{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# LLM Random Number Picker\n",
    "\n",
    "Inspired by this [Information is Beautiful viz on what random number ChatGPT guesses](https://twitter.com/infobeautiful/status/1778059112250589561), I tried the same with 3 LLMs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import json\n",
    "import httpx\n",
    "\n",
    "\n",
    "# If we have prior cached data, load it\n",
    "data = {}\n",
    "if os.path.exists(\"llm-random-numbers.json\"):\n",
    "    with open(\"llm-random-numbers.json\", \"r\") as f:\n",
    "        data = json.load(f)\n",
    "\n",
    "\n",
    "def claude_haiku(temperature):\n",
    "    r = httpx.post(\n",
    "        \"https://api.anthropic.com/v1/messages\",\n",
    "        headers={\n",
    "            \"x-api-key\": os.environ[\"ANTHROPIC_API_KEY\"],\n",
    "            \"anthropic-version\": \"2023-06-01\",\n",
    "            \"content-type\": \"application/json\",\n",
    "        },\n",
    "        json={\n",
    "            \"model\": \"claude-3-haiku-20240307\",\n",
    "            \"max_tokens\": 2,\n",
    "            \"temperature\": temperature,\n",
    "            \"messages\": [\n",
    "                {\n",
    "                    \"role\": \"user\",\n",
    "                    \"content\": \"Pick a random number from 0 - 100. Write ONLY the number NOTHING ELSE\",\n",
    "                }\n",
    "            ],\n",
    "        },\n",
    "    )\n",
    "    r.raise_for_status()\n",
    "    return r.json()[\"content\"][0][\"text\"]\n",
    "\n",
    "\n",
    "def openai_gpt_35(temperature):\n",
    "    r = httpx.post(\n",
    "        \"https://api.openai.com/v1/chat/completions\",\n",
    "        headers={\n",
    "            \"Authorization\": f\"Bearer {os.environ['OPENAI_API_KEY']}\",\n",
    "            \"content-type\": \"application/json\",\n",
    "        },\n",
    "        json={\n",
    "            \"model\": \"gpt-3.5-turbo\",\n",
    "            \"max_tokens\": 2,\n",
    "            \"temperature\": temperature,\n",
    "            \"messages\": [\n",
    "                {\n",
    "                    \"role\": \"user\",\n",
    "                    \"content\": \"Pick a random number from 0 - 100. Write ONLY the number NOTHING ELSE\",\n",
    "                }\n",
    "            ],\n",
    "        },\n",
    "    )\n",
    "    r.raise_for_status()\n",
    "    return r.json()[\"choices\"][0][\"message\"][\"content\"]\n",
    "\n",
    "\n",
    "def google_gemini(temperature):\n",
    "    r = httpx.post(\n",
    "        \"https://europe-west2-aiplatform.googleapis.com/v1/projects/{GOOGLE_PROJECT}/locations/europe-west2/publishers/google/models/gemini-1.0-pro-001:generateContent\".format(**os.environ),\n",
    "        headers={\n",
    "            \"Authorization\": f\"Bearer {os.environ['GOOGLE_API_KEY']}\",\n",
    "            \"content-type\": \"application/json\",\n",
    "        },\n",
    "        json={\n",
    "            \"contents\": [\n",
    "                {\n",
    "                    \"role\": \"user\",\n",
    "                    \"parts\": [\n",
    "                        {\n",
    "                            \"text\": \"Pick a random number from 0 - 100. Write ONLY the number NOTHING ELSE\",\n",
    "                        }\n",
    "                    ]\n",
    "                }\n",
    "            ],\n",
    "            \"generationConfig\": {\n",
    "                \"maxOutputTokens\": 2,\n",
    "                \"temperature\": temperature,\n",
    "            },\n",
    "        },\n",
    "    )\n",
    "    r.raise_for_status()\n",
    "    return r.json()[\"candidates\"][0][\"content\"][\"parts\"][0][\"text\"]\n",
    "\n",
    "\n",
    "# Get 200 random numbers\n",
    "for attempt in range(0, 200):\n",
    "    # At each temperature from 1.0 to 0.0\n",
    "    for t in range(100, -1, -10):\n",
    "        temperature = t / 100\n",
    "        # For each provider\n",
    "        for provider, method in [(\"O\", openai_gpt_35), (\"C\", claude_haiku), (\"G\", google_gemini)]:\n",
    "            # Store data as a key-value pair. The key is \"Provider,Temperature,Attempt\"\n",
    "            key = f\"{provider},{temperature:.2f},{attempt}\"\n",
    "            if key in data:\n",
    "                continue\n",
    "            print(key)\n",
    "            data[key] = method(temperature)\n",
    "            with open(\"llm-random-numbers.json\", \"w\") as f:\n",
    "                json.dump(data, f, sort_keys=True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>m</th>\n",
       "      <th>t</th>\n",
       "      <th>#</th>\n",
       "      <th>n</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>C</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0</td>\n",
       "      <td>42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>C</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1</td>\n",
       "      <td>42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>C</td>\n",
       "      <td>0.0</td>\n",
       "      <td>10</td>\n",
       "      <td>42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>C</td>\n",
       "      <td>0.0</td>\n",
       "      <td>100</td>\n",
       "      <td>42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>C</td>\n",
       "      <td>0.0</td>\n",
       "      <td>101</td>\n",
       "      <td>42</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6595</th>\n",
       "      <td>O</td>\n",
       "      <td>1.0</td>\n",
       "      <td>95</td>\n",
       "      <td>56</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6596</th>\n",
       "      <td>O</td>\n",
       "      <td>1.0</td>\n",
       "      <td>96</td>\n",
       "      <td>74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6597</th>\n",
       "      <td>O</td>\n",
       "      <td>1.0</td>\n",
       "      <td>97</td>\n",
