Coding Task 1/Smarter Robot Navigation.ipynb

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      "source": [
        "# **Coding Task 1 | Algorithms 2023 | EC31205**\n",
        "#### Submitted by Irsh Vijay | 21EC30025\n",
        "****\n",
        "### **Question 2: Smarter Robot Navigation Problem**\n",
        "Please run the following code cells in succession and provide input parameters in the fifth cell.\n",
        "\n",
        "The function is called in the sixth cell.\n",
        "\n",
        "**For Input:**\n",
        "```\n",
        "maze = [[1, 1, 1, 1, 1],\n",
        "[1, 0, 0, 0, 1],\n",
        "[1, 0, 1, 1, 1],\n",
        "[0, 1, 1, 1, 1]]\n",
        "\n",
        "start = (0, 0)\n",
        "\n",
        "end = (3, 2)\n",
        "\n",
        "all_direction = False\n",
        "```\n",
        "\n",
        "**Expected Output:**<br><br>\n",
        "![expected-maze-output.png](data:image/png;base64,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)\n",
        "\n",
        "(True,\n",
        " [(0, 0),\n",
        "  (0, 1),\n",
        "  (0, 2),\n",
        "  (0, 3),\n",
        "  (0, 4),\n",
        "  (1, 4),\n",
        "  (2, 4),\n",
        "  (3, 4),\n",
        "  (3, 3),\n",
        "  (3, 2)], 11.0)"
      ],
      "metadata": {
        "id": "v3xW1M3u8vtV"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# A plot maze function to visualise the path taken\n",
        "\n",
        "def plot_maze(maze, start = False, end = False, path = False):\n",
        "  rows = len(maze)\n",
        "  cols = len(maze[0])\n",
        "\n",
        "  grid = [[(255, 255, 255) if maze[row][col] == 1 else (0, 0, 0) for col in range(cols)] for row in range(rows)]\n",
        "\n",
        "  if start:\n",
        "    grid[start[0]][start[1]] = (160, 4, 252)\n",
        "  if end:\n",
        "    grid[end[0]][end[1]] = (160, 4, 4)\n",
        "  if path:\n",
        "    for path_row, path_col in path:\n",
        "      if(grid[path_row][path_col] != (160, 4, 252) and grid[path_row][path_col] != (160, 4, 4)):\n",
        "        grid[path_row][path_col] = (100, 255, 100)\n",
        "\n",
        "  plt.imshow(grid)\n",
        "  plt.xticks(range(cols))\n",
        "  plt.yticks(range(rows))\n",
        "  plt.show()"
      ],
      "metadata": {
        "id": "p1JJFgJK3c6b"
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def check_valid_move(maze, row, col, all_direction):\n",
        "  return 0 <= row < len(maze) and 0 <= col < len(maze[0]) and maze[row][col] == 1"
      ],
      "metadata": {
        "id": "8iIFcPHrw8I7"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import math\n",
        "\n",
        "def directional_cost(prev_direction, direction):\n",
        "    # Calculate the directional cost based on the change in direction\n",
        "    ang_prev =  math.atan2(prev_direction[1], prev_direction[0])/math.pi*180\n",
        "    ang_new =  math.atan2(direction[1], direction[0])/math.pi*180\n",
        "    if ang_prev == ang_new:\n",
        "        return 0.0  # No turn\n",
        "    elif abs(ang_prev - ang_new)==45 or abs(ang_prev - ang_new)==135:\n",
        "        return 0.5  # 45-degree turn\n",
        "    else:\n",
        "        return 1.0  # 90-degree turn"
      ],
      "metadata": {
        "id": "kDegEtiYyATr"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import heapq\n",
        "\n",
        "def smarter_robot_navigation(maze, start, end, all_direction):\n",
