{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction\n",
    "\n",
    "In this notebook, we will explore the use of matrix representations of graphs, and show how their are direct matrix parallels for some of the algorithms that we have investigated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "import networkx as nx\n",
    "from networkx import bipartite\n",
    "import matplotlib.pyplot as plt\n",
    "import nxviz as nv\n",
    "from custom.load_data import load_university_social_network, load_amazon_reviews\n",
    "from matplotlib import animation\n",
    "from IPython.display import HTML\n",
    "import numpy as np\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For this notebook, we will specifically see the connection between matrix operations and pathfinding between nodes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Toy Example: Linear Chain\n",
    "\n",
    "To start, let us use a simple four-node network, in which nodes are joined in a chain. Convince yourself that this is is a linear chain by running the cell below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "nodes = list(range(4))\n",
    "G1 = nx.Graph()\n",
    "\n",
    "G1.add_nodes_from(nodes)\n",
    "G1.add_edges_from(zip(nodes, nodes[1:]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Graph Form\n",
    "\n",
    "When visualized as circles and lines, the graph looks like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 320,
       "width": 481
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(G1, with_labels=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matrix Form\n",
    "\n",
    "When represented in matrix form, it looks like the plot below. (Explain row by columns = node by nodes.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 344,
       "width": 344
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "nv.MatrixPlot(G1).draw()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Playing with the matrix form\n",
    "\n",
    "NetworkX provides a `to_numpy_array()` function that will return a numpy array of the graph. That is used behind-the-scenes in `nxviz` to generate the MatrixPlot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 1., 0., 0.],\n",
       "       [1., 0., 1., 0.],\n",
       "       [0., 1., 0., 1.],\n",
       "       [0., 0., 1., 0.]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1 = nx.to_numpy_array(G1, nodelist=sorted(G1.nodes()))\n",
    "A1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One neat result is that if we take the adjacency matrix, and matrix-matrix multiply it against itself (\"matrix power 2\"), we will get back a new matrix that has interesting properties."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 1., 0.],\n",
       "       [0., 2., 0., 1.],\n",
       "       [1., 0., 2., 0.],\n",
       "       [0., 1., 0., 1.]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# One way of coding this up\n",
    "np.linalg.matrix_power(A1, 2)\n",
    "\n",
    "# Another equivalent way, that takes advantage of Python 3.5's matrix multiply operator\n",
    "A1 @ A1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Firstly**, if we look at the off-diagonals of the new matrix, this corresponds to the number of paths of length 2 that exist between those two nodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 2., 2., 1.])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.diag(A1 @ A1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, one path of length 2 exists between node 0 and node 2, and one path of length 2 exists between node 1 and node 3.\n",
    "\n",
    "**Secondly**, you may notice that the diagonals look like the degree of the nodes. This is a unique property of the 2nd adjacency matrix power: for every node, there are $ d $ degree paths of length two to get back to that same node.\n",
    "\n",
    "Not convinced? To get from a node and back, that's a path length of 2! :-)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see if the following statment is true: The $ k^{th} $ matrix power of the graph adjacency matrix indicates how many paths of length $ k $ exist between each pair of nodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 2., 0., 1.],\n",
       "       [2., 0., 3., 0.],\n",
       "       [0., 3., 0., 2.],\n",
       "       [1., 0., 2., 0.]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.matrix_power(A1, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed, if we think about it, there is, by definition, no way sequence of graph traversals that will allow us to go back to a node within 3 steps. We will always end up at some neighboring node.\n",
    "\n",
    "In addition, to get to the neighboring node in 3 steps, there are two ways to go about it:\n",
    "\n",
    "- node -> neighbor -> node -> neighbor\n",
    "- node -> neighbor -> neighbor's neighbor -> neighbor\n",
    "\n",
    "Or for the case of this chain graph:\n",
    "\n",
    "- 0 -> 1 -> 0 -> 1\n",
    "- 0 -> 1 -> 2 -> 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Toy Example: Directed Linear Chain\n",
    "\n",
    "Let's see if the same properties hold for a directed graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nodes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 320,
       "width": 479
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "G2 = nx.DiGraph()\n",
    "G2.add_nodes_from(nodes)\n",
    "G2.add_edges_from(zip(nodes, nodes[1:]))\n",
    "nx.draw(G2, with_labels=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall that in a directed graph, the matrix representation is not guaranteed to be symmetric."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 1., 0., 0.],\n",
       "       [0., 0., 1., 0.],\n",
       "       [0., 0., 0., 1.],\n",
       "       [0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A2 = nx.to_numpy_array(G2)\n",
    "A2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the 2nd matrix power: the number of paths of length 2 between any pair of nodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 1., 0.],\n",
       "       [0., 0., 0., 1.],\n",
       "       [0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.matrix_power(A2, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that there's only one path from node 0 to node 2 of length 2, and one path from node 1 to node 3. If you're not convinced of this, trace it for yourself!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise\n",
    "\n",
    "In this directed graph, how many paths are there from node 0 to node 3 of length 3? Compute the 3rd matrix power and verify your answer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 1.],\n",
       "       [0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Enter your code here.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Real Data\n",
    "\n",
    "Now that we've looked at a toy example, let's play around with a real dataset!\n",
    "\n",
    "This dataset is a residence hall rating dataset. From the [source website](http://konect.uni-koblenz.de/networks/moreno_oz):\n",
    "\n",
    "> This directed network contains friendship ratings between 217 residents living at a residence hall located on the Australian National University campus. A node represents a person and edges contain ratings of one friend to another.\n",
    "\n",
    "For the purposes of this exercise, we will treat the edges as if they were unweighted.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "G = load_university_social_network()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise\n",
    "\n",
    "Use nxviz's MatrixPlot to draw the graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 344,
       "width": 344
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Enter your code below.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise\n",
    "\n",
    "Using what you know from the previous material, find out how many connected component subgraphs there are in the subgraph.\n",
    "\n",
    "**Hint:** You may need to convert the graph to an undirected one first."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<networkx.classes.graph.Graph at 0x1a18810d30>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Enter your code below.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise\n",
    "\n",
    "Since there is only one connected component subgraph, pick two nodes in the graph and see how many shortest paths there exist between those two nodes.\n",
    "\n",
    "**Hint:** You will first need to know what the shortest path length is between those two nodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[30, 196, 115, 100]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Enter your code below to find shortest path between two nodes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "40.0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Find out the number of possible shortest nodes between those two nodes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Message Passing\n",
    "\n",
    "Message passing on graphs is a fascinating topic to explore. It's a neat way to think about a wide variety of problems, including the spread of infectious disease agents, rumours, and more. As it turns out, there's a direct matrix interpretation of the message passing operation.\n",
    "\n",
    "To illustrate this more clearly, let's go back to the directed chain graph, `G2`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 320,
       "width": 479
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(G2, with_labels=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we have a message that begins at node 0, and it is only passed to its neighbors, then node 1 is the next one that possess the message. Node 1 then passes it to node 2, and so on, until it reaches node 3.\n",
    "\n",
    "There are two key ideas to introduce here. Firstly, there is the notion of the **\"wavefront\"** of message passing: at the first time step, node 0 is the wavefront, and as time progresses, node 1, 2 and 3 progressively become the wavefront.\n",
    "\n",
    "Secondly, as the message gets passed, the number of nodes that have seen the message progressively increases. \n",
    "\n",
    "Let's see how this gets implemented in matrix form."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matrix Message Passing\n",
    "\n",
    "To represent the data, we start with a vertical array of messages of shape `(1, 4)`. Let's use the following conventions:\n",
    "\n",
    "- `1` indicates that a node currently has the message.\n",
    "- `0` indicates that a node currently does not have the message.\n",
    "\n",
