GaussianMRFExample_cbp.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a href=\"https://colab.research.google.com/github/gtbook/gtsam-examples/blob/main/GaussianMRFExample_lbp.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Clustered Belief Propagation\n",
    "\n",
    "Instead of \"vanilla\" loopy belief propagation, we now introduce more a structured approximation. In particular, we could treat a number of variables $X_c$ as a cluster and use a Gaussian density for the entire cluster. This could easily be implemented using vanilla LBP, by introducing new clustered variables and proceeding as before. However, here we instead adopt a different approximate density as a collection of Bayes trees.\n",
    "\n",
    "If we group several variables together, and build a variational mean field approximation on those clusters, we can get much more accurate marginals, much faster. This is because we are making less of an approximation, and because we use the power of GTSAM to optimize over a bunch of variables at the same time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pip -q install gtbook  # also installs latest gtsam pre-release"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import defaultdict\n",
    "from dataclasses import dataclass\n",
    "from typing import FrozenSet\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import gtsam\n",
    "import numpy as np\n",
    "from gtbook.driving import planar_example, marginals_figure\n",
    "from gtbook.display import show\n",
    "import gtsam.utils.plot as gtsam_plot\n",
    "\n",
    "GaussianPrior = gtsam.GaussianDensity.FromMeanAndStddev\n",
    "ConstrainedOrdering = gtsam.Ordering.ColamdConstrainedLastGaussianFactorGraph\n",
    "Keys = FrozenSet[int]\n",
    "Edge = FrozenSet[int]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## A Linear SLAM example \n",
    "\n",
    "We use a planar SLAM example that we linearize at the ground truth, in order to illustrate structured LBP."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<gtbook.display.show at 0x110633f40>"
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     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nonlinear_graph, truth, graph_keys = planar_example()\n",
    "x1, x2, x3, l1, l2 = graph_keys\n",
    "graph = nonlinear_graph.linearize(truth)\n",
    "show(nonlinear_graph, truth, binary_edges=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Gaussian marginals around the non-linear solution are shown below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x560 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "marginals = gtsam.Marginals(graph, truth)\n",
    "marginals_figure(truth, marginals, graph_keys)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cluster Nodes\n",
    "\n",
    "In the example below we create three clusters: the Markov chain x1-x2-x3 in one cluster, and the two landmarks l1 and l2 each in their own separate cluster. For each we create an initial belief *in the form of a Gaussian Bayes net*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "belief0 = gtsam.GaussianBayesNet()\n",
    "zero = np.zeros((3,), float)\n",
    "belief0.push_back(GaussianPrior(x1, zero, 1.5))\n",
    "belief0.push_back(GaussianPrior(x2, zero, 1.5))\n",
    "belief0.push_back(GaussianPrior(x3, zero, 1.5))\n",
    "\n",
    "belief1 = gtsam.GaussianBayesNet()\n",
    "belief1.push_back(GaussianPrior(l1, zero[:2], 1.5))\n",
    "\n",
    "belief2 = gtsam.GaussianBayesNet()\n",
    "belief2.push_back(GaussianPrior(l2, zero[:2], 1.5))\n",
    "\n",
    "key_sets = [{x1, x2, x3}, {l1}, {l2}]\n",
    "beliefs = [belief0, belief1, belief2]\n",
    "node_specs = list(zip(key_sets, beliefs))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's then create a set of `Clusters` that each approximate the density of a cluster:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "@dataclass(frozen=True)\n",
    "class Cluster:\n",
    "    keys: Keys\n",
    "    belief: gtsam.GaussianBayesNet\n",
    "\n",
    "variable_nodes = [Cluster(keys, initial_belief)\n",
    "                for keys, initial_belief in node_specs]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can't currently update a Bayes tree in python yet, but in C++ we would use a `gtsam.BayesTree` so we can easily get covariances and incrementally update the custer. Soon! \n",
    "\n",
    "## Visualizing the Covariances\n",
    "\n",
    "For now, we can visualize the covariances by converting to a Bayes tree. Note that we add the linear solution to the non-linear values for visualization purposes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x560 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_covariances(variable_nodes):\n",
    "    \"\"\"Plot all covariances.\"\"\"\n",
    "    graph = gtsam.GaussianFactorGraph()\n",
    "    for q_j in variable_nodes:\n",
    "        graph.push_back(q_j.belief)\n",
    "    bt = graph.eliminateMultifrontal()\n",
    "    mean = bt.optimize()\n",
    "    cov = {key: bt.marginalCovariance(key)\n",
    "           for q_j in variable_nodes for key in q_j.keys}\n",
    "\n",
    "    plt.figure(0, figsize=(12, 7), dpi=80)\n",
    "    for key in [x1, x2, x3]:\n",
    "        gtsam_plot.plot_point2(0, truth.atPose2(key).translation() + mean.at(\n",
    "            key)[:2], 0.5, bt.marginalCovariance(key))\n",
    "    for key in [l1, l2]:\n",
    "        gtsam_plot.plot_point2(0, truth.atPoint2(key) + mean.at(key), 0.5,\n",
    "                               bt.marginalCovariance(key))\n",
    "\n",
    "    plt.axis('equal')\n",
    "    plt.xlim([-0.8, 6])\n",
    "    plt.ylim([-0.8, 3])\n",
    "\n",
    "\n",
    "plot_covariances(variable_nodes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that above all beliefs are just uniform Gaussians with a large standard deviation. \n",
    "\n",
    "## (Super) Factor Nodes\n",
    "\n",
    "We also parse the factor graph in \"super-factors\" that bridge different cluster nodes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# First figure out which nodes every node is connected to.\n",
    "factor_indices = defaultdict(set)\n",
    "for i in range(graph.size()):\n",
    "    factor = graph.at(i)\n",
    "    for j, (keys, _) in enumerate(node_specs):\n",
    "        if keys.intersection(factor.keys()):\n",
    "            factor_indices[i].add(j)\n",
