n}{2r}$$ \n",
    "\n",
    "**Number of ways of selecting 0 pairs from the remaining (n - r) pairs:** = $$\\binom{n - r}{0}$$\n",
    "\n",
    "**Number of ways of selecting r pairs from n pairs:** = $$\\binom{n}{r}$$\n",
    "\n",
    "$$\\text{P(Exactly r pairs)}= \\frac{\\binom{n}{r}(n - r)}{\\binom{2n}{2r}}$$"
   ]
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   "source": [
    "<h2>Question 2 - Conditional Probabilities & Entropy (30 Marks)</h2>\n",
    "\n",
    "<span style=\"color:red\"> **Warning, no built in functions to calculate probability or entropy from R should be used for this part. The only help you can get from R should be dataframe manipulation. Answers using functions will not be marked even if the answer is correct.**</span>\n",
    "\n",
    "Sports analytics (i.e., the application of data science techniques to competitive sports) is a rapidly growing area of data science. In this question we will look at some very basic analytics applied to the outcomes of consecutive games of English Premier League (EPL). The file chelsea.csv contains a record of the outcomes of games of EPL played by **Chelsea football club (CFC)** in the seasons from 1993 to 2018. The data is sequential, in the sense that each row recorded the result whether the home team wins (H), the away team wins (A), or there is a draw (D).\n",
    "\n",
    "**Please show all working including code and presentation for this question**\n",
    "\n",
    "<h2>Part 1: Analyzing Home/Away performance (17 Marks)</h2>"
   ]
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   "source": [
    "<h3> Question 2.a (3 Marks)</h3>\n",
    "\n",
    "Find out the probabilities **P(Chelsea Wins), P(Chelsea Loses), and P(Chelsea Draws)**. This includes all the results both home and away."
   ]
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   "source": [
    "# Reading the dataset into data\n",
    "data <- read.csv(\"chelsea.csv\")\n",
    "\n",
    "# Calculating the total number of games\n",
    "total_number_of_games <- nrow(data)\n",
    "\n",
    "# Number of games won \n",
    "chelsea_wins <- subset( data, (home == \"Chelsea\" & result == \"H\") | \n",
    "                              (away == \"Chelsea\" & result == 'A') )\n",
    "chelsea_wins_games <- nrow(chelsea_wins)\n",
    "chelsea_wins_probability <- chelsea_wins_games/total_number_of_games\n",
    "round( chelsea_wins_probability, digits = 4)\n",
    "\n",
    "# Number of games lost \n",
    "chelsea_lost <- subset( data, (home == \"Chelsea\" & result == \"A\") | \n",
    "                              (away == \"Chelsea\" & result == 'H') )\n",
    "chelsea_lost_games <- nrow(chelsea_lost)\n",
    "chelsea_lost_probability <- chelsea_lost_games/total_number_of_games\n",
    "round( chelsea_lost_probability, digits = 4)\n",
    "\n",
    "# Number of games in draw\n",
    "chelsea_draw <- subset( data, (home == \"Chelsea\" & result == \"D\") | \n",
    "                              (away == \"Chelsea\" & result == 'D') )\n",
    "chelsea_draw_games <- nrow(chelsea_draw)\n",
    "chelsea_draw_probability <- chelsea_draw_games/total_number_of_games\n",
    "round( chelsea_draw_probability, digits = 4)"
   ]
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    "\n",
    " 1. **P(Chelsea Wins)** = chelsea_wins_games/total_number_of_games = 0.5459\n",
    " 2. **P(Chelsea Loses)** = chelsea_lost_games/total_number_of_games = 0.2098\n",
    " 3. **P(Chelsea Draws)** = chelsea_draw_games/total_number_of_games = 0.2443"
   ]
  },
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   "source": [
    "<h3> Question 2.b (6 Marks)</h3>\n",
    "\n",
    "Find out the conditional probabilities: \n",
    "\n",
    "1. **P(Chelsea Wins| Playing at Home)**\n",
    "2. **P(Chelsea Wins| Playing away)**\n",
    "2. **P(Chelsea Draws| Playing at Home)**\n",
    "4. **P(Chelsea Draws| Playing away)**\n",
    "5. **P(Chelsea Loses| Playing at Home)**\n",
    "6. **P(Chelsea Loses| Playing away)**\n",
    "\n",
    "Please make comparison and a general conclusion."
   ]
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   "source": [
    "# Reading the dataset into data\n",
    "data <- read.csv(\"chelsea.csv\")\n",
    "\n",
    "# Calculating the total number of games\n",
    "total_number_of_games <- nrow(data)\n",
    "\n",
    "# Games at home\n",
    "home <- subset( data, (home == \"Chelsea\"))\n",
    "total_games_home <- nrow(home)\n",
    "\n",
    "# Games away\n",
    "away <- subset( data, (away == \"Chelsea\"))\n",
    "total_games_away <- nrow(away)\n",
    "\n",
    "# P(Chelsea Wins| Playing at Home)\n",
    "wins_playing_at_home <- subset( data, (home == \"Chelsea\" & result == \"H\") )\n",
    "wins_playing_at_home <- nrow(wins_playing_at_home)\n",
    "wins_playing_at_home_probability <- wins_playing_at_home/total_games_home\n",
    "round( wins_playing_at_home_probability, digits = 4) \n",
    "\n",
    "# P(Chelsea Wins| Playing Away)\n",
    "wins_playing_away <- subset( data, (away == \"Chelsea\" & result == \"A\") )\n",
    "wins_playing_away <- nrow(wins_playing_away)\n",
    "wins_playing_away_probability <- wins_playing_away/total_games_away\n",
    "round( wins_playing_away_probability, digits = 4)\n",
    "\n",
    "# P(Chelsea Draws| Playing at Home)\n",
    "draws_playing_at_home <- subset( data, (home == \"Chelsea\" & result == \"D\") )\n",
    "draws_playing_at_home <- nrow(draws_playing_at_home)\n",
    "draws_playing_at_home_probability <- draws_playing_at_home/total_games_home\n",
    "round( draws_playing_at_home_probability, digits = 4)\n",
    "\n",
    "# P(Chelsea Draws| Playing away)\n",
    "draws_playing_away <- subset( data, (away == \"Chelsea\" & result == \"D\") )\n",
    "draws_playing_away <- nrow(draws_playing_away)\n",
    "draws_playing_away_probability <- draws_playing_away/total_games_away\n",
    "round( draws_playing_away_probability, digits = 4)\n",
    "\n",
    "# P(Chelsea Loses| Playing at Home)\n",
    "loses_playing_at_home <- subset( data, (home == \"Chelsea\" & result == \"A\") )\n",
    "loses_playing_at_home <- nrow(loses_playing_at_home)\n",
    "loses_playing_at_home_probability <- loses_playing_at_home/total_games_home\n",
    "round( loses_playing_at_home_probability, digits = 4) \n",
    "\n",
    "# P(Chelsea Loses| Playing away)\n",
    "loses_playing_away <- subset( data, (away == \"Chelsea\" & result == \"H\") )\n",
    "loses_playing_away <- nrow(loses_playing_away)\n",
    "loses_playing_away_probability <- loses_playing_away/total_games_away\n",
    "round( loses_playing_away_probability, digits = 4)"
   ]
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    "1. **P(Chelsea Wins| Playing at Home)**  = 0.6347\n",
    "2. **P(Chelsea Wins| Playing away)**     = 0.4572\n",
    "2. **P(Chelsea Draws| Playing at Home)** = 0.238\n",
    "4. **P(Chelsea Draws| Playing away)**    = 0.2505\n",
    "5. **P(Chelsea Loses| Playing at Home)** = 0.1273\n",
    "6. **P(Chelsea Loses| Playing away)**    = 0.2923\n",
    "\n",
    "**Comparison :** We can observe the following from the data :\n",
    "    * Chelsea wins more number of matches while playing at home than playing away.\n",
    "    * There is only a slightly higher probability of the match ending in a draw, when Chelsea is playing away, then at home.\n",
    "    * Similarly, the probability of Chelsea losing is higher when playing away, than playing at home.\n",
    "\n",
    "**General Conclusion :**\n",
    "    * Thus, we can conclude that for Chelsea phas it's best performance when the team is playing at home as it has it's familiar with the ground and turf and has it's crowd for support.\n"
   ]
  },
  {
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   "source": [
    "<h3> Question 2.c (3 Marks)</h3>\n",
    "\n",
    "Find $H($Chelsea Results$)$ this includes results in both home and away games"
   ]
  },
  {
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   "execution_count": 600,
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   "source": [
    "#log(value, base)\n",
    "# We have the probability values from the above calculations\n",
    "pw = chelsea_wins_probability \n",
    "pl = chelsea_lost_probability\n",
    "pd = chelsea_draw_probability\n",
    "\n",
    "p1 = pw*(log2(1/pw))\n",
    "p2 = pl*(log2(1/pl))\n",
    "p3 = pd*(log2(1/pd))\n",
    "\n",
    "Chelsea_Results_Entropy = round( p1 + p2 + p3, digits = 4)\n",
    "Chelsea_Results_Entropy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**$H($Chelsea Results$)$** = 1.4461"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Question 2.d (5 Marks)</h3>\n",
    "\n",
    "Is knowing whether Chelsea plays at home or away a good indicator in knowing the result of CFC games? Show your justification (answering just yes or no will not be given any marks) by calculating all the information necessary using the knowledge you have learnt so far in the unit. \n",
    "\n",
    "**Note that this is a challenge question, only attempt if you are comfortable with your progress. You should not use consultations to ask for this question as the tutors will proritize answering queries about other questions.**"
   ]
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     "output_type": "stream",
     "text": [
      "\n",
      " Probability of Chelsea playing at home: 0.5\n",
      " Probability of Chelsea playing at home: 0.5"
     ]
    }
   ],
   "source": [
    "#Calculations which will used in the answer:\n",
    "\n",
    "chelsea_home <- subset( data, (home == \"Chelsea\") )\n",
    "chelsea_home_probability <- ( nrow( chelsea_home ))/total_number_of_games\n",
    "cat(\"\\n Probability of Chelsea playing at home:\",chelsea_home_probability )\n",
    "\n",
    "chelsea_away <- subset( data, (away == \"Chelsea\") )\n",
    "chelsea_away_probability <- ( nrow( chelsea_away ))/total_number_of_games\n",
    "cat(\"\\n Probability of Chelsea playing at home:\",chelsea_away_probability )"
   ]
  },
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    "**ANSWER:**\n",
    "\n",
    "Yes, knowing whether Chelsea plays at home or away a good indicator in knowing the result of CFC games. \n",
    "\n",
    "**Step 1:**\n",
    "* Clearly, we know from **2a** that the Chelsea has **higher chances of winning**, than losing or the match resulting in a draw. \n",
    "* Similarly, from 2b, we know that when Chelsea, plays at home, the probability of winning is higher than the game resulting in a draw or a loss.\n",
    "\n",
    "**Step 2:**\\\n",
    "Now, we calculate the following:\n",
    "\n",
    "* Probability of playing at home: P(H)\n",
    "\\begin{eqnarray*}\n",
    "   P(Home)   &=&  0.5 \\\\                         \n",
    "\\end{eqnarray*}\n",
    "\n",
    "**Step 3:**\\\n",
    "Now, we can calculate the following:\n",
    "* The probability that Chelsea played at home, given it won the game.\n",
    "\\begin{eqnarray*}\n",
    "   P(Home/Wins)   &=&  \\frac{P(Home) \\cdot (Wins/Home)}{P(Wins)} \\\\\n",
    "          &=& 0.5812                \n",
    "\\end{eqnarray*}\n",
    "\n",
    "* The probability that Chelsea played at home, given it lost the game.\n",
    "\\begin{eqnarray*}\n",
    "   P(Home/Loses)   &=&  \\frac{P(Home) \\cdot (Loses/Home)}{P(Lost)} \\\\\n",
    "          &=& 0.3033                \n",
    "\\end{eqnarray*}\n",
    "\n",
    "* The probability that Chelsea played at home, given the match resulted in a draw.\n",
    "\\begin{eqnarray*}\n",
    "   P(Home/Draws)   &=&  \\frac{P(Home) \\cdot (Draws/Home)}{P(Lost)} \\\\\n",
    "          &=& 0.5129                \n",
    "\\end{eqnarray*}\n",
    "\n",
    "**Conclusions:**\n",
    "* Thus, from we can conclude that:\n",
    "    * Given, Chelsea has won a game, the probability that Chelsea played the match at **home** is quite high."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Part 2: Analyzing effects of previous results on future results (13 Marks)</h2>\n",
    "\n",
    "<span style=\"color:red\">**This is a new part of the question, this part will focus on a different aspects compared to part I. Objectively speaking, this part is harder compared to the previous one; thus, it has lower mark allocation, students are advised to spend time on this part if they want to achieve desirable outcome.** </span>\n",
    "\n",
    "Based on the data given to you, please create another column named \"binary\". This column will record a win $($corresponding to $1)$ or a loss/draw $($corresponding to $0)$ in the order in which the games were played by CFC.\n",
    "\n",
    "A simple question regarding this type of data might be regarding the existence of (de)motivativing effects on a team if they have won / not won their previous game. Let $W_t$ denote the binary outcome of a game in round $t$ and $W_{t−1}$ denote the outcome of the game played in the previous round. Answer the following questions; **you must provide working/justification.**\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 602,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Adding a new column named binary to the dataframe\n",
    "\n",
    "data <- read.csv(\"chelsea.csv\")\n",
    "\n",
    "data$binary <- ifelse( ( data$home == \"Chelsea\" & data$result == 'H') | \n",
    "                       ( data$away == \"Chelsea\" & data$result == 'A'), 1,0 )     "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Question 2.e (4 Marks)</h3>\n",
    "\n",
    "Using the data in **chelsea.csv** and the new column you just created for this task, write R code to **find the frequency** with which CFC won / did not win a game after it won / did not win its previous game. Using these frequencies, calculate the joint distributions $P(W_t = 0, W_{t-1} =0)$, $P(W_t = 1, W_{t-1} = 0)$, $P(W_t = 1, W_{t-1} = 1)$, and $P(W_t = 0, W_{t-1} = 1)$. We suggest students create another column from the original dataframe to solve this question. Please read this question carefully before attempting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 603,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Creating counters\n",
    "count_LL <- 0\n",
    "count_LW <- 0\n",
    "count_WW <- 0\n",
    "count_WL <- 0\n",
    "\n",
    "for (i in 2:total_number_of_games) \n",
    "{\n",
    "    if ( data$binary[i] == 0 & data$binary[i-1] == 0) \n",
    "    {\n",
    "     data$current_previous[i] <- \"LL\"\n",
    "     count_LL <- count_LL + 1\n",
    "    } \n",
    "    else if ( data$binary[i] == 0 & data$binary[i-1] == 1 ) \n",
    "    {\n",
    "      data$current_previous[i] <- \"LW\"\n",
    "      count_LW <- count_LW + 1\n",
    "    } \n",
    "    else if ( data$binary[i] == 1 & data$binary[i-1] == 1 ) \n",
    "    {\n",
    "      data$current_previous[i] <- \"WW\"\n",
    "      count_WW <- count_WW + 1\n",
    "    } \n",
    "    else if (data$binary[i] == 1 & data$binary[i-1] == 0 ) \n",
    "    {\n",
    "      data$current_previous[i] <- \"WL\"\n",
    "      count_WL <- count_WL + 1\n",
    "    } \n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 604,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " (Wt = 0, Wt-1 = 0) : 198\n",
      " (Wt = 0, Wt-1 = 1) : 236\n",
      " (Wt = 1, Wt-1 = 1) : 287\n",
      " (Wt = 1, Wt-1 = 0) : 236"
     ]
    }
   ],
   "source": [
    "# Frequencies\n",
    "cat(\"\\n (Wt = 0, Wt-1 = 0) :\",count_LL)\n",
    "cat(\"\\n (Wt = 0, Wt-1 = 1) :\",count_LW) \n",
    "cat(\"\\n (Wt = 1, Wt-1 = 1) :\",count_WW)\n",
    "cat(\"\\n (Wt = 1, Wt-1 = 0) :\",count_WL)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The different **frequencies** of the Joint Distributions are as follows:\n",
    "\n",
    "$P(W_t = 0, W_{t-1} =0)$ = 198 \\\n",
    "$P(W_t = 1, W_{t-1} = 0)$ = 236 \\\n",
    "$P(W_t = 1, W_{t-1} = 1)$ = 287 \\\n",
    "$P(W_t = 0, W_{t-1} = 1)$ = 236"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 605,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.2067"
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       "0.2067"
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       "[1] 0.2067"
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     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
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       "0.2463"
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       "[1] 0.2463"
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       "[1] 0.2996"
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     "data": {
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       "[1] 0.2463"
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculating the probabilities\n",
    "LL <- subset( data, (current_previous == \"LL\") )\n",
    "WL <- subset( data, (current_previous == \"WL\") )\n",
    "WW <- subset( data, (current_previous == \"WW\") )\n",
    "LW <- subset( data, (current_previous == \"LW\") )\n",
    "\n",
    "w00 <-  round ( ( nrow( LL ) ) / total_number_of_games, digits = 4 )\n",
    "w10 <-  round ( ( nrow( WL ) ) / total_number_of_games, digits = 4 )\n",
    "w11 <-  round ( ( nrow( WW ) ) / total_number_of_games, digits = 4 )\n",
    "w01 <-  round ( ( nrow( LW ) ) / total_number_of_games, digits = 4 )\n",
    "\n",
    "# Displaying the answers\n",
    "w00\n",
    "w10\n",
    "w11\n",
    "w01"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The different **probabilities** of the Joint Distributions are as follows:\n",
    "\n",
    "$P(W_t = 0, W_{t-1} =0)$ = 0.2067 \\\n",
    "$P(W_t = 1, W_{t-1} = 0)$ = 0.2463 \\\n",
    "$P(W_t = 1, W_{t-1} = 1)$ = 0.2996 \\\n",
    "$P(W_t = 0, W_{t-1} = 1)$ = 0.2463"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Question 2.f (2 Marks)</h3>\n",
    "\n",
    "What is the probability that CFC will win a game given that they won their previous game?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 606,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.5488"
      ],
      "text/latex": [
       "0.5488"
      ],
      "text/markdown": [
       "0.5488"
      ],
      "text/plain": [
       "[1] 0.5488"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_wins <- nrow( subset( data, (current_previous == \"WL\" | current_previous == \"WW\")) ) \n",
    "\n",
    "n_WW <- nrow( subset( data, (current_previous == \"WW\")) ) \n",
    "\n",
    "n_win_won <- round( n_WW/n_wins, digits = 4 )\n",
    "\n",
    "n_win_won"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, the probability that CFC will win a game given that they won their previous game is:\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "     Required Probability &=&  \\frac{P(W/W)}{P(W/W) + P(W/L)} \\\\\n",
    "          &=& 0.5488                \n",
    "\\end{eqnarray*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Question 2.g (2 Marks)</h3>\n",
    "\n",
    "What is the probability that CFC will win a game given that they didn't win their previous game?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 607,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.5438"
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       "[1] 0.5438"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_losses <- nrow( subset( data, (current_previous == \"LL\" | current_previous == \"LW\")) ) \n",
    "\n",
    "n_WL <- nrow( subset( data, (current_previous == \"WL\")) ) \n",
    "\n",
    "n_win_loss <- round( n_WL/n_losses, digits = 4 )\n",
    "\n",
    "n_win_loss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, probability that CFC will win a game given that they didn't win their previous game:\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "     Required Probability &=&  \\frac{P(W/L)}{P(L/W) + P(L/L)} \\\\\n",
    "          &=& 0.5438                \n",
    "\\end{eqnarray*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Question 2.h (2 Marks)</h3>\n",
    "\n",
    "Do you think winning/not winning the previous game had an effect on the CFC players in their next game? Justify your answer? **(Note that this is different compared to 2.d)**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Yes, **winning/not winning** the previous game had an effect on the CFC players in their next game.\n",
    "\n",
    "* Clearly, we can see from the above numbers that -\n",
    "    * the probability of CFC winning, given they have won their previous game is **higher**.\n",
    "* The contributing factors could be -\n",
    "    * High Energy, morale after the previous win!\n",
    "    * Greater confidence levels to keep th momemtum of winning high.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Question 2.i (3 Marks)</h3>\n",
    "\n",
    "Calculate the probability of CFC not winning their next two games given that they won their previous game."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 608,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.1086"
      ],
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       "0.1086"
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       "[1] 0.1086"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "count <- 0\n",
    "\n",
    "for( i in 2:total_number_of_games)\n",
    "{\n",
    "        if( data$binary[i - 1] == 1 & data$binary[i] == 0 & data$binary[i + 1] == 0 )\n",
    "        {\n",
    "                count <- count + 1\n",
    "        }\n",
    "}\n",
    "\n",
    "answer <- round( count/total_number_of_games, digits = 4)\n",
    "answer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus, the probability of CFC not winning their next two games given that they won their previous game\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "     Required Probability &=&  \\frac{Number Of Binary Occurrences of (1,0,0) }{Total Number Of Games Played} \\\\\n",
    "          &=& 0.1086               \n",
    "\\end{eqnarray*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Question 3 - Expectation - Challenge Question (10 Marks)</h2>\n",
    "\n",
    "Randomly place a point $P$ inside triangle $ABC$. Let $X$ be the continuous random variable representing the distance from point $P$ to $AB$. Find out $E(X)$ & $Var(X)$ (**5 Marks each**)\n",
    "\n",
    "\n",
    "**Note that this is a challenge question, only attempt if you are comfortable with your progress. You should not use consultations to ask about this question as the tutors will prioritize answering queries about other questions.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**ANSWER:**\n",
    "\n",
    "**Calculating the pdf of x:**\n",
    "* Let us draw a line from the vertex C to base AB.\n",
    "* Since Point P can lie anywhere inside the triangle, let us assume that P lies on this line.\n",
    "* Let x be the the distance of the point P from the base AB. \n",
    "* Let h be the height of the triangle.\n",
    "* Hence, from the question, \n",
    "    * we know that X is the continuous random variable representing the distance of this point P to the base AB.\n",
    "* Now, \n",
    "\n",
    "**The pdf can be calculated as:**\n",
    "\\begin{eqnarray*}\n",
    "     f(x) &=& \\frac{d}{dx} \\cdot P[X<=x] \\\\ \n",
    "          &=& \\frac{d}{dx} \\cdot (\\frac{h - x}{h})^{2} \\\\\n",
    "          &=& \\frac{2(h - x)}{h^{2}}          \n",
    "\\end{eqnarray*} \n",
    "\n",
    "\n",
    "**Hence, The pdf of X can be given as:**\n",
    "\n",
    "\\begin{equation*}\n",
    "    f(x)=\\left\\{\n",
    "                \\begin{array}{ll}\n",
    "                   \\frac{2(h - x)}{h^{2}} \\text{ if  }  0 \\le x \\le h\\\\\n",
    "                   0 \\text{ otherwise  }\n",
    "                \\end{array}\n",
    "              \\right.\n",
    "\\end{equation*}\n",
    "\n",
    "where $h$ =  Distance from vertex C to AB\n",
    "\n",
    "**Now, Mean of X can be given as:**\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "     E[X] &=& \\int_{0}^h{ x \\cdot f(x) \\cdot dx} \\\\\n",
    "          &=& \\int_{0}^h{ \\frac{2x(h - x)}{h^{2}} \\cdot dx } \\\\\n",
    "          &=& \\frac{h}{3}                     \n",
    "\\end{eqnarray*}\n",
    "\n",
    "\n",
    "**Now,**\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "     E[X^{2}] &=& \\int_{0}^h{ x^{2} \\cdot f(x) \\cdot dx} \\\\\n",
    "          &=& \\int_{0}^h{ \\frac{2x^{2}(h - x)}{h^{2}} \\cdot dx } \\\\\n",
    "          &=& \\frac{h^{2}}{6}                     \n",
    "\\end{eqnarray*}\n",
    "\n",
    "**Hence, Variance of x can be given as:**\n",
    "\\begin{eqnarray*}\n",
    "     V[X] &=& E[X^{2}] - E[X] \\\\\n",
    "          &=& \\frac{h^{2}}{18}                     \n",
    "\\end{eqnarray*}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Question 4 - Distribution (10 Marks)</h2>\n",
    "\n",
    "The teaching team of FIT5197 is required to prepare 4 questions each week for the next week’s tutorial. The number of questions created in a week is said to have a Poisson distribution with mean 6."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Question 4.a (2 Marks) </h3>\n",
    "\n",
    "Find the probability that the teaching team manages to write enough questions for the following week?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**ANSWER:**\n",
    "\n",
    "Here, it is given that the teaching team manages to write enough questions. \\\n",
    "Hence, $x = 4$ and $\\lambda$ = 6\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "     P(x=4 | \\lambda) &=& \\frac{ \\lambda^4 \\exp \\left(-\\lambda \\right) }{4!} \\\\\n",
    "                      &=& \\frac{ 6^4 \\exp \\left(-6 \\right) }{4!} \\\\\n",
    "                      &=& 0.1339\n",
    " \\end{eqnarray*}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 609,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.1339"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Checking with the r function\n",
    "round( dpois(4,6), digits = 4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Question 4.b (4 Marks) </h3>\n",
    "\n",
    "Since some of the tutors in the teaching team are also responsible for other units from FIT, for each week, there is a probability of 40% that only half of the team will work on the questions. If that is the case, the teaching team can only create 3 questions on average. If the teaching team fails to finish 4 questions one week, what is the probability that only half of the team works that week?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "YOUR ANSWER HERE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 610,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] 0.6472319\n",
      "[1] 0.1512039\n"
     ]
    }
   ],
   "source": [
    "# Probability of failing, when only half the staff works.\n",
    "print ( dpois(0,3) + dpois(1,3) + dpois(2,3) + dpois(3,3))\n",
    "\n",
    "# Probability of failing, when the entire the staff works.\n",
    "print ( dpois(0,6) + dpois(1,6) + dpois(2,6) + dpois(3,6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**ANSWER:**\n",
    "\n",
    "**P(Full)** :- Probability of full staff working = 0.6 \\\n",
    "**P(Half)** :- Probability of half staff working = 0.4 \\\n",
    "**Now,** \\\n",
    "Here : **Failing** means making less than 4 questions in one week. \n",
    "* When half staff works, lambda = 3 \n",
    "    * Probability of half staff failing = 0.6472 \n",
    "    * Which Implies, Probability of half staff not failing i.e passing = 1 - 0.6472 = 0.3528\n",
    "* When full staff works, lambda = 6\n",
    "    * Probability of full staff failing = 0.1512 \n",
    "    * Which Implies, Probability of full staff not failing i.e passing = 1 - 0.1512 = 0.8488 \n",
    "    \n",
    "**Here, it is given that the teaching team fails.** \\\n",
    "**Hence, the required probability can be calculated as:**\n",
    "    \n",
    "\\begin{eqnarray*} \n",
    "\tP(Half/Fail) &=& \\frac{P(Half) \\cdot P(Fail/Half)}{P(Half) \\cdot P(Fail/Half) + P(Full) \\cdot P(Fail/Full)} \\\\\n",
    "\t&=& \\frac{ (0.4)(0.6472) }{(0.4)(0.6472) + (0.6)(0.1512)}   \\\\\n",
    "    &=&  0.7405\n",
    "\\end{eqnarray*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Question 4.c (4 Marks) </h3>\n",
    "\n",
    "On week 12, the teaching team decides to no longer limit to 4 questions, and instead use every question they create. If a student has a 40% chance of correctly answering questions, and this student is expected to answer 2 questions correctly in the coming tutorial, what is the probability that the whole teaching team worked on creating the questions that week?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**ANSWER:**\n",
    "\n",
    "**P(Full)** :- Probability of full staff working = 0.6 \\\n",
    "**P(Half)** :- Probability of half staff working = 0.4 \\\n",
    "Now, \\\n",
    "Here, let the number of questions generated by the teaching team be N. \\\n",
    "And, student has a 40% chance of correctly answering questions. \\\n",
    "Also, student is expected to answer 2 questions correctly. \\\n",
    "Hence,\n",
    "\n",
    "\\begin{eqnarray*} \n",
    "\t\\Rightarrow& 0.4N &=& 2 \\\\\n",
    "\t\\Rightarrow& N &=& 5 \\\\\n",
    "\\end{eqnarray*}\n",
    "\n",
    "Hence, we now know that the number of questions generated are 5. \\\n",
    "Which, implies the teaching team has passed.\n",
    "\n",
    "Probability of full staff failing = 0.1512 \\\n",
    "Hence, Probability of full staff **passing** =1 - 0.1512 = 0.8488 \\\n",
    "Probability of half staff failing = 0.6472 \\\n",
    "Hence, Probability of half staff **passing** =1 - 0.6472 = 0.3528 \n",
    "\n",
    "**Here, we have found out that the teaching team has passed.** \\\n",
    "**Hence, the required probability can be calculated as:**\n",
    "\n",
    "\\begin{eqnarray*} \n",
    "\tP(Full/Pass) &=& \\frac{P(Full) \\cdot P(Pass/Full)}{P(Full) \\cdot P(Pass/Full) + P(Half) \\cdot P(Pass/Half)} \\\\\n",
    "\t&=& \\frac{ (0.6)(0.8488) }{(0.4)(0.3528) + (0.6)(0.8488)}   \\\\\n",
    "    &=&  0.7830\n",
    "\\end{eqnarray*}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Question 5 - Maximum Likelihood Estimation (15 Marks)</h2>\n",
    "\n",
    "The exponential distribution is a probability distribution for non-negative real numbers. It is often used to model waiting or survival times. The version that we will look at has a probability density function of the form\n",
    "\n",
    "$p(y | v) = exp(−e^{−v}y − v)$\n",
    "\n",
    "where $y ∈ R_+$, i.e., y can take on the values of non-negative real numbers. In this form it has one parameter: a log-scale parameter $v$.  If a random variable follows an ``exponential distribution`` with log-scale $v$ we say that $Y ∼ Exp(v)$. If $Y ∼ Exp(v)$, then $E[Y] = e^v$ and $V[Y] = e^{2v}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Question 5.a (4 Marks) </h3>\n",
    "\n",
    "Imagine we are given a sample of n observations $y = (y_1, . . . , y_n)$. Write down the joint probability of this sample of data, under the assumption that it came from an exponential distribution with log-scale parameter $v$ (i.e., write down the likelihood of this data). Make sure to simplify your expression, and provide working."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**ANSWER:**\n",
    "\n",
    "The likelihood is equal to the product of the individual probabilities.\n",
    "\n",
    "**Step 1:** Multiplying the individual probabilities. \\\n",
    "**Step 2:** Taking out the common values outside. \\\n",
    "**Step 3:** Simplifying the expression.\n",
    "\n",
    "**Thus**, we have\n",
    "\n",
    "\\begin{eqnarray*} \n",
    "\tp({\\bf y} | v) &=& exp(−e^{−v}y1 − v) \\cdot exp(−e^{−v}y2 − v) \\cdots \\exp(−e^{−v}yn − v) \\\\\n",
    "\t&=& xe^{−xy1} \\cdot xe^{−xy2}  \\cdots xe^{−xyn}   \\\\\n",
    "    &=& x^{n}e^{−xy1} \\cdot e^{−xy2}  \\cdots e^{−xyn} \\\\\n",
    "    &=& x^{n}e^{-xy1 -xy2  \\cdots -xyn} \\\\\n",
    "    &=& x^{n}e^{-x (y1 + y2  \\cdots + yn )} \\\\\n",
    "    &=& x^{n}e^{-xm}\n",
    "\\end{eqnarray*}\n",
    "\n",
    "\n",
    "where $m = \\sum_{i=1}^n y_i$ \\\n",
    "where $x =  e^{−v}$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Question 5.b (2 Marks) </h3>\n",
    "\n",
    "Take the negative logarithm of your likelihood expression and write down the negative loglikelihood of the data $y$ under the exponential model with log-scale $v$. Simplify this expression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**ANSWER:**\n",
    "\n",
    "The negative loglikelihood of the data $y$ under the exponential model with log-scale $v$ is given as follows:\n",
    "\n",
    "**Step 1:** Take the negative logarithm of the likelihood \\\n",
    "**Step 2:** Taking out the common values outside. \\\n",
    "**Step 3:** Substitute the value of $x =  e^{−v}$ \n",
    "\n",
    "**Thus**, we have\n",
    "\n",
    "\\begin{eqnarray*} \n",
    "\t -ln (p({\\bf y} | v)) &=&  -ln ( x^{n}e^{-xm} ) \\\\\n",
    "\t&=& -nln(x) -nln(e^{-xm})  \\\\\n",
    "    &=& -nln(x) + xm \\\\\n",
    "    &=& -nln(e^{−v}) + e^{−v}m \\\\\n",
    "    &=&  nv + e^{−v}m \n",
    "\\end{eqnarray*}\n",
    "\n",
    "\n",
    "where $m = \\sum_{i=1}^n y_i$ \\\n",
    "where $x =  e^{−v}$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Question 5.c (4 Marks) </h3>\n",
    "\n",
    "Derive the maximum likelihood estimator $\\hat{v}$ for $v$. That is, find the value of $v$ that minimises the negative log-likelihood. You must provide working."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**ANSWER:**\n",
    "\n",
    "The maximum likelihood estimator  $\\hat{v}$ for $v$ for a given data sample ${\\bf y}$ is given as follows:\n",
    "\n",
    "\n",
    "**Step 1:** Differentiate the negative log-likelihood function with respect to  $v$. \\\n",
    "**Step 2:** Set the derivative to zero. \\\n",
    "**Step 3:** Solve for $v$.\n",
    "\n",
    "Begin by differentiate the negative log-likelihood with respect to our parameter of interest $v$:\n",
    "\t\\begin{eqnarray*}\n",
    "\t\t\\frac{d \\, \\ell({\\bf v} ; v)}{d v} &=&  \\frac{d \\,(nv)}{dv} + \\frac{d \\, (me^{-v}) }{dv} \\\\\n",
    "\t\t\t\t\t\t\t\t\t\t&=& n + m(-e^{-v}) \\\\ \n",
    "                                        &=& n - me^{-v}\n",
    "\t\\end{eqnarray*}\n",
    "\tThen we need to set this to zero and solve for $v$:\n",
    "\t\\begin{eqnarray*}\n",
    "\t\t& n - me^{-v} &= 0 \\\\\n",
    "\t\t\\Rightarrow& n &= me^{-v} \\\\\n",
    "\t\t\\Rightarrow& e^{-v} &= \\frac{n}{m} \\\\\n",
    "        \\Rightarrow& v &= ln( \\frac{m}{n} )\n",
    "\t\\end{eqnarray*}\n",
    "    \n",
    " \\begin{eqnarray*}\n",
    "     \\hat{v}_{\\rm ML}({\\bf y}) &= ln( \\frac{m}{n} )\n",
    " \\end{eqnarray*}\n",
    "\t\n",
    "where $m = \\sum_{i=1}^n y_i$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Question 5.d (5 Marks) </h3>\n",
    "\n",
    "Determine the approximate bias and variance of the maximum likelihood estimator $\\hat{v}$ of $v$ for the exponential distribution.\n",
    "\n",
    "**Note that this is a challenge question, only attempt if you are comfortable with your progress. You should not use consultations to ask about this question as the tutors will proritize answering queries about other questions.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**ANSWER:**\n",
    "\n",
    "Here,  $Y ∼ Exp(v)$,then \\\n",
    "**Mean:** $E[Y] = e^v$ \\\n",
    "**Variance:** $V[Y] = e^{2v}$.\n",
    "\n",
    "We can **approximate** the maximum likelihood estimator to be the **probability density function** \\\n",
    "The maximum likelihood estimator helps us in determining the parameters that best help us describe the data \\\n",
    "This data is also given by the probability density function which provides the likelihood of the variable in the data\n",
    "\n",
    "**Step 1: Calculating the Mean and Bias** \\\n",
    "Here, it is given that y follows and exponential distribution. \\\n",
    "And, y takes values from $y_1$ to $y_n.$\\\n",
    "Hence, the Mean is given as follows:\n",
    "\n",
    "\\begin{eqnarray*}\n",
    "     E[ \\hat{v}_{\\rm ML}({\\bf y}) ] &=& \\int_{0}^v{ x \\cdot f(x) \\cdot dx} \\\\\n",
    "          &=& \\int_{0}^v{ x \\cdot ln( \\frac{m}{n} ) \\cdot dx } \\\\\n",
    "          &=& \\frac{v^{2}}{2} \\cdot ln( \\frac{m}{n} )                  \n",
    "\\end{eqnarray*}\n",
    "\n",
    "Hence, Bias can be given as:\n",
    "\\begin{eqnarray*}\n",
    "     b[ \\hat{v}_{\\rm ML}({\\bf y}) ] &=& E[ \\hat{v}_{\\rm ML}({\\bf y}) ] - v \\\\\n",
    "          &=& \\frac{v^{2}}{2} \\cdot ln( \\frac{m}{n} ) - v\n",
    "\\end{eqnarray*}\n",
    "\n",
    "**Step 2: Calculating the Varince**\n",
    "* The variance of the maximum likelihood estimator can be given as:\n",
    "\\begin{eqnarray*}\n",
    "     V[ \\hat{v}_{\\rm ML}({\\bf y}) ] &=& E[ ( \\hat{v}_{\\rm ML}({\\bf y}) - E[ \\hat{v}_{\\rm ML}({\\bf y}) ])^{2} ]\\\\\n",
    "          &=& E[ ln( \\frac{m}{n} ) - \\frac{v^{2}}{2} \\cdot ln( \\frac{m}{n} ) )^{2} ]  \\\\    \n",
    "          &=& E[ t - \\frac{v^{2}}{2} \\cdot t ) )^{2} ] \\\\   \n",
    "          &=& E[ \\frac{t^{2}( 4 + v^{4} - 4v^{2} )}{4} ] \\\\\n",
    "          &=& \\int_{0}^v{ v \\cdot \\frac{t^{2}( 4 + v^{4} - 4v^{2} )}{4} \\cdot dx } \\\\\n",
    "          &=& \\frac{v^{2}t^{2}( 12 + v^{4} - 6v^{2} ) }{24}\n",
    "\\end{eqnarray*}\n",
    "\n",
    "where $m = \\sum_{i=1}^n y_i$ \\\n",
    "where $t = ln( \\frac{m}{n} )$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Question 6 - Central Limit Theorem (15 Marks)</h2>\n",
    "\n",
    "Sampling Process: Assume that we randomly select samples of the same size $n$ an infinite number of times from a population that follows a Poisson distribution with mean of $\\lambda$, and then, we calculate the mean of scores in each sample. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Question 6.a (2 Marks) </h3>\n",
    "\n",
    "What does Central Limit Theorem tell us about the sampling distribution of the sample mean?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**ANSWER:**\n",
    "\n",
    "The **Central Limit Theorem** states that if you have a population with **mean μ** and **standard deviation σ** and take sufficiently large random samples from the population with replacement , then the **distribution** of the **sample means** will be approximately **normally distributed** **as follows** for large values of n.\n",
    "\n",
    "$$\n",
    " =\\begin{align}\n",
    "N\\left [ μ,{\\frac{1}{n}σ^2} \\right ]\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "In Poisson Distribution, we know:\n",
    "* **Mean = $\\lambda$**\n",
    "* **Variance = $\\lambda$**\n",
    "\n",
    "**Pois($\\lambda$)** approaches **N($\\lambda$,$\\lambda$)** for large **$\\lambda$**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Question 6.b (3 Marks) </h3>\n",
    "\n",
    "For three different Poisson populations with mean of $\\lambda_1$ = 1, $\\lambda_2$ = 5 and $\\lambda_3$ = 20, we will do the sampling four separate times -- for small samples (n=10), for samples of 100 subjects (n=100) and 1000 subjects (n=1000), and once for big samples (n=10000).\n",
    "\n",
    "Based on your answer from 6.a, compute the parameter values for each sampling distribution in R. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 623,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to calculate mean and standard deviation\n",
    "calculate_mean_sd <- function(n, lambda) \n",
    "{\n",
    "        # Displaying the n and lambda values\n",
    "        cat(\"\\n n =\",n)\n",
    "        cat(\"\\n lambda =\",lambda)\n",
    "    \n",
    "        cat(\"\\n\")\n",
    "        # Storing the mean and sd values in a list names result\n",
    "        result <- list()\n",
    "        result$mean_value <- mean(rpois(n,lambda))\n",
    "        result$sd_value <- sd(rpois(n,lambda))\n",
    "        \n",
    "        #return (result)\n",
    "        cat(\"\\n Mean =\",result$mean_value)\n",
    "        cat(\"\\n Standard Deviation =\",result$sd_value)\n",
    "        cat(\"\\n --------------------------------\\n \")\n",
    "          \n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 624,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " n = 10\n",
      " lambda = 1\n",
      "\n",
      " Mean = 1\n",
      " Standard Deviation = 0.5163978\n",
      " --------------------------------\n",
      " \n",
      " n = 100\n",
      " lambda = 1\n",
      "\n",
      " Mean = 1.09\n",
      " Standard Deviation = 0.8348471\n",
      " --------------------------------\n",
      " \n",
      " n = 1000\n",
      " lambda = 1\n",
      "\n",
      " Mean = 1.036\n",
      " Standard Deviation = 0.9763982\n",
      " --------------------------------\n",
      " \n",
      " n = 10\n",
      " lambda = 5\n",
      "\n",
      " Mean = 5\n",
      " Standard Deviation = 3.198958\n",
      " --------------------------------\n",
      " \n",
      " n = 100\n",
      " lambda = 5\n",
      "\n",
      " Mean = 5.14\n",
      " Standard Deviation = 2.38336\n",
      " --------------------------------\n",
      " \n",
      " n = 1000\n",
      " lambda = 5\n",
      "\n",
      " Mean = 4.994\n",
      " Standard Deviation = 2.258932\n",
      " --------------------------------\n",
      " \n",
      " n = 10\n",
      " lambda = 20\n",
      "\n",
      " Mean = 19.4\n",
      " Standard Deviation = 3.683296\n",
      " --------------------------------\n",
      " \n",
      " n = 100\n",
      " lambda = 20\n",
      "\n",
      " Mean = 19.91\n",
      " Standard Deviation = 4.398932\n",
      " --------------------------------\n",
      " \n",
      " n = 1000\n",
      " lambda = 20\n",
      "\n",
      " Mean = 19.925\n",
      " Standard Deviation = 4.404919\n",
      " --------------------------------\n",
      " "
     ]
    }
   ],
   "source": [
    "# Calling the function to calculate the mean and sd values\n",
    "\n",
    "for (lambda in c(1,5,20))\n",
    " for (n in c(10,100,1000)) \n",
    "        calculate_mean_sd(n,lambda)        "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Question 6.c (5 Marks) </h3>\n",
    "\n",
    "In this question, you are asked to experimentally justify the result in the CLT Theorem.\n",
    "\n",
    "For different sample sizes of $n$ = 10, 100 and 1000, use 50000 simulations (i.e. to approximate the infinite times we drew samples as mentioned before) to implement the sampling process.\n",
    "\n",
    "From those 50000 sample means, compute the mean and standard deviation parameters (3 sample sizes and 3 $\\lambda$ rates, 9 pairs of parameters in total).\n",
    "\n",
    "Discuss how the results reflect the CLT. Plot the results ( mean and standard deviation separately) to demonstrate any effects you want to discuss."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**How the results reflect the CLT:**\n",
    "\n",
    "* As the sample size **increases**, the mean and standard deviation **decreases.**\n",
    "    * This is because as the sample size increases, the sample means cluster more and more around the true mean.\n",
    "    * Hence, the standard error i.e standard deviation **decreases.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 625,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to calculate the parameters\n",
    "simulate <- function(n, lambda) \n",
    "{\n",
    "    # To store the different mean values\n",
    "    sample_mean = rep(0,50000)\n",
    "    for (i in 1:50000) \n",
    "    {\n",
    "        sample_mean[i] = mean(rpois(n,lambda))\n",
    "        \n",
    "        # Storing the mean and sd values in result \n",
    "        result <- list()\n",
    "        result$mean_value <- mean(sample_mean)\n",
    "        result$sd_value <- sd(sample_mean)\n",
    "        \n",
    "        # Returning this result value\n",
    "        return (result)\n",
    "    }\n",
    "    \n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 626,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "$mean_value\n",
      "[1] 1.4e-05\n",
      "\n",
      "$sd_value\n",
      "[1] 0.003130495\n",
      "\n",
      "\n",
      " ------------------- \n",
      " $mean_value\n",
      "[1] 1.96e-05\n",
      "\n",
      "$sd_value\n",
      "[1] 0.004382693\n",
      "\n",
      "\n",
      " ------------------- \n",
      " $mean_value\n",
      "[1] 1.946e-05\n",
      "\n",
      "$sd_value\n",
      "[1] 0.004351388\n",
      "\n",
      "\n",
      " ------------------- \n",
      " $mean_value\n",
      "[1] 7.2e-05\n",
      "\n",
      "$sd_value\n",
      "[1] 0.01609969\n",
      "\n",
      "\n",
      " ------------------- \n",
      " $mean_value\n",
      "[1] 0.0001014\n",
      "\n",
      "$sd_value\n",
      "[1] 0.02267373\n",
      "\n",
      "\n",
      " ------------------- \n",
      " $mean_value\n",
      "[1] 0.00010184\n",
      "\n",
      "$sd_value\n",
      "[1] 0.02277212\n",
      "\n",
      "\n",
      " ------------------- \n",
      " $mean_value\n",
      "[1] 0.000456\n",
      "\n",
      "$sd_value\n",
      "[1] 0.1019647\n",
      "\n",
      "\n",
      " ------------------- \n",
      " $mean_value\n",
      "[1] 0.0004018\n",
      "\n",
      "$sd_value\n",
      "[1] 0.08984521\n",
      "\n",
      "\n",
      " ------------------- \n",
      " $mean_value\n",
      "[1] 0.000397\n",
      "\n",
      "$sd_value\n",
      "[1] 0.0887719\n",
      "\n",
      "\n",
      " ------------------- \n",
      " "
     ]
    }
   ],
   "source": [
    "# Calling the function to calculate the parameters\n",
    "for (lambda in c(1,5,20)) \n",
    "{\n",
    "    for (n in c(10,100,1000)) \n",
    "    {\n",
    "        print( (simulate(n,lambda)) )\n",
    "        cat(\"\\n ------------------- \\n \")\n",
    "    }\n",
    "    \n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 627,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to plot the mean\n",
    "plot_mean <- function(n,lambda)\n",
    "{\n",
    "    sample_mean = rep(0,n)\n",
    "    \n",
    "    for (i in 1:50000) \n",
    "        sample_mean[i] = mean(rpois(n,lambda))\n",
    "        \n",
    "        # Plotting an histogram of the means\n",
    "        h = hist(sample_mean, xlab =\"Mean\", \n",
    "        col=ifelse(n<11, 'blue', ifelse( n<101,'red', ifelse(n<1001,'green','yellow') )),                                                   \n",
    "        breaks = 30, freq = F,\n",
    "        main=sprintf(\"n=%s, lambda=%s\", n, lambda),\n",
    "        cex.lab=2, cex.axis=1.5, cex.main=2.5, cex.sub=1.5) \n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 628,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to plot the standard deviation\n",
    "plot_sd <- function(n,lambda)\n",
    "{\n",
    "    sample_deviation = rep(0,n)\n",
    "    \n",
    "    for (i in 1:50000) \n",
    "        sample_deviation[i] = sd(rpois(n,lambda))\n",
    "        \n",
    "        # Plotting an histogram of the standard deviations\n",
    "        h = hist(sample_deviation, xlab =\"Standard Deviation\", \n",
    "        col=ifelse(n<11, 'blue', ifelse( n<101,'red', ifelse(n<1001,'green','yellow') )),\n",
    "        breaks = 30, freq = F,\n",
    "        main=sprintf(\"n=%s, lambda=%s\", n, lambda),\n",
    "        cex.lab=2, cex.axis=1.5, cex.main=2.5, cex.sub=1.5)  \n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 629,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PAaAis6gbUnsMjAyCcJLEYGeA2BFZ3A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\nH7zU2hSNLZU9KD0omxYFVv4E4RBYkbA/ChBY7o3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skcatsZAKD0qPVL2pCfXd17+3v7p++QksuX/lj47AQhHXs9fYR8UnkB5qLJHGrbGQ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\nlUGwAAAAAFbmfzg0D9IECZoRAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"n=1000, lambda=20\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 1200,
       "width": 1200
      },
      "text/plain": {
       "height": 1200,
       "width": 1200
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calling the function to plot means\n",
    "\n",
    "par(mfrow=c(3, 3))\n",
    "options(repr.plot.width=20, repr.plot.height=20)\n",
    "\n",
    "for (lambda in c(1,5,20)) {\n",
    "    for (n in c(10,100,1000)) {\n",
    "        plot_mean(n, lambda)\n",
    "    }\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 630,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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3V/0Fc/CCwOXm+7u73A+kVgMUHgiQqs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Pn//fnJ/j6qvbrbhAixTE0poV6bF55PJ8\nFCGwPOF85NJSUTNL0iOyo/s5Gqfv71M3fPDh5nl+FMTSmhXpsXnk8nwUIbA84Xzk0lJRM0vS\nI7Lj+sue/3XnY+LngCiIpTUr0mPzyOX5KEJgecL5yKWlomaWpEdkxzWw3rrN8CcvB0RBLK1Z\nkR6bRy7PRxECyxPORy4tFTWzJD0iO65fIrz8msFPN19DVxBLa1akx+aRy/NRhMDyhPORS0tF\nzSxJj8iO8ze5v50/w3v4/j72w689z71AixTE0poV6bF55PJ8FCGwPOF85NJSUTNL0iOyo7s+\ng8n5Qw9Hz2OiIJbWrEiPzSOX56MIgeUJ5yOXloqaWZIekR0/ozy+dcMneL/7/boLNEhBLK1Z\nkR6bSx7PRxECyxXORyYtFTWzJD0iO/hdhFKxtGZFemzI5nDPCCwkc7gpWipqZkl6RHYQWFKx\ntGZFemzI5nDPCCwkc7gpWipqZkl6RHYQWFKxtGZFemzI5nDPCCwkc7gpWipqZkl6RHYM34M1\nfJvixZoLNEhBLK1ZkR6bSx7PRxECyxXORyYtFTWzJD0iO7rzD9d27g6IglhasyI9No9cno8i\nBJYnnI9cWipqZkl6RHZ05yfh/Sq6QIsUxNKaFemxeeTyfBQhsDzhfOTSUlEzS9IjsuP8q3IO\nZRdokYJYWrMiPTaPXJ6PIgSWJ5yPXFoqamZJekR2dGt+f9T9BVqkIJbWrEiPzSOX56MIgeUJ\n5yOXloqaWZIekR3d93b4PegFF2iRglhasyI9No9cno8iBJYnnI9cWipqZkl6RHZ03x/de9kF\nWqQgltasSI/NI5fnowiB5QnnI5eWippZkh6RHd35t3Xuj0UXaJCCWFqzIj02lzyejyIEliuc\nj0xaKmpmSXpEdpy/B8vhj9kqiKU1K9Jj88jl+ShCYHnC+cilpaJmlqRHZAeBJRVLa1akx+aR\ny/NRRG1gBUlPq3Wcj1xaKmpmSXpEdvCrcqRiac2K9NiQzeGeqQ2s4F9KT8s5h/PXUlEzS9Ij\nsoPAkoqlNSvSY0M2h3tGYCGZw/lrqaiZJekR2UFgScXSmhXpsSGbwz0jsJDM4fy1VNTMkvSI\n7BhG+bXfnL96vlvzlLxt7oWCWFqzIj02p/ydjyIEljOcj0fhb/i7UFJRM0vS07PjPMrd9dsT\nu+5z3QXaoyCW1qxIj80nh+ejCIHlC+cjQEsqrVuSnp4d3fmpeLdfwy88+Fzza6Xa3AsFsbRm\nRXpsLnk8H0UILFc4HyFaUmndkvT07Dg/k/v2+/obpT66txUXaJGCWFqzIj02j1yejyIEliec\njyAtqbRuSXp6dpx/F+H5w47hgJy6fsUFWqQgltasSI/NI5fnowiB5QnnI0hLKq1bkp6eHd31\nt6Hf/m/mBVqkIJbWrEiPzSOX5yNR5Jt4X9lHxReQnmHrOB9BWlJp3ZL09OwgsKRiac2K9Ng8\ncnk+Einoo+ILSM+wdZyPIC2ptG5Jenp2nL9E+PV9PRpfw5fTcy/QIgWxtGZFemweuTwfiRT0\nUfEFpGfYOs5HkJZUWrckPT077r7Jfdt9rLhAixTE0poV6bF55PJ8JFLQR8UXkJ5h6zgfQVpS\nad2S9PTsGJ6mYTP8mO3XzwurLtAgBbG0ZkV6bC55PB+JFPRR8QWkZ9g8zkeIllRatyQ9PTsu\nH3hcbY/rLtAeBbG0ZkV6bD45PB+JFPRR8QWkZ9g+zkeAllRatyQ9PTuGUX6+bbqu3614Ht5W\nD4iCWFqzIj02p/ydj0QK+qj4AtIzNIDz8UhLKq1bkp6eHfyyZ6lYWrMiPTZkM71nCvqo+ALS\nM3TO6vy1pNK6Jenp2UFgScXSmhXpsSGb6T1T0EfFF5CeoXNW568lldYtSU/Pju70b7fpum7z\ntuoTvK0eEAWxtGZFemwO+TwfiRT0UfEFpGfYOM5HmJZUWrckPT07bp5/uc//GdvvVg+Iglha\nsyI9Nn/efZ6PRAr6qPgC0jNsG+cjQksqrVuSnp4dXbf/Ov38//Hzret2ay5Q+x69hIJYWrMi\nPTZ/nJ6PRAr6qPgC0jNsG+cjQksqrVuSnp4d3d9P1h76Fb8MvdEDoiCW1qxIj82f3uf5SKSg\nj4ovID3DtnE+IrSk0rol6enZcTvKY9/lP5FJm3uhIJbWrEiPzZ/bA+HofCRS0EfFF5CeYds4\nHxFaUmndkvT07Lgb5Xv3XnaBZiiIpTUr0mNzzs/5SKSgj4ovID1DQzgff7Sk0rol6enZcTfK\nw4qvore5Fwpiac2K9Nic83M+Einoo+ILSM/QEM7HHy2ptG5Jenp23I+yy59sm3uhIJbWrEiP\nzTs35yORgj4qvoD0DC3hfPzSkkrrlqSnZweBJRVLa1akx+adm/ORSEEfFV9AeoaWcD5+aUml\ndUvS07ODwJKKpTUr0mPzzs35SKSgj4ovID1DSzgfv7Sk0rol6enZQWBJxdKaFemxeefmfCRS\n0EfFF5CeoSWcj19aUmndkvT07CCwpGJpzYr02LwLnY+v993wRNa7/VfwP3n2fZKkoI+KLyA9\nQ0vcvP9YpiWV1i1JT88OAksqltasSI/Nu8fzcdrc/LKpbeg/ecHdEqOgj4ovID1DS9y8/1im\nJZXWLUlPzw4CSyqW1qxIj827x/Ox7/p/h+Gl42ff7QP/ydPvlCAFfVR8AekZWuLm/ccyLam0\nbkl6enZ0E/kXeMKdej4FsbRmRXps/iydj747/L586PrABZ5694Qp6KPiC0jPsG1O338s05JK\n65akp2eH0wOiIJbWrEiPzZ+l83H3N6HjY3rPFPRR8QWkZ9g2p+8/lmlJpXVL0tOzo3iUbe6F\nglhasyI9NkzxGSzhPiq+gPQMnbM6fy2ptG5Jenp2EFhSsbRmRXpsmNp3/eflN9zyPVgifVR8\nAekZOmd1/lpSad2S9PTsILCkYmnNivTY8GB78/WRzelx3fSeKeij4gtIz9A5q/PXkkrrlqSn\nZweBJRVLa1akx4ZHX/vhebD63TvPgyXQR8UXkJ6hc1bnryWV1i1JT88OAksqltasSI8N2Uzv\nmYI+Kr6A9Aydszp/Lam0bkl6enYQWFKxtGZFemzIZnrPFPRR8QWkZ+ic1flrSaV1S9LTs4PA\nkoqlNSvSY0M203umoI+KLyA9Q+eszl9LKq1bkp6eHQSWVCytWZEeG2bxPFiv76PiC0jP0Dmr\n89eSSuuWpKdnB4ElFUtrVqTHhlmTZx1d+dSLDVHQR8UXkJ6hc1bnryWV1i1JT88OAksqltas\nSI8N2UzvmYI+Kr6A9Aydszp/Lam0bkl6enYQWFKxtGZFemzIZnrPFPRR8QWkZ+ic1flrSaV1\nS9LTs4PAkoqlNSvSY0M203umoI+KLyA9Q+eszl9LKq1bkp6eHQSWVCytWZEeG7KZ3jMFfVR8\nAekZOmd1/lpSad2S9PTsILCkYmnNivTYkM30ninoo+ILSM/QOavz15JK65akp2cHgSUVS2tW\npMeGbKb3TEEfFV9AeobOWZ2/llRatyQ9PTsILKlYWrMiPTZMdfcCN3j9fXodBX1UfAHpGTpn\ndf5aUmndkvT07CCwpGJpzYr02DD1QWDJ9lHxBaRn6JzV+WtJpXVL0tOzg8CSiqU1K9Jjw4ND\nv51dN71nCvqo+ALSM3TO6vy1pNK6Jenp2UFgScXSmhXpseHRodvPLZveMwV9VHwB6Rk6Z3X+\nWlJp3ZL09OwgsKRiac2K9NgQ8NEdZlZN75mCPiq+gPQMnbM6fy2ptG5Jenp2EFhSsbRmRXps\nyGZ6zxT0UfEFpGfonNX5a0mldUvS07ODwJKKpTUr0mNDNtN7pqCPii8gPUPnrM5fSyqtW5Ke\nnh0EllQsrVmRHhuymd4zBX1UfAHpGTpndf5aUmndkvT07CCwpGJpzYr02JDN9J4p6KPiC0jP\n0Dmr89eSSuuWpKdnB4ElFUtrVqTHhmym90xBHxVfQHqGzlmdv5ZUWrckPT07CCypWFqzIj02\nZDO9Zwr6qPgC0jN0zur8taTSuiXp6dlBYEnF0poV6bEhm+k9U9BHxReQnqFzVuevJZXWLUlP\nzw4CSyqW1qxIjw3ZTO+Zgj4qvoD0DJ2zOn8tqbRuSXp6dhBYUrG0ZkV6bMhmes8U9FHxBaRn\n6JzV+WtJpXVL0tOzg8CSiqU1K9JjQzbTe6agj4ovID1D56zOX0sqrVuSnp4dBJZULK1ZkR4b\nspneMwV9VHwB6Rk6Z3X+WlJp3ZL09OwgsKRiac2K9NiQzfSeKeij4gtIz9A5q/PXkkrrlqSn\nZweBJRVLa1akx4ZspvdMQR8VX0B6hs5Znb+WVFq3JD09OwgsqVhasyI9NmQzvWcK+qj4AtIz\ndM7q/LWk0rol6enZQWBJxdKaFemxIZvpPVPQR8UXkJ6hc1bnryWV1i1JT88OAksqltasSI8N\n2UzvmYI+Kr6A9Aydszp/Lam0bkl6enYQWFKxtGZFemzIZnrPFPRR8QWkZ+ic1flrSaV1S9LT\ns4PAkoqlNStx0gNFhOmdUdBHxReQnqFzVuevJZXWLUlPzw4CSyqW6q5IDxQRpndGQR8VX0B6\nhs5Znb+WVFq3JD09OwgsqSSquyI9UESY3hkFfVR8AekZOmd1/lpSad2S9PTsILCkkqjuivRA\nEWF6ZxT0UfEFpGfonNX5a0mldUvS07ODwJJKoror0gNFhOmdUdBHxReQnqFzVuevJZXWLUlP\nzw4CSyqJ6q5IDxQRpndGQR8VX0B6hs5Znb+WVFq3NEd6sm0hsKSSqO6K9EARYXpnFPRR8QWk\nZ+ic1flrSaXaS3x2Kw+BJZVEdVekB4oI0zujoI+KLyA9Q+eszl9JDxFYwggsqSSquyI9UESY\n3hkFfVR8AekZOmd1/kp6iMASRmBJJVHdFemBIsL0zijoo+ILSM/QOavzV9JDBJYwAksqiequ\nSA8UEaZ3RkEfFV9AeobOWZ2/kh4isIQRWFJJVHdFeqCIML0zCvqo+ALSM3TO6vyV9PmsBawA\nACAASURBVBCBJYzAkkqiuivSA0WE6Z1R0EfFF5CeoXNW56+khwgsYQSWVBLVXZEeKCJM74yC\nPiq+gPQMnbM6fyU9RGAJI7CkkqjuivRAEWF6ZxT0UfEFpGfonNX5K+khAksYgSWVRHVXpAeK\nCNM7o6CPii/A01WLsjppJT1EYAkjsKSSqO6K9EARYXpnFPTRky4gPVk3rE5aSQ8RWMIILKkk\nqrsiPVBEmN4ZtX1UfAHpybphddJKeojAEkZgSSVR3RXpgSLC9M6o7aPiC0hP1g2rk1bSQwSW\nMAJLKonqrkgPFBGmd0ZtHxVfQHqyblidtJIeIrCEEVhSSVR3RXqgiDC9M2r7qPgC0pN1w+qk\nlfQQgSWMwJJKoror0gNFhOmdUdtHxReQnqwbVietpIcILGEEllQS1V2RHigiTO+M2j4qvoD0\nZN2wOmklPURgCSOwpJKo7or0QBFhemfU9lHxBaQn64bVSSvpIQJLGIEllUR1V6QHigjTO6O2\nj4ovID1ZN6xOWkkPEVjCCCypJKq7Ij1QRJjeGbV9VHwB6cm6YXXSSnqIwBJGYEklUd0V6YEi\nwvTOqO2j4gtIT9YNq5NW0kMEljACSyqJ6q5IDxQRpndGbR8VX0B6sm5YnbSSHiKwhBFYUklU\nd0V6oIgwvTNq+6j4AtKTdcPqpJX0EIEljMCSSqK6K9IDRYTpnVHbR8UXkJ6sG1YnraSHCCxh\nBJZUEtVdkR4oIkzvjNo+Kr6A9GTdsDppJT1EYAkjsKSSqO6K9EARYXpn1PZR8QWkJ+uG1Ukr\n6SECSxiBJZVEdVekB4oI0zujto+KLyA9WTesTlpJDxFYwggsqSSquyI9UESY3hm1fVR8AenJ\numF10kp6iMASRmBJJVHdFemBIsL0zqjto+ILSE/WDauTVtJDBJYwAksqiequSA8UEVZ2pgt6\nUt7IX0B63G5YnbSSHiKwhBFYUklUd0V6oIiwsjNt9VHxBaTH7YbVSSvpIQJLGIEllUR1V6QH\niggrO9NWHxVfQHrcblidtJIeIrCEEVhSSVR3RXqgiLCyM231UfEFpMfthtVJK+khAksYgSWV\nRHVXpAeKCCs701YfFV9AetxuWJ20kh4isIQRWFJJVHdFeqCIsLIzbfVR8QWkx+2G1Ukr6SEC\nSxiBJZVEdVekB4oIKzvTVh8VX0B63G5YnbSSHiKwhBFYUklUd0V6oIiwsjNt9VHxBaTH7YbV\nSSvpIQJLGIEllUR1V6QHiggrO9NWHxVfQHrcblidtJIeIrCEEVhSSVR3RXqgiLCyM231UfEF\npMfthtVJK+khAkvY4rhOb123/bzeOHDrNuetIInqrkgPFBFWdqatPiq+gPS43bA6aSU9RGAJ\nWxrXqR9+JcbucmMCS+uK9EARYWVn2uqj4gtIj9sNq5NW0kMElrClce27j5/K+ui3w40JLK0r\n0gNFhJWdaauPii8gPW43rE5aSQ8RWMKWxtVfbnDsN0cCS/GK9EARYWVn2uqj4gtIj9sNq5NW\n0kMElrClcY1NddpuCSzFK9IDRYSVnWmrj4ovID1uN6xOWkkPEVjClsa16U7jS1sCS++K9EAR\nYWVn2uqj4gtIj9sNq5NW0kMElrClcX10b9eXjt2WwFK7Ij1QRFjZmbb6qPgC0uN2w+qklfQQ\ngSVscVz736r67AgstSvSA0WElZ1pq4+KLyA9bjeannQ3Q0cPEVjClsd12I0vHd8ILK0r0gNF\nhJWdaauPii8gPW43mp60kughsPTimdylkqjuivRAEWFlZ9rqo+ILSI/bjaYnrSR6CCy9CCyp\nJKq7Ij1QRFjZmbb6qPgC0uN2o+lJK4keAksvAksqiequSA8UEVZ2pq0+Kr6A9LjdaHrSSqKH\nwNIra1x8k7vaFemBIsLKzrTVR8UXkB63G01PWkn0EFh6rQ+s8aclKt+h11CQRHVXpAeKCCs7\n01YfFV9AetxmnN66bvt5ednOB+hXSqKHwNKLLxFKJVHdFemBIsLKzrTVR8UXkB63Fad++Cj8\n8pPoBFb7SwRWHgJLKonqrkgPFBFWdqatPiq+gPS4rdh3Hz+V9dFvz38gsNpfIrDyEFhSSVR3\nRXqgiLCyM231UfEFpMdtRX+Z5LHfHAksC0sEVp7lcX297y6f5d1/rbuARgqSqO6K9EARYWVn\n2uqj4gtIj9uKsalO262l7+G9UhI9BJZeS+M6bW6e/X+74gI6KUiiuivSA0WElZ1pq4+KLyA9\nbis23Wl8actnsAwsEVh5lsa17/p/h+Gl42ff7fMvIGnmN0XJJ1HdFelRI8LKzrTVR8UXkB63\nFR/d2/WlY7clsNpfIrDyLI2r7w6/Lx+6Pv8CkhSEz6tWpEeNCCs701YfFV9Aetxm7H+r6jP4\n9cCmJ60keggsvZbGNfmyef4FJCkIn1etSI8aEVZ2pq0+Kr6A9LjtOOzGl45vjb3/WKQkeggs\nvfgMlo0V6VEjwsrOtNVHxReQHrcbTU9aSfQQWHolfA/W53F4qcXvwZIPn1etSI8aEVZ2pq0+\nKr6A9LjdaHrSSqKHwNJrcVzbm+8M35we1zXPW0H4vGpFetSIsLIzbfVR8QWkx+1G05NWEj0E\nll4Jz4O1H54Hq9+9N/c8WArC51Ur0qNGhJWdaauPii8gPW43mp60kughsPQy/UzuCsLnVSvS\no0aElZ1pq4+KLyA9bjeanrSS6CGw9CKwbKxIjxoRVnamrT4qvoD0uN1oetJKoofA0ovAsrEi\nPWpEWNmZtvqo+ALS43aj6UkriR4CSy8Cy8aK9KgRYWVn2uqj4gtIj9uNpietJHoILL0ILBsr\n0qNGhJWdaauPii8gPW43mp60kughsPQisGysSI8aEVZ2pq0+Kr6A9LjdaHrSSqKHwNKLwLKx\nIj1qRFjZmbb6qPgC0uN2o+lJK4keAksvAsvGivSoEWFlZ9rqo+ILSI/bjaYnrSR6CCy9CCwb\nK9KjRoSVnWmrj4ovID1uN5qetJLoIbD0IrBsrEiPGhFWdqatPiq+gPS43Wh60kqih8DSi8Cy\nsSI9akRY2Zm2+qj4AtLjdqPpSSuJHgJLLwLLxor0qBFhZWfa6qPiC0iP242mJ60keggsvQgs\nGyvSo0aElZ1pq4+KLyA9bjeanrSS6CGw9CKwbKxIjxoRVnamrT4qvoD0uN1oetJKoofA0ovA\nsrEiPWrnPjZdt/sMrVjZmbb6qPgC0uN2o+lJK4keAksvAsvGivSoveqGyW+7wT50gxffoWdp\nq4+KLyA9bjeanrSS6CGw9CKwbKxIj9qrIbD23f70/X3cdx+BG7z8Lj1HW31UfAHpcbvR9KSV\nRA+BpReBZWNFetReDYHVd6fzy6duE7jBi+/Qs7TVR8UXkB63G01PWkn0EFh6EVg2VqRH7dUQ\nWF1384fpDV56d56nrT4qvoD0uN1oetJKoofA0ovAsrEiPWqvhqZ6GwOrD9zgpXfnedrqo+IL\nhElvgkFNz1RJ9BBYehFYNlakR+1V1+3ePz67fz8vnvah73K3sjNt9dGTLiC9CQY1PVMl0UNg\n6UVg2ViRHrVXN5/b6Lr+FLjBy+/ScyjIG/kLSG+CQU3PVEn0EFh6EVg2VqRH7dbh8PGx2w3f\n6r4P9JXq85FDQd7IX0B6EwxqeqZKoofA0ovAsrEiPWpEWNkZBXkjfwHpTTCo6ZkqiR4CSy8C\ny8aK9KgRYWVnFOSN/AWkN8GgpmeqJHoILL0ILBsr0qNGhJWdUZA38heQ3gSDmp6pkughsPQi\nsGysSI8a3zwP1pPzRv4C0ptgUNMzVRI9BJZeBJaNFelR43sSWMaeO0lB3shfQHoTDGp6pkqi\n57WBNUN6PxQisGysSI8aEVZ2RkHeyF9AehMManqmSqLntYE1syS9HwoRWDZW+KhCKSvzV5A3\n8heQ3gSDmp6pkughsPQisKyvSG+Cc1bmryBv5C8gvQkGNT1TJdFDYOlFYFlfkd4E677ed8Nn\nCnf7r9CylfkryBv5C0hvgkFNz1RJ9BBYehFY1lekN8G20+bmq7HbwA2szF9B3shfQHoTDGp6\npkqih8DSi8CyviK9Cbbtu/7fYXjp+Nnzy56fmjfyF5DeBIOanqmS6CGw9CKwrK9Ib4JtfXf4\nffnQ9Y83sDJ/BXkjfwHpTTCo6ZkqiR4CSy8Cy/qK9CbYNnnqq8ANXnZXnktB3shfQHoTDGp6\npkqih8DSi8CyviK9CbbxGazX5Y38BaQ3waCmZ6okeggsvQgs6yvSm2Dbvus/j8NLfA/Ws/NG\n/gLSm2BQ0zNVEj0Ell4ElvUV6U0wbnvzU4Sb0+O6lfkryBv5C0hvgkFNz1RJ9BBYehFY1lek\nN8G6r/3wPFj97p3nwXpu3shfQHoTDGp6pkqih8DSi8CyviK9Cc5Zmb+CvJG/gPQmGNT0TJVE\nD4GlF4FlfUV6E5yzMn8FeSN/AelNMKjpmSqJHgJLLwLL+or0JjhnZf4K8kb+AtKbYFDTM1US\nPQSWXgSW9RXpTXCuvfl3YfJ5I38B6a0xqOmZKokeAksvAsv6ivQmONfe/NXmjfwFpLfGoKZn\nqiR6CCy9CCzrK9Kb4Fx781ebN/IXkN4ag5qeqZLoIbD0IrCsr0hvgnPtzV9t3shfQHprDGp6\npkqih8DSi8CyviK9Cc61N3+1eSN/AemtMajpmSqJHgJLLwLL+or0JjjX3vzV5o38BaS3xqCm\nZ6okeggsvQgs6yvSm+Bce/NXmzfyF5DeGoOanqmS6CGw9CKwrK9Ib4Jz7c1fbd7IX0B6awxq\neqZKoofA0ovAsr4ivQnOtTd/tXkjfwHprTGo6ZkqiR4CSy8Cy/qK9CY419781eaN/AWkt8ag\npmeqJHoILL0ILOsr0pvgXHvzV5s38heQ3hqDmp6pkughsPQisKyvSG+Cc+3NX23eyF9AemsM\nanqmSqKHwNKLwLK+Ir0JzrU3f7V5I38B6a0xqOmZKokeAksvAsv6ivQmONfe/NXmjfwFpLfG\noKZnqiR6CCy9CCzrK9Kb4Fx781ebN/IXkN4ag5qeqZLoIbD0IrCsr0hvgnPtzV9t3shfQHpr\nDGp6pkqih8DSi8CyviK9Cc61N3+1eSN/AemtMajpmSqJHgJLLwLL+or0JjjX3vzV5o38BaS3\nxqCmZ6okeggsvQgs6yvSm+Bce/NXmzfyF5DeGoOanqmS6CGw9CKwrK9Ib4Jz7c1fbd7IX0B6\nawxqeqZKoofA0ovAsr4ivQnOtTd/tXkjfwHprTGo6ZkqiR4CSy8Cy/qK9CY419781eaN/AWk\nt8agpmeqJHoILL0ILOsr0pvgXHvzV5s38heQ3hqDmp6pkughsPQisKyvSG+Cc+3NX23eyF9A\nemsManqmSqKHwNKLwLK+Ir0JzrU3f7V5I38B6a0xqOmZKokeAksvAsv6ivQmONfe/NXmjfwF\npLfGoKZnqiR6CCy9CCzrK9Kb4Fx781ebN/IXkN4ag5qeqZLoIbD0IrCsr0hvgnPtzV9t3shf\nQHprDGp6pkqih8DSi8CyviK9Cc61N3+1eSN/AemtMajpmSqJHgJLLwLL+or0JjjX3vzV5o38\nBaS3xiD9M+1mvLBslCwRWHkILOsr0pvgXHvzV5s38heQ3hqD9M9USdkoWSKw8hBY1lekN8G5\n9uavNm/kLyC9NQbpn6mSslGyRGDlMRBYM5/Blc8b+RXp7XGuvfmrzRv5C0hvjUH6Z6qkbJQs\nEVh5LASWfMRoXpHeHufam7/avJG/gPTWGKR/pkrKRskSgZWHwLK+Ir09zrU3f7V5I38B6a0x\nSP9MlZSNkiUCKw+BZX1Fenuca2/+avNG/gLSW2OQ/pkqKRslSwRWHgLL+kqc9Ma50N6U1eaN\n/AU4RtXpH5+SslGyRGDlIbD8rkhvnAvtTVlt3ii9gPR+tU3/+JSUjZIlAisPgeV3RXrjXGhv\nym3ljfwFpPerbfrHp6RslCwRWHkILL8r0hvnQntTbitv5C8gvV9t0z8+JWWjZInAykNg+V2R\n3jgX2ptyW3kjfwHp/Wqb/vEpKRslSwRWHgLL74r0xrnQ3pTbyhv5C0jvV9v0j09J2ShZIrDy\nEFh+V6Q3zoX2ptxW3shfQHq/2qZ/fErKRskSgZWHwPK7Ir1xLrQ35bbyRv4C0vvVNv3jU1I2\nSpYIrDwElt8V6Y1zob0pt5U38heQ3q+26R+fkrJRskRg5SGw/K5Ib5wL7U25rbyRv4D0frVN\n//iUlI2SJQIrD4Hld0V641xob8pt5Y38BaT3q236x6ekbJQsEVh5CCy/K9Ib50J7U24rb+Qv\nIL1fbdM/PiVlo2SJwMpDYPldkd44F9qbclt5I38B6f1qm/7xKSkbJUsEVh4Cy++K9Ma50N6U\n28ob+QtI71fb9I9PSdkoWSKw8hBYflekN86F9qbcVt7IX0B6v9qmf3xKykbJ0ux/NkN6F6UQ\nWH5XpDfOBc1TjrwtfGWdGLiA9C62Tf/4lJSNkqW1V5TeRSkElt8V6Y1zQfOUFdSJgQtI72Lb\n9I9PSdkoWSKw8hBYflekN84FzVNWUCcGLiC9i23TPz4lZaNkicDKQ2D5XZHeOBc0T1lBnRi4\ngPQutk3/+JSUjZIlAisPgeV3RXrjXNA8ZQV1YuAC0rvYNv3jU1I2SpYIrDwElt8V6Y1zQfOU\nFdSJgQtI72Lb9I9PSdkoWSKw8hBYflekN84FzVNWUCcGLiC9i23TPz4lZaNkicDKQ2D5XZHe\nOBc0T1lBnRi4gPQutk3/+JSUjZIlAisPgeV3RXrjXNA8ZQV1YuAC0rvYNv3jU1I2SpYIrDwE\nlt8V6Y1zQfOUFdSJgQtI72Lb9I9PSdkoWSKw8hBYflekN84FzVNWUCcGLiC9i23TPz4lZaNk\nicDKQ2D5XZHeOBc0T1lBnRi4gPQutk3/+JSUjZIlAisPgeV3RXrjXNA8ZQV1YuAC0rvYNv3j\nU1I2SpYIrDwElt8V6Y1zQfOUFdSJgQtI72Lb9I9PSdkoWSKw8hBYflekN84FzVNWUCcGLiC9\ni23TPz4lZaNkicDKQ2D5XZHeOBc0T1lBnRi4gPQutk3/+JSUjZIlAisPgeV3RXrjXNA8ZQV1\nYuAC0rvYNv3jU1I2SpYIrDwElt8V6Y1zQfOUFdSJgQtI72Lb9I9PSdkoWSKw8hBYflekN84F\nzVNWUCcGLiC9i23TPz4lZaNkicDKQ2D5XYmT3lJDNM9SQZ0YuID0LrZN//iUlI2SJQIrD4HF\nyuOK9JYaonmWCurEwAX4GKWE/kEpKRslSwRWHgKLlccV6S01RPMsFdSJ2QtI720r9A9KSdko\nWSKw8hBYrDyuSG+pIZpnqbZODFxAem9boX9QSspGyRKBlYfAYuVxRXpLDdE8S7V1YuAC0nvb\nCv2DUlI2SpYIrDwEFiuPK9JbaojmWaqtEwMXkN7bVigZ1MxP/CgpGyVLBFYeAouVxxXpLTVE\n8yzV1omBC0jvbSuUDEpJvuhfIrDyEFisPK5Ib6khmmeptk4MXEB6b1uhZFBK8kX/EoGVh8Bi\n5XFFeksN0TxLtXVi4ALSe9sKJYNSki/6lwisPAQWK48r0ltqiOZZqq0TAxeQ3ttWKBmUknzR\nv0Rg5SGwWHlckd5SQzTPUm2dGLiA9N62QsmglOSL/iUCKw+BxcrjivSWGqJ5lmrrxMAFpPe2\nFUoGpSRf9C8RWHkILFYeV6S31BDNs1RbJwYuIL23rVAyKCX5on+JwMpDYLHyuCK9pYZonqXa\nOjFwAem9bYWSQSnJF/1LBFYeAouVxxXpLTVE8yzV1omBC0jvbSuUDEpJvuhfIrDyEFisPK5I\nb6khmmeptk4MXEB6b1uhZFBK8kX/EoGVp5nAmvlVBvJBYm3lRXvqgZJZhk/Ok+KCCxBYqZQM\nSkm+6F9ae8UZ0nv/VO0Elnx2+Fl50Z56oGSWbdWJgQtIb3grlAxKSb7oX3rCK5Pe+6cisFh5\nXHnRnnqgZJZt1YmBC0hveCuUDEpJvuhfIrDyEFisPK68aE89UDLLturEwAUcfjVkFSUjUZIv\n+pcIrDwEFiuPKy/aUw+UzLKtOjF7AemHgT5KRqIkX/QvEVh5CCxWHldetKceKJmlgrjgAgTW\nIyUjUZIv+pcIrDwEFiuPK05/4uMZlExMQVxwAQLrkZKRKMkX/UsEVh4Ci5WclRftth1KJqYg\nLrgAgfVIyUiU5Iv+JQIrD4HFSs7Ki3bbDiUTUxAXXIDAeqRkJEryRf8SgZWHwGIlZ+VFu22H\nkokpiAsuQGA9UjISJfmif4nAykNgsZKz8qLdtkPJxBTEBRcgsB4pGYmSfNG/RGDlWf7Xfb3v\nhm9v3u2/1l2gDgVxwQqB9UjJ+VigIC64AIH1SMlIlOSL/iUCK8/Sv+60ufkRsu2KC9SiIC5Y\nIbCm1JyPBQriggsQWI9eOZK5X4j3yqJoeYnAyrP0r9t3/b/D8NLxs+/2+ReoRUFcsEJgTak5\nHwsUxAUXILAevTSwXpkNRpcIrDxL/7q+O/y+fOj6/AvUoiAuWCGwptScj79XGCYfF1yAwHpE\nYLW1RGDlWfrX3T21ZOh5JgksVys8Bek9Nefj7xU+qQ24QIULcHKmCKy2lgisPHwGi5U6Ky96\nHCij5nz8vcIntQEXeNYFXv0IUYXAamvpCa/M9EftCd+D9XkcXuJ7sFghsKbUnI+/V/jKNuAC\nBFYZAqutpdfejxc+OJ5k8Z+wvenJzWnFBSpRkBCsEFgPtJyPv1f4yjbgAgRWGQKrrSUCK0/C\n82Dth+f56XfvPA8WK/GVFz0O1FFyPv5e4SvbgAsQWGUIrLaWCKw8PJM7K3VWXvQ4aM0T55Lx\n84Jq44ILWA+sVz8R79y39CjJhpaXCKw8BBYrdVYsf6digWcGlnwbcIEKF7B8al7/RLxKQsTq\nEoGVR1lgzbyblk8IVkivbAQWF1h1gec9bl7p9U/EqyRErC699n60/74j634+/3l+FOQAK3xZ\ncaXnnY/w25gnvWvnAhou0PS7lV9PehqTufe8StrA6JKW+9HKSVgfWItHfu4QAC+09nRk4nyg\nSS87EoGH/8x/CqhQcgAK/lsAAGIWP4MFWEZgAQCeYfGJeAHLCCwAwFMsPREvYFnCE43OP48J\n4BrnA4hbeCJewLKlwFp8HhPAMc4HACAo4Zc9zz+PCeAY5wMAELQUWPwUCBDH+QAABC0FVvx5\nTABwPgAAQXwGC1iP8wEACEr4HiyexwSI4HwAAIIWv6jB85gAcZwPAEBIwvNg8TwmQBTnAwAQ\nwLflAgAAVEZgAQAAVEZgAQAAVEZgAQAAVEZgAQAAVEZgAQAAVEZgAQAAVEZgAQAAVEZgAQAA\nVEZgAQAAVEZgAQAAVEZgAQAAVFYcWB2gQ43z8BzSkwGupI+CUtLbAs1KHljFj8zSCxTjHnAP\ndNyDKMV3rYjVfxf/MG+UzIW7cUfJ/SCwuAfSd4B7MEfxXSti9d/FP8wbJXPhbtxRcj8ILO6B\n9B3gHsxRfNeKWP138Q/zRslcuBt3lNwPAot7IH0HuAdzFN+1Ilb/XfzDvFEyF+7GHSX3g8Di\nHkjfAe7BHMV3rYjVfxf/MG+UzIW7cUfJ/SCwuAfSd4B7MEfxXSti9d/FP8wbJXPhbtxRcj8I\nLO6B9B3gHsxRfNeKWP138Q/zRslcuBt3lNwPAot7IH0HuAdzFN+1Ilb/XfzDvFEyF+7GHSX3\nQzSwAAAAcI/AAgAAqIzAAgAAqIzAAgAAqIzAAgAAqKwssPZ91+9Ple7KSh/CjfixEZ7B6a3r\n3g6Cd2DwJboN5b/1/BnuH5o672O+hwe8hrcCNUz/YVY27PENhJUdKxR40y3x3uThbsi8S5m+\nVqn3K6F/vcB7l0pvDYru+HZ4lZuSSxQ7CL8F3A8z6AXfWvXDPRAurFMvuQ0Hle8L7x+aOu9j\nvocHvIa3AjVM/2FWNuzxDYSVHSsUeNMt8d7k4W7IvEt5eK1C71dC/3qB9y613hqU3PGvrj98\nH/ruq+AapX5evehbwEP3djp/3PMmdg/259e973Zid2CwE92Gg/Q/P2Ty0FR5H/M9POA1vBWo\n4eEfZmTDHt9AWNmxQoE33RLvTQKPO4l3KQ+vVej9SvBf//r3LtXeGpTc8X33+fO//7r3gmsU\n+ui2soG1u7x2wTvRdyfZO3D2T/Yj/Q/Jx2DE9KGp8T6u8PCAV/BWoIqHf5iRDXt8A2Flxwo9\nvukWeW/ycDdk3qU8vFah9yuhf73Ae5dqbw1K7viuO34Lf6DX7aXT4kL8TnS95Gs/CnfuR/ch\n+NrDpg9Njfdxvdv3B+JvBWq6fZNqasP+3kAY27FCN4dU8r3JwyuWuSfT1yr1fuX2fgi+dyl/\na1D0LPDin735Pihomx+nbit7B/ay7wy23VF0G3bd51vX7wXvwaPpQ1PjfVzt5gGv4K1ARTf/\nMFMbdvsGwtaOFbp90y343uThPYjMu5Tpa5V6v3J3P+Teu1R4a9B4YMm/+sHH8El3Mf+6TvT9\nwHv3T3YbdpdvQBSu3AeTwFJ5H9e5ecDreCtQy80/zNCG3b+BsLVjhSZvuqWG8vAeROZdyv1r\nlXu/cns/BN+7VHhrQGBVcOxlP9v+seslv6Fi+GKD6DZ0P2fw+yT8abxHdzNReh9XuX3A63gr\nUMn9P8zMht2/gTC1Y4Wmb7qFhvLwHkTmXcrktYq9X7m9H4LvXWq8NSCwyp16+Y9y3wTfD2zO\nP8wqvw3fJ20/eR6Yibr7uMbdA17HW4E6AifZxIZ9372BsLRjhR42XGYoD3dD5l1K4LWKvF+5\nux9y712qvDUoueO9ioMq/3Ziq+BN8Enuu9zfhs+jym+DjvtwK3R/tN3HNe4e8DreCtQROskm\n/mF3byAs7Vihhw2XGcrD3ZB5lxJ4rSLvV27vh+B7lypvDcp/ivAo/NMo0m8njpvtUfYeDOTG\n0P2Sugd/90T6HtyzGViTB7yOtwI1hE9y+xt2Mf25Tws7Viiw4RK7/XA3ZN6lE5w5NAAAIABJ\nREFUaHn4398PsfculcZRcrffh7j8lP0Ga+k3gJ/S3wV7eb6So9xXMhQE1jgDZe8y7iai9D5m\nmz7gdbwVqGD6D7OyYQ9vIMzsWKHQm26BN2IPd0PmXUrs4f/q9yuT+yH13qXWW4OSu63jGYFl\nA+so3VeXZ9w97aS/F1d0G/bndxanvezPcj66m4nS+5jr4QGv461AuYd/mJENe3wDYWXHCgXf\ndAt8wmZ6N2TepQQe/iLvV8L/+td//qrWW4OiO77R8HPMsoH1Jv7Zm+vvjJLuPNFtOF1moO1D\n8nEmw/8rvY+5bh/wl3+fircC5R7+YUY27O4NhKkdK/T4SP6WeDP2cDdk3qU8TkPm/UpwV16/\nLdXeGhTd8dPwW9lLrlCBbGDJf3nsJ677biP+s+Sy23BSMYOpu8BSeh9zdQ9vAFW8FSgX/oe1\nv2Hft28gTO1YoccN/5Z4M/ZwN2TepQSmIfLwD+7K67el2lsDI9/BCQAAoAeBBQAAUBmBBQAA\nUBmBBQAAUBmBBQAAUBmBBQAAUBmBBQAAUBmBBQAAUBmBBQAAUBmBBQAAUBmBBQAAUBmBBQAA\nUBmBBQAAUBmBtcq/Xdd1m/3h+sev9P8y7feC393q9zd7b39fYe4r+Mp43UApzgcQx/nwgpGt\n8NWPD9nd8Oe3jCmWHJAfb6tewfUOckDwCpwPII7z4Qcjy3fsuuFDgdNn323Pf5HzwFt1QK4v\nHN6vrzAXJwOvw/kA4jgfjjC5fG/dv/HFTff5/boD8nM2++49/XVlvlKgBs4HEMf5cITJ5bt5\nuH0On+R93QE5f/RzSn9lea8UqIHzAcRxPhxhcvluH6M/D73rV7d//vD51p+/dfE4rnxsu+7t\neL3l+Q/bz/GxOr3pvuv2j7f6fR1/9tcPf4Ybfvy8cOr638X+5549voLfOzhe6Pe/DdxNoBDn\nA4jjfDhCYOXbdtvbjwJ+H3+78TsJD5e/3g9/6I/X/2iwvzxIpzd96y4H5P5Wv6/g5g9fl2+M\nvN7w/BX1v884f56v8fgKJgfkuLn+t8fA3QRKcT6AOM6HIwRWvq/zo+vj5ideLw+8j25z/mnW\nr+34nYvd++n7sLn84MbPX/4sfm2GB+rjTfvP79PDre4vf3XqNr83PGzPp+Uw/M3Z5nIcQq/g\n5kLXVxK8m0AxzgcQx/lwhMBa4fPyY7ab/eflz5cH3uby4cTPQ7i7/OXwOduv4TOwn+ODuB8W\nH256+c7Dya1G918BP//p94bb7uv8P5/X//z3C/oPr+DvQr//7fgNljd3E6iA8wHEcT78ILDW\nOP27fop1c/006d3q+KA8/v3p7foY/nl4Pjzaz/97eThHbvX4n7x116em+zo/vD+vP3u7C/xI\nyuMBuXklu+ndBGrgfABxnA83GMtah4/ztwH258/M/j24Tl8fu/7uQTl+RHD9qvvp97aBmwZu\ndbv896fN798MH05cPt64fqp35hUM/9f/vZJ+ejeBWjgfQBznwwXGUuJrO3yC9PrgOu3HZ+j9\n/p488v4efpeXZm46eWn6h+P5GHQ3vs9fMT9/LHH9+ZCZVxC6KxwQPA3nA4jjfJjHWLLdPpRu\nK/50/oBk93H4Xj4gczd9eB33f/g8fzfh5ID8fFRx/P1x25lXwAHB83E+gDjOhyeMJdu2u/nd\nnDcPsrdud/r7u8ineC9/jNx0cqvv0B+GL4H3k23b/3wgtL9+p+PMKxj+j0/x4qk4H0Ac58MT\nxpLt/forOs8uX7e+f5h/BQ7I5NsPIzdN+CbFw/Co3nX3v3/9/FgfH/gzr2B6V26fRZgDgjo4\nH0Ac58MTxpLt1F9+MvVs252f0Pb+Yb4NHJDD+FOsm7vH7+Smk1uNbv5w7IdXOP7cx/VBfj4x\n+/FOzbyC4f8efsz24ZUABTgfQBznwxPGku/n44PN5+n829A34w9enD8g2A1P0Pt1/gHc2x8N\nufz/7uc/uS7Gbzq51ej3D+ffhn45EJcnezt9jD+ge+jGl77Dr+Dr70LTJ4qbvBKgDOcDiON8\nOMJYVvgcf8Li+usC3oZvFjxe/+7n2JwfjpNH3vWJT96HP0ZuOrnV6PZbEq/Plzv+uoLx07U/\nH07sfm/9+Aoud3B8Pddfg3D/HCwcENTC+QDiOB9+MJZV/p2fIaR/Gx+ePw/A/udRef6//fH6\n656mj7zP82/I/Lr+MXzT6a2+xytc7d7/fuHT+Tds9m+/v2/h8/eohF7B9Q7+3pW3u1/Weff/\nQDnOBxDH+fCCsQAAAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEA\nAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEA\nAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEA\nAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEA\nAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEAAFRGYAEAAFRGYFV06n78/ulz9/On3Wf8\n5t3dzdMt/HfZl/13vqPb/eHvbxbvOpBs6VhwUOBQ/rHgoLSHwKro7faBuO0uttGb6zgOX/31\njnb78a+W7zqQbOFYcFDgUfax4KA0iMCq59/tA3F8SM08qFQch0P353oeEu46kGrhWHBQ4FH2\nseCgtIjAqua9u3kgft48ymKfGFVxHDY3d7T7Ov9Nyl0HEi0cCw4KPMo+FhyUJhFYlRzHSr/8\ncXN5MA0PrU3kP9FwHIY72B++T8Pdfzv/VcpdB5IsHgsOCvxZcSw4KE0isKo47X8Tffjz8fzS\n+fOjw98fw/+RhuMwfCPAx88LX+N/lnTXgQTLx4KDAnfWHAsOSpsIrFmXh8jh7afBN++n37+6\n9feX/d+fPy7Nfu35j/jFr/M/vZ9/yuL3By8uC1/Dqx3+6rQfXjzd/ncfPx8ibG8uPf55/rKT\nu775fcyPf5N01+FavWPBQYEZzzwWHJQ2EVizhofIbnz4fI5/FTwy2+Pfn4eMPz8Gh+/4e4tf\n/HLzmy9Sv48rv59F/on/98d7cLz+qEZ//Yjg78/zl53c9Y+33ba7uzdJdx2u1TsWHBSY8cxj\nwUFpE4E1azgKf4+f03f0yPR3pb+7O0y7+MWHG33dXu/zutL//dXNtw0ex//ud/lyHo5/f56/\n7MNdvzqOdzTprsO1eseCgwIznnksOChtIrBmXR42b6fvw/Ao239HHlObf7+3/o69FL74+YXz\nZ2J/Cv+4Gx+Av6/2dD2vu+P1+yL/7sF2/Kvt9RI3fzV72fBxGL4+/i/1rsO1eseCgwIznnks\nOChtcvbPzdWNj6TLJ0cXnsVj7sjM3fz4vhm+pD08t29/92ovHzNsf1/cjKs3P1rydbM2/pRs\n8LIzDr+3cX0ckKTeseCgwIxnHgsOSpuc/XNzddeH2/UxtTCtuSMze/Pp3/y92suLn4+rwwdB\nl2er2998tDB5ArvYK5q6fD44+oEVcKveseCgwIxnHgsOSpuc/XNzDY+I49+LCbeOvjRz88Hx\n3/buAX/zAx739+Dmr4YPE7bXL3Pf/FX4snF/z1ni+zggSb1jwUGBGc88FhyUNjn75+a6eUTc\nPRhvBG+dexyOH7vbCwZe7fQe3F8j8Fexy4bu+t9X3p0fBySpdyw4KDDjmceCg9ImZ//cXPWO\nzNzFT7vJBesch/BlA3f95qMN58cBSeodCw4KzHjmseCgtMnZPzfX2iOT90O1l5+D3bwf717H\n/D24v0bwOIQv+3jXhy+3//7ic9c/VIsk9Y4FBwVmPPNYcFDaRGDNKjoyqU8LNzzp2/b4HXzA\nJxyHPnwcIpd9uOvD7d5/71XSXYdr9Y4FBwVmPPNYcFDaRGDNCj8ul2+d9YsNhh+DPd3+TcJx\nuPyqguEhu7t5DN98S+LjZYOGn8f99/dn17/YAEnqHQsOCsx45rHgoLSJwJq19sgMj7HUX835\n+5/lfEL38gHCv+uL738P3Y/4ZUNO50/73n5UkXTX4Vq9Y8FBgRnPPBYclDYRWLPWHpnLV6s/\nL82+ifz3d4/b8+PuPeM49MNHEuPHFDfP/NbHLxvy94vdxxs93nXgTsVjwUGBFU89FhyUJhFY\ns1YfmY+bx9jndHFy8+GXYW5P438TfbV3q+ffWXD6/V0Hl0f1/S82eLxswOnuNHThuw7cqXgs\nOCiw4qnHgoPSJAJr1uoj8/33Sz8fng1kevO7X6E5fOF7+Tj8/eLO7fT19dHLBvx7PA6Pdx24\nU/FYcFBgxVOPBQelSQTWrPVH5ns3eUjFj8PvJ1V3Q+r/SzkOx83k8r+vb3OMXjbg7olNxlc0\nvevAnYrHgoMCK556LDgoTSKwZhUcme/P82dUd5/hxfu/+fq5af92uHx6dZtyHH4+Ujg/aN9u\nPuN6eX3/xvXAZWN3eXocpncduFPxWDz+DQcFbXrqsXj8Gw5KAwisF3L3HX7AGhwUIAEHRTsC\n63X+/T25LYAYDgqQgIOiHoH1KqeP2LcFAvjFQQEScFAaQGC9ys7fj6gC+TgoQAIOSgMIrFc5\nbPloA1jEQQEScFAaQGABAABURmABAABURmABAABURmABAABURmABAABURmABAABURmABAABU\nRmABAABURmABAABURmABAABURmABAABURmABAABURmABAABURmABAABURmABAABURmABAABU\nRmABAABURmABAABURmABAABURmABAABURmABAABURmABAABURmABAABURmABAABURmABAABU\nRmABAABURmABAABURmABAABURmABAABURmABAABURmABAABURmABAABURmABAABURmABAABU\nRmABAABURmABAABURmABAABURmABAABURmABAABURmA9R5dC+k4CreAMAUt4p6MN836O7j/L\nmD2QqPtfEGcI+NX9dwkH5rWY93MQWEBFBBawhMDShnk/B4EFVERgAUsILG2Y93MQWEBFBBaw\nhMDShnk/B4EFVERgAUsILG2Y93MQWEBFBBawhMDShnk/B4EFVERgAUsILG2Y93MQWEBFBBaw\nhMDShnk/B4EFVERgAUsILG2Y93MQWE6c3rpu+3l5madJfh4CC1hCYGnDvJ+DwPLh1A+/f2I3\n/IHAeh4CC1hCYGnDvJ+DwPJh3338VNZHvz3/gcB6HgILWEJgacO8n4PA8qG/bOKx3xwJrGci\nsIAlBJY2zPs5CCwfxqY6bbcE1jMRWMASAksb5v0cBJYPm+40vrQlsJ6IwAKWEFjaMO/nILB8\n+Ojeri8duy2B9TwEFrCEwNKGeT8HgeXE/reqPjsC63kILGAJgaUN834OAsuLw2586fjGjj4N\ngQUsIbC0Yd7PQWABFRFYwBICSxvm/RwEFlARgQUsIbC0Yd7PQWABFRFYwBICSxvm/RwElkN8\nk/vzEFjAEgJLG+b9HASWQ3eB1V2J3RtbCCxgCYGlDfN+DgILAza5DgILWEJgacO8n4PAwoBN\nroPAApYQWNow7+cgsDBgk+sgsIAlBJY2zPs5CCwM2OQ6CCxgCYGlDfN+DgILAza5DgILWEJg\nacO8n4PAwoBNroPAApYQWNow7+cgsHzo7gVu8Pr7ZBKBBSwhsLRh3s9BYPnwQWC9BoEFLCGw\ntGHez0FgOXHot7PrbHIdBBawhMDShnk/B4HlxaHbzy2zyXUQWMASAksb5v0cBJYbH91hZpVN\nriMWWDHS9xd4PQJLG+b9HAQWBmxyHbHACv81n9mCRwSWNsz7OQgsDNjkOggsYAmBpQ3zfg4C\nCwM2uQ4CC1hCYGnDvJ+DwMKATa6DwAKWEFjaMO/nILAwYJMzxb5rncACFhBY2jDv5yCwMGCT\nM+WVFIEF/CKwtGHez0FgYcAmZyKwgJUILG2Y93MQWBiwyZkILGAlAksb5v0cBBYGbHImAgtY\nicDShnk/B4GFAZucicACViKwtGHez0FgYcAmZyKwgJUILG2Y93MQWBiwyZkILGAlAksb5v0c\nBBYGbHImAgtYicDShnk/B4GFAZucicACViKwtGHez0FgYcAmZyKwgJUILG2Y93MQWBiwyZkI\nLGAlAksb5v0cBBYGbHImAgtYicDShnk/B4GFAZucicACViKwtGHez0FgYcAmZyKwgJUILG2Y\n93MQWBiwyZkILCCoW0ZgKcO8n4PAwoBNzkRgAUEJ+URgKcO8n4PAwoBNzkRgAUEEVnuY93MQ\nWBiwyZkILCCIwGoP834OAgsDNjkTgQUEEVjtYd7PQWBhwCZnIrCAIAKrPcz7OQgsDNjkTAQW\nEERgtYd5PweBhQGbnInAAoIIrPYw7+cgsDBgkzMRWEAQgdUe5v0cBBYGbHImAgsIIrDaw7yf\ng8DCgE3ORGABQQRWe5j3cyQFVgrpfwjKsIGZCCwgiMBqD/POlxRGKYHFZ7nsYwMzEVhAEIHV\nHuadr1o8EVj2sYGZCCwgiMBqD/POR2AhGRuYicACggis9jDvfAQWkrGBmQgsIIjAag/zzkdg\nIRkbmInAAoIIrPYw73wEFpKxgZkILCCoSmDxk+svxTDzEVhIxgZmIrCAoCqBtXgLPslVE8PM\nR2AhGRuYicACggis9jDMfAQWkrGBmQgsIIjAag/DzEdgIRkbmInAAoIIrPYwzHwEFpKxgZkI\nLCCIwGoPw8xHYCEZG5iJwAKCCKz2MMx8BBaSsYGZCCwgiMBqD8PMR2AhGRuYicACggis9jDM\nfAQWkrGBmQgsIIjAag/DzEdgIRkbmInAAoIIrPYwzHwEFpKxgZkILCCIwGoPw8xHYCEZG5iJ\nwAKCCKz2MMx8BBaSsYGZCCwgiMBqD8PMR2AhGRuYicACggis9jDMfAQWkrGBmQgsIIjAag/D\nzEdgIRkbmInAAoIIrPYwzHwEFpKxgZkILCCIwGoPw8xHYCEZG5iJwAKCCKz2MMx8BBaSsYGZ\nCCwgiMBqD8PMR2AhGRuYicACggis9jDMfAQWkrGBmQgsIIjAag/DzEdgIRkbmInAAoIIrPYw\nzHwEFpKxgZkILCCIwGoPw8xHYCEZG5iJwAKCCKz2MMx8BBaSsYGZCCwgiMBqD8PMR2AhGRuY\nicACggis9jDMfAQWkrGBmQgsIIjAag/DzEdgIRkbmInAAoIIrPYwzHwEFpKxgZkqBVaE9L8O\nWI3Aag/DzEdgIRkbmKlSYEX+WvpfB6xGYLWHYeYjsJCMDcxEYAFBBFZ7GGY+AgvJ2MBMBBYQ\nRGC1h2HmI7CQjA3MRGABQQRWexhmPgILydjATAQWEERgtYdh5iOwkIwNzERgAUEEVnsYZj4C\nC3++3nfDEwDs9l+hZTYwE4EFBBFY7WGY+QgsjE6bmydZ2gZuwAZmIrCAIAKrPQwzH4GF0b7r\n/x2Gl46ffbd/vAEbmInAAoIIrPYwzHwEFkZ9d/h9+dD1jzdgAzMRWEAQgdUehpmPwMLo7pev\nhH4TCxuYicACggis9jDMfAQWRnwGqzYCCwgisNrDMPMRWBjtu/7zOLzE92DVQWABQQRWexhm\nPgILv7Y3P0W4OT2us4GZCCwgiMBqD8PMR2Dhz9d+eB6sfvfO82Bl6SIILCCEwGpP6jA/+m7z\n8dR70g4CC8nYwJgqJUVgwQ0Cqz2Lwzzsuv7j+z36RIoOEVhIxgbGEFhADgKrPUvDPAxlte/e\nTt/HXcfnsM4ILCRjA2MILCAHgdWepWG+nX8yan/5+fNTt3nBPdKPwEIQz4OVg8ACchBY7Vka\n5uV9Rre7+YN7BBaCJs86eiF2b7QjsIAcBFZ70gLr3+Vrg6EnUnSIwEIyNjCGwAJyEFjtWf4S\n4dv45D6nt9ATKTpEYCEZGxhDYAE5CKz2LA3z1P9+kaPjE1gXBBaSsYExBBaQg8Bqz/Iw92NW\n9Xz+6oLAQjI2MIbAAnIQWO1hmPkILCRjA2MILCAHgdUehpmPwEIyNjCGwAJyEFjtYZj5CCyM\nJr9HL3CD19+nRhBYQA4Cqz1Zw+RJfQYEFkYfBNZaBJYj/C7bCgis9qwPLL9PpEhg4dehn/8N\nnWxgDIHlAb/Lth4Cqz3Fw3S4GwQW/hzmnx2ODYwhsBzgd9lWRGC1h8DKR2Dhxkd3mFllA2MI\nLAf4XbYVEVjtIbDyEVhIxgbGEFgOxH+Xrd9vMVmNwGrP8jC/3nfDQdjtv9ZdwBwCC8nYwBgC\ny4HF32XLjqQjsNqz+KtyNjc/IxX6JkWHu0FgIRkbGENgObD4u2zZkXQEVnuWhrnv+n+XbzE5\nfvYckAGBhWRsYAyB5cDi77JlR9IRWO1ZGmZ/8x28Bz7FOyCwkIwNjCGwXFj4XbbsSDoCqz1L\nw5x8X2L+BQwisJCMDYwhsMD5yEFgtYfPYOUjsJCMDYwhsMD5yEFgtSfhe7A+j8NLfA/WiMBC\nMjYwhsAC5yMHgdWexWFub36KcHN6XHe4GwQWkrGBMQQWOB85CKz2JDwP1n54Hqx+987zYF0Q\nWEjGBsYQWOB85CCw2sMzuecjsJCMDYwhsMD5yEFgtYfAykdgIRkbGENggfORg8BqD4GVj8BC\nMjYwhsAC5yMHgdUeAisfgYVkbGAMgQXORw4Cqz0EVj4CC8nYwBgCC5yPHARWewisfAQWkrGB\nMQQWOB85CKz2EFj5CCwkYwNjCCxwPnIQWO0hsPIRWEjGBsYQWOB85CCw2kNg5SOwkIwNjCGw\nwPnIQWC1h8DKR2AhGRsYQ2CB85GDwGoPgZWPwEIyNjCGwALnIweB1R4CKx+BhWRsYAyBBc5H\nDgKrPQRWPgILydjAGAILnI8cBFZ7CKx8BBaSsYExBBY4HzkIrPYQWPkILCRjA2MILHA+chBY\n7SGw8hFYSMYGxhBY4HzkILDaQ2DlI7CQjA2MIbDA+chBYLWHwMpHYCEZGxhDYIHzkYPAag+B\nlY/AQjI2MIbAAucjB4HVHgIrH4GFZGxgDIEFzkcOAqs9BFY+AgvJ2MAYAgucjxwEVnsIrHwE\nFpKxgTEEFjgfOQis9hBY+QgsJGMDYwgscD5yEFjtIbDyEVhIxgbGEFjgfOQgsNpDYOUjsJCM\nDYwhsMD5yEFgtYfAykdgIRkbGENggfORg8BqD4GVj8BCMjYwhsAC5yMHgdUeAisfgYVkbGAM\ngQXORw4Cqz0EVj4CC8nYwBgCC5yPHARWewisfAQWkrGBMQQWOB85CKz2EFj5CCwkYwNjCCxw\nPnIQWO0hsPIRWEjGBsYQWOB85CCw2kNg5SOwkIwNjCGwwPnIQWC1h8DKR2AhGRsYQ2CB85GD\nwGoPgZWPwEIyNjCGwALnIweB1R4CKx+BhWRsYAyBBc5HDgKrPQRWPgILydjAGAILnI8cBFZ7\nCKx8BBaSsYExBBY4HzkIrPYQWPkILCRjA2MILHA+chBY7SGw8hFYSMYGxhBY4HzkILDaQ2Dl\nI7CQjA2MIbDA+chBYLWHwMpHYCEZGxhDYIHzkYPAag+BlY/AQjI2MIbAAucjB4HVHgIrH4GF\nZGxgDIEFzkcOAqs9BFY+AgvJ2MAYAgucjxwEVnsIrHwEFpKxgTEEFjgfOQis9hBY+QgsJGMD\nYwgscD5yEFjtIbDyEVhIxgbGEFjgfOQgsNpDYOUjsJCMDYwhsMD5yEFgtYfAykdgIRkbGENg\ngfORg8BqD4GVj8BCMjYwhsAC5yMHgdUeAisfgYVkbGAMgQXORw4Cqz0EVj4CC8nYwBgCC5yP\nHARWewisfAQWkrGBMQQWOB85CKz2EFj5CCwkYwNjCCxwPnIQWO0hsPIRWEjGBsYQWOB85CCw\n2kNg5SOwkIwNjCGwwPnIQWC1h8DKR2AhGRsYQ2CB85GDwGoPgZWPwEIyNjCGwALnIweB1R4C\nKx+BhWRsYAyBBc5HDgKrPQRWPgILydjAGJHAipCehV+MPh2B1R4CKx+BhWRsYIxIYEX+WnoW\nfjH6dARWewisfAQWfh3fuv79+/tj0/X70DobGENggfORg8BqD4GVj8DC6NSfv8L08T58oWkb\nuAEbGENggfPxJ/bl6xsEVnMIrHwEFkb7bv/zP333dvo+DS9PsYExBBY4H39ek08E1msRWPkI\nLIz6YYO67jT8X/94AzYwhsAC5+MPgWURgZWPwMKo6/7+9zv002hsYAyBBc7HHwLLIgIrH4GF\nUX8TWCc+g5WDwALn4w+BZRGBlY/Awmj8Hqz96fryFBsYQ2CB8/GHwLKIwMpHYGHETxEui/1M\nFIEFzscvAssiAisfgYVfPA/WomeWFIHVOEY/IrAsIrDyEVhIxgYSWIhj9CMCyyICKx+BhWRs\nIIGFOEY/IrAsIrDyEVhIxgYSWIhj9CMCyyICKx+BhSCeByuIwEIUox8RWBYRWPkILATdBdb4\ns3Ji90YNAgtRjH5EYFlEYOUjsJCMDSSwEMfoRwSWRQRWPgILydhAAgtxjH5EYFlEYOUjsJCM\nDSSwEMfoRwSWRQRWPgILf77ed8P3Wu32X6FlNpDAQhyjHxFYFhFY+QgsjE6bm9/9wq/KCSKw\nEMXoRwSWRQRWPgILo33X/zsMLx0/e37ZcxCBhShGPyKwLCKw7sV+Me0dAgtXfXf4ffnQ9Y83\nYAMJLMQx+hGBZRGBde+l8ZRyG+mBYNbkqa8CN3jZXVGLwEIUox8RWBYRWPcILOTgM1jLCCxE\nMfoRgWURgXVPXWClkB6aY/uu/zwOL/E9WDEEFqIY/YjAsojAuqcusFJuIz00z7Y3obs5Pa6z\nOQQW4hj9iMCyiMC6py6eUm4jPTTXvvbD82D1u3eeByuMwEIUox8RWBYRWPfUxVPKbaSHhjg2\nh8BCHKMfEVgWEVj31MVTym2kh4Y4NofAQhyjHxFYFhFY99TFU8ptpIeGODaHwEIcox/pCSx+\nrKoeAuueunhKuY300BDH5hBYiGP0Iz2BtXwL6Vm1g8C6py6eUm4jPTRqxe+2AAAgAElEQVTE\nsTkEFuIY/YjAsojAuqcunlJuIz00xLE5BBbiGP2IwLKIwLqnLp5SbiM9NMSxOQQW4hj9iMCy\niMC6py6eUm4jPTTEsTkEFuIY/YjAsojAuqcunlJuIz00xLE5BBbiGP2IwLKIwLqnLp5SbiM9\nNMSxOQQW4hj9iMCyiMC6py6eUm4jPTTEsTkEFuIY/YjAsojAuqcunlJuIz00xLE5BBbiGP2I\nwLKIwLqnLp5SbiM9NMSxOQQW4hj9iMCyiMC6py6eUm4jPTTEsTkEFuIY/YjAsojAuqcunlJu\nIz00xLE5BBbiGP2IwLKIwLqnLp5SbiM9NMSxOQQW4hj9iMCyiMC6py6eUm4jPTTEsTkEFuIY\n/YjAsojAuqcunlJuIz00xLE5BBbiGP2IwLKIwLqnLp5SbiM9NMSxOQQW4hj9iMCyiMC6py6e\nUm4jPTTEsTkEFuIY/YjAsojAuqcunlJuIz00xLE5BBbiGP2IwLKIwLqnLp5SbiM9NMSxOQQW\n4hj9iMCyiMC6py6eUm4jPTTEsTkEFuIY/YjAsojAuqcunlJuIz00xLE5BBbiGP2IwLKIwLqn\nLp5SbiM9NMSxOQQW4hj9iMCyiMC6py6eUm4jPTTEsTkEFuIY/YjAsojAuqcunlJuIz00xLE5\nBBbiGP2IwLKIwLqnLp5SbiM9NMSxOQQW4hj9iMCyiMC6py6eUm4jPTTEsTkEFuIY/YjAsojA\nuqcunlJuIz00xLE5BBbiGP2IwLKIwLqnLp5SbiM9NMSxOQQW4hj9iMCyqPvevB/LLmCKunhK\nuY300EzjfJQisCzjfFRCYFnUfXddt/13KriAKeriKeU20kMzjfNRisCyjPNRCYFl0c+o/m1/\nzsjuc/0FLFEXTym3kR6abZyPQgSWaZyPOggsi4ZRHd/7nzPytuqMGJu1unhKuY300KzjfBQh\nsIzjfNRAYFk0jupr/3NE+v3X6gsYoS6eUm4jPTQHOB/rEVj2cT6KEVgW3Yzqc3c+I7nfsmhs\n1uriKeU20kPzgfOxEoHlAuejDIFl0d+ohi+ln72tvIAJ6uIp5TbSQ3OB87EWgeUB56MQgWXR\nZVSHj+Gjj/3n9/HfJu+EGJu1unhKuY300MzjfJQgsKzjfFRAYFnU/RyJt/PHHdvxc7unLmt8\nxmatLp5SbiM9NNM4H6UILMs4H5UQWBYNz4PVv33ePJFJt8m7gCnq4inlNtJDM43zUYrAsozz\nUQmBZdH5mdzzf/Tj7gKmqIunlNtID800zkcpAssyzkclBJZF/C7Ce+riKeU20kNDHJtDYCGO\n0Y8ILIvOXyK8+VO/4gKmqIunlNtID800zkcpAssyzkclBJZFk8DKn5yxWauLp5TbSA/NNM5H\nKQLLMs5HJQSWRXeB9RU4IKe3rttefwlC6PwYm7W6eEq5jfTQTFs4H4v/ec370iYCyzLORyUE\nlkXdvYenMDn1w9/vrjcOXODpd/Gl1MVTym2kh2bY0vlYvsAT7lRjCCy7OB/VEFgWLZ2Pfffx\nU1kf/fZy48AFnn4XX0pdPKXcRnpohpW+/7B2PtYgsOzifFRDYFnULXzdvL+sHvvNkcCqHUa1\nbiM9NNNWfNnj7j+vdDcaRmBZxvmohMCyaCmwxtXTdktg1Q6jWreRHpppvAMpRWBZxvmohMCy\naGlUm258jt7NlsCqHEa1biM9NMSxOQQW4hj9iMCyaGlUH79fVz92WwKrbhjVuo300BDH5hBY\niGP0IwLLom7ybYoPN9j//t1naNnaAVEXTym3kR6aaQvnY/E/f8JdagyBZRnnoxICy6LFwPo+\n7MaXjm8EVtUwqnUb6aGZxjuQUgSWZZyPSggsi/hdhPfUxVPKbaSHhjg2h8BCHKMfEVgWEVj3\n1MVTym2kh4Y4NofAQhyjHxFYFhFY99TFU8ptpIeGODaHwPLM2a9aK0BgWfQ7quO269+Xbmz/\ngKiLp5TbSA/Ng5TzEcLmEFgeRM6Ht1+1VoDAsuhnVO/ncV0Ownbhxt3dH1Z+W6Nq6uIp5TbS\nQ7Mt/XyEsDkElm2z58Pbr1orQGBZ1H0fhof9e9cdT9vuc8UFTFEXTym3kR6aaZyPUgSWZfPn\nw9uvWitAYFnUXT7G+N50++/vr263+B88XsAUdfGUchvpoZnG+ShFYFk2fz7iv2rN5ldAChBY\nFnWXX4Zz6oYPPngeE3XxlHIb6aGZxvkoRWBZNn8+vP2qtQIElkXXX/b8rxsOQugEfL3vLt+n\nuP8KX8AUdfGUchvpoZm2dD6W/vPqd6g5BJZl8+fD269aK0BgWXQNrLduM/zpYXKnzc3T9Ia+\nx9fYrNXFU8ptpIdm2vz5WP7Pa9+f9hBYli2cD2e/aq0AgWXR9UuE/flL6D9H4OFr6Puu/3cY\nXjp+Xm70cAFT1MVTym2kh2ba/PlYxOYQWKYtnQ9fv2qtAIFl0fmb3N/On+E9nH/Uo/s3Xe+7\nw+/Lh64PXcAUdfGUchvpoZk2fz4WsTkElmmcj0oILIu66zOYnD/MCH0NcPKDH6ELmKIunlJu\nIz000+bPxyI2h8AyjfNRCYFlUTd85vbytb8+8BVAPoP1xDCqdRvpodk2ez4WsTkElm2cjzoI\nLIuWRrXv+s/j8BLfg1U9jGrdRnpoiGNzCCzEMfoRgWXR4qi2Nz9FuDk9rhubtbp4SrmN9NAQ\nx+YQWIhj9CMCy6LlUX3th+fB6nfvPA9W5TCqdRvpoSGOzSGwEMfoRwSWRcP3YPV/n6RacwFL\n1MVTym2kh2bb/Pk47c/fmPi+6bpt8Eeo2BwCyzbef9RBYFnUnX+4tuOAjNTFU8ptpIdm2vz5\nOK9ef5DKxRPxrkFgWcb7j0oILIu685PwBr/2l3wBU9TFU8ptpIdm2vz5eOt2p5//eTsOP01l\n/4dA1iCwLOP9RyUElkXnX5VzWL7Z3AVMURdPKbeRHppp8+dj+B1sl1/E9n1y8DQmaxBYlvH+\noxICy6Juze9Xu7+AKeriKeU20kMzbf58DKt9F78pm0Ngmcb7j0oILIu6720XePKFnAuYoi6e\nUm4jPTTT5s/H2/nj9/fLB/Gn0DdhsTkElmm8/6iEwLKo+/7o3ssuYIq6eEq5jfTQTJs/H4eu\n3x++d/1PYX1uus/HG7A5BJZpvP+ohMCyqDs/Wfv+WHQBS9TFU8ptpIdm2/z5+Lz5IarQexo2\nh8CyjfcfdRBYFp2/B4sfs/2jLp5SbiM9NNMWz8e/t83w627fg+9m2BwCyzTef1RCYFlEYN1T\nF08pt5Eemmmcj1IElmWcj0oILIuKR2Vs1uriKeU20kNDHJtDYCGO0Y8ILIsIrHvq4inlNtJD\nQxybQ2AhjtGPCCyLCKx76uIp5TbSQ8MFz4MVRGAhitGPCCyLhlF97Tfn9w27NU/Ja2zW6uIp\n5TbSQ7Mu9XzcBdbq70oxh8AyjvcfNRBYFp1Htbu+I+hCz+OTcgFD1MVTym2kh2Yc56MMgWUb\n56MKAsui7vxUvNuv4YPvzzW/VsrYrNXFU8ptpIdmG+ejEIFlGuejDgLLov+3d65dqSNBFM0s\nENHrg+X//7EjLyWESBK6u05V7f1hRr0l1TndbTavsL+S+/4DPg5PZbx2zwtuIBRy8jSlxjq0\n0LA/HgXBigz7oxAIVkT2n0W4v9tx2CC7brXgBkIhJ09TaqxDC829/fH+cnyKZLN9v/XrTA6C\nFRrOH4VAsCLSnV6Ze/nfmTcQCjl5mlJjHVpo/t4fu/XFVRZvfNZztP2xBAQrMpw/CoFgRQTB\n6iMnT1NqrEMLzd/7Y9ut/h1fePL5tuq2N3696uBcgGBFhvNHIRCsiOyfItw/tXHYGu8374Pf\nu4FQyMnTlBrr0ELz9/5YXbyu9+PWMyRMDoIVGs4fhUCwItJ7kftT97rgBkIhJ09TaqxDC83f\n++Pq0lfDX2dyEKzQcP4oBIIVkcNlGtaHt9m+f3+x6AYiISdPU2qsQ4vNn/uDR7Dug2CFhvNH\nGRCsiBzveJxfpPu57AYCISdPU2qsQwvOX/tj263ejj/lNVhjIFix4fxRBAQrIoeo3p7XXbfa\nLLgOb7gNIidPU2qsQ4vOX/vj6eJdhOvd8N+ZHAQrOpw/SoBgRYQPe+4jJ09TaqxDS8379nAd\nrNXmhetg3QbBglGI/gyCFREEq4+cPE2psQ4NxmFyECwYh+jPIFgR6Xb/NvtrJa6fFz3AG26D\nyMnTlBrr0CLD/ngYBCsw7I9SIFgRuXgFyWr+e2y/wm0QOXmaUmMdWmBe2B8P40CwRrBOTh/2\nRzEQrIh03fZ9/9Lcz7fnrtssuYHSI7JFTp6m1FiHFhj2x+M4EKyRH1snpw/7oxgIVkS633fW\nfqwWfBh6tA0iJ09TaqxDC8yK/fEwCFZc2B/FQLAichnV56qbfyGTYFnLydOUGuvQAnO5Idgf\ny0Cw4sL+KAaCFZFeVC/dy2M34B85eZpSYx1aFtgfi0CwksD+eAQEKyK9qD4WPIseLGs5eZpS\nYx1aFtgfi0CwksD+eAQEKyL9qBa8byZY1nLyNKXGOrQ0sD+WgGBlgf3xAAhWRBCsPnLyNKXG\nOrQ0sD+WgGBlgf3xAAhWRBCsPnLyNKXGOrQ0sD+WgGBlgf3xAAhWRBCsPnLyNKXGOrQ0sD+W\ngGBlgf3xAAhWRBCsPnLyNKXGOrQ0sD+WgGBlgf3xAAhWRBCsPnLyNKXGOrQ0sD+WgGBlgf3x\nAAhWRBCsPnLyNKXGOrQ0sD/+YuwT/RCsLLA/HgDBisjDH28aLGs5eZpSYx1aYNgf06krO7N+\njGA1gv1RDAQrImyQPnLyNKXGOrTAsD+mg2Dlg/1RDAQrIg9HFSxrOXmaUmMdGoyTaHIQLJgN\nGZ9BsCKCYPWRk6cpNdahwTiJJgfBgtmQ8RkEKyIIVh85eZpSYx0ajJNochAsmA0Zn0GwIoJg\n9ZGTpyk11qHBOIkmB8GC2ZDxGQQrIghWHzl5mlJjHRqMk2hyECyYDRmfQbAigmD1kZOnKTXW\nocE4iSYHwYLZkPEZBCsiCFYfOXmaUmMdGoyTaHIQLJgNGZ9BsCKCYPWRk6cpNdahwTiJJgfB\ngtmQ8RkEKyIIVh85eZpSYx0ajJNochAsmA0Zn0GwIoJg9ZGTpyk11qHBOIkmB8GC2ZDxGQQr\nIghWHzl5mlJjHRqMk2hyECyYDRmfQbAigmD1kZOnKTXWocE4iSYHwYLZkPEZBCsiCFYfOXma\nUmMdGoyTaHIQLJgNGZ9BsCKCYPWRk6cpNdahwTiJJgfBgtmQ8RkEKyIIVh85eZpSYx0ajJNo\nchAsmA0Zn0GwIoJg9ZGTpyk11qHBOIkmB8GC2ZDxGQQrIghWHzl5mlJjHRqMk2hyECyYDRmf\nQbAigmD1kZOnKTXWocE4iSYHwYLZkPEZBCsiCFYfOXmaUmMdGoyTaHIQLJgNGZ9BsCKCYPWR\nk6cpNdahwTiJJgfBgtmQ8RkEKyIIVh85eZpSYx0ajJNochAsmA0Zn0GwIoJg9ZGTpyk11qHB\nOIkmB8GC2ZDxGQQrIghWHzl5mlJjHRqMk2hyECyYDRmfQbAigmD1kZOnKTXWocE4iSYHwYLZ\nkPEZBCsiCFYfOXmaUmMdGoyTaHIQLJgNGZ9BsCKCYPWRk6cpNdahwTiJJgfBgtmQ8RkEKyII\nVh85eZpSMwnrZJOSKHcEC2ZDxmcQrIggWH3k5KlQDQ9zGZEodwQLZkPGZxCsiCBYfdTECMFy\nTqLcESyYDRmfQbAigmD1URMjBMs5iXJHsGA2ZHwGwYoIgtVHTYwQLOckyh3BgtmQ8RkEKyII\nVh81MUKwnJModwQLZpMl4wlvQ2qiTwhWWxCsPmpihGA5J1HuCBbMJkvGKvqEYLUFweqjJkYI\nlnMS5Y5gwWyyZKyiTwhWWxCsPmpihGA5J1HuCBbMJkvGKvqEYLUFweqjJkYIlnMS5Y5gwWyy\nZKyiTwhWWxCsPmpihGA5J1HuCBbMJkvGKvqEYLUFweqjJkYIlnMS5Y5gwWyyZKyiTwhWWxCs\nPmpihGA5J1HuCBbMJkvGKvqEYLUFweqjJkYIlnMS5Y5gwWyyZKyiTwhWWxCsPmpihGA5J1Hu\nCBbMJkvGKvqEYLUFweqjJkYIlnMS5Y5gwWyyZKyiTwhWWxCsPmpihGA5J1HuCBbMJkvGKvqE\nYLUFweqjJkYIlnMS5Y5gwWyyZKyiTwhWWxCsPmpihGA5J1HuCBbMJkvGKvqEYLUFweqjJkYI\nlnMS5Y5gwWyyZKyiTwhWWxCsPmpihGA5J1HuCBbMJkvGKvqEYLUFweqjJkYIlnMS5Y5gwWyy\nZKyiTwhWWxCsPmpihGA5J1HuCBbMJkvGKvqEYLUFweqjJkYIlnMS5Y5gwWyyZKyiTwhWWxCs\nPmpihGA5J1HuCBbMJkvGKvqEYLUFweqjJkYIlnMS5Y5gwWyyZKyiTwhWWxCsPmpihGA5J1Hu\nCBbMJkvGKvqEYLUFweqjJkYIlnMS5Y5gwWyyZKyiTwhWWxCsPmpihGB5obudcKLcESyYTZaM\nVfQJwWoLgtVHTYwQLC8gWAgWzCZLxir6hGC1BcHqoyZGCJY2XZ8bBe3HZAWCBbPJkrGKPiFY\nbckkWN0UGkoPguWf9xWCdQbBgtlkyVhFnxCstqQSrIZCo1aDYFVit+mePvdf8BQhggWzyZKx\nij4hWG1BsOoIjVoNglWNf1337wvBQrBgAVkyVtEnBKstCFYdoVGrQbDq8fnUbXYIFoIF88mS\nsYo+IVhtQbDqCI1aDYJVk5du9YZgIVgwmywZq+gTgtUWBKuO0KjVIFhV+VjffIX7l6v98SgI\nFswmS8Yq+oRgtQXBqiM0ajUIVmWeESwEC2aTJWMVfUKw2oJg1REatRoEy4hEuSNYMJssGavo\nUxnBuo913iogWHWERq0GwTIiUe4IFswmS8Yq+lRGsO5XWOetAoJVR2jUahCsBnCh0YqyM+vH\nCJYXsmSsok8IVlsQrDpCo1aDYDWgJ1j5HitHsGA2WTJW0ScEqy0IVh2hUatBsIxIlDuCBbPJ\nkrGKPiFYbUGw6giNWg2CZUSi3BEsmE2WjFX0CcFqC4JVR2jUahAsIxLlHk+weIdUdbKEqaJP\nCFZbEKw6QqNWg2DV4v1lczjrbrbvt/45Ue7xBGvkx9ZBRyJLmCr6hGC1BcGqIzRqNQhWHXbr\ni0c2nm4UJModwYLZZAlTRZ8QrLYgWHWERq0GwarDtlv9+zh89fm26rbDgkS5I1gwmyxhqugT\ngtUWBKuO0KjVIFh1WHUfP19/dKthQaLcESyYTZYwVfQJwWoLglVHaNRqEKw6XF366kZBs6GY\ng2DBbLKEqaJPCFZbEKw6QqNWg2DVgUewfkGwYDZZwlTRJwSrLQhWHaFRq0Gw6rDtVm+fh694\nDRaCBbPJEqaKPiFYbUGw6giNWg2CVYmni3cRrnfDf0+UO4IFs8kSpoo+IVhtQbDqCI1aDYJV\ni/ft4TpYq80L18EykB2LntZBRyJLmCr6hGC1BcGqIzRqNQiWEYlyR7BgNlnCVNEnBKstCFYd\noVGrQbCMSJQ7ggWzyRKmij4hWG1BsOoIjVoNgmVEotwRLJhNljBV9AnBaguCVUdo1GoQLCMS\n5Y5gwWyyhKmiTwhWWxCsOkKjVoNgGZEodwQLZpMlTBV9QrDagmDVERq1GgTLiES5I1gwmyxh\nqugTgtUWBKuO0KjVIFhGJModwYLZZAlTRZ8QrLYgWHWERq0GwTIiUe4IFswmS5gq+oRgtQXB\nqiM0ajUIlhGJckewYDZZwlTRJwSrLQhWHaFRq0GwjEiUO4IFs8kSpoo+IVhtQbDqCI1aDYJl\nRMTcuxEsZMeip3X+kcgSpoo+IVhtQbDqCI1aDYJlRMTclWTHoqd1/pHIEqaKPiFYbbkXxNV9\n1Pk3IISa9CBYCYiYu5LsWPS0zj8SWcJU0ScEqy33gnhFsELUIFhGRMxdSXYselrnH4ksYaro\nE4LVlrtBfKyeHrsBHdSkB8FKQMTclWTHoqd1/pHIEqaKPiFYbbkfxEe3fewGZFCTHgQrARFz\nV5Idi57W+UciS5gq+oRgtWVCEK/dx2M3oIKa9CBYCYiYu5LsWPS0zj8SWcJU0ScEqy28i7CO\n0KjVIFhGRMxdSXYselrnH4ksYaroE4LVFgSrjtCo1SBYRkTMXUl2LHpa5x+JLGGq6BOC1RYE\nq47QqNUgWEZEzF1Jdix6WucfiSxhqugTgtUWBKuO0KjVIFhGRMxdSXYselrnH4ksYaroE4LV\nlllBcB0stzUIlhERc1eSHYue1vlHIkuYKvqEYLVluWCNX3tUFTXpQbASEDF3Jdmx6GmdfySy\nhKmiTwhWW3iKsI7QqNUgWEZEzF1Jdix6WufviEgftfYQKvqEYLUFwaojNGo1CJYREXNXkh2L\nntb5O2L8o9b8PQPyECr6hGC1BcGqIzRqNQiWERFzV5Idi57W+Xsi0EetPYSKPiFYbbkfxPvL\n5nBPY7N9X3YDMqhJD4KVgIi5K8mORU/r/F0R56PWHkJFnxCsttwLYre+eID31n0RR0mqSQ+C\nlYCIuSvJjkVP6/x9Eeaj1h5CRZ8QrLbcC2Lbrf4d98fn2+rWfRFHSapJD4KVgIi5K8mORU/r\n/CORJUwVfUKw2nIviNXF3Y+PbjX/BoRQkx4EKwERc1eSHYue1vlHIkuYKvqEYLXlXhBXb/yY\nfwNCqEkPgpWAiLkryY5FT+v8I5ElTBV9QrDawiNYdYRGrQbBMiJi7kqyY9HTOv9IZAlTRZ8Q\nrLZMeA3W2+fhK16D5bkGwTIiYu5KsmPR0zr/SGQJU0WfEKy23A3i6eJdhOvdghvQQU16EKwE\nRMxdSXYselrnH4ksYaroE4LVlgnXwdoeroO12rxwHSy/NQiWERFzV5Idi57W+UciS5gq+oRg\ntYUrudcRGrUaBMuIiLkryY5FT+v8I5ElTBV9QrDagmDVERq1GgTLiIi5K8mORU/r/CORJUwV\nfUKw2oJg1REatRoEy4iIuSvJjkVP6/wjkSVMFX1CsNqCYNURGrUaBMuIiLkryY5FT+v8I5El\nTBV9QrDagmDVERq1GgTLiIi5K8mORU/r/CORJUwVfUKw2oJg1REatRoEy4iIuSvJjkVP6/wj\nkSVMFX1CsNqCYNURGrUaBMuIiLkryY5FT+v8I5ElTBV9QrDagmDVERq1GgTLiIi5K8mORU/r\n/CORJUwVfUKw2oJg1REatRoEy4iIuSvJjkVP6/wjkSVMFX1CsNqCYNURGrUaBMuIiLkryY5F\nT+v8I5ElTBV9QrDagmDVERq1GgTLiIi5K8mORU/r/CORJUwVfUKw2oJg1REatRoEy4iIuSvJ\njkVP6/wjkSVMFX1CsNqCYNURGrUaBMuIiLkryY5FT+v8I5ElTBV9QrDagmDVERq1GgTLiIi5\nK8mORU/r/CORJUwVfUKw2oJg1REatRoEy4iIuSvJjkVP6/wjkSVMFX1CsNqCYNURGrUaBMuI\niLkryY5FT+v8I5ElTBV9QrDagmDVERq1GgTLiIi5K8mORU/r/CORJUwVfUKw2oJg1REatRoE\ny4iIuSvJjkVP6/wjkSVMFX1CsNqCYNURGrUaBMuIiLkryY5FT+v8I5ElTBV9QrDagmDVERq1\nGgTLiIi5K8mORU/r/CORJUwVfUKw2oJg1REatRoEy4iIuSvJjkVP6/wjkSVMFX1CsNqCYNUR\nGrUaBMuIiLkryY5FT+v8I5ElTBV9QrDagmDVERq1GgTLiIi5K8mORU/r/CORJUwVfUKw2oJg\n1REatRoEy4iIuSvJjkVP6/wjkSVMFX1CsNqCYNURGrUaBMuIiLkryY5FT+v8I5ElTBV9QrDa\ngmDVERq1GgTLiIi5K8mORU/r/CORJUwVfUKw2oJg1REatRoEy4iIuSvJjkVP6/wjkSVMFX1C\nsNqCYNURGrUaBMuIiLkryY5FT+v8I5ElTBV9QrDagmDVERq1mv+6KVjPUEAiZqokOxY9rfOP\nRJYwVfQJwWoLglVHaNRqpt2Q9QwFJGKmSrJj0dM6/0hkCVNFnxCstiBYCzzEYQ2CZUTETJVk\nx6Kndf6RyBKmij4hWG1BsBZ4iMMaBMuIiJkqyY5FT+v8I5ElTBV9QrDagmAt8BCHNQiWEREz\nVZIdi57W+UciS5gq+oRgtQXBWuAhDmsQLCMiZqokOxY9rfOPRJYwVfQJwWoLgrXAQxzWIFhG\nRMxUSXYselrnH4ksYaroE4LVFgRrgYc4rEGwjIiYqZLsWPS0zj8SWcJU0ScEqy0I1gIPcViD\nYFVi99x1T2/Hr29dSCxipkqyY9GTy8iVI0toKvqEYLUFwVrgIQ5rEKw67FaHU+vm8A2C1V52\nlHpaz4tHsoSmok8IVlsQrAUe4rAGwarDtnv9tqzX1dP+GwSrudVI9bSeF49kCU1FnxCstiBY\nCzzEYQ2CVYfVMbPP1foTwRoTj/Y/RrC8kCU0FX1CsNqCYC3wEIc1CFYdzk61e3pCsMbEo/2P\nESwvZAlNRZ8QrLYgWAs8xGENglWHdbc7f/WEYLW3Gqme1vPikSyhqegTgtUWBGuBhzisQbDq\n8No9n7767J4QrOZWI9XTel48kiU0FX1CsNqCYC3wEIc1CFYltj9W9XbzjfoRM/UgOxY9refF\nI1lCU9EnBKstCNYCD3FYg2DV4mNz/urzGcFqbTVSPa3nxSNZQlPRJwSrLQjWAg9xWINgGREx\nUw+yY9HTel48kiU0FX1CsNqCYC3wEIc1CJYRETP1IDsWPa3nxSNZQlPRJwSrLQjWAg9xWINg\nGRExUw+yY9HTel48kiU0FX1CsNqCYC3wEIc1CFYDeJF7c6uR6mk9Lx4JEdrop1Ne0MZrClQg\nWCVBsBZ4iMMaBKsBPcEK/AnAHmTHoqf1vHgkRGitrKVJBYJVEgRrgYc4rEGwjIiYqQfZsehp\nPS8eCREagjWosJ4SFRCsBR7isAbBMiJiph5kx6Kn9bx4JERoCIjjlyQAABmqSURBVNagwnpK\nVECwFniIwxoEy4iImXqQHYue1vPikRChIViDCuspUQHBWuAhDmsQrFq8v2wOr7XabN9v/bPr\nTMdesDtTPNr/GMHyQojQEKxBhfWUqIBgLfAQhzUIVh126wvveLpR4DpTx7Jj0dN6ujwSIjQE\na1BhPSUqIFgLPMRhDYJVh223+vdx+OrzbdVthwWuM3UsOxY9rafLIyFCQ7AGFdZTogKCtcBD\nHNYgWHVYdR8/X390q2GB60wdy45FT+vp8kiI0BCsQYX1lKiAYC3wEIc1CFYdri59daOg2VAq\n4Fh2LHpaT5dHQoSGYA0qrKdEBQRrgYc4rEGw6sAjWBPEo/2PESwvhAgNwRpUWE+JCgjWAg9x\nWINg1WHbrd4+D1/xGiwp2bHoaT1dHgkRGoI1qLCeEhUQrAUe4rAGwarE08W7CNe74b+7ztSx\n7Fj0tJ4uj4QIDcEaVFhPiQoI1gIPcViDYNXifXu4DtZq8xLwOlhlxKP9jxEsL4QIDcEaVFhP\niQoI1gIPcViDYBnhOlPHsmPR03q6PBIiNARrUHEf60lrA4K1wEMc1iBYRrjO1LHsWPS0ni6P\nhAgNwVpQYT1pbUCwFniIwxoEywjXmTqWHYue1tPlkRCh6VhLgQoEqyQI1gIPcViDYBnhOlPH\nsmPR03q6PBIiNB1rKVCBYJUEwVrgIQ5rECwjXGfqWHYselpPl0dChKZjLQUqEKySIFgLPMRh\nDYJlhOtMHcuORU/r6fJIiNB0rKVABYJVEgRrgYc4rEGwjHCdqWPZsehpPV0eCRGajrUUqECw\nSoJgLfAQhzUIlhGuM3UsOxY9rafLIyFC07GWAhUIVkkQrAUe4rAGwTLCdaaOZceip/V0eSRE\naDrWUqACwSoJgrXAQxzWIFhGuM7UsexY9LSeLo+ECE3HWgpUIFgliSJYE64c26lJD4KVANeZ\nOpYdi57W0+WREKHpWEuBCgSrJGEEq5RjBK1BsIxwnalj2bHoaT1dHgkRmo61FKhAsEqCYOWo\nQbCMcJ2pY9mx6Gk9XR4JEZqOtRSoQLBKgmDlqEGwjHCdqWPZsehpPV0eCRGajrUUqECwSoJg\n5ahBsIxwnalj2bHoaT1dHgkRmo61FKhAsEqCYOWoQbCMcJ2pY9mx6Gk9XR4JEZqOtRSoQLBK\ngmDlqEGwjHCdqWPZsehpPV0eCRGajrUUqECwSoJg5ahBsIxwnalj2bHoaT1dHgkRmo61FKhA\nsEqCYOWoQbCMcJ2pY9mx6Gk9XR4JEZqOtRSoQLBKgmDlqEGwjHCdqWPZseg5gvUsShMiHR1r\nKVCBYJUEwcpRg2AZ4TpTx7Ij1NN6FqUJkY6OtRSoQLBKgmDlqEGwjHCdaTzZsehpPYvShEhH\nx1oKVCBYJUGwctQgWEa4zjSe7Fj0tJ5FaUKko2MtBSoQrJIgWDlqECwjXGcaT3YselrPojQh\n0tGxlgIVCFZJEKwcNQiWEa4zjSc7Fj2tZ1GaEOnoWEuBCgSrJAhWjhoEywjXmcaTHYue1rMo\nTYh0dKylQAWCVRIEK0cNgmWE60zjyY5FT+tZlCZEOjrWUqACwSoJgpWjBsEywnWm8WTHoqf1\nLEoTIh0daylQgWCVBMHKUYNgGeE603iyY9HTehalCZGOjrUUqECwSoJg5ahBsIxwnWk82bHo\naT2L0oRIR8daClQgWCVBsHLUIFhGuM40nuxY9LSeRWlCpKNjLQUqEKySIFg5ahAsI1xnGk92\nLHpaz6I0IdLRsZYCFQhWSRCsHDUIlhGuM40nOxY9rWdRmhDp6FhLgQoEqyQIVo6aaTc0BeuZ\ndobrvOLJjkVP61mUJkQ6OtZSoALBKgmClaOmXDPrmXaG67ziyY5FT+tZlCZEOjrWUqACwSoJ\ngpWjBsEywnVe8WTHoqf1LEoTIh0daylQgWCVBMHKUYNgGeEjr7Hng6uKR8UfS/W0nlxpQqSj\nYy0FKhCskiBYOWoQLCN85JVGdix6Wk+uNCHS0bGWAhUIVkkQrBw1CJYRPvJKIzsWPa0nV5oQ\n6ehYS4EKBKskCFaOGgTLCB95pZEdi57WkytNiHR0rKVABYJVEgQrRw2CZYSPvNLIjkVP68mV\nJkQ6OtZSoALBKgmClaMGwTLCR15pZMeip/XkShMiHR1rKVCBYJUEwcpRg2AZ4SOvNLJj0dN6\ncqUJkY6OtRSoQLBKgmDlqEGwjPCRVxrZsehpPbnShEhHx1oKVCBYJUGwctQgWEb4yCuN7Fj0\ntJ5caUKko2MtBSoQrJIgWDlqECwjfOSVRnYselpPrjQh0tGxlgIVCFZJEKwcNQiWET7ySiM7\nFj2tJ1eaEOnoWEuBCgSrJAhWjhoEywgfeaWRHYue1pMrTYh0dKylQAWCVRIEK0cNgmWEj7zS\nyI5FT+vJlSZEOjrWUqACwSoJgpWjBsEywkdeaWTHoqf15EoTIh0daylQgWCVBMHKUYNgGeEj\nrzSyY9HTenKlCZGOjrUUqECwSoJg5ahBsIzwkVca2bHoaT250jhIp7uPjLUUqECwSoJg5ahB\nsIzwkVca2bHoaT250jhIx5O1FKhAsEqCYOWoQbCM8JFXGtmx6DmC9Zxr4CAGT9ZSoALBKgmC\nlaMGwTLCR15pZEeop/Wca+AgBk/WUqACwSoJgpWjBsEywkdeSuKRpaf1nGvgIAZP1lKgAsEq\nCYKVowbBMsJHXkrikaWn9Zxr4CAGT9ZSoALBKgmClaMGwTLCR15K4pGlp/Wca+AgBk/WUqAC\nwSoJgpWjBsEywkdeSuKRpaf1nGvgIAZP1lKgotVA7mM98SVAsHLUIFhG+MhLSTyy9LSecw0c\nxODJWgpUyAzEwdK4D4KVowbBMsJHXkrikaWn9Zxr4CCGWNZyt0JmIA6Wxn0QrBw1CJYRPvJS\nEo8sPa3nXAMHMcSylrsVMgNxsDTug2DlqEGwjPCRl5J4ZOlpPecaOIghlrXcrZAZiIOlcR8E\nK0cNgmWEVl6jrycVEo8sPa3XggYOYohlLXcrZAbiYGncB8HKUYNgGaGVl4WPeJAdi57Wa0ED\nBzHEspa7FTIDcbA07oNg5agp12wK1qtBCK0sECydntZrQQMHMcSylrsVMgNxsDTug2DlqGk7\nIOvVIIRWFgiWTk/rtaCBgxhiWcvdCpmBOFga9/EgWJMeNGnpDw5rECwjtLJAsHR6Wq8FDRzE\nEMta7lbIDMTB0riPC8Fq6QZBaxAsI7SyQLB0elqvBQ0cxBDLWu5WyAzEwdK4D4KVowbBMkIr\nCwRLpyevX9zj4HhjWcvdCpmBOFga90GwctQgWEZoZYFgyfe0XiKNcXC8sazlboXMQBwsjfvc\nP4j3l83hntVm+77sBh5GTVY81iBYtbDfHzNAsOR7Wi+Rxjg43ljWcrdCZiAOlsZ97h3Ebn3x\n6PXTghsogJqseKxBsOqgsD9mgGDJ97ReIo1xcLyxrOVuhcxAHCyN+9w7iG23+vdx+OrzbdVt\n599AAdRkxWMNglUHhf0xAwRLvqf1EmmMg+ONZS13K2QG4mBp3OfeQay6j5+vP7rV/BsogJqs\neKxBsOqgsD9mgGDJ97ReIo1xcLyxrOVuhcxAHCyN+9w7iN67Wm69xQXBclGDYNVBYX/cYuw9\nalXdwODG4/W0WS9mODjeWNZyt0JmIA6Wxn14BCtHDYJVB4X9cQshH3EsOxY9bdaLGQ6ON5a1\n3K2QGciU64tbr427THgN1tvn4Steg+W5BsGqg8L+uIWQjziWHYueNuvFDPPjnXAWLyALOtZy\nt0JmIFOGar167nJ3hE8XC229W3ADj6MmKx5r2g4oxH2PaQjsj1sI+Yhj2bHoGXu7DDA/MKxF\ndSA5BOvrfXu4zs9q88J1sPzWyA1If2tMxH5/3Gxr4QYGN56mp80yqo/5gWEtqgNJIli1b2BC\ni5bn/aA1cgPS3xplQLDiyY5FT5tlVAD1C/FiLaoDQbCK3MCEFi3P+0Fr5AakvzXKUPs4x55S\n0nGDeLJj0bPyMqqF/oV4sRbVgSBYBW5g0st1Wp73g9bIDUh/a5ShumCVOH07Fo8sPZ2+Nsv6\nQrwTzi6NVMBNhcxA8glWhev8yJ33g9bIDWiSWT+2tppjcR0sfTeIJztKPcV3jvVlTHRUwE2F\nzECmDFX+HLJcsO4ewKRTKEB9lu6OmbA/wCXNtsSN5f/HrwJI8MgGeOB3AQAAxrj7CBZAZBAs\nAACowd0L8QJEBsECAIAq3LsQL0BkJlxo9O/rmACkhv0BMM6dC/ECROaeYN29jglAYtgfAABw\nkwkf9vz3dUwAEsP+AACAm9wTLN4FAjAO+wMAAG5yT7DGr2MCAOwPAAC4CY9gASyH/QEAADeZ\n8BosrmMCMAL7AwAAbnL3SQ2uYwIwDvsDAABuMeE6WFzHBGAU9gcAANyAl+UCAAAAFAbBAgAA\nACgMggUAAABQGAQLAAAAoDAIFgAAAEBhECwAAACAwiBYAAAAAIVBsAAAAAAKg2ABAAAAFAbB\nAgAAACgMggUAAABQGAQLAAAAoDBRBKsDZ1ivmHZYJw2wCLYNiGO7RCegP8JpqB2H2njkBqQ2\nnopYHCo96emxp077XxjINQxkMvojnIbacaiNR25AauOpSJaTIz3pGaf9LwzkGgYyGf0RTkPt\nONTGIzcgtfFUJMvJkZ70jNP+FwZyDQOZjP4Ip6F2HGrjkRuQ2ngqkuXkSE96xmn/CwO5hoFM\nRn+E01A7DrXxyA1IbTwVyXJypCc947T/hYFcw0Amoz/Caagdh9p45AakNp6KZDk50pOecdr/\nwkCuYSCT0R/hNNSOQ208cgNSG09Fspwc6UnPOO1/YSDXMJDJ6I9wGmrHoTYeuQGpjaciWU6O\n9KRnnPa/MJBrGMhk9EcIAAAA4AwECwAAAKAwCBYAAABAYRAsAAAAgMIgWAAAAACFCSFYr+tu\ntd1Zj6LHu1SwH89d9/xpPYofdtuV3IQVZrdP/OPyJ/WPedCz0SfO99d6m7nt9WxwnMMW9Y9z\n0LPFfA7+VDTfqxbLacJADE8yg5OJ1dml39fwrNIbiPTpRMoDFrI9/NlZKSW8WykF+6YV0Ofq\nOB4d4yvP8RAvbOfp8IN1y54fbQSrv9YbHOd1zwbHOWxR/zgHPVvM5+BPRZv5vMBiOU0YiOFJ\nZnAysTq79PsanlV6A9E+nSh5wEI+uufvSX7tnq0HcsGm/uMGM1itPr52m25rPY4Tz4eRbKUm\nrDCHg9t2m58fvHffc/Cx6t4b9vy4+LoivbXe4DgHPRsc56BFg+Mc9Gwxn9d/KhrN5wUWy+n+\nQCxPMoOTidXZpd/X8KzSG4j26UTJAxayOR6DktL8a/DEzHT+HVbgrltZD+REpzdhpVl1+zt2\nF0e47d6+9jPx0rDna81uP/TXeoPjHPRscJyDFg2Oc9CzwXEO/lS0mc/eCNovpwkDMTzJDE4m\nVmeXfl/Ds0p/INqnE81RLUEo4M/uSWg034r/cb+oIafHd2WErxoXR7jp9o9gN3gM4qLna/da\nu9tgrTc5zqueDY5z0KLBcQ56NjjOwZ+KZuv2hMVymjKQEwZ/1gcDsTq7XPW1O6tcDUT7dCLk\nAY+x656sh/DDU/epJFjr7utldXiIW4OX02O6BndLm7K9OCG2upt12XPTvT13q8oP4V+t9SbH\nedWzwXEOWjQ4zkHPBsc5+FPR+uEBi+U0ZSBHLE4yg4FYnV2u+tqdVa4Gon06EfKAx3g9PJgs\nwUv3T+nxtO+xbA6vArQexw+v+5clrho8vGLJv65re0Ie9NwcXxNd9ZxwvdZbHOd1zwbHOWjR\nRLCuejY4zsGfisaGY7GcJg3kiMFJZjAQq7PLcGqMziqDAKRPJ0Ie8BCfq/aPIo9weEBbS7D2\nL0d81lH8l8OJQmY4dXjdrC4Osc2Z4rrnv/17mGs+sTRY6w2O80bP6sc5aNHgOG/0bHCcV38q\n2hqOxXKaNpADBieZwUCszi43psbmrDIMQPp0IuQBj7Bb6TxBuN6/c1VLsPbPln/avNn5Bq/7\nh1m+t6bofY5yPDc9IQ96HtnVnPfBWm9wnCP7q+pxDlo0m8/BYVU9zsGfiraGY7Gcpg1kj8VJ\nZjAQq7PLjamxOasMBqJ9OhHygEd4UpGH/Rlu/zCylmBd/s+e9eHtbg1OiNZcvMVm1e6EfP2g\nfcWew7Ve/zhH91eD9f3botl8DlvUfdTsqkW74/yyWU4TB7LH4CQzGIjV2WXY1+isMhyI9ulE\n5aT7EJ/rJ52rjHU/WI/kjNp1LNSErx6/h3h8O9Rng7dDtTwhD9d6/eMc3V9NZSfmfA7/VLQ7\nzi+b5TRxIEYnmcFArM4ut6bm9A/WA9E+nWiOah5vQm8gVBSsl4P0f8qkdLxbqnNdrgocr0l1\n8fj5cQ7eal6Wb9Dz/IOWslP/OIc96x/nsEXD+dyM/qA8gz8VDY7zF4vlNHEgRicZYcEyOqvc\n2v77/6qeTmQsYDk65nCBjl4dzrm7/ZPU/6wHcmLb7T84aitzZfkKHK4rvNv8vi6g1ZXcL3se\nEt5tq7/z6XKtt7r09mXPBsc5aNFkPq96NjjOwZ8Kg0upWyynuwMxPclYPFh7k34ihmeVq+0v\nfDoR8oClPKs9YrRHajTHt1noaOiT2HgqsPo9xONSWNc/5uueu+MPqv/h6T1G3+A4r3s2OM7L\nFq2Oc9CzxXy+GKzbKyyW092BmJ5kBk+CGQvW8X+WZ5XeQKRPJ0oesBCjB03/Rms0b0/VLzg5\ni8PHn1sPoi7fh7g+PpZ0XAq7Bsd8q+e6/ptren/tWhznrZ6Vj3NnMJ83e9aez98/FU3n8wKL\n5XR3IKYnGU3Bsjyr9AeifDqR8gAAAACACCBYAAAAAIVBsAAAAAAKg2ABAAAAFAbBAgAAACgM\nggUAAABQGAQLAAAAoDAIFgAAAEBhECwAAACAwiBYAAAAAIVBsAAAAAAKg2ABAAAAFAbBAgAA\nACgMgrWIf5uu69bbj9O379N/c9oHofeqfj7J/emn4dwG7zN6AzwK+wNgHPZHFohsAe+r85Ld\nHL5/npHiIxvkm+dFDU4DZINAC9gfAOOwP/JAZPP57LrDXYHd26p72v9gzsJbtEFOX3y8nBrO\nhZ0B7WB/AIzD/kgEyc3nuft3/nLdvX212yDfe3PVvUzvNbMpQAnYHwDjsD8SQXLzuVhub4cH\nedttkP29n930ZvOaApSA/QEwDvsjESQ3n8s1+r30Ts9uf3/z9rzav3Tx8/wvr09d9/x5qtx/\n8/R2XqvXpduu2w6rfnr8sj3d/TkUvn5/setWP/+4+h7ZsMHPAM839PO7N4YJ8CDsD4Bx2B+J\nQLDm89Q9Xd4L+Fl/m/MrCT+OP94evll9nn7pwPa4SK9Ln7vjBulX/TS4+Ob9+MLIU+H+GfXf\nR5zf9rcxbHC1QT7Xp9/9vDFMgEdhfwCMw/5IBII1n/f96nq9eMfrceG9duv9u1nfn86vXOxe\ndl8f6+MbN75/+P2P7+vDQh2Wrt6+doOq/s2f2HXrn8KPp/1u+Tj8ZM/6uB1uNbi4oVOTm8ME\neBj2B8A47I9EIFgLeDu+zXa9fTt+f1x46+Pdie8l3B1/eHjM9v3wCOzbeRGvDv84KD2+8vCq\n6kz/GfD9dz+FT937/j9vp1//eUJ/0OD3hn5+9/wCy4thAhSA/QEwDvsjDwjWEnb/Tg+xrk8P\nk/b+9bwoP3+/ez6t4e/lOVjt+/8el/NI1fBXnrvTpene98v77fTe282Nt6QMN8hFk831MAFK\nwP4AGIf9kQZiWcrH6/5lgKv9I7O/i2v3/rpZ9Rbl+R7B6Vn33U/tjdIbVZf//Pvd+ucnh7sT\nx/sbp4d6/2hw+N/qt8nqepgApWB/AIzD/kgBsTzC+9PhAdLT4tptz1fo/fq6Wnm/y+/41R+l\nV19df/O53wbdBV/7Z8z39yVO7w/5o8GtobBBoBrsD4Bx2B/hIZbZXC6lS4vf7e+QbF4/vu5v\nkL9KBz3637ztX014tUG+71V8/rzd9o8GbBCoD/sDYBz2RyaIZTZP3cVnc14ssudus/v92chD\nvMdvR0qvqr5ufXN4Cnx1NW3b7ztC29MrHf9ocPgfD/FCVdgfAOOwPzJBLLN5OX1E557j89b9\nZf5+Y4NcvfxwpHTCixQ/Dqt60/U/f32/1s8L/48G10O5vIowGwTKwP4AGIf9kQlimc1udXxn\n6p6nbn9B2/4yf7qxQT7O72Jd99bvVelV1ZmLbz5Xh4bn932cFvl+x2zPg/qjweF/g7fZDpoA\nPAD7A2Ac9kcmiGU+3/cP1m+7/aehr89vvNjfIdgcLtD7vn8D7uVbQ47/33z/yukfx0uvqs78\nfLP/NPTjhjhe7G33en6D7kd3/urrdoP33xu6vlDcVROAx2B/AIzD/kgEsSzg7fwOi9PHBTwf\nXiz4efrZ97bZL8erlXe68MnL4duR0quqM5cvSTxdL/f8cQXnh2u/705sfqqHDY4DPPc5fQxC\n/xosbBAoBfsDYBz2Rx6IZRH/9lcIWT2fl+f3Alx9r8r9/7afp497ul55b/tPyHw/fXu79Lrq\n63wLJzYvvx/4tP+EzdXzz+ctvP1slVsNTgP8Gcpz78M6e/8HeBz2B8A47I8sEAsAAABAYRAs\nAAAAgMIgWAAAAACFQbAAAAAACoNgAQAAABQGwQIAAAAoDIIFAAAAUBgECwAAAKAwCBYAAABA\nYRAsAAAAgMIgWAAAAACFQbAAAAAACoNgAQAAABQGwQIAAAAoDIIFAAAAUBgECwAAAKAwCBYA\nAABAYRAsAAAAgMIgWAAAAACFQbAAAAAACvM/WickWcZ41FUAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"n=1000, lambda=20\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 1200,
       "width": 1200
      },
      "text/plain": {
       "height": 1200,
       "width": 1200
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calling the function to plot standard deviations\n",
    "\n",
    "par(mfrow=c(3, 3))\n",
    "options(repr.plot.width=20, repr.plot.height=20)\n",
    "\n",
    "for (lambda in c(1,5,20)) {\n",
    "    for (n in c(10,100,1000)) {\n",
    "        plot_sd(n, lambda)\n",
    "    }\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3> Question 6.d (5 Marks) </h3>\n",
    "\n",
    "When rate $\\lambda_1$ = 1 and $\\lambda_2$ = 5 and sample size $n$ is 10 or 100, obtain the z scores of the sample means (from 50000 simulations). Plot their distributions in a histogram with the theoretical Gaussian curve overlaid.\n",
    "\n",
    "Note that for sample size 100, the plots overlay very nicely. But what happens with sample size 10? Explain the\n",
    "differences between the four plots.\n",
    "\n",
    "For each simulation: the z score of the mean can be calculated as:\n",
    "$$\n",
    "\\frac{(\\bar{X}-\\mu)}{\\sigma / \\sqrt{n}}\n",
    "$$\n",
    "where $\\bar{X}$ is the mean of the sample, $\\mu$ is the population mean and $\\sigma$ is the population standard deviation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 631,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function for calculating and plotting the zscore\n",
    "plot_z_score <- function(lambda,n)\n",
    "{  \n",
    "    # Calculating the population mean and standard deviation values \n",
    "    mean_value = lambda\n",
    "    sd_value = sqrt(lambda/n)\n",
    "    \n",
    "    # To store the values of the z_Score and sample means\n",
    "    z_score_values = rep(0,50000)\n",
    "    sample_means = rep(0,50000)\n",
    "    \n",
    "    for (i in 1:50000) \n",
    "    {\n",
    "        sample_means[i] = mean(rpois(n,lambda))\n",
    "        z_score_values[i] = (sample_means[i] - mean_value)/(sd_value/sqrt(n)) \n",
    "    }\n",
    "    #f = function(x, mean = mean_value, sd = sd_value) dnorm(x, mean = mean, sd = sd)\n",
    "    \n",
    "    hist(z_score_values, xlab =\"Z Score\", col=ifelse(n<99,'green','yellow'), breaks = 40,freq=F)\n",
    "    #curve(f, from = min(z_score), to = max(z_score), add = T)\n",
    "    curve( dnorm(x, mean = mean(z_score_values), sd = sd(z_score_values)), add = T )\n",
    "         \n",
    "} "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 620,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iPJTALWArsEnYmGgQLWljNYacpEO9iPCtxPyqWHkFkm5EoJWH1ZepuG94fGgQc8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      "text/plain": [
       "Plot with title \"Histogram of z_score_values\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 600,
       "width": 1200
      },
      "text/plain": {
       "height": 600,
       "width": 1200
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calling the zscore function to plot the graphs\n",
    "par(mfrow=c(2, 2))\n",
    "options(repr.plot.width=20, repr.plot.height=10)\n",
    "\n",
    "for (lambda in c(1,5)) {\n",
    "    for (n in c(10,100)) {\n",
    "        plot_z_score(lambda,n)\n",
    "    }\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Difference between the four plots:**\n",
    "\n",
    "\n",
    "* When N = 10, The calculated values of the zscore are **slightly different** from the theoretical values of zscore.\n",
    "* Also, When N = 10, the values of zscore lie in between 0 and 0.20\n",
    "* When N = 100, We can notice than an increase in the value of N, causes a **significant** decrease in the value of zscore.\n",
    "* Hence, When N = 100, the values of zscore lie in between 0 and 0.04\n",
    "* As the value of lambda increases, there are **higher variations** in the values of zscore.\n",
    "* For lambda = 1, the values of zscore increase evenly and then they decrease after a point.\n",
    "* However, for lambda = 5, the values of zscore do not follow any pattern. \n",
    "    * They gradually increase till a point, then there is a sudden spike and then they decrease suddenly.\n",
    "    * These variations of sudden increase followed by a sudden decrease are greater as the value of N increases.\n",
    "    \n",
    "**Also, we notice that the graph is not smooth when N=10. However, as the value of N increases, the graph becomes smoother.**\n",
    "   "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}