diff --git a/notebooks/book1/04/laplace_approx_beta_binom_jax.ipynb b/notebooks/book1/04/laplace_approx_beta_binom_jax.ipynb
index dfbf9f86204..8b5b29e21a0 100644
--- a/notebooks/book1/04/laplace_approx_beta_binom_jax.ipynb
+++ b/notebooks/book1/04/laplace_approx_beta_binom_jax.ipynb
@@ -7,12 +7,14 @@
    "source": [
     "# Laplace approximation ( Quadratic approximation) \n",
     "\n",
-    "In this notebook we will approximate posterior of beta-bernouli model for coin toss problem using laplace approximation method"
+    "In this notebook we will approximate posterior of beta-bernouli model for coin toss problem using laplace approximation method\n",
+    "\n",
+    "author: @karm-patel @nipunbatra"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 1,
    "id": "f9c1338c",
    "metadata": {},
    "outputs": [],
@@ -58,17 +60,20 @@
     "import warnings\n",
     "\n",
     "warnings.filterwarnings(\"ignore\")\n",
-    "dist = tfp.distributions"
+    "dist = tfp.distributions\n",
+    "\n",
+    "import os"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": 2,
-   "id": "76d8b346",
+   "id": "2bced3b9",
    "metadata": {},
    "outputs": [],
    "source": [
-    "latexify(width_scale_factor=2, fig_height=2)  # to apply latexify, set LATEXIFY=1 in environment variable"
+    "os.environ[\"LATEXIFY\"] = \"\"\n",
+    "os.environ[\"FIG_DIR\"] = \"figures\""
    ]
   },
   {
@@ -133,7 +138,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": 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\n",
       "text/plain": [
        "<Figure size 432x288 with 2 Axes>"
       ]
@@ -229,7 +234,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 8,
    "id": "9749aaa5",
    "metadata": {},
    "outputs": [],
@@ -252,7 +257,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 9,
    "id": "36236690",
    "metadata": {},
    "outputs": [],
@@ -267,13 +272,13 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 10,
    "id": "d94f5415",
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": "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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -292,7 +297,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 11,
    "id": "67f02005",
    "metadata": {},
    "outputs": [
@@ -326,7 +331,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 12,
    "id": "15b14b76",
    "metadata": {},
    "outputs": [
@@ -351,7 +356,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 13,
    "id": "35d513a0",
    "metadata": {},
    "outputs": [
@@ -385,15 +390,33 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 14,
+   "id": "f95d1dd9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "latexify(fig_width=0.45 * 6, fig_height=1.5)  # to apply latexify, set LATEXIFY=1 in environment variable"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
    "id": "291fb43e",
    "metadata": {},
    "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "saving image to figures/bb_laplace_latexified.pdf\n",
+      "Figure size: [2.7 1.5]\n"
+     ]
+    },
     {
      "data": {
-      "image/png": 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\n",
+      "image/png": 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\n",
       "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
+       "<Figure size 194.4x108 with 1 Axes>"
       ]
      },
      "metadata": {
@@ -405,9 +428,8 @@
    "source": [
     "plt.figure()\n",
     "y = jnp.exp(dist.Normal(loc, scale).log_prob(theta_range))\n",
-    "plt.title(\"Quadratic approximation\")\n",
-    "plt.plot(theta_range, y, label=\"laplace approximation\", color=\"tab:red\")\n",
-    "plt.plot(theta_range, exact_posterior.prob(theta_range), label=\"true posterior\", color=\"tab:green\", linestyle=\"--\")\n",
+    "plt.plot(theta_range, y, label=\"Laplace approximation\", color=\"tab:orange\", linestyle=\"--\", lw=3)\n",
+    "plt.plot(theta_range, exact_posterior.prob(theta_range), label=\"True posterior\", color=\"tab:blue\")\n",
     "plt.xlabel(\"$\\\\theta$\")\n",
     "plt.ylabel(\"$p(\\\\theta)$\")\n",
     "sns.despine()\n",
@@ -417,138 +439,84 @@
   },
   {
    "cell_type": "markdown",
-   "id": "29bf9a93",
+   "id": "2c9f554b",
    "metadata": {},
    "source": [
-    "## Pymc"
+    "# Grid Approximation"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
-   "id": "cbadfd36",
+   "execution_count": 16,
+   "id": "ac8d875a",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "WARNING:theano.link.c.cmodule:install mkl with `conda install mkl-service`: No module named 'mkl'\n",
-      "WARNING:theano.tensor.blas:Using NumPy C-API based implementation for BLAS functions.\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
-    "try:\n",
-    "    import pymc3 as pm\n",
-    "except ModuleNotFoundError:\n",
-    "    %pip install -qq pymc3\n",
-    "    import pymc3 as pm\n",
-    "try:\n",
-    "    import scipy.stats as stats\n",
-    "except ModuleNotFoundError:\n",
-    "    %pip install -qq scipy\n",
-    "    import scipy.stats as stats\n",
-    "\n",
-    "import scipy.special as sp\n",
-    "\n",
-    "try:\n",
-    "    import arviz as az\n",
-    "except ModuleNotFoundError:\n",
-    "    %pip install -qq arviz\n",
-    "    import arviz as az\n",
-    "\n",
-    "import math"
+    "n_points_grid = 20\n",
+    "theta_range = jnp.linspace(0.01, 0.99, n_points_grid)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
-   "id": "0022fcbc",
+   "execution_count": 17,
+   "id": "16050b3d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "likelihood = jax.vmap(lambda x: jnp.prod(likelihood_dist(x).prob(dataset)))(theta_range)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "7e43ffc2",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "unnormalized_post = prior_dist().prob(theta_range) * likelihood\n",
+    "grid_appx = (unnormalized_post / unnormalized_post.sum()) * n_points_grid  # Done so that the area under curve sums to 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "id": "074adfa4",
    "metadata": {},
    "outputs": [
     {
      "data": {
-      "text/html": [
-       "\n",
-       "<style>\n",
-       "    /* Turns off some styling */\n",
-       "    progress {\n",
-       "        /* gets rid of default border in Firefox and Opera. */\n",
-       "        border: none;\n",
-       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
-       "        background-size: auto;\n",
-       "    }\n",
-       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
-       "        background: #F44336;\n",
-       "    }\n",
-       "</style>\n"
-      ],
-      "text/plain": [
-       "<IPython.core.display.HTML object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "text/html": [
-       "\n",
-       "    <div>\n",
-       "      <progress value='8' class='' max='8' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
-       "      100.00% [8/8 00:00<00:00 logp = -7.6246, ||grad|| = 4.5]\n",
-       "    </div>\n",
-       "    "
-      ],
       "text/plain": [
-       "<IPython.core.display.HTML object>"
+       "20"
       ]
      },
+     "execution_count": 19,
      "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n"
-     ]
+     "output_type": "execute_result"
     }
    ],
    "source": [
-    "# Laplace\n",
-    "with pm.Model() as normal_aproximation:\n",
-    "    theta = pm.Beta(\"theta\", 1.0, 1.0)\n",
-    "    y = pm.Binomial(\"y\", n=1, p=theta, observed=dataset)  # Bernoulli\n",
-    "    mean_q = pm.find_MAP()\n",
-    "    std_q = ((1 / pm.find_hessian(mean_q, vars=[theta])) ** 0.5)[0]\n",
-    "    loc = mean_q[\"theta\"]\n",
-    "\n",
-    "# plt.savefig('bb_laplace.pdf');"
+    "len(grid_appx)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
-   "id": "73a0b4f8",
+   "execution_count": 20,
+   "id": "db5aa5e9",
    "metadata": {},
    "outputs": [
     {
-     "data": {
-      "text/plain": [
-       "<matplotlib.legend.Legend at 0x7fe99724c130>"
-      ]
-     },
-     "execution_count": 21,
-     "metadata": {},
-     "output_type": "execute_result"
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "saving image to figures/bb_grid_latexified.pdf\n",
+      "Figure size: [2.7 1.5]\n"
+     ]
     },
     {
      "data": {
-      "image/png": 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\n",
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\n",
       "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
+       "<Figure size 194.4x108 with 1 Axes>"
       ]
      },
      "metadata": {
@@ -558,24 +526,31 @@
     }
    ],
    "source": [
-    "x = theta_range\n",
-    "\n",
     "plt.figure()\n",
-    "plt.plot(x, stats.norm.pdf(x, loc, std_q), \"--\", label=\"Laplace\")\n",
-    "post_exact = stats.beta.pdf(x, n_heads + 1, n_tails + 1)\n",
-    "plt.plot(x, post_exact, label=\"exact\")\n",
-    "plt.title(\"Quadratic approximation\")\n",
-    "plt.xlabel(\"θ\", fontsize=14)\n",
-    "plt.yticks([])\n",
-    "plt.legend()"
+    "plt.plot(jnp.linspace(0.01, 0.99, 100), exact_posterior.prob(jnp.linspace(0.01, 0.99, 100)), label=\"True Posterior\")\n",
+    "plt.plot(theta_range, grid_appx, label=\"Grid approximation\", linestyle=\"--\", lw=3)\n",
+    "\n",
+    "plt.legend()\n",
+    "plt.xlabel(\"$\\\\theta$\")\n",
+    "plt.ylabel(\"$p(\\\\theta)$\")\n",
+    "sns.despine()\n",
+    "savefig(\"bb_grid\")"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9da5b77f",
+   "metadata": {},
+   "outputs": [],
+   "source": []
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python [conda env:pymc_exp]",
+   "display_name": "Python [conda env:py3713]",
    "language": "python",
-   "name": "conda-env-pymc_exp-py"
+   "name": "conda-env-py3713-py"
   },
   "language_info": {
    "codemirror_mode": {
@@ -587,7 +562,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.0"
+   "version": "3.7.13"
   }
  },
  "nbformat": 4,
diff --git a/notebooks/book1/04/laplace_approx_beta_binom_pymc3.ipynb b/notebooks/book1/04/laplace_approx_beta_binom_pymc3.ipynb
new file mode 100644
index 00000000000..d431376b9b3
--- /dev/null
+++ b/notebooks/book1/04/laplace_approx_beta_binom_pymc3.ipynb
@@ -0,0 +1,328 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "29bf9a93",
+   "metadata": {},
+   "source": [
+    "## Pymc"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "cbadfd36",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import jax\n",
+    "import jax.numpy as jnp\n",
+    "from jax import lax\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "try:\n",
+    "    from tensorflow_probability.substrates import jax as tfp\n",
+    "except ModuleNotFoundError:\n",
+    "    %pip install -qqq tensorflow_probability\n",
+    "    from tensorflow_probability.substrates import jax as tfp\n",
+    "\n",
+    "dist = tfp.distributions\n",
+    "\n",
+    "\n",
+    "try:\n",
+    "    import pymc3 as pm\n",
+    "except ModuleNotFoundError:\n",
+    "    %pip install -qq pymc3\n",
+    "    import pymc3 as pm\n",
+    "\n",
+    "try:\n",
+    "    import scipy.stats as stats\n",
+    "except ModuleNotFoundError:\n",
+    "    %pip install -qq scipy\n",
+    "    import scipy.stats as stats\n",
+    "\n",
+    "import scipy.special as sp\n",
+    "\n",
+    "try:\n",
+    "    import arviz as az\n",
+    "except ModuleNotFoundError:\n",
+    "    %pip install -qq arviz\n",
+    "    import arviz as az\n",
+    "\n",
+    "import math"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "7b6487c1",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Dataset: [0 0 0 0 0 0 0 0 0 0 1]\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Use same data as https://github.com/probml/probml-notebooks/blob/main/notebooks/beta_binom_approx_post_pymc.ipynb\n",
+    "key = jax.random.PRNGKey(128)\n",
+    "dataset = np.repeat([0, 1], (10, 1))\n",
+    "n_samples = len(dataset)\n",
+    "print(f\"Dataset: {dataset}\")\n",
+    "n_heads = dataset.sum()\n",
+    "n_tails = n_samples - n_heads"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "c04b4e84",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# prior distribution ~ Beta\n",
+    "def prior_dist():\n",
+    "    return dist.Beta(concentration1=1.0, concentration0=1.0)\n",
+    "\n",
+    "\n",
+    "# likelihood distribution ~ Bernoulli\n",
+    "def likelihood_dist(theta):\n",
+    "    return dist.Bernoulli(probs=theta)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "6d16a8df",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 2 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# closed form of beta posterior\n",
+    "a = prior_dist().concentration1\n",
+    "b = prior_dist().concentration0\n",
+    "\n",
+    "exact_posterior = dist.Beta(concentration1=a + n_heads, concentration0=b + n_tails)\n",
+    "\n",
+    "theta_range = jnp.linspace(0.01, 0.99, 100)\n",
+    "\n",
+    "ax = plt.gca()\n",
+    "ax2 = ax.twinx()\n",
+    "(plt2,) = ax2.plot(theta_range, exact_posterior.prob(theta_range), \"g--\", label=\"True Posterior\")\n",
+    "(plt3,) = ax2.plot(theta_range, prior_dist().prob(theta_range), label=\"Prior\")\n",
+    "\n",
+    "likelihood = jax.vmap(lambda x: jnp.prod(likelihood_dist(x).prob(dataset)))(theta_range)\n",
+    "(plt1,) = ax.plot(theta_range, likelihood, \"r-.\", label=\"Likelihood\")\n",
+    "\n",
+    "ax.set_xlabel(\"theta\")\n",
+    "ax.set_ylabel(\"Likelihood\")\n",
+    "ax2.set_ylabel(\"Prior & Posterior\")\n",
+    "ax2.legend(handles=[plt1, plt2, plt3], bbox_to_anchor=(1.6, 1));"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9ed5c361",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "0022fcbc",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "<style>\n",
+       "    /* Turns off some styling */\n",
+       "    progress {\n",
+       "        /* gets rid of default border in Firefox and Opera. */\n",
+       "        border: none;\n",
+       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
+       "        background-size: auto;\n",
+       "    }\n",
+       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
+       "        background: #F44336;\n",
+       "    }\n",
+       "</style>\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "    <div>\n",
+       "      <progress value='8' class='' max='8' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
+       "      100.00% [8/8 00:00<00:00 logp = -7.6246, ||grad|| = 4.5]\n",
+       "    </div>\n",
+       "    "
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "theta ~ Beta\n",