    "Since the message starts at node 0, let's put a `1` in that cell of the array, and `0`s elsewhere."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0, 0]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "msg = np.array([1, 0, 0, 0]).reshape(1, 4)\n",
    "msg"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to simulate one round of message passing, we matrix multiply the message with the adjacency matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 1., 0., 0.]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "msg2 = msg @ A2\n",
    "msg2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The interpretation now is that the message is currently at node 1.\n",
    "\n",
    "To simulate a second round, we take that result and matrix multiply it against the adjacency matrix again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 1., 0.]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "msg3 = msg2 @ A2\n",
    "msg3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The interpretation now is that the message is currently at node 2."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Let's make an animation of this. I have pre-written the animation functions for you; your task is to implement the message passing function `propagate()` to precompute at each time step the message status."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fig, ax = plt.subplots()\n",
    "\n",
    "def propagate(G, msg, n_frames):\n",
    "    \"\"\"\n",
    "    Computes the node values based on propagation.\n",
    "    \n",
    "    Intended to be used before or when being passed into the \n",
    "    anim() function (defined below).\n",
    "    \n",
    "    :param G: A NetworkX Graph.\n",
    "    :param msg: The initial state of the message.\n",
    "    :returns: A list of 1/0 representing message status at \n",
    "        each node.\n",
    "    \"\"\"\n",
    "    # Initialize a list to store message states at each timestep.\n",
    "    \n",
    "    \n",
    "    # Set a variable `new_msg` to be the initial message state.\n",
    "    \n",
    "    \n",
    "    # Get the adjacency matrix of the graph G.\n",
    "    \n",
    "    \n",
    "    # Perform message passing at each time step\n",
    "    for i in range(n_frames):\n",
    "        \n",
    "        \n",
    "        \n",
    "    # Return the message states.\n",
    "    return msg_states"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The rest of the `matplotlib` animation functions are shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:matplotlib.animation:Animation.save using <class 'matplotlib.animation.FFMpegWriter'>\n",
      "INFO:matplotlib.animation:MovieWriter.run: running command: ['ffmpeg', '-f', 'rawvideo', '-vcodec', 'rawvideo', '-s', '432x288', '-pix_fmt', 'rgba', '-r', '5.0', '-loglevel', 'quiet', '-i', 'pipe:', '-vcodec', 'h264', '-pix_fmt', 'yuv420p', '-y', '/var/folders/mn/tfgkzcm91g189p7tsghp_jkc0000gn/T/tmpuev6ursm.m4v']\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<video width=\"432\" height=\"288\" controls autoplay loop>\n",
       "  <source type=\"video/mp4\" src=\"data:video/mp4;base64,AAAAHGZ0eXBNNFYgAAACAGlzb21pc28yYXZjMQAAAAhmcmVlAAAQXW1kYXQAAAKtBgX//6ncRem9\n",
       "5tlIt5Ys2CDZI+7veDI2NCAtIGNvcmUgMTQ4IHIyNzk1IGFhYTlhYTggLSBILjI2NC9NUEVHLTQg\n",
       "QVZDIGNvZGVjIC0gQ29weWxlZnQgMjAwMy0yMDE3IC0gaHR0cDovL3d3dy52aWRlb2xhbi5vcmcv\n",
       "eDI2NC5odG1sIC0gb3B0aW9uczogY2FiYWM9MSByZWY9MyBkZWJsb2NrPTE6MDowIGFuYWx5c2U9\n",
       "MHgzOjB4MTEzIG1lPWhleCBzdWJtZT03IHBzeT0xIHBzeV9yZD0xLjAwOjAuMDAgbWl4ZWRfcmVm\n",
       "PTEgbWVfcmFuZ2U9MTYgY2hyb21hX21lPTEgdHJlbGxpcz0xIDh4OGRjdD0xIGNxbT0wIGRlYWR6\n",
       "b25lPTIxLDExIGZhc3RfcHNraXA9MSBjaHJvbWFfcXBfb2Zmc2V0PS0yIHRocmVhZHM9NiBsb29r\n",
       "YWhlYWRfdGhyZWFkcz0xIHNsaWNlZF90aHJlYWRzPTAgbnI9MCBkZWNpbWF0ZT0xIGludGVybGFj\n",
       "ZWQ9MCBibHVyYXlfY29tcGF0PTAgY29uc3RyYWluZWRfaW50cmE9MCBiZnJhbWVzPTMgYl9weXJh\n",
       "bWlkPTIgYl9hZGFwdD0xIGJfYmlhcz0wIGRpcmVjdD0xIHdlaWdodGI9MSBvcGVuX2dvcD0wIHdl\n",
       "aWdodHA9MiBrZXlpbnQ9MjUwIGtleWludF9taW49NSBzY2VuZWN1dD00MCBpbnRyYV9yZWZyZXNo\n",
       "PTAgcmNfbG9va2FoZWFkPTQwIHJjPWNyZiBtYnRyZWU9MSBjcmY9MjMuMCBxY29tcD0wLjYwIHFw\n",
       "bWluPTAgcXBtYXg9NjkgcXBzdGVwPTQgaXBfcmF0aW89MS40MCBhcT0xOjEuMDAAgAAADAhliIQA\n",
       "Ev/+963fgU3AQO1rulc4tMurlDQ9UfaUpni2SAAAAwADjh6zXRqSe5rQaAAFyZoHnr/P+YAWqlkl\n",
       "qorVQJXhNFk7TC85N6aCh/vPR8fzEyHB6fLQpRbCR+67hkqqH/D1s5z6LTz8Ba+6ntCXge3e7Xlq\n",
       "iQdBoiU4WHu05tpsAS/sVZbuY0/Z7gVA/BE1Ej+S/D+kPB1rJ4fQx8xGdd5givCQ7281BrC4GsmC\n",
       "aM4SBpN3ZO/hcnaipmn4Q0uK5gBZI1sdvlnoTjWkxAQH+KTWH0bEq8/++qmkAADNPqwUVS/KgytO\n",
       "IaYhyYtSD9lh2PsS2Un6ZIpJWH4Dgd+uvqpDem8P+3OQ4WGX2hmFllvvcYU8qv80GTF7A5Bp1MD5\n",
       "8dvJrXy6+rCiOubeMrAw3msfEbCi24VyhcOj5caHi7tGRL4LhjQk5r5XGbfMcL7rX3CkYKI/n+uZ\n",
       "HQU06kPJB/msvjVOH1E8cQz8/9uBbI1Ty6uehSLwv7ZOBY4dS5NmxL2ZbngE0YbIIum7D2fxz4Li\n",
       "8TRjZ5LtC3PrpTNvPF6IiU1iERzVufevcoEIyk8loCDxGwbRtXIqHvnATrSV+p7FEqBIjN6gOY4h\n",
       "0kOySGrucX9cqG9OugbG8XoXqUegsSBPKCybQEbmmCf7FmyxfeuxHZdn7us6zSlQn+GQecReCEF7\n",
       "+XA0Lh4UDMrQsmoGPJHjVWkfksDVfmveDxgnwK9Z/3WoCTGKdrAaFcyXbqVLVYfE3ofKyyIU0VT7\n",
       "PrVshW6mLGs/AtnKY/Lx1r6o+/c/8BO7OB655qeHldhH5lV4fNzit13VEjIQc/7D45HvyFW3q+7h\n",
       "KU2zV46t0SpVfIBnDGMlI+mw0sxB3nIE1yc9X4wcLh3Usi4IJ70JppvwujmA+8HprV0BIwpcT5to\n",
       "mNEshXLJNGJBpupSs90N7Xj3w5KB/2z2i+euLkYtIRYJq76Z7dBGDe3sDo9erZ3McpS1BaY8h35z\n",
       "h6DLIkVKSDGAbQyQqQ6Ucu8TaAZim0yBTMHW7WYac+Z2A6Y9jIswL4V8cLY1NtOdbGiyNj3TsfuV\n",
       "HDHh1FzmItpmAVKw1MXAw2YkdT1C255GsL/Me3ID1m4p052FiMH00IbdfaOtbPn9rwLCC6sHJoxp\n",
       "c5i9OLX5pB38buFJcGCoFi5vumFxSgwmXwXIz9yF5RUJ02ZEf3vFgfky//YRGFq6vYXxMfDXjByM\n",
       "7OTCMDzwXSc6q6968x9Hj7MBam9pQ+4YTgyhPuPq6F4QCk7QvjaL9bywFyIGI+FBcRgDwO2RuyAu\n",
       "9ugKgGhfYMXJBkGGvL2kAvYdrEYT85Y7G9kGCG4yLT2WpynzNc0VTEE8G4ojtaeywRXQSbikfU6K\n",
       "xhi1RR/1M6dWwrXEYeH+lTEc/YTX7+CxVPfobO2U6suoRjVIjtE6PKP3o8lKkMs8kmxu4OBx/rAW\n",
       "M1eF8m8L63clPtNPsOMrR5xHL7WiuHuBD5A1RrXlQOgW/3r9HW4sSQiAKH/CXl4128yidYDQcV+o\n",
       "IWBsotFEAQW9eBqLosvZ/mhILlT3A5dWR5edZ3bD2S+Y0XrhGkYpOYFMTjmEOhJK4t5Yp+AMm5es\n",
       "BHSxWEFLwWwAZmBRVHGCKmXLg0GGrNYWEDueeLT5kuoVb7ts2jOhjWBW2+XmAi7d16Y4bBTAQBxU\n",
       "Ks9SJKWBvKWiC7coBtiiI0HdOUNayzAqpYUX5oD8S5QY7QlC6U9dGmQgRFUjSZ2/Mq48JyFL4rGv\n",
       "Biwqw9ootWaPJW+EuXwgs01oqI/MXjOUBqZ/R7o2b2jcErEPTDMoO6ELh9QpInp2xFgF6fhz8DLF\n",
       "aXRJ+L6PQgMXCjYbotkRAfTBLtLmwyzijoZ0Wo+BlqkxVqWRxEe2rO8baa9QtwSv/dxKq8J+k6uv\n",
       "51sfeFjD9GQWMNXU5+eK8IZPo39TLZt4j4M5f8dGtBlD/qpsZSzMn4N6VWexECNrZwJ0T5oFSAXX\n",
       "8KXiV1RwrDRZyUMRUlRNE5pfrsH7GPy02UDAr5DCVEBXM9Fscdw+CqOFor9WQBL8m3oBlHIpAeLt\n",
       "bhkHxABZ4YM6kqdn+oEzzpXlHtKzFa54ipX/r99tosLChhCcBXoSVq4mBfgl0WExL6XfNh4jNBnD\n",
       "ZRzcB943nSGFcsUVDqEsaft9oXsSTSv2ITzubBlD5no7NXbFC83ZDVxdNHkPrTOEKT9+3nUvVJi7\n",
       "lftL5FsUPiL1FlVH6vuULYC8DpSc2x4IbUyyPtqH6IPytoBvMzUzEYHGbWy+S48aw3BFdbxNvD/u\n",
       "kAtf+x+W1/CEJ9kx8ZOdg7uPSxXE6Yn9qterq/zibDcUvPBuZVoVWZWAYjKPuo0A5Qiw1DwCEH17\n",
       "AJpWw86aEKGS9FUc/sp+H6czvYAGoeaAiXl6ub0uIqKOgrbUWO5AACWcngm/5TH8/UgwAZiItPJL\n",
       "8UUmisi/7wNkHjQ/jzQl4Hm7h8XBUtWzaWDyZNC0JmnzXrhyUvgdgvy3qyeXfy98PN0Ums1BHo7w\n",
       "kSsojnWHNbweG7vg58kjyVTRSAKhekirruPlA9u1KOI+UFLutethdx5WMIhFNmA3vW/6qwrnLYAA\n",
       "67JETbjln2P850wvYywU85ft3Sx6P/XOk8bSFedOFtDOdcepKeAkED2o8Aa8ZF9bzFJBqYNJEVh5\n",
       "MX8yfvy3qt43doLxiEslV4v9lXxiL16yL3wds5R3q7/95BnDXcu2YuJTAEslJP0Ez2r0Eng73Kwx\n",
       "m3VsB8bhLxuMzZc6DKRHlvpGseZvxAGj5AvIKqvJGx/PPiwoZjcwPYqaQgWbKoWurP5Ajtq7Jl3S\n",
       "HDLZz7mbKds64Y3BrsUyzcpTk0BKLSsuHY9/5stDtBaSkMZ/0EItPWidx52esg5/OwS+xxyWymRW\n",
       "4Sb0+dkn6EUKKh67JWDfYYfFzF7fUl46pRl01hHa+pyu4fnjfgkjSkugW+qqd1JGfMIPba2UoLiZ\n",
       "mdvsG8dTLiyKynmWRlF7gSzdchuRYUFBo0uJfZ5XMvh2i4doQCmWZf9WVo24/pkNjERwmB+s335u\n",
       "1XvggABaDYK4619IqEZjR66cgSGUNcRFmwyzgRVlIKyL9nCANnuzMIrpSaZZlloDkaSN6a1+f3Oa\n",
       "sVb37GaYT8BZY/c4WHY9lNd8MCY4FfJ2tLhscS3Es7CkrQfRbrj/ged4WzytUM07UzXBA/wEmaig\n",
       "WD6FmuYrmXFjy5vpys46MGsAKboGlDgKe19DOZyzzOedvjp/XdYeDgJvDH4mDAf/1XjkmB7+NHfp\n",
       "7GigW7yrnO9aukXAdXo3WCVPDJCRotvNez0LHzixfvV41ABgt8OsZGUK6ulBCCYj/I3Ol9WImqSp\n",
       "SM9/r24c3GODDXKBdcrWP9fEZhGt9T+q8On6lZdE13B37eO6hzxrpHJf7hdP4GrJJECjMGRxh7WQ\n",
       "AUUZlbDCJKX+AvSsSxyQK5vq7M4UP11NCedYtxOjoMVSJxAZtufIUo6ScBJ4YWR9FKdv0Kvul1dA\n",
       "GaER9o5ZEu2R46RxLicepX/1yRLiKWXjPrLUOvryimFZmi54kl5k410jmD/X7kp3Fw9Ys1w5QbjG\n",
       "30hnR7EqANgHPYSFgViznl7Igpz4zTyU32ZjCdyvVmKhcKeA+EtM42b4gIJOBhAF9EAhrT4UddLa\n",
       "2cHnejwwPEYPZ56OwQgYDVVpgG0cfxGWEbXgy/LLrBVSWxGKVvOrEwKlVVB2M547/NvMkRydVVgb\n",
       "L3lTRQZOFyRXeon5ByCW/jos0YVmvQT/lvpfPz+LR4/GWqhXhRHE10U8vqkh01KqsXGB4v2YD7Ee\n",
       "n+L+1stO70SOUuvNTq5/mlu9NHR4Qw5eEGZgnJjuRHS/Xb/MwO/9HwybwtNgQhC88d+rY3jYLrnC\n",
       "q/Z4SPmgStvVSjPdHMFlPeE3lFyHu38jy7XSroVzaZA2XnNodfvHjeJ1Z85+YZyaNls2/S0/3iDU\n",
       "ghIgIHGhMBLawPvtsEYwDTzRgFax1wqG0icA+rTnt3Sg6J9N0U/Z9nfQi54hs2o5nfKNZuYGPt0B\n",
       "F2DZnXp8MqqPsjV72nQ8Y7oJMOAw/JOJcZsAPyASj7irfFcm4tQSKmeGQQY/KO6IugB7kAyR0wAA\n",
       "AMhBmiNsQ//+qZYAREI0sSQATkmS7rExUJgCiSpSfXgmHQLEXs0UjiKbD60HluOukiPneGEFUKIf\n",
       "B+Fr76ZgEXNuio6q/PfX/l3skgL8RqBT2bh1HrWy1uAR02QnhENrJyCS07BMcycMRSHxndskLnvK\n",
       "mNNjj9FAKXp93p9fsvWEzLHJPf982GhOq+HQ1fRdP0A0esmrEyct8eqsPXFd51xNbhC5Ik8GDZKI\n",
       "vogGZDi91Io0XusNk9c0ItWvEVuIryMj1HWwxRicQAAAAGdBnkF4gh8ACwvh/mlNX8IgIAALAdaw\n",
       "lmvvf/pio2Uv9GlcBCVuK787/IYB6p7JMOs5lQST+yDLPzW2pMYjvgSNJTkOLTmPOeBM9JpP/e57\n",
       "ASSF0cVg1DTKAoFHgaAVxNXkX1raTq/xAAAAXQGeYmpD/wADiYS2UHDoYoTBrUUALDJXjJQ8ikow\n",
       "03afBBHadJ5sxujz9BpfHjderURzf4WzPgIN922tg//hO7R+xOZXvF9susRruF9nDMS2oVBvISd0\n",
       "14ajZsW9WAAAA1Ztb292AAAAbG12aGQAAAAAAAAAAAAAAAAAAAPoAAADIAABAAABAAAAAAAAAAAA\n",
       "AAAAAQAAAAAAAAAAAAAAAAAAAAEAAAAAAAAAAAAAAAAAAEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA\n",
       "AAAAAAAAAAACAAACgHRyYWsAAABcdGtoZAAAAAMAAAAAAAAAAAAAAAEAAAAAAAADIAAAAAAAAAAA\n",
       "AAAAAAAAAAAAAQAAAAAAAAAAAAAAAAAAAAEAAAAAAAAAAAAAAAAAAEAAAAABsAAAASAAAAAAACRl\n",
       "ZHRzAAAAHGVsc3QAAAAAAAAAAQAAAyAAABAAAAEAAAAAAfhtZGlhAAAAIG1kaGQAAAAAAAAAAAAA\n",
       "AAAAACgAAAAgAFXEAAAAAAAtaGRscgAAAAAAAAAAdmlkZQAAAAAAAAAAAAAAAFZpZGVvSGFuZGxl\n",
       "cgAAAAGjbWluZgAAABR2bWhkAAAAAQAAAAAAAAAAAAAAJGRpbmYAAAAcZHJlZgAAAAAAAAABAAAA\n",
       "DHVybCAAAAABAAABY3N0YmwAAACzc3RzZAAAAAAAAAABAAAAo2F2YzEAAAAAAAAAAQAAAAAAAAAA\n",
       "AAAAAAAAAAABsAEgAEgAAABIAAAAAAAAAAEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA\n",
       "AAAY//8AAAAxYXZjQwFkABX/4QAYZ2QAFazZQbCWhAAAAwAEAAADACg8WLZYAQAGaOvjyyLAAAAA\n",
       "HHV1aWRraEDyXyRPxbo5pRvPAyPzAAAAAAAAABhzdHRzAAAAAAAAAAEAAAAEAAAIAAAAABRzdHNz\n",