        "    allowed_directions = [(1, 0), (-1, 0), (0, 1), (0, -1)]\n",
        "    if all_direction:\n",
        "        allowed_directions.extend([(1, 1), (-1, 1), (1, -1), (-1, -1)])\n",
        "\n",
        "    visited = set()\n",
        "    cost_map = {}\n",
        "    queue = [(0, start, [], (None, None))]\n",
        "\n",
        "    while queue:\n",
        "        current_cost, (row, col), path, prev_direction = heapq.heappop(queue)\n",
        "\n",
        "        if (row, col) == end:\n",
        "            plot_maze(maze, start, end, path + [(row, col)])\n",
        "            total_cost = calculate_total_cost(path)\n",
        "            return True, path + [(row, col)], total_cost\n",
        "\n",
        "        if (row, col) in visited:\n",
        "            continue\n",
        "\n",
        "        visited.add((row, col))\n",
        "\n",
        "        for dr, dc in allowed_directions:\n",
        "            new_row, new_col = row + dr, col + dc\n",
        "            new_direction = (dr, dc)\n",
        "\n",
        "            if check_valid_move(maze, new_row, new_col, all_direction):\n",
        "                if prev_direction[0] == None:\n",
        "                    step_cost = 0.0\n",
        "                else:\n",
        "                    step_cost = directional_cost(prev_direction, new_direction)\n",
        "                new_cost = current_cost + step_cost\n",
        "                heapq.heappush(queue, (new_cost, (new_row, new_col), path + [(row, col)], new_direction))\n",
        "    return False, [], 'inf'\n",
        "\n",
        "def calculate_total_cost(path):\n",
        "    total_cost = len(path)\n",
        "    for i in range(len(path) - 2):\n",
        "        intermediate_cost = directional_cost(\n",
        "            np.subtract(path[i], path[i + 1]), np.subtract(path[i + 1], path[i + 2])\n",
        "        )\n",
        "        total_cost += intermediate_cost\n",
        "    return total_cost"
      ],
      "metadata": {
        "id": "6j8MZnI_1Kmo"
      },
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "maze = [[1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1],\n",
        "[1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0],\n",
        "[1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0],\n",
        "[0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1],\n",
        "[1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0],\n",
        "[1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0],\n",
        "[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1],\n",
        "[1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1],\n",
        "[0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1],\n",
        "[1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1],\n",
        "[0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1],\n",
        "[1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1],\n",
        "[1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0],\n",
        "[1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0],\n",
        "[0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1],\n",
        "[1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1],\n",
        "[1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1],\n",
        "[0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1],\n",
        "[1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0],\n",
        "[1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1],\n",
