{ "cells": [ { "cell_type": "markdown", "id": "dc99bd62", "metadata": {}, "source": [ "# Fermion mean field\n", "\n", "Mean-field states, including determinants and Pfaffians, are often the starting point in the study of fermionic systems. In this tutorial, we will introduce how to train these states in Quantax." ] }, { "cell_type": "markdown", "id": "5e27ec7b", "metadata": {}, "source": [ "## Hubbard model\n", "\n", "We utilize the 16x4 Hubbard model at 1/8 doping for illustration. As we will see, this system will exhibit stripe pattern, which is also observed in cuprates." ] }, { "cell_type": "code", "execution_count": null, "id": "12b4154a", "metadata": {}, "outputs": [], "source": [ "import jax\n", "import jax.numpy as jnp\n", "import matplotlib.pyplot as plt\n", "import equinox as eqx\n", "import quantax as qtx\n", "from quantax.operator import number_u, number_d, annihilate_u, annihilate_d\n", "\n", "lattice = qtx.sites.Grid(\n", " (16, 4), particle_type=qtx.PARTICLE_TYPE.spinful_fermion, Nparticles=56\n", ")\n", "N = lattice.Nsites" ] }, { "cell_type": "markdown", "id": "1a0382a0", "metadata": {}, "source": [ "## Determinant state\n", "\n", "The mean-field determinant state is defined as\n", "\n", "$$\n", "\\ket{\\psi_0} = \\prod_\\alpha \\left(\\sum_i U_{i\\alpha} c_i^\\dagger \\right) \\ket{0},\n", "$$\n", "where $U_{i\\alpha}$ denotes trainable mean-field orbitals, and $i$ iterates over both spatial and spinful degrees of freedom." ] }, { "cell_type": "code", "execution_count": 2, "id": "e11b37a6", "metadata": {}, "outputs": [], "source": [ "det_state = qtx.state.GeneralDetState()" ] }, { "cell_type": "markdown", "id": "55ed6311", "metadata": {}, "source": [ "The variational energy of mean-field states can be computed exactly, so we can train\n", "these states with exact gradient descent. Here we choose interaction $U=3$, weaker than the usual strongly-correlated regime around $U=8$, because the optimization of mean-field states are unstable under strong interactions." ] }, { "cell_type": "code", "execution_count": 3, "id": "e5e3647f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-67.80696117567832\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "H = qtx.operator.Hubbard(U=3)\n", "\n", "energy = qtx.utils.DataTracer()\n", "\n", "for i in range(1000):\n", " step = det_state.get_step(H)\n", " det_state.update(step * 0.1)\n", " energy.append(det_state.energy)\n", "\n", "print(energy[-1])\n", "energy.plot()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "a4166641", "metadata": {}, "source": [ "As the energy is computed exactly without stochastic error, one can also optimize it with BFGS to obtain better accuracy as shown below.\n", "\n", "To use BFGS, install `optimistix` by `pip install optimistix`." ] }, { "cell_type": "code", "execution_count": null, "id": "5f05e916", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-67.80696117575035\n" ] } ], "source": [ "import optimistix as optx\n", "\n", "params, static = eqx.partition(det_state.model, eqx.is_inexact_array)\n", "loss_fn = det_state.get_loss_fn(H)\n", "solver = optx.BFGS(1e-8, 1e-12)\n", "out = optx.minimise(loss_fn, solver, params, max_steps=10000)\n", "E = loss_fn(out.value)\n", "model = eqx.combine(out.value, static)\n", "det_state = qtx.state.GeneralDetState(model)\n", "print(E)" ] }, { "cell_type": "markdown", "id": "a789e151", "metadata": {}, "source": [ "One can also check how single-particle orbitals look like in the determinant state." ] }, { "cell_type": "code", "execution_count": 5, "id": "0740d54d", "metadata": {}, "outputs": [ { "data": { "image/png": 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XpccjMPiLVkoxKq5IkyNMDkLiVOD3CVh8UQKpsEKDdD48xSGE9YUd/LE6y5Fpz1cywyZShzghSI0jM36zzmkQvqgTO4eyBdZC34UMXUjPFd/bD/iEybeYA3NvJfz8PrbbGsC0Am0FSgmULPMtZSlfSkEQKILy98KCEA4lJbVQEwfeU0iNJTeOQEuasSaOfICQGgdSQ7sDgNtcxZkCNxyAcIhOBzE7i6vVMHmGSRKUUrjONC6qk21vMSgSnyiu1wkXmsh+gDkrKZIhstYkaDZQ8/Owk5Bc36CbZcSBpB1rQuWrhBbIjENGMbX5EGENNl/HXitwRYGqRcQLcygZwFZCup1iHNRqIbU4oBkqgkCP3pNOI6QRB2gpCLUcYdbkz7FNVg/HsVfl6Yz9pHFB0U34T2/wvsTETyFGUZ9w4yDNTaxSJfcnWQrjX93Ev917deUrcaL0IydCRSlGvmUZXvqwVgpGAWEVcr4xKHZl8Lib+rFnb5/d1gAGPrRQ0oNY4WA7s+jUorTi4EydQW4oELywNkAJiCLNI4enEQK2U8NnX9tEAJ1I8Z4jHXBwcTvl4lYyWlsIwVQScfDOB2geOc52e4lzXUeWdqmpaVqn3onIM653DrKxMiRXBYV1nFpsoSQ4pXl1O0ekEtM6jDkcIGpNlG0gN4ZsJwVhoFhoR3S042DN0NIOpODsuuKc1HRixUI9IJCCJJhmOHUHzlriaJbYCAprMRaUEGhpmDI9mm6IMgE2gVUp0VhqoqCGRSKR1hM8q1yTKJPunjDqSgAomQkTF6sQoCZuW7wnJQEtKjAUmJJ/URUIhFA4HXrgEAorhH9ilcsqEdQhS4Arva7qPM6fSAg98qhdWViYhEuB84UGZyeqkP6R6ohCBrigXjp9IZLxa61IstrmaFcghEDIACsUAkudnBCDJPmufpa/nb3lKuSeB/b9aUKAkgItJYWDzdSCsqhAc2iuQWosBfDstT5aCvY1Ix4/2iApLN+8ss2TF7eZijV/6Y5pHtjfZGUn43++ss5zq32k8F6KkoK7ZmL2nXqEVivg6nbBN1dSNtMuh5qznDy9j1AKLmwkfPNKH+sEdy40uW9/GyFgY5jz8mYOTqE6R5HtQz5ZbDVufYh1jihULOmYpSDnvlrGrC54fWj58nXLRi45NFVDLijqgWQnmGFruo7FMR3HTBnP5TLOoaQgtI599NjvNkhtxEoSsWYiGsqyHKTUlQE0zgoQZRVRqNKr8lVcKHNdu4CrpEsw9nt8ct2bFKAE5V48sbWqLkoBTvgcpSs9mcrDkjhcSdvwGOXzbkKM1QZMuSaAkLq8mMUYcMQ4eyacRdkc4QxWaAqhPGRPrqcCcjzjXiuJrnhoIzfTEdqM2CY4qTAojAgRIqdBhiBF3soq5B6A3dRuawCzFqxwZV7YjaqSZtRFIlDOc8Jy49DSuwdx4HMshbHsDHOC8oNdDySBEqS5ZXuYEyqJkroER8GAgB1CEmuweQ55QW4VfQIyoRhSUFiwznoeWNJHAHKQ45Ici6DQAU5FPmdjHLbwrTCBzQmsIRKG2OXEGIRx9BPBTirpaRiGFhlIMicpZODZ4gWIQQYOiixDm4LApqhkgEi7oAoSMnrOADlp0icnRYQRsh0glKYKxUZOiht7Kt/KRsl/3NiDEjd/RlVTnDxwVH0cmWNXGflGcxNRrIAS9nZVTd/whJLUOnnAJN/MiXFiW2BHu6zyglXx9MbXNHr8W+92z26R3dYA1ksLBlbS7WcM04JhWng6BZ4W0U8LksJSGEthPYClhSW3lqywdHsZ6xtDVGZI0xysxRSe6Lq5PmT/VMQDh5ocnI7pJwVfeGmNJLNMiT5H5RahKFhda/GV6zOkaOJYszxVI7AF7QtnyL9yFukKWiXDPwlqXJw6wrXmIhZf7TLO0U52OLb+GjPDDaY7NfThGWwrprsZcOFyzOWhpOiuUts4R8tl6LvuInjwAUQU8/LFbS5c3UG5gnunMu5qZ+h0SHHmDJcvXaZba/P8Ebi4qGl3N+m//g3m1q/QOHSAhQ+8m/rBZcY5rt3AJRh7LIIJxKnQypWhmil8yCfVqE1IlRwy7xHdWDCswlU5WqeiPAhrQJgRejghRwUEJUqImUyK2bI9iHE4SeVFyjLF4AwSi3USM6qe+hYinEM5gyo8qTkUGqmUf+UiIrdqHM7aHOcsmQxxWpPoW0ejEFIi3orixfdQLePttNsewIZG0Bt4AEsS43lhDjJj6aeGYW58+GEdofIAVhhHVlh6/ZzNzSGRsWSpb1uxhaXfS9naHHKgrrhvNubBQy2+enabPzizwcsrfd430+OxAxscqOU8sTXN19YyNmzIg0dneHyxRcNmhF99neL/fBpZpDQXW9TmGuzUOrx6QHNlvkXhBJnxe9m3c417zj7N4sY56vvmUfVTWDdDfyPk0tU6Z3sSd+YFmk99hnbSZfbHf5Sle+7GRTFnLm/zma9dILQZi3ckfPBoiuz1ufKNZ1n/+mtstOd4cbjIq9ksUyuXsE98kaUzzzH78Gnap+6icXD/yItCjHlYMJn3cuVDVXhVuSXOVwON55mhQ5wIEBUg4cBWHhi71h6Hk+Xj1tM3ECVbH+lzYaXJ6jgcruzP9MBmAYNz0rcEVS5T6V0JPMHWlb2exvnQVUsISiwUxiBMCgikFuiq51KE5C5EOEvgCpTNMU6Qy5BCKlJlvpsf529reyHkze22BjDP4BZIKcbNw5Muf/ll7DtGymOqh8pjpRSjhHB1vFK+v1JjUWkf3beE2ZCGhlasqWtBYHJUlhLZjJYqKISi6VJqWY/YZgTCEtRCVOEIQkWgIJKOOjlNl2CcIHMW4xxNMiJhCZRDS/+akAIh/T4CJQmjgLhZIw4K4lAQmRRTDGnIgk4EoRXUlENZ723oUKPrMUE9JgwDokARhZqwERO0Guh6jFBqlPx+IyG1SsW/0SYdMVd6J558OsrWj725Ku6rElWMK5Vucn0hRoAlcLiyiXsy6BuFmGLiPpxv5BbV4+XtXfudTPBXS4yzcBUHbQSmzgDCr+MYrVcFo54rh/cW9+xttdsawNq1kNAF7AwjwlBRrwdoJT3fR3r1AOt8Y7eSglB5CoVWgkBJ6o2QzlSNdiskjAOQmiAMmZ2pc2BfzozsUTz3NbZe2GGqPs+PnjjBzr37WNw6S7xyhmRjmyNNzUcPzZIqzXRxkZlXnyewhnhWEf/Qe71Ui+khzYBIBTzQ6nFYnvd+g3A4BfVml337a7Snlwhm5wlmZlGtKVo25HBWJxhK7l66m0furzHlUqLFGWrJeWwR8ANzipPvnEG5gjuVQ8sBIg6ZeeBOGsePMR21yPYfY256mtaC4o7ZDzK3fQ/xviXi/Ys4qccZMCdG0dmoKjjyeiYrfWMgQgagy6qhlCOvyjdHezCRmFEezJVEYyYAQAiB02WzvrMIOya1ViVMUfU2IkbVRe8B+mqj53mVIOm8zA7OlZw1NZL/CUrPUNrC88lwvkm78lBMjjAZwoG2XkLICYlTEZkKEM4Q5n1Ck1Fk3e/NB/sm5kPIt+KB7YWQ33fWjBRaBDTrAVJLapFGSe+JKSk8UDlJqCVR6cnEgUQL/1gt1jRbIfVGiC4Z7zrQdNoxC3MF7Z1NitdeoLd1nvad9/Ge0/cRHNhH/so1huf6ZBub7Gu0ObZokJEhubDK8OIZcI7GybtonHgAAHP9ImZ9hZpztOUQJ67gL87SU5AG5mIwc6jODLrdRjbaNAhZKmqoXHGsVefU7H6mtcVuXcNuXIWhZd/sPh45tt97H2td3DqIKKBzch+y2aEtY0y4jyndpiHqHD7ZYEZkuDDGNGewFWnUeZiSiJI6WvobNzRtj3ybKpsu9ejil4ycrJInRSl1Y8YFgpEihC0BzIFQnpAq8CFp4fXAhBt7csLZUf+lEMq/d670lqwtsc4yrpF678kJMELhhPS5LmG892VyRJF470pHnt4BCJMiyvNLa8BZrAzIZEghNMoZomKIzvpkae+7+Gn+9vaWeyHFXgj5fWfGOgqqymPZF1lKw1S3C+PbVqRwgE/mF875n8b3ShpjseV1ah2+LzIzFE4imm2UnEfokGJ9E1xAttUjC5vYpkE6jd7YRuo+bpigA9+g3HOaraH/1rN5hHN1lDXU84TYluqy5cVeOEnfRWSyRkzElHFEeU6RwTDR9FPLhiy4FBR0laGRWFrOM+CLbp8ivebxJCsgaPgEeT9DDjYZ6Drd1hTbcQNjU/rZFnHR868rbCGDeOxpucmKIYz0uKrNigma6g3Vv8pjqoKtMTmVifDwBr5WJWy4K7QUIw/tJvU/v9aEAoZPtu8Oe8fH+p+VNyYq+qkrqwpC4YQbNZCD883jpZyPkLu9PWkNovTIrAyw8i0IDH6nptRbaiVye83c33/WTQqGTtId5Ayzgn6SM8gMUWAYZAU7w5wkt2glRmFjK1C0I80gLdjpZmyVSfw8820heWFY3xxyeaVLo1UjeODdTHUcwyvXWfmfnyVd38EtL+JO3Q3H6qizZ9GfeRqZDGkfmqNzfB9FGPF02uJrL2RkThKLNqGo0SyG3Ld9hqP9K1TpawRsRh2enzrJtdosy8bwSDdhIRuwtR7y6vkG5weKC6Q8xZCaMDw+n/OhJUUDx+ozr3Dl+SsYpak/8iDxA/dCMsQ9+TXcCy+y3ZjiG3c9zvllmNpeo/fCl1lavUDzjqPs+ys/TOOOepnr8VVAyjCwUmf12lh41YlKUG+SM+FsqVgxBgyc71eUZXVwpKSK98ycE55IKyTIifDUlWGpUGUaTY7BTepRItqJcZOSrzyWoaozo0JA1QIlrCEovAqrwI1SnU4oXFT3yXokBb7aGSiJUuEICj22O7QtUHkPhyDXdVLdYFC8eYHBPfvu2G0NYIPMA9gwLRhmBUlmyIynSCSFZZj5KqSSPgcWKMkgMySFJcktgySn388YaElReB6QMY5eP2N9a0iv0UYdOULjSIek9xW2nvlv7Dz3EvJ970U//kHk8jLutVX45uvIrQ2C2gPMPXwXrtbg/PmIP75oSJyj1arTaIbM5jvMbBkWNzdQzvlEvYCNRsTLjTZn6/sZ2C53JVeYK/oMtiJWVg0Xu5oiGZINugQYWndp3rcYUBeCrXNXOP9/nsQEMZ2Dd9JuLIPdwZzfxHzxm2y0Z3lNHeEVuY/ZlWu0vvQs5tXnmNnsMfvex2k5HyZ5OkJJK5UaEGCNBzFcSUtwJT6N65PjEkBZHazudz50dGX4hpA4B7aUg0bIka4hjPPzrsyluYnV/a8TYDbhydmya0BWuTPn13AjmR+LtJlXax1RMAQEGqcjnJAYA4X1r01KNUoXuep4WyDTHGkSChGQ6gaFisiDb8Nb+y7bW61CvqXw8/vYbmsA8xggiEP/jS2koJcalCyQOBYbAZmR7CSG7WFBhsPqjMhtYXNL06V0GiHNAOzadQZnuti+YSEwnFxsMteKWO/nvLzSJ88VcnmZZmHI9i0xFBqTWVxQx87tQ0YNguYc0tbJi5iBCAhDjRCK+VbE/FRMPS0YbLQ5yzRxAHOtiHZNI/UMidN0+zl9nZKZAbnuEQ1TlosMYyW5GZLlfRSW2HRYdy1SAoYyJAgVUksy69hOCqSBaHaO8I7jxGGdRp7QvnKBaHudflzn2vwycmqePIh2h20wLs+WXCpXqaNWFcFd3NFJkugYykS1TqmAINwESbT01ASWSitoTLuolpoArlHlcWJ95305GHHvqwLyaCduFCaOdcLKs453UnqeFRyPzlo9d2JFJxRWBjihkDiUK0od/VtjewB2c7utAcxaRxgr5jsx1jm0VlzYGhL1Ug40Ne891EACf/r6Fi9f6EGWcXL1CrNqhVwGHK0dZXDoAM20j3nqK1z+X+cw03O89x2P88g9x9noZ3zt3BaffnaVY1HA+370L3M4sFxUdV4XETsbA0x7H+bxD0Oe8fpMhyibwhaKlUAwMyuJAsUjh9qc3t9i2GvxtZ2TfO56zGIz5EdOz3PgYItgy7HxYs75K1tM6XU2o8v01RbzfccPDyy93JGlKWkyxDlBkN7D0/lJlFbU41naMw2MUqwWhmvXekRacuKRx1h84B7C9S2OfPFp9Ge+RlZvcmn5CK+efAcnji1ysjPLovAKDqLsSXTSq0FQSigzuvgn8mEjYuoY7Cb7Jh0ghSr7ivCenCtASKTUOCF9FbDIfH7KGk+IBZyOsWEdDzC2VFWtwsWywmiLkvAqEMqDiq+aVsn7MmAt9fFdUAN8h0ZeblADgSlKjFMoURUiKjD1OT/KyqnVMU4G4ByBLQhMTmZvXS/knt3cbm8Ac45QCqJaMJKr2hhkKCE43FLcMR0RSsHzFwTdboYZDrDmKg37CjaMmTmywOJMjWhrgL1wju1nv0z96FGOv+sRpk7M8uylHf7om6s8fW4Tc8cMP/DOe5nb32L1Wp+d1ze53s8wtTb5sbvHuvJFKTkjHY2GoxVpjs01eHB/i+s7IU805vmaKDgS1Xj//kPEd86iLnXpP3+OzY0ttnWfYbhFqjZoZAWn8gRrDLnJSbKEAsX54jiv2iaFjTisG8w0QqyQJNax2kupNWocO3yE+kITce48s3/8efKXv8nm0kHO3/0QK3fcS3Nfk6TWHCXMXRXPjTTrS22tMiwUpQrrJCnVh3FyVKIf8aSgBB2FrzaWFUSpxz6NcwibI6wpybC5/5uW4asrw7/K69vlETnr9yMluNIzqUB1khNWeWDKa30Z4Ys3/qGCwOZlTkyWOCwoW9MnzunvtzLACo20BdpmSJsR2FunB+ZD2z0i6412WwNYGCiiQI4GdlTf/kr4ZGwVDkkl0aFCGoU2Gmk0ItCerKr88I8gVgT1AF3TSOVzMI1IccdCHWsNi52I1V6KuybY2NxhZrhGnGf0RcS2bvhSfRXtOEuU9YlNn0YhaG4OKPQ6InUcrFkeODLFbDMkcYLXNlM2UsvybJ13FHDSJHTyGtrGyNCgohBnLbpuUPUcg2RuOiYJUwrtaM+1scdPYqWkvrTAfCumVgtphZJYOUSomF5oYY7MEi/MkOxvM7XU5PBMnXpY5roE5VCNyav2RisrgIixh3PjEZUHBIypDGX4KdXYSxsdJUYhnj+718+vMmp+NxVo+d7Q0frVeqLkm0GZV1OjqqEH3MqT8ik8VQ4HkdWEIvByO9VpEBg3WQkt77Xl+DZrKEpFjFzcusvnrfLA3lIb0vex3dYA1ql5NdaRthT+c6eEoBbpUgQOgkhTb4ZYbYhNTGhquCAmroXUQ00UaxrTNRqLTaLZOiryH5TFdsRfeWCBfjLNSj/na5d32HxtgyPFGg9mZ2m7IZcaB3i1eQdDHZXqCQLtcg5tb3IoOUuY5TTP5CQv5ui4yfsP3c9Dp47TLxznthP++yvbtALFe04t8GMPKupbIfPnrlLrGv+B1V6M0TmBtd4zmZ2a4lhrm0IFbN17lM3jd2CkZmFmlvnODFEgOdjSTGmL6Wji+/ezHN5NMbufex8+THpgmVakmW9HPs8FZSszVH1/lY1+GyXRXZnw381Cr6CpYq2LCfByQvl5Hp4V5vNT+HFn3okLcNIPF7FSY8qKpFe/mCCs2mLkUVnlia8G6bXOEKhJ7X07nmg0zpEJP5yEUtW1DFul0KgSnK0T5M5r/EtZqpI5iyqGSJN5ER0RUoiQvsi/C5/iPXsrdlsDWBz4HFNlPgrwAx90OY7MV/ElQaCw1ntgygTYQKO18vQKLQliTdgICGoaUXlgoeLEQgPpLE9f6fHE2W1eXR/SklvMqDX2ywGZm2IlAAI/fksJCK1lUSUctRvoIiHd7JLt9JHtGQ7deS/RkSmu9gpe2kp4dSPl8FTEe47WuGu+jlvdptiq40yECEJkXPP8H6m8coQUiChGhgmFNNjmftbD/VjpxQvrgSKU0Aohlg4XSoLFFq1kDjc9g9vfwS15nbJIVV6Vf/d2+VRV3p7JkLAEsAlxw0kbeWAlr8y3BOFDvbIpu8qTUa3pPO/KE1nL5p6JiuTYtTYTKqxhSc1grEQiqvmP+ChwYvDI+MttPCSECT6YH8NXBo9OYKpX6soAusy7KZNhhcbImEwGZNw6HtheEv/mdlsDWG4csrDlB94hyn5HJcuZf+XFaSzkucFmBXmRUxQZ1gjStCDJDWSGpJeRbKfQynC5QeIw3S6D8+cw29sIG3FHvU271uHoYItw22CylIh1Zs1rNFQNqaTvo3QF9e517GCIcRY688jZQ6AiepfX6G18iaEMWdQd7llsMuNS7Ctn2HhpiBiso9auI4Z9hEoQYQJSsamarAQz5FIzrwv2BesgJdfCmNfDFk4qjugh00FKGCjs7CzDTgeTGLqXtxm+sko+q9ie3iRxO3RizZHpmHa8+yMgRl5USUYdVQTdBNfBt+hApShRPlN4T9FPFBp7YNXMyUnc8g3hCoTFliPTKnrELrGJ0m9ClFO9R15cFfB6CmolVOHKEzihPBGVyepixeYva6iqDKGdQxQJEoFEo0Qll+05bsJZnNQYFeGQaGHAZWS30Vi1PQD7PrQ0t9jMlInZcc+jkoK0cP6jLQRF7hgOcuwgI80TsryPDQ2DfsrOMCftZeysDWhc2sEEPaaSDOUsyeoK137/0/Rfehl91yk++CM/ijq4n/DCJrX1nGy7T2PzLMfMRQwSFWpUGCAFRPmAvBhiohry7hMEd5wm39xh7Q//D9tfeQa9b4m7PvrjPPDwQxTnztH/b/+Hsy+8QNSQtOc0YW3MOHcIvhEe5DPxAXZkjce5zA9yjhDLK6HlC0GEFNBQF7lbXSao1TF3P8p2Y4pkp+DKN6+w8ccvsrPY4xV3J2vrLY7P1vmxexZ2AZiAkjdVjHNXFUCVwz4c4IQuk+2UXxr+cIPCljCkqwZp5yjwk78rh0pQcr2E1yIzTpC7kuAqxUjt1eF19oVwSBUgS0KsFQpjfd5LYfFMMM/2r+71UriuDOvLyqTJESbx1UkV4YIYEIh8iEz6/v0O6sigDvgp4VW/plEhRsXgDFGREtsUa4ff88/4nn17u60BzDiHLFuCqqZtW14IxkHVdmKdH7Hm/xlsbjDCUBSGvLDIwpInBcUwp0gKXFFO5UkSkstX6Z95nc7sHPtCR2MmJlsLSJzD5AVBNqSZZOAcKgxQceibk51va3I6RtTbyPllnA1JN7v0XnqVeprRKVLm2yE9ZemtrNB75TXMTI1YzyCIS6fHVzc3ooKzRrMpQ446S2J6IAq6us/10Mtlp3IDLVcIsiZZOiS3kOaO3uaQ7ZUdNtnhylqfq9NDmqEiKcbcqypSqyp5AgtO4vCqEKJMegtKEckyAT/ihAm/113qFq7ygqu+SJ+rGolMVADtxKh3clLyq5LA8RucILK6ar3dwW/pN44rlv7FUOniYxjrh2nKHs4yz2Vz/5seTzuS5c79mrKsQlaeWYHe44G97XZbA5jEN22DV52ovK/qH/gPt1LCkz2NJtAhQVhDBhFhHPhKZqiodWLqcw3imToyCrBCoqamaD/8IMHsDNHCLMXV8wyGG/R3dths7acIZqj1N2nurKJMjopCdC3CSsmmarOlmhRhnSyrkV3eQfZyGsfvYOGHPkjYaSCSLYbfeJJiY5vmncdQnTahLmjUBmhV+MqRVFghmY9mOdaYYls2mFUHcVJjKThYtHhvkaCE41hQox7sQ9XqqHpMIA2qJlg4PE18epnphf2oO+Y4fGSaQ1MxrUhX6SoYQQ9+ys9I3JAJb0yVIZ5AYkeM+lE45yyqkqkpQaTy0IAJD8x7bqKsfErhPTYHvsVoHAuOqoEWMZqRCVAp4Us3gj4fzo4IsSW4Od80PtIS06EHWqFHEtW+eqnHxxdpuborW5XwOTCXg3MUKJARmbyFIeRbbOYWe83c339WKU5UYCVL4NJCEJQVJBAo5UeuWQIiUSMSLWwQEjdiaqGiVgtoLTToDKYI97VQ9RCLJFhcYv4v/zA2ScmvnCN55k8ZrK+ysXCUi8cfJqm32b/+Gq2Vgijvo+KQoB6Tq5CN+lFeqh1liObaULHx0hodLfjgQw9z1wcfge4myYtPs/O/n0TNLDDz+GOoxYOIravI808jdq77JH4U45TmUO0gDzUX6ekGy9ECpn4PBsM9m5c5vXkJ5QztRotWbRYRxtipJk4VmKakcXofWf1uipkl7nrwENnyEjWtmK0H+A6aCghK96cir1ozUoxwUpVcIt9fKGxRhnN+zJpfo6QaABURVgiJlmNPajKlVt2QzhJiJh4oG79FWQoo82gVgGkJVXelKCuiQkikMyV/DEZDdK1Bmgycn9LtdA0nJcaVdAnnAIVUEaJUzpD5wHtcOsaqEKxB5X2ESTFCk6oahdQk8hYKGr7FZu63NFPy+9huawCrRApHnS8+3Vt+y/sPL2VSWSmJ0BIllGeJa+VHi0kItCCIQ4JmDV0LPW3BGNAaNTeHRGB6G5hhn2L9OllrH8OwybAxSza4hg0jHBmEISKKQIWkcZNufZq+VWwOB6x1E2xdY9pzRIfb2OuK5LkUs7aCiGvo6Q7h4YO4msVttCDvIoMQXa+DCqjFMVONgFBravUQ0YwBQytfZ3qQe9nkWgPZaEIQIrTGYRFaUGvXCBbauOk2zakarh0jBQTVyJ/JiuKI0Fn9HFMRRvkwISZEA92uJcaTrMVoncklR1yziaWrTB9UIeh4tYqZ5lzVPORtPJl7XFhg9HgVTDrGfZ7WUzmk9Ox83ITQhvALOlkqwxqvUuF8JVSU74O0BisEVgmMUJgJTf09e3vstgYwayyhkszUA0Il2RhkXNlOyAvD/nyTtJ8ghCXeDphvBNggJNzOSXe2kUHAfHMDJTYIajmLx4/QWGojdEC+cpl8Y4Nu2OBCYx87YZNOX7N8x2ka+w+RzRxgdqZDEof0e9M8Ex5EuiFzzToLMw2sDLheTHG9n2NMxlK2xh12gygPSbcl31jVhNsZU0FEfaZN1qhzeWBIrw/IdwSJnccozVwgOBJBXUOj6LO4+jIpms78PNP1fQQCdG+L9NoaEksYNgln6hQqZC2XbO9YZKYJ2wfQB2JUo01cbxGU6aTR5TeZyBoHkgDeo7mRM1GBAiCkHIWICImlmoIudh8/kqEWY0SaaP0Zs4CBckDtOJ9Wendl+5B0E90CUiFcBZiV1ljJP3POs5qrBJ9UVIqryrpRgr5SzfBgVXqAYnIqksCq0OdXhUQLrz2Wilutib9HZL3RbmsAy50j1n7kWCvSvLBiWd1O2O6nHLp+iYF4HSUK6o072N++C1tI4vWMwco6Uag5MH+NO2QHUauhD96Fas6SX19h+3NPkLz6IhfqSzyx7zHONpe5Zy7mx+9/D0udEGEVxgYkFl7pzvNMaBlScGenxemlDlIKrqwmXN0cEhYJ9xVXeMReIM1rPLce80JaYypLeTiMmVuaYVhv8FovZ+VKl2ECm+YAqVrgVJgyX+/RDHLa169z6OKLmKygLu6isVhDKs1we53hxcs+pzSzTBg3yWXI5YHmbGoIZMTc9Ana8yeIA0XcqBNVszTK93HM87oBqETFExt7U54GZsEW3uOVXlMLKD0btevp3nWarGqWj4+0xqoU/4TXVYHTmFKGcoVXlRASZFiu4z2nqnG7mic5wZvw/1fB6Jyiypk5gyqVNsaj5NwIsIWQY/gUAqNjrIx8hRWDdAUZe0n8t9tuawArFWmIlKQW+G/GvLCkuSG3KdZ2cSJHRimhFFgtEdZhswKHJbQZTTJQEa5eh840Ra+LTRPyjXWyPGbQSegFBQMrSKMGeb2OzQr0MCMsLM4JBqpGXxt6qk5P1lBCkJONmpTrNmPKDRlaENmQwTAhMjm5UJjQ58wGBXSzgkEOWzYgQdITYFUKyssBqiJD5CkqG6KyxOc18hSb5SAlhXGkTpE6xdD6kWuBEl6xItAI7cMwafKyUXsstexN3ORdvhHYJkmsVUvRZPVxN49rlEzfFR7eBCy//V+aSX7aLk4Z3BDy3rB3MToKKOftOTfR9lQCKxNrlB7dRD2VykOjDEv35nJ/f9htDWDjoR6+fagKW3x+w+KMwQqDLWkWxjiKzJAPc5RRmDTHFRmiyD03SAichXyQk26nNOuOx/bXOXVgCpzg6dc3eOa1DaYH6+zfukiUJ0w15jnZOcBQ1XHW8fVzm0gsHdvlfY0esUk4sDOAYY7CspyfQ6otpJKshzV26ifp6garJqSbFPSTgs1uyjAz9JTB6BARa3baS5xbrJGmBTMDw/xTT6OtwXXXCGohuQp4PVFcu2oolGGgHFIJcmO5sDnAGMeszGhG27T0EGotxOwBRK1ZvpsTifZd6a0JoCnDPCclwmnv9ZQM+zEQjJ2tse1WYmUkgHgj6HlPyvPNRImV42NGYaMTZfHBrz1ed1yBFHYMTiO6xITX5ypGf7VGhV/WMEnZ8EoaDmU9c985yLygDgN768KyPQ/s5nZbA1hVolclgVWOcivgrB+RZoXFGjuWmM4M+aBAFxab5rg8gyLH2ZLXbRx5vyDZTmktWt673KR+aoZnLnb5ra+u8tq1Aae3X+OHVp9kId9m+sHHOfWBI6StNt88v8VXX19HFAU/utjnBxf71GyG7fdxaYoyloN5l6XCsRVP8+z+d3CxecQPzTWSPM/pDnPWd1IGSUG3JrEqQsSC7U6HVzlCL3Xsf+0peP4rxNmA+kKb+kKHPKhxZqj48qUCGUgOzDoW2pAax7n1Add2Ug6KLsf06+wX64iZfVBvI+I6FV9u5BndkKB/4xsvx2HZROjpSt7XpJ818cfavWZZpRzHshOenTMlxUKyS62r4vVRVSRF+SXmnz9i/5fUCZz1ObKJPs7K87JCYaXeBaw+dFTIss/TK2b4dZTJUbagQJGJmBRN3906UJDSk3zf/AJ/Mf3F2xvAJv47vi7EOGqYSIe4MnSoQgjnqiHykxdWFaL4C0FaS2xS6mZIZDKEs14Qz1mkzVEmIzQZ1qQo40esaWvAFUQ2o14kxDZj4CCREbgC6RJikxG6HCcVmYqx1vrw0BivUeUmc0LeCqEYyoiBcmQiwJYXdyEDUh2T6phcBljh1RjcRELev+zyf5XczC6gmnwfKrsRvG4I3G44/A2Xx4gVe6N9qzBVTLh+4/O/EQQn8nETR4rxU3bfd8N6k+d0N6zln1Oew1WBsZt4xp59v9ltDWCqTNjm1pEaT6wMtCQKFaHUaKE9m1r5srkFhBTIQKFChYwiRK2OiGo+9VFknmEdSoJ6AEmX7tNfJbt0jmY8y4cOH+PhOxbYtw1HVwY00x2Gsab38lcoVMgDUZvlw9PgBEe21+m/eI6+EFxrLrK+eAhtMpa2LzLdu0ZUj2jVQ6brAVHaY6Z7ntpgixVXh9o81+MardigbIZLHcMBrHUl27lkceEgtfd/mNgVrFrJqhUYFdCYWeZ903NYKSkcFM4RKMHhmTrLnZg5WWcqCpF6CLU21NpjL6iyEYfK/6yUUt1o2s+3zl9N4opg/GUxAsuKeT8qCIxB0Y0oCROKFsLzvcCHQBUo+6bscYaqwkopRCkpXVYxhSsJs5WfJXDKa4e5avybc2WHwPg1GZTv58SVfesCK0Oc9LpiIX5mqJW3sgopRr2db/b5fxHttgaw6o9SGEdmPEAFWhIHikAoFL4vkVJdwgEogdQSGXgAk3EDEcVevM9kCFegA+EBLO3R/+ZTDJSicfdp3v+XTxEcOkCwo4lWDCLp0j93Afni09gsY//dp2ideAAhJd2nNuieeY1Ehly85ygXFu6jbhIaLmXe7hDWIpq1kKl6SMfmnEwvMtu9yOvhEteaM9gwohknSJNjs4JkCBtdxabRJAeXqR2/h1hJ1q90+fqVHYQQPLQ0zf3LHXILZzYGXNpJ0Uqy0IxohYqGhnZ9HhH6PJYX+pO7VSdGntkN9AbcDR7STf8i5X/fuEaVxHdVf6VzI0/TMQ4nywARqAYSj/7YowpmJfgzcqrLbXkZr7J1SVYcMofCTgCoxsnx83w6rqqE4j3bMtxUE6RcKzVGeBpGVA4PKW4lgN1ITXkTz/+LaLc1gLnRGLUyJCz/Td4ehYuO0c+bmxh5CH5x/4EXYYwIA5RSBEmfoLeNTRK6aJyIKFSA0hJpBKErCJKB5+wgsFEDo0Jy7eVXlDP0VcyOqpOIEFHk1NIucdonzBKCPEXJDGcMxpQKr+WGAwxNUgpnkK5O3ykyFEOp/R4AkWeo7rbXx8rKXKDzvaJpIQgBW1iv7Ce1H0pbIsEoic4YeG4mWvitrcwxTf59uBEUb3L/TYK93V7exOO7YsXdod+329XoKCdKmf4q11cGkqMuhPK40pMbryB2/bYr1Nyzt9VuawDrZQXDchJRbh1pYUlSwzApSIucPEspRE4eFWSFwRYOYyxu178CbKmdrkKc0BSZIx8UhEtzNB57J9HyMmYwZOdrX8MkX+RafYpXp/YxCBocU4vcc8JSNyk2L9h65utYBP3GHMPH/hKJikhqC6QGMqN5Tu/ntVpMTMH86iWOrJwlzPqozSukSY9+0Gct77MaNNjCYGYlUsEBPeQDep0Bjv7OkD99TWBkQGodzSggLFLcy8+xvXGeIghJl+/CzR9mmAuud/skmWFRpXTidaZ0HxrT2KXj0JgqvSFTXrRl03aFEbsoCpOhX2lluAbsojmU8699f+QkE96VQeEElUFUOTm/ClaUAOHceE/VecUNQ0jcRK5v5Ee5MhFfBZ1VgtRVOOYri6Vn5sUNS1KrVIhSaVXgRq9NlURaP4bNe4wpt7IK+daS+G4vhPz+s2FaMMwNufFa57mxJLkhzQxZXmCyHENGUS/IC4s1nkphrfNVR2vAVJOdJajAN/kWjiIpCGstavc9RPP0ffSeeYbNz32Bwauv8tryKT5/ao7N9hQfmJ7jvkMhTZGx89IZui++ROEE6WN/ifT042Q6IttIyLYTciu5qucZxtPMpxu8f+1r7N85C8Zgs4zcWIbBgK1iyLoe0q0JLycjFYsqYUZfI7M5X+zB57dr9EXE0lTM/qkasXNw/lV6T/8Jpt4kf3cLZg+RFpaLm0NWthN2ZJfT4VmcXsfNLOOm9uHqUyN5ZVHxpEZemByLCt40yT8REpaeDCWr3Uvr+NYuWVUF8R6Qq7yo0vMZeTSighzp+WpiLPs8kvNx1fkm9zQJYpQzIsehaHWUpeyvdD7nJauBt6ZAWK+uKgn8xV5VgspwVzr/RWeExBBSoMhvYRVSiLeYA9sLIb//TAiBEoJQCWIFQaVc4By2MBRJRkFOjGOmpnFO0JruEC0uobXAGEGyvoUdGPphj0QkmKGlaHWI9u+H6Vk2nabbMxRW49pThAsL1GenmWnXUM0QqXOu50E5sq2BmJpFOcFQx2wmjlQUmO4O9a1tCgQqqFFrRHREQGAtLkkRUqEaLYTS1PU0C3GdgQ6pR46N1BIpR2gCalEDqQqivqM13EIR0GrN0NQNolARCHyjdZERJl3q/Q2wkmlhMTXBlFCosEahWoigVoa6Y0KmKyuBolSi+LbgVSXanfNM/F0h14Tz5ijzV3Yiy19p2Ffqq+OQrjrVCOOqVUe5NErm/+5gbtfZq5O7MaiNt25H3t14t7tD3JsRY8cVS5+nk44R3eJW2F4S/+Z2WwOYVoJmKNlXl8w3FJcigbSWIjck20O6q5sokbFvv2H2cBsRxUzte5TOA8dgMGD48ots/a8n6cUtnj0mOL/omFEFj973GEceOM2qi/j8puTKVy9xUIY8/N4fZElk1GsdFjoLJCri2tomf3g5x+Sa+9p38dAH70QKybODBl9+ZR2bZRy+/CLHV19FNxvUH36U+ORdqPWU+tmCwbUdwvl52nc9QLR8gDtkjR/Xs+yImO1+wp9c3yHJck7OzPHw/gM0Ncy/cpbHrjxFUVhaUw/SnlpCFjV0I0AFEuly5ldeZkb0cPUmJ5ePYZYXiWRAR7foKYeOa9Siuqd9CEbDNMTkxXxTln4JJOWgWJ+Cn/BEyou8cmKElAgReDJpydvz+lzCCxpWubaR/PM4PHTIMrnv/EzdkTcmxkA32TA+kYPz8yzH7UDgny9MzggpJ9uOqlFqiJHqxgjYhMBUw3atJTAZgbVk5i++oOGnPvUp/uk//aesrKxw//338y//5b/k0Ucfvemx//pf/2v+w3/4Dzz33HMAPPTQQ/zjf/yPv+Xx3w27rQFMSUFNC6ZjyVwsaWpfMreFI+9nDNd71MiYxbKwUEe1WiCmceIu8vV1tp97hfWvv8Ja2OKp/jLf2Jjh6EKT+951J9PHp1lZ6fHcVy7xzSvrPHSww8OP3c/0fJNpLEeswVjHHw1zvrq1w9ZA0lya5/HTiwRKsv71a3zzzDVkr8u+C2dYuvwUjblZFh89xfT+JpnY4bq17GwPkDOK4OBx6vfcQx3BvrKS9sVzO/yv1/uc3yxI621OTO0nqis6r1/grvUzuCwlzA8RNjTOCJI4IFESYQuaW5cJig30zCztowvU9h0gkyHbqs1QRkQSatohMVBW3kZUCbE7Gb/LXOUNleFZKSDpb/hmau8AlWAgAKcYjWdjIt1fAYid5L75HJeX6qkEo0tgtaW44kTYuTuInACwcmCIY5xrw7rxsA+pyt7Nco2Ki1H1awpGr9Hn9DzvToqCoOzLDG/hXEgpxIg68mbMvYnn/s7v/A4f//jH+Y3f+A0ee+wxfu3Xfo2PfOQjvPzyyywsLLzh+M9+9rP8jb/xN3jXu95FHMf86q/+Kh/+8Id5/vnnWV5eftN7/3Z2WwOYFONa0FhRfRz1iDIEqojYo2hoVJKuqpT+81tVL31i2Q8N2dcO2RlGtGPFWi9HywG1fEg73UGanLhvONAO6dQClJJc2s68PpkQHJqO0bFhLp+noQ8RNRuQJmQXL5BvbSIbDaJDR7BzS6wWmmubGbVQMVUPibQnpBrr9f27qeHKTkqaK+oipDm/gMxTpLPY1cs4axFKofcf9NLJMgf8xWqFwpRTpRWG0OZoAQK5az7Hzfq5d6tElHkqcSN0VD/fYpgyigyrpL4sE+7jc/vDxuf5lpVSdyPFweezPLB5r2rMDhPlbEux+7kjoPZho3AleAqFk3pi4vf33t6OEPKf//N/zt/+23+bn/3ZnwXgN37jN/iDP/gD/t2/+3f8wi/8whuO/4//8T/uuv1v/s2/4b/8l//CE088wU//9E+/uY3/GXZbA1igvFien+5cqghIPwdSaYkMJQrpqzeTbSbCqylI4RBKIpX/cIzCEVsgioyFGvzQySnedajJtV7On766xtag4OjORR5efY5O1mPx2N189N5HyWotLm4O+N3n1rDWcXQm5qfesUQsDPODDjPJaVwyJDl/lmv/5XeQjSbR0TuoP/xOVnLFn3ZDLjy9xtHZOh84OcdyJ6RA+/anwnJurc8fvXiNRih5RzTNe971ARouo3/1Gv3P/HecUAQHDhP9yE9COsSdeQZ38QwWSaJqFEEH4Qy1YkjDbCN0gFINEHrkNTnGnpNjLBborZKqwf9U/qMzIsKKiX832g1s928LdH7M0MQXzMRzJs81ApsyBBUT4acrh+m6sjhThq9VGOs7E6qKJSipqaZRAgiTMc6xlcc4N/IhnQ4xRJjg1vHAvlu2s7Oz63YURURR9Ibjsizjqaee4hOf+MToPiklH/rQh/jSl7705zrXYDAgz3NmZmbe2qa/jd3WACbL/kcfIpTSLJW3pTyQSSHLb5+xcgIT+RR//KQoYglytqAdCu5ZrOOAJy/s8IfPrfHyap/B2kUOnfs6Mt1iujPFHUt17PQ013oZX7/cozCWY7M1Hj7Yoh4qYBaAfO0a/Reepfv1pwn3LVN/6DEa73gUc73PK09e4uuXthlayYNHYElqP63HgjWO9X5Gb8USacnysTrBsQXqIie5cpXi5WdxKiA8epzwngcg6ZOvX8RcPOPnHMqQQtUIbErNbhObPk7EWBuVuaKbwYoYVfS81yEnvDCJG/tt3yJX9sbbfy5W2Yhd6kPZkVM2zs5PnHPM2sftBjb/pWZL3pcaPceVXp3vp/SfBSkUTtqJXsobZ15WnwuvTGtl5CW99Rsv/O+Vfbc8sIMHD+66/5d+6Zf4h//wH77h+LW1NYwxLC4u7rp/cXGRl1566c91zr//9/8++/fv50Mf+tCb2/Sfw25rAHPOs+9dxdIuJYyFFKNK02jQRBU+TBA0fcpGIkoPTErhfy89CTtMyNbXsIMBYU9wtC0JdJujjQWmwxM0sh1ULSa9cA67tka777hzroZxjs5wm+HLG+RasR236UZN6OUE7XniE3dhp+e4akKK1R5r/Yy5RsippRaHZ2o0AlkNDxs18U7HiuWZiHooibTk7E5B3RUEYYvwwCGcVGyrGlc3hshkSCs1NIQo9eYLlM2QznjumKohZDCheVW+n3wb3+hGVv7oCdX9Yvz7aJE3xqS7w7/xb15+2pXMhzH9QZbA5UUL5U0dvPFmKgAqPxOy8trKx934/J5qMU4XeA+TifD1xpcvRiBaNXj7gsCtsbfazF3xwC5evEi73R7dfzPv67thv/Irv8Jv//Zv89nPfpY4jr8n54DbHMCMdVgnsDLw2uU6QGofPvpIompgFiXzXO2aKi2VRIUSFSp09U977XEnFdnGBpuf/WOS82dpHDjGjzz0fsz8PprZLLPDYwRFSnL+HJuf+SNMmnH4nnfwUw88DlKivvYlrv/RlxhawdPLp3lh4U5aseIDR+/n/gcfYD0TfHlT8tLXLjPbCHhguc2H756nGUoWGwrtDFpYP6RXS07MRfzwnW2m65rXNjP+8PUh1hgebR/ksQ/OYBE8m7T56ktrxGmPRzYT7pZ+RmbsEiLTxSBJdZ2ebhEIqEsx+gBUGPStQWycuJ9sDxpFXmKikOff3fHvI27ZhGTPKDD0+SiULvdg/BRuvNdQqV4LOR6M+y1RzJkqDi6ngVc5Lr9nhxh9oUlnkc6UTqUAGXqvcsRZm3zlgkJIr/1vDbpIUc6g8/63+GR+/1q73d4FYN/K5ubmUEqxurq66/7V1VWWlpa+7XP/2T/7Z/zKr/wKn/nMZzh9+vRb2u+fZbc1gFnnSnKiLPMbclfP2O4+ufLbuMxa+5tlmCkFUlUeWCW9IjFJQnLhPP0XX6AZxRzoKGoH2+BaYBfAFOTXVknPvU6xvc3M4cPMLdQQSrMy2OLaCy+wVUjODWf5RraP2ekmD584SHzXAmwnXFm7zPNXNzmx0ODDd0ac3t8aha9Y6xvRy2/emZrmrrmIubrmcrfg1a2ctLCcmGoTHZ7HOth6PeXVywPq2YCTqac5CAHaFYQ2I5cBfVEnlRFOWGI/sXH0fo7aBf9MmwCvEe2iyra7sWe2G8FGPydaq8dLViGqHfPFBDeKI95YONi9p7GHWP2tb0jKU+lL+H3K6pbQZRIfr9PzBrULgcVr4CvhQ0xhsjJXdmtMTKQg3+zzvxMLw5CHHnqIJ554gp/4iZ8AwFrLE088wcc+9rFv+bx/8k/+Cf/oH/0j/uiP/oiHH374zW/4z2m3N4DZCsSY6H/0oaWzzrcKOeuZ94yjm0mpGZhwEGAihHCoep34jpO4MELPzZNcOE++vU0vbLBWmyKTmlg2qd11L/GwjwhC+i88D8KDTuuB+1Fo7th3lHx+hiiO6KaGpy9s0c8KZmLJw8t1lrRBnXuV7asG3WwS7ltCNhqYCYlk091meHaDJIJW0uCu2SYJCqscz214RrmWcHpWEaeK+VQiBz6BXciQVEYYIdEuJzaWoApJxPgcY57phHfEGHDG3wZu9+/VuzjKXYld7/dY/dSfZCJTNTp+bBMbmYxAJ6gbk0z8iZXLNasw1s+1HLuIHlNlOb5NWOPzZLt8TjEOP8tzVrVKWXYpCBxI7dUu1K0cq3brm7k//vGP8zM/8zM8/PDDPProo/zar/0a/X5/VJX86Z/+aZaXl/nkJz8JwK/+6q/yi7/4i/zWb/0WR44cYWVlBYBms0mz2fyW53krdlsDWGEshXFlKAnG+W8Ja8pBtpnFYLBlY3RVEJdlPszdAGIV+FUXSzA7R/sDP0gjSUkvXmD7ya+QXb/Ga7NH+fLBh9iuT/HQzDw/+JEfY0oaes8/x/of/HecMTTvvZ99f/2vYaOYmajNI1GT7aTgyfNbfP61dWZqincfavCRozO4q1cwf/JZrpx7ndrJO5n6kR8hrLcpJoZLZCuX2bn4EpFIWTrxDj5877tJwzpnVrf57+d2UFgemJV89FhAkASEiUbvKJzWJLpGqlooVxAXfRo2Q+gQoRs4GcJkLmykElG+K2V3w/hdYhcPbPINFKIK2RlpSviWHd8G5GVw5ERCftIbG5/PjWYYVgjmxiPehBi1+jjKeZF4eoPCjFe15Q4mLlzfl1m2Dznj16xCY6dLGR5VFjbwHLkS5PwE8HK9IPaef3j7VSG/E/upn/oprl+/zi/+4i+ysrLCAw88wKc//elRYv/ChQvIiWEhv/7rv06WZfy1v/bXdq3zrQoF3w37rgPYJz/5Sf7rf/2vvPTSS9RqNd71rnfxq7/6q9x5552jY5Ik4e/9vb/Hb//2b5OmKR/5yEf4V//qX72h4vFn2ViJggk1igqEGN+248dgFACNvngrPuXoW7zig0URwdIySkjy7R2ytesMX3+VjX7I+egE662II7NzqAP7iULov/wS6cULuDyndfp+4qNHkfU6dQSLCFa7GZ87s85r13pkUyGtoMGJmYj+uuHytSv0XjkD9QaNQYKqAFf4VI4dDEg3VkjdgNrBE0y1AtJazCvX+5zvWjSGh+YkR1sCHQh6kWQofWhthC5Z7z7vE9gMbDlKo+LKjd7ViST2RES26+HR45Mh4O4E2siPLf/jA7fKs/t2NukKjhcbV5B3J9krH+mNfLCJ11ABZgXOFZ3GluRZUVI3KJv68QWFSQrcpDdapSucunXf/1LyFpP4b+55H/vYx75lyPjZz3521+1z5869uZO8Bfuu/wX+5E/+hJ/7uZ/jkUceoSgK/sE/+Ad8+MMf5oUXXqDRaADwd//u3+UP/uAP+M//+T/T6XT42Mc+xk/+5E/yxS9+8Ts6l3VAliC711BGIvtDKBPAKg6ozTSoOY3KtzFnX6CoNbhKkxUaiEGPTlindccBRNTi3uMLNJZmqIeKK9sZnz2z6XMfpexwoy+ZPXmKqYUFDjfmeHQ6YCfMaZk+z5zfIJbQLhRTh/cjjOEqIS+d3UIFPfbZHeZND5nkHN3c5DHTY26oaV1eJ8lizMoqUU3QOjCNUgXJ88+SrV6jXijeUQs4tgSdqMVZd5QrJmXZBhy+dg4dxogdgzUGi8P0timuJ1hT0Is77CyfQuiAYPUaqvdl8jCk1+lAHBNFik4EUQkItorm3O6Qz40Hi42AiPKeSe7XZK8gJaBILNWYMrsLmLyNVpoEper3MhnvD6iqlBNVgt0VAyqtsYqYW+1UMFFtHIWx3qcySpbgKMrQUmCsxZR70QiUGDPERjnCCgTtXi/k223fdQD79Kc/vev2v//3/56FhQWeeuop3ve+97G9vc2//bf/lt/6rd/iB37gBwD4zd/8Te6++26+/OUv8853vvPPfS5jLW7YRV3fQQcZalNDHoKDsBXTOjhD2w0JhtfIn/4sQxXxpDjC58UhYmH4oUab9zx2ioVak/mjx0gWD7CynfLEi9d46cpOeVH6j/59swE/8fgHWepoZpI+J7ob5EXCU1uW//mNhH4B7480P/zAXWhh+eow5jNPraBtwQ9kr/B4dg7pDA8auNuC7kLrRUHvFcAaGh1Bo7VM0s3Z+uPPkPULpk4c4Uff+whqboZvXJ/nT/QU3dTyrmKHQ689QygdcriEyRdBOIq1FfLeCgQhG53jXFt6B7q3Rfu5r1C/eIbhzCIr97+f7v5jzBnNqRrEgS1ziF61VjqHKkMrrxs/Hoixq3m5Ai5RTeyGXbkmoAra3QTLfTx4hYrxgKxCupFNuHIjz05OhJaMAMxVmq0VFUJ6z6lwoly7nLZdAWTJBTNCUOBfs7YF0uXgvHR3aq3POSm5K7dvBeWADzPRV3lrbE+N4ub2PfeBt7e3AUZs3Keeeoo8z3eR2+666y4OHTrEl770pZsCWJqmpGk6ul2xiT1/tUCkA6RNEHmMcIFPomuJroUErkCYFLe9RkHIlpzmkhjSCCCZDwinWwT1JvF0HTdVIy0cvdRwYTMFwWjS93Inwk7PoRcbhDvXaJtNbJrznIW1Lmyl0JsXyE4LKRy9RHNlJyMoUnaSbfL0GqGwdKKAGa1whcMmhsJYZKDQjToyjBD9LYr1NbK1Ls35JktBTtyA1wYRO7UG68LRo48Z7BAIA0UHVVbUyMtRcmGNfCYiac0S5IZiOMSurVCgGQwzdgpFzXjZ6clQayRzM2EViI8F/sbJeDfphU0+VYwJplXQ+MZxa7sDwRvv2fV7lQq76UU4mYRn9PsEbXnXceMvJYmtYE2YakoIlfS4nHjt1bNdFcqWoahwu9+rPbv19j0FMGstf+fv/B3e/e53c++99wKwsrJCGIZMTU3tOnZxcXFUtbjRPvnJT/LLv/zLb7g/UBIlK/dYIKREa4kOJFpotAxQLvQ5LevjIyUFgVYEgUBFETKuI0I/JNbiUAKCQBHGmqlYccdsjZm6phUHvHS9z4XthLntqxy+9hpx1mOead4/u8iAgE4U8c1i2l/c7Rana22UKQiGx7k0rBG7jAW7zZTt46zF5gXOGNKwwfXpZZK4jTCr6MUBDS2Ip2tI5a/e+WbIQwdb7BSSxrDghUGBcoaoNc97ak0Cm3Ngw1Js9TGhI09zjHXoICDev0jbHSeeWoSlKeamI9qhoBYoSoge5doE5bxIHAiJLOkQ4zYdMRo8W3JRJhLx4/ByDB4TYZ6r7hsXA3ZVD0c2rkK6ibrxbppEFeA6BKbc13hErnLGe5Qw2mPVPuSoRISEh7AqJwZo4YikJ7cqHH74th/wUgGWB35FdgsFDd+OZu7bwb6nAPZzP/dzPPfcc3zhC194S+t84hOf4OMf//jo9s7ODgcPHiTQEq1K91hKlJIEoSJyklAHBDZGO4dNM4o0xzmLkoIoUoShQtdqyDrIqIZVfgCIkhBGirgWcGA25ofvmeOu+RovXx/y6Vc2uLiVcu/OOT60+hwL2Rb7jxzj8KkWpt7kG70aX+zVyFAsz7R490wLAfT6U7zav4N60aex8yILg4tgTTmX0tCrzXF+4W5Wm/uZ0ec4trNBp+mozzeRgUQ4x8FOzA8szZGIkFdXYr5yqYExhgcXa/yVfXWiPME+aynOdUlDQ5Z4gcQwDGkcPcTsUohrTDF3cBYzVUMJCKX3OKrxdKNqhtOM64P438sQzQugqjGITViVTHeAFXIEYGL0eNm+41fyADFKzFdWeT2T2hLjFSpnrLpPlaGnhzHtK5LOopzxcFX1QuJnSeZulAmbKN6MASwQFqXKPVZ9mc6hbD4SNCxESCE06a0s4r/FHNjeWLXv0D72sY/x+7//+3zuc5/jwIEDo/uXlpbIsoytra1dXti3Y/h+q4bTscJE+T1ecmWqfIFAIGzlOYxLSlXvo5Dlh1uqXddixXkNFEwFjvnQcUn6id/d1A+fzdKcIs+JTc60zHEqJ5QxA0JSNFIpOuXoxH4YMTAackkW1inyEGEMxggshlxHDII6vaBBPaxBEPipSVqOLv9QOjoaYglaa/qyRuEMSmmmtSVyhq6AvhMUVmCqZLYQyCBAEUMUIgOFUxMeU8UBYwIYJqt2NwRiu96kP9NufszIE/uWQ0L+/BdbRagdh783AzsYc9PGfuIkm2wSKiUwfjcmqp9V3k3wrd6VPbvF9l0HMOccP//zP8/v/u7v8tnPfpajR4/uevyhhx4iCAKeeOIJPvrRjwLw8ssvc+HCBR5//PHv6Fx5YTFOgQoQoUMoPU4SFxaT5xibYfNxgthaP+TCGIE1laS0GQGcc179Ic8Mw2vrbHzxFa7pIUFtmnfOHOLupXlm+xBtKtKsjzAJvHwWENTnTnLXwhKF1CxsXCJ69TIFgmFzH2v1BQIskZtlIxRgHVb5qeH9oMHVPGJ7kBN3U/qbfWprfdRUgrXWY8X6Ku7sRZxxREwxHc5RoJDXrrBz6TLaFlxL4fr+BzBhTNKcRwgJacbw8hW2114nb8+zIxdJig51LVioSRpBVS8cX/4TeoEjgHhDfmrEAxuj3ySVoQoNJy/00XdItX617qS6xK4D2bWimPDqKtUJnAVbcswmJhEh1aijsvoSkPgQ0QHCWWTFCcMrTFSbG4k1jjhpzk85Ep4Eq7Eol5O6W5jE36tC3tS+6wD2cz/3c/zWb/0Wv/d7v0er1RrltTqdDrVajU6nw9/6W3+Lj3/848zMzNBut/n5n/95Hn/88e+oAgmQG0vhNAQhIpCg9cgzsKaUlDYZ47J8BWAexKwxOOPzUGMAgyL3ADa4fp31c1/g6vZF6ved5n0fPUx0dJFBOsNm/whJlpN/80mSz38a+j0aj01x7z2PgNLIV84hv/gZhk7RP/Eurh1ugtZ0g3lei+ZhgsNmEKSFwhQZ8U5Cb61P7XqXYCHBmnJfa1dxL7wIg4T4wGlmj81iZIA8f4Htl76IE4ILJ97JheMPI4KIVrNOXQpcljG4cJmtV19gMLvMxeYJtsUC8zVFU4c0tM8PWTGmCYgRfkyEd7vwa0KMpsyLTZoY/Wf81o/zX5N+UQVvpcsrhG+vmBziMbnqqB+mAk1/vLA5COVzRGWC3o1UVf15BGWOT5T7L9uBwHlmvfIevm/j8gCGCnz+TIARGuO8jLS2GdIaInv7NHO/pane38f2XQewX//1XwfgAx/4wK77f/M3f5O/+Tf/JgD/4l/8C6SUfPSjH91FZH3zNg4fd1nFqq++4EcxZxUWjA684V/1w+GsxRmDNAV1k1GzKTmCXMcMCQlUhEMhnW/0jYsUXAFFijAZuVNegthkOOkwRCTSx5YVgOEs0hQoV6BdMQaO6qp33mMQ1iBsQWBzYpNhnEXbwhcEhCKTAUNdQ+iQ2mgQLCWJ147IvhMQwWSZbSSsyhtre+P35IYHRl7U7gdGMCXGb/Ubk/WTf8Lv9AITE1uvQuIKhKtuxxsJruPq6C7u2cTe3YTHtvuF3Gh7QeT3g31PQsg/y+I45lOf+hSf+tSn3tK5AiXRalye97l8r8AgpSiHVshStFCiRYhUysvICFHmwCRCSr9vW3imuhaEsaZRX2D28AdYVAOEcAxefJbBS89yqb7A81NH6eoa89EsBx56P1GeEChB8NTnUDhi1yd+xz10hOT+WLDgXiezNTaCZbr1OSxgjMM4R8MMWE5WaZkudX2NmSlJjTZRO0ZgcEWOnp6jcfphosIwn1jM5W9gHXTaMfV3/yCZDMiDRbYTgyhy4nLAbxgE1A7sZyoeUu8soPfPMpyt0wgEtbCaOiR3gdcorVi5TuCT3KOEuYIytBqROvEM9XEf4a7EWplDrqqJ/j4rxkTSCjTEjYAxcqImvEFZ5TzL4bxSj4BKOIMf5yZGa41AzBa7NfGr5L4Y79sJjZOyzIUJRFl9VNYgnW9JyxBYQgYEb+pz+2Zsb7Dtze227oXUWqKkZDzYwU8p8gAmy4ESEhloVBigRIhC+8tFihF4VfkUYQqkswTaVyrrs/PMnL6HhYU6gxeeZeN//FeS8+e4tO9unj0Zs9mc48TsLFPvOATSIL/xp0RPfgZlMhr33c30O+4BIZheX+Xk5jn6rs4LwTQX6gHGQWYchbUsZIYH0hWW7TUK3SOZVpiwRdiKkBhckaGnZ1BH7sYJhXj+68RnvogtCvQD7yZ48D0IFZFf7LJ1pYfMctpxQGEcLgipHdhPZzHA1aeYWp7FtOtI4QiwZci1OwflI7Fd2SvfglMN3pCloKFjpNrqmfDVVGt2AdVkglyUFU0LGCdHRZUqoX6j5yd2/Zx4tAoVy6nrwlmkyaiqiTeGtUCptJuAsz5kDKIy3PRSOR7MJLZ8RzTGVzOdQ9kMjKEQiqGIyNEktxLAbrEaxe1itzWASeFL5i7LsDYDA1pG3jMLQyRNpFX+W9kYnDAoDZGWBFpipKJPQGAkajhEsQUDQ1NZZuoB9Tggk5odNJkMsWGMjGO0ltRsSmqGaEJMEFBIjVMS6QzSFVipSAPP4xJRjTiOMTKk5nLipIsVikCH2FBTtxDZgiBPsM5hojoZAUEU+1DPGCwCo0KvfaYjXBj5vr0wwoYxVoZIPSQs5YFiJYi1ILQSG8RkooEIYoSUBHLcQbi72jbOf/3ZhcAy3yTwY9gqd+fGTP23Cr9cdXYxeS+7tCrEzZ4+WVSYBN4bCgG7njIG40pboiLiuqqAMI7Wy/vcSHp6tLMKnJ1DiMm2qj17u+y2BjAtBSQD0u0LDG0XKRaZjloQx0zVD1NvzhK5jPTcKySvvkhqBa0lw5HZOioI2I5qPGMMcZowd/4lOjtryLjNw0t3cvyeRTIDL652+caVLot5yKlH3s3cgw8is4JassHQruOKZbKkTqE0cRRSW5xG2ZzN5hwXxDxSBSwuzTG3PydKUubPX0W89gqi2SG86zR630GijR3CSwMGqxt0oylWlu9lELaZDXNqJkP3tuipJtt1Qa41Secgw7veg7OGaPYQUSEohKVVCzg+1yBQgiNTEUvNAApJtzvHZlKjpkL2GWhnfU9WVaEPl1w1CHYiA1QmsPzj4MTE/MiyNxFASF3OafQXtnJeT943OleTgRgh0UjKG/8FVEGAraJDNw53ds9GmiwolIKHQvgm9ZFW/8jHK1n20rcRlVOPrAOjYv8qZRUG+6lK1fyhyapnqcgGovLUfR4xsl5fzbhbN1ZtL4l/c7u9AUwJRJqQr66QJuuIqYDOwnFkHNNenCZebhCKgnRjm3T7KbLC0liyLE/VMEHIjoAXnaA+WKd45Szi7DOE+5a59/BhandM88r6kP/07BovXBvwwFKdu+99iOnpiPblM+x//suY3hYXipCXswOkSjAbBERzbaQ1bNeneJ0ZtIyJ52rMT8eEW+vMvPgi0Zkn0fNLdE4dozZfo8g1/eGQ4do23YVZri2cZGfmACK5yv7uS9TSHsMoZS2FxGmy1j7SY/PgoBYF1I0ALI1Ic2imTqjgaDtgf0PRyxUv5dNcKppMS8e0hal8iFNBOYlcAiWlgInZiOAvcKG8l7WrcXlcEXRCjooOwmQIa0rpbjUCr7Ej5kbeUCVn7YQHL1cVTcpQdCIQnTBXaiZ6sHVCgpKM1F+FwE8Tl6MxaMrhq4rWYmVAoUKvrIoY8ejdDT+r382kzJD090pXENgMZTNym3KrbI9GcXO7rQHMGIcxFlsU2KLAFWYssYMApf1FYqFIDUVuMIX1YZr1zbm5dYjckiU5+SBFJTnSObSSxFrRiTWzdU2oFVuJ5WqvIBgUxGmGyFL0sE/U3QQdY4ucrm4icPRExKBwKGlZHxjqOkcNLAQxQWcKVathdnpkl65gNrdAR6ipOVyjTSoDhlaQFs5TQfIEF/VR/W10XtA3iu1CYRHkzmCdD6VNr4fs91GBwgVTmHqT3MDOsGB9JwNtGBRDsjBHxA3ETIRQVR6nBIdKRubGbLoQN3g6YxtX+75VCLc7JzZx97e9vStcHPUeTory7A4hx4oYE6+H8UyEqgrtlV53+3eTJ3dl7FqN6tu1FzfuNLC3MLG0l8S/ud3WANZNcvpFRjZMKZKENM4YpAUDacgKO8ppZIOc/rU+w9zQ3UrYGeTkgcRYi7XQ2E5YXBvQXulj4yGdzOGkZrYZ88Hj0zy4v8lmL+NzL6/TG+Yc617lsbU1prItwo2c5avXyVTITn2apxonyVTIlphmcyfHYjh7ZQeXGTqy4F0zxzn1A/sodvpsfO15+r/3J0SzHaYfOEnt1IOIImRjWOfq1pBoe4ftlVVUsgHrA6Y2Nsl1zEU7y1eLRYYiYL4TM9eOCfOEmZe+wdSZ55GNOoP3vZvr95/mei/nmVc3+Pq5LZbdDlPF6wR2jfDAIVrvej/hcn1iGk8p+ShGhUUqH8rzqjxXyk2I2E2k+cvpPoyAYsywqCqVYw/M4Tyj3d0MuMoVqz05t4uf5UPfiiYix3sQvsKM856SKL/IjKxIqhJdKmOISrq7en3+AIyQnhyNbx9Srti1d6+P72cwJPLWyens2c3ttgawQWpIioI8LTBpTp4VpJkh0YbcVvrngiIpSLYSksww7HuQy60iM5bcWEw/o7+TkmwmqJmMogCkol2TnN4nwVm+8voWv3+py0tXu7zTrHMi3aHuugSuy6y7TCE1awcf4szcaYZBncw4sqEhyzOuXutzbb3PYivk5Dv3UT81w/D183R/73Nc+8wXaN93is573kV836OwPqB7ZoON7SEz230Ga5vUB+voXp9GfwOjQwbmEGdMwI6M2Z/kDIylnvaJXnqZma98HtHpkBw/hrv7XtYHhteudHn21XW62XUe6D7LUnqB+naP2n3vIBhVCisAq5q7PWeskrZ3wlf8bmYV1c4JgajySojd6g2T4SNjie9vC2LVgA1nwRQIW5T78Dptkx5f5X15J9KgyucaqUtNN4ksK9QCEKakhbhKtbVsBncCV6ppSOunOY1VWx1GaFJVo5Ah+S2UlN7Lgd3cbmsAC7VEo1CBQhYarRWhloTVwFvKD6uU/hjn0FoSaonQ42/uQEs/kShWqEh5DSjncGmC2d7AJUPCnZx9DUk6X2c665APF+jaGkGeEOcDtJBexUIrrFbU7ABphxRYdF3QoM5UXVMIwZV+gTESNzdP844jqP1LbBIw2MlYHxa48rWFYYCuxWhRQ9fr6FYLqQKmcs3BLKUvHAuBZFFrYpsz1QpozLXQ7SZRPSRUglog6DRDZqdipk2TRn2euCgI5+YQYbj7DRVipNA6BocKeMqq4k1qb2/gblEBVZXJGoMXQpT5LnHD83evOioniLJqWCpkeNlnMcqZVWn7UUAoxvtEynFRAkqvy5bbm+gkoLotEMIiS0VWqmExrtK1sDghkc567+wWMvH39MBubrc1gE01QtomIh7UCYM69VaNTjNExSH1UPvWEgc6VkTtEFdoWq2I6UZIHoSkuSEzlmYR0Zqt0VxqEs/W0KFA2Jx8fZXul79AevkindkD/NgdD5K095P3ptnemGcrS1joXubQxqtENqc93WS2FVNoxdL2BkvZeYRSZEeOkc8cInOCtWHO75/ZoW00p973Po696x2sy5hnTJ2V51Z9UlsI5lsRM7pFW+2jlddQrSn0zBxOB9zfzZnZ3iC3UO+0qTdTlCmo3T1NbfpeRL2JPjyDrAkUAfcfnyZshizKOY7GcyzqIbIzjZ6dHVMXRDm1mlIXXlB6ISX3aySlAyOFVca581ELUsV0x1FJNWO9Jr4TomyeH+evqnqjnOBvVGvLctYn+JDeudBXGMueSAGlWKHF4XNSzpVhpQqoUNXLIHoBQlmkHqyk8qP2hABjynASlMJPpgJQGlsKJtpSlhxn0SYltIa86H0vPtZ79h3YbQ1gtVBTs5ogDtAiIowD6pHGRt4Tq750vLhhQFAY4lhTjzS5Vigp0IWlFilqzZC4ExE1A5TCV616XYZnXmbw8gs07s25/52PEh2Z49x2i6ca02wnOY11iTTXCIshtXpEM9ZYqTgg+5wwKwQqQM0dRR6fZiN1/P5L63zz2pClRsDdd55kYV+d3mbKhefXee7yDlP1gEOzdVpxQEPWqIkOkZGozgxqbj9CBxwMV9ln18EYZA1k5Bntdn8dO7WMCOsw20QEngpwYL5BEQXMhjA/s0i7Bk6FFGHjBu6Tr+jZMuHtQyxTejieSelnz44T6SOHB6qVYMLroSQ1+FCtBKSKgsE4/KyC04rMQbWnciE7ydOqWrDwBFuJLWkQshzQ7ZuwPcDZMXXDFogi9WCqw5LqUbqP1vhOjnJMCGWS3grl+1WFZ+FLkxHYAm0SApN8lz7Jf7YpKVDfhcG2f9HstgYwYyyFtZjc58CK3JAXltw4jLWjvAXliDVrvCROPy0orPJTjaxXn8iGOWkvQwxy30AtBDKuES4fxJkC2ewwvHCZdGdI10b0TZ2BlWy4iCvBDJFIGGSWxsYVBBBsr1H0B5AosguXcUlEimY6jzg2HVMPJGvdjG8aw2ZiaIeKE3M1lJI4B/20YJCkpDs9sqJLIhr0YrBaEK6nRJc3kUVGOG0IMouVkvUUNrI6ytaYyTUtA/3MsbadcOX6kCIo6Pb7JFEG9RZy8SDUg3HIWFYfxSh5P1maK/8jBJMk2FEBgIrLNQ4bK6fKq7FW5NHxcu6G5d9ImmDUmuZ/FxPQOR55NvLdROXXTZ672lO599J7s8iyE8AXH2QFZqORbaXnWPqDrmwpEtZQIDEiJBW3jokv3yKA2T0A+/6zYW5IspysOyQb9knDhEFS0JcFWV7gTIFwnmJhMkOeGbZ7GStbCUXo0GViVAwLutcH7FzcwegBU4kPMfTcAp33fhDTf5TBuUtc+8znSVbXuHTwBCv3Pk63PUPPtLlav5vQ5iztXOHgxc8TFin1vEeS93HWMXxhlWT4BehMc/J9H+TkfQ+w3s/58svXefVql8VOzON3zvK+49Nc6WY8faXH1Z2cxvYWWyuXUckG52ZDns2OMNCK5Ze2OPL1l4izAa0Ds7QOzjAMYr4kD/A1sY+4XuexxRqnUsH1bs43X9vka69vcMjtcJAztLlOcPAIzff8JcJGC3/BqlH3zYRozYSNEUEIygGvvjrouV+CAl1yrEBXnheU+SsmIGd34l4w9rRw419t2Xs4Bj03WluWiXZRkskqUcZxcGpHT7TleaVQCOWnMxVCkzpfcNBSEqiwDIer1+mQJvOFA+dQpoASvIYiIpMxXXnz+ume3Tq7rQEsN5a8MBRZ7j2wLCcvvBdmjFdgwFnvfRUWU1iSzNBNcoxVRIFP6Oe5IRvkJDsZQT/DFt4fkPUG0aGjACQbA/qvX2DnhZfYHkp6h07Tj9oMZcRmEBO4gnZ6iea189Tygd8fYHND/9I2/ZUu4eIiB975CHNzdV4XQ1a3Ur56dpt7li0/fHqRUwsNpBA8dblLNyno91OSzR3S4TZrasirTdgJJObakM75NRppDykNYc0yDBtcDPfxjaBBgxqHsoAjBXRTy+pmwoWrXbTZYCs7x8BcIhaKRjIcg9Qb+FMwGvGzy25oQap6JIWnWhgkkvK9H03nnuRniRvz9buCzkntSd8v+cbzI8oZAKIsY1b5++pljJxHRyUfXf5Fqdj3VkgMAuckQgqUKomtzg+8FVVYafJygEeGMAYrA3JVJxERibh1RNa3GkLueWDfj+bAFoZimJP3UuSUpR1pdD0gd3B+O6dmc5xQRLMtRGFYbguK2oBUGdaKgK0sQKIIjxxhOjaEUx3Sa9fZ+NJXGQYR12szDIIY1RdEJ04w026RT82zvXOVXtZFTM/A/CJKhsRA3k2ReQbzCzC3QGFgXW5zPdwhbjdpbHepv/hN8r4jKjI67Yi6NrjVi6T2KiJVzKqQtBOjsjavhUtcyWN6UYfDDUse5KhmjVeb+wiCIXdOTTE3N0WgYuxQM+wNEGlK8kqPZOMsYpBy8Np17s93mHIJ10WDZ9Qyc3KWe50iLsFnVxhJBVw+pHK7UEyM3vsRulWemyuHy5ZIMtKzd3bsWYkqJJysdrpSB8x7S9V4WmEt6oYBuqLMu71Rh5+b7bJskyqo2F6ezyaR1qFNBgK00MhyspL3KL3XZRwYAgQWJSVSGpwTPvdVZBRZ9zv7vL4F2wOwm9ttDWDOOYq0YLjRZ7DVJZzPOdCKSGfqDNKCP73URxQZd4iAu+9YInCGmX2S050NtmzA/15v8PJWTBEFNN77Ho7MvZ/s2nXWP/clVn7vD7ncXODzBx/mYmsf98wqfvzDP8SRlqTz2ms0vvwkyfY2xb0PURzfB7UG9Zcdgys7JHmGOH4Y8cj7SaTmzMVtzlzdoVEMCS9doHbuGQZBm1bnNAf3H2DObGGe/wY7xXXUzAGOH3+MhYUZLrOfz67cS9f2eaBV4wfnDK1owOcWpvj9pfvJsoK/erjOfSfqCATFS4LNlQ3SPGHr2dfYGV5GKng0VjwYSNZUk6+Gh/nf6k7uUXMs2oj5IvEXtQo9j2vEeWLkVQET+lkTWayJIRs+tDPlMA2JExorfCO9sHmZSBdUum1OKAza32XNiFRqUeRoTyVxXvusYkVUz3cEI6VU4exoT1VYOvb1fJVSmbysPGqcCkGAyhJqRc+HwUEMsubXy1NEkeIQDIkYiggpINJ+hoAoUuq9dUTWRw72qpBvt93eAAY4Y334mORIY2kEijDS7CQFq/0Ck+fsE4qgXacuCoKGIAgTmsYQ2YBhqknDmGDfEs0TMwyDgHxri+7zL7He6fGaOcyZmQZTjRnEgQM0l1uYnQ2SwQbp2lXy4XGyQOBi37ZUDHIoDCJsIeYPkOiInWyL62aH4WCT7rmXSFbOUjTnCJsnaTYC4r6BrWvk2+cRIqStLGEjYqXW4GowwzVV484AFmPHfFSg6xFXarMMtGW7FSE7Mdo6rByQJ0Oyfo/s6mXytVeIIsnCcpPaTA0pYFvEvKrmmJIdEmRZfROetLor8+2AccXQUbXy3OybfOxpVRGcoawiVkzV0tOrhHN8Yt+NvLSq4OJKORsHYO1oaMf4vLIUZCwDWTGOdCcix10eGOUcRyeV7yIQAikc0ub+nC7wIS+UgFvgkBRCkKGQ0ufJjBYoW6BthsoHhPmta+be88Bubrc1gIXag1VQCwnSABtrAu0FDGMtiUOFxZNLpVb+slE+kSvQRKGmUQuoxxqtytAiUMRTNZpLLZbmOjx25xxHlhZYmq5xqZczvNwltiHNE8epL86QTtdIrr2G2YwglriHH8Y62J7fx3YvJ1X+w7d/KiautRHmODstTR7GHGgJGuIaM8EOM52IOJiG6TZZHKICSacesDBdQ2lBp56iiiFCGg63BT9wskVqYP9ijfWohnGChQM573I5tXTAyeUeC5uaMBDUZmLPAwtmeLC5TDtc5I7FOu1mreRCea5VFcZNMtNHHNYby4aVYoRQOFkpWIwpC9JZnC3bcIT08swwFjwUsgREr7c14WZR/ebbhcaVvhHbfrIH0bmRd1fRJkb7EyVnTAZ+b4jxMFoHTkeAw8oAUxI5lAyQ2uf5QuewLkMiCFAo67XnTNjECklubl0VUstSfeVNmtvTA/v+s0aoqNcC4nZE7GqIZoQNFYVWNEJNO9ZYZYlzjUq0ZzkFAUIHKBlQr4dM5xGdRkQYeoKligNa+9uoE7PMHFjk5PsOw5HjXNpJ+eqVHmsXdrgnrvOhxx9jXuUMVlfpvfZVirzALJ+k+ImfINMx5waClzcSrMiYqgXcudRCuwZyqcm14j5iM+SewUU66Wvo2NBYrBO4ZYKZeWjXyGLNYifmjgMd5gY1loINVL6OMDkPLLQ4ujxFIQK2dYOL2l9Qx+9RHL9HERYJy1tt5rtHvKehJUIJGlGb5vQJurV5mpFksR3gtGLUB1mCjZMlqdVVk3x8ZXIXODABEGhftStDRZ8AL0pMkqD0WHerNFEpvNqq4lmpwgpERZiVGiv0KLE/gs9dBQdfRPBcsioZp3DSK21YKf0Ebud7G4N8iHQ+F+bCOr63UVOUU7+dlmgdgHPU8ozYDH2V04Z4ZQ5B3pjBuhkSsZcDe7vttgYwqfwsSKUVMlDIUsxPSv8H10pirUTJctRalTj22tN+jqSWaFWpuvp2DRVrgnpI2AxpT0dEMxH9wtDPDKu9nIORgulpdGQJttcJBlvIJCHXd2KX9iGCOvnVbfpbO4Bhtq5phxIhFDaeYuhAZ9s084sspn2QAqc1TobIOEIrhVWCKJDUY03mLKHwPZlYQzuAqY6mUJrXTcSqqWGFYrammIk0gdHMhB3qjWSc5BYgohYLM0069TqBgiioEunlZJ8JlhUltaEijI69rxvDyEr+ZiLZXvU+wjiZXwLEmI4hqGYuUkaaQCmOWJ1B+PeG3dm30dkrdJ1k/0PJxi9/Lz02i0NB2UpkQUpcycR3bjyct2pVEtaWtIxylBoWnG/2diLwwK1vXRVyz25utzWAWWMpckM2yMi6KfkwH5FT08ITVk2WMxxkZL0higLRSFB5hrUwHGbs9DI0grzwF6DJLclmQm+li0ovMxRfRM2+iql1ODVzgOWpKWKT8JUrXQKTsbCtONRqE9RjLueCV85ukukBOutyWu+gnKG1mdJcy8hkwKV4nvWww1TWZ99Gl5nuNn1d40LcYVs3CZM2jUSgdcHqTsLF1R6b/YyptuTK7CJDVVBcWSd/8qsYB90jp9DHTuGsI3nhVa5fuoguUtJknZ18B6Xl/5+9Pw22LDvru8HfGvZw5jsPOY81D1KpVCUhUQVIIAzY0Ma0edvdpgkHH9rGxsgfMA4HmAhHYPvFRmEbg4OwiXD368DDG/ZrBxaTQCMlqVQqlWoeMivn8c73THtYa/WHtfY+52alsKUqpUhFPhk377377Onsu/f/PMP/+T+kMylRM2JT93ihpbkcDVnupTxypMdyN8zblN5LqR5gwHtVbopPVTHob6haykBXETdK7ohqZNukullL1DhTN2p7LX0VigiCKLQdCcBYfy4WVzeHK2eohqYhAKUneTZn/TRtU4KwSAQKzxGTUvrxac7ipK4FCwWTAbnWCfJ6xzpIjQmk0F7U0BhUtoUsC/TurfPA3i6R1dzxwP7sWWEdeVaS7YwZb40oBhlFYSmNY1RYdkaeHzboj8i2+0hKZHtE1B1jrGXQj1nf1kgLWR5u4MIwvNZn++wm9sw25ZfP4Zyi/ei7ePwn/jfSu5Z45vQ6/9eXNri2Nea7Oor9s/O0dcn5oeD3X7pGIRTfN9/nu+f6JCYju3yB/PJVtlSTl+bfxavd4yzkOxxZ22C5v8bleJ5Pz/Q43VhlMW5yT18wS8aF9RGvn99mbWdMeqjLgf2HmI2hf+oMO//nH2KzjO4PS3pH7gZj6X/haQb/4/cQeUZbWhrCErdiZo/P0l5uc4YZ/geW59jiocMz7O9FLHdjKi8KOaEneO+mEjp0WKEwgUMlBWHMvZtq1ak8rqDCGtqGPOtdTIFPaBayBmzhJW+ExIaBIAJLFHoojZOUwbsyrgIw30gtXeH3r+PQcG2nSLWVByiQUiGqnkelIGjoGydruobCEGFwDjInyVwl1RPjRIQUgkhKlBBIOyDqr6FG2+T9wa250QEl/PyHt7P9t6Pd1gAG+CpSaBVyoeHW4WphQ+Mc1jqscTgRiK0hJLLWCyIa6+oci3POk15zgy1LivHIE1v7fbqUtCNHLGA3g/Wxo99SlFGCiTT5UDDICkpnkEVG141J3ZhBPkCMtolVCdmIMs8pi6Juexpbwa6L2XQpiY3JrPDgHFqfstyQWcFYJIykYJTDYHsA4zGtUYayvmeR4YByYwORZxRKopRPWpeDFDPSFIzZtRmbLqc/KiinWaJTSfRqqdzz2+T16e/ixnUqjlatiV+t4abWDV9T1cOJ2KDnkyE8aN24pS+UVr2V1THlngKDIDRei2n6x6QwMX3+1WZVfm96yG+9vph6h6GdyBNbb52czh27ud3WANaIFY00ImknxHmKaERYrRBS0ogU3TTCSEer3SDN2iSiRHe6qFYPZSNanSazWUqvHRNHPkcjtSKda9BZ7SBaXdS+Y8j2DMlsi+L86/Q3z9Mp2zy6f47jq13mdYvXdINEGJKZhO9ta6SzHMt3KC5eAlcilKC5bwVkzAONMTP6IpGyyJV9XLCLbOs2s60ljsUt5lsxC62YmTRisZNwcLlNsxkx00sxQOYE6Ynj7P+//RCqzJi9ax+zo4sIa5k5uUD2w9+JKEsiWxI5g4olrcUmSTdhn5rhO9MjHIiWObLQZL7X8F5PeCi9ieA5+YdXyIpvFUJFAZMZQoRQL4xYw9UfDsKWVFwyGYQGK2+tbg5XQc5HqpCjnMp94UUrdNhnDWXCIa3PYSLklHcnkTKqE+17clrIqYLERDu2EsWQFSAhiKTwRQccoiy9lwgoJ5AWcIai0aPQKWNx63hgbzeJ/3a2/bNstzWAtRNFsxmTdlNS20C0EkzkW0OasWKmGWNj6NgmDbqkwqBnZpDdGbTRtIcJ80XEbCsmjn3YICJFc6GFONgjOnCU7nf/APHhE2RnXqf/uT9kePUi3eMP8cHHvp98ZolrO0Ne3JjFlCX3z+T8cCenYTKK17bJz52lABr7lmke2k9TQKcY8VB5lr7u8Eb3JG82VnBCMq9j5oSim2qWOwntWDGYaXBkX5eZUcFcK6YExg4W77ub1YfvInaGzu45Ojtnkc4i7l9CvOeY90ZGA1zuk/giTCFK0x7N+ZMMW4s0IsV8K0yeDvmoiis1mcElPUWiCt2m8mEVyE1mSjqfIA9BI6F3UAhZjV/069S6YBIbJl9DVVisMlJVaBf6MmvXy3/5gosKyXmBccKHtDpGVmfgJsn/qp/SBnY9DiIl0MJ7a9KWiNJ7U1GsUdqvI8scYQLXKzQsGBSjxixlUzOSO+/8Tf017A6A3dxuawATwlccZRh4IKWfC+mkz9NUn9xCaUTSQAgDUmJLA1aSSGgnmkbkE9jDwnhduyRBd9uobhvX7WK6PWyj4fcWvJu2LDHKsK0FTscYFFqVdEVBKgr6wlEEXS2jY/IoRQiIGZMKi4kkNkoYRU2UFKRaEklBU0FsC3RRklDSSSQWTTMSRJRoK4mSlKTXIMESF1fQWznKOWQjRs32cA7KocaMY/+ABs8nSlt0WzFJKyKS4gZeUQiaHNVVq65yUCidrFOtPiGi+vX2NDJyw/o3/V38Kb9NLauYqiEkrSrGe5rD63Ngat2bHL7OFdx4xEkls4JvMbWsOg3PxZFhGtJt/fh8W9ht/RcojU/YW2tx1pJIaDYUtqm5tjvm6vaYvCjZ357HLjyMczmja1cozz5PpmKOLN1LemQJIyTXdjP+YCejXRqOH76fpeVVdpIuXx3GbJ/eYiZvcOiBx+ievIdCKEbnX8ZceJX9vWVaC4exSrN0/SqjV1+mLHNco0PjvU9SCMV5F3HNRcRScHRBsdqQWBOxPWhyZXvMbENzaLHFYitC7W6QvHkaNdhmuTVPNH+YPO6SZNs0h1dQWUm7sUhX7UMLiIRXGXUCXNzEtBYpHFwrm2wVY2IpWGwouolCSkWqICp2kEqjVYoQwd2oeh4FU2HepC9ROudzUwAEKWbw8jRiCkQqORqFb90JBQKHDB84AVkciKBoWgHSjcNC9s5zlJMCgRP1+TknvE4XFfD685d2wuyfSPmU6DILNI8IJ5Pg3AVlC/CMfGtwQCEijPI+YSRBhZxabMZoO6Io7nhg32q7vQHM4gdzGK84EUvophrR0AjnuLo9ZpAb7pqbwxw+gTVjxmcuMfjq84gk5fDiAe453GYtg4+/vskzlwbs60QsnbyPY8tN1ndynj+9w6lLW9w9m3Lg/kfptTXZ6ZeRX/wU5fYG3fse5chdJxCNFsXlXcavvkxWljQe/y6ajz6BExEXzu/wzKVd2lLRnu+wutzEDEq2Tu1wdWdELFIWG4qTcynl7oDhm89hLp+ldfx+Dh4/jJrvIK6tw/ZFRDZEdCVSLiGUwk8R8lr2NmpCe4HMCq6MWpwbZbQiSTLToNOJEaYgHW1DuQMkOKuC0F2VDPLZ6iqhbZFYp270xyaMfcBJVefEbKBNCFEtD0WR2oEKfDzhKQ/SlCEZL+vc1Z7pR6HK6RC+QlpxyUJ/phd79cWYan3C+fk2IR8SSxmHlqMCaUZgDUY2KZ2vwE4XKypirEWQi4hMxh64lPNpN5MT5wNEMabIb2EOTPjo4u1s/+1otzeAGYspfdXQlhasd/+FAGcdRWnJS+u9CB2BMJjSUQzGSAPKWFItiUu/bn9UMEwUVkXItIEaCyKliJVPaPeNZKNU4DROR6goRlmLGuwiSoMpCkQo64+JyArBSEgKFDqKkFoyNJKNMezk3ntpRopUWOSgj5MZZmuLcmuHYmsXNRwT4YiUBK1wWoPRFHlOtr6Jk5JonBPpBCskw9wx2h4yNIK1nRHrOxlFqslmfcuQLQqK3QG2v4NsNNHzDT9WTUClAvY1w7gqhAxY4SavUC0RVWPi9Gs1p6z6zzFNPp1sHb5PFzSn15uUIG8sejItyr83etxbFqjXDUn+CvesA1XTRxxeUseTWYWr+P1T07w9FNfS13fsW2e3NYBtDHJmdsb0N0bEG0Oi3Rxn/G2VF4bdfk4/K8kyE+5Lx3hzxPbZbVQzp7mTeblgY9ndzVhbG9J2jiw3OAQzqebRfU1OzGq2+wV//OIaw3HBsVTz2N2PM6tKxmtb7P7eH2DLknSuQ/Pd76eQmi8POzz7qbOgFIeXW3xwf5O8tLx+YZvPvXCNNNHsX+7wvSfnidevU/zxFzh75SLZ1ia7Z06R726zEB8g/UBJJIDWDGLfXZhszIUXzvD605+nLAzH3nWM4+++i1xIPvPGFk994tMMC8PGMGdnXLBvocvSdz3E4dnDDK5vcu7jn2XzldfoHT3E0Y98F70jh7x0spS191Rllnx90T/lcnouo1C1N7Rn2pAzE9UJNZmYXXVAeF2tgord7oUOdRBxllWKvgYoZS26UqPATcLWcByB77GUspqEhNf4EqIuLEgkqgIcGeGiJjhHhmZU+iM20Kio4austkCORggHqXVEzoHSSNHBqgZGRIxli1LF7KpbB2Bvl8h6ZyrRn0HbHubs9DNGW57I2hjk2OCFFaVlOCwYZIUHJOe5QdlOxu7lXXTLUAxycA5jHIN+zubGiLlIUhSeLtBJFA8spjgb8YVT2/yfb2zwyuUB33XfIg8/9BDxbMLgj/6Irc99jnJ7m8Xv+zCNJ59EJC1e++wF/ssXL5JEkp988hDvvn+OjUHOp7/a53efv86hxRZ/bV+P9x+eYdC/zLkvfpGLn/8SWWHYHuXkxsKBLfZnBSCg2YW0jcsyrl58jmf+0+9SDEfE7f+NI9/7ITIUX/qjz/L/+/jTjMY5xhqctRw/uMgT9x3E3HeYwcYOpz/9Zc7/8efY996HWXr3g/QO7Qfpq3aWiqRaeWMucNUrzylwpeREZocKtJzzjdLWhCS3CESyyUBWUdErrPFUBRn7dZ2vJFoq5yxAmXWTnkpAyHAeYcQaUqGkQqqgWx/yYa4OZ33eqhaJlhojI5yDvLSMCr8/P8Q4wTmDHI8RWR/hLIk1PpzUCWWcYkSTUigGskEmU/q3UJH1Tg7s5nZbA5hWvo9RKoGUnj4xVRPzFcpa490vFUqiIv8lggaxJ2lLokii9aQvkrKA/g4iHxNnY2YSwUInJk00/VKwmcNIJajeDEJK8rTJZikZS4HQmvluQqoETZcjdzdRI0NHGRa6CXMNRcOMUP1NVDEiajdJFhdwWUa600fmBVEa+fYVoHSCwkJhJTQatBfnKEZjZKvF2CkyJGkzZWmuwygryIuS0hi6nRZx5P/MKtKkvTatxTkasx1UNKWHL/YGhFNRGZME+/TVvYnV+avJ6xWpVEyx46fVLibruqmfpo55s2ng1fK6G2ASWlbhbuUtTtMypikVIFBVFVUIL/+DAKFQ0stOe19+0jNZ7d9rnFgkt26wrX5L1fjrszutRH8GbambMp+lNHsJiUmImrqenacjSdqMKJUkjlU9Vy+dSegd7CIbDeKOT+IqJen1EpaWWszNNUkSf1nK7U2Gz36e4spFZltL/IW77qHf2E8hBC9c6/P8NTjQXubED/4QiS05m87xxYs5uTTMzrf5f3/PCRKbc3jnNKOnvoRUKR+YP8GJw0dpmhEHtk+RPb2ONJKlJ9/L3AfeR752hcFrX6XcXKd7zzJxM8Eh2M4MV/oFWVES33M33/H/+StgSuSRY5wbQSkcD99/jINLM4wLw5V+xvqwYKHX5MD+JaSA9uIs9/75Jzn8rmM0V5bpHFj148eEROE7FSazGKk9JwcIoXAqAAZA6B0UFR1B+InZqBsyac75tp9qOIdSgA4cLllXFHXobTRUoOVARWGY7iRMxQlf3ZS6rphSZoBAV+Gj883pXkZDIYIyhbGQG4fF1yvasQyFBsHY+vceRy3iILNThi4NISVSJUislw43A0yZoctb1wt5x25utzWAzTQjOq2ItBUTZxE60VWlHaUkSaIpECjtFwoJcTumtdREpg2iZhSEKQTNZszMTINOJyGKfObH9PuMXn2J8esv0b7nQb7jkXcRHVzhuct9Pv7aBtcHBerALA8/eJR2onj+zA5fPrVJaeF7js/xXcfniMd9hp/9MuMXn0W2uzzwXUd4z0MruK01si9epjj9AmrpADOPfy/6wAmK868z7gwoL0dEh2aJ0ggnBIPScmlQMC4thw8e5OT9R9ASzvQtb/YtQsDxI6t890OHyYzjtfUR53YyWpFicbGJFILGTIfD73sI8cgJiFJsaxZUFCgEASDElOMF1N6LlD5JH8CkltaZAjwXZkv68K8itVZho61lbqohHxXZVE2Fqh7Y/H6FUPVgWYLUM0HNFenVOURNmPVFEc8nsX5957xyBBEgsDgK66uiqRY0tPfPxgbGpQczqTVa+fMqjKOwIIUjkQ4V8nyxHSHsCOzwm3l777E7IeTN7bYGsNI4SuMwpcUWnkpRFcpcGJdWljYMJQ35FevXp/S9k+CXF4VhPC7IU42xPngQUYSemSNaWkHEKfmV65QZyJFgTgtEO0I4uLCVkWrJqLDMNWKcsySDXfIzfVwxwpUWNbeISBqU233c6TMw6mNRiJlF8kaPzaGjWB8h10dEGyPk5gj6OUkoSmgpaEYKKWCUFZy5NkACAxnRUJ6wmq9vsHZ1xNg4rvQtl0eWbiPhcFtBJ/HKHFfXKbc20J0uyYEmWgc1irp2d8P3Gs0msFYn25mu8zGhPFBRYadCzgCMlTLFHj/NWi87DYhK9aGCVFcFgv5fBbXW4SuFhJFtdSjp/9B+0K2bomT4PSrhz1A6F7YH6UJbUdh3WR3YFCgTwFGrIO3jKIXCiYj8Fo5VuwNgN7fbGsC2RwUzg5zRbkayk5GMSp/Ed74KORzkDMYl2bjEWIexjnxUkm1lyKbE5P6BK41hY33ExfM7xJlhPMzBWfTMLJ3HPkDz3vsZXLjGxd/5Y8ZrW4h77+U7nnwCNz/Hqct9/vPnLzIqDCf39/jgkRlSV6Kf/iIXn3kaLWH24ZP0PvBhzHDM2pdeYec//xHRXI+59z9M+7EHuDqAT5zKOfXsKZYvnebBZ99k4fp5emqV+P05qYNuojk+K8gKw5devMpnvvQ6eWn4joeP8oF3HUXlGaf/6PN88Y//hF3jeL45z6mkx4HlWVZ/4DGOL3UYXNvgjf/rj1l/7gVm7z7ByR/788ze1X5L7qoawjEJ3dhDPzAhYQ6ghdfZqrwkGaRwnIywgQuGtGEgrqRwHnyk8NtK/LBYmQ8QzqKiJiQtED4hH+opvpIofbI+d5IygJeWERKHdAZVjhGmxEpFIROsVEgRqpDOorE0hcHhVTFk4auhSmgiGXnwst7zErYkGW/RyHdBakSzg4iblE4wkC1y3WBXK+7Yt9ZuawAb5iXjrKQYlZQjP/vRhkSrKR15ZsjHpffCghyLyQ3FqESJ0nPH8NHNYJCzuTliPlEUQVpHNZvooyfAWYZbX2Trq6+w/cKrrEjJie//TtLlFmcu7fL06U02BjmL3QYn51t0XM6l65e4/OnPoZKYzj3HSU/eT3Z9g+GFT3HtDz9N8+hhOu9/HHn0fvqXdnju2dM8fWqDE1evM/fGGnp9DX1sBxPOJdWShpZkhWRza8AnnzvHcFxwZGWWuVigrOMrr7/Bi//jj9gq4SvLR3h9bpWtIytsvP8ecJDtDLjy7Cuc+6PPs2834+CHn2SPL1SJJtZJ8YlEtKMKD70XVYbrLAXUUx+d8RXCIBZYJchFpavvJMb5hLnG787PdywRxRjhDLKWnhZ176LA+V5HUUnhCAob5kAGGSCMQwYCq0NglKIUEVr4pgAPgg4tQmhbad+7IIwpw/uyjtw6lDGk+ZBovAUqxsYxTidYJxmLmJGUDGX5zbq132JKvE0P7A6R9c+e+ZBDILVERhLpSsRoBzFoENsx7VRhhSB3cGU3p2VzXNqgsW8RFUXYwS7D11/HZIJ9ccmDB7ss9hK2RgUvXtgJD7CnCZSFRh8+xIwUJLNdskuXsPmY1saQu1sZO5FlYbRG9nqOtgWyHNM5tIiLE3ajhNNbOXnfcqk1z9qBoySLKwgTsbM54ko/xylBqxWRzveQx47iFlsU3R7D8xdwRearlLMdlIPuYJP9/XVG45yZwQZyuI3MxsRlTlMKrLQcIEe6ISvlkOHOkDfWh2z2DReSGS7P7ifpLJDruPa0nJhAWV3VY7o2uPe6V0NkJ+t4gBFB1wuYaIWF+N0Dkd8mkP7ryp/TPvT2QoPUIDoZVuvC38Mz53WoLnvvKwSWtRy2RDo/EEQQ2o2oFHklAi+15MIwX1vvKwCy8PeVUTG5boYZCgJpS6SFOKgXFeWty4Hd4YHd3G5vABMCFUmiZkQ8jojcEHX9NMps0StjDi6m7JSSXev4k3NbNCm5d36Bu558FJln9C+f48oLL1G2e3znw+/nsY/cw+bI8JXzO3zi5esAqFCtP56mfPcPfT/7opL88hU2P/lJzGDA6r4V/p9HjmDjCH32NFufP8OuKeksdzn0/e9lHDf4SnuWl17doshLxvsfIP/wPmQjJclaRC9cZZgbXKrZv7/LwqEm0Xv246RhtHaFK3/wR0TDPjP3HmH5fQ+gmylHLr3Md1/4Kvk45+SlJvGVGShLuvkOq4mkVHBU9RHOYUaCK2ev8J+7l9m9nvHm7N2s39ejf3Q/jze7+HxVxZ/y3CsVSKt1a890ZRI/lbtu9gkUBISX9BYq9BUGgUGgBjEpIRKE9iVvFhA69VVF57BBKbWiLESBfuFZ8SUgiIVG+ym0SGcQNoyvVRonJRKIXIE2OU5GlKJqGRLowF8rUeTOBa6YQof3qWX1vjRZOsNYN1FYmq4gyQZoa+jkOS1Tokd3xqp9q+02BzC8hn0kUbFCuhw53ETGjsTM0Gu2wGpy5zi/PaYhLEeaLVpz+xH9XXZeP8fu8y8RLy5x+LFHmTsxx+vXhnzi5TW+eHrTA6QOk5sPd4gePcnCUoONzz3F2u+/SXbxMgs6556HVtBtyZWXrnD+uedwpaH3ofcwc/Je+lGDra0GL6+NKRDI7jKitwzgRRavDZBSEGlJt5PQ7HRRKx1cK6b40ufp/+Fp1MXzpCrD3b2Ism1mdq9xdOcq5Thnfvc6qr+ONZbUjOkor2o6K3I6zrFVtvjCVp83rvQZ9EsupQvsLDVYmZkni9Kap2WFd3pUnffyTHeHnIBY8Lk8P9XVSXlTJdgDzjlnEaWZ0hirKpcS5d1mPxqtilSl9qqpYZkNWX4lvMdWyfnUXpz0YFh7dtXoNSHrMFiFXsgSgZOx98CqRL0AI6AI70EKWeuReQ/MdwZkKqUQCdqVpOW2T+rbElX6eaNleQsVWe8k8W9qtzWARYHIqiKFihRSa9/CohRaK5JIkdpJ428sQGvlR6tpjU4j4laMbvo+RfD5kDTVtNsxzVix2k1oJ4r9swnXRgbWM4xsY0/ci55fRizNUA6HUGboZkzvniMYC4P5FU6bDmMRkVJyr96mEIph1GasUmDyAMeuoGcGpC6nqzrMRm1akUK3EpLFDtL0YLbHdtxDRR3Yd4ClR+7F5Tmd1Xkvpewc6YF9zLzvUYQpmU0sndiiOnPs3z9HMdckb8UsSsd4scU9+7u0m0kI92Sto1WFghNV1b0e2MSq2uC0/Ey9E8+w98wsf/GFCyKE07O0q+0mojhysnASvIoJJXWalFpzY4I3hpua1x0mcIsQTlYk2hLhqRY4dDiAl6j2uT6FAuFH8MWUKGf8a1JjZYozfjo3qiTPb51M8x0Au7nd1gDWiBSNVBM1InQWoxoxMk6QUUJCTE9GSBt5eWnrSIQgjiNEnCDLgrjXpLnYQs010alnpWutmJlJWV5qc6CX8N3HZjgym3B9UPLyxpCnLo/ZFy1x7/f+EB1hEBtnGV15CVWMaczPcvAHvpNCxbwg53ixnEcUlqNc48+nG+Qq4Uz7KFcb7ZoOANDNtznev85ctoGLljGNRVwzIlrqkNy7glwSjI4c5ELnIKbZo/fuFvcdPYA2ObHIEOUYhGLm8Uc49P7vQ1rDXH6dbrHFKGqh5k9woD2PBGK3hHKOmWbE8nzT87Jq4HABqKZvi4rjVf0c6Aohd+ZDyrCtm4COk8oTTmvOmJsA441WhZwhnK0oDVV11LnJVpXXVxcI8LwwUfHNAnm1Ys8LZ4lsCdbTH3J8cUEJSKTnn8lijCpHgEBGDVTUwGFJ3Bhs7kE3SshVC+ccRWmw1jJwd4is32q7rQFM12PVpE/kKxkGNyiUU0ROkViJcZ5CEeFQSiGk98JUrNGNCJVECO1pBFIK4ljTaETMdmKOLza5Z7HBi9eGPHWpz7ntnGixzV0H96MaGl7bpTyT4Ya7xItLNI+skkcNRltNLm410LbgHgxHVZ9cl4wSS9bQ074Gs1JwYDRiWe4wVh22tSWPJFEjIplpIUWbUbdNP+pQRB16C5KZlZTE5pj1y9i1AUII4uVF2sv3+ElI/Q6d0TVimbCYdlFxSqQkvURNxBPjSXg4IaYyFTLezKah5GutJajUGwJ/grpEcJMN6iT9HnbZlFhiDZ4Tm7xWLQ9TkQhy1UFy2lM7ArCF5h+LB91akdUZr8gqBFLHVOUFiUG4AisUhVRYlWCd73ow1lHoW9dKpOTb86LUt+dMj9sbwEpjKTJDtpuTbY9JBjmuKHBlSZ4X9McFO4H/VVpHKgxjcpwscHlB3h8z2hgRMcKOC3AGYwzDYc7OzpitcZ+1/nmuJyUuanE8XWButU2sJGfWBpwXsJgn7F8+QVyOuaJn2bqqKJRjQykW2ymxEcQbY0Zba5QiIt2JmUu3J6PLgHbRx/UvMyq2GNkO/cWMcWyIdsYkl7aQ6xtkzQHKOZyUXNwuOLfRR5qCxShlqbUfg+TUhuXM9UvEZcZd26c42L/IKGlzbjXiykwC1iEKgzCWhU7MAwe7LLQ9kXUCX6IO1qgVKHzBZM9E7CkAqWHHVcM2guCgE2/Fq+kp2nvAcLpdqNq1wwUJHQvYmhBxs6exEk4UdcUSZ0N+T+HwLP+QaUPZcqKM4Ww9Odw3peee3IzEysRXLq1FmQxpLaIssNaSF7fPYNs7IeSfQcuNZTzMGawN0Nf6xIsDzHiMzDOGo4y1fsaWKSmNn/DTlIZdO8bIEW40YrzeZ/fCNnGe0B2MwZSYLGdrc8jVq30au1c5d+Fp4t1LpA/ez+N/8YeJju7jhSt9/uC1DdYGOQ/Mt4lOvp+mFjx7oc/nT+1QOse9R2LuPdKmUQga5/rsvH4OrKUdXyCNEqY9CuUM1ozZtSWDcYO15SGjKEdf3SV5+TLy8kVE+zjxey1KSb50OeMzX94gz0s+eP8S3/nAcYx1fPK5y3z2pZdpjvp87/WvUm69Qb83z3OPpJw52mI8Lrh+eZfB7pgHDvZYbB1lsRUFcAgKFHXSPNApbOnBKAzeAPZ4RI6gPFFXHquE+lTuLEz69sM+JhPAZWjIrvJkNfBUgokhKe+AEkmJDws1khsppPXwXIFvLbIFwhrvPQnfeymFIwnBuyzGqGwAWJzyHK96T8UIhyQjJpMpEkfD5iQ281r/2QBhcuzwzlCPb7Xd1gDmnB+XZjKDyUpMYcBYnLMYY8lLQ24EubEUpUVJS2kMWIuzBpOXlOMCOQ6kVuf5QUVhyDLDuD9kdPkqw7VzpKvLzElDu6U4JWF7kHFtJ2Nrtsm4PY+KFZsKzg/7lMZy1AjakaTpJMqUFMMx0hTo8Zj4Bn/e4ekIOZCPC/LCkBuLzUrYzVA7I/QoJ3Ze5b+fGc5s5GS54WQeMYg7GONYH1/mwvVd2sMdNq9uMNxcYzAWbG8P2RzmDIYFlzaGbG8OWerEZEVJFdoF3wevOR+WugAo1UnWJuoFrkqw12KDrn65nj40vU0Aqmk1/Xrnk5MI3yvJQN+kbURovv4az+J0WDkRQ/R0ECs8fyzMMQraX2UYZBLhQvuSlwTyOTsrBaXQKIz3Xl0ZZk/mCJOh7oxV+5bbbQ1gjUjTaEY0ZhqkZZO4myKTGBnFxElMu4wwRvtQ0zga0tBIU2SSI4uSpNeiudgmmm+iGzEojYo0nU7K3FyDhc4KSwuPsVKcJF2cpbh0hv5wjd5Y8r62ZiuVtJOMtd0RG0qTJppHjs4hTMlxtuieuURkCsq4wfbJ96BsTq/YplEOQiTky/eZTNiOZxjLFLOwStLtESWaaLZJemQe1cjQs4p4fAW7m3F3p+C7Hlghs4LDyx0KCzjLPcsJzQd6NPKIh7ZPsNJv0WnNsHVilWSlQ5EbjrdjslHB8aUWs+00POwgp4NIN6kKVo3XTshJVxFV+Fcl36emFUkfxtV1vwAmFQ3C73UqdKwKAlV1Uiick/VaIgBiRXEQ1ALWkxuhbiYITftu4vUJCJVEE76Xk+6CuOm9Oxlh8CGk93QMOIicATf2+5ASJ1KcNBgncKpknN+6Xsg7RNab2zcdwP7RP/pH/PzP/zw/8zM/w8c+9jEAxuMxf+fv/B1++7d/myzL+MhHPsK/+lf/iuXl5a9r352GpttNaC+1aEcd0rk2stFAxCkNlzBLjDa6TuKnwtJqF8imRQKNxS7dAzOo2S5Ru4FTEVFsmZtrsm9k2N+Z4fDhuznS1eQX3mT4zGcZrl1hYd9+fuie+6Dd5ZVixDMbuwyc5kCvwYcfXCG1Od3XnqbzwtNYobh+8EHWjz9CYjJ6W6/S7p8PDcJBmSHusd05yXoyT7ORMDc7Q5rExEsdGvftQ+9T6EVFMjgD5hrp7H4OHz5KIWMGxjEwnnz6+OEmf+HAItqWNPJZ0vI+RrpB1DnM/nQOJQQNJYgFtGLlp3IHZrqqQr/pVqKqmkfF2/KgVTHVcXgO1lTI51uIwCCxlVROrdQarJaZnlK0COFmNSoN8OPOguZWxc/yGTA7GTBSdw1M6YtJX0n1xFxDFDhhwhTIMgMcLmpg0y5OSAoryMKpJNIiwwDkpMxIyrEvCEQNnIoxzpGpFsY5Rib9uu7Xt2N3NPFvbt9UAHv66af51//6X/PQQw/tWf6zP/uz/M7v/A7/6T/9J3q9Hj/90z/NX/yLf5HPfe5zX9f+pfRaXjrxnC4VTfI0SgoSrSikpDCOHOv/iFJhhC/xi6oKmWoQDleWCGtJIkmroWm2U6L5WdR8A7l9HZtnmJ1t0vkZZlWBTkoulCWmyMmdIxYJcw1JwyoSMuLhNqXUoDWmO4+xY2zRwZUNnxqKY6TSiLhN3uoxSmbRseeoKSl8lbTdQNmWf4+2QJiMTuSgG1GohKvDgsHAT/fpppL9SqOQOKvAtkAkdKKEQglfhWxEpFoRKUEc1Vql4YpWlcUQek2TWKdCSDetfV95VwQZZzE9QFbUZJGKIvFWPlmwWntM1AUOJ/Ye92vXRt2UFxbWrHNwdpJjq0JiF1aWnvNlnfPk2eqYIVT1uwvvjUkRw0l8Q7u8dR7YHbu5fdMArN/v81f+yl/hN3/zN/mH//Af1su3t7f5N//m3/Dv//2/53u+53sA+K3f+i3uvfdePv/5z/O+973vf/kYeWEwUhF1mqSig9KOcvM6cjyg15bcPbvCUCScWh9ycTNDOMuMk2jRIsmhm/ZoLcwgIk3+5qsUm1u4qMVdrX3MHp1DCccbG2Pe3BwzM0o4cM+76Rw+RpwqKDPs1nXm810eLrfJnGJxWzNrYiJXosYb6HaK1gnz3ZSkm1CWkktbC5x2Ba1IcmyuzWI7ITcxa0PNheGITqIoraMVKSLboDF/EtVapdFq0prpoHWEFJrG5nkSoRiINgPdQTqBzkfYYsOLOrZmoNVGGkt75yoMz6HTBs2FFeJ2B2kV0sW4oBg/oU7YqSSTuAEYwjIxRYkQAtxERd8FSqxyJdK6QOWSTDeD13bDYI+w90l4OrVcYsEZqiSYnWpt8jWFOuitIdkvl15oUVqsVH6eIw4hI19wEEFWJ3ii1V6cIGwXtP9tichLlIPYed3G3NzCXkgRhve+je2/Efu1X/s1/vf//X/nypUrPPzww/yLf/EveOyxx2667osvvsgv/MIv8Mwzz3D27Fl+9Vd/lb/9t//2N3zO/yv2TQOwv/E3/gY/+IM/yIc//OE9APbMM89QFAUf/vCH62X33HMPhw4d4qmnnvq6AGxUWEoliWY6pGmG1GDWr2BUxOyRHjPzCVnU5Pr2mCtbI8alRZDSVy06VvFgc4aFlTncOGP3tecZbXwetbKfBz78F4jvOsHZzRG/++oap9YG3LeQsPLg++l1NVw/B2e+gtneZhnFrPBhk9w0yLUQLpU5otOAtEk622RxNmUri/lMvMzzLmZRx7QW5lhcaZNt51x5Y4czGwPaiWZUWpqJJnJN0sX7UDg6acRsMyGWjtndiyyunUY4w7B7lGGvi3AS3R9it69DFCM6i9BdQg536Gy/QfPqGUR7lqglUU0NIsKhITQ0i5qL7z2gKQirwWBShKyG3U5VGisag5DgjKcp2NKLD6qkBoLaQrvSW6yKAJk+B9+wLYVnwVuhMAQBQjGV6KeqAUyBn5BBBRaMc5TS+1raGSJrEBgkGolkQiAJ10H7TgVhS0TWR5ZjIMygdFAUt7AKSUUY/sa3/3rtP/yH/8BHP/pRfuM3foPHH3+cj33sY3zkIx/h1VdfZWlp6S3rD4dDjh07xo/92I/xsz/7s9/4yX4d9k0BsN/+7d/my1/+Mk8//fRbXrty5QpxHDMzM7Nn+fLyMleuXLnp/rIsI8uy+vedHT9Q1NowylQIL4LnHLYoEMairCFSQalC+CEOWWEYlLBbenXRAulnKwJ2OKLc3ES2uzSwtNJqYjfk1pE7xThqMI4TUAnOSihBiZKG8FQDW5TYvMDhuUeljkHHKONQ2QiV+zxSoVJyFTESMQMbMQ4aWpVCQ1ZahDAUSmB0EqRUNKmIMMLRsIJxViBtiU0zVDH24VE2wgxHuNgijENIT5h14xFuZxuBgsEAmgOIUoga4c7eA1PAjf7PW9ywiYkQUk4BSA0CQQv/rX7W1MZ/yqt71/xa61WtSlOnerPzrsqXQob1Rejl8m1O0w5K1bbkqvdXvbcpj3Hyjr997Z/9s3/GT/3UT/GTP/mTAPzGb/wGv/M7v8O//bf/lr/7d//uW9Z/73vfy3vf+16Am77+zbB3HMDOnz/Pz/zMz/AHf/AHpOk7k+T85V/+ZX7pl37pLcsHecnQFuTDMeV4DNLr3gulEXlR5ztMYcjHBVlu2ennXNOS3GX0+2OK4QjXH5NtjxhtjnHdDJP76TqzqeR9h3ocm29SFiVfOLXJn5SGNM/pZCtEcoaVbJ3DoyskJsNZizMGIxRX2/u42l4FJ5h58Rzdp1+jTBocPXic2cP7KIzj1QvbfOXUBnGkWO6kHJptsj0uOb89ZmOQI4Uf5CAFdFLNdjMmkvDauqC81kaWBavrV9gXXSIyOfm1S1xfv4xsdYgah9ALkmLXsP3SFYZffg3dbtE5u0s6N4deWqXxrkfRiytTeSr/sNpqZFrgaHlPy1IN4RFVpQ/P5/JKpb7yaJ1DWGouGRW3y01r24ejTZFgJ9ggJjUEqn2E/FMl0yOoK5FyakKRV7RWVNXRetxboEUoR131lGGYG3hNMl3l75wXXRQ4lMmRzk+0KlBY3Qpn48PncXTrAExK8bYqidW21Yd/ZUmSkCTJW9bP85xnnnmGn//5n5/ah+TDH/4wTz311Dd8Hu+0veMA9swzz3Dt2jUeeeSRepkxhk9/+tP8y3/5L/m93/s98jxna2trjxd29epVVlZWbrrPn//5n+ejH/1o/fvOzg4HDx5kmBlGpqAYZhTjsQcvKRGqROUFzhpwFlN6YcNxZtiOFShB6cb0B2OK0Rg7GDPeHjPeHCNmMmxWIJxhLlU8fqiHQfDlM5v8Hy9c442rfWY6EfsWVmnGggfykpmtN+kWu/Wnf65izrd7vNg8CeOMQy98gn3P/gnJ3AxHfvwvMfueuzi3lfP/fW2dP3l9k5OrHf5fHzzMu4/M8ur1AafWBlzaHO1xHjqNiJ1xiZKCy2uCc1c7yHzMh8s3OJK/RlqOGV3eYvv6DnJmnsax9xDfLcn6JZdevMLGp18jbUYsnr5Aa7ZB4+77UIdPoBZX6mOABzATSK2KoLaKm9LNJ3gy1foBwBxe9dZ5ueY9Ict08txNVSyFDqAB9i3P5g2emxC+GggheHQTKWpT4Kzy4oYqiDLaAFDWz3oUzqtuyKmEvwjhssLVIGzwaq/SGWSZI80Ii6LQLXLlH/QKRzJ1C1uJ3qEq5MGDB/cs/8Vf/EX+wT/4B29Zf21tDWPMW5gBy8vLvPLKK9/webzT9o4D2Ic+9CGef/75Pct+8id/knvuuYef+7mf4+DBg0RRxCc+8Ql+9Ed/FIBXX32Vc+fO8f73v/+m+/xanxLTonr+4aie+OqFt/7BRf21t81FBOUFIcUeikBUZGjrS+qx8FOyldJY7SceFTolUyljV+4BsEynlDpBaIeLIkQUobQisgVxNiAuChJniLQgFpakHBNnfaJijMLWI+Kq3FNEpY7gpZhRGnSMtBItHVo4nI4oogYySkmkDpdBIFXoFdW+wim19oocX7MiOP1DnVn6U2ziwU18KqYKA9w0YV9t+aftfa8KxfS+wteUQ3fjcSadlaKGwwmdQ+45Py/JI+p7aFIxnVRFpw8zUee/vez8+fN0u93695s9V7eTveMA1ul0eOCBB/Ysa7VazM/P18v/2l/7a3z0ox9lbm6ObrfL3/ybf5P3v//9X1cCH7xX0ioidKyRpUZqhYwUQmlkFDhWYfCpjhQxgk4zYrGb0rOOpotRJkKmJelsislbpHMNVOI9A7u9xei1FynXrzMbz/KRY4d4312LjB3sWjA4RLqfc21FbHKvZWUdRir63RXazZS4EbH0+HvYf/cqWlhkMWD3s39ApJp8YO4AJ1ZW6Jkhs+eeY3B6F1SXBX2AYq6NlhBJr6G1rMYcUjskGM4tJiy1Z3HWcqwY0MsN2hq2jyX0xwm62WTm0CG6kcB0Nfr+FeaLu4k6bdrHjpEszKMXlonnZuvWocqE8PrzDq92WvVC+pT7dAgXAk7nux/AbyfxrHwR5GzAP+xuyvMC/JizKfZDLZDIFBzWo9yYAhvvdWGCnLOUOOlbs4SzYHLPJRNBy0xKH1aGHkdlCs++1wlWh+1sicpzf2yV4GSMEBKnE0wYmhsBCj8rQZYlOHNLeyHfqSpkt9vdA2BfyxYWFlBKcfXq1T3L/7RI6Vth3xIm/q/+6q8ipeRHf/RH9xBZv15rJ5qm1OhII4MemFeW0Ig4qnk+Qkl0pIiAdiNivhXTdYZmHqEyDTYi6aW4MieeSVFxqFrt7jB+6VmyN19j5sT9PPndd6H37+fCTs6LawN2M4Ntr3KpXMLhMMZSWP+5H0cR7VjT0IKFQw+y0n0XbnuD3c/8PoNnv4SeX+K9TyyT3LNEefkCw8+8zPDM67jFY8zdu4CYWSBWkkakiAQctBn3mF0armCxtUhX9zBIDpc53SL4A2qZoVoijhRqLqUTAe2I1t1LmPQosjtHfPe7UYv7w1i1nr+QVeuN/6UOkUJJD/DgVRNMCVGkI/Qd+unZIsg5+92oILsV1FQxIWwMua9qErcNxNjqoFNOlRNez2uPk+Xwuvtl7sFLJ0HN1dbj25xUWKWxQu5JzisXtKCt8ax6FYMQyMwPFXGAjSVSeQVXpxMMiR8IYjJkmDwuyhHCluTFrRM0rKSu3872X4/Fccx73vMePvGJT/AjP/IjAFhr+cQnPsFP//RPf+Mn8g7bLQGwT37yk3t+T9OUX/u1X+PXfu3X3tZ+rQNbz0sDQp6jnqE2va51k6+gD1at66zDFtYPBSkNLiR9hZTItIlsd31hoL8D69fRg4K0P6YsLCOhGRJTIjDOS/cIB0mRkZYDYiUYxS2uRQ1kLnA6Rba7yDiFwRB77TpuewchFarVQaQNrJBergWLEl49tCxzRDlG2gwtdoh9QEkhMrZkhEGwhWLbQSIEY4ufNm0dxaik6GcoOUbsDnDpLiK1iLQDUeKvAV+rzlil9vf+XqHKRLBQTBaLGwL0UAGcBF1TwVcNlnbqSJNt6/OqlSrqA9feWrVNlTXYW0etTqraTnlJ61qbTNzw7kIBoEojML1tAF+hcMJi96hzfHPtnUrifz320Y9+lJ/4iZ/g0Ucf5bHHHuNjH/sYg8Ggrkr+1b/6V9m/fz+//Mu/DPjE/0svvVT/fPHiRb7yla/Qbrc5ceLEN3zuf5rd1r2Qw7xkXJSUeYkpSl8FdA6hLbIoqSRVysKQjwrGhWUwKtgeFuAKxuOCMiuww5zBtQG7F3ZoyF26gwxhSlS3S+OR7yC+60HyjW02PvMU5W6fPFIspRFzSnGmtY/TvWMMVaN+7iJbsrB7lgP9c1gkLzUO8PFklbZ2vH/+Lu49eJhyp8/as68x/O+fI5nrMPvAUTr3PsSGSdkpmlzbyfxUHusfKJVd5/D4DMIMYcvQWjNkKM6uHuSr+w+RyYjL45Kr2TrtNKIl55htJpjtgo2vXqT/hVeI2g1mTq3TmO8R7ztI530fJF5NQr5HBs75lNV5xL1Zw3pYR1VhxAX5GRH4WaKeBoQA5yRC+BF2xoUqYwA5Lxlt/IBaCJ5bkM2psdL5tiJrqMDEST8Ot8RPOpIVmyu8ARWkdKrBLBXw2cRXEm0AfT/GSvppSM43eWuThfcZGs8DaJUqxUlLSYSzlmH0bSqyFewv/+W/zPXr1/mFX/gFrly5wrve9S5+93d/t07snzt3Dikn1+DSpUu8+93vrn//lV/5FX7lV36FJ5988i1OzDtltzWAjQvj2filwRUGa12VrEGXpv7UtqWlyA15bhhlJf2sRLuSLC+xRYnJCsZbIwZXB9AZYUa5F8JrtEhO3o8TiuKZL7H7336P4Wuvkcw2mN3XRTQSLs2P2XKLbMWiHn2V2Bx9/QJLV7/CyErOyJzfk5KFmRbHnzjEIw8uMT51hp3/+mmu/v6n6D1wN7Pvf4zmu96D3sgYntphazcnLy2DrMRay9J4i2H/KmmxAxc2Sd68jrOKqw88wfOtEwx1ysZ2xubOkJlmxN3LbXZLQTEouXJ6nc0vnyVtRpRra3RmGzTv3qFx74PEK6tUkjUugMZUapvpYR5VrkzUwDDxfp0Ag+fWSRcE9KoagPAMfV/lE0FtP0z/IQyZrcBJAEpNnKZqH9aALer9eaCTk6ohIU/kRGggtyHMNWBCFVLH2KjhwTpUTT2lIqi6Cuf7LE1O7e05H5KWUROjIqyDnBhj3S2tQn6rmPg//dM//TVDxhtB6ciRI3u4crfCbmsA8yPVNKrZRMk2zpSYPIfSYvp9zOZ1bDxE5QPSWGKEv7mL0pIDWdRi3FnAiRF61dA0TZLFecxwyPj8BfIoZacxQ64blKWC+XnSA/tJOhHxXAOZaFpa+NFm4zFxMyVuNUhsQdt50URhBB09YFVv0ytLTDZmbWQoCoeJFEk7QqSavhUwdgyGGcnWOr3NIUWUECctrIyRrsH6uEvhBFlLMpqT5E6RNdoUzifEtZa0Uk0z1QjpZYQyJP12j+2FVfKmpj3XQ8+mqM4sVut6mnbdPTQVbk1ka8QeWecb/gp1gl1UkjWCqZzadOgnAkhM/LnKyasbsae7APaUiQMP7AYXUYT7wId+00esVqzyaG6vIKOzXlKnJp3dKHEUkDM0mAvnkKHhvcoBSnHrHlb1NnNgb2fbP8t2WwOYkoKo1abZOkzbzTG6fI3+G29SjsZY9SquzCjjJo1sgX3zS/SdprSOzUFOoQXX5o9xpXeExBm6945YynPsaMD4/Fn6zz/LtdYiz+57iMvtZY4ozfuf/BCrMkeTEbkhwpUcObdB8doXGWeG7olDzKwcRwtHdGEXsz1AlJaHW2c50NjBZl3GVxt8stEk3Ryyuthm+V37GK/M8erY0T8/QFy8wOpzT7F67TL28AnKRz+AnZ1nuO74vFCYLKMzAzN3+Yd+S3YZ4XNm892UwwstmrEijjWbo5K+anDqvvdwXi/RaUYU+7vM9xLm53sstnu+mid947YTag/B07ftBGmbikPFJIPlRBha67wskK65Sm4CDpUmvnM1YdQx1SwtfA3SqThQHSZh4CRPJvy8SCmnvD8/6VEFoq8AhK3ycF47zCKR0voZkhDamfzO/XShzJ+fVDidBm+vyqxVDdwiVDALdJl5YUQZea9M3qQV6o7dUrutAUwK0GlK3JgnUS3ynSHFuKDYGSDVFZQdY+KUaOY+Zmf2E4mYjX7OTj8Dp9ltLbK9OkM7Eiy1BAspjM+e5dLzX2H76S9xqXeAZ7fneWNOkx3s8h0P3cfsUhM52kbuXINsxOLaNub6aYp+n4VVwVK6hFCKdcasD3MoCw5FaxyP+/SLGZ7ZOc7r14fMjgpP5zg0Q9Ftc7lwXNrImL+2yV3nX2Pm0pswk+LaErfY5mXrOLUt2JUlqzMNDs03UVIwXB9SrA3AOjqNiJWZlERLdCQZFIYdGXFt31EuRov0GhG91S6ymxA3JGWqfWiGwI9iDGyp+iHeWwHcw3uaUo+o3Cgl5STkmwKuisTq6RdyKhYN+6hDWCYUvmC1IydlOB8X8mUuHDN4gFMqh44g5yO8r1fPoRRTIbEzPlR0DidTnNI1WFWy1zaEqSKAnTAZSIWUvpoaiVsHYN+qEPLPut3mABbyHTIMcZAysPHF5EkQfj0lvXdQ/x1FCEGF8HMBpQijmf1wEKW9pM6huRS11GauFXN9UCLXx4isQA4cohA42UQvLRB1mqgkotjeRkhFGTcwB474kr/K0bIgjgRzDNlXrtOwA4q0xVp3H9vtRVwYuhHHirgRE7cSbBJRSg8bnUhwqC0ZxpI0BmMtxgk6ieLwXAPpLAtyyNzuFlprIj2HiTsIAb1GxEqvQTfVLLZjFpoRvUQQaRXivYlHtLcGOPm5rja+5RWAG5e7vYtrDtekOaiqInLDlnsY/9PVwSq0rVRWq9ech6sqRK1ajqpwds9j67yqarUrK1XI38mgdVadZQhlRVhRCIxQCBGFfKEEJ+ptboXdkZS+ud3WAKaEQErpKQ7Ks8tlNaEoTClyShJpSRpJCqHQcpJn0VIQa+mbvqVviRFa+0nfnZj9yy0WH1zCHNvPtUHO05f6bJ8OssLGopzi/niZ9z32CB2XYXZ36L/+BhbJcOk4xYceR1iDvPwy8fVTaKW4z13h2DBjKGIuLuzn7MJduKSBmVmkl2q63ZTOSo9ONEs236KvJdY5DrUFxw8qnHG8OXK82i8okRyZaXD06CxRmaNOPYc88xJllLAhHmY3PYEQghOLLY7ON+nEiiOzCbMNTSKhGQmcBCEkUvqslJgCKSEm/CERvCqf9VZ1PqnW2LqpVE4VagagrPJloQeykuWaqEcEry3kmqZ5ZcKaevn0sapRap68qsI8SDEBoWmUrAZ5ON9sb3UDh/CVTAsgiKT/ojqf4JUWMsZoHd6Dr7Rm35DGwx17J+22BrDKg0KK4H1VX1NeWODPaCXR7HXD67xNkHYGv72MFDpRtNsx86ttGod6fPniLp84tcUba6M6EtFCMDffIVpVdFTB7muvMzi1RukkxcGHMCfu9yO9zCaqf5EIS4s+Ks9Yj2Y43TnMpcZBIqXopZo0UqSJJukkJGUT00xCjx7MxHAwlSgnGazBC1uGzDlmGxH3LrdJ8hHZm33yrbOMdYPB0lE2jUVpxXw7oRkpWpFgfydiJvENz9ON1dVkamBCe2IKK6YAyb9YJb3fQr6YWMUPE2Ky/nR7UQCxSXg6yW/5zfe2dVFN4EZ5DXvnfK+jsz4EFjpQMKaOIKgbz4W1Pvx0FrTCyshr7VsojT8RxZSckINKiNFITTG9X+fD1Ftld0LIm9ttDWBQFc38w+icwxmLM85/eabrW0u7YZlzDuMCsRWJrW7m3FCMSsTGDoPX3qAclahMcayZ0FhtY5wjt+G4Ebyym3MBR6TmiFdPYJ3gquxw9foQ4QyLZYO55iqRLZi1I9rjjNLkZEnJWFtUkdPOB/QoaG9cwm3tkG17Ood0Hihtv89w4yyqGJNmMQfHCQWS1pV1skGELTPY2kDFGhXHKK0QwlMF1vs5a87RiRUax7jUxBI6GrwoqwwqqyGMqm72G276uq1ouim7GqU2SX5RhV22TppP6Uq4+j+qWl89jaj6W+49KggPImJq0d47IBQLgrfk8ARn56Y8yOA5IRU4GaSrqQFUTRU4jZ0cpsrrS0IPagBTL8Nd3PSe/GbYnSrkze22B7D6U1gYXGkwhcHk/rstDVYZD2bhmXEVG984SuMojKNQzjPpUZRGkO0WDNdHZIPzjDc/jmo2SY6d5ENPfghWl+kXjrWxJSsdF69t8V8u5BS54t6Fkzz07geRUvDCmuPZl9ZwOA405lmen6FTDrhv/SUO76wzijW7asyWy4mLLZZ3XuJgdh23uU155jw7O32Y6aOtRSuBuXyZjS98BrG7SW92hvcvznsv5I0ttq9tIXG052Jasw1c2kInEUoI+qXlzNqA67sZ3VSzPmqz1EmYjQUne4rZOFT4as9FQJh0vVckaxpkoM5fV3ywqZyWg8BWF/Xvfs+u7q8MeX//SggbxXST9o0ZuZpmMTmlCviENXUzpcCDV2Yc1npgiqUMqT5dqzKYEDY6qnW8D2icH9dXHbI6AyUckXBBAcMTnXMz+sbv2zv2jthtDWD141G3EFmcdZ6Rb20YnzbRhQpr196Xrb+80KATwk9ezi3luMRkfcr+EISg12qxL4XWYpPNzNIYGIaF49JGzOm+op85uksznFxcQknJ+sY1zm9e95p5y21s2mJU7HDYRZisoHSFH99WGlw2prm7xszgAtnWiO2dPvnuGDUuiJ13HOxwwPjSJcTmddp2SK9rEUqydf0KW6cugxA0o/2o5RVUHHnlieCBbQ0LLm+PGeYRc+0EqRTSSUoTqnehSugCqohpdJlctfoaChcGzrrKKwsy1GKaguArdXXunemapl9Yp82nK5Z7/7jBBRJTy26Sa6tbx1y9yFoog0JJrT8hZK0E5GxNFgl0DL+dCV/VkQSh2k3wYoRFOgOuRLnyf3aLvmMm3mYI+TWVR25zu70BTE41HgMIUcvGyEghI42LNFL5HJcQgTumJVqrIBbo96GcQVpQGLQW6ESh2h0ahw6iuj2SxQXyi2dxgy1yA7qExAoWRhEnFxKGtkmaaC5uj5ECeqrgfUs+QxR3JTpWaJUymN3HVWUYiphFmXF/doGFcodeZIiaKbawJN0GQkloxhiB7yyYmSe+9yFkfxsVlZgyR5SGaH6BTnMBIxSbczNcjnqUusm2aIIQJEqy2k2JlaSbag71EhbbEb1YEKuJh1Tl6EUAJm70wKrwiwn01FhSSUszNaW7DusCRNyYUIe9ebWp5H61cyemcmRC1vmtybaA1JPKo3PgSiReCFI4gRIeOGXYxkxOGh2OraytvULpFKoWTpxwzPB/BhySMuiY5SL+02/Qd9DuVCFvbrc1gEVKoOXk00UoiYo1NtE+hEpjRBIjI+2bYRFEkSRJNGmsiCKFVqFvz5XoskC7nCgRxK2Y9PAq89//ERonTpJfOEv/mc9TXL8GkSJOImKtOXrwfpon38co7XB5Z8wLl3cQzvKe9pgfOAlOCE45xVmnEa7NeuNeBivHSLNdTlx/nUd2TxFj6aUlcaOFUApbliTDjGymwUAIjHHoA0doLC+iywxOv0DxyhehzEmP3Uf32H2MZcQbm47nthwozYKaZQZBM5bcs9JBAO1IcqgXMZMqNJaGMFD7IWBxU2FcsDofpnDqBlVVN8lNOTGliY/PE0nn6ik/E/5VtWO35zAVOLnQduRD0kl6XwiFrI5vTd1BgPLUhiqUFGWJEAohI6yQYQSbByjjfMXR4cUao0DalaZAmgInQOkGTnlSq2Qi8+0clM63QZVCYJVjJG9dDqzqcHg723872m0NYLLi6tShT8ULE1MVSU8RkIElrqWnVUQqML6ru3Mq3BRaImONajWJV1dJDh3G7G5Rbm+TXbqATiKidoKINO2lQ5iGJGvFrA8ydseeZtHoGA41LUjJZu64Uvi8SxF1MLKLVIq2KFkptrzcTxwjdIxKLbrhReaKWPtCgzGQNlCzXTQGs3aB0oIwDtlqkexbxciEkRlzdTdHSkGLiBkcWniuWBopWpFkNlX0EglWeKnlIIVaYxKw11Wazj1NJeqnZjo6MRWeMxmlBm6Sr7+R9eWml4kpoKwIq1OrETJoQkxC1vomkCBUyMuFCqMQyKBz772qSWhbtcsqfCuQrHJ7tqx7KKuhIlJQA1ilXVZJbhvnMHdoFN9yu60BrDCWUiW41hwuKjHRdfKxpejnONfHFA6XpHSaBffMN8ijBru9hP648JhlLM9f2CKS8GbsaGtHOoCFI/fQa/cY9RZ4blcyfH2Ddl+zfPJ+equryEij0hikpKCB+uqzKKHZ11kgWl5CEjO/fZXti2/ijEXaFnO2CWmDxtFjxCsrJE4h+yP6lzbRvR7N1WPE8wuoLCdd3PXDQWSD0emXcWdOIfetIo4fx8UJ16IZLrSOYYqcQ/Eyh2WDMZp+kbEzKohdSVJcY35jRNRo0Nx/mKS9QKR8M/Ww9A9whAxMdoWUlYghN4DLDWGeY6ryWL2q6nKdCEHaNJ/Mrx/Ab9rDq9apwVGEOLZSHmMqkg3eWMC6SdVU1Cn/m1r1AYVv1NZiSqyxWkdIUJpKlaM6XB3MuokahnQelK1zZC7/X7pP3wm7M9j25nZ7A1hpKVWKnZnFNSQmuUw2MOSbI7LtMeLqLiJNmTucc3BfB9luB00wy/ao4PdfWeMzb25hnSNWPsdwoKP58/e/j6OLCae2Cj71xi6vnrrMA/OaH3nPB5nv+qG46AjnHPlTX0T9j98n2u1z8skneO9Dh5GRZviJq1z/4z/BjscopVmVCj2/wOxyi/bCMUwZMdjss3XqCumRBsnS3Yj77iMyJXE+9nyl115j+MlPwdo6+tHHEftWsEnKuWSRT/ceIi8NjzeX6ck2hYOtvM96P6dVDEhHL7MvO0M0M08810I3VgBB6Ry7ha+6tbX2Dkz1cASMqcNIBxNvZ5I7qsI1h6dKWKEQDiSmbnieIICbTO6esum2pFoDLNQB9kzxZhqsJltPg5dfhyl1DDelMB7OF4cUMrT/TIOp8MKIIgIEQk5JbVffnEWZzIsogidrOCjtratC3uGB3dxuawCz4KWDdQKR9nQA46cQeSuRVhBZSy9RqDQKn7xhCo2DrUFOYZ3XjZeCRqIp2z2i5RlwfXbtgPVBzs5MTNnuwVwj5IMizzNTEXJ3B7W1RTMfMh85ROQwZc7OzgAzHiG1JFWSqBHTLDNawlBgGRqLKR3GKcq4SdHooZwhbvhpOCqKEbvbiPVriJ0tyDJcWZKj2I3aZNIykClj54fhmhpzDHo8IBlsEMWayORo6a+XMX49H0pNQsPJ7X1jpn3a3A0vV75PCCOtX1YFmrVHxV7AesvmtU223Lu06tL8nzyEN3t5KudWn0N9mEBTDSTm6VBWTH35UHiigVYdRt5sruUdu6V2ewOYdYH+UBETZaBRuPAB66DwxNa9Nrk1K1F4Z714oCnDdwvdhubxQ10O9SISLXnh6pDX1kbe80AhnGNe9Vj9zidI8iG61WDrqT8JxHPJ3Hc/6R9gpfz8SaUwWxtsf+L3wZSk+/aRfN+fo9+a5dldxfYL11hqa+5bajDXiLFSV2+U4tJFBp/9FHS6LCVdPjg3SyEjlB3zzPlNrBMkWvEdR+dojjX7zjVQuUYpiM2IKN/BAdp68FJaoUipbwFnJuFW8Fgm8jPCv24nGamqZafqOawuJciAWVPJfqZyY3vC06kfpzPUbyGzgsBSDebwKhFyCnY9CDmhECqEgTUpN/wXyKuVJI91EosLXp9vMK8EfupaqJs6uoqpNf4rZ1XfOhqFCgOX3s723452WwOYsYHDhfRj4xE+3RJY+M46nDTYirEI4Y52ddne34wCay3OgjHWE1ytY7ah+e4TM1jT5aWrA/77S+uc3RqHqV0OKeCJg7Oc/P7vZz6ybH/+KTY+8Ye4smT2iSdY+sEfQKapb1lRmnJjg80/+Di7zzxNvLTE3Ed+gPaDD7OzmfHUS5s8/8ZFHljtsNjZx2w7xkmNcwJnLfnZM+SXLiOiiNX3vJt7n/gOimbMp6+M+OTFEQjFo4d6PH5kkWSU0Bq20ZsapQSxGZKON6eIpQJEgnMRCF2DVsVmnwBI8HpE4GkF1VSnIpAh5JrybPbISNfM+MkHhadEVEqu1f5hT5vRnmOzd3+BD2ZD36P3myaDR5C6cqwQTP62BD2wqhrqhMAKzxNz1LcCAmraxbQz54QHMCtjf8wquR/fOgDzx3w7IeQ7eDJ/huy2BrC9tueWq8mqeybu3HRdn9NwwWNzU0lmhSPxmp+krsQYw7j0ZFlrPIDlQlO02hQRlCrC5jmuLH3vXLODaDR8uCk15SjzOvXZGFuUlDohb3bJh0Myt01WWArjpZCnHyHngNIPrBCmJC5GtF1G6SIiKzClAOmIbUlXlMSiRAs75SoQvKoq1xTyRPW1cFPgNbkqey+S27uspkVMh31TebI9f5qv9+lxNwkvq/1OB3d/ynFu3FZM/1AFpaIGvMkR9u5zAqd7svr/q2/kjn2T7bYGMK3CoAMxyZLUhS0h/Og/FUrqzkxm/1WeiKs8NfaEnlXfW7m5wfZzX6G4doWkOccH5o/w4L6FGuxwfljCp09tobAcSBc58t0fRjjLm519nH15E6P6dQjZKEYc23eCfd/XoB+1eKYfceVLFwE4MZ9yYj5hXzdhPnHIcgxl7oeMGEe6f4n2iWPoZhMZSXae+ypGafZ39vO9y/tBOFbWX4cLm5hihLh+DlGUGAu5buCSGRzU+S+lImKhqFufKy+lhs5JYv1PNcGkwrhn+UT7HlHll5xPyNdgaZmGiBpoQyHAUalLTB0q7HtyjvXWe3624WbwHpPY6ys6f38oOblnpoGqgmq/PJQYnKlFGqUtfU4sG/5PLs47ZxUN6O1s/+1otzeAiQk7+aY9wEIEmRimkrAhjABfIHMBvELlCudC3xsUmxtsffaz9F98keaDD/LEXzpCcnSxPoRxjs+c3ua/PH+d3XHJR04s88Ajd6OF4PTLm/y3l7YYFRYV5H2Wmpr/+z0nePDQQ4y2C57+yiafe/EiJ5aa/D/eu8LD+zsoEby+cowoc1zptf7T5WUWPvg+opkeO889x8ZTT2GLggPvfYx7794H1rD7pVcYfOVZjDXIVGNjBRYy1aCMe1gEufEN7LESqBrAqKt61B8F4SJ+jcT65HVXFwL2eE4VeDHR6Kplc0Twju0e5Aie4UROx6mKGHsTIK0PWx9sDxgZW+m7etVYIdwecAJPLXD4+Z7WTvl34WG3eMAVOLQt/Vg2axBlhrAlsuh/jevyztudKuTN7bYGsD26UHt+2Ctc6O//+nPVL39LruWGB7V6doP3pATE+ZhkPKhfNs4RlxlaOJQUlFIzlEn4OUJJiVbeS1PCf89lRF8mDKXAKuVbm7B+DFsmEUoidMWrEvUpFlIxVAlaJWQq9kll66fvJPkIrGVsS5QU1MoNwcOcZteLkDMS02J8e6JA8TUS7dUFCT8HwKnD0Olwvf7upoCRve+pzn9NDrMXJ92eRTfC6N7NqusUKqA37KcKjeu3RnU/hHflJr/XP00dWNwYZ7LnTroldieJf3O7vQEM6kRuPeWvAqzAyJc6DDcNDcMOwHqPzLlJcl9Kn6yVSlLNDIzmF5h78kna992LKwp2nn2W7ae/VB/YCcnC/H5+8MgJxnGD3MLvvb6JA+JI8yPvXg0hjK/qWeu4Nij5j8+vI4Xk8FKHYysz9MbbNF7+MmvPrBEtr9B48F3o+QVKFQXvRXB21/KFswXllmFf8zBHvrNLYgry0TYbX3jaH6fZYOY7PojNc/JLZymvX0UVOVG2SzLewCHquZgyilFxBwhDXMXkgWa6HzKggZMSZOj9ExKwvsCArw/ifM6wAkthvUqqkw6BxFG1CgWNfcAJOwV6QQGCCehNix5Oc15FqJL6M5yMP6omG3mvKwC5s77jAOc9Man9nq0BW4Z9elXean/O+X1Kpu4loXBO4qQFoXHOUkZv48a9Y++I3fYAVn3CeqJiaB8RAqECgCkZilxVojqAWKXAEB7UOtysc2oCPTtH732P+/Dsua9y5T/+J0anTvkcjAShFHNPPMFdjz6Am53jD97Y4vff2KC0jh+4b4nvu3eRpvaa6sKWXOvn/MevXOdTp7dY7aX8pXfv472HZynODNn9/PNsvvw86b0PIo7cRbKYYGQUSJZwYWD5zMWC/q7hA4f3c+Thh4gpyT7zBwy+8hmkhLkPPkH3kfdixyO2syH5lcvIoiDK+zSyrfp64cCJJtY1vRjFlHdVB2Nico28+xJadm5YbsNcRv9BErat23PCsFrpgvdThYJVfXI6NNxbIJjug9wrUuFQzoa/42TwhvcqfZ7K919qqqqmsF5D30ntm5SEAGcQ1fg0oZFSgRCU+HYjEe6lOvQSuj4XG3JnJv72H6v2Z91uawCrwgVjoQyTqIWckpSOFDLVSFfiBjtYTMh5gR0bGq5gthlhnKu7/XupZlwYrvdzBDYwwwUZEa7VRvV6PkkMPsEsJWrcxw00UZmRakFpBXExRu9uobRPFkvpSIqClhnSMUM6xtIoByRFhChHKEqkdBhn6eclo3FJhsJ0ZmBuSNRs0HQZrhiQ0EFGkfcoqgZnwGmFS1KsExSNDlmzh03bWASUOVXLTDU/YJK7uonVMdIkr1Wr2uxBlSpzNAlS69R3HT7eJE68Mf7aE/dNbeOcV8io0/bhxFzV6zipHIt6/RtoszfSM/aEy6JOMdSh4x6PbyK685bzvwlf7ZtlFdXj7Wz/7Wi3N4AJQguNRUpD4QSqFZF0Y6J2g6TXQsYROt8ke/4phNLk/RHFYMxYpRyfvwt9/2GklHQiaGjIjOPN9QHPX971xwgPzD7b4OEnPsSqHTMqHduZobSOwo3YffYLCAELnUO8/8AJjBAsrZ1m97XTZNLSXJqhMd+lWVjeO9pmNR7SsoqDFy8i+il6e5tWR5AcXWa91+bF6yO2y3W6tsvS+76HNB+xfzjgw/0LmPF5VktLg2WUlMTNBDHXRggJrS5Z3CVXjuuHHuKqWqYZQRprWttrEDdhdgUaHZyMcDIK73Hqma68J/z3uiJYTdSGMEk7CCzLaEJ4FTIk6D2p2AYwkVV/YfCSJg++2HtcQoipKh18O1E9rRUtXFCXsHWKTYmp6UeTu8O/KCUOPXmHoa3Jc7uScGzrPTMHTnhuoag+pkKaYSIP5OqWJV2O387te8feAbutAQzhJaD7hUUJiXQCmWpUKyadbdJc6iEjDeUOxekXccYyXt9mvL6LbXfZ98Qyy0dmiWLNQuLoRXBmY8z/8exVvnButzoECMEj+zu865H3MLfQZDsz9AclZVFSvPRFhl/4InLUZ+bBmPtPPoiTivT0ZYZPf5Ycgz55gOTIKomDe7MhJ3WOsAK1phCbEmksjabAJnNciRu8vjXm/HCHg70m7fseIUkUi2e/yokX3kCPdpHlEhKDEAqdRIhOw882bDTJoxajSLG5dIKryQE6dshqeR47WPOpLRVD2mNCbwiXsv5pAmCi0psHpmW5nbUhLBOACnr01G6CA4z0w3anh9jWoFhJ4QSQqVp06hOp1GGFRdqKLBoGibjJ4I9Kx9/nuia3xXSo6nXMAkT7Dn7/s1B1p4N0JS6EmRWI1e+TMnhbk7BZBHkeZW9dM7ckDCp5G9t/O9ptDWDWTtp+jJsqzVuvjW+NRUg7uZmtxRmDLUtc6TWlqjyHDyF9/swYR1EaEq2YbUakkaIZK9aHJfFWxm7hWB+X5KWlS4TqzKGjxPOrNq6BEETlmKiVInEMoyaZayKc9W09RRFybQ7rJIWT7MommZBsyBYDIxnnhsI6kAqhNUopP5hECdx4gL1+Badisrwka8zipMLaCLuTkwvFoLQ4KXEGyuGIYriDKEB2t5EqBh1B0pqIpdd6OlWIVl3lqRu/7msEpugNom7DmYRaokqve9fLY8ZUs3VdkHRQb12Dzp/yRxciNHfLqbhKTAoPYvr93OCRVaEt0yBH7WG5Opx8azuRz7VVJw0Id0uHetwJIW9utzWADfKSYV6SlZZcC1RhcOMSOSookhzdH2EjjUwiVBL5mz80e7vcUoa+R2kdNky6sUJRFI5sVLI8F/Gh47McXWyyvpvz2dfW2BmVGCEwIdl/LJrhgQeepEWBuHYF/ZnfR5qCdlvSu+84hYp5LV3ljF4mLkacHA3Zt3PVA2aaoGLNhurwXHyIy3qGDRNzbqzZcRkLzRgX8nM61kStFC3GZJfPMrpwlVJorrUXuLbvETIVsz7ssfHidaRSzLZjOo0Il+cMzpxn4+Ir6G6b1mBIsrAA7VnYdxLRmgmgMh3aBRPUXpoPnULSWkqc8NVLJUKPo6iqjWEVURGIJx5LHZIGza6qi9IJiVPVyLJpVdeJl+im6BhOTm7bCV5NAEvg6gqjE9KrhwiBdRJTtTSJyqOZBipXtwlNZ+6cExRCYQOIVd7oWN46D+yO3dxuawDLC0NuLIW1lFbiSocoLK6wmLzEjAuctURKIpKoTs660mGNrSkFlvAQSYVDYkpLmRuaSvDASptHDvX4wpub/M5XrvDy5T5RrIgbEVpL5IEeh44fQmhHcvU66SvP+clBD99N+567GUYN1vIVXiwWadJnNn+DxWGG88QwhIABitNqkdfjVUZ5yeYoZ1yUZEFVQwnhPbAkRpUR7tIa+bmr5E6x8cCTXDh8jKFKOLM25MKVHVIteeBAj24zwhUl2bV1+mfOk/RaJE1FXG7D3D7EwgFozQB2Ei7WHk3lpUwl053xz7nwjengHR8VYKue8iMmoSM4X42sNMRqLbFQfKhDz4q+MmViasTZlAviwnBZEY46XUKYhIr+OEJqXOBDOAEmeFl7fKc9bVJu0jdYeV8CLIoibFUFvIW4dTyKCljfzvbfjnZbA1iltFr9bfxzMKXIqiVSKaq2luqTczI3MmwYchzCBUXOQL+gyCmuXCIza8SbhoNthV1po4UlkgVKlnRlzvYwp1Awr2O6C3PoMmPQ7DE0TUYiZShiIq1QLmLcmmWzWEVJkGmCjDRbegYTJWglibUijRVS+KG7Ai+e1xcxmex67OgqotUIgUJ0uhTO5wJnU0nc00Ra0ou9WoPUiqjbIVmcJ+62UTOL0JvzwKWiUHQLQoHTF8RNXZ8pmyT8J6EUbm/Vz1VJ7+kYrNpGiJDjqkCr2teE2TUpB+JBzaPmVCVwOmM3VYIQIkSSMlQuZd3AXt8zhEDSgZgKMV0NnpXqa3W0ygO1qElBFgeoWyincyeEvLnd1gCWRopIT0mnSIGKJDJW6FSjGwkq0gglw6Qi53O6sYTI63+ZKoywJaI0SFcSxYKkoRH9TXY+8wWumQ06K4f5oQffTzG7jBxuIDcvQD7mjIOXLytyJ3lPo8tdjz1M5AxfVUu8MF4klxE0O3RbCdoqrkf3MVg85GtcIVwaiYhCdugITRpJYi0pjaPXjBFCUDi4JHqcjU5SpBn3LsC73u080z/v0M/BipIH5jTHDvlhrZsuYgfQjZTOyWPMrybIZgd98ARiZgGiBNfoUoGHmAYCYPKoVkAFuBvoEYIpUAl5IiooclVDYv0aUuK1YKt9TlQo3LSnV1U+hcAJXa++Jzkf9uyxzp+PFD4B7wFITtzBGooCJcPhK6nWSwhZIT3nDi8/LcO0ISEETmqEs0TGoG0eztUTnXNunRrFHbu53dYAppUMOZhgAt+8rbznoSLtq5BAxdsRFdteyamPpSrs8PkapQQ6UrAzYvzmKfrbZ2kLwX1PfCeN47OwMUIIgxlm9Hcj1rZG7BjFPbMJjdV9RMKxtd3l5a0OpdCsNhMWI4UQmn68zI5bwjo/l9KEMNZYR+J8g7qSAmMdaeyJo9bBJimn1QIjbViaT4gPpyRaIC7lZJdypLCstCLevaQpELzUV/SHAhlFJAtztGaBZhe7chA6i5OAKXg3ogKmG9qO/MvV8imbAhIPZNyAf9V+Jt7RxOsSe5bt8dGm6RBC1RSNG/y4qcNMJKUtVd4seFA3OGz10QRhHkAAIBFPTTwqQ1W08hb98SWFzxNOgWjEDdfkm2h3qpA3t9sawN4ycduBM17qZtKgbSeTuI31w25DhdJYS2ktyiosMtABJDbogpE0SA4fpVV20LPzjM9foNwdQH8dsXYOm49oyAVORAmDOEY5xyt9jRSCkUhZ6TUAWGLAwmCDUkg2RIsdkWIdGGexFiKTM5dtk5RjdmzEBdOg7zRzSQTO58AiJUm0wljHdmZ5aT0nEY7xTp8D+S7KWRpXDcMdQ6EiTLKMiGehKMk3txj2LyObfRQpYjSEKMW1ZiDyXCifH7wxTpl4RaHXoV4uAt3A3RA+Tpj4VVK9Aq7Ka6oAR+zZ/yThdPOwbO9ZTVrAJvuZ9BNUrHyf05uMg8N5OSLP73J79jrJgE2fF/W6/v5Q9XVwCIpbCQpvM4T8NsWv2xvAKu9FVAlO57CFxYXJ3M5YnBTYoqJOWMpx4Sd3x5a8sIwKi1MWgxcddLKkLB1FViJm5+g99iEWFyLG586z+bk/Ib92DUyBKEaAY/bEcf7cwwllq8WLO5r/eqVBIRRHVrs8sn+OxOXMXTpL7+ob9Il5pnGMzXgflToXwHy2xcmNF1kdXuN1N8Mr9ihn6dJVEuwMiRY0Y0WvEaGU4MxOwavXRmhb8KC9zPvsJZIyQ72+wdr6pmfhP/wE+sQsZBn910+zduZ5ok6L9tHLJPMzMLMMR98FM0sAQeHUhbFmVVhp63yQQ2LEpEdQhVyVB2L/cFWTfqi5UiYUR3SdoK+iSiGmAlRn63YfmIajiU2cZR9iVlwyIZVXYg00jarPUZjMJ/Kl8pLjQiBMjijGHtikxqm4Hge3hzZShbbOIoKqhREKKyIvyx3e99jdusfnThL/5nZbA5itexmhimNcxQOzU16YtdgK0IyXmHbGYqyjtJbSOl/LCrkNGwQLiVPiA4doHOpRbPfJLl9m8OprNblVKMnC0hz7ohEujXhlR/HGUJOhWRUJS52ElnX0xIjO8CoRKUqskGGwobdNCJBFzsxwnZX+Ja66ksItsUvKKPMhjhSCSPqkfmwk67nl7GaOKnPuinZZ1es0ihFb1y+zffYaRXsGc2zHA4QxFFvbjK5cwwwaNNoK6waeuV9mASYmOS2mroPnc1baXF751q8x8blqYUAHSkxYVrWXIyq0Cq+ERHjVgl3tb0JmnT6XyZ+Wt6xv/F6cqndfA1hF17AmcLcsCOUBzfgQ0VUFhBvD2OoauMpXtN7jEhIjFM55JVfjHIX7NkWF28huawDTUlJax8awICsMbetYaKfEZYtkZZX42BFkFDE8d4HRlbPYogDn0I0YFUua/evoS6+ipSR3lk0cplScSFI4McdsM+Ls2pD+qCQZSLon72Vmbo7trORqvyC3DteeZXanjyoLRDZHM2qjkTT6ayTnr3t1VKVQB04SZ46Zy1ssv/ksstmkfewQyeICnTWF2BiwdWkDlUru7l2hl2QsZCXXNroMCkN2/TrdC+dojjMaxjFnHNIa5vtXGIyuU5QZ5bggasaIVkIjjbCxoogS3lTzjMR+YpcyUy7RyDp08y6HS0HXFHUyfsK1qoBowsSfBpSa04X3x6pG4UlGMYRZovLkKk/LB1/OVSKBYlIcqCZr18cJyfYq6c7U8tpL8l4itiLGBgUKIZEq8qAlVb2uC14XzgVuWN1+PpUTFDXoei0wz3OTzqLAzw41JdpacnvrWommAttvePtvR7utASxWksxYzm+NUAIOFo6VhQ7ttiW59x6a7/kg6JjdnU+wfeEF7GhIa7lDa6mNiBWN9VO4F9awWcnwwiZb633kyj4++JEf4Mn3nuD8xog/eukab14fcv98xA8/8SH2dTQ7a0Nee3OLzWFO4a6yfO0cDVGiEsVsY5UCSff6G7TOnaIRa9J7HyK+5wma61vs+/LvYj/9NOm+FQ4c+wvMHTtKVmo2zm9y+dnzRIu7fNd9FhF3uTjY4YVzbXaSEQfOvcTdrzxFa7hNvNAhXu4hhcCdv8zmucsIZ2nON0lnW7huG9lpkDZjro1bfDE6zHMSImJmxrM0Bg3uGnb4kVwwW46wQlOqGIdECocKqh2Tth8AOYVQBpxvJVIyqlt6Ku/L54dUnVSPahCb5Kb2aGwJvNcXwExME1KnCgp1pUCAl+fxIE7wqGw1jVsK38FQg50/ulURJgzBlWK6CUFg615MgroF1M3eOJTzFWqs8ekDU2Dy3W/OjX0Tu6NGcXO7rQFMSn/jDQtPkcicQyYRWibobhe9sOLzH3GLYlhihznOOq9SoQUq6yPMiHKY079wjdGlbRoOlrRhdqnFKDdsDgpOXxuw2JnFLa6QrHZwaZ+dQYuN3Yzd/oB8KycyI4QqSJRAAUnWR29cQTcSrzU1s4jMBM3xmN7VizQbgiVyFluanUiwMcoZb47oNGKWzS5N4eiXs+wOx1wrEua3d0jXr9AZbtJJ5+gtOISSbI522dgcAI6klyKTCNKIKFagJEJp1mWLM3KGSMTM2g4N06BrGmRW+FBLTip9PrddJdRvpFWE766iKvjfbyR++h8FBvAwMnl4poeA1BQLJ6nFt5h4XBNKBhPwCnuhBruqajmlcy+CXI+YPireK5Sy5qm5MEC3rjlMrV+fmwieIhUZtwKyAmXv0Ci+1XZbA1glgVOlLbRWKK2QTnmqBCG5nCiSbozVCXEnJWo3kFp59VMpcBbiTkI6k5J0Y6QWYC0zqeLRIz0WWpq5TsKbm2PWMsPVQUGkFbOtGCvnuaiOk5oMrVPutVcQzrFPD0lbMcQJ5/sFm+d3YFCQHj/Jwp8zxJ0GIu8zeuEZ7Po2M/efIJ6fJW04GrOGKIV2O2W5l6LjJu0D+8l4D/18QGM2IlqK0cLRMQnEqfeeDuwjW1lBtNpEs3M0IstcKjm62mVjVNJINStLXbqthMMzMd1mUksCVVn1ul9xGizC/yrkw/YEjM4GZYrKfGejFAotJp5XHQaKvTN/KprGjRONvFXVxklhAZjky6rmbGu8g+iiiXhlyME5BHaKiuGnFVWJ/gKBQwkdaBReC6ww/lpIJz39QPjxfRYZtOZShIjIo1tIZOXtVSG/Pf2v2xzAtPL0Aif9zRxphUoiH9ZoH2KAI2poGvNNXAsacy3SmXbQ0fImlKIx30IKSzzfQMcCbMlyW/FDDy6SlfOc2hjzqTPbXO7ndBsxS72UbjOibO/n1d4cypYcGl7gg/03SUxGGmUkvSZDkfDiZsbTo2u0Y82TjzzGQx/6DsTOBsULX2Dnk19CzS6y+MR70EsHYPsK4tzzuN01Zrsdji51mEs7JAt3Mzx+iNyV9KI+abRD4grixSW6R1copWZr6S62Fo6jo4iFbkovsqiO4KET8zTm2nRTzYmFFguthFYE8w18HFXnk8L1sIZKGbUimEocsuqFFFUavlJerSRvqgS8QEuJlbLOH03CuclMgj0kmCCVI8yU6gOTFJwTCiv9LE4JNVVC2DLwuRwoO0nmh8EbVijf/4ioq9UCr0AhizFgUSpB6gSHIHOC3IIIhRMd+LA5Dj+LXCN0hADG0a2DBckN7U/fwPbfjnZbA9jkUyl8Mgsx+ZpeLzD0nfEihyJ4X1VJTFYiiJHcI0EdK5hPvVbMtT4Mc8P6oPCqEFgaUpDriIGI/KSasWLGDmjYcZgYrilFxLCEzWGJEYqi00Wt9iASWGcwO1uIVgfZ66L3rUJUYK8liJFCa0kSKdJIIaIGebNJiaUQMVZarC0QZeEfRqmxvVmK7jxOKYgtWjpiKWilmk4buolmthUz34qIpUOrUCUMD/eekA0X4qdJuFaDCntDqxskUwmu3M0Tz9NN2W5q0WTjKXNU2q3TSybnV33fG3bWy8J3h6t7KmtfbqqBXagpOR83PRxk7yQFGzBY4iufdmpi0h371thtDWBZGRq3g8zqOC8os4KyKFBl8BYcmNyQ7WTYcUa0MyJuj0KfpERISZkVjNaHDK7skuoh7czipCJf36D//Etk164jGzO8e+4gxxbmaY23mF17FV2OuRbPsdNYwgjJoD9ivLmLNTnXWstcay2RRymtmVU+2J3DIbm8PuS/XxvQLgccnzvK0ns67OgWz12FjY0rzO9e5+TlTXqDbbaKXS7oPhtpQlka8twgnGMrzdlqJsRohjslg23nQ0ElcWJEGmsiNLHSrI9KXj+3wVfPb9NMI64u9ZjtpCy3NO9aSVlq6xDCBWespgaEXJKs2n0mODaZkB3UJkTIQVUVv5AEF9Mhp9gLZ6HxAYdDBgoGlde3BxhEfWx5E8FCJ3SYxh0G3VaqGkKA8yGfH3QC0hqkLRAEmkV9nJALFAItCJy4MOQ2eIYxJTpMLw+LiG6hHlj1wfx2tv92tNsawMaFocxKSuu5XqNxQT7KMEWGLcr6I74clYy3MuxwRNwaErdi32qUxqgkohwVDK4O2Hpzm6buMzuyWKkZX9/g6sf/kJ3nXqD1yLv4zr/y4yQnlinfuE726rOUm2sUs3fzxnKTkU7pbw8ZXtsic4ZX1XGemzlJ1Gjy2L5FvvPgHJuDnP/8+fN85pXr7Osl/Pij93DoWJfz14b83heu8NyF89xvrvCjxRrH7QZroxlOuR2uphHDYcHuToa1jjdnE04vpCgpWN8SrG1GSClYQbJkh7RTTVO3aaaaa8MRz79+jc8+f4E4TZhfnafVaXHfcpOD7UWWWj7NLgN1oOK4gX+QJy02YpL2cq7WjZfOBTqEl63xUjeu5mH5uE2/JYHjcJg6eW6Dzn04toqqA1EXDagKBxO3zeGLFNUQjj2SP3XYKOpqo3AFshgEgqv2Ej51D6ZBOB82KumVZcWU96kpJqFyyBPeShrFHSLrze22BrCKFFnNdHTB969/n15vmtxqKx31ek9h2nYgudY5ZIvJcsxwiMzGtChpS0PmcmQxpMgHxOUIbXKUUDhrKUKqeyxjBrJBolKUknSVIRcGZ0qGWcmojMl0Qp52yCIYWckwt4ytxRg/MakSbCyNw5QGWxRYaynKiKFVKCHpu4g+BukgMwJrClwZSL541nhhLFle4qRinBtUYciNqakDk6DshuT61PJp/HEhRKzSWnuaDidx3J7wb1rocHrvbjoUrMPPSX/jxJuaClWnjlfxvm56c0y/OzFZ7qkhrs79seecHBJLpcYxXZy8sXr6bYoJt5Xd1gDWiBRRrCiNBGdJE02UxmgV+ybuEM5ILVGpQrqIqJ0S91qoSKGSGBn79ZqLLcrRmMZSgyiRSGdJ5udY/J4n6NxzEt2MKd58hZ3Lb8DuOjoCNdvhQJpjzVkylxB3Y642HvGiiN0DzHWaJNKhL51mdHkT5RSPdmaYe2wFqTVbWcEn3linyA0PH53l3n0dVoaKA2tXaI0E8505Di92aCctGsOCTnOAMgViLkUuNLFKs9pO2J7NUViOJCMOJBukccRKlNCNWiy0Iu4+usjACVqNmEMrM8x2Guzrxsy2UxBByLF6WmEqd+VD8yqNXwGHqPTDaq8omC2mPKDQQuTXnoBUnYMCjcMJao174RxWVtr7AcQqGelKxjooRHiCKp7DBTULv6Z4hFDSSt/n6oRAugB2EozUmHpyUfW+HdIUqGLsNfN1A6vj8B40rnJjAuE2E7cyhHyLE/t1b//taN8UALt48SI/93M/x8c//nGGwyEnTpzgt37rt3j00UcB7zH94i/+Ir/5m7/J1tYWH/jAB/j1X/91Tp48+XUdp5FI4ljXObBGGqHT2FeVoio8EMhIEaUahybupCS9NjJSqFgjtUYqRWu5DTYnWW4RpxLhDMnCLIvf991YY8lOvcLupz5OcdkLA7ZXZlDtDgfJWCnPUArN2d5x3ph9iEynGKGYl5okH6LffIPR+a+gWx0ee++TfMddJ7kyNPzeqW2+em6HgzMp33/3AncttFDrkui1C8gtx3xrjqMLXebjNgdGO5xs+wLBxsw81xeaFCphVBhGhSVyBUezAYfyNVQUo+JZZAS2HXPPsUV0r81MI+L+5TYrnYREQjcWuNDAXiWsp1t8fOjmFRg8pvhwUgY+1CTNHSqItso/Sc+/k2pPMrxOnjMtNw2TqekegKpkeSXsLAIHS5h8AoxS1Yl1V4WztgzeUxg64iy4CBN6GDXCj09z0pN3ha5bikQ4j8iMEHnfH0dorIqxTlCKCCv1BIeB7BYqst6pQt7c3vH3tbm5yQc+8AGiKOLjH/84L730Ev/0n/5TZmdn63X+yT/5J/zzf/7P+Y3f+A2+8IUv0Gq1+MhHPsJ4/PXlFGRVPXMhnyIkMoqRcYyVisw4RsZhhPCy0mmMSBu4RguXNn1rifVMc9VoEM30UK0m2BI76GPyjExFZGmTIk5DU7LASMVYJYzCJ3SqJU0tkFqT65RMJQitaSlHU3mPI7e+hy4Wlo42tJSnKpThCWxIS1cbmhFESYxMU6JI0aCgZTNa0tKOFe0kohVBk4ImBS0N7UTRihVN5UgpSSmJXIm0JRGGtnbMpIJeIugmkm4saUYSJScf65UjNcVP3WO1Rzb1ws0/1N1NfnRveana/q1B6w0r7Qk3p0UPp3IEe+LbG45flxSrlqgJ522Sd2CPHpnPhwWQngZXJp6e9ytvpaCheNtf3472jntg//gf/2MOHjzIb/3Wb9XLjh49Wv/snONjH/sYf//v/31++Id/GIB/9+/+HcvLy/zX//pf+fEf//H/5WNZ5zxbfphTlJZlEaGWV4lFxtW4w4XrIwpyZpRm9ugyypa44/ewc+QuhC3R515FXT6DiBLiE/eTzCwDjvL6ZXavXmA76fHG7DE201nms4TjD72P3r0PcK0UfDWDkRUcajru6TpiJcjNHOujkhw40So53jIoXTJePcD5tEWiBIfKksa5l4hMxL6ox+5ym9W4pLV5FoY5whTIdg8aTTojw4GrrzAuHa1el2zxICaKUEXB4tZpLIJhe5lhewnpNOnIQpHhrEEONhBa0ygtR8shMyIjJWHBWNKyiZAKKRMfQlaZqdCrWOebaj2uEDraqQdWKt/T6EomOllBfx78PiqPKejJy7cgWFXhtFOh3DQYmVB59FVWF6UhLwaYHFFL3KgaeKqpQ9V4NgFokwdGiAAVh4pkSVQM/H2kE6xOAv3G1ftSxQhh/aBcKRRWKGrirjXkt7CV6I7d3N5xAPtv/+2/8ZGPfIQf+7Ef41Of+hT79+/nr//1v85P/dRPAfDmm29y5coVPvzhD9fb9Ho9Hn/8cZ566qmbAliWZWRZVv++s7MD+Ps4Kw0b/ZxxXtLvRciFZeLYsl22eXl9zMgI7lcRBw4tEEvB9tGT7B5+N4yHxGfPE13ZQM/M0X3fXTQfftyD1yf/B9lrz3OltY8vH4g414F7FlKO3vsInW7MmWsDvvrGFmvDAtN13LXq0BrydcXmVUPpDO1Gzj1RDrHkpeVVLs+eIDUj5gevs3DxNSLdZql7L0V3gblim8b2RcjXEM0Ocn4VmTZpXb7IyvorlLs7mOhB8t6D5K0ujetv0L3+OsKWDJKIfrKCcIJUOihyMAUMt5FSkFrLwXLIfnIEDaSJESWgYmwUgdBUeXRXeysTT6tiqNf6WhCAKvDobEnVyoOMAwXC1cM76vYd4W7Ap6mkTj3haNp7qlQlwnCOSv7GOaTxQF+Bqwt9j16ksKp8Ts5bmRzhHE77bgyEROYFqhyA8x56qcOMSCplDJDFGGmKEBLH3gO3xhNgbUFe9L/ex+MbtjtVyJvbOw5gp0+f5td//df56Ec/yt/7e3+Pp59+mr/1t/4WcRzzEz/xE1y5cgWA5eXlPdstLy/Xr91ov/zLv8wv/dIvvWV5aaAUjrK05KXFmElYYaxjXFrGBopqmCl4ZrbUIBRl6RDjEpEbrykVJyA1ZlyQbw+wYkyCoxX7BuGtHJLR/5+9Pw+27Dzr+9HP+75r2vOZz+nT86TZsiRrsOUxYIIxTiD39wNS17dwSCqkSFGJQxWUncJAHMBFBsoJSeFybqWK3MQh8Evi+0sIDsbYBmMhSx4la2xJPfc53Wfc4xre4f7xrrX3Pq0W2JYs0779qI7OPmuvd621d6/93c/wfb6PY7eQWBUiQ0GGYSPTjLQfMtLAYJ0lGg2xO0OcVGREDBBoq9jRimYhSa2D0YCa3SEqujDsY/IhUoYo7YeRuKLA9ofY3oBhd0S3m2FMzmwGoQhRQlAMM/LLVxDOYQYjn+R2oHsD7LAkapoMTIFNc7QOcXGKqDVQCzGyFo2xYzw2rPSG9ujN/7kmJmHZ1UtEVSucJNnHFcer49Zx7uuqY4/NTf1Mnh/XN6tQqWpXEsLPOZgKn4RzOKphteUgXphq5pZjKghClR5kqawhKu6ZHG9/Ne27FINelr3iAGat5d577+VXf/VXAbj77rt5/PHH+chHPsJ73vOeb+mY73//+/mZn/mZ8d/dbpeDBw+yM8pJHXQHOWmmGUUpZjTAWkOaheymTYYaBv2MrDcEJcjSnFQbXGYodlLUWp/IJDRH/pteZ5ruhV12n95AHpvlntfH3HVyhq1ezmcev0xvVBDXI9qdGrONmO3+gP/2VB+MZiXMeCAeEVPQeu4iV9YvksqI0yuv4dTizQgcl/IWzWI/NZ2xfPYpltIeCQVW9umLgnBmACokaA1JL66x9eQFRps7nLrc4kuXlxk0ZrhjKeC+/cdJMOx+/Xl2HvsTlLDIWxfpnJzH5jkbX3qG3efXkRLiVkBYU+gC+gNBngkax46w/APfR+NY039WhW9CF1LiCCdg4iplCKY8JqZyRwqh/M5uqpJZfcgFIEthxLFWlz+hT+VX5xgz/T2NoapATip/FqmnkubCD2sRFXeNSo1CjUFMVNdXtiDhLKIYjakcNqoBAi0isnJ8qAhqSOUBrFJedeVxPLHX+ZFyzpLmN5j432l7xQFs37593HbbbXu23XrrrfzX//pfAVhZWQFgfX2dffv2jfdZX1/nrrvuuuYx4zgmjuMXbe+PClInGY4K0kyTjTJMOsJhyNM6/bRgqAWjUUYxzJBKUGQFufYCh0UvQ24NsUGKyXw/nc0Nw8sDds/s0J4ZcksnYvZQi4dObfN/Pb/Fkxf73H5klu9ZaDHXiXlse8TnT+ekacZfX+7x/atd2qRcufAsG198hp5MuHTHLOflAbQKeMHVca7G0uAKbzvzAkeuPI0KFbaZMIoDbF4QtptIV5Bd2aB7+gr9tR2e2ejwqSun2al3yF53hP0nj9CSlq0XvsDW//jfhMKxGL8Zces+TKrZeeosFz/7VVQgaO1vUputkQ1yNs50GWynzN9/N53776Nx7MjE63EewKiyVZUwYMWZuopNDw6kwO1RJq04CeX+zpV5rMlsyIrbJbBTHtskSY6ziNLTsaIMD7VG2KrncsL4H1+7EOMqocAz6Mew6qTP100rsgYRLkiwQqKtoCjTeEEQY1UCTMbEjaudlAUjGfv+yOAb8U5fGbsRQl7bXnEAe+Mb38jTTz+9Z9szzzzD4cOHAZ/QX1lZ4VOf+tQYsLrdLg8//DA/9VM/9U2dK1QS7QRKSZSqWoMUCIeUkqBUq5CyfE6VI9eEl+IJIoVMQoKkbEcBkF69IqiHqMBBfwe7eZk4TVmqK3qzNRYTaGa71PsBbZcx3wzJQkEj6COyEc5mECWIxWWUiGjVApbEkEIEpCqmECGJDomTiKgeQxiSNzsQx1Bv0YgSCEJUHHneWjuh00nYPxvRqkfM1D13zQoI2w2aq4uEwiFabQaqhg1BdDrUludQgSCeqxN1IlxsqGURNAqSxTlUHL24UOjGpInJxgq0KqARlPQGxrkq/8xUXstVYdqk0jc+1l5W7GTt1KmqNdNOX4VObry/B0hRtln7cLJExLHgYpWUH/MtAIkVnvtWrZNTcmfjUsV4IO+4jOEB2Vqfi7PTKhzfXrvRSnRte8UB7B/9o3/Egw8+yK/+6q/yoz/6o3zhC1/gox/9KB/96EcB/0a+973v5Zd/+Zc5efIkR48e5QMf+ACrq6v88A//8Dd1rpl6REzEINOEoaRWN6hajowMkYxpigiloZ7HRHmNSAniJCIJFMQB8UKT6Mgc4WyHqBEhnCWIJK3VFtw0T9Q25E8+wu7lU8y1VvjhW25nUJ+l0b3E3NpXCPIBtfYB9t1+Aq0iDq1vYy6uM7A5dv8RotvejBKCu/Iet+TPk6mE8+3DXKnNMZMZVsJVZpcyhlGbizNH6dbmmEug1YF6DLXVEQt3HKC906a27yAnju0nr7dRnTaBgkIoFu+5lZNLpTrCvv08V9+HCnNabzAcP7aKFI4gFqgADAHzroZxIeHiIsnKwtizqBL5shIyrMI8WQ2wrbhf4CjDKef7CynldIQKS316C7rwFUqqnFGZm6raisbA50M1O06625IMK8ZrROVWlcCpURh8WBjYAllJRKvIe2zOIp0eh6bTNAhXJuu1CMidxDkvFFhTJdw5yIwnw4Ym9aPUKIsIQvoiQZGBLSiyG1XI77S94gB233338d//+3/n/e9/Px/84Ac5evQoH/7wh3n3u9893ufnfu7nGAwG/ORP/iQ7Ozu86U1v4hOf+ARJknxT56rHCikC6omfHRjFITKMEKEhdBE1o0BCHHuCa6AEQRgQKgmBJGnHJIsNgk6DIPaleBVIarM12NcCYdHnn0NfELRufg333/M6wgPL5M+sM3rmBcz2Bu1GjdWDd+GSJkFfYXZ2MEZjjywS3P0AEZbl04/SuvACQ1UjqR8g7CS0iwYzcpZmq0+RzNOfu5mN2gqBSjHhNlJmRLMdWgcXMHMxSwfnee3Ns9Boc07XOKX9TMvO0QMcuWkOCzyX11nPE6JQM3sTLJ+cR1iD04WvFoYJorMISRMbJBS1tieNMj1boORB4Tw9QVbIMd3K40oPzPmp21WlTiooKQ3CFh7YhPTTsYUstWzKKUF2UtX0oaL/N5TWIWyV8J9Okk88CINA47slVNmgbaUCGYzzXcLqcfgrSm/QqQBUgENinCC3PlROpCAqY6zcQmE8YIc6R5myMKJ8FVLYAqGHCJ0R5YNv6n59OXYjhLy2fVuY+O9617t417ve9ZLPCyH44Ac/yAc/+MGXdZ7COAoshbZobTHG4IzBWYMxhtxYcg1FodFZgVICow3a+mkzOjfoVCOSAmv8h8laP7ko7+eoekI8v4hqNBBJg/TCGnk/x1257AURG3V0nmHOnsWGCXaQotuLWGBX1NjdyVBOs787IumPsNIQB1domYTQZmynYGyLrq6xmQl2haapCrTNcHKEGY7IuwOK7oBcbTKU53BJnbwxR6NlMFKxO0h5Uqc4IenFETISSOsodroMe+t4mPOkSytCio0UoxJku0N0MEG2J2PVgKlwqfp7Kvyb6kEU1RrBpAI5vb+Q40S7k2pSuSu9nGoO5Vi6makDCkmleLEXOCfVxck1i1I9wntvWD0OaaucnSsTZb48MKmJKlF1H0waxaV1KFuSV4XAynDiiZbsfCFDUGDUqxhCctW/y7ew/rvRruteyF5aMHKC3iBnlGlGUYbJUhyGLM3oDnOGGvpdL3PjlCAdpKSFgVzjdkeY9S6RDmmM/MAPm2kG6322X9imfvQwrdc8SOOmEwzPXGD9E58hvbxBa1+bpVsWCRdnyS5sMXzkv5PnFnv8OPbWN5CHCU8OQp56/ApRPuTBjYvE22tIIeis9YijJ+mFdb7a2M9acgRdRIy0owj6uKDP7bUNTDBgVFYh040d+vYS2/pxjApYvvsmDjz4Gmwt4XNnC/74TI5TIXfeLrn15g5RVtB7/Bn0448ihSNqBoSJIh0ZLl/KGHQLOrfexJEf/SE67Vb5bo7JCJM3uBwrVoVzriKpIsaSMhPPq8pBlaFaNUqt1Kp3sqrolWEbAiV8vnIaAJ1Q2Krn0hlEVXkUjHsrq0SYQ0zNfHQok+F0WSCQaswFq+gOGknhPHhJIYjLvKeyGqk9ny00msCUXLIgxETJhAQiBFiHFRHOWUY6ekXv5xv2zdt1DWBpYUitIc0NWW7QhcHqAqcMWmvSwjAqIEsLimGKVJIiLyiMA21RowLRzxBJji18uGG1JevljDaHhAcUwb4j1G55DaONIb2nTtH7+lOoe29C3LmfaHYG8ewaxeOPkQ0y9NwyxcIR0nqT889u8sSlTZKsz/HdLmmvR4ghCXrUlCRP5rm4vMpjahZhBKEBKTIWoxG562ODAcVul+H6LsPLO2zsZFzYGKKdoNkQdO5cxNHkyprmT5/RuDBifnWFO4RAWUN26QrZE8+hlKM2VyNqhgx2My4/ucnO5QFF4dj/jv6EHT92qZgUEssEuCegVlN8pnan8sXkVV/xJbC40utSXrLZOTDV8UoPaOwhleZbeiZk2ElzuPJA6TkNU6cqz20NwuixztfEY5p4gtaCLlWqw6rAAx6kS89N2RxhdTlGLcaouMz3lQonCowIsA60evU08W8M9bi2XdcAdnS2hpYJc5EiyzWHWhFxRyEiQyducSyukWpYCRaoxccIlaAxO4uLBbiA8MAq4W13EHbaqE7Hf4vXEhrHDmP6ferHjhA0an6MVqtB87abkfUajZv2o2YXodEkWt1P847bidMCfWgV0wjJYsWRuYRR2ibKA/bN7Kc2SAlwiDBEKEUzbHNodg5dTxBCEihPlj2oHLVkHlSdcB80bitQq31cd4Tb6mMczJ44hpxbgVqN/asF944KnAo5ulCnE0tCHSEOrCBuPYlUgqhTJ2xE0MtYCDdItgbUjx+kp0JMv6AwfsCvsY52rFiqK0Il2BlpNga5P2cjZr7pQ7XtUcFOqpE45mPohAJtYWNU0Ct8W9VCLaAZKUbGcaWfMdRQCyWz9ZBYSYa5YXeUo62lGYfM1EKUFOykmq2hp7TMxYK52IPmbmrpFRlSCBpRQBIqtLGspwVpromVYz4S1FXAyMBWqsmsph4GzNT9BKtcO3Zzh7HQjCRhrHDCMdKONPUhZF0GJErikAyMILUGKSBWklBN8dzYS6f9dtt3So3i3/7bf8s//+f/nLW1NV772tfyG7/xG9x///0vuf/v/u7v8oEPfIDTp09z8uRJfu3Xfo13vvOd3+JV/8Um3F5hrOvCut0unU6Hh586Ta3eJCu8ttWMLFgJMiJp6RrFlgmxDlrFgHbRQwC63sbUW14TrNuF/gAZBiTzs0StBibNSNcuo3d7qEaNZHmRoFGn6A8ZXd7GpBlRLaDWiZGBoBgWpKXQIDMzuNk5rFR0M0c3t352Y7rBbLbtS9lhggtiCiHZkQkDEYL0wnwISUMUzIuUGpoi1WT9DFNYzLCP7m3jrKG2vEzjwH5cEHK5m7HeTUFI5uY6zMy0kDpHXDyD2FxDKIWotyBOsFlKsXEFM+jTrc9wdv4Y3doM28OcC9sjRrnhjpUG33N8lplayJfOd/ns89uMtOWBgx3edHQGKQSPnO/xpUs9YiV4YH+T1y7X6WaGz5/r8uSVEQuNkDce6nBiPuFir+BzZ7uc2805MpvwhsMzLDcjntsc8oVzu+yONLcs1rlvf5NaKPnypQEPn+thnOO+A23u3d/COsdjlwc8szGiFkjuXKpxdDZmJ9U8cqHPC9spS42Q1+9vcLAdcqFX8MW1EZcHmsMzMa/b12A2UVwaGJ7valLjONAMOdKJCCSc72ac7+YIAQdaIfsaIcbBxYFhI7XEgWR/M2QuURgHmQVjodftcvLwKru7u7Tb7W/rvb6+tvayztHtdlleWfmmrvW//Jf/wo//+I/zkY98hAceeIAPf/jD/O7v/i5PP/00S0tLL9r/85//PG95y1v40Ic+xLve9S4+9rGP8Wu/9mt86Utf4o477viWr/3Ps+vaAzs8k9Bu1ycbqkkzztLB0RljcwLMAxBPESl1cx9GRWU5PgerUUlM4+hh/5VlLZgCYTVhq4GaW/DzBnWOKIYIawjbEcFB319HOfIeYLYe4FToGeR5iChmfR4pauDCmNhaWjoFo/1aFfiePheDrYOzBDMBKohASGTaRQ02vVJG0sE25kAoVhsj9i94FQ8XxDglIYyQ+5eRi02cDLBJGxfVEcUItW8WkfWxeUhvELI2KLjSy3l2Y0g/1czWQ3Lj80vbqeHUZko/Nxydq3nZIuHYHOY8vzkiCSS3LNSwQlA4WO9rTm2lDLXjrsKCkKTacqmb8fzmiDgQFNrP9x4WlvO7GVcGBQv1AGMtzgl2RzkvbA3RFo7P1zFIDI6d1HKum9MMJSdmI6RzGGO5Mih4fjtDWxhqcCIgNZpLfc25bkYtlBTagJPkxrKbaUbaMRdLnPPnHGrHVuarF3MNhVUR2jqGxrCTaepGousKIdRYvqVU2n9V7vPvlP36r/86f/fv/l1+4id+AoCPfOQj/N7v/R7//t//e973vve9aP9/9a/+Fe94xzv42Z/9WQD+6T/9p3zyk5/k3/ybf8NHPvKRb8s1XtcApq1XHK0mzUwPTp1OLu8hU1byMWW1yz/Gj94qk9RVOluM/XYx7pdzzmsQqSqxLSZVrauGg02xzkuAEiWB0lXHV6VO4ERVtBoDNj6ec4B/PTasIZzBqMjncoTzI+RkWE7pcWMdLCcUOqiV+SCf/HYiwAV1KCkEefmhzgpDmmrSUUGR6bFardHWb881ujDjfFieG/rDAhNKCu3reMZCf1iwvZ3SBPLC4hDUo4Ajc3WiQNEKFc+s9Tm3MaSXa1abIQt1hXSOr5zZRQlBLzOcmK8jnKW1tU734edwQtKKO5zotBBCcGlrxO72kNxCLAS3LdbpmJT8iadYK4ZcKkLWR3XWdchqJNC6Dk5RCwSL9ZBUW3Z7Iz6/vuXTBvUac7UEaS356TOc37rCyMITOuaMCZlpJszftMRyvUN/qHnqUo/L3ZTh4NVr5vb30suQ7ynXVkIIlb1Ul0ue53zxi1/k/e9//3iblJK3v/3tPPTQQ9c8xUMPPbSn5Q/g+7//+/n4xz/+rV/3X2DXNYAV1utphSUIeAkXn4x1QeQ9IOHVWr3MCmXSV5aAJMZg4kSAKCfpBFeNAfMQIkrAdAS2Sor6JLEp5eak8I3Cfj6FRVQjwUrvCsAIhWdsCBAhqKAERN95Z5EUCKwQKByhNZ5brkKodbBA4RSp8UytQAQESiGwBDojMEOcEBgVY8LGuCInhMSqCFObxUYdRhSM7JBRrhkMC7q7Kb1BwXBYlE3xjjw39LopvVSTjrRvMJeCwShnY3tIPQoYZhYrFdoKNjdHnD27Q5A2GN66iBWSmXrMGw4rcm15Zq3PHz6+zoXtEXfsb/F9t80z34x49IUd/uuj6/RTzf0nF3jrbUs0XEH6R19k/TN/hAhDlv/q93H0zW9kK3X8/pfXeOTUFkudhB+4Zx9vOjZDeuoFrvyv/836