       "      <td>79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6598</th>\n",
       "      <td>O</td>\n",
       "      <td>1.0</td>\n",
       "      <td>98</td>\n",
       "      <td>47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6599</th>\n",
       "      <td>O</td>\n",
       "      <td>1.0</td>\n",
       "      <td>99</td>\n",
       "      <td>67</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>6600 rows × 4 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      m    t    #   n\n",
       "0     C  0.0    0  42\n",
       "1     C  0.0    1  42\n",
       "2     C  0.0   10  42\n",
       "3     C  0.0  100  42\n",
       "4     C  0.0  101  42\n",
       "...  ..  ...  ...  ..\n",
       "6595  O  1.0   95  56\n",
       "6596  O  1.0   96  74\n",
       "6597  O  1.0   97  79\n",
       "6598  O  1.0   98  47\n",
       "6599  O  1.0   99  67\n",
       "\n",
       "[6600 rows x 4 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Convert data into a Pandas DataFrame with columns \"t\" (for temperature), \"#\" for attempt, and \"n\" for the random number\n",
    "import pandas as pd\n",
    "df = pd.DataFrame([{\"m\": k.split(\",\")[0], \"t\": float(k.split(\",\")[1]), \"#\": int(k.split(\",\")[2]), \"n\": int(v)} for k, v in data.items()])\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## OpenAI GPT 3.5 Turbo prefers 47\n",
    "\n",
    "- Clearly prefers 47!\n",
    "- No single-digit numbers\n",
    "- Prefers numbers ending with 7: 37, 47, 57, 67, but not 27, 77, 97.\n",
    "- 72, 73 are also popular."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1600x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Draw a heatmap of the random numbers. X-axis is the random number n, Y-axis is the temperature t, and the color is the frequency of that random number at that temperature.\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize=(16, 4))\n",
    "pivot = df[df[\"m\"] == \"O\"].pivot_table(index=\"t\", columns=\"n\", values=\"#\", aggfunc=\"count\").fillna(0)\n",
    "sns.heatmap(pivot, cmap=\"viridis\", cbar_kws={'label': 'Frequency of random number'})\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Anthropic Claude 3 Haiku loves 42\n",
    "\n",
    "- Clearly prefers 42!\n",
    "- Guesses numbers in a much smaller range (23-87) compared to OpenAI.\n",
    "- No single-digit numbers\n",
    "- Prefers numbers ending with 7: 37, 47, 57, 67, also 27, 87, but not 77.\n",
    "- Prefers multiples of 9: 72, 45, 54, 63 are pretty popular.\n",
    "- 72, 73 are also popular.\n",
    "- Avoids multiples of 10."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 1600x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16, 4))\n",
    "pivot = df[df[\"m\"] == \"C\"].pivot_table(index=\"t\", columns=\"n\", values=\"#\", aggfunc=\"count\").fillna(0)\n",
    "sns.heatmap(pivot, cmap=\"viridis\", cbar_kws={'label': 'Frequency of random number'})\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Google Gemini 1.0 Pro likes 72\n",
    "\n",
    "- Clearly prefers 72!\n",
    "- Guesses numbers in a much smaller range (23-87) compared to OpenAI.\n",
    "- Few single-digit numbers\n",
    "- Prefers numbers ending with 7: 27, 37, 47, 57, 67, 77.\n",
    "- 73 is also popular.\n",
    "- Avoids multiples of 10, with rare exceptions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABKQAAAF4CAYAAABq5yEjAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8pXeV/AAAACXBIWXMAAA9hAAAPYQGoP6dpAABu80lEQVR4nO3deXgUVdr38V9nhQAJhBASRHYBUUCJgqACGobNQQUExI1NGBQiBlEMLiiOBpVFcQQcJERcBvV5cYMRBhFxi4RElnFGECLIBEgQERhAmiR93j98yGObrauXVEK+n+uq66KrTt91d1dXdefmnFMOY4wRAAAAAAAAUEmC7E4AAAAAAAAANQsFKQAAAAAAAFQqClIAAAAAAACoVBSkAAAAAAAAUKkoSAEAAAAAAKBSUZACAAAAAABApaIgBQAAAAAAgEpFQQoAAAAAAACVioIUAAAAAAAAKhUFKQAAAAAAAFQqClIAAAAAAABVUGpqqi6//HLVq1dPsbGxuvHGG7Vz5063NqdPn9akSZPUsGFD1a1bV0OHDlV+fr5bm3379um6665TRESEYmNjdf/996uwsLAyX0oJFKQAAAAAAACqoI0bN2rSpEn66quvtG7dOhUUFKhv3746efJkcZvk5GR98MEHevvtt7Vx40YdOHBAQ4YMKd5eVFSk6667TmfOnNGXX36pV155Renp6Xr00UfteEnFHMYYY2sGAAAAAAAAqNCPP/6o2NhYbdy4UT179tSxY8fUqFEjvfHGG7rpppskSTt27NCFF16ojIwMXXHFFfrwww/1xz/+UQcOHFDjxo0lSYsXL9b06dP1448/KiwszJbXQg8pAAAAAACASuR0OnX8+HG3xel0Vvi8Y8eOSZKio6MlSdnZ2SooKFCfPn2K27Rv317NmjVTRkaGJCkjI0MdO3YsLkZJUr9+/XT8+HH961//8ufLsiTEtj0H0B+ChtmdAgAAAFCp1h7YZql9vyadA5QJgJpknettu1OwhSuvrU/PT118ix5//HG3dTNnztRjjz1W9j5dLt1777268sordfHFF0uS8vLyFBYWpvr167u1bdy4sfLy8orb/LYYdXb72W12OScLUgAAAAAAAIHiksun56ekpGjq1Klu68LDw8t9zqRJk/TNN9/o888/92nfVQUFKQAAAAAAAAuKjG8FqfDw8AoLUL81efJkrVq1Sp9++qmaNm1avD4uLk5nzpzR0aNH3XpJ5efnKy4urrhNZmamW7yzd+E728YOzCEFAAAAAABggUvGp8VTxhhNnjxZ77zzjj7++GO1bNnSbXtCQoJCQ0O1fv364nU7d+7Uvn371L17d0lS9+7d9c9//lOHDh0qbrNu3TpFRkaqQ4cOPr4T3qOHFAAAAAAAQBU0adIkvfHGG3rvvfdUr1694jmfoqKiVLt2bUVFRWncuHGaOnWqoqOjFRkZqaSkJHXv3l1XXHGFJKlv377q0KGDbr/9dj3zzDPKy8vTww8/rEmTJlnqpeVvFKQAAAAAAAAs8HUOKU8tWrRIktS7d2+39cuWLdPo0aMlSfPnz1dQUJCGDh0qp9Opfv36aeHChcVtg4ODtWrVKt11113q3r276tSpo1GjRmnWrFmV8hrK4jDGeN5XzM/+/e9/6y9/+YsyMjKKq3xxcXHq3r27Jk+e7HXXMe6yBwAAgJqGu+wBsENNvcve8QPNfHp+ZJN9fsqk+rKth9SHH36oG2+8UV26dNENN9xQfMvB/Px8rVu3Tl26dNF7772nfv362ZUiAAAAAABACVbmgULpbOsh1blzZ91www1ldhF77LHHtHLlSm3fvt1ybHpIAQAAoKahhxQAO9TUHlI/HWhacaNyNGyS66dMqi/b7rL33Xff6dZbby1z+8iRI7Vr165KzAgAAAAAAKBilXWXvXOZbQWpFi1aaPXq1WVuX716tZo3b16JGQEAAAAAAKAy2DaH1KxZs3TLLbfok08+UZ8+fdzmkFq/fr3WrFmjN954w670AAAAAAAASlVk3/3hzhm2FaSGDRum8847TwsWLNDcuXNL3GXvk08+Uffu3e1KDwAAAAAAoFQuuxM4B9hWkJKkHj16qEePHj7FcDqdcjqdbutcpkhBjmCf4gIAAAAAAJSmiHmgfGbbHFL+kpqaqqioKLdlj3bYnRYAAAAAADhHFRnfFlThgtSMGTM0duzYCtulpKTo2LFjbktLta+EDAEAAAAAQE3k8nGBzUP2ypObm6vc3NwK24WHhys8PNxtHcP1AAAAAAAAqq4qW5Bavny53SkAAAAAAACUUCSH3SlUe7YWpA4fPqy0tDRlZGS43WWvR48eGj16tBo1amRnegAAAAAAACW4mAfKZ7bNIbV582a1bdtWCxYsUFRUlHr27KmePXsqKipKCxYsUPv27ZWVlWVXegAAAAAAAKUqksOnBTb2kEpKStKwYcO0ePFiORzuB8MYo4kTJyopKUkZGRk2ZQgAAAAAAFASRSXf2VaQ2rZtm9LT00sUoyTJ4XAoOTlZl156qQ2ZAQAAAAAAlM1lKEj5yrYhe3FxccrMzCxze2Zmpho3blyJGQEAAAAAAKAy2NZDatq0aZowYYKys7OVmJhYXHzKz8/X+vXrtWTJEs2ZM8