        "[1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1],\n",
        "[1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1],\n",
        "[1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0],\n",
        "[1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1],\n",
        "[1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1],\n",
        "[1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1],\n",
        "[1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1],\n",
        "[0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1],\n",
        "[1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1],\n",
        "[1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1]]\n",
        "\n",
        "start = (0, 0)\n",
        "\n",
        "end = (29, 29)\n",
        "\n",
        "all_direction = True"
      ],
      "metadata": {
        "id": "1tqV5rwA21tR"
      },
      "execution_count": 33,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "smarter_robot_navigation(maze, start, end, all_direction)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "nUAvJv0p3wqe",
        "outputId": "7a949aec-8c9b-4473-804b-5b35d178084c"
      },
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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9SqWCSqVSP2dQKhFR3SP5kZG9vT169uyJZcuW4c6dOygpKcGOHTuQnJyM7OzscvURERFQKpXqh5eXl9RdIiIiE2eUc0ZffPEFhBBo3LgxrK2t8a9//Qtjx44tFxMEMCiViIiM8DUdADRv3hxJSUkoLCxEQUEB3N3dMWbMGDRr1qxcLYNSiYjIqPcZ2dnZwd3dHQ8ePEBcXByGDRtmzOaIiKiWMsqRUVxcHIQQaNWqFTIzM7FgwQL4+vpi8uTJxmiOiIhqOaMMRvn5+QgPD8etW7fg6OiIUaNGYfny5bC0tKzyPJRKZZVr5ZKRtRmb9ZtAz8Wehmn6TVANjJ2RZWgbpsYU93G5ZK4ZW3VkQsqBUQajkJAQhISEGGPWREQkQ8ymIyKiGqf3YHTixAkMGTIEHh4eUCgUOHDggMbfhRB4//334e7uDltbWwQEBCAjI0Oq/hIRkQzpPRgVFhbCz88P69ev1/r3VatW4V//+hc2bNiAM2fOwM7ODoMGDcKTJ0+eu7NERCRPep8zCgoKQlBQkNa/CSGwZs0avPfee+rLuLdv345GjRrhwIEDePXVV5+vt0REJEuSnjO6fv06cnJyEBAQoH5NqVSie/fuSE5O1jqNSqVCQUGBxoOIiOoWSQejnJwcAECjRo00Xm/UqJH6b89iNh0REdX41XTMpiMiIkkHIzc3NwDA3bt3NV6/e/eu+m/Psra2hoODg8aDiIjqFkkHo6ZNm8LNzQ3Hjh1Tv1ZQUIAzZ86gZ8+eUjZFREQyovfVdI8ePUJmZqb6+fXr15GWlgZHR0d4e3tj7ty5+N///V+88MILaNq0KRYvXgwPDw8MHz5cyn4TEZGM6D0YpaSkoH///urn8+fPBwBMnDgR0dHRePvtt1FYWIjp06cjLy8Pffr0QWxsbLlffiUiIiqjECaWwFhQUAClUon8/Hyjnj/SN4hQDoGNhpgqpupVr2/YqykGpZrYW8JgprgPGnvd1tXwVlPbZw35HK/xq+mIiIgkz6bbv38/AgMD4eTkBIVCgbS0NIm6SkREciV5Nl1hYSH69OmDlStXPnfniIiobpA0mw4Axo8fDwD45ZdfDO4UERHVLUb5cT19qFQqqFQq9XNm0xER1T01fgEDs+mIiKjGByNm0xERUY1/TWdtbQ1ra+ua7gYREdWgGj8yIiIikjyb7v79+7hx4wbu3LkDAEhPTwfwZ6K3ruRuIiKq2/Q+MkpJSUHHjh3RsWNHAH9m03Xs2BHvv/8+AODQoUPo2LEjgoODAQCvvvoqOnbsiA0bNkjYbSIikhNZZNOZYvaTKfZpGqbp3UZ1ZM3py8R2WQCmmQOnLzmsVzksQ3UwZD0ZshzMpiMiolqFgxEREdU4SYNSnz59ioULF6J9+/aws7ODh4cHJkyYoL6YgYiISBtJg1KLiopw/vx5LF68GOfPn8f+/fuRnp6OoUOHStJZIiKSJ0mDUpVKJeLj4zVeW7duHbp164YbN27A29vbsF4SEZGsGT2BIT8/HwqFAg0aNND6dwalEhGRUS9gePLkCRYuXIixY8fqvLyPQalERGS0wejp06cICQmBEAKRkZE66xiUSkRERvmarmwg+vXXX5GQkFDhTU8MSiUiIskHo7KBKCMjA8ePH4eTk5PUTRARkcxIGpTq7u6O//mf/8H58+dx+PBhlJSUICcnBwDg6OgIKysr6XpORESyoXc2XWJiIvr371/u9YkTJ2LJkiVo2rSp1umOHz8Of3//SudvSDadIYydeWVIjpOxs+Y+V3yuVz2ZDmaumQ5T/CyoDsbOptP7yMjf37/CFWWKK5GIiEwbs+mIiKjGSZpNBwBLliyBr68v7Ozs0LBhQwQEBODMmTNS9ZeIiGRI0mw6AGjZsiXWrVuHS5cu4eTJk2jSpAkCAwNx79695+4sERHJ03P9uJ5CoUBMTAyGDx+us6bsgoSjR49i4MCBlc6TFzBUHS9gqDtM8VwsL2CoGl7AYKQLGPRRXFyMTZs2QalUws/PT2sNs+mIiMgoFzAcPnwY9evXh42NDVavXo34+Hg4OztrrWU2HRERGWUw6t+/P9LS0nDq1CkMHjwYISEhyM3N1VrLbDoiIjLKYGRnZ4cWLVqgR48e2LJlCywsLLBlyxattdbW1nBwcNB4EBFR3VIt9xmVlpZqnBciIiL6K0mz6ZycnLB8+XIMHToU7u7u+O2337B+/Xrcvn0bo0ePlrTjREQkH3oPRikpKRrZdPPnzwfwZzbdhg