From 68bd9e008f7da35a15084aae0a4b4a94de2cad5d Mon Sep 17 00:00:00 2001 From: Kevin P Murphy Date: Sat, 23 Nov 2024 09:56:16 -0800 Subject: [PATCH] fixed legend in plot (based on https://github.com/probml/pml-book/issues/655) Commented out old jax.config which no longer works --- notebooks/book2/18/deepgp_stepdata.ipynb | 1679 ++++++++++++++++------ 1 file changed, 1236 insertions(+), 443 deletions(-) diff --git a/notebooks/book2/18/deepgp_stepdata.ipynb b/notebooks/book2/18/deepgp_stepdata.ipynb index fed16c16f78..aa5daa4cf66 100644 --- a/notebooks/book2/18/deepgp_stepdata.ipynb +++ b/notebooks/book2/18/deepgp_stepdata.ipynb @@ -1,445 +1,1238 @@ { - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Step Data using Deep Gaussian Process" - ] + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "id": "view-in-github", + "colab_type": "text" + }, + "source": [ + "\"Open" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "N9ZmMDgBH72h" + }, + "source": [ + "# Step Data using Deep Gaussian Process" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "id": "BSfDIrLLH72i", + "outputId": "d84b2812-8858-4e45-9e1d-d6857a346252", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 141 + } + }, + "outputs": [ + { + "output_type": "error", + "ename": "RuntimeError", + "evalue": "module was compiled against NumPy C-API version 0x10 (NumPy 1.23) but the running NumPy has C-API version 0xf. Check the section C-API incompatibility at the Troubleshooting ImportError section at https://numpy.org/devdocs/user/troubleshooting-importerror.html#c-api-incompatibility for indications on how to solve this problem.", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mRuntimeError\u001b[0m Traceback (most recent call last)", + "\u001b[0;31mRuntimeError\u001b[0m: module was compiled against NumPy C-API version 0x10 (NumPy 1.23) but the running NumPy has C-API version 0xf. Check the section C-API incompatibility at the Troubleshooting ImportError section at https://numpy.org/devdocs/user/troubleshooting-importerror.html#c-api-incompatibility for indications on how to solve this problem." + ] + }, + { + "output_type": "stream", + "name": "stderr", + "text": [ + " /usr/local/lib/python3.10/dist-packages/probml_utils/plotting.py:25: UserWarning:LATEXIFY environment variable not set, not latexifying\n" + ] + } + ], + "source": [ + "try:\n", + " import deepgp\n", + "except ModuleNotFoundError:\n", + " %pip install git+https://github.com/SheffieldML/PyDeepGP.git\n", + " import deepgp\n", + "\n", + "try:\n", + " import GPy\n", + "except ModuleNotFoundError:\n", + " %pip install -qq GPy\n", + " import GPy\n", + "\n", + "try:\n", + " from probml_utils import latexify, savefig, is_latexify_enabled\n", + "except ModuleNotFoundError:\n", + " %pip install git+https://github.com/probml/probml-utils.git\n", + " from probml_utils import latexify, savefig, is_latexify_enabled\n", + "\n", + "try:\n", + " import tinygp\n", + "except ModuleNotFoundError:\n", + " %pip install -q tinygp\n", + " import tinygp\n", + "\n", + "# import display\n", + "import seaborn as sns\n", + "import jax\n", + "import jax.numpy as jnp\n", + "import matplotlib.pyplot as plt\n", + "from tinygp import kernels, GaussianProcess\n", + "#from jax.config import config\n", + "\n", + "import numpy as np\n", + "\n", + "try:\n", + " import jaxopt\n", + "except ModuleNotFoundError:\n", + " %pip install jaxopt\n", + " import jaxopt\n", + "#config.update(\"jax_enable_x64\", True)\n", + "\n", + "latexify(width_scale_factor=2, fig_height=1.75)\n", + "marksize = 3 if is_latexify_enabled() else 4" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "JhmIXzNJH72j" + }, + "source": [ + "## Step Data" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "id": "RXOCMd-zH72j", + "outputId": "87bc9535-a91c-489e-812e-f337459c1416", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 504 + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stderr", + "text": [ + "2024-11-23 17:51:56.411379: W external/xla/xla/service/gpu/nvptx_compiler.cc:893] The NVIDIA driver's CUDA version is 12.2 which is older than the PTX compiler version 12.6.77. Because the driver is older than the PTX compiler version, XLA is disabling parallel compilation, which may slow down compilation. You should update your NVIDIA driver or use the NVIDIA-provided CUDA forward compatibility packages.\n" + ] + }, + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "(-2.0, 2.0)" + ] + }, + "metadata": {}, + "execution_count": 2 + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ], + "source": [ + "num_low = 25\n", + "num_high = 25\n", + "gap = -0.1\n", + "noise = 0.0001\n", + "x = jnp.vstack(\n", + " (jnp.linspace(-1, -gap / 2.0, num_low)[:, jnp.newaxis], jnp.linspace(gap / 2.0, 1, num_high)[:, jnp.newaxis])\n", + ").reshape(\n", + " -1,\n", + ")\n", + "y = jnp.vstack((jnp.zeros((num_low, 1)), jnp.ones((num_high, 1))))\n", + "scale = jnp.sqrt(y.var())\n", + "offset = y.mean()\n", + "yhat = ((y - offset) / scale).reshape(\n", + " -1,\n", + ")\n", + "\n", + "fig = plt.figure()\n", + "plt.plot(x, y, \"r.\", markersize=marksize)\n", + "plt.xlabel(\"$x$\")\n", + "plt.ylabel(\"$y$\")\n", + "xlim = (-2, 2)\n", + "ylim = (-0.6, 1.6)\n", + "plt.ylim(ylim)\n", + "plt.xlim(xlim)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "7cF70vS2H72j" + }, + "source": [ + "## GPy" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "id": "RrLtZFmRH72j" + }, + "outputs": [], + "source": [ + "def neg_log_likelihood(theta, X, y):\n", + " kernel = jnp.exp(theta[\"log_amp\"]) * kernels.ExpSquared(scale=jnp.exp(theta[\"log_scale\"]))\n", + " gp = GaussianProcess(kernel, X, diag=jnp.exp(theta[\"log_diag\"]))\n", + " return -gp.log_probability(y)\n", + "\n", + "\n", + "theta_init = {\"log_scale\": jnp.log(1.0), \"log_diag\": jnp.log(1.0), \"log_amp\": jnp.log(1.0)}\n", + "obj = jax.jit(jax.value_and_grad(neg_log_likelihood))\n", + "solver = jaxopt.ScipyMinimize(fun=neg_log_likelihood, method=\"L-BFGS-B\")\n", + "soln = solver.run(\n", + " theta_init,\n", + " X=x,\n", + " y=y.reshape(\n", + " -1,\n", + " ),\n", + ")\n", + "\n", + "kernel = jnp.exp(soln.params[\"log_amp\"]) * kernels.ExpSquared(scale=jnp.exp(soln.params[\"log_scale\"]))\n", + "gp = GaussianProcess(kernel, x, diag=jnp.exp(soln.params[\"log_diag\"]))\n", + "\n", + "xnew = jnp.vstack(\n", + " (jnp.linspace(-2, -gap / 2.0, 25)[:, jnp.newaxis], jnp.linspace(gap / 2.0, 2, 25)[:, jnp.newaxis])\n", + ").reshape(\n", + " -1,\n", + ")\n", + "cond_gp = gp.condition(\n", + " y.reshape(\n", + " -1,\n", + " ),\n", + " xnew,\n", + ").gp\n", + "mu, var = cond_gp.loc, cond_gp.variance\n", + "\n", + "var = var + jnp.exp(soln.params[\"log_diag\"])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "miYy2kU_H72j" + }, + "source": [ + "## Plotting GP Fit" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "id": "0BVePSE6H72j", + "outputId": "3d63ca35-9f5b-4515-905a-0ef3a2787960", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 449 + } + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" + }, + "metadata": {} + } + ], + "source": [ + "fig = plt.figure()\n", + "latexify(width_scale_factor=2, fig_height=1.75)\n", + "\n", + "plt.plot(x, y, \"r.\", markersize=marksize)\n", + "plt.plot(xnew, mu, \"blue\", markersize=marksize)\n", + "plt.fill_between(\n", + " xnew.flatten(),\n", + " mu.flatten() - 1.96 * jnp.sqrt(var),\n", + " mu.flatten() + 1.96 * jnp.sqrt(var),\n", + " alpha=0.3,\n", + " color=\"C1\",\n", + ")\n", + "\n", + "sns.despine()\n", + "legendsize = 5 if is_latexify_enabled() else 9\n", + "plt.legend(labels=[\"Data\", \"Mean\", \"Confidence\"], loc=(0.5, 0.2), prop={\"size\": legendsize}, frameon=False)\n", + "# ax.title(\"$(l, \\sigma_f, \\sigma_y)=${}, {}, {}\".format(length_scale, sigma_f, sigma_y))\n", + "plt.xlabel(\"$x$\")\n", + "plt.ylabel(\"$y$\")\n", + "\n", + "savefig(\"gp_stepdata_fit\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "WVEdD1O9H72k" + }, + "source": [ + "## Deep GP" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "id": "W60n-Fw0H72k" + }, + "outputs": [], + "source": [ + "num_hidden = 3\n", + "latent_dim = 1\n", + "\n", + "kernels = [*[GPy.kern.RBF(latent_dim, ARD=True)] * num_hidden] # hidden kernels\n", + "kernels.append(GPy.kern.RBF(np.array(x.reshape(-1, 1)).shape[1])) # we append a kernel for the input layer\n", + "\n", + "m = deepgp.DeepGP(\n", + " # this describes the shapes of the inputs and outputs of our latent GPs\n", + " [y.reshape(-1, 1).shape[1], *[latent_dim] * num_hidden, x.reshape(-1, 1).shape[1]],\n", + " X=np.array(x.reshape(-1, 1)), # training input\n", + " Y=np.array(y.reshape(-1, 1)), # training outout\n", + " inits=[*[\"PCA\"] * num_hidden, \"PCA\"], # initialise layers\n", + " kernels=kernels,\n", + " num_inducing=x.shape[0],\n", + " back_constraint=False,\n", + ")\n", + "m.initialize_parameter()\n", + "# display(m)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "CaCQ3_JSH72k" + }, + "source": [ + "## Optimizing Deep GP" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "id": "vnH_Xkq3H72k", + "outputId": "ea8708b7-fdb9-4aea-9656-92c897e8250e", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 893, + "referenced_widgets": [ + "eaf1964d8b4c4c6480722678e242458f", + "ee99017b75aa4376abaa36f4b80a9402", + "a9ed49507ee74da79ed618c2c0f67f90", + "e7eadc86cf654b9f9b44b007fee83538", + "3799d26f887c4264bb07b11e31d43369", + "878560e078e6482da563103bc1378595", + "b8103675ef734bd1a2601ed4817d0ca6", + "e6362925324e4930865e7656163315f4", + "cb29faba796c43ad84ae109dc9fb1721", + "2e7487b13000429e915141609c7862c1", + "44ca4b0c25524af285e70a213f1d5c73", + "168de9f254df447287980729a0e84021", + "79e87d8bfd0047c2bb3f532c7e965188", + "bd30bce9da304d2297bbe490f5a88e62", + "20e3c7e4814a44ccac35569b0c3fe5b1" + ] + } + }, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "HBox(children=(VBox(children=(IntProgress(value=0, max=10000), HTML(value=''))), Box(children=(HTML(value=''),…" + ], + "application/vnd.jupyter.widget-view+json": { + "version_major": 2, + "version_minor": 0, + "model_id": "eaf1964d8b4c4c6480722678e242458f" + } + }, + "metadata": {} + } + ], + "source": [ + "def optimise_dgp(model, messages=True):\n", + " \"\"\"Utility function for optimising deep GP by first\n", + " reinitiailising the Gaussian noise at each layer\n", + " (for reasons pertaining to stability)\n", + " \"\"\"\n", + " model.initialize_parameter()\n", + " for layer in model.layers:\n", + " layer.likelihood.variance.constrain_positive(warning=False)\n", + " layer.likelihood.variance = 1.0 # small variance may cause