9_01_Shortest_Path_Routing.ipynb

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        "# Shortest-Path Routing\n",
        "\n",
        "Welcome to this class on shortest-path routing where we will be building on concepts learnt throughout the semester to work through some graph/network examples.\n",
        "\n",
        "Today we will cover some basic introductory graph theory, followed by covering Kruskal's algorithm, eventually fitting our own minimum spanning tree.\n"
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        "## A Basic Intro to Graph Theory\n",
        "\n",
        "Before we get into some code, we need to briefly cover some introductory terms and concepts.\n",
        "\n",
        "Here, we treat a 'graph' as representing a set of relationships between objects. Think of a network of cities, with roads between them, each having a specific distance.\n",
        "\n",
        "This field provides a mathematical framework for spatial problems by treating phenomena of interest as networks (e.g., a graph).\n",
        "\n",
        "The nodes in the network are known as 'vertices', which are then linked by graph connections called 'edges' (so cities would be the vertices/nodes, and roads would be the edges in a transportation network).\n",
        "\n",
        "\n"
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        "Such an approach supports a wide variety of spatial computing applications pertaining to the modeling, analyzing, and solving of spatial problems. We have already covered in this class that understanding spatial relationships is central to spatial computing.\n",
        "\n",
        "* A **graph** (G) consists of a set of **vertices** (V) and a set of **edges** (E). We are able to measure graph networks based on different properties, including (i) directed vs. undirected, (ii) connected vs. disconnected, and (iii) weighted vs. unweighted edges.\n",
        "* Whether or not vertices are directly connected or not by an edge is referred to as **adjacency**. The degree of adjacency is symmetric in undirected graphs.\n",
        "* When we have a sequence of vertices connected by edges, this is called a \"path\". This indicates a possible way to traverse from one vertex node to another, along a particular set of edges.\n",
        "\n",
        "\n",
        "By way of an illustrative example, the figure below shows how a graph theory approach could be applied to a road network (Figures are credited to Wilson Chua, 2024).\n"
      ],
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      "cell_type": "code",
      "source": [
        "from IPython.display import HTML\n",
        "HTML('<img src=\"https://wilsoncwc.github.io/assets/2022-10-02-road-graph-neural-networks/primal_dual.png\">')"
      ],
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      "execution_count": 25,
      "outputs": [
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            "text/plain": [
              "<IPython.core.display.HTML object>"
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              "<img src=\"https://wilsoncwc.github.io/assets/2022-10-02-road-graph-neural-networks/primal_dual.png\">"
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        "Within graph theory, we have a variety of different types of graphs:\n",
        "\n",
        "* **Undirected Graph**: Edges do not have a direction associated with them.\n",
        "* **Directed Graph**: Edges do have a direction associated with them.\n",
        "* **Weighted Graph**: Where each edge has an associated weight or cost (e.g., distance).\n",
        "\n",
        "See the graphical example below of these three types of graphs (Figures are credited to Haque and Andrejevic, 2021):"
      ],
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VxPXSEHbB5T2jh37g7f1nEzd9dxLL/aot2ddETXZGzJ4skn8kCVBc4Pqpomi8tDKf3jQarK2F8gE39sG4MWJpQAgTtpSINFD2w7Cw5zZdZNz+RjwB02aP3h/qNuKoVV9iSpHjpzyRwl5v3XrXtfmyksWDF5QOr0/GuHaRO3yerd+3i33umbNFnfP+07I70Ek6w2l8+QTr7nybN9+s209AUBpy7JDvgQiWUvIckBxThw/G5K/BCZd13YD/3dV7bV8+Xq3DePxx7rWc1IYkggfIAABCEAAAhCAAAQgAAEI1BFIPwHAm4TLrNofZCKuCaImXPqbOeM7/+3ge03YtS9fcbTlwAsXzl9xK+zaHy+TbMUrLSlzE0adTiDnc316jXTPyQmfF65nZpsc3Sm9n39e512O6uuoEV+49Dt36l1v9VoZaUI5oH/dCrkc//lDrASArKxce/bp7o6ZzPAjhe5vDHDl1mp/eJgwfo67J27vvD2oQU/6Wp2XMKN44u8PqvfwGz4RdP/jfmP8t23nzgNu4q57+lsftnrvRdbWD1lWaBuCThfwgl8AePnFD5y/Au+e//WNG0ct+gUAfX8Gffq5y3fa1Hn+6G77gredQVszmnKKQEgCfIAABCAAAQhAAAIQgAAE0pFA8gkAmiw1FNasrluxbcgCQPvIZaqtyZy82/uDVljlVO1Wkz3PB4DieRP5bdv22tDBcvL3lJsI6ug4nSagCXeH9u+5fd86BUDPaBX+l59vTng1EZYzO92Tqfj0aQuchYBW+hs6ns5f7lu914r1o4/U1cu/+u1/TnvPO73ay51UoP39/hArAWDZ0jVu8q+JcVGE4/q0PUPOFsVFpu7hYcni1cG2akis0TPbtu516cjJoSwh/EFbCbwTAZTPpM+/9t+2o0dPuVV23dOff8uIP6LnA0B5HPY5lvQEAAlL/jb3P6v3kQQAWQrou6Nn1/+2PeQRHcEop5XDP5vqnCWG3OQDBCAAAQhAAAIQgAAEIACByASSTwDQUXENhf37j7mJWkMCwOcTv3YTcE3mws3KNRn0JuLPPfOWO3ouUj6aIGu1V2bhcoSnoEmsN0nUqyb7ciIo021NMOXFX1sXxoyeYTpuMCcnLyTptWu22KuvfOjS1fMyF3/sL12cR3yZjWvLgKwItCrc3KBJv1am5bSwuLg04uM68k+TV5VZ3vf9wRMAfv4petYJcmqo7Qyq65zZiyy8WnWr3xODTPv0HuUvknt/4EBdWyuNhoQNRfy47xiXjlb35VHfC8pj2bI6nw3au690/BYdiqfTG7yTIDq9+lGI4z8vHb16J0gort9UX3kqXVk6hLe5//nGBAAJRqNGfmmXL1111iThfhL86fAeAhCAAAQgAAEIQAACEIBAIwSSTwB4+MGGjwFsTADQZE4O4DTZ06TqzTcGhHApKyu3jq/WmYp7K/shEW6YyuvYNU3q5CzQO7v95IlzptMCdH3Y0CnueMFz5y7b9cwcN+luysRdk3NNauWsT/vbdVqAthMoTYkNmsDLssBvJh5evkiftaqtND4ZOCHEiZwXV2WbPet7F0d1CN+j7gkAi75f4T3S6tdLFzOcVYLa4tTJ8/XS275tX7DuKnskAeDihYzg6ny4U0MvQZ0C8MhDnVzd9u457F12r57lhY5aHHlji8SvK0IdLGZkZAa3Z3hiT0giN5z4eVtCdJKAF2S98e4NkUPbKxoLkQQAiSISFvQd0Pf10Ue6WPvn33VOE5We/CPoOMBoWIk0VjbuQQACEIAABCAAAQhAAAIpQyD5BACtsjYUGhIAtGoqJ3cy0R896ku3Qv/OW6GnCejYOHmk14RTWwkihT27DztP7oqjyZl/Yv/ZsKnuWU3MGgvad7571yHLzMxuMJqc/umYOR2Rt/jHlSZTcjnxU74vtH/PSkoir+RHStBzcud3WOiPp5VpnVogU/Offlrrv+Xe97rhJC+aAsDmzbudqCGrh+KikpA8tWVB4ofq6u1zV9uFB/F74obvhIYEgC1b9jjzfznoU/t6QW2g9tLEWj4AZIWg/MItCZSHhBfdk6ATKci0X/fl5V/t6oWK8krzfBjMnrXIuxzxVab+SiNc3JEYIz8EshyROPNCu/eCx1MqvgSUEcOnW4WvbhEz4CIEIAABCEAAAhCAAAQgAAGz5BMAdJRaXgSP8WpNTwDQxMvvGO2nZWvdSqqOutNqvVZVwwUA7at+/90hbiIWySmdTLs9b+0dX/kwxNRbeesMek3Khg+b2ugXa8vm3W4yr0mdF44cPmm//rrRHQnnXfO/asK6auUml75WrP1HzfnjRXrf/c06R3obNoQeP6e4Slc+B1RuTcYj7cV//YaDuqlTvomUfIuuydReeX7cb2yIiKI2G+J8KTztGMkpouKNHvllvXy0ut/++Xfc/YYEgC+/+Nbdlz8Gv2WDBB75F9DkXn4hZs5Y6OKFCwBqc0+MOHEi1EO/CqRtGZ5/BQkl4ukFvwDwne+0CO++/9UTMvwCgCwAdCKDdyqDvp/5eYUmfwOHDp1wosV993RwIkBD1gn+PHgPAQhAAAIQgAAEIAABCKQ9geQTAO6750W7fj0nYsvJ0/59977o9uR7k1mZfmuSpn35WzbvcRO+SAKAJoh9+4x2E8GpU0K9rus89pHDp7tVawkQO3ccqJf/6lWb3Yryyy99EDIR9CLKWkATVa1qa7Vdk1MFOeCTDwGt5mqbQkNBk1NNhvW8nmlq8OoUyYO9zqSXPwP9bdu2L2KSngAwYcKciPdbcnHGl3UTbr8Iosmz/CNoYq4tD0sWr7J9e4+4Ovvjefk1RQDQc2Km1X7PWuPMmYv24P2vhlg8eALADz/86iXvXmU14DkJVPv6g7ZsvNX9E5e+/DWEOwj0CwCNWU9o64knIvgFgJKSMrfaL+eMkYJOmnji8W52913t61kORIrPNQhAAAIQgAAEIAABCEAg7QkknwCgyWpDK57FxSUmZ2333N3eFi9eZUuXrjGdk65J4NgxM90Ku1ZtIwkA+ioMGzLZxfWvhmuiqQmkTLz1p8mcf6XX+wrJieAjD3dyDvd0frwXNPG8evW6TZ823x748ysujfHjZpkmfgp61TF3KqNWkWX67w8y0ZfH+8ce7eImrfPnLfPfvuX7RYtWuAn1pwMnBM3gxUCTbVkTeGJEpDop8VgIAPO+Werq+85bn5jEFa1uz/tmSdAJoqwpZA3QWgFAdZeZvyw2JA6pXbTdQddkaeA51FM88ZePhfCgCbju9e83NrjfPuNKpr337mCXjpwn7tp5MPwx03fRa1cJLQ2FzGvZ9tADr7o8/AKAth9ICFH6v67YEGIdoi0g+g7pvo44LIxwikJD+XEdAhCAAAQgAAEIQAACEEhbAskjAGgSpImYVogjrcB7Tag92Zo0Kd4dtz3jnvnwg8+CkyR5U5c1QPgWAD0/ZfJcF99NrF79yAYP+jx4Vv29f+pgmnw35nRt+fL1blJ27z0dnOO6oUMmuyPeHn6oo5ssyn+B9uKHp6Fj3rw4Wg3WFoa3u3/izPL1WfWQ8DFr5nchWxu8Ojf2KmHirTcHujQ0+ZUFwSMPdXQnDdx15/POAaB/u0R4Wp4AMGrkF+G3Wvz5yuVr1r7du66NPuo53JXPOyZxxGfTguJIawUAiSnymaAJv3wo6Duh75CcLGqC7gVN0HVd3vp1zKM/9Hi/bluITlLQd0YigVux//1TzqnkunXbgtYF/ufE/aUXe7h0N2/a7b8V8v7smYtOiFH+Eim8ID8QEyd85QQjfZ8lSg0dPNkJF3IGqO+EHBw29r/gpcUrBCAAAQhAAAIQgAAEIAABSyYfAFoJ/2TABJs4YU5wJTtSE+qIOTmzkyWA9m9PmzovZL/+saOn3aQqkgAw+4YzOE0En33mLTdJ1uqsJox79hyOuPLvL4NW0TWZ7Nyxd3CyqcmnjhccN2amM/GPtNIuK4EL56+4Cb7OvNee8L883MkdBdi5Yy/37KmT50yTwpaEoqJi5zW+U8de9vijXZ0I0LvXCNP2CP/e+EhpL5i/zJV/9epQE/hIcZtzTUKMTlTwjtn7y8OdbeG3P5tM573QmAAgy4lBn0y0N17rbzoRoKEg03xZcMgKoGuXPm7rhX/yr+e0119izTffLHHWCP60vKP8tE1D7NSej/2lq3PMePbsJX/UkPcSVfRdlZ+CkxH8B3iRdSJChxfedyz8jgp1v7q6xg4ePO7K36H9+yZhSdYrii+LlnPnLkUUH7y0eYUABCAAAQhAAAIQgAAEIOAjkDwWACq0Js/+s9x9FQl5qwm1JlPaRx0+4T7aiACgs+61Equ94zKzlvm/zKtlot6coLy1+nz0yCnnr6CkuLReORpKT9YB8owvHwZaRVZa3v71hp5p6nWlpTS1f12Ty6YECQQqf0vFh8byUBnEV0cByvt/eD0bEwCUrlhJMAh/LjxPlb2srKJRlooTKZ0J42a774R8EoidHFDqtSn8tMVA36NI6Xpl1D3FacwKQ99hHTkpoUKc9D78e+2lxysEIAABCEAAAhCAAAQgAIEGCCSXANBAJZp1uTEBwPO0r9VVQvwJ7Ni+302+td89XmHK5G9cGZYtXROvIpAvBCAAAQhAAAIQgAAEIACBaBBIPwHgwP5jzlFfzx7D6gFEAKiHJK4X5M9BFhnNdXwYzUIjAESTJmlBAAIQgAAEIAABCEAAAnEkkHoCgEyqGzO51l52OfmL5NTOEwDkbI0QOwIy3R8yaJJN+vxrk8+GhsKsmd+7toq2/4GG8ot03RMAvl3wc6TbXIMABCAAAQhAAAIQgAAEIJAsBFJLAMjKyrUX2r1nb7/1idvnHqkVvvziW7eqrKPfwoMnAPT8oL51QHhcPrecwJUrmc7RoYSYHxb9GtERofwuvPjC++7EhjNnLrY8s1Y+6QkAciZJgAAEIAABCEAAAhCAAAQgkMQEUksAuHLlmvPUriPb1q7dWs8SQI7T5FVfntwjeXBHAGibr7La4Yvp37qtGBIB5IH/zJkL7vg/efc/f/6y9es72gk1L3Z4PyYOCJtaUwSAppIiHgQgAAEIQAACEIAABCCQ4ARSSwCQ6f/kSXOd2biO79Mech35VlVZ5TzAz5+/zO647VnTOeqRvKh7AoCOiyPEloBW+JcsXm2PPtLZCTLa668jAR984FU38ddnHYfY2BF6sS1hXeqeADBi+LS2yI48IAABCEAAAhCAAAQgAAEIxIpAagkAoqQV5OGfTbM7b3/OTSSfevINe7v7J/ZShx5OGJAAsLQBj+6eAKBtBIS2IXA9M8e+mvODs8x46MFXnQjw7NPdnZCTk5PXNoVoJBdPABjw8bhGYnELAhCAAAQgAAEIQAACEIBAwhNIPQFAyOVkbsXy9da5U2+7/76X7e672tk9d7/gtgd8/dWPEVf/9dy6tdvcavSrL3+Y8C2XigUsLCw2+XFozIljW9fb8xkxeNCkts6a/CAAAQhAAAIQgAAEIAABCESTQGoKAB6hmpoat9d/966DdvDgcSsoKPJuRXwtKioxeXvftetgxPtcTD8CVzOu29yvF9uZ0xfSr/LUGAIQgAAEIAABCEAAAhBIJQKpLQCkUktRFwhAAAIQgAAEIAABCEAAAhCAQCsIIAC0Ah6PQgACEIAABCAAAQhAAAIQgAAEkoUAAkCytBTlhAAEIAABCEAAAhCAAAQgAAEItIIAAkAr4PEoBCAAAQhAAAIQgAAEIAABCEAgWQggACRLS1FOCEAAAhCAAAQgAAEIQAACEIBAKwggALQCHo9CAAIQgAAEIAABCEAAAhCAAASShQACQLK0FOWEAAQgAAEIQAACEIAABCAAAQi0ggACQCvg8SgEIAABCEAAAhCAAAQgAAEIQCBZCCAAJEtLUU4IQAACEIAABCAAAQhAAAIQgEArCCAAtAIej0IAAhCAAAQgAAEIQAACEIAABJKFAAJAsrQU5YQABCAAAQhAAAIQgAAEIAABCLSCAAJAK+DxKAQgAAEIQAACEIAABCAAAQhAIFur2gsAACAASURBVFkIIAAkS0tRTghAAAIQgAAEIAABCEAAAhCAQCsIIAC0Ah6PQgACEIAABCAAAQhAAAIQgAAEkoUAAkCytBTlhAAEIAABCEAAAhCAAAQgAAEItIIAAkAr4PEoBCAAAQhAAAIQgAAEIAABCEAgWQggACRLS1FOCEAAAhCAAAQgAAEIQAACEIBAKwggALQCHo9CAAIQgAAEIAABCEAAAhCAAASShQACQLK0FOWEAAQgAAEIQAACEIAABCAAAQi0ggACQCvg8SgEIAABCEAAAhCAAAQgAAEIQCBZCCAAJEtLUU4IQAACEIAABCAAAQhAAAIQgEArCCAAtAIej0IAAhCAAAQgAAEIQAACEIAABJKFAAJAsrQU5YQABCAAAQhAAAIQgAAEIAABCLSCAAJAK+DxKAQgAAEIQAACEIAABCAAAQhAIFkIIAAkS0tRTghAAAIQgAAEIAABCEAAAhCAQCsIIAC0Ah6PQgACEIAABCAAAQhAAAIQgAAEkoUAAkCytBTlhAAEIAABCEAAAhCAAAQgAAEItIIAAkAr4PEoBCAAAQhAAAIQgAAEIAABCEAgWQggACRLS1FOCEAAAhCAAAQgAAEIQAACEIBAKwggALQCHo9CAAIQgAAEIAABCEAAAhCAAASShQACQLK0FOWEAAQgAAEIQAACEIAABCAAAQi0ggACQCvg8SgEIAABCEAAAhCAAAQgAAEIQCBZCCAAJEtLUU4IQAACEIAABCAAAQhAAAIQgEArCCAAtAIej0IAAhCAAAQgAAEIQAACEIAABJKFAAJAsrQU5YQABCAAAQhAAAIQgAAEIAABCLSCAAJAK+DxKAQgAAEIQAACEIAABCAAAQhAIFkIIAAkS0tRTgh4BAKBgFVX15heCRCAQGIT0P9qbW1tYheS0kEAAhBIcAI1NbWMexK8jShe0hBAAEiapkrxgmZn59nqVZutoqIyxWva+ur9tGytvdShhx08cLz1iZECBCAQMwKXL121Lp372IwvFyIC3IKyBvf6Ddi4Yaehbd4CFrchkGYEiopK7P33htjkSXMtUJvYix8lJaU29+vFdvFCRpq1EtVNIgIIAEnUWCld1GVL19gf/uUp++XndUlTz2vXsmz37kOmgWtbhokT5jhWi39c1ZbZkhcEINBMAocOHrd7/vSCvdX9k6QSNysrq6y4qKSZtW1d9MLCYnv6yTfsySdeM70nQAACEPAIXLqYYffc/YL96Y/trbq62rt8y1fFlXjQllZYW7futTtue9aGDZ1yy/IRAQJxIoAAECfwZBtGQKvaEgAWLvwl7E7ifhw98ktX5rZeiZ8963uX74L5yxIXDiWDAATs5Mlz9sCfX7ZuXftaWVl50hDRKtsjD3W03Jz8NitzUVGxPffMW/bEY90sN7egzfIlIwhAIPEJZGfl2n33dHACobZVNTUsXbLaHrj/FTty5FRTH2l1vJ07DjgB4NOBE1qdFglAIEYEEABiBJZkm0lg08Zdduftz9UTAKTcLv5xpa3/bXubr7Tfqgojhk93E3GZrbZl+GHRCpevzIoJEIBA4hK4dOmq/eXhzvbyix9YcfHNFfWLFzPsm7lLbM+ew1abgOasn34y0fUxp06ebzO4paVl1vGVDxEA2ow4GUEgtgQkemoCvmrVZqupafqkPVKptIIvMVUWQs0RAGbPWuT6sjVrtkRKNibXjh09bXfd8ZwhAMQEL4lGhwACQHQ4kkprCciU/u672oUIAHJyN2L4NNd5S/m9cP5Ka7OJ6vOeALB//9GopnurxCSIyFoCAeBWpLgPgfgSuHz5mj36SH0BYOCA8e5/WGaiJ0+ci28hI+SOABABCpcgAIFmEZAlkcYqt9/2jJ061Xox8cH7X0EAaFYLEBkCDRJAAGgQDTfalMDpU+ft3ns6hAgAKsC8b5Y61VcraAUFRW1apltl5gkA2ufblmHd2m0IAG0JnLwg0EICMmV/8q+v17MAWLZsjf3xrnbO6gkBoA4uFgAt/JLxGAQSlMCSJatNk/ZnnnrTcnNbv52ofbt3EQAStK0pVtIRQABIuiZL0QJnZFy3++97yb6a82NIDWU2pn20OiUg0UK8BIDNm3YjACTal4HyQCACATmz0+A3fAuAzFm3bNnjvN5HeCzul7AAiHsTUAAIJD0B9XNa+c/MzI5KXV595UMEgKiQJBEIGAIAX4LEIJCXW+CU4nFjZyVGgZpQingJAMePn0EAaEL7EAUC8SagbUwd2r9XTwCId7lulT8CwK0IcR8CEGhrAggAbU2c/FKYAAJACjduVKqWk5Nn2sfqP0JFppr5+YUhZzXLg/PZMxdNTq+aeiyejmfJysq10tJy00BZzrJGjpju3nuF1/W8vIKQa1VV1XbhwpXgsVoqmxTm06cv2NWr10PK6qWj7QOKo7yaGlTH8+cuW3FxacRHPAFgx/b9zrxNZ34fOXzSOSzU6p6fmRJQfa9cybTz5y8Hyx4x4bCL5WUVruzioDTF+Y93Po8PgDBOfIRAvAmo75O1kvq1iopKV5yuXfpEFAD0/ywnp15QPyPnUeXlFe6S+j6lpX5N/WplZV16XnzvVQ6xrl3NMh2T1ZSTBpRuTnaenTt3yaWvz+Fh2JApTmSUE0CVRxZa6tt+WPSrfT7xK/ds+DOydlCaWddzQvrr8Hj+zzk5+c4796GDJ1wdOnfsZc8+3d3UxxMgAIHoE/DGXZU3+qdb5SArzIb+H2+OaW6Ox8LT0+JOUxydamxz/XqOnT170fLzCsOTcZ8jCQAap+kZje8i9WVytio/BHICqONNM69l2/HjZ+3nn9bZpM+/tnAfTkrjemaOG2c1NPYLL5wYXbl8zQ7sP2YnTpy1w4dPOieAkyZ+HR6VzxBIFAIIAInSEvEqhwapUyZ/Y/MbOFJuzJgZ1v75d1yn6ZVx1Mgv7MUX3nedtX4YdISfPmuvlxxeTRg/Jzj49Z7xv6qz3LZ1r/V4b6gzj+3SubetXbPVXmj3nvXuNTJEQNCgst3z79ivKzYEk5AJ/F8e7mR7dh92nf7wz6bZU3993W0h+Ovjr9ny5euDcTUg/mrOD24VTitxXTr1tp07DwTvR3qjOv3yy2/20osf2EMPvmqvd/vYDh86ERK1rLTcur850P2wyMT3+Wfftsf+0sXuuvN5d01HWXmDe/2gaPD8Yc/P7PHHutrDD3a0994d7LY2hCQa9kGixdyvl1jnjr3tqb++Ye2ee8fkPGztmi320AOvIgCE8eIjBOJFQANh9UsffvCZm8CqT3jj9f62YvkGe//dwfUEAJ0I8FKHHjZ08ORgkXV29J/vfdH27jnsBqpzv17s0tLWqEcf6WK9PhphGRmZwfh6c/TIKevTe5T99YnX7C+PdHbHDeoIqoaC+tNZM7+3Z595y/Vt6lO+W/iLy8//zOTP65x3vfvOIOv06kfOM79ERw2kVcbt2/cFo6uP1ZGkqo/6paefetNmzfwuKGQEI/reaGA9c8Z39tyzbzkxU84QX+zQwz2rvpQAAQjEhsC6ddvcuEv/f7cKEjSnT5vv+h7/KSYa0xw6dMJ6fjDMHn+0bkzT470hTqz0p6nxZYf27zvh0H89/L0EzuHDptrTT77pxpEvv/SBHT16Ojya+QUAjdN+/HGlG59q7Pn0k2+4slbcEFC9h70jprt16Wv6k0+We+5+wfVl6tOWLF7lRXXjySGDJtlTT77hfE916tjLNm/eHbwf6Y0E2oEDxtljj3a1237/tN37pw72ztufumMAv/zi20iPcA0CiUAAASARWiGeZVCnro5Lg7dIYdCnE92gTqvbXvio52eu89y6ZY9bDdLxfZr4jx832yQO/OmP7d2g0ovvf5UCqwGovPqro9TqmCbEGuQ++MAr1v2NAW6l3HtGK+YadA769HPvkhMclOea1VtMPzrq/LUa7wa2T3e3YUOnOCVYeX02bKrdefuzrlzyJdC/31gnHmhlP1KQUi0v+zqRQD8C8mKrHznx0cqWF2QVoQG3yvbE493spRd72Gvd+lnvj0bYxAlzXNk8NXrXzoNuAK2VrW+//dk2bthpr778oRNNtAIWKWjl7803Btjtf3jGiQtqh359x7gfpT/f+5Krk9RrAgQgEF8CGohqMK1BpSbAH/QY6vodCafqR+750wtukKrJtxeuXctyE9933vrUu2RbNu+2u+543gkJEi317CcDJ7gBqE78UL+qwakEVIUdO/bb4491cyKBBrFayZLYoP4w0p7bkpIy6//xOLcy1afXSHcE4cJvf3bxdVSX118pbU8A0ID8zdf727Ahk23u3MX2668b3SDfO4ZLg+2RI+r6/L69R9mGDTtMx26pf//668UhaXoVVTnUb6vvlNXXwP7jXJ8t0UTXEAA8UrxCIPoE5s9b5v7PJk746paJ63/1+efedv+nsmryggRATfyfe+YtN9bT/738nGjRRJZNXtDqv8ZqEkYbCnKCqvGVhEWNHzVh12KNFoO8RRTvWU8AqKqqsrFjZrq+7JWXerqjBseMnuH6zwXzf/Kiu1dPAFB5u3Xta9repD5KFgASGTxLLfXJHW4sZEn02LZtnyuDxqeRxAglfuDAMSc8aOKvRTCdWtWvz2jX/6kvQwAIaQo+JBYBBIDEao+2L40nALzVfWDEzCMJAEOHTHY/IP0/Hus6d60S6VxrBXXMGtzph0FbBfxBavLsWd+7ga9WyzUR1uqRlGStcKvDfOXlniGrUTJ/13VN5L2gDl2Dba2IPfaXriYT/NqaWndbA1+ZtypoUKvJvybOXid/NeO6m1TLjDVSkAnuIw91cqvtcl4j69jLl6/aIw93Mg2W/UGDcZVNK38a3Ht5+ONINJBlg35EZEXgDbLlHVc/GqtXb/ZHd+/1o6vVQ03+9aPmiQQykVMaHV/5yOWrHzICBCAQPwLq0+bNW+osfzQ41Yq8NznOzs61MaNmuD5IFktev6TSRhIA9Kz6qymT57oB5JDBk4Kr6NVV1U5YaP/8u26AnZuT70QF9UvHj50JAlCfpX5Dp6f4g4RNXdNKu/pDbzVPlgtvvPaxG7wX+k5ZmTr5G9fHyMpKQmqkoL5RYqnKLMskb+tCWVmFaVCuQb0/TS8N9Wnq+7p27mPnzl0O9okSVTWIllCqchEgAIHoE1j0/Qr3v92UyamsEDUxl6WQ16/JhF5WmerT1Gd5YxptD9L/9W/rtoUUWqKmxMFIQSv/+p9/4M8v26qVm4LWn19MX+D6KlkW+YMnAEggveO2Z6xrl75uu5XiaAwmawP1O/7+45eff3P11XjQ66P8aeq9xlayylTfqXJ4dZI5/+1/eNot6oQ/o0UaWSqoHFqM8YQPpbVx407XL7JIE06NzwlEAAEggRojLkVpiQDgne161x3P2dtvfVJPpfVWgNR5+oP2xWtlSCtU2gLgdbKKIxN/padVdX8n7QkAE8fPCSYlAUA/NFoh04+ZPx0vksQHDZbvu+dFu3ihTpzQPa2eabtAp1d7eVGDr1rJk6ghszDtF/PC4UMnXbn9IoTueT4AGjsGUGq0yipm/nLKzPfuP7azObN/8LIJvnp8NQEIH3yr/J4AgwAQRMYbCMSFgPZ6qo/RpFWT2fCwZfMe1081RQDQpF6TafVrSi98FX/RohVuIK0+WwNjb6Lv71f0/pGHOrpVKH9ZtD9Vfav6Pk20vaD47783xB5+qKPzn+Jd//675W7QLB8ADYW6AXeduCm/JP7Qt89ot2ooocMfNGGQeCtBVNZd/iCxQOa52j7lDab993kPAQi0noAm6E1dndb/r+L2/mhkMGPtqdeYRqvk/r5Hlo7qu3TfHyQAaLEkPEgo7PXhCLeIJHFSE2cvSABQvlOnzvMuuVcJAMpDf1pE8haedFPPy8JT20D9Rw7KUkpp+cd0IYma2b69R5zg8Fb3T0LKoXTUV3304fDwR0xlFId+fUfX872ifl/CwCAWaepx40LCEEAASJimiFNBWiIATJs633Wo6hjljC88SEG9847n3Mq4d08DOq0KadC66Pvl9ZzCrF+/wwkAui/V2QuRBIBNG3e5/KVC5+ffjOs9o1dZBWgiLxNardIpaIKvrQwqx8MPvuqP7t7LFO3eP71gr7/2cYgIIQFh8KDP6/kOuJUAIIeDSkuczpy5EJKfzHXvubu9W+H338i4kukGyLJCkAPG8HDmzEV76IFXXP0RAMLp8BkCbUdA4pwGhjJx1epSeKiqrHLbhzT4bIoAUFJS6gavGlRq/394UP8lYVMCqbYQqQ8Ln2DrGZnQaw+qP2jFTOlqm5Q/qA7atiRzW7/DK+2tVbk1YW8oyJeK0pSVmH8ioPgDPh7rBunhvw9aCVS68jsQHtat3erSkwCQm3vTjDg8Hp8hAIGWE9i794jbTjR65JchicgiQAsgfsvNI0dOuf/XSZ/PdXFlnah99LI8ksNPf9iz57BLd8L42f7Lziw/kgCwYsUGN0nWyrt/0Ud9yUc9h7t8IwkA6j/0J79R4UFbRTV2kmWBF/bsPuTi+/1Iefe8V/mRUpqy5vQHbWHQ9tbOnXr7L5vGaU8+8Zob250+VV8k1TYApffpwAkhz/EBAglEAAEggRojLkW5lQDwyYDx9XwAeALApIlf1Rv4qRLaD6bOT6ZXXtCAT4NF7fEvCfOqr0GolFc9oz//fiv9MEgU8FsAbN2y18UL/wHz8tKrV0btX5UIoL1fcpSlPboyg9WrJwx4z2l7gvIPN/XX/fABrq7dSgDQCpf268spliYIWu2fPm2Bm/R/8P5QV47p0xd42btXbU1QGSJZBmgCoLpolVDiBgJACDo+QKBNCZw4ftb9L2oyHul0Ea20/fGuds7XSVMEAG0hkln8vfd0aHDircG5nJzKZ4q2WWm1beqUb9wWqZ49hrlrsqTSViovSFiQaawGxuGr7oqj++Hll38VrWBt33bT2Z+Xnvc6dco816dr8PzjDytd3yaHsrKUkkMuWXppoOwFWSGoP9S+f50a4w/6DXj37UGu70MA8JPhPQSiS0Ae8zX++bjvmOBqtxzZyVeJxh5Ll64JZrhpU91ii/6/FXTSiLYEyImoG9PMWlQ3phk1w239VJ8R7lzQ810STNTM/f/LQlP9wcGDx/237ML5K66vUlnCBQA5DdV1OWAOH78pEQkAsmbyW31KxGjML5We0xhN48LFP65yW6U0TpOQoa1NsjZ4751BIWWUNZbGs3Li6vlk8SIobzFSOREAPCq8JiABBIAEbJQ2LZIm49p//1rXfvXy1cDw1Zd7uv1Z6vi94E2uN6zf4V0KefUEgJ9/XueuKx0NbDVplePA8LDy141u9f/JJ153g06tBHlBR1/JeYsc+3nBEwDkqb+hIMd9Eg60H0yig8y0NLmWECHfA9or6w8afL/15kB74P5XrDGzV/8ztxIAdu066H4E9EOgv/v//LKrywvt3nWnESi/ffuOBJOUCZvM18TJ2/cfvGnmHAtq8i//ALJi6BXBLM0fn/cQgEDsCHgT4G8XhDqdUo46zqrdc2/bgw+86gaB2iaga17Qyr3+z/1OALVvVQ4ENVH3O9zyntGrJuYSFbw+Ra8y7Vd/oH5Ozv3UL/k9V9f5BXjaDdAjCZn+9L33OpFAQoLfQ7Z3T68qqxx7eeXQ4FkrZRJZ5aNE/f2oEV9YaclNPzDLlq5xfbIcfYWX48CB424A7urzcGeTrxYCBCAQfQJ5eYWmsZacDHsr71pMkGCnsYnGTFpsUNAYT/+Tv9wYy0kQ9P7n9aq9+xqfyc+RTljSmEb/y/7w7DPdXb/kvyYHfLf9/qkQEUL31S94PkKUfrgAoPx0XSchRQqRBACt0Os5nU4VKcjMX5N8r17aoqQ6aRuW6iQrTvVdXpDwoH5afV6kE6UkHKhuSk8nPxEgkKAEEAAStGHarFj6AdBRJ1JAw4P22mvCKaVTHvS94AkAUlYjBU8A8DpNKbpSYOUwRWKAP2hQ/MxT3d1gc+HCX1xHPHPGwmAUrQxpUjyg/7jgNU8A0FaAhoLMYDUgVfpKI5JarH2r3kBbDl20/1TP+bcgNJS+rsvBizr5hnwA/PTTWndfQoXOtdWeWZnZarVN3FUu7cf1nOvIpE6TApnYhQet3GlVTT9ku3cfcj9MOnWAAAEItD0B/e/Kcaom9rIE8AeZ/kuwVL8p7/1ff/Wj6wf8q+GRBAANfuVt323/ueHI1J+u3stpqkx11e/MmLHQCYXFRSWm/bR1/VzdCQH+57x+qClOv7znJBpoIBzJU7icgOl4Q/e78eSbJt8FOotb1mQSlNW3SVCVB2+/6CEmKve6taFOwjTZkBmw+r6Or9RtbQjfOuCVi1cIQKB1BNTP6GhPnVyk8Yi3qj9u7Eznm0kLJ57wJ2tIHW28bdtel6mu639YizaNjWn8q+I6RUD/315QP/Xu25/aH+9s5/LzrutViyZaPdekW1YKskD1B41/ZGWgsVSkEEkAUH+lsZ0m4+HCo/yOfDH9WzeZV/1VJ43/xEXbHby+TONEb+yqrZmyvtIWgHA/LVr9Vxl1MpQsmeQjiwCBBCWAAJCgDdNmxVIHp/1NsgLwBw0ApYJqEKgO3690egKAPOZHCp4AMOOLuon85htmZFJ2/UE/BNpzJrVUDu/OyAzt7hfcypLnEEZxJADIU7UXmiIAPPN0d+ckpqEfCnXmUq2191VBA3KZjnV89SMvm5BXDWbD09I+XcemgXO3JYDofvi+Mi/ha/pheuK1oNOc9eu32+23PeOOt/Hi6FVtJPNY/fB9NedH90MkZbpzx15Bpd4fn/cQgEBsCWhwqEGe+khNyv1B3rAlnL7e7WPnBf+br5e4fkD9mxc8AUDHTvnDyBHT3cA3o5EVcG9VLpLfAS8tWVotuGGZoOP71A+tWL7eux3yqpNbZGnlDxIVNJDVtgKvL9Z9Dew1KNcWBK30N3Zk39dfLXZ9tyeyvt6tnytH+BGsq1dtdmKJBsvTp893fljCzYL9ZeM9BCDQOgIybdcEW5NZHacn58wZGZkWqA04C8NHH+nixEU5G5UwJ59KCtoKoL5ER+RFClevXndHk/qtoiQA6Fg/L0gs1BHQWtDw951aiddRgvIvIC/6WsCRLxF/UJ/018e7BRdN/Pc0udcWSVlE+cVWjZ+0JUpbtTSO8wfPkZ/qpPeRghZsZF31cb8x7ra2UKgcXTr3CSm/+kk5P1Va2iIgawpZgREgkKAEEAAStGHarFieAKCJqGf2JYd9mlzqB+LHH351q1w6O9YLtxIANKBTJ+g5epJaHN7BqrNUhyu1WRYA2Vm57pis++590V5o/57VVNetZKlMHV54z51F6+XfFAFA52HL6kBHcYUHTeRlwqW85clWwRMApIyHBzHSnn1NwvXeCzKL0yrf8rCtCKqbTHX1A6Z6y6N2eBBjlVH3NWFQ8Dxv+/fQydRWkwKJJHI4ph9M7QOWAKAf1fAftPB8+AwBCESfgFaJZAKqs+v9QVZJ99/3smkA7R3P5wkAu3cdCkb1BIDw5/W/L6uCY76j/YIP3XjjThC5q12DJq3yjK0J+uOPdXNPeKt2339fvx/SSleP94c6c1dvou7lJwsjORr0D9JPnz7vnB7qNAGt0jXksX/9b9vdIFnCsueRW35Y1N/5fcBcvZrlhFrlIwsoOSlUv+3fGuWVh1cIQCA6BLR9Sf+L3v+p/HjoqFAF9R9aiOnTe5RbnPALAHKkp+fkJDQ8yHGnnI/qvo459oLGKjqZxAtHDtc5FlT6XlA/pGOdNSbTyU5y1tyQAKAtCn4LAy8NZ1nwziAnOsp5nz8MGzLF9avnzt50XKixoXyzqLz6+/ST+g77lOa4sbPcOE+OoBXkiFnbOf1WDbouSyux0jHYek7jWIkcBAgkKAEEgARtmDYrlibY77832E321fFfz8xxx0JpT5Sc+GklSoO8vn1GBVeCbiUASDVWh+r5ANBxgEpP5q1SaTVpleos79nad3bk8MlgffVZA2t1oAoyj9fK0YMPvOJMsnTNEwAaO9ZFk2md36pVepn/K1/VVZN21Ud5qx7eD4lUXg1QZX4rhziKrz8p5Do3W2nJUaF/MCwzVZVV1guKq4m/9pvph0zCgI6p0Y+YzqrVhEFxVC9NEp5+ss7pzMQJc4LCi4QS/QDKV4HiSpGX6KC0tO9fyrmCJwDIMkKKOwECEGhbAjJ316RVfYn+pyUMzpm9yPVzOqXDWzFTqTwBwO8U1RMAdESWP8ipnyx9Vq/e7L8c8l59iVbeNbj0Ju11/U/ACY/KXytUWkVT0DYjrfBJ1NXAWHH1l3U91x0rqL5aq1Uy5feH2bMXub5Hq37/bXHN9WFaRZN1g6ybtLVB/agmA5o8KE1tpZKll+olC4nDh04Ek9QKv/I6e2MQrrjtn3/Hbf/yPHpLAFAcvx+YYAK8gQAEokLA25akPkSTVq1q+4PGcPo/f7FDjxALAI0HNWmW+KeFFP3Pq//bsGGnO2JU4yEdY6yFCy/omFGlJasiBW291P+4VssV1JfqOECNcwYPmmSySFKfFS4AaCymfkyOnTXWCg86MUqipcZd6l/9Yc3qzW6spi1NGg9qHKdxmsqhcaAsD9RnXrua5eqkOBJh5ctEYzItAHkWoNrSqpOdZDnrOU+VkCKrBgm61zOzXdYSAFQnAgQSlAACQII2TJsWS6bnGrCp89LKkSbrGoiqk1VHKcX1UV+n6gkAOl81UtAAUB2rN+DVxFtn12tlxztCRvc1gT2w/1hIEt261pmJqpNVkAAg8391/OfP152zLd8Eej6St34vMSnKcrClHySZ9UuZ1g+KBtcaxEYqu47m04+HfuCkTmvyrdU4/UBqkh9ptV2edPUD0bVLH/cjonLJjF9llkDg9tDd8bwTOlR3lUE/Cpo4rF27NcQ3gawClL+OIvygxzCnwssRl7xqV1TctDwQz7e7f+LKpXPICRCAQNsSkHA4fNhU17/ogwC+YwAAIABJREFUf10Daf1fv/xSz3oORuVVW/2C/3gsTcTVz+oZ/z75X29YS8m/SGNB5vxapdPEXelqK5W2PUmobN/u3RC/BBqkL1u21u2tfeD+l+2N1/o7k1jlr75NfZgGvuFB+2G111X5fDZ0inuvgfz4sbNcvyVBUhZT6mPl0Vv79/U7os86Bit8EK6+UH2lxF+JnbIi0KDZvzUBASC8FfgMgegTqFtseNr1Szqiz1sI8XLSZ+2ZV7+lfkJH6SmoL5k/b6kT7WQhqkUTjZfUj2k8p4lw+ORcFkb6v/f8SGlMqX5DY7rx42ZZu+fecfe1LcE7gjCSAKB+sjEBQOMzTbo1xtKJI/6gLVsaD6ouH/cb68RQlUnHkqo8OsJQfZHua9IvB4Cqu8Z/GgvLp4kXJPZqbKixssaisiJVH/niC++bf3sTAoBHjNcEJYAAkKAN06bFUoetPaOa9Erp3LJ5T0gnruP21BF63l21+qNO1jNxDS+sTKFk9nX8+JngLTmp0oqSvM/qB0MmZ+EOVBRZez/1o6AJvIJ+cLSaLxU554ZjLJ1j+9ijXW3Vyk3B9CO9URra/ypTLa0+DR08ybZs3l3vx87/rBTuaVPnuf1dUrm1Gq9TAVSOSEHqt6wMdIqC9pnJTGzLlj3BVX09J5NdCQjyN6CBulbUvNX88DRl+qb6K64m/rt3HQyP4j7rKDCJKlpFI0AAAm1PQAPBhd/+Yv37jXX7Q2Vqr4FmeLh44Yo7Tir8SD05CBw9KvQsbomcWhnb2YBfEX/a27fvd/21zGu1IiUhQqvx/sGqP77OxtZgVsKFTGK1rcs/YPXH9d5r0C2v/RJRtQXJsyrw7suXitKUhZj6LE3u1d9FcroqEVOmxxI5Zekl4eGUz7ms0tR2qMcf6xoiYHh58QoBCESHgFbjdWSnxkaRjgZVLrI00jhNCz7+PkVjGjki1mq9/ucHfDzOHZ+n+JGCFoK0au8f72lbkPoKLcZocUZjRi1seCGSAKD748fNdltHI43HNJGXo1EJjeEihNJV+VQXLdao3jqJwHPArPuygFVfpzppLPzVnB/qCQle+dRvyoJAgqoWzjRmDK+/xpyRTtfy0uAVAnEmgAAQ5wZIiuylBmt1OlKnmhQVoJAQgAAEIJDwBDSw53cm4ZuJAkIgpgTkMFUWBuFOAGOaaZQTjySCRjkLkoNAawggALSGHs9CAAIQgAAEIAABCEAAAtEhIEtQmdXLqz8BAhCICQEEgJhgJVEIQAACEIAABCAAAQhAIISArHxWrtzo/CBFMuf3fKHo2GMCBCAQEwIIADHBSqIQgAAEIAABCEAAAhCAQAgBnTgiPyDy5XTpYkbIPQkC2ssvh81N8YUS8jAfIACBphJAAGgqKeJBAAIQgAAEIAABCEAAAi0nIKeC3ikD774zyB3751kCaP+/HIXqhAEdEUiAAARiQgABICZYSRQCEIAABCAAAQhAAAIQqEdAR4/26zvaHb331JNv2MTxc9yJIq+81NMeeaiT7d5Vd/RgvQe5AAEIRIMAAkA0KJIGBCAAAQhAAAIQgAAEINA0AjpGecOGne7YvWef6W5P/fUNe++dwbZr18EGj15uWsrEggAEbkEAAeAWgLgNAQhAAAIQgAAEIAABCMSAgMz/c3Pz7fr1HNOx0wQIQCDmBBAAYo6YDCAAAQhAAAIQgAAEIAABCEAAAvEngAAQ/zagBBCAAAQgAAEIQAACEIAABCAAgZgTQACIOWIygAAEIAABCEAAAhCAAAQgAAEIxJ8AAkD824ASQAACEIAABCAAAQhAAAIQgAAEYk4AASDmiMkAAhCAAAQgAAEIQAACEIAABCAQfwIIAPFvA0oAAQhAAAIQgAAEIAABCEAAAhCIOQEEgJgjJgMIQAACEIAABCAAAQhAAAIQgED8CSAAxL8NKAEEIAABCEAAAhCAAAQgAAEIQCDmBBAAYo6YDCAAAQhAAAIQgAAEIAABCEAAAvEngAAQ/zagBBCAAAQgAAEIQAACEIAABCAAgZgTQACIOWIygAAEIAABCEAAAhCAAAQgAAEIxJ8AAkD824ASQAACEIAABCAAAQhAAAIQgAAEYk4AASDmiMkAAhCAAAQgAAEIQAACEIAABCAQfwIIAPFvA0oAAQhAAAIQgAAEIAABCEAAAhCIOQEEgJgjJgMIQAACEIAABCAAAQhAAAIQgED8CSAAxL8NKAEEIAABCEAAAhCAAAQgAAEIQCDmBBAAYo6YDCAAAQhAAAIQgAAEIAABCEAAAvEngAAQ/zagBBCAAAQgAAEIQAACEIAABCAAgZgTQACIOWIygEAsCNTUWm1ZhdUUlri/2qIS99lqa2ORG2lCAAIQiDmBQMCsvKrWisqqraC02gpLq62kosaqawIxz5sMIAABCESDQHVtuZVWZllh+WX3V1xxzSqqCy1g9GPR4EsaUSGAABAVjCQCgTYiEKiotKpL16x01xErXr/HilZtt6KV29xr8YY9Vrb7qFVdvm6Byqo2KhHZQAACEGgdAU3wr+ZV2N4zhbb+UK6t3Jtty3dn2YrdWbZmf45tO55vpzJKrbi8hiF061DzNAQgEBMCASsuz7DT15fbzvMTbMPJAbbm2Afu77cTfWzrmeF2+Mo3ll18zGpqK2JSAhKFQDMIIAA0AxZRIRA/ArUBq7qabSVbDtRN+DXpb+SvZOsBq87MMdOSGgECEIBAghLIL6my7SfybcWeLDfp18S/ob91B3Ls7LVSLAIStC0pFgTSkUBVTZmdyVoRMun3Jv/hr+uOf2T7L82wovKMdERFnROHAAJA4rQFJYFAAwRqa63i5AUrWr2j0Ul/uCBQvGaHVZy5jAjQAFYuQwAC8SVwObvcrfA3NOGPdF1Cwf6zhVZVjbgZ39YjdwhAoLwqz03o1x7rGVzxD5/0R/q85fRQyyo6YoZNE1+i+BBAAIgPd3KFQBMJBAJWceriTVP/Rlb9wwUAb2tA5dkrTcyMaBCAAATahkBmfmXQ1D/SRP9W1yQC1NQiArRNa5ELBCAQTqCqpsT2XfqyWRN/vxiw8dQnlld6OjxZPkOgLQggALQFZfKAQEsJVGflNXvlv54QsHqH1eQVtrQIPAcBCEAgqgTKK2tt7f6cBk39bzX5131ZAmg7ABJAVJuGxCAAgSYQCFitncxcas1d+fcLAHq//exoq6guaEKORIFAVAkgAEQVJ4lBIIoEAjW1VrrtYLPM/utN/m9YDJTuOIylWRTbhqQgAIGWEzhwrqhVk39PIFi9P8fKKmtaXhCehAAEINACAoVll2zDyf4tXv2/KQT0tLNZK1tQAh6BQKsIIAC0Ch8PQyCGBOTEr6EJfUuu1+Tkx7C0JA0BCEDg1gQ0Yfe8/HsT+da8nsoouXWmxIAABCAQRQLHrn4fhcl/3SkBW898hhVAFNuGpJpEAAGgSZiIBIE4ECg/eCqqAkD5kbNxqAVZQgACELhJ4Pz1sqis/nuiweajeVaLL4CbgHkHAQjElEBldZE71u/mKn7dRL6ln7WNIKvocEzLTOIQCCOAABAGhI8QSAwCgYCVbNwXVQFARwgSIAABCMSTQLTM/z0BQL4AKqpq41kl8oYABNKIQEHZRfvtRO+oWQBIODh9/Zc0IkhVE4AAAkACNAJFgEB9ArWBqE7+3ZaBNTvq58MVCEAAAm1IYOux/KhaAEgIKCitbsMakBUEIJDOBLRa39LV/oaeO3h5Tjojpe5tTwABoO2ZkyMEmkAgFgLAagSAJpAnCgQgEEMCm47kRV0AyC6simGJSRoCEIDATQIZBTujLgDsvTjtZga8g0DsCSAAxJ4xOUCgBQQkAKzZEVUrgOJ1u1pQEB6BAAQgED0CO08WRF0AKC7nJIDotRApQQACjRHILTkVdQHgSMb8xrLkHgSiTQABINpESQ8CUSEQCFjptkNRFQBKdx6JStFIBAIQgEBLCRy9VBxVAUAnClTjBLClzcFzEIBAMwmUVFyzDScHRFUEuJDzWzNLQXQItIoAAkCr8PEwBGJIoOLkhagKAJVnL8ewtCQNAQhA4NYEMvMrTI77PCd+rX3ddarAAoFb50sMCEAAAtEgUFNbZbvOT4yaALDueG8rKDsfjaKRBgSaSgABoKmkiAeBtiZQW1xqRau2R0cEWLXdassq2roK5AcBCEAghEBtIGDrDuZETQC4kku/FgKYDxCAQMwJXMzdaGuO9YyKCLDrwudWU1sZ8zKTAQR8BBAAfDB4C4HEIhAIWPmh01ERAMqPnk2sulEaCEAgbQlcuF4WFQFgy7E8q8H8P22/R1QcAvEiUFFdaFvPjGi1ALDueC/LLNwfr2qQb/oSQABI37an5slAIFBeYSUb97ZKBCjZtM8CVRyTlQztTRkhkA4EZLK/82TrjgNctS/b8orx/p8O3xfqCIFEJJBZeMB+O9G3FSJAT5Pzv9oA47NEbN8ULxMCQIo3MNVLAQI1uYVWvH5Pi0SA4g17rKagOAUoUAUIQCCVCJRX1VpLjwSU47/L2eXG1v9U+kZQFwgkG4GAnc1ebdrDv+bYB83862l7Lky1yhrGZ8nW6ilSXgSAFGlIqpHiBGryCq1k64FmiQCl2w4y+U/x7wXVg0AyEyitqDE58WuOU8DfDuZYRm4Fjv+SueEpOwRShEBtoMYu5W2xjScHNlkAkNn/oStzraK6KEUoUI0kJIAAkISNRpHTlECgotIqTlxo3Bpg1TbTqn/FqYsWqMQ8Nk2/KlQbAklDQEf4nb9eZhsO5zYqBKzZn2P7zxZaURnmsknTuBQUAmlCoLDsoh24PNvWn+jXoBCw9vhHtuPcWMvI32m1AcZnafLVSNRqIgAkastQLgg0RKC2tNyqLmda+cHTVrr9kJVuO2SlOw47h4FVV67j7b8hcFyHAAQSlkBlda1dzauwIxeLbfuJfJODv63H8mzvmUI7l1nmJv4c95ewzUfBIJD2BAKBWpMQcD5nrR24NNN2nhvv/vZcnGonMpdYVtFhq64tq8eprKbKymsQNuuB4UIsCSAAxJIuaUMgEQgEqmus9NzlRCgKZYAABCAAAQhAAAIQMLPMsmJ7c/My++LYLnhAoC0JIAC0JW3ygkCbEwgE7MoPK+3owPFWkZ3b5tmTIQQgAIFYEdh7Ms+mLTtjO4/lWlEpK2ix4ky6EIBAdAlU1dbYqsun7I6l0+13MwbYf/lhkhMDopsLqUGgQQIIAA2i4QYEUoRAxpLVdrjXSLuyaEWK1IhqQAACEDCb+cs56zRil3UZtdv6zThkP23NsIzsMhwE8uWAAAQSmkBOean91x8n29/M6O/+/nbmAJt8ZHtCl5nCpRQBBICUak4qA4EIBCpz8+3ogPF2tP84q7ieEyEGlyAAAQgkH4EDp/Ot2+jddSLAyLrX9z7fb9OWnrEj5wutoqo2+SpFiSEAgZQnELCAjTiwMSgASAj4Lz98jhVAyrd8wlQQASBhmoKCQCCGBLACiCFckoYABOJCoKY2YCPmH3cCwKQfT9sXP521tybsdZ9fG7PHhs49Zmv3ZFpeUWVcykemEIAABBoicKm4wP7hu3FBEQArgIZIcT0GBBAAYgCVJCGQcAQq8wqcBYAsASoysxOufBQIAhCAQEsIHDxTYF1H7bYPpx6wsooau5pTbku3ZFj/mYedENB55C7r9+Uhu3y9tCXJ8wwEIACBmBBwVgD761sBXC8riUl+JAoBHwEEAB8M3kIgpQlgBZDSzUvlIJCWBGQFMPyGFYBW+71QXFZtu47n2rjvTzr/AIfPFXi3eIUABCCQEARkBfCPPiuA380cYFOO7kiIslGIlCaAAJDSzUvlIOAj4HwB9B9nxwZOsHKsAHxkeAsBCCQzgUNnC6zLyDorgPB9/1XVtVZSXo1jwGRuYMoOgRQlEDCzEWFWAP+86HPLKscKIEWbPFGqhQCQKC1BOSAQcwKBgGEFEHPKZAABCLQxgdpAwIbPO26dR+yyNT4rgDYuBtlBAAIQaDaBcF8AOhYQK4BmY+SB5hFAAGgeL2JDILkJ1FkBjHdWAGVXbprLJnetKD0EIJDuBPafznd7/j+cdtDKK2vSHQf1hwAEkoSArACGh1kB/OdFE01HBRIgECMCCAAxAkuyEEhMAoGAXV26xg73GmkXv1mamGWkVBCAAASaSSAQCNiAWYdNTv/W7EbcbCY+okMAAnEkcLmkwP7jwrHBEwF+N6O/OyZQ4gABAjEggAAQA6gkCYGEJlCZk286DUB/pRcyErqsFA4CEIBAUwnI6V+nEbvsI6wAmoqMeBCAQIIQGL5/Q1AA+JsZ/e3/XDDaMsuKE6R0FCPFCCAApFiDUh0I3JpAiBXAklvHJwYEIACBJCAgXwADb1gBrMYKIAlajCJCAAIegSslhSFWABIBJApgBeAR4jWKBBAAogiTpCCQNAQqc/KcH4A6K4ArSVNuCgoBCECgMQK7b1gB9Jp+0CoqaxuLyj0IQAACCUVAvgBk/q/Jv/7+3YJRdh0rgIRqoxQpDAJAijQk1YBA8wjUBuzqMp8vgAAac/MAEhsCEEhEAtU1Aft0zhHrMmq3bTqYnYhFpEwQgAAEIhLIaNAKgDFaRGBcbCkBBICWkuM5CCQ7gYqsXDv2ycQ6XwDnsQJI9vak/BCAQB0B+QKQM0A5BayowgqA7wUEIJA8BGT2/7uZA4JWAH8/f6RllZckTwUoaTIQQABIhlaijBCIBYGAzwrg0rxlps8ECEAAAslOoKq61gZ9ddS6YgWQ7E1J+SGQdgQySovsP/hOBMAXQNp9BdqiwggAbUGZPCCQqAQqrufYsU8/t6MDJ1jp+cuJWkzKBQEIQKBZBDwrgIGzj1h5ZU2zniUyBCAAgXgSGLF/o/2tzwrgf58/0rLLS+NZJPJOLQIIAKnVntQGAs0jEKittavL1trhXiPt0nxZAWAu2zyCxIYABBKRgEz/B3+NFUAitg1lggAEGieQU1Fq/3nRxOA2AM8KoPGnGr5bVFVhNfh6ahhQ+t1BAEi/NqfGEAglUJGZbccHTcIKIBQLnyAAgSQnsPlQtnUescs+mXPEyiqwAkjy5qT4EEgrApOObLe/mzkwKAL823kjLLei+VYAuRVl9uSqeTbm4GYrr6lOK4ZUtkECCAANouEGBNKEgLMC+MlnBVCDFUCaND3VhEBKEygpr3aOAPEFkNLNTOUgkJIENHH/p+8nBAUAWQF8tn9Ds+oasICNPbTZ/vG7cfav5wy24/lZzXqeyClLAAEgZZuWikGgGQQqs/PsxLCpN6wAOBGgGeiICgEIJDCBDQey3IkAOhqwFCuABG4pigYBCIQTCLcC+N+cFUBZeLQGP2vC/y+Lp9qck3udCHC5pLDBuNxIKwIIAGnV3FQWAg0RCAQsc+WmG74AfrIAVgANkeI6BCCQRASKy6pNjgCxAkiiRqOoEICAI5BfWW7/z/fjW2QFIHP/l3/73gbv/c2O5l23//rjJLtWWgRZCIgAAgDfAwhAoI5AZU6+nfhsmh0dMN5KL2AFwPcCAhBIDQKeFcCQr49yIkBqNCm1gEDaEJjsfAEMCIoAOhEgpwknAsw+sdfu/ulLyywrthP52QgAafONaVJFEQCahIlIEEgHAn4rgAWyAsBpVjo0O3WEQKoTKLphBdBt9G7T8YAECEAAAslCoKCy3P7xu5tWAL+bMcCG3cIXwIXifPv/Fk+xJeePumoiACRLa7dZOREA2gw1GUEgCQhU5uRhBZAE7UQRIQCB5hHwrABGzD+OFUDz0BEbAhCIM4HJR7fb3868aQXw9/NHWVZ5ScRSyfHfp3vWWbu13wa9/ksA+OdFE21r5kU7WZBtNQGcPUeElz4XEQDSp62pKQSaQAArgCZAIgoEIJBsBIpK63wByApg9wmsAJKt/SgvBNKZQFFVhf3HhWOD2wAkBgzbvz4ikovF+faf/tvpAUP3rbfxh7bY65uW2r8smWr/w+xPnQhw29JpJt8ChLQmgACQ1s1P5SEQgUCdL4CpdrT/OCu9mBEhBpcgAAEIJB+BDfvrTgTACiD52o4SQyDdCUw5usN+N6N/UAT4dwtG2fWy4npYVl0+Zf9h4Vj766pvbNDedbbwzEH74dwR+6dFE2x/zlW7VlZstYFAvee4kFYEEADSqrmpLASaQiBglrly440TAZZZoBpfAE3BRhwIQCCxCRSWVln/mYetq7MCyEvswlI6CEAAAj4CJdWV9n9/OyYoADRkBVBRU23Z5SWmVy/gA8AjwesNAggAfBUgAIH6BJwVwLCpdqTfGCs5fbF+BK5AAAIQSEICv+68Zp1G7DKsAJKw8SgyBNKcwNSjO4ICwN/M6G+yArhQlH9LKhIAdJzglZLCW8YlQloQQABIi2amkhBoAYHMX+usAC7M+cECVTeV5BYkxSMQgAAEEoJAfnGl9fnikHUdtdv2nMQKICEahUJAAAJNIlBaXWX/l88KQFsCeu9cectnJQD8r98Mt3NF9Hm3hJUeERAA0qOdqSUEmk+gMjffTgydYkf6jraSM1gBNJ8gT0AAAolIACuARGwVygQBCDSFQLgVwL+dN8LO32JiX1VbazuuXwrZFtCUvIiTsgQQAFK2aakYBKJAIGgFMPsHfAFEgSdJQAAC8SeQX1zlrAC6jNxt+0/f2nw2/iWmBBCAAATqCIT7AtBWgD5NsAKAHwR8BBAAfDB4CwEIhBGozCuw47IC6DPKSs5eCrvLRwhAAALJScCzAhj3/UmrquZM7ORsRUoNgfQkMO3YzhBfALICwLw/Pb8LLaw1AkALwfEYBNKGQNAKYNYirADSptWpKARSm0DBDSsA+QI4eh7HWKnd2tQOAqlFoKiqwv7hu3EhIkBTfAGkFgVq0woCCACtgMejEEgLAlV5hXVWAL2xAkiLBqeSEEgTArIC6Dxyl43HCiBNWpxqQiB1CIRbAfwf80famcLc1KkgNYklAQSAWNIlbQikCoEQK4CamlSpFvWAAATSmABWAGnc+FQdAklOIL+y3B3tJx8A3p98AQSSvF4Uv00IIAC0CWYygUCSE6jKL7TjQybbEawAkrwlKT4EIOAnsGLHVWcFgC8APxXeQwACyUBgzsm99ruZA4ICwN/PH2WnC3KSoeiUMb4EEADiy5/cIZA8BJwVQO9Rdn7m9xaowWlW8rQcJYUABBoikFNQYR9OPWDyBXDsAr4AGuLEdQhAIPEIyBfA75dMDQoAdScCrLIAdgCJ11iJVSIEgMRqD0oDgcQlUJVf5KwADmMFkLiNRMkgAIFmE/hx42WsAJpNjQcgAIFEIDDv9AH7W58VwL9bMMpOYQWQCE2TyGVAAEjk1qFsEEg0AlnrtpkEAGcFUMtOs0RrH8oDAQg0n0B2QYX1nHLAumAF0Hx4PAEBCMSVQEFluf1hybQQK4C+O1dZIMAYLa4Nk9iZIwAkdvtQOggkFoGakjI78dk0JwKUnL2UWIWjNBCAAARaSCBoBfDdSauuYeDcQow8BgEIxIHAvFP7sQKIA/ckzhIBIIkbj6JDIC4EstbvqLMCmPGdGQpzXNqATCEAgegSyC6otA9uWAGczSiJbuKkBgEIQCCGBHQiwG1L61sB1DJGiyH1pE4aASCpm4/CQyAOBGpKy+3EsKl2pM8owwogDg1AlhCAQEwI/HDDF8CUJWesli1OMWFMoqlHoLS6ymSGzmQzvm37DVYA8W2A5ModASC52ovSQiAxCGTLCqDXSDuPFUBiNAilgAAEWk0gp7DSekzeb91G77ZzV7ECaDVQEkhZAjWBWtuZddl6bFtudy37wu5c9oU9s2a+rb96DiEgTq2eV1Fmty+dHuoLYNcq2iNO7ZHg2SIAJHgDUTwIJCSBmrJyOzF0ih3pO9pKzlxMyDJSKAhAAALNJeBZAUxecpodTs2FR/y0IFBeU23D9q23f79gtL279Wdbn3HWDuVes69O7rV/WjTBDuVmpgWHRKykrAD+zn8iwPxRdpoTARKxqeJdJgSAeLcA+UMgWQlgBZCsLUe5IQCBhgjkFVXa+5P2W9fRu+38NawAGuLE9fQlsOzCMftP30+wDVfPWVVtbRBEdW2t/b8/TLKlF44Fr/GmbQlEsgLohxVA2zZCcuSGAJAc7UQpIZB4BGrKKuz4kMl2pN8YKz59IfEKSIkgAAEItIDAd+svWacRu2zS4tMteJpHIJDaBBaeOWT/vGiiXS4pCKmorv/nRRPtamlRyHU+tC2BOiuAgcGtAH8/f6SdKcxt20KQW6ITQABI9BaifBBIZAKeFcDZqfMsUHNzJSCRy0zZIAABCDRGICu/wrqP32tdR8kKoLSxqNyDQNoR0BaAPjtX2VOr59n5ojxX/7VXztg/fT/Bfrl4wjhE8+ZXQo4RNSGfc3KvzT213/19fWqfjTqwyQbtXWfiFu0QyQqg145frTrAGC3arJM4PQSAJG48ig6BuBO46QtgjBUeORX38lAACEAAAtEg8M3qC1gBRAMkaaQkgbLqKhu2f739y5KpNmD3GvvH78bZwjMHcTgX1toSAD7cscLu/2WWPbZyrvvrsO47e/m37+3fzB1mYw9tCXsiOh8lNvzdzJtWAP/L3GF2JO96dBInlVQggACQCq1IHSAQTwJBK4ApWAHEsx3IGwIQiB6BnIIKe2PsHnciAL4AoseVlFKHgI7+e2LlN/a7Gf3t9U1LTZYBhPoE5BtBbCpratyfTlD47uwh+/Mvs6ywqqL+A1G4kl9ZbrctnRbcBvA3M/rb21t+MuVNgICZIQDwNYAABFpHoKa0zE4Mm2pH+o6xwsMnW5cYT0MAAhBIEAKeFcCUJdE3002QKlIMCLSIgMzM26391h5aMcfWZpxxk9lum5ZYaXVVi9JLp4fyK8rsnp9n2MrLsbWaDLcC+DdfD7Vj+VnphJq6NkwAAaBhNtyBAASaSiDUCqCmqY8RDwIQgEDCEtCJAK+N3m2vj9ljV3PKE7acFAwCbUmgoqbaum4IN7FFAAAgAElEQVRcbE+ummcSAhRkDfDg8jn2yZ61FgjgBaCx9tDq/90/zTBxjGVQm/xhyVSsAGIJOXnTRgBI3rZrXclrS8ut6lq2VZ657P6qLmVaTWGxcfBxGNeAWW1xqVVduW6VZ6/UsbqSZbVFOIbyk6opwQrAz4P38SFQUVVrmfkVduZaqZ2+WmrnM8ssu7DSamoZkIa3SFllrV3NrbCzN1hdyCqz3KIqq4VVCCrPCmDW8nMh1/kAgVgQqA3UWEHZRbuSv93OZa+28zlrLbNwn5VWauU2MfqxkwXZ9vcLRtmmq+dDEMw6scduXzrdSqorQ67H6kNtbZXll561S3lbbrBaZ9eLDlp5VX6ssmxRuvID8FvGWVtw+oB9c3q/3bFsuj3669f22f4NdjTG+/LDrQD+56+GmNqPkPYEEADS6itQG7CqK1lWsuWAFa3cFvGveP0eqzh1yQIVbdOBJyr/QHWNVZ7PsJJN+yJyEr+SDXtdnEANK95qx+wNO+1wr5F21vkCgEmifrdTrVwaEmcVVtrOkwW2Yk+WLd9d/2/l3mw7eL7IisvT+3upgagm/VuP5dmKCJzEbtW+bDtysdjKKtKblfd/4qwAxuyx1/+bP4CM7LrVTu8erxCIFoGK6gI7df1n23TqU1tz7IOIfzvOjbFrBXssEIjv/2ZmWbH986LPbfj+DW4VW/vKdfSfHN1127TYtOc9lkGsTlz70X470Scip7XHP7TdFybZ9cKDFkiAPe/yvv/xrtXWZeNia79uoWkS/v62X2zovvW2L+dqLFFZUVWF/T7MCqD7lmX4Aogp9aRIHAEgKZopCoXUinXp9kMNTmbDBYGSDXus+lpOWloE1OQWWsmW/U1ntXGvVecWRqGVkjuJ6uJSOzF8mh3phy+A5G7J5Cm9Vvz3ny1scOIfLgb8ujfbTmeUpqWn6tKKGtt1qiCiQBLOyRMCLmaVpb1RmASm+WsuuhMBsAJInr4hWUqqCeq1wr22sZGJf7ggsOv8RCupiK9H953XL9v9y2fbPy+a6Fa0/+G7cfbB9uVWWBkbp3ZqT7G6nLfV1p/oG3HiH85pzbGetu/SDCuryk2Yr4MsAf79gtGWU9F2VqQ6hvC/m3XzRID/6avBWAEkzDcibgVBAIgb+jbMuCav0Ip/293kCW1QDFi9w5m9p9MIsCojy4rX7mwRq+prmFUFrQCmzrfa6tjub2vDfyGySkACmtBuOZrX5Amtf5J74FyhVdckhjltU9FqW21VdW2LTPQLS6ttw6HcFrE6mVGSTj8BEZsjp7DSnQjw5ri9djkLK4CIkLjYbAJayT+bvdrWHe/VxAntTcuAjScHWGHZpWbnGe0H5G3+YnG+VdXG1ipBrE5lLrO1x3o2m9XWM8OtsPxytKveovRGH9xsdy37okXPtvQhWQHc/dOXIb4A6qwAkus3sKX157mIBBAAImJJoYta+ZdZf3BS34Dpf4P31+xw2wZSCEmDVanJKbDidbtazKp4zU6rzk6svWcNVjZGN6qLSuzkiC+cFUDBIU4EiBHmtE+2srrWtp/Ib9GE1hMCZOaeTNvd5YRu5ILj9uPGy1ZZ1XQT2/LKWtt4uGWTf4+VfCqkc5D4MnvF+aAVAD7O0vnbEK26ByyjYJetPf5Rsye03kr3xlMDb/gGiFaZEjWdgJ3NWmlrj33YYlY7zo2Lu28AbcF6ef0i67LxxzYHvfj8UfvvZ38aFAH+9ZzBdqogp83LQYYJQwABIGGaIgYFCdTUWumuIy2e0HqigASE2uLUXvUIVFQ16hvBY3Gr15LN+y1Qmd7H4AStAKbNt9qq9GYRg3/rtE9SaxbHL5e0avKvia38AlzLi525arQb6lpuufWcesA6j9xl3667aNr+cKsggePAuaJWs9LWiYLS9LbouZJV5k4D6D5+r126nt6CyK2+d9y/NYGSyuu24eSAFk9oPRFgz4WpcfcJcOvati5GXumZBvf7exya8nr06rcmJ4vxChU1NfbYyq+t++ZlbV6E8ppqd/Tg38zoHxQB3tyyLC23w7U5/MTMEAEgMdslOqWSw7+iVdtbLQBo0lt+5GxK+wOoPJcRFU5ipZMV0jnICuDU2Fl1vgCwAkjnr0JM6l5UVm1r9ue0elIrEUDO8KqSaCvAvlP59u7n+5wIsHRLxi23MeQVVzXZP4K32t/Qq/wHpLPBqE5HkA+ATiN2uVesAGLy750WiWov+5GMBa2e/GvSq1XxzML9IdzkhE/H8yXjn8zV/f2MWO29ODUqrLTVIr80fqd5aJtExw0/WK8dK0Paq60+hFsB/I9zBtnpQqwA2op/guWDAJBgDRK94gQCVrb7aNQmtc4KoCx5VsuaAzJQVW0lWxs+GeFWq/7h93VyQLqfDJC7fb8d7j3Kzk1fYLVpbhHRnO8icW9N4OSV1q/+e5PcX/dk2fWC5DrxZOvhbNMqdLfRu235jqsNigCaoB6Mwuq/n5XEl3QOl7JKnS+Atyfss4v/P3vvGd5Ydl2J/nFLsmQ5yB5ZY8t6zuNsOT9JtuUg57FGHnvssfX8/NzdklrqVupuda5cXV1k5WJlslg550AWcyjGYg5IJMEEgiRyzmm92YcNFkASROAFcC9wzvfdD8C9556wziWIvc7ea+u4F0AxPwsbmTulqWtWvSWIUUskAHkBxJYph4Upv3/6Vhmkdny3sypuV9rmmUZTyqJ/TzUSEnkEyBeuIYKn3lPuYIAZwVqXHVa/B/4saxmYvG4YvK7Y5crZ+zW9ANruxhEuORsM7yjfCHACIN8rkK3+wy5PZsJ/62gEsKwA2RpwHtsN2ZyCeUowMqC+G5RJoJhL0OXBxP5KnhGgmB+CLMw9FI6gQ7Gx2P+oQRt9JS0AKRUy7FuGDMskQNOAPu4Hc3QuhFXjkDCeElGsJotcC4AwjXoBXKyb4T+cow8bf00LgQVbn2DGPxm6ZCD7g47lMeg9Lvzy9QPLrt6xbt9if0+p8WLLtKlBUKw61bsRCD01wBc9TvzYuZ346cul+L07x/C3j87ha213sWuwBZfVQ+jQzTLF/Hm3A/aAb83v2tjxiv39Wl4Aau4FIPZly8b4OAGQDVTF0GZQbxHWqK3phG9sJm5qtLMbsDsld4S88Z4MAa1eME+JqDdAYHYxDqti/PDUC+AKwn5p7bIW43pJYc6k/N84LKxRS2KCJM4ULZQdwOoMwOr0i/ag3PTXmzV4vrSX7Ug/HjasUup3eUOChElEjX96HZgsPGLT5Q3icsMs+sYscc9B9HlY+Tqrd4OyAXynbBAkzMgLRyBdBMZ09wQ1ahuV34PJpVoehivoXxXvLXbDPzq+i+Px4QxDc5WCYkWii25/fMam/3rhvXXJkh85uwOU5vCzd0/gizUX8M2OB9g/0o7bU3L0GOYYQaDzOEHeBGIvvlAQn39QHjdfmg8vRYcAJwAKdckDC0bBjVrv8HgcXNa+UYyVnJLcoa9ri5uHb0IjOFYrdQDIGF64Ww/T417YZWPwaBbgN1oQdLoRCeZPlCYOCIE/BF1uTBw6i8kjF+A3F3d2BIGhLdrmKJ1d7YBRUMOWUgnGpgSc0DrxTsUoXj85LOrjtePDjACgmPSv7u2DbCreODfa/YLiRAQAeV/EFjKGz1RP42HnAp4ozCDs5o0eEEGRikhhbFv5em+w+vDdI4Mgt/7Jhac7g4nGw7wAqqfwvePDGJ2yJarGz3ME1kSAYtpHtOeFNWoVr2DR1r/cH2kA/I/aC3FGXtTAFvtrg1a9PA9682TqgKBYkceE1T0Z18dv3DycMVYfrNiEH7+wC7964yD+6P4p/GP9JbzcVY2j8m5UaVToM2pZiAG5/QfCT0MP4gaQ4w93puX48Okt+EjlFvactCzkTxchx1Pn3T1FgBMAT7EorHe5IAAsvSMYe++E5A5dbe4JgPlbNRh9rWT5kL25B8odRzC+twKTRy9i9vwdLD5ogrlzAA7VJDxzi/CbLAh5vJIWX/TO60FEAC8cASEQyAkBMOfEW+UjzMAjI08KB5EVsul4AsCQFQLAEreMw5M2JopHJAQdz5X04qVDA3j9xDC2n5Pj4I1xkKt8zZNFDIxboJ53grIZ2F2BONIlrtEcfyBxvwt1M0xYcfclJTy+5IQsERx6C9/9z/FSFUR3RAAMz50V1KhtYARA3zI+wUgYX6q9mLFRm0+SoHEVAbBfUKyIALAISAAkw+oHKrfipy6VgEiGP3lQji83XcNbPXUoV/aCyI4B0zymHRZY/d6UPJCWF3kDbygbAY3j5tRo1jUPNjBMfmt2EeAEQHbxzV/rOQkB8PkRsNoldzCjOmZpAnM64T0AZuJDALwLBmbcL1Y1Q3PxLiaPX2LGv3J7GWRv7FkmBqIkgfyd/VDtPIqJ/acxeewS5i4/gK6mFZaeYTgnZuDR6hCw2KQrsBeJsHSJYbd3KW2ilBKyxzw7/G1uEWAhAALHtXcq40MAAsEwzHa/pA6rw78qBMCZgxAAmzOAthEjbrXO4eT9SZRcVmJzpQwvHx3CV/f0xZEDUU8Fcp1/89QIdpyT4+idCVxr0qChX48htRVTCy7orT5Q+EJMVEbWHzKaB3l9UIpFyq4QGxKSTucUSELPDz2nXn8Y5C3AC0dgJQKqxduCGrXk1h4bAkCu6H/6oEKSBMDFifgQgEFNheBYrQwB+ImLu/OC1TMVm/CxczvwM1f24NM3y/DnD0/j2dZb2N7fhHPjA2ien8SweRFzLrvg4QWeUOJwhVDYD2/QCk/AxPQSIlztZOWfcCF85gRAIaziWnNYEgHsEdSwJa+CQiwhq0NQnBx13QiZ1ncNjQSDCDpdLAyAjHmHfAKm9j4s3KvHzNlbmDx6AWMlJ6HYfHAVOUDq+ootB6HadZwJ7U2dvALt9WroGzpg7ZfBpZ6Fd9GAoN0prmwE4QgIa9KScHeNgLIlOFv62Ct99imnl8QTc/nLvxAf6AKeUygUAbnsx8alb/T96MxT8SyCzh8IQ2fxsp1q2q2W0kG72dFCYQ1CpUuMYpxMBJAMXqcnCKPNBwoPGJm0oXlAjxvNc8zYf++SEm+Xj+Lb76cyjHoO0CsZ3xRbT+TBW+Wj2HlBgRP31LjdqkXrkIG528/o3IyYoTUSuhABQf2/sK8P49rUhSEJccqOoF50o3vMitZRM9OpaBo2o01uwfC0A4sWn2g8HoTGjbeXPgIL1h5Bjdom1RugzALRYvS68Gs3DuXFqE22I57s+rsrRAAnDTWCYtWh3hUnAkhYffTMNlFi9f2nt+Dj53fh56/uw2/dOoK/qj6Db7TfQ+nQY1ybHEHrwhQUVgMMHhdCkY19JwZDHhgcMlCWhK7JPWif2InHE9vQod6N/tkTIDFGl28RnAyI/pVJ/pUTAJJfwkQTiETg7h4VzLB1NvWCdmsLsbA0gG2DgmHlau3fcFx/2OdnBrzPYGZ6AbZhJYzN3dDerMFM5Q2oD5+D6r3jTGU/6jUQfZW9tReKrYeheu8E8yCYOX0D83fqYGx5AmrHNakBtRtye3K2nGGHC55BFZwNT9bF2VnfDU+fAiF78ljcnA2edyQqBBQap2AEQHWfATprvEBlVdcCE3ijnWqpHbSDHi3Eo5FoX9R43+grpUx0uDeWBtAfDMPhDoDi7jV6N/rHLajr1TERvkM3x5nRT+EMlOYwlhyg98+V9uKlg/145dgQIxHIXb/i4RTud8yjU2aCfNrO2qTwgkw4RCJPrjRqGBGx7aw8pVAA0jlQzrmSEi30nHUoLIwIiK4Pfy1eBLwBC8hoT5SqLt3zvTNlQMwu7YzTij+4cwy/fuOQ5I5Xu6vjjExy1xcSK/n8FVAYRrSM20z46+qzbAf+Exd2iZIISESaUHjBT1x8D794dT9+5/ZRFs//nc6HODTaCYrzb9fNMP0Buz9e+Do69+irwTHKtBbIk2S9Z691bDPGdHfgC8aHm0Xb4a+SQoATAJJarjQHG5jTC5YJwDuqlnQsejLo/JPadQ3TqLp/Kq++sdlk3W3oeiQcBmUyoB1+v9EM15QG1v5R6Os7mCfAdPk1TBw4wzQGyFsgSgxEX+Vv7weFHoztPoGJA5Xv6w80Mg8E++g43DNa+M02hAOJXcTSmUBQZ2I7/algF61DhFNAa0inG163SBAgHQChdrZph5aM0thC7uwUy05G54sH+5lr+KbTo5DCQdkAYovJHkB1r0EQEqBLaY0xMWJ7EeY9OS94/SHYXEsEwfSiiwkLEiFzrmYaRBCQYf7K0SF8Zc/S+sSSBBRyQEJ+rxJBUDGKfdfG2H1V3QvoUZqh0jiYav96Mf4uTxBbKmVs7W8/1q5LJNBz2K5Izxulpt/ICINYTw1h0OOtSAmBSCSEUe3FdY2t9Qyx2GsNilexaH8qAEg4kAggic5J8aBY+Kd+TEA4EkLfzFFBsGpUvgaLa2LVo0Lu8CavG0ScyCx6Jt53WNaJl7uq8M8NV5hqPqVV/OGz2yVDEHygYhMb709e3M0yGHyh6jSmHPEaLuFIEBOGKjSpXk8D31cYWWD3ZPd37qpF4ieERoATAEIjKqb2SF1eCC8AtvvvKGwht4jXD5cAXgBs998njOGc6bNE4QWkc0AEAe30O8enYe4egu5RK+auPMDUicsY31MO+RrhBbI3SiHfdIARBORBoC47zzQL6F5qw6FQM4HCgC3ebTrRWIOLJjgbMwtFIW8BStHIC0cgFgHa3ZXPbtwL4FGfEVrT6p0Rci+nnWDacf7avj7U9iwyt3ZKFyf2Y6XyPhma/eqNewHQDrbZmd/vNQovIOM9ShCMzznRJTPhbts8TldNMYP/ndOj+OahgVXeAxReQGtJ18iDgHQKDt8aZ54Htb069I9ZoNY6WejCsNrKwgAoswJlNVirkMt/84g5I2KFsJRrnOuSC2v1yc8VFgIO7zyax95Ow/B6ec26vdNlzEguLHTiZ2NyjaFRmY6RujZWlH2BjN50CumBUFpFChWYdVrRb5zH7Wk5SwP4Yvt9/EPdRXzm7gkWx08u+4l26/N9/utt9xgxFJ07ufKP6e6CBCRjCaVU31OIAD3DvEgWAU4ASHbpUhw4xVyTAR/dWU37tbYLxZLTnoQTnfXru6ivhx+5rwf15hRXJk/VIhG2s88IAocTPr1pWX9g8UEjNBfvMdFB0hegTAVRr4Hoq+zNvUsEwbYypkEwdfwS5q4+hKGxkxEOsbMKO9xp7/yvxJfIg5Bt7R/hsX3x98WFABm66e6+rnSBp9jsRDuxFD8fJQHIEKQYdKkWEqSjePSV80/n85j2aWiBWHEIhCJMfI8IAr3FB/mMHa3DBtxoeSpQSOKDRATEeg7Q++dLe/HC/iWCgFICfm3vUp13LyhWTZeejS6VdUN4EgmgMRZmSN0qwPiJBAhEoLG0ZWyAkaFGLtlO30KC9gvndARhTOgfbgirDvV78PhNgoMSCIfgCPgYQUBifZ26WVxWD+O9wRZ85fFt/O2jc/itW2XIZ3jBx8+/ixFzvDD1vK0H5BGRqsG/Vj0KPSHtAF4kiQAnACS5bGkOmozSjHZha7vgm5gjH6w0e5Ro9UiE7TiTIb/SEE36ua4bgXlDbBieJEGg8AJy/WcEgdMNz7wOthEV0w8gHYHZs7eY/oByW1kcOUApDSksYbmEw/AMjaWPY03nqns8vfKCDj9Zxoy/SQsBUrl/LEvPBTtq9A5O2kEG43qFkQANGhYOQC7nK93r17tXbNdo974hw+wJjChZHyqxTXfVeGgXj9T5yYOAdAy0Rg9op7+xX8+yEBy9o8bO8wrmHRAN/yBigMiflWVa59mQ8R99Bmk9vFkQM1w5Xv5ZvAgsuWBXZ2TYkveA0SkX7+QEHlk4EsDo/CXUZ7Bj3TaxAzbPjMAjSt4cfW36QkFGEJh8buZB0DQ/iUpVH7b0NeDZlltM+f+Xrh/AD2ZRiJDCGALhp6FuvqADjye2b8j4XyIEXsG0qTE5ELyGGBHgBIAYVyUbYyJPAFd76kJ3SzHY+uIx/qOgRyIIGixwtQ6sMkQTkQCkZE/eA8VQlgiCIMJeHwJ2J9MLsA4qYBuK3ymjXXvKhpAIs7TO13UjaHyqcFwMOPM5poaAxx9C77gtZYOM3P5JtI2M+1QKuZ0/6JxfJgGseXaDT2XMieo4PSFQysOoAZrsleLVSfU/05R4icYhxvPkCUIEAWkQEEFA+gN9KgsozCC20HOTqev/WniPzxd2aF0sdvz92giQHoDW2oWWsXdSNshIpb0YY7BJD2DKWJ9WOADpB7j84gwlpO9WIghcAT9I+2DMZkTd3ASOK7rxxpMafLnpGj537yQ+dakUlDIw0zCCSxNDcQ8fKfpnQqSs5QXQrn4X/pD4PcTiAOAfCAFOABTTc0CaAP6pebha+hMaZuQp4FNMIeyJ2c0tJpDen2vEF4BvfBbO5r7EWDX3spR2VJeXeAQo1V9aRv4aO/+x93tlk/Ed8E8cgfcRIE2AeZMPHesYt4/6jeibsIMM+HQV4qk+KdVTjnuK/ZZyIUJjzuhd13OCDP+hKQfTPZDyXLMxdoPNnzKBspbBv/IcpQzkhSNAroPknq5cvLWuLgAZW7PmVgTDxRw+EmFhD+QNkNiF/RWWym7R1odQWLq/z0KRCPzhEDzBAGx+L3Pjvz+rxIGRdpDa//+su4TfvX0UP3puZ0Jy4IfObMeoRbf8R0ax/91T+1Imm9Yy+leeKyZPlGUgpf+GEwDSX8MMZhCJsLhq/+wifBMadvintGyXlUgCXp4iEAmFWW56/8zCU6ymF5by1RdLaMRTOFJ6R5i5e2SCEgAk0Ji25ZbSaHmlQkGADHWXN8QMXIpZp2Ni3s1Sr5HSf2p7/mujQfcW0k44fXURmaExeBlODKsFN/Q2P9sJXxsFflaldQlKABDZQs8sLxyBJQQizLg3uVTMtVpteAQ6SCvA7tWkLWBXyKiSIRsIuUAp7MgrIIqV1trJCILYVH+xONBue6EU+p8UioRBOgR6jws9hjlcnxzFnuHHeKHtLv6m+izTIDB4nu7Qu/3GtLxNVhr7a31W6e4UCqTFNA9OABTTavO5ZhkBJrAn7R1CIRCK+ANwtaUeQhG705/oPXliUKYGXjgCHAGOQD4QIIKpf2LjGRVivQAe9RlgtPPvtXysJ++zuBAgV/t3B5qZYVxIZG66q2h2jacVQrGWwb/y3KCmouAzUaSLswTqcwJAAouUnyGSMevzIxLiuxOpLAAJ4DGRvPOcCSVDfUOZJ9YIB6DQlLCTq82m8izyOusjQBkEKNabl9QQWDB5cbVRA8WMHRRCUKwlGwQAZQPQWYs73K5Yn6eNzJt2fZVWA86ODWykmaK4NxgO44lhDl94eJrF0f/q9YMweYtXe8PkVK4TOrF2+sSVBv/Kz4Oacu6dIr2/Jk4ASG/Nsj9iEnoztj7B2O6TcM/yPJ+pIB6wOUAp8pTbyxByF7ehyjwAHnMPgFSeG14ntwiMTtnwTsUoHnQWfuosoZCt7l5gafOeLenBoZvj0OjdCdMnCtWnGNthBIBaeA8A0hXghSOQCgJEv9VrJ/CvjVfxA5Vb8clLJQUVmpQKBunUIdf4l9rv48OVW5Zj5D9QsYml6kunnUKqa3aNcQ+AQlrQzOfCCYDMsSvsO2k3m3K/U353XpIjQJ4Sk0cvMhLALp9IfkMB1yAs3E+yoAEQk8amgOHjU8siArSL/ezuHmw/J+ex7iniTKQJGf+UFo+lxtvThzOPpqEze4tOloMySMS68G/0PdcASPEh5NUYAmTQ/tyVvXHGLO1u85IYga88vrOMV1RFf3Nfw4Y0YRL3Jv4rXANA/GuUoxFyAiBHQEuuGzJiR18vxfSpqzwMIMXV09d3MNJk4U5dincUbjWfSuAsAKPqwgWLzyxnCNhcAbx6fAgvHRzArK543UDTAZwEFL9xoB/Plfbi2F01XjzYz4iAFw/042bLHEw2f9EQAXqrsFkAWkbNRWuIpPMM8rpPEVhp0O7ob3p6kb9bhcDtaTlo1z9q/NPrH98/BVewOD1vKO0kpZFc6ca/kc96x8gq3PkJ0SPACQDRL1GeBug326B69xhzafcZeKqiVJbBq9Ux0mSs5BQiweIWAwxZHXDUdQuTCaCuG0GDJZUl4HU4AusiQOJPp6ummAFb27O4bl1+8SkC5PpPXgCtQwZoDR6cvD+Jr+9fIgJeOTYE+bT9aeUCfhcIRtA8YhbMC2B8npNQBfy4ZGVqd6bl+FDF5mWD9rN3T2Sln0JpdMZhxc/GeE0QAfDh01swbjMVyhTTnse0qQH1ilcEIQHaJnbAH3SmPQZ+Q94R4ARA3pdApAMgHYCZs7fYjrZ1UC7SUYprWGF/AON7yiHfdIBrJ4TD8AyqBCEAKJwA3P1fXA+7hEfTN2ZhBMDuy0oEQ8UrapfOEpLhT+7/R+8shTdRPPyYxoED18fwrcODuNOmTac5Sded0rkFIQAahkzw+sOSxoIPPvcIGLyuuLzvH6ncijlXcRBwmaAdikTwP2ovLBMmUU+AY/LuTJoriHt8ASsej28VhACYMpLHK/8/KsEHgxMAEly0nA3Z1N7PCIC5Kw94DvZUUI9EWCYApp3Q1JXKHQVdJ2R3gdL3JUrtl8p5Uv8nbwJeOAJCIWB2+PHy0SF8u2wQC6biFuxMFVPC7LmSXnzr8AAoi0K0hEIRLJi9RaWnEAhF0Km0bogEIPX/aT1/9qLPEX9ND4G/rKpcNmjJvf0czwawLoAnFE/wTPk7y5gRCfCl2ovwh4s3G4zW2oUG5fc2RAL0TB9CIORaF3t+UbQIcAJAtEsjgoF55/VQbDnEdrWDDv5HnsqSOJSTjDSZPHaRkyYAggtGOBt6MiMB6rsR0OhSgZ3X4QikjAClsjt+T83EAJsG9CnfV8wVacd/6xkZni/tBYkCFnuxu4NoGs4sFKC61wD5rLNodBOK/VnJxvwPj3bGGbT/1ng1G90UTJvD5lv+wnEAACAASURBVEV8/Py7cQTAj1/YBZ2neF3XI5EwVIu3Mw4FINd/u2e2YJ6RIpwIJwCKcNFTnjK5tKvLzkP2xh64prjSbCrABV1uKLeVscNv5NoJ9Cs3uGBI2xPA2dTDjf9UHjheJyME2keNzKX9wI0xnkYrRQTvPNYyzK41aVK8o7CrWZ0BtMktaXkCPOozQqFx8meusB+NrM9OZtHj+08/TW33Exd3wxHwZb1fqXbgDQXxmbsn4ggA8gK4P6OQ6pQEGXco7MO4/j4ala+l5QnQPbUXVs+UIGPgjeQNAU4A5A16iXS88KCR7WjrHrVKZMT5HWYkFMbs+TtMDNDSM5zfweSj90gEIY93Vc8huxOefmVyYcDaLrh75QhZuNv/KhD5CcEQ0Ft9+E7ZIAsFoPe8JEdgQutkBMDb5aMIh4sv5tPlCa7atff4QpDNOlE3aFyXCKBdfyIL5s2+VW0kR57X4AjEI0Bipr9249CyQUuidnVzxZ1+OB6h1Z829dYv4xXVAXih7W7Rk3HkCaCzD6F7al9Sb4CWsU1QLt6AJ8A3t1Y/YZI7wwkAyS1ZjgfsHJtmue0nj11C2F+caVPShdzcNchIk9kLd9O9Vdr1IxHYhpWYPHoRHs3CqrkQORIy2+BVTMHdNQJXaz8oxp9e3Z3D8MrUCBqtoHq8cASyiQCJ/x28saRs3zFavGrQ6WBMsf/fPTKEF/b3Yc5QXPHrGoMHO88r0KNc/cOXwiMoJIAU/btVVlBqv/pBExqHTHgss2BAbce8yQtKp8gLR0AoBF7pqo4zaN/sqRWq6YJsp3F+Ej9QuTUOs1+6dqCo0gGSWOSbT2ph86/epAmE3NDZBzCiPc/SBD4e3wYy+DvUu9A3cxRqwyM4vPMgwoCXgkCAEwAFsYxZnETQ7sRYyUkoNh+ET89/KKcCtd9khfztfVC9dxzFop1AWSNMbX0sAwKFjOgbOtYVho0EQ4h4/Qi7POy12NMmpvJc8TrCIkDx/6RsT7ntyYjjZX0ECKOKh1MsHWBDX/Foc6g0DuYp8uzuHhy8Ob6u4CF5RhBR4vKG4PaFuNG//iPFr24Agdq58TgdgE/fKkOQZ8tJiKjZ58avXD8YRwA8U7EJPYbiCG+VWXT4/P1yvNxVBXcwkBAn+uFGwn60y+/2G+AL2hGOrFd/nab4JTEjwAkAMa+OKMYWiWD2wh22o215MiSKIYl9EKSdMHn8EmRv7QWJAhZ6IWN+saqZzZeID31DJ8IB/g+j0Ndd6vObN3rwzUMD+N7xYZjt3LsplfXskpsYabLv2lgq1SVfh3b8Xzo4wEiPw7cm4HAHJT8nPoHCQMAXCuJj53YsG7Q/fHY7Rs3FQ8xlsorPtd5exisaBrC1rzGTpiR1T+vCFH7v9lGUDD0GPTe8cAQAcAKAPwbJEbD0jmD09RKQSzvt9PKSHAF9bRsjTRYfFPY/l7DXh7nLD5hQJGWMsDwZRiRUvKl1kj8ZvIZYEAiGwii9omLGXa/KIpZhiXocJHz3tb19LIWizVW4JB9JHNT36vDCvj72fFyom4lLfyjqReKDKxoE/rHu0rJBS+kAjyueFM3cM5notckRfKhi8zJmRAL84b2TBZsOMBKJ4MbUKH7z5mFUqvq4h0gmD03h3sMJgMJdW+Fm5tUZmap9Mbm0bxQ9ioEnV/iJA5Ugj4BCLBTeMHXqKiOHlDuPwiFXp5X6MBwIshCJQsWnENe80OZU1b3AdrQrq6d5GEAKi0vaCUSaUDrAQiVNAqEwbrTM4St7evFcSS/ud8yD5s0LR0BsCJxS9sQZs/+95pzYhiiq8cw6rfjUpZI4zD50ejOmHYVHAFM4yBFZF37j5mFUadLLdhNBBGafh6VJ5B4DonqEhRwMJwCERLNQ2yJRNkoHOPp6KUgUkJfkCITcHozvrWAx8Z7Z1YJ4yVsQdw2fwYyJA2eYl8NYySm4Z+fTHrBtUAHl9jKYuwbSvpffwBEQAoFZnRvfONCPN0+NoJB3tIXAKtpGVdcSaXKupvD+F5Cq/+nqKWb4f3VvHx4PG9NWCff6Q+iWmzA574pCxl85AllBQOuy44MxO9o/eXE39EWW294Z8OPWlAzVmjF2XFWPoFzZiyvq4VWpEcmw/Zvqs3EEAHkBUP1CKpT28J3eevzu7aPoMWhB806n+MMhfLnpOn72yl6062bSuZXXlQ4CnACQzlrld6T6+nZm7C3cL2yXdsFQjkSgvfGIYWZsKSy3PPe0Fqpdx9nc1IfOwW/MjD1noSWvlcDY2iMY7LwhjkA6CJBgG6m7P1vSg9EpWzq3Fm1djd7NvCaINKHd8kIpNmcAB66PsWeB4v6HJqwZeYU86FxgBAK1xT0HCuXpEOc8KB3g7985tmzQUjrAB7NKcQ42S6PqN87jI5Vb8Ad3juO/15zHP9Vfxj/UXQSl+DN53at6pV3xZ8rfWcaMCIAv1V5Im+hb1bBITjgCPpDWwZ8/PI1J++qsJakM0x8K4e9rzuOjZ7aheaHwdaxSwaQA63ACoAAXNStTcqlnmbK9+vA5hH1cMCsVkO2jY8xInjp5pWC0E2hOiq2H2LymK64j5Fr9DzYVbKgOJwBSRYrXyyYCtx9rmUF7qX42m90UTNu0w/12+SiLjx+fcxbEvBbNXkYEUVaIV44NYWohs917yhjw0qEB9jxRqARP/VcQj4eoJ/FWT12cMfti+31Rj1fowRm8LnzyUgk0LhvIcA2Ew+wIJkhXR4TBj57bGYcZiSm6AtL/XWv0uvHF2gv454Yr0Hsy+w6j9eEEgNBPqSjb4wSAKJdFhIMKeX0sHSDFtfN0gKktUMBqh3LHEXaQy7zUi6m9D/K39zPjX3u9esPaBpwAkPoTURjjJ1dtEnt7p2KUq7ynsKSUDvB87QwzcikcQOplcsGFN06OsPm8c3oUOsvqHNmpzJE8CDadHmXtEJHACYBUUON1NopAt14TZ8z+2o1DIBfwYimdulkmcpfqfCk2/tM3y+IwIy+ARxppZzah3f7P3D0BIoAoLGIjhRMAG0FPMvdyAkAySyWCgZLRN/paCUxthRUvlS1oKWPC7NlbDDNrvyxb3WS93Ug4spTm7809bC6U4UCIbBCcAMj60vEOUkCA4r7JcCPBN/V8YexopzDtDVUZGLcyQ3fXRcWG2sn3zSOTNpbRgAz23ZeVGetABEIRnLw/yTD5TtkgvrqnjxMA+V7cAupfYdUnTN9Gxv4nLz4VtvuRsztApECxlGvqEeb2T/OlHXDPujnul1B5q6d2FQHw9bZ7koWsz6jFr14/iJ0DzYIo/XMCQLKPQjoD5wRAOmgVe13bkIIJAU6fvgHK/c5LcgRI4I5IE81labrlkUL/3NWHbN1lb++DpWckLaX/9RDiBMB66PBruUTgerOGGW/0yktyBBzuIL59eBDfOjwAcp+XWiEvhvYRI76+v5/F/B+/p95Qmr+6Xh1r57tHBtE8qGceJdwDQGpPhTjHK7fo8YkLu/CFqkrY/b5VgyQdgH9vvhFn0JYOPV5Vr1BP7Ohvwl9Vn8Fv3iwDaSCQe38yQ7hhXo0fqNwah9mnLpWmKZWXf0RJ3K9Ko2JifWfH+gUbECcABINSzA1xAkDMqyO2sfnNVubOTvneg87MY7/FNq9sjsenM7JMAOOlp1jKu2z2JXTblOZvuvwaIzBIrd+hUAvaBScABIWTN7YBBJSzdpDq+9azMri9nNxMBmUoFMHhW+PM6O2SmZJVF9X1UDiCh10LLM3f83t6cbVJsyExwzGNAy8e7GfPT6fMhAmtkxMAolpx6Q6G3NW/3HQNf/foHD52dgemEqSro/z25MYePb7w8LTkjNlMVilKfvzUpRLcm1Ew1/fauXH8/NV9IEwSFXvAx4zmKF7R1wFj+tmMEvWR7fOhSBinVX1sHnVzE4J2xwkAQeEUa2OcABDryoh1XCRoRzvaJAbHS3IEwn4/Jo9dhOzNPXCOTSW/QSQ1SOeBFP5prcdKM0vzl2wqnABIhhC/nisEXJ4g3iofYUYhpQbkJTkC9X065jVBru9SKT5/GJcbZvFcaS++tq8P1U8WQYRApsX6ftw/ZZGgdqktTgBkiia/byUCd6bl+Ny9k2ianwTF9q+lak/3LLod+MEz25YJAEoHqM5QAX7lGMT8mf5ymxem8MQwFzfMTb31eL71dty5lR/+o/nmMl5RAmDHQPPKaqL8TAY6eT788vWDGDItCj5GTgAIDqkYG+QEgBhXRcxjMjR3M6NQe/ORYK7gYp6vEGPTPWplmC1WSeCfSyQC99QcE3wcfb0Ek0cuIFsChpwAEOLp4m0IhcCFuiVhu3vt0tkFEmrumbSzYPayXe/XTgzD6RG/6BiFLZy4p2akxbcODaBDZsoozV8sVpQ5gukHXFIuY8AJgFiE+PtMEZh321mKP3Lxlln0TOjO5FubnKS87X9RVbls0H6wYjMuTwxn2rXk79s/0o7/p+n6uvO4rB4G4RQ1/un1s3dPiN5zwh0M4KuP7+Cz905gzpWd1LWcAFj30SmUi5wAKJSVzNU8PJqFJZf2PeU8HWCKoLumNMwDQH3orLgxC0dgHxmDcvsRFvM/c+YmAvbsiaJxAiDFB4hXywkCQ2orni/tBQnb0U4xL+sjQOkAd5yTMxJAPm1fv3KerxqsPibKR8b6q8eGQOJ/QhTa9d9cKUOs1wgnAIRAtrjbIPduUnN/rvUWfKFQUgKA0KK4/1hjlu4t9NKyMIUOXXz6VjKQKWRi73DbutOfd9nx4+d3xWH2/ac3Q+MU5rth3c4zvEgih39fcx5frDkPi8+TYSvJb+MEQHKMCqAGJwAKYBFzOgUS/xvfU852tD1aXU77lmpnQacL43srGHEiVswioRDMnQNQbD7IyArtjUcIeVYLDgm5BpwAEBJN3tZGEbC5AqDdbHINXzBJT9huo/PP5P7rzXNsB/xWa7wLbiZtZesejd6NLf/HSCfjn7I9TC1knh975Rj9wfAqLwJOAKxEiX9OFwEybH/j5mEorQZ2azIPAKo0aFrABys2LRu0v3z9AMxZNBLTnZPQ9UkA71sdD/C3j87CFVxKe0evZbJO/PatIyntjv/5w9PLeBF58kz5JpxRCSemJ+ScJ+wmluaPdv+zneaREwBCrpxo2+IEgGiXRsQDm79dxwgAfUOniEcpoqFFItBeq2KYGVt7RDSwpaGQ0r+upg2yt/ZB/vY+6GoeIxLIvksvJwBE9ygU/YDKHy6lcqvpET6ushDBJfFEin8nT4BgKPNY+mxgQ0r/ihk7vnd8mI3xvUvKnGQs4ARANlazeNr0hYL454YrLMabdrN1HieqNWP4mSt7cGi0ExWqPgTCq4VKHQEf0wmIegF89Mw2Fh9fyMiNWnQsNILCH97sqcVfV59hYROPF6dTmjaFCjwTI55I2P1T/eWU7s1lpS79LJvntv5GQdL8JRs7JwCSIVQQ1zkBUBDLmONJ2GXjkL25FyQISDvHvCRHwDaiWkqhWH5NVCkUQ24P5m/WQPZGKdv9N3f0IxLOjfszJwCSPze8Rm4R6FGamUDcnqsqBIK5+TvI7QyF7Y28JsjA/uahAdBOu1gKGf+9SjNLU/hsSS+O3J4AjTUXhRMAuUC5cPvo1mtY2r9/abiCL9VeZLH9v3nzMH7o7HZ8sfYC/qP5xpo7wKSI/1L7/bgd7e39TYUL1PszI4LkinoY+0bacX58EHpP6mGLI+bFOPFEIgA+fv5d2P3i8AAjL4e7Mwr8yvWDqFD2gtY4F4UTALlAOe99cAIg70sgwQFQCkCKE6cd42zGiEsQmoRD9pusUO08CuWOo6D3YigBqx0zZ24xzwTlzqOwDStzKuzICQAxPAV8DLEImB1+vHx0iOWHN9qyGwIT269U34fDEZy4r8azu3vQPLjkrpzvudCYKEPBC/v7mabD+dqZnKZ25ARAvp8AafdPMe0Uv39c8QRP9HOYcVrRb5xfVwQwOuP7M8o4AuCP7p8CeRTwsjYClGaRsitEvSbo9UOnNzOPi7XvyN3ZYCSMk4onbHwPZ1U5M/5phpwAyN0657EnTgDkEXxJdz19+gYzHK39MknPI1eDp131mcqbzAvANqTIVbcJ+/EuGpnCP6X5I00H12S8kE7CGwW8wAkAAcHkTQmGwNE7EyxevGlAH9emLxDG/Y55DIxb4s4X+4f2ESPDq+z2xKp4+FxjQ2EIpEfwlT29TJzwbvs8/IHcenJwAiDXq174/aWiAUAoLHqczHsgatB+4sJ7TECw8BHKfIavP6mJIwAIO/KkyGfxhAIsBOT37xxDl14D8gTIZeEEQC7RzltfnADIG/QS75gE40ZfL8XclQc53TWWMmym9j5Gmsxdq8orZizNX+kpNpbJsvPwLuZn544TAFJ+mgt37I+HjXiupBeHb03E5YhvG14ydEkngJenCCyavXjp4AALBSAPinwVytxwumqKxfu/eKAfROCEwrn94Uxz5wRAvp6Awu2XCIBPXS5legDrzZLSAVLYQJQA+EDFJlSq+ta7peiv1WvVbNc/ihm9/tK1A2vqLOQCLKvfi2+032OhH1ERyJX90rea2m4GeQlko3ACIBuoiq5NTgCIbkkkMiCfzgj5O/uh3F4GEpHjJTkC3nkdFFsOsR13ygyQj2IfHWehCETekEdCwObIxzBYn5wAyBv0vON1ECDX/28fHsSLB/thdS59t1Ho5dYzcmZcUv54Xp4iQEr4JZeVzN1+WKD0ek9bT+2d3RXAwRvjzBOB1q5/zJI3bwROAKS2ZrxW6ghMOywgd36DN/nvhjJZ1zIBQMbs/6q/nPMd5NRnlv+apKj/Xy+8F4fZRyu3sfCLXI+OUhPSev1r41VoXYlTqz6YVeLnr+6D3BLvpSbUeDkBIBSSom6HEwCiXh4RDy4SiWDiwBm2i+yeFm8KKDFBGPb7oT58jgnuuSY1uR1aJPI0zd8bpdDeqEbIk1+hG04A5PYR4L2lhgAZ+/uujTFjsvN9Y18162DG/yvHhkAGLy/xCNxtm2d4Xaybib+Qg096iw/bz8lZ/5TGcXwudRGwbAyPEwDZQLW426TfWyavO6U4cPIW+EjllmWD9r9d248Fd/6Ifims3L81XlvGi0gTygxQMtSa06HTbv8Xqk7jmx0P1k3fOOu04hev7QdleZi0m7MyRk4AZAVWsTXKCQCxrYiUxrNY3cIIAN2j3H5RSgmjlWNdrGpewqy6ZeWlrH2OBEPQ1bZB9vY+lr2B0vyFc5DmL9mEOAGQDCF+PV8INPTrmcF/8v4kSFQuqgtAMeW8rEaAjG6Ku996Vg6PL3eZYSbnnXjz1Agz/jdXyrBgzi+pSchwAmD188HP5A4BSgf42Xsnlg3aD5/egtq5idwNQII9UfaAZ8o3LWNGJMDn75fnbCYk/PgHd45h50AzXMHEHrUUHvCXVZV4rvU2y16gcdqyMkZOAGQFVrE1ygkAsa2IlMbjHJ+G7M09mNhfmdeYdmlhNgPZW3uZAF/Im32VcepDe/MRZG/sYSEbpN2QqzR/ydaFEwDJEOLX84WAzrIU107p7SYXXExR/mt7+2DJY4x7vrBIpV+HJ4h3To+y7AnTi8ndlFNpM1mdYbUV3z0yyIx/SttoeT9cI9l92b7OCYBsI8zbXw8Big9/rftRnDH7Slf1ercU/TWDx4WPVG6Nw+y/nH+XxdlnExwS97s3o8Snb5XhtKoPpOGQqJDxT/oORO4suh2cAEgEFD+fKgKcAEgVKV5vNQK0i6zcVsbEACmlHC/JEaAUimOlpyB/e3/WxfeCdudSmr/XS6HYegh22ThyLCa7LiCcAFgXHn4xjwhQGMCO80tu5bsuKpiReeoBF/9LtCSEFwnw/efuHtQ8WUxUTZDz1FfrkAEvHRpYWpf7kzlN85dsEpwASIYQv55tBBq06jhj9jN3T8AZyJ9AZ7bnK0T7f/KgIg6zD1ZswtmxfiGaXrONUCSMCmUvPn2zDBTTT5/XKwPGeaYNQHoQE3YTJwDWA4tfSwUBTgCkghKvkxgBzaV7zKXd3D2UuBK/EocAZU6g9Hvmjuz9c/EZzFAfucD6Ue06DveM+FyXOQEQ91jwDyJD4NGTRZbf/tmSHmZokicAL4kR6FGaGU77r49lTX2f0vw97FrAC/v6WIjG9eY5UHpGMRVOAIhpNYpzLDqPE79wdf+yQfuxczswZMouMSd1pPcMty3jRSEAdPzvhitZmRa52G/vb8Jv3zqylOaPWM0khWoEwkvfdaQX8INntoGHACQBjV9eDwFOAKyHDr+WHAFmxJGi/JmbySvzGgwB26CceU2QCj/F5wtdyNgfLy1nxj+FZ/iN4sxbzgkAoVeetyckAjM6NzM0aVd710Ul0wIQsv1Ca0tv9TGX/O8cGQQJ8wldKM3fpfpZpjXwlT19qOlZBBECYiucABDbihTfeILhMNstjhqy9ErZAXhJjIDCalhFAHzqUum6gnyJW0t8hTwxvt52j2kMJErzl/jupSucAEiGEL+eAgKcAEgBJF5lHQQCdicTlpNvPohwILF4yTpNFN0lMsiVO45AfegsQm5hRavs8gnWNnkYTJdfQ9DlFi2+nAAQ7dLwgWFJ1oSE5YgA6Bjlqf+SPRShcIRlT3jxQD8TwktWP53rTk8QJ+6p2a7/Nw70o1thSkkRPZ0+hKrLCQChkOTtbASBClVvnEH7pdoLSd3MN9Kf1O+lTAuUMYHIkg9UbAKFTewZfiwoAUBpHP+h9iKL5d9IZgYiAH7k7I6sfQdyEUCpP80pjZ8TACnBxCuti8DkkQtQbi9DwJIdRdJ1O5fixQhAaQDDPgFj8ijNX9cg5JsOsJ1/CjMQtP0s4MwJgCyAypsUFIEFkxe9Kgvf/U8R1cl5FxNKTMGjNcUWAZPdj5LLKhaO8Z2yQcin7WKSMlk1D04ArIKEn8gDAuM2E37s3E5m0P7enWOomRvPmsGYh+llpctXu6vxpw8q0Dg/ua4gXyadU+z+H947ia+03gZlathIiRIAG2ljvXs5AbAeOgVzjRMABbOUeZyIQzmJoIPHx+ZrCSiMQF/XzjwxZG+UQlfdmpXQAqHnxwkAoRHl7XEECguBeaMHm06PMi+M108OQ6MXr0dTFHlOAESR4K/5RMAdDOBvH53D9oEmuIICbjbkc1JZ7tvkc2eFJCH9hV+/cQibexuW4/g3MhVOAGwEPX7v+whwAoA/CllEIBJBxB9A2OFCyO5CxOsHwuKL2cwiAqk3TVj5AgwnhhV5B6SwjUZp/uZv1jBNAfk7+2Hq6EdEIhhzAiD1x4PXFA8C9GdJsecub4ilnnP7QsxDgH+zrV4jwioQjIDSBFpdQXj8IfYDOxWsphZc+HbZUpq/50t7WXhBxcMp3GiZw+3HWnbcadOiedDAsgKQCGEKX5mrBynwGU4ACAwoby5jBMw+T4J7I4hEQvAGLLB5ZuH0LSIQciGSRIk+QWMFfZpS9YUjAXgCZtg8M3D5dAiGvSlhRd9z9Vo1fvryHqb4vxGghs2L2NLXgM299fhG+z18uHILe//tzoe4rB7eSNOr7uUeAKsgKcQTnAAoxFXN65wiEYSdbvjGZuBqG4SjpjPucDb3wjs6gZDVkZKBm9e5ZLvzSIQZ/F75JJwtfXE4EW6u1n74FFOszlq/bMn4n71wl7n8UzpG27BKUphyAiDbDxhvX0gEAsEw1ItutCssqO4zoKr36VE7YETfhA2LFl/WFPCFnEs226IfvR5fCGPzLrTJV2NVP2hCv9oOg82/Lh/8eNjIBP+eK+3FcyVPD9JkSHRQCEK+CycA8r0CvP9ECJDRb3aNY3T+IlrHt6Be8XLc0TlZign9Q3gCpHmSCk2XqCfpnw+FA9A7hjE8dwbNY2/H4dSgfBXdU3sxZWqAL0gpsNfG6uLEIDP+azTjGwZEbTdj30gbKFvByqN5YWrD7cc2wAmAWDQK9j0nAAp2afMwsUgwCJ9qBo66rlXG7EoiwFHbBc+gCmHPxmKh8jBNQbqM+PzwjqpTxorqkjdFbImEwlisasJYySmmKRB7TQrvOQEghVXiYySHmlmDBw1DpjijP5YAiH1PBIHFGUjwk7Cw8STPCPWCG3UDxpSw6lZZ4fCsnQklGAqDvAD6xyzoVZnZ0a0wo75Ph7repaO6ewFXGjW43DCLW63iSAnICYDCfsalOjvauR7UlKNB8WqcMbuSBKDPTao3MGmoQShcjKEDEbbT3zN9MClOhFXr+GZozG3MSyD22QhFwvjHukvoM4ovBXPsONd6zwmAtVApuHOcACi4Jc3ThMi93901ktzwX+ERQLvcIQsxqMVTQjYXXO1DaWPl7hhm3hWxSIW9PgTIm0KChRMAEly0IhsyKdsPTztSMmZjSQDyCNAYyU20eADzB8NsZ786xjMiFpNE78kjwGgvHEODEwDF88xLY6YRmJxKPB7fmpJBG0sIDMyehD+Uf6+a3OEcgc4+iGbVW2ljJZu/hEBI/BolqWDJCYBUUJJ8HU4ASH4JRTABEqEj43TVLv8KYz/RdWdzH9MJEMFUsj6EsMuzZmhEImxWnifiICxw6sCsTzpBB5wASAAMPy0KBGjnfyQD4z9q6Nb0G6E1ScvDidLtmR3+tLMeUJw/ufVH557uayGRAJwAEMWfLx/E+whY3Gq2Sx1r2Kfzvn/2JIt5LwZA9Y4RNCpfT9v4j+JJJACFDki9pEsAkLcDZTbwh9f25pI6HgU6fk4AFOjC5m5aEcA7MpGx8R81cMl7IBII5m7ceeiJiBJPn2LDWHkGVEA4nIcZCNslJwCExZO3JiwCM3rPqlj/dA1bChuwu6XzvVZZNcXi7h90zoM0D1Ip5OUwpnUh3Z3/lVi2jJrh9afWZyrjylcdTgDkC3ne70oEfEEbi1WPGqiZvDYoXsG4/kHCOPeVfUr1Mwkitoxtytj4j2KrMT+WPFapEgDk4DZoWsDzrbfxF1WV+HLTNahsRqk+7T5hxgAAIABJREFUAsU2bk4AFNuKCz1fct+neP6oIb+R18DsotDDE1V7gQWjMFjVdSG4SCI90i6cAJD2+hXy6H2BMJpGzBnvaMcatwOT9qyklsoG/u2jRnzjQD+eLenBpfpZeP3Jd3SI4KgbTC3mPxaXtd7LZ53ZmFZO2+QEQE7h5p0lQIDU69WG6g0btGTYkku83TOboKfCOC2bvywIVqQJQMSLlEuqBMCAcR6/cHUfvttZhSf6OZQMtTIiIFgAG1RSXr8Ux84JgBSB4tUSIOAZUApi/BNxQFkDaJe8EEskFIL7iUwwrNw9Msl7AXACoBCf9MKY05TOs+Ed7aiBS6EAUvECoN38LrkJ3zo8wJT2j99Tg8IC1isKjVMQooTwIo8JqXsBcAJgvaeFX8sVAmSEtk+8K4hRSySAYuFaroae834oxd9GXP+ju//R1yljXc7nIGSHqRIA/9lyC3REXf+JBPipSyXwhdb/nyHkWHlbGSPACYCMoeM3MlV6Z8MTwYxaIgFCFmkK2iV7HEJ2J5z1wmHlbOxB2CFtwRlOACR7avj1fCBAbo2dSqtgRi0ZtqSML6Uin7bj1WNDjAQouaxkugBrjZ9i/x/LLIJhRekVpaabsBIXTgCsRIR/zgcCFM8eNUiFeCUyIVCggoAaS5ugWD2ZOoBwRLqbWakSAJ++VYaHs6rlx7tS1YfP3TuJAPcAWMZExG84ASDixRH90IJGqzAu7TFigf4prejnnckAA/MGQYkSIkuCi9KOteIEQCZPEr8n2wjQDnSqKf+iu/zJXvsmbJLLCDCjc+PtilFGAmyplEFr9KyC3ukN4VGfQTACgHAcnZF2GAAnAFY9JvxEHhCguH0hDP9oG02qN2H1TMfNZNJuxohZl6djMeN+SbAutgxrzwmKVaPye5LOCJAqAXBhfBCLnqXv60A4hL+uPoP3BluKMgVu7PMkkfecAJDIQolymIE5veBGrVcxFTdXh3ISc9eqJHfYBuVx8/Cr5wTHitqUcuEEgJRXr3DHTu76lMYvmVGfzvV2uQXB0NOcgHqLDyS4V/FQ3Aft/j9f2stIgO8dH8b4XLxxbnIEBMWJMO0Zl3b8LCcACve7QUozG9GeF9SoJTFAg2M0DoK/e3QOP3Zup+SO1oX435ndU/sExYpIE6dPuppWqRIAsQ/D3RkFfu7K3mVCIPYafy9KBDgBIMplkcig/DMLghu13uFxxG6VmTsHMPpaieQOfW1b3Cr6VDOCY+Ub18T1IbUPnACQ2ooVx3gtzgAobj8dAz9ZXXKTD8QQAGQkRg3r/9zdwwxsKbw2DejjHgKj3S8oTowAGOMEQBzI/ANHIAMERgTe1SajVm8fihvJ5x+U4/vK35Hc0TQ/GTePzskSwQkAu1e6GzTpEgAGjwu/desIjsq7ESEhGV6kgAAnAKSwSmIdI3NrFygDQDR7ABnKscVnMMM+opLc4Z2P/6Hsn54XnAAgAkbKhRMAUl69wh07ubXXDZoENWy7lFaEwk9/GJGwXt+YBb0q6RyDE1a4vPHiTlan8B4AfRN2ST9c3ANA0stXMIOnnPRR930hXhuUr8LofOrZSN9mL7bfxx/fPyW5o9cQH2raO1MmKFaEtycg3UxN6RAAwUgY3+x4gC/WXIAz4C+Yv58imAgnAIpgkbM2xZDNCUddt6CGbUAbbzhnbfA5bjioNwuKE6VeJA0GKRdOAEh59Qp37OSq3zQsTArAqGfA0NRqcVOjzYd5o0dSx4LJi3AMkeHxC0+WjM27JP1wcQJA0stXMIOfMTUJatS2jL0Dpy9+08ETDMAV8OflIGMz075XpqlTLt4QFKvmsbcQCkvXGE6HALgwMYjfuX0UE3bpEh4F80ef3kQ4AZAeXrx2HALhCFwt/cIZtrVdCLtWC03F9SnRD2GPF86WPsGwcrX0IeyJF7KRGjScAJDaihXPeAfUdkE9ALQmbxx4g+NWfPfIIL55aEBSxytHh0AkQLSQV0P3mHAZEx71G2GwS/eHM+HCCYDo08Ff84mAzTONBuX3BDNsu6f2IxyJ9wDK5/yE7FtnH0K94hXBsBqaO41IJCzkEHPaVqoEQKNWjV+/cQg1c+Nc+C+nKyRIZ5wAEATGIm7ENyZcbLunTwHE7C4VFKyRCEjfIBrqsNFX76ha8vBwAkDyS1iwE9BZfXjUJ4wOQNPw6tz2smn7sgbAs7t78NapEZDSvtiPrWdkGBiP9zyaNXgEI0va5Ja4UAkpPmCcAJDiqhXemINhH/pmjghk1L6CaVNj4YH0/oxot751fItAWJFWwrCksUqFAKD0f//X5VL8+cPTeLX7Ef696Qb+qvoMfunaAfzK9YMYMsV7i0gakMIcPCcACnNdczeriM8Pykm/UYOWXNpDJmmLPyVDPWR1CIIV4R2yS9tNlrDiBECyJ4ZfzxcC5OZOcftRF/6NvKoX3KumQTpJXXIzXjo4wAQAKd3e1IILHl9I9EdsNgOamD8YBhnuG8GI7q3uM2AuxrtgFWgSOcEJAIksVBEMU+8YFsQLoEP9HnzB3GlzmH0eUFq5XJZZc6sgBEDP9GFJu/8T5qkQALsGW/B3Nefwclc19g634Yp6GNcnR5cPrgeQy6c3o744AZARbPymOASESAfoU0zHqf/HdVAoHyIASwe4EeHE2i74J+MFbKQKDycApLpyxTFumyu4YTFAIhHIQE5UNHo3yPinDAAUEkBCe1Isept/w5kTSPwvVl9AijjQmDkBINWVK7xxhyMByOYvb8iwbVS+DiISsl18oRAor/zn7p3Er984jN++dQQKqyHb3S63H46E0LtBj4lm1Zug0Aupl1QIANJRoHq8SBYBTgBIdunENPBIBL6x2Yy9ADwDKkSCxfFFEgmFQO77mXpMeEcmCiZMghMAYvoj5mNZC4FFiy9jw7Z5xAyXN/n3msMdRNmtCUYCvLCvD/c65iXnBk+K4FOLHjzqM2TkCdCusMAbSEyUrLU2Yj3HCQCxrkxxjssfdKBv5mhGJAAp/08aahDJcoQ3iQmSkvzn75ejS6eBI+DDvzVew+7B1pwumjdoRfvEzoywIqJkwdYLZBmrXACSCgGQi3HwPrKKACcAsgpvMTUeicA/NQ9y5U/ZuK3tgnd0ApFgYQrLJFz+UAg+5XR6WNV1gfQWsEIjIWB1IGB3JuxKzBc4ASDm1eFjiyKgt/pRn2ZawE6lFW5fcuM/2ge51d/vmMdzJb3sOH5PzUIBotel8EphDRqjF7UD6Wkn9I7b4Fth/FN2Aa1RmoKwnACQwtNaXGMkEmBYey4tobtG1euYs3Rk3finlbg1JcPv3j4KjfNpGOg/1F1EuZIM6twWb8CaticAZUjQ24dWYXV2rB+Vqr7cTkCA3jgBIACI4m+CEwDiXyNpjZBSA7p7ZElJAFf7EIKLpsJ3+19n+YIGC9ydI+tjVdvJ6qyljxByezB59CJUO4/CNqhAJCytHTROAKzzcPBLokLA6w9jeNqRdIe7fsgEivkPriDqUpkMGdAUAkCZAZ4v7cWQWprhAE5PEL0TNhbTv54uQOOQCRqDFzTv2EJkyMX6WZA3xK3H2lXkQGxdMb7nBIAYV4WPiVzc5209aFe/m2SH+xX0z56Ay6fLGWj2gA86z9ONjNaFaaYuP2k352wMsR1RtoNZcwtaxjati1Wj8nsY1V6A22+MvZ29HzQt4MfO7cQHKjbh72vOY871lNxYVVlkJzgBILIFyc5wOAGQHVx5qyG7E74JDTz9SpCx72obhLtXzna+Q2ZbURv+cU9HJAISB/SNz8LTK2c4EVaEG4VV0LVEJWCxY6byJkZfL2WH9loVgs7VgmOJ7s/3eU4A5HsFeP/pIkBEwIzeg361nQnftYyaQbv9I9MOzJt9WCmQl277VF9v8aJtxAizQ9rp8Cj8Qb3oBsX2P5aZEcVKNuuEzupfZfhHsSJvgGtNGnx1bx8Li9hyRobxOWfC+tH7xPLKCQCxrAQfx1oIkHFrdCqg0t1hoQEd6t3onCzB0Fwlpox1OTX8V46PdADuzSjwyUsl+E7nQ1j93rw61IfCAejsg1Au3kTP9CGQGGLX5B4Mz50FiQZ6/KaVU1j+/KXai3im/B183/vHx8+/y7wBQisZz+U7xPOGEwDiWYssjoQTAFkElzfNEcg6AqQpYO4ahGLrYYy+VoKx907ALhuXhDcAJwCy/njwDjgCkkSAfiMrZx3YdHoUz5b0MDLgapMGLo/4w8U4ASDJR44POs8IjNtM+IM7x/CJC7vwZw8r8KcPKliauVPKHoQlYDSvhM8dDODNnlp8uHLLMglA3gD/0nAVs05rXomNlWNd+ZkTACsRKcjPnAAoyGXlkyo6BLwLBkyXX4XsjT1L3gDXqxF0iDtVICcAiu4x5RPmCKSFgMsbxJVGDV7Yv+QNsLlSBsWMuLMFcAIgrSXmlTkCDAFKG/dIMwaT96kXY41mHD95cTcm7Il32sUOX4duBr91q4yFAkS9AX768h5cVg/Dn+NUh6lixQmAVJGSdD1OAEh6+UQ4+EgoDIpNl1o8ugihTHtIkUAQxtYeKLcteQOM7ymHc2xKtGvBCYC0l5jfkEcEbK4AAuuk9Mvj0Aq6a9r8U8zaseO8HM+V9OBre/tYiIBDpN4AnAAo6MdR0pMjdX2b3yu6HfVAAkPY4HUxL4DHC9JOrWf3+/Bq9yN89My2ZW+AD53ejP9ovsG8AcT2UHECQGwrkpXxcAIgK7AWcaO2QTlU7x6FoamriFHIbOruGS1cUxoEXRtTv/ZodZg8dgmy10she3MPFu7VI+gUnzcAJwAye074XblHwOLw49uHB3H41nhB5KrPPYIb79HjC+Fm6xxePNi/rA0gnxafNwAnADa+1rwF4REgN/r/r+UmE9er004I30GGLZI7/Nfb7sLgWf0bpW1xBp+6VAJ1nsQAY6ekt/hgtPliT6X1nvAnDwfyBnimYtMyEfBL1w7g9rRcVN4AnABIa2mlWpkTAFJdOTGOm3b9pyuuYfSNUpi7B8U4RNGOibwmFNsOQ/bmXlBqv42WsD8AfUPHsjbA+N4KOCdmEMlAnXyjY0l0PycAEiHDz4sNgZqeRWZ0Hrkjnh/OYsNorfFYnQGWzi8QEi5DiUrjwM7zCqYNsOwN4BaPNgAnANZ6Evi5fCNARvSnLpXiY+d2Qmk15Hs4y/2Tkf+L1/Zjxhmf9YTc/j979wS+3fkQiTwElhvJ8ht/IIx918YwMB4/xky61XtcTODwh89uXyYBPlK5FV97fFc03gCcAMhkZSV3DycAJLdkIh6w32RlO87K7WWijz8XG4zWvlHI3ijF9KlrgmZI8GgWmDcAZQqQv70fi1XNLERDDPPnBIAYVoGPIRkCtHOz7aycEQCUpo+X5AiQ4V/bs4jvHR9mKQ3JKBayuL0h3Gqdw0sHB+K9AUQgFsYJACFXmrclFALHFU/wTPkm/GPdJZDavliKM+DD/6q/jP9ovok+oxZyix4nFT343dtH8XzrbZD7fL6L1ujB1jMy2N0BQYYSioRxf1bJvDFiMwX8yvWDeDCrzLs3ACcABFlmsTfCCQCxr5CUxqeva2dK9HNXH0pp2KIY60zlDYYdKfoLXUJeH3Q1j6HYfJD1oT50Fi7mDSDcrlwmY+YEQCao8XtyjcD0ogtf2dPLQgCE3MnO9Txy0Z/TE0TLkAFvlY/g2d09zDh/fk8vZnVPhb2EHAfzBrggLm8ATgAIucK8LSEQIEX6P394mgnRXVWPCNGkoG0suB1440kNfuf2Efz2rSP4y6pKXJoYgi8kDs+e+x3zOPNIeB2COZcNX2u7ix+M0Qb4oTPbmdeD1mUXFON0GuMEQDpoSbYuJwAku3QiGziloxsrPcVc2J1jwn9Rimy6gg4nYLFDsfUQ5JsOZNVzwjWpwWTZeZYlgPrSPWrNqzcAJwAEfYx4Y1lCgHLS/+fuHlysn81SD9JvluLzu+Vm5ilBafuIMPnW4QFGApB4n9efvR1H5g3wWIsXDyxpA2w9K4Nsyp43oTNOAEj/eS60GXTpNSCX8/92bT/m3RsPMcwWPpQJwOLz5O1vd6150XdX6RUVZNPZMcgpvOHWlAy/cfMwYr0BiAh5OKvKS/gDJwDWehIK7hwnAApuSfM0IZd6lu0uk/I8kQG8pI6AqaOfGeUzZ29lXbGftAbIG4AIAAoLILFAIgaQB9dZTgCk/ozwmvlBgGI/Xz02xOLNJ+dXi1TlZ1Ti6ZWyIlBYxK6LSubq/1xpL7aelaNLbsKxu2pGnNxrn8/JgMfe1wYgsubr+/txtUkjmMtuOhPgBEA6aPG62UYgAuC17hoWb/7dzipRGdfZnrsQ7c/o3KD0o0RyZrOQBsJ/ttzERyu3LmsD/NDZ7fhe9yOQbkAuCycAcol23vriBEDeoC+wjjVXHjACQF/fUWAzy/J0IhFMn7rKsLMOyLPc2fvNRyJwqqagPnSO9UveB/ratpx7A3ACIDfLzXvJHAEybp8v7cWm06MIiUhAM/MZCXsnGfpf3dvHCJJ3KkbRMmgAhQFQysTXTw4zTwD6AZ2r4vIGcfuxFt840M/GRNoNw2pb2mvnD4ZBOgaZFE4AZIIavydbCOg8TvzajUP4aOU2tOtmstVNQbZL5MmNljmWdjQXE/SGgrg8MYRfvn4gzhvgD+4cB2VuiORoo4YTALlY7bz3wQmAvC9BAQyAdpXl7xyA/O19ICFAXlJHwKc3QbHlEMsAQDjmsgQdLiw+bF72Bpg6cRnu2XmA/uvloHACIAcg8y42hMCJ+5NsF/th18KG2inUmztlJuy5qkLNk8U4g5kRJ3t68d4lJXyB3GqN0G9k0gZ494KCrd0L+/pwoXYmbnzJ1uPWYy0jMBbN3mRVV13nBMAqSPiJDSBAgn0zDius/vSfReqW3Ms/WLEJn79fDkcg/4J6G4Ai57fSrj99h43N5TZsgjI2kDfA95/esuwN8CNndzBvAJM3+4QqJwBy/qjlo0NOAOQD9ULr09w5wHaSp09fL7SpZX0+xpYnzBV/7vKDrLv/rzUZSt1I3gATB8+wNVRuK4OhqQskHJjtwgmAbCPM298IAhaHn8WxUzz7RvI/b2QMUrg3GIqs4gwrq6eY8V3dvZi3KZAnwp02LV46uOQN8M7pURaukIonx8n3iZ8nCnPa4+cEQNqQ8RvWQICyj1TNqph43x/dP4U/fVCB2rnxVX9ra9y6fIriy/+l4QozIg/LOpfP8zepIUBE4pZKGcgjKNeFvAHOjPXjZ6/sXSYBvq/8HXzm7gm0L2bXk4MTALle7bz0xwmAvMBeYJ2q3xeWsw0pC2xm2Z0OGd+TRy8yw9suz29+8YDNgfm7dSxVoOyNPZg6eQXu2YWsegNwAiC7zxdvfWMIkJr9cyW9LP9zmLv/pwym2eHHayeGWRy+1pBbr6aVgyQjSj3vRMllFQsJIG+A8yl4A9zrmGcEBhEI6RZOAKSLGK+/FgJtizP4uSt7cWCkHbNOG65NjuD37xwDCeWlWpRWAz5xYRc+eWk3VDZjqrfxeliSRbrcMIu77el/BwgJ4JjNiH9tvMq8OIgAoOPHzu3Elr6GjL1Cko2PEwDJECqI65wAKIhlzOMkPFodU/5XbDuMsD+zmMk8Dj+vXXs0C8z9XrXreM7j79eaOIk3OuQTmNh/eskbYHsZjI97s7aunABYaxX4OTEgQG7kpPxMgnIdMpMYhiSZMfQozYw42Z0H9/9EILm9QVR1LeClQwPLegUUppCI2OmWm9gcjt9TJ2oy4XlOACSEhl9IA4F/b7qOF9vvIxhe2n3uNWjZbnA6oQClQ4+ZwfhvjddAued5SR0Bcv8nDZGphdwK8K01QvIGODc2gJ+8uHvZG+ADFZvwuXsn0akTPjsNJwDWWoWCO8cJgIJb0hxPaPFhEzMWF+7V57hn6XdHgomjr5VAe6M6Lyr8iRAM2J3Q3njEiB3Zm3swXXEN3gVDouoZn+cEQMbQ8RuzjMCc3s3SypHBSK7kvKSGABEnJ+4vqf+TLoCYCnkD0I/5ksvKOG8AEixcWagehX5sOytbeSnpZ04AJIWIV0gBATLu7s0olmtWKHtZHL8nuPp5Xa4U88bm9+Kzd0+wOPIHs9w7MwaalN6OTNpAKUwTkYQpNSJwJZXVgC/WXlgmAcgb4OPn38WuwRa4gql7hiQbFicAkiFUENc5AVAQy5inSdCOv+rdY8yIJU8AXlJHIBIMQn3oLMPOOSE8g5v6SNauSd4A9pExjO0+ycao3F4GU3ufoDoFQacb7mktiHDghSMgJgQedC65gJ+umuJps9JYGLPdj+8dH8ZLBwcwb8qv+3+iYbt9IeYN8OL72gBvlY9gSG2NW2eHO4iv7esDhQykWyhvOIUdaI2efGRXTXe4vL5IEXiin4PZt/Q35AsF8WcPT2P/SHvKGgAUQkAicr95swy5EI4TKYwZDYuIzLM106jpEReJSZPxhAI4oXiCT1x4b5kI+GDFZqYR0WcUJuUqkaUKqwFdeg2ISOKlIBHgBEBBLmuOJmUbUYHixScOnBHVDnaOpr+hblxTc5C/sx/jeyoQcov3C5a0AbTXqtg601rPVN7kmR42tPL8ZrEjEAiFWdo/cv+XTdvEPlxRjY/c/58t6WG6CSQOKNZCP/CnF11M4ZvGS6kMSRuADP9oeeXYEAsByTQdYLQd/soR2CgCF99PDWdIMR88GXAvtN1lBuLbPXUb7b7o7nd7Q3i7YpSReGKcPMmukjbAX1adWSYBot4Au4daQSEDvHAEkiDACYAkAPHL6yAwe/Y22x2mnWFe0kNgsaqZYbdwv1H05AmJFdqGFFDuPLrkDbCtDObuwfQmzGtzBCSCgGLGzgxC2hmmOFBeUkOAXGUP35pgRnNDvz61m/Jci3brKcXjNw4sZQp44+QIRqZsbOe+9PKSBoR82p7nUfLuixmBOZeN5YW/ODGY8u7/gtuBn7myh4nF9RnzK2InxbXrH7eANEyIKMxXISM+6gGSaAzuYAAHRzvwsbM7lokASvn419VnIbNI4zs40dz4+awjwAmArENcoB34zVbINx+E7K29IFduXlJHIOzzLwntvV4K96wwLlup9555zYDVDs2Fuyxt4ejrpcwbIMjd9zMHlN8pSgRoJ5h2/2+0zKX8g1uUE8nxoAxWH14+OrTk/m8Up/v/WpDQj/xZnRvvXlDg2d09eL60l3kDVDxcSmXYNMB/SK+FGz+XfQQojd//23wDX266jlRj/2lUlyaGmEH4F1WV8Ic5iZnOSpH3xKkHk2jME4k5ZFrAP9Zdws9f3YdPXirB9v4mhNZhIsgbgIx9ShMZzRJArz9+YRco9SOFj/DCEVgDAU4ArAEKP5UCAsaWbmYIai7dE/0OdgrTyWkV5/g0ZG/tY6ETIY943f/XBCUSgXVQDuW2smVtANvgU6GiNe+JORnxB+DX6OAZGoOrYwiuxwPs1TOggn92ERGfcEI2Md3ytxyBlBAgF/BXjw0xATiNnhObKYH2fqVOmYkRJweuj0HM7v+J5hQIhvGwc4HF/RMBRKEB9HqpIblGSygcwaLFh5FpBzoUFjSPmNEyakbPuA0T8244PEFOJiUCnp9PiECZrAv/993jWHQ7EtZZeYEMvr99dA7PVGxChap35WX+OQkCJPpKRKbJnvvfIlWzKvzC1X04qehhbvwtC1P49K0y2FOIwyePAcr68ENnti8TAc+Ub8LfPDoLtd2cZNZ0OQKXT4dJYy0GNeXoUL+HdvW7eDJ9EPKFq9A7hhEK+1Joh1eRCAKcAJDIQolqmOQSTnH/pGDvUE6KamxSGMzC3QaGna7msRSGu+YYA1YHpiuuL3sDkGcA6QUkKmT4+5TTcDY8gaOmM+HhrOuGVzaJiC81peNE/fHzHIFMEHhCKexKe1lsuD/A02aliuGS+/84M5jbR6Wdb3zO4MbO84plAoAIjUSFDP8ZgweNwyZU9RrWPZ6M2RgRkKgtfp4jEEWAdnVvTsnwy9cOoFOnYakAaSefjDw6aJc6UVFaDfiByq0sBIDCB3hJDwEiMg/cSPw3n15rqde2+Dz4zN0TuKIeXr7p4awKf/awAuTqn2qhkI8/vHeSEUBRj4AfP78Llaq+hN4gZPiT0V+veHnd4/H4VsyaHyMUzj05kur8eb2UEeAEQMpQ8YrLCLjUM5C/vQ9j751AOJD6F9NyA0X8Juh0YazkFAud8M5L37XU3DUIxbbDjNBQ7TwKj2Zh1eqGbE64Hg8mNPrXIgScLX0IWXjs7Sow+YmsIUC/qQ/dXDJipRLDnjUw0mxYb/Hi22WD+O6RQegsEvNqWmOu5MHwoGMe39jfz56JNarA6w+zHf5khn/s9Zp+I2b0PDvAWnjyc08ROD8+iB85uwO/f+cY/qn+Mv7kQTl+9cZB/OCZbWyHt3lh6mnlFe829dWzHeDnWm+vuMI/JkOA/gccuTOBfJGYRNhEyR1S3/+r6jMsxj8x3bP2jCgl4M6BZvzouZ3L3gCUEaJdNxN3AxFNWmsXmlRvrmv4ryQG+mePwxuwxLXFP0gOAU4ASG7JRDDg+Vs1kt/BzheMdvkEU9SfPHoBpAVQCMVvsmK6/BrGSk8h6HDFTYkZ/y39aRn/UULA2dSLkJmTAHGA8g9ZQ2DR7MV3ygZZDHs+3D+zNrEcNNw8qGe7/wdvjosqb/ZGp+76P2rgwdBqTxAy/jsU1nV3/GMN/5Xv1YtuHhKw0cUp4PsvjA/imx0PWLq3+zNKUEpASvEWPShP+1rF6vfiN28exkfPbEODVr1WFX5uHQTsrgAjMmOzgaxTPSuXyNODvDj+vuY8fu7KXpaKj1L/ZVI6dLOMRPpAxSb8e9P1FR4AEcyYm9GgeCUt4z9KBnRP7Yc3kEpoQSYj5/fkAAFOAOQA5ILqggw82umllHA+namg5pb1yUQi0F6vZuSJseVJ1rvLZQeRYBA+Xbzrb9jjg6stvZ3/qPE5IOeEAAAgAElEQVQffXU29yEs4jSJucSY95VdBOp6dczt++gdNci1m5fUEKDdcnKTp5j59pH474DUWpBWLXo2+tX2jI1/IgMe9RmgtxUGASyt1Svs0dZr1WzH93duHwHtAvOSHgJEZB67m1/i5DudD/FTl0rw2Xsn8K+N1/DrNw4xTwC9x5neZN6vTZ4Em3vrMWJejLvf6JSjUfV6RsZ/lAQYmqtEkOsCxOEqoQ+cAJDQYoliqJbeEWb8045vJLg2Cy2KgYpwEKSiT2ET8k0H4F00iHCEAg4pEoFXPpXRzn/U+I++kmBgXvPxCAgLb0qcCJAA3HuXlMyIpVz2vKSOgM7sZV4TrxwbgtFW+CJRWpMX1Uni/Vfu+K/1mYQCpSiWmPqTwWvmEoFgJMwyBpDw267Bllx2XTB9lVxWoleVX9f2QdMC5Bb9cigAxf//ZVUlXntSA3LZF6IEw150qndvyPgnEoC8B+athbWZJQS+EmmDEwASWShRDJPE/6ZOXWU72JaeEVGMSUqDsI2omGgeYRj2Z+bSJZX5hp1uOBt7BCEASDgwZE0sMCgVTPg4xYuAet7J4r1fPzEMm6uw/zaFXoWo+z/tnK2jTSZ0t3lpjwz2NrllQ7v/sWTAlE466RLzAjjvNGUEFtwO/Jfz74IE38iA5CU9BEx2HwsB8/rzs7EVDIeZ2ONaoybj/383XF03HeBa9yU6N2fpQIPi1Q0TAEQCdE3uRSDEM+YkwlrE5zkBIOLFEd3QPFodFFsOQbnz6KpYb9ENVmQDioQjoJSJlDnB3DkgstEJPxz/pFYQ4z/qBeBTxYvXCD9i3mIxI3CzZY7FsJ+vnSl4I1bIdaZMCXuuqvBcSS+65YUfEmZ2BAQz/okIaFfkd7dRyGeBt5VfBI7Ju5n7P8WOR4Xk8jsiafVe26tDZXViccVsziYUiTA3fcr8sLJQ1ocvVJ3G1r5GQfb/yYugZ/qQIMZ/NBTA5FKtHDb/LH4EOAEg/jUSzwh1tW3MgNXefAQyaHlJHQESyiPtBMXWw/DpC/yHcjgMT69cUALA1THEwwBSf9x4zTQQoLzP71SM4it7ejGm4Z4maUCHBZMHX9/fj1eP5SdvdjpjFaLumNYlKAFQO2Bk2QSEGBtvo3gR8IWC+OP7p/D9pzfjckwaueJFJL2Zk+fStrNyjEzmJ20ird9fVFVi/0h7nJHvCQXxZk8tfuX6Qcw6hRkbqfe3jL0jKAEwoX+YHuC8thgQ4ASAGFZBCmMIeX0Y33eaxf+71LNSGLKoxmjtG2Xu/zOVNwteOyESCMLVvjHxv+jOf/SV0gJGfNw1W1QPdYEMZlhtw/Olvdh+Tg63Lz/un1KFsqZnkXlOHL9X+O7/ZCQMTG5M/C/W/Z/eP+ozwmjnYm1Sff7FMm7KDvCh05uZarzZx8NK0l2XeaOHkZj51OS4NS3Hb90qQ6WqD0OmBdydUeB/1l3C790+in7jfLpTSljf7JpAo3Jj4n/Rnf/o69DcGUQi/H9nQtDFeYETAOJcF/GNyqFQQ/bWPqgPnUPYW/hCT0KuAIklkuFP7v/FoJ0Q8fpBKfyixrsQr86mHoRd/IeNkM8lb2vJqaT84RQzYu93CPcjqxiwJff/0isqRp70jxW+KzsRAP0TwhIA1X0G6Kz8/2kx/L1ka47k0v1KVzVz/3+5qypb3RR0u/Tdf7E+vxtbJOJYpRnDF2sv4HP3TuKP75dje38TtC5hUyGbnEo0Kl8T1ANgUFOOcCRY0M9IAU6OEwAFuKjCTylC8ev3mQFraOwSvv0Cb/H/b+/Og+O48vuA/7OXvXbWTmxvUrErttflY53Kxq5Ubexyys7GsStlx3Zsx+UkLru00mq9Xu1hURIlSiS1FCmJJHhTvO/7pngTF8EL930NZgY3BgNg7vvu6W/qNTUQAOKYwTRmunu+XYUCZjDT/d7njSC+X//e78WdHvRt2KPUTki4S+Afyokkwo9a1Q0A1DRDbCvIgwJqCrgDCby+v0OpYm9zMsCUi