4B. Receptive fields.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "73e9ab10",
   "metadata": {},
   "outputs": [],
   "source": [
    "#default_exp receptive_fields"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e325bc2c",
   "metadata": {},
   "outputs": [],
   "source": [
    "#hide\n",
    "#skip\n",
    "! [ -e /content ] && pip install -Uqq fastai fastcore imageio imageio-ffmpeg Pillow==9.0.0 # upgrade fastai on colab"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "baa2acee",
   "metadata": {},
   "source": [
    "# Investigate ResNet receptive fields"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e3a3852f",
   "metadata": {},
   "outputs": [],
   "source": [
    "#exporti\n",
    "from fastai.vision.all import *\n",
    "import imageio"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db787ada",
   "metadata": {},
   "source": [
    "## Prepare the network\n",
    "\n",
    "We load a standard ResNet18 and drop the clasiffication head."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fc2ae874",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Sequential(\n",
       "  (0): Conv2d(3, 64, kernel_size=(7, 7), stride=(2, 2), padding=(3, 3), bias=False)\n",
       "  (1): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "  (2): ReLU(inplace=True)\n",
       "  (3): MaxPool2d(kernel_size=3, stride=2, padding=1, dilation=1, ceil_mode=False)\n",
       "  (4): Sequential(\n",
       "    (0): BasicBlock(\n",
       "      (conv1): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (relu): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "    )\n",
       "    (1): BasicBlock(\n",
       "      (conv1): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (relu): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(64, 64, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(64, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "    )\n",
       "  )\n",
       "  (5): Sequential(\n",
       "    (0): BasicBlock(\n",
       "      (conv1): Conv2d(64, 128, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (relu): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(128, 128, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (downsample): Sequential(\n",
       "        (0): Conv2d(64, 128, kernel_size=(1, 1), stride=(2, 2), bias=False)\n",
       "        (1): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      )\n",
       "    )\n",
       "    (1): BasicBlock(\n",
       "      (conv1): Conv2d(128, 128, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (relu): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(128, 128, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(128, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "    )\n",
       "  )\n",
       "  (6): Sequential(\n",
       "    (0): BasicBlock(\n",
       "      (conv1): Conv2d(128, 256, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (relu): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(256, 256, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (downsample): Sequential(\n",
       "        (0): Conv2d(128, 256, kernel_size=(1, 1), stride=(2, 2), bias=False)\n",
       "        (1): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      )\n",
       "    )\n",
       "    (1): BasicBlock(\n",
       "      (conv1): Conv2d(256, 256, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (relu): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(256, 256, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(256, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "    )\n",
       "  )\n",
       "  (7): Sequential(\n",
       "    (0): BasicBlock(\n",
       "      (conv1): Conv2d(256, 512, kernel_size=(3, 3), stride=(2, 2), padding=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (relu): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(512, 512, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (downsample): Sequential(\n",
       "        (0): Conv2d(256, 512, kernel_size=(1, 1), stride=(2, 2), bias=False)\n",
       "        (1): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      )\n",
       "    )\n",
       "    (1): BasicBlock(\n",
       "      (conv1): Conv2d(512, 512, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn1): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "      (relu): ReLU(inplace=True)\n",
       "      (conv2): Conv2d(512, 512, kernel_size=(3, 3), stride=(1, 1), padding=(1, 1), bias=False)\n",
       "      (bn2): BatchNorm2d(512, eps=1e-05, momentum=0.1, affine=True, track_running_stats=True)\n",
       "    )\n",
       "  )\n",
       ")"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = nn.Sequential(*list(resnet18().children())[:-2]) # drop the pooling and linear layers\n",
    "model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f77e34d4",
   "metadata": {},
   "source": [