+      "[[133.09999067]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Laplace\n",
+    "with pm.Model() as normal_aproximation:\n",
+    "    theta = pm.Beta(\"theta\", 1.0, 1.0)\n",
+    "    y = pm.Binomial(\"y\", n=1, p=theta, observed=dataset)  # Bernoulli\n",
+    "    mean_q = pm.find_MAP()\n",
+    "    std_q = ((1 / pm.find_hessian(mean_q, vars=[theta])) ** 0.5)[0]\n",
+    "    print(theta)\n",
+    "    print(pm.find_hessian(mean_q, vars=[theta]))\n",
+    "    loc = mean_q[\"theta\"]\n",
+    "\n",
+    "# plt.savefig('bb_laplace.pdf');"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "2ef00785",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(array(0.09090909),\n",
+       " array([0.08667842]),\n",
+       " {'theta_logodds__': array(-2.30258505), 'theta': array(0.09090909)})"
+      ]
+     },
+     "execution_count": 9,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "loc, std_q, mean_q"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "73a0b4f8",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<matplotlib.legend.Legend at 0x7fd94c0bb590>"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "x = theta_range\n",
+    "\n",
+    "plt.figure()\n",
+    "plt.plot(x, stats.norm.pdf(x, loc, std_q), \"--\", label=\"Laplace\")\n",
+    "post_exact = stats.beta.pdf(x, n_heads + 1, n_tails + 1)\n",
+    "plt.plot(x, post_exact, label=\"exact\")\n",
+    "plt.title(\"Quadratic approximation\")\n",
+    "plt.xlabel(\"θ\", fontsize=14)\n",
+    "plt.yticks([])\n",
+    "plt.legend()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "2f568bea",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c9d11b7d",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python [conda env:py3713]",
+   "language": "python",
+   "name": "conda-env-py3713-py"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.13"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/notebooks/book1/04/laplace_approx_beta_binom_pymc4.ipynb b/notebooks/book1/04/laplace_approx_beta_binom_pymc4.ipynb
new file mode 100644
index 00000000000..c05c4953ba0
--- /dev/null
+++ b/notebooks/book1/04/laplace_approx_beta_binom_pymc4.ipynb
@@ -0,0 +1,339 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "29bf9a93",
+   "metadata": {},
+   "source": [
+    "## Pymc"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "cbadfd36",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import jax\n",
+    "import jax.numpy as jnp\n",
+    "from jax import lax\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "try:\n",
+    "    from tensorflow_probability.substrates import jax as tfp\n",
+    "except ModuleNotFoundError:\n",
+    "    %pip install -qqq tensorflow_probability\n",
+    "    from tensorflow_probability.substrates import jax as tfp\n",
+    "\n",
+    "dist = tfp.distributions\n",
+    "\n",
+    "try:\n",
+    "    import pymc as pm\n",
+    "except ModuleNotFoundError:\n",
+    "    %pip install -qq pymc\n",
+    "    import pymc as pm\n",
+    "\n",
+    "# try:\n",
+    "#     import pymc3 as pm\n",
+    "# except ModuleNotFoundError:\n",
+    "#     %pip install -qq pymc3\n",
+    "#     import pymc3 as pm\n",
+    "\n",
+    "try:\n",
+    "    import scipy.stats as stats\n",
+    "except ModuleNotFoundError:\n",
+    "    %pip install -qq scipy\n",
+    "    import scipy.stats as stats\n",
+    "\n",
+    "import scipy.special as sp\n",
+    "\n",
+    "try:\n",
+    "    import arviz as az\n",
+    "except ModuleNotFoundError:\n",
+    "    %pip install -qq arviz\n",
+    "    import arviz as az\n",
+    "\n",
+    "import math"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "7b6487c1",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Dataset: [0 0 0 0 0 0 0 0 0 0 1]\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Use same data as https://github.com/probml/probml-notebooks/blob/main/notebooks/beta_binom_approx_post_pymc.ipynb\n",
+    "key = jax.random.PRNGKey(128)\n",
+    "dataset = np.repeat([0, 1], (10, 1))\n",
+    "n_samples = len(dataset)\n",
+    "print(f\"Dataset: {dataset}\")\n",
+    "n_heads = dataset.sum()\n",
+    "n_tails = n_samples - n_heads"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "c04b4e84",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# prior distribution ~ Beta\n",
+    "def prior_dist():\n",
+    "    return dist.Beta(concentration1=1.0, concentration0=1.0)\n",
+    "\n",
+    "\n",
+    "# likelihood distribution ~ Bernoulli\n",
+    "def likelihood_dist(theta):\n",
+    "    return dist.Bernoulli(probs=theta)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "6d16a8df",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 2 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# closed form of beta posterior\n",
+    "a = prior_dist().concentration1\n",
+    "b = prior_dist().concentration0\n",
+    "\n",
+    "exact_posterior = dist.Beta(concentration1=a + n_heads, concentration0=b + n_tails)\n",
+    "\n",
+    "theta_range = jnp.linspace(0.01, 0.99, 100)\n",
+    "\n",
+    "ax = plt.gca()\n",
+    "ax2 = ax.twinx()\n",
+    "(plt2,) = ax2.plot(theta_range, exact_posterior.prob(theta_range), \"g--\", label=\"True Posterior\")\n",
+    "(plt3,) = ax2.plot(theta_range, prior_dist().prob(theta_range), label=\"Prior\")\n",
+    "\n",
+    "likelihood = jax.vmap(lambda x: jnp.prod(likelihood_dist(x).prob(dataset)))(theta_range)\n",
+    "(plt1,) = ax.plot(theta_range, likelihood, \"r-.\", label=\"Likelihood\")\n",
+    "\n",
+    "ax.set_xlabel(\"theta\")\n",
+    "ax.set_ylabel(\"Likelihood\")\n",
+    "ax2.set_ylabel(\"Prior & Posterior\")\n",
+    "ax2.legend(handles=[plt1, plt2, plt3], bbox_to_anchor=(1.6, 1));"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "2bf9afc8",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "0022fcbc",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "<style>\n",
+       "    /* Turns off some styling */\n",
+       "    progress {\n",
+       "        /* gets rid of default border in Firefox and Opera. */\n",
+       "        border: none;\n",
+       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
+       "        background-size: auto;\n",
+       "    }\n",
+       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
+       "        background: #F44336;\n",
+       "    }\n",
+       "</style>\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "    <div>\n",
+       "      <progress value='3' class='' max='3' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
+       "      100.00% [3/3 00:00<00:00 logp = -7.6246, ||grad|| = 18]\n",
+       "    </div>\n",
+       "    "
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "[[2.18550173]]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "array([[88.80087443]])"
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# Laplace\n",
+    "with pm.Model() as normal_aproximation:\n",
+    "    theta = pm.Beta(\"theta\", 1.0, 1.0, transform=None)\n",
+    "    y = pm.Binomial(\"y\", n=1, p=theta, observed=dataset)  # Bernoulli\n",
+    "    mean_q = pm.find_MAP()\n",
+    "    std_q = ((1 / pm.find_hessian(mean_q, vars=[theta])) ** 0.5)[0]\n",
+    "    print(pm.find_hessian(mean_q, vars=[theta]))\n",
+    "    loc = mean_q[\"theta\"]\n",
+    "normal_aproximation.compile_d2logp(vars=[theta], jacobian=False)({\"theta\": 0.66})\n",
+    "# plt.savefig('bb_laplace.pdf');"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "71772ba9",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(array(-1.42857143), array([0.67643243]), {'theta': array(-1.42857143)})"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "loc, std_q, mean_q"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "73a0b4f8",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "<matplotlib.legend.Legend at 0x7fbb72cd6750>"
+      ]
+     },
+     "execution_count": 12,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "x = theta_range\n",
+    "\n",
+    "plt.figure()\n",
+    "plt.plot(x, stats.norm.pdf(x, loc, std_q), \"--\", label=\"Laplace\")\n",
+    "post_exact = stats.beta.pdf(x, n_heads + 1, n_tails + 1)\n",
+    "plt.plot(x, post_exact, label=\"exact\")\n",
+    "plt.title(\"Quadratic approximation\")\n",
+    "plt.xlabel(\"θ\", fontsize=14)\n",
+    "plt.yticks([])\n",
+    "plt.legend()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "183d93df",
+   "metadata": {},
+   "source": [
+    "Currently this is not giving right answer, see this issue: https://github.com/pymc-devs/pymc/issues/5443"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "aa5d2330",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python [conda env:py3713_2]",
+   "language": "python",
+   "name": "conda-env-py3713_2-py"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.13"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/notebooks/book2/07/advi_beta_binom.ipynb b/notebooks/book2/07/advi_beta_binom.ipynb
index 535c473d9db..90a63c89e57 100644
--- a/notebooks/book2/07/advi_beta_binom.ipynb
+++ b/notebooks/book2/07/advi_beta_binom.ipynb
@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 1,
    "id": "05bdb330",
    "metadata": {
     "colab": {
@@ -36,7 +36,15 @@
     "id": "05bdb330",
     "outputId": "a5ee2f3a-3334-4378-9800-94312d169a08"
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Note: you may need to restart the kernel to use updated packages.\n"
+     ]
+    }
+   ],
    "source": [
     "try:\n",
     "    import jax\n",
@@ -108,7 +116,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 2,
    "id": "TBUwCk3r1oEw",
    "metadata": {
     "id": "TBUwCk3r1oEw"
@@ -153,33 +161,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
-   "id": "1e88faaa",
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/",
-     "height": 68
-    },
-    "id": "1e88faaa",
-    "outputId": "a9196127-9239-49bd-a3e4-dab9b394fb84"
-   },
-   "outputs": [],
-   "source": [
-    "# preparing dataset\n",
-    "# key = jax.random.PRNGKey(128)\n",
-    "# n_samples = 12\n",
-    "# theta_true =  prior_dist().sample((5,),key)[0]\n",
-    "\n",
-    "# dataset = likelihood_dist(theta_true).sample(n_samples,key)\n",
-    "\n",
-    "# print(f\"Dataset: {dataset}\")\n",
-    "# n_heads = dataset.sum()\n",
-    "# n_tails = n_samples - n_heads"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": 4,
    "id": "YajB06WPxMNJ",
    "metadata": {
     "colab": {
@@ -190,6 +172,13 @@
     "outputId": "6b780e95-f6d2-411c-b5ff-f64bd85f518c"
    },
    "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "WARNING:absl:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n"
+     ]
+    },
     {
      "data": {
       "text/html": [
@@ -227,7 +216,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 39,
+   "execution_count": 5,
    "id": "bc027abf",
    "metadata": {
     "colab": {
@@ -240,7 +229,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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",
+      "image/png": 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\n",
       "text/plain": [
        "<Figure size 432x288 with 2 Axes>"
       ]
@@ -320,7 +309,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 6,
    "id": "fb8f583e",
    "metadata": {
     "id": "fb8f583e"
@@ -339,7 +328,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 41,
+   "execution_count": 7,
    "id": "9ba6a667",
    "metadata": {
     "id": "9ba6a667"
@@ -379,7 +368,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 42,
+   "execution_count": 8,
    "id": "e834dfe3",
    "metadata": {
     "colab": {
@@ -437,7 +426,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 43,
+   "execution_count": 9,
    "id": "48dcd6e8",
    "metadata": {
     "id": "48dcd6e8"
@@ -471,7 +460,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 44,
+   "execution_count": 10,
    "id": "r-nFedcOSnLH",
    "metadata": {
     "colab": {
@@ -485,8 +474,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 2.09 s, sys: 20.1 ms, total: 2.11 s\n",
-      "Wall time: 2.03 s\n"
+      "CPU times: user 2.03 s, sys: 20.4 ms, total: 2.05 s\n",
+      "Wall time: 1.96 s\n"
      ]
     }
    ],
@@ -514,7 +503,30 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
+   "execution_count": 29,
+   "id": "808e2ffd",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{'loc': DeviceArray(-1.9149526, dtype=float32),\n",
+       " 'scale': DeviceArray(0.21098873, dtype=float32)}"
+      ]
+     },
+     "execution_count": 29,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "optimized_params = jax.tree_map(lambda x: x[-100:].mean(), output[\"params\"])\n",
+    "optimized_params"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
    "id": "JtMxRokq6DmD",
    "metadata": {
     "colab": {
@@ -569,7 +581,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 46,
+   "execution_count": 31,
    "id": "a__PZbi740j0",
    "metadata": {
     "colab": {
@@ -582,7 +594,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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",