    "\n",
    "# Then store based on those index tuples.\n",
    "factor_nodes = defaultdict(gtsam.GaussianFactorGraph)\n",
    "for i, edge in factor_indices.items():\n",
    "    assert len(edge) <= 2, \"Invalid interaction between nodes.\"\n",
    "    factor_nodes[frozenset(edge)].push_back(graph.at(i))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Every super-factor is really a factor graph. For example, one of the super-factors is intra-cluster:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.50.0 (0)\n -->\n<!-- Pages: 1 -->\n<svg width=\"248pt\" height=\"59pt\"\n viewBox=\"0.00 0.00 247.93 59.12\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 55.12)\">\n<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-55.12 243.93,-55.12 243.93,4 -4,4\"/>\n<!-- varx1 -->\n<g id=\"node1\" class=\"node\">\n<title>varx1</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"68.93\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"68.93\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">x1</text>\n</g>\n<!-- varx2 -->\n<g id=\"node2\" class=\"node\">\n<title>varx2</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"140.93\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"140.93\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">x2</text>\n</g>\n<!-- varx1&#45;&#45;varx2 -->\n<g id=\"edge2\" class=\"edge\">\n<title>varx1&#45;&#45;varx2</title>\n<path fill=\"none\" stroke=\"black\" d=\"M96.15,-18C101.88,-18 107.93,-18 113.67,-18\"/>\n</g>\n<!-- factor0 -->\n<g id=\"node4\" class=\"node\">\n<title>factor0</title>\n<ellipse fill=\"black\" stroke=\"black\" cx=\"1.8\" cy=\"-49.32\" rx=\"1.8\" ry=\"1.8\"/>\n</g>\n<!-- varx1&#45;&#45;factor0 -->\n<g id=\"edge1\" class=\"edge\">\n<title>varx1&#45;&#45;factor0</title>\n<path fill=\"none\" stroke=\"black\" d=\"M46.58,-28.43C30.1,-36.12 9.55,-45.7 3.53,-48.51\"/>\n</g>\n<!-- varx3 -->\n<g id=\"node3\" class=\"node\">\n<title>varx3</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"212.93\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"212.93\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">x3</text>\n</g>\n<!-- varx2&#45;&#45;varx3 -->\n<g id=\"edge3\" class=\"edge\">\n<title>varx2&#45;&#45;varx3</title>\n<path fill=\"none\" stroke=\"black\" d=\"M168.15,-18C173.88,-18 179.93,-18 185.67,-18\"/>\n</g>\n</g>\n</svg>\n",
      "text/plain": [
       "<gtbook.display.show at 0x13543a2e0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "edge0, edge01, edge02 = frozenset({0}), frozenset({0, 1}), frozenset({0, 2})\n",
    "show(factor_nodes[edge0], hints={'x':0}, binary_edges=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And another one is between cluster 0 and 1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.50.0 (0)\n -->\n<!-- Pages: 1 -->\n<svg width=\"134pt\" height=\"116pt\"\n viewBox=\"0.00 0.00 134.00 116.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 112)\">\n<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-112 130,-112 130,4 -4,4\"/>\n<!-- varl1 -->\n<g id=\"node1\" class=\"node\">\n<title>varl1</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"27\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">l1</text>\n</g>\n<!-- varx1 -->\n<g id=\"node2\" class=\"node\">\n<title>varx1</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"27\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">x1</text>\n</g>\n<!-- varx1&#45;&#45;varl1 -->\n<g id=\"edge1\" class=\"edge\">\n<title>varx1&#45;&#45;varl1</title>\n<path fill=\"none\" stroke=\"black\" d=\"M27,-36.17C27,-47 27,-60.71 27,-71.59\"/>\n</g>\n<!-- varx2 -->\n<g id=\"node3\" class=\"node\">\n<title>varx2</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"99\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"99\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">x2</text>\n</g>\n<!-- varx2&#45;&#45;varl1 -->\n<g id=\"edge2\" class=\"edge\">\n<title>varx2&#45;&#45;varl1</title>\n<path fill=\"none\" stroke=\"black\" d=\"M83.73,-33.27C71.51,-45.49 54.46,-62.54 42.25,-74.75\"/>\n</g>\n</g>\n</svg>\n",
      "text/plain": [
       "<gtbook.display.show at 0x135404190>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show(factor_nodes[edge01], hints={'x':0, 'l':1}, binary_edges=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Messages\n",
    "\n",
    "Finally, as in our vanilla LBP implementation, we only have one type of message, from factors (indexed by `frozenset` edges) to clusters (indexed by int). Again, messages are entire factor *graphs* now:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "Message = gtsam.GaussianFactorGraph\n",
    "\n",
    "messages = defaultdict(dict)\n",
    "for i, factors in factor_nodes.items():\n",
    "    if len(i) == 1:\n",
    "        j, *others = i\n",
    "        messages[j][i] = factors\n",
    "        continue\n",
    "    for j in i:\n",
    "        messages[j][i] = Message()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We initialized the messages $m_{i->j}$ above to empty, except the ones that correspond to unary \"factors\". There is only one here, which is exactly the intra-cluster factor graph from above:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F_[0] -> X_0: size = 3\n",
      "F_[0, 1] -> X_0: size = 0\n",
      "F_[0, 2] -> X_0: size = 0\n",
      "F_[0, 1] -> X_1: size = 0\n",
      "F_[0, 2] -> X_2: size = 0\n"
     ]
    }
   ],
   "source": [
    "for j, messages_j in messages.items():\n",
    "    for i, message_ij in messages_j.items():\n",
    "        print(f\"F_{list(i)} -> X_{j}: size = {message_ij.size()}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cluster Belief Propagation\n",
    "\n",
    "With these three data structures in hand, the code to update the belief of one cluster is easy: just add all \"message\" factor graphs to a big graph, and then eliminate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_node(j: int):\n",
    "    \"\"\"Update cluster j.\"\"\"\n",
    "    graph = gtsam.GaussianFactorGraph()\n",
    "    for message in messages[j].values():\n",
    "        for i in range(message.size()):\n",
    "            graph.push_back(message.at(i))\n",
    "\n",
    "    # Eliminate into Bayes net.\n",
    "    new_belief = graph.eliminateSequential(gtsam.Ordering.OrderingType.NATURAL)\n",
    "\n",
