{ "cells": [ { "attachments": {}, "cell_type": "markdown", "id": "9f5de6a8", "metadata": {}, "source": [ "# Gaussian Processes from scratch" ] }, { "attachments": {}, "cell_type": "markdown", "id": "5eb6a396", "metadata": {}, "source": [ "Loading the Data\n", "First, we need to load the dataset that we'll use for training and testing the GP model. Here, we're using the UCI Machine Learning Repository's \"bike\" dataset, and using only the last feature so that the predictions can be easily visualized." ] }, { "cell_type": "code", "execution_count": 1, "id": "19f964ca", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "--2023-10-13 14:55:46-- https://www.andpotap.com/static/bike.mat\n", "Resolving www.andpotap.com (www.andpotap.com)... 143.42.238.119\n", "Connecting to www.andpotap.com (www.andpotap.com)|143.42.238.119|:443... connected.\n", "HTTP request sent, awaiting response... 200 OK\n", "Length: 434829 (425K) [application/octet-stream]\n", "Saving to: ‘bike.mat’\n", "\n", "bike.mat 100%[===================>] 424.64K --.-KB/s in 0.05s \n", "\n", "2023-10-13 14:55:46 (8.22 MB/s) - ‘bike.mat’ saved [434829/434829]\n", "\n" ] } ], "source": [ "!wget -O bike.mat \"https://www.andpotap.com/static/bike.mat\"" ] }, { "cell_type": "code", "execution_count": 2, "id": "0fafacc0", "metadata": {}, "outputs": [], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")" ] }, { "cell_type": "code", "execution_count": 3, "id": "9a64e181", "metadata": {}, "outputs": [], "source": [ "from jax import numpy as jnp\n", "import os\n", "import numpy as np\n", "from math import floor\n", "from scipy.io import loadmat\n", "import cola\n", "\n", "\n", "def load_uci_data(data_dir, dataset, train_p=0.75, test_p=0.15):\n", " file_path = os.path.join(data_dir, dataset + '.mat')\n", " data = np.array(loadmat(file_path)['data'])\n", " X = data[:, -2:-1]\n", " y = data[:, -1]\n", " X = X - X.min(0)[None]\n", " X = 2.0 * (X / X.max(0)[None]) - 1.0\n", " y -= y.mean()\n", " y /= y.std()\n", " train_n = int(floor(train_p * X.shape[0]))\n", " return X[:train_n], y[:train_n], X[train_n:], y[train_n:]\n", "\n", "\n", "train_x, train_y, test_x, test_y = load_uci_data(data_dir=\"./\", dataset=\"bike\")\n", "dtype = jnp.float32\n", "train_x = train_x[:3000]\n", "train_y = train_y[:3000]" ] }, { "cell_type": "code", "execution_count": 4, "id": "b4b32532", "metadata": {}, "outputs": [], "source": [ "def rbf(ls, uscale):\n", " def f(x, y):\n", " # (n, d) and (m, d) -> (n, m)\n", " inner = x@y.T\n", " sqdist = (x**2).sum(1).reshape(-1, 1) + (y**2).sum(1) - 2*inner\n", " return uscale*jnp.exp(-sqdist / ls**2)\n", " return f" ] }, { "attachments": {}, "cell_type": "markdown", "id": "d742eee5", "metadata": {}, "source": [ "For a Gaussian Process, the predictive distribution of the function values at test inputs $X_*$\n", " given the training inputs \n", "$X$ and training targets \n", "$y$ is given by:\n", "\n", "$$f_* | X, y, X_* \\sim \\mathcal{N}(\\mu_*, \\Sigma_*)$$\n", "\n", "where:\n", "\n", "$$\\mu_* = K(X_*, X)[K(X, X) + \\sigma^2_n I]^{-1}y$$\n", "\n", "$$\\Sigma_* = K(X_*, X_*) - K(X_*, X)[K(X, X) + \\sigma^2_n I]^{-1}K(X, X_*)$$\n", "\n", "Here, $K$ is the RBF kernel, $X$ are the training inputs, $y$ are the training targets, $X_*$ are the test inputs, and $\\sigma^2_n$ is the noise variance." ] }, { "attachments": {}, "cell_type": "markdown", "id": "df66ecf0", "metadata": {}, "source": [ "We will get the variances from the diagonal of the predictive covariance." ] }, { "cell_type": "code", "execution_count": 6, "id": "c5ed6118", "metadata": {}, "outputs": [], "source": [ "from cola.linalg import Cholesky\n", "\n", "ls, uscale, noise = .2, .5, 1e-2\n", "\n", "def predicted_mean_std(ls,uscale,noise):\n", " kernel = rbf(ls=ls, uscale=uscale)\n", " Kxx= cola.ops.Dense(kernel(train_x, train_x))\n", " Kzx = cola.ops.Dense(kernel(test_x, train_x))\n", " Kzz = cola.ops.Dense(kernel(test_x, test_x))\n", " K = cola.PSD(Kxx + noise * cola.ops.I_like(Kxx))\n", " invK = cola.inv(K, alg=Cholesky())\n", " mu = Kzx@invK@train_y\n", " Sigma = Kzz - Kzx@invK@Kzx.T\n", " std = jnp.sqrt(cola.diag(Sigma))\n", " return mu,std" ] }, { "attachments": {}, "cell_type": "markdown", "id": "d8b7176e", "metadata": {}, "source": [ "### Visualization\n", "Next, we visualize the GP's prediction with the initial hyperparameters:" ] }, { "cell_type": "code", "execution_count": 8, "id": "9dd4eb89", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING:jax._src.xla_bridge:CUDA backend failed to initialize: Found CUDA version 12000, but JAX was built against version 12020, which is newer. The copy of CUDA that is installed must be at least as new as the version against which JAX was built. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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6Y5VasYDLF2A8EKRayuP2haiXC9RKRaaOP4Y3GOmfz/DUYUq5NL5QZM/1FAiGdtIuu9kd4divrXa/uTAfRKQQkUg+ANyLVMnb3ef29jaXL18G4OTJk3tESY/etolEgnQ63d/HnaIp72Xqp9To7LTGNslUTOFxr7pU3il3GnDWEyEub+C2gtHzL/0p2e1Njj31sdtufPtFSYQwoyH51BaNWplGtUJsdIrI4BhrNy6xvTLP9Mkn9nS/KIrK4sXv47DVCLqXsXvSuB0Fxh73EvC9il1N43PlcNqrcIeATEe3U6oP09aOo9tP0xCHuHw+x/ZaGhSFqWOPUi7kWD6XxOULEhkao1oqoqoqE8dOm1EGIRg9HGBowqw5cfvmcbi9IAxc3gCNWhmhmCJCIPrRpc3Fa6TXlxGIfdMlt9ZuvONOlX1+/kGpB9kPKUQkkg8A9yJVcqd9XrhwgXQ6vUd0AGSzWa5cuUIymexHO3YLlIsXL5JMJjl16hRw52hK7/mlS5dIpVKcPn36tvPRNNP86e2cl2EIam1zcFu1ac5SKdQ75GtmbUer82BMib1TGqZnqrW1fKNfW+ELRm4rpCzl0lx+9QWSq4sMjM/gDUb27GdrcZbk2iID49N73EYrxRyhgSHmzq1SKWSJjU7y1Ge/yPf/9N/jtKY5eRTi4W/iKX2PIX8FzdjCEUjjOJTHor21YGt2gjTFGMmUg2zeQ9MYJVuO44k9iTcY60cRKoUshdwWbp8flzeINxjpR3t6XTMuX2Dn/E1TMm/wZuSinEvj8gU4NXnQfJ437dhvjW4AjEwf6++jd413X+8fhLcjVj6oSCEikXwAeKtUyTtt2etFJHrRid37vH79en+7XnQiGo2Sy+V44403CAQCKIpCPH7zP+bLly+TTKZw+cPMJcrYfGHOL+dJfv86dm+QdqeLMxDFU6xiXJvfsdVOUCtdZeTNdSYPHqOSz1ItpLFYLGjCIBLXiaQEys30O4YQ6AZ0dIN216DR0Wl1DIwHpU3lLtwpDbO5eI1qIW/WcAiBoigMTx/t24srioLbF2Dt+kXyqW384TiTxx7Zs6+txVkSqwuomkpybRGA4enD2NQkxw5XKKy/xMQz54lGu8Rj38Xv/b/52N+9Q/vrLgwDqnUX9VaQSsNPsWijqcdoGTF0bQrDfphO106tnAehgGLWWghbAc+uOS/lQoZKPsfgxEz/3LaXzU4UZafCVVUUDj3+7L4pkDulRXqv92bA7OaDLg7eS6QQkUgeEt5JKmS/7QYHB0mlUly6dGnP9j+Ib0AvGjI0NNQ/ZiKRIJPJEA6Hicfje6IdAJlMBoBCocDXvvY1RsYnOHj6aV49e46VzSTVtk5kyIO/mcEXVijrTlY2k3h8LTyBECF/hHwm2W8LHZyYoVIIsr4wRz6TMdstVHB7g+YnaNVLJbv/sLCHEV84RjmfZWt57ubznYFqtXJxR3AJ3L5Qf4CaAlRLBTbmryAMA6fHSzg+QmJtCW8gSLVUYOHSazitRQ5NVoiF02jNy/hcacJaBUtsR2yE9l9Ts+2kVPFQawVodmMUinYqDR+1hp/lhTy5rIpmc2FzuBiZPgLQj9AcOPUk/nCczYVruH2hfsGqKZyCewo4hSH6BZ7914BGpYjTG2Dq+GMYhrFHUOwWWm/HbVRy/5BCRCJ5SHg7qZBbt4O99RfJZJJCoUA0Gr1NrCQSiX5dxt3ETu8YPQEyNDSEoihkMhkWFhZ45plniMfjpFKpPe87efIkxXqbP/zTP2e1At/71ps4z84jDIHbF6BaKuDyBhg9eByASiGLokC1XKBeKYJiRgV2DxXzhWNUijkym6s0ahXGDp7Y94ZzP7nVnbQ3dO3WltfdQ9fuFMb3hSKkNhZZvPg6sbEphBB4g2HqlSK1chG3P4iimqPla+UCA+PTZBPrFDNJAtEBRmeOoXWWsIkrRKybxCM5huMFXI79BZtuqOSLbrIFHx11mmRKY3urSzZnpVC0448f4uiTHyW1tkQ2uUGrUScQidOs12h2LAwfHKJeKRMZHKVeLhEeHkdRzL9JBcU8f2F2zVSLebyBcD/i0RMSt4qIfufJ1CHKhQwI5bb33CowZFrkwUYKEYnkIaEnDnbXRuwu7oSbHSdDQ0N7IhKJRILLly9TKBTQdZ1sNkskEukLj921FW+nlmR3NOTy5ctks1kKhQJAP0XQO26h1mIj32C2HWZ5bZOtugWLfxDSOZKrC9idHqLDE7j9QSqFHFuLs+YxdwQHwPLVc6xcO79nqFjvUz8CGrUKTrcXlAfvxnKrO2mlmKNazO0ZF99Po+x6z53Ow+MLMXf+e9RrZSJDYyDA6Q30r1+tVEAIgaoapOafZ8S3xrN/pUU8dJaI/99hszRu26chFMqNQSrtadrqMRr6OOdfX2N+No8QKlPHHqNeLVOvllAUBXvQA9UVHC5Pv1ajXivTrFVo1qukN1bwhaMIA/P3AhgIGuVif2ptL7XiC4Zx+4J4A+F9oxq3CsvdwmS/2o396jo+aGiqgtOqUWs/OOZ4d0MKEckHnofJfGtwcJArV65w5swZZmdnCYfD/UjI5cuXOXfuHH6/n4MHD5LL5QiHw1y+fJlcLkehUCAQCHD8+HF0XSeXyzE3N0ckEiEcDu8pBDVrNsyi0p4IUVW1vwagL1yy2SzFYhGAZ599Fl3XKTU6LGeqnLu+RanRNW+M2xd32jwPUSlksbs82F1uHE4Pme01Tj37GTz+LLOvv4xA4dhTH+u3TkZHJhAC6uUCwzuum1vLc9TLBUBh7OAJUKBazLO1OLvHp+IH5d0a2nbrTXV46hCXv/sC6/NXOPbUc5Tz5oRYty/A0M612Vq6QbmQoVrK4/GFGZm5+YnfEwjh9Pq4fvZl3P4ghx/9CEOTQ3isK6i+c4Q8W4R9CULebSza7T4mXV0jkfayseWhUB8nVxqmph/AYg/uqcFooeEN2WBHZAhhtsU6PF6a1TKx0UlioxNsLc/RqBRxuL0E40OAit3pwuF0gyKIjUxSKeSIj04iDEG5kNkpBDVTR0Jwm8/G7uv2g3SovB+xW1U8dgseuwWXzYLLpuG0aTit5nfXrsd2i1msXWp0uLJZ4tp2iXr7wej02g8pRCQfeB42860TJ04wPz/PysoK+XyekydPkkwmWVxcRAjBxsYGa2trfPrTnyYcDvP973+fs2fPcvDgQZ555pl+JGVubo5Lly7h8/n4whe+cJsQS6fTnD9/fo8Q232dUqkUZ86coVQqIYQgMjjKZtPKSrbD1b/4Zt/SemTkZjFkL8JRLmSJj04SHZ4gt71Go1ph4eLrxMemcLh9/ahKby5Jr3YAzG4HXyjSFyHs8nDoHQd4R2JkP9GhoLC1fIPE6jwDEzN7OklKuTT1cpHEyjxDk7f7R5hmYlm8oTD+cHyPGFEUBafXT6NWYeXa+Z1PrGZRbWJ1Hpc3YKZg1pfYXJojFBskvbmMMAyGJkYRzTkePZHn1ESGWHCWsdFvEQ5U9z2vdtdOpT1FqTFJqTnF9Wstrs9WKOcLDB84yuHHn6WUvojD7e132GwtzlIu5FAVhdDACIXUFomVBQanDuJwefD4ggyMHUBRFJavnqNZrxKKDzM4Pk1ybYmt5evYnW6zilSYQqMXxeodo1zI9AXl7hbZD2JUQ1HAbbPgcVhw2y147TuPbRa8O6957BZsFvUd79vvtPLsTIQPHQgzn6pwebPIdrF5D87ih0MKEckHnne7o+TdZr+IzczMDAsLC2xsbPDlL38Zv9+Pz+cjEAjg9/splUpkMhnOnj3L1taWaZ99S6eKEIJTp06xsrKyx7tje3u7n1bpdWHsPnbvOjU7XZa30nQ0B5bgCLr7APPn5nYsq8EbuOk86QmGGQTKhRyVQq7fXtqLEGyvzLM+Z6aSJo890l9fr4Dx1k/MiZV5eiLE5Qv219YTH+V8Fu9OiP/tRDZ66ZOeyOmF/ROr86xdvwSYwmR7ZQ4EeINhDCFoVIpcPvMC0ZEJBicO9vfVSzvUynkq+SwjM8d2ik3N9tr42BQKsLl0g1B8kMjwBBvzV1m6+ibTJx4lFusyEllkZmATS/ebBH0FhgZ1fO7qHeenVBteys0Jat1p0sUohcoYOI9gGPSHw20mrmDoFcKDY4zOHKNWLuwRIZmtVYRh7IilQL8O4/rZ75BYnmdwcoaBsQP9vwu3LwAoeAIhDMPA4w8yPHWERrWE0+PHEwhiGEa/Vbh3fXaLj1t5v4gPi6qYEYudaIXLZukLDo9d6wsMt82CqipvvcMfAk1VODLo48igj3SlyeWNEnOpCu3ug9GaLoWIRMJeMfLDdpS829xafLq9vU0sZrpWbmxskEwmSSaTHD58mHw+TygUIhAI8MILL1Cr1Thw4AA/9mM/xtmzZ3n++ef50Ic+RCaT6UcY/H4/2Wz2tuhH72aj6wZzy+s4/RFyHQfzFQtf+coLLC8tma25I3GsDrMOwB+OsbV0A18osici4Q/H8YfjiIVZqqV8X4TsvunUSmZRamp92bzB7aRadguanmdGpZjDEwgztOMJsTucPzx9FO8to+PvOo5eVfAFo/2ha6n1JQbGD5i1D4YgMjxGamOFzMYqqIBQ+tEegMuvvsDlM98ks7XG5NFHqBRyZgOPqpiPBf16lt41rRSztKvXGQhcZyBwgWGfwZOfKBLw5gh4/wBNu3Niv9m2U6yGaegT1PQZLpzNcOl8Ebtvgqc+++PmdZ2I0e1FbipF0purtGoVBDB14glcHr9Z3OoL9KMV9UrRtEJXIDw43h/Q5gvHqJbyNOtVQPTtzreWbhAfO2Bey0LWNFDzBRjc5dMhxE0PE3OQ24M3P0VVFOxWFYdFxW7VsGoqVk3BoqpoqoJVU9DUnS9l12NVwaqpWDTzu01TsVtU7BZTfPwgEYz3gpjXwaeOOnh2JsL1RPmBSNkoQjy4pSzlcrn/6c7n893v5Ug+APRuxoqi8Oijj75r+90d1bg1wrFb+NypJuXChQt873vfIxgM8vGPf5xUKsXXv/51coUSis3Bme98ByxW3P4gLl+I1NYG1VKB2NgBfMEIHn+QerlEq14hOjiMoir4/QF8gSChSIzN5Xl8gRD+UBh/OEomlcQdjOHwhUkkEhSze10hz3/7q9TKJTMSMHmw31Lr3xVa73WC3FpLcWuEYrfHQ6WQJbm2hMsXwBsIoyjsES27x8h7guH+fjcXZqkUc/2b52563Si9SMzuDoveereW50zBE4qwcPF1csmNvk24Lxhm5ep56rUKCoLQwCgAA+MHGJ4+ytybZzj30ldpNxsMHzhKOD4CioJh6PhDPrz2FFaxSCxcJh6t47Ks4lBWsVr2tzAHaLdVckUf6ZyLQjlAtuAjmbJQqsewOEcYP3yq75paLmRZvHSWZq3C4ORBnv3LP93fT8+krFEpExke70++9QbDCEPsEVS9dFO1lGdgfPpmdGnXNReCfrrpViG325l097XfHQW5H0LEqin4XTaCLitBlw2/04rXsRONsFuwW9S+KJe8e7yT+7eMiEgkO+xORdxtFsoPwu6oxn4Rjp4IuVNNysDAAMVikaWVVSo4yJSbnJldJ5sybwTFWptut4aj3qG7sUW33cIXjjFy6BSr1y+yePUCkycewx0eZGlhDrvTjZhyE5mZpArUFRfpjQTqRhLXTtGk3e6n2uriDUX79RrATreHIDoygdsXvG3ce++T7603+x67b0a3bmMYBjM7XRXm8dQ9FuXlfAZVVXeJiZRZgxGKkF5fYuHS68yceqp/8+vtxx+OUSsVWLp6jtT6Ek6vH2/gprOoAqTWF818vd/P9uocma1VXN6d/0BVaDUqOJxeFEUQH5smsbpApWhGPKLDk5TTC9i7rxJWGhyY0hkZquB3JlDV/T9x6oZGqRokX/KRLwXYWNfZ2ICWMkliq06r2UZBcOTJj9GolEhvrWGz23HQQBiin07xBSOc/uhfYu3GJfLJTebOneHQY6axl2EYuP2h/kA5wc77dANfKGJGfXYJBF842hcNPd6OB8eDkGaxqAohj42ox07EayfithNwW/HaLVJoPODIiIhEArfVhLzdGpF30nFzq9C41fDrTsertrrMJSu8+N3XeOGrz4Oi4HC6cXp8rM9f3vGIGCI6NMrClTcoprZxeHycePoToCoU0wkUTcNmcxCKD1OvlXC5ze6HwfHpPZGMxUuvYwg4ePqpOxZg9myxd0cWdluJe4LhfjrkrTw9bvXY2P2JenNhlmo5h9sbvG2/ma0VhCGYOf00AkF1p/akXi4iAI8/iCEEua01IiMTDE0epJRLs3bjUn9qbHzsQD/60uvkWb56jmI2RbNWQVE1bE4n7XoNXziGy+unXimhoHD6w6cwyt/Da1tkMJon7NvC787ue44d3UVDn6BUH2BtHYqVCMJ5EtV5mHKhCCpkNldJrS2ZXTKBCPnUFsqOQ9vAxAEcTg/hgRFq1SKFdAqn28PozDGzVmVXxGju3BlSGyscOP4YnmB4T6TqbhGlhw2bRSXisRHzOoj57ES9dsJuO9o9rrWQvH1kREQi2cVbiYVkMolhGHtEwH4FrPvxTjpudvuA7P6Etluw9Oo9Tp46zXKmytXtEmu5OkJAttIiGBtife4y2dY6kcGxHQ8HiA6N0mzUwTBweLyEooNsrdzAarUTG5tiZPoYm/NXAYHT7UNgUEhvUa+UOHD8sf5NKjoyeduQtN0IYexxuNzdDdITI5V8FiH2/xR9K7tvhLfeFH2hSL/GwDAMKoUsCIXM1iqbC9cJDZjXtlrIsXz1HG5fEJc/SGZzhVxq04xsGQbZ7dUdXw0Fh8sDQCaxQS6xgdPj3ym4NLs7itkkzVrVFG52F+n1eSLBBkO+JY6f8hIPpfE5VvA49+9SKZQcrG+6WdtwUmpOMXjsZwhPfJRyPkMpl6ZWK+AOBM0iXLvSb9ddv36Z+PgB7BkPidV5QrER7C4XydUFNhauMTpzjPhO3UpiZZ61uSv913dPfT302LN4/CHKBVMU3VqLs6d7h4fjpu22a0Q8ptiIeu1EPXZCbpuMcryPkEJE8r5nt1jY3QWy2x/jVqMuuCkc7hY0HBwcJJlM9qMbt0ZT9tvnSy+9RD6fZ2Zmhmg02l8TwPlLV1nPVfnmahOLJ9w/ztbiLEtX3iQ+NgUI1ueuUM6n8QVjHH7sWa5875vUK0VcviBP/6WfYGt5juz2Gp12i2a1Qi6xQXhwpF+gKAQ7NyJl3xHlvdz+bnoh+t72u6MYvdcTK/NUiwU8AbPTpZc66XEn/43efnbXGfRumlvLc6iKQq2cI7V+HUV0GT90FIc7yMLF7wEaiqqSTawTwUwZbcxfI72+wviRkwjDYHPhCkJAZGiMRrVMYmWecHwYp8dLKGwns/inVLOzHBhMEPDkiIVrDAx0iIYqOOy3p1YMAfmSn3JjkuVVG8srFjLFAQYOfJhapcjG3FXarSbT+iYTndkdIXSzDbmXWgFIri2axmTA+txVbHYn/kis3wLbqlURQiG1voQ3GOHQ48/iCYRYvnoe1NvFYq9Yt5zPPDS25ooCHruFoMtG0G0l5LYTdtsIe2y4bPI29X5HpmYkHwh2O4fqut7//k5TMftx4cIFrl+/TjgcJhqNkk6nGRgY6M9bicVi/WmzFy9eZHZ2lnw+T6lUYnJyksOHDzO7vMGlxU0qwoEnsDfc3vPGMMPwglxijcTqIp1mA4EgNnaAzflrdDstXB4/sfEDiG4XRVXJbK5Sq5QIxgaYPPoYA+MHKBdypgRRFarFAgKBxxfc88n6btxe6HkDRVFRFKgUcqiq2hc88bED/Smot6ZrSrmUGeXArNGwqRn8zk2sxnX8zjQeVw2rksFhLWCzNPY15wIzkqEbKrquYQgLhqHR6UCnI0B10Gp10XUVXTfrTVSlhdVi4HIL3M4GFu3uLYydrkYqG2A75afYnKBhHKGjHaWYb5BPbdCs12nVq9hdHoKxARxuH41qiWImRateYer447h8gdvakLeW52iUi/2anMVLr7O1NIfD7cbh8hAbneynu2rFAigQHZm8TSw+DOkVq6b021W9Dgteh1kw6nNY8Tmt+BwWLNqD2WUi+cGQqRnJB4p3Uqexvb1NNpslk8kQi8VuKxLt7ePChQtkMhlOnDixp4C1F7lIJpPE4/E94eE333yTxx9/nHw+Tz6fZ3bWtCrveXdcvHiRM2fOcPDgwf72S1sZXl3IkszkEMIgNjJJan0ZoQiqpTyLl15HCNE3Aps9+wqNWg2H2wMCapUCq1fOMzA5QzA6wOKVN1g4/z1OfuSznPzwp3jlf/wXaqU8oFKvFikXcv16iMTqgvkp3RsEZW/B4d28N8AUMX1REYxw/qWv06zXOPnsp3D7g6zOXiCX2DDnjAyNUS3lwTCjU4qq4AtH8ViW8dhfwG+9yGB4FY+r/gP9/hUFLJqxIyh2OlGcvZ++vaF39bpGpWajWndRqkcpVcNsbausr+notiMMjB+ikElg6DrRoTEe/cSnuPHmdxHCoFmrEB2ZILO1Sr1cZvLoo3iDERYvvc7m0hy55KbZqXJLG/L2yjzVSpH4uNkC6/T6efTjn0cgSK8v4/YH8QWjppuqP9SvkXmQzL40VembcLntFtx2rd+N4raZz912Cw6rdr+XKnmAkUJE8tDzdus0epGPSGTHXEkIvv3tbxOJRDh58uSedtp0Ok0ul+Py5cvE4/F+FCWVSvWt002PDfP1HgsLpqvn5uYmXq+XJ598El3XefHFF5mbmyMUCuH0Bnnj1QssF7ro+Qz2bBWBwqFHP0Rma43E6jyD4wdpVMrUy0Vc3gDVUp71uSs0a1Wcbi9CGDhcHmrlAp2uOSHV5QsQjo9gsztplItsL8/xyEc/T3rqMEtX3qBZq/WrAsr5LM16Dafba3ZTiJvplnIuTXJlAcMwIwV7Rs7vapPtTYKtl4uAaZi2fuMKTo+XRq1Ks1GnlEvTqJX7dt5TY0UmHMtMKws4Iwm42biCrivkSgFKtQE2NjWyOQu6GieXg1IRfJExYpOnURSNxUvfp1HOYnM6cLkd6O0KhfQGitHCHw4wMDaKoTdILF0B0cQb8GN069jsDlz+QXzhMSqVNnNX1tlcy2MIGzOnniIYH8LQDVrNGsHoIF3rAv5wnGa9SjA6iKqqOD1+5s6doVrM4wmEcPtD1EoFwoPjTB4N9+tZnN4AIwcOIYToG37tnqMyODmDN2AKDIFgeGpX7c1OO+zuNMr9inx47Bb8u1pffc6bkQy3TZO1GpIfGilEJA89b9cZdXd7biQS6Q