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AbxiJfwIzgEXAe3FKx1hgsaruitPxYvblXSfF9Xi+/gfPz1rHxRPnxvXYxhgTbzFVDKvqHQGfHxOR+Ti5gHg1G72cCEVBidazdXwrcUWgOGAI6nnr9zCie4u4nsMYY+KlQk1kVPVrVf00HpPLiEgD4HSc3EaNlyJCQXHJ13LZpHlJTI0xxpQt1iaiXxO+f9URYCvwgar+ryIJUNUcoPa8KgsU2WQ0xpgaItacwEycsYJmAW+4/3YBFgK7gH+KyN0JSF+NkyJiM5IZY2qMWEcRPQM4U1VX+FaIyJvAv1T1WBH5AKdM/9EEpLHKdGhar9Kjg67Zlc2ADk3ilCJjjEmsWHMCfYD1Ies2Ab0BVHUB0CaO6apS153QjbH923L9id0qfayHpqxguw0zbYypIWINAl8Br4hITxGpKyI9gReB2QAiMgDYkaA0Jty95/Rl4s+HkhqnoUU/XVZjvwpjjMfEGgSudvddDuTizCOQClzjbs/HaeZZo8Wrt++zM9ZF38kYY6qBWPsJ7AUuE5EUoBWQGdg81B0IrsazER+MMV4Ta8UwItIHuBRoo6q3ikhvIENVf0hY6qpYZWYbM8aYmijWieYvBb4GOgC/cFc3Ap5IULqSIlKVwKm9q/d4RcYYU1Gx1gk8AJymqjcBRe6674FBCUlVkkSqE2jXtF4Vp8QYY6pGrEGgNeAr9tGAf2tVr6hIhUGVLSRSrVVfkzGmFok1CCwCrgpZdxmwIL7JSa5IdQKVrSqwHsTGmOoq1orh24DPReQ6oIGIfIYz0cwZCUtZEqRECIlSybxAQVFxwqazNMaYyoi1iehKt3XQOcDHOHMLf6yqhxKZuKqWqJxAVnY+aakFtLe6BWNMNRNzE1FVzQXeSWBaqq3K1gmc/uQsjhQWs3HC2RzILWDC1BX86Zx+1EtPjUv6jDGmosoMAiIyg7Irf1VVR8c3SckTOSdQuTBwpNDpV6eq/GP6GiYv2MJRbRpx7fGVH6vIGGMqI1pO4I0I6zvg1BPUj29ykivRncUO5hXiqyO2umJjTHVQZhBQ1ZcDl0WkBTAeuB54G6f/QK0RKQbEKzZkZh+Jz4GMMSZOYu0x3FhEHgTW4gwZPURVb1DVrQlNXRUL12N4wkUDYmod1Kdt9LmKc/MLK5IsY4xJmDKDgIjUE5HxOHMJHA2coKpXqWqtHCYzXNl/rEVEsdQb5BUU+3MV1oHMGFMdRKsT2IgTKB7FmUqyjYgETR6jqtMTk7SqF/YxLnC4oCjcliCxdAPIi+E4xhhTlaIFgcM4rYNujrBdge5xTVES+VrxhMo5UlKM06VFfXKOFJJ1KD9on1hyDJGCwBfLd5GbX8j5gzuUI7XGGFN50SqGu1ZROqqFcG/8xcUaFARm/vYUALqN/yRov1iKgw4XFIXNbVz/2kIACwLGmCoXc2cxLzgSJggUFiv5RSU5hEgP+9QYqg7mrd/D1n0l8w9f+vxc+rRt7F9+Y94mfj6iSzlSbIwxlZP0AW1EpKmIvCciK0VkhYiMTFZa8gpKFwcVq1IUQ6P+Ds2id5mYvGALX6/J8i9/u3Efr8/b5F9+Z+GWGFNqjDHxkfQgADwFTFXVPjjzE6xIVkLCFQcVFsUWBO45q0+5zhWucZDNa2aMqWpJLQ4SkSbASbgT1qtqPs6k9UnRqXnpAd6KiqMHgRN6tqRuWhzGAbLpLY0xVSzZOYFuQCbwiogsEZGXRKRB6E4icoOILBSRhZmZmQlLzAVhKmaLVKPOB9C6UUZchpyINL2lMcYkSrKDQBowBJioqscAOcC40J1UdZKqDlPVYa1aJW6+33CVvkXFSnGUjl0dm9dHyvlNBlY2+88P5BcWM3dtVulfMMaYBEh2ENgKbFXV+e7yezhBodooKlYKi8oOAs3r1yl3TuBvn60qtU5EePzzVVzx0ny+37K/XMczxpiKSGoQUNWdwBYR6e2uGg0sT2KSSomlTiA1ReJSlCPAmt3OPD022JwxpipUh34CvwbeFJF0nDGKrk1yeoIUFStFUYqDUlIkYk6gZcMMsg7F9kAXcQIKEPWcxhgTD0kPAqr6HTAs2emIpDAgJ3DjSeFHyEgRiUvDHhEh1T1QtCIoY4yJh2TXCVR7xaoUFjuVuFcc2znsPikCdSLNUl/mxGzBBEh1ux4fOlJQnmQaY0yFWBCIorBIcWOAv6gmlIiQEodKAZGSgeiy82zuAWNM4lkQiOLMfm38OYFIQSA1hrKghhnRS94Eocg9V7gmpMYYE28WBKI4tnsLf51ApCAQsSQoQNsmdaPu8836PWzemwtAQaHVCRhjEs+CQAx8QSAt4Gn/1GWD/Z/L6iPQr30TAAZ3ahrTuZZtOwhAgeUEjDFVwIJADHzDRgQW+5w/uANnD2gHlB0Ezh7Yjum/OZlzB7Uv1znnrMsiP8IkN8YYEy8WBCI4b1B7fj2qJwAXHuOMKVQ3Pfjr8g0nUVYQqFcnle6tGlKnnBXHSzbv5/EvSvcqvm3yEm55c7F/efn2g0z4dKXNWWyMqZCk9xOorp6+/Bj/5/vO7cfvzuxNRshIob4gUNb8wnXruL9TgcZDL8xaz4yVu/n8zpP96/77/XYAnnWXr3llAbuzj3DjSd1p1iC9/Ccxxnia5QRikJoiNKpbp9R6X7F9WVNL1q3jfMUVHWV09a5DZW73HXdfbtJG4DbG1GCWE6gEXxFMWU1EfS2K4j1K9C1vLSb3SCH1M5ycRmgQ2L7/MIcLiujRqmGcz2yMqU0sJ1AJvvF9YmkiGstE9OUx5YcdzFiVSYN0J47vORQcBI6bMJ3Rj8/yL3+ydIcNSmeMKcWCQCX4BheNpagnURPG+E6d57YkUtVSrYoOHSnk/95czNX/XJCYRBhjaiwLApVQXBy9dVDfdo2B0jNHPvHTQeU615HCIn737vel1vse+IVuBcVd73zPcROm+7erlgyAt8XtiGaMMT5WJ1AJ0ZqIbpxwdsBS8D5tGkfvQRzouRnreHfR1lLrV+7MBpy+DKrKh0u2BW3PPlIYdT4EY4x3WU6gEkqCgLP81vXH8uq1Pwm7b4OM4Oalx/Vowd8uGchDF/SPep45a7NY5T7sI/lg8Va6jf+k1Pr9OQX+XIKFAmNMKAsCleCvE3CjwHE9WnJK79Zh9+3TtnHQUBMiwqXDOtGobvTM2JUvzWfqjzvL3Gfe+r1h1x/MK6DATah1KDPGhLIgUAnnDHSGjejSon5M+58/uEOpdZEGpYuX7LxCywkYYyKyIFAJV43owsoHx9CuSb0KH2Nk9xb0bN2QB8/vF8eUlTiYV0CBR2cpe3bGWrqOm+KvwDfGlGZBIMS1x3flJ12bxbSviJQMC1FBLRpm8OVdJ3PVyK6VOk4k2XmF7Hc7kkUrDVqfeYjjJ0xn54E8dhw4zEmPzqjRLYoe/9wZe8nmZjAmMgsCIe47tx/v3nRcpY5xzXFdg8r/Az10QX/+fcOIsNveuXFkpc4bTnZeAZc8/w1QUpEdyWvfbGLb/sOMeGQar87ZyOa9udz70bKgfab8sIO9OfkUFyvfbdlfrVse+VJWG4fl/nH7AUY9NpMDh20aUlM5FgQS4P7z+oUt/wf4+YgujOjeIuy2WHMg5fHn/y33f1ZgY1YO+3PzOZhXQNdxU/jNO07fg8zsI8xem+Xfd8mW/QDMXJXpX5d16Ai3vLWYG15byJx1WVzw7BxufH1R3NMcL76YVxuLw578YjXrs3KYt35PspMS1fgPfuCbddU/nV5lQaAaiffQEqHyC4s55bGZ/PLVb1m0cR8A7y/eiqpyw+sLWbu7ZLC6vIKiUr/ve+vfuCfH/wb65YpdbN9/OKHprqzamBOoKQqKipm8YAuXvzgv2UkxEVgQqIbuOK1XQo+/cU8uU5eVNDk9UljMrgN5Qfsczi8JAr7WRb7JdQqLlX05JWMV/fLVb3n7282JTHKlJGNynrnrspixcncCzxD/gQkDmxBv2ZvLgdzKFzXl5pd+mTDVS9KDgIhsFJGlIvKdiCxMdnqSbeOEs7njtKMqfZzjeoQvcgLo3Lw+by/c4l/uc+9UtocEgTUBuYLrX3Nui+9hWlSk3PvRj/7tK3dm8/v3l9J13BTeWbgFVeV/328nM/sI2/YfrlT/hH05+ew5VLmB7xKZEzicX8T4D35gb07wAH5XvDifa1/9NmHnjbd7Plwa1NnwxEdnMOiBz/l2Y/j+J7EKl6OszRZv3seb8zclOxnlkvQg4DpVVQer6rBkJ6Q2GNWnNW9dH77yGYLf8mMxY1Umqup/mGYfKYy4718+WcHny3fx68lLuP3fSzh+wnQmLygJOOECQlkPimMe/IKhD30ZcfuSzft48OPlZQaaitQJ7DqYx/wYytvfW7yVyQu28I/pa8p9jurkrflOTi70e7zUbVRQUSuj9HSvSqrK3HVZCe00edFzc/nDh8ui7xjB4s37yCnj/1ciVJcgYMpw+fBO5drf90f+9d2nht1+qAJ/ZN3Gf8IZT34Vdb/9uQX+SsBFm5x6B19RUXGxMvD+z7n/vz+y+2AeK3YcpOu4KfS5dyqrdzkPi6VbD3DRc3PIzgtfFDF12c6gYopLn/+Gl2dv4HBAIAn9T15WTuCTpTuYE1AhDs5/xFGPzeRnk0rKsQuKivnPkm2ljp3rfpdlzSkRSlVjfkOev35PmZW/vsZZL329nq7jprBk875SuZLyyCso/V3F0gJsy95c1u4u/cCPZeTagqLiuDyYfek8UlhEbn4hqsqiTXv9x/5g8TaueHE+//luW1mHiWrqsh08+PHyMvcJvZ68giI2ZuWU+TsHDhdw0XNzuf3fSyqVvvKqDkFAgc9FZJGI3JDsxFRHdcqavzIM359fp+bhezIfjPCAjRdfy6IjbvHR91sPMHPVbrrf8wnZRwp5de5Ghv9lGmOf+tr/O2c8+RUzV+3mwY+Xs3jzfuasDX7wbdmbS9ahI9z0xiLGPPUV/3On2fTVU/iWH/jfcrqN/4QFG0qKMSL1EyguVv7vzcVc+dJ8fxDavv8wFz03lxw3t/T6PCdrP+mr9dzx9ndMWboj6Bi+a9y6L/bK8Zdnb6DPvVOjFnNt23+Yn02ax2WTIleq5hcVM2/9Hh6asgKAC5+by8UT5wLOd/aR+8Bbvv0g+3Pz2brP6fex48DhsJ3ocvNLvyD0uOeToKB861vOsOQH8woodgcuPPHRGZz2hPOScOBwATtDihcBXp2zgey8ArbtP8z2/YfZm5PP7uw8ev3hU178en2Z30Wol2dv4M//KymS/Oi7bfS45xN2HDjM2U/Ppu+fPmPmqkwunviN/x7uPOikacWO2HMnv3v3ex76eHnQi8RNbyzm5dkb/HVl4YT+zd3y5mJOeWxm2Pqp6St3MW/9Hn+QWLJ5P2t2ZQcFklfnbGDp1gMxp7s8qsMooieo6jYRaQ18ISIrVTXoldMNDjcAdO7cORlprHLv3DiSSV+t58sVu0gvZxAI/L/doWk9toW03snOK19OoG6dlLBviJF87waBQNe8Er18/Ivlu1jglkHf9MYiHr1koH/biY/O4JKhHQHYcSCPX09ewqg+JeM0/f79pby1YIv/3D99oaQY4+KJc/n39SMY3q05xeoM1ZFXUMT9/y15iGzbd5ivVmeWaqF173+WcdWILv7vcO3uQzzxxWqGdG5K1xYNeOKL1QBM/XEnH323jZHdW3DPh0v9v3/gcAHLth2gsFgZ2qUZ6akp/gf209PWcNnwzuzLzWdgx6Y8PGU5153QneU7DnLeoPYcHzAk+Al/nc4LVw1FEF6evYEvV+wC4LbJpd8aN7gPk6tfWcD6zBwGdWzKWU+XBNxrjuvKq3M3AvDuTSPZkFnyhnrRxLl8ctuJpY454P7PGdG9OSf2asXHPziBcOD9n3PHab24/sTuQfue84+v2bL3MJf9JDgHe///lnP//4LfoId1cZpF/+WTlZzSuzVtGtWlWDXsfNnZeQUc+5dpPHvFEP+b+H3nOj3t/+OOnjttxW5/K7fpbsX83LV7+MXIrtRPdzp2TvpqPfecdXSp4+/Lyee1bzaRk19I95YNGNixqX/k3pdmb2DDI2cF/X18smwns1ZlknOkkOevGhoUFDZm5dK7bSPAedmY5qblzne+4/Sj23DH29/x+KWDWLrtgP9e+OzJyef0J7+ibeO6TL5hBA3SU/3fW/DIxPEh1WlQMRG5Hzikqo9F2mfYsGG6cKE36o8f+XQFL8xaz82n9GDizHUR9wt9SJ/YqyWvX3csAI99topnZqyN+LutGmVEnXHsrxcPYNbqTD5ZWvYgdlVtUMcmfF+Bt6M+bRuVq6x6aJdm/qKtsvRu04i8wiI27Yncy/riIR15f3HpIcFDpaWIP5dTEYH39c7TjuLJL1dX+Fjl8eVdJ/lzBBUxvGtzFmzcy7NXDKFXm4Y8OnUVQ7o05dOlO6mfnsr8DcEV1RsnnE3XcVP8yw3SU/25OJ/BnZoyvFtzJn1Vktu47CedGDe2D9l5hdz70TI2ZuUwqFNTPvpue8S0HdO5Kacd3Ya/fbaq1LbAwOrzr18Op0/bRpz2xKxyv3hFUskgELbMMqlBQEQaACmqmu1+/gJ4QFWnRvodLwWBh6cs58WvN3Db6F48PS1yxWPDjLSgcv4TerbkjV/FFgR+Oqwj7yws/VBq3SiD3e5D5LFLB7FmVzYvfFU6y/7+zSO5eGLpysOj2zVmxY6DYc956dCOYedG8BnRvXnEUVGNd/x6VE/+MT3y3y6UP5caKlzQqM4SEQSSXSfQBpgtIt8DC4ApZQUAr/HlLtNTg+9daM/i0DsbODxEaH3lGX3bBC3fNrpX2OEqPrn9RB44vx/NG6Rz8lGtIo5AOrRL87DrG4cZIrtN4wyGdWnGjSf38K+76/SjOO3o4DS9eu1w5owbVer3j3ZnaYunv10ykDH92sa0r684KhbDu4X/XipqQIcmcTvW8K6xp+3Mfm34x+XHlFr/+zF94paeSKIFAAhfkV0eoQGgRZhiqGRo1Sgj7PpENHdOahBQ1fWqOsj96aeqDyczPdWN72EeWjEcOrZRw5AHbqTMXbP6dXg65D90Rlqq/4HVulEGt4/uxQWD29OyYQa/GNmVxfeeTqtGGWW23vj7zwaXWlcnNYVXrvkJk68fwVOXDea2UT2ZO240b984ks7N6zOsSzMevKA/t43uxUtXl7QMvvLYztStk0qHpqVHZq1bp/Sfa+B/2reuPzZiGn1Ddg/r0oyMNOc4M397CpcO68TzVw0ttf8xnZtyw0ndmRsQjB6+sGQCoP4dnIB08yk9mP6bk4N+9+8/G8zjl0afPrRBevDgg6HHCfTHs4/mbwF1JD5f/e5Urjy2M9/+4bSg9c9dOQSA+umpPHXZYBpmlPyNvHbdcAA6NqtHy4bhHzbgBIsXrhrGuYPa8/ilgzh/cHveuXEk5wxsx5UjStfNfXHnSdx0cg9uPbUn3Vo2iHjcaO45K3yAOfmoVoBTvBPO5cNLp6l9k7r+eodPbz+RlQ+OYeKVQ6iTGr4119zxo2jT2PlO/vXL4QzsWDr4jhvbp9TLlM+Xd50UNCLw+zePJN39e7ttdC+GdWnGj38+078unD+efTQvXz2M43s6Iwz3aFXyXSaid351qBg2EfiCQLg/mElXDWVDVg6PfLqS9k3rscNtjTG8a3P+eE7pSq/Lh3fmkYsGAM5b5dJtTlm6r9J58b2nk5YqNK5bJ2xayio1vOCYDvzhw6VBb1XDuzXn1D7hJ9hJTRHeuzn8IH33ntPX//mjW45nx4HDfL0miw7N6jGgQxOu+9dCHjq/P3e//wMAI3q04LNlOyksVkZ2b8HTlx+D4HSIO//ZOYDzIJj+21P4/fs/cOdpR9GwbhoFRcVBQ4B//OsTyM0v4qcvfEOKwIf/d7x/26qHxnAgt4CMtJKHdqdm9Vm27SADOjShe6uG/vXfjB/lP+47N45kYMcmzFi5mzP6taXHPcEzv/34wBgumTiXhW59Q/dWDZn1u1M4+W8zS30vzRukM7BjU373nnPdX9x5Em2a1KVx3To8fKFzX7+++1RmrtrtH5F2zrhRZKSl0LJhBucP7kDXcVNo3iCdunVSWfXQGAShTqqwPiuH0Y/PApy/h47N6rE+K4e+7UtyXhcP7cjFbk7I99Lw3JVD2JebzxfLd/HIRQNo16Qe48b28e//3qItDOncjIkz1/mvMZqJVw7h2O4t+MsnKwFn1r5iheN7tvDP2icibNmby/Oz1nHt8d34YPFWrji2Mx2b1eeRiwawZPM+bn5jMe/cOJIWDdOpVyeVvbn5/oA3dkA7lvZpTWqKsC83n+EPT/OfPyMt1d/LuXWjDCZdNYynpq3m1N6tufPt78jJL+LcQe351q2buPb4rrwyZ6M/7T1bN6JHq4b+zpStG9Vl6f1nsGbXIfp3aMJdpzsdQafddTL/mruRl2ZvCLr+6b852f/39Povj0XEud4ftx/g2w17g4J5vFgQqMZ87Z7Twkw8c0a/tsxc5bQ4qJ+eSqOMNG4d1TOoqCVQ24A5jQMnsklz34iaR8kG33xKD3YczOOSIR3D9oT98YExnPfMbAqLlNtG9+T0vrEVsYQKHJp7UKemDOrUlDH92/nXrX5oLAcOF/iDwGOXDOJ3Z/Rm454cRITzBrX377txwtnkFxaTliKkpAhPXVa6WMOnf4cm/u/7FyHDemekpdK6sZOur+8+ldQUKdVO/KaTe7Ah61BQYPE9LMcOaEco37ZnrhjCiEem+e9PlxYNuOGk7v5KzDtO68Xfv1xD2yZ1g14GerVpVOqYnZrXDxqSPDQ3NWfcKOq7329gQOse8Na++uGxvD5vE/f+Z1nUIbjPcq/rymO7lNrWrWUDfnemExCen+U0anjuyiHUS0/l2oCWYqkp4v/ef3l8N/939filg/hm/R7Gj+3DyAnTufXUXkEtczo1r+8PfneHFE0d07kZ8+4ZHbQuNMfj+ztr3aguU247gbvf+8Gfo/UFgZYNM2jVKINHLnJyYHPHj2bO2iw6NK3HqX1aM23lbq49rhvrM3OYtTrTX2QqIpw9oB1Tlu6gcb06ZKSl0j+kOK9T8/r88Zy+LNt+gHnr9/LoxQMZ2aNFULPulID/p/3aN6Ff+/gVCQayIFCN+ecwDvhjuPXUnv7PvmKiwiJl6Z/PDHuMcJneTs3r892W/dx3bl8axPhm0aJhBs9eMQRV5bFLB/Hbd78vtc9/bz0hpmNVVr2AQFEvPZWuLRvQNULxQ1nZ7lCpKcKKB8b4i4vC8f0n/fWoXqzYcdA/PIfvDbgsfzqnL03r16Fbywb0aO287bVpnMHvx/Th7IBA0S/gDfz20b24fXSvuAwuGK6IDUoPXOgrYmtaL3yusLx8uchWjZw6od+ecRSPfb6a5g3S+fT2E3nxq/W8NHsDeYUlOcnAnMfqh8bGJR2R9GvfhCkBzWKHdmnGgg17S70YNalXJyDwdea8we1pXLeOf4rYwLq4xy4dxM2n9KBJlO/w6cuO4d1FW7l0WMeEDyAZiQWBasz3hhTYG/W3Z/b2f/blEAqLy1dZ9JcL+3PyUa3KVdHpIyJcMrRj2CBQVSKV58ZDvfTYJgnq274xM38Xvkd2JL88oVupdSLCzacE596O79kSgD+f1y8pD4ax/dvy6MUDOW9w++g7x6Bzi/os3LSPhhlpiAi3jurFVSO6kpYqNMhI4yg3V3OkkpW88fLS1cPYuvdwmVO/ipQUnf7x7L6kp6YENXCol1767T+c1o3rckvAi10yWBCoxkInsg/lK8op79g4jerWqVAACPTA+f1iajufCL4HY5JenBKuZcOMhHQKKsvTlx/jL5ISEX76k/INVVKWB8/vzxl92wS17mpSv+QNOcOt8A/MCSRT47p16Ns+9lxQ2yZ1eSJM44iawoJANXbxkI68t2grI7qFHxHUXxwUQ05A4zzN/C9Gdi1Vdl4Zf7lwQNR6iUCTrhoatlzcVExgXUq8NchIC6rXCXVir1a0apTBTSeFr88yiWVBoBob2aNFmW+EvvLu1JQyyr1ryOvyFceWbziQM2Js22+qv+YN0ks1cTVVJ9mdxUwl9G7TiFtP7ckzYTrz+Fw8pAONMtK48Jjw010aY7zNcgI1mIgEVRSH06VFg4gth4wxxoKAMTXIkntPJ6WGFPGZmsGCQA3x6CUD6dqi4l3xTe0QbohlYyrDgkAN8dNh8WuyZ4wxPlYxbIwxHmZBwBhjPMyCgDHGeJgFAWOM8TALAsYY42EWBIwxxsMsCBhjjIdZEDDGGA+TsiYQr45EJBPYVMFfbwlkxTE5NYFdszfYNXtDZa45S1XHhK6scUGgMkRkoaoOS3Y6qpJdszfYNXtDIq7ZioOMMcbDLAgYY4yHeS0ITEp2ApLArtkb7Jq9Ie7X7Kk6AWOMMcG8lhMwxhgTwIKAMcZ4mGeCgIiMEZFVIrJWRMYlOz3xICKdRGSGiCwXkR9F5HZ3fXMR+UJE1rj/NnPXi4g87X4HP4jIkOReQcWJSKqILBGRj93lbiIy3722t0Uk3V2f4S6vdbd3TWrCK0hEmorIeyKyUkRWiMjI2n6fReRO9+96mYhMFpG6te0+i8g/RWS3iCwLWFfu+yoiV7v7rxGRq8uTBk8EARFJBZ4FxgJ9gctFpG9yUxUXhcBvVLUvMAK4xb2uccA0Ve0FTHOXwbn+Xu7PDcDEqk9y3NwOrAhY/ivwpKr2BPYB17nrrwP2ueufdPeriZ4CpqpqH2AQzrXX2vssIh2A24BhqtofSAUuo/bd51eB0A5c5bqvItIcuA84FhgO3OcLHDFR1Vr/A4wEPgtYHg+MT3a6EnCdHwGnA6uAdu66dsAq9/MLwOUB+/v3q0k/QEf3P8co4GNAcHpRpoXeb+AzYKT7Oc3dT5J9DeW83ibAhtB01+b7DHQAtgDN3fv2MXBmbbzPQFdgWUXvK3A58ELA+qD9ov14IidAyR+Uz1Z3Xa3hZn+PAeYDbVR1h7tpJ9DG/Vxbvoe/A3cDxe5yC2C/qha6y4HX5b9md/sBd/+apBuQCbziFoG9JCINqMX3WVW3AY8Bm4EdOPdtEbX7PvuU975W6n57JQjUaiLSEHgfuENVDwZuU+fVoNa0AxaRc4Ddqroo2WmpQmnAEGCiqh4D5FBSRADUyvvcDDgfJwC2BxpQutik1quK++qVILAN6BSw3NFdV+OJSB2cAPCmqn7grt4lIu3c7e2A3e762vA9HA+cJyIbgX/jFAk9BTQVkTR3n8Dr8l+zu70JsKcqExwHW4GtqjrfXX4PJyjU5vt8GrBBVTNVtQD4AOfe1+b77FPe+1qp++2VIPAt0MttWZCOU8H03ySnqdJERICXgRWq+kTApv8CvhYCV+PUFfjW/8JtZTACOBCQ7awRVHW8qnZU1a4493G6ql4JzAAucXcLvWbfd3GJu3+NemNW1Z3AFhHp7a4aDSynFt9nnGKgESJS3/07911zrb3PAcp7Xz8DzhCRZm4O6gx3XWySXSlShZUvZwGrgXXAH5Kdnjhd0wk4WcUfgO/cn7NwykKnAWuAL4Hm7v6C00pqHbAUp+VF0q+jEtd/CvCx+7k7sABYC7wLZLjr67rLa93t3ZOd7gpe62BgoXuv/wM0q+33GfgzsBJYBrwOZNS2+wxMxqnzKMDJ8V1XkfsK/NK99rXAteVJgw0bYYwxHuaV4iBjjDFhWBAwxhgPsyBgjDEeZkHAGGM8zIKAMcZ4mAUBYxJIRA6JSPdkp8OYSCwImFpNRDaKyGkico2IzE7wuWaKyK8C16lqQ1Vdn8jzGlMZFgSMiUHAUAXG1CoWBIwXHA08D4x0i2f2g38iksdEZLOI7BKR50WknrvtFBHZKiK/F5GdOCN4NhORj0UkU0T2uZ87uvs/DJwIPOOe4xl3vYpIT/dzExF5zf39TSLyRxFJcbddIyKz3fTsE5ENIjLWdwHu9vUiku1uu7Lqvj5Tm1kQMF6wArgJ+MYtnmnqrp8AHIUzJENPnOF3/xTwe21xxrPvgjOJRwrwirvcGTgMPAOgqn8AvgZudc9xa5h0/ANnYLPuwMnAL4BrA7YfizNGfEvgUeBld5yYBsDTwFhVbQQchzNEiDGVZkHAeJI7KNkNwJ2quldVs4G/4AxK51MM3KeqR1T1sKruUdX3VTXX3f9hnId5LOfzzYw1XlWzVXUj8DhwVcBum1T1RVUtAv6FM2GIbyz5YqC/iNRT1R2q+mOFL96YABYEjFe1AuoDi0Rkv1tENNVd75Opqnm+BXdEyxfcopyDwFc4QxunxnC+lkAdYFPAuk0ET/6x0/dBVXPdjw1VNQf4GU5uZoeITBGRPrFeqDFlsSBgvCJ0pMQsnOKcfqra1P1poqoNy/id3wC9gWNVtTFwkrteIuwfer4CnKIkn87EOO67qn6mqqfj5A5WAi/G8nvGRGNBwHjFLqCjO58EqlqM8yB9UkRagzO5uYicWcYxGuEEjv0Bk3uHniNsnwC3iOcd4GERaSQiXYC7gDeiJVxE2ojI+W7dwBHgECVTaxpTKRYEjFdMB34EdopIlrvu9zjjr89zi3e+xHnTj+TvQD2ct/p5OMVHgZ4CLnFb9zwd5vd/jTM15HpgNvAW8M8Y0p6CEzC2A3tx6iFujuH3jInK5hMwxhgPs5yAMcZ4mAUBY4zxMAsCxhjjYRYEjDHGwywIGGOMh1kQMMYYD7MgYIwxHmZBwBhjPOz/AZtouVhc4PIzAAAAAElFTkSuQmCC\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -634,7 +646,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 59,
+   "execution_count": 32,
    "id": "4cf71065",
    "metadata": {
     "colab": {
@@ -647,7 +659,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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More//bbdnpJS9PYPP7TbExLKFt9jjz0mvXr1kn379kl6err06NFDYmNjRUSkdu3asnLlylP2T01NlerVq8vPP/8sM2bMkPbt20t6oZnV7rrrLhk/fnzB67Fjx8rYsWOLPHbhiURyc3OlS5cuMmnSJMnOzpbt27dLfHy8LFq0SETsLFiJiYmSm5srH374oVStWlWSCv2/0KRJE+nUqZMkJCTI0aNHpUmTJnLeeedJYmKipKWlSevWrWXGjBmlHis7O1saN24s06ZNk+PHj8snn3wilSpVOmVmLH/hs5OXiMhEEWkkIk2B4cBiEbnRG8cuk02bCobeLFtm76+qSJddBjVrwofHBkJenta5Vx6TkpLCtGnTmDVrFvXq1SM6Opp+/frRoUMHwJZAjoqKOuU9tWrVYvz48YwaNYopU6awYMECoqOjC7ZHRUWRnp5e8Hr69OlMnz691FhWrVpFSkoKjz76KOHh4TRr1ozbbruNDz/8EIChQ4fSoEEDQkJCGDZsGC1atGBlfpeqy7hx44iLiyvodho3bhwNGjSgZs2aDBgwgF9//bXUYy1fvpwTJ05wzz33EBYWxpAhQzjvvPPK/Lf1V5WcDsBnZGXBrl0wYgQ5OfbG1rFjK/aQ4eEwZAjs3RuDtGuP+egjuOuuij2oqlCF5ug+Q9WqJW+vXbvk7XFx7sfx3Xff0aZNm1Nq2qelpRUk+xo1apCRkXHG+zp37sykSZOYNWsWcacdMCMjg5iYGPeDcNm9ezdJSUmnvDc3N5cLL7wQgJkzZzJt2jR27doFwJEjR0hNTT3lM06PpV69egXPq1atSlJSUqnHSkpKomHDhhhjCrY1adKkzOfjr7x+U5WIfC8i/b193FJt22Zb161asXmzzf2dO1f8YadPh/nzwQwfBj/9BHv2VPxBVcBLTU2l8HWvnJwc5s6dWzC1YMeOHdmyZcsp71m3bh1jx45l1KhRvFXEtGybNm2iU6dOZY4lLi6O+Ph40tPTC5aMjAwWLFjA7t27ue222/jXv/5FWloa6enptG/fPr/7t0DhBF3eY9WvX5/ExMRTPjvBk7fH+zi9gzbf5s32sXVrXL8IvZLs82vkHx0wzD7RrhzlAa1bt2bZsmXs3LmTgwcPMnbsWHbu3FnQsu/bty8//PBDwf6JiYkMGDCAV199lenTp7Nu3Tq+L/QzIysrizVr1nD55ZeXOZbu3bsTFRXF1KlTOXbsGLm5uaxfv55Vq1aRmZmJMabgi+ntt99m/VlM7FPSsXr27EmlSpV46aWXOHHiBLNnzz6juyiQabLP9/vv9rFlS2JjbfdKq1beOfT06VD/ohZkdOilZY+VR1x22WUMHTqUTp060aNHDzp06EBISAjt2rUDYOTIkSxYsIBjx45x+PBh+vbty7333svAgQOpWrUqEyZM4OGHHy74vHnz5tG7d28aNGhQsG7MmDGMGTOm1FhCQ0P58ssv+fXXX4mPj6d27drceuutHDp0iLZt23LffffRs2dPYmNjWbduHRdccEG5z7ukY4WHhzN79mzeeecdatasyUcffcSgQYPKfSy/U9LVWycXr4/GGTFCpFEj7x7TZelSOyrn/WFz7JOdOx2JQ5VNCSMifM5XX30l55xzzinrJk6cKM8//7xb7+/evbusW7euAiJT5VGe0Th6gTbf5s3QujVg5xUpNAihwl1wAdSrB7MPX8oNAJ98AhMmeC8AFfA2bdpU0IWT7+mnn3b7/SvyqwIqv6XdOGAnGP/9d2jVikOHICYGXnzRe4cPCbE3WC1cGsmxLhdoV47yuE2bNhVcnFXBSZM92ElmDx+GVq3YuNGuatbMuyEMGmSrJnzT8T5Ys8aODlLKQ1599VWeeOIJp8NQDtJkDycvzrZuTX5hP9d1LK/p3RueeQY63+66yeOzz7wbgFIqoGmyh5PDLl0t+ypVoNC9KF4RFma76eN6NrK1eTTZK6U8SJM92JZ91arQqBEbNkCbNrYf3duys+Hjj2Ftr7GwahXs3u39IJRSAUmTPdiWfcuWEBLCzTfD+PHOhJGXBzffDK+lDrYrZs92JhDlNjntTk+lKlp5/81psgeb7F13UA0fDjc6VKKtShXo2xc+XxxNXodO2pXj4yIiIkhLS9OEr7xGREhLSyMiIqLM79Vx9llZsHMnjBhBairs22eH23t6KkJ3DRpkKyYs7zeOXm/dagOqX9+ZYFSJGjVqxN69e3Fkoh0VtCIiImjUqFGZ36fJfts2O86+VSvmzIHbboPt270/9DJf3772i2Z27jX0kr/C55/DHXc4E4wqUVhYGPHx8U6HoZRbtBsnf9ilgyNxCouOtnXu1+6tZX9iaFeOUsoDNNnnD7ts2dLRkTiFffQRfP01MHiwLXCu3QRKqbOkyf7336FRI4iMZMMGaNvW6YAgKgqMwZbezMuDL75wOiSllJ/TZL9tG7RowaFDkJjo/Ttni/PUU3D1xE4QH2/77ZVS6ixosk9IgKZNqVwZvvzSNqZ9QUgILFpk2Hf5SPj2W1u7Rymlyim4k/3x43ZoY1wcERHQrx+cc47TQVkDB9rHL2NutHEuWOBsQEopvxbcyT4pyQ67bNyY5ctdF0V9RLt2tgfni/XNITZWu3KUUmcluJN9/mTDcXG8+CK4McOa1xhjW/fffmfI7He9nZU8K8vpsJRSfiq4k/2ePfaxcWO2brXlcXzJsGEwdiwcveJaV7H7b5wOSSnlp4L7DlpXy14axbFlC/Tq5XA8p+nZ0y4c/5O92+rzz2HAAKfDUkr5IW3Z16xJ8pFqZGRAixZOB3SmnBz4cWU4uf0Gwty5doVSSpVRcCf7hARo3JgtW+xLX+vGAVst4cILYUW7WyAtDZYudTokpZQf0mTfuDE9esDatb7XjQNw5ZVQqRLMTetlC/foqBylVDkEd7Lfswfi4qhcGTp2tGUKfE1MDFx8McxdGA5XXAFz5tjhokopVQbBm+wzMiA9HRo35t13fbu45MCBsGkTbO05EvbuhdWrnQ5JKeVngjfZ5w+7jIvj2WfhvfecDack+QNwvsy5EkJDtStHKVVmwZvsXcMu8xo1zq+F5rPi4+HHH+FvE6pB796a7JVSZRb0yX5PpXiys31zJE5hF1wA4eHAddfZssz5k64opZQbgjfZ79kDISFsORQL+H6yz8yEBx6ABVHD7Apt3SulyiB4k31CAjRsyM6EUMD3k32VKvDuu/DewtrQvTvMnu10SEopPxK8yd417PL22+29SvXqOR1QyUJCbAnmhQvhxMDBdkRO/kVmpZQqRfAme9cNVQA1a7qmAfRxAwbAoUPwU9xwu2LOHEfjUUr5D68ke2NMhDFmpTFmrTFmgzFmkjeOW6y8PNsqbtyYe++FDz5wNBq3XX65vUg7b21jO1mu9tsrpdzkrZZ9NtBHRDoB5wJXGWPO99Kxz5SSAsePk9uwMa+8Ar/84lgkZRIZaQfjGAMMGgQ//ACpqU6HpZTyA15J9mIdcb0Mcy3O3fPvGnaZVK0Fx49D8+aORVJmH34Izz2Hzfp5ebYSplJKlcJrffbGmFBjzK/AfuAbEVlRxD63G2NWG2NWp6SkVFwwrgub2/PiAf9K9vkyW3aGJk10VI5Syi1eS/Yikisi5wKNgO7GmPZF7PO6iHQTkW516tSpuGBcLfvtR+sD/pfshwyBfv2N7cr55htb50cppUrg9dE4IpIOLAGu8vaxCyQkQNWqHJFq1KgBcXGORVIurVvb8gkHLxsKx4/DggVOh6SU8nHeGo1TxxgT43peBbgccO5+f9cY+7vvMaSl2Xrx/qR/f8jNhYUHekDdutqVo5Qqlbda9vWBJcaY34BV2D77L7107DO5kj34x/j603XvbnP8vPkhcO21tmWfleV0WEopH+at0Ti/iUhnEekoIu1F5AlvHLdY+/ZB/fpcfbVvlzYuzhl30x45YvvulVKqGMF3B60IJCdzoHpTFi2yQ+790ejR8PLLkHdRb4iO1q4cpVSJ3O6tNsZcA8wXkZwKjKfiHT4M2dlsD7WVz/xtJE6+Hj3sAuF2KqsvvoATJyAszOnQlFI+qCwt+yeAfcaYfxljelRUQBVu/34Atuc0Afw32YMdVPTvfwODB8PBg7BkidMhKaV8lNvJ3lXq4DLgGPCZMWazMeYRY0zTigquQiQnA7A905a5bNbMyWDOzrx5cNttsCX+SqhWzbcn0lVKOapMffYislZEJgBxwN+AocB2Y8xSY8xfjDG+fw3Alewj61blwguhalWH4zkL/fvbx3nfRNgXc+bYMZlKKXWaMidnY0xz4FFgBhDhev4GcCfwqUejqwiuZH/3vaEsXepwLGepSRPo0MG28Bk82HZR/fij02EppXyQ28neGPM3Y8xyYCUQC4wQkVYiMllE3gMuBa6ooDg9JznZDq6vXdvpSDxiwADX3bTnXw0REfCp73/fKqW8rywt+6uBfwINROQOEVleeKOIHAUGeTK4CpGczLFajYhvUYmZM50O5uwNGGBHk67cGAlXX22HYOblOR2WUsrHlCXZfy8in4hIduGVxph785+LyNcei6yiJCezM6Yzu3b5X5mEopx3nu29ufJKbFdOUhKsOKOgqFIqyJUl2T9azPpHPBGI1yQns71qB8C/h13mCw2FWrVcL/r3t1NZaVeOUuo0pSZ7Y0wfY0wfoJIx5pL8167lVsC/6usmJ7MttBUQGMkeYMcOuPRSWLo22jbxP/nE9u0opZSLOx0Zb7oeKwNvFVovwB/AXZ4OqkIlJ7M9qinVqxdqEfu5unXtRdovvoCLhg61w3NWrIDznZv5USnlW0pt2YtIvIjEA7Pyn7uWZiLSS0T8Z168zEzIzKR142P8+c/+WfGyKJGRcMklriGYAwfarpyPP3Y6LKWUDynLHbQjKzIQr3CNsb/zukRmzHA4Fg/r3x+2boUtyYW6cnRUjlLKpcRkb4zZVOj5HmNMQlFLxYfpIcnJCJBTu57TkXjcgAH2cd484PrrYe9eHZWjlCpQWp/9bYWe31iRgXhFcjK7aUKL665i5ntwww1OB+Q5TZrATTdBo0bA1QOhcmXbldOzp9OhKaV8QInJXkR+LPT8h4oPp4IlJ7Od5uTkGmJjnQ7G895+O/9Z9ZNdOf/8p53tRCkV1MpSLuFeY8y5rufnu7pwdhpj/Kfp6Er2EDjDLk936JCddZHrr4fERFi+vNT3KKUCX1mafOOBna7nU4BpwFPACx6OqeLs38/2yu0IC3N1dwQYEWjXDh58ENuJX7kyfPSR02EppXxAWZJ9tIgcMsZEAZ2Al0XkTaBVxYRWAZKT2R7emvh4e+dpoDEGLr/czk2bU7U69O1r++217LFSQa8syX6PMaYXMBxYKiK5xpjqgP9kkuRk+jX4hbFjnQ6k4vTvD+np8NNP2CvQf/wBP/j/5Ral1NkpSymwCdh69ceBwa51/bElj/1DcjI3n/sL3ON0IBXniivsPVXz5sHFT/Szd1x98AH06eN0aEopB5XlpqoFItJARJqKyBrX6k+AgRUTmudl/3GQpGotArpsTFQU9O7tGm9ftSpcc42drvD4cadDU0o5qExj8owx0caY7oWKo13oWnxfVha/HG5Gw7efYv58p4OpWFOm2BkKAduVc/AgfPWVkyEppRzmdjeOMeYm4BXgCHC00CYBfH/a7v37A37YZb4uXQq9uPxyqFkTPvzw5G22SqmgU5aW/WRgiIjEnl4QraKC8yjXGHtjhPh4p4OpeN98A5MnYzvwhwyxJTGPHi31fUqpwFSWZF8J8P2ZqIrjSvYN6xwnIsLpYCrekiXw2GO2B4cbbrAVP+fNczospZRDypLspwKPGGP88957V7JvHh/AV2cLGTDADq9ftAi48EJo0ABmzXI6LKWUQ8p6B+0jQIZfVr1MTuZepjH+3gApYl+K7t2hTh1XYz40FP78Z3u3VWqq06EppRxQlnH2/l31MjmZQVHfwvWVnY7EK0JDoV8/OyrnxAkIu/FGeO45e0ftHXc4HZ5SysvcTvb+XvXyQMIRtkZfQcdjUKWK09F4R//+8N//2sJozTp1gg4d4L33NNkrFYTKUvWysjFmsjFmhzHmkGvdFcaYOysuPM/5YWsDzt/7KRs3Oh2J91x3nZ29qln+eKkRI2wVzK1bHY1LKeV9Zemzfx5oD/wFO7YeYAPgF5VmtqdUBwJ/jH1hISG2ONqJE7YiJjfcYFfohVqlgk5Zkv11wJ9F5H9AHoCIJAINKyIwT9uWUZealY8QE+N0JN61bBnUqwcrV2LrOvfpA//5DwFdM0IpdYayJPvjnNbHb4ypA6R5NKKKIML2rIacU/Og05F4Xdu2cOSIvS4L2K6c7dvhf/9zNC6llHeVJdl/ArxrjIkHMMbUB/4FfFgRgXlUZibbpRnNYzOcjsTrYmJOzlCYlwcMGmSvUM+c6XRoSikvKkuy/zuwA1gHxABbgX3ApNLeaIyJM8YsMcZsNMZsMMbcXZ5gy+3AAd7mZu7rv8Wrh/UVQ4faETkrVmDLYg4aZGvlHDvmdGhKKS8pS7I/B9gMPA08BvQUkXtExJ3auTnAfSLSFjgf+Jsxpm2Zoy2vtDQuZilduwRnP/XAgbZETkFXzi232MlqC0pjKqUCXanJ3lhvYVv0fwcGALcBvxhj3jbGlHpLqojsE5GfXc8zgE148cLujvVH+YQhHKlSx1uH9CnR0fDSSzB8uGtF797QtCm89ZaDUSmlvMmdlv3tQG/gfBFpIiI9RaQx0BNby350WQ5ojGkKdAZWFLHtdmPMamPM6pSUlLJ8bIkWfl+F6/mEw+G1PfaZ/mb0aOjRw/UiJARGjYLvvoME/6h2oZQ6O+4k+xHAOBFZVXil6/U9ru1uMcZEAp8B94jI4dO3i8jrItJNRLrVqeO5Vvj23ZWowlHqt6rusc/0R8uXw+efu16MGmWHX777rqMxKaW8w51k3xYorlTCD67tpTLGhGET/SwRme1eeJ6xPTGCZuzA1KzhzcP6nKlT4c47XaNy4uPtmPu333atUEoFMneSfairn/0MrvVu9fsDbwKbRGRa2UI8e9tTqtM8ZFfwFMUpxtChkJRkb7QC4OabYedOWLrU0biUUhXPnWQfZoy5JH/e2dMX3CumdgG2u6ePMeZX19L3rCJ3kwjsSK9B86r7vHE4nzZwoJ2D/D//ca0YNAiqV4c333Q0LqVUxTNSym3zxphdnKyFUyQR8fhEf926dZPVq1ef9eeIwI4rxhC2dyeNN+mk2yNGwJdfwr592Bm77rjDjspJSrJz1Sql/FmxoyNLbdmLSNPT5pw9Y/FsrJ5lDDTP2kDjeu7cDhD4Ro60jwXVP2+/HbKz9Y5apQKcf04xWAb//S+8sLUfx2PqOh2KT+jTx7bqu3RxrTj3XDut1euva3E0pQJYwCf7OXPg4f3jqFQ7xulQfEJoqO2+EbGljwE7CH/TJvjxR0djU0pVnIBP9lu2COewjZBawT3ssrCDB6FVK3jtNdeKYcPshdqCFUqpQBP4yf53oaVs1ouPhdSoAdWq2SH2gH0xYgR8+imk+X7FaqVU2QV0sj9xAnbsMrRkiyb709x6K/z8M6xZ41oxerS9UKt31CoVkAI62e/ZA7m52GRfq5bT4fiUv/zF3mP2xhuuFR06QK9eMGOG3lGrVAAK6GTfrBlkzv+B6/lYW/aniYmxXfWzZtmZrABbS2HbNvhK70dQKtAEdLIHqJKZShWyNNkX4d574Z13oHJl14rBg+2EtS+/7GRYSqkKENDJfsYMmPRuU/tCk/0ZOnSw+T0szLUiPBzGjIGFC2FLcM7qpVSgCuhk/+mnsGhtfftCk32R0tPhiSdg7VrXitGjbfZ/5RUnw1JKeVhAJ/stW6Bl1D57JTLIK16W5JlnYFp+LdJ69eD66+24zIzgm6BdqUAVsMk+MxP27oWWEQnaqi9BTIytdPzBB/DHH66Vd91lE73Wy1EqYARsst+2zT62CNmuyb4U48bZexJmzHCt6NHD1st58UUdhqlUgAjYZJ+WBnXqQMvcTTrGvhQtWkD//jbZZ2W5Vt53H2zdCnPnOhqbUsozAjbZ9+kD+/dDp+yV2rJ3w/jx9p6qAwdcKwYNgqZN4dlnnQxLKeUhAZvs85mDBzTZu6FPH1shtEED14pKlexA/GXLCs1jqJTyVwGb7IcPh6n/ENufo8nebdu2QcEEYbfcYqumPfecozEppc5eQCb73Fz44gvYn5QDx49rn72bROw8tbff7prHpFo1O23hnDl6k5VSfi4gk/2uXfZCY7vGrnHi2rJ3izEwYQL88ou9iRawwzDDwwsNxFdK+aOATPYbNtjHtrGu2uya7N12443QuDE8+aSrdR8bC6NG2ZusEhOdDk8pVU4BmezzJ9NuW2OffaLJ3m1hYfDQQ7B8OXz9tWvlgw/avjEdmaOU3wrIZB8dDVdcAdWz9tsVmuzL5JZb7LSF+V+aNGtmm/yvvQbJyY7GppQqn4BM9mPHukqy5w8a1wu0ZVK5Mvz2mx17X+Dvf7cXu//5T8fiUkqVX8AlexFXXzOcTPbasi+z8HD7+OOPNsfTsqWd7WT6dEhNdTQ2pVTZBVyy37ULatd23eV/4ABERGjFy3JatQouvND23gDw8MO2wtwLLzgZllKqHAIu2W/caHN87droDVVnqVs3e2ft44/bPyXt2sGQIbZAmrbulfIrAZfsC4ZdtsVmfe2vLzdj4KWX4NAheOQR18onnoCjR2HKFEdjU0qVTcAl+40bbX2XmBhssteW/Vlp187eV/Xaa/Dzz0CbNjBypJ3Jas8ep8NTSrkpIJN927auF5rsPeLxx6F1a0hIcK147DFb5/6JJ5wMSylVBgGX7Pv1s7PqAdpn7yHR0bB+PVx7rWtF06Z2YvK339aaOUr5CSMF4xR9S7du3WR1QfnFcsq/iFi79tkHpMjLgzfesF+ojcKSoXlz++Kjj5wOTSllmeI2BFzL/hS1a2ui96DERFvifswYkLqx9sXHH8P//ud0aEqpUgR2slceFRcHkyfD/Pnw/vvAAw9A/fr2Vludq1Ypn6bJXpXJXXdBz57wt79BwoFIOwRzxQr44AOnQ1NKlUCTvSqT0FD4z39sEcyRI0FuHAFdu9rKmJmZToenlCqGV5K9MeYtY8x+Y8x6bxxPVaxmzexAnIcfBhMaYssnJCbq9IVK+TCvjMYxxlwEHAFmikh7d97jkdE4yiuysiBi1DCYN8/ewhwf73RISgUrZ0fjiMhS4IA3jqW866WXoFMnyJg0zfbx3HlnobKjSilf4VN99saY240xq40xq1NSUpwOR7mhSxfYtg3++mhDZNITsGABzJ7tdFhKqdP4VLIXkddFpJuIdKtTp47T4Sg3/OlP8I9/wCefwPO54+Dcc2HcODh82OnQlFKF+FSyV/7p/vth0CB4YGIoP4x+H/btg//7P6fDUkoVoslenTVj7OicNm1ga6U2dl7Il1+GZcucDk0p5eKt0TgfAL2B2kAy8JiIvFnSe3Q0jv85cQLCwoCMDOjQwc5t+OuvULWq06EpFSwcH41zg4jUF5EwEWlUWqJX/ikszD7OXRLF3879Edm61U5UrpRynHbjKI/79VeY/kUjnuk5x05h+MMPToekVNDTZK887v/+D264ASYuH8jnsWPg5pvt3IZKKcdoslceZwy8+SZ072648dC/+Hl3LRg9Wm+2UspBmuxVhahSBebMgdp1Q5lz8fN2gpN//9vpsJQKWpWcDkAFrnr1YNUqqFOrF1x1mb3ZqmdPaO9WeSSllAdpy15VqLp1bWXMjY+8zxD5mMwho+DIEafDUiroaLJXXrH9cB0+P9GfoZuf4sSIW3RmK6W8TJO98ooBA+C11wwLuZoRcwaR88TTToekVFDRZK+85tZb4dlnhI8YzqhJ8eTO/sLpkJQKGnqBVnnV/RMMOVknWPRsa7JG9qVafGPo3NnpsJQKeNqyV1730P+F8c26+lSrWZmjVw8md9tOp0NSKuBpsleOCGvSgOy5X3FF6vsM67yZrL2pToekVEDTZK8cU/ncNgy5oy6fHbmKq9omkL5Xh2QqVVE02StH3fNSM96/dxXLMtpzces/SNp21OmQlApImuyV427453nM//sydmTGcuN5v8NRTfhKeZome+UTLp/cm6WTf+TlQ6NgwADyMjKdDkmpgKLJXvmMzn+/mnYzH0SWfM/o5t8yelQWmZrzlfIITfbKt9x4I/LpZ9Q8sJU3ZobTpeMJ1qxxOiil/J8me+VzQgZdy9TF3fmu2jUc3Z3C+ecLTz9t57hVSpWPJnvlmy66iEuWTea32CsYJJ8x5ckTpKQ4HZRS/kuTvfJdHTtSY823fNj9eX7LakmDGf+H5OYxdSqa+JUqI032yrfVq4dZspj4v14KTz3Fr73u4JFHhHPOgcmT0Qu4SrlJk73yfZUrwxtvwBtv0HndTNZGXUjvtsk88giccw68+irk5DgdpFK+TZO98g/G2BrJa9bQNi6DL5bX48drnuWc+BymTDk5l7nOaa5U0TTZK//Spg2sWAH33ccF8x5iaUI8Pz25mLAwyM621ZInT4b0dKcDVcq3aLJX/iciAp57DpYtw8RE02jUpTB4MGm/JNCwITzyCDRuDHffDZs2OR2sUr5Bk73yXz16wJo18NRTsGgRDXq3ZP65D/Prj0cYOND25bdtC7/84nSgSjlPk73yb5Urw8MPw5YtMHQoPP00nQY24T8dprLn90ymT4dzz7W7TpoEEybA2rXat6+CjyZ7FRgaNoT33oNVq2yL/6GHqHt+M8Ye+gcm/SAA27bBCy/Y5N+xI0yZAlu3Ohq1Ul6jyV4Flm7dYMEC+Oknm9UnToS4OLj7bt57dCv79sH06VC9Ovz97zb5A+TlwX//ay/yKhWIjPjo79lu3brJ6tWrnQ5D+bu1a2HaNHj/fTsYv3dvuP12uO469qZGkJsLTZrA8uXQsydUqQK9esEll9jlvPMgLMzpk1DKbabYDZrsVVDYtw/efhv+/W/YudM27a+7DoYPh0svJSMrjCVLYMkSWLwYfvvNvm3xYpv0f/vNXug97zxo1QpCQ509HaWKocleKcD21yxebFv6s2fDoUMQEwNXXw0DB8KVV0KNGqSkwA8/wFVXQWSkvbj7+OP2IyIioHVrO9Jnxgz7vXH4MFStCpUqOXlySmmyV+pMWVmwaBF88QXMn2+rqxkDXbvCpZfaLp/zz4eYGHJzYfNmWL0a1q2DDRtgxw7YuBFCQmzP0Ntv2/H9zZpBfLz9BXDfffZQ6en2S0O/DFQF02SvVIlyc+2dud98A999B//7n+3jNwbatbMjfLp2hS5doEMH24wvZNEiWLrU9hDt2HGyp2jbNrv9iivg228hNhYaNLBL587wxBN2++LFdjho7dpQq5ZdqlTx8t9ABQJN9kqVyZEjsHIlLFtmR/asWgVpaXabMbb53q6dLd/QooVdmjeH+vVtUx/7wyEiwr7lk09g/XpISjq5NG0Kn39ut7drZ38lFNa3r/3BATBqlK3wGR1tv0SqV7ffO9dcY7cvXmy/HPK3RUXpL4kg5XyyN8ZcBbwIhAL/FpF/lLS/JnvlU0Rgzx57x+5vv9l+nA0b7ED9wlNohYfboZ6NG9ux//nN+NhYu9SpY5vvNWvafV02b4Y//rDfJ6mp9rFhQxg50m6/6ip7+MOH7WWGjAwYMQJmzrTbq1SxXy6FjR5t7yLOy7PfRZGRJ78EoqJg0CC44QY73HTatDO3t25tRyrl5sLBg3Z95cr2u075LGeTvTEmFNgCXA7sBVYBN4jIxuLeo8le+YWcHJuFt261/Te7dtklIeFkE764+RQjI+3F4ZgY22SPirLN8shIqFbt5FKlysklIgIqVyYvrDInQipTOTIMwsNZtjGGw9mVOZwVzqGjYWQcq0T7NrlccckJsnNC+ev9MRzJDCEjM4QjmYYjmYa/3pTLvffkkZwSQr24M8eXTpkCDz1kT6t5c7suLMyGGh0NTz5pvywSEuDRR0+uz1/69LE/gA4dsr9aXKEXLHXq2MfcXLuEhNgvkvxHVS6OJ/uewOMicqXr9UQAEZlS3Hs02auAkJcHBw5AcjLs32+XtDS7HDhgM2F6ul0yMk4umZl28UKhfgGyqcwRIskgquCxEYk0DtnLQWowi7+QQSSHieYQ0RyiOreEzuTS0O/5Na8j1xz/hENU5zDVEde9mh+Fj+D6SrP5Lrc3l2XPP+O4X1YeTL9KX/F5zgAGZX9wxvalVa7kwtBlzDpxPfdkTyUlMr6C/xI+om5d2L69vO92PNkPAa4SkVtdr0cAPUTkztP2ux243fWyFbC5nIesDaSW873+KhjPGYLzvIPxnCE4z7us55wqIlcVtcGnLt+IyOvA62f7OcaY1SLSzQMh+Y1gPGcIzvMOxnOG4DxvT56zt2rjJAJxhV43cq1TSinlBd5K9quAFsaYeGNMODAcmOulYyulVNDzSjeOiOQYY+4EvsIOvXxLRDZU4CHPuivIDwXjOUNwnncwnjME53l77Jx99qYqpZRSnqP17JVSKghosldKqSDg18neGHOVMWazMWabMeahIrZXNsZ85Nq+whjT1IEwPcqNc77XGLPRGPObMeY7Y0wTJ+L0tNLOu9B+g40xYozx+yF67pyzMeZ613/vDcaY970do6e58e+7sTFmiTHmF9e/8b5OxOlJxpi3jDH7jTHri9lujDEvuf4mvxljupTrQCLilwv2Qu92oBkQDqwF2p62zx3Aq67nw4GPnI7bC+d8CVDV9Xysv5+zu+ft2i8KWAosB7o5HbcX/lu3AH4Barhe13U6bi+c8+vAWNfztsAup+P2wHlfBHQB1hezvS+wEHt37PnAivIcx59b9t2BbSKyQ0SOAx8C15y2zzXAu67nnwKXGuPXVTdKPWcRWSIiR10vl2PvafB37vy3BngSmApkFbHN37hzzrcBr4jIQQAR2e/lGD3NnXMWoLrreTSQ5MX4KoSILAUOlLDLNcBMsZYDMcaY+mU9jj8n+4bAnkKv97rWFbmPiOQAh4BaXomuYrhzzoX9Fdsi8Helnrfrp22ciJxZhMU/ufPfuiXQ0hjzkzFmuauyrD9z55wfB240xuwFFgB3eSc0R5X1//si+VS5BOU5xpgbgW7AxU7HUtGMMSHANOAmh0PxtkrYrpze2F9wS40xHUQk3cmgKtgNwDsi8k9XgcX3jDHtRSTP6cB8nT+37N0pwVCwjzGmEvZnX5pXoqsYbpWdMMZcBjwMDBSRbC/FVpFKO+8ooD3wvTFmF7Zfc66fX6R157/1XmCuiJwQkZ3YMuItvBRfRXDnnP8KfAwgIv8DIrDFwgKZR8rN+HOyd6cEw1xglOv5EGCxuK54+KlSz9kY0xl4DZvo/b0PN1+J5y0ih0Sktog0FZGm2GsVA0XEn2tku/Pvew62VY8xpja2W2eHF2P0NHfOOQG4FMAY0wab7FO8GqX3zQVGukblnA8cEpF9Zf0Qv+3GkWJKMBhjngBWi8hc4E3sz7xt2Asgw52L+Oy5ec7PApHAJ65r0QkiMtCxoD3AzfMOKG6e81fAFcaYjUAuMEFE/PaXq5vnfB/whjFmPPZi7U1+3oDDGPMB9ku7tutaxGNAGICIvIq9NtEX2AYcBW4u13H8/O+klFLKDf7cjaOUUspNmuyVUioIaLJXSqkgoMleKaWCgCZ7pZQKAprsVdAzxjR1Vcr026HISpVGk70KSsaYXa47jc/2c/SLQvkFTfZKKRUENNmroGOMeQ9oDMwzxhwBrndt+osxJsEYk2qMebjQ/iHGmIeMMduNMWnGmI+NMTVdm5e6HtONMUeMMT2NMc2NMYtd+6YaY2YZY2K8doJKFUGTvQo6IjICW2NlgIhE4iqsBfwJaIWtvfKoq/YK2DK612IriDYADgKvuLZd5HqMEZFIV3EuA0xx7dsGW8Tq8Qo8JaVKpcleqZMmicgxEVmLnSWpk2v9GOBhEdnrqiL6ODCkuH56EdkmIt+ISLaIpGDLLwd8qWnl2/SiklIn/VHo+VFsQTmAJsDnxpjCNdNzgdiiPsQYEwu8CFyILb8cgv01oJRjtGWvglVZKgDuAa4WkZhCS4SIJBbzOU+71ncQkerAjdiuHaUco8leBatk7MTW7ngVmGyMaQJgjKljjMmfGzUFyDvts6KAI8AhY0xDYIJnQlaq/DTZq2A1BXjEGJOOndimJC9iJ5D42hiTgZ0cpQeAa3L3ycBPxph01+QSk4Au2DmP5wOzK+QMlCoDrWevlFJBQFv2SikVBDTZK6VUENBkr5RSQUCTvVJKBQFN9kopFQQ02SulVBDQZK+UUkFAk71SSgWB/we/PVWT2K2f4AAAAABJRU5ErkJggg==",
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evmSJ2Z6UVLP4Hn74Yd23b1+dnp6us7KydO/evXVUVJTWWuvGjRvrDRs2lNn/6NGjukGDBvrXX3/V//73v3WnTp10VlZWyfbbb79dT506teT95MmT9eTJk/9S7oEDB3S9evX0iRMntNZaFxYW6qZNm+off/yxZJ8PP/xQp6am6qKiIr1kyRIdHBys09LStNZmtqauXbvqpKQkffr06ZJ1Z2ZwqurY8vuWf5+fn69bt26tH3/8cZ2Xl6fXrl2rQ0JC9I4dO0r2Pf/883VqaqrOzMzU5557rv73v/9td9xVzaLVsWNHnZSUpDMzM3Xfvn1LZuSqKqYdO3boFi1alMyctX//fr1nz54KyysqKtLdu3fXs2fP1nl5eXrv3r06Pj5er1692q7P1Z7PpvzxFTmbmarkzr6cnTvh4Ydh91cHoG9fiIhw2LkvHR9Pi6AMFn1W34yJLzxaRkYG8+bNY9GiRTRt2pSwsDAGDx5M586dATMEcmi5HteNGjVi6tSpjB8/njlz5rBy5UrCSg2cFBoaWmbo5AULFrBgwYK/lB0bG0v37t1L7nq//vprgoODueCCC0r2GTFiBNHR0fj5+TFy5EjOOeccNmzYULL9jjvuICYmpsJqpuqOrcpPP/3EyZMnuf/++wkMDKR///4MGTKExYsXlyk7Ojqahg0bMnToUDZv3uyQsqdMmUJMTAwNGzbkwQcfLCmzqpj8/f3Jy8tj27ZtFBQUEBcXR+vWrSs8/8aNG8nIyGDmzJkEBgbSqlUrJkyYwJIlS8pcW2Wfq72fTWXH14aMjVPO3r3mZ+u9a+CfNzr03H5+MPraHOYt7k/Gy4uInP4Ph57fV1TVsCE4uOrtjRtXvT0mxv441q5dS/v27YmLiytZl5mZWZLsIyIiyM7O/stx5513HrNnz2bRokXElCswOzub8PBwu8ofPXo0ixcvZty4cbz//vuMHj26zPaFCxcyb968kjHoT548ydGjR0u2ly+7JsdWJS0tjZiYmJIJxcF8OaWmppa8b1oy6BQEBweTlpbmkLJLX1NsbGzJeauKqU2bNjz//PPMmjWLxMRErrrqKubNm0d0dPRfzn/w4EHS0tLK/I6Kioq4+OKLK4yhPHs+m6qOrw25sy/nTLJvxT64/HKHn3/M/TEUEsCHzyYjXWo929GjR4mMjCx5X1hYyPLly0vmkO3SpQu7du0qc0xCQgKTJ09m/PjxvPnmm3855/bt2+natatd5Y8YMYJ169aRkpLC0qVLyyT7gwcPMmHCBF5++WUyMzPJysqiU6dO6FL/5pSqeLrS2hwLEB0dTXJyMsXFxSXrkpKSaF7p/J41K7sqycnJZco8k7Cri2n06NGsX7+egwcPopTivvvuq/A6Y2JiiI+PJysrq2TJzs5m5cqVJfvU9rOp6vjakGRfzv790Cz4OPXq+0P37g4/f+cuiqlXJtL58FdV32IKt3fuuefyv//9j/379/PHH38wefJk9u/fX3JnP2jQIL799tuS/VNTUxk6dCivvPIKCxYsICEhoUz769zcXH755ReuuOIKu8qPjIykX79+3HTTTcTHx5eZgPrUqVMopUq+jN566y22bt1q13ntOTYqKop9+/ZVeHzv3r0JDg7mqaeeoqCggHXr1rFixQpGjRrlkLKrMn/+fFJSUjh27BiPP/44I0eOrDamnTt38vXXX5OXl0dQUBD16tUrufMuf529evUiNDSUuXPnkpOTQ1FREVu3bmXjxo12xVebz6a2JNmXk5oKsRww9fUBAU4pY96yVlzSMBEqqIsVnmPAgAGMGDGCrl270rt3bzp37oyfnx8dO3YEYNy4caxcuZKcnBxOnDjBoEGDuPvuuxk2bBjBwcFMnz6dBx98sOR8K1asoF+/fmWqD2699VZuvfXWSmMYPXo0//3vf/9ShdOhQwemTZtGnz59iIqKIiEhgQsvvNCu67Ln2BkzZvDYY48RHh7OM888U2ZbYGAgK1asYNWqVTRu3JjbbruNhQsX2jVfb23iBvN5XHnllbRq1YrWrVvz0EMPVRtTXl4e999/P40bN6Zp06YcOXKEOXPmVHid/v7+fP7552zevJn4+HgaN27MLbfcwvHj9nWYrM1nU2tVPb21crGqNU5RRqb+g3CtH33UqeXsuvlJ/Y1ff61TUpxajqerotWB21mzZo1u06ZNmXUzZszQzz33nF3H9+rVSyckJDghMt9QVUsdb3M2rXHkAW05fj/+QDhZcMklTi1nUuIdpBRfy87/vIp6ZLZTyxKusX379pIqnDOeeOIJu4//+eefHR2SECVcWo2jlPJXSv2mlPrcleXa69gxmPhQJBvq9IVevZxa1pgJ9dhNWzbO3wAFBU4tS7jG9u3bSx7OCuFuXH1nfyewHWjg4nLtsn8/vLblAga1vajmY9fX0HXXwW23FvHesYH0WrnScT11hWVeeeUVq0PwaWeaaoqKuezOXinVAhgMvO6qMmsq6UARAC3Pa+T0ssLCYOgwxRK/0RS8/o7TyxNC+DZXVuM8D9wLFFezn2WSNmUA0PLiWJeUN2asH8dVOFtWpiCT1AohnMklyV4pNQQ4orX+pZr9JiqlNimlNmVkZLgitDKSNmdSj9M06te5+p0dYOBASP9hPz2KN8K777qkTCGEb3LVnf2FwDCl1AFgCdBfKfVe+Z201q9qrXtqrXuW7pnoKjkpx2it9qPObeeS8gIDoWHvc+Cii9BvvCk9aiuh5XMRosTZ/n9wSbLXWs/QWrfQWscBo4CvtdZjXFF2TSwIuZctF04Gf3+XlZmRAX3TP+G9XefD//7nsnI9RVBQEJmZmZLwhcAk+szMTILOogGJtLM/o6AANm9GTZ7s0mIbN4b0wsa85z+esW++CTXoLegLWrRoQUpKClZU6wnhjoKCgmjRokWNj3N5stdarwPWubrc6uQl7OKa3E/5lwpiiAvLVQpuHOPHnCf6k754Es1eOGmmQhQABAQEEB8fb3UYQng8GRvHJuW7faxmIBlhbVxe9o03QrH244OcobBsmcvLF0J4P0n2NsmbDgPQ8vwol5fdvj2cd55mUeBN8N5fnlsLIUStSbK3Sdp2EoCWbQItKf/++xX/7H8Q/eVX4OIJp4UQ3k+SvU3SAdPX6yyeezjE3/8Ok+edg9LFUGqKMyGEcARJ9gCnTlH3j3R6RKfh4Gkfa+RYVHvejfs/9ELpYCWEcCxJ9gCJiUznGTbNt29SY2dZuhTGHXiETb/5wbZtlsYihPAukuwBzkx7ZvHwtNddB4GBmkVqDCxaZGksQgjvIskeYOtWeqsNvPJlK0vDCA+HIUMUSwLGUvjeEih22zHjhBAeRpI9kL31IBv0+Zw4af3HceONcDi/IV8ntYb1660ORwjhJazPbm4gfXsWAM2aWRsHwKBBEBam+V9AP2lzL4RwGEn2eXmkp5rqEndI9kFBsHevYtaoHfDhh5CXZ3VIQggvIMl+3z7Stek1Gx1tcSw2jRoBN9yAPn4c1qyxOhwhhBeQZL9rF6Fkc3G3bLdJ9gBTVlzJyMCl0sFKCOEQkux37mQwK/luXTHh4VYH86e69fz5rHAwx5d9A6dOWR2OEMLDSbLftQuioswM4G5kxAjILw5gec4A+Pxzq8MRQng4Sfa7dnFt4YeMcbN5s3r3hpgYzUd1x0pVjhCi1iTZ79rF9sJz3K7Ri1Jw/fWKNYX9Of7FesjKsjokIYQH8+1kf/w4HD5Mem5Dt2h2Wd64cXD/Pw5TWFAsk5oIIWrFt5P93r2cIpgTeXXdqiXOGd26wezXomkUHyZVOUKIWvHtZL9vH+mYW3p3vLMHyMtXrOgxixNf/Qwy6bYQ4iz5drLfvx9/irjh+nw6drQ6mIr98gsM+3gcy4sHw8cfWx2OEMJD+Xyyj484zvsfBdKzp9XBVOyCC6B5c81HIf+ExYutDkcI4aF8O9nv20dxnLXDGlfHz8/WKif3Ek58vxlSUqwOSQjhgXw72e/fz4xTD9GkCWhtdTCVGzEC8grr8AWDzeBoQghRQ76b7IuL4cAB0urEEBxs2rW7qz59oEkTWNd4hFTlCCHOiu8m+/R0yM8nvSjKLZtdlubnBxs3wiv37oNNm2DPHqtDEkJ4GN9N9vv2AZB2Otxtm12W1rIlqFEjzZsPPrA2GCGEx/HdZL9/PwDpx+t5RLIHmPZ8DLNbvi5VOUKIGvPpZK+BibdorrzS6mDss28fvJH9d3RiImzdanU4QggP4tPJXkVHM/fZOgwbZnUw9hk2DJL/CGWz6i7DJwghasR3k31SErkx55CdbXUg9hsyxLQa+iz+LlOV487tRYUQbsV3k31KCiv8htOgAWzZYnUw9omMhL594bPCQaZOZ+NGq0MSQngIu5O9Umq4UqqOM4NxGa0hOZn0unGA+0w0bo/x46HXZSEUBtSD99+3OhwhhIeoyZ39I0C6UuplpVTvmhSilApSSm1QSv2ulEpUSs2uWZgOlpkJubmk+7cgIAAaNbI0mhqZMAH+83Zd6gy52jTBLCqyOiQhhAewO9lrrbsCA4Ac4BOl1E6l1ENKqTg7Ds8D+tvO0Q24Wil1wVnE6xjJyQCkFTahaVP37j1bEa1hd78JcOgQfPut1eEIITxAjerstda/a62nAzHAv4ARwF6l1HdKqRuVUhWeTxsnbW8DbIt1Txdtg4ml54R7VBXOGbNnQ6fpV3OyfpRU5Qgh7FLjB7RKqdbATODfQJDt9WvAFKDSAdeVUv5Kqc3AEeArrfXPFewzUSm1SSm1KcOZE3XY7uxvGl/MlCnOK8ZZLrkE8vMVX59/H3zyCW43ga4Qwu3U5AHtv5RSPwEbgChgrNa6ndb6ca31u8DlQKXdk7TWRVrrbkALoJdSqlMF+7yqte6pte4ZGRlZ02uxX3Iy1KnDDZMaMGaM84pxlosugpAQWFnvOjMR+erVVockhHBzNbmzHwg8C0RrrW/TWv9UeqPW+jTwt+pOorXOAr4Brq5B2Y6VkkJhdEu27fTn1CnLojhrgYEwYACsSoxBN2oswycIIapVk2S/Tmv9kda6TJ2BUuruM6+11l9WdKBSKlIpFW57XQ+4AthR83AdJDmZlCbd6djRc8cUGzQIkpIU2wbcAcuXw8mT1R8khPBZNUn2MytZ/5AdxzYDvlFKbQE2YursP69B2Y6VnEx6eHsTmIcMglbe8OGwYgW0uqU/5OTAZ59ZHZIQwo1V20lKKdX/zL5KqcuA0g0VWwHVDjigtd4CnHdWETpacTGkpJDWqQ3gucm+SRMzfALFfSAmxlTl3Hij1WEJIdyUPT1i37D9rAu8WWq9Bg4Btzs6KKc6etRMWhIYC3hW79nyDhyAd97xY+q142mw4EnTWcyTeogJIVym2mocrXW81joeWHTmtW1ppbXuq7Ve7oI4HcfW7DJdN6VOHWjc2OJ4auHgQZg1C9a2vAkKC+HjSlu+CiF8XE160I5zZiAuY0v2fxtexKuvmin/PFXfvtCgAazcHg/nniutcoQQlaqyGkcptV1r3d72OplKer1qrVs6ITbnsPWe7XFlI3pEWRxLLQUEwBVXwKrVCj3hBtTsWeb6WrSwOjQhhJuprs5+QqnXHtj9qAJpaVCnDv/bHUl0DsTFWR1Q7QwcaDrRJnQfTxf9sGlLOm2a1WEJIdxMlZUYWuv1pV5/W9ni/DAdKD0doqIYfq0fc+daHUztDRwI9erBjpxY6NlTxsoRQlSoJsMl3K2U6mZ7fYFSKkkptV8p1cdp0TlDejr5UTEcPeq5zS5Li46GP/6Av/8duOEG+PVX2LXL6rCEEG6mJo8npwL7ba/nAPOAx4DnHRyTc6WncyjCsztUlVe3ru3FyJFmvGZ5UCuEKKcmyT5Ma31cKRUKdAVe0lq/AbRzTmhOkp5Oeug5gGe3sS8tKcnU4Czb2BwuvRQWLZL5aYUQZdQk2ScrpfoCo4DvtNZFSqkGgOdMlVRQABkZpAXGA95zZ9+smam5WbkSGDsWdu+GDRusDksI4UZqkuynY8arfxB41LZuCGbIY89w5AgAfXvk8dln0LatxfE4SECAbRTMVaCvux6CgmDhQqvDEkK4kZp0qlqptY7WWsdprX+xrf4IGOac0JwgPR2AqHbhDBtmxoT3FgMHmib221IawLXXwpIlMqmJEKJEjfqPKqXClFK9lFL9bQOkXWxbPIMt2X9/6By++cbiWBzsatvsAKtWAePGwbFj8MUXlsYkhHAf9gyEBoBS6h/AfOAkcLrUJo0Z/dL92ZL9nA/iOXICNm2yOB4HiomBKVPMqAkMGABNm5qqnL9VO5+MEMIH2J3sgceB67XWq5wVjNPZkn1aZl1iPGeAB7u99NKZV3XMcMcvvGBG+fTk0d6EEA5Rk2qcOkCFM1F5jPR0aNyY9EN+XtPssrzUVDMaJuPHm5EwlyyxOiQhhBuoSbKfCzyklPLccSIPHaIgqgVHjnhPs8vSCgpMNc6TTwKdO0O3btIqRwgB1LwH7UNAtm2ohJLFSbE5Xno6hxt6V+/Z0gICoH9/WxNMjXlQu3EjbN9udWhCCIvVJNmPAQYAg4Cx5RbPkJ5Ok5ZB/PILXHON1cE4x8CBphpn507MWDn+/vDuu1aHJYSwmN0PaD1udMvytIZDhwhs0YTu3a0OxnkGDjQ/V62Cc6c2hauuMsn+scc8e6YWIUSt1GTUy7pKqceVUvuUUsdt665USk1xXngOlJkJBQVsKujKa69Bfr7VATlHbCy0b29rbw+mKiclBdatszIsIYTFanKr9xzQCbiRP2esSgQmOzoop7A1u1x+oAuTJnn3Te5bb8GbZ6aGHzYMwsLg7betDEkIYbGapLxrgdFa6x+BYgCtdSrQ3BmBOdyhQwCk5zUkKgrq1KSHgYfp3bvUzIT16sGoUWYy8uPHLY1LCGGdmiT7fMrV8SulIoFMh0bkLLZB0NKyQ722jX1p77wDr79ue3PLLZCTI+PcC+HDapLsPwLeUUrFAyilmgEvA57RaycjA4C0P4K8stlleR9/bGtvD9CjB3TtWir7CyF8TU2S/QPAPiABCAd2A+nAbMeH5QRHjoC/P6mH/GnuGRVPtTJwIOzda4a2Rylzd//LL/Dbb1aHJoSwQE2SfRtgJ/AE8DDQR2t9l9baM9q1ZGRAZCSJiYpHHrE6GOcrMwommLFy6taFN96wLCYhhHWqTfbKeBNzR/8AMBSYAPymlHpLKaWcHKNjHDkCTZoQGQlRUVYH43ytWpnJWVavtq2IiIDrr4f33jP190IIn2LPnf1EoB9wgdY6VmvdR2vdEuiDGct+khPjc5yMDPbU78rMmZCcbHUwrjF4MGRnl5qO9uabTYucTz6xNC4hhOvZk+zHAndorTeWXml7fxeeMlzCkSP87n8ejz5q5vXwBc88A99/b6rsATMZeevW8qBWCB9kT7LvAFQ2VMK3tu3uLyODVD8ziL0vNL2EPzuOFRWVWnHzzfDtt7Ynt0IIX2FPsvfXWmdXtMG23v37oubmwokTpOpmBAb61lweTz0F7dpBcbFtxfjxZnC0ki62QghfYE+iDlBKXXZm3tnyC3YMpqaUilFKfaOU2qaUSlRK3Vn70GvgTBv7/Eiio0tVa/iA6GjTBLNkCsboaFOZ/9Zb3jtAkBDiL+wZNOAIUNVt4BE7zlEITNNa/6qUCgV+UUp9pbXeZk+QtWZL9odzw3ymCueMwYPNjfyyZdCrl23lrbfC8uWwdCmMHGlleEIIF6n2zl5rHae1jq9qseMc6VrrX22vs4HtuHJMHdtQCWvm72HNGpeV6hYiIqBfP5PsS1x1lWmbOX++RVEJIVzN5fXtSqk44Dzg5wq2TVRKbVJKbcqw3Y07hO1cqkkkISGOO62nuOYaM1nVzp22FX5+MHmyaaqTkGBlaEIIF3FpsldKhQCfAHdprU+U3661flVr3VNr3TMyMtJxBR85wknq88/ZsXz/veNO6ymuuQYefhhCQ0utvOkmCAqCBQusCksI4UIuS/ZKqQBMol+ktf7UVeUCkJFBSp143loUSJLnzJjrMC1awKxZ5ZqcNmpkhj5+910Z+lgIH+CSZG8bUuENYLvWep4ryizjyBFSw0x3AF8YBK0ieXnmmWxKSqmV//oXnDolc9QK4QNcdWd/IaanbX+l1GbbMshFZcORI6TVPwfwnQ5V5R06BMOHl8vrPXuaJjoLFpQaU0EI4Y1ckuy11uu11kpr3UVr3c22rHRF2YDpPVvXNBry1Tv72Fjo2xeWlJ994LbbzNPbb76xJC4hhGu4f+9XRzhyhNygCKKioH59q4OxzqhRsGULbCvdu2HkSNOl+KWXLItLCOF8vpHsMzKYNWD9mTnHfdaIEabV5QcflFoZFGSaYX72GezZY1lsQgjn8v5kf/q0eQjZpIlPDZNQkaZNTQerH34ot+G22yAgAF54wYqwhBAu4P3J/uhRAEYvvV5G9gU+/BC++qrcyqZNYfRoMzjaH39YEpcQwrm8P9lnZlKM4sNNrdi3z+pgrNeokRkIrmQUzDOmTjV/Bb36qiVxCSGcyyeS/RGaUFTs57PNLsv74AMzNE526YGru3SBAQPgxRdlNEwhvJBPJPtkYgBo2dLiWNxEbCwcPFjuQS3A3XdDWhp89JElcQkhnMcnkv1BYgFJ9mf07g0dO1YwO+FVV0H79jBvnnSyEsLL+ESy1yjatNbExlodjHtQCm65BX7+udygl35+pu7+119h7VrL4hNCOJ5PJPsRoWvYvUcREWF1MO5jzBjTxP7ll8ttGDsWmjWDJ56wJC4hhHP4RLKnYUOro3A7jRubRD9hQrkNQUFwzz1m+IQff7QkNiGE4/lEsr/u+Bs89JDVgbifm282Y6H9xcSJ5gtyzhyXxySEcA7vT/bHjvHtqZ5kZlodiHvaswduvx1yckqtDAmBu+6CFSvMYDpCCI/n9cn+VMZpMgvCpCVOJZKTTXXOe++V2zBlikn6cncvhFfw+mSfdDQYkGaXlenXD7p3hyefhIKCUhsiIsyYOR9+CLt3WxWeEMJBvDvZFxWRdCIcQJpdVkIpM2Xhvn3w9tvlNt59NwQGwmOPWRCZEMKRvDvZ//EHdcnlsnOSiY+3Ohj3NWSI6Wj1yCOQm1tqQ1SUmbrwvfdgxw7L4hNC1J53J/vMTPrxLV8//J3PzlBlD6VM1fw115i5asu47z6oV8/c/gshPJbXJ3vADPUoqnTZZWayqrCwchsiI03LnA8+kJY5Qngwr0/2g/mcMS+cb3UkHuOHHyqYoXDaNPMt8PDDlsQkhKg9r0/22+gAdQOtjsRjvPOOGR4nMbHUyogIk/CXLYNNm6wKTQhRC16d7IsyjpFCC1q2DrA6FI/xxBPQoIHpaFVm4Ms77zTVYQ8+aFlsQoiz59XJ/lBSPoUE0LJNXatD8RiNG8Pjj5uhcd5/v9SGBg1Mov/yS1izxrL4hBBnx6uTfVKymWE8Ns7HZxqvoYkT4YILzN39oUOlNtx2m5niavp0KCqyLD4hRM15dbIPOXWYcWHLaNfO6kg8i7+/qbu//37TGKdE3bowd64ZBP+ttyyLTwhRc0q76YxEPXv21Jtq+zDwssugsBC+/94xQfmoggIIOPPYQ2u46CLT5Xb3bjN+jhDCXVRajeHVd/anjuagI2Qs+9r44Qc45xzYvt22Qil49llTv/P005bGJoSwn1cn+6G7nmXAJhm1sTbi4uD0aRgxAk6dsq284AL4+99Nsk9KsjI8IYSdvDrZ7214Ps3Ob2F1GB6teXNYtAi2bTPPZ0tq/Z56yvycOtWy2IQQ9vPaZJ+XB8mHA2ndrYHVoXi8K66AmTNh4cJSvWtjY+Ghh+DTT2HVKkvjE0JUz2uT/YED5i60dWurI/EOM2eagdI2bix1dz9tGrRrZyY6KTPVlRDC3Xhtst+71/yUZO8Yfn6weLG5u1dnnvfXrQvz55uWOXPnWhqfEKJqLkn2Sqk3lVJHlFJbXVEemFqGGTPg3HNdVaL3Cwoyif7AAejfHw4eBC6/HEaONFNd7dljdYhCiEq4pJ29UuoS4CSwUGvdyZ5jHNLOXjhFQgJccgk0aQLr10NkQRq0b2/mN1y71vwZIISwgrXt7LXW3wHHXFHWGXv2QHa2K0v0HZ07w4oVZrLygQPhREg0PPMMrFsH//mP1eEJISrgVrdgSqmJSqlNSqlNGRkZtTrXVVfBhAkOCkz8xUUXwUcfwebN5sFt7phbYMAAuPdeW/2OEMKduFWy11q/qrXuqbXuGVlmUJaayc019cpSX+9cgwebScqzs+HUaQWvvWaa6kyYUG58ZCGE1dwq2TvKnj1QXIwMgOYCY8bAjz+aoe4LmsdR/ORT8NVXUp0jhJvxymS/Y4f5KcneNerUgfx8GD4c7to5GT3gCrj77lID6gghrOaqppeLgR+BdkqpFKXUzc4sb+dO87NtW2eWIkoLCDDVZi+9rJjV+ROoXx9uuMF0ZRZCWK6OKwrRWt/ginLOGD4coqNl9F1XOjMYZlYWPPJcKBG3rOOu1zuZzg7z5lkdnhA+zyXJ3tU6dTKLcC2l4NVX4cQJmPp6RyIGvMv458aajleDB1sdnhA+zevq7IuKzNhcZabTEy5Tp44ZJXPsWOj8yAjo1s08xT0zfoUQwhJel+z37YPrroOVK62OxHfVrWvG0Onepy588gnHaWB+KadPWx2aED7L65J9QoL52bmztXEI49FFrehRbxtHf0+FSZOk/b0QFvHKZK8UdOxodSQCzFj4Kcfqc23LX8h770N4/nmrQxLCJ3llsm/TBoKDrY5EgJnB8J13YH1SSya2XI2+exosW2Z1WEL4HK9M9lKF415GjoTZs2Fh0mU82eJlGD0aZERTIVzK65perlwJBQVWRyHK+7//M+OjxfcaDU8+DUOGwE8/mRnNhRBO55Lx7M+GjGfvxbZvJ69PP+pGNoDvvoNmzayOSAhvYe149kKU9tHW9pwbfJDUVMwT3MxMq0MSwutJshcud+65cDQ7iCHNfyVrd4aZfOD4cavDEsKrSbIXLte5s5n4JPFgKINabSd7815zh3/MpZOZCeFTJNkLS1x9NXzwAWzY3ZAh5+6mcPNW6NcPDh+2OjQhvJIke2GZa6+Fd9+FPkMaU+eLz8ysM5deaia3FUI4lCR7YakbboAnnwSuuIJfX1zP5uRGpifWb79ZHZoQXkWSvXALWsOtr3anV/73PHlyCoUX9YMvvrA6LCG8hiR74RaUMh3ihl/jx4wTM+jD//h26DNm4hM37QsihCeRZC/cRuPG8OGHsHgxpIe3p5/+hv9OWwkjRpgZUYQQZ02SvXArSsGoUbB7jx+vvarp/9RAWLaM/5zzNK89nCJD4gtxlmS4BOH+vv+eKwcU81X+pUTUy+HmyXWZ/C8/WrWyOjAh3I4MlyA82MUXsyapPd9d9ABX5CznuXnFtGmjmTvX6sCE8ByS7IVHUFFNuPi7x/lgYT4HQzvzf/5zuCTpPcjPZ+dOeOklOHXK6iiFcF+S7IXnUArGjqV54pfMHrKRPgvGQteuLH92N3fcAS1bmqGUjxyxOlAh3I8ke+F5YmJg6VL4/HPIz2f6a2354aL7uKTbcR5/3CT9u+6yOkgh3Iske+G5Bg+GxER4/HH6bnmFpd9EsGPIPYy/9niZpvm//25diEK4C0n2wrMFBcEDD8D+/XDvvbT97wL+81EjXsgYDb/+yo8/QrducOGF8OmnkJ9vdcBCWEOSvfAODRuaQXb27jV1OJ9/Dj160GXGYF6ckEBamua666BpU5g0CY4etTpgIVxL2tkL73T8OLz2Gjz/PKSmUti0BV9e/CiLcv/Gul8asHev+aNg0SLIyYHLLoNWrcwzYCE8WKX/giXZC+9WUGAG3XnjDTOwWnExhRdcRJ0R18J113HlhFi++srs2rAhdO9uxtqfNs2sy8uDunWtC1+IGpJkLwRpabBwoZk1ZfNmAHTP89l+wU18F3w1v2TG8suvfrRrZ8bnAdPwR2to185Mp9iuHfTtCz17WncZQlRBkr0QZezdC598Ah9/DJs2mYweHg6XX46+rD+qbx90p87MfbYO27fDzp2wY4epHZoyxXTiKigwfwm0agVt28I555ifnTtDo0ZWX6DwUZLshajU0aOwdi18+aVZUlLM+vr14fzzzWQq3bqhO3XmcFhbtH8dmjUzU+ZOmAC7dsHu3abKB2DuXLj3XkhPh9tvh6goM6JnZKT5eeGF5i+G/Hw4eRLCwsDf37rLF15Fkr0QdtEaDh6EH3/8c9m8GQoLzfbAQGjf3ty+t20LrVtDq1YUx7UiOTeS3XsUrVqZu/3ff4eRIyEjo+xc6osXm5E9v/kG+vc3D4XDwiAiwiwvvmi+ELZuNdM2RkSYPzrCwqBBA1ONFBEBp0+bL4zQUPmyECWsT/ZKqauBFwB/4HWt9ZNV7S/JXriN3FxTh5OQYJYtW0wmTk0tu19ICMTHQ7Nmf1kKI5vxR0ATjhZF0LRtAyKa1iUpybT9/+OPssujj8J555laptGj/9o34OefoVcv88z5llv+LLpBA6hXD9asMd9BH38Mr79u1tWrBwEBZnn6afNl8dVX5g+aM+vPLHfcYb7T9uwx8TRpYv46CQpyzcctasXaZK+U8gd2AVcAKcBG4Aat9bbKjpFkL9xeTg4cOGDq//ftM8v+/ab+Jj0dDh368y+C8urV+/NWPjzcLPXrQ3BwmUUH1ycnoAHHCeN4cSgnCurRsVUO9Rv4szUlnP/+Hsnx3EBO5ARyIieAnAJ/nn3gGFHN/Fi0ogEvvhVCTq4iJ1dRUKgoKFBs/j6byCaKR5+qy2NPB1JQAFr/mSNOZRcTXF9x512KF1/8M+QGDSA62nRa9vODjz4y1VdNm5olIsLs07Gj7TynoE4d8wXiJz16XMXyZN8HmKW1vsr2fgaA1npOZcdIshcer7gYMjP/TP7Hjv15+56VVfZ2/vhxUy9zZjl1ynyZuEgRfhQQQAEBhHASBeyhNTtUBw4TxWEVxWGiOKlDeKPOJADGFL7NIj26zHmiSSU10Ew0MLhgGSv1wJJtfhTRUW1jS+D5fx5QVceG6jo9nO2x7t6ZokkTcwNxdixP9tcDV2utb7G9Hwv01lpPKbffRGCi7W07YOdZFtkY8LU+kr54zeCb1+2L1wy+ed01veajWuurK9pQxzHxOIbW+lXg1dqeRym1SWvtUy2hffGawTev2xevGXzzuh15za6qSUsFYkq9b2FbJ4QQwgVclew3AucopeKVUoHAKGC5i8oWQgif55JqHK11oVJqCrAG0/TyTa11ohOLrHVVkAfyxWsG37xuX7xm8M3rdtg1u22nKiGEEI4jrV+FEMIHSLIXQggf4NHJXil1tVJqp1Jqj1Lq/gq211VKfWDb/rNSKs6CMB3Kjmu+Wym1TSm1RSm1VikVa0WcjlbddZfa7zqllFZKeXwTPXuuWSn1d9vvO1Ep9b6rY3Q0O/59t1RKfaOU+s32b3yQFXE6klLqTaXUEaXU1kq2K6XUi7bPZItSqvtZFaS19sgF86B3L9AKCAR+BzqU2+c24BXb61HAB1bH7YJrvgwItr2e7OnXbO912/YLBb4DfgJ6Wh23C37X5wC/ARG2902sjtsF1/wqMNn2ugNwwOq4HXDdlwDdga2VbB8ErML0jr0A+PlsyvHkO/tewB6t9T6tdT6wBBhebp/hwDu21x8Dlyvl7n2lq1TtNWutv9Fan7a9/QnTp8HT2fO7BngUmAvkujI4J7HnmicA87XWfwBorY+4OEZHs+eaNdDA9joMSHNhfE6htf4OOFbFLsOBhdr4CQhXSjWraTmenOybA8ml3qfY1lW4j9a6EDgOePK0EvZcc2k3Y+4IPF2112370zZGa/2FKwNzInt+122BtkqpH5RSP9lGlvVk9lzzLGCMUioFWAnc7prQLFXT//cVcqvhEoTjKKXGAD2BS62OxdmUUn7APOAfFofianUwVTn9MH/BfaeU6qy1zrIyKCe7AXhba/2sbYDFd5VSnbTWxVYH5u48+c7eniEYSvZRStXB/NmX6ZLonMOuYSeUUgOAB4FhWus8F8XmTNVddyjQCVinlDqAqddc7uEPae35XacAy7XWBVrr/ZhhxM9xUXzOYM813wx8CKC1/hEIwgwW5s0cMtyMJyd7e4ZgWA6Mt72+Hvha2554eKhqr1kpdR7wH0yi9/Q63DOqvG6t9XGtdWOtdZzWOg7zrGKY1tqTx8i259/3MsxdPUqpxphqnX0ujNHR7LnmJOByAKVUe0yyz3BplK63HBhna5VzAXBca51e05N4bDWOrmQIBqXUI8AmrfVy4A3Mn3l7MA9ARlkXce3Zec1PAyHAR7Zn0Ula62GWBe0Adl63V7HzmtcAVyqltgFFwHSttcf+5WrnNU8DXlNKTcU8rP2Hh9/AoZRajPnSbmx7FvEwEACgtX4F82xiELAHOA3cdFblePjnJIQQwg6eXI0jhBDCTpLshRDCB0iyF0IIHyDJXgghfIAkeyGE8AGS7IUQwgdIshfCTkqp82zj0JxWSm1QSrW0OiYh7CXJXgg7KKVaYDq3zMUMprcPeMjSoISoAUn2QtjnWeA1rfVyrXUOZvjd8y2OSQi7eexwCUK4ilKqAWZM8balVvvhHePmCx8hyV6I6l2OGatkS6m5b+oCn1kWkRA1JNU4QlQvDjOUcPiZBfgGWG1pVELUgCR7IapXFzPaIABKqXjMxDBeN9qm8F6S7IWo3kbgUqVUtFIqBngfeFBrXdW8oUK4FamzF6J6XwOfY2aCygTmaq1fszYkIWpGxrMXQggfINU4QgjhAyTZCyGED5BkL4QQPkCSvRBC+ABJ9kII4QMk2QshhA+QZC+EED5Akr0QQviA/wdJJRXtUOGGRgAAAABJRU5ErkJggg==\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -664,14 +676,14 @@
     "q_learned_samples = q_learned.sample(1000, seed=key)  # q(z|D)\n",
     "transformed_samples = transform_fn(q_learned_samples)  # transform Normal samples into Beta samples\n",
     "\n",
-    "theta_range = jnp.linspace(0.01, 0.99, 100)\n",
+    "theta_range = jnp.linspace(0.01, 0.99, 1000)\n",
     "plt.figure()\n",
     "plt.plot(theta_range, exact_posterior.prob(theta_range), \"r\", label=\"$p(x)$: true posterior\")\n",
     "sns.kdeplot(\n",
     "    transformed_samples,\n",
     "    color=\"blue\",\n",
     "    label=\"$q(x)$: variational posterior\",\n",
-    "    bw_adjust=1.5,\n",
+    "    bw_adjust=1,\n",
     "    clip=(0.0, 1.0),\n",
     "    linestyle=\"--\",\n",
     ")\n",
@@ -695,7 +707,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 60,
+   "execution_count": 33,
    "id": "FaU7odF-9TFn",
    "metadata": {
     "colab": {
@@ -755,7 +767,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 61,
+   "execution_count": 34,
    "id": "MDigrSzC8GE7",
    "metadata": {
     "colab": {
@@ -782,11 +794,11 @@
     {
      "data": {
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+       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">-1.9149526</span>\n",
        "</pre>\n"
       ],
       "text/plain": [
-       "\u001b[1;36m-1.9198773\u001b[0m\n"
+       "\u001b[1;36m-1.9149526\u001b[0m\n"
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@@ -795,11 +807,11 @@
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      "data": {
       "text/html": [
-       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.8108946</span>\n",
+       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0.8041958</span>\n",
        "</pre>\n"
       ],
       "text/plain": [
-       "\u001b[1;36m0.8108946\u001b[0m\n"
+       "\u001b[1;36m0.8041958\u001b[0m\n"
       ]
      },
      "metadata": {},
@@ -814,7 +826,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 62,
+   "execution_count": 35,
    "id": "Ou1lgfiH531a",
    "metadata": {
     "colab": {
@@ -827,7 +839,7 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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",
+      "image/png": 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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -839,7 +851,7 @@
     },
     {
      "data": {
-      "image/png": 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",
+      "image/png": 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\n",