    "We then convert the network to a linear model to make the receptive field calculations easier. This will shows us the biggest possible receptive field for a neuron. In a fully trained network most of neurons will focus on smaller areas as determined by their weights.\n",
    "\n",
    "We set all the weights to a small positive number, clear out all the biases and pacify the batchnorm layers. This means every positive value in the input tensor will be linearly multiplied and added up in each layer and will turn up in the output feature map."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f5cbdb44",
   "metadata": {},
   "outputs": [],
   "source": [
    "# based on: https://learnopencv.com/cnn-receptive-field-computation-using-backprop/\n",
    "for module in model.modules():\n",
    "    # skip errors on container modules, like nn.Sequential\n",
    "    try:\n",
    "        # Make all convolution weights equal.\n",
    "        # Set all biases to zero.\n",
    "        nn.init.constant_(module.weight, 0.05)\n",
    "        nn.init.zeros_(module.bias)\n",
    "\n",
    "        # Set BatchNorm means to zeros, \n",
    "        # variances - to 1.\n",
    "        nn.init.zeros_(module.running_mean)\n",
    "        nn.init.ones_(module.running_var)\n",
    "    except:\n",
    "        pass\n",
    "    \n",
    "    # Freeze the BatchNorm stats. \n",
    "    if isinstance(module, torch.nn.modules.BatchNorm2d):\n",
    "        module.eval()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "447842d6",
   "metadata": {},
   "source": [
    "A helper function for rendering:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "072a97c9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def torch2img(x, vmin=0, vmax=None, color=(255,255,255), size=(224*2,224*2)):\n",
    "    \"\"\"Converts a torch tensor to a PIL image of size `size` while mapping\n",
    "       values from `vmin` to `vmax` to colors from black to `color` (RGB\n",
    "       or grayscale).\"\"\"\n",
    "    if vmax is None:\n",
    "        vmax = x.max()\n",
    "    vmax = vmax - vmin\n",
    "    x = (x - vmin) / vmax\n",
    "    if len(color) > 1:\n",
    "        x = x[:,:,None]\n",
    "    x = x * torch.tensor(color)\n",
    "    return Image.fromarray(x.detach().numpy().astype(np.uint8)).resize(size, Image.NEAREST)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f786667",
   "metadata": {},
   "source": [
    "## Calculate the receptive fields\n",
    "\n",
    "Let's calculate some receptive fields for a few output activations (14x14) of the penultimate convolutional block:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6b8f0bea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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60Epc14Oif+ZtPFuXrxqk9ww/UC5/JZdEtgpo1nWGHyiNw+/hB6p0oMoPlP/QrQOl62orYD/TfrrOH1R8WV2qYtnyvfShXoEaY0xPVopbBjjopTj4FPmBnq6wl5+9vndmXTAcARj+IuVtnzQAhr/yAgB4aCZv+AL+ngfijSrfAMBLBgCGPz/z6aHf5PZv1QCGlA+9Ur6ZOw2AwftJhyj0idVoDKB417wOMS63eOd8vBg3abxp8ngR/pVcfwMAg3cLv1HWUSq/0XGub421ZNIPY+F/Wgn95ijXw7b+nny94e/5dtZ7AsDgzeT7Gf35ehJGKr1n9OerhB8o6z2nFYCCxmFTVwCKF+U+oXgB6z0BADcLP9Bl88VzfCp0oxGn4SP1oRFX5ZX+dNnyHFf60G4d67I+p4vrQNXZrRm8AjXGmJ54AjXGmJ54AjXGmJ54AjXGmJ54AjXGmJ7s6UAf3dfQNVdIELVVA2jCpfHcvswsfCGb8fZc8fDfxH/aBoCLMzrQUfh7kk4wdJ0Xyfezu3xTAyhnVKjN0yX29twPlA8dKOtDw/eT/UPDv7ISPp6j3K8z0Wmer7C3587xRDe6Gn6dFL8QeeHz8g35V8Y9qr5JfqMXaqT+pOE3+vX54u11jefL12fKjvKqfxrW254X/p6hA+XyF2ukfqPh+1mSDvRyDSRZ2mPMJz6emw2Q+YGGDpR8aff8QGmzdix8PyfX1A+U+kfGm5lP4fJMd3mlP122POtVl813v2z5a+srCsArUGOM6U2rAy1mdKDDj5GO8myJPb3n7PmZ6htjAMNfmNeBVn+/i6sZ25+a0YGG4/eLF9Z7rneWf/EAwPAz+62tIk99ovcM/0rOew6kOsfpOI8j1y2GnnFAOs26AIDBT1A89JVcz2Oi/MMAMHg3xR8FgMG7FtV7Ng9NARTv5fYIHajwJ42zN6p8we0MH1LWhz40Qar3rIQO9LEpgOKNJCCsSgDF63MBYfHjQu/5Svb3FL6fkf/9JaI860CVH+gWgEwHut3k8ZHwCR0J3ehE6EMnop5pZ3lVP9dzbeOqPcvqXpWeVC0aF9eBzqxYvQI1xpie8GmAa8yn/7fdq/+u/mEX2cml+B1z5dfmne2rv9sFMPgMOcn/9S6A4c/Px40x5vuJV6DGGNMTT6DGGNMTT6DGGNOTldYD8cl9sVY12p0vtdVgT1XXagYB7Oklq2a+fPNkCaD6/Hy8fmoKZP6MT5QAqr+h8k9Okeocny4BVP8ofD9Z9xd6z/mPRXOiBFBz/Z3+nkm+8tB1Pkz1h36T/TQjj/kjnMc8/DpFPVz/qvADjfY8MB/H+Rp7nk8Hyit/0nNL+pmeE/2zrL/nqvD3DL1nNf8fNJcrINFLyvzvMeZZX7kldJ2h9+QRNBY+oTGi5uXR2g80Wkiy3TZO47ltCOtV2ytdWB8a5YuF6+/+3MV1qVVn/YvX0x1nroM+1CtQY4zpyUqo1YrbZvxAKa93rCAir3r98P66oC4mSHWX4Rf5yfl4rE0Sv85tUX7aABjeSbvw27sAhpSvPNaegw+R3jPqZx/M8ANlP83dMYCC9JhtvnLOSx7+lW9hPSNw0Gu1jUc7Od6I8lNRf5R/G8WnQKqjbKZIdaZTACjesaQ/KZcPfSjXPxbtjP55i+ifN3H5KYDidpKORHteR/G6BFC8cl4Q2ET5l1M8/D1Z71nWAIoXc/73Ah1+oKwDjRXN81kHKuLxSjY/nPd0oEo3ung81rwsZonyz6fVVRuneuIsH/uf7naW57jSt+7WwPI6WaUbZX1oTGmL54W3DtQYYw6PJ1BjjOmJJ1BjjOmJJ1BjjOmJJ1BjjOlJEXtnxctmPJMoW2Hskhe3DQHg4r6MKnbnZ3fw2/jJEkDxBoofL5HtojbPiniUp93VtvzrqJ0nK2TuO5HHHK+i3dKzFdLd2HMivircelZrAMWPUfxSjTSb41pneY5H+ZctHL9YAyhersqL63oFxS+Kfjgvykc9qn7VTu6fiHM/R//cSrvhlyNO5TfEbvim2DVWrkg7NZDtDqvd3n5ZMzkeCsels2CqekRctZPjy5bvF1+2fxbP4qncmFo9LMWdldMYY64fK+0KdGaVN3gP6ftWawCDj/0IgObojA70wSmAAekx66ZB6r85wNV6DsQj3/edFA8/zY9QXOVzb8bI9J7VVORJh/CjLIWeMfw6WadZTZHqNJ+aAijeREuIoyWAgvSPeKoEMLiD6jk6Rao/fUrEj0wBDN5B1xv18PU+0iD1Mz0CpP0Q+lMuH/3Des+HRX8eKZHmeQ/fT4pH/7RvQhx/LS85gEwHWscbEq+sLwgdaN0AKMiXNk46JTpQtfINP1