frechet_mean_esm_2_v2.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Computation of Persistence Diagrams and Fréchet Mean for Protein Sequences with ESM-2\n",
    "\n",
    "This notebook demonstrates the process of computing persistence diagrams for protein sequences and their Fréchet mean using the ESM-2 model. We will compute context vectors for protein sequences using ESM-2, then convert these context vectors into a form suitable for computing persistence diagrams. Finally, we will compute the Fréchet mean of these persistence diagrams.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Install the necessary Python packages\n",
    "\n",
    "# numpy: a package for numerical computations in Python\n",
    "# matplotlib: a plotting library in Python\n",
    "# transformers: a library for transformer models in NLP\n",
    "# gudhi: a library for topological data analysis\n",
    "# scipy and sklearn: libraries for scientific computations and machine learning in Python\n",
    "\n",
    "!pip install numpy matplotlib transformers gudhi scipy sklearn -q"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Definition of Protein Sequences\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the protein sequences\n",
    "\n",
    "protein_sequences = [\n",
    "    \"VHLTPEEKSAVTALWGKVNVDEVGGEALGRLLVVYPWTQRFF\",\n",
    "    \"VHLTPEEKSAVTALWGKVNVDEVGGEALGRLLVVYPWTQRFFES\",\n",
    "    \"VHLTPEEKSAVTALWGKVNVDEVGGEALGRLLVVYPWTQRFFESF\",\n",
    "    \"GLSDGEWQQVLNVWGKVEADIPGHGQEVLIRLFKGHPETLEKFDR\"\n",
    "]\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computation of Context Vectors for Protein Sequences\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Some weights of the model checkpoint at facebook/esm2_t6_8M_UR50D were not used when initializing EsmModel: ['lm_head.bias', 'lm_head.dense.bias', 'lm_head.layer_norm.weight', 'lm_head.layer_norm.bias', 'lm_head.dense.weight']\n",
      "- This IS expected if you are initializing EsmModel from the checkpoint of a model trained on another task or with another architecture (e.g. initializing a BertForSequenceClassification model from a BertForPreTraining model).\n",
      "- This IS NOT expected if you are initializing EsmModel from the checkpoint of a model that you expect to be exactly identical (initializing a BertForSequenceClassification model from a BertForSequenceClassification model).\n",
      "Some weights of EsmModel were not initialized from the model checkpoint at facebook/esm2_t6_8M_UR50D and are newly initialized: ['esm.pooler.dense.weight', 'esm.pooler.dense.bias']\n",
      "You should probably TRAIN this model on a down-stream task to be able to use it for predictions and inference.\n",
      "Some weights of the model checkpoint at facebook/esm2_t6_8M_UR50D were not used when initializing EsmModel: ['lm_head.bias', 'lm_head.dense.bias', 'lm_head.layer_norm.weight', 'lm_head.layer_norm.bias', 'lm_head.dense.weight']\n",
      "- This IS expected if you are initializing EsmModel from the checkpoint of a model trained on another task or with another architecture (e.g. initializing a BertForSequenceClassification model from a BertForPreTraining model).\n",
      "- This IS NOT expected if you are initializing EsmModel from the checkpoint of a model that you expect to be exactly identical (initializing a BertForSequenceClassification model from a BertForSequenceClassification model).\n",
      "Some weights of EsmModel were not initialized from the model checkpoint at facebook/esm2_t6_8M_UR50D and are newly initialized: ['esm.pooler.dense.weight', 'esm.pooler.dense.bias']\n",
      "You should probably TRAIN this model on a down-stream task to be able to use it for predictions and inference.\n",
      "Some weights of the model checkpoint at facebook/esm2_t6_8M_UR50D were not used when initializing EsmModel: ['lm_head.bias', 'lm_head.dense.bias', 'lm_head.layer_norm.weight', 'lm_head.layer_norm.bias', 'lm_head.dense.weight']\n",
      "- This IS expected if you are initializing EsmModel from the checkpoint of a model trained on another task or with another architecture (e.g. initializing a BertForSequenceClassification model from a BertForPreTraining model).\n",
      "- This IS NOT expected if you are initializing EsmModel from the checkpoint of a model that you expect to be exactly identical (initializing a BertForSequenceClassification model from a BertForSequenceClassification model).\n",
      "Some weights of EsmModel were not initialized from the model checkpoint at facebook/esm2_t6_8M_UR50D and are newly initialized: ['esm.pooler.dense.weight', 'esm.pooler.dense.bias']\n",
      "You should probably TRAIN this model on a down-stream task to be able to use it for predictions and inference.\n",
      "Some weights of the model checkpoint at facebook/esm2_t6_8M_UR50D were not used when initializing EsmModel: ['lm_head.bias', 'lm_head.dense.bias', 'lm_head.layer_norm.weight', 'lm_head.layer_norm.bias', 'lm_head.dense.weight']\n",
      "- This IS expected if you are initializing EsmModel from the checkpoint of a model trained on another task or with another architecture (e.g. initializing a BertForSequenceClassification model from a BertForPreTraining model).\n",
      "- This IS NOT expected if you are initializing EsmModel from the checkpoint of a model that you expect to be exactly identical (initializing a BertForSequenceClassification model from a BertForSequenceClassification model).\n",
      "Some weights of EsmModel were not initialized from the model checkpoint at facebook/esm2_t6_8M_UR50D and are newly initialized: ['esm.pooler.dense.weight', 'esm.pooler.dense.bias']\n",
      "You should probably TRAIN this model on a down-stream task to be able to use it for predictions and inference.\n"
     ]
    }
   ],
   "source": [
    "# Import necessary libraries\n",
    "from transformers import EsmModel, AutoTokenizer\n",
    "import torch\n",
    "\n",
    "def compute_context_vectors(protein_sequence, layer, head):\n",
    "    # Load the tokenizer and model\n",
    "    tokenizer = AutoTokenizer.from_pretrained(\"facebook/esm2_t6_8M_UR50D\")\n",
    "    model = EsmModel.from_pretrained(\"facebook/esm2_t6_8M_UR50D\")   \n",
    "\n",
    "    # Tokenize input and convert to tensor\n",
    "    inputs = tokenizer(protein_sequence, return_tensors=\"pt\")\n",
    "\n",
    "    # Forward pass\n",
    "    outputs = model(**inputs, output_attentions=True, output_hidden_states=True)\n",
    "\n",
    "    # Obtain the attention weights\n",
    "    attentions = outputs.attentions\n",
    "\n",
    "    # Obtain the attention weights for the specific layer and head\n",
    "    S = attentions[layer][0, head]\n",
    "\n",
    "    # Obtain the value vectors\n",
    "    model.eval()\n",
    "    with torch.no_grad():\n",
    "        hidden_states = outputs.hidden_states[layer]\n",
    "        all_W_v = model.encoder.layer[layer].attention.self.value.weight\n",
    "        num_heads = model.config.num_attention_heads\n",
    "        head_dim = model.config.hidden_size // num_heads\n",