       "text/plain": [
        "<Figure size 432x288 with 1 Axes>"
       ]
@@ -873,326 +885,6 @@
     "plt.show()"
    ]
   },
-  {
-   "cell_type": "markdown",
-   "id": "f5db58f0",
-   "metadata": {
-    "id": "f5db58f0"
-   },
-   "source": [
-    "\n",
-    "## Comparison with pymc.ADVI() \n",
-    "\n",
-    "Now, we compare our implementation with pymc's ADVI implementation. \n",
-    "\n",
-    "\n",
-    "**Note**: For pymc implementation, the code is taken from this notebook: https://github.com/probml/probml-notebooks/blob/main/notebooks/beta_binom_approx_post_pymc.ipynb"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 63,
-   "id": "c3ab49e8",
-   "metadata": {
-    "id": "c3ab49e8"
-   },
-   "outputs": [],
-   "source": [
-    "try:\n",
-    "    import pymc3 as pm\n",
-    "except ModuleNotFoundError:\n",
-    "    %pip install -qq pymc3\n",
-    "    import pymc3 as pm\n",
-    "try:\n",
-    "    import scipy.stats as stats\n",
-    "except ModuleNotFoundError:\n",
-    "    %pip install -qq scipy\n",
-    "    import scipy.stats as stats\n",
-    "\n",
-    "import scipy.special as sp\n",
-    "\n",
-    "try:\n",
-    "    import arviz as az\n",
-    "except ModuleNotFoundError:\n",
-    "    %pip install -qq arviz\n",
-    "    import arviz as az\n",
-    "\n",
-    "import math"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 64,
-   "id": "2d7794f3",
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/",
-     "height": 37
-    },
-    "id": "2d7794f3",
-    "outputId": "a8cd71c2-f09b-4c38-c4bd-05faf33f9117"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "\n",
-       "<style>\n",
-       "    /* Turns off some styling */\n",
-       "    progress {\n",
-       "        /* gets rid of default border in Firefox and Opera. */\n",
-       "        border: none;\n",
-       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
-       "        background-size: auto;\n",
-       "    }\n",
-       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
-       "        background: #F44336;\n",
-       "    }\n",
-       "</style>\n"
-      ],
-      "text/plain": [
-       "<IPython.core.display.HTML object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "text/html": [
-       "\n",
-       "    <div>\n",
-       "      <progress value='20000' class='' max='20000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
-       "      100.00% [20000/20000 00:01<00:00 Average Loss = 4.9174]\n",
-       "    </div>\n",
-       "    "
-      ],
-      "text/plain": [
-       "<IPython.core.display.HTML object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "a = prior_dist().concentration1\n",
-    "b = prior_dist().concentration0\n",
-    "\n",
-    "\n",
-    "with pm.Model() as mf_model:\n",
-    "    theta = pm.Beta(\"theta\", a, b)\n",
-    "    y = pm.Binomial(\"y\", n=1, p=theta, observed=dataset)  # Bernoulli\n",
-    "    advi = pm.ADVI()\n",
-    "    tracker = pm.callbacks.Tracker(\n",
-    "        mean=advi.approx.mean.eval,  # callable that returns mean\n",
-    "        std=advi.approx.std.eval,  # callable that returns std\n",
-    "    )\n",
-    "    approx = advi.fit(callbacks=[tracker], n=20000)\n",
-    "\n",
-    "trace_approx = approx.sample(1000)\n",
-    "thetas = trace_approx[\"theta\"]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 65,
-   "id": "4W8e7Dp9N1As",
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/",
-     "height": 282
-    },
-    "id": "4W8e7Dp9N1As",
-    "outputId": "7c84681f-bc08-4f04-a2e2-53b4230a3a57"
-   },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plt.plot(advi.hist, label=\"ELBO\")\n",
-    "plt.xlabel(\"Iterations\")\n",
-    "plt.ylabel(\"ELBO\")\n",
-    "plt.legend()\n",
-    "sns.despine()\n",
-    "plt.savefig(\"advi_beta_binom_pymc_loss.pdf\")\n",
-    "plt.show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 66,
-   "id": "w4ZWgVXua04j",
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/",
-     "height": 65
-    },
-    "id": "w4ZWgVXua04j",
-    "outputId": "806caad6-d32f-47b0-c50a-838fac7a641d"
-   },
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">ELBO comparison for last <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1</span>% iterations:\n",
-       "JAX ELBO: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">4.899871826171875</span>\n",
-       "Pymc ELBO: <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">4.941951796589394</span>\n",
-       "</pre>\n"
-      ],
-      "text/plain": [
-       "ELBO comparison for last \u001b[1;36m1\u001b[0m% iterations:\n",
-       "JAX ELBO: \u001b[1;36m4.899871826171875\u001b[0m\n",
-       "Pymc ELBO: \u001b[1;36m4.941951796589394\u001b[0m\n"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "print(f\"ELBO comparison for last 1% iterations:\\nJAX ELBO: {elbo[-10:].mean()}\\nPymc ELBO: {advi.hist[-100:].mean()}\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "53f16a33",
-   "metadata": {
-    "id": "53f16a33"
-   },
-   "source": [
-    "## True posterior, JAX q(x), and pymc q(x) "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 67,
-   "id": "f46083ff",
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/",
-     "height": 282
-    },
-    "id": "f46083ff",
-    "outputId": "b1ae81e7-23c2-4540-e324-479cf7dac55a"
-   },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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hRL1Wq//MK6XslVJblVJLavO4VbFxIwQHQ5MmsPHPfRTbO3BN94jL3u9tXULJzC9m+c5kYziziwsvtfyc116rhtBCCCFsVm23p/4NJNTyMaskM9NYSADgt5QiTCVFdG7pf/EvVUL3Fr6E+rgwb/MR8PSEmBiYNw9dVMyhQ5e9eyFEHfX000/zzjvvVGrbrl27snPnzkrvOyQkpP2CBQs8Kt7SNoWHh7ddsmRJnc1fptYKrVKqCTAE+KS2jnkpFi2C774DiopYZwqiq8rE2aHKq0Cdw85OMbxjCOv3pWLOKjDW3jOb+fzu1URFyT21QjREZrOZL774grFjx1Zq+yeeeIIpU6bUcKrqUR1FPjExcefQoUOzqiuTtdRmi/Yd4EnggsufK6UeUEptVkptNpvNtRbsbHZ2YN68nUTfUHo2ufgCAlUxtEMwFg3L/joOgwaBhwfXZ3xLTg4sWFBthxFC1BGfffYZgwcPxsWlcoMtY2JiWL16NcnJyTWc7OKKioqsevy6plYKrVJqKJCitb7oWola64+01l201l38/S+/u7aq3nzTqH8lJbD5j10AdL3y8q/PlokI8qBVgDuLdxwHkwmGDydw/U+0DC3kyy+r7TBCCBtisViYNm0aAQEB+Pv7M2vWLJycnDCbzSxdupTevXufsf2TTz7J8OHDy19PmjSJ6667jsLCQkwmE507d2b58uWXlOXAgQOOAwcObNmoUaPokJCQ9q+88kpA2WfPPPNMUGhoaDs3N7dOLVu2bPvFF194n/7dkJCQ9pMnTw5q3bp1lJub2xWBgYEdpkyZEti6desoDw+PjkOGDGmRm5urAIYPH978+PHjTiNHjmzl6ura6dlnnw28lLynt4ovlG/nzp3OXl5eHdetW+dado6NGjWKtqUuZ4daOs5VQIxSajBgAjyVUl9pre+speNXyurVcKR0XolNh05hcnCnXZfqXeJqSIfGzFi1lxOZ+QSOHIn68kum9F/BPT8O5fhxaNy4Wg8nRMPz2GOwbVvNHqNjR6jkddWXXnqJlStXsmPHDlxcXBg4cCA+Pj74+/sTHx9PRMSZv8w/9dRTtGjRgq1bt7Jx40aWLVvGunXrcHJyAiAyMpLt27eXb//ggw8CMGvWrIvmKCkpYciQIeGDBg3KWLhwYVJSUpLjgAEDIiIjI/NHjBiRGR4eXvDbb7/tDg0NLZozZ06jsWPHNu/du/dfzZo1K2++/vjjjz6xsbF7g4KCiiMiItrNnz/fZ8WKFXtdXFwsPXr0aDNz5ky/J5980rxgwYL9ISEh7u+///6B4cOHV0vX74XytW3btmDKlClHxowZ03zbtm0Jd955Z9gtt9ySZktdzrXSotVaP621bqK1DgNGAr/aWpEFSEiAtm2N55sKTXTMPYGT4+Vfnz3d0A7BaA2x8cehXz/w8SEm71ssFlmnVoj6xmw289ZbbzF37lyCgoLw8vJiyJAhtG/fHjCW0fPwOLPh5evry+OPP86YMWOYNm0asbGxeHn9s2qYh4cHGRkZ5a9nzZpVYZEFiIuLczt58qTD9OnTj5tMJh0VFVU4evRo8zfffOMDcO+996aHhYUV2dvbc//996c3a9as4LfffnM7fR/jxo07ER4eXuTu7q4Bxo8ffyIsLKwoMDCwZMCAAae2bdt26RMOVOBi+SZOnJjarFmzgs6dO7dJSUlxnDFjxtGaynEpaqtFa/Py8+HAARg9GrJz8tnpHshDuvqHA4cHuNMmyIMlO45zz1XN4aab8P72W37+IY/e19fY31EhGo5KtjRrw6pVq4iMjDxjTdq0tLTyQtuoUSOyss5teHXq1IkXX3yRuXPnEhoaesZnWVlZeHt7VzlLUlKSk9lsdvLw8OhY9p7FYlFdunTJApg5c6bvzJkzA48ePeoEkJeXZ282m8+oEae3bgGCg4PLX7u6ulqOHz/uWNk8H3zwgc/EiRObAXTp0iV77dq1ey+2fUX57rvvPvMdd9wRPn369IMuLi66sjlqQ61Pl6C1XqO1Hlrbx61IYiJYLBARAds37MRiZ0+XFn41cqxh0cFsOZjO0Yw8GDkSsrMZTCxubhV/VwhRd6SmpnL6eJPi4mIWLVpEu3btAOjQoQN79uw54zvx8fGMHz+eMWPGMGfOnHP2mZCQQHR0dJWzhIWFFYaEhBRkZWVtK3vk5ORsjYuLS9yzZ4/ThAkTms2YMeNQenr6tqysrG3h4eF5Wp9Zr5RS1VbAxo8ffzI3N3drbm7u1oqKbEX5Tp06ZffUU0+F3nrrramvv/568IkTJ6q3K/IyybxEpUpKYMAAaN8etu3YD0DHrpE1cqwh7Y0Lscv/SobevSEgAP3Nt7z2Gnz7bY0cUghhBW3atGH9+vXs37+f9PR0xo8fz/79+8tbtIMHDyYuLq58+6NHjzJs2DBmz57NrFmziI+PZ82aNeWf5+fns2XLFvr371/lLH369Mlxc3MrmTx5clB2drYqLi5m06ZNpri4ONesrCw7pRRBQUFFADNmzPBNTEy8rC42Pz+/osTExKoveXYeFeW7//77Qzt06JD73XffHbzuuutO3XPPPc2q47jVRQptqehoWL4c2rWDbcezaXHyKF4domrkWGF+bkQEerBiVzI4OMAtt6B+XsLir7NsqddLCHGZ+vXrxy233EJ0dDTdunWjffv22NnZ0bZ0MMhdd91FbGwseXl5ZGZmMnjwYCZMmEBMTAyurq5MmjSJyZMnl+9v8eLF9OnTh+Dg4PL3xo0bx7hx4yrM4uDgQGxsbOKOHTtcwsLCOvj4+HS87777wtLT0+07d+6c/8ADD5zo1atXpL+/f3R8fLxLp06dsi/n3CdNmpT85ptvNvbw8Og4ZcqUSxp1XOZi+b766ivvNWvWeM2ZM+cgwOzZsw//9ddfrh988IHP5RyzOqmzuwZsRZcuXfTmzZtr7XgWi3H/rNaark/M42rzXt7+YnLFX7xEb67YzfurE9nybH8a/bkRevVi4W1fM/y729m/H067pCOEuIiEhAQiI2um96m6rVixgoceeoi9e//pKX3mmWcICAjgscceq/D73bp149NPPy3vej6Pi95CWdc0bty4/Zw5c/YPGjTosop+bdi+fbtfdHR02Pk+kxZtqWuugTFjIDkzH7OjGx1dS2r0eAOigrBoWPV3Clx1FQQFcV2msQjuvHk1emghhJUkJCSUdxuXmTp1aqWKLMDGjRsvVmTrlWPHjjmkp6c7hoeHF1o7y+WSQgtoDX/9BR4esP3vYwBEh3rX6DHbhXjS2MvEip3JRlN6+HDc42K56oo8YwpIIUS9k5CQ0GAK5eWIi4tzjYiIaHf33XentGrVqs4XWrm9B0hONhYTiIiA7X8dwLGkiMh2zWv0mEopBkQF8t3mw+QVluBy000wezZPdVrB+0duID/fmDxKCFF/zJ4929oR6oTevXvnZmVlbbN2juoiLVpg927jZ0QE7DqaQXjqYZzbt63x4w5oG0R+kYXf9pqhTx/w9mZY0U8sWyZFVggh6gsptPxTaNu0gYQcRVTaoVoZjdS1uQ+eJgdW7DoBjo7G0nmLF0NREWlpNX54IYQQtUAKLdCqFdx/Pzh7FZCinImyzzOum9YwR3s7rosMZFXCCYpLLHDTTZCezspn4wgIgIMHazyCEEKIGiaFFujbFz76CHafyAQg0rf2+m0HRAWSnlvE5oPpxowZrq5ceeQnLBb46adaiyGEEKKGSKEFjh0z7qNN2J8CQFSLy7q3ukp6tfbHycGOFTtPgIsLDB6M96/ziW5v4ccfay2GEEKIGtLgC21+PoSGwiuvwK69xwg5lYJ3++pdGu9i3JwduCbcjxW7ktFaG93Hycn8u9sG1q+H48drLYoQQoga0OALbdliAq1awa6UHCJT9kNUzUy9eCED2gZyJD2PXcczYcgQcHIipvgntIb582s1ihBCiGrW4Att2YjjsJYlJBXYE3XyMDSv2Xtoz9a3TSBKwS+7UsDTE/r1wzfuJ+Z8qhk+vFajCCGEqGYNvtD+/bfxU3lnUaLsiDIV1cqI49P5ezjTKdSbXxJOGG/ceCPs3889XeI5be5wIYQQdVCDL7S7d0OTJnAgo3TEcaCHVXL0jwoi/ugpjp/Kg6HGcr0lCxbx2WewcqVVIgkhasHTTz/NO5Vctqtr167s3Lmz0vsOCQlpv2DBAuv8oybKNfhCe/vtMHUq7DqQintBLqER1lnGsH9UAAC/JKRAUBB064bdkkW8+CKydJ4Q9ZTZbOaLL75g7Nixldr+iSeeYMqUKTWcqnpIkf9Hgy+0gwbB6NGQcDCVyJT92EXW3ojj07X0d6e5nxsrd5V2H8fEoDZt4u4Bx/jlF2MuZiFE/fLZZ58xePBgXFwqt8Z6TEwMq1evJjk5uYaTXVxRUZFVj1/XNOhCW1wMGzbAyXRNQnqhMeK4dWurZFFK0S8ygD/2pZKVX2RMxwiM8lpCYSHExlollhDiMlksFqZNm0ZAQAD+/v7MmjULJycnzGYzS5cupXfv3mds/+STTzL8tFGQkyZN4rrrrqOwsBCTyUTnzp1Zvnz5JWU5cOCA48CBA1s2atQoOiQkpP0rr7wSUPbZM888ExQaGtrOzc2tU8uWLdt+8cUX3qd/NyQkpP3kyZODWrduHeXm5nZFYGBghylTpgS2bt06ysPDo+OQIUNa5ObmKoDhw4c3P378uNPIkSNbubq6dnr22WcvaXKCkJCQ9k8//XRQy5Yt23p6ena8+eabw3Jzc9Vzzz0XOHDgwJanb3v33XeH3nPPPaFl33vuuecCW7duHeXi4tLp1ltvbXb48GGHXr16tXJzc+vUs2fP1maz2b7su4mJiY4DBgxo2ahRo2hvb++Od911V9NLyXshDXr1niNHoEcPmP5BHtkWRUTqQWjZsuIv1pD+UUF8/Nt+1u5JZUj7ttC8OeE7FxEY+ADz58PIkVaLJkSd8eLinew6VrNdQFHBnjw/rHILj7z00kusXLmSHTt24OLiwsCBA/Hx8cHf35/4+HgiIiLO2P6pp56iRYsWbN26lY0bN7Js2TLWrVuHk5MTAJGRkWzfvr18+wcffBCAWbNmXTRHSUkJQ4YMCR80aFDGwoULk5KSkhwHDBgQERkZmT9ixIjM8PDwgt9++213aGho0Zw5cxqNHTu2ee/evf9q1qxZefP1xx9/9ImNjd0bFBRUHBER0W7+/Pk+K1as2Ovi4mLp0aNHm5kzZ/o9+eST5gULFuwPCQlxf//99w8MHz48q3L/Vc/vhx9+8F2+fPkeDw8Py6BBg1r95z//aTxx4kTz9OnTg1NTU+39/PxKioqKWLRokc/ChQv3ln1v0aJFjVatWrWnuLhYde7cOWrgwIGuH3/88YFOnTrl9+3bt9Vrr70W8Oabbx4vLi5myJAhra6++uqsH374Id7BwUH/9ttvbpeT+WwNukV7+LDxU3llA9DasRCcna2W54qm3jRydTRGHytldB+v+oVbBudw7Jixbq4Qou4wm8289dZbzJ07l6CgILy8vBgyZEj54u8ZGRl4eJx5GdPX15fHH3+cMWPGMG3aNGJjY/Hy8ir/3MPDg4yMjPLXs2bNqrDIAsTFxbmdPHnSYfr06cdNJpOOiooqHD16tPmbb77xAbj33nvTw8LCiuzt7bn//vvTmzVrVnB2wRk3btyJ8PDwInd3dw0wfvz4E2FhYUWBgYElAwYMOLVt27bK9YFXwf33358SHh5eFBgYWPLUU08dnz9/vk+zZs2KrrzyyuzPP/+8EcAPP/zg1ahRo+Jrrrkm97SsKaGhocXNmzcvuvLKK7M7deqUc9VVV+W5urrqYcOGZWzfvt0VYM2aNW4pKSmOs2fPPuzp6WlxdXXVAwcOzK7Oc2jQLdpDh4yfuY7GL1yt/FytmAYc7O3o2yaQXxJOUFRiwTEmBmbM4O3BK3G4ebhVswlRV1S2pVkbVq1aRWRkJGGnrQaWlpZWXmgbNWpEVta5Db5OnTrx4osvMnfuXEJDQ8/4LCsrC29v7ypnSUpKcjKbzU4eHh4dy96zWCyqS5cuWQAzZ870nTlzZuDRo0edAPLy8uzNZvMZNeL01i1AcHBw+WtXV1fL8ePHHSub54MPPvCZOHFiM4AuXbpkr127du/5tmvatGn5wu8tW7YsMJvNTgB33nln6scffxwwceLE1Llz5/reeuutZ6x51rhx4/JsJpPJEhgYWFz22sXFxZKbm2sPcODAAaeQkJBCR8dKR68yadECaUXZ+Oek493SOiOOT9c/KoBTeUVsPpAO11wDXl44xC4CjBmshBB1R2pqKv7+/uWvi4uLWbRoEe3atQOgQ4cO7Nmz54zvxMfHM378eMaMGcOcOXPO2WdCQgLR0dFVzhIWFlYYEhJSkJWVta3skZOTszUuLi5xz549ThMmTGg2Y8aMQ+np6duysrK2hYeH5+mzutGUUtXWrzZ+/PiTubm5W3Nzc7deqMgCHDp0yKnseVJSkpO/v38hwJ133pmxe/dul02bNpl+/fVXr3vvvffkpeQICwsrPHbsmFNNDvBq0IX20CHw8YH9J9JpZT5ktYFQp7umlbHIwMqyNWoHD4YlS5g5o4QWLYwBXEKIuqFNmzasX7+e/fv3k56ezvjx49m/f395i3bw4MHExcWVb3/06FGGDRvG7NmzmTVrFvHx8axZs6b88/z8fLZs2UL//v2rnKVPnz45bm5uJZMnTw7Kzs5WxcXFbNq0yRQXF+ealZVlp5QiKCioCGDGjBm+iYmJl9UN7OfnV5SYmHjZ1+I++eQT/3379jmeOHHC/vXXX298ww03pAO4urrqwYMHp99xxx0tOnTokNOqVavCivZ1Pn369Mnx9/cveuihh5pkZmba5ebmqhUrVsg12uoybhzMmaNJTM2hVdohY8JjK3NzduCqlr6sTChdZCAmBsxm2uVs5OBBWLvW2gmFEJXVr18/brnlFqKjo+nWrRvt27fHzs6Otm2N7u277rqL2NhY8vLyyMzMZPDgwUyYMIGYmBhcXV2ZNGkSkydPLt/f4sWL6dOnD8GnTRk3btw4xo0bV2EWBwcHYmNjE3fs2OESFhbWwcfHp+N9990Xlp6ebt+5c+f8Bx544ESvXr0i/f39o+Pj4106dep0WdcpJ02alPzmm2829vDw6DhlypRLXhJtxIgRJwcMGNA6PDy8fbNmzQqmTZtWvtTKPffck7Z3716X22+/Pe1i+7gYBwcHlixZkpiUlOTctGnTDiEhIR2+/vprn0vd3/mos7sGbEWXLl305s2ba/w4x0/l0WPar7y8/H1G/zgTWrSo8WNW5OuNh3hmfjzLH+tFhKkE/P0pfHQi3h+8xr/+Be+9Z+2EQtiOhIQEIiMjrR2jUlasWMFDDz3E3r3/9JQ+88wzBAQE8Nhjj1X4/W7duvHpp5+Wdz2fx5ZqCWojQkJC2l9s5PLevXudOnTo0Pbo0aPbfXx8rHpxbfv27X7R0dFh5/usQQ+G+uknKPYzfmlrdeo4NLP+NVqA6yIDYD78knCCiGvDoXdvnJYuYsCA11iwAN591xiULISoWxISEsq7jctMnTq10t/fuHFjdUeqs0pKSpg2bVrg0KFD061dZCvSYLuOs7JgxAhYuKZ0xLGnA9jbV/Ct2hHoaSI61JsVp80SRUICd/XYy5EjsKVe/c4qRMORkJBwsdaoqKTMzEw7Dw+PTmvXrvWcNm3aUWvnqUiDbdGWjTguNGXjk56NbzPbWianf2QA01fsISUzn4Bhw+Df/+b6osU888wEThvEKISoQ2bPnm3tCHXK0aNH48/3vqenpyU3N3drbee5VA22RVt2D22GziLcfNAmRhyfrn9UEFC6yEDz5tC+Pa6/LOLVV22mh1sIIUQlNNhCa7RoNcnZmbSywULbOtCdUB+Xf9aoHTYMfvuNwuSTLFv2T4tcCCGEbWuwhfbQIXDwKCCryEKrVNu4h/Z0Sin6RwaxLjGVnIJio9BaLGTNW8agQfDVV9ZOKIQQojIabKF98EF474vSOY5TbeMe2rP1iwqgsNjCb3tToWtXCAjAd/1iunaF+fOtnU4I22GrtymKhsFisSig5EKfN9hC27gxOPsbI47D81KNN2zMlWE+eLk4GrNE2dnBkCGwdCkjYorYtEm6j4UAMJlMpKWlSbEVtU5rTUFBgePBgwe9gXUX2q7Bjjr+5BPYUJyNZ0kB/sH+NnljqqO9HddG+PPr3ycosWjshw6F//6XkU3W8RTXsmABPPKItVMKYV1NmjThyJEjmM1ma0exusLCQj9rZ2hgLEqpUyUlJe9aLJYPLrRRrRRapZQJWAs4lx7zB63187Vx7POxWOChhyD6sRxanEpGWXEN2or0jwpiwbZjbDmYTtcBA8DJiaY7lhAVdS1r1kihFcLR0ZHmzZtbO4atCLN2AHGu2uo6LgD6aq2jgY7A9Uqp7rV07HOYzVBYCLn22bRITrLqYu8V6dXaD0d7ZYw+dneHa6+FxYtZvhzmzbN2OiGEEBWplUKrDWUTVDuWPqx2QeXQIVCOxWRbCmiRetimC62HyZEeLf1YueuEcQ1q2DDYu5cmObuxa7BX2IUQou6otX+qlVL2SqltQAqwUmt9zqSdSqkHlFKblVKba/J6y+HD4NAoB4AWJ4/adKEFY5ao/ak57DPnwNChxpuLF/Pqq3D//dbNJoQQ4uJqrdBqrUu01h2BJkBXpdQ5E35qrT/SWnfRWnfxr8F5Bg8dAkdfo9A2rwOFtl+UscLUyl0njGmh2reHJUtIS4MvvjDmbRZCCGGbar3zUWudAawGrq/tY5cZNw4mPl9aaLNSIDTUWlEqpbGXC+1CPM+cJWrdOm7pl05hIcTGWjefEEKIC6uVQquU8ldKeZc+dwH6A3/XxrHPx2SCUzqbkOJsTE2CwcH273LqHxnEn4fSMWcVGIW2pIRuJ5cSEGAs9yeEEMI21VaLtjGwWim1A9iEcY12SS0d+xzvvAN/7jVu7bH1buMy/aIC0BpW/51izBLl74/dz4sZPtxo0ebnWzuhEEKI86mVppzWegfQqTaOVRlvv61xuC2Ha4/b9q09p4tq7EmItwsrdp3g1itDjVmiFixg1Lwiiosdycw0WupCCCFsS4O7QURrMGcVUGJXTIs6VGiVUvSLDGBdopm8whKj+zgjg94Ov/PppxAQYO2EQgghzqfShVYpdYNSyvYvZlYgMxMs7nXn1p7T9Y8KIr/Iwtq9ZiidJYrFi9Eatm2DoiJrJxRCCHG2qrRoXwKOK6VmKqW61VSgmpaSAo4+defWntN1a+GDt6sjS+OPnzFL1LJl0KkTrFlj7YRCCCHOVulCWzp9Yj8gD/hRKbVbKfWsUiqspsLVBLMZHHyycdQWQjLN0KKFtSNVmqO9HQOjgvglIYWC4hJj8oq9e7k2ZA9ubvDDD9ZOKIQQ4mxVukartd6utZ4EhAIPAbcA+5RSa5VSdyilbP6ab8+ecMOdOTQvzsKucRC4ulo7UpUMah9EdkEx6/amGtdpAdPKxQwZYqxRW3LBFRGFEEJYQ5ULo1KqJTAF+AAwlT7/GHgYqBNtqkMnc2iZWXdu7Tldz5Z+eJociI1P/meWqMWLGTHCaK3/9pu1EwohhDhdVQZDPaSU2gD8DwgERmutI7TWr2qtvwSuAwbUUM5q8933Fvabc2l+bF+dLLRODnb0jwpi5a5kCost5bNEDe6RjslktGqFEELYjqq0aAcBbwLBWusHtdYbTv9Qa50L3FSd4WrCkjW5aKVpcejvOlloAQa3DyIzv5j1+1LLZ4lyX7eMVatg6lRrpxNCCHG6qhTaNVrreVrrgtPfVEpNKHuutV5RbclqyNHMshHHx+psob26lR8ezg4sjU+GK68Ef39YvJiePcHNzdrphBBCnK4qhXbKBd5/tjqC1JbUAqPQtjx5pM4WWmcHe/pFBbJ8VzJFKGOWqKVLoaiIN9+Ed9+1dkIhhBBlKiy0Sqm+Sqm+gINS6tqy16WP+4A6tUhblsrGtbAE7/zsOltoAQa1CyIjt4gNSWnls0Tx+++sWQPTpxszYAkhhLC+ysz09GnpT2dgzmnvayAZeKS6Q9Uk7Z5DSE4meHqCr6+141yyXq39cXOyJzY+mWv69y+fJerWW/uwZAls3Ajdu1s7pRBCiApbtFrr5lrr5sDcsueljxZa655a60W1kLPa+LfMIVqX3tqjlLXjXDKToz19IwNZsTOZYlc36NMHliwhJsaoud9/b+2EQgghoGozQ91Vk0FqQ1Z+EeasAlrU0Vt7zja4XRBpOYX878BJo/t4zx68Tuxh4ECYNw8sFmsnFEIIcdFCq5RKOO35YaXUofM9aj5m9Vj1P2MgVNi+nfWi0PaJCMDF0d4YfVw6SxSLF3PHHdChA6SnWzefEEKIiq/R3n/a8ztrMkht2LLHKLThqQeh5Wgrp7l8Lk729G0TwLKdybwQ0xb70lmiblszkdtus3Y6IYQQUEGh1VqvO+15XM3HqVn7U3NAQ9P04/WiRQvG3Mc/xx9n04GTdB86FP7v/4ymbKNGHDsGQUFgZ/MzUAshRP1VlSkYJyilOpY+717abbxfKdWjxtJVs2NZObicKsZUUlRvCm3fNkb38eLtx8pniWLZMpYtg5AQ2LCh4n0IIYSoOVVp6zwO7C99Pg14C3gFeKeaM9WY1MJsAjMywdERmjSxdpxq4erkQP+oQGLjj1PUucsZs0Q5O8N331k7oRBCNGxVKbReWutTSikPIBp4T2v9KRBRM9Gql9aaHLscWuUkQ/PmYG9v7UjVJiY6mPTcItYlpZfPEuXpUsTgwcZtPrJ0nhBCWE9VCu1hpVRPYCSwVmtdopTyBOrEP+MnMgsoUSX0Uon1ptu4TK/W/ni5OLKorPs4IwPWr+f22yE5GeLq/NV1IYSou6pSaCdhrDc7GXi59L2hGMvm2byk1GwAmifG17tC6+Rgx+D2QSzfmUxen77ls0QNHQru7vDNN9ZOKIQQDVdVJqyI1VoHa63DtNZbSt+eB8TUTLTqlWQ2bu1pcWQvhIdbOU31i4kOIbewhFVHco1ZohYvxsUFfvgBXn65wq8LIYSoIVW68UMp5aWU6nraQgPXlD5s3t7kHCiCoKy0eteiBeja3IdAT2cWbjtWPksUe4xZooKCrJ1OCCEarqrc3nM3cAxYjLHQQNnjkxpJVs12H8vGNb0YO3S9LLT2doqhHYKJ223mVP9BxptLlgDGgKjXX7diOCGEaMCq0qJ9FbhZax149uICNRWuOu1Py8H/ZCZaKWPUcT10Q8dgCkssLMt0hHbtYPFiAFatgpdegpwcKwcUQogGqCqF1gFYUVNBalJBcQkpObmEnTxOoX8ImEzWjlQj2od4Eebr+s/o499+g/R0br8dcnPLG7hCCCFqUVUK7evAs0qpOjeh3+GTuWjgiuxEaFH/uo3LKKWI6RjCH/vSSOk/pHyWqGuugeBgmDvX2gmFEKLhqerMUM8CWXVt9Z59pSOO+xTswDmq/hZaMCavsGhY4hBkzBK1ZAn29jBqFCxdCqmp1k4ohBANS0Wr95yuzq7eU3ZrT/PEeLijTtyNdMnCA9yJauzJoh3J3DtkCCxcCMXF3HmnA6tWwdGj4Odn7ZRCCNFwVLrQ1uXVe5LM2biU2OFZmFsv76E92w0dg5m29G8O9htGs88+g99/J7p3b/7809rJhBCi4anK7T3OSqlXlVJJSqlTpe8NUEo9XHPxqsf+1Bw8MoqNF/Xw1p6zDYsORilY0Ki1MUvUokXln2VlyYLwQghRm6pyjfZtoB1wB6BL39sJjK/uUNUtKTUHv9RTxosGUGiDvV3o0cKXn3aa0f37G9NDaU1mpjEo6p13rJ1QCCEajqoU2huBUVrrPwALgNb6KBBSE8GqS0ZuISdzCmmScoxsZx/w9rZ2pFpx0xVNOJiWy5aho+DQIfjf//D0hG7d4KuvQOuK9yGEEOLyVaXQFnLWNV2llD+QVq2JqlnZiOPWKYmk+9T/1myZQe2CcHG050fv0u7j778HYPRoSEqCP/6wckAhhGggqlJo5wGfK6WaAyilGgMzgW9rIlh1STIbq/b0yt2OJazhFFo3ZwcGtQtiyd9p5F8/GObNA4uFm24CFxf44gtrJxRCiIahKoX2GSAJiAe8gb3AceDFir6olApVSq1WSu1SSu1USv37UsJeiv2pOTjYKTqZt9Gsb8MptGB0H2flF/NL/5Fw+DD87394eMBNN8G330JBgbUTCiFE/VeVQhsO7AamAs8DPbTWj2mtCyvx3WJgotY6CugOPKSUiqpy2kuQZM6hqYcjjkWFDeLWntP1aOlLYy8TPzmHntF9/OyzxuyMzs5WDiiEEA1AhYVWGeZgtGSfAYYB9wNblVL/VUqpivahtT6utf6z9HkWkEAtDaJKSs3GN7cIgITChtWitbdTDO8UQtz+DMxDbizvPm7TBtq3t3Y6IYRoGCrTon0A6AN011o301r30Fo3BXpgrEU7tioHVEqFAZ2Ajef57AGl1Gal1Gaz2VyV3Z5XiUVzIC2X4FMZxv7DG1ahBRhxRQglFs3C3jfDkSOwYQMAiYlw551w8KCVAwohRD1XmUI7GnhUa73p9DdLXz9W+nmlKKXcgR+Bx7TWmWd/rrX+SGvdRWvdxd/fv7K7vaBjGXkUFltoknKMXFzwjGh82fusa8IDPIhu4sWPJX5GX/G8eQA4OBiLDHz+uZUDCiFEPVeZQhsFXGj6xbjSzyuklHLEKLJztdY/VS7e5dlXOuK4+ZFEkmiBj2+Fvdz10ojOTUhIyWHnDaPKu4/DwqBvX/jsM7BYrJ1QCCHqr8oUWvvS66rnKH2/Utd5gU+BBK31W1WLeOnKFhOIPLiNA/Yt6+sytBWKiQ7GycGO77sMNVYVWL8egHvugf37Ye1aKwcUQoh6rDKF1lEpda1Squ/5HlRuYYKrMLqY+yqltpU+Bl9W8kpISs3Gw+RA65QdmOr58ngX4+3qxKB2QczPcSPfw8uYGgrjNh9PT/j0UysHFEKIeqwyRTIFmFPB5xeltV4H1Hq/bZI5hxZeTjgW5tFvXMO6tedst10ZysJtx1g28mGGf/c+vPMOrq4mHn0U7O2tnU4IIeqvCgut1jqsFnLUiP2pOfRwM27tISLCumGsrHtzX5r6uPKtd0+GZ7wKS5bAzTfz8svWTiaEEPVbVSasqFNyC4s5fiqf5rknAfj3+62tnMi67OwUt10ZyoYMzYGIaPjyy/LPSkpg1SpZaEAIIWpCvS20ZQOhWqQeIg8X8n1tepGhWnFz5ybYKfj+hrEQGwul9yp/+y306wfr1lk5oBBC1EP1t9CmGoW2+YEE9tKKRr719lQrLdDTRN82AcxzCaO4xGJUWGD4cGNQ1IcfWjefEELUR/W2+uxLyUYpCIvfwm5a4+tr7US24bYrm2LOt7C6363GTbSAm5uxfN4PP0CaTS96KIQQdU+9LbSJ5myaNnLBJWk3e2iNj4+1E9mGayP88fdw5rueN8Gff8KWLQCMHWus5iMzRQkhRPWqv4X2RDat3O1QxcU0H9Ca6GhrJ7INDvZ23NK5Cb8WuHLUPxQ+/hgwFhno2dO4dCuEEKL61MtCW1xiISk1m3CLcZ121Aut6dLFyqFsyKhuTQH4+tZHjQmPs42pKr//HpYts2YyIYSof+ploT14MpeiEk2rzOMA5IU27Ft7ztakkSt92wTyrU8UBXn55YOiQkKMxQaKi60cUAgh6pF6WWj3njBaaK2O7SPfzQfXUF+OHrVyKBszpmcz0go1sf1Gwkcflb+/Zg2EhsKePdbLJoQQ9Um9LLSJKcYaCC33bCPNx2jNymCoM13V0o8Wfm58ceVw2LTJGBgFtGljjDx+/33r5hNCiPqiXhbavSnZhHi74Pb3TpI9WuHiAi4u1k5lW+zsFKN7NGNrkYn4sHYwYwYAQUFw663w3/9C1nnXbBJCCFEV9bPQnsimlZ8LHD7MIZPc2nMhIzo3wdXJni9uehi++QaSkwF45BGjyH7xhZUDCiFEPVDvCm2JRbPPnE0rB2MxgUR7KbQX4mly5MZOISwyhZLu4AIffABAt27QtavRyJVF4YUQ4vLUu0J7ND2PgmIL4XnGFEftb2rNww9bOZQNu6tHGAUlmu9ve9QotPn5ALzxhjFGStX64oZCCFG/1LtCu7d0IFS4+QAA1z8czgMPWDGQjYsI8qBbcx8+b9aDorSTRhcy0KsX9OkjhVYIIS5XPSy0xq094Xt3QNOmHEh1L5uPQVzA/de04Fi+Jrb/KJg+vby/+ORJePRR2LDBygGFEKIOq3+F9kQ2gZ7OeP21Dd22LRER8Mor1k5l2/q2CaClvxsfdr8ZvWsXLFgAgLMzfPUV/N//WTefEELUZfWu0CamZNHK3x3+/pviVlEUFso9tBWxs1M80KsFu/Lt+b3nEOM3E61xc4MHHzTqrkxgIYQQl6ZeFVqtNXtTsgk3WSA/n6zQKEAKbWXc0DEEP3dnPhp4L2zdCkuXAsatPk5O8NZbVg4ohBB1VL0qtBYNM0Z24mb7VADSAqXQVpbJ0Z57rgpjba4zuzr0gJdfBq0JDIQxY4wJLGQaSyGEqLp6VWjt7RT9owJpd2gXAMe8jUIri75Xzp3dmuHh7MDMEY8bI6BWrADgP/+BUaNAaysHFEKIOqheFdpyu3ZBkyY0j/bk3XchIsLageoGL1dH7r4qjNhcV3ZH9zAqrMVC8+ZGi7ZJE2snFEKIuqd+FtqdOyEqiqZNjWuMQUHWDlR33HtVc9yc7Hn3tkmwbRt89135Z1u2GKOQhRBCVF79K7QWCyQkQNu2HDli1Fzp8qy8Rm5OjOkZRmymE3t79oNnn4XCQsAYEDVuHKSmWjmkEELUIfWv0B48CHl5EBXFu+9Cly4yu1FV3XdNC1wc7Xl3xOOQlAQffgjA5MmQmwvvvGPdfEIIUZfUv0K7c6fxMyqKkydlxPGl8HFz4p6rwlicovlr6Eh44QVISyMqCm6+2VhsQFq1QghROfWv0O4yRhwTFUVamhTaSzW2d0t83JyYet196FOnjC5k4MUXjVbttGlWDiiEEHVE/Sy0wcHg7c3Jk3Jrz6XyNDnyaN9w1ifns+bfLxjdx3/+SWSkMVuU/AIjhBCVU/8KbemIY0C6ji/TqG7NaObrymvBV1ESEAAPPwwWC++9Z1yvFUIIUbH6VWjLRhyXFtrXX4fHHrNupLrMycGOJwe2Ybc5l2/+MwP++AM+/hgwRnIvWgSJiVYOKYQQNk5pG733pUuXLnrz5s1V+1JJiTFHb5Mm0LFjjeRqaLTW3P7xBnYdy2TVhvfxX78Gdu0i1dSEsDAYMuSMW22FENYl91jYoPrVorW3h6FDpchWI6UUrwxvT15RCVNvnmT8MjNuHH6+mgkT4PvvjYauEEKI86tfhVbUiPAAd8b1bsn8xEzWT3kLfv4Zvv6aJ5+Exo3h8cfL14oXQghxFim0olIeujacZr6uPGPXmtyresFDD+F+8hDTpsHGjfDNN9ZOKIQQtkkKragUk6M9r4/owMGTubx831SjC/nOOxk9qoSYGHBxsXZCIYSwTbVSaJVSc5RSKUqpv2rjeKJmdG/hy9heLfnm7wyWT/sIfvsNu/97jYUL4aabrJ1OCCFsU221aD8Drq+lY4kaNKF/a9qFePKfk74k33EPPP88/O9/FBXBm2/C/v3WTiiEELalVgqt1notcLI2jiVqlpODHe/c1on8Igvjuo4hv2kYjBqFOSmLF16Ahx6S1ZKEEOJ0NnWNVin1gFJqs1Jqs9lstnYccQHhAe68fVs0245l88zjs9D79xP83L946UXN0qXw00/WTiiEELbDpgqt1vojrXUXrXUXf39/a8cRF3F9u8ZM6N+an44W8eHzH8O8eTxa8jYdO8Kjj0JmprUTCiGEbbCpQivqlkf6hjO0Q2Neyw3k+7ufwv7pJ/l6bBzHj8Nzz1k7nRBC2AYHawcQdZdSijdvjSYrv5inuAbHPoe48flbefepP+kcE2LteEIIYRNq6/aeb4A/gAil1BGl1L9q47ii5jk72PPh6M50b+HLxCvv4KcmV/Bw3C30uKIAkIFRQghRvxYVEFaTW1jMfZ9vZv2+NJ5Y+wUPtjLxmOdn2Dso3n7b2umEaDBkUQEbJNdoRbVwdXLgs3u6cmOnEKb3uounU7zo/ef/8c47EBdn7XRCCGE9co1WVBsnBzveujWa0EYuvAv8lZzI6JT53HPPjWzdCl5e1k4ohBC1T1q0oloppZgwIIJPRnbgiG8Ifw4txs1tHQ+M1XK9VgjRIEmhFTWiX8dQYsd2pU3mMbKGnGKTXsv6bXnWjiWEELVOCq2oMSGtm/LdY9cx5fcvcQ5N44Gf1jA7bh8FxSXWjiaEELVGCq2oUfbt23Hva4+w/MvH6X48gdeW/k2/N9eyctcJbHXEuxBCVCcptKLmXXUVTT9+j0/+O4lHvl+EOVlx/xebGf3p/9h57JS10wkhRI2SQitqR0wM6sMPmbj/I55790O6O7Thr2OnGPreOiZ8t42jGXL9VghRP8ntPaL23HcfOj2DO56cBK/accN3n3LQ4wBzft/Pkvjj3HNVGA/2CcfLxdHaSYUQotrIzFCi1hW9/BqOU57mG8fRDDjyX/KdCnlzxW7mbz2Kl4sjD18bzugezXB2sLd2VCHqGpkZygZJoRVWkfnUq3j+37Nw993wySdgb8/OY6d4benf/LY3lSaNXJg0MIJhHYKxs5N/O4SoJPmfxQZJoRXW89JL8PzzmHuNQM39Cr8mJgDW7jEzbenfJBzPpH2IF08PbkPPln5WDitEnSCF1gZJoRVWlTv1HVwnP86fHr1pvWsB7k28ASixaBZsPcqbK3Zz7FQ+fdsE8NT1bYgI8rBuYCFsmxRaGySFVljdponfEP3WGA65RRK8bSmu4cHln+UXlfDZ+gO8vzqRnIJibukcyuP9WxPkZbJiYiFslhRaGySFVtiENZNX0nnqTeQ6N8Lzl/m4XN35jM/TcwqZuTqRL/44gL2d4r6rWzC2dws8TDJCWYjTSKG1QVJohc1YOnUrbSffQLCjGYf/fgJ33HHONofScpm+YjeLth/Dx82Jf1/XilHdmuJoL7eEC4EUWpsk/zoJmzHomU6kLt2Mfc9ucOedMHYs5OScsU1TX1fevb0TCx+6ilYB7jy/aCeDZ/zGhqQ0K6UWQoiLkxatsD1FRWQ8/CyeH71BSYtWOH7/NXTufM5mWmt+SUjhhUU7OZqRx01XhPDM4Ej83J2tEFoImyAtWhskLVphexwd2TXmdW5wW4X5YC66e3eYOhWKis7YTClF/6hAfpnQmwf7tGTx9mP0nb6GrzYcpMRim79ACiEaHim0wib17Amvrr+WAYE7+FHfBJMnG63a338/Z1sXJ3uevL4NS/99DVHBnjy74C9u+mA9fx2VBQuEENYnhVbYrA4d4JctjXi767cMZz45xzLg6qvh3nvBbD5n+/AAD765vzvv3NaRo+m5xMxcxwuLdpKZX3TuzoUQopZIoRU2LSgIfl2tuOLF4bArAZ58Ev3llxAeDq++es5gKaUUwzuFsGpiH+7s3ozP/zjAdW/GsXDbUVn/VghhFTIYStQpOTkwvvcu3nB4msCNi4xK/Pzz8K9/geO599TuOJLBswv+YseRU/Rs6ctLN7QjPMDdCsmFqBUyGMoGSYtW1ClpabC9KIqgjQt544Z1FDcPh/HjjRbue+9Bbu4Z23do4s38B6/i5eHtiD96ikEz1vLG8r/JKyyx0hkIIRoaKbSiTmnaFDZuhIkT4T+Lr6L5obVseuFnCA2FRx+FsDCjSzkjo/w79naK0d2b8evEPgyLDub91fvo91Ycv+w6YbXzEEI0HNJ1LOqsjRuNHmMvL1i3DtTv62DaNIiNBQ8PuOceGDcOIiPP/F5SGs8t/Is9J7Lp2yaApwe1oVWgLFYg6gXpOrZBUmhFnVZQACkpRoM2ORlmzYInB27H/YM3YN48KCyEPn3gwQdh+PDy67hFJRb++/t+3luVSE5hMbddGcrj/VoT4CmLFYg6TQqtDZJCK+qNTz6B++8HHx948kl4+NYU3L6bAx9+CAcOGAOn7rzTeHToAEpxMqeQ937dy1cbDuJgZ8eYnmH86+rm+HvI7FKiTpJCa4Ok0Ip6ZfNmmDIFli6FgACj4E58rASWLTMK7tKlUFwM7drBqFFw443Qpg0H03KYvmIPS3Ycw8nejpFXhnJ/rxY0aeRq7VMSoiqk0NogKbSiXlq/Hl580Si2X35pvHfoEDR1TTW6lL/6ytgIoHVruOEGGDqUpJbt+PCPI/y09Qhaw3WRAdx2ZSi9WvnjICsECdsnhdYGSaEV9VpRkXFZdscOiI6Ga681updvvBFMqUdg0SJYuBBWrzY2dnGBnj051nsAnwVdwY/JFtJyigj0dOamK5owsG0QHUK8sLOTf8+ETZK/mDZICq1oEMxm+Phj4zru/v3g6WkU26lTITgYOHUK4uKMgvvrr0ZlBgpd3Pi1781836Y3axz8saDwc3Pi2jYB9I7w54qmjWjsZUIp+fdN2AT5i2iDpNCKBsViMero118bl2337AF3d6NRm5cHAwdCo0YYlTkuDjZsgE2bYMsW0kvsiGvRmVWtu7OmRWeyHF0ACHTUdAp2p12rxoQHeRIe4E4zXzdZjF5YgxRaGySFVjRYJSVgb288v/56WL4clDIWCbruOqPoXnvtaRvv3m2MtoqPp2hnAjuTs9imPNka3IY/Q9pw2DuofN8O2kKwfRGNXR0I8XElOMCb4BBfAr1dCfAw4e/hjJ+7k1z3FdVNCq0NkkIrBEYd3bgRVq6EVavgjz9gwAD4+Wfj86efNmaluuIKaN8eXMsGI2dnQ0IC7NpF9t+JJB07SWJGIfsK7Tni4MExT3+OefqT7OFLiZ39GcdUWuOjivF31Pib7Ahwd8Lf2xV/X08CAhvh7+tBgIcz/h7OuDs7SPe0qAz5S2KDpNAKcR7Z2XDypFFc8/ONn2Ur8ykFLVoY00COH2/cLbR+PbRsCY0bg11ZIzUry7ggfPAgxUePkXIslRPmU5jTczDnFJFSBGacSHFrhNmtEWZ342eR/bmLI7iUFOFvySNAF+JvX0KAI/ib7PB3dzRayN6uBPh54uPnhYO3lzEzlrs7ODjU3n80YQuk0NqgWvu/UCl1PTADsAc+0Vq/VlvHFqKq3N2NB4DJBCdOwOHDsGWLMU5q587Sa7kYtbR3b+O5k5MxS1XTpvDkkx5cf30H0kI6sHIlBEaAvz908DMm1XBywhjpfPIkpKZCWho6NY2MlOOY07JIycjFnF2IOa+ElGKFGWdSHFzY6+TO767eZFrcIRdIAbAAGdhZ0vDJzcQ/J52AnJP452cSUJSLvyUff4oIsC/G30ETYLLDzc30T0H28Djz+dk/y547Oxu/aQghKq1WCq1Syh54H+gPHAE2KaUWaa131cbxhbhcShnFs2lTY7Ty6YKDjeu7SUnGBFQHDhj37Fosxufx8XD77efuc+FCiIlx5PfEQJ56KhAPD2M0dFmRf+QRuDrcuDT8668QYjKKvrMzODta6No+k/ycNBL3ZrDvYDZZ+TlkFpRw0smJdPcATqpA9ljsMeNEsTr3WrCpuBD3wjxcT+bimpyPe2EuroUncSvKx7m4EMeSYpxKinAsKca5pMh4ri04Odrj6OSIk7MjTs5OOLk44+jijJOLCUc3F+zdXHFwc8PB3Q17dzccTU7YOzkZP52dcHQxYW9yxtHkjL3JGQdnJxwc7LF3sMfR0QE7O4Wyk2vXov6orRZtVyBRa50EoJT6FrgBkEIr6jw3N+N67oV062a0gE+cMOZlTkszHmVrHWhttG5TU43WcVaWsdrfqFHG6n9//GFM1XwmO7Zv96ZDB28WroZHHjv3uPv2GV3c06Zpnn25CHu3fOzdC7B3Mx6PTCpE2xfz+8Zitu0pxNGpEHtTIXaexSh7C/6BFoosmpx8TaEGi4OquDVbDJwqfQBQAuSVPqpGaQtKaxTG9WyNohhH0Eb3vJOTEccpvh37V4We8d1rrzVukQZjErCDB8/c97BhxshzgGbNjE6F040aZUwkBuDnZ8ypfboHHoA33zQ6JHx8zs3++OPw0kvGfps1O/fzKVNg0iTjF7K2bc/8bMsWYw4VUX/UyjVapdTNwPVa6/tKX48GummtHz5ruweAB0pfRgC7L/GQfkDqJX63rmqI5wwN87wb4jlDwzzvqp5zqtb6+poKIy6NTY2U0Fp/BHx0uftRSm3WWnephkh1RkM8Z2iY590Qzxka5nk3xHOuj2rrQshR4PS+nSal7wkhhBD1Wm0V2k1AK6VUc6WUEzASWFRLxxZCCCGspla6jrXWxUqph4HlGLf3zNFa76zBQ15293Md1BDPGRrmeTfEc4aGed4N8ZzrHZudsEIIIYSoD+RmNSGEEKIGSaEVQgghalCdLrRKqeuVUruVUolKqf+c53NnpdR3pZ9vVEqFWSFmtarEOU9QSu1SSu1QSq1SSp3ndvm6p6LzPm27EUoprZSq87dEVOaclVK3lv5571RKfV3bGatbJf5+N1VKrVZKbS39Oz7YGjmrk1JqjlIqRSn11wU+V0qpd0v/m+xQSl1R2xnFZdJa18kHxqCqfUALwAnYDkSdtc2DwOzS5yOB76yduxbO+VrAtfT5+Lp+zpU979LtPIC1wAagi7Vz18KfdStgK9Co9HWAtXPXwjl/BIwvfR4FHLB27mo4717AFcBfF/h8MLAUY8GA7sBGa2eWR9UedblFWz6to9a6ECib1vF0NwCflz7/AbhO1e21xio8Z631aq11bunLDRj3LNd1lfmzBngZeB3Ir81wNaQy53w/8L7WOh1Aa51SyxmrW2XOWQOepc+9gGO1mK9GaK3XAicvsskNwBfasAHwVko1rp10ojrU5UIbAhw+7fWR0vfOu43WumwWVt9aSVczKnPOp/sXxm/CdV2F513anRaqtf65NoPVoMr8WbcGWiulfldKbShdIasuq8w5vwDcqZQ6AsQCj9RONKuq6v/3wsbY1BSMovoope4EugC9rZ2lpiml7IC3gLutHKW2OWB0H/fB6LlYq5Rqr7XOsGaoGnY78JnW+k2lVA/gS6VUO621xdrBhLiQutyircy0juXbKKUcMLqa0molXc2o1FSWSql+wGQgRmtdcPbndVBF5+0BtAPWKKUOYFzHWlTHB0RV5s/6CLBIa12ktd4P7MEovHVVZc75X8D3AFrrPwATxsT79ZlMYVvH1eVCW5lpHRcBY0qf3wz8qrWuyzN0VHjOSqlOwIcYRbauX7Mrc9Hz1lqf0lr7aa3DtNZhGNemY7TWm60Tt1pU5u/3AozWLEopP4yu5KRazFjdKnPOh4DrAJRSkRiF1lyrKWvfIuCu0tHH3YFTWuvj1g4lKq/Odh3rC0zrqJR6CdistV4EfIrRtZSIMdhgpPUSX75KnvMbgDswr3Tc1yGtdYzVQleDSp53vVLJc14ODFBK7cJY+HWS1rrO9thU8pwnAh8rpR7HGBh1dx3/5Rml1DcYvzD5lV57fh5wBNBaz8a4Fj0YSARygXusk1RcKpmCUQghhKhBdbnrWAghhLB5UmiFEEKIGiSFVgghhKhBUmiFEEKIGiSFVgghhKhBUmhFg6eUCitd8afO3u4mhLBdUmhFg6SUOlA6g9bl7keKtBDioqTQCiGEEDVICq1ocJRSXwJNgcVKqWzg1tKP7lBKHVJKpSqlJp+2vZ1S6j9KqX1KqTSl1PdKKZ/Sj9eW/sxQSmUrpXoopVoqpX4t3TZVKTVXKeVdaycohLApUmhFg6O1Ho0xZ+4wrbU7pZPUA1cDERhz6U4pnUsXjKXYhmOshBQMpAPvl37Wq/Snt9bavXSiewVMK902EmNC+Bdq8JSEEDZMCq0Q/3hRa52ntd4ObAeiS98fB0zWWh8pXQ3pBeDmC12X1Vonaq1Xaq0LtNZmjCX86v1yhUKI85MBHEL8I/m057kYizMANAPmK6VOX/O0BAg8306UUoHADOAajCX87DBawUKIBkhatKKhqspqGoeBQVpr79MeJq310QvsZ2rp++211p7AnRjdyUKIBkgKrWioTgAtKrntbOBVpVQzAKWUv1LqhtLPzIDlrH15ANnAKaVUCDCpeiILIeoiKbSioZoGPKuUygBurmDbGRiLb69QSmVhLCzfDUBrnQu8CvyulMooXZj7ReAK4BTwM/BTjZyBEKJOkPVohRBCiBokLVohhBCiBkmhFUIIIWqQFFohhBCiBkmhFUIIIWqQFFohhBCiBkmhFUIIIWqQFFohhBCiBkmhFUIIIWrQ/wMNVIysa/ca4gAAAABJRU5ErkJggg==",
-      "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "plt.plot(theta_range, exact_posterior.prob(theta_range), \"b--\", label=\"$p(x)$: True Posterior\")\n",
-    "sns.kdeplot(transformed_samples, color=\"red\", label=\"$q(x)$: learnt - jax\", clip=(0.0, 1.0), bw_adjust=1.5)\n",
-    "sns.kdeplot(thetas, label=\"$q(x)$: learnt - pymc\", clip=(0.0, 1.0), bw_adjust=1.5)\n",
-    "plt.xlabel(\"theta\")\n",
-    "plt.legend(bbox_to_anchor=(1.3, 1))\n",
-    "sns.despine()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "82994180",
-   "metadata": {
-    "id": "82994180"
-   },
-   "source": [
-    "## Plot of loc and scale for variational distribution"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 68,
-   "id": "KRG3SGdPcxkW",
-   "metadata": {
-    "colab": {
-     "base_uri": "https://localhost:8080/",
-     "height": 530
-    },
-    "id": "KRG3SGdPcxkW",
-    "outputId": "54d1e49d-fcf8-4d59-d919-16facee37b9d"
-   },
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 720x288 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "image/png": 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",
-      "text/plain": [
-       "<Figure size 720x288 with 2 Axes>"
-      ]
-     },
