{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "483c3aa5-62e1-4347-b584-edcefcd80a28",
   "metadata": {},
   "source": [
    "# Parallel Tempering using pure Python (Multiprocessing)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eab6bd29-ad75-4634-b6d2-60ddcbbd7402",
   "metadata": {},
   "source": [
    "Parallel tempering is a technique for improving the efficiency of MCMC, especially in the case of multi-modal target distributions. The core idea is to build a sequence of distributions starting with an easy-to-sample reference (e.g. the prior) and ending with the difficult-to-sample target (e.g. the posterior). Given the target $\\pi$ and the reference $\\pi_0$, this sequence is constructed using a \"temperature\" parameter $0 < \\beta < 1$:\n",
    "$$\\pi_\\beta = \\pi_0^{1-\\beta} \\cdot \\pi^\\beta$$\n",
    "Here, for $\\beta = 0$ (also referred to as \"cold\" chain) the distribution is equal to the target, for $\\beta = 1$ (also referred to as \"hot\" chain) it is equal to the reference. By running multiple chains with an ascending sequence of temperatures $\\beta_0 = 0, \\beta_1, \\dots, \\beta_n = 1$ and allowing theses chains to pass states based on Metropolis-Hastings, the simpler properties of hotter distributions improve the exploration of the state space and can result in faster convergence of the cold chain to the target distribution.\n",
    "\n",
    "*hopsy* implements parallel tempering. This notebook illustrates it by sampling a mixture of Gaussians that has two distinct modes. Depending on the starting point, vanilla MCMC approaches have trouble capturing the multi-modality. This is because once the chain has found a mode, Metropolis-Hastings proposal are very unlikely to propose high-density points in the other mode. With parallel tempering, the hotter chains are less effected by this and can better sample broadly. By passing these states on to the colder chains, other modes can be explored.\n",
    "\n",
    "We highly recommend using MPI for maximum performance when using parallel tempering. For examples see parallel_tempering_MPI.py or ParallelTemperingMPI.ipynb.\n",
    "However, using MPI and mpi4py requires compiling hopsy with your MPI distribution.\n",
    "This is because we can not assume and/or suppport all possible MPI implementations.\n",
    "\n",
    "Instead, we provide parallel tempering using Pythons multiprocessing.\n",
    "The usage is demonstrated in this notebook.\n",
    "\n",
    "This notebook is the same as parallel_tempering_multiprocessing.py but with iPython and more comments to check whether the example works in Notebooks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "66ea2c41-6c2a-46ce-bf3a-2cc0025b66d8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import time\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import hopsy\n",
    "import multiprocessing as mp\n",
    "import sys"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7c15025-f8d2-47d4-a679-fd1d4f193f76",
   "metadata": {},
   "source": [
    "## Defining model type with multimodal density"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "219ee847-f2e7-4a0a-915f-44a6abdb5853",
   "metadata": {},
   "source": [
    "## Important note:\n",
    "Functionality within multiprocessing requires that the __main__ module be importable by the children. See https://docs.python.org/3/library/multiprocessing.html#using-a-pool-of-workers.\n",
    "This means, that the gaussian mixture needs to be imported from a file and not defined here\n",
    "\n",
    "\n",
    "E.g. the code below is will not work with multiprocessing and jupyter due to python limitations\n",
    "\n",
    "    GaussianMixture:\n",
    "        def __init__(self, mu1, mu2):\n",
    "            epsilon = 0.05\n",
    "            cov = epsilon * np.eye(2, 2)\n",
    "            self.model1 = hopsy.Gaussian(mean=mu1, covariance=cov)\n",
    "            self.model2 = hopsy.Gaussian(mean=mu2, covariance=cov)\n",
    "    \n",
    "        def log_density(self, x):\n",
    "            return np.log(\n",
    "                np.exp(-self.model1.compute_negative_log_likelihood(x))\n",
    "                + np.exp(-self.model2.compute_negative_log_likelihood(x))\n",
    "            )\n",
    "\n",
    "Instead, we import the Gaussian mixture, like below\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1aac7983-07b8-4fb1-9d7c-23d5b471145e",
   "metadata": {},
   "outputs": [],
   "source": [
    "from custom_models import GaussianMixture"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "611f08a7-d19a-48a7-95f2-33b8ecde3576",
   "metadata": {},
   "source": [
    "<!-- ## Setup problem and sampling configuration -->"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0eea7ee7-955b-4446-a5e5-17d79e61bc94",
   "metadata": {},
   "outputs": [],
   "source": [
    "replicates = 3\n",