0b8PPPP2Pbtm347bff4OTkhK5du+L7779H27Ztpes1ERHJynPdZ2QMZfcZ6cOQRZDDfUb6tjFVTNWr3hCbsdnobZgiY+9PhmCfTIMpfhYYQp8+GXK/KLPpiIioxkmeTfdXM2bMgEKhwJo1a56ji0REJHeSZ9OViYmJwenTp+Hh4WFw54iIqG7Q+wKGoKAgBAUFVVhz+/ZtzJo1C3FxcQgODja4c0REVDdInk1XWlqK8ePHY8GCBVW6go7ZdEREJPkFDCtXroSFhQVmz55dpXpm0xERkaSDUWpqKv75z38iOjq6ypcaMpuOiIgkHYy+//575ObmwtvbGxYWFrCwsMCvv/6Kf/zjH2jSpInWaZhNR0REkp4zGj9+PAICAjReGzRoEMaPH4/JkydL2RQREcmIpNl03t7ecHJy0qi3tLSEm5sbWrVq9fy9JSIiWZI0my46OlqyjhERUd1hstl0+mQamSK55FHpS9/8u88VnxupJ4arjqxDOZDLejLF911t7xOz6YiIqFaSPJtu0qRJUCgUGo/BgwdL1V8iIpIho2TTDR48GNnZ2erH7t27n6uTREQkb0bJprO2toabm5vBnSIiorrFKOeMEhMT4erqilatWmHmzJn4/fffjdEMERHJhORBqYMHD8bIkSPRtGlTZGVl4Z133kFQUBCSk5Nhbm5erp5BqUREJPlg9Oqrr6r/3b59e3To0AHNmzdHYmIiBg4cWK4+IiICS5culbobRERUixj90u5mzZrB2dlZI7XhrxiUSkREkh8ZPevWrVv4/fff4e7urvXv1tbWsLa2NnY3iIjIhEmaTefo6IilS5di1KhRcHNzQ1ZWFt5++220aNECgwYNkrTjREQkH5Jm00VGRuLixYvYtm0b8vLy4OHhgcDAQCxbtoxHP0REpJMssunkkgNnYpsCgP7Lre8yTMM0veoBYDM261Vv7GWQi+pYT3LYFqa4DKb2+cRsOiIiqpU4GBERUY2TPCgVAK5cuYKhQ4dCqVTCzs4OXbt2xY0bN6ToLxERyZDkQalZWVno06cPfH19kZiYiIsXL2Lx4sWwsbF57s4SEZE8SR6U+u677+Lll1/GqlWr1K81b97csN4REVGdIOk5o9LSUnzzzTdo2bIlBg0aBFdXV3Tv3l3rV3llVCoVCgoKNB5ERFS3SDoY5ebm4tGjR1ixYgUGDx6M7777DiNGjMDIkSORlJSkdZqIiAgolUr1w8vLS8ouERFRLSD5kREADBs2DPPmzcOLL76IRYsW4ZVXXsGGDRu0TsNsOiIikjSbztnZGRYWFmjTpo3G661bt8bJkye1TsNsOiIikvTIyMrKCl27dkV6errG61evXoWPj4+UTRERkYxIGpTq7e2NBQsWYMyYMejbty/69++P2NhYfP3110hMTJSy30REJCOSBqVGR0djxIgR2LBhAyIiIjB79my0atUKX331Ffr06SNdr4mISFZMNijV2ExssQEYP+xQLoGNU8VUveo/V3xupJ6YNu7jVcM+SY9BqUREVCtJnk2nUCi0Pj7++GOp+kxERDIjeTZddna2xmPr1q1QKBQYNWrUc3eWiIjkSfJsOjc3N43nBw8eRP/+/dGsWTP9e0dERHWCpDe9Puvu3bv45ptvsG3bNp01KpUKKpVK/ZzZdEREdY9RL2DYtm0b7O3tMXLkSJ01zKYjIiKjDkZbt27FuHHjKvwtI2bTERGR0b6m+/7775Geno69e/dWWMdsOiIiMtqR0ZYtW9C5c2f4+fkZqwkiIpIJybPpgD8vQti3bx8+/fRT6XpKRESyJXk2HQDs2bMHQgiMHTtWml4SEZGsmWw2nT6ZRtVB36woU8yjMoSxdw9DllnfPk3DNL3qDcmyM8X1ZIqMve2oajZjs97TGLIPMpuOiIhqFcmz6R49eoSwsDB4enrC1tYWbdq00fmT40RERIARsunmz5+P2NhY7NixA1euXMHcuXMRFhaGQ4cOPXdniYhIniTPpjt16hQmTpwIf39/AMD06dOxceNGnD17FkOHDjW4o0REJF+SnzPq1asXDh06hNu3b0MIgePHj+Pq1asIDAyUuikiIpIJyRMY1q5di+nTp8PT0xMWFhYwMzPD5s2b0bdvX631DEolIiLJj4zWrl2L06dP49ChQ0hNTcWnn36K0NBQHD16VGs9g1KJiEjSI6PHjx/jnXfeQUxMDIKDgwEAHTp0QFpaGj755BMEBASUmyY8PFx94yzw55ERByQiorpF0sHo6dOnePr0KczMNA+4zM3NUVpaqnUaBqUSEZHk2XT9+vXDggULYGtrCx8fHyQlJWH79u347LPPJO04ERHJh+TZdHv27EF4eDjGjRuH+/fvw8fHB8uXL8eMGTOk6zUREcmK3oORv79/hflSbm5uiIqKeq5O6UsuuV2mqDoy+fRl9D5VQ1pjdeyz+i53dfSpOnICqQoM2Mf12Z/KMkb1wWw6IiKqcRyMiIioxkkelHr37l1MmjQJHh4eqFevHgYPHoyMjAyp+ktERDIkaVCqEALDhw/HtWvXcPDgQVy4cAE+Pj4ICAhAYWGhJB0mIiL5kTQoNSMjA6dPn8bly5fRtm1bAEBkZCTc3Nywe/duTJ069fl6S0REsiTpOaOyjDkbG5v/a8DMDNbW1jh58qTOaQoKCjQeRERUt0g6GPn6+sLb2xvh4eF48OABiouLsXLlSty6dQvZ2dlap2E2HRERSToYWVpaYv/+/bh69SocHR1Rr149HD9+HEFBQeUigsqEh4cjPz9f/bh586aUXSIiolpA8p+Q6Ny5M9LS0pCfn4/i4mK4uLige/fu6NKli9Z6ZtMREZHR7jNSKpVwcXFBRkYGUlJSMGzYMGM1RUREtZzkQan79u2Di4sLvL29cenSJcyZMwfDhw/nL70SEZFOkgelZmdnY/78+bh79y7c3d0xYcIELF68WLoeExGR7ChEdSRb6qEsYC8/Px8ODg413R01Uwy2rA6mGJSqr+rYdlOFfvfQbcZmveoNWQZ9+1QdjL3cprj/GcIUw5/12Z+KC4qxXbldr89xZtMREVGN02swioiIQNeuXWFvbw9XV1cMHz4c6enpGjVPnjxBaGgonJycUL9+fYwaNQp3796VtNNERCQveg1GSUlJCA0NxenTpxEfH4+nT58iMDBQI3du3rx5+Prrr7Fv3z4kJSXhzp07GDlypOQdJyIi+dDrAobY2FiN59HR0XB1dUVqair69u2L/Px8bNmyBbt27cKAAQMAAFFRUWjdujVOnz6NHj16SNdzIiKSjec6Z5Sfnw8AcHR0BACkpqbi6dOnCAgIUNeURQQlJydrnQez6YiIyODBqLS0FHPnzkXv3r3Rrl07AEBOTg6srKzQoEEDjdpGjRohJydH63yYTUdERAYPRqGhobh8+TL27NnzXB1gNh0RERmUTRcWFobDhw/jxIkT8PT0VL/u5uaG4uJi5OXlaRwd3b17F25ublrnxWw6IiLS68hICIGwsDDExMQgISEBTZs21fh7586dYWlpiWPHjqlfS09Px40bN9CzZ09pekxERLKj15FRaGgodu3ahYMHD8Le3l59HkipVMLW1hZKpRJTpkzB/Pnz4ejoCAcHB8yaNQs9e/bklXRERKSTXoNRZGQkAMDf31/j9aioKEyaNAkAsHr1apiZmWHUqFFQqVQYNGgQ/v3vf0vSWSIikidZZNMZkuOk72KbYjZddeR2mWJGlhzWU3Xkxn2u+NzobRhbdXw8GXsfr479Sd82pmGaXvWAfrmChnyOM5uOiIhqnOTZdJs2bYK/vz8cHBygUCiQl5cnZX+JiEiGJM+mKyoqwuDBg/HOO+9I3lkiIpInSbPpAGDu3LkAgMTEREk6SERE8idpNh0REZEhDEpgALRn0xlCpVJBpVKpnzMolYio7qnxbDoGpRIRkUGDUVk23fHjxzWy6QzBoFQiItLrazohBGbNmoWYmBgkJiaWy6YzBINSiYhI0mw64M/fNMrJyUFmZiYA4NKlS7C3t4e3tzcvdCAiIq30+pouMjIS+fn58Pf3h7u7u/qxd+9edc2GDRvQsWNHTJv2Z9xE37590bFjRxw6dEjanhMRkWwwm66KqiPfTF+m2Cd9yWXbmWK+mb7q6v5kbKaYdVhduYXMpiMiolqFgxEREdU4SYNS79+/j1mzZqFVq1awtbWFt7c3Zs+erU5qICIi0kbSoNQ7d+7gzp07+OSTT3D58mVER0cjNjYWU6ZMMUrniYhIHp7rAoZ79+7B1dUVSUlJ6qDUZ+3btw+vv/46CgsLYWFR+ZXkvICh6kyxT/qSy7bjBQymgRcwVI0pXsBgcDZdWUNAxUGpZZ3RNRAxm46IiAy+gKEqQam//fYbli1bhunTp+ucD7PpiIjIaEGpBQUFCA4ORps2bbBkyRKd82E2HRERGfQ1XVlQ6okTJ7QGpT58+BCDBw+Gvb09YmJiYGlpqXNezKYjIiK9joyEEAgLC0NMTAwSEhK0BqUWFBQgMDAQVlZWOHToEGxsbCTrLBERyZOkQallA1FRURF27NiBgoIC9QUJLi4uMDc3l34JiIio1tNrMIqMjAQA+Pv7a7weFRWFSZMm4fz58zhz5gwAoEWLFho1169fR5MmTQzvKRERyZbev2dUEX9/f5O890AKdfU+D1O8b6Muqo77sUxxf6qOZTDF950p0me5y+4X1Qez6YiIqMZJmk0HAG+++SaaN28OW1tbuLi4YNiwYfj5558l7TQREcmLpNl0ANC5c2dERUXhypUriIuLgxACgYGBKCkpkbzzREQkD0bPprt48SL8/PyQmZmJ5s2bVzpPU82mqw6m+N21KZ4zqovZdIbgPl41cuhTdWTTGXLOyGSy6QoLCxEVFYWmTZvqjPlhNh0RERklm+7f//436tevj/r16+PIkSOIj4+HlZWV1vkwm46IiIySTTdu3DhcuHABSUlJaNmyJUJCQvDkyROt82E2HRERGSWbruwo54UXXkCPHj3QsGFDxMTEYOzYseVqmU1HRER63/Q6a9YsxMTEIDExUWs2nbZphBAa54WIiIj+StJsumvXrmHv3r0IDAyEi4sLbt26hRUrVsDW1hYvv/yyURaAiIhqP73OGUVGRiI/Px/+/v5wd3dXP/bu3QsAsLGxwffff4+XX34ZLVq0wJgxY2Bvb49Tp07B1dXVKAtARES1n6TZdB4eHvj222+fq0PVxRTvCzE2udyPRVUjh33cFO8B0ld1bIfN2KzfBKa3mphNR0RENU/ybLoyQggEBQVBoVDgwIEDUvSViIhkSvJsujJr1qyRxdcERERkfHqdM4qNjdV4Hh0dDVdXV6Smpmpk06WlpeHTTz9FSkoK3N3dpekpERHJ1nOdM9KWTVdUVITXXnsN69evh5ub2/P1joiI6gSDg1J1ZdPNmzcPvXr1wrBhw6o0HwalEhGRwYNRWTbdyZMn1a8dOnQICQkJuHDhQpXnExERgaVLlxraDSIikgGDvqYry6Y7fvy4RjZdQkICsrKy0KBBA1hYWMDC4s+xbtSoUfD399c6LwalEhGRpNl0ixYtwtSpmj/y1L59e6xevRpDhgzROk8GpRIRkaTZdG5ublovWvD29q5SqCoREdVNkmbTERERGULSbDqppqkO+vZLDhlZhjD2jcuGrCdTvJnaFLe3HPZZU9zW+qqOfbxa1pMei1GMYr1nz2w6IiKqcRyMiIioxkkelOrv7w+FQqHxmDFjhqSdJiIieTFKUOq0adOQnZ2tfqxatUrSThMRkbwYJSi1Xr16zKUjIqIqkzwoFQB27twJZ2dntGvXDuHh4SgqKtI5D5VKhYKCAo0HERHVLZIHpb722mvw8fGBh4cHLl68iIULFyI9PR379+/XOh9m0xERkUIYeHPBzJkzceTIEZw8eVIjn+5ZCQkJGDhwIDIzM9G8efNyf9eW2u3l5YX8/Hw4ODhUqS+GXGNfF+8zMsV7NkzxPiNT3HaGqIv7bHXsT9WxnkzxvTpVTK286P8rLijGduV2vT7HDToyKgtKPXHiRIUDEQB0794dAHQORsymIyIiSYNStUlLSwMA/uIrERHpJGlQalZWFnbt2oWXX34ZTk5OuHjxIubNm4e+ffuiQ4cORlkAIiKq/fQajCIjIwGg3G8TRUVFYdKkSbCyssLRo0exZs0aFBYWwsvLC6NGjcJ7770nWYeJiEh+JA1K9fLyQlJS0nN1yBCmeOLVEMY+kSqXk7umyBQvqjD2tqiOC4eMfaGRIarjPWGK287YmE1HREQ1TvJsOgBITk7GgAEDYGdnBwcHB/Tt2xePHz+WrNNERCQvkmfTJScnY/DgwQgMDMTZs2dx7tw5hIWFwcyMB2FERKSdwTe9AsC9e/fg6uqKpKQkdTZdjx498NJLL2HZsmUGzbOgoABKpVKvm6WqA2++qxpT7JO+eCNu1VTHOSN9meK5ELlsO2Pf9CppNl1ubi7OnDkDV1dX9OrVC40aNUK/fv1w8uRJnfNgNh0RERk8GGnLprt27RoAYMmSJZg2bRpiY2PRqVMnDBw4EBkZGVrnExERAaVSqX54eXkZ2iUiIqqlDB6MQkNDcfnyZezZs0f9WmlpKQDgzTffxOTJk9GxY0esXr0arVq1wtatW7XOJzw8HPn5+erHzZs3De0SERHVUpJm05VF/rRp00ajvnXr1rhx44bWeTGbjoiI9DoyEkIgLCwMMTExSEhIKJdN16RJE3h4eJS73Pvq1avw8fF5/t4SEZEsSZpNp1AosGDBAnzwwQfw8/PDiy++iG3btuHnn3/Gf/7zH6MsABER1X6SZtMBwNy5c/HkyRPMmzcP9+/fh5+fH+Lj47X+fAQRERHwnPcZGUPZfUb6kMt9IaZ4j4S+qiNLzMR22Wohh33DEKa4reVwz6Hs7jMiIiKSgqTZdL/88gsUCoXWx759+yTvPBERyYOk2XReXl7Izs7WeCxduhT169dHUFCQURaAiIhqP70uYIiNjdV4Hh0dDVdXV6SmpqJv374wNzeHm5ubRk1MTAxCQkJQv3795+8tERHJkkE3vZZ5NpvuWampqUhLS8P69et1zkOlUkGlUqmfM5uOiKjukTSb7llbtmxB69at0atXL53zYTYdERFJmk33V48fP8auXbswZcqUCufDbDoiIpI0m+6v/vOf/6CoqAgTJkyocF7MpiMiIr0GIyEEZs2ahZiYGCQmJpbLpvurLVu2YOjQoXBxcXnuThIRkbxJmk1XJjMzEydOnMC3334rbW+JiEiW9DpnFBkZifz8fPj7+8Pd3V392Lt3r0bd1q1b4enpicDAQEk7S0RE8mSy2XT6ZBpVh+rIo9KXKfZJX9WRTcdcN9NhittCDvsTs+mIiIgkwMGIiIhqnKRBqQCQk5OD8ePHw83NDXZ2dujUqRO++uorSTtNRETyImlQKgBMmDAB6enpOHToEC5duoSRI0ciJCQEFy5ckLzzREQkD5IGpQLAqVOnEBkZiW7dugEA3nvvPaxevRqpqano2LGjRN0mIiI5ea5zRtqCUnv16oW9e/fi/v37KC0txZ49e/DkyZNyP1VeRqVSoaCgQONBRER1i+RBqV9++SWePn0KJycnWFtb480330RMTAxatGihdT4MSiUiIsmDUhcvXoy8vDwcPXoUKSkpmD9/PkJCQnDp0iWt82FQKhERSRqUmpWVhXXr1uHy5cto27YtAMDPzw/ff/891q9fjw0bNpSbF4NSiYhI0qDUoqIiAICZmeYBl7m5OUpLS5+zq0REJFeSBqX6+vqiRYsWePPNN/HJJ5/AyckJBw4cQHx8PA4fPmyUBSAiotpP0qBUS0tLfPvtt3BxccGQIUPQoUMHbN++Hdu2bcPLL79slAUgIqLaTxZBqXIJ2zSxTQGgboaxmuIyVAeup7rDkM+zaIuqf5H2WAjMLClhUCoREdUukmfTZWVlYcSIEXBxcYGDgwNCQkJw9+5dSTtNRETyImk2XWFhIQIDA6FQKJCQkIAffvgBxcXFGDJkCK+mIyIinZ7rnNG9e/fg6uqKpKQk9O3bF9999x2CgoLw4MED9feE+fn5aNiwIb777jsEBARUOk+eMzItcjiPIIdlqA5cT3WH7M4ZPZtNp1KpoFAoNG5itbGxgZmZGU6ePKl1HsymIyIiSbPpevToATs7OyxcuBBFRUUoLCzEW2+9hZKSEmRnZ2udD7PpiIhI0mw6FxcX7Nu3D19//TXq168PpVKJvLw8dOrUqVwqQxlm0xERkaTZdAAQGBiIrKws/Pbbb7CwsECDBg3g5uaGZs2aaZ0Xs+mIiEjSbLq/cnZ2BgAkJCQgNzcXQ4cOfb6eEhGRbEmaTQcAUVFRaN26NVxcXJCcnIw5c+Zg3rx5aNWqlfS9JyIiWdBrMIqMjASAcr/aGhUVhUmTJgEA0tPTER4ejvv376NJkyZ49913MW/evCq3UXa5qLGvqjPFq/ZMsU/64jLUHVxPdctjPS7lL6vV5/J/k8umu3XrFq+oIyKSgZs3b5a7rkAXkxuMSktLcefOHdjb25e7MaugoABeXl64efNmlW6kMnY9+1R7+ySHZWCf2CdT7ZMQAg8fPoSHh4fOK6mfZdDVdMZkZmZW6Ujq4OBQ5ZVbHfXsU+3tkxyWgX1in0yxT0qlUq82mdpNREQ1joMRERHVuFo1GFlbW+ODDz6o8k2yxq5nn2pvn+SwDOwT+1Tb+lQRk7uAgYiI6p5adWRERETyxMGIiIhqHAcjIiKqcRyMiIioxtWawWj9+vVo0qQJbGxs0L17d5w9e1Zn7YkTJzBkyBB4eHhAoVDgwIEDFc47IiICXbt2hb29PVxdXTF8+HCkp6frrI+MjESHDh3UN3r17NkTR44cqfKyrFixAgqFAnPnztVZs2TJEigUCo2Hr69vhfO9ffs2Xn/9dTg5OcHW1hbt27dHSkqKzvomTZqUa0OhUCA0NFRrfUlJCRYvXoymTZvC1tYWzZs3x7JlyyrMn3r48CHmzp0LHx8f2NraolevXjh37pz675VtKyEE3n//fbi7u8PW1hadO3fGgAEDdNbv378fgYGBcHJygkKhwJYtW3TO/+nTp1i4cCHat28POzs7eHh4YMKECdi/f3+FfVqyZAl8fX1hZ2eHhg0bonPnzujTp0+V9rcZM2ZAoVCgbdu2OusnTZpUbpu4urpWOP8rV65g6NChUCqVsLOzg6+vLwICAnROo227KxQKODg4aK1/9OgRwsLC4OnpCVtbWzRp0gQdOnTQOf+7d+9i0qRJ8PDwQL169dCyZUu0b9++wvfYkydPEBoaCicnJ9SvXx/t2rXDiy++WOE0mzZtgr+/v7rfnTp10ll///59zJo1C61atYKtrS0aNGiARo0aVTj/N998E82bN4etrS1cXFzQpk2bSpejjBACLVu2hEKhgK2trc56f3//ctvBysqqwvknJydjwIABsLOzg7W1Nezt7XX26ZdfftG5vZVKpdY2cnJyMH78eLi5ucHKygp2dnYVLkNWVhZGjBgBFxcXODg4ICQkBHfv3tW6XnSpFYPR3r17MX/+fHzwwQc4f/48/Pz8MGjQIOTm5mqtLywshJ+fH9avX1+l+SclJSE0NBSnT59GfHw8nj59isDAQBQWFmqt9/T0xIoVK5CamoqUlBQMGDAAw4YNw3//+99K2zp37hw2btyIDh06VFrbtm1bZGdnqx+6frodAB48eIDevXvD0tISR44cwU8//YRPP/0UDRs2rLAvf51/fHw8AGD06NFa61euXInIyEisW7cOV65cwcqVK7Fq1SqsXbtWZxtTp05FfHw8vvjiC1y6dAmBgYEICAjA7du3AVS+rVatWoV//etf2LBhA86cOQNLS0ucP38eq1ev1lpfWFiIPn36YOXKlQCAx48f65x/UVERzp8/j8WLF+P8+fPYv38/0tPTsXDhwgr71LJlS6xbtw6XLl3CyZMn4ezsjHPnzuGjjz7SuR4AICYmBqdPn4ajoyMaN25c4f45ePBg9XbZsWMHJkyYoLM+KysLffr0ga+vLxITE3Hx4kWMGTMG7du31znNX7d7dna2+j9GZevtWfPnz0dsbCx27NihHvguX76MiRMnlqsVQmD48OG4du0aDh48iAsXLuDx48e4c+cOEhISdL7H5s2bh6+//hr79u1DUlISbt26hcLCwgrfl0VFRRg8eDDeeecdAH/ub7rq79y5gzt37uCTTz7B5cuX1QNFz549dc6/c+fOiIqKwpUrVxAXF4fffvsNd+7cwQ8//FDpZ8WaNWvw4MED9XqtqH7atGnIzs6Gv78/1qxZg++//15nfXJyMgYPHozAwECcPXsW3bp1w/jx43HixAmt03h5eWlsa39/fwwfPhy2traIjY3V2saECROQnp6OQ4cOoUePHhg0aBBUKhXWrl1brr6wsBCBgYFQKBRISEjADz/8gOLiYgwZMgSlpaVa9yetRC3QrVs3ERoaqn5eUlIiPDw8RERERKXTAhAxMTF6tZebmysAiKSkpCpP07BhQ/H5559XWPPw4UPxwgsviPj4eNGvXz8xZ84cnbUffPCB8PPzq3L7CxcuFH369KlyvTZz5swRzZs3F6WlpVr/HhwcLN544w2N10aOHCnGjRuntb6oqEiYm5uLw4cPa7zeqVMn8e6775arf3ZblZaWCjc3N/Hxxx+rX8vLyxPW1tZi9+7dFW7b69evCwDiwoULOuevzdmzZwUA8euvv1Z5mvz8fAFAHD16VGf9rVu3ROPGjcXly5eFj4+PWL16tc75T5w4UQwbNkxrW9rqx4wZI15//XWd/avKMgwbNkwMGDBAZ33btm3Fhx9+qPFa2XZ8tj49PV0AEJcvX1a/VlJSIlxcXMTmzZuFEOXfY3l5ecLS0lLs27dPPc2VK1cEAJGcnKx1mr86fvy4ACAePHigfq0q7+Mvv/xSWFlZiadPn1ap/scffxQARGZmZoVtXLhwQTRu3FhkZ2drrB9t9RV9Fmir7969u3jvvfd09rEqy/Hiiy+q38va6u3s7MT27ds1pnF0dBSbN28uVx8XFyfMzMxEfn6+ujYvL08oFAoRHx+vsw/PMvkjo+LiYqSmpiIgIED9mpmZGQICApCcnGyUNvPz8wEAjo6OldaWlJRgz549KCwsRM+ePSusDQ0NRXBwsMayVCQjIwMeHh5o1qwZxo0bhxs3buisPXToELp06YLRo0fD1dUVHTt2xObNm6vUDvDnet6xYwfeeOONcgG1ZXr16oVjx47h6tWrAIAff/wRJ0+eRFBQkNb6P/74AyUlJbCxsdF43dbWtsKjvDLXr19HTk6OxvpSKpXo3r27Ube9QqFAgwYNqlRfXFyMTZs2QalUws/PT2tNaWkpxo8fjwULFqBt27ZVmm9iYiJcXV3RqlUrzJw5E7///rvOeX/zzTdo2bIlBg0aBFdXV3Tv3r3Sr6b/6u7du/jmm28wZcoUnTW9evXCoUOHcPv2bQghcPz4cVy9ehWBgYHlalUqFQBobHczMzNYW1urt/uz77HU1FQ8ffpUY1v7+vrC29tbva31eV9WtT4/Px8ODg6wsLCotL6wsBBRUVFo2rSp+pcFtE1TVFSE1157DevXr4ebm1uV+rRz5044OzujXbt2CA8PR1FRkdb63NxcnDlzBq6urujVqxcaNWqEfv36abyfKluO1NRUpKWlqbe3tvpevXph7969uH//PkpLS7Fnzx48efIE/v7+5epVKhUUCoXGja82NjYwMzOr0vtcrcrDVg25ffu2ACBOnTql8fqCBQtEt27dKp0eeh4ZlZSUiODgYNG7d+8K6y5evCjs7OyEubm5UCqV4ptvvqmwfvfu3aJdu3bi8ePHQoiK/zckhBDffvut+PLLL8WPP/4oYmNjRc+ePYW3t7coKCjQWm9tbS2sra1FeHi4OH/+vNi4caOwsbER0dHRFS/w/7d3715hbm4ubt++rbOmpKRELFy4UCgUCmFhYSEUCoX46KOPKpxvz549Rb9+/cTt27fFH3/8Ib744gthZmYmWrZsWa722W31ww8/CADizp07GnWjR48WISEhkh8ZPX78WHTq1Em89tprlU7z9ddfCzs7O6FQKISHh4c4e/aszvqPPvpIvPTSS+ojzsqOjHbv3i0OHjwoLl68KGJiYkTr1q1F165dxR9//FGuvux/3vXq1ROfffaZuHDhgoiIiBAKhUIkJiZWablXrlwpGjZsqN43tdU/efJETJgwQQAQFhYWwsrKSmzbtk1rfXFxsfD29hajR48W9+/fFyqVSqxYsUIAEIGBgVrfYzt37hRWVlbl+ta1a1fx9ttvV/q+fPbIqCrv43v37glvb2/xzjvvVFi/fv16YWdnJwCIVq1aqY+KdE0zffp0MWXKFPXzsvWjq37jxo0iNjZWXLx4UezYsUM0btxYjBgxQmt9cnKyACAcHR3F1q1bxfnz58XcuXOFlZWVuHr1apWWe+bMmaJ169YVLsODBw9EYGCgens7ODiIuLg4rfW5ubnCwcFBzJkzRxQWFopHjx6JsLAwAUBMnz5dZz+excHoGTNmzBA+Pj7i5s2bFdapVCqRkZEhUlJSxKJFi4Szs7P473//q7X2xo0bwtXVVfz444/q1yobjJ714MED4eDgoPOrQEtLS9GzZ0+N12bNmiV69OhRpfkHBgaKV155pcKa3bt3C09PT7F7925x8eJFsX37duHo6FjhgJeZmSn69u0rAAhzc3PRtWtXMW7cOOHr61uutiYHo+LiYjFkyBDRsWNHja8bdE3z6NEjkZGRIZKTk8Ubb7whmjRpIu7evVuuPiUlRTRq1EhjkK9sMHpWVlaWzq8By94fY8eO1ZhmyJAh4tVXX61SG61atRJhYWEVLvPHH38sWrZsKQ4dOiR+/PFHsXbtWlG/fn0RHx+vtT4lJUX4+fmpt/ugQYNEUFCQGDx4sNb3WGWDUWXvy2cHo8rq8/PzRbdu3cTgwYNFcXFxhfV5eXni6tWrIikpSQwZMkR06tRJPH78WOs0Bw8eFC1atBAPHz4stz6r+tly7NgxAUC89tpr5erL3hPh4eEa07Rv314sWrSo0jaKioqEUqkUn3zySYXrKSwsTHTr1k0cPXpUpKWliSVLlgilUilGjx6ttT4uLk40a9ZMKBQKYW5uLl5//XXRqVMnMWPGjAqX9a9MfjBSqVTC3Ny83M4+YcIEMXTo0Eqn12cwCg0NFZ6enuLatWt693PgwIE6/xcQExOjflOWPQCoN9wff/xRpTa6dOkiFi1apPVv3t7eGv8bE0KIf//738LDw6PS+f7yyy/CzMxMHDhwoMI6T09PsW7dOo3Xli1bJlq1alVpG48ePVIPKiEhIeLll18uV/Pstir7EP7rgCKEEH379hWzZ8+WbDAqLi4Ww4cPFx06dBC//fZbhX3SpUWLFuKjjz4qV7969Wr1dv7rtjczMxM+Pj5Vnr+zs7PYsGFDuXqVSiUsLCzEsmXLNOrffvtt0atXr0qX4cSJEwKASEtL07nMRUVFwtLSsty5vylTpohBgwZVOP+8vDyRm5srhPjz3G+7du20vsfKPoD/es5HiD/36969e1f6vvzrYFTZ+7igoED07NlTDBw4UDx+/Fiv971KpRL16tUTL730ktZp5syZo3V7AxDW1tZVauPRo0cCgHB2di5Xf+3aNQFAfPHFFxqvh4SEiBdeeKHS5di+fbuwtLQUubm5Opc7MzOz3Dk/If58/9vZ2VU4/3v37qm3YaNGjcSqVasqXd4yJn/OyMrKCp07d8axY8fUr5WWluLYsWOVnqOpKiEEwsLCEBMTg4SEBDRt2lTveZSWlqq/K3/WwIEDcenSJaSlpakfXbp0wbhx45CWlgZzc/NK5//o0SNkZWXB3d1d69979+5d7nLLq1evwsfHp9J5R0VFwdXVFcHBwRXWFRUVlfuhLHNz8ypdMWNnZwd3d3c8ePAAcXFxGDZsWKXTNG3aFG5ubhrbvqCgAGfOnJFs2z99+hQhISHIyMjA0aNH4eTkZNB8dG3/8ePH4+LFixrb3sPDAwsWLEBcXFyV5n3r1i38/vvvWre9lZUVunbtavC237JlCzp37qzzfBfw5zp6+vSpQdteqVTCxcUFV69exdmzZ5Gdna31Pda5c2dYWlpqbOuff/4ZN27cQHp6epXflwsWLKjwfVxQUIDAwEBYWVnh4MGDeOutt/R635dt53PnzmmdZtGiRRrb+8KFC+r18O2331bahhACEyZMAABs3bq1XH2TJk3g4eGhsb2FEEhISNC5bv+q7FaHpUuX6lzusvNVZdu77PPx3r17CA4OrnD+zs7OaNCgARISEpCbm4uhQ4dWuLzPLrzJ27Nnj7C2thbR0dHip59+EtOnTxcNGjQQOTk5WusfPnwoLly4IC5cuCAAqL9LL7tC6lkzZ84USqVSJCYmiuzsbPWjqKhIa/2iRYtEUlKSuH79urh48aJYtGiRUCgU4rvvvqvyMlX2Nd0//vEPkZiYKK5fvy5++OEHERAQIJydndX/y3zW2bNnhYWFhVi+fLnIyMgQO3fuFPXq1RM7duyosB8lJSXC29tbLFy4sNI+T5w4UTRu3FgcPnxYXL9+Xezfv184OzuLt99+W+c0sbGx4siRI+LatWviu+++E35+fqJ79+6iuLhYCFH5tlqxYoVo0KCB+hxKcHCw8PDwEKdPn9Za//vvv4sLFy6Ib775RgAQ0dHRYs+ePeqvk/5aX1xcLIYOHSo8PT1FWlqaertnZmaKs2fPau3To0ePRHh4uEhOTha//PKLSElJEa+//rqwtLQU//nPf6q0v3l5eYm33npL6/wfPnwo3nrrLZGcnCyuX78ujh49Kvz8/IS3t7c4c+aM1vnv379fWFpaik2bNomMjAyxdu1aYWZmJrZu3VrheyA/P1/Uq1dPREZGVrod+vXrJ9q2bSuOHz8url27JiIjI4WVlZUIDw/XWv/ll1+K48ePi6ysLHHgwAFRv359YWlpWeF7bMaMGcLb21skJCSov940NzevcJrs7Gxx4cIFsXnzZgFA1K9fX2zevFn89NNP5erz8/NF9+7dRfv27UVmZqaYOHGicHBwEF999ZW4detWufqsrCzx0UcfiZSUFPHrr7+KH374Qfj4+AiFQiFiYmKq9Fkxc+ZMAUAsW7ZMa31mZqb48MMPRUpKirh+/boICgoSZmZmokOHDjrnv3r1auHg4CD27dsnMjIyROfOnQUAsXPnzgr7lJGRIRQKhQgODq7w8664uFi0aNFC/O1vfxNnzpwRr732mrCxsVEfkWmb/9atW0VycrLIzMwUX3zxhXB0dBTz58/Xuk50qRWDkRBCrF27Vnh7ewsrKyvRrVs3cfr0aZ21ZYfszz4mTpyotV5bLQARFRWltf6NN94QPj4+wsrKSri4uIiBAwfqNRAJUflgNGbMGOHu7i6srKxE48aNxZgxY9QnTnX5+uuvRbt27YS1tbXw9fUVmzZtqrQfcXFxAoBIT0+vtLagoEDMmTNHeHt7CxsbG9GsWTPx7rvvCpVKpXOavXv3imbNmgkrKyvh5uYmQkNDRV5envrvlW2r0tJSsXjxYtGoUSNhbW0tOnXqVGF9VFSUzu35bH3ZV3lVfUycOFE8fvxYjBgxQnh4eAgrKyvh7u4uevXqpdf+1qhRI531RUVFIjAwULi4uAhLS0vh4+MjgoODK53/li1bRIsWLYSNjY3w8/MTy5Ytq3SajRs3CltbW5GXl1fpdsjOzhaTJk0SHh4ewsbGRnh5eVVY/89//lN4enoKS0tL4e3tXaX32OPHj8Xf//530bBhQ1GvXr0qTfPBBx9Uut3K6nUto67627dvi6CgIOHq6iosLS2Fp6en3p8VldXfuHFD9O3bVzg6Ogpra+sqzz8iIkJ4enpWeT0JIUR4eLjO7fZs/dWrV8XIkSOFq6trleoXLlwoGjVqJCwtLcULL7wgPv30U523iOjCn5AgIqIaZ/LnjIiISP44GBERUY3jYERERDWOgxEREdU4DkZERFTjOBgREVGN42BEREQ1joMRERHVOA5GRERU4zgYERFRjeNgRERENY6DERER1bj/B7Z2gLl4u96sAAAAAElFTkSuQmCC\n"
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(True,\n",
              " [(0, 0),\n",
              "  (1, 0),\n",
              "  (2, 0),\n",
              "  (3, 1),\n",
              "  (4, 1),\n",
              "  (5, 2),\n",
              "  (6, 2),\n",
              "  (7, 2),\n",
              "  (8, 3),\n",
              "  (8, 4),\n",
              "  (9, 5),\n",
              "  (10, 6),\n",
              "  (10, 7),\n",
              "  (11, 8),\n",
              "  (12, 7),\n",
              "  (13, 6),\n",
              "  (14, 7),\n",
              "  (14, 8),\n",
              "  (15, 9),\n",
              "  (16, 10),\n",
              "  (17, 11),\n",
              "  (18, 12),\n",
              "  (19, 13),\n",
              "  (20, 14),\n",
              "  (21, 15),\n",
              "  (21, 16),\n",
              "  (20, 17),\n",
              "  (20, 18),\n",
              "  (20, 19),\n",
              "  (19, 20),\n",
              "  (18, 21),\n",
              "  (18, 22),\n",
              "  (18, 23),\n",
              "  (18, 24),\n",
              "  (18, 25),\n",
              "  (18, 26),\n",
              "  (18, 27),\n",
              "  (19, 28),\n",
              "  (20, 29),\n",
              "  (21, 28),\n",
              "  (22, 27),\n",
              "  (23, 27),\n",
              "  (24, 28),\n",
              "  (25, 29),\n",
              "  (26, 29),\n",
              "  (27, 29),\n",
              "  (28, 29),\n",
              "  (29, 29)],\n",
              " 63.5)"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "-yt36qrCxNVj"
      },
      "execution_count": 88,
      "outputs": []
    }
  ]
}