    "        W_v_heads = all_W_v.view(num_heads, head_dim, model.config.hidden_size)\n",
    "        W_v = W_v_heads[head]\n",
    "        V = torch.matmul(hidden_states, W_v.t())\n",
    "\n",
    "    # Compute the output O\n",
    "    O = torch.matmul(S, V)\n",
    "\n",
    "    return O\n",
    "\n",
    "# Set the layer and head to use for computation\n",
    "layer = 3\n",
    "head = 2\n",
    "\n",
    "# Compute the context vectors for each protein sequence\n",
    "context_vectors = [compute_context_vectors(seq, layer, head) for seq in protein_sequences]\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computation of Persistence Diagrams for Protein Sequences\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.spatial import distance_matrix\n",
    "import gudhi as gd\n",
    "import numpy as np\n",
    "\n",
    "def compute_persistence_diagram(context_vectors, protein_sequence):\n",
    "    # Detach the tensor and convert to numpy array\n",
    "    context_vectors_np = context_vectors[0].detach().numpy()\n",
    "\n",
    "    # Compute the pairwise Euclidean distances among the context vectors\n",
    "    distances = distance_matrix(context_vectors_np, context_vectors_np)\n",
    "\n",
    "    # Compute the persistent homology of the distance matrix\n",
    "    rips_complex = gd.RipsComplex(distance_matrix=distances, max_edge_length=np.max(distances))\n",
    "    simplex_tree = rips_complex.create_simplex_tree(max_dimension=2)\n",
    "    persistent_homology = simplex_tree.persistence(min_persistence=0.001)\n",
    "\n",
    "    return persistent_homology\n",
    "\n",
    "# Compute the persistence diagrams for each protein sequence\n",
    "persistence_diagrams = [compute_persistence_diagram(context, seq) for context, seq in zip(context_vectors, protein_sequences)]\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Computation of the Fréchet Mean of Persistence Diagrams\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fréchet mean of the persistence diagrams:\n",
      "[[0.1019498  0.12332781]\n",
      " [0.08684006 0.09949496]\n",
      " [0.07449247 0.08628009]\n",
      " [0.10522105 0.10783894]\n",
      " [0.09807877 0.1007339 ]\n",
      " [0.08884561 0.09302715]\n",
      " [0.07123579 0.07324044]\n",
      " [0.07947653 0.08141049]\n",
      " [0.08064701 0.0822148 ]\n",
      " [0.06087262 0.06149911]\n",
      " [0.09250238 0.09664686]\n",
      " [0.10109362 0.10325347]\n",
      " [0.05193209 0.05452511]\n",
      " [0.05545235 0.05710111]\n",
      " [0.08130216 0.08294133]\n",
      " [0.05534306 0.05575815]\n",
      " [0.05091841 0.05128485]]\n"
     ]
    }
   ],
   "source": [
    "from gudhi.wasserstein.barycenter import lagrangian_barycenter\n",
    "\n",
    "def convert_persistence_diagram(diagram, dimension):\n",
    "    return np.array([point[1] for point in diagram if point[1][1] != np.inf and point[0] == dimension])\n",
    "\n",
    "# Convert the persistence diagrams to the appropriate format\n",
    "converted_diagrams = [convert_persistence_diagram(diag, 1) for diag in persistence_diagrams]\n",
    "\n",
    "# Compute the Fréchet mean of the persistence diagrams\n",
    "frechet_mean = lagrangian_barycenter(pdiagset=converted_diagrams, init=0)\n",
    "\n",
    "print(\"Fréchet mean of the persistence diagrams:\")\n",
    "print(frechet_mean)\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualization of Persistence Diagrams and Their Fréchet Mean\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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tt/jkk0+YM2cOFhYWOjsI3Rnvb7/9hrOzc6lWckWVJMPk5ORyX6+kU0RFP4DKo1ar2bp1K87OzuW2yj/88ENat27N7t27MTMz01nmgQce4Pz581WK55tvviEjI4P9+/fTo0cPAL799tsqnVOX7t27c+jQIeLi4pg4cSKjRo3i9OnTpXrKljh//jwbNmzg+eef55tvvgGo0sQKDg4OFBQUkJ+fX+rLkTHUr1+fBg0akJiYaND3l6HpG2fTpk05f/48ubm5VR42Y4jPpvI89thjTJo0idWrV3P16lWeeOIJnX9j+tb9o48+omHDhvz888+almZteI9JB6QaMnToUG7cuMHSpUurfK62bdtqOr2cOHFCr2NsbGx4++236dixo9YxJX+Id/YqHjp0KECFBpmXpXnz5rRp04bNmzdz+fJlnWUM+Xq3W7RoEefOneOtt94q91tqZmYmrVq10vyRX7t2DUCr12PHjh25cuWKVkItKCjQdK7Q51twSSv99sSu67UMpVu3brz33nsUFRVx+vTpGourZFzhgQMHtLYfOnSowucylCFDhhAfH8+OHTuMFoM+9Ilz6NChqNVqzRefqtD3s8nCwqLU54Q+bGxsGDp0KFu3buWXX37RuvR9J33qnpmZiYeHhyaR5uXlkZOTU6MT5OgiybSGzJgxg1atWjF16lRmzZrFTz/9xNatW5k6dWq5H3Ilvv/+e1588UUiIyPZt28fc+bMwczMrNxWaVZWFn379uXbb7/l559/JjQ0lJMnT2rd32zdujX169fn888/58cffyQ+Ph4oHirTq1cvFi5cyOTJk/nxxx+Jiorirbfe4qeffqpw/T///HMKCgro2bMnK1euJDY2lm+//VbTQu7fvz+jR49mw4YNjB49mu3bt7Nnzx7+97//6by/osuJEyf47bffOHjwIBs2bODxxx/n9ddfZ+LEiXe9HO7r68vOnTtZvXo1kZGR+Pj40KhRI/bv38+xY8cAePXVVzE3N+fJJ58kKipKU65kuJA+3459fX2B4vtp+/bt49lnnyUuLg4obqHquj9ZUfPmzeO1115j27Zt7N27lwULFmBnZ0e3bt3KPKZNmzY4OjqyZMkSfvzxR7788kumTp2KhYUFmzdvJikpqUIxTJo0CRsbGyZMmMCmTZvYuXMnQ4YMYd++fVWtXqV9+OGHNGnShMcff5wFCxawb98+Nm7cyAsvvEBGRobR4rqTPnFOnjyZhx56iFdeeYXZs2cTExPD5s2bee211yr8evp+Nj3yyCNERUWxZs2aCn8peuqpp8jPz7/rWGF96u7r68vx48f59NNPiYqKok+fPiiKwu+//27U95f05jWAu/U2LJGRkaEEBwcrLi4uipmZmeLs7KwMHTpUuXjxoqYMZfSYi42NVfz9/ZVGjRop9evXV7y9vZWdO3dqlbmzN29ubq7y1FNPKZ6enoqFhYXi4eGhzJo1S8nPz9c6LjIyUmnRooVSv359ZdasWZrtt27dUt566y3lwQcfVMzMzJQHHnhA6d+/v1bvOA8PD8XX11frfGX1EP7ll18UPz8/xcrKSrGxsVEefvhhTQ9bRVGUwsJCZeHChUrr1q0Vc3NzxcHBQenVq5eye/fucn+vJfUueZiamipNmjRRhgwZomzbtq1UeV29CJOTk5V+/fop1tbWSufOnZWoqChl06ZNio2NjdK7d29NuT179igdO3ZUzM3NlWbNmimfffaZ8sYbbygqlUqrd6uvr6/i4eGhM9633npLady4sdK0aVNl1qxZytWrV5V27dopdnZ2ysmTJ8s8vqQn7Z09Ye98z0RGRio9evRQ7OzsFBsbG6VPnz569V7ct2+f0rZtW8Xa2loZMmSIcubMGWXmzJmKpaWl8vbbb5cbg6549+/fr3Tp0kUxNzdXXF1dlffff1/57rvvqqU3752vXVaP7aSkJGXs2LHKAw88oJibmyseHh7KqFGjlBs3bpR5XFnv57KUlF+wYMFdy5R1zrvFqSiKkpmZqbz44ouaMp6enlrvA129+xVF92eMPp9Np0+fVrp3765YW1tr/U3oUtKbt0RBQYFy+PBhJTExUbOtsv9H165dU4KCgpQGDRoorVq1UlatWqUcOnRIady4sfLggw+WW8+y3r+GoPrnRYUQldS7d2/++usvva4wCCHqJumAJISe1Go106dPp0ePHjg5OZGVlcW6deuIiYnR2RNSCHH/kGQqhJ5u3LhBfHw869evJz09HXNzc9q3b88PP/ygczYXIcT9Qy7zCiGEEFUkvXmFEEKIKpJkKoQQQlSRJFMhhBCiiqQDkg5qtZrU1FRsbGx0TrgshBDi/qAoCjdu3LjrvNySTHVITU3VrLMphBBCJCcnl7tYhyRTHWxsbIDiX151LRklhBCi9svOzsbNzU2TF8oiyVSHkku7tra2kkyFEELc9ZafdEASQgghqkiSqRBCCFFFkkyFEEKIKpJ7ppWkKAqFhYUUFRUZOxRRi5mZmWFqamrsMIQQ1UySaSXk5+dz+fJlbt26ZexQRC2nUqlwdXWlQYMGxg5FCFGNJJlWkFqt5sKFC5iamuLs7Iy5ublM7CB0UhSFtLQ0Ll26RMuWLaWFKkQdZvRkunv3bqZNm0ZCQgI9evTg22+/xdPTs8zyKSkp7N27l7179+Li4sIHH3xQZtnk5GTatGnD9OnTmTt3rkHizc/PR61W4+bmhrW1tUHOKeouR0dHEhMTKSgokGQqRB1m1A5IZ8+eZfjw4UyfPp2EhARatmzJwIEDy70P+cILL7Bu3Tp27dpFampqued/6aWX+Pvvvw0dNkC500oJUUKuWghxfzBqRliyZAl9+vThmWeewdnZmdDQUK5evcrWrVvLPGb79u3s3Lmz3GmdAMLCwjh8+DCDBw82dNhCCCGEFqMm0/DwcHr37q15bm5uTvfu3dmwYUOZx+jzTf/69euEhISwZMkSHBwcDBKrEELcb4rURcQkxrDu5DpiEmMoUsvohbIYLZnm5+dz9erVUhPKu7m5cfHixSqd+/XXX6dr166MHDlSr/J5eXlkZ2drPeoiPz8/VCqV1qNVq1Z6HVtUVERAQABPPPEEeXl5eh0zd+7ccu9/G8r48eNRqVTMmDGj1L5Dhw6hUqnw8/Or9jiEqEsi4iPwDPWk94rePBnxJL1X9MYz1JOI+Ahjh1YrGS2ZZmRkoCgKlpaWWtstLS1JT0+v9HljY2MJDw/n888/1/uYefPmYWdnp3nU5RVjhg4dyrVr1zSPw4cP63XcrFmzaNu2LevWrcPCwqKao/zXggULOHr0qF5lIyJK/5GXd5VDCKFbRHwEQWFBXMq+pLU9JTuFoLAgSag6GC2ZNmrUCJVKRW5urtb2nJwcHB0dK3XO/Px8JkyYwPz583F2dtb7uDfeeIOsrCzNIzk5uVKvX1HqIjWJMYmcXHeSxJhE1EXqan9NMzMzGjZsqHmUtRLCna3PefPmsWjRohrvUPP666/z+++/37Xcf/7zH/7v//6vVNnw8HC8vLyqKzwh6pwidREhUSEoKKX2lWybGjVVLvnewWjJ1NzcHCcnJy5d0v7mk5SUhLu7e6XOGRcXx