Be+ap46ECX1V1yPJI2vEjoTzke7bklL59c76Z4A4j4LRS/IuJb6o0BeTzamehqQ086H27fGHglO+7UhzIzK1OvQI0xpieeQI0xpieeQI0xpieeQI0xpieeQI0xpicrsWMVzphBknc78mJfqYGDOtDwqfw6lT9RAai/SvnBT5VI/R/Dr/OrFD8Zfp0crwDUZKDYnK4A1NPcx1P6ZnL94Uf5qPDrZL/LSzWA+gkqf6kGkgtu40/m8cQHs7N+5ZsZe/FJ+9lvVF3vqipfYW/P/UBc+Z9Gex6n64320Ae0+dyfZt/P6E+qfyMX7LUjlv8YY56NQtv87/QfjACgYXMe5QfKDp5B6Bl3KB56xnl7273yrE9U5bvrIZvftjzHVflpA6DZyf1PsziWLC/6p7v9fL3xDZ1Qx3X7pTL2AzXGmOvHSpy7mD1VUpBOEJcqAMP3/wiA+tj8umDwTtIbjifI9KStvvI9VH6nycu3fp3z8WqnRuZHGU88bn+xK3w8Q3/KOsTwM6X847H25BNWmERecoo3Il5O83qa/AQXyhKpnhSho+TrCl0qtR8AMHhbfl2JPjTKK50s6z1DH5r0c5O3J/xDRfuT/O+N0HtOGwDFaygeCzg+MVUKP9BG6ECriPMJqAKpnrEWOsdwwmfdZegclU5T6B8T3eVW1+cm13VFxNfFSbD1BunJMXWC7nLnSTyu/7LwXe08aVa8ML8uqbedn372chMM2b9VLEFnXl28AjXGmJ54AjXGmJ54AjXGmJ54AjXGmJ54AjXGmJ4UrWfJjNMM746Fi0nsZrY7XACu7r7xLme42rCvaMQ5S+I5Uf58p1+n+lzeDVR+nWtiF3JN7B6ud+4Scj2xS6hcfJL6xS7n5fAhpetVu6WXhE+o2i1V/qEXRT2rneVV/ys/U+UH+tKFd2NVXO3GKj/QnV5+oCrO2SInIj4W9ajyk87yHB93ZuVMsoEumWVz2fIqK+euaGcbnw+38cV9Widitz10pryYJMV6i7NyGmPM4VmJ+XvWRZz1j/EkDz/H1t0dwJ4mNNED1gAwIJ1m6+9JecZbPSaXjwfDsjpE9usshb+k0l1WQof4TDjnk96wFvUcrwAUr6fyx0LXSTrWcNrnz30aAIq3Ujz6n31IHxf5358U9+vRCYDBu0if+7jwD31YlH9smtcf5bk9UT/nfz/S6QdKmQjizFKiDz0JdPiB8hvMeZFx4AKQvxl0OuTzm8dGp56RyyufzQ3x5rGh3mDEG8MlEY83Bn4jVJkLzotMEOfFG+fZzjdOzmhwrjOjAffbWoVUD7teA9nKd1P4hCod6MzK1CtQY4zpiSdQY4zpiSdQY4zpiSdQY4zpiSdQY4zpSdF6k8zs9LGeMXRkocc8oANd79QJ8u7bmthlU7t1Ks94qw9dOJ94d972RAcqdmNDp6l0oLz7Gbui7OLT6jEX1nWude6iLtv/Ks/74ruuahdV3S+l272odr0775fadVW73ktkzRR6xq0ldYs7Yrc3nCtVtkhVfnHd5ahT38puTyq+2SDd/d8W/XmlU0WgsnKqLJ7KXSnJHir6batTN8r60JGzchpjzPedlTjnMPv0SHwVtxpc9aM8P2OGF36Ltyl/TKonfCfJH7P13+R4+Day7jJORvHnhm/m6yg+niLVCUb90l+S6gm952vF53IcZd7OSvTPcSDVgcbnsi4ydKDsv9kI/eZRINVjhm6X9bmR5531uRWQ5oV/RNRfqbzwQKrbDR0uxcPDP7vvYjwcL5HqE8PXVZ2I4zeDSpxwUyfZGqHH7H6DWfakmXojUSf0qB8QbyrcP2cqAMVtVP4MkOpwTwBAcTv1/ynxvYj7wvWHbvfVef14FV3vWXG/lK9rvKm8IPdvBcmyk2QMbXz/n16BGmNMTzyBGmNMTzyBGmNMTzyBGmNMTzyBGmNMT1ba3NarM3vrnBd+0gAoQj23s//XyALIWbBb3dajFN+osbfnfiB+ucbenvuBeLincHsizuWjhVx/lK8oz3i0cyrinM89siqWovyzIs6fuyHynm80+edG+5/I86TXlNg+dofDYymJc171yPP+MMUjzzulT2/jDy1cXuWdj7zwfB/XaqD1yjoQvyT6P/rzhIhTe0JVEnu1SZwvYLfZbxXHOS/8qAHQXKY93IhTc8KXs816n9QjPvcSxSOv/cU83z0uzJdvv79sQhTxMxSP8Xya4vG9OCX6n2w12/JczxW6opn2FOfpD+o+Rv9wuvcRcHXPfZbwA62pI1S++Bm8AjXGmJ6shAve7KkA1pHFyYpWzzX73DsPpLqteLApXSTHKxFvOsurPOAcr0Q70dl+rid0cMp3UungOB46OMqH3saF/jHRY0ac9ZWPTgEM3se6zimAwbvJx/O7EwCDD8zHm4emAIr3UD33TQAM3k/lH5wCKFgfGuXfQ58bPqHsH/rgBKmO9YjwaT0CAMUbhO8q63nD15Xue3O6AgDWV54VJ7hWxUmqVSA9IXZJ6DrjBN0rhc5U6Tp5fJ6P72l+XQXprHFa+NhG/9wh/GpZj/yE8Jl9agpgQOM8fGCLtwi/V27nE1N0fI/oRFwdcXUijk9Gxfs3nyjbdF54Y4y5bngCNcaYnngCNcaYnngCNcaYnngCNcaYnhSIra1ZTz32E5wCaLMPNrszO1M7DTr8/pbNMsjllW+gym642elXyOW3evkbqvaw+86VcOUR7ju8S3hZ+Hte7PT3VK5CapeW3Hfq0yWAAblYtbvPvFt9skK62yt8QutTJYDBq6n+cxUAvIKu97S4rgud/qHKtYizZl7qyiO/tB+l8hXl+I7w69xuAOCWPJ58vzaFC5SKrwv/WZXds939V7604r7w/brY6efL6oJV4XrVfX+p39o4f69Df8p55EP3ylk5SVHe4qycxhhzeFZaH+aZFah0pI8nxsaMI32cwaAnQ3tGiFZSRfynFG9PAnD5SpSf5OXDb5R1fG17KF7EA4aetFEPr6Ta/2px3esZoQMNfeubcv1d4u+JKVIdaPh7sq6zmQAYvI90mg9PAQx+cj4e+tnBh6ie0G9+cN5Cva7HAAYfpvh3xnn94TdKOtP6/glS3WgZeec5vzwADEg/2PqHsj7xSZFHvhK+sSdyXWFT5+NhLzOC8KNUGRYWzqseZ4eS8RZ6ZPY/PdOp62TdpRpvR6cABu+k+3VUjMO4L6wXfhRIfWYfANL7G+Xfwn61kzx+dIr0PtZTpD6nJyJDBK1MS+Fsz2fYgpmzc16BGmNMTzyBGmNMTzyBGmNMTzyBGmNMTzyBGmNMT4p2F/55MztQnLc6dqNil2rW/XM8E59F5a1W8e1eurnFy+90llc6vuuny9vozAuvsj8urgM9n+s3Wx2ocCHi3eo2OyPpSaUO9Ey+m9ycEnrSsxUAsAuR0oGeX1InGP3GWTCVDlTlkV9WB7op8q1vi/iWyMO+1alXTXTHERfjivXFl0V2z8jWyaqD1U7dMd/386K80Au35ZVulO/7RaHXXhOuS+Gry/PVptCBkhNxi3WgxhhzeFbaKXRGnZ8o+6czea63Zxzp46QNPwFqsfKCiFfiidqIlUUt4hAruEY8gZXfIjp1eXzC5zSQ+hjGSor9K0N/x36Xx4TvZ/h7sl9nxMmXs9Vvfox0mhH/KJW/ewxg8Kmb5+PfHOf1fCXKU/zrYwCDj3L5UV7PtybIdKNtPeK6CvY/jet6O+lDwz+UdZER5/v1TKd/qPLZ5JNXcbKL6pErtajndhpXZ4FURxx+l6SLjLjUdb5X6DpZR/zgBMDwQ3S/Hsp9YOt7YlzxeIv7SPEYVx+mer4zSdtT3TNGqht9aApgQN+v0KUmeecjBwTPD5HXnt4kkhwEgXWgxhhzeDyBGmNMTzyBGmNMTzyBGmNMTzyBGmNMT4p2Cp3d4HqecCWJrHXTGW1UaEI5m91IuJuMZuo5EA99Fs3mI1H/sjpTpffcFfFuf0aly+PdvVApKB9D1j9eEnrP8xWAAbk9tfo43h0OnSbtPjeRhZFcfJpn8myLzfE8m2Pz9BRA8ab5XdEmsjbSbnLzVO4S1BzPs6423bve1D/1yTKNS/3g+V7+oUrPy3pD5W/b009W6DfZr/PSklk8hduTUgW0Ol/2jT0u7u/J3PWqvb+kLmjLc3uOCx3xmQpIXNnadnK/heqG5ofoT5CJ2Kzi6ADT/X96BWqMMT3Z04HeNDMr88qxBIDiRQWAZjQTjzzsLxC6Tnb2Dv0mncRoqiKPhw8j61IrEY/28BNe6Uy7daO0osGq8GcEkPozxgkc9v2E0IFGnnfW5T2c521v86ez/g5jAINPsP4OAIak96y+NAIw/Nnnz8e/OgIw/DSVrxsAw58T9XyS4tVuXs9XRwAGH6F2lk0e/9YYWX750CkrPePgDtIJlp3+oawfrPOVe+sfSitlHAeyk12tXlj5kLJeNd4kuJ1PqTzsJVK95CNAprdtHpkCGHxQ6DpZt3uviN8FpOPq7hGA4cd5/IwADD5J9dyNvD3VGOn4v2cCoODv0XSMVH/9eIl05T5pkJ5AmwpD0Kl1oMYYc2g8gRpjTE88gRpjTE88gRpjTE88gRpjTE8KxFb27IYh++LF9nbs1M944bWuJDfxrr2Ix+4V60wnIt5dnvM7q3jkd2ad6bhTN8o60B3hB7rVqePjXf5uHZ/wSUzytp8TPp5KB3pS6PVCl6d0nVz+6TyraFuP0o2qz1U6QdaBnhLuR0oHGv3Dvqsqv/ya0G9eqvL4Rqeuk8tfEXGVn31djJ9LneOH++FChdQdSumITwn97ymh31Tj5IQof0yME6ULflboQ09XQJJtt9Wxcn+GioZdl1odKOu+hRvTZP+fXoEaY0xPVtoV6OyqM3GkL4DMkT7+4+SkEPbLMxyPKpMTQSIeek+1ElRPeOXgrXxC2Q80nmBK38d6vZMVUr3eE1OkeduPlkj9Fu+fINV13jdBqrv8ygjA8BeFrvPnKf73uwCGvzofr/9xBGD4C/Px8nM7AFZ+9QXz9fzDLoDBZ6g9n0NaT/WPu3n7/17E7xoh0wPiq0Dab98ROsHwqeT4Y1Ok+sEjQKrnPZafvIJYoeN4/maAY1MABY2T1jeWx8/jU6S6zsfF+Lmva/wM7qT418YAhj9P/R/xn6H4fx0BGP4SjZ8vjgAMfpbK/91uXv8XRgCG1J7qvwg/2fCxffd8/1QR5357aILUj/XxKdI3iVKcRJpYB2qMMYfGE6gxxvTEE6gxxvTEE6gxxvTEE6gxxvRkTwc6O5Gy2VBsOsVOfTWzMxVmJbnZ0LXQhy6rA5126kDJNar1G1X54skXstWBKn0f57PeEHm3L4rsnrHLr3R5rLs8lWf9bHV2b8vjA8rm2O7qvpPVAiLL4yMTAIN3iiyPbyH3o3D9EWqEpP2PC53pMaEPfbpTN0r+mPWpTv9Q1g9eEK5dyid0TZRfF3rPi53+sMLfcwl/2O7xw/pNoQpox88dYvxwttRwh2I3rMfEeHhS6IUf79QR8676MxUAsE72rMgXf6ECMjXRFaEDHe//0ytQY4zpycpCJ5FiIo4FRzn7V7GibE8u0ac1M/Uk9Qt9KD8ZonxygghIff0a4TReAOmKAMIP9GK+Qmx1oKwfPCF8P0OvR3m6m3gyf5j0boXw9/zWBKkv5z8JXV7Ef3k+Hv08/Bfzuk58fhfA8NcpXjUAhr9J8b/ayeuf7iDTmeJvAGDA7Z/sAhiyfjB0guQTWo13kfqHRv5x8glt/UN5xd0AHf6hFG/9Q/m+17nDf6sb5XqaJf09HwYyHWjrG8v98O3O8cO6zi8AmW63/kI+rsK3N7m/oef9JRonpRgnfwcAA27PBACGn6b7HjpT1r2OxgAKvr/lBOmbX7yJ8pvlROhAx9aBGmPMofEEaowxPfEEaowxPfEEaowxPfEEaowxPdnbmJ6dSHlSbWbisxtTtSgfcdaTKt1o1Vmed/O7daZKT8q7+eHrp/LLsx/orsgLv7mkDnRNZPdUOtAzQu95Uuj7lA70aaHrPCp0fEeFiuDRCYDBO2j388gUwOCtQvcnPjdp/+P57rbUgar4SZFHPnSgrK9UeeSVDnRNuHxdEnrPy531sG5xrdPfc3Ed6Ole44fuYzt+WEcc7mI8TiLO5Y+I8aB0wUfDP1Tcd/YJVTrQ+B7x99c6UGOM+f6zpwOdnXzVCjT0oTVpo9RJJNaTRkXK8V6tHPlkEYSTfOSsp/zy4SuanBjZbJD6gV4SK8TQgZLDNk7lT2w8WyHzK4wVGesZWx0f5dGuvzEGMPxn5Kd5t/D9/PtdACu//cI0PvwN0uX92TaAlX/7orlw+Rc7AFZ+e758+UcAsPJ78/WXf7YDYIXqL/94C8CQ2oO/2EnbX/7ZNjK9Yesj+YncX3Lw8dzXMvFdvbtBpsOtvztBujJ6YIJ0hRUr9zeLFRaXf1KcwInylO++PeFD7W/b81N0vQ8If8+7x0j9WL+W+7224+e3xPhhvfBntwEM/xXd39AFc/k/3QYwpPrxlztpe8qon31s/2EXwJB009V/3UXWn1XoYW+jN6TQe/KbxNQ6UGOMuW54AjXGmJ54AjXGmJ54AjXGmJ54AjXGmJ4Uc/93/t+zxGQ7K42a1YfOonSgy+pGI652+XnXvlsHytlAO3Wgie/njvB/3BB6vcsiz3vo+Dhf9jmRjzvyYtOubsSTXePHxa5u7Bqzj+eDE2SuNs0jUwAFqwjuE+UfmiJ1wYny3J7wFeVdabXrrXwhj3T6Rb564TzjZ0Se8TO5r2iz2pl3nsuvVQCKl4vyShcs2pmMkzMiP/szYvw8s+T4Ub6xDwq1wKPCNzayzL6H9cVCH/qAGCehI34d60anSPvtRAUA/P09UwLZ/LAhduF3vQtvjDGHZm/yXkQHqlaOi5ePOK80A+VUr/xG+eRAnBBIHOaB9ATCVgPtNI5XzceLVQAoSEeGk8Kp+xnh5/gIAAw+yPq+KVIdH4DM97P+yhgd/p6s9/z8LoCV3yGdZtUAWPld0nX+5+08PgGAlX9L8T/ZBrDyOxQfN/nn/mcg9ZHcbZBeVw0Ag0+TDnTUIM0jX+d55Otxg9RPs54AKPhE1mSC9KTWY0DqwF81AAZ0Eqx+Ank9cV3vEv6w3M5mAmDwUYp/B0j7oRkBGH6G/D2/LPxhayD3h91Bpg8ty20AK/+K7u+fAamOuB0PrCPeBjD8ZfrcGA+kC46TipwvvtoR93c6BlDcTifTdmoA4JNj42r+E2faE3gFaowxPfEEaowxPfEEaowxPfEEaowxPfEEaowxPck0n0oHGvFZaVT3brswUVpaB7q4PjQ2zZbQgXbmi2c/0MgLn7g6CT/QdaEDXa0ADFi/Fn6OrA89WQIoyFdR6kDDh5F3/8Pfk3V8D0+RuhOFTpOyWra6PC7/kND9RflEjSD8Qx8RPpKh72P9Y/hIcr89I/Sexytk+cTr0FGyTvOs0G+uCv/QcO1il6/w91T1cH7zGCesY4320G6y1IeeEONH6UCfEHrPGD/vEPdR6Tq5/EOi/ijPqoaon1UurQ6U+uGpEtn3ro7vEeu7z1VANj+sCx3oyLvwxhhzaDIdaPcKdJH4srrRg23ZR5046naYVzpQfvJsdfmBDl5DT/JYKdBJD5yskOr7jpXoyN/N/pXfnQAY/jTp+L4yAjD8FdLxfWmENG/7X+0AWPk35O8ZcdZ1/uE2gJX/ab589SfbAIb/jsr/X1t5+T/cBjDk+qM81xO6UdIbln+4hVSH+Fc7SPOG/yWQ9tsXdwEMPkT9HPnESYeLe4D0JNW9agUNpCem4v6SrrP1/UzeAAB9EmzwIaon2kN6z/reMYDhz5BvZowT0tu2ed65n/+yc/yQ72f5R1sAVv4HKv+n2wBW/jWV/3+2AKz8nihP47kdD78qxgPlu68+t4tM/4uvAdn3tx6PkZ0oqyflfA2BV6DGGHN4PIEaY0xPPIEaY0xPPIEaY0xPPIEaY0xP1M76YmW79Z6H37VX7k39dKDs+9ntB8p6z22RB3yjAVCQe1PrB0r6Ppyrkea/PtOVpzvR06l47N7yru5jUwDFe6n8dyZIs4SGfpNVBN+eABh8WPg8kj60+tYY2a5o88AUQMHt/07oSfNspgPqn7jepN+eFvniVfyUyCN/MtcVtj6eSjcqdJ2JT+i5Tl2waidfr4o/LfS/Ty05fh6dAihY73nfBMCQ1Q4PivFwzziv/8EpUjes+5QbVuiCqX8i/trcBzbJvhn9RvNA68rG2I3JGGMOD6/iljmJxDnlZ1lcB9p94kj5hHK++CmAdEUJAMUtvKLs8gPlFQfCD5Tzwp+okJ6ciRUin+RB1wpu+EnStTUAMPhn87o/fDHX94Uzf+LDGHneWZc3ATK9J/4YAFb+/bxebzraTOMltgAMySe02RF+o/U2gJXfpHZuN0j1rdUOMl/UuI+JDrQaIe3n3QbA4AO0YqrGAArSexbhH6r0m6wDnTZ5HMjrqYFsZYeon9tZj5H5YMabQdIPdZ7/Hf80AjD8NTF+fmvx8dMAGP4bGj8DINMFN7tNXk8jdMHbNfQ4Zz1stdUg1c+OG2RvfrXyBd4VJ5G8AjXGmMPjCdQYY3riCdQYY3riCdQYY3riCdQYY3qyjA708HV360MPny9e7dqXwr1p2ukHeiuVj1171pFdqZHq+1Re+PB5pOyebV54zut9vARQkG9j6wcq8mUnu/+R15tdgh7K9Z7Nw0L3d78oHzo+di26X/iKPizyfT8k4pH/nfWzj5dI9YDL5oU/XQHAKxbOCx86UPaBVXnhL3bWw3nhL9QAitccOi/8sxWAgrKEtvrixcfPEeEz+5DIC69cqUJf/G7hS6vGA6tcHp8iy5Lb+sOyDlflhT9bAiien+u4E+zGZIwxhyfTgSpYBzobn2XZleay+eLVilKdLBoBqR+o0oGqE0ThNE5P/tYPlHV/yg/0IeEHGjpQ9ruM/O/sBxo6UM7/Hno9ztsecdLrlX8ApP6ef7yNVAf6HzcB3PS/3DJfz+/nOtDyP24BWPn3FA+dKetAfx8AhhTHn+c60HK6A2D4s9Rv/yR0oF8InSDrKHMdaF2pFROQ3veHGqQrtSPI4w8B6cmcWJF9mNoZJ3k+xe0vkPVP9YURgBXy04z+Gf4G6Sv/XIyTvxB+sn+Q+4FW/0n4w/7fWwBW/vuF/WH/QOiC/2IHqQ50InSgXx0j1YGOxDwwtiO9McZcN5ZZgRpDfOl/3l9PNRduBVDcQ0/y8y8GUDzCuYNWABT3U3z1JgA4OgDw6f8wurYNNjcUX/7f99eJ7Xi4Lx8nOEpvhJeeBwBHaBV46WYAOFkA+ORvbF67xiZ4BWqMMT3xBGqMMT3xBGqMMT15LutAybxm+bzwALIsnuEHyrv2O0v6gYarE+v7foj8QL/6d7fu/2En911ts58m2VLz+9KqI55fAPjEx9f3P9d+oLPt/KHwA73rn168/4cFxsOBeHxP5z92L/68AsCdb720H7cfqDHG3Dhci114tdJUJZfOF08fEAaZyUoTQLbSjA9P/EDFirKoAeCV8/HiIgAUtFKIBPaDN9OT+Zl48tMKrpkgc2hv88KTPrSqGgAD0vch8n3/c9LxTRsAK6QPLQc7AFZ+h/R3owaZXi9Q/p4Rn91zb1ZrAMXL6EZWNVKdXVMDKH6Uy1dAu1IY/vLM1YX/I+lkY4U7ZD1gKfLC7zRIV9blBFle+GLUIHVEr4H05Ez4gXI8fF25ngrI9KfxfUnaGbpUfmOIvPDcD+GL+hkaP4MR5no4iPHDesxiB8DKb4vx89/Nl28aEd+ur9Yzq8H4HuOBThAVTQUA9L0uqhpo3ywHH9zvvVbvyXnhN2N80krffqDGGHP98ARqjDE98QRqjDE98QRqjDE98QRqjDE9uZ460MU/83rnhS9VFs9OP9BbFtaHxi4e6wHXa2S6wvCFlLo/yvrZhA7xDvIDPV4CGJBPaP3EFKnu74lO3R/rQx8RvpAP7Ov77vryvo4vducTvV7EWWfXlkcev7kA8IkPrO9