9+y2azJJPJ/v56zqJgdrbMzs72t1tdXcXn8/X/8909ZfaJJ54gk8mwurpKuVxmdHQUwzDIZrO8+M1voltcNEPTvPLKFYQ9wvixR1m6/AatZgO708n63FUatTIHjj9BvVokn9wmNDBMo1Liyqvfwu5yE4wNER4aQ1Egs7WG1W5nZvophDBHpT/68S/0p9Fmt9fMdEsoQr1col4tUS0X2F6eo1ErU68Wcbq9fYOqUi5tmoUVctTKBTyBEFtLN6gUsv0OmUoxR6NS3JmDUmBz4QpOj28nneBGAMn1JaqFHDaHC38kxMGpNCOhC8yMLeP3tvrXuavb2EgOsLgSYHUrytycRqlQxuULMnX8MdIbK1QLGUqFHMOThzh1+vOAOQDP4gihVzqsL67gjwzgC8XJ5jJ0uyq1jo/tVIlyLo3TO47V5iBVFtQrZQKRON5GlPL1NHanh3RaEIhNmm2xLg8Ol4dmo4bQdZr1KoMTMzTr1R1B6Cc6PNE3XYuPTXHosWfZXJilXi7gC5qTY7cWZynnswwfOAzQt3q/1VitZ/K2H/sNc7vXeOwWIl4bkZ1i0LDbTtBt7c8tkUjuFVKISN4XvJUz6q3C5OLFi2QyGaLRKJFIhOvXrzM7O4uiKBw9erT/vlQqxcLCAisrKyQSCQzD4NixY+RyOZaXlwkEAgAEg0FisRhvvPEG5XIZn8+HEIKzF69Rx858Xqejl5hL/AUOt5n/FzsdLs1qhUo+R2J1icGJGVw+P7nEOk6PF4fbS6NaRghhFs3udH9UiwWKmSSxkUlGZ46z0+lphu0FuHx+EAqLF1/H6Qtw8tlPU85nSK0vs3DxdQLROOOHTiIMwdbyHMNTh6hXiqzduEJ4YASPP4RhCFRN7ftluH1BfMEw9XKR62e/058l0qhWaNSqOF0eFAVa1TRHZxI8frrMsUNpHPab4qPRtLCWOsL15QlePdME1YMvFMbh8jB21MPS5XPkE5vUK6ZIqhRzuFxe2s0a1VJ+Z8y9SrNaRVEhNjJJIbNNu1kjNjqJ3ekmubpAp93EYrfj9gawOlwMjh+gUa3QbJjdLp1Wk1qlRLfbwWa34wlGcHq8qJqGoeu4/EHC8RHUnboFl9eP0+PrG4IdOPF4P8IxMnMUX8gczlfOpfEEw3iDkds6VXrc7yJRRYGgy0bMazdbXz0Ool47TpsUHJL7gxQikvcNvUjIrfNRbhUhFy5cIJ1O96fQ9ibIKorSHyQHZrQjmUwSCoXY3NzsCwxjZxZHIBDg5ZdfJhaL8eyzz3LmzBmKpTLC4iBXazN3aZVmVycUH6ZrCJr1Og6Xi2ImRTGdBE0hEI5T3Mlb2FoOQDB/4TUcbjfhgREalRLB+PBOOkZQyCbJp7dpt5r4QhHCgyMIYdqJr12/TKtVJxCOM3X8MaqlPKs3LhPFHKZm6AaNWplyIY3D7WFwwqxV2V6e49J3X6BRK6MoCh5/kMHJg2wvz5HeWO3fvLPb6zjdXuq1Es1GjUoug0Ch02oQDCkcOlxjIj7L4b+ew267ebOt1p3cWBlnefsI584Z5FMpIEOtXGR46jAIhVI2xer1i3RaTZqNCiiCbqeDw+khODiMMATnvvWnREcmCQ8MU0gnsNtdDE8fYfmKQbvZwOZw4nB7sNjsphCx2mi3mkSHJ5g4+gjp9WU2l+fIJzZAUei2WviCUcYOnyI6PM76jSvUq2ZNi6Hr+EIRPMHwjigzi0Z7s2h6EaJb6zXeKoXyXtd1KAqE3D3R4TC/ex0PrP245IOJFCKS9w13ckbdHR3ZXf8Rj8f73h2RSGRPfcfv//7vc/r0aaLRKCsrK5TLZZrNJo1GA4/Hg2EY1Go1Go0G88srVA0LHcVO2+LE6fZR18tsrt7Aanfi8vgoZlI43G5zQu3SHJtL13C5/YBCOZfG7nQTGhgll9gAAcPTh2lUy9SrZRq1Mg6X14wE1Ct0Wm1ajSoDE9M4PQFyiTXqlTLZ5Abteo1gbIhyIUe9UmDi8EnTd2PpOqGBYRwuD+OHT9GolFi4/DozJ58CBRq1Mk63D0WFaqlApZDFEwyxsXCV9MYKpWya6s5rA2MzWJQOB8YzHBjPMjG8zYGJCuque1uh5ObsOTdn3/TQsjyJLzQAClSKF6mVSqCC3u2aa241qVdLlHMZNKsVjz9Mt9sBw8DmcuELhHH5gySW51mdvUAplyI+OoXbH6RaKjB17HFc/gBXX/s2m/PXCMQGiAyNUsnnEeg4vV4zlaZAu1Gj02nCzuj58aOniQyMYhiC8KB5/evlItGRib7h126r+p4TKdwuKu538aimKn3REd0RHlGPXYoOyQOPFCKS+8Y76XZ5K3pRjl7RaS8KAvSFCZgFqidPniSVSnH16lUymQyhUKjf2ZLP51laWkJVVS5evIjf7wdgZGQEn8/HwuISV2/MY2h2hGqlbglQLOcoLK4TG5kgFI8jhHljB0GtnCe5usDg5AxOtw+XN4DT7cYfipPaXKJeLRGIDjAwcYBCKkm71SAUHzHXktzC6fMjdB1FVUGAw+Wl3TTrG+rlIi63F2EIsltr5qyTg8dwujw0KnmsaotuYxO7pYbT0cGi1giEYsQfeZzX/uJPWL5ygXxiE4RpctaslWnWaxSUJLmUOWvFF7BjE11E8zxHRmqcOO0lGnyJaDCN1bK37XV5xcrl2SgriYMsLAg6nTaBcJxofIBmrUqlmKPTaoMi6DSbWB1Os3alUkLTLNhcLiyaFV8khtVio14t067XabWbjMZHcLm9XD7zAghBMZs0HVS9AaZPP0VidZ52vYbLF2Ds4ElcPh851yYoCoVUgkb1FZwe/44/h4tgfIjo8DiVQg5FVcAQxMYmiY9NUSnkGZiY2RPZuN8iYzeKAj6HlbDHrOOIeM3vIbdNOotKHkqkEJHcN96JK+nd6EU5dtMzGnv++ecBeOaZZxgaGtqzz2984xu8+OKLPPnkkzz99NN9MSKEYGVlhdXVVfzBEN5wHF1zUNY9FK1Blq+fw+nxEYwN4Q/H0Owucol1itkk4YERUKCYSeINxUAImo06k0cfwRuMcPnMizRqVexuNxiCbrdNu9lg7fplfOEoofgIrUaNZs2J0+enmNpmcOoQLreXzaXrKCjExg7QKJdo17YJOrKM++b5yLESPk+JSOh1nPY6VkvnjuPiAT76c9DtqnS7CrphwcBiPu8YWC1d7HawWjt39dio1N2kige5cEHw6pkG6YyC3eGm1UiiWWyMHTrGiQ9/CoFg4cLrFDNJut02wwcOUyuVKGYTdNpNAFyRASwWC7GxA9hsDhRV5dDjH6GQ3qZRKZFLbuB0+wgNjqIomJNgs0lOf+SzAKQ3V4iOTDJ26ATCEKBAfPQAlUKOjYWrpi2+28Pk0dN75qv0Ckt7aZgHyZPDYdUIuqwEXFYCLhtBl42Q2xzeJj03JO8npBCR3DfebrfLfuyOpvSiHL3XU6kUsVgMRVEoFotUKhVmZ2eJx+P9Y7z00kuUSiVyuRyzs7MEAgEikQiNdpeG6mIxXSXbtbOynMJb0Bk+cBhXMIA9m8Pp8eHaGVOPYtqGhwdHaTXqbC6a1uOB2GA/kjF84DDlQo5KMUe9Wsbp9uJwe5h59EMIAZvzV+l22nRaTYanj9Csu3C4PISig4Tjw9QrRTaXbhAZjBHxzDE1dI7J4TUigfwPdf0tFgOLBUAHWnfcrlpTKVddZHN2VtetzF9vs5UJYlimQVGw2exYPSoBo0Bme5VOq0UwPmR2pWys4PYFcLg8BCID1CoFhICBsQO4fX6yyQ1K2RQWixWr3Y7d7iQYG8Th9uLxB3j8kz/C+Ze+xtKVN7E7XYRiw0SGxshur5NPbZFYnWdgYobJY4/iC0ZvM/oq59J4AmF64+vv5EJ6v9pjXTaNgMuK32nbERxWAjuPpfeG5IPCPXVW/c53vsO/+lf/inPnzpFIJPjjP/5jfvRHf/Rtv186q34w6ImPXgrl7bib3kmwvPDCC8zPzzMzM0MkEkHTNGZnZ1lZWSEQCDAzM4MQgsXFRTY2NiiXK6RzRXTNRltzEBqdoVYqoKgKLreferVMYm2BTrOBNxilUsggBPgiUcrZNIqq4g1ECMYGaeykNir5DNHhcZxeP4auEx+bYm3uMuVsBrvTzfCBQzi95pj79OYy5771pzRqZSxWG/7wALHRCZxuH06Pj8HxcYz8HzEZO8vM+AZ2297R8dmcg+VVJ4VqnHp3AF0dY321wNr8KqVSG5sjyOjBY+STGxTSW9gcdhx2DYtFEIyGadTSVLPbON02jj/1YZwuJ/lsmY3FZQq5CrW6Rr1uYLM50HWdZr2CoetYbXZUiwWb3YU3GMZqs5NcX6RZKeHw+nF5/ESGRjn82LP9up16tUSjWsHp8lLIJskl1s2ZKDvW6za7A1CYOvYoLn+AajGPNximWiyQT20SHhzB5Qn0R9cnVudZu36J8SOnOPTYs/fgL/PdQVUUAi7rTkusjaDbjG5IsSF5P/PAOKvWajVOnTrF3/7bf5svfvGL9/JQkoeM3RGNW7tdej+/W2rmTtGU3bpaURROnz5NPB5ndXWVl19+mdnZWVwuN8sb2zSx4hmYIE+H5PK8Wb9w7RIun5/hicOEB8dxB4IU0gkK6QS1cpGBiRkcbjfp9RUUTcNqtZNLbtBq1vGFIjjcHpKrC6AoPPrcF6hXS6zduMz28hz1SpHY6BRC3LyRLl95E7cvSDA+RKtep5RLYXO6sBlzPH46z8GRK7iO3HQcLZVtXF+IMr8+wuJykEbTgUBQr5bNmo6Ig1JWpd7yohtVGrU6zXqDarlCo9ZCUR006i1qpTwbq1n0bher3YvPiPL976ZwewPUKkVyiSqaxWq2BQuDaimHzeFG1SxYbQ40qxW93QYVGtUy2+ltVFXj4BMfwesLsbF4jVajAYDLF0QBXP4A9WKRXGqTci6Dze5k8sijoEKzVsEfHQRDJ5vc5Nj4ARRFYe36JbPu49AJXN5A31a+lEv3u36qxfweo7D7iduuEfXaiXhufsnaDYnk7txTIfK5z32Oz33uc/fyEJKHlN31IXBzGF0mkyGTyfRTLQDnz59HVdV+uqW37eXLl7lw4QKjo6NEIhGzvbVQQFEUXnrpJbxeb1+weL0+DM3G5YV12oqNfGobl89PGKtZvBgbYnt5nlxyA48/TDg+SqNaJLe9id3lYvLYI5QyKRxON+H4CM16jezWGragk067yfbydfzR53A43bj9IRAG2eQ64YExyvkMVpsdlzdAu9mgUS2RWJln7uJrtJtNvEEzotKqFzk6vcKHH/sah2fK/fOvN91cnpvg6sIMq2tOUttrNKtlQgNBTnzoWebOn0EYBvVqaceILMzIzFEUYOHCWebPfw+rw0l4cJRiNoHe6dJu1MyWVIuFkeljeEMR0uvLJAvLoJh+JbrexeZw0ixVEQKatTKaxUYwPkQgFCO5sUyzUqLTbqMICA+NEYmPoGgqM6eeolmrkU1sEFEAw9Q0jVppZ47KFAidscMnEQZsLF6hUSkxMnMUDEGlmGNw0hQahm7g9oXwhSJ7xIZAcOixZ/cd0Pde4HVYiPkcxHd1qXjsMtstkbxTHqh/Na1Wi1brZq66XC7fZWvJw0xPIPSm1vaERyaTAeg7nQ4OmrbaV69eJR6PEwqFyOfz6LrOxYsXefPNN9na2uKpp56iXC5jGMYez4//8fW/YLvU4sr1FbZydWqlCm5/kEBskFqpwMbcVQKxQTAMKsUcVpsNgEo+zXKthj8aJTI4ZtqYRwWh2AgCYba9CkGrXsXlDRCMDZNZX8bmdBEZGqPVrJFYXiC5uogQBnaXBxQVhKBRq3Lle9+kkE5gtTuhu8nx0fM8cXIej7MCgGHAlRtx3rw8xfxKhPDQNA63G6GsgGG2kXaaDa5875sgBKGBESr5LN1OG5vNzsFHnsbrD7Nw6XVazV5ERaCpFgr5BHqnjaF3sTpcdDtt7HYnLq+fcj6DZrHi8gdp1Ss0qhU01YKh67j9IewuD06Xh3arydjMMRYvv4E34AMVRqeP0Go2CETjnHr2s1QKWZLrS7i85rTfermIy+MnPnYATzBMtZDrD/fzBIOkN5aJjUziC0X7NRu7W2fv5DZ6ryMhmqoQdNuIemw7Y+gdxHx2mVaRSN4lHigh8qUvfYl//s//+f1ehmQXu1Mot7bb7m6xTSQSfd+OH6Qdt/fzXtQjlUr1O2FOnz4NwJkzZ1BVFV3XqdVqdDodfD4fy8vLAMRiMdLpNIVikeDwJAsFg9TCJbaWrmNzOLE53NicLlr1Ou1WHavdSTGXIrO5gsXuQNMsaA4HertDcmOZsekTOD1+ctvrNBt1/JE4igK1csm8DpOHKCQ3adRqhAYGWZ+7SrtRp9WoEYjEWUpsYLU58IWjYAjajTo2p5tGrUy7WWd8JMPHn0ny6Kk8Fs38RF9rOPju92O8dCZCpe6j02qBksXtj9OsVWg3aljtDjqtJuWCmd4IDYzQrtdQFIVOq0k+nSC7vUF2ax2vP0y70aBWzpFYnkPXdYTexTB0NM2MBlUKGRrVMkNTh3HlM6CALxChbrWh1co0alUUwO7yMHHkFPnUNvVygXIxSyg+jCcQot2ok0tu4fEHUBTz9z88fZTh6aP9AXqw1/Brt8gYmT7GyPSxff82ekJDVRQ0lX76TgiBboDxLpS52a3qzpA2C36nWTQa3JmvEnTZUGVqRSK5Z9zTYtU9B1KUtyxW3S8iMjo6KotV7yO3ttLe7bGmaei6flsB6Z0KS3vC5lY31O3tbXK5HACGYTAwMEA8Huf5559nbW2NdDpNJpMhHo/jcDhoNBpkMhnaukGmUEFxegkMjJDdXKfbafcLQUemj6GoCpVchnarRWZ7hWatgqqZtRA2hwO3L0itXKRZr+D2hfAGQlgdDkKxER77xBcQAlZnL1BIbxOMDzFx5DSr1y6QXFui3arvCJ0anU4bq9WGoioIQ6CoKjaHE7oVjk7P89yHtxkeqPSvxeKKh+++PsrZN72Ehmawu1wkVhdQAKvNgccfpt2sAQrtVoPM9hp6p4PN6cTh9ACC0UMnAFi5doFWrUZ0ZJzh6cNsLc+xcO77NBoVVBQsNgdufwBD17FY7Ti9PpqVMg6PF28wgtVqw+Z0027UyCTW0TQNi83B4PgMiqpSSG1RKefR220mTzxObHiCUjZFs1bF4fHgcLgID44yfeqpdxSt8DosRL1mTUXAacPntOCyWXDaNBwW9Y4tq4Yh6BgGXV3Q1Xc9Ngx0Q2CIm2JFVRQ0RUHTFGyait2q4rRqWGU7rETyrvLAFKu+U+x2O3a7/X4vQ7KL3UWhPR+OW9Mpu0XGbiOxt2rH7UVSdruh9l7PZrMAaJrGmTNnAJiZmaFYLAL0oyDhSAR/fIyXXj2LYnNisdlw2QTJ5QWsTiedWoNWo47FYqPdatBu1KhVilSKOVq1KqpmxWZ30KxVaVRKtFtNbHYHqmahWS1RK+dx+0IMTx3FG4ywcPF1EMKc0moY1MoFXF4/KMJ8r8NFp9OinM1gcdiJDo7TbdWYOVDm6cfmODg2h92mA9Bqq5w9H+GlMwNsbLtp1io4XBpg4HC5OPr4RymkE1QKGQqZLQCsVsdOp4nA5nABgnIhgy8YpVWvM3X8EXKJTdZSW2wtN+i0W1itNlz+AK1mDSEEmkVlYGKGRqVEKZem3ayjWiyAQjA6AIqC3ekiWS5gtzuIDE9is9soZJJYrFZQFSyahYGZaXyBMKpi1oTUqyU2F2ZB1RBCsL08B9w5dRL22BgNuRgJOBkMOH/g+gpVVbCrGrI8QyJ5OJH/dCVvyW4xsnvk937D5d5q+NxubhUpu5+fPHmSy5cvk06nKZVKCCF4+eWXcblcqKpKMBQhU6qxvZIm9eob1ApZNJs5QdVqs+P2BylmkpTzWTSLBavdQXp9mW6njcVqw+H2oHc62J1u03sinyG5PI+yY7Bltqt2UBUrICjlUlw+84I5zl6FyaOPUC3lmTv/PZxuL1MnHmfpynm2V27gDUbxRaJQfZNT45f51Kd0wsFG/7xTaQd/8U0333rZRbNtR++WsdnbZm2G10+1WMAfjhMdGaeQ3kYAbl+A7PYGmdIqVpuD6Mgk7WadarGAze7E6nCQ3lgGIQjHh6hXS6RXFslsrRCIDuF0+2h5qtgcZhtuJZ/F4fHij8SxWGx0ux18gfDOIDtBOZ/H7fUxMDHN8OQhtlbmIJ3AG4ziD8VoNqsMTRzC7Q+CEHiDYQanDuL2BRCGYGjqEOVCZk8RqaYqjIacHIh6mIi48Tms7/JfqkQieRi5p0KkWq2yuLjYf76yssLFixcJhUKMjY3dy0NL3mV2t8dGo+bY+FuHy+237a0/3y1m9ouUqKq6J+VTLBYRQpBMJrlw4QLD41MMH32CLJsU63kq5QLNagVDGFg1C3aXm1xik2I2id7pmiPuFbPFtNWoEYgOYrXZqVdK2F1unG4v7WYDXzBCa7BGIblJJZfBEwxisTqw2Z1YrHYK6W3ajRpjR04SGRqjXMihAKH4MInVBTKbq1g0wZNPOTk4eYNTRzNEQrX+eTVbFt68FOXMayGWVrw063WajRLtRhkBZq1HfLi/fSmXYf78azhcblqNGq1Gg0oxR7tp1rZ4fAFaNgcKCpVSnmIqgd3jIZ/eJhQfwh+MghB0O21qpRy6rjMwMUMgGie7vUG1lMMbjBAbmqBSKoAQDB88itANysUMdoeNqeNPEB+bIrm2yMzJpxmeOkx2e53Rw8cYmjhEKZfut9PuLi7t4QvHsKgKY2EXMzEvU1G3LPCUSCS3cU+FyJtvvsnHP/7x/vNf/dVfBeDnfu7n+E//6T/dy0NL3mV2C4teZ0s0Gt0zXG6/bW/9ea9tV1XVvgjZ3t4mnU7360vA7JrJ5XKsr6+TTKVRHT669iA3NtJs1d7AZndRzKWpFk2nU02z0GrWKWW7NMplUATBgWFQFGrFPO12E6fHS6fVIBAdxOZwUKuUqOSzoMLY9Ak8gRB6p0MxvU2zVsMf9eBweynn0rQaVawOB/nEltmHiqDTKDAU3Wbq9DkOjGY5MFnHar0ZAeh0FG4shjjzqpOL16LU6zp6t43d1SUUGyS5UcfQa9icDtw+/87cmUG8wTArV8/hdPt47JM/gtPj58zXfp9OvcbIoeOgC7ZX5hmaPITd5TJt0l1uU3i0m+RTW9jsTkamj5FaX6RayCEQjB4+welnP8vF7/w5Cxdfp1GtMHH0EY5/6BPUKyUMQ0fVNMIDI3gCQbPbBcHM6af76ZWtxVmEEHedNrtbfByIubFbpPiQSCR35p4Kkeeee473qBZWcg+5tWC1J0TejkX7rTUjt74HIJ1O893vfpfDhw/z2GOP9WfHtHUD4Y4wl1xAN0pExqbJbm+wvTSLLxLHbnfStNmw2ZxYvDY6qRaVfBZVVbG7PLSbTRB5UBSMbgdQiI5MEYjGSW+s0Gk1CcWHyae2SG+tYLXa0awWbA4XLn8ABNRKBTSLBc1qo5xeZnJglUcmbQyGVhgfqWCx7P37LpY0rlxzcPFqmNn5EB3diaIolPMpdN2sDUFAfsfSXbNaEQJQFKw2O8V0guTaIhaLFbc/wNLlNylmE9jsDsKHRnG5fdSrJSxWG4X0Nm5fgNjoFHaHi5VrF3B6vXRaTWw2J+1GHbcvSCfaMiffZtPUK0Uefe7ztOo10ptmse7Q1CF84Rhbi7MkVhcYnJjZM+Z+d43H8PTR/uPdr9ssKhNhNwdibiYjUnxIJJK3j6wRkdyV/bpmbi1SHRoa6s94ubVrpjd8rlfgeqsYuXz5MkIIDh8+TCqV4sUXX8Tl9fP92TVmV7fRdYPQ4PhOhAUiQ6MUs0nTvRRwe4N4g2EatQqtRhVd7wIWOq0G7VYDm92JPzKAOxDG4XSjaCrp9RVyqU267SYuTwCH20M5lwGEOTvFYTfbZK1Njh7p8sTjDg4frDIx1kC75f6ayarML/m4dBkuX1JJpm1YbA40iwWb3cBibbMzlIZWrYrN6UCz2WjWynQ7bcLDY2CYgicQHaDZrFEr5hmYnGH04AmWrrxBp9XkxDOf5sjjH+HCK3+Gzemi02ogDEw/j0MnKGSSOD0es90XBZvTiT8cpdGoMXb4JAiDtetXWJ+7yujBY3zo8z9JamOZaqnQP5eeyOh9eLhbx4tFVYj7HIwEnYyFXQz5nbLFVSKR/EBIISK5K7uLTfer6djtDZJIJPYtTB0YGCCdTpNMJvv7SaVSzM/Po+s60WiUT3/607z+xjn+w+//IalKG4vDTSGdoN2q4wtGiQyO4vQG2Fy4hi8cJZdYp9Nsors7oChU8hmMro7d4UTvdul2OoBA1yzo3TaHn/gIrXqd9dmLNOpVbHYHgeggnXYDlzeA1Wqn09jm8HSV04+qjA9mmJzo7giPm2226YyFK1c0Ll/VuLHgZmWhgmYVqKqCbnRQ0Gk1amhWG1rIisPtoVmrolktaFYrjVqNTrsNgN3polWt4vYFiRw4SnJ9kVoxx8DkQVweHxvzV7Fa7YwePE4oNkx6Y5nByUMkVuZoN+ooioLbF6CQTSIMg8c++ZeplQtsLc7idDgYmzyAx+dDRWFk+jDrUzNsry0RjkYZmjrCyMxRStm9rqS7Ix6qouCwqrjtFnxOK36nlbDb1rcwl7blEonk3UAKEcm+9IpKdxuQ7RYct5qT3cnIDEyxEo/HSSaTXLx4kXg8zve+9z3W1taYmJjAMAS/81+fZ6tuYavQpFGr4OwahOKDJFcXyW6voQDOahlh6DjcHuJj01RLeYqpbUrZJKpqxWJzAALNakPvdk330G4XzWr6hNidLmqVInq7bfpl2KwEvSkeObHGiSM5JkbLqLfYSWxtKVy6DLNzTuYXfWysN0CA1W7H0HUEAqHrGEIFw8DAQNVULBYbCEExvY3D4yMQGcDucFMt5WhUK6iaRi9r2azXyCbW0DstBiYPcuSxZ1mfv4owDGKjkxx98mPMvv4KAkFkaIxAZABQ8Pu8BNx2UmtLPP3hD/GLv/ALVAoZXv3OK5TLZbxeL/F4nGPHju38rp687XfX1afpGgJDmH4bCqYAsWiK9NaQSCTvCVKISPZl9yyY3amUW4tKe9zNOVVRFHRdp1Ao8OabbxIMBikWi6iqSrJYY3kpz43Lb1LKpYkNT+KPxDAMQaNaxe7yUEgnyCY28AUihIfHqOayhOJD2BwOyrnkjmungWa1IHQDzWpFVTUEBoZu0G422Ji/SrmQASF45EkvH30mwYnDl4hG9k6zTWU9XLlq4fIVlWvXLBTLNoqZNIbeRNXaqKqGzemi3WgghI6mmi2ohtHF6OoomgpYELqOrndRNQu1omnO5nC6iQ5PkEts0mk3MfQugegAybVFHE4PwweO8rEv/izf/8YfghDERidpVCvMvvEK4YERitlt6tsLfP6zn+Hw5AjrywsUCgXUQ6N4vV42Fq9z+vRp7J/4BEII0uk0hmHcJhh3Y9FUZDmHRCK5n0ghItmX/QpR0+k0V69e5fjx43d0Tr3VBn73vl577TWuXLmC3W4nFBugrHpJLiZoVirkkptUC1lAwR+JUSlm2F66gdPjN+s/6jWS5SL1ahkUyKcT1Ep5VEXD7vTQbNZoVMp4AkGa1SqqxYLHH6ZVq1JMbRNwbPPjP6Ly0WfqDAwY/bW12nDlqp0r1yOsJGZYWcxTyiQxhI7D5aLbru+Yk5sOqUIRtOp1s8NE1bA5bAgh6Lba6N0uGhoubwDYma3iC+Dw+Gg3auidNm5vAF84RrfdotWoUSnmzSJZmxVPIMTsm9/B5nQwMHaAk89+muUrb1DZWuCTj00T9xyjVCry0Y8+ZZrBjY+QTCaJx+N90bH7et9terFEIpE8KEghIrkj+5mTHT9+HF3X+y25d+uS2e0jkkwmKZVK2Gx2NrMlLq+mCQ2NIQyDzaVZLBYrQ9NHqZeKbC3NMTx9iEI6QWptASHA4fKgd3USa/Ooqmaaknm8AJSySYRuAIJ6pWxalwMue53PfarJxz5SZ/rAzfNqNOD1Nx1897tW3njTQNft+MJeOu1Vuu0W3U4bVdNo1au06jteIMJACNANA0VVEQicngCdZoN2p4UiFFSLBVVV6bRbOJwuujvmaHani5YQaBYrXb2L0+7GH46RS25SLxcYmDzIgeOPsbE4S3JtkaNPP8dzn/48hwY8/PqP/wNuXLvC1atXGZwZ53Of+0t7fj9SdEgkkocdKUQkd+VWc7LTp0/3xcZ+zqlCCDRN2zN7JpVKcf36dQq1FjlctDSdWjWD2NqgXMjQbbfwhqK4dyIJwjDYWrwOQiAEGIZOq16l2ajTbTVRFBVhN7DuDKrzRwaol4tUywW6nSZPPW3nC1/o8uRjaaw75p2dDrzxhsJLr1h47fsquurE6XTTbpVQNZ1SNmHWleg6NpsdQ++aRaVCYLU5sDqcNKslQNk5RwudVgshBMIwi1VdvgBOj49WvWaalDndNKpljG6XQGyQbqdNt93CGopid7vBMAgPjjE0dRC3P4jXH2Qw7GfSo3PYUeLTTzwJ3Bz614t4SCQSyfsJKUTeh+yXHunxVlNw77T9reZkd3JO7U3Njcfj6LpONpvltdfOcmMrTarcolmrUSvl6LbbJPOLGN0u0ZFJxo+cYvHS61itpj17cnUJFHAHQlRyGapFs83U4fbQbrVp1qu0mnXi49MMTExTWD3DT/wV+PSnBPF4vb+eG3MKf/EXGi+9DKWiwO6wY7HbcTicdNpt/JE4tXKBZrWMoqogoN1q9G/6DqcHm9NJq1Yzvd0VsFhs6LputtACFosFtz+Eyxtg4shpMttr1Ep5AtEBGrUKvarUoYlDoCgUUlsUklscefo5jjz2EYqJFUaCDn7y2Z/ApppusreKjp4YkUgkkvcbUoi8D9mv0BRMUXHp0iUGBgb2FSK3ipQ7pV1SqdQdnVN7rbqpVAqArtXDpe0ySzcWQQg8wQigUK+W6LSadNttipkEVrudZr1KuZGhUspTq+RpNxugQLvRQO+0QVHotKxoVo1Oy0BVVcbiq3zhuTmeeqLV9/io1lReetnKn31NYXHJQFE1DKOLxWrpRzDq5RKKpqI2anTbLTSrBdViw+h0aLdaIAxsTgeoCq1aDV3v4PYHsdpsdDptOo0GnW4XFTPlYne58UfidFotLBYbwweOYnM4cdWr2N0ehCGwu1wcfORDzF94jUo+zalHHuVv/ugn8BoVshmzxkPTNE6ePClTLRKJ5AODFCLvQ+7meDowMLCnxqPHrcZl+03NHRwcJJVK9QtWY7EY6XR6X+fU//D/+11m15JokXGa7S42u6M/Wr5cyIABqmZB1XSqxTwoYHd6KGVTVIo5XD4/wjBo1qsY3Q6qxYIQBo16Ba9H5ce/qPGFLzQZG70ZObg+7+Trf6bxnVcE7ZZCq9MEXaBqBoYhzLZaVUPXOygoqIrWb+e12h10223TEE0YqJoFvWtg6A1A4HB78AZjtJsNnF4/9XIJqmUURcETjODy+FBUhXarhs3hJDoyisPlRVE1HE433mCYarFAs1rk7/39X0IrbNCuFQkqNQZHhhkdGX7H0SqJRCJ5PyCFyPuUu03BvdV2fXekpBfhuHX7XjtoMpnsixBFUUgmk2i77EYHBwe5vrTOpY0CqyubRLsarVqN6MgEzXqN7ZUb5k1cBU2xgA06zTqVfIa2q4HN4cLQS9QrJTqtBka3C6qKqlmIRbv8+I91+dzndJxOs+22XodvfUvjGy+6WVuzmCJD1eh26tDtomgWVFVD0xS63S7tdh27y4sC6N0ORsc0ROu22xiGGWXR7A66nTboBh5fEM1qxRuK4nC5sbtcFFPb6N02Lo+PQHyI8MAY9UoBq9VOeHAUEDSqNcKxUWJjB1BUiLisTD8yw3DAzsRYlMHBk/3reuvvTCKRSD5ISCHyPuZOtRz7iZRepGS3T8hu0aJpGslkkoGBgX69Qu/1XhomHh/g977+Cn9x5g3qHUEpm6SUTxMIRxmePsLW0g26nTYun596pWR2pCjQabVMUaAbuHx+VNVKrZRHEQLVonHokOCv/kSTj3yEfvplbU3ha1+z8t3XfJTyLdrtBoqiomkqnWYHQzcFjKKoqBYLVqsNvVbDMHS6rSaqqtFuNwAVVVHQu11Ui2bWf3TNIlWL1da/lt5AaGf2TB6by43HFmZgYobo8ATNWoXYyASlbAqHy0N4YAQQDA1EOTEe4Ec+8Qz1YnZPOmv370EikUg+yEgh8j7mblNw79YN0+t66c2O6XW/nDp1as9+FEUhFAqRzWY5f/kaX339BluJNMV8itzWBl29S71QpFmvAArtVhNvIEwuuUk5n0HTVGwOM8pQr5ZpNeoIw0AYAqsGTz8t+Kt/VXD82M30y7nzNv7bf4cL5xVzUJxDx+nzo9atdNtNDMPoG5arioqqabh9QfROG5fHi653MTpdOh1TbKiaOQfGajdnxBiiiyosWOwOXF4/AFa7AyGg22mjWe1Eh4cZPnAIp9uLAJxuLy6vj/jwCKNDcZ594hGeOj7TFx9+pxW/U4oOiUQi2Q8pRN6nvNUU3N0iJJ1Oc/HixT2Rjmw2SyaTQVVVQqEQp06d2pPGSaVSffGykq3yje+8gWEYtFstipkELm8QXyhCq1GjUa2wvnAVBKBCo1JGGAZd3UChicVmxWpzoLfLNGslnnsOfu7nFMbHTUnR6cC3X9L4o+etrKwI00fEYUcY3X53id1l+nZ0Oy2zS0XRUFXNjIR02zjcPnS9S71aQhc6CgLVZoed2hGXx2cWqXYFVrud0OAYeqeD3eliaOow7UaDWjlPYPQAhx97hvj4AWqlHNZOncmRAQ5PjnDswChjoyP934EUHxKJRPLWSCHyPuROhabAvlNyL168yNWrVwH64iISibCwsEAgEOhHVC5cuMDAwAADAwNcvXqVcqPDjZLCmfPXSWysUC8X0TQLFpt9xx/EHO7WqlXptJroehchTAt2BRVV1TAMnXbLoNNu8MyHO/zcz8HUFICgUoGvfhX++E9UylU7RlfHMLpmAajbDTtRimoxhzBMUYWimLNgHDY8/jDdbptOs4miaKiahtFum9uqGlaLHV1v4wvHsNqd2Dod9G4XbyhCt93C7nJz5MmP4HB6KKYThKMRjp04xcRQlIOTcY5OPcHsNfO6nTw0IVMtEolE8gMghcj7kFtNxnr0ul6SyWQ/wgE3PSquXr1KJpNB13WWlpZYW1tDVVWOHDnC1atXyWazXL9+nYOHDlPExVf+v/+VeqNObnsDvd3B7nDRatRpNxu0GmY9ht7t0G210LtdAPSu2ZnicHuxWG00qiUOH2zz9/++4MgRc53VKvz3/w5/9EdQqwEKKEprx1LdhaF3KOcyONwebHanmW7RDSxWKzabnXarjejo/fZfgaBeLqIooKoWnG4vmtVKu9XEZnHRabcwOl1GDp3A4wuS3lzBYrMS8AeIe2wcOzRB8PEZRgZjnDx5cs81tmgqyWRyT9GpRCKRSN4+Uoi8D7lb+2csFiMej98mUk6fPk0mk+HGjRtomkY+n2dqagqv10s+nyeTybC2tkax3uLPzy/iCA1Tb9RZuXqOUi6NPxxn8uijJNcWSG+tmkPdOl3a7SZGtwOowE6th2HQbTWJR9r8rX/Q5mMfM2/ijQb8t/8Gf/S8hUq5e3Nxium2qhs6VocDi9VOt9Oh22oidIHVakdXOiDAQOBwuRCGgdHVsbucKEJB73QwULDZ7XiDEVAU7J123yfEFx/gxGNPYTOaTERcHDwwQSQYoFQqceLAMJ/97Gff8dRhiUQikbw1Uoh8wLiTSEkkEoRCISKRCLquEwwGMQyDcrkMQLpQ5PzCJolcGbvDSe7s9ykXMrSaDVTNQrfbplLMgaLQbtTR2x263c6OCIG+CEHBYlX4Gz/V4md+BqxW0HX4xjfgd38XCgVzW63XvQJmbclOCWqrUWd4+igIyCbWaLcaqJqK1e6g026ZduualdDICO1mHc1i6Xe6GLppC293uhmaOkSn3aSSXCc2PcPpk8c4OBVhenoaVVVJpVLE43EikQiGYdzmuyKRSCSSdwcpRD5A3M36PZlMksvlCAaDKIrSrxGZX1wiW+vQsPjI17tUiznSlRK1coFGtYRmtTN57FFWrp3n8ne/gd3lRe+aXSlGT0jsYvqQyq//I53pafP52bPwf/9bWFu3IPReFMTYESEqKKJvka5YragCcltrBOJDWDQLrW4NvQuKXcHtCwJgd5r1I5rFQrNWxega+MIxApE4doeDoNfDQMjNUHSE5vQgbrcbn8/HzMwMJ06cQAhBNBrFMAweeeSR2/w+JBKJRPLuIYXIQ87bnSuzvb3dr/M4evTontklL7zwAm+++SZ+v58Pf/jDxONxvvnSS6xmqnzv2gr51DYoKoHIAJntNUrZJA6X25y30qkw9+YZOs0mum5QrxTQLNbbbtwWC/z0T8PP/IyOxQKlEvz2b8NLryhggGZR0TXNDI/0MVBUc6KtuQ8b3W6HRrWCMLZweNxY7Q70dgurzYHLG+Dw48+ysXCVXGIDVbMQHhjFanfgtKp85Jln+Os//pdZWpjj8uXLeL1envj0JwH6k4X3m2YrIyESiURy75BC5CHnbnNldlu29zpfCoUCZ86cIZ1Oc+LECVKpFN/+9rdJJpMcPHiQdtfgm+fn+cOXzpFYN4e3NRt1SpkkW0vXTeOxbhfNYsVitVEt5ek06iiaht3upt1p0u10EMbNGo8DB+A3foN+FOSVV+DLX4ZiESx2c9Ktvk/0BEDoOjanG5vTRbtRx2g3QYGu3qbTtuJwulA9XgBa9Qq51CZOt5eB8WkCwRAffvpp/spnnuPy+bOsra1RLub5+Mc/TiQSAeD48ePSUl0ikUjuI1KIPOTcba7Mfu27uVyO1dVV3njjDd544w0AvF4vdqeb1WyNf/Fvfw+r00dXKFSLObrdDt5AiEJqi3a9gt7VsdjMyESn1ei36ArdoNttY7PZadZrpjOpBX7mZ8xIiMViCo/f/m14+eXdZyBQFHXvSWkW6KdpBJ12C9Vi/qna7S4sNhvtptmdY7FaiY9PY7HYaDaqFJKbHDxyhJ/963+dEzPjGIbB0NAQ0xMjPP/882SzWVlgKpFIJA8QUog8xNyalulZtqfTaTRNY3BwcM82PTfUUqlEtVolnU5TrtY4/MRH6HqGuPbmi1TLRRACm92OJxRma2GWTruJruvoXTNt0m130PUyCuquFIzY8QkRKKrKgUmD3/gNMxoCe6Mgu+m2WrefmGGgaFYUDAxdp9vpQKOGxx8kEBumVa9SyWdpt+pomvkn/PQnP8+wz86l117GYzGwGc3+NNteeuqLX/yirPWQSCSSBwwpRB4ibhUeu9MyANlslkgkQj6fxzAMotEo8Xic7e1tkskkiqJgGIY5MTeZoljv0BQWki9/B08gSLvVpNNoYHU6KWbTZtSj3aRWLiEMHc1qA0Wgt9sIHQQ6oPSPb3asdPnZn9X56Z8258IUi6YAeeUVdm17BzGgarDjlGqz27A53DRqFYShm625hg4IXL4gdpcbhGBoaBi/Q+NwUOELX/g0o2EXb775Jvl8nqGhoT3ttjIKIpFIJA8eUog8RNxaD9K7sV6+fJlcLkc4HCabzWIYBvF4HH2n8HNoaIiXXnqJ5eVlUFRurG6yvrGJyxcAoVLOpdGsVty+IFa7nXq5SLmQoV4q7rTE6uiGjmHoCMO4ZVU3RcXMtM6v//rNKMjLL5upmJtRkLtHIxRVRbNYsTlc6N0OQug4PV7sThfNahW9q9Oq1zh48jDPfeSjjEbc2FVBpVIhl8uRTqf54he/yMzMDJFIRAoPiUQieQiQQuQhYr96EDDrPvL5POFwmEgk0hchveF1iqIQDof59vfe4Lvffx1DKPjCAzTrFbrtDp1Ok2a9TL1cJDo6Qa1SpFEt06xXMAwdVbOAYFd77V4sFvibf5M7REHuhMIeYaKoKIDV6cTl8VEp5ui220SGJxk7dJz0xgr1YoaDUxN88ZNPc3BmnJMnT/adYqenpwmHw7L+QyKRSB4ypBB5yNgtRnZHQnoipDdJ9+LFi1y7dg1VVRken+IPX3qD6+tpNKuDdrUECtQrRfRul3argdANhNIhuTqP3t2JfgiB0TXt0xG3RkJMDh6EX/u1vVGQL3/ZbM+9O4LdYkTTNBRNw2h3aDXq+CNxbHYXA+PTHDl8mM9/5AkquSTJZJKtzU0OHTzYL8iNx+O3OZ5KJBKJ5OFACpGHkF5nDEA+nycajaLrer9G5OLFi+i6TqlUYnEjwYuzKeZmr1Mt5gjGBqkUcxQzKwgBqkXD6HZRFA293aLZaaOpGjaHE522GeLY4+1hYrfDz/4s/LW/Zm5SKJhpmLtGQRR1j6BRVBWrzbaTQjKH1WlWKxa7jfDACB//1GcZCdjxOW1MT08Tjz/Hq6++iqIoHD9+vN+SLAWIRCKRPLxIIfIQ0UuzAH33z8XFRc6ePcuBAwfQdZ1CoUAmk0HTNFYyVW4kqyCq2J1u2o066c1VKrkMrXoNq9NBu1IHFNqtOkIINEXB0HX0TgdV01CFwGCvEHn8cfiH/xB69/+3HQURxh4xomoWAvFhNM1COZ9Bb7fxhMIcPHSYkXCAZ4+N89xzz5FMJgFzTk6v80WKD4lEInl/IIXIQ4SiKFy+fBmgPwU2GAyyvr7O0tISgUCA1dVVNM3C1dUEhVoHu8tNpZDFGwyDqpLdWqHdbqJaNVq1ihkJ0bvoegeh61gdToTRodVqoKgqyq4yjmAQfuEX4NOfNp+n02YU5Hvfe5vr1ywoioKiWM3hdG636Xxqs6FZbHjdTmYmhnnysUdRFIV8Pg/AI4888q5dQ4lEIpE8WEgh8pDQs2jv1YSAGRU5evQohUKBs2fPcvDgQQKBIN+9eINEKoPHH6LZqAOCldkLtBo1bA43QoDebe+kRMzWWIGKorLjFSLA0BGGjlAt2B0qP/HjBn/jb4DLZXbYPv+8OaSu0di9ylsKUHdhdTjNnwuBqmn4IwOEB0cRCII+H5/7+Ifw2kyh4vf7mZmZQQhBMpmUxacSiUTyPkYKkYeEVCrFwsICwWCw7w2iKAqZTIZSqYTX62Vra4vlTI1cqWIOgFMEDqeLYmqb7NYaQgicbtMO3TAMDMMw23EFqFYLqmKh2+5gTspVUFXBJz7R5e/8HRgYMNdx/boZBZmb22+V+4sQm9ONZrHQabVQVBVvMEJ4cJRAMEDc7+RTH/kwzzzzDLOzsyiKQigUQghBPB4nFovdi8spkUgkkgcEKUQeEgYGBpieniaXy5FKpfqvf/WrXyWVSvGJT3yCnBrk0te/Rq1YIDjgotWos3L9Is1aBUVREUKnVi7Q7bRRFQ2bzUGrUQXA6LRRrTZQFVTgU58S/PRPw9iYeZxUCv79v4dvf7s/DBdQMUXLrexERhQNzaKhaVZQFdz+IHanm+jwKCePHSNgEwwPDXLw4EFisVi/+0VRFJLJJLFYTNaCSCQSyfscKUQeEnably0uLlIoFNje3iadTuP1evnOheuUuxbTcVRVSK+vUMgmqOQyKIqCZrXSaZkD43Rdp6u3EYrCnnSKaPP5vwR/42/A8LD5UrkM/+2/wR/+Iex2Y9csVvRuF1XTMHZ11ahWG4YwsCgaqmZBs1gx9C7+8ADHnvw4NqXDoNfCk48eRdd1yuXyvsWnMh0jkUgkHwykEHmIGBwcJJVK8cYbb1Aul/F4PIyOjrJVqHP++2+CAuGhUdzeIDfmv0uzXkNTVax2B129g941DckMwwDREw8KVit84QvwUz8F8bj5arFoCpA/+ROo12+uQVE1VIsFvdtBUTWM3SZnioowBC6POUTPH4lTKeRQFJg8fJKnTh5kyG/HYrHg8/mIxWIIITh+/Ph7cv0kEolE8uAhhcgDyH7D7FKpFIqiMDs7S6VSAaBarVJrGZydXQLV9OHIba2T2V6nUSljCAPN7kQXOqLbQdVUuu2bYQ2bDX7kRwQ/9VMQiZivZbPwB38AX/saNJu3r00YOnrbFDGil5ZRLbg8Puq1MggDTbMyMn0MRVMZmjiEz2UjYOkyGnIxPT2NYRgMDAzI1ItEIpFIpBB5ELl1poyiKKTTac6dO8fW1hZDQ0NMTU3x+rlzfO2FV9CFIDIwCopCdnudWjGHqmkIXdCqV0BRcTjdaBaNbrvVj4D89E/fFCCpFHzlK/D1r0On87ZXCoA3GMLmcKFZNAxh4AkE6XbbhIIDfPTpRzk2PkCpVOLAgQN85jOfIZFISC8QiUQikQBSiDww7I6C3DpTBmBpaYmLFy/idDoJBoOEQmFKSgBFs9KqFCjm0jTrFTLrK4AwJ+UizDQM0KybUZSPftT0Aul1wSST8F//K/z5n0N3/1Eyd0S1WLG73Ti9PkKxYTzBMB5fiHx6C7/TyV/55IexqYJYLMbHP/5xOQVXIpFIJLchhcgDwu4oSK9zZGhoiMuXL/PGG2+QSCRwOp14vV7W19f5i++exRIZZ/TwCW6c/Q6ptUVajRqGYaAoINotUMDh8tCsV5mYgF/+ZXj0UfN4mQz8P/8PfOMb71yAoGrY7Hbc/hD+2AAW1YonGOaRj34Oi0XDVUsxGfPxoQ89jaqqGIYhox8SiUQi2RcpRB4QdkdBNE3rT8/NZrMEg0HK5TKjo6PMzs6ysrlNug7trbNYbQ7sbg/FbApFAUVVEF0dgcBqc6B3G/zUX9X5238brFaz8+UrX4H/9//d2wXztlE1nC6v6QUyPEowEqfdbiO6Oq1Cil/8//x1RKOMYRg82lM9EolEIpHcASlEHiB2i5FsNsvCwgKhUIgPfehDALz00ksUiiXWUwXK5SKddhPNYqVVr5viwxAIQ8cwuiiaBae1zD/9X+H0aXP/r74K/+f/adaD/EAoKm5fgFMf/UtgCFrNOnaPl4FQHEenzONjfk4dmvrhL4REIpFIPjBIIfKAsXuyLtC3cw8Gg7RaLZY3tqi3OnTaLerlMnrXrCzV9a7pCKKoCGBmvMX/+r+a7bj1uilA/vzPf7A1aRYbmsWCZrHhi8TwByOMHT5JZmsNo1nhxz/1JEcmRoj3en8lEolEInmbSCHygLB7sm4mkyGbzTIzMwPAjRs3WFlZ4fSHnuPi/DqdVoVuuw0qdDvt/jRbAVjtTp5+qsNv/SY4HLC+Dv/L/wIbG+98TYqmYbFa8YUHCEYHQVFo1iqszl3G6fHx4UdPcnTISzwWlYPpJBKJRPIDIYXIA8Luybq5XI5YLEY0GuXMmTNsbm5id7pZLNZwuNyUMgk6nfYeEdLjo882+M3fBE2D116Df/EvoFZ75+tRLVbc/iA2h4vhqcN4AmHio1MU8ynUdoNPPzrNk6enZB2IRCKRSH4opBB5AIlGo8zNzTE/P08oFCIUCvFHL77K9dlZrHY7/tgg2c0VMwSiqDtiROGznxX8439sipBvfAP+9b82J+W+bTQLFosFVbNgtduZPPYYwwcOsbV4g3azRiAU4ic+/wkOD/oZGIjLThiJRCKR/NCo93sBH2S2t7f79SAvvfQShUKBkydPYhgGm5ubnD17FlVVOXt5jvNvvE6jXsFqc+Bwe3YEiABFAVXlYx8T/NqvmSLka1+Df/WvwDCUfY6632uAqqEAVqudocnDDE4cxGaz43T5GJ05QshlZdxa5ehwQIoQiUQikbxryIjIfURRFC5dukQqlSIajfLaa68RDodZXFwEQFVV/vN/+T3m1xP4wjE6zRYbC1epV0oYesccKGcYHDui81u/BaoKX/0qfPnLvQm5Yp+j7vca2OwO3L4gmsWCLxxheOoIzXoVtZ7lxz76IVz2JxBCSFt2iUQikbyrSCFyH+kNsbt69SrHjx/n6aef5vd+7/dQFIV4PM7GxgZXbswTHjnA8NQhtlbnqRRydLsdVFVFRTAy1OVf/AtzbsyZM/Dbv90TIW8TVUNRFBRVZWByhmB0iGoxi1LP8bmnHmdkMMKhQ4dkLYhEIpFI7glSiNxnTu+YfFy9ehVN0/B4PKyurlKr1dhKptHRqBRzXH/zDK1GDZvTgV7pYHTaON3wv/1v4PfD7KxZmPpOakKCAyOomgVD79JuNkitLnDi+HE++WOfJbO9zqnjh/jMZz5zb05cIpFIJBKkEHkgOH36NH/2Z3/G5uYmPp8PVVWp1mp0VDvDB4bZXr5BtZBDtVhNt1Rbm1ajy6/9GoyOmvNi/uf/+Z05pYaHx4kNT+L2h1CBbiWL0m0yGXbx9/7W3+wPppNIJBKJ5F4ihcgDQCKRwO/3Mzc3x8bGBhsbG7QVG25/mHqlTLtRQ+92EYZBt9NGCIOf/ElzgF2nA//8n0Ox+PaOpWpWXF4/Tq8fXyDEYMTPR558hMGYOYb30KFDgBxMJ5FIJJL3BilE3gV2T869lTuNvN9tYHbp0iXC4bDpnLq8TK3Zxupz06lXSK8v0mw2MAwD3dBBwLEjbf6n/8ncz+/8Dty48fbWqVpsxEancHk90Krj0ks8efxxjh85xPHjx2URqkQikUjec6QQeRfYPTl3txhJJBJsb2/ve4NXFIVvf/vbrK6uEgqFeO2117hx4wYWi5V6u05l6Rp6p4NAIHQdXTdACDxunX/yT8w23W99C/7kT97uIjU8gQAej5OjU6O4HHY2NjbY2tri53/+52UERCKRSCT3BSlE3gV2D6vrPd8tQoQQJBKJPTf7wcFBotEoL774ItVqFZ/PRyQSYS2Zo16r0G40MLptNJsd0atAFTq//MsQjZqW7f/6X7+99dndXiKDI4hGhZDTSjgYwG63E41GicfjshZEIpFIJPcNKUTeJXaLkd3pGCEE6XQaXdf3bNfD7XbTaDQol8s4Q3Gamxm6zRZCmNvr7V4FqsJHPgKf+QzoOvzv/zs0m3dfk2q1ERkaIxIM8uTpY9RqNQqFArFYjPHxcXw+H5/4xCdkNEQikUgk9w0pRN5FepEQIUS/ZiSRSKDrOpqm9SMmQgiuXbvG/Pw8w8PDeL1eVte3OHv+ErVSAUXT0DQrXUP07dsDAcE//Ifmcb7yFbNd963QNI1jh2c4Oj1FMpnk8ccfZ3x8nFAoxIkTJ1AURUZDJBKJRHJfkULkXWS3CLk1HbO9vc38/Dxzc3MUCgXOnj3L4cOHTXfVK1e4sbJFpZClVW/QrFXZ64BqipBgEJaX4T//57dYiKJiczjxupwUUgmO/ZUf4ejRoxiGwXPPPScjIBKJRCJ5YJBC5F1id03I7hoRuJmOmZub48yZMwAUCgVeffVVIpEIG6kcyfVlhGHQabdgJy3T41OfMlt1u1340pfMlt07oqgMjc8wMRTF6bQTCoVYXV3lV37lVwBkBEQikUgkDxTvydC73/md32FiYgKHw8FTTz3F2bNn34vDvmfcKkLAFB9DQ0P9mpHe616vl0wmA0Amk+Gb336FtaUlDL1Lp93C0Lt79h2JwD/4B+bj//yfYWcMzf4oKtGBUQbDXkZGhvjiF7/IqVOnALhy5Up/TRKJRCKRPCjccyHyB3/wB/zqr/4q/+yf/TPOnz/PqVOn+OxnP0s6nb7Xh37P6BWm3pryEEKgaRqJRIIXX3yRS5cuoSgKjzzyCPV6na3tbZKpBLVSgXarfZsIAfhH/wi8Xrh+HX7/9++8Bs1mJxCNEwm4sVg0DMPA7/fz5JNPcurUKSKRyLt92hKJRCKR/NDc89TMv/k3/4a/+3f/Ln/rb/0tAP7tv/23fP3rX+d3f/d3+Y3f+I17ffj3hDtFGRRFQdd1FhYWWFhYYGJiAl3XKZfLdA2DelvHMAyEMNhvKu4XvgBPPQXtttklc6c5MprFSnRolMNT4+idNgDT09McPXqUeDwuoyASiUQieWC5pxGRdrvNuXPn+NSnPnXzgKrKpz71Kb7//e/ftn2r1aJcLu/5epgZHBxE0zQymQzhcJipqSlUVeVrf/ZnzC2s0e3qCH1/ERKPw9//++bj//AfYH19/2NYbA68oQhuC3TbLaamphgcHMTr9fLII49IESKRSCSSB5p7KkSy2Sy6rhOPx/e8Ho/HSSaTt23/pS99Cb/f3/8aHR29l8t71zh//jwXL17c92fpdBpN0wgEAiwsLPDtb7/EwtIqpWJ+xyvkdhGiKPDrvw4uF1y6BH/0R/sfV7PZGTl8nOnJSbweD6qqIoRgcnKSxx577N07QYlEIpFI7hHvSbHq2+U3f/M3KZVK/a+NjY37vaS3haqqXL169TYx8sILL/DNb36z385bLpe5vryGaneid9vUyiVTdWh7M2Q/+qPwyCPQaMD/8X/sn5KxOlw4XB5cCJ56/BGeeeYZJicnOXz4MJ/4xCc4ceLEvTthiUQikUjeJe5pjUgkEkHTNFKp1J7XU6kUAwMDt21vt9ux2+33ckn3hNOnTwNw9erV/vOLFy8yPz9PIBAgn89TKBR449oCwuZG72Zod9ug66hWK8ZOXQfA8DD8vb9nPv53/w52OoD3YHU4GZ4+gtNqwWM1nVt/7Md+jHA4TCQS4dFHH73XpyyRSCQSybvCPRUiNpuNxx57jG9961v86I/+KACGYfCtb32LX/qlX7qXh37P2S1Grl27hhCCZ599FoCvfOUrXFtaI1lq0Wm3aVYr2Kx2FJtGq1Ht70NV4Td+AxwOOH8evvrVWw6iaYQHRhmeOgzdFienRxkZNm3kw+Ewn/nMZ96js5VIJBKJ5N3hnnfN/Oqv/io/93M/x+OPP86TTz7Jl7/8ZWq1Wr+L5v3E6dOn+yJkdXUVi8VCMBjE6ovy5oU/oVEuYRg6iqpgd7qplQs7Fu4mP/mTcPw41GpmSuZW7zGny8uhRz7EwMQM3lYC2m1GRkZ45plniMVi7/HZSiQSiUTyw3PPhchf+2t/jUwmwz/9p/+UZDLJ6dOn+fM///PbClgfVra3t/tzZS5evNi3eFcUheeff57w4ChV1wgKCvVKEQBFVem024juTYvUgwfh7/wd8/H/9X/BLdksbA4X4aExUBU+9vgJItZDrK6uEgqFiMVisjtGIpFIJA8l74nF+y/90i+971IxPRRFYXt7m6tXr5JKpTh+/DinT5/mxRdf5PK1G7x28TrBgQpuX4DMhkG33ebWThmnE/7JPwGrFb7zHfizP9t7DNVixR0I4Q2EcVs0wpYWR48eIxwOSxEikUgkkoeaB6pr5mFkcPD/3969R0dVHfoD/54zk3llMpOEyWMmCZDwRghBLI8URRQFi1WvrRXtUmhdtLX02lavhdCKVa+CwrK/u7yKtguBddsrWq+vtvguSCuI8n6GEggQMpPJY5KZTDKZzGP//hhnyJAQkpDMQM73s1aWzJl9zuw9J5P5us/e+1jhcrnwxRdfICcnByUlJXA4HNAbTWg3ZsPv96F81z/R4KiCMT0TkDq/5Q89BOTnA7W1wJo15z0pqZAzbCRklRruBgcmFNpgsViQnZ2N4uLiQdOzREREysSb3vWDIUOGYMiQIairq8OePXvgqHHirc92o7a2Fk31NfC46qAzpKG93Q9ZJSMcPHdTuxtvBObNA0Ih4OmngebmDgeWZKRlDIFWb0BW3nCkawR8LW7IssxeECIiGhQYRC5BdHzI1VdfHVkx9a9/BQCU13hQeeoMvA11aG12IxTwo60VCLa3IdxhXEhhIfDII5F//8//AAcOxB8/e2gRhlgL4Gt2I9NkxOJ77oDb7Ub4Qmu9ExERXWEYRC5BdHwIEFktNj09Hf/Y8RUOnKlFe2srXPUOBNraAFkFv68FQX9bbF+jEXjqqcj4kN27I0GkoxSdASpVClLUWmSPHo9br/0Gxo0bx3vHEBHRoMIgcgmid9vdsmULGhsbAUg43dgGr8uFOvtpNLvqYje16xhCZBn49a8ji5c5HMCTT8avnqrW6GAako1QKABPUx3GFuaheMI4TJ48OcEtJCIiGlgMIv2kqakJu4+eRG2NCxq9DqmmDDTW2xEOBtDeIYQAwIMPAtOnA21tkdkycff2k2RoDanQG9OgS01DvjUPJeNG8HIMERENSgwil0gIgXHjxsHXHoL/RB1avSchwkAw0AYRCqO9rTWu/N13A9/9buTfzz0HnDgRfzyNVotUUwbUai0yLNm4dc61uGHWTPaGEBHRoMTpu5fIZrNBkiQcq3FDQIYICwSDfvh9rfD7WuLKzpkD/OQnkX+/+CKwZcv5R5OQotNBozdAn2qEzWyAXqPiFF0iIhq0GEQukcPhQKO3DTXNAYhQCNai0UjRaNFYUx038GPKFGDp0si/33gDePPN8w4kq6DVp0KdogMgkG5KxdiiAkyfPp2DU4mIaNDipZlL4HA48Pe//x2Ha5oRDofh9/vQUF2F2rOn0N7uhySrISSBUUUhPPkkoFYDn34KvPxy/HEkWQ3TkCykaLVI0eiQnmnBnGtn4I5bb+GddImIaFBjELkEQgiYMy049sUx+LzNaKiugv1UOdp9rdBodQiFghiS4cOqVYDBELmj7rPPnn8zOxlavR5pQ7KQk1eEQMCP8cNtmDn9GwwhREQ06DGIXAKbzYZ9VY0wpKXj+L6dqK+pQlgAkIAUrRY64cOzqwQyMyODUlesAAKB+GPojSakWSzQ6VJhysrGiGFDccOkIlgslqS0iYiIKJEYRC7B7t278ennRyDCYWhTjQi1t0OEgpAlGf42F556OoChQyP3kFm6FGhp6XwMgzkdmdkF0Gh1SDOm4offmYtheTaOCyEiIkVgEOmjDz/8ELsPlaOmth1tvhakqDXQ6FMBSKhvOI2yXwUwaRLg9QLLlgENDV0cRJKhSlHDaM6A39cKqx7QqVUMIUREpBgMIn0kyzL2HjqGBl8IIhxGU4MT7b5WNDqr8W+3BTBnDhAMAo8/DlRWdt5fUqmhUqkQCgSRlTcMNrMOxaPzOVWXiIgUhUHkAqI3tIsu496Rw+HA2HHjkVZwGJXbt8LdWIeWpkY0N9Zj9Oj22FohL70UGaB6Po3eAH2aGYa0dKjUKqTpNPjtoz+DLIG9IUREpCgMIhfQ8YZ2HcOIw+GA3W6Hw+PHsPHXoKa6CqfL96G5sQFaTQC/WR6CWg1s3Qq8/XbXxxYAMix5KJxYgtYmF6z6IFRy16GHiIhoMGMQuYBoKOgYRqIhxGaz4bi3DtUnvsSQbBsgSYAAfvgDP3JzgepqYPXqro8rqVKgUqdArdNAp0/F1SPzMOWqMRDxc3qJiIgUgUGkGx3DiMPhgBACNpsNubm5OPS3L1Fx4Esc378TEMDESRJuvy2y3+rVQGtrV0eUkZpmRnqODW3NHvhrT6PwmlEYO3YsL8kQEZEicYn3i7BarZAkCUKI2H8PHj+FtoBA1fHDqDtzEu3+Fix5MLJAyN/+Buzf39WRJKRoNdCmGqHTp2KIJRMFWWaMGjWKA1SJiEix2CNyEdGekGgIqa2txf7TDXBWnYQhNQ3GTAuumeTE8KFtaGkBfv/7ro4iQ6s3QGdMgwQgzZiKRd+7HdfO/CZycnLYG0JERIrFINKNjmNChBA4dOgQhBBwtghUHPgKgWA7cocOxf3fPwMA2LQJaPaqAITijiPJMjQGA7IKChH0eXFVUR7u+u53ODiViIgUj0HkAjqGkOhA1fr6elScqMSB2nbIahlNdQ5Mu7oONlsYLlfkjroiHOp0LEmWIMsq6DQazJg6ExkmIw4ePMggQkREiscxIhcQHZhqtVpjM2fGjx8Pe109ju//Ct6mRoQCAcyb0wgAeOstoK0t/hiSSg21RgutwQCVSoVMnYQMkxGTJ0/mvWSIiIjAHpELio7bsNvtqK2tRSgUisyYKRyHwM59aHCeRX62HWNGh+H3A3/96/lHkKBSqaEzGGEekoXCglzkZFlgNpuRmZnJO+sSERGBQaRbHUNIQ0MD6uvrYcgeiowcG04f249bF0W6QD75BHC7z99bQITDSLNk4Vtz56Fk/EhkZGRg7NixnCVDRET0NQaRbkiShJqaGqhUKtTX18PlasS2PSfQ6HTAlKbCN78ZWYTsnXc67QkACIXDMAC46/ZbcNVVV3F2DBER0XkYRC4geq8ZWZZx7NgxyLKMXfsPYM9n/0BbazPmzVNDkwKcPAlUVJy3swSo1CmQIUGnjeyflZXFIEJERHQeDla9gOi9ZrKzs5GZmYktW7Zg29Zt8DY1wOdtxrTJTgDAxx93sbMQCIeCSEtLRUpKCsrLy+F0OhPbACIioisAg8gFWK1WyLIMp9OJ8ePHw+/3w+1