    "n_temps = 4\n",
    "n_samples = 40_000\n",
    "thinning = 10\n",
    "\n",
    "A = np.array([[1, 0], [0, 1], [-1, 0], [0, -1]])\n",
    "b = np.array([1, 1, 1, 1])\n",
    "\n",
    "model = GaussianMixture(np.ones(2).reshape(2, 1), -np.ones(2).reshape(2, 1))\n",
    "problem = hopsy.Problem(A, b, model)\n",
    "\n",
    "sync_rngs = [hopsy.RandomNumberGenerator(seed=4321 + r) for r in range(replicates)]\n",
    "\n",
    "temperature_ladder = [1.0 - float(n) / (n_temps - 1) for n in range(n_temps)]\n",
    "\n",
    "mcs = [\n",
    "    hopsy.MarkovChain(\n",
    "        proposal=hopsy.GaussianHitAndRunProposal,\n",
    "        problem=problem,\n",
    "        starting_point=0.9 * np.ones(2),\n",
    "    )\n",
    "    for r in range(replicates)\n",
    "]\n",
    "\n",
    "try:\n",
    "    epsilon = 100 \n",
    "    for mc in mcs:\n",
    "        mc.proposal.stepsize = epsilon\n",
    "except:\n",
    "    pass\n",
    "\n",
    "# Creates one parallel tempering ensemble for each replicate.\n",
    "# Each ensemble will have len(temperature_ladder) chains.\n",
    "chains = hopsy.create_py_parallel_tempering_ensembles(\n",
    "    markov_chains=mcs,\n",
    "    temperature_ladder=temperature_ladder,\n",
    "    sync_rngs=sync_rngs,\n",
    "    draws_per_exchange_attempt=20,\n",
    ")\n",
    "\n",
    "rngs = [hopsy.RandomNumberGenerator(i + 1234) for i, _ in enumerate(chains)]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e680bc05-6f06-40b8-9ab3-509fcde3fe59",
   "metadata": {},
   "source": [
    "## run and benchmark sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "076683fc-136d-414e-ad38-22741b4e0d85",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "sampling 40000 samples with thinning 10 and 12 chains took 100.14002706602332 seconds\n"
     ]
    }
   ],
   "source": [
    "start = time.perf_counter()\n",
    "acc_rate, samples = hopsy.sample(\n",
    "    markov_chains=chains,\n",
    "    rngs=rngs,\n",
    "    n_samples=n_samples,\n",
    "    thinning=thinning,\n",
    "    n_procs=len(chains),\n",
    ")\n",
    "end = time.perf_counter()\n",
    "print(\n",
    "    f\"sampling {n_samples} samples with thinning {thinning} and {len(chains)} chains took {end - start} seconds\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "dbd00cd1-b418-4175-a5de-e034fcd711bb",
   "metadata": {},
   "outputs": [],
   "source": [
    "## Check convergence and plot posterior marginal for first dimension"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "251bf37a-0fb4-4236-a650-c89e2b478f0c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "convergence check for hot samples (rhat<1.01 & ess > 400 means converged)\n",
      "min ess 117989.07529181667 rhat:  1.0000070989126177\n",
      "convergence check for cold samples (rhat<1.01 & ess > 400 means converged)\n",
      "min ess: 25741.320276520106 , rhat:  1.0002144991000597\n"
     ]
    },
    {
     "data": {
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dUVxcDD8/vz7HCQkJgZ+fH7Kzs7WWGxENLB5hIaIh7+DBg1i1alW/Yhw9ehQzZsyAvb09JBJJr48DICLt4hEWNVTWt4gW2020yETUydraut8xWlpa4OvriwULFuC5557TQlZEpAkeYSEinero6EBmZibc3NwglUrh6OiI1atXq7QpLy9HaGgoZDIZfH19UVRUpFxWX1+PqKgoODg4QCaTwdvbG/v27VNZPyQkBPHx8cppJycnZGRkYMGCBTA3N4ejoyO2bdvWY57Tpk3D22+/jWeffbb/nSYijbFgISKdSk5Oxtq1a5Gamopz585h7969sLGxUWmTkpKCxMRElJSUYNy4cYiKikJ7ezsAoLW1Ff7+/sjLy0NpaSliYmIwd+5cnDp1qsftbtiwAQEBASguLkZcXBxiY2Nx8eJF0fpJRP3DU0JEpDNNTU3IycnBpk2bEB0dDQBwdXVFcHCwSrvExEREREQAANLT0+Hl5YWysjJ4enrCwcEBiYmJyrZLly5Ffn4+cnNzERgY+MBtT58+HXFxcQCApKQkbNy4EUeOHIGHh4e2u0lEWsCChYh05vz585DL5ZgyZUqP7Xx8fJQ/29nZAQBqa2vh6ekJhUKBjIwM5ObmoqqqCm1tbZDL5ZDJZGrHlEgksLW1RW1tbT96Q0RiYsFCRDpjZmamVjtjY2PlzxKJBMDdsS8AsG7dOuTk5CA7Oxve3t4YNmwY4uPj0dbWpnbMzridMYlI/3AMCxHpjLu7O8zMzFBQUNDnGMeOHUNkZCTmzJkDX19fuLi44NKlS1rMkoj0AY+wEJHOmJqaIikpCcuWLYOJiQkmTZqEuro6nD17FgsXLlQrhru7Ow4cOIDjx4/DysoKWVlZqKmpwfjx2r2PeHNzM8rKypTTFRUVKCkpgbW1NRwdHbW6LSLqigUL0VCnxTvPiiE1NRVGRkZIS0vDtWvXYGdnh8WLF6u9/ooVK1BeXo7w8HDIZDLExMRg5syZaGho0Gqep0+fRmhoqHI6ISEBABAdHY3du3drdVtE1JVEEARB10n0V2NjIywtLdHQ0AALCwutx/+i8BOtx+wUFvIb0WLTw6W1tRUVFRVwdnaGqamprtMhNXCfkbYNtu8rTb6/OYaFiIiI9B4LFiIiItJ7LFiIiIhI77FgISIiIr3HgoWIiIj0HgsWIiIi0nssWIiIiEjvsWAhIiIivceChYiIiPQeb81PNMSdrj49oNsLsA3QWqzKyko4OzujuLgYfn5+fY4TEhICPz8/ZGdnay03IhpYPMJCREPewYMHsWrVqn7FWLNmDZ588kmYm5tj1KhRmDlzJi5evKilDImoNyxYiGjIs7a2hrm5eb9ifPnll3jllVdw4sQJfP7557hz5w6eeeYZtLS0aClLIuoJCxYi0qmOjg5kZmbCzc0NUqkUjo6OWL16tUqb8vJyhIaGQiaTwdfXF0VFRcpl9fX1iIqKgoODA2QyGby9vbFv3z6V9UNCQhAfH6+cdnJyQkZGBhYsWABzc3M4Ojpi27ZtPeZ5+PBhzJs3D15eXvD19cXu3btx5coVnDlzpv9vAhH1igULEelUcnIy1q5di9TUVJw7dw579+6FjY2NSpuUlBQkJiaipKQE48aNQ1RUFNrb2wHcfeKxv78/8vLyUFpaipiYGMydOxenTp3qcbsbNmxAQEAAiouLERcXh9jYWI1O8TQ0NAC4e/SGiMTHQbdEpDNNTU3IycnBpk2bEB0dDQBwdXVFcHCwSrvExEREREQAANLT0+Hl5YWysjJ4enrCwcEBiYmJyrZLly5Ffn4+cnNzERgY+MBtT58+HXFxcQCApKQkbNy4EUeOHIGHh0eveXd0dCA+Ph6TJk3CY489pnG/