/7tEpUr/LJ4QvpPL9PJ7rNOvw01S6To6HrpPVBRdzNUKzJsbJapdudMB+ptGe2xf2CT1RAijITzP8UpcYP0c7xw/rQx+d5uUf2q//rrtfst+eBcbDgfhoX++ZxG8qANz5xrX9z43vEX9/z1VApt5ZtxuTMcZcN66nG1N3fnlm8ZVmCWCZE0fhB3qr0IGS7qxdOXJe+FhB0EoHp+MJT/FnK6Q+ko8CqU/lg1MAA8oLX98NAEPKCx/+huwTis8DwJD0evi80IGGD+O/ozzv/3kbaf7u/xfY83M84LF0Mdd7YlXE4wZT/7f6vtCB/vrM1X0OAAafzv0fh5+i+JdHSPW20/2TMAf4DgAUrNMsJ0hXZI8BwIDue7vy4nriDYDjjwDA4D35ybGk/fdNkOaFjxNl3D9fyfPC118eIR0/nwOA4W+J8UPx8k+3kfqH/lnoRklP+of746o44KVUA8lJoaKu8ng4xrMOtJ7Rgc66qYbellbuoQ/lcdiMK6R4BWqMMYfHE6gxxvTEE6gxxvTEE6gxxvTEE6gxxvTkh0sH2i8vPOWDlnnhlQ5U5YXfEDrQCxWAAes9lQ408sKTu4/UgUb+d9rVbfN9827yg8L/MXw2WUUQu8Dh5/iFhf0cWQe6K/R94bsafqAfXp+7rkQHekTEl80Lf6YCgJcvnBe+1YEunBd+TehJVV741dxPNvLXJ9er8sJHP1D2UKkDVePn8c7xw3nhHw31AsXvn2BPN3rXV1+y354FxsOBeOsHKuLhB/qmfR2ozAt/pgQy9c6G3ZiMMea6cSPpQJfNF690oLzSjMSOifM8ABQvoSfYBpCtFFodKK8UAGRPfpwQT/jwheQn/MMTpPmsKwAYfoJ8Qu8GgAHlQ29CF/mLpO8DAAx/hfJr724DWKG822W9g9RXdHvfb3QhP0el42tqIPN5jA568QAHr669rjtJ57jVIPXHnAKpI3qsaGgl1Sgfz/ADvYP0nuHT+maKT0W8EfWU4nMxzdtZCj/TAZD2QwkAw09QvxUjdIwf0o3G93H4y/n4Gf4qla+bPL5d4+o4fGj/7n+P8UA67lbv+SLhB/qCAge/ZdVoDGBAOu56K9efNqNyvuXB7v4/vQI1xpieeAI1xpieeAI1xpieeAI1xpieeAI1xpieXM9deJWbU5XkJMwR562wiI/pA6KGXaooatikeqYN0uzPY+CqS+Asof86Qc2JXbwnpvPxKw329tYPxNdqANW3x/MVrdYA6mo+HjrE6r+M5uOnSgDVfPWtvq/8s+35+LFy/ypmCH1o+UdbFC8BlNvz/RP52cvfbwA0q/tDqIndyWq+31pdXiPi9Xx79srXAKq/3t/yjPzm1dbufPlnSgD1hOo5VWEvB+eB+JkKex5LB+LnKwA1javINlrXdH/XagD1lOKXauz10oH45bi/op4H83FS0w0O3Wj9DRon0f4ptf90BaD6B+q3kxWAakLxYyWA8rM0fp4W4ydG/p/Ml2/j21T+yBQAptsAcHFfY9D6eKrxUM+Pw2bc4OqeO8VjNpj9lrX3fYvqX6+BAx5LLSor5wxegRpjTE++vzrQRsQDlS9+cef5qXCej4DSgSYnixqkjuKXhQ70HJA5geN0BWBATuD1k/lJjzhRk+hA750AGNxJ+r5vFwCGpOOrvjBCpgOtvyDyyIf/I+lA8be7SHV81Q6AYehDj+73RqH8HNdEXu8oT/3f6gFvHeDg1VUYARh8hPpn0mDO+THi3xoDGLyL+jnKUx72GG6JfrOcAihIvxmvNsUbKf5ECaCgenCszOtpSqQ60KfKvJ0PA6kO9GGRL/7bYwAD0hHX35oAGP4MjZ9G+IfG+Pml+XjzuQapr+jfA8Dwl2hclTu4mo/+qRkd6Pr+fZ+lXXty/Mq+7+eBeMwzz5/XgcY7R/Ea+v6O9nXHB66L3mlaZt5RvAI1xpieXM8VqPlvgE//n/u/oFWf20W2wq0+u4NsJVv97S6ykzBtPRQ3P3x8+n+dGT9/twtgwCviGA+fppN4Xxwh83CovzRGdoLreuAVqDHG9MQTqDHG9MQTqDHG9OS54Ad6rfLFq7zw7AMYu2zk8hK7dQVlAQwdaJIfXO3mXxK7+ZHVknYJW//HN5HPo/KFjN3et+W+kAPKL9/6PHL+7ifDTUpkneTykTecs1RG3nDeZX5S+Hg+XiK93riu11L/PC3ipypkfqz1qRKpX2f4cnJ2xvPi/oYqg/0l14RPaGR7ZdefcPl6pRgnop2D1wo/WdUP3J+n1PiZIvWfPdY5fjjbaKgI2H3qsWXHQ6ff64/T9T5TAcArqD/PVki/vxcqIHNxu8LSdACtTjzwCtQYY3ryXNCB8kozVpTKeZ5XmhOx0iwAoKCVZgOxstiogcSxHE2DzPkcRYVUH1rHSo2ewEWn/yM7fmOCNL98+Dl+nHYtayDLOx8nPQY/Tbve1QjZrmg4zHMc0xGyvO1N+HV+ij53Gu1kf89dpNc1Fj6Y0Z53c/73CbKVeLFTI9d7Nkh9XcdTZJkC4j4Wr6MBOm3yeIO8nipfYYXOVLaTritQ/ZD0W9M5fijvfDt+SE/ajp9PifFD8Xb8cD3qczcbAIMPkY51DAADyphQbY6Rfr/iDZJXrNs1gIJ0pg2fTQqsAzXGmMPjCdQYY3riCdQYY3riCdQYY3riCdQYY3pyI+lAF8/i2U8Hyu5N3bv2lMe81X8lrk4iX/yW0P1tNAAKzj9+WeSRj/zj7CIT+kTW/Z3Od//DPzSJP5u7CjXHhU7w6SmA4k15nvHidmrPsc7PZT3j8RKpHlbpOk8LXed5oeu8kGcPbfWYL6YsrXFf+P5uiN3bdaHiuNJZjxonrD9t9aEizuMndKOvWVI3qsYPqQj0+BHlnxHx42I8RP2km45xzqqYdvzz/V2tART0/Y37m8wP5ITbMmPQ6hWoMcb05MbWgX6PlSZVVDWA9glNThwBAF7ETx4gXUFsipVjnCAifRkuAKnu74TwhYyTQnyi4zEgy2/exAmfDwp930dJN3cPAAxIH9rmnf8k6THvHgMYkm60KhsAQ9J1VgWQ6k9DH8qfCyDV90Ve9Q9SvBkDKMgfswh/Tz4ZFbrFJG97rKBzX85Ev1lFXPiB8omyCkjfGEJ3zPU0+QodJ/MTRK1/6FvFyR/uh9CfvpfciR4BgMEHaPzUMX4oHuOHdJrt+Lkzzzuf6Hy7xwOP57i/op3F2+l6x2OkPq1lvKnQ9zec7VkPTt7+LRPrQI0x5tB4AjXGmJ54AjXGmJ54AjXGmJ54AjXGmJ78IHSgiuutA2X3pmV37UP/xTrQHaED3e5ydSpeLvwiOX6xQrrbu5r7iu7pQCl+pkK2C9zq71jHd6JCh65T6UZvE+VZ93dS6PuO57rXVvfHu6hxvYv7e14QusvQe966pA6U/SU3RPlNoRu9ItoTfrKqnUoHqvqBVQEXOscP3/fu8cN64ZO5ekHqQE8Jf8/j+fiP9oD9dqOdyneV9N17OlDMQxntW6b7//QK1BhjevKDyMp5eB1oJeIBrzSjIk7yOC6A7MTRDpCuLLbESjPymNOTsAjd36uooTWQnQBp/6s3sK6wQeoE3kyR6eDavOfvFPq+9+Q+iYnfaCl8JHeFL2f4TnI94f9IOsRW70l526udcdd1sc9jtIdWxFF/cRsN8tEUaf+XuV9kvHnwyq4dh7QSbE+4UTzylfNJoVY3yp/b5CeFYjwk1xX6UNEPSb91jx+6L+34If/Ndvy8h8dP3HeK70R5MR5o3LbjgTMsRDtJJxv1J3re0G/SG0l7kpBPKE3ESaQZfahXoMYY0xNPoMYY0xNPoMYY0xNPoMYY0xNPoMYY05MfxC68EFeBt7xUyYiXIj6m/yxq3qV47KJuUT1lgz1V5gGmDYDmItUzBq6q0mYZNQCaisqHvuyp+QsInWC7hzsb32gA1A9O5uOXawD1dDwfX60BVN/keIUs12BzrgLQfJXaea7G3h73LPWZEjighmvrOVsBqHbm+y16hr1t2s8ltV34VNaT/Lq4PW18Ot+g0EXGnvuBeOj+Sur/KzX29nYPsNl5H9mzZ7vBnqvmAXYaoM2xmpR/VtRf5e3EUbquKzXaVKEH4zFOvivGj+jnpccPj9vzFYBmR5Tn8dBZvqb70t53Ln+xApJ5oP1G8zwQ94XvO0cIr0CNMaYnN4YO9Frli4+4yhe/+ImjEYDMJzT0oawDjZMk7By+3uUQnpwsOgek/qHipBCeFfnl6ylSX9HHAWBAeefDz5F1f03kqSfdXxF6SYq3fyW/zlYfyp/bAMDgbUIPyH6XjcifHv6edHImPqAgJ/bWFzLRXQLIHM6rzpNOL6N4XaHjRBnHm9xpvz0pJNrJzu04k2cEaPuBfUWf6Rw/7LNZAKnfaIwf1h0Xkzwe+mLhW5rc96nQQddTpP6qE6HnjVeCl7DeswKyeYDfcdu4daDGGHNoPIEaY0xPPIEaY0xPPIEaY0xPPIEaY0xPbmw/0NjsUi5Ni8eVT6jK7qnyxceu/c2c3bMBgBfSB4diLsn62ekfqnwnf4x2bzfE7n9kCX2l8EPkXeDYTSbXqDYfPe8+nxPlL4hd5nOinqif2x/57tnncU34q8buNsfXhV+niocOl925tuL+5vcxKb8tyu901pOoPpqOdmZZY0V8vXP8sF/qWqffKKsOLuQqAqk6OCfKr3b6t3L8kvBvXRP3N/Sz/L3eqoFsHmBFeTCzO+8VqDHG9OS5oANdVh+ap+/W+tD59NR7H8m6sPD3pJVm+IEmT8L4j9gZuxb+ofG/yi+SdaOhB2Qd3DR3/I5DKolfpPJVDH0fx8eifCnKj4RfZ+hJOR/6SORhj+tiZ/XI682+qyWQrnzjhAmtfFufTV7plGJlV4k3hlLEaxGvhCN9+Myyf2WciSK9qvQbjX5Ixo/wzYz7IsYPZzoI3eWA9Ll1JeIxHui+t/6t/LnKv3Wa3/f2rBR9v9ryvDKdiDdOPjPWxvf/6RWoMcb0xBOoMcb0xBOoMcb0