{ "cells": [ { "cell_type": "markdown", "id": "5bfe6a46", "metadata": {}, "source": [ "# Triangular Heisenberg model\n", "\n", "The Heisenberg model on the triangular lattice is much more difficult compared to the square case. In this tutorial, we will show how to search for its ground state in Quantax." ] }, { "cell_type": "code", "execution_count": 1, "id": "31b7f2af", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import jax\n", "import jax.numpy as jnp\n", "import jax.random as jr\n", "import equinox as eqx\n", "import quantax as qtx\n", "from IPython.display import clear_output\n", "\n", "lattice = qtx.sites.Triangular(6, Nparticles=(18, 18))\n", "N = lattice.Nsites\n", "\n", "lattice.plot()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "9f09d44f", "metadata": {}, "source": [ "## Sign (phase) structure\n", "\n", "Similar to the square Heisenberg model, the first step is to find the sign structure of ground state wavefunctions. Unfortunately, the triangular Heisenberg model is frustrated and its sign structure is unknown. Nevertheless, one can still look at its classical counterpart for a reasonable starting point.\n", "\n", "![Classical triangular spins](../images/triangular.png)\n", "\n", "The classical ground state has the Neel $120^\\circ$ pattern as shown above. We can construct a corresponding quantum product state $\\ket{\\Psi_0} = \\bigotimes_j \\ket{\\psi_j}$. The single-spin state on each site $j$ is\n", "\n", "$$\n", "\\ket{\\psi_j} = \\ket{\\uparrow} + e^{i\\phi_j} \\ket{\\downarrow},\n", "$$\n", "\n", "where $\\phi_j = 0, 2\\pi/3$ or $4\\pi/3$ depending on the sublattice of $j$.\n", "\n", "$\\braket{s|\\Psi_0}$ provides a good reference phase structure for any input spin configuration $s$. It also suggests that expressing the wavefunction amplitudes by complex numbers is more natural. To activate complex numbers in Quantax, one should set the default dtype before any computation." ] }, { "cell_type": "code", "execution_count": 2, "id": "1c4dfab3", "metadata": {}, "outputs": [], "source": [ "qtx.set_default_dtype(jnp.complex128)" ] }, { "cell_type": "markdown", "id": "49cf0ab6", "metadata": {}, "source": [ "We can manually define a function for this phase structure. In Quantax, we also provide a pre-defined function {py:func}`~quantax.nn.neel120_phase`." ] }, { "cell_type": "code", "execution_count": 3, "id": "d19e0960", "metadata": {}, "outputs": [], "source": [ "def get_phase(s):\n", " Lx, Ly = lattice.shape[1:]\n", " sublattice_idx_x = jnp.arange(Lx) % 3\n", " sublattice_idx_y = -jnp.arange(Ly) % 3\n", " sublattice_idx = sublattice_idx_x[:, None] + sublattice_idx_y[None, :]\n", " sublattice_idx = sublattice_idx.flatten() % 3\n", "\n", " phase = jnp.exp(1j * sublattice_idx * 2 * jnp.pi / 3)\n", " phase = jnp.where(s > 0, 1.0, phase)\n", " return jnp.prod(phase)\n", "\n", "s = qtx.utils.rand_states()\n", "phase1 = get_phase(s)\n", "phase2 = qtx.nn.neel120_phase(s)\n", "assert jnp.isclose(phase1, phase2)" ] }, { "cell_type": "markdown", "id": "b26c2085", "metadata": {}, "source": [ "## Define model\n", "\n", "![Residual convolutional network](../images/ResConv_triangular.svg)\n", "\n", "We will utilize a residual convoluional network as shown above. The pair complex function in the end converts real values from previous layers to complex outputs. In {py:class}`~quantax.model.ResConv`, this pair complex function is called automatically when one needs complex outputs." ] }, { "cell_type": "code", "execution_count": 4, "id": "c7b759a9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Network type: \n", "Number of layers: 7\n" ] } ], "source": [ "model0 = qtx.model.ResConv(\n", " nblocks=4, channels=8, kernel_size=3, dtype=jnp.float32, out_dtype=jnp.complex128\n", ")\n", "\n", "print(\"Network type:\", type(model0))\n", "print(\"Number of layers:\", len(model0.layers))" ] }, { "cell_type": "markdown", "id": "8054d74d", "metadata": {}, "source": [ "Then how to include the reference phase structure? `model0` is a {py:class}`~quantax.nn.Sequential` network that performs forward pass layer by layer, so one can append a new layer to multiply the network output by a phase structure factor." ] }, { "cell_type": "code", "execution_count": 5, "id": "5da1db86", "metadata": {}, "outputs": [], "source": [ "class PhaseLayer(qtx.nn.RawInputLayer):\n", " def __call__(self, x: jax.Array, s: jax.Array) -> jax.Array:\n", " phase = qtx.nn.neel120_phase(s)\n", " return x * phase\n", "\n", "layers = model0.layers + (PhaseLayer(),)\n", "model = qtx.nn.Sequential(layers)" ] }, { "cell_type": "markdown", "id": "8243c4d2", "metadata": {}, "source": [ "Here we define the new layer to be an instance of {py:class}`~quantax.nn.RawInputLayer`, which allows it to take two inputs, the output from last layer x, and the original input spin configuration s. `Sequential` will pass x and s to `RawInputLayer` automatically. \n", "\n", "Here we perform a forward pass to check whether the network works. The scatter plot shows the distribution of output wavefunctions $\\psi(s)$, in which the color represents the reference phase of the inputs. " ] }, { "cell_type": "code", "execution_count": 6, "id": "97c39751", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "s = qtx.utils.rand_states(64)\n", "psi = jax.vmap(model)(s)\n", "phase = jax.vmap(qtx.nn.neel120_phase)(s)\n", "\n", "plt.scatter(psi.real, psi.imag, c=jnp.angle(phase), cmap=\"viridis\", alpha=0.7)\n", "plt.axis(\"equal\")\n", "plt.xlabel(r\"Re $\\psi$\")\n", "plt.ylabel(r\"Im $\\psi$\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "58bae3ba", "metadata": {}, "source": [ "Before training, the reference phase structure dominates the output." ] }, { "cell_type": "markdown", "id": "289db350", "metadata": {}, "source": [ "## Optimization\n", "\n", "We can train this model as we have done previous tutorials." ] }, { "cell_type": "code", "execution_count": 7, "id": "98e92143", "metadata": {}, "outputs": [], "source": [ "H = qtx.operator.Heisenberg()\n", "E_exact = -80.6937689612426\n", "\n", "state = qtx.state.Variational(model, max_parallel=32768)\n", "sampler = qtx.sampler.SpinExchange(state, nsamples=1024)\n", "optimizer = qtx.optimizer.SR(state, H)" ] }, { "cell_type": "code", "execution_count": 8, "id": "fc4080b3", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "energy = qtx.utils.DataTracer()\n", "VarE = qtx.utils.DataTracer()\n", "\n", "training_rate = 5e-3\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=E_exact)\n", " plt.show()\n", " VarE.plot(batch=10)\n", " plt.show()\n", "\n", "state.save(\"/tmp/triangular.eqx\")" ] }, { "cell_type": "markdown", "id": "aaa139b4", "metadata": {}, "source": [ "Now we can symmetrize the wavefunction. The symmetry consists of a {py:class}`~quantax.symmetry.D6` group (including rotations and mirror flips) and local spin inverse. By default, the center of transformations like rotations is fixed at the center of the lattice. In this special case, however, we need to specify the center to be (0, 0) to ensure that the lattice transforms back to itself under rotation and periodic shifts." ] }, { "cell_type": "code", "execution_count": 9, "id": "d34d2512", "metadata": {}, "outputs": [], "source": [ "from quantax.symmetry import D6, SpinInverse\n", "\n", "symm = D6(center=(0, 0)) @ SpinInverse()" ] }, { "cell_type": "markdown", "id": "c30ac8b6", "metadata": {}, "source": [ "Then we can keep training the symmetrized state." ] }, { "cell_type": "code", "execution_count": 10, "id": "a7e76222", "metadata": {}, "outputs": [], "source": [ "symm_state = qtx.state.Variational(\n", " model, \"/tmp/triangular.