eu9AAAAAAAAErFkD3f2VaQmjRpkmJiYjR//nwtXLhQRUVFkqTg4GAlJCQoPT1dw4cPtys9AAAAAACAUhXZN+DsnGFbQUqSRowYoREjRqigoECHDx+WJMXExCg0NNTOtAAAAAAAAMrEHFK+s7UgdVZoaKji4+PtTgMAAAAAAKBCDNnzXZUoSAEAAAAAAFQXRYYhe76iIAUA56iQxrGW2hfmHwpQJt4JiW1kqX3hoR8DlAngI4fFH6zGFZg84JlqfLxmHOpkqX1IfJyl9oUH8yy1BwCgPBSkAAAAAAAALHAxqbnPKEgBAAAAAABYwBxSvqMgBQAAAAAAYAFzSPmOghQAAAAAAIAFLnpI+YyCFAAAAAAAgAVFzCHlsyr7Dubk5Ojaa6+1Ow0AAAAAAAD4WZUtSJ04cUIbN260Ow0AAAAAAAA3RSbIp8WKTz/9VIMGDVKTJk3kcDj07rvvum13OBylLs8++2xxmxYtWpTYPnv2bH+8FV6zbcjeggULyt2+f//+SsoEAAAAAADAc65K7N9z8uRJde7cWWPHjtWQIUNKbD948KDb4w8//FDjxo3T0KFD3dbPmjVL48ePL35cr169wCTsIdsKUvfee6/i4+MVFhZW6vYzZ85UckYAAAAAAAAVKzK+TWrudDrldDrd1oWHhys8PLxE2wEDBmjAgAFlxoqLi3N7/N577+maa65Rq1at3NbXq1evRFs72TZkr3nz5po/f7727NlT6rJ69Wq7UgMAAAAAAChTkYJ8WlJTUxUVFeW2pKam+pxXfn6+Vq9erXHjxpXYNnv2bDVs2FCXXnqpnn32WRUWFvq8P1/Y1kMqISFB2dnZGj58eKnbHQ6HjDGVnBUAAAAAAED5XBbngfq9lJQUTZ061W1dab2jrHrllVdUr169EkP77rnnHnXp0kXR0dH68ssvlZKSooMHD2revHk+79NbthWkZs2apVOnTpW5vUOHDtqzZ08lZgQAAAAAABB4ZQ3P81VaWppuvfVW1apVy239b4tfnTp1UlhYmP70pz8pNTU1IHl4wraCVIcOHcrdHhoaqubNm1cYp7Rxly5TpCBHsE/5AQAAAAAAlKbIvhmQyvTZZ59p586devPNNyts261bNxUWFmrv3r1q165dJWRXUtV7By0qbdzlHu2wOy0AAAAAAHCOKjIOn5ZAWLp0qRISEtS5c+cK227dulVBQUGKjY0NSC6esK2HVEVmzJihvLw8paWllduutHGXg6NGBzAzAAAAAABQk7kqsX/PiRMntHv37uLHe/bs0datWxUdHa1mzZpJko4fP663335bc+fOLfH8jIwMbdq0Sddcc43q1aunjIwMJScn67bbblODBg0q7XX8XpUtSOXm5io3N7fCdqWNu2S4HgAAAAAACJQiHyc1tyIrK0vXXHNN8eOznXJGjRql9PR0SdKKFStkjNHIkSNLPD88PFwrVqzQY489JqfTqZYtWyo5OblE557K5jDn4K3s/hA0zO4UAMB2IY2tdb8tzD8UoEy8ExLbyFL7wkM/BigTwEcOiz9YjSswecAz1fh4JWy19rN+24B4S+0LD+ZZag+gZljnetvuFGzx8ndX+/T8O9t+5qdMqi9be0gdPnxYaWlpysjIUF7er19wcXFx6tGjh0aPHq1Gjaz9MQIAAAAAAICqz7ZJzTdv3qy2bdtqwYIFioqKUs+ePdWzZ09FRUVpwYIFat++vbKysuxKDwAAAAAAoFRFJsinBTb2kEpKStKwYcO0ePFiORzuM8wbYzRx4kQlJSUpIyPDpgwBAAAAAABKKrKvf885w7aC1LZt25Senl6iGCVJDodDycnJuvTSS23IDAAAAAAAoGwuU7KWAWtsK+nFxcUpMzOzzO2ZmZlq3LhxJWYEAAAAAABQsSIF+bTAxh5S06ZN04QJE5Sdna3ExMTi4lN+fr7Wr1+vJUuWaM6cOXalBwAAAAAAUCoX80D5zLaC1KRJkxQTE6P58+dr4cKFKioqkiQFBwcrISFB6enpGj58uF3pAQAAAAAA1GiFhYV66qmnNHbsWDVt2tSvsW0rSEnSiBEjNGLECBUUFOjw4cOSpJiYGIWGhtqZFgAAAAAAQJmKVDPmkAoJCdGzzz6rO+64w/+x/R7RC6GhoYqPj7c7DQAAAAAAgArVpCF71157rTZu3KgWLVr4NW6VKEgBAAAAAABUFzWlh5QkDRgwQA8++KD++c9/KiEhQXXq1HHbfv3113sVl4IU4CNHcLCl9uZ/50uDDRwW/xfDuAKTRyU50+48S+2D8g8FKBPvmLgYa0849GNgEgF+z+K1JCgszFJ7l/O0pfY1ToCv5Za/1wurznfFW+t7WGrftuERazs4mGetfaDVsO91AFVLTeohdffdd0uS5s2bV2Kbw+EonhPcKgpSAAAAAAAAFhTVoIKUyxWYgn7NeQcBAAAAAADgtdOn/deTm4IUAAAAAACABS45fFqqk6KiIj3xxBM677zzVLduXX3//feSpEceeURLly71Oi4FKQAAAAAAAAuKTJBPS3Xy5JNPKj09Xc8884zCfjM35sUXX6yXX37Z67jV610AAAAAAACwmcs4fFqqk+XLl+uvf/2rbr31VgX/5uYfnTt31o4dO7yOa2tB6uDBg3rttdf097//XWfOnHHbdvLkSc2aNcumzAAAAAAAAEpXpCCflupk//79atOmTYn1LpdLBQUFXse17V3YvHmzOnTooEmTJummm27SRRddpH/961/F20+cOKHHH3/crvQAAAAAAABKVZN6SHXo0EGfffZZifX/8z//o0svvdTruCG+JOWLGTNmaPDgwXr55Zd18uRJTZ8+Xb169dK6det8ekEAAAAAAADwj0cffVSjRo3S/v375XK5tHLlSu3cuVPLly/XqlWrvI5rW0EqOztbL774ooKCglSvXj0tXLhQzZo1U2JiotauXatmzZrZlRoAAAAAAECZXNVs2J0vbrjhBn3wwQeaNWuW6tSpo0cffVRdunTRBx98oD/84Q9ex7WtICVJp0+fdnv84IMPKiQkRH379lVaWppNWQEAAAAAAJStqJoNu/PV1VdfrXXr1vk1pm0FqYsvvlhffvmlOnXq5LZ+2rRpcrlcGjlypE2ZAQAAAAAAlK26zQPlD1lZWfr2228l/TqvVEJCgk/xbCtI3XHHHdq4caMmTpxYYtsDDzwgY4wWL15sQ2YAAAAAAABlc5maM2QvNzdXI0eO1BdffKH69etLko4ePaoePXpoxYoVatq0qVdxbXsH77zzTr366qtlbp8+fbr27NlTYRyn06njx4+7LS5T5M9UAQAAAAAAaqQ777xTBQUF+vbbb3XkyBEdOXJE3377rVwul+68806v41b7kl5qaqqioqLclj3aYXdaAAAAAADgHFUkh09LdbJx40YtWrRI7dq1K17Xrl07vfDCC/r000+9jltlC1IzZszQ2LFjK2yXkpKiY8eOuS0t1b4SMgQAAAAAADWRyzh8WqqT888/XwUFBSXWFxUVqUmTJl7HrbIFqdzcXO3du7fCduHh4YqMjHRbghzBgU8QAAAAAADUSC4T5NNSnTz77LNKSkpSVlZW8bqsrCxNmTJFc+bM8TpulX0Xli9fro8//tjuNAAAAAAAANy45PBpseLTTz/VoEGD1KRJEzkcDr377rtu20ePHi2Hw+G29O/f363NkSNHdOuttyoyMlL169fXuHHjdOLEiTL32aBBA0VHRys6OlpjxozR1q1b1a1bN4WHhys8PFzdunXT119/7dHItrLYdpc9STp8+LDS0tKUkZGhvLw8SVJcXJx69Oih0aNHq1GjRnamBwAAAAAAUEJRJQ67O3nypDp37qyxY8dqyJAhpbbp37+/li1bVvw4PDzcbfutt96qgwcPat26dSooKNCYMWM0YcIEvfHGG6XGe+655/yWf1lsK0ht3rxZ/fr1U0REhPr06aO2bdtKkvLz87VgwQLNnj1ba9eu1WWXXWZXigAAAAAAALYaMGCABgwYUG6b8PBwxcXFlbrt22+/1Zo1a7R58+biGssLL7yggQMHas6cOaXOAzVq1CjfE6+AbQWppKQkDRs2TIsXL5bD4V5ZNMZo4sSJSkpKUkZGhk0ZAgAAAAAAlOTrPFBOp1NOp9Nt3dnhcN745JNPFBsbqwYNGujaa6/Vn//8ZzVs2FCSlJGRofr167t1+OnTp4+CgoK0adMmDR482KN9HDp0SIcOHZLL5XJb36lTJ69ytq0gtW3bNqWnp5coRkmSw+FQcnKyLr30UhsyAwAAAAAAKJuvd8pLTU3V448/7rZu5syZeuyxxyzH6t+/v4YMGaKWLVsqJydHM2bM0IABA5SRkaHg4GDl5eUpNjbW7TkhISGKjo4unj6pPNnZ2Ro1apS+/fZbGWPctjkcDhUVFVnOWbKxIBUXF6fMzEy1b9++1O2ZmZlq3LhxJWcFAAAAAABQPqsTk/9eSkqKpk6d6rbO295RN998c/G/O3bsqE6dOql169b65JNPlJiY6FOekjR27Fi1bdtWS5cuVePGjUvtWOQN2wpS06ZN04QJE5Sdna3ExMTi4lN+fr7Wr1+vJUuW+HT7QAAAAAAAgEDwtYeUL8PzKtKqVSvFxMRo9+7dSkxMVFxcnA4dOuTWprCwUEeOHClz3qnf+v777/X//t//U5s2bfyap20FqUmTJikmJkbz58/XwoULi7t4BQcHKyEhQenp6Ro+fLhd6QEAAAAAAJTK1zmkAik3N1c//fST4uPjJUndu3fX0aNHlZ2drYSEBEnSxx9/LJfLpW7dulUYLzExUdu2bTt3ClKSNGLECI0YMUIFBQU6fPiwJCkmJkahoaF2pgUAAAAAAFAlnDhxQrt37y5+vGfPHm3dulXR0dGKjo7W448/rqFDhyouLk45OTl64IEH1KZNG/Xr10+SdOGFF6p///4aP368Fi9erIKCAk2ePFk333xzqXfY+72XX35Zo0aN0jfffKOLL764RM3m+uuv9+p12VqQOis0NLS4cgcAAAAAAFCV+Tpkz4qsrCxdc801xY/Pzj01atQoLVq0SNu3b9crr7yio0ePqkmTJurbt6+eeOIJtyGBr7/+uiZPnqzExEQFBQVp6NChWrBggUf7z8jI0BdffKEPP/ywxLZqOak5AAAAAABAdeTrpOZW9O7du8Td7X5r7dq1FcaIjo7WG2+84dX+k5KSdNttt+mRRx7x683nKEgBPjKusi8MqFocQda+NIzVQr/D4jhy47K4A2uCTxVaal/VPskFDWpbal91R/F7yMrnJ8CfnarGERxsqb3l67LV99Nie0erZtbif/udtfbVnCPE4lQNFt9/y9fyanx+xWZba2/CAvungOVz1+L/sFuOX1h9j22NVMV+VwG/V5k9pOz2008/KTk52a/FKOkc+P0OAAAAAABQmVzG4dNSnQwZMkQbNmzwe1x6SAEAAAAAAFhQ3YpKvmjbtq1SUlL0+eefq2PHjiUmNb/nnnu8iktBCgAAAAAAAKV6+eWXVbduXW3cuFEbN2502+ZwOChIAQAAAAAAVIaa1ENqz549AYlLQQoAAAAAAMCCyrzL3rnK1oLUunXr9Pnnn6tXr1669tpr9emnnyo1NVVOp1O33367xowZY2d6AAAAAAAAJdSkHlJjx44td3taWppXcW0rSL322msaM2aMOnXqpHnz5umFF15QcnKybrrpJrlcLk2cOFH16tXTTTfdZFeKAAAAAAAAJdSkgtTPP//s9rigoEDffPONjh49qmuvvdbruLYVpObOnau5c+fqnnvu0fr16zVo0CA9+eSTSk5OliR16NBBzz33HAUpAAAAAABQpdSkgtQ777xTYp3L5dJdd92l1q1bex03yJekfLFr1y4NGjRIkpSYmKjCwkIlJiYWb7/uuuu0Y8cOu9IDAAAAAABAKYKCgjR16lTNnz/f6xi29ZAKDQ3VmTNnih+Hh4erbt26bo9/+eUXO1IDAAAAAAAoU03