{ "cells": [ { "cell_type": "markdown", "id": "a01a167a", "metadata": {}, "source": [ "# Square J1-J2 model\n", "\n", "In this tutorial, we use neural quantum states and variational Monte Carlo to study the J1-J2 Heisenberg model on the square lattice.\n", "\n", "We will work on the 4x4 lattice. Due to the spin conservation in the Heisenberg interactions, we limit the number of both up and down spins to 8." ] }, { "cell_type": "code", "execution_count": null, "id": "847bdc40", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import jax.numpy as jnp\n", "import quantax as qtx\n", "from IPython.display import clear_output\n", "\n", "# 4x4 square lattice, 8 spin-up, 8 spin-down\n", "lattice = qtx.sites.Square(4, Nparticles=(8, 8))\n", "N = lattice.Nsites" ] }, { "cell_type": "markdown", "id": "da1ca2e7", "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. \n", "\n", "## Heisenberg model\n", "\n", "A nearest-neighbor Heisenberg model has $J_1=1$ and $J_2=0$. In this special case, the exact sign structure of the model is given by the Marshall sign rule. In the code below, `msr=True` encodes this sign structure by rotating the local basis of the Hamitltonian, such that its ground state wavefunctions are positive in the new basis." ] }, { "cell_type": "code", "execution_count": 2, "id": "2faf7eb7", "metadata": {}, "outputs": [], "source": [ "H = qtx.operator.Heisenberg(msr=True)" ] }, { "cell_type": "markdown", "id": "e84f1727", "metadata": {}, "source": [ "In this function, we define $J_1 = 1$ and $J_2 = 0.5$. The neighbors are determined by the distance of spins in real space. With `msr=True`, the function returns a Hamiltonian corrected by Marshall sign rule (MSR), which is equivalent to the original J1-J2 model but has simpler sign structures.\n", "\n", "In this small lattice, one can use exact diagonalization to obtain the reference energy. " ] }, { "cell_type": "code", "execution_count": null, "id": "bfa40131", "metadata": {}, "outputs": [ { "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" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Exact ground state energy: -44.91393283371544\n" ] } ], "source": [ "from quantax.symmetry import TransND, Rotation, Flip, SpinInverse\n", "\n", "full_symm = TransND() @ Rotation(np.pi/2) @ Flip() @ SpinInverse()\n", "E, wf = H.diagonalize(full_symm)\n", "exact_energy = E[0]\n", "print(f\"Exact ground state energy: {exact_energy}\")" ] }, { "cell_type": "markdown", "id": "2b5123a8", "metadata": {}, "source": [ "We can utilize a pre-defined ResNet for solving this Hamiltonian. Its architecture is shown below. By default, its output wavefunctions are strictly positive. Here we define a residual convolutional network with 2 blocks, 8 channels and 3x3 kernels.\n", "\n", "![ResConv architecture](../images/ResConv.svg)" ] }, { "cell_type": "code", "execution_count": 4, "id": "7b9b14f9", "metadata": {}, "outputs": [], "source": [ "model = qtx.model.ResConv(nblocks=2, channels=8, kernel_size=3)" ] }, { "cell_type": "markdown", "id": "fff01a9c", "metadata": {}, "source": [ "In Quantax, we usually define a variational state by `state = qtx.state.Variational(model)`. Here we should be careful about one more thing - the batch size. There are two benefits to set a maximum batch size in the forward pass.\n", "\n", "1. Sometimes the forward batch is too large and can cause an out-of-memory error. Set a maximum batch size can force the batch to be splitted into smaller pieces and forwarded piece by piece to avoid the memory bottleneck.\n", "\n", "2. When computing the local energy $E_\\mathrm{loc}(s) = \\sum_{s'} H_{ss'} \\psi(s')/\\psi(s)$ in systems like the Heisenberg model, the number of nonzero $H_{ss'}$ depends on $s$. A direct computation of $\\psi(s')$ involves non-constant length and triggers re-jitting. When a maximum batch size is given, Quantax will pad the number of $s'$ to a multiple of batch size to avoid re-jitting." ] }, { "cell_type": "code", "execution_count": 5, "id": "9f36f5f3", "metadata": {}, "outputs": [], "source": [ "state = qtx.state.Variational(model, max_parallel=25000)" ] }, { "cell_type": "markdown", "id": "58cbaa37", "metadata": {}, "source": [ "Here the forward and backward batch sizes are both set to 16384. You can also set them to different values by giving a tuple like `max_parallel=(25000, 2048)`. When running on multiple devices, the batch given here is the size on __each machine__. For example, the actual batch size on all machines is 8*25000 if you are running your code on 8 GPUs.\n", "\n", "Then we can define the Monte Carlo sampler and SR optimizer for training the state." ] }, { "cell_type": "code", "execution_count": 6, "id": "70757bdf", "metadata": {}, "outputs": [], "source": [ "sampler = qtx.sampler.SpinExchange(state, nsamples=1024)\n", "optimizer = qtx.optimizer.SR(state, H)" ] }, { "cell_type": "code", "execution_count": 7, "id": "6c4e5f07", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "energy = qtx.utils.DataTracer()\n", "VarE = qtx.utils.DataTracer()\n", "\n", "training_rate = 0.01\n", "\n", "for i in range(200):\n", " samples = sampler.sweep()\n", " step = optimizer.get_step(samples)\n", " state.update(step * training_rate)\n", "\n", " energy.append(optimizer.energy)\n", " VarE.append(optimizer.VarE)\n", " if i % 10 == 0:\n", " clear_output()\n", " energy.plot(batch=10, baseline=exact_energy)\n", " plt.show()\n", " VarE.plot(batch=10)\n", " plt.show()" ] }, { "cell_type": "markdown", "id": "cbf33766", "metadata": {}, "source": [ "Then we can save the trained model for reference in the future. Internally, we call [`equinox.tree_serialise_leaves`](https://docs.kidger.site/equinox/api/serialisation/#equinox.tree_serialise_leaves) to save the model." ] }, { "cell_type": "code", "execution_count": 8, "id": "1e63d3ff", "metadata": {}, "outputs": [], "source": [ "state.save(\"/tmp/Heisenberg.eqx\")" ] }, { "cell_type": "markdown", "id": "2b99886b", "metadata": {}, "source": [ "To get better accuracy, one can apply symmetry projections on the variational state. For a symmetry group $G$ with elememts $g$ and characters $\\chi_g$, the projection is defined as\n", "\n", "$$\n", "\\psi^\\mathrm{symm}(s) = \\sum_g \\chi_g \\psi(T_g s).