2 Cellular Automata + Agent-Based MOdels.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "be29de1c-3651-4c78-ad34-b6971e40c284",
   "metadata": {},
   "source": [
    "# Rule 110 Cellular Automation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2c2c3437-19c9-4233-ba89-2e9d7d115675",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "def ca110(seed,gen=10):\n",
    "    grid = np.ones(shape=(gen,len(seed)))\n",
    "    grid[0] = seed\n",
    "    for row_num in range(1,gen):\n",
    "        new_row = np.ones(shape = len(seed))\n",
    "        for i in range(0,len(seed)):\n",
    "            current = [grid[row_num-1][i-1],grid[row_num-1][i],grid[row_num-1][(i+1)%len(seed)]]\n",
    "            if current == [1,1,1]:\n",
    "                new_row[i] = 0\n",
    "            elif current == [1,1,0]:\n",
    "                     new_row[i] = 1\n",
    "            elif current == [1,0,1]:\n",
    "                     new_row[i] = 1\n",
    "            elif current == [1,0,0]:\n",
    "                     new_row[i] = 0\n",
    "            elif current == [0,1,1]:\n",
    "                     new_row[i] = 1\n",
    "            elif current == [0,1,0]:\n",
    "                     new_row[i] = 1\n",
    "            elif current == [0,0,1]:\n",
    "                     new_row[i] = 1\n",
    "            elif current == [0,0,0]:\n",
    "                     new_row[i] = 0\n",
    "        grid[row_num] = new_row\n",
    "    return grid\n",
    "            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6b7abfad-3a59-439b-8ba3-6fdd511a6f19",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x22477907f40>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ini_string = np.array([0,1,0,0,1,0,0,1,1,1])\n",
    "implement = ca110(ini_string)\n",
    "plt.imshow(implement,cmap= 'Greys')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8f724625-438d-4d33-8fb2-aeaacd5b293a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x224779fe6a0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ini_string2 = [1,0,0,0,1,1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,1,0,1,1,1,1,1,0,0,0,1,0,0,1,1,0,1,1,1,1,1,0,0,0,1,0,0]\n",
    "check = ca110(ini_string2,len(ini_string2))\n",
    "#plt.imshow(check, cmap = 'Blues')\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(5, 5))\n",
    "ax.imshow(check, cmap = 'Blues')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ec8edf2-7435-4aec-8878-79ca93668010",
   "metadata": {
    "tags": []
   },
   "source": [
    "# Why are they called rules?\n",
    "Rules are just mappings from 3 bits to 1 bit. For 3 bits, we can specify 8 different configurations (e.g. 000,001, ... , 111). Each configuration maps to 1 bit, which gives us 8 bits of information (ways to set rules). Hence there are $2^8 = 256$ possible rules. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d53577a8-b739-444b-b230-1837bfb4b838",
   "metadata": {},
   "source": [
    "# Generalized CA Rule"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3e596c67-fb14-426e-a2f9-3af50a57817f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ca_rule(dec_num,seed,gen=10):\n",
    "    if type(dec_num)!= int:\n",
    "        raise Exception(\"First positional argument must be an integer!\")\n",
    "    if dec_num < 0 or dec_num > 255:\n",
    "        raise Exception(\"First positional argument must be in [0,255]!\")\n",
    "    #convert to binary\n",
    "    bin_num = np.binary_repr(dec_num)\n",
    "    #zero padding\n",
    "    for i in range(len(bin_num),8):\n",
    "        bin_num = \"0\" + bin_num\n",
    "    \n",
    "    grid = np.ones(shape=(gen,len(seed)))\n",
    "    grid[0] = seed\n",
    "    for row_num in range(1,gen):\n",
    "        new_row = np.ones(shape = len(seed))\n",
    "        for i in range(0,len(seed)):\n",
    "            current = [grid[row_num-1][i-1],grid[row_num-1][i],grid[row_num-1][(i+1)%len(seed)]]\n",
    "            if current == [1,1,1]:\n",
    "                new_row[i] = bin_num[0]\n",
    "            elif current == [1,1,0]:\n",
    "                     new_row[i] = bin_num[1]\n",
    "            elif current == [1,0,1]:\n",
    "                     new_row[i] = bin_num[2]\n",
    "            elif current == [1,0,0]:\n",
    "                     new_row[i] = bin_num[3]\n",
    "            elif current == [0,1,1]:\n",
    "                     new_row[i] = bin_num[4]\n",
    "            elif current == [0,1,0]:\n",
    "                     new_row[i] = bin_num[5]\n",
    "            elif current == [0,0,1]:\n",
    "                     new_row[i] = bin_num[6]\n",
    "            elif current == [0,0,0]:\n",
    "                     new_row[i] = bin_num[7]\n",
    "        grid[row_num] = new_row\n",
    "    return grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "a122fadd-3d54-411b-a372-d8e73dc868bc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Rule 110')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x720 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "length = 100\n",
    "initial_cond = [1 if i==int(length/2) else 0 for i in range(length)]\n",
    "r90_val = ca_rule(90,initial_cond,length)\n",
    "r110_val = ca_rule(110,initial_cond,length)\n",
    "\n",
    "\n",
    "fig, ax = plt.subplots(1,2,figsize=(20, 10))\n",
    "ax[0].imshow(r90_val, cmap = 'Greys')\n",
    "ax[0].set_title('Rule 90', fontsize = 20)\n",
    "ax[1].imshow(r110_val, cmap = 'Greys')\n",
    "ax[1].set_title('Rule 110', fontsize = 20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b29d1c0b-9b04-42b3-81b8-cdbc6c757c18",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x22477d0f640>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "check = ca_rule(120,ini_string2,100)\n",
    "plt.imshow(check,cmap='Greys')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "efc75488-7846-4a70-b73d-d137b1e4e38a",
   "metadata": {},
   "source": [
    "# Schelling's Model of racial segregation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "23c8b915-d401-465e-ac16-92ad0b64d7d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\"\\nfrom os.path import basename, exists\\n\\ndef download(url):\\n    filename = basename(url)\\n    if not exists(filename):\\n        from urllib.request import urlretrieve\\n        local, _ = urlretrieve(url, filename)\\n        print('Downloaded ' + local)\\n    \\ndownload('https://github.com/AllenDowney/ThinkComplexity2/raw/master/notebooks/utils.py')\\ndownload('https://github.com/AllenDowney/ThinkComplexity2/raw/master/notebooks/Cell2D.py')\\n\""
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "from os.path import basename, exists\n",
    "\n",
    "def download(url):\n",
    "    filename = basename(url)\n",
    "    if not exists(filename):\n",
    "        from urllib.request import urlretrieve\n",
    "        local, _ = urlretrieve(url, filename)\n",
    "        print('Downloaded ' + local)\n",
    "    \n",
    "download('https://github.com/AllenDowney/ThinkComplexity2/raw/master/notebooks/utils.py')\n",
    "download('https://github.com/AllenDowney/ThinkComplexity2/raw/master/notebooks/Cell2D.py')\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "745be17f-ed2e-4f55-8706-967028148f58",
   "metadata": {
    "tags": []
   },
