{ "cells": [ { "cell_type": "markdown", "id": "c477b5c3", "metadata": {}, "source": [ "# Neural Jastrow\n", "\n", "In this tutorial, we use neural networks as generalized Jastrow factors to study the Heisenberg J1-J2 model.\n", "\n", "Reference:\n", "\n", "[Y. Normura, et al., Restricted Boltzmann machine learning for solving strongly correlated quantum systems, Phys. Rev. B 96, 205152 (2017).](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.96.205152)\n", "\n", "[Y. Normura and M. Imada, Dirac-Type Nodal Spin Liquid Revealed by Refined Quantum Many-Body Solver Using Neural-Network Wave Function, Correlation Ratio, and Level Spectroscopy, Phys. Rev. X 11, 031034 (2021).](https://journals.aps.org/prx/abstract/10.1103/PhysRevX.11.031034)" ] }, { "cell_type": "code", "execution_count": null, "id": "f894e8f8", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import jax.numpy as jnp\n", "import equinox as eqx\n", "import quantax as qtx\n", "from IPython.display import clear_output\n", "\n", "lattice = qtx.sites.Square(4, Nparticles=(8, 8))\n", "N = lattice.Nsites" ] }, { "cell_type": "markdown", "id": "d5be1b4d", "metadata": {}, "source": [ "The Hamiltonian is\n", "\n", "$$\n", "H = J_1 \\sum_{\\braket{ij}} \\mathbf{\\sigma}_i \\cdot \\mathbf{\\sigma}_j\n", "+ J_2 \\sum_{\\braket{\\braket{ij}}} \\mathbf{\\sigma}_i \\cdot \\mathbf{\\sigma}_j,\n", "$$\n", "\n", "where $\\braket{ij}$ and $\\braket{\\braket{ij}}$ represent nearest and next-nearest neighbors, respectively. " ] }, { "cell_type": "code", "execution_count": 15, "id": "bdbad6ca", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Exact ground state energy: -33.83169340557937\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/home/aochen/quantax_env/lib/python3.12/site-packages/quantax/symmetry/symmetry.py:288: GeneralBasisWarning: using non-commuting symmetries can lead to unwanted behaviour of general basis, make sure that quantum numbers are invariant under non-commuting symmetries!\n", " basis = spin_basis_general(\n" ] } ], "source": [ "from quantax.symmetry import Identity, TransND, C4v, SpinInverse\n", "\n", "H = qtx.operator.Heisenberg(J=[1, 0.5], n_neighbor=[1, 2])\n", "\n", "full_symm = TransND() @ C4v() @ SpinInverse()\n", "E, psi = H.diagonalize(symm=full_symm)\n", "exact_energy = E[0]\n", "exact_state = qtx.state.DenseState(psi, full_symm)\n", "print(\"Exact ground state energy:\", exact_energy)" ] }, { "cell_type": "markdown", "id": "0a3725b8", "metadata": {}, "source": [ "## Gutzwiller-projected fermionic wavefunction\n", "\n", "The Hamiltonian in spin degrees of freedom can be mapped to fermion ones by\n", "\n", "$$\n", "S^\\alpha = \\frac{1}{2} (c_\\uparrow^\\dagger, c_\\downarrow^\\dagger) \\sigma^\\alpha\n", "\\begin{pmatrix} c_\\uparrow \\\\ c_\\downarrow \\end{pmatrix},\n", "$$\n", "\n", "where $\\alpha = x,y,z$ and $\\sigma^\\alpha$ are Pauli matrices. Quantax utilizes this relation internally such that the mean-field state can be optimized in spin systems.\n", "\n", "A fermionic wavefunction $\\ket{\\psi_0}$ contains redundancy of zero occupancy and double occupancy when it is used for spin systems. Therefore, one needs a Gutzwiller projection to obtain\n", "\n", "$$\n", "\\ket{\\psi_G} = \\hat P_G \\ket{\\psi_0},\n", "$$\n", "\n", "where $\\hat P_G = \\prod_i (n_{i\\uparrow} - n_{i\\downarrow})^2$ projects the state to spin degrees of freedom. In variational Monte Carlo, this is done by sampling suitable sectors instead of modifying the mean-field state.\n", "\n", "Here we show how to optimize the Gutzwiller-projected fermionic mean-field wavefunction. {py:class}`~quantax.state.GeneralPfState` is a subclass of {py:class}`~quantax.state.Variational`, so one can train it directly with {py:class}`~quantax.optimizer.SR`." ] }, { "cell_type": "code", "execution_count": 3, "id": "9a20bd9c", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "state = qtx.state.GeneralPfState(max_parallel=32768)\n", "sampler = qtx.sampler.SpinExchange(state, 1024, n_neighbor=[1, 2])\n", "optimizer = qtx.optimizer.SR(state, H)\n", "\n", "energy = qtx.utils.DataTracer()\n", "VarE = qtx.utils.DataTracer()\n", "\n", "for i in range(500):\n", " samples = sampler.sweep()\n", " step = optimizer.get_step(samples)\n", " state.update(step * 1e-3)\n", "\n", " energy.append(optimizer.energy)\n", " VarE.append(optimizer.VarE)\n", "\n", "energy.plot(batch=10, baseline=exact_energy)\n", "plt.xlabel(\"Iteration\")\n", "plt.ylabel(\"Energy\")\n", "plt.show()\n", "VarE.plot(batch=10)\n", "plt.xlabel(\"Iteration\")\n", "plt.ylabel(\"Energy variance\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "d4acb9eb", "metadata": {}, "source": [ "## Neural Jastrow factor\n", "\n", "The neural Jastrow factor modifies an existing wavefunction by utilizing a neural network. The new wavefunction is given by\n", "\n", "$$\n", "\\psi(s) = J(s) \\psi_G(s),\n", "$$\n", "\n", "where $J(s)$ is the neural Jastrow factor, and $\\psi_G(s)$ is the original Gutzwiller-projected fermionic wavefunction.