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": null, "id": "3b082975", "metadata": {}, "outputs": [ { "data": { "image/png": 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gALp3744pU6Zg1apV+Oijj1BRce+Vo+Pj4/Hyyy/j888/h5+fn2a7QqHAuHHj0LNnT/Tv3x/fffcdnJ2dsX79+lqPO2/ePBQVFWkeV65ceahxNDdT+3eEncQcZ3OV+OnMNUOXQ0REZFANXrg9e/ZsjB8/vs42Xl5eiIuLQ3R0NAoLCzXn+9auXYvY2Fhs2bIFUVFRkMvlSEpK0nrt9evXAQByubzeNQUFBUGlUuHSpUvw9vbWbP/ll18wfPhwvP/++xg3blydfVhYWCAgIADnz5+vtY1EIoFEIql3XcbGwdYSk/t74b/7M7FqfyaGdnOFpTmvEkFERC1Tg0OSs7MznJ2d79uutLTmCs5isfaHrFgshlqtBlAzm7NkyRLk5+dDJpMBAGJjYyGVSuHr61vvmpKTkyEWizV9ADWXAQgLC8N7772HV1999b59VFdX4/fff8ewYcPqfVxT9EpwB2xOuIzsW6XYfjwb4xSehi6JiIjIIPQ2TaBQKODg4ICIiAikpKQgMzMTc+bMQVZWFkJDQwEAQ4YMga+vL8aOHYuUlBTs27cPCxYsQGRkpGbGJikpCT4+PsjJyQFQs9h7zZo1SElJwcWLF7Ft2zbMnDkTY8aM0ax1io+PR2hoKKZPn46RI0ciLy8PeXl5uHXrlqa+xYsXY//+/bh48SJOnTqFMWPG4PLly5g4caK+3hKjYGNpjjee6AQA+PDgeZRU1L0gnoiIyFTpLSQ5OTkhJiYGxcXFGDRoEHr37o2jR49i9+7d6NGjBwDAzMwM0dHRMDMzg0KhwJgxYzBu3DgsXrxY009paSkyMjJQVVUFoOaU1/bt29G/f3/4+flhyZIlmDlzJj777DPNa7Zs2YLS0lIsW7YMrq6umsczzzyjaVNYWIhJkyaha9euGDZsGJRKJRISEho0g2WqXnjEHe5tbHCjuAIbj2YZuhwiIiKD0Nt1kloCU7pO0j/tTs7BG9uTYScxxy9vDUQbW93XrCIiIjI2Br9OEhm34d3boqurFHcqVPj0UO2L2YmIiEwVQxLpJBaL8NZTNd8U3JJ4GTm3ywxcERERUdNiSKJaDejijKAObVCpUuODA5mGLoeIiKhJMSRRrUQiEd56ygcA8O3Jqziff8fAFRERETUdhiSqU6CHA570dYFaAFbuyzB0OURERE2GIYnua06IN8QiYF/adZzOLjR0OURERE2CIYnuq4uLHZ7p1R4A8F5MzX35iIiITB1DEtXLjMGdYWkmxm8Xb+HwuRuGLoeIiEjvGJKoXto72GCswgMAsCImHWo1Z5OIiMi0MSRRvb02oCNaScyRdk2JPb/nGrocIiIivWJIonpzbCXBpH5eAIBV+zNQVa02cEVERET6w5BEDTKxXwc42lri0s1SfHP8iqHLISIi0huGJGoQW4k5Xh/UCQDwwcFzKK1UGbgiIiIi/WBIogYbFeSO9g7WKLhTgU2/XjJ0OURERHrBkEQNJjE3w+whXQAA6365gNullQauiIiIqPExJNEDebpHO/jI7XCnXIVPD10wdDlERESNjiGJHoiZWIQ5Id4AgM0Jl5BbVGbgioiIiBoXQxI9sEE+Mjzi6YAKlRofHjxn6HKIiIgaFUMSPTCRSIS5T/kAAHacuIoLBcUGroiIiKjxMCTRQ+nt2QaDu8pQrRawan+GocshIiJqNAxJ9NDeDPGGSATs/T0PKVduG7ocIiKiRsGQRA/NRy7Fv3q2AwCs2Jdu4GqIiIgaB0MSNYqZT3aBhZkIv56/iaPnbhi6HCIioofGkESNwq2NDUYHeQAA3otJhyAIBq6IiIjo4TAkUaOZNqgTbC3N8HtOEfb+nmfocoiIiB4KQxI1GqdWEkzs5wUA+O/+DFRVqw1cUdOqqlbjt4s3sfzndIR+eAQTtxxHeVW1ocsiIqIHZG7oAsi0TOzXAf/77TKybpTg25NXMepRd0OXpFfXleX4JaMA8Rn5OHruBu5UqDT70q4p8e/vf8eq53pAJBIZsEoiInoQDEnUqOysLBA5sBPejf4Daw5kIrxnO1hbmhm6rEajqlbj9JXbiE/Px6GMAvyRq9Ta38bWEo93dkIXuR1W7c/Ed6dy0K2tPV4J7mCgiomI6EExJFGjG9PHHRuPZiHndhm2JF7ClP4dDV3SQ8m/UzNbdCijAEfOFUBZ/tdskUgEdG9njwHeMgzwdkb39q1hJq6ZNZKYm+Hd6D+wZO9Z+LjaoW9HJ0MNgYiIHoBI4NeQHphSqYS9vT2KiooglUoNXU6z8u3Jq3hzZwqkVuY48tYg2NtYGLqkeqtWC0i+Uoj49AIcysxHao72bFFrGws83tkZA32c8XhnZzi2kujsRxAEzNqRgu9P58DBxgI/TguGWxubphgCERHVob6f33pduJ2ZmYkRI0bAyckJUqkUwcHBiI+P12qTnZ2N0NBQ2NjYQCaTYc6cOVCpVLX0WMPT0xMikUjrsXz5cs3+S5cu3bNfJBLht99+0+pn586d8PHxgZWVFfz9/bF3797GG3wL96+Aduji0grKchXWHb5g6HLu60ZxBXadvIrXvz6NXu/GYuSnifg4/rwmIPm3s8f0QZ2wa2pfnFzwJD4cFYB/BbSvNSABNfe2W/aMP7q1k6KwtAqT/3cSZZVcyE1EZCz0erotLCwMnTt3RlxcHKytrbFmzRqEhYXhwoULkMvlqK6uRmhoKORyORISEpCbm4tx48bBwsICS5curbPvxYsXY9KkSZrndnZ297Q5cOAA/Pz8NM8dHR01f05ISMCoUaOwbNkyhIWF4auvvkJ4eDhOnTqFbt26NcLoWzYzsQhzQnwwaesJbPo1C+P7esJFamXosjSq1QJSrt7GofR8HMoswJmrRVr7pVbmeLyLMwZ4y9C/izOc7WoPQ3WxsjDD+rG98fRHR/FHrhJR353Bmhd6ciE3EZER0Nvpths3bsDZ2RmHDx9Gv379AAB37tyBVCpFbGwsBg8ejJ9//hlhYWG4du0aXFxcAADr1q3D3LlzUVBQAEtLS519e3p6YsaMGZgxY4bO/ZcuXUKHDh1w+vRp9OzZU2ebF154ASUlJYiOjtZs69OnD3r27Il169bVa4w83VY3QRAw8tMEnMq+jZeC3LH0X/4GredmcQUOn6tZW3Q4swCFpVVa+/3aSjHA2xkDvWXo6dYa5maNN9H628WbGLPhGFRqAfOHdcWkx70arW8iImoYg59uc3R0hLe3N7Zu3YqSkhKoVCqsX78eMpkMgYGBAIDExET4+/trAhIAhISEQKlUIi0trc7+ly9fDkdHRwQEBGDlypU6T9E9/fTTkMlkCA4Oxo8//qi1LzExEYMHD9baFhISgsTExFqPWVFRAaVSqfWg2olEIsx9ygcA8M3xK8i6UdKkx1erBSRfuY01BzIx4pNf0XvJAcz8JgW7k6+hsLQKdlbmGOYvx4pnuyPp309gz/R+mBPig96ebRo1IAFAHy9H/CfMFwCw7OezvHULEZER0NvpNpFIhAMHDiA8PBx2dnYQi8WQyWSIiYmBg4MDACAvL08rIAHQPM/Lq/2KzdOnT0evXr3Qpk0bJCQkYN68ecjNzcXq1asBAK1atcKqVavw2GOPQSwWY9euXQgPD8cPP/yAp59+us5j13XcZcuW4Z133mn4m9GCBXk5YqC3M+IzCrBqfwY+fqmXXo9XWFKpNVt0s6RSa39X179miwLcW8OikcNQXcYpPJCaU4SdJ69i2ten8GNkMNwduZCbiKi5anBIioqKwnvvvVdnm7Nnz8Lb2xuRkZGQyWQ4cuQIrK2tsWHDBgwfPhzHjx+Hq6vrAxc9a9YszZ+7d+8OS0tLTJ48GcuWLYNEIoGTk5NWm0ceeQTXrl3DypUrNSHpQcybN0+rX6VSCTc3twfur6WYE+KD+IwCRJ/JxeTHi+Df3r7R+larBaReK8KhPy/omHLlNtR/O4HcSmKO4E5OGOjjjP5dZJDbG25dlEgkwrvh3ZCZX4yUK7fx6v9O4LvX+sLGklfiICJqjhr823n27NkYP358nW28vLwQFxeH6OhoFBYWas73rV27FrGxsdiyZQuioqIgl8uRlJSk9drr168DAORyeb1rCgoKgkqlwqVLl+Dt7V1rm9jYWM1zuVyuOdbfj13XcSUSCSSSB1vA25L5tpViRM+22J18DSv2peN/E4Ieqr+i0iocPlcTig5nFuBGsfZskbeLHQb4OGNAFxkCPRxgad587r5jZWGGdWN6YfhHvyI97w7mfHsGH48K4EJuIqJmqMEhydnZGc7OzvdtV1paCgAQi7U/oMRiMdTqmnt6KRQKLFmyBPn5+ZDJZACA2NhYSKVS+Pr61rum5ORkzem8utr8ffZKoVDg4MGDWou/Y2NjoVAo6n1cqr/ZT3pjz5lcHDl3Awnnb6Bvp/pfWFEQBKRdU+JQRs1Vrk9lF2rNFtlamuGxTk6aCzq2bW2thxE0Hld7a3w6phdGffYb9pzJRbe29pg6wLgvuElEZIr0Ns+vUCjg4OCAiIgILFy4ENbW1vj888+RlZWF0NBQAMCQIUPg6+uLsWPHYsWKFcjLy8OCBQsQGRmpmbFJSkrCuHHjcPDgQbRr1w6JiYk4duwYBg4cCDs7OyQmJmLmzJkYM2aMZq3Tli1bYGlpiYCAAADAd999h40bN2LDhg2a+t544w30798fq1atQmhoKLZv344TJ07gs88+09db0qK5O9rgpSB3bE28jPf2ZeCHjo51zp4UlVXh6LkbNcEoswAFdyq09neWtdKsLert2aZZzRbVxyOebbDoaT8s+CEVK/alo6urHQZ41x7yiYio6ektJDk5OSEmJgbz58/HoEGDUFVVBT8/P+zevRs9evQAAJiZmSE6OhpTp06FQqGAra0tIiIisHjxYk0/paWlyMjIQFVVzde1JRIJtm/fjkWLFqGiogIdOnTAzJkztdYKAcC7776Ly5cvw9zcHD4+Pvjmm2/w7LPPavb37dsXX331FRYsWIB///vf6Ny5M3744QdeI0mPpg3qhJ0nriLlym3sS8vDU93+mtkTBAFnc+/gUGY+DqUX4GR2Iar/Nl1kbXF3tsgZA7yd0d7B+Bc8jw5yR9q1InyddAXTvz6NH6cFw9PJ1tBlERHRn3hbkofA6yQ13Kr9Gfgo7jw6Otti19S+SLxwE4cyam7/cV2pPVvU0dkWA7xlGOgtwyMdHCAxN50b5d5VoarGqM9+w6ns2+ji0grfvfYYWkm4kJuISJ/q+/nNkPQQGJIaTllehcdXxON2aRVEIuDvf/usLMR4rOPd2SJZi7nP2XVlOYZ/dBT5dyrwlJ8cn47pxYXcRER6xJDUBBiSHswXR7PwbvQfAAAvJ1v0/3Nt0aMd2sDKwvRmi+rj5OVCvPhZIqqqBbw5pAumDeps6JKIiEwWQ1ITYEh6MIIgIPHCTbRzsIaHI9fg3LU9KRtR3/0OkQj4IqI3Bvm43P9FRETUYAa/LQlRbUQiEfp2cmJA+ocXH3XHmD7uEATgja+TcaGg2NAlERG1aAxJRM3IwjA/POLpgDsVKry69QTulFfd/0VERKQXDElEzYiluRifjO4FudQKFwpKMGtHCtRqnhEnIjIEhiSiZkZmZ4V1YwNhaS5G7B/X8WHcOUOXRETUIjEkETVDPd1a4//Cay5suubAOcT+cf0+ryAiosbGkETUTD3f2w3j+3oCAGZ+k4zz+XcMWxARUQvDkETUjM0P7YqgDm1QXKHCq1tPQsmF3ERETYYhiagZszCrWcjd1t4KF2+UYMb2ZC7kJiJqIgxJRM2cUysJ1o/tDYm5GHHp+Xj/QKahSyIiahEYkoiMgH97eyx7xh8A8FHcecSk5hq4IiIi08eQRGQknunVHhOCOwAAZu1IQUYeF3ITEekTQxKREZk31Ad9OzqitLIar/7vBIpKuZCbiEhfGJKIjIi5mRgfv9QL7Vpb4/LNUkzffhrVXMhNRKQXDElERqaNrSU+GxcIKwsxfskswH/3Zxi6JCIik8SQRGSE/NraY8WzPQAAnx66gOgz1wxcERGR6WFIIjJST/doi8mPewEA5uw8g7O5SgNXRERkWhiSiIzYW0/5oF9nJ5RV1SzkLiypNHRJREQmgyGJyIiZiUX4aFQA3NvY4MqtMkzffhqqarWhyyIiMgkMSURGrrVNzUJuawszHDl3Ayv2cSE3EVFjYEgiMgE+cin++1zNQu7PDl/E7uQcA1dERGT8GJKITERod1e8NqAjAGDurjNIzSkycEVERMaNIYnIhMwe4o0B3s4or1Jj8v9O4hYXchMRPTCGJCITYiYW4YMXAuDpaIOc22WI3HaKC7mJiB4QQxKRibG3scBn43rD1tIMiRdvYunedEOXRERklBiSiExQFxc7rHq+JwBg469Z+O7UVcMWRERkhBiSiEzUU93kmD6oEwAg6rvfcebqbcMWRERkZBiSiEzYjMFd8ISPDJWqmoXcN4orDF0SEZHRYEgiMmFisQjvv9gTXs62yC0qx2vbTqGKC7mJiOpFryEpMzMTI0aMgJOTE6RSKYKDgxEfH6/VJjs7G6GhobCxsYFMJsOcOXOgUqnq7NfT0xMikUjrsXz5cs3+RYsW3bNfJBLB1tZW02bz5s337LeysmrcN4CoGZBaWeCzsb3RSmKOpKxb+L/oPwxdUrP3xzUlVsSk49fzNwxdChEZkLk+Ow8LC0Pnzp0RFxcHa2trrFmzBmFhYbhw4QLkcjmqq6sRGhoKuVyOhIQE5ObmYty4cbCwsMDSpUvr7Hvx4sWYNGmS5rmdnZ3mz2+++SamTJmi1f6JJ57AI488orVNKpUiI+OvWziIRKKHGS5Rs9VJ1grvv9ATk7aewJbEy/BrZ4/ne7sZuqxmpayyGtFnrmHbsWwkX7kNAFh76AKm9O+I2UO6wMKME+9ELY