       "AAAAAAAAAAEAAAABAAAAKGN0dHMAAAAAAAAAAwAAAAEAABAAAAAAAQAAIAAAAAACAAAIAAAAABxz\n",
       "dHNjAAAAAAAAAAEAAAABAAAABAAAAAEAAAAkc3RzegAAAAAAAAAAAAAABAAADr0AAADMAAAAawAA\n",
       "AGEAAAAUc3RjbwAAAAAAAAABAAAALAAAAGJ1ZHRhAAAAWm1ldGEAAAAAAAAAIWhkbHIAAAAAAAAA\n",
       "AG1kaXJhcHBsAAAAAAAAAAAAAAAALWlsc3QAAAAlqXRvbwAAAB1kYXRhAAAAAQAAAABMYXZmNTcu\n",
       "NzEuMTAw\n",
       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 250,
       "width": 382
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def update_func(step, nodes, colors):\n",
    "    \"\"\"\n",
    "    The update function for each animation time step.\n",
    "    \n",
    "    :param step: Passed in from matplotlib's FuncAnimation. Must\n",
    "        be present in the function signature.\n",
    "    :param nodes: Returned from nx.draw_networkx_edges(). Is an\n",
    "        array of colors.\n",
    "    :param colors: A list of pre-computed colors.\n",
    "    \"\"\"\n",
    "    nodes.set_array(colors[step].ravel())\n",
    "    return nodes\n",
    "\n",
    "def anim(G, initial_state, n_frames=4):\n",
    "    colors = propagate(G, initial_state, n_frames)\n",
    "    fig = plt.figure()\n",
    "    pos = {i:(i, i) for i in range(len(G))}\n",
    "    adj = nx.to_numpy_array(G)\n",
    "    pos = nx.kamada_kawai_layout(G)\n",
    "    nodes = nx.draw_networkx_nodes(G, pos=pos, node_color=colors[0].ravel(), node_size=20)\n",
    "    ax = nx.draw_networkx_edges(G, pos)\n",
    "    return animation.FuncAnimation(fig, update_func, frames=range(n_frames), fargs=(nodes, colors))\n",
    "\n",
    "\n",
    "# Initialize the message\n",
    "msg = np.zeros(len(G2))\n",
    "msg[0] = 1\n",
    "\n",
    "# Animate the graph with message propagation.\n",
    "HTML(anim(G2, propagate(G2, msg)).to_html5_video())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Visualize how a rumour would spread in the university dorm network. You can initialize the message on any node of your choice."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO:matplotlib.animation:Animation.save using <class 'matplotlib.animation.FFMpegWriter'>\n",
      "INFO:matplotlib.animation:MovieWriter.run: running command: ['ffmpeg', '-f', 'rawvideo', '-vcodec', 'rawvideo', '-s', '432x288', '-pix_fmt', 'rgba', '-r', '5.0', '-loglevel', 'quiet', '-i', 'pipe:', '-vcodec', 'h264', '-pix_fmt', 'yuv420p', '-y', '/var/folders/mn/tfgkzcm91g189p7tsghp_jkc0000gn/T/tmp70glgllz.m4v']\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<video width=\"432\" height=\"288\" controls autoplay loop>\n",
       "  <source type=\"video/mp4\" src=\"data:video/mp4;base64,AAAAHGZ0eXBNNFYgAAACAGlzb21pc28yYXZjMQAAAAhmcmVlAAB72G1kYXQAAAKtBgX//6ncRem9\n",
       "5tlIt5Ys2CDZI+7veDI2NCAtIGNvcmUgMTQ4IHIyNzk1IGFhYTlhYTggLSBILjI2NC9NUEVHLTQg\n",
       "QVZDIGNvZGVjIC0gQ29weWxlZnQgMjAwMy0yMDE3IC0gaHR0cDovL3d3dy52aWRlb2xhbi5vcmcv\n",
       "eDI2NC5odG1sIC0gb3B0aW9uczogY2FiYWM9MSByZWY9MyBkZWJsb2NrPTE6MDowIGFuYWx5c2U9\n",
       "MHgzOjB4MTEzIG1lPWhleCBzdWJtZT03IHBzeT0xIHBzeV9yZD0xLjAwOjAuMDAgbWl4ZWRfcmVm\n",
       "PTEgbWVfcmFuZ2U9MTYgY2hyb21hX21lPTEgdHJlbGxpcz0xIDh4OGRjdD0xIGNxbT0wIGRlYWR6\n",
       "b25lPTIxLDExIGZhc3RfcHNraXA9MSBjaHJvbWFfcXBfb2Zmc2V0PS0yIHRocmVhZHM9NiBsb29r\n",
       "YWhlYWRfdGhyZWFkcz0xIHNsaWNlZF90aHJlYWRzPTAgbnI9MCBkZWNpbWF0ZT0xIGludGVybGFj\n",
       "ZWQ9MCBibHVyYXlfY29tcGF0PTAgY29uc3RyYWluZWRfaW50cmE9MCBiZnJhbWVzPTMgYl9weXJh\n",
       "bWlkPTIgYl9hZGFwdD0xIGJfYmlhcz0wIGRpcmVjdD0xIHdlaWdodGI9MSBvcGVuX2dvcD0wIHdl\n",
       "aWdodHA9MiBrZXlpbnQ9MjUwIGtleWludF9taW49NSBzY2VuZWN1dD00MCBpbnRyYV9yZWZyZXNo\n",
       "PTAgcmNfbG9va2FoZWFkPTQwIHJjPWNyZiBtYnRyZWU9MSBjcmY9MjMuMCBxY29tcD0wLjYwIHFw\n",
       "bWluPTAgcXBtYXg9NjkgcXBzdGVwPTQgaXBfcmF0aW89MS40MCBhcT0xOjEuMDAAgAAATNhliIQA\n",
       "Ev/+963fgU3AQO1rulc4tMurlDQ9UfaUpni2SAAAAwADjh6zXRqSe5rQaAAGAwP44d7H+IAewKtb\n",
       "1EHRrF6gy1h6AHqgJD9RGssFNqPrrq6cEfDc99MHqjqa+wazhb3Y6d2PbnlGzHfHx/rZSuJU/ES3\n",
       "KjVOmBf2OIEx5mtwAvIrLNEeUoLw6Sz0dzmYaQzRHXUyzzhYYRwUUsBjh5txPgYR+2notF5ep6Oq\n",
       "7hJ7fdOAydOpUUOLOskE+4YBLYQc3gOFpPutFgsDcw7JRuOUvV0qmOMPXIS0HPT7AtEAYF0YUZxe\n",
       "Wdw/NhydqKEGvW0LyrOUxIg9fosBuBRkYT1kJBTrKMLk58h28vUtPjL3kxDtnlL4p0sMaInWHaBG\n",
       "EceGRgAOX/6LZGfWT9rgau32pCbDb2H++vvWNWvkOA4L+/yk3VoOTd1NEZS2CG30g6s6Cx0oFe6P\n",
       "W7Nku20H0FlTc3CIUIuNswZO5ue9kqeGjOmNVVbQepwnXuz62Z4RRt/Lt5a4ruUQThmGy4HT7WDu\n",
       "65ACypFAvPk8fASo3qcL5VOh7VXIHhaL/yuiGkGMkAk8hNa05DDP6Z2BVfQxF0xJTt/ZQ3JS5Gbw\n",
       "nl7PbjNJzq9v2g9l2eLer9elFQTDcec4nLsawL4m7PjrXwYt31uV5OuG+gNsdJB8EuxLzKbTpFmv\n",
       "wNN7cHqM5WhrGUozvK0rDJZ2wnbv7eKZz2erTRQ7AgI1U8BoFKcllZHkDeqVVgO06qcMvn8ZUSy/\n",
       "L5QyJeULAJfDa2CJ0iEX7Cd2LerYoTU87qCHTn2JCGq8vEb8Bmdx6oF6pEbFtvZO9uNhfLnfJlkM\n",
       "XGeIxpsk+GbDGoDHk+CGRBOsgnbrRAWV7DV8ocSaORa9k4Ug9Yug/a3wqJCwLpn1JO5uZfEqXku2\n",
       "vkTwJIjUhZ/PrnhHUtHO3I12Yj9MJrrhy9e14ButUtVBzUj7tOQqFvnEGvU88u5QBtQMqkMws+sw\n",
       "dGrwPaq/rLWQVdLa7kADFlh0mchBqbcYHUt8WH+txnUITTYaOk6ZSLhgSaD8oTFosuDoEQSo29EQ\n",
       "V1bqvjJRoDx/wEnDNkc+qGVNqDrct8sRpzzftSVoJ+QwvUf/zw9fI453dcYmUFo8P0rtGSCwHHUk\n",
       "XxGMiuesL/6dCyr3HSZnw+dA+9a1lPXLNd92sh1OPWcMTJvgklpjhKwCtIPZx6IUlHlRpo077SNQ\n",
       "Q/OKHeIsC8cgmYcWTYKk+5sww1ExsVT2aLMDaZpVC5B/aAeeTukxxycgQsdVlt1eZAAR6nElalwi\n",
       "6nPo5PNzbXcbfyjVMEuY29u2Hfho5TKaCjUXMZtXyhwwlGeEdL6ZcFau/7EPD5P4M/UOqn8SM8Te\n",
       "i3df8kMHbtmmMmqtDSA+k2U+u+7bhxct5+Os8W5OCiQYiQckrIoqQcukZ4jdjD9HUhJ7O2PDM9oQ\n",
       "ajxbJOHJC+L8Rs+q+b3jhORMknXaUme+sdpU4TeeIR4B9ZY9fQfpmf0u0BWIZXtUm+umCsHlDwF0\n",
       "EPnjXOHUAqfTX0h3JZHCJS3cGmULwqt97ncgaZWyz+v84AQJaZdT6RtDIISkwpKN8SyZqd7O1bbN\n",
       "jcNsK9EwoZUhBjZhwytHdG6eMAXttwmPXE3IbnRHw7rUHD/3RG3N0Fz3FWzP81N/Yqmk2eLSHRiv\n",
       "SGniVyKhG9KOp/5NOudn4N9WVxeqMmeGX6IuEy5O0hP2T7IFZAoPessbWdJl5avtdWuaRoblgKZ4\n",
       "uywWgXI12nSukDkvvUhLNRVcQhh5JN8AQPmLD1rEzK00P22XqM12f/yaCdhA171YtDxMYfRTDtmc\n",
       "OPz0dXNmUAstADQRef2HjCNR/TljWZRikx/5APX/FG0j/oXTBsx7fi12mnr99KK5wKXLnC7uo6WZ\n",
       "KuE4J7PqyfUI7gozuFfZn6KXb3s097yXmoTd9aFVb3uwmUTpmZoJW0Wuaa5Wsj45lkerSwZ7YAON\n",
       "dHmYa7McDC96dFqqJvaDlnRUiI4bNnwZWz402AdDkLeFkMpLfLGkr4JDyStzXgAHldUQTcxHN3oO\n",
       "G0ejkHbBrncmMiw8XCP/hKMvGZncMr5BuBw0PY4R/TZNstfX6T+BYiSb2SSuxppOyP3BfeFfzr8o\n",
       "Ilxy5Fy9WBUDyRbcYID3rpH+c2FTQryn3ep4aIIZKdPnH4gi66dj/qtYTeq1/vXwcxEHHp/WSD2g\n",
       "2XbLZEDtgWawDg/FquX0xO++/6EDw33eGJ6aoWKZywYSW8ujrokbS8K6HQs+mZYLzySBUAOW/nUt\n",
       "HAxXWL+uP6Xf3XOasDXKUFCSw//nQ6Sw6s/HeLOkaAHvAvmW0Ke44cEjoelQQSWgr8ylwqXKrYTy\n",
       "rlV0hF314PWCDzRZIcERVnwyVSIuCmzSkHWd8VsKTRsiFLQTeyTnh+/O+Dv4+oxa0FWtaHNN6ksW\n",
       "T8v2ZU+1XaxS15EZQmm9HKmUrnFr2GSWHoYVSpp9DSC0AtMeMZd8L2x0yUu5bLVzyc9hsmZcYNn4\n",
       "cThZJQaDtnTcV8FAuumOUM8OOTAmtlG2M1tz+p/zRhJXVakg73Y8SURd3/Ok6jgIY5ccmB4rH68r\n",
       "NlajF1Ax5366BnG3OkSxHL/uh6NVLPIeWAXjuqwZIEYtm+BsaVyw5E+XfIti6w6VgSSD3zriNtkl\n",
       "R9CSupumNrM4WB+R9dznsbYzq9JnhrcLH0+ZYOdS2xlZeQ4qrrGUkZEWGCsUVRyD+OELKIZXY6Kt\n",
       "oCtt40EL723Zy/QxrspeG44B7dzZds1qbJQ9Ji3lztTlKW5/QgDVdgJlohJzQ3m/dY1QFmz1OeFq\n",
       "2HERloTiAfwf0A9W7V8R3YOQ9HCmPBqy3OJJAAKush6Y30cBDdjfpFHoIJnJM0WgiIozCT4NM5IS\n",
       "iJxhwByYeZNKHU4AytyZOP488VOesH7Qy4OF0Scb91sLk7Cw9DfRVPTvioMrrN+A9zuoeyKLu9zt\n",
       "V5bMs6k8Q7WG9sgMkyWAFkRZo8ns6XB9mnPXHzE4YPOFW1Je5nGfwfZYHsvPNvEhrIBbSv2HqNiv\n",
       "7woU/B7j6eijqFF6PK6kAisgujkbGHIniWZPVLV2oG9/+K2LfpNLO23FRZMDY4fdVH9kLtAL+0yw\n",
       "1msmh0y2te2d6DQ3rrlVucZOfbXfpWtUj1b7xotZldskR1KnmZE490iQXlCOkwk2d2XSzcseeqiA\n",
       "EVSlR3qciV4r4LdQtB+bSx48szgS/iegB2WsxD79SriO+mOU6a3D3bMesXZNgy5MlDZa75ryZkTD\n",
       "kAGg8tyBYI9nVUrY+2oYNS0Knb5I4AP2kK4PlZ7p6WT6Y0RnZ846cF8/w8+dndf2FNyMZ3IEhB0n\n",
       "NNHU2hp9Ef95AeoUnMuGAB5icScmbnEE9q76Orb0rpOE+uYo1OlTVpdrOQRHGwFVT3Q4o1XkL37D\n",
       "udU+xgStxCVBxO6I+THhykcZAjQBHCeN5OE84pop54Jh0Xiv33VkM0K3M0EKJJjONWHhUO0WnbMd\n",
       "DK20ZgPAfnPxLhJ7Qr3log1fZP9VETjrykI5uKvme5xMQfjBg4glaKFKYHQJtTzNkyp1yOKyRzf+\n",
       "MPaWa6Cf+goTfox0Q0daNxB5Dy0lOOxWxQ9+fhL4yMHZ1iiDzxxBaV2x1p5qfGt/vzn+Vx7b9Y/h\n",
       "82DrybVao+D9n/LxERLJNcsu+WeYfUPdtvqJli87fCGkJiy+Akw+As5upXOqBQaIzbtKb4ebuuFs\n",
       "whN2lP1Hnh1AsRQ+m1hH846VuK1YL7N1Ii8XOp/soRIeHnHx6ssvTZbnUbH9wsWeDPQe3UWbtS4f\n",
       "tspe/0ZG0Pva8nis2fuz8M2dDIZS+XhYJi5zMdb3vYZH+6yMetGrMx7n4BZAJvLFWbx+mwhMG//U\n",
       "tX5LOB57k09cFvfW6okvGfAoDe1P8fhE0tx0sCec/zoACGLtXeOmqkdpj/gJ/3heRlcoJpswWdVz\n",
       "Yd+KDiWkr7uxe218uTdyom/wOrxhXFS14ausuxDoEZO25vpLqO7+KE0QJyZji4PAeXy2F0aQWnjE\n",
       "J/XnH2GC56tkvitkel8OFobDVVUwXysgvaTMXOWKcWjw/MnQL1+3bFTURwEMFuDqfww719pOSKUT\n",
       "y40vlMLMntg+QMyt9IF2wiCzHoyvheyIXwWxPPgpO63KMADYIxPIgMXuNdMwRiU/eE7QJ4k6AKjL\n",
       "bZLovdFMo8bkUX6nRTXhO90arnjHnu4dx1WyaAGbouEdOl3bwMlzG4RrPTmyEL6uK6TY95c8et2g\n",
       "Mbz8i4h7NjvRojMqcIBRcAXHykbBsX0cMOj8zzrhuPx8Rf7mvccm4hTrjwwpzkV+Xd+2tMvGVWEh\n",
       "xiFVbwLIrlBiAisUn6sdn/sw+DaAq+urCkNKjcv3zlLCSH0aofDYQ6u1UNrGSQYi+h1MNsuNMnW0\n",
       "sP3FWFN4+KDx/xU/D+O2C97ewhiHmo0Khp90ho1vV1rds7RtY5SnoEpEODzMS/Lm9h/NzGZ2F5yv\n",
       "te7t7o/4L0ZTJFtbiQBgnc8YNgpqZYfTaM+Bm19qRv1KMV/IiGdAJKQPuo9YHAPS5NmuSIUf3Dtz\n",
       "7Lf+O9q/HAHpLqxvIFcG6NyZH3MMvzCGxLrEe4IW1rjEKNRrMWluei2aeYjxb5g4I/GzEc2pafsu\n",
       "V7qbup2dG9ot1NSirgFmE3QNr3rNnYA5RWZuR244N0t/feJ7FpYMxqM0RS2OpdHnnzZvBd8kJhsb\n",
       "iRmbhThlZtCL1+Q5EYI7AT807POr4u8QQexLf9LdfolL/pU/8e6AAUM/Lw7Aqptf9GcTAthr0E+A\n",
       "lm4em9Re6nvCOrExO4Yi+/SgwgYPABVuczobJkvlbfyyHkwLB7+uzCJ4wVjxqx5+tsARbfG1antk\n",
       "eg3MuJM4558qHUOLkONN4M1TB4N7q4ztogacHkEuS1mCJ1FXyMSKhfS5idWqEjyJgUkSGAKpDU2q\n",
       "SkFUY3eiQ5FXKYd3W8VsoSY5RJ5lztOqaaRMHg1W9qqKYVurvJX6JPNRJrvJVJPn8l/A1cVw/5s5\n",
       "a2H3s3fugUg1zZIPQM7UkpTepSSoBgkGmH2KscfS4csBXx9sHsF3NgRo61YtWGNSe99COKz6JoUJ\n",
       "kJVqv6ynxczMWCpYFhTjLbhSqD9D2zFxLkCZqtZdOinT6PlYZWrIgdbiJIyQ3ehMsP5/+swEz+Ha\n",
       "/MLCyV1j/dFcR9xc1Oz0CqvR8Fo+a2/YMD7q7FMtnY5umMw3nyoRrgbNUV0PEgffr1StRlH6XJVY\n",
       "wNabQ7zL5sk1TKT9aaraICK5xbDbV52cnWiK0xfsiAsjrV07vfuz7y1spRmvQUqAINb0EQvAmMD5\n",
       "8DR9zzpueypfdkR5V+BGii7fP5WbPnYuKNxfGOdiZFUpXVmso+Ht9FQsACoPjR/+/FM4SE5Bx6bV\n",
       "PorDTlsbBuhIskR5cxDg9wnbXedh4KHnZXZOyFdpf+5geR8sFxBhxb9hZuQaqK3jqR3eaRvb8+C4\n",
       "1BCtYGi41Q3iQ5F5fSlt35ETDo2vl4QrAJ+fkK06KtnCnCGrZa2n8SlOzNVJBXYqO/vyLD9J+Vng\n",
       "hySZKb5Ra1M9Wb7eqZPWaMAvBlKYoNy0tUFvAqvk9Rfxs8JfNshSIr96RJfHZOKWkns0Q8iSTOtd\n",
       "p4KlLB/VOe6tum0vyMdifrrPRqRbu4QYa/Nut0DjFW0yx3sCzWLophX2CVDgUyfPl9UK1lfVEuGB\n",
       "kcA4sUZfAy93c5C3ONxXYQfHzhLVFzL2QXNCWjEkolij8kFAlBsVd0Sxabk0Akhjzvhdmhmjol5J\n",
       "5CesxwkGgL2qkQg/u7bBeGWQXm2+W8/n2GMcgfe3wlgXlfw8QY1Tm9YF5FFqwiEuYdq7U3Ty6Cw4\n",
       "tmLOPURWWKwc3Z+FWoIunBFyHf8wDhxHADfNfXwhe6p2WvH8GbnipngUhTyaGTG4mAdlrtIAib5y\n",