xBOoMcb0xBOoMcb05Mb2A1Xxbp9Q8qls4+zut6xPaNXg6t7oLOETeoni4wYAF299Qtk/dLfTd/IY+UKGfo19FUPvdkT4ik6EL+RD8x8b+sGafRUvhe9k7rNZs1/kpQrap1L7dXL7ayDzeQwfT94z3RQ+j1vRz8Kvc0o3bLcG0NRUj/J7HQnf2O7yPKpHop27ffxG9fgRfqNHcr9R/h61952uq1lvANRjMd74/oZfJ4+f9a52NqzWvBL3kfonfFfHuW9vMm8oN6YZvAI1xpiePBd0oErvubhPaDxyFj9xNBE+oWHRvXge+SL0g6QP3QBSveFlcVKoyU/+4DyQ6iKVPrQokeYTV/q+40Cq06ymeRxCfxr6SvapDB0i+1pWQu8pdI6xpkv0nrU46VSJky2N0m82AIpblf5X6D05DlF/+7kL64ghTqAVXeMHdDKtCF0z60NrINVdngbScVUJ3S7EeFPlm7jvwr9V6KBZ79mUFbT+Osn/XooTSvzO0bZ//59egRpjTE88gRpjTE88gRpjTE88gRpjTE88gRpjTE9uJD9QxeF9QruzePLmYeyycdLJ0IWp7J7sEzrp9A99gfAPVX6R5PbU+oou7hd5RewCrws3oCvhW0q7lpdF+Q1R/pJoz4bYrV4X8dAhcv9sdvYb9/+2UFmEIvjm+XAb513asYiPOtUdqrxSfXD7R8KHtHv83LLk+OFxsiV8Njd6jTeV3fZFov7F/Vs3xX2P+8jf6+g3nh/mBax7zAiFvQI1xpie/CB0oIpr5QeqHgqsA42zE+wTGktZXmkG/GSLlS8/CQGkT9RldX+1cBQPfR/5QkLoIlt9n/LNTPKPi/z1U+Tx0F1yPRPxudEe1nVOcr/L9rrYEX0qdH+VWBmFTpD9W0Pvyfcr/D2FD2xy3+MNhleCoWPleuqu+gtaObbtVONnWb9R4Yua+I3G/WK9bfiHsg+pKN+OH45Hv/F9nwr/1vhcvq6p8OetxEq/9QueD4PPjAVegRpjzOHxBGqMMT3xBGqMMT3xBGqMMT3xBGqMMT15LutAF9+176cbvVb6UKUHlLpRoQ9Vur/EHaoBZJ7xJL7ZqRPkXelNocvbEjq+0G9y/Vui/d152HkXtVvXyVlXR0JlMV4yPhEqjmmvuBo/6nOVvljFn7/wuFL565fNa78tym91llfjQbWTv1+7NaDvI6txoj95HlB+oN6FN8aYw3Nj60CX9QmN8tIPVMRVvvjFTxyNAGRPyF0A2ZN2C0j1erGyeynp19aB1P+x9Q+l+GqNVF+5WuXxRug3z9dI826HjyeXPwcg8Z0MX8Xkc1Eh9a8MPSnrPdHp8yh0jpnec8mTTrHi4HiQrIgBSN9YGU9WdgD0+OGVvvIbVSeFNjr7bUm/0SSu7m93+WX9W5P7W0Drr5Pvr9KDKz9Qr0CNMebweAI1xpieeAI1xpieeAI1xpieeAI1xpieWAd6A+pAF97l76cDVbq8xXWgV8Qu9lanX+e10v0dXgfa7e/Ju7HL6j1V+VLoEPvpQLn9aryNRf/EuFL9xvdxV9wXpQPd6Sy/+P1VcXV/lT40+mG4sA6UEsi3eBfeGGMOzw+jDnRZR/pldaD8ZINYOQb8pA1fSHWSR+UfZ73eeqc+jv1Du3WX7PN4oQKAVwi/SI43uQ9pU3XqAVnvGeXVdbGeser09+R+rsRKWfm6xjjhFVCU5/tei/hIxFU96PxcoSeVfqPKl1b1m8pfn/R/p55U+bQuW579T9X9LYVPa9wX/l5X4s1A6UBn8ArUGGN64gnUGGN64gnUGGN64gnUGGN64gnUGGN68sOlA+2n91S784vnkW+z+h16N7/b53FxHZ/ShyodX7f/o9LxLVv+8Lq/iC+bt537X/mBKv3mROzStrpOas8UeTx0hTyuVFbIiKvPXXy8Kd1od3xxv9FRp4+t0m+quLq/6nPV/ZX3keqP+8XzidKBzmzOewVqjDE9+W9bBxo1qxMm6qSHejInJ4UApCdwgFTvud3p5/ijpJfcEL6NazVSPeaa0Huer5D6fq6K8udE+QtC73lO+JBGedarXhC+kGtCh3ixyuPrXfrHzJkfgNTtZismAKmus87Lj8S4GnWeQFNvHslJIREHkOolt7t8UTP/0AapX+1loUdeF7rOS6L8ZTH+m173NznhBiDr/7oGspX+WOhAZ1amXoEaY0xPPIEaY0xPPIEaY0xPPIEaY0xPPIEaY0xPfrh0oN3ln8N+oLHLv2Re72vkByr9PZctf638QLl/lD60Wye4uA5U+YROO/09pa6T4qFDXFYHer39QxO1CfL4KFQHC+tAlV5Y6T13RTbNfjpQ9gOdCj9QlRfeOlBjjDk8P4w60OdKXnjh6J7p3Rr0yAvP+k2VFx65rjPywuNVnH9c5JE/VwNJXvhWx8e60XOd/qTqumReeKFPZP1jI/SDm50+kiqfe6ID7fSN5bgsL+pX+lCIdsb3QumRVf+wHrPVh1I/rxfo8Ktd3PcTYvx3+5Ny+2uVGQFAqgNd0g/UOlBjjDk8nkCNMaYnnkCNMaYnnkCNMaYnnkCNMaYn1oHeSDrQbt/Pw+eFV/m7lQ50q7P84nGlA93q1KX+oHSgvBvbnRd+cT9QpQNdNt6qSg6tD11aB9qpU15cB/o9/EAPrQNVul3rQI0x5sbhxtaBdscX14G2+d8p3r1yTE4KAdAnKHiFtQukes9N4Yd4Reg9wweTdZRrQtd5vgIweM38zW19P19N5U9VAIrbKH6mAlC8huInKwDF6yh+WtR/ogJQvFbUT+2vT5cd15X4h57r9A/lvOeXhA/mhtAPXgGwjA50p3PFtLgfaJz8USu1xf1AI1+80h0rvSfrNGN8cvyy8KVV8Ys1gOJl4n7x9+Iiuj6X3pzaOOt8r4j7siXePBqhA51ZmXoFaowxPfEEaowxPfEEaowxPfEEaowxPfEEaowxPXku60CvVf7366f3lO5NsYu6pL8n6zR3GmhXocTVZrNr9zkpf0Xs0l4Wu7Qbov71zt1edtNZF/Et4Za0uaRudLuXv+TiulHlE1p2+4eK8kp/uqwf6LXyn11cFaB8P5Uv7Y6oX/nGSl1wDWh9qNL5Lq4Drff/6RWoMcb05AehAz38yaJg8ZVmsLjvpzwpBED6fsq820l+7U7dnPLxZP/NCzUynSZOA5lOE2cAoLiNbvrxEkDxBoqHfvN27lBR/niuJ8UzJYDidq6/RKYbjfuorguvYP9H4Ssa+eUT/9AG6X1R+sFa5JGPPOO8YlJxmUe+8wTa4r6fyn82fD8X14Gi8w1D6W2VrlPdFzXOWefbCJ0vRPvj/vL3cUO8eSiduPID9QrUGGMOjydQY4zpiSdQY4zpiSdQY4zpiSdQY4zpiXWg1zNb56RzdzVx0+nUx4k87Mnu6pVOXWeS9VPtuqrd6tjdpt3SVu8p3HHU5yrdqLgumXde+YoqXSH7h+52uiUpf8nF48vqQ6+VDrSnL+2SOmU1bjm+vaRudFvcx24d6OL3cWwdqDHGfN+5kXSg13tFyU/msvMJzE/IWDkmzu1AuoLbFP6elzv9PUW+ddZjNmdDpyl0nXeQsO3ZEkDxJir/VAmgeCvFny4BDKie+nEAGLyN4k9O8/qPlgCKN+f1F6+neNSjrov6pzme91t9pkSHfyj7Tq4Jf8lL4mSUXBED0P6hyYoYeT27nfWw3lP5fm6KN4zNTn9P1tteEjrlC7kPbOiU8Sqq54wof64GgFeK8soflu/jeSB947lUASjohFW88eB5881pV7iMV6DGGHN4PIEaY0xPPIEaY0xPPIEaY0xPPIEaY0xPbiQd6OFdmrqzch7e97Ps1NMp/0Sld6NskVLXqXZRI0si70LGbunLRZxdc1ZrpLucF4XL0XmxKxpuOi8T5bk9F0UWxlURvySybF5eNstmp56R76/SFar84+NOly+lG13W31P5z6p2sq5z3Md/Ntn9j918dkXa6lIvyHEuXJSS+GanP6zSjfJu+25nvnim2v+nV6DGGNOTG0kHurjvZ5RXK0p1omPxE0Th+3l4nd0V4Yd4sQIweDXlbb+Q51vHKQAo3kgXHPnZWV/5VIlUpxnxt8+Xrx+dAhi8k8ofAYDBOygeBzfeRfFHAWDwdorXTV7PkRLAgNpf11Po60r6J+KUdz5g3WJdl0hXytH/rB+sxQprXfiHqpVvwCumGM8in7uqR/rPKud/XtFvdPp4st7zYq63bVAh9W89C6T35SSQ+sbGOGd9aCPi4Q/Lbza10IfGmw19r5tKONgrP1CvQI0x5vB4AjXGmJ54AjXGmJ54AjXGmJ54AjXGmJ48l3Wg19v3c/E872OhA1WuTjtC7/k9dlFp97M7SyK76agsiauduk7ejVU60AudulH1udz+C53Xxf0TLjsq3/0LhYuS8p1c1l9y2Tzyyt9zcd/P7jzvSge6rE45UaGIbJeb4r5sdvm6JuU3uvS810wHyrrv3c588Yx34Y0x5vA8F3SgakXJ8ahBrSiTJzaA7Ak2AjpWiMq5nVd8cUJG5XN/vdDNcb71ZysABek3I996ors8MgUweO/8kYs2/h6Kf3cCYPDB+Xjz4BTA4H3z8ereMYDhB38krad4D7Xn3klaT/3gJG//AyJ+ZIq0f44AaX8+k/uH4lkAme/kWaEfPAek9z1Wvrwyuty5YkpO8iCPRz73xVd8W2J8Xm6QngS7LE6gXagADF5HOuV4k2BdZ+g3+b6cFH6vcV9Y13xc6KCPlQCK26j8iRJIfHXriPMbzzlxvy5WQLZytw7UGGOuH55AjTGmJ55AjTGmJ55AjTGmJ55AjTGmJze2DlTFu7N4Hj5bp9J7TjvzZfMu6m6nvyfv9l4RWTzDB5N3jVWWxPPCHedCrgpoTue7n+2uNLngNCdF+TPCredk3p6oH6xeON2pM02yMHb6hy6eZTN2yVk/qHSFbR75+bDML698QsedPrOqPLcnXMRYVbLbNT6T+FaD1JUqxi3H1zt1yqwKWBMuUJdF