3eQtKNGzdw7tw5fPHFF+jevTsAYPny5Vi7di1SU1Mhl8uxf/9+/PHHHzhw4ABcXFzQs2dPvPvuu5g7dy4WLVoES0vLWvu3s7ODXC7Xua9Vq1Zo1aqV5nlKSgr++OMPrFu3TqudSCSqtQ8iU/OkrwtmDu6C9w9kYsH3qegsa4UAdwdDl2Vw5/PvYNuxbOw6eRXK8ppZbAszEXq0b40Tlwux7pcLOH7pFj4aFYC2ra0NXC0RNSW9/dPI0dER3t7e2Lp1K0pKSqBSqbB+/XrIZDIEBgYCABITE+Hv7w8XFxfN60JCQqBUKpGWllZn/8uXL4ejoyMCAgKwcuXKOk/RbdiwAV26dEG/fv20thcXF8PDwwNubm4YMWLEfY9ZUVEBpVKp9SAyJq8P6oQhvi6orFZjypcnkX+n3NAlGUSFqhq7k3PwwvpEDF59GJt+vQRluQpubawx9ykfJM57At9O7Yu1o3vBTmKOk5cLMezDIzjwx3VDl05ETUhvM0kikQgHDhxAeHg47OzsIBaLIZPJEBMTAweHmn+95uXlaQUkAJrneXl5tfY9ffp09OrVC23atEFCQgLmzZuH3NxcrF69+p625eXl2LZtG6KiorS2e3t7Y+PGjejevTuKiorw3//+F3379kVaWhrat2+v87jLli3DO++806D3gag5EYtFWP1CT4R/8ivO5xfjtS9P4atJfWBp3jJOJV2+WYKvkrKx88RVzS1bzMQiPOEjw+g+HujXyQli8V+n3Yf5u6JbW3tM+/oUzlwtwsStJzAxuAPeesqnxbxnRC2ZSBAEoSEviIqKwnvvvVdnm7Nnz8Lb2xvh4eGoqqrC/PnzYW1tjQ0bNuDHH3/E8ePH4erqildffRWXL1/Gvn37NK8tLS2Fra0t9u7di6FDh9arpo0bN2Ly5MkoLi6GRCLR2vf1119j3LhxuHr16j2B7O+qqqrQtWtXjBo1Cu+++67ONhUVFaio+Osr1EqlEm5ubigqKoJUKq1XrUTNwcWCYoz45FfcKVdhdJA7lvzL39Al6U1VtRoHz17HtmPZOHLur4XYcqkVXnzUDS884gZX+7pPo1Wq1Fj+czo2/poFAOjh1hofjwqAWxsbvdZORPqhVCphb29/38/vBoekgoIC3Lx5s842Xl5eOHLkCIYMGYLCwkKtAjp37owJEyYgKioKCxcuxI8//ojk5GTN/qysLHh5eeHUqVMICAioV01paWno1q0b0tPT4e3trbXviSeegFQqxffff3/ffp577jmYm5vj66+/rtdx6/smEzVH8en5eGXLcQgCsOwZf4x61N3QJTWqnNtl+CYpG9uPX0H+nZp/3IhEQP8uzhgd5IGB3s4wb+Bi7P1peXhzZwqU5SpIrcyx4tkeeKob1zUSGZv6fn43+HSbs7MznJ2d79uutLQUACAWa/8SEovFUKtrrtOiUCiwZMkS5OfnQyaTAQBiY2MhlUrh6+tb75qSk5M1p/P+LisrC/Hx8fjxxx/v20d1dTV+//13DBs2rN7HJTJmA31keHOIN1buy8DC3ano4tIKgR5tDF3WQ6lWC/glMx9fHctGXHo+1H/+E9CplSWe7+2GUY+6P9TszxA/Ofa2leL1r0/jdPZtTPnyJMb39cS8YT6QmJs10iiIqLnQ25okhUIBBwcHREREYOHChbC2tsbnn3+OrKwshIaGAgCGDBkCX19fjB07FitWrEBeXh4WLFiAyMhIzWmzpKQkjBs3DgcPHkS7du2QmJiIY8eOYeDAgbCzs0NiYiJmzpyJMWPGaNY63bVx40a4urrqPG23ePFi9OnTB506dcLt27excuVKXL58GRMnTtTXW0LU7Lw2oCPSrhVh7+95mPLlKUS/HgwXqfFdLyxfWY4dJ67g66QryLldptnet6MjRgd54Elfl0ZbQ9TewQY7Jivw330ZWH/4IjYnXMLJy4X4+KUAeDja3r8DIjIaegtJTk5OiImJwfz58zFo0CBUVVXBz88Pu3fvRo8ePQAAZmZmiI6OxtSpU6FQKGBra4uIiAgsXrxY009paSkyMjJQVVUFAJBIJNi+fTsWLVqEiooKdOjQATNnzsSsWbO0jq9Wq7F582aMHz8eZmb3/guvsLAQkyZNQl5eHhwcHBAYGIiEhIQGzWARGTuRSISVz/bAhfwSZFy/gylfnsT2V/sYxayIWi0g4cJNfJV0GfvTrkP157RRaxsLPNurPUYFuaOjc6v79PJgLMzEmDesK4K82mD2jhT8nlOEsA+PYvnI7gjt7qqXYxJR02vwmiT6C9ckkam4fLMEwz86CmW5Ci/0dsPykf7N9uKqt0oq8e3JK/jqWDYu3SzVbO/t4YDRfdwxtJsrrCyaLuTlFpVh+tencfxSIQBgTB93LAj1bdIaiKhh9LZwm/7CkESm5JfMAry8KQlqAXg3vBvG9vEwdEkagiDg+KVCfHXsMvb+nofKP+8/10pijmd6tcNLQe7wkRvu/0FVtRqrYzOx9tAFAEBXVyk+eSkAXnqaySKih8OQ1AQYksjUrPvlApb/nA5zsQhfTeqDRzsYdiF3UVkVvj91FduOZeNcfrFmu387e4wOcsfwHm1hK9Hr3ZUa5JfMAsz6Jhk3Sypha2mGpc/4Y0TPdoYui4j+gSGpCTAkkakRBAGvf30a0Wdy4dTKEj+9Hnzfawjpo4YzV4uw7dhl/JhyDeVVNbNG1hZmGNGzLV4Kckf39q2btKaGuK4sxxvbT+O3i7cAAC8+4oa3h/vB2pKn34iaC4akJsCQRKaotFKFZ9YmID3vDnq0t8c3kxVNsr6mpEKF3cnXsO3YZaRd++uWP94udhjdxx3hAe0gtbLQex2NoVot4IOD5/BR3DkIQs0YPhkdgE4yu/u/mIj0jiGpCTAkkam6cqsUwz8+itulVRjZqz3++1x3vS3k/uOaEl8lXcYPp6+huKLmHoyW5mKE+btidB939HJ3aLaLyO8n4fwNTN+ejBvFFbC2MMO74d3wbKDu2x4RUdNhSGoCDElkyo6eu4FxG49BLQCLhvti/GMdGq3v8qpqRJ/JxbZjl3E6+7ZmewcnW4wOcsfIXu3hYGvZaMczpII7FZj5TTKOnq+5Jcozvdrh/8K7wcay+aylImppGJKaAEMSmboNRy7i//achZlYhC8nBEHR0fGh+jufX4yvjmVj16mrKCqrufaZuViEED85Rge5Q9HR0WhnjepSrRawNv483j+QCbUAdHS2xSejexn0G3lELRlDUhNgSCJTJwgCZn6TjB+Sr6GNbc1C7natG7aQu0JVjX1p1/HVscuaxcwA0K61NV4KcsdzvdtDZmd8V/l+EL9dvIk3tp/GdWUFJOZivPO0H154xM0kgyFRc8aQ1AQYkqglKKusxrPrEpB2TYlu7aT4dkrfei3kzr5Ziq+SsrHzxBXcLKkEAIhFwCAfF4zu447HOzvDTNzywsHN4grM2pGCXzILAAAjerbFkn/5o1UzupQBkaljSGoCDEnUUlwtLMXTH/+KWyWV+FdAO6x+vofO2Q9VtRoH0/Ox7Vg2Dv8ZAgDARSrBi4+444VH3NC2gTNRpkitFrD+8EX8d38GqtUCOjjZ4uOXAuDX1t7QpRG1CAxJTYAhiVqSxAs3MeaLY6hWC1gQ2hUT+3lp9l27XYbtx6/gm+PZuK6s0Gx/vIszRge54wkfGczNGucGs6bk5OVbeP2r07hWVA5LczH+E+aLMUHuPP1GpGcMSU2AIYlamk2/ZuGdn/6AmViEzS8/AlW1gG3HshGXfh1/3l8WjraWeP4RN4x6xB3ujjaGLdgIFJZUYs63KThwNh8AEOrvimUj/Y3mmlBExoghqQkwJFFLIwgC3tx5BrtOXb1nXx+vNhgd5IEhfi6QmPPq0g0hCAK+OJqF5T+nQ6UW4N7GBh+/FNCsryxOZMwYkpoAQxK1ROVV1XhhfSJSrhZBamWOZwPd8FKQOzrJeDPXh3U6uxDTvjqNnNtlsDAT4d/DumJ8X0+efiNqZAxJTYAhiVqq4goVTl0uxKMd2jTJLUtakqLSKry1KwX70q4DAEL8XLBiZA/Y2/D0G1Fjqe/nN1dSElGDtZKY4/EuzgxIemBvY4F1YwKxaLgvLM3E2Jd2HcM+PILT2YWGLo2oxWFIIiJqZkQiEcY/1gG7pvaFexsb5Nwuw3PrEvH54Yvg5D9R02FIIiJqpvzb2yN6ejBCu7tCpRawZO9ZTNxyAoV/XpyTiPSLIYmIqBmTWlng41EB+L/wbrA0F+Ngej5CPzyCE5du3f/FRPRQGJKIiJo5kUiEMX088P1rfdHByRbXisrxwme/Ye2h81CrefqNSF8YkoiIjIRfW3v89HowRvRsi2q1gBUxGXh583HcLK64/4uJqMEYkoiIjEgriTnWvNAT7430h8RcjF8yCzDswyM4dvGmoUsjMjkMSURERkYkEuGFR9zx47RgdJK1wnVlBUZ9/hs+OngO1Tz9RtRoGJKIiIyUt9wOP057DCN7tYdaAFbFZmLcxmMouMPTb0SNgSGJiMiI2ViaY9XzPfDf53rA2sIMv56/iaEfHMGv528YujQio8eQRERkAp4NbI+fXn8M3i52uFFcgTFfHMPq2EyefiN6CAxJREQmopPMDj9EPoYXH3GDIAAfHjyHlz7/DdeV5YYujcgoMSQREZkQa0szLB/ZHR+82BO2lmY4lnULwz44gl8yCwxdGpHRYUgiIjJBI3q2w0+vB6OrqxQ3SyoRsTEJ78WkQ1WtNnRpREaDIYmIyER5ObfC96/1xZg+7gCATw9dwIuf/YZrt8sMXBmRcdBbSMrMzMSIESPg5OQEqVSK4OBgxMfHa7XJzs5GaGgobGxsIJPJMGfOHKhUqvv2vWfPHgQFBcHa2hoODg4IDw9vcL+HDh1Cr169IJFI0KlTJ2zevPlhh0xE1OxYWZjh/8L98fFLAbCTmOPE5UIM+/AI4tKvG7o0ombPXF8dh4WFoXPnzoiLi4O1tTXWrFmDsLAwXLhwAXK5HNXV1QgNDYVcLkdCQgJyc3Mxbtw4WFhYYOnSpbX2u2vXLkyaNAlLly7FoEGDoFKpkJqaqtlfn36zsrIQGhqKKVOmYNu2bTh48CAmTpwIV1dXhISE6OstISIymLDubeHfzh7TvjqN33OK8MrmE3gusD0e8WyDjrJW6OTcCvY2FoYuk6hZEQmC0OjfD71x4wacnZ1x+PBh9OvXDwBw584dSKVSxMbGYvDgwfj5558RFhaGa9euwcXFBQCwbt06zJ07FwUFBbC0tLynX5VKBU9PT7zzzjuYMGGCzmPXp9+5c+diz549WuHqxRdfxO3btxETE1PvcSqVStjb26OoqAhSqbTeryMiMpQKVTWW7U3H5oRL9+xzaiVBJ5ktOslaoaNzK3SS1TzkUiuIRKKmL5YAAIIg4LqyAhdvFOPSjVJk3ShG1o1SXC0shbfcDlP6d0RXV34GNUR9P7/1MpPk6OgIb29vbN26VXNKa/369ZDJZAgMDAQAJCYmwt/fXxNkACAkJARTp05FWloaAgIC7un31KlTyMnJgVgsRkBAAPLy8tCzZ0+sXLkS3bp1q3e/iYmJGDx4sFbfISEhmDFjRp3jqqioQEXFX1eyVSqVDX5viIgMSWJuhkVP++GJrjIcPJuP8/nFOJ9fjDxlOW4UV+BGcQV+u3hL6zW2lmaa2aaOsr/Ck3sbG1iYcWlrYxAEAbdKKnHpZgkuFpTg0s0SZN0oQdaNUly6UYKyqmqdr0vPu4PdydcwuKsLpg3qhJ5urZu2cBOnl5AkEolw4MABhIeHw87ODmKxGDKZDDExMXBwcAAA5OXlaQUZAJrneXl5Ovu9ePEiAGDRokVYvXo1PD09sWrVKgwYMACZmZlo06ZNvfqtrY1SqURZWRmsra11Hn/ZsmV45513GvJWEBE1S/06O6NfZ2fN8zvlVbhQUIIL+cU4X1ATnC7kF+PyrVKUVFbjzNUinLlapNWHhZkIHo626PTnrFNHmS06Oduho8wWNpZ6W81h1JTlVbh0424AKtH6s7K89jW5ZmIR3Bys4elkiw5/PlykVvgx5Rr2/p6LA2ev48DZ6wju5IRpgzohqEMbzv41ggb9LY6KisJ7771XZ5uzZ8/C29sbkZGRkMlkOHLkCKytrbFhwwYMHz4cx48fh6ur6wMVq1bXfHV1/vz5GDlyJABg06ZNaN++PXbu3InJkyc/UL/1NW/ePMyaNUvzXKlUws3NTa/HJCJqCnZWFujp1vqemYhKlRqXb5ZoZpwuFNSEqAv5NbMbd7cjTbu/dq2t4eVsq5l1ujsL5WhrafIf3mWV1bh0888AdLMEWX+bGbpRXFnna9vaW6GDsy08Hf8KQx2cbOFWy6xdiJ8c5/OL8emhC/ghOQdHz9/A0fM30NvDAZGDOmFAF2eTf7/1qUEhafbs2Rg/fnydbby8vBAXF4fo6GgUFhZqzvWtXbsWsbGx2LJlC6KioiCXy5GUlKT12uvXa75tIZfLdfZ9N1z5+vpqtkkkEnh5eSE7O1vz2vv1K5fLNdv+3kYqldY6i3T3WBKJpM7xExGZEktzMTq72KGzi53WdrVawLWiMlwo+FuA+jNE3SypRM7tMuTcLsORc9r3kGttY6GZefr72qd2ra0hFhvPh3mlSo0rhaWaAHTxb7NCuUV1X+HcqZUEHZxs0MHJFp5OtvD6878ebWxhbWnW4Fo6yVph1fM9MGNwZ6w/fAE7TlzFicuFeHnTcXRrJ0XkgE4I8ZMb1fvbXDQoJDk7O8PZ2fm+7UpLSwEAYrF26hWLxZrZIIVCgSVLliA/Px8ymQwAEBsbC6lUqhWC/i4wMBASiQQZGRkIDg4GAFRVVeHSpUvw8PCod78KhQJ79+7V6js2NhYKhaJe7wMRUUsnFovQ3sEG7R1s0L+L9udCYUml1im7u3/OuV2G26VVOHG5ECcuF2q9xspCDC+nVpq1T3dDlKeTDSTmDQ8OjaFaLeDa7TLN6TDNKbKbJbhaWFbnffGkVubo4NyqJgA52sLTyQZeTjXjsbPSz7cI3drY4P/C/TF9UGd8fuQivvwtG6k5SkzddgqdZa3w2sCOGN69Lcy5jqze9PbtNh8fH/Tv3x8LFy6EtbU1Pv/8c3zwwQc4fvw4evTogerqavTs2RNt27bFihUrkJeXh7Fjx2LixImar+onJSVh3LhxOHjwINq1awcAmDFjBr799lts3LgRHh4eWLlyJX766Sekp6fDwcGhXv1mZWWhW7duiIyMxCuvvIK4uDhMnz4de/bsadAlAPjtNiKi+iurrMbFG9rh6UJ+TfCorOVK4GIR4N7G5s81T9qLx6WNEDYEQUD+nYp/LJaueWTfLK21LgCwtjDTOiX29/VCDjYWBj/NdaukEpt+zcLmhEu48+d6J/c2Npg6oCOe6dXOYOGzOajv57deQhIAnDhxAvPnz8eJEydQVVUFPz8/LFy4EEOHDtW0uXz5MqZOnYpDhw7B1tYWERERWL58OczNaya4Dh06hIEDByIrKwuenp4AamaO5s2bh//9738oKytDUFAQ1qxZAz8/v3r3e7fvmTNn4o8//kD79u3xn//8576nEv+JIYmI6OGpqtW4Ulj215qnv52+u1NR+2JmmZ3knssVdJK1gsxOohVQBEFAYWmVzsXSl26WoLRS9zfHAMDSTAx3RxvtMORoCy9n23uO01wpy6vwv8TL+OJoFm6V1KyJkkut8OrjXhj1qPsDneIzdgYPSS0BQxIRkf4IgoCCOxU1oamgWCtEXVdW1Po6O4k5vGSt0NbeCteKynHpRgmKyqpqbS8W1Zyq+udi6Q5Otmjb2hpmJrKWp7RSha+TruCzwxc075+jrSVeCe6AcQoPvZ0GbI4YkpoAQxIRkWEoy6v+XCiu/c27yzdLUNtSIVd7K+3F0o626OBsCzcHG1iat5x1OhWqauw6mYNPfzmPK7dq7uMntTLH+L6eePmxDnCwvfdizqaGIakJMCQRETUvFapqXL5ZivP5xcgtKkdbeyt4/hmIWuJppbqoqtX4MeUa1h66UHMZBwA2lmYY08cDE4M7QCa1MnCF+sOQ1AQYkoiIyNip1QL2peXh4/jzSLtWcycJS3MxXujthsn9vdDewcbAFTY+hqQmwJBERESmQhAEHMoowMfx53Hyz0s0mItFCA9oh9cGdISXcysDV9h4GJKaAEMSERGZGkEQ8NvFW/gk/jyOnq+5GKhIBIT6uyJyYCeTuJkuQ1ITYEgiIiJTdjq7EJ/En8eBs/mabYO7yhA5sBMC3B0MWNnDYUhqAgxJRETUEpzNVeKT+PPY83su7qaG4E5OiBzYCX28jO9mugxJTYAhiYiIWpILBX/eTPd0DlR/Xmsh0MMB0wZ2wgBv47mZLkNSE2BIIiKiluhqYSnW/3IR35y4gkpVza1b/NpKMW2gcdxMlyGpCTAkERFRS5avLMeGo1n48rfLmtu7dJK1QmQzv5kuQ1ITYEgiIiICCv+8me6mf9xMd0r/jhgZ2PxupsuQ1AQYkoiIiP5y92a6G49m4ebfbqY76XEvvNSMbqbLkNQEGJKIiIjuVVZZja+TsvHZ4YvIU5YD+OtmumMVHpAa+Ga6DElNgCGJiIiodhWqanx3KgefHrqA7FulAAA7K3O8bOCb6TIkNQGGJCIiovtTVavx05lr+CRe+2a6o4PcMamfV5PfTJchqQkwJBEREdWfWi1g/x95+ChO+2a6z/duj8mPd4Rbm6a5mS5DUhNgSCIiImo4QRBwKLMAn8Sdx4l/3Ex36oCO6Kjnm+kyJDUBhiQiIqIHJwgCjmXdwsdx2jfTHebviml6vJkuQ1ITYEgiIiJqHMlXbuPjuPM4cPa6ZtvgrjLMCfGBt9yuUY9V38/v5nkpTCIiImpRerq1xoaI3vj5jX4Y3qMtRCLgwNl8FJVVGawmziQ9BM4kERER6cfFgmL8nJqHyIGdGr1vziQRERGR0fJybqWXgNQQDElEREREOjAkEREREenAkERERESkA0MSERERkQ4MSUREREQ6MCQRERER6cCQRERERKQDQxIRERGRDnoLSZmZmRgxYgScnJwglUoRHByM+Ph4rTbZ2dkIDQ2FjY0NZDIZ5syZA5VKdd++9+zZg6CgIFhbW8PBwQHh4eGafSkpKRg1ahTc3NxgbW2Nrl274oMPPtB6/aFDhyASie555OXlNcrYiYiIyPiZ66vjsLAwdO7cGXFxcbC2tsaaNWsQFhaGCxcuQC6Xo7q6GqGhoZDL5UhISEBubi7GjRsHCwsLLF26tNZ+d+3ahUmTJmHp0qUYNGgQVCoVUlNTNftPnjwJmUyGL7/8Em5ubkhISMCrr74KMzMzTJs2TauvjIwMrcuRy2Syxn8jiIiIyCjp5d5tN27cgLOzMw4fPox+/foBAO7cuQOpVIrY2FgMHjwYP//8M8LCwnDt2jW4uLgAANatW4e5c+eioKAAlpaW9/SrUqng6emJd955BxMmTKh3PZGRkTh79izi4uIA1MwkDRw4EIWFhWjduvUDj5P3biMiIjI+Br13m6OjI7y9vbF161aUlJRApVJh/fr1kMlkCAwMBAAkJibC399fE5AAICQkBEqlEmlpaTr7PXXqFHJyciAWixEQEABXV1cMHTpUayZJl6KiIrRp0+ae7T179oSrqyuefPJJ/Prrrw8xYiIiIjI1ejndJhKJcODAAYSHh8POzg5isRgymQwxMTFwcHAAAOTl5WkFJACa57WtDbp48SIAYNGiRVi9ejU8PT2xatUqDBgwAJmZmTqDUEJCAr755hvs2bNHs83V1RXr1q1D7969UVFRgQ0bNmDAgAE4duwYevXqVeu4KioqUFFRoXmuVCrr+Y4QERGRsWnQTFJUVJTOBc9/f6Snp0MQBERGRkImk+HIkSNISkpCeHg4hg8fjtzc3AcuVq1WAwDmz5+PkSNHIjAwEJs2bYJIJMLOnTvvaZ+amooRI0bg7bffxpAhQzTbvb29MXnyZAQGBqJv377YuHEj+vbti/fff7/O4y9btgz29vaah5ub2wOPhYiIiJq3Bs0kzZ49G+PHj6+zjZeXF+Li4hAdHY3CwkLNub61a9ciNjYWW7ZsQVRUFORyOZKSkrRee/36dQCAXC7X2berqysAwNfXV7NNIpHAy8sL2dnZWm3/+OMPPPHEE3j11VexYMGC+47t0UcfxdGjR+tsM2/ePMyaNUvzXKlUMigRERGZqAaFJGdnZzg7O9+3XWlpKQBALNaeqBKLxZrZIIVCgSVLliA/P1/zrbLY2FhIpVKtEPR3gYGBkEgkyMjIQHBwMACgqqoKly5dgoeHh6ZdWloaBg0ahIiICCxZsqReY0tOTtaEsNpIJBJIJJJ69UdERETGTS9rkhQKBRwcHBAREYGFCxfC2toan3/+ObKyshAaGgoAGDJkCHx9fTF27FisWLECeXl5WLBgASIjIzVBJCkpCePGjcPBgwfRrl07SKVSTJkyBW+//Tbc3Nzg4eGBlStXAgCee+45ADWn2AYNGoSQkBDMmjVLs77JzMxME/DWrFmDDh06wM/PD+Xl5diwYQPi4uKwf/9+fbwdREREZIT0EpKcnJwQExOD+fPnY9CgQaiqqoKfnx92796NHj16AKgJLdHR0Zg6dSoUCgVsbW0RERGBxYsXa/opLS1FRkYGqqqqNNtWrlwJc3NzjB07FmVlZQgKCkJcXJxmQfi3336LgoICfPnll/jyyy81r/Pw8MClS5cAAJWVlZg9ezZycnJgY2OD7t2748CBAxg4cKA+3g4iIiIyQnq5TlJLweskERERGR+DXieJiIiIyNgxJBERERHpwJBEREREpANDEhEREZEODElEREREOjAkEREREenAkERERESkA0MSERERkQ4MSUREREQ6MCQRERER6cCQRERERKQDQxIRERGRDgxJRERERDowJBERERHpwJBEREREpANDEhEREZEODElEREREOjAkEREREenAkERERESkA0MSERERkQ4MSUREREQ6MCQRERER6cCQRERERKQDQxIRERGRDgxJRERERDowJBERERHpwJBEREREpANDEhEREZEODElEREREOjAkEREREenAkERERESkg95CUmZmJkaMGAEnJydIpVIEBwcjPj5eq012djZCQ0NhY2MDmUyGOXPmQKVS3bfvPXv2ICgoCNbW1nBwcEB4eLjWfpFIdM9j+/btWm0OHTqEXr16QSKRoFOnTti8efPDDpmIiIhMiLm+Og4LC0Pnzp0RFxcHa2trrFmzBmFhYbhw4QLkcjmqq6sRGhoKuVyOhIQE5ObmYty4cbCwsMDSpUtr7XfXrl2YNGkSli5dikGDBkGlUiE1NfWedps2bcJTTz2led66dWvNn7OyshAaGoopU6Zg27ZtOHjwICZOnAhXV1eEhIQ06vtARERExkkkCILQ2J3euHEDzs7OOHz4MPr16wcAuHPnDqRSKWJjYzF48GD8/PPPCAsLw7Vr1+Di4gIAWLduHebOnYuCggJYWlre069KpYKnpyfeeecdTJgwofZBiUT4/vvv75lhumvu3LnYs2ePVrh68cUXcfv2bcTExNR7nEqlEvb29igqKoJUKq3364iIiMhw6vv5rZfTbY6OjvD29sbWrVtRUlIClUqF9evXQyaTITAwEACQmJgIf39/TUACgJCQECiVSqSlpens99SpU8jJyYFYLEZAQABcXV0xdOhQnTNJkZGRcHJywqOPPoqNGzfi71kwMTERgwcP1mofEhKCxMTEOsdVUVEBpVKp9SAiIiLTpJfTbSKRCAcOHEB4eDjs7OwgFoshk8kQExMDBwcHAEBeXp5WQAKgeZ6Xl6ez34sXLwIAFi1ahNWrV8PT0xOrVq3CgAEDkJmZiTZt2gAAFi9ejEGDBsHGxgb79+/Ha6+9huLiYkyfPr3OYyuVSpSVlcHa2lrn8ZctW4Z33nnnAd8VIiIiMiYNmkmKiorSuSj674/09HQIgoDIyEjIZDIcOXIESUlJCA8Px/Dhw5Gbm/vAxarVagDA/PnzMXLkSAQGBmLTpk0QiUTYuXOnpt1//vMfPPbYYwgICMDcuXPx1ltvYeXKlQ983LvmzZuHoqIizePKlSsP3ScRERE1Tw2aSZo9ezbGjx9fZxsvLy/ExcUhOjoahYWFmnN9a9euRWxsLLZs2YKoqCjI5XIkJSVpvfb69esAALlcrrNvV1dXAICvr69mm0QigZeXF7Kzs2utKSgoCO+++y4qKiogkUggl8s1x/r7saVSaa2zSHePJZFI6hg9ERERmYoGhSRnZ2c4Ozvft11paSkAQCzWnqgSi8Wa2SCFQoElS5YgPz8fMpkMABAbGwupVKoVgv4uMDAQEokEGRkZCA4OBgBUVVXh0qVL8PDwqLWe5ORkODg4aAKOQqHA3r17tdrExsZCoVDcd2xERETUMuhl4bZCoYCDgwMiIiKQkpKCzMxMzJkzR/PVewAYMmQIfH19MXbsWKSkpGDfvn1YsGABIiMjNWEmKSkJPj4+yMnJAQBIpVJMmTIFb7/9Nvbv34+MjAxMnToVAPDcc88BAH766Sds2LABqampOH/+PD799FMsXboUr7/+uqa+KVOm4OLFi3jrrbeQnp6OtWvXYseOHZg5c6Y+3g4iIiIyRoKeHD9+XBgyZIjQpk0bwc7OTujTp4+wd+9erTaXLl0Shg4dKlhbWwtOTk7C7NmzhaqqKs3++Ph4AYCQlZWl2VZZWSnMnj1bkMlkgp2dnTB48GAhNTVVs//nn38WevbsKbRq1UqwtbUVevToIaxbt06orq7WOnZ8fLzQs2dPwdLSUvDy8hI2bdrU4DEWFRUJAISioqIGv5aIiIgMo76f33q5TlJLweskERERGR+DXieJiIiIyNgxJBERERHpwJBEREREpANDEhEREZEODElEREREOjAkEREREenAkERERESkA0MSERERkQ4MSUREREQ6MCQRERER6cCQRERERKQDQxIRERGRDgxJRERERDowJBERERHpwJBEREREpANDEhEREZEODElEREREOjAkEREREenAkERERESkA0MSERERkQ4MSUREREQ6MCQRERER6cCQRERERKQDQxIRERGRDgxJRERERDowJBERERHpwJBEREREpANDEhEREZEODElEREREOjAkEREREemgt5CUmZmJESNGwMnJCVKpFMHBwYiPj9dqk52djdDQUNjY2EAmk2HOnDlQqVT37XvPnj0ICgqCtbU1HBwcEB4ertm3efNmiEQinY/8/HwAwKFDh3Tuz8vLa9T3gIiIiIyXub46DgsLQ+fOnREXFwdra2usWbMGYWFhuHDhAuRyOaqrqxEaGgq5XI6EhATk5uZi3LhxsLCwwNKlS2vtd9euXZg0aRKWLl2KQYMGQaVSITU1VbP/hRdewFNPPaX1mvHjx6O8vBwymUxre0ZGBqRSqeb5P/cTERFRCyboQUFBgQBAOHz4sGabUqkUAAixsbGCIAjC3r17BbFYLOTl5WnafPrpp4JUKhUqKip09ltVVSW0a9dO2LBhQ71ryc/PFywsLIStW7dqtsXHxwsAhMLCwgaOTFtRUZEAQCgqKnqofoiIiKjp1PfzWy+n2xwdHeHt7Y2tW7eipKQEKpUK69evh0wmQ2BgIAAgMTER/v7+cHFx0bwuJCQESqUSaWlpOvs9deoUcnJyIBaLERAQAFdXVwwdOlRrJumftm7dChsbGzz77LP37OvZsydcXV3x5JNP4tdff73vuCoqKqBUKrUeREREZJr0EpJEIhEOHDiA06dPw87ODlZWVli9ejViYmLg4OAAAMjLy9MKSAA0z2tbG3Tx4kUAwKJFi7BgwQJER0fDwcEBAwYMwK1bt3S+5osvvsBLL70Ea2trzTZXV1esW7cOu3btwq5du+Dm5oYBAwbg1KlTdY5r2bJlsLe31zzc3Nzq94YQERGR0WlQSIqKiqp1UfTdR3p6OgRBQGRkJGQyGY4cOYKkpCSEh4dj+PDhyM3NfeBi1Wo1AGD+/PkYOXIkAgMDsWnTJohEIuzcufOe9omJiTh79iwmTJigtd3b2xuTJ09GYGAg+vbti40bN6Jv3754//336zz+vHnzUFRUpHlcuXLlgcdCREREzVuDFm7Pnj0b48ePr7ONl5cX4uLiEB0djcLCQs3C6LVr1yI2NhZbtmxBVFQU5HI5kpKStF57/fp1AIBcLtfZt6urKwDA19dXs00ikcDLywvZ2dn3tN+wYQN69uypOcVXl0cffRRHjx6ts41EIoFEIrlvX0RERGT8GhSSnJ2d4ezsfN92paWlAACxWHuiSiwWa2aDFAoFlixZgvz8fM23ymJjYyGVSrVC0N8FBgZCIpEgIyMDwcHBAICqqipcunQJHh4eWm2Li4uxY8cOLFu2rF5jS05O1oQwIiIiIr2sSVIoFHBwcEBERARSUlKQmZmJOXPmICsrC6GhoQCAIUOGwNfXF2PHjkVKSgr27duHBQsWIDIyUjNbk5SUBB8fH+Tk5AAApFIppkyZgrfffhv79+9HRkYGpk6dCgB47rnntGr45ptvoFKpMGbMmHvqW7NmDXbv3o3z588jNTUVM2bMQFxcHCIjI/XxdhAREZER0st1kpycnBATE4P58+dj0KBBqKqqgp+fH3bv3o0ePXoAAMzMzBAdHY2pU6dCoVDA1tYWERERWLx4saaf0tJSZGRkoKqqSrNt5cqVMDc3x9ixY1FWVoagoCDExcVpFoTf9cUXX