qIVWWnJwcFRYWev182wpSbdq00Y4dO9SuXTtJ0v79+1WvXr3i7Tk5OWratKld6QEAAAAAAJTK1KCC1NSpU90eG2N08OBBrV69WqNGjfI6rm0FqRkzZqhBgwbFjyMjI922Z2Vlafjw4ZWdFgAAAAAAQLlcqjkFqS1btrg9DgoKUqNGjTR37twK78BXHtsKUoMHDy53+4MPPuhRHKfTKafT6bbOZYoU5Aj2OjcAAAAAAICy1KQhexs2bAhIXNsmNfeX1NRURUVFuS17xGToAAAAAAAgMIxx+LSgChekZsyY4VHXr5SUFB07dsxtaan2lZAhAAAAAADAuS0/P1+33367mjRpopCQEAUHB7st3rJtyF5FcnNzlZubW2G78PBwhYeHu61juB4AAAAAAAiUmjRkb/To0dq3b58eeeQRxcfHy+Hwz2uvsgWp5cuX250CAAAAAABACTVp2N3nn3+uzz77TJdccolf49pakDp8+LDS0tKUkZGhvLw8SVJcXJx69Oih0aNHq1GjRnamBwAAAAAAUEJN6iF1/vnnyxjj97i2zSG1efNmtW3bVgsWLFBUVJR69uypnj17KioqSgsWLFD79u2VlZVlV3oAAAAAAAClMsa3pTp57rnn9OCDD2rv3r1+jWtbD6mkpCQNGzZMixcvLjH+0BijiRMnKikpSRkZGTZlCAAAAAAAUJJLNaeH1IgRI3Tq1Cm1bt1aERERCg0Nddt+5MgRr+LaVpDatm2b0tPTS50My+FwKDk5WZdeeqkNmQEAAAAAAED6tYdUINhWkIqLi1NmZqbat29f6vbMzEw1bty4krMCAAAAAAAoX02a1HzUqFEBiWtbQWratGmaMGGCsrOzlZiYWFx8ys/P1/r167VkyRLNmTPHrvQAAAAAAABKVZMmNQ8U2wpSkyZNUkxMjObPn6+FCxeqqKhIkhQcHKyEhASlp6dr+PDhdqUHAAAAAABQquo2MXlVZFtBSvp1YqwRI0aooKBAhw8fliTFxMSUmCALAAAAAACgqqhJQ/YCxdaC1FmhoaGKj4+3Ow0AAAAAAIAKUZDyXZDdCQAAAAAAAKB0n376qQYNGqQmTZrI4XDo3XffLd5WUFCg6dOnq2PHjqpTp46aNGmiO+64QwcOHHCL0aJFCzkcDrdl9uzZlfxK3FWJHlJAdRYUFmapvct5OkCZWOcIsTY81hQWBCiTymFcgR3obfWzYPX9NP87156nHBYHtle1YfCuUGv/Z1Lt/4fFuOzOoNIE+tpjOb61U0uO4GBr7Y8ctbaDmqaKffaDYxpaal+YfyhAmVhX+0dr50rQqTOW2gf6SFk9tyx/LwY4fo3jsPjNW8XO9WqfP2xXmZOanzx5Up07d9bYsWM1ZMgQt22nTp3S119/rUceeUSdO3fWzz//rClTpuj6669XVlaWW9tZs2Zp/PjxxY/r1avn0f5Pnz6tF154QRs2bNChQ4fkcrmfD19//bVXr4uCFAAAAAAAgAWVOan5gAEDNGDAgFK3RUVFad26dW7r/vKXv6hr167at2+fmjVrVry+Xr16iouLs7z/cePG6R//+Iduuukmde3aVQ6Hf4pxFKQAAAAAAAAs8HUOKafTKafT6bYuPDxc4eHhPsWVpGPHjsnhcKh+/fpu62fPnq0nnnhCzZo10y233KLk5GSFhFRcFlq1apX+/ve/68orr/Q5t9+q9iMcAAAAAAAAKpMxDp+W1NRURUVFuS2pqak+53X69GlNnz5dI0eOVGRkZPH6e+65RytWrNCGDRv0pz/9SU899ZQeeOABj2Ked955Hg/vs4IeUgAAAAAAABb4OmIvJSVFU6dOdVvna++ogoICDR8+XMYYLVq0yG3bb/fVqVMnhYWF6U9/+pNSU1Mr3O/cuXM1ffp0LV68WM2bN/cpx9+qcgWpPXv26Pzzz/eo2xgAAAAAAEB146/heWedLUb98MMP+vjjj916R5WmW7duKiws1N69e9WuXbty21522WU6ffq0WrVqpYiICIWGut9A5siRI17lXOWqPu3atdO2bdt04YUX2p0KAAAAAABACb7OIeVPZ4tRu3bt0oYNG9SwYcV3jN26dauCgoIUGxtbYduRI0dq//79euqpp9S4cePqP6n5729VeFZRUZHuueee4vGJK1eurMy0AAAAAAAAyleJd9k7ceKEdu/eXfx4z5492rp1q6KjoxUfH6+bbrpJX3/9tVatWqWioiLl5eVJkqKjoxUWFqaMjAxt2rRJ11xzjerVq6eMjAwlJyfrtttuU4MGDSrc/5dffqmMjAx17tzZr6/LtoLUu+++q549e6ply5YlttWtW1dRUVE2ZAUAAAAAAFC+yuwhlZWVpWuuuab48dn5oEaNGqXHHntM77//viTpkksucXvehg0b1Lt3b4WHh2vFihV67LHH5HQ61bJlSyUnJ5eYw6os7du31y+//OKfF/MbthWk3njjDd1///0aNWqUxowZU7z+tdde05NPPqkOHTrYlRoAAAAAAECZTCX2kOrdu7dMOTssb5skdenSRV999ZXX+589e7buu+8+Pfnkk+rYsWOJOaQqmq+qLLYVpG6++WZdccUVuu2227Rq1Sq9/PLLHnUVAwAAAAAAsFNVmkMq0Pr37y9JSkxMdFtvjJHD4VBRUZFXcW2d1LxFixb69NNP9fjjj6tz585asmSJ3ybHAgAAAAAAgG82bNgQkLi232UvKChIjz/+uP7whz/ojjvu8LqyBgAAAAAAUClqUA+pXr16BSSu7QWps6666ipt375dOTk5atOmjcfPczqdcjqdbutcpkhBjmB/pwgAAAAAAFCpc0hVBUePHtXSpUv17bffSpIuuugijR071qcb0gX5Kzl/qFu3rjp37qywsDCPn5OamqqoqCi3ZY92BDBLAAAAAABQoxkfl2okKytLrVu31vz583XkyBEdOXJE8+bNU+vWrfX11197HbdKFaR+a8aMGRo7dmyF7VJSUnTs2DG3paXaV0KGAAAAAACgJjLG4dNSnSQnJ+v666/X3r17tXLlSq1cuVJ79uzRH//4R917771ex60yQ/Z+Lzc3V7m5uRW2Cw8PV3h4uNs6husBAAAAAICAqWa9nHyRlZWlJUuWKCTk/0pIISEheuCBB3TZZZd5HbfKFqSWL19udwoAAAAAAAA1WmRkpPbt26f27d1Ho/3nP/9RvXr1vI5ra0Hq8OHDSktLU0ZGhvLy8iRJcXFx6tGjh0aPHq1GjRrZmR4AAAAAAEAJ1W3YnS9GjBihcePGac6cOerRo4ck6YsvvtD999+vkSNHeh3XtoLU5s2b1a9fP0VERKhPnz5q27atJCk/P18LFizQ7NmztXbtWp+6fwEAAAAAAPhdDRqyN2fOHDkcDt1xxx0qLCyUJIWGhuquu+7S7NmzvY5rW0EqKSlJw4YN0+LFi+VwuFcWjTGaOHGikpKSlJGRYVOGAAAAAAAApak5PaTCwsL0/PPPKzU1VTk5OZKk1q1bKyIiwqe4thWktm3bpvT09BLFKElyOBxKTk7WpZdeakNmAAAAAAAA5ahBPaTOioiIUMeOHf0Wz7aCVFxcnDIzM0tMinVWZmamGjduXMlZAQAAAAAAVOAcL0gNGTLE47YrV670ah+2FaSmTZumCRMmKDs7W4mJicXFp/z8fK1fv15LlizRnDlz7EoPAAAAAACgRoqKiir+tzFG77zzjqKioorn+c7OztbRo0ctFa5+z7aC1KRJkxQTE6P58+dr4cKFKioqkiQFBwcrISFB6enpGj58uF3pAQAAAAAAlO4cv8vesmXLiv89ffp0DR8+XIsXL1ZwcLAkqaioSHfffbciIyO93odtBSnp11sHjhgxQgUFBTp8+LAkKSYmRqGhoXamBQAAAAAAUCZzjg/Z+620tDR9/vnnxcUo6dfORFOnTlWPHj307LPPehU3yF8J+iI0NFTx8fGKj4+nGAUAAAAAAKo24+NSjRQWFmrHjh0l1u/YsUMul8vruLb2kAIAAAAAAKh2zvEhe781ZswYjRs3Tjk5OerataskadOmTZo9e7bGjBnjdVwKUvA/h8WOd8b7impAWMw/KKqepfauQ6cttQ8kR5i1HommsMDiDqrWZ8ERZO1LwxRZ3IHl+FZ3YI0rNLjiRlVYyEmLn7fqzsr5Us2vm5Y/+1avJRY5gi2eK1bf/9q1rbW3qopda60KqlvXUvuiY8es7cDi++M6/l9r8auQsCMWf2P8HNj30irjstZlIKh2LUvtXadOWWpf3Vm9tlm+Nlexa4llFvMPCrf4eXNWnd/8CAxHNevl5Is5c+YoLi5Oc+fO1cGDByVJ8fHxuv/++3Xfffd5HZeCFAAAAAAAAEoVFBSkBx54QA888ICOHz8uST5NZn4WBSkAAAAAAAAralAPqd/yRyHqrCoxqTkAAAAAAEC1YRy+LdVIfn6+br/9djVp0kQhISEKDg52W7xFDykAAAAAAAAralAPqdGjR2vfvn165JFHFB8fL4fDPwU1ClIAAAAAAABW1KCC1Oeff67PPvtMl1xyiV/jVpmC1IEDB/TSSy9p9+7dio+P15133qn27dvbnRYAAAAAAECNdf7558sY/1fgbJtDKiIiQj/++KMk6d///rc6dOigN954QwUFBVq9erUSEhK0fft2u9IDAAAAAAAonfFxqUaee+45Pfjgg9q7d69f49rWQ+r06dPFFbYZM2aoZ8+eWrlypUJCQuRyuXTrrbfqoYce0gcffGBXigAAAAAAACVVs4nJfTFixAidOnVKrVu3VkREhEJDQ922HzlyxKu4VWLI3tdff63XX39dISG/phMUFKQHHnhA1113nc2ZAQAAAAAAuHNUs15OvnjuuecCEte2gpTD4SiemT0oKEhRUVFu2+vXr6+ff/7ZjtQAAAAAAADKVokFqU8//VTPPvussrOzdfDgQb3zzju68cYb/y8VYzRz5kwtWbJER48e1ZVXXqlFixbpggsuKG5z5MgRJSUl6YMPPlBQUJCGDh2q559/XnXr1q1w/6NGjQrEy7JvDiljjNq2bavo6GgdOHCgxHxRu3fvVlxcnE3ZAQAAAAAA2O/kyZPq3LmzXnzxxVK3P/PMM1qwYIEWL16sTZs2qU6dOurXr59Onz5d3ObWW2/Vv/71L61bt06rVq3Sp59+qgkTJljO5fTp0zp+/Ljb4i3LPaT27dun888/v7h301nGGP3nP/9Rs2bNPIqzbNkyt8dt2rRxe/zVV19p8ODBVtMDAAAAAAA4ZwwYMEADBgwodZsxRs8995wefvhh3XDDDZKk5cuXq3Hjxnr33Xd1880369tvv9WaNWu0efNmXXbZZZKkF154QQMHDtScOXPUpEmTcvd/8uRJTZ8+XW+99ZZ++umnEtuLioq8el2WC1ItW7bUwYMHFRsb67b+yJEjatmypceJVNTl65FHHvEojtPplNPpdFvnMkUKcgR79HwAAAAAAAArfJ1DqrRaRnh4uMLDwy3F2bNnj/Ly8tSnT5/idVFRUerWrZsyMjJ08803KyMjQ/Xr1y8uRklSnz59FBQUpE2bNlXYGeiBBx7Qhg0btGjRIt1+++168cUXtX//fr300kuaPXu2pXx/y/KQPWNMid5RknTixAnVqlXL60S8lZqaqqioKLdlj3ZUeh4AAAAAAKCGMA6fltJqGampqZbTyMvLkyQ1btzYbX3jxo2Lt+Xl5ZXoVBQSEqLo6OjiNuX54IMPtHDhQg0dOlQhISG6+uqr9fDDD+upp57S66+/bjnn4hw8bTh16lRJv05G/sgjjygiIqJ4W1FRkTZt2qRLLrnE60R+b8aMGcrLy1NaWlq57VJSUopzO2tw1Gi/5QEAAAAAAODGxx5SpdUyrPaOqixHjhxRq1atJEmRkZE6cuSIJOmqq67SXXfd5XVcjwtSW7ZskfRrD6l//vOfCgsLK94WFhamzp07a9q0aV4n8nu5ubnKzc2tsF1pXdoYrgcAAAAAAALGx4KUN8PzSnP2ZnD5+fmKj48vXp+fn1/caSguLk6HDh1ye15hYaGOHDni0c3kWrVqpT179qhZs2Zq37693nrrLXXt2lUffPCB6tev73XuHhekNmzYIEkaM2aMnn/+eUVGRnq9U08sX748oPEBAAAAAAC84escUv7SsmVLxcXFaf369cUFqOPHj2vTpk3FvZe6d++uo0ePKjs7WwkJCZKkjz/+WC6XS926datwH2PGjNG2bdvUq1cvPfjggxo0aJD+8pe/qKCgQPPmzfM6d8uTmv/+7ni+OHz4sNLS0pSRkVE8bjEuLk49evTQ6NGj1ahRI7/tCwAAAAAAoLo5ceKEdu/eXfx4z5492rp1q6Kjo9WsWTPde++9+vOf/6wLLrhALVu21COPPKImTZroxhtvlCRdeOGF6t+/v8aPH6/FixeroKBAkydP1s0331zhHfYkKTk5ufjfffr00Y4dO5Sdna02bdqoU6dOXr8uywUpf9m8ebP69euniIgI9enTR23btpX0a7eyBQsWaPbs2Vq7dq3bLPAAAAAAAAC2q8QeUllZWbrmmmuKH5+de2rUqFFKT0/XAw88oJMnT2rChAk6evSorrrqKq1Zs8btxnOvv/66Jk+erMTERAUFBWno0KFasGBBhfsuKChQ//79tXjxYl1wwQWSpObNm6t58+Y+vy7bClJJSUkaNmyYFi9eXOKufcYYTZw4UUlJScrIyLApQwAAAAAAgFJUYkGqd+/eMqbsHTocDs2aNUuzZs0qs010dLTeeOMNy/sODQ3V9u3bLT/PE0EBieqBbdu2KTk5uUQxSvr1zUxOTtbWrVsrPzEAAAAAAIByOIxvS3Vy2223aenSpX6Pa1sPqbi4OGVmZqp9+/albs/MzFTjxo0rOSsAAAAAAIAKmJKda85VhYWFSktL00cffaSEhATVqVPHbbu3E5vbVpCaNm2aJkyYoOzsbCUmJhYXn/Lz87V+/XotWbJEc+bMsSs9AAAAAACA0lWzXk6++Oabb9SlSxdJ0nfffee2rbRRb56yrSA1adIkxcTEaP78+Vq4cKGKiookScHBwUpISFB6erqGDx9uV3oAAAAAAAA13oYNGwIS17aClCSNGDFCI0aMUEFBgQ4fPixJiomJUWhoqJ1pAQAAAAAAlKm6zQNVFdlakDorNDRU8fHxdqcBAAAAAABQMQpSPqsSBSkAAAAAAIDqgh5SvqMg5Q1HUGDjG1dg4wdaoPO3+v5bzcdie1NYaC1+FeIIC7P2hFOnrLWvYp/loNq1LbU3BRaPrQ8T+nkW39pnP+TQMUvtq9on2VFg8VwMUB5nOYKDLbU3LosZVbHzxRKLuVt9LwN93bd6rCx/Fo5aOxcD/lkL9PdogFm9lrt++SVAmfyvKvR+Bv18wlJ7E13f2g7yD1lrL2ufZUeQxe/RosBee6rcdTzQf4NUMVY/D6bI8g4sNXc5T1sLH+L5NDSmsMBSbMuq0HXqnEJBymc166oGAAAAAADgK+PjUsV16dJFP//8syRp1qxZOmW1c4IHKEgBAAAAAACg2LfffquTJ09Kkh5//HGdOGGtF64nGLIHAAAAAABgwbk+h9Qll1yiMWPG6KqrrpIxRnPmzFHdunVLbfvoo496tQ8KUgAAAAAAACiWnp6umTNnatWqVXI4HPrwww8VElKyhORwOM6dglRhYWGpLxIAAAAAAKBKOMd7SLVr104rVqyQJAUFBWn9+vWKjY316z5sm0NqzZo1+uc//ylJcrlceuKJJ3TeeecpPDxcTZs21ezZs2XMOX6EAQAAAABAteMwvi3Vicvl8nsxSrKxh9S9996rJUuWSJKefvppPf/883rooYd04YUXaufOnUpNTZXD4dD06dPtShEAAAAAAKCkalZU8lVOTo6ee+45ffvtt5KkDh06aMqUKWrdurXXMW3rIbV37141b95ckvTGG29o0aJFSk5OVv/+/TVlyhQtXbpUL7/8sl3pAQAAAAAA1Hhr165Vhw4dlJmZqU6dOqlTp07atGmTLrroIq1bt87ruLb1kIqOjtaBAwfUrFkz/fjjj2rTpo3b9rZt22r//v02ZQcAAAAAAFCGGtRD6sEHH1RycrJmz55dYv306dP1hz/8wau4tvWQGjx4sJ588kkVFRXphhtu0MKFC93mjHrhhRd0ySWX2JUeAAAAAABAqWrSHFLffvutxo0bV2L92LFj9e9//9vruLYVpJ566inl5eWpffv2+uWXX/Taa6+pZcuW6tu3r1q1aqXly5dr/vz5dqUHAAAAAABQOuPjUo00atRIW7duLbF+69atPk12btuQvaioKH355ZdaunSpPvjgA7Vo0UIul0tnzpzRyJEjddddd6lp06Z2pQcAAAAAAFCq6tbLyRfjx4/XhAkT9P3336tHjx6SpC+++EJPP/20pk6d6nVc2wpSkhQaGqqJEydq4sSJXsdwOp1yOp1u61ymSEGOYF/TAwAAAAAAKKkGFaQeeeQR1atXT3PnzlVKSookqUmTJnrsscd0zz33eB3XtiF7/pKamqqoqCi3ZY922J0WAAAAAABAtedwOJScnKzc3FwdO3ZMx44dU25urqZMmSKHw+F13CpbkJoxY4bGjh1bYbuUlJTiN+Ts0lLtKyFDAAAAAABQI9WgOaR+q169eqpXr55fYtk6ZK88ubm5ys3NrbBdeHi4wsPD3dYxXA8AAAAAAARKTZpDKlCqbEFq+fLldqcAAAAAAABQEgUpn9lakDp8+LDS0tKUkZGhvLw8SVJcXJx69Oih0aNHq1GjRnamBwAAAAAAUBIFKZ/ZNofU5s2b1bZtWy1YsEBRUVHq2bOnevbsqaioKC1YsEDt27dXVlaWXekBAAAAAACUymF8W6qT77//PiBxbeshlZSUpGHDhmnx4sUlZmU3xmjixIlKSkpSRkaGTRkCAAAAAADUbG3atFGvXr00btw43XTTTapVq5Zf4trWQ2rbtm1KTk4u9RaBZ28puHXr1spPDAAAAAAAoDyVeJe9Fi1ayOFwlFgmTZokSerdu3eJbRMnTvTHq5Qkff311+rUqZOmTp2quLg4/elPf1JmZqbPcW0rSMXFxZX7AjIzM9W4ceNKzAgAAAAAAKBilTlkb/PmzTp48GDxsm7dOknSsGHDituMHz/erc0zzzzjt9d6ySWX6Pnnn9eBAweUlpamgwcP6qqrrtLFF1+sefPm6ccff/Qqrm1D9qZNm6YJEyYoOztbiYmJxcWn/Px8rV+/XkuWLNGcOXPsSg8AAAAAAKB0Ps4D5XQ65XQ63daFh4crPDy8RNvf3/Bt9uzZat26tXr16lW8LiIiQnFxcb4lVYGQkBANGTJE1113nRYuXKiUlBRNmzZNM2bM0PDhw/X0008rPj7e43i29ZCaNGmSXnnlFW3atElDhw5V9+7d1b17dw0dOlSbNm1Senq67r77brvSAwAAAAAAKJ2PQ/ZSU1MVFRXltqSmpla42zNnzui1117T2LFj3aZAev311xUTE6OLL75YKSkpOnXqlF9friRlZWXp7rvvVnx8vObNm6dp06YpJydH69at04EDB3TDDTdYimdbDylJGjFihEaMGKGCggIdPnxYkhQTE6PQ0FA70wIAAAAAAChTydmwrUlJSdHUqVPd1pXWO+r33n33XR09elSjR48uXnfLLbeoefPmatKkibZv367p06dr586dWrlypY9Z/mrevHlatmyZdu7cqYEDB2r58uUaOHCggoJ+7ePUsmVLpaenq0WLFpbi2lqQOis0NNRSty4AAAAAAIDqqqzheRVZunSpBgwYoCZNmhSvmzBhQvG/O3bsqPj4eCUmJionJ0etW7f2OddFixZp7NixGj16dJm1m9jYWC1dutRS3CpRkAIAAAAAAKg2fJxDyhs//PCDPvroowp7PnXr1k2StHv3br8UpHbt2lVhm7CwMI0aNcpSXApSkuSwOJWWcQU2vlWBzj/AHMHBltobl8UzP9Dvf3VmAnwVrWKfTVNQaK19UZG1HRQWWGruCLE4PNni++OqF2EtvlUBPr6OAmvvv+VPs8X8LV97LL7eoPBaHrd1nTkT0FwCzREWZqm967Sz4ka/jW/xe0WyeK5b/SyHVbGpCKrY58EUWLt2Gquff4vnuqO25+eiJOmXX6y1t5JPoL8Xf8i11N7yuWX1Omv1e9die6vfu5Y/a4Fm+fNg9VpYtVj+3rW+A2vtA/m7J9C/qYKsDS4zFk/FmsrqnfL8YdmyZYqNjdV1111XbrutW7dKkt9Goi1btkx169Z1u6ufJL399ts6deqU5ULUWfylDgAAAAAAYIWPk5pb5XK5tGzZMo0aNUohIf/XtygnJ0dPPPGEsrOztXfvXr3//vu644471LNnT3Xq1MmXV1gsNTVVMTExJdbHxsbqqaee8jouPaQAAAAAAACsqOQeUh999JH27dunsWPHuq0PCwvTRx99pOeee04nT57U+eefr6FDh+rhhx/227737dunli1blljfvHlz7du3z+u4FKQAAAAAAAAsqOwhe3379pUpZcqV888/Xxs3bgzovmNjY7V9+/YSd9Hbtm2bGjZs6HVchuwBAAAAAACgVCNHjtQ999yjDRs2qKioSEVFRfr44481ZcoU3XzzzV7HpYcUAAAAAACAFTZMam6XJ554Qnv37lViYmLx/FUul0t33HFH9ZxDatCgQRo+fLhuuukm1a5d2640AAAAAAAALLHjLnt2CQsL05tvvqknnnhC27ZtU+3atdWxY0c1b97cp7i2FaRWr16tNWvWKCkpSSNHjtSdd96phIQEu9IBAAAAAADwTA0qSJ3Vtm1btW3b1m/xbB2yt23bNv3jH/9QWlqa/vrXv6pjx4668847deutt6pBgwZ2pgYAAAAAAFCqmtRDqqioSOnp6Vq/fr0OHTokl8vltv3jjz/2Kq6tk5rHxMTo3nvv1fbt25WRkaFu3brp4Ycf1nnnnadbbrnF6xcFAAAAAAAQMMbHpRqZMmWKpkyZoqKiIl188cXq3Lmz2+KtKjOpedeuXdW1a1fNnz9fb731lpYuXao//OEPKioqsjs1AAAAAACAGmnFihV66623NHDgQL/GtbWHVGkiIiI0evRoffbZZ/r222/tTgcAAAAAAMBdDeohFRYWpjZt2vg9rm0FqV69eiksLKzcNv6cLAsAAAAAAMAfHMa3pTq577779Pzzz8sY/yZu25C9DRs2+CWO0+mU0+l0W+cyRQpyBPslPgAAAAAAgJtqVlTyxeeff64NGzboww8/1EUXXaTQ0FC37StXrvQqbpWZQ8pbqampevzxx93WtdSFaq2LbMoIAAAAAACcyxx+7i1UldWvX1+DBw/2e9wqW5CaMWOG8vLylJaWVm67lJQUTZ061W3d4KjRAcwMAAAAAADUaDWnHqVly5YFJG6VLUjl5uYqNze3wnbh4eEKDw93W8dwPQAAAAAAAP8oLCzUJ598opycHN1yyy2qV6+eDhw4oMjISNWtW9ermFW2ILV8+XK7UwAAAAAAACihuk1M7osffvhB/fv31759++R0OvWHP/xB9erV09NPPy2n06nFixd7FdfWgtThw4eVlpamjIwM5eXlSZLi4uLUo0cPjR49Wo0aNbIzPQAAAAAAgJJqUEFqypQpuuyyy7Rt2zY1bNiweP3gwYM1fvx4r+PaVpDavHmz+vXrp4iICPXp00dt27aVJOXn52vBggWaPXu21q5dq8suu8yuFAEAAAAAAEqoST2kPvvsM3355ZcKCwtzW9+iRQvt37/f67i2FaSSkpI0bNgwLV68WA6Hw22bMUYTJ05UUlKSMjIybMoQAAAAAACgFDWoIOVyuVRUVFRifW5ururVq+d13CBfkvLFtm3blJycXKIYJUkOh0PJycnaunVr5ScGAAAAAABQDofxbalO+vbtq+eee674scPh0IkTJzRz5kwNHDjQ67i2FaTi4uKUmZlZ5vbMzEw1bty4EjMCAAAAAADAb82dO1dffPGFOnTooNOnT+uWW24pHq739NNPex3XtiF706ZN04QJE5Sdna3ExMTi4lN+fr7Wr1+vJUuWaM6cOXalBwAAAAAAULpq1svJF02bNtW2bdu0YsUKbd++XSdOnNC4ceN06623qnbt2l7Hta0gNWnSJMXExGj+/PlauHBh8XjE4OBgJSQkKD09XcOHD7crPQAAAAAAgFJVt2F3vgoJCdFtt93m35h+jWbRiBEjNGLECBUUFOjw4cOSpJiYGIWGhtqZFgAAAAAAQNlMzalILV++vNztd9xxh1dxbS1InRUaGqr4+Hi70wAAAAAAAKhQTeohNWXKFLfHBQUFOnXqlMLCwhQREeF1Qcq2Sc0BAAAAAABQtf38889uy4kTJ7Rz505dddVV+tvf/uZ13CrRQ+qcZ1zW2jss1gmtxg80i/mb/50/zOPwIdaGdFqNb5X55bS1J1Sh42sKCgIW+9cdVK3PpiPU4iUvyGFxBxbbF1l7f1xOa8cr+MQv1uJbah14QRZfrwkOttbeZe2/tYLCwiy1dzmtXRssXauq+feKKSgMaHyr+QfVCrfU3mHxs2CcZ6y1t/jZdFj97BdWrc+POWPtXLf6/svi582ctHbtrErMkaOW2gfFW7ujdeH3P1hq7wiy9llwWPzetfq9bvnaU9WutVZ/Y1u8llS1/Ksaq5/PgP4NYvG9rGp/P50zalAPqdJccMEFmj17tm677Tbt2LHDqxgUpAAAAAAAACxwVLX/zbVBSEiIDhw44P3z/ZgLAAAAAADAua8G9ZB6//333R4bY3Tw4EH95S9/0ZVXXul1XApSAAAAAAAAFlTWpOaPPfaYHn/8cbd17dq1Kx4md/r0ad13331asWKFnE6n+vXrp4ULF6pxY2vDsstz4403uj12OBxq1KiRrr32Ws2dO9fruBSkAAAAAAAArDCV10Xqoosu0kcffVT8OCTk/0o5ycnJWr16td5++21FRUVp8uTJGjJkiL744gu/7d/lCsz4xCpZkDLGyGF1cmAAAAAAAIBzTEhIiOLi4kqsP3bsmJYuXao33nhD1157rSRp2bJluvDCC/XVV1/piiuuqOxULbGtIOV0OvXQQw8pMzNT1113naZPn64///nPmj17tiTp+uuv1+LFixUZGWlXigAAAAAAACX4OmTP6XTK6XS6rQsPD1d4eMm7/+7atUtNmjRRrVq11L17d6WmpqpZs2bKzs5WQUGB+vTpU9y2ffv2atasmTIyMvxWkJo6darHbefNm+dxW9sKUikpKXrzzTc1cuRIvfLKK9q3b59WrVqll156SUFBQXr00Uf18MMPa8GCBXalCAAAAAAAUJKPBanU1NQSc0PNnDlTjz32mNu6bt26KT09Xe3atdPBgwf1+OOP6+qrr9Y333yjvLw8hYWFqX79+m7Pady4sfLy8nxL8De2bNmiLVu2qKCgQO3atZMkfffddwoODlaXLl2K21kd6WZbQep//ud/9Morr6hPnz66++67dcEFF2jlypW64YYbJEkxMTEaP348BSkAAAAAAFCl+NpDKiUlpUTPo9J6Rw0YMKD43506dVK3bt3UvHlzvfXWW6pdu7ZvSXho0KBBqlevnl555RU1aNBAkvTzzz9rzJgxuvrqq3Xfffd5FTfIn0lacfjwYbVt21aS1KpVKwUHB6tNmzbF2y+44AL9+OOPdqUHAAAAAABQOmN8WsLDwxUZGem2lFaQ+r369eurbdu22r17t+Li4nTmzBkdPXrUrU1+fn6pc055a+7cuUpNTS0uRklSgwYN9Oc//9mnu+zZVpA6O6ZRkjZv3iyHw6HMzMzi7Zs2bdJ5551nV3oAAAAAAAClchjfFm+dOHFCOTk5io+PV0JCgkJDQ7V+/fri7Tt37tS+ffvUvXt3P7zKXx0/frzUDkM//vij/vvf/3od17YhexMnTtTo0aP18ssvKzs7W3PmzNGMGTO0Y8cOBQUFadGiRV53+wIAAAAAAKjupk2bpkGDBql58+Y6cOCAZs6cqeDgYI0cOVJRUVEaN26cpk6dqujoaEVGRiopKUndu3f36x32Bg8erDFjxmju3Lnq2rWrpF87Ed1///0aMmSI13FtK0jde++9io2NVUZGhsaOHauRI0eqY8eOevTRR3Xq1CklJyfroYcesis9AAAAAACA0vk4h5SncnNzNXLkSP30009q1KiRrrrqKn311Vdq1KiRJGn+/PkKCgrS0KFD5XQ61a9fPy1cuNCvOSxevFjTpk3TLbfcooKCAklSSEiIxo0bp2effdbruA5jTCW9jYFR2q0SB0eNVpAj2PMgDosjF43LWnurqlo+VgU4f0dIqLXwRUWW2lsVVKvicb6/5TrtrLjRbwXw+AZFRFhq7zp1KkCZVI7gunUttbf82bF4VwkVWTu2LudpS+1DWre01L4wZ4+l9oE+10PaX2CpfdGu7y21Ny5rX39BYWGW2ls9XlaubaawwFLsqva9EujruCPI2rnosHhsrba3qui4ta7vjmALv3lU9T4/Vj8PjlBr/59qCgqtxbf4flo91y29nxbfy+Df3WWpwlQaNqi40W8Ufv+DtfgWz0WrrJ6LVj8LVe1csRw/0Kpa/oH+7rJ6rQ3k3yAW38tA/4ZZ53rbUvtzRa9B3hdiJGnjB/f7KZPKc/LkSeXk5EiSWrdurTp16vgUr4pd1axLTU1VVFSU27JHO+xOCwAAAAAAnKtcxrelGjp48KAOHjyoCy64QHXq1JGv/ZuqbEFqxowZGjt2bIXtUlJSdOzYMbelpdpXQoYAAAAAAKBGMj4u1chPP/2kxMREtW3bVgMHDtTBgwclSePGjfNp7u8qW5DKzc3V3r17K2xX2q0SLQ3XAwAAAAAAsMCuu+zZITk5WaGhodq3b58ifjPty4gRI7RmzRqv49o2qXlFli9fbncKAAAAAAAANdo//vEPrV27Vk2bNnVbf8EFF+iHH6zNL/hbthakDh8+rLS0NGVkZCgvL0+SFBcXpx49emj06NHFs8YDAAAAAABUGdX7/nCWnDx50q1n1FlHjhxReLi1m3z9lm1D9jZv3qy2bdtqwYIFioqKUs+ePdWzZ09FRUVpwYIFat++vbKysuxKDwAAAAAAoFQ1acje1Vdf7TaKzeFwyOVy6ZlnntE111zjdVzbekglJSVp2LBhWrx4sRy/u1W6MUYTJ05UUlKSMjIybMoQAAAAAACgFNWsqOSLZ555RomJicrKytKZM2f0wAMP6F//+peOHDmiL774wuu4tvWQ2rZtm5KTk0sUo6Rfq23JycnaunVr5ScGAAAAAABQDocxPi3VycUXX6zvvvtOV111lW644QadPHlSQ4YM0ZYtW9S6dWuv49rWQyouLk6ZmZlq3759qdszMzPVuHHjSs4KAAAAAACgAi67E6gcBQUF6t+/vxYvXqyHHnrIr7FtK0hNmzZNEyZMUHZ2thITE4uLT/n5+Vq/fr2WLFmiOXPm2JUeAAAAAABAjRYaGqrt27cHJLZtBalJkyYpJiZG8+fP18KFC1VUVCRJCg4OVkJCgtLT0zV8+HC70gMAAAAAAChVdRt254vbbrtNS5cu1ezZs/0a17aClCSNGDFCI0aMUEFBgQ4fPixJiomJUWhoqJ1pAQAAAAAAlK3m1KNUWFiotLQ0ffTRR0pISFCdOnXcts+bN8+ruLYWpM4KDQ1VfHy83WkAAAAAAABUrAb1kPrmm2/UpUsXSdJ3333ntq20G9V5qkoUpAAAAAAAAKoLRw2oR33//fdq2bKlNmzYEJD4FKQkyVicHt8RFNj4Fts7goMthg/wmVPD3k/L7YOsVZBNkaXm1mKfKQhccCnwx9ZifFNk7c00Z85Yah9Uu7al9i6n01J7y+/nqV+stbfK6vGyyFUn3FL7QF/bTKHF8yXAn09rwavWdTmoToSl9q6Tpyy1t/y9aPFcd/1i7dwKrlvXUnur76cpDPBtfqx+j4ZYm3ohqJa1c73I4ufBquAGUZbau348HaBMrHPUt5Z7oL8nrH4WrF9nLf6vfIC/t6p9fIssX2sD+T3nDYvfdY6wMGvxLXy3WH5vrH5PVLX3/lxRA3pIXXDBBTp48KBiY2Ml/Trt0oIFC4pvSucri784AQAAAAAAcK4zvyu6/f3vf9fJkyf9Fp8eUgAAAAAAABY4qlanxWqJghQAAAAAAIAVNWDInsPhKDFpuS+TmP8eBSkAAAAAAAArzv16lIwxGj16tMLDf53v8fTp05o4caLq1Knj1m7lypVexacgBQAAAAAAYIGjBvSQGjVqlNvj2267za/xbS1Ibdu2TXPnztXnn3+ugwcPKigoSK1atdKNN96o+++/X5GRkXamBwAAAAAAUFINKEgtW7YsoPFtu8ve2rVr1b17d506dUpXXnmlgoKCNHbsWF133XVasWKFunTpory8PLvSAwAAAAAAQIDYVpB68MEHNW/ePP3P//yPXn31Vb377rv66KOPNHv2bP373/9WixYtlJKSYld6AAAAAAAApXP5uMC+gtSOHTvUv3//4sd9+vRRTk6ODh48qNDQUM2cOVOrV6+2Kz0AAAAAAIBSOYzxaYGNBanzzjtPO3fuLH6ck5Mjl8ulhg0bSpKaNm2qEydO2JUeAAAAAABA6YzxbYF9k5rfcccduvPOO/XQQw8pPDxc8+bN0/XXX6+wsDBJ0tatW9WyZUu70gMAAAAAACgdRSWf2VaQmjFjhk6ePKknnnhCTqdT/fr10/PPP1+8/bzzztOiRYvsSg8AAAAAAKB0zAPlM9uG7IWEhOjpp5/W/v37dfjwYb3++uuKiYkp3t61a1f17NmzwjhOp1PHjx93W1ymKJCpAwAAAAAABFxqaqouv/xy1atXT7Gxsbrxxhvdpj+SpN69e8vhcLgtEydOtCljz9lWkPKX1NRURUVFuS17tMPutAAAAAAAwDmqsiY137hxoyZNmqSvvvpK69atU0FBgfr27auTJ0+6tRs/frwOHjxYvDzzzDP+fsl+Z9uQvYrMmDFDeXl5SktLK7ddSkqKpk6d6rZucNToAGYGAAAAAABqtEqaQ2rNmjVuj9PT0xUbG6vs7Gy3UWURERGKi4urlJz8pcr2kMrNzdXevXsrbBceHq7IyEi3JcgRHPgEAQAAAABAzeTjXfZKm37I6XRWuNtjx45JkqKjo93Wn50G6eKLL1ZKSopOnToVkJftT1W2ILV8+XJ9/PHHdqcBAAAAAADgzseCVGnTD6Wmppa7S5fLpXvvvVdXXnmlLr744uL1t9xyi1577TVt2LBBKSkpevXVV3XbbbcF+h3wma1D9g4fPqy0tDRlZGQoLy9PkhQXF6cePXpo9OjRatSokZ3pAQAAAAAAlOTjXfZKm34oPDy83OdMmjRJ33zzjT7//HO39RMmTCj+d8eOHRUfH6/ExETl5OSodevWviUaQLb1kNq8ebPatm2rBQsWKCoqSj179lTPnj0VFRWlBQsWqH379srKyrIrPQAAAAAAgIAobfqh8gpSkydP1qpVq7RhwwY1bdq03NjdunWTJO3evduvOfubbT2kkpKSNGzYMC1evFgOh8NtmzFGEydOVFJSkjIyMmzKEAAAAAAAoCQrd8rzhTFGSUlJeuedd/TJJ5+oZcuWFT5n69atkqT4+PgAZ+cb2wpS27ZtU3p6eolilCQ5HA4lJyfr0ksvtSEzAAAAAACAclRSQWrSpEl644039N5776levXrF0x1FRUWpdu3aysnJ0RtvvKGBAweqYcOG2r59u5KTk9WzZ0916tSpUnL0lm1D9uLi4pSZmVnm9szMTDVu3LgSMwIAAAAAAPCAy/i2eGjRokU6duyYevfurfj4+OLlzTfflCSFhYXpo48+Ut++fdW+fXvdd999Gjp0qD744INAvXK/sa2H1LRp0zRhwgRlZ2crMTGxuPiUn5+v9evXa8mSJZozZ45d6QEAAAAAAJSuEofslef888/Xxo0bKyUXf7OtIDVp0iTFxMRo