59//smLL75IvXr1qFevHitXruTdd9+lRYsWZR5nYWGhWSGmplaKiY+IJ9QzlBW9VxDxZAQreq8g1DOU+Ij4an9tXWJiYlCpVOzcuZMuXbrw0EMPafZ9/PHHuLi44ODgwPPPP09OTo5mX0FBAW+99Rbu7u6YmZnh5OTE9u3btc594MABHn74YRo0aMCYMWO0emunpaURFBRE/fr1adGiBWvXrtXsK7lE/Mwzz6BSqYiJiSkz/q5du+Ls7MzGjRs123799VfUajXe3t5aZYuKipg5cyaNGzemadOmzJgxQyum7777jocffpj69evTtGlTFi5cqHW8SqVi6dKlTJs2DXt7ezw9PYmOji7ntyvEvSM2KbZUi/R2CgrJ2cnEJsXWYFS1n1E7IAUFBWl9COXm5nLgwAGCgoIqdb5HHnmEkydPcvz4cc2jc+fOTJo0iR07dhgq7CqLj4gnLCiM7Eva92azU7IJCwozWkKF4pbgBx98oPl/Wbt2LR9//DEREREcOHCAQ4cO8b///U9T/s0332ThwoXMmjWLxMREtm/fTuvWrTX7MzMzefnll1myZAl79+7lhx9+0Ep4Y8aMwcLCgj///JN58+YxduxYzp49C6BpZX7++edcu3aNnj17lhm3SqXiscce07rUu2HDBoKCgkq1pufPn8+OHTvYt28f27dvZ9WqVXz//fea/fXq1WPJkiUkJCTw6quv8vrrr5f60jd37lysra35/fff6dq1K5MnT9b7dyxEbXb5xmWDlrtfGDWZBgcHs3fvXlatWkVqaipTpkyhadOmDB06FAB/f3/Gjh2rdczNmze5fv06RUVF5Ofnc/36dc20fvXr16ddu3Zaj/r16/PAAw/wn//8p8brp4u6SE1USBQ6rqBotkVNjaq2S75btmzRuswbH6+duBcsWEC/fv1wcnIC4MMPP+Sll17C29ubVq1a8eyzz7J+/XoAbt26RWhoKBMnTmTChAm4uLjw8MMP8+CDD2rOV1BQQFhYGD169MDb25umTZty5swZAI4ePcru3btZsGABbm5ujBw5krZt22ruc5ZcIbC2tqZhw4bUq1f+HCOBgYGcOnVKk4zDw8NLdUJTq9V89NFHzJw5k7Zt29K5c2dGjhypqRPAuHHj6NGjB02bNmXEiBEoisKFCxe0zjN48GD+97//4ebmhr+/v6ZOQtzrnGycDFrufmHUZNqyZUsiIyP54IMPaN68ORcuXGDnzp2amWISEhJISkrSOmbw4MHY29tz/Phx1q1bh729PS+99JIxwq+UpNikUi1SLQpkJ2eTFJtUdpkq6Nu3r1bL/c7L37f37i0sLCQ+Pp7//e9/muT71ltvae4pnzt3joKCAq3hTXdq0qQJzZs31zw3MzPTXFI9efIkAG3atNGc//Tp05W+Z+3r60vjxo3ZuHEjhw8fprCwkK5du2qVSU5OJisri4kTJ2pe8+uvv9Z6zf/7v/9j0qRJtG/fnkceeQSg1EQi3bt316qTWl3997uFqAk+7j642rqiQnf/CBUq3Gzd8HH3qeHIajejTyfYv3//Uq2jEomJiaW2lXffTJeKlq9uNy7fMGi5irK2ttZ7uIparaaoqIg333yTMWPGlNpf0lKsbKek/Px8TExMiIuLw8rKSrO9spPCm5qaMnToUCIiIrh27ZrOS7z5+fkAfPbZZ/j6+mq2l9QlLS0Nb29vOnbsSGhoKPXq1dMqJ0RdZ2piSmhAKEFhQahQaXVEKkmwiwMWY2oi02PeTubEq2E2Trp7z1a2XHUyNzenY8eOHDp0CE9PT60HFF9ZsLW1rXTnG29vb9RqNfHx8Vrnbty4saaMiYkJhYWFep9zxIgR/PbbbyxfvpxRo0aV2v/ggw/SuHFjjhw5ovWaJTNqRUdHk5mZSVhYGH369Kl0Zzgh7mWBrQMJHxWOi62L1nZXW1fCR4UT2DrQSJHVXkZvmd5v3H3csXW1JTslW/d9UxXYutri7lM7PsTfeecdhg0bxuzZs3nmmWdQFIWYmBiee+45zM3NmT17Nm+99RZt2rRh8ODBJCcnY2ZmRufOne967g4dOjBixAiCg4OpV68eXbp04dKlS2RmZvLoo48C0KJFCyIjIxkwYACNGze+6xjXvn37Ymdnh4WFRalLvFDcep0zZw7Tpk2jRYsWDB8+nFu3bnHkyBHGjBmjGWO8fft2unTpwttvv029evU4evQoPXv2vOt9WyHqisDWgQzzGkZsUiyXb1zGycYJH3cfaZGWQVqmNczE1ISA0IDiJ3deHf3necDiAExMa8d/zZAhQ4iMjGTbtm20bt2a7t27ExkZqdk/ffp0Zs+ezTvvvEOLFi147rnnuHr1qt7nX7NmDU8++SQTJ07E09OTMWPGcP78ec3+zz77jD/++IM2bdrw559/3vV85ubm7N27l+3bt5d5+Tk4OJgvv/ySzz//nBYtWuDv78++ffsA6NatGzNmzODll1/mscce4+mnn+bll19m9uzZ/Pbbb3rXS4i6wNTEFD9PP0a3H42fp58k0nKoFEXR1T66r2VnZ2NnZ0dWVlapMae5ublcuHCBZs2alZq9qSLiI+KJConS6oxk62ZLwOIAWge2LudIcS8x1PtFCGEc5eWD28k1KyNpHdgar2FeJMUmcePyDWycbHD3ca81LVIhhBD6k2RqRCamJnj6eRo7DCGEEFUkzSAhhBCiiiSZCiGEEFUkyVQIIYSoIkmmQgghRBVJMhVCCCGqSJKpEEIIUUWSTIUQQogqkmR6H/Hz80OlUqFSqTAxMcHe3p5evXoRHh6uVS4mJgaVSqVz1Z57kVqt5vDhw8yfP5/+/ftz8OBBY4ckhKhjJJneZ4YOHcq1a9dISUkhKioKLy8vRo4cyeLFizVlevbsybVr1+rMiilJSUkEBgbyyy+/sHv3bnJzc40dkhCijpEZkIyoqAhiY+HyZXByAh8fMK3meaTNzMw0i2I7OTnh7e1NTk4OM2fOZNSoUTg7O1OvXj0aNmxYrXHk5+djbm5era9RwsPDg+TkZE6dOsXWrVtr5DWFEPcXaZkaSUQEeHpC797w5JPFPz09i7fXtJkzZ5KXl8emTZuA0pd5b926xXPPPYeHhwdWVlZ06tSJo0ePap3js88+w8XFBRsbG6ZMmULPnj0JCgrS7Pfz82P8+PHMmTMHe3t7wsLCAJg2bRotW7bEysoKLy8vdu/erTmmJI5ffvmFgIAArK2t6datG1euXGHJkiU4OTnh6OjI6tWry61fZRcvF0IIfUkyNYKICAgKgkuXtLenpBRvr+mE2qZNG8zMzIiPj9e5v6CggA4dOrBr1y7OnDlDgwYNmDFjhmb/jh07CAkJ4e233yY+Ph53d3ed9yW3b9/OlStXOH78OEOHDgXA2dmZiIgIEhIS6NChAy+99FKp4yZOnMikSZM4fPgwp06dol+/fhw4cIADBw4QGBhIcHAwsviREMKY5DJvDSsqgpAQ0PXZryigUsHUqTBsWPVf8i1hYmKCg4MDeXl5Ovfb2dkREhKied6nTx+t1uDChQsZMGAAEydOBODVV1/VeTm1RYsWfPXVV1otxddee03z74EDBxKh45vE/PnzGTRoEAAtW7bEwsKCNWvWYGJigr+/P0uXLuXatWs4ODhUsOZCCGEY0jKtYbGxpVukt1MUSE4uLldTCgsLSUtLo3HjxmWWiYyMJCAggObNm/PRRx9RVFSk2Xfy5Em8vb21yuu6tOrl5VVqe0xMDIGBgXh5efHyyy+jVqtLHde2bVvNv01MTPDy8sLExETzHNB5nBBC1BRJpjXs8mXDljOE48ePo1ar6dKli879y5YtIygoiK5du7Jx40ZNC7RETk4O1tbWFX7dPXv20KdPH5ydnVm9ejVz586tTPhCCGF0cpm3hjk5GbacISxatAgnJycGDhyoc394eDgDBw7UJLs7e/o2a9aMCxcuaJ6r1WoyMzNxdHQs93UjIiJo27Ytn332GQCnT5+ufCWEEMKIpGVaw3x8wNW1+N6oLioVuLkVl6sOBQUFXL9+nczMTE6cOMHkyZOJjIxk+fLlWFhY6DzGzc2N06dPc+bMGXbs2MHq1av566+/NL19x40bx5o1a9i3bx/nzp3jqaeeIjU1FTMzs3JjcXNzIzk5maNHj7J//36WLFkCwKFDhwxaZ7VazfXr17lx4wYAN2/e5Pr16xQWFhr0dYQQ9y9JpjXM1BRCQ4v/fWdCLXm+eHH1dT7asmUL9vb2NG7cmH79+nH16lXi4uLo379/mcfMmTMHFxcXOnXqxNKlS9m8eTMuLi4MHz4cgJCQEEaOHMmgQYPw9fXFx8eHNm3a0KBBg3JjCQ4OxsfHBx8fH2bPns3y5cvx9vZm8ODBBk10SUlJ2Nvb0717dwCGDBmCvb09+/fvN9hrCCHubypFxhSUkp2djZ2dHVlZWdja2mrty83N5cKFCzRr1gxLS8tKv0ZERHGv3ts7I7m5FSfSwMBKn7ZWUKvVuLu7ExwczMyZM40djlEZ6v0ihDCO8vLB7eSeqZEEBhYPf6npGZCqw9mzZzlx4gT//e9/KSoq4tNPPyUtLU1r0gYhhKjLJJkakakp+PkZO4qqS09P5/333ychIQEzMzM6dOjAvn37aNGihbFDE0KIGiHJVFRZ9+7dOXHihLHDEEIIo5EOSEIIIUQVSTIVQgghqkgu8wohRB2mLlKTFJvEjcs3sHGywd3HHRNTaUcZmiRTIYSoo+Ij4okKiSL7UrZmm62rLQGhAbQObG3EyOoe+XoihBB1UHxEPGFBYVqJFCA7JZuwoDDiI3QvuSgqR5KpEELUMeoiNVEhUaBrSp5/tkVNjUJdJKstGYok0/uIn58fKpUKlUqFiYkJ9vb29OrVi/DwcK1yMTExqFQqzdy797pPP/2UTp060aBBAzw8PHj33Xe1lpAToq5Jik0q1SLVokB2cjZJsUk1F1QNOnbsGBMnTqzRv3O5Z2pEReoiYpNiuXzjMk42Tvi4+2BqUr1TIA0dOpQVK1aQk5NDUlIS3377LSNHjuSTTz5h6tSpAPTs2ZNr166VO3XWveTXX3/l3XffpVOnTvz666+MGTMGa2trXn31VWOHJoRhFBVpTad2I6WhXofduHyjeuMygl27dhEUFMTNmzdp1qxZjU1pKsnUSCLiIwiJCuFS9r+T87rauhIaEEpg6+qbnNfMzIyGDRvSsGFDnJyc8Pb2Jicnh5kzZzJq1CicnZ2pV69eqWXWDC0/Px9zc/NqfY0Sq1ev1vzb1dWVoKAgwsPDJZmKukHHRN+tHZvSil78SZtyD7Vxsqnu6GrU999/zwsvvEBRURH+/v68+OKLNfbacpnXCCLiIwgKC9JKpAAp2SkEhQURER9Ro/HMnDmTvLw8Nm3aBJS+zHvr1i2ee+45PDw8sLKyolOnThw9elTrHJ999hkuLi7Y2NgwZcoUevbsqTU3r5+fH+PHj2fOnDnY29sTFhYGwLRp02jZsiVWVlZ4eXmxe/duzTElcfzyyy8EBARgbW1Nt27duHLlCkuWLMHJyQlHR0etZKkPCwsLcnJyKvGbEqKWiYiAoCDtFTMA0/SrjCKMVvyh+zgV2LrZ4u7jXgNBVj9FUXj33Xd59tlnKSoqYsyYMezYsQM7O7sai6FWJNPdu3fTrl07rKys6Nu3713v1aWkpLBy5UrGjRvHm2++WWr/rl276NOnDw4ODjg6OjJ27FgyMjKqKfqKKVIXERIVgqKjZ0DJtqlRUylS19y1/jZt2mBmZkZ8vO7efQUFBXTo0IFdu3Zx5swZGjRowIwZMzT7d+zYQUhICG+//Tbx8fG4u7tz8ODBUufZvn07V65c4fjx4wwdOhQAZ2dnIiIiSEhIoEOHDrz00kuljps4cSKTJk3i8OHDnDp1in79+nHgwAEOHDhAYGAgwcHB6Lv40d9//822bdt49NFH9SovRK1VVFTcItXx3lcpCqAigChU3NHJ6J+lHgMWB9SZ8aYnTpzgnXfeAYobB6tWraqxK18ljP6bPHv2LMOHD2f69OkkJCTQsmVLBg4cWO6N4xdeeIF169axa9cuUlNTS+0/ePAgo0eP5rfffmPbtm0cPHiQcePGVWc19BabFFuqRXo7BYXk7GRik2JrLCYTExMcHBzIy8vTud/Ozo6QkBBatWqFu7s7ffr04fz585r9CxcuZMCAAUycOBFXV1deffVVevToUeo8LVq04KuvvsLDw0NzP/a1116jffv2ODs7M3DgQK3zlpg/fz7Dhw+nbdu2tGzZkgYNGrBmzRqaNWuGv78/WVlZXLt2Ta+6vvTSSzg4ODB79my9ygtRa8XGlmqR3k6Fgh3ZtG6crrXd1tWWUeGj6tQ4044dO/LFF1/w+eefM2/ePFR3LhZdA4x+z3TJkiX06dOHZ555BoDQ0FCcnJzYunWrZvHpO23fvh2VSsUjjzyic/+cOXM0/37wwQeZMWMGEyZM4NatW1hbWxu8DhVx+cZlg5YzhMLCQtLS0mjcuHGZZSIjI/n66685d+4cqampNGnSRLPv5MmTTJkyRau8rjezl5dXqe0xMTF8+umnnD59mpSUFNTq0l3127Ztq/m3iYkJXl5emJiYaJ4DOo+70+TJkzl06BDR0dHY2NSte0XiPnRZv8+IEYu708WlR52bAenq1avk5OTg6ekJFF/BMiaj/0bDw8Pp3bu35rm5uTndu3dnw4YNZR5T0W8dFhYWqNXqMlteNcnJxsmg5Qzh+PHjqNVqunTponP/smXLCAoKomvXrmzcuLHUmzYnJ6dSX1L27NlDnz59cHZ2ZvXq1cydO7cy4evlzTffZM+ePezbtw8np5r73QpRbfR8H5u4uODp50n70e3x9POsE4n0zJkzdOvWjYCAgFpzC8+oLdP8/HyuXr2Km5ub1nY3Nzd+//13g73ODz/8QJcuXbC3t9e5Py8vTyvRZmeXMz6rinzcfXC1dSUlO0XnfVMVKlxtXfFx96m2GO60aNEinJycGDhwoM794eHhDBw4UJPs7uzp26xZMy5cuKB5rlaryczMxNHRsdzXjYiIoG3btnz22WcAnD59uvKVKMemTZv4+OOPOX78uFaLWoh7VVERxBb50MXBFevMFFS6ZmdQqcDVFXxq7rOkJhw4cIChQ4eSkZFB8+bNycrKolGjRsYOy7gt04yMDBRFwdLSUmu7paUl6enpZRxVMcuWLSMmJoalS5eWWWbevHnY2dlpHncmd0MyNTElNCAUKE6ctyt5vjhgcbWNNy0oKOD69etkZmZy4sQJJk+eTGRkJMuXL8fCwkLnMW5ubpw+fZozZ86wY8cOVq9ezV9//aXpKDZu3DjWrFnDvn37OHfuHE899RSpqamYmZmVG4ubmxvJyckcPXqU/fv3s2TJEgAOHTpksPrm5+fz8ssvM3z4cJo2bcr169e5fv16tX5hEqI6RUSApyf07mvK05mhKID6js8SSq7eLV4MptU7dr0mRUZG4u/vT0ZGBl26dOHAgQM8+OCDxg4LMHIybdSoESqVitzcXK3tOTk5d23V6GPdunVMnz6dHTt20LFjxzLLvfHGG2RlZWkeycnJVX7t8gS2DiR8VDguti5a211tXQkfFV6t40y3bNmCvb09jRs3pl+/fly9epW4uDj69+9f5jFz5szBxcWFTp06sXTpUjZv3oyLi4vmnnZISAgjR45k0KBB+Pr64uPjQ5s2bWjQoEG5sQQHB+Pj44OPjw+zZ89m+fLleHt7M3jwYAoLCw1S39TUVC5dusT69euxt7fXPDp06GCQ8wtRk+4cCRNJIEGEk4L2ZwmurhAeDoHV91lS0z7//HNGjBhBbm4ugwcPJjo6mgceeMDYYf1LMTJnZ2fl448/1to2cOBA5cknn7zrsZ07d1bGjRunc9/27dsVOzs7Zf/+/RWOKSsrSwGUrKysUvtycnKUP/74Q8nJyanwee9UWFSoRF+IVtb+vlaJvhCtFBYVVvmctUFRUZHi4uKizJs3z9ihGJ0h3y/i/lZYqCiuropSPBZG+2FCoeJHtDLZYa1SuCe6uHAd8vnnnysUzyqsTJgwQSkoKKix1y4vH9zO6L15g4KCiI6OZtq0aQDk5uZy4MABli1bVulzXrx4kdGjR7N48WKdQzRqC1MTU/w8/YwdRpWdPXuWEydO8N///peioiI+/fRT0tLStCZtEEJUTXkjYdSYEoMfMZkQZAp+defKLgAjRoxg0aJFPPvss7z55ptGGfpyN0ZPpsHBwXTs2JFVq1bh7+/P3Llzadq0qWZQv7+/Py4uLqxcuVJzzM2bNyksLKSoqIj8/HyuX7+Oubm5pkfp66+/jp2dHcOHD+f69eua42xtbTVDKYThpKen8/7775OQkICZmRkdOnRg3759tGjRwtihCVFn6DkSRu9ytd3tU442adKEEydO3PXWkTEZPbO0bNmSyMhIPvjgA5o3b86FCxfYuXMnpv/cNE9ISCApSXtlg8GDB2Nvb8/x48dZt24d9vb2WjPnHDp0iOTkZBwcHLTuk915HmEY3bt358SJE9y8eZNr166xb98+unbtauywhKhT9B3RVRdGfiUnJ/PII4+wYsUKzbbanEgBVIqi5zxs95Hs7Gzs7OzIysoqtXJKbm4uFy5coFmzZqV6IQtxJ3m/CEMpKiruxZuSonMGQc1ImAsX7u0OvCdPnmTAgAGkpKTg4eHBn3/+adS/nfLywe2M3jIVQghxd6amEFo8qo47bxnWlZEwP/30Ez179iQlJYXWrVvz888/3zNfQiWZCiHEPSIwsHjEi0tlR8Koi+BqDCSuK/5Zgwtq3M3atWsJCAggOzubXr168csvv+Dufu+samP0DkhCCCH0FxgIw4ZprQWOj48eLdLkCDgSArdu6xJs7QqdQ8HNuONR58+fr1nEe9SoUaxYseKeaZGWkGQqhBD3GFNT8POrwAHJERAbBHdOO3grpXi7T7hRE+qtW7cAeOWVV1iwYME9OepCkqkQQtRl6qLiFqmu+XspXveUI1PBZRhU0zSmdzN37ly6d+9+T68zfO+lf1Fpfn5+qFQqVCoVJiYm2Nvb06tXL8LDw7XKxcTEoFKp7rpI+73i448/5sEHH8TCwoIHHniAoKAgLteVwXhC3E1arPal3VIUuJVcXK6GpKen89JLL2lapCqV6p5OpCDJ1LiKiiAmBtatK/5ZzoLohjJ06FCuXbtGSkoKUVFReHl5MXLkSBYvXqwp07NnT65du3ZP3fwvj5eXF2FhYSQlJREREcH+/ft59dVXjR2WEDUjR88vjvqWq6KEhAS6d+/Ol19+qTU/wL1OLvMaS0QEhIRozw/m6lrc970aJ6c2MzOjYcOGNGzYECcnJ7y9vcnJyWHmzJmMGjUKZ2dn6tWrV2qZNUO7fXaT6jZo0CDNv5s0aUK3bt0MtiqRELWelZ6zOOhbrgoOHz7MoEGDSEtLw8PDQ9PpqC6Qlqkx3Ln0Q4mUlOLtERE1Gs7MmTPJy8tj06ZNQOnLvLdu3eK5557Dw8MDKysrOnXqxNGjR7XO8dlnn+Hi4oKNjQ1TpkyhZ8+eWnPz+vn5MX78eObMmYO9vT1hYWEATJs2jZYtW2JlZYWXlxe7d+/WHFMSxy+//EJAQADW1tZ069aNK1eusGTJEpycnHB0dGT16tV61bOgoICIiAji4uLq1B+xEOVy9CnutXvnMm0aKrB2Ky5XjbZv346fnx9paWl06tSJuLg4WrVqVa2vWZMkmda0oqLiFqmuKUxKtk2dWiOXfEu0adMGMzMz4uPjde4vKCigQ4cO7Nq1izNnztCgQQNmzJih2b9jxw5CQkJ4++23iY+Px93dnYMHD5Y6z/bt27ly5QrHjx/XzL3s7OxMREQECQkJdOjQQedln4kTJzJp0iQOHz7MqVOn6NevHwcOHODAgQMEBgYSHBzM3Sbyat++PRYWFjzzzDOsXLmS3r17V+RXJMS9y8S0ePgLUDqh/vO88+Jq7Xz0zTffMHToUG7dusWjjz7Kvn37cKoL8x7eRpJpTStv6QcoTqjJycXlaoiJiQkODg7k5eXp3G9nZ0dISAitWrXC3d2dPn36cP78ec3+hQsXMmDAACZOnIirqyuvvvqqztV6WrRowVdffYWHh4dmWq7XXnuN9u3b4+zszMCBA7XOW2L+/PkMHz6ctm3b0rJlSxo0aMCaNWto1qwZ/v7+ZGVlce3atXLruGPHDvbv389zzz3H4MGD2bhxY0V+RULc29wCi4e/WN8x24O1a7UPi7l27RpvvfUWarWaZ555hq1bt2JjY1Ntr2cscs+0ptXCpR8KCwtJS0ujcePGZZaJjIzk66+/5ty5c6SmptKkSRPNvpMnTzJlyhSt8rqWSPLy8iq1PSYmhk8//ZTTp0+TkpKCWq0udVzbtm01/zYxMcHLy0szDq3kp67jbufm5oabmxvdu3cnPT2d1157jREjRpR7jBB1iltg8fCXtNjizkZWTsWXdk1MKSqqxCQQerK3t2fbtm3s2rWLWbNm1crl0wxBWqY1rRYu/XD8+HHUajVdunTRuX/ZsmUEBQXRtWtXNm7cyMSJE7X25+TkaJa/q4g9e/bQp08fnJ2dWb16NXPnzq1M+BXm7e1NYmIiRTV4KV2IWsHEFJr4gefo4p8mpkREFE+g37s3PPlk8U9Pz6p13cjOziYuLk7z/L///S+zZ8+us4kUJJnWPB+f4l67Zb2pVCpwcysuV0MWLVqEk5MTAwcO1Lk/PDycgQMHMnfuXDp27Fiqp2+zZs24cOGC5rlarSYzM/OufzgRERG0bduWzz77jC5dupTbMjakM2fO4OLiolnmT4j7VXX0hUxNTcXX15d+/fpx5MgRwwR6D5BkWtOMvPRDQUEB169fJzMzkxMnTjB58mQiIyNZvnw5FhYWOo9xc3Pj9OnTnDlzhh07drB69Wr++usvTW/fcePGsWbNGvbt28e5c+d46qmnSE1NxczMrNxY3NzcSE5O5ujRo+zfv58lS5YAxevRGtL8+fOJiYkhJSWF5cuXs3Tp0jo1vk2IyqiOvpB//PEH3bp14/jx49SvX/+uHQPrEkmmxlDlpR8qb8uWLdjb29O4cWP69evH1atXiYuLo3///mUeM2fOHFxcXOjUqRNLly5l8+bNuLi4MHz4cABCQkIYOXIkgwYNwtfXFx8fH9q0aXPXxXyDg4Px8fHBx8eH2bNns3z5cry9vRk8eDCFhYUGq/P58+cZPXo0zZs3Z968ebz33nu8/vrrBju/EPciQ/eFjI2NpUePHiQlJdGyZUvi4uJ45JFHDBPsPUAWB9ehxhYHr867/kakVqtxd3cnODj4vh/PKYuDi9pq3brie6R3s3YtjB5dfpkNGzbw1FNPkZ+fT7du3diyZUuN3bapbvouDi69eY2pwks/1E5nz57lxIkT/Pe//6WoqIhPP/2UtLQ0rUkbhBC1i6H6Qu7evZtRo0YBMHz4cNauXYuVlVUVo7v3SDIVVZaens77779PQkICZmZmdOjQgX379tGiRQtjhyaEKENJX8iUFN33TVWq4v136wvZu3dvBg4cSLNmzQgNDb1vO/ZJMhVV1r17d06cOGHsMMS9rI7e8qjNSvpCBgWBSqWgKP92iFSpipdmK6svZG5uLvXq1dM8IiMjMTMzq9NDX+5GOiAJIYyrOgY6ilKK1EXEJMaw7uQ6YhJjKFIXERgIi1+9hK3JTa2ydiY3WPzqJZ19ITMzM+nXrx8vvfSSpreuubn5fZ1IQVqmQghjKhnoeOd1xpKBjtXcu/1+EREfQUhUCJey/+2+62rrymsNX+PawmuEKCou4s5NbGjADTyKkri2UCG+6yhaB7bWHJOYmMiAAQP4888/+f3333njjTdo1qyZMapU60jLVAhhHLVw0Yd7QgXXQY6IjyAoLEgrkQKkZKcQcjGEP1r9gQkKzbhIe07RjIuYUPz7j5oahbqoeKrOY8eO0a1bN/78809cXV3Zv3+/JNLbSDIVQhhHLVz0odar4CXxInURIVEhKJT+wlKyLSogCrVKx9zWCmQnZ5MUm8SuXbvo1asXV65coX379sTFxdG+fXsDVuzeJ8lUCGEctXDRh1qtEnP/xSbFlmqRalFBtl02Fz0ulllkbdhaBg8ezM2bN+nTpw+xsbG4urpWthZ1liRTIYRx1MJFH2qtSl4Sv3xDvy8iNxvcLHOfs4cziqIwZswYdu7ciZ2dnb5R31ckmd5H/Pz8UKlUqFQqTExMsLe3p1evXoSHh2uVi4mJQaVSaeberUsiIyNRqVTExMQYOxRRCxd9qLUqeUncyUa/LyINbuqY+lMFtm62jH11LHFxcaxcuRJzc/OKRH1fkWRqTOoiuBoDieuKf6qrv6PF0KFDuXbtGikpKURFReHl5cXIkSNZvHixpkzPnj25du0a7u7u1R5PTcrOziY4OPi+78Jfaxh50Yd7RlER7N2rX9k7Lon7uPvgauuKCt3veRUqbLNs8Ujy0GzLI49IIslQMghYHICJqQldunTRrB0sdJOhMcaSHAFHQuDWbd82rV2hc2i1rnpvZmZGw4YNadiwIU5OTnh7e5OTk8PMmTMZNWoUzs7O1KtXr9Qya4aWn59f499yZ86cSdu2be+6mo2oQSWLPoSEaLe8XF2LE+n9PiwmIqL076Y8d1wSNzUxJTQglKCwIFSotDoilSTY99q/R5FzEdmXsrnJTdayllRSyfXIZfHwxYaqSZ0nXzWMITkCYoO0EynArZTi7ck1O1h95syZ5OXlsWnTJqD0Zd5bt27x3HPP4eHhgZWVFZ06deLo0aNa5/jss89wcXHBxsaGKVOm0LNnT625ef38/Bg/fjxz5szB3t6esLAwAKZNm0bLli2xsrLCy8uL3bt3a44pieOXX34hICAAa2trunXrxpUrV1iyZAlOTk44OjqyevXqu9YxLi6O1atXs3Tp0ir+toTBBQZCYiJERxfPqh4dDRcu3NOJtIKjV3Qrq8ORLuVcEg9sHUj4qHBcbLVXqXK1dSV8VDhTnplCSGIIPit9+OGBH0gllcaNG7P8h+XSGq0A+U3VNHVRcYtUR1d1zbYjU2vkkm+JNm3aYGZmRnx8vM79BQUFdOjQgV27dnHmzBkaNGjAjBkzNPt37NhBSEgIb7/9NvHx8bi7u3Pw4MFS59m+fTtXrlzh+PHjDB06FABnZ2ciIiJISEigQ4cOOtcZnThxIpMmTeLw4cOcOnWKfv36ceDAAQ4cOEBgYCDBwcHlrptYUFDACy+8wHvvvYenp2cFfzuiRpQs+jB6dPHPe/jSrkEmdCqvw9Gd9LgkHtg6kMSQRKLHRbM2cC3R46K5EHKBwNbFX1gO/XqIUdNGcemvSzRv3pwDBw7QtWvXCgQs5DJvTUuLLd0i1aLAreTick38aiQkExMTHBwcyMvL07nfzs6OkJAQzfM+ffpotQYXLlzIgAEDmDhxIgCvvvoqW7duLXWeFi1a8NVXX2nds3zttdc0/x44cCAROj5x5s+fz6BBgwBo2bIlFhYWrFmzBhMTE/z9/Vm6dCnXrl3DwcFBZ/zz58/HxsaGl19+ubxfgxBVZrAJne7W4eh2ZVwSVxepSYpN4sblG9g42eDu446fp1+pwzdt2sTo0aPJzc2lS5cubNu2jQceeEC/1xYakkxrWo6eY+b0LWcAhYWFpKWllbv+YGRkJF9//TXnzp0jNTWVJk2aaPadPHmSKVOmaJXX1cnHy8ur1PaYmBg+/fRTTp8+TUpKCmp16cHjbdu21fzbxMQELy8vzeWnkp+6jgM4d+4cCxYs4MCBA3LJSlRdORPy3230ikpVPHpl2DA9Gt76jq2dNQvmzi11wviIeKJCosi+lK3ZZutqS0BogNb0gGq1mgULFpCbm8vgwYP54YcfqF+/vn6vLbTIp0tNs9JzzJy+5Qzg+PHjqNVqunTponP/smXLCAoKomvXrmzcuFHTAi2Rk5ODtbV1hV93z5499OnTB2dnZ1avXs3cuXMrE3651q5dS3Z2Ng899JBmhYuLFy/i7+/Pc889Z/DXE3XYXa7fGnRCJ33H1vr760ykYUFhWokUIDslm7CgMOIj/r2dY2JiwqZNm3j77beJjIyURFoF0jKtaY4+xb12b6Wg+76pqni/Y82NrVu0aBFOTk4MHDhQ5/7w8HAGDhyoSXZ39vRt1qwZFy5c0DxXq9VkZmbi6OhY7utGRETQtm1bPvvsMwBOnz5d+UqU4cUXX2TEiBFa29q3b8+3335L//79Df56oo7S4/rt5Tz9Okzp1eis5GKj6iI1USFRZXfJUMG2kG2cVp/WdBB0dHTknXfe0St