\n", "\n", "We can take the pre-trained Pfaffian state as a good initialization." ] }, { "cell_type": "code", "execution_count": 4, "id": "47ec4e5a", "metadata": {}, "outputs": [], "source": [ "pf_model = state.model" ] }, { "cell_type": "markdown", "id": "659964e1", "metadata": {}, "source": [ "We still utilize {py:class}`~quantax.model.ResConv` as the neural network. `trans_symm=Identity()` means network output is not summed in the last layer, so the output is a matrix $\\mathbf{J}(s)$. Then we define {py:class}`~quantax.model.NeuralJastrow` with `trans_symm=TransND()`, which means the output is\n", "\n", "$$\n", "\\psi(s) = \\sum_i^{L_x} \\sum_j^{L_y} \\mathbf{J}_{ij}(s) \\psi_G(T_{ij}s),\n", "$$\n", "\n", "where $T_{ij}s$ is a translation of the original input $s$. One can view this formula as a translation symmetrized form of $\\psi(s) = J(s) \\psi_G(s)$." ] }, { "cell_type": "code", "execution_count": null, "id": "e29a6dd3", "metadata": {}, "outputs": [], "source": [ "net = qtx.model.ResConv(nblocks=2, channels=8, kernel_size=3, trans_symm=Identity())\n", "model = qtx.model.NeuralJastrow(net, pf_model, trans_symm=TransND())" ] }, { "cell_type": "markdown", "id": "42b527c9", "metadata": {}, "source": [ "Then one can perform the usual SR optimization on this wavefunction." ] }, { "cell_type": "code", "execution_count": 11, "id": "702c778f", "metadata": {}, "outputs": [], "source": [ "state = qtx.state.Variational(model, max_parallel=16384)\n", "\n", "sampler = qtx.sampler.SpinExchange(state, 1024, n_neighbor=[1, 2])\n", "optimizer = qtx.optimizer.SR(state, H)" ] }, { "cell_type": "code", "execution_count": 12, "id": "01389040", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "energy = qtx.utils.DataTracer()\n", "VarE = qtx.utils.DataTracer()\n", "\n", "for i in range(500):\n", " samples = sampler.sweep()\n", " step = optimizer.get_step(samples)\n", " state.update(step * 2e-3)\n", "\n", " energy.append(optimizer.energy)\n", " VarE.append(optimizer.VarE)\n", "\n", " if i % 10 == 0:\n", " clear_output()\n", " energy.plot(batch=10, baseline=exact_energy)\n", " plt.xlabel(\"Iteration\")\n", " plt.ylabel(\"Energy\")\n", " plt.show()\n", " VarE.plot(batch=10)\n", " plt.xlabel(\"Iteration\")\n", " plt.ylabel(\"Energy variance\")\n", " plt.show()\n", "\n", "state.save(\"/tmp/neural_jastrow.eqx\")" ] }, { "cell_type": "markdown", "id": "aaf73158", "metadata": {}, "source": [ "This state can also be symmetrized to achieve better accuracy" ] }, { "cell_type": "code", "execution_count": null, "id": "b5dbd83d", "metadata": {}, "outputs": [], "source": [ "symm = C4v() @ SpinInverse()\n", "state = qtx.state.Variational(\n", " model, param_file=\"/tmp/neural_jastrow.eqx\", symm=symm, max_parallel=2048\n", ")\n", "\n", "sampler = qtx.sampler.SpinExchange(state, 1024, n_neighbor=[1, 2])\n", "optimizer = qtx.optimizer.SR(state, H)" ] }, { "cell_type": "code", "execution_count": 14, "id": "6ae3fc8f", "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAlQAAAGwCAYAAABvpfsgAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjcsIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvTLEjVAAAAAlwSFlzAAAPYQAAD2EBqD+naQAAXjlJREFUeJzt3Xlc1NX+P/DX7MM6IDvKIi6A+25oZqSltmiLN7OSNMsWvd2yumrZtfzdm0vL7d7WW5Faaje/V8vK3Mql3BBEXAEVF5BdkGGHYebz+wNmFFkEZvnMDK/n4zGPYObMZ94fBplX55zPORJBEAQQERERUYdJxS6AiIiIyNExUBERERGZiYGKiIiIyEwMVERERERmYqAiIiIiMhMDFREREZGZGKiIiIiIzCQXu4DOwmAwICcnBx4eHpBIJGKXQ0RERG0gCALKysoQHBwMqbTlfigGKhvJyclBSEiI2GUQERFRB2RlZaFbt24tPs5AZSMeHh4A6t8QT09PkashIiKitigtLUVISIjpc7wlDFQ2Yhzm8/T0ZKAiIiJyMDebrsNJ6URERERmYqAiIiIiMhMDFREREZGZGKiIiIiIzMRARURERGQmBioiIiIiMzFQEREREZmJgYqIiIjITAxURERERGZioCIiIiIyEwMVERERkZkYqIiIiIjMxEDl4Cpq6nAyWyt2GURERJ0aA5UDK6vWod+b23Hvh/tQWq0TuxwiIqJOi4HKgXmoFQj0VAMAzuSViVwNERFR58VA5eCiAj0AAKkMVERERKJhoHJwUUGeAIC03FKRKyEiIuq8GKgcnLGHKp09VERERKJhoHJwUYENPVR5ZRAEQeRqiIiIOicGKgcX4ecGhUyC8po6XL5aJXY5REREnZLDBKrJkycjNDQUarUaQUFBmDFjBnJyckyPp6enIzY2FgEBAVCr1YiIiMDixYuh07W8nMDq1ashkUiavRUUFJjaffzxx4iOjoaLiwsiIyPx9ddfW/Vc20Mhk6KHnzsADvsRERGJRS52AW0VGxuL1157DUFBQcjOzsYrr7yCqVOn4sCBAwAAhUKBuLg4DBkyBF5eXjh27BiefvppGAwGvP32280ec9q0aZg4cWKj+2bOnInq6mr4+/sDAD799FMsWrQIX3zxBYYPH47Dhw/j6aefhre3N+677z7rnnQbRQd5Ii2vDGl5pRjfJ0DscoiIiDodhwlUL730kunrsLAwLFy4EPfffz90Oh0UCgUiIiIQERHRqM2ePXvwxx9/tHhMFxcXuLi4mL4vLCzErl27EB8fb7rvm2++wTPPPINp06YBACIiIpCYmIgVK1a0GqhqampQU1Nj+r601HpX4XHpBCIiInE5zJDf9YqLi7Fu3TqMGjUKCoWi2Tbnzp3Dtm3bMHbs2DYf9+uvv4arqyumTp1quq+mpgZqtbpROxcXFxw+fLjV4cRly5ZBo9GYbiEhIW2uo70ieaUfERGRqBwqUC1YsABubm7w8fFBZmYmNm/e3KTNqFGjoFar0atXL4wZMwZLly5t8/Hj4+Px6KOPNuq1mjBhAr788kscOXIEgiAgKSkJX375JXQ6Ha5cudLisRYtWgStVmu6ZWVlte9k2yG6YS2q84XlqNbprfY6RERE1DxRA9XChQtbnBRuvKWlpZnav/rqqzh69Ch27NgBmUyGuLi4JksFfPfdd0hOTsb69euxZcsWvPvuu22q5eDBg0hNTcXs2bMb3f/GG29g0qRJuOWWW6BQKDBlyhQ88cQTAACptOUfn0qlgqenZ6Obtfh7qODtqoBBAM4VlFvtdYiIiKh5EkHExYsKCwtRVFTUapuIiAgolcom91++fBkhISE4cOAAYmJimn3u2rVrMWfOHJSVlUEmk7X6OrNnz0ZycjKOHj3a7OM6nQ75+fkICgrC559/jgULFqCkpKTVUHW90tJSaDQaaLVaq4SrRz4/iEPni/HunwZi6tBuFj8+ERFRZ9TWz29RJ6X7+fnBz8+vQ881GAwA0Gjid3NtdDodDAZDq4GqvLwcGzZswLJly1pso1Ao0K1bfVD573//i3vvvbfNYcoWogI9ceh8MbegISIiEoFDXOWXkJCAxMRE3HrrrfD29kZGRgbeeOMN9OjRw9Q7tW7dOigUCvTv3x8qlQpJSUlYtGgRpk2bZpq4/v3332PRokWNhhGB+mHCuro6PP74401e+8yZMzh8+DBGjhyJq1ev4v3338fJkyexZs0a6594O0QH1U9MT+PEdCIiIptziEDl6uqKTZs2YcmSJaioqEBQUBAmTpyIxYsXQ6VSAQDkcjlWrFiBM2fOQBAEhIWFYd68eY2WW9BqtUhPT29y/Pj4eDz44IPw8vJq8pher8d7772H9PR0KBQKxMbG4sCBAwgPD7fW6XZI5HVb0BAREZFtiTqHqjOx9hyqyto69F2yHYIAJL4+Hn4eKou/BhERUWfT1