   "source": [
    "#### Mini tutorial for boolean indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "177b7cfb-853c-4284-9853-4c976e335772",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Orignal Series\n",
      "[1 2 3 4 5 6]\n",
      "Example 1: Greater than 2\n",
      "[3 4 5 6]\n",
      "Example 2: Greater then 5 and less than 2\n",
      "[3 4]\n",
      "Example 3: Not less than 4\n",
      "[4 5 6]\n",
      "Example 4: Set all values greater than 2 to 0\n",
      "[1 2 5 5 5 5]\n"
     ]
    }
   ],
   "source": [
    "ser1 = np.array([1,2,3,4,5,6])\n",
    "\n",
    "print(\"Orignal Series\")\n",
    "print(ser1)\n",
    "print(\"Example 1: Greater than 2\")\n",
    "print(ser1[ser1 > 2])\n",
    "print(\"Example 2: Greater then 5 and less than 2\")\n",
    "print(ser1[(ser1 < 5) & (ser1 > 2)])\n",
    "print(\"Example 3: Not less than 4\")\n",
    "print(ser1[~(ser1 < 4)])\n",
    "\n",
    "#editing values:\n",
    "print(\"Example 4: Set all values greater than 2 to 0\")\n",
    "ser1[ser1 > 2] = 5\n",
    "print(ser1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "124d8cf7-16e1-44ea-a495-20a85878dcfa",
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "from matplotlib.colors import LinearSegmentedColormap\n",
    "\n",
    "# make a custom color map\n",
    "palette = sns.color_palette('muted')\n",
    "colors = 'white', palette[1], palette[0]\n",
    "colors2 = palette[1], 'white', palette[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "2a3ece51-c578-466f-a814-049407588b61",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.signal import correlate2d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "a0e4b9ac-2d00-4a7d-9e33-c91bbd27da07",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from matplotlib.colors import LinearSegmentedColormap\n",
    "\n",
    "\n",
    "from scipy.signal import correlate2d\n",
    "from time import sleep\n",
    "from IPython.display import clear_output\n",
    "\n",
    "\n",
    "class agent_Schelling():\n",
    "    \n",
    "    \"\"\"Creates a grid of Schelling agents\"\"\"\n",
    "    options = dict(mode='same', boundary='wrap')\n",
    "    #moore neighborhood; we use this for the count neighbors function\n",
    "    #instantiated as a class variable so that we can easily change neighborhood for an instance of agent_Schelling()\n",
    "    #vonNeumann at the moment for quiz\n",
    "    kernel = np.array([[0, 1, 0],\n",
    "                       [1, 0, 1],\n",
    "                       [0, 1, 0]], dtype=np.int8)\n",
    "    \n",
    "    def __init__(self, p_happy, n, m=None, ):\n",
    "        \"\"\" Initialize instance variables\n",
    "        n: number of rows\n",
    "        m: number of columns\n",
    "        p_happy: happiness threshold on the fraction of similar neighbors\n",
    "        \"\"\"\n",
    "        self.p_happy = p_happy\n",
    "        m = n if m is None else m\n",
    "        #set possible choices; dtype to ensure boolean masking is easy; \n",
    "        #-1 is red, 0 is empty, 1 is blue\n",
    "        choices = np.array([-1,0,1], dtype = np.int8)\n",
    "        probs = [0.45,0.1,0.45]\n",
    "        self.array = np.random.choice(choices, (n,m), p = probs)\n",
    "\n",
    "    def count_neighbors(self):    \n",
    "        #boolean masking\n",
    "        #generates 2D array of boolean values for red, empty, and blue neighbors\n",
    "        red_bool = self.array == (-1)\n",
    "        empty_bool = self.array == 0\n",
    "        blue_bool = self.array == 1\n",
    "        \n",
    "        #counts number of red and blue neighbors; moore neighborhood\n",
    "        num_red = correlate2d(red_bool, self.kernel, **self.options)\n",
    "        num_blue = correlate2d(blue_bool, self.kernel, **self.options)\n",
    "        \n",
    "        #computes fraction of red and blue neighbors; boolean indexing to set elements with zero neighbors to zero:\n",
    "        num_neighbors = num_red + num_blue\n",
    "        frac_red = num_red / num_neighbors\n",
    "        frac_blue = num_blue / num_neighbors\n",
    "        frac_red[num_neighbors == 0] = 0\n",
    "        frac_blue[num_neighbors == 0] = 0\n",
    "        \n",
    "        #compute fraction of neighbors with the same color; important to have NaN data type for empty cells to ignore when comparing with p_happy\n",
    "        frac_same = np.where(red_bool, frac_red, frac_blue)\n",
    "        frac_same[empty_bool] = np.nan\n",
    "        \n",
    "        return empty_bool, frac_same\n",
    "    \n",
    "    def segregation(self):\n",
    "        #useful for testing segregation for a single time step\n",
    "        _, frac_same = self.count_neighbors()\n",
    "        return np.nanmean(frac_same)\n",
    "    \n",
    "    def locs_where(self, condition):\n",
    "        #returns list of tuples (i.e., locations)\n",
    "        return list(zip(*np.nonzero(condition)))\n",
    "    \n",
    "    def step(self):\n",
    "        \"\"\"Executes one time step.\n",
    "                \n",
    "        returns: fraction of similar neighbors, averaged over cells\n",
    "        \"\"\"\n",
    "        empty, frac_same = self.count_neighbors()\n",
    "        \n",
    "        # find the unhappy cells (ignore NaN in frac_same)\n",
    "        with np.errstate(invalid='ignore'):\n",
    "            unhappy = frac_same < self.p_happy\n",
    "        unhappy_locs = self.locs_where(unhappy)\n",
    "        \n",
    "        # find the empty cells\n",
    "        empty_locs = self.locs_where(empty)\n",
    "\n",
    "        # shuffle the unhappy cells\n",
    "        if len(unhappy_locs):\n",
    "            np.random.shuffle(unhappy_locs)\n",
    "            \n",
    "        # for each unhappy cell, choose a random destination\n",
    "        num_empty = np.sum(empty)\n",
    "        \n",
    "        for source in unhappy_locs:\n",
    "            i = np.random.randint(num_empty)\n",
    "            dest = empty_locs[i]\n",
    "            \n",
    "            # move\n",
    "            self.array[dest] = self.array[source]\n",
    "            self.array[source] = 0\n",
    "            empty_locs[i] = source\n",
    "        \n",
    "            # check that the number of empty cells is unchanged; why would it ever not be?\n",
    "            num_empty2 = np.sum(self.array==0)\n",
    "            assert num_empty == num_empty2\n",
    "        \n",
    "        # return the average fraction of similar neighbors\n",
    "        return np.nanmean(frac_same)\n",
    "    \n",
    "    def animate(self, frames, interval=None, step=None):\n",
    "        \"\"\"Animate the automaton.\n",
    "        \n",
    "        frames: number of frames to draw\n",
    "        interval: time between frames in seconds\n",
    "        iters: number of steps between frames\n",
    "        \"\"\"\n",
    "        if step is None:\n",
    "            step = self.step\n",
    "            \n",
    "        plt.figure()\n",
    "        try:\n",
    "            for i in range(frames-1):\n",
    "                self.draw()\n",
    "                #print(self.segregation())\n",
    "                plt.show()\n",
    "                if interval:\n",