       "7Ft2DYSsIGMUGt1GuEDhIxKRipVh/uxZG/PPjZxfCLdgryUfrehvhVT23uYzKQfbO7sniF3ex+0x\n",
       "DGxzVUtV+uYJCNLSsXvCzEr2wnRHMTcpKEFdWMN5o5ZOoHRwKiPhAC0OxEYA4h9keAMi+lIlDOpF\n",
       "SSi7VTiYUz0NUC1doYVmVONqgiRKMsYtou1gJwD+dQd1GKhyKRzwy51bxu9Omba5S2NxTsU6MvQP\n",
       "1oToBzk+ufaJ8XeH1KqHEWPGS5RMKZgj0sy0bNgkjcNsPXVpsiSukrif7Pm8ktVBy/B8TvUoHs7t\n",
       "Q35VnxZQZFJblF0wfmzAeuyi18QpppnZALHih2PXsXZ4YZO1dfTGo3BtqZi9+Ez5zcS8Lr2JW7F7\n",
       "RDmL4Sk1CnGerYzugC/GAkK9SL/rtPV4F26EwMhP1CpiLJcZ60lRPzuWAk8c/M9/mZMwAypT2AbY\n",
       "Orij9C3KWGiiMgcT10BvEG4EksjgjXJBgypWtiPDt7QJOzBe+JQ4d2uX3kqRbG/Vx85Cyy/jZ8pP\n",
       "xqUka8i3MUuewC/KnHFd+ZtVwobPeFlB5OUcedZpRns5ooIbar22UzhEVfLi5WfcdGNwXMDxpG+7\n",
       "qbZxrvIwnWx12qWZVAtdCIdn4ItlPTKW1YuVvjQl5v86KnWksuLMAa6IWxKpohRiu0LF1y8oACXM\n",
       "t08mAsArW0Ajd+mU9qUZ14xuenTusqblrRDQJM8ophCFG3IBXp6j6wVngGlaq4s8JFrbUey8wpRC\n",
       "C+7oiJ2bJgVRvMBzVCPGHSFR7vTbT7H6Oz3cLf6zlD1MAAjmUvzBzfJmyYjk10rBPTgutTRCCq5t\n",
       "BxjggIRtg6wx/EPLMCWa6MGvDxOO8JTQqHg+kPu72LYgejjC2u/v7dumr221KTU/mwaTbBh7HeAZ\n",
       "F0rbVhOJhTf7Td1zV8/Qz01wVwHS2g3bYw9tqEFiiBukn/otaAX90Ek5khNeHyKsZlVTblsf3oEA\n",
       "S2VFvx7tAo3cD9JVegRK1tNkdxT9XpLs73nC6o38gPmfsEh9NdQJ9UyA1Y1Kd5cjyIDKxuk5ERrm\n",
       "K9/5TTIh0yhWsRX908sCdEjfHobfTHcsUxTpOW46SlCNmlx61bD+bsyt2t2ZP8e8lEV083Jganv8\n",
       "zoNYzekVA1eXVO2wo99TTDkiknqXBPI6sFMvSvRQ8+ubhBdsJvEeF/OZHvjqa+QR5ncIPU6cyAVs\n",
       "v/VoTPTkFEZhnel/+LDCy2TqUSc3JrJ3qMirPeeM7ObgHPLS9iEpwisXgmzccyMXrkM5pzW6DyIu\n",
       "CxPvHr3wOR2RNVI8ZT+9khPxOEKJSd9R1A9nFdcDt7MnuQuymwPA27PN4TDG08MyskpYvqPC3gmQ\n",
       "EQeOGOYgj2zusFV/GkhADYti+nR0XRNRzYGHSZe6gX8QgafqpS1jQQ2hoaHRRHQh2zOLh8HUduin\n",
       "Wg3JE7Xet5ngOknVj04SyZiBgRlJTM0YkxWfVibgeyKAqDANxQ23vRsj+xoJFvWZRXhW6NK5g2HM\n",
       "NTX6+DC7M/hQXyrv9GCvVL1zK1Xc2mV+L62CrFR+kWKkhnIzju/lcSZ7McUoUTySPGLrkkUc/PVW\n",
       "gsT4MbEY1bceQJr1MVeLayv9lfiCsGk3NbT00FNzn/YrrYeiTV2pw+Ax1gzJ0DYfI7R0rn0ZbV34\n",
       "mDKjAcxDUGcESbWt3R/zC7jkTrzv88sdbHvUwfYx0qDF1hL5n9HUx8zOyGikgytgMlq/iVjFTE+D\n",
       "5ujsnPLnAzJCgUqNQlTLC7MHJk8SOWV0dskpGElCYa1EJ4Jk8n6s3Ry53TRE06WP7PL6QSGjwxNm\n",
       "UxZ0eeCbMh1NdK9xQw7MKQW+QP/xGaioBpwGWi3+79aRwK1J0mSuO1DVdi09ydrGoO2KEMQq05gH\n",
       "oZf6Rn7zwGJ8AoSBBRjHEDJ6T07UlveiXOjuakZjpopIc716fpoAJyWb2IAKierDci0dOD+EQcOa\n",
       "sOB3zZnt10DBIj5I3pjEjsB01Cimo4QT8jXy0dhbcUf1dKUEtlDz0X/1Bo6dEJHHLVlaYGmayYsY\n",
       "rfdCu+onbMwY6Q66i8SHWHxjnCIQAb8Y8xWjlB5J6gyo1CjzNW1f4vTjMyFfDtFxiEcbWKGoZlDm\n",
       "cM6tipsvsf0gwixLOBqkZmxaZrTbCJKgbe30xvAJrLHdt9PCdHeWpyZcAO+M5l/WhvPQ2qe7PV4S\n",
       "RCWCfGOhP6RbdQOUkZEIZG6nXplIP2sb/F9eONfrF6s7/Ao02S42ifOf/soYI7fD8u2R+bGfP1CS\n",
       "7CU6OI+52Nm7ak/NdsY0d4NxUpfF2GfBT4+nSOKEpL3937VI4Hrv5IEle4EfCZXOpeAX5XIMQwAj\n",
       "ai0kIZzn7MZ8T5ip3zohGTIZWfZ6fVj0qZUhTYDyo/tcaJ+InKpDrEyUI6LYsMOMBCuBkMhnqRPt\n",
       "tzhbF7O6/KzqZwJGDV0rtmD9Kz9g31P3+ao6LDIKsetTEF1vCcIncF0On/qHSM+m9IA3hzjePblF\n",
       "/78uYWPbN8jM/0O2p2PP2jD9c48nagQl4NUVAJ9XUFfLtB4hiFVn/86C3VG8+Oar1AD68FUYqsqL\n",
       "Px+CI+PkJ6ieRp7K4LnA7nvHpT7MkBbwKqnkYEYwFZExO3r7UvQAsIFDesHc6di+VlKrq95KTHfI\n",
       "f0dUIYu/EhIBYpDwpemiW/mE0VoynvEwa46QDlQ2Uma6HDSxWxPtweFsV0f0sGq1eN5qFeLSw1S2\n",
       "COC+97jUucAemnZ36/sMy0xac+VMtb0Xjz11hePkfRJNrCUtEzNxmMIWdNP/chhz+WIHp6DbzxDs\n",
       "93S8KLER3ZjGiTDQQMUSp3m4zum+W7m48GwKBFt1c2dP3nMhwiN/zapa3V12xgv2CtludlQDMdKy\n",
       "DNdTMyoAV0RJ0lI1fO9WVUfbF2k+Ib9turNLnoxWtNIsvldoL+qUlUz/AqE7y6uL3q6Hwxj+YH0D\n",
       "yFnp6po9KPrkyYCz1lVvLgZ6129kmRoGDKsUAYSYqNfGo9fmo0egnwD94osj0FX0EDDJ+drLLEwm\n",
       "qnZoGIpY45jf8p67RGXBHDkP4+j6RRNZWDWwvjHuVw6E4q7pKJwksTCMcf8VSoEwbnm19Lvuou/D\n",
       "KQc9NnqmNaBQzELWQf5UIrqIs5mVxA+ssA/4gZ8qwKKtKmsyCFcrFWDCeYQsMvZRCx0dFsAL9Pfu\n",
       "f7jE601DwLw8Ep3Tdg7VEOQGpvGvOhc0/8+WRCJy/9bwtjFhoLUlsJjwU2Pw2DHjYwgdEM7GVci6\n",
       "IcMvtQs0PFI8Nc0y79A60zUxxM9v2ZyTR5rkEQKMKFROsIuIRMfxzVU3zuDk06Vu8DFFPe1KxoMT\n",
       "saYLjOT9wsK10OR6IgI5OyR7pMUgu5BR9VBO+kNyTHrWMWjWQWCwEqWQKfd3FsONtVrQlkG+ZIim\n",
       "moTH4znMmMmit1NpK3XxMj7NY1ASIs+1b+K/s6p5S7FARhkmB7dpfCKfKJD3JIq5RDdmxqQOMex1\n",
       "DTYYirnzxpzpMeEWgZW7umc5BzBQgChwtUwgCEfqOMD7XMgTi4JSoGs/GKqGgMUb1r1jXnStEEzu\n",
       "DLhGZlzkKu5qMb0Gz/bNzhG68n/ytyifGsFiWhyC2LXG6nYrITIPyHCulDe2uzLUKW2Qr3qFzqF2\n",
       "UOtTNYkW0nEZoLscXT+XBFCaXx/5xR3wf2D4KNp7JQXaLPidM6dwAahl2NAYWKKxSOn8euiJNBHX\n",
       "qqOmp3Cx7Jw9P239TUbVgBEG0TkIBs1qx8zuK1kNFBqhgNxJJwTbtvFYAe5ZrJm6ZfoNGTzxbVxq\n",
       "RuSl9HlAylgKkoaqB2xUM8JJ7zLXqpX8U8pE4KpW6mUw/rfE3XaD9MvGnrsz3yCR1YWRrQsUOXQo\n",
       "V0f8P4eWZEmOecfLvX/kQK74ye7PV/SKoE0HFkahe8Cr43EmbcvNaB4So8QbvGYHagQ4xBgJFRZa\n",
       "G++RjBsNZYeVzuZlrr9n+KgK5y2Plf6Ykuj38cAiG2WnT3p7aEpcOvAw1NiIOWoQjdSo/2zAu0QT\n",
       "Get5rkFHINjbFq4WR1+zHxkGcdm0b+EFUEUdwP+zUPrH5/nBdA77k/JHM6NzUL0gPMbS324vY+uv\n",
       "f/TMRXsDV2FknxmTq1d1P/ijGBsMRyWo4q+C0l1bHaDyronzbigPeQXPQrFqB9aSaSwIyV9DgnIk\n",
       "Exg1jPu9jR3YfE3OtL6+/pNvciJqSZ0Iw0aCbx8iDw4cy3kLyDMJBkDdbiSnFumGWePILDjgim01\n",
       "YTbwQbIpMXKr5OPOjnSkaYMXDFf5z9uYJcznq1uzoPn+kqYTAUuvNDUgOrsp5YVXcYZRFCxCgUm7\n",
       "0pY5a4oy0/+VjXiu3Y4GIr6+L8q1v65Ptk9GNStL1/+EAKIrGUU9PWNyDmXvA7UEswgKvgp12+n4\n",
       "p+nuAaGQUBtRbw4ajOJM//1KYjqfhgB6DQ7prFue68JOLiA5luHy3x2UWIpiKWYYyeqCrsrV1jw0\n",
       "xIWtavtMv1EfU52mqV4urj72y3oCeT/LexFABnF+JMVwkgmJ8IchWtA/Iwi8PXRjakoOxbQQqLfY\n",
       "0eT5lRHJzcwkbaPNuSAis5fybi7dM9n81NAQKeN7z5UAuMVGEZ6aMGZsT2tluWlXvgEv30z289Pl\n",
       "LrQBKq0VuF7lSoQVSReDJu5yWkFwjVEUMMiTZFUP7025NmsbUu/kpq2D3Q8qyKKC2mLAC/uRE+7f\n",
       "7OYJai3YtnYXjeDXmYBJB7UNsr2zKNQ53APzLQTzF0CvzamammT8/V2oDjx/MIY/GHv5TPjm9v/F\n",
       "sKOViCigObeFOpM/Xv5+CjXEQduM9zlL6yZ6bUeIdgJxwEJvuEc6RZsrG09I8lndhv6szseCgG0u\n",
       "oEtDtKo8vXCvcasDk5/q8xpmibXtOProFozg8r3jv4q+mHinRvo2nQ+11hI12PydL0c4JOcaeCun\n",
       "UOcp2JTZ7/7ZRVrkI10z9yR+R9LwhE/+MpEGdkt82xZgGIeCcqStLrKReqdCct43Taps/E6TxIPI\n",
       "V95FVU3ScTrpt9LQLlY4gi879BlADauCA/Gt0jpixag/TcTqO+m4019liYMhEECUdJrXeYNi1Xn6\n",
       "DQ1ofTmZg9PBY/RigYV4aiaZXZI8bxwGoCMiXhAHghHJqJH+XjCgN/fO1Hh9qJqEsZY1g2EDx60L\n",
       "s8hABvqH1bdRsfmHbVMRHklVYiAGH9iqLvpbsqT2TBxBevxhxa9T2I5wnf0jhsfPODIawcKSHrhK\n",
       "fij1TGIEKTgyaQgm7vDbRghejo8SqSLlm1rUOf876jT2f5t/4y4KB0tiWSuqyhQ7dDhTpcZaGM5R\n",
       "wwz8FT3Vgd9+QVKPLqz9gG1q2Nwd7v7YQu4FTm1ar45veQn8N08jWlHtbzXWRq9GRgXib7ReK6hL\n",
       "nYW/+LtDCUy3GsnStRbfM3A2abPdnK4iEFDEKTQeVLHz3xhZgrZ7T4bR8d6181QZMSBnrtmgmiH9\n",
       "klCcU3GLLnd4uSyeRPJtW+LyZYU5EcFOfo9Kx1JorsVVX1xdubgC2M6eg8Dgxjn2TIDzOpA9tHZG\n",
       "S3BRJcy2UzLDQ3pIWEhQf1vfa9jsYBfNie2I7D+qvLxgsc9CJfxxPtllNws3W64gL0PN0AOPkloP\n",
       "SoPqIS2vHXijGg1J4x4J4X2mNPqiJu1mG4Tw8ne1nukUoEyuPYF0aJUe0OIxVyQDMNS59eYcTu5r\n",
       "f4B80WBGTArbE+uvq4Ls2MbLFYcmmKltHz/YEqO1RiDp5s579S+igI5rdhwL6W3Trpq1V1Y5g53e\n",
       "4aV4wVA71g5w0Lo6oL6GG3GDO8HOo5PvQLPELQXWoHD/UQ0E+I4WZ43eWsNu73RpqnemX/fFkRO0\n",
       "v4ncMBZbf6na8/JaGD1NpG+T1wKC6PaFt0ShFisM47ZC4HEhC9ex9AZJ6eJQpKEqCSUwZOAdNXpj\n",
       "AA6LbvJNrp19ltbMOP3GhvndLhLtRNzuv6ntr0ha4gUDYCbmire9KpY3D9zW0uCrOI0bU2n1Z703\n",
       "P8XrbcBkiDnnEj5/wyOuAW1NpbjMgUYzIwiFp6hV92nO55IwRbndSb2TLQaR7OtVBMpvWHenKIAU\n",
       "DohFexxBYa8ruDcYg5WHsrWb/aq11mv0RRf0XNTUvav+EFYfzIWCHGkoOXv7XAtmgfNYGJuOtOfv\n",
       "gv4jgn5Ri+G7ooUXIm1fYKptv6fBzQlXQrxfKPvzfDN0QIbVrqJF5jyVs1Mwnt7yZaaSOEBil+mr\n",
       "W95TX7z2608/+aMNcQJ4gQpkCS+oYVWCcq8TIosmeyDNiD7i7Axwde1me0L6z+TQmLiZOHIwLIcp\n",
       "EDHIiBqpeeE5+HN/JbaNbtvcG38sFWbwRhvwUDJIWxxJmAscAl4w5MhuSCR1lprarY1DZMxE4et8\n",
       "EBMI/ZEBqpIW1lCSiou3+Ah7O9a1njhHF8HJHlv/cWALOLNfgxJ7HnXfU0vK0JkF2H4LoXrrS3Ww\n",
       "TN6QwLh8urh7IYk5IoHyhA26ry7j/9QeC9/FLCsv5EWp25RiZZqefIamipY/kxJJW4GLrnZdwUb2\n",
       "q7Cy1xIjBy5cKPaOhZGJ8Al2S7+1UDRlHDzuIZX4XgGtXrLV9GbMNvHzFrkGgtYi84RMlve5vHrV\n",
       "wzw58zIxfU9IScKc2bdqJEfX4C03vGcCOpJG1XrcHoCAANh9BTAaKNQJLknf6sQh8+O50TRP8Ihh\n",
       "G0sb1btUx5i+GNqeD+4iZIo42e0HMqNMuWbMuK2RIcHOZa9mD0VW+so/1i13SMJkn8PROsGGAKDg\n",
       "D3X/9b/F7OLukr3LQccSzHKUMzs5KqJTIUUttZG5UgjXC2WIx5VdlDK/yk/Yz465EtNbf7AQbd+k\n",
       "6cqhQHUMfGW6ngCVjonmKpHExJWybzzPgueVBa2W1iMS7cPWnWsWu14bY/DEI3y+HT+EXELikO2a\n",
       "5BSpZX7ru+vcvXW28hRIGkDL+d9dPda9TPUYI5XcI7joVsVTrOrC59uZsEORlUnWxaTxXtBVnDhO\n",
       "izsDlnYi9QuCsNGtBf69VClJwytM+k5VPBxcR37jhXBnKTSdt6xFIJGNPjD3cYMyDzX/gMbzeTya\n",
       "iPWc+hmqMU83DLaO941qShcbQCjjCMWAjOP6A0ViO/Mr/gCTgaj29f0xYIzF8nXmpnCyJn3GcMLP\n",
       "mGDK3ya5D6ivn6ke3AXfiVCIBqR7NjvU4J8mXzhptuh/13ECpk67qtAH3POlpwJa6kAxCT4xcpOs\n",
       "q5yjc9hWVZRRzOEkN9dRhfHtIweCoojjgNKcmqH94m33LW9zlMV5YqM5hQG18WB3t5tpvZqOe86a\n",
       "Wkl4c9ovaLu1ZeVA0zQJNOCUqr0GPVNWfDH3WJJrQPsGx5MzkaohhH+CMRSKa4ktoRFNG6vBdR8r\n",
       "WmJ+E0QMTqNDcOj6Dh+OwUlrPicXAu2ABGO8QHGeAGnQzdTKqZ5VPs0t8BiIJxlxWoQG8agVaUjZ\n",
       "89HGrWCHSUX2oCVAJK9Ev7lDHAQPnSpZPDmJUPR/MR+f5jzw7YDA/51oJ/DMHdoJdJFHE85XAuzr\n",
       "YoPWMfkaPbiDqGMLGkGSnAEcwYVEmvmyAPGFOibVXCQdJDv+S+Rtm8HQDS6+AmyKUNihJ0czMJD/\n",
       "cPWLzPBnOGdTqkKkSVeLSxqT1Sl/kVDEJSDoJhbASqR9Dwdu3AL2tne/AYROAA0UWNgxp7qnlIJu\n",
       "g1LVUGk6Dao1KAgGVd3UNp3y94DJm24RB/5VTK8pQs8tn5IftdSJWzVoq2PoeiAqEgIpmfQz3UQv\n",
       "AozLLxboZj8CCWp3EWFSF9AoHJdLiBtMmpX1tzPYAQcNAYk1v6v+XlLIvenCEwdZyQx5pE0Plpkk\n",
       "8Tja2qKTpaHFmBUJWehsme98dl+0WLVChfF1c4t0phRisbuWnF7FVJe3h6+RK69IeALbja0DBvmN\n",
       "RSNssa8BNTCbChW/5g8VXFCEGHAOMoJ82tUXyHJgpmfT2xR18BDrHeiPBdkA7xgbrdM7MgzAg4LF\n",
       "Pd0M+bRrf6V6XaMXD2P/hYHvLgz0JIA6opjTbWPEb1q1PA/wNU7roPTLPjGorWyUyYBQ5hPvHqkK\n",
       "LCGLtBOzajpI3OLszaFKnDaESs3Oh7jlu39JUIGzgl9sF+4awkpnXYsybisCQ3Kiz++bvdTz/4zw\n",
       "DfGp5ggRS6tXeH6jNgamMk6a/6Up50fOCPZTNftDMzCRX4jxKeWwRmzqZcGpM+ze//tE0N4wizWr\n",
       "Q23QTQRKHB8mnNjKDP4UjrVG7I9Pb4S5AuSYsX2eSFpontBWNNIwQBMJby+tlx2M9xFBNIjyPgbe\n",
       "NFrg6h1HErwuCuJBvpV2903Y3maN8f5deWZYy+4A3kpHdy54/fMrYut2R6FPWhF63AKkJeIwfu+N\n",
       "LJpDWnoLP/l6H7PWgMReOdey8D1qjkyvuIML56dw6CRRH1ILOjCKzz1f+YLGjxmO/9q6t0Cxqj42\n",
       "8E95JhJemL4CGc+iugXMnSCypR/rF9/SOu/5qD4PTjR4r4g75sN6PWrncGvQ5lU5yXa1pMC37qV/\n",
       "1jm0zshex3R/WZ+elCiWtEc0xYNaO4gi3otg9cL88yxR5uUcrpMg2rg6JMo/RydQS/3WP9sQEPYG\n",
       "bSeBTPOo/NjafkwIHh9qxYgrzXKrjJJmPq0iZqgJQvrEzGcDb3rJgpQ3XARYmViRuJVrJuYe3Pt4\n",
       "VhfDGx0Dj8dWCUfwpzkzb796V78eY9DXjhI70KBdjuUIplADiMLpRs/SefSkmERPCa9CCPzv/sLI\n",
       "Ge9TmY0DxghUjn/GUYDqtSuWkZrJPN8kfCsk/SDoS6Y9PG/Jtnj9YtLR4p5mo1QeFEKLWpB5YIg6\n",
       "/znfBDVjbi9pJTK0BgHK1ZEuO9i3xSaqSaScd0xb94cKbEmyRJuf+eBGOSOlzYWWS+HzthT5ov+q\n",
       "26qcwc4wncETaDpvzOiXBPi9uWuI11o0O2oZsqhGEK9TcudTWYhPDVfByyy25EL/gtzfpS5BWz4I\n",
       "HAqNPt+CM6h/ji0vOwwvAM+YB8eGevpoEJZRPCogt1mX7ZSuu+MMRISUMt/KZd1tReTiEgLVq4Qa\n",
       "AzqKnihirXdtLhuQyWnwT+RIHKCTPHZ8uyU4Z4Cy59o8IYIn8k9ITNPHeZat0x2UWtb2Q3Et4bFA\n",