s9v+5kERGZxVcoR7uMGgOtRERER2RoDlROJDDDOo+LEdCIiIltioHIiUZyYTkREJAoGKicSZZqYzh4qIiIiW2KgciLGTZLP5pejTm8QuRoiIqLOg4HKiYR2cYWLQoaaOgMuFlWKXQ4REVGnwUDlRKRSCSIDOTGdiIjI1hionIxx2I9LJxAREdkOA5WTMQaq1FwGKiIiIlthoHIyUUG80o+IiMjWGKicjLGH6vLVKpRV60SuhoiIqHNgoHIyXq5KBHqqAQBn8jnsR0REZAsMVE7IuGI651ERERHZBgOVE4rklX5EREQ2xUDlhKK5BQ0REZFNMVA5oes3SRYEQeRqiIiInB8DlROK8HWHXCpBWXUdcrTVYpdDRETk9BionJBSLkVPf3cAQFouh/2IiIisjYHKSUUFXhv2IyIiIutioHJSkaaJ6QxURERE1sZA5aRME9M55EdERGR1DFROyrh0wvkrFaip04tcDRERkXNjoHJSAZ4qaFwU0BsEnCsoF7scIiIip8ZA5aQkEsm1iencgoaIiMiqGKicWHQQV0wnIiKyBQYqJxbJpROIiIhsgoHKiXEtKiIiIttgoHJivQM8IJEAhWU1KCqvEbscIiIip8VA5cTcVHKEdnEFAKSzl4qIiMhqGKicnHHYL5WBioiIyGoYqJxclHELGq6YTkREZDUMVE7O2EOVns8eKiIiImthoHJyUQ1rUaXnlUFvEESuhoiIyDkxUDm50C6ucFHIUFNnwMWiCrHLISIickoMVE5OJpWgd4A7AF7pR0REZC0MVJ0AJ6YTERFZFwNVJxAVxKUTiIiIrImBqhMw7unHIT8iIiLrYKDqBIxDfpnFlSivqRO5GiIiIufDQNUJdHFTIsBTBYC9VERERNbAQNVJRAZeW4+KiIiILIuBqpOIbphHlZbHK/2IiIgsjYGqkzBe6ZeWyx4qIiIiS2Og6iQiA+qH/FLzSiEI3IKGiIjIkhioOoke/m6QSyUoq65DrrZa7HKIiIicCgNVJ6GSy9DDr34LGs6jIiIisiwGqk7EuMBnKudRERERWRQDVSdinJjOpROIiIgsi4GqE4k2bpLMIT8iIiKLYqDqRIxDfhmFFaip04tcDRERkfNgoOpEgjRqeKrl0BsEZBRUiF0OERGR02Cg6kQkEgmigjjsR0REZGkMVJ1MlGkLGk5MJyIishQGqk4myjQxnYGKiIjIUhioOplre/pxyI+IiMhSGKg6md4B9YGqoKwGxRW1IldDRETkHBioOhl3lRyhXVwBcGI6ERGRpTBQdUKmiencgoaIiMgiGKg6oWtX+rGHioiIyBIYqDoh41pU3NOPiIjIMhioOiFjD1V6fhn0BkHkaoiIiBwfA1UnFObjBrVCimqdAZeKuAUNERGRuRioOiGZVGJaPoHDfkREROZjoOqkjMN+qQxUREREZmOg6qRMW9BwxXQiIiKzMVB1UtdPTCciIiLzMFB1UpENgepSUSUqaupEroaIiMixOUygmjx5MkJDQ6FWqxEUFIQZM2YgJyfH9Hh6ejpiY2MREBAAtVqNiIgILF68GDqdrtXjJiYmYty4cfDy8oK3tzcmTJiAY8eONWpz/PhxjBkzBmq1GiEhIVi5cqVVztGWfNxV8PdQAWAvFRERkbkcJlDFxsZiw4YNSE9Px8aNG5GRkYGpU6eaHlcoFIiLi8OOHTuQnp6ODz74AF988QWWLFnS4jHLy8sxceJEhIaGIiEhAfv27YOHhwcmTJhgCmKlpaW46667EBYWhiNHjuCdd97Bm2++ic8//9zq52xtxl4qXulHRERkHokgCA65suOPP/6I+++/HzU1NVAoFM22mT9/PhITE/HHH380+3hSUhKGDx+OzMxMhISEAABOnDiBAQMG4OzZs+jZsyc+/fRTvP7668jLy4NSqQQALFy4ED/88APS0tLaXG9paSk0Gg20Wi08PT3bebbW8fYvqfj89/N4IiYMb03pJ3Y5REREdqetn98O00N1veLiYqxbtw6jRo1qMUydO3cO27Ztw9ixY1s8TmRkJHx8fBAfH4/a2lpUVVUhPj4e0dHRCA8PBwAcPHgQt912mylMAcCECROQnp6Oq1evtnjsmpoalJaWNrrZGy6dQEREZBkOFagWLFgANzc3+Pj4IDMzE5s3b27SZtSoUVCr1ejVqxfGjBmDpUuXtng8Dw8P7NmzB2vXroWLiwvc3d2xbds2bN26FXK5HACQl5eHgICARs8zfp+Xl9fisZctWwaNRmO6GXvA7Mn1Q34O2lFJRERkF0QNVAsXLoREImn1dv2w2quvvoqjR49ix44dkMlkiIuLaxIEvvvuOyQnJ2P9+vXYsmUL3n333RZfv6qqCrNnz8bo0aNx6NAh7N+/H/369cM999yDqqoqs85t0aJF0Gq1pltWVpZZx7OGnv7ukEkl0FbpkFdaLXY5REREDksu5ou//PLLmDlzZqttIiIiTF/7+vrC19cXvXv3RnR0NEJCQnDo0CHExMSY2hh7gvr06QO9Xo85c+bg5Zdfhkwma3Ls9evX4+LFizh48CCkUqnpPm9vb2zevBmPPPIIAgMDkZ+f3+h5xu8DAwNbrFulUkGlUrX+AxCZSi5DDz83nMkvR1puGYI0LmKXRERE5JBEDVR+fn7w8/Pr0HMNBgOA+rlKrbXR6XQwGAzNBqrKykpIpVJIJBLTfcbvjcePiYnB66+/Dp1OZ5qvtXPnTkRGRsLb27tDtduTyEDP+kCVV4bYKH+xyyEiInJIDjGHKiEhAR999BFSUlJw6dIl7Nq1C9OnT0ePHj1MvVPr1q3Dhg0bkJqaivPnz2PDhg1YtGgRpk2bZgpC33//PaKiokzHvfPOO3H16lXMnTsXqampOHXqFGbNmgW5XI7Y2FgAwKOPPgqlUonZs2fj1KlT+O677/Cvf/0L8+fPt/0PwgqME9PT8uxv0jwREZGjELWHqq1cXV2xadMmLFmyBBUVFQgKCsLEiROxePFi07CaXC7HihUrcObMGQiCgLCwMMybNw8vvfSS6TharRbp6emm76OiovDTTz/hrbfeQkxMDKRSKQYPHoxt27YhKCgIAKDRaLBjxw7MnTsXQ4cOha+vL/72t79hzpw5tv0hWEl0UEOgyuWVfkRERB3lsOtQORp7XIcKALJLqjB6+S7IpRKcXjoRSrlDdFoSERHZhFOvQ0WWE6xRw0MtR51BQEZhudjlEBEROSQGqk5OIpEgOrA+cXMeFRERUccwUJFpgc80rphORETUIQxUhChOTCciIjILAxUhikN+REREZmGgItOQX35pDa5W1IpcDRERkeNhoCK4q+QI6VK/7QznUREREbUfAxUB4LAfERGRORioCMC1LWjS2UNFRETUbgxUBOBaD1UqAxUREVG7MVARgGtLJ5zJK4PBwN2IiIiI2oOBigAA4T5uUMmlqNLpkVlcKXY5REREDoWBigAAMqkEvQOMK6ZzYjoREVF7MFCRiXFieipXTCciImoXBioyieSVfkRERB3CQEUm0UFci4qIiKgjGKjIxDjkd6m4EpW1dSJXQ0RE5DgYqMjEx10FX3cVBAE4k18udjlEREQOg4GKGoluWI8qLZfDfkRERG3FQEWNGIf9uEkyERFR2zFQUSOR3CSZiIio3RioqJHre6gEgVvQEBERtQUDFTXS098dMqkEJZU65JfWiF0OERGRQ2CgokbUChm6+7oB4LAfERFRWzFQUROcmE5ERNQ+DFTUhGnFdC6dQERE1CYMVNREZAB7qIiIiNqDgYqaiGpY3DOjsBy1dQaRqyEiIrJ/DFTURFcvF3io5NDpBZy/wi1oiIiIboaBipqQSCSINE5Mz+WwHxER0c0wUFGzjMN+nEdFRER0cwxU1KwobkFDRETUZgxU1KwoDvkRERG1GQMVNat3Q6DKK61GSWWtyNUQERHZNwYqapanWoFu3i4AOI+KiIjoZhioqEXXhv04j4qIiKg1DFTUIuPE9PR89lARERG1hoGKWmRcOiGVE9OJiIhaxUBFLTIO+Z3JL4PBIIhcDRERkf1ioKIWhfu4QSmXorJWj6yrlWKXQ0REZLcYqKhFcpkUvQPcAXDYj4iIqDUMVNSqyACumE5ERHQzDFTUquiGienpXIuKiIioRQxU1Kpre/oxUBEREbWEgYpaFdlwpd/FogpU1taJXA0REZF9YqCiVvl5qODrroIgAKdzOI+KiIioOQxUdFNDQr0AAMmZV8UthIiIyE4xUNFNDQ3zBgAkXWSgIiIiag4DFd3UsPD6QJWceRWCwBXTiYiIbsRARTfVN1gDpUyKK+W1uFTEFdOJiIhuxEBFN6VWyNC/mwYAcOQSh/2IiIhuxEBFbWKaR8VARURE1ESHAlVFRYWl6yA7ZwxUyQxURERETXQoUAUEBODJJ5/Evn37LF0P2akhofWB6kxBGbRVOpGrISIisi8dClRr165FcXEx7rjjDvTu3RvLly9HTk6OpWsjO+LnoUK4jysEATjK9aiIiIga6VCguv/++/HDDz8gOzsbzz77LNavX4+wsDDce++92LRpE+rquEWJMxrSMOzHielERESNmTUp3c/PD/Pnz8fx48fx/vvv49dff8XUqVMRHByMv/3tb6is5CX2zmRYWBcADFREREQ3kpvz5Pz8fKxZswarV6/GpUuXMHXqVMyePRuXL1/GihUrcOjQIezYscNStZLIjBPTU7JKUKc3QC7jRaJERERABwPVpk2bsGrVKmzfvh19+vTB888/j8cffxxeXl6mNqNGjUJ0dLSl6iQ70MvfHR5qOcqq65CWV4Z+XTVil0RERGQXOtTFMGvWLAQHB2P//v1ISUnBvHnzGoUpAAgODsbrr79uiRrJTkilEtPVfkkXi0WuhoiIyH50qIcqNzcXrq6urbZxcXHBkiVLOlQU2a9hYd7Ye6YQRzJLMHO02NUQERHZhw4Fqrq6OpSWlja5XyKRQKVSQalUml0Y2SfjPKoj7KEiIiIy6dCQn5eXF7y9vZvcvLy84OLigrCwMCxZsgQGg8HS9ZLIBoZ4QSaVIEdbjZySKrHLISIisgsd6qFavXo1Xn/9dcycORMjRowAABw+fBhr1qzB4sWLUVhYiHfffRcqlQqvvfaaRQsmcbmp5IgO8sDJ7FIcuXQVwV4uYpdEREQkug4FqjVr1uC9997Dww8/bLrvvvvuQ//+/fGf//wHv/32G0JDQ/GPf/yDgcoJDQvrYgpU9w0MFrscIiIi0XVoyO/AgQMYPHhwk/sHDx6MgwcPAgBuvfVWZGZmmlcd2SWumE5ERNRYhwJVSEgI4uPjm9wfHx+PkJAQAEBRURG8vb3Nq47s0rCGQHU6txSVtdxmiIiIqEOB6t1338U///lPDBw4EE899RSeeuopDBo0CB988AHee+89AEBiYiKmTZtmsUInT56M0NBQqNVqBAUFYcaMGY02ZE5PT0dsbCwCAgKgVqsRERGBxYsXQ6fTtXrcxMREjBs3zjTRfsKECTh27Jjp8erqasycORP9+/eHXC7H/fffb7FzclTBXi4I0qihNwhIySoRuxwiIiLRdShQTZ48Genp6bj77rtRXFyM4uJiTJo0CWlpabj33nsBAM899xzef/99ixUaGxuLDRs2ID09HRs3bkRGRgamTp1qelyhUCAuLg47duxAeno6PvjgA3zxxRetroVVXl6OiRMnIjQ0FAkJCdi3bx88PDwwYcIEUxDT6/VwcXHBCy+8gPHjx1vsfBydcfmEZA77ERERQSIIgtCeJ+h0OkycOBGfffYZevXqZa26burHH3/E/fffj5qaGigUimbbzJ8/H4mJifjjjz+afTwpKQnDhw9HZmamaajyxIkTGDBgAM6ePYuePXs2aj9z5kyUlJTghx9+aHe9paWl0Gg00Gq18PT0bPfz7c2q/Rfw1k+ncXukH1bPGiF2OURERFbR1s/vdvdQKRQKHD9+3KzizFVcXIx169Zh1KhRLYapc+fOYdu2bRg7dmyLx4mMjISPjw/i4+NRW1uLqqoqxMfHIzo6GuHh4WbVWFNTg9LS0kY3ZzIsrAuA+h4qg6FdmZyIiMjpdGjI7/HHH292Urq1LViwAG5ubvDx8UFmZiY2b97cpM2oUaOgVqvRq1cvjBkzBkuXLm3xeB4eHtizZw/Wrl0LFxcXuLu7Y9u2bdi6dSvk8g6tKGGybNkyaDQa083YA+YsooI84KKQobS6DucKy8Uuh4iISFQdClR1dXX49NNPMWzYMDzzzDOYP39+o1tbLVy4EBKJpNVbWlqaqf2rr76Ko0ePYseOHZDJZIiLi8ONI5bfffcdkpOTsX79emzZsgXvvvtui69fVVWF2bNnY/To0Th06BD279+Pfv364Z577kFVlXmrgC9atAhardZ0y8rKMut49kYhk2JQiBcALp9wPb1B4JWPRESdUIe6YU6ePIkhQ4YAAM6cOdPoMYlE0ubjvPzyy5g5c2arbSIiIkxf+/r6wtfXF71790Z0dDRCQkJw6NAhxMTEmNoYe4L69OkDvV6POXPm4OWXX4ZMJmty7PXr1+PixYs4ePAgpFKp6T5vb29s3rwZjzzySJvP5UYqlQoqlarDz3cEQ8O8cfB8EZIuXsX0EaFilyMqQRCw5UQuVm5LR35pNX7+863oFeAhdllERGQjHQpUu3fvtsiL+/n5wc/Pr0PPNe4TWFNT02obnU4Hg8HQbKCqrKyEVCptFAKN33MfwpsbGt5wpV9m5+6hSrxYjH9sSW20hMTO1HwGKiKiTqRDQ35G586dw/bt203DY+28YLDNEhIS8NFHHyElJQWXLl3Crl27MH36dPTo0cPUO7Vu3Tps2LABqampOH/+PDZs2IBFixZh2rRpponr33//PaKiokzHvfPOO3H16lXMnTsXqampOHXqFGbNmgW5XI7Y2FhTu9OnTyMlJQXFxcXQarVISUlBSkqKVc7VkQwJqQ9UF65U4Ep5y8HWWZ0vLMcz3yThT58dREpWCVyVMtOip8e4PhcRUafSoR6qoqIiPPzww9i9ezckEgnOnj2LiIgIzJ49G97e3qbFPS3F1dUVmzZtwpIlS1BRUYGgoCBMnDgRixcvNg2ryeVyrFixAmfOnIEgCAgLC8O8efPw0ksvmY6j1WqRnp5u+j4qKgo//fQT3nrrLcTExEAqlWLw4MHYtm0bgoKCTO3uvvtuXLp0yfS9cdsdawVIR6FxVaB3gDvO5Jcj+dJV3NU3UOySbOJKeQ3+9etZrD+cCb1BgFQCPDIiFC+O74WLVyrx8H8OcsFTIqJOpt3rUAFAXFwcCgoK8OWXXyI6OhrHjh1DREQEtm/fjvnz5+PUqVPWqNWhOds6VEaLNh3Ht4ez8MxtEVh0d7TY5VhVVa0eX+2/gE/3ZKC8pn7i+fhofyycFIWe/vXDe5W1dej/5g7oDQIOLRqHQI1azJKJiMhMbf387lAP1Y4dO7B9+3Z069at0f29evVq1JNDzm9oWBd8ezjLqa/00xsEbEq+jPd2nEFeaTUAoH9XDV67OxoxPXwatXVVytE7wAOpuaVIybqKiZqg5g5JREROpkOBqqKiAq6urk3uLy4udvor26gx4xY0x7O1qKnTQyVvOvnfkf1+phBv/5KKtLwyAEBXLxf8dWIk7hsQDKm0+StaB4VoGgKVFhP7MVAREXUGHZqUPmbMGHz99dem741Xxa1cubLRZG5yfuE+rvBxU6K2zoCT2c6zGnxqbilmxCcg7qvDSMsrg6dajtfujsJvL4/FlEFdWwxTAEzrc3FiOhFR59GhHqqVK1di3LhxSEpKQm1tLf7617/i1KlTKC4uxv79+y1dI9kxiUSCIWHe2Hk6H0cuFZt6rBxVrrYK7+04g43JlyEIgEImQVxMOObF9oS3m7JNxxjYEKiOXy6B3iBA1kr4IiIi59ChQNWvXz+cOXMGH330ETw8PFBeXo4HH3wQc+fObXR1HHUOw0yBynHnUZVV6/DZ3gzE77uAal39GmT3DgjCXydEIdSn6fB2a3r5e8BVKUNFrR4ZheXozfWoiIicXoc3rNNoNHj99dctWQs5KGOv1JFLVyEIQrtWyxebTm/At4cz8a9fz6KoohYAMCK8C167J9o0dNdeMqkE/btqkHChGClZJQxURESdQIcDVUlJCQ4fPoyCgoImq4rHxcWZXRg5jn5dNVDKpLhSXovM4kqE+biJXdJNCYKA7afysXJbGs5fqQAARPi5YeHEKNzZJ8DsUDgoxMsUqB4e5lwbYxMRUVMdClQ//fQTHnvsMZSXl8PT07PRh49EImGg6mTUChn6dfVEcmYJki5etftAlZx5Fct+SUXixfohSl93Jf4yvjceGR4ChcyszQNMODGdiKhz6VCgevnll/Hkk0/i7bffbnb5BOp8hoV3QXJmCY5kXsVDQ7vd/AkiyNVW4e8/p2LLiVwAgFohxdNjIvDM2B5wV3W4s7ZZxonpaXllqNbpoVY413ISRETUWIc+RbKzs/HCCy8wTJHJkNCGeVQX7XNiuiAIeOabIzh+WQuJBPjT0G6Yf2ek1VYyD9Ko4eehQmFZDU5mazEsvItVXoeIiOxDh8Y3JkyYgKSkJEvXQg7MODH9TEEZtFU6katp6lROKY5f1kIpl2LLn8dg5dSBVt0WRiKRmIb9uK8fEZHz61AP1T333INXX30Vp0+fRv/+/aFQKBo9PnnyZIsUR47Dz0OFMB9XXCqqxNHMq7g90l/skhr535HLAIA7+wSgT7Bt9lIcFOKFnafzceyy1iavR0RE4ulQoHr66acBAEuXLm3ymEQigV6vN68qckhDw7xxqagSyZfsK1DV1hnw47EcAMBUG87vGtjNCwCQkmWfw6BERGQ5HRryMxgMLd4Ypjov47Bfkp0t8LknvQDFFbXw81BhTE9fm73ugBANACCruApF5TU2e10iIrK9dgWqu+++G1rtteGL5cuXo6SkxPR9UVER+vTpY7HiyLEMC6ufeJ2SVYI6veEmrW1nY3L9cN8Dg7tCbqFlEdrCU61AD7/6JSSOc9iPiMiptevTZfv27aipufZ/2m+//TaKi4tN39fV1SE9Pd1y1ZFD6eXvDg+1HJW1eqTllYldDgCguKIWu9IKAAAPDbH9cg7G5ROOcmI6EZFTa1egEgSh1e+pc5NKJdeWT7CTYb8fU7Kh0wvo31WDyEDbbwEzmAt8EhF1CrYb/6BOwd7mUW1MzgYAPDSkqyivb+yhOna5hP8DQkTkxNoVqCQSSZM9zhxpI1yyvmENgSrZDgJVel4ZTmRroZBJMHmQOIEqKtATSrkUJZU6XCqqFKUGIiKyvnYtmyAIAmbOnAmVSgUAqK6uxrPPPgs3t/qJt9fPr6LOaWCIF2RSCbJLqpCrrUKQxkW0WoyT0e+I8kcXN6UoNSjlUvQN9sTRzBIcu1yCcF/73ueQiIg6pl09VE888QT8/f2h0Wig0Wjw+OOPIzg42PS9v78/N0bu5NxUckQH1c9VEnMeVZ3egO+PGof7xN1b0Lge1dHMElHrICIi62lXD9WqVausVQc5kaGh3jiZXYqki1dx74BgUWr44+wVFJbVoIubUvRFRgeHemH1gfp5VERE5Jw4KZ0sbmjDRsDJmeL1UP2vYbhvyqBgKOXi/pobe6hO5ZSits5+1uciIiLLYaAiizNe6XcqpxSVtXU2f31tpQ47T+cDEH+4DwDCfFzh5apAbZ0BaXmlYpdDRERWwEBFFtfVywVBGjX0BgHHsmy/QvhPx3NQW2dAVKAH+tpoI+TWSCQSUy8V16MiInJODFRkFUPCjAt8Ft+kpeUZr+57aEg3u1nWw7geVYoIAZOIiKyPgYqsYliYOCumZxSW42hmCWRSCaYMFmdCfHMGNWyUnJIl/vpcRERkeQxUZBVDrwtUBoPtVgjf1NA7Nba3H/w91DZ73ZsxDvllFFagtFonbjFERGRxDFRkFdFBnnBRyFBaXYeMwnKbvKbeIGBTsn2sPXUjH3cVQrrUL3J64jKH/YiInA0DFVmFQibFwIZhLlvt63cwowi52mpoXBQYFy3u2lPNMfZSpXBiOhGR02GgIqsZFla/HpWt5lEZJ6PfNzAIaoXMJq/ZHoNME9NLRK2DiIgsj4GKrGaoDSeml1XrsPVkLgD7G+4zuj5QCYLt5pUREZH1MVCR1QwJrQ9UF65UoKjcuhtnbz2Rh2qdARF+bqbgYm/6ddVAJpWgsKwGudpqscshIiILYqAiq9G4KtDL3x2A9XupjFvNTB1qP2tP3UitkCEqsH7jaC7wSUTkXBioyKqGhTcM+1lxX7/MokocvlAMiQR4YHBXq72OJQzkPCoiIqfEQEVWZRz2O3LReoHKOBn91p6+CNK4WO11LIET04mInBMDFVnVsPD6K/2OZ2tRU6e3+PENBgGbjl4b7rN3xkB1IlsLvQ0XPCUiIutioCKrCvdxhY+bErV1BpzMLrX48RMvFiOruAruKjnu6hNo8eNbWg8/d7gpZais1eNsQZnY5RARkYUwUJFVSSQS00bJyVaYmP6/I/W9U/f0D4KL0v7WnrqRTCrBgIYFPjkxnYjIeTBQkdUZ16NKulRs0eNW1tbhlxMNa085wHCf0bWJ6dyChojIWTBQkdUNMy3wadkFLbefykNFrR6hXVwxvOFqQkcwqGFLHk5MJyJyHgxUZHX9umqglElxpbwGmcWVFjuucbjvoSH2u/ZUcwaF1Ie/M/llqKytE7kaIiKyBAYqsjq1QoZ+XT0BWG6Bz5ySKhzIKAIAPDjEvteeulGgRo0ATxX0BgGnciw/UZ+IiGyPgYps4to8KssEqu+PZkMQgFsiuiCki6tFjmlLAxsmpqdklohaBxERWQYDFdnE0LD69agscaWfIAiNhvsc0aBQLwBAyuUSUesgIiLLYKAimzD2UKXnl0FbpTPrWMmZJbhwpQIuChkm9Q+yRHk2N4hLJxARORUGKrIJPw8VwnxcIQjmX91m3GpmUr9AuKvkFqjO9vp300AiAS5frcKV8hqxyyEiIjMxUJHNDDXt69fx9aiqdXr8dCwHgGNsNdMSD7UCPf3cAbCXiojIGTBQkc0MbVgr6khmx+dR7Tydj7LqOnT1csEtET6WKk0UA7lRMhGR02CgIpsxzqM6mlmCOr2hQ8cwDvc9MLgrpFLHWXuqOYMYqIiInAYDFdlMb38PeKjkqKzVIy2v/RsDF5RW4/czhQAca6uZlhgD1bEsy64gT0REtsdARTYjlUow2LQNTfuH/b4/mg2DUN/T1d3XzdLl2VxkoAdUcilKq+tw4UqF2OUQEZEZGKjIpoZ1MFAJgmAa7nPUtadupJBJ0a9r/b5+x7geFRGRQ2OgIpsa2sFAdTK7FGfyy6GUS3HPAMdce6o5A03rUWnFLYSIiMzCQEU2NSjEC1IJkF1ShVxtVZuf978jWQCACX0DoXFRWKs8mxsYUt9DdZQT04mIHBoDFdmUm0qO6KD2bZRcW2fAjw1rTz3kYBsh38zgkPoeu9ScUtTU6UWuhoiIOoqBimyuvfOodqUV4GqlDv4eKozp5WfN0mwupIsLvF0VqNUbkJbb/isfiYjIPjBQkc0NaWegMm6E/MCQrpA5+NpTN5JIJFzgk4jICTBQkc0NC+8CADiVU4rK2rpW2xaV12BPegEAYKqTXN13o+vXoyLLSrpYjKmfHsCRSx3f7oiIqC0YqMjmgjVqBHqqoTcIN726bXNKDuoMAgZ006BXgIeNKrQtUw8Vl06wuH/9dhZJl67iz+uPoqxaJ3Y5ROTEGKjI5iQSiWlfv+Sb7OtnXHvKkTdCvplBDUsnnC+sgLaSH/qWoq3U4WBGEQAgR1uNt39JE7kiInJmDFQkiqGh9YEq6WLLQzGpuaU4lVMKhUyC+wYE26o0m/N2UyLMxxUAcDy7RNxinMjO1HzUGQT4uisBAN8ezsQfZwtFroqInBUDFYlimKmHqgQGQ/P72G1smIw+LioA3m5Km9UmhmsLfJaIWocz2XYyFwDw+C1heCImDACwcOMJDv0RkVUwUJEoooM84aKQQVulQ0ZheZPHdXoDfkhpWHvKiYf7jAbxSj+LKqvW4fczVwAAd/cPwl8nRiGkiwuyS6qwbCuH/ojI8hioSBQKmdS0Snhzyyf8fqYQV8pr4OOmxO2RzrX2VHOuLZ2ghSA032NHbbcrrQC1egMi/NzQy98dbio5Vj40EACwPiET+85eEblCInI2DFQkGuO+fknNBCrjZPQpg7pCIXP+X9O+wZ6QSyW4Ul6D7JK2b8lDzdt2Mg8AMKlfICSS+rXLYnr4IK5h6G/BxuMor2l9yQ4iovZw/k8qslvDwurXo0q+IVCVVNbi19P1a089NNS5tpppiVohM23Jw42SzVNZW4c96fWTzyf1a7yR9oLrhv7e/iVVjPKIyEkxUJFoBod6AQDOX6lAUXmN6f6fjuWgVm9AdJAn+gZrRKrO9oxDoMe4HpVZ9qYXokqnR0gXF/QN9mz0mJtKjhUPDQDAoT8isiyHCVSTJ09GaGgo1Go1goKCMGPGDOTk5JgeT09PR2xsLAICAqBWqxEREYHFixdDp2v9ip7ExESMGzcOXl5e8Pb2xoQJE3Ds2DHT43v27MGUKVMQFBQENzc3DBo0COvWrbPaeXYmXq5K9PJ3B1B/tZ/R/5KzATjfRsg3Y7zSL+W6nwW131bTcF+QabjveqN6+GLGLRz6IyLLcphAFRsbiw0bNiA9PR0bN25ERkYGpk6danpcoVAgLi4OO3bsQHp6Oj744AN88cUXWLJkSYvHLC8vx8SJExEaGoqEhATs27cPHh4emDBhgimIHThwAAMGDMDGjRtx/PhxzJo1C3Fxcfj555+tfs6dwbV5VPXrUZ0rKMexrBLIpBJMGdS5ApWxx+5EthZ1eoO4xTiomjo9dqXVDxdP7BfYYruFk6LQzbvhqj8HGfqrrePvBJE9k4tdQFu99NJLpq/DwsKwcOFC3H///dDpdFAoFIiIiEBERESjNnv27MEff/zR4jHT0tJQXFyMpUuXIiQkBACwZMkSDBgwAJcuXULPnj3x2muvNXrOX/7yF+zYsQObNm3Cvffe2+Kxa2pqUFNzbRirtLS03efcGQwN88Z/E7NM86iMk9Fv7+0HPw+VmKXZXISvO9xVcpTX1OFsQblpThW13b6zV1BeU4dAT7VpBfrm1F/1NwCPfpmAdQmZuLt/EEb39LVdoe20av8FLNuahgcGdcXfH+jXKS7UIHI0Dvmvsri4GOvWrcOoUaOgUCiabXPu3Dls27YNY8eObfE4kZGR8PHxQXx8PGpra1FVVYX4+HhER0cjPDy8xedptVp06dKl1RqXLVsGjUZjuhkDGzVm7KE6dlmLap0emzrBVjMtkUolGNCtfh4V16PqmF9O1A/3TewXCKm06XDf9Ub19MXjt4QCAP76P/sd+vvm4EW89dNp1NYZ8F1SFp5cnWi3tRJ1Zg4VqBYsWAA3Nzf4+PggMzMTmzdvbtJm1KhRUKvV6NWrF8aMGYOlS5e2eDwPDw/s2bMHa9euhYuLC9zd3bFt2zZs3boVcnnznXcbNmxAYmIiZs2a1WqtixYtglarNd2ysrLad7KdRHdfN3RxU6K2zoD/7D2P/NIaaFwUuCPaX+zSRGFc4JMrprefTm/Ar6n5AOqXS2iLRZOiTUN/y7fa39DfhsQsvLH5FADg3gFBcFHI8MfZK5j2n4MoKK0WuToiup6ogWrhwoWQSCSt3tLSrq1q/Oqrr+Lo0aPYsWMHZDIZ4uLimiyC+N133yE5ORnr16/Hli1b8O6777b4+lVVVZg9ezZGjx6NQ4cOYf/+/ejXrx/uueceVFU1XQto9+7dmDVrFr744gv07du31XNTqVTw9PRsdKOmJBIJhjTs6/fJnnMAgMkDg6GSy8QsSzQDuWJ6hx3MKIK2SgdfdyWGhbfeg2xkHPoDgLWHMnHgnP1c9ffD0Wws2HQcAPDk6O74cPpg/HfOLfBxU+JUTike+OQAzhU03WWAiMQhEURclrmwsBBFRUWttomIiIBS2XQft8uXLyMkJAQHDhxATExMs89du3Yt5syZg7KyMshkTT+g4+Pj8dprryE3NxdSaX22rK2thbe3N+Lj4/HII4+Y2u7duxf33HMP3n//fcyZM6c9pwmgfg6VRqOBVqtluLrBZ3szsPy67UA2zx1tChadTUFpNUa8/RukEuDEmxPgpnKYaY6iW7TpBL49nIlHR4bi7Qf6t+u5i384gbWHMtHVywXbX7oN7iL/3H85kYt565NhEIDHbwnF/5vSz3TF4qWiCsxclYgLVyrg5arAl3HD2hwgicSQklUCd5UcPRuu6nY0bf38FvWvhp+fH/z8OratiMFQf8XL9RO/m2uj0+lgMBiaDVSVlZWQSqWNLq02fm88PlC/dMK9996LFStWdChMUeuM86gAoKe/u2keUWfk76lGkEaNXG01TmZrMTLCR+ySHILeIGDHqWuro7fXwknR2J1WiOySKqzYmob/d38/S5fYZr+ezscL3x6FQQD+NLQblk7u1+hvVJiPG/73bAxmr0lCSlYJHv0yAf9+ZBAm3rCIKZHYdHoDlm9NQ/y+C1DKpfgybhhu6+28W4k5xByqhIQEfPTRR0hJScGlS5ewa9cuTJ8+HT169DD1Tq1btw4bNmxAamoqzp8/jw0bNmDRokWYNm2aaeL6999/j6ioKNNx77zzTly9ehVz585FamoqTp06hVmzZkEulyM2NhZA/TDfPffcgxdeeAEPPfQQ8vLykJeXh+LiYtv/IJxU/64aKGT1HxgPDenW7NpBnYlxPSou8Nl2hy8Uo6iiFl6uCtzSgRDqrpJj5dT6ob9vDl0Sbehv75lCPL8uGXUGAVMGBWP5QwOanVzv467Ct0/fgvHRAaitM+C5dclYvf+CCBUTNS9PW43pnx9C/L7638vaOgOe+joJv58pFLky63GIQOXq6opNmzZh3LhxiIyMxOzZszFgwADs3bsXKlX9pfVyuRwrVqzAiBEjMGDAALz11luYN28evvzyS9NxtFot0tPTTd9HRUXhp59+wvHjxxETE4MxY8YgJycH27ZtQ1BQ/f/trVmzBpWVlVi2bBmCgoJMtwcffNC2PwQnplbI8MjwUPT0d8efhnW+q/tuNKhhPSrOo2q7bSdzAQB3Rgd0eEmB0T198djIhqv+Nh5HhY2vpDuQcQVzvk5Crd6ASf0C8d6fBkLWypWKLkoZPnt8CB4dGQpBAN786TSW/ZIKg4Gba5O4DmRcwb0f/oGkS1fhoZLjo0cH484+AU4fqkSdQ9WZcA4VtdXBjCJM/+IQunq5YP/CO8Qux+4ZDAJilv+G/NIafDVzGO6ICujwscpr6jDhn78ju6QKM24Js9nQX+LFYsTFH0aVTo/x0f745LGhUMrbFgwFQcAnezLwzvb6/1mcPDAY7/xpQKe9sIPEYzAI+Oz3DLy7PR0GAYgK9MCnjw9Fd1831NYZMHd9Mnaezne44b+2fn47RA8VUWfSv5sGEgmQXVKFgjJeGn8zR7OuIr+0Bh4qudmLczYZ+suw/tBfSlYJZq1KRJVOjzG9fPHRo0PaHKaA+itl58b2xHt/Ggi5VIIfj+Vg5leJ0Fa1vu0WkSVpq3SY880RrNxWH6YeHNIV3z8/Gt193QAASrkUHz86xKl7qhioiOyMu0qO3v4eAIBjWVqRq7F/WxsW8xwX7W+RXpnRPX3xaMPQ3wIrD/2dzNYiLj4B5TV1uCWiCz6fMQxqRcfO4aGh3fDVzOFwU8pw8HwRHv7sIHK1TZd/IbK0Uzla3PfhPvyamg+lTIq3H+iP9/40EC7Kxr/Lzh6qGKiI7NDAkPorHbnAZ+sEQTBthmzJq9wWTYpCVy8XZBVXYcW2tJs/oQPS88owIz4BpdV1GBrmjfgnhjf5AGqv23r7YcOzMfDzUCE9vwwPfnIA6XllFqqYqKkNiVl48JMDyCyuRDdvF2x8bhQeHRna4sVFzhyqGKiI7BAX+Gybk9mlyC6pgotChrEWnI/hoVZgRcOCn18fvISDGa2vl9deGYXleOzLBFyt1GFgNw1WzRpusTXH+gZr8P3zo9DDzw252mpM/eyATYYuqXOp1unx1/8dw183HkdNnQGxkX74+c+3on8blr25MVQ97SShioGKyA6ZtqC5XMKrtlrxS8PVfbFRfmb37tzo1l6+mD7CeNXfMYsN/V0qqsCjXxzClfIaRAd5Ys2TI+Cpbn5P0o7q5u2Kjc+NwvBwb5RV12HmV4n48ViORV+DOq/Moko8+MkBbEi6DIkEeOWu3oh/Yji8XJsuwt0SY6gaHx2AGicJVQxURHaod4AH1AopyqrrcKGoQuxy7JIgCNh20riYp3UWtXzt7mtDfystMPR3+WolHv0iAfmlNejl7461s0e060OoPbxclfhm9khM6heIWr0BL3x7FJ//ntFkuy6i9vj1dD7u/fAPnM4tRRc3Jb55ciTm3dHrppuRN0cpl+KTx5wnVDFQEdkhhUyKfsH1XecpmSXiFmOn0vPLcOFKBZRyKWKjrLOZtodageUP1W9js8bMob88bTUe+zIB2SVViPB1w7qnR8LHXWWpUpulVsjw0aNDMHNUOADg7V/S8NZPp6Fnrye1U53egJXb0vDU10kora7D4FAvbHnhVtzay7wra50pVDFQEdmp64f9qCnj1X239fKz6t57Y3r5YfqIEAD1Q3+Vte0f+issq8GjXx7CpaJKhHRxwbqnR8LfQ23pUpslk0qw5L4+eP3uaADA6gMXMW99Mqp1epu8Pjm+wrIazIg/jE/2ZAAAZo4Kx3dzYhCkcbHI8Z0lVDFQEdkp48R0XunXvK0N86c6sndfe712dzSCNeqGob/0mz/hOsUVtXj8ywScL6xAsEaN9U/dYrEPoraSSCR4+rYI/Hv6YChlUmw9mYfHv0xASWWtTesgx5N0sRj3fvgHDp4vgqtShn9PH4w3J/dt11ppbdFcqPrjrGOFKq6UbiNcKZ3aK6u4EmNW7oZCJsGJNyd0eH0iZ5RRWI5x7+2FXCrBkcV3QuNq2Undzfn9TCHivjoMAPjvnFvatGegtkqHR784hFM5pfD3UGHDMzEIb1joUCwHM4ow55sklFXXoYefG1bPGoGQLq6i1uRoaur0+DElBwVlNab7BEGAIAACAOOnqoBr90EQIJjaNn7s+vYw3Vd/Z7CXC4aEeiM6yNPiIaY1giDgq/0XseyXVNQZBPT0d8dnjw9Bz4Y18qylts6A59cdwa+pBVDJpfjyiWEY00vcFdXb+vnNQGUjDFTUXoIgYNjff0VRRS2+f34UBod6i12S3fh49zm8sz0dY3v7Yc2TI2z2uos2Hce3h7MQ2sUV214cA1dly0ONZdU6zIg/jJSsEvi4KfHdM7dY/cOordLzyjBz1WHkaqvh56HCqpnD0a/rzS93J2B3WgHe+ukULhZV2vR1lXIp+nfVYHCIFwaHemNImJfVejrLa+qw4H/HseVEfS/wfQODsfzB/hZb2uNm7C1UMVDZGQYq6ognVydiV1oB3ryvD2aO7i52OXbj3g//wMnsUix/sD8eaVjawBbKqnWY8M/fkaOtxsxR4Xhzct9m21XW1uGJrw4j8eJVeLkq8O3TtyA6yL7+3edqqzBrVSLS8srgppTh08eHOszeamK4eKUC/+/n0/gtrQAA4Oehwu29/SCRABJI6v8rAdDwdf1XaPw40GjByxsfM90nkUACwCAIOFdQjqNZJSipbLqVUKCnGoNDvRpu3ujfVWN2T/aZ/DI8u/YIzhdWQCGT4PW7o/HEqPAWF+q0FnsKVQxUdoaBijri37+dxfs7z+D+QcH44JHBYpdjFzKLKnHbO7shlQCJr4+3+pVyN7rZ0F+1To8nVyfiQEYRPNRyrH/qljYtdiiG0modnvn6CA6eL4JcKsHyhwZg6tBuYpdlVypr6/Dx7nP44vcLqNUbIJdK8OSt3fHnO3rCw8Lrh7VEEARcLKrE0cyrOJpZgqNZV5GaW9bkak25VII+wZ6mXqzBoV4I7eLa5jD0w9FsLNp0AlU6PQI91fj4sSEYGiZez7i9hCoGKjvDQEUdsfdMIZ746jC6+7ph9yu3i12OXfj89wy8/UsaYiJ88O2cW0SpYeHG4/hvYhbCfFyx9S/Xhv5q6vR45psj2JNeCDelDN88NRJD7HyotqZOj1f/77hp4c/eAe7w91DD30MFv+tu/h5q+HvWf+2hktu8x8LWBEHAlhO5+MeWVORq6zcpH9PLF0vu64ue/u4iVwdU1epxIluL5MyrOJp5FcmZJSi8bk6XURc3ZUPA8sKQUG8MCPFqclVsTZ0ef/85Fd8cugQAuLWnL/71yCCb/89Kc+whVDFQ2RkGKuqIkspaDFq6EwCQ8rc7rbYIpCN54JP9OJpZgv83pS9mxISLUkNpw9Bf7nVDfzq9Ac+vS8bO0/lwUciw5skRGNG9iyj1tZfBIGDF9jT8Z+/5NrVXK6SmkOXnrqoPWsb/Gu/3UMHHTQm5zPEuJk/PK8ObP57CwfP1645183bBG/f2wV19Auw2SAqCgBxttakXKznzKk5ll6JWb2jUTiIBIgM86ocJQ7zR3c8Nf9+Sarqa+M939MSL43tD1oGFOq2lpk6PueuSRQtVDFR2hoGKOir23T24cKUCa54cYdH96hxRrrYKMct2QSIBEhaNg7+nbdZyao6x9xAA1j89EusOZWLLiVwo5VKsmjkco3uat+ChGLKKK3GxqAKFZTUoKKu57r/V9f8trUFZO7bgkUgAHzcl/BoCln/DbWSED0b38LG7sKWt0uGDX8/g64OXoDcIUMmleO72Hnh2bA+HvMq2pk6P0zmlDcOEJTiaeRWXr1Y121bjosA/pw3EHVEBNq6ybW4MVfFPDDd7UdG2YqCyMwxU1FEv/vcofkjJwfw7e+OFcb3ELkdUq/ZfwFs/ncawMG/877lRYpeDBf87ju+SsqCQSaDTC1DIJPh8xjCrrdxuD6pq9Sgsq0FheTUKSmtQWF5T/9+yGhQYg1dZDa6U16C1Bdl93ZW4d0AwJg8KxuAQL1F7fgwGAf9LvoyV29Jwpbx+ba4JfQOw+J4+TrekREFZNVIyS5CcWR+wTuWUok+wJ97700C7P1exQhUDlZ1hoKKOMoaIcVH+iJ85XOxyRPXwfw7i8IViLL4nGk+NiRC7nEZDfzKpBJ88NgQT+lp/oVFHoDcIKK6oRUFZdaMer8yiSuxMzUdxxbVFRUO7uGLKoGBMGRRs86UljmWVYMmPp5DSMOTVw88Nb07uK/raR7YiCILdDmM2R4xQxUBlZxioqKOOZl7FA58cgI+bEkmLxzvUHz9LKiyrwYi3f4UgAPsX3oGuXrZdbbwlRy4VY+W2dMwa3R0TbbBquzPQ6Q3Yd/YKNqdkY8fpfFTWXtsGp2+wJ6YMCsZ9A4OtuqJ8UXkNVm5Lx4YjWRAEwE0pw1/G98LMUd1tuoAmtV9NnR7Pr03Gb2m2CVUMVHaGgYo6qlqnR/83t0OnF/DHX2PtvlveWtYlXMLr35/EwG4abJ53q9jlkIVU1tZh5+l8/JiSg71nClHXME4okQAju3fBlEFdMalfoMUuyKjTG7D20CW8v/MMSqvr54M9OLgrFk6KEnVOHrWPLUMVA5WdYaAic0z+aB+OX9biw+mDcd/AYLHLEcXjXyZg37krWDAxCs/d3kPscsgKrlbUYsuJXPyYkoPDF4tN9ytkEtwe6Y8pg4IxPjqgwxPED50vwps/nkJaXhkAoE+QJ5ZO6Yth4Y5xNSY1ZqtQxUBlZxioyBx/23wSXx+8hKdu7Y7F9/YRuxybu1pRi2H/+BV6g4A9r9wu+n54ZH3ZJVX4MSUHm1OyTQEIqB+am9AvEFMGdW3zlYK52iq8/UsafmpYa8vLVYFX7orE9BGhdrU8ALXfjaFq43OjLL6NUls/v22zMQ8RmWVgNy8Al3DsconIlYhjZ2o+9AYBUYEeDFOdRFcvFzx3ew88d3sPpOeVYXNKNjan5CC7pAqbkrOxKTnbdKXglEHBGNTMlYI1dXrE77uAj3adQ2WtHhIJ8OiIULxyVyS83bimmzNQyWX45PEheH5tMlQKKSIDxdsvk4GKyAEMCvUCAJzI1kKnN0BhZ+v3WNu2k3kAgLv7B4lcCYkhMtADf50YhVcnROLIpavYnJKDLSdycaW8FqsPXMTqAxebXCm4O60AS38+jQtXKgAAQ8O88dbkvtwE2gkZQ5VUIhH1byMDFZED6O7jBg+1HGXVdTiTX4a+wZ3nQ6G0Woc/zhYCACbxKrpOTSKRYFh4FwwL74K/3dcH+85dweaj9VcKZhZX4sNd5/DhrnPo6uWC7JL6BSz9PFRYNCkKDwzu2mmvkO0MVHLxF15loCJyAFKpBAO7eWHfuSs4lqXtVIFqV2oBdHoBPfzc0CtAvO58si8KmRSxkf6IjfRHZW0dfk0twOaj2dh7phDZJVWibGJMnRsDFZGDGBRSH6hSsq7i0ZGhYpdjM1tP5gIAJvXjcB81z1Upx+SBwZg8MBhXK2qRcKEIkYGe6M75dmRDDFREDmJgiBcA4FiWVtxCbKiipg570huG+/pzuI9uzttNiYkM3ySCzjWzlciBDQypH+Y7U1CG8nZsUOvI9qQXoqbOgNAurugTxOVGiMh+MVAROQh/DzW6erlAEIATlztHL9W14b5ATigmIrvGQEXkQIy9VJ1hPapqnR670woAgHvkEZHd4xwqIgcysJsXfjmRh2NZJWYdx2AQUFxZi9ySauRqq5BXWo2ckmrkaauQo61GnrYacqkEb9zXB7GR/pYpvp3+OHsFFbV6BGvUGNQwf4yIyF4xUBE5EGOwSGklUBkMAooqapGnrQ9Ludrqhlv913kNt1q94aav98zXR/CfuKGihKqtJ+qH+yZwuI+IHAADFZED6ddVA6kEyNVWY1PyZZRV1yFHW9UQnupDU762pk1hSSIB/NxVCNKoEaRxQaBGXf+1lwuCNGp8te8