    "                    sleep(interval)\n",
    "                step()\n",
    "                clear_output(wait=True)\n",
    "            self.draw()\n",
    "            plt.show()\n",
    "        except KeyboardInterrupt:\n",
    "            pass\n",
    "\n",
    "    def draw(self):\n",
    "        \"\"\"Draws the cells.\"\"\"\n",
    "        n, m = self.array.shape\n",
    "        \n",
    "        palette = sns.color_palette('muted')\n",
    "        colors = palette[1], 'white', palette[0]\n",
    "        cmap=LinearSegmentedColormap.from_list('cmap', colors)\n",
    "\n",
    "        plt.axis([0, m, 0, n])\n",
    "        plt.xticks([])\n",
    "        plt.yticks([])\n",
    "        return plt.imshow(self.array,\n",
    "                        cmap = cmap, \n",
    "                        alpha=0.7,\n",
    "                        vmin=-1, vmax=1, \n",
    "                        interpolation='none', \n",
    "                        origin='upper',\n",
    "                        extent=[0, m, 0, n])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "f0b18b5d-fc60-4f89-a6df-f37dfe37cd28",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "grid = agent_Schelling(0.6,80,150)\n",
    "grid.animate(frames=50, interval=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "12777807-1e3f-42f6-abf4-79b0293586d4",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-84-9e7861803538>:50: RuntimeWarning: invalid value encountered in divide\n",
      "  frac_red = num_red / num_neighbors\n",
      "<ipython-input-84-9e7861803538>:51: RuntimeWarning: invalid value encountered in divide\n",
      "  frac_blue = num_blue / num_neighbors\n"
     ]
    }
   ],
   "source": [
    "#thresholds\n",
    "thresholds = np.arange(0,1,0.1).round(1)\n",
    "\n",
    "#number of steps\n",
    "num_steps = np.arange(50)\n",
    "#dimensions\n",
    "N = 80\n",
    "M = 150\n",
    "\n",
    "von_models = [agent_Schelling(p, 80, 150) for p in thresholds]\n",
    "deg_segs = [[von_models[p_count].step() for i in steps] for p_count in range(len(thresholds))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "a7857602-7efb-4191-a57f-16b8bb1b3630",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Degree of Segregation')"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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lwCpnsM8UMtGBcHTbOmhO/BtkgHLaMVw2lMuG4bKBoaLvG6a2gr++j33m0RplN8BmoOwKZTesQK1n3mFguG1WGrthBXUKK6BTyjr3GHkfrOesdarnPRmGBGRCCCHEMLTWVsASjgRBI82H+rSqhMLooB4c/AxY1mE9qNUluq7vfNi08ou03IwmDxtN+94cPoEC5TAigUeflqLIY9/53nVWgKF1JCi03qDelqG+LVo9jzYrgFFuG0aK05rvO9kNlNMKbpRd9QYyPcFLNMBjUCConLZ+QVc0+LIbowY/05EEZEIIIaY167SWxgyErSCm5zEYRgcip46gX8uM6ttK0/Mjbv2xTmN1h6zJF0L3zPdZZ3Zb6ye8BaenlaXPhK2nFUb1Bih91tEvveoNcmwGymGdZou21kTy33/wdS5du7p3G47+21S2mRewzHYSkAkhhBgTrbUVFPn69Nnxh3r78viH6MsTCEf6CNF7Sqynz1DPqbCeU2daW6fjApGAKxjpAzRJlNuGkWDHcNsxEuw4shJQCda81XoT6VtkqN55WyQQsqnoPDbV2+rTMzkGBF7G1ARCvhpw5qdMybbExJCATAghLiA6bGL6wmhfCNMXCZh8vYFTxglFq/cU2h/ql65nuSddTAFST18etw3lNHqDmr6nwGwKHAbGgFNlVkuRgXLY+j0aA5Z7WpOsnYs89HSe7tMh3Jq3ZpTLHgnAbCi3fcqCJCFGIgGZEEJMU7qnL064b0drq+XI7O4NpKKn3XqWu0O9p+UGBFyjnYLLxKDzVA2GqzdgMVw2DE8CDrcNw223+uq47VbLUr8+PH06Urtnbl8eIeJBAjIhhJhAOmhieoNWMOTt7Y/UMw3qr9QdxPSFIx3DGXRV21gph2GdbosET0aiA8Pj7hNA9Qm0+gZckeef2/siG9+xccLfFyHEyCQgE0KIPrSprc7iA/tH+cK9QVZ30Hr09jz2rhutBSraXykyOXISrdNmPZfPDxwfaYhl5TQiAVQk8Erone8ZR+m8yXDhQsSFBGRCiFnNDIQxOwKE2yNTZN5s9xPuDEZP5UUHmQzE0D/KpqyAKtGBkWjH5nHjSEjGSOxd1zfo6pmkv5IQYjgSkAkhZhQdNKOtUeGu4OAWq85gb/DVHkD7QoMzsStsqS5syQ4rgMpw9/aDcvcfUFK57RjOyHKiHSMxcuWd9I0SQkwgCciEENOGNjXhdj+hhm5C9V6Cjd2EGrsxO3sDrpFOCSqHgZHkwJbqxJGTgGtxmhV4pTp7pxQnKsEuAZUQYlqRgEwIMeXMQJhQYzehBi+hhm6CDb3zfQMu5bJhz07AlubCMTfJas1KipwW7HPK0EhyYEu0oxy2OO6VEEKcPwnIhBDjorXG7AjibAff8ZbeU4ddfTu99z6GvdaVhlEKbBlu7FkJJC1Mw56diD07AUdOIkayQ1qyhBAXBAnIhBCj0sEwoRY/oWYf4aZuQs2+6BRu9qGDJvOx0fjiwX6vU05btAXLSLTj8LhxJdqxJTuxZydgz07EkeWWli0hxAVPAjIhLnA6ZBLu7LnysPcqxHCbPxpwhdsD/V6jnAZ2jxt7ZgLuogzsHjeHzxxl5dpV2CLBl5HosG4XI4QQYlQSkAlxAQi1+ghUthOs90avPuwZCsLsCg5+gQG2FCc2jxtXJOCye9zYPG7smW6MpMGnErsCR3EvTp+aHRJCiFlGAjIhZhltakINXvyn2vFXthGobCfc6reeVGCkWFca2tJdOOenWPOpLozIFYi2VKcVcMl4WUIIMWUkIBNihtMhk8DZTgI9Adjpdkyv1WneSHHgKkzDeUUersI0HHOSem/ELIQQYtqQgEyIGUJrjdkZJFjvtcboqvMSrOsiWN0ZHSrCnpWAe1kmrsJUXIVp2DLdcpWiEELMABKQCTHNaK0JtwWsoKtv8FXv7TdchHLZcOQmknTZHJyFabgKU7GlOONYciGEEOdLAjIh4sz0BvGf6SBwut2aajrR/nD0eSPRjj03kcSLsrDnJOLIScSRm4iR4pTWLyGEmCUkIBNiCmlTE2rsJnC6HX8kAAs1dFtPGuCYl0zipTk4cpNw5CRgz0nEliytXkIIMdtJQCbEJDL9YQLVHQTOtBOobMd/piN62tFItOOcn0ripbm4FqTgyE/BcMoAqUIIMduEw2Fqa2tHTCMBmRATRGtNuNlH4EyH1fp1pp3guS6I3JrRnpNI4oosnAtScC5IxZ6VIKcchRBiFjJNk/r6ek6dOsWpU6c4ffo0fr9/xNdIQCbEedLBMIGaTgKnewMws9MaZFU5bTjnp5CysQDnglRcBSkYiY44l1gIIcRk0FrT1NQUDcAqKyvxer0AeDweVqxYQWFhIdu2bRs2DwnIhIiRDpn4T7fjP9aK/0QrgbOdENYA2DPduIsycC5IxTk/xRrvSwZWFUKIWUNrjc/nw+v10tXVhdfrpaOjg6qqKk6dOkVHRwcAqampFBUVsXDhQgoLC0lPT48pfwnIhBiG1ppQvRffsVb8x1rwn2yzxvsywFmQSsqGvGgAJh3vhRBiegqHw/j9fkKhEMFgMDoNtxwIBKIB18BH0zQH5Z+YmMjChQujk8fjOa/uKBKQCdFHuDOA/3grvqMt+I63YkZuqm3PSiBxTS7uogxci9Iw3PLREUKIeAiFQtTV1UWDpO7u7ujUd7lnPhAIjHkbLpeLxMREkpKSSEtLY968eSQlJUXX9X1MS0ubkP7A8qsiLnihVj/efefoPtREsLYLsK6AdC1OtwKwonTsGe44l1IIIS5MgUCA6upqTp8+zenTp6muriYUCg1Kl5CQQEJCAomJiSQnJ5OdnR1d53K5cDgc0clut4+6PNUkIBMXJB0y6X6zia59dfiPtYAGZ2EqqZsW4C7KwDEvWfqACSHEGGmt8Xq9tLW10d7ejs1mIzExMdqi5HSO3r3D7/dTVVVFZWUlp0+fpqamBtM0UUoxZ84c1qxZw/z580lNTY0GXG63G8MwpmAPJ48EZOKCEjzXRdfL5/Dur8fsCmFLc5Lyjvkkrc7F7pFWMCGEGEkwGKStra3f1N7e3m95qNarHna7vV+A1jOfmJiI3+/n9OnTnD17Fq01SinmzZvHunXrWLBgAfPnz8ftnr3f0xKQiVnP9IXwHmjA+3IdgaoOsCkSlmWStCYXV1GGtIQJIS44Wmu01pimGe3E3nfq7OwctK6rq2vIsbRSUlJIS0tjzpw5FBcXk5aWRlpaGqmpqYTD4X6d4numnuXm5ma8Xi9+vx+bzUZeXh4bNmygsLCQ/Px8XC5XHN6d+JCATMxKWmsCp9vpermO7gMN6KCJPSeRtPcsJPGSHLkqUggxrfl8Ps6ePUtNTQ1nz56ltbW1XxDVMz/c5PP52Lt3bzTtwEet9YjbV0pFW7GSkpKindp7Orn3TCkpKRPS36qnVS0efbemiwt3z8WsZHqDdL1aT9fec4TqvSinjcRVOSSuzcVZkCIj4wshpp1gMEhtbW2/AKypqSn6fEZGBllZWRiGgVIqpuncuXPk5eVFXzPSo9PpjAZbycnJJCUlkZCQMKV9si7kQKyHvANixou2hu09h/dAI4RMHPnJZLy/iISLsjFccn9IIcTU0VpHx7Pqmfx+f795v99PQ0MDNTU11NfXR1usUlJSmDdvHhdffDHz5s1j3rx5JCYmjrkMFRUVbNy4cYL3TEwmCcjEjGV6g3S9FmkNq/OiXDaSVueQdNlcnHnJ8S6eEGIGC4VCdHV1Rce08vl80Wmk5Z6ga7RTggBut5u8vDyWLl1KXl4e8+bNIzU1dQr2TkxHEpCJGUVrTeBMB117aqU1TAgxKq014XCYUCgUHYnd6/VGO60P9djZ2YnP5xsxX7fbHZ0SEhLIysrC7XbjdDpxuVw4nc7oNHC5Z11CQoJ0oxBREpCJGUGHTLyv1tPxQo20hglxAdNa09HRQV1dHXV1dZw7d47W1laCwWC/wKvvNBqn00lycnJ0MNGFCxdG+1MlJiZGg66eAMzlcs34Ma/E9CMBmZjWTF+Izpdq6XyhBrMjiCNPWsOEmA78fj9dXV3RQGUyWnpCoRANDQ3RwKsnCPN6vdE0qampZGZmkpSUhN1ux263Y7PZovNDTT0jufcEXQ6HY8LLLsRYSUAmpqVwe4COF2roeqkW7Q/jKkon5YP5uBanSxO/EHGgtaauro7jx49z/Phxzpw5E73Rcs8QCT23rek79axzu93RFqy+N3Lu+9j3Zs8tLS00NjZGt2G328nJyaG4uJjc3FzmzJlDbm4uCQkJ8XxbhJgwEpCJaSXY4KXz2Rq6Xq0DU5OwMouUqwrktKQQcdDd3c3JkyejQVhHRwcAubm5rFu3jqysrH43cu6Zmpubqa6uxuv1RgOqkfS9l2BPK1ZaWlo0+MrNzSUzM1NOE4pZTQIyMS0EqjroqKii+80msBkkrZ1DyhV52DPlv18hpoppmrS3t/PMM89w/Phxqqur0VrjdrtZtGgRS5YsYcmSJTFfCai1xu/39xuJvW/g5XA4sNls0uotBBKQiTjSpsZ3tIV5ew3qd+xHJdhJubqA5LfPk5H0hZgCgUCAmpoaqqurqaqqoqqqiu7ubgDmzp3LFVdcwZIlS8jLy8NmG3ufTaVUtCO8EGJkEpCJKRfuCuLdV0fnnlrCzT4cbkh7zyKSLsvFcMkhKcRk0FrT0tLSL/iqq6uLjpeVmZlJcXExPp+P66+/nuRk6SYgxFSSXz8xZQLVHXTursX7egOETJwLU0m7tpC9jYdYeEVevIsnxKwQDofp7Oykvb2djo6OaH+uqqoqurq6AGuYh56bOBcUFJCfnx8dDb6iokKCMSHiQAIyMal00MR7oIHOl2oJVnWgnAZJq3NIXjcPx5wkK1HFFJdJa7S2HjH7L2ttnUpFD0gXeTRNjRkO03cQbq0B3T//YZ/rWRhiEO8