iUhzLFiISGfOnz8PuVyOKVOm9NjOx8dH+bOdnR0AoLa2Fp6enlAoFMjIyEBubi6qqqrQ1tYGuVwOmUymdkyJRAJbW1vU1taqlfcrr7yC0tJSfPXVV2q1J6L+Y8FCRDpjZmamVjtjY2PlzxKJBMDdoxwAsG7dOuTk5CA7Oxve3t4YNmwY4uPj0dbWpnbMzridMXuyZMkS/POf/8TRo0cxevRotfInov7jGBYi0hl3d3eYmZmhoKCgzzGOHTuGyMhIzJkzB76+vnBxccGlS5e0mOVdgiBgyZIl+Pjjj/Hvf/8bzs7OWt8GET0Yj7AQkc6YmpoiKSkJy5Ytg4mJCSZNmoS6ujqcPXsWCxcuVCuGu7s7Dhw4gOPHj8PKygpZWVmoqanB+PHjtZrrK6+8gr179+Lvf/87zM3NUV1dDQCwtLRU+0gREfUdCxaiIU6bd54VQ2pqKoyMjJCWloZr167Bzs4OixcvVnv9FStWoLy8HOHh4ZDJZIiJicHMmTOVV/Foy5YtWwDcvUT6Xrt27cK8efO0ui0i6ooFCxHplIGBAVJSUpCSktJlmZOTEwRBUJk3fPhwlXnW1tY4dOhQj9soLCxUma6srOzSpqSkpMcY9+dBRANL4zEsR48exYwZM2Bvbw+JRKLWLwqJRNLl1Xk4tdPmzZvh5OQEU1NTBAUF9XoPBSIiInp4aFywtLS0wNfXF5s3b9ZovYsXL+L69evK16hRo5TLPvjgAyQkJGDlypX45ptv4Ovri/DwcLUvMSQiIqKhTeNTQtOmTcO0adM03tCoUaMwfPjwbpdlZWXh5Zdfxvz58wEAW7duRV5eHnbu3Inly5d3aS+XyyGXy5XTjY2NGudDREREg8eAXdbs5+cHOzs7PP300zh27JhyfltbG86cOYOwsLD/JmVggLCwMJXnhdxrzZo1sLS0VL7GjBkjev5ERESkO6IXLHZ2dti6dSs++ugjfPTRRxgzZgxCQkLwzTffAABu3LgBhULR5dkhNjY2Xca5dEpOTkZDQ4Py9eOPP4rdDSIiItIh0a8S8vDwUHk2x8SJE/HDDz9g48aN+Otf/9qnmFKpFFKpVFspEhERkZ7TyZ1uAwMDUVZWBgAYMWIEDA0NUVNTo9KmpqYGtra2ukiPiIiI9IxOCpaSkhLlA8xMTEzg7++vcmvujo4OFBQUYMKECbpIj4iIiPSMxqeEmpublUdHAKCiogIlJSWwtraGo6MjkpOTUVVVhffffx8AkJ2dDWdnZ3h5eaG1tRV/+ctf8O9//xv/+te/lDESEhIQHR2NgIAABAYGIjs7Gy0tLcqrhoiIiOjhpnHBcvr0aYSGhiqnExISAADR0dHYvXs3rl+/jitXriiXt7W14Q9/+AOqqqogk8ng4+ODL774QiXGrFmzUFdXh7S0NFRXV8PPzw+HDx/uMhCXiDR3++uvB3R7sief1FqsyspKODs7o7i4GH5+fn2OExISAj8/P2RnZ2stNyIaWBoXLCEhIT3eonr37t0q08uWLcOyZct6jbtkyRIsWbJE03SIiHp18OBBGBsb9yvGli1bsGXLFuVt/b28vJCWltan+1IRkeZ0MoaFiGggWVtbw9zcvF8xRo8ejbVr1+LMmTM4ffo0fv3rXyMyMhJnz57VUpZE1BMWLESkUx0dHcjMzISbmxukUikcHR2xevVqlTbl5eUIDQ2FTCaDr6+vyk0l6+vrERUVBQcHB8hkMnh7e2Pfvn0q64eEhCA+Pl457eTkhIyMDCxYsADm5uZwdHTEtm3besxzxowZmD59Otzd3TFu3DisXr0ajzzyCE6cONH/N4GIesWChYh0Kjk5GWvXrkVqairOnTuHvXv3dhm/lpKSgsTERJSUlGDcuHGIiopCe3s7AKC1tRX+/v7Iy8tDaWkpYmJiMHfu3F4foLphwwYEBASguLgYcXFxiI2NxcWLF9XKWaFQYP/+/WhpaeHVjEQDRPQbxw0FFwTxblIX1nsToiGrqakJOTk52LRpE6KjowEArq6uCA4OVmmXmJiIiIgIAEB6ejq8vLxQVlYGT09PODg4IDExUdl26dKlyM/PR25uLgIDAx+47enTpyMuLg4AkJSUhI0bN+LIkSMqN7q833fffYcJEyagtbUVjzzyCD7++GOMHz++z/0nIvWxYFGD8e3uHxFARP1z/vx5yOVyTJkypcd2Pj4+yp877+FUW1sLT09PKBQKZGRkIDc3F1VVVWhra4NcLodMJlM7pkQiga2tba9PiPfw8EBJSQkaGhpw4MABREdH48svv2TRQnpjKP+BzYKFiHTGzMxMrXb3XuEjkUgA3B37AgDr1q1DTk4OsrOz4e3tjWHDhiE+Ph5tbW1qx+yM2xnzQUxMTODm5gYA8Pf3x9dff42cnBz8+c9/VqsfRJ1OltfrOoVBhwULEemMu7s7zMzMUFBQgEWLFvUpxrFjxxAZGYk5c+YAuFvIXLp0aUCOenR0dEAul4u+HSJ1yRvqdJ2CaFiwqKG1qUHXKRANSaampkhKSsKyZctgYmKCSZMmoa6uDmfPnsXChQvViuHu7o4DBw7g+PHjsLKyQlZWFmpqarResCQnJ2PatGlwdHREU1MT9u7di8LCQuTn52t1O/RwaPqxWdcpDDosWHSs7LuC3hv1gZt3z2MC6OGhzTvPiiE1NRVGRkZIS0vDtWvXYGdnh8WLF6u9/ooVK1BeXo7w8HDIZDLExMRg5syZaGjQ7h8atbW1eOmll3D9+nVYWlrCx8cH+fn5ePrpp7W6HaL+MGr9SdcpiIYFCxHplIGBAVJSUpCSktJlmZOTU5c7aw8fPlxlnrW1NQ4dOtTjNgoLC1WmO+9We6+SkpIeY+zYsaPH5UQaEf6j6wwGHd6HhYiIiPQeCxYiIiLSezwlpGOV9S2ixHUTJSoREZFu8AgLERER6T0WLERERKT3WLAQERGR3mPBQkRERHqPBQsRERHpPRYsREREpPd4WTPREHft+5sDuj17dyutxaqsrISzszOKi4vh5+fX5zghISHw8/NDdna21nIjooHFIyxENOQdPHgQq1at0lq8tWvXQiKRID4+XmsxiahnPMJCREOetbW11mJ9/fXX+POf/wwfHx+txSSi3vEICxHpVEdHBzIzM+Hm5gapVApHR0esXr1apU15eTlCQ0Mhk8ng6+uLoqIi5bL6+npERUXBwcEBMpkM3t7e2Ldvn8r6ISEhKkdDnJyckJGRgQULFsDc3ByOjo7Ytm1br7k2NzfjxRdfxPbt22Flpb1TX0TUOxYsRKRTycnJWLt2LVJTU3Hu3Dns3bsXNjY2Km1SUlKQmJiIkpISjBs3DlFRUWhvbwcAtLa2wt/fH3l5eSgtLUVMTAzmzp2LU6dO9bjdDRs2ICAgAMXFxYiLi0NsbCwuXrzY4zqvvPIKIiIiEBYW1r9OE5HGeEqIiHSmqakJOTk52LRpE6KjowEArq6uCA4OVmmXmJiIiIgIAEB6ejq8vLxQVlYGT09PODg4IDExUdl26dKlyM/PR25uLgIDAx+47enTpyMuLg4AkJSUhI0bN+LIkSPw8PDotv3+/fvxzTff4Ouvv+5Xn4mob1iwEJHOnD9/HnK5HFOmTOmx3b3jRezs7AAAtbW18PT0hEKhQEZGBnJzc1FVVYW2tjbI5XLIZDK1Y0okEtja2qK2trbbtj/++CNee+01fP755zA1NVW3e0SkRSxYiEhnzMzM1GpnbGys/FkikQC4O/YFANatW4ecnBxkZ2fD29sbw4YNQ3x8PNra2tSO2Rm3M+b9zpw5g9raWjzxxBPKeQqFAkePHsWmTZsgl8thaGioVl+IqG9YsBCRzri7u8PMzAwFBQVYtGhRn2IcO3YMkZGRmDNnDoC7hcylS5cwfvx4reU5ZcoUfPfddyrz5s+fD09PTyQlJbFYIRoALFiISGdMTU2RlJSEZcuWwcTEBJMmTUJdXR3Onj2LhQsXqhXD3d0dBw4cwPHjx2FlZYWsrCzU1NRotWAxNzfHY489pjJv2LBh+MUvftFlPhGJgwUL0RCnzTvPiiE1NRVGRkZIS0vDtWvXYGdnh8WLF6u9/ooVK1BeXo7w8HDIZDLExMRg5syZaGhoEDFrIhpoLFiISKcMDAyQkpKClJSULsucnJwgCILKvOHDh6vMs7a2xqFDh3rcRmFhocp0ZWVllzYlJSXqptxtTCISF+/DQkRERHqPBQsRERHpPZ4S0rGfb1zVdQpERER6j0dYiIiISO+xYCEiIiK9x4KFiIiI9B4LFiIiItJ7GhcsR48exYwZM2Bvbw+JRNLr/Q8OHjyIp59+GiNHjoSFhQUmTJiA/Px8lTZvvfUWJBKJysvT01PT1IiIiGiI0vgqoZaWFvj6+mLBggV47rnnem1/9OhRPP3008jIyMDw4cOxa9cuzJgxAydPnsTjjz+ubOfl5YUvvvjiv4kZ8QImIiIamqSNl3WdwqCjcVUwbdo0TJs2Te322dnZKtMZGRn4+9//jn/84x8qBYuRkRFsbW01TWfQu2RkoesUaIi7eq50QLc3erz2nq1TWVkJZ2dnFBcXw8/Pr89xQkJC4Ofn1+X3ERENHgN+GKOjowNNTU2wtrZWmf/999/D3t4epqammDBhAtasWQNHR8duY8jlcsjlcuV0Y2OjqDmLyaj1J12nQDTkHTx4EMbGxv2K8dZbbyE9PV1lnoeHBy5cuNCvuESkngEfdLt+/Xo0NzfjhRdeUM4LCgrC7t27cfjwYWzZsgUVFRV46qmn0NTU1G2MNWvWwNLSUvkaM2bMQKVPRIOQtbU1zM3N+x3Hy8sL169fV76++uorLWRHROoY0IJl7969SE9PR25uLkaNGqWcP23aNDz//PPw8fFBeHg4Pv30U9y6dQu5ubndxklOTkZDQ4Py9eOPPw5UF4hIyzo6OpCZmQk3NzdIpVI4Ojpi9erVKm3Ky8sRGhoKmUwGX19fFBUVKZfV19cjKioKDg4OkMlk8Pb2xr59+1TWDwkJQXx8vHLayckJGRkZWLBgAczNzeHo6Iht27b1mmvnqevO14gRI/rXeSJS24AVLPv378eiRYuQm5uLsLCwHtsOHz4c48aNQ1lZWbfLpVIpLCwsVF5ENDglJydj7dq1SE1Nxblz57B3717Y2NiotElJSUFiYiJKSkowbtw4REVFob29HQDQ2toKf39/5OXlobS0FDExMZg7dy5OnTrV43Y3bNiAgIAAFBcXIy4uDrGxsbh48WKP63SeunZxccGLL76IK1eu9K/zRKS2ASlY9u3bh/nz52Pfvn2IiIjotX1zczN++OEH2NnZDUB2RKQrTU1NyMnJQWZmJqKjo+Hq6org4GAsWrRIpV1iYiIiIiIwbtw4pKen4/Lly8o/aBwcHJCYmAg/Pz+4uLhg6dKlmDp16gOP0HaaPn064uLi4ObmhqSkJIwYMQJHjhx5YHtNT10TkXZpPOi2ublZ5chHRUUFSkpKYG1tDUdHRyQnJ6Oqqgrvv/8+gLungaKjo5GTk4OgoCBUV1cDAMzMzGBpaQng7i+jGTNmYOzYsbh27RpWrlwJQ0NDREVFaaOPRKSnzp8/D7lcjilTpvTYzsfHR/lz5x8ytbW18PT0hEKhQEZGBnJzc1FVVYW2tjbI5XLIZDK1Y0okEtja2qK2tvaB7e+9OtLHxwdBQUEYO3YscnNzsXDhwh63RXS/c4ZinRloECmu7mlcsJw+fRqhoaHK6YSEBABAdHQ0du/ejevXr6scJt22bRva29vxyiuv4JVXXlHO72wPAFevXkVUVBTq6+sxcuRIBAcH48SJExg5cmRf+0VEg4CZmZla7e69wkcikQC4O/YFANatW4ecnBxkZ2fD29sbw4YNQ3x8PNra2tSO2Rm3M6Y6ejt1TdST1qahW1iIReOCJSQkBIIgPHB5ZxHSqbCwsNeY+/fv1zQNIhoC3N3dYWZmhoKCgi6ngdR17NgxREZGYs6cOQDuFjKXLl3C+PHjtZlqF52nrufOnSvqdojoLj5LiIh0xtTUFElJSVi2bBnef/99/PDDDzhx4gR27Nihdgx3d3d8/vnnOH78OM6fP4/f//73qKmp0XquiYmJ+PLLL1FZWYnjx4/j2Wef5alrogHE+98TDXHavPOsGFJTU2FkZIS0tDRcu3YNdnZ2WLx4sdrrr1ixAuXl5QgPD4dMJkNMTAxmzpyJhgbtHnLnqWsi3WLBQkQ6ZWBggJSUFKSkpHRZ5uTk1OUU9PDhw1XmWVtb9/oQ1vtPTVdWVnZpU1JS0mMMnrom0i2eEiIiIiK9x4KFiIiI9B4LFiIiItJ7LFiIiIhI77FgISIiIr3HgoWIiIj0HgsWIiIi0nssWIiIiEjvsWAhIr1VWVkJiUTS603dehMSEoL4+Hit5EREusE73RINcfLygX0qrNTFckC3p46DBw92eTpzX1RVVSEpKQmfffYZbt++DTc3N+zatQsBAQFayJKIesKChYiGPGtr637HuHnzJiZNmoTQ0FB89tlnGDlyJL7//ntYWVlpIUMi6g1PCRGRTnV0dCAzMxNubm6QSqVwdHTE6tWrVdqUl5cjNDQUMpkMvr6+KCoqUi6rr69HVFQUHBwcIJPJ4O3tjX379qmsf/8pIScnJ2RkZGDBggUwNzeHo6Mjtm3b1mOe77zzDsaMGYNdu3YhMDAQzs7OeOaZZ+Dq6tr/N4GIesWChYh0Kjk5GWvXrkVqairOnTuHvXv3wsbGRqVNSkoKEhMTUVJSgnHjxiEqKgrt7e0AgNbWVvj7+yMvLw+lpaWIiYnB3LlzcerUqR63u2HDBgQEBKC4uBhxcXGIjY3FxYsXH9j+k08+QUBAAJ5//nmMGjUKjz/+OLZv397/N4CI1MKChYh0pqmpCTk5OcjMzER0dDRcXV0RHByMRYsWqbRLTExEREQExo0bh/T0dFy+fBllZWUAAAcHByQmJsLPzw8uLi5YunQppk6ditzc3B63PX36dMTFxcHNzQ1JSUkYMWIEjhw58sD25eXl2LJlC9zd3ZGfn4/Y2Fi8+uqreO+99/r/RhBRrziGhYh05vz585DL5ZgyZUqP7Xx8fJQ/29nZAQBqa2vh6ekJhUKBjIwM5ObmoqqqCm1tbZDL5ZDJZGrHlEgksLW1RW1t7QPbd3R0ICAgABkZGQCAxx9/HKWlpdi6dSuio6N77SsR9Q+PsBCRzpiZmanV7t4rfCQSCYC7BQQArFu3Djk5OUhKSsKRI0dQUlKC8PBwtLW1qR2zM25nzO7Y2dlh/PjxKvMeffRRXLlyRa0+EFH/sGAhIp1xd3eHmZkZCgoK+hzj2LFjiIyMxJw5c+Dr6wsXFxdcunRJi1neNWnSpC5jXC5duoSxY8dqfVtE1BVPCRGRzpiamiIpKQnLli2DiYkJJk2ahLq6Opw9exYLFy5UK4a7uzsOHDiA48ePw8rKCllZWaipqelyNKS/Xn/9dUycOBEZGRl44YUXcOrUKWzbtq3Xq4uISDtYsBCRTqWmpsLIyAhpaWm4du0a7OzssHjxYrXXX7FiBcrLyxEeHg6ZTIaYmBjMnDkTDQ3avWHek08+iY8//hjJycn44x//CGdnZ2RnZ+PFF1/U6naIqHsSQRAEXSfRX42NjbC0tERDQwMsLCy0Hj9n/7tajym212a/qusUaIC1traioqICzs7OMDU11XU6pAbus4cXv1fu0uT7m2NYiIiISO+xYCEiIiK9x4KFiIiI9B4LFiIiItJ7LFiIiIhI77FgISIiIr3HgoWIiIj0HgsWIiIi0nssWIiIiEjvsWAhIr1VWVkJiUSCkpKSfsUJCQlBfHy8VnIiIt3gs4SIhrjKysoB3Z6Tk9OAbk8dBw8ehLGxcb9iODk54fLly13mx8XFYfPmzf2KTUS9Y8FCREOetbV1v2N8/fXXUCgUyunS0lI8/fTTeP755/sdm4h6x1NCRKRTHR0dyMzMhJubG6RSKRwdHbF69WqVNuXl5QgNDYVMJoOvry+KioqUy+rr6xEVFQUHBwfIZDJ4e3tj3759Kuvff0rIyckJGRkZWLBgAczNzeHo6Iht27b1mOfIkSNha2urfP3zn/+Eq6srJk+e3P83gYh6xSMsRKRTycnJ2L59OzZu3Ijg4GBcv34dFy5cUGmTkpKC9evXw93dHSkpKYiKikJZWRmMjIzQ2toKf39/JCUlwcLCAnl5eZg7dy5cXV0RGBj4wO1u2LABq1atwptvvokDBw4gNjYWkydPhoeHR685t7W14W9/+xsSEhIgkUj6/R4QacvV5qH71G8WLGowudO/c989aTO+I1psIn3X1NSEnJwcbNq0CdHR0QAAV1dXBAcHq7RLTExEREQEACA9PR1eXl4oKyuDp6cnHBwckJiYqGy7dOlS5OfnIzc3t8eCZfr06YiLiwMAJCUlYePGjThy5IhaBcuhQ4dw69YtzJs3T9MuE4mqpaNV1ymIhgULEenM+fPnIZfLMWXKlB7b+fj4KH+2s7MDANTW1sLT0xMKhQIZGRnIzc1FVVUV2traIJfLIZPJ1I4pkUhga2uL2tpatfLesWMHpk2bBnt7e7XaE1H/aTyG5ejRo5gxYwbs7e0hkUhw6NChXtcpLCzEE088AalUCjc3N+zevbtLm82bN8PJyQmmpqYICgrCqVOnNE2NiAYZMzMztdrde4VP5ymYjo4OAMC6deuQk5ODpKQkHDlyBCUlJQgPD0dbW5vaMTvjdsbsyeXLl/HFF19g0aJFauVORNqhccHS0tICX19ftS/jq6ioQEREBEJDQ1FSUoL4+HgsWrQI+fn5yjYffPABEhISsHLlSnzzzTfw9fVFeHi42n/tENHg5O7uDjMzMxQUFPQ5xrFjxxAZGYk5c+bA19cXLi4uuHTpkhazVLVr1y6MGjVKeYqKiAaGxqeEpk2bhmnTpqndfuvWrXB2dsaGDRsAAI8++ii++uorbNy4EeHh4QCArKwsvPzyy5g/f75ynby8POzcuRPLly/XNEUiGiRMTU2RlJSEZcuWwcTEBJMmTUJdXR3Onj2LhQsXqhXD3d0dBw4cwPHjx2FlZYWsrCzU1NRg/PjxWs+3o6MDu3btQnR0NIyMeEadaCCJ/okrKipCWFiYyrzw8HDlJYZtbW04c+YMkpOTlcsNDAwQFhamcuniveRyOeRyuXK6sbFR+4kT0YBITU2FkZER0tLScO3aNdjZ2WHx4sVqr79ixQqUl5cjPDwcMpkMMTExmDlzJhoaGrSe6xdffIErV65gwYIFWo9NRD0TvWCprq6GjY2NyjwbGxs0Njbi559/xs2bN6FQKLptc/+ljZ3WrFmD9PR00XImGkr08c6z9zIwMEBKSgpSUlK6LHNycoIgCCrzhg8frjLP2tq617F0hYWFKtPd3f1Xndv/P/PMM13yIaKBMSiPaSYnJyMhIUE53djYiDFjxoi2vZaOn0WLbTw4dwER0ZB3srxe1yloTKoQ7zYcuib6t6WtrS1qampU5tXU1MDCwgJmZmYwNDSEoaFht21sbW27jSmVSiGVSkXL+X5Vt9W7kqEvnKS8DwsREVFvRL81/4QJE7pcAfD5559jwoQJAAATExP4+/urtOno6EBBQYGyDRERET3cND7C0tzcjLKyMuV0RUUFSkpKYG1tDUdHRyQnJ6Oqqgrvv/8+AGDx4sXYtGkTli1bhgULFuDf//43cnNzkZeXp4yRkJCA6OhoBAQEIDAwENnZ2WhpaVFeNURERDTQzGt4PzB9onHBcvr0aYSGhiqnO8eSREdHY/fu3bh+/TquXLmiXO7s7Iy8vDy8/vrryMnJwejRo/GXv/xFeUkzAMyaNQt1dXVIS0tDdXU1/Pz8cPjw4S4DcYeixo4WXadARESk9zQuWEJCQnocJd/dXWxDQkJQXFzcY9wlS5ZgyZIlmqYz6JndEWcszoFvvhQlLgD87gk+nZaIiAaW6GNYiIiIiPqL19QSERENMJM7Q/fyY7GwYBmimuprem9EREQ0SLBgISK9VVlZCWdnZxQXF8PPz6/PcUJCQuDn54fs7Gyt5UbUHz+2iHUvMXnvTQYpFixEQ9zNmwN7aaaVVeCAbk8dBw8ehLFx/w7BKxQKvPXWW/jb3/6G6upq2NvbY968eVixYgUkEomWMqWHxc/C0C0sxMKChYiGPGtr637HeOedd7Blyxa899578PLywunTpzF//nxYWlri1Vdf1UKWpG9uVbMQ1Se8SkjHqm6bifIiGiw6OjqQmZkJNzc3SKVSODo6YvXq1SptysvLERoaCplMBl9fX5UnudfX1yMqKgoODg6QyWTw9vbGvn37VNYPCQlRPiEeuPtQxYyMDCxYsADm5uZwdHTEtm3beszz+PHjiIyMREREBJycnPC73/0OzzzzDE6d4s3FiAYCj7AMUT+1tOk6BSK1JCcnY/v27di4cSOCg4Nx/fr1Lk9qT0lJwfr16+Hu7o6UlBRERUWhrKwMRkZGaG1thb+/P5KSkmBhYYG8vDzMnTsXrq6uCAx88OmpDRs2YNWqVXjzzTdx4MABxMbGYvLkyfDw8Oi2/cSJE7Ft2zZcunQJ48aNw3/+8x989dVXyMrK0ur7QfrjrCGv5NEnLFiISGeampqQk5ODTZs2ITo6GgDg6uqK4OBglXaJiYmIiIgAAKSnp8PLywtlZWXw9PSEg4MDEhMTlW2XLl2K/Px85Obm9liwTJ8+HXFxcQCApKQkbNy4EUeOHHlgwbJ8+XI0NjbC09MThoaGUCgUWL16NV588cV+vQekv27fuqHrFOgeLFiGKKPWn3SdAlGvzp8/D7lcjilTpvTYzsfHR/mznZ0dAKC2thaenp5QKBTIyMhAbm4uqqqq0NbWBrlcDplMpnZMiUQCW1tb1NbWPrB9bm4u9uzZg71798LLywslJSWIj4+Hvb29stgiIvGwYCEinTEzU2+81b1X+HRekdPR0QEAWLduHXJycpCdnQ1vb28MGzYM8fHxaGvr+bTo/VcNSSQSZczuvPHGG1i+fDlmz54NAPD29sbly5exZs0aFixEA4AFCxHpjLu7O8zMzFBQUIBFixb1KcaxY8cQGRmJOXPmALhbyFy6dAnjx4/XZqq4ffs2DAxUr1MwNDTsscihQc5ExBtwtnB8jKZYsBCRzpiamiIpKQnLli2DiYkJJk2ahLq6Opw9exYLFy5UK4a7uzsOHDiA48ePw8rKCllZWaipqdF6wTJjxgysXr0ajo6O8PLyQnFxMbKysrBgwQKtboeIuseChYh0KjU1FUZGRkhLS8O1a9dgZ2eHxYsXq73+ihUrUF5ejvDwcMhkMsTExGDmzJloaGjQap5/+tOfkJqairi4ONTW1sLe3h6///3vkZaWptXtEFH3JIIgCLpOor8aGxthaWmJhoYGWFhYaD3+61u2aD2m2Jys7ogW+7XZvEmWPmptbUVFRQWcnZ1hamqq63RIDdxn+i1n/7uixa68OfhOCW2MjdV6TE2+v3njOCIiItJ7LFiIiIhI77FgISIiIr3HgoWIiIj0HgsWIiIi0nssWIiIiEjv8T4sQ5TJncF3yRwREdGD8AgLERER6T0eYRmifmyR6joFIqJB7WqzmDfzU4gYe2jiERYi0luVlZWQSCQoKSnpV5yQkBDEx8drJSci0g0eYSEa4opuNQ/o9iYMf2RAt6eOgwcPwti4f+O6mpqakJqaio8//hi1tbV4/PHHkZOTgyeffFJLWRJRT1iwENGQZ21t3e8YixYtQmlpKf7617/C3t4ef/vb3xAWFoZz587BwcFBC1mSvmnpaBUtthS8MEJTPCVERDrV0dGBzMxMuLm5QSqVwtHREatXr1ZpU15ejtDQUMhkMvj6+qKoqEi5rL6+HlFRUXBwcIBMJoO3tzf27dunsv79p4ScnJyQkZGBBQsWwNzcHI6Ojti2bdsDc/z555/x0UcfITMzE7/61a/g5uaGt956C25ubtgyCB+OSjQYsWAhIp1KTk7G2rVrkZqainPnzmHv3r2wsbFRaZOSkoLExESUlJRg3LhxiIqKQnt7O4C7Tzz29/dHXl4eSktLERMTg7lz5+LUqVM9bnfDhg0ICAhAcXEx4uLiEBsbi4sXL3bbtr29HQqFossTlc3MzPDVV1/1o/dEpC6eEhqifhbkuk6BqFdNTU3IycnBpk2bEB0dDQBwdXVFcHCwSrvExEREREQAANLT0+Hl5YWysjJ4enrCwcEBiYmJyrZLly5Ffn4+cnNzERgY+MBtT58+HXFxcQCApKQkbNy4EUeOHIGHh0eXtubm5pgwYQJWrVqFRx99FDY2Nti3bx+Kiorg5ubW7/eB9JNUwdM2+oRHWIhIZ86fPw+5XI4pU6b02M7Hx0f5s52dHQCgtrYWAKBQKLBq1Sp4e3vD2toajzzyCPLz83HlyhW1Y0okEtja2ipjduevf/0rBEGAg4MDpFIp3n33XURFRcHAgL9GiQYCP2lEpDNmZmZqtbv3Ch+JRALg7tgXAFi3bh1ycnKQlJSEI0eOoKSkBOHh4Whra1M7ZmfczpjdcXV1xZdffonm5mb8+OOPOHXqFO7cuQMXFxe1+kBE/cOChYh0xt3dHWZmZigoKOhzjGPHjiEyMhJz5syBr68vXFxccOnSJS1mqWrYsGGws7PDzZs3kZ+fj8jISNG2RUT/xTEsRKQzpqamSEpKwrJly2BiYoJJkyahrq4OZ8+excKFC9WK4e7ujgMHDuD48eOwsrJCVlYWampqMH78eK3mmp+fD0EQ4OHhgbKyMrzxxhvw9PTE/PnztbodIuoeCxYi0qnU1FQYGRkhLS0N165dg52dHRYvXqz2+itWrEB5eTnCw8Mhk8kQExODmTNnoqGhQat5NjQ0IDk5GVevXoW1tTV++9vfYvXq1f2+IR0RqUciCIKg6yT6q7GxEZaWlmhoaICFhYXW47/O+yyo2Bgbq+sUqButra2oqKiAs7Nzl8tvST9xn+k3/u5XJcbvfk2+vzmGhYiIiPQeCxYiIiLSeyxYiIiISO/1qWDZvHkznJycYGpqiqCgoB5vgR0SEgKJRNLl1XnXSgCYN29el+VTp07tS2pEREQ0BGl8ldAHH3yAhIQEbN26FUFBQcjOzkZ4eDguXryIUaNGdWl/8OBBlRs41dfXw9fXF88//7xKu6lTp2LXrl3KaalUqmlqRERENERpfIQlKysLL7/8MubPn4/x48dj69atkMlk2LlzZ7ftra2tYWtrq3x9/vnnkMlkXQoWqVSq0s7KyqpvPSIiIqIhR6OCpa2tDWfOnEFYWNh/AxgYICwsTOVx7z3ZsWMHZs+ejWHDhqnMLywsxKhRo+Dh4YHY2FjU19c/MIZcLkdjY6PKi4iIiIYujQqWGzduQKFQdHn0u42NDaqrq3td/9SpUygtLcWiRYtU5k+dOhXvv/8+CgoK8M477+DLL7/EtGnToFAouo2zZs0aWFpaKl9jxozRpBtEREQ0yAzonW537NgBb2/vLo98nz17tvJnb29v+Pj4wNXVFYWFhd0+xTU5ORkJCQnK6cbGRhYtREREQ5hGR1hGjBgBQ0ND1NTUqMyvqamBra1tj+u2tLRg//79aj0fxMXFBSNGjEBZWVm3y6VSKSwsLFReRDT0VFZWQiKRoKSkpF9xQkJCEB8fr5WciEg3NDrCYmJiAn9/fxQUFGDmzJkA7j7ivaCgAEuWLOlx3Q8//BByuRxz5szpdTtXr15FfX097OzsNEmPiLpxsvzB48HEEOTyiwHdnjoOHjzY72f+HD16FOvWrcOZM2dw/fp1fPzxx8rfg50EQcDKlSuxfft23Lp1C5MmTcKWLVvg7u7er20TUR+uEkpISMD27dvx3nvv4fz584iNjUVLS4vyiaUvvfQSkpOTu6y3Y8cOzJw5E7/4heovs+bmZrzxxhs4ceIEKisrUVBQgMjISLi5uSE8PLyP3SIi+i9ra2uYm5v3K0ZLSwt8fX2xefPmB7bJzMzEu+++i61bt+LkyZMYNmwYwsPD0dra2q9tE1EfCpZZs2Zh/fr1SEtLg5+fH0pKSnD48GHlQNwrV67g+vXrKutcvHgRX331VbengwwNDfHtt9/iN7/5DcaNG4eFCxfC398f//d//8d7sRA9BDo6OpCZmQk3NzdIpVI4Ojpi9erVKm3Ky8sRGhoKmUwGX19flasS6+vrERUVBQcHB8hkMnh7e2Pfvn0q699/SsjJyQkZGRlYsGABzM3N4ejoiG3btvWY57Rp0/D222/j2Wef7Xa5IAjIzs7GihUrEBkZCR8fH7z//vu4du0aDh06pNmbQkRd9GnQ7ZIlSx54CqiwsLDLPA8PDzzoodBmZmbIz8/vSxpENAQkJydj+/bt2LhxI4KDg3H9+nVcuHBBpU1KSgrWr18Pd3d3pKSkICoqCmVlZTAyMkJrayv8/f2RlJQECwsL5OXlYe7cuXB1de0ywP9eGzZswKpVq/Dmm2/iwIEDiI2NxeTJk+Hh4dGnflRUVKC6ulrltg+WlpYICgpCUVGRysUFRKS5Ab1KiIjoXk1NTcjJycGmTZsQHR0NAHB1dUVwcLBKu8TEROXjPNLT0+Hl5YWysjJ4enrCwcEBiYmJyrZLly5Ffn4+cnNzeyxYpk+fjri4OABAUlISNm7ciCNHjvS5YOm8tUNfb/tARD1jwUJEOnP+/HnI5fJub19wLx8fH+XPnYPxa2tr4enpCYVCgYyMDOTm5qKqqgptbW2Qy+WQyWRqx5RIJLC1tUVtbW0/ekNEYuLTmolIZ8zMzNRqd+8VPhKJBMDdsS8AsG7dOuTk5CApKQlHjhxBSUkJwsPDVZ5h1lvMzridMfui89YOfbntAxH1jgULEemMu7s7zMzMUFBQ0OcYx44dQ2RkJObMmQNfX1+4uLjg0qVLWsxSPc7OzrC1tVXpS2NjI06ePIkJEyYMeD5EQw1PCZHG3j99XJS4LwVMFCUu6S9TU1MkJSVh2bJlMDExwaRJk1BXV4ezZ8+qdZNJ4G7Rc+DAARw/fhxWVlbIyspCTU0Nxo8fr9Vcm5ubVW5mWVFRgZKSElhbW8PR0RESiQTx8fF4++234e7uDmdnZ6SmpsLe3r7L/VpIu05Xn9Z1CjQAWLCQxozq+n7YnOh+qampMDIyQlpaGq5duwY7OzssXrxY7fVXrFiB8vJyhIeHQyaTISYmBjNnzkRDQ4NW8zx9+jRCQ0OV052PB4mOjsbu3bsBAMuWLUNLSwtiYmJw69YtBAcH4/DhwzA1NdVqLkQPI4nwoOuNB5HGxkZYWlqioaFBlNv0v75li9ZjDmZPOnmLEvd/pgX33ogeqLW1FRUVFXB2duYX5CDBfaYdYh31Lf76P6LEHaw2xsZqPaYm3988wkJERIMaj/o+HDjoloiIiPQeCxYiIiLSeyxYiIiISO9xDAtp7PaNel2nQESkxN9JDwcWLERENLi1/KTrDGgAsGAhjVUamOg6BSIieshwDAsRERHpPRYsREREpPdYsBCR3qqsrIREIkFJSUm/4oSEhCA+Pl4rORGRbnAMC2muVbvPaCGRVR4b2O05TRrY7anh4MGDMDY27leMo0ePYt26dThz5gyuX7+Ojz/+uMtDDQ8ePIitW7fizJkz+Omnn1BcXAw/P79+bZd6V2lsJk7gtlZx4lKf8AgLEQ151tbWMDc371eMlpYW+Pr6YvPmzT22CQ4OxjvvvNOvbRFRVyxYiEinOjo6kJmZCTc3N0ilUjg6OmL16tUqbcrLyxEaGgqZTAZfX18UFRUpl9XX1yMqKgoODg6QyWTw9vbGvn37VNa//5SQk5MTMjIysGDBApibm8PR0RHbtm3rMc9p06bh7bffxrPPPvvANnPnzkVaWhrCwsI0eAeISB0sWIhIp5KTk7F27Vqkpqbi3Llz2Lt3L2xsbFTapKSkIDExESUlJRg3bhyioqLQ3t4O4O4Tj/39/ZGXl4fS0lLExMRg7ty5OHXqVI/b3bBhAwICAlBcXIy4uDjExsbi4sWLovWTiPqHY1iISGeampqQk5ODTZs2ITo6GgDg6uqK4OBglXaJiYmIiIgAAKSnp8PLywtlZWXw9PSEg4MDEhMTlW2XLl2K/Px85ObmIjAw8IHbnj59OuLi4gAASUlJ2LhxI44cOQIPDw9td5OItIAFCxHpzPnz5yGXyzFlypQe2/n4+Ch/trOzAwDU1tbC09MTCoUCGRkZyM3NRVVVFdra2iCXyyGTydSOKZFIYGtri9ra2n70hojExIKFiHTGzEy9qzvuvcJHIpEAuDv2BQDWrVuHnJwcZGdnw9vbG8OGDUN8fDza2trUjtkZtzMmEekfjmEhIp1xd3eHmZkZCgoK+hzj2LFjiIyMxJw5c+Dr6wsXFxdcunRJi1kSkT7gERYi0hlTU1MkJSVh2bJlMDExwaRJk1BXV4ezZ89i4cKFasVwd3fHgQMHcPz4cVhZWSErKws1NTUYP368VnNtbm5GWVmZcrqiogIlJSWwtraGo6MjAOCnn37ClStXcO3aNQBQDuK1tbWFra2tVvMhetiwYCEinUpNTYWRkRHS0tJw7do12NnZYfHixWqvv2LFCpSXlyM8PBwymQwxMTGYOXMmGhq0e4PD06dPIzQ0VDmdkJAAAIiOjsbu3bsBAJ988gnmz5+vbDN79mwAwMqVK/HWW29pNR+ih41EEARB10n0V2NjIywtLdHQ0AALCwutx399yxatxxzMhplYiRL37YWzRYn7sGhtbUVFRQWcnZ1hamqq63RIDdxn2rFix35R4ra03RQl7mC1MTZW6zE1+f7mGBYiIiLSeyxYiIiISO+xYCEiIiK9x4KFiIiI9B4LFqIhZgiMo39ocF8RqY8FC9EQYWhoCAC93uGV9Efnvurcd0T0YLwPC2lMMLyl6xSoG0ZGRpDJZKirq4OxsTEMDPj3iD7r6OhAXV0dZDIZjIz4q5ioN/yUEA0REokEdnZ2qKiowOXLl3WdDqnBwMAAjo6OyucjUd/cblPoOgUaACxYSG/Iy7V7Z9J7SV0sRYutT0xMTODu7s7TQoOEiYkJj4QRqYkFC9EQY2BgwLumDnGVlZWixXZychIttlgkxrdEiSvcEa+YNJTfESWuQmrce6NBigULacyptVyUuF9fF+8IS/BDcoSFSF+JeQSVHg59Klg2b96MdevWobq6Gr6+vvjTn/6EwMDAbtvu3r1b5WFgACCVStHa2qqcFgQBK1euxPbt23Hr1i1MmjQJW7Zsgbu7e1/SI5Ep7ohzvv1K4xVR4t7lKGJsGsxuf/21aLFlTz4pWuzBZsfXx0SL3SHikRDSHxoXLB988AESEhKwdetWBAUFITs7G+Hh4bh48SJGjRrV7ToWFhbKx6wD6DLALDMzE++++y7ee+89ODs7IzU1FeHh4Th37hwPbeuhOx0duk5BY9dPfCRKXDtbW1HiAgCcJokXm2gIcWkT56hvuYmLKHGpbzQuWLKysvDyyy8rj5ps3boVeXl52LlzJ5YvX97tOhKJBLYP+MUuCAKys7OxYsUKREZGAgDef/992NjY4NChQ8rHs+uSWOcaAfHON4r1ARaT5FqNeMHFecA03UessRWj6upEiQsANyr+T7TYjjzCQgNsMP5BqS6NCpa2tjacOXMGycnJynkGBgYICwtDUVHRA9drbm7G2LFj0dHRgSeeeAIZGRnw8vICAFRUVKC6uhphYWHK9paWlggKCkJRUVG3BYtcLodcLldONzY2atINjY1prxAttnG7OKdX5IbiHSKVKgbfB+LOFZEu8xXzCItILh4+LFpss8Zz4gR2fkqcuCIT7XTTyJHixCUVYn7581aBmtOoYLlx4wYUCgVsbGxU5tvY2ODChQvdruPh4YGdO3fCx8cHDQ0NWL9+PSZOnIizZ89i9OjRqK6uVsa4P2bnsvutWbMG6enpmqT+0DFQiHlfAt4zYiCIVViIVlRQFwb134oTeOQUceJC3CuQBhvXNvH+WK2ScFydpkS/SmjChAmYMGGCcnrixIl49NFH8ec//xmrVq3qU8zk5GQkJCQopxsbGzFmzJh+50rquQNxnn8ysvVi7436ypxjoQYzMU/biKm2cfBdGSOtPiNKXMmN1t4b6RlR//AT6dvX4E67OIH1gEZv2YgRI2BoaIiaGtWxBjU1NQ8co3I/Y2NjPP744ygrKwMA5Xo1NTWws7NTienn59dtDKlUCqlUqknqNAg0i3qzM3EKlusPOAqoHcNEjE2DmfwBR7S1waBRnNOndm3inbr/kRcJKbm2V+o6BdFoVLCYmJjA398fBQUFmDlzJoC7z8MoKCjAkiVL1IqhUCjw3XffYfr06QAAZ2dn2NraoqCgQFmgNDY24uTJk4iNjdUkvUFJrKMVNPjx1A09CP9vqOoYhEcVXEQqLMS7RET3ND4olZCQgOjoaAQEBCAwMBDZ2dloaWlRXjX00ksvwcHBAWvWrAEA/PGPf8Qvf/lLuLm54datW1i3bh0uX76MRYsWAbh7BVF8fDzefvttuLu7Ky9rtre3VxZFRPpKtMG8RDSk8Y9VzWlcsMyaNQt1dXVIS0tDdXU1/Pz8cPjwYeWg2StXrqg8G+PmzZt4+eWXUV1dDSsrK/j7++P48eMYP368ss2yZcvQ0tKCmJgY3Lp1C8HBwTh8+DDvwUJEREQAAIkgCIO+zGtsbISlpSUaGhpgYWGh9fg561/XekzqaqyheLfPf8JB+/8viEh931SJN4blsmLwDW4ejF5L3Kj1mJp8f3OoEhEREek9FixERESk91iwEBERkd5jwUJERER6jwULERER6T0WLERERKT3WLAQERGR3mPBQkRERHqPBQsRERHpPRYsREREpPdYsBAREZHeY8FCREREeo8FCxEREek9FixERESk91iwEBERkd4z0nUCRANB0SxOXMNHxIlLpCs1t2tFimwqUlx6WLBgIb1RY2Si6xSIiEhPsWAhvdF+p0202P9pECf2E49YiBKXaKipunNHvOAc3PBQYMFC+qNdxF9oxsbixSYiItGxLiUiIiK9xyMsRESk9ONtsY5GdogUlx4WPMJCREREeo8FCxEREek9nhIiIiIlA7mhSJF5Soj6h0dYiIiISO+xYCEiIiK9x4KFiIiI9B4LFiIiItJ7LFiIiIhI77FgISIiIr3HgoWIiIj0HgsWIiIi0nssWIiIiEjvsWAhIiIivceChYiIiPQeCxYiIiLSeyxYiIiISO+xYCEiIiK9x4KFiIiI9F6fCpbNmzfDyckJpqamCAoKwqlTpx7Ydvv27XjqqadgZWUFKysrhIWFdWk/b948SCQSldfUqVP7khoR0ZBX3izei0hfGWm6wgcffICEhARs3boVQUFByM7ORnh4OC5evIhRo0Z1aV9YWIioqChMnDgRpqameOedd/DMM8/g7NmzcHBwULabOnUqdu3apZyWSqV97BLRwDl946ZosQNGWIkWm2ig3VF0iBZbwnMFDwWNC5asrCy8/PLLmD9/PgBg69atyMvLw86dO7F8+fIu7ffs2aMy/Ze//AUfffQRCgoK8NJLLynnS6VS2NraqpWDXC6HXC5XTjc2NmraDSKtMJAb6joFegj91CpeoWwA/p8m/aRRXdrW1oYzZ84gLCzsvwEMDBAWFoaioiK1Yty+fRt37tyBtbW1yvzCwkKMGjUKHh4eiI2NRX19/QNjrFmzBpaWlsrXmDFjNOkGEdGgZiA3FO1FpK80OsJy48YNKBQK2NjYqMy3sbHBhQsX1IqRlJQEe3t7laJn6tSpeO655+Ds7IwffvgBb775JqZNm4aioiIYGnb9ACUnJyMhIUE53djYyKJlCFAoRPxlaSxeaCLqndAh3udbIlpk0icanxLqj7Vr12L//v0oLCyEqampcv7s2bOVP3t7e8PHxweurq4oLCzElClTusSRSqUc4zIESUzEHPFnIWJsIiISm0anhEaMGAFDQ0PU1NSozK+pqel1/Mn69euxdu1a/Otf/4KPj0+PbV1cXDBixAiUlZVpkh4Nch2CINqLiIgGN40KFhMTE/j7+6OgoEA5r6OjAwUFBZgwYcID18vMzMSqVatw+PBhBAQE9Lqdq1evor6+HnZ2dpqkR0REREOUxheDJSQkYPv27Xjvvfdw/vx5xMbGoqWlRXnV0EsvvYTk5GRl+3feeQepqanYuXMnnJycUF1djerqajQ33z3839zcjDfeeAMnTpxAZWUlCgoKEBkZCTc3N4SHh2upm0RERDSYaTyGZdasWairq0NaWhqqq6vh5+eHw4cPKwfiXrlyBQYG/62DtmzZgra2Nvzud79TibNy5Uq89dZbMDQ0xLfffov33nsPt27dgr29PZ555hmsWrWK41SIiIYIA2mLrlOgQa5Pg26XLFmCJUuWdLussLBQZbqysrLHWGZmZsjPz+9LGkRERPSQGNCrhIh0pcbIRJS4Nu1tosQlIiJVvKExERER6T0WLERERKT3eEqIHg7trSIFZs1PQ0ybSINjedd/6icWLEREpFRjYiZOYEWTOHHpocE/D4mIiEjv8QgLPRTa7yjECWzMmp+IaCCwYCEiIiXRinvW9tRPLFiI9JRCpIdXGz4iTlzqqlzMB5ATPWRYsBARieSn1puixDXgJTf0EGLBQqSn/tPQKErcJx6xECUudWUgZ2FBpC08q0hERER6jwULERER6T0WLERERKT3WLAQERGR3mPBQkRERHqPBQsRERHpPRYsREREpPdYsBAREZHeY8FCREREeo93uiV6yNTcrhUtto1slGixiejhxoKFHgoKhUi3SDcWJywNnLI6QdcpEJEaWLAQPWSqbpqKFttGJlpoInrIsWChh4Kio0OkyBwGNtg1tjXpOgW9ckchzmdFwo8K9RMLFqJ+qBLxbIKDRLzYNMi1tYgYnF8LpJ/4P5MeCgZSkX7Bt4t4DsSYA2Soe1USExGji3U0kqh/WLAQEZGSxLhV1ykQdYsFCxFpzekbN0WJa21qJUpcIho8WLAQkdYYyMW5fPyWvFGUuEQ0eHDcNhEREek9FixERESk91iwEBERkd5jwUJERER6jwULERER6T0WLERERKT3eFkzUT+I9hRoAHfkt0SJa/zIcFHiUldVd+7oOgWiIYMFC1E/CMbiPTiv1nCYKHEdRIlKA0lh1Cxe8A4eeCf9xIKFiGiQEVhU0EOoT//rN2/eDCcnJ5iamiIoKAinTp3qsf2HH34IT09PmJqawtvbG59++qnKckEQkJaWBjs7O5iZmSEsLAzff/99X1IjIiKiIUjjguWDDz5AQkICVq5ciW+++Qa+vr4IDw9HbW1tt+2PHz+OqKgoLFy4EMXFxZg5cyZmzpyJ0tJSZZvMzEy8++672Lp1K06ePIlhw4YhPDwcra18CBcRietOa6toLyLSHokgCIImKwQFBeHJJ5/Epk2bAAAdHR0YM2YMli5diuXLl3dpP2vWLLS0tOCf//ynct4vf/lL+Pn5YevWrRAEAfb29vjDH/6AxMREAEBDQwNsbGywe/duzJ49u9ecGhsbYWlpiYaGBlhYWGjSHbXkrH9d6zGJemPUIdN1ChpzMDbWdQoaG4wDY9sNbus6BXoIvZa4UesxNfn+1mgMS1tbG86cOYPk5GTlPAMDA4SFhaGoqKjbdYqKipCQkKAyLzw8HIcOHQIAVFRUoLq6GmFhYcrllpaWCAoKQlFRUbcFi1wuh1wuV043NDQAuNtxMbS2yntvRKR14vy/MxSxECoT6bNiZCze1VjtdxSixVawsKAhRIzv2M6Y6hw70ahguXHjBhQKBWxsbFTm29jY4MKFC92uU11d3W376upq5fLOeQ9qc781a9YgPT29y/wxY8ao1xEiIiLSyPLULaLFbmpqgqWlZY9tBuVVQsnJySpHbTo6OvDTTz/hF7/4BSQSiVa31djYiDFjxuDHH38U5XSTrg31/gFDv4/s3+A31Ps41PsHDP0+itU/QRDQ1NQEe3v7XttqVLCMGDEChoaGqKmpUZlfU1MDW1vbbtextbXtsX3nvzU1NbCzs1Np4+fn121MqVQKqVSqMm/48OGadEVjFhYWQ/I/Yaeh3j9g6PeR/Rv8hnofh3r/gKHfRzH619uRlU4aXSVkYmICf39/FBQUKOd1dHSgoKAAEyZM6HadCRMmqLQHgM8//1zZ3tnZGba2tiptGhsbcfLkyQfGJCIiooeLxqeEEhISEB0djYCAAAQGBiI7OxstLS2YP38+AOCll16Cg4MD1qxZAwB47bXXMHnyZGzYsAERERHYv38/Tp8+jW3btgEAJBIJ4uPj8fbbb8Pd3R3Ozs5ITU2Fvb09Zs6cqb2eEhER0aClccEya9Ys1NXVIS0tDdXV1fDz88Phw4eVg2avXLkCA4P/HriZOHEi9u7dixUrVuDNN9+Eu7s7Dh06hMcee0zZZtmyZWhpaUFMTAxu3bqF4OBgHD58GKamplroYv9IpVKsXLmyyymooWKo9w8Y+n1k/wa/od7Hod4/YOj3UR/6p/F9WIiIiIgGGh9IQURERHqPBQsRERHpPRYsREREpPdYsBAREZHeY8FCREREeu+hL1hWr16NiRMnQiaTqX23XEEQkJaWBjs7O5iZmSEsLAzff/+9SpuffvoJL774IiwsLDB8+HAsXLgQzc3NIvSgd5rmUllZCYlE0u3rww8/VLbrbvn+/fsHoksq+vJeh4SEdMl98eLFKm2uXLmCiIgIyGQyjBo1Cm+88Qba29vF7Eq3NO3fTz/9hKVLl8LDwwNmZmZwdHTEq6++qnxIaCdd7r/NmzfDyckJpqamCAoKwqlTp3ps/+GHH8LT0xOmpqbw9vbGp59+qrJcnc/kQNKkf9u3b8dTTz0FKysrWFlZISwsrEv7efPmddlXU6dOFbsbPdKkj7t37+6S//23rRjM+7C73ycSiQQRERHKNvq0D48ePYoZM2bA3t4eEolE+TDinhQWFuKJJ56AVCqFm5sbdu/e3aWNpp9rjQkPubS0NCErK0tISEgQLC0t1Vpn7dq1gqWlpXDo0CHhP//5j/Cb3/xGcHZ2Fn7++Wdlm6lTpwq+vr7CiRMnhP/7v/8T3NzchKioKJF60TNNc2lvbxeuX7+u8kpPTxceeeQRoampSdkOgLBr1y6Vdve+BwOlL+/15MmThZdfflkl94aGBuXy9vZ24bHHHhPCwsKE4uJi4dNPPxVGjBghJCcni92dLjTt33fffSc899xzwieffCKUlZUJBQUFgru7u/Db3/5WpZ2u9t/+/fsFExMTYefOncLZs2eFl19+WRg+fLhQU1PTbftjx44JhoaGQmZmpnDu3DlhxYoVgrGxsfDdd98p26jzmRwomvbvf/7nf4TNmzcLxcXFwvnz54V58+YJlpaWwtWrV5VtoqOjhalTp6rsq59++mmgutSFpn3ctWuXYGFhoZJ/dXW1SpvBvA/r6+tV+lZaWioYGhoKu3btUrbRp3346aefCikpKcLBgwcFAMLHH3/cY/vy8nJBJpMJCQkJwrlz54Q//elPgqGhoXD48GFlG03fs7546AuWTrt27VKrYOno6BBsbW2FdevWKefdunVLkEqlwr59+wRBEIRz584JAISvv/5a2eazzz4TJBKJUFVVpfXce6KtXPz8/IQFCxaozFPnP7rY+tq/yZMnC6+99toDl3/66aeCgYGByi/VLVu2CBYWFoJcLtdK7urQ1v7Lzc0VTExMhDt37ijn6Wr/BQYGCq+88opyWqFQCPb29sKaNWu6bf/CCy8IERERKvOCgoKE3//+94IgqPeZHEia9u9+7e3tgrm5ufDee+8p50VHRwuRkZHaTrXPNO1jb79fh9o+3Lhxo2Bubi40Nzcr5+nbPuykzu+BZcuWCV5eXirzZs2aJYSHhyun+/ueqeOhPyWkqYqKClRXVyMsLEw5z9LSEkFBQSgqKgIAFBUVYfjw4QgICFC2CQsLg4GBAU6ePDmg+WojlzNnzqCkpAQLFy7ssuyVV17BiBEjEBgYiJ07d0IY4PsQ9qd/e/bswYgRI/DYY48hOTkZt2/fVonr7e2tvIMzAISHh6OxsRFnz57VfkceQFv/lxoaGmBhYQEjI9WbWw/0/mtra8OZM2dUPj8GBgYICwtTfn7uV1RUpNIeuLsvOtur85kcKH3p3/1u376NO3fuwNraWmV+YWEhRo0aBQ8PD8TGxqK+vl6ruaurr31sbm7G2LFjMWbMGERGRqp8jobaPtyxYwdmz56NYcOGqczXl32oqd4+g9p4z9Sh8a35H3bV1dUAoPJF1jnduay6uhqjRo1SWW5kZARra2tlm4GijVx27NiBRx99FBMnTlSZ/8c//hG//vWvIZPJ8K9//QtxcXFobm7Gq6++qrX8e9PX/v3P//wPxo4dC3t7e3z77bdISkrCxYsXcfDgQWXc7vZx57KBoo39d+PGDaxatQoxMTEq83Wx/27cuAGFQtHte3vhwoVu13nQvrj389Y570FtBkpf+ne/pKQk