{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "Cygv_wPHYa5R"
   },
   "source": [
    "# Learning Fixpoints\n",
    "\n",
    "We want to learn a function $f$ such that $f(x) = x$ for an initial $x$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "DTY3MwI4TrMG"
   },
   "source": [
    "## Related Work\n",
    "\n",
    "- Random NNs: https://arxiv.org/pdf/1710.06570.pdf\n",
    "- Attractors: https://en.wikipedia.org/wiki/Attractor"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 103,
     "output_extras": [
      {
       "item_id": 1
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 3128,
     "status": "ok",
     "timestamp": 1522832183139,
     "user": {
      "displayName": "Lenz Belzner",
      "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
      "userId": "102800868167498000139"
     },
     "user_tz": -120
    },
    "id": "dXGZLAQARYjV",
    "outputId": "e96a4de3-9eae-4f6b-ab96-eeaae849846c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: keras in c:\\miniconda\\envs\\keras\\lib\\site-packages (2.2.4)\n",
      "Requirement already satisfied: numpy>=1.9.1 in c:\\miniconda\\envs\\keras\\lib\\site-packages (from keras) (1.15.4)\n",
      "Requirement already satisfied: scipy>=0.14 in c:\\miniconda\\envs\\keras\\lib\\site-packages (from keras) (1.1.0)\n",
      "Requirement already satisfied: six>=1.9.0 in c:\\miniconda\\envs\\keras\\lib\\site-packages (from keras) (1.11.0)\n",
      "Requirement already satisfied: pyyaml in c:\\miniconda\\envs\\keras\\lib\\site-packages (from keras) (3.13)\n",
      "Requirement already satisfied: h5py in c:\\miniconda\\envs\\keras\\lib\\site-packages (from keras) (2.8.0)\n",
      "Requirement already satisfied: keras_applications>=1.0.6 in c:\\miniconda\\envs\\keras\\lib\\site-packages (from keras) (1.0.6)\n",
      "Requirement already satisfied: keras_preprocessing>=1.0.5 in c:\\miniconda\\envs\\keras\\lib\\site-packages (from keras) (1.0.5)\n"
     ]
    }
   ],
   "source": [
    "!pip install keras"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 34,
     "output_extras": [
      {
       "item_id": 1
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 7843,
     "status": "ok",
     "timestamp": 1522832191020,
     "user": {
      "displayName": "Lenz Belzner",
      "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
      "userId": "102800868167498000139"
     },
     "user_tz": -120
    },
    "id": "0yvVUGjTSYW3",
    "outputId": "b087262b-51af-4e63-fe91-a45bce9e54e8"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pylab as plt\n",
    "from keras.models import Model\n",
    "from keras.layers import Input, Dense"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "JUVIsqO9TjOX"
   },
   "outputs": [],
   "source": [
    "DIM = 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "RunnmxYmhhnm"
   },
   "source": [
    "Setup the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "06pEyryrSdHG"
   },
   "outputs": [],
   "source": [
    "def make_model():\n",
    "  a = Input(shape=(DIM,))\n",
    "  b = Dense(DIM)(a)\n",
    "  model = Model(inputs=a, outputs=b)\n",
    "  model.compile('sgd', 'mse')\n",
    "  return model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "MOhqMK8iUCAj"
   },
   "outputs": [],
   "source": [
    "model = make_model()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "edL4F3vXhj5L"
   },
   "source": [
    "We use a random initial point $x$, and train the network by minimizing $(f(x) - x)^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "arfIdBXbTZw_"
   },
   "outputs": [],
   "source": [
    "x = []\n",
    "x.append(np.random.uniform(size=(1, DIM)))\n",
    "for _ in range(100):\n",
    "  new_x = model.predict(x[-1])\n",
    "  x.append(new_x)\n",
    "  model.fit(x[-1], new_x, verbose=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "FJrlXoLMh52E"
   },
   "source": [
    "This is the resulting trajectory of $x$, plotted by dimension."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 366,
     "output_extras": [
      {
       "item_id": 1
      },
      {
       "item_id": 2
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 641,
     "status": "ok",
     "timestamp": 1522832197171,
     "user": {
      "displayName": "Lenz Belzner",
      "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
      "userId": "102800868167498000139"
     },
     "user_tz": -120
    },
    "id": "AnoQzZmNUfLf",
    "outputId": "4d68c369-a25e-468d-e673-ca3ba623a60a"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2439cf7b898>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([e[0][0] for e in x])\n",
    "plt.plot([e[0][1] for e in x])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "4MElxuYKh-wz"
   },
   "source": [
    "Same data, in 2D."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 364,
     "output_extras": [
      {
       "item_id": 1
      },
      {
       "item_id": 2
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 470,
     "status": "ok",
     "timestamp": 1522832197784,
     "user": {
      "displayName": "Lenz Belzner",
      "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
      "userId": "102800868167498000139"
     },
     "user_tz": -120
    },
    "id": "bw5I9K4bUgL6",
    "outputId": "907a2322-b3db-49aa-a8f3-269e1242edfe"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2439d011320>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter([e[0][0] for e in x], [e[0][1] for e in x], alpha=.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "k930dBsyiB7h"
   },
   "source": [
    "This is what happens if we initialize the recurrent function application for new points $x$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 348,
     "output_extras": [
      {
       "item_id": 1
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1170,
     "status": "ok",
     "timestamp": 1522832199086,
     "user": {
      "displayName": "Lenz Belzner",
      "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
      "userId": "102800868167498000139"
     },
     "user_tz": -120
    },
    "id": "UoZHRg0PVEy6",
    "outputId": "0207091e-9895-4892-b572-e5f7176a0e68"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for _ in range(4):\n",
    "  x = []\n",
    "  x.append(np.random.uniform(size=(1, DIM)))\n",
    "  for _ in range(100):\n",
    "    new_x = model.predict(x[-1])\n",
    "    x.append(new_x)\n",
    "\n",
    "  plt.scatter([e[0][0] for e in x], [e[0][1] for e in x], alpha=.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "WgSISiDwhYH3"
   },
   "source": [
    "## Untrained Network with Random Weights\n",
    "\n",
    "It's tempting to credit the learning process for this effect, but not training at all yields similar results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 347,
     "output_extras": [
      {
       "item_id": 1
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1382,
     "status": "ok",
     "timestamp": 1522832200496,
     "user": {
      "displayName": "Lenz Belzner",
      "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
      "userId": "102800868167498000139"
     },
     "user_tz": -120
    },
    "id": "m8qfSihbgE6f",
    "outputId": "50b40d91-0780-4ce3-90f3-5b7ade328cf9"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = make_model()\n",
    "\n",
    "for _ in range(4):\n",
    "  x = []\n",
    "  x.append(np.random.uniform(size=(1, DIM)))\n",