/WvCJWs9dKm5P6zyLU36ebsGMh3oWOzCz+SL9wrUGGN6cmPoQAN1skjFlz1ZtLgOdBdYSge6nq8EESsd9jEMvSfr404Jf8+nhd7zyRLA4N0UfwgABj9Jus6HpgAGHyA9ZjMBMPgw6TrvGwMYfIji9RjA4KMUv2cMYPB+ildjZDrT+jsTAAW3v5x0Xdcd5B9ainz0Twqf0LJEel9OAQB4ZVR15pFnh/y68wQO+4c2XStiWQ+vyL5HhgJaIa7lbwyRnz3ptzMAUNzOXzyl6xTxpoQe54meNPxYOR56UvLVRVUCmc43fEJZP6vmh8orUGOMuW54AjXGmJ54AjXGmJ54AjXGmJ54AjXGmJ7c2DrQbr3n918H2p3/fXEdqHLNWVYHutblppPsMp/PVQGtfpN1nadz9x2pAz0l9J4nhZ70TAVku6VnOn1IuX+UDlTtkl8Wu+HKJ3RL+YRGfD4sdaCjTn3o4nHlB7qsDlTlf79WOtD1Tn2uGudKN/pScR9ZvbAusqIuqwMd2Y3JGGOuGze2DrR7RcnO0t0rSj5BNFFPZiB90saTWZ2g4BXfxRrQ+a/voAs4IfK5P5H7crb+nqT3rO+fABh+bH5pFPHBR6j8N8YABp+k8t8aAxh8jHSdXxkDGHyK4l8fAxh8hOJfHQEY/BTFvzVJ2199fdRxXYkeNuJvFf6h7CP5xBSpzvEEgCzP+Cmx8l0VvpxrQm+onNU3Oh3dVT3q5A+3f0340q7mes/2DYB1yvFGwrrO8Ot8Wx4fvIXuy+NT5LrmKYDBm8V9ZN3oU0Ln+1TuA1uHPyl/r8+Kk13VfGAvvr8y9QrUGGN64gnUGGN64gnUGGN64gnUGGN64gnUGGN6cmPrQFW8n96TXZqqTp0d6+lCZ6fyvPNu6bbQzW0IdxwVXxX+nqtC13k630VtTufZDZtnS2RuRs2JCkBxO9V/LHfZaSKrIqkOmqfz7IxNZE98jWgP60lDN8q7zKc7885z/6+KXfJ1kUd+o1ceeY4rHeiu8vcU9Ud5amdbP7cz9J6kh23HrXJ7Un61Sm/Lvq6XhO/nqvCxvSjUDheEbnRNfL8uiuybG8Lv9UpnvnjGbkzGGHN4rqcOdNn870ufLBIrStaBTjodvHlFGc1MdHnipFBRA8Cr5uPFKpDqEE/mK77wTxyQnq61RX03+Xs+NgUweL/y92T/TSDVddYAMLxzXgdafX0MYPiJ+fJVOQIwJN1oddcYwJDqr6aj/HMBpP6kkwb6uoqfIJ3gZIK038JHkvWMkwbpfalLpCujMvS/FG/ECrcWbySN8Pfs9g9V9ShfWl7xxUqN8qe3bzD8ZgMg9f08JXSgjdB7PjVFqmuuI0736ygADN6S+70m9T8hdL7TBqkuOwYc99ukAlDQyr0p6/kagtI6UGOMOTSeQI0xpieeQI0xpieeQI0xpieeQI0xpic/jDpQ6d608K79dMld+12hs9sWvoqxu/pjC7vpXBRuOiLe5nNnPWbr+0m6y5NCp3myUzeqdJ1c/7MifjLPjtnqT8V1JTrQuC6lN1Q6Qd713vgB6UBHyt9TxEedvrTKD5R9P5UOdFPs8m8IHejlzjzvrFq52DnOleuV0oG+mHbP17pcr5L+3FrSD9Q6UGOMOTw/jDpQdbJIrSjZD3QbyB25hR/opRrAgPJTtydeWE8XKy/Su7U60HcI30/SRTaPTpHmW793AmDwcdJdqvhdADD8GdJ13i10oF8YARj+rNCBUv1RfkD11Hcjb/9dIo/8vRMAxTtID1gJn9BHJ0h1oFWDbEWMWCmzw3+U55NO54UOtBFvHutiZdQIvafK/66c3pd9g4mVHWUWaP1qOQ97ZBa4I/flTPr/KaFrDv3yO+n+hk8o60AfmSL1ez06Rfr9qqZI9a3HAQDcb6cBoKD5oamsAzXGmOuGJ1BjjOmJJ1BjjOmJJ1BjjOmJJ1BjjOnJD6MOdPH87+U19QPl3dJuP1B2/bks4qsVgMFraZf/gsjDHq45tIva+oHSrmXr70nZEJvjZV7PU9O8/DOi/iif+IcKP9Bn8myLre8n9U99qkS6Sx79w3rGC2L3XOWLV3nGt4S6I/KM3yx0mvNihA4dKIAs73y3DpTbud3pV6uyfiqdstJjvlLElXqB3KFa1Qq7Xp0Lv1ehLljS7zW5XxvCD1TpQKf7//QK1BhjevKc1oFSXDnPo/MJr/xA+YTGljiJEQ2iJ3DrB0orxzjKkOjsBiWAwVtJB9cAQPFOekQ+BqT54kMXyTrKAkjztk+B1McTQKrrHDd5vBb1jJv8cysg9QMdNdDXxX6gRZTnfgv9JusExw3S+1IJP9Cp8AOtxUo2/EP5hEwjTv7UQh8K4RPa7QfKK8SmBgByjG/HJ/tmxnijk2xSH1qXSPO5Q+g6yyaPN8jj0yavvxZ+oBPhBxoniLjfxkv6gU6tAzXGmEPjCdQYY3riCdQYY3riCdQYY3riCdQYY3ryXNaBLrtrzzqv2JVT+lDetZ8AWMZvcbfTb5F3Sze63J6kbo59M89VAAbsvxk+oayvDN0o+36eEj6eJ4RPaLhMsV71hNB1nsrbX0c9fL1nRf730AmyOuKi0DmudfmBJvd3U+g9d1Se9zqPj4X/7LhTj6zqUe5iHO/2A+Xd/y2hr1Q+oZfFuL0sXKPWOrOHKv9Q/txLwg/0ktDzXrEfqDHG3DBcTx2oYlkdKMeXPXE0XVIHugMspQONJy35SCKeqLTywhkAKN5AS+KToQPN818PSAdaPw6kesnvCh1oxD9MesxvjpHmbf82AAx+iuJfbQAM7qT4N5DXXwkd6LfHaftDd5lcFyL/O/VDlOe84Y3QCYZOk/0iY7zxyqiq0OGUzitclRd+o8spXa4EVb74JNNBk7fzUn7CrR2frJc8C6T9dlrol0PX/GaKHxP54o8Kf88np0j1nuHvyfU/FW9IrPcskb6Z1eLEoMpAUc4H9uLWgRpjzKHxBGqMMT3xBGqMMT3xBGqMMT3xBGqMMT2xDnSZvPDXWAdKu4RXOv0WeVfxovBVVDrQc8I/9GSePbT1D1V53lUeefb3PJ7vlrb+ntR+qQM9J/wiz4pd8jWxi20daLC0DrQBULyUdJdtXnjhb6t0nUrvzCqXVRGP+m89tA50swYyFzfrQI0x5vpxY+hAlU9otw508XzxpXjyB/zEjua8kJ5ghXjihX+i0N8lPoxRnvV38dckz3UJYPAm4Z/IeropkPlmRv8M3jWvr6zGYwCD97DfYpPHd0W8zOPVbp1+bj0V/p474e+ZX1fSD7vC93MaK2Lq5/ADZd/P0If+KPuBCt/PSoyHqkC6AmqEs32MW47HOOFx2O0fyvpT5R8aH0xO7zGw+A0ghNbFq1lXm5802/MV5fsi8rnX+Qk3TKZI9Z6V8P2MlTh971r9L795TIROfOoVqDHGXDc8gRpjTE88gRpjTE88gRpjTE88gRpjTE9ubB3oslk8v8fuPMVVFk+VL166OkU+bpGn+0UL5+lW+rueebqFbpR3ny8IPWnEuZ5zovx5Uf+5zs9l/eD5Tl2n8vcUecCT3fCNzjzvfH93hK5zJNQdKh67vTzepp1xVY8an0o3unge+R2hG93u1DVz/6v4euc4V+WVKxWrFK4IPW/c33lTsL3rHYp+Zqr9f3oFaowxPbmxdaDB4j6hQW5XmD3hC/FEiqYkJ46AdEWj9HdFZ55uziNfANqnsrid4icBoHijyNN9B+klAaT6yvDrfDvn9QaAAek0Wz0mx0OXyvVMha4zdKnczsjrLa4r0QNOhb9nrBRYDxjleUVfi5Vs1ZXPPVnBxefy+GlEfBuA1CPLepI3G6BLH0p61RhvfMIndKPs/F9UQNafoRulk3JBotOsgPR+qfIl8vpjgCq9J19X6Hap35qpeMOovAI1xpjrxg9iBWp+iLjrrpdc/XcTJ4LW6Am/UwMoNmhFEOUvz9fZxjcLAHe+j/5szMJ87fzL9v+feBNdp0Kx0JxQPF8iAzfv/9MrUGOM6YknUGOM6YknUGOM6ckP4jdQsbWVxCNSL1nDVMRZ1RU1s+tf/FayRfWUDa6qzGaZNACaSxXFAaC5QOV3Guy5YR4gfBuPz4dDT4en55MEhj9jeDUdiF+uANSPUj3rNfY8kw7EL9YA6gfnfwQK3WVNnjRxRfUDDfZ+32yZAnu5Dw9QAle1B0l8PtzW0zQAmqP7Vxft5/vYxqk7236j6w09YOy5HyDuS5nfl3bPfZbQV/L4VPrB6MltEd8R8aR/GgDYzOOtypXaE+6ZBxgDe26bBxg12FPvHmBX9Nt2gz0XV45z/7TfIB7nkZ+dqonyybgKXae6vxXVFi05/Dwzg1egxhjTkxt7F76Y+V9m8ZNI8cjkkwYQJ0CaTn0on1SpAaCgkx6tno51Z5U4iRRrNPJtbJ+xpCctQtfGOriJ8HMshV5vLHwVw1eU/R93p1fjs3vubd5tOjkTa8mC+lnG6/34gaub5P3QvkNwv02FfnNcIb0v0T98H0MnyDrNGFdKPzhvf7o3PhePxwqIx2EjPjfi3M5+45P1pLXQO5fiZFEtxnPcR9Jptv0myif1l+KE0mTm/q7P/gGA1pXz9KBmnpmVqVegxhjTE0+gxhjTE0+gxhjTE0+gxhjTE0+gxhjTkxtpF34B1dWBkiRHayEd2Z4+lD4gAqwDjV3RHYrHJ7IerQJS/d1U6AdDl3eedaMNgIZ1rKHLq4Quj1WH26FnpIoiPqJ46OkmpCcNXd4u6S5DxzeZYu/ceksNpHq9qn+8PjbTqtAV8v2K65pQ/4xqAM2Yykd/lrmus91znyV6mMdbqCPYsyeaLK4rKa/GVd1Zz3auq03Kh952ncvP6CVniXG4Shcc45l1l9FvZzkOdNyX0/PhdjyPRXn+/o7E+B/N3MfZPzaYjwTRAcolrhOvQI0xpic30gp02SfA9XOwD1g32nTqRikNO+oCyBzF4xEr9aRCl0e+k2088TcEUh2f0s3Fs5r8IlEWeXw8E9+dicfSlvuzWTI+c19m3Vfb/OzcD6ET5H4rhW43VmqJfhNApsdsMxeIdq7wfWyAbPxEnMs3Ij69RvXUQpfaiPEZ18X91oh49E+iP+26LwWV39PhivuodLhJPncAe/d39nidWmkqvblXoMYYc/3wBGqMMT3xBGqMMT3xBGqMMT3xBGqMMT25kXbh1Z6XirN/n4or/Veg/EPZqHJZ3WjEt4SO74rQ67Eubyr0emWXbrFhveFE6OZa/aOIKx3llNSRym+xXzxcQS/MfED0w0RcL+s6o4WsW4w7zvH4KNYRK/1mt05T6Tp5XPWL8zhsOj9Xjc/F26/6YTrz11nKrvsix7O8j3n9ib67nGnnrMZDqXS654dOvAI1xpieeAI1xpieeAI1xpieeAI1xpieeAI1xpieeAI1xpieeAI1xpie3Eg60GvFsnpSFVd+o4vrT7vrkX6mokEq3p2FnGFdZ3c93eVvpviy16viSnWr2in77Rq153rf92sVv+7jU5Vf9r4sOW773V8en730ngqvQI0xpieeQI0xpieeQI0xpif/P9Yb75g9rKtAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=448x448 at 0x1084BFBB0>"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create a dummy input\n",