collapse\n", + " model.optimize(messages=messages, max_iters=10000)\n", + "\n", + "\n", + "optimise_dgp(m, messages=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "id": "VsoQxjUrH72k", + "outputId": "c91d4a71-30d2-4d0e-b761-b1e9f4a7d52e", + "colab": { + "base_uri": "https://localhost:8080/" + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stderr", + "text": [ + " /usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py:68: UserWarning:Explicitly requested dtype float requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", + " /usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py:68: UserWarning:Explicitly requested dtype float requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n" + ] + } + ], + "source": [ + "# m.optimize_restarts(num_restarts=5)\n", + "mu_dgp, var_dgp = m.predict(xnew.reshape(-1, 1))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "aRLBU-0pH72k" + }, + "source": [ + "## Samples from Data" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "id": "-h_tNF_8H72k" + }, + "outputs": [], + "source": [ + "def sample_dgp(model, X, num_samples=1, include_likelihood=True):\n", + " samples = []\n", + " jitter = 1e-5\n", + " count, num_tries = 0, 100\n", + " while len(samples) < num_samples:\n", + " next_input = X\n", + " if count > num_tries:\n", + " print(\"failed to sample\")\n", + " break\n", + " try:\n", + " count = count + 1\n", + " for layer in reversed(model.layers):\n", + " mu_k, sig_k = layer.predict(next_input, full_cov=True, include_likelihood=include_likelihood)\n", + " sample_k = mu_k + np.linalg.cholesky(sig_k + jitter * np.eye(X.shape[0])) @ np.random.randn(*X.shape)\n", + " next_input = sample_k\n", + " samples.append(sample_k)\n", + " count = 0\n", + " except:\n", + " pass\n", + "\n", + " return samples if num_samples > 1 else samples[0]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "symBskJkH72k" + }, + "source": [ + "## Plot Deep GP fit without samples" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "id": "nhJW7QcdH72k", + "outputId": "3af886dd-5ff3-40ab-e232-e92cb97d6c34", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 660 + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stderr", + "text": [ + " /usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py:68: UserWarning:Explicitly requested dtype float requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", + " /usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py:68: UserWarning:Explicitly requested dtype float requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", + " /usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py:68: UserWarning:Explicitly requested dtype float requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", + " /usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py:68: UserWarning:Explicitly requested dtype float requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", + " /usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py:68: UserWarning:Explicitly requested dtype float requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", + " /usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py:68: UserWarning:Explicitly requested dtype float requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", + " /usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py:68: UserWarning:Explicitly requested dtype float requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", + " /usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py:68: UserWarning:Explicitly requested dtype float requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", + " /usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py:68: UserWarning:Explicitly requested dtype float requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", + " /usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py:68: UserWarning:Explicitly requested dtype float requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", + " /usr/local/lib/python3.10/dist-packages/probml_utils/plotting.py:25: UserWarning:LATEXIFY environment variable not set, not latexifying\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
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\n" + }, + "metadata": {} + } + ], + "source": [ + "plt.figure()\n", + "num = 5\n", + "sample = sample_dgp(m, xnew.reshape(-1, 1), num, include_likelihood=False)\n", + "latexify(width_scale_factor=2, fig_height=1.75)\n", + "plt.plot(xnew, mu_dgp, \"blue\")\n", + "plt.scatter(x, y, c=\"r\", s=marksize)\n", + "plt.fill_between(\n", + " xnew.flatten(),\n", + " mu_dgp.flatten() - 1.96 * jnp.sqrt(var_dgp.flatten()),\n", + " mu_dgp.flatten() + 1.96 * jnp.sqrt(var_dgp.flatten()),\n", + " alpha=0.3,\n", + " color=\"C1\",\n", + ")\n", + "sns.despine()\n", + "legendsize = 4.5 if is_latexify_enabled() else 9\n", + "plt.legend(labels=[\"Mean\", \"Data\", \"Confidence\"], loc=2, prop={\"size\": legendsize}, frameon=False)\n", + "plt.xlabel(\"$x$\")\n", + "plt.ylabel(\"$y$\")\n", + "sns.despine()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "P6vo0KM0H72k" + }, + "source": [ + "## Plot Deep GP fit with samples" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "id": "s4WhEj-uH72k", + "outputId": "aa9dcb48-a255-435b-c617-0d8ead7a2a95", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 473 + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stderr", + "text": [ + " /usr/local/lib/python3.10/dist-packages/probml_utils/plotting.py:84: UserWarning:set FIG_DIR environment variable to save figures\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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7NuvXr2/6/vDhw/nDH/7A0UcfTXp6Oscffzy7du1q+n55eTkXX3wxhYWFOBwOjjvuODwe1U5k//79XHTRRRQWFlJUVMT111+P15sEj6fwlmjoeLePPQtqdqiZWyFAzTiGglLUtB9IuoDp448/Zv78+RQVFWEwGHjllVc6Pf5f//oXJ510EoMGDSIjI4OZM2fyzjvvtDrmd7/7HQaDodVlzJgxMfwpkoTRqF4AckpUAGUwqF5C61+Hdf+EnZ+pZEbRbZs3b2bbtm0sWLCg3e/X1NQwd+5cLrjgAg4cOMDDDz/MlVdeyf/+97+mY9555x2OO+44qqqq+P3vf88Pf/hDXC4X1113HY888ggTJkzA7Xbz5JNPtjn/HXfcwfLly1m3bh1fffUV//rXv1p9/+GHH+axxx7jtddeo7KykrPOOov58+fj8zUnzf/jH//gueee48CBA6SmpvKb3/wGgGAwyPz58zGZTHz77bdUVlZy5513YjQaCYVCnH766RQUFLB161bWrl3L119/ze9///so/FZjLLyEDR0v69oyoMGlCvYJofuherssx/UTSRcw1dXVMWnSJB566KGIjv/444856aSTePPNN1m5ciUnnHAC8+fP56uvvmp13BFHHMG+ffuaLp988kkshp+8jBqk5KilBscwlfO0+wsVPO1cAb76eI8wqRw4cACAwYPbL3T4xhtvMGjQIH76059iNps5/vjjufDCC3nqqaeajjnyyCM577zz0DSN73//+/h8PjZt2hTR/T/zzDPcdNNNFBUV4XA4+O1vf9vq+w899BC33XYbo0aNwmQycd111+HxeFixYkXTMT/+8Y8ZMWIENpuNiy66iJUrVwLwxRdfsH79eh5++GGysrIwmUzMmjULq9XKl19+yebNm7nnnntISUkhJyeHm266iWeffbZbv7+48NWBp7GPnNZBcqDBqL5Xva3vxiUSl7sCPFVSTqCfSLo5wnnz5jFv3ryIj3/ggQdafX3nnXfy6quv8tprrzFlypSm600mEwUFBdEaZv+mmdSyXeogtTa/8zOo3al2BzmG978ddjEQXoLbs2cPhx3WNt9l9+7dbXarlZSU8PHHHzd93fLxajAYsNvtuFyRLQXt3bu3VY7UoflS27dv5+KLL0bTmnf1+Hw+du/e3e79p6amNt33jh07GDx4MHZ723y37du3U1NTQ3Z2dtN1oVAIXdcjGndc1VcCEdSASckC1x71tyEvlAObcx8EQ13XGBJJYcC9sgWDQVwuV6snbFBLJEVFRZSUlHDRRRexc+fOTs/j9XpxOp2tLgOS3aFmnTwHYdM7sO0j9UIhOnX44YczfPhwnn/++Xa/P2TIELZv397quu3btzNkyJCo3H9RURE7duxo+vrQx3txcTEvvfQSNTU1TZf6+voOlxBbGjZsGHv27KGhoW0CfHFxMXl5ea3OW1tbmxw7+NyNTXetXSyvWNLVspxLluUGND2gZhpt/WCXsQAGYMB077334na7Oe+885qumzFjBk8++SRvv/02Dz/8MNu2bePYY4/t9N36kiVLyMzMbLoUFxf3xfATk1GDzGJIzYPyNaoyecW36gkj0QQa1PJhLC7d2CFnMBh48MEHueuuu3jwwQepqqoCYNOmTVxxxRXMmjWL/fv385e//IVAIMB///tfnnnmGS655JKo/BoWLFjAXXfdxd69e6mpqeG2225r9f2f/OQnLF68mI0bNwLgdDp59dVXI5rBOuqooxg9ejQ//vGPqampIRAI8Mknn+D1ejnqqKMoLi7mlltuweVyEQqF2LFjB2+99VZUfq6YChc9taR2fpzBABY7VG1VO+vEwFS3Xy3H2RzxHomIkgEVMD377LPceuutvPjii+Tl5TVdP2/ePM4991wmTpzInDlzePPNN6mpqeHFF1/s8FyLFi2itra26dJyh9CAZUmBnFEqv2nrMtjyLrgq4j0qRbOoJ65wraRYXAIN6j4inH4/7bTTeOutt3jjjTc47LDDcDgcnHPOOYwZM4bCwkLeeust/vGPf5CTk8NVV13Fww8/zKxZs6Ly67jllluYNm0a48ePZ/LkyZx55pmtvn/ttddy2WWXcdZZZ5GRkcHYsWMjzjMyGo289tpr1NfXM3r0aHJzc7nlllsIBoNomsbrr7/Onj17GDt2LJmZmZx66qls2bIlKj9XTIV3hkZSx8uerTZE1FfHdkwicbkqVJDd0Y5KkXQMoVDyvgUyGAz8+9//bvNk357nn3+eH/zgB7z00kuceuqpXR5/1FFHUVpaypIlSyIai9PpJDMzk9raWjIyorgjwu+BNS+AyZ5cOy0CXtVs0pICBZOgYEL8m5JKaxTRU0EdVj2ltogPGhtZLa/KzXDYCeqxLwaWoA7f/Fu1tUovjPdo+odwL7nx58TttTDpkr574rnnnuMHP/gBzz//fETBktvtZuvWrXz/+9/vg9H1Uyarym2qr4Yd/1Nbsod9J74J4Wa7BDOiZ7yu5ty8SGcMLClQtQXyjpCNEANNXSXUV6k0BdFvJN1fsdvtZvXq1axevRpQFY1Xr17dlLS6aNGiVnkezz77LJdccgn33XcfM2bMoLy8nPLycmpra5uO+eUvf8lHH33E9u3b+fTTT/ne976HpmkRJbiKLqRkqwrhe1dD+dfxHo0QPVNXqYJ+iLwfmD1bJYrXV3Z9rOhf3OVqlt0cozZMIi6SLmD68ssvmTJlSlNJgIULFzJlyhQWL14MwL59+1rt+Pnb3/5GIBDgJz/5CYWFhU2Xn/3sZ03H7N69mwULFjB69GjOO+88cnJy+Oyzzxg0aFDf/nD9lSVVBU67PofKJMhVEeJQ7sZcPHM32uqY7epFM7y7TgwMwSBUl3W9OUAknaRbkps9ezadpV0dWtX4ww8/7PKcHW3tFlGUkq2Sonf8Tz2RZMi6vkgi3sayId0JmEAliNfuhoLx0R+TSEyeajUjmZLd9bEiqSTdDJNIYhlFKnFv+ydSq0kkl2Bjwcru7niyZajlGW8S1JkS0eHapzaYdDe4FglPAibRt7KGqe3W2/+nnlSESAbhGaZISgq0ZElXwVLdgeiPSSSeYFAVq5TNJf2SBEyibxmMKmiq2qxaqiRicUshWtL9qs4WdD+JN7w7zi0B04BQX6Xy3WQ5rl+SgEn0Pc0MjmIoX6d2zyVvKTAxENRXNQdMPekJZk2Dmh2qNo/o35y7ZTmuH5OAScSHOQVSc2H3F1C5Kd6jGfC2b9+OwWCgpqYm3kNJPO6K5mDH0IOnTGsGNBxU/RZF/6UHVDscq/SO668kYBLxY3eonls7/qd2Eg1AGzduZP78+eTm5pKRkcGYMWO4++674z0s0VJ4Oc3SwxdCsx38DZLH1N/V7Vf/x3ZZjuuvJGAS8ZWWDwGf2jk3APtunXrqqUyaNImdO3dy8OBB/vnPf1JSUhLvYYmWwk2VI2mH0hHNMmDfFAwYNbtB16V3XD8mAZOIP0exehe//ZOESQLXdZ2amhp0PXZ5J5WVlWzdupUf/ehHpKSkoGkaRxxxBOeeey4A999/P6NGjSI9PZ3DDjuMP//5z023DS+hPf7445SUlJCWlsYNN9zAvn37OOmkk8jIyOD444+nvLy86TYGg4E//vGPjB49GofDwfnnn9+q4n1LoVCIP/3pT4wZMwaHw8Hs2bNZv3590/fvv/9+hg4dSnp6OsOHD+fvf/97jH5LCSDQuJuzuzvkWrJlqO3mvvrojEkkloAXqreCLT3eIxExJAGTiD+DEbKGQs0ucO6J92jQdZ2lS5fy3HPPsXTp0pgFTTk5OYwePZrLL7+cF198kR07drT6/rBhw3j//fdxOp38/e9/51e/+hX/+9//Wh3zwQcfsHbtWj7//HP++Mc/ct555/HAAw9w4MABLBYLd955Z6vj/9//+3988MEHbN++nYMHD3L99de3O7aHH36Yxx57jNdee43KykrOOuss5s+fj8/nY9OmTdxyyy28++67uFwuVqxYwfTp06P6u0kY/gbw1qnPezNzYE2HBqe0SemvXPvU5gBZjuvXJGASiSG8+6hyc3zHAbhcLsrKyqivr6esrAyXyxWT+zEYDHz44YdMmjSJW2+9lZKSEsaNG8d7770HwNlnn01xcTEGg4ETTjiBOXPmtKlcf8stt5Camsq4ceOYNGkSs2bN4ogjjsBqtfK9732PVatWtTr+hhtuoKioCIfDwe23386zzz5LMFyUsYWHHnqI2267jVGjRmEymbjuuuvweDysWLECTdMIhUJ88803eDwe8vPzmThxYkx+R3HnczfvkOvNDJPRpHaDSnmB/qlmF2AALemaZ4hukIBJJI60QWr7dV1VXIeRnp5OSUkJKSkplJSUkJ4eu2n2goIC7rvvPr755hsOHDjAvHnz+N73vkd1dTXPPPMMRx55JNnZ2TgcDt58800qK1vPUOTn5zd9npKS0uZrt7t1helhw4a1+tzn83HgQNsX8e3bt3PxxRfjcDiaLgcPHmT37t0cdthhPPXUU/z5z38mPz+fk08+uakZdr/TUKuCJuhZSYGWrKmN5QXaBqgiifnq4OB2tYlF9GsSMInEYW2sily9La7D0DSN0tJSFixYQGlpKZoWYXf6XsrOzuZ3v/sddXV1rF27lksvvZQ//OEP7N+/n5qaGk455ZRO+yhGouWy386dO7FYLO02mS4uLuall16ipqam6VJfX8+CBQsAOO+88/jggw+oqKhg0qRJfP/73+/VuBJWNHe2WTPVxobwjJXoH5z7VKsnmyPeIxExJgGTSCwpWVC1Me5tUzRNw+FwxDRYOnjwILfccgsbNmxA13Xq6+u5//77yc7OJjc3l1AoRF5eHkajkTfffJN333231/d5zz33sHfvXmpqali8eDEXXHABRmPbp4Gf/OQnLF68mI0bNwLgdDp59dVXcblcbNy4kffeew+Px4PFYiEtLQ2TqZ8uRTSVFIhC53mzXT2upbxA/3JwGxi15qruot/qp89yImnZs6G6TOUEDDo83qOJKYvFwp49ezjllFPYv38/NpuNI488krfeeosjjjiCm2++me9+97vous7pp5/O6aef3uv7vPjiiznhhBMoLy/n5JNP5o9//GO7x1177bVomsZZZ53Frl27SE9PZ9asWXz3u9/F5/Pxm9/8hm+//Raj0cikSZN48sknez22hBMKNQfu1igsyxoM6oXVuRcGje79+UT8eWpUuYiUnHiPRPQBQ6i3c/wCUO/AMzMzqa2tJSMjI3on9ntgzQtgsqutyQNB7S5IK4Axp8m7tigyGAx89dVXTJ48Od5DSQ6+elj7onpBzBoRnf5g9dUqEJtwTvf70onEs389bH4PckaqgFjEjq9ONcEef07cXgvl1UgkntRBqryAa1+8RyIGMq+reYYpWsUIrRngrZXyAv1BKKRaoZhsEiwNEBIwicRjsqneXdVb4z0SMZD53Kp2EkQvYNJMENIlj6k/qK8CV3l0Zh5FUpCASSSmlBz17s1TE++R9BuhUEiW47rD64KgX31ujGK6pzkVDu5QMxQieTn3qmWiaGwIEElBAiaRmGyZar364PZ4j0QMVK7yro/pCWuGlBdIdkEdqraAtYcNmUVSkoBJJCaDQb2wHNiomvMK0ZeCweaAxtyLprvtsaSqmYk4F2gVveDery6yHDegSMAkEldKrnpSqt0V75GIgcZfB/7GRrnR3pETLi8gmxqSV+0e0H29a5cjko4ETCJxaSZ1qdwk+R6ib3ndqvEuqJyjaLOmqzcCMnuafHQ/VG9RaQNiQJGASSS21Dz1wuLeH++RiIHE64JAuKRADGYRbBngqVU7rURyce1T/2/2rHiPRPQxCZhEYrOkgN+r2g8I0Vf8dS1qMPWy6W57NAuE/FJeIBnV7FIz3po53iMRfUwCJpH4UrLVspzXHe+RiIEivBwHYIjR06TJDjU7uj5OJA6/R7VusjviPRIRBxIwicRnd6h6TDU74z0SMVD462J/H7YMNcMULo4pEp9zLzTUgs0R75GIOJCASSQ+g1EtzR3YAHog3qMRA4GnVn2M5S4oSxp462RZLpkc3KGej4xavEci4kACJpEcUgepZEvnnniPRAwEQV19jOVOKINRXVwVsbsPET0NTjXLLcneA5YETCI5aBYIAZWb4z0S0d8FgxBqnMm0psf2vqxp6kVYZk4TVyik6i7tWK6KmUa7LpdIGlFskCREjKUNUkmydVWQmhPv0Yj+KuhvnmEy22N7X7ZM1YKlvgrS82N7X6L73PuhfB1UbYZgABzDYrcJQCQ8CZhE8rCmg3OfqsskAZOIFd3foulujLeOm6yqYnTdAQmYEkl9Nexfry4BD6QXqJwzMaBJwCSSi8Xe2FJicrxHIvor3adqf4FqYxJrJptqMm2yqvwYW6bU+ImXBifs3wD7v1HNv9MKIHNwvEclEoQETCK5mFPVklzAF5uCgkIEAxBo6Pq4aEnLU7uvqsvAbFOP8fR8SMtX29ftWaphb18EbwNRKKT6BlZuUstv9dWQmgs5o+R3LlqRgEkkF0uKyivwOsGUG+/RiP7IXw8hXW006AsmK+SUNN53A/jcULkF9n8LGNVSkD0T0gerx7/BABhavJgbmvNqwt9rVzv9GNv0aAx1cH0Ht49IO+NpFYgYOvleF+dpd7yhFl+HIBRUQXAwoN5oBbyge9VMYsDbvATrOQj2bMgdKXlKol0SMInkojXmfDTUqneBQkRbfbVK+o7H9nGzTV3Cj+2gDr46NabaPfQ8aOmBUCh6MyzhAKYPZ2x0PYirvoH0FCuaptEUWIbrKDV91MBoguyRYJRASXQs6QKmjz/+mHvuuYeVK1eyb98+/v3vf3PmmWd2epsPP/yQhQsX8s0331BcXMwtt9zCZZdd1uqYhx56iHvuuYfy8nImTZrEgw8+yPTp02P3g4ieMRjUa4anJt4jSRq6ruNyuUhPT2984WjL5/Oxb98+CgsLsVg6nllxu92sXr2ayZMnk5bWuyTYSMYVF+4KNSsR65ICkTBqahu7bGXvFl3XWfrpasp2l1MypIDSYyYn1mMsQfl8PvYdOEjhoKxOnwdqa518+vUmjpl0OJmZHT82Izku8vus49NVazim+CQy4/T3kHThdF1dHZMmTeKhhx6K6Pht27Zx6qmncsIJJ7B69Wquv/56fvjDH/LOO+80HfPCCy+wcOFCfvvb37Jq1SomTZrEnDlz2L9/f6x+DNEb5nDit+iKruu88847PP7447zzzjvout7mGJ/Px5IlS7j22mtZsmQJPp+v3XO53W7OOOMMFixYwBlnnIHb3X5vP5/Px44dOzo8T3hcr732Gr///e957bXX2h1Xy2Nramo6PSZadF2nxulGD/hVjaSujutq3F0cM5D05e/MVeehbHc59R4vZbvLcdV5enW+gcDn83H3oy+x8K5HufvRlzr8+62tdXL8pYu46Jd3c/yli6itbb+1TyTH+Xw+7njkeX60+EHueOT5zu/zh7/lolv+xvEnn0ptbW3Pf9BeSLoZpnnz5jFv3ryIj3/kkUcYMWIE9913HwBjx47lk08+4f/+7/+YM2cOAPfffz9XXnkll19+edNt3njjDR5//HFuvPHG6P8QA0ik7x4iOU7XdVx1HtI1G5rnoMr3MLdtXZGwMxdxUFNTwxtvvMGuXbvYunUrM2bMICendUmGHTt28PLLL1NZWcn27du58MILGTVqVJtzrVy5krVr1+LxeFi7di0rV67k+OOPb3VMOPj68ssvmTZtGosWLWr3/3Pfvn3ceOONlJeX8/rrrzNt2jSGDBnS5jhd13nzzTf5+uuvmTRpEqecckq7/6cej4fNmzczatQo7Pae1U7SdZ13br2VDR//mzFH5DLnJ0eiAaxYAWvXwoQJMGOGGtOjz7Dmi6+ZeNQkTrnyIjWmFsfp06bx+ocr+PytD5muBTjtzJPQZs5Ud3To+ZYvx7XyK9KnTmn3mOBRM6j3aNR/+jXBbzfAmLGEphxJKAShVV/Bhg2ExowlNHmKuu1X6jrGjIEpHV9nWP0VbFgPY8ZiOHKyOq7xfIaxLY9bBevXw9ixMOXIxvM1XxeafGSL+1Dna32/69EPH81HgSC79u2juK6O40JBtHHjCE1pvq3+7Td8oIf4Fhh32EhOsFnQNm1sPl+L83vGjGHbnr2MqKrEXra1zc8QXP8NKUHYHoLxhxfg/WwrBzd9i/GIsWjTp6JpITRjCE0LYTQOjNzupufPVHu7f0O7y6tYunw1B6qdVB6s5aL536VkaGGb4z79ehM79+7H5w+wc+9+Pv16E/OOm9aj48p2VvD0K+9TXetm47bdLDjlBMaMLO7gXJX4/EF27tzJp59+2q04IFqSLmDqruXLl1NaWtrqujlz5nD99dcD6gl+5cqVLFq0qOn7RqOR0tJSli9f3uF5vV4vXq+36WunUxpoHsrn83HPY/9k3eYdjB81jF9dcXa7L54+n48lf3uRld9sYeoRI1l01XltjtN1ndc+XMGXazczbdwI5h9ZjOZ1tgmYdF1n6dKllJWVUVJSQmlp6YAOmnRdZ9euXezcubPp6/aOcbvd1NfX43Z3/O7+sMMOIzs7m/LycrKzsznssMPaHBMOvg4cONBp8LV161aqq6vRdZ3q6mq2bt3absBUVVXFX//6V8rKyvjss8+YMWMGeXl5rY7xeDxcddVVrF27lgkTJvC3v/2tR0FTzXPP8cbtt7MrFbZuNjDjiKPISUuBO+5QuS3/+Q/cfDNVTjd/feR5ygKwfOV6Zhw2mLyMtFbH7f/JT7nzgefZtWMfS00w/evPKLz1t+qOWhznPv0Crn4EvvEXYvybFdvQMdT57Lj3jcIdTMMdTKMuFJ7pOrmdUX/3kK91YAqQDrR83J/Qzm3bu+7Q80XruhrgOdRLTgqwAHAcMpb9wA+BXUAl8Hcg75BjADzAlcDXwCTgUaDl//d3AR9wB/A5UAzcAHT8hi0tJUBxYQNDCz1NH4cWNlDc+HFIQQM2a7DD2ye6SJYo7TYzXl8AZ109GWkp2G3tl7Y4ZtLhDC3KY+fe/QwtyuOYSYf3+Lg6jwdfIECIEL5AgDpP+zOB6ly56lxDh3LMMcd08zcQHf0+YCovLyc/v3VBuPz8fJxOJx6Ph4MHD6LrervHbNiwocPzLlmyhFtvvTUmY+4v9h04yNpN26lx1rF203b2HTjIsMFti/Pt2LOfl9/5hAPVTrbtLufCU2czakTrF8/9lTUseeRFdpVX8t7/cplx68UUNtSqLdktuFwuysrKqK+vp6ysDJfLhcPhiOWPmdA0TaO4uJhQKERxcXG7wWN2djZHHHFEU5CZnZ3d7rkKCwu56667+OSTT5g1axaFhW3ffYaDL4/H02nwNXXqVCZMmMCmTZs4/PDDmTp1arvHVVdX880331BdXY3H46G6urpNwLRhwwY+++wzXC4XdXV1bNiwgSnhGY5u0D/+mF3ATj/QEEJf9y2kWlVwEwyqj+vWUb2/lm98UB0ETxCqV64hLze91XF7P1/N7opq3CHYHYC9uoHCdetU8nPjcSGDkR/+Yy4vuJ1APZACW7JoHUi0ZkC9aBsMIbVnLBTCgLqEDEFCLINQGTAcIydiCNdzCrZ4sTcaVQ52sEUCuVGdpc11IUPrHWjhqZgW14UMhqaxdHRcCDshhmFgGzAUAzYM+MFowEAIgiF0qglSAzQANWhUoRnCvfwMhBPe/aGvCPE+4AaqMPAVJqaBUd1nKAgBtgD/AqqAPcDFQNvAPcxdb2L91jTWb+14GbZgUAM/+/4Ofn1lWdLNSLW3ROnIaP2zWswWjhxXgiMjlZIh+VjM7QeYmZkZfPTUki5zkyI5btzIYk6YMZE1G7cxcfQIxrUzu9R0rr/fyqervuKY839BZmYMezx2ot8HTLGyaNEiFi5c2PS10+mkuLj9/+yBKi87A6vFQmXNPvJzs8jLbv8PS9dDuOsa8DT4cNc1oOttdwLt3V/N7opK3PUedldUsrfaSWH9wTbHpaenU1JS0vTin56eAIm7ceRwODj11FNZv349Y8eObTd4zMnJ4eqrr25K5j50yS5M0zTmz5/P7NmzO1zujDT4SktL49VXX+0ygVzTNNLS0vB4PKSlpbV7nwUFBeTk5ODxeMjJyaGgoKCT30jHtOOOo/jRRwlZoNgK2hHjID1FzSyFg6Hx49HKK0kzLsUDpBlBG3s4FOS2Oq5o+mSGLN/I7h17GWKCIi0E48erO2o87k9VP+GFAxdg4B1OT/0TIy06My50kGkPkPbCo6RpdaThIu0XV5Jm9WG/53cYtMZx3HyzOld4tioYpOb6X/DM8jVUv/E22WYDF6UZcCy+pc1x7d22L67TFy3C5fGR/n8/U/+PhxznCYX40V6dtTn5TBhi5q8VR2A3m9Vx554LL70ERiMb6nzMq8+kus5Lts/FW8WzGGPVWp1rsy/I2XuCVKakkpsW4CXjaEpS7AR10G+4Cf3Io9CDBnTdgB40UOM0savczs69Nnbus7Or3MbOvXZ27rOxq9xGvcdE+QEbi+4fzf4qC/fduCGpgqb0VDslQwqaZpjSU9vOwDoyUjnthKNZX7aLsSXFODJSOzxfZmZGu8tw3T3Obrfz6G0/ZfPOckYNLeh0ZjgzM5V5x0yEOAVLMAACpoKCAioqWncDr6ioICMjA7tdreVqmtbuMZ098VqtVqxWa0zG3F94/TrTxo9kcGEuhTkOvH6d9v4esh2pHDFqKGW7Kigpzifb0fYPtSgviyH5uewqr2RIfi5FBQXtJn5rmkZpaankMDXSNI05c+ZwzDHHdPj70DSNefPmMWvWrC5/Z5qmdTpjF2nwBSpomjVrVqfjHzZsGOecc05TTtSwYcPaHJOXl8dNN93E559/zvTp09vMQEXKsWABp65fw/pP32DsuHwcJxwHWuML8bp1KuCZMYNhPh/nfLaOL7/ewLRJYxg27ySwWFodlzdtGjebUvn8rY+YrgXIO7MUZsxQd3TzzXz4ZohfvPRbwMi9F4T4wSAL6UdORpvpUMdM+G6L+2wMtKytxxE+V/i6lClTqF6/m9UjRjPZZiDlB2e1e1y8rtNmzFBzZ6m2do/zfrmKo6r8FKdnUpDrwDv4FOzbtjQfd/jhsG4dJWPGcMnKrXy+ZhPTc9IoKcmByRNbnWvY6jWcva2aL2s8TBs/khFTRmDesKHxXEeili5bPIZyfBw+or7dx0UoBNU1Zp5+dTAL7xrL/z01Ane9xsO/+4ZkeXrRNI3SYyZ3msOkaRpzZh3JMVPGdnhMLNjtdiaOHtEn99VbhlCo3QplScFgMHRZVuDXv/41b775JmvXrm267sILL6S6upq3334bgBkzZjB9+nQefPBBAILBIEOHDuXaa6+NOOnb6XSSmZlJbW0tGRlR3PLo98CaF8BkT7qtxZFu7dV1nbc+/oLVG7YxecwI5h13VJvjdF1XSbRrNzN9wihOmzEGjQBMPC/2DVITVKImt0d7XJGUPIjWfer7N+Ha+DHpITda/ujOxxTpJoVDXnx27rUx9ezvUHnQwsWn7+Hpu9dEZbai6qCTxQ/+P3buPcDQokHc9tPvk5OVPM8Z3SkFEMnvP9INJ93xxD8H88PfTCAYNHDhaXt5cskazOakfQlNLr46VbB4/Dlxey1Muhkmt9vNli1bmr7etm0bq1evJjs7m6FDh7Jo0SL27NnD008/DcDVV1/Nn//8Z2644QZ+8IMf8P777/Piiy/yxhtvNJ1j4cKFXHrppUybNo3p06fzwAMPUFdX17RrTvRMJO9qwsfNO+4oZk0d3+m7n9Nmz+D4oyaqYwiqQn4NtQMyYErk5PauZqG6y2KxtDuzFIv71DKLcKRawdD5Y8pisbSbj9dmTIfkiXgajHzv2iOpPGhhyrha/nrruugt7YSCGA0GzCZN1YsJ6q1zl6CdYtmNV8R7fSkUQjMaKZ05CVfdKPU3bjSohKSmY5o/tZhMDCsc1JjaFKR15fPGYyL4P+quy8/eQ2qKzkW/msSzrxdR59F44f9WY7Ukb0K4iFzSBUxffvklJ5zQvLsjnEd06aWX8uSTT7Jv376mHUEAI0aM4I033uDnP/85f/zjHxkyZAh///vfm0oKAJx//vkcOHCAxYsXU15ezuTJk3n77bfbJIKL7mvvRaOnx7U+RoNQQAVM6T3LWUlmktweIwaDCjSiNCPRUigEP/rteFZ9m0lulo9/P7iKFHuwy+3e+BugoQa87tYBT4iWudA4gkHmTBzM6i0weeRgHMEqqGmb59emjcih5zvk6s46knTo0HF29b3G6zTAgQFaltnpKpgLhZpPdMjvpPV9GdTXxsbK3k0XTTU7NkfWr++8eeWk2HTO+dkUXl2Wz+nXHMm//6z+L0X/ltRLcolEluTioGorDJ4Kw2bGeyR9LpFnmJKapwbWvgwpWWBOieqp//T0MH525zg0Lch7j33BCUdXd7wM5auHhoPqo8kKKTmQXaKqjx/aN66x3YceDPLO0o9Yv2ULY0eNYk7p7NaPiYj6xh3Sh63D29L2GDWoQ77soGdcyz547R7fQeByaEDTKlhq/LxVH7nGXnK6r7F3nE89p/rr1Ue9AfSA6ikX8ELWUBVERWDZ8hzO+MmR1NWbOHZaNa8/spKMtEBEtxU9IEtyQvSCJQVc5dHteZUkJLk9RnS/arxriO5T44crsll49xgA7r1hIyccXQ203O7dQNn27biGp+GwG1WwlpoLQ0ogLV99buz8/9hVU8OOqjqwZrKj0o3LkI4jwxHVn6PfCYXU/7nnIOz6TL0JyxwClo53iIWdOLOKd//+Baf8aBr//TKbEy87ircf/ZKcLH8fDFzEQ9K1RhGiiTlVLcn529/d0t+F83a6Cpb6srVI0gv6VVf7CGcZIrFzr41zr5+Crhu5aP4efnbJ9qbvpafaKSnIJEWvpSQ/g/TCEhh5IhzxPRh7OhROhPT8LoMlaC6pkZKSIiU1ImUwgMmifsejTobBR6pegu7I2mIdc2QN7z/5OTkOH1+uczD7khmUH4j+cq5IDLIkFyWyJBcHwQDU7FQvLhlF8R5NQpKlu246uAO+/Q/kjozK6TwNRmZdeDSrvs1kyrhaPnnmsza5Lnr1LlzGDNKPOAktNbtXs6WJunMyaQSDcGAD7FqhnnsdQyMKVr/dkkbp5Uex74CNUcPq+N9znzEou+NeiqIHEmBJTmaYRPIymlSCbkN8GjEmg/aSw0UndH+H6TPdFQrB1b89glXfZpLjaE7yPpQW8uEoLEFLyxlwS8sJx2iE/HFw+Fy1maR6qwqcujBupJv/PrOCYUX1bN6Ryv89OTz2YxV9TgImkdyMGtRXxXsUCUuWabopGL38k4eeGcrTrw5B04K8+MBXDBvc0MGRoai8Yw7PJj733HMsXbpUlmB7I6MQDp8DBRPBuQfqKru8yWFD63ngpvUAPPpSMQ1eeXntbyTpWyQ388BN/I6EJId3k+5T2897KRSC2x9Wy3p/+OVGvtuY5N1GsLGGUARJxl2RUhNRZkmFEcdBSjbs/lIt12YWq1moDpw2+wBDizzs3GvnhTcLufR7e/pwwCLWJAQWyc2Sqta1fe54jyRhRZocLojaklz5ASv7q6wYjSGuWbCz4wMDDWCygbXrWmVdkdnEGDBqUDhJJYSn5MDBbZ0ebjKFuOYC9f/94D+GdVyNQSQlCZhEcjOnNNaskTwmEQV+T0RJvl1Zu0kFK4cPr8Nu66SgYaBBVaq39D64Cc8mLliwQJL7o81RDEOPbixs2nmtpSvO2Y3VorPym0w+XxO/RrEi+iRgEsnNqKnCdBIwiWiIUsC0ZqMKgCYc3kWSfcADtkzQopMdIbOJMWTPUqVMfJ2XMRmU7eOCU1Rj8D8/03lLH5FcJGASyc9oiigpU4guBTxRqcG0dpNaYps4uouAyd8AqYN6fX+iD1hSVXDrr+vy0J9evAOAF98qpKJS6jL1FxIwieRnSQVXRdtGo0J0l78BDFGYYdqkdr11OcMUCkp9tWRhMKjdc13MMAFMHe/k6EkH8fmNPPpScR8MTvQFCZhE8rOkqKRvn9QYEr2gB6JS5dvvN/DtlghmmEJB1QfO0vuEb9FH7Nnq/y0C116skr8feX4ofr/s4O0PJGASyc+UotqjSB6T6I2gX116GTBt3pGKz28kLSXAsKJOih6Gd8hFoaSA6CO2TNAsqolvF86ZU05ejpc9FTZeXZbfB4MTsSYBk0h+RiMgid+il3SfWtbtZdJ3y4TvTkr2qOU/sx2ssv0/adgyVYAbQR6T1RLkqvN2AfDnZ4bGemSiD0jAJPoHowXcB+I9CpHM9EBUZpjCCd+R7ZDLAM3cq/sTfchsU/WYIshjArj6gp1oWpCPvshh7UZZek12EjCJ/sGSojqMB6UdhOgh3aceP72eYVJJ3LJDrp9KL1DBbgQG53s566QKQEoM9AcSMIn+wZyqEr+9zniPRCSroL8xEbt3AVPEM0yEwCo75JKOLRNCEGkZ72svUiUG/vFaEQdrpRtZMpOASfQPZpsqOih5TKKndD/Qu56EtS4TO/amAF0ETKHGHnJRaIki+pg9S+WeBTpqptzasdMOMuFwJ/UeE0/+e0iMBydiSQIm0T8YjGAIScAkek739/oU6zarAGhIgYeszE5aaAS8jTvkJGBKOtYMlfjt6zrxG1T8fe1FqsTAQ88OlXJxSUwCJtF/aFZw7Y/3KESyCvY+YIo8f8kjAVOy0kyQNijigAngovl7cWT42bozlXc+yY3h4EQsScAk+g9zCtTtV7udhOgu3adyU3oh8h1yDWDPBJO0zUhKafkQ7LoWU1hqis4PztoNSPJ3MpOASfQfllRVwFISv0VP+L1Rq8E0sauAye+BFJlpSFq2TMDYrXZM1yzYicEQ4q2PB7FlR0rsxiZiRgIm0X+YbGqrdkNNvEcikpG/vlc1mEIhWLupuWhlF0c3vuiKpGRzqFIm/sjqMQGMHFbPvOMOEAoZ+MuzUsgyGUnAJPqP8O4mSfwWPRHw9GqGaedeG063GbM5yOgRneS3hHfISUuU5GVNV5cIKn63FC4x8Pi/hlBX3/smz6JvScAk+hezFVzl8R6FSEaBhl7NMIVnl8aMcGOxdJIMFfCCySotUZKZwQDphd1K/AaYM6uSkcPqqHWZeea1ohgNTsSKBEyifzGnQl1VRM0xhWgS1NVjphczTE35S13tkGtquis75JJaSk7jbGHkjEb4yYWqxMCD/xgWae1LkSAkYBL9iyVFTZNL4rfoDt0PIb1XVb6b85fcnR/o96haPrJDLrnZHOrx0s36XZd9bzepKQHWbU7n/c9yYjM2ERMSMIn+RbOq7eGSxyS6I+iHYEDV2OmhNZvCM0xdBOsB6SHXL9gyu1XAMsyREeDy76kSA/c/OTwGAxOxIgGT6F8MBlVLx1MT75GIZKL71bKcoWcBk9dnZOM2lcTd5QxTUFc1mERys6SoWaZu7JQL+9klOzAYQrz5UR4byiT5P1lIwCT6H7MdXPviPQqRTHS/Knjaw6Tv9VtT0XUjWZk+Bud30mMsFFJtfCR/qX/IKOpRwDRyWD2nf1d1JXjgqeFRHpSIFQmYRI/puk6N042u6/EeSmuWFPAcVDWZhIiE7oNQoMdJ3035S6PcnffuDe+Qk4Cpf7Bn9bg6/MLLtgHw9KuDqTxojuKgRKxIwCR6RNd1ln66mufe+Iiln65OrKDJ3FhQzttV8UAhGgX96oWv02inY8075LrKX2rsIWeVgKlfsDtU8n6g+2/Ojp12kCPH1eJp0PjrC1LIMhlIwCR6xFXnoWx3OfUeL2W7y3HVeeI9pGaaRW0R78FUuRig9AD0LFYCurFDLtCg6i+ZrD2/M5E4bJlqttDX/ecagwEWXr4dgD8/MxSvT16OE538D4keSU+1UzKkgBS7lZIhBaSn2uM9pGYGg3rx8ydQECcSm967ul0R12Dyyw65fkUzQ2put3fKhZ07Zx9FeQ2UH7DxwpsFUR6ciDYJmESPaJpG6TGTWXDq8ZQeMxlNS7Ay/yFkhklELti9WjotVR40s++ADYDxo7oImEIB6SHX36Tlq9y0HrBYQvz0YtUu5f+eGiGFLBNcUgZMDz30EMOHD8dmszFjxgw+//zzDo+dPXs2BoOhzeXUU09tOuayyy5r8/25c+f2xY+S1DRNw5GRlnjBEqh3fpLDJCIV8Krdaz2wtnF2qaS4nrTUTnL5QiEIGSR/qb+xO9THblb9DrvqvF2k2AOsXp/BhyuyozcuEXVJFzC98MILLFy4kN/+9resWrWKSZMmMWfOHPbv39/u8f/617/Yt29f02XdunVomsa5557b6ri5c+e2Ou65557rix9HxIrJonbKCREJv6fHVb7XRlqwUveqXocW6SHXr9gyGzsM9CwFINvh57Lv7QHg/idHRHNkIsqSLmC6//77ufLKK7n88ssZN24cjzzyCCkpKTz++OPtHp+dnU1BQUHT5b333iMlJaVNwGS1Wlsdl5WV1Rc/jogVzaLyCoIJtHtPJC6/p8dVvtdE3BKlAUx2VR1a9B/WnlX8buln39+OwRDi9Q/z2LQtJYqDE9GUVAGTz+dj5cqVlJaWNl1nNBopLS1l+fLlEZ3jscce44ILLiA1tfWT1ocffkheXh6jR4/mmmuuoaqqqtPzeL1enE5nq4tIIJpVvaOXPCYRiUBD72eYDu+q6a5H7agy23p0P9Gk6zo1NTWJVQ4kWRmNkFbQq+eaw0fUc9rsxkKWTw+P0sBEtCVVwFRZWYmu6+Tn57e6Pj8/n/Ly8i5v//nnn7Nu3Tp++MMftrp+7ty5PP300yxbtoy7776bjz76iHnz5nX6ZLJkyRIyMzObLsXFxT37oURsNJUWkOKVogvBoMph6kGV72AQ1m1WOUkTugqY/A2QFv8dcrqus3TpUp577jmWLl0qQVM0pA3q1cYBgIWXbQfgyX8PobpGClkmoqQKmHrrscceY8KECUyfPr3V9RdccAGnn346EyZM4Mwzz+T111/niy++4MMPP+zwXIsWLaK2trbpsmvXrhiPXnSLZlZPYDLDJLoSDKhLDwKmsl0p1HtM2Kw6I4d1sSQT0hNih5zL5aKsrIz6+nrKyspwuWRzRK/ZMtUMZTDQ41McP72ayWOdjYUs5Q14IkqqgCk3NxdN06ioqGh1fUVFBQUFndewqKur4/nnn+eKK67o8n5KSkrIzc1ly5YtHR5jtVrJyMhodREJJFyxuQcVeMUAo/t6HDCF6y8dMdJNp5tFQyFV6iIBWqKkp6dTUlJCSkoKJSUlpKdLEnqv2RxgTu3VGzSDobldyp+fGYbP14tKqiImkipgslgsTJ06lWXLljVdFwwGWbZsGTNnzuz0ti+99BJer5eLL764y/vZvXs3VVVVFBYW9nrMIo6kFpOIRNCvNgf0oI9c8w65LmZpdK/auWmNf3CiaRqlpaUsWLCA0tLSxCwLkmwsqWDL6FXiN8D58/ZROKiBvfttvPi2vP4kmqQKmAAWLlzIo48+ylNPPcX69eu55pprqKur4/LLLwfgkksuYdGiRW1u99hjj3HmmWeSk5PT6nq3282vfvUrPvvsM7Zv386yZcs444wzGDlyJHPmzOmTn0nEiGaGBknGF13Q/Y0zTN0PHMIzTBHlL5ntCTHDBI011BwOCZaixWCA9MIetUhpyWIJce1FjYUsnxwuhSwTTM/20cbR+eefz4EDB1i8eDHl5eVMnjyZt99+uykRfOfOnRiNrePAjRs38sknn/Duu++2OZ+maaxZs4annnqKmpoaioqKOPnkk7n99tuxWqXfU1LTzNBQG+9RiEQXDpgMPViSi3SGKdCg8lwSYIeciJGUnB4Xr2zpR+fv4vePjGTVt5l8/EU2x0+vjsLgRDQkXcAEcO2113Lttde2+732ErVHjx5NqINQ3W63884770RzeCJRmKyq2ncPl1vEAKH7gJDaHt4NdfUaW3eqmjldzzB5IGdkDwcokoItU+3O1X3qYw/lZPm59Mw9PPL8UP7vqeESMCWQpFuSEyJi4ScvacIrOtPDnU3fbEkjFDKQn+slL6eL5r3BQHMLDdE/2XpfwDLs+ku2A/Cf9/PYvF0KWSYKCZhE/6VZJWASXdN7Vj9nxdcOIILZpVBI5bgkSP6SiBGzDexZvc5jAhhdUsepx+8nFDLw+4cPi8LgRDRIwCT6L82sAqaABEyiE3oXs0MduO6OcQDkZXdx+/ASjQRM/V9GUdSeb265ZisGQ4inXx3Cmx/Fv+CpkIBJ9GfhWkwywyQ6o/uB7tW8qfc0P3Wm2rtY0vN7wGQDqwRM/Z4tU5UzicL2tqMn1zQtzV21eDw1zqRMOe5XJGAS/ZvUYhJd8dd3u2jlsuW5TZ9fed7uzg8ONKj6S2Z7T0Ynkok9Sy3NRalg7u+v38SoYXXsqbCx8K6xUTmn6DkJmET/ppmgQVo/iE74Pd3eRfnoS0OaPh8/KoKSAik5nR8j+gdrRtQSvwFS7EGeWLIGgyHEE/8awlsf53Z9IxEzEjCJ/k2zQENNvEchElnA0+0Zptc+yAd0oAaLuYuk8aBfzTyI/k8zqeA4inmT3zmyeWnuyt9MkKW5OJKASfRvmgV8blWLSYhDhUIQ8PagTpcOLAWeY+mnq9H1Th5fIYPkLw0ktiwI9GwjQUdaLs394u4xUT23iJwETKJ/M1nVC6Ikfov2BAOg96TxrgsoA+op212Oq66Dx1fAp3rIWeLfQ070EWsqKnkyelLsQR6/cy0GQ4jH/1ksS3NxIgGT6N/CxSujlIQp+pke95FLB0oYWxKkZEgB6akdJHQHGnfIWVJ7O1KRLEy2aMdLAMyaepCftViaq3XJ0lxfk4BJ9G+aRb0oyk450R7dByG9WzNMZbvsgAaUcu+vJ1N6zOSOm9j6PSpYkh1yA4c5RQXgPawg35k7rt/EyKZdc7I019ckYBIxpes6NU535zkesWQwqDwVv8wwiXYEA91uvHvfEyMaP9OYe2yg42AJ1HJwSm5zTTDR/5ntjakA0c1jgsZdcy2W5t7+ryzN9SUJmETM6LrO0k9X89wbH3WdGBtLBmSGSbRP93V7Se4vzw5r+rzLfr1BP6TIDrkBxZzSOLPtjcnpWy/NjZeluT4kAZOIGVedh7Ld5dR7vJ0nxsaa0QQNzvjct0hsuh+CwR7kMEUohLREGWhMFrUMG4hNwATNS3O7y+2ya64PScAkYiY91U7JkAJS7NbOE2NjTbOAtzY+9y0SWzDQ3a4o3Tu30SQJ3wORLbPHPQojkWIP8vgdamnusZdlaa6vSMAkYkbTNEqPmcyCU4/vPDE25gOxgNelZhKEaKkXL2rDirpY5g0GQNPU408MLLbMxh6FsXPstINc9/0dgFqaq6iUx1msScAkYkrTNBwZafELlkBNkQd8Ua2+K/oJ3a8KS0bI728+9pc/2Nb5weEZpm7XeBJJz5xCTGoLHOLOn29sWpo79qKj2bHHFvP7HMgkYBL9n2ZVCZhSvFIcSvd3a0nuhbcKmz6//Kw9nR8c1MEgM0wDUh+VkUixB3nrb18yrKiezTtSOfbio9lYJkvAsSIBk+j/NHNjLSYJmMQhAh4wRP40eO/jI5o+T03pYtdnsLG+k2bu6ehEsjKnqP/7GC/LAYwcVs8nz65gTImbXfvsHHvxDFavl8rysSABk+j/DEYgJAGTaMvvUQ1TI/T1hozIzx0MqNmlWO3AE4krXIspRqUFDjWkoIGP/7GCKeNqOVBtZfYlM/jfKkef3PdAIgGTGBhCBqnFJNrye9SyWSwEA2CWnJIByZyiUgFiULyyI4OyfXzw1OfMmlpNrcvMyVccxbufyO65aJKASQwMRiP43PEehUg0AW/skrKDOpikJcqApJnAktJnM0xhmekB3vn7F8w99gD1HhPzr5nKv97N79Mx9GcSMImBwWQFz8F4j0IkkqCuygr0IGCaf0JFBOcPSA+5gcyW1aczTGEp9iCvPrSSc+bsw+c3cu71U3jyX4P7fBz9kQRMYmDQLOB1Sy0m0aypLUpkAdOeCmvT512WFAAVkEWwJKfrOjU1NfFrHSRiw5ahWuPEgcUS4vn7V/ODs3cRDBq4/KaJ/OnpYV3fUHRKAiYxMJgsavlFajH1Sz0KOnR/4062yHKY/vj08KbPj50WwWylgS5LCui6ztKlS3nuuedYunSpBE39iTklrnevafD336/j55eq4P5nd47jhntGU++Rl/2ekt+cGBg0CwR94G+I90hElPU46ND9EIq88W7LkgKGSGs3GTsvKeByuSgrK6O+vp6ysjJcLleEJxYJz2wHDBCKfQHLjhgMcN+NG7j1p5sBuOexEsadeiz/ejc/nsNKWhIwiYFBa5xhkp1y/U6Pg46gH/TIl+RC3agI3qSLGkzp6emUlJSQkpJCSUkJ6elSP6ffMKc014CLI4MBFv9kC//80yqKCz3s2JvC2dcdyclXHMX6rVLksjskYBIDQ7g4odRi6nd6HHSEl+RiUVYgFAIMXQZMmqZRWlrKggULKC0tjW8LIRFdZrt6o9bHO+U6ctbJFWx482N+8+MtWC06Sz/NZeIZs/jl3aNxuqV9TyQkYBIDR8ggOUz9UI+DDt2n8owiXl9TLOYINg6EdBWkR9AWRdM0HA6HBEv9Tbh4ZSAxAiZQO+huu24z377xX07/bgWBgJH7nihh9LxjefqVItkT0wUJmMTAYTSCV3JE+qMeBR3BQMSHtsz3+NUVZRGcW1e1eLrIYRL9mFEDa7oKzBNMSbGHV/+yijf/9gWjhtVRfsDGpTdO4tiLjmbVN92oZj/ASMAkBg6TBRpq4z0KkSi68UL2/mc5TZ9fe9GOrm8QDIBB+sgNeNbMhAyYwuYdV8na1z7hrl9sJDUlwKdfZTHtnGOY+8NpvPBmAQ1eCRFakt+GGDg0KzS4pBaTULqRjNtyh1zBoAheAMPlCiRgGthsGd2ayYwHqyXIr68sY+NbH7Pg1L2EQgbe+WQQFyycQtFxJ/CT28bxxdpM2VWHBExiINEsEGhQFyH8DREnfL/930HdO3e4IKYsyQ1sca7F1B2D8708e9/XbH7nI26+egtDCjwcrLXwl2eHMf3cY5hw+izue3w4FZVd5+X1VxIwiYHDFK7FJInfArUBIMIaTN0WDKgAXZPdRwNaUy2m5JnVHjmsnt9fv5ntyz7k3cc+Z8Gpe7FZdb7ZnM4v/zCWwcefwOnXHMkLbxYMuOBJ/prFwKFJtW/Rgt8Tw8a7AbVDSgxsZrt6o6b7wNR1m5xEomlw0neqOOk7VdQ4TbzwZiFP/HsIK7528NoH+bz2gWrqO3qEm+OmVXPcUQc5blo1Q4v67wx+Us4wPfTQQwwfPhybzcaMGTP4/PPPOzz2ySefxGAwtLrYbK0fuKFQiMWLF1NYWIjdbqe0tJTNmzfH+scQfU1qMYmWAg3dnmE6akJNZAeGdGm8K9RjwGhJ6MTvSDgyAvzogl189sJyvn3jY3595VYmjXFiMITYuC2NR18ayvdvmMSw757A8O8ez6W/nsBjLw9h8/aUfpX7lHQzTC+88AILFy7kkUceYcaMGTzwwAPMmTOHjRs3kpeX1+5tMjIy2LhxY9PXhkPqrvzhD3/gT3/6E0899RQjRozgN7/5DXPmzOHbb79tE1yJJBcySLVvoRL/dV9EM0wti/pF1HQXVAVxCZiEKVyLyQf9ZMJx7GF13PWLTdz1i00crDXxycpsPv4yi4+/zGblNxns2JvC06+m8PSrQwBISwkwpsTNmJI6xpTUMbbx85FD67BYkiua6lbAtGvXLoqLi2M1lojcf//9XHnllVx++eUAPPLII7zxxhs8/vjj3Hjjje3exmAwUFBQ0O73QqEQDzzwALfccgtnnHEGAE8//TT5+fm88sorXHDBBbH5QUR8GI3grYv3KES8Bf2NidldJ2X//aUhTZ+fdVJFZOcPBSVgEur5xpYBrn3xHklMZGUGmP/d/cz/7n4A3HUan36V1RRArfjagbvexJfrHHy5ztHqtpoWpGSIh7GHuTl8eB1DChooyvNSlKc+Fg7yYrMmVu5XtwKmMWPG8Itf/IIbb7yRlJS+z/73+XysXLmSRYsWNV1nNBopLS1l+fLlHd7O7XYzbNgwgsEgRx55JHfeeSdHHHEEANu2baO8vJzS0tKm4zMzM5kxYwbLly/vMGDyer14vc0VXJ1OZ29/PNEXTBZoiKDTvOjfdF9jnlHXQU3LkgImU6TviEOyQ04oNgccjKB2Vz+Qlqpz8qxKTp5VCYDPZ2DrrhQ2lKWxoSyV9Y0fN5Sl4aozsXlHKpt3dNzPLjvTR2Gel6JBXopy3RRl17LoD5Aep4WfbgVM7733Hj//+c957LHHuOOOO7jssstiNKz2VVZWous6+fn5ra7Pz89nw4YN7d5m9OjRPP7440ycOJHa2lruvfdejjnmGL755huGDBlCeXl50zkOPWf4e+1ZsmQJt956ay9/oq69/E8j5j3FpKUbSXNYSUvRSUsJqI+pOhZzsLudHQY2zaKqfYdC3W6JIfqRcB+5Q5bkdF3HVechPdXeVDV834EePjtLDSYBYE1TOW0DkMUSYuxhdYw9rPWsfigE+/ZbmwKoLTtT2Lvfxt791qaPDV6N6loL1bUWvtmcDuQCsPj/4jc50a2A6ZhjjmHFihU8/fTT3HzzzTz44IM88MADHHvssbEaX6/NnDmTmTNnNn19zDHHMHbsWP76179y++239/i8ixYtYuHChU1fO53OmCxXXvIDCx7PiR1+X9OCjUGUzqBsHwW5aiqzIFddCvNafD7IS1rqwPzDbaJZ1S45vwcsyVMjRUSZHl6Sa0761nWdpZ+upmx3OSVDCig9ZnLv+rtF0EdODADmFEiuVJ2YMxigKN9LUb6XE2dWtfl+KAQ1TlPrIGqfgepqsNmGxWHESo+Svi+55BLOOecc7rrrLubNm8fcuXO55557GDFiRNc37oXc3Fw0TaOionUeQUVFRYc5Socym81MmTKFLVu2ADTdrqKigsLCwlbnnDx5cofnsVqtWK2xzeILheCYmUHc+6upazDj9lhw15tw12s0eNUTua4bqXUZqXWZ2VPR9TvhjDQ/4w5zM/5wNxNGuRh/uIsJh7sZlJ3cuzgiZrKAt1btkJKAaeAKtg2YXHUeynaXU+/xUra7HFedB0dGWs/vI1YlC0RyMdtVhBAMqpwm0SWDQeVHZWW6OWKUW13pqwOvE0iygCns5JNPxul08uCDD/LGG2/w05/+lMWLF5OW1osnmU5YLBamTp3KsmXLOPPMMwEIBoMsW7aMa6+9NqJz6LrO2rVrOeWUUwAYMWIEBQUFLFu2rClAcjqdrFixgmuuuSYWP0bEDAZY+rYP1ryhci1szU0RAwEDdR6NunoNd72G023iwEEL5Qes7DtgpbxSXcKf7ztgpa7ehNNt5rOvs/js66xW95WX42X8KBU8jR/l4uhJNRwxyt3/Vq00i9qx4q8HsuM9GhEvul+96zc0v4Clp9opGVLQNMOUnto6v+mKc3ZFdu6grs4rM0wC1AyTydq4K1N2XSezbgVMjzzyCF988QVffPEF69evx2g0Mn78eK6++momTZrE888/z7hx4/jXv/7FtGnTYjLghQsXcumllzJt2jSmT5/OAw88QF1dXdOuuUsuuYTBgwezZMkSAG677TaOPvpoRo4cSU1NDffccw87duzghz/8IaB20F1//fX8/ve/Z9SoUU1lBYqKipqCskRkMoXITA+QmR55nyJ3ncaOvXbWbU5j3eZ01m5KZ93mNMp2pbC/ysr7VVbe/yy36fhhRfXMP2E/p80+wOwZ1VgtibVjoUcMRiAktZgGOt0Ph7wZ0DSN0mMmt8phWrep+c3fLy6PsKRAuC2K5DAJUDNMmgV0L5glYEpm3QqY7rjjDmbMmMEll1zC0UcfzdSpU7Hbm9+FXXXVVdx5551cdtllrFu3LuqDBTj//PM5cOAAixcvpry8nMmTJ/P22283JW3v3LkTY4tpz4MHD3LllVdSXl5OVlYWU6dO5dNPP2XcuHFNx9xwww3U1dVx1VVXUVNTw6xZs3j77bf7XQ2mtFSdI0apKc7zaU5or6vX+HZrGus2pbF2UzprNqXzv1VZ7Nibwp+fGc6fnxlOWkqAk79TyfwT9nPK8QfIy0nyJTwJmAa2oJ/2Eks0TWu1DHffE81pBocmrnZ8bl3tkJOASYCq8G2ySQ/LfsAQCkW3DmdFRQVFRUXo+sBKLnY6nWRmZlJbW0tGRkbXN4iU3wNrXmizJBdr9R4jy5bn8toHg3j9w7xWO4UMhhBHT6ph/gn7ufTMPRTlezs5UwKq3gaFk2H4MfEeiYiXvV/Btk8gd2SnhxnGzGv6PLThrcjO3eBUGwsmnCd5ckLZ+BbU7obMIV0fK9oXzmEaf06fvha2FPWsxLy8PN5///1on1b0sRR7sKkgWTD4Dau+yeC1D/J4/cM8Vn2byfLVWSxfncWtD43k6gt28esfllGYlySBk9aY+C0GroAvdmUlwgUxJYdJhNkcULU13qMQvRT1lH2DwcDxxx8f7dOKODIaYdoEJ7det4WV//qU3R+9zyO/W8cxUw7i9Wn88enhlJx0PAuXjEmO7tUmCzTU0q+aHInu8dfHtvGu0QSa7JITjaxpqvq7SGqyx1F02+B8Lz+6YBefPPsZ7z72OTMnH6TBq/F/T41gROlsfvWH0eyvSuDASbNCwCs5BQNZoKFbAVNxYTdy3kK62hUlRJg5RQrl9gMSMIkeMxjgpO9U8b/nPuOtR79g+sQaPA0a9z5ewojS47nxvsOpPJiAia9aY/dwSfweuPwNrWowtScQaH6B+2WkO+RAzTCZJXdJtGC2qx26wYGV29vfSMAkes1ggLnHVvLZC8t5469fMm18DfUeE3c/ehgjTpzNb/44Cp8vgd5daRY1wyQB08AUCkU0w/TyO83FcH9w9u7Izx/UpfGuaM1sVzPbepLkeYp2ScAkosZggFOOP8DnLy3nP39ZyZRxtbjrTfz+4ZGc9IPpiTPbZJRaTANaU1uUzgOmex5rLinQrZZCEjCJQ4WLVwaSvBzLACcBk4g6gwHmf3c/K//5KS8+8BUZaX4+/jKbGecdw/qtHXem7nP++niPQMRDO21R2rPq28yenT+E1GASrZmsqhaTzDAlNQmYRMwYDHDu3HKWP/8ZI4bUU7YrhZkXzOTdT3K7vnHMB2dUdT3EwKP7GotL9qKxbmcMISkpINqyZarHnkhaEjCJmBs30s2KF5cza2o1tS4zp/xoKg89MzS+g9Ks0FAT3zGI+NADES3J9YpRZpjEIWwOWZJLchIwiT4xKNvH0ie+4NIzd6PrRq69/QiuvW1cq51IfUozq4rMUotp4An61dZ/Q2QB06nH7+/e+WVJTrTHmkp77XhE8pCASfQZqyXIE0vWctcvNgLw0LPDOPVHU6l1Rfedvq7r1DjdnbfnMVnVTimpxTTw6D4IBhuT/9u3t6K5jtIvf9CdkgK6Oq8ETOJQZrvES0lOAibRpwwG+PWVZfzrwVWk2AO8+79BzLxgJlt3Rqduja7rLP10Nc+98RFLP13dcdCkWdVuKdkpN/DoAehiYvPBfwxr+vz46dWRnzuoN1b5lhwmcQhzinps6IF4j0T0kARMIi6+d1IFnzyzgsH5DazfmsaM82byycqsXp/XVeehbHc59R4vZbvLcdV1EBBpFrVjRQKmgSeCxNt7n2guKdCtAs3h3KhY5keJ5GSyqZltSfxOWhIwibiZMs7J5y9+ytQjaqmqsXDa1VPZscfWq3Omp9opGVJAit1KyZAC0lM7qIdjNKreTrIkN/AE/RDqPAoKBHr41BgKgEGTGSbRljlFLdVKaYGkJQGTiKuifC8f/+MzZkyqodZl5uIbJvUqEVzTNEqPmcyCU4+n9JjJaFoXW8elFtPAE/B1uSTXY3q48a7kMIlDmCxgSVVdBkRSkoBJxF2KPciz964mPTXAJyuzWfK3kl6dT9M0HBlpXQdLBiN43b26L5GE/J6IazCZTN3sMB/SQZMlOdEBqcWU1CRgEgmhpNjDX377DQC3PjSST1c5Yn+nmgUaamN/PyKxBDydBjQtK038qjs75EDlMJls0pletM/mUJtNRFKSgEkkjItP38tF8/eg60Yu+tWkqJcbaMNkA0+N2mIuBo4uZpg++jy76fOfXryje+cO6upxJUR7LClIbYHkJQGTSCgPLf6WEUPq2b4nhZ/cNi62d2a2qRwmnyu29yMSRyikckg6mWG69/HmHXKFed3MNwkGVHKvEO0x2SReSmISMImEkpke4Jl7vkbTgjzz2mD+8Z+i2N2ZKUUFTF4JmAaMYEAtiRg6nmF646O8XpxfVwUKhWiPOUXluMmyXFKSgEkknJlTavjtT7YA8ONbj4haUcs2wqUFJGAaOHS/2vofq6