       "RaQb7xrY6KADHwhsJB3b2dG2/naDv1plk7+XN+ftzz3tB9FUop1mvx61pOwRQV+K1lcNojye7nvq\n",
       "PuIkSSFEk6f+eBrAzwzC4Y9odTWQGEWE98aAgfbZsuSeUCG3Z2hriae9TZyeoHyOdi6KhQjn94vK\n",
       "/GBwtFQERc2twym1efuwItKz5ql4/T6jFr0dnOzn8Qyvdzo5e11sxRXjINginGtetmdrPpEX73c8\n",
       "OuicAa1IZgT7Li8ba0EGYlM7EuyeNrMRxFdcMSeFrPFxRQZ8c8RVWmZXeWK74CvLTUW+ycAAU9cD\n",
       "EPLyF1yX7bxMsF/j9yCri60FOSidyM7thWZDllJ6fNnnyHVRoxyTfQoPFfTcoBOwnd98fSA+26ZG\n",
       "tBLswFV0TaPbO7RG5ed3OUhwa1D20StYLnBpNP4mNTS097XWj5ap5Iund33nQookHjNa8w1nX3sk\n",
       "QT56f6Z8bGtUZIQKW6rOJJNG6hMIL+a2TcFcSOTB/Vtza5gYYSr+7S2K+lD2ihE/RPbrLQrOaJ3t\n",
       "zdOfp21LRz+DdrByxfG3h4Mh2Is8IjUp97vg+AricHcbIhMrpmh/41qWEi0xW+8wGKXZZHw0XYBz\n",
       "qCXDj5hbzUbf1uLB+UaacvXBk8ozUJFgUtMIJGxARSx7XKjmy+kWRGdZGo/uvwi0EYRFXZsi95/p\n",
       "N88xB2CfEvfv4TBckReVORwplqINavfQblhGNFJffpth1ul1kef/hGJvRTUysyXo7HfCcgCtb8eJ\n",
       "VXumtbid166KEIs37rIfHnFCL/6bI49j6KkcXKbDt30js2nzP6oB5aFhz1SOku51JSCALEsF5ECf\n",
       "5sX2Rdg7hb7yBocSzd8Pat1yYhOS6Ni11J19B9xOgdNm3AWEqFk76zLcPNvtTRNmSEwgKvBspC6N\n",
       "L1amu5NIYrFgLTlq79u2/toHZ2PNs7tDcdRVkeGqYppxomOg9ungWsHm5n5HYzbvlrit9smvTCd/\n",
       "oZLYPdBwy0Z4mAzTWxTa6X+U7mUx7vZ97At3WYVuJni+0nT5QpNfB/DQDigUoS3wVZXtz/ywACnc\n",
       "E9SaG9Qs/4vtW7fzIjo+94NWPJH6vUS9qzqCeUKHYBGbtQjKT7ruPsCbHqoGkd+P2MbUO+P5qrMA\n",
       "COftG2LRt9amWryM6CLdWqNASkwipEHLE+kwSQRXoJc+So/LYCAsVI7cvjNBQWr3Lvgi206CVmUF\n",
       "NM26+HnNIXSg+N9GFMp5/BgjUJ2tWHykztcwc7muXa91q23f+9lEY4YzOebxK65iKErtBUDfZbuw\n",
       "mTCC/RO2nKfZO25l790Sl97iw4BArF0obKEpxDvmnJE3BLGAlqoDw7C2mu6TnnNSIqVHGzpvCLwM\n",
       "4K2nz5b3u4BuoDkqfVufSBEC7O41qHADG3tPwtQT5KXsjwreR6KMjjPfW6LLH48KAm4C9gSFEYN/\n",
       "IU1ws8TTMKKRgR9zF+qFWBGEuLXGWgGTpGfY/pMUeLkZAIVB3j0i1QwcFVct3uVA/zh7ygVWxg7E\n",
       "V/RsXt5Mrl983oktZI1WXSDmM4clYOJyeHUZBuyBMy1rRTGl/Zl0L/JwCV5HnzRCSX16gLgSot9w\n",
       "r2Dy1vUD6GZJX7QK8fT0ojpMHDKwhvJqyJaG194FZbM8vTXUbwLGOX7ThNFWVnr9QbFV0FabXXj+\n",
       "V0A1i68BFHbUHLfeG26xgzXGElXAKN+pZAPgWLMRAPbinfoICCPYCeZABxRqK/TTWggVJA1UdZe7\n",
       "/H0cG1C1uA6XLX+k+332/LbixfgUQwMsVnySNWVAQK8hFHEY1oLpEQra9LmeqHT+xx4vP6dJTqgr\n",
       "+fptEdA3wF8UhqQwToiC7ureNEUzfWQCbHejFh/uft6RAbQ8BP9PdJDYnzZ9FVe7Ku0pgiSXIY6U\n",
       "GBdQydWQ3YyHGGKXmrMO4L5tqCp9tcR+mr4BOlIEt6dDEOTycAbSQTrN5Cs8RAQeR9GzgQfO+tIn\n",
       "NLfXjo5SV1DosTCmr8IgsS1nfFnQq4eZB9sF7k9pSy1F8/oN1Jj5D8nZ+yuTB9uGWhpiXAUfYNaK\n",
       "STjuFS908y+OvGkdsV0IIdOP8kYqXw9uDROmWJQEalr3gdH2Eta7+H/shdqxOIVt01ZYMvZJODJW\n",
       "kTt6P3k0WnMVyJ5Z7KsA5d68TU0eqnco8s8fEYjQFMx1M8zfHu2lOtU01fP2fJDPpvK3aCKTVpIq\n",
       "FC4+nrVWoxuFTNxUHLDk0B8yNuyQ9VY0LAXmbnO+FayLv2nlOf6ID1MhUKNDIwVZEJbgOu4FbFcR\n",
       "yYY2VKOaUw4OVcJKhA48IJSYXoHqNwVUsk4vlAiGQ5IbO1NJSgqePsQ2+NMH/w4k8QAzj4FG0tSR\n",
       "w3y39/3IP2PpjCZnW3c+Fto+v998opVTnoKDq1NM3Ge7Ff7tHuZgaCh4QPvZF3u1RuAYhWl10eAK\n",
       "7tf6hgRd/h2xlz/XYSlV4RFsKpMzvIOtiVlUvZiqjPvTqMCWVbYjXK3jNNhRjU3BapMEkgsgKOMm\n",
       "hv7+2JznQ6Nd8vcFdVKGA//5cBMFeDckLqiC39eUnTzGft+AjPnbtcUQnb+JZVof+U+AID1Yh4mM\n",
       "VGZ5pesbyFVA6TfZPxmPNsCjTLG+8C/ERa3dXnUWuQ60djCgMX8zZJLAsFqLtKq1XGbOtI7UAce4\n",
       "L+UFYJPlx+Eo1TF482IJrYO71A7vugp9Wv5aV+bx0/G3waj52lDV9WwynI2VCV4Hug7Vj4IElQzD\n",
       "OA4KLKMSLygL358RV/hCxDZDgSgOZvD0605LrT3v6iPknS+163rwUNZCEDnJ9wvpEBTTD3Cw0Ioe\n",
       "oItUTyJGvcEzv9mS1rX9vDqK+mZeZdleASBymcxtBr3XWDKWiBjmo6WPpP8+UiZtvg2oIf+k69xp\n",
       "PWX3S5DpS3fDAcFEbF9IWGwmOywbfxVbLzZtJJbDOiFz+3bceNFQrqzxbRxB/n2o5ZbTnHztD2dg\n",
       "iiXKo1xTdgvNaWlyiWgEUePfiV2hEmA0KT/zA+saeZiLRX7lXLMrLgW0QM4G7Zk0aXr4s2Qblvvw\n",
       "M69NY9Kq+Vn+urKrxjTuBFkeDtARm73LyvQXwO7LW0ati/9f4wx63lFnUabjgn4l/4SD2vey4Syt\n",
       "6NjFZFbXFFjS8POZPGVXGT3IyY1t/78WnpiYpzIewWGoLHHqcfIlcFnnlZkglR1+/c5Y0hayzilN\n",
       "rgeB/LrUGtS6ccFHFf05+rxyUSTwnfc4diYTkRfB5qgu0B6SRTQpy3xb6f5nGE48EPytFEsRikn2\n",
       "97k5WujZGyEzpMNjVf2s+Z1Q1Qpvp1kmDjK5fAlEWeir75Fgxrxh0dhbeNuE0Nngu0Mrc0pP3cvb\n",
       "vkbhnBw5Kv0n1OmZDbrh5DSSLCZsRuEwyTwrMtX+cYFsccKt7FQLqGhvnBb5V6DeJbrsVcuGP7NI\n",
       "ZBdfPV24xrJcBBTUfRQNKj291o6TLjel2hgMH00bQ7TvyhA7SErGcbqmgDl2deDpPGAOnnzcbHrG\n",
       "TIJ2OEEEYYYSfaEa9ovXbS15ITHD09v2o4H/SCSjUbBLvimgElwKIMJbjbnIJSIhtBJLjNFifkXK\n",
       "I5Z8Eyv7lNtSwVf4cHNxzy/pONLJraNp1X/RD0wTqoLUv4vSmEh8Y06hG0YjNU8z1U4CtqTzYz/8\n",
       "ghz8VZzQDWsN3XieqmpMku/U85Lng/oVaZYh9H9ZTURViHez+jCGgdavkPFolmp/TOjq9w8gjSPM\n",
       "UjJw1erx9yW26UWpWFOhzunjQ9GK/5XMkPrBbhoJDwGqLC8EQ+Ye1o/PoWW5xMoYNtQ3GcV9tuO3\n",
       "NEbxU3qmlizT6c8WqPhUP/x9dzBkzD7A5bShVlv4p22IHAgYcx98iIxV99ec5O8xK/ZZ3ttb3Mxa\n",
       "++xC4sj1PYYlZ0z77ij0Ftn2onqeURX/tZIzpTQov9Qs/vaDSXZH2T9KZjfoxHR+pA11tEp+JwFq\n",
       "gErjKl6pMs43g9a9AKCNdsTnVT3B3+jlPqGySnahLA+BnYs9/08z4g+KNB0knten/cj012pXp/XF\n",
       "vwi6SV3oIbMw8iicXJQJivolNYBSspsJUEkEujrb9gsej8XwMcNJXh5RQ5Cs5qKwRbnjm1nYFDFS\n",
       "eTvg6Gk4XbUzEWDVrj8TnPDeUgR1b9SX7DUAlOjc+tIdtKrd30Ub4GW1nzAxiGju5WaRfiB+UxyX\n",
       "MVA+iaWi1fKDleLqGmRVaE0RHd+x+2xkoU8pa0H0Qgd6q2nHZeUU1tCpzL9YSsYg+N5pMX/hILgM\n",
       "nymyK7hoH5gIUlIm+KqsHjdWvBqaZpu3nsUj51t1Px8Uh6ALUiOHe4ghLhCkQK6lstQQbXezxt75\n",
       "61EDL0tdxKdsdxsg4w52vQ8gRFvpw0ZVJZMeeMIAAKqcdBZGepFTZV2YGxr9sbeS/TIeFLZfYeX2\n",
       "s+OTDyQS6tg7lWbT6O39hASl0wfvKG+Mhk9JihElCV3RK+SeybnG0EUNP50oWSTEfnb/TaYfLj6T\n",
       "jr8PBKOONYtgsBarjFowb0LZH4kbNKbyJQ7crE9gAsmgT2LLjGiZnumyK66fiMDCRsQRDILSmUdW\n",
       "z8GQURMvzyz8Ih/vLCitnnvYpjpZI8z2txsbBlWQzs33B+BGAUnyVYRcvyHUAQACBHknPp2a356r\n",
       "j0SPrm0Xm4rdrEnRXM0hweMR8Arq3F56hYLrNyzowU4yznMj5SQRmKoPvKey4qnkC2NRXqh699B6\n",
       "mO2+YzrNtVuEsIt2jWRYfONmmPbhMmpGODZbY+HKyfqL9biyAtLWgklOrz26fXKN/Gp28rToQ+yG\n",
       "p/lHGN8YjrS9v2bV9bW71vXAXTbVKS+RYcls+YW2O92Jg9E+g7lFHsk4aehmZjyhamQ2ULYLnoNP\n",
       "tslTuZNqLCXjJy14oCHuj8w0hCkNFatxJ9oEayZHZD2/U2OuQMMZ6jP69a4z/0bin1XJVSZoptlN\n",
       "ZHQ8xMJ63kBdbPNnL3YZLc8dR/C+SkaKBOe3I2R0gqiufRnUrqvkjN1Z25+FeNuFwTFFbWLK0Z5F\n",
       "zdbk9k5v8LpPBCxxX+CB/eDAdCJ3vRDHev9nOa6tBQPh+5VcvaRv+0lDlCrGlzHlnf6quggJAYM5\n",
       "n9SBpqTgpQI11GoFwPg1oiFUPPQqEnIEFaGIURwORsOTwi/bvbkiFMvhlX7dUfBwjeYuO6An7dBF\n",
       "Qulsr6Johw7+HoJplbYgx1Bx4+cL5QRgARwNsWq0eELeKv6+9SUNuCu2jLbDg00xZKa5kGuXc0cu\n",
       "q5U/vkL0u6Rp/8M6PMhPgBrnEn/mQh+EcGt+LqXo2419cioY/hchZeB4IR7dSqmRZUtnFNJMW6lY\n",
       "6aEhdnrS+B9/trmYWHXqfoaAVH60IGXmPT47W2oKY5n+HBrt3v9E4Gm1QzCKByY+JiGq0JpN2PvV\n",
       "Hfl91KIb+6WivKG8MopGkXDQFpnw6ymditYkzsztpy+Di+aWrRJz/YY1F7ZQa/iUxeGdMownItHs\n",
       "Rg5xpAb2E3JPiFaTbz10vWbroZJQSj2lxRguX/YzaJYAFiAB83+ujqS11f1PjeGvCoOFII91+Xen\n",
       "D876c+YFsUeOdgX3JT+4KasIojBQ3BPHQavRXTgGLpSAFcxuTgissunSd79QForEp4is4nvS7OZZ\n",
       "0+igQgT+TtnFfEedcZi/fTj3O2PGtnOcpZGoDhbRbWl/6g7wIp6GHiQPFwDe+8hjZKxCXjKgOGIQ\n",
       "57yAykSby9kQoyjdEpaOrtBxLH5DJ1blspftals/TfOrmLf/KBsJfVBfxiDBFqmCBlfpiPpLtlXA\n",
       "L47PItm7BwaRWgIKA0QP6KXrkcvL7Did1YRdKmKag6kyPZ6jTaRrxjxzxVjUZU2cgZ6lA2ryOH5q\n",
       "nRlnzCTK1pRlzAoHI+YEwEYSQ09IiUAVrzSBOOcNpyyAuV14Bvd1J47ne0+UtBaS0yfSYW0Tu0zV\n",
       "O7/awoYC+oao/17ljv/kzOtV+IJHJVso9/SZzH9Jo7pZn+gvszefPNtPkWhWp77358/9bf2lN2Dq\n",
       "kKKJ3YOxxQ1hz7aSJ7rou5/ozrr5dHZSrvJXDrBX65/yL8MOjA31Y0yIxaytKtK6+5MMqvxFm/ni\n",
       "Ht0erGi0hZ5HzVhq5SAdY1ydIa8qeFU6VzZJqCjZiN3RsH52pAuoahcozZ+UwozBqGjvZGZ5LVfh\n",
       "FKMDlgRaQJV+D7M3Iup+jOf0ciqTTyv7BufTk6ECURBVFMyoftTUd4cq/5r35guyfAQDYaY/c5Or\n",
       "Uiru1NsnhbVA0LAUz1o0ux4TZxbwwrQj0TE/J+dHZquT4Y/gIywKZ3j/lztozfEv+2xIjisZy1fY\n",
       "KsOIXgqCf/znrAyv5sw4bVGvFhSWXZuedWnkKTesPlZv80QS1UGv+31y4Sm218xkZl7DxCldxFVG\n",
       "foSx69Zh/fxLwAu0N8i4kvrBt6w462DDWRcMWwAT1iNeYyG8SiIfrJ6DGR2dTl7DTxIFUTuupgiz\n",
       "wUm0tHclQletc2bBC4du3kcQT3ZxQX7OGoj4PclklgBxSXi/DgrUfa2M+0VoYmWpCdy8xpzNCRTn\n",
       "rEd7BWEJ8UQTlsV3QGrBpDx9pdQuHVsTCjRKlHYXBGPSGAkLzU0kwiNJGGuhSOBG8ScUuHWQZfAN\n",
       "M4wGkqDspSrBfhPuQ9LQOxBluoV4XEVW4toXPZ429z11aTQTFQammaOZmCHYuNm/7sQz8quQnJsl\n",
       "j8MAjJw8iof9xOTZuPdxU9H9uwNXfmRSMsSzw++v3egzuayAoNYQXwSbDdh4p+xAiUltPtQ82GuI\n",
       "LUc7/W2NiVOm58t/GqCfnFidt7heYLKoKbFPvFX279iGL/1vhKvomyMFGzW0ZujqkasdiaAZGPoh\n",
       "v8wgehMcZuMaJH0pgK3RLL44rxHPe1ub9xhMy7+E3S2FrbUWSal+95A7HDoSrB8QIUVh7GqnUrks\n",
       "NfMJpelF8qGV3JijEArrGf7brDuZIZ/sBmhPYwHORxl8ki0JvtAlQIUossyE49vIBHybgYb7D6XU\n",
       "hAQAdS5ITCcCPhTvPqhnQ+f4w2Xhagr1G/X/W1nI8RzIs4/7OkY9FywpFDZnQKU/4U4XB3BrDt1z\n",
       "7Fs7vgBgsmR2tWUhmd0Lsc3JLwwgmQ3VkdxOo5eS4oJPrdZFk/lFvL1Yxs2o+b/fc9sMJIUqK68F\n",
       "X5owBgi/1vjhRNcYRSKBL6mk0qz2hnRBGaZCHIzmIAMzq+Ti/KUBZcFX6ZQ3eRy5TTm1OKsPiMub\n",
       "nhtP5KJv9J+r9oDy5jIftZK1oWl4GhCD8dASx7PetaczkgyyYxRNc92Ul6NFRVOGs4dHSUR5lYW9\n",
       "/gEkySfUjn5on3m1fab3x9+ujVSpgbz1XV5yzbHRRE+eAwr4dAZeyiFSSwYRaslXDD4HTx4VNa2Y\n",
       "AAvCVec7VSV4WESTlV5lOg+u44cD8DLYqijWGcvSMg4Icbapwbg0PaI1l0qA+BB9FivZseOB5gZn\n",
       "HXTRj3tY2qjnheeGne7/Q3Ggl9ayrQTSh2nYUBme+oZPKXLZqx7zw7H7BHef0aDAkBvDTy4D26HP\n",
       "pBVmGdFtooC6pFBXSmFjQK2ZX29fdocBMF5qPUjjGFRpnfpLJdGb4HL9pHwfHgRy7UUGmM224xEl\n",
       "LZzIC4juPt4gwbPh3I9dqToy7+MTGmFqb3/OyfUq6ZiWnMcPR2u6d4xosYDCtAWucyNpPvZtEUd7\n",
       "8cuNRs+CsQQxLCF3trTC53Of/mmIBOV6mF6LDibRQUD9CFSS/6iPZvcUnQI1s1/i9jurVLepxcWA\n",
       "VBNvgvG+k0b798W7zkEad9DU0gtUFdsQa038AUlZCRZnjeNZKfvkhaJ10vfaOacCOYdv1Wj+cj+S\n",
       "yvhzNjwPyqodxSDzYRK/mD74pkgMBV5RP/+4VB1hKeeb/nSRZOmUAzrJOSMqIK1/8t3JP/H0my62\n",
       "jpXi4t7pQq064/f0Ph13t494khgFsHgRBM3MzFPIkIlMknBzZNgIVpWpKDrsN/9G0Bl+syWmNC3Y\n",
       "ZhVfRNJMJanCpHC0O/n/JHwKKk8M98LRPz6euvIOt2yXScVrPX1UNPgH8G0mW+A0taod58SKURKs\n",
       "Zzhrw+MWzzakvWu8Ifw8JIoqiYbkJcd/6xwVO4pP0jXvGDI/+jG+HMGO5U7ShHsmpDAOvpgQ6AD7\n",
       "CSbiHI4Vtkj3AOQCS2Dfsd7IIYor0duNHQhozE9nV3ntUwJK6tIHAndH/v/JZ/zV10QbUfy+MTiT\n",
       "kpJYSedyV110EEIBRZ32kX2WAhNObfGD1l9wCEo5ewtM8XnSQsqDGdKsGHIQ8z4NLMab02XF2WsD\n",
       "0anlJehQmuM3617baY4kQPt0r5yIAXmlYq00bPr/ZxhAfq5xaWYA3h5wAvyP5pfFmDldY29oTpCi\n",
       "8j+6/a4/lJIxEsHG76cIozUeV6pRCtwP9hUKjAy41zl/IGE17/f9xZnWtlzuol98YZr0MNufY/bc\n",
       "O3M049Nyz6I6gj4voonnEcWPGm0n1Mpjyv+seHEXaEAYndqGBDO8oPvybsh8UsyD3XVnlt9wI488\n",
       "/+qSMh//n3ROKq48haZgVQ9DZjoqJegYsn4tw8QZDtQxcUfFY2jBpNpRHJcZxP5AJXWsEbAJWOrA\n",
       "nsMuUPy4nf9fKwQ5fN74CzFzl2NDwEdlSEP+5jOX6PcqBRuL7Kg0w26zKLObgX8rff4IUEQeVe4w\n",
       "fo4WciHxF3YDko9+PoManPEnvkuIPCDG4KCybTKnM2+bq1wF6aws4raciG9s6W51LXQ60O+gzq1Q\n",
       "kA7TAfxrdXO3X3heufki6iVjoxxJae35O1CKqMtMfYxjwFrXxaJ4soZ8lx8bKufYq2UJm2P2gWHL\n",
       "kXw9YHgVSNN7c+/F4+hEzBNhHMBxeT73mDTXPUnS73L1mog9zWKnb/pSH26p7ay156qnptxBGbqe\n",
       "+nQhDbquemPos0tG+UnsNU5el+uH4IwuKd/hP5G/F75tJFup5mv5JR7EIBWWxwL3SP8fimFgiDD9\n",
       "Ev1cUqkveltaL2MgGQgMSn/94j7g5+R71/r2vtr5xcEXrT0YqxNRkAyygDROoHi42C/UJIzs+USO\n",
       "u7ybxjZBoOGhKfdtgJTf7PTCwYu9GOYqV1tNazMtRYfPV+fUcuMhxQu+OEgTrChHB/pxKltKDnqk\n",
       "Hk6DGU0vlvZ7+GxaST7q/5Tv+F07kKRe4ZG6u08T7XG27gJ5WFoB4XXb7kEpKZFguFsoKd3tBWnI\n",