2UTZpmdY0E9Pi4S8ApcZ+/fO88+LictWgoKCA69evk5mZyYkTJ5g8eTKRkZEsX74cCwsLnce4ublx+vRpzpw5w44dO1i9ejV//fWXprfvuHHjWLNmDfv27ePcuXM89dRTpKam3nUIipubG8nJyRw9epT9+/ezZMkSAA4dOmSw+j7wwAO0a9dO6wHFXwBcXFzucrQQ6D37kNMD+nUa1KvRWckxuEmxSaVapLfLUXL44tIXjBw5km+//VaveIV+JJkag1sg+ISD9R0f5tauxdurcZzpli1bsLe3p3HjxvTr14+rV68SFxdXbittzpw5uLi40KlTJ5YuXcrmzZtxcXFh+PDhAISEhDBy5EgGDRqEr68vPj4+tGnThgYNdMyqcpvg4GB8fHzw8fFh9uzZLF++HG9vbwYPHkxhYaEhqy1E5el5/daHWMNO6FQyBvfOL32urmX2ZLpx+UaZp8sii+/5nkQSqW9VHw8PjzLLiopTKeWNKbhPZWdnY2dnR1ZWFra2tlr7cnNzuXDhAs2aNcPS0rJqL6QuKu61m3O5+B6po0+1tUhrklqtxt3dneDgYGbOnGnscIzKoO8XYRzr1hXfI72btWuJsBhNyfDq2z9ZSxJspZZn1dHpSY2qVE9dE1MTEmMSWdF7RalTXOUqq1nNDW7QgAas/2Y9A5/XfVtHaCsvH9xO7pkak4lpjQ1/qU5nz57lxIkT/Pe//6WoqIhPP/2UtLQ0rUkbhLhnVWBC/kC/apjQqWQM7j/K66nrNcwLW1dbslOyNfdNz3Oe9awnjzwa05hJTpMIeCagEoGI8tSKy7y7d++mXbt2WFlZ0bdv37tOsJ6SksLKlSsZN24cb775pkHOKSovPT2d999/n7Zt29K5c2eOHTvGvn37aNGihbFDE6LqKjghf3VO6HS3nrpnNp8hIPSfRKmCa1xjDWvIIw933HmO53jysycxMa0VH/11itF/o2fPnmX48OFMnz6dhIQEWrZsycCBAykqZ/6tF154gXXr1rFr1y5SU1MNck5Red27d+fEiRPcvHmTa9eusW/fPpk9RdQd5XQGUlChKKD++GOtzkDVMaFTQb6azyae4qTSjgt4oL69A+M/rdCoqVF4DfNiVPgobF1ssceeXvSiDW2Y7DqZcRvHaY0zFYZj9HumL7/8MomJiZoZc/Lz83FycuK7777TdHC5k6IoqFQqHnnkEdq1a8fy5curfM7b1dg9U1HnyfvlHlTWxAw6Jp3PwpYoAkh17VpqQgRDioiAyZMKuZL27505W7IIIIo2/KlV9qk9T+HwsAN2tnbFvXtTs2nQtAGevp7SIq0Efe+ZGv03Gx4eTu/evTXPzc3N6d69Oxs2bCjzmLstoVWZc1aU9NsS+pD3yT2mvIkZAgOJ/3gnyxnHRkawnHGEMpU/aaNzQgRDhhQUBFfStJu32dgSxij+oJVmWz75vDDjBfr168etnFt4+nnS4ckOPNjnQUmk1cyoHZDy8/O5evUqbm5uWtvd3Nz4/fffa+yceXl5WvPSZmeXPU6rZOzkrVu3sLKyqlSM4v6Rn58PgOk9PHH7feMuEzOow8KIeiWZbJqVPvafCRFKLrMaKnFpD3HVNS5dIYoAWnGGHG6yjnVcOnIJCwsLjhw5gq+vr0HiEHdn1GSakZGBoiilLn9ZWlqSnp5eY+ecN2+e3jOAmJqa0rBhQ/766y8ArK2tZbFpoZNarSYtLQ1ra2vq1ZOO87WaHhPrql+awo20Fyjzgp4C2cnZJMUm4ennaZCw7j7fvYps7DiFJTGEkkkm9vb2bN68GR+9B7QKQzDqX3ijRo1QqVTk5uZqbc/JybnrVHSGPOcbb7zBK6+8onmenZ1dqmV7u6ZNmwJoEqoQZTExMcHd3V2+cNV2ekzMUC/tMu5c5KKulultyps4oaL0m+/+MNv5gDyycHZ0Zs++PbRuLZ2MappRk6m5uTlOTk5cuuNNnJSUhLu7e42d08LCosyp9HRRqVQ4OTnxwAMPUFBQUKk4xf3B3NxcVqu5F+i5SosNN+9exsmmqtFo3H2I6x5gGHnconWz1uz9ZS9O+o6LFQZl9GtPQUFBREdHM23aNKC49+OBAwdYtmxZrTqnLqampnIvTIi6QM8EpG7cBDIoc40KW1db3H3u3hDQtdaorvusd5vvHh7ERNWAvn17Er4xHBsbwyVyUTFG/8ocHBzM3r17WbVqFampqUyZMoWmTZsydOhQAPz9/Rk7dqzWMTdv3uT69esUFRWRn5/P9evXuXXrlt7nFEIILXpOzNDuixf/eX7n/uIfAYsD7tr5KD4inlDPUFb0XkHEkxGs6L2CUM9QnT2B7zbfvUr1IJ8u+YVt27dJIjUyoyfTli1bEhkZyQcffEDz5s25cOECO3fu1LT4EhISSEpK0jpm8ODB2Nvbc/z4cdatW4e9vT0vvfSS3ucUQggteq7S0npkO82ECLezdbVlVPiou44zrchaoyW057svAJ4Dtmjmu588ucVdV2gS1c/okzbURvoO0hVC1DE6JmbAza3UxLr6Xqa9nbpITahnaNlLpP1zmTjkQojOc127lk3//kH89tturK1tSExMxNHRoTK1FBUgE90LIURFBQbCsGG6Z0C6jYmpSYWHv9xtrdHyhtakpqYyaNAgjh8/jrW1NRs2/CCJtJaRZCqEELe7Y5UWQ9F3yMyd5eLj4wkICCApKYkHHniA7du388gjjxg8PlE1Rr9nKoQQ9wN9h8zcXi42Npbu3buTlJREy5YtiYuLk0RaS0kyFUKIGuDu446tq23pnsAlVGDrpj20ZuPGjVy/fp1u3bpx4MABHnzwwZoJVlSYJFMhhKgBJqYmWmuNailjaM2iRYv46KOP2Lt3L40bN66ZQEWlSDIVQggDURepSYxJ5OS6kyTGJKIuUmvtbx3YutyhNV7Dvfj66681M6uZmpry2muvyaIa9wDpgCSEEAYQHxFPVEiUVo9dW1fbUuuctg5sjdcwr1JDa/IL8nniiSfYsGEDhw4dMviMbaJ6STIVQogqKpmM4c5pBksmY7hzQoc7h9ZkZmYybNgw9u/fj5mZGX379q2hyIWhyGVeIYSoAnWRmqiQKN3z9f6zLWpqVKlLviUuXrxIz5492b9/P7a2tuzatYsnn3yy+gIW1UKSqRBCVEFFJmO407Fjx+jatSvx8fG4uLiwf/9+evfuXY3Riuoil3mFEKIKdE3GoEbFRdy5iQ0NuIEHSaXK5ebmMnjwYK5cuUK7du3YuXMnrq6uNRW2MDBJpkIIUQV3TsbwB62IIoBs7DTbbMnC6Vwe7W8rZ2lpyffff8/HH3/M+vXrsbOzQ9y7ZKJ7HWSieyGEvjQT2Kdk84fSijBG/bPn9sGkCioVbNgA//3vJdzc3P7doyioylr6TRidvvlA7pkKIUQVlEzGoFZURPHPpAw6ZmVQlCLGjZtIx44dOXPmzL97JJHWCZJMhRCiiloHtubBd8b9c2lXV3L8GxjO339/w/Xr1zl06FANRyiqm9wzFUIIAzBv6VHGnqvAYOA3wJKpU39g7NhhNReYqBGSTIUQwgCcnHRtPQsMAM4DjYCtDBnSrSbDEjVELvMKIYQB+PiAqyv8ewv0NNCd4kT6IHAAN7du+PgYK0JRnSSZCiHuTeoiuBoDieuKf6qLjBqOqSmEhhb/uzihPgh4AY8AB1Cp/sPixcXlRN0jl3mFEPee5Ag4EgK3Lv27zdoVOoeCW6DRwgoMhA0bFKZOVXHpkhWwFbDAza0+ixcX7xd1kyRTIcS9JTkCYoMoNRnurZTi7T7hRkmoarWaN998ExMTExITPyA2Fi5fdsDJqfgSsLRI6zZJpkKIalGkLiI2KZbLNy7jZOOEj7sPpiZVzCjqouIWaZmzyqvgyFRwGQZVfa0KyMvL49lnn2Xt2rUAjBgxAj+/zjX2+sL4JJkKIQwuIj6CkKgQLmX/exnW1daV0IBQAltXrtWoLlLz154NNL390m4pCtxKhrRYaOJXqdepqKysLB577DGio6OpV68e33zzDZ07SyK930gHJCGEQUXERxAUFqSVSAFSslMICgsiIj6iwueMj4gn1DOUX94J1++AnMsVfo3KuHTpEj4+PkRHR9OgQQO2b9/O+PHja+S1Re0iyVQIYTBF6iJCokJQdFyGLdk2NWoqRRXoeVuy8Hb2pWxuXG+g30FWOgd9GtTJkyfp2rUrJ0+exMnJidjYWPr371/trytqJ0mmQgiDiU2KLdUivZ2CQnJ2MrFJsXqd786Ft5P+9CArwxZF9zrbgAqs3cChO0TvhbWzYcdsuLzX4ENnTp06RUpKCq1btyYuLo6OHTsa9Pzi3iL3TIUQBnP5hn6XV/Utd+fC24piQtTKAEZNDUOtBhOt5sA/syUUPAFDnGFQRvGkQ9eB6PeBRuCz1GA9fUePHg1AQEAA9vb2BjmnuHdJy1QIYTBONvpdXtW3nK6FtyN+C+TpxStJuaa9kHaW0piietNRFixAeToDHO44UJ0BsSOKh9ZUgqIofPHFF6Smpmq2jR49WhKpACSZCiEMyMfdB1dbV1Q6V04BFSrcbN3wcddvTj1dC2+HMYo1vz2F51cf43emMaMvg98laHw2jcsTFsHT/7RR7wzBhOLLxb+FVPiSb1FREVOmTGHy5MkMGjSI3NzcCh0v6j5JpkIIgzE1MSU0oHhOvTsTasnzxQGL9R5v6u7jjq2rLahAzW3rhbaORD3ycfap0vnhJuzLgR4XwdVZQdUI3aug8c/2nEvFQ2f0lJOTQ1BQEJ999hkqlYqxY8diaWmp9/Hi/iDJVAhhUIGtAwkfFY6LrYvWdldbV8JHhVdonGnJwtsAF3EvXi9UpYaAfyZuuC1pOt0EGup5Yj2HzqSnp+Pv78+mTZuwsLBg/fr1TJs2Te/4xf1DOiAJIQwusHUgw7yGGWQGpNaBrRkVPooPXrgAmYBHLNiV7jF8uQHFnY30oLZoQlJMIjcu38DGyQZ3H3dMTLXbFufPnycgIIBz585hb2/P5s2b8ZElX0QZJJkKIaqFqYkpfp5+BjlX68DWPGPnxeq+QAPdrcpYD0jeBK4ZoLJH53U3RYFCVVM+9z5GVvK/l3ptXW0JCA2gdWBrzbbnn3+ec+fO4eHhwc6dO2ndunXpEwrxD7nMK4S4J/j6meDqCtzU3RNYbQIhj4KyEhQVcMdY1JKxqRGf9CIr+abWvuyUbMKCwoiPiNdsW758OYMGDSIuLk4SqbgrSaZCiHuCZr3QJB/Icv0nY2qLbANBD0LGUuCa9r7MPBVhS0bx529tSp/8n0khlk9ejrqoOOu6u7uzbds2nJyqfzYlce+rdDK9fPkyv/76K/n5+QAkJSVx7tw5gwUmhBB3CgyEjRtMaXT4n1W4y0ioTfygzxF492d473fokwSTPx7Bn4d0JFKKZ2aKVqL56MpHLP3f0mqsgairKpxML168SK9evXBxcaFbt25cuXIFgBMnTvDss88aPEAhhLhdYCBcjQnknbbhOJhp9xhuZNWIRlaNUJtAdDOY4wQfFzXEceUoWv/RTuf5iihiM5vZxz4ATp86Xe11EHVPhTsgPf/883h4eBAaGoqfn59me+fOnTl16pQhYxNCCJ1MTeHtkYG8pS7dYxiK5wj+7affOPXeKTwuemCi6G435JFHGGEkkIAKFYMZzPSXptdkVUQdUeGW6cGDB/nwww/p1KkTJrdNjJmRkUFhYWGlgti9ezft2rXDysqKvn37kpiYWG75Y8eO4e3tjZWVFd7e3hw/frxUmf3799OtWzcaNGiAh4cHCxYsqFRsQojaq6TH8Oj2o/Hz9MPUxBRTE1N6ufXCdI4pzRKblZlIb3CD7/meBBIww4zRjKa3W2/cfdxruBaiLqhwMvX09CQuLk7zXKVSkZuby+zZsys1Buvs2bMMHz6c6dOnk5CQQMuWLRk4cCBFRbqn+8rMzKR///4MHTqU8+fPM2TIEB599FGuX7+uKXP58mUGDRrE+PHjOXfuHIsWLWLWrFls27atwvEJIe49d06Qf6db3OJbvuUKV6hPfcYznv/wHwIWB5QabyqEPir8rlm0aBHjxo0jICCA3NxcgoODad68Ofv372fhwoUVDmDJkiX06dOHZ555BmdnZ0JDQ7l69Spbt27VWf7777/HycmJt956CycnJ2bNmsUDDzzA8uXLNWXi4uIwMzNj4sSJODk5ERQURIcOHTh79myF4xNC3Ht0TZB/OyusaEUrHHDgOZ7D1dSVoA1BWuNMhaiICifT/v37c+rUKby8vOjWrRsZGRk88cQTHD9+nDZtdPeUK094eDi9e/fWPDc3N6d79+5s2LChzPK336sF8PPz0yrfvHlzMjIy+OGHHwBITU0lISGBIUOGVDg+IcS9584J8kuo/xl8qkLFozzKC7yAAw6MWDeCtkFtazJEUcdUagakZs2aERoaWuUXz8/P5+rVq7i5uWltd3Nz4/fff9d5TFJSEoGBgaXKR0ZGap4/9NBDzJkzhzFjxvDLL79w5MgRVqxYQcuWLXWeMy8vj7y8PM3z7OyyLw8JIWq/kgnys1OyNWNID3KQs5zlSZ6kHvUwwYQmrk1KzXwkRGVUejrB69evo1aXXu7eweHORQTLlpGRgaIopVZgsLS0JD09Xecx6enpepU3MzOjY8eO7Nixg8zMTDIzM8uMY968ebzzzjt6xy2EqN1KJsgPCwpDjZrd7CaO4r4epzhFRzri944fPm/5yD1SYRAVfhetWbMGBwcHGjVqhKOjY6lHRTRq1EjTgel2OTk5ZZ7L0dHxruVXrlzJN998w08//cTJkycZMWIE48ePZ+3atTrP+cYbb5CVlaV5JCcnV6geQojap3Vga4atHcYWqy2aRNqXvvi4+jBq4yh83/aVRCoMpsIt02nTpjFq1Cj8/f21hsZUhrm5OU5OTly6pL0CRFJSEu7uurune3h43LX8V199RVBQEHZ2dgB8++23JCYm8umnn/Lkk0+WOqeFhQUWFhZVqosQonbJzMxkyhdTOJ5zHLN6Zrw78V2eCHpC5woxQlRVhZNpvXr1eOONN/Dw8DBIAEFBQURHR2vWCMzNzeXAgQMsW7aszPLff/+91rbo6GheeOEFzfO8vLxSl3U9PDyIj49HCFH3Xbx4kQEDBhAfH4+trS