    "  for _ in range(100):\n",
    "    new_x = model.predict(x[-1])\n",
    "    x.append(new_x)\n",
    "\n",
    "  plt.scatter([e[0][0] for e in x], [e[0][1] for e in x], alpha=.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "UM7ttSvmij8u"
   },
   "source": [
    "More layers, more parameters, same effect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 371,
     "output_extras": [
      {
       "item_id": 1
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1289,
     "status": "ok",
     "timestamp": 1522832201928,
     "user": {
      "displayName": "Lenz Belzner",
      "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
      "userId": "102800868167498000139"
     },
     "user_tz": -120
    },
    "id": "SIOil5pugtHJ",
    "outputId": "2769b8a6-3ec4-4d43-ea2d-e4f69e0ee210"
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = Input(shape=(DIM,))\n",
    "h = Dense(4)(a)\n",
    "b = Dense(DIM)(h)\n",
    "model = Model(inputs=a, outputs=b)\n",
    "model.compile('sgd', 'mse')\n",
    "\n",
    "for _ in range(4):\n",
    "  x = []\n",
    "  x.append(np.random.uniform(size=(1, DIM)))\n",
    "  for _ in range(100):\n",
    "    new_x = model.predict(x[-1])\n",
    "    x.append(new_x)\n",
    "  \n",
    "  plt.scatter([e[0][0] for e in x], [e[0][1] for e in x], alpha=.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "v5Z3yxTnUTT-"
   },
   "source": [
    "## Multiple Untrained Networks\n",
    "\n",
    "We can build a chain of networks and use the prediction of a network as the input of the next network. We can do this in a circular manner."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 677,
     "output_extras": [
      {
       "item_id": 1
      },
      {
       "item_id": 2
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1566,
     "status": "ok",
     "timestamp": 1522832203577,
     "user": {
      "displayName": "Lenz Belzner",
      "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
      "userId": "102800868167498000139"
     },
     "user_tz": -120
    },
    "id": "RBq9UbI3UhaV",
    "outputId": "5c88e9ba-804a-4eb5-ed44-964bc67d8542"
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAD8CAYAAACfF6SlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvDW2N/gAAIABJREFUeJzt3XmYHPV95/H3t8/RzGhGxwhJaCQkGXGbywPB2E6IDYnAXuRNbAPxvY61+8TkcjYJiRPiOE/2seM4voK90foCJzbG2GtkowQDxseaIwgDAiRAAgMaaXSiYw7N9PXdP6p6pqenW1f3zIiqz+t59ExXdamrSq3nM9/+1q/rZ+6OiIjES2K6D0BERKaewl9EJIYU/iIiMaTwFxGJIYW/iEgMKfxFRGJI4S8iEkMKfxGRGFL4i4jEUGq6D6Cerq4uX7p06XQfhojIK8ojjzyyx93nHWm7Ezb8ly5dyvr166f7MEREXlHM7MWj2U5tHxGRGFL4i4jEkMJfRCSGFP4iIjHUlPA3s6+Y2S4ze7LO82ZmnzOzLWa2wcwubMZ+RUTk+DSr8v8asPIwz18JrAj/rAa+2KT9iojIcWhK+Lv7T4GXD7PJKuAWDzwIzDKzhc3Yt4iIHLup6vkvArZWLPeG65qufzjPP939LI++tG8yXl5EJBKmKvytxroJkweb2WozW29m63fv3n1cOyoUnc/du5nHtu4/rr8vIhIHUxX+vcDiiuVuYHv1Ru6+xt173L1n3rwjfju5prZs8KXlwZHCcf19EZE4mKrwXwu8Jxz1cwlwwN37JmNHmVSCdNIYzBUn4+VFRCKhKff2MbNvApcBXWbWC/wNkAZw9/8NrAOuArYAQ8D7m7HfelozKYZU+YuI1NWU8Hf3647wvAMfasa+jkZbJsnAiCp/EZF6IvkN37ZsiqGcKn8RkXoiGf6t2ZR6/iIihxHJ8G/LJDXaR0TkMKIZ/tmUwl9E5DCiGf6ZJENq+4iI1BXJ8G/VBV8RkcOKZPi3Z1MMqO0jIlJXJMO/NZNkOF+iWJpw+yARESGi4d+WCb67ptaPiEht0Qz/0Zu76aKviEgtEQ3/JACDqvxFRGqKZPi3lts+qvxFRGqKZPi3ZYLKXyN+RERqi2b4Z3XBV0TkcCIa/uWev9o+IiK1RDL8x3r+qvxFRGqJZPiX2z7q+YuI1BbJ8G8NL/jq5m4iIrVFMvzTyQSZVELj/EVE6mhK+JvZSjN7xsy2mNkNNZ5fYmb3mdmjZrbBzK5qxn4Pp1339BcRqavh8DezJHATcCVwFnCdmZ1VtdlfAbe5+wXAtcAXGt3vkbRmkvqSl4hIHc2o/C8Gtrj78+6eA24FVlVt40BH+LgT2N6E/R5WWyalto+ISB2pJrzGImBrxXIv8CtV23wU+KGZ/T7QBlzehP0eVms2qRu7iYjU0YzK32qsq76R/nXA19y9G7gK+LqZTdi3ma02s/Vmtn737t0NHVR7VpW/iEg9zQj/XmBxxXI3E9s6HwBuA3D3B4AWoKv6hdx9jbv3uHvPvHnzGjoo9fxFROprRvg/DKwws2VmliG4oLu2apuXgDcBmNmZBOHfWGl/BOr5i4jU13D4u3sBuB64C9hEMKrnKTP7mJldHW72J8AHzexx4JvA+9x9UudYbNNQTxGRuppxwRd3Xwesq1p3Y8XjjcDrmrGvo9WaTerGbiIidUTyG74QtH1yhRL5Ymm6D0VE5IQT3fDPajYvEZF6ohv+Gc3jKyJST2TDv1WzeYmI1BXZ8B+bx1dtHxGRatEN/6xm8xIRqSe64R9O5ajhniIiE0U2/Fuz5dm8VPmLiFSLbPi3ax5fEZG6Ihv+o/P46oKviMgEEQ7/cs9flb+ISLXIhn8yYcxIJ3VzNxGRGiIb/gBturmbiEhNkQ7/1kxK4/xFRGqIdPi3ZVP6hq+ISA3RDv9MUuP8RURqiHT4t2ZT6vmLiNQQ6fBvy2i0j4hILdEO/6wu+IqI1BLt8M9oqKeISC1NCX8zW2lmz5jZFjO7oc427zCzjWb2lJl9oxn7PZLWbEoXfEVEakg1+gJmlgRuAq4AeoGHzWytu2+s2GYF8BfA69x9n5md1Oh+j0Z7NkW+6IwUimRTyanYpYjIK0IzKv+LgS3u/ry754BbgVVV23wQuMnd9wG4+64m7PeIdHM3EZHamhH+i4CtFcu94bpKpwGnmdnPzexBM1tZ64XMbLWZrTez9bt37274wNp0czcRkZqaEf5WY51XLaeAFcBlwHXAl8xs1oS/5L7G3XvcvWfevHkNH1h5KsdBVf4iIuM0I/x7gcUVy93A9hrb3OHueXf/JfAMwS+DSVWezUuVv4jIeM0I/4eBFWa2zMwywLXA2qptvgf8OoCZdRG0gZ5vwr4Pq9z2Uc9fRGS8hsPf3QvA9cBdwCbgNnd/ysw+ZmZXh5vdBew1s43AfcCfuvveRvd9JOULvprKUURkvIaHegK4+zpgXdW6GyseO/Dh8M+UKc/jq7H+IiLjRfobvmM9f7V9REQqRTr8x3r+qvxFRCpFOvwzqeD0RgqlaT4SEZETS6TDP5UwzCCn8BcRGSfS4W9mZJIJckWFv4hIpUiHPwStH1X+IiLjRT78s6mEev4iIlUiH/6ZpCp/EZFq0Q//lHr+IiLV4hH+BX3JS0SkUkzCv0bl/6+/DY9/a+oPSETkBBD98K811DM/DFvuge2/mJ6DEhGZZtEP/1qV/8DO4GdheOoPSETkBBCD8E8eJvxHpv6AREROANEP/2SNcf79O4KfqvxFJKYiH/7ZWkM9VfmLSMxFPvxr9vxV+YtIzEU//Gt9w1eVv4jEXPTD/7BtH1X+IhJPTQl/M1tpZs+Y2RYzu+Ew273NzNzMepqx36Nx+LaPKn8RiaeGw9/MksBNwJXAWcB1ZnZWje1mAn8APNToPo/F4cf5K/xFJJ6aUflfDGxx9+fdPQfcCqyqsd3fAf8ATGmvJZNMUCg5pZIHK0pFGNwdPFb4i0hMNSP8FwFbK5Z7w3WjzOwCYLG7/6AJ+zsm5Xl8R/v+g7vBS2AJ9fxFJLaaEf5WY52PPmmWAD4N/MkRX8hstZmtN7P1u3fvbsKhBeP8oWIS93LLp2ORKn8Ria1mhH8vsLhiuRvYXrE8EzgH+LGZvQBcAqytddHX3de4e4+798ybN68Jh1ZR+ZfDvz8M/1mnqPIXkdhqRvg/DKwws2VmlgGuBdaWn3T3A+7e5e5L3X0p8CBwtbuvb8K+jyiTrGr7DIQjfWYtgeIIuNf5myIi0dVw+Lt7AbgeuAvYBNzm7k+Z2cfM7OpGX79R9Sv/JcFPtX5EJIZSzXgRd18HrKtad2OdbS9rxj6P1oTwH9gBLbOgpTNYLgxDumUqD0lEZNpF/xu+yerKfwfMXACpTLCsyl9EYij64T861DOcx3dgF7TPh1RY7euir4jEUGzCf6Sy7TNzwVj4F3PTdGQiItMn8uGfrez5uwcXfNvnQyobbKDKX0RiKPLhn0kmgTD8h/cHwzvHtX3U8xeR+Il++Ffe3qE8zHPmAlX+IhJrTRnqeSIbN9Sz/AUvtX1EJObiU/kXSsFIH6iq/NX2EZH4iX74V97eob+y8tdQTxGJr+iH/7jKfyekWyE7U5W/iMRa5MN/3C2d+3cEVb8ZJNXzF5H4inz4j7u9w0A4xh9U+YtIrEU+/BMJI5WwsZ7/zHL4a5y/iMRX5MMfKiZxH9gF7QuClar8RSTGYhP++XweRg5A65xgZSIJibR6/iISS/EI/2SCUj6s8FMV9+5PtajyF5FYikf4pxJ4/lCwkJ4x9kQqq8pfRGIpPuFfDvlyrx9U+YtIbMUj/JMJvGbbR5W/iMRTU8LfzFaa2TNmtsXMbqjx/IfNbKOZbTCze83slGbs92hlUwkohG0fhb+ISOPhb2ZJ4CbgSuAs4DozO6tqs0eBHnc/F7gd+IdG93ssMqkENtr2qQ5/tX1EJH6aUflfDGxx9+fdPQfcCqyq3MDd73P3oXDxQaC7Cfs9aplUYizkJ/T8VfmLSPw0I/wXAVsrlnvDdfV8APj3Juz3qGWSCRLFOpX/4ebwffCL8MTtk3twIiLToBnhbzXWec0Nzd4F9ACfrPP8ajNbb2brd+/e3YRDC2RSCRLlkE9Xj/MfX/n/2e2Pc/P9LwQL938efvKJph2HiMiJohnh3wssrljuBrZXb2RmlwMfAa5295qNdndf4+497t4zb968JhxaIJNKkijVG+0zdijuzvcf7+PODX1QLEB/H+x5Fg5sa9qxiIicCJoR/g8DK8xsmZllgGuBtZUbmNkFwL8QBP+uJuzzmGSSCZLFeuP8xyr/lwdzHMoXeWZnP97fB14Knnj+x1N3sCIiU6Dh8Hf3AnA9cBewCbjN3Z8ys4+Z2dXhZp8E2oFvm9ljZra2zstNiqDtU678q7/hO1b59+4LhoMeOJRnf98vx7ZT+ItIxDRlAnd3Xwesq1p3Y8Xjy5uxn+OVTSVIlo482qcc/gA7e59jNsD8c4Lwdw8mgRERiYB4fMM3lSBZCi/4Hqbn37tvaPTxgZ0vBA8ueBcM7oJdG6fgSEVEpkY8wj+ZIF3rgm8y/IavB4OTtu4bonNGmq72DIWXX4JsB5z5X4Jtn7tvio9aRGTyxCP8Uwky5PFkBhIVp5xqCS7qlgpA0Pbpnj2DFSfNJDWwHToWQWc3zF2hvr+IREpswj9Lfny/Hypm8wr6/uXwP33BTNpHduKd4ReRX/Xr8OLPdSsIEYmMeIR/MkELObyy5QMV8/jmcHd69w3RPbuVFfPbmc9eBlvC+X6XXwb5Ieh9GIAtu/rZuP3glB2/iEizxSP8UwmylseT1eE/VvnvHcwxnC/RPXsGZ8xN02UH2WVdwfNLXw+WHO373/CdJ7hmzQNsfXkIEZFXouiF/8gAPHAT9G0YXRW0fXKUkpnx245W/sOjwzy7Z7dy2oygqn+hEM7329IJJ58PLz2Iu7Op7yD9wwX+8NZHKRRLk35KIiLNFr3wL4zAXX8JLz0wuiqbStBCnlKiXs9/ZHSY5+I5M5g5shOAp4dmjm170pmw51l69x1iMFfkDSu6+MVL+/ncvZsn9XRERCZD9MI/0xr8zA2OrUoGlX9xQttnYuW/aNYMONALwKMH2sa27ToNBnfx3EvBc390+Qre/ppuPn/fFh58fu/knIuIyCSJXvinWgALLtCGyj3/iW2fscp/68tDzGpNM7MlDQeDG7k9uKeFYim8QWnXaQDsefEpAFbMn8lHrz6bU+a08vd3bprUUxIRabbohb8ZpFshVxX+5ChMaPuMr/y7Z4f3/TnQy3BmDv2F1NhF3TD8h/s2sWjWDDpa0rRlU1z56oU8veMguYJ6/yLyyhG98Ieg9VNZ+SeDcf7FCeEffhIIe/7ds8KW0YFeSh3BfDTP7OwP1s06BRJp0vue4/QFY9cCzlzYQb7obNk1MP61dzwBL/y8qaclItIs0Qz/dOvEtg95ClZ7tI9XV/4Ht5GZE0xRsLkc/skUPudVzD70AqfNHwv/sxYGjzf1heP+S0X46T/CmsvgG9dASZ8IROTEE93wr7zgG/b884na4d8/MMBIoVTR9tlGavYSumfP4KmKL3MNzFzGcrZzRkXlv6yrnZZ0Igj/g31w89Xwo7+D2Ush1w97t0zaaYqIHK9ohn+mFfJjt2cOhnrmyFvtoZ77+oOWzeI5rTB8IAjtjkW8/tQufvrsbobzRQD60ks4xXZy2ryxUUPJhHH6/Jls2nEQfvgR2PYIrPoCvOOWYIO+xybxREVEjk80w7+67ZNMkiVPvk7b52B/0Nrpnt06OsyTzkW8+dyFDOaK/OTZYD7hzaUFpK3Iqenx8wufubCDTX39eO96OO034YJ3QtfpwcQx2x+dpJMUETl+0Q3/6rYPeXITwj+o/PsHgm0XzZ4xNl9v52Jeu3wus1vTwZy+wGNDJwWvt++5cS9z5sIOCoMvY/tfhIXnBSuTKVjwatiuyl9ETjzRDP/q0T6JEmkrkqN25T8wOMDs1jTt2RQcDCv/jkWkkglWnrOQezbtZDhf5Gf7OoPn9jw77mXOXNjB2YkXg4Vy+ENwS4gdG4KLwEChWOIf/uNpfuf/PMhQrhB8G7lvgy4Ki8iUi2b4p9vG9fwzBLN45Sw9frtECizBoaHgbp5A0PaxJMxcAMCbX72QoVyROzf08fS+BAOZLtgz/pYOZyycyTkWzvk7LvwvgNwA7N3CnoER3v3l/+QLP36O+5/byz/98NngNhT/8gb47Llwz0dh9/hfKiIik6Upc/iecDJVbR/PAzDiVeFvBqkWhg8N0n3S2EgfOk6GRBKAS5bPYU5bhs//KAj8XOerJlT+HS1pLmrpZZ/NY3Zb19gTC88HYPumB/it/9fLvqEc//j28/jFS/u47/77+Uj2q9ipVwAOP/8c3P/P8MF7YeF57BvMkUwabZkUyYTmDhaR5mpK+JvZSuCzQBL4krt/vOr5LHAL8BpgL3CNu7/QjH3XlJ4xru2TLgWTtYyQnrhtMkNxeJiTZoYjgQ5uC2bwCgWtnwV846GXgtdacAZs/t6ECd1fnXiBjb6M11W+dtdpkJrBxkd+ykjhWr77e5dy9smd/MbZ8/nPJ/6M4VKa5Fs+T2bWQji4PfhuwB3X8/lT1/Cpe54ffZn5HVk+fc35XLpsTjCaaHh/8MkmmYZTrwiuL4iIHIOGU8PMksBNwBVAL/Cwma1198oZzz8A7HP3U83sWuATwDWN7ruudBsUc1AsQDKFFYO2z3B1zx/wVAuJ4gjtLeE/xYFeWHThuG3e8uqFfOOhl2jNJGk7+Ux44mYY3A3twQVgRgZYkN/KtwoX8Zp8kZZ08KmBZIrS/HOY1fsUb7ngZM4+Obhm0LF3A5eX7uezhd/CHhngD95E8Gnjqk/Cbe9hcOtnWHn2anqWzmZgpMCdG/r43a88wN3Lv8Wird8ffwKveiP+tq/y9P4E2/cfYs/ACP3DBV5zymzOP7kN6304mKYy3Rp8Iuo6LfilISKx1oyS8WJgi7s/D2BmtwKrgMrwXwV8NHx8O/DPZmbu4czpzVa+s2d+CJIdo9M0Dle3fQBPZcmQpz2bDqr5gZ0wc+G4bS5eNoe5bRm657SSmBfc44c9m8fCf+eTGM4TpaU8s6Of8xbPGv27vTPO4ExuY+iMsB3kDnf/DbTOZevC/8Z37nmW3n1D/M/fPJ2+mb/GztJFfDj9XfiND5OZvxyA9180ny03/TaLtj7MY8tXc85lbyeVaYWtD+L//uds+9Sv8rsDH2Yb88iS43TbiiXv55TU/czhwLhzyaU7eKLtUr6fu5BthU6SXiBNnjOyL3NuZhtLfRutDJMwI5EwDmXmsjOzmBcT3RwstWClAlbK08YhZicG6WSALAUSZlgiQSGRZcjaGLC24JetlzAgSZGs5cl6jpQVMSBhhpMgbylyZCiQwnDAMS+RMCdJkSRjn7IMKJGgSILSuEtWTvBqwc/KT2U4uAXPlAX7CZ8cfeXK5fK6Wuvrrz7ME1C3e6e2noyX7jiJC1e+b1L30YzwXwRsrVjuBX6l3jbuXjCzA8BcYE/lRma2GlgNsGTJkuM/onRF+Ld0QL5++JcSWbLkaM8mg4uz+aGxUA+lkgk+c+35ZFNJmB1eS9jzLCwNmzx9jwPwZGkZG/sOjgv/Bw4t5hob4ZJZ+4AFsPmH8MLPYOUn+NsLXsucezfz1Z//kjs39NGSTtI9439wOX9M4o7/DmetAozOp+/kwtx6bpn7x9y48SLan9vHRUuhq/0idoz8OTelP82P2v8Ky7SSGQrmIigm0jzacgk3HryIXcU2ZliOTgb4teLjXJH/GR/lP8b/Q+RhiBY2l07ml942GqQL7EnOsh9xnhVr/lMf8gwjpLEwdFvIkamzrYgcnWdSp8MrIPxrlS3VZc/RbIO7rwHWAPT09Bz/p4J01T39w8p/qDQx/IvJDBkKtGVTMLArWNk+f8J2b1gxL3hQmhW8fuWIn74NeGsXgz5v7B4/QLHkfHdHF9cAmZ2PA0X4zgeDL4D1vJ+2VIq/vOpMfufiJfyvdZtY/+I+PvH+3yCx61Pwvd8b+4JYuhV7+9f4nTOuZu5TO7n/uT08+PxefvLsbq65aCWl11xJ9qFPQqY9uK3EnOUkX/VGelrncG6hxK7+YXYcGGZX/wjLutpo78rCtoeDO58mU5BIw6zFtHYuYelwkf2HcgyMFBjKFRnJpBhoTzJrZBtWOBRsm0xDph1v6aRQSpPLFykUnUIx+AXQlizQWhog4zksYZglKJIkZ1lGSJHzBO5GyR28SNoLpH2EpBexRFBtO0aJJEUSFN1wI6jg3YOa34Pa3yoq/OAZo0TlOseccG2J8f8VRz9njHuvzQg+odX5b1z/P/fRPzP2xOR8+JVXtgXpiS3qZmtG+PcCiyuWu4HtdbbpNbMU0Am83IR911bZ9oHR8D9Uo/IvWlD5ezYF/eFY/RrhPyqRgLmnBsFcvujb9zi28DzOGOhgQ+9Ym+WxrftYPziPQtsMUpu+D3ffCJk2eNftY3MJAEu72ljznh7cPQizBe+As94KXgQvBYGbypAC3nzuQt58btCWKhRLpJJh6+OUW2r/U6QSdM9uHRvKOrrT19fcvrM1QWdrrWsCp01YY8BMCOZAmPhK45aSwIzwj4hMv2aM838YWGFmy8wsA1wLrK3aZi3w3vDx24AfTVq/H4ILvjA21r8wAsCh0sTfdflEhqzlgy94DQQtk8OGP8A5vw0v3Q+PfSNoKe3eBAvP4/Kz5vPY1v18e33QBfvhxp0kyt/0ffoHwXG8+7swq3ZLq7KKJZUJRi1l2sZuPV1lNPhFRI5Rw5V/2MO/HriLoMD7irs/ZWYfA9a7+1rgy8DXzWwLQcV/baP7Pax0WF+Otn2CXwK12j550mTJkWhJwZ4w/MMveNV16e/Dlntg3Z8GLZBSARaexwfPXM5Pn93NX9/xJK/u7uTujTu5ZPlcUosvgZ1PwDu/HcwFLCIyzZoyQNzd1wHrqtbdWPF4GHh7M/Z1VCa0fYLKf8gnnm7OMmTJkylX/ok0tMyasN04iST81hr44qVwx4eCdQvPI5kwPnvtBVz1uZ/xvq88zI6Dw7zv0qXQ8xF47YeO/EtFRGSKRLNvMKHtE/T8B4oTw3+ENFnKbZ9dwUifxFH8s3ScHNy6uZiDbGdwoRWYNzPL56+7gF39wT4vP3M+pFsU/CJyQonmV0MzVaN9wqGeg8WJbZ+cp2gv9/z7dxy531/pjKvgsr8M2koV/fpLls/lY6vOYWPfQU6epUucInLiiWb4p2uP9qlV+Q97mrnkac0kg8q/s/vY9nXZn9dc/a5LTjm21xERmUIRbftUj/MPev6DxeSETQ95mhbywUibgR0w8xgqfxGRV6hohn8qC5ao6PkfIm9pcsWJo0uHSimylg/uAzS459jaPiIir1DRDH+z8J7+Y6N98pYlV5g4acqhUpo0BRjcBfiEWzuIiERRNMMfgrH+Fbd3KCay5IoTw3+gFLaC9ge3bKZdo3JEJPqiG/6VUznmhykkMjUr/8HyReDR8FfbR0SiL7rhXzmVY7nyrxH+/fmw8t8X3tdHF3xFJAYiHP4zxo32KSaDtk/1LYX6yyOA9ofh36aev4hEX3TDv7LtUzhEKRncRbO673+wUNHzb+kMvo0rIhJx0Q3/qtE+pWQQ6pWtH3fnYC78J9j/oi72ikhsRDf8M63BZCUAhWG8XPlXhP9IoTR2j/8DvRrmKSKxEd3wT88YV/l7jbbPwEiBEcLwLxV08zURiY0Ih3/bWOWfP4SnJrZ9BkcKjFTO7qVhniISE9EN/3EXfEfw1MS2z7jKH9T2EZHYiG74p9uglIdiHgrDWFj5j1SG/3B1+KvtIyLxEOHwr5jKsTA8OoSzsuc/mCswQsX8uKr8RSQmohv+lVM5VlT+49s+xfE9f13wFZGYaCj8zWyOmd1tZpvDn7NrbHO+mT1gZk+Z2QYzu6aRfR618lSOwwfBSyTSNcJ/QttHF3xFJB4arfxvAO519xXAveFytSHgPe5+NrAS+IyZHWGG9CYot30OvQyA1Qj/wcoLvok0zJjwu0tEJJIaDf9VwM3h45uBt1Zv4O7Puvvm8PF2YBcwr8H9Hlm57TO0F4BEJvhlUNnz7x8pkCvPZNk+f9w8vCIiUdZo+M939z6A8Odhr5ia2cVABniuwf0eWbntMxRU/snwk0B15d+aSUMyo4u9IhIrR5zA3czuAWpdCf3IsezIzBYCXwfe6+4T760cbLMaWA2wZMmSY3n5icqVf9j2SWRqt33asilItOhir4jEyhHD390vr/ecme00s4Xu3heG+64623UAdwJ/5e4PHmZfa4A1AD09PRMn3D0W5Uncy5V/NlgeqWr7tLekIN0Fc5Y3tDsRkVeSI4b/EawF3gt8PPx5R/UGZpYB/i9wi7t/u8H9Hb30+Mo/lWkBfELl355Nwbt/AC0dU3ZoIiLTrdGe/8eBK8xsM3BFuIyZ9ZjZl8Jt3gH8KvA+M3ss/HN+g/s9stG2z34AUpnaPf/2bAo6F0F25qQfkojIiaKhyt/d9wJvqrF+PfC74eN/Bf61kf0cl6oLvqlsKzA0Lvz7hwssntM65YcmIjLdovsN32QaLDk61DOVmUFHS4rdA8OjmwzmwspfRCRmohv+ZpBpG+35k2phWVcbL+wZGt1kYFjhLyLxFN3wh+Ci76F94eMWTpnbxgt7B0efHhwpBkM9RURiJuLhPyOYoQsg1cLSrja27z/ESKHISKFIrlhiZovCX0TiJ9rhn2kbe5zKsqyrlZLD1pcPMThSBKAtk5ymgxMRmT7RLnvTFSN5Ui2cMjcY6fPCnkGyqeD3nto+IhJHEa/8y+FvkMywbG7wSeCFvYMMjATtILV9RCSOoh3+5co/1QJmzGpN09GSGhf+qvxFJI5iEv7B5O1mNjrcsxz+GuopInEU7fAvt33KE7vA6HDPgWGFv4jEV7TDv3yLh7DyB0aHe+4bygFq+4hIPEU8/MOKP5y8HRgd7rmp7yBAcEtnEZGYiXb4Zyou+IZOCUf8PLktCP+2jMJfROIn2uE/2vapqPzD8H9mRz+tmSTJhObtFZH4iXj4l9s+Yz0VxbykAAAFuElEQVT/8nDPXLGkfr+IxFa0w798e4eK0T7l4Z6gkT4iEl/RDv+qcf5lSxX+IhJz0Q7/Ghd8Yeyib1tWN3UTkXiKdvjXqfyXdQXr27PpqT4iEZETQkPhb2ZzzOxuM9sc/px9mG07zGybmf1zI/s8JqPhP2Pc6nLl367KX0RiqtHK/wbgXndfAdwbLtfzd8BPGtzfsclM/IYvjA331GgfEYmrRsN/FXBz+Phm4K21NjKz1wDzgR82uL9jk67d85/Vmua87k7OPrlzSg9HRORE0WjpO9/d+wDcvc/MTqrewMwSwKeAdwNvanB/x6bGOP/wmLjj+tdP6aGIiJxIjhj+ZnYPsKDGUx85yn38HrDO3beaHf7btGa2GlgNsGTJkqN8+cNo6YQ3/jWc/V8bfy0RkQgxdz/+v2z2DHBZWPUvBH7s7qdXbfNvwBuAEtAOZIAvuPvhrg/Q09Pj69evP+5jExGJIzN7xN17jrRdo22ftcB7gY+HP++o3sDd31lxUO8Deo4U/CIiMrkaveD7ceAKM9sMXBEuY2Y9ZvalRg9OREQmR0Ntn8mkto+IyLE72rZPtL/hKyIiNSn8RURiSOEvIhJDCn8RkRhS+IuIxNAJO9rHzHYDLzbwEl3AniYdzitF3M45bucLOue4aOScT3H3eUfa6IQN/0aZ2fqjGe4UJXE757idL+ic42IqzlltHxGRGFL4i4jEUJTDf810H8A0iNs5x+18QeccF5N+zpHt+YuISH1RrvxFRKSOyIW/ma00s2fMbIuZRfLW0Wa22MzuM7NNZvaUmf1huH6Omd1tZpvDn7On+1ibzcySZvaomf0gXF5mZg+F5/wtM8tM9zE2k5nNMrPbzezp8P1+bdTfZzP74/D/9ZNm9k0za4na+2xmXzGzXWb2ZMW6mu+rBT4XZtoGM7uwGccQqfA3syRwE3AlcBZwnZmdNb1HNSkKwJ+4+5nAJcCHwvO8AbjX3VcA94bLUfOHwKaK5U8Anw7PeR/wgWk5qsnzWeA/3P0M4DyCc4/s+2xmi4A/IJj34xwgCVxL9N7nrwErq9bVe1+vBFaEf1YDX2zGAUQq/IGLgS3u/ry754BbCSaZjxR373P3X4SP+wkCYRHBud4cbnYz8NbpOcLJYWbdwJuBL4XLBrwRuD3cJFLnbGYdwK8CXwZw95y77yfi7zPBJFMzzCwFtAJ9ROx9dvefAi9Xra73vq4CbvHAg8CscObEhkQt/BcBWyuWe8N1kWVmS4ELgIeA+e7eB8EvCOCk6TuySfEZ4M8IpgQFmAvsd/dCuBy193s5sBv4atjq+pKZtRHh99ndtwH/CLxEEPoHgEeI9vtcVu99nZRci1r415ohPrLDmcysHfgO8EfufnC6j2cymdlbgF3u/kjl6hqbRun9TgEXAl909wuAQSLU4qkl7HOvApYBJwNtBG2PalF6n49kUv6fRy38e4HFFcvdwPZpOpZJZWZpguD/N3f/brh6Z/njYPhz13Qd3yR4HXC1mb1A0M57I8EngVlhewCi9373Ar3u/lC4fDvBL4Mov8+XA790993unge+C1xKtN/nsnrv66TkWtTC/2FgRTgyIENwoWjtNB9T04W97i8Dm9z9nyqeWgu8N3z8XuCOqT62yeLuf+Hu3e6+lOB9/ZG7vxO4D3hbuFnUznkHsNXMTg9XvQnYSITfZ4J2zyVm1hr+Py+fc2Tf5wr13te1wHvCUT+XAAfK7aGGuHuk/gBXAc8CzwEfme7jmaRzfD3Bx74NwGPhn6sIeuD3ApvDn3Om+1gn6fwvA34QPl4O/CewBfg2kJ3u42vyuZ4PrA/f6+8Bs6P+PgN/CzwNPAl8HchG7X0GvklwTSNPUNl/oN77StD2uSnMtCcIRkI1fAz6hq+ISAxFre0jIiJHQeEvIhJDCn8RkRhS+IuIxJDCX0QkhhT+IiIxpPAXEYkhhb+ISAz9fxVGnTG0H5XEAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_models = 4\n",