       "LfC0ZrvKhuDLUN8Kd0k0GMJeEsgsXQm6frQ8+mM5d8MQbdcXcokEtCYzVe7im0Z5O0/JA/cQ7EdB\n",
       "rgjTd1zYCEe49i6w1SzSxeOZS9WL4iMFSnMdGV6s8i+yB9sl/VHfAwEZ0DBcdljvuC4PJ+BzTvUE\n",
       "WA4rzG58ffm/pmj/IwQ3bJWiiESPqTqBVracV69Cylnd4K1rn6hqbZHY/mkCzQYMG4bNCmbXxfAA\n",
       "l1HrICxHs+72psLKX7JhU8bMBmXy0M08oglUgaXU7FOO0RqmlXBtdvLt+qUmKvMlWcY3mG0bMvVw\n",
       "yGtExcP2NNGJqcNz2BmULmY1tJelZlNujZ4nXgMi94ZZA2+8v0wbVGRVl71TW3giBVnwDKLC9AuH\n",
       "n4DJYQZoqRuOf4yVnGhoW1MkXPatcJMKhmttn0tEOF2LxLGoX26oN+EQkjxJ0M6RZPQOHoWuCWSR\n",
       "zT1Sm6VOTux5Al5lJaLzwjKtn8CEtPo0KOGS5GdgE9NLRK7rwZoPvfZeTftSj32hS4H/7PB/AD+Y\n",
       "J3hz1e3dbe1JWj1xllLzI74ANTlvQVrq3CSxBZ7oTUKGZYAzcTwjd6oY2kk0v/wrp0h6sckXe9nn\n",
       "Q0MdSH7zzdz34Ix/4Y8r5WQTaSsYLDpPPd9jEV38KcgWUcCtmXwzw5jRdH/Wy5JP4Gsq49mKYDnP\n",
       "1CBJsk6HqfiRqtCW+a86ZDxwnmJCmCmtwqc4bk0hn2zz3hjeIfS65Cuh/8omAEmKQEOHwYVwOJ8B\n",
       "aaAm2jxu3evvjD7ovQncfem9wlYxkjvHp1tP/CEehgNSrg47mUvvXpGQq9Pd6twfzNgevW2l8IEJ\n",
       "CSBS0P6fmyx5nYnjUsZNbos3ZiQxg20sP4FZMzeuWAzKwiqCPqwm2YfQ3Wi0CA4JUkfdqh3QiXUw\n",
       "0Kt1zCuKeosdIJpMVoZLO5RDv/NZaICG+KuA5T3sJ1wQEzysWoLebhGht90AcKesR7aZUixJz9ED\n",
       "Zu9KSmlOQoavjZrMjfJ8G94abWZHCrVV5kQdY4CapQVS5wLmZ43vhyHwhyei32yofb31A3VD/sjm\n",
       "pTkmYxWPJURzeRWRHHhYkV1aeKkABzZ8/eE+YIn7bEOVnnZyganADlnor+/QRNhxCo5X8kr/5Y9h\n",
       "B2bVfBqcy4zvoGjthqv5g27YDalqT/nQseUTcGWgtjPArgzr2zwD6uYZJXcDAXasud5R0MmtVOts\n",
       "HC3PduedTVh3/ilnBCitOrXu1+EI+qPWRg9H74ge6v1GriZtJ3xLH8zNPluDS4Fpx9F2acDl/wry\n",
       "hw7hXKSxp5mMf4GcroNcg3uewxDUemP1R6G6j96/yeTVynew1b3NKTsn079Hx0J+rewk1PCp+LHa\n",
       "LhEDaFNtG59+NQVjZe0TbHH3GyyE+VY3uemt8gpoogJs+E0QtOMYuc5BbdRDYFLSr0x7ygVQYMxj\n",
       "kSIgojskfJZ6ZerSWwxcLBcLtCg+gE34FLE66zFhzjAHm2Y+B09MOvB0mB1Pm/45zTBVsi3FM3pz\n",
       "a9Xyaa+Sb4MW2+YEfnPAMDp/lKlT0PgtBH+ctcFAnZXI3a1jhMBN4ftRV9iQNhsK+Wtg5lKNSlW+\n",
       "l8kU9ZaJjyvFtpGaGOEKAq6ZxTYpeK3uMr76qVqZsJSrEoKVT+Dfiv7lW85SPoALjR/zOE84gJoM\n",
       "4+QQNihmreJ1Vg6Nx+0eLdsuy9ORVRJuXrMIWaN61bwPNs1WhpAfSra2upX/5LTxczdhj+8xcgA0\n",
       "iw53yYq2hKpzJFpk1aeJ61N4g+hGAadHn6A8ZJRWB4wIbrlWyLFWqIgvHP/7gwTBCuSjzy26O75w\n",
       "wH78QiRKiNq4YQ7oZSUk9KDszlltBwTVlKK277D3p6D7dtoUR4T0wNBk5ktfSPr3+s3pXjWjlNLA\n",
       "0woOmmZyTPSFYf+j/ffRBdexYvIBi1TvEK6lo9ivLC5omofaBOWSKZGBQhOTE8L5O/K1B9hUAAfI\n",
       "HcKhAAALyEGaImxBH/61KoAKV+urhIASqcujdiOYcpheDuRIgOcpIdePeUmBBBlo5t2Edzn2OR3O\n",
       "sT3lf7CZz7m5U4ww4umYjggarXfnsAbU1eWtZXfQnn4fc4C8xFmEQ3MXS+l5QWXFfgi4/HxKsFs2\n",
       "PV2S1BrJIowCJkN4I8R/0m4uk5et3uSYSwX/K12C1ilkhGGZqtujCq0329RdHKjhpJLWZuJeQhw6\n",
       "F4qRdYoOI+v+u0YonrkXfFrdI0X+1BgMnyRSLe2UrRbnJHOdEVbSMidX9IIr4fT9Y8aUd/jnP/I2\n",
       "A1V+G29QXsFk4bR4DA+VErXtf1Hs388/o13GZuEl5hWJh6xbQTI8dJoiFOrpw891L/tY4YcrRrud\n",
       "cXe2XNxtOSKquuYGPfzrBqw6wNe2tqDmo7OtWGtCB7HbeJP2Gzi63y77+tSy+8vmmy9AW6ayu+4p\n",
       "Lo53AkoXXBIyTHVED52sW7inT++sH9RieNW/xycaZk8B9az/tn8e09jnQfQOolRVDiiRHs5gNpGa\n",
       "oBIKsVbqE86CEAHoDx8ZtwGuKZWInFBPAAyN8tQwPsYd4XtGxfgxwXJO7HJlx/o7er1iLoSp1Jge\n",
       "kMieKdZ4uA0/iuLJVq+PEcSLWr+p7ysmuHkpmRPix4SGsOYa2biGaFWMwjIj6Dx5SlStgDEMtJjc\n",
       "Dt6nV26531wQ9mQElBp2f2sFP9Sd2mqYQLtHBOfsXbkIrJp3jCcR6DsGPXBC8CpVmUMfkS59BNei\n",
       "CIkQ2G17u4WrgLifoXHeFanbNO/gRiDRGZa984AtVxK84hwWtK+sIUUNukoi5UGcVEW1PMqxDXVK\n",
       "qGzWPQlS/RxKU0kcTQIrbIgeJ+cBebMf8U24Ve6amQqPHrq1s9jKdO4ufVveyNlzSAz+/M+3NNu1\n",
       "lEcN2IUTG3xqznt8Jt+UVNrcdEQCfyh1AS0R/bJSEAx2CD6wnUqrHdI1EHW/VGTssULps84c7ysd\n",
       "YHECrjusFYd/MgVloeFvgjeDJ6PNF368S2n2eW0+d8mlWwoBahqNt5ja8k3B19T+Bq83oK1Wa7jV\n",
       "+nB/GnHmAXQ7Zz0VzMsh6SzSRl5Bbt7sK1WSGknXgG0KN1HsYRCOESc6REhH5KjrhjXJmmbBilr/\n",
       "zaD1vVHXcPcqNcxX1mB1xndAHNZl3HgzMectlqCxJFLM+rRDn3W3UpZM6pnDlv+2KTF4MZmuF1uw\n",
       "HDFf0bOKyk0z5bfjVtYSlxtONGBgRgH9zGG9owcsJ8WQEdnSJoPhsVchVV1qZjFSDMFPSTqEnd/m\n",
       "uUj7GSqORf1JHpnnF67EGkk/vpO2iJrJqFEY/+5HCSosOYhOK7BrKX3Gyu7g4PuiBbaZc3SGJIaq\n",
       "jPNhAtc/mHnEOWZpRVPnmOTKl0ZsuZbRLkpqwirB8R9d9M/2MQzeolk5vHER/bAYhmsLn5niIrB2\n",
       "10Ddk7RlcjSy+sHk1ZSPwk+nRRr8nBPJk3p429OheeL1MJ7Ln7EA/gBfnsI9SfBXvUoNSZVaGR2C\n",
       "Ultx6bsqOPoldgP5iA+Sq13dQL+XUbhErWyCkZYScBWNQyIofoZrvMI01+GLdVZe+6prqNqtvVnY\n",
       "8fHwLo1W+deSd8af08rA2SMaVcf1/C23+EzgWl93RwCMjhJi3Ypgzf/2coes+LjvZQM0q2U29HLG\n",
       "QmYetCEKy9lKn9OrXAe979N83v0OSpUeAOLHzpu7o9P56xNWc3WfO1o9XIY7mtNbX2j/7pAFL5re\n",
       "HEmZdtx6nfxvzYxW9L4y7NMnV9v3yWmqNqPDl0WI0ANeDCWZGQlfd+K8Xf2ct00CBg2MynluUpOB\n",
       "pe1XXDNYYZ3xNSO2CxH1VUVvLSgK6PNZAOCKZsIOy0unhqkZttbMpIwXOnzuOHHqgbsIPwmtQbch\n",
       "kHO4GrrAgjf/XbIayW7eQcJo1QhyFW39hpcGpv1McZqneQ6Yt8D5Zr+P0jHtIlYgn260+RtgGabd\n",
       "IDA9QpjvnX/+PhKt4ETF34B9+Jx3HnyETviA5gKssVKKXjQrLKzUAqEwCqGZNKVe0IerEaYBg2BV\n",
       "fJ6+8Z8y6PU6XcnzvItLMxMsxSSOgVpVP2PiJPvbDvSkvtxrvznJFr7hXwkY274iyx0MgLpT+bbd\n",
       "5XFX5ES34uKcrYfzSHoiALa4y6OQv/86wqezjPCk6UA4yrHP9fyp0/XYcqP9hnfCbrNZA6qr2YbG\n",
       "1RUNxEx3+6fhI+xAt9tClgXMy4ZN4QmzeNFmZdVnN3kdrFcxEZJsnpD/JEV70eXqnn8BTOxJi6Cu\n",
       "UGSZa4Y4glLJ6SLGplXihUkZrI4Fh6P9MJkF3A4pc9JFyXeH+wBzwamrJp91hJQ6+LfrBjglOhzL\n",
       "f+XnJLt229+FA+QzKSOay9EH34NlqkiyhuMNlaHIo37fg0fmpdVoqSSlQptOj5KgRS6ijBSaJ07n\n",
       "EQWsb9owiRb34J40STbEU2kiDc2rixLUCSyGQg1RSEZAiszN6LE940NxVD1saDtB9MCGPly8bCOW\n",
       "2o65tLg2//F8k6lwqD0oFOD0IXZxI0Q00RqQYo3SU5Z3d0DlrQQvRPJDf26IQ+s48Qv4uDBe0QBT\n",
       "OqenhVi7yAJLmbkEcHzcrDa95sNRxPAt+koboJX31BAQU8kAfG3Z+q9ZsUcJAutWfyUm3qTXSXZf\n",
       "zLlFlngpnKGf/Mf/hL/vDWaxPcktXU2us/FCvQkHDnYNnR8n0gYaZYQwNdOvbgRk2R9wYpeX2lJQ\n",
       "AA9x9dwvfomNkeUnaQFqcj3zTgxFUxN1FajFMcfn4YQ8qvVqso6Ueh+msDEGuyNh6rNiiFPSPJGC\n",
       "qMTZOrADPBDXkJ7MG9plj/HK03kcZff1RdWquPpdbf6Ay5DGfP5/D8zRmnqskCBpXNs1R88LICQF\n",
       "u42BSLF4eaL+k2n5Cbzyl8a6UmI08JtDNZrwElrKv4g92fLJnv+A3D0uAinJEhnbmBDO5ruDW0Ch\n",
       "vlSH7aWK74NgoVJM5pu1mRMGpmndr/MWRlHihCnVVdEoqjbUWyiyiX1uQrUoIO0nvwcDTS/hwQYy\n",
       "UaFbEBTaURL3T3IEAACLUyKkyqoz6w86D/fCIxMPrrr+5otvHADCfq/E/m3EtLe+qo56FDiVOtqw\n",
       "CVpRw0ItH6kwlE+BSAPPKACKq5Uy9WSqZvzaJ3rmho9mP+7voNONbyYLoWfT00QBTq+2dEGxQmC7\n",
       "k/lPnYyv9XmQUoJBXE4ZI2Pk7xCOg9kLZYlEJbM5K/bluncVkvgc7DmG9ySQSjdreKQ/DoOamP2X\n",
       "sLsJRGL++lX8JwGQUoXznbr8HF2l8BxrP/eNk80k+pypq/vj3L2PIZlTmppnrXLKA4SiGX0t0K8Q\n",
       "a2NH/8k5WxqRSzud26LA+xoMagTj9AcSznOE7GFZQHJoMLOrmuUvDElkQ21Oi1bPjmWJX0/NMczl\n",
       "szzJ2sEpLQJOEIgGWVogcdJgtzbfWKHDhKC3UDl574RfM+andwazsLYHKyCW1Vc0oi+nJLBcdsHB\n",
       "ixikWrgWnmymSahINZFzPGjkU3/TjfodPSJdmdW/acPb2Ehqgux60aelOs5EXvnMd3KUrLGuNQKs\n",
       "iudvGKFeK1eCqfxJ3dF7FuFJ4BC8An58/p3jFTPT3Z/jvyGqNS00mw601LjhrodejfjOPqiTgH0p\n",
       "L0IvFyy0YU+lCnqr+Rxk2PAZrximElHNnvf6sOiUytCrlgioPY+iU1hI9CeRvLvX2npWzOmFT0tv\n",
       "+3gPsPOf3e+rv9OoKSPQ6RLr6z6mT64D031nafiu5f87Xdy49pn7YOYYwpHQnw2VnOh1yUe4rz+H\n",
       "yaZUXEBCkmhasiQxthQHbMPWWvFaAc5pD24k34hUEShUb+JmTL0ZZzC3TI1SgqT1MdZFj0ghbq7b\n",
       "/p+lT0u7BoUk+xIuwydBh31eTM/acF7qvReHwnJbyHLi1CJBajM5Ryb6iK7O+UrelpMrJ0otxNgk\n",
       "GpHOGDpKKEBNZynGhzTsJVWDBQ1w+exR9CHQuX4yUDroGHm+FW+XZHcg7En/CpcqVeon9eWZ93rp\n",
       "lVAAAADMAZ5BeQ//ABxP0bZO1GMWCgDkoij0ZcgsugBxrFTHaCXrwaaXpS8WFbRXo3k1Mc40puCF\n",
       "iQ4wxE+iRI0At6WP1No/D/QpPRTPXyReziC57UIXFtmbID79jPTDtQ3nDUGOp7wcZp2gQ52mtMhp\n",
       "Jc2Wo4scKM/7WlCUxbptO5IqhVITdjDZhXMnhM0dMaR+eR4y3Do8S3akTIfQohLaP4dkMY12eXrj\n",
       "Qk2tbiJMQ+5//0QacS218WjJ9mK1bQ0AuSCdjtF0h5fqVu8mKIKBAAAXzUGaQzwhkymEEP/+qlUA\n",
       "GLMb4m+ZIoAOErMpBHxDsk/VsWZlOXX4lx8/+o6Fi55JRGW0zxvmHwXztPh/hhZmOKjV69NZkvHY\n",
       "YsT2cloS7jNUit21935pOa2QcWK03r+A+p7PYOy+5O5L1jMjoF5HyudJsxgIelT35XRpcvJryGyI\n",
       "FfYjOuzUHnqviEzm40ebbqFg7S8th2IMFhoDk1EFEF2yMDHR8cfIVHGnRD2TdnzT71TamGaK3bb/\n",
       "0V0DbJ87SSfS40W6uJyr802WElZoAhwctGMSKQYGkzh01jI3pYpWpGeLk8b0xXT3T33r+40pZFqQ\n",
       "JuWJSqj5raB6Oxu1Kwy6wYYXg71AiWymq0eHSWZcm23+MRIPXP2OEqVFSfrIiTdtpkixugB0ptQz\n",
       "sgEGzfI+lNrWgR3nQgMvJTzKcBWeQNW9mpa32bV3YNbOrTmQlAH2OYhFBP01WLDuyMzOMkPyKtXg\n",
       "T9kdsz0jxUqgF5Xq2vndIZAEXm+Khp+raYSM7ozcJU6Kk/v2GjFBX3ZftKGobEFnNfjgzV/t+L0v\n",
       "vVKOdHc5DWtdnK0rFIYvx/17lTBe7YS4Gq6ttp4tl3TxY4+nECb6tpSCCDE7kH0hB704QsjDjpdI\n",
       "eH9jplXw92Qml7awPFh1LlzLIVvtnO888DFUw/MmH4ozZYdtVOd+5row9kKzZ0zMY7ymiduwxBUa\n",
       "FpVDiRCtAZVd51k/jLR+0CZBdU/uRh4pTmWKhjVGQ+jSelgZFcMelgSc4hlOn27msyHoeiydTMSf\n",
       "e6hfisPlvnAIdnlMnaN/E9nRGg8pKRgb2B00T10xWAuwjNJSsoyCkIQzehyZLYFlioCmWdDKNUW0\n",
       "DEY+UO7ZU76kjgcEFmS9sZOFtVLQbdR0yS4KTC4FLQs3Ufk7pKz8mypqcwdc4iL3CS0t7QPmuI7y\n",
       "jWiP7EQ9IM4DEanLeuZ57AU33oNpIyR9cS2Nt5K4rYMJFRx/SaxShbExqy7GhvuUNtWSX887i9EY\n",
       "gHXLMXroCMW3g0trVOzG5svOipmsdx4lr5cV2Z1962/chf+R6WDfr7LWFL8XJcJNqpogJhybSrle\n",
       "IRWxgr91KuxCrAsMvXdaDnEW3/UqkbHop37cWzAacNvavXYEfv0nEKtFxfhoZwSQ4+vGbo8XpIwR\n",
       "WCqrjwTELOnwMjEM7ax364wlT+8t87yc+SLcBc/iNiD4Iazhl/+ICer+wHt4nJqvolK5KgHy/QtU\n",
       "bOQA8r7NXQ9V4OwAKkBUPaOyaZZpQi2Dgp4XRjGeYG7CLLlABr38/1APcocYUee3ueJfre5UO0K+\n",
       "1JLzDpfKdwKkFcQHJxiK7nlnX6O53G0JZL1Xi1v1OlzmbkK0F3NC7GmzzhAGqy1IL+w0e8S4+Jmc\n",
       "KwBlqQY33kNP8Ydw7bKYLQT+4RXgbBV5uOCp+21YCa30xRPsyT9bY0+O7P4rKpBkwBuV45tYcVTn\n",
       "2ieCXiTqKD5WUlMzQYv63kRtFU5AGF1feWMWeS0RDn3AH3UqFLVweExNKx66FlfK1U9Kho9pKWsO\n",
       "wzB+rKZI4D+3eGPyswO/3LedE/Vk6tG5sKgFrusKtJ6768DO1PRcZVhJmNn32IwlbuXOTfQNooJp\n",
       "xhlMw3Qw+r9zTAw0R8ZutAZgO00lBQGkDxeZWyIhZD/vr5UaXh+wfmuYEDi8b5JxTIaclxSOSkGk\n",
       "MmCXPMmrXQU3pXHzK/mhKm6eyBhjq5HjAisLnfnoNOCHz3af8vHb/qsy8Hjx575S7CiDVMAmkNS5\n",
       "RVMjuy5vyChky2DrxELyP++LHZG4PW1uOBQ31LJLiHize3aZ9UWH0m/bw1ZFLZwgb2/ED9Pq2gmF\n",
       "CUrQHteJtYKl5MRi3hxSJE5zWduIt8RV3Yc8ldBPFXwlP6OxjEFAkYFMgaAtVWpf2vR2v1Uq3q6S\n",
       "jlr57G3szD72Bo0sxOI87sSXhrq+fsuOfMTALfH7Ese8rPDUTmix2h/635hlTGABdiz1L9ox4mtg\n",
       "CruW0of3jw4dq5X1dro1+HDu21OmEd0zHV/fx8gZO6VtdtnD0+7CrIU/qyTqtfgNoefsG1xsQTht\n",
       "EXt2sP2BpOTcsfLDWvDzpI+XJ9o/dbxRzE/ERNHLJBsXQ7LZm6UF0xHf5ZVT1zAMdY/vbc4r938T\n",
       "8iWoSUz5n28eLArWrvz8nsVV+k/x8xIPd6PvW1zW218F9jPqIvqD4y6d8kw8HUuCgYP42z786k4p\n",
       "KiPWYZQhNwF3v2awJlXH8tF7L+5yLjc/9xnpcYIiSPYYWibdSohkmxYdRvDPnGAumP0d936aJvhp\n",
       "N6ge20uhbMkORV5275dxI6eKEIozGcayOo4Zsa2aUHY44lQXzz/Wou28AVTPq4pb+0L0XOhNGfhT\n",
       "DucnY+gs5L/c7MKdSTPy/J9rtmhVlOk0B12gzePTL14fR0wbZkkgpOKUmhKyiei+Ozk+52ij5unI\n",
       "4slrteIdXTkxXnCCGxMPbcZLiA6eMAMT9gPpE71lPNPxud069zWTKFJuSZeAzYHX6Wv/Ye8DLd6x\n",
       "T6aIuMSBCSUeuzFqEbA8/ZT/7GGdFbwDhLDoUTvB1YXdtl4v8acMcuSdqnGYpVrAMf1ZYLyAoJQl\n",
       "uher0AoLsc7mULU2Dzgo2msiltwfnNnZaXWHynuaD9rYjDYYdtB6D+kRheVsqQg+bRGZjxCL8y17\n",
       "V9mORVMKxnovU3AUcSezt98Lx90kObSbl7KPZuKqgW7TkchpRod/2DG1yUQD22yv1h85q/ICBAQV\n",
       "cmsdBVi6/v0G8N0EnIpy970VVWWvMtZSb7Ymdjgr7wjMRGdkpAzm+rDgl5ZBW8ZRaH2MhRrrkM4T\n",
       "z2pSJ0u5fY9yx1Bbt2Z0GH3oIFIFVd2vi2kNXxOsBAHwIkga+duyY0j1lSuuaEijZZu33FOuaBNi\n",