Ctp7MwzPfHMHnM4bidhuGqto6A3am5gPgcglE5BgYqIgciJtKjt4BHkjLK8P8DcdabNdcWAr2UiNQ49Jwnxr+Hmoo5S1PoxwU4oU/rz+KbafyMOebI/gibhjG9vazxmk1cSDjCsqq6+DrrsLQMG+bvCYRkTkYqIgczJO3dsdHu87B21XRJCwFa9QIbENYaguFTIoPHx2MeeuTsf1UPp7+Oslmocq4d9+EvgGQSTncR0T2TyIIgiB2EZ1BaWkpNBoNtFotPD25ng45jto6A+atT8aO0/lQyqX4Mm4YbrNiqKrTGzD8H7/iaqUO654aidE9fa32WkREN9PWz28um0BErVLKpfjo0SG4s08AausMePrrJNNmxdZw+EIxrlbq4O2qwMjuXaz2OkRElsRARUQ3pZRL8XFDqKqpM+CpNUnYd/aKVV5ra8Nw3519AiCX8U8UETkG/rUiojYxhqrx0fWhavaaRIuHKoNBwLZT9YGKV/cRkSNhoCKiNlPKpfjksSEYH+1vlVB1JPMqCstq4KGWY1RPH4sdl4jI2hioiKhdlHIpPn5sCMZFXQtV+89ZJlRtPVHfOzU+OgAqucwixyQisgUGKiJqN5Vchk8eH4I7rgtVB8wMVYIgYHvDcB/37iMiR8NARUQdopLL8GlDqKrWGfCkmaHq+GUtskuq4KqU2WwBUSIiS2GgIqIOM4aq2Ei/a6Eqo2Oh6peT9Xv3xUb5Q63gcB8RORYGKiIyS32oGorbjaFqdSIOZhS16xiCIJhWR5/E4T4ickAMVERkNrVChs8eH4qxva+FqkPn2x6qUnPLcKmoEiq5FLE23ISZiMhSGKiIyCLUChn+M6M+VFXp9Ji1qu2halvDcN9tvf3gpuIWo0TkeBioiMhijKHqtutCVUIbQtUvHO4jIgfHQEVEFqVWyPD5jKEY08u3PlStTsThC8Uttj9XUIZzBeVQyCQYFx1gw0qJiCyHgYqILE6tkOGLuGEY08sXlbV6zFx1uMVQZVzMc3RPX2hcFLYsk4jIYhioiMgqmgtViRebhqqtHO4jIifAQEVEVmMMVbf2rA9VT3zVOFRdKqrA6dxSyKQS3NmHgYqIHBcDFRFZlTFUje7pU99T9dVhJDWEKmPv1C0RXdDFTSlmmUREZmGgIiKrc1HK8GXccIzq4YOKhp6qpIvFpkA1sV+QyBUSEZmHgYqIbMJFKUP8E9dCVdxXh3EsqwQSCTChL6/uIyLHxkBFRDZjDFUxEfXDfwAwLMwb/h5qkSsjIjIPAxUR2ZSLUob4mcMQE+EDAHhoSDeRKyIiMh/3eCAim3NVyvHN7BFIyytD32BPscshIjIbAxURiUIuk6JfV43YZRARWQSH/IiIiIjMxEBFREREZCYGKiIiIiIzMVARERERmYmBioiIiMhMDFREREREZmKgIiIiIjKTwwSqyZMnIzQ0FGq1GkFBQZgxYwZycnJMj6enpyM2NhYBAQFQq9WIiIjA4sWLodPpWj1uYmIixo0bBy8vL3h7e2PChAk4duyY2cclIiKizsNhAlVsbCw2bNiA9PR0bNy4ERkZGZg6darpcYVCgbi4OOzYsQPp6en44IMP8MUXX2DJkiUtHrO8vBwTJ05EaGgoEhISsG/fPnh4eGDChAmmwNSR4xIREVHnIhEEQRC7iI748ccfcf/996OmpgYKhaLZNvPnz0diYiL++OOPZh9PSkrC8OHDkZmZiZCQEADAiRMnMGDAAJw9exY9e/bs0HGbU1paCo1GA61WC09PbrVBRETkCNr6+e0wPVTXKy4uxrp16zBq1KgWw9S5c+ewbds2jB07tsXjREZGwsfHB/Hx8aitrUVVVRXi4+MRHR2N8PDwDh8XAGpqalBaWtroRkRERM7JoQLVggUL4ObmBh8fH2RmZmLz5s1N2owaNQpqtRq9evXCmDFjsHTp0haP5+HhgT179mDt2rVwcXGBu7s7tm3bhq1bt0Iub7zNYXuOCwDLli2DRqMx3Yw9YEREROR8RA1UCxcuhEQiafWWlpZmav/qq6/i6NGj2LFjB2QyGeLi4nDjiOV3332H5ORkrF+/Hlu2bMG7777b4utXVVVh9uzZGD16NA4dOoT9+/ejX79+uOeee1BVVdXh4wLAokWLoNVqTbesrKwO/ISIiIjIEYg6h6qwsBBFRUWttomIiIBSqWxy/+XLlxESEoIDBw4gJiam2eeuXbsWc+bMQVlZGWQyWZPH4+Pj8dprryE3NxdSaX22rK2thbe3N+Lj4/HII4906LjN4RwqIiIix9PWz295i4/YgJ+fH/z8/Dr0XIPBAKB+rlJrbXQ6HQwGQ7PBp7KyElKpFBKJxHSf8Xvj8TtyXCIiIupcRA1UbZWQkIDExETceuut8Pb2RkZGBt544w306NHD1Du1bt06KBQK9O/fHyqVCklJSVi0aBGmTZtmmrj+/fffY9GiRaZhxDvvvBOvvvoq5s6diz//+c8wGAxYvnw55HI5YmNj23xcIiIi6twcIlC5urpi06ZNWLJkCSoqKhAUFISJEydi8eLFUKlUAAC5XI4VK1bgzJkzEAQBYWFhmDdvHl566SXTcbRaLdLT003fR0VF4aeffsJbb72FmJgYSKVSDB48GNu2bUNQUFCbj0tERESdm8OuQ+VoOIeKiIjI8Tj1OlRERERE9oSBioiIiMhMDFREREREZmKgIiIiIjKTQ1zlR62rqKho8TGZTAa1Wt2mtlKpFC4uLh1qW1lZ2WTVeiOJRAJXV9cOta2qqmp1TTA3N7cOta2uroZer7dIW1dXV9NaZjU1Nairq7NIWxcXl0YLzup0Oou0VavVpvXT2tNWp9Ohtra2xbYqlcq0ZVN72tbV1bW6npxSqTQtUdKetnq9HtXV1S22VSgUpkWD29PWYDA02Umho23lcrnpSmVBEFBZWWmRtu35d8+/Ec235d8Ix/wbISqBbEKr1QoABK1Wa/FjA2jxdvfddzdq6+rq2mLbsWPHNmrr6+vbYtthw4Y1ahsWFtZi2z59+jRq26dPnxbbhoWFNWo7bNiwFtv6+vo2ajt27NgW27q6ujZqe/fdd7f6c7ve1KlTW21bXl5uavvEE0+02ragoMDU9vnnn2+17YULF0xtX3nllVbbnjx50tR2yZIlrbY9fPiwqe3KlStbbbt7925T248++qjVtj///LOp7apVq1ptu2HDBlPbDRs2tNp21apVprY///xzq20/+ugjU9vdu3e32nblypWmtocPH2617ZIlS0xtT5482WrbV155xdT2woULrbZ9/vnnTW0LCgpabfvEE0+Y2paXl7fadurUqY1+h1try78R9Tf+jbh2c+S/EdbQ1s9vDvkRERERmYnrUNmINdehYnd++9uyO98xu/M55MchP/6NuIZ/I+pZe8ivrZ/fDFQ2woU9iYiIHA8X9iQiIiKyEQYqIiIiIjMxUBERERGZiYGKiIiIyEwMVERERERmYqAiIiIiMhMDFREREZGZGKiIiIiIzMRARURERGQmBioiIiIiMzFQEREREZmJgYqIiIjITAxURERERGaSi11AZyEIAoD6XauJiIjIMRg/t42f4y1hoLKRsrIyAEBISIjIlRAREVF7lZWVQaPRtPi4RLhZ5CKLMBgMyMnJgYeHByQSSattS0tLERISgqysLHh6etqoQvF11vMGeO6d8dw763kDPPfOeO6OfN6CIKCsrAzBwcGQSlueKcUeKhuRSqXo1q1bu57j6enpcL94ltBZzxvguXfGc++s5w3w3DvjuTvqebfWM2XESelEREREZmKgIiIiIjITA5UdUqlUWLJkCVQqldil2FRnPW+A594Zz72znjfAc++M594ZzpuT0omIiIjMxB4qIiIiIjMxUBERERGZiYGKiIiIyEwMVERERERmYqCyMx9//DHCw8OhVqsxcuRIHD58WOySLG7ZsmUYPnw4PDw84O/vj/vvvx/p6emN2tx+++2QSCSNbs8++6xIFVvGm2++2eScoqKiTI9XV1dj7ty58PHxgbu7Ox566CHk5+eLWLHlhIeHNzl3iUSCuXPnAnCu9/v333/Hfffdh+DgYEgkEvzwww+NHhcEAX/7298QFBQEFxcXjB8/HmfPnm3Upri4GI899hg8PT3h5eWF2bNno7y83IZn0X6tnbdOp8OCBQvQv39/uLm5ITg4GHFxccjJyWl0jOZ+T5YvX27jM2m/m73nM2fObHJeEydObNTGEd9z4Obn3ty/e4lEgnfeecfUxlHf9xsxUNmR7777DvPnz8eSJUuQnJyMgQMHYsKECSgoKBC7NIvau3cv5s6di0OHDmHnzp3Q6XS46667UFFR0ajd008/jdzcXNNt5cqVIlVsOX379m10Tvv27TM99tJLL+Gnn37C//3f/2Hv3r3IycnBgw8+KGK1lpOYmNjovHfu3AkA+NOf/mRq4yzvd0VFBQYOHIiPP/642cdXrlyJf//73/jss8+QkJAANzc3TJgwAdXV1aY2jz32GE6dOoWdO3fi559/xu+//445c+bY6hQ6pLXzrqysRHJyMt544w0kJydj06ZNSE9Px+TJk5u0Xbp0aaPfgz//+c+2KN8sN3vPAWDixImNzuvbb79t9LgjvufAzc/9+nPOzc3FV199BYlEgoceeqhRO0d835sQyG6MGDFCmDt3rul7vV4vBAcHC8uWLROxKusrKCgQAAh79+413Td27FjhL3/5i3hFWcGSJUuEgQMHNvtYSUmJoFAohP/7v/8z3ZeamioAEA4ePGijCm3nL3/5i9CjRw/BYDAIguCc77cgCAIA4fvvvzd9bzAYhMDAQOGdd94x3VdSUiKoVCrh22+/FQRBEE6fPi0AEBITE01ttm7dKkgkEiE7O9tmtZvjxvNuzuHDhwUAwqVLl0z3hYWFCf/85z+tW5yVNXfuTzzxhDBlypQWn+MM77kgtO19nzJlinDHHXc0us8Z3ndBEAT2UNmJ2tpaHDlyBOPHjzfdJ5VKMX78eBw8eFDEyqxPq9UCALp06dLo/nXr1sHX1xf9+vXDokWLUFlZKUZ5FnX27FkEBwcjIiICjz32GDIzMwEAR44cgU6na/T+R0VFITQ01One/9raWqxduxZPPvlko43CnfH9vtGFCxeQl5fX6H3WaDQYOXKk6X0+ePAgvLy8MGzYMFOb8ePHQyqVIiEhweY1W4tWq4VEIoGXl1ej+5cvXw4fHx8MHjwY77zzDurq6sQp0ML27NkDf39/REZG4