    "models = [make_model() for _ in range(n_models)]\n",
    "\n",
    "for _ in range(2):\n",
    "  x = []\n",
    "  x.append(np.random.uniform(size=(1, DIM)))\n",
    "  for i in range(100):\n",
    "    new_x = models[i % n_models].predict(x[-1])\n",
    "    x.append(new_x)\n",
    "\n",
    "  plt.figure()\n",
    "  plt.plot([e[0][0] for e in x])\n",
    "  plt.plot([e[0][1] for e in x])\n",
    "    \n",
    "  # plt.scatter([e[0][0] for e in x], [e[0][1] for e in x], alpha=.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "TFS3YznBWZRl"
   },
   "source": [
    "## Adding Offset\n",
    "\n",
    "We can add an offset to each prediction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     },
     "base_uri": "https://localhost:8080/",
     "height": 677,
     "output_extras": [
      {
       "item_id": 1
      },
      {
       "item_id": 2
      }
     ]
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1474,
     "status": "ok",
     "timestamp": 1522832205162,
     "user": {
      "displayName": "Lenz Belzner",
      "photoUrl": "https://lh3.googleusercontent.com/a/default-user=s128",
      "userId": "102800868167498000139"
     },
     "user_tz": -120
    },
    "id": "2H6bn029WmRf",
    "outputId": "cbc65f97-7f13-4869-b1c8-b6aa4f8606a3"
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAD8CAYAAACfF6SlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvDW2N/gAAIABJREFUeJzsvXm0JMdZJ/qLzNqrblXdtfdNUmtpbZbdkm3ZGGwLIRks29jwbOCAgTdieBgwvGEwi80cM37ngOe9mfMeghlgWMdgg8EH4RHjBWzAkqzu1mLtSy+39+57b9VdqrKWrMqM90dEZEZkRua9cldL9q34naOjrrpfZcYX+cUXv++LLyIJpRQGBgYGBuMF69VugIGBgYHBKw/j/A0MDAzGEMb5GxgYGIwhjPM3MDAwGEMY529gYGAwhjDO38DAwGAMYZy/gYGBwRjCOH8DAwODMYRx/gYGBgZjiMyr3YAkzMzM0L17977azTAwMDD4tsKjjz66RCmdXU/uW9b57927F0eOHHm1m2FgYGDwbQVCyMmNyJm0j4GBgcEYwjh/AwMDgzGEcf4GBgYGYwjj/A0MDAzGEMb5GxgYGIwhjPM3MDAwGEMY529gYGAwhhgr5//FZy7gwmrv1W6GgYGBwauOkTh/QshdhJAXCCFHCSEf0fz9g4SQRULIE/y//30U93058H2Kn/7UY/jUIxva/2BgYGCwqXHJO3wJITaA+wB8N4AzAA4TQu6nlD4bEf0MpfRDl3q/bxau58PzKda6g1erCQYGBgbfMhgF878NwFFK6XFKqQvg0wDeNYLrjhQDzwcAtPrDV7klBgYGBq8+RuH8dwA4LX0+w7+L4r2EkCcJIZ8lhOwawX1fFgYeBQC0esb5GxgYGIzC+RPNdzTy+e8B7KWU3gTgywD+VHshQu4lhBwhhBxZXFwcQdNCCObfNs7fwMDAYCTO/wwAmcnvBHBOFqCUNiilff7xDwC8TnchSunvU0oPUkoPzs6ueyLpy4I75M7fpH0MDAwMRuL8DwPYTwjZRwjJAXg/gPtlAULINunjPQCeG8F9XxZckfPvmQVfAwMDg0uu9qGUDgkhHwLwBQA2gD+ilD5DCPk4gCOU0vsB/Bwh5B4AQwBNAB+81Pu+XARpH8P8DQwMDEbzMhdK6QMAHoh89zHp378C4FdGca9vFoOhWfA1MDAwEBibHb6u5wEA+kM/yP8bGBgYjCvGx/kPwwIkk/oxMDAYd4yN8xc5f8CUexoYGBiMpfNv9U3Fj4GBwXhj8zv/xjFg0FOdv2H+BgYGY47N7fxdB/i924EnPoX+0KR9DAwMDARGUur5LYvWBWDYA7pNDCyz4GtgYGAgsLmZv8PPB/K9SM7fOH8DA4PxxuZ2/u2L7P/eIJLzNwu+BgYG441N7vwX2P/9gbKxy+T8DQwMxh1j4vy94GC3YtY2OX8DA4OxxyZ3/lLah+/wnSrnTKmngYHB2GNzO/9gwZfl/C0C1IpZ4/wNDAzGHpu71FNi/q7lI5exUClk0DY7fA0MDMYcm5v5t8NST3foI2tbmMhnTM7fwMBg7LF5nT+lIfPnaZ+czZi/SfsYGBiMOzZv2qe/Bnj8tcHeAAPKmX8hY0o9DQwMxh6b1/mLMk8A8IdwfZ7zz2fNDl8DA4Oxx+ZN+0Sc/8CjyNoEE4UM3KGP/tB79dpmYGBg8CpjEzt/nu/Plli1jxemfQCzy9fAwGC8sYmdP2f+1e2c+Yu0D3f+JvVjYGAwxti8zt9ZAIgNlOdYzn/Iq3248zcVPwYGBuOMkTh/QshdhJAXCCFHCSEfSZF7HyGEEkIOjuK+qWhfBMqzQCYXnOqZ5aWegHH+BgYG441Ldv6EEBvAfQDuBnAAwAcIIQc0chMAfg7AI5d6zw2hvQhU5gAry5i/R5HNWKgWsuzPJu1jYGAwxhgF878NwFFK6XFKqQvg0wDepZH7TQC/DaA3gnuuj/ZF7vwzbJPX0EfOJlLO3xzxYGBgML4YhfPfAeC09PkM/y4AIeQWALsopZ9PuxAh5F5CyBFCyJHFxcVLa5WzCFS2AHYG8IZwvfBsH8BU+xgYGIw3RuH8iea74IW5hBALwH8G8H+udyFK6e9TSg9SSg/Ozs5+8y2ilFX7lGeDtM8gUuq5Zpy/gYHBGGMUzv8MgF3S550AzkmfJwDcAOCrhJB5AG8AcP9lXfTtLgP+gDF/Ke2TtS3kMzZytmVy/gYGBmONUTj/wwD2E0L2EUJyAN4P4H7xR0rpKqV0hlK6l1K6F8DXAdxDKT0ygnvrIWr8K3OAneVpH4qszdStmPN9DAwMxhyX7PwppUMAHwLwBQDPAfgrSukzhJCPE0LuudTrf1MQu3uDBd8h3KGHfIY7/3zGvMTdwMBgrDGSg90opQ8AeCDy3ccSZL9rFPdMhXiDl5z24Wf7AGAne5q0j4GBwRhjc+7wFcy/PBukfcSCLyCYv3H+BgYG44tN6vwXWJVPcRKwMqD+EEM/zPkb5m9gYDDu2LzOvzIHEBKkfQAglxHO37zE3cDAYLyxOZ2/w50/wNM+3PlLaR/D/A0MDMYZm9P5ty+y0zwBwMqCgILADxZ8TamngYHBuGOTOv/FkPlbNgAgCw9ZqdTT9Xz0BuZtXgYGBuOJzef8fY+f6yOlfQBk4AVpn2rBvNDFwMBgvLH5nH+nCVCP1fgDrOoH3Plnwh2+gDnczcDAYHwxkk1e31LIV4Af+mtg9mr22WIqZuBJdf7mTH8DA4PxxuZz/tkicPWd4Wc77vzDkz3NEQ8GBgbjic2X9olCl/bJm7SPgYHBeGMMnD9n/sRTzvYBTNrHwMBgfLH5nT+v9sliqGzyAsxL3A0MDMYXm9/56xZ8DfM3MDAYc4yR8/eDnH8+YyOXscyCr4GBwdhi8zv/YJPXMGD+AFDIWOgP/FerVQYGBgavKja/85fSPjnJ+ecyNlzPOH8DA4PxxBg5fx/ZDAm+ztkEg6Fx/gYGBuOJze/8RdqHDCPM3zLM38DAYGyx+Z2/JUo9w1M9Ae78DfM3MDAYU2x+58+Pd7BjOX/j/A0MDMYXI3H+hJC7CCEvEEKOEkI+ovn7vyWEPEUIeYIQ8jVCyIFR3HdD0NT5A0DWNmkfAwOD8cUlO39CiA3gPgB3AzgA4AMa5/4XlNIbKaWvAfDbAP6fS73vhsHTPnnLh23JC76G+RsYGIwvRsH8bwNwlFJ6nFLqAvg0gHfJApTSNeljGQAdwX03Br7gm7NUR28WfA0MDMYZozjSeQeA09LnMwBeHxUihPwMgF8EkAPwthHcd2Pgr3EsRJx/PmOh6Rjnb2BgMJ4YBfMnmu9izJ5Seh+l9EoAvwzg17UXIuReQsgRQsiRxcXFETQNQdqnQNT39WZtCwPD/A0MDMYUo3D+ZwDskj7vBHAuRf7TAN6t+wOl9PcppQcppQdnZ2dH0DSEaR9bnY9MtY+BgcE4YxTO/zCA/YSQfYSQHID3A7hfFiCE7Jc+fi+Al0Zw342BV/vkSSTnbxZ8DQwMxhiXnPOnlA4JIR8C8AUANoA/opQ+Qwj5OIAjlNL7AXyIEHIHgAGAZQA/dqn33TCE87fUtI9Z8DUwMBhnjOQdvpTSBwA8EPnuY9K/f34U9/mmEFT7qGmfrGH+BgYGY4zNv8OXM/9cZME3b5i/gYHBGGNsnb9Z8DUwMBhnbH7nTwiGsJGNLPhmbQs+BYaG/RsYGIwhNr/zB+DBRi5a7cNP+Bx4r9xmYwMDA4NvFYyR84+kffghbyb1Y2BgMI7YdM6/N/DwtZeWcHalG3w3JBlkNTl/AOh76vcGBgYG44BN5/zb/SF+5L8/gi8/ezH4bkituPM3zN/AwGCMsemc/0SBVfesdQfBd0PYyELP/E3O38DAYByx6Zx/PmOjkLWw1gud/wAZZBIWfA3zNzAwGEdsOucPANVCFmvdYfB5CCvO/E3ax8DAYIyxOZ1/Masyf2ojg6EiI17m7poFXwMDgzHEpnT+Na3zj5/qCQDu0OT8DQwMxg+b0vlXC5kg7eP7FENYsBMWfM35PgYGBuOIzen8JeY/8H0MkYmlffJmwdfAwGCMsTmdfyEblHq6Qx8D2MjQ+Gscxd8NDAwMxg2b0/kXM1jrDUEpxcCj8KidmPYx7/E1MDAYR2xO51/IwvMpOq6HgceYvx1J+5g6fwMDg3HGSN7k9a2GapG9vWutN8DQoxjChkVdRUZU+/QN8zcwMBhDbE7nX2DOf7U7QNa24MGGTc0mLwMDAwOBzZn2KYrzfYZB2seKOn+T8zcwMBhjbE7nz5n/WneAwVCkfUzO38DAwEBgUzr/mpTzdz2fO3+V+dsWgW0R4/wNDAzGEiNx/oSQuwghLxBCjhJCPqL5+y8SQp4lhDxJCPlHQsieUdw3CcGCb3cAd+hjSG1YdBCTy9rE7PA1MDAYS1yy8yeE2ADuA3A3gAMAPkAIORARexzAQUrpTQA+C+C3L/W+aQjO9O+xnL8u7QOwRV/D/A0MDMYRo2D+twE4Sik9Til1AXwawLtkAUrpVyilHf7x6wB2juC+icjaFko5m+X8ufMnfvz0zlzGNszfwMBgLDEK578DwGnp8xn+XRJ+EsA/6P5ACLmXEHKEEHJkcXHxkhpVLbDzfQLnr2H++Yxh/gYGBuOJUTh/ovlOe04yIeRHABwE8End3ymlv08pPUgpPTg7O3tJjaoW2cmefX62D/ETcv7G+RsYGIwhRrHJ6wyAXdLnnQDORYUIIXcA+DUA30kp7Y/gvqkImT+Fl5j2sUZa5y+uJQ6NMzAwMPhWxSi81GEA+wkh+wghOQDvB3C/LEAIuQXAfwNwD6V0YQT3XBfiWGexyYv4A4CqAUluxGmfT/zP53DbJ76Mr7zwiqhoYGBg8E3jkp0/pXQI4EMAvgDgOQB/RSl9hhDycULIPVzskwAqAP6aEPIEIeT+hMuNDOKFLgOPlXoCAPz4EQ+jXPB95EQTy50BfvyPD+O3/tfzGJrFZAMDg29RjORsH0rpAwAeiHz3Menfd4ziPi8Hgvm7Qx8ehPMfAnaocta20B8R8/d8imOLbfzoG/dg4Pn4va8ew6lGB/f98GtHcn0DAwODUWJTHuwGhC90EQu+AAB/AKAQyOQyFtr9eBXQN4OTDQfu0McNO2r4wYO70B/6+PKzF0dybQMDA4NRY9M6/1oxC58CKx0XQ+H8PbXiJ5+x0HRGw/xfvNgGAFy9ZQIAsL1WRLvPXihDiK4gSgWlFJQClpUs23GH+KOvnUDDcdHuDUEI8NHvO4AJfpaRDi9dbOHYYhsX1/pY6QzwgdfvwtxEIVH+6EILz5xbw2Krj6W2i3fevA3Xb68lyl9c6+Gxk8tYaPWx2Orjtn1TeMvVyZVaa70Bvn6sEcjvmirhfa9L3vbhDn08dGwJF1Z7WGz1kc1Y+Km3XJHYp5RSPHKiiTPLXSy0eui5Hu79zitRySeb+tNnV3F0oY2FVo/10W27sWuqlCg/v+TgqbOrvI/6+J7rt+LmXfVE+cVWH4+ebGKh1cfCWh+v2VXHHQe2JMo7/SEePtbAxRbTeUu1gA/ctjtRfuj5eOhYAxdWe1ho9QAAP/1dV8FOsaUj802cbHSw0Oqj4w7xk2/eh3oplyj//IU1vHChhcVWH03HxQ8c3IV9M+VE+dPNDp48s4oFrsPbrp3Dwb1TifJNx8WhE00scvnrtlVx943bEuW7roeHjy/h4hrr03opix+7fW+ivOdTfP14A2dXulhs9TH0KH76u64MzvjS4fFTyzix5GCh1Ue7N8SP3b4XsxP5RPmXLrbw7Pm1oI/efcuOwB/ocG6liydOr2BhrYfFdh9vunIGt181kyg/amxa5y9O9my0XUwQrmY05z/CBd+XLrYAAPvnKgCASiEDnwId10M5wfH4PsU/Pr+Af35xAf/84iI6fQ8PfuRtKGRtrfznnzyP//TFF1HJZ5DLWGg6Lr7vpu2JzvZ0s4M7/8u/KOvclUIGP/nmfVr5gefjPfc9hJYUDTWdPn77fTcn6n3vnz+Kb5xeCT7f/FIt1fl/4vPP4TNHwm0h+YyV6vz/x9dP4uOff1b57u4btmLPtN7xPHSsgR/+w0eU767fUcP3XL9VK39xrYd7fudr8KU+KmRt/Nzb92vlfZ/iff/1YSy1w4K1k80O7vuh5PTehz/zOB482gg+XzVXSXX+/+mLL+CPH5xXvvuB1+1EJqGK7G8eO4Nf/punlO/edu0WHNhe1co/cXoF7/uvDyvfXTFbxntu0T+H1c4A7/z/voaBF3aSRyl+5e7rEnX44T98BKeaneDzs+fX8Cc/flui/C//zZP4khQpb68VUp3/fV85it/5ylHlu/e8dkdwqGMUDzx1Hj/7l48r391+1TRuTZiQXrzYwnt+9yHlu621An7kDfqTaXoDD/f8zoPoDkIf0+oN8ZvvviFRh5/4k8N4/kIr+Hz4xPIr6vw3bU2iMILFdh/UktM+IbIjXPB9caGNHfVi4OjFEROtXnJa6Y8ePIF/82dH8LePnUU+Y6PhuIpTieLIfBP1UhZP/sad+Mt/84Z1r//w8QYoBf7wRw/i0K++HQCCdxvr8PTZVbT6Q/zHd9+Ab/zGnbh6SwVr3eTrt3oDPHVmBR+8fS+O/Pod+N6btmEtpT0A8NDxJbzl6lk88qtvx4fv2I/+0Ed/GC/DDeSPNbB7qoSv/fJbAweb1qaHji3Btgi+/ItvwRd/4S3r6vzIiSZ83kdP/oc7UczaqfJHF9tYavfxK3dfi8c/+t24eVc9Vb4/9HB4fhnvv3UXDv/aHfjBgztT5QHg4WMN3LZ3Cg//ytvwq++4FkD6c37oWAOzE3n8679/K/74g7cynXvJ93jo2BIA4PM/+2b8679/K5NP6dMjJ5sYeBT/7wduwTd+407MVPKp8meWOzjV7ODn374fj330u3H7ldOpOgtWfs/N23Ho196OD96+d307OraEG3fU8NBH3oZPvOcGrkOazg1M5DP4l196Kz5z7xvWlX/4GJusP/tv34gjv86WLNP69PFTK+gOPPzWe2/ENz52J/ZMl1Llm46L5y+08FNvuQKP/voduOO6uVT5y4HN6/z54W6NtgtqcTYQSfvkbAuDETL/q7dUgs8izdDuJz/QLz17Eddtq+KJj92Jf3fnNQDWG4TLOLhnEpZFpPOLkq9/+EQTk6Us3nbtHOaqBVTymXT5+SYA4Huu34paMYuJQhatlPY/enIZPgXuuG4LZip51IpZtFKuf2G1h9PNLt6yfwZbqgVM8jRDkmPzfYojJ5t4/b4p7JwsYboi5NN0XsYN26u4am4CczxET3Och080Uc7Z+K5rZlEtZDFRyKTKHzoR9tFkOYfqOvJPnVmFO/Tx1mvnMDsh+ihZfrUzwAsXW3jz/hlsqxXX7SOhw217p7BrqoSZysZ0vmqught21LClWuDyyX16aL6JrE1w54EtqBWzXOf17ejO67dgqpxDtZCu8wsXWmj1hnjrtbOYmyigVsyi3R/C87V7RdEbeHjq7Cpuv2oa2+tFTG2kj+abeN3eSeyeLmFmA3ZxaL6J7bUCDu6dwnQ5h6xN1r0+IcBd129DrbS+HYk+uuPAFkxX8qiuYxeXA5vX+XPm33D6IJZI+8TP9B8F8x96Po4vOkp+L3inQMID7boeHj+1grfsn0EuY6G6jjNvtPs4vugEeVMxua03CA/unQrWEdZ3bMvYN1MO8pqiXDYJR+aXYVsEt+yuBzqnyR/iBn/bPqGDeOmOXoeji22sdAa4VcgXwqO6degPPTxxZiUI5cUEvN6E99o9k0FKRVSJpcnPTuSxZ7q0IXmhs2hTtZBFd+Albi48crIJSiX5YrrOZ5Y7OLfaw617J7l8ep96PsWRk8vB9XMZC4Wslcq0D59o4sYdtSAdOVHMpsofOrGMiXwG126tBm3aCOmI6txOuMfjp1Yw8Chui/ZRgs5Nx8XRhbbyDIDkPqWU4vCJZmB3hJCggCRNh2u2TKBWygb3SJU/0UQuY+GmnbUNyV8ObF7nL+X8A+avcf6jKPWcb3Tgej72S85fMPMkAz4834Tr+UGOL3TmevkjJ5cBAAf3sEFeztmwSHKksLDWw3yjEwwQIN3ABMsWToTpkM7kD803ccP2qpLqcj0fvYE+jSNY9oFtzClM5NN1Fixb6CCf1qrDk5xli0GbsS2Uc3bi9QXLlvO+6zI2zrLFgvN6zF+w7KlyTtEhUWfOssWEul6EFzjOfaKP0kmBYNm37dvYcxYsW1wfwIaY/+v2TgYLzhPrMH/BsndOlrj8+joTAhzco9pF0j0OR0jHevKnmmwhfKN2MfR8PCZNqOvJiza9Zmcd+QybUKuFDNruEH5CtHM5sHmdPx8EQ58Cgvlr0j6jWPAVi71K2mcdA3vw2BKyNgkZWyGdvRyZZ0zhRs4UCCGpg/ZQxCkA6QYZsGx5sihmEh1tf+jhidMrEfl0RqVj2evJR1k2kNxHYrKItimxTyMsGwiPBdEhyrID+Q2y7I3oEGXZoV0kTZAqy15vgoyybHaP5AgvyrJFmzbKsoV8x9VHO1GWLeSZDsl2EWXZqfIRll3I2shlrHXt6LZ9ETtKuP6z59fguF5MhyR5pz/E0+fWcKs0AVeLWVAKpdjicmPTOn8xCACA2Mlpn1Gc7fPixTYIYVUc4f3TGdhDRxu4ZfckSjl1gTjJYI6cXMbNO2sBUxC/SWQ7J5ooZm1cL1V8pBmwzuDF5EJpnI08FWHZAILUla5NSSw7SR5gaSWZZYs0TrK8yrLFPZIZ4bLCsteTPzLPoq/ohJq0aJ3EspN00LPsdDs6EmHZWdtCMWunkgKZZYs2JdpdhGULndOeARC1o+QoWMey0+woiWUnyQPA4ZPLCssW90ibIOulLK6alcdzuh0BUCbItGjnidMr8HyaoMMrl/rZtM5fhPwAADsh7WNb8Cku+RiGFxda2DVZChw5IC/4xg1gpePi6XOreNOVYVlXmgF3XQ9Pn12N1UmnDdpD88t43Z5J5ZC5dANmLHu3VN9eLWQx8Ch6g3j/RHPZQh7Qs9pHT2lYdgoLPrvSxdmVrsKybYtgImHRWseyRZvSGKTMskWbEhnhfFNh2bIOun5NYtmAfpJ/4rSGZReTmfyy4+KlCMsWv9ExeR3LFjokOcJDEZYdyif3qcyyhTzTIf6bJJYN6O3iufOtGMueSLG7jjvEM2dXFZYNrGcXyzi4Z0rZc5MW7Rw+0cSuqSK21sL9M9ViJnHR+tCJJiwCvG6PGkEC6YvQo8amdf5AaERIqvYRL3G/ROcfrfQB5MXG+MP8Oi/BfNNV08F3YrLSGdg3zjCnIDtCIJm9rHYHeP7C2styhFGWDaSzkWguW5WPt+nQCT3LTpI/fCKethK/0cnrWHaafG/g4ckzKxu+vmiTzLLX0yGJZTN5fZ9GWXYY7WjkNSxb3ENXpaVj2UIH3fV1LBsAJvIZ9Aa+Nmo+NB9n2anPOYFlJ8kHRQNSm8SitS5l8vipFQwjLDvUOS6/0OrhxJKzYTuilOLwfFNz/eRF68PzTVy3rapszkybwC4XNrXzFy9yT0r7CFZ8KXn/gefjxJKjLPYCjKVW8hntw3/waAPlnB3bFZrE5EUo/drdUYPUs5FHRS47wYCjaRwdywaSGVsSy05LaehYdiWXASF6x6Zj2aJNaY4wzoL18jqWDbAJUrdonciyE5x5MstOJgU6lp22aK1j2axNeuavY9lCB931dSyb6aB/zmksG9Az/ySWza6vnyCjLDvUQR9ZRFm20EEnH6T2NM9ZJ398yUHDcTV2pI/wBp6Px0+taKM1wDD/kUEYkRWkfdZn/l97aQkvSLvuBH7mU4/h1z73VOz7+SUHA4/GmD/AWJvOYB48toTb9k3Fzv2vFvXs4sjJZVy9pRLbfp8kH7DsXXGD93yKjqs6tjSWDcQdlWDZ8clCb/ABy44YvMUnSJ0jPHyCLQ5HjyiYSHJs801sqxWwo16My6dEFjGnkDBokyaXkLGp9xAsW5eqY/Lq9QXLPhjpU/Eb3SR/aD6+DiTkkybIWlFl2YCYLPQTMIDYcw7sIvIbwbLjOgt5tY8Ey45ev5JgdwHL3qNeX9xDZxeH55u4dqvKskN5/WRRyFqxI00mClk4rhdLEQs7SnzOkefw9NlVdAdesh2ZnP9oIJxRkPP34gu+gMr8P/K3T+I3I8cJ9AYevvTcRTx1djV2D3Gmz/65+BkeE4VMLOd/YbWH44sO3qTZxq1j/p5P8ejJZe25KElpnMPzTdywo4ZiLuoU9OwikWUnMPn1HGHU8QiWrdtKr9NBsOwoQxX3iKY0ApYdSVsF8ppFa8Gy4xNqss45O86yk1Jj0TJVgaRF64Bl6/pIM8kHLFsjnzjhzS/j1r2TsfOjkhatD59oYudkEdtq0QlV30eHeNoqPqHq7UK3gA4kL1oLlh2VF21KYtlaO8rro53D803csmsyduZPsGjdj4+d6XIOV86qx40kLVqHpbl60mGY/4iQyvxf+F+o988DUJ3/aneAw/NNJex//NQK3KGPRtuN3ePFiy1YkUofgYomT/jgUba1/vYr485fF66/eFHPsoV8u6/WBguWrTP4pPA7iWVXExieYNk7J1WnkLT3IGRHOlYb1zlpchFtSmLZOqegW7QOctn79O0BdDov4+Zdtdi5S0mpMcGy90fsImnROroBTm1T3LEFuWydzpqURsiy9fKA6ngEy45OXkB6dHTd1mrsfJ2kVJdg2TdoDg7ULVoHEWqCDtHrJ7Hs4PqR9rd6Azx3fi2xTwGNbc83cXDvZIx0JC1aHzqxjL3TpdjhiibnP2KIB2BlNDn/z/4Erpr/CwBh2odSinafvff38VPhYWVfP87O+Wg4/RiDPLrQxq6pkvYwNl34/fyFNeQzFq7dGo8UdIP2+QtrAIAbd8RPjZwosNpgxw31OrbYxsCjuHmnTj7OUgeej5cW2rh5Z3wAJjG8Fy60cNPOWszgk/YePH+hhb3TJe2pkXqdWdotyrJFm5Lk9TrEdT6z3IXjerhJ00e6aIdSiufPr2nlk6Ip0Ue6U1p1i4fPn1/D7EQ+xrJZm+Lyz51ndpH0nGMk4gKLUDeqw2K7j4bjJj4DJh9/DjfvissnLVq/cKFfdcL8AAAgAElEQVSFA9uq2pM1dRHe8xdaqOQzMZYtdHi5dtQb+Arxe2mhDZ+m25E8YTj9IU43uy/LLp6/oLejtEXry4XN7fz5A7Bs7nREtY83BAYOcl4XADAYMofecb3gBExx+BUAPHKCOf/ewI/lyy+s9WJ5ZoGJfCb2MJvOADOVfKJTiLIXEW3ojpLV5eTT5HXsZdlJk9czvEa7n3i0rW5j2FKavFbnPiYKGe2EKq4vT8Ib0lnSoeH0E+V1uVfH9dAf+lp5sWgdZWxLbRezlaQ+iufwG06yvI75NxwXGYtgspSNyesWrdN01pXohn0aP/47PEIifG6eT7Hc0esQVrJFnrOzjl3E5F3MVHLa47x1R4s02mk6xyekVDvS2EUzbewkRNmNtpuoc9LazuXC5nb+gvlHq30GDgAg67Ozz12PDRJHctQiPdMbeHjs1EpQ0igeuMBSux8cphWFjuE1nT4my/pjZ0UtseLYHBdZmwTGqtOvpTHISR3L1rCXBpefKsd1KGZt2BZRru/5FCvdgVYeELlU1YCbjquUhKptiss3HBfTCfITBbZoLR+d2+SOTXePtAlSdw9d1UWzLfooLp+0aJ2ms84uGo4bHFyna1PMjtouJstJjlDznFN01kV4TSdZZ90EudxxQaleXvxGbxfJjjAu30+xozjzbzguyjk7MSoHojqvb0eyvBg7uj7V7fDvuh66A+9l2cXlxOZ2/vwBkyzvbOH8Xeb8M5Q9bHG+j2DpOyeL+MaZVbT7QzxxmuX7xXnw0SOXF1vpzj9a6tnsJDvOajGLYdSxtV1MlvSDXFdFkWaQusPm0gY5O9BKZWBikCc5Z12uNn2Qx6su1pssgLjOlXwmVvWiyscnyFTH1o1HCok6R5h5MMiTnLmGyac5tokEUpD8DPTO3LZIUP6syieTAt2ENJHn0Y7OjhKjHTXH7vsUy51Bqg66KDht7EQXrZuOm/wMtBGhGDvxe9Q0Ofy0ySJrWyhF9u28XDu63Njczp8btR1N+wjn73Hmz52/cNR3HtgKz6c4dKKBrx9vgBD2AhFAZf4dd4iO6yWGcZV8/ATHZcfFlCZUB5LZxXqOUGX+/cRBrsvVpg1y8RtdZJHqqGKDPN1RRRet15ssojqkTxZpjC1+D7FovVEWLNqkXj99kGsjwnb6cx766qJ1+mQRX7RuOC4mS9mEdKPGjtrJjs2yCCq5jDZlkhaxyTqvdgfwfLpOn8ZJQVqfMh3U57a+HakRXjFrx6rkkuRDnTcW+W/EjtZ7j8EosbmdPzfqTDaS9nHZ4pftMQMXbygSZVzfec0schkLDx1t4JHjTVy/vRq8sk6u+FlqsX/P6BznoItpm00yTn9jBqlnqf0Ux6w3+KRBXshasXPJ0wY5EM/hrzfIoxuGVroD+KnpAPbGM3nReiOsNpp7TW6/Xj5pkItF640yQnEPfWSRIi9dvzfw4Ljeuo5twzonpDTWmyDlaKrpuCBEnz4MdOhu3LGxtZ2Nk45oDp9SRiLSoimmgzohpdlpVD6tT3XHg4fRzsaY/Lo6r/M+jFFjJM6fEHIXIeQFQshRQshHNH9/CyHkMULIkBDyvlHccyMIc/6Rs30487f5gq9g/mKwzFRyeN3uSXz1xUU8dmoZr983HTywhsT8F9ssctAy/6/8X3jnoz+hXLc/9NDuDzGly/mffQxvOPJh2PA0g1xz/dWz2P3Zu7EFzY05haEL8mf34E35Y6rBdwbJg/xzP413eF/VM3+dAf/LJ3FP84+0A0Rr8E//Lb7nuV8FEPYRpZRFRzr5c0/gdf/4ARTQj01I2kHuLGHm0+/ATrKgOMLlpD7yPeDPvx9vzT0Tk0/U+fO/iHe6/6CNLLT3ePg+vPPCfcpO6+VOymTxwj/g7U98GACNPQetzosv4Pp/eC8m0FFz8s5A357eKir/4x3Yb51Rr99xUS9m4+8BphT4yx/Cd9uPxuSBBFLwxV/HPZ3PqX3aSemjw/8d33fqt5VF67XeEAOP6q9//Kv4jkfuhQU/dg/t9ZdP4sq/uwdTWFMnyE7CuovbQeZPvxe35k7GiFYuI50hJuOzP4m78KDejnTP+Z8+gXetfir1fRijxiU7f0KIDeA+AHcDOADgA4SQAxGxUwA+COAvLvV+Lwe1oNRTn/YRzF8s+ArmP5HP4k1XTePoQhv9oY83XDGN0tLTuCl7JqggAIDFlovryEnsbj8Zv3njKCrdswBCtrDssP9P6gzy6Jcxe/oLmMWK6tiSBvnZR5G5+CSus+IGqTX41dPAiX/BG+0XY4wwcZA//Vm8dvhEhOGlRArPfR7XtR5U0jipjPDol7H7/BcB0KCP1npDDP2EQT7/NVQuHsYOsrQxxnb+G7DPPYrX2sdjKRDtIHcWgWP/iNeT52LXTxzkz3wOr+k/qk54adHR8w/g6pV/UXZaN1IWlHHsn7Dtwj8hjwFW+XMYeD7WekO9Ezn5EIoXH8M+cj6WitJGLgvPg5w5hDfmjsdy+Nr2uG3ghf+JW+kzWp21tv3M3+HG7iFtNZH2Hi9+AVc2vgogHDupdnT8q5i+8DXU0Q7kKaXJY+f0IeQvPo5rrNMbI07N48Cph/DG7NG4HekW3b0h8PTf4KD/pD5S0I6dv8f17Ye/7Zj/bQCOUkqPU0pdAJ8G8C5ZgFI6Tyl9EsBo3pm4QYjQzs5ENnnxtI8VYf5t3vGVQiZ4yQohfJfm3/88Ppr9lJLzX2z38e8yf4XdD/1q/ObOImyvhyyGwVpCwIJ1D7/NXl5dJZ3AwNwhYzJaY3EWAABTdldjkJpB3pbkN2LwvVXAc1FFJ8I4+QSmixScRRS9NigF2q7QOWWyaC+AwEcZvcBRpQ4QrnMNjhIpNJPSAc4iAGA229vYBMn7aNLuxpi8fpAPgG4TFak9gMRqtW1aQH7I7C+qs3ZC4m2qwgmeQ2okwnWW7ShVZ96nM5lerDoozY5qVidGIqqFTOzIErYRZQFl6ijRTjgWNPdwFpAbshr9DdlFW+gcPgfH9eAO/VSdq3BiEWSa/HSmu7EIstMAQPnYUe0oqXIPzgJKfnvdd1qPEqNw/jsAnJY+n+HfveqoFjP4hTuuxnffuJN94fNO5cyfDEWpp5rzL+dt3LSjhko+gwPbquygrZVTmCFrWJKc/1KrjxmyCtu5GL85HyQTkgEIp6B1nO3Qsa1F5NMc1ZZsL8bYtKWkjnBsEYNMGuTciVQiA6Tp9FErZvWDvB13bKn5cjHhSRPMepMFwBxbdJCnTaizmd7GFojFMyCdjU2QvI+YYwurccQgn8hrBnn7IndsVNJ5/ecs65xW0SV0rkmOMCzPTZafyby8CbIamfBYNKV5xv01YNhD0W8ri9biOWtttb0I23eRhxufIDdqR2mRBZefy8btQt+n7DlP2V1l41liMQa//oQ0YYs2aSv3vAHQaaDgqWPncmMUzj++sgh8U+8iI4TcSwg5Qgg5sri4eInNYot3P3/Hflw5x3fsRdI+ZBjJ+feHyGUs5DM2MraFj37fdfiFO64G3A7QbaKGVmC0AGP+U5YD0lsBhmoJKBy2T6BKnGBSSV3wCQZ5aDCpi6ttwdhCJj/0fKwklZLKji3CCPUDkBlwyW8p55InGnx3GfAHyA1bsOAH9wjTAboJaZG3yQlSS6npABG9WKFzDq6fMqFO251IKq0fvPRbbU+yY0trT9Fr8UVrL2iTdpAP+0BvFRb1UEbItIM1gpQ2MVKgThZpOjNSwCOFtBp87tgmLZ1dJLdnQmpPIK+rYuPXL3AmL+usLc/lkQLAmXlXJQVpxEaxo1QSwdo0l+kG8qI8V6szHwt16fpC57RIoUzbsZJkvTzzFbnhGgD6im30GoXzPwNgl/R5J4Bz38yFKKW/Tyk9SCk9ODs7O4KmcRDCXuUYSfuQQTTtM1TY2v92627ccWALsMZy9xP+Ghqt0MkvtfqYBLuWcGTsgk6wkWwC3Vi4rh+0zMCmrNAg01Mggo30pMiC3Sdtsog6tsQF5cCxMf3EBLYeCwaAClSWqh3kvh+mKCSGtJG0z6zE2IKyypQUSN0Kn0HHHaI38PUpExGt0ahjS6iU4dcPo53Qsa3XR1WEE1Jaea4upZFKIvg9ZCa/kT6tS5FFanku76Oy346lcbR2xK+vi3b06cYVwHO5zrpoR2ergkR0XpYdTWU0dpSWJiLRFGgSKWDtKXltZdE62Y7Y9W1/gDwG31bM/zCA/YSQfYSQHID3A7h/BNcdLaxsrNqHeH0QhOd7tPvDYGeegtUzAIAsddHptEKDb3VQAbuWcN4A1EFOnGDzWIOXz+nOuBG/mct1JXbUhwUf2zvPx+UFG7E2aPBcviw5to0McpF7DRlYeqjLdO6sL99dDp5HlYSOMH2QS9FObIJMTgfUrE4sskjTueS31UXrpFwwv3522AaBL7UpoTxX6SNH6SNtee6gB/TZSbJ1qytFU2mslt1jOhPKb0TnKgntIrU8V5ACv60uWiemTFh7LOqhhH6waL1eWgmIRDtJNfi+r5CCjdkRJ1p2R7OgnGx3E1IKVFTupemc58Rpbb0JT9K5GomoLicu2flTSocAPgTgCwCeA/BXlNJnCCEfJ4TcAwCEkFsJIWcA/ACA/0YIeeZS7/uyYWfDI5258weAsjUINmG1e8OgnlcBd/4AUB6uBSy43w7P/xGzPYAgjAOASRIuEi07CeVzrhNEI1HGdof1KHZ99h3A0lH1N5o0TtNxMYU13PmFtwJnH1Pl+eRS8tvo8HPJ2SCn+KnH3w0c+eOIPLt+1usig6HCwD689B+Af4hU9CqDthPkRpuOiw/hL4E/vUd7fUBdhG46Lt6b+zqKv3MjMJSO0vD9oF9ZtBOy7OvISdz0ZweAlVORNonIQp0gq3Dwni99B3DsK9o2Ff1w0VrU4P/M8z8GPPy7Wp0JqBLhNR0XH179JPB3H9K2J2xTOCH9H/bfAX/w9sQ+mstG7MJ+FNO/d71iy/I9Jq2uIr+XnMfrP3MTsPiiVocKdST5Pgro44f+9Q7guc9r2ySv7Yjy3J+d/xngnz+ZorOa0vxw93eBv/5xbXsAlWk3HRf35r8E3PcGVb63EpAIedG66bh4o/UMdv3BAaDT1LapJo3NhuNiKxp42+deC5x7Qtumsh+u7TQdFzY8/PihdwLf+Eykj9j1w2hHGjvnfxn40m+so/O3D/MHpfQBSunVlNIrKaWf4N99jFJ6P//3YUrpTkppmVI6TSm9fhT3fVmwbCntEw6YCXsYnOrZ7g9R1jl/nvYBgEnSRtNxQSmF35aMSmb+0sOczYWOqtlxcXf+G8BnfgSQTweV5Kdkhue42E74PZrHQ3lKAwObgBMZ5BeQ71wAzhxWdeD3kBeVmo6LCXQx0TsHnH1UKw+IFMUgGOQ7ey/Frx+JdmRmfi09AZw5kqjzbDZk8suOi9dkT7M+b0nZw24ToIxlTtmOlDJxcTU5DWvgABeejrQpdGyBfMfFDrKEnLuSqLMc7Sx32CCfcV4Czh5J11makPYMjjGdNe2Jyi932ASGc4+prxqVHKe8ttPsuLgldxbEWQSW50N5twO4rO116frNjov95CzsgQOc/4a2TSUqO7YB5sgKCv2luM68TUG00xsE5blbOy9q+kgiBUQtZrjCS+8jRmxCx3mDfRJYfA7orUntCeWnM6od3WCfBuktAw2JOEXSjWEZtosrrPOwB23g3OORNjH5ot8OjgdvtF1Moo1y77ymj1ibRLSz1mUEs9UbYnvvpbjdOWq080qVe27qHb4KlLRPO/i6ag+UtI+2QmM1LGaqkxaW2i4c10NpKL3cRXqAslOYzvTCUs+2izeTp4Dn/p6lPQQkA56UFjMbjottuQ77w1oYfcBtAwP2fcVvS2ynj0nC30ImRSvyPfJ8UUk4/7qQlya4aJtEvnmtywZ5yVvVXF9KaURy+DW02RpIgs6zGZXJz2U6cR2U66uMcJbvpFbkvWEQKciL1s22izppp/aRHO002i5q0Fw/0qYaZ/KiPLfsraXKT1lqPnuStAHqA63zWvlpW2XyWzKaNkk2qJACRWe5MC/UWV60bjp9TCLJjlibWLTDnkPTYZU5Gb+3jl10ggmm4biY8FvM7nyptLEdjXbC5zxtcZ1lW431aWhH28XYkXWWSESUOAXrdwk6FILy04E6dlLtgt2DrfdRFIZric8AUInT5cb4OP+EtE/FHgYHuyXn/M8COXb+/iQY819qSY4WUB6gPAjlQbvccTFlaQahMBZiqbngtostgSOUDX4hkC/67eBl2oETAVSDFBUUxAoWldZ6A7bBK8mxcXmAM//uAA2njxwGyHpd1mY5LdNeDOSnM93g2OWm42LC50xNHrROqAOr3gkH4XTQR3qdJ6Dm8Lfluvz6kg681hrECqKdNp/wAscWnfA0OjcdV5pQNROkkOfPjZXnUhSHq4yF9ySCIPXRXLanRHg1aO4h9ZFcjdNou5i1dRPkYiBfUaqD+tiWFSRCun6fkwhiIS9FO6odpfQRZ+bpk8VipI+GQXluyVtljjgaNXP52WxXsYu6to9CnWtEtaO5dcZOSVq0bjguZux2vI98j9kSsZRoJ3WycCI691ifVtGBRT1g7RyLQDQ61yKLypcT4+P8E9M+G8j5r50Ftt4AAKiTNhrtPhbb/ZBNZYoR578E5KtAocYqTaQF38BgViTnLwb55D5lX0DTcTFj69gOl6/viaVxtmoHOau1Rn0PgDDcbUQdm5KWWQzlScjw6qL9oGpapn0xkBdMvt1nKbWSx51/lMnbOaCyVanGaSqOR54gQ50rVI4s+noWLBxKfU/o2LjOwSBXIgVWax3q7ITRkdC5dU59FWh7QepT5ngabRcVdGHRob5N9d0AWETY6g2D8tyyto+Ezru5U5AWSy2NDpLOJd8JFq0bjhs6/wR5OdpptiWdoyRC0rnG04GNtvTMeitsUlF0ZvLiOTfbLJUmnksseqlsATIFTEl20XD6mKBCXkOc6nvUNQU5UkjQWV60bsokYjVCIqgP1PcEaztrvWFk7GiYv2QXYZTN+8Vz1epASX4usm/ncmKMnH8k7ZNhL6moSGmflo75U8oe7hbm/CfRQkMwfzFAZq+OOP9FoDwL5GvBTkiRL69qDXgBAAGmr0SFtiFX+2gHuZgsZq4OFpUEY9uW1RiwYIQzVwOQGJs8yOW0jIgUhDyvclAMHoiz1OkrAWIF1ThNx4UFXz/I24tAeQ4oTirRjjLIdZHCzNUo+e3gZdpNxw0O0NOy5pmrgw1DItoJB7ksv6T2kXBs8mREfaB9Qb0Hl5/ki9bKII/dYxGY2A7kJoJFblGeW/R4hLAWcf6FOlCeU87qUSKFhD6Sd1o3HRezOhbsqHYxIekckIjWuTAt028xEhHYEbOLmM5rkXtw+Tm+96Dh9MNUGhCf8MqzQKHO+rQ7DMpzgwkySoTsHDC5h0U7XU0KNNoernOUFGxJSzcqY4fZ0ZSYXLpNtt4CMHLQaap9JKIpSGNHfs5SH0V3Wl9OjI/zt7PqJq8y20dQsZjz7w9ZKBrL+XeXWWg8tQ/ITWA246DRdrHU7mOStEGtLDB1hZrzDwy4hio6aPcHaPV5vtznBrASYS+laaA0jaLXDl4v13Rc1HSOUEw0M/uDRSXB2GYFC26dD1mqE8oD4aKSMsjle4haay4/k+kGzH8yaZC3F4HKViBfxaTdCwZUDW0QsecvxvDmgEItiHbCQb4al28vsAm7thMFj/VJuz9Uo6loeySdZQYWDPL+arh4GOkjUXXRlCdguU1Dl9kGl9+SZem9hiORAiDuzLnOdStsTx4usvx48dgEVtkCFGrB8QiiPHfCT5hQAWD6Kr62gyB1NSWeW7Q9MZ0HagTpD0M5R9enGscmiI2IFBQ7GqqptJgOoc5ipzUrVeX58lgfcRJRqCvRTrOdRrSYDkq04/TVtI9Iy0T7CGFEGKwpACyVAwCdJQA0kK/zqqsm9xeJOtd3sWjH7pqc/8hhZdQ6/9I0AKBkuXA9H06fsZtY2kc8pOoOoDSJLZkOmk4fiyLnX5pixhpN+1Rm+aDtBI4ZAMsFA8CqVJbYXuROoR6kcVa6Lla6A1TEIF87F6ZlRKQwdQVrGk/jLHekfLm8eBiwFzHIQ8a2TXb+YlBFHOdsthcw+brs2MSgErXWXOdJcf122mRxMXCEYtE6GOQD0UeRCa88BxTrUrTDFtKqkPpIsFSdzl2R9pFYp2hTOz5BCsepDHJhD8IRTl0BgGCan7G0vK5j484/aE8/0qd6+TJftG44LnyKsNggylKLU0B5WjkeoSEvTnaXw7RnpI+YzkOeL9cw84j8lNWR5DV21FsFvD4wsQ3IVdhOa/4MFJ2jzJzrLBztcodVpYWptAhx4nYnFq2bHVaQUfE1k0X7ImDngRrblyqv7UwRrrPncieO2IRX4zl8hUTIbYr00Vw2jAgndREhPx+KTWA1ZdH6cmN8nT9n/mXiYuD5QUVOpRDZZSkMs7YLKE5h2nbQcFwstpnBk9I0M9b+GsB3DMMRzL+KMm0HA9CGh9yAG2SU+XODF8cjnGp0QClQ9NZYymrY44uY/Po8UgDEOS7yoOL7CIJBG0n7SFUabNAK+YgBT+4FrAxbtO4LgxdOgUiDnNdac8amXyMgmrQPH7R80Xqh1UMZPdh0GJeXJhcR7Sy2+2yQe2tMnnpAi6dlnEUgW2KTNsKqi5AFR/soTJkAwHSmg1af5fAZC47Ii0hhYitQqLJzXwJWK+vM+0hs2IpEOzH5KDPnfSRIwammAws+nwCJungoRVPiOa/yCYlFCkKHs2EfgQBTVzJ5EjL5GcsJ5df0fSR2WjflqjT5uQnHGUx4SX3E5UWkUBbEqR1EkMHkBRKPgrnjFGmckw1mo8Uht4vOkjQ2+eRSrHOdnWB8sig7YSxMxyNIFmWLPooQp2k12mms20ezUrRjmP9oIdI+vs+dPzu1s2QN0B/6waakROZf2wGUpjGFNhptl72+0XI405pjMu2FMOcnHJvHFpXOrXTDPCexVfYihfcAOx5hvtFBBkPkhm1g7jq1Le1FRb7Kq1+WHZfly3lEEBrkRXbPyX0AgFmek284LqbtNluEtLKhvHBs/B4iFGWDnA+i6avijJDrXKGcQXYkFjx9Veh0RK11ZQtQrAdpnPmlTugUpq9S0zLthYjOjjTIV5m80kcXg9wxIHYRD8J8uU4ekAZtP6jembU7wRpOLFLgbapb3cBRbdf1kejTsmDyzLEpkYIsL+ssRTvzS50wlTZ9FStiENcOIoXQsZ1b6WLoU5YvD3SWHJtEIsTazrLI4cf6iN9n6koAhO89kFJp2TJj+bLdAYHzr/Ey5mW5PFfWmZ8PJfpUpHGU9TVhR3IUzJ25iHbmlzqs9NTrhjqItIxEtJjOHTQcFiFVfLmPpOecKQI1djhk3QqjlyniBJFfzI6qLNoR+3aWOyLKJiyFvBaR5zpPEFPnP3oI5j/sAqCh8ycs5y+Y/0R0wXf1DHOM