       "CnC5xMUAYT5hADpX0M09LlpdEXEbUSWb+p0Z4UzOUTwaTZrWaCC8KCc2CBybRAUeaQ2Lzlj7Kb7D\n",
       "IBcCxcxl+6XivEq9Qi3a3jBnUIBsp5GV09g4nSQj6RdYOgss5ZmeSlrfL52P6phfBNFh/7XQV3+D\n",
       "Qs90v0KBn7VQMm3NNAq20zoIgH56ei5Ju9ZLt8ixDyvWe3XpHaFa6uNdr/VvXUa07ROVSyXgsVLu\n",
       "YsT30lG+QoHwcBTFYA1ISaS5wmi2Shfei/fKI+Eb1g611quWESGXZs792B1UrC4jKagwsQ5+OFck\n",
       "n+Xt7cb/lSI9VoDX3/MiDZqiM/mC0qSTFAMqZUdguVfqoxSrdGWdMINsvs7t0Jx5WZHxiIeq/iQP\n",
       "SOYTqB2Q1NLzWPp0DsQ/4k/tl4bhkkq5/z4Zzzsn4USfJLO3XZ2OD3LE7lSVPGp2Z+MEp1fhCQ+b\n",
       "CZKQUxHQXBsB82Dnfayl66GyxhHxc1t+wokEfJJh795zVR1SNxsn/ubrDSOUi4yXe5gZzdPZhaoa\n",
       "V6AaehZtXlUJur48qXXyotbq6rl2D6ZLY2OWz/j9kB74Cr9uhF1m6oSDOfXg1uXfz1ZOiX4yo/oX\n",
       "bBR5pl1Ftx0PgJooJZHisVqYpgrm9BNoSzXUWjpfwgE9iRJMRA9v/EGTe4B1jbbwnKbZhcYYNOI3\n",
       "3M5pf/Rr/V/Y56Lzm+pfi1pxGQPgKDzI5sAqCb13jI6p42CqVWFrMDwCXYLprFh8gs2aosJ80R2o\n",
       "qRvMChhetDLWw31wH+ZnY2WwAJFTLbcEmCqvrbIRRhgZIzmhCk9W1id2c5d5WT2vU2Ubh8KEyOnF\n",
       "GRIGRRnGxAGAXZg32AKY7zA3GF0Cjx7MbBo3HWS8HJjaPY6ikRXilFwoJBzU/I1kXyHlh6XEsLyE\n",
       "dID71xHv+JTtT5vbfJlTllbaO/l9inQXUG5E4GU7ckSsvpsRwYXNXtiu79CMeGrqMPdyl70l6IuQ\n",
       "PgLeWyU6HrbhlMo6UTPjy/I+ZNfx/BMhGqd+AUwUT4wKbW4Y8eBAUCspgZ2NGBxJJSZ/DSGTVZ4B\n",
       "vbamFfxJjdhnXwDdcZg1wftaWDWKq/kBaXEA3UN9fgktaSssIF29KiDibtVE/kXuqC1rgPu062sf\n",
       "lV28yjHEXTfqTg0DVY2QjCBJMO7g0aE/ifvgy6qypHm8gSKdRYRUL31W0cRnwzQq/XBpc4bQ2oNL\n",
       "BUJs2d4yjdkwpGZJ/eWlMlOu4SkyeJWKL///5Mt8nHrcxuWEq7M4RzXzjyJQZoFNYGaXPtaP6XLP\n",
       "08OmU7gAAORehj6gv/q3gVTe4q13kmWkelhmuOdXLEAwzm4cs0XQSTVGlvfv3r3RxGU4oH2SiHGv\n",
       "oa8eaDySPDORfIMpK5awQCJuBgBxGdTF9z+J5prL1lNfeEjt/9+n/63NIn9C1scrAvttTducrNOX\n",
       "atY/cDl0AjBFILQagStzn1tqKe2mxvdr846uutWJWPXGdlkV229XCYck/d1yuLFOlxVgnMGKhSDS\n",
       "o3VVbUkysjgNOZJP1+6oxtgcdKpr7A4GjkXIMYoxcTKfDy4Y+dwzIt+kFtMvYwut84ZEJqB/OB2q\n",
       "g0rEY6I9gqzoaB2hHmJkc+MaBOlMkAJGVV5UaHG5XetfzOcdyUQkAocwCLdyMlv7H4c7DBVi2V/F\n",
       "9L7G3OhCBNgejsrUIIseHjTp5HHrJBkAj2s5j8luXMEh/zNlZTDdfBMmYNKnAzHeT27TZNGoVZM2\n",
       "eWyhI3g62iuFJDXb8HHFYskEWQEey5HRwv/I/qESbipHltfLykyOU8y4MasHVGAO09LTODBmIsHa\n",
       "7KzKI+4GqdCNuemeOO0D2cViBBNep9TKl54wC6TbeNH1OLM3hZdjH2ac/tU5F+P1DFJkJVGfjqB/\n",
       "gSCI5kKVZyqnS64lChtyKd8/h4xXBKQws7WhPKWhgtBrqITqJd8t07f1r4rrcRtn2/+PQdheSCq5\n",
       "mytPquLHPXh2b1pgXQpxZwqnXYjRSkdGfpUqu3QTRKFqeynasG+OMUvp/UujbKb59M+8rvZ9vlHE\n",
       "NBXlbbQUvOJzZjWFQypKHLdk5m1Q5OZYuIB0N0YNOZxnfw30+l12HR8BhxJAtfo+HfwGmuSC6v5t\n",
       "0ZyB8bkzD8q2mSHxXGfZ7fIfyE/K2w53FpWOOCApCPMTpYdED8Qmd9LQgioALGpBXMls/Pyd/Rt5\n",
       "pLBGUliTKdIImADRjKQ5eq4MLnxgrFVFI/6jTUqBFrOuLAQZMdHSYNrjGYLKFTwW50aP4KOCZw1L\n",
       "C6kSO6iw5XhZVhKkpKuzQIUk4ELwdmzhdSljt64HfBaxWb2nXarERm9lFMt+kYq6IGzi1Bj68xts\n",
       "DPiD7bdeiI9jZIahSY8VHUAKkrObbvZU0qCFLlEde8STGTtoDac3JGr3mrbMibDnCJlgwmVtbNlC\n",
       "vObWeyaKJn1/WbUMiFQGyDWtHHMyfMW7x4Me0a9ZJH6jMZyTsuMmQPXqQVZDA1l30DdBx3Qtybdh\n",
       "HQYjQjAeyRcg+p513f9f5flhpq3lNjSGqpGZRuYWUs59FHGc0RomVxVBgD2KLX3tmZxTHtOJNEZa\n",
       "WuRnovTFCIijlX5qJ0Gktk72muKQal/1dqVp0JpxCmM7/Ouv8ah8mrVqMihmLB2cWVviOZGVhFsB\n",
       "jvhNUVq5BkwKHETpPjeGi3ZctHRAfdA5BJYDVtdhzost2o4IJeu3HOQBNlbc9/o4k+2kahcwqJBa\n",
       "Ttl3WfIRto6afTtZ1Bf6vdBVtzhI9WODi4nDT9J24Oau2hF8GIFkEwOsswaBn3DCAOJi3DEV7OEC\n",
       "vEGseAmkig+t0yIg2v6uZYqQUABC/KAy0t6AoAeTc55QSfVK7G4cHumVGSGAX4nbGfPApPgisB0N\n",
       "JIoUuhQnV8ZiZy/CEEbvLQsnKCu6mCmCdftIDEdUh1sLrsDq5UddrbbVB6YsdkoFXfmWThxm+j3p\n",
       "Z4jAtzZnfcxDNyr/U+lJ0KG38J+4Sw4CX+AXMedPAbGWUIlegb7Io3N++ZK5DOQ00h/H7HltOm3Z\n",
       "9a0QYTkbNbgBUnYpOWOWnpQzbEk/+WFg0PRpfLF5h+yM2Jwl8QsZJ3LiqhCAGsxz4nb8QwtvFUeh\n",
       "ND1ZhQn8NGWTIxnLzwqGEkkpXSW9/UN7f67jqni6MscC9Dulna/HWBCZIO1ICzFYvlEZYcU1LKNA\n",
       "9Ttyvw5VB40Xf+BbomegAW3G+MVhFL1k1Jh9lFpT9ZGgMVGzOJMjIJmIB4nn0oMCpN6q8S7CZ7Ly\n",
       "WbVXV0SNOiJ5KoI91Scph5mWhb//j4bs/mAkZ/0MCfl3HXQNfYUMDCKmQ0NJNUNj7gv5EFbT9+cQ\n",
       "y0d8BWSTP+IR7YTbUAttcCbc2vBvVfxAhT3v6fFIAABvA9e45EQk7JGEddCITrnvPxM8Z23rdDkZ\n",
       "WeCSGFq/nEc9wTf97oAlbwTtBKQPjj5Me6mkBGvGvCIUYfvzSFLP8M3IUMjyvTuAImKWobATQLKz\n",
       "/0dgzrCmF6PPb2Q7dkPZvrniiTlfp7pIhlpozYwbvDsNSnKqvUvTkhWvFrknVumMw6CzOLB4LDOm\n",
       "LmGgw4buhfr8fgJppGBNr9QFh8MGfxCENw0iSohjvTjALkCK/pj8knJExtGZHloQjO7Izx86+q0B\n",
       "hy9H/s1ZNwTGJKKeVTl5vDTVSTbI5lHQDFhY/vHUBYgmw4TFpNoBrN/kecNkicQRArqZUHJB4ZB1\n",
       "slIq6BV4oVr/FTfCVBRHAzZniaAAB7oCkH/3rSKjfyMTG+Fr6/jrjCmhwXyCPth+CqLPDYnb1Pwa\n",
       "mmpGE9LhN8PD0nykN3kXGB1yl6qFXA3T0FcDMg+Ugi5GJYFn6wjgbiScaCACJaqDJlP2EK8GnEFa\n",
       "ahLfRA0uB7crSKTGHRTcB1A+/jC9N4cOq6BLq13MjZIfTutceZULjet1mNSk85NWUgh+TZlm1fXX\n",
       "TVoD2eUw1f0N8ENSJAxjtlzgD0ml07LUYTs9e87b76qEfZHBJuT9KkMD9eyAWGMPwa2SK77sPkil\n",
       "KAe7MhyVndjT4SL4KswdalN68R4z1B5XuW0adPwPwHsOTnjc20PY8MWxA0iPwwvnsda3IEVlYo3H\n",
       "bf+ClsyVd5gzbskS6UqKS7xYwBWgROT05iMudnfQFHS41na2Wl6e9MQzGUULC09SrL2BDgC/WcoL\n",
       "Wz/hAicEZtkGoTpDvsnbFo0+csJ+x1p4vRtXerziP5LN750Qot5w1m3fAKSgbqnd8yJe0Vs2BfXp\n",
       "Z10CkU/eFvLkAYqqgCgCDyV/PuTZR0i+SI4+dru12Hn73Y2yIXGaCkF0elU985hM/sO36SG7FUIC\n",
       "NmGok71KrmgkXR4A0NHloIleKeSZ7jKTHFs6QoPJ8LRVh9DH4obNqk2MJrysVU5ouS7ihUlIrH1w\n",
       "/ByOKtij8F/BWu2GYtWEkX1BfQvyhmrUC6yQatWnz6xltu3rUQ9jYy4/dPFiiQMyrOMNu+pIc+/v\n",
       "EjTSUIj9DuklO1Z8A7zQFaGRFKvRxAWYGrkf0ZTE5FZkTwZFH0VeBlQ47u8wq7o8yzMjciIdE8Ht\n",
       "YZtbEw1GFKY2lQMqbDNlWqRboelgQwA/RhqiHziRVjbhJ7l3L+zeghjlfrxvXJfELtUUgy4zK6H4\n",
       "MsF4x6pTtbJZPVDU/jSRsiJ0bAtcK/chmGEvxpFp5cCGMKCgSsYaamhBbi619juuoH2WrZLqZbPd\n",
       "pUKj3mXxVrFn6TuA7V87113+6rkFHWyPRBZsQE8z0Daz0cAUuRJsAgCYBsiRKOqztzDfcuAD+gX6\n",
       "GJncN1fKuYPO4JoZmbkA5KJ0NwZYP5BK/WBCf9nNnQmfzkY0lLZP6UF4kdurdbSomXrJyMSxePUp\n",
       "7uADmH/kj6Q3ND+2INcrPmSpSucbLEPsH2cDlmSzVkgfJ8fzJAlMOIlKS8W2wzNLCZeKxzicrOjV\n",
       "gnMhF8SOCAXGcvNzJgsfo6bbr6G3T/Wsbkfpfi+fglGkmlQliOGsKvN95awXkYhkRMJx1wg8nDii\n",
       "B7BVLoW64KigQnYL3ZtEzgV4YoUKwkrKmyu6bXsvqsTFXa6ynFopFN5sPTi3D+jj5cMouwTXkHPS\n",
       "n66/qel+k4Ic49LFhxDxzlPc+ohjXBf1CIbcTK9nFadQvkNcEQAQMLlwu8WKNxrua+qMv7d5gxYy\n",
       "Ypyu1Um4T7llAtbQnI1C57dfLbZOeAzjvbEjxvdkfrpb+dVBlQAAB9JBmmRJ4Q8mUwIf//6plgBX\n",
       "USF4oAAc5bYlGns3qhfuiGt2w/hrk5gK8xpnTFCyn9jjwX8fdPMVcbiCOFTcDPcVGpbTfOgrLvx0\n",
       "BprNp7JEoLue9CsestX7ygnqyTtxMXUfpKpymW5ZbG6F0pad6WVAqn9337vheSGEoJTMA8p+wyXP\n",
       "chRPBWQ9jdCtYnt0HjNf6Y1QALXo27fa//oCJiSfea6Ylni2aivdTPDan+3p9J0sqDHGLU+/+/eY\n",
       "F7vx/pEaU5m2A8c/NqokVmjwJ321wRku2NcdzYnjgPSw9fd3Uk6WG8vb3ljFBQGeGw/yQavfu6HN\n",
       "WpPoQkaQ4E9wHvqd4VbUGIvjpmKeMAgEFmz8hqausYKUjfzkeRemjKBmaTgbP4z1HwnAlLd4vY4Q\n",
       "ki3Ap+AJ4QXaMO8flEBgzpRcUpT1mMZUQczFw0voFFt7hweFl4zXklGzFOBbHYN6lRyXh3+ObBqv\n",
       "sA/+aBVIJrps1OQXOT8uGE2nLs33CmX/3HhtRYYcyQ5AtqcI0a6lVMVTuEW5gYhHU2Y5Ke0Qv8FT\n",
       "iU6QWhkrUw+k80SeHRq6+u0aLmn2hpdoJ0wgoQnRP3/YLsQuXPDpEGs8RQn026KzX/SVROONHf6P\n",
       "yGyDaERCh2aDJBig7AuhuNngZfq8Juf1IxBjNUJXMtK49Jxzr197jHsQ8ABbRPmefpNo4oaHBsDQ\n",
       "6ez7qdFyAc1a2quYpUkZ0zgLGHsuoTv4QyrusmuwdtNMXqB6AQ8jwaia/MKmb+jwjJpF7PRueO6p\n",
       "DugJ34B3M1e6OPPFd/JwOGdXpCqaRyq4IXtWKzgRQAULDIDm0Bhkm8Mjd4fa6b70Fx7w+nC+XmV7\n",
       "d7q6tpQr4ZwhP6DxgDNM+/18873sti3woSbMex8xyJKToSI2TpSoO/VPHY0oLo3/vYfehrjpb3eG\n",
       "fqyG8Drzyh+BdPBiWdwVULH7BrcfRoYnzcJ0+6PhaSzmTeQWVxZQiXjE+i3tKrjcJ3m62n+Ma59l\n",
       "4lbrCvl80Uw3kJ/gtw/WgcrX2IWQrdBAg2VgoBSFF3griDfI0LnHmmhPtseapJYj0d7+MY6QXNle\n",
       "/4EkdAa9aB4Pb/uIgSOD4NB5k79ExknILNAdMGgi+ZVtgoD27gGIsImFVgUkI3dkjOFpbB3/ZAed\n",
       "EhvqIheuOa1dBaih/oeNwlUS7VgYGBHsiE+qu/kclv8WhRaImCgHK8+jhNTEOxpe3Qu7buyH+AbV\n",
       "ExiJQzmGNXFOAyovPvsEzmloVEzPJwNVXcDKzljAMwTI6+CGB5IXxFbEJv0lSlRtMFHgLZuqmq2N\n",
       "aJTdmk39XyhgjPkTucWyGOnqAmHXu/OQVYphf9I+tGd9IzdavlozEyYfszYUwHs0duY2P/hGf9Ex\n",
       "oYrNmlknNq8/LfT2r/eq0gaY8TL/e2OO2fHsYAnotLbFM7o92lJ/q8n6Ut7h8qhpADW02ovtL8xH\n",
       "UF/YKP70p8t8DV6vBjAykU2qAn8poQJpGTzaU2CYRp5E+iqxSg1GAeagbrDySGW0cJQ4AjgfC0PZ\n",
       "2xV2U/jWIHbAonrtMS7PoNm26DMicJN4EPDk3fLgFh4ToUhyLP72M9C1msksj3o4/kHWiIdnMRRe\n",
       "kl/56Z6Ff0NDZTTLS5G2jF/4H8uTyW0Tn33juhgvCpGfbn2U+GUvchFe+BHNVtHUVy5SjOkvIh4Y\n",
       "pkTskAlIJ+mhjdiMKrlvhySTk0P9Taq+lPsmve8X4ciVP+QT7OmzgJa7eujKHFAh2CcVSmUQzbsV\n",
       "K1l+De7CLx/CMfqeHKUfdf1vMMGiTd3IXKSuu4JD8iO14xsC31HxA//bSvETWL0dydVk59v0xlGP\n",
       "JyeIxtu42rQNUkrF4dshrHE2nwmGFlmucxthyIPHF4p88K/MVb9prRWDA/LPgkMGgoVrX6CSDqCR\n",
       "vk4HX4//6AG8KCn2uY4zYR5b1Gh/5dST8V/NT7b9Ff0CUFhbs2khlw6NeYfqKwT8P5YHnsPj04PC\n",
       "xvQktkmiLctDTyW/tvPTY55aXxNmJSAe06CTn0JjhWYkjF9tFKXZJd9apTujWKProD4biG/lqzJV\n",
       "Bxrk/fS32JeXcyBRYYBFO031Leg7A3Uu6ekI7BEL8lVJCaUzH8+t5pqPeHNBZvJlz0mVegXoU8Z+\n",
       "RoNgyvj3FaA24QzkusEk9yPe4c9Yg0eweABoNn8vUA2gNeZ2fDRyCkL42+WwXmquvk/ZSkVvzPdY\n",
       "Clnf4J+E2GKYSX2spsAmMGKvp3b9vHTykGTWu3fMwq+6rB9to0dyb1HsTZpOraSHsHTDCybeXSfD\n",
       "iTrzRfLxz1YpYpqAlT2Jw+UyO5kcgPQiqrjVKbkTTiNnFV9f/MptEYiAy/OKyqD+qj7JWn4ITJCA\n",
       "QuCvRCw65hB0Qy2rgIvpC26T68s3JKv3qUN1NJQ+JU/SPhRgf5/7nq5vFv1qi0JJvydwmOAJS2Ww\n",
       "oOeDRj2eTKbgdIUPJVAFOnuupBmB9nefEqMeZTP3bOng8rTbQR2USyS7V368SrJ6/vh9BGsDhzSj\n",
       "77y9wXgM0jUTqDkdkXbec2mCwGqjmpjps+tCHFGnJymF9tnMgMHaTjH/7y6G7J0ZbIOiFz8L/YWN\n",
       "HP2oWzbCtQcd0mTjud2nqV0ScFZlpWB6/KdrQvGWZ/kKtqc+iyvrdVY+7XburIZBAAADYm1vb3YA\n",
       "AABsbXZoZAAAAAAAAAAAAAAAAAAAA+gAAAPoAAEAAAEAAAAAAAAAAAAAAAABAAAAAAAAAAAAAAAA\n",
       "AAAAAQAAAAAAAAAAAAAAAAAAQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAIAAAKMdHJh\n",
       "awAAAFx0a2hkAAAAAwAAAAAAAAAAAAAAAQAAAAAAAAPoAAAAAAAAAAAAAAAAAAAAAAABAAAAAAAA\n",
       "AAAAAAAAAAAAAQAAAAAAAAAAAAAAAAAAQAAAAAGwAAABIAAAAAAAJGVkdHMAAAAcZWxzdAAAAAAA\n",
       "AAABAAAD6AAAEAAAAQAAAAACBG1kaWEAAAAgbWRoZAAAAAAAAAAAAAAAAAAAKAAAACgAVcQAAAAA\n",
       "AC1oZGxyAAAAAAAAAAB2aWRlAAAAAAAAAAAAAAAAVmlkZW9IYW5kbGVyAAAAAa9taW5mAAAAFHZt\n",
       "aGQAAAABAAAAAAAAAAAAAAAkZGluZgAAABxkcmVmAAAAAAAAAAEAAAAMdXJsIAAAAAEAAAFvc3Ri\n",
       "bAAAALNzdHNkAAAAAAAAAAEAAACjYXZjMQAAAAAAAAABAAAAAAAAAAAAAAAAAAAAAAGwASAASAAA\n",
       "AEgAAAAAAAAAAQAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABj//wAAADFhdmNDAWQA\n",
       "Ff/hABhnZAAVrNlBsJaEAAADAAQAAAMAKDxYtlgBAAZo6+PLIsAAAAAcdXVpZGtoQPJfJE/Fujml\n",
       "G88DI/MAAAAAAAAAGHN0dHMAAAAAAAAAAQAAAAUAAAgAAAAAFHN0c3MAAAAAAAAAAQAAAAEAAAAw\n",
       "Y3R0cwAAAAAAAAAEAAAAAQAAEAAAAAABAAAYAAAAAAEAAAgAAAAAAgAAEAAAAAAcc3RzYwAAAAAA\n",
       "AAABAAAAAQAAAAUAAAABAAAAKHN0c3oAAAAAAAAAAAAAAAUAAE+NAAALzAAAANAAABfRAAAH1gAA\n",
       "ABRzdGNvAAAAAAAAAAEAAAAsAAAAYnVkdGEAAABabWV0YQAAAAAAAAAhaGRscgAAAAAAAAAAbWRp\n",
       "cmFwcGwAAAAAAAAAAAAAAAAtaWxzdAAAACWpdG9vAAAAHWRhdGEAAAABAAAAAExhdmY1Ny43MS4x\n",
       "MDA=\n",
       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 250,