YBvae1rqbw9SfaY93MWa1UChIe0c7nV0ddHk7e6cu67HT20l3t3fQ69JS08mbM585ufOYkz0PT0b/DvKdjSE6sepO6nF2kHqceVQst3eYroqLi/WRI0fiXYwLnhkO093RQVt9K+2NLXQ0tRFu9ZN0ziClxYndNPDZAtQ5mzhnNOAPdhMOBgkHA4RDQbq9XTidTtDaCoJMMxIMmb3rrEgpMh9Gm+HIcjiSLowm8qhNrEjLpDfyGa7T8MD1esC8HmK9EJNDA9ruwHS40E4XpsOF6XBG57VjcN9KFQpGJyMYiMwHMEJBVDBgrTPDU78zQohB7nr8j69ordcM9Zy0kIlBAt1eOltaaGtopLW2gbaGRjqbW/G2t+Pr7MDv7STQ7SUU6CIc7Eab/uhr5yQsZEnqpeQlLEajOes9xrH216j3nY6kUIAdZdhBRR4xCPsMUApF5DEyoQyUUhiGiqy3oQxrlGxl2KKT0fNos0eXrTS9rQBKMSj+si7u0tZ6DcpQKGWgDCuxVQSrDAoFRp+y9ctowKwa4ol+2xzGDL7YrL6unpzcnHgXY1rRWhPWmpA2CZsmIR2ZTJNw5NFaDuM3w/jDoUGhv9Ow4bLZcfU82uw4DRtOw4bDsGFM8BWKUo+zg9TjNPX4H4d9SlrILjCB7gDVh09Qc+QErfX1dLU2093eir+rjUB3O6FAO9oMDvFKA5Qbpdwomxu7MxGHKxFnQjLJSWkUOOaRG8jAGbJhOiC00A3FyTizknAluK0p2Y3D5bCCqz4qKirYuHHjlOy/mDwXej2Gw2Fqa2s5efIkJ0+epL6+nu7u7hFvMu10OqODp6anp5ORkdFvSktLw26f2v+bL/R6nC2kHqcnpZS0kF1Igv4w7Y3d1J+qo+bYcRqrKmmvr6K7rZZQoBHoe/rCibIlYXek4HDPJclTQkJKGolpGSR7PKRkZpKem01qVhpJaS4SUpw4XDbrJt9VHXTtrsX7RgN4Nc6FqSRfPo+E5ZkouwzgKGY3rTVNTU3RAOzUqVP4/VZrcW5uLqWlpdFgq2e0+p75nul8hpIQQsxOEpDNAh3NPg49e5yje16mo7GKgLcOM9wAurdzr82RQmLaXNJyVpC9YCFzixaTszCf1KxUHM7YfxTMQJjOvbV0vVRL8GyXdZPvNXNIvnxubyd9IWapjo6OfgFYe7vVaTo9PZ3ly5ezaNGi6I2phRBiLKYsIFNKXQt8C7ABD2utvzbg+fnAdiA9kuZurfWTU1W+mcbXGeTNF0/xxl8qaK7ejxmqAjTKsJOUPpeMeZeQu3AR+SVLmLt0CYmpaePaXrDeS9dLtXS9Wof2hXHMSST9piUkXpItY4eJWScUCtHc3Ex9fT0NDQ3U19dTX19PU1MTAAkJCSxcuJBFixaxaNEiPB5PnEsshJjppuSXVCllAx4EyoBq4GWl1O+01m/2SfZF4HGt9XeUUsuAJ4HCqSjfTBH0hzn68mle3/kMdadexQyeBkwSUrIpfvvNrLj6KrLnF2JM4GmQcGeA1t+doPtAI9gUCSuzSL58Ls4FqXK7EzHjhcPhQYFXQ0MDTU1N/W6cnZGRQU5ODpdeeimLFi0iNzdX7qsohJhQU9W0cRlwXGt9EkAp9XPgRqBvQKaBnhukpQFnp6hs01o4bHLytRpe2/EMZ4/uI+w/BYRxJWawZP17WLXpHeQuXDLhwZHWmu4DDbT+7gSmL0zKO+SWRmJ2CIVCHDt2jNdff51jx44RDvf2qewJvIqLi8nJySE7O5usrCwcDkccSyyEuBBMVUCWB1T1Wa4G3jYgzZeAXUqpvweSgHdOTdGmp642PxWPPsWJl/9KsPsEEMbhTmPJ28u49N3vZG5R8aS1UIU7ArT85ji+N5tw5CeTfctSHLnSJ0bMXFprzp49y/79+zl48CDd3d0kJyezZs0a5s2bFw28nE75h0MIER9TMuyFUmozcK3W+vbI8keBt2mtP9MnzT9FyvNfSql1wCPACm2N8tk3r08DnwbIzs5e/fjjj096+adSyKepfbWZxjcrMIOnMOyJpBYsJXtlMSnz8if3NKGGlLOKrLcUKgzNRZrWBRom+cxMZ2en3KplFpiO9ejz+airq6Ourg6v14thGGRlZZGbm0tGRoacdhzCdKxHMXZSj9PT1VdfHfdhL2qAgj7L+ZF1fX0SuBZAa71bKeUGsoD6vom01t8DvgfWOGSzZZwVb3uAl588yps7f0nQ+yqGzcFlN32Ut9/yPmz2yT9dEm7zW61ibzXjXJBKxuYi5mcnTvp2QcbLmS2mSz0GAgEOHz7M66+/zsmTJwGYP38+F198McuXL8ftdse5hNPbdKlHMT5SjzPPVAVkLwNFSqmFWIHYh4CPDEhzBrgG+JFSqhRwAw1TVL646e4I8OrOSl7buRN/x3Oguyl620auKS8nKT1j0revtca7r47WP5wEU5N2/SKS3z4vMlK9ENOb1+ulsbGRxsZGmpqaaGho4NSpUwSDQdLT07nqqqu4+OKL5SpIIcS0NyUBmdY6pJT6DLATa0iLH2itDymlvgzs01r/Dvhn4PtKqc9hdfD/uJ7JtxEYRXdngP1PneG1XXvxtf0FHa4jp3ApZZ++kzmLi6akDKEWHy2/Pob/WCvOhWl4Nhdhz0yYkm2LC1MwGOT06dM0NjZit9txOByjTjabjdbW1n6BV898d3d3NG+bzYbH42HlypVcfPHFzJ8/X64EFkLMGFM2gFRkTLEnB6y7r8/8m8D6qSpPvPg6g7z25zO8/ufDdLc9gxk4TGJaBhs/+s+UbNg4JT8gWmu69p6j7Y+nAE36jYtJettcaRUTk6K5uZljx45x/PhxTp06RSgUGld+SUlJZGVlsWzZMjIzM8nKyiIrK4u0tDQZ+V4IMWPJvSyn0KkDjTz1gwN0t+7BDLyMUpo1772Zy266Bad7alqmwl1BWn51DN+bTbiWpJPxviLsnt4+Ndo00YEA2u+3HgMBTH8AHQxCOIQOh9GhEITD6FAYHY7Mh8O960IhdCiIDloTwd756BTona+tqWZO7hzQ2prQ1v3/NL3rIutHNlRAOXxeg9aLcWlqaiQzM4sQcM7ppMrlpNrppD1yL8aUUIiCQIB8f4CsYBBTKcJKEVIQUooQynrsM4UVhJUiKWySFgqRFg7jkrqaVD31KGY2qcfpaf53vxP3Tv0XNK01r+48zYu/2ovp+z2hQAtL1q7jqo9+kvTcOZOyzXBnF+HGBkINDYQaGwk1NBCo8RNqW4DWTsL1z+J79QVaf+KPBmBmJHiabMrpRDkcKIcDHHacoTBdpypBgUKBGjgNWD+UoX6ktR46L6VgmO2IsdNAu8tFpdvNywluziUnEzYMbKZJbmcnxR0d5HV0kBoITMj2Jv8IvbAZHZ0Ex9mKKeJP6nHmkYBskgUDYZ7+8WGOvLSfcPcTuJLc3LT1Kyy4aNW48g23thKoqiJw+gyBM6cJnj5DoLo6GoBpb+99LFEGzpLrcS69Du1rJtz4BPYUE8dFF6FcTpTTieF0WYGSy3o0IutVz3qHA+Wwg82GstlRNgNsdpTdhrLZovPYbCi7PRpwDZyw2QadlpWrgWaWYDDI2bNnqaqqik7eyPHm8XhYvWQJRUVFFBYWyoCqM1BFRQUXyedxxpN6nKZG6JYkAdkk6mj28afvvsG5E68T7v4jqdnZbP7Cl0nLia1VLNzZif/oMSvgOnMmEnxZk9nW1i+tfc4cnPn5JKxYgT07G3t2FvbsbEjMpPsNO6H6IImrc0i/YQOG6+bJ2F0xS3V0dEQDrzNnzlBbWxu9rZDH42Hp0qUUFBRQV1fHddddF+fSCiHEzCQB2SSpPdHGn/7nDbpbXyfUtZOchYt5379+adSbfAeqquh8uoLOiqfpenlf7ylEw8Axbx7O+fNJve7dOAvm41wwH+f8+TgKCjCGGFvJe6CBll8fA23i+VAxiatyJmNXxSyitaa5uZnKykpOnz7NmTNnaG1tBayrGPPy8li3bh0FBQUUFBSQlNR7B4eKior4FFoIIWYBCcgmwZsvnKXip29hU6/ha3uaBRddwg3/9K84EwYPtKrDYbpff53Op5+m4+mnCRw/AYBz0SI8H/soiWvX4lywAGdeHirG27qYgTCtvzuBd18dzvkpeD5U0q/jvhA9tNY0NTVRWVkZDcI6OjoA62rG+fPnc9lll1FQUMDcuXOx2+UrQwghJoN8u04gM2zywq+O8/pfqnAnvERb7W5K1l/FtX/7j/1G2w93dtL1/PNWS9izzxJuaQG7ncQ1a8i45RaSN27EuWDBeZUhcLaT5p+9Raixm5SrC0h953yrv5cQDA7AKisr6ezsBCA5OZnCwkIKCwtZsGABWVlZMo6XEEJMEQnIJoivK8jO7x+k6nAjySnP0VT1Kpe++wY2fux2VOR+ed0HD9HwrW/R9dJLEAxiS0sj6aorSdm4kaQNG7Clpp739rXWdL54lrYnT2EkOsj65ErcS9InaO/ETKK1xuv10traOmg6e/YsXV1dQP8ArLCwkMzMTAnAhBAiTiQgmwDNZ7v443cO0NHcTkrqX2g88yYbPnwbl924GaUUoZYWGr75LVoffxybx4PnYx8l5eqrSVi1CjUBp4DCnQFafnkM31vNuEs8ZNyyFFuSXN02m4VCIZqbm2lqaqKlpWVQ4BUYMMSE2+0mPT2dRYsWRQMwj8cjAZgQQkwTEpCNU83RFv740AEMm59E9x9pqq5k0x2fZcXVZehwmJZf/IKGb3yTcGcnno99jKzP/B22lJQJ277veAvN/3sU0xsk7b2R+1DKj+ysYJom7e3tNDU1RaeeWwe1tbXRd1Bnp9NJRkYGGRkZLFy4kPT09H5TQoLcEksIIaYzCcjGwdcZZNcjh3AldBPs/BVtLU3ceNcXWLz6bXhffY1zX/k/+N88TOLb3sacL34BV9HE3aNSh03ad52m49lq7FkJZH1iOc55yROWv5haWmsaGho4ceIEVVVV0QCs722GHA4HWVlZ5Ofnc/HFF5OZmUlmZiYZGRkkJCRIIC6EEDOYBGTnSWtNxWNH8LaeQ5m/RYdDbL73q+R6sjj7L3fT9sQT2HNzyfvG/yPl2msn9Mcy1NRN08+PEKzqIOmyOaRdvwjDKffwm2m6uro4efIkJ06c4MSJE9GrG9PT08nOzmbRokXRoCszM5OUlBQJuoQQYpaSgOw8Hd1bx/F9Z1DmHzBsivff81WMZ57jxH9/GzMQIPPTnybrbz6N0Wecpongfa2elt8eB6XwbCkhcWX2hOYvJk8oFKK6ujoagJ09exaw+nctWrSIxYsXs3jxYtLT0+NbUCGEEFNOArLz0NHs45mfHcHQT+H3tnLj5ltp//vPEjh+gqQrriD3nn/FtXDhhG7T9IdofeIE3lfrcS5IxfOhYuwZMrbYdBYKhaitraW6uppTp05x6tQpgsEgSikKCgq4+uqrWbx4MfPmzcMwZGgSIYS4kElANkba1Pz1x4fxd7xAoPMYlxUswX/PvTjy88l/6EGSr756wk8rBao7rLHFmn2kXDOf1HfMR9nk1NV0orWmtbWV6urq6HTu3DnC4TAAGRkZrFq1isWLF1NYWIh7iDsrCCGEuHBJQDZGByqqOf3GKwQ7d7MoPYvMP+wk/cMfIvdf/mXI2xeNhzY1nc/X0LazEluyg+xPXYRr0ci3XhJTw+/3U1NTEw2+ampqouN72e128vLyuPzyy8nPzycvL4/UcYwxJ4QQYvaTgGwMmmu7eOEXrxD27SDd5abo2b1kfrKcnLvumvBWMR00afrZW/jebMK9PBPP+4swEmVssXhqbW3lrbfe4q233uL06dPRYScyMzNZsmQJ+fn55Ofnk5OTg80mF1kIIYSInQRkMQqHTXY98jr+jt9hM4OseuMkOXf8Ddn/8A+TEIyFafzJYfxHW0i7fhHJ62VssXjQWlNXVxcNws6dOwdAdnY269evZ8GCBeTl5ZGYOPgepUIIIcRYSEAWo5f/cIraI7/BDNaz+uRZFtz5t2TdeeeEb8cMhGnafgj/yTYy3l9E0to5E74NMTzTNDlz5kw0CGttbQWgoKCAsrIySkpKyMzMjG8hhRBCzDoSkMXg3Mk29j7xBGbgMEW1zSy/4+/I/OQnJ3w7pj9E4w8PETjdTsYtS0m6NHfCtyEGCwaDnDx5ksOHD3P06FG8Xi82m41FixZxxRVXUFxcTHKyDLorhBBi8khANoqgP8yTD+4k2FVBVns36z95B5m3fWzCt2P6QjT+4CCB6g48HywmcVXOhG9D9PL5fBw9epS33nqLY8eOEQwGcblcLF26lJKSEpYsWYLL5Yp3MYUQQlwgJCAbRcWPX6al5le4giabPvxxMj/20QnfhukN0vDDQwRrOvF8uJTElVkTvg0BHR0dHDlyhMOHD3Pq1ClM0yQ5OZmLL76YkpISCgsLsU/Azd6FEEKIsZJfnxGc3HuGNyp+iDK9XPeem5gzCcFYuCtI4yNvEKzzknlrKQnLpH/SRGpubuatt97i8OHDVFVVAdaYYJdffjmlpaXk5eXJoKxCCCHiTgKyYXTVtfDH//4uOlTDlW9/B4s+efuEbyPcGaDx4TcINnaT+dFlJJR4Jnwbs5nWmu7ubtrb2+no6KC9vb3f1NLSQnNzMwBz5sxh48aNlJaWkpOTI1etCiGEmFYkIBtCqK2NX279JoHAARYvvpi1//hPE76NcEeAhu+/QbjFR9Zty3EXZUz4NmYLrTXNzc2cPHmS6upq2traokFXKBQalD45OZnU1FRycnJYu3YtJSUlZGTI+yuEEGL6koBsAG2aPP13X6ExeIyU1Hm898tfmvBthNv8VjDW7ifz48txL06f8G3MdF6vl1OnTnHy5ElOnDgRHX4iOTmZjIwM5s6dS3FxMampqf2m5ORkGZRVCCHEjCMB2QBNO/7CwfA5DJuTD33tfmz2iR0dP9Tqo+H7b2B2BMkqX4GrUG6FBNaNuKurqzlx4gQnTpzg7NmzALhcLhYuXMjb3/52Fi9ejMfjkdONQgghZp2YAjKllAe4C1gF9BuQSWt95cQXKz601jz96B8xzRau+PDfkzrBA4CG2vw0/M8BzO4QWbevwDX/wr6/YTgc5sCBAxw4cIAXXniBYDCIUor8/HyuuuoqFi9eTF5enrR4CSGEmPVibSF7DHABjwPeyStOfLX+pYJqsxGHM5O1N5RNaN6mN0jjIwcxvSGyb1+JsyBlQvOfScLhMG+88QbPPPMMLS0tuN1uVq1axaJFi1i4cCHuCb5JuxBCCDHdxRqQvR3I1lr7J7Mw8aS15ukf/g5Tt/K2996