TsEGo3lBDtMdsbazHJTrlkJAGTSEg3/Wgrx06rxlVn4qJfTcLvj1ESrUFTeUxiYAj6m6txx4IhJI13RcfMKarLgDThTUoSMImEpGnwjz98TWa6nxVfO7jtLyNjc0cWO7jLY3NukXh0f2M17q7LCpwwo6pn9yFFK0VHNJNK/JYZpqQkAZNIWEOLGvjbbesAuOORw1rtXooak10tyfml4veA4KtTQVMHhSVbVppfdNXW7p8/hHpRFKIjtiyZYUpSEjCJhHbevHIuP2s3oZCBi2+YyMHaKL8YmVPUNnPJYxoYvC4gqIqWtuOBp4c3ff7do7s5wxQMqrw4mWESnbFlSNJ3kpKASSS8P938LaOG1bG73M5Vi8e3KizYayaLqrzrdUbxpCJheQ6CoeOg+4GnmksKdFUovo2mxruSwyQ6YU6JXWseEVMSMImEl5aq8+y9qzGZgrz8TiHPvV4Y3TsIIQHTQBAKQd2B2G37b2q8KwGT6ITZDhiI7js/0RckYBJJYdoEJ7+5RuWU/P6RkdEtzm2ygrsyiicUCcnvUYFxrAKmoDTeFREwp6jHiCzLJR0JmETSuP7S7WSk+Vm/NY03PxoUvROb7VBfpbabi/7L61JBUwcBk8/XvE4y9rAeNGUO6mr3neQwic6Y7eoxIjvlko4ETCJpZKQF+NH5uwC457GS6J3YbJeK3wOB16VmgToIaDZsS2v6/CcXdrOHHKiASTPFrsaT6B/CxSsDEjAlGwmYRFL52SXbMZuDfPxlNp+vyYzOSU122Sk3EHidnfbxeuvj5lnL+Sfs7/75gwHQbGCQjF7RCaMG1nS12UQkFQmYRFIZnO/lwlP3AnDPYyO6ODpCRiMgLVL6vboD6p19B7bubF6qG1rUg7pc0kdORMrmkIApCUnAJJLOLy7fBsC/3iuIXp85g1FapPRnQV3lqXUS0OzYq763ZOHGHt5HIGkCJl3XqampQdclby8urOnq8SKSigRMIulMGO1m7rEHCAYN/N+Tw6NzUrMd6iqicy6ReLpI+Ab4emMG0IuWKMGAWt5NcLqus3TpUp577jmWLl0qQVM8mGPUUFzElARMIin96ooyAB7/1xAqD0ZhG3dTixRP788lEk/4/7aDgKai0kJFpRWDIcT4UT3YIQdASBVCTXAul4uysjLq6+spKyvD5ZKl6D4XDtxD0ayPImItKQOmhx56iOHDh2Oz2ZgxYwaff/55h8c++uijHHvssWRlZZGVlUVpaWmb4y+77DIMBkOry9y5c2P9Y4heOGFGNUeOq8XToPGXZ4f1/oTSIqV/87nVi5Ox/ae8NRvTARg5tJ7UlF7MuCRBSYH09HRKSkpISUmhpKSE9PT0eA9p4DGnqHw6yWNKKkkXML3wwgssXLiQ3/72t6xatYpJkyYxZ84c9u9vf1fLhx9+yIIFC/jggw9Yvnw5xcXFnHzyyezZs6fVcXPnzmXfvn1Nl+eee64vfhzRQwYD/OoKlcv052eG4mno5UO5qUWKBEz9kqdGVeHuQDhgmjSmlxXfk6BopaZplJaWsmDBAkpLS9G63QNG9Jo1rXl3rkgaSRcw3X///Vx55ZVcfvnljBs3jkceeYSUlBQef/zxdo9/5pln+PGPf8zkyZMZM2YMf//73wkGgyxbtqzVcVarlYKCgqZLVlZWX/w4ohfOmVPO8MH1HKi28tQrg6NzUmmR0j+5K8Bs6/Db4YBp4uheBsxJUoNJ0zQcDocES/FisoI9S9V/E0kjqQImn8/HypUrKS0tbbrOaDRSWlrK8uXLIzpHfX09fr+f7OzsVtd/+OGH5OXlMXr0aK655hqqqjpP/PR6vTidzlYX0bdMphA/v3Q7APc9MYJe565q0iKlX/I3qJnDThJtwwnfPQ6YgkG10zIJluREgkjNU49NkTSSKmCqrKxE13Xy8/NbXZ+fn095eXlE5/j1r39NUVFRq6Br7ty5PP300yxbtoy7776bjz76iHnz5nW6e2TJkiVkZmY2XYqLi3v2Q4le+cHZu8nK9LFlRyqvLsvv+gadSbIWKbI1PEI+t3on38EOOb/fwLdbVZXvST0NmJoa70rAJCJkd9BpJVWRcJIqYOqtu+66i+eff55///vf2GzN0/MXXHABp59+OhMmTODMM8/k9ddf54svvuDDDz/s8FyLFi2itra26bJr164++AnEodJSdX68YCegCln2qgG42Q7+uqTIY5Kt4d3gdULA13FLlLJU/H4jGWl+hg3uYU5JU+Pd5FiSEwnAlqEeM9KEN2kkVcCUm5uLpmlUVLSul1NRUUFBQUGnt7333nu56667ePfdd5k4cWKnx5aUlJCbm8uWLVs6PMZqtZKRkdHqIuLj2ot2YDEH+ezrLP63qhe5Z0nUIkW2hndD+P+zg5YlazY1L8f1uKuJNN4V3WVNb+5jKZJCUgVMFouFqVOntkrYDidwz5w5s8Pb/eEPf+D222/n7bffZtq0aV3ez+7du6mqqqKwsDAq4xaxVTDIxyVnql2PvWqXkkQtUmRreDfUVXW6ey0qCd9BXc0WGBN/l5xIEOYUsGbITrkkknTzxwsXLuTSSy9l2rRpTJ8+nQceeIC6ujouv/xyAC655BIGDx7MkiVLALj77rtZvHgxzz77LMOHD2/KdUpLSyMtLQ23282tt97K2WefTUFBAVu3buWGG25g5MiRzJkzJ24/p+ieX1y+jb+/VMx/3s9nQ1kqY0rqenYig5YULVLCW8NdLhfp6emy26kjwSDUVXZe4XtDY0mBXgVM4SU5CZhEhAwGSCsA1754j0REKKlmmADOP/987r33XhYvXszkyZNZvXo1b7/9dlMi+M6dO9m3r/kB+PDDD+Pz+TjnnHMoLCxsutx7772AeuFZs2YNp59+OocffjhXXHEFU6dO5b///S9Wa8eNOkViGVNSx+nfVUu19z3Ri1kms11tQU8CsjU8Aj43+N2d7pCLzgxTAEy2Dpf9hGiX3ZE0m0wEGEKhXqXJikZOp5PMzExqa2ujm8/k98CaF1R+jU3ypDrzycosjr3oaCzmIDve/4CCQT2oouupUQUsJ56XNI1URSece+Gbf4NjaLs1kg5UW8g75kQMhhDOL98jLbWHL161eyBzMIye18sBiwGldjd8+yo4hqkcONExX53awDH+nLi9FibdDJMQHfnOkQc5etJBfH4jD/6jh+1SLNIipV/xutSyXAcFJcOzS4cNre95sARJ03hXJBhrRmPit+QxJQMJmES/0bJdysPPD6Wuvgfv2DSL2uYrAVP/4KlVBSU7EM5fmnh4L/+/gwGZkRTdZ0kDc5rslEsSEjCJfuWMEysoKa7nYK2FF97q4S5HA9BQG9VxiTip2w/mjnMRm3vI9TJgCoVUuwshusNohLQ8mWFKEhIwiX5F0+Cq81QR0b+92MPq6yYr1B2I4qhEXAR8Kietk6WyNZvCCd+9bG1kQHbIiZ5JzVF5kyLhScAk+p3LvrcbkynIiq8dTUsu3WJKrhYpogM+NwQ8nbZE+WZzlJrugtRgEj1jTVfLxqFgvEciuiABk+h38nN9nHmiKg3waE9mmczhxG9pqJzUvE7V3NRka/fbm7an4vMbSU8NMLynLVFakhkm0RPWDPUYDUgj3kQnAZPol8LLcv94rYh6Tzcf5mZbY8DkjsHIRJ/xutRSWQe1kcKzjxMOd6ki7z0VCgIGCZhEz4R3yvkk8TvRScAk+qUTZ1YxYkg9tS4zL73dzeRvgxEIyQxTsquv7rCcADTnL00a08v/52BA+siJntNMkJqrlo9FQpOASfRLRiNceW4vkr+TpEWK6EAopBL3O1iOgyhV+IbGPnLmToMzITqVlgcBb7xHIbogAZPoty4/SyV/f/pVFus2pXXvxknUIkW0w1+vllQ7aYny9QZVLbhXPeSgMWCSGSbRC9YMCKECfZGwJGAS/VbBIB/zT9gPwKMvdXOWyWxXOTCSV5CcvC6Vh9bBDrnKg2b27lezT+NHRaFopTTeFb1hzQCTRcoLJDgJmES/Fk7+fvrVwXgauvFwD7crkIrfycnrglCgwyAmvBxXUlxPelovy0eEAyYpK5CUdF2npqYGXY9jGRFbRuPuXHmDlsgkYBL92knHVDKsqJ4ap5mX3ymI/IaaBYLSIiVpNThRW+Tat2Zj43JcbxO+obGPnJXebbUT8aDrOkuXLuW5555j6dKl8QuaTFawOyRgSnDyFy76NU2DH567G+jBslyIfrFTLiHeQfe1ugNqiaMDUeshBxDSpS1KknK5XJSVlVFfX09ZWRkuVxzfIKXmg18SvxOZBEyi37v8rN1oWpD/fpnN+q2pkd/QnPwtUhLmHXRf0gOqUntnLVGi1UMufH+dJJeLxJWenk5JSQkpKSmUlJSQnt6DzgDRYncAsav2res6NU73wHgOiBEJmES/Nzjfy2mzVeDTrcrf4RYpeiBGI4u9hHoH3Vd84YTv9oOYQMDAN1vUrsmotEQJ6R0ml4vEpmkapaWlLFiwgNLSUjRNi99grOlgMIHuj/qpdV1n6aeree6Nj1j66WoJmnpIAiYxIISTv596ZTAN3ggf9uYUtUvOl7xBRkK9g+4rXrdqM2HuuCWK16eRlhJgxJAo5IwEg7Ikl8Q0TcPhcMQ3WAKV+G1p3GwSZa46D2W7y6n3eCnbXY6rTopk9oRUWhMDwpxZBygu9LBrn51/vZvPhfP3dX0jsw1cDSrx254V+0HGQPgdtMvlIj09Pf4vCn3B6wKCjRXb2wovx/W6JUqYgV7tkNN1fWD9/4j2mVNUeYGGWhU8RVF6qp2SIQWU7S6nZEgB6akyI9oTMsMkBgRNgx+eo5K/I678He4gnuQ75RLmHXRf8dSoSu0daEr4jsZyXFgPi1YOyBwz0T6DAdLyY7JTTtM0So+ZzIJTj6f0mMkD57kgyiRgEgPGD87ejdEY4qMvcthYFmHyt9EEnoOxHZiILndFpzlFzT3kohQwhVD9wHpgQOaYiY7Zs1Tl+BjQNA1HRpoES70gAZMYMIYUNHDKcY3J3y8NiexGZju490vLgmTh96icswh2yE0cHYWSEaGgWpLr4QzTgMwxEx2zZaiZ7RgFTaJ3JGASA0pz8vcQvL4IHv5mu6rFFINETBEDXnenO+Sqa8zsLlfB1ITD3b2/v6DeqyrfCbVLS8SfNR0sKfJ8k6AkYBIDyrzjDjA4v4HKgxZeWZrX9Q2kRUpy8Toh4OuwaGV4dmnEkHoy0qJQLiIcMPWij9xAyTEbkAVUu8uSDuY0qfidoCRgEgOKyRTiirPVLFNEyd+aRdVFqdsf45GJqPC66Kwlytcbo5zwHQyAUZPGu12Q5PYIGY2QmiszTAlKAiYx4Fxxzm4MhhDvf5bL5u0RVGi2ZcDOz6DiG8llSnT1lWDqOHhpqvAdjfwlaAyYzD3OYRooJLm9G1JzQffFexSiHRIwiR5L1lL7Q4samNeY/P3wc0O7vkFaPphsUPYR7FmlChWKxBMMQl1lpzvkvt6g6ttEfYapF3WYBgJJbu8GWwZgUBsKREKRwpWiR8Kl9sOF0JKttsc1F+zkzY/yeODp4RwzpYZz5pZ3foPUXJWrsuNTCHih+ChZhkk0PrfK/bC0/2LcsiVK9EoK6KDZiU4FzP5rQBZQ7Slrhgr6Aw3SozDByF+56JFkL7V/6uwDXH3BTkIhAxffMJGPv4igkrfdAekFsOdL2P4J+BtiPk7RDd5wD7n2Z5h+9+eRNHg1MtP9lBRHKak2GJA+chEaKMntvRYOmCSPKeFIwCR6JFxqP8VuTcpS+wYD/Pk333BmaTlen8bpP57K2o1pXd/QmgaZQ2DfGij7UG1jF4nB61LLGMa2L8h/fHoYdzwyEoB7b9gQlQkhXdepqXWhG2SmUUSRZmpM/JadcolGAibRI/2h1L6mwbP3fs13jqym1mVm3lVHsXNv+w1bWzHbIXs4HNgIW5dJJfBE0VBLezvknnmtiOvvHAfA76/fxA/P3d3ru2rq/v7OCpZ+9k3S5fGJBJc6SC39i4QiAZPosf5Qat9uC/Kfv6xi3EgXeypszL3yKKprIpgx0CyQUwIHd8KWpaoauOh7DU6oLoOdK6BqS5vlsbc+zuWyRRMA+Nkl27npR1ujcrdNS9INDZTt3S+7vkR02TLjPQLRDgmYxICX7fDz9qNfMji/gfVb05h/zVQ8DRH8aRhNkF2igqUt70HNTlWzSUoPxE7AC7V7YN/XsP41WPdPWP8G7P5cbcVOay5GuvwrB2dfdySBgJELT9vL/Teux9BxiaZuaVqStlooGT5cdn2J6LJmqDdlMsuUUGSXnBBAcWED7/z9C2ZddDSffpXFgl9M5uU/foXJ1EXwYzRC1ggVLG16W/Uw0yxqpsOcoi6Wxus0i9pZZzTT/MptaPy88evw5y1f2bsMwFp8v9WxHV1/yPd6pOV4W3zd0XVtvtdyKCE1nlCocSt1O5/7PeDcC849qpp3UFe/Y2uGCpIMrQPcbzancerVU/E0aMw99gBP3LkmqhvZwkvSrmIz6ZOOTepZVpGArOnqucNfDyZrvEcjGknAJESjI0a5+c9fVnLSD47i1WX5/OS2cTxy6zddz0oYDJA1DHx1apZD94K/DvSA2kUVapHfEmo8vtVJw0FSi687utMOg6dQu5+2/iLaM1+HBEaG9r4X/rKTX2JTwAQQbH0d4Q8hFWxaMyCzuNOSDjv22Jjzw6M4WGvh6EkHefmPX2GxqHPpuo6rzkN6qr3dIKer77ekaRqO9BSwRJD3JgYEXdcjKp3Q5XFmG9gd6LX7cPnNnT4eI33MduexLdonAZMQLRw77SDP3vs15/xsCn97cSiD870s/smWyG5sSQVSuz4uXJAuHAg0BQvtfd2oy6Wk9mZ6Ojqmg6/DX3YYV3UwS9VugNbBSdq72tD4T9NMm+GQ6yJ3oNrCyVccxZ4KG+NGunjjrytJTVEBa1e1w7pdWywcvErRSoF6/Lz22mt88cUXHHXUUcyfP7/DoDyi42w5vPrvV/nflmq+c+RYzvjuzDbH6brOGx+u4PO1m5k+YRSnzp7R4X0mc928RJGUOUwPPfQQw4cPx2azMWPGDD7//PNOj3/ppZcYM2YMNpuNCRMm8Oabb7b6figUYvHixRQWFmK32yktLWXz5s2x/BEGjGSsBn7WyRU8tPhbAH774CgefXFIdO/AYFQXo7GxSrRJbSXWGpu4ahbVPLblRevqYm68tDiX8dCLdsjF2PrSalztXQ69vemQsZtajKODcR76c5laLlWamsdlMHY7WHK5NU65aiqbtqcxtMjDO3//kmyHv/n7XdQO63ZtsaAOBlNStkVJ1Ea4iTquSOzfv58lS5bwxBNPsGTJEvbvb38jSKTH7av1ctMj/+Gxl9/hpvueZF9FVdtzVR3kjr++yBP/fI87/voi+6va37HrqvOwaftudpdXsmn77qSrm5coki5geuGFF1i4cCG//e1vWbVqFZMmTWLOnDkdPug+/fRTFixYwBVXXMFXX33FmWeeyZlnnsm6deuajvnDH/7An/70Jx555BFWrFhBamoqc+bMoaFBChP2RtPW6zc+Yumnq5PqSfCaBTu5+Wo1s3TV4gkMPWE2x188g8tunMCtfx7J068U8fEXWezaZ6PLH2vFCvj739XHWFwX6/MnwXUN/13JWWfn8+U6B7lZPt79+xcM2fFRq+PSv1lLybqvSCnf21w7rMW5mhK5y/dSsu4r0r9Z2/k4Pl8O/34F3ltKMom0EW5fBy/J3qB379697N69G7fbze7du9m7d2+nx9XV1XV63La9B6l21qPrOtW1brbtqWh7ropqdu87gKvew+59B9hbUd3uuaxmjS/XbeGdT1by5botWM0dL+8l2xvcvpR0S3L3338/V155JZdffjkAjzzyCG+88QaPP/44N954Y5vj//jHPzJ37lx+9atfAXD77bfz3nvv8ec//5lHHnmEUCjEAw88wC233MIZZ5wBwNNPP01+fj6vvPIKF1xwQbvj8Hq9eL3NOxiczig184whj8fD5p3ljBpagN3ecaFJn8/HvgMHKRyUhcXS8bvnro5r7x27IyOC4pC9FK01/dt/tpnK6hB/fdHCrn2F7NqXzcdfZrc5zmwOMiS/mtSUDaTaSjCbbWjGEEYjaO4ajNs0NMPRGNEJlQyitmEjjp2jMZmPxBAKwujh6kQbvRgMk9F1D67hXjJsxWibJwKTgBCMGaaO2+ABJhEM6fgLLZj3jcdgmKyOaTpXA6CuCx3efH4MU9RS0ujoXmcY0/Z+DYeMt72fIQQwerha3droJWQ4svE+RqjrNvkJGabRELTiGXI4Hp8Zz96heEKX4gna8Fiz8PhM+ALzAEg1uHnzumcZfWAv3HGHmq36z3/g3HPRXnqJUoMBVyBI+glT0b78stUx2s03U2oK4vrfO6SbjGhrP4ebb1bjbXmu8HX33gN2Df74LryUDqef3s6jrGuR5r1ES3uNcB0OR5sxvf7663z++edMnz6d0047rcOxud1uVq9ezeTJk0lL6/jv2+fzsW/fPgoLC9t/vohgXLHg8XjYvHkzo0aN6vp5sZPxFxUVMWTIEHbt2sWQIUMoKipq9zyRHjfl6O8wcVQxG3ZWMGZEMVPGjmh7rrxchhTksqu8kiEFuRTl5bZ7rv3VTrw+HzlZGXh9PvZXOxk2uPXPKst2XUuqgMnn87Fy5UoWLVrUdJ3RaKS0tJTly5e3e5vly5ezcOHCVtfNmTOHV155BYBt27ZRXl5OaWlp0/czMzOZMWMGy5cv7zBgWrJkCbfeemsvf6KuqSejTUweM5o0W0aHx9XWOvn0600cM+lwMjPbHufxeLhy8YOs2bCNiWNG8OhtP233ycHn87Hkby/x5TebmXbEKBZddW67Tw4+n497Hvsn6zbvYPyoYfzqirPbHBd+xx7+A+yLauC6rvPOJyvZULabMSVDmDNraodr+l2t/fv9PvIG/ZYTZmxheNF4TphxNbvKM9m2J4Vtu+1s253Czn02/H4v23YvBNYCE4C/AuGfNQc4rPFzN6w9A9gEHA7eV4E0WBW+x7GAB/ghrF8DTAT+3nyuL8PHjQN04E3YshwVjJwCaLCy5bkareqD69q731bj7eS6Tsc8pvm6TeFPWrzAtCiGnG2s4oXBF3NUfSqsDakAJxhUH1euBKMRLRjEYdbg229VYNbymHXr0EIhHGYNXyDA7qCRwtVrsGiGNscRCoHJCAEdzBp8+GGPAqbwrEpZWRklJSWUlpbG/EUqPT2dYcOGsX79eoYNG9ZuSYT9+/dz5513smvXLpYuXcr06dMpLCxsc5zb7eaMM85g06ZNHH744bz66qvtBk0+n4+77767KbD69a9/3fb5orFBb/h30RelGjweDz/60Y9Yu3YtEyZM4K9//WuHz4t33HEHK1asYMaMGdx8881txp+Xl8dNN93UFGTm5eW1OU/4uEWLFjXlMHV0XFpWHq88eAur161j8pQj2/295uVmsujqC/hi7SaOmnA4ebnt128qHJTFhMOHNz1fFw5q2woqXm9wk0lSBUyVlZXouk5+fn6r6/Pz89mwYUO7tykvL2/3+PLy8qbvh6/r6Jj2LFq0qFUg5nQ6KS4ujvyHiYDb7eaMs85j47erGT1sMK8+/Nt2/2hqa50cf+kidu7dz9CiPD56akmboOnbLbv4YMUaXHUeqmpdfLtlF1MnHN7mXDv2HOCf735C1UEXO/ZUcOGpsxk1YnCb4/YdOMiaTdupddaxZtN29h04yLDBrX+HTVuv+3BnRo3TzVsff8me/dVs213OjImjyclq+yQSXvvfva+S9z79iqMmHE7hIe/OynaW8//+vYxqp5ttu3ZwwxUz+P6ZQ1sdEwgYePd/O7ly8fu46zzYrZX88vJ/M3TwWHTdQHDzVvRXXyeIxrf15fyl4Uv8uhezfoAfZVzM4bYiOEXNjoTefJvt3v08XPsGXg2s5j1cY/k+w+0F6gV6njqOt97CqdfzD+cHVNuCZDcY+H7GCWRoKU3n4s23VA5QKASnzFM51G++CUYDBENwyimNx3XvulCQDu+j5XWhEK3G23TcIdeFQmCYNxeDIQRvvqWqAwRDGE5VxxnefAMMBmx4sJ9zCnZLAPuLT2DXvNipx/7jy7Cb/dgf+gMZJjeWkBfGN84A/ec/zYHO1KlQVoY7GGR1XYDJI0eSZrO1Pmb8eAB8r7zCHVVBVjQEmbG1kpvPOA5LO8fpH/0Hl8dIeoofbfbsCB6dbUU6qxLpLEikgsEgHo+HYDDY7vfbW15qL2BauXIla9euxePxsHbtWlauXMnxxx/f5rjdu3ezbNkyqqqqqKqq4qKLLqKkpKTVMfFo0Ltx40Y+++wznE4ndXV1bNy4kcmTJ7c5rqysjKeffprq6mo2btzIggULGDNmTKtjNE3jtNNO4/jjj+90/JqmMX/+fGbPnt35z2kwkFYwjFmhWuhg5k7TNObPns7soyZ0+hxrsVj41RVnd7oiEI83uMkmqQKmRGK1WrFaY1sfY9WqVaxZt46GOg9rNu9k1fptHHfUhDbHffr1Jnbu3Y/PH2Dn3v18+vUm5h03rdUxqXY7FpMJIwYsJhOpHT7phgiFQujBIKGWW7sPkZedgc1iYWvNPvJzs8jLbn/2K1wNvO8YCIZC+AMBgqEQHW0v21txsHHtv6Fx7f9gm4CpzuPF5/cTCoXw+f3UedoWkTOZQkwcZSXdHqKuvgFHuo0LTvEzpCgcbKfAMcNg3Tp2F43kP39cTXlVgIIUGz8/w8+Q7+TBjMY/wxMGseHDzbzwHwvVXj/ZGRYu+2keY6rL1Yv0jMYnw+8Oouy/n/Hmf0OEgkayjSHOPrackmOPbnGuPDUTMn58i+vyo3xde/fR8rrm8UZ0XavbNu48m13Y4rrGx9ikWS2uU/3hyLm6xXUz1HU339zqOvfQoZx5x2Ns9vgY9cTbvPLnm0k75BiAsh/8iKfveoKDoSAbv9zIgqsuZswhx+m6zpvTjmXNmj1MPPUUTjn1VHry8h7JrEqksyCRqqmp4Z133mHPnj1UVFQwc+ZMcnJyWh0T6bLRYYcdRnZ2NuXl5WRnZ3PYYYe1e1xaWhoZGRnU1taSkZHR4dJduEFvX8nPzyc7O5v6+nqys7PbvHEOq6urw+fzqecCn4+6urp2j4t0/BH/nCm5jaVJQh1ugoj0OdZisbR5U3voefr6DW6ySaqAKTc3F03TqKhonfxWUVFBQUFBu7cpKCjo9Pjwx4qKilbvoCoqKtp9p9GXSkpKyMnOpryhjpzMVEqGtP9gP2bS4QwtymuaYTpmUtuZo5Kh+Vxy5omsWLORGRNHUzK0/XMNKchh0piSpqW7IQU57R7n9etMGz+KIQW5FORm4fXrROGNb6+lp9ooyHFQfuAgBTkO0lPbr5FTlJfVuPZ/oHHtv+0U9biRQzhh5mS+Xl/GpLEljBvZ/m45u93G8dMnsWXnHkYOHYzdfsh9zpgBM2ZQqOvcpaXyyVfrmTVlLIUnzlQN7VocVzJlCpem5Db/P506Bw59NzhjBkOmTOHElJf4ev02Jo0dwZAfntv6uMb7bG8cA/W61Wm5bPZDAwY279jD6o07mNXO7epGjcZnSyGoe/AFAtR5PG3OVXXQyaOr97Cz2suKb7Ywo6qqw6WVzkQyq7Jx40aWL1+O0+nE7XZ3OAvSXYZOdiFGurxUWFjIXXfdxSeffMKsWbPanYUCyMnJ4aqrrmpakjs0QIuXvLw8brzxxi6Xx8aNG8cJJ5zAmjVrmDhxIuPGjWv3uKjLKFRFLBtqwe6I+d31/Rvc5JJUAZPFYmHq1KksW7aMM888E1BTy8uWLePaa69t9zYzZ85k2bJlXH/99U3Xvffee8ycOROAESNGUFBQwLJly5qehJxOJytWrOCaa66J5Y/TpcLCQpb8/jb+9+oTfOfIIyjMa/9JJjMzg4+eWtJpDpPFYuHmq8/vMpnb69eZMXEMw4ryOw2E0lPtHD58MCaTllDTt/UNPrIdGUwZexhZmWnUN/ja/VnzcrO46erzm3KY8nLbBkx2u51Hb722y0R5R0YqZ5x4NOvLdjG2pBhHRvu1mDRNY/6JM5l99OQO38FZLBZu+lHX/08Wi4Vf//DciJLzhTJ59DBGDRvM5h17GDVsMJNHD2v3uHEjizlhxsSmNw3jRrZdanfXN+Cs86LrQZwuF263u0cBE3Q92xB+o+j1etE0jdzc9hN7I+VwOJg3bx7r169n7Nix7d53tJeXNE1j3rx5zJo1q8+W2yIR6fjtdjuPPvpoVJdFI2LLhKzhsH99nwRMonOGUCi5Gl+98MILXHrppfz1r39l+vTpPPDAA7z44ots2LCB/Px8LrnkEgYPHsySJUsAVVbg+OOP56677uLUU0/l+eef584772TVqlWMb8xFuPvuu7nrrrt46qmnGDFiBL/5zW9Ys2YN3377LTZbZFV8nU4nmZmZTVPO0aI3uHF99jTpGVloqY6onbfD++vGTolErBwbr/F3eK5QUNXrCeoQCqgcmHDLD2i/lUlP/iTbzBZEUMOoO3WOIhpTb8dv6Phzo6ZaoRh6VwnF7XazeuMOJo8e1umOrq52lPp8Pu6+/4+s3tPA5GPntZvEHC1VVVXcdNNNbNmyhZEjR3LnnXf2eoamr3fmiV6oLoMNb6puAsakmuOILl+daos0/hzoZANULCXdb//888/nwIEDLF68mPLyciZPnszbb7/dtPa8c+dOjC2aRh1zzDE8++yz3HLLLdx0002MGjWKV155pSlYArjhhhuoq6vjqquuoqamhlmzZvH2229HHCzFUlP7Ba1vSmZ1Zx07Eadv4zV+LeDB4d8PNcHmfIMQzUUYw0UZDUYwhMfUTj82Q4sq151qJyiJJFBpeUxHfedajq0j7QZbjde1adoWSWAWah5PsEVAGb4+qIOrHAiCsbFXnyW120FUWloas6Ye0eVxdrudiaPbbuMOs1gs/Pr849hnGU7hrAtjOsPncDg444wzOp0R6q6+zhUSvZBeBClZ4KmB1N7NLoreSboZpkQVqxkm/B5Y84Jq6hqnqFp0IqirhrChIOSNg5Rs1SpDMzdWrQ5/Hq6KbVYBU5vmu42fQ7crXHfaWLfdP++e/sl31Uw3wv5xh14fCgdLnXwMeNW7y4ZacB+Auv3gq1fNScNBlCUF7DntBGwxENRh32oYPBVGz4v53cmM0AC3cwXs+gJy20+qHxBkhkmIJNZQC64KyBysXjizhnc/2ImGeNxnNLVpRtwOs711Dkcw2BxAeZ0qiHLtBdc+9f8Ra/56Ips5iw6ZERrgHMWwdxUEGsAU/5WPgUoCJiG6Sw9A7S41WzR0BhRMVLMbou8YjSqAahlEla+FrR/0zf03ONUYUhJjt5fo59Ly1aW+GjLaL/EgYk8CJiG6o74a6ivVbNLgaX0zmyEikzpINcINeMEU2xppNNSopVUJmERfMGqQOwq2vh/vkQxoEjAJEYmAT80qWVJg+HGQPy72L8qie1JywZ6llunSerbFP2KBhubEcyH6QsZgsKSB1w3WxNpsM1D0zdYrIZJZfRXU7IScEhh9KgyeIsFSItJMauu1t48aYZtsKqlfiL5gz4KMIer5SMSFzDAJ0ZlQUC3DDZ8FBRNU3pJIXGn5gEHtYjPGaDdZeOehyS6PB9F3DAb1pq1yU3MjaNGn5DcuRGe8btWaIGekvDgmg7Q89f/ldcXuPnS/+mjUVM6UEH0lowjsmSqHTvQ5CZiE6ExDDaQXSg2sZGFJVf9fDbWxu4+AR30M19USoq9YUiG7BDwH4z2SAUkCJiE6E2gAx9B4j0J0h6MYdF/szh/OkQpXbxeiLzmGquW58Eyn6DMSMAnREV89mFMb82JE0kjNA3NKY3HJGGgIB0wSLIk4SC9UO0I91fEeyYAjAZMQHWmogdQctTtFJA97lmpRE6tluUCD+miVZVoRB5oZcg9vDtxFn5GASYiO+OpUgUrZjZJcjEb1/+ati+39SHV3ES+Zg8Fsi90sqmiXvBII0Z6AT72TSyuI90hET6TlqcBJD0T3vMFg4ycGVURQiHhIyVXPTVKTqU9JwCREexpqwJ6t2m2I5JM6CKyZ4I3yspzeuBxnSVXlC4SIB6NRtUrxNzTXBRMxJwGTEO3xulTVaE1quyYlk1Xtlot2noe/MWAy2yVgEvGVUdRYc0xymfqKBExCHCrYuIyTXhjfcYjeyRisKn6Hgl0fGylfY16UBEwi3myZ4BimOhGIPiEBkxCHanCqJ6NYN3AVsZWaC9bU5iAnGsI770w2FTQJEU/Zw9UbgmCUc/VEuyRgEuJQDbWQWSwviMnOlqlymaJZXkD3qo9Sm0skgvQiSMkCT028RzIgSMAkREuhoFrGyRwS75GI3jIY1JJFLLZep+ZG/5xCdJfZBtmHScDURyRgEqIlrxusabIc11+k5YFmhYC39+cKt1sxp0j+kkgcjqFqc0o0HuOiUxIwCdFSQy2kF0iz3f4iJVdV/o7GslzLCt9Sg0kkirR8tWPOuTfeI+n3JGASoqVAg1rGEf2DZlLvwL2u3p9LSgqIRGTUYMhRaiOC7JiLKQmYhAjz16vlFlmO61/SG6u1B3tZXsDvUR/NdlUFXohEkVEEg6eogCngi/do+i0JmIQI89RASo6q8C36j7S86BT4C99eluNEIsofr6p/1+6U6t8xIgGTEGG+OlXXRJrt9i+WVFWEtLd5TOGk73QpKSASkGaG4ulgc4C7It6j6ZfklUEIaNFsV14M+yVHcXPA0xPh5TyjJv0FReJKyVZBk78efDEopzHAScAkBKhmu7YseTHsr1IHqdyjntZkCjfdtTkk4VsktpxRkDcOnLt7n7cnWpGASQhQu6iyh0syb39lz1b5aT1dlvO3CJjMqVEblhBRZzTCkGmqCrhzT7xH069IwCREMKCqQod3U4n+x2iErOHg7WFfuXANJnOK5LiJxGdNh+KjgFB0WwMNcPKXL0SDUxUjlPyl/i11kAp29B40Kg1XUTZZojsmIWIlazgUTgFXRc8e86INCZiEaKhVveOk2W7/lpYH1kzw9uAdd7ikgD0rumMSIpYKJ0L2CFVqQPSaBExiYAsFISTNdgcEk1XtlmvoQT2mYOM7dClqKpKJ2QbFM9SbwbrKeI8m6UnAJAY2n1vV6ZEXwoEhowiCugqUIxUuRyDLtiIZpefD4GmqMG84F0/0iARMYmDz1EJaAdgy4z0S0RdSB4E1VQXKkQq/yNgyVXAtRLLJGwd5Y6BmV/Nsqeg2CZjEwOb3QJY02x0w7A41S9SdnUMtSwoIkYw0k2rQ6xgKVVub+yKKbkmqgKm6upqLLrqIjIwMHA4HV1xxBW53x+8Uq6ur+elPf8ro0aOx2+0MHTqU6667jtra1k+WBoOhzeX555+P9Y8j4s1fD5YUWWYZaLKGNwdBkdBlh5zoB+wOGHUSFEyE2j3gORjvESUdU7wH0B0XXXQR+/bt47333sPv93P55Zdz1VVX8eyzz7Z7/N69e9m7dy/33nsv48aNY8eOHVx99dXs3buXl19+udWxTzzxBHPnzm362uFwxPJHEYlAmu0OTGn5zVW/zSldHx9uMWGyxnZcQsSaJRVGHKd2e+75Qj22M4pUHTrRpaQJmNavX8/bb7/NF198wbRp0wB48MEHOeWUU7j33nspKipqc5vx48fzz3/+s+nrww47jDvuuIOLL76YQCCAydT84zscDgoKIi9c6PV68Xq9TV87nb3shC76nq8OBk+VQoQDTVPV75oIA6bGWWyZiRT9gWaCwVPAngk7l0N1GTiGqetFp5LmlWL58uU4HI6mYAmgtLQUo9HIihUrIj5PbW0tGRkZrYIlgJ/85Cfk5uYyffp0Hn/8cUKhUKfnWbJkCZmZmU2X4uLi7v1AIr78DWrGIL0w3iMRfc1ohKwRkSV+h3txaVYJmET/kl0Co+aqvKbqrdKsNwJJEzCVl5eTl9d667fJZCI7O5vy8vKIzlFZWcntt9/OVVdd1er62267jRdffJH33nuPs88+mx//+Mc8+OCDnZ5r0aJF1NbWNl127drVvR9IxJenWu2YSs2N90hEPKTng8HcXDKgI+Gmu3aHNN0V/U9qjsprKpoCzr1QXxXvESW0uM/B3Xjjjdx9992dHrN+/fpe34/T6eTUU09l3Lhx/O53v2v1vd/85jdNn0+ZMoW6ujruuecerrvuug7PZ7VasVolpyFp+epg8JFg1OI9EhEPqYNUHoenpvMaXOHkcGuG5DCJ/slsh+HHqjcFu75QpQcyB4MhaeZT+kzcA6Zf/OIXXHbZZZ0eU1JSQkFBAfv37291fSAQoLq6usvcI5fLxdy5c0lPT+ff//43ZnPnHelnzJjB7bffjtfrlaCoPwqEl+Pa5r2JAUIzq3ISe77sPGBq2iFn65txCREPRiMUTlKlM3Yuh6otjbl+2RI4tRD3gGnQoEEMGjSoy+NmzpxJTU0NK1euZOrUqQC8//77BINBZsyY0eHtnE4nc+bMwWq18p///AebresnvtWrV5OVlSXBUn/lOaiSfmU5bmDLKIQ9RlX5u6OZRm9jnpPW+ZssIfqFrGFqpunAJjiwASo3q69TcmU2ngQImCI1duxY5s6dy5VXXskjjzyC3+/n2muv5YILLmjaIbdnzx5OPPFEnn76aaZPn47T6eTkk0+mvr6ef/zjHzidzqbdbIMGDULTNF577TUqKio4+uijsdlsvPfee9x555388pe/jOePK2LJ61ZdvOUJYGBLywdbhipimdJBaYlw011pnSMGClsmFB+lKoNXl0HFt1C9DSx2SM0b0G8ekiZgAnjmmWe49tprOfHEEzEajZx99tn86U9/avq+3+9n48aN1NerbP9Vq1Y17aAbOXJkq3Nt27aN4cOHYzabeeihh/j5z39OKBRi5MiR3H///Vx55ZV994OJvhNoAM2iZhfEwGa2q6bL+9d3HDABYJDZSDHwWNPVMl3uaDi4Tf2d1OwEo0ltmhiAy9SGUFf750VEnE4nmZmZTWULosbvgTUvgMmu3g2L3nGVqyeCI74nM0xCLTlsfBtyStrmaug+KF+r8jomXSBBkxjYdL8KmPZ/C7W7IRRq3j1q7IO5F1+dmvEdf07cXguTaoZJiF7zOqFwsgRLQknLa27Gaz3kSTjQmPBtSVOzUUIMZJoZcg5TrYWce9SbDeceOLhDBU/WVLBmqr+Vflo5XAImMXAEvGo5Lj3yiu6in7NlQlqBesd8aMAUblBqsqoZXiGEerPpGKouvnqorwTXfqjdCfXVKogymtTfljWjX1UQ7z8/iRBd8RxUyyqSwCtayhqm3i0fyutSH01WaZ8jRHssKWBpDJ4GH6naDdUdUEUwa3erICqoqwDKbFetiMw29cY1CUnAJAYOn0slMcpynGgpLV898R/ajLehRn2U5sxCdM1oVJsnUrJh0GhV9LW+Ur1Rra9WgZTPrbos6AEwoAIns13N4JqsKrBK4OU8CZjEwBDwgtEsy3GirXAzXs/B9pvxpub0/ZiESHZmm9qFmjlEfR0KqTclXreavfW5wF0Jnir1eX1lcyAVQr2x1Swqd0qzQDAQz58GkIBJDBSeg6r4Wqosx4lDhJvx1rboBxlqbLobXkYQQvSOwQCWVHVJb9HIOhhUM09+DwQ86s2t36Pyo7y1KsAKNKhdepbUuK4QSMCUDAwauPZB3X7AoB54BqO63mBs/tpoUhfNpGZTjCZZfgrzuqBgYr9KQBRRlJ4PRgsEfGCyNO+QM0nAJERMGY2qTEBnpQICPhVMBXUVNMWJvHokOpMNhh6tIuygDiFdPXh0PwT96qPuU9OVAW/jR0/j9wPN75TVHKcKokwWdV6TTa0b9/deQQGfCiClWKXoSLgZb0ON2hTgV8VvMdlUfpMQIn5MFnWJ9zDiPQDRBYMBckdFdmwopIKngLcxkPK2/dxXp5LuvG6ViBdoQAVThsbt07bmS3+ZjWkI946T5TjRAc0M2cNhd2MzXk9N4/UWmWESQgASMPUvhnDQE0HT4IBPrRv76horqLqgvkq9UPhcavkvqKtzWdPBkp68AVSDC4aOT97xi76RXqD+hoKB5h1yZtuA7p0lhGgmryADlckCpuy2PbSCQfC3CKCce8HdWJQspDcuUaSDNa1vyuH3VsCnxinLcaIrafmq0F6Ds/m61EHxG48QIqEkwSue6FNGo5pRsqZDRhEUTFA7FuqrVQBVu1vV06jZqd6JW1LVcleiNmJsOKiCQilWKbpitkNmseqVBYBB+jcKIZpIwCS6ZrZD5mB1KZzYWA6/Sl0OblMNbfWAasRoz0qsnXkNbhh6hCyriMhkDoF9q9XnZhuY47cjRwiRWCRgEt1nSVEXR7GagXJXqBmnyi0qgDKa1KyTNT2+49R9asYsoyi+4xDJIy1P9cDyuZurEAshBBIwid4yaiogyShSbUdq90DVVnDuBuc+sKWDPSc+W0I9NbIcJ7rHlqFmSp171IYH2SEnhGgkAZOIHrMdckdCzmGqsnbtLtXU1LkbMKjigH35AtTgVDWsZDlOdIfJBhhBs0oNJiFEEwmYRPQZDM1NGPOOANdeqFgPB8tUIc20gti/EDUtx8nuONFNwSCkZDU2BE3QzQxCiD4nAZOILc0EjqGQMUQFTvvXQ3UZuAJqxilWZe49NWopMC2/y0OFaC2ocvBsmQndOV0I0bckYBJ9w2hUO5AyBqvaTvvXQ/VWtcMuPR8sadG9P68ThsyQ5TjRPUEdMKjHY3pBvEcjhEggEjCJvmUwqPIEGUXgGgf7N0D1FnBVqOTs3u6sC/jAXa4SdjNld5zoprpKwAA5I2HQ4fEejRAigUjAJOLDYFBBU3oh5I9TM05VjTNOdgfYs7tXzyngA9c+VY08sxjyj1CzWUJ0l5SiEEK0wxAKhULxHkR/4HQ6yczMpLa2lowMqQ7cbaH/397dxzR1vXEA/xaFAmrpEKQwFQEdRkURnKQsEQxMULbJZG4qUTQq6nTxbc6XbCOaODdnptGY4LKoMfFlM0HN3NQhik5FpohREYkw1KkUNxngOwjP7w9GYwVaitBb+H0/SRN6e871eThc++Tce8+VuoUwy24A9wuAR2V1SxF08TS/Fs7zZ3VF1ouFktaXz42jlqup5qlcImqA3ypkH1QqoItH3Us3sO4RLH8X1K2H87yq7o47Fy2gcqhrX18o1db8t4DmIMCtNwslenUsloioEfx2Ifvj6AJ49APcA+pWEf/3BnD/OnC/sO5RFbXP62aUtL51p/O0vvb1OBYiIupwWDCR/apfR0njXfcIlvJbwD8FgIPjf6feerNQIiIim2DBRO2DumvdbJJn/7rTd1wfh4iIbIgFE7UvDg5KR0BERP+H+O1DREREZAELJiIiIiILWDARERERWcCCiYiIiMgCFkxEREREFrBgIiIiIrKABRMRERGRBe2qYCorK0NiYiI0Gg20Wi2mT5+Ohw8fmu0TGRkJlUpl8po9e7ZJm1u3biEuLg6urq7o0aMHlixZgufPn7dlKkRERNSOtKuFKxMTE1FSUoL09HRUV1dj2rRpSE5Oxq5du8z2mzlzJlatWmV87+rqavy5pqYGcXFx0Ol0OHPmDEpKSjBlyhQ4Ojriq6++arNciIiIqP1QiYgoHURz5OfnY8CAATh37hyGDRsGADh8+DDGjBmD27dvw8fHp9F+kZGRCA4OxoYNGxr9/NChQ3jnnXdw9+5deHl5AQBSU1OxdOlS/P3333BycmpWfJWVlXBzc0NFRQU0Go31CRIREZHdajen5LKysqDVao3FEgBER0fDwcEB2dnZZvvu3LkTHh4eGDRoEJYvX47Hjx+b7DcoKMhYLAFATEwMKisrkZeX1+Q+nz17hsrKSpMXERERdUzt5pScwWBAjx49TLZ17twZ7u7uMBgMTfabNGkSfH194ePjg0uXLmHp0qUoKChAWlqacb8vFksAjO/N7XfNmjVYuXJlS9MhIiKidkTxgmnZsmX45ptvzLbJz89v8f6Tk5ONPwcFBcHb2xtRUVEoKipCQEBAi/e7fPlyLFq0yPi+srISvXr1avH+iIiIyH4pXjAtXrwYU6dONdvG398fOp0O9+7dM9n+/PlzlJWVQafTNfvfCwsLAwAUFhYiICAAOp0Of/zxh0mb0tJSADC7X7VaDbVabXxffykYT80RERG1P926dYNKpWryc8ULJk9PT3h6elpsp9frUV5ejpycHISGhgIAjh07htraWmMR1BwXL14EAHh7exv3u3r1aty7d894yi89PR0ajQYDBgxo9n4fPHgAAJxlIiIiaocs3bTVbu6SA4DRo0ejtLQUqampxmUFhg0bZlxW4M6dO4iKisKOHTswfPhwFBUVYdeuXRgzZgy6d++OS5cuYeHChejZsydOnDgBoG5ZgeDgYPj4+GDt2rUwGAyYPHkyZsyYYdWyArW1tbh7967FCtVa9af6/vrrrw55911Hzw/o+Dl29PyAjp8j82v/OnqOtsjP7meYrLFz507MmzcPUVFRcHBwQEJCAjZu3Gj8vLq6GgUFBca74JycnHD06FFs2LABjx49Qq9evZCQkIDPP//c2KdTp044ePAg5syZA71ejy5duiApKclk3abmcHBwQM+ePVsn0UZoNJoOeRDU6+j5AR0/x46eH9Dxc2R+7V9Hz1HJ/NpVweTu7m52kco+ffrgxQmzXr16GWeSzPH19cWvv/7aKjESERFRx9Nu1mEiIiIiUgoLJjunVquRkpJickdeR9LR8wM6fo4dPT+g4+fI/Nq/jp6jPeTXri76JiIiIlICZ5iIiIiILGDBRERERGQBCyYiIiIiC1gwEREREVnAgsnO3LhxA9OnT4efnx9cXFwQEBCAlJQUVFVVme339OlTzJ07F927d0fXrl2RkJBgfCaevVm9ejXCw8Ph6uoKrVbbrD5Tp06FSqUyecXGxrZtoC3UkvxEBF9++SW8vb3h4uKC6OhoXL9+vW0DfQVlZWVITEyERqOBVqvF9OnT8fDhQ7N9IiMjG4zh7NmzbRSxeZs3b0afPn3g7OyMsLCwBs+XfNnevXvRv39/ODs7IygoqF2s42ZNjtu3b28wVs7OzjaM1jonT57Eu+++Cx8fH6hUKuzfv99in8zMTISEhECtVqNv377Yvn17m8fZUtbml5mZ2WD8VCoVDAaDbQK20po1a/Dmm2+iW7du6NGjB+Lj41FQUGCxn62PQxZMdubatWuora3Fli1bkJeXh/Xr1yM1NRUrVqww22/hwoX4+eefsXfvXpw4cQJ3797FuHHjbBS1daqqqjB+/HjMmTPHqn6xsbEoKSkxvnbv3t1GEb6aluS3du1abNy4EampqcjOzkaXLl0QExODp0+ftmGkLZeYmIi8vDykp6fj4MGDOHnyJJKTky32mzlzpskYrl271gbRmvfjjz9i0aJFSElJwYULFzBkyBDExMQ0eNh3vTNnzmDixImYPn06cnNzER8fj/j4eFy5csXGkTeftTkCdSsqvzhWN2/etGHE1nn06BGGDBmCzZs3N6t9cXEx4uLiMHLkSFy8eBELFizAjBkzcOTIkTaOtGWsza9eQUGByRjWPy/V3pw4cQJz587F2bNnkZ6ejurqaowaNQqPHj1qso8ix6GQ3Vu7dq34+fk1+Xl5ebk4OjrK3r17jdvy8/MFgGRlZdkixBbZtm2buLm5NattUlKSjB07tk3jaW3Nza+2tlZ0Op18++23xm3l5eWiVqtl9+7dbRhhy1y9elUAyLlz54zbDh06JCqVSu7cudNkv4iICJk/f74NIrTO8OHDZe7cucb3NTU14uPjI2vWrGm0/YcffihxcXEm28LCwmTWrFltGuersDZHa45NewNA9u3bZ7bNZ599JgMHDjTZ9tFHH0lMTEwbRtY6mpPf8ePHBYD8+++/Nomptd27d08AyIkTJ5pso8RxyBmmdqCiogLu7u5Nfp6Tk4Pq6mpER0cbt/Xv3x+9e/dGVlaWLUK0iczMTPTo0QOBgYGYM2cO7t+/r3RIraK4uBgGg8Fk/Nzc3BAWFmaX45eVlQWtVothw4YZt0VHR8PBwQHZ2dlm++7cuRMeHh4YNGgQli9fbnzuo1KqqqqQk5Nj8rt3cHBAdHR0k7/7rKwsk/YAEBMTY5djBbQsRwB4+PAhfH190atXL4wdOxZ5eXm2CNcm2tsYtlRwcDC8vb3x9ttv4/Tp00qH02wVFRUAYPZ7T4kxbFfPkvt/VFhYiE2bNmHdunVNtjEYDHBycmpwvYyXl5fdnrO2VmxsLMaNGwc/Pz8UFRVhxYoVGD16NLKystCpUyelw3sl9WPk5eVlst1ex89gMDSY2u/cuTPc3d3Nxjtp0iT4+vrCx8cHly5dwtKlS1FQUIC0tLS2DrlJ//zzD2pqahr93V+7dq3RPgaDod2MFdCyHAMDA7F161YMHjwYFRUVWLduHcLDw5GXl9emDxm3labGsLKyEk+ePIGLi4tCkbUOb29vpKamYtiwYXj27Bl++OEHREZGIjs7GyEhIUqHZ1ZtbS0WLFiAt956C4MGDWqynRLHIWeYbGTZsmWNXoT34uvl/7zu3LmD2NhYjB8/HjNnzlQo8uZpSX7WmDBhAt577z0EBQUhPj4eBw8exLlz55CZmdl6SZjR1vnZg7bOMTk5GTExMQgKCkJiYiJ27NiBffv2oaioqBWzoNag1+sxZcoUBAcHIyIiAmlpafD09MSWLVuUDo2aITAwELNmzUJoaCjCw8OxdetWhIeHY/369UqHZtHcuXNx5coV7NmzR+lQGuAMk40sXrwYU6dONdvG39/f+PPdu3cxcuRIhIeH4/vvvzfbT6fToaqqCuXl5SazTKWlpdDpdK8SdrNZm9+r8vf3h4eHBwoLCxEVFdVq+21KW+ZXP0alpaXw9vY2bi8tLUVwcHCL9tkSzc1Rp9M1uFj4+fPnKCsrs+rvLSwsDEDdLGpAQIDV8bYGDw8PdOrUqcEdpeaOHZ1OZ1V7pbUkx5c5Ojpi6NChKCwsbIsQba6pMdRoNO1+dqkpw4cPx6lTp5QOw6x58+YZbyKxNJOpxHHIgslGPD094enp2ay2d+7cwciRIxEaGopt27bBwcH8RGBoaCgcHR2RkZGBhIQEAHV3R9y6dQt6vf6VY28Oa/JrDbdv38b9+/dNCoy21Jb5+fn5QafTISMjw1ggVVZWIjs72+o7CV9Fc3PU6/UoLy9HTk4OQkNDAQDHjh1DbW2tsQhqjosXLwKAzcawMU5OTggNDUVGRgbi4+MB1J0SyMjIwLx58xrto9frkZGRgQULFhi3paen2+xYs1ZLcnxZTU0NLl++jDFjxrRhpLaj1+sb3IJuz2PYGi5evKjosWaOiOCTTz7Bvn37kJmZCT8/P4t9FDkO2+xycmqR27dvS9++fSUqKkpu374tJSUlxteLbQIDAyU7O9u4bfbs2dK7d285duyYnD9/XvR6vej1eiVSsOjmzZuSm5srK1eulK5du0pubq7k5ubKgwcPjG0CAwMlLS1NREQePHggn376qWRlZUlxcbEcPXpUQkJCpF+/fvL06VOl0miStfmJiHz99dei1WrlwIEDcunSJRk7dqz4+fnJkydPlEjBotjYWBk6dKhkZ2fLqVOnpF+/fjJx4kTj5y//jRYWFsqqVavk/PnzUlxcLAcOHBB/f38ZMWKEUikY7dmzR9RqtWzfvl2uXr0qycnJotVqxWAwiIjI5MmTZdmyZcb2p0+fls6dO8u6deskPz9fUlJSxNHRUS5fvqxUChZZm+PKlSvlyJEjUlRUJDk5OTJhwgRxdnaWvLw8pVIw68GDB8bjDIB89913kpubKzdv3hQRkWXLlsnkyZON7f/8809xdXWVJUuWSH5+vmzevFk6deokhw8fVioFs6zNb/369bJ//365fv26XL58WebPny8ODg5y9OhRpVIwa86cOeLm5iaZmZkm33mPHz82trGH45AFk53Ztm2bAGj0Va+4uFgAyPHjx43bnjx5Ih9//LG89tpr4urqKu+//75JkWVPkpKSGs3vxXwAyLZt20RE5PHjxzJq1Cjx9PQUR0dH8fX1lZkzZxr/s7c31uYnUre0wBdffCFeXl6iVqslKipKCgoKbB98M92/f18mTpwoXbt2FY1GI9OmTTMpCF/+G71165aMGDFC3N3dRa1WS9++fWXJkiVSUVGhUAamNm3aJL179xYnJycZPny4nD171vhZRESEJCUlmbT/6aef5I033hAnJycZOHCg/PLLLzaO2HrW5LhgwQJjWy8vLxkzZoxcuHBBgaibp/42+pdf9TklJSVJREREgz7BwcHi5OQk/v7+JsejvbE2v2+++UYCAgLE2dlZ3N3dJTIyUo4dO6ZM8M3Q1Hfei2NiD8eh6r9giYiIiKgJvEuOiIiIyAIWTEREREQWsGAiIiIisoAFExEREZEFLJiIiIiILGDBRERERGQBCyYiIiIiC1gwEREREVnAgomIiIjIAhZMRERERBawYCIiIiKygAUTEVEjdu/eDRcXF5SUlBi3TZs2DYMHD0ZFRYWCkRGREvjwXSKiRogIgoODMWLECGzatAkpKSnYunUrzp49i9dff13p8IjIxjorHQARkT1SqVRYvXo1PvjgA+h0OmzatAm///47iyWi/1OcYSIiMiMkJAR5eXn47bffEBERoXQ4RKQQXsNERNSEw4cP49q1a6ipqYGXl5fS4RCRgjjDRETUiAsXLiAyMhJbtmzB9u3bodFosHfvXqXDIiKF8BomIqKX3LhxA3FxcVixYgUmTpwIf39/6PV6XLhwASEhIUqHR0QK4AwTEdELysrKEB4ejsjISKSmphq3x8XFoaamBocPH1YwOiJSCgsmIiIiIgt40TcRERGRBSyYiIiIiCxgwURERERkAQsmIiIiIgtYMBERERFZwIKJiIiIyAIWTEREREQWsGAiIiIisoAFExEREZEFLJiIiIiILGDBRERERGTB/wDt3Q37oFaFbAAAAABJRU5ErkJggg==\n" + }, + "metadata": {} + } + ], + "source": [ + "plt.figure()\n", + "latexify(width_scale_factor=2, fig_height=1.75)\n", + "plt.plot(xnew, mu_dgp, \"b\")\n", + "plt.scatter(x, y, c=\"r\", s=marksize)\n", + "plt.fill_between(\n", + " xnew.flatten(),\n", + " mu_dgp.flatten() - 1.96 * jnp.sqrt(var_dgp.flatten()),\n", + " mu_dgp.flatten() + 1.96 * jnp.sqrt(var_dgp.flatten()),\n", + " alpha=0.3,\n", + " color=\"C1\",\n", + ")\n", + "plt.plot(xnew, np.array(sample).reshape(-1, num), \"k.\", markersize=3, alpha=0.3)\n", + "sns.despine()\n", + "legendsize = 5 if is_latexify_enabled() else 9\n", + "plt.legend(labels=[\"Mean\", \"Data\", \"Confidence\", \"Samples\"], loc=(0.2, 0.8), prop={\"size\": legendsize}, frameon=False)\n", + "plt.xlabel(\"$x$\")\n", + "plt.ylabel(\"$y$\")\n", + "savefig(\"deep_gp_stepdata_fit\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "id": "AEKHEme9H72k" + }, + "source": [ + "## Plot Input to each Deep GP layers" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "id": "NGwe5EFUH72k", + "outputId": "0199931f-5582-4ec2-9288-2979b4dea79d", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 1000 + } + }, + "outputs": [ + { + "output_type": "stream", + "name": "stderr", + "text": [ + " /usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py:68: UserWarning:Explicitly requested dtype float requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", + " /usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py:68: UserWarning:Explicitly requested dtype float requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", + " /usr/local/lib/python3.10/dist-packages/probml_utils/plotting.py:84: UserWarning:set FIG_DIR environment variable to save figures\n", + " /usr/local/lib/python3.10/dist-packages/probml_utils/plotting.py:25: UserWarning:LATEXIFY environment variable not set, not latexifying\n", + " /usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py:68: UserWarning:Explicitly requested dtype float requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", + " /usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py:68: UserWarning:Explicitly requested dtype float requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", + " /usr/local/lib/python3.10/dist-packages/probml_utils/plotting.py:84: UserWarning:set FIG_DIR environment variable to save figures\n", + " /usr/local/lib/python3.10/dist-packages/probml_utils/plotting.py:25: UserWarning:LATEXIFY environment variable not set, not latexifying\n", + " /usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py:68: UserWarning:Explicitly requested dtype float requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", + " /usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py:68: UserWarning:Explicitly requested dtype float requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", + " /usr/local/lib/python3.10/dist-packages/probml_utils/plotting.py:84: UserWarning:set FIG_DIR environment variable to save figures\n", + " /usr/local/lib/python3.10/dist-packages/probml_utils/plotting.py:25: UserWarning:LATEXIFY environment variable not set, not latexifying\n", + " /usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py:68: UserWarning:Explicitly requested dtype float requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", + " /usr/local/lib/python3.10/dist-packages/jax/_src/numpy/array_methods.py:68: UserWarning:Explicitly requested dtype float requested in astype is not available, and will be truncated to dtype float32. To enable more dtypes, set the jax_enable_x64 configuration option or the JAX_ENABLE_X64 shell environment variable. See https://github.com/google/jax#current-gotchas for more.\n", + " /usr/local/lib/python3.10/dist-packages/probml_utils/plotting.py:84: UserWarning:set FIG_DIR environment variable to save figures\n" + ] + }, + { + "output_type": "display_data", + "data": { + "text/plain": [ + "
" + ], + "image/png": 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\n" 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\n" 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\n" 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\n" + }, + "metadata": {} + } + ], + "source": [ + "def plot_dgp_layers(model, X, training_points=True):\n", + " \"\"\"Plot mappings between layers in a deep GP\"\"\"\n", + "\n", + " num_layers = len(model.layers)\n", + " layer_input = X\n", + "\n", + " # The layers in a deep GP are ordered from observation to input,\n", + " layers_name = [\"layer1\", \"layer2\", \"layer3\"]\n", + " layers = list(reversed(model.layers))\n", + " for i, layer in enumerate(layers):\n", + " plt.figure()\n", + " latexify(width_scale_factor=2, fig_height=1.75)\n", + " mu_i, var_i = layer.predict(layer_input, include_likelihood=True)\n", + " plt.plot(layer_input, mu_i, \"blue\")\n", + " plt.fill_between(\n", + " layer_input[:, 0],\n", + " mu_i.flatten() - 1.96 * jnp.sqrt(var_i.flatten()),\n", + " mu_i.flatten() + 1.96 * jnp.sqrt(var_i.flatten()),\n", + " alpha=0.3,\n", + " color=\"C1\",\n", + " )\n", + "\n", + " plt.ylabel(layers_name[i] if i < len(layers) - 1 else \"output\")\n", + " plt.xlabel(layers_name[i - 1] if i > 0 else \"input\")\n", + " if training_points: # Plot propagated training points\n", + " plt.plot(\n", + " layer.X.mean.values if i > 0 else layer.X,\n", + " layer.Y.mean.values if i < num_layers - 1 else layer.Y,\n", + " \"r.\",\n", + " markersize=marksize,\n", + " )\n", + "\n", + " legendsize = 6 if is_latexify_enabled() else 9\n", + " if i == 3:\n", + " plt.legend(labels=[\"Mean\", \"Confidence\", \"Data\"], loc=(0.5, 0.2), prop={\"size\": legendsize}, frameon=False)\n", + " sns.despine()\n", + " savefig(\"deep_gp_input_layer{}\".format(i + 1))\n", + "\n", + "\n", + "plot_dgp_layers(m, xnew.reshape(-1, 1))" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "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": "3.10.4" + }, + 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optimizerL-BFGS-B (Scipy implementation)
runtime11s98
evaluation00059
objective -7.470E+01
||gradient|| +1.983E+02
statusConverged
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\nModel: deepgp
\nObjective: -74.69549181478446
\nNumber of Parameters: 708
\nNumber of Optimization Parameters: 708
\nUpdates: True
\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
deepgp. valueconstraintspriors
obslayer.inducing inputs (50, 1)
obslayer.Gaussian_noise.variance8.190950723380839e-05 +ve
obslayer.Kuu_var (50,) +ve
obslayer.latent space.mean (50, 1)
obslayer.latent space.variance (50, 1) +ve
layer_1.inducing inputs (50, 1)
layer_1.Gaussian_noise.variance 0.01938008363828453 +ve
layer_1.Kuu_var (50,) +ve
layer_1.latent space.mean (50, 1)
layer_1.latent space.variance (50, 1) +ve
layer_2.inducing inputs (50, 1)
layer_2.rbf.variance 0.5690875141858986 +ve
layer_2.rbf.lengthscale 0.6685296477093707 +ve
layer_2.Gaussian_noise.variance 0.03606230658517032 +ve
layer_2.Kuu_var (50,) +ve
layer_2.latent space.mean (50, 1)
layer_2.latent space.variance (50, 1) +ve
layer_3.inducing inputs (50, 1)
layer_3.rbf.variance 0.7661055514379832 +ve
layer_3.rbf.lengthscale 0.654213286105518 +ve
layer_3.Gaussian_noise.variance 0.033991288120161514 +ve
layer_3.Kuu_var (50,) +ve
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install git+https://github.com/probml/probml-utils.git\n", - " from probml_utils import latexify, savefig, is_latexify_enabled\n", - "\n", - "try:\n", - " import tinygp\n", - "except ModuleNotFoundError:\n", - " %pip install -q tinygp\n", - " import tinygp\n", - "\n", - "# import display\n", - "import seaborn as sns\n", - "import jax\n", - "import jax.numpy as jnp\n", - "import matplotlib.pyplot as plt\n", - "from tinygp import kernels, GaussianProcess\n", - "from jax.config import config\n", - "\n", - "import numpy as np\n", - "\n", - "try:\n", - " import jaxopt\n", - "except ModuleNotFoundError:\n", - " %pip install jaxopt\n", - " import jaxopt\n", - "config.update(\"jax_enable_x64\", True)\n", - "\n", - "latexify(width_scale_factor=2, fig_height=1.75)\n", - "marksize = 3 if is_latexify_enabled() else 4" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step Data" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "num_low = 25\n", - "num_high = 25\n", - "gap = -0.1\n", - "noise = 0.0001\n", - "x = jnp.vstack(\n", - " (jnp.linspace(-1, -gap / 2.0, num_low)[:, jnp.newaxis], jnp.linspace(gap / 2.0, 1, num_high)[:, jnp.newaxis])\n", - ").reshape(\n", - " -1,\n", - ")\n", - "y = jnp.vstack((jnp.zeros((num_low, 1)), jnp.ones((num_high, 1))))\n", - "scale = jnp.sqrt(y.var())\n", - "offset = y.mean()\n", - "yhat = ((y - offset) / scale).reshape(\n", - " -1,\n", - ")\n", - "\n", - "fig = plt.figure()\n", - "plt.plot(x, y, \"r.\", markersize=marksize)\n", - "plt.xlabel(\"$x$\")\n", - "plt.ylabel(\"$y$\")\n", - "xlim = (-2, 2)\n", - "ylim = (-0.6, 1.6)\n", - "plt.ylim(ylim)\n", - "plt.xlim(xlim)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## GPy" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "def neg_log_likelihood(theta, X, y):\n", - " kernel = jnp.exp(theta[\"log_amp\"]) * kernels.ExpSquared(scale=jnp.exp(theta[\"log_scale\"]))\n", - " gp = GaussianProcess(kernel, X, diag=jnp.exp(theta[\"log_diag\"]))\n", - " return -gp.log_probability(y)\n", - "\n", - "\n", - "theta_init = {\"log_scale\": jnp.log(1.0), \"log_diag\": jnp.log(1.0), \"log_amp\": jnp.log(1.0)}\n", - "obj = jax.jit(jax.value_and_grad(neg_log_likelihood))\n", - "solver = jaxopt.ScipyMinimize(fun=neg_log_likelihood, method=\"L-BFGS-B\")\n", - "soln = solver.run(\n", - " theta_init,\n", - " X=x,\n", - " y=y.reshape(\n", - " -1,\n", - " ),\n", - ")\n", - "\n", - "kernel = jnp.exp(soln.params[\"log_amp\"]) * kernels.ExpSquared(scale=jnp.exp(soln.params[\"log_scale\"]))\n", - "gp = GaussianProcess(kernel, x, diag=jnp.exp(soln.params[\"log_diag\"]))\n", - "\n", - "xnew = jnp.vstack(\n", - " (jnp.linspace(-2, -gap / 2.0, 25)[:, jnp.newaxis], jnp.linspace(gap / 2.0, 2, 25)[:, jnp.newaxis])\n", - ").reshape(\n", - " -1,\n", - ")\n", - "cond_gp = gp.condition(\n", - " y.reshape(\n", - " -1,\n", - " ),\n", - " xnew,\n", - ").gp\n", - "mu, var = cond_gp.loc, cond_gp.variance\n", - "\n", - "var = var + jnp.exp(soln.params[\"log_diag\"])" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Plotting GP Fit" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "fig = plt.figure()\n", - "latexify(width_scale_factor=2, fig_height=1.75)\n", - "\n", - "plt.plot(x, y, \"r.\", markersize=marksize)\n", - "plt.plot(xnew, mu, \"blue\", markersize=marksize)\n", - "plt.fill_between(\n", - " xnew.flatten(),\n", - " mu.flatten() - 1.96 * jnp.sqrt(var),\n", - " mu.flatten() + 1.96 * jnp.sqrt(var),\n", - " alpha=0.3,\n", - " color=\"C1\",\n", - ")\n", - "\n", - "sns.despine()\n", - "legendsize = 5 if is_latexify_enabled() else 9\n", - "plt.legend(labels=[\"Mean\", \"Data\", \"Confidence\"], loc=(0.5, 0.2), prop={\"size\": legendsize}, frameon=False)\n", - "# ax.title(\"$(l, \\sigma_f, \\sigma_y)=${}, {}, {}\".format(length_scale, sigma_f, sigma_y))\n", - "plt.xlabel(\"$x$\")\n", - "plt.ylabel(\"$y$\")\n", - "\n", - "savefig(\"gp_stepdata_fit\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Deep GP" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "num_hidden = 3\n", - "latent_dim = 1\n", - "\n", - "kernels = [*[GPy.kern.RBF(latent_dim, ARD=True)] * num_hidden] # hidden kernels\n", - "kernels.append(GPy.kern.RBF(np.array(x.reshape(-1, 1)).shape[1])) # we append a kernel for the input layer\n", - "\n", - "m = deepgp.DeepGP(\n", - " # this describes the shapes of the inputs and outputs of our latent GPs\n", - " [y.reshape(-1, 1).shape[1], *[latent_dim] * num_hidden, x.reshape(-1, 1).shape[1]],\n", - " X=np.array(x.reshape(-1, 1)), # training input\n", - " Y=np.array(y.reshape(-1, 1)), # training outout\n", - " inits=[*[\"PCA\"] * num_hidden, \"PCA\"], # initialise layers\n", - " kernels=kernels,\n", - " num_inducing=x.shape[0],\n", - " back_constraint=False,\n", - ")\n", - "m.initialize_parameter()\n", - "# display(m)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Optimizing Deep GP" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "def optimise_dgp(model, messages=True):\n", - " \"\"\"Utility function for optimising deep GP by first\n", - " reinitiailising the Gaussian noise at each layer\n", - " (for reasons pertaining to stability)\n", - " \"\"\"\n", - " model.initialize_parameter()\n", - " for layer in model.layers:\n", - " layer.likelihood.variance.constrain_positive(warning=False)\n", - " layer.likelihood.variance = 1.0 # small variance may cause collapse\n", - " model.optimize(messages=messages, max_iters=10000)\n", - "\n", - "\n", - "optimise_dgp(m, messages=True)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "# m.optimize_restarts(num_restarts=5)\n", - "mu_dgp, var_dgp = m.predict(xnew.reshape(-1, 1))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Samples from Data" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "def sample_dgp(model, X, num_samples=1, include_likelihood=True):\n", - " samples = []\n", - " jitter = 1e-5\n", - " count, num_tries = 0, 100\n", - " while len(samples) < num_samples:\n", - " next_input = X\n", - " if count > num_tries:\n", - " print(\"failed to sample\")\n", - " break\n", - " try:\n", - " count = count + 1\n", - " for layer in reversed(model.layers):\n", - " mu_k, sig_k = layer.predict(next_input, full_cov=True, include_likelihood=include_likelihood)\n", - " sample_k = mu_k + np.linalg.cholesky(sig_k + jitter * np.eye(X.shape[0])) @ np.random.randn(*X.shape)\n", - " next_input = sample_k\n", - " samples.append(sample_k)\n", - " count = 0\n", - " except:\n", - " pass\n", - "\n", - " return samples if num_samples > 1 else samples[0]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Plot Deep GP fit without samples" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "plt.figure()\n", - "num = 5\n", - "sample = sample_dgp(m, xnew.reshape(-1, 1), num, include_likelihood=False)\n", - "latexify(width_scale_factor=2, fig_height=1.75)\n", - "plt.plot(xnew, mu_dgp, \"blue\")\n", - "plt.scatter(x, y, c=\"r\", s=marksize)\n", - "plt.fill_between(\n", - " xnew.flatten(),\n", - " mu_dgp.flatten() - 1.96 * jnp.sqrt(var_dgp.flatten()),\n", - " mu_dgp.flatten() + 1.96 * jnp.sqrt(var_dgp.flatten()),\n", - " alpha=0.3,\n", - " color=\"C1\",\n", - ")\n", - "sns.despine()\n", - "legendsize = 4.5 if is_latexify_enabled() else 9\n", - "plt.legend(labels=[\"Mean\", \"Data\", \"Confidence\"], loc=2, prop={\"size\": legendsize}, frameon=False)\n", - "plt.xlabel(\"$x$\")\n", - "plt.ylabel(\"$y$\")\n", - "sns.despine()\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Plot Deep GP fit with samples" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "plt.figure()\n", - "latexify(width_scale_factor=2, fig_height=1.75)\n", - "plt.plot(xnew, mu_dgp, \"b\")\n", - "plt.scatter(x, y, c=\"r\", s=marksize)\n", - "plt.fill_between(\n", - " xnew.flatten(),\n", - " mu_dgp.flatten() - 1.96 * jnp.sqrt(var_dgp.flatten()),\n", - " mu_dgp.flatten() + 1.96 * jnp.sqrt(var_dgp.flatten()),\n", - " alpha=0.3,\n", - " color=\"C1\",\n", - ")\n", - "plt.plot(xnew, np.array(sample).reshape(-1, num), \"k.\", markersize=3, alpha=0.3)\n", - "sns.despine()\n", - "legendsize = 5 if is_latexify_enabled() else 9\n", - "plt.legend(labels=[\"Mean\", \"Data\", \"Confidence\", \"Samples\"], loc=(0.2, 0.8), prop={\"size\": legendsize}, frameon=False)\n", - "plt.xlabel(\"$x$\")\n", - "plt.ylabel(\"$y$\")\n", - "savefig(\"deep_gp_stepdata_fit\")\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Plot Input to each Deep GP layers" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "def plot_dgp_layers(model, X, training_points=True):\n", - " \"\"\"Plot mappings between layers in a deep GP\"\"\"\n", - "\n", - " num_layers = len(model.layers)\n", - " layer_input = X\n", - "\n", - " # The layers in a deep GP are ordered from observation to input,\n", - " layers_name = [\"layer1\", \"layer2\", \"layer3\"]\n", - " layers = list(reversed(model.layers))\n", - " for i, layer in enumerate(layers):\n", - " plt.figure()\n", - " latexify(width_scale_factor=2, fig_height=1.75)\n", - " mu_i, var_i = layer.predict(layer_input, include_likelihood=True)\n", - " plt.plot(layer_input, mu_i, \"blue\")\n", - " plt.fill_between(\n", - " layer_input[:, 0],\n", - " mu_i.flatten() - 1.96 * jnp.sqrt(var_i.flatten()),\n", - " mu_i.flatten() + 1.96 * jnp.sqrt(var_i.flatten()),\n", - " alpha=0.3,\n", - " color=\"C1\",\n", - " )\n", - "\n", - " plt.ylabel(layers_name[i] if i < len(layers) - 1 else \"output\")\n", - " plt.xlabel(layers_name[i - 1] if i > 0 else \"input\")\n", - " if training_points: # Plot propagated training points\n", - " plt.plot(\n", - " layer.X.mean.values if i > 0 else layer.X,\n", - " layer.Y.mean.values if i < num_layers - 1 else layer.Y,\n", - " \"r.\",\n", - " markersize=marksize,\n", - " )\n", - "\n", - " legendsize = 6 if is_latexify_enabled() else 9\n", - " if i == 3:\n", - " plt.legend(labels=[\"Mean\", \"Confidence\", \"Data\"], loc=(0.5, 0.2), prop={\"size\": legendsize}, frameon=False)\n", - " sns.despine()\n", - " savefig(\"deep_gp_input_layer{}\".format(i + 1))\n", - "\n", - "\n", - "plot_dgp_layers(m, xnew.reshape(-1, 1))" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3.10.4 ('pyprob')", - "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": "3.10.4" - }, - "orig_nbformat": 4, - "vscode": { - "interpreter": { - "hash": "2c5a0c76092399a6bd22c426573677968c7f47e4ef0855af24014a5bf1c5bd34" - } - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file