2Nvbq/zynzp1Kp577jk4Ozvjhx9+wJtvvolp06ahqKgIhoaGWu1Db/rSRw8PD+zcuRM+Pj5oaGjA+vXrMXHiRJw9exajR48eUvvw1KlTKC0txY4dO1Tm69M+1NSDPoONjY34+eefcfPmzX7/v1fHkCxYli9fjnfeeafHNufPn4enp+cAZaR96vaxv37++Wfs3bsXqampXZbdO+/xxx9HS0sL1q1bp5UvPLH7d++Xt7e3N+zs7DBlyhT88MMPcHV17XNcdQ3U/mtsbERERATGjx+Pt956S2WZmPuP+mbt2rXYv38/CgsLVQalzp49W/mzt7c3fHx84OrqisLCQkyZMkUXqWpkwoQJmDBhgnJ64sSJePTRR/HnP/8Zq1at0mFm2rdjxw54e3sjMDBQZf5g34f6YEgWLH/4wx8wb968Htu4uLj0KbatrS0AoKamBnZ2dsr5NTU18PPzU7apra1VWa+9vR0//fSTcv3+UreP/c3lwIEDuH37Nl566aVe2wYFBWHVqlWQy+X9fkDWQPWvU1BQEACgrKwMrq6usLW17TLCvaamBgC0sg8Hon9NTU2YOnUqzM3N8fHHH8PY2LjH9trcfw8yYsQIGBoaKt/LTjU1NQ/sj62tbY/t1flMDpS+9K/T+vXrsXbtWnzxxRfw8fHpsa2LiwtGjBiBsrKyAf+y608fOxkbG+Pxxx9HWVkZgKGzD1taWrB//3788Y9/7HU7utyHmnrQZ9DCwgJmZmYwNDTs9/8JtWhtNMwgp+mg2/Xr1yvnNTQ0dDvo9vTp08o2+fn5Oh1029dcJk+e3OXqkgd5++23BSsrqz7n2hfaeq+/+uorAYDwn//8RxCE/w66vXeE+5///GfBwsJCaG1t1V4HetHX/jU0NAi//OUvhcmTJwstLS1qbWug9l9gYKCwZMkS5bRCoRAcHBx6HHT7//7f/1OZN2HChC6Dbnv6TA4kTfsnCILwzjvvCBYWFkJRUZFa2/jxxx8FiUQi/P3vf+93vn3Rlz7eq729XfDw8BBef/11QRCGxj4UhLvfI1KpVLhx40av29D1PuwENQfdPvbYYyrzoqKiugy67c//CbVy1VqkQery5ctCcXGx8rLd4uJiobi4WOXyXQ8PD+HgwYPK6bVr1wrDhw8X/v73vwvffvutEBkZ2e1lzY8//rhw8uRJ4auvvhLc3d11ellzT7lcvXpV8PDwEE6ePKmy3vfffy9IJBLhs88+6xLzk08+EbZv3y589913wvfffy/87//+ryCTyYS0tDTR+3M/TftXVlYm/PGPfxROnz4tVFRUCH//+98FFxcX4Ve/+pVync7Lmp955hmhpKREOHz4sDBy5EidXdasSf8aGhqEoKAgwdvbWygrK1O5jLK9vV0QBN3uv/379wtSqVTYvXu3cO7cOSEmJkYYPny48oqsuXPnCsuXL1e2P3bsmGBkZCSsX79eOH/+vLBy5cpuL2vu7TM5UDTt39q1awUTExPhwIEDKvuq83dQU1OTkJiYKBQVFQkVFRXCF198ITzxxBOCu7v7gBbP/eljenq6kJ+fL/zwww/CmTNnhNmzZwumpqbC2bNnlW0G8z7sFBwcLMyaNavLfH3bh01NTcrvOgBCVlaWUFxcLFy+fFkQBEFYvny5MHfuXGX7zsua33jjDeH8+fPC5s2bu72suaf3TBse+oIlOjpaANDldeTIEWUb/P/3q+jU0dEhpKamCjY2NoJUKhWmTJkiXLx4USVufX29EBUVJTzyyCOChYWFMH/+fJUiaCD1lktFRUWXPguCICQnJwtjxowRFApFl5ifffaZ4OfnJzzyyCPCsGHDBF9fX2Hr1q3dthWbpv27cuWK8Ktf/UqwtrYWpFKp4ObmJrzxxhsq92ERBEGorKwUpk2bJpiZmQkjRowQ/vCHP6hcFjxQNO3fkSNHuv0/DUCoqKgQBEH3++9Pf/qT4OjoKJiYmAiBgYHCiRMnlMsmT54sREdHq7TPzc0Vxo0bJ5iYmAheXl5CXl6eynJ1PpMDSZP+jR07ttt9tXLlSkEQBOH27dvCM888I4wcOVIwNjYWxo4dK7z88sta/SLoC036GB8fr2xrY2MjTJ8+Xfjmm29U4g3mfSgIgnDhwgUBgPCvf/2rSyx924cP+h3R2afo6Ghh8uTJXdbx8/MTTExMBBcXF5XvxE49vWfaIBGEAb4OlYiIiEhDvA8LERER6T0WLERERKT3WLAQERGR3mPBQkRERHqPBQsRERHpPRYsREREpPdYsBAREZHeY8FCREREeo8FCxEREek9FixERESk91iwEBERkd77/wB6KlWZ9GdKuQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plots all chains, also the tempered ones\n",
    "plt.figure()\n",
    "plt.title(\"All chains\")\n",
    "for i in range(samples.shape[0]):\n",
    "    plt.hist(\n",
    "        samples[i, :, 0], density=True, alpha=0.245, bins=20, label=f\"chain {i}\"\n",
    "    )\n",
    "plt.legend()\n",
    "# DO not check convergence on all chain samples. It does not make sense, since they sampled different distributions.\n",
    "# Instead, fetch all samples for a certain temp for convergence checking & plotting\n",
    "\n",
    "# Fetches and plots the chains with the highest temperature (beta=0):\n",
    "high_temp_samples = hopsy.get_samples_with_temperature(\n",
    "    0, temperature_ladder, samples\n",
    ")\n",
    "print(\"convergence check for hot samples (rhat<1.01 & ess > 400 means converged)\")\n",
    "print(\n",
    "    \"min ess\",\n",
    "    np.min(hopsy.ess(high_temp_samples)),\n",
    "    \"rhat: \",\n",
    "    np.max(hopsy.rhat(high_temp_samples)),\n",
    ")\n",
    "\n",
    "plt.figure()\n",
    "plt.title(\"High temp samples (should look uniform)\")\n",
    "for i in range(high_temp_samples.shape[0]):\n",
    "    plt.hist(\n",
    "        high_temp_samples[i, :, 0],\n",
    "        density=True,\n",
    "        alpha=0.245,\n",
    "        bins=20,\n",
    "        label=f\"chain {i}\",\n",
    "    )\n",
    "plt.legend()\n",
    "\n",
    "# Fetchs and plots the chains with the colds temperature (beta=1):\n",
    "cold_temp_samples = hopsy.get_samples_with_temperature(\n",
    "    1, temperature_ladder, samples\n",
    ")\n",
    "print(\"convergence check for cold samples (rhat<1.01 & ess > 400 means converged)\")\n",
    "print(\n",
    "    \"min ess:\",\n",
    "    np.min(hopsy.ess(cold_temp_samples)),\n",
    "    \", rhat: \",\n",
    "    np.max(hopsy.rhat(cold_temp_samples)),\n",
    ")\n",
    "plt.figure()\n",
    "plt.title(\"Low temp samples (original posterior)\")\n",
    "for i in range(cold_temp_samples.shape[0]):\n",
    "    plt.hist(\n",
    "        cold_temp_samples[i, :, 0],\n",
    "        density=True,\n",
    "        alpha=0.245,\n",
    "        bins=20,\n",
    "        label=f\"chain {i}\",\n",
    "    )\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d2c7ebd1-e748-43ce-a6fa-799db23ff529",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c5d3bbd5-02f5-4f94-bcb8-0ab6de2c7be0",
   "metadata": {},
   "outputs": [],
   "source": [
    "    "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}