uQjAYwJAMPyYVRy7LfPpp1/tLACZMmACbzQan0wlJkhJXeSIioisEL810Izc3F7W1tdi8eTPS09NhsmRDNLowY3ozgMhS7nV1XxeWJKDDjetMJhOys7MxZcoUhEKd1xYhIiIiBpFuCSHQ2NiI8vJyGFLTYBsxAcHjhzBtWmRdkc8/71haAhAJIjqdDnl5eZAkCUajETNnzkR2dnbC609ERHS5YxDpRm1tLbZt2wa/34+Tp6pwpsYFtboNxRPDAIAvvuhQWES26XQ62Gw2GI1GGAwGDBkyBNnZ2RyoSkRE1AUGkS5EZ8wIISDLcmQ9EZcb7X4fCm2nodEA1dVAVVXnfQOBAPR6PaZMmYKWlhY0NjYyhBAREV0Ag0gXJEnCli1bAADf/OY3UVtbi1N2J1zOaky9KwAA2Lmz631DoRDa2towfvx4uN1uZGRkJKraREREVxzOmumC1WqFxWKBy+UCANxxxx1Qaw2QEMY3vhEpE3dZpoOUlBSo1WocPXoU11xzDWbNmpWgWhMREV152CNyARMmTIDL5cLu3bshq1TQG9MxdLgROTl+BIPAwYOd9zEYDMjLy4MQAmfOnOEiZkRERBeh6CASHQtitVo7PVdbW4sTJ06goaEBZ6qrUWs/jWklXgDAsWOd77QLAHq9HoWFhcjLy8PIkSN5TxkiIqKLUHQQia6eCiAujDgcDoRCIbS0tOBf//oXTp+thrveifHj/AC67g0BAJ/PB5PJhJEjR+IHP/hBlwGHiIiIzlH0GBGr1QqbzQa73Q6HwwEgEkLsdjtUKhUmTJiA1NRUeJo9CIeCKC6O7Ld//4WPWV5eDo/Hg5qamgS0gIiI6Mqm6B4R4FxPiN1ux4EDBwBEekrq6+uRlZWF3NxciDBgsahQUBBAOAwcOtT5OEajEXq9Hi6XCy0tLbwsQ0RE1AOK7hGJslqtsfBx/PhxAEBlZSXefvttNDY2QpbVGDe2HUDkbrteb/z+KpUKsiwjMzMTV111FXJzczlIlYiIqAcU3yMCRC7HCCFgsVjQ2NiI+vp6FBUV4fjx46hvaABUKowbG1m+/fDhzvvr9XpYLBaMHj0aS5Yswdy5cxPcAiIioiuT4oNIdEyIzWbDlClTIEkSvvrqK6SnpwOIXLJpbXZj1OhIEDl2rPMxoqupZmRkQJbZyURERNRTiv7W7BhComNFJk6ciMLCQhw+fBgulwutPj+AEEaPiuzzr3+d21+SJKhUKggh0NDQAL/fj3A4nPiGEBERXaEU3SMihIgLIXa7HVu3bsXp06dRV1eHM2fOoL09AFtOGEYj0N4OnDoVfwyDwYDU1FSkpqbCYrHwsgwREVEvKDqInD+gVJIknDp1Cu+88w48Hg+am5vR1taKopIgAODECSAUOldeCAFJkjBq1CgUFxejtLQ0kdUnIiK64in60kxXhg8fDrPZDK/Xi0AgACEExozpPD5ElmVoNJrY49LSUsyePTvR1SUiIrqiMYh0UFNTg8bGRtxwww3IyMiAy+VCe5sPo0dHnu84PiQcDkOSJGRlZUGj0aCpqQlCiORUnIiI6ArFINJBTk4ORo8ejXA4jJycHKhUkStXo7oYqCrLMkwmE6699lrceeedmD59OtcOISIi6iVFjxHpaM+ePZBlGUIIOByOr5doF8jKAoxGIBgETp+O3yc7Oxt6vR5CCN5XhoiIqA8YRL4myzIOHTqEqqoqnD59Gj6fD8FgCMOHR54/ezYSRjry+XyYMGEC0tPTeVmGiIioD3hp5mvhcBhVVVXYs2cP3G43WltbEQ6HUFgYef78abvhcBgulwtnzpzB7NmzeVmGiIioDxhEvibLMkKhECRJAgB4v76hTLRHpLIyvrxKpYJOp4PD4cDBgwcTWFMiIqLBg5dmEFnITAiBESNGYP/+/Th58iTMZjN8/gCGD/cD6Nwjkp6ejueffx5DhgyBxWJJfKWJiIgGAQYRRBYyq62thRACdXV1cLvdCAQCCAf9sR6RjkEk2mvyySefYN26dQmvLxER0WDBSzMArFYrJEnCgQMHYLFYoNfr0d7ejuxsQK8HAgGguvpc+ejsGq1Wm7xKExERDQIMIl9zuVyw2+1ob2+HXq+HJEmxgapVVfFLu4dCIahUqtgdeomIiKhvBiyIPP300ygtLYXBYLjsvrDtdjscDkfc48zMTOTl5eHQoUPweDzQaLVxl2XUWh20Wl1sn1AohFDHdEJERES9NmBBpL29HXfddRcefPDBgXqJPpMkKS6MSJKE+vp6OBwOGAwGBINBtPl8yM+PlD9zBgj62xAMBqBSqaBSqeD3+1FfX5/EVhAREV35Bmyw6hNPPAEA2LBhw0C9RJ9FV0G12+3YsmULsrKycPr0aTQ0NKCoqAiVX8/VzcuLlI+ODwmFQtBoNLBarcjMzETw/BXOiIiIqFcuq1kzfr8ffr8/9tjj8QzYa0XDyBdffIEPP/wQkiRh2LBh2L59OwKBAIBzQeTs2XP7hUIhDB8+HGVlZSguLh6w+hERESnBZTVYdeXKlTCbzbGfgoKCAX09q9WKGTNmYPTo0WhpaYEsy0hNTcXQoUNhSFUjKytSruOMGb1ejwkTJiA7O5vLuhMREV2iXgWRZcuWQZKkbn/Ky8v7XJmysjK43e7YT1VVVZ+P1RMOhwNCCBQWFsLv9+ODDz6A1+uFVqtFfoEKAOB2A83NkfJ6vR7Dhw9HeXk5jh07xmXdiYiILlGvLs088sgjWLRoUbdlioqK+lwZrVabsLU5HA4H7HY7bDZbbLl2j8eDUCgEt9uD4pJIb0e0N0SSJKSkpKC1tRUGgwHhcDgh9SQiIhrMehVEsrKykBW9XnEFczgc2L9/P2RZhizLKC8vh9PphFqthsPhgK+tDTlZHYKIJEOtViEUCqGxsRFNTU2D4n0gIiJKtgEbrHrmzJnY3WlDoRD27dsHABg5ciSMRuNAvWyPCCGQm5sLp9OJo0eP4uOPP0Z9fT20Wi10Oh18HabuVjtUyMjMRCgQGUiblpYGq9XKHhEiIqJ+MGBBZMWKFdi4cWPs8eTJkwEAW7ZswfXXXz9QL9sjNpsNNpsNDocD69evh9frxbRp01BVVfV1T4kKeXmRxcpqa7XIKxiKdKMedXV1CIVCGDFiBObOnZvUNhAREQ0GAxZENmzYcFmuIdJRdJyI2+1GeXk57HY7PB4PwuFQbOruqZNtqKr6F3JysmGxWOD3+7miKhERUT+5rNYRSTRZlmG1WmNjRDweD4LBILRaxKbunq0W8HqbEQoFoVKp8Itf/OKyXC2WiIjoSnRZrSOSaCUlJZg6dSp0Oh1k+dxbkZMT+a/XCzR7IoNWhRAoKSnBHXfckYSaEhERDU6KDiJ79+7F22+/DbvdDq/XG1uyPRpEnM5zZYPBIBobG7mIGRERUT9SbBBxOBw4evQoGhoa0NLSElvWHQBycyP/rak5V16j0cDn82Hbtm0JrikREdHgpdggIoTAuHHj8MADD2DMmDEwGAyQJAlA1z0ixcXFuOeeezhtl4iIqB8pNohE7d69G0eOHIHP54uNE+mqR6SiogKSJOHee+9NQi2JiIgGJ8XOmpEkCdu3b8ff//531NXVxd31t6seEa/Xi//+7/8GAM6aISIi6ieKDSJWqxWjRo3ClClT4Pf7sXPnTrS3twPoHETy8/Mxbtw4aLVaXpohIiLqR4oMIna7HU6nE1lZWZg0aRK2b98Og8GA9vZ2pKScW0OkpgZQqVTw+/2YPXs2ysrKkltxIiKiQUaRQUSSJNTW1qKiogKfffYZKisr0draCuBcCGlrA1paU6DRqNHU1ISXX34ZhYWFWLBgQRJrTkRENLgoMohYrVYAQH19PQAgLy8PjY2NaG9vjw1UdTqBcCiEjKwsDB06FCkpKbwsQ0RE1M8UGUSil2a2b9+OPXv2wOPxQJIkyLKM3NxI2KhxSgiHw6itrcXMmTPx+uuvJ7nWREREg48ip+9KkoSjR4+iqqoKTqcTdXV18Hq9UKvVGDrcAABwfj11NxQK4aOPPsKqVauSWGMiIqLBSZFBxGq1Yty4cZg+fTpGjRoFlUoFAAiHw8jMiMycqa0FjEYjRo8ejTFjxvCOu0RERANAkZdmACA3NxfDhw/HzTffDKPRiF27dsHn8yEjPfK8pyUVkydPRmlpKRYsWICSkpJkVpeIiGhQUmQQ2bt3L15//XUcOXIEhw8fhsvlAgCo1GpYLJEb37k9WlRXV2PdunX4/PPP8cILLzCMEBER9TNFBpEop9MJl8uFpqam2Lbo9N3K4w2oqfEgNTUVmZmZnDFDREQ0ABQZRCZPngxJkuD1euF0OmNBRK8HUlMjZerrI2NG5s2bh9deey15lSUiIhrEFDlY1eFwwOl0orW1Fc3NzbHBqhZL5HmvF/D5AI1Gg/LycmzatCmJtSUiIhq8FNkj8uqrr+LAgQPYtWsXmpubkZKSgpycHFitdQACqK+PhJBwOIy6ujpeliEiIhogiuwRyczMRHV1NXw+H0KhEPx+P2pra5GREQAA1NUB7e3tCIfDmDt3Lu69994k15iIiGhwUmQQefDBB3HrrbdCr9cjJSUFQggEg8HYpZmvV36HSqXCqFGjkldRIiKiQU6Rl2YcDgfS0tJgMBjiLrtEZ8zU1wN6vR4qlQovvPACAGDZsmXJqCoREdGgpsgeESEEMjIyMH/+fJjNZmi1WkiSFOsR8XgN+PnPf47S0lLk5+dzVVUiIqIBosgeEZvNBgBYu3YtWltboVarIYSIBRGH3Y+/vvf/YDab8dhjj2HJkiVJrC0REdHgpcggAgCffvopmpubY+NDJEn6+tKMQK0zhLa2ENrb2yHLiuw0IiIiSghFfsuuXbsWx44dQ0ZGRmybSiWQni4AxA9W3bVrVzKqSEREpAiK7BEJh8MoKSmBTqfDgQMH0NjYiMzMIGQZCAQAt0fG2LGjEQgEEAwGk11dIiKiQUtxPSJ2ux2lpaUoLy/HZ599BrVajcWLFyMzM/K8ywWkp2fgxIkT8Hq92LhxY3IrTERENIgpLohIkoTa2lq0tLQgGAzC4XBg7dq1cUHE1dCAQCDA8SFEREQDTHHftFarFcXFxfjtb3+LkSNHxrZ3DCJRjz32WIJrR0REpCyKCyJAJIycPHkSdrs9ti0aRBobz5VbunQp1q5dm+DaERERKYcigwgAmM1mGAwGmEwmaDSauB6R1157DXl5eZ1WXiUiIqL+pchZMwAwe/Zs/PGPf8Ty5cuxZ88eRGfyNjYCDz/8cFxvCREREQ0MRfaI3HTTTSgqKsItt9yCPXv2AAAsWZG3wuWK3ItGkiQsXbo0mdUkIiIa9BQXRBwOB7xeL9ra2iBEZAEzvV6PwlE5AOIHq0ZveEdEREQDQ3FBRAiBl156CZnRQSEAhAhDDtUAiA8iJpMp0dUjIiJSFMUFEZvNhsmTJ6OhoQG33347ZFmGJPmh1UZ6R1patSgrK4MQAjU1NUmuLRER0eCmuCDS0TvvvIPMzMzYjJnWVqCwcCKeeeaZ5FaMiIhIIRQdRO644w64XK64qbvlRw9h+fLlya0YERGRQiguiOzZsweLFi2CJEl49913EQ6HkZ2TAiASRNra2rBy5Uou705ERJQAivu2lWUZmzdvjtt2w9xSAICnOSW2TQjBnhEiIqIBprggUlJSgrFjx8ZtO/WvfwAAap2B2LasrCyEQqGE1o2IiEhpFLmy6rZt27Bv3z6sWLECf/nLX5CeHlnG3eWKrCnS2tqa5BoSEREpg+J6RKJKSkpw9913o7CwMLa8e1MTGEKIiIgSSLFBZN++fXj99ddRWVmJ9PTItqYmwGAwJLNaREREiqLIINLxsgyAuCDi8/kYRoiIiBJEcUHkpZdewowZM2IhRK/XIzs3EjxybBMARMKIJElJqyMREZFSKC6ICCFiN7sDgKzsDKikyLiQ8iPVyaoWERGRIikuiCxZsgR/+ctfYLVaAQBtPjsAIBAA7NWNAID8/Py4sEJEREQDQ3FBBABuuukmbNy4EVarNW58CBAJIVVVVcmqGhERkaIoMogAkTDy05/+FJmZkbegqQmQJIkhhIiIKIEUG0Q+/vhjvPTSSzCZIouZNTVFxo8UFBQkt2JEREQKosgg8vHHH2PhwoVwOBwwmyPbWtu0AICzZ88yjBARESWI4oJIxxACALa8VADAiKtuiA1gZRghIiJKDMUFkXA4DL1eD0mSkJ+fj/l33QoAsA0twcaNGzFixAjIsoxwOJzkmhIREQ1+igsiu3btwsmTJ6HRaFBVVYVwqB4AkJKShd27d+PkyZNQq9WoruaaIkRERANNcUFEpVIBAPx+P3Q6HRBuAAB8/ulOlJWVQQjBVVWJiIgSZMCCyKlTp/DAAw+gsLAQer0eI0aMwOOPP4729vaBeskeWbZsGVauXAkgEkYaqvcBAP746usAAK1Wi7a2tmRVj4iISFHUA3Xg8vJyhMNhvPLKKxg5ciQOHTqExYsXo6WlBWvWrBmol+2RZcuWAQDKysriFjRjCCEiIkosSSRwLfPVq1dj7dq1OHnyZI/KezwemM1muN1umEymfq/PTTfNxq9/vRUAcOutgNfLZd2JiIguVW++vwesR6QrbrcbmZmZF3ze7/fD7/fHHns8ngGry6pVq7B//1YAkfvMtLQAOp2OPSJEREQJlLDBqhUVFXjhhRfw4x//+IJlVq5cCbPZHPsZqLU8Vq1aFXdZpi1gBNBhACsRERElRK+DyLJlyyBJUrc/5eXlcftUV1dj3rx5uOuuu7B48eILHrusrAxutzv2MxD3fYmGEAAYMiQFAKAx5McNYGUYISIiSoxeX5p55JFHsGjRom7LFBUVxf5tt9sxe/ZslJaW4ve//323+2m1Wmi12t5WqVdCoVDstdZuXIsm+w8h5PTYANbly5cjgcNmiIiIFG1AB6tWV1dj9uzZmDJlCv74xz/G1vDoqYEerLrz0Gr46n+FdvW3cPPMv/X78YmIiJSoN9/fAzZGpLq6Gtdffz2GDh2KNWvWoK6uDjU1NaipqRmol7wou92Om266CZIkwWg0IhCILGYmqzLhcDgwd+5cSJIEg8GQtDoSEREpyYDNmvn4449RUVGBiooK5Ofnxz2XrEsfkiTFFlRraWnBnzeuwb/dAQTatViwYAG2bdsGAJBlxS04S0RElBQD9o27aNEiCCG6/EkWq9WKTZs24brrrgMApBoi40U++ssnsRCSmpoKr9ebtDoSEREpieL+179jGIletio/fBoAQwgREVGiKS6IAJEw8rvf/Q7p6ZHmR9dNYwghIiJKLEUGEYfDgV/+8pcwGsMAzgURo9GYxFoREREpj+KCiMPhiA1MjV6aGTHiagCRAawMI0RERImjqCDSMYTIMhDNHKufXxcbwMowQkRElDiKCiJCCGg0GgBAVpYe0Vm6RcPGY9OmTbj55psBAOFwOFlVJCIiUpQBXVn1Ug3kyqq1jYdxZP8EhGDEjdc39+uxiYiIlOyyWFn1ctfaVgcAEMhIck2IiIiUS7FBpL09sry7kNOTWxEiIiIFU2wQCYUaAQCSnJnkmhARESmXooLInj17IEkSJElCKOgCELnhHQDs27cv9hwRERElhqKCSMeb2f3u2aUAAJU6A/v27cPkyZOTVS0iIiLFUlQQKSkpwd69ewEgtpiZpykUF0Iu40lEREREg46igghwLoxEg8iGlzfGnmMIISIiSix1siuQDCUlJThrHwfgaOw+MwwhREREiae4HhEgMjDVUX0UwLkb3nGQKhERUeIpLohEB6ampUUeP/f8+thzDCNERESJpagg0nF2jNkc2TZpYmlsACvAMEJERJRIigoi0ZvZpaQAen1km0FniZtNQ0RERImjqCBy9dVXQwiB5mY7AEBARkpKOoDIAFYhBAetEhERJZCigkhUIBC5z0wY6ZAkRb4FRERElwVFfgsHg1/f8E5KT25FiIiIFE6hQcQDQALkjGRXhYiISNEUuaCZxfJtjJzkwaGqmmRXhYiISNEU2SMCAJKkgk5rSnY1iIiIFE2xQQQAdCmqZFeBiIhI0RhEiIiIKGkUHUT0DCJERERJpeggoktRdPOJiIiSTlHfxEuXLkVqaioKCgoAxF+aWb58OVJTU5GXl5es6hERESmOooKISqVCe3s7zp49i2vGj4JWHWn+8uXLsXr1arS2tkKWFfWWEBERJZWi1hF55plnAACrV69GjaMaE0YX4f7778fq1asRDAaRn5+PqqqqJNeSiIhIOSRxGd/lzePxwGw2w+12w2TqvzU/li9fjueeW41QKBjbxhBCRETUP3rz/a3I6xDPPPMMiktKYo8lSWIIISIiSgJFBpHly5fjwP59scdCiNgAViIiIkocxQWR6MDU0NdjQsrKyqBWq3H27FmGESIiogRT1GDVaAjpamDq6tWrY2GEl2mIiIgSQ1FBJBQKQaPRIDc3Ny5sRGfT/Nd//RfC4XCyqkdERKQ4ipw1Q0RERAOHs2aIiIjoisAgQkREREnDIEJERERJwyBCREREScMgQkREREnDIEJERERJwyBCREREScMgQkREREnDIEJERERJwyBCREREScMgQkREREnDIEJERERJwyBCREREScMgQkREREnDIEJERERJwyBCREREScMgQkREREnDIEJERERJwyBCRERESTOgQeS2227D0KFDodPpYLVacd9998Futw/kSxIREdEVZECDyOzZs/HGG2/g2LFj+L//+z+cOHEC3/3udwfyJYmIiOgKIgkhRKJe7L333sMdd9wBv9+PlJSUi5b3eDwwm81wu90wmUwJqCERERFdqt58f6sTVCe4XC786U9/Qmlp6QVDiN/vh9/vjz32eDz9Wofc3FzIstzl5SGbzYZwOIyampp+fU0iIiK6sAEfrLp06VKkpqZiyJAhOHPmDN59990Lll25ciXMZnPsp6CgoF/rIssyHA4HbDZb3HabzQaHwwFZ5thdIiKiROr1N++yZcsgSVK3P+Xl5bHyjz76KPbu3YuPPvoIKpUK999/Py50NaisrAxutzv2U1VV1feWdcFut8NqtcaFkWgIsVqtHEhLRESUYL0eI1JXV4eGhoZuyxQVFUGj0XTafvbsWRQUFGD79u2YMWPGRV9roMaIRMNHFEMIERFR/xnQMSJZWVnIysrqU8XC4TAAxI0DSQa73Q5JkuIeExERUeIN2GDVnTt34quvvsLMmTORkZGBEydO4LHHHsOIESN61BsykLoaI8IwQkRElHgDNjrTYDDgrbfewo033ogxY8bggQceQHFxMT777DNotdqBetmL6jgmRAjRacwIERERJU5C1xHprf4eI3KhgakcsEpERNR/evP9raj5quFwuMuwEZ1NEx3DQkRERImRsAXNLgfdLVbGnhAiIqLEU1SPCBEREV1eGESIiIgoaRhEiIiIKGkYRIiIiChpGESIiIgoaRhEiIiIKGkYRIiIiChpGESIiIgoaRhEiIiIKGkYRIiIiChpLusl3qP34/N4PEmuCREREfVU9Hu7J/fVvayDSHNzMwCgoKAgyTUhIiKi3mpubobZbO62jCR6EleSJBwOw263Iy0tDZIk9euxPR4PCgoKUFVVddFbFF+p2MbBgW0cHNjGwYFt7BkhBJqbm2Gz2SDL3Y8Cuax7RGRZRn5+/oC+hslkGrS/TFFs4+DANg4ObOPgwDZe3MV6QqI4WJWIiIiShkGEiIiIkkaxQUSr1eLxxx+HVqtNdlUGDNs4OLCNgwPbODiwjf3vsh6sSkRERIObYntEiIiIKPkYRIiIiChpGESIiIgoaRhEiIiIKGkYRIiIiChpBm0Qefrpp1FaWgqDwYD09PQe7SOEwIoVK2C1WqHX6zFnzhwcP348rozL5cL3v/99mEwmpKen44EHHoDX6x2AFlxcb+ty6tQpSJLU5c+f//znWLmunt+0aVMimtRJX97v66+/vlP9f/KTn8SVOXPmDObPnw+DwYDs7Gw8+uijCAaDA9mUC+ptG10uF/793/8dY8aMgV6vx9ChQ/HQQw/B7XbHlUvmeXzxxRcxfPhw6HQ6TJs2DV9++WW35f/85z9j7Nix0Ol0mDhxIjZv3hz3fE8+m4nWmzb+4Q9/wLXXXouMjAxkZGRgzpw5ncovWrSo0/maN2/eQDejW71p44YNGzrVX6fTxZW50s9jV39bJEnC/PnzY2Uut/O4bds2fPvb34bNZoMkSXjnnXcuus/WrVtx9dVXQ6vVYuTIkdiwYUOnMr39jHdLDFIrVqwQzz//vHj44YeF2Wzu0T6rVq0SZrNZvPPOO2L//v3itttuE4WFhcLn88XKzJs3T0yaNEl88cUX4h//+IcYOXKkuOeeewaoFd3rbV2CwaBwOBxxP0888YQwGo2iubk5Vg6AWL9+fVy5ju9BIvXl/Z41a5ZYvHhxXP3dbnfs+WAwKCZMmCDmzJkj9u7dKzZv3iwsFosoKysb6OZ0qbdtPHjwoLjzzjvFe++9JyoqKsSnn34qRo0aJb7zne/ElUvWedy0aZPQaDTi1VdfFYcPHxaLFy8W6enpwul0dln+888/FyqVSjz33HPiyJEj4je/+Y1ISUkRBw8ejJXpyWczkXrbxnvvvVe8+OKLYu/eveLo0aNi0aJFwmw2i7Nnz8bKLFy4UMybNy/ufLlcrkQ1qZPetnH9+vXCZDLF1b+mpiauzJV+HhsaGuLad+jQIaFSqcT69etjZS6387h582bx61//Wrz11lsCgHj77be7LX/y5ElhMBjEww8/LI4cOSJeeOEFoVKpxAcffBAr09v37WIGbRCJWr9+fY+CSDgcFrm5uWL16tWxbU1NTUKr1YrXXntNCCHEkSNHBADx1Vdfxcq8//77QpIkUV1d3e91705/1aWkpET88Ic/jNvWk1/WROhrG2fNmiV+/vOfX/D5zZs3C1mW4/5Irl27VphMJuH3+/ul7j3VX+fxjTfeEBqNRgQCgdi2ZJ3HqVOniiVLlsQeh0IhYbPZxMqVK7ss/73vfU/Mnz8/btu0adPEj3/8YyFEzz6bidbbNp4vGAyKtLQ0sXHjxti2hQsXittvv72/q9pnvW3jxf7WDsbz+Lvf/U6kpaUJr9cb23a5nceOevI34Ve/+pW46qqr4rbdfffdYu7cubHHl/q+nW/QXprprcrKStTU1GDOnDmxbWazGdOmTcOOHTsAADt27EB6ejquueaaWJk5c+ZAlmXs3LkzofXtj7rs3r0b+/btwwMPPNDpuSVLlsBisWDq1Kl49dVXIZKw7t2ltPFPf/oTLBYLJkyYgLKyMrS2tsYdd+LEicjJyYltmzt3LjweDw4fPtz/DelGf/1Oud1umEwmqNXx97FM9Hlsb2/H7t274z5Hsixjzpw5sc/R+Xbs2BFXHoicj2j5nnw2E6kvbTxfa2srAoEAMjMz47Zv3boV2dnZGDNmDB588EE0NDT0a917qq9t9Hq9GDZsGAoKCnD77bfHfZ4G43lct24dFixYgNTU1Ljtl8t57IuLfR77430732V9991EqqmpAYC4L6fo4+hzNTU1yM7OjnterVYjMzMzViZR+qMu69atw7hx41BaWhq3/cknn8QNN9wAg8GAjz76CD/96U/h9Xrx0EMP9Vv9e6Kvbbz33nsxbNgw2Gw2HDhwAEuXLsWxY8fw1ltvxY7b1XmOPpdI/XEe6+vr8dRTT+FHP/pR3PZknMf6+nqEQqEu39/y8vIu97nQ+ej4uYtuu1CZROpLG8+3dOlS2Gy2uD/m8+bNw5133onCwkKcOHECy5cvxy233IIdO3ZApVL1axsupi9tHDNmDF599VUUFxfD7XZjzZo1KC0txeHDh5Gfnz/ozuOXX36JQ4cOYd26dXHbL6fz2BcX+jx6PB74fD40NjZe8u//+a6oILJs2TI8++yz3ZY5evQoxo4dm6Aa9b+etvFS+Xw+/O///i8ee+yxTs913DZ58mS0tLRg9erV/fYFNtBt7PiFPHHiRFitVtx44404ceIERowY0efj9kaizqPH48H8+fMxfvx4/Pa3v417bqDPI/XNqlWrsGnTJmzdujVuMOeCBQti/544cSKKi4sxYsQIbN26FTfeeGMyqtorM2bMwIwZM2KPS0tLMW7cOLzyyit46qmnklizgbFu3TpMnDgRU6dOjdt+pZ/HZLiigsgjjzyCRYsWdVumqKioT8fOzc0FADidTlit1th2p9OJkpKSWJna2tq4/YLBIFwuV2z/S9XTNl5qXd588020trbi/vvvv2jZadOm4amnnoLf7++XmyAlqo1R06ZNAwBUVFRgxIgRyM3N7TTC2+l0AsAVdR6bm5sxb948pKWl4e2330ZKSkq35fv7PHbFYrFApVLF3s8op9N5wfbk5uZ2W74nn81E6ksbo9asWYNVq1bhk08+QXFxcbdli4qKYLFYUFFRkfAvsEtpY1RKSgomT56MiooKAIPrPLa0tGDTpk148sknL/o6yTyPfXGhz6PJZIJer4dKpbrk341O+jSy5ArS28Gqa9asiW1zu91dDlbdtWtXrMyHH36Y1MGqfa3LrFmzOs2yuJD//M/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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "mu, std = predicted_mean_std(ls,uscale,noise)\n", "pstd = np.sqrt(std**2+noise) # prediction interval std\n", "order = np.argsort(test_x.reshape(-1))\n", "plt.plot(train_x.reshape(-1), train_y, 'kx', alpha=.2)\n", "plt.plot(test_x[order].reshape(-1), mu[order], 'y')\n", "plt.fill_between(test_x[order].reshape(-1), (mu - 2*pstd)[order], (mu + 2*pstd)[order], alpha=.5, interpolate=True)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "901ae2f5", "metadata": {}, "source": [ "As you can see, we have chosen the noise value too small for the data.\n", "But lets fix that by optimizing these parameters using the marginal log likelihood" ] }, { "attachments": {}, "cell_type": "markdown", "id": "80638eb8", "metadata": {}, "source": [ "## Hyperparameter Optimization\n", "Often, the initial hyperparameter values may not fit the data well. We can optimize these parameters using the marginal log-likelihood:\n", "\n", "$$\n", "\\text{NLL} = \\frac{1}{2} y^T (K + \\sigma^2_n I)^{-1} y + \\frac{1}{2} \\log |K + \\sigma^2_n I| + \\frac{n}{2} \\log 2\\pi\n", "$$\n", "\n", "Here:\n", "\n", "- $y$ is the vector of target values.\n", "- $K$ is the kernel matrix computed using the RBF kernel between the training inputs.\n", "- $\\sigma^2_n$ is the noise variance.\n", "- $I$ is the identity matrix.