\n", "$$\n", "\n", "In this system, the symmetry operation includes translation, rotation, mirror flip, and spin inverse. As the translation symmetry is already enforced in the convolutional network, we enforce the remaining symmetries by projection." ] }, { "cell_type": "code", "execution_count": 9, "id": "b656d560", "metadata": {}, "outputs": [], "source": [ "symm = Rotation(np.pi/2) @ Flip() @ SpinInverse()\n", "\n", "symm_state = qtx.state.Variational(\n", " model, \"/tmp/Heisenberg.eqx\", symm, max_parallel=2048\n", ")\n", "\n", "sampler = qtx.sampler.SpinExchange(symm_state, nsamples=1024)\n", "optimizer = qtx.optimizer.SR(symm_state, H)" ] }, { "cell_type": "code", "execution_count": 10, "id": "2ec93492", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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R+W5Nc5sV+wouAwDmjEvs9/OJNTXcqSEid2NQo3DiLkByVBBSorhTowTVV+0wqD0F9cmZy2g2WzEwKgipyf0/jZujEojIUxjUKJzY+WRPP9lPcC2qUX+6Q8nE9NO4pHBoNOpPQYkH7s0Z1//UE8BCYSLyHAY1ClcspZ+CMKg9/cS2bnlVNdp3GEYnhGPakGgA6k1BtVqsyDlVCQC4bXz/up5EHJVARJ7CoEbhxB2AgVFBrKlRCHGnJjZUj7kT7DUm7x9XZ1Cz/5tq1LdaEBdmwKSUKLc8J0clEJGnMKhRMFOzGfUtFgBAUmQQBkbZ00/1LRaYmnjEvFzEmpqYUD3mpCZAowHyitSZghK7nrLGJUCr7X/qCeCoBCLyHAY1CiZ2PsWE6BGsD0CwPkCqR2AKSj5i91NMiAFxYUbVpqAsVhv+e9I9pwh3xlEJROQpDGoUrHPnk0gqFmYKSjZigWtM+3krt6s0BXXwQg2uNJkRFRyIaUOj3frcHJVARJ7AoEbBOnc+idjWLT8x/STummV1SkEVqyjY3P21fZfm22PjEaBz77cKdkARkScwqFGwkk6dTyLu1MjLZhNQ0+i4U+OYgiqXbW3uZLMJnU4R7v+Be1fjqAQi8gQGNQompZ867dR0tHWrryjVF9S1mGGx2Tt2otsLXoGOFJRaDuI7WnQFlfWtCDMEYPqIGLc/vzgqgTU1RORODGoUTJr71J5yAjrST8VMP8lCTJeEGQNgCNBJ96stBSXuOM0aE+fwPt2FZ9UQkScwqFGwzmfUiMSzaoqvNMNm4xkf3ialnjrt0gD2FFT6UHWkoARBkOpp3Nn11BlHJRCRJzCoUaimNov0A7Rz91NihBE6rQZtVhsq6lvkWp7f6jijxnDN1+aOb++C8vEU1NeldSi+0gxjoBYzr4vzyGuwUJiIPIFBjUKJRcJhxgCEGwOl+wN0WiRFGgFwBpQcqrrYqQHsKSitBjhWVOvT3Wn/aZ/1dMt1cQjSuz/1BHScKsydGiJyJwY1ClXspEhYxLZu+XS3UxMXZpTOcxEDA18kdT25adaTMwM6BTUclUBE7sKgRqE62rmDr/maFNSooCDV13Se++TM3AlJAIAPfLSu5mxFPc5dboRep8Ws0Z5JPQEclUBEnsGgRqGKnZxRIxoUw2ndcqlun9DtLP0EAHPG+XYK6j/tuzQ3johBWKe0p7txVAIReQKDGoVydkaNSAx0illT43UdIxKuTT8B9rRK+lD7uS6+mIL6jwcP3LuaeADf5XoWCxORezCoUaiS9tSSs50asa2b6Sfv6zyhuyvfEQ/i87FZUJeqG3GqrA46rQbfHhvv8dcTi4Uvc6eGiNyEQY1CdRy85yT91B7UlNe1oNVi9eq6/J04oTu2i50aoFMKqtjkUykosUD4hmHRiOoiveZOHJVARO7GoEaBWi1WaXqxs/RTTIgeQYE6CEJHQTF5ntlqQ22Tvai1q5oawDEFtcuHzqwRU09zxnmu66kzjkogIndjUKNAZbX2Q/WCAnUO84VEGo2m02BLBjXecqV9l0arASKDu9/JEFNQvhLUlJmakVdUC40GyPJSUMNRCUTkbgxqFKhz6kmj0Ti9RkxB+VJ6w9eJqafoED10Wuefi8jXUlAftu/STBkUhbhwo1dek6MSiMjdGNQoUEmt/Yegs9STaCAP4PM68YwaZ7tnV/O1FJSUevLQrCdnOCqBiNyNQY0ClXRzRo2IHVDe13FGTddFwp3N9ZEUVFVDK766WAPAe6kngKMSiMj9GNQoUHedT6KU9q9x/pP3dJxR07vOoDmpvpGC2nOyAjYBGJ8cIQXL3sBRCUTkbgxqFKi7uU8inirsfeIZNd21c3cWG2rADcOUn4KSI/UEcFQCEblfn4KajRs3YsiQITAajUhPT8fBgwe7vX779u0YPXo0jEYjxo8fj127djl8/Z133sHs2bMRExMDjUaDvLw8p8+Tm5uLWbNmISQkBOHh4bj55pvR3Ky+nYru5j6JxPlPpmYz6lr4A8EbxJqa7tq5r/ad8e0H8Sk0qDE1mbH/myoA3g9qOCqBiNzN5aBm27ZtWLlyJdasWYMjR44gLS0NWVlZqKysdHr9/v37sWjRIixduhRHjx7F/PnzMX/+fOTn50vXNDY2YsaMGXjhhRe6fN3c3FzMmTMHs2fPxsGDB/HVV19h+fLl0GrVtdlksdpQXmdv6e6upibEECAVrCo5taEmUk1NL3dqgI4U1HGFpqByTlfAYhNwXXwohg8I9frrc1QCEbmTyxHBunXrsGzZMmRnZ2Ps2LHYtGkTgoOD8frrrzu9/tVXX8WcOXPw+OOPY8yYMXj++ecxefJkbNiwQbrm/vvvx+rVq5GZmdnl6z722GP42c9+hieffBLjxo3DqFGjcM8998BgcP4DprW1FXV1dQ43X1Be1wKrTYBep5W+4XclhW3dXuVqTQ3gmIJS4m7Ne3mlAIA5Xpj15AxHJRCRO7kU1LS1teHw4cMOwYdWq0VmZiZyc3OdPiY3N/eaYCUrK6vL652prKzEgQMHEBcXh+nTpyM+Ph4zZ87E559/3uVj1q5di4iICOmWkpLS69eTk5h6Soo0QtvDWSgsFvYucacm1oWgBuhIQSmtrmZfQSU+OXMZOq0G8yYmybIGjkogIndyKaipqqqC1WpFfLzjsLv4+HiUl5c7fUx5eblL1ztz/vx5AMCzzz6LZcuWYffu3Zg8eTJuvfVWnD171uljVq1aBZPJJN2Kiop6/XpykqZzd5N6ErGt27s6amp6n34CHFNQhdXK+KxazFasfu9rAED29CGypJ4AjkogIvfyiYIUm80GAHjooYeQnZ2NSZMm4ZVXXsGoUaO6THsZDAaEh4c73HyB1M7dTeeTKIUH8HlNU5sFTW324aGupJ+Aq7qg8pWxW/N/+86hsKYJCeFGPPrt62RbB08VJiJ3cimoiY2NhU6nQ0VFhcP9FRUVSEhw3jmRkJDg0vXOJCbat+/Hjh3rcP+YMWNQWFjY6+fxBb3pfBKJoxLY1u154i6NPkCLUEOAy48XD+L74Lj8Qc35yw3YtO8cAGD1HWP79H7chfOfiMidXApq9Ho9pkyZgpycHOk+m82GnJwcZGRkOH1MRkaGw/UAsGfPni6vd2bIkCFISkpCQUGBw/1nzpzB4MGDXXgHylfSizNqROJQy+IrzTy8zMNq2uc+xYbou5zH1Z2s9llQJ0rkTUEJgoDV732NNqsNM68bgNu83MZ9NY5KICJ3cvlXtJUrV+KBBx7A1KlTMW3aNKxfvx6NjY3Izs4GACxevBjJyclYu3YtAGDFihWYOXMmXn75ZcydOxdbt27FoUOHsHnzZuk5a2pqUFhYiNJSeyeGGLwkJCQgISEBGo0Gjz/+ONasWYO0tDRMnDgRb775Jk6fPo233367338ISlLcXh/Tm5qapMggaDVAq8WGy/WtXhtE6I/EIuFoF1NPothQAzKGx+CLb6rxwYky/OSW4e5cXq+9f7wMn39TBX2AFs/NG9enAM2dOCqBiNzJ5aBm4cKFuHz5MlavXo3y8nJMnDgRu3fvloqBCwsLHc6OmT59OrZs2YKnn34aTz31FEaOHIkdO3YgNTVVumbnzp1SUAQA9957LwBgzZo1ePbZZwEAjz76KFpaWvDYY4+hpqYGaWlp2LNnD4YPl+eHgyfYbAJKa3s+o0YUqNMiMSIIJbXNKKxpYlDjQVV9LBLu7DvjE/HFN9XYJVNQU99ixvPvnwQAPHzLCAyOCfH6Gq7WuVBYEATZgywi8m19SqYvX74cy5cvd/q1ffv2XXPfggULsGDBgi6fb8mSJViyZEmPr/vkk0/iySef7O0yfU5VQyvarDbotBok9DJASYm2BzVFV5owdUi0h1fov6r7cEbN1eaMS8AzO/KlFJQ46sJb1u05g8r6VgyNDcFDM4d59bW7IqafxFEJkcF9//MlIvKJ7id/UdReJJwQbkSArncfTUcHFM+q8SRX5z45E9OeggK8fxBffokJb+6/CAB4bt44GAN1Xn39rnBUAhG5E4MaBXHljBrRIJ4q7BXVja7PfXJGjoP4bDYBT+/Ih00Abp+QiJtGDvDaa/cGRyUQkbswqFEQqZ27F51PohS2dXuFuIvgytwnZ+bI0AW19asi5BXVItQQgGduH9vzA7yMxcJE5C4MahTElc4nUee2bvIcd9TU2B/v3RRUVUMrXth9GgCw8tvXIV6BxeQdOzUMaoiofxjUKIiYfupN55NIrKkpMzWjzWLzyLqo09ynfnQ/ieaOt89Z+uBEab+fqydrd52GqdmMsYnhWJyhzDOdOCqBiNyFQY2ClEgjEnrfFTMgzABDgBY2ASit5W6NJwiC4LadGgDIGhcPnVaD/JI6XKpu7PfzdeXA+Wr860gxNBrgf+5K7XXxubdxVAIRuYsyv8v5IUEQOuY+ubBTo9FoONjSw+qaLbDY7Cc2R/ezUBhoT0EN82wKymy14Zn38gEA914/CJMGRXnkddxhQBhPFSYi92BQoxBXmsxoNtsHJiZFulb3kNIeBLGt2zOq2lNPYYYAt7VCe7oL6s+fX8CZigbEhOjxxJxRHnkNd4llTQ0RuQmDGoUQU09xYQYYAlz7wTmIOzUeJc59ckfqSeTJFFRJbTNe/egsAGDVd8Yo/kA7dj8RkbswqFGIvnQ+idjW7VnVbmrn7syTKahf7/wazWYrpg2Jxt2Tk9363J5w9agEIqK+YlCjEK5M577awPYOqGIGNR4h1nq4o56ms7kT7CmoD467L6jJOVWB/56sQIBWg9/cleoTs5SuHpVARNRXDGoUQiwSFgMUV4hn1RTxrBqPEDufYt2YfgKArHEJ0Gk1+Lq0Dher+p+Cam6zYs3OrwEAS28aiuviw/r9nN7AUQlE5C4MahSiL51PIjH9VNPYhoZWi1vXRR1n1PRnQrcz0SF6t6agNnx8FsVXmpEUYcTPZo3s9/N5E0clEJE7MKhRCOngvT6kn8KNgYgMDgTAGVCe4M4zaq4mpqD62wX1TWU9Nn96HgCw5s5xCDEE9Htt3sSzaojIHRjUKERJe6GwK6cJd9YxrZtBjbu5a+6TM+5IQQmCgGd2fA2zVcCto+Mwe2y8m1fpeeJZNWzrJqL+YFCjAHUtZtS12NNGfUk/AZ3bullX427ihO5YNxcKA/YU1PR+zoJ6L68UueerYQzU4tk7x/lEcfDVOCqBiNyBQY0CiGfURAUHIljft7TBQLFYmDs1bueJlu7OxIP4+tIFZWo24zcfnAQAPDJrpFRf5WuYfiIid2BQowAl/eh8EjH95BkWqw1Xmuxtxp6oqQE6UlAny1xPQb383wJUNbRh+IAQLLtpmEfW5w2xHJVARG7AoEYBpIP3+lAkLOKpwp5R02T/IavRAFEeOpm3rymo48W1+OuXlwAAz89LhT7Ad/85D+CoBCJyA9/9Lqgi0sF7faynATrauotqmnkqqxuJnU/RwXrotJ6rVZnrYgrKahPwq3fzIQjA/IlJmD4i1mNr8waOSiAid2BQowBSO3c/gpqkSCM0GqDZbOUWvht5Yu6TM7M7paAu9CIF9fcDl3CixIQwYwCemjvGo2vzBrFQuLqhjUE5EfUZgxoFkA7e60f6yRCgQ0K4fbo3U1DuI7Vzu/ngvat1TkH1dGZNZX0LXvywAADweNYoxIW5NtVdicRC4TarDXXNPECSiPqGQY0ClPTjNOHOOlJQDGrcRUo/eXinBuh9Cup/PziF+hYLJgyMwH3pgz2+Lm/oPCrhckOLzKshIl/FoEZmzW1W6RyU/nQ/AeyA8gRxRIInzqi5Wm9SUPu/qcKOvFJoNMBv5qd6tM7H2zgqgYj6i0GNzEpq7QFImCEAEUGB/XouabBlDQ/gc5eOEQmeTT8BPaeg2iw2PP1ePgDgB+mDMWFgpMfX5E08q4aI+otBjcz6M8jyamzrdr8qD859ckZMQb3vJAX1p8/O4/zlRsSGGvCLrFFeWY83DWAHFBH1E4Mambmj80kk1tQUMv3kNp6a0N0V8SC+U2V1OH+5Qbq/qKYJr+WcBQA8PXdMv3f1lEjsgOJZNUTUVwxqZOaOzieRWFNTZmqBxWrr9/NRR/op1ks7NVFOUlCCIGDNzq/RarEhY1gM5k1M8spavI3pJyLqLwY1MnNX5xMAxIUZoA/QwmoTUGZiB4k7eHrukzO3T2jvgjpRDgD478kK7D1diUCdBs/PT/XJgZW9wVEJRNRfDGpk1pF+6v8gQq1WI6Wx2AHVf81tVjS2WQF4r6YGAGaP7UhB5ZeY8OudXwMAHrx5GEbEhXptHd42gDs1RNRPDGpk5o65T52JKSjW1fSfWE+j12kRZujb9PS+iArR48b2sQc/evMQSk0tGBgVhOXfGum1NchB3KlhTQ0R9RWDGhm1WWyobP8G7o70E9CprZsdUP1W3anzydspn7njEwAA5XX2NOKv7xyHIL3Oq2vwNo5KIKL+YlAjozJTMwQBMAZqEeOmw90GdRpsSf3jrblPzogpKPt/x+PWMfFeX4O3cVQCEfUXgxoZde58ctdOANNP7uOtuU/ORIXokT19CK6LD8WaO8d5/fXl4DgqgSkoInKd9woF6BodnU/9LxIWiWfVFDP91G/i+Ap37aK56unbx8ryunIaEGpAfYsFl+tbVV0UTUSe0aedmo0bN2LIkCEwGo1IT0/HwYMHu71++/btGD16NIxGI8aPH49du3Y5fP2dd97B7NmzERMTA41Gg7y8vC6fSxAE3HbbbdBoNNixY0dflq8YxW48eE8k7tRUNbShqY1b+P3R0c4tT1Djj3hWDRH1h8tBzbZt27By5UqsWbMGR44cQVpaGrKyslBZWen0+v3792PRokVYunQpjh49ivnz52P+/PnIz8+XrmlsbMSMGTPwwgsv9Pj669evV805He7ufAKAiOBAhLdv4YvpLeobb859IrvYMHsAyaCGiPrC5aBm3bp1WLZsGbKzszF27Fhs2rQJwcHBeP31151e/+qrr2LOnDl4/PHHMWbMGDz//POYPHkyNmzYIF1z//33Y/Xq1cjMzOz2tfPy8vDyyy93+Vqdtba2oq6uzuGmNGL6yZ07NUCncQnVTEH1R5XM6Sd/1DGpm0ENEbnOpaCmra0Nhw8fdgg+tFotMjMzkZub6/Qxubm51wQrWVlZXV7flaamJnz/+9/Hxo0bkZCQ0OP1a9euRUREhHRLSUlx6fW8wZ1znzoTU1Bs6+4fMf0Uy50ar2H6iYj6w6WgpqqqClarFfHxju2l8fHxKC8vd/qY8vJyl67vymOPPYbp06dj3rx5vbp+1apVMJlM0q2oqMil1/M0i9UmjTJIjnRfoTAADIphW7c7VHt5QjdxVAIR9Y9PdD/t3LkTe/fuxdGjR3v9GIPBAINBub9hV9S3wmoTEKjTIC7MvetMad/5YVt33wmC0DGhmzs1XsOdGiLqD5d2amJjY6HT6VBRUeFwf0VFRZcpoYSEBJeud2bv3r04d+4cIiMjERAQgIAAeyx2991345ZbbnHlLSiGWE+TFBkErda9hc8D2dbdb3UtFpit9lNtWVPjPQM4KoGI+sGloEav12PKlCnIycmR7rPZbMjJyUFGRobTx2RkZDhcDwB79uzp8npnnnzySRw/fhx5eXnSDQBeeeUVvPHGG668BcXwROeTqONU4SYeN99HYj1NqCEAxkB1jydQEo5KIKL+cDn9tHLlSjzwwAOYOnUqpk2bhvXr16OxsRHZ2dkAgMWLFyM5ORlr164FAKxYsQIzZ87Eyy+/jLlz52Lr1q04dOgQNm/eLD1nTU0NCgsLUVpaCgAoKCgAYN/l6Xy72qBBgzB06FDX37UClHQ6TdjdxOdsbLPiSpMZ0dxpcFm1jCMS/NnVoxIiggNlXhER+RKXW7oXLlyIl156CatXr8bEiRORl5eH3bt3S8XAhYWFKCsrk66fPn06tmzZgs2bNyMtLQ1vv/02duzYgdTUVOmanTt3YtKkSZg7dy4A4N5778WkSZOwadOm/r4/xRI7n9w1yLIzY6AO8eH2Hw6sq+kbqUiYAaFXcVQCEfVHnwqFly9fjuXLlzv92r59+665b8GCBViwYEGXz7dkyRIsWbLEpTX4+tZ0sXRGjXs7n0QpUcGoqGtFUU0TJqZEeuQ11IxFwvLhqAQi6isOtJSJtFPjgfQT0KmuhsXCfSLu1MQy/eR17IAior5iUCMDm03w2MF7ooGdioXJdWKhMOuRvI+jEoiorxjUyKCqoRVtFhu0GiAhwuiR1xDPquEBfH3TMSKB6SdvG8CdGiLqIwY1MhCncyeEGxGo88xHwPRT/3BCt3xiOf+JiPqIQY0MpHZuD6WegI6hliVXmmG1+XZRtRw6amq4U+NtHJVARH3FoEYGnu58AoD4cCMCdRpYbALKTExBuYrn1MiHhcJE1FcMamRQUuu504RFOq1Gen7W1bjGYrXhShNrauQijkqoYvqJiFzEoEYG3kg/AR0pKNbVuOZKkxmCAGg0QBRPtPU6sY2+iqMSiMhFDGpk0JF+8lJQw7Zul4gH70UF6xHgoUJu6trVoxKIiHqL37G9TBAEjx+8J0qJYlDTFzUckSArY6AOYQaOSiAi1zGo8bLaJjOa2qwAgCQPBzUdbd2sqXFFFYuEZSfV1TCoISIXMKjxMjH1NCDMAGOgzqOvlRItFgpzp8YVHWfUsEhYLjyrhoj6gkGNl3mj80kkpp8q61vRYrZ6/PXUQjqjhukn2XBUAhH1BYMaLyv2UucTAEQGB0q1CcXsgOo1sVA4mu3csuFZNUTUFwxqvMxbnU8AoNFoOg22ZF1Nb4kn2bKmRj7S/Kd6nipMRL3HoMbLpOncXkg/AR2DLQtZV9NrYk1NLIMa2YijEtj9RESuYFDjZd46eE/Es2pc1zEigeknuTD9RER9waDGy8TaFk/OfeqM07pdV81zamTHUQlE1BcMaryovsWMuhb7Cane6H4COrd1s6amN1rMVjS02j8j7tTIh6MSqCfFV5rw8N+P4NDFGrmXQgrCoMaLxHqayOBAhLR3JXla51OF+cOhZ2LqKVCnQbjRO58RXYujEqgnz/37JD44UYYXPyyQeymkIAxqvKi4xnudTyIxzVXfaoGp2ey11/VV0sF7IQZoNBqZV+O/OCqBupNfYsJ/T1YAAA5dugJTE7+3kR2DGi/y1synzoL0Oqk+gSmonlVzRIJicFQCdWX9R2ek/7baBHxy9rKMqyElYVDjRR1BjXeKhEVs6+49qUiY9TSy46gEcuZYUS0+OlUJrQbIGhcPAPj4dKXMqyKlYFDjRR2dT97bqQE6tXWzA6pH0hk17HySHUclkDPiLs1dkwZi6YxhAICPCyphtbFmkBjUeJW3z6gRDeJZNb3G9JNy8KwautqRwiv4uOAydFoNfnbrCEweFImIoEDUNplxtPCK3MsjBWBQ40Vy1NQAnTqgrrCmpidVnNCtGEobldBituJkaR27CGX0yh77Ls3dk5MxOCYEATotbhk1AACQwxQUgUGN1zS3WaWZQileOnhPNFA6q4Y7NT0Ra2qimX6SndJGJbz0YQG+89pn+B1biGVx6GINPjtbhQCtBo/MGindP2t0HABg7ykGNcSgxmvEXZpQQwDCg7x7/omYfiq50gwb887dEid0c+6T/JSWfvq0vcPmD/vO4b28EplX439eaa+lWTA1RaoTBICZ1w2AVgMUVNRLdYvkvxjUeEnn1JO3zz9JjAhCgFaDNqsNFfUtXn1tX9MxIoHpJ7lJpworoPupvsWMs5UN0v//5dvHcby4Vr4F+ZkD56vxxTfVCNRpsHzWCIevRQbrMXVwNAB2QRGDGq+Rq/MJAHRaDZLa63gKq/mbTFcEQejU0s2dGrl1nFMj/6iEE8UmCAKQFGHEraPj0Gqx4cG3DqOyjr8keIO4S7Pw+hSnNYmzxthTUKyrIQY1XiJX55NImgHFYuEu1bda0Ga1AeBOjRIoaVRCXvuuzKRBUVh/70SMiAtFeV0LHvrbYbSYrbKuTe32n6vCl+droNdp8fC3Rji95tb2upr956rR1MaxGv6MQY2XyNX5JGJbd8/EXZoQvQ5Bep3MqyEljUrIK6wFAExMiUSYMRD/b/FURAQF4mhhLZ7ekS/7TpJaCYKA9XvOAgAWTUtBYoTz758j4kIxMCoIbRYbvvim2ptLJIVhUOMlxTLv1AyMYlDTk2q2cytOrEJGJRxr36lJS4kEAAyJDcHG70+GTqvB24eL8efPL8i3OBX74ptqHLxYA32AFj/tYpcGADQajbRbs/d0hbeWRwrEoMZLxPTTQC+3c4t4qnDPePCe8gxQQAdUmakZFXWt0Gk1SE0Ol+6fMTIWv/rOGADA/+46hU/PcP6QOwmCINXS3Jc+CPHhxm6vnzXGPjJh7+lK7pz5MQY1XtBm6eg6kj/9xJqarrDzSXnEUQlyzn8SU0/XxYchWO94HEP2jUNwz9SBsAnA8i1HcKGqUYYVqtOnZ6tw+NIVGAO1+Mktw3u8Pn1oNIL1OlTUteLr0jovrJCUqE9BzcaNGzFkyBAYjUakp6fj4MGD3V6/fft2jB49GkajEePHj8euXbscvv7OO+9g9uzZiImJgUajQV5ensPXa2pq8Mgjj2DUqFEICgrCoEGD8LOf/Qwmk6kvy/e6MlMzBAEwBGhlO/9EHGpZUd/CwsYuSHOfuFOjGEo4q0YsEp7YnnrqTKPR4Pn5qZgyOAp1LRb86M2vUNdi9u4CVUgQBKxrPz34B+mDERfW/S4NYK/BmjEiFoB9t4b8k8tBzbZt27By5UqsWbMGR44cQVpaGrKyslBZ6fwv0f79+7Fo0SIsXboUR48exfz58zF//nzk5+dL1zQ2NmLGjBl44YUXnD5HaWkpSktL8dJLLyE/Px9/+ctfsHv3bixdutTV5cuic+eTt8+oEUWH6BGs10EQOoqWyRHTT8qjhFEJ4k7NJCdBDQAYAnT4ww8mIzHCiHOXG/Ho1jwOV+ynfQWXcayoFkGBOjw0s+ddGtGtbO32ey4HNevWrcOyZcuQnZ2NsWPHYtOmTQgODsbrr7/u9PpXX30Vc+bMweOPP44xY8bg+eefx+TJk7Fhwwbpmvvvvx+rV69GZmam0+dITU3Fv/71L9xxxx0YPnw4Zs2ahf/5n//Bv//9b1gsym/fK5a58wmw/0bJDqjuSXOfmH5SDLkLha02ASdK7DvCaV0ENQAQF2bE5vunwhCgxd7TlXiRoxT6rPMuzeLpg6XzinrjW6PsQc2xolpZU5YkH5eCmra2Nhw+fNgh+NBqtcjMzERubq7Tx+Tm5l4TrGRlZXV5fW+ZTCaEh4cjIMD5yIHW1lbU1dU53ORSLBUJyxfU2F+fgy27w4P3lEdMP8nV0n22sh5NbVaE6HUYERfa7bXjB0bgd9+bAADY9AlHKfTVR6cqcaLEhGC9Dg/d3PtdGgCICzdifHIEAODjAu7W+COXgpqqqipYrVbEx8c73B8fH4/y8nKnjykvL3fp+t6u4/nnn8eDDz7Y5TVr165FRESEdEtJSenz6/WX3J1PohQOtuyWOPeJOzXKIfeoBDH1NGFgJHTanlPH8yYm46ftRa0cpeA6QRCkSdxLpg/p02BZccAlRyb4J5/rfqqrq8PcuXMxduxYPPvss11et2rVKphMJulWVFTkvUVepaTWHkTImX4COqaDM6hxjjs1yiP3qISrz6fpjV/MHsVRCn304dcVOFlWh1BDAJbdNKxPzyHW1Xx65jLaLDZ3Lo98gEtBTWxsLHQ6HSoqHA83qqioQEJCgtPHJCQkuHR9d+rr6zFnzhyEhYXh3XffRWBgYJfXGgwGhIeHO9zkIvfBe6JBPKumS1abgJomBjVK4zAqocX79XNHO50k3FtarYajFPrAZhOwvv1cmuwbhyCqD7s0AJCaFIEBYQY0tllx8EKNO5dIPsCloEav12PKlCnIycmR7rPZbMjJyUFGRobTx2RkZDhcDwB79uzp8vqu1NXVYfbs2dDr9di5cyeMxp5b/JTAahNQbrL/piZ3TU0Kz6rp0pWmNogbAdHBDGqUwmFUgpdTUI2tFpypqAfgWlADgKMU+mD31+U4XV6PMEMAfjSjb7s0gD2onDVK7ILi6cL+xuX008qVK/GnP/0Jb775Jk6dOoWf/OQnaGxsRHZ2NgBg8eLFWLVqlXT9ihUrsHv3brz88ss4ffo0nn32WRw6dAjLly+XrqmpqUFeXh5OnjwJACgoKEBeXp5UdyMGNI2Njfjzn/+Muro6lJeXo7y8HFarsn8DqqhrgcUmIECr6dVZC54kBlWmZjNMzTxLozMx9RQVHIgAnc9lZVVNrg6o/BITbAKQEG5EQoTr/3aHxIZgw/cnQasB3j5cjNe/uOj+RapE512aH84Yiojgrnfhe+Nb7XU1Oad4urC/cfm798KFC/HSSy9h9erVmDhxIvLy8rB7926pGLiwsBBlZWXS9dOnT8eWLVuwefNmpKWl4e2338aOHTuQmpoqXbNz505MmjQJc+fOBQDce++9mDRpEjZt2gQAOHLkCA4cOIATJ05gxIgRSExMlG5y1sr0hph6Sow09qrQ0JNCDAFS4SXrahxx7pNyyTUqIa+oFoDruzSd3TRyAJ6eOxYA8D8fnOQohS58cKIMZyoaEG4MwA9nDO33880YGQu9TovCmiacu8xTnv2J837oHixfvtxhp6Wzffv2XXPfggULsGDBgi6fb8mSJViyZEmXX7/lllt8NtoWi4QHRsrb+SQaGBWMqoY2FF9pQmp76yN1Onivj3l88hy5RiWIQY0rRcLOZN84BKfK6rD9cDGWbzmC95bPwNDYkP4vUCWsnXZplt00DBFB/dulAYBQQwDSh0Xjs7NV+Ph0ZY/t+KQe3Gf3sBKFFAmLxLqaQu7UOOgYkcCdGqWRa1TCMTfs1AD2gy9/c1cqJg+K5CgFJ94/XopzlxsRGRyIJTcOcdvzilO7WVfjXxjUeJjU+SRzO7dInAHFYmFHHJGgXLEyjEqorGtBqakFWg0wYWD/dzQNATpsun8KRylcxWK14dWPzgKw79KEGfu/SyOaNdpeEvHVxSusIfQjDGo8TJyzJHfnk4ht3c5VcUK3Yg2QoVBYTD2NjAtDiKFPWfprcJTCtd7LK8X5qkZEh+jxwPQhbn3uQTHBGBEXCqtNYC2TH2FQ42FKTT+xUNhRR6Ewd2qURo5RCe4oEnaGoxQ6WKw2vLbXvkvz4M3DEOqm4LEzMQXFqd3+g0GNB9lsgjTMUimFwimd5j/ZuP0tYaGwcskxKsFdRcLOcJSC3TtHS3CpugkxIXoszhjskdcQRybsK6hkus9PMKjxoKrGVrRZbNBq0KdzLjxBbC1vs9hkGxKoRGzpVq6OQmHvjEqw2QQcL7ZP5nb3To3I30cpmK02/L59l+bHM4cjWO/+XRoAmDI4CuHGAFxpMiOv6IpHXoOUhUGNB4mpp/hwI/QByvijDtRpkdgeYDEF1YFzn5RLrKnx1qiEc5cb0NBqQVCgDtfFe6YV2NkohVaLsg8Sdad/HS5GUU0zYkMN+MENntmlAYAAnRa3jOo4iI/UTxk/aVVKaZ1PIjEFxbZuuxazFfWt9h+WsSwUVhxvj0o42p56Gp8c4dHTpa8epfCrd/1jlEKbxYbf7/0GAPDTW4YjSK/z6OuJAy5ZV+MfGNR4kNI6n0SDOAPKQU17PU2AVoPwIM9sg1P/eHNUgnQ+zaBIj7+WP45S2H64CCW1zYgLM+D76YM8/nozrxsArQY4XV6PYnZ9qh6DGg9SWueTKCW6/awa/gMH4Jh60mjkHWVBznlzVIKnOp+64k+jFFotVmxo36V5+FsjYAz07C4NAEQG6zFlcBQA4GPu1qgegxoPEn8rSFZI55OIbd2Oqhrbi4SZelIscVSCpzugWsxWnC63T+b2ROdTV7JvHIIFUwbCJgDLtxxBYbU6/21u+6oIZaYWJIQbsfD6FK+9rngQH1NQ6segxoOUmn4aGMWgprMaFgkrnrfOqskvMcFqEzAgzIAkL3YsiqMUJqbYRylsOVjotdf2lhazFRs/bt+lmeWdXRqRWFfzxblqNLV5vtic5MOgxkMEQVBs+kmsqSmra0GbxSbzauRX3ci5T0rnrVEJ0vk0AyO9noo0BOhwz1T77sXXpSavvrY3/ONgISrqWpEcGYR7pg706muPjAvFwKggtFls2P9NtVdfm7yLQY2H1DaZ0dhmb9FUWvdTbKgeQYE6CAJQWstiYammhgfvKZa3RiWIQc0kLxQJOzMuKRwA8HVpnao6oVrMVvzfvnMA7LU0hgDv7dIA9p2wjgGXTEGpGYMaDxFTT7GhBq9us/aGRqORUmJs6+4094k7NYrlrUnd3i4SvtqohDDotBrUNLahXEUH8v3ty0u4XN+KgVFB+N4U7+7SiL7VHtR8fLpSVQEjOWJQ4yHFCk09iTjYsoOYfmJNjXKJoxI8eU5NVUMriq80Q6Oxz2iSgzFQhxED7Af+fV1SJ8sa3K2pzYJNn9h3aX42a6RsB5HeMCwGQYE6lNe14GSZOv5s6VoMajxEKhJWWOpJlMKzaiRi+imWQY1ieWNUgng+zfABoQg3BnrkNXpjXLI9BZWvkrqav315CVUNbRgUHYy7JifLtg5joA4zRsYCAPbydGHVYlDjIWI7t9I6n0TiurhT0zH3KZot3YrljVEJcqeeROOS7LtEX5f6/m5CY6sFmz45DwD42a0jEejBE5p7g3U16segxkOU2vkk4lk1doIgoIoTuhWv86gET9XVeHIytyvEYuGTKghq3sy9iJrGNgyNDcH8iUlyL0eqqzlWXOuVkRvkfQxqPERMPymt80k0iEENAKCh1SK1tbOmRtnEUQme+GFkswlS+mmSzEHN2PagpqS2GVcaPdvC7kn1LWZs/lTcpRnh0TlavRUfbkRqcjgEAdhXwN0aNZL/b5lKKb1QWNypudJkRn2LWebVyEespwnW6xCs59wnJRNrnjyxU3OhuhF1LRYYArQYlRDm9ud3RbgxUPqlw5cLWt/cfxG1TWYMGxCCO9Pkq6W5Gk8XVjcGNR7Q0GqBqdkeKCh1pybUEICoYHsxpD8XC7PzyXdIZ9V4YKdG3KVJTY6Qve4D6HxejW8WC9e1mPGnzy4AAFbcOhI6rXJmqol1NZ+dreLhoyok/79eFRLraSKCAhEmYxdFT9jW3emMGhYJK54nRyUopUhYlJpsLxbO99G27u2HimFqNmNkXChunyB/LU1n45MjEBtqQEOrBV9drJF7OeRmDGo8oGOQpTJ3aUQDWVeDmka2c/sKT45KUEqRsGisj+/UfHXBHix8b8pARe3SAIBWq8Gs0QMAADls7VYdBjUeoNRBlldLaR9sKdb/+COxnZs7NcrnqVOFW8xWnGqvXZG7SFgkpp/OVzX65ADG48W1AJSz83U1sa4m53QFTxdWGQY1HqD0dm6RmH7y51EJVZzQ7TM8Nf/pZFkdzFYBMSF6xfwiEhdmxIAwAwQBOFVWL/dyXFJZ14JSUwu0mo40mtLMGBmLQJ0Gl6qbcL6qUe7lkBsxqPEAqfNJ4emnlOj2A/j8OKipbuTcJ1/hqVEJxzqlnrw9mbs7HefV+FYK6lixfb3XxYchxKDMjsJQQwBuGBYDgKcLqw2DGg8oltJPwTKvpHti+qnoSpPfbsGK6SfW1Cifp0YlKK1IWNR5YrcvkYLEgZGyrqMns9q7oNjarS4MajxATD8pZSu7K0mRQdBogBazzSMdJb6gmt1PPsNToxKUViQsSm0fl+BrM6COtdfTTEhRZupJJAY1X12skY7gIN/HoMbNWsxWKeev9PSTPkCLpAgxBeWfxcLiOTXRHJGgeJ4YlXClsQ2Xqu3p14kK21kQZ0CdKW+A2eob56l0PplZ6Ts1g2NCMCIuFBabgM/OXpZ7OeQmDGrcTOx8CtHrEBms3DNqROJuUrEfnlVjtQls6fYx7h6VkNe+qzAsNgQRCvv3mhIdhDBjANqsNpytaJB7Ob1yUUEnM/eGlIJiXY1qMKhxs86dT0oqOuyKPw+2rG1qg629NCOKOzU+wd2jEvIKawEoL/UEABqNBmMTfeu8muPtRcJKOZm5J2JQ83FBJaw2/6wrVBvl/63zMb7S+STy57ZusfMpMjjQJ74Bk/tHJRxT+HkqYgrKV4qF83wk9SSaMjgK4cYAXGkyS2sn38bv5G5WUmsPDpTe+STqaOv2v5qaKungPe7S+IrOHVD9JQgd9R/KDWrEtm7fCGrEIDFN4UXCokCdFjNHiV1QFTKvhtyBQY2b+crBe6LObd3+poZn1Pgcaf6TG3ZqCmuacKXJDL1Oi9GJyqz/EA+v+7rUBJvC0yNtFpu0o6TUINEZccAlRyaoQ5+Cmo0bN2LIkCEwGo1IT0/HwYMHu71++/btGD16NIxGI8aPH49du3Y5fP2dd97B7NmzERMTA41Gg7y8vGueo6WlBQ8//DBiYmIQGhqKu+++GxUVyousfS39JNbUlNY2+0yHhbuI7dwsEvYd7hyVIKYbxiaFwxCg6/fzecLwASEwBGjR2GbFJYWniAvK69FmsSEyOFBKa/uCmdcNgFYDnC6vlxo9yHe5HNRs27YNK1euxJo1a3DkyBGkpaUhKysLlZXOo9z9+/dj0aJFWLp0KY4ePYr58+dj/vz5yM/Pl65pbGzEjBkz8MILL3T5uo899hj+/e9/Y/v27fjkk09QWlqK7373u64u3+N8Ze6TaECoAYYALWwCUFbbIvdyvIpzn3yPO0clHG0vElbyrkKATovR7V1ESi8WFjvJJgxU1snMPYkK0WPyoCgAPIhPDVwOatatW4dly5YhOzsbY8eOxaZNmxAcHIzXX3/d6fWvvvoq5syZg8cffxxjxozB888/j8mTJ2PDhg3SNffffz9Wr16NzMxMp89hMpnw5z//GevWrcOsWbMwZcoUvPHGG9i/fz++/PJLV9+Cx7RZbKioswcGvpJ+0mo1UgDmbymoqkbOffI1Hd1P