/vz5WrhwoYqKiiRJwcHBSkhIUHp6uoYPH25XegAAAAAAAKWrpILUucy2gpQkjRgxQiNGjFBBQYEOHz4sSYqJiVFoaKidaQEAAAAAACCAbC1InRUaGlrlZ38HAAAAAACQRA8pP6gSBSkAAAAAAIBqw8LE5CjdOVmQcgQHW2pv/nf+Ks+f4LLWvqoJdP4O227eWDqr+QQ4f6ufN0eItSGsVuI7Qi1eAix+diyfWxbfe0eQw1r78HBL7c2ZM9baFxRaam/52FrMR1aPbxU7d4NyD1lqbyx+HozFHxGWPz+nTlmLb+HzYAoDfB0P8PeE5c+y1WtPgN+foPBaltoH+lpoWaB/B1iM7/rlF0vtg8LCrMW3ei3/5bSl9oFk9TetCgosNTdOp7X4FplCi/lYPFeC69W11N5VZPFaYvWPTavnVoDPdau/k6yyfG2zqor9LnGdDtz5Eui/X6vc99C5orrXBaqAc7IgBQAAAAAAEDAM2fMZBSkAAAAAAAArGLLnM/riAQAAAAAAoFLRQwoAAAAAAMAKhuz5jIIUAAAAAACAFRSkfFalClLO/73TR7jFOxkBAAAAAABUGgpSPrN9Dql169Zp4MCBatCggSIiIhQREaEGDRpo4MCB+uijj+xODwAAAAAAwJ3L5dsCewtSr7zyigYOHKioqCjNnz9fq1at0qpVqzR//nzVr19fAwcO1KuvvmpnigAAAAAAAO6M8W2BvUP2nnzyST333HOaNGlSiW2jR4/WVVddpVmzZun222+3ITsAAAAAAAAEgq09pPbt26c+ffqUuT0xMVG5ubmVmBEAAAAAAEAF6CHlM1sLUhdddJGWLl1a5va0tDR16NChEjMCAAAAAACogMv4tsDeIXtz587VH//4R61Zs0Z9+vRR48aNJUn5+flav369vv/+e61evdrOFAEAAAAAANwYw8TkvrK1INW7d2998803WrRokb766ivl5eVJkuLi4jRgwABNnDhRLVq0KDeG0+mU0+l0W+cyRQpyBAcqbQAAAAAAUJPRy8lnthakJKlFixZ6+umnvX5+amqqHn/8cbd1rRwXqXXwxb6mBgAAAAAAUBLzQPnM1jmk/CElJUXHjh1zW1oGXWh3WgAAAAAAACiD7T2kyjNq1Cj95z//0ccff1xmm/DwcIWHh7utY7geAAAAAAAIGBdzSPmqShekmjRpoqCgat+JCwAAAAAAnEsYsuezKl2QSk1NtTsFAAAAAAAAN4YeUj6r0t2P/vOf/2js2LF2pwEAAAAAAPB/jPFtQdUuSB05ckSvvPKK3WkAAAAAAADAj2wdsvf++++Xu/3777+vpEwAAAAAAAA85KKXk69sLUjdeOONcjgcMuV0V3M4HJWYEQAAAAAAQAUMc0j5ytYhe/Hx8Vq5cqVcLlepy9dff21negAAAAAAACUYl/Fpgc0FqYSEBGVnZ5e5vaLeUwAAAAAAAJXOuHxbLHrxxRfVokUL1apVS926dVNmZmYAXlTlsrUgdf/996tHjx5lbm/Tpo02bNhQiRkBAAAAAACUrzJ7SL355puaOnWqZs6cqa+//lqdO3dWv379dOjQoQC9uspha0Hq6quvVv/+/cvcXqdOHfXq1asSMwIAAAAAAKg65s2bp/Hjx2vMmDHq0KGDFi9erIiICKWlpdmdmk9sndQcAAAAAACg2vFxUnOn0ymn0+m2Ljw8XOHh4W7rzpw5o+zsbKWkpBSvCwoKUp8+fZSRkeFTDrYzNcTp06fNzJkzzenTp4lP/BoVvzrnTnziE59rA/GJT/zKi0184hOfc9eu+DXRzJkzjSS3ZebMmSXa7d+/30gyX375pdv6+++/33Tt2rWSsg0MhzE1Y9bw48ePKyoqSseOHVNkZCTxiV9j4lfn3IlPfOJzbSA+8YlfebGJT3zic+7aFb8m8rSH1IEDB3Teeefpyy+/VPfu3YvXP/DAA9q4caM2bdpUKfkGAkP2AAAAAAAAKlFpxafSxMTEKDg4WPn5+W7r8/PzFRcXF6j0KoWtk5oDAAAAAACgdGFhYUpISND69euL17lcLq1fv96tx1R1RA8pAAAAAACAKmrq1KkaNWqULrvsMnXt2lXPPfecTp48qTFjxtidmk9qTEEqPDxcM2fO9KhLHPGJfy7Fr865E5/4xOfaQHziE7/yYhOf+MTn3LUrPso3YsQI/fjjj3r00UeVl5enSy65RGvWrFHjxo3tTs0nNWZScwAAAAAAAFQNzCEFAAAAAACASkVBCgAAAAAAAJWKghQAAAAAAAAqFQUpAAAAAAAAVKoaU5B68cUX1aJFC9WqVUvdunVTZmamX+IuWrRInTp1UmRkpCIjI9W9e3d9+OGHfol91v79+3XbbbepYcOGql27tjp27KisrCy/xC4qKtIjjzyili1bqnbt2mrdurWeeOIJeTvX/aeffqpBgwapSZMmcjgcevfdd4u3FRQUaPr06erYsaPq1KmjJk2a6I477tCBAwf8El+SHA5Hqcuzzz5bYezU1FRdfvnlqlevnmJjY3XjjTdq586dxduPHDmipKQktWvXTrVr11azZs10zz336NixYx7lXlH83zLGaMCAAaW+Rl/jZ2Rk6Nprr1WdOnUUGRmpnj176pdffvFL/Ly8PN1+++2Ki4tTnTp11KVLF/2///f/PMq/onPp9OnTmjRpkho2bKi6detq6NChys/P9yh2RfF9PbaeXge8Oa6exvf2uHoS35fjWprZs2fL4XDo3nvvLV7317/+Vb1791ZkZKQcDoeOHj3q1/h/+tOf1Lp1a9WuXVuNGjXSDTfcoB07dvgtfu/evUtcdyZOnOhz7L1795Z5XXv77bf9kntOTo4GDx6sRo0aKTIyUsOHD7d0bj322GMlcmvfvn3xdl+PbUXxfTm2FcX29biWF98fx7ai/H09tlLFv0FWrlypvn37qmHDhnI4HNq6datf4z/22GNq37696tSpowYNGqhPnz7atGmT3+KPHj26xHvYv39/v8U/ceKEJk+erKZNm6p27drq0KGDFi9e7FHsFi1alPr5mDRpkiTfz62K4vt63awovq/nV3nxfT2/Ksrd13PLk9/fvpxbnsT35dzyJL4v55Yn8X35ze9J/Pz8fI0ePVpNmjRRRESE+vfvr127dnmUvyT997//1b333qvmzZurdu3a6tGjhzZv3ly83Zf3v6LYkvTtt9/q+uuvV1RUlOrUqaPLL79c+/bt80t8X65rQAmmBlixYoUJCwszaWlp5l//+pcZP368qV+/vsnPz/c59vvvv29Wr15tvvvuO7Nz504zY8YMExoaar755hs/ZG7MkSNHTPPmzc3o0aPNpk2bzPfff2/Wrl1rdu/e7Zf4Tz75pGnYsKFZtWqV2bNnj3n77bdN3bp1zfPPP+9VvL///e/moYceMitXrjSSzDvvvFO87ejRo6ZPnz7mzTffNDt27DAZGRmma9euJiEhwS/xjTHm4MGDbktaWppxOBwmJyenwtj9+vUzy5YtM998843ZunWrGThwoGnWrJk5ceKEMcaYf/7zn2bIkCHm/fffN7t37zbr1683F1xwgRk6dKhHuVcU/7fmzZtnBgwYUOpr9CX+l19+aSIjI01qaqr55ptvzI4dO8ybb75pTp8+7Zf4f/jDH8zll19uNm3aZHJycswTTzxhgoKCzNdff11h/IrOpYkTJ5rzzz/frF+/3mRlZZkrrrjC9OjRw6P3pqL4vh5bT68D3hxXT+L7clw9ie/Lcf29zMxM06JFC9OpUyczZcqU4vXz5883qampJjU11UgyP//8s+XY5cV/6aWXzMaNG82ePXtMdna2GTRokDn//PNNYWGhX+L36tXLjB8/3u36c+zYMZ9jFxYWlriuPf7446Zu3brmv//9r8/xT5w4YVq1amUGDx5stm/fbrZv325uuOEGc/nll5uioiKP4s6cOdNcdNFFbjn++OOPxdt9PbYVxffl2FYU29fjWl58fxzb8uL749h68htk+fLl5vHHHzdLliwxksyWLVs8fn88if/666+bdevWmZycHPPNN9+YcePGmcjISHPo0CG/xB81apTp37+/23t45MgRv+U/fvx407p1a7NhwwazZ88e89JLL5ng4GDz3nvvVRj/0KFDbnmtW7fOSDIbNmwwxvh+blUU39frZkXxfT2/yovv6/lVXmx/nFue/P725dzyJL4v55Yn8X05tzyJ78tv/oriu1wuc8UVV5irr77aZGZmmh07dpgJEyaU+bu9NMOHDzcdOnQwGzduNLt27TIzZ840kZGRJjc31xjj2/tfUezdu3eb6Ohoc//995uvv/7a7N6927z33nse/+1bUXxfrmvA79WIglTXrl3NpEmTih8XFRWZJk2amNTU1IDsr0GDBubll1/2S6zp06ebq666yi+xSnPdddeZsWPHuq0bMmSIufXWW32O7ckf3ZmZmUaS+eGHHwIS/4YbbjDXXnut5djG/PpjRJLZuHFjmW3eeustExYWZgoKCvwWf8uWLea8884zBw8etFy4qCh+t27dzMMPP+xVPE/i16lTxyxfvtytXXR0tFmyZIlX+zh7Lh09etSEhoaat99+u3jbt99+aySZjIwM716AKf9c9eXYlhbbX8e1tPj+PK6lxffXcf3vf/9rLrjgArNu3TrTq1cvt4LOWRs2bPC6IOVJ/LO2bdtmJFkq7pcXv6L9+TP3Sy65pMR129v4a9euNUFBQW5/BB49etQ4HA6zbt06j2LPnDnTdO7cucJ23h5bT+OfZeXYVhTb1+NqNXerx7a8+P44tlZ+g+zZs8fyH83e/MY5duyYkWQ++ugjv8QfNWqUueGGGyzlYCX+RRddZGbNmuW2rkuXLuahhx6yvL8pU6aY1q1bG5fL5bbel+umJ/HP8ua6WV58X8+viuL/njfXztJi++PcsvL725tzy5vf91bOLU/i+3JueZO/ld/8FcXfuXOnkeT2H4tFRUWmUaNGHv32OXXqlAkODjarVq1yW1/eue/p++9J7BEjRpjbbrutwjy9je/P6xpwzg/ZO3PmjLKzs9WnT5/idUFBQerTp48yMjL8uq+ioiKtWLFCJ0+eVPfu3f0S8/3339dll12mYcOGKTY2VpdeeqmWLFnil9iS1KNHD61fv17fffedJGnbtm36/PPPNWDAAL/tozzHjh2Tw+FQ/fr1/R47Pz9fq1ev1rhx47x6/tnhWtHR0eW2iYyMVEhIiF/inzp1SrfccotefPFFxcXFWY5ZXvxDhw5p06ZNio2NVY8ePdS4cWP16tVLn3/+uV/iS79+nt58800dOXJELpdLK1as0OnTp9W7d29LsX9/LmVnZ6ugoMDtPG7fvr2aNWvm1Xnsybnq7bEtLbY/j+vv4/v7uJaWv7+O66RJk3Tddde5HUd/8jT+yZMntWzZMrVs2VLnn3++3+K//vrriomJ0cUXX6yUlBSdOnXK77lnZ2dr69atlq9rZcV3Op1yOBwKDw8vXlerVi0FBQVZ+gzt2rVLTZo0UatWrXTrrbd6PCzA3/G9ObYVxfbluFrJ3dtjW1Z8fxzbQP8GsRr/zJkz+utf/6qoqCh17tzZb/E/+eQTxcbGql27drrrrrv0008/+S3/Hj166P3339f+/ftljNGGDRv03XffqW/fvh7t46wzZ87otdde09ixY+VwOCw91x/xvb1uVhTf1/PL0/y9Pb9Ki+2PcyvQv7+txrd6bnka39tzy2r+Vn/zVxTf6XRK+vW4nhUUFKTw8HCPjnFhYaGKiorcni9JtWvXLvX5Vt7/imK7XC6tXr1abdu2Vb9+/RQbG6tu3bp5PFWEJ7n767oGSDr3h+zt37/fSDJffvml2/r777/fdO3a1S/72L59u6lTp44JDg42UVFRZvXq1X6Ja4wx4eHhJjw83KSkpJivv/7avPTSS6ZWrVomPT3dL/GLiorM9OnTjcPhMCEhIcbhcJinnnrKL7FVQS+QX375xXTp0sXccsstAYn/9