2bNm3S6ugohKFV+OvZG2+8wZtvvmmwAIKDg9m7dy+rVq0iNTWVKVOm0LRpU4YOHQqAv78/Y8eO1ZQfP348V65cYf78+Vy5coW5c+eSnp7O+PHjNWUCAwNZu3Yt69atIzU1lfDwcH744QfGjRtnsLiFELXXjRs3SE1NxcXFhf3790siFdVOpSiKUpEDrl69Sr9+/bCxscHLy6vU/rJalOX58ccfCQkJITExkZ49e/LNN9/g6ekJFE8S4enpSUxMjKb80aNHmTBhAqdOnaJjx458+eWXdOrUSbO/qKiI+fPns2zZMlJTU2nWrBkhISFMmDBBr3iys7Oxs7MjKysLW1vbCtdHCPGvInWRQRYJr6hffvkFDw8PXF1dq/21RN2lbz6ocDLt0aMHJ0+epGXLlqXumapUKn799dfKRVyLSDIVwjAi4iMIiQrhUva//RxcbV0JDQglsHVgOUdW3MqVK/H09KRXr14GPa+4v1VbMq1fvz6//fZbnV4sV5KpEFUXER9BUFgQCtofMSqKl00LHxVukISqKAoffPABs2bNomHDhpw4caLMDoxCVJS++aDC90x79erF//3f/1UpOCFE3VakLiIkKqRUIgU026ZGTaVIrXsObn0VFhYyadIkZs2aBcDEiRPlsq4wigr35p09ezaTJk3CzMxM5/SB8o1QCBGbFKt1afdOCgrJ2cnEJsXi5+lXqdf4+++/efzxx9m+fTsqlYolS5YwefLkSkYsRNVUOJn27NkTgIEDB6JS/bvKvaIoqFSqMld7EULcPy7fuGzQcnf666+/GDx4MIcPH8bS0pJ169YxfPjwSp1LCEOocDKNjo6ujjiEEHWIk42TQcvdaf78+Rw+fJhGjRqxdetWunXrVqnzCGEoFU6mvr6+1RGHEKIO8XH3wdXWlZTsFJ33TVWocLV1xcfdB3WRmqTYJG5cvoGNk41eMxR98MEHZGRk8Oabb/Kf//ynuqohhN4q3Jv3fiC9eYWoupLevIBWQr29N2/r+NZEhURpLeRt62qrcyWXQ4cO0aVLlypPYypERRi0N6+pqalmWTITExNMTU3LfAghBEBg60DCR4XjYuuitd3V1lWTSMOCwrQSKUB2SjZhQWHER/w7/efnn39O9+7dmTFjRo3ELkRF6XWZd9myZVhbW2v+fXvHIyGEKEtg60CGeQ0rNQOSSlER2j8UHVeAi7epIGpqFC2HtGTW7FnMnz8fgKysLNRqtbRORa0jl3l1kMu8QlSvxJhEVvReUW6ZQgo56X+SzXs3A/Dee+/x1ltvyZd5UaOqbdKGPn36cOvWrVLbMzMzZSJ5IYRebly+Ue7+XHJZzWo2791MvXr1+P7775k1a5YkUlFrVTiZxsTE6BxL+ttvvxEZGWmQoIQQdZuNk02Z+9SoWclKEkmkvlV9tm3bprUqlBC1kd5DY0JDQwkNDUWlUtG+fXutexaFhYWkpqby+OOPV0uQQoi6xd3HHVtXW7JTskvdNzXBhB70YJfpLn76+Sc6P9LZOEEKUQF6J9Nu3bpx7do13n33XUaPHo2lpaVmn6mpKS1atCAoKKhaghRC1C0mpiYEhAYQFhQGKkApvkdaj3qggra0ZcbKGZJIxT2jwh2QVqxYwZgxY6hXr8LzPdwzpAOSEDUjPiKeqJAo9l/aTzTRjGc8bm5uBCwuPc5UCGOotg5I48aNq9OJVAhRc1o91or8yflEEME1rpEzOoeQCyGSSMU9RwZrCSGMoqioiJdffpmZb8wEYOrUqXy++vO7TiUoRG0kTUwhRI3LycnhySefZNOmTahUKhYtWsS0adOMHZYQlSbJVAhRozIyMhgyZAhxcXGYm5uzevVqRo4caeywhKgSSaZCiBpVr149bt68ScOGDdm8eTO9evUydkhCVFmFk6miKGzcuJEzZ87onLzh7bffNkhgQoi6yc7Ojh07dpCdnU2bNm2MHY4QBlHhoTFPPfUUP/zwA02bNsXMzEz7ZCoV58+fN2iAxiBDY4QwrB07dpCQkMDLL79s7FCEqBB980GFW6abN28mLi6OLl26VClAIcT94dtvv2XSpEkUFRXRpk0b/P39jR2SEAZX4T7o//nPf3Re3hVCiNspisKcOXN44YUXKCoqYty4cXJ/VNRZFU6mn332GS+//DKJiYnVEI4Qoi4oKCjg2Wef5d133wVg1qxZfP/996VuDQlRV+h1mbdZs2ZaSx9lZGTQtm1bmjRpUqpsXbhnKoSovBs3bjBy5Eh27dqFiYkJX375JRMmTDB2WEJUK72S6bhx42QdQSGEXrZs2cKuXbuwtrZm/fr1DB482NghCVHtKtyb934gvXmFqJr333+fRx99VDoqintetU10/+yzz5Kbm1tqe1ZWFrNnz67o6YQQdcDBgwe5du2a5vmsWbMkkYr7SoWT6YoVKygoKCi1PSEhgcWLFxsiJiHEPSQ8PBw/Pz+GDx+u84u2EPcDvceZLl++nJUrVwIwaNAgrWXYCgsLOX78OD179jR8hEKIWmvx4sW88sorKIpCw4YNUavVxg5JCKPQO5m6uLjg7u6Ooii4ublhbm6u2WdqasrAgQN58cUXqyVIIUTtolaree211/j4448BePHFF1myZAmmpqZGjkwI49A7mfbr149+/frRrFkzZs6ciYWFRXXGJYSopXJzcxk3bhxhYWEAfPjhh7z++uvS41/c1yp8z3TOnDk6E+nff/8t6xEKcQ8qUhcRkxjDupPriEmMoUhd/gxnL7zwAmFhYZiZmbF69WpmzJghiVTc9yo8NCYrK4svvviC8+fPa00rGB8fz5kzZ8jMzDR4kDVNhsaI+0VEfAQhUSFcyr6k2eZq60poQCiBrQN1HhMfH8/AgQP57rvv6NOnT02FKoRR6JsPKpxMBw0axKFDh2jXrh0HDhygc+fOWFpacuzYMTZv3oyvr2+Vgzc2SabifhARH0FQWBAK2h8BKopbmV+0+YIJgRMwMTXh5s2bNGjQQFOmoKBApgYU94VqG2f6888/89NPPxETE0PTpk1Zvnw50dHR/O9//2Pr1q1VCloIUTOK1EWERIWUSqQACgqKojAjbgafNPuE7+Z8h6enJ9HR0ZoykkiF0FbhZGptbY2DgwMAbm5u/PrrrwAMHTqUZcuWGTY6IUS1iE2K1bq0W4oKsu2y2ZSziQnvTiAjI4NPP/205gIU4h5T4fVMu3btSlxcHCNHjmTkyJFMnz6d9PR0fv75Zxo3blwdMQohDOzyjcvlF1CAWNifvh+ATtadWLtmbfUHJsQ9qsIt0/nz5/Pggw8C8NJLLxEQEMCsWbOIj4/nu+++q1QQu3fvpl27dlhZWdG3b9+7Lu927NgxvL29sbKywtvbm+PHj5cqc+jQIfz8/Khfvz4ODg707duXmzdvVio+IeoaJxunsncWAduAn4qf9qAHQ24N4eqvV2siNCHuSRVOpq1ataJz584AmJubs3LlSv7++2/+/PNPfHx8KhzA2bNnGT58ONOnTychIYGWLVsycODAMhcgz8zMpH///gwdOpTz588zZMgQHn30Ua5fv64pc/LkSfz9/Rk4cCDnzp3j559/ZsCAARWOTYhaSV0EV2MgcV3xz7sMZdHFx90HV1tXTWcjjQJgPXCk+OkABtCPfphgwo3LN6oYuBB1V6VXjbl8+TLJycl07NgRc3NzkpKSyMvLo2XLlhU6T8lC4yWdl/Lz83FycuK7775j+PDhpcovWrSIFStW8Pvvv2u2tW/fnueee46pU6cCMGzYMCwtLVm/fn1lqia9eUXtlRwBR0Lg1m33O61doXMouOkeylKWkt68wL8dkRQgEvgDejTtQb9L/TTlx0WPw9PPs2rxC3GPqbbevBcvXqRXr164uLjQrVs3rly5AsCJEyd49tlnKxxoeHg4vXv31jw3Nzene/fubNiwoczyfn5+Wtv8/Pw05fPy8ti5c6fORCzEPS05AmKDtBMpwK2U4u3JERU6XWDrQMJHheNi4/LvRhXY+NnQ363/v4lUBbZutrj7uFexAkLUXRVOps8//zweHh4cOXJEa9xZ586dOXXqVIXOlZ+fz9WrV3Fzc9Pa7ubmxsWLF3Uek5SUVG75c+fOUVBQgIWFBYGBgTg7O9OrVy9iY2PLjCMvL4/s7GythxDVriKXa9VFxS1SHUNZNNuOTK3wJd/A1oH80PUHfKN9CQwPZNzycUxbMo3uF7oXF/jnKnDA4gBMTCv8cSHEfaPCfx0HDx7kww8/pFOnTpiY/Ht4RkYGhYWFFTpXRkYGiqJgaWmptd3S0pL09HSdx6Snp5dbvuTe6axZsxgzZgw7d+7Ezc2N/v37k5CQoPOc8+bNw87OTvO4M1kLYXDJEbDFE/b2hgNPFv/c4ll26zIttnSLVIsCt5KLy1XAli1b6Ne3H/v27aNF5xY8VPgQJsq/f9e2rraMCh9F68DWFTqvEPebCidTT09P4uLiNM9VKhW5ubnMnj27wh2QGjVqpDn+djk5OTg6Ouo8xtHRsdzyJavZvPHGG4wYMYKHHnqIpUuXUq9ePVavXq3znG+88QZZWVmaR3JycoXqIUSFVOZybc5dhrJUtBzw5Zdf8thjj5GTk8OgQYN4+/O3CUkMYVz0OALXBjIuehwhF0IkkQqhhwqPM120aBGPPfYY3377Lbm5uQQHB/Pbb7+Rl5fHzz//XKFzmZub4+TkxKVL2h8qSUlJuLvrvj/j4eFRbnkPDw8AmjZtqtlfv359PDw8ymztWlhYyCo4ombc9XKtqvhyrcswMLltOTOrcoay3H56iyYkxSRy4/INbJxscPdxL3V5VlEU3nzzTT788EOgeOL6L774QrNGsXQyEqLiKtwy7d+/P6dOneI///kP3bp1IyMjgyeeeILjx4/Tpk2bCgcQFBSkNU1Zbm4uBw4cICgoSK/yANHR0ZryTZo0oW3btlqt5/z8fFJTU2ndWr5hCyOr7OVaR5/iXrt3DmXRUFFAUz71PsaK3iuIeDKCFb1XEOoZSnxEvKZUfn4+Y8eO1STSd999l6+//lqTSIUQlVPpoTGGcu7cOTp27MhXX32Fv78/c+fOJTY2llOnTmFqaoq/vz8uLi6sXLkSgGvXruHl5cX06dMZN24cX331FV988QVnzpzB3t4egHXr1jFp0iS+//57HnnkEebPn8/mzZv5888/tTpNlUWGxohqk7iu+B7p3XRfC56jtbeVXB4GtFu2KhQUosP9uHalETeuNyDpTw8UxUSTe0vue544cYKuXbtSWFjIN998w/jx4w1QKSHqLn3zQYW+jl65coVNmzYRHx9PXl4ejRs35r///S8DBgyo9MTXLVu2JDIykpCQECZMmEDPnj3ZuXMnpqbFl7gSEhK0JnCwt7cnKiqKCRMmMGfOHDp27MiuXbs0iRRg9OjRXLt2jWnTpnHlyhW6du1KVFSUXolUiGql5+VaneXcAsEnvNQ4U8XcgdxrOfQJitFsy8qwJWplAH/+1gZUEDU1Cq9hXjz00EOsW7cOKysrHn300SpWRghRQu+W6aeffsrMmTPJzc3FzMwMBwcH0tLSUKvVODs7s2LFCvz9/as73hohLVNRbdRFxb12b6Wg+76pqvhy7tAL2vdM7zxHWmxxZ6Mb51BOzgVF4fb1uRV18anCFo9i32+NUFCYET1D7ocKUUEGnbRh48aNTJ06lREjRnDy5Elyc3O5fPkyeXl5/Prrr/j4+DBkyBCtWYmEEDqYmBbPVgSUvv/5z/POi8tOpCXnaOIH7qMg4RtAO5ECqEwABep33cb3LGM1qzl78qwhaiCE0EGvlqmvry+tWrXi66+/LrPM5MmTSUtLIywszKABGoO0TEW10zktoFtxItV3WsCrMcXjU8uw7gCM/xryC8EddyIjInn4sYerFLYQ9xuD3jM9efIkCxcuLLfMxIkT6d+/f8WiFOJ+5RZYPPyl5HKtlVNxj90yWqTqIjVJsUnaQ17KGFOqKLBwO7y+rvh5VwcX/DOfpqFtw2qqjBBCr2SalZVV5rjPEm5ubmWO4xRC6FByufYu4iPiiQqJIvvSv9Nc2rraEvixAx53lC1Sw9RV8NmPxc+nBkD7RH+SM834+6+/DRe7EEKL3uNMra2tyz+RiQlGHmUjRJ0THxFPWFCYViIFyE7JZsUT5ymgCcpt914/2lqcSFUqWPQkzB1gy6UzngDYONnUZOhC3Ff0apkqisLYsWPLHf5SUFBgsKCEEMWXdqNCosqcLEnBhKhVAxj89AoUpTiBBveHrcdg6qMwsiuELQ5AwURWfRGimumVTHv16qW1+HZ55YQQhpEUm1SqRapFgaNRnrQY9xHNixZgzl/YWMH+t+FGpi1hiwP480jxrGSy6osQ1UuvZBoTE1PNYQgh7nTj8o27lkkhhZ4TN/L6G6/yRHNnTq/Yw1/nTTUzINm62RKwOEAmqxeimsmEnELURuoiHB1O067bSe3pAW9zlrNsYAMF2QWsD9vA1Lg43AKfLt3rV1qkQlQ7SaZC1Db/jEFteusSI4KLN2lNDwgc4Qjb2IaCQt++fdm4caNm5SOZ5UiImidfWYWoTcpY69TWPptRU8Pw6nyaaKLZylYUFIb7DWfHjh0yuYgQRibJVIjaopy1TkumB9xpvol97ANgUtAkIn6KqPQiE0IIw5FkKkRtcZe1TlUm0K1VAaYmJnz55Zd8ueFLVHdOyiuEMAq5ZypEbVHG9IC3m9QXTC4M4vkXJtRAQEIIfUnLVIjaQscapvEpEDAfMm4bJWN+1YGk2KQaDEwIcTeSTIWoLRx9yKdJ8VqkwP4z0OMd2PU7TFtdvEZpVrotSX966DUGVQhRcySZClFbmJhy3X4uqGDDQeg7D679DV1bwMLRgAqiVgWgKCYyz64QtYzcMxWiFmncfwIvtF3GsrOHURQY1hnWToaCG/9ODyjz7ApR+0gyFaKWUKvVvPb6a3x35jAAve29eNKsLWELbIpnQPrnQpLMsytE7SPJVIha4vr160RGRgLwylOv4BLtQvzBf++Nyjy7QtRekkyFqCUcHByIioriyJEjjB49GnWRWubZFeIeoVJkRe9SsrOzsbOzIysrS6ZpE9Xq4sWLHDlyhMDAQGOHIoTQQd98IF9zhTCS48eP061bNx5//HH27Nlj7HCEEFUgyVQII9i9eze9evXi8uXLeHl54eXlZeyQhBBVIMlUiBq2cuVKBg4cyI0bN/Dz82P//v24ubkZOywhRBVIMhWihiiKwv/+9z/GjRtHYWEhTzzxBFFRUTRs2NDYoQkhqkiSqRA1ZNu2bcyaNQuA119/nTVr1mgW9BZC3NtkaIwQNWTw4ME899xzdOzYkeDgYGOHI4QwIEmmQlSjtLQ06tevj7W1NSqVim+++UbWIBWiDpLLvEJUk3PnztGtWzdGjx5NUVERgCRSIeooaZkKUQ0OHTrE4MGDSU9PR61Wc/XqVZydnY0dlhCimkjLVAgD27JlC7179yY9PZ3OnTsTFxcniVSIOk6SqRAG9OWXX/LYY4+Rk5PDgAEDiImJoUmTJsYOSwhRzSSZCmEg8+bN46WXXkKtVvPcc8+xZcsWGjRoYOywhBA1QJKpEAbSp08frK2teeedd/jmm2+oV0+6JAhxv5C/diGqQFEUTQ9db29vzpw5g6urq5GjEkLUNGmZClFJKSkp9OzZkyNHjmi2SSIV4v4kyVSISjh16hRdu3blwIEDPP/888iywELc32pFMt29ezft2rXDysqKvn37kpiYWG75Y8eO4e3tjZWVFd7e3hw/frzMsr/99hv16tVj+fLlBo1Z3L9iYmLo2bMnly5dwsvLi8jISJmMQYj7nNGT6dmzZxk+fDjTp08nISGBli1bMnDgQM2MMXfKzMykf//+DB06lPPnzzNkyBAeffRRrl+/XqpsYWEhL7zwAmq1upprIe4XP/zwA48++ihZWVn06NGDAwcO4OnpaeywhBBGZvRkumTJEvr06cMzzzyDs7MzoaGhXL16la1bt+os//333+Pk5MRbb72Fk5MTs2bN4oEHHtDZ8vz4448pKCiga9eu1VwLUdcpisLChQsZPXo0+fn5jBgxgj179uDg4GDs0IQQtYDRk2l4eDi9e/fWPDc3N6d79+5s2LChzPJ+fn5a2/z8/EqVv3DhAu+99x7fffcd5ubmBo9b3F/UajXR0dEATJ06lbCwMCwtLY0clRCitjBqMs3Pz+fq1au4ublpbXdzc+PixYs6j0lKStKr/KRJk3j++efx9va+axx5eXlkZ2drPYS4nampKWFhYaxcuZJPPvkEExOjfw8VQtQiRv1EyMjIQFGUUt/wLS0tSU9P13lMenr6XcuvXr2as2fP8v777+sVx7x587Czs9M87kzW4v6UkZHBokWLND1169evz9NPP23kqIQQtZFRk2mjRo1QqVTk5uZqbc/JycHR0VHnMY6OjuWWz8jI4JVXXmHp0qXUr19frzjeeOMNsrKyNI/k5ORK1EbUJRcuXKB79+68+uqrLFiwwNjhCCFqOaPOgGRubo6TkxOXLl3S2p6UlIS7u7vOYzw8PMotv23bNtLS0hgwYIBmf1FREbGxsaxatYq9e/eWOqeFhQUWFhZVrY6oI44cOcKgQYO4evUq7u7uDB482NghCSFqOaPf+AkKCtJ07ADIzc3lwIEDBAUF6VUeIDo6WlN+2LBhnDx5kuPHj2sezs7OvPvuu3z77bfVVxFRJ+zcuRNfX1+uXr3KQw89RFxcHG3atDF2WEKIWs7oyTQ4OJi9e/eyatUqUlNTmTJlCk2bNmXo0KEA+Pv7M3bsWE358ePHc+XKFebPn8+VK1eYO3cu6enpjB8/HoCGDRvSrl07rYeZmRkuLi40a9bMGFUU94jvvvuOIUOG8Pfff9OvXz9+/vlnWYdUCKEXoyfTli1bEhkZyQcffEDz5s25cOECO3fuxNTUFICEhASSkpI05e3t7YmKimLDhg14enoSFRXFrl27sLe3N1YVRB2QkJDAxIkTKSoqYuzYsWzfvh1bW1tjhyWEuEeoFJlUtJTs7Gzs7OzIysqSD9T7yHfffacZnyzTAwohQP98IEuwifvWzZs3ycjIwMPDA4DnnnvOyBEJIe5VRr/MK4QxXLlyBV9fX/z9/UlLSzN2OEKIe5wkU3Hf+fPPP+nWrRtHjx4lOzublJQUY4ckhLjHSTIV95VffvmFHj16kJiYSIsWLYiLi6Njx47GDksIcY+TZCruGxs3bsTf35/MzEy8vb05cOAAzZs3N3ZYQog6QJKpuC+EhYUxcuRI8vLyGDp0KD/99FOZU1YKIURFSW9ecV/o3bs3zZs3p1+/fixZskQzjlkIIQxBkqmos4qKijRJ09HRkUOHDmFvby9jSIUQBieXeUWddO3aNfz9/bXmY3ZwcJBEKoSoFpJMRZ2TlJREz5492bdvHzNmzOD69evGDkkIUcdJMhV1yokTJ+jatSt//PEHLi4uREdH07BhQ2OHJYSo4ySZijpjz549+Pj4cPnyZdq2bUtcXBwdOnQwdlhCiPuAJFNRJ6xatYoBAwZw48YN/Pz82L9/P25ubsYOSwhxn5BkKuqEpKQkCgsLeeKJJ4iKipJLu0KIGiVDY0Sd8Oabb9K6dWuGDx+OiYl8RxRC1Cz51BH3pFu3bjFjxgxu3rwJgEqlIjAwUBKpEMIopGUq7jl//fUXQ4YM4ddffyUhIYHw8HBjhySEuM9JMhX3lP/7v/8jICCAhIQEHBwceOWVV4wdkhBCyGVece84dOgQ3bp1IyEhgWbNmnHgwAG6d+9u7LCEEEKSqbg3bNmyhd69e5Oenk7nzp05cOAAXl5exg5LCCEASabiHnDr1i1efPFFcnJyGDBgADExMTRt2tTYYQkhhIYkU1HrWVtbs2XLFoKDg9myZQsNGjQwdkhCCKFFOiCJWik/P58TJ07QpUsXADp37kznzp2NHJUQQugmLVNR62RlZTFw4EB8fX05dOiQscMRQoi7kmQqapWUlBR69erF3r17MTExISsry9ghCSHEXcllXlFrnD59moCAAC5dukSTJk3YsWMHDz/8sLHDEkKIu5KWqagVYmJi6NGjB5cuXcLLy4uDBw9KIhVC3DOkZSqM7vDhwzz66KPk5+fTo0cPtmzZgoODg7HDEkIIvUkyFUb38MMPM2DAAOrVq8eqVauwsrIydkhCCFEhkkyFURQVFaFWqzEzM8PU1JQffvhB828hhLjXyD1TUeNycnIYNWoUL7zwAoqiAGBpaSmJVAhxz5JkKmpURkYGffv2JSIignXr1nHq1CljhySEEFUmyVTUmAsXLtCjRw8OHDhAw4YN+fHHH2nfvr2xwxJCiCqTe6aiRhw5coRBgwZx9epV3Nzc2LlzJ23btjV2WEIIYRDSMhXVLioqCl9fX65evcpDDz3EwYMHJZEKIeoUSaai2pmampKXl0ffvn35+eefcXZ2NnZIQghhUHKZV1S7fv36sXfvXrp27Yq5ubmxwxFCCIOTlqkwuIKCAqZNm8aZM2c023r16iWJVAhRZ0kyFQZ18+ZNhg4dyuLFixk8eDD5+fnGDkkIIapdrUimu3fvpl27dlhZWdG3b18SExPLLX/s2DG8vb2xsrLC29ub48ePa+1fu3Yt3bp1w9bWFmdnZ0JCQrh161b1VUAAcOXKFXx9fYmKisLKyoqPP/5YWqNCiPuC0ZPp2bNnGT58ONOnTychIYGWLVsycOBAioqKdJbPzMykf//+DB06lPPnzzNkyBAeffRRrl+/rilz8OBBpkyZwqlTp1i1ahXr1q3j9ddfr6Ea3Z/OnDlDt27dOHr0KI0bNyYmJoYhQ4YYOywhhKgZipEFBwcrgwcP1jzPy8tTHBwclMjISJ3lFy5cqLRv315rW7t27ZRPPvmkzNeYNWuW0qRJE71jysrKUgAlKytL72PuZ/v371ccHBwUQGnevLly7tw5Y4ckhBAGoW8+MHrLNDw8nN69e2uem5ub0717dzZs2FBmeT8/P61tfn5+ZZYHsLCwICcnxyDxCm2KojB37lwyMzP573//S1xcHC1atDB2WEIIUaOMmkzz8/M1M+Lczs3NjYsXL+o8JikpqULl1Wo1GzZs4NFHHy0zjry8PLKzs7UeQj8qlYoffviBKVOmEB0djaOjo7FDEkKIGmfUZJqRkYGiKFhaWmptt7S0JD09Xecx6enpFSo/d+5crl69yscff1xmHPPmzcPOzk7zuDNZC21qtZqdO3dqnjdq1IjQ0FCsra2NGJUQQhiPUZNpo0aNUKlU5Obmam3Pyckps4Xj6Oiod/mPPvqIb775hp9++glXV9cy43jjjTfIysrSPJKTkytRm/tDXl4eY8aMYeDAgXz55ZfGDkcIIWoFo86AZG5ujpOTE5cuXdLanpSUhLu7u85jPDw89Cr/9ddf8/HHH7Nv3z68vLzKjcPCwgILC4tK1OD+cv36dYYPH86+ffuoV68eDRo0MHZIQghRKxi9A1JQUBDR0dGa57m5uRw4cICgoCC9ygNER0drlT98+DAvv/wya9euvWsiFfpJSkqiZ8+e7Nu3DxsbG3bu3MnTTz9t7LCEEKJWMHoyDQ4OZu/evaxatYrU1FSmTJlC06ZNGTp0KAD+/v6MHTtWU378+PFcuXKF+fPnc+XKFebOnUt6ejrjx4/XOucjjzzCww8/zPXr1zUPUTknTpygW7dunD59GmdnZ2JjY+nbt6+xwxJCiFrD6Mm0ZcuWREZG8sEHH9C8eXMuXLjAzp07MTU1BSAhIYGkpCRNeXt7e6KiotiwYQOenp5ERUWxa9cu7O3tNWV+/fVX4uLisLe313qIiktLS8PX15fU1FTatm3LwYMHeeihh4wdlhBC1CoqRVEUYwdR22RnZ2NnZ0dWVha2trbGDsfoPvroI3bu3ElkZCQNGzY0djhCCFFj9M0Hkkx1uN+TqaIo3Lx5ExsbG83zwsJCzMzMjByZEELULH3zgdEv84rapbCwkJdeeolevXppJq9QqVSSSIUQohySTIXG33//TWBgIF999RUnTpzgp59+MnZIQghxTzDqOFNRe6SlpTF48GB+/fVXLC0tWbNmDcOHDzd2WEIIcU+QZCr4v//7PwYMGMD//d//4eDgwJYtW+jRo4exwxJCiHuGJNP73JEjRxgwYABpaWmaoUYy0YUQQlSM3DO9zzk6OmJmZkbnzp2Ji4uTRCqEEJUgLdP7nLu7Oz/99BMuLi4y164QQlSStEzvM4qiMGvWLCIiIjTbvLy8JJEKIUQVSMv0PpKfn8/zzz/PqlWrsLS05Ny5c+UuTSeEEEI/kkzvE9nZ2YwYMYI9e/ZgamrK559/LolUCCEMRJLpfSA1NZUBAwbw+++/U79+fcLDwwkICDB2WEIIUWdIMq3jTp8+zYABA0hOTqZJkybs2LGDhx9+2NhhCSFEnSLJtI5bs2YNycnJeHl5sXPnTpo1a2bskIQQos6RZFrHvf/++1hYWBAcHEyjRo2MHY4QQtRJMjSmjlEUhfXr15Ofnw+AiYkJc+bMkUQqhBDVSJJpHVJUVMTUqVN54oknePbZZ5GlaoUQombIZd46Iicnh6effpqNGzcCSCcjIYSoQZJM64CMjAyGDRvGL7/8grm5OStXruTxxx83dlhCCHHfkGR6j7tw4QIDBgzgzJkzNGzYkE2bNuHr62vssIQQ4r4iyfQeVlRUpEmkbm5u7Ny5k7Zt2xo7LCGEuO9IB6R7mKmpKV9++SVdunTh4MGDkkiFEMJIVIp0+SwlOzsbOzs7srKysLW1NXY4paSlpeHo6Kh5rlarMTGR70VCCGFo+uYD+QS+hyiKwjvvvIOXlxd//PGHZrskUiGEMC65Z3qPKCgoYNKkSSxbtgyAnTt30qZNGyNHJYQQAiSZ3hNu3rzJyJEjiYqKwsTEhM8//5xJkyYZOywhhBD/kGRay125coVBgwZx9OhRrKysWL9+PUOGDDF2WEIIIW4jybQWS0pKwtfXl8TERBo3bsy2bdvw9vY2dlhCCCHuIMm0FmvSpAkeHh6YmpoSFRVFixYtjB2SEEIIHSSZ1mIWFhZs2rSJ/Px8HnjgAWOHI4QQogwypqKWWbJkCTNmzNA8b9iwoSRSIYSo5aRlWkuo1WpmzJjBwoULAXj00Ufp06ePkaMSQgihD0mmtUBeXh7jx4/nhx9+AGDevHn07t3byFEJIYTQlyRTI7t+/TrDhw9n37591KtXj2XLlvH0008bOywhhBAVIMnUiJKTkxkwYACnT5/GxsaGiIgI+vbta+ywhBBCVJAkUyM6cuQIf/zxB87OzuzYsYOHHnrI2CEJIYSoBEmmRjR8+HCWL1+On58f7u7uxg5HCCFEJcnQmBq2fv16Ll26pHk+duxYSaRCCHGPqxXJdPfu3bRr1w4rKyv69u1LYmJiueWPHTuGt7c3VlZWeHt7c/z48VJl1q5dS/Pmzalfvz5BQUFkZGRUT/B6UhSFefPm8cQTTzBgwABu3Lhh1HiEEEIYjtGT6dmzZxk+fDjTp08nISGBli1bMnDgQIqKinSWz8zMpH///gwdOpTz588zZMgQHn30Ua5fv64ps2/fPiZMmEBoaCjx8fEUFRXx5JNP1lCNSissLOSll17izTffBCAgIID69esbLR4hhBAGphhZcHCwMnjwYM3zvLw8xcHBQYmMjNRZfuHChUr79u21trVr10755JNPNM8HDx6sBAcHa55fuXJFMTU1VY4dO6ZXTFlZWQqgZGVl6V2Psvz999/KkCFDFEBRqVRKaGholc8phBCiZuibD4zeMg0PD9eaoMDc3Jzu3buzYcOGMsv7+flpbfPz89OUv3XrFjt27NA6Z5MmTWjdunWZ56wuaWlp9OnTh61bt2JhYcGGDRuYMmVKjcYghBCi+hk1mebn53P16lXc3Ny0tru5uXHx4kWdxyQlJZVbPiUlBbVaXaFz5uXlkZ2drfUwhEmTJnHo0CEcHBzYu3cvI0aMMMh5hRBC1C5GTaYZGRkoioKlpaXWdktLS9LT03Uek56eXm75kp8VOee8efOws7PTPO5MxJX16aef0qtXL3755Rd69OhhkHMKIYSofYyaTBs1aoRKpSI3N1dre05ODo6OjjqPcXR0LLd8yc+KnPONN94gKytL80hOTq5Ufe7k4uJCTEwMrVq1Msj5hBBC1E5GTabm5uY4OTlpjbuE4ku5ZY299PDwKLe8i4sLpqamFTqnhYUFtra2Wg9DUalUBjuXEEKI2snoHZCCgoKIjo7WPM/NzeXAgQMEBQXpVR4gOjpaU97KyopBgwZplbl8+TJ//vlnmecUQgghqsLoyTQ4OJi9