    "    variable_nodes[j] = Cluster(variable_nodes[j].keys, new_belief)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, updating cluster 0 we get an updated Bayes net on the Markov chain x1-x2-x3, which we show below as a Bayes net (it was eliminated in the x1,x2,x3 order, which is why the past is conditioned on the present), and below that we show the updated covariances:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.50.0 (0)\n -->\n<!-- Pages: 1 -->\n<svg width=\"206pt\" height=\"44pt\"\n viewBox=\"0.00 0.00 206.00 44.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 40)\">\n<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-40 202,-40 202,4 -4,4\"/>\n<!-- varx1 -->\n<g id=\"node1\" class=\"node\">\n<title>varx1</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"27\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">x1</text>\n</g>\n<!-- varx2 -->\n<g id=\"node2\" class=\"node\">\n<title>varx2</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"99\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"99\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">x2</text>\n</g>\n<!-- varx2&#45;&gt;varx1 -->\n<g id=\"edge2\" class=\"edge\">\n<title>varx2&#45;&gt;varx1</title>\n<path fill=\"none\" stroke=\"black\" d=\"M71.78,-18C69.36,-18 66.89,-18 64.4,-18\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"64.26,-14.5 54.26,-18 64.26,-21.5 64.26,-14.5\"/>\n</g>\n<!-- varx3 -->\n<g id=\"node3\" class=\"node\">\n<title>varx3</title>\n<ellipse fill=\"none\" stroke=\"black\" cx=\"171\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"171\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">x3</text>\n</g>\n<!-- varx3&#45;&gt;varx2 -->\n<g id=\"edge1\" class=\"edge\">\n<title>varx3&#45;&gt;varx2</title>\n<path fill=\"none\" stroke=\"black\" d=\"M143.78,-18C141.36,-18 138.89,-18 136.4,-18\"/>\n<polygon fill=\"black\" stroke=\"black\" points=\"136.26,-14.5 126.26,-18 136.26,-21.5 136.26,-14.5\"/>\n</g>\n</g>\n</svg>\n",
      "text/plain": [
       "<gtbook.display.show at 0x1353b1160>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "update_node(0)\n",
    "show(variable_nodes[0].belief, hints={'x':0})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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cZYXIwmbPno2+ffuyrOQDLi4uCAkJwZw5c1RHIdKar68vGjRogIiICNVRrIKFhfKtefPmITQ0VHUMIq1du3YNv//+O8daPhISEoLFixcjIyNDdRQirYWEhOSbPWMsLJQv7d+/H4mJiXjxxRdVRyHSWmRkJMqXL486deqojkJW0qBBAxQvXhyrVq1SHYVIay+99BJiY2Nx9OhR1VEsjoWF8qV58+ahS5cuKFy4sOooRFoLDw9HaGgon2yfjwghEBISgvDwcNVRiLRWrFgxdOjQIV/MsrCwUL5jMpkwf/58LlEhsrDz589j/fr1ePnll1VHISsLCQnBypUrcfnyZdVRiLQWGhqKefPmaX9nPhYWyne2bNmCGzduoE2bNqqjEGktIiICzz//PLy9vVVHISvz9fVFrVq18Ouvv6qOQqS1jh074vz589i1a5fqKBbFwkL5Tnh4OHr16gVHR0fVUYi0lrccjPInLgsjsjxnZ2f06NFD+7HG57BQvnLz5k2UKVMGa9asQYMGDVTHIdLWsWPH4OfnhzNnzqB48eKq45AC586dg6enJ44fPw4vLy/VcYi0FR0djZ49e+L06dM2dTHW5p7DIoRwFkIsFUIkCiHihBBrhBDe9zkuSAhxPfeYvFdBBZHJRm3YsAHFixfH888/rzoKkdYWL16Mtm3bsqzkY+7u7mjRogWXhRFZWLNmzeDo6Ijo6GjVUSzGEIUl108AfKWU/gBW5L59P4eklP53vG5YLSHZvMjISHTp0oV3LCKysMjISHTt2lV1DFKsa9euWL58ueoYRFqzs7NDcHCw1mPNEIVFSnlTSrlK/v/6tB0AKqnMRPoxmUxYvnw5goODVUch0trZs2exe/dudOzYUXUUUqxz587YunUrLl68qDoKkdaCg4MRGRmp7d3CDFFY7uMdAA+qib5CiBghxG4hxKD7HSCEGCGESM57paenWy4p2Yw9e/bgxo0baNKkieooRFpbuXIlAgMD4e7urjoKKVa+fHk899xzWL16teooRFpr0aIFLly4gP3796uOYhGGKyxCiA8BVAXw0X3+OAaAp5SyLoAXAbwthOh570FSynFSSs+8l6urq2VDk01Yvnw5OnToYFMb0ohsEWcy6U55V36JyHKcnZ3Rpk0bbceaoQqLEGIkgG4A2kspr9/751LKq1LKK7m/TwawAEBT66YkWxUZGcmTKCILu3HjBtatW8exRrcFBwdj9erVyMzMVB2FSGs6XxwwTGERQowA0AdAaynl5Qcc4yGEsMv9vRuATgBirRaSbNaJEydw6NAhtGvXTnUUIq1t3LgRHh4eqFGjhuooZBB16tRB4cKFsWnTJtVRiLTWsWNHxMTEICUlRXUUszNEYRFCeAL4D4CiAKJyb1e8M/fPZggh8i7VdQewXwgRj1sb89cD+EVBZLIxy5cvR/PmzVG0aFHVUYi0ljeTyTvxUR4hBDp37qztlV8ioyhVqhQaNGiAFStWqI5idoYoLFLKZCmlkFJWvuN2xc/n/ll/KWVk7u8nSSn9pJS1c3/9XOp6OwQyq+XLl6Nz586qYxBpTUrJsUb3pfsdjIiMQteLA4YoLESWlJGRgS1btqBt27aqoxBp7dChQ7h69SrvxEf/EBQUhLNnz+L48eOqoxBprW3btti0aROysrJURzErFhbS3s6dO1G0aFH4+vqqjkKktejoaDRu3BgFChRQHYUMpmDBgmjQoIHWT+ImMoJatWrB0dERMTExqqOYFQsLaS86OhpBQUFcU09kYXljjeh+goKCWFiILMzOzg7NmzfXbqyxsJD2oqKieBJFZGEmk4mFhR4qKCgIUVFR3MdCZGE6XhxgYSGt3bx5E//73/94EkVkYYcOHcL169cRGBioOgoZVIMGDXDhwgUcO3ZMdRQirbVo0QJbtmzRah8LCwtpbceOHShevDh8fHxURyHSWlRUFJo0aQJHR0fVUcigChYsiIYNGyIqKkp1FCKt1axZE87Ozti7d6/qKGbDwkJa4/4VIuuIjo5GixYtVMcgg9NxqQqR0ei4j4WFhbTGNfVElmcymbBp0yaONXqkvMLCfSxElqXbxQEWFtJWRkYGduzYgebNm6uOQqS1w4cP48aNGwgICFAdhQyuQYMGSE1N5T4WIgsLCgrC1q1bkZOTozqKWbCwkLYOHDgAZ2dn7l8hsrDdu3cjICCA+1fokZydnVG7dm3s2bNHdRQirdWoUQMAcOTIEcVJzIOFhbS1d+9eBAQEcP8KkYXljTWixxEQEKDVZmAiI7K3t4e/v782Y42FhbS1Z88enkQRWQHHGj0JFhYi6wgICNBmNpOFhbTFq75ElpednY34+HiONXpsAQEBiImJgclkUh2FSGs6XRxgYSEtZWRkYP/+/TyJIrKww4cPw87OjnvF6LH5+fkhIyMDx48fVx2FSGv16tVDXFycFhvvWVhISwcOHICLiwsqV66sOgqR1vbu3Yu6devC3t5edRSyEQUKFECtWrW0WapCZFS+vr4QQmix8Z6FhbTEDfdE1sGll/Q0dFqqQmRUOm28Z2EhLXETMJF1cKzR02BhIbIOXTbes7CQluLj41GnTh3VMYi0ZjKZsG/fPo41emJ16tRBXFwcn3hPZGF5Y83WsbCQdqSUSEhIQLVq1VRHIdLa6dOncfPmTVSpUkV1FLIxvr6+uHz5Mi5cuKA6CpHWqlWrhsTERNUxnhkLC2nn/PnzuHLlCqpWrao6CpHWEhMT4e3tDScnJ9VRyMa4urqiXLlyWpxIERmZj48Pzp07hytXrqiO8kxYWEg7iYmJKFeuHFxdXVVHIdJaYmIib2dMT83Hx4eFhcjCihcvjhIlSuDo0aOqozwTFhbSDk+iiKwjISEBvr6+qmOQjfLx8UFCQoLqGETa8/X1tfmxxsJC2mFhIbIOjjV6FpxhIbIOHcYaCwtphydRRNbBsUbPQoeTKCJboMNYY2Eh7SQmJnKZCpGFZWZm4s8//2Rhoafm6+uLY8eOIScnR3UUIq2xsBAZTE5ODo4dO8aTKCILS0pKQoECBeDp6ak6Ctkob29v5OTk4NSpU6qjEGktr7DY8nOPWFhIKykpKcjMzIS3t7fqKERaO378OCpVqgQ7O/4zQk/H0dERFSpUwPHjx1VHIdJa5cqVkZ6ejvPnz6uO8tT4Lw1pJSUlBaVLl4ajo6PqKERaS0lJQdmyZVXHIBtXtmxZpKSkqI5BpDUXFxcULVrUpscaCwtp5cyZMzyJIrICjjUyh7Jly+LMmTOqYxBpz8PDw6bHGgsLaSUlJQUeHh6qYxBp78yZMxxr9Mxs/SSKyFbY+sUBFhbSCq/6ElkHl4SROXBJGJF1eHh42PRYY2EhrXCGhcg6OMNC5sAZFiLr4AwLkYFwhoXIOjjWyBxs/SSKyFbY+sUBFhbSCq/6ElmeyWTC2bNnOdbomeUtU7Hl50MQ2QJbX37JwkJa4ZIwIsu7cOECsrOzOdbomXl4eOD69etIS0tTHYVIa5xhITIIKSXOnz+P0qVLq45CpLW///4brq6uKFiwoOooZOOKFCmCAgUK4O+//1YdhUhr7u7uNj3OWFhIG9euXYOUEoULF1YdhUhraWlpHGdkFkIIuLm5cYaFyMLc3Nxw8+ZNZGdnq47yVFhYSBvp6ekAbg1KIrKctLQ0jjMyGxYWIsvL+5ltq2ONhYW0kZaWBicnJzg6OqqOQqS19PR0FhYyGzc3t9sXnIjIMlxcXADAZscaCwtpIy0tDa6urqpjEGmPY43MydXV1Wav+hLZCjs7O5seaywspA1e9SWyDi4JI3PikjAi62BhITIAnkQRWQfHGpkTCwuRddjyWGNhIW1wmQqRdXCskTnZ8lVfIlvCwkJkAFwSRmQdHGtkTtx0T2Qdrq6uNjvWWFhIG9euXbt9FwwishyONTKnQoUK4dq1a6pjEGnPlseaIQqLEMJZCLFUCJEohIgTQqwRQng/4Ng3hBBHhRDHhRA/CSEcrByXDMpkMsHBgf87EFkaxxqZk729PUwmk+oYRNqz5bFmpH9xfgKwWkophRBDct9uc+cBQoiKAL4CUAfA3wCWAXgDwDQrZyUDMplMsLMzRAcnMqvMlHRc3XASWWfS4ejhisIveKFAWXV7SDjWyJzs7OwMcRKVlnYIf/75I9LSD8PNtToqVnwHbm7VVcciMhujjLWnYYh/caSUN6WUq6SUMvddOwBUus+hPQD8LqU8l3vsVAB9rJWTjC0nJ4cnUaSdzJR0/B0Wh5uHU5FzKQM3D6fi77A4ZKaoW4fMwkLmZGdnh5ycHKUZ0tIOYfee7jh/YQNu3jyF8xc2YPeebkhLO6w0F5E5GWGsPS2j/ovzDoDl93m/F4C/7nj7RO77iHgSRVq6uuEkkCOBvMs5EkCOxNWNJ5Vl4lgjczLCSdSff/4IKbMB5F19NkHKbPx5YqLKWERmZW9vr3ysPS3D/YsjhPgQQFUAHz3gEHnn4Q/4HCOEEMl5L1u9IwI9GSHu+78DkU3LOpN+9089AJBAVoq6jZMca2ROUkrlBTgt/TD+v6zkMXGGhbRihLH2tAyVWggxEkA3AO2llNfvc8hJAN53vF0h9313kVKOk1J65r34vID8wZbXZhI9iKOH6z8vzQjAsWwhJXkAjjUyLyPM2Lm5Vsc/T4ns4OZWQ0UcIoswwlh7WoZJLYQYgVv7UVpLKS8/4LAlAF4UQriLW5f43gaw0EoRyeB4EkU6KvyCF2Av/r+0CAD2AoVbqVsNy7FG5mSEk6iKFd/BrZuO5uWwgxAOqOg9VGUsIrMywlh7WoZILYTwBPAfAEUBROXe2nhn7p/NEEIEA4CUMgnAZwC2ATiOW3cKm6kkNBmOEdZBE5lbgbKuKD3IH841SsC+mDOca5RA6UH+Su8SxrFG5mSEkyg3t+oIrPcbSpV6Ac7O5VGq1AsIrPcb7xJGWrHlmxMZ4rbGUspkPGA/ipSy/z1vTwcw3Rq5yLY4ODggOztbdQwisytQ1hUl+xpnaYq9vT3HGplNdnY27O3tVceAm1t11HpuiuoYRBaTk5NjiLH2NGyzZhHdhy0/wZXIlnCskTldu3YN3GtKZHnp6ek2O9ZYWEgbbm5uSEtLUx2DSHsca2ROaWlpcHNzUx2DSHu2PNZYWEgbrq6uPIkisgIWFjInWz6JIrIl6enpNjvWWFhIG25ubuAzd4gsz9XVlWONzMaWl6kQ2ZK0tDSbHWssLKQNXvUlsg6ONTInzrAQWQdnWIgMIG9JmJT3PhaciMyJhYXMiYWFyPJycnJw/fp1mx1rLCykDTc3N2RnZyMjI0N1FCKtsbCQObGwEFle3jJeWx1rLCykjbxByLX1RJbFPSxkTtzDQmR5eT+zCxUqpDjJ02FhIW04OzvDwcEBV65cUR2FSGuFCxfmOCOzkFIiLS0NhQsXVh2FSGtXr15FoUKF+OBIItWEEHB3d8e5c+dURyHSWpkyZXDjxg0uC6NnlpqaiuzsbLi7u6uOQqS1s2fPokyZMqpjPDUWFtKKh4cHUlJSVMcg0lrRokXh5OTEsUbPLCUlBUWKFIGLi4vqKERaS0lJgYeHh+oYT42FhbRStmxZnDlzRnUMIq0JIeDh4cGxRs/szJkzNn0SRWQrbH2ssbCQVjjDQmQdZcuW5VijZ5aSkoKyZcuqjkGkPVsfaywspBXOsBBZB2dYyBxs/aovka2w9bHGwkJa4UkUkXVwrJE52PpJFJGt4B4WIgPhMhUi6+BYI3Ow9WUqRLbC1scaCwtphVd9iayDY43MgTMsRJYnpbT5scbCQlopV64cUlNTcePGDdVRiLRWrlw5JCcnq45BNu706dM2fdWXyBZcvXoV165ds+mxxsJCWildujRcXV1x/Phx1VGItFalShWcOHECWVlZqqOQjbpx4wZOnTqFqlWrqo5CpLWjR4+iRIkSKFasmOooT42FhbQihICPjw8SExNVRyHSmpeXF+zs7HDixAnVUchGHT9+HIUKFbLpp28T2YLExET4+PiojvFMWFhIOz4+PkhISFAdg0hr9vb2qFKlCi8O0FNLSEiAj48PhBCqoxBpjYWFyIA4w0JkHRxr9Cx0OIkisgU6jDUWFtIOT6KIrMPX15djjZ5aYmIifH19Vccg0p4OY42FhbTDwkJkHVx+Sc9Ch6u+REYnpby9/NKWsbCQdnx8fHDhwgVcvHhRdRQirfHiAD0LHU6iiIzu7NmzSE9PR5UqVVRHeSYsLKSdIkWKwN3dnSdSRBbm4+OD06dPIz09XXUUsjGpqalITU1lYSGysMTERHh5eaFgwYKqozwTFhbSkq+vLw4fPqw6BpHWSpUqhWLFinFZGD2xI0eOoEyZMihcuLDqKERaO3z4sM3vXwFYWEhTderUQUxMjOoYRFoTQnCs0VOJiYlB3bp1Vccg0p4uY42FhbQUEBCAPXv2qI5BpD2ONXoae/bsQUBAgOoYRNrTZayxsJCWAgICEB8fj+zsbNVRiLQWEBCAvXv3qo5BNmbv3r1anEQRGVlGRgYOHDigxVhjYSEt+fr6ws7OjvtYiCysXr162L9/PzIzM1VHIRtx7do1HD58WIuTKCIj279/P1xdXVGxYkXVUZ4ZCwtpyd7eHnXq1OGVXyILq1SpElxcXHDgwAHVUchGxMfHo2TJkihXrpzqKERay5vJFEKojvLMWFhIW1yqQmR5QgjUrVuXY40em04nUURGptPSSxYW0hY3AxNZB8caPQldNgETGZ1OY42FhbTFjfdE1sHZTHoSe/fuRb169VTHINKaThvuARYW0pivry8cHR2xb98+1VGItFa/fn3s27cP169fVx2FDO7KlSs4fPgwAgMDVUch0lpsbCwKFy6sxYZ7gIWFNGZvb4+mTZsiOjpadRQirXl7e8PDwwPbt29XHYUMbsuWLahcuTLKli2rOgqR1qKiohAUFKTNXjEWFtJaUFAQCwuRhQkhONbosURHRyMoKEh1DCLt6TbWWFhIa0FBQdi8eTNycnJURyHSWlBQEKKiolTHIIPT7SSKyIgyMzOxdetWrcYaCwtprU6dOpBSIi4uTnUUIq21aNECu3btwrVr11RHIYO6fPkyYmNjtTqJIjKiPXv2wMXFBTVq1FAdxWxYWEhr9vb2aNasGZeqEFmYt7c3ypUrh23btqmOQga1ZcsWVKlShftXiCwsb/+KnZ0+p/n6fCVED9CiRQsWFiIr4Fijh4mOjkaLFi1UxyDSno5LL1lYSHvcx0JkHdx4Tw+j40kUkdFkZmZi27Zt2o01FhbSXu3atWFnZ4fY2FjVUYi0FhQUhN27dyMtLU11FDKYS5cuIS4uDs2bN1cdhUhru3btgqurq1b7VwAWFsoH7O3t0apVK6xevVp1FCKtVahQAZUqVcLGjRtVRyGDWbduHWrUqAEPDw/VUYi0tnr1arzwwgvaPH8lDwsL5QvBwcGIjIxUHYNIexxrdD+RkZHo0qWL6hhE2tN1rBmisAghJgohTgghpBCi5gOOCRJCXBdCxN3xKmjtrGSbOnTogNjYWJw+fVp1FCKtde7cGStWrOCeMbotKysLq1atQnBwsOooRFpLSkpCQkIC2rVrpzqK2RmisAD4FUATAH894rhDUkr/O143rJCNNFCyZEk0bNgQK1asUB2FSGuNGjVCTk4Odu7cqToKGcTWrVvh7OyMevXqqY5CpLXly5ejefPmKFKkiOooZmeIwiKl3CylTFadg/QWHByM5cuXq45BpDUHBwd07NiRY41ui4yMROfOnbV6JgSRES1fvlzbmUxb++nhK4SIEULsFkIMUh2GbEtwcDA2bNjAJ3ETWRj3sVAeKSWWLVuGzp07q45CpLXLly9j06ZN2o41WyosMQA8pZR1AbwI4G0hRM/7HSiEGCGESM57paenWzUoGZOvry8qVKiA9evXq45CpLW2bdvi2LFjOHbsmOoopNihQ4dw9uxZtGrVSnUUIq2tWbMG1atXh7e3t+ooFmEzhUVKeVVKeSX398kAFgBo+oBjx0kpPfNerq6u1oxKBta5c2de+SWyMDc3NwQFBXFZGCEyMhKtW7eGi4uL6ihEWouMjNR2ORhgQ4VFCOEhhLDL/b0bgE4A+CRAeiJ5+1iysrJURyHSWnBwMH7//XfVMUix33//XeuTKCIjyMjI0P5OfIYoLEKIyUKIZACeADYIIY7lvn+GECLvv353APuFEPEAdgBYD+AXJYHJZjVp0gTOzs7YsGGD6ihEWuvRowd27NiBkydPqo5Cihw9ehTx8fHo1q2b6ihEWlu1ahVKlCiBwMBA1VEsxhCFRUo5OHf5loOUsoyUskru+/tLKSNzfz9JSuknpayd++vnUkqpNjnZGjs7O/Tp0wfh4eGqoxBpzd3dHa1atcL8+fNVRyFF5s2bhw4dOqBYsWKqoxBpLTw8HCEhIdo93f5OhigsRNYUGhqKpUuXgjdjILKs0NBQhIeHg9eW8h8pJebNm4fQ0FDVUYi0dvnyZaxcuRIhISGqo1gUCwvlO7Vq1ULlypWxdOlS1VGItNa1a1ecOHEC+/btUx2FrGzXrl04f/48OnbsqDoKkdZ+/fVX1KpVC76+vqqjWBQLC+VLISEhXBZGZGGFChVC165dOdbyofDwcPTo0QPOzs6qoxBpLW85mO5Efpiq9/T0lMnJyapjkIGcOnUKlSpVwqlTp1CmTBnVcYi0tWbNGrzxxhs4efIk7O3tVcchK8jKykK5cuWwaNEiBAUFqY5DpK2TJ0+icuXKSE5Ohru7u+o4T0wIcVpK6fk4x3KGhfKl8uXLo0mTJoiIiFAdhUhrL7zwArKzs7Fp0ybVUchK1q9fDycnJzRr1kx1FCKtLViwAC+88IJNlpUnxcJC+VZISAjmzp2rOgaR1hwcHNC7d2+OtXwkPDwcL7/8MuzseIpBZClSynyzHAzgkjDKx65cuYKyZctiy5YtqFu3ruo4RNqKi4tD48aNcfr0aRQtWlR1HLKgCxcuoHz58oiJiUH16tVVxyHS1o4dO9C2bVukpKSgUKFCquM8FS4JI3oMRYoUQWhoKKZMmaI6CpHW/P39Ubt2bcyZM0d1FLKwX375BQ0bNmRZIbKwsLAw9OvXz2bLypNiYaF8beDAgZg3bx4uX76sOgqR1gYNGoSwsDA+k0VjJpMJU6ZMwaBBg1RHIdLa+fPnsWjRIgwcOFB1FKthYaF8zd/fH3Xq1MHs2bNVRyHSWo8ePZCamoqoqCjVUchC1q5di5s3b6JLly6qoxBp7eeff0bjxo1RrVo11VGshoWF8j1e+SWyPGdnZ7zxxhsICwtTHYUsJCwsDG+99RYcHR1VRyHSVk5ODqZOnZrvZjJZWCjf69GjBy5evIg//vhDdRQirQ0YMACRkZE4ffq06ihkZidOnMC6devw5ptvqo5CpLU1a9YgMzMTwcHBqqNYFQsL5XtOTk7o378/r/wSWVjFihXRpk0bTJ8+XXUUMrNp06ahU6dOKFeunOooRFrLrzOZvK0xEW5dHfTx8UFSUhI8PR/rDntE9BRWrVqF/v3746+//sp3/+DqKiMjA56enli4cCFatWqlOg6RtpKSklC9enX8+eefKFu2rOo4z4y3NSZ6Qt7e3mjfvj1+/PFH1VGItNa2bVu4uLggIiJCdRQyk/DwcJQqVQotW7ZUHYVIaxMmTEDXrl21KCtPijMsRLm2b9+Odu3a4eTJk3y4HZEFTZs2DT/++CP27dvHp6HbuJycHFSvXh0ffvgh+vXrpzoOkbbOnz8Pb29vrR52zRkWoqfQqFEj1KlTB5MnT1YdhUhrr776KlJTU7FixQrVUegZ/fbbb8jIyEBISIjqKERamzhxIpo0aaJNWXlSLCxEd/jggw/w3//+F9evX1cdhUhbzs7OGDFiBEaPHs3bidswKSVGjx6NkSNHcj8SkQVdvXoVkyZNwgcffKA6ijIsLER3aNu2LcqXL4+ZM2eqjkKktbfffhtHjhzBpk2bVEehp7Ru3TokJyfjjTfeUB2FSGvTpk1DtWrV0Lx5c9VRlGFhIbqDEAKjRo3CDz/8gKysLNVxiLTl5uaGIUOGYPTo0aqj0FMaPXo03n33Xbi4uKiOQqStmzdvYty4cfjggw8ghFAdRxkWFqJ7dO/eHU5OTpg/f77qKERae+edd7B161bs3btXdRR6Qtu3b0dMTAwGDx6sOgqR1mbPno0SJUqgU6dOqqMoxcJCdA97e3u8//77+O6772AymVTHIdJWqVKl0L9/f4wZM0Z1FHpCo0ePxsCBA3lHRSILys7Oxvfff49Ro0bl+zsq5u+vnugB+vbti7S0NCxevFh1FCKtjRw5EitWrMD+/ftVR6HHtHfvXvzxxx8YPny46ihEWps3bx6klOjdu7fqKMqxsBDdh5OTEz7//HN8/PHH3MtCZEHly5fHgAED8NFHH6mOQo/pgw8+wNChQ1GmTBnVUYi0lZGRgU8//RRfffUVHBwcVMdR7rEKixDiSyFEUXHLSiHEBSFEd0uHI1Lp1VdfhYODA+8YRmRhH374IaKiorB161bVUegRNm7ciN27d+Pf//636ihEWpsyZQqKFi2KPn36qI5iCI87w9JFSnkZwAsAsgE0BsDLYaQ1BwcHfPPNN/jiiy9w7do11XGItFW6dGmMHDkSo0aN4nNZDExKiVGjRmHUqFEoVqyY6jhE2rp69Sq++eYbjB49Ot/vXcnzuP8V8nYeNwewWEqZYKE8RIby4osvwsvLCxMnTlQdhUhrI0aMQGJiIlauXKk6Cj3AkiVLkJKSgqFDh6qOQqS1//znP6hevTrat2+vOophiMe5miWE2ApgBYD+uDW7ch7APillTcvGMw9PT0+ZnJysOgbZqKioKLz44otISkpC8eLFVcch0tbEiRMxffp0xMXFwd7eXnUcukN2djb8/Pzwr3/9C2+99ZbqOETaOnfuHKpUqYK1a9eiUaNGquNYlBDitJTS83GOfdwZln4AygB4X0p5DkAlAPOeLh6RbWnRogUaNGjAB9wRWdiAAQOQnp6OefP4z4vR/Pzzz5BS4rXXXlMdhUhrX3/9NVq2bKl9WXlSjzXDYus4w0LPKjY2Fo0bN0ZCQgLKly+vOg6RtubOnYtPPvkECQkJcHJyUh2HAFy/fh1Vq1bFf//7X7z00kuq4xBpKykpCX5+ftizZw/8/PxUx7G4J5lheWhhEUJ8J6X8txBiMYB/HCil7Pn0Ma2HhYXMISQkBAB49ZfIgnJychAQEIDevXtj1KhRquMQgM8//xyrVq3Czp07IYRQHYdIW927d0eRIkXw888/q45iFeYsLJ2llMuFEK/e78+llLOfMqNVsbCQOZw+fRrVqlXDihUr0Lx5c9VxiLS1ZcsWtG/fHocPH+aMpmJJSUmoWbMmoqOjUb9+fdVxiLS1bt069OzZEwkJCXB3d1cdxyrMVlge8ZcUkFJmPtUHWxkLC5nL2LFjMWfOHMTExMDR0VF1HCJt9e3bFxkZGVi0aJHqKPlacHAw3N3dMX36dNVRiLSVkZGBWrVqYfDgwXjnnXdUx7Eas2+6F0KsEEIUu+PtSgD+95T5iGzWu+++i+zsbEyePFl1FCKtff/991i7di02bNigOkq+tXLlSmzdupU3HCGysPHjx8PZ2RmDBg1SHcWwHvcuYZsA7BFCNBRC9Mx9+3vLxSIypgIFCmDSpEn47LPPcPbsWdVxiLTl4eGBzz//HEOHDkVmpk1M5mvl5s2beOedd/DNN9+gZMmSquMQaevUqVP4+uuvMWnSJDg4OKiOY1iPvSRMCNEcwFoAqQCaSSmPWzKYOXFJGJlbr1694OTkhDlz5qiOQqStrKws1K1bF6+88gree+891XHyla+++gpLly7Frl27+EwcIgvq2bMnnJ2d8+X5hNn3sAghvAEsAhALoCaAIwAGSylvPkNOq2FhIXNLTk5G9erVsWrVKjRt2lR1HCJtbd68GR07dsThw4fh6flY/67RMzpx4gT8/PywceNGNGjQQHUcIm1t2LAB3bt3R0JCAsqUKaM6jtVZorCcAjBSShkhhLAH8B2ANlLKWs8W1TpYWMgSvvvuO8ybNw979+7lBnwiCwoJCUF2djYiIiJUR9GelBJdu3ZFyZIlMXPmTNVxiLSVkZEBf39/DBgwAMOGDVMdRwlLPOn+BSllBABIKXOklCMBfPC0AYl0MHz4cEgpMWbMGNVRiLT2ww8/YP369Vi6dKnqKNqLiIjA9u3b+XONyMK+/PJLFCxYEIMHD1YdxSY80W2NhRAOAArkvS2lvG6JUObGGRaylL1796Jp06bYsWMHatWyiQlHIps0d+5cvPfeezh48CBKlCihOo6Wzp07Bz8/P0yZMoVPtCeyoD179qBZs2b5/tzBEkvC6gOYCaA6gNuPuZVS2sROPBYWsqSPP/749lOguTSMyDKklOjSpQvc3Nwwb9481XG0I6VEjx49YG9vz2ffEFlQRkYGAgIC0KtXL3zyySeq4yhliSVhEwH0B7AfQFEAnwLgLVuIAHzyySfIysriEgoiCxJCYNq0aVi9ejWXhllAREQENm/ezGdMEVnYl19+iQIFCmDUqFGqo9iUxy0sjlLKnQAcpJRpUspvAARbMBeRzXBycsIvv/yC0aNHY9++farjEGnLw8MDEyZMwNtvv43U1FTVcbRx7tw5DBkyBGFhYShVqpTqOETa2rNnD8aPH49Zs2ZxRcYTetzCkp37a6oQwl8IURJABQtlIrI59erVw/Dhw9GvXz9kZWWpjkOkrdDQUNSvXx/vvPOO6ihakFJi0KBBaNmyJfetEFlQRkYG+vXrhw8++CBf71t5Wo9bWBYKIUoA+BbAZgAnAXDemOgOn376KZeGEVkYl4aZF5eCEVkHl4I9mye6SxgACCEcAThLKdMsE8n8uOmerCXvzh+bNm1CYGCg6jhE2goPD8eIESMQHx8PDw8P1XFs0qlTp+Dv74+pU6dydoXIgrZt24bWrVvn+7uC3csSm+5vk1JmmbusCCEmCiFOCCGkEKLmQ457QwhxVAhxXAjxU+5tlokMo169evj888/Rq1cvXLlyRXUcIm2FhISgbdu2CA0NRU5Ojuo4Nic7Oxt9+vTBiy++yLJCZEGpqano06cPRo8ezbLyDJ54hsUiIYRoBiAJwFYAnaSUB+5zTEUA2wDUAfA3gGUAVkoppz3q83OGhazJZDKhQ4cOKFy4MCIiIiCEePQHEdETS0tLQ0BAAPr27Zvvbw/6pD766CMsXboUu3fvhouLi+o4RFqSUqJr164AgKVLl/J84B4WnWGxBCnlZinloxpFDwC/SynPyVstayqAPpZPR/Rk7OzsMGfOHGzduhU//fST6jhE2nJzc8OiRYswZswYbN68WXUcm7F+/XpMmDABixYtYlkhsqCJEyciNjYWv/zyC8vKM3poYRFCDLdWkMfgBeCvO94+kfu+fxBCjBBCJOe90tPTrZGP6LbSpUtj/vz5GDFiBG91TGRB/v7+GDt2LPr06YMLFy6ojmN4Z8+eRWhoKCZMmAA/Pz/VcYi0tWfPHnz44YdYsGABihcvrjqOzXvUDEtbIUS0EOK+xUCBO9evPbCqSinHSSk9816urq5WiEZ0t6CgILz33nvo1asXrl27pjoOkbYGDhyIhg0bol+/fjDCMmejMplM6Nu3L1q1aoXXX39ddRwibV29ehW9e/fGxx9/jMaNG6uOo4WHFhYpZTsA8wBsE0K8Zp1ID3QSgPcdb1fIfR+RYX3yyScoU6YMhgwZojoKkbaEEJgxYwYOHjyI8ePHq45jWGPGjMGJEycwdepULk8hshApJd566y1UqlQJ//73v1XH0cYj97BIKacDaAlgnBDighDibyHEeSHE35aPd5clAF4UQriLWz9p3waw0MoZiJ6Ivb095s2bhxUrVuDnn39WHYdIW0WLFsXChQvxySefYNu2barjGE50dDS++eYbREREoHDhwqrjEGlr6tSp2LRpE+bOnQs7O0NsFdfCI/9LCiECAPyGW+WgPoBAAPVyfzULIcRkIUQyAE8AG4QQx3LfP0MIEQwAUsokAJ/h1p3CjuPWncJmmisDkaWULVsWERERGDp0KLZv3646DpG2nn/+eYwdOxbdunXDyZOcgM+TlJSEHj16YOLEiahbt67qOETaio6OxsiRI7Fo0SK4u7urjqOVh97WWAjxNYAQAG9LKddaLZWZ8bbGZASTJ0/GV199hd27d6N8+fKq4xBpSUqJgQMHYteuXdi6dWu+vwtWWloaGjVqhJYtW2LChAmq4xBp688//0RgYCDGjBmD/v37q45jE57ktsaPKizhAIZIKS+bKZsSLCxkBFJKDBgwADExMdi8eXO+P5EispTMzEy88MILKFu2LBYsWJBv92uYTCZ0794daWlpWLNmDRwc+KxlIktIT09Ho0aN0Lx5c/z444+q49gMsz2HRUoZautlhcgohBCYNGkSChYsiDfeeIN3MyKykAIFCmDJkiXYsWMHRo8erTqOMp9//jn279+PiIgIlhUiCzGZTHjllVdQqlQpjBs3TnUcbXE3EJEV5Z1Ibd++HWPGjFEdh0hbpUqVwrJlyzB69GgsW7ZMdRyrW7RoESZMmIBly5ahRIkSquMQaeuLL75AfHw8Fi1aBEdHR9VxtMXCQmRlpUuXxrJly/Dtt98iMjJSdRwibdWuXRuzZs1C3759ceDAAdVxrCY2Nhavv/46wsPD+XBIIgtavHgxxo8fj8jISF4YsDAWFiIF/P398fPPPyM0NBSxsbGq4xBpq3v37hgxYgQ6d+6Ms2fPqo5jccnJyejSpQs++ugjdO7cWXUcIm3t2rWLFwasiIWFSJGXXnoJH330Edq3b4+kpCTVcYi09emnn6JJkyZo3749rl69qjqOxVy6dAnt2rVD69atMWrUKNVxiLSVmJiIjh074quvvkJwcLDqOPnCQ+8SpgveJYyMSkqJESNGYMWKFdi2bRtKly6tOhKRlrKyshAcHIzMzEysWrUKTk5OqiOZ1Y0bN9CmTRsUK1YMv/32GzfZE1lISkoKGjVqhN69e3Mv6jMy222NdcHCQkZmMpkQGhqKxMREREVFwc3NTXUkIi2lp6ejZcuW8Pb2xoIFC2Bvb686kllkZ2eje/fuSE1Nxbp163jLdCILuXz5Mpo3b446dergl19+ybe3TDcXs93WmIgsz87ODrNmzUKxYsXQrVs3ZGZmqo5EpCVXV1esXLkS8fHxePfdd7W4tXjegzKPHz+OyMhIlhUiC7l58ya6dOmC8uXLY/r06SwrVsbCQmQABQoUwG+//YZLly6hX79+MJlMqiMRaalUqVJYu3YtfvvtN3z77beq4zyzTz/9FGvXrsWaNWtQvHhx1XGItJSTk4OQkBBkZmby9sWKsLAQGYSbmxtWrVqF3bt3Y8SIEVpc/SUyIm9vb6xZswZjx47FjBkzVMd5apMnT0ZYWBjWrl0LT8/HWlVBRE9ISonBgwfj8OHDWLFiBWcxFeGuPCIDKV26NNatW4dGjRqhcOHC+PLLL1VHItJSrVq1EBkZiQ4dOsDV1RW9e/dWHemJzJkzB6NGjcK6detQvXp11XGItCSlxKhRo7By5Ups27aNz1pRiIWFyGAqVqyIjRs3okWLFnBwcMCnn36qOhKRlpo1a4YlS5agW7dusLe3x0svvaQ60mOZN28eBg0ahMjISDRs2FB1HCItSSnx8ccfY+7cudi0aRO8vLxUR8rXWFiIDKhGjRp3lZYPP/xQdSQiLbVt2xaLFi1Cz549YW9vj27duqmO9FAREREYMGAAfv/9d7Rs2VJ1HCJtffHFF5g5cyaio6NRtWpV1XHyPRYWIoOqWbMmNm7ciJYtW8LOzo4PgiOykI4dO2LBggXo06cPhBB48cUXVUe6r0WLFuGNN97Ar7/+itatW6uOQ6StL7/8EmFhYYiOjka1atVUxyFw0z2RodWqVQsbN27EDz/8gK+//lp1HCJtBQcHY/78+QgNDcWvv/6qOs4/zJ8/H6+//joWL16Mdu3aqY5DpCUpJT799FNMnjwZf/zxB2rUqKE6EuXiDAuRwdWuXRtRUVFo1aoVsrOz8dlnn/H+70QW0KVLF0RERKBXr17IyclBr169VEcCAMydOxcDBw7Eb7/9hjZt2qiOQ6QlKSU+/PBDzJo1C9HR0byZhcGwsBDZgOeeew5RUVFo2bIlbt68idGjR7O0EFlAp06d8Ouvv6JHjx64efMmXn31VaV5ZsyYgeHDh2PZsmVo1aqV0ixEujKZTHjvvfewcOFCREdHw9fXV3UkugcLC5GN8PPzw+bNm9GmTRucP38e06ZNg4MDhzCRubVv3x6RkZF48cUXcf78eYwcOdLqGaSU+PbbbzF27FisXLkSzZo1s3oGovwgKysLr7/+OrZt24ZNmzahSpUqqiPRfYj88HA6T09PmZycrDoGkVmcPn0a7dq1Q8WKFbFw4UI+xIrIQvbu3YsOHTogNDQUY8eOhZ2ddbZ95uTkYNiwYViyZAnWrFmDWrVqWeXvJcpv0tPT8dJLL+Hs2bNYvXo1ypQpozpSviKEOC2lfKyn3nLTPZGNKVeuHDZv3oxLly6hTZs2uHjxoupIRFoKCAjAtm3bsHTpUrzyyivIzMy0+N+ZkZGBPn36YN26ddi+fTvLCpGFXLhwAa1atUJGRgY2bdrEsmJwLCxENqhYsWJYt24dSpYsiaZNm4IziESWUaVKFWzbtg0HDx5EcHAw0tPTLfZ3Xb16FR06dMCJEyewdetWeHt7W+zvIsrPTpw4gcaNG8PLywurV69G4cKFVUeiR2BhIbJRBQsWxK+//orGjRujUaNGOHz4sOpIRFoqU6YMNm3ahMzMTLRs2RLnz583+99x9uxZNG/eHI6Ojvjjjz9QqlQps/8dRATs27cPjRo1QuvWrbFw4UI4OTmpjkSPgYWFyIY5ODhg2rRp6NevH5o0aYKtW7eqjkSkpcKFC2P16tXw9vZGkyZNcOzYMbN97oSEBDRu3Bg1a9ZEZGQkXF1