rnnnkNRUZHpsc7ynufn52PLli2YPXt2k8ec4X3n5sh24sqVK9Dr9QgICGh0f0BAANLS0kSqyvoMBgNefPFFjB49Gv369TPd/+ijjyIsLAzBwcE4fvw4FixYgPT0dGzatEnEas0zcuRIrF69GpGRkcjNzcVbb72FMWPG4OTJk8jLy4NSqWzy4RIQEIC8vDxxCraSH374ASUlJZg5c6bpPmd8v5tjfC+b+3dufCwvLw/+/v6NHpfL5ejSpYvT/C5UV1djwYIFmD59eqONcl944QUMGTIEXbp0wYEDB7Bo0SLk5ubi/fffF7Fa802cOBEPPvggunfvjoyMDLz22muYNGkSDh48CJlM1inecwBYs2YNPDw8mkxlcJb3nYGKRDV37lycPHmy0VwiAI3mDvTv3x9BQUEYN24cMjIy0KNHD1uXaRGTJk0yfT1gwACMHDkSYWFh2LBhA1xcXESszLbi4+MxadIkBAcHm+5zxvebmqfT6fDwww9DEAR8+umnjR6bP3++6esBAwZAqVTimWeewbJlyxx6y5JHHnnE9HX//v0xYMAA9OjRA3v27MG4ceNErMy2vvrqKzz22GNQq9WN7neW951DfnbC19cXMpmsyVVd+fn5CAwMFKkq65o3bx5+/vln7N69G926dWu17ciRIwEA586ds0VpNuHl5YXevXvj3LlzCAwMRG1tLUpKShq1cbb3/9KlS/j111/x1FNPtdrOGd9vAKb3srV/54GBgU0uRKmrq0NxcbHD/y4Yw9SlS5ewc+fORr1TzRk5ciTq6upw8eJF2xRoIxEREfD19TX9fjvze270xx9/ID09/ab/9gHHfd8ZqOyEUqnE0KFD8dtvv5nuMxgM+O233xATEyNiZZYnCALmzZuH77//Hrt27UL37t1v+pyUlBQAQFBQkJWrs53y8nJkZGQgKCgIQ4cOhUKhaPT+p6enIzMz06ne/1WrVsHf3x/33HNPq+2c8f0GgO7duyMwMLDR+1xaWoqEhATT+xwTE4OSkhIcOXLE1GbXrl0wGAymoOmIjGHq7Nmz+PXXX+Hj43PT56SkpEAqlTYZDnN0ly9fRlFRken321nf8+vFx8dj6NChGDhw4E3bOuz7LvaseLrmv//9r6BSqYTVq1cLp0+fFubMmSN4eXkJeXl5YpdmUc8995yg0WiEPXv2CLm5uaZbZWWlIAiCcO7cOWHp0qVCUlKScOHCBWHz5s1CRESEcNttt4lcuXlefvllYc+ePcKFCxeE/fv3C+PHjxd8fX2FgoICQRAE4dlnnxVCQ0OFXbt2CUlJSUJMTIwQExMjctWWo9frhdDQUGHBggWN7ne297usrEw4evSocPToUQGA8P777wtHjx41Xc22fPlywcvLS9i8ebNw/PhxYcqUKUL37t2Fqqoq0zEmTpwoDB48WEhISBD27dsn9OrVS5g+fbpYp9QmrZ13bW2tMHnyZKFbt25CSkpKo3/3NTU1giAIwoEDB4R//vOfQkpKipCRkSGsXbtW8PPzE+Li4kQ+s5tr7dzLysqEV155RTh48KBw4cIF4ddffxWGDBki9OrVS6iurjYdwxHfc0G4+e+7IAiCVqsVXF1dhU8//bTJ8x35fb8RA5Wd+fDDD4XQ0FBBqVQKI0aMEA4dOiR2SRYHoNnbqlWrBEEQhMzMTOG2224TunTpIqhUKqFnz57Cq6++Kmi1WnELN9O0adOEoKAgQalUCl27dhWmTZsmnDt3zvR4VVWV8Pzzzwve3t6Cq6ur8MADDwi5ubkiVmxZ27dvFwAI6enpje53tvd79+7dzf5+P/HEE4Ig1C+d8MYbbwgBAQGCSqUSxo0b1+RnUlRUJEyfPl1wd3cXPD09hVmzZgllZWUinE3btXbeFy5caPHf/e7duwVBEIQjR44II0eOFDQajaBWq4Xo6Gjh7bffbhQ67FVr515ZWSncddddgp+fn6BQKISwsDDh6aefbvI/yo74ngvCzX/fBUEQ/vOf/wguLi5CSUlJk+c78vt+I4kgCIJVu8CIiIiInBznUBERERGZiYGKiIiIyEwMVERERERmYqAiIiIiMhMDFREREZGZGKiIiIiIzMRARURERGQmBioiIiIiMzFQERHZQHh4OD744AOxyyAiK2GgIiKnM3PmTNx///0AgNtvvx0vvviizV579erV8PLyanJ/YmIi5syZY7M6iMi25GIXQETkCGpra6FUKjv8fD8/PwtWQ0T2hj1UROS0Zs6cib179+Jf//oXJBIJJBIJLl68CAA4efIkJk2aBHd3dwQEBGDGjBm4cuWK6bm333475s2bhxdffBG+vr6YMGECAOD9999H//794ebmhpCQEDz//PMoLy8HAOzZswezZs2CVqs1vd6bb74JoOmQX2ZmJqZMmQJ3d3d4enri4YcfRn5+vunxN998E4MGDcI333yD8PBwaDQaPPLIIygrK7PuD42IOoSBioic1r/+9S/ExMTg6aefRm5uLnJzcxESEoKSkhLccccdGDx4MJKSkrBt2zbk5+fj4YcfbvT8NWvWQKlUYv/+/fjss88AAFKpFP/+979x6tQprFmzBrt27cJf//pXAMCoUaPwwQcfwNPT0/R6r7zySpO6DAYDpkyZguLiYuzduxc7d+7E+fPnMW3atEbtMjIy8MMPP+Dnn3/Gzz//jL1792L58uVW+mkRkTk45EdETkuj0UCpVMLV1RWBgYGm+z/66CMMHjwYb7/9tum+r776CiEhIThz5gx69+4NAOjVqxdWrlzZ6JjXz8cKDw/H3//+dzz77LP45JNPoFQqodFoIJFIGr3ejX777TecOHECFy5cQEhICADg66+/Rt++fZGYmIjhw4cDqA9eq1evhoeHBwBgxowZ+O233/CPf/zDvB8MEVkce6iIqNM5duwYdu/eDXd3d9MtKioKQH2vkNHQoUObPPfXX3/FuHHj0LVrV3h4eGDGjBkoKipCZWVlm18/NTUVISEhpjAFAH369IGXlxdSU1NN94WHh5vCFAAEBQWhoKCgXedKRLbBHioi6nTKy8tx3333YcWKFU0eCwoKMn3t5ubW6LGLFy/i3nvvxXPPPYd//OMf6NKlC/bt24fZs2ejtrYWrq6uFq1ToVA0+l4ikcBgMFj0NYjIMhioiMipKZVK6PX6RvcNGTIEGzduRHh4OOTytv8ZPHLkCAwGA9577z1IpfUd/Bs2bLjp690oOjoaWVlZyMrKMvVSnT59GiUlJejTp0+b6yEi+8EhPyJyauHh4UhISMDFixdx5coVGAwGzJ07F8XFxZg+fToSExORkZGB7du3Y9asWa2GoZ49e0Kn0+HDDz/E+fPn8c0335gmq1//euXl5fjtt99w5cqVZocCx48fj/79++Oxxx5DcnIyDh8+jLi4OIwdOxbDhg2z+M+AiKyPgYqInNorr7wCmUyGPn36wM/PD5mZmQgODsb+/fuh1+tx1113oX///njxxRfh5eVl6nlqzsCBA/H+++9jxYoV6NevH9atW4dly5Y1ajNq1Cg8++yzmDZtGvz8/JpMagfqh+42b94Mb29v3HbbbRg/fjwiIiLw3XffWfz8icg2JIIgCGIXQUREROTI2ENFREREZCYGKiIiIiIzMVARERERmYmBioiIiMhMDFREREREZmKgIiIiIjITAxURERGRmRioiIiIiMzEQEVERERkJgYqIiIiIjMxUBERERGZ6f8DivLT15wW7kgAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "energy = qtx.utils.DataTracer()\n", "VarE = qtx.utils.DataTracer()\n", "\n", "for i in range(200):\n", " samples = sampler.sweep()\n", " step = optimizer.get_step(samples)\n", " state.update(step * 2e-3)\n", "\n", " energy.append(optimizer.energy)\n", " VarE.append(optimizer.VarE)\n", "\n", " if i % 10 == 0:\n", " clear_output()\n", " energy.plot(batch=10, baseline=exact_energy)\n", " plt.xlabel(\"Iteration\")\n", " plt.ylabel(\"Energy\")\n", " plt.show()\n", " VarE.plot(batch=10)\n", " plt.xlabel(\"Iteration\")\n", " plt.ylabel(\"Energy variance\")\n", " plt.show()\n", "\n", "state.save(\"/tmp/neural_jastrow.eqx\")" ] }, { "cell_type": "markdown", "id": "024091b4", "metadata": {}, "source": [ "Then we can check its accuracy against the exact ground state." ] }, { "cell_type": "code", "execution_count": 16, "id": "9c86b9a8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Relative energy error: 0.00017402258135205257\n", "Fidelity with exact ground state: 0.99964914257028\n" ] } ], "source": [ "dense = state.todense(full_symm).normalize()\n", "\n", "E = dense @ H @ dense\n", "print(\"Relative energy error:\", abs(E - exact_energy) / abs(exact_energy))\n", "\n", "fidelity = abs(dense @ exact_state) ** 2\n", "print(\"Fidelity with exact ground state:\", fidelity)" ] } ], "metadata": { "kernelspec": { "display_name": "quantax_env", "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": "3.12.11" } }, "nbformat": 4, "nbformat_minor": 5 }