-     "metadata": {
-      "needs_background": "light"
-     },
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "fig1, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4), sharey=True)\n",
-    "locs, scales = params[\"loc\"], params[\"scale\"]\n",
-    "\n",
-    "# plot loc\n",
-    "\n",
-    "# JAX\n",
-    "ax1.plot(locs, label=\"JAX: loc\")\n",
-    "ax1.set_ylabel(\"loc\")\n",
-    "ax1.legend()\n",
-    "\n",
-    "# pymc\n",
-    "ax2.plot(tracker[\"mean\"], label=\"Pymc: loc\")\n",
-    "ax2.legend()\n",
-    "sns.despine()\n",
-    "\n",
-    "\n",
-    "# plot scale\n",
-    "fig2, (ax3, ax4) = plt.subplots(1, 2, figsize=(10, 4), sharey=True)\n",
-    "\n",
-    "# JAX\n",
-    "ax3.plot(positivity_fn(jnp.array(scales)), label=\"JAX: scale\")\n",
-    "# apply softplus on scale\n",
-    "ax3.set_xlabel(\"Iterations\")\n",
-    "ax3.set_ylabel(\"scale\")\n",
-    "ax3.legend()\n",
-    "\n",
-    "# pymc\n",
-    "ax4.plot(tracker[\"std\"], label=\"Pymc: scale\")\n",
-    "ax4.set_xlabel(\"Iterations\")\n",
-    "ax4.legend()\n",
-    "\n",
-    "sns.despine();"
-   ]
-  },
   {
    "cell_type": "markdown",
    "id": "gf2lVoeQOF07",
@@ -1209,16 +901,6 @@
     "5. Github issue: https://github.com/pyro-ppl/pyro/issues/3016#:~:text=loc%3D%27upper%20right%27)-,Bandwidth%20adjustment,-Another%20thing%20to\n",
     "6. Blog: https://ericmjl.github.io/dl-workshop/02-jax-idioms/02-loopy-carry.html"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "5e5a2980",
-   "metadata": {
-    "id": "5e5a2980"
-   },
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {
@@ -1230,9 +912,9 @@
    "provenance": []
   },
   "kernelspec": {
-   "display_name": "Python [conda env:pymc_exp]",
+   "display_name": "Python [conda env:py3713_2]",
    "language": "python",
-   "name": "conda-env-pymc_exp-py"
+   "name": "conda-env-py3713_2-py"
   },
   "language_info": {
    "codemirror_mode": {
@@ -1244,7 +926,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.0"
+   "version": "3.7.13"
   }
  },
  "nbformat": 4,
diff --git a/notebooks/book2/07/advi_beta_binom_pymc.ipynb b/notebooks/book2/07/advi_beta_binom_pymc.ipynb
new file mode 100644
index 00000000000..c46008e5e35
--- /dev/null
+++ b/notebooks/book2/07/advi_beta_binom_pymc.ipynb
@@ -0,0 +1,501 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "f5db58f0",
+   "metadata": {
+    "id": "f5db58f0"
+   },
+   "source": [
+    "\n",
+    "## pymc's ADVI implementation for coin toss problem\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "c3ab49e8",
+   "metadata": {
+    "id": "c3ab49e8"
+   },
+   "outputs": [],
+   "source": [
+    "try:\n",
+    "    import jax\n",
+    "except ModuleNotFoundError:\n",
+    "    %pip install -qqq jax jaxlib\n",
+    "    import jax\n",
+    "\n",
+    "import jax.numpy as jnp\n",
+    "from jax import lax\n",
+    "\n",
+    "try:\n",
+    "    from tensorflow_probability.substrates import jax as tfp\n",
+    "except ModuleNotFoundError:\n",
+    "    %pip install -qqq tensorflow_probability\n",
+    "    from tensorflow_probability.substrates import jax as tfp\n",
+    "\n",
+    "try:\n",
+    "    import optax\n",
+    "except ModuleNotFoundError:\n",
+    "    %pip install -qqq optax\n",
+    "    import optax\n",
+    "\n",
+    "try:\n",
+    "    from rich import print\n",
+    "except ModuleNotFoundError:\n",
+    "    %pip install -qqq rich\n",
+    "    from rich import print\n",
+    "\n",
+    "try:\n",
+    "    from tqdm import trange\n",
+    "except ModuleNotFoundError:\n",
+    "    %pip install -qqq tqdm\n",
+    "    from tqdm import trange\n",
+    "\n",
+    "\n",
+    "import seaborn as sns\n",
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "import warnings\n",
+    "\n",
+    "try:\n",
+    "    import probml_utils as pml\n",
+    "except ModuleNotFoundError:\n",
+    "    %pip install -qqq git+https://github.com/probml/probml-utils.git\n",
+    "    import probml_utils as pml\n",
+    "\n",
+    "\n",
+    "warnings.filterwarnings(\"ignore\")\n",
+    "dist = tfp.distributions\n",
+    "\n",
+    "plt.rc(\"font\", size=10)  # controls default text sizes\n",
+    "plt.rc(\"axes\", labelsize=12)  # fontsize of the x and y labels\n",
+    "plt.rc(\"legend\", fontsize=12)  # legend fontsize\n",
+    "plt.rc(\"figure\", titlesize=15)  # fontsize of the figure title\n",
+    "\n",
+    "\n",
+    "try:\n",
+    "    import pymc as pm\n",
+    "except ModuleNotFoundError:\n",
+    "    %pip install -qq pymc\n",
+    "    import pymc as pm\n",
+    "\n",
+    "\n",
+    "try:\n",
+    "    import arviz as az\n",
+    "except ModuleNotFoundError:\n",
+    "    %pip install -qq arviz\n",
+    "    import arviz as az\n",
+    "\n",
+    "import math"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "1c7e8ec2",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def prior_dist():\n",
+    "    return dist.Beta(concentration1=1.0, concentration0=1.0)\n",
+    "\n",
+    "\n",
+    "def likelihood_dist(theta):\n",
+    "    return dist.Bernoulli(probs=theta)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "FZEmTzoHfbg9",
+   "metadata": {
+    "id": "FZEmTzoHfbg9"
+   },
+   "source": [
+    "## Dataset\n",
+    "Now, we will create the dataset. we sample `theta_true` (probability of occurring head) random variable from the prior distribution which is Beta in this case. Then we sample `n_samples` coin tosses from likelihood distribution which is Bernouli in this case. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "YajB06WPxMNJ",
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 33
+    },
+    "id": "YajB06WPxMNJ",
+    "outputId": "6b780e95-f6d2-411c-b5ff-f64bd85f518c"
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\">Dataset: <span style=\"font-weight: bold\">[</span><span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">0</span> <span style=\"color: #008080; text-decoration-color: #008080; font-weight: bold\">1</span><span style=\"font-weight: bold\">]</span>\n",
+       "</pre>\n"
+      ],
+      "text/plain": [
+       "Dataset: \u001b[1m[\u001b[0m\u001b[1;36m0\u001b[0m \u001b[1;36m0\u001b[0m \u001b[1;36m0\u001b[0m \u001b[1;36m0\u001b[0m \u001b[1;36m0\u001b[0m \u001b[1;36m0\u001b[0m \u001b[1;36m0\u001b[0m \u001b[1;36m0\u001b[0m \u001b[1;36m0\u001b[0m \u001b[1;36m0\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1m]\u001b[0m\n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Use same data as https://github.com/probml/probml-notebooks/blob/main/notebooks/beta_binom_approx_post_pymc.ipynb\n",
+    "key = jax.random.PRNGKey(128)\n",
+    "dataset = np.repeat([0, 1], (10, 1))\n",
+    "n_samples = len(dataset)\n",
+    "print(f\"Dataset: {dataset}\")\n",
+    "n_heads = dataset.sum()\n",
+    "n_tails = n_samples - n_heads"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fa96ac0d",
+   "metadata": {
+    "id": "fa96ac0d"
+   },
+   "source": [
+    "## Prior, Likelihood, and True Posterior  \n",
+    "For coin toss problem, since we know the closed form solution of posterior, we compare the distributions of Prior, Likelihood, and True Posterior below."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "bc027abf",
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 282
+    },
+    "id": "bc027abf",
+    "outputId": "24cdcf89-13a0-4d98-923b-2675cb17b5e3"
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 2 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# closed form of beta posterior\n",
+    "a = prior_dist().concentration1\n",
+    "b = prior_dist().concentration0\n",
+    "\n",
+    "exact_posterior = dist.Beta(concentration1=a + n_heads, concentration0=b + n_tails)\n",
+    "\n",
+    "theta_range = jnp.linspace(0.01, 0.99, 100)\n",
+    "\n",
+    "plt.figure()\n",
+    "ax = plt.gca()\n",
+    "ax2 = ax.twinx()\n",
+    "(plt2,) = ax2.plot(theta_range, exact_posterior.prob(theta_range), \"g--\", label=\"True Posterior\")\n",
+    "(plt3,) = ax2.plot(theta_range, prior_dist().prob(theta_range), label=\"Prior\")\n",
+    "\n",
+    "likelihood = jax.vmap(lambda x: jnp.prod(likelihood_dist(x).prob(dataset)))(theta_range)\n",
+    "(plt1,) = ax.plot(theta_range, likelihood, \"r-.\", label=\"Likelihood\")\n",
+    "\n",
+    "ax.set_xlabel(\"theta\")\n",
+    "ax.set_ylabel(\"Likelihood\")\n",
+    "ax2.set_ylabel(\"Prior & Posterior\")\n",
+    "ax2.legend(handles=[plt1, plt2, plt3], bbox_to_anchor=(1.6, 1));"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "2d7794f3",
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 37
+    },
+    "id": "2d7794f3",
+    "outputId": "a8cd71c2-f09b-4c38-c4bd-05faf33f9117"
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "<style>\n",
+       "    /* Turns off some styling */\n",
+       "    progress {\n",
+       "        /* gets rid of default border in Firefox and Opera. */\n",
+       "        border: none;\n",
+       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
+       "        background-size: auto;\n",
+       "    }\n",
+       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
+       "        background: #F44336;\n",
+       "    }\n",
+       "</style>\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "    <div>\n",
+       "      <progress value='20000' class='' max='20000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
+       "      100.00% [20000/20000 00:03<00:00 Average Loss = 4.9009]\n",
+       "    </div>\n",
+       "    "
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Finished [100%]: Average Loss = 4.9012\n",
+      "INFO:pymc.variational.inference:Finished [100%]: Average Loss = 4.9012\n"
+     ]
+    },
+    {
+     "ename": "KeyError",
+     "evalue": "'theta'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
+      "\u001b[0;32m/tmp/ipykernel_2708/1222123001.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     10\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     11\u001b[0m \u001b[0mtrace_approx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mapprox\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msample\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1000\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 12\u001b[0;31m \u001b[0mthetas\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtrace_approx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"theta\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
+      "\u001b[0;32m~/anaconda3/envs/py3713_2/lib/python3.7/site-packages/arviz/data/inference_data.py\u001b[0m in \u001b[0;36m__getitem__\u001b[0;34m(self, key)\u001b[0m\n\u001b[1;32m    251\u001b[0m         \u001b[0;34m\"\"\"Get item by key.\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    252\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mkey\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_groups_all\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 253\u001b[0;31m             \u001b[0;32mraise\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    254\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mgetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    255\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
+      "\u001b[0;31mKeyError\u001b[0m: 'theta'"
+     ]
+    }
+   ],
+   "source": [
+    "with pm.Model() as mf_model:\n",
+    "    theta = pm.Beta(\"theta\", 1, 1)\n",
+    "    y = pm.Binomial(\"y\", n=1, p=theta, observed=dataset)  # Bernoulli\n",
+    "    advi = pm.ADVI()\n",
+    "    tracker = pm.callbacks.Tracker(\n",
+    "        mean=advi.approx.mean.eval,  # callable that returns mean\n",
+    "        std=advi.approx.std.eval,  # callable that returns std\n",
+    "    )\n",
+    "    approx = advi.fit(callbacks=[tracker], n=20000)\n",
+    "\n",
+    "trace_approx = approx.sample(1000)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "id": "72d8a3f8",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "thetas = jnp.array(trace_approx.posterior[\"theta\"]).flatten()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "id": "4W8e7Dp9N1As",
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 282
+    },
+    "id": "4W8e7Dp9N1As",
+    "outputId": "7c84681f-bc08-4f04-a2e2-53b4230a3a57"
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.plot(advi.hist, label=\"ELBO\")\n",
+    "plt.xlabel(\"Iterations\")\n",
+    "plt.ylabel(\"ELBO\")\n",
+    "plt.legend()\n",
+    "sns.despine()\n",
+    "plt.savefig(\"advi_beta_binom_pymc_loss.pdf\")\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "53f16a33",
+   "metadata": {
+    "id": "53f16a33"
+   },
+   "source": [
+    "## True posterior & pymc q(x) "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "id": "f46083ff",
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 282
+    },
+    "id": "f46083ff",
+    "outputId": "b1ae81e7-23c2-4540-e324-479cf7dac55a"
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.plot(theta_range, exact_posterior.prob(theta_range), \"b--\", label=\"$p(x)$: True Posterior\")\n",
+    "sns.kdeplot(thetas, label=\"$q(x)$: learnt - pymc\", clip=(0.0, 1.0), bw_adjust=1)\n",
+    "plt.xlabel(\"theta\")\n",
+    "plt.legend(bbox_to_anchor=(1.3, 1))\n",
+    "sns.despine()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "82994180",
+   "metadata": {
+    "id": "82994180"
+   },
+   "source": [
+    "## Plot of loc and scale for variational distribution"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 43,
+   "id": "KRG3SGdPcxkW",
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 530
+    },
+    "id": "KRG3SGdPcxkW",
+    "outputId": "54d1e49d-fcf8-4d59-d919-16facee37b9d"
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# pymc\n",
+    "fig, ax2 = plt.subplots()\n",
+    "ax2.plot(tracker[\"mean\"], label=\"Pymc: loc\")\n",
+    "ax2.legend()\n",
+    "sns.despine()\n",
+    "\n",
+    "# pymc\n",
+    "fig, ax4 = plt.subplots()\n",
+    "ax4.plot(tracker[\"std\"], label=\"Pymc: scale\")\n",
+    "ax4.set_xlabel(\"Iterations\")\n",
+    "ax4.legend()\n",
+    "\n",
+    "sns.despine();"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5e5a2980",
+   "metadata": {
+    "id": "5e5a2980"
+   },
+   "outputs": [],
+   "source": []
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "07d5485b",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python [conda env:py3713_2]",
+   "language": "python",
+   "name": "conda-env-py3713_2-py"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.7.13"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}