\n", "- $n$ is the number of training examples." ] }, { "cell_type": "code", "execution_count": 13, "id": "4545800a", "metadata": {}, "outputs": [], "source": [ "# compute the MLL\n", "y = train_y\n", "alg = Cholesky()\n", "def NLL(params, key):\n", " ls,uscale,noise = params\n", " kernel = rbf(ls, uscale)\n", " Kxx= cola.ops.Dense(kernel(train_x, train_x))\n", " K = cola.PSD(Kxx + noise * cola.ops.I_like(Kxx))\n", " invK = cola.inv(K,alg)\n", " minus2MLL =y.T@(invK@y)+cola.logdet(K,alg)+jnp.log(2*jnp.pi)*y.shape[0]\n", " return minus2MLL/(2*y.shape[0])" ] }, { "attachments": {}, "cell_type": "markdown", "id": "e0d99566", "metadata": {}, "source": [ "Using optax and jax, we create a training loop to optimize the hyperparameters:" ] }, { "cell_type": "code", "execution_count": 14, "id": "0d9642e3", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "loss: -0.268\n", "loss: -0.377\n", "loss: -0.423\n", "loss: -0.443\n", "loss: -0.451\n", "loss: -0.454\n", "loss: -0.454\n", "loss: -0.454\n", "loss: -0.453\n", "loss: -0.453\n" ] } ], "source": [ "import optax\n", "import jax\n", "# create the training loop\n", "opt = optax.adam(3e-3)\n", "\n", "@jax.jit\n", "def step(params,opt_state, key):\n", " loss, grads = jax.value_and_grad(NLL)(params, key)\n", " key = jax.random.split(key)[0]\n", " updates, opt_state = opt.update(grads, opt_state)\n", " params = optax.apply_updates(params, updates)\n", " return params, opt_state, loss, key\n", "\n", "params = list(map(jnp.array,(ls,uscale,noise)))\n", "opt_state = opt.init(params)\n", "key = jax.random.PRNGKey(0)\n", "for i in range(10):\n", " params,opt_state,loss,key = step(params,opt_state,key)\n", " print(f\"loss: {loss.item():.3f}\")" ] }, { "attachments": {}, "cell_type": "markdown", "id": "bc5d2bf3", "metadata": {}, "source": [ "Now we have a new lengthscale, uncertainty scale and noise level." ] }, { "cell_type": "code", "execution_count": 15, "id": "63ec6dd8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "ls = 0.17, uscale = 0.53, noise = 0.03\n" ] } ], "source": [ "ls, uscale, noise = params\n", "print(f\"ls = {ls:.2f}, uscale = {uscale:.2f}, noise = {noise:.2f}\")" ] }, { "attachments": {}, "cell_type": "markdown", "id": "54481a36", "metadata": {}, "source": [ "### Final Visualization\n", "Finally, we visualize the GP's prediction with the optimized hyperparameters. The new plot shows a better fit to the data:" ] }, { "cell_type": "code", "execution_count": 16, "id": "c90e19c0", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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TanbomG3mTz3Nc5/9S46w2l+l3WzgC4RoVxvYthuzVERaFunJOY4/+zy1Yg6jWkYIp+5ESoa/3/trVznc2WR0Zn547NF0EhqEI0nAERrhWHIoSvY3VqiVCkSO/LfyfhPqSogoFIq3jWVL9vtpl7Vcg4bpbA6uUJJo0rqnzbTie+dehYl7a1doVEpMzB+/4/GBaVY4kbx3TUE8Tb1cIruzhkDgD8fYW72ElIJAKIw/EmN/7erQUyN626f6SDzJ7spFhLaHLxgGIfCHotTK+eE5DjZXQEoSSReJ0UNo/QXpWIlkNEfEv4tHq0LizrX1ehrV1ihte4lMLsjurk7P/ST1dpL83h6pyVmkLTnYuA5C4EuEkEadVnOXUCRO26iT2bpBIBwjHHdEQrvZwLZsQjFHFIWicQLh2C3RGIBwPEkonhxe11A8yeLpZwn1n+f26x1Jpm+pcbn98WoxNzzH+/G/DSVEFIr3AQcHB29oWPRWhlxJ6UyA3S+32O4XnL6RqdfRUPPB5nWQYtjlcE8XytWrIOTQafIob+Rqebdj3g+fKN9owNne2hVyOxsgnU/cRx+/fu4b5Pe2SU3MEkmkbnm+26+dE60osLd2hVa9hj8Uplo4xBsI88Rzn6BRLXHuq18gMTbOmY/ejHLUSgXWzr8CQCASpZQ9oGXUeeIDZxlJdenW/oBgPU8skOfkyTyxUBGPq3nX1yilwGSWtjzG7r6X9TWbQiXJ+Ikfp1qu0KyVnSshoLizR6t5g6mlk/hDUYr728RHJ/AHIwQjMQqZHZASfyhEy2iys3KZmeNPEgjHAAhG40TiKWrlAsFIjLG55Vuu8dTSE3f9/YomR9/w9+2o8+rdRMjRKMj7FSVEFIrHnFbH8cNod2zMntPyaver3gc+G6VSi2IhS7FhMj01iUfXcOuCfO7wjiFXA6+NZsei0e5RbXUpNTsUGx1y9fZwVsobfRqvFg9plIuE4s6n7VopD1LQqJXJbN6gVs4TiadvKXqM9gVJrVSgXikiYPgJccDtaZ27OV8OjtH6bZvvdTHyRp0pjXIJfzhGJJ6kXi4OxUi9XGD3+mUkksiRT/TgXLv9jetE4qlbrpsQIG2bUu4Ad9lDJJlmYv44m1dfp1mrInRBs16jUc7g1Q/waXmWJg5JWi/hEVni0RahQJVoqIHP+8bdKFIK6s0IRneKijFJrhinKZcJjX6CUHJmaA6maYLgaJxQfBRbOu9zs1YmEIkjJSAki2c+SL1UJBxLgpD9yI5jYDZ/6mkkkkalTH5/m0alzPjcsWHUIpIcITxoMT7y+z0QCm83YnE/3SzvV5QQUSgeI2rtLnulFtla6y3bjNeKki9feZ1ocm+4YdVKOeKpUWLVBlxbxbIZiph7MRAbtu2c++gf0uzWKoe7myw++SwCp0gxFEvQrFfYWbmILxxm4dSzaJo2dJ0EONhYwahVGJ1ZJJJI3SI07jY9VAjn54Fbjhl0YAw8J94rvJHwk0ia9QqNamnYmTJxpP5ACIGQkovf+BKl3AGJsUnmTz19awFov/5DaIJaqQBrV4fX1LZtogk/7UKedFowMVVidGwN2d4klZTEoh3CwQZ+zz+5dcGxu78Oo+XH6E7StmYwuhM02uPkSyE215v4QmlGpheoV0qEY0kiiRTlYo5q+Sq1UoHxueXhugb1KuFYgmatglGtMDqz4NiVc3OuCzB8HbcX1oaiCeqVInCrUHinxIfi/lBCRKF4xMnV2tw4bHDu2jqVZvdtpyOOfnoebFjR5AjBeJqu9dbCwgIx7Ag4+ml8f+0q9XKR0el5auUi9XJxuCnWKyWSQLNe48orL5Aam2Z8bplauUh2ew0QBCOxocnVoDujXikSjMSHXQT7a1exbZuJ+WO3HONUUUIwHH9P1qG8URqm0b/OmqYRiiYQ4mbKSwCNapl2o0rTqDnmXVIipVNwOvDiAButu8lIuo1XbOPT9hlvS5aTeTypAzxPmPe1xp7lwmiFKVV8lKt+KjU/lXqIStWPO3IKS5uiVmmCgLPPf5ZIcoTs6hXqzSKJCUEomkBKSTiWGAqJerngWK/fJiIkTveNEM7vjQQiCccf/fbr5Py3cefvxNTyqVvSfUd5r/3+PMooIaJQPII0Oz2uHtS4clCjZHQAqDW7b1gP0CiXhhv+veovauU8ud1NRqbnhxvWgNvndNzO7fUZRz0gnDoQx1hqZGqe8bljw0+sA9Ez6BJYPf8yAIXsLlLIodV2s15hbHZxeO5wPEV2Z41GpUSzViGSTNMoF4dRlEFhX71SJL+3RcuoM3Ps9CMnQo6+H0f9NW5/f2rF3BF/jTsF5aBeY/X8y4zNLt0SsQjHkxzubtK8doHkxPRwbkoknqJZr1A6PEBoglh6DNOokF/9A6YmqpxKZxlL5kmE9/G4O/d8HW3TS70Zolxxky+A0Y4i9SmEdxbDjGG7pjnYLdGsVamVi0hpE0uPIW2bQDgKNUlycoR0CIxq2Ym8QF94JKlXSjQqJUIxR4wMojWheJJw/KYD6yDyNblw3BEpJUekONf67j4cKi3yaKOEiELxCJGttvnuTpnVXOOOIWuDP5i3pywa5dLw89ztQ71unwK6deU8trQxamWCkfgtofmjouLo+eDO+ozb/+Dndjdo1qsgYHz+GBInPTAQIUc/pQcicYKROIX9bQ42VmgbDcbmlgiEY9TLxb4NtZNWCIYd74bCwQ4A6al5xueWh2kFACS0jDr+YBjEo7exHI1kHPXXuL0+ZmBbPjjubq9DCGg1alx5+QUOd9ZJT807E1xt2f9qU8zskt/bZnRmnvzuddydC3z4mRwTIxUmRstE/bu49DtbXy3bhdEZp9kdwzBHOcy52d23Odi1wDtLt+cBadNuGkgEjXKBmWNPMv/kM7TMInvXLtNq1BGahrQtfMEwXn8QDUFqYobc3hatWoWlvvvpwcYK9UpxKFAbldJdoxq3i4ij0Q2JvEWk3Hx8dHhb8eijhIjifc871VHydpFSsp43eH27zH7l3rMpIskRDrZW2Lh8juz2OsFIbBgJOdhYYffGZXzhEM1wlUalxOLpDyCRrJx7iZ3rTn3G4hPPYts2Rq1Cfm+TQDR2SzpjkH+vlfPDLoFqMYfoD5a73XjJqJUpZfdoGQ2Wn/4+gOEn/IEIkfJmSmWw8TTrFTI7a/iCIUAwNrtIrVxk7cIrSOnMDAnHkwSjN/0ljFqZEx/42HDjHnRMzBw7DcLZzPb79Q3fK+/U0Lbbr9fkwnEufuNL7Ny4xBPPfZJaqcDhzs33sl4usL9+nVo5T6NaIhRJDlMItm0z/8QzvP7Cn3HhpS+Rmpxl+cxzNGsVRidHCIirJMJ7xAPbJCP7JGNFdO3OzbjVdrF7EKRUn6ZQnaCjn6ZUTzE2e4LJpVPs710ls73qDI6TEr/Lgy8QpN00iI2MIwBfIEggEsO2bVr1Cr5ACHA6S9Yuvoq0baqFDJMLJ5ESFp981hGa/WLlQWplIMhuRvTu7S56e7fK3a717bcVjzZKiCje9wgh7jp1MpPJ3NFR8k5i2ZLr2Rrf2SoP0y/3w8TccfK7287mX68O/4A3axUkkkouSzmbYWr5FLZts37hVdYvncMXCHLquU8OIyn53U32Nq7jD4Q49dwn7si/N8qlI8ZSd3ZnAKxdeIX99WuOa+TiSSJ946vbrbqPjkMHRzRJCYtPPEuzUaXVqDvCKhqjmNkFIQhGY8M6lPTU/NB5c3/tKuF4aihC6Edfjp4HeEti5G6iQyDY37hOZusGY3PLN9NbfWHWrFWolwv3bDM+2gY7uH5CCPzhKC2jzuaV151ODyRCMPS1iCRSHO6ss7e+QmJknNzeBtK2WX7qw9TLBeIxQcydZTx1meOJLzH3dJuI//Cur63dDVEzF6m2F1lbhbUNF7tbJm5fkNGZhX5K6yTBqCP2BoJR0zTG549Rzh30W3cjxEcnCEXihGJOLUpma5XtlYvYPYtQNIY/FKGY3UXaNkLTiKVG+1fSSbWF4ymnRqmcHwrSWil/RzpNRTXeXyghonjfMxAfR8XIURHyTs9e6PRsLu1X+e5O+b7mrtxtk0xPzpLf36acz/D1P/htfIEwibEpUuPTNGoVzGaDQCjK9rXzlHMHdM0W43PLhOM3fSNsJFMLJyge7g47B47m329Pq9xcjyNGnE/u1/AFw0wfe5KJ+ePOBl13rK4HdRzgGD6Nw7CAFY1bozmbN9hZuQhAYnwagSQYiQ9TSNHkCNPHnnRqH0oFGpUSAxESiNz08x6Ij1qpQLifdrqfyMYgfVIrFYb1G5HkCJmtG2xfuwA426ljvuUYWtlScri9QW5ng9GZRcLx1C3PpWka2c1VgtE4U8tPDB1EpZSMziwggL316yRGx0lNzrF74zLrl7/D4pMfJBiNOcdNJOhUXsBDltNn44z5f4twdIsfPXn3yFnTjFM1lyhUxyk3Zui4ztLsxDFqFaSE4sE25WoGl6/FwpNPE4jEyO9tkT/YJj0xS7NewbZsNN3pPArFEgSjcYrZPUqZPRJjk4zNLCKlJJJI06iWKGX3SU3OkJ6cI7+/RbNWITE+SXJsBk0TwxqW263LjzqrHkVFNd5/KCGiUHCrGDmajnknRUjD7HF+p8LF/crQi+N+OFpjAI4QCMUTCE1QzmdolIsUMvu0WwZef4BAOEpidJLV869QyOwghGDp7IdAwo3zrzA247RHagikAF8gTLNWuSP6cTStcrvro5MGujQUIQN77mhyhEalNHSeHDAwfJKrV2lUSwTDsTs+BRvVMs16hUA4RqAvQhqDNs7+cZNLp6Af9QjFkkzMHxteE3A2rsmlU4RvK6y9V92L0ASReJpocoT9jRUOd9YZm+0LC1uSmpzhcHeT/O4WaIAUw7kh9XKBq69+nf3160wunmB05ub8kcOddYxahTQM61kG17ReKVE83KdeyeMSBWK+G5ycrxI8XiDo+zaJqMHYWYuwv/yGvxe1ZpJ8dYqVa13W1nU6rrMc+9BPONd1bARZzNHsC8Pc3hamUQcE8ZEJAuGIE4mRsNBPmRi1inO9NIFtWbe0yjbrFfzhCP5QeFjDMahpmT15Zvia/cEIsyfPEgjHhm3UR7++X4zmFG8NJUQUij6DSMhgs3inRMh+pcXXzl1ns9gkFE/f8Qn99s6J2/9YD7olLr70JQLhKEtnn6NeLrB9/SJCCNJTc6xeeIXdG1UCkRiLTz7LwfYqu6uXCIRjJMamaDUbTnjdqCGAVqNKIBx1hnfNLJLZXht2LMARi+4jhayDtUSSI6xdeBlfMEx6ao7x+WM0ysWbNRCLJ97w9Uwtn7rr668Wcyw/5byu7Pa64w8RTRKOJe/wu7Btm/G55Vsstmulwi0OoncMYdPEG/qSgLOpDuZ/rJ5/hSuvvEAgFCU5McPo9CLN6us0jToCSWJsepiWmVw6xeHuOhdf+jL1cqF/Mihm9vAFQoxMz6PRJbf6x4ykTBaSTQLuQ/TkBr7jGeKR2hvOTBlQN3wcFmLs7Xsp1cfouZ6gJRdxB0aJxJNkO2vs5r+J29Mjv7fJ9LEnh9ehXnaiRxqC6WOnKWS2kbZNMBpH2o5UG6RMDjZWaDYqNKplRqfnb0ltBcJxguE44Xjy5nvbN58LReP9mo+bhaNHI01HvyoRorgbSogoFH2OihApJZlM5m2LEcPscT1b5+pBlUKjQ61oUC3msG151whHNDlyx+Z4lEgiRdOoUc5lCERiIMFsNakV884GKKHX69Kslbn08ldpN2qE4ykWz3yQw90NslurjC8eR0rYuPK6EzkJRW9OAy0XadTKNGsVZz7JwvE7QudHUzK2LUlPzRGMxIfGZoOOm2i/XfKNXs/Rzej2Y2zbZrnfVeGcT7ulk6dWyqNp2hExcUg0OUokkSK3s87qhVdYPvvccPMbbJaTC8cxqmXWL5/jcGcdfziKJrRhNEQAhztrCAHBaJSDrRXy+1sEwhFnoRqYrTo+fxghJKMzS0P/En8oRnpyEi9b6NV/y+hIl7PPtJmc1IgESwQ8FYS4d51D3QiRL3rJ5V0Y5giZjOQw5+Iw72f6iR+kVa+S29/G6wsgabP4hJdk3BFpY7NLBCNxdlcvs7d2jWA0Phy8Zts2wagzOTYUSzCYpmtbNpFEaphOGta/lPKMTotbolmSm63Xt4vKgeC4V3pFoXgzlBBRKOCOmpDBfeCeYuRox0293WUjb7Caa7BfblEpHA7/cN/eOTFIAwi4o1vgbn/EI8kRnvjQJzn3tS+wev4VfP4g8fQ49XKeSj5DLD1BemKarZWLZLdW8QXDzJ14yhFVlkVifArZsxA+gTcQIJGewEbe0bGwduEVZ6rqXc4PTuShXr7V4fKom+kg/H6/A+6OtmLePoujVioMW5EHzwuCWrnI4df+BGlLlp/68NDlFaBVq7J6/hVC0Ti2lBQPdvCHItTLhWG6oHCwQyASIzk+Q25ng3q5NEyzbFw+R6VwSNuo4/WH2Nu4TqdpEEmOEB+ZpFmv0KtfZTRUZGzpPGHvDul4ieiH8+ia9Yavs2f5qLfTVOtRaq0kppzCds2TL/gwukkOd/c53F53umRiKUqH+4i+Q1s5d4DPH+Lks89TzO5RLeYoHu4T6HcVDd6/iYXjrF14lcPdTULRBKF4Ek3TCEZid0S3NE27JaI0eI/v9l4pDw7Fg0YJEcV7njdrz81ms84f8yM1IXcrYL2dhtljs2Dw0ivn6HoiBCeWho/dbebJUR8QIUS/1JJbXE5rpcKwbfZuJEYmWLvwKt1Om7F+8amUkJ6YBiHottu4vT6C4Shb188TS40zPn+M5PgMezcu4w+G8AVDSGzKuX2a9SqLTz473KQGvhR3q6kAkPJWm+yjAmsgRuqlwvD1vNlGdc9WzEQKKW/WGNTLBYQQFDM7ZDZXGZ93rnejXOTqKy/gD0VIT8+R292keLiHEAKvP4jQnO6OdtNwrN91nVJ2DyT4Q5FhC2m9XKJSyNI2GghdI5mQuHuvMj7dYGa6x9ysJBE+xKXfvcOp1Xaxn/FxmPNTaUSx3ct4Y08hvccwe+Hh3B0p5c0i3IkRKBdo1a8xOruINx8is3WDxMgU3kCA7NYqu6tXmF5+gtHZRZaeeo7M5g22Vy4Nv380evXMD/zo0MwMuKVz6fb3671mga94fFFCRPGe52h77tH6j0HUQ9O0YYvu0Xbdgfjo9Cxy9TYlwxn8VmiY5OvmsOMl3/ORWbvCeLPD5NIp9lavUq8UifQ/rd7+B79w4EwATU/NEe5bWgvhHHO4sw4449ePbuL7a1dZv/QdRmcWQEjWzr9KIbNNamyWE88+z/VzL1EtZAF4/sd/hvJhhszmDcr5DLH0GK16leT4FEat4thhy0FTpbhrBONutteD6MXg+KMdKYPvZzZv0KiUCcXifR+IwztSMbfXChx1Gx2kVIauqeUC2e01QtEERq1MMbOHBMbnl/EHI6yef5lWow5C0DLqGNUy6ak5dm9cIbez6RRSWhblfIZKPoPPH8ZsNeh0THzBMAFvnWSkjFX5M1Jij7nncqQTZSZGGwT8d49w9CwXh4UwhUoS6T3L2rrF5e+WMMw4Jz7wMYrZPfbWrxGKxll8Mkl6KjJ8f4epv74BGUB2e43UxAwAOyuX8Xj9RFMjeP1BEALTaCCl4HBnnXA8xfEPPE8olmDj8uug3SkWB8W6d2uLBTXtVfHoIaS8jwlXD4larUY0GqVarRKJRB72chSPMQPRoes6lmWh6zrZbJaxsTGeeuopMpkMmzu7eMJJ3OEkq5u7lJsmIpigYfaQ8t7TZtcvvkajUmJkeh4poVWvDKefDqfQ9o3CjFqFZqNCq1EnNTbNyMwCjUpp2LUQisUJHOkqGU4d1XVsW6IJ2N+4RvFgD4RgcvkUW5dfp2XUSI7NMHvqLM1qGaFp7K9dp9moMjI9z/ypZ4amYQKngLNRKSORhCLxWz5Z34u7TcEVQkMIhjNPBoJndGZxWMQ4qI05moqplwsIJFbzBrHAPulEA2HtE/DU8LkraBjoWg9Ns8A20UQPW7rQXAFMU9Ltgtm2sfFg2RpCuLFsnW7Hwmx38fjDGLUSbpeFz+ciEBS4RI1goEc03MXleuN0imULCqUQ5cYY+xkf2VyEllwC3wlCsREalTKl3B7V/CGddotwIk18ZAxfMEL5cJ/83hZur5/F088SCMeGnTYDobe/sUKrViHQb2N2PFlW8AWDw0LXQbrLqJRBOM6yt4tFVQCq+F5YGgnxY2ffea+kt7J/q4iI4rHnrTijHhwcUCgUyOVy+CIJivtlvnHjy+TrLfRggkjSola8PNxcJ/p25aL/v4FZ19HNNbN1A9uy0HSdRqVE26gRCMVo1Ss0a2XG6HtQbKw4DpizC+R2NthduUy7aYCQNOt1pLQZmZ4nt7eF0ATJsWnWLrzibOrROIFQlN21y7QaBv5QhOT4NLtrV7n00pcYm1ni5Ic+zs7KJS5+44uc+dhnOfORT/P11r+luVKh027RbFSolYvDeoj1S+fQdI3U+IwzKv2ICNlbuwLy1gmmcHPqrtBuigohNC5/6yt02k1OfPB5RqYX2Lr6XYqZXYrZfRKjkzSqJbCd6JRLbzOZWiMRegGf/9skglu4Xfdv6OZQA/9b/U25E9uGStVDseylXPVTM2JU21NUGmNsb1tUCmVSE7OMzy1TrmawLYv0hJvjzz7P9e98A6NWJpoaZeb46b6HRo35U88wPrvEVQntlkG/S/aWuFgkOcLB5g0a9Qqjs4sA+MNRnvn+H0Yiye1sEOx3o1SLuWHNx6D7ZPAcCsUAXRO4dIFb03DpApcmKBnd+5qm/bBRQkTx2HO/zqipkVFevbLGTgXWDi30molRy/bbVpNMzCeGn/Yj8RS1cnE4Gt22nNoITdNYv3wOTROkJ+f6XTCOwRVA26jTMhqUc1kmF0447pPba07KRYI/EkMgaDaquL1+Ou0m++vXkQiOP/N9GNUy5VwGfyDEXuMq0rIQuo4EitldsCX+YAhp2/hCYdxuDwTChBNp0pOzlA+d69CqVTjYWOHpj/8wkwsnWL/0Gm3DGG6GtVIBzaVj9ywQEIwkhumW/bWrHG5vEIjEht8bcHToXKNaJre7iRDQaTfptNsUM3s0a1XK+Sz1ch5pSxCSTv0ay9MbHJ/fZjK97RR2hm6+h72eRq4YolCO02iHKeah2Qmj+0YpZvO02z0So3Okppdx6TZbV14Bq4XusvH7Xeh6j7ZRxu62CEZChKNh2s0qzWoONBcef4JWs4NlefCE57CIcphpsXb9ELPdAwHzJ58mPjqBbdmYbYPpY+O4PKtEU6O0mw3i6XHHKyMUZeXcS7dEwIxqmeT4LPOnktTLRSRw6rlP9P05ykT6g9uO1t6Mzy8TjjkCw+lMOVJ702+HvXV6rIp8vFdw6wKfW8fj0nDrzj+PS8Oji1vuu3UNj67hdonhbY9Lw6UJXLqGWxe4NOfrIP13lGy1zZevHVKo39/05IeFSs0o3hO8UdfL+Pg4li/GlYMar1/foHCYHbbnDgoGjVoZJDRqZUR/5smgI2T1/Cs065V+pGKbtlEnOTpJ06jSrFVJTcwwOuOkO1r1KkatTKWQxWwajM0uk5qcAQmrF75NPD1Jqu9e6Q9HaTWqrF98DaFpeP1+QKPdNDjzkU9h1CusX3zNGRzm8yN0nVajjj8UZmrpCVr1Cvvr1zHbTcZml/oTbCPMP/HMcBqtEIIzz38GgIsvfZlmo0pibIpQJE6zUR36RRw1nxq4ogpdIxSJD9s8j3bI5Pe3MKrlYdGnPxihX3SClHCweZ1aMc/yMT8f+5jFiYVd0tG9W96vZidNrrrI9RtBrt/wUayEaDc7VAoZAuEYi2c+QCV/SPFgm1rZqR858/xnGJ1e4OorL9BuNTFbBuXDA4LRBEibSv4QdEEgEKZp1GgbdcKJNIFQBIGG2W4STqSQto1RKYEQznULR/F4vaQn54mPTtBuGTSrZQKRGL5AiHazQbNWITU5S3pyjma9wuHOBqMzCxx/9nn2Vq9yuLM2nIh7NJpU67u1hhM303NKVDyaaELgdjmRBE04G7suQNOOVHn1N3vRP14TzleXLtC1m2LB59bxujV8Lh2fW8Pr0vF5NPxuHb9bx6Vr79rrsmzJd7ZKvLpZomffud0/CqkZJUQU7xkG4kMIgdntUdPCZDo+ys3uLXUNEkl2a5V6uehYWB8RI7s3LpMYn2T57IcBhjUd+5vXKWX2CEbiLJ5+FltK2o2aUyipCaS0CQSjlHMHTC6coGnUKB0e4AuESI5NOlNmWy1iqTTStklNziJtm4OtG7QbdadupF5h+thplp96jvzeFpVillhyjHaz4czu0PXhSPXS4QGdtsHCE88ODc42rrxOMBwjEI5i1MsgnT+g/ohTqzJwzzzYWCGWHmXkNhGyff0Cma0bLJ7+IKPTCzfrUiyrP5odWvUqjVoZs92kVavSMdtIaRFLjZMcm+Rw5Y84NnuNjzzXZGKsOXxvpITNnRiXro9Q4wfJZD3sr1/D7fUTSSQZ2LUXD/Yo5fbxBUO43F7azTrhmON3MTo9j9A1WvUa7aaB2WyA0GiU83h8AQDCiTS7q5f7wkiQnpxFCJ35U09Ryu7TbjUwjSZoTrKknDvA5fYQjiUZm10iEInRqJbRdJ3k6BSarjl1L7qOPxQZXqtIPHVLR8r9tisr3n00IQj7XMQCbmIBN1G/m5DXTcCj4/c4wmAQfXgvUzI6/Jerh3cM1nwUhIhKzSjeM4yPj7O2tcv1TI31vMHoQgzo3rFJ7K9dpV4uEo4nCYRjNOuOiZemaXiDIUqH+1x46YukJuYIxxM06xU6TQO314vQBIWDXfzhMMFwjLVLr9GsVZg+9iSBYBRfIEjxcBcpwR8MORsiAl8whNkyQEqErnPt1a8jdBfTS6c4bDZxe7zEUmP4AkEufeurIGDx1DMUsrv4g+FhaiCztUp+f4uuaXL6I58mGImzv7FCJJ5ECMH173yDcCLFM5/8ERrVElvXLxJs1IbFsy2jRq2cwxcMEYwkEMJp8dy+dp5mvUosPe5EOIBQLMnO9YuYZpNoY5RqIUs0NUYoGkcA+d0NbNtmJFHk7Nx5zpzYY/yzjeH70bMEK+spVjbnub4xQY+000ZrfBuX2+PYn0/NUS+X6LQMmkYdt9uDZfXodTu0mwY+f4BwIkUknqJSPKRtNIilx5C2xBsIMblwvJ/akvgDYaqlPC6XB6EJAqEoXbNDamKaYDROq1Ent7/Zr7Nwpv8Gw1FOfPDjSFtysHmdZqNGamIG27KIJFKE4klC0cSwaHQwi2YQIbq9XkN1ojw8NCFIBN2kQl5SYS/JoIdYwEPU70bXVKtyIujhv/nAFBf2qnxzrUCnd/9jJh40Sogo3hNUW12++No1Xruyjy25ZT7KUdOsgdukYx0unSFf/aFc9XKR0el5dlYuUsllAKf7ZW/tGtHUCNVinoON6zSSJSbnj1PJHYIEt9eHLxAGJMnxGQqZHUd0IEBCKbuLRDA2u+z4dxxmaTZqdM02nXaLTqtJYmyKSCLF1tXzdDsm08tPgHA203L+AGlL2q1VqqUcPdPE7fHRMmoEIjGKmW12b1xyPCoQ+AIhDrfXkUKSnpihmNmlnDsgPjKOLxhm9sRZSrkDtq6dZ/bEGbavXximKPyhCHvr1/AeBAhFYpidFpmNG2Q313B73PiCIabn4rjqX+LpT+1y+mSZWKQ9fB96PcHG3hSvXxrha19p02xpzBxfAinxBiQen59SZg80sHo98vtbBMNxEIK2UactBF5fABD4/AHcXj8ej6/vJiuplwr9NlxHhEgJy099GAS8/rUvUDjYZv7JDzAxd4zNq991hv/125VbRg2vL0Sn3UQISTw9QTQ9SiAUJRxPIvrW7M2+QBp0Ox1NqQycSOHew9oUDxaXJkiFvYyEvYyEfaTDXlIhz7ua8ngcEULw1HSMhXSQr13PsZE3HvaSACVEFA+Rt9Lt8kbU2l1e3SjxpRe/TbVUHLagHp2PcrTTYCBKosmRYUdKemqOQDhGKJqgXi3iDYQByG6v4/MH8YfC+IMR2objsNltt9m6fqE/i2QabMn+2hWCsSSLTz7L7PEz3Dj/MpmtVTxeL5OLJ0mNTg1TJK/n/4xYapzM9iq1wiGRlJMm2Vu9QsuoMbFwgsmlk+ytXUMA8ZEJWkaN3O4GmqaRHJsCTVDK7jsXwbbo1K7jo8TJp+eZmheU8+fotFt4fCECo22qpSrd5h7CPcKHPv4jnPvaAcXMJUqZaxi1Fm5/GLNlsLN6iU6zxdLTz2F3MgRY5fTJLJNjHUaSVU6ceIV4pAofvPkemB2N8xdcvPyqn0L7o9hanNzOBu1Wl8ToBNHECO1Wg3q5RLfdwhPw0ygVELqO1e3Rbhm4dBcujxekJJIawe3y0O12wLYRLo3k6BRIidzfQgjHZbWY2XOm/i4cZ+3iq3RaBhOLJ1k68yFajUo/laNTyuw5Qiw1RnJsimJ2H38ozPypp28Z9rZ09jlGZxapl0uMzS3fMe9H8XAIenWSQS/p8M1/iYAHTUU53jYRn5v/+qlJrmdr7JfvPsn53UQJEcVD4367Xe7G6uYO53crZLp+yvlDqqXiMCg+HLilCS6+9CUkgoUnnh5+uh0c02zU2L1xGYRGKOoMe2uUSyw++SyHuxvsr69QyR0QH50EKYmlx5lcPMF3vvan9Mw2TQTheBJ/OEowliSWGnVa5YQTkUmMjA+Ntkb701wvvvRlpG3T7Zpg27i8PrBtLn/rKwRCESYWT+DxBtm4dA5vIIjPH6DVrCElzJ48S6uyyUhslbnpGtMTFeKREpFgHZc+CLO+5nw5ea8r/2957qdu/Y5tO50rPUtDSg2/70to2t3TDLYN2XyQw+opzl8K8fq5Ho16E5fLQ7u1S6e14gzTm10gHEvjC4fwh6MUD/aoV0okRieHRaBto06n1cSXHAFpMzKziMfjQ2ga4/PHaRt1mrUye+tX8fqDRJIjxNJjVPJZqsVDZrTTgNO1cuZjn2XpzIc42HDOPzrtTMIFCTbMnXqaSCLF0tmbXSiDYlKEdDpXlk7d9TUrHiy65tRxxAMeYgE3iaBn+C/gUdvUg+LEWITjo+GHvYwHK0RefPFFfv3Xf51z586RyWT4wz/8Qz73uc89yFMqHiPuZqN+e/fL7TQ7PV7bKvON87uU8ofD4tPBrJSj81sEglajRrtlcLgduWUy6Or5lynnM3TMFrsrF2k3aviCIRaefJZGtcTe6lUmF0+AEFRyWdotg+njp9m9cQWP24vH66fTajoOnbbN+NwS2HCwvoLZbhJLjxIfGaN8eIA/GCa7vcbV116knM8QT0/gC4ZIT80RT0/w6pf+gHazgdvrxeMN9l1ZE0zMH0doAprfZW50heOLe0ykM9ztg6BlC8yOl54dpNmUWD0LTRdIu4fbJdBdNh43CDq4dAuXW6IfERqaBh6PjYdb88ZGUyd76OYwH2BnF9bWXFxfdeH2jeMPh+i2W8RS4xx75jRrl16lmN0ddhh4fAEm+4P2Wo0awViSbrcNUjK1dIpOu8XBxgrl3AFIidvrw+v1D1NIoWiMD3zqx3jpT36H7WvniSTSRFNjLDzxLFLC1tXvktvdRCI5+7HP3hK1OCo0Tn/k02/YpfJG81UU7xyaEAQ8OkGvi6BXJ+R1Efa5CXldRPzO7bDXpSIcD4m7tf2+2zxQIWIYBmfPnuVv/s2/yV/6S3/pQZ5K8ZhyVIwcTcfcLkJaHYvvbJe4sFuha0mC8TSWLe+wJW/2w+yDmR6nnvsk2e11itk9mt+skZqYxaiW2Lx6HrNpMLl4CqSkUjxElHK0201yOxuMTM5x6kOfGHaT7Fy/xMt//p/pmm0CkTgzx5+k3WxQyWUoHGwzc/wMrWYNoQmMSolYOs3CE89yGIlRONjl0re+QsdskRibJp4eG46xf/XL/z9cLrczXl1K9tYuk56YY2wyzlPHX2cm9lVG4tlbrkWxEiFbnGBjO8T1qwbZrAstsNT3MhHUS3kqhUN6vQ4ul4eR6XkalRKlw318gSA9q0c1nyWWHsWt25jNAqFIkOWzT5FIx9m6co7DbJ1SoYNlCTz+AJ12E6vbo9Nugujhch/SrFcZm1smPTXHtddeJL+/BYDL6+0X5sLI9AL1SpGWUSOWSuPz+/EGgwihUS8XcHk8hONpApGYU5PSahIIRQlEYzQqJVbOvYQvEGZkeoHE6ARjM0vDbpUzz/8gq+dfwahUbrk+tw9yUzwY3LroiwsXIa9rKDYCHp2gx0WgLzr8bv2R2OwUjy4PVIj80A/9ED/0Qz/0IE+heEw5Wh8yiIQcnbkyiIo0Oz3ObZe5uFclf5gZ1ns4I97zNOsV5/jNFaSUhGJxcrubbF09jz8U4dlP/RjheIpXvrjH6vlXyGytIYBy/oBgOIY/GKZl1Jw00eYK1159keTEDCc/8LGhrwa2pGO2qZXyTCyeIJpIc7i9RjQ9hi8YppLPcu21bxAfGcPrC4KA/O4Om8HXSY7PIrR9OmaLXreL2WzQbhpMLp3iy7/7L9m8fI7xxeNMzC1zsHkDt3mO/+rT3+DJ4/u4XU7EwrI11ncnuHZjnM3MIvmCTjm3T9c0iaWO0+pW6BaydNptQrE4IHB7vfS6Ju2mQTmXodWoYlk9jFoVb8BpdS1lDzANg7GFY/hjU1y/lEWIQ7odnWKmjqa78AfD1Et5pO04x7o9boTLjcfrR9fdIBhGl6TVY3r5NB6fD6NaxuMPIIQgEk9R2N8GYHLxBMFonJXXv023bTK9/CS+UJjc9jreYBifz08hu8cTs4sIIdi+doHUxCwnP/BxIonUHa2yy089R62cV90qDwCfWx+2u0Z8bsI+FxG/ux/RcOFz6w97iYr3CI9U8s00TUzzpgNcrVZ7iKtRPEiO1ofAzWFg+XyefD5PMJrg2+tFMl0fm9cvI4QYOlM26xVsy6ZlVNlbcybZjs8tO6PiJVQKh9RKOUamFqj1C1YlzvMb1QKhaIpAOAZCsLNyEbcviFEpYTabSNui1zFp1qvk9zcpHjhj15Njk0wunSCeHndqG5oG+d0NZk6cxWw1Odi4RnxkgvjYBGarSTmfIbO1DggquQwebwBBy3FptS2+/Du/yeHeBh5/gEbxkODUNj//l64zPbI9vCbbuwGubp3l0o0FcI3gCwbJFzYpH+7TMuq43B4QGt1OG9Domi3qFUk4liA9PYs/GObVL/8Re2tXcLk8RFOjmG2D4sEOZtOg1+3g9vjwB0OkZxYwLr9OMbPrGHkFQ5hGw/FXwbEo9/iCePx+wrEkbq+PrtnmYPUa3a6JrumMzi2RHJvCGwzw7A/8KDvXL3HllRdITUwTCMeG17xeLpIYmSAxOoE/GCEYieMPhilldklOzIAtqVeKjM8fAxiaqt0+QXaQflFRj7ePEBDzu0mGnHbXeNAzrNNQQkPxbvFICZHPf/7z/MN/+A8f9jIUb8CbdblkMplhhONujx/tghkcc/HiRQDOnDkDwPrOAau5BhXZptez+rNMnDHuAJqmDT1AmrUae6tXAIkvGMLnD3K4s0mnbTAyNY8/GOblv/jPjsFZs0nXbFMvF/B4A0QSKYrZPfJ7W+guDwhJq17BEwjS63a4+K0vE0uO4vEH8PoDxMcm8AcitBo1mo0ak4vHKQYCZLdu4PGHeOYHfozs5g0ym6vEUqN4/QGKh3vsXL+Ixx8gMTZFo1zE43HSFrndDbpmmY99uMZHnrnO5LjTAmvZGt9+JcLXvjVNoTpJs14hlm5x/JkJSocH1MtFWs06kXiabtekUSng9voJhqN02m26ZotOu8X08mnCsQQXv/kV6pqO2TYw+zbsZtMYzsaJjozRMuqsvv5tApEYuttNs1Yhkkjj9Qep5rP9667j8fuZWT4NAsrZfdAFUkjiIxMgYPbEU5jNOqnRacbnjhGKJsjurBMIxYY1PAcbK4T7gwAHfpUSyfjCMtmtVYKROJFEeigyjrbOHkWJj7eOx6Xd7DwJ9btPgp73vJGX4tHnkRIiv/Zrv8av/MqvDO/XajWmp6cf4ooUR8XH7V0uR9Mpg8m2b7cL5uKNTa4e1Nir9BD4qJXzwzHpgymvV175OoFQhEAkws7KZSqFLIFwFID9tWtOAanptKK1mwbtZgMQ/c4YiKXGcfv8VPJZCtk9kE7KpVMp4fJ48PiDBMJRzKZBrZSjbTRIjE7inQhSzhzgX4yQnpylUXVcWH3BCEhoGYbTSiIE3VYTJMRHJyhmdzHqFZACrz9IemqG/P4O5f3v8vEPbfOJD+8QjTjTX1ttF69dWuYvvhzFaMfxeL0g2iA0Om2DUu6AVqOG0AUul4d8ZtspFB0ZJz016fie2JJur0vhYIfXv/anhBMp3G4P4USKwv4O+b0tpLTQNKdV1uPzAeAPhsnvbdFuGnh9AVxhD7HUGPQLV3tmB8vukhiZ7CfFJG6/n/zeNumJeUKxOI1KiVopx/ypZ5zfm40VJhaO39GFci8Bca+CUsVbw+PSGAl7GY34GI34GAl7iQXcqlZD8UjySAkRr9eL1+t92MtQHOFuLbYHBwccHh5iWRa6rmNZ1h0zXgbH36sLxrZtopOLvHD+BrmqMwMmknCmjWqahm3ZGLUKRtUZgS6QlHMHZLfXyO1tEEuPkRibchxFz32DYCSO2+3F7fc5Nt9A2zBoGTX8wTCeKR8en49aKUezWqHbNdF0Fy6PByTobje9TgcQdFpN7J5Ffn+bbqfN3MmnGZt12kFDsQSbV16nbdSZPn6awt422e116pUS4XiC/fVrgCAUc4pHzbaB2WqQjFX42Gdf55nTO3g9ziZfrnh56dwyX30xxuFeAShz4oOn8QWCtOp1JhdPsLd6nf3VqyQnZ0iOTFIr5ui0WuguFy63F6NaodtuExuZIBxPsnnlddYvvYYvEGb+iWcIxhI0a84wPRB4PB6Wn/4wtXKByuE+xewemu4CJBPzx0GA1xugmNvD5XLjD4ZBgsfnRwjppIaaBsFIjMT4JJFYkvT0PK1aldLhHonRKRDilgFvigfHINJxVHjElehQPEY8UkJE8ehxtxbbw8NDLl++TDqdJpVK3SIy7qcLxrYl17N1zu102djOUq22h4Po4GYERNM0auUie6uXkVISCEedAL1w/s+oVvD4gpRz+7SNBl2zjdvjJ5Yewx+KUTjYolmv4PZ4CceTNCplmvUKvU4HTyBIt2qiu1zER8YdwVO+6UWiu3Q0lwur26VeKdJuNpyJtbrmTJzVBInRKQSiH5WRCAGNSolOt4NAsrN6Gbdb58PfF+D5D65xavlweA02t7x85RvTnF+ZJLu5BaKOx+sjlh6neLDD0tnnOPXBT/D6176A1+/HbLfYvPw6ZruJ1xfAH4oAkvz+FuFYgkhqlEo+4xiCJdJOp0qjws6NiyTS4wjNha670XUXbo+HWrmAS3fhj8bAkqAJRmcW+x4oNrg0pC0JhGOcef4HKWZ32bpyHpBOG27HZGR2kZGJOUKxOOnJOfL7W+ytXqUVqjEyPe/U7Kgi0neUiN9NKuQhFbqZYlGRDsXjzgMVIo1Gg7W1teH9zc1Nzp8/TyKRYGZm5kGeWvEOcjdxMRAhd6sZuT1tM3jcsiVXD2q8ulWi1rpzBszR+9HkCNVijla9QqtRp2O2KOxv9Ws2ggTCYbqdDuXcAfVyCYCu6UQ4KoUsXn+QTrtFIBRFd3toGXXq5SIut4fE6CTNepVOu0kgHCWWGicQjlIv5umYLQSCYCyGrrsIJhL0OibFzC6+YBBfIEy7VWdq6TSaJti+fhGz7UzaLecz7N64jNvjJRSs87Fnt/jU9zcZSfWG1+b85Thf+Is4Fy8Jep02tnUDW1r4AhFiqXHG5pbJbKyys3KJluEUxSIlXp+Pg0oR06hDcoQTz36UerlIdnuNSj6Dy+0hEIk5E2ZjCSYXT5LdXqXTapHP7GBbPRLjU0TiKcr5LNVCFl8wTDQxQq/XBWkjhMDjC9DptCnsbTG1/ATJsSkalTIzx07TNhrUinlGpmeYOX4anz9EOJ4YDs5bPPNBgpEY0pZDfxc1ZfatowlB1O8aFo4OjL2SIQ9elyogVbz3eKDTd1944QW+//u//47v/9zP/Ry//du//aY/r6bvPlq8/vrrSCkpFApDEXK3iMfRKbhSSsbGxikT5JXNErt7e8MixaPTcAffq5UKSGn3LdhfppjZAyHwByNc/OaXcXu8zD3xFNVCnp0bF2k16viDEVpGjW6riebSMVstpJTER8eJpcap5DNOtMTrJxiJMjK94NQ0lPOYzSZef4CJhRMcbK2Q3VzF6nYIRmO4PF7cHj+6240vEHQs3cenmZw/QbNZxbZsqqVDinu7oMHYiMXpExmOz2+yOGfQL3Gh2dL57pVZ/uTP/KyvGPjCEcKxBMXMHpXcAd5AiNHZRQACoSiTy6e49srXAXj+x3+GZr3Kt//s9zAqRRIT0yAlqck5UuMzHGyusLtyCbfPx9jMEsnxaaSEUnaHbsekXi7RKOfwBEI88dz3E0+PsX39MlvXv4vH52Ny6RRTi6fQNJ1mvYrQABv8kSjJsSlnBgvO+xhJpMls3UDakhMf/NhNB9t+S7USHfeP160R8TmtsUf/xQJOq6wy91I87jwy03c/+clP8gB1juJdZBDhKBQK5PN5RkdHeeqpp960JuRbl1b5v794DgJxIskRBE7tgNDELZGQg40VJDA56K7YWqGY2evXGWi0jQYj0wt0WgZbV84TjMQBkFYPy+o6tuACGpUivU4Xt9eL1etRLxexej1aRh3N5WL6mFN/UT50xr9HptJkt1fZvPI60dQYkWSaai5Lt9vB4wvSMVvYRh2X202tXKBjtoiPTlDK7tMzNlicLfGR49scX2owPdW75Zpdvurn69+Mc+HaKNVSHTDR3E66p9sx6bQNXB6fk2pyhvSS39ty0iZuD7H0KMWDXfY3VuiaLXyhCKnxGTpmi8rhAZ1WCyltpo+fpmu2KB06s2c8Xi/djtOaG4471vUujxuz1SQ1MUvLqGPUyggN0uOzLD75LKF4kka5yPrlc4xMzXPiA88PhcYbzVxRtR9vjEsTRI4IDOe2i4jPua1aYxWKm6gaEcWbMhAXuq6TSqUYHR3Fsqxhuy7cWsA6MTGBHorze9/ZZa8sqZk9GtkV4ObmNShkrBVz1Mp5GrUKR5sI83vbIJyJtdntNdCceTH7G9fJ7qxTrzoCQ3O5wLax7B5GtUzXdDw17J5FNX+Iy+shGI4TSabx+oLUKwXMZqM/7bWB2+PD4wvSatQoZXfQ3R48/gDStjHqJQSC1EiAqZF95mYl8wuCqYlLjKZqRCO3Cg/LgqvX/bx+Mc658xHKVU9fYFjompt2u47P78x1ONxdp9fukJyeAdvp8kmMjtHrdikf7jGxcJITzz7PxW/+F2rFHMee+Shjs4tkt26AlHR9PrpmE7fXz9LpDzgtuOdfptmoUit3SI3NEE6kAMncqTBto0HxYIfd1StMH3uS5Pg0xYMdEuOTw86WgeAYfHhQQuPeCAFhn5tE0E084Bn+iwUdy3JVt6FQ3B9KiCjuydEIx9Gaj9sjIYNjE+lRrld1LlzZYRAMi8TT1MslaqUCkX4qxqiXye9tYktJKBJnfHaRernIxW9+mVa9Nhwc12rV8foDSBua9Sq+QJhwLMnhzhpm00BzuXHH/XRbJl3TRGguhNCwbQvbthCahu5yMf/EBzCbBtmtNTpmC4/PTziepNtp4wsEcbncWGaZ+fkmy8dCxAL7TE10mZ21iceLd702lgUbmxpXrnm4eFFw8aJGq+1B6Ca+QJtwLIDL46NtNLDsLj3TpNo00F1ueh0Tl9cLlhOtcLk81MolzGad9PQCSMmFb36ZnmmSnJhlbGaR1PgMrUbVEWmAROD2+kBzUlfTx06T3VqlbRh4/AGe+eQPk91eQ2iCQCiGLxACJKFYghMf+Bj7a1eplQrUirmh6FBD3+5O2OciGfKQDHpJ9otF4wEPHpfy4FAovleUEFHclaM1HnerARl8f/DpeXx8nLoW4ssrOQyzectzSSSReJJaqcD+2lXC8RTNSoW9jWskRicIRWOE4ynqlRLZrVU8/hCTC87At41Lr9Ex24TjaVpGg5ZRY2x+mXq5hNBdtOpVivvbaLqG2+vFtiyEpiNtG4mN0DWCkThenx+kjVEr0zFbBCNRTj7hYzS6x/x0mdnpFqlEc1jXcTvZQ439Ay+bmzY7Ozo7+252dgS1SotQNI7V7WK2DCRNBAJd00GkaDfqdDpO0azV62EaDWzbwuML4PJ4MWolRyAEBI1ygVA8yZmP/CA7KxfotFqMzS1x7OnvI7e7SeFgB38ogsfnByA9NUdybJq9tasITfDMJ38EieS7L/z58H1ZfurD1Ep5Iok0EwvHqZXzhOMpwBEd4buYhb1f0TVBxHdrkWgy5HxVRaIKxYNDCRHFXRn4hxwVIQcHB+RyuVt8QwAaZo/fe/Ei20XjrgWLAoFt27QaNXZXr5Aan+p3rbQoHx7QatRZvfAKxcweHo+faGqEYnYXfziMNximnM+S3VnH5w8yfew0tWKBxNgEtbKHrtmka7awLfD6AsNz2paF1tOwu12MRoXs1gqtepYPf7DJ889bnH3yIsFA9461VqoetrbdbG4JNrcke/serl+p0+loCOFs2C6Pjt3tDLfvtlFDd3mdKE5PInSNjtmh1+nQ6bSwel3MdhN/MIw/FKFZKSKFwDJNYmMTVHIHWN0uEwsnWTr7QbavXUAImFw6SatRJ7+/zcj0PDe++23ahsGZ5z8NEnJ7myDAHwozCD9NLT1BJJ4ms3lj6EY7tfzE8PXdnm55lNIvg7qKiN9FwOMMS/O4NNy6QBNimOqwpcS2JV1LYtmSrmXTtWznti2xbBvLdiJq/dIbNCFw6QK3ruF1afjcOv7+cLaQz0XE5wxuU+kUheLdRwkRxV25m39ILpfj8uXLPPnkk8PHrx7U+KNvXyafzfZbbg8RiLsWNW5du0Bhf5taMQtCJ5IYQWiC/O4m+xvXQcDkwkkcE7A629cv4Pb6qOSzWL0eVrfL7uoV2kbDKb5sNtGEjtZPdbTqNcKJFGazge72EEmOUC9mmB9f44d/aI0PPNvD67n56b/VgmsrHq7fCLCbiVOsjpPPdygcbNJrd/FHInTaLcyOU3MidBsBTleOLXG5XbjdXqxeB6vXwOpZCKGhuVxomkYpu0c0Neq0xLYMrG6XSDyFK+0UjlpdRwh5vAE8gQCJ0QlA4PX7iaZHee4zP8nahVfZX7+GPxhhcuEECBibWyaaHCUUS7B++Rwzx08TiiZuqe2IJEfYX7v6yBaL65pgLOJjPOZjLOIjpfwwFIr3LUqIKN6Qu/mHPPnkk1iWxfr2LlcqOt+9tnFXLxBg2NoZSY5QK+dpGzUkNuV8FmmDN+AUhVaKh+huN+FYkk67RX5vi3AyTcuok9lYQeg6vkCITrtNtXgNJHgDQXyhMLrHi9Zv17Vlj0bFKTCNxgT/9X+1y6e/3yCZvLkZHxwIvvVtndfOBbl6FTpdC5dLIzEawrLLtI06PbODcLnomm26ZhtNaNiyg+w5dRn0N0tdd2NZPayeU4+iaTout4dgJIrVs2gbddrNOsFIHN3lxusP0LN6+AMhkmPTVIs5jEqJ5MQ0ozNLlA73KGb3OPuxz7B05kNIJM/8wI8SiEbJ726x8OSzt9RwTC6dIhxPvWHr7KNW7xEPuJlPh5hLBpiI+dWME4VCASghongTbjcne+qpp/jWpTX+9Rdfx+zZSCmHIgQc8aFp2k2bdtumXi6Q29lwjLn8QQSCSvGQ4v4utXKeXsckMTaNx+ulUjyk02nTabfodbpYtoXLpdM12zTrZXqdDpqm0zLqSNvC5fYSTqTwtPw0KiVCoTY/81d0fvSHm/h8jgCpVuGLXxJ85Ss6m9supA1uj8Dj90OnhmV1KWZ3nKiLZeFyuxHSptNqO6F9IXB5vPQ6NydDa5rupGJsC9u2+8e4CSfS6C4XQuvh7nbpdTu0m3ViqXFnFo3Zxu0LEEmOUC1kCcYSjM4uMrV4ErNl0O20Mapl6uXCUEicePZjhKPJu0Y3HqXUyt1Ih70sj4RYGgmRDKnxDQqF4k6UEHkP8mZTco9OwX0zjooQs9vjd164wGHXPxQhQtyahqmXCzTKJcLxJLbtFIfurFzGbBmAU8rQMVv0Oh2ypTXsXo/01DyTi8dZPf8KCAiFY2S3N3B53EN/C8NwxtH7Q2E6Zoeu2cLqmIzOHSMxPkl1/1X+3z+n8ZlP23i9zhyXGzc0/uPv6Xz72wLTlNiWjdfnwhXw4guG6bSahBNp2s067XoNoWkgcXw+bAsJeFweNJ8H2bXo9XpgW+gut1Oj0DH71wD8oSiJ8Ul8/tCwIHRkco78/ia+QAi310ssNY7QNMqH+2S3bjB9/DTHzn6YRrWMtCVnPvppGpUyLaNGvXJrp86jFt24F6mwl2MjIY6NhokHPQ97OQqF4hFHCZH3IHcbVAeOqLhw4QJjY2N3FSK3i5SjrbtdT5T/9OJFDg7WnRkifREipbyl/XPQqlsvF0FAMBJHaFDM7IKUhOIpQNBsVOmabXqdDpV8hn2Pl3arQatRo1bKD0fVI6DVqGF1uwhNo2u60d06XVMiXC7c9i6f+dAqn/l0C7fbeR3Xb7j5d/+Pi+98R2BbNpqmIUQP3aVjWT00S6dZLSM0zTFE63YQugtd17Asm163A7bE7fUiXC6kbWNLG38o4sxhsSTdXhvLstE1ge7yEIhEcLncBCIx2i0DZyZLArfHC5rA7fHhC4ZYfvo5Vr/7CoWDbSYXTnC8bxxWK+eRtuzXekA4kXygvyPvNKMRH4vpoBIfCoXiLaOEyHuQuxWaDkTF2NjYHWZkcKvoOHo/NTLGtarGxb099FACTcuS2VplfG55GK04OmV1IEhe+eLv0zYaTCwcdya3en14/EE6LYNaOQ82aLoLTbdo1quUcgcgBaZhYNkWvmAQs92k225hdbtoLh0pbVrNOpqmMz3j4af/G5NPf8oYCpBrKz7+3b938fo5CVLQMdsIIZG2htWv4XC7Pf2iUonHE6RRrdAxm7g9XizLxup1wbYRugvbtpEdEyHA4w/iD4Wxuj3cPh/NWplWo4GmCWIjE3h8flxeH0hJOJogGIsTisVJHD/tdPBoOrZt0axU+cRP/HUyWzccm/m+iBvU1zwuVulet8Z0PMBsMsB8KkjY537YS1IoFI8pSoi8R7nXFNy72bIPIiVSyuHxPW+ML2+Z7O9vIpE0ykVqpcJQhAgEtXIB7Yj5RiQ5Qr1cAOjPiQGk43nRbhocbF6nWati2T0E4PJ46bablDJ7uL1e3D4fsm3Qbhp0222sbgc0DU1zYfV6TI73+NmftfnBH+yg960dvnte43f/U4BLFxwjMyGg2zXBtpCahtQ0dLfT+dLpNPEGwkjbxmw16XZaCDSsbg/bdqInusdDr9vFkjahSBzNpeHzRwhEowBUDp1rF4xECUaTpCfn6HZauD0+QrEEIPH4gkzNn2BkZhEhwLZtmvUKtuWkjY4/e9NC/ei1+17QNYHXpaFrTrurxGlh7VqSnmXTs99eB43PrZMIukkGvYxEvIxFfaRDXtXholAo3hGUEHkP80ZTcO8mUgaRklwuR71lst3ykrcCwy4YTdOolQsITSMcTznFlsVDNE1z0jCA0AQHWyvkdrdot5s06xVqVxwzrTPP/yD769cde3UN7E7PSb0AZruF3esBErfXhy0lrUYDISVaPzIxPtrmZ/+a4FM/ALrubKjf+Y7G7/1hhIvnLcx2y0nB6Dq9TgdsC4SGQKDpGl6vj5ZhYNsWPbONEIJOuw0CdF3v28XruFwerF4HpMTlcv7zkBIiqTRut5dKIYMnECTkSTI2t0w47rQLR1MnqBYOiSZHSY5NARJ/OAY49R1O5CM9HBAHb194hH0uxqN+RiJeEkEPUb+bkNf1pvNLLFvS6dmYPav/1REnA98NAE04gsbj0gh4XAS9ujLzUigUDxQlRN7DHBUhg0jHUTFyezfM3v4BL3z3OpczDTqd3rDrZfB1cuEEAPvr16mXC4TjKQLhmFOQev0S/mCYVrNOtZR3hsJZPZr1Ks1GFV6CbsfEGwjRqBRpGXUEAo/Pjz8Yotmo0Wk1nXoMq4dAIDRYWtL46Z+y+OQnQNOcDfzlVzR+53fcrNzQ0V3g9vkRmkavayJte5gGEZqGrruc0fSWRSAUdtptu1263Q5Cc9JDIHB7Pbg8PmzZQ5MuXF4fgbATAXF7fbjcXrrdDrrbS3pyksnF4/iD4b5hliAQjpAcnyQQijO+4Ph8HI14fC/RDk0IphN+Fvqtr7HA26vB0DWB3+MYeSkUCsWjghIi71Fun4J7t3TMQITkcjn++KvfpOSdYLvhodPpYdTKNColNE3DH4oObcEHqZeBa6fQBMXsPnsb1whHk3TMFo1qGY/XT69rorvddNottq9fAEDrRyyk5QyqE0Kgu9xomouu3abXqAJw9imdv/L/snnuuZuD5b71LZ1/++8F6+tuXLobIWyksBEC3F4vvW6HXtcEJAgdXddwe3xYnS7eYAjb6tGtVbEsC13TEbrHES66RiAUoWOa0HOKVBPjM1jdLl5/gImFE3RaLYxaidj0Iiee/Sij/dk4Rq1CKBonGIsTjqfecFLt22Es6uPUeIRjo2ElHhQKxXsWJUTeg9wuQoA3nJJr+2P8l2s5Llz8FuNzy04aoZQnGImzu3IZXzBEIBIjkkixv3F96G/RqJZYv3wOTdOo5DO0jBqF/W28gSBIQbtVp9fpODNYmg3MpoGU0ula0QSa7sLrD2JZlmMc1mkjLYsPfxj+6l+FJ5900jaWBS98XfB7v+/lxg0bKS1cLonudQbFATTrFaTtiCpnzkwPl9tNOJFC2hadtkm7H4GxpSN+hBBOGsbqEEmO4Pb68XS7WL0e4USKXsfEGwhy8kMfw+cPUcllCCeSTCwcJxCOIZFMLBznYGMFW0oi8fQ74unh1gUnxiKcmY4yEvZ9z8+nUCgUjzpKiLwHudugOnDEyOHhIdlslsmF47yStdks7OIeWWB8rk1ma5VGtYRt2xQzu7SMev8JoVbOo2kaG5fPcbi7TnpyHrPZILe76aRebAhG47QNg47ZxGw6viGddpNex0mZ2LbttMvaztRYITS67Tp2z+QHfgD+yl+BhQXnlJ0OfPGL8B/+g+DgABAmmq7j9vixrK5j7x7SEYBl9bAtG5fbje7S6XUtpG3Rbhn9tFKXXruLrrtwuTy4A16EptMx23hcAbodE7vbY+r4aUKROLm9TVxuN4FgDCybYDhGIBIlGIo5XUD0B/n1hUetVPieB8eFvC7OTsc4MxV901oPhUKheC+hhMh7kHuZlbmCUXJuyfWdLlLeHPo2iHIc7myi6RrNWoWp5VP4Q1GatQr5g20EgnbToJzLUMzu0TYaVIs5yvkD/MEop7/vB9i6dp7cfg2z3cTudeh2ekjr6HA5AQh6nS5g8iM/1OGnfxoGmqnZhD/+Y/i934NS6cjPSBu710O4wRcKYZkdTKOO5nLhdnmwdekUv0qJPxQBKZC9HsLtRaCjaT0kNrrLhy8YQXe78XY7oDktw5HRMZbOfIBWwxFf0fQo/kCIVrNGIBLlxAc+dtf22qMty2+HRNDDs7NxTo5H0DXVhaJQKN5/KCHyPqHe7vKn377Cas4gnEjf8fj+2lVsyyYUjWHbNoFQBNtyIiOBYJh