/a+pUXqRsGisjxQLS/VJA32jnqazWWPE1m7l7f77ktc/v4Ayk7y7XS4FNW1tbTh8+LBD8KHVapGZmYnc3Fynj8nNzb0mWMnKyuryemcOHz4Ms9ns8DyjR4/GoEGDunye1tZW1NXVOdw8rdzUAptgP9Qu1od++/fXtm5pp4Y1NT6jc01Nf0Yl+FL9h6+MSzguFQlHyrqOvri1fWr3/nPVaG6zyrwa3/TJmct47v2TyHrlU1lPaHYpqKmqqoLVakV8fLzD/fHx8SgvL3f6mPLycpeu7+o59Ho9IiMje/08a9euRUREhHRLSUnp9ev1VbHY+RQZBK3Wd7Zf/bWtW6qpYfeTz3DXqIRTZXVS/cfgGGXXf0hBTYlJsTPaGlotOFtpPyBwgo+0c3d2XXwokiOD0GqxYf+5KrmX43NazFY8s8NeUrJgagoiguQ7yFK13U+rVq2CyWSSbkVFRR5/TV/rfBJ1dED5V5EcJ3T7HneNSpBaj32g/mNMYjh0Wg2qG9tQUafMGW0nik0QBHuDhBh4+hKNRoNb21NQOayrcdmGvd+gsKYJiRFGPPbt62Rdi0tBTWxsLHQ63TVdRxUVFUhISHD6mISEBJeu7+o52traUFtb2+vnMRgMCA8Pd7h5mq91Pok6zqrxr50a8Yci5z75llg3HMCX5wNFwiJjoA7DB4QAUG6xsK/UJ3Wn88gEpe6IKdE3lfX446fnAABr7hiH0PZfOuTiUlCj1+sxZcoU5OTkSPfZbDbk5OQgIyPD6WMyMjIcrgeAPXv2dHm9M1OmTEFgYKDD8xQUFKCwsNCl5/E0X+t8EokHBfpTUNNqsaK+PX3Blm7fIn5e/Zksn+djP4SVfrKwWCQ8wQeLhEU3DItBUKAO5XUtOFmmzD9npREEAb96Nx9mq4DMMXHIGhff84M8zOWQauXKlXjggQcwdepUTJs2DevXr0djYyOys7MBAIsXL0ZycjLWrl0LAFixYgVmzpyJl19+GXPnzsXWrVtx6NAhbN68WXrOmpoaFBYWorS0FIA9YAHsOzQJCQmIiIjA0qVLsXLlSkRHRyM8PByPPPIIMjIycMMNN/T7D8FdfDX9NKi9pqC6sQ2NrRaEyBxpe4N48F6AVoNwo7IGGVL3pLNq+rhTY2oy4/zlRgC+U9Q6Likc7x4tUe5OjTgewUf+PJ0xBupw44hYfHSqAh+frpQCSerav46U4MCFGgQF6vDsneMUkcp1uaZm4cKFeOmll7B69WpMnDgReXl52L17t1QMXFhYiLKyMun66dOnY8uWLdi8eTPS0tLw9ttvY8eOHUhNTZWu2blzJyZNmoS5c+cCAO69915MmjQJmzZtkq555ZVXcPvtt+Puu+/GzTffjISEBLzzzjt9fuOeIBYKJ0cqu/DwauHGQKmwq9hP6mrEIuHoEL1PFXVT57Nq+tbWLaZKBkUH+0zqcayCO6Aq61pQamqBVgOMT/btQIB1Nb13pbEN/7vrFADg0cyRihkN1KdfyZcvX47ly5c7/dq+ffuuuW/BggVYsGBBl8+3ZMkSLFmypNvXNBqN2LhxIzZu3OjKUr3GahOkw+t8Lf0E2OtqTCVmFNU0YVSCMo+Md6cqtnP7rP6eKqz0eU/OjEu0BwvFV5phajIjIlg5u4vH2idzj4wL8/ld3m+1z4HKK6pFVUOr9HeNrvXb/5xGTWMbRieE4Yczhsq9HIlqu5+8rbK+BRabgACtBvHhRrmX4zJ/a+sW00+sp/E9/Z3/lOeDQU1EcKBU0K+0FNRxHxti2Z2ECCNSk8MhCMC+gstyL0exDl6owbZD9o7i/7krFYE65YQSylmJjxPTNgkRRuh8MJ3hb4MtxfQTJ3T7nv6MShAEQQpqfK3+Q9ytUVoKylf/PLsyi1O7u9VmseFX754AACyaloIpg6NlXpEjBjVuIhYJ+2LqCQAGSqcK+0dNTVUj00++qj+jEoqvNKO6sQ0BWo10qJ2v6DhZWDk7NYIgdBQJ++Che87MGmOvD/30TBXaLP415Lc3/t/n53G2sgExIXo8MWe03Mu5BoMaNxHbuX2tSFg0yM9GJUg7NUw/+Zz+jEoQdxXGJIbDGKjMydxdGZesvGLhi9VNqGuxwBCgVU0t3oTkCMSG6tHQasGhizVyL0dRimqa8FrOWQDAr+aOQWSw8r5/Mqhxk+L2tI2vtXOLUtrXXVjThAtVjTKvxvPEuU++NKOL7PozKsEX62lEYovxucsNiplPJO7SjEsKV1RdRX9otRqpYJhdUB0EQcAz7+WjxWxDxrAY3DUpWe4lOaWOv4UKUOzr6aeoYCRHBqHZbEXW+k/x6kdn0WpRxjdOT6jmhG6f1Z9RCb7Y+SSKCzMgNlQPmwCcLlfGbo3a6mlEYmv3XgY1kv/kl2NfwWXodVr85q5URZxJ4wyDGjeRThP2sREJIn2AFn//UTpuGhmLNosNr3x0BnPWf4bPz6pzuFtH+ok7Nb6oL6MSzFYbTpTY61F88YewRqORdmvyFZKCUsN4BGdmjByAQJ0GF6oacf5yg9zLkV19ixm//vfXAIAf3zIcwweEyryirjGocQNBEHz2NOHOhsSG4K0fTsPvF03CgDADLlQ14gd/PoAVW4+isr5F7uW5jSAIHefUsPvJJ/VlVEJBeT1aLTaEGQMwLDbEU0vzKLFY+KQCioXNVptU36OWImFRqCEA6UNjAHC3BgBe/u8ZVNS1YkhMMH56y3C5l9MtBjVuUNXQhlaLDRoNkBjhu0ENYP9t8I60JOT8fCaWTB8CjQZ4L68Ut778Cf765SVYbb4/6K2xzYrW9q4Gpp98U19GJXSup/HVU6SVNAOqoLwebRYbIoICMTjGNxskuiMOuMw55d9BzYliE97KvQgAeH5+quIL7BnUuIGYeooPM0IfoI4/0nBjIJ69cxzee/hGjE+OQH2LBc/syMd3/+8L5JfI/1tif4hFwkGBOgTrffsEVH/Vl1EJeSpoPRZ3ak6X18NslbfduHM9jVLrK/pDrKv56mIN6lrMMq9GHlabgF/tOAGbANyZloSbRg6Qe0k9UsdPYJn5eudTdyYMjMSOh2/Ec/PGIcwQgGPFJty54XP8+t9fo95H/6FXsZ3b5/VlVIIvFwmLBkUHI9QQgDaLDedkrvXoOJ/G908SdmZwTAiGDwiBxSbgszPqrC3syd++vITjxSaEGQPw9O1j5F5OrzCocQOpnsZHi4R7otNqsDhjCHJ+PhN3pCXBJgBvfHERmes+wa4TZS6fFSK3as598nmujkqobzHjm/YgwBeLhEVarQZjE9vPqymRNwUlFgn78s5XT25tP4jvw6/LZV6J91XUteDFDwsAAL+cMxpxYb4x/odBjRtInU8q3KnpLC7ciN8vmoS3fjgNg2OCUVHXip/+/QiWvPEVLlX7ztk20twnFgn7rI5ThXsX1BwvNkEQ7L94iKkrXyUewpcvY7FwQ6sFZyvtQeIEFcx86src8YkAgN355X0eoOqrnnv/JBpaLZiYEon7pg2Sezm9xqDGDYpV0PnkipuvG4APH70ZK24dCb1Oi0/OXMbsVz7Fhr2+cbYNz6jxfa7W1EhFwoMiPbQi71FCsfCJTkGir/wG3xdpKZFIS4lEm9WGfxwolHs5XrOvoBIfHC+DTqvB/9yV6lOF9Qxq3EDt6SdnjIE6PPbt67D70ZswY0QsWi02vPTfM/jOq58h91y13MvrVhXTTz5PSj819G5UghTUqCBVIhYLnyqtg02mbkQ1TebuSfb0IQCAvx24JHtxtjc0t1nxzHv5AOzvXQyifQWDmn4SBKFT+kl9bY09GTYgFH9dOg2v3jsRsaEGnLvciEV/+hIrt+UpdruWE7p9nzQqwdLzqITOk7nVsFMzIi4U+gAt6lstKLoiz6w2f6inEX1nfCJiQw2oqGvF7nz119Zs+PgsimqakRhhxGPfvk7u5biMQU0/mZrNaGi1f1P1p52azjQaDeZNTEbOz2fi/hsGQ6MB3jlaglkv7cOWA4Wy/TbZler2Cd2x3KnxWcZAHUJ7OSqhzNSCy/Wt0Gk1SPWx3zqdCdRpMSrePjxSrhTUsSLfPZnZVfoALe5Lt9eU/GX/RXkX42FnK+qx+dPzAIBn7xyHEIPvHXnBoKafxHqamBA9gvTKPpTI0yKCAvH8/FTs+OmNGJcUjroWC5569wTu3rQfJxVwWJiIE7rVYUAvRyWIuzSj4sNU829UTEF9LUOxcGV9C0pqm6HRAKnJvh8k9sZ96YMQoNXg8KUrOFHs2+d0dUUQBPzq3XyYrQIyx8Qja1yC3EvqEwY1/TQ0NgRbfpSO3949Qe6lKEZaSiTee/hGrLljLEINAThaWIs7NnyO37RX08tNOqeGE7p9WkcHVPfFwsdUlHoSjWsPJvJlaOs+3r5LMzIuVNotU7u4cCPmTrB3Qql1t2b74WIcvFiDoEAdnr1zrNzL6TMGNf0UYgjA9BGx+PbYeLmXoigBOi2ybxyKnJ/PxNwJibDaBPy/zy/g2+s+wccyzlKx2QTUSOkn7tT4so6zarqfS3ZURUXCoo6dGu8HNf5UT9PZkvaC4X8fK1VsvWBf1TS2Ye2uUwCAx7490qfrQxnUkEfFhxux8fuT8Zfs6zEoOhhlphY89NfDsg3IrG02QyzxiWKhsE/rTVu3xWqT0gVq2qkZkxAOrcZeT1RZ591/S53HI/iTSYOikDYwAm1WG7YeVFd799pdp3ClyYzRCWHIvnGo3MvpFwY15BW3jIrDfx+7GaPiw9BmteHzs/IcOy6eJhwRFIhAHf/6+7LejEo4W9mAZrMVoYYADB8Q6q2leVyQXodh7e/Hm7s1giDguBgk+llQAwBLbhwCAPjrl+pp7z5wvhrbDxcDAP7nrvE+/33Rt1dPPsUYqJOGxH0mU1DDuU/q0ZugRtxVGJ8cAZ0PHSDWG3IUC1+qboKp2Qx9gBajEsK89rpKYW/v1qOirlUVoxPaLDb8aof9TJpF0wZhyuAomVfUfwxqyKtmjIwFYA9q5JgZJbVzs0jY54k1Ud3Nf1JjkbBIjroasZ4mNSnc53+j7wtDgA7fTx8MAPjLFxflXYwb/Omz8/imsgExIXo8OWe03MtxC//7W0mymjI4CkGBOlQ1tOJ0eb3XX7+GIxJUozc1NXkqmMzdFfHMHW/OgBL/PCf4WZFwZ2J796FLV5Bf4rvt3YXVTXgt5ywA4OnbxyAiOFDmFbkHgxryKkOADjcMiwYAfHb2stdfn+kn9ehpVEJjqwVnKuyBsxqDmrHtOzVFNc0wNZu98prHVBwk9lZ8uBHfGe/b7d2CIOCZ9/LRarFh+vAYzJ+YLPeS3IZBDXndTSMHAJCnrkYsFOYZNb6v86iEeifnH50oMcEmAIkRRsSHq2/oYmSwXjrF3BuHW5qtNuS3v46/dT5dTSwY3nmsVPqe4kt2nSjHJ2cuQ6/T4vn5qdBo1FNvxqCGvO7m6+x1NQcu1KDF7N2p3uJpwjyjxvd1HpXgrK5Gaj1WcarEm8XCBeX1aLPYEG4MwJAY3z3HxB0mpURiwsAItFls2PpVkdzLcUldixm//vfXAICf3DJcVV2BAIMaksHwAaFIjDCizWLDwQs1Xn1tsVCYE7rVobtRCXmFtQDUWSQsEicoe2OnpvP5NGr6zb4vNBqNdBjfX3N9q7173X/PoLK+FUNjQ/CTW4bLvRy3Y1BDXqfRaDBjhNgF5d26Gk7oVpfuRiWInTpqrv/wZgfUcT/483TF3An29u7yuhb89+sKuZfTK8eLa/Fm7kUAwPPzUmEMVMcstM4Y1JAsbrpOnroa8UwT7tSoQ1ejEirqWlBmaoFWYz+jRq3EgZLfXG7weCpXmsyt4nSeKwwBOnx/mji9+4LMq+mZ1SbgqXdPQBCAeROTpOM11IZBDclixohYaDTA6fJ6rx3z3maxoa7FXlDKmhp16DiAz3GnRkyVXBcfhhAVD12MDzcgJkQPq03w6BEJDa0WnKm0P/+EFPUGia6674bBCNBq8NVF5bd3v5V7EfkldQgzBuDpub