63dHcU/bmvB6/tLo3CiEgDIc/u/5zMAuB1gLp85vvZ5gWAyjl88twX/4viPlD3jn38Fn1lMIJ2W8fbhblhty9tmb7FzL+d3ohigLxFDXFqZO+pivb76AYAjSDMDYDnDXcz3MABQTH29XHt6/fr6nRCTWR65CYiif+Lu/9iZjyF2UjD6IUsSIg3dqgYAwk/aIUvGtzP6Z0Nr/XvS5VK2/tt+yQKxFSCP7AVu1dmVzAmRQVEqR+9oSNUaAPdbXQhGeeesVD4/K9HPq0M9yt3/3/34wIJV5FfiukY559BEGGuPdkMqkbpWofgkasxrVM0A6Ju8bJSPQyn1gwGAUhrt5fbVXduqrF8fPXENYnLHI3uBdDKFYbF14uot8HeYsn+jzl8ZNw2pGgCIdVp1LsLma01ArPfccdmqBAAedTq11jxNtyeeTGPTaRNe2tqMUkj/zwyG3RNXNQBQ0+VBicw7MoT8rqKALMv4i4oz+NyRtdjbw+zM5dBefDCGyw9ty3mrLt8j1urXDnygagBgwt+iS4sSbzQDACX+AViy+2ICO7jv7LMJbGffkq/nC2YLxCZdMK3bCfMH+5H0qbuWa/aVtPVI8vgRLK9XJwhQUY/UlMF3TtDW8JVEa2zOCF7Z1YZV+zrg5DrsnMZcLJcQk//VBzohdlEolUMEPqo63KoFAUxj2kg7LpXxM1o/x0J+fPHYevzsqU2whdWpEm80o8X6I4LA4m/Y6FRp7WPf77iFStMqVYIAj6zrEUv6FmPm77QpwACANsdFO62KjIyjd+0OWLYcQioY1k7DdNISZ02Dkv5vu3inpLaxE4UPIyptBRip6zT8zgk6+Tgbqpl36ieUFPaDNwch1nfzyF4gk/5/snwk+zcZ4JXiY9JnU2crQLEFIHedMMCHoohd2NLxWEn//7/VF4vYCv1e2jQSwMZTJhSz+n8x9CIJJx5a1qoSALBMfQwZXD5XjHHM85oMAOQJaPi3T9ysViawEzeqSmoCq8bApuMJDO47o2ydGOgpvRR2yRNAqKoxvyyAygaknMYvnKjG543nyF4gGpfw3imTUsG+o593L7KXA8Rd8PXHe/Dy1haILRRL7RD9f9TtyTsLwGpnQL3UPjtq9leSZfz7y7vwhSPrcGfUrOapS+Zcp8pHcCPL3V9iUkrZnk+SjTHZHXZXoyrPLACxlCCW5L/PdPofDAMAOh24gjRb3PG3bj2M3re3QWQC8MhNIDbhQM/b22DZfAipUAn+Y0+WkRieWP5SgPJ6xPvHGHjK7WPHV2chYLEF8a2tzXj7SPd0CrtYBnDt8TjEnvZjjtJKCc2CbPolI5NhpW7CGwc6EU2UZk0YTzCZ11KAJqsfaaadTH+m+EPuAk8mR5S1/185XwYxOeWRm0AsIUH8DZvyxpZ8o5j0r2upwm9e2onRkDECxmLbvk7biWVnAYgMArGjAA/dCjAAoNuhK0DDA10W5e61qAGQTiQLcEVjXWLq/mMle8J+rcJYHculN2kZiSE7QpUNuWUCZCb/rJCVizZfm4WAmHedrRxV0v/PV49hZCqC43eH8f3dbcrE9qUtzRCVoXk8LyBS4K88tCl2pZb+P1fDHUyiehn1AFr6AyWXcjzXjo/zF/j244+V9P+1zZX5n6wEzyCyl7aeNyOZxe5Cd8YsSp2Fr17aCVfMOMFhKZ1YVhBArPt3h0RNMK6d0/F/OgwA6HjwVrTpYru60ZPXlAms+wkrfOaKLcXiGNh1Aj1ryhA0l842WfM6yTJSLh/CtR1ZBQHCj9uQcnh4539eTD6Zr0AgnMRbh7qUyb74/u1tLcqE9uWyFnx0vR+WsSDvzi6AnEillS2zvl3Wgr7R0ilqugAHQlEJ4m7+3WbnkksCKtpcGJqK8LO1ECafz1pA7BP/c6c24fNH1sLid2X9Pr7wU4FDtwZR3jT56RML/NTpmcRvXNyBH9bdVjIAPHHjBABEl9OyhBFPTZZbA65C2+hBhOITnPwv8HnR0dMMAOhosAra1LjDDdO7u9D33l4kXFzjkyt+1DapZE9Ytx2FqAXAA5ClNJITLkRbTM/XBqhsQKSpF0mbQ3kdvSiwUgIdAz5lwv/Ch03K93/a0apkBEy4Y5ycLYE+PBFWzFYf7EIyZYy1sEt0eclfiyQldyCJ9sHAc8sC7rY48aTXi4GJCGIJei2JyRdkJXDC0qak/3/j9lHeg81KbPaLxM4lIv3f7Y/P/sWcRz1eB37t4na8UnsLzc5xQwYAMl2OpwIQdQEah3agqu+1WUsDHlnXocd+Tkn5FwEDHoYQYADAEMO4Ap1wfVK9fuzcLd6JzdVXBqaLJ956kOu7S+P1aRnpaBzpSEz5Yhn20hh2LfTySZdLufsvtv8TOwEEIlzelM24iGTPc1XPlk6IvbN5PC8glpeIIoGiur/4ktIyJ2jPM/GZPAX+8PYxJf3/pLUtzzOV5tsbTB7sumJdcilO1fgA3mt9gEgqievDvYYOAGQ+CeIvllgaEE26lS8RGGCV/4yOob4zAGCo4VSxM9HxKdjO30LIUuLp68swlaIxiDv/vW9vR3iQ/1BeBiHfQoEVExBbPk16YhDp7DyyFxB3/F/b1wGxVMI8Fsz+jXwlBSigmoCYoF0b7sUf3zmOYHLxO9iqXdRgJ9p9tR8PO5w59apUAgA5ofDFehZgAEDPo8e2a1MgPDCq1E7o33mc+9drc4jYKgpQIEcBqy2opP+Lugmltm92jlR8OQVWXIC5Jcsj9gQTyu4v3mBuSzNFAEBsu+iNR5d3Yb6LAtoSYABAW+NR4Nak08p6a1mSgHSaBT3V4JdljF+5rwQAHOVP1Dgjz0EBCuQgINZki9RrMUlVUrBZqDgHvYVfmkn/F1sl8qAABVZOQEzu03ISUjqupGOLLdt4qCPwqNOpFHuVpNz+xyACAL/z8QF1GsGzUKD4AgwAFH8MCtwCKQ3JG0DcMoJIcy8idZ0IP21HpKEbsZ5BpBxeyEn+z2a5oyJFYrB8cACmdTshCgHyoAAFVl5ATPpDMQn9ExE09/vx1OTDo24Pak0+dAwFMeqMIpZMcz32ModCBFN+uLddSf8fnuQWictk5NsosIiAjKQUhiPYBdPERTQN70bd4BY0DG1TKq9bHbfgiw5BklmzZBHERX8lanRsu2hBU59n0dfN90sGAOZT4XM6FmAAQMeDl1vTZRmSJ4BIU8+SW7GJbdiStikomQG5XaXkXx3o7Vfu/g/sOQWxlSIPClBgZQXExF9UYL/X4lp0K7bKdjfM42EkkvzvMtcR6R7yK+n/7xzphgi28KAABdQTEEXXxn31qB14f1b19UrTq7MeV5lWoXX0ALyRQXAJQO7+ovbL+mM98IdyD6LMDAAkRfasiCbwoIB+BRgA0O/Y5dByKY3EoA2hyoYlJ//B+3XPXlNej1iHFXIst3VSObTKcC+V0zJsF26je/UWOGsaDNc/dogCWhIQ//ya8MSf23rtzhJ7sj/t9cIfYZZTLmN57O6QEgBg+n8uanwtBZYWiCd96LQdR6Vp1azJ/tzJ/8zH1X1vYNhdBS4NWNp35ivKm6dw6NagsjRs5vML/fzxsAn/UHNZ+frG7SP48un3lZ//V8UZ3B41L/Q2Pk8BPQgwAKCHUcqrjWkZ8b5hBMvrs5/8Z4IA9+uUPdtl7mOf1RBI4Sj6NuyBaf0uxKdcWb2HL6IABZYnYHfHUN62+F3/hYIBD7s9CDAIkBW8SP///u52fGtrM2xOFsDKCo0vokAWAmKLtZaRj7Ke+M8MAoifrY6bkGVmNGVBrUz6t5w3o2PAl83LlddY/C5cGuye92so6M36PHwhBTQowACABgdF1SaJVP5gxfIm/5lsgFj3wLMigaq2zHgn87eblPT/oQPnwX3tjTe+7JF2BHzhJKra3Yum/C80+c88X2vyKnu2a6dX2mxJ56Af39zchB+d6NVmA9kqCuhQQKzl77afWfbkXwQAqvpeg93fpMPeF77Jo44INpzshT+ce/p/4VvLK1JgxQUYAFhx4iJeIB2JIfSwZVl3/jOTf+V7RQNSjtyLphSx6wW/tFjvP3rqupL+737aUvDr84IUKBUBUdm/0eLPa/KfCQL02VjQbqnPjUiZfeHDJtypn1jqpfw9BSiQpcBUoEOZwM+9q5/r40fW9UikQlletXRfdrtuAifuDfPeTOl+BNjz2QIMAMz2MNajuHU0/8n/J8sBxI4BLAq48OcjGQgplf9N7+5Cwutf+IX8DQUokJfAlC+xZMG/zAR/qe/VHW5E4lJe7THym6NxCa/sbMOLW5ohCmjxoAAF8hcQRf+ahnfldff/00DBKgw6y/NvlIHPkEyl8f6ZPvSOBAzcS3aNAjkJMACQE5eOXiynJISftKsWABAFBNNB3i1b6CPgbexU0v+Hj1xa6CV8ngIUUEGgbTCgyt3/THBAbBHIY36BFrMXL25uxgam/88PxGcpsAyBYGwcVabXVAoAvKrsHiDLxQtkRlJJ7Dc14v89uARfQnuBwgF7CJtOmxBk3ZdlfFr5FoMKMABg0IGF5A8hVNWoWgBALAVIjnJf+3k/L7IMMfHveXMrvC3d876ET1KAAvkLJFJpPOr2qBoAaB3gXaGFRubgzWfp/xXNUwu9hM9TgAI5Coy4H6g2+ReZANV9qxGKF2eJjicewcuPr+NrV/bgpLUNiXTxAhELDYPYveTigzGm/y8ExOdLUYABAKOOemrKrerkXwQAYr2DRuXKq19JXwA9a8pgenc3UqFIXufimylAgYUFgtEUKvMs/pe585/5LooBiroCPGYLhGMpfG9XG17a0gxvkNvBztbhIwosV0BG78QFVQMAVX2vwxnsWW6Dlv0+bzyKv6o4iz8vP43BgDbrRIllTOLuv8UWXHY/+UYKGFCAAQADDqrSpaTdqXoAINphMSpXXv1yP2lW0v9HT13L6zx8MwUosLiA2LpvuVv/ZSb8c78/7fVCbHXHY7bA026Xkv7/wdk+3jmbTcNHFFi2gNi2r9N2XNUAQKVpFey+xmW3aTlvFHf6f1B3W5n82yPazaLqGw3i/TMmiIAmDwpQYFqAAYBpCoP9kJp0qR4AiHX3G0xJne4M7j2tpP8HuhggUUeUZ6HA/AIiA6Ci3aXqEgAGAOa33n21X6n+X9nC9P/5hfgsBXIXkCGj235W1QCA2A5Q7CpQyOPjERO+fn0/hoLeQl4252udrxrF9cfjOb+Pb6CAwQUYADDqAEueAEThvlnb+X1S0X+5zyUGbEblWna/4k6PsvWfSP9Px5kmu2xIvpECWQjEEmnUdKlbA6DJ6gfv/8/GF3tli/T/l8ta4A9x3+zZOnxEgfwEBpz3VA0AVPe9AX90ZFajRKBhpY5AIo4/vHMMl4ee1TxyxsKoHO9Hr9exglfNvTehaAobT5kwNMEC1rnr8R0GF2AAwKgDLCeSCD1sUS8AUF4PEVTgMVvA+aBeSf+3Xbg9+xd8RAEKqC4gy4CYsM9N48/ncf8E63bMHahM+v/Oy1akBToPClBANQF32KxqAOCRZR3E1oKZYyISxN89uIQLA50Qk3W1j2r7IL5x+yjEdT5of4hfPl+mFAH8zcs7cW24V+3LLft83UN+fHiuD/Fketnn4BspYFABBgAMOrBKt2Jd/aoFAMJPOyCCCtMH/1GoUPRvO6pkAIQsw9M0/IECFFg5gVFnTLUAgKgn4A9zbejc0dp+yaKk/z/udM39FR9TgAJ5CqSkKJ4ObFItCNA7cXFWi2qnRvDZI2vxhaPr8CsXtmFdSxXMPvX+W97YVoMXHl7BN24fwe/fOow7o2b4EzHs623AX5Sf1sxOACfvj+BuQ3F2R5g1IHxAAe0JMACgvTFRr0WSVywDUGcrwMSwfVbDQpYhDB++CF9bL9LJ0vwHdNQ2qaz979uwF7Kkva1vZg0YH1DAIALibs5DlbYCbB8MsMDdnM+F0xfHKzvb8G2R/h+eEfSd8zo+pAAFlisgY9hdpUoAoNq8GsHYp2vcRb7OmqZyfObwO9Nfnz38Dr50YgP+rPw0boyY8p6gv1J7Ez91YgPebCyfzjCQZBl/U3Uebzbex0ouP8hWXCxd2nCyFyNTzPDK1oyvKykBBgCMPtxx03DeWQCRhm7Icyb5IuW9+43Nyt1v88Z9mLr/CAm3tovBqD3WU/cfKwYTH1eqfWqejwIUWETA7onjXkt+xQCrOtwQRQXnHjXtTry2rwMn7w8r/3gstQT4h+1OfHNzE3ZdsXJ7xLkfDj6mgEoCIgugYWh73kEAy9T1WS1yxSL49Ys7pif/MwMB4ufPH1mH37i0A5vaamAL+2e9N9sHqxvv42dPbUK399MCoeLu/1fOl2mmKGCb1Yct5838G5btoPJ1pSbAAIDRR1xOSYg09Sw7CCDqCKSDzxdQkWJxeBo7MLDrhBIEEMGAnje3YuTYFQRN/ZAlY6+5ktNpWDYfVAIAkZFPo+9G/zyxfxTQgoBYgdQ7FsLdZueylgPcb3VBBBHmOy4/tCnp7y982KRMhDec6EVVqwOReGlk+Ww9b1b632jS5r7e840Zn6OAHgXEnftH1vXLDgK0jHwEsa3gzGNXd92Ck/+5wYCfOPYu/k/1RdRMDCE15zwzzzn3Z1H877ev7sVkJAhvPIpV9XfxC2c3o9o+MPelRXks/v9w+PYQqlsdRbk+L0oBHQgwAKCDQcq7ieLufaSpN+cgQPhxGyRfcMnrR0ftEBkBvet2onv1ZmVSbP7gAByVT5EU7zdgvYDw4Bh63toK8/v7l/ThCyhAAfUF0mkZvaOhnDMBxLp/mzu2YIOstiD+cVsLXtzSrFTCF3fDRTBAPHf83jAG7CHD3lWa8saUPoslAMHI89kRC6LxFxSgwLIEfNEhPO3fmGMQYBVaRw9ASs8OYoaSCfzp/VPK2v+5k/2lHn/10k7s7K6FyCBYqvBnNJXE92pv4VculOHnz27Gn9w7iXa3dtbauwMJrD/eg3FXdFljwjdRoAQEGAAogUF+1kUpjXi/DaHqpqUDARUNiHVaIee4rV0qHIHrUROsZUfQ81aZEgjofXs7xs58jJB1+LllBHq2n7hRpfRv6t4jPXeDbaeArgVEev6EJ44HnZ4lswHutjhR1+dbsuiflJbxoxO903fBG0welF0wK2vip7MCTvYqd5fEJHmpfyzrCbi8aRLf/LAJ+z4eMGyQQ0/jwbaWhkAs6UPX+CmI7fwqTa8u+vXQ8g6GXBVIy/NnJElyGk8mR/Dio2v4mZMb8bkja7POCBBBgi8d34CXHl1Dk3MccWnxIKA7FoEnrr1JtsheEjuYGPDeU2n8B8FeFkKAAYBCKGvpGnIsgcSADZG6TiUYEKpsgPJV1Qhxxz/WO5jVXf/F+iTS40WRwLEzN2Bav+vZEoHVW9C/47gSIEj6gxCv0euRTiTRt/EjpV8xO1PM9DqObLdxBJKSjFFnFA1mHyra3RAp/uJL3O2v7nCjbTCAKV88638Q3hcT4c3PJsIi00Ac484oxPKAVR91KNkBIhjwyq42nLg3jP7xEBIp/f5NE/0T/1j+4EzfdODDOJ8O9oQC2hcQhfN8kUGYJi8pGQE15jV4YH5T+aqxvI2GoW0YclUinsp+3f54OIAdXU/xW1f34IvH3s0pECACB7974wAOmprgjIZ1E+gUAVwRwHzc6dT+oLOFFCieAAMAxbMv/pXFtn7pQPjZVzQOrEC1q4TbB2d13aysABEUGL90F+EhG8RkWm9HsG9QyXDo33FM14EMvbmzvRTIRiAlyUpxP7G9XzgmITOBz+a9mddMemLK5P4721ufq4QfS0io63ErWQHi9yIQIJYLbDptQlWLAyL9dDnXzFy7WN9tzohS/f+He9sRYPX/Yg0Dr0sBZV1/LOlFIGZDMG5HUnq+DlMuTAlJwr0xC/626gK+fPp9ZYvApZYEzPy9WN//w7rbSlaASP/X8iF2MVl3rAfiOw8KUGBBAQYAFqThL1QVEBP9QJcZoyevPcsK+KRo4MDe0/A0dEBkBWR9e07VluV+MhG8EEUPnQ/qc38z30EBCuhCYMdlizK5f9A2f5aPuGMutpgSWQFvHerCS1ubldd/b1cbjt4ZQt9oECJYoJcjk/5/5M6Qbu726cWW7aSAVgT6A25lB4DfvLwTP35sfU5ZAT92dD3++O5xnOnvgCMa0uTfCXHn/6Pr/VrhZjsooFUBBgC0OjKGbZcsIz7lglg7b9lyaLpWgEipt18rR9Q2ifScLQe1ZCFFYuh7by963tyCuJNVsrU0NmwLBdQUaOj14KVP7uyLtNLFjmhcQlPfs3WnooCekhWwuRnvnexFRfOUcjdKy1kBImsik/7fZi2t7VwXG1f+jgJGFRAFA2+MmPA/75/Cz53alFMgQGQH/OqFbXirsRydnknElqgVUChDsQxLrP2v73UX6pK8DgX0KsAAgF5HzgjtliJR+NpNGD58ESaxg4DIClhThuFDF+Bt7kIqGNJcN/1dZqX6/+C+s5Al/dzd0xwkG0QBjQuIbf9e/ahDCQL4QtmlvcqyDJFKf/XRON4+3K28VwQDfrC7HeLOumkkABEs0NoxNBnGd3e0YtW+DgQi2fVVa31geyhAgdwFRBFTMYlf21wJsRPA53MsGvhTJzbgz+6fxtWhHmUHgcVDpbm3L5d3iF1M1h7tRrZ/r3M5N19LAYMJMABgsAHVZXdEQUBx53/y1gNYPjz4rGjgG5th2XwIk7cfIGqfgpxavBptoTouChuKQIX7aUuhLsnrUIACRRJosXiVIn9LZQDM17xwLKVkBey6YlW21svUCnjv1LOsAPGPVa1kBdyqm1CyFpj+P99I8jkKlIaAqOp/tr8D/+PuCWUHgZl1AJb6WRQN/NqV3VjXUoVerwPJdOEDnSLb6vCtwdIYLPaSAvkJMACQnx/frbZA0h+Ct7kbQwfPo/ed7cpku/edHRg5dgX+joX0iNgAACAASURBVD6kgvkVw8mnvaJOQd+GvUqWQsLjy+dUfC8FKFAiAuIO25jjWVaAuDv1rU9qBfxgdxsO3BhA95AfkVjh/7Gc4U+m0th4yqTseiDawoMCFChtgZScRpPThn+uv4NfvbA956yAnz21CX9TdR63Rs3wxCMFwYwn00ph1lYLlzAVBJwX0bsAAwB6H0Gjtl+k10eGbbBfvQ/LBweUQED36i2wbjuCqfuPEZt0QpYKu+2Wr6UbPW9uxcjRy0z/N+oHj/2iwAoKiKyA9n4f9l7vx/d3P6sVIOoMvHu8B3cbJiB2HxABg0IemfR/UcgwGNFGplUh+89rUYAC8wuIv0T2cAAnLK34b7eP4kvHN+RUK+ALR9YpWxBu63wCs9+1on/b7K4o3j7SDfE3lgcFKLCkAAMASxLxBUUXSPoC8NS1YXDfGfSs2aYEA0w/2o3Rk1cR6LFCisYK0sbwwKhSr8Db0l2Q6/EiFKCAMQVE6r/dHcXNWruyZlVsIyiWCPxwT7uSFdA56IeoQVCIw+GL4+DNQVyqGdPLRiyFYOE1KECBGQJi+7+nUyP47tOb+KVzW/HZw2tzCgb82zMf4u8eXELV+ABEAUK1jwF7CLfrJtQ+Lc9HAaMKMABg1JE1Yr/S8QTEJHz84h2lEr9SNPCtMvTvPA5ndT3iU+4V30pQ1CLQ8i4FRhx39okCRhYIRZ9lBYitq8QWgiIQ8PLWZ1kBdwqUFSBqHER1tGWhkT8P7BsFtCwgMpSGgl7s723E7988jB8/mttWgj9x7F387o0D2Nldq5xHzb4WOntKzbbzXBQosAADAAUG5+VUEJDTMhIuL1yPmzCw+6SSli+CAWJ9/ti5mwj2DSKdYCVrFah5CgpQoEACYhI+8UlWwLpjPRBZAd/c/CwrYO+1foi1rVrcQaBAPLwMBSigMYFgMo4H9kG88PAqfv7s5pwyAkTRwF88txXfenwdNfYhzWwlqDFiNocCKyXAAMBKyfK8hREQ6f9B86Ay8Te9u1tZHiCWCfTvOgH3k2YkPFkWtZJlpANhJMcdiFtGETcNIW4eQdLmgBQIrXhmQWG0eBUKUEAPAiIrQBTkE6n5mawAUTxQFBG88dSuLB/ItlRAOCZhwhOHxR5Gz2gIvWMhDE1F4QkmkZIKW29AD/ZsIwUokJuAKBoosgK2dT3B16/vz7looKgt8NeV5+CKzV/kWUrH4Y0MwOZ9CvPUNfRNXsWg8z6mAu2IJFy5NZavpgAFhAADAPwcGENAFASMOz1wVNXCuu3os60EV29RlgrYLt5Rlg7Mu8BVlpGa8iDa1ItQdROC9+ue+wpVNSLS2INUAZYYGGM02AsKUEANAZEVILYLvNc4qRQKfHFzk7JEQAQF9lztR6vVi0Ry/mKo/nAKbYMBVLa7cbfFiTvNs7/ut7rwqMeLwckIxE4APChAAQrkK+BLxFBh68ffVl3Avzz5XlZZAT994j1cHep5rkhgSopizPsE9YNb8MD8JipNr876qjK9hkfW9egaPwV/dCTfpvP9FCglAQYASmm0S6WvSlaAaQAjJ65ObyU4cuwyxNKBmYecSCLWaUWwouG5Sf98gQDxumi7BXJM/QI2M9vFnylAAQrMFRDp/z3DARy8NYjv7mhVAgGrD3QiEJ693ElkBljtYZS3uZ6b9M8NAojHIjhQa/LCN+c8c6/PxxSgAAWyFUimJQwGPNjUXoOvXtq5YCDg80fWYVNbDSR5dhBSTOibhnehqu+1WZP+uUGAzOOHlrcx6CpHWi5M8dRsHfg6CmhUgAEAjQ4Mm6WCgJySnmUFlD9Rvs88ZTqWQKS+K7uJ/5ysAPG+dCw+83T8mQIUoEBBBERWgMsfV7ICRF2AmWFNMfkXaf5359ztn2/iP/e56g433IHZwYSCdIgXoQAFDC0gsgI+Hu7FX1WchSgC+JnD70x//d6NgxC/n3l4I/140r8hq4l/JgAgvotgQY/9HKQ0b9LM9OTPFJhHgAGAeVD4lNEF0mlEW0zLmvxnMgMiDd0Qyw54UIACFNCKgGU8PG+6/9zJ/kKPqzvdCEa5j7ZWxpPtoICRBERWQJ/PiTVNFfil81vxxWPrldT/mX0MxSfxpH9jzpP/TCBABAH6HbchzwqNzrwCf6YABVgDgJ+BkhRIDNvzmvxnggDx/rGS9GOnKUAB7Ql4Q0nca80u7X+hAIB4vsnqh8gy4EEBClBgJQTE5NyfiD1X/T+dTqJt7NCyJ/+ZIECNeQ3cYfNKNJ3npIBRBJgBYJSRZD+yE5BTqQWL/WUm9tl+D1U2QI4z1Sw7eb6KAhRYSYEGiy+rNf+LTf4zv3MF+HdtJceK56YABZ4XcAZ7UNX3et4BABEIaB3dz3oAzxPzGQpkBBgAyEjwe2kIJMemVLn7nwkSiGwCHhSgAAWKKeCPpFS5+58JALQOBObdNKWYfeS1KUAB4wqIrIBO2wlVJv8iAPDA/BZ3BjDux4U9y1+AAYD8DXkGPQlEW/tUDQCI7QF5UIACFCimwMBkRLW7/yIIUNHuRjLFZQDFHFNemwKlJBBLevE0j7X/mfT/md+H3dWlRMi+UiAXAQYActHia/UvEKppUTUAEKpq1D8Ke0ABCuhaoH0woGoAQAQBAhEWA9T1h4KNp4COBALRUVSrlP6fCQJ0jZ/UkQCbSoGCCjAAUFBuXqzoApnUfTW/F71TbAAFKFDSAvVm9db/Z5YBTPlYB6CkP1TsPAUKKOAJW1VL/88EAJpH9hSwB7wUBXQlwACAroaLjc1bIFhep2oGgAgk8KAABShQTIGGFQgAOPwMABRzTHltCpSSgDfSr3oAoGVkbykRsq8UyEWAAYBctPha/QuEH7aqGgAIVTfpH4U9oAAFdC3QORxUfQlAMMolALr+ULDxFNCRQDBmwwPzalWDAN32szoSYFMpUFABBgAKys2LFV0g2mFRNQAQaTEVvU9sAAUoUNoCI46oqgGASlEEUGIRwNL+VLH3FCicQDwVQO3AB6oGAMa8TwvXAV6JAvoSYABAX+PF1uYrkJpwqRoASIxO5tskvp8CFKBAXgLhmITyNpdqQQBRVFDm/D+vMeGbKUCB7AXENoA99rOqBQAeWt5BMMZtmrMfAb6yxAQYACixAS/57sopCeFH6iwDCD1ohpxkmmzJf6gIQAENCLQOqLMTwN0WJ9yBpAZ6xCZQgAKlJCAKAT4wv6lKEKDTdgKyLJUSH/tKgVwEGADIRYuvNYZA0uZQJQuAd/+N8XlgLyhgBIFANIUKFbIAxN3/NG//G+EjwT5QQNMC3ngU4dSnxUbTcgo99nN5BwAeWtbCHx3WdN/ZOAoUWYABgCIPAC+/wgIxuwOux82Q0zPyWdMyYl39eQUBou1myFJ6hVvP01OAAhR4XiAQTuJe4yTCsdkZSKIWgLiDn9nKL9fvj3u8iMR51+x5cT5DAQqoJSACjLVTo/ivt47gtLV91mmjSTcahrYtOwhQ3fcGRj2PAMz4N9+sK/ABBSgAgAEAfgyMKSBLErxNXTBv2oeeNWWI2admdVSk7kfbl1cQMNpigpxgiuwsUD6gAAVWXEDcmLfagth4yoQXNzejus0x65ri9+bxMO615F4P4FG3B77w7IDCrJPzAQUoQIE8BcLJBHZ0PcWXT72Pzxx+B1+7shuT0dCsswZiY6gf3JJzEKC6bzUGnPcgMgl4UIACiwowALAoD3+pS4GkP4jxS3eViX/Pm1thO38LqWD4ub6IIEDcOgaxlV/wft2SX6HKRsT7hrnu/zlJPkEBCqy0QCKZxv2mSfxgdxte+LBJCQIMTszzd00GbK4YHnR6ssoEuNfiRHO/H6EY7/yv9Bjy/BQoZYGBgAd/WXEWXzi6Tpn8iwDAV86Xoclpe44lknCi03YcVX2vZxUIeNK/EXZfIyf/z0nyCQrMK8AAwLwsfFKfArKMkHkI/TuOoXv1FvS9txeehnbIqUWiwbIMyRdUlgSEHs5fHDBU04xYpxWSNwiWxtbnR4OtpoCeBRy+OPZ9PICXtjbj5bIWnK4YgT+8eBZSNC4p2QAPuz3zLgsQ9QKaLH5MeuOQZi6R0jMU204BCmhOQCTjXx7qVib7YtIvvj5/ZC3+5N5JdHumFkzWl9IJOIKdaBs9iBrzmnkCAatQN7gZVsdNRBIuzfWbDaKAhgUYANDw4LBpOQik4wk4yp/AtG4nut/YjKGD5xEVaf/ZFrOSZcixBCS3H6JIYHJsSvlKuXxIx+LZnyeHNvOlFKAABRYTEGtl26w+vHWoS7nr/9q+DjT0upGSsl/fGk+m4QsnlayAEUcM4mvKl0A4LnHivxg+f0cBCuQt4IlH8L3aW/jJ4z+avuv/0yfew8a2Bwgk4lmdPy0nlQm+CAbYvLXKl7jbLwr9JSSxfCD7v4dZXZAvooDxBRgAMP4YG7+HotDf8OGLEOn+ve9sx9T9x5AiMeN3nD2kAAUMKxBNSLj80IbvbG/FNzc3YdtFC+zuaNYxTcPCsGMUoIAuBBodNnz9+n589vDa6cn/b13di2r7IKRsb87ooqdsJAV0J8AAgO6GjA2eFhBV+DOF/sRdf2vZYYQsQ5DTrM4/jcQfKEAB3QmMOSL44GyfUuhPBABu1tohUvp5UIACFNC6QExKYXvXU/zMqU3TE//PHVmLlx9ff67gn9b7wvZRwKACDAAYdGAN361UIATbxTvoeasMPW9uUQr9JX1Bw/ebHaQABYwrkE7LeNLlwg/2tCsp/2sOd6N3OACxFIAHBShAAa0LjIR8+PPy07MK/f3cqU0419+BRJpBTK2PH9tXMgIMAJTMUBulozIQ7h+FtezIs0J/P9oDT2Pn4oX+jNJ39oMCFDCsQDiWwqFbg3hpS7Ny5//grUH4QosX+jMsBjtGAQroTuDqcA9+8dxWfPaTQn+i2N8f3DoMs8/FVfq6G0022OACDAAYfIAN1T05JcFR8QS9b29TCv0N7juD2KSTBfoMNcrsDAVKT8BqC00X+ntlZxsedThZoK/0PgbsMQV0KeBLRPG92pv4iWPvTqf8//jR9Xi3pRpiOQAPClBAcwIMAGhuSNigeQXiTg+G9p9T7vr3rCnD5N2HSCd4d2xeLD5JAQroQkBsv3enfgIvb21RUv43nOzFuCuqi7azkRSgAAVaXOP4T9c+mnXX/9cubkeNfYhLl/jxoIB2BRgA0O7YsGWKgCzD19oD0/pdyl1/y4cHEeofIQ4FKEABXQt4AglsPm9WJv4i7f9SzRjEln08KEABCmhdQNzZ39ldC7Gln0j1F1+fPbIWf19zGZ5YROvNZ/soUOoCDACU+idAy/2XwlHYLtxWJv5ii7+xMzeQCvF/LFoeM7aNAhRYXEDU82u1eKcL/b26twOdg/7F38TfUoACFNCAgChHmin0Jyr7Zyb///r0+zhhaUNKZhBTA8PEJlBgKQEGAJYS4u+LICDLiAzZYNl8UJn8m97dDU9jB+Q0K2EXYTR4SQpQQCUBsZXfmYoRpcjfi5ubsf2SBf4wlzKpxMvTUIACKyiQSqdxfbgX/+7clumJvwgCfOPWEZh8zhW8Mk9NAQqoLMAAgMqgPF2eAulkEo6qWvS8tVVZ7z+49zRiU648z8q3U4ACFCiegLjrPzwZxoYTvUrK/z9tb8W9hkkW+ivekPDKFKBADgKuWAQ/rLsNUdwvc9dfpP+va6lEJMUgZg6UfCkFtCDAAIAWRoFteCYQn3Jh6OB5dK/ejN63t2PyTg3SSVaQ5eeDAhTQr0AylUZVyxRe2dmqTP7XH+/BwHhIvx1iyylAgZIRSMsyGh02fP3j/dMT/88eXouvXdmN+zYrZBHd5EEBCuhNgAEAvY2YEdsrtvfztXSj7729Ssq/dcthBM1DRuwq+0QBCpSQgMsfx4EbA3hxSzNeLmvB8XvDCEYZ1CyhjwC7SgHdCoSSCezqrsXPnNw4Pfn/4rF38cLDK7BHArrtFxtOAQqAAQB+CIorkPQFMH75rpLy3/NWGcbO3kTSHyxuo3h1ClCAAnkIiO39OgZ8ePtwt3LXf9W+DtR2u5jyn4cp30oBChROYDDgwV9VnMXMQn9i7f/hvmYkJKlwDeGVKECBlRBgAGAlVHnOpQXkdBoh6zD6dxxT7vqLu/+ehnaIbAAeFKAABfQqEI6lcO3xOL6zvVW581920QKbM6rX7rDdFKBACQkk0xKuDffil8+XTd/1//yRdfijO8fQ6Z4sIQl2lQKGFmAAwNDDq9HOSdE4HJVP0bt2h1Lob+jAOUTHpwAuJdPoiLFZFKDAUgJiKeyYI4KtF8z45uYm/NOOViUQEEswqLmUHX9PAQoUX8ATj+AHdbfxxWOfFvr7Vyc3Yl1LFQLJeFYNtEeCeDI5gorxfgQS2b0nqxPzRRSggJoCDACoqclzLS0QszswfOQiut/cAtO6nZi69whSNLb0G/kKClCAAhoVEIX+Hne68OpHHUrK/9qjPega9EMU0OJBAQpQQOsC9Y4x/OdZhf7ewX+8sgf3xqxZ/R2LSSns7anH7988jL+sOIuvX9+PV57ezOq9Wrdh+yhgQAEGAAw4qJrskkjt9zZ1wrxpn5Ly37/tKIKmAYilADwoQAEK6FXAG0woxf1Ekb9vbW3G4VuDEMX/eFCAAhTQukA4mcD2rqf48qn3p1P+xVZ/33x0FePh7Ar9SbKsZAn8l5uH0OS0KZP+6vEB/PbVvUjx33ha/wiwfaUpwABAaY57YXud9AYwfukuetaUQRT6s52/jYTHX9hG8GoUoAAFVBQQN/f7RoNYf6xHuev/wz3tqG5zQGQD8KAABSigdYH+gBt/XXkOXzi6bnry/wtnN+OouQVxKfvdSjzxKP535Tl0zKgRsKenXnmOWVBa/xSwfSUqwABAiQ58YbotywhZhtC/4zi6V29G38aP4GnoQDqZLMz1eRUKUIACKyAQT6Zxt2EC393Zqqz3f/+MCYMTYZYxWQFrnpICFFBXQBT6uzzYjV+9uH164v+Zw+/gv985hh6vY1kXEzUCMgueOj2T+Oqlnai2Dy7rXHwTBSiw4gIMAKw4cYleQIrF4ah4qqzz7169BUMHzyNqmwS4JrZEPxHsNgWMITDljWHnZatS4f/bZS24WDOGYCT7u2XGUGAvKEABPQq4YhF8v/YWvnR8w/TkX/z8bmt13kX7bGG/sk3gV86X4ZfPb8W+3gaI53hQgAKaE2AAQHNDYoAGxSZdGD50AT1vbkHvOzswdf8xpAgL/RlgaNkFCpS0QFOfB6/v71RS/sX3FrMXUjpz36ukadh5ClBA4wK1U6P4nY8P4HNH1k5P/v/Dld1KxX6xjj/f42+rLuD3bhzEW03l2N/bgL+vuYxfv7gDAwF3vqfm+ylAAXUFGABQ11PnZ5NlpKNxSN4AUm6f8l08zvquvSzD29yFvvf2KoX+rFsPI2geZKE/nX8s2HwK6F0gkUrDF07BFUjAHUggFJNyqk4dTUg4XTECccdfbPG364oVTh8L/en9c8H2U0AvAmk5hXDcAU/YAnfYDH90BEkpnFXzI6kkyjqf4N+c/mB64i/W/b/46CrskewK/WVzIZFdMHPrv2Q6jT+9fwqvN9zL5u18DQUoUDgBBgAKZ63dK8mJFBIjE4g0dCP0oBmhygYEKxqU7+JxpL5L+b0cTyzYiVQorBT3E0X+RMr/2JkbSHqZ+rUgGH9BAQqsqIAoPmX3xNFk9aOqw43yNhfutbpwv9WFinYXHvd40GcLK8GAxRoyNBHGeyd7lYm/CADca5xEIslCf4uZ8XcUoIA6AsGYHdapG6gd+AAPLe+gum81qvvewAPzW3hsfRcdtqNwBDshy9K8FxwMeJRt+X7s6Prpyf/Pn/kQxyytEFv3qXGI9f9Raf7aTt96fB0vP76uxmV4DgpQQD0BBgDUs9ThmWQZyQkXwo9aESyvR/B+3cJf5XXK65J217wZAWKNf/cbm5U1/56Gdsgpdf7HokNVNpkCFCiygD+cQq3Jh7stTtxpXvyrst0Ny3h4wVR+cbf/hQ+blC9x93/VRx0ou2hWMgKqWqfQMxyAqAuQkvJPoS0yGy9PAQpoRCCVjqPfcUeZ9FeaXsViX9V9r6NlZC+CsfHnWn93zDJrvX+m0J+sQsq/uJgIIvzx3eM4P9D53LUd0RB+6fxWnOnveO53fIICFCiqAAMAReUv5sVlGXHLCIIVS0z85wYFKuqV92HO3q7B3n4M7DmF2KQT06Vgi9k/XpsCFChJAbsnhoo215IT/5mBgbvNTjRb/RBLBeYenQN+HLs7jA/P9uEHe9qngwGZoMC3tjbjO9tbIbYBbLV4576djylAAQrkJBBP+dE2eghVplWLTvznBgUeWtbCGeyeda1UOo3v1d7CTx7/kSqF/madHIA4/x/dOY6d3bWQZ/zjT0z+/+DWYWUJgFgKwIMCFNCUAAMAmhqOAjYm3j+GYPkid/znTvxnPi6vg3j/rNoAon5Aknf9CziEvBQFKDBHwOGLKyn+Myf3ufwslgvMdydf3CwTz4vt/7yhBHpHAqhudShZAFvOm/Havg68XNaCp12uOS3iQwpQgALZC6SkKNrGDuU08Z8ZCKixvA13qG/WBW3hAOodYznVPZl1giUePJkcwa9c2IZ/fPIxjppb8M91dyCWGfxDzRUEk6yVsgQff02BYggwAFAM9WJfU/IElj/5zwQCyuuRcvmK3RVenwIUoIAiEEumUd3pzunO/3zBAas9POM+1tK4otaAJMlKgEClrNqlL8pXUIACBhSQYXXcXPbkPxMIeNq/ESKLoJDHaMiHDa0P8A81l/FGwz08nRqBJPPOfyHHgNeiQA4CDADkgGWMl8oywk/aF17rn5ngZ/E9/LQdkPgH3hgfDPaCAvoW6BoJ5j35FwEBUSwwFJ2/oJa+hdh6ClBAywKB6BhqzGvyDgCIQIB58qqWu8q2UYACxRVgAKC4/oW/esrpVWXynykYmHJ4Ct8JXpECFKDADAGxTV+u6/7nu/ufec40Fppxdv5IAQpQYOUF+iavqjL5FwEAsUNANOFe+UbzChSggB4FGADQ46jl0+ZYV7+qAQBxPh4UoAAFiikw5opBFPLLTODz/f6ox4skq/oXc0h5bQqUlEAiFULd4GbVAgCVplWY8LeWlCE7SwEKZC3AAEDWVAZ5Yfhxm6oBAHG+WcUADeLEblCAAvoR6BpWJ/0/EzgQ2wdG4lwGoJ9PAFtKAX0LhOJ2VPe9oWIAgMsA9P2JYOspsKICDACsKK8GTx6saFA1ACC2EZy7JaAGu80mUYACBhaoN/tUu/ufCQJ4Q0kDi7FrFKCAlgRE5f5MET+1vrePHdFSF9kWClBAOwIMAGhnLArTEtUDAPfrGAAozNDxKhSgwAIC9X0MACxAw6cpQAEdCDiCXaoHAJpH9uig52wiBShQBAEGAIqAXtRLhqoaVc0ACFU1AWm5qH3ixSlAgdIWaOn3q54B4I+kShuVvacABQom4IsOQ6zbV+vuvzhP1/ipgrWfF6IABXQlwACAroZLhcZGGntUDQBEGrpZA0CFceEpKECB5QuYbWFVAwBiR4F4klucLn9E+E4KUCAXgUjChUfWdaoGAAZd5bk0ga+lAAVKR4ABgNIZ62c9jfePqRoASPSPlRoh+0sBCmhMwOlP4F6LS7UgQKPFD4mZTRobZTaHAsYVkNJJtI7uUy0A8MC8Gp6w1bhg7BkFKJCPAAMA+ejp8b3pSAyq1QGobEA6HNUjA9tMAQoYSEBM1h/3elULANhcMQPpsCsUoIAeBGzeWlSptAygaXg3pHRcD91mGylAgcILMABQePPiXzHWM6hKFoA4D7cALP54sgUUoAAw7o5BbN+XqeK/3O9PTV4kU6xrws8UBShQWIFEKoSGoW15ZwGI7QQnA62FbTyvRgEK6EmAAQA9jZZabZUTSYQft+UVBBDvl2MJtZrE81CAAhTISyAty2gdCOQVABBr/10B/l3LayD4ZgpQYNkCrpAJNeY1eQQBVqHbfhZpmduYLnsQ+EYKGF+AAQDjj/H8PZT8IYRqWpYVBAg/bIXkC85/Yj5LAQpQoEgConBfvXl5WwKWt7kgUv9l3vwv0ujxshSggCynMeZ9ggfmN5cVBGge2Yt4KkBIClCAAosJMACwmI7Rf5cOhBGu7cwpCBCp6+Lk3+gfDPaPAjoWEEGAthwzAao73bB74pz863jc2XQKGEVAliXYfY14bH036yBAlek1dI+fRjzFmzNG+RywHxRYQQEGAFYQVxenFssBRCX/0MPWRQMBoYctiFtHIceZHquLgWUjKVDCAqIo4JgrhidLFAYUKf+dQ0EEo1IJa7HrFKCA9gRkhOIT6LafwQPzW4sGAkTdgAl/C8ROAjwoQAEKZCHAAEAWSCXxErGePzXhgijsF20xIdpsUr7HegaQnHA9W+/P3NiS+CywkxQwioAo5ifW9JvGQmjp96PJ8uyrfSiIYUcUoZgE7vZnlNFmPyhgPIG0nEI44cCo55Fyh79t9CDEV/vYEVgdt+AOW5CSuBuT8UaePaLAigowALCivHo9eToNKF9cDKvXIWS7KUCB2QJiop9Oy8oXY5mzbfiIAhTQvoAMGSIg8OyLWUvaHzG2kAKaFWAAQLNDw4ZRgAIUoAAFKEABClCAAhSgAAXUE2AAQD1LnokCFKAABShAAQpQgAIUoAAFKKBZAQYANDs0bBgFKEABClCAAhSgAAUoQAEKUEA9AQYA1LPkmShAAQpQgAIUoAAFKEABClCAApoVYABAs0PDhlGAAhSgAAUoQAEKUIACFKAABdQTYABAPUueiQIUoAAFKEABClCAAhSgAAUooFkBBgA0OzRsGAUoQAEKUIACFKAABShAAQpQQD0BBgDUs+SZKEABClCAAhSgAAUoQAEKUIACmhVgAECzQ8OGUYACFKAABShAAQpQgAIUoAAF1BNgAEA9S56JAhSgAAUoQAEKUIACFKAABSig1ysvuAAAA8xJREFUWQEGADQ7NGwYBShAAQpQgAIUoAAFKEABClBAPQEGANSz5JkoQAEKUIACFKAABShAAQpQgAKaFWAAQLNDw4ZRgAIUoAAFKEABClCAAhSgAAXUE2AAQD1LnokCFKAABShAAQpQgAIUoAAFKKBZAQYANDs0bBgFKEABClCAAhSgAAUoQAEKUEA9AQYA1LPkmShAAQpQgAIUoAAFKEABClCAApoVYABAs0PDhlGAAhSgAAUoQAEKUIACFKAABdQTYABAPUueiQIUoAAFKEABClCAAhSgAAUooFkBBgA0OzRsGAUoQAEKUIACFKAABShAAQpQQD0BBgDUs+SZKEABClCAAhSgAAUoQAEKUIACmhVgAECzQ8OGUYACFKAABShAAQpQgAIUoAAF1BNgAEA9S56JAhSgAAUoQAEKUIACFKAABSigWQEGADQ7NGwYBShAAQpQgAIUoAAFKEABClBAPQEGANSz5JkoQAEKUIACFKAABShAAQpQgAKaFWAAQLNDw4ZRgAIUoAAFKEABClCAAhSgAAXUE2AAQD1LnokCFKAABShAAQpQgAIUoAAFKKBZAQYANDs0bBgFKEABClCAAhSgAAUoQAEKUEA9AQYA1LPkmShAAQpQgAIUoAAFKEABClCAApoVYABAs0PDhlGAAhSgAAUoQAEKUIACFKAABdQTYABAPUueiQIUoAAFKEABClCAAhSgAAUooFkBBgA0OzRsGAUoQAEKUIACFKAABShAAQpQQD0BBgDUs+SZKEABClCAAhSgAAUoQAEKUIACmhVgAECzQ8OGUYACFKAABShAAQpQgAIUoAAF1BNgAEA9S56JAhSgAAUoQAEKUIACFKAABSigWQEGADQ7NGwYBShAAQpQgAIUoAAFKEABClBAPQEGANSz5JkoQAEKUIACFKAABShAAQpQgAKaFWAAQLNDw4ZRgAIUoAAFKEABClCAAhSgAAXUE2AAQD1LnokCFKAABShAAQpQgAIUoAAFKKBZAQYANDs0bBgFKEABClCAAhSgAAUoQAEKUEA9AQYA1LPkmShAAQpQgAIUoAAFKEABClCAApoVYABAs0PDhlGAAhSgAAUoQAEKUIACFKAABdQTYABAPUueiQIUoAAFKEABClCAAhSgAAUooFkBBgA0OzRsGAUoQAEKUIACFKAABShAAQpQQD0BBgDUs+SZKEABClCAAhSgAAUoQAEKUIACmhVgAECzQ8OGUYACFKAABShAAQpQgAIUoAAF1BNgAEA9S56JAhSgAAUoQAEKUIACFKAABSigWYFT/x+k0p0yDAA5iAAAAABJRU5ErkJggg==)"
      ],
      "metadata": {
        "id": "EgJ2-07w1l-z"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "There are a range of algorithms which can be utilized to understand and traverse a graph.\n",
        "\n",
        "Our focus today is understanding how these types of techniques can be used to support modern mapping software, especially the navigation tools embedded within your smartphone, as well as infrastructure planning approaches, as explored in our class tasks."
      ],
      "metadata": {
        "id": "ulFkHQs_4dHM"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Kruskal’s Minimum Spanning Tree (MST) Algorithm\n",
        "\n",
        "A minimum spanning tree (MST) is a network graph with a weight less than, or equal to, the weight of every other possible graph specified between a set of nodes/vertices.\n",
        "\n",
        "Here we will apply Kruskal's algorithm to find the MST for a connected, undirected graph.\n"
      ],
      "metadata": {
        "id": "sciDSutBVgIy"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Our Objective\n",
        "\n",
        "*To unify all nodes/vertices with the minimal edge weight, avoiding any cycles.*\n",
        "\n",
        "Importantly, when we say \"avoiding any cycles\" in the context of graph algorithms, we mean ensuring that no sequence of edges forms a closed loop.\n",
        "\n",
        "So if you start at a node and follow the selected edges, we do not want to return to a node without retracing an edge.\n",
        "\n",
        "Take the example below, with the full graph on the left (e.g., a full road network). Next, we have a spanning tree in the middle (non-optimized path). Finally, on the right we have an MST providing the lowest total weight to connect all nodes/vertices.\n",
        "\n",
        "(Figure credited to Terun Jain, 2022)"
      ],
      "metadata": {
        "id": "qGsVZeBVuGgF"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "VUip6or9us8U"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "For the sake of this example, you can consider the weight of each edge as representing the distance to travel along a transportation network between locations (e.g., so the weight is a cost incurred, which we want to minimize).\n",
        "\n",
        "Kruskal’s algorithm undertakes the following:\n",
        "\n",
        "- Sort all edge links in ascending weight order.\n",
        "- Pick the smallest edge.\n",
        "- Check if it forms a cycle with the spanning tree formed so far.\n",
        "- If the cycle is not formed, include this edge. Else, discard it.\n",
        "- Repeat this process until there are (V-1) edges in the spanning tree.\n",
        "\n",
        "See the input graph below containing 9 vertices and 14 edges. We expect the final spanning tree to consist of 8 edges."
      ],
      "metadata": {
        "id": "XFS3sJsuuLxd"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "rOufEbyaVI0M"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "2qJZsV1kqlms"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "pRSYrvC1qhG6"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "fqY1-HQwqswC"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "isHDdhYfqvhL"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "hSrlMrvBq0wy"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        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pNSJiv6lGRNqq2qMtRr9sO3NKc/r90y9JnKShotGtVbfYvNj/xfzvUsalEM8QNYHa87LnQ04MSRIntdNuN8xsWGh66Ja7W+7n3T87/KxipxPR/PD5FzMuttNuF5kVeS713Ohzo2+Nv8Xn8TvrdX7f+v3BxoMFPIGbmVvY07DC8kITTZPu+t0Vw3orC0kPuZJ5paNuR47j7ufdnxg08eroq72MehHRtxHfrolew+fxh7cbnluWezrldFhmWNS4qCrfle8Fv3c8+bi2qrarqWtMTsyRxCPhT8PvTbzH9q/XRS/2xRgrHauEgoThZ4ZXmL3GCarfmBpnx5lTy+7Te7SffUy2EFmwmzzdz7uv3Kn1fcz3ErlEha9yfcz1iLERUeOjEsWJykuocYLK5xNPS5620WgTMz7mgOuB0JGhfB5/W+w29lmyxqVtuL1BIpcIeILwMeHR46OjxkWxreXz+LVZfjUSxYlfX/+anUxUOG+oIC4vjr+Db/6n+ZknZyZZTbrgeaE2t+5lnwrTi9OtdazvT7ofNznO2cSZfUyuPPGHNh8ud1jOHu9y3qUcovmS/DxJXs4HOU+nP2W/RqZYQj1eu4yTvWv2rqJnL0+SF/Y0TFtVu1/rfsqTze48mw0uWH9rfevdrXse6Tk/fP6J5BMvu6hTGwceH2ir0bZ3694RYyPODj87u/Ns1n/I/rrv0T4immkz8+qYq2c8ztybdK9P6z6G6oapRamVF7W299rh5sOTC5Pb/9m+88HOX1z5orVG630u+6o8vpfKStntYESqog9DP9TbqacdoO0Z6PmyDu3V0auTxElCvjBybGTkuMiIsRECniD8aTjrYziXeo7juPba7UM8Q467Hd8xeAd78nHBY1K62BybF/vwvYcRYyPYJ7+7uXcjsyKJqHfr3ntd9s7uPFuVrxo4PJBt8DCzYYHDA0e2H/my0l1/dj16fPSdCXeuj72uwleRyqUb72xk53DsTjRre6894X4ibHTYBKsJ+ZL8VVGrquzAuJ17u712+58H/vyP2z/XxlzjES+zOPNo4lEielTwiCXHex3ee/Teo/jJ8YONByvfy6bGCarfmBpnRzg1IkV3E28Hr3JfWXOQJ8lj98WYaDWRvSXYFQjlrb2YcZGInI2d2QWGTrqdKowjqnGCClhfv1s7N3ZVo4d+D1s9WzknZ8/XuLRLGZeIaIjxEHayYqtnW+Ezb/XLf5m7uXcHHx/8tOSpSFW003knn8eXc/Jrz64p/qvy23Kl0tIEccKjgkd1Kjs7MxDwBOx3KYulxc9KntV+djkn/6HvD7pCXUN1Qy8bL+Ul1OO1cxzHvkLOTsXOpJyRyqVuZm5CwX/GrRlrGl8fe316x+naqtoyThaVHeV/13/U2VHmf5ofTjxcv+a3qd+mpKlJ18Zcyy7NTi1KZferTC1KZR2MrIPu7JOzv9z/JT4v3kjd6NqYa8fdjlc5wESNr2ajayNSFT0vex6XF8cRZ6plys6kK+9HxR2cfW767H64m4iKpEWnUk69e/pd5d8KUGAHa1cz1y6tuhBR11Zdz404d8L9BDtrnNxhctLUpKSpSQZqBqlFqQZqBopjt/JC5nady3rwJneYzJ5JKkyq9zt3rMVYdisAewN7Z2NnIgrPDCeiwCeBrF+UvaNZjwjbuZUX0l67feKUxKSpSeMsx6UVpck4GWs2bMsvpl9kk33R9QsWsV/ZffWfN35NE1S/MTXOjm69Fu1wwmF2G8AxFmOkcimf+CPbj9z7cO9fj/9a23stmyajOEPRq8NUuIltjRMoK5eXs+l3P9it/FPCRMS+2lzL1Sn3UXTS7VT75VfpcublUYGj8iR5rdRanfY43UO/Bzvi9zv279nDUvul/+v94u6INno2BR8WpBWl+UX5/fnoT48zHtHjorvpd6tNzXnE66DTgT1mg1DYumq/13jEY8lNRKZapool1O+1E1F3/e6WIstEcWJUdtTJlJNEVGUfl6XIcvc7u8vl5ZFZkVcyr5xNPRuSFvKs5Nm0kGn2E+0VL6r2EsWJC68uDHwSWOH0SyqXkoAWdl/IRlHOuTyHiNpotBnVftQyh2XKbUNhRuiMQwmHOul2uvbuNXNt81/u/7L42uKx58ZeHnXZzsCuwn5cZr+MPdYT6t2ecNtMyywgPmDWxVlJ4qT9j/ezvFc+s0wuTCYiC22Lf3sRTVyUL9t8E/FNQHyA8lUo1hSV/6loxvXb6RUot3lWELbrUwpT2JNW+//TiZdblptTmsMuKivbHrt9bcxaxVzKW55enP5i+TqWihUJeALFRcEaJ6h+Y2qcHeHUsvv0Hr8YON7pQCfl55PESdeeXevbui+7uFJhrgqn3jVOUOHAyh7YG9gPMR6i/KferXvXfnXKQ/OVh3HXuPzK2G1ESqQlnXQ7nXA/ofy2r/pUgzjWI2SrZ/v7kN//Tvi7XF5+IOFALcOJz+MLeIIKW1u3rgMen50TsNOvV3ntCqMtRm++szkkLeR86nkBTzDCfESV4w+JSJWv2q9Nv35t+i2xW3Iy5eTIwJGlstJTKafmdZtXp1fBETfm7JjbubdNNE1WO6020jA6mXxS+Sekexn1ujvx7o77O4LSgmKyY56WPP017tcTKSdujLnRTrtdhQ6AQwmHiOizrp+xk5sve3y5LmZdVmnW7oe7fzCo+O0rkapIXaBeKisdbzmenYd52Xh9efXLPEnevef3Kp9ZvmhmJK/yhSy9sXTr3a2qfNW1vdd2adXlSeGTL8K+qLJur7LTK7eBf9s/yRWdxgpzusxR46tV7lVWdiTxyKdXPiWiWbazRpiPUOWrTg2eKi4Xv+x9zRGn/GSNE1S/MbWfHeHU4mQWZ4amh740tx7tZ+FkrGmcVpSmfOGnwq/61jjBf3YeX8VE0yS9ON1Gz2Zz/82VJ6hxaW002mQUZyhPoHxaUOPyK3e7jzo7qkRa0rt179Pup5U/WmqranOz//NWicqOGnV21LOSZwddD7LORj6Pz95OLxtF1qRvjDq+9v+EU/vRm+9s/jn256zSLGcT5wo/H5Nblvvl1S9j82KnWk+d322+4vmhJkN5xOOIyy7NruvWJomTbufeJqLFdovZPZGvZF6p3O+0xmnNGqc1ZbKyM0/OTL8wPbM482DCwQrfE1esXREARCTgC9iWV96PLL+vPbum+PAu5+RSTlp9VZWv2/0R/8fTkqe2erZjLMawwd8e7Ty+tv+alO4f3aiU2zzbMDaEp73oxTW2+d3m2+rZVr+Qf5L/ISJdoe6vg3/lEa9IWqR8MqcYE5RYkMgeP8h/oPxBsMYJqt+YGmd/E2FARMM4mHCQnUFHjI3gZnOK/zzaebC/soYysO1AIgrNCGXjDu7k3mFDjRVqnKCC4ebDiehUyinWW5Jdmu16ynXMuTERWRG1WVr/Nv3ZBOyjfezzWOXv6NS4/ApmX5r9vOy5pormb4N/K5eXZxZnsv8Unx+VdW3VNV+SXy4v/+bGN5FZkU8Knyy+tpid2Nkb2DdG2LAHT4qe1HKWOr12ZYOMB+mr6bPIH92+Yp+evpp+ZHbkjWc3vrnxza9xv2YWZxZLi+Pz4j+78hnLZjZOrE4UJ8SsTy+lMOX3uN/ZM4XlhTJONuH8hE4HOp1PPU9EagK1ke1HVjmEkojMtc3Z5Zy/E/5m16supF9g31hS9H9W8J71e0R0KOHQieQT4nLxmug17EJUhWEgzCiLUWyZbDBn7PPYOZfnLLuxjA15YC+EvYpyefnq6NWKV1HvnV7j7UCPJB5h+RSVHaW4CktEbmZu7KRqW+yL8Z+b7mx69/S7Vd7shm05R5xEJiEi35u+7IDAtpy9E4nI/64/O6dZG7228hu/mgmq35gaZ0c4teA+vUf7ichWz7bCkWVGpxkvzqsyQoloUfdFAp5AKpf2PdbX4bCD01EnNnRb8Rmnxgkq8Hb0NlA3KCwv7P5398HHB3c+2Dk4LfhJ4RM7A7tara7HIj6PL5VL+x3r1/1Qd8cjjqwnp5bLV5ZalHou9RwRFUuLexzqYbzXWPGf703fyluuJlD7acBPRHQ/777TUSfzP8233t1KRF1adZlqPbXBd5Cig3HM2TG9j/au/CNhda1tNVhX3otjcftRlSfY6byzlVqrYmnx7EuzjfcaawVo2R603flgJxF5mntWM67sZax0rKx1rInIL8pv7LmxTked3rd+nx2ax54beznjsqmW6cP8h56BnkNODBkROKLTgU4P8h+0UmulGFCgIOQLV/RcQUSh6aGme007H+w87NQwIjLTMvusy2dVrn1O5zmOho4SuWTU2VE6f+isiFxBRH1a9xlrWcXNQXwcfUw0Tcrl5b2P9u51pFevo70kcom9gT37Vhwb63g29az7aXe7Q3ZsOUS0PGJ5PX5wgO30kPQQh8MOlb/kp3gXdG3V1f6wvcNhh/7/9JdxMjWB2mK7xSyn2Wnl1rtbu/7d1emo06Kri4LTgp1aVzH6lG15gaSg/z/9h5wYEhAfMLPTTCL689Gfn1/53FbPlu3WgwkHrfZbWf5peSf3DhuVyjoSa5yg+o2pcXaEUwvFrioR0fSO0yv38LBBOyy9erfu/fewv9mgryJp0dYBW9kVY444NrSpxgkqf869Pub6FOsp6gL168+ua6tqL+qx6ILnBXZbsxqX1r9N/4OuB1kvQam0dHO/zewHtBRd6tUvv8oP77U3o9OMoBFBrqaubTXbqvJVLUQW87rNuzzqsuLrLA2oS6suPj19Wqm1KpGVSOSS2lyrqP1rr6Jnz2I0EXXT71blF2J6GvaMHBv5WZfPbPRsNFQ0BDyBgbrBOybv7Bi845jbsXpcRxHwBEfePTLYeDCPeJFZkXO7zt3Yb6O3o7e2qvaD/Adl8rJN/TZt7Lexm363O7l3QtJCiGh259kRYyOqHK23uMfiU+6nXExchAJhcmFyR92OC7oviB4fbahuWOXa1QRqwZ7Bc7vNNdUyVeGrtNNut6D7gvMjzitfw1Noq9n2+tjrH9p8qKemdzv3dmv11l/2+DJ0ZCgbT/hDvx+mWk/VV9O/kXWjd+veJ91PrnBc0UajTXpRej16O/16+fUy6iXkCzOKMzQEFb+foBg58nHnj9f3Wc++6utg6HDK/RT7UgERfd/n+20Dt9kZ2D0uePwo/5GzifNpj9NsmFzlxuzT08dMyywuL06FpxLqGerT06ebfrcSWQk7Kdz9zu5pHaeJVEW5ZbmOho4n3U+ysYhF5S++9F3jBNVvTI2zv3F4HMf5+vquNF7ZcrJkZc+VPj19kKlV+vLalxtvbzRSN3o24xmqAQBNzNfXl4h8fHxew5kTj3jTOk47N/zc0+lPS2eVJkxJOOl+0r2dO/ZK0zuYcNDpqJPpXlP2ZczC8kJ2RXpA2wEoDgC8Rk09Wk9LReuY2zFXU1fFM5YiS0uR5QjzEbsf7P4g9APskqbU07Dn44LHz8ue2x+279O6z+2c26lFqRoqGiscV6A4APAaNfWZ0z6XfcrJpGxGpxkVvrIHja2DTofLoy6/1+E9Nb7a+dTzZbKycZbjwkeHOxg6oDgA0FLOnIabD1d8W/50yunF1xY/KXribOy8x2UPu9HyErslAfEB2CtNqWurrvuH7kcdAKDlhpPil2ke5j8cd34cGy1zMuXkxPMT22m3e1L4pMrbUAIAAMKpsWiraituqv9r3K/KdwALSgvCngAAgNcQTt31uyu+IHL92XULkcWcznOcWjtpqmgmFCQcTDiIn60EAICmDicbXRvF4y6tupxyP6X4qem+rftOtZ56JPHIlOAptfnqPgAAvN2abrSe8m1AN/XbpEgmhXGW49b0XoNdAgAATRdOWipaisfqAvUtd7e029eu9e7Witt9EtHcrnNfdosUAABAODU85R8XuZB+YUH4gtSi1KzSrB9u/6AYPq4mUFMMmgAAAIRTo1P+acvTKaeV/6T8Mw3V/PArAAAgnBqY8u/olMn/80vST0ueKh6zmxMDAADCqSnczrn97+mRzn9Oj9potFE8fl72HHsFAADh1EQeFTx6mP+QPZ5iPYX9EBbDfqWbYb/ZCgAACKcm8lvcb+yBobrhny5/ttVsq62q/VmXz9hPRhJRVmnW5czL2CsAAC1ck95bb8vdLTNtZnbW68zOlsZYjOGIU/7dz5WRK6v8vVcAAMCZU2Mpk5W5nXaLz4tXPKOcTD/c/mFb7DbsEgAAaOofG3xS+MTusN1nXT6baDXRVs9WW1U7qzQrLDNsW+y20PRQ7A8AAHgN4cTOnzbd2bTpziZUHwAAqsRHCQAAAOEEAACAcAIAAIQTAAAAwgkAABBOAAAACCcAAGhpVIgoVDu0Rb3mlTdXrry5EvseAKC5cddy71vUF2dOAADQHCGcAACg2VEhIudCZ+dCZx8fH5QDAABeI19fX5w5AQBAM4VwAgAAhBMAAADCCQAAEE4AAAAIJwAAQDgBAAAgnAAAAOEEAACAcAIAAEA4AQAAwgkAAADhBAAACCcAAACEEwAAIJwAAAAQTgAAgHACAABAOAEAACCcAAAA4QQAAIBwAgAAhBMAAADCCQAAEE4AAAAIJwAAAIQTAAAgnAAAABBOAACAcAIAAEA4AQAAwgkAAADhBAAACCcAAACEEwAAAMIJAAAQTgAAAK9CBSWABpGSnxKUEBSSFBKVHpVRlCEuE8vkMgFfIFITGWsZO5o4uli4uFq5muuao1aoM+oMCCdodAHRAVsjtsZlxakKVcVSMfGJeERqRDyScbI8yssrzLsfd//4o+PlknJbI9u5TnO9HLxQN9QZdYZq8DiO8/X1JSIfHx+UA+pke+R271Dvcq48X5ZPgtrNIyNdga4qT9XP2W9OrzmoIeqMOoMyRR7hmhPUR3RGtP0v9ssuLMuWZedTrd/JRCSgfMrPlmUvu7DMYYdDdEY0iok6o85QGcIJ6tPv4bjD8VburTzKq2cL4lMe5cXkxDjucAyIDkBJUWfUGRBO8ErWXF6z4OwCUm+I65UqROq04OyCNZfXoLBvfZ1zcnLc3d15/+Xu7p6Tk4M6A8IJXvWdvD58vZgvbrCGwycxX7w+fD3ez299nQ0MDAIDA7n/l52d7ebmNn36dAMDA9QZEE7wSr0f68LW5fPyidegy+VRPi9/Xdg69Ie0qDpv27bNwsJi3LhxqDMgnKD+ojOiZx2fJeaJG/id/P/vZzFPPOv4LFxPbiF1DgsLO3z48MKFCzU0NFBnQDhB/Xmd8CJhY7YXPpGQPjz+Ier81te5pKRkz54948ePt7GxQZ0B4QT1tz1ye1J+UqN/Y1uFkguSt0duR53f7jqnpKQkJiZOmjQJdQaEE7wS71DvPHleE6woT57nHeqNOr/ddY6MjLS0tDQ3N0edAeEE9RcQHVDOlTdRS+FTOVfeMq8kt5A6l5SUXL58edCgQa/rahPaM8IJ3hJbI7bmy/KbbHX5svytEVtR57e1zsXFxUlJSRYWFqgzIJyg/lLyU+Ky4upwN5dXJ6C4rLiU/BTU+a2sc3Z2NsdxhoaGqDMgnKD+ghKCVIWq9Zhx1cBVZYvKUj9NdTF3qeu8qkLVoIQg1LlG97zucUs4bglXtqhs1cBVb0Sds7OzeTze6wqnetR5etfpBfMLWJ3ved2rx0pbYHtGOEGjC0kKEUvFdZ3LxdzFq7uXUCCs30rFUnFIUgjqXGMydTHowh4LBcKlvZfWNZ9eS50HDBgQGBj4uu4KUdc6u5i7rB28ViQUsX92MehSj3xqge0Z4QSNLio9qq5tZHrX6cfGHjPVNn2VVhmVHoU6V1/kdqJ2EpnE76rf0AND0wrThAJhf5P+qHPD1tnZ3NlIw0gsEc84PcPvqp9EJmknaje963TUGeEEr1lGUUadvkI/vev0n1x/EglFOSWvcDdPHmUUZaDO1RjSbohIKMoqyQpNCQ1JCYnLiUOdG6POK66sUNuoprNFZ8+9PeyZAklBmjgNdW4C+CVcqLZHokxManWbpUxWtvnqZhNtk1ndZ73SelHnl/so8KOPAj9ij13MXWwNbCUySXh6OOrc4O2ZCZoUNLT9UIlMEnAnICQlBHVGOMFrJpPL6vRJc8+9Pewz5m/uv73KmZNMLkOda2mr61ZTbdPYnNgVV1bUo848X17LatP1ernG2sZEJBQIx3caX78642CCcIKGJOALZJyMmvjwxZGAL0Cda4MNi0grTJsbNLd+dZZ6S1vQ8c5PpX517hrQ1cXcZfeI3V0Muvzm/pvitBXtufHgmhNUR6QmalHrfbPqrEimGadm1KOvCXWuUdCkIMUIcsW1PQsdC9QZ4QSvmbGWMXFNvlaOjLWMUecaj5tdDLqIJeJll5bVL5lQ5xolFSQRERuhx67tKZ5EnRFO8Do5mjiSvMnXKidHE0fUuRqrBq4aZDaIiERC0e7hu9lXRIMmBaHODVvnP2P/TCtMY0UOnhxsqm2aVpj2Z+yfqDPCCV4zFwsXkUpT90iIVEQuFi6oczX6m/Sv93ecUefaTx+SEjLj1Iy0whdjx+vXg9oC69wgMCACquNq5VouKae6HwaVxzrXVbmk3NXKFXWubvqDDVAf1LmW+WT2sxnqjDMnaF7Mdc1tjWypKcfBysjWyNZc1xx1Rp1RZ4QTwEvNdZqrK9BtstXpCnTnOs1FnVFn1BnhBFAdLwcvVZ5qEw2LkJMqT9XLwQt1Rp1RZ4QTQA38nP30+HpNsCI9vp6fsx/qjDqjzoBwgprN6TWnvU57auw7CUjJQtdiTq85qDPqjDoDwglq5Y9Rf5CEGrEzRE4koYCRAagz6ow6A8IJasvB2OH3Ub+LOFGj3DCCIxEn+n3U7w7GDqgz6ow6A8IJ6sDLwWuMzRhNqWYDv5850uV0lw5YiuvGijovHbBUl9Nt8DprybXe7/4+6tzYdUZ7RjhBkzr14NSe23vGdx4vkosarD9ETiK5aEn/JcsHLUeFFZYPWr6k/5IGr/Mwy2HRGdEob2PXGe0Z4QRNmkye+z1PTjm5e+zuzW6bqZQa4HqylKiUNrttxju5yuNmg9f56OSj1vrWS4OWoryNWme0Z4QTNHUyjeg0goi8HLyiZkfZG9jrkV49P3LKSY/07PTtomZHoffjZRqjzv4e/n/e+fPMozMob6PWGRBO0NTJxDgYO0TPjl77zlpDgaEu6dbhfjAy0iVdQ4Hh2nfWxnwSgyvG1WvwOutr6Pt7+M87M6+4vBjlRXtGOMFblUwKc3rNyVqctdF1o72+vbpEXUQikhLJiTh6cZGZPZATSUlEInWJur2+/UbXjVmLs/D9j9pr2DqPtR07vOPw+YHzUVi05+aMx3Gcr68vEfn4+KAcUPtkqiAlPyUoISgkKSQqPSqjKENcJpbJZQK+QKQmMtYydjRxdLFwcbVyxR0wX1FD1dluu92S/kum9ZiGkqI9NyuKPEI4QQMkE7zOD5i+PM6nzqOhLyZfHPvX2Nuf3jbTMUMNoRmGE7r1AMnUEg1pP2R+3/nzzsxDKaB5QjgBkqmF8hnik1ea53/dH6UAhBMgmaAZ8ffwXxC44FbmLZQCEE7QKPz8/Pz8XvXm/EimlqZb627+Hv7zAtG5BwgnaARhYWErVqxAMkE9fNH7CyNNI59QjIcChBM0qJycnB9//PHdd99FMkH9+Hv4b4vYdiHpAkoBCCdoGCUlJcuXL/f09Bw4cCCSCerHRGTCbhsh5+SoBiCcoAEcOXKEiMaNG4dkglcxpduU/u36Y2Q5IJygAcTHx+/evXvhwoUaGhpIJnhF/u7+5xPOH4o9hFIAwgnqr6SkZNOmTTNmzLCxsUEywatTU1Hzd/efd2ZednE2qgEIJ6inlJSUa9euTZs2jcfj8Xi8FStWrFixwt3dPScnB8kE9eNm7TbTfiY69wDhBPVnY2MTExPD/b9Vq1atWrUqMDDQwMAAyQT19t3Q75Lykn65+QtKAQgnaFJIJqiev4f//MD58TnxKAUgnADJBFXw8/Pj/b+wsLCmWWkvk16r31mNzj1AOEED8Pb29vb2RjK9ZcmUlpZWXFzMcVxcXNznn3/eZPm0uP9ioUC49spa7AVAOAHOmeBfOTk5YWFh06dPZ98TsLGxGT9+fEhISJNtgL+H/3eXvwt/Eo59AQgnQDLBCwYGBoGBgQMGDHhdG2CpZ8luG4F9AQgnQDJBdSdSVlZWTbnSD+0/7Nq66+Jzi1F/QDgBkgkqYndQtLCweJX7VNWPv7v/odhDJx+cxF4AhBMgmeA/ybRw4cKkpKQ1a9bU+z5V9aarrst+8ElcJsa+AIQTIJngP8m0b9++2ny9ujGMshk1xmYMfpAQEE6AZIJ/k4mIjh49+rqSidnotvFW5q1dt3ZhpwDCCZBMLd2GDRuIaNOmTU3fm1cZG7mXnJ+M/QIIJ0AytVzx8fGHDx/+5ZdfNDU1FTeJmDNnTklJyWvZnoHmA78a8BVGlgPCCZBMLVqFG/sy27dvf41nUcsHLS8uL954dSP2DiCcAMkEzYi/h//SoKVRGVEoBSCcAMkEzUVnw87sBwlRCkA4AZIJmpFPnT410zH7NuRblAIQToBkgmbE38P/t6jfzj8+j1IAwgmQTNBctNZq7e/hP//s/HJ5OaoBCCdAMkFzManrJOf2zrj4BAgnQDJB8+Lv4X8p+dKBewdQCkA4AZIJmgsVvgq7bURmYSaqAQgnQDJBczHUcujsnrPRuQcIJ0AyQfPi945fRmHGtohtKAUgnJBMSCZoRtjXcmOzYlEKQDghmQCaCwdjhw3vbkDnHiCckEwAzcuCvgu0hdp+l/xQCmgoKihBI0nJTwlKCApJColKj8ooyhCXiWVymYAvEKmJjLWMHU0cXSxcXK1czXXNkUzwKu2KiFT8VOrRrhqWv4d/j597OFs4DzIfhN0ECKfmKCA6YGvE1risOFWhqlgqJj4Rj0iNiEcyTpZHeXmFeffj7h9/dLxcUm5rZDvXaa6XgxeSCZqyXTU4c11zNrI8+pNo7Cx4dejWa0jbI7cbbTBaFLQoJjemVFgqJjGp0IuDCI+I/v8Bn0iFxCQuFZbG5MYsClpktMFoe+R2JBM0TbtqJDPsZjgaOy48uxC7DBBOzUV0RrT9L/bLLizLlmXnUz4Jaj2ngPIpP1uWvezCMocdDtEZ0UgmaNR21aj8PfyPxx8/FncM+w4QTq9fQHSA4w7HW7m38iivnhXlUx7lxeTEOO5wDIgOQDJBI7WrxqalquXv4T8/cH5eaR72ICCcXqc1l9csOLuA1Bvi+p0KkTotOLtgxtEZSCa0qwZvV2sur2mCLR/RccSkrpNecWS5n5+fnx/G/iGc4BWOIOvD14v54gYrJJ/EfPGR+CPTe0xHMqFdNWy7Wh++vmnyaf2w9XE5cfU+VwsLC1uxYgWaAcIJ6ikgOmBd2Lp8Xv6Li9INhUdF/KJj8ceaph8GWk67yuflrwtb1zTtit024nHu47rOmJOT8+OPP7777rtoCQgnqI/ojOhZx2eJeeIGPoL8/3FEzBPPOj6rya5jA9pVw+pr1vfbwd/OPzu/TnOVlJQsX77c09Nz4MCBaAwIJ6gPrxNeJGzM+vGJhPTh8Q9RarSrN7RdfT3wa6lMuj58fe1nOXLkCBGNGzcOLQEQTvWxPXJ7Un5So3+DWYWSC5Kb8nsqgHbVsPw9/FdcWBGRHlGbiePj43fv3r1w4UINDQ00BkA41Yd3qHeePK8JVpQnz/MO9UbB0a7e0HbVyaATu21EjVOWlJRs2rRpxowZNjY2aAmAcKqPgOiAcq68iSrHp3KuHCMj0K7e3Hb1sePHVq2svg76uvrJUlJSrl27Nm3aNB6Px+PxVqxYsWLFCnd395ycHLQNhBPUytaIrfmy/CZbXb4sf2vEVpQd7erNbVf+Hv57bu8JfBRYzTQ2NjYxMTHc/1u1atWqVasCAwMNDAzQNhBOULOU/JS4rLg63EXm1QkoLisuJT8FxUe7ekPblYGGAevcK5WWYl8DwqlRBCUEqQpV6zSLi7lL6qep3BKOW8KlfprqYu5S15WqClWDEoJQfLQrZasGripbVMbaVcH8guldpzfndjW+83h3a3f8ICEgnBpLSFKIWCqu0yxbXbeaapuyx6bapltd69yXIpaKQ5JCUHy0K4XpXacv6LlAKBCyf4qEop9cf6prPjVxu9rivuVa6rV9t/fVZmJvb29vbwwFQjhBrUWlR9WpZqsGrrLWsxZLxDNOz5hxeoZYIrbWs141cFVd91JUehSKj3alMKTdEJFQlFaYNvTA0KEHhqYVpomEoiHthjTndsXj8fw9/OefnZ8mTsMeB4RTA8soyqjTV/dNtE2EAuET8ZM99/bsubfnifiJUCA00Tap49uaMooyUHy0K4X0wnSJTPLidFxkqiPUkcgk6YXpzbxdOVs4f+H0BTr3AOHU8NivYteehY4FEWUUvjgEsAfsyUZdL7zd7WrFlRWXUy+bapsGTw7ePXy3SCi6nHp5xZUVzb9drXRemVuSu/UGBqACwqlByeSyRrnpWU2fcGVyGYqPdqXMWNu4mn8253a1xX3LvDPzbj+9jf0OCKcGI+ALiGvytXIk4AtQfLQrhd/cf+ti0EX5mlMXgy6/uf/2RrSrHm16sB8kxH4HhFODEamJ6jR9UkGS8qda9oA92ajrhbe7XbGe4bicuJCUkJCUkLicOKpXd/Hraldze8/V19BfGboSux5eRgUlqBNjLeO8wrza98CwC9ftRO3YMN92onb1uXDN1avTBt7edsXYGtiyr83ZGtjW74z8NbYrf3d/u1/snC2cnS2c0QAAZ06vytHEkeR1mD40JTSrJEskFO0evptduH6U96jOF67l5GjiiOKjXSnsurdLLBGzARHBk4NNtU3FEvGue7veoHZlqmPKfpCQ4zg0AEA4vSoXCxeRSh16QkJSQmacmpFW+OKLHWmFaXOD5tZ1pSIVkYuFC4qPdqWw596ez4M+F0tejLUTS8SfB32+596eN6tdTe0+ta9Z37r+ICG0EOjWqxtXK9dySTkJ6zBLSEqI2c9mr7LSckm5q5Urio92VSGf6ppGzbBd+Xv49/i5x+H2h8d3Ho9mADhzqj9zXXNbI1tqyvG3MrI1sjXXNUfx0a7evnalrqLO7gmbU4KfxgCE06uZ6zRXV6DbZKvTFejOdZqLsqNdva3tyt3afYbdDNw2AhBOr8rLwUuVp1qny9f1JydVnqqXgxfKjnb1FrertUPXJjxP+DXqVzQDQDi9Ej9nPz2+XhOsSI+v5+fsh4KjXb317Yp17j3IeYBmAAin+pvTa057nfYkbeTVSMlC12JOrzkoONrVW9+unEycVr2zCp17gHB6VX+M+oMk1IidMHIiCQWMDECp0a5aSLta0n+JikDlf1f+h2YACKf6czB2+H3U7yJO1Ci32uNIxIl+H/W7g7EDSo121XLa1Ra3Lasvrb6Weg0tARBO9efl4LV0wFJdTreBjyMc6XK6SwcsxTgItKuW1q466Hfw9/CfF4jOPUA4vZrlg5Yv6b9EJBc1WD+MnERy0ZL+S5YPWo7yol21wHbl5eBla2C75PwSNAOEE7zqcWSz22YqpQa4ji0lKqXNbpuRTNCS25W/h//BewdPPTyFZoBwglf9rBc1O8rewF6P9Or5UVdOeqRnp28XNTsKvXnQwtuVnroe+0HCovIiNAOEE7wSB2OH6NnRa99Zaygw1CXdOtyHRka6pGsoMFz7ztqYT2IwAgLQrohojO2YUTajMLIc4QQNY06vOVmLsza6brTXt1eXqItIRFIiORFHLy5uswdyIimJSKQuUbfXt9/oujFrcRa+zwRoV8o2uW2KyojafWs3GkDLhLuSNzwvBy8vB6+U/JSghKCQpJCo9KiMogxxmVgmlwn4ApGayFjb2NHE0cXCxdXKFXd0BbSrl/H38B/550hnC2e8TRBO0GDMdc3Z0QSlALSr+hlkPmhx/8Xzzsw79t4x7PqWBt16ANB8fTv420JJ4eZrm1EKhBMAQDPi7+G/+Nzi6IxolALhBADQXHQx6oLbRiCcAACanc+cPjMRmXhf8EYpEE4AAM3IFvctO27uCE4MRikQTgAAzUVb7bbsBwmlcimqgXACAGguJnedPLj9YNw2AuEEANC8+Lv7hyaHHrx3EKVAOAEANBeqAtUtblvmnZn3rOgZqoFwAgBoLoZ1GPaR40fo3EM4AQA0L6tdVqcWpP4c+TNKgXACAGhG2Mi9+9n3UQqEEwBAc+Fo7LjOdR069xBOAADNy6J+izRVNddcXoNSIJwAAJoRfw//78O+v5JyBaVAOAEANBftdduzi08oBcIJAKAZ+cDuA7u2dovOLkIpEE4AAM2Iv7v/sbhjx+OPoxQIJwCA5kKkJmI/+JRfmo9qIJwAAJoLz06eEzpPwA8SIpwAAJqXDe9uiM2K/SPmD5QC4QQA0Ixscd8y78y8xLxElALhBADQXPRv1/+bQd9gZDnCCQCgeVk2cJlEJtkQvgGlQDgBADQj/h7+3174NjI9EqVAOAEANBc2BjbsBwlRCoQTAEAz8kmvTyz0LL4J/galQDgBADQj/h7+O2N2nn10FqVAOAEANBeGmobsthFl0jJUA+EEANBcTOgyYZjVMNw2AuEEANC8+Hv4hz8J3393P0qBcAIAaDYHOB6f/eBTujgd1UA4AQA0F+9YvPOZ02cYWY5wAgBoXnydfbOKs3688SNKgXACAGhG/N39552Zd/fZXZQC4QQA0FzYtbXb7L4ZnXsIJwCA5mVen3l66nq+F31RCoQTAEAz4u/hv+XalovJF1GK5k8FJYAGkZKfEpQQFJIUEpUelVGUIS4Ty+QyAV8gUhMZaxk7mji6WLi4Wrma65qjVqjz62KmY8ZGlt+acwt1RjjBWy4gOmBrxNa4rDhVoapYKiY+EY9IjYhHMk6WR3l5hXn34+4ff3S8XFJua2Q712mul4MX6oY6vxbTeky7mHxxfuD8Le5bUOfmjMdxnK+vLxH5+PigHFAn2yO3e4d6l3Pl+bJ8EtRuHhnpCnRVeap+zn5zes1BDVHnpldcXmy33e77Yd+PtR2LOjc3ijzCNSeoj+iMaPtf7JddWJYty86nWr+TiUhA+ZSfLctedmGZww6H6IxoFBN1bmKaqpqscy+3JBd1brYQTlBnAdEBjjscb+XeyqO8erYgPuVRXkxOjOMOx4DoAJQUdW5iHtYeU7tPZSPLUWeEE7wN1lxes+DsAlJviOuVKkTqtODsgjWX16CwqHMTW+e67lHuo7EHxqLOCCd4G46Y68PXi/niBms4fBLzxevD1+P9jDo3PQdjh/OJ51FnhBO82QKiA9aFrcvn5ROvQZfLo3xe/rqwdegPQZ2buM777uwr4hehzggneINFZ0TPOj5LzBM38Dv5/9/PYp541vFZuJ6MOqPOgHCCOvA64UXCxmwvfCIhfXj8Q9QZdUadAeEEtbI9cntSflKjf2NbhZILkrdHbkedUWfUGRBOUDPvUO88eV4TrChPnucd6o06o86oMyCcoAYB0QHlXHkTtRQ+lXPlLfNKMuqMOgPCCepga8TWfFl+k60uX5a/NWIr6ow6o84IJ4CXSslPicuKq8PdXF6dgOKy4lLyU1Bn1Bl1RjgBVC0oIUhVqFqH6ScFcUu4Cv8FTQqq00pVhapBCUGoc+2rXTC/YHrX6XWdHXWujVUDV5UtKlM05rJFZasGrkKdEU7wmoUkhYil4iZeqVgqDkkKQZ2rd8/r3tD2Q9ljkVC0dvBaF3MX1LnB62yibSIUCNGemx5+zwmqE5UeVacPMK4HXZU/ci7tvbRMVrbr3q66fmSKSo9Cnav/OG+tZy2WiD8P+pyIfnL9yUjDyNncOSQlBHVuwDoTkYWOBREFJwcrt220Z4QTvGYZRRn1+wq9i7mLV3cvoUC4J3bPnnt76jYzjzKKMlDnGj/OX069zGpb5wqjzrVuxrYGtkQ0tP1QbgknkUnW3Vi34soK1LkJoFsPqu2RKKtnn943fb8x1TaNzYn9KPCjplxvC6kz+zivoaLBLofU75oT6lwjU5GpjlBH8U+hQLig54J6lLql1RlnTtDoZHJZPc6c2OdNiUxy+MHh+n2il8llPF9ey6p13V9uf9P+7IFIKPrJ9ac6n0KhzjXp2KqjmkCNdZ+midN2j9htqm36QdcP6lFnHEwQTtCQBHyBjKtzPk3tMtVU2zStMC00JbQ+a+VIwBdIvaUt6H3op1KPOqcVps04NYOI6nnQRJ1rsuLKCuVOvLicOFNtU2Nt43q0ZxxM6grdelAdkZqoHnP1M+nH3sl1uz7/yuttOXVOKkhSVDgkJSQuJw51bozXywbr3/O691reRwgngJcy1jImrm6zuJi76KrpSmSS8PTweq6VI2MtY9S5GumF6RKZxNbA1sXcRXHRniUW6tyAdQ5PD5fIJNZ61qsGrlLU+Wr6VdQZ4QSvmaOJI8nrNgu7hlwmK3v4/GE91yonRxNH1LkaK66seJT3yFTbNHhycPDkYFNtU7FEfPHJRdS5MeosFAi9+3mzOqcVpv0Z+yfqjHCC18zFwkWkUrceCXYNuUBSkCZOq99KRSoiFwuX1/J64+Pjp0yZkpOT0/zr3DWga2xOLHvMrtjXdUD5a6mzn58f7/+FhYU1/zrPDZqbVviiJbOLfHXtrH6N7fmNhgERUB1XK9dySTnV5QvyFa4h10O5pNzVyrXpX2x8fPzkyZPbtm37RtSZ5dObVWc/P7+0tLTi4mINDQ1W7Z9++mnAgAHNuc4hKSFmP5u9ie0ZZ07wNjPXNbc1sqWmHAcrI1sjW3Nd8yZ+pfv27bO1tbW1tUWdG0lOTk5YWNj06dM1NDSIyMbGZvz48SEhIagzIJygPuY6zdUV6DbZ6nQFunOd5jbxa8zJyTl58mRcXNzcuXNR50ZiYGAQGBjYlOdJLbY9I5ygRfBy8FLlqdZ1WEQ9yUmVp+rl4NXEr9HAwGD//v02NjaocxOfSFlZWaHOgHCCevJz9tPj6zXBivT4en7OfqjzW1/nkpKS5cuXW1hYjBs3DnUGhBPU05xec9rrtKfGvpOAlCx0Leb0moM6v911LikpWbhwYVJS0po1a9j1J9QZEE5QT3+M+oMk1IidIXIiCQWMDECd3+46K5Jp3759BgYGqDMgnOCVOBg7/D7qdxEnqusNI2qFIxEn+n3U7w7GDqjzW1xnlkxEdPTo0deYTGjPCCd4q3g5eC0dsFSX023g9zNHupzu0gFLcd34ra/zhg0biGjTpk2vpTcP7RnhBG+t5YOWL+m/RCQXNVh/iJxEctGS/kuWD1qO8r7ddY6Pjz98+PAvv/yiqampuEnEnDlzSkpKUGeoDHeIgDq/n421jWcdn0XCV24+UiIJbR61ufl8xhwwYEBgYCDq3BhsbGxiYmLQngFnTtBYvBy8omZH2RvY65FePT9yykmP9Oz07aJmR+GdjDqjzoBwgobhYOwQPTt67TtrDQWGuqRbh/vByEiXdA0FhmvfWRvzSQyuGKPOqDMgnKCBzek1J2tx1kbXjfb69uoSdRGJSEokJ+LoxUVm9kBOJCURidQl6vb69htdN2YtzsL3P1Bn1BmqgWtO0AC9Il4OXin5KUEJQSFJIVHpURlFGeIysUwuE/AFIjWRsbaxo4mji4WLq5Ur7oCJOqPOUBs8juN8fX2JyMfHB+UAAIDXSJFH6NYDAIBmB+EEAAAIJwAAAIQTAAAgnAAAABBOAACAcAIAAEA4AQAAwgkAAADhBAAAgHACAACEEwAAAMIJAAAQTgAAAAgnAABAOAEAACCcAAAA4QQAAIBwAgAAQDgBAADCCQAAAOEEAAAIJwAAAIQTAAAgnAAAABBOAAAACCcAAEA4AQAAIJwAAADhBAAAgHACAACEEwAAAMIJAAAQTgAAAAgnAAAAhBMAACCcAAAAEE4AAIBwAgAAQDgBAADCCQAAAOEEAACAcAIAAIQTAAAAwgkAABBOAAAACCcAAEA4AQAANCEVlKDZ8r3piyIANCqfnj4oAsIJ6mblzZUoAgDCqWVCtx4AACCcAAAAEE4AAIBwAgAAQDgBAADCCQAAAOEENdvQdwM3m+Nmc7KPZUbqRsp/2tRvE/sTN5vTVtVmTxqpG33f5/s7E+4UeRVJP5Zmz8i+4HlhWsdpFZb2sv8Uy2koK3uu5GZz0o+ljV0f5S3XEepEjI3gZnPiD8X92vRrpFW/ykurMG/46HBuNrel/5YG30hWnG8dv23UVlphLXwe39vRe4zFmCbeDEA4wevYnTy+Z3tP5WdGmI+oMI2RutHNcTeX2C3ppt+NiPLK8gzUDZxNnPe8s2dxj8WvZbMLygvSitJSi1KbbI0aKhon3E70MupVIi3xDPS8+vRq89+54nKx4v9vorSitLSitAJJAfvngDYDVvVapRxOAAint1O+JJ+IRrUfpXjGRs+mo25HxeGA+bTLp+202xHRxKCJ2gHahrsNrfZb3cm9Q0Tejt4aKhrfRnzbamcr9t+P935kc5ntM1M8WVhe2LBbvvH2RrN9ZhZ/WjRNoYR84ZFhRwYbDy6TlY05N+ZixsWXTYZwahCqfFXWhMz2mfnf9WdPjrYYjfcsIJxahOjsaIlcMsxsmLpAnT0z0nwkEUVkRShPZqVjRUQFkoLDCYc54ogoUZw4M3TmZ1c+mxg0kYhKZaV5kjz2X5msTJF8iicrr3qvy15uNhc3KU7xzLeO31bozvI09wz2DH46/WnJrJJH7z1a33e9rlCX/alC/9W6Puu42dzdiXcN1Q33D92fNzMvc3rmjsE7tFS0FEt71+zdqHFRpbNKk6YmLey+cFrHaaxTiB0HqyHgCfYP3e/ezr1cXj4paNK51HOKP33f53u2XnsD+9hJsYVeha/+0iow1zZ/NuMZN5vbMXgHe6Z/m/6n3E9lTs8s8iq6M+HO3G5zBTxBdeEkeRFOhuqG6/uufzD5QbFXcdaMrKARQW5mbtWcKfr09Lk/6X6RV1H6tPTDww7b6Nm8bGItFa2fB/6cPSO70Kvw7PCzVjpWj957xM3m1jitUUwz1HTo2eFnn898XvZRWcKUBP/+/or+ZE0VTbYvJlpN9O/vL/5QvNR+KSn12qkL1LnZ3Jc9viSiDzp9wM3mvuj6hWLJUrnU09zz9oTbRV5F0eOjh5kNU7wEtoQJVhM+7fLpk/efFHoVBg4PNNY0bq/d/vyI84VehQ/fezi943QcCt4OuH3R20PGycIzw51NnIeaDj2VcoqIWBff1adXh5oOVUyWKE4kIh2hzro+6/4X87/cslwiisqOisqOarxtm2A14W/Xvznirj+7nleW19Oo5+Ieiwe0GdD/n/6VJy6VlRJRK7VWx949ZqBukFWaZa1j/bHtx1K59LMrnxGRg6HDCfcTQr5QIpc8L3u+xmlNdE40EXHElcvLq9kMHvEChgSMsxwn42Tvh7x/PPm48l9ZEuuo6gQMCeik20nGyRr2pWmqaP7j9o+RutH51PPshfRt3TfEM0RNoBadHZ1VmjXMbJh/f3+Rqui76O8qryg0PVSVr8rOcfk8frBncA/9Hs9KnoVmhBqoGQw1HfqOyTsjz448nXK68rx/Df1rVPtRheWFQWlB9gb24yzH9W/Tv+vfXdner2Cn884JVhOI6EnhE2sd65PuJ/XV9BX1ISIvG6/fhvzGI152aXbs89hurbrN7TbXs72n01GnnNIcxWTvW78/2mJ05T0i42RnU88OaDNAW1U7vTj9Tu6d5MJkxV8763Ve7bRaxsmEfKG9gf0JtxMdD3R8UvikVFqqWOzAtgMzizPNtMzczNy2DdxmKbLkiJPIJNY61rve2RWRFRGXF4cDAs6coLkQ8ATsPID17OkJ9Qa0GVBYXnj12X8uqOy4vyOrNIuIltgteTbj2c1xN7f03zKy/Ug1gVrjbdv71u8T0c74nf2O9fM449H1YNfrz65nl2abaZlVnpjjOCIy0TR5VPCo88HOtgdsQ9ND2adsNsHiHouFfKGMk/U/1t/hsIPjEUc7AzsiknPy6jdj64CtMzrNIKKfY3/+O+HvygdNIjLTNntW+kx/l752gHYDvjQe8XY577I3sL/3/N7EoIlSuZSIJneYnFmSeePZDaejTm6n3Xbc38H6Xatc0a4Hu6aFTLuceZmIuut376Hfg4icjjoNPzO8z7E+30Z8eznzso1uFedD7bXb99DvkVyY/OmVT0efHd33WF+OuLaabcdajq08cUfdjiyZjiQesdhv0eGvDuGZ4a3UWhGRnOREZKBusHXAVh7xzqaeNdtn5nDYYciJIXJObimy9HH0UZSRiIabD/cM9FT7TW1dzDrlVZTLy91Pu7NAOp963v20+4nkE4q/TrGeMuH8BPXf1OdcnkNEagK1KR2msE8ebAJnE+ceh3r0ONSD9ceOsRhz/dl1thmszhOtJuJogHCCZoTH451MOUlEI9uP5BHPw9xDha9yNvWsRCZRniyjOKPP0T57Hu4pLC8U8ASOho7zus077nY8ZWrKeMvxjbRtxdJiInJr5/ZJ509s9GyySrP6Hus76uyo6gdBsBMIGSc7lHiInXm01mhNRIONBxPRxYyLN7NvElFcXtw/Sf/UZjMU8fahzYddWnV52dnV8hvLCyQF1Z+E1fWleTt6T7CakFWa5Rnoya4OEtHCqwst/rToe6yvobqhmZZZelE6EZlpmSk6ZqtfKRGtcVrjauoqUhWtiV7jfMJ5051NlSdOLky23G9p8afFkcQjplqmAp6AXYa01rGuPDGrLRFtvrOZhf26W/+JFk9zT00VTbZ32ElS+NPwkPQQlhPKU55NPXsq5VSNp7MVBD4JPJZ0jCPu17hfWaEsRBbKExxLOpZRnMERd+bJGfbMr3G/EtGd3Dus5uba5jgaIJygebmTeydRnGisaexo6Ohp7klEVR61E8WJMy7M0N+l3/+f/l9d/yo4LZgjrrVG670uezvodGiMDdt0Z1NheaGJpsn2QdvjJsWxa0iWIstqZuGIe1zwmD1+VvJM0TNGRMaaxkSUUJCgmPhB/oPabMb9vPseZzzyJflaKlqHhh1SvoilLDYvtmFfmoAnWNlrJRGp8dVKpCWK5y1FlsfePVYyqyRzeuaT95/49nrxIykq/Br62x/mP/zr8V9ENK3jtPMjzud+kHtl1JVZtrNeNv2cLnOSpyYXeRWlvp/65P0n7JJYldfnTDRN2IME8YvyPi54rNzDqYg05ZqzPdVOu53ylsc+j61HU7mde5s9kHPyjOIMxU7/N2vFL/oAc0tf9EkmiZNePFOWS0QaKho4FCCcoNlhaeRi6jLMbJiMk7GLT1Uql5dffXp1/a31rqdcRwWOIiJ1gXrloed1OnVTPK5w4IvMiuz2d7fvor+78eyGRC5po9HmY9uPw0eHs3GDVZJzcsUxUdGlozi5qfAkn1erlux8wjnwSeCsi7OIqLNe518G/1J5GhknU86Phnpp95/fTy9OZ5f6FK/imNux0Rajc8pyvC56jQwc+cv9X2pf7anBU98Lfu9gwsH04nQVvsqAtgN+G/zbaqfVlaccZznu54E/m2ub/x73+7hz40YGjqxmyB+rraJzlT2jePKlxxEen+0RxVxU34GF7IqjYl9UnkDKSSu0CtZHqrzNgHCC5hdOyf8Q0addPjVSN7qccbnCFW99Nf0/nP+4Pub6/G7zlZ8PTg9mb3VDdcN699opz9tRp2PlzqXlEcv7HOuj84fO2HNjC8sL22q2nWQ1qR6re1rylJ12KJ7ppNup9tt5OPHwT/d+IqL3rd+f02VOE7w0GSdzOur0bcS3RDSj04y+rfuy3ip23WjDrQ1/xP9xMuVkXlle7YvAEXfg8YHJQZNN95pa7bdil9Aq7FZmdPvRRJQvyf/40sdHk45eSL9Q4VxEWWZJ5ouzOp0X5bXWtVbO/ocFD9kD5etb7HFCQUItR5EAIJxaHBZI7MDNgkpZblluL8NevVv3/q73dx/bftxWs62miqaNns22gdvYp+PIrMh6rJT1q+ir6buauhJRl1ZdlC+2C3iCQ8MOPZj8gA0LLpOVnUg+kV6cXu/XGP40nIicjZ0dDR3Z6pS/3VUbX177Mjo7mog299vMFtLYL61YWrzrwa6YnBge8X4c+COfx1f0gLGhKOba5op+uRrvwTHWYmz46PCT7ifZuPNEcSIbeVjhFJNhK+IRTygQEpFPTx82V5VrYbUlooXdF7JM+tr+a+UJTiafLJIWsefZSaSrqesg40FEdODxgdrvAna6U82pMyCc4K2i3JVXYag0MzN05vOy55oqmjsG78iYllHkVRQ3KW5mp5lEdDLlpPK4qdrb/2g/u+h93O341TFXb4y9wXoX2dFNxsnSitI66nY86X7y4siLp9xPPZj8oJNup+dlz+t0OFPYeHujnJOr8FWujrl6Z8KdqHFRdb28USYrmxQ0SVwuVhOoHRp2SE+o1wQvTc7JF19bTEQ9DXvOspmVUJDwqOAREXk7eh9992jE2Ih9j/axQ/bRd486mzhXs/0xOTGdW3UeYT7iweQHp9xPXRx58bfBvxFRlR2DbAynjlAnfHT4xZEXvWy8dj7YSURTraf+NPCnChPfzb0b+CSQiMZbjk+empw8NbmXYS/F6HD2+WZu2FyOOPd27ilTU25PuB04PJBHvFs5t6ocAf8y7JKVi4lL9PjoKk/4AOEEb13PXtI/7CijPGRA4Wb2zV5He22L3RafF18iLZFxspzSnAvpF2Zfmj3m7JgqP3rXKFGcOPrs6Nu5t3k8Xithq48vfXw48TD7tM4Gni28unDR1UV3c+921+/uYupCRDvu73A66lS/WxaFPw2fFDSJfZdFXUV9wdUFRxKPUB0vOTwqePTxpY9Z9+BO550vu6zSsC8tOC2YfXT4rvd3OkKdcefGXcq4xBHXy6jX1ntbF11d5BflV1he2Em3kxpfrfqCDzo+aP+j/ap81aGmQ7u06nIz++aHoR9+de2ryhPvfrDb96ZvalGqrZ6tlJM6n3T2vel7N/euhkCjyvEvU0Om7nu0T1wu1hXqxuTEDA8czi65Kcr7R/wfbqfdgtOC2Wl3QkHC2pi1g44PYmdUteQd6R2ZFSmRS4w1jUtkJXjbQgU8juN8fX2JyMfHB+VoXvtmBw9FqKUf+v6wqMeirNKs1rtboxoNS6QqKviwgIg+v/L5tthtb9mr42ZjDEXzosgjnDnBm2eS1aSIsRFp09LYF121VbXZjdrCMsNQnFekwlc56X7y4XsPN/V78ZWp9zu+rzhhRX2g6ZoiSgBvnJvZNzvodGil1ipmfMz1Z9d7GPQw0zIrkZasilqF4rwiqVz6uODxCPMRC7ov6Numb5msbFDbF4MdYnJiUB9oMjhzgjfP44LHg44P+uvxX2XysmFmw9QEakcSj/T/pz8bgAevaOHVhQvCF8TkxHRt1bVv676xz2O/vvH1tAvTUBnAmRNADe49vzcleArq0BjknHzL3S1b7m5BKQBnTgAAAAgnAABAOAEAACCcAADgDYYBEc3Xyp4rUQQAQDhB8+LTE/fsAIAWCt16AACAcAIAAEA4AQAAwgkAAADhBAAACCcAAACEEwAAIJwAAABeO47jVq5ciToAAEBzsHLlSo7j/g++KObuUUHCDAAAAABJRU5ErkJggg==)"
      ],
      "metadata": {
        "id": "kShedtlyq2wc"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "69-tHHLyq427"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "KVjKxPAkq7zy"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Notation\n",
        "\n",
        "The labels `u` and `v` are commonly used in graph theory and computer science to represent the source and destination nodes/vertices of an edge.\n",
        "\n",
        "This convention originates from traditional mathematical notations used in graph theory and has been widely adopted in algorithm textbooks and literature.\n",
        "\n",
        "Additionally, it is common to refer to the edge weight by `w`, which is important here as we want to approximate distance/cost via the weight parameter.\n",
        "\n",
        "You will find this as common notation in other graph algorithms, including Dijkstra’s, Breadth-First Search (BFS), Depth-First Search (DFS) etc.\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "3Qlggs1z2OSb"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Code example\n",
        "Now let us get into some code to show how this plays out when utilizing the Python programing skills learnt in this class.\n",
        "\n",
        "Our approach will have the following steps:\n",
        "\n",
        "- Define our full data structure.\n",
        "- Define our Union-Find (or Disjoint Set) function.\n",
        "- Specify our Kruskal function to implement the algorithm.\n",
        "- Obtain returned output.\n",
        "\n",
        "Now we can begin by defining the full data structure as a source-destination pairing (essentially, a graph structure defined in code format)."