dzfa5iej/RUVFoXnz5hg0aBB+/PFH2Nvbq45Ej4mFhcjGCSHw5Zdf4ttvv0Xbtm0xY8YM1ZGItOTk5IQFCxagY8eOeP7557Fx48Zn/pyrV6/G888/j5deegmzZ89GgQIFzJCUiO4kpURYWBg6deqE//znP/j444/5aAAbw3uiEmliwIAB8PX1RY8ePbBv3z6MGzeOtz0mMjN7e3uMGzcOzz33HIKDgzFmzBgMGTLkiU9+pJQYN24cPvvsM0ybNg0hISEWSkyUv2VmZuKdd97B77//jrVr16JJkyaqI9FT4G2NiTTz559/Ijg4GO7u7oiIiECJEiVURyLS0vbt29GtWzd07twZkydPfuzZkZs3b2LAgAHYsGEDli5disDAQAsnJcqfzp8/j+7duyMtLQ3Lli2Dl5eX6kh0B97WmCgfq1ixIrZv3w43NzfUr18fBw8eVB2JSEuNGjXC7t27ERsbi5YtW+LcuXOP/JiUlBQEBQUhISEBe/bsYVkhspD4+HgEBgaiTJky2Lp1K8uKjWNhIdKQm5sblixZgpCQEDRs2BDLly9XHYlIS+XLl8fmzZtRvnx5BAYGIjY29oHH7t69G4GBgfD19UV0dDQ8PDysmJQo/1iyZAmaNGmCN998ExEREShUqJDqSPSMWFiINGVnZ4cvv/wSM2fOxMsvv4zPPvsMOTk5qmMRacfFxQXz58/HwIED0bRpU8yePfuuP5dSYvr06WjRogX+9a9/YdasWXB2dlaUlkhfWVlZ+OCDD/Daa69h7ty5+Oijj7i5XhPcw0KUD+zbtw+9evWCu7s75s2bh3LlyqmORKSlNWvW4JVXXkG7du0QFhYGk8mEAQMGICoqCvPmzUOrVq1URyTS0smTJ9GnTx9cuXIFixYtQo0aNVRHokfgHhYiukutWrWwe/dueHt7w9/fH6tWrVIdiUhL7dq1Q1xcHE6dOgU/Pz/4+fkhNTUV8fHxLCtEFrJs2TL4+/vDz88Pu3btYlnREAsLUT7h6uqKWbNmYdy4cejVqxfef/99ZGVlqY5FpB0PDw8EBwfjzJkzOHfuHLp06YLSpUurjkWknYyMDAwbNgyvvPIKwsLC8NNPP8HFxUV1LLIALgkjyocSEhLQs2dPFCxYEAsXLoS3t7fqSERauHjxIl577TXExsZiwYIFyM7Oxssvv4yGDRtixowZKFq0qOqIRFo4duwYevXqBSEEFi5ciCpVqqiORE+IS8KI6KF8fX2xc+dOBAQEoE6dOli0aJHqSEQ2b/PmzfD39wcAxMXFoXHjxmjevDni4uJw/fp11KlTB9u3b1cbksjGSSkxb948BAQEoFmzZti2bRvLSj7AwkKUTzk7O2Py5MmYMWMGBg0ahJ49e+L8+fOqYxHZnGvXruHdd99F+/btMXLkSCxduhTFixe//eelSpXCihUrMHToULRu3RojR47EjRs3FCYmsk1nz55Ft27dMGLECMydOxfjx4+Hk5OT6lhkBSwsRPlc9+7dcfDgQeTk5KBGjRpYvHix6khENmPLli2oXbs29u7di7i4OLzzzjv3vY2qnZ0dRowYgT179mDr1q3w9/fnbAvRY5JSYv78+fDz84OzszMOHjyI4OBg1bHIilhYiAju7u749ddfMWnSJAwcOJCzLUSPkDer0q5dOwwePBibNm1C1apVH/lx1atXx7Zt29C/f3/OthA9hrxZleHDh2P69OlYsGABSpYsqToWWRkLCxEBAIQQ6NWrF2dbiB7h3lmV4cOHw97e/rE/3t7eHu+99x5nW4ge4n6zKt26dVMdixRhYSGiu9xvtuXMmTOqYxEpd/Xq1aeaVXmQe2db/vWvfyE9Pd2MiYlsU3JyMmdV6C4sLET0D3fOttjZ2cHX1xfjxo3jc1soX8q7K5Gvry/27duH2NjYJ55VeZA7Z1t27dqFatWqISIiAvnhkQNE98rMzMR3332H6tWro1ChQpxVodv4HBYieqSNGzdi6NChsLOzw6RJkxAUFKQ6EpFV7N+/H0OGDMGxY8fwn//85/ZzHyxBSonw8HC899578PPzw48//sgndlO+sX79egwdOhQFChTApEmT0KxZM9WRyML4HBYiMqtWrVohLi4O/fr1Q+fOndGnTx+cPn1adSwii7ly5QqGDRuG+vXr4/nnn8eRI0fQu3dvi5UV4NbMZt++fZGQkIBatWohICAAI0eORFpamsX+TiLVTp06hZdeegk9evTAwIEDERMTw7JC/8DCQkSPpUCBAhg5ciSOHDkCIQSqVauGH374gcvESCtSSsyZMwe+vr44cOAAYmJi8P3338PNzc1qGYoUKYLx48dj165d2L17N6pVq4YFCxZwmRhpJSMjA6NHj0b16tXh4uKChIQEvPvuu3BwcFAdjQyIS8KI6KlER0djyJAhyM7OxrfffosXX3zRolefiSxt8+bN+Pe//41Tp05h/Pjx6NGjh/L/p6WUWLBgAUaOHInKlSvju+++Q6NGjZRmInoWJpMJv/76Kz766CO4uLhg8uTJaNKkiepYpACXhBGRxQUFBSE2NhbvvvsuBg8ejAYNGiAqKkp1LKInFh8fjw4dOqBTp07o0KEDjhw5gpdeekl5WQFuLRN7+eWXkZCQgJYtW6Jt27bo0qULDhw4oDoa0RNbv3496tevj+HDh+P999/H3r17WVbosRiisAghqgohtgshEoUQu4QQ/9hlKIQIEkJcF0LE3fEqqCIv3bIkYg6azF+Kqiu3osn8pfht0VzVkcjKHB0dMXDgQBw7dgxdunRB165d0a5dO8TGxqqORvRISUlJCA0NRYMGDVCtWjUkJSXhk08+gaurq+po/+Dm5oYvvvgCx48fR4UKFRAYGIh+/frhr7/+Uh2N6JF2796NF154AT179kTPnj1x7NgxvPnmm1z+RY/NEIUFwDQAP0kpfQB8D2DmA447JKX0v+PFxwMrsiRiDt4p6YdjZbyQ5uKKY2W8MLREDZaWfKpQoUL48MMPkZSUhOeeew6NGzdGnz59cOzYMdXRiP7h3LlzGDp0KPz8/ODo6IiEhASMGzfOJp7zULp0aUycOBGHDh1CTk4OqlWrhuHDh+PChQuqoxH9Q0JCAl566SUEBQUhMDAQSUlJeP/991GwIK8305NRXliEEKUB1AUQnvuuJQAqCiG8lYWiRxqfUxg5QgAi938hYQeTEBifZbwrk2Q9JUqUwNixY5GQkIBChQrhueeew4ABA5CUlKQ6GhH+/vtvfPjhh6hcuTJOnTqFPXv24JdffoGXl5fqaE+sYsWKmDt3Lnbu3ImjR4+iUqVK+PTTT1lcyBCOHj2K/v37w9/fHyVKlMDRo0cxevRoFCtWTHU0slHKCwuA8gBSpJTZACBv3QXgJID7/QviK4SIEULsFkIMetAnFEKMEEIk57345GDzO1ek5P+XlVxS2OFc0VKKEpGRlC9fHjNmzEBMTAyuXbuGGjVqICQkBPv371cdjfKhEydOYMiQIfD29kZcXBzWr1+PpUuXws/PT3W0Z1arVi2sWLECK1euxM6dO1GhQgUMGzYMp06dUh2N8qHY2Fj06tULzz33HLKzsxEfH4+pU6eibNmyqqORjTNCYQGAe29Vdr+djjEAPKWUdQG8COBtIUTP+34yKcdJKT3zXkZcj2zr3K9cAKTprvcJaYL75fOKEpERVa9eHeHh4Th8+DCKFCmC+vXro3Pnzti+fbvqaJQPHDp0CK+88gqqVauGCxcuYPv27Vi1ahUaNmyoOprZNW3aFGvXrsXmzZtx+vRpVK1aFa+//joSEhJURyPNSSmxefNmtG/fHo0bN4a7uzsSEhIwa9Ys+Pj4qI5HmjBCYTkFwFMI4QAA4tZtWcrj1izLbVLKq1LKK7m/TwawAEBTK2elXCMc0mAvJURuaRHSBDspMdyRs1n0TxUrVkRYWBj+/PNP+Pn5oV27dmjevDnWrFnDZ0uQ2e3cuRNdu3ZF3bp14ezsjAMHDmDhwoXw9/dXHc3iAgICsHjxYsTHxwMAateujR49emDv3r2Kk5FupJRYsWIFmjRpguDgYAQEBODEiROYOHEiKlSooDoeaUZ5YZFS/g0gFkBo7ru6AzghpTxx53FCCA8hbq1BEkK4AeiU+3GkQLeeffFj6iFUOfMXCl9PR5Uzf+HH1EPo1rOv6mhkYGXKlMGYMWNw8uRJtG3bFq+88grq1KmD6dOn49q1a6rjkQ3LzMzEokWL0Lx5c7zwwguoUqUKkpKS8NNPP6FKlSqq41mdr68vfv75Zxw9ehSenp5o1qwZWrZsiSVLlvBhr/RM0tLSMHXqVNSqVQv9+/dHcHAwTp48ia+//hqlS5dWHY80ZYgHRwohfAHMAlACwFUAr0opDwohZgCIlFJGCiGGABgIIBuAA4DFAL6Qj/EF8MGRRMZ0/fp1zJs3D2FhYUhKSkK/fv0wcOBAVKtWTXU0shHJycn46aefMH36dLi4uGDgwIF4/fXXUbx4cdXRDOXChQuYOXMmpkyZgqysLAwYMAD9+/fn3gJ6bAcPHsSUKVMwZ84c+Pj4YNCgQXj55Zfh7OysOhrZqCd5cKQhCoulsbAQGZuUEjt27EBYWBgWL16Mxo0bY9CgQQgODoajo6PqeGQwUkps3LgRYWFhWLFiBdq1a4dBgwahTZs2sLNTvnDA0HJycrBmzRqEhYVhw4YNCA4OxqBBgxAUFGSIB2WSsWRmZmLp0qUICwvDzp070bt3bwwaNAiBgYGqo5EGWFjuwcJCZDvOnz+PX375BVOmTEFmZibefPNNvPLKK6hUqZLqaKTYuXPnMH/+fEydOhWXLl1C//798dZbb8Hb21t1NJuUlJSEadOmYebMmShdujQGDBiAl19+GaVK8W6P+d2xY8cwe/ZszJgxA4UKFcLAgQPRr18/lChRQnU00ggLyz1YWIhsT05ODtauXYtp06Zh9erVCAwMREhICHr27GkTD/gj80hPT8fSpUsRHh6OjRs3onHjxnjrrbfQvXt3ODk5qY6nhZs3b2Lx4sWYPn06duzYgdatWyM0NBTBwcEoVKiQ6nhkJefPn0dERATCw8MRGxuLDh064O2330br1q05c0kWwcJyDxYWItt24cIFLF68GOHh4di9ezfatWuHkJAQBAcH84nJGsrOzsb69esRHh6OpUuXolKlSujbty/69OmD8uXLq46ntb/++gvz589HeHg4/vrrL3Tr1g2hoaFo2bIlHBwcVMcjM7t27RoiIyMRHh6O9evXo0GDBggNDUWPHj24D4wsjoXlHiwsRPpISkq6fUKVkpKCbt26oVevXmjRogU3f9qw7OxsbN++Hb/++isWLlyIAgUK4OWXX0ZoaChq1aqlOl6+I6VEfHw8wsPDMX/+fJhMJvTp0wc9evRAgwYNYG9vrzoiPaUbN27gjz/+QEREBH777Td4eXndviDA5ZVkTSws92BhIdKPlBIxMTEIDw/H77//jgsXLqBt27YIDg5Ghw4duA7fBqSlpWHt2rWIjIzEypUrYW9vj+DgYISEhKBZs2Y8KTaInJwcREdHY968eYiMjIQQAp06dULnzp3Rpk0b8OHMxnfu3DmsXLkSkZGRWL9+PUqXLn179szf3583XCAlWFjuwcJCpDcpJfbv34/IyEhERkYiJiYGDRs2RHBwMIKDg+Hr66s6IuU6deoUli9fjsjISERFRaFy5cq3v0/PP/88S4rB5eTk4H//+9/tsXbixAm0bNkSwcHB6Ny5M8qVK6c6IuHWz8TDhw/f/j7t2rUL9erVuz3W/Pz8WFJIORaWe7CwEOUvKSkpWLFiBSIjI7FhwwZ4eXmhVatWCAoKQvPmzVGmTBnVEfONy5cvY/PmzYiOjsYff/yBgwcP3n4ydufOnfPlQx11kpCQgOXLl2P58uXYtm0batWqhZYtWyIoKAhNmzZFkSJFVEfMN86cOYPo6GhER0djw4YNOHPmDFq3bo3OnTujU6dO/LlHhsPCcg8WFqL869q1a9i4cSOio6MRFRWFffv2wdfXF0FBQbcLjLu7u+qY2rhy5Qq2bNmCqKgoREdHIy4uDlWrVkVQUBBatGiB1q1bczOvplJTU7Fu3brb3/vjx4+jbt26t7/3TZo0QeHChVXH1MbZs2dvF5To6GgcPXoU/v7+aNGixe2Xi4uL6phED8TCcg8WFiLKc/HixbtOqPft24fq1aujadOmqFevHgICAuDn54cCBQqojmp4OTk5SExMxJ49e7B3715s3boVsbGxqFKlyu1CGBQUBA8PD9VRSYHTp0/fdUL9559/om7dumjSpAkCAgIQEBAAHx8f3jL3MWRmZuLAgQPYs2cP9uzZgy1btiAxMRG1a9e+XQibNm2KokWLqo5K9NhYWO7BwkJED5KamorNmzdj27Zt2Lt3L2JiYnDz5k3UqlXrdoFhiflnOdm7dy9iY2NhMplQu3Zt1KtXDw0aNEBQUBD3MdB9nTp1CtHR0dixYwf27t2L+Ph4ODg4oG7durfHGUvM3eUkb6zt378fBQsWvP3fqkmTJmjatClnK8mmsbDcg4WFiB6XyWTC8ePHsXfv3tsnDHklpkaNGvDx8bn98vX1hY+Pj1ZXNa9du4bExMS7XgkJCTh06BBMJhP8/f3vOrmsXr06n89BTyUrKwuHDx++a6zllZgaNWrcHl95r6pVq2r1IMtLly7dHl93jrUjR46gYMGCd42zgIAAVK5cmRvlSSssLPdgYSGiZ5FXYg4ePHjXyUViYiL+/vtvlCpV6naB8fb2hoeHBzw8PFC2bFl4eHigVKlShrj7lZQSqampOHPmDFJSUm7/evLkydtfz+nTp1GkSBH4+vredcJYo0YNVKtWjeWELCo7OxuHDh3C4cOH7zqZT0hIwNWrV+Hp6Xn7/0kvL6+7xlnZsmVRvHhxQ5zU5+Tk4O+//8aZM2fuGm8nTpy4/TVduHAB7u7u/7gAUrNmTVSqVMkQXweRJbGw3IOFhYgs5fLly3ddHT158uRdJykXL16Evb093N3db59UlShRAq6urnBzc7v9uvNtV1dXODs7w87O7q6XlBImk+n2KyMjA+np6UhLS7v9uvPt9PR0XLx48XaeM2fOICsrC0WKFLmrVOWdBOadMJUsWZInS2QoUkqcP3/+rgsGycnJt4vAmTNncPXqVRQoUABlypS5XWKKFSt23/F159grUKDAXeNMCHHXODOZTLh58+Y/xte9b995MeDcuXMwmUwoUaLEXaXKy8vrrgsBvIsa5WcsLPdgYSEiVTIyMnD27Nm7ZjQuXbr0wJOevFdGRsZdJ0w5OTmws7ODvb397RMrR0fHu0687ncyVrRo0X/M+PDOQaSja9eu/WNG4/Llyw8tGWlpacjKyrprnJlMprvGmZ2dHZydne87vu58u3jx4rfHmIeHB8qUKQMnJyfV/1mIDIuF5R4sLERERERExvEkhSX/3oaDiIiIiIgMj4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMi4WFiIiIiIgMy0F1ACIiIiJVrl+/jhMnTiAtLQ2ZmZnIycmBg4MDChQogGLFisHb2xuOjo6qYxLlaywsREQGdfz4caxduxbbt29HWloaChYsiICAALRt2xbPPfcchBCqIxLZDCklEhISsHr1asTHx+P48eM4fvw4zpw5AxcXFxQpUgSOjo6wt7dHdnY2srKycPHiRWRnZ8PLywuVK1dG5cqVUb9+fbRv3x5ly5ZV/SUR5RtCSqk6A4QQVQHMBlASwGUA/aSUh+5z3BsARuHWUraNAAZJKbMf9fk9PT1lcnKyWTMTEVnKhQsXMGjQICxbtgxNmjRBUFAQihUrhvT0dGzbtg1RUVGoV68eZs6cicqVK6uOS2Roqamp+OmnnzBr1iycPHkSLVq0QP369W8XkMqVK6N06dL3vQCQk5OD06dP3y43x44dw+bNm7Fz5048//zz6NevH/r164cCBQoo+MqIbJsQ4rSU0vOxjjVIYfkDwBwp5SwhRA8A/5JSNrznmIoAtgGoA+BvAMsArJRSTnvU52dhsYyDKVcwfl0CEs6lo4ZHYbz7gg9qlC2sOhaRTbt58yb8/f1Ro0YNhIWFoUyZMjhy8QimxE9BwsUE+Bb3xatVXsUv3/+C+fPn48CBA/Dw8FAdm8iQoqOjERoaiqpVq+Ltt99G586d4eLict9jz59Kw+6Vf+JCcjpKerqifqeKKOnpdt9jL1y4gIiICEyePBkuLi5YuHAhqlSpYskvhUg7NlVYhBClASQCKCmlzBa3LnGcAdBASnnijuPeA+AtpRyc+3YHAO9LKYMe9XewsJjfjF/X4OudNyGFHYSdPSBNKOBgj6WDm7C0ED2DL7/8EpGRkdi5cyfs7e1x5OIRhKwMQbYpGyaYYAc7ONg5YH7H+fhs0GdwcHBAeHi46thEhhMXF4eGDRti3LhxePvttx+6hPL8qTQs+W4PcnIkIAEIwN5eoMeoeg8sLQCQkZGB9957D4sWLcKRI0dQtGhR838hRJp6ksJihLuElQeQkre0S95qUCcBeN1znBeAv+54+8R9jiEr+fK3PYC9w62yAgDCDlk5JkzYmKg2GJGNi46OxsCBA2Fvf2tsTYmfcrusAIAJJmSbsjElfgqGDBmC6OhohWmJjGvmzJkIDQ3FwIEDH7nfa/fKP/+/rACABEw5ErtXnHjoxzk5OWHChAnw8PDAsmXLzBOciP7BCIUF+P8fEXke9JNFPsYxEEKMEEIk573S09OfOSDdraBHFdz7LZAQOJRyVU0gIk0UL14chw8fvv12wsWE22UljwkmHLl4BIcOHUKJEiWsHZHIJvj4+GDbtm24ePHiI4+9kJz+jzMRKYELyWmP/NiEhAQcO3YMPj4+TxuViB7BCIXlFABPIYQDAOQuCSuPW7MsdzoJwPuOtyvc5xgAgJRynJTSM+/l6upq/tT5XPPalSHu+eluJwC/skUUJSLSw8cff4zJkydj06ZNAADf4r6wu+dHtR3s4OnoiY8++giff/65gpRExvf222+jSpUqqF27NlatWgWTyfTAY0t6uv7jMqgQQMnyD14OdvPmTUybNg2BgYEYNmwYGjZs+MBjiejZKC8sUsq/AcQCCM19V3cAJ+7cv5JrCYAXhRDuuaXmbQALrRaU7jLsBV84OtjDLvcHvJ0AHOzt8E6rqmqDEdk4f39/TJgwAe3bt0f//v1RO702HOwcbpcWAQGYgCUjl+DNN99E165d1QYmMihHR0csW7YM//73v9GvXz9UqlQJ7733HqKionDt2rW7jq3fqSLs7QXyVo4JAdjZCwR29L7ruIsXL2Lp0qV48803UbZsWfzwww9YtGgRvvrqKyt9VUT5k/JN9wAghPAFMAtACQBXAbwqpTwohJgBIFJKGZl73JsA/o1bResPAAOllFmP+vzcdG8Zh1KuYsLGRBxKuYoaZQvj3Va8SxiRuSQmJmLcuHFYs2YNzpnOocyLZVDAswBM50yofa02Rr46Eg0aNFAdk8gmZGVlYfXq1Vi2bBlWr16NM2fOwN3d/a5bGxcpUBoOlzwgbjpDOt1AVvEzOJ+WfPuWxsePH8fly5fh4+ODDh06oHv37mjcuDGfh0T0lGzqLmHWwMJCRLZKSokzZ84gLS0Nzs7OKF++POzslE+OE9ksKSUuXLhwVxFJSkpCeno6MjMzkZ2dDUdHx9tPur+z1FSuXBmFC/PCHJE5sLDcg4WFiIiIiMg4bO22xkRERERERPfFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIbFwkJERERERIalvLAIIVyEEAuEEMeEEIlCiG4POVYKIfYJIeJyX02tmZWIiIiIiKzLQXUAACMBZEgpqwghKgL4nxAiSkp56QHHN5JSplsxHxERERERKaJ8hgVALwCTAUBK+SeAzQC6KE1ERERERESGYITC4gXgrzvePpH7vgeJFkLECyHGCSEK3e8AIcQIIURy3is9nRMyRERERES2yOKFRQixRQhx4QGv8rmHyTs/5CGfroKUsh6ARgBKARh7v4OklOOklJ55L1dXV/N8MUREREREZFUW38MipXzoxnghxEkA3gDO576rAoBVD/hcJ3N/vSaECAPwk/mSEhERERGR0RhhSdhiAIMBIHfTfXMAkfceJIQoJoRwyf29HW7tfYm1Yk4iIiIiIrIyIxSWsQAKCiGOAVgLYLCU8iIACCHeFkJ8mXtcNQA7hBDxAPYDKAFgmIK8RERERERkJUJK+eijbJynp6dMTk5WHYOIiIiIiAAIIU5LKT0f51gjzLAQERERERHdFwsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZFgsLEREREREZlpBSqs5gcUKIDADnVefQmCuAdNUh6Inwe2ab+H2zPfye2R5+z2wTv2+2p4yU0uFxDnysg2ydlNJJdQadCSGSpZSeqnPQ4+P3zDbx+2Z7+D2zPfye2SZ+32yPECL5cY/lkjAiIiIiIjIsFhYiIiIiIjIsFhYyh3GqA9AT4/fMNvH7Znv4PbM9/J7ZJn7fbM9jf8/yxaZ7IiIiIiKyTZxhISIiIiIiw2JhISIiIiIiw2JhoacmhKgqhNguhEgUQuwSQtRQnYkeTggxUQhxQgghhRA1VeehRxNCOAshluaOszghxBohhLfqXPRwQoh1Qoh9ud+zLUIIf9WZ6PEIIT7jz0jbkftv2pHcsRYnhOilOhM9nBDCSQgxSQhxVAhxUAgR/qiPyRfPYSGLmQbgJynlLCFEDwAzATRUnIke7lcA3wPYqjoIPZGfAKyWUkohxJDct9sozkQP11NKeRkAhBBdAfwMoK7KQPRoQoi6ABoAOKk6Cz2RHlLKA6pD0GMbA8AEwCf33zWPR30AZ1joqQghSuPWP755rXgJgIq88mtsUsrNUsrHflATqSelvCmlXCX//w4pOwBUUpmJHi2vrOQqglv/OJOBCSGcAEwGMAgA70hEZAFCiEIAXgPwYd6/a1LKM4/6OBYWelrlAaRIKbMBIPd/upMAvJSmItLfOwCWqw5BjyaEmCOEOAXgawCvqs5Dj/QlgHAp5Z+qg9ATmyeE2C+EmCGEKKU6DD1UZQCpAD4WQuzJXTLb6lEfxMJCz+LeK1BCSQqifEII8SGAqgA+Up2FHk1K+YqUsjyAjwGMVZ2HHkwI0RBAIIAw1VnoiTWTUtbGrVUfqQBmK85DD+eIW6sEDkkp6wEYAmDho4omCws9rVMAPIUQDgAghBC4NevCdb9EFiCEGAmgG4D2UsrrqvPQ45NSzgbQQghRQnUWeqDmAKoB+FMIcQKAJ4C1Qoj2SlPRI0kpT+b+mgXgvwCaKg1Ej/IXbi2RnQcAUsp4AH8C8HvYB7Gw0FORUv4NIBZAaO67ugM4IaU8oSwUkaaEECMA9AHQ+p69EWRAQojCQoiyd7z9Im5d+b2oLhU9jJRyjJSyrJTSW0rpDSAZQFsp5WrF0eghhBCFhBBF73hXH9w6NyGDklJeALARQFsAEEJUAFARQMLDPo5PuqenJoTwBTALQAkAVwG8KqU8qDQUPZQQYjKALgDKALgAIF1KWUVtKnoYIYQnbs1oJgFIy313hpTyeXWp6GGEEOVx60YkBXHrSuJ5ACOllHEqc9Hjy51l6cQ7TxmbEKISbo01e9xalp4E4F1ePDW23O/bz7h1/pgD4Asp5e8P/RgWFiIiIiIiMiouCSMiIiIiIsNiYSEiIiIiIsNiYSEiIiIiIsNiYSEiIiIiIsNiYSEiIiIiIsNiYSEiIiIiIsNiYSEiIqsRQhQVQpwUQjS8431DhBBRQghhpr/jbSHEcHN8LiIiUo/PYSEiIqsSQnQAMB5AHQDlAGwB0IAPeyMiovvhDAsREVmVlHIVgK0AxgKYDeCTB5UVIcRYIcRuIUScEGKTEKJq7vubCyGOCyGK5749WQgxJff3nwshfsj9fQMhxN7cjz8ghBhohS+RiIjMiDMsRERkdUKIwgBOANgrpWz9kONKSikv5P6+N4BQKWWn3Lc/ANAIwBwAHwJoKKW8KYT4HICrlHKkEGIZgAgp5fzcjykmpbxkwS+NiIjMzEF1ACIiypeaA7gOoJIQwlVKmf6A49oIIYYCcMOtVQGF7/izMQBWA5gOIFBKefM+Hx8F4GMhRBUAf0gpt5rtKyAiIqvgkjAiIrIqIUQJAGEAugFYg1tLw+53nBeAiQBCpJQ1AfQG4HzHIW4AKgK4BqD0/T6HlPK/ADoBOAPgWyFEmHm+CiIishbOsBARkbVNBjBXSrlLCHEQQLwQopWUcuM9xxUBkAngbO4dxIbc8+czAcwHsAFAuBCinpQy9c4DhBC+UsoEAElCiFMAvrXEF0RERJbDwkJERFYjhOgBwA/AKwAgpbwmhHgDwC9CiNpSyrS8Y6WU+4UQiwEcBHASwPo7Ps8QAMUBfCWlNAkhpgGYI4TodM9fOVQI0QK3ik8OgH9Z8MsjIiIL4KZ7IiIiIiIyLO5hISIiIiIiw2JhISIiIiIiw2JhISIiIiIiw2JhISIiIiIiw2JhISIiIiIiw2JhISIiIiIiw2JhISIiIiIiw2JhISIiIiIiw/o/UinpEz9b1+MAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 960x560 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_covariances(variable_nodes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above we see that the Markov chain has been updated in one fell swoop, and has the correct covariance structure. However, we did not use all information: we should have updated the messages using the other cluster's beliefs first. Let's correct that now.\n",