BmsChEMxAmMbtbxJq6ibrEysu2GDMNE0OHjzIM888Q1NTE3PnzuUjH/kINTU1XH311fEunhBCCBE3sQZkB4B84MQkliWu2p59ntPhJuz2dC7f/O4Jy1eHNc2PvUXgTDuej5TgXpI+YXnPFKZp8uabb1JRUUFjYyM5OTl88IMfpKSkBKVUtL+YEEIIcaGKNSD7K7BDKfVD4FzfJ7TWP5jwUk0xrTXPfP83mLqZ1e/+JIYxMX2WtNa0/PoYvreaSb9pMYkrsyck35lCa81bb73F008/TX19PVlZWdxyyy2UlpbKYKxCCCFEH7EGZFcA1cDAjlUamPEBWceLL3Eq1IzNlsLbP3j9hOXbvrMS7yt1pFwzn+TL501YvtOd1pqjR4/y9NNPc+7cOTIzM3nf+97HihUrJBATQgghhhBTQKa1ntUdfJ773q8I60YueedHsTsmZpiLjudr6KioJultc0h95/wJyXM6C4fDnD17llOnTnH48GFqa2vJyMjgpptuYuXKlXKlpBBCCDGCmMchU0plAO8F8oAa4Pda65bJKthU6dz7Msf9zRi2ZK649eYJydP7Wj1tfzhJwvJM0m9cMivHzTJNk7q6Ok6dOsWpU6c4ffo0gUAAgNzcXG644QYuvvhiCcSEEEKIGMQ6Dtk64I/AW8Bp4Hrgm0qp92itd09i+Sbd8w89TkjXs/LKD+JwOsedn+9oC82/OIpzYRqeD5WgjNkRjGmtaWpqigZgp06doru7G4DMzEwuuugiFi5cSGFhIUlJSXEurRBCCDGzxNpC9k3gb7XWP+9ZoZT6IPAAsHYSyjUlvK+9xlFfM4aRyMaP3zLu/AJVHTQ9+iaO3ESybluGcszs/lKmaXLmzBneeOMNjh49SkdHBwCpqaksXbqURYsWUVhYSFqa3G1ACCGEGI9YA7KlWIPC9vVL4LsTW5yp9cK3f0ZQ11H69ptxjnMw0mCDl8YfHcRIdpL1iRUY7pl5VyqtNTU1NRw8eJBDhw7R0dGBw+GgqKgoOnCr3L5ICCGEmFixRg3HgA9hjdjf4xZm8Lhk3jcOcrirBaXcvOP2D48rr3C7n8ZHDgKKrPIV2FLHf+pzqtXV1XHw4EEOHjxIS0sLNpuNJUuWsHLlSpYuXYpzAk7nCiGEEGJosQZk/wj8QSn1D1h9yAqBIqy+ZDPSnv/+KUFdS9Ha63EnJp53PmZ3iIaeWyJ9eiWOrIQJLOXkam5ujgZh9fX1KKVYuHAhV155JSUlJSQkzJx9EUIIIWayWIe9eFEptRh4DzAP+D3wpNa6eTILN1m6Dx/mUFsTSjl5599sOe98dMik8cdvEmrsJuvjy3HmT/9bIoXDYd5880327NlDdXU1AAUFBVx33XUsW7aM5OTkUXIQQgghxESLuaNTZIiLRyexLFNm3wOP4ucsiy7eRGLK+QVRWmtafnmUwKk2PB8sxl2UMcGlnFher5dXXnmFvXv30tHRgcfjoaysjOXLl5Oenh7v4gkhhBAXtGEDMqXUDq31tZH557BG5R9Ea33lJJVtUnQfOcKB5kZQDt51x8fOO5/2p07j3d9A6rsWkHhJzgSWcGI1NDSwZ88e9u/fTygUYtGiRbz3ve9lyZIlMmq+EEIIMU2M1EL24z7zD092QabKaw/8BB9nWbDsapIyzm+4hq6Xz9Hx1yoS1+SScnXBBJdw/LTWnDhxgpdeeonjx49js9m46KKLuPzyy8nNzY138YQQQggxwLABmda67xWVb2mt9wxMo5S6bFJKNUn8J0+yv7EBsPGuO287rzx8x1po+c1xXEXpZNw8vUbhDwaDvP766+zZs4eGhgaSk5O5+uqrWbNmjQzWKoQQQkxjsfYhewpIHWL9DsAzccWZXPu/9SO6OUt+8QZSszPH/PrguS6aHj2MIyeBzC2lKFv8T/l5vV5OnjzJ8ePHOXLkCN3d3cyZM4ebb76Z5cuXY7fPzPHQhBBCiAvJiL/WSikDUNasUpH5HouB0CSWbUIFTp/m1dp6UIqyOz4+5teH2/w0/vAgymUjM44Dv5qmSU1NDcePH+f48ePU1NQA4Ha7WbJkCWvWrGHBggXTquVOCCGEECMbLaoI0duZf2DwZQJfnfASTZI3HvgRXlXL3MWX4Zk3tn5Upj9E448OYXaHyb7jIuxprkkq5dDa29s5fvw4J06c4MSJE/h8PpRS5OXlsXHjRpYsWcK8efOkk74QQggxQ40WkC3EahV7Buh7NaUGGrTW3ZNVsIkUrKlh35laMDRld5aP6bU6rGn66VsE67rIum05znlTM05XW1sbr776KocPH6a+vh6A5ORkSkpKWLJkCYsWLSJxHAPaCiGEEGL6GDEg01qfjswumIKyTJrjv9pJp1FLTsEqsgvmxfw6rTWtTxzHf7SF9JuX4C6e3O5ypmly8uRJ9u3bx5EjR9BaU1hYSFlZGYsXLyY3N1dORQohhBCzUMwdoZRSNwBXAVn06UumtT7/wbymyBuvHQbCbPzkR8f0uo5nqunae46Ujfkkv23u5BQO6OrqYv/+/ezbt4+WlhYSExNZv349q1evJiNjeg84K4QQQojxiykgU0r9G3AH8HOsm4r/D/AR4H8nr2gTQ4dCNHhbMYwk8kuWxPw67+sNtO+oJOHibFLfVTjx5dKaqqoq9u3bx6FDhwiHw8yfP593vOMdlJaWytWRQgghxAUk1l/9cqBMa31QKfUJrfXnlFI/A744iWWbEO3738CnWsjMWBTz6T5/ZRvNjx/BWZiKZ/NSlDFxpwn9fj8HDhxg37591NXV4XQ6ufTSS1mzZo0M2iqEEEJcoGINyNK11gcj8wGllENrvVcpddVkFWyiHPzDc6B9LLxsbUzpw11Bmh49jD3DTeZHl6EcE3Plotaa1157jZ07d+L3+5kzZw7XX389K1euxOWa2qs2hRBCCDG9xBqQnVBKLddaHwIOAncqpVqAlskr2sQ4edK6LmHVdRtjSt/25ClMb4isT67EluSYkDK0tbXx+9//nuPHj7NgwQLe+c53kp+fLx30hRBCCAHEHpB9EegZ2v5fgZ8CycDfTkahJorp99MSaMNhTyctJ3vU9L7jLXhfqSNlYwHOueO/1ZDWmv3797Njxw5M0+Td7343a9eulfHChBBCCNFPTAGZ1vrJPvN7gNh7x8dR/bN7CepG5uauHDWtDoZp+c1x7JluUq8Z/w3D29vb+f3vf8+xY8eYP38+N910Ex7PjLnLlBBCCCGmUKxXWS4a5ik/UKu1NmPI41rgW4ANeFhr/bUh0nwA+BLWwLOva60/Ekv5hvPGn18CQhRftWHUtO1/OUO4yUfWp1aiHLbz3qbWmtdff50dO3YQCoW4dtO7uGzVMoyQD5pOQLAbzBBoE7QGHY7MRyaz77Km90YJMW2878IQ68eQ1xTKbHwDjsyIMYbFCKQeZwepx9lB6nHmifWU5XF6f817Oj71LJtKqd8Bf6u1rhvqxUopG/AgUAZUAy8rpX6ntX6zT5oirNOh67XWLUqpnLHtymBVNWcBxfJrRg7IArVddDxbTeLqXNyL04dPaIah4xy0noaW09HHYEct3mAXDf4gFa0lVAfmkGGrY4nrGRqff5BfvmjQrRReQ+FVBmHV++ZpFCag+63rO6nocxrrflXR16n+aWe0IY8cMeNIPc4OUo+zg9TjjBJrQPYpYCNW61UVMB+rX9lurNsq/QdWwLV5mNdfBhzXWp8EUEr9HLgReLNPmk8BD2qtWwC01vVj2I9BQh2dtIdbcTuzcCcP3x9Mm5qWXx3FSHCQ/p6F1srG43Du9WjQFWqu5Fz7aaq766m2QY3dTrXdTrXDTo3DSYtSFPgKWNW0Fpu2cdDzOsdTj4OyYY2j28ttOLBhoJSKRLYqOq+i85FnIvNG5L7uRr+0BkpZr+lZP7LpewGBz+fD7XbHuxhinKQeZwepx9lB6nG6OjXsM7EGZNuAJVprX2T5uFLqb4GjWuv/UUp9HDg2wuvzsAK5HtXA2wakWQqglHoB67Tml7TWOwZmpJT6NPBpgOzsbCoqKobcYOClQ4TNRtLSlw2bBiCtUpFdbXDuIpNzTz1M9plfsDtwhDddzkjQ5eCczUY4FUi1rmuwofAYaWQ6clhBLpm1mdjabKgkReKiRN6Z+E7eo96DS7lwGa7oo1M5MZR06B+os7OT5OSpuUeomDxSj7OD1OPsIPU4Pf2Bp4Z9LtaAzAAKgbf6rJuPFTgBdI0hr5HKUoTVEpcPPKuUWqm1bu2bSGv9PeB7AMXFxXrjxo1DZva7X78IaNZ94GZKrrh8yDShVh91f30FV36Qgu5/52cNb/F4aiodhgePM5X8lAIuSp3Pdcn5FKQUkJecR35KPjmJOeiwZvfu3Tz33HNorXnHu97B5ZdfLldQnoeKigqGq0cxc0g9zg5Sj7OD1OPME2sQ9U3gr0qpH2K1dOUDn4isB7gO6/TlcGqAvpcu5kfW9VUN7NFaB4FTSqmjWAHayzGWsZ/apjrAxpLLVw/5vA4Faf3x85hBxcOhu/lfWzdmejrXFFzNbSvLuTj74qFfpzWHDh3iqaeeoq2tjdLSUsrKyuQKSiGEEEKct1iHvfi6UuoA1n0sLwVqgU/2nFLUWv8W+O0IWbwMFCmlFmIFYh/CuhdmX78FPgz8UCmVhXUK82SsO9KXr66RLrOF5MQ52B0DBncN+tCvPcr+Z54nu+mTfC/nl+zMDPOBog9x6/LbKEgZfsiL6upqdu7cSVVVFXPmzOHmm2+msLDwfIoohBBCCBEV82nGSPA1qE9XjK8NKaU+A+zEOs35A631IaXUl4F9WuvfRZ57l1LqTSAMbNVaN53P9o488QzabCZ/6Tt7V/raCOz9Hn98/RF+4Ujg7tb/w8mEKha8YwVPlX6ZNFfasPm1t7fz5z//mQMHDpCUlMQNN9zAqlWr5PSkEEIIISZErOOQuYD7sFqwMrXWaUqpdwFLtdbfjiWPyOCyTw5Yd1+feQ38U2QalyOvHgLgohveBUCo9g1+9Mv38dNEB42pDu5r+AQZZipLyjdwZUH6sPkEAgFefPFFXnjhBUzTZMOGDVxxxRVy70khhBBCTKhYW8i+gXWl5BbgT5F1hyLrYwrIplJDewNKOckvLQHgFxX38K1UN2/PXMn/zfk7cg+bJF+VT+IwwZhpmhw8eJA///nPtLe3s2zZMsrKysjIyJjCvRBCCCHEhSLWgOxmrGEvupRSJoDWukYplTd5RTs/7cfO4DMbyUidhzIMzLYaHus6zoqELL7zrp9Q/8BraI8m9Zr5Q76+tbWVX//615w5c4a5c+fy/ve/nwULFkzxXgghhBDiQhJrQBYYmFYplQ2cVx+vyXToiWdBd7Dw4msAeOG5r1LpsHP/RZ+k4+kqQo3dZH1yBYZz8O2Rjhw5wm9+8xtM05R+YkIIIYSYMrEGZL8AtiulPgeglJqLNeTFzyepXOft+OGjAKy8cRMEu/np2afJdrm5JvNmmn72BomX5OAu6n/qMRwO85e//IUXX3yROXPmcMstt5CZmRmP4gshhBDiAhRrQHYP1u2R3gASsUbl/z7WCP7ThmmatHQ3YzMSyczL5+Tub/CCy87fLXg3Hb89hZFgI+36/vdJb21t5Ze//CXV1dWsWbOGTZs24Rg4VIYQQgghxCQaNSCL3Bj8i8DdWuvPRU5VNkauipxW6vcdIWjWkpu1AAU89uZPcNjhZuMTBM6cI+MDS7El9QZbR44c4be//S3hcJjNmzezYsWK+BVeCCGEEBesUQMyrXU4ct/KL0WWGya7UOfr4JPPg/az9O1vo/3ok/zOFuB9KZcTeroR16I0Ei/JAeQUpRBCCCGml1hPWf4YuAN4aBLLMm5nKisBWPbuMn71h1voNgy2dH8K7Q+RfuNilFK0tbXxy1/+kqqqKjlFKYQQQohpIdaA7DLg75VSn8e6l2X0dKXW+srJKNhYhQJB2gJNOO2pJIQa+Jn/LDeqy3AcDpJ8ZR6O3CSOHj3Kb37zG8LhMO9///tZuXJlvIsthBBCCBFzQPb9yDRtnf7La5jhc8wpWEbFc1+h1u7g4/W3YaQ6Sb46n6eeeooXXniB3NxcbrnlFrKysuJdZCGEEEIIIPabi2+f7IKM15sVe4EQpVes5r/qfs2HvZtwNztI//AiXnz5JV544QVWr17NtddeK6cohRBCCDGtxHovy/JhnvID1cBLWmv/hJXqPJytrQYU2vUqx2wZ3Nd0E67FabTnhql4ooLly5fz3ve+N55FFEIIIYQYUqynLD8GrAPqsAKwfCAX2AcUAiilbtRa75uEMo7K1+alK9RIojODx08/waeaP4YjbCfl+oVsf+Ix3G431113XTyKJoQQQggxqljvC3QI2Kq1nq+1frvWej7wz8BrWMHZd4D/nqQyjurok3vQ4Tpys1I4GV7ENW3rSL4in73HXqO2tpbrr7+epKSkeBVPCCGEEGJEsQZkHwG+PWDdd4AtkQFi/xNYNpEFG4u3dr8GaBo8h/h03YfQyQa+lW4qKqxTlcuWxa1oQgghhBCjijUgqwMGdsB6D1AfmXcDwYkq1Fg1tJxDYaM5YRmL/QWkX7+YJ/74OzlVKYQQQogZIdY+ZP8A/EIpdRBrHLICYAVwS+T5txGnU5Zt1S34Q3WkOdJZ33wj3rwwJ9uPUltbywc+8AE5VSmEEEKIaS/WYS92KaUWA+8G5gFPAn/UWjf1PA/smrRSjuDN37+INptYPHcTbu3Efs0CKn75EzlVKYQQQogZI9YWMrTWjUqpCiBPa/3S5BVpbE68fpAsVx5LnKuoXHqOQ88dlVOVQgghhJhRYupDppSar5R6AXgL+HNk3Wal1MOTWbhYNHc2sDrzXTTam/HNT6e2tpb3vOc9cqpSCCGEEDNGrC1k/wP8EbgCaIqsewr4r8koVKzMoElhgod0Vw5/XvQCZ14IsHz5cpYvXx7PYgkBQGMgxKvtXbza7sVnmmQ67GQ67WQ57GQ67Hgiyyk2A6VUvIsrZimtwyhli3cxZp2QqTnq9bG/w8vr7V5e7+imxh/gak8Km3M9rM9IxiafazEGY7m5+Hu01qZSSgNorduUUmmTV7TRaW+AFRmXcSJ8lE5fEm63IacqJ0hbMMSr7V72tXfxSpuX5mCIJUluihPdLE1ysTTJTWGCa8gvHNMMYhgX1u2pgqbmcFc3+9q6eKXdyyvtXVR2BwCwK7Arhc/UQ77WqRQehx2Pw0am00663Y7bpnAbBi5D4Yo8ug0D96BlgwUJThYnunAasV40Pbm01mgdIBz2Eg53Ewp3ReYjU6gL0/RhmgFM0x95DGDqQO+86UdH5rUO4XRm4XbnRaZ5uN15uFw54wo0tDbROoRhOCdw7ydfZyhMWyg8aH3P0WWGu2lre42W1j20tO4h5K9lceYq5s25iaysjRiGa2oLPEZBU3MuEMTjsJFkmx6BZFhrjnv9vB4Nvrwc6uymO/KZTrEZXJSSyPr0ZP7U0Mbj51rIddq5KTeDzbkZrEhOGPM/Xd6wyZ7WTipaOni2uYNaf5DFidZ379JEt/WY5CbP5cCQwG9ctA7j9Z6iveMgHR0HCfgbSEoqIiVlGcnJpbhcc6bkn+ZYA7I6YAlwtGeFUmoZcGYyChUrh7ZjU3aeyT2AWZ/BLbfcMq5TlVprjnh9PN3UQWMwhKk1GtAaTDSmtr70wjpMKOQlGPYSCndj093k2LrJNrzk2LrINjrwqA5s2t/nhyZo/cDoIErZUMqOYTgxlANlOAY89qy3o1DWa3UQU4fQOoQ2Q5g6OGheKTsZGZeTlbkRt3tezPttas2RLl80kNjX1sUxr3UnLAMoSXKT43Swp7WTX9e1RF/nMhSLE1wUJdooUPXkhg+T6X2BZO8LYMsg6FpCwFmI31GAz56L15ZNF+l0kkxb2KAlFKI1GKZdJ/PYoUqyHHaynXayIq1I2U4HWU472Q47iWNsRdLaJBzuxmZLHPV1tf4Az7d0Uu0L4DYMEmxW4JNgM0gwIlOfdW7DQANvdHjZ1+7llbYuXu/wRr+cc5121qQl8dF5WaxJTWRlSiIJhsJrmjQFQjQFwzQFQzQFQjQHQ9Z8ZLkpGKLW343PNPGbGn/0cehgroddweJEN6VJbkqTEihJdlOS5KbA7ZyUL2vTDNLVdYz29gO0dxygo+MgYfMszzwbIhzuRuvQmPNUymF9JgwnhnJanwPDiVI2Wtv2EQy2DEhvx+Wa0y9IS3DnYRgugqF2QsE2QqF2QqEOgqHIfLDdei7URijUAShSUy/Ck7GOjIy3k5a2Gpvt/AMWn/8cba2v0Nq2D7+vFps9Gbs9BbstGbs9GVt0PiU62WzJOByp2GzJ/Y7VlmCIo10+jnn9HO3yWZPXx1l/LCMMpQObIhPYmkJ4GpvIVr8hP8HNotQCFqfNpyDBRZ7LyTy3Y0zBj9Yan+8sgUDPyEcKlELR91gbuE6hdZhu06TGb01n/ZqzQajxw9kAnA0a1AcVJgqH0qxODHJFapArkoMsdGmib080X2vShDHDvug/AWHTSzjsw4wsd4SC7Pel8logmzeDuQRxYjcMHMqG3bBhN+w4DIf1aHPiMJzWeqU45w/yRmc3XWETgERDsSLZwYdznCxPCFHq9pFv70KHqwiHu7krNcjznYk82Z7GI1UB/qeqgUJHF+9KrOWdiTXMsXWgTeu73G5PwenKweXKxeHI4WTYw+5OF8+2drO3rQu/qXEqxWVpSaxJS+KE189Tje38LNgcfZcTbQZFCU4WJ8AiZ5CFji7ybW006KO8XmOiDDsoJ0rZQTlA2VHKCYY9Mm8nzabw2AKRf5R8hE0/Zrjbmg9H1kWWtda4XDm43HNxu+bics0d8jPjC5uc6vbjDZuYkWPGhMjvqPXbGjKDBAKt+IMtBAItoIMkOZNJcqaQ5Egj2ZlGoiMJt80W/WfUYYzt+0xHfscVoJR1DHZ1naCj42A0AOvsPEw47AXAMFw4ndnU1f8hmofDkUFycikpyaUkpywjJbmUxMRFGIYDX9jEZah+n12tNeFwJ4FAE8FgM4FAE4FgM8FAEyNR1riuI4vcy/Ju4H7gW8DfAPcAX9Na/3RM784Eumhuid72/k9wIMdHaUkpH/jABwalCYe9dHS8SVfXMUChDHuf4MeOXzt42evm2Q4Hz7bbqAlYb6pTaQw0Cg2YKEyUNq15Hcb6SbbSBHDiVf0DQYVJBm1kqVayVCvZRgfZRic5Rie5qok5qg6n9qLNYG/ApoPRx8E/aAaGYX2QrGDO+iAp5aBLpVKr51AXdhEItgLgds0lJWU5KcnLSExciDJs/b4se4OwLl5r99IR+bLJsNtYnZbE6tRE1qQmcUlqIsn23i/qzlCYN9sbeb3xCIfa6jnWHeZ0KINGldNn3zWa4T80Tu0nRXWRYgRIs5n4A5oueyotpotOPXRrhUuF8RgBsu1+FttbKLI1sNhWTT5nIdwZaYXpmbzRD5fNlkRi4iKSkhaTlLiYxKTFhJyLeM3v4fnWbp5r6eC49/xvw+pQipUpCaxOTWR1ahKr05LIdznGGDxax5jWIbQ2AR2t2558TK0J9AnQegK2rsiX3uHObg53+Xiry0eVLxDNO8lmUJwUCdSSE8hxOghpTcA0CWkij1beIa0JaE3ItB5NDTZlBXuEWgkH6ggHzhLynyXsP4tN+7ARwmk4SU6YR3cXZGbmYjOc2A0XNsOJzebCZliTPTrvBsNJt7bhM234tIHPNPCamm7TxBvunbpNk6CpWZWayNXpTkqdzYT8Z+n21eDzncXnq4lOfn89YPZ7bw0jAYc9FbsjFbs9FYc9Dbs9Fa8tk9eD8zkaSML0n0b5K3FpLwkqTGZSPtkpxcxJX05WyhKS7Q6SbAaJNgN7pD6sf9RMOruO0dr6Cm1tr9La9go+f621XeXGmVBAIBzAH+rGH/YRRhHGTggbYWyEsRPGRggbAVzUqfmcsy2hhvlU6RxazITofiQYmiUJDoqTk1ialEiGEaTTe5yuzqN0dR0lFGoHwOXKITmpmKSkpSQmFqIMO35TU9Pt41RHLae7mqkN2mjWGegBrYseh418lxOjs52lc3KsU+wO65+jFNpwB07h9B/G7t1PsHN/vwA5gIMOUmknjfZBj9Z8G+k0kU37gBMrhg7joYksGqJTJk3UMpf9XMpZVQBAtq7jYl7jYl5jGW/gZvjPrR8nRynhsLqYQ6zkJIWY2LATYqmtlkTdRVCHCekwpjYwMQhjw8TAjNSPVjZM5SBFdbOIUyzUx1hgvsk8ajAGHGfD6SSZPazjBa7kiLKu+i/mCFeoPbzdeBVvOMABvYw3uJhDXBR9bwqo5hL7Kda6Grg0yUeaKwubLZFgqJVgoJkGv5dTAQeVwSROhzKo1nOoIZ8WlRlTuYaSrDuYRzV5/aYqPDSN8G1u1X2DfRl19mWcNRZSpedxJpxOddCNOeIrz4+BiUuZOKyTdWgUYW09Rr49I0Ff7zKAkzBpqpNk3UyKbiGVdlKVlxyXm5yEDOYlzSE/tZC8lAUkOxzUdbdT3VFJTcdZznobqe/upDEYpE2n0EYaHSqNNjLw48RBmEyjg0xayaCBdPMcGbqeTJrIoBkPTaTTioHJO685+YrWes1Q+xZTQAbWvSqxArEFWGORfVdr/dvxvrnjsWJOkf7gJ96HKyOTv/u7v8PtttPZeZj2jjfoaD9Ae8cbdHWdYOCXdCNZ7Gc1r3Epb7KSgHLh0j6Wc4BLeJWLeYVMev8DsdvTcLvm4HLPweWag8s111qOrHM6MunWDs4FFDWBMLX+ENW+AGf9Qc76A9T4rMeBp6zmOB0sTHSyKMHFwgQXCxNdLEpwsSDBRYKhIoGZxjAceE1NZXeAE14/J70+TnT7OeX1c7LbT3Nw8OmLWBhAabLbCiRSk1iTlsiiBFdvEGAGCAbbCIZa8XpP0tKyh9bWvXR2vgVoDMNFWtqlZKS/DUfq5TTYizjqNans9pNoM0h32Miw20m320hRHSSE63EFq9GBGny+arq7q/D5qvF6m3E47IAmYCraSaJVp9Kmk2gjtXfSKTSSw2lViA/rx8pJkEW2eorsTRQ72ylxdbHYZeKyJ2DYEvD7a2nuPMOrXYr9wXwOsZJTLEQrG278rHTUcVmSjyvSEylOTsEX9uMN+fGGAnSFA/hCQbrCQbrD4cgUotvUhMwQC416FhlncRDobb3U4T6PwchjOBpsDXwE6/nhWEGZHcNwRFqQeh97WlGtU4S9+XaZds6YOZzRczhtzuGMzqOKPDpIiem4sGNiVyY2rCAthEE49guyx8VlKBINK/hJjLRQouBQZzdhDel2G1d5UrgmM5WrPSlkO3tPjZtmEL//HKYZxBEJwHpORwZMk5fbuni2pZNnmjs40OHFxPqvObZvwKmRqALMNxrI01XMMY8zT1eSRzWZNEb+CQSHw0Mo1IbWYez2FDwZG8jMvBKP5wrc7rmjbiMU6uJcw585VPtnTrRW0kgmHa4VdLkvpsXIp7K1jW6Hg+YQBPTQrWYuQnjsJjbDRkvIoMsc+ofXoTQem4nHbpJhN5nr0MxzauY5TfKcinlOyHUa2JWBUoZ1CloZKAxQCrSmxm/ybDs806Z5qQO8ppXv2mS4KlVzRZom32lwoNvJnk4bL7Wb7O8MENTWPxOrUhJZn5HChvRkVqclkWjrPbWvtWm1oEZaMazHZoLBlkiLRjOmDmK3JWGzJ2GzJWG3JWKzJWOzJWKzJ2LvmbclYbMlRP/Z7/3sWvNVviC/qWvll3XNHPP6sSkIRw6+LDusSw6yNqGZS+xnSA3X4A/U4/fXE/DX4Q80oHUQmy0Zp8ODw5mBw2FNTocnOt9t83Am7KE6mMDxU5UUFhaADqEi30PoMOgQmhDKDKGxlptDDipDiZwKuDnpd9Aa7n2PkgxYkmBnSaKL4uQEsh12jne28FZnF8e6TaqDjmjgZRBmDnXk6dPkRwK6BLyRxg0Thy0ZpzMDpyMdlyMdp9OD2+HB5fTgdGailQNvsBNvoIOuUCfeoJfuYDfekI/ucIDuUABfOIjPDOM3rQYTAxMVyV+ho9vqOw+agEqh21FAp5FrBVNmAk0hhu1KMpBNYfX9tZmkG12k6BaSw7W4gtV0q2RaVI4VeulUGsNJBAdcM2kDcpx29m9YOf6AbDpaMDdL/+u/vQudqUhJaiDVVYepIIydjlA6DYGFNAXm0xiYT0N4Hg0JCTQkuehwWl/SScEAc7s7mOdrI9ffikOFsKkQBiECZiJdIQ9doQxC2j3usmogaAO/XdHtMOh2KrodKvJoELT3/0JzBU3cQSu29zoMAo7+zzuDmsSgSUJAkxDUJAR60/ewKx+57uPMTXiLOQlvkWDvBKDJn8e57hJcIUhVLbhsnbhtXbhsnbiMTty2Tly2TpyGr982Q6aTc76l1HpLONtdSoN/EaYef1+x1tZW0tPTY06vgW6HosNt0OE26HQpOt0G4UhTtmFqkvyaZL+J16lodxtoQ6G0JtPvZX7wHEvNo5QYb5DlqCLNWYehhg+KTK0IaRch0xl9DGsnYW23vg60Da2t/6xNbUNjs/7r1rbe5/s9GtZXReQ1OvIfutYGGusH0CCMoUKRKYxBCJuy1tl61kWe15H8zMjrre2oSLki//VrGx0qCb/hxKF8OPHjUt04jW5c+HAa3biVF6fhw6H82I0ABibNgQIafIuo9y2k3r+IluA8TGVgqkgrkVLWvIL2jg5SUqygT/c5EDXQc2D2HKEKjWGCTYPN7J0f7v/pkAEtiQbNSTaak2wE7NaPdYpf4+kK4+kKk+LrPf414HUqWhINWpJstCYYmIb1mlSfSYbXJKPLJMVn/bMWNiBsWPsSNsBm95LmPkOKu5YkVwPYQvhwoyNfst2hVLpCHjpDWXQGs/CbiQwsvYrsj9IaQ/ddBkPrAcuQEDRxhvrmonEZnSTZW0iyt5Bob47Od4dSqfJeTL1vcfSYOR8JtlYWp7xEUcoLZLtP9XsurG2c8y/iTLCEmuBi6sLzadbZ+A0HQRsE7db5A0cYHGGNM6xxhDSOMNZ8WGMzh6/T82EqaEswaI4cC15X5EdP62gAl+LXpHvDpHtN0rpNbNPsJ04DnS5FY7INuwkZXWGSAiOdUwAibXfmGP4xGuv3al8BG3idBl6nwus06HIqvC7D+twBaE1ioGcySfJrkgImCUHrWHcYXpLtTSTZWwiaLryhDLrCGRPye9HLjJzBirx3SvdZtipdEfngASGz9/PbV1hB0KYI2K3HoE0RVvQ7jp0hjX0Mx3LP733ArvAPmA7cvPb8AjKl1GrAr7U+GFnOBr6JNUr/buAurXVnjGWccM7iUp35nZ+iVWydmZXWpHWbeLpMMjvDJARH+xBMnZBBJEAzrMdIsKZRJEYO9MRAbwA29i8ZTabrNPMTX6cgaT+57uMopTG1ImAm4Qsn4wun4DeT8IeT8YeT8YWT8ZtJ+MIpdIU8NPgWjekLIVbj+eLoMVSQ1uUycAd7v5zTh/lyVoRIddTjtnUSNF39gy/txNR2JvZnZXaaiHqMRc8PmhWcGbS7rdYUR0iT4Q2jNLT0BG1AQqAnAAuT3m1ij+1sU78tpjjqmZvwFt2hVOp9RfjN5InerbhLd9ZQmLSP1k6DLmMZzYECwsN0IZgufHZFc5KBz6FI7TbPs35np8n4PIYMCNgU7pAVeImxe/yOt593QPYcsE1r3TP22BNYI/X/CPgwcEBr/bcTXuIYZSxeoP/hiT+QmpSF07D6dzgMhUNZk91QOJXCrhSJNoM1aUmk2qfHVTvxFgp1oLWJ3Z6CijGgnSwVFRVs3LgxrmUQ4xevemwOhnimuYO/NLXz12arL9UVGSlclZHCFZ4UCtzTO6iYbuTzODtIPU5PSqlhA7LRmjtKgecimaRj3Tpphdb6qFLqd8CLQNwCMo9psG3Fynhtfkaz22PrTyTEdOdx2Lk5N4ObczPo+QdTxnUTQsw0ozWN2IGeS7YuB85prY8CaK2rsK6tjhu7U/7zFUL0UkpJMCaEmJFGC8gOAbdE5j9E5LZJAEqpPKBtksolhBBCCHHBGO2U5b8Av1dKfRcIAxv6PPdB4IXJKpgQQgghxIVixIBMa/28Umo+sBQ4qrXu6PP0H4GfT2bhzkcwGKS6uhqfzzd64guQ2+0mPz8fh+PCurWREEIIMZ2NOoZBJAh7ZYj1RyalRONUXV1NSkoKhYWF0pdkAK01TU1NVFdXs3DhwngXRwghhBAR0+NuxBPI5/ORmZkpwdgQlFJkZmZK66EQQggxzcy6gAzkkveRyHsjhBBCTD/DBmRKqRv6zEuHozjbvn07RUVFFBUVsX379iHTNDc3U1ZWRlFREWVlZbS0tAyZTgghhBDTy0gtZI/2mW+a7IKI4TU3N7Nt2zb27NnD3r172bZt25DB1te+9jWuueYajh07xjXXXMPXvva1OJRWCCGEEGM1UkB2Tin1GaXUOwC7UupqpdQ7Bk5TVdCZorKykpKSErZs2UJpaSmbN2/G6/WOK8+dO3dSVlaGx+MhIyODsrIyduzYMSjdE088wW233QbAbbfdxm9/+9txbVcIIYQQU2Okqyw/DnwZ+CzgBH4wRBoNLJr4Yk2Mbb8/xJtn2yc0z2XzUvm39y