47sLInDGpIFtEheumcjc+/8c5ujXhGjU6rQbhRHWcy+LuOs2oca2rUfD5NZxqNRmrt9mSxcH6JCYIAJEUYERemvk6yvooPN+K29vbuNxXc3l1masbL/z0DAHhizmjp340aMagh2dzU6XRhbxB/8EWH6KFV2ZH5/qqrUQlikbA/tB6LxcKerKs55qdDLHtDLBh+71ip9IuTkgiCgCf/dQINrRZMGhQppczUikENycbbIxOqG1kkrDbORiVYbQJOlPjP0EVvFAuLRdcMaq41eVAkxifb27v/ocDp3f88VGQ/kyZAixe/N0H1v9AxqCHZeHtkgnhIViyLhFUj1smohHOXG9DQakFQoA4j49R1BoczYlBzuqwOFg+1FrNIuGud27v/9uUlj30GfVF8pQnPv38KAPCL2ddhRJz6h5D2KajZuHEjhgwZAqPRiPT0dBw8eLDb67dv347Ro0fDaDRi/Pjx2LVrl8PXBUHA6tWrkZiYiKCgIGRmZuLs2bMO15w5cwbz5s1DbGwswsPDMWPGDHz88cd9WT4phLdHJnDuk/oMcDIqQUw9jR8YgQA/GLo4JCYEIXodWi02nLvc6Pbnv1zfipLaZmg09j9TutbtaYmICdGjzNSC/55URnu3IAh44l/H0dBqwZTBUVg6Y5jcS/IKl//Fb9u2DStXrsSaNWtw5MgRpKWlISsrC5WVlU6v379/PxYtWoSlS5fi6NGjmD9/PubPn4/8/Hzpmt/97nd47bXXsGnTJhw4cAAhISHIyspCS0tHV8ztt98Oi8WCvXv34vDhw0hLS8Ptt9+O8nLfH//uz7w5MkGa+8QRCarhbFRCXnuqZJKfpEq0Ws8WC4vn04yMC5VOcCZH9und7e3dCpne/bcDhfjim2oYA+1pJ53K004il4OadevWYdmyZcjOzsbYsWOxadMmBAcH4/XXX3d6/auvvoo5c+bg8ccfx5gxY/D8889j8uTJ2LBhAwB7NLl+/Xo8/fTTmDdvHiZMmIC33noLpaWl2LFjBwCgqqoKZ8+exZNPPokJEyZg5MiR+O1vf4umpiaH4Kiz1tZW1NXVOdxIebw5MkGa+8SdGtVwNirBn4qERZ4sFj7Gydy9cl+6vb374MUar4yt6E5hdRPW7rKnnX6ZNRrDVDYKoTsuBTVtbW04fPgwMjMzO55Aq0VmZiZyc3OdPiY3N9fhegDIysqSrr9w4QLKy8sdromIiEB6erp0TUxMDEaNGoW33noLjY2NsFgs+OMf/4i4uDhMmTLF6euuXbsWERER0i0lJcWVt0pe4s2RCWKhMM+oUZfOoxKa26woUPFk7q54cqcmr7i9nsaP/jz7IiHCiDmpCQDkbe+22QQ8/vYxNLVZMW1otFTv4y9cCmqqqqpgtVoRHx/vcH98fHyXaaDy8vJurxf/t7trNBoNPvroIxw9ehRhYWEwGo1Yt24ddu/ejaioKKevu2rVKphMJulWVORbQ8f8hTdHJnBCtzp1HpWQX2qC1SYgLsyAxAj/OU9FLBY+WVrn1k5CQRCknZqJ3KnpUXb79O738uRr734z9yIOXKhBsF6Hl76Xpvpup6v5RBWdIAh4+OGHERcXh88++wwHDx7E/Pnzcccdd6CsrMzpYwwGA8LDwx1upEzeGpkg1dRwp0ZVOp9V0zn15E9DF0fGhSFQp0FdiwXFV5rd9ryXqptgajZDH6DFqAT1d8701+RBUUhNDkerxYatX3m/vftCVSNe2H0aALDqttEY5IfT1F0KamJjY6HT6VBR4VjdXVFRgYSEBKePSUhI6PZ68X+7u2bv3r14//33sXXrVtx4442YPHky/u///g9BQUF48803XXkLpEDeGJkgCII0oZst3erSMf+pVSoS9qfUEwCHoMOdx/WL59OMSwqHPsAnfgeWlb29eygA4G+53m3vttoE/GL7MbSYbbhxRAzuSx/stddWEpf+lur1ekyZMgU5OTnSfTabDTk5OcjIyHD6mIyMDIfrAWDPnj3S9UOHDkVCQoLDNXV1dThw4IB0TVNTk32xWsflarVa2GzKOROA+sYbIxOa2qxoMdv/rnCnRl06j0oQd2r8LagBgHGJ7i8WFsdN8Hya3rt9QiKiQ/QoNbVgjxfbu1///AIOX7qCUEMAXrhb/YfsdcXl0HvlypX405/+hDfffBOnTp3CT37yEzQ2NiI7OxsAsHjxYqxatUq6fsWKFdi9ezdefvllnD59Gs8++ywOHTqE5cuXA7BHto8++ih+85vfYOfOnThx4gQWL16MpKQkzJ8/H4A9MIqKisIDDzyAY8eO4cyZM3j88cdx4cIFzJ071w1/DCQ3T49MqG5PPQUF6hCsZ1uqmog7NafK66XzVCb44Xkq45LdXyx8vNh/TmZ2F2Ngx/TuN7xUMPxNZQNe/G8BAODpuWMwMMr/0k4il4OahQsX4qWXXsLq1asxceJE5OXlYffu3VKhb2FhoUOdy/Tp07FlyxZs3rwZaWlpePvtt7Fjxw6kpqZK1/zyl7/EI488ggcffBDXX389GhoasHv3bhiN9kK/2NhY7N69Gw0NDZg1axamTp2Kzz//HO+99x7S0tL6+2dACuDpkQlVjR1zn0hdxEJhsaB1xIBQhPnhwFJ3j0swW21SKssfg8T+uO+GQdBpNTh4oQYnPTi+AgAsVht+vv0Y2iw2zLxuABZe79+dvn36lXX58uXSTsvV9u3bd819CxYswIIFC7p8Po1Gg+eeew7PPfdcl9dMnToVH374octrJd9w9ciEMYnuLewWd2rYzq0+sVdNHPbX1uPRCeHQaIDK+lZcrm/t9yTmgvJ6tFpsCDcGYEhMiJtW6R8SI4IwJzUBHxwvw5v7L+KF703w2Gtt/uw8jhXVIswYgN/ePd6vCuSdYeUXKYKnRyZ0HLzHImG1GXDVZ+qvqZIQQwCGxtqDD3ekoDoPsfTX+oz+yG4/H2ZHXgmueKi9u6C8Huv32EcKrbljHBIjgjzyOr6EQQ0phidHJnBCt3pdvSPhr0ENAKng3h0pqGMsEu6XKYOjMC5JbO92/zlpZqsNP9+ehzarDbeOjsPdk5Pd/hq+iEENKYYnRyZUS2fUcKdGbTqPSjD4+Xkq49x4srA0mduPg8T+6Dy9+6+5F93e3v2HfeeQX1KHiKBArP0u004iBjWkGMMHhCIh3DMjEzrOqOFOjRqJn+v45AgE+sFk7q64awZUY6sFZyvt4ybSWCTcZ3ekJUnt3R+dcl9799elJryWY087PTdvHOLC/ef07J74779+UhyNRiO1drv7vJpqniasamIKyt93FcSdmkvVTahrMff5efJLTLAJQFKEkT8w+8EYqMOiafZupDfcNL27zWLDz/95DBabgDnjEnBnWpJbnlctGNSQoogjEz49495i4SrOfVI1cYL0raPj5F2IzKJC9Ehqn3l1qh+7NWKRMCdz998PbhgMnVaDAxdqcKqs/7VOv997FqfL6xEdosdv7kpl2ukqDGpIUTw1MkEqFOZOjSr96jtjcOCpWzG9fTiqPxvrhhQU62ncJzEiCHPGuWd69/HiWvzfvnMAgOfnpXLkixMMakhRPDEywWYTpIm5/CagTlqtBvFMkwAAUttPFs7vR7GwNB4hhfU07rCkfXr3u0f73t7darHi5/88BqtNwO0TEjF3QqIbV6geDGpIcdw9MsHUbIbVZj+lOCqYOzWkbmKxcF9Psr1c3yqNmxifzKDGHaYOjsLYRHt797ZDfWvvfmXPWZytbEBsqB7PzUvt+QF+ikENKY67RyaInU8RQYGcNEyqJxYLn61s6NPRCMfb62n8ddyEJ2g0Gmm35q99mN59pPAKNn9qTzv9713jOe6lG/wOT4pz9ciE/qpq4MF75D8SI4yICg6E1SbgTIXr/36kQ/dYT+NWd6YlISo4ECW1zfjoVGWvH9dituIX24/BJgB3TUrG7Pb6HHKOQQ0pjrtHJrCdm/yJRqPp13k1x4pZJOwJ9vZu+/Tuv+y/0OvHvfRhAc5fbkRcmAHP3jHOU8tTDQY1pEjuHJlQ08h2bvIvfT1ZWBCEjplPPHTP7cT27i/P1+B0ec8B58ELNfjzF/YA6Ld3j0dEMNOBPWFQQ4rkzpEJVdypIT8zrr3AN7/EtZ2awpom1DaZoddpMToh3BNL82tJkUHIGhcPoOf27qY2Cx5/+xgEAVgwZSBmjY73wgp9H4MaUiR3jkwQC4U594n8hbhTc7q8Tur86w2xlXtsUjiL6j1kyfShAOzt3bVNXbd3/253AS5VNyExwohn7hjrreX5PP6tJUVy58gEsaaGc5/IXwyNCUGwXocWsw3nLzf0+nHioXv+POnc064fEoUxieFoMduwrYvp3fvPVeEv7Ts5L9w9AeHsQus1BjWkWO4amSAVCrOmhvyEVqvBmESxrqb3KSipnoaH7nmMRqNBdvv07rdyL12zk9bQasEv3z4OAPh++iDc3P59kHqHQQ0plrtGJlRJ6Sfu1JD/cLVY2Gy1Ib+kvfOJM5886s6Jndu7Had3/++uUyi+0ozkyCA89Z0xMq3QdzGoIcVy18gEpp/IH3UENb3bqSkor0erxYZwYwCGxIR4cml+zxiow71ie3en6d2fnrmMLQcKAQAvLpiAUEOAHMvzaQxqSNH6OzKhzWKDqdkMgOkn8i/iWTX5JaZencx9vP18mgkDI6HVcvKzp/3ghsHQaoDc89UoKK9HXYsZT/7LnnZ6IGMwpg/ncNa+YFBDitbfkQlX2rsLdFoNIoJYbEf+47r4MATqNKhrsaD4SnOP1x/jEEuvSo4MQlb76cB/2X8Rv3n/JEpNLRgcE4wnbhst8+p8F4MaUrT+jkyoarDX00SH6PnbJ/kVfYAWI+PCAPQuBdVx6F6kB1dFnS1pLxh++3AR/nmoGBoN8OL30hCsZ9qprxjUkKL1d2RCNec+kR8T62pO9lAs3NhqkeZEsZ3be6YNjcbohDCYrfZd6B/eOBTThkbLvCrfxqCGFK8/IxOq2flEfqy3xcL5JSbYBPswzLhwozeWRrC3d/9whv0wvmGxIfjF7FEyr8j3cY+LFO/qkQnGQF2vH8szasifieMSegpqmHqSz4IpAxFuDMDkQVEI0vf+exs5x50aUrz+jEyobuTcJ/JfYxLDodEA5XUtUn2ZM+JJwpzM7X0ajQZzUhO5Q+YmDGpI8fozMqG6/Rt5LOc+kR8KNQRgaPuZM93t1nAyN6kFgxryCX0dmcBCYfJ3Y3s4WbiqoRXFV5qh0QCpDGrIxzGoIZ/Q15EJVVL6iTs15J/EQ/i62qk53r5LM3xAKAcnks9jUEM+oa8jE8T0E2tqyF91tHU7D2ryijjvidSDQQ35jBl9GJkgzX1i9xP5KTGouVDViPoW8zVfF08SnsiThEkFGNSQz7jJxZEJTW0WNJutALhTQ/4rJtSAhPbOmlNljqdyC4LQUSTMzidSAQY15DNcHZkg7tIYA7UI5vkP5MdSk50XCxfWNKG2yQy9TovRCeFyLI3IrRjUkM9wdWSCeC5HTIgBGg3nPpH/GttFsfCx9sncY5LCoQ/gjwPyffxbTD7FlZEJUj0NU0/k57oalyDV07CVm1SiT0HNxo0bMWTIEBiNRqSnp+PgwYPdXr99+3aMHj0aRqMR48ePx65duxy+LggCVq9ejcTERAQFBSEzMxNnz5695nk++OADpKenIygoCFFRUZg/f35flk8+7OqRCd0R5z5F84wa8nNiUHO2oh6tlo5/N2JQw3oaUguXg5pt27Zh5cqVWLNmDY4cOYK0tDRkZWWhsrLS6fX79+/HokWLsHTpUhw9ehTz58/H/PnzkZ+fL13zu9/9Dq+99ho2bdqEAwcOICQkBFlZWWhp6TiP5F//+hfuv/9+ZGdn49ixY/jiiy/w/e9/vw9vmXyZKyMTqnlGDREAIDkyCBFBgbDYBJytaAAAmK025JdyPAKpi8tBzbp167Bs2TJkZ2dj7Nix2LRpE4KDg/H66687vf7VV1/FnDlz8Pjjj2PMmDF4/vnnMXnyZGzYsAGAfZdm/fr1ePrppzFv3jxMmDABb731FkpLS7Fjxw4AgMViwYoVK/Diiy/ixz/+Ma677jqMHTsW99xzT9/fOfkkV0YmSKcJM/1Efk6j0Ui7Nfkl9kDmTEU9Wsw2hBk7RikQ+TqXgpq2tjYcPnwYmZmZHU+g1SIzMxO5ublOH5Obm+twPQBkZWVJ11+4cAHl5eUO10RERCA9PV265siRIygpKYFWq8WkSZOQmJiI2267zWG352qtra2oq6tzuJE69HZkgjT3iWfUECH1qondxzoduqfVspCe1MGloKaqqgpWqxXx8fEO98fHx6O8vNzpY8rLy7u9Xvzf7q45f/48AODZZ5/F008/jffffx9RUVG45ZZbUFPjPAWxdu1aRERESLeUlBRX3iopWG9HJnBCN1GHcVfNgOqop2GRMKmHT3Q/2Ww2AMCvfvUr3H333ZgyZQreeOMNaDQabN++3eljVq1aBZPJJN2Kioq8uWTyoN6OTKhqYE0NkUgMak6V1cNq6zh0bwLHI5CKuBTUxMbGQqfToaKiwuH+iooKJCQkOH1MQkJCt9eL/9vdNYmJiQCAsWPHSl83GAwYNmwYCgsLnb6uwWBAeHi4w43UozcjE6S5T+x+IsLQ2FAEBerQbLbiZGkdzlTYD7CcyCJhUhGXghq9Xo8pU6YgJydHus9msyEnJwcZGRlOH5ORkeFwPQDs2bNHun7o0KFISEhwuKaurg4HDhyQrpkyZQoMBgMKCgqka8xmMy5evIjBgwe78hZIJXoamWCzCahpFM+p4U4NkU6rwejEMADAtkOFsAlAQrgR8e0jFIjUIMDVB6xcuRIPPPAApk6dimnTpmH9+vVobGxEdnY2AGDx4sVITk7G2rVrAQArVqzAzJkz8fLLL2Pu3LnYunUrDh06hM2bNwOwV+U/+uij+M1vfoORI0di6NCheOaZZ5CUlCSdQxMeHo4f//jHWLNmDVJSUjB48GC8+OKLAIAFCxa448+BfMzVIxPGJDruxNW1mGGx2YMdnlNDZDcuKRxHC2ux42gpANbTkPq4HNQsXLgQly9fxurVq1FeXo6JEydi9+7dUqFvYWEhtNqODaDp06djy5YtePrpp/HUU09h5MiR2LFjB1JTU6VrfvnLX6KxsREPPvggamtrMWPGDOzevRtGY8dvEC+++CICAgJw//33o7m5Genp6di7dy+ioqL68/7JR4kjEz4uuIzPzl6+JqgR62nCjQE8/p2onViL1tBqAcDzaUh9NEJvxh2rQF1dHSIiImAymVhfoxKvf34Bz71/EjeNjMVfl6Y7fO3A+Wos3PwlhsWGYO8vbpFngUQKc6LYhDs2fC79/y0/Ssf0EbEyroioZ678/OavsOSzxLoaZyMT2M5NdK3rEkIR0H4mjUYDpHLmE6kMgxryWSPiuh6ZIHY+sZ6GqIMhQIcRcaEAgGGxIQg3Bsq8IiL3YlBDPqu7kQmc+0Tk3Lj2uhrW05AaMaghn9bVyARx7lMsd2qIHCydMRQZw2LwoxnD5F4Kkdu53P1EpCRXj0yIaz9zo7qx/eA97tQQORibFI5/PHiD3Msg8gju1JBP62pkQhUndBMR+R0GNeTznI1M6BiRwJ0aIiJ/waCGfJ6zkQnV0ogE7tQQEfkLBjXk864emWC22lDbZAbAmhoiIn/CoIZ8njgyAQA+O3sZV9p3abQaIDKI53AQEfkLBjWkCjeNtLd2f3a2SioSjg4xQNt+eioREakfgxpShc4jE0pqmwGwnoaIyN8wqCFV6Dwy4T/5ZQDYzk1E5G8Y1JAqdB6Z8GF+OQB7+omIiPwHgxpSDXFkQmObfWJ3DEckEBH5FQY1pBriyAQRa2qIiPwLgxpSjc4jEwCeUUNE5G8Y1JCqiCMTAKafiIj8DYMaUpWbOgc13KkhIvIrDGpIVaYMjkKYMQBaDZAcGST3coiIyIsC5F4AkTsZAnR464fTcKWpDQkRRrmXQ0REXsSghlRn0qAouZdAREQyYPqJiIiIVIFBDREREakCgxoiIiJSBQY1REREpAoMaoiIiEgVGNQQERGRKjCoISIiIlVgUENERESqwKCGiIiIVIFBDREREakCgxoiIiJSBQY1REREpAoMaoiIiEgV/GZKtyAIAIC6ujqZV0JERES9Jf7cFn+Od8dvgpr6+noAQEpKiswrISIiIlfV19cjIiKi22s0Qm9CHxWw2WwoLS1FWFgYNBpNj9fX1dUhJSUFRUVFCA8P98IKlcFf3zfgv+/dX983wPfuj+/dX9834LvvXRAE1NfXIykpCVpt91UzfrNTo9VqMXDgQJcfFx4e7lMfvrv46/sG/Pe9++v7Bvje/fG9++v7Bnzzvfe0QyNioTARERGpAoMaIiIiUgUGNV0wGAxYs2YNDAaD3EvxKn9934D/vnd/fd8A37s/vnd/fd+Af7x3vykUJiIiInXjTg0RERGpAoMaIiIiUgUGNURERKQKDGqIiIhIFRjUEBERkSowqHFi48aNGDJkCIxGI9LT03Hw4EG5l+RWa9euxfXXX4+wsDDExcVh/vz5KCgocLjmlltugUajcbj9+Mc/lmnF7vPss89e875Gjx4tfb2lpQUPP/wwYmJiEBoairvvvhsVFRUyrth9hgwZcs1712g0ePjhhwGo6zP/9NNPcccddyApKQkajQY7duxw+LogCFi9ejUSExMRFBSEzMxMnD171uGampoa3HfffQgPD0dkZCSWLl2KhoYGL74L13X3vs1mM5544gmMHz8eISEhSEpKwuLFi1FaWurwHM7+nvz2t7/18jtxXU+f+ZIlS655X3PmzHG4Rm2fOQCn/+Y1Gg1efPFF6Rpf/cydYVBzlW3btmHlypVYs2YNjhw5grS0NGRlZaGyslLupbnNJ598gocffhhffvkl9uzZA7PZjNmzZ6OxsdHhumXLlqGsrEy6/e53v5Npxe41btw4h/f1+eefS1977LHH8O9//xvbt2/HJ598gtLSUnz3u9+VcbXu89VXXzm87z179gAAFixYIF2jls+8sbERaWlp2Lhxo9Ov/+53v8Nrr72GTZs24cCBAwgJCUFWVhZaWlqka+677z58/fXX2LNnD95//318+umnePDBB731Fvqku/fd1NSEI0eO4JlnnsGRI0fwzjvvoKCgAHfeeec11z733HMOfw8eeeQRbyy/X3r6zAFgzpw5Du/rH//4h8PX1faZA3B4v2VlZXj99deh0Whw9913O1zni5+5UwI5mDZtmvDwww9L/99qtQpJSUnC2rVrZVyVZ1VWVgoAhE8++US6b+bMmcKKFSvkW5SHrFmzRkhLS3P6tdraWiEwMFDYvn27dN+pU6cEAEJubq6XVug9K1asEIYPHy7YbDZBENT7mQMQ3n33Xen/22w2ISEhQXjxxRel+2prawWDwSD84x//EARBEE6ePCkAEL766ivpmv/85z+CRqMRSkpKvLb2/rj6fTtz8OBBAYBw6dIl6b7BgwcLr7zyimcX52HO3vsDDzwgzJs3r8vH+MtnPm/ePGHWrFkO96nhMxdxp6aTtrY2HD58GJmZmdJ9Wq0WmZmZyM3NlXFlnmUymQAA0dHRDvf//e9/R2xsLFJTU7Fq1So0NTXJsTy3O3v2LJKSkjBs2DDcd999KCwsBAAcPnwYZrPZ4fMfPXo0Bg0apLrPv62tDX/729/wwx/+0GFqvVo/884uXLiA8vJyh885IiIC6enp0uecm5uLyMhITJ06VbomMzMTWq0WBw4c8PqaPcVkMkGj0SAyMtLh/t/+9reIiYnBpEmT8OKLL8JiscizQDfbt28f4uLiMGrUKPzkJz9BdXW19DV/+MwrKirwwQcfYOnSpdd8TS2fud9M6e6NqqoqWK1WxMfHO9wfHx+P06dPy7Qqz7LZbHj00Udx4403IjU1Vbr/+9//PgYPHoykpCQcP34cTzzxBAoKCvDOO+/IuNr+S09Px1/+8heMGjUKZWVl+PWvf42bbroJ+fn5KC8vh16vv+YbfHx8PMrLy+VZsIfs2LEDtbW1WLJkiXSfWj/zq4mfpbN/5+LXysvLERcX5/D1gIAAREdHq+bvQktLC5544gksWrTIYWLzz372M0yePBnR0dHYv38/Vq1ahbKyMqxbt07G1fbfnDlz8N3vfhdDhw7FuXPn8NRTT+G2225Dbm4udDqdX3zmb775JsLCwq5JqavpM2dQ4+cefvhh5OfnO9SVAHDII48fPx6JiYm49dZbce7cOQwfPtzby3Sb2267TfrvCRMmID09HYMHD8Y///lPBAUFybgy7/rzn/+M2267DUlJSdJ9av3M6Vpmsxn33HMPBEHAH/7wB4evrVy5UvrvCRMmQK/X46GHHsLatWt9embQvffeK/33+PHjMWHCBAwfPhz79u3DrbfeKuPKvOf111/HfffdB6PR6HC/mj5zpp86iY2NhU6nu6bbpaKiAgkJCTKtynOWL1+O999/Hx9//DEGDhzY7bXp6ekAgG+++cYbS/OayMhIXHfddfjmm2+QkJCAtrY21NbWOlyjts//0qVL+Oijj/CjH/2o2+vU+pmLn2V3/84TEhKuaQ6wWCyoqanx+b8LYkBz6dIl7Nmzx2GXxpn09HRYLBZcvHjROwv0kmHDhiE2Nlb6+63mzxwAPvvsMxQUFPT47x7w7c+cQU0ner0eU6ZMQU5OjnSfzWZDTk4OMjIyZFyZewmCgOXLl+Pdd9/F3r17MXTo0B4fk5eXBwBITEz08Oq8q6GhAefOnUNiYiKmTJmCwMBAh8+/oKAAhYWFqvr833jjDcTFxWHu3LndXqfWz3zo0KFISEhw+Jzr6upw4MAB6XPOyMhAbW0tDh8+LF2zd+9e2Gw2KdjzRWJAc/bsWXz00UeIiYnp8TF5eXnQarXXpGZ8XXFxMaqrq6W/32r9zEV//vOfMWXKFKSlpfV4rU9/5nJXKivN1q1bBYPBIPzlL38RTp48KTz44INCZGSkUF5eLvfS3OYnP/mJEBERIezbt08oKyuTbk1NTYIgCMI333wjPPfcc8KhQ4eECxcuCO+9954wbNgw4eabb5Z55f3385//XNi3b59w4cIF4YsvvhAyMzOF2NhYobKyUhAEQfjxj38sDBo0SNi7d69w6NAhISMjQ8jIyJB51e5jtVqFQYMGCU888YTD/Wr7zOvr64WjR48KR48eFQAI69atE44ePSp1+fz2t78VIiMjhffee084fvy4MG/ePGHo0KFCc3Oz9Bxz5swRJk2aJBw4cED4/PPPhZEjRwqLFi2S6y31Snfvu62tTbjzzjuFgQMHCnl5eQ7/9ltbWwVBEIT9+/cLr7zyipCXlyecO3dO+Nvf/iYMGDBAWLx4sczvrGfdvff6+nrhF7/4hZCbmytcuHBB+Oijj4TJkycLI0eOFFpaWqTnUNtnLjKZTEJwcLDwhz/84ZrH+/Jn7gyDGid+//vfC4MGDRL0er0wbdo04csvv5R7SW4FwOntjTfeEARBEAoLC4Wbb75ZiI6OFgwGgzBixAjh8ccfF0wmk7wLd4OFCxcKiYmJgl6vF5KTk4WFCxcK33zzjfT15uZm4ac//akQFRUlBAcHC3fddZdQVlYm44rd68MPPxQACAUFBQ73q+0z//jjj53+HX/ggQcEQbC3dT/zzDNCfHy8YDAYhFtvvfWaP5Pq6mph0aJFQmhoqBAeHi5kZ2cL9fX1Mryb3uvufV+4cKHLf/sff/yxIAiCcPjwYSE9PV2IiIgQjEajMGbMGOF///d/HX7wK1V3772pqUmYPXu2MGDAACEwMFAYPHiwsGzZsmt+WVXbZy764x//KAQFBQm1tbXXPN6XP3NnNIIgCB7dCiIiIiLyAtbUEBERkSowqCEiIiJVYFBDREREqsCghoiIiFSBQQ0RERGpAoMaIiIiUgUGNURERKQKDGqIiIhIFRjUEBERkSowqCEiIiJVYFBDREREqvD/AUdBtxpNxPJhAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "energy = qtx.utils.DataTracer()\n", "VarE = qtx.utils.DataTracer()\n", "\n", "training_rate = 0.01\n", "\n", "for i in range(200):\n", " samples = sampler.sweep()\n", " step = optimizer.get_step(samples)\n", " state.update(step * training_rate)\n", "\n", " energy.append(optimizer.energy)\n", " VarE.append(optimizer.VarE)\n", " if i % 10 == 0:\n", " clear_output()\n", " energy.plot(batch=10, baseline=exact_energy)\n", " plt.show()\n", " VarE.plot(batch=10)\n", " plt.show()\n", "\n", "state.save(\"/tmp/Heisenberg.eqx\")" ] }, { "cell_type": "markdown", "id": "c1919643", "metadata": {}, "source": [ "We can check the variational accuracy against the ED result." ] }, { "cell_type": "code", "execution_count": 11, "id": "8702be1d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "NQS energy: -44.91365075323898, relative error: 6.280467076974902e-06\n", "Fidelity: 0.9999925315217684\n" ] } ], "source": [ "dense = symm_state.todense(full_symm).normalize()\n", "nqs_energy = jnp.asarray(dense @ H @ dense)\n", "rel_err = jnp.abs((nqs_energy - exact_energy) / exact_energy)\n", "print(f\"NQS energy: {nqs_energy}, relative error: {rel_err}\")\n", "\n", "fidelity = jnp.abs(dense @ wf[:, 0]) ** 2\n", "print(f\"Fidelity: {fidelity}\")" ] }, { "cell_type": "markdown", "id": "3332ff21", "metadata": {}, "source": [ "## J1-J2 model\n", "\n", "To enter the next level of complexity, we look at the $J_1$-$J_2$ model at the most frustrated regime $J_2/J_1=0.5$. In this case, the Marshal sign rule is still an approximate sign rule, but no longer exact. Nevertheless, defining a Hamiltonian with basis rotation still makes it easier to train a network." ] }, { "cell_type": "code", "execution_count": 47, "id": "3ca9e153", "metadata": {}, "outputs": [ { "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" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Exact ground state energy: -33.831693405579394\n" ] } ], "source": [ "H = qtx.operator.Heisenberg(J=[1, 0.5], n_neighbor=[1, 2], msr=True)\n", "\n", "full_symm = TransND() @ Rotation(np.pi/2) @ Flip() @ SpinInverse()\n", "E, wf = H.diagonalize(full_symm)\n", "exact_energy = E[0]\n", "print(f\"Exact ground state energy: {exact_energy}\")" ] }, { "cell_type": "markdown", "id": "96ddf55e", "metadata": {}, "source": [ "Now the wavefunction is no longer strictly positive but still real. To allow the network to produce negative outputs, we replace the defaul activation function in the last layer, $f(x)=\\exp(x)$, by the new activation function $f(x) = \\sinh(x) + 1$. To avoid overflow, it is implemented by {py:func}`~quantax.nn.sinhp1_by_scale`." ] }, { "cell_type": "code", "execution_count": 48, "id": "d742a378", "metadata": {}, "outputs": [], "source": [ "model = qtx.model.ResConv(\n", " nblocks=2, channels=8, kernel_size=3, final_activation=qtx.nn.sinhp1_by_scale\n", ")\n", "\n", "state = qtx.state.Variational(model, max_parallel=20000)\n", "sampler = qtx.sampler.SpinExchange(state, nsamples=1024)\n", "optimizer = qtx.optimizer.SR(state, H)" ] }, { "cell_type": "markdown", "id": "3550bfc3", "metadata": {}, "source": [ "Then we can train as usual." ] }, { "cell_type": "code", "execution_count": 49, "id": "00d77d9d", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "energy = qtx.utils.DataTracer()\n", "VarE = qtx.utils.DataTracer()\n", "\n", "training_rate = 0.01\n", "\n", "for i in range(200):\n", " samples = sampler.sweep()\n", " step = optimizer.get_step(samples)\n", " state.update(step * training_rate)\n", "\n", " energy.append(optimizer.energy)\n", " VarE.append(optimizer.VarE)\n", " if i % 10 == 0:\n", " clear_output()\n", " energy.plot(batch=10, baseline=exact_energy)\n", " plt.show()\n", " VarE.plot(batch=10)\n", " plt.show()\n", "\n", "state.save(\"/tmp/J1J2.eqx\")" ] }, { "cell_type": "markdown", "id": "aaddaafb", "metadata": {}, "source": [ "It becomes harder to converge due to the sign structure. But we can still apply symmetries to improve the performance." ] }, { "cell_type": "code", "execution_count": 50, "id": "5ec2f7f6", "metadata": {}, "outputs": [], "source": [ "symm = Rotation(np.pi/2) @ Flip() @ SpinInverse()\n", "\n", "symm_state = qtx.state.Variational(\n", " model, \"/tmp/J1J2.eqx\", symm, max_parallel=2048\n", ")\n", "\n", "sampler = qtx.sampler.SpinExchange(symm_state, nsamples=1024)\n", "optimizer = qtx.optimizer.SR(symm_state, H)" ] }, { "cell_type": "code", "execution_count": 51, "id": "1ba6b31b", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "energy = qtx.utils.DataTracer()\n", "VarE = qtx.utils.DataTracer()\n", "\n", "training_rate = 0.01\n", "\n", "for i in range(200):\n", " samples = sampler.sweep()\n", " step = optimizer.get_step(samples)\n", " symm_state.update(step * training_rate)\n", "\n", " energy.append(optimizer.energy)\n", " VarE.append(optimizer.VarE)\n", " if i % 10 == 0:\n", " clear_output()\n", " energy.plot(batch=10, baseline=exact_energy)\n", " plt.show()\n", " VarE.plot(batch=10)\n", " plt.show()\n", "\n", "symm_state.save(\"/tmp/J1J2.eqx\")" ] }, { "cell_type": "markdown", "id": "0298d207", "metadata": {}, "source": [ "A benchmark against ED shows that the $J_1$-$J_2$ model is indeed more difficult than the nearest-neighbor Heisenberg model. The accuracy can be improved by increasing the amount of samples or utilizing deeper and wider networks." ] }, { "cell_type": "code", "execution_count": 52, "id": "0dde70a7", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "NQS energy: -33.782434819834265, relative error: 0.001455989363423509\n", "Fidelity: 0.9971699670582732\n" ] } ], "source": [ "dense = symm_state.todense(full_symm).normalize()\n", "nqs_energy = jnp.asarray(dense @ H @ dense)\n", "rel_err = jnp.abs((nqs_energy - exact_energy) / exact_energy)\n", "print(f\"NQS energy: {nqs_energy}, relative error: {rel_err}\")\n", "\n", "fidelity = jnp.abs(dense @ wf[:, 0]) ** 2\n", "print(f\"Fidelity: {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": "3.12.3" } }, "nbformat": 4, "nbformat_minor": 5 }