e/eyatUqUlNTmTJlCk2bNmXo0KEA+Pv7M3bsWE358ePHc+XKFebPn8+VK1eYO3cu6enpjB8/XlNm+vTpLFu2jKioKC5evMiECRPo06cPnTp1qunqCSGEuA8YPZm2bNmSyMhIPvjgA5o3b86FCxfYuXMnpqamACQkJJCUlKQpb29vT1RUFBs2bMDT05OoqCh27dqFvb29pkyvXr346quvmDRpEm3atMHS0lKzVqgQQghhaCpFURRjB1HbZGdnY2dnR1ZWlkHvnwohhLi36JsPjN4yFUIIIe51kkyFEEKIKpJkKoQQQlSRJFMhhBCiiiSZCiGEEFUkyVQIIYSoIkmmQgghRBVJMhVCCCGqSJKpEEIIUUWSTIUQQogqqmfsAGqjkhkWs7OzjRyJEEIIYyrJA3ebeVeSqQ43btwAwM3NzciRCCGEqA1u3LiBnZ1dmftlonsd1Go1qamp2NjYVGlx7+zsbNzc3EhOTq6zE+ZLHesGqWPdcD/UEWq2noqicOPGDZydnTExKfvOqLRMdTAxMcHV1dVg57O1ta3Tb2yQOtYVUse64X6oI9RcPctrkZaQDkhCCCFEFUkyFUIIIapIkmk1srCwYM6cOVhYWBg7lGojdawbpI51w/1QR6id9ZQOSEIIIUQVSctUCCGEqCJJpkIIIUQVSTIVQgghqkiSaQXs3r2bdu3aYWVlRd++fUlMTCy3/LFjx/D29sbKygpvb2+OHz9eqszatWtp3rw59evXJygoiIyMjOoJXk+GruPatWvp1q0btra2ODs7ExISwq1bt6qvAnqqjv/LEr/99hv16tVj+fLlBo25oqqjjocOHcLPz4/69evj4OBA3759uXnzZvVUQA/VUcf9+/fTrVs3GjRogIeHBwsWLKie4PVU0TqmpKSwcuVKxo0bx5tvvmmQc1Y3Q9dx165d9OnTBwcHBxwdHRk7dmz1f7YqQi9nzpxRrK2tlWXLlikpKSnKpEmTlNatWyuFhYU6y2dkZCiNGzdW3n//fSU1NVV57733lAceeEC5du2apkxMTIxSv359ZevWrcrFixeV4cOHK/3796+hGpVWHXV8+eWXlbVr1yoXL15U9uzZozg6OiqTJ0+uoRrpVh31LFFQUKB07NhRUalUyvfff1+9FSlHddTx999/V+rXr6/Mnz9fSUlJUU6ePKksXLhQuXHjRg3VSlt11DE1NVWxtbVVvvrqKyU1NVXZsGGDYm5urmzdurWGaqWtonVUFEUZMGCAEhAQoDRp0kQZN26cQc5ZnaqjjnPnzlWWLl2qJCQkKAcPHlRatmypDBo0qBproSiSTPUUHBysDB48WPM8Ly9PcXBwUCIjI3WWX7hwodK+fXutbe3atVM++eQTzfPBgwcrwcHBmudXrlxRTE1NlWPHjhkydL1VRx3vNGvWLKVJkyaGCLfSqrOe8+fPV9q2bat069bNqMm0Ouo4dOhQZdSoUdURbqVURx03btyoNGrUSKvMI488oixatMhgcVdEReuoKIqiVqsVRVGUzp0760w0lTlndaqOOt7p22+/VUxMTJS///67quGWSS7z6ik8PJzevXtrnpubm9O9e3c2bNhQZnk/Pz+tbX5+fpryt27dYseOHVrnbNKkCa1bty7znNXN0HXUxcLCgpycHIPEW1nVVc8LFy7w3nvv8d1332Fubm7wuCvC0HXMy8tj586dDB8+vLpCrrDq+H9s3rw5GRkZ/PDDDwCkpqaSkJDAkCFDDF8BPVS0jsBd5xOvzDmrU3XU8U4WFhao1Wry8vIqHefdSDLVQ35+PlevXi21ioybmxsXL17UeUxSUlK55VNSUlCr1RU6Z3WqjjreSa1Ws2HDBh599FHDBF0J1VnPSZMm8fzzz+Pt7W3YoCuoOup47tw5CgoKsLCwIDAwEGdnZ3r16kVsbGz1VOIuquv/8aGHHmLOnDmMGTOGl19+maCgIFasWEHLli0NX4m7qEwdjXHOqqipeH744Qe6dOmCvb29wc55J0mmesjIyEBRFCwtLbW2W1pakp6ervOY9PT0csuX/KzIOatTddTxTnPnzuXq1at8/PHHhgm6EqqrnqtXr+bs2bO8//77hg+6gqqjjtevXwdg1qxZjBkzhp07d+Lm5kb//v1JSEgwfCXuojrfr2ZmZnTs2JEdO3YQHx9PZmamYYPXU2XqaIxzVkVNxLNs2TJiYmJYunSpQc5XFkmmemjUqBEqlYrc3Fyt7Tk5OTg6Ouo8xtHRsdzyJT8rcs7qVB11vN1HH33EN998w08//WTQFXkqqjrqmZGRwSuvvMLSpUupX79+9QReAdVRx5LL1m+88QYjRozgoYceYunSpdSrV4/Vq1dXQy3KV13v15UrV2repydPnmTEiBGMHz+etWvXGr4Sd1GZOhrjnFVR3fGsW7eO6dOns2PHDjp27Fjl85VHkqkezM3NcXJy4tKlS1rbk5KScHd313mMh4dHueVdXFwwNTWt0DmrU3XUscTXX3/Nxx9/TExMDG3atDFs4BVUHfXctm0baWlpDBgwgHr16lGvXj327dvHc889h7+/f/VUpBzVUUcPDw8AmjZtqtlfv359PDw8jNKiqa7361dffUVQUBB2dnZYW1vz7bff4u/vz6effmr4StxFZepojHNWRXXGs2PHDl588UW2bdvG/7d3fyFNvX8cwN9Lm9uKMWZaGDqpQVMvLA0lBReyO6OoRikkjiLKym4MkpCSMAq98GqiJJRaIxmOWoJUhBiRF2Jowkrp3wIbRW2hN2na87sIx3da6jo7bf54v2AX55xnn/N8dO7tOfN4ioqKJNVaCYbpClmtVvT19QWXv3//jmfPnsFqta5oPAD09fUFx6vVapSUlISM8fl8ePXq1R9ryi3SPQLA4OAgqqqq4HA4sG3bNnkmHqZI97lv3z6Mjo5ieHg4+EhJScHly5fR1tYmXyNLiHSPGzduRFZWFgYGBoLbZ2Zm8PHjR2RkZMjQwfLkeL1OT08vOq1rMBiWvCm0nMLtMVo1pZBjPl6vF2VlZWhqakJhYWEkprk82f5O+P/M+Pi40Gg0oqOjQ0xMTIjjx48Lk8kUvBaquLhYlJeXB8f7/X6RlJQkrl27Jnw+n7h06ZJISkoSfr8/OKa/v1+sW7dO9Pb2ivfv34s9e/YIi8Xyz3ubJ0ePeXl5YteuXSIQCIQ8okmOPhcyGAxRvTRGjh4dDofQarWiu7tbeL1ecerUKbF58+aoXWcqR4/19fUiISFBOBwOMTExIZxOp9BoNKKlpeWf9ydE+D0KIcTU1JQIBAJi+/btoqysTAQCgZBLQpar+a/J0eOhQ4dEamqq8Pv9Ie87c3NzsvXBMA3DgwcPhMlkEiqVSlgsFvHu3bvgNoPBIMxmc8j4oaEhkZubKxISEkR+fr54/vz5opqdnZ3CYDAIjUYjrFar+PLli8xdLC3SPQL47SPa5Phe/le0w1QIeXq02+0iLS1NKJVKUVRUJEZHR2XuYmmR7nF2dlZcuXJFbN26VajVapGZmSlaW1v/QSd/Fm6PZrN50c/bwmsxl6oZDZHu0WAw/PZ9R84+eQs2IiIiifiZKRERkUQMUyIiIokYpkRERBIxTImIiCRimBIREUnEMCUiIpKIYUpERCQRw5SIiEgihilRDNu9ezcUCgUUCgWSk5NRVlaGT58+BbfbbLZFN7xeKSnP/a+6ujqkp6dLrkO0mjFMiWLc3r174fP50Nrait7eXpw+fTq4rbm5GT09PcvWcDqdcLlckufy8OFD3LhxI2RdTU0NXrx4Ibk20WrGMCWKcWvXrsWmTZuwf/9+VFRUYHBwMLhNo9Fg/fr1f3zu9PQ0AMBut8Ptdkuei8PhQHt7e8g6lUoFrVYruTbRasYwJVpFJicnQ06pLjxVO3/K1eVyIT09HWfOnIHNZkN/fz/a29uhUChQV1cXUvPevXswmUzQarWorq7+477r6urQ3t6O/v5+KBQK2Gy2kH3Ou3nzJhQKBTweDwoKCqDRaFBSUoKpqSnU1tZCr9cjNTUVjx49Cql/+/ZtbNmyBVqtFgcOHFh0KzSiWBYf7QkQ0fLm5ubQ09OD7u5u3L17d8mxX79+hd1ux/3795GSkgK1Wo3Xr18jLS0Nzc3NUKlUwbEejweNjY3o6urCmzdvcPDgQRw+fBh5eXmL6tbU1GB8fBwfPnxAT08PlErlkvM4duwYrl69iri4OJjNZhQUFMBisWBkZAQnT57EuXPnMDIyAgB4+vQpKisr4XK5YDQacfToUZw9exa3bt0K/4tFFAUMU6IY53a7oVarMTs7i5aWFhQXFy/7nK6uLmzYsCG4HB8fD6VSCZ1OFzJuzZo1cLvd0Ov1yMzMBACMjY39NkxVKhWUSiXi4+MX1fmdtrY2ZGVlAQB0Oh0yMjLQ1NQEADCbzaivrw+ObWhoQGlpKSwWCwCgqqoKpaWl6OjoiNqNuYnCwVcpUYyzWCwYHBxEQ0MDqqurlzwVCwCJiYkhQboUk8kEvV4P4Ndns8Cvo+BImA9S4Fdoz4f1/PLPnz+Dy6Ojo+js7IROp4NOp0N5eTlmZmbw+fPniMyFSG48MiWKcRqNBtnZ2cjOzkZycjIqKipw5MgR7NixI9pTi5iZmRnYbDacP38+ZP1KfykgijaGKdEqMn+09/bt27DCNC4uDrOzs5L3H6k6C+Xn52NgYABpaWk8rUurEl+1RDHux48f8Pv98Hg8uHjxIpRKJXJzc8OqYTQa8eTJE4yNjWFycvKv52I0GjE8PIyhoSF8+/btr+ssVFtbi5cvX+LEiRMYGxuD1+vFnTt3IroPIjkxTIlinNvtRmJiInbu3Amfzwen0xn2fxy6cOECUlJSkJOTA4fD8ddzqaysRGFhIYqKitDY2PjXdRbKycnB48eP4fF4kJ2djZycHFy/fj1in98SyU0hhBDRngQREdFqxiNTIiIiiRimREREEjFMiYiIJGKYEhERScQwJSIikohhSkREJBHDlIiISCKGKRERkUQMUyIiIokYpkRERBIxTImIiCT6H6u+XI5JYStCAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Convert the Fréchet mean back into a list of tuples format for plotting\n",
    "frechet_mean_as_tuples = [(1, tuple(point)) for point in frechet_mean]\n",
    "\n",
    "# Separate birth and death times for plotting\n",
    "birth_times_frechet, death_times_frechet = zip(*[point[1] for point in frechet_mean_as_tuples])\n",
    "\n",
    "plt.figure(figsize=(5,5))\n",
    "\n",
    "# Plot the Fréchet mean\n",
    "plt.scatter(birth_times_frechet, death_times_frechet, color='purple', label='Fréchet Mean')\n",
    "\n",
    "# Plot the original diagrams\n",
    "colors = ['blue', 'green', 'red', 'orange']\n",
    "for idx, diag in enumerate(converted_diagrams):\n",
    "    birth_times, death_times = zip(*diag)\n",
    "    plt.scatter(birth_times, death_times, color=colors[idx], label=f'Diagram {idx+1}')\n",
    "\n",
    "plt.plot([0, max(death_times_frechet)], [0, max(death_times_frechet)], 'k--')  # diagonal line\n",
    "plt.title('Persistence Diagrams and Their Fréchet Mean')\n",
    "plt.xlabel('Birth time')\n",
    "plt.ylabel('Death time')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Convert the Fréchet mean back into a list of tuples format for plotting\n",
    "frechet_mean_as_tuples = [(1, tuple(point)) for point in frechet_mean]\n",
    "\n",
    "# Separate birth and death times for plotting\n",
    "birth_times_frechet, death_times_frechet = zip(*[point[1] for point in frechet_mean_as_tuples])\n",
    "\n",
    "plt.figure(figsize=(5,5))\n",
    "\n",
    "# Plot the Fréchet mean\n",
    "plt.scatter(birth_times_frechet, death_times_frechet, color='purple', label='Fréchet Mean')\n",
    "\n",
    "plt.plot([0, max(death_times_frechet)], [0, max(death_times_frechet)], 'k--')  # diagonal line\n",
    "plt.title('Fréchet Mean of Persistence Diagrams')\n",
    "plt.xlabel('Birth time')\n",
    "plt.ylabel('Death time')\n",
    "plt.legend()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "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": "3.11.3"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}