4fMc2RI0d45JFHWL9+PeXl5Tz00EPcdddd/dL853/+Jz/96U8HvfbKK6/kgQce6LeupqaGgoKC6HJ+fj41NTWDXltXV8fcuXMBmDNnDnV1dTHvlxBCCCHiZ9iATGv9IvBOAKXUca31kikr1QxXUFDA+vXrAbj11lt54IEHBgVkW7duZevWrZNWBrmFjBBCCDFzjDoOGUBPMBYZJDYPqI7cy3JaG60la7IMDISGCozG0kKWl5dHRUVFdLm6upqNGzcOem1ubi61tbXMnTuX2tpacnJyzm8HhBBCCDGlYhr2Qik1Ryn1DHAc+DVwQin1rFJq3qSWboY6c+YMu3fvBuCxxx5jw4YNg9Js3bqV/fv3D5oGBmMAmzZtYteuXbS0tNDS0sKuXbvYtGnToHQ33HBD9ArM7du3c+ONN07wngkhhBBiMsQ6Dtl3gdeBDK31XCADeC2yXgxQXFzMgw8+SGlpKS0tLdx5553jys/j8XDvvfeydu1a1q5dy3333YfH4wHg9ttvZ9++fQDcfffdPPXUUxQVFfHnP/+Zu+++e9z7IoQQQojJF9MpS6ybis/VWgcBtNZdSqnPA4N7lgvsdjuPPvro6AnHoLy8nPLy8kHrH3744eh8ZmYmf/nLXyZ0u0IIIYSYfLG2kLUAywasKwZaJ7Q0QgghhBAXoFhbyL4O/Fkp9QhwGlgAfAK4d7IKNlMVFhZy8ODBeBdDCCGEEDNIrFdZfl8pdQL4CHARcBb4iNZazo8JIYQQQoxTrC1kaK3/Cvx1EssihBBCCHFBirUPmRBCCCGEmCQSkAkhhBBCxJkEZDPE9u3bKSoqoqioKDr460C/+MUvWL58OYZhRMcmE0IIIcT0F3MfMgCllAHkaq1rJ6k8YgjNzc1s27aNffv2oZRi9erV3HDDDWRkZPRLt2LFCn7961/zN3/zN3EqqRBCCCHOR6y3TkpXSj0G+LBun4RS6gal1Fcms3AzUWVlJSUlJWzZsoXS0lI2b96M1+sdV547d+6krKwMj8dDRkYGZWVl7NixY1C60tJSiouLx7UtIYQQQky9WFvIvos1OOwC4M3Iut3AfwFfnIRyTYw/3Q3n3pjYPOeshHd/bcQkR44c4ZFHHmH9+vWUl5fz0EMPcdddd/VLM5abi9fU1FBQUBBdzs/Pp6ZGbpIghBBCzBaxBmTXAPO01kGllAbQWjcopXImr2gzV0FBAevXrwfg1ltv5YEHHhgUkG3dupWtW7fGo3hCCCGEmGZiDcjagCwg2ndMKTW/7/JolFLXAt8CbMDDWushm5mUUu8Hfgms1VqPr2f6KC1Zk0UpNeIyjK2FLC8vj4qKiuhydXU1GzdunJCyCiGEECL+Yg3IHgZ+pZT6AmAopdYB/451KnNUSikb8CBQBlQDLyulfqe1fnNAuhTgs8CeGMs1LZ05c4bdu3ezbt06HnvsMTZs2DAozVhayDZt2sQ999xDS0sLALt27eL++++f0DILIYQQIn5iHfbiP4D/xQqqHMAPgCewWrxicRlwXGt9UmsdAH4O3DhEuv8T2ZYvxnynpeLiYh588EFKS0tpaWnhzjvvHFd+Ho+He++9l7Vr17J27Vruu+8+PB4PALfffnt0iIvf/OY35Ofns3v3bt7znvewadOmce+LEEIIISaf0lpP/kaU2gxcq7W+PbL8UeBtWuvP9ElzKfAFrfX7lVIVwF1DnbJUSn0a+DRAdnb26scff7zf82lpaSxZsmTS9mU0p0+f5gMf+AB79kzfRr7jx4/T1tYW72JEdXZ2kpycHO9iiHGSepwdpB5nB6nH6enqq69+RWu9ZqjnYh6HTClVBnwIyNFav1cptQZIjdzjclwi45v9P+Djo6XVWn8P+B5AcXGxHtiX6vDhw6SkpIy3SOctOTkZwzDiWobRuN1uLrnkkngXI6qiokL6xM0CUo+zg9Tj7CD1OPPEOg7Z3wPfAY4BV0ZWdwOxjkNWAxT0Wc6PrOuRAqwAKpRSlcDlwO8iQd+MUlhYyMGDB+NdDCGEEELMILH2IftH4J2RKyPNyLq3gFhHIX0ZKFJKLVRKObFa2n7X86TWuk1rnaW1LtRaFwIvATeM+ypLIYQQQogZINaALAWoisz3dDpzAIFYXqy1DgGfAXYCh4HHtdaHlFJfVkrdMIbyCiGEEELMOrH2IXsWuBv4ap91/wA8HeuGtNZPAk8OWHffMGk3xpqvEEIIIcRMF2tA9vfA75VSnwJSlFJHgA7g+kkrmRBCCCHEBWLUU5aRKyBLgSuADwAfAW4DLtNan5vc4oke27dvp6ioiKKiIrZv3z5kmq1bt1JSUsJFF13EzTffTGtr69QWUgghhBDnZdSATGttAk9orbu11nu11r/QWr8UWS+mQHNzM9u2bWPPnj3s3buXbdu2RUft76usrIyDBw9y4MABli5dKqP5CyGEEDNErJ36n1VKXT6pJZklKisrKSkpYcuWLZSWlrJ582a8Xu+48ty5cydlZWV4PB4yMjIoKytjx44dg9K9613vwm63zkJffvnlVFdXj2u7QgghhJgasfYhOw38SSn1BNbVltHh/YfrmD8d/Mfe/+Ct5rcmNM8STwn/ctm/jJjmyJEjPPLII6xfv57y8nIeeugh7rrrrn5pxnJz8ZqaGgoKeodxy8/Pp6amZuBL+/nBD37ABz/4wdF2RwghhBDTQKwBWQLw28h8/uQUZfYoKChg/fr1ANx666088MADgwKysdxcfKy++tWvYrfb2bJly6TkL4QQQoiJFVNAprX+xGQXZDKM1pI1WZRSIy7D2FrI8vLyqKioiC5XV1cPe0uMH/3oR/zhD3/gL3/5y5DbFUIIIcT0E1NAppRaNMxTfqBWOvj3d+bMGXbv3s26det47LHH2LBhw6A0Y2kh27RpE/fcc0+0I/+uXbuG7LC/Y8cOvv71r/PMM8+QmJg4vp0QQgghxJSJtVP/caz7WB4bMH8G8CulfqWUyp2cIs48xcXFPPjgg5SWltLS0sKdd945rvw8Hg/33nsva9euZe3atdx33314PB4Abr/9dvbts+4w9ZnPfIaOjg7KyspYtWoVd9xxx7j3RQghhBCTL9Y+ZJ8CNgJfwurUPx/4IrAbeAb4D+BBYPOEl3AGstvtPProoxOaZ3l5OeXl5YPWP/zww9H548ePT+g2hRBCCDE1Yg3ItgFLtNa+yPJxpdTfAke11v+jlPo4VouZEEIIIYQYo1hPWRpA4YB18wFbZL6L2IO7Wa2wsJCDBw/GuxhCCCGEmEFiDaK+CfxVKfVDrFOW+cAnIusBrsM6fSmEEEIIIcYo1mEvvq6UOgDcAlwK1AKf1FrviDz/W3rHKRNCCCGEEGMQ82nGSPA1+H49QgghhBBiXGLqQ6aUcimlvqqUOqmUaouse5dS6jOTWzwhhBBCiNkv1k793wBWAFvovY/lIWB8A2yJmG3fvp2ioiKKiorYvn37kGnuvfdeLrroIlatWsW73vUuzp49O8WlFEIIIcT5iDUguxn4iNZ6N2ACaK1rgLzJKpjo1dzczLZt29izZw979+5l27Zt0VH7+9q6dSsHDhxg//79XH/99Xz5y1+OQ2mFEEIIMVaxBmQBBvQ3U0plA00TXqIZrrKykpKSErZs2UJpaSmbN2/G6/WOK8+dO3dSVlaGx+MhIyODsrIyduwY3J0vNTU1Ot/V1SX3shRCCCFmiFg79f8C2K6U+hyAUmou1pAXP5+kck2Ic//+7/gPvzWhebpKS5hzzz0jpjly5AiPPPII69evp7y8nIceeoi77rqrX5qx3Fy8pqaGgoKC6HJ+fj41NTVDbvsLX/gCP/7xj0lLS+Ppp5+OdbeEEEIIEUextpDdA5wC3gDSsUblP4s1gr8YoKCggPXr1wNw66238vzzzw9Ks3XrVvbv3z9oGhiMjdVXv/pVqqqq2LJlC9/+9rfHlZcQQgghpkas45AFgM8Bn4ucqmzUWutRXhZ3o7VkTZaBpwqHOnU4lhayvLw8KioqosvV1dVs3LhxxDJs2bKF6667jm3bJGYWQgghpruYAjKl1DLgCsADNAPPAW9OYrlmtDNnzrB7927WrVvHY489xoYNGwal2bp1K1u3bo0pv02bNnHPPfdEO/Lv2rWL+++/f1C6Y8eOUVRUBMATTzxBSUnJOPZCCCGEEFNlxIBMWU07jwC3AdVYpynzgHlKqZ8A5TOhpWyqFRcX8+CDD1JeXs6yZcu4887xjQ7i8Xi49957Wbt2LQD33XcfHo8HgNtvv5077riDNWvWcPfdd3PkyBEMw2DBggV897vfHfe+CCGEEGLyjdZC9mlgI3C51vrlnpVKqbXAz4C/AeRXfwC73c6jjz46oXmWl5dTXl4+aP3DDz8cnf/Vr341odsUQgghxNQYrVP/R4F/6BuMAUSW/zHyvBBCCCGEGIfRArJlwDPDPPdM5HnRR2FhIQcPHox3MYQQQggxg4wWkNm01h1DPRFZH+uwGUIIIYQQYhij9SFzKKWuBoYb8j3WgWWFEEIIIcQwRguo6oEfjPK8EEIIIYQYhxEDMq114RSVQwghhBDigiV9wGaI7du3U1RURFFREdu3bx8x7X/913+hlKKxsXGKSieEEEKI8ZA+YDNAc3Mz27ZtY9++fSilWL16NTfccAMZGRmD0lZVVbFr1y7mz58fh5IKIYQQ4nxIC9kEq6yspKSkhC1btlBaWsrmzZvxer3jynPnzp2UlZXh8XjIyMigrKyMHTt2DJn2c5/7HF//+teHvH+mEEIIIaanWd1C9tzjR2ms6pzQPLMKkrniA0tHTHPkyBEeeeQR1q9fT3l5OQ899BB33XVXvzRjubl4TU0NBQUF0eX8/HxqamoGvfaJJ54gLy+Piy++eCy7JIQQQog4m9UBWbwUFBSwfv16AG699VYeeOCBQQHZWG4uHguv18u///u/s2vXrgnLUwghhBBTY1YHZKO1ZE2WgacLhzp9OJYWsry8PCoqKqLL1dXVbNy4sV+aEydOcOrUqWjrWHV1NZdeeil79+5lzpw557knQgghhJgKszogi5czZ86we/du1q1bx2OPPcaGDRsGpRlLC9mmTZu45557aGlpAWDXrl3cf//9/dKsXLmS+vreYeEKCwvZt28fWVlZ49gTIYQQQkwF6dQ/CYqLi3nwwQcpLS2lpaWFO++8c1z5eTwe7r33XtauXcvatWu577778Hg8ANx+++3s27dvIoothBBCiDiRFrJJYLfbefTRRyc0z/LycsrLywetf/jhh4dMX1lZOaHbF0IIIcTkkRYyIYQQQog4k4BsghUWFnLw4MF4F0MIIYQQM4gEZEIIIYQQcSYBmRBCCCFEnElAJoQQQggRZxKQCSGEEELEmQRkM8T27dspKiqiqKiI7du3D5nmS1/6Enl5eaxatYpVq1bx5JNPTnEphRBCCHE+ZByyGaC5uZlt27axb98+lFKsXr2aG264gYyMjEFpP/e5zw26b6YQQgghpjdpIZtglZWVlJSUsGXLFkpLS9m8eTNer3dcee7cuZOysjI8Hg8ZGRmUlZWxY8eOCSqxEEIIIeJtVreQPf2j71F/+uSE5pmzYBFXf/zTI6Y5cuQIjzzyCOvXr6e8vJyHHnpoUKvVWG4uXlNTQ0FBQXQ5Pz+fmpqaIbf97W9/mx//+MesWbOG//qv/xqyFU0IIYQQ04u0kE2CgoIC1q9fD8Ctt97K888/PyjN1q1b2b9//6BpYDA2FnfeeScnTpxg//79zJ07l3/+538+77yEEEIIMXVmdQvZaC1Zk0UpNeIyjK2FLC8vj4qKiuhydXU1GzduHPTa3Nzc6PynPvUprr/++jGWXAghhBDxMKsDsng5c+YMu3fvZt26dTz22GNs2LBhUJqtW7eydevWmPLbtGkT99xzDy0tLQDs2rWL+++/f1C62tpa5s6dC8BvfvMbVqxYMY69EEIIIcRUkVOWk6C4uJgHH3yQ0tJSWlpauPPOO8eVn8fj4d5772Xt2rWsXbuW++67D4/HA8Dtt9/Ovn37APj85z/PypUrueiii3j66af5xje+Me59EUIIIcTkkxaySWC323n00UcnNM/y8nLKy8sHrX/44Yej8z/5yU8mdJtCCCGEmBrSQiaEEEIIEWdTFpAppa5VSh1RSh1XSt09xPP/pJR6Uyl1QCn1F6XUgqkq20QqLCzk4MGD8S6GEEIIIWaQKQnIlFI24EHg3cAy4MNKqWUDkr0GrNFaXwT8Evj6VJRNCCGEECLepqqF7DLguNb6pNY6APwcuLFvAq3101rrniHtXwLyp6hsQgghhBBxNVUBWR5Q1We5OrJuOJ8E/jSpJRJCCCGEmCam3VWWSqlbgTXAVcM8/2ng0wDZ2dn9BkwFSEtLo6OjY5JLObP5fL5B71s8dXZ2TqvyiPMj9Tg7SD3ODlKPM89UBWQ1QEGf5fzIun6UUu8EvgBcpbX2D5WR1vp7wPcAiouL9cAR6w8fPkxKSsrElHoa2b59O1/5ylcA+OIXv8htt902ZLr//u//5sEHH8Rms/Ge97yHr399cFc8t9vNJZdcMqnlHYuKiooh7zwgZhapx9lB6nF2kHqceaYqIHsZKFJKLcQKxD4EfKRvAqXUJcD/ANdqreunqFwzQnNzM9u2bWPfvn0opVi9ejU33HDDoBuHP/300zzxxBO8/vrruFwu6uvlbRRCCCFmginpQ6a1DgGfAXYCh4HHtdaHlFJfVkrdEEn2n0Ay8Aul1H6l1O+momwTrbKykpKSErZs2UJpaSmbN2/G6/WO/sIR7Ny5k7KyMjweDxkZGZSVlbFjx45B6b7zne9w991343K5AMjJyRnXdoUQQggxNaasD5nW+kngyQHr7usz/86J3mbr708QONs1oXk65yWR/t7FI6Y5cuQIjzzyCOvXr6e8vJyHHnqIu+66q1+asdxcvKamhoKC3jO++fn51NQMOuPL0aNHee655/jCF76A2+3m//7f/8vatWvHsntCCCGEiINp16l/NigoKGD9+vUA3HrrrTzwwAODArKx3Fw8VqFQiObmZl566SVefvllPvCBD3Dy5EmUUhO6HSGEEEJMrFkdkI3WkjVZBgZAQwVEY2khy8vL63e1THV19ZCdNfPz83nf+96HUorLLrsMwzBobGwkOzv7/HZECCGEEFNiVgdk8XLmzBl2797NunXreOyxx9iwYcOgNGNpIdu0aRP33HMPLS0tAOzatYv7779/ULqbbrqJp59+mquvvpqjR48SCATIysoa384IIYQQYtLJzcUnQXFxMQ8++CClpaW0tLRw5513jis/j8fDvffey9q1a1m7