    "\n",
    "Calculating a new messages $m_{i\\rightarrow j}$ takes the super-factor and adds the belief of the cluster \"on the other side\" to it, *minus* the messages that was sent to that other cluster:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_new_message(factors: gtsam.GaussianFactorGraph,\n",
    "                          keys: Keys, downdated_belief: gtsam.GaussianFactorGraph):\n",
    "    \"\"\"Calculate message from factors and belief for sending node.\"\"\"\n",
    "    graph = gtsam.GaussianFactorGraph()\n",
    "    graph.push_back(downdated_belief)\n",
    "    graph.push_back(factors)\n",
    "    ordering = gtsam.Ordering()\n",
    "    for key in keys:\n",
    "        ordering.push_back(key)\n",
    "    _, remaining = graph.eliminatePartialSequential(ordering)\n",
    "    return remaining"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With that, we can write our final iteration code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_messages_and_node(j: int):\n",
    "    \"\"\"Update messages into cluster j and calculate belief q(X_j).\"\"\"\n",
    "    for edge in messages[j].keys():\n",
    "        if len(edge) == 2:  # only update binary messages\n",
    "            j1, j2 = edge\n",
    "            k = j2 if j1 == j else j1\n",
    "            other_cluster = variable_nodes[k]\n",
    "            downdated_belief = gtsam.GaussianFactorGraph()\n",
    "            downdated_belief.push_back(other_cluster.belief)\n",
    "            message_to_subtract = messages[k][edge]\n",
    "            for i in range(message_to_subtract.size()):\n",
    "                downdated_belief.push_back(message_to_subtract.at(i).negate())\n",
    "            messages[j][edge] = calculate_new_message(factor_nodes[edge],\n",
    "                                                      other_cluster.keys,\n",
    "                                                      downdated_belief)\n",
    "    update_node(j)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that above we down-date the belief for the \"other node\" before eliminating the variables associated with it. Otherwise we are double-counting information."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Running Cluster-BP\n",
    "\n",
    "Below we run this to convergence, which is very fast."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x560 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "update_messages_and_node(0)\n",
    "plot_covariances(variable_nodes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We update the two other clusters as well:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x560 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for j in [1,2]:\n",
    "    update_messages_and_node(j)\n",
    "plot_covariances(variable_nodes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, these are remarkably close, after *one* round-robin iteration. Doing a few more rounds does not make a difference, and when overlaid on the *true* covariances you can hardly see the difference:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x560 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for round in range(5):\n",
    "    for j in range(3):\n",
    "        update_messages_and_node(j)\n",
    "marginals_figure(truth, marginals, graph_keys)\n",
    "plot_covariances(variable_nodes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Different Initial Beliefs\n",
    "\n",
    "Of course, we started from beliefs that already had the mean correct. But, We get a more interesting animation when we start different points and pretend to be rather confident:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "rng = np.random.default_rng(42)\n",
    "new_belief0 = gtsam.GaussianBayesNet()\n",
    "minmax = -3.0, 3.0\n",
    "new_belief0.push_back(GaussianPrior(x1, rng.uniform(*minmax, size=(3,)), 0.1))\n",
    "new_belief0.push_back(GaussianPrior(x2, rng.uniform(*minmax, size=(3,)), 0.1))\n",
    "new_belief0.push_back(GaussianPrior(x3, rng.uniform(*minmax, size=(3,)), 0.1))\n",
    "\n",
    "new_belief1 = gtsam.GaussianBayesNet()\n",
    "new_belief1.push_back(GaussianPrior(l1, rng.uniform(*minmax, size=(2,)), 0.1))\n",
    "\n",
    "new_belief2 = gtsam.GaussianBayesNet()\n",
    "new_belief2.push_back(GaussianPrior(l2, rng.uniform(*minmax, size=(2,)), 0.1))\n",
    "\n",
    "key_sets = [{x1, x2, x3}, {l1}, {l2}]\n",
    "new_beliefs = [new_belief0, new_belief1, new_belief2]\n",
    "\n",
    "new_node_specs = list(zip(key_sets, new_beliefs))\n",
    "variable_nodes = [Cluster(keys, initial_belief)\n",
    "                  for keys, initial_belief in new_node_specs]\n",
    "messages = defaultdict(dict)\n",
    "for i, factors in factor_nodes.items():\n",
    "    if len(i) == 1:\n",
    "        j, *others = i\n",
    "        messages[j][i] = factors\n",
    "        continue\n",
    "    for j in i:\n",
    "        messages[j][i] = Message()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x560 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# marginals_figure(truth, marginals, graph_keys)\n",
    "plot_covariances(variable_nodes)\n",
    "for round in range(5):\n",
    "    for j in range(3):\n",
    "        update_messages_and_node(j)\n",
    "    plot_covariances(variable_nodes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Still, for this small graph we converge rather fast."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "A cluster-based belief propagation approach is still a \"mean-field\" approximation, but on clusters rather than individual variables. We recover \"vanilla\" BP if make the clusters contain only one variable, but note that even then these variables are multivariate. Finally, if we use *one* cluster, because we call sparse factorization (`eliminateSequential`!), we converge to the *true* posterior density.\n",
    "\n",
    "We'll do a larger example in a non-linear SLAM notebook."
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3.8.12 ('gtbook')",
   "language": "python",
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