       "width": 388
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "msg = ____________\n",
    "msg[____] = _____\n",
    "HTML(anim(G, propagate(G, msg), n_frames=5).to_html5_video())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bipartite Graph Matrices\n",
    "\n",
    "The section on message passing above assumed unipartite graphs, or at least graphs for which messages can be meaningfully passed between nodes. \n",
    "\n",
    "In this section, we will look at bipartite graphs. \n",
    "\n",
    "Recall from before the definition of a bipartite graph:\n",
    "\n",
    "- Nodes are separated into two partitions (hence 'bi'-'partite').\n",
    "- Edges can only occur between nodes of different partitions.\n",
    "\n",
    "Bipartite graphs have a natural matrix representation, known as the **biadjacency matrix**. Nodes on one partition are the rows, and nodes on the other partition are the columns.\n",
    "\n",
    "NetworkX's `bipartite` module provides a function for computing the biadjacency matrix of a bipartite graph."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start by looking at a toy bipartite graph, a \"customer-product\" purchase record graph, with 4 products and 3 customers. The matrix representation might be as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "# Rows = customers, columns = products, 1 = customer purchased product, 0 = customer did not purchase product.\n",
    "cp_mat = np.array([[0, 1, 0, 0],\n",
    "                   [1, 0, 1, 0],\n",
    "                   [1, 1, 1, 1]])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From this \"bi-adjacency\" matrix, one can compute the projection onto the customers, matrix multiplying the matrix with its transpose."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 1],\n",
       "       [0, 2, 2],\n",
       "       [1, 2, 4]])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c_mat = cp_mat @ cp_mat.T  # c_mat means \"customer matrix\"\n",
    "c_mat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Pause here and read carefully!**\n",
    "\n",
    "What we get is the connectivity matrix of the customers, based on shared purchases. The diagonals are the degree of the customers in the original graph, i.e. the number of purchases they originally made, and the off-diagonals are the connectivity matrix, based on shared products."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get the products matrix, we make the transposed matrix the left side of the matrix multiplication."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[2, 1, 2, 1],\n",
       "       [1, 2, 1, 1],\n",
       "       [2, 1, 2, 1],\n",
       "       [1, 1, 1, 1]])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_mat = cp_mat.T @ cp_mat  # p_mat means \"product matrix\"\n",
    "p_mat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You may now try to convince yourself that the diagonals are the number of times a customer purchased that product, and the off-diagonals are the connectivity matrix of the products, weighted by how similar two customers are."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises \n",
    "\n",
    "In the following exercises, you will now play with a customer-product graph from Amazon. This dataset was downloaded from [UCSD's Julian McAuley's website](http://jmcauley.ucsd.edu/data/amazon/), and corresponds to the digital music dataset.\n",
    "\n",
    "This is a bipartite graph. The two partitions are:\n",
    "\n",
    "- `customers`: The customers that were doing the reviews.\n",
    "- `products`: The music that was being reviewed.\n",
    "\n",
    "In the original dataset (see the original JSON in the `datasets/` directory), they are referred to as:\n",
    "\n",
    "- `customers`: `reviewerID`\n",
    "- `products`: `asin`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 64706/64706 [00:01<00:00, 44848.08it/s]\n",
      "100%|██████████| 64706/64706 [00:00<00:00, 378986.83it/s]\n",
      "100%|██████████| 64706/64706 [00:00<00:00, 285943.74it/s]\n"
     ]
    }
   ],
   "source": [
    "G_amzn = load_amazon_reviews()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "NetworkX provides [`nx.bipartite.matrix.biadjacency_matrix()`](https://networkx.github.io/documentation/stable/reference/algorithms/generated/networkx.algorithms.bipartite.matrix.biadjacency_matrix.html#networkx.algorithms.bipartite.matrix.biadjacency_matrix) function that lets you get the biadjacency matrix of a graph object. This returns a `scipy.sparse` matrix. Sparse matrices are commonly used to represent graphs, especially large ones, as they take up much less memory."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Read the [docs](https://networkx.github.io/documentation/stable/reference/algorithms/generated/networkx.algorithms.bipartite.matrix.biadjacency_matrix.html#networkx.algorithms.bipartite.matrix.biadjacency_matrix) on how to use the `biadjacency_matrix()` function. \n",
    "\n",
    "You probably would want to first define a function that gets all nodes from a partition."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_partition_nodes(G, partition):\n",
    "    \"\"\"\n",
    "    A function that returns nodes from one partition.\n",
    "    \n",
    "    Assumes that the attribute key that stores the partition information\n",
    "    is 'bipartite'.\n",
    "    \"\"\"\n",
    "    # Put your code here.\n",
    "    return _________"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Now, use the `get_partition_nodes()` function to get the `row_order` and `column_order` nodes from the Amazon music review graph, then get the biadjacency matrix using `nx.bipartite.biadjacency_matrix`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "customer_nodes = get_partition_nodes(G_amzn, ________)\n",
    "mat = _________"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Let's find out which customers reviewed the most number of music items.\n",
    "\n",
    "To do so, you can break the problem into a few steps.\n",
    "\n",
    "First off, compute the customer projection using matrix operations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "customer_mat = ________"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, get the diagonals of the customer-customer matrix. Recall here that in `customer_mat`, the diagonals correspond to the degree of the customer nodes in the bipartite matrix.\n",
    "\n",
    "**Hint:** SciPy sparse matrices provide a `.diagonal()` method that returns the diagonal elements."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get the diagonal.\n",
    "degrees = ___________"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, find the index of the customer that has the highest degree."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "294"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cust_idx = ___________\n",
    "cust_idx"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It should be customer 294 in the `customer_nodes` list.\n",
    "\n",
    "### Exercise\n",
    "\n",
    "Verify that this holds when looking at the degrees of each customer in `customer_nodes`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "294"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute the degree of each customer according to the order\n",
    "# in customer_nodes\n",
    "cust_degrees = ________________\n",
    "np.argmax(cust_degrees)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise\n",
    "\n",
    "Let's now also compute which two customers are similar, based on shared reviews. To do so involves the following steps:\n",
    "\n",
    "1. We construct a sparse matrix consisting of only the diagonals. `scipy.sparse.diags(elements)` will construct a sparse diagonal matrix based on the elements inside `elements`.\n",
    "1. Subtract the diagonals from the customer matrix projection. This yields the customer-customer similarity matrix, which should only consist of the off-diagonal elements of the customer matrix projection.\n",
    "1. Finally, get the indices where the weight (shared number of between the customers is highest. (*This code is provided for you.*)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.sparse as sp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(294, 86)"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Construct diagonal elements.\n",
    "customer_diags = __________\n",
    "# Subtract off-diagonals.\n",
    "off_diagonals = _________\n",
    "# Compute index of most similar individuals.\n",
    "np.unravel_index(np.argmax(off_diagonals), customer_mat.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Performance: Object vs. Matrices\n",
    "\n",
    "Finally, to motivate why you might want to use matrices rather than graph objects to compute some of these statistics, let's time the two ways of getting to the same answer."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Objects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "27.772 seconds\n",
      "Most similar customers: ('A3HU0B9XUEVHIM', 'A9Q28YTLYREO7', {'weight': 154})\n"
     ]
    }
   ],
   "source": [
    "from time import time\n",
    "\n",
    "start = time()\n",
    "G_cust = nx.bipartite.weighted_projected_graph(G_amzn, customer_nodes)\n",
    "most_similar_customers = sorted(G_cust.edges(data=True), key=lambda x: x[2]['weight'], reverse=True)[0]\n",
    "end = time()\n",
    "print(f'{end - start:.3f} seconds')\n",
    "print(f'Most similar customers: {most_similar_customers}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matrices"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.672 seconds\n",
      "Most similar customers: A9Q28YTLYREO7, A3HU0B9XUEVHIM, 154\n"
     ]
    }
   ],
   "source": [
    "start = time()\n",
    "mat = nx.bipartite.matrix.biadjacency_matrix(G_amzn, customer_nodes)\n",
    "cust_mat = mat @ mat.T\n",
    "degrees = customer_mat.diagonal()\n",
    "customer_diags = sp.diags(degrees)\n",
    "off_diagonals = customer_mat - customer_diags\n",
    "c1, c2 = np.unravel_index(np.argmax(off_diagonals), customer_mat.shape)\n",
    "\n",
    "end = time()\n",
    "print(f'{end - start:.3f} seconds')\n",
    "print(f'Most similar customers: {customer_nodes[c1]}, {customer_nodes[c2]}, {cust_mat[c1, c2]}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You may notice that it's much easier to read the \"objects\" code, but the matrix code way outperforms the object code. This then becomes a great reason to use matrices (even better, sparse matrices)!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "nams",
   "language": "python",
   "name": "nams"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}