di333XcfHo8HgNtvv519+/YBUF5ezsmTJ1mxYgUf+tCH2L59u5yuFEIIIWYAaSGbBHa7nUcffXRC8ywvL6e8vHzQ+ocffjg673Q6J3y7QgghhJh80kImhBBCCBFnEpBNsMLCQg4ePBjvYgghhBBiBpGATAghhBAiziQgE0IIIYSIMwnIhBBCCCHiTAIyIYQQQog4k4Bshti+fTtFRUUUFRWxffv2IdN88IMfZNWqVaxatYrCwkJWrVo1tYUUQgghxHmRcchmgObmZrZt28a+fftQSrF69WpuuOEGMjIy+qX73//93+j8P//zP5OWljbVRRVCCCHEeZAWsglWWVlJSUkJW7ZsobS0lM2bN+P1eseV586dOykrK8Pj8ZCRkUFZWRk7duwYNr3Wmscff5wPf/jD49quEEIIIabGrG4h+9Of/sS5c+cmNM85c+bw7ne/e8Q0R44c4ZFHHmH9+vWUl5fz0EMPcdddd/VLM5abi9fU1FBQUBBdzs/Pp6amZtjtP/fcc+Tm5lJUVBTLLgkhhBAizmZ1QBYvBQUFrF+/HoBbb72VBx54YFBANpabi4/Vz372M2kdE0IIIWaQWR2QjdaSNVkG3tB7qBt8j6WFLC8vj4qKiuhydXU1GzduHHLboVCIX//617zyyitjL7gQQggh4mJWB2TxcubMGXbv3s26det47LHH2LBhw6A0Y2kh27RpE/fccw8tLS0A7Nq1i/vvv3/ItH/+858pKSkhPz///HdACCGEEFNKOvVPguLiYh588EFKS0tpaWnhzjvvHFd+Ho+He++9l7Vr17J27Vruu+8+PB4PALfffjv79u2Lpv35z38upyuFEEKIGUZayCaB3W7n0UcfndA8y8vLKS8vH7T+4Ycf7rf8ox/9aEK3K4QQQojJJy1kQgghhBBxJgHZBCssLOTgwYPxLoYQQgghZhAJyIQQQggh4kwCMiGEEEKIOJOATAghhBAiziQgE0IIIYSIMwnIZojt27dTVFREUVER27dvHzLN/v37ufzyy1m1ahVr1qxh7969U1xKIYQQQpwPGYdsBmhubmbbtm3s27cPpRSrV6/mhhtuICMjo1+6z3/+8/zbv/0b7373u3nyySf5/Oc/3++WS0IIIYSYnqSFbIJVVlZSUlLCli1bKC0tZfPmzXi93nHluXPnTsrKyvB4PGRkZFBWVsaOHTsGpVNK0d7eDkBbWxvz5s0b13aFEEIIMTVmdQvZ0aP/h47OwxOaZ0pyKUuX3jtimiNHjvDII4+wfv16ysvLeeihh7jrrrv6pRnLzcVramooKCiILufn51NTUzPotd/85jfZtGkTd911F6Zp8uKLL45l14QQQggRJ9JCNgkKCgpYv349ALfeeivPP//8oDRbt25l//79g6aBwdhYfOc73+Eb3/gGVVVVfOMb3+CTn/zkeeclhBBCiKkzq1vIRmvJmixKqRGXYWwtZHl5ef36glVXV7Nx48ZBr92+fTvf+ta3ALjlllu4/fbbz6P0QgghhJhqszogi5czZ86we/du1q1bx2OPPcaGDRsGpdm6dStbt26NKb9NmzZxzz330NLSAsCuXbu4//77B6WbN28ezzzzDBs3buSvf/0rRUVF49sRIYQQQkwJCcgmQXFxMQ8++CDl5eUsW7aMO++8c1z5eTwe7r33XtauXQvAfffdh8fjAeD222/njjvuYM2aNXz/+9/ns5/9LKFQCLfbzfe+971x74sQQgghJp8EZJPAbrfz6KOPTmie5eXllJeXD1r/8MMPR+c3bNjAK6+8MqHbFUIIIcTkk079QgghhBBxJgHZBCssLOTgwYPxLoYQQgghZhAJyIQQQggh4kwCMiGEEEKIOJOATAghhBAiziQgE0IIIYSIMwnIZojt27dTVFREUVER27dvHzLN66+/zrp161i5ciXvfe97ozcaF0IIIcT0JgHZDNDc3My2bdvYs2cPe/fuZdu2bdFR+/u6/fbb+drXvsYbb7zBzTffzH/+53/GobRCCCGEGCsJyCZYZWUlJSUlbNmyhdLSUjZv3ozX6x1Xnjt37qSsrAyPx0NGRgZlZWXs2LFjULqjR49y5ZVXAlBWVsavfvWrcW1XCCGEEFNjVo/Uf++xag52dk9oniuSE/g/Rfkjpjly5AiPPPII69evp7y8nIceeoi77rqrX5qx3Fy8pqaGgoKC6HJ+fj41NTWDXrt8+XKeeOIJbrrpJn7xi19QVVU1ll0TQgghRJxIC9kkKCgoYP369QDceuutPP/884PSbN26lf379w+aBgZjY/GDH/yAhx56iNWrV9PR0YHT6TzvvIQQQggxdWZ1C9loLVmTRSk14jKMrYUsLy+PioqK6HJ1dTUbN24c9NqSkhJ27doFWKcv//jHP55H6YUQQggx1WZ1QBYvZ86cYffu3axbt47HHnuMDRs2DEqzdetWtm7dGlN+mzZt4p577ol25N+1axf333//oHT19fXk5ORgmiZf+cpXuOOOO8a3I0IIIYSYEnLKchIUFxfz4IMPUlpaSktLC3feeee48vN4PNx7772sXbuWtWvXct999+HxeADrysp9+/YB8LOf/YylS5dSUlLCvHnz+MQnPjHufRFCCCHE5JMWsklgt9t59NFHJzTP8vJyysvLB61/+OGHo/Of/exn+exnPzuh2xVCCCHE5JMWMiGEEEKIOJOAbIIVFhZy8ODBeBdDCCGEEDOIBGRCCCGEEHE2KwMyrXW8izBtyXsjhBBCTD+zLiBzu900NTVJ4DEErTVNTU243e54F0UIIYQQfcy6qyzz8/Oprq6moaEh3kWZltxuN/n58RkwVwghhBBDm7KATCl1LfAtwAY8rLX+2oDnXcCPgdVAE/BBrXXlWLfjcDhYuHDh+AsshBBCCDFFpuSUpVLKBjwIvBtYBnxYKbVsQLJPAi1a6yXAN4D/mIqyCSGEEELE21T1IbsMOK61Pqm1DgA/B24ckOZGYHtk/pfANWqom0AKIYQQQswyUxWQ5QFVfZarI+uGTKO1DgFtQOaUlE4IIYQQIo5mXKd+pdSngU9HFv1KKRmFdebLAhrjXQgxblKPs4PU4+wg9Tg9LRjuiakKyGqAgj7L+ZF1Q6WpVkrZgTSszv39aK2/B3wPQCm1T2u9ZlJKLKaM1OPsIPU4O0g9zg5SjzPPVJ2yfBkoUkotVEo5gQ8BvxuQ5nfAbZH5zcBftQwmJoQQQogLwJS0kGmtQ0qpzwA7sYa9+IHW+pBS6svAPq3174BHgJ8opY4DzVhBmxBCCCHErDdlfci01k8CTw5Yd1+feR9wyxiz/d4EFE3En9Tj7CD1ODtIPc4OUo8zjJKzgkIIIYQQ8TXr7mUphBBCCDHTzNiATCl1rVLqiFLquFLq7niXR8RGKfUDpVR93+FKlFIepdRTSqljkceMeJZRjEwpVaCUelop9aZS6pBS6rOR9VKPM4hSyq2U2quUej1Sj9si6xcqpfZEvlv/N3IhlpjmlFI2pdRrSqk/RJalHmeYGRmQxXgrJjE9/Qi4dsC6u4G/aK2LgL9ElsX0FQL+WWu9DLgc+LvI50/qcWbxA+/QWl8MrAKuVUpdjnXbum9EbmPXgnVbOzH9fRY43GdZ6nGGmZEBGbHdiklMQ1rrZ7Guou2r722ztgM3TWWZxNhorWu11q9G5juwfgTykHqcUbSlM7LoiEwaeAfW7etA6nFGUErlA+8BHo4sK6QeZ5yZGpDFcismMXPkaq1rI/PngNx4FkbETilVCFwC7EHqccaJnObaD9QDTwEngNbI7etAvltnim8CnwfMyHImUo8zzkwNyMQsFRkMWC79nQGUUsnAr4B/1Fq3931O6nFm0FqHtdarsO6echlQEt8SibFSSl0P1GutX4l3WcT4zLh7WUbEcismMXPUKaXmaq1rlVJzsf5bF9OYUsqBFYz9VGv968hqqccZSmvdqpR6GlgHpCul7JHWFflunf7WAzcopa4D3EAq8C2kHmecmdpCFsutmMTM0fe2WbcBT8SxLGIUkf4pjwCHtdb/r89TUo8ziFIqWymVHplPAMqw+gM+jXX7OpB6nPa01v+qtc7X/7+9ewuxqorjOP79ZZmkppTdNGfM8iGJLm9JglJBZZoPkS+jUUHUQ/aQU1QUgWh2IQiDILpQKV0kwbIMMkqxC11IrKgXCc2yIitzLKpJfz3sNXg6zOgpoj1Hfx8Y2Gfvvfb+7zkw8ztrr32WPYHqf+EbtrvI+9h22vaLYcungQfZNxXT4norilZIehaYDowBvgPuAlYBK4AOYCswx3bzwP8YJCRNBTYAn7BvzMrtVOPI8j62CUlnUg32HkL14XyF7YWSJlI9KHUMsBGYa/v3+iqNVkmaDnTbnpn3sf20bSCLiIiIOFi06y3LiIiIiINGAllEREREzRLIIiIiImqWQBYRERFRswSyiIiIiJolkEXEIUPSIkk7JH07CGp5W9I5ZXm+pHvrriki6pNAFhGHBEkdwAJgsu0T/2HbLZIu/A9rmQX02N5YVj0KdEk6vumcE/6rc0bE4JZAFhGHig7gB9uDYUqn64FlfS9s/wa8ClxZW0URUasEsoj435Xen25JH0v6WdLzkoY1bL9W0mZJP0p6SdLYFo87StLTkr6XtFXSHZIOK71ba4GxknZLerKftmMkvSxpZznvhtJ2GVWYW13a3lL2P1fSO2X/TeVb0vuOtU7SEknvS9ol6UVJx5RtQ4HzgfVNJawDLh3gumZI+kxSj6SvJXW38vuIiPaRQBYRdZkDXAycApwJXAUg6XxgSdl+EtU0TM+1eMyHgFHARGAaVY/T1bZfBy4BttseYfuqftouAL4CjgNOoJoOyrbnAV8Cs0rb+ySNA14BFlFNTdMNrJR0XMPxrgSuKdfwJ7C0rJ8E7LX9VdP5PwfO6nthe4LtLeXl48B1tkcCZwBvtPj7iIg2kUAWEXVZant7me9yNXB2Wd9FNT/tR2XuvduAKQcaTyVpCNXkyrfZ7ilh5gFgXov19FKFp07bvbY3eOC55eYCa2yvsb3X9lrgQ2BGwz7LbH9q+xfgTmBOqXE00NPPMXuowuRAtU2WdLTtn2x/1OI1RUSbSCCLiLo0Pun4KzCiLI+l6hUDwPZu4Adg3AGONwY4orFtWT5Quz73A5uB1yR9IenW/ezbCVxRblfulLQTmEoV6Ppsa6rjiFLjT8DIfo45Evh5gPNdThX2tkpaL2lKKxcUEe0jgSwiBpvtVIEHAEnDgWOBrw/QbgdVT1Jnw7qOFtoBUHrVFtieCFwG3CTpgr7NTbtvo+oBG93wM9z2PQ37jG+qo7fUuLm6LDUHxdOBTQPU9oHt2cDxwCpgRSvXFBHtI4EsIgabZ4GrJZ0t6UjgbuC9hvFU/bK9hyqoLJY0UlIncBOwvJWTSpop6TRJouqp2gPsLZu/oxqX1mc5MEvSRZKGSBomabqkkxv2mStpsqSjgIXAC7b32P4DeJ1qjFujaVRPWjbXNVRSl6RRtnuBXQ11RcRBIoEsIgaVMgD/TmAl8A1wKtXYMCR1lCcdOwZoPh/4BfgCeAt4BniixVNPogpKu4F3gYdtv1m2LQHuKLcnu21vA2ZTDfz/nqrH7Gb+/jd1GfAk1a3ZYcCNDdseoWFsW3nCdAbw1AC1zQO2SNpF9ZUZXS1eU0S0CQ08ZjUiIv4NSeuA5bYf288+bwM32N4oaT4w3vYt/1eNETG4HF53ARERhyLb5zUsP1RnLRFRv9yyjIiIiKhZbllGRERE1Cw9ZBERERE1SyCLiIiIqFkCWURERETNEsgiIiIiapZAFhEREVGzBLKIiIiImv0FRv0/VIRbO3cAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (10,6))\n",
    "\n",
    "for p_count in range(len(thresholds)):\n",
    "    ax.plot(steps,deg_segs[p_count], label= 'p = ' + str(thresholds[p_count]))\n",
    "ax.legend()\n",
    "ax.set_ylim(0,1)\n",
    "ax.set_xlim(steps.min(),steps.max())\n",
    "ax.grid()\n",
    "ax.set_title(r'Degree of segregation over 50 steps with grid size $80 \\times 150$ for different thresholds $p$', fontsize = 12)\n",
    "ax.set_xlabel('no. of step()\\'s', fontsize = 12)\n",
    "ax.set_ylabel('Degree of Segregation', fontsize = 12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "757ea9d5-4f0b-48b9-845d-cc2ea5f8a5c5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Degree of Segregation')"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (10,6))\n",
    "ax.plot(steps,deg_seg, label = 'von Neumann')\n",
    "ax.plot(steps,deg_seg2, label = 'Moore', ls='-.')\n",
    "ax.legend()\n",
    "ax.set_ylim(0,1)\n",
    "ax.set_xlim(steps.min(),steps.max())\n",
    "ax.grid()\n",
    "ax.set_title(\"Degree of segregation for 50 steps with grid size 80 x 150 and happiness threshold p = 0.6\", fontsize = 12)\n",
    "ax.set_xlabel('no. of step()\\'s', fontsize = 12)\n",
    "ax.set_ylabel('Degree of Segregation', fontsize = 12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "18183bda-96fb-4aa4-959d-be06dd24e4e1",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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