      ],
      "metadata": {
        "id": "oEflNjs4rVOL"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Example: Define the graph as an edge list (u, v, w)\n",
        "# This equates to source,\tdestination, weight\n",
        "edges = [\n",
        "  (7,\t6, 1),\n",
        "  (8,\t2, 2),\n",
        "  (6,\t5, 2),\n",
        "  (0,\t1, 4),\n",
        "  (2,\t5, 4),\n",
        "  (8,\t6, 6),\n",
        "  (2,\t3, 7),\n",
        "  (7,\t8, 7),\n",
        "  (0,\t7, 8),\n",
        "  (1,\t2, 8),\n",
        "  (3,\t4, 9),\n",
        "  (5,\t4, 10),\n",
        "  (1,\t7, 11),\n",
        "  (3,\t5, 14),\n",
        "]\n",
        "edges"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OUeSfmz6lCib",
        "outputId": "d2122548-ac04-4710-8cfa-3dc286f674e3"
      },
      "execution_count": 77,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[(7, 6, 1),\n",
              " (8, 2, 2),\n",
              " (6, 5, 2),\n",
              " (0, 1, 4),\n",
              " (2, 5, 4),\n",
              " (8, 6, 6),\n",
              " (2, 3, 7),\n",
              " (7, 8, 7),\n",
              " (0, 7, 8),\n",
              " (1, 2, 8),\n",
              " (3, 4, 9),\n",
              " (5, 4, 10),\n",
              " (1, 7, 11),\n",
              " (3, 5, 14)]"
            ]
          },
          "metadata": {},
          "execution_count": 77
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Next, we can create our Union-Find function to manage and merge groups of elements that belong to distinct sets.\n",
        "\n",
        "The purpose here in Kruskal's algorithm is to determine if adding an edge would form a cycle (breaking a key MST property)."
      ],
      "metadata": {
        "id": "Y2q9_oy6sX_h"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Suppose we have three nodes A, B and C with edges A-B, B-C, and C-A.\n",
        "\n",
        "- Adding edges A-B and B-C, the graphic is still acyclic.\n",
        "- Yet, adding C-A would form a cycle A-B-C-A, leading to a closed loop.\n",
        "- To avoid a cycle in our MST we need to exclude C-A.\n",
        "\n",
        "By defining the following `Union-Find` function we can avoid this outcome."
      ],
      "metadata": {
        "id": "UGUDkhUEy0CA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Example: Defining our Union-Find class\n",
        "class UnionFind:\n",
        "    def __init__(self, n):\n",
        "        \"\"\"\n",
        "        Initializes a Union-Find (Disjoint Set) data structure.\n",
        "\n",
        "        Parameters\n",
        "        ----------\n",
        "        n : int\n",
        "            The number of elements in the Union-Find structure.\n",
        "        \"\"\"\n",
        "        self.parent = list(range(n))\n",
        "        self.rank = [0] * n\n",
        "\n",
        "    def find(self, u):\n",
        "        \"\"\"\n",
        "        Finds the root of the node `u` with path compression.\n",
        "\n",
        "        Parameters\n",
        "        ----------\n",
        "        u : int\n",
        "            The node whose root we are searching for.\n",
        "\n",
        "        Returns\n",
        "        -------\n",
        "        int\n",
        "            The root of the node `u`.\n",
        "        \"\"\"\n",
        "        if self.parent[u] != u:\n",
        "            self.parent[u] = self.find(self.parent[u])\n",
        "        return self.parent[u]\n",
        "\n",
        "    def union(self, u, v):\n",
        "        \"\"\"\n",
        "        Unites two sets containing nodes/vertices `u` and `v`, using union\n",
        "        by rank.\n",
        "\n",
        "        Parameters\n",
        "        ----------\n",
        "        u : int\n",
        "            The first node to union.\n",
        "        v : int\n",
        "            The second node to union.\n",
        "\n",
        "        \"\"\"\n",
        "        root_u = self.find(u)\n",
        "        root_v = self.find(v)\n",
        "\n",
        "        if root_u != root_v:\n",
        "            if self.rank[root_u] > self.rank[root_v]:\n",
        "                self.parent[root_v] = root_u\n",
        "            elif self.rank[root_u] < self.rank[root_v]:\n",
        "                self.parent[root_u] = root_v\n",
        "            else:\n",
        "                self.parent[root_v] = root_u\n",
        "                self.rank[root_u] += 1\n",
        "\n",
        "# Instantiate our class\n",
        "uf = UnionFind(10)\n",
        "uf"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VjkkODsJloNZ",
        "outputId": "6ded412f-f0c1-47fb-86ab-63d7b21ee548"
      },
      "execution_count": 100,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<__main__.UnionFind at 0x7c629daf7a00>"
            ]
          },
          "metadata": {},
          "execution_count": 100
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Some comments on this `UnionFind` function:\n",
        "\n",
        "- The `find` method helps us identify the root of a node's set, indicating the connected component. This helps us avoid cycling.\n",
        "- The `union` method enables the merging of two sets into one, for example, connecting two previously unconnected nodes/sets.\n"
      ],
      "metadata": {
        "id": "G8yVDlVg3YQr"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Next, we are able to specify our Kruskal function to implement the algorithm."
      ],
      "metadata": {
        "id": "PAYOx4KN3Dg5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Example: Define Kruskal's\n",
        "def kruskal(edges, num_vertices):\n",
        "    \"\"\"\n",
        "    Finds the Minimum Spanning Tree (MST) of a connected, undirected graph\n",
        "    using Kruskal's algorithm.\n",
        "\n",
        "    Parameters\n",
        "    ----------\n",
        "    edges : list of tuples\n",
        "        A list of edges in the graph, where each edge is represented\n",
        "        as a tuple (u, v, weight), with `u` and `v` being the connected\n",
        "        nodes and `weight` the weight of the edge.\n",
        "    num_vertices : int\n",
        "        The number of vertices in the graph.\n",
        "\n",
        "    Returns\n",
        "    -------\n",
        "    tuple of (list, int)\n",
        "        A tuple containing:\n",
        "        - `mst` (list of tuples): The edges in the Minimum Spanning Tree,\n",
        "        where each edge is represented as (u, v, weight).\n",
        "        - `mst_weight` (int): The total weight of the Minimum Spanning Tree.\n",
        "    \"\"\"\n",
        "    # Sort all edge links in non-decreasing weight order.\n",
        "    # Here we are sorting using a lambda function on the weight x[2]\n",
        "    edges.sort(key=lambda x: x[2])\n",
        "\n",
        "    # Set up our union find algorithm to ensure we avoid cycles.\n",
        "    uf = UnionFind(num_vertices)\n",
        "\n",
        "    mst = []\n",
        "    mst_weight = 0\n",
        "\n",
        "    # Loop over our sorted edges\n",
        "    for u, v, weight in edges:\n",
        "        # Check if u and v are in the same set\n",
        "        if uf.find(u) != uf.find(v):\n",
        "            uf.union(u, v)\n",
        "            # if not to our output list\n",
        "            mst.append((u, v, weight))\n",
        "            # and add the weight\n",
        "            mst_weight += weight\n",
        "\n",
        "    return mst, mst_weight # Return the mst and weight"
      ],
      "metadata": {
        "id": "0eBEjUw-lr72"
      },
      "execution_count": 101,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "And now we have specified our functions/classes, we can generate results.\n",
        "\n",
        "Here we need the edges, number of vertices, and the `kruskal` function and `UnionFind` class."
      ],
      "metadata": {
        "id": "uv6Rbiv247ts"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Example: Run Kruskal's Algorithm\n",
        "num_vertices = 10\n",
        "mst, mst_weight = kruskal(edges, num_vertices)\n",
        "print(mst)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "s6OeQBHalth6",
        "outputId": "db4cd8ec-6067-4eda-ceaa-4ac1855d3073"
      },
      "execution_count": 104,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[(7, 6, 1), (8, 2, 2), (6, 5, 2), (0, 1, 4), (2, 5, 4), (2, 3, 7), (0, 7, 8), (3, 4, 9)]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The output we have obtained should match up with the graphical explanation illustrated earlier in this class.\n",
        "\n",
        "Next, we can interrogate the edge properties of the MST define:"
      ],
      "metadata": {
        "id": "2MHAFCKX5Vsd"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Example: Display the result\n",
        "print(\"Edges in the Minimum Spanning Tree:\")\n",
        "for u, v, weight in mst:\n",
        "    print(f\"({u}, {v}) - Weight: {weight}\")\n",
        "print(f\"Total weight of MST: {mst_weight}\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rvpAQOc3lvKk",
        "outputId": "881ce556-2ae2-42b9-d081-bd6493b20eba"
      },
      "execution_count": 103,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Edges in the Minimum Spanning Tree:\n",
            "(7, 6) - Weight: 1\n",
            "(8, 2) - Weight: 2\n",
            "(6, 5) - Weight: 2\n",
            "(0, 1) - Weight: 4\n",
            "(2, 5) - Weight: 4\n",
            "(2, 3) - Weight: 7\n",
            "(0, 7) - Weight: 8\n",
            "(3, 4) - Weight: 9\n",
            "Total weight of MST: 37\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from IPython.display import HTML\n",
        "HTML('<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/JZBQLXgSGfs?si=cBUswiVWRNaai3qm\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen></iframe>')\n"
      ],
      "metadata": {
        "id": "hA_yunZOwn8T",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 372
        },
        "outputId": "ca98a794-1187-4d8f-ee0d-bb3c8e0acac3"
      },
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/IPython/core/display.py:724: UserWarning: Consider using IPython.display.IFrame instead\n",
            "  warnings.warn(\"Consider using IPython.display.IFrame instead\")\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/JZBQLXgSGfs?si=cBUswiVWRNaai3qm\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen></iframe>"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "<iframe width=\"560\" height=\"315\" src=\"https://www.youtube.com/embed/EFg3u_E6eHU?si=38RtZ8Mn_AW5Wrb3\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen></iframe>"
      ],
      "metadata": {
        "id": "I1RXJN2lo7O9"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Working With Real Data\n",
        "\n",
        "We can begin by loading in the `botswana_settlements.shp` data, which you can download from the GitHub, followed by unzipping.\n",
        "\n"
      ],
      "metadata": {
        "id": "cmJ8lMjf6EBT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from google.colab import files\n",
        "files.upload()"
      ],
      "metadata": {
        "id": "huLkEUphCreF",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "outputId": "95fc5f29-7679-40a9-e773-5fc52b8c4c9b"
      },
      "execution_count": 106,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "     <input type=\"file\" id=\"files-eeed0c6d-3a78-4fec-b4b5-5e6e1a25d9f1\" name=\"files[]\" multiple disabled\n",
              "        style=\"border:none\" />\n",
              "     <output id=\"result-eeed0c6d-3a78-4fec-b4b5-5e6e1a25d9f1\">\n",
              "      Upload widget is only available when the cell has been executed in the\n",
              "      current browser session. Please rerun this cell to enable.\n",
              "      </output>\n",
              "      <script>// Copyright 2017 Google LLC\n",
              "//\n",
              "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
              "// you may not use this file except in compliance with the License.\n",
              "// You may obtain a copy of the License at\n",
              "//\n",
              "//      http://www.apache.org/licenses/LICENSE-2.0\n",
              "//\n",
              "// Unless required by applicable law or agreed to in writing, software\n",
              "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
              "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
              "// See the License for the specific language governing permissions and\n",
              "// limitations under the License.\n",
              "\n",
              "/**\n",
              " * @fileoverview Helpers for google.colab Python module.\n",
              " */\n",
              "(function(scope) {\n",
              "function span(text, styleAttributes = {}) {\n",
              "  const element = document.createElement('span');\n",
              "  element.textContent = text;\n",
              "  for (const key of Object.keys(styleAttributes)) {\n",
              "    element.style[key] = styleAttributes[key];\n",
              "  }\n",
              "  return element;\n",
              "}\n",
              "\n",
              "// Max number of bytes which will be uploaded at a time.\n",
              "const MAX_PAYLOAD_SIZE = 100 * 1024;\n",
              "\n",
              "function _uploadFiles(inputId, outputId) {\n",
              "  const steps = uploadFilesStep(inputId, outputId);\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  // Cache steps on the outputElement to make it available for the next call\n",
              "  // to uploadFilesContinue from Python.\n",
              "  outputElement.steps = steps;\n",
              "\n",
              "  return _uploadFilesContinue(outputId);\n",
              "}\n",
              "\n",
              "// This is roughly an async generator (not supported in the browser yet),\n",
              "// where there are multiple asynchronous steps and the Python side is going\n",
              "// to poll for completion of each step.\n",
              "// This uses a Promise to block the python side on completion of each step,\n",
              "// then passes the result of the previous step as the input to the next step.\n",
              "function _uploadFilesContinue(outputId) {\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  const steps = outputElement.steps;\n",
              "\n",
              "  const next = steps.next(outputElement.lastPromiseValue);\n",
              "  return Promise.resolve(next.value.promise).then((value) => {\n",
              "    // Cache the last promise value to make it available to the next\n",
              "    // step of the generator.\n",
              "    outputElement.lastPromiseValue = value;\n",
              "    return next.value.response;\n",
              "  });\n",
              "}\n",
              "\n",
              "/**\n",
              " * Generator function which is called between each async step of the upload\n",
              " * process.\n",
              " * @param {string} inputId Element ID of the input file picker element.\n",
              " * @param {string} outputId Element ID of the output display.\n",
              " * @return {!Iterable<!Object>} Iterable of next steps.\n",
              " */\n",
              "function* uploadFilesStep(inputId, outputId) {\n",
              "  const inputElement = document.getElementById(inputId);\n",
              "  inputElement.disabled = false;\n",
              "\n",
              "  const outputElement = document.getElementById(outputId);\n",
              "  outputElement.innerHTML = '';\n",
              "\n",
              "  const pickedPromise = new Promise((resolve) => {\n",
              "    inputElement.addEventListener('change', (e) => {\n",
              "      resolve(e.target.files);\n",
              "    });\n",
              "  });\n",
              "\n",
              "  const cancel = document.createElement('button');\n",
              "  inputElement.parentElement.appendChild(cancel);\n",
              "  cancel.textContent = 'Cancel upload';\n",
              "  const cancelPromise = new Promise((resolve) => {\n",
              "    cancel.onclick = () => {\n",
              "      resolve(null);\n",
              "    };\n",
              "  });\n",
              "\n",
              "  // Wait for the user to pick the files.\n",
              "  const files = yield {\n",
              "    promise: Promise.race([pickedPromise, cancelPromise]),\n",
              "    response: {\n",
              "      action: 'starting',\n",
              "    }\n",
              "  };\n",
              "\n",
              "  cancel.remove();\n",
              "\n",
              "  // Disable the input element since further picks are not allowed.\n",
              "  inputElement.disabled = true;\n",
              "\n",
              "  if (!files) {\n",
              "    return {\n",
              "      response: {\n",
              "        action: 'complete',\n",
              "      }\n",
              "    };\n",
              "  }\n",
              "\n",
              "  for (const file of files) {\n",
              "    const li = document.createElement('li');\n",
              "    li.append(span(file.name, {fontWeight: 'bold'}));\n",
              "    li.append(span(\n",
              "        `(${file.type || 'n/a'}) - ${file.size} bytes, ` +\n",
              "        `last modified: ${\n",
              "            file.lastModifiedDate ? file.lastModifiedDate.toLocaleDateString() :\n",
              "                                    'n/a'} - `));\n",
              "    const percent = span('0% done');\n",
              "    li.appendChild(percent);\n",
              "\n",
              "    outputElement.appendChild(li);\n",
              "\n",
              "    const fileDataPromise = new Promise((resolve) => {\n",
              "      const reader = new FileReader();\n",
              "      reader.onload = (e) => {\n",
              "        resolve(e.target.result);\n",
              "      };\n",
              "      reader.readAsArrayBuffer(file);\n",
              "    });\n",
              "    // Wait for the data to be ready.\n",
              "    let fileData = yield {\n",
              "      promise: fileDataPromise,\n",
              "      response: {\n",
              "        action: 'continue',\n",
              "      }\n",
              "    };\n",
              "\n",
              "    // Use a chunked sending to avoid message size limits. See b/62115660.\n",
              "    let position = 0;\n",
              "    do {\n",
              "      const length = Math.min(fileData.byteLength - position, MAX_PAYLOAD_SIZE);\n",
              "      const chunk = new Uint8Array(fileData, position, length);\n",
              "      position += length;\n",
              "\n",
              "      const base64 = btoa(String.fromCharCode.apply(null, chunk));\n",
              "      yield {\n",
              "        response: {\n",
              "          action: 'append',\n",
              "          file: file.name,\n",
              "          data: base64,\n",
              "        },\n",
              "      };\n",
              "\n",
              "      let percentDone = fileData.byteLength === 0 ?\n",
              "          100 :\n",
              "          Math.round((position / fileData.byteLength) * 100);\n",
              "      percent.textContent = `${percentDone}% done`;\n",
              "\n",
              "    } while (position < fileData.byteLength);\n",
              "  }\n",
              "\n",
              "  // All done.\n",
              "  yield {\n",
              "    response: {\n",
              "      action: 'complete',\n",
              "    }\n",
              "  };\n",
              "}\n",
              "\n",
              "scope.google = scope.google || {};\n",
              "scope.google.colab = scope.google.colab || {};\n",
              "scope.google.colab._files = {\n",
              "  _uploadFiles,\n",
              "  _uploadFilesContinue,\n",
              "};\n",
              "})(self);\n",
              "</script> "
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Saving botswana_settlements.cpg to botswana_settlements.cpg\n",
            "Saving botswana_settlements.dbf to botswana_settlements.dbf\n",
            "Saving botswana_settlements.prj to botswana_settlements.prj\n",
            "Saving botswana_settlements.qmd to botswana_settlements.qmd\n",
            "Saving botswana_settlements.shx to botswana_settlements.shx\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "{'botswana_settlements.cpg': b'UTF-8',\n",
              " 'botswana_settlements.dbf': b'\\x03|\\x04\\x01\\x0c\\x00\\x00\\x00\\x01\\x01K\\x01\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00id\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00N\\x00\\x00\\x00\\x00\\x12\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00GID_0\\x00\\x00\\x00\\x00\\x00\\x00C\\x00\\x00\\x00\\x00P\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00GID_2\\x00\\x00\\x00\\x00\\x00\\x00C\\x00\\x00\\x00\\x00P\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00population\\x00N\\x00\\x00\\x00\\x00\\x18\\x0f\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00type\\x00\\x00\\x00\\x00\\x00\\x00\\x00C\\x00\\x00\\x00\\x00P\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00lon\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00N\\x00\\x00\\x00\\x00\\x18\\x0f\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00lat\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00N\\x00\\x00\\x00\\x00\\x18\\x0f\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\r                  2BWA                                                                             BWA.1.3_1                                                                          48375.335937499992724>20k                                                                                  27.165550000000000     -23.118430000000000                  7BWA                                                                             BWA.1.8_1                                                                             45.099712371826165<0.25k                                                                                25.943750000000001     -20.066250000000000                  7BWA                                                                             BWA.1.8_1                                                                             37.008594512939453<0.25k                                                                                26.506840000000000     -20.431539999999998                  9BWA                                                                             BWA.3.1_1                                                                          97115.515625000000000>20k                                                                                  27.497309999999999     -21.176829999999999                 10BWA                                                                             BWA.4.1_1                                                                         171852.281250000000000>20k                                                                                  25.931120000000000     -24.619140000000002                 11BWA                                                                             BWA.5.1_1                                                                            748.1848754882812500.5-1k                                                                                22.354550000000000     -21.117360000000001                 11BWA                                                                             BWA.5.1_1                                                                            492.4983825683593750.25-0.5k                                                                             21.745570000000001     -22.107540000000000                 11BWA                                                                             BWA.5.1_1                                                                             26.942081451416016<0.25k                                                                                22.198060000000002     -22.862919999999999                 14BWA                                                                             BWA.7.2_1                                                                            370.8496093750000000.25-0.5k                                                                             22.976320000000001     -23.955439999999999                 16BWA                                                                             BWA.8.1_1                                                                         114261.765625000000000>20k                                                                                  26.323290000000000     -24.188099999999999                 21BWA                                                                             BWA.12.1_1                                                                         53775.171875000000000>20k                                                                                  23.559229999999999     -20.040360000000000                 27BWA                                                                             BWA.15.3_1                                                                         80909.054687500000000>20k                                                                                  25.334070000000001     -24.858709999999999\\x1a',\n",
              " 'botswana_settlements.prj': b'GEOGCS[\"GCS_WGS_1984\",DATUM[\"D_WGS_1984\",SPHEROID[\"WGS_1984\",6378137.0,298.257223563]],PRIMEM[\"Greenwich\",0.0],UNIT[\"Degree\",0.0174532925199433]]',\n",
              " 'botswana_settlements.qmd': b'<!DOCTYPE qgis PUBLIC \\'http://mrcc.com/qgis.dtd\\' \\'SYSTEM\\'>\\n<qgis version=\"3.30.1-\\'s-Hertogenbosch\">\\n  <identifier></identifier>\\n  <parentidentifier></parentidentifier>\\n  <language></language>\\n  <type>dataset</type>\\n  <title></title>\\n  <abstract></abstract>\\n  <links/>\\n  <dates/>\\n  <fees></fees>\\n  <encoding></encoding>\\n  <crs>\\n    <spatialrefsys nativeFormat=\"Wkt\">\\n      <wkt>GEOGCRS[\"WGS 84\",ENSEMBLE[\"World Geodetic System 1984 ensemble\",MEMBER[\"World Geodetic System 1984 (Transit)\"],MEMBER[\"World Geodetic System 1984 (G730)\"],MEMBER[\"World Geodetic System 1984 (G873)\"],MEMBER[\"World Geodetic System 1984 (G1150)\"],MEMBER[\"World Geodetic System 1984 (G1674)\"],MEMBER[\"World Geodetic System 1984 (G1762)\"],MEMBER[\"World Geodetic System 1984 (G2139)\"],ELLIPSOID[\"WGS 84\",6378137,298.257223563,LENGTHUNIT[\"metre\",1]],ENSEMBLEACCURACY[2.0]],PRIMEM[\"Greenwich\",0,ANGLEUNIT[\"degree\",0.0174532925199433]],CS[ellipsoidal,2],AXIS[\"geodetic latitude (Lat)\",north,ORDER[1],ANGLEUNIT[\"degree\",0.0174532925199433]],AXIS[\"geodetic longitude (Lon)\",east,ORDER[2],ANGLEUNIT[\"degree\",0.0174532925199433]],USAGE[SCOPE[\"Horizontal component of 3D system.\"],AREA[\"World.\"],BBOX[-90,-180,90,180]],ID[\"EPSG\",4326]]</wkt>\\n      <proj4>+proj=longlat +datum=WGS84 +no_defs</proj4>\\n      <srsid>3452</srsid>\\n      <srid>4326</srid>\\n      <authid>EPSG:4326</authid>\\n      <description>WGS 84</description>\\n      <projectionacronym>longlat</projectionacronym>\\n      <ellipsoidacronym>EPSG:7030</ellipsoidacronym>\\n      <geographicflag>true</geographicflag>\\n    </spatialrefsys>\\n  </crs>\\n  <extent/>\\n</qgis>\\n',\n",
              " 'botswana_settlements.shx': b\"\\x00\\x00'\\n\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00b\\xe8\\x03\\x00\\x00\\x01\\x00\\x00\\x00\\x9aU\\xe3\\x9a\\xdd\\xbe5@\\xb4\\xed\\x87\\x19\\xd4\\xdb8\\xc0\\x9dj\\x08\\xcfO\\x7f;@CPq\\xebT\\n4\\xc0\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x00\\x002\\x00\\x00\\x00\\n\\x00\\x00\\x00@\\x00\\x00\\x00\\n\\x00\\x00\\x00N\\x00\\x00\\x00\\n\\x00\\x00\\x00\\\\\\x00\\x00\\x00\\n\\x00\\x00\\x00j\\x00\\x00\\x00\\n\\x00\\x00\\x00x\\x00\\x00\\x00\\n\\x00\\x00\\x00\\x86\\x00\\x00\\x00\\n\\x00\\x00\\x00\\x94\\x00\\x00\\x00\\n\\x00\\x00\\x00\\xa2\\x00\\x00\\x00\\n\\x00\\x00\\x00\\xb0\\x00\\x00\\x00\\n\\x00\\x00\\x00\\xbe\\x00\\x00\\x00\\n\\x00\\x00\\x00\\xcc\\x00\\x00\\x00\\n\"}"
            ]
          },
          "metadata": {},
          "execution_count": 106
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can now load in our node data for selected settlements in Botswana.\n",
        "\n",
        "Please also take a moment to view the data in a piece of GIS software, e.g., QGIS."
      ],
      "metadata": {
        "id": "ZBZuFkX0He-T"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Example: Load in our node data\n",
        "import geopandas as gpd\n",
        "from shapely.geometry import Point as shapely_point, LineString as shapely_linestring\n",
        "\n",
        "# Load in using geopandas\n",
        "nodes = gpd.read_file('botswana_settlements.shp', crs='epsg:4326')\n",
        "\n",
        "# Convert to projected crs\n",
        "nodes = nodes.to_crs('epsg:3857')\n",
        "print(nodes.head(3)) # inspect geodataframe\n",
        "\n",
        "# Convert our geodataframe to a list of dictionaries\n",
        "nodes = nodes.to_dict('records')\n",
        "print(len(nodes))\n",
        "print(nodes[0]) # inspect first dict"
      ],
      "metadata": {
        "id": "J-1JJAKFC8E8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f942825f-4f9f-4f2c-8d16-ee3f4480014a"
      },
      "execution_count": 152,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "   id GID_0      GID_2    population    type       lon       lat  \\\n",
            "0   2   BWA  BWA.1.3_1  48375.335937    >20k  27.16555 -23.11843   \n",
            "1   7   BWA  BWA.1.8_1     45.099712  <0.25k  25.94375 -20.06625   \n",
            "2   7   BWA  BWA.1.8_1     37.008595  <0.25k  26.50684 -20.43154   \n",
            "\n",
            "                           geometry  \n",
            "0  POINT (3024055.289 -2646346.907)  \n",
            "1  POINT (2888045.029 -2280880.769)  \n",
            "2  POINT (2950727.725 -2324223.904)  \n",
            "12\n",
            "{'id': 2, 'GID_0': 'BWA', 'GID_2': 'BWA.1.3_1', 'population': 48375.33593749999, 'type': '>20k', 'lon': 27.16555, 'lat': -23.11843, 'geometry': <POINT (3024055.289 -2646346.907)>}\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.10/dist-packages/pyogrio/raw.py:198: RuntimeWarning: driver ESRI Shapefile does not support open option CRS\n",
            "  return ogr_read(\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Next, we can specify all the possible edges in our network, creating a fully connected graph (e.g., connecting each node to all other nodes).\n",
        "\n",
        "We will write these out as `my_edges.shp` so that you can view these in your GIS software.\n",
        "\n",
        "We require this step to enable the mst algorithm to find the shortest path."
      ],
      "metadata": {
        "id": "Q5QWrsg36z1u"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Example create a fully connected graph\n",
        "my_edges = []\n",
        "\n",
        "for item1 in nodes:\n",
        "  for item2 in nodes:\n",
        "    if item1['id'] != item2['id']:\n",
        "      line = shapely_linestring([item1['geometry'], item2['geometry']])\n",
        "      my_edges.append({\n",
        "          'geometry': line,\n",
        "          'properties': {\n",
        "            'from': item1['id'],\n",
        "            'to': item2['id'],\n",
        "            'length': line.length\n",
        "          }\n",
        "      })\n",
        "\n",
        "edges = gpd.GeoDataFrame.from_features(my_edges, crs='epsg:3857')\n",
        "edges = edges.to_crs('epsg:4326')\n",
        "edges.to_file('my_edges.shp')\n",
        "\n",
        "print(len(edges))"
      ],
      "metadata": {
        "id": "MyS2bmkE60M8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "78948dd9-2efa-470c-a467-004aa7e1b3b8"
      },
      "execution_count": 154,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "124\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Finally, we can utilize `NetworkX` to fit a minimum spanning tree, thanks to its handy `.minimum_spanning_edges()` function.\n",
        "\n",
        "`NetworkX` provides a range of useful tools for creating, manipulating, and studying complex networks or graphs (including algorithms visualization capabilities etc.).\n",
        "\n",
        "This `.minimum_spanning_edges()` function will iterate across all possible paths in the network that connect all points, and then rank these options, selecting the shortest distance instance as the minimum spanning tree."
      ],
      "metadata": {
        "id": "tWqwyRNK6DiT"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 157,
      "metadata": {
        "id": "LVkqQhRhnuJS",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4655f67d-b8aa-42f3-d704-41bf67a5e0ce"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "<generator object kruskal_mst_edges at 0x7c62695aff40>\n",
            "[(10, 16, {'object': {'geometry': <LINESTRING (2930295.494 -2776345.817, 2886639.429 -2829036.104)>, 'properties': {'from': 16, 'to': 10, 'length': 68426.00634555693}}, 'weight': 68426.00634555693}), (10, 27, {'object': {'geometry': <LINESTRING (2820176.259 -2858399.687, 2886639.429 -2829036.104)>, 'properties': {'from': 27, 'to': 10, 'length': 72660.66955598944}}, 'weight': 72660.66955598944}), (7, 9, {'object': {'geometry': <LINESTRING (3060986.718 -2412976.519, 2950727.725 -2324223.904)>, 'properties': {'from': 9, 'to': 7, 'length': 141541.76851955632}}, 'weight': 141541.76851955632}), (11, 14, {'object': {'geometry': <LINESTRING (2557712.627 -2747979.326, 2471076.233 -2615449.089)>, 'properties': {'from': 14, 'to': 11, 'length': 158335.49377697895}}, 'weight': 158335.49377697895}), (2, 16, {'object': {'geometry': <LINESTRING (2930295.494 -2776345.817, 3024055.289 -2646346.907)>, 'properties': {'from': 16, 'to': 2, 'length': 160282.92475872982}}, 'weight': 160282.92475872982}), (2, 9, {'object': {'geometry': <LINESTRING (3060986.718 -2412976.519, 3024055.289 -2646346.907)>, 'properties': {'from': 9, 'to': 2, 'length': 236274.56152335138}}, 'weight': 236274.56152335138}), (14, 27, {'object': {'geometry': <LINESTRING (2820176.259 -2858399.687, 2557712.627 -2747979.326)>, 'properties': {'from': 27, 'to': 14, 'length': 284745.1746610878}}, 'weight': 284745.1746610878}), (7, 21, {'object': {'geometry': <LINESTRING (2622601.446 -2277812.532, 2950727.725 -2324223.904)>, 'properties': {'from': 21, 'to': 7, 'length': 331392.32106432255}}, 'weight': 331392.32106432255})]\n"
          ]
        }
      ],
      "source": [
        "# Example: Fit our minimum spanning tree\n",
        "import networkx as nx\n",
        "\n",
        "G = nx.Graph()\n",
        "\n",
        "for node_id, node in enumerate(nodes):\n",
        "    G.add_node(node_id, object=node)\n",
        "\n",
        "for edge in my_edges:\n",
        "    G.add_edge(edge['properties']['from'], edge['properties']['to'],\n",
        "        object=edge, weight=edge['properties']['length'])\n",
        "\n",
        "tree = nx.minimum_spanning_edges(G)\n",
        "print(tree) # inspect networkx generator object\n",
        "print(list(tree)) #inspect underlying data structure"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "To export our minimum spanning tree, we will convert our tree from the format which `NetworkX` creates (source, sink, geometry), into a list of dictionaries, utilizing the geojson format.\n",
        "\n",
        "We can then easily export this using `GeoPandas`."
      ],
      "metadata": {
        "id": "LknHH7knJb6C"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Example: Fit and export our minimum spanning tree\n",
        "import networkx as nx\n",
        "\n",
        "G = nx.Graph()\n",
        "\n",
        "for node_id, node in enumerate(nodes):\n",
        "    G.add_node(node_id, object=node)\n",
        "\n",
        "for edge in my_edges:\n",
        "    G.add_edge(edge['properties']['from'], edge['properties']['to'],\n",
        "        object=edge, weight=edge['properties']['length'])\n",
        "\n",
        "tree = nx.minimum_spanning_edges(G)\n",
        "# print(tree) # inspect networkx generator object\n",
        "# print(list(tree)) #inspect underlying data structure\n",
        "\n",
        "mst = []\n",
        "\n",
        "# Convert our networkx mst into a geojson list of dicts\n",
        "for source, sink, geojson in tree:\n",
        "    if geojson['object']['properties']['length'] > 0:\n",
        "        mst.append({\n",
        "          'geometry': geojson['object']['geometry'],\n",
        "          'properties': geojson['object']['properties']\n",
        "        })\n",
        "    else:\n",
        "      print(source, sink, geojson)\n",
        "\n",
        "# Create geodataframe\n",
        "edges = gpd.GeoDataFrame.from_features(mst, crs='epsg:3857')\n",
        "\n",
        "# # Convert crs to export in 3857\n",
        "# edges['geometry'].set_crs('epsg:3857')\n",
        "\n",
        "# Convert crs to export in 4326\n",
        "edges = edges.to_crs('epsg:4326')\n",
        "\n",
        "# Export to .shp file\n",
        "edges.to_file('minimum_spanning_tree.shp')"
      ],
      "metadata": {
        "id": "B1MpF2C9_B85"
      },
      "execution_count": 161,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Inspect the resulting files within your GIS software and think critically about the implications of using method.\n",
        "\n",
        "Consider the range of uses within your own field of research, from routing users through to planning new infrastructure (e.g., roads, fiber optic links etc.)."
      ],
      "metadata": {
        "id": "894sWEzrJ5x6"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Task 1\n",
        "\n",
        "Go find the `botswana_settlements_task.zip` file from the GitHub.\n",
        "\n",
        "With this larger set of settlements, try to find a minimum spanning tree to connect all these nodes.\n",
        "\n",
        "Once you have your results, think critically about how you could improve this.\n",
        "\n",
        "Do you have the most cost-efficient network?\n",
        "\n",
        "What could you do to reduce distance travelled/cost?\n"
      ],
      "metadata": {
        "id": "PGUFSo9jpip0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Enter your attempt below\n"
      ],
      "metadata": {
        "id": "7zDD57TKLfCK"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Task 2\n",
        "\n",
        "Now find your own set of nodes, such as OSM Points of Interest (PoIs), building centroids, electricity infrastructure etc. and fit a minimum spanning tree.\n",
        "\n",
        "Prior to exporting your results, make sure you have the distance of each link, so that you can estimate the total distance covered in kilometers."
      ],
      "metadata": {
        "id": "NIFU6Rs2L38J"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Enter your attempt below\n"
      ],
      "metadata": {
        "id": "Q_gTU40JL4Pj"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}