5TmgNIUqWmg4/SDnj9Ike3AAM5Ruk1+fOcK8x4z8VLMTDvLZaxiLdx2V7RRDRzW/5IRlmFtvZP+XBxVnCkzewRl5kAt5McidBaZvcZLdnjO2ZZEvL88wY41GCjyXWpciiy3ZDhsM01dpHCEbhOKUS1atxNnOtpvCmm5Ra80HYXbogMDHySZzbIG8ovOC4sxrxMF8o4Mshsh6HUleclQyw0MHy8EgbwFbDrDyOpmB5SqsL6yMwtimLIel92o74o6Qt6lG2mHFlXD+W2+Q2iOx4GIdRd9Bx/Ww2JIWP7fdxNMyHcZU3VYs2jnZ7KBOJHlho0Efhc6/BtZHAEV+uKrpU5UFT0mL1oxE7GN9siqRAmKxPipU+dHX4jnLfXQ6bI9kRxM0ZNnBBLntJn2kwEkBpcDp5W64oLztJpZKcpYkEqE6c2ZH0T4SbVpU+qhKOjjVZDZa9NbifeossmfA+0gcDx7sX5nYyu6vneTrQc6/0XYxm+my69R3J441RpyM8x8thPMX+U6e9imSPnP+vBwzxvzXzgLV7YBlAcUpVLw1NB3G/Ku0xZh/hR9C5yxEnEItqA0+2XDCFMi217D/r54JyzAlVluDgxMNJwx1A2cuDcKy6tjml5hehcEqWzwq1NUcfmUOyBbCRSU+aKvgOtR2SfI8UihORlIUPNqJOsJg0G4Jop3+0MeF1R52BI7wxrCmW54sCrWghG5+yQmZv6yz77HQPRLtsAlSIy/aJMlPZ7rcEfJ0QHmWVd7Ik0tljh0CWKhh0uqqkUJxirG/6CAX6xY0TJnM2Q67b31PmJaJyAfRTqMTrinIk3wksmA6O6yPELUL2VFJ8pxElNCH7Q+AuQNQUlGRNNFstofzKz24ns9YsNBZnlDLs6xsOrJoPUnazF5qOyNppVAHkQJtOi625DpsTM5ey9MyvVikwI6QoJhfcngaSu6jM2yipB6/fhjtMDtKGTvKZMHkLfgsJTt1JSM3CtHawvf5EEzbPSx3XKx0Bpiga6HO8oSaLQP5irJoHexfCewoGmXPKdEOlcuuLxPGx/mLtI/Y3VtizL8IVucfOH8d8+chH0pTKHgt+N4Q51Y7KPur4YIvwAxFZi/5auDYTjY6YbndtpvZ/1dOqYxQGrQnG04Y6s7sZ+Vsa2d4pBAuEAOshO5kw0EBfdh+P+6o2hfD1BRP41xYZYO87PFF6+oO1bFV5tiEV6gFx/cGC7jC4EVNt5L2qaPAS/JONhw2yIkNzIrU1VlJXtaZpXFmrIgzXzsT1lpX4vIBI6zvYXsrommffBUA2zB0ssEijPxADNodiX1UtxysdAZskPstJl/doU4W+SqQLYb5aZ4amxbpwNrOsKY7onNOIgXb5AkSYCxVYc2cFER1licLcT6UHBFC2BF3hJUtjKlGdc6WWLRjd4NUWmGwGrcLEVnwPhKL4g2nz/Llch9RGiMRwrEttvosIko4oAEAACAASURBVBR2JHSI6GzRIYt2Gg6256N9dCaWbgQYcTrZkEgEL9EOos5IpDBlsT6qwmGptFiExyMFywIKVUxnOjjNI4XScE3TRxdDMigtWgfrX8VJoLoTwSbJyIQXPR78cmJ8nL+VZflEwfwLVcDOoYg+XMn5x0o9V8+GBlqcAgDU0UaFdmFTj+f8+cNuL4bOvzyrOPPTzQ52CANWnL/68AHBRqQ0UWmaRR+rZ3mtdTeYXADGak8sSZNFKcLYhMEDnI04OLEk5cvFIBQ13YLhcfmS3w7WCBgL5gYMhIPWygaDXJTQnVhyWG63OMmiEYA5Nic+4dXQwYklJ+yjOSktE4mmWB91uM68j2TH4w3YuktlSxDtTNusj6rogMDXMPnFyKDtBI6w7K2y9F5tJ0/XdSJ9VEfRc9AdeFhY67GITXFsZ2KTvCAFJ5YctoieKaj55oARxnUOKrSmrmAsU+kjybHZTD6YLAKWGiERItrh8kEqLZggZdYc6jyBDi6u9dAb+CyVVuIRpChOCCIFS4l2TjYcTBOJBQOqDpGxcGLJCUtPhTNX+kglTieWnLC0dWIr65PV08wmqK/00Wy2x+wo6CMNcZLsos6vH1SlydGO2B8jyCAnBas851+lrXBsik2S7UUWVXASIe/budwYI+efYY5NOP9cGcgUkSeukvNXDnbzPZ724S8mK3HnT9phSqY0xaKK4pTK/MszgYFNoIPza71w0M5dy9qzejqyuMqY/CR/AUyQFy1OMWe7ekYNpe0MkKsEC2/BZFGU2IhgYIHzrwe7UTMYIjsUg3BHWNPdVg246LNzyftDng4oyYP2dCxlInRe6w3ZIBTsCOCThTzhheH6Wm+IrWKTWnmWLR7KkYLUR0LnYBenaNPqab5hiyqDlqVxpD4SbRJpGRHe8z4Kj++lyA9WVUe1di7WR8KxrfWGqPotVWfBUgs1IJNXHFWgQ3GKpaHE4qFGZ9FHAQsuSixVkyaazfa5zhIpEHYhkwiuQ533UV2eUGu7mI0O+zGdWTUOGzeMRPD2BDovKNfPBccjDBmJiNqFw0lEoR7rozm7wxbc+e5fJTqS+4jb3Y5YH0XsLlcGiB0cRRKQiBIfa2tnefFGQ9FZVOOU0YNFB6FdiE2SMeLE9x5QsOMslD46q47NYl3Zt3O5MT7O386oaZ9cBcgWUaBhzp8QoCSfF96+yHKK4mHxBdNJtEKWzaMBVLYw43UWJQNmzLwKVrY5l+F5zkKdGf2KPryfybINP0E6QISiSmgssRGLTSoqw9vBjLF1gaUepHC9TJnDDBaUBWMDwglGMkhxoBXA8+VRA3YWlMkFYIMWAFsUK04x3XKV0CnY+eAIDNFHAFj5XL7KJtTqjsRIYZb3UdwRnlUnVN4m0UfKc6vtZIuHrfOsr6Q+KvlMrog+bN+NOPPTKgsu1pH1WHUWAJTlfLnSR2F7mM6s/yfFBJnJMRk5UohEOwC3I8Ly7oEzlyOFINph8kF5rpxvdqSFRt4mpT2AZtKORzsAQOCzt1BFJzzZLor1INoBEK4pKBPkohQpqH00ZfHiCkLCCE8TEU5ynQOiJU94cqRACFCsY8pi7Zm0ZLvYwcZN6zyC4g2u88RG+kg8Z6mSDeATpJhcgj5So3Kh8yuxy3d8nH807ZMrA9kCcmCbvFr8XB/l1Xsi3BWOkTP/SdJWHz7ABl17ITRgiQVXeXUGY3jcgOu7OXvhedHSFHOOxMJMhjk2Nllk2feCpYqNW0oahxnw1oxk8KLN5/i5/hHGBiCMXkTKBAgZlTS5iBI6gCIncsET2xDUXEdywUDoqCZEpEBIGE47arpB6SOxpgCEC2nyIOfRzrTNdA4WS8Wg6iyF5/pLbZrg7QkGuRy9nH8ifIZcvsidf2yyABJ1FvcI8uXFSZZPXzsb5o7lPuITZFXkywF1AitOsklQinYAYFa2o1gfqWs7AEIWLHQedoHF52M6B32EiCMEgIXn2EQp2Z1wbFV0QKhIpe2S+ihZZ5Yvn2QTVXk2jHak9sjydbHoHu0jO8dkpWgH4GMnU2TplNquxD4SpGBHju+wFuk90PD4a0nnkDhJUbawi+V5VsmmiXayGCIz7Kh9unYmNtaEzq9EuecYOf8MC+MU519CXmL+8Xw/Lw8TjlHk/ElbffgAc64i7RMx4GBQEdmAd4XMX1RQ8NyoYGxB+RwhzGCoB1x8OrwfoLARhQWLNouXukhtKgwjjq0kGeTFZ8Jaa0mHKjrhqYRFnuqa2CaF96rONe7Mg1BX9GMwyFWnMMcnvLpgwYAarmeKQH4i+I0YtHN2h0UR2VI4CM/FnfkEn/CC6iN5wjsbnyBFtKMyvO3s383jbLE72keko6bSBEsVk3y0j/hzC1JpQDhBKmmocNEa4BOYLN++yHPUJChhFikKAGG+fB2dy3w3eXBEiEwiNPIi2lFSaeUZ9jxWTkUiwpDVslTaStwuIvlyuY8mRL4c4JVpZ0KWTQibROx8UFo8LarSAGZHbhtYeonrELZJkJRgA5Y8dsS5/tJYK3kau4janeTMRbQT+IvSJPM9xUnNc5aY/ytwxMP4OH87UuqZqwCZAnP+no9WbxCv9Al294bVPgBj2FNWhPmX5/iCrzST53kahzu2CSoN2vpuxuLXzoZOAQgWlQBuYPJkAbBBSKxgYw4rM2Q6bZVD3cAgHwvbBwDFOvIeW1SaldMBhTrrkyBSiKZxHNSi0U5tBx/ki1oDBoC8yxdLRT9GGWG+CrFhCOCRgqyz1wcWnmV9JKIyqY+m7bY6Qep0ltI425VU2i69vLRhqC6vo2TyTM/AKUQYGzpqKk3oLNIssclCXnQXjnBnPMVis+hvymZ2VFNYsBS9iPUnfg/BmmdtKZWWZBe8RBcAdiokYntEPkx1AYzYKJGCeA4Lz7J0Y9T5k46aShM6xCIFdv1pbhflKIloX2C/KUtjp8gOgwOiREvSOVNQSIQgTlvkVFrMLsLnLF7NqKzHledYhK6JsoXOyoKyaFNAItQ+qr1CG73Gx/kHaR+R82fMP0v7oBRY6Qz0u3tzleChIFcB7By25jr84ZPASFGZY4s+y/OSsYTVOICU5wR49QtljkQYC8AYG2e1NZntyGykNM0iBS4vHNuM3WHVH5k8H7REw17CDUM75XSAYKlno84/ZGCxdY7aTuDCUywiKUcNmO2yDEpPhbyzCKyeCq/PS+hEiqLsa3Q++1isj8TkUidOfJCffSystebyIo0zl+2wyTNf43n2QqLOVXSwPUgHSG3SsGCmszRBymmcxlG2nyMS3s/YPZYvF2kiocOgAyy+ENN5kttFZYN9JKKdSaujptKEvNiwxeWFY9siT5DZIiuLTtC5Sjrhqaob6SNImxfl57ZyOhIpsLEjiFN+EImOqA+cfzKmsyAFjGhxnauSziLdyOVFCnRGVKXJJEKjQ87rwIankgjLYuMt0Y6k/SglaZIPItQI0cIrc8TDGDl/seDrMKPPFFjO32c5wuWOGz/XZ/UMM2RhLIQAxSnM2Q7b6VqosYgCCB9gd1llbNlywNgKQ5kF75Lk58J78p2QgJgsJCcCqOkGAKI2GADbRCKMy86yMrfuclhrzeUBZpBKqAuEtfuANlc7qxvkQl5a2APYgqxShimuD7ADvyqyzqzSBEBYPqfIr8T6qMwdSFU3QcpsirdJbBiasRw2yCwrzJlHdZCinbBqRGpTrI/CxUmlagRgzzm4Pn9uItrJ9jCBbpgvByLPWe2jmpwvL0bsqLeisuBCPSAFdUh9VOJpmd6KSiKKdWT8PvJw1VSaaFOsj8IJcmesjySdpcVS0aeTRGMXA4efD8Wvz6OdaburptJifaRGzSLaKStjJ9mORLQzKa81ibRMb4X1gSARUrSzRU6liXsk2lEnLN7YgB3J77S+nBgf529nw1LPXIXnCYvIUub8m46r5vy9AQtdheEIlKZw45SP187QcEAB6kBVBmEVdc5q8+5K+PBF3Xv0t9KiUlAdADDDyJY11w8XleqQFg6B0BmKDVtcHuDOPNNlC2Y5fl0xqOQ2SWxESQcAat8Ieb5haNruxhfFq9L1y3HHZsNDdrCWcH1VZ+HYKp40WWTyYd9E+tSiQxTRDytron0kaq3lPkInPLkxrU1Sn26P9lFV06dStFOP9ZF0/bLesbF8uWC12+PX5/Ii2mGb1KbCe4vfRJ4BAEygG5IIQXpEm4gdXkdKXW0T0VGUqMht4vLTdk8tz432UUTnSbsbT6UpfaTqUJHHTrAeN8fIn6aPRLRTkydI+R6R9jCdO2oqLaZDnPnviI0dXR/xaIefonu5MT7O38qEaR/h7DJFZPg56svRtM8XP8pycq/9UfU6xSlszXJHWJSdv8TGo6yWdFBAH5YnpUCqOxGcCBhh8syx8coaIS+HoxF5AooKeuqiGBA6Ko0B1+Dw7eaT4SAXLNIKK0zklIZSeipfX24Tr+CZyvTC46XTJgsgWLSuRQd5aTp46U482mHXLogSw6jOlbhjq6Kj5stlnXXyYpDnKqwMM6pDZJDPZqTjLLR9pN5j0upI0VFKn3L5CnVYKs3rhdfPlcL1n4i8iHZK3uoG+khm5u1IH0l2FCUR6LBSUhKWZ2p1kNZ2dhaijnBXXJ7fo0Y6alUaEHGcCWPHlXS27HDCizwDEe1UvDW9zpHrM50dtuYnEy0hn5tgz0SWJx11PS6msxTtZMv81a+G+Y8OctpHOP9sERme9vF8Gi74Pv03wCO/B7z+p4Hr361epzTJdgp2m+qAkhmIyKMCECV0k9GcXybH0jJAzCALwxbbROIPEpi8usgFMIMsJxpwwiBHZJCL62sG+Uy2Hx7/LNZA0hgbcbAjr8mXC1SijK2tblIDwnUIzfVzwzY7j8VdSdAh7sxrxFErawBpQo33US0Y5Jrr52uswgQINgzNZKRBrnPmsWjHiTuF8iybfDVtKvmt+GSh6Kz2kTgeoSCTCLlNmgmvBicszw3kNXYnHbA3bUupNCBkzWJPC8D+lq9iOtPF9mx0gky2iyqk3bpCPj8R2mCkTSWvxUtPvUgfiQlMTwqK3kbsQlrboe0N9JGIdjiJkFNpSVFwsc7P9P82Yf6EkLsIIS8QQo4SQj6i+XueEPIZ/vdHCCF7R3HflwU7yxYm+23V+Ys3KAGM+S88D/zdzwK73gDc+Zvx6xSnmOPvLKvGVZ4JXsKsDMJ8FRXqxB0boGedxToyfg+7s2vss87AdAZMOmq+HEhlL9N2l23AWs+AeQndtlyXOapCLcwTi/aLWmvpHpN2F3tLIh0wFV6Ln6mktqmOEpWOLSjJOiRHO1vRZC/4UHROYfJweL5c4zg18jOZLt+hrOtTSZ5HO3NZ/opIKxvaWOIEWUeddLGvxMhHoINlJTqeotcOX5qiZfLx5zxFWjyVlpAOjMjXSIevNdU3dP1teemwv0BeslPLUn4zk+liR5T5V7YkpmWqcHBF2eXyuucciXa8dngI3AYn+Spx1JQskNpHU1aXH4ioaY88Nnm0sy3P35shp9JqGhLB7yGOvr7cuGTnTwixAdwH4G4ABwB8gBByICL2kwCWKaVXAfjPAH7rUu/7siHYVG+VhfEAkC3C9kPnP1HIAH//8yxs+4E/DvN5MkpTbMt3p6Eal2WH4XfEOU8QB9dPeuHvBeo6A2YG+bkfUvcWAAjZi2YQ/pd7diPjRsJ7LSNk1/+l79yGLVln/QHF7/GO/SUcnIusc4iablFrLclfXfPwwzdNxHVOSEVVaBuf/L7dcZ1TnPmn3junuX7yoP2/37mXL7rr2hOX/5nbZ7Gr2FufNfPffOeeHN6y01YHea7Efl+cDFNHXH5XaYCfum0yrnMCS80N2/jd9+j6SLQpzjr//Pv5s9ygzv/xrl0sfbhee3i082O3TGL/hJswoUrt4fe4dauNu67Iqak0y2ZHW9i5MFLg8ltyffzSd8zEdU6I8Cw6xJ+8d1tcPiXa