NNPmwYNGphffvnFcuyioiJz3XXXmSuvvLLMNj/++KNp1qyZmTFjht/iT5gwwYwbN674cUWv0Ur8jIwMI8lER0ebtLQ08/XXX5t7773XhIWFme+++84v+f/888+mb9++RpIJCQkxkZGRZu3atR7HLetcev31101YWFiJ9pdffrl54IEHfI7/e94c2/Ji++O4lhXfX8e1vPx9Pa7GGPO3v/3NXHzxxcXno797SHkS/8UXXzR16tQxkky7du0s/S9/RfFfeukls2bNGrN9+3bz2muvmfPOO88MHjzYb7mfddddd5kLL7zQ47wrin/o0CETGRlppkyZYk6ePGlOnDhhJk+ebCSZCRMmeBT/73//u3nrrbfMtm3bzJo1a0z37t1Ns2bNzPHjx93aeXtsPYnv7bGtKLYvx9XT3M/y5tiWF98fx9bKbxBvenF4Gv+DDz4wderUMQ6HwzRp0sRkZmb6Lf7f/vY3895775nt27ebd955x1x44YXm8ssv92hYmifxT58+be64447i62dYWJh55ZVXPHyH/s+bb75pgoODzf79+0ts80cPqbLi+3LdrCi+r+eXJ/mf5c35VVZsf5xbVn5/e3NueRrf23PLk/i+nFtW/z6x+pu/ovhnzpwxzZo1M8OGDTNHjhwxTqfTzJ4920gyffv29Wgf3bt3N7169TL79+83hYWF5tVXXzVBQUGmbdu2xW28ff/Li322J35ERISZN2+e2bJli0lNTTUOh8N88sknfsndX9c1wJgaMGSvMgpSTqfT7Nq1y2RlZZkHH3zQxMTEmH/9619+iR0aGmq6d+/uti4pKclcccUVfon/t7/9zTRt2tT87W9/M9u3bzfLly830dHRfil4lfdH95kzZ8ygQYPMpZdeanmeFU/iG2NMu3btzOTJk72KPXHiRNO8eXPzn//8p9Ttx44dM127djX9+/c3Z86c8Uv89957z7Rp08ZtbgNvC1Klxf/iiy+MJJOSkuLWtmPHjubBBx/0Ob4xxkyePNl07drVfPTRR2br1q3mscceM1FRUWb79u0exS3rXPJXQcqTc9XbY1tWbH8d17Li++u4lvfe+Hpc9+3bZ2JjY822bduK1/mzIOVp/KNHj5rvvvvObNy40QwaNMh06dLFox+vVvI/a/369R4NbbES+9SpUyYqKsrMmTOnwpytxF+7dq1p1aqVcTgcJjg42Nx2222mS5cuZuLEiR7v57d+/vlnExkZWWI4rL+GFZUW39tj62nuZ3l6XK3G9+bYehLf12Nr5TeIN380exr/xIkTZteuXSYjI8OMHTvWtGjRwqO5ULz5DZWTk+PxsCVP4j/77LOmbdu25v333zfbtm0zL7zwgqlbt67HQ7vO6tu3r/njH/9Y6jZ/nFtlxffXuVVe/mf5cn6VF9/X86u02L6eW1Z+f3tzbnka39tzy5u/H6ycW1bjW/3N70n8rKws07lzZyPJBAcHm379+pkBAwaY/v37e7SP3bt3m549exY///LLLze33nqrad++fXEbb9//8mKf/dt35MiRbs8ZNGiQufnmm/2Su7+ua4AxNaAg5XQ6TXBwcIk//u644w5z/fXXB2SfiYmJHv8PSUWaNWvm1rPCGGMWLlxomjRp4pf4TZs2NX/5y1/c1j3xxBOmXbt2Pscu64/uM2fOmBtvvNF06tTJHD582O/xjTHm008/NZLM1q1bLcedNGmSadq0qfn+++9L3X78+HHTvXt3k5iY6NWPsrLiT5kypfiHzdlFkgkKCjK9evXyOf73339vJJlXX33Vbf3w4cMt9VIrK/7u3btLjLc35tfz4U9/+pPH8X//3AkTJhT/SP39j+1mzZqZefPmeRX7t/HP8vXYlhbbX8e1rPj+Oq5lxffHcX3nnXeKf9T89j04+7789n9LvfnDykr8s5xOp4mIiDBvvPFGQOKfOHHCSDJr1qzxW+zly5eb0NBQjyY89Sb+jz/+WPy+N27c2DzzzDMe7+f3LrvsshIFUX8VpMqKf5aVY2s1tqfH1Wp8b46tlfjeHlsrv0G8+aPZ2984bdq08ag3t7fxY2JizOLFi32Of+rUKRMaGlpiLpZx48aZfv36VRj/rL1795qgoCDz7rvvlrrd13OrovhneXtueRrf2/Orovi+nF8Vxfb23LLy+9ubc8vb3/eenlvexvf03LIS35vf/FbiHz16tPiz07VrV3P33Xd7vB9jfv1cHzhwwBjz62+zgQMHltnW0/e/vNhOp9OEhISYJ554wq3tAw88YOlmQGXF99d1DTjrnJ9DKiwsTAkJCVq/fn3xOpfLpfXr1/ttnqffc7lcxWOPfXXllVdq586dbuu+++47NW/e3C/xT506paAg949BcHCwXC6XX+L/XkFBgYYPH65du3bpo48+UsOGDQOyn6VLlyohIcGjcfBnGWM0efJkvfPOO/r444/VsmXLEm2OHz+uvn37KiwsTO+//36J8dW+xH/wwQe1fft2bd26tXiRpPnz52vZsmU+x2/RooWaNGni9eepovhn533w5+fp7LmUkJCg0NBQt/N4586d2rdvn0/n8W/PVV+ObXmxfT2uFcX39bhWFN8fxzUxMVH//Oc/3d6Dyy67TLfeequ2bt2q4OBgr/P0Nr759T9kPLpWexP/7HGOj4/3W+ylS5fq+uuvV6NGjSrM2Zv4MTExql+/vj7++GMdOnRI119/vcf7+a0TJ04oJyenwtfurYriWzm2VmN7elytxvfm2FqJ7+2xDfRvEG/je/o7y5v4ubm5+umnnzw6xhXFLygoUEFBgc/fi8uWLVNsbKyuu+46j59jhafxvT23PI3v7flVUXxfzq+KYnt7bgX697e38T09t7yJb+XcshLfm9/8VuJHRUWpUaNG2rVrl7KysnTDDTd4vB9JqlOnjuLj4/Xzzz9r7dq15T7f6t+QpcUOCwvT5Zdf7pdrd2nx/XVdA4rZVQmrTCtWrDDh4eEmPT3d/Pvf/zYTJkww9evXN3l5eT7HfvDBB4tvibt9+3bz4IMPGofDYf7xj3/4IfNf70IXEhJinnzySbNr1y7z+uuvm4iICPPaa6/5Jf6oUaPMeeedV3zb05UrV5qYmBhLw6B+67///a/ZsmWL2bJli5FUPHb5hx9+MGfOnDHXX3+9adq0qdm6davbrVqdTqfP8c86duyYiYiIMIsWLbKU+1133WWioqLMJ5984pbbqVOniuN269bNdOzY0ezevdutjSfj4SuKXxpZGNrlSfz58+ebyMhI8/bbb5tdu3aZhx9+2NSqVcuj7vEVxT9z5oxp06aNufrqq82mTZvM7t27zZw5c4zD4fBoXrWKzqWJEyeaZs2amY8//thkZWWZ7t27lxgq4W18X4+t1euAlePqSXxfjmtF8X09rmX5/bCxgwcPmi1bthTf3vrTTz81W7ZsMT/99JPP8XNycsxTTz1lsrKyzA8//GC++OILM2jQIBMdHe3xLZDLi797924za9Ysk5WVZfbs2WPee+8906pVK9OzZ0+fY5+1a9cu43A4zIcffuhVzPLip6WlmYyMDLN7927z6quvmujoaDN16lSP4913333mk08+MXv27DFffPGF6dOnj4mJiSn+H2Vfj2158X09tuXF9sdxrei9Mca3Y1tRfF+PrSe/QX766SezZcsWs3r1aiPJrFixwmzZssUcPHjQ5/gnTpwwKSkpJiMjw+zdu9dkZWWZMWPGmPDw8BK9Nr2J/9///tdMmzbNZGRkmD179piPPvrIdOnSxVxwwQXm9OnTfnl/evXqZS666CKzYcMG8/3335tly5aZWrVqmYULF1YY35hf57pp1qyZmT59eolt/rhulhXfX9fNsuL767pZ3vtjjG/nV3mxfT23PPn97cu5VVF8X8+tiuL7em55+veJt7/5PYn/1ltvmQ0bNpicnBzz7rvvmubNm5shQ4Z4vI81a9aYDz/80Hz//ffmH//4h+ncubPp1q2bOXPmjM/vf3mxjTFm5cqVJjQ01Pz1r381u3btMi+88IIJDg42n332mc+5G+P7dQ34rRpRkDLGmBdeeME0a9bMhIWFma5du5qvvvrKL3HHjh1rmjdvbsLCwkyjRo1MYmKi34pRZ33wwQfm4osvNuHh4aZ9+/bmr3/9q99iHz9+3EyZMsU0a9bM1KpVy7Rq1co89NBDHheIfu9st/HfL6NGjSruclzasmHDBp/jn/XSSy+Z2rVrm6NHj1rKvazcli1bVu6+JZk9e/b4HL+s53hauPA0fmpqqmnatKmJiIgw3bt39/jLyZP43333nRkyZIiJjY01ERERplOnTmb58uUexa/oXPrll1/M3XffbRo0aGAiIiLM4MGDPfpR5kl8X4+t1euA1YKUJ/G9Pa6exPfluJbl90WRmTNnWj4/PI2/f/9+M2DAABMbG2tCQ0NN06ZNzS233GJ27Njhl/z37dtnevbsaaKjo014eLhp06aNuf/++72eH6+0glRKSoo5//zzTVFRkdc5lxV/+vTppnHjxiY0NNRccMEFZu7cuWXeNr00I0aMMPHx8SYsLMycd955ZsSIEW7FUF+PbXnxfT225cX2x3Gt6L0xxrdjW1F8X4+tMRX/Blm2bFmpx3fmzJk+x//ll1/M4MGDTZMmTUxYWJiJj483119/vccT/1YU/9SpU6Zv376mUaNGJjQ01DRv3tyMHz/e0n9YVvT+HDx40IwePdo0adLE1KpVy7Rr187ScVi7dq2RZHbu3Flimz+um2XF99d1s6z4/rpulvf+GOPb+VVebF/PLU9+f/tyblUU39dzq6L4vp5bnv594u1vfk/iP//886Zp06YmNDTUNGvWzDz88MOW/j568803TatWrUxYWJiJi4szkyZNKs7T1/e/vNhnLV261LRp08bUqlXLdO7cucIhs1bi+3pdA37LYYwxHnWlAgAAAAAAAPzgnJ9DCgAAAAAAAFULBSkAAAAAAABUKgpSAAAAAAAAqFQUpAAAAAAAAFCpKEgBAAAAAACgUlGQAgAAAAAAQKWiIAUAAAAAAIBKRUEKAAAAAAAAlYqCFAAAAAAAACoVBSkAAAAAAABUKgpSAAAAAAAAqFQhdicAAABqrt69e6tTp06qVauWXn75ZYWFhWnixIl67LHH7E4NAAAAAUQPKQAAYKtXXnlFderU0aZNm/TMM89o1qxZWrdund1pAQAAIIAcxhhjdxIAAKBm6t27t4qKivTZZ58Vr+vatauuvfZazZ4928bMAAAAEEj0kAIAALbq1KmT2+P4+HgdOnTIpmwAAABQGShIAQAAW4WGhro9djgccrlcNmUDAACAykBBCgAAAAAAAJWKghQAAAAAAAAqFQUpAAAAAAAAVCrusgcAAAAAAIBKRQ8pAAAAAAAAVCoKUgAAAAAAAKhUFKQAAAAAAABQqShIAQAAAAAAoFJRkAIAAAAAAECloiAFAAAAAACASkVBCgAAAAAAAJWKghQAAAAAAAAqFQUpAAAAAAAAVCoKUgAAAAAAAKhUFKQAAAAAAABQqf4/27vnLa9yJPcAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 1600x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(16, 4))\n",
    "pivot = df[df[\"m\"] == \"G\"].pivot_table(index=\"t\", columns=\"n\", values=\"#\", aggfunc=\"count\").fillna(0)\n",
    "sns.heatmap(pivot, cmap=\"viridis\", cbar_kws={'label': 'Frequency of random number'})\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "gramex39",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}