2s87e6jW8fj/hxAh7q9cpHGyju9zoupu2UePSy1/F5fbQqlexux06g+6V2/D74cd/rM1P/RQkEs73KhX4z/8Z/uiPoGE4RabgCBiha8h+W0en02b6xBmMWpny4R5Wr4cQOgInNaPpOrruJjY6QafdBAnNWgWP349tWXj8ATy+AGOzC4BGYX+L5Ng0YzNLYMP08pPMHBfUy0XC8STBSAIp7VtM294JJmI+np1NsJgOqjZYhULxvkYJkfc4Pcvm3HaZ//Kda+yu38CWkkkpb9lUr5/7Brsrl0iOT+MPR2nWq/jDMVqNKpmtFYTQQNp4/QGyO2tkdzawel2a9QoAE0snyG6tcrB+Dbfbg3C5sHrWHSIkHIaf+AnJT/6kJBJxvpfNwn/6PcGf/4VGuzk43nZaaAEQSKsHCITuAiTbV19ndO4YXn+IRrmAZXVw+7xEkilcHi+67hlOtu20DISuEYjEiKVGCUZiePwBOk0Dj9/HxOJJvD4fvkCQ1PQsE3PHkcjhNNup5VN3+H28XYSAxXSIZ2bjTMb83/PzKRQKxXsBJUQec+41V+bctXVevJGHQIKeDbaUFDJbtGoVlp56bjgqfvf6JdpNg2a9xsj0ApMLJ3jlL36fdsug2zapFLL0+sKgWSvTqFTwh8K4PF6Mapn186+gCRcut5tet4uweljWzW6XYBB+6qfgL/9lCASc7+3swO/+LnztBRdmuwfChr7guRWJ0F14PD40XafdbtI1TQq7W4QSCTSXG+ji9QYIROLMHDtDbm+DYmYXt9fH0tPPgdSo5A8Ym1vmmU/8MLVykb21yyBh5thppJAgYXzu2FCgvZPdLz63zqmJCE9NxYgGlAOpQqFQHEUJkcecu82VsWzJH3/rCi9dvEEkMUIkcHMzbdUqFLJ7NF+qEQhHMGoV/OHIMBJiVMtE4mnQNHZvXKLX64KEavGQTqdFt9mi1+ti2wF6HROr16HbboOu4fUF0HTbGQ4nbdxu+NznnC6Yvikpa2vw7/89vPgi2LbA7fOgu7R+BOTuUQdfIIjHF6DVqDkVJi4X3a5JvVjA6wvg9vnQdRdGtURuz5nyO338NMnRCSYXTrJ09jnWLr7K+sXXONzdYOnMhwjHEyAF4UTygViqCwFT8QCnxiMsj4bUyHuFQqF4A5QQeYwZREMmJiaGYiQUT/H/fPU83z1/kXAsecun+UhyhEA0hsjtsbNyESklI9PzTB87jVEtUc5nOfeVPyaUGCExMk4sPUF2ew2X14PZMmgbDaSU6LqOaTRAgNV3RMWy6JothOZCWj0+/nH4xV+EsTHn3Nvb8K//NXzjG0dfgXQGzN1WIiFcLmTvZkSl1zERQsft9eENBHG5PRjVIpbVxS28TC+f7vuXFGkbDcbmlnn6Ez9MpD8BGOCZ7/9R54y2/J4LTN8IIWAi6mdxJMSx0ZCav6JQKBT3gRIijzGDaMjExAQTExNcurHJi6uvsbm2igZMLhynWjwc2ooLHP+MSi4LArptk731qwyUQK2Qo9moYtSrlDK7JCemKWR2KGf36Q5s2IWgZ9tAF4TjKjrA7vWYm5f88i/Bs88638vl4Ld/22nFtW/PukC//uOWV4W0nKFzmnAiJV3TSQtFUmPERyYwqmV63Q5Wr4vuclMr53j+x34GgAvf+BJISavhGI1pmjas7xiIkXcKIZyul8mYn+lEgJlEQLXeKhQKxVtECZHHiNvrQY6alOXqHf70lRW6lk27USU1MQs4QmEwKya7vcbB1gqVQpauaeL2eGg1Dc6/+OfE0uO4vV6khF7XpF4pcrB5nVajTqfVxOX2Ykv602n7RaXyZjLF7Yaf+zn46Z+2cLkcH5Df+R2nDqTTuf2VvAGaPlQruttNMBylWa8h++frdUzaRgOvP0BsZBRpgSfgh77vyXOf/UkA1i++BhKiyZF3bJqtx6WRCHpIBD2kQh5Gwj7SYa8SHgqFQvE9ooTIY8Td6kHGx8c5v7LFv/79P8OWgkAoQnJilnA8SbWYI5ocIZocYX9jhYOtG2Q310AI3F4vXdPEbDZoVEt0zDbheBJ/IIzb46WU2aVWzjtGYS433a6J1enbp9/G8ePwq78Kc3PO/W9+E/7Fv4BM5i2+QNvum5b5kNLGbLWIj0zg8Qco5/YxW00CkS4zx55k4YlnneF5lmNc1qxVyGze4Jnv/1FGpxeQt3UG3S9hn4tUyEs86CER8BALuIkHPYS86j8VhUKheBCov66PEUcjIIP7566t8yevXMWWgvTELKFYgkgiTbWYw6hVMKplQrEErXoFadm4vT66ZptWs47ZahKMJmjWqzQqRdpGnZnjZ8hur9JuNEA64+st2+p3wdwqQtxu+Ot/3XFE1XXHgOw3fsMRIvfkbt0xwjE6c7ndBKIxet0OAkiOTzN38iz7mytkNlYJhmOMzS/jj0SYXDhBvVygViqQnpghGIkDjjnb/eD36EzE/ExEfYxGVIRDoVAoHgZKiDxmHBUjL778Hf7i9VW6XUkgFHUMSKUjFjRNI7+/RduokxybYn/9OkLXSE5Mcf3Vb9DtmnRN06n9sC00TaPbbrJ2/mXQBLruRmg6Qlj9SMitLC87UZCBJftXvgL/9J9CrXYfL2IoQoQjQKQzMVd3uRFCo9ftkByfJhIfIRSN4Q9FOP3hH2DpzIfYvnqB8uE+8yefGkZ8wvHUfadgxqI+FlJB5lNB0mGvMhNTKBSKh4wSIo8h4+PjbGzv8u31ItsrV4mPTjJ/6mlqpQLNeoXc7iatRpV2y6BaOKRt1KlXSzQqJYSm0aiX6RgG4WQas9kcupNKCV2zBbqOLxbC6nWGwmaAywV/7a85Lbm6DuUy/J//5+3dMBpwl8rU2yIhLq8HfzCK2WxgSxuha4QTaXyBCC6Xm6WnPkQgGMaWMDa7SCieJD0xg1EpE4onh0W4byZA4gE3pyaiHB8LE/WrThaFQqF4lFBC5DFiUKxq2ZIXb+RpdS18gRDNeo1GtYTQBbndTdpNg2oxR6fl2Lmb7SbYkl6vS353E2zwBII0SiW6XRMpbZAS27LRXG5sW9KoVtCEQNP0fgusZHERfu3XYHHRWc/Xvgb/5J9AtXr7Su8iQgCk7EdAJE4axoc/HCEUSziD8yTERsZZPvN9tI06zXqNMx/5tPOjfcFxv4WnmhAsjgQ5OxVjOhF4O5dboVAoFO8CSog8JhwcHHD58mUKhQK7hk4nPMn4fIRwLMnV117k3Ff+mPTUPADVYp5Oy8DtC2K2mjQqRZqNKm3DAIljcd5qYppNNM0x2rKtHqARSaSoFPPIXgcLcHt9aAL+6s/Az/6sExGpVOAf/2P4+tfvf/2ay420bRAC3e1CFzpuj5fk+DTBcBSkxBMMIXsSpM3k0gmkLamV80wtPXHf5/G4NJ6YiPD0TFxFPxQKheIxQAmRx4TDw0NWV1dZ3T2kQJTlpyaJJkdplIu0G3U6Zpu20QAh6bQauH0hYqk0baNB2TQpZnYBCCfS1Mt5up2WU4xqWU5ERGhomk4lf3jLeWen2/zqr96Mgrz4opOKqVTussi7WrSDy+PD5fX2C1AFbo+XaHoM3eWm225z4vt/lGAkxva1CwSicaQtkbYcpmPuB69b46mpGE/PxPF7VMGpQqFQPC4oIfKYMDY2hjcQJtPO4/HhtONurnDjuy9Tyu6RHJ/BFwhQLeRBaAghye9tUSnmMKolep2O40hac2pFpJS4PV46baN/BoHQBPSn3Lq9Oj/7M9awFqRScdIwL7xwj0XeRYQI3YXQBHa3h9vlJRCNER8ZZ3r5CUBgtgyMWpWlMx/qP4VkYuE4tXKeUPzN7de9bo2np+M8PRNTHS8KhULxGKKEyGPC6OgYvbGTRDNdWvUKezcu0WoaNMp5PF4/ZssAIalXy7TqFQKRKNmtNSr5A1xuH7rHRb2Sx7ak4zQqJZ1288gZbKyu4zz28Y/DL/yCxdSU88gLLzgi5GgURNN1bMvCcWU9UtCq646DK6C5XAjh3PaHI6Sn5nB7vIzNLjM5fxwENOs1/OEIEsnxZ58fPs2beYB4XBpPT8d4ZjauBIhCoVA8xigh8pjw2laJlivK5MJxLn7jS1SKh3TaLTxeP7HRCXI7GzQqJcKxJK16hY2L36HbNdF0N5qm0Wm16HW6TtRC02+6ox7h5En4238bnnzSuV8qOS25t9eCCN3drykRoGtg3XwuDYE3EHRu6xq9bg9fIMTS2Q8ze/IM2a0bmE2DZqNGIBQhPTnL2PzyfRehunXB2ekYH5hNqBSMQqFQvAdQQuQx4OKNDf7zVy8RiiWplwuUchl8/iA+fxDTbJPb2cDrDyIQNMoFet0OZsugZ3Xx+oJYvV5/LovLGVJ3mwiZmIBf+AX45Ced++02/Kf/BP/hP0Crded6pNW9eacvQjTdhW1Lp8NGCpITM/hCIXodE/rNMv5AiNMf+TS5vS0C4QgjMwuE46n7EiEuTXB6KsoH5xIElcupQqFQvGdQf9EfQY7OlHFadYtUSwU2rrxOdmsNjz/IxMIJSod7ZHfWaRl1UmMzePx+jHqZZqOCpmlo0kW7UQcBHq8X3R+kVSsPzxMOO54gn/uc45Jq2/AXfwH/5t9AoXD/6/WHowQicRqVItKyCERjJMYnCIbijC8co3x4gNmsI4TG2Nwy43PH7tuAzK0LTk/F+MBsXAkQhUKheA+i/rI/IhwVH0dnymw1PRQbJq16hbULr9I128w98TRCE7QMg27HpNftUMjsgpAU9rfotswjfh0SpKDb7dBpO+ENt9sRH3/trzliBOC11+Bf/ktYX7+f1TqOqMLlwq27CETijEzNMbl0km67Rbdj4vH4GJ9fxu71OPb0h5FIQpHEfadgPC6Ns1MxnpmNEfCoX1OFQqF4r6L+wj8iHBUfUkp0XefK6hZfupbjYHOVg+1VQBKMJWg1GqxffI3YyDix9Dj7a1cwqmXHJbVrYtk9bNsCKXD7/HRNE9lPoXzyk04aZmLCOe/6uiNAXnvtvhfqFKBqOl5vgNjoGF5/kGAkxsd/4q8jELz+tS8AgrmTT/f1kGRq+f68QAIenadn4pyZiqoiVIVCoXgfoITII8LRGTK6rtPt9vjKxQ32dw9oNxvIXo/k5Cy1/CGl7B4er4/9tWsgQXd7aTdzWJ02lmUjpYWUApdL7wsSiyeecApRT/XnwRUK8Fu/BV/8opOSuS+EhqYJdJcHTyBAenKeSDwN2Hi8AXI7GyydfY5nvv9HqFeKhBNv3n47IB5w88xsnFPjEVy69tYvoEKhUCgeS5QQeYQ4KkZeub7Fzu4BmqYxe+IsANvXLlAt5+mZJs16hW6njdvrx2wayJ7lZExwIhCartPtdknELP77/x4+8xnnHK0W/O7vwu/9nlOU+paQNi5PkJlTZ4nGR+maLULxOF5fkHopT/Fwn0XkfU+/BRiP+nh2Ns7SSEgNoFMoFIr3IUqIPGKMj49zY2OHHUNH0zRs2ya3u4Ft23S7HdqNGh2zTbdj0m40aFTKSNui1+sBIDQNENAz+cmfgJ//eQgGnajHn/2ZEwUpl++9htvRdDe6ywWa4wcyNX+SqeVTFLM7tBoGk4vHYfE4gVDsviMgc6kAH5hNqDkwCoVC8T5HCZFHhEGxqpSSlzcKVMslbNt2ZsFIqBayTC4cp1bK0TYa2JaF0DW6RvsWR1Oh6aTTFr/69+Gpp5zvXbvmGJKtrLy1NQldx+V2E0mOEU+PgxC0jTqHexvER8aZOXYGKSEUjd9XDYgQsJgO8dx8gpGI760tRqFQKBTvSZQQeUQQQnDx4kU28g0uX9lGIgnHk+R2Nynns/gDIdA0kBKz1aTbMel22nfYqn/kwx3+/t+HUMhJw/xf/xd84Qv9Bpq3gOZyE4zG8fgCTC6cIBRLMjq9QKV0SLvRIBiNEYzcnwABWBwJ8eGFBCNhJUAUCoVCcRMlRB4hDLPH5YMqCChl92g1agTCMYKRGPsbK+zeuARCIxRPUszs9i3Wb/JX/yr8t/+tc/vqVfhH/wj6jTj3h6ajuVy4XG7cXi/zTzzL5OJx9teu02kbBKNR5k49haZp9zUHBmAy7udjyynGo/63sBCFQqFQvF9QQuQhcnBwwOHhIWNjY3zta1/jO1tlRhbO0u2tUL18jtXzL7P89EdAwOaV1+n1Ovh8IXouN9iW0xorNDRh8z/8D/DDP+w87x/8gRMJse50cX9jNB0hBF6Pj9HZZVweNx6PF38gwuTSCfK7WxQze4xOL96XCIn63Xz8WIqlkfDbv0AKhUKheM+jhMhDRAhBLpcjl8uxX25xbeUGs5qf4v42AG6vn2uvfZ1et0NidBIpBTvXz2NUSyDB5fJgCZNf/Xvw6U87wuOf/BP4kz9562vxeH0EI3F0l4tIMsXkwknazQbl3AGTSydIjk47pmRvIkJcmuCD8wk+MBtXbbgKhUKheFOUEHmIDNp1v/Xq62wZgtTkLN/5L39Mt2OSHJsiGImT29vE4/Ph8QbodFsYtQq9Xg9N08Hq8mt/3+JTn4JeD/63/w1efPEtLqIfCRGaxtj8MvH0BI1ygWrxkLG5JQKBKCNT8/dVCzKTCPCpkyPEAp63cTUUCoVC8X5ECZGHzOjoGAXPKL1elma1Qrdj0qxV8Hj9FLI7eLx+dJebjUuv0u128PoDgE3PNPnbvwyf+hR0u/C//C/wrW+9lTNrxMcmnGF1Vo9Ou8Xh1ipjs8ssPPEMxewuqbFZTnzw+Td9Jq9b4+PLaZ6cjL7Nq6BQKBSK9ytKiDxkXt0q0XRFKOzvkN1ZIzk+Sbdj0mk3QUJ6cpbs9hpGvQrSxuML4nL7+MnPmfzkTzrP8fnPv1URAuFEirGZJYLRBACVQoZ200BKyTM/8KPUijkkb95qM58K8ulTo4TUQDqFQqFQvA3U7vEOcHRg3e1kMhmklEwMhrscYa/c5JWNErVijnLhgEalRLmQpZLPoLs9hKNx8pltaqVDrG4XXXfRrFd49pke/91/5zzHP//n8LWv3f9aPb4AwVgCXXfR7Zp4vD7GZpc48exHkUhGpxcAiCRH7v08Lo1PHFNREIVCoVB8bygh8g5wdGDdUTGSyWQ4ODi4qwhZ39rht79yga21GxSze/j8IWqVIvVSAdvuoWkujFqJZqWCZfWwbRtbdhhNdfif/oFjKfLHfwy///v3v07d4yWSGCE9M0+33caolumkx0lNzDK+sHzfrqhTcT+feWKMqN99/ydXKBQKheIuKCHyDnB0Rszg/lERIqUkk8kMj7NtyVdX8myt3eD6uW9itpp4/UF6nQ69ronV7dJs1rE7HTSXe2j17nX3+F//V4hEHJ+Qf/7P73eFAo/PTyASxReJIC2LkdlFGqUCbq+XiYVjbxoBAacj5iNLSZ6Ziau5MAqFQqF4R1BC5B3iqBg5mo45KkoGx31jrUBDc/w1PF4fHl+A0uE+4XgSl8fDwfpVZK8HSBCCXq8LEv7W34KlJSiV4H/+n50i1TfDFwjjj0bx+UN0zDY+X5DExAx2r8fSU8+RGp++r1qQ0YiPzz4xSjLkfdvXSKFQKBSK21FC5B1kIDqklMOakUH9yMTEBAcHB1zP1Pj6jRyNchGAaMpJh3TaBoWDXeqVItJ2BAiaht01AXj6afjc55zz/O//OxQKb74el8dHfHyKYDhKIBoHW9LttInEU6TGp7Ftm4n54/eMhuia4Ln5BB+cS6BpKgqiUCgUincWJUTeQY6KkEE6ZlA/MjExQa7e4Y9ffglbwo3XX8YfcqIiW9e+i9sbwGw3aRt1JBIhNGTfGtXvh7/395xz/NEfwblz97EYTUfTNXSXm5HpRTqtBumZBZLpKQLRKOPzxxCIe0ZDJmI+Pn1SRUEUCoVC8eBQQuQd4mhNyO01IhMTE1xZ3eLPXrtObnebZrNOo1rEbBsIXadeKVE8uIAtLXpmB6sfBRnwt/4WjI1BJgP/8l+++Vo8gSAerw/d5aHTMgCYOXkWXyDM0lMfetN6EK9b46OLKc5MRVUtiEKhUCgeKO+KEPkX/+Jf8Ou//utks1nOnj3LP/tn/4wPfehD78ap3xVuFyFwa81IKJ7mu0VBuViinM9QzO7RNVugaVRyGZr1Kr1OG9uWWN3OLc/97LPw4z/u3P4//g9nou690N0eJpZO4g+ECYajSCmoVwo8Of4DTMwfu2cERAg4NR7h+eUUAY/SqAqFQqF48Dzw3eY//sf/yK/8yq/wm7/5mzz33HP843/8j/nsZz/LysoKIyNv3qnxOHC0MPUo4+PjNDs9/t1Xz9NoWzTrFeIjE/iCQbauXSS/u0mjUqLXc8TH7ZGQQAD+x//Ruf2Hfwjnz997Hf5QFM3joprLkjozwzOf+GGEJjCqZULR+D0jIVNxPx8/lmY04nvLr1+hUCgUirfLAxciv/Ebv8Ev/MIv8PM///MA/OZv/iZf+MIX+K3f+i1+9Vd/9UGf/l3hbj4hAFs7e3zxSpZG22Lj8jnKhUP8gSCJ0Wn216/TMup0zRY2OAWqt/GLvwijo3BwAP/qX73x+YXmIjYy6viACI1aIUvhYBuEYGzu3v4gqbCXjy4mWUiH3urLVigUCoXie+aBCpFOp8O5c+f4tV/7teH3NE3j05/+NN/+9rfvON40TUzzZlSg9v9v797jm64P/fG/Prk3aXPpNekNKIVypwjjphOZiDi3ydk5O6LbhM3jbXp2Np1H4EycehQUH9vO1+Oc86fi48wzdIq3M7xOkTkuChQQKEixQGnSpG3SpEnTtEnevz9CQkNboKVJoJ/X8/HIw+aTdz6f9zsf2rz8vC8fny+V1UupaFTgo4Mu1NU3oMPXBkmSkGUwoNPvx65N/4fmxqNQKJSIRAUgorFHD1/7GvCtb8V+fvxxoLOz/2Mp1Sro9EYY84qg0WhhtBQgz1YK26j+Q4hFr8bs0XmoKsrhOBAiIsqYlN6nvaWlBZFIBEVFyV+GRUVFaGpq6lV+9erVMJlMiUdZWVkqqzdkdu3ahd2n9Zts+tIFr5SN5sajOLjr79AbzSitnIRWZyOOHdyDQJvnZEnRK4QYDMAvfhH7ecMGYM+e/o9tMOchx5KPoL8NvlYXcnILMHryDEyb980+Q0iOToWrJhThpjkjMc5qZAghIqKMSmkQGagVK1bA6/UmHg0NDZmu0jlRKBTYt29fIox8ccKLPQ1eHNz5Nxz54nMoVCpEIxG0Oo6jw+eBVmdAJNyNgM8DRCO99veTnwCFhUBjI/Dss/0fV6XRwZhbiLKxk2EuLEa4O4R2dwskhQRIyV09OrUSl48twLK5IzGpxMQ1QYiI6IKQ0q6Z/Px8KJVKOJ3OpO1OpxNWq7VXea1WC6324luzorq6GgCwb98+uP0h7A/lorHuAJobjsKcb4NWb0Bnhx9upx36HDPC4W60uZ2x1VMVyqQwMnMm8M1vAtEo8Nhj/XTJKBTILy6HQqmMBQ4hMH7G5egM+qHLMiC/uBw5lvxYUUnClFIT5ozOg06tTMOnQUREdO5SGkQ0Gg2mT5+Ov/71r1h8clnQaDSKv/71r7jrrrtSeei0q66uRnckimff2ISO7iiEEKiYNB05lnxsf+81nKg7COnk9SeP0w6VQoWoWkIkHE7so2eXzGuvAV980fs4am0WLNYSWMsqkVdSjs6AHxKAvKJSjK7+WlJ3TKFRi6vGF6GQM2GIiOgClfJZM3fffTeWLl2KGTNmYObMmfjtb3+LQCCQmEUznHTklCVCiMfZiBxz3slXJNjraxGNRBAJd6GzowMqrS62lkiP8SF33gkUFAANDcBzz/Xev0KlwfhZVyCvqARNx+oQCrRj9OQZENEoCssrEiFEkoCZI3MxuyKPXTBERHRBS3kQuf7669Hc3IxVq1ahqakJ1dXVePfdd3sNYL1Yxe8lo8y24P8+2pJY4h2ShK3vvopsoxnWkWOg0enhavgKIiqgkCR0d4UgwqfuWjd7NnDNNbEumccfB0LJS4pAUqpgzM2DRqtFSeV4AEBr0wm0OhowYeY8ZFtioSdLo8Q3J9lQnqdP22dAREQ0WGlZPvOuu+4adl0xcfF7ybyx7WPYjzfCNnIMSion4NDOT9FYVwuPywGtPhsGoxkiKhANdyF62j6MxlNdMq++Cuzb1/s4Wdk5yC8Zha7OIAK+Noy9ZA6OH/oCWQYjsi15MOUVIS9bg+umlsCkV6e83UREREOB63ifJ5vNhg//vgM7PtuOEeOnoqRyAnytLuhzzCipnICjtTU4uONTdHa0w5ibh7ZWFxBJnilz991AXh5w9GjvLhlJpUbJ6PHoCnYg4HWjbOwkFJSMgHXkGNhGxpZsN+UVwWbSYfG0Eg5IJSKiiwqDyBBo6FBixPip0OeYceLwfgghEPB50BkMoL2tFZ0d7dBlGdAZDECt0qA7cuqGMVddBcybB4TDwKOPAl3Jt5qBPseIbFMecsdNgd/dgs6AD5IkJQ1KLTFnYfG0EmhUF9RsbCIiorNiEDkPdrsdjZ4gsmyVMPhDcDV8hYLSUXA1fAW3y4FOvx9dnUF0d3YiGo4gFOqIDVA9qagI+OlPYz+vWwccPpy8f1OBDTm5BegM+KDVVmLODbfBefyrpOXgi4w6XDetmCGEiIguSgwi50GSJGze8yX8ihwEfB6cqKtFh98Hj8uOpvo6dIe7EOrwo7sriM6gH+HQqUVBFApgxQogOzs2JuRPf0ret0KlhkqjhS4rG2qtBpAEfJ5WVE6dmbh5nVmvxuJpxdCq2B1DREQXJwaR86A35cOvzMHhmm0I+n2QlAocP7gXmiwDusMhOOq/RHcoBElSIBwKJL33X/4FmDoVCASA1atjs2XiJIUSBqMFSpUK4XAI+mwjdPoc5JjzIBC7GqJTK7G4ugR6DU8hERFdvPgtdh72272AAIJ+HzwuB0LBDgTa2wAA4e5uhLtC6AoFey3jfumlwA03xH5+/PHY3XV70hqyYSoogs6QA3NuIQpKK1BWOQGlYyYAiK2Weu1kGywGTaqbSERElFIMIoMkhMABhw8CAqMmXgKBnWhzNcGQY0bA5wWEgBDoFUJKSoDly2M///nPwObNyfvVGnKQby2DSqWFObcQ5VVTMHLCtEQIAYC5lXlcJ4SIiIYFBpFBOuEJor0zDFNeESRIyC8eCQBodTaiva0FAZ8naWAqAJhMsfvHxMeFPPNM7/1qdVnILSmDWnXynjsSkJObl3i9osCAGSMsqWoWERFRWnGqxSAddrUDAHytLnhbXSipqIIEBdzORnSFggj6vRA9roZotbHpuSUlgMMBrFp1+nIiCmh0Weju7obP5UJheUXsasj46sRU3WytCgsnWGMrtxIREQ0DvCIyCEIIHHEF4Gt14fDubZAUEppPHEXTsToAAgGvB6GODkBSACIKhQL45S+BCRMArxe47z7A4+m5RwmmgiIolEpIAEKhDnibmzDhmu+hpDLWJSNJwNUTrcjScIYMERENHwwig9Dk64Q/FIaAQLY5F66GejgbvoKn2QGVWgMJEhQqJSCASHcX7roLuOyy2GJlv/xl7KZ2PWWZzNCbzCiwlqM73AUIAa3eACFOrRdSXWbmuBAiIhp2GEQGob45NhW33d0CIQCDyQLP541w2Y9BrdVBa8hGd6gToaAf118P/MM/xKbnPvJI7/vIZJvzYS4qhkqlQnZePopKRsFgtKCwbBRKx0wEAOQaNLisMj/dzSQiIko5BpFBqG+NBRFJkuA6UQ9vixNqvR4anQ6dAT/CXV3o7gpi/nzg9ttj73n66d4zZABAUiiQbcpFtjkXGnUWCstGwTpyTGJciEKSsHBiEVRKDuchIqLhh99uA9TRFUZzewgHP/8b/F43Rk+aDggBjVoLgzEXCqUKfq8HkyZGEtN0X3019jidpFIh25KHbJMFiEaRZcyBwWhJuo/MJSPMsJmy0tQ6IiKi9OIVkQFqcAchBCApJBzauQW5thKUVI7Dtnc3wHW8DoF2L2xF3XjoIUCjiV0Fefrp3vtR63RQKNWAECgoHQWIKHILSxLdMQBg0asxpyKv95uJiIiGCQaRftjtdkiSBJvNlrS9wd0BX6sL1pFjEPC1ofazzeju7jo5UyYAnaYLjzwaWzOktjY2LqTn8u0AoMnSI9ucC2N+EcKhELwtTZhzzfeQbTkVOiQJWDCBXTJERDS8MYj0Q5Ik2E+uvd4zjOw7fBTeVhckhYTC0go01h/C5+9uQGfQj0i4G7/8lcDIEUBzM3D//bGZMr0IQG/MxfjpX0dnMABdVjayLXlJXTJTSk0otXCWDBERDW8MIv2Ih4+eYeTI0QYcP9EIU14h7PWHsG/rR/C47IAESJIC131HJE3TbW3tvV9JqYJSo4VOn43OgB+WIhtGTpiWFEJydCpcylkyREQkAwwiZ9AzjDgcDhxr8UNSxFY1zTHnwd/mwdH9u6FUq1BZZcAdt3cAAP7wB+DLL3vvT6XWQmvIhsFkQWfAj6bjddAZcgCRvFLqgvFF0Kq4cBkREQ1/HIBwFjabDZIkQQiBlkA3jJYCeFtdyLHkI6+4FEqVCl2dHbjtxx5oNMBnnwGvvdZ7P5JSBa1eD1tFFXKLSpFjyYOlsBhlYycm3UtmvM2IkfmGNLaQiIgoc3hF5CwcDkcshLS0YO++g9Dmj4AprxDvvfQ0HEcPoWzcZIws2IapU8IIhYDf/KavvSigzcqCLtuETn87xlwyB8Ujx6Jy6sykLhmDVokrqgrS1jYiIqJM4xWRM3A4HLDb7SguLsbESZPhaHZj16a/oG7PZwh43Wj3tMLt+ArLftAJAPif/wGamvraUxRKpQY5lnwAEtpbXRgzdVZSCAGAb4wrgk7NLhkiIpIPBpF+9AwhQgh4AiGMHD8NoWAHdn70NjRZeihVKsyd3ojCQoHmZuCVV/rel0qtRVREASFgHVmJbHM+HPXJg0jG23JQWZidhpYRERFdOBhE+iGESIQQl8uF/XXHkGPJR8WkS9DdHUL9/p0IeOy4YUkYAPDSS0B39+l7UUBnyEGW0QSd3oBQZwdENIJcawkMJkuiVI5OhSuqCtPXOCIiogsEx4j0o7i4GHa7HS6XC5FIBEftTthdfhSVjUZh6SicOFyL+ZcHUVAAOJ3Axo2996FUqWAw52HU+Gpo9AZARGEtH4t8a1liBVVJAhZOsLJLhoiIZIlB5AwkSUJTUxOUSiUa7E60uFrRcHgfPE4H1BoNrrtOAiDwxhunXw2JTceNRKNQqlSYfuW3k25k19Ml5RaU53HhMiIikicGkX7El3hXKBSorT2I5lY3mo5/ifr9e9DZ0Y7J0/SoGhtFVxfwzjunvVkClCo1AAEAcDXUI9uU2yuIWE06LlxGRESyxjEi/Ygv8V5YWAitwYhDNVtRt3cH/G2tCPrb8fWvNQAAPvkE8HpPe7MQiITDUGtjA1qdDfVob0teZlWnVuKbk2xQKiQQERHJFYNIP2w2GxQKBZxOJwpHjEZ3VzeC7T6Ew91QKrrw9csiAIC33+5/H9ZRY2DOs8Lf1op4dw0QGxdy9cQimPTqFLeCiIjowsaumTOwWq1wuVx4Z+O70OcYYcorQqDdg0lj/TAYYje227fvZGFJAoRIvFerN8BoykfJ2AlAJBrvpQEAzK7IQ0UBp+oSERHxisgZCCHg8Xjw5Ze10GZlo7xqMgymXFx+eexqyKZNPbPHqSseCrUmNh5ECeiy9Jgwax5sFWMAAFXWHMwalZvehhAREV2geEXkDFwuFzZv3oxARxBtbQ50+gOQpE7MmR0FEBsfkiBi25RqDYx5hdBk6aFR62DIsSDbkgdTXhGKzTosnFAESeK4ECIiIoBBpE/xGTNCCEQhocXlRCgYRCTcjcoRxxLdMgcO9H5vJByGWqND+dhJ6Ap2oCPghSmvCBa9Gt+ZWgKVkhehiIiI4vit2AdJkvDxxx+jtrYWU6fPhDG3EJFwN9zORkyvji0YsmVL0pCQU0QU3V2dsI6oREHpKGTpjcjWqvAP00qRpeGiZURERD0xiPTBZrMhPz8fbrcb/s4wpsxdAE2WHhIEZsyIldmxo583K1RQKlVoOnoE5WMnYcKM2bhuWjFnyBAREfWBXTP9mDRpEtxuN9788FM427uQbbRAXW5AeXknIhGgpqb3e1TaLJjyiyAAeJrtMFlycdOV01CYo0t7/YmIiC4Gsg4i8bEgNput12sulwtHjhyBs7kZDkcTmu3HMWe6HwBw8CAQCPTen1qthaWoGOY8KwpKyvGtORNQauHy7URERP2RdRCJr54KICmMOBwORCIRBAIBNHx1BK2tTrS7WzFtaghA/90y3d2dyNLnoKBkBP71jn/B16eOTXkbiIiILmayHiNis9kSd9l1OBwAYiHEbrdDqVRiwoSJkLRahAIdiEa6UV0de9/Onf3sUADOE0dgUIRgVYfS0gYiIqKLmayviACnroTY7Xbs3bsXQOxKSUtLCwymXJgshTiBWpSWKpGbG0ZXV6xr5nRqXRZUGh1C7T4UZUkoKup9p10iIiJKJvsgAsTCiMPhQEtLCzweD8aOHYv6+nrU1m1CoN0LlUqNsWO7AACHDwPd3aftQFJAkhTIMZowYczoxJUWIiIiOjMGEcS6Y4QQyM/Ph8fjQUtLCyoqKrBt9z4E/T4olEpMHB8r29ciZmqtDtlmC8aMGYfl9/0MV199dXobQEREdJGSfRCJjwkpLi7G9OnTIUkSPv/8c5jNZoS6w/C2OtHR7sWECbHVy/pcTTUShlarQ0VpIRQKWQ+7ISIiGhBZB5GeIcRms8Fut6Ourg4OhwPbtm1Dbe1h+Ns8UKlCGD069p79+3vvR0SjCHf40NUVQjQaTW8jiIiILmKyDiJCiEQIAZC4v4zL5YLL5UKwIwCICMaOjkCpjN1fprk5eR8qrQ6G7BwYc3KQn5/PbhkiIqIBkHU/Qs8QAsQGrV566aUIBoNobm5GOByBUqHCuHGx12tre+9DazBgyuRJWLRoEebOnZummhMREQ0Psg4ip3M4HHA6nRgxYgSUShU6A350d3ehsjL2+pdfniorKVRQa7MQDXUDkTDmzp2L+fPnZ6biREREFykGkR6amppQV1eHCRMmILegAKHODkTCXYnxIUeOnCoromFEohHk5edCo9Ggra0Nos/b8RIREVF/GER6KCoqwtixY3Hs2DG0+/xQKCSo1UB5eez1urrk8lqdHgvmX4Hvfve7mD17NtcOISIiGiBZD1btadeuXVAoFGhpacHOnTvR6nZDUigxckQYSiXg9QItLcnv0WdlIRqNQgjR543ziIiI6MwYRE46dOgQPv30UzQ0NKC1tRUdAT8iXaHE+JCe3TJxba0tUCgUidk2RERENDDsmjlp/PjY0qkdHR2oqqqCPscIAH2OD4mzWgtRWVmJxYsXs1uGiIhoEBhEELvhnRACl112WWJl1YDfDyiU/QaRkvKR+MEPfgCTyQSXy5X+ShMREQ0DDCKILWTmcrkghEBZWRmcTieCgXZACFRUxMqcPlA1z2zG1KlTMXbsWK6mSkRENEgMIogtZCZJEjweD/R6PZRKFaLhbljMURiNQCQCHD9+qrykUKKh4Ri2bt2KhQsX4pJLLslc5YmIiC5iDCInFRYWoqGhAXv37oVGqwEgJabtNjUB3d2nyopoBCqVCuFwOCN1JSIiGi5SFkQeeeQRzJ07F3q9HmazOVWHGRS73Q6Hw5H0vLm5GU1NTThy5AgCHR2QVKpEEGloABQqDSTlqUlGPp/vgmsXERHRxSZlQaSrqwvf+973cMcdd6TqEIMmSVJSGJEkCZ999hncbjd0Oh3C3WGIcDfKymLljx8HouEuiEgYgAQACIVCePvttzPUAiIiouEhZeuIPPjggwCAdevWpeoQgxZffMxutyeeWywW6HQ6XHPNNXjj/95F47EjiSsiPceHWAqKMKN6MlpaWjB58uR0V52IiGhYuaAWNAuFQgiFQonnPp8vZceKh5HXXnsN7e3tiEajqKiowMcffwynvQFKjRZlZbG6NDScel+Hrw2dnZ1YvXo1pkyZkrL6ERERycEFNVh19erVMJlMiUdZvG8kRWw2GxQKBQ4cOACHw4GcnBx0dXVBrdVBpeyG1Rord7xBglKlASQJXd1d8Pv9KCws5GqqRERE52lAQWT58uWQJOmMj4MHDw66MitWrIDX6008GnpeikgBh8OBWbNmoaSkBJ9//jlee+01jBkzBrnWEpTYolAoAJ8PaPMIRMJdgBDItViQm5uLQ4cOcTVVIiKi8zSgrpl77rkHy5YtO2OZivgKYIOg1Wqh1WoH/f6BcDgcsNvtKC4uxpIlS7BlyxYcPXoUza2tcLe1Y+Z0BYBoUreMQqWGyWSCXq/nImZERERDYEBBpKCgAAUFBamqS9o4HA7s2bMHCoUCCoUCBw8ehNVqxVdffYXW5mYEg0GMKItdLIoFEQWUajVyLbnweDxoa2sbFp8DERFRpqVssOrx48fhdrtx/PhxRCIR7N69GwBQWVmJ7OzsVB32nAghYLVa4XQ6UVtbi6NHj6KpqQkAEDl5pcNmi/33xAnEZ+xCqQRGV1TBZrPxiggREdEQSFkQWbVqFV588cXE82nTpgEAPv74Y1xxxRWpOuw5KS4uRnFxMRwOB/bu3Yu9e/fCaDSitLQUXd1RuD1u2GyxGTPOZjUKy0fA73EjGolg/vz5ePTRRzNafyIiouEiZUFk3bp1F+QaIj05HA785S9/wSeffIK2tjb4fD54fe0Q0Qji41AbG8LwOBuRlZWNrq4uPPvsswDAMEJERDQELqh1RNJNoVDA5/NBqVTC7/ejvT0WQtRqIC8vVsZuF+juDEISAgX5eSgqKkIkEslsxYmIiIYJWQeR6upqfP/730dLSwvsdjskKTYYxGoFFAqgowPweuOlBS699FL89re/TSyGRkREROfnglrQLN1qamrw+uuvw263w+/3J+6mG88ZPe6Lh2gkAo/Hw0XMiIiIhpBsg4jD4UBtbS1aW1sRCATQ3d2deC0+PuTkrWgAABqNBsFgEJs3b05zTYmIiIYv2QYRIQTGjx+Pm2++GVVVVdDr9Ymumb6uiEyZMgU33HADp+0SERENIdkGkbidO3fiwIEDCAaDUChiH0dfQaSurg6SJOHGG2/MQC2JiIiGJ9kOVpUkCVu2bMFHH32E5ubmpLv+9tU14/f78d///d8AgDvuuCOdVSUiIhq2ZBtEbDYbxowZg+nTpyMUCmH79u3o6uoCgMRdd+NXRAptNkydNAlarZZdM0RERENIlkHEbrfD6XSioKAAU6dOxZYtW6DX69HV1QWjETAYYuWamgBICkS6ujF//nysWLEio/UmIiIabmQZRCRJgsvlQl1dHT755BPU19ejo6MDAFBYGCvjdgNRoYFKo4DP58Xvf/97jBo1CkuWLMlgzYmIiIYXWQaR+IJkLS0tAICSkhJ4PB50dXUlgojLBUSiYZjNBRhXOQpqtZrdMkRERENMlkEk3jWzZcsW7Nq1Cz6fLzZ1V1KgsDAWNlwuCYhG4XU3o7x8Hl5++eUM15qIiGj4keX0XUmSUFtbi4aGBjidTjQ3N8Pv90OhVKB0hB4A4GqOlRXRKN5//32sWbMmgzUmIiIanmQZRGw2G8aPH4/Zs2djzJgxUCqVAIBoRCDXHJvG63IBap0eIysrUVVVxRvdERERpYAsu2YAwGq1YuTIkVi4cCGys7OxY8cOBINB5J+8667Pn42S0WPx7YVX4Mc3/QDV1dUZrS8REdFwJMsgUlNTg5dffhkHDhzA/v374Xa7IYSApFCioCB25cPdpoHX7cT//s+LqPl8O5588kmGESIioiEmyyAS53Q64Xa70dbWBgBQKICCgthr9V+2wutRwpiTg9zcXM6YISIiSgFZBpFp06ZBkiT4/X44nc5EEMnNBZRKIBw+uY4IBBYtWoQ//elPma0wERHRMCXLIPLII49g27Zt2LFjB5qamhLb42uItLQAsQsgUbz77rtYv349FzIjIiJKAVnOmlEqlWhoaEAgEEhsU2u1KCyUAMRmzMQZDAZ2yxAREaWILK+ILF++HCaTCc8//zwOHz4Mr9eL7lAocUWk+eQaIpOmTMUXe3ZnrJ5ERETDnSyviADA4sWLMXr06NiKqifFg4jTCQAKtDa7uJAZERFRCsnyiojD4cCGDRsQCATQ2dmZ2J6fH/uv26OCqaAA7e3tePLJJwHErqIQERHR0JLlFREhBPbv34/33nsvKYjknVzMrNkVhrfZgWAwCJVKxVVViYiIUkSWV0SKi4sRCoUQDoeTtucXKABEcfKmvBBCYPny5bjjjjvSX0kiIiIZkOUVkaeffhqHDh2CxWJJ2p6XKwAAra2x50qlEjt27Eh39YiIiGRDlldEotEoqqurodPpsHfvXng8Huj1YajVsSDidgMjRldCBdHrqgkRERENHVkGkTvvvDPp+dKbb8Pmj/4AAPB6gfGzr8bLr7yCcVZjJqpHREQkG7LrmrHb7aipqcGCBQugVqthNpvxxmsvJ2bMtLQAe//2HsbbTLBarZmtLBER0TAnuysikiTB5XIhEAggHA7D6/UCAAqtKgDhxPgQAOjo6MhMJYmIiGRCdldEbDYbpkyZgnnz5iVtt1iSB6rGPf300+mqGhERkezILogAsTBSXl4Oi8WSWFk11xxbK6S1FdBmZaOkpAR6vZ73mSEiIkoh2XXNxP3kJz/B7NmzUVtbi1tuvR35+X4AsSDy0t9q8Y/TSzNcQyIiouFPlkHkW9/6Fj766COo1WrodDoEO/zIzY291toK/NOMMhQUFOBHP/oRHnvsscxWloiIaBiTZRAJh8MIBoMIBoPw+XwAgIICCYBIrKra3NwMpVKZuUoSERHJgOzGiDgcDvz85z+HyWRK2p6b13uw6rp169JYMyIiIvmRXRARQqCwsBAzZsxIbDMaAfXJa0MerwolpWVQq9UcqEpERJRisuuaKS4uRnFxMT788EMAQEFBAXJyYv0xXi9QNHI89u7cAYtBk8lqEhERyYLsroj0tHjxYrjdbsTvfefxAI6vvsRjD6/KbMWIiIhkQnZBZNeuXVi2bBkkScKbb76JaDSK3LzYhSG3G4h0h/DYY49BoZDdR0NERJR2svu2VSgU2LhxY9K2GVd8DQDQHlAntgkhsHLlyrTWjYiISG5kF0Sqq6sxbty4pG0tx7YDAFqbuxPbCgoKEIlE0lo3IiIiuZHdYFUA2Lx5M3bv3o1Vq1bh7bffhtkYmx3jdgMarQ6hzmCGa0hERCQPsrsiElddXY3rr78ettIRicGqbW3A5gMnMlovIiIiOZFtENm9ezdefvllOE4cS5o1M28i7zFDRESULrIMIj27ZQAkBZFQZyf0en0Ga0dERCQfsgsiv/vd7zBnzpxECFFrtSgs0gEAdLlVAIBgMAhJkjJWRyIiIrmQXRARQkAIkXiem2+CQuoEANR/6chUtYiIiGRJdkHkzjvvxNtvvw2bzQYAUAoXAKCzE2hrjt2Jt7S0NCmsEBERUWrILogAwFVXXYUXX3wRVqsNZnNsm9sd+29paSkaGhoyVjciIiI5kWUQAWJh5Nbbb4clLzYWpK0ttp0hhIiIKH1kG0Q++OAD/P53T8NiinXBeDyx7WVlZRmsFRERkbzIMoh88MEHWLp0KVyupkTXjL9DCwA4ceIEwwgREVGayC6IxEOIwxGbIVNkywIAlE5YgPyCQgAMI0REROkiuyDyxz/+MRFCCq02XLroCgCAyVqNyxcsTJSLRqOZqB4REZGsyO6md+PHj0/87HG3QoVWAMCuLTXY8KeNAACtVovGxsaM1I+IiEhOUnZF5OjRo7j55psxatQoZGVlYfTo0XjggQfQ1dWVqkOek+XLl2P16tUAgO6uLrQ2fAYA2PT6qRDS2dmZsfoRERHJScquiBw8eBDRaBTPPPMMKisrsW/fPtxyyy0IBAJ44oknUnXYc7J8+XIAwIoVK2Axx7Z5PAwhRERE6SaJNC4hunbtWjz99NP46quvzqm8z+eDyWSC1+uF0Wgc8vpUz7kUv129BQCweDHQ1sbVVImIiM7XQL6/0zpGxOv1Ijc3t9/XQ6EQQqFQ4rnP50tZXdasWYOGL2MhJBIBfD5Ap9PxiggREVEapW3WTF1dHZ588kncdttt/ZZZvXo1TCZT4pGqKbRr1qyJdctYYs+DXXoIEQtCOp0uJcckIiKi3gYcRJYvXw5Jks74OHjwYNJ7GhsbsWjRInzve9/DLbfc0u++V6xYAa/Xm3ikYrn1eAgBAEtu7IKQUleKH/w0Nm6EYYSIiCh9Btw1c88992DZsmVnLFNRUZH42W63Y/78+Zg7dy7+8Ic/nPF9Wq0WWq12oFUakEgkkjjWXavXAPg5wsKMpbf9DBNtJqxcuZJ33iUiIkqTlA5WbWxsxPz58zF9+nT88Y9/hFKpHND7UzlYtbM7gj9vfghlyofgiV6NohF/xNzR+UN6DCIiIjkayPd3ysaINDY24oorrkB5eTmeeOIJNDc3o6mpCU1NTak65FnZ7XZcddVVkCQJuWYjVIjd6S4izOjwtODqq6+GJEnQ6/UZqyMREZGcpGzWzAcffIC6ujrU1dWhtLQ06bVMdX1IkpRYUC3Y0YFt//c7/MN1QCCowWP334wdW2OzaBQK2a18T0RElBEp+8ZdtmwZhBB9PjLFZrNh/fr1uPzyywEAxuzYeJEt73+cCCEGgwF+vz9jdSQiIpIT2f2vfzyMzJo7F/Fuq6OHTgBgCCEiIko32QURIBZGfvXoWpgtseZ7vbHtDCFERETpJcsg4nA48KuV9yInOwrgVBDJzs7OYK2IiIjkR3ZBxOFwYMmSJdi+ZQtMptg2i20SACAQCDCMEBERpZGsgkg8hGzevBlqNZCVFdt+0y/+X2IAK8MIERFR+sgqiAghoNFoAABFRbqT21Sw2cZg/fr1WLhwIQAgGo1mrI5ERERyktKVVc9XKldW/cqxHccPzUa3yIco/AILJ1qHdP9ERERydUGsrHqhi4RbAQBhmKHXpGxdNyIiIjoDGQcRNwAgLCzI0gzsHjhEREQ0NOQbRCItsf/CDD2DCBERUUbIKojs2rULkiRBkqRTV0RggV6jxO7duxOvERERUXrIKoj0vJnds089DCDWNXOkdh+mTZuWqWoRERHJlqyCSHV1NWpqagAgcZ8Zd0sIV359dqLMBTyJiIiIaNiRVRABToWR+Kqqb72wLvEaQwgREVF6yXLeanV1NRxNIwAcS9xnhiGEiIgo/WR3RQQAdu/ejTbPMQCnbnjHQapERETpJ7sgsnv3bkybNi3RNXPrqmcTrzGMEBERpZesgkg8hKjVgF4f2zZq7JzEAFaAYYSIiCidZBVE4jezi8+YEUIJncaSNJuGiIiI0kdWQeSSSy6BEAJHj+4BAIRhgl6rBhAbwCqE4KBVIiKiNJJVEInr7o7f8M6CLDWXdyciIsoUWQYRISJQaUaiWxRDxyBCRESUMbIMIrm5CzBqwgEcifx/vPMuERFRBskyiPTErhkiIqLMYRBhECEiIsoYBhF2zRAREWWMrIOIQpKgVcn6IyAiIsooWX8L69QKrqRKRESUQbIKIvfddx8MBgPKysoAJHfLrFy5EgaDASUlJZmqHhERkezIKogolUp0dXXhxIkTmDFhTGINkZUrV2Lt2rXo6OiAQiGrj4SIiCijVJmuQDo9+uijAIC1a9eiydGIO66dhd03L8PatWsRDodRWlqKhoaGDNeSiIhIPiRxAd9cxefzwWQywev1whi/U90QWLlyJR5/fC0ikXBiG0MIERHR0BjI97cs+yEeffRRTJ5SnXguSRJDCBERUQbIMoisXLkSX+zdnXguhEgMYCUiIqL0kV0QiQ9MjUTCKLTasGLFCqhUKpw4cYJhhIiIKM1kNVg1HkLC4TCsthJ8uucgRhdkA4gNYI2HEXbTEBERpYesgkgkEoFGo4HVasW2L75MbI/Ppvmv//ovRKPRTFWPiIhIdmQ5awYAGtuC0KkUyMvWDul+iYiI5I6zZs4Rb3hHRESUWbINIhIAnYpBhIiIKJNkG0Q0KgUUCt7wjoiIKJNkG0Ti95khIiKizJFvEFHJtulEREQXDNl+G6uUsm06ERHRBYPfxkRERJQxDCJERESUMQwiRERElDEMIkRERJQxDCJERESUMQwiRERElDEMIkRERJQxDCJERESUMQwiRERElDEMIkRERJQxDCJERESUMQwiRERElDEpDSLf+c53UF5eDp1OB5vNhh/+8Iew2+2pPCQRERFdRFIaRObPn49XXnkFhw4dwmuvvYYjR47gn/7pn1J5SCIiIrqISEIIka6DvfXWW1i8eDFCoRDUavVZy/t8PphMJni9XhiNxjTUkIiIiM7XQL6/VWmqE9xuN1566SXMnTu33xASCoUQCoUSz30+35DWwWq1QqFQ9Nk9VFxcjGg0iqampiE9JhEREfUv5YNV77vvPhgMBuTl5eH48eN48803+y27evVqmEymxKOsrGxI66JQKOBwOFBcXJy0vbi4GA6HAwoFx+4SERGl04C/eZcvXw5Jks74OHjwYKL8vffei5qaGrz//vtQKpW46aab0F9v0IoVK+D1ehOPhoaGwbesD3a7HTabLSmMxEOIzWbjQFoiIqI0G/AYkebmZrS2tp6xTEVFBTQaTa/tJ06cQFlZGbZs2YI5c+ac9VipGiMSDx9xDCFERERDJ6VjRAoKClBQUDCoikWjUQBIGgeSCXa7HZIkJT0nIiKi9EvZYNXt27fj888/x2WXXQaLxYIjR47g/vvvx+jRo8/pakgq9TVGhGGEiIgo/VI2OlOv12PDhg248sorUVVVhZtvvhlTpkzBJ598Aq1Wm6rDnlXPMSFCiF5jRoiIiCh90rqOyEAN9RiR/gamcsAqERHR0BnI97es5qtGo9E+w0Z8Nk18DAsRERGlR9oWNLsQnGmxMl4JISIiSj9ZXREhIiKiCwuDCBEREWUMgwgRERFlDIMIERERZQyDCBEREWUMgwgRERFlDIMIERERZQyDCBEREWUMgwgRERFlDIMIERERZcwFvcR7/H58Pp8vwzUhIiKicxX/3j6X++pe0EGkvb0dAFBWVpbhmhAREdFAtbe3w2QynbGMJM4lrmRINBqF3W5HTk4OJEka0n37fD6UlZWhoaHhrLcovlixjcMD2zg8sI3DA9t4boQQaG9vR3FxMRSKM48CuaCviCgUCpSWlqb0GEajcdj+Y4pjG4cHtnF4YBuHB7bx7M52JSSOg1WJiIgoYxhEiIiIKGNkG0S0Wi0eeOABaLXaTFclZdjG4YFtHB7YxuGBbRx6F/RgVSIiIhreZHtFhIiIiDKPQYSIiIgyhkGEiIiIMoZBhIiIiDJm2AaRRx55BHPnzoVer4fZbD6n9wghsGrVKthsNmRlZWHBggU4fPhwUhm3243vf//7MBqNMJvNuPnmm+H3+1PQgrMbaF2OHj0KSZL6fPz5z39OlOvr9fXr16ejSb0M5vO+4ooretX/9ttvTypz/PhxXHvttdDr9SgsLMS9996LcDicyqb0a6BtdLvd+Nd//VdUVVUhKysL5eXl+OlPfwqv15tULpPn8amnnsLIkSOh0+kwa9YsfPbZZ2cs/+c//xnjxo2DTqfD5MmTsXHjxqTXz+V3M90G0sZnn30WX//612GxWGCxWLBgwYJe5ZctW9brfC1atCjVzTijgbRx3bp1veqv0+mSylzs57Gvvy2SJOHaa69NlLnQzuPmzZvx7W9/G8XFxZAkCW+88cZZ37Np0yZccskl0Gq1qKysxLp163qVGejv+BmJYWrVqlXi17/+tbj77ruFyWQ6p/esWbNGmEwm8cYbb4g9e/aI73znO2LUqFEiGAwmyixatEhMnTpVbNu2Tfztb38TlZWV4oYbbkhRK85soHUJh8PC4XAkPR588EGRnZ0t2tvbE+UAiBdeeCGpXM/PIJ0G83nPmzdP3HLLLUn193q9idfD4bCYNGmSWLBggaipqREbN24U+fn5YsWKFaluTp8G2sYvvvhCfPe73xVvvfWWqKurE3/961/FmDFjxD/+4z8mlcvUeVy/fr3QaDTi+eefF/v37xe33HKLMJvNwul09ln+73//u1AqleLxxx8XBw4cEL/85S+FWq0WX3zxRaLMufxuptNA23jjjTeKp556StTU1Ija2lqxbNkyYTKZxIkTJxJlli5dKhYtWpR0vtxud7qa1MtA2/jCCy8Io9GYVP+mpqakMhf7eWxtbU1q3759+4RSqRQvvPBCosyFdh43btwo/uM//kNs2LBBABCvv/76Gct/9dVXQq/Xi7vvvlscOHBAPPnkk0KpVIp33303UWagn9vZDNsgEvfCCy+cUxCJRqPCarWKtWvXJra1tbUJrVYr/vSnPwkhhDhw4IAAID7//PNEmXfeeUdIkiQaGxuHvO5nMlR1qa6uFj/+8Y+Ttp3LP9Z0GGwb582bJ/7t3/6t39c3btwoFApF0h/Jp59+WhiNRhEKhYak7udqqM7jK6+8IjQajeju7k5sy9R5nDlzprjzzjsTzyORiCguLharV6/us/w///M/i2uvvTZp26xZs8Rtt90mhDi33810G2gbTxcOh0VOTo548cUXE9uWLl0qrrvuuqGu6qANtI1n+1s7HM/jb37zG5GTkyP8fn9i24V2Hns6l78J//7v/y4mTpyYtO36668XV199deL5+X5upxu2XTMDVV9fj6amJixYsCCxzWQyYdasWdi6dSsAYOvWrTCbzZgxY0aizIIFC6BQKLB9+/a01nco6rJz507s3r0bN998c6/X7rzzTuTn52PmzJl4/vnnz+lWzkPtfNr40ksvIT8/H5MmTcKKFSvQ0dGRtN/JkyejqKgose3qq6+Gz+fD/v37h74hZzBU/6a8Xi+MRiNUquTbR6X7PHZ1dWHnzp1Jv0cKhQILFixI/B6dbuvWrUnlgdj5iJc/l9/NdBpMG0/X0dGB7u5u5ObmJm3ftGkTCgsLUVVVhTvuuAOtra1DWvdzNdg2+v1+jBgxAmVlZbjuuuuSfp+G43l87rnnsGTJEhgMhqTtF8p5HIyz/T4Oxed2ugv6pnfp1NTUBABJX07x5/HXmpqaUFhYmPS6SqVCbm5uoky6DEVdnnvuOYwfPx5z585N2v7QQw/hG9/4BvR6Pd5//3385Cc/gd/vx09/+tMhq/+5GGwbb7zxRowYMQLFxcXYu3cv7rvvPhw6dAgbNmxI7Lev8xx/LZ2G4jy2tLTg4Ycfxq233pq0PRPnsaWlBZFIpM/P9+DBg32+p7/z0fP3Lr6tvzLpNJg2nu6+++5DcXFx0h/zRYsW4bvf/S5GjRqFI0eOYOXKlbjmmmuwdetWKJXKIW3D2QymjVVVVXj++ecxZcoUeL1ePPHEE5g7dy7279+P0tLSYXceP/vsM+zbtw/PPfdc0vYL6TwORn+/jz6fD8FgEB6P57z//Z/uogoiy5cvx2OPPXbGMrW1tRg3blyaajT0zrWN5ysYDOJ///d/cf/99/d6ree2adOmIRAIYO3atUP2BZbqNvb8Qp48eTJsNhuuvPJKHDlyBKNHjx70fgciXefR5/Ph2muvxYQJE/CrX/0q6bVUn0canDVr1mD9+vXYtGlT0mDOJUuWJH6ePHkypkyZgtGjR2PTpk248sorM1HVAZkzZw7mzJmTeD537lyMHz8ezzzzDB5++OEM1iw1nnvuOUyePBkzZ85M2n6xn8dMuKiCyD333INly5adsUxFRcWg9m21WgEATqcTNpstsd3pdKK6ujpRxuVyJb0vHA7D7XYn3n++zrWN51uXV199FR0dHbjpppvOWnbWrFl4+OGHEQqFhuTeA+lqY9ysWbMAAHV1dRg9ejSsVmuvEd5OpxMALqrz2N7ejkWLFiEnJwevv/461Gr1GcsP9XnsS35+PpRKZeLzjHM6nf22x2q1nrH8ufxuptNg2hj3xBNPYM2aNfjwww8xZcqUM5atqKhAfn4+6urq0v4Fdj5tjFOr1Zg2bRrq6uoADK/zGAgEsH79ejz00ENnPU4mz+Ng9Pf7aDQakZWVBaVSed7/NnoZ1MiSi8hAB6s+8cQTiW1er7fPwao7duxIlHnvvfcyOlh1sHWZN29er1kW/fnP//xPYbFYBl3XwRqqz/vTTz8VAMSePXuEEKcGq/Yc4f3MM88Io9EoOjs7h64B52CwbfR6vWL27Nli3rx5IhAInNOx0nUeZ86cKe66667E80gkIkpKSs44WPVb3/pW0rY5c+b0Gqx6pt/NdBtoG4UQ4rHHHhNGo1Fs3br1nI7R0NAgJEkSb7755nnXdzAG08aewuGwqKqqEj//+c+FEMPnPAoR+17RarWipaXlrMfI9HnsCec4WHXSpElJ22644YZeg1XP599Gr3oN6l0XgWPHjomamprE9NSamhpRU1OTNE21qqpKbNiwIfF8zZo1wmw2izfffFPs3btXXHfddX1O3502bZrYvn27+PTTT8WYMWMyOn33THU5ceKEqKqqEtu3b0963+HDh4UkSeKdd97ptc+33npLPPvss+KLL74Qhw8fFr/73e+EXq8Xq1atSnl7+jLQNtbV1YmHHnpI7NixQ9TX14s333xTVFRUiMsvvzzxnvj03YULF4rdu3eLd999VxQUFGR0+u5A2uj1esWsWbPE5MmTRV1dXdI0wXA4LITI7Hlcv3690Gq1Yt26deLAgQPi1ltvFWazOTFL6Yc//KFYvnx5ovzf//53oVKpxBNPPCFqa2vFAw880Of03bP9bqbTQNu4Zs0aodFoxKuvvpp0vuJ/j9rb28UvfvELsXXrVlFfXy8+/PBDcckll4gxY8akPRwPto0PPvigeO+998SRI0fEzp07xZIlS4ROpxP79+9PlLnYz2PcZZddJq6//vpe2y/E89je3p74/gMgfv3rX4uamhpx7NgxIYQQy5cvFz/84Q8T5ePTd++9915RW1srnnrqqT6n757pcxuoYRtEli5dKgD0enz88ceJMji5zkJcNBoV999/vygqKhJarVZceeWV4tChQ0n7bW1tFTfccIPIzs4WRqNR/OhHP0oKN+l0trrU19f3arMQQqxYsUKUlZWJSCTSa5/vvPOOqK6uFtnZ2cJgMIipU6eK3//+932WTYeBtvH48ePi8ssvF7m5uUKr1YrKykpx7733Jq0jIoQQR48eFddcc43IysoS+fn54p577kma+ppOA23jxx9/3Oe/bQCivr5eCJH58/jkk0+K8vJyodFoxMyZM8W2bdsSr82bN08sXbo0qfwrr7wixo4dKzQajZg4caL4y1/+kvT6ufxupttA2jhixIg+z9cDDzwghBCio6NDLFy4UBQUFAi1Wi1GjBghbrnllkH/YR8qA2njz372s0TZoqIi8c1vflPs2rUraX8X+3kUQoiDBw8KAOL999/vta8L8Tz29/ci3q6lS5eKefPm9XpPdXW10Gg0oqKiIul7Mu5Mn9tASUJkYF4mEREREYbxEu9ERER04WMQISIiooxhECEiIqKMYRAhIiKijGEQISIiooxhECEiIqKMYRAhIiKijGEQISIiooxhECEiIqKMYRAhIiKijGEQISIiooxhECEiIqKM+f8B3IDGmJaVLjMAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "mu, std = predicted_mean_std(ls,uscale,noise)\n", "pstd = np.sqrt(std**2+noise) # prediction interval std\n", "order = np.argsort(test_x.reshape(-1))\n", "plt.plot(train_x.reshape(-1), train_y, 'kx', alpha=.2)\n", "plt.plot(test_x[order].reshape(-1), mu[order], 'y')\n", "plt.fill_between(test_x[order].reshape(-1), (mu - 2*pstd)[order], (mu + 2*pstd)[order], alpha=.5, interpolate=True)" ] }, { "cell_type": "code", "execution_count": null, "id": "99204e6b", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.13" } }, "nbformat": 4, "nbformat_minor": 5 }