+YP37IIlp9IAvTPn8r/29u3h2UQxnSV5Hu2890AFN01FIpGJbYwsavrompqPj9x1LS43RsH8bwNwlFJ6nFLqAvg0gHdFZN4F4E/5vz8L4O1E2Ur7CkCw1d6KxPxLsPwBLLA3IVXyGWDpReC6e9SFNBnFKVaVMHDUhwmETjOS9qmSLn7rHbvC3wvU+UDW5OQLLb5LdYOh5TX5ZXYq4bp5S7FhqAeruxyZLDQLgQBQZOeMx1IshLDflKMGXEfWbbEzbkTpqdwmudaa60BcB9tsTbSjm8A4K91n8R2b6zoFJr8n3wYZdKCPjiR5Hu1M213YvUgfiZruqM7FOkpeG4XBStwuajvifVqoI+Ou8XQgiTBtoYNqRwQUO8GPZdD2kRpBAgl9lJIO3Fnsg0TtQmd3PNqpWx1k+hH5QpUxWo0dFYbtePQl7iF2xkttsvqr8QXipDbxsbAbF+PyKX10ha3ro+RU19ZcWh9FdWZp36y7osrbWaCyVWMXLNp5/RXTuNzIrC+yLnYAkF5LhTMAXp8kQykdEkJWAUwDWJKFCCH3ArgXAHbv3j2CpkmwZeYvFnxZuFWAiw4KqOQtXgI3lXARqH+T0wEAM16xJV+gUAXprYJ0m+yz7Hhe88PMYOXvBPNpHufy0v12vQGYuSY82RAI0y1CXm7f7DXAnjcDe98UfsdL6NBdYWsX8vWzReDAu4Gr3qbqVaixfusux437hu8P85gx+Wa8L695B/t7JFIAwPZIRHW+8m3AqYfVBbJA/kRc512vB3a8DtjxWkm+niw/uRfY9xZg73fodYj2kWUBN/0gsOdNenk7G9f5wLvYefU6+W5TTaUBwNV3sQ1Sih1FdJbbdMV3AbvfCExfmSwv2+r2W4AdB4Fdt8XlV88wchNlqVfdwe6j06GzDGy5Uf3bje8L30AnyzdPcLuIjJ3r3qm+xUzI99dYlC2OOfn/2zv7YLnq8o5/nvuW3RtKXiBEIAaixggiDfRKw0szDglWlAFbXyq+RRHpjDJS29LSocPYTv9opx3fRnQmA7apY9GKjqbUQTE4U/8RDeooGpQIsUZTAiS5vOUmueTpH7/zu/fs2bO7v9/unt2bc57PzM7d3fvsOc/v7Xue33PO+R3P2tfC0/vmVrbNLXO6DGs2wqpXN/rUrh+tfCWsughWXzL/XTLb4fmn3FPm0tuvLYV1b3D9NVsG349WrGv836velCv+7N/FIOiH+OdF8NknEYTYoKpbga0AU1NT/X2agU/7HD7UkPMHqHOE56mxZGTG3TxSX9ZiIzQ2eDZ6OfPCRlED15jHZ+c7drqDnboWLvtwsz24QZK1X/FyuPF7+fZ5wjmxGN77381lqC1x64ocP9YsVG/dlm///FNu0K7ITEc33ZZvP3PIHSzSES3ABe9wrzTe5sBjLvebnhWcdTG8557m7Xt7aI7Y3n9/xv7kjH2qfccWwZb/ai5DfakbsDPTzf3hjZ9utq8tcWsvjYzNP0bTs/HmfPujz7ib3rJtcN4fu1fWn1ZlOGM9XHdvZvtZ+0y67v07Gu2T2U5uvxsZhXd+ubkM9aVuPB0+2FxHV3202d73i4nJZvuLP5hvr8fdXeTpVBrAuivdK+sP5NfRinVw/beat9/KvrYErr+v0d6vReXHWrqORODa/8gpQ5s6eu0/5Nv76/8Lph/ivxdIhWWsAn7bwmaviIwBS4ADfdh3OD6ymj3ckPMHqMtRUOYfIdhO/Bsi/8ygbSWE4DpMNgWSR1P00sYXSJaQkPzopd0+8g4W7ewPPOoivNDtz8645StCtw+uDOlLT0PsobNPySV0uRFhu30c+hWg4WWemQYEVk2F2YNrh9g6Gp9sPEnYyR4i+kVkHT2336VAs5F8K/uZaTfjTs/k2tlD0i8i6yibSutoT/g+Yu0PPJo/C25lP/O0W2Z8pNiLMfux9e8Da0VkjYhMAG8DtmdstgNbkvdvBu7XQTynLE16Cp2J/N2KlcndotC+USdPyX/fCj8tPfhYWOP7DntwT+NNJK1ITirlRi+tqC2BA3vi7J970kWqMYPwwJ7wDu/tY7cPjScJ2/3G24f6NFdHgfaHD7lBvhDrKFioEvui6ujos/mznVb2EFFHPvLf05xKy2Os5k4yd1vm0APe9G+aU2nt7FE31gqmZ/FX1VngRuAbwC7gP1X1pyLy9yJydWJ2J3CKiOwG/hxouhy0cEZyxH9sPu0DzK1q2HXaJ49aSsxDhRZc5Bxi73/jp4qhg+TIdKS9Pxkb4JP3O5sXbbn9JfP2If742c6Raffb0YAJbD1V5lCfYuvohSMuVx9zkO+qjgLawM92jkw3p9La+VR0HYHrSyHbb6ijiLET2o9EGsdCqE9RdRQ71pIyzEx3tu2RfqR9UNWvA1/PfHdb6v0M8JZ+7KtrRlJFzaR9aknkv/iFEPFfijuFEZEOAJfze9H5ne19NBIqIn4f08wvWBbqE8QJTzf2MaIQun0/2wkVzkH4tNDqyO/DX5UWcnHdIOsoZux0Yx9TR8/tD0ulDcKnAYp/de7wTUeH2RO+4sR/0bEkem4n/iPJsq/+QRGdqKWuRoiJRiBe2NJ3WYbYh/o0qA4PYVFt+jcxB0iIaLdIn9JCWEQdJTcMBW8/vY9YewhPpXmK7hch9n62E+pPeh/dBBFFHPD8bOdw8Sd9qyP+eWmfVORfHx9ldG4616HjTy7vbkDFdrBBDPKY6XQ39iE++UvoIL6OYlJjof6k7UN96qlOA4TWz3ZC/UnvI7aOFgWm0gqf7UTWafo30WMtcvuhqTSL/BcAeWmfuZz/Ubeuz+GDbmGmTidZ68uLSzekfxPa4etdzhRCTiin7UP3EWufepxj4RFbrL1/wEeofeg+eukXRddRsBAOYrYTsf30PgrvRwFXpaXtQ3060XL+JwTtrvaRZDnnvGtx8zj/T1xOPoR0Dr9ooQrt8HMHi8iDS+g+GnLBERHV4QPxPgUPcl/mgCjb++PtQwZ5bB1NnOQOLNkFyDr5NE0XdRQp5rH9bqwWlkpL11HQbGfUzUK6ObcTHTgVVEfpcsak0kz8+8hIm5w/R+Yj/5BO+fs3hO9XxEUwzz8ZL86FR3iRwplelbAd/oahF47ElfkgC/AAWVAqzc92Qq//7sWnhVhHMX079OqdBp+KSgd2OTZDU2n+SjZL+/SRNlf7TEqyln9o5B9Lt7nXos8RdDNAQpdkGlROfsEcICNTaYP0aaHU0cRJ7oq00KvSBuHToNKHobMvf25nAHf5Vkf889I+Sc5/8cjRAYl/wSehijq4xJ5o9PtIP+Cj3z4VfnCJjGp9ei+m/yxYoSqoDfxsp74s/O7VhXYA63psRo4dS/v0kbyrfUZGYHQRJ3HMpX0eL0r8E/EsSniKnrqOTbh0T6i99yn00lNvH+PTQhMFL2yxdRSaSuvGp6IPeLHb978ZCZwZpfdR9AyyqAOqP7cTW0cm/n0kfat3erCN11m9WBhbtQQeXiBpn7nn0K5sbze3/YJzwX4fMXVTXxrZ4Qd04q2oqNb7FFOnvo6CU2kLrI7G6+7gFduPOq1vlfUpKpUWOxYiyxxbR3OzHRP/4eE7z/hk5kBQZ9NLfwd+71T45mxx4h+TAjnvTW51yvTj7dpxxnq3PPTZl4X7c/nfuuWbQ3nNX7vlj0O56E/dSqChnP9WV/ehwvCyzXDxjW7p3RBOO9fZv+yKMPvRcdj8EXjppjB7gI1/GTfIp65rXgK4Ha/8I0DD++iajbDhA26J6xCWnQ2X3uSW3Q5l80cal4buxKU3hQs5uGdon74+3P6cq9xJ9JMDx87qDe5xrWdd0tkWXEC28Wb3zI9QLr8VVpzT2c6zZqO7M7tgZNDrq4UyNTWlO3fu7N8Gn/gF3P5qF1XfvHv++09e4AbHptvg46+Cqz8FF76rf/sF+NFd8LOvwtu/2N/tGoZhZBCRB1W149Ky1Yn8fbTv8/2esTocO+xO9kIxkf/6a93LMAxjgVC9q33STwMCl7csWvwNwzAWGNURf3+FQTbyN/E3DKOCVEj8kwxXnvjPmvgbhlEtqiP+oy3Ef6yWifwDr8gxDMM4gamO+I+0yvlPzot/6FrvhmEYJzgVEv9WaZ9U5G8pH8MwKkJ1xH+01QlfH/kfMvE3DKMyVEf8R0bh5VfC6sydfGO1+RO+Jv6GYVSE6tzkBfD2LzR/Nz4Jx2fh2f2wYt3gfTIMwxgCPUX+IrJcRO4TkUeSv7mhs4jcKyKHROSeXvZXCP4E7zP7LPI3DKMy9Jr2uQXYoaprgR3J5zz+Gejzgjl9Yrzm/h59Nm4VSsMwjBOYXsX/GmBb8n4bkLtMpKruAJ7pcV/FkF7e2SJ/wzAqQq/iv1JV9wEkf0/r3aUBM1abf2/ibxhGReh4wldEvgW8KOdft/bbGRG5AbgBYPXq1f3efD4W+RuGUUE6ir+qbm71PxF5XEROV9V9InI6sL8XZ1R1K7AV3Hr+vWwrmHGL/A3DqB69pn22A1uS91uAr/W4vcFjkb9hGBWkV/H/R+AKEXkEuCL5jIhMicgd3khEvgN8CdgkIntF5A973G//sJy/YRgVpKebvFT1KaDpIaequhO4PvX5D3rZT6FY5G8YRgWpzvIOrfA5/9GJxgOBYRhGiTHx94JfXwYiw/XFMAxjQJj4+5y/pXwMw6gQJv4m/oZhVBAT/5ERdwAw8TcMo0KY+INb2bNmz+41DKM6VGs9/1Zsug1WnjdsLwzDMAaGiT/A1HXD9sAwDGOgWNrHMAyjgpj4G4ZhVBATf8MwjApi4m8YhlFBTPwNwzAqiIm/YRhGBTHxNwzDqCAm/oZhGBVEVAfzqNxYROQJ4Fc9bOJU4Mk+uXOiULUyV628YGWuCr2U+SxVXdHJaMGKf6+IyE5VnRq2H4OkamWuWnnBylwVBlFmS/sYhmFUEBN/wzCMClJm8d86bAeGQNXKXLXygpW5KhRe5tLm/A3DMIzWlDnyNwzDMFpQOvEXkdeJyM9FV+ya6wAAA3dJREFUZLeI3DJsf4pARF4sIt8WkV0i8lMRuSn5frmI3CcijyR/S/dsShEZFZEfisg9yec1IvJAUuYvisjEsH3sJyKyVETuFpGHk/a+uOztLCIfTvr1QyJyl4jUytbOIvJZEdkvIg+lvsttV3F8MtG0H4vIhf3woVTiLyKjwO3AlcC5wLUicu5wvSqEWeAvVPUcYAPwwaSctwA7VHUtsCP5XDZuAnalPv8T8LGkzAeB9w3Fq+L4BHCvqr4C+F1c2UvbziJyJvAhYEpVzwNGgbdRvnb+N+B1me9ateuVwNrkdQPwmX44UCrxBy4Cdqvqo6p6FPgCcM2Qfeo7qrpPVX+QvH8GJwhn4sq6LTHbBrxxOB4Wg4isAt4A3JF8FuBy4O7EpFRlFpGTgY3AnQCqelRVD1HydsY9YbAuImPAJLCPkrWzqv4PcCDzdat2vQb4d3V8F1gqIqf36kPZxP9M4Nepz3uT70qLiJwNXAA8AKxU1X3gDhDAacPzrBA+DvwVcDz5fApwSFVnk89la++XAE8A/5qkuu4QkcWUuJ1V9TfAvwD/ixP9aeBByt3OnlbtWoiulU38Jee70l7OJCInAV8G/kxVnx62P0UiIlcB+1X1wfTXOaZlau8x4ELgM6p6AfAcJUrx5JHkua8B1gBnAItxaY8sZWrnThTSz8sm/nuBF6c+rwJ+OyRfCkVExnHC/3lV/Ury9eN+Opj83T8s/wrgUuBqEdmDS+ddjpsJLE3SA1C+9t4L7FXVB5LPd+MOBmVu583AY6r6hKoeA74CXEK529nTql0L0bWyif/3gbXJlQETuBNF24fsU99Jct13ArtU9aOpf20HtiTvtwBfG7RvRaGqf6Oqq1T1bFy73q+q7wC+Dbw5MStbmf8P+LWIrEu+2gT8jBK3My7ds0FEJpN+7stc2nZO0apdtwPvTq762QBM+/RQT6hqqV7A64FfAL8Ebh22PwWV8TLctO/HwI+S1+txOfAdwCPJ3+XD9rWg8r8GuCd5/xLge8Bu4EvAomH71+eyrgd2Jm39VWBZ2dsZ+DvgYeAh4HPAorK1M3AX7pzGMVxk/75W7YpL+9yeaNpPcFdC9eyD3eFrGIZRQcqW9jEMwzACMPE3DMOoICb+hmEYFcTE3zAMo4KY+BuGYVQQE3/DMIwKYuJvGIZRQUz8DcMwKsj/A0qKjJwYsaZhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "n_models = 4\n",
    "models = [make_model() for _ in range(n_models)]\n",
    "\n",
    "offset = .1\n",
    "\n",
    "for _ in range(2):\n",
    "  x = []\n",
    "  x.append(np.random.uniform(size=(1, DIM)))\n",
    "  for i in range(100):\n",
    "    new_x = models[i % n_models].predict(x[-1])\n",
    "    new_x += offset\n",
    "    x.append(new_x)\n",
    "\n",
    "  plt.figure()\n",
    "  plt.plot([e[0][0] for e in x])\n",
    "  plt.plot([e[0][1] for e in x])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "tXjCfO6AKyRj"
   },
   "source": [
    "## Next\n",
    "\n",
    "- Is a trained net also an attractor?\n",
    "- How do trained or random density nets behave?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "autoexec": {
      "startup": false,
      "wait_interval": 0
     }
    },
    "colab_type": "code",
    "id": "w4SRxuKdK4Gg"
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "accelerator": "GPU",
  "colab": {
   "collapsed_sections": [],
   "default_view": {},
   "name": "fixpoint.ipynb",
   "provenance": [],
   "toc_visible": true,
   "version": "0.3.2",
   "views": {}
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}