    "inp = torch.ones((64,3,224,224), requires_grad=True)\n",
    "m = model[:-1] # remove the last conv block\n",
    "\n",
    "# run the forward pass\n",
    "out = m(inp)\n",
    "\n",
    "# hand-craft a new feature vector\n",
    "grad = torch.zeros_like(out) # 14x14x256 features\n",
    "grad[0, 0,  1,  1] = 1\n",
    "grad[0, 0, 6,  12] = 1\n",
    "grad[0, 0,  0,  6] = 1\n",
    "grad[0, 0, 13,  6] = 1\n",
    "grad[0, 0, 13, 13] = 1\n",
    "grad[0, 0,  6,  6] = 1\n",
    "grad.requires_grad_(True)\n",
    "\n",
    "# calculate the input pixels that would change the feature vector the most\n",
    "out.backward(gradient=grad)\n",
    "\n",
    "# render the image\n",
    "din = torch2img(grad[0,0], color=(250,10,30))\n",
    "dout = torch2img(inp.grad[0,0], color=(10,250,30))\n",
    "frame = Image.composite(din, dout, torch2img(grad[0,0], color=(200,)))\n",
    "imageio.imwrite('14x14-receptive-fields.png', frame)\n",
    "frame"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51cb7556",
   "metadata": {},
   "source": [
    "We can also make a video showing the receptive field of every activation on the diagonal:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "98eed035",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video controls  >\n",
       " <source 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type=\"video/mp4\">\n",
       " Your browser does not support the video tag.\n",
       " </video>"
      ],
      "text/plain": [
       "<IPython.core.display.Video object>"
      ]
     },
     "execution_count": null,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "images = []\n",
    "for i in range(14):\n",
    "    inp = torch.ones((64,3,224,224), requires_grad=True)\n",
    "    m = model[:-1] # remove the last conv block\n",
    "\n",
    "    # run the forward pass\n",
    "    out = m(inp)\n",
    "\n",
    "    # hand-craft a new feature vector\n",
    "    grad = torch.zeros_like(out) # 14x14x256 features\n",
    "    grad[0, 0,  i,  i] = 1\n",
    "    grad.requires_grad_(True)\n",
    "\n",
    "    # calculate the input pixels that would change the feature vector the most\n",
    "    out.backward(gradient=grad)\n",
    "    \n",
    "    din = torch2img(grad[0,0], color=(250,10,30))\n",
    "    dout = torch2img(inp.grad[0,0], color=(10,250,30), vmax=9.15) # force the same vmax for all frames\n",
    "    frame = Image.composite(din, dout, torch2img(grad[0,0], color=(200,)))\n",
    "    images.append(frame)\n",
    "\n",
    "imageio.mimsave(\"14x14-receptive-fields.mp4\", [frame for frame in images], fps=2)\n",
    "from IPython.display import Video\n",
    "Video(\"14x14-receptive-fields.mp4\", embed=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c39a9ae9",
   "metadata": {},
   "source": [
    "## The surprising results\n",
    "\n",
    "The red squares show the feature positions and the pixels affecting them are show in green.\n",
    "224 (the input image size) / 14 (the feature map size) = 16 so you would expect each feature to cover an area of aproximately 16x16 pixels in the input.\n",
    "\n",
    "In reality:\n",
    "1. The receptive fields are much larger.\n",
    "2. They are biased to both the left and top by about 8px.\n",
    "3. The rightmost and bottom 8px are pretty much invisible to the network.\n",
    "4. The 7th pixel row from the top is much more important than you would expect. This means the 2 topmost feature rows are calculating subtly different representations than the rest of the network for the same pixel content (no translation invariance).\n",
    "5. The path to the last row and column of features is so suppressed that it has little chance to generate meaningful activations.\n",
    "\n",
    "The first point is surprising but not difficult to explain: these features would have a 16x16 receptive field if all the convolutions were 1x1, otherwise it spreads out quite a bit with each layer.\n",
    "\n",
    "My hyphotesis for 2. is that the strided convolutions are always calculated for the top left position in the 2x2 grid. After a few layers this adds up into a pretty big error.\n",
    "\n",
    "I am not sure how to explain the 3rd, 4th and 5th effects."
   ]
  }
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