157g+Zn9PHnkfi60l1kUhux4C+ECOpHixGxEZhyf/tJl/sefPktWaN7xwHHe+cBxwnzEC7/3BZ75H3/AjhU8NHeEx1srHNw3y+HGPdyy0uLKzoDfe/gFHj21gc6Gr9q9PhF9/NbXAxw8eHDP9l/8xV/kl37pl160/8bGBsaYa4ouPPXUU9c8x9ra2jcl0vBK2HUNYJVHBJOK2WRSMxOwcm7SSlFJwUDZ7OYfToaAVSO4rmp/QZS9cW7cylL5WxPd93LfsSzMVCuOlGUv3ZQqvJgEJNXQWO8NCozz1+CcH7jhVRIiL3VsHEaXLAYhkCUPylFW04TEBR6wYFKBchWICdBSYBihrUMbS1FY8txg9ORDYq1FFxZdGEzJk3POq39kuUEhfFiJ/yLIcsNwWDBKNdr47ZHyXg84zm8I1ndTnrs84OBMxGwkWW0EKGs5tzVie1Dw2sOG5WZI2zkuDXbZfeE0MopYGPZYShTWWrqDnGfXBxTWEeJYbYbsSM2li2vsPnWK7gp0Wz26cpbRSHuOn3NEEgIlSbUjTXOeu7TLMCt4Yz+lEQoiA2Zzk+2nT7FpJJf2hZxbCAil76cFR1ZoLm72OXVhB1OMvvGb9S+JnTt3bk8O7Fre1/Vk1zWAKeHHcYmSFzTmKlWDWq0BcdXcQuy42U0wKU1XRMaKl0mlRCBL0BISJUrSgBA4AiwOJ9R4CISAUp55L5/K4r09T3q3VCN3TUmspFznZyk6AmuQrpJdngzn0M7nXqyDcMxo8Gq0AgiEwikvjyOtJiiG/riB1/2SzhIUKcoURNqgnEUJP9E8qQUUzhHGgZ9WLgRSKaIkIAKCUI1LYSpQRHFAFClUyaWSUtJoRMzM1Wi3E6JQevLsoI9eO4/td2mNAu5biTg4u8BNSYZ47nEGyrAwTHjzkQYDKzkR9HDPfJXcFkSthNm3vAmhJGEiyZ99DGUUt7VDijtXWL2Uz6UAAPPkSURBVEgcC4M18qcvIrrbzL/2ZqL5WYraAgfmVhFJi/m5GmEU+C+ttA/DHqrQHK3n/NW79pMbx82zgnDrLKrIWTi6zPF3vZ1FK+k3V2jU5tm30GJhzvPl2vWI151copbE5OmA//A7r9z9/OfaKxRCttvtbyiJv7CwgFKK9fX1PdvX19fHggxX28rKyje1/yth1zWAxRL8cOQppnYQlX9a385SkS3HfKFSGUF4IqUshfmmPTefj5JY4TAoqsYZJfwb5lBlnqqaWO1DTldxlRBUssQO0E5QlB5ViCXAYhEY50HMkzT9b+kM0ubgDGM2exm+jqzDIIilIynbC3MryH0cTCADAukZ6VJnKOP1yKxsYWXgixHZLiIfEmeSwAUoKYgjRaMZQ6io1UOvSCEkQaRIGhE6kISxBwEhBGEcUKuH1EJVAhsEgWRmtsa+1TaLMzG1WPrXv7PJ6EufIz/3AvP7j/HX7n4rbn4fnHoc92efZXdnk4O33s2P3fc2RK2JfPYr2If/jJHRJCdfS/P/9WNgDfa5rzH6wh8R1Jq85dYHecO9NyH72yRPPcToyVOI9jz73/4GxNw+kr5h7XJBa2g5sFwnSiIvzNjfRpx/kjBLubtzkON/9WacVLR2z5Jc+DoCx8G7jrH84OtJnWRxJLkzh2YccHCliUCw2KnxzvuO8OY7Df1+j//wfl4dm5K//pbXfxMWRRGve93r+NSnPjXuUbbW8qlPfYqf/umfvuaaN7zhDXzqU5/ive9973jbJz/5Sd7whjd8q1f9F9p1DWBTku6l1yOmiI1u8o9e0cbHBEhXLRjzNyczB8XkiWq0lhOl8+G9Ig+BleSMmRQJRDVGbG86f5ozJFyld1USQKdtLA8zOd70euPwSlkOpJgOeqsQVo7XVP2A/olK08sXOaQtkFbhFcCkrzEoQRBID+jjcFsglf8RU2+2EAIp/c90F5AKJFGkCEPlnwOcLrC9LmZni3h+ibnIETQVQ6nZ6e2gtzdp5kM6NYFqKobkDHrbGGMIwgC1tOLFGE9LTH8XaS0zgSZqh1grSIshRW8bVW8SznZQB/cTb6fUhtvUbEoUKmQ1bNdqXDZEZENaStPsxKACxNAh8gFOSMJmjWDfPqRTzPRysoGmFgjiyPdqBkoy24ppNAS90HxzN+x1Zj/zMz/De97zHu69917uv/9+PvzhDzMYDMZVyR//8R9n//79fOhDHwLgH/7Df8hb3/pW/uW//Jf84A/+IL/927/No48+OhZy+HbYdQ1grsxL6TJKVMJ7SWKaVQ6MZVGEV2R1TMTwKjMInJNeaqdMnAshkHhvZLpfTpQVSuFK9QSdgXN+gg2qxEmvo+69NEEgfEVRVv16QqJkUOqt48Nf/DonQyr2OKUaqBSORBicc4TOIrUPPpUIiWRYAp9XahAInIoBz0aXQiKdl5zRYR1EQKotQ2MYZJpBqhmNNKNMk+d7q5DZSJNlGl2UDdFCkGeaQS/HRYrCcy5w1jEaFex2U2aUoCg8aKpmi+TmOwjml9BGsvWFr2Ds11A2Izl6EnHkGJqQ9U9+Dockii3xzXdjlOKU7fDCl9dQWE6KOY7cdi/OOLaeOUf6tfOoQNBsN0nueD3bos5TZ1IunzvN5rDgmY0hOyPNrO2QH2j6gkl9BrFyHJuN2Fzrc/mLf4CxjsXVFourh9FC8fjFlKeefJzUODaHBd3MsNBOaNx5iKXGPDuDjEef2+DcxpDR8PqrQn4z9mM/9mNcuXKFX/iFX2BtbY277rqLT3ziE+NE/dmzZ/0XXmkPPvggH/vYx/j5n/95/vE//secPHmSj3/84982Dhhc5wBGmezOrc8LBRISKUvmw9Q/2FRDsFMSIz04VB18vsXF842kc36ijzMgFFJFlOmpiSBfqfaJwKselCJ5zgmM8In2yj30IONBSliBNF7nXQpFoBxSVaSN0mEUEqdCf7klKAEooQlEgZ/JqEutdgjDOioIfXLfKbRzgMIohZXeY4zxlVUnBEXUwoQwyjL6xQ69tKA/LBgMcoapJks1rgxJTWFJhzmjVFPkpeaWg3Sk6e6MMHFAnpZCkMbS7+dsbY6YkYK88N6JbM9Se+39OK3Z/fLjXP7tjzN47gxz993Jgf/zB0iWF1j/9MOc/93fo+j22feD30vnx/46ea3BY1+6wn975BxxIPmb9y5z0323YjY2ufL/+e+c/+TnaB5a5cTf+lE6D9zPzqUB/+uzZ/niCxfR1pEZPxh4KXCkdyz6L4PWHKLehixn/dE/4Iv//v9Cj1Je8//868ze/cMMRcCffOWr/M5nnmSUFRS6wBjD0dU5bl5s8Joji2x0Uz7xhdN8/slLmPzVS+KLKd21b3X9t2I//dM//ZIh42c+85kXbfuRH/kRfuRHfuRbOte3Ytc3gDEJr+xUi8fExNSW6fBQTG3ZG6ZVPW/TRx/7aVM3wfSRp/e9+vxlFOqDxSrcnQpfxVVHKAO98bpqh+oYkyv3oWRVdCj7jCdVzlLRwT+uyq1TvDUhsfjZAdY5rHVYaz131/kfhyuBG6x1FMZ6785BUH4BGOtIC0NWusGhnxuL1pZhbjwAB3UIHLmKKEY5Ra9PURiKqI6qt8lFQDYYUXQHZBryuEGeNBmyzW6qiQPJSITopEkRDhmmmv52F2ZmyAgokhZpYNnJLBu9DClcSUsBkxdkuWGUW6RUqDDEOsWosOxu7pIPRwxSjQ4SChGwm1nWtvukaY7UOdIUDOsBaZqTasso0/S6fXY3d7HFNzcG8Ia98nZ9A5jz1TpVpr58Y64pP+WunJwzcXHHtIPym8w6ga6ySFYTVlOohUAzqWZWQOE9rwoIPWg4GaDDGjiHUxFByaodh6eT3XEI3whcTnVVCF/B9Eeb5MmEuBodx6oOYEt99rDc2evXO+d5cYX1Rwqw+HGuHiYNng8XFCMCq4m0JsISBb4PUwWSIFAUwE5qiCKNU4qlhTqNzDBw8KVLfQIpqDUi3nTbMgLYGGn+76+u4ZxjtRPxf9yzjBSC5y/3ObMxLKNgnyub6ccceNObWbn7TrZmlvjDi4Z0c4uGWqD9vd+HKgpO7zvGY6d2KYIRKYLX37aMkoI8UDx0vk/RNVzYd5KNBw3J/Cw9XWfm+W3WdkYEzYSDh2aZkzknVJeOLIhrfb5w6jJfutBnZbbG0aUWgXC8EM/x9QO3k6UZM/Ul9o8smSsYahAqpC4LTupdDo62aXVzNs5f5g+f3aJ7fp39507xPZdOkeucj73sm/gbtO9ACHk92HUNYMJ6IkIgZEn8tJMBEUL4ypOEku7u1ziLctZ/4J2gcL7cn1hNiMYKiRERRgbj8E2UAKam9bDKx1aFfkQ9Dim8woIQ1ZzFau+JFTIkdwolfGinprSrxDQ8XtV9a8s5hwBGOKz03pUsc3EewCA3nhAbCUMkvCyMIUSjkE4TFkNUMSQuIBJeljsMJGEoyY2kwDdCi0BBoNi32GRYGPoOHrnQJVKSA50a37OvwzDXPPTsBn/41BUWGgH/x52LPHh0kTObIz728CW+8MIuQvrigJCCu/c3+Zt/5XtZXahx5vQuv/+lNS7ubnHXgSXe+s5baESKUxf7/NlTO2jruPPwLG98zQpCCM7vjvjjM10Kbejvv4V07ihSSZ7XNcJnNzHWEbQTDjdiTgQ9vj/a5ZDKeLTX4788tcaFPOa1R2Z5WxDSSgJOJQt89fCdZFnBcnOZY0OLtpaBEQgV0pCSu/MdHhyeY7Sb8czZdb7a2qB98RInzj7FPRe+ztCaGwD2HbbrGsC8Tapx0+O7nBOTuG1C7iorkROvZ2xlEmqSkXpxcDet074nmKwqltU1ODd1VRMnbC+BtQoD3fiATkyFsjBVGfVHtuXBHHvB7cVjtfcGzu6qLeMjSoGSlHMDJlVF6zxJWEgIA0lUFkBy44NSpQSNUgXXAYPceHWHQNKqBdQjn4vr54ZACepKEAqBVQF5XCNNGuhwVL5GiwsUulanSAJMmJcSjI4IQ0t60cDIZFCk/p8uDv1QDgFGSpzxld26tEhpmQksM4lgJpAkI4FxfsReoQ1O515KKZBE7RauMIg4RjsfDsehZLYR0pARs1nIrPFaaqHyLWBCCBpxwGwjJDJX/Tt8O+0GgF3TrnMAK5PkzpS0U3hR7FWZm/5Ie8wIROVdCaST4Lz6phTlxGkxgcZJK4cr49UqSe9KL8ohrfEa8QAyxJY9iBO6gz+nkh5kFbbK3GOmJ2TjYUbaaiirpRABuQhxCAIsgSiHVpTqoX6Nl0zGgXaKofOKp35/g3OWTNWwROSRJYpyGtr3QjZq/rUnUUAYSAIpiQJJLVLjIShSCEIlSAIvtxMpSS0JaDUi6o0QFYY4GSLCiEYzYWa2xmIz4q79LVbaMUJJnt0ccGp7hBsN+N5DElYjbB2u9Ea4oaJZC3nLzYsEVnMoX2fluacQztBwkqNOkIqIi81lNsJZH4aX11UrBiz312jmXRYixUwzQcV12qrGUdrEWcjxlubg8Czt3HHfgqT25uPkTrG81AEpCBA8cHyWW2qHifMRJ7sxB/urjBozuBOHWV6ZpbUgONZ8C/PbN9EfpfBPH33lb+sb9g3b9Q1gJYBMD20QlUc0beO4bC+4eTDxm4VTOOf/qLofvVdVhZ/VlGhXKn1WjeK23Nd5QT2TezBRwo+ir05dAlkgnO+5LCuawlksfnzYiwoRViN1irSaXHoJHiMkUlgCWYK21V7vHgFKIGTg+ykNpNb3UzZsQYBBI8lUjVxKirAgigUNU5AWhnriKR1J7L2NQApiJamFfs6ikh7EIimJQ0koJaFy1OKARiOkXo9QUeh148OQWjOmPZNwaKHO996+xK3LDZ68POD3ntrk3E7K3bOGv3ZAspSEfLUHf7w9omcVJ+cb3Ht4lprNqT/5NPXTX0TaggOdJkGrzjBs8lRjlrOtuqeXUObXRgNuGV1m0V4ikDMk9SPIZot2nHA4bNHQAUfcZVaH52mLnNbcUY7dfJJCxexkXnVCKcG9RzscOKZQtkANZhGjHllQpzZzkAONWWo0Wbm5TculdHt9+Ke/9Mrcy3+ROVuSsF/G+u9Cu74BDJiEcP6xG5MwfUVuL5hd3eP44kOV46kZjw0Dqorf3tJjGf658vFUSOg9rgn3jDJK3NOvyXS4WpbJy7YhMfWsf7JUphCeU7ZnQKybzM8WuHGBQoz/q56ZPJLlOmstxtqyAsne386V1UiHsf66lAONm1Qux9VL/zMd3lrrMMZh8wJ6XWSYEQwKasJSjySJy1GDATLXhGmNugVrFUkGUVcTuoKgSAnK4owyBSodERhFnPaphV1fVBH+fUmyPmGeEhQZSudelcNojDYUhSEvBEYYhLAoLDIbIXZ3EDIiQBA7z5WTeoDVXYQpcKMBZClFpMjqBVls/JdJNqLQQ4r+9dfM/d1m1zWAWSF9or7KIQHTeSdbVRBF9YGm9Lb8nt5v8/tPtUOPexQlDuVcSW4vQ8dqTdmSROUBVhyxEpykNQQipyKj+o+h3y6cKYsMASjfcqOMHw82GT0mfUtPmOCcRYmAmvRhZmgMUqf+vDIYa9UrkyN0VvYxJoRhBM5LOWdIsJbIjIiNYSvX9Ic5Gz3DziCnO8gYZYbeMKeXaQIl2B0VbA1y0sKMATRUkk4cMFMLGWWa3UHO7m5KZF3J/XIYbRn0MnY2h2xcWePC18/StLuw7wAP3Hkv9xxeonHmGXqffZi0u0W8b5X7jh7FRjHquQ30hcukVlObD0hWVhDWkF3ZYHDpEloENJsDDtZO+XA/DJBSEukRYrDOMO8TpgYR11CjPtvdOk+vpVzIQjozQ4oliZOS7tef5txTD6ENzNx2mMO3HwZr2fnKk5x7/BRCaxquIMEwbM/z/GsV64djmrubHH/iC8yvnaWfZ9/+m/yG/bl2XQOYKweUTmuyVw6S9xD8Y7+HhydPjHDj/0/8lcoBEyWpVSKxyBLOqvIAUnivp9JqrxLtFchV022c8VxaITzIVEUCq720jyybrKUCC9JlCKP9BJ+qnUdIkKH3fvCMegBpfK8jzuFCCTLCT8DOUUWGkxKpQqwSWCcorFeNUOTUTE5gRgSFYzjS7I4c3WHBYFiQ5oZhphnmmiiU9DNNb1QwLCYtM5GSdNOIQW4Ylbpg/X5OQ0nP1geMcQwHXqJnZ3udy099nvbmaWYevJ/XvP4emkdn2DqTceFLj5OeO8/i627itoM1wqTGlfNPsvYnXyMzFvGmO4lP3gnOMrh4mcGFDZxz1OJNGmGAUBIVh8hAgXU4Y0id57KFzRroEb3NJmfOw+lRxE22oFgQEEiGz59h/fceQqcFs/p+Vg8rjLGc/8rXeOJ/fQFyzVykaAeS/uIKT0XHOBfuZ+biJfj0I/SffpyhffU08W8k8a9t1zWA7QmMqlCNKgCsQrZq76u2jSVvphlY09XMSidiqs4pGIeWYwgUouyVdExEFN1U1ROmG3HdlEc27TFeXYDYm7ar/MkJQPoBF248YRoEClnSOyq9M7yUkLOVtkZJEwlwwqKkJZCWQFXTzS1KilKixyfIQyWJ7OS6qvyYn1PoKRJhqEpNf3/NUkAYSuJYETcSksU5knhE1G4g0z5sX0GYHDk7i8oLRKMBeQYjR6AEyWwLax15rckmCeAYJh2yziLCGhJlCKVFSIEMFTIIMAgyQgokrl6nHtcRYUwQRSRJSOICRCRIA8kwCHGtNo3leUyWEzcTKtpv1GlRW90HhaamLHXlsHMdGq2EVhzQbMTUF+eo95dBF7D2xDd/434r9io3c18vdn0DWKX4UOphMaZC+HBOjUO7CUhVNAfwU6grPpco818CX7VTpYaYkL4XETeGEO+ZlZW/qiJpKT0tOalIei+tzHc578VZEeCCEiaFKkNaxoqqFVTZcnCrtLpM+BvvvTm8wkTU9K1BTlI4hcARyYgw9PCbOUVeeOCKXEHkNNZBoRIylaBjTb0+ZNZ6Ku8g04S5olHzKhNJIGklAQut2LPsSwukoFPuIxzMNGMW5mrMNSKSSCKcIQoc87MJ+/e1OXgo4fAD8xwNc6TNMGefoH/mqxhRp/Z930tEgBquM7pyjtxkRJ0mq9/3IIUKOd1Y5pFiGScErYNzNFbuJDYpK/2zNEeXvXNbDknpqQbrtQNsB20WEmjOOBoxtJOYI6pJlAY05hQXWgH90BHf0+TWfQdQpqDdCZDS4aRk6cH7MK95EGk0s9kmraLLKGkTHzrOvoVZmsshx/e9g7nB/fRGI/ipz7wq9/oNu7Zd5wBmmfaeGHtk5WNnXhziTVaXCqxT24QPD1XprnvGeymKWKa9XJkLGw8DqzTIAOuUJ/47h8CHhGMPrHQPnQwwZXWyvExkVQMo/7al/yecK09ajgwzZdgYNbBR4mWjjSM3XgVWyYCAUj3WCXLjqRqxKwgp0EKRyYRChJgwJ441jQIKY6klAUhBEvkqZFhWINtJSGb2Alg9CoiVxAaOei2g3Yxp1gOiwHc5BBJazYi5uRrzszMs3nwTS/MJ2fNP0f/jT1CsnceceC3xG96EnVlEfv3PyP7sSeRgl+bN87TuuJk8qtHdqfP13TpWKA4sJOxrJzSKPlxxJDu5p/kpP427F82y0znJWryECjJMrYsKcuoqZMkmuFwRNWO2ajXSUHDoeJsDt+wndgVuew27tYYTis7NJxALJ1BOM9s9S2t4mZGMsckyzahBQ9U4eNMsM4Gh2+u93Fv4G7cbIeQ17boGsIlczlXVwGmwGlcOq7+rSc1icoxy+zhMLMOwspQ5XluFlC+qZJbVRjF9TQDjwa2y/KkKBm4qinXjUHSyT1k/FGIskOiPEzAOLqtqYxk2jxU4ykZz5RyBsEjnz2/K7kBfmNCoMqyUwkvE1KPA0yWUJNWGQe7DxNnEy0XvZobdkUYJh1U5sQC0IzGaJJREWOzWBqndhEIwJyWHZhJmagHd3HKuV6BMSDCzhHKQt+foWYnODUomhK1FZFBDJ7MUokbhEnIZEoV+QG0jCmjHAZGM6MsG52kTSUGnHlOPAqxskaEYFpbUFmiGWJUSZwGLpkA6yZxN6FhLYhXCGnpWkQKRjIjCGISiEJLUOpQT6CCGpIFEEZsRjeEGSRhAFKNliJbht3rnftP2nWrm/stu1zWAifJbaZwshwl4+E894z/Kf3wnPdnSP1turwCrAjcpx3m0sSeHH+QxISVMaA7+OvxvV0rxIMRYHXV8fMrsVFWtHHuHrgxVAxAeSDwrX1LI0Oe6CDDCJ+sDAZHOS7kfhRRBeZpS1dVBLCyh0x4EpSIjRDhLaAsia6g5Syh8zqsRKZY7CdpY4lCxPsjZTgv2NUJes5gggEfP93hscwC64FB8hbl4Ey0Ui2I/C81FmvmA4muPsblzGttZ4K7XvJ7bbjtONy14emvIFy4M2B/Wufv2B5kPDDsu4XSm6KdDgmCB6PgbkEYTNJuEto3Til6omGsqokByZCbh2GzCKBV8fWMfp23AbBzw+uU2x+cT9EiwfVmy1kups8uI82i6zFrFfTokQ5LoJvWig3QRu6bJs7oNQrAq2+xv5iAkfULW+jmhFDSSDp1mA5UNmV07R31nE1Hv4KKb6SctBiJ/5W/qG/ZN2XUNYGPQAJgClMmTMBYxHPdHSqxUfm+rp5L6jL0fVzleOGRJXq1AaQxcYvw/xh6am0yS9hSJSrBnwkcT1jAmvk7J/Ph9JhVIASXB1V+PwaHxSXlJgbC5B1I50RObUDZ8MzcYrJDkIkSLAOU0oUkJXE7oSsUGKYgCiZJV/6ajl2mkgP2NgNWm14R/TDq2+zk2T9HBFRrBWUwQ0Wx3aDZXSHKDuXCWwXNfJjlwiP133UNzpclzmyO+cK7LM1eG6OUmd+zbTzSboLdGbJ7vsp3mhKpBstAqX4Kflu0HMQkaCdQCyVw9YKkesC1gQ3V43AlWVMht7TnEQgO7mzFc36U7GjGwIwqzjbHb1KXkcOBpKdKMUNpiRUzPhVxxPpxvywSX1AFBaiXdzBAFkrxRwzX8KLV61qW2cxZtFxnqY+QEZLx6HtiNEPLadn0D2BhExPSG8UM33dso1fiJvRW/q700wfQxnfDtOFc3V0+bmzr/VYPVpo599bV7SmlFXp1+DdUoNVmCqCvP78rLklN5NUk5tKOskBa20u1X5ewS3wYVOD8v0yBxIiTHUtiCQlusoySruvGlOsFkYhMCa0EXBpsbtNUYk2M05IkmzQ1khmxUUAwK1EhjtW+YTwLB/laINQmtQHB2Y8B2N6Pf61Lf2iDIc7K4wShpe9nrsropsbSLAS09IMbhdmA3EIycZDZPODEXUw8lV3YzvlwY+oWlEQiOzSYsjwKCrYIi9XpdXmJIoFJDYCQuCBE6J9F9CqHoNSWnm77L4Zy2XNIpSajYV5Ok9QCXGtK1Lvlzl8lmBJv1XQa2z6D/3S1oeD3Y9Q1gZZ5orO9VeliA7xEsS3ye7Fr2JQqfPxJ7AMz5obRljdETSSvPSVXJKl6MQlUGq3Kv/L6VtzZes6eQUJ6zvO6xg1gdo/TMhK0qpeVm4ZulQSC1K709h1KOSIkSvCyZ9SAaSkkg/WDdQGcIW2CQZCJEi5gBOf2iYJDpcfP2+OqEV7bV1o3fz6KwDAcFNs1IxZBU9NBBTFcM2SSn1k3Z3Rgyc6mPqQ2ZSTXGOWaSgDceapGuJDx/ZcSnH19jbSfjpL3M64vnmHVDnm8f5rG5WxmGdZT09I3IapZ2TnFs51mCNCU/u80LF3eRMzOc/P63c9vr7mZzoPnc05s8c6nPvpmEt962wBsPtwkubRKfHzC8vIXJNcUowxlL2GwQzW74aeU7BTObGRkB54/ezheP30GqItaGOVeGOa0kYCZSzDdrFDsFlx89w86ffIXdxf08vXuIK0cS8u9yRdbrwa5vAJt2dqYar11ZYZxgVDVKTUxoFtPHKGkMPh8GewoAY2/sGl4Uk+e9k1SBaRWTTtmeULECPB/y7T2sb0ES7L3hxoWH6ldZLJBlqFx1FegSEaXwvCxpS9qHLXAiwIiYfOyBlQoTpYhj5WhK4cPtcV+B8KPcdGEwuUFTYMjRgSDLNaNcQ27IhwV5vyAaaYz2oX3lgUmn2NhJOXtlwJOX+jTlFRrqPItiwCXRJKtn9E1EUPLMrC0IetvMbJ1H9vtcfvYSu0+tE68ss/LWB9g3l/A8GZd3M750psvtheUHA8nx2ZhsN6BXFBSDETrNybtDbGGwWQ5OI5VEXO4RX9gGAnrNfbywIhkGAZvdjO1+xkwtZDczjKwgzwzbl7psnLrMZi/m+cO7XKz10engWjfEDXsV7boGsGnJmolVgyamwEGwJ2H+IiQqP6zVBKBx+DjGrPJMbhIsuj0h5VTn4p4q53RIOz3AY5ITq8LWyfGqgsLeesR46jYl4MiQClSFyZEIlPMqEgI/ck6W1+FFFCMsksAZcBmRKwilI1SeiLvHA6OU2JlK90klCEKFMIpAhAQyxgURSRxSjwNqSUDSiklmYqJmhAr9ddjhkOLSWVx/l6SveM1iyFxzjluzPq1BjdBo5sKCE+YKAzFAWa+7FjrNghwS1UKkatK6+RgsHCFsNZAuJ332CVQmuKklyE/OcbAB9e0LpM9ewGxcQmIIGzVUHKNqNe/AtGco5pdwKoBkg0ZYI3aSheVZ9nVqZCpkyfbJzS7NJGJ/MENDGuJEsnBwlvD2/TQW95EfmWPpQIdspPhTXh270Qt5bbuuAWwMBFMOjc8F4cGr/ASKsftdJs6t97R8aOmJqrYKBctEMvjjVMNzJY6gpGm4Mn9VeWZjkqwAr1LBJKlePXZTXtkeQPVnciVXXpT5OofCle1QDt/nGJjM57FUiAkTQKBMjswHCARRkCCDBD/v0jPirZNoFWNE6EmmJiOxBQ1nqSlIQt8rWQGYB+0pccbymlUgiZIAK0KisEYUNFBBTLtdY74ZU3MxM0t12t0W8XKdsOYT3Hprk+6ffpb89Ck6B0/wQ/f9FeziKrU1Q+fUGYKB44gasahPYawcvx/SORoqpd6pI4OI5LUnWVo4is1S9Okn6X76fxK15vje297AW+45idpep/7E5+lePotSjjAEudBBBCEyTkAF9DoH2F66CR0ktLbOMHf5FDiDWTpIuDyDczCjLtDhAmEcM5PM0FTz2E5A+95DFPMD8s4yN99+lNHKKoNej4+8krfzn2f2ZapRvJy1f4nt+gawPZXAqzