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  7.     "Before you turn this problem in, make sure everything runs as expected. First, **restart the kernel** (in the menubar, select Kernel$\\rightarrow$Restart) and then **run all cells** (in the menubar, select Cell$\\rightarrow$Run All).\n",
  8.     "\n",
  9.     "Make sure you fill in any place that says `YOUR CODE HERE` or \"YOUR ANSWER HERE\", as well as your name and collaborators below:"
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  18.     "NAME = \"Juraj Vasek\"\n",
  19.     "COLLABORATORS = \"\""
  20.    ]
  21.   },
  22.   {
  23.    "cell_type": "markdown",
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  25.    "source": [
  26.     "---"
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  44.     "# CS110 Pre-class Work 4.2\n",
  45.     "\n",
  46.     "## Part A. The Hire-Assistant Problem.\n",
  47.     "\n",
  48.     "Imagine that you need to hire a new assistant. Every day an agency sends a new assistant for you to interview. If the assistant is better than your current assistant, then you fire your current assistant and you hire the better assistant. You may assume that assistant quality is uniformly distributed between 0 and 1.\n",
  49.     "\n",
  50.     "## Question 1.\n",
  51.     "Write a function, named hire_assistant, that takes applicants (a list of the numbers that represent the level of qualification of the applicants; the higher the number, the better qualified), and returns the number hires if the applicants are presented in the exact same order as the input list applicants. Note that your function should not randomize anything (or else it would be called a randomized algorithm)."
  52.    ]
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  70.     "def hire_assistant(applicants):\n",
  71.     "    \"\"\"\n",
  72.     "    Return the number of assistant hired.\n",
  73.     "    Inputs:\n",
  74.     "    - applicants: a list of the numbers that represent the level of qualification of \n",
  75.     "    the applicants; the higher the number, the better qualified\n",
  76.     "    \n",
  77.     "    Outputs:\n",
  78.     "    - hires: Number of assistants hired\n",
  79.     "    \"\"\"\n",
  80.     "    best = -float(\"inf\")  # initialize the best variable with the lowest possible\n",
  81.     "    counter = 0           # Initialize the counter variable\n",
  82.     "    for i in applicants:  # Lets interview all aplicants\n",
  83.     "        if i > best:      # Check if the applicant is better than current one\n",
  84.     "            best = i      # You are hired!\n",
  85.     "            counter +=1   # Yes, another employee \n",
  86.     "    return counter        # Finally, we went through all applicants and we found the best"
  87.    ]
  88.   },
  89.   {
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  105.    "outputs": [],
  106.    "source": [
  107.     "assert(hire_assistant([1])==1)\n",
  108.     "assert(hire_assistant([-1, -2, -3, -4])==1)"
  109.    ]
  110.   },
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  125.    "source": [
  126.     "## Question 2. \n",
  127.     "Assuming the applicants are presented in a random order, write a function that receives the number of applicants as input and returns the average number of assistants hired.\n",
  128.     "\n",
  129.     "**N.B.:** Don’t forget to run the simulation several times for each given number of applicants to better estimate the number of hires (please refer to task 3 of the Study Guide)."
  130.    ]
  131.   },
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  149.     "import random\n",
  150.     "def experimental_hires(N):\n",
  151.     "    repeats = 100  # Configuration constant that tells us how many times we want to repeat the simulation\n",
  152.     "                    # This variable has significant impact on performance and precision\n",
  153.     "    resutls = []    # Empty list for resutls\n",
  154.     "    for i in range(repeats): # Making multiple trials\n",
  155.     "        applicants  = random.sample(range(N*100), N)\n",
  156.     "        resutls.append(hire_assistant(applicants))        \n",
  157.     "    return sum(resutls)/repeats\n",
  158.     "        \n",
  159.     "        "
  160.    ]
  161.   },
  162.   {
  163.    "cell_type": "code",
  164.    "execution_count": 5,
  165.    "metadata": {},
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  167.     {
  168.      "name": "stdout",
  169.      "output_type": "stream",
  170.      "text": [
  171.       "For 1 people: 1.0\n",
  172.       "For 10 people: 2.9\n",
  173.       "For 100 people: 5.2\n",
  174.       "For 1 000 people: 7.33\n",
  175.       "For 10 000 people: 9.85\n"
  176.      ]
  177.     }
  178.    ],
  179.    "source": [
  180.     "print(\"For 1 people:\", experimental_hires(1))\n",
  181.     "print(\"For 10 people:\", experimental_hires(10))\n",
  182.     "print(\"For 100 people:\", experimental_hires(100))\n",
  183.     "print(\"For 1 000 people:\", experimental_hires(1000))\n",
  184.     "print(\"For 10 000 people:\", experimental_hires(10000))"
  185.    ]
  186.   },
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  201.    "source": [
  202.     "## Question 3.\n",
  203.     "\n",
  204.     "Use the function below, `analytical_hires(N)`, which returns the analytical expected number of hires, given the number of applicants, along with the function you created in question 2 to create a graph with two curves such that:\n",
  205.     "* The x-axis shows the total number of applicants (make sure label the x-axis)\n",
  206.     "* The y-axis shows the average number of hires (make sure label the y-axis)\n",
  207.     "* The graph contains two curves;\n",
  208.     "    * Curve 1: the theoretical performance estimates computed calls to the function `analytical_hires`.\n",
  209.     "    * Curve 2: the simulated or experimental estimates using the function you created in question 2.\n"
  210.    ]
  211.   },
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  227.    "outputs": [],
  228.    "source": [
  229.     "def analytical_hires(N):\n",
  230.     "    \"\"\"\n",
  231.     "    Return the analytical expected number of hires if there are N applicants\n",
  232.     "    Inputs:\n",
  233.     "    - N: Number of applicants\n",
  234.     "    Outputs:\n",
  235.     "    - hires: Average number of assistants hired\n",
  236.     "    \"\"\"\n",
  237.     "    # from the textbook, we know that the analytical result is \n",
  238.     "    # 1 + 1/2 + 1/3 + ... + 1/N\n",
  239.     "    hires = 0\n",
  240.     "    for n in range(N):\n",
  241.     "        hires += 1/(n+1)\n",
  242.     "    return hires"
  243.    ]
  244.   },
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\n",
  264.       "text/plain": [
  265.        "<Figure size 432x288 with 1 Axes>"
  266.       ]
  267.      },
  268.      "metadata": {
  269.       "needs_background": "light"
  270.      },
  271.      "output_type": "display_data"
  272.     }
  273.    ],
  274.    "source": [
  275.     "import matplotlib.pyplot as plt\n",
  276.     "%matplotlib inline\n",
  277.     "stop = 1000      # Maximum number of aplicants in our simulation\n",
  278.     "precission = 10  # Incresement between the values\n",
  279.     "step_list, experimental_list, analytic_list = [],[],[] # Initialize the lists for the chart\n",
  280.     "for step in range(1, stop, precission): # Generate the data\n",
  281.     "    step_list.append(step) \n",
  282.     "    experimental_list.append(experimental_hires(step))\n",
  283.     "    analytic_list.append(analytical_hires(step))\n",
  284.     "plt.plot(step_list, experimental_list,label=\"Experimental curve\") # plot the first curve\n",
  285.     "plt.plot(step_list, analytic_list,  label=\"Analytics curve\")      # plot the second curve\n",
  286.     "plt.legend() # show legend \n",
  287.     "plt.xlabel(\"Number of aplicants\")\n",
  288.     "plt.ylabel(\"Number of hired applicants\")\n",
  289.     "plt.show()"
  290.    ]
  291.   },
  292.   {
  293.    "cell_type": "markdown",
  294.    "metadata": {
  295.     "deletable": false,
  296.     "editable": false,
  297.     "nbgrader": {
  298.      "checksum": "f5c0fc54ac7e38140eacf7a0d3877a00",
  299.      "grade": false,
  300.      "grade_id": "cell-8720f8d8a6a98422",
  301.      "locked": true,
  302.      "schema_version": 1,
  303.      "solution": false
  304.     }
  305.    },
  306.    "source": [
  307.     "## Question 4.\n",
  308.     "\n",
  309.     "Plot a graph with the x-axis showing the total number of applicants and the y-axis showing the probability that exactly one assistant is hired."
  310.    ]
  311.   },
  312.   {
  313.    "cell_type": "code",
  314.    "execution_count": 8,
  315.    "metadata": {
  316.     "deletable": false,
  317.     "nbgrader": {
  318.      "checksum": "99500575978918dad34be4dfe49fff36",
  319.      "grade": true,
  320.      "grade_id": "cell-d3fe1b7d6d175ad7",
  321.      "locked": false,
  322.      "points": 0,
  323.      "schema_version": 1,
  324.      "solution": true
  325.     }
  326.    },
  327.    "outputs": [
  328.     {
  329.      "data": {
  330.       "image/png": 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\n",
  331.       "text/plain": [
  332.        "<Figure size 432x288 with 1 Axes>"
  333.       ]
  334.      },
  335.      "metadata": {
  336.       "needs_background": "light"
  337.      },
  338.      "output_type": "display_data"
  339.     }
  340.    ],
  341.    "source": [
  342.     "def experimental_hires_target(N, target_value):\n",
  343.     "    repeats = 100  # Configuration constant that tells us how many times we want to repeat the simulation\n",
  344.     "                    # This variable has significant impact on performance and precision\n",
  345.     "    resutls = []    # Empty list for resutls\n",
  346.     "    for i in range(repeats): # Making multiple trials\n",
  347.     "        applicants  = random.sample(range(N*100), N)\n",
  348.     "        resutls.append(hire_assistant(applicants))        \n",
  349.     "    return resutls.count(target_value)/N\n",
  350.     "\n",
  351.     "\n",
  352.     "stop = 100      # Maximum number of aplicants in our simulation\n",
  353.     "precission = 2  # Incresement between the values\n",
  354.     "step_list, experimental_list = [],[] # Initialize the lists for the chart\n",
  355.     "for step in range(1, stop, precission): # Generate the data\n",
  356.     "    step_list.append(step) \n",
  357.     "    experimental_list.append(experimental_hires_target(step,1))\n",
  358.     "    \n",
  359.     "plt.plot(step_list, experimental_list,label=\"Experimental curve\") # plot the first curve\n",
  360.     "plt.legend() # show legend \n",
  361.     "plt.xlabel(\"Number of aplicants\")\n",
  362.     "plt.ylabel(\"Probabilty of hiring only 1 applicant\")\n",
  363.     "plt.show()\n"
  364.    ]
  365.   },
  366.   {
  367.    "cell_type": "markdown",
  368.    "metadata": {
  369.     "deletable": false,
  370.     "editable": false,
  371.     "nbgrader": {
  372.      "checksum": "998ef0b673bc47c929e5543e6f86ccb2",
  373.      "grade": false,
  374.      "grade_id": "cell-2bd2500c3ca4cf02",
  375.      "locked": true,
  376.      "schema_version": 1,
  377.      "solution": false
  378.     }
  379.    },
  380.    "source": [
  381.     "## [Optional] Question 5.\n",
  382.     "Assume that an assistant is able to perform an amount of work each day that is equal to their “quality”. You have a total amount of work M that needs to be accomplished. Your costs are as follows:\n",
  383.     "* X = daily salary for the assistant,\n",
  384.     "* Y = fee to the employment agency,\n",
  385.     "* Z = retrenchment fee for the old assistant.\n",
  386.     "\n",
  387.     "Try to formulate an optimal stopping rule (ie. at what point should one stop requesting new potential hires from the agency?) Make any necessary assumptions to ensure the problem is well-formulated.\n"
  388.    ]
  389.   },
  390.   {
  391.    "cell_type": "code",
  392.    "execution_count": null,
  393.    "metadata": {
  394.     "deletable": false,
  395.     "nbgrader": {
  396.      "checksum": "43b6a51878665a39b0ede1313448eaa6",
  397.      "grade": true,
  398.      "grade_id": "cell-af2f0291eced6982",
  399.      "locked": false,
  400.      "points": 0,
  401.      "schema_version": 1,
  402.      "solution": true
  403.     }
  404.    },
  405.    "outputs": [],
  406.    "source": [
  407.     "# YOUR CODE HERE\n",
  408.     "raise NotImplementedError()"
  409.    ]
  410.   },
  411.   {
  412.    "cell_type": "markdown",
  413.    "metadata": {
  414.     "deletable": false,
  415.     "editable": false,
  416.     "nbgrader": {
  417.      "checksum": "b0c67a7805b6596f1ba87521c45df302",
  418.      "grade": false,
  419.      "grade_id": "cell-92211f5b42929c46",
  420.      "locked": true,
  421.      "schema_version": 1,
  422.      "solution": false
  423.     }
  424.    },
  425.    "source": [
  426.     "## Part B. The Hat Check Problem.\n",
  427.     "\n",
  428.     "There is a coat check at a party, where an attendant stores everyone’s hat while they attend the party. The attendant receives the N hats from everyone attending (all attendees come with a hat). Unfortunately, the coat check attendant forgets which hat belongs to whom. Rather than admitting a mistake, the attendant simply returns random hats back to the party goers. \n",
  429.     "What is the average number of correct hats returned? Here are some guiding questions to help you to simulate this problem. \n",
  430.     "\n",
  431.     "## Question 1. \n",
  432.     "Knowing that everyone’s hats are unique and every guest has a hat. Do you need to generate a random sample in a similar way as what you did for the hiring assistant problem? "
  433.    ]
  434.   },
  435.   {
  436.    "cell_type": "markdown",
  437.    "metadata": {
  438.     "deletable": false,
  439.     "nbgrader": {
  440.      "checksum": "259c6115bee56676178f28ab36d6db2f",
  441.      "grade": true,
  442.      "grade_id": "cell-e786799fc4eb1499",
  443.      "locked": false,
  444.      "points": 0,
  445.      "schema_version": 1,
  446.      "solution": true
  447.     }
  448.    },
  449.    "source": [
  450.     "I can generate numbers from 0 -> N and shuffle them. Also I think this may be easy to solve analytically. Now I think that maybe better approach in the Part A would be to get numbers from the standard distribution, because there is less high skilled people and more of average, what can be better represented by the normal distribution. The sampling of the range in my case is sampling from uniform distribution"
  451.    ]
  452.   },
  453.   {
  454.    "cell_type": "markdown",
  455.    "metadata": {
  456.     "deletable": false,
  457.     "editable": false,
  458.     "nbgrader": {
  459.      "checksum": "c9f8182f3dd59f572cb797f373fb7464",
  460.      "grade": false,
  461.      "grade_id": "cell-e2f68e2bd4c2d099",
  462.      "locked": true,
  463.      "schema_version": 1,
  464.      "solution": false
  465.     }
  466.    },
  467.    "source": [
  468.     "## Question 2. \n",
  469.     "Which of the following commands do you think is the Pythonic way to implement that? \n",
  470.     "```\n",
  471.     "import numpy as np\n",
  472.     "n = 100 #the number of party attendants `\n",
  473.     "```\n",
  474.     "**Command 1. **\n",
  475.     "```\n",
  476.     "hat_list = [np.random.integers(0,n) for i in range(n)]`\n",
  477.     "```\n",
  478.     "**Command 2.**\n",
  479.     "```\n",
  480.     "hat_list = list(range(n)) \n",
  481.     "np.random.shuffle(hat_list) \n",
  482.     "```\n",
  483.     "**Command 3.**\n",
  484.     "```\n",
  485.     "hat_list = np.random.sample(n)\n",
  486.     "```"
  487.    ]
  488.   },
  489.   {
  490.    "cell_type": "markdown",
  491.    "metadata": {
  492.     "deletable": false,
  493.     "nbgrader": {
  494.      "checksum": "b5e83025692b2772640e9e58f0f36af1",
  495.      "grade": true,
  496.      "grade_id": "cell-b8da78e72c1c0738",
  497.      "locked": false,
  498.      "points": 0,
  499.      "schema_version": 1,
  500.      "solution": true
  501.     }
  502.    },
  503.    "source": [
  504.     "Command np.random.integers does not exist (see np.random.random_integers(n)). Command 2 sounds ok, it is similar approach that I used in the part 1. Command np.random.sample requires list as argument. Therefore the best (and only working) python approch is command 2. "
  505.    ]
  506.   },
  507.   {
  508.    "cell_type": "markdown",
  509.    "metadata": {
  510.     "deletable": false,
  511.     "editable": false,
  512.     "nbgrader": {
  513.      "checksum": "ec25d5c32cc709928fa50666f21d9808",
  514.      "grade": false,
  515.      "grade_id": "cell-8915979a0b8cf6ce",
  516.      "locked": true,
  517.      "schema_version": 1,
  518.      "solution": false
  519.     }
  520.    },
  521.    "source": [
  522.     "## Question 3.\n",
  523.     "Now write a function `hat_check(N)` that has: \n",
  524.     "* Input: N the number of party attendants. \n",
  525.     "* Output: the number of hats correctly returned despite the fact that hats are randomly handed back to the guests.\n",
  526.     "\n",
  527.     "You should use the command you picked for question 2. "
  528.    ]
  529.   },
  530.   {
  531.    "cell_type": "code",
  532.    "execution_count": 9,
  533.    "metadata": {
  534.     "deletable": false,
  535.     "nbgrader": {
  536.      "checksum": "c37f6cdc2ca8cbb92644fa2746445779",
  537.      "grade": true,
  538.      "grade_id": "cell-c8499aeb1b1d76c7",
  539.      "locked": false,
  540.      "points": 0,
  541.      "schema_version": 1,
  542.      "solution": true
  543.     }
  544.    },
  545.    "outputs": [],
  546.    "source": [
  547.     "import numpy as np\n",
  548.     "def hat_check(n):\n",
  549.     "    hat_list = list(range(n)) \n",
  550.     "    np.random.shuffle(hat_list) \n",
  551.     "    counter = 0\n",
  552.     "    # lets simulate returning of hats\n",
  553.     "    for correct_hat in range(n): # correct hat is value and index of hat_list in the same time\n",
  554.     "        if correct_hat == hat_list[correct_hat]:\n",
  555.     "            counter += 1\n",
  556.     "    return counter\n"
  557.    ]
  558.   },
  559.   {
  560.    "cell_type": "code",
  561.    "execution_count": 10,
  562.    "metadata": {},
  563.    "outputs": [
  564.     {
  565.      "name": "stdout",
  566.      "output_type": "stream",
  567.      "text": [
  568.       "For 1 people: 1\n",
  569.       "For 10 people: 2\n",
  570.       "For 100 people: 1\n",
  571.       "For 1 000 people: 2\n",
  572.       "For 10 000 people: 2\n"
  573.      ]
  574.     }
  575.    ],
  576.    "source": [
  577.     "print(\"For 1 people:\", hat_check(1))\n",
  578.     "print(\"For 10 people:\", hat_check(10))\n",
  579.     "print(\"For 100 people:\", hat_check(100))\n",
  580.     "print(\"For 1 000 people:\", hat_check(1000))\n",
  581.     "print(\"For 10 000 people:\", hat_check(10000))"
  582.    ]
  583.   },
  584.   {
  585.    "cell_type": "markdown",
  586.    "metadata": {
  587.     "deletable": false,
  588.     "editable": false,
  589.     "nbgrader": {
  590.      "checksum": "1ff8b95312de63513a2107ffb7ab9d5a",
  591.      "grade": false,
  592.      "grade_id": "cell-086d4cc0fc5b0155",
  593.      "locked": true,
  594.      "schema_version": 1,
  595.      "solution": false
  596.     }
  597.    },
  598.    "source": [
  599.     "## Question 4.\n",
  600.     "\n",
  601.     "Plot a curve with the x-axis showing the total number of party attendants and the y-axis showing the average number of hats correctly returned. As always, remember to run several trials. "
  602.    ]
  603.   },
  604.   {
  605.    "cell_type": "code",
  606.    "execution_count": 11,
  607.    "metadata": {
  608.     "deletable": false,
  609.     "nbgrader": {
  610.      "checksum": "c4d1251529b962f3d3ce28f6ac9f244e",
  611.      "grade": true,
  612.      "grade_id": "cell-597031ea2a5a512a",
  613.      "locked": false,
  614.      "points": 0,
  615.      "schema_version": 1,
  616.      "solution": true
  617.     }
  618.    },
  619.    "outputs": [
  620.     {
  621.      "data": {
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\n",
  623.       "text/plain": [
  624.        "<Figure size 432x288 with 1 Axes>"
  625.       ]
  626.      },
  627.      "metadata": {
  628.       "needs_background": "light"
  629.      },
  630.      "output_type": "display_data"
  631.     }
  632.    ],
  633.    "source": [
  634.     "def generate_several_trials(N):\n",
  635.     "    repeats = 100  # Configuration constant that tells us how many times we want to repeat the simulation\n",
  636.     "                    # This variable has significant impact on performance and precision\n",
  637.     "    resutls = []    # Empty list for resutls\n",
  638.     "    for i in range(repeats): # Making multiple trials\n",
  639.     "        resutls.append(hat_check(N))        \n",
  640.     "    return sum(resutls)/repeats\n",
  641.     "\n",
  642.     "\n",
  643.     "stop = 1000      # Maximum number of hats in our simulation\n",
  644.     "precission = 2  # Incresement between the values\n",
  645.     "step_list, experimental_list = [],[] # Initialize the lists for the chart\n",
  646.     "for step in range(1, stop, precission): # Generate the data\n",
  647.     "    step_list.append(step) \n",
  648.     "    experimental_list.append(generate_several_trials(step))\n",
  649.     "    \n",
  650.     "plt.plot(step_list, experimental_list,label=\"Experimental Hat curve\") # plot the first curve\n",
  651.     "plt.legend() # show legend \n",
  652.     "plt.xlabel(\"Number of guests\")\n",
  653.     "plt.ylabel(\"How many guests get correct hat\")\n",
  654.     "plt.show()"
  655.    ]
  656.   },
  657.   {
  658.    "cell_type": "markdown",
  659.    "metadata": {
  660.     "deletable": false,
  661.     "editable": false,
  662.     "nbgrader": {
  663.      "checksum": "aad5d529ed9af56148bfc12691cdb950",
  664.      "grade": false,
  665.      "grade_id": "cell-f74b2078132a5177",
  666.      "locked": true,
  667.      "schema_version": 1,
  668.      "solution": false
  669.     }
  670.    },
  671.    "source": [
  672.     "## [Optional] Question 5.\n",
  673.     "As $N$ tends to infinity, the number of correct hats returned tends towards a well-known statistical distribution. State the distribution with all its parameters. Plot several samples using your code. Does the empirical distribution match your theoretical prediction?"
  674.    ]
  675.   },
  676.   {
  677.    "cell_type": "markdown",
  678.    "metadata": {
  679.     "deletable": false,
  680.     "nbgrader": {
  681.      "checksum": "33f94a80e6d5d9c371e6c39790bd67eb",
  682.      "grade": true,
  683.      "grade_id": "cell-32fe26c1d99fdd2a",
  684.      "locked": false,
  685.      "points": 0,
  686.      "schema_version": 1,
  687.      "solution": true
  688.     }
  689.    },
  690.    "source": [
  691.     "This distribution looks like the constant distribution. The constant distribution has always the same expected value and mean. we can verify it by generating very large n values, see cells bellow"
  692.    ]
  693.   },
  694.   {
  695.    "cell_type": "code",
  696.    "execution_count": 12,
  697.    "metadata": {},
  698.    "outputs": [
  699.     {
  700.      "data": {
  701.       "image/png": 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lEDI7qI2Y0Xyg3AAArC459cAZzZGPhmFMa2RQYIyVGWPzAN4OJzDUGGPz0vefNyCm0GuK2hhR6jsMkDOOjEUyLTqhzVT8wZmC9aC1Xsqy6vY0XDcs1AwLtz6yr/0vjxBkj29YCr+SYsEN0OPu+M2spoDz4SjEjAwKnPMi57zk/q1wzvPS16WlXOSgQQyh10ZzIzWwu4Zl9U4+InnokCsXEWarwxEUiKl0uw76f1u27e7ZmoYBFCQ1hY2cfERBoZiloOA0nh40KwXSyWuJ0K9BHlSsMmoX9DBAZgqLLV6jTXOmEggKteHwFEgeWwxTAIA7HzuAQ4HXOMqg+3GykBk5tr1QDzAF3dmKh4HxpEEhAUT2Uc+ZQiofdQvZU1js6YqCc5ApCE9hwAYg1WEshikcu6YI0+b4r1/t6eXSBgpi2FMFfeSK1xYaJhQG5HWHIWQ1NygMQQZSGhQSoF+50IKBpPJRxzB98lFvPIUo+WjQlJ5YUfdMwcbJh0/hBSvHnlMSEt2XU2OjxxTKdRNjWQ2MMQCO0QyMSFBgjH01yfeey6g1HapXbZo9zQ5ImUL38KWkLrJ4jT6HQy1G85DIRyYFhW6ZgoWcruCizetxz44Z7Jl7blRoU5CcKuhomvZIpXZXGqbwEwDPUxiGtNQkTOF4+QvGmArg1P4sZzhBm7bNexvJ6QJIPYXOYUmBoLlIpkCb/kLD9N2Uw1K8Rhkp3W4YDcNGTldx0UnrwDnwnQeeGxISBcllYxnn6yHYUJNioWEKPwHw5KNBX2tAfErquxljZQAnuqmo8+7X++FUOT9vIHsJvdzABVNI5aOOYfQw+0jebEkykv896BvVM5o7X4fltunIagqOXDGGEzdM4Lu/HN6g8Kkf/hrXfuOBRL8rG83AaDXFW2iYGA9lCoN/DXEpqR/inBcB/KObikrpqMs55+9ewjUOHLK800uzuTHCveAHDTKaFda77CPAn4E0NyR1Cl5KaufXCQW0nGtoblpdxL75eu8W12Ns3XkI//XLPYmkIDpMLRNBYXTuI/IUCF720RAHBQn3uK2zAQCMsUnG2O+0+0+MsX9hjO1njP0q4ufHMsZ+xhhrMMau7WDNSw75JN/LDdyTjwZ/IYwayFPI6+qiW2fLN6KcsklMwbT5QPVqCnrdbBi0UZI8MZbVhrqyudo0UW1a2JWgM63HFHTf16OASsNEUZKPMioZzYN/DUmCwnWc8zn6gnM+C+C6BP/vBgDnx/x8BsDbAHw0wWMNFL6g0EOmUE+ZQtcgySifURfd5qIh/f8ZNwOJqoCJ4g8yA8lYBFNoBJhCIaMO9fVGTDzYhyoMdcOCqjAUc7r4elTQIh/pI5R9FPE7SeYw/AjOxh/18/2c83vhTXYbWsjdUfvDFEbnYh4WEFPI6Wpi+ci0bPzfO59oeb/lgiFiCvOudLSqmHV+Z4A3a3MRngK91pzuMQXD4gP3SaJAh65H95YT/W5eV5HPOAGvl/fRDx7eh1/ummv/i21woNzAV362oyVrcaFuYjyri69FRfMQfC5JgsJWxtjHGWMvYIwdxRj7BID7+r0wGYyxKxljWxljWw8cOLCUTw3Azw566imkRnPXsKSgkLRfzLZnZvGh721vaSzn9xScYEB9j1a6QWGQN2svmAJtOgV3A602h1NCovvr0X0JgoLhpNrmXGmslzLse7c8hC/++MlFP86WB3bjPTc/hH3zDfE92+ZYaJoYz6rie17x2uD3giRB4WoATQA3Afg6gBqAq/q5qCA451/gnJ/GOT9t5cqVS/nUAJxNm6heLzfwtE6he9BGmdfVxHUKh1yPIPh+0+dQzGmigI38BOpiOUj5yGuI1wOmkHGu48qQHkQoWCViCoaFnMQUenlvLjTMnhwAKVmBal4AR3ngHL6U1GEqXksiA1UAvIsxNs45766h+4ijalhYNpbBQsNEzejdCYtkizQodA5LNpoT3kizkl8go2FayGgKlo9lRPYR/a6Qjwb4GfWUKbin0+qQms01wwJjwJMHK2iYllh3GOqGIx+RX9KrOgXOOSo9utdJhpRTncno98tHI5R9xBh7OWPsYQAPu19vZox9tu8rGyLUm5YokKk1e1m8ZovHT9EZSDLK6kri1tl0aqsHgkjTdPL4p8YyHlMIykcDZAo99RSGmCk0TRuGxXHMqiIsm+OJ/ZXY3681LeQzqugf1M37M1czWupcGqYN0+Y9YR5hQaEcaIYHjF5F8ycAvBrANABwzh8A8Mp2/4kxdiOAnwHYxBjbxRh7A2PsTYyxN7k/X8MY2wXgGgD/2/2doWzJXTVMLHeDQq+0WM55Kh8tApbPaE7KFNy6gxD5KKupmCp4TEEYzaUh8BRMr6K50zYrkZ7CEDIF2oRPPnwSAPDovvgMJJKPKHOn0/vItjnO/sfbceO9z/i+Tyf5XshH83XnOpqT5CMxS0HyFHSVgbHhMJqTzGgG5/wZatzkou27xTm/rM3P9wLYkOT5B41a0/ZK6Xu0gcvaYRoUOgf5CHldhc2dIKEqLPb/kK7bmn3kMoVCRmjZs1UDqsKwbGwIgoIb9Gx3CEtGi3+dMsKyj4DhZApVV645fl0JusqwvY2vUDNsTOZ1wRQ6lfgapo1DVQO7Zqq+71cavcsKnK85r0lmCqJttiQfMcbckZyDDwpJmMIzjLGXA+CMsYxbaPZIn9c1VKg1TZTyOjSF9Sz7yBcUhvAGHXaQ+UobQpJaBboxgzKDo10rWDame55CrYmJvD4UPWnk4rxOdfNRyj6ie6uU1/GCleN4rE1QqDf9nkKn9xFJNeUAa6o0e88U5JG7Cw3n33KdAuAUsI1KUHgTnGyj9QB2ATgJS5x9NEhwzlFzDa28rvYwKPSnn9LzBcJodjc5M4GvIDyFEPko43oKNcNCrWlhtmpgUgoKjUEWr5nea+vUiBQVzUGm0Bi+a4429byu4tg1xbYZSDXD8RR0VXGmr3UZMOnkTiD5qBcMfi7EU1hw33u5ohkAsro6FJ5CrHzkdkT9X5zzP16i9QwdGqYNmzubTz6j9k4+cm9uTWGpfBSC/7jnaTRMG3/68o2hP5eL14BkTfEEUwjceE3TRlZXRQ+dQ9Um5moGJgq6lyo4wKwQmQV1ev2NElOgzbiQ0XDMmiL+37bdzueQ10N/nzwFwLkOOk0CIfYXbPtBmn8vjWafp1APZwpZTRn+7CPOuQXgdUu0lqEE3YSFjIpCppdMwfnwJwt6Kh+F4Nu/eBbfvG9X5M/JUyCtPEl2kOcphMtHU65vNFNptjCFYWhzAXSexx70FAqZ4WUK1Dkgn3GYAgA8FlPERvIR4Ly+zplChHzkvjemvbjKb9OyhXfjZwrO842FBYURmdF8F2Ps04yxsxhjp9Cfvq9sSFCVKG1O713fGLogJ/KjN0pwKVBtmrGN24KeQpJWF3PVaPnI8RQ8pjBba2KykEFGHXz7Abliu2Om4Ob9U8M1VWHI6cpQMgU6HI1lVWxa4yQixpnNjnzkvK6c3jmLp/uuRT6S3pvF3O/z0uP6UlIbJjKaIlgoIaupQ8EUkmQfvdz9+/3S9ziA3+j9coYPNen0UsioPTvVe0whgycOVGBaNjQ1nY5KqDYtcaIKg8cUkgUFy+biJm1hCoaN5WNO9hHgMYWJvCcfDUP2EdA5U6CAJ2cPjmU038Y3LKADWEHXsG4ih2JOw6MRjfEMy6klyEvyUbfSWvA6kw8jtaYVKV+1A0lHmsKEt0CPX8y2br0ZTRkJT0EB8DnO+deXaD1DB9n8yvewwyRdwJPuBVc3bYx3GBR+/uQ0Xrx+ooWG9ht1w8LPnpjG2ZtWIpCq3DPUmlY8U7AD2UdtWl3MSzdl8MajytkptwXzgXID5bqJyYIcFAZf0Qx0nnZZN1qrggtZFdUhlI9o7G0+o4Ixhk2ri3hsb3gThZqQxZzXltfVjhk3XQexQWFRTMG55jZM5XGg7PU+Wqj7p64RRiIllXNuA3jrEq1lKFETnoKGvK713FOYoF7wHT7uoUoTl33xbnz7/mjdvV943y0P489uuBdPHOhf15Nq00KlaUXOMbBcZpDLJEtJlVMCgxSdJpNN5HUwBuycdvLWnwueQsO0hZ9AGFamQPo7meFHrx6PvMaoCwBln+V0peN7qBnBFBakgLkYmY3YwWHLCqg0LfE5LjRMUVkuw8k+GvKg4OIHjLFrGWOHMcaW0Z++r2xIIDyFjNKX7KOpLqdGHVxowOZeV8+lwq0P78ON9zwNwH/z9Bp0g0ed1Ki1BXXIbCcfUS8jhbVmHzUMJyVVU53AsGPaaa8wWcgMSfYRF8Gpc93cy9Ah5HuYMNFLyP4d4DQjnK40Q6U7IevK8lGXKalN0/axR5kpLOZ+p8K1I5YXAHhBohzDFIahojlJULgCTl3Cj+C0zL4PwNZ+LmqY4MlHGgq62jODji5Cko86palUZLWUJ76DCw2869sPipNcvy5gw7LFyTxKQrJsG6rCoLuSW1KmsLKYjTSaAWe045MHnKAwUXAKFhkbPFOgnPZuPQUZY5nhnL5Wa5rI6yoUtzKdOtQeXGi0/m5IUOi8eM17L+VsLPmeWkzwJPnosCknKJDZvBDhKWSHxFNoGxQ450eG/DlqKRY3DKBOiVSn0HujuUv5SLrAlgKcc7zrWw9ivm7ib197HID+BQX5Rox6fabNoUlBoV3xGmUerSnlwlNS3c1laiyD3XPOKMjJvA7GGDLqYE9wTlDobrpYGFPoZWp1L1FtWuLAAXgdasNmStNnmMt4QaHjgCm9l3IGUtBo7hbkYx2+jJhCUzx+GFPIjEKdAgAwxnTG2NsYY990/7yVMdadHT+CqEo6Zy+NZs9TcLuvSo/7+P4yXvahH2LPXPScWurmuVSNzW7bvh+3PrIf7zz/WLx4nTOyu1+nGvlGjMqnNy0nKGiqc6ps1z6b5KPVpZxvY6XGhHSanipkQD3nJt3PJjNgA7Bp8d4yhWz/PIWmaePVn/gRbtu+r+P/S11PCcQU9pdDmEJAasrrStfZRwBQbsjZQZZIOkh6v3/t50/jD7/wM9/35mpO/6y1k3kAfqYQLFwD3JTUEZGPPgfgVACfdf+c6n7veQG6+HJumwvD4oueCQx4p5Qw+ejhPWXsmavjoWeju0SSfNRPXV/Gs7NOgPqdk9aJlgn9YwrehhXFFKgBnk5BoQ1TIPkoGBRMm4Nzr5/9sjHvvEOfTVZTBisfmbbYRHrGFPp03cxUmnh0XxmP7Gk/JCeIStP0MwW3Q+3+UKYQIh91+N40I+SjhYaJFePOcydlVL98dhZ3Pznje8z5upPWTAGGgkK5HhUUhkM+SpLLeDrnfLP09W2MsQf6taBhQ01iCnTB1gxLyBbdIigfyTMViHbujmMKFY+KLgXoYtc1RRRC9etUI9+IUR6OYdluzxsymtsxBQPFrIZCVvXNU6DXQIYyVTUDTmM2wDnBDVI+Mm1bpB13wxSWjS0dUyAdvZtro9q0kJeycpaPZaEw+EZZEuT6IYBSUrtnCgsNfx3BivEsfr1/IbF8RNfsgYUG1rvMYL5mopTTMJl3rqnZmuGa2nZ4UNBHx2i2GGMvoC8YY0chQevs5wpqhiW06267MYaBKk1LuVamQDcWnc7DMFNdWqOZTsoZVRH6+yA9BY8pJDOa591eRjl3g6dUV2JslMtP2WDFnCZacQ9aPjIsp0hLU1hXTCEbwhTqhi2aCvYSdKDp5sRba1oYk5iCqjCsLGaxv9zKFILyUdatU+hk3oS8xnLdby6vcP2MpOyDrlmZ1czVDJTyOoo5DYwBc9WmN3UtLPvI7ZLa6cyMXiMJU/hrALczxp4EwAAcAeDP+rqqIUJV0jkFU+hFUHC1Xpl9ECh1bc9s681AOCTko6UJCtSpU1dlptCfs4HMDiI9BWE0u/JRu5TUmoHJgi4Ce8O0kc94Gq6cfQR4DA6AazQP7hzUNG1xKOm8QCs8+whwrrmwE+tiQNduN4ZptWn53ncAWFXMxTIFuXgNoLqM6BGeMvxMwS9ZLivoUFjye51+T14ryUeKwjCR1zFbM6QBO+F1CgDVzSR7Df1AkhnNP2SMHQ1gE5ygsJ1z3vopPUdBc2ABucNkr4KCKrInaj75yLlwdscyBefmW6rKVMOyoTDZbKbfAAAgAElEQVTn9NbvIeN+ozki+8htC6KJ7KP2RvNkPiMKuepu22URFHS/fESUH3CYwqCzj3SVdaU5143WTVKe09zroLAY+cjpZeRfz+pSFs+GHI6Cjf7o71qz1UOJQsNw0potm4vsI5rPPJbVUMgkL1alg8wBidXM1wysm3CkpMm8jtlqm6Ag3VeDDApJso+uApDnnD/ojuIsMMbe0v+lDQfkNDkhH/UgA4k6c8onHALdWHFBYak9BcOyRTDI9jkodJaSmpwpTEhMgQqdmoIpON8no9nHFAZsNJs2XwRTsCKZQj+mr9GBptN2HICzsRYCG/rKYi7UaJYTQACPKXRSwNa0LFHFTvcRzWcey2odZRtWQ5mCiVLeea8nChk/U4goXgMGP5IziafwRs75LH3BOT8E4I39W9JwQT69UNvh3ngKNrK6Al1VoCoswBScoLB3vh5poB6SiteWQoNsusYu4HXc7JunIN2IUUZzp57CnNsK22MKzu/TyZteE3kKchO0gdcpuPJRN0yhEcYU3ENOPw4UnqfQhXzU8KekAg5TmK40Wz5fJ9nD+/xFsO8gaDYMGzlNwXhWE+2zK9JJPq+roh9T27WTp1Bu9RQAhynMVZvSKM7wlFSgf4etpEgSFBQmdT1zB+9kYn7/OYVa00Le3UjyPWQKddNrVJYPpNPRjWVzYF9IjnbTtFFuOOl7No9fz1zV6EkVdtO0xcapKKyvowOp9mIso0am3BoWd+Qj1wyOa3PBOfc8BY02D+dxg/IRtc+WmcKgs0Kalg1dY8JMTQrb5qKvkwzKZOpHAdtcl0Yz5xxVw8JYNhgUnFqFA4H7oBZItZXlo6RouMOVxrOa2KzluqTCIphC3bDQNG2RSDJZcDwFCj7BqWsApJYqg83jSRIU/gfA1xlj5zLGfgPAjQD+u7/LGh7UDEswhLzwFBa/ydKweKA1x3q+boqTapiERMNiqHw+zmz+03+9Bx/47uJHahsSUwD6q7PTDbZ8PBvb5sIpXmvPFBYaJiybu55CICgYfvmolHOyRda5aYXA4GfnGpYTkDtlCrTmSKbQh8y1bj2FpuVkQxUCnkJUVbPs9QFokQWToGFayKgOU6B7SNb8cx2M3yVGQeuk94GYwoTrKdD1HNbZuN+ybFIkcZneCeBKAG+GYzR/H8D1/VzUMKHatISkQEGhF03x5CyJfEZpqVM4dk0RP39qJjQoHKpQ98U8Ht1XdszmYvjz7DpU64mZaFgcuua1ye5noY1zCnRu1kij2ebQVCbYS1ybCyoamijoghEE5SO6IRWF4b/edhZWupsRMFij2bI5bA5oioKc3lkbBDGfOYop9CFJwfMUOnu/gimmhKiq5mD1swgKHTMFR75dCMhHjtGcrK0NsRzAYzTE9ksuI5jM65ivG+L7UXUKtK5BIkn2kQ3g8+6f5x3qhmc0kwnWm+wjzwCU5SPOOeZqBo5bW8LPn5oJrVWgauYNCZhCuW6I318MmkvKFJzWwuMxRVadtLkgScPxFCKMZqm99GFurxrCIOsUiAHpGkNOV4WXlASDZQqd3SOybCODmELQbK4FmEJXRrObrpvT1RamMOZ6CvJwnCg49RHOGqir65wbHInxT7jtU/bMOa8jtHW2Nvgpf0Ay+eh5jarbuRHwmEJvso/s0KBQMyyYNseaiRwmC3porQL1Pdow5UgcUadpqp6k318MDMlTAPrb+oFqQ8ayamSdAhnN5CnEtbkgpjBZyAhPoRHwFOTXFsQg21wYctGgpnTkKQTTNgm0IfWjb9Zcl0ZzVRqwI2P5uFPV3MIUAga6V1jagdHspn6GeQrjlH2U4ABIa6cW2QcXGi3yEbVM2XWoivGsJjrByvDko+H3FJ7XkGmqM9awh9lHWmvbX6LfpZyOdRP5UPmITv50oo068ZXdC3Om0lx0hpKckgr0t6NjteGws7EY+ciwHebCmBMY4tpckAfjFK9FyEcxue1h2UfX//hJ/MtPnkr+oroEpdpSSmrchvEP/70dN297VnztFeaF1yn0JSW1Hj4Hux1oMw6eoKmqucVTaEYwhQ6el9h6mKcwllVbEkDarf3IFWMAHF/Bk4/8Kc5xcu4wzO4AktUpXJLke89V1AwvKDDG3DS1HslHlNUkDe/xThiO2RkmHx2q+JlCVIYOle43THvR7CYoH2U1tX9MwU0Dlm/WIIgpAM6GGWc0y/IRbf60uQYrmsOQ1Vt7H928bTe+cV//p97R69Lc4rU4pnDjPU/jfx7aK76OYgoZN2urV7NBZAhPoWOmEC4fAU5VcytTCHoKbrDvxGh2hyuN5zymIDyFjJa4xTjdWxvdoLC/3BBBgeQjOSgEM6wIo5SS+u6E33vOwbBsGBb3FdQUMqovj75b1I1w+WhOupjWT+bCmUK1ifGsJgzwKBlA7ueyWF/BMLkoFAP6O2S85hYxFWKGwZCnADgbZlzxGslHpbwuJrUJpmC0DwpO9pH/tVYaZmxr815BeAptmIJh2ZitGmJTBqKZAmMMhUy0NNctbJt3nX0kjOaQoLC6lG1pdRH0FLJCPurQaNYUFLMaFtx6H9loziVMSaXAsdGVj/bP1zFf96eeTrgV8gsNE+O58MkDwyIfRRrNjLHXAPhtAOsZY/8s/agEYPjGNvUBwU6MQHcTnsLQMC1fNSY9l0w7107mMV83Ua4bYsgK4DCFqTFdUO2o0zTJR87/MbBhqvv1Ni0bRd27XPo5OrDatLB2Qsd41gnAts1bNFjTtkWHVF1VYttczNUM5HRnU6UmcHSKFo3+4oKCpsDmXmsNwJHsKMUwLL2wV6Bg185ToKAvG6NRTAGA28Kht7exs7E6I087zbX3mELre7mymMMvnp71fS/YziKsM0A7NMlTyGng3FnDQsNJU81oCgq6hqZp+1hp6Nrd+++wqQJUhWHffAOG5ZnYgL/uJWzqGoC+t6RPijimsBvO2M06vDGc9wHYAuDV/V/a0oBzju8/tDdUfggOBweQOE2tHWSjOZdRhUEmG1SUK08ZC4SZqoFlhYygoVEnvnmJKSzWbKZceUKSjJzbt+/vauOpuS2Ux7LOzRp2WjNtDlUl+YjFFq9R3yOgtfKVNq84o5kChiyX0Xveb7YQZAp10wr1h2hk5bx0EIhiCoDjK8iewvRCAz/59cFFrZUONMvHsx0zBfLFwuSjsKpmp3eV95npKottYHfrw/taNluScCmoLzRMJ/Mt66WKA+0TS4Q5ndOwYjyD/eU65mqGrype/nekp9DnlvRJEXkncM4f4Jx/GcALAXwdwN2c8y9zzr/ttrp4TmD73jKu/Op9uH37/pafBQeJ0797IR/JTa/kXvA0NpLkI6C1hbbDFDLQ3NNjO6MZ6FFQ0GRPIZ4p7J+v489uuBffvv/ZyN+JQsWVj+hmDZOQTItDJ/lIic8Omq0a4qRGg3nqkqfgJBBEnwSDbT045+I9D2vW1kuIORaup8B5eJ+ngwvO5zufkCmMZTSf7Pivd+3A67/0c+w6VO16rSRdrRzPwrR52xkXMmptPAXAX9UclI/I7wszmp88sIA//8pW3PqIfxocffa0SZfrJhYk5kftbdodbGg/KGRUrC45XV3n616LC8AJ6vQ8Ucwy6HcNCkk8hfMBbINbxcwYO4kxtqWvq1pCkGlLurOMMPMrn1E7KpAJg+lWbwY9Bc65T4skphD0FQ5Vm6LFc5wZ21NPweKBOoX40YE0Q7qbkzSlpI5no+Uxh9KTfNSGKQRObTlN9bW5iPMTAIkpuK+32rTEyM64poW9ABXlyfM8wszUacEUvF5YsUwh42cKz7jB4DsP7ul6rSRd0cS0ThIR4uSj1TSBzQ0KnPOWoABET1+jdQVrDhqmc9Ah3X+hYTpyIPU6S+hT1EQ6rYZVxaxrNJuicI1A12BYiwtA8hSGPfsIwHsBnAFgFgA459sAbOzfkpYWtAmHbTzBnu2Aq8Uai9Nig/128hlH6zYsjvmagUJGha4qWFXMQVVYS60CMQXAOXVEGc30mhhDR0VPYaCe/oR2TeKIpYT1wm+HWtNLSQXC5THTbXMBAFo7T0FiCgB8PYQcCSG+TXGw/YDMXPodFGT5KG7TIPnIsrnY7EVFcxhTyPo9BbrGbt62u+u1knS10h1l2UlNRa1pgrFwVkNVzZSW6gyigWg7T4jqIkubupxJ5B3MVIxnnWtjoW6i0rAk+ShZXZIIaLqKVSWnq6vcDI9AQSFKPtIURwIbWvlIgsk5n+v7SgYE2rxCg0LI6aUXKanBE5zcknu+bojcZlVhWFPyZyDVDQuVpiUatxVimsaV6wbyuoqpQkZMausWTctGRm5zocdnHxFLCRu6Hvs8buviQkYVU7jC5DHT4qKa2UlJjWMKTd98BKddhMcU4vwEAC3zI+QTdtx0vF7AkOWjmFz86QXv8w12Ko1iCnKbi2dna8ioCh7ZM49f7+t8vrL8vNQipBMZpOrWHYTJeKKquew1mwNaW2LkdCWURdGmLXc8JRYjy0cLjaB8lKyDQVXyHlcXc5iuNDG90PCxU8Azm8PaZgOOBNbPVO+kSBIUfsUY+yMAKmPsaMbYpwD8tM/rWjKUEzCFoHy02KAQ7EkjF94EDar1gVoFkrmmJPkoKm2zXDdRzGmYKuiiX1K3aGmI16ZJHJ0aw3rhx0EOxLGegu2lpOoqi61TmA0wBTJsAa//TRyCfe7l9cRNx0uCh3bP4dS/+0FLF1ACbRC6prQwFhkH5aAQKCCL8hQo2Fo2x975On7n5HVQGLDlge7YgpCPKCh0wBSqUjuZIERVs3stERsIBoUoaZc0f3lzl1ORxwNGM30t7su2QcGEwpzHIuls91xdHO4IIijEZKs5RaHD7ylcDeB4AA04HVLnAfxlu//EGPsXxth+xtivIn7OGGP/zBh7nDH2IGPslE4W3itQUJD1dwLR62Dq22ILwYI9aUSWQ9NytMi8d9Gsncxht6TLkzdAw2DihrBTUFg2lulBnUKgzYUeHxS6ZQpyFspYQk/BqWgOZwp1w0LDtDHhCwqKr06h3ZSrYPYRrWfFeMb32XSDJw5UMF1pCk0/CDklNdjhVQbJR4CXrNAwbTAWnllVyHpMYX+5Dsvm2HzYJM584QpseWB3VxXw83VHAlohmEIHQaFhhtYoAA5jXjHuVTWHpYoDrlcUwhSIIfiCgpBwVXFyX6gbrnxE81OSM4WxjAbGmPA/APjuY8CrVYgLCtkBzwMHEgQFznmVc/63nPPTOeenuf9Ocjy6AY5JHYXXADja/XMlgM8lWXCvQfJR2Gm0HsIUklY5xiHYmTMfIR8BwLrJPPbO1UV+PWURTSUwmufd+oapQqYH2Uccupx95HoKUZsHBYWZSrNjGQGAz2gO8xRoRCXgeApRTMGrZpbkI5/R3DqZLIiM6m9URtfK0auK2DNbhx3Td6kdSB6K6lhqShXN8nzpIKYrDaxwtXzyyRqGFZlZRUyBcy7kyXWTeVy4eR12TlfxwK7OFeP5miGG0zjr7OxzD2sSR1hd8qqag1PXCFE1RHT9yB6KPFyJPAQhH2X809zaHQLlVjiUKQUgWj6KCwptDltLgSRtLm5hjG0J/PkqY+ztjLFc1P/jnP8IwEzMQ78OwFe4g7sBTDLG1nb+EhaHOPkoLCXVqSq1F7URCOoq5st6F19QPlo3mYdhcXES9JgCGc1q5IbSK6bAOW9tc+GuOUrLl9Nho6SRMPjlo+gJYXJBUUZVIltne83wAvLRIrKP6Fo5evU4mpaNg5XuR5YT+4hie81QozmEKZSbOGql02ZB9hSiWFAh6wxoapi2SKtdP5nH+S9eg4ym+HooJQUdaLpp1xBsWxGEXNVci/QUIozmMPlISvbIaioymoIyZR8FPIV2crE8sneVzBSC8lE+3lMAHP9nFFJSnwSwAOCL7p95APsAHON+3S3WA3hG+nqX+72+4L6dh3DV1+5v0bjLDddoDpGPwmhqIWFGQhyCBqCsXc4HshaoVmHXIec0Ryf+yQIZzXGeguF4CmMOU+i2KZ4nYUhtLkShTXzfJaAzCakqyUcFMUvY//o45+48BVc+CngKe+fqeMfXH8DVN/4Cf/edhwF4NyTgl4+aph1bzQxInoLl31yOXjUOANidwFfYcbCC/3vnEy3f99JcIxr/hchHwc2Wc47pSgNHub13iB3V3bkUYRBzmhsm9rhMYe1EDqWcjnM2rcR3Htwj2ClhoWHiw9/bHtl0jq5dMRegE0+hGe0pAE5V8775OjjnntHckn2khK6N3lt5cw/O5h7PaphZaIr5zEA4U7j90f343i/9abvVpjeyd/lYVhxWgtlHiZjCAGd3EJIEhZM553/EOb/F/fN6AGdwzq8CsBgfIKxaKHTXYoxdyRjbyhjbeuDAga6ebHqhge8+uKdlgxKeQkT2EWP+vji9aJ/dIh+JLBsL5YY/v3nTmhIA4OdPTQPwmIJ8gUXNaS7XTRSzOpYVMjAsHjt3IQ5yWiShXUm+zBQ6MZvlQiBVcQqSgkGPNitNKl6TGcuPfn0A37p/Fx54Zha7Z2s4ccMENq3xphBlg0ZzQk+BNjkhH612HjNJWup3HtyND31ve8tr8SSp6J5GgJ8pBDe++boJw+KiIZtsNAclFoKsl++eraGU00QrlVccvRIHyg2fTwEAdz8xjc/f+QTufnI69DHnayYm8lrkOuPgZB9Fb5anHTGFmUoT/3b3Tk8+CnxuUcVrFMT9TMF/D45nNTH6dlx4Cq1jSz93+xP4px/+OvD4png/Hf+jdc43AJxx5HK86piVgtGFYZCzOwhJgsJKxtjh9IX77xXul4sRqncBOEz6egOc1hot4Jx/wfUzTlu5cmVXT0Yn62CRmlen0JqdU2taKATS5MTpYRG+QnAEJD3mwYUGOEeAKeRxyuGT2OLmjx+qNFHKaWKDHstqkXOaST6iABJWoJcEYUGhXUl+uW4K062TWgWSwuiGHMtqLSm3JBWpitzmQm5B4XymN191Jm679mxseesrsHzco/U5TRWfgdytNgpRRrPHFNoHBZmZyKDHjGIKSTwF2rzXlHIYz2q+TqVR0pg8p/nZ2bpv/ChtZnJgB7xgE2y7Iv+8W/lI3ljDcPEp6/GqY1biA999BL/a7fgdcpsLgLLKYuoUpHsk2AhxPKthHw3Acd8b+pmcykotLPxr97McqqsIykdHrhjDl684I7RAj5DtY0v6pEgSFN4B4CeMsdsZY3cA+DGAv2aMjQH48iKeewuAP3GzkF4KYI5z3n05ZRuIjbHmj2MLwmgOT2ULUtSkuctxoFNq0FPY616UQdp50eZ12L63jEf3lp2+R2OeaToe0f/IsJx22cWcLn6/W18hrGlce6Zg4ohlY9AUhv3lDphCoAfOeLaVKXhVvuGts+Pm4AJ+mUGelR2FYACsNEzkdAXLxjIoZNRE8hGdTIM56I02TKEpzVOIOoFTjcLy8QxKOa0jplBpmtg9W8N6KShQxe18QFKlYBgVBIV81EW3z2rTimwpDTg5/P/4+yeikFHx6dseB9BqNEeli1NdiVzkKYYrUVDIadg7T1PRnMdVXKYqT0XcN99oOVzVAkGBUnKD2UdJMBKeAuf8v+BkCP2l+2cT5/y7nPMK5/yTUf+PMXYjgJ8B2MQY28UYewNj7E2MsTe5v/JfcPyKx+F4E29Z5GuJBWnKwQ9UGM0hnkK92RoUeuIpuCeBXKB4jTbP4AnjtSdS/vizmK161cwAInP5F6R2GfT73Rawybo2gTJyok6D1PvFGZDSgdEc0IvDBu1YFjEF2VPw5CO502UYWo3mZBXNQuppWhjPOimI6ybDByEFEckU2noK7uYVk5JKTGHFeBalvO6bftaWKTQs7J6rYe2klzNSEima/jXRvRJVsEdJEnFZUlGotZGPAGBVKYcPXXyCOBS0GM2aEtowMDYl1f3si1lNvG/yYULONiw3TNQMCzXD8m3cVcP0nf5XRTCFJBiGlNREoYxz3gDwQCcPzDm/rM3POYCrOnnMxYBO30HqRxd607Ld9ETvQqMqSxl0wS+m7XBYmwvAk1mCJ4yVxazIHy9mdayd8G7gQkT77LIUFKhPUretLkRTNrmiWWvPFEo5rxdMUgT7TclFVgRqaSGK1xR/mwsngyR6o3cqX2mTTpCSGlK8Ru/7usl8oloFOQVWhhxowiBXNNs8XLKjvkfLxzMo5XWRfVQ3rEi2RO/vgYU6ZquGTz4ibyFYu0MMJCwImpaNStNy5aPoLKkwcM7bykeE81+8FpecugFbHtjd8tpyGRXczaiSWYSoaJblowBblx9L/rfcT2m/dLiZqxlYVfSkZPnweNSKMRRzWmSPozj0c/Z5UjxvxnHmdGe83qx0WiaJhYyh4MmoZnhZBQTaDDodNygjaHLR4BcqzgkaVIAjIT0zU8P2vfM+pjAewRToBi7mdI8pdBkUQj2FNhLBQsPxM6gXTFJUXXOfWFTYnGY6KYo2F5q/eK3SjJ9xkNOo15SdKCVVDFS3vKBAjx81CCkI2siDG7rIaIoaO2o5BWiqwiT5KOgpNMEYsKyQQSmne3UKcUzBvY4f37/gvg4vKHhdQ8MPUGGeAv2slNe87KOEm1vDtGHz8AE7Yfjw752IW695VWudgpi/7X9ez2gOG0DkyUeE8QBTIElKvo7nJMWh0rB8g7j+5GUbces1rxLZcZ0g26bR5FLgeRMUAMdXkOUjCgJr3JN3cPNxKK3/LUpa5RiHIHXVVAUZVfGYQgjtfLWbP25z+DwFkcvfDGcKpZyGUk6DqrCuC9i89s2tQSHsVMM5d4OC7uaXdxAUGibyuiqG6oTJR2ZI9lEz4CnEFULJMkwndQq02Sw0TOHlrJvI4+BCs+0hQQz1Cbxfhum8lkimYHPoijuL2h2jGQzEBxcamCo4rdRLec3HFKKa/dGcZgoK60I8hSBTEEEhpGBvThoO1elcgLhRnGFQFSbmk8vIhaSQAp7RXDdskbkWJh8RZJaZl6avyYx31n29tu10bC1I/z+jKcJs7hTteootBZIUr53pmspgjL2eMfZxxtgR/V9a7zGR18WHCXgX+doJ54YoBzKQaobVkinQy+wjWfPO6QqmKyQftQaFUk7Hb2xaBcCrZgYQWfVblpgCY8xpitdl/yMjzGiO6cNTbVqwbO4whWIOh6pG4gs92AMnrGKbMnKiWmfLnS7DQLn79LjtuqSqCoOqMHGql1shRA1CCqIh5KrOso8M06vcdtbeWqA1vdDEcvegUMrpgeK1eKbw65Cg4LRsCGMKhlhzsGCPmOlEXo8MXlGg1x4XyJOAspGCAVo+MNVEgoFb0SxlHxHGAg0wKWjJhxs6XFLSSNKA1g6jkn30OQBVxthmAP8fgJ0AvtLXVfUJkwXdR/voQl7nMoWgfFRtmqFNt4DFGc1104KuMt+Iv7yrhzIWPa7vdSetAwBMSdW5kUZzwz8jdtmY3rWnEGo0xwQFz8/QRVpq0qrmoD4bxxTkNheypyB3ugwDBQE63bZjCoC/VbgsT5FB205CCo7/JCSpU9ADh4cwprBcyo0vN0xYNkfdsCOzj+i63jldhcKA1UUvZVdRmJPaGsEUgNaCPUqDpQNN3OjQIOLmM3cCko/CmAJllVMAkrukAtGeQj7jJSXICRMkQ3fKctphVOQj0zWFXwfgnzjn/wSg2Ob/DCUm8xmf0VwW8pFzSgqeSIMbFNA7phBWeAM4ASE4j5hw7nGr8fZzj8a5x60W34ua0ywbzQAW1T47tHhN5KKH1UcQS9FEL5ikZnO1aaKgy6c2b04zwWqpU3CK1yjrpNIwY6tGaaOkA0K7imb6HdloprRF0uLbtdCOYgr0/Sim0AwMN8pqIUyh0hR9j0pSjUFcXydKt7RsjjWlXIv+XcrpIfKRgcNd2SYYBL0xsm6Ov548tbJXG2vUAanatASTovu2pU7BvU+CWWty9tH+cl34j7SPiIDWhm0mRUZzpNBuuw/0AkmCQpkx9m4ArwfwXcaYCqDzXKshgCMfeRsjbV6UzdMSFEKmO+VF9tHijOZgwRRtVGHSESGjKfir844R/eoByVOIkI/GBVPILD77SE2WfSRPj6NeMEnN5mrTEno3gNA5zRSkNJKP3OBADMLJeY8vEAI6ZAqaIhnN3uOTH9WuhbacAitDfswwmJYtXh8QrjkfXPCa4VE66XzNdA4fMZsVXTuydEQo5rRQo5kqw4NBQfYUACd5IqkMUu0RUwjzQkjzp/eHnoumrlFhKrHzoOwoN9nbP9/AUSvHoSpMyEdeV9/FSV+EOFl2qZAkKFwKp232Gzjne+H0J/rHvq6qTwgazZ6nEB4UwvqxKG4WyOKyj1pz4+mG6DS3OWpOc7luIqMp4nmo/1E3aIYyBX+Vr/+5PabgTc1KyhT873nY6a+lzYW7LvIV5E6XYci1yEftNyOaH0HzmYmJZDUVK4vZtvJRM8pTMFszY2QE5aMgU6gbFsp1s6W1wmytiaYVb6LTRrY2Mii0XlMbpvIYCynYIx+Dnj+rJ5dBqj3aWCmVdl4KZqT5k7zmBQU/i6LDU/AwUfAZzXWsLuV8h0vBcmI8rE4wKkHhrzjnH+ec/xgAOOdPw5mvMHKYKOhomLbY0GnzopPSQuCE0TDt0NNLp+2zn5mp4mdPeP1iwgxAYiBh6ajtEDZoZ77u76G0rJDBoarRFS0NM5qDGTkyZE9hWSHTUVVzsAdO2Jxm0eZC9dpcAIBhu5t2G0+BUoCJ0SRhCtTSmOYzy4+fpFYhKvuobZ1CQD4KegqUZrw8IB+RhxPHFCj4rptszZQp5nRf4oVlexllYQV783UDqsLEYzpFWP7XdPeT03hmpnVuBN1LcYE8CUohTIEY2PIxYgrh6bp0nQXNbsdoNkU18+piFpN573Apuvr2SD4iv2uQGUhJgsJ5Id97Ta8XshSgnvr0gdJGs6qUBWP+jWchJiOiEFJQFYfP3P44/uKrW8XXDY9dD3wAACAASURBVMNq0bHzQj7q/LQUZsaW3VkKhKmxDCybt5iHSSBX1RKCufv+5/bkI0VhHVU11wJFTGFzmokR6CL7yPnbMJ26A7nTZRiCTCGRp+AazfS5y4+/qphta6SLOoWg0Wx5DCJsJkRLy/KALEPVzHL2EeB5OHEBz6u1aM8U6N4o5TSsDQmCNKie5Jiwytyrb/wFPnWbv5kc0DujWQzLke4FeuwgU2gG2Pp4hHyUz2ioGzbm60418+pSDhMFr2rc80N6Kx8NsoAt8ophjL2ZMfZLAMe6k9Hoz1MAfrl0S+wdgv2PynUTWVdiGc/4bwLqJ7OimGl5nOB823bYPVfHfN0UtNYZARnQLruUj2g9waZx1AyPQJPauvEVKJdeT8wUvHRYwNk0k9YqtMhHIXOaKdNIFfKR5ylQcExiNM93IB9RS2MKTvKpNsk0vnZMAQj3qUzL9rUszwUMXO86dU7CNGGOqm8TMYWJ9kFBlgTDCvaCc0CyUtNB8TtVIzR1t1fyUV53OuvKXkjVoCl5zvtTkzyFpPIRADw97TCcVSU/U6C1LzagEYZdPvoagAsB3Oz+TX9O5Zz/8RKsrecI9j+ar5ti4xrP+fPhvRNYFkHEjcAMA5msdCPVjdaskF7LRzRLgUBdYrvJQPI8BW9zUhUGTcrd9z+3M7OWNs5VpVxHKany5hDmKRBTEBXNLmMwLNuTImKDQsBobtMlFfCyj8Ka7UW1bJYRWafgCwqt15RhcV9mUDDVU/Q9GvMbzSTXRc1TADwWHG406yjXPbnRS3HWQwv2qNeVWKeu+EZjNkwLTcv2tYoQrztkwmE3YIy1BDO6HlYGjeYAW6dDRPAwQffljukKAGey2mQh0+op9DooDLBWIfKK4ZzPcc53APjfAPZyzncCOBLA6xljk0u0vp5iItBCulw3xE0U3FjlfjJBxI3ADANRecpQCfZmAWT5qPOgEBakaJYCYTH9j2jjCs76zURkmJTrhmgYByRnCmTihslHC7FGs8sUpJkRnRnNybOPFkKYSE5XYlOUTcsWPkhQKzYsLt7XMKbQtFqL1+THOCh1SAWcjV5hsnwUwxSy/rRaGcWcBsPiIpjJkmBYwd58zT9GNihzkV8X5i2FzS3pFsGg0CofSZ6CLjPScKZADGAnBYVS1jGaq375aLGFd4S4VO+lQpJP4VsALMbYCwF8CU5g+FpfV9Un0Gl5TpKP6DTdyhSc31k5HsYUkstHTdMWZiDlsocazUI+6vziCmcKQfmo+/5HYXUKgCupRHgKsp+xupSsqjmsB05YxbbX5iLgKVjhJ/kgqEakE/lIeAohj5/LhPfxl18XIaxOgWTNsGvKCPEUZKYwvdBAXlfFehSFoZjTRVCIYwqTeafVdpiPRSmaJHmKFOesFBQkCWmuZvgeJ1inQJ9f2HVQaXiD7xeLYlb3yUf0edH178s+kt5XRWGYKui+CX2AzBQc+Yiyj8p1E6Zliw6szyX5KMkOZHPOTcbYxQA+yTn/FGPsF/1eWD8QlI9kM3Y86z9hEC2Xm88RxjpgCgek6VW7RVBolY/o9DpR6IYptDaNCzOaAXSVlhqWfURfhzGF+UBAkquaN0y19qwh1EKoeNicZnnwDCBlH8lMoc1wdKAzozmrqa7R7KxxXDIkc+7P5LnRMmSZJSwlde1EHvvLjVBJ0rBsH0PLSVPjAH81M2Eir+NgAqbwplcdhYtOWhe6GcudUlcV/Rlly8ec9cgFe/N1M+Ap+I1mOZMpeB3UDLNnm2ox56/EJq+nlNehq8xnNAevkX/9szNaMrEKElMoZFSMZ72hVfN1E9WmBU1hia6hJIjrKbZUSPJKDMbYZQD+BMB33O+NZPFaIaNCV5nof+RjCoGNfnqhiamC3nI6BsLbOUdBlk1EUDBC6hRIPurKaNZa8vgrTcu3MY9lVGRUpav+RzToRQtseFlNjaxTkF8HVTW3y0AK05bD5jSHNcRzvu8Zwe3m4DLWuXzUMC3xPsu+R65NGqGPKYRkH9FBIMxTMC0ugh89lxyIpytN31Q5wMlgO5CAKawq5XDSYeFKcLAQjDbaUk7D6gnn+eRahVb5yF+nIKd7B6+DdvOZO0ExUIkta/6FjCZO9mFs/aTDJsW1SqD78qmDVVFz400ybLrzmXuzdkCWj4Y7KPwZgJcB+HvO+VOMsSMB/Ft/l9UfMMYwkc9ITMEfFCoBozl4sxHCUkCjQMZaMauJm8jRM4NGs/N1N55CcE6zPGCHwBjDVJf9j+i0GjxR0kYZRFC6WiWYQryvUAvJQgmb09zS5kIj+YhLKaPRNypjTgFix55CpNEc3tKaEM8UbNHLKqyqOSwlVR4kc3ChiZUBplDK6VJvn+42LI8p+OWjojtuUy7Yo26zpSBTkF63fOAKVreHzS3pFqVAJbacMirXFyUZrgR4stDBhYaYqCZS22tG4jkQSeG1HR9iT4Fz/jCAdwK43/36Kc75h/u9sH5hsqBLnoKB8ayUfRRISV0RYjIDjnTgmHDtPzgy1k46fFLyFEKyjxaRkhqc0zwvpQ/KmCpkMN1VSqrf7CTITeJk0CwFQlKmUGm0MgWgdU5z0OOgNhA+T6GN8ZeTKm7bdUkFWo1m2ciOatlMkIOF/H6ZluOhUNfb8OyjVvmIc69J4cGFRkuGnCzjxDGFOASZQrluQlOYeDy5YI8OWbIfRsV+BF9QCGSiBcdZLgYt2UeC2anIu320gPB7MAwyC6CJasTs5mqG01KlRyYz4B1QkjYT7AeStM6+EMA2AP/tfn0SY2xLvxfWL1COcVBiKWY1LDRN0XjtYCWeKQDhxmAQ++cbUBWGF6+fwN75Oiybh/akOePI5fjtE9bgiOXRmnsUgnOaZf1XxmHLCnjiwELHj98MtFogBG98QtDPWDaWAWNoG5CieuAE5zQHmYLc5iKJ0QzA15AwaZfUhssUcrriSxOl9UalpTZ8qZmtUhIlQIQxBcMMNsRzNw3TwkyliQPlBg4PXDNBGacb0H2xIIKCk+JMbHH9ZE4ccv7ph4+BMeCkw6Z8z0ttQQB/UAhmoh0oN7AsJPW7u3XrWGh4rLlqOB2JdVVx64tc+ciwE/kAcnPG1YIpuEGhaoQ2zVwMyBDvZAZJr5HkGPFeAGcAmAUAzvk2OBlIIwnqfxSUWKjxGp0kDpYbWBFiMtPvAq29ksKwb76OleNZbJjKw7I59s7XQ3vSHLliDJ/941Nji42iEMzlD7bNJpx2xBSeOlgRJnpSBDNgCLRRyuCct8hHKrVirsX7GTUjvIgpKNcZESmphm23nc9MoBMvY61eSRhE8Zo7n9n/s/jOufKpLywTaSrOU7Bt/xhU8i8MG/ftPAQAOH3jMt//8WcBdcsU/H2Eghll6yby2DNbxw8e3ocb73kGf/HKF+CEDRPe8wayaBYkT0JmCpxz7JypYGMXh6HwdWuwbO6N4JSkqUJG84zmNn2hCLmM9zskg1IQJ0+hl/JRMadj/WQej+4t9+wxO0XS1tlzge8Nrq/rIkGDzSkboiQVrwHOxds0nbL2FVFMIcT8jMK+cgOrSlmRxrfzoJPv3O0JLgzBOc3BimLCae7msXXHoY4ev2nylhoFwNmggvJR3XBy8oPP7YyJjA8KUYVAwToMS2QfOWvKSEyh2oyfz0yg4JvVWr2SMFD6rTyfmUAnxWijWfIUrNagUMhqyKhKaP+jpmkLI53WATisZOvOGWRUBSdKmzGAlsribuCN5PTkIznQr53Mo2ZYeMfXt+FFa0u45rxjfP/fM9+9aXWMOYcf+RS8v9xA3bBxxIqxrtYZRHC+tKP5O+uWm9s1jNauAmGQP2symkkmm60ZqIaM7F0sNq0pDn1Q+BVj7I8AqIyxoxljnwLw0z6vq2+gmQrBeQNy4zWagBYtH7WmSUZh/3wdq4o5USD0pAgKvUlhA1rnNAdfG+HF60vIagq27pjp6PENK5xqhzGFcoSfIQ+Uj0JkUMiooXUKwTYXhqv5t5OOAO/EnXTTzGgKOHf085aB8e57U2tGGc3O94tZTXRFBaRBL6qCQlYNndNsWDwwoc/bbLfuOIQTNky0sMtSDzwFYnflgHxEWO+mbtZNG5/8w5Narg+PKXiS5njG6ZorVzXvcO+HXjIFWi/gb8VORjPnPLmnIL235I1pqoJiTsNs1XB6dfXIJCccs7qIJw4sDCwtNckVczWcrqgNADcCmAfwl/1cVD8xWXA0R8rCoZOF0FAbptdPJtJopt9NYjQ3sLqUFe25n6Kg0OXNGobgnOaojTmrqdi8YRL37uyMKRhWuNGc1RXfJgf4ZynImMhrYjpXFKoh6Z5Aq3zUMnlNanPRbj4zgTbypMGZNr1D1aavRgHwz3wOA22MxZzmu9FFpbimuGnOUcVrrXMs5moGfrlrDqcdMdXyf4j9MtZahd4J5JkKQfnohavGAQB/85pjcczq1plbwXYNlYaJcXe+hlzVvNMtCtu4vDdMgRj/vGAKnryT1zXUmhZMm8PmyT57VapBIPkIoIQVA5WG1bO22YRj1xRh2lzsFUuNJNlHVc7533LOT+ecn+b+e3AuyCJBOca7DjkmmccUnO8v1E2v71Fbozl+k6Nq5lXFHIo5HcWc5gWFHspHwapfL6e8NZPptI1TeOjZuY4mxzXNcE8h2wlTSCIfRfTAGc9qvhYQrZPXvDYX7eYzE4R8lDA40+Y6U2lGtkKoR8lH7sZYyut++UgqCnROsf7riXMO0w62znaea+uOGTQtW0iCMsT0s4TSWBTkTJ6gfPTCVUX8/G/OxeVnhtuL2RD5aDyrYXVgZveO6Qp0lYlD02JRamEK3iS/QkZFpWmKNSUtOKPrkeQjwFEcZqtNd457b4MCDTLavne+p4+bFEmyj25njN0W/LMUi+sHSG995pBzQvGMZueDXWgYosVFe6YQHxSompkqetdP5qWg0Eum0Cof6SoLfY7TNy6DaXNse2Y28eMHc+UJDlMIBoXwzCfycuIQ1QMn797MBNEQL6TNRVL5iGSVpCfpjBvED4UEhVwbo7ktU1AVFLJaS/YRpZ2GZR/95PGDAIBTQ5iCGHSzyIOHPFMhWJAI+DfJIILyEX0uqwIzu3dOV7FhqtAyDnQxa6bnA/wjdQtZRz6i9z3p+5PXVVHNTHAG7Rg+z6JXeMHKcWgKG5ivkOTVXCv9Owfg9wB03pR/SECZAzTsQ8hHWc+gov5AkUZzxCzYIKhIh26EdZN53PnYAQDxLY07RXBOM6WEhp0STznc2US27pjBy16wPNHjd+YpRMlHyTyFgq62rHvMzRrhnIMxBtO2wViIp2A7RnOSU2euC08BcIbhBJvtUYZKVP8j8hRKUk8iQBpzqinOLOoAU/DqMfwVzQBwz1MzeMHKMZHCKEOMxFykRFnMaZipNME5b6k9aYdgvj0xjVXSJL4NUwXsmK50lYYdt2Z6PsC5ptZNukFBd4Iyvc9JD2b5jNpyv04UdOw6VEXdsHtWeEfIaAqOXDE2sKCQRD66T/pzF+f8GgAvWYK19QWTgikE5KOct9EfXGggpyuRtJC+HzUti0DFWmRQrZvMCemjt0xBdZ/PCUJBqi9joqBj0+oitkq+wmdufxzX3LQt8vHlTp4ywrKPojKfSjkdlaYl+haFwWkZEDLUKOsMmKcAZNrcl0ZKrbNNy/bNT44Dne6Tykfy59XCFMhTaMMUSnk9milkWvtXhTUizImKV7slFZVARvNiDx5kNFeaFmzeGujjEOz2KctHgHNg4pxj53S1Z34C0FqJXZVasdN9S8V2ST/7Qkb1zUUHnH2EusT2Wj4C3AykfUMaFBhjy6Q/KxhjrwawZgnW1heQp/DMTBUZVRE3jicfmW41czZSj81qCjSFtZWPyFAjmi33re9lUNBUBb953Gp85Wc78et95ZZMkSBO2ziF+3cegmVz/PSJg/jo9x/Flgd2R2Y7RBnNDlNoHe4DhGUf+U9wYYhKJyUmRL6Cadm+xnPB1tlJxjrS5tqp0QxE99yPMprrhsNsxrL+INrweQpaC1MIn43tvbYwPwGQ5aPFMgWn42hUoI+DHLwA12iW5KP95QZmKk0sNMyeMoWxjAqFBVNSXaPZ/ZuaQiZlie/4rU0tKbeT7mhfwEkp7jWOXVPErkO1jlr09wpJrpr7AGx1//4ZgHcAeEM/F9VPUN+S/eWGb+PKak7DuHLDxMGQJmMyGGMYy2ptjWaqZqZRiXLf+iQ50p3ggxe/GGNZDW//j22YqTR9sxSCOH3jMpQbJu55agbv+PoD0BQG0+aR1c6RRrOmwObwnf7LdQOMAeOBEz9JGnG+QlQPHMHM3PfbtLlgB4C3aVIdQTJPwXnMTIfyEdDKFHRVgaqwyDYXDdNCTlORUdVQppDVFKfTbYBpkHeSCWEKAHD6xlY/gR5PPvB0i5LbcTQq0MdBMAXDK14bz2liZve++bpoR91LpsCYP5VWzj4qiKDgdsdN6GOcs2kVXnqUX2qlfQTo3XxmGZvWlABgIBJSEvnoSM75Ue7fR3POf4tz/pOlWFw/4JTqO/8eD1zk1P8orppZ/G6gH08YqJpZcU+1/WIKgCNRffjiE/Dwnnk8sGuu5bXJIHPyrV+7HwfKDXzwd08AADwWQVej2lyIkZzSRjfv5qMrgSphOr3GZSBF9cAR2V7upmnZHKrEXCgoVJtm2/nMhKxUvJYEcu/9sMfPBeYcyKgbTgPEjKb4ZjTLKamFTOshwxBFenJKqrPuFeNZHL4s/ITNGEMpr/WAKTgaPGXjdcIU5MZuts2x0HSYAs3s3l9uiME1vWQKtM75uiEkR2E0uweVWWIKi/Bc5Bb3/ZCPjnUzkIYyKDDGLg75cy5jbNVSLLDXUBQmNqjgyYc6pU5XGpEmM2Es0I8nDPvdamaCbID2OigAwG8dvwZ/ePphAOJPdRum8lhTymG60sTbzj0av3Pyeugqw/aICzDYlI0Q1vs9ys8gnTuuViEqk8PzcEx3PX5PQVUYGPO04ri22QR6/7uRj8LkqXxGjU5JJabgtsqgvjxiToXqGs2GJXpvyT8P8xRO3zgVm25ayumLZgoUBGhiYDdGc8O0UTUscO59LqtKOcEUFIbYGRvdrdthCrVAirNgCpXkw5WiIA/j6WXvI8L6yTwKGRWPDiAtNcmn/AY4rbNvd78+G8DdAI5hjL2fc/7VPq2tb6CmeEGJZTzr0OXphWboGE4ZhQQzFfbN130X/OpSDgoDbN7b7CMZ/+eCF+HhPfPYvCF6YipjDBduXovte8t4y9kvgKYqeMHK8chTiRHV5iKk93uwGR6BPIU4+cgZ6NKaORRsQGjZ/tYPgLNx0pyMTuSjTrOPoh4/q6mRRnPdsJHTFbFROn13VD9TcHtv1U3PGG2arSmpOU3FCesn8NoT18au9yVHLY9MqU4KCgLUIruTqYDytUGHJ2Kvq4pZPD1dxc7pCtZN5ns2oIZQcr2QaqAVe6HFU+j+eSmLUX78XkJRGI5ZPRizOdHkNQDHcc73AQBjbDWAz8HJQPoRgJELChOFDDBdbWUKOQ27Z2swbd6WKSSZ03yg3PDlkeuqgtWlHPbM1fvCFABnw9ry1le0/b2/fe2LfF8fs7ooGqwFYVj+pmyEMKYQlbqYRD6arjRxxpGtG1mQKZghE850hWHOZQodGc2Js4+8xwxjIu2YAnlWgPN+yQOKMm5KKuAUINImY9r0c++1KgrDLVe3/3w/dPEJSV5WLCi4U4vsruQjwxL6Pr1vq0tZbN0xg1xG7amfQCjmNOydr4tDRNBo7oV8NNln+QhwJKT/eWivSMVeKiR5VzZSQHCxH8AxnPMZAJ2P8RoCTAr5qJUp7HB1znZMod2c5qZpY9qtZpZBvkKvjebFYtOaIp6drYVu2pHFa4ECJSBGPqKumxFMwbRsHKo2Q4Oxl33kBgWLt2RDaaqCWXdORicpqcmL19p4CroS2yU1pytiE6IgGvQUAH8BnPAUlP4cINqBPsdnXfkoiSxHkOUjOjyJoOBWNT+5f6HnfgLgyUfBXlp0HXVqNIdBlo/6FRQ2rSniUNUQhX5LhSTvyo8ZY99hjP0pY+xPAdwM4EeMsTG47bRHDXGeApmFK9t6CvFM4WCgmpkggkKfmEK3IGPr1yF0tZ2nkEQ+KmRUqAqLZAoz1SY4D68iLwTmRYTNQtZVJrTijuSjpG0ufCmpIZ6CrsZOXvMxBXezb0h1CsH+VUC4fLSUkOUjVWEdbX7OpD6HKSwEmAL5bOWG2Sem4MhH1Io931KnQEyh+8285AsKvZePALndxdJKSEmutqsA/CuAkwCcDOArAK7inFc45+f0c3H9AlG/oEYqZ+zEpaQC3gjMKOwLVDMTNi4vIK+riXr4LyXiLsC4lFTA3w46iikwxlDKaZGegteEsD1TMKxwT4EeO8mJ1qtTSOgpSK8/bBPI6WpMSqqXfQSEMAXVYwpyrYIwokOku6UAsbvdszWMZ7WOJAwaeeowBfdzIU9Bao+xlEwhH0hJXczBLKer4hrqh9EMAMe6aam/fDY4uaC/SJKSyjnn3+Kc/xXn/C8559/klD7RBoyx8xljjzLGHmeMvSvk50cwxn7IGHuQMXYHY2xDNy+iU0TJR8WsHBQSGM0xTCFYzUz487OOwk1/8dIl1QiTYP1kHuNZrcVsttyOkqFtLgKdMAG3RXJUNXVej8w+imtCSLULMlPQWuQjr5iw03kKSZDIaI4sXnOZQjAoWDY0hUFRmNSOPXrs6FKDgntVmlDYCWj6GqVuU2LHKqk6+Ig+MIXxnAbT5qJdTSGQktoLoxnwahX6JR8tG8tg82GT+O6De/ry+FHo29XGGFMBfAbAawC8CMBljLEXBX7towC+wjk/EcD7AXyoX+uRMeFmDoTJRwCgMG9ubhTazWk+EKhmFs+d13FiTGbQoMAYwzGrx1uYQtzGRKdsYgp1w0LTsiPnTJfy0Z1SiSmEBWPFlS6qktEcZFpyMVui1tkdVjRnE6Skho0mBZwgkNMVwTYaElOgQBHOFAYrH8mMqxOTmeAwBQsLdT9TkO+JqFqLxYDWSmyd3ltqg03G92IbBk4WdDHqs1+4aPM6PLxnHo/vXzoJqZ9X2xkAHuecP8k5bwL4DwCvC/zOiwD80P337SE/7wuimAKdAJeNZVo06yDazWneF6hmHgVsWlPCo3vLkIlgM6QpG8HrmR+cDR2+KZdy0Z1SiSlEZX0VpHkDpm23fD4yc0hUvKZ1yBTcGz84n5mQ0+KMZj9TCAsKYppfKFMYDKvUVK//V1dMQVfQMOwWBkdVzWtKub5ILyQLE1uXT/JyQF/s+zqR1/vmJxAuPHEtGAO2bNvd1+eRkaR47QLGWDfBYz2AZ6Svd7nfk/EAnK6rAPC7AIqMsWStOxcB8hTCUlKB6I1JRrs5zfvL/mrmUcCxa4qYqxm+Tp5GTO/5oKcQNUuBENcp9eBCExlVicyFH5Mmk5kWb9mY6bSWZD4z0HmdgqIw6CqL9CviU1KpTsFlVnJQcNdNZnqYpzAopgB4bKGTGgUCyUflhomM6r1+qmruh58AeNff/9/euUdLVpUH/vfdet5nd0O/b/NsmuYZXi1Ko9CjBkEjRBQHIkGFGV8THB+sWbBQx9HlmqgxUTNmEA1iXJpAxBDCYEhiEDXL4aG8mmDzHqWbbrobu++lu+/tW1V7/th7nzp1qk7VuY+qOnXv91ur1q06dapq77PPPd/53l5TCAsefxGfba8JsNeRdpmOPMtHipx19KHc8cg2ElrtZ02Ss+1S4CkR+YKIHD+N7250xKOzugY4V0QeAs4FttKgLLeIvE9EHhSRB3fu3DmNITTmjCOW8NZTVtcleHmfQit/AoQa28Q4m1/cO1EXeZR2Gjmbm5kwoj4Fb6tdHGN6G+nPBg2Aoux+ZZJDh/Kx/6jhpuvlBuYjLySS+BPAmi0uPn00cflwqHUIRynmMok1BS9EwyXJq32/0+NTgOoFdqbmowkXfRT1M71n45H8wasPn5MxRvFj9W0/w7WJvICYi+i/t502yh+edcSsv6cVF526mud37+fRFzrjcE7iaL4cG3X0DPAtEfm5u0jX9+Cr5QXgsNDrNUCNDmSM2WaMudgYcxpwvdtWN3NjzI2u69uGZcuWtRpySxYP5Pnzy06rqV8CVU3h0MHkmkKcs3nbngOMLulv+F5aWb/C11upptYHNf8T+BS8ur4ypvnKSLGZpjDZVBgPuv66YPsm1GkKTkgkMR2BFWh/+s5TOWwaNu18ti/2+4s5e1ccLlPhqWoKtY7myZBQKOZsCGe4/lG3fQpQ3652Ovhj4iukhnn/uWu56NSo4WBuCDSF8Qny2Vpzn7+zn4s8ofNPWsWHNh0z6+9p+TsnriKXEe54pDMmpERnmzFmDLgN6xdYhTX1/FJErm7ysQeAdSJylIjksRrHHeEdXCluP4brgJumOf45xf/DJzIf5X2p7fq7Q2MM2/ZMsHpRbwmFJYN5lg8XajSFcNZtlHzEpxCE4Q43Pn4j/bbccKMond37DjYVxuHua7bMRTRPofaOux3ks30NcxSgvlS0p1SuUKoYirkG0Uch85GI1PVp7rZPAcKawkzMR87R3EAotJOwozlq3umfZtRZGlg0kGPT+uX8wyPbgn4s7SSJT+GtIvJ3wL8COeBMY8wFwCnUdmWrwRhTAv4IuBt4ArjVGPO4iHxGRC50u20CtojIk8AK4HOzmcxsmY75qFmf5j37pzgwVa6pitorrF85XBOWWi3a1qTMhdvnpfFJchmJjdwaaVLqYtd48yKEg/ls4NQvleuT17yjOan5aCY00xTieip4IeHLWdttdh9b7qL2LjZtPoWRYuOgjCT4PIXxiU4LBftbE1OVurLWfv3mut5Su7nwlNW8ND7Jfc/tbvtvJVmpS4A/M8b8JLzRGLNfRK5s9kFjzF3AXZFtnwo9/z7w/eTDbS/Lh4sUc32sWz7Uct9mfZq3fa8LaAAAGyVJREFUugJivSgUjlk+xC0PVOMDmoek1voUoqXCo3hn5diBEstDxkdjDLv2HWxawG2gkKmpfRS9ew40hTZefEYX98eGUAbd1yLOZi8k4jSF8HEdjPRpTof5aDaaQobJqQrlimnaz3muGcrb8vjG1CeWVX0K6Soz04o3Hr+CgXyGHz62nY1rl7b1t1qutDHmiibv/SjuvV5k0UCO+69/Y00SWxzNfArbAqHQuX+EuWLJQJ79B8uu21pfU6GQdSWrA01hbLImWzWK1xSiYamvTJY4WKq08CnUOpozkYxmb05q5x3pze89k74YR7g3H0WdzWFNIRqtZaulxmsKVX9OGsxHM9AUctZ8NFlq77pE6esThvJZxifrS7EP9KD5CKwwu+V9Z3HsytY3rLMlifnoYhF5SkT2isiYiIyLSOeLfHeIkZiG91GqtWrq7eO+d2svagrRxufN6u+ESxmADcNtFnEVVyl1V5MSF56BUP+KqXIDn0K2/ZpC+G4/StV8VOtTaKUp5CNCIawplCq2DWo3s99n42iulrmIz3JvF368UZ/CwBxGH3Wak9cs6oiGk+TIfAG40BizyBgzYowZNsaMtHtgaSefie/TvG3PAfLZvp5KXPNEG583czSDPQ7+IrdjbLJhPwRPXKXU3U1KXHgG81kmSxVK5UrDkNQg+qjNceNx+GiWaP2jGp9Co+S1SE2laEZztyqkevzFdaZ5ChOudHYS7Xsu8edxnVDoUZ9CJ0lyZHYYY55o+0h6jGZ9mrfuOcDo4v7U1TdKQlRTCJLXYuzaBRd2ODFVZu+Bqaaagm+0ExUK1WzmJj4F98+9f6psy1w0KJ0N7dUUmuE1hcmpJj6FTERTKFciNZVq+zRbn0N3zyGv3cWVLmlGMdfHvskyk6VKx9elqinEmY96y6fQSZKs1IMicgtwOxCkuhpjftC2UfUIcX2at+050JP+BKj+M3kTT+BTiKnUmc9Yu7Gv+Z5IU4gksCUxH4XLipTK9WUucpnp5SnMNcUYTcGbk3wGrT1eceajbCRPodL1O9rfPWEFn37rCRyTIPgiSriRUCd9ClA9j2MdzbNosDPfSbJSI8B+4LzQNgMseKEQ16d5254JXreuvREC7cJfuH0N/IMtwiILOWs+iisVHqaYy1DI9sVqCoc0MbeFu6/ZgniNy1x0+uLjifMp+PBTb17yfZqh3tE8mK/VFGwzoW6bj3K85+yjZvTZ8Nw67VMYijMfhcpcKI1JEn303k4MpBcZbNBTYapcYcf4RE86maF6UQ3MRy4sMs585O98fb2kVqGHjSql7n7loKs4Gf+PGvRUmCzb2kfRPIW+7pqPfPRRNE8hrCmAEwrlap5CjU+hEPUpNO5j0SuE78Y771NorCkM9GhIaidpuVIiUgSuAk4Egv94Y0zTHIWFwGCDngrb905gTG+Go0LYp+AczU3KXIC9A67RFGKymT2NGu3s3jfZ0ik/EOpMVm5U5iLTXUdznPnIawrh/g1x0UeDeVuO3W8/WK7U+U56ifCFt1s+hWiGey9HH3WKJEfmO8BK4E3AvdgaRp3tD5dSrPmo9iKwrYcT1yAcfVQN/4T4aI2C8ym0ymb2NGq0s2u8cW/mMOHua6UGZS6yKfEp1GU0N9IUQuajXCT6CGo7zM2mj3C36ab5aETNRzMmyZE5xhjzSWCfMebbwFuAk9s7rN6gUZ/mbXt7WyjkXZLV+GStUIiLggn7FJYPF1uWCm9kPtq1r3mJC6jmhYxPlKgYGjia02k+imoK+YzVAMoVQ7li6qKPgCBJLw0+hdmQRvPRXFZJna8kOTL+P3iPiJwELAKObNuIeohGfZq37XGJaz1WDC+Mb3wOrR3NgU9hbJJlLUxH0LjRzq7x5hVSoXqH5yOX4spcdMvRnM/00SeNktfsay808lnbeCboz5yN1xSsJtG75qNiyHyUuuS1OaiSOl9JslI3isgS4JPYKqdDwKeaf2RhYGvVRIXCAQ4ZzLetmXcnGClW+x5MNclohqqm8NL4BEctbd1vN9po52CpwthEKbH5yH82rsxFOwviNUNEKObq+zQH0UfZUPRROSQUMvWagjdJTpUrDbu89QphTaHjIamuH3R/Tn0K0yVJ9NE33dN7gaPbO5zeYqiQrXEMQm/nKHiGi9kan0KmT2Lbk3pNYe+BKV59VOuGNb7RjjEGEQmaq7fSFLyQ9aanqE9hpD9Htk+C+krdoD+XaZin0CdVzcYfr8myFxZhR7P9d/Sa1FTZBKGuvUiNo7nNbSuj+NDo6Hm1qD9HpsvnSdpJEn20GLgCazIK9jfGfLh9w+oNgtj5yRL5rD35tu2ZaFubwU4RNR81c3bms32MTUy1zGb2jBRzlCuG/QfLDBayQY5Cq8ZGeVd62jupo1E5bzttlJNHF80o83ausJpCfZ5CIZsJstsLuQxjB6aqob4hoeA1rWd2vsI5xy5jqlyZUXmJtOAF3mA+0/G2tCePLuK2D27k9MNruysuHsjz9//l7Bkl4y0UkpxxdwH/F3gMqLTYd0ER7tO8ZNALhQPTavGYRoaLWba7ENNWpRYK2Qx79lsB0qxCqidcKTUsFJYNt64TNVDIBOajqKZQzGU4aXRRy+9oJ4VcX8M8hWLIjOJrRTXyKSwbLrBkIBf0s5jqdUez0xQ67U8Aa84744glDd/r9nmSdpKsVtEY87G2j6QHifZpHpuYYnyyNE/MR9UyF81KLYTfa5WjALWVUlfTH5S4SNICdSCXqZqPUnix7I/xKYTNKIU6n0L1PRHh2BXDQee7qXIlqP7ai3ifQrec/8rMSJSnICL/WURWicgh/tH2kfUA0Z4KvZ6j4LHmo6pPodndatgmnqSRSrVSqv1+XyF1aQKBMlDIhhzN6YvKKcb4FGo0BdeispGmAHDcymGe2jFOpWLssU/hPJPiz42hLpr0lOmTRIQfBL4IXI+teYT7u+CdzkORaJH5IxRsQ5tSudLShDFdTcFXSvXO1N37DlLI9iXKRB7MZ4LPRc1HaaA/V9skB+o1hcB85BzNUaGwfuUI+w6W2brnAFOl3i5z4XMz4vpaK+kkiVD4GDaBbVe7B9Nr+LhyrylsdTkKoz0vFFxRvMlSy1h5f8FLks0MIfORu7j73sxJyowP5LP85rdW8KbRfFTM9fHyvvo8haimcLBUCSqlRo/t+pW2T+mvto8zVTG9bT7KqvmoF0lyxj2OrZKqRIj2ad625wC5jLCsRcx92hkOFcWz4bbxd3r+TjdJNjOEy2c7odCiN3OYwSaO5jQQl6dQoylkax3N0Xj5Y1fYqJgt28fmQZkLrymo+aiXSCLCy8DDInIPtf0UFnxIatSn8OKeA6xclOzimGbCjXbshamZpmAvWkmymcPffd+zLzNSzPHcrldYt3w40WcH8llKFWvBTKtPoVH0UbiVZTNHM1gtbXRxv9UUSvU1nnoJf8Mwk1aeSvdIslq3u4cSIdynedcrk/zs6V3zItwt3JKzlaPZ/+MnyVEAa/YZXdzPPz6+nX98fDsAbzphZaLPhrOV01j+oZjra+BoLtdka+ezfUyVTWA+ahTZddzKYZ7cMW79OT1sPsr0CaOL+xNluivpIUlG87c7MZBepJDNkMvYPs3X3vYYYwdKXHvBcd0e1qyp0RRKzR3NhUAoJA/Dvfuj5/CyC0UFGF2SzAcTbq0YLXORBvobJK8dLNX7FKBqcmwkFNavHObeJ3dSqvR2ngLAPdds6mltZyGiet0sGchnuf2hrby4d4JPvOV4jls50u0hzZpAKExOcbBcYSQfbxMuBD6F5H6UoUJ2Rs7HcIRSGkM1fUiqL+EBVlMo5mqjj6Da2S5OKHgzWTPTXS/Q7XaiyvTRFZslQ4UsL+6dYOPaQ7lyhm0L00a4p0IrZ6d3JibJZp4tA4WwppC+i6W/+HvTkH8ediYXoppCg2PrI5AgvhChorSLlmeciCz4fIRmDBezjBSz/Mklp/S8g9kTNh/Z6KP4efkL4coOCIWwppDGjmSBUAiZkOo0hQTmo6OXDgUmlzSG3irzmyQ6/M0iMgo8APwE+Kkx5rH2Dqt3+MRbTqA/n+n5hLUwxVzGFp9L4Gh+1ZFL+NzbTmJjB+o9hX0K2ZT6FMC25FyE1bbqNQW7jzcfNSrhnM/2sXbZEFt2jPe8+UjpPZI4ms8RkTzwKmAT8H9EZMgYo6UugNeuW9rtIbQFXz67VUZzNtPHu159REfGFI4+Sqf5qLb7WqlcoVQxTTWFuGO7fuUwW3aMq/lI6ThJSme/FnideywG7gR+2uZxKV3GC4VoH+FuUqMppPAOuhjSFKDqWwhrA96HMDYx1bRPxfqVw/CI+hSUzpPEfHQv8CDwP4G7jDEHW+yvzAN8T4VWyWudJKwppNl85DUF/zdOU2jmwF+/wjqb0yj8lPlNEqFwKHA2cA7wYRGpAD83xnyyrSNTukpgPio1L53dSWp9Cum7WPpS0U01BS8UJkpNj+uGI5dwymGLOXF174c4K71FEp/CHhF5FjgMWANsBLSYyTxnuJhl1659qTIfDebTHZLaH4k+aqkpNBEKvkOYonSaJD6FZ4AtwM+AG4D3qglp/jNUyDF2oLWjuZMM1JS5SMeYwhQj5qNGmkIhpClon2AljSQxH60zxmgbzgXGcDHLy/ut7E+P+Sjd0Uf9EUdzI00hEAoHS4mLCCpKJ0ny375aRP5ORF4SkR0icpuIrGn7yJSuMlLMBpU801J8rpjN4NsupGVMYaqagj1ujaOP7D7GpEfYKkqYJGflt4A7gNXAKPAPbltLROR8EdkiIk+LyLUN3j9cRO4RkYdE5FERefN0Bq+0j+FQC8W01PTv6xMG3IW3lzSFQgOfQvS5oqSFJGflMmPMt4wxJfe4GVjW6kMikgG+BlwAnABcJiInRHb7BHCrMeY04FLgL6Y1eqVthGvgp6l8s69/lMaQ1EIkec1rCo2qpEJ6hK2ihElyVu4SkctFJOMelwO7E3zuTOBpY8yzzjH9N8BFkX0M4GPuFgHbkg5caS9hTSFNTl1f/yiN8fuFbB8i9XkK0c5rnjQdV0XxJDkrrwTeCWwHXgTe4ba1YhT4Tej1C25bmE8Dl4vIC8BdwNUJvlfpAGFNIU13tD5XIZOgp3OnERGK2Wr3NR+aWqMpZNR8pKSbJHkKvwYunMF3N/qvNZHXlwE3G2O+JCJnAd8RkZOi0U4i8j7gfQCHH374DIaiTJca81GKhMJgIUOfkNqKtMVcX8jRXK8p5DKCiDqalfQSKxRE5M+pv4gHJOjR/AI24c2zhnrz0FXA+e77fi4iRWAp8FLkt24EbgTYsGFD7JiUuaPWfJSeC/BAPpvqctL9rtEOVKOQwpqCiJDP9DGZokxxRQnT7Kx8EPiFe1wYeu4frXgAWCciR7kqq5dio5jC/Bp4A4CIHA8UgZ3TmYDSHkbC5qMUXbwGC5lUlrjwFHMh81EDTQGqx7OQYuGmLFxiNYVwb2YR+ch0ezUbY0oi8kfA3UAGuMkY87iIfAZ40BhzB/Bx4Bsi8lGsVvIeY4xqAikgjSGp4DSFHhEKE1MV+qRe0ypk+xgnXcJWUTxJG+XO6EJtjLkL60AOb/tU6Pm/Y4vtKSmjmOsj2ye2eXyKLl5rlw1x+KED3R5GLN6nMFWu8OMnX2L5cDHo1+zxQlaFgpJGpt89XVkQiAhDxSx79k+lytH8gXOP5oOb1nZ7GLEUnU/hK//yFJu3jnHD5afX7eOFQZo0MEXxNHM0j1PVEAZEZMy/BRhjjNb0necMB0IhPeaa6F132ujPZdi8dS8P/fq3XHLGGs4/aVXdPt7HoJqCkkaa+RSGOzkQJX0MF3LAAb2jnQbFXIaxiRKHHdLPf7/wxIb7BJqCCgUlhehZqcTicxX04pUcn0fxZ+88laFC43sufzzTZJZTFI/6FJRYfASSXryS8/5z13LByavYcOQhsft4zaugwlZJISoUlFh8roIKheSsXTbE2mVDTfdR85GSZvSsVGIJzEcqFOYUjT5S0oyelUosgfkom+6In16joJqCkmLUfKTEsnHtoTy5Y5xipEyDMjvUfKSkGRUKSiwbj1nKxmOWdnsY846Cmo+UFKNnpaJ0GC1zoaQZPSsVpcOo+UhJM3pWKkqH0egjJc3oWakoHSaf0dpHSnrRs1JROkwhp+YjJb3oWakoHSZwNKv5SEkhelYqSodRTUFJM5qnoCgd5g3HrWD76ydYvai/20NRlDpUKChKh1m5qMjHz1vf7WEoSkNUf1UURVECVCgoiqIoASoUFEVRlAAVCoqiKEqACgVFURQlQIWCoiiKEqBCQVEURQlQoaAoiqIEiDGm22OYFiKyE/h/M/z4UmDXHA6nV1iI816Ic4aFOe+FOGeY/ryPMMYsa7VTzwmF2SAiDxpjNnR7HJ1mIc57Ic4ZFua8F+KcoX3zVvORoiiKEqBCQVEURQlYaELhxm4PoEssxHkvxDnDwpz3QpwztGneC8qnoCiKojRnoWkKiqIoShMWjFAQkfNFZIuIPC0i13Z7PLNBRA4TkXtE5AkReVxE/qvbfoiI/LOIPOX+LnHbRUS+6ub+qIicHvqud7v9nxKRd3drTkkRkYyIPCQid7rXR4nIfW78t4hI3m0vuNdPu/ePDH3HdW77FhF5U3dmkhwRWSwi3xeRX7k1P2u+r7WIfNSd25tF5K9FpDgf11pEbhKRl0Rkc2jbnK2tiJwhIo+5z3xVRKTloIwx8/4BZIBngKOBPPAIcEK3xzWL+awCTnfPh4EngROALwDXuu3XAp93z98M/BAQ4DXAfW77IcCz7u8S93xJt+fXYu4fA74H3Ole3wpc6p7fAHzQPf8QcIN7filwi3t+glv/AnCUOy8y3Z5Xizl/G/hP7nkeWDyf1xoYBZ4D+kNr/J75uNbAOcDpwObQtjlbW+B+4Cz3mR8CF7QcU7cPSocO/FnA3aHX1wHXdXtcczi/vwd+F9gCrHLbVgFb3POvA5eF9t/i3r8M+Hpoe81+aXsAa4AfAa8H7nQn+i4gG11n4G7gLPc86/aT6NqH90vjAxhxF0iJbJ+3a+2Ewm/cRS7r1vpN83WtgSMjQmFO1ta996vQ9pr94h4LxXzkTzLPC25bz+NU5dOA+4AVxpgXAdzf5W63uPn32nH5MvDfgIp7fSiwxxhTcq/D4w/m5t7f6/bvtTkfDewEvuXMZt8UkUHm8VobY7YCfwL8GngRu3a/YP6vtWeu1nbUPY9ub8pCEQqN7Gg9H3YlIkPAbcBHjDFjzXZtsM002Z46ROT3gJeMMb8Ib26wq2nxXs/M2ZHFmhf+tzHmNGAf1qQQR8/P29nQL8KafFYDg8AFDXadb2vdiunOc0bzXyhC4QXgsNDrNcC2Lo1lThCRHFYgfNcY8wO3eYeIrHLvrwJectvj5t9Lx+Vs4EIReR74G6wJ6cvAYhHJun3C4w/m5t5fBLxMb80Z7HhfMMbc515/Hysk5vNavxF4zhiz0xgzBfwA2Mj8X2vPXK3tC+55dHtTFopQeABY56IX8lhn1B1dHtOMcREEfwk8YYz509BbdwA+8uDdWF+D336Fi154DbDXqaV3A+eJyBJ3d3ae25Y6jDHXGWPWGGOOxK7fvxpj3gXcA7zD7Radsz8W73D7G7f9UhexchSwDuuMSyXGmO3Ab0Rkvdv0BuDfmcdrjTUbvUZEBty57uc8r9c6xJysrXtvXERe447jFaHviqfbTpYOOnPejI3SeQa4vtvjmeVcXotVAx8FHnaPN2PtqD8CnnJ/D3H7C/A1N/fHgA2h77oSeNo93tvtuSWc/yaq0UdHY//Rnwb+Fii47UX3+mn3/tGhz1/vjsUWEkRjdPsBnAo86Nb7dmyEybxea+B/AL8CNgPfwUYQzbu1Bv4a6zeZwt7ZXzWXawtscMfwGeB/EQlYaPTQjGZFURQlYKGYjxRFUZQEqFBQFEVRAlQoKIqiKAEqFBRFUZQAFQqKoihKgAoFJdWIiBGRL4VeXyMin56j775ZRN7Res9Z/84lrrrpPe3+rcjvLhaRD3XyN5XeR4WCknYmgYtFZGm3BxJGRDLT2P0q4EPGmP/QrvHEsBhbQVRREqNCQUk7JWzbwY9G34je6YvIK+7vJhG5V0RuFZEnReSPReRdInK/qy2/NvQ1bxSRn7r9fs99PiMiXxSRB1zd+veHvvceEfkeNnkoOp7L3PdvFpHPu22fwiYb3iAiX4zs3ycifyG2b8CdInKXn4+IPO8FoYhsEJEfu+eDYmvwP+AK5F3ktp/o5vewG/M64I+BtW7bF0VklYj8xL3eLCKvm9GKKPOabOtdFKXrfA14VES+MI3PnAIcj62B8yzwTWPMmWIbEl0NfMTtdyRwLrAWuEdEjsGWA9hrjHmViBSAfxORf3L7nwmcZIx5LvxjIrIa+DxwBvBb4J9E5PeNMZ8RkdcD1xhjHoyM8WL3+ydjK2E+AdzUYl7XY8s4XCkii4H7ReRfgA8AXzHGfNeVcslgC+edZIw51Y3x49jyB59zms5Aq4OoLDxUKCipxxgzJiJ/BXwYOJDwYw8YV35YRJ4B/EX9MSBsxrnVGFMBnhKRZ4HjsLVjfiekhSzC1s05CNwfFQiOVwE/NsbsdL/5XWwDldubjPG1wN+639+e0OdwHrYw4DXudRE4HPg5cL2IrAF+YIx5SuqbbD0A3CS2mOLtxpiHE/yessBQ85HSK3wZa5sfDG0r4c5hV/ArH3pvMvS8EnpdofZmKFrnxZccvtoYc6p7HGWM8UJlX8z4Wrc5nN5ngrlhL/zhz7w9NLbDjTFPGGO+B1yIFZp3O+2kBmPMT7CCaivwHRG5YgZjVuY5KhSUnsAY8zK2HeNVoc3PY801YOvv52bw1Zc42/5abMG1Ldiqkx90d9SIyLFiG9s04z7gXBFZ6kwzlwH3tvjMz4C3u99fgS3053me6tzeHtp+N3C1E4KIyGnu79HAs8aYr2Kraf4OMI5t14rb5whsT4pvYKvsno6iRFChoPQSXwLCUUjfwF6I7wdeTfxdfDO2YC/ePwQ+YIyZAL6JLdX8S7EN1b9OC1OrM1Vdhy3v/AjwS2NMqzLFt2ErY/rfuA/bNQxsldCviMhPgXLoM5/FCr9H3dg+67b/R2CziDyMNYH9lTFmN9Yfstk5uTcBD4vIQ1hB85UW41MWIFolVVG6iIgMGWNeEZFDsWWfzza2h4KidAV1NCtKd7nTRRHlgc+qQFC6jWoKiqIoSoD6FBRFUZQAFQqKoihKgAoFRVEUJUCFgqIoihKgQkFRFEUJUKGgKIqiBPx/m/Y2ZWMM0KYAAAAASUVORK5CYII=\n",
  702.       "text/plain": [
  703.        "<Figure size 432x288 with 1 Axes>"
  704.       ]
  705.      },
  706.      "metadata": {
  707.       "needs_background": "light"
  708.      },
  709.      "output_type": "display_data"
  710.     }
  711.    ],
  712.    "source": [
  713.     "# chart for very large numbers that I can compute in reasonable timeframe\n",
  714.     "stop = 10000      # Maximum number of hats in our simulation\n",
  715.     "precission = 100  # Incresement between the values\n",
  716.     "step_list, experimental_list = [],[] # Initialize the lists for the chart\n",
  717.     "for step in range(1, stop, precission): # Generate the data\n",
  718.     "    step_list.append(step) \n",
  719.     "    experimental_list.append(generate_several_trials(step))\n",
  720.     "    \n",
  721.     "plt.plot(step_list, experimental_list,label=\"Experimental Hat curve\") # plot the first curve\n",
  722.     "plt.legend() # show legend \n",
  723.     "plt.xlabel(\"Number of guests\")\n",
  724.     "plt.ylabel(\"How many guests get correct hat\")\n",
  725.     "plt.show()"
  726.    ]
  727.   },
  728.   {
  729.    "cell_type": "code",
  730.    "execution_count": 13,
  731.    "metadata": {},
  732.    "outputs": [
  733.     {
  734.      "data": {
  735.       "image/png": 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\n",
  736.       "text/plain": [
  737.        "<Figure size 432x288 with 1 Axes>"
  738.       ]
  739.      },
  740.      "metadata": {
  741.       "needs_background": "light"
  742.      },
  743.      "output_type": "display_data"
  744.     }
  745.    ],
  746.    "source": [
  747.     "# chart for small numbers with high precission and extra repeats\n",
  748.     "# we can see that as we increased the precision, the average fluctulates between 0.97 and 1.02.\n",
  749.     "def generate_several_trials(N):\n",
  750.     "    repeats = 10000  # Configuration constant that tells us how many times we want to repeat the simulation\n",
  751.     "                    # This variable has significant impact on performance and precision\n",
  752.     "    resutls = []    # Empty list for resutls\n",
  753.     "    for i in range(repeats): # Making multiple trials\n",
  754.     "        resutls.append(hat_check(N))        \n",
  755.     "    return sum(resutls)/repeats\n",
  756.     "\n",
  757.     "\n",
  758.     "stop = 100      # Maximum number of hats in our simulation\n",
  759.     "precission = 1  # Incresement between the values\n",
  760.     "step_list, experimental_list = [],[] # Initialize the lists for the chart\n",
  761.     "for step in range(1, stop, precission): # Generate the data\n",
  762.     "    step_list.append(step) \n",
  763.     "    experimental_list.append(generate_several_trials(step))\n",
  764.     "    \n",
  765.     "plt.plot(step_list, experimental_list,label=\"Experimental Hat curve\") # plot the first curve\n",
  766.     "plt.legend() # show legend \n",
  767.     "plt.xlabel(\"Number of guests\")\n",
  768.     "plt.ylabel(\"How many guests get correct hat\")\n",
  769.     "plt.show()"
  770.    ]
  771.   }
  772.  ],
  773.  "metadata": {
  774.   "kernelspec": {
  775.    "display_name": "Python 3",
  776.    "language": "python",
  777.    "name": "python3"
  778.   },
  779.   "language_info": {
  780.    "codemirror_mode": {
  781.     "name": "ipython",
  782.     "version": 3
  783.    },
  784.    "file_extension": ".py",
  785.    "mimetype": "text/x-python",
  786.    "name": "python",
  787.    "nbconvert_exporter": "python",
  788.    "pygments_lexer": "ipython3",
  789.    "version": "3.7.0"
  790.   }
  791.  },
  792.  "nbformat": 4,
  793.  "nbformat_minor": 2
  794. }
RAW Paste Data
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