+CZZ55B69at76mvsrISs2fPRk5ODmxsbNC9e3ccOHAAAwcO1MfbQUREREZIJAiCYOgijJVSqYS9vT2Kioq0LkpJREREzVd9P7957zYiIiIiHRiSiIiIiHRgSCIiIiLSgSGJiIiISAeGJCIiIiIdGJKIiIiIdGBIIiIiItKBIYmIiIhIB4YkIiIiIh0YkoiIiIh0YEgiIiIi0oEhiYiIiEgHhiQiIiIiHRiSiIiIiHRgSCIiIiLSgSGJiIiISAeGJCIiIiIdGJKIiIiIdGBIIiIiItKBIYmIiIhIB4YkIiIiIh0YkoiIiIh0MDd0AaRbSUlJrfvMzMxgZWVVr7ZisRjW1tYP1La0tBSCIOhsKxKJYGNj80Bty8rKoFara63D1tb2gdqWl5ejurq6Udra2NhAJBIBACoqKqBSqRqlrbW1NcTimn+bVFZWoqqqqlHaWllZwczMrMFtq6qqUFlZWWtbiUQCc3PzBrdVqVSoqKiota2lpSUsLCwa3La6uhrl5eW1trWwsIClpWWD26rVapSVlTVKW3Nzc0gkEgCAIAgoLS1tlLYN+f+evyN0t+XvCOP8HWFQAj2woqIiAYBQVFTU6H0DqPUxbNgwrbY2Nja1tu3fv79WWycnp1rb9u7dW6uth4dHrW19fX212vr6+tba1sPDQ6tt7969a23r5OSk1bZ///61trWxsdFqO2zYsDrft7979tln62xbXFysaRsREVFn2/z8fE3b1157rc62WVlZmrZvvvlmnW1TU1M1bd9+++062yYlJWnarlixos628fHxmrYff/xxnW2jo6M1bTdt2lRn2x07dmja7tixo862mzZt0rSNjo6us+3HH3+saRsfH19n2xUrVmjaJiUl1dn27bff1rRNTU2ts+2bb76paZuVlVVn29dee03TNj8/v862ERERmrbFxcV1tn322We1/g7X1Za/I2oe/B3x18OYf0foQ30/v3m6jYiIiEgHkSDUMv9J96VUKmFvb4+ioiJIpdJG7ZtT6Q1vy6l045xK5+k2nm7j74i/8HdEDX2fbqvv5zdD0kPQZ0giIiIi/ajv5zdPtxERERHpwJBEREREpANDEhEREZEODElEREREOug1JGVmZmLEiBFwcnKCVCpFcHAw4uPjtdpkZ2cjNDQUNjY2kMlkmDNnTp0r/w8dOgSRSKTzcfz4cU27M2fOoF+/frCysoKbmxtWrFhxT187d+6Ej48PrKys4O/vj7179zbe4ImIiMio6TUkhYWFQaVSIS4uDidPnkSPHj0QFhaGvLw8ADVf0Q0NDUVlZSUSEhKwZcsWbN68GQsXLqy1z759+yI3N1frMXHiRHTo0AG9e/cGULNqfciQIfDw8MDJkyexcuVKLFq0CJ999pmmn4SEBIwaNQoTJkzA6dOnER4ejvDwcKSmpurzLSEiIiJjoa+rWRYUFAgAhMOHD2u2KZVKAYAQGxsrCIIg7N27VxCLxUJeXp6mzaeffipIpVKhoqKiXseprKwUnJ2dhcWLF2u2rV27VnBwcNDqY+7cuYK3t7fm+fPPPy+EhoZq9RUUFCRMnjy53mPU5xW3iYiISD8MfsVtR0dHeHt7Y+vWrSgpKYFKpcL69eshk8kQGBgIAEhMTIS/vz9cXFw0rwsJCYFSqURaWlq9jvPjjz/i5s2bePnllzXbEhMT8fjjj2su/na334yMDBQWFmraDB48WKuvkJAQJCYm1nqsiooKKJVKrQcRERGZJr2FJJFIhAMHDuD06dOws7ODlZUVVq9ejZiYGDg4OAAA8vLytAISAM3zu6fk7ueLL75ASEgI2rdvr9lWn35ra1PXcZctWwZ7e3vNw83NrV41EhERkfFpcEiKioqqdeH03Ud6ejoEQUBkZCRkMhmOHDmCpKQkhIeHY/jw4cjNzW2U4q9evYp9+/ZhwoQJjdLf/cybNw9FRUWax5UrV5rkuERERNT0zBv6gtmzZ2P8+PF1tvHy8kJcXByio6NRWFioueT32rVrERsbiy1btiAqKgpyuRxJSUlar71+/ToAQC6X37eWTZs2wdHREU8//bTWdrlcrumntn5ra1PXcSUSieY+S0RERGTaGhySnJ2d4ezsfN92d2/UePfme3eJxWLNzQgVCgWWLFmC/Px8yGQyAEBsbCykUil8fX3r7F8QBGzatAnjxo275yZ4CoUC8+fPR1VVlWZfbGwsvL29Naf6FAoFDh48iBkzZmheFxsbC4VCcd+xERERkenT25okhUIBBwcHREREICUlBZmZmZgzZw6ysrIQGhoKABgyZAh8fX0xduxYpKSkYN++fViwYAEiIyM1MzZJSUnw8fFBTk6OVv9xcXHIysrCxIkT7zn2Sy+9BEtLS0yYMAFpaWn45ptv8MEHH2DWrFmaNm+88QZiYmKwatUqpKenY9GiRThx4gSmTZumr7eEiIiIjEiDZ5Lqy8nJCTExMZg/fz4GDRqEqqoq+Pn5Yffu3ejRowcAwMzMDNHR0Zg6dSoUCgVsbW0RERGBxYsXa/opLS1FRkYGqqqqtPr/4osv0LdvX/j4+NxzbHt7e+zfvx+RkZEIDAyEk5MTFi5ciFdffVXTpm/fvvjqq6+wYMEC/Pvf/0bnzp3xww8/oFu3bvUeoyAIAMBvuRERERmRu5/bdz/HayMS7teCanX16lV+w42IiMhIXblyRevb8f/EkPQQ1Go1rl27Bjs7O4hEIkOX0yiUSiXc3Nxw5coVzYJ7U2PqY+T4jJ+pj5HjM37GPkZBEHDnzh20bdv2nrXTf6e3020tgVgsrjOBGjOpVGqUf/EbwtTHyPEZP1MfI8dn/Ix5jPb29vdto9d7txEREREZK4YkIiIiIh0YkkiLRCLB22+/bdIXzTT1MXJ8xs/Ux8jxGb+WMEaAC7eJiIiIdOJMEhEREZEODElEREREOjAkEREREenAkERERESkA0NSC3X48GEMHz4cbdu2hUgkwg8//KC1XxAELFy4EK6urrC2tsbgwYNx7tw5wxT7AJYtW4ZHHnkEdnZ2kMlkCA8PR0ZGhlab8vJyREZGwtHREa1atcLIkSNx/fp1A1XcMJ9++im6d++uuZCbQqHAzz//rNlvzGPTZfny5RCJRJgxY4Zmm7GPcdGiRRCJRFqPv9+L0tjHBwA5OTkYM2YMHB0dYW1tDX9/f5w4cUKz39h/z3h6et7zMxSJRIiMjARg/D/D6upq/Oc//0GHDh1gbW2Njh074t1339W635mx/wzvS6AWae/evcL8+fOF7777TgAgfP/991r7ly9fLtjb2ws//PCDkJKSIjz99NNChw4dhLKyMsMU3EAhISHCpk2bhNTUVCE5OVkYNmyY4O7uLhQXF2vaTJkyRXBzcxMOHjwonDhxQujTp4/Qt29fA1Zdfz/++KOwZ88eITMzU8jIyBD+/e9/CxYWFkJqaqogCMY9tn9KSkoSPD09he7duwtvvPGGZruxj/Htt98W/Pz8hNzcXM2joKBAs9/Yx3fr1i3Bw8NDGD9+vHDs2DHh4sWLwr59+4Tz589r2hj775n8/Hytn19sbKwAQIiPjxcEwfh/hkuWLBEcHR2F6OhoISsrS9i5c6fQqlUr4YMPPtC0Mfaf4f0wJNE9IUmtVgtyuVxYuXKlZtvt27cFiUQifP311wao8OHl5+cLAIRffvlFEISa8VhYWAg7d+7UtDl79qwAQEhMTDRUmQ/FwcFB2LBhg0mN7c6dO0Lnzp2F2NhYoX///pqQZApjfPvtt4UePXro3GcK45s7d64QHBxc635T/D3zxhtvCB07dhTUarVJ/AxDQ0OFV155RWvbM888I4wePVoQBNP8Gf4TT7fRPbKyspCXl4fBgwdrttnb2yMoKAiJiYkGrOzBFRUVAQDatGkDADh58iSqqqq0xujj4wN3d3ejG2N1dTW2b9+OkpISKBQKkxpbZGQkQkNDtcYCmM7P79y5c2jbti28vLwwevRoZGdnAzCN8f3444/o3bs3nnvuOchkMgQEBODzzz/X7De13zOVlZX48ssv8corr0AkEpnEz7Bv3744ePAgMjMzAQApKSk4evQohg4dCsD0foa68Aa3dI+8vDwAgIuLi9Z2FxcXzT5jolarMWPGDDz22GPo1q0bgJoxWlpaonXr1lptjWmMv//+OxQKBcrLy9GqVSt8//338PX1RXJystGPDQC2b9+OU6dO4fjx4/fsM4WfX1BQEDZv3gxvb2/k5ubinXfeQb9+/ZCammoS47t48SI+/fRTzJo1C//+979x/PhxTJ8+HZaWloiIiDC53zM//PADbt++jfHjxwMwjb+jUVFRUCqV8PHxgZmZGaqrq7FkyRKMHj0agOl9VujCkEQmLzIyEqmpqTh69KihS2lU3t7eSE5ORlFREb799ltERETgl19+MXRZjeLKlSt44403EBsbCysrK0OXoxd3/zUOAN27d0dQUBA8PDywY8cOWFtbG7CyxqFWq9G7d28sXboUABAQEIDU1FSsW7cOERERBq6u8X3xxRcYOnQo2rZta+hSGs2OHTuwbds2fPXVV/Dz80NycjJmzJiBtm3bmuTPUBeebqN7yOVyALjnWxjXr1/X7DMW06ZNQ3R0NOLj49G+fXvNdrlcjsrKSty+fVurvTGN0dLSEp06dUJgYCCWLVuGHj164IMPPjCJsZ08eRL5+fno1asXzM3NYW5ujl9++QUffvghzM3N4eLiYvRj/KfWrVujS5cuOH/+vEn8DF1dXeHr66u1rWvXrppTiqb0e+by5cs4cOAAJk6cqNlmCj/DOXPmICoqCi+++CL8/f0xduxYzJw5E8uWLQNgWj/D2jAk0T06dOgAuVyOgwcParYplUocO3YMCoXCgJXVnyAImDZtGr7//nvExcWhQ4cOWvsDAwNhYWGhNcaMjAxkZ2cbzRj/Sa1Wo6KiwiTG9sQTT+D3339HcnKy5tG7d2+MHj1a82djH+M/FRcX48KFC3B1dTWJn+Fjjz12z2U3MjMz4eHhAcA0fs/ctWnTJshkMoSGhmq2mcLPsLS0FGKxdkwwMzODWq0GYFo/w1oZeuU4GcadO3eE06dPC6dPnxYACKtXrxZOnz4tXL58WRCEmq91tm7dWti9e7dw5swZYcSIEUb1tc6pU6cK9vb2wqFDh7S+oltaWqppM2XKFMHd3V2Ii4sTTpw4ISgUCkGhUBiw6vqLiooSfvnlFyErK0s4c+aMEBUVJYhEImH//v2CIBj32Grz92+3CYLxj3H27NnCoUOHhKysLOHXX38VBg8eLDg5OQn5+fmCIBj/+JKSkgRzc3NhyZIlwrlz54Rt27YJNjY2wpdffqlpY+y/ZwRBEKqrqwV3d3dh7ty59+wz9p9hRESE0K5dO80lAL777jvByclJeOuttzRtTOFnWBeGpBYqPj5eAHDPIyIiQhCEmq92/uc//xFcXFwEiUQiPPHEE0JGRoZhi24AXWMDIGzatEnTpqysTHjttdcEBwcHwcbGRvjXv/4l5ObmGq7oBnjllVcEDw8PwdLSUnB2dhaeeOIJTUASBOMeW23+GZKMfYwvvPCC4OrqKlhaWgrt2rUTXnjhBa1rCBn7+ARBEH766SehW7dugkQiEXx8fITPPvtMa7+x/54RBEHYt2+fAEBn3cb+M1QqlcIbb7whuLu7C1ZWVoKXl5cwf/58oaKiQtPGFH6GdREJwt8unUlEREREALgmiYiIiEgnhiQiIiIiHRiSiIiIiHRgSCIiIiLSgSGJiIiISAeGJCIiIiIdGJKIiIiIdGBIIiIiItKBIYmIiIhIB4YkIiIiIh0YkoiIiIh0YEgiIiIi0uH/AXDngcDfjWjNAAAAAElFTkSuQmCC", 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ktL4ZFewbIT/l3Ivm2pz+nRVxynZumselGiK/5vEwMnXqVCxfvhw33ngjtFotEhISoNfrz7nMs3TpUuj1etctNTXV02V6XERwEEYn2f/K28arasgPHao2YX+lEUFqCTPH9GyH3u5wB1+iwODxMLJ//34sXrwYjz32GHbu3InPP/8cx44dw4IFC7p8zZIlS2AwGFy3srIyT5fpFa6lmqNcqiH/s9bRuPqLYXGICtW65Xs6m1j3njDAYrW55XsSke/RePoNli5diqlTp+Khhx4CAIwdOxZhYWG48MIL8Ze//AWJiWf+BaXT6aDT6TxdmtdNHhyL17YUc94I+R2bTWBdgX2Jpjc79HZnyMBwROg0MJktOFhtwqgkvdu+NxH5Do+fGWluboZKdfrbqNX2TbOEEJ5+e5+Smx4NlQQcr2tGpYF9I+Q/8o6fQnlDC8J1Gkwb0fMderujUknIYt8Ikd/rdRhpbGxEQUEBCgoKAAAlJSUoKChAaWkpAPsSy9y5c13PnzVrFj766CO88sorKC4uxtatW3Hfffdh4sSJSEpyT5ObUkQEB3WaN8KlGvIfax3j36/qww693XE2sXL4GZH/6nUYycvLQ05ODnJycgAADzzwAHJycvDYY48BACorK13BBABuu+02PPfcc/jXv/6F0aNH4/rrr8fw4cPx0UcfuekQlIX71JC/abPYsGGvY4febPct0ThxLDyR/+t1z8jFF198zuWVd95554z77r33Xtx77729fSu/NHlwDF7fUswwQn5j86FaNDS3Iy5ChylDer9Db3ecZ0aO1jbB0NIOfUiQ29+DiOTFvWm8LDc9BioJOFbXzKmS5BecV9Fck5UEdR926O1ObLgOaTH2AWq7uVRD5JcYRrwsMjjIdUUA542Q0pla2/HVgWoAwGw3XkXzc+wbIfJvDCMy4D415C8+L6yC2WLD0LhwjErq+w693XH2jTCMEPknhhEZcJ8a8hfO2SKzs5P6tUNvdzrGwp8KuJEARIGAYUQGzr6RkpNNqDayb4SUqdrYiq1HTwIArvXAVTSdjUyKhFatwqnmdpTWN3v0vYjI+xhGZKAP6egb4VINKdXHuysgBDB+UDRSY/q3Q293dBo1RjqWgTj8jMj/MIzIZFKGs2+ESzWkTM5BZ55sXO2MTaxE/othRCbOvpFtPDNCCnSkxoTCciM0Kvft0NsdDj8j8l8MIzKZkBEDSQKKTzahhn0jpDBr8+2Nq78YNhAxYe7Zobc7OanRAID9lUa0tlu98p5E5B0MIzKx943Y18B/KuFSDSmHEALrdtuXaK710hINAKTGhCA2TIt2q8C+CqPX3peIPI9hREaTMrhPDSnPrtJTKKtvQZhWjctHxHvtfSVJYt8IkZ9iGJERN80jJVrjGP9+5egEhGjdu0Nvd9g3QuSfGEZkNDHd0TdSy74RUoZ2qw2f7vHcDr3dyXb0jfDMCJF/YRiRkT40CCMT7X0j29g3Qgqw5VAtTjW3Y2CEDud7YIfe7oxN1UOSgBOnWlBrMnv9/YnIMxhGZMa+EVIS5xLNrLFJ0Ki9/+MjMjgIQweGA+DZESJ/wjAiM26aR0rRaLZ02qE3SbY6OjbNY98Ikb9gGJHZRMe8kaO1TagxsW+EfNcXhVVobbdh8IAwjEnWy1aHs2+EY+GJ/AfDiMyiQrUYkWDvG9nOvhHyYZ3Hv3tyh97uOC/v3XPCAKuNO/gS+QOGER8wiUs15ONqTK3YesS5Q698SzQAMCw+HKFaNRrNFhypaZS1FiJyD4YRH9Axb4RnRsg3fby7EjZh79cYFBsmay0atcq1TMS+ESL/wDDiAyY5+kaO1DTyckXySescSzTXeXH8+7nkpLFvhMifMIz4gKhQLTLZN0I+6mhtI/acMEDtxR16u8Ox8ET+hWHER0zKYN8I+aZ1jtkiF503ALHhOpmrsXNe3nuw2oRGs0XeYoio3xhGfAT3qSFfJITA2oIKAParaHxFfGQwkvTBEALYc6JB7nKIqJ8YRnyE88zI4ZpGnGxk3wj5hvyyBpTWNyNUq8blI723Q29POPtGuFRDpHwMIz4iOkyLzIQIAOwbId+x1rlD76gEhGo1MldzOmffCJtYiZSPYcSHcKmGfEm71YZPHDv0yj1b5Gw6xsI3QAgOPyNSMoYRH8J9asiXfH/4JOqb2jAgXIsLhg6Qu5wzjE7WQ6OSUGsyo7yhRe5yiKgfGEZ8yETHDr6HqhtRx74Rkplz/PvVMu3Q253gIDUyE+1Lm+wbIVI23/sJE8Bi2DdCPqLJbMGX+5w79PrOVTQ/l8NN84j8AsOIj+G8EfIFX+6vQku7FemxochKkW+H3u5w+BmRf2AY8THcp4Z8wdr8jtkicu7Q2x1nE+vecgPaLDZ5iyGiPmMY8TETHWdGDlabUN/UJnM1FIhqTWZ879ihd3a27y7RAEDGgDDoQ4LQZrGhqMoodzlE1EcMIz4mNlyH4fHOvhEu1ZD3fbKnAlabQFZqFNIHyLtDb3ckSeK8ESI/wDDigya5LvHlUg15n2v8uw/OFjkb9o0QKR/DiA/i8DOSS8nJJuwua4BaJeHqscoII86+kfzSU/IWQkR9xjDig5x9I0VV7Bsh73KOf79g6AAMjPCNHXq74zwzcqyuGaf43wuRIjGM+KAB4ToMiw8HwHkj5D1CCKxzDDqbnaOMsyIAEBWqxWBHb0sBd/AlUiSGER81KYNLNeRdu08YcKyuGSFBalwxMkHucnqFTaxEysYw4qPYN0Le5lyiuWJUPMJ0vrVDb3c6b5pHRMrDMOKjnFfUFFWZuA5OHmex2vDJHudVNL49W+Rssh1j4QtKT8Fm4w6+RErDMOKjBoTrcF6co2/kGPtGyLO+P3ISJxvbEBOmxQXn+d4Ovd3JTIyATqOCsdWCkromucshol5iGPFhHfNGuFRDnrXOMVtk1thEBPngDr3dCVKrMCbZvocO+0aIlEd5P3UCCPepIW9obrPgi31VAIBrfXiH3u50DD/jvBEipWEY8WHOK2qKqoxoaGbfyNl8tOsEnv/qENqt3CStrzbur0ZzmxWDYkOR4/iFrkQ5afa+EZ4ZIVIehhEfNjBCh6Fx4RCC80bO5v2fjuOBD3fj+a8O46lPD8hdjmI5r6K5NivJp3fo7U6244qaoioTWtqs8hZDRL3CMOLjJmVwn5qz+WxvJR5bV+j6+p0fjmFVXpmMFSlTXaMZWw7bd+hV8hINACTpgxEXoYPVJrC33CB3OUTUCwwjPo7zRs70U3EdFq8sgBDAnElpWDztPADAo2sLOWeilz7ZUwmrTWBsih5DBobLXU6/dN7Bl30jRMrCMOLjnFfUHKgywtDcLnM18jtQacSd7+ahzWrDVaMS8H/Xjsbiaefh8pHxaLPYsOD9nagxtcpdpmKsdYx/v1aBs0XOxtk3wlBKpCwMIz4uLiIYQwaG2ftGAnzeSFl9M+a9tR0mswUTM2Lw/E3ZUKskqFQSnrshC0PjwlFlbMU9y3ahzcKG1u4cr2tCfmkDVBIwKytR7nLcgmPhiZSJYUQBJnGpBvVNbZj31nbUmMzITIjAG3NzERykdj0eERyE128dj4hgDfKOn8KTH++TsVplcM4WmTp0AOIigmWuxj3GpuihkoBKQyuqDDxDRqQUDCMKEOh9I81tFtz+zg4Un2xCclQI3p0/EfqQoDOeN3hgOF68KQeSBCzfVooV20plqFYZhBCuq2iUOP69K2E6DYbFRwBg3wiRkjCMKMBkxxU1+ysDr2+k3WrDPct3YXdZA6JDg/Du/ImIj+z6r/hLMuPw4BXDAQCPry/EzuOBvbTVlb3lBhSfbEJwkApXjlbWDr3dcW6al8++ESLFYBhRgLjIYAx29I3sCKC+ESEEHv7vHnx7sBbBQSq8edsEDI3r/oqPey4eghljEtBuFViwbBdP15/F2nz7Es3lIxMQrrAderuTk8rhZ0RKwzCiEM5prIG0VPPM50X4aFc51CoJL88Zh3GOKyW6I0kS/v6/WchMiECtyYzfLNuJ1nYOwXKyWG1Yv9u5Q2+SzNW4n3P42d4TBlg4mZdIERhGFGKyc9O8ksAII29+X4LXNhcDAJ755Rhcmhnfq9eH6TR4/dZc6EOCsLusAX9cWwghuLU8APxwtA4nG82IDg3CRcMGyl2O2w0dGI4InQYt7VYcrDbJXQ4R9QDDiEI4m1j3VRhhaPHvvpF1BeX48yf7AQC/v2o4rs9N7dP3SYsNxb9uzoFKAlbvPIH3fjzuzjIVyzlbZKZCd+jtjkolYWyqfQdfzhshUgb/+0nkp+IjgzF4gL1vJM+P+0a+O1yLB1ftBgDcdn467v7FkH59vwvPG4gl00cAAP7vk/348WhgnFnqSkubFV8U2nfovU7h49/PhX0jRMrCMKIgzmms/to3sveEAQve34l2q8DVYxPx2NUj3bJx2x0XZuDa7CRYbQILV+xCeUOLG6pVpo0HqtHUZkVqTEiPe3CUqGMsfIOsdRBRzzCMKEjHvBH/OzNyvK4Jt7+zHU1tVkwdGotnb8iCSuWeHWQlScIzvxyLUUmRqG9qw13v5QXsrq7rXDv0Jit6h97uOJtYj9Q0+v2yJpE/YBhREOcVNfsqDDC2+s8P2FqTGbe+uR0nG9swKikSr94yHjqNuvsX9kKIVo3Xbh2PmDAt9lUYseSjPQHX0Frf1IbNh2oBALNz/O8qms4GhOuQGhMCANhzokHeYoioWwwjCpKgD0bGgDDY/KhvpNFswe3vbEdpfTNSY0Lw9u0TEBF85nRVd0iJDsVLN4+DWiVhbUEF3vy+xCPv46s+3VsJi01gdHIkhsZFyF2Oxzn7RgrYN0Lk83odRrZs2YJZs2YhKSkJkiRh7dq13b7GbDbj0UcfxaBBg6DT6ZCeno633nqrL/UGvEkZzr4R5YcR5y67heVGxIZp8f78SR7fI2XKkFg8dvVIAMDTGw7g+8MnPfp+vsQfx7+fi2vTPPaNEPm8XoeRpqYmZGVl4aWXXurxa2644QZ8/fXXePPNN3Hw4EF88MEHGD58eG/fmuA/+9TYbAIPrtqN74+cRKhWjbdvn4D0AWFeee+5Uwbh+vEpsAlg0Qe7UFrX7JX3lVNZfTN2Hj8FSQJmZfn3Eo2Tcyx8QVlDwC3JESlNr+dAT58+HdOnT+/x8z///HNs3rwZxcXFiImx/1Wfnp7e27clB+cVNYXl9r6RSA8taXiSEAJ/+fQA1u+ugEYl4dVbxmNsSpTX3l+SJPx59mgcqmnE7rIG3PV+Hj6653yEav1rLHpn6xyzRaYOGXDOvX38ycikSGjVKtQ3taG0vhmDYr0Tdomo9zzeM7J+/Xrk5ubib3/7G5KTkzFs2DA8+OCDaGnp+vJKs9kMo9F42o3sEvUhSI8NhU0AO48pc1fS17YU462t9n6Nf1yfJcsU0OAgNV67ZTwGhOtQVGXCQ6v8t6FVCIE1zqto/HD8e1d0GjVGJEUC4CW+RL7O42GkuLgY33//PQoLC7FmzRo8//zzWL16Ne65554uX7N06VLo9XrXLTW1bxM4/ZWS96lZvfMEnvmsCADwx5kjMFvGwVsJ+mC8ess4BKklfLq3Eq9sPipbLZ60r8KIo7VN0GlUuMrPdujtTo6zb4RNrEQ+zeNhxGazQZIkLF++HBMnTsSMGTPw3HPP4d133+3y7MiSJUtgMBhct7KyMk+XqSiThyhz+Nmmoho8/N89AIC7LhqMOy4cLHNFQG56DJ68ZjQA4O9fHMSmgzUyV+R+zsbVy0bEe+xKJV/l7BthEyuRb/N4GElMTERycjL0er3rvhEjRkAIgRMnTpz1NTqdDpGRkafdqIPzzMjecgNMCpk3kl96Cvcs3wWrTeC6nGQ8clWm3CW53DwpDTdPSoMQwH0f5KO4tlHuktzGahMdO/T68fj3rjgv791fYeDOzUQ+zONhZOrUqaioqEBjY8cP+EOHDkGlUiElJcXTb++XkqJCMMjRN5J33Pf7Ro7WNmL+OzvQ0m7FRcMG4m//O9Zt01Xd5YlZo5A7KBqmVgvuen+nYkJed348WocakxlRoUH4hR/u0Nud1JgQxIRp0W4V2F/J3jMiX9XrMNLY2IiCggIUFBQAAEpKSlBQUIDS0lIA9iWWuXPnup5/8803IzY2Frfffjv279+PLVu24KGHHsL8+fMREhLinqMIQB3zRnx7qaba2Iq5b27HqeZ2ZKXo8cqccT65U6xWo8LLt4xDfKQOR2oa8cCHu2GzKb+h1blD74wxidBqfO+fu6dJkuTqG+HwMyLf1eufTnl5ecjJyUFOTg4A4IEHHkBOTg4ee+wxAEBlZaUrmABAeHg4Nm7ciIaGBuTm5mLOnDmYNWsWXnzxRTcdQmBSwj41hpZ2zHtrO8obWpAxIAxv3TYBYTrfvXw2LiIYr92aC61ahY37q/HiN4flLqlfWtut+DwAdujtDoefEfm+Xv9muPjii895CeQ777xzxn2ZmZnYuHFjb9+KzmGSI4wUlhvQaLYg3Md+ybe2W3Hne3koqjJhYIQO782fiNhwndxldSs7NQp/uW40fr96D57/6jBGJkbiilHKvALlqwPVaDRbkBwVgvF+vENvd3Icx15Q5vtLmkRyaGmzQqWC2/cE643AO2/rJ5KjQpAWEwqrTfjcPjVWm8D9KwuwvaQe4ToN3rl9AlJjQuUuq8duyE3FbeenAwB++58CHK42yVtQH63NtzeuXpud5HM9Ot40NlUPSQLK6ltwstEsdzlEPuflb49g2rOb8U1RtWw1MIwomC/uUyOEwOPrC/H5vipo1Sq8Pnc8RiXpu3+hj3l05ghMyohBU5sVd72/U3Hb0Dc0t2HzIftlyoF4FU1nkcFBGDowHAD7Roh+rsrQije+K8aJUy1os8jXJ8cwomC+uE/NP785gmU/lUKSgP93YzbOHzJA7pL6JEitwstzxiE5KgQlJ5uweGU+rApqaP10byXarQIjEyMxLN7/d+jtTkffCJdqiDp79suDaG23IXdQNK4cFS9bHQwjCubcp2avo29Ebh9sL8VzGw8BsF8qO3NsoswV9U9suA6v3ToeOo0K3x6sxXMbD8pdUo+5dujNCZzx7+fS0TfSIG8hRD5kf4URq3fZ5309OnMEJEm+5VyGEQVLiQ5FakwIrDaBnTLPG/lyXxUeXbMXALDwkiGY5+i5ULrRyXr89X/GAgBe2nQUn+6plLmi7p041Ywdx+w79F6TFdhLNE7OMyO7ywyKOsNF5ElLPzsAIYCZYxNdgV0uDCMK5wv71OQdq8e9H+TDJoAbclPw4BXDZavFE2bnJOPOCzMAAA+u2o0DPj48a12BvXF1yuBYJOgDY4fe7gyLD0dIkBqNZguO+tGEXaK+2nyoFt8dPokgtYSHr5R/IjbDiMLJ3TdyqNqE+e/sgNliw7TMODx93RhZT/V5ysNXZeLC8wagpd2Ku97PQ0Nzm9wlnZUQomOJJptnRZw0ahXGptgbqfNL2TdCgc1qE1i64QAAYO6UdKTFyn+1I8OIwjmvqNlzwoAmL/eNVDS0YN5b22FstWBcWhT+dfM4aHxwuqo7aNQq/PNXOUiLCUVZfQvu/SAfFqtN7rLOsL/SiMM1jdBqVLhqjDLno3hKtmPTPPaNUKD7784TKKoyITJYg3svHSp3OQAYRhQvNSYUKdHe7xtpaG7D3Le2o9LQiqFx4XjrtgkI0co3MMcbokK1eH3ueIQEqfHd4ZP42xe+19DqXKKZlhmHyADbobc7zk3z8nl5LwWw5jYLnnU049976XmICtXKXJEdw4gf8HbfSEubFb9+Nw9HahqREBmM9+ZP9Jl/oT0tMyESz96QBQB4fUsx1jn2fvEFVpvA+oLA3aG3OzmOMyOHqk1eP4tI5Cv+/V0Jqo1mpESHYO75g+Qux4VhxA9MHuy9TfMsVhsWrdiFncdPITJYg/d+PRFJUYG14eGMMYlYeMkQAMDvV+9BYblB5orsthXXocrYishgDS4eHng79HYnPjIYSfpg2IR9WZMo0NSYWvHq5qMAgN9flSnr+PefYxjxA84m1j0nDGhu89xffEII/GHNXnxdVAOdRoU3b5sQsAO1Hrh8OC4ZPhBmiw13vZfnE2PGnTv0zhyb6FM/ZHyJs2+Ew88oED3/1WE0t1mRlRqFWT42B4phxA+kxoQiOSoEFg/3jTz75SF8mHcCKgn4569yMCE9xmPv5evUKgnP35SDjAFhqDC0YuHyXWiXsaG1td2Kz/bad+i9llfRdMnZN8Kx8BRoDleb8J8dZQCAR2fIO+DsbBhG/MQkDy/VvPvDMfxr0xEAwFPXjVHsTrbupA8JwhtzxyNcp8G2kno89ekB2WrZVFQDk9mCJH0wJgZwSOxOx5mRhnPuPk7kb575rAhWm8AVI+MxMcP3fkYwjPiJjnkj7t8079M9lXji430AgN9eNgy/mpjm9vdQqqFxEXjO0dD6zg/H8GFemSx1rHHMFrkmOzmgd+jtzugkPTQqCbUmMyoMrXKXQ+QVPxw9ia+LaqBWSXh4uvwDzs6GYcRPTHGEkd1lDW7tG/nh6En89j8FEAKYMykN903zjWvSfckVoxJw/2XnAQD+uKbQ60O1DM3t+PZgLQDuRdOdEK0amYn2PicOP6NAYLMJPO0YcDZnUhqGOHaw9jUMI34iJTrE1Tey63iDW77n/gojfvPeTrRZbbhqVAL+79rRPrfO6Cvuu/Q8XD4yHm1WGxYs24kak/f+6t5QWIk2qw2ZCRHITIj02vsqlXOfGvaNUCBYv7sCheVGhOs0WDztPLnL6RLDiJ+QJMk1jdUdfSNl9c2Y9/Z2mMwWTMyIwfM3ZUPN0/9dUqkkPHdDFobGhaPaaMbdy3ahzeKdhtaOHXrZuNoTruFnnMRKfq613Yq/O4Yz3n3xEMSG62SuqGsMI37EXfvU1DWaMfet7ag1mZGZEIE35uYiOIiXinYnIjgIr986HhHBGuw8fsrVZ+NJ5Q0t2FZS79ihl0s0PeFsYi0sN8h6BRSRp73zwzGUN7QgUR+MX1+QIXc558Qw4kecYWT3iQa0tFn79D2azBbMf2cHSk42ITkqBO/Onwh9CMeK99TggeF48aYcSBKwYlsplm877tH3c05cnZgeE3DD5/oqIzYM+pAgmC02FFWa5C6HyCPqm9rw0jf2KyAfvGK4z/9ByTDiR1JjQpCkD0a7VWBXH5rz2q023L18F3afMCA6NAjvzp+I+EhuQd9bl2TG4cErhgMAnli/D3nH3H+Fk5NzHP11XKLpMZVKQpajb4TDz8hfvfj1YZjMFoxMjFTEzweGET8iSRIm9XGpxmYTeHj1Hmw5VIvgIPt01aFxvtl1rQT3XDwEM8YkoN0qsGDZLlR54DLSA5VGFFWZoFWrMH2Mb01T9HU5bGIlP1ZysgnLfrKflX105ghFXO7PMOJn+rpPzV8/L8JH+eVQqyS8PGccxqVFe6K8gCFJEv7+v1nITIjAyUYzfrNsJ1rb+7Z01hXn+PdLMgdyKa2XOg8/I/I3f/u8CBabwMXDB2Lq0AFyl9MjDCN+xtk3UlDW876Rf39XjNe2FAMAnvnlGFyaGe+x+gJJmE6D12/NhT4kCLvLGvDHtYVum/ppswl87Nyhl+Pfey07JQqA/S/IU01t8hZD5EZ5x+rxWWEVVBKwZPoIucvpMYYRP5MWE4pER99IT4Y6rc0vx18cY8x/f9VwXJ+b6ukSA0pabCj+dXMOVBKweucJvPvDMbd83+3H6lFhaEVEsAaXZMa55XsGkugwLTIGhAEACk40yFsMkZsIIfCUY8DZDbmpGJ6gnI1MGUb8TG/mjWw5VIsHV+0GANx2fjru/sUQj9cXiC48b6DrL5Q/f3oAPx7t/xwY52yRGaMTfb5L3lexb4T8zYa9VcgvbUBIkBoPXD5M7nJ6hWHED/Vkn5o9JxqwYNlOWGwCV49NxGNXj+R0VQ+648IMzM5OgtUmsHDFLpw41dzn72W2WLFhbyUA4FqOf+8z9o2QP2mz2PDXz4sAAHddNBhxCrsSkmHED3XuGzlb02TJySbc/vYONLdZMXVoLJ69IUsR3dZKJkkSnvmfsRidHIn6pjb85v2dfZ4Fs6moFsZWCxL1wZicEevmSgOHcxLr7rIG2GzcwZeU7f2fjqO0vhkDI3S466LBcpfTawwjfmhQbCgSIoPRZrWdMW+kxtSKuW9tQ11TG0YlReLVW8ZDp+Fpfm8IDlLjtVtzERumxb4KIx75aE+fGlqdSzTXZCUxRPZDZmIEdBoVDC3tKKlrkrscoj4zNLfjn98cBgA8cPkwhOk0MlfUewwjfkiSpE6X+HYs1Zha23HbWztQVt+C1JgQvH37BEQE85JQb0qOCsFLc8ZBrZKwrqAC//6upFevN7S045uiGgDAtbyKpl+C1CqMTtYDYN8IKdtL3x5BQ3M7hsWH4/rxKXKX0ycMI37q58PPzBYrfvP+TuyvNCI2TIv3509CXISy1hT9xeTBsXjs6pEAgKWfHcB3h2t7/NrPHTv0DosPx4hE5XTK+6ocTmIlhSurb8Y7W48BsF/Kq1Er89e6Mqumbrn6Rkob0NxmwQMf7sYPR+sQqlXj7dsnIN1xWSPJY+6UQbh+fApsAli0Ih+ldT1raF2b75gtkpPMhmM3cDaxFrCJlRTq718cRJvVhqlDY3Hx8IFyl9NnDCN+Kj02FPGROrRZbbj97R34dE8lNCoJr94yHmMdA59IPpIk4c+zRyMrNQqGlnbc9X4emsyWc76m0tCCn0rsZ7q4Q6975DgmDRdVmvrcUEwkl91lDVi/uwKSY8CZkv9AYRjxU/a+EfvZkW0l9r6Rf1yfhYuGKTc5+5vgIDVeu2U8BoTrUFRlwkOrd5+zoXV9QQWEsO/QmxId6sVK/VeSPhgDI3Sw2AQKKwxyl0PUY50HnF2Xk+zqf1IqhhE/NqnTZZ9/nDkCsxWwc2OgSdAH49VbxiFILWHD3iq8/O3RLp+7tqBjiYbcQ5IkDj8jRfrqQA22l9RDp1G5dglXMoYRPzZzTCKmDo3Fw1dl4o4LlXfdeaDITY/Bk9eMBgD848uD2OS4Wqazg1UmHKg0IkgtYcaYBG+X6Nc6hp+xiZWUod1qw9LP7GdFfn1BBpKiQmSuqP8YRvyYPjQIy++YjLsv5ph3X3fzpDTcPCkNQgD3rcxHcW3jaY87d+i9eHgcokK1cpTot5zDz3hmhJRi5Y4yFNc2ISZMiwV+8vOdYYTIRzwxaxRyB0XD1GrBXe/vhKm1HYB9h9713KHXY8am6KGSgApDK6qNrXKXQ3ROptZ2PL/xEADg/svOQ6SfzIpiGCHyEVqNCi/fMg7xkTocqWnEAx/uhs0mkHf8FMobWhCh02DaCO7Q625hOg2GxdtntuTz7Aj5uNc2F6OuqQ2DB4ThVxPT5C7HbRhGiHxIXEQwXrs1F1q1Chv3V+OFrw9jjWP8+1WjE7hDr4fksG+EFKDS0II3visGADw8PRNBCh1wdjb+cyREfiI7NQp/uc7e0GoPIycA8CoaT8rmFTWkAM9+eQhmiw0T0qNxxch4uctxK4YRIh90Q24qbjs/HQDQ2m5DXITONTeG3M85/GzPCQMsVpvM1RCdaX+FEf/dZf/D5A8zlD3g7GwYRoh81KMzR2BShn3Dw+vGJUPNHXo9ZsjAcITrNGhpt+JQdWP3LyDyIiEEnt5wAEIAV49NdIVnf6K8fYaJAkSQWoW3bpuAr4tqcPkI/zol62vUKglZqXpsPVKHgrIGjEyKlLskIpfNh2rx/ZGT0KpVePiqTLnL8QieGSHyYWE6Da7JSkKIlo2rnubsG8kvZRMr+Q6rTWDphiIA9g02U2P8cysIhhEiInQafsYdfMmHrN5ZhoPVJuhDgrDo0qFyl+MxDCNEROgYC3+kthFGx8A5Ijk1t1nw7Jf2AWf3XjrUr6cvM4wQEQEYEK5DakwIhAD2lHEHX5LfG1tKUGMyIzUmBLdOGSR3OR7FMEJE5JDtWKph3wjJrcbUite22Hfx/v2VmdBp/LtvjGGEiMghxzn8jH0jJLP/t/EwmtusyE6NwtVjE+Uux+MYRoiIHLJdY+EbIISQtxgKWIerTfjPjlIA9nlD/jbg7GwYRoiIHEYlRUKrVqG+qQ1l9S1yl0MBaulnRbAJ4MpR8ZiQHiN3OV7BMEJE5KDTqDHCMfCMm+aRHH44chLfFNVAo5L8dsDZ2TCMEBF1kuMaftYgax0UeGw2gac2HAAAzJmUhsEDw2WuyHsYRoiIOslx9I2wiZW8bd3ucuyrMCJCp8F9086TuxyvYhghIurEORZ+f4URZotV3mIoYLS2W/H3zw8CAO6+ZAhiw3UyV+RdDCNERJ2kxYQiJkyLNqsN+yuMcpdDAeLtrcdQYWhFkj4Y86dmyF2O1zGMEBF1IklSp03zGmSthQJDXaMZL286AgB48MrhCA7y7wFnZ8MwQkT0Mxx+Rt70z2+OwGS2YFRSJGZnJ8tdjiwYRoiIfqZj+Bkv7yXPKq5txLKfjgMAHp0xAiqV/w84OxuGESKin8lKjYIkAWX1LTjZaJa7HPJjf/v8ICw2gUuGD8T5QwfIXY5sGEaIiH4mMjgIQxwzHgrYN0IesuNYPT7fVwWVBCyZMULucmTV6zCyZcsWzJo1C0lJSZAkCWvXru3xa7du3QqNRoPs7Ozevi0RkVexb4Q8SQiBpz61Dzi7cUIqhsVHyFyRvHodRpqampCVlYWXXnqpV69raGjA3LlzMW3atN6+JRGR17FvhDzp072VKChrQKhWjd9eNkzucmSn6e0Lpk+fjunTp/f6jRYsWICbb74ZarW6V2dTiIjk4Ly8d0+ZATabCNjGQnI/s8WKv35eBAC466LBiIsMlrki+XmlZ+Ttt99GcXExHn/88R4932w2w2g0nnYjIvKm4fERCAlSw2S24Ghto9zlkB95/8fjKKtvQVyEDnddNFjucnyCx8PI4cOH8cgjj2DZsmXQaHp2Imbp0qXQ6/WuW2pqqoerJCI6nUatwpgUPQAOPyP3MTS345/f2AecPXD5MIRqe71A4Zc8GkasVituvvlmPPnkkxg2rOdrYkuWLIHBYHDdysrKPFglEdHZ5bj6RhpkrYP8x782HYahpR3D4yNwfS7/0HbyaCQzmUzIy8tDfn4+Fi1aBACw2WwQQkCj0eDLL7/EpZdeesbrdDoddLrA2iSIiHxPjmssPJtYqf/K6pvx7g/2AWePzMiEmn1ILh4NI5GRkdi7d+9p97388sv45ptvsHr1amRkBN5mQESkHDlp0QCAQ9UmNJktCNPxlDr13d++OIg2qw0XDB2Ai4cNlLscn9Lr/7IaGxtx5MgR19clJSUoKChATEwM0tLSsGTJEpSXl+O9996DSqXC6NGjT3t9XFwcgoODz7ifiMjXxEcGI1EfjEpDK/acMGDKkFi5SyKFKihrwMe7KyBJwJIZmZAknhXprNc9I3l5ecjJyUFOTg4A4IEHHkBOTg4ee+wxAEBlZSVKS0vdWyURkUycfSMcfkZ9JYTA044BZ7/MScGoJL3MFfkeSQgh5C6iO0ajEXq9HgaDAZGRkXKXQ0QB5PUtR/H0hiJcMTIer8/NlbscUqAv9lXhN+/vhE6jwrcPXYxEfYjcJXlNT39/c28aIqJzcPaN5Jc1QAF/u5GPabfa8NfP7APO7rgwI6CCSG8wjBARncPoJD3UKgm1JjMqDK1yl0MK88H2UhSfbEJsmBYLfjFE7nJ8FsMIEdE5hGjVGJFo38SMO/hSbxhb2/H8V4cBAPdfdh4igoNkrsh3MYwQEXUj27WDL+eNUM+9+u1R1De1YfCAMNw0MU3ucnwawwgRUTeyUx19IzwzQj1U0dCCN78vAQA8Mj0TQWr+uj0X/tMhIuqG8/LeveUGtFtt8hZDivCPLw/CbLFhYnoMLh8ZL3c5Po9hhIioGxmxYYgM1sBssaGo0iR3OeTjCssNWJNfDgD4w8wRHHDWAwwjRETdUKkkZDsu8WXfCJ2LEAJLPzsAIYBrspJc/UZ0bgwjREQ9kO3aNK9B1jrIt317qBZbj9RBq1bhoSuHy12OYjCMEBH1AMfCU3csVhuWbrCPfb9tajpSY0Jlrkg5GEaIiHogOyUKAFB8sgkNzW3yFkM+afXOEzhU3Qh9SBAWXjxU7nIUhWGEiKgHosO0yBgQBoBnR+hMTWYLnt14CABw37TzoA/lgLPeYBghIuoh9o1QV974rhi1JjPSYkJx6+RBcpejOAwjREQ9xL4ROpsaYyte21wMAHj4qkxoNfzV2lv8J0ZE1EMdY+G5gy91+H9fHUJLuxU5aVGYMSZB7nIUiWGEiKiHMhMiodWoYGhpR8nJJrnLIR9wqNqE/+woAwA8OoMDzvqKYYSIqIe0GhXGJOsBcKmG7JZuOACbAK4alYDc9Bi5y1EshhEiol5gEys5bT1yEpsO1kKjkvDw9Ey5y1E0hhEiol5gEysBgM0m8NSn9gFnt0we5Lrsm/qGYYSIqBecZ0YOVBrR2m6VtxiSzZr8cuyvNCJCp8F9086TuxzFYxghIuqF5KgQDIzQwWITKCw3yF0OyaC13Yp/fHkQAHDPJUMRE6aVuSLlYxghIuoFSZLYNxLg3vy+BJWGViRHheD2qelyl+MXGEaIiHqJfSOBq67RjFe+PQoAePDKYQgOUstckX9gGCEi6qWOMyOn5C2EvO6Frw+j0WzB6ORIXJuVLHc5fkMjdwFEREozNiUKKgmoMLSi2tiK+MhguUuSzc7j9Xh5k/1MQWy4FrHhOsSGaTEwQofYMJ3jPi1iQrXQqJX99+/R2kas2FYKAPjDjBFQqTjgzF0YRoiIeilcp8Gw+AgUVZmQX9qAq0YH5gjwD3eU4dG1e9Fu7X40viQB0aFaxIZpXaFlQJjjf8PtoWVAuNYVYMJ1Gp+bZvrXz4pgsQlMy4zD+UMGyF2OX2EYISLqg5y0KBRVmVBQFnhhxGK14akNB/D21mMAgOmjE/CLYQNR19SGk41m1DV2/G9dkxn1TW2wCaC+qQ31TW04XNP9e+g0KldIiXWElthwLQa67nMGGB1iwrQI8vBZl+0l9fhyfzVUEvAIB5y5HcMIEVEfZKdG4YPtZSgoC6y+kYbmNixakY/vj5wEADxw+TDce+nQc57FsNoEGprb7GHFZMbJpjbUdQortSb7/9Y12u9varPCbLGhvKEF5Q0tPaorKjTIFVoG/CysDOi0fBQbrkNkcO/Ouggh8NQG+4Czmyam4bz4iB6/lnqGYYSIqA+yU6MBAHtOGGC1CagDoH/gcLUJd7yXh+N1zQjVqvHcDdk9OiukVkmOMxs6DOvBL/KWNivqmsw42dgRWk42nX7G5WSjGXWOMy32sNOOhuZ2HK3tfgNDrVrl6mU5I7R0+jo2XIuYMC2+3FeN3WUNCNWqcf9lHHDmCQwjRER9MDQuHOE6DRrNFhyqNmFEYqTcJXnU1weqsXhlARrNFiRHheDf83I9dswhWjVStKFIiQ7t9rk2m0BDSzvqGh3hpdMZllpnmOl0JsZktqDNakOloRWVhtYe1ePMmQt+MQRxEYHbrOxJDCNERH2gVkkYm6LHD0frkF/a4LdhRAiBVzcX429fFEEIYGJGDF6ZMw6x4Tq5SwMAqFQSYsLsZzDOi+/++a3t1tPCifMMy0mT+bSeF2eosdgEbAJIiQ7BHRdmeP6AAhTDCBFRH+WkReGHo3UoKDuFmyelyV2O27W2W/Hwf/dgXUEFAGDOpDQ8PmsUtBrlXqIbHKRGclQIkqNCun2uzSZgbG3HycY2xEfqEKrlr0xP4T9ZIqI+cvaN+ONY+CpDK+56Pw97ThigUUl4/JpRuHXyILnL8iqVSkJUqBZRodx7xtMYRoiI+sg5ifVIbSOMre2IDA6StyA3yS89hbve34lakxnRoUF4ac44ztUgj1LuuTYiIpkNjNAhJToEQgB7yvxjB9//7jyBG1//CbUmM4bHR2DdwgsYRMjjGEaIiPohJ82+VKP0eSNWm8DTGw7gd6t2o81iwxUj4/Hfe85HWmz3V7QQ9RfDCBFRP3Rsmtcgax39YWhpx/x3duD1LcUAgPsuHYpXbxmPcB1X8sk7+G8aEVE/5KRFAQAKyhoghPC5/VS6c7S2EXe+m4fik00IDlLhH9dn4eqxSXKXRQGGYYSIqB9GJkYiSC2hrqkNJ061IDVGOcsamw/VYtGKXTC1WpCkD8brc3MxOlkvd1kUgLhMQ0TUD8FBaoxMsv8C31WqjL4RIQT+/V0xbn97O0ytFowfFI11iy5gECHZMIwQEfVTjqNvpKCsQdY6eqK13YoHV+3BXz49AJsAbsxNxYo7J2FghG9MVKXAxGUaIqJ+UkoTa42xFb9ZthP5pQ1QqyT8aeYIzDs/XXF9LuR/GEaIiPrJ2cS6v8IIs8UKnUYtb0FnsedEA+56byeqjK3QhwThpZvH4YLzOD+EfAOXaYiI+iktJhQxYVq0WW3YX2GUu5wzrCsox/Wv/ogqYyuGxoVj7cKpDCLkUxhGiIj6SZIk11KNL/WN2GwCf/u8CItXFsBsseHSzDisued8ZAwIk7s0otMwjBARuYGv9Y2YWttx53t5ePnbowCAuy8egjfm5iLCT/bPIf/CnhEiIjfoPPxMbsdONuGO9/JwpKYROo0Kf/vfsbg2O1nusoi6xDBCROQGY1OiAACl9c2oazQjNlyeS2W3HjmJe5bvgqGlHfGROrx+ay6yHGdtiHwVl2mIiNxAHxKEoXHhAOQ5OyKEwDtbSzD3re0wtLQjOzUKHy+6gEGEFIFhhIjITeRqYm2z2LDko7144uP9sNoEfjkuGSvvmoy4yGCv1kHUVwwjRERu4uwb8WYT68lGM25+4yes3FEGlQT8ceYIPHt9FoKDfG/WCVFX2DNCROQmzjMju8saYLMJqFSenWy6r8KAO9/NQ4WhFRHBGvzzVzm4eHicR9+TyBMYRoiI3GR4fARCgtQwmS04WtuI8+IjPPZen+6pxIOrdqOl3YrBA8LwxrxcDBkY7rH3I/IkLtMQEbmJRq3CmBT7zrf5HuobsdkEnvvyIBau2IWWdisuGjYQaxZOZRAhRWMYISJyoxwPDj9rMluwYNlOvPjNEQDAnRdm4O3bJkAfwkFmpGxcpiEiciNPDT8rq2/Gne/loajKBK1ahad/OQb/Oz7Fre9BJBeGESIiN8pOjQYAHKwyoslsQZiu/z9mfzxah3uW78Sp5nYMjNDhtVvHY1xadL+/L5Gv4DINEZEbJeiDkagPhk0Ae8sN/f5+7/90HLe+uQ2nmtsxJlmP9YumMoiQ32EYISJyM3dsmtduteHRNXvxp7WFsNgErslKwqoFU5CoD3FPkUQ+hGGEiMjNOvpGTvXp9fVNbbjl39uwfFspJAl4+KpMvHBTNgeZkd9izwgRkZs5+0bySxsghIAk9Xz42YFKI+58Lw8nTrUgXKfBCzdlY9qIeE+VSuQTGEaIiNxsTLIeapWEGpMZlYZWJEX1bGnli31V+O1/CtDcZsWg2FD8e26uRwenEfmKXi/TbNmyBbNmzUJSUhIkScLatWvP+fyPPvoIl19+OQYOHIjIyEhMmTIFX3zxRV/rJSLyeSFaNTIT7CGiJ5f4CiHw4teH8Zv3d6K5zYqpQ2OxbuFUBhEKGL0OI01NTcjKysJLL73Uo+dv2bIFl19+OTZs2ICdO3fikksuwaxZs5Cfn9/rYomIlKJj07xz9400t1mwaEU+ntt4CABw2/npePf2iYgK1Xq6RCKf0etlmunTp2P69Ok9fv7zzz9/2tdPP/001q1bh48//hg5OTm9fXsiIkXITo3Gsp9Kz3lmpLyhBXe+m4f9lUYEqSX8+drRuGlimveKJPIRXu8ZsdlsMJlMiImJ6fI5ZrMZZrPZ9bXRaPRGaUREbuO8vHfPCQParTYEqU8/Eb3jWD0WvL8TdU1tiA3T4tVbx2NCetc/F4n8mdcv7f3HP/6BxsZG3HDDDV0+Z+nSpdDr9a5bamqqFyskIuq/wQPCEBmsgdliw8Eq02mPrdxeipvf+Al1TW0YmRiJ9fdewCBCAc2rYWTFihV48skn8eGHHyIuLq7L5y1ZsgQGg8F1Kysr82KVRET9p1JJyHINP7P3jVisNjyxfh8e+Wgv2q0CM8ckYvXdU5Dcw6ttiPyV15ZpVq5ciTvuuAOrVq3CZZddds7n6nQ66HQ6L1VGROQZOWnR+O7wSeSXNWBWVhsWrtiFrUfqAAC/u3wYFl06tFczSIj8lVfCyAcffID58+dj5cqVmDlzpjfekohIdjmOMyM/HKnDtS9txfG6ZoRq1XjuhmxcNTpB3uKIfEivw0hjYyOOHDni+rqkpAQFBQWIiYlBWloalixZgvLycrz33nsA7Esz8+bNwwsvvIBJkyahqqoKABASEgK9Xu+mwyAi8j3OJtYqYysAICU6BP+el4vMhEgZqyLyPb3uGcnLy0NOTo7rstwHHngAOTk5eOyxxwAAlZWVKC0tdT3/9ddfh8ViwcKFC5GYmOi6LV682E2HQETkm6LDtBgaFw4AmJQRg/WLLmAQIToLSQgh5C6iO0ajEXq9HgaDAZGR/A+ZiJSjsNyAPScMuD435YzLe4n8XU9/f3NvGiIiDxqdrMfoZC5JE50LYzoRERHJimGEiIiIZMUwQkRERLJiGCEiIiJZMYwQERGRrBhGiIiISFYMI0RERCQrhhEiIiKSFcMIERERyYphhIiIiGTFMEJERESyYhghIiIiWTGMEBERkawUsWuvEAKAfStiIiIiUgbn723n7/GuKCKMmEwmAEBqaqrMlRAREVFvmUwm6PX6Lh+XRHdxxQfYbDZUVFQgIiICkiTJXY5bGI1GpKamoqysDJGRkXKX4xH+fow8PuXz92P09+MD/P8YlX58QgiYTCYkJSVBpeq6M0QRZ0ZUKhVSUlLkLsMjIiMjFfkvWG/4+zHy+JTP34/R348P8P9jVPLxneuMiBMbWImIiEhWDCNEREQkK4YRmeh0Ojz++OPQ6XRyl+Ix/n6MPD7l8/dj9PfjA/z/GP39+JwU0cBKRERE/otnRoiIiEhWDCNEREQkK4YRIiIikhXDCBEREcmKYcTDtmzZglmzZiEpKQmSJGHt2rWnPS6EwGOPPYbExESEhITgsssuw+HDh+Uptg+WLl2KCRMmICIiAnFxcZg9ezYOHjx42nNaW1uxcOFCxMbGIjw8HP/zP/+D6upqmSrunVdeeQVjx451DRyaMmUKPvvsM9fjSj62s3nmmWcgSRLuv/9+131KP8YnnngCkiSddsvMzHQ9rvTjA4Dy8nLccsstiI2NRUhICMaMGYO8vDzX40r/OZOenn7GZyhJEhYuXAhA+Z+h1WrFn/70J2RkZCAkJARDhgzBn//859P2c1H6Z9gtQR61YcMG8eijj4qPPvpIABBr1qw57fFnnnlG6PV6sXbtWrF7925xzTXXiIyMDNHS0iJPwb105ZVXirffflsUFhaKgoICMWPGDJGWliYaGxtdz1mwYIFITU0VX3/9tcjLyxOTJ08W559/voxV99z69evFp59+Kg4dOiQOHjwo/vCHP4igoCBRWFgohFD2sf3c9u3bRXp6uhg7dqxYvHix636lH+Pjjz8uRo0aJSorK1232tpa1+NKP776+noxaNAgcdttt4lt27aJ4uJi8cUXX4gjR464nqP0nzM1NTWnfX4bN24UAMSmTZuEEMr/DJ966ikRGxsrPvnkE1FSUiJWrVolwsPDxQsvvOB6jtI/w+4wjHjRz8OIzWYTCQkJ4u9//7vrvoaGBqHT6cQHH3wgQ4X9V1NTIwCIzZs3CyHsxxMUFCRWrVrles6BAwcEAPHjjz/KVWa/REdHi3//+99+dWwmk0mcd955YuPGjeIXv/iFK4z4wzE+/vjjIisr66yP+cPxPfzww+KCCy7o8nF//DmzePFiMWTIEGGz2fziM5w5c6aYP3/+aff98pe/FHPmzBFC+Odn+HNcppFRSUkJqqqqcNlll7nu0+v1mDRpEn788UcZK+s7g8EAAIiJiQEA7Ny5E+3t7acdY2ZmJtLS0hR3jFarFStXrkRTUxOmTJniV8e2cOFCzJw587RjAfzn8zt8+DCSkpIwePBgzJkzB6WlpQD84/jWr1+P3NxcXH/99YiLi0NOTg7eeOMN1+P+9nOmra0Ny5Ytw/z58yFJkl98hueffz6+/vprHDp0CACwe/dufP/995g+fToA//sMz0YRG+X5q6qqKgBAfHz8affHx8e7HlMSm82G+++/H1OnTsXo0aMB2I9Rq9UiKirqtOcq6Rj37t2LKVOmoLW1FeHh4VizZg1GjhyJgoICxR8bAKxcuRK7du3Cjh07znjMHz6/SZMm4Z133sHw4cNRWVmJJ598EhdeeCEKCwv94viKi4vxyiuv4IEHHsAf/vAH7NixA/fddx+0Wi3mzZvndz9n1q5di4aGBtx2220A/OPf0UceeQRGoxGZmZlQq9WwWq146qmnMGfOHAD+97vibBhGyG0WLlyIwsJCfP/993KX4lbDhw9HQUEBDAYDVq9ejXnz5mHz5s1yl+UWZWVlWLx4MTZu3Ijg4GC5y/EI51+XADB27FhMmjQJgwYNwocffoiQkBAZK3MPm82G3NxcPP300wCAnJwcFBYW4tVXX8W8efNkrs793nzzTUyfPh1JSUlyl+I2H374IZYvX44VK1Zg1KhRKCgowP3334+kpCS//AzPhss0MkpISACAM7q+q6urXY8pxaJFi/DJJ59g06ZNSElJcd2fkJCAtrY2NDQ0nPZ8JR2jVqvF0KFDMX78eCxduhRZWVl44YUX/OLYdu7ciZqaGowbNw4ajQYajQabN2/Giy++CI1Gg/j4eMUf489FRUVh2LBhOHLkiF98homJiRg5cuRp940YMcK1FOVPP2eOHz+Or776CnfccYfrPn/4DB966CE88sgjuOmmmzBmzBjceuut+O1vf4ulS5cC8K/PsCsMIzLKyMhAQkICvv76a9d9RqMR27Ztw5QpU2SsrOeEEFi0aBHWrFmDb775BhkZGac9Pn78eAQFBZ12jAcPHkRpaalijvHnbDYbzGazXxzbtGnTsHfvXhQUFLhuubm5mDNnjuv/K/0Yf66xsRFHjx5FYmKiX3yGU6dOPeNy+kOHDmHQoEEA/OPnjNPbb7+NuLg4zJw503WfP3yGzc3NUKlO/3WsVqths9kA+Ndn2CW5O2j9nclkEvn5+SI/P18AEM8995zIz88Xx48fF0LYL9eKiooS69atE3v27BHXXnutoi7Xuvvuu4VerxfffvvtaZfeNTc3u56zYMECkZaWJr755huRl5cnpkyZIqZMmSJj1T33yCOPiM2bN4uSkhKxZ88e8cgjjwhJksSXX34phFD2sXWl89U0Qij/GH/3u9+Jb7/9VpSUlIitW7eKyy67TAwYMEDU1NQIIZR/fNu3bxcajUY89dRT4vDhw2L58uUiNDRULFu2zPUcpf+cEUIIq9Uq0tLSxMMPP3zGY0r/DOfNmyeSk5Ndl/Z+9NFHYsCAAeL3v/+96zn+8BmeC8OIh23atEkAOOM2b948IYT9kq0//elPIj4+Xuh0OjFt2jRx8OBBeYvuhbMdGwDx9ttvu57T0tIi7rnnHhEdHS1CQ0PFddddJyorK+Uruhfmz58vBg0aJLRarRg4cKCYNm2aK4gIoexj68rPw4jSj/HGG28UiYmJQqvViuTkZHHjjTeeNoND6ccnhBAff/yxGD16tNDpdCIzM1O8/vrrpz2u9J8zQgjxxRdfCABnrVvpn6HRaBSLFy8WaWlpIjg4WAwePFg8+uijwmw2u57jD5/huUhCdBrxRkRERORl7BkhIiIiWTGMEBERkawYRoiIiEhWDCNEREQkK4YRIiIikhXDCBEREcmKYYSIiIhkxTBCREREsmIYISIiIlkxjBAREZGsGEaIiIhIVgwjREREJKv/D9FiTjJCXNjuAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "energy = qtx.utils.DataTracer()\n", "VarE = qtx.utils.DataTracer()\n", "\n", "training_rate = 5e-3\n", "\n", "for i in range(100):\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=E_exact)\n", " plt.show()\n", " VarE.plot(batch=10)\n", " plt.show()\n", "\n", "symm_state.save(\"/tmp/triangular.eqx\")" ] }, { "cell_type": "markdown", "id": "7524d94b", "metadata": {}, "source": [ "Let's check how the phase structure changes after optimization." ] }, { "cell_type": "code", "execution_count": 13, "id": "f56d7510", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "s = qtx.utils.rand_states(64)\n", "psi = symm_state(s)\n", "phase = jax.vmap(qtx.nn.neel120_phase)(s)\n", "\n", "plt.scatter(psi.real, psi.imag, c=jnp.angle(phase), cmap=\"viridis\", alpha=0.7)\n", "plt.axis(\"equal\")\n", "plt.xlabel(r\"Re $\\psi$\")\n", "plt.ylabel(r\"Im $\\psi$\")\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "2ac68a2d", "metadata": {}, "source": [ "There are two interesting phenomena in this plot.\n", "\n", "1. The wavefunctions lie on the same line in the complex plane, so they become nearly real after multiplying a constant phase. This is because the ground state wavefunctions should be real in this system.\n", "\n", "2. The new sign structure after optimization is quite different from the initial reference phase we show above.\n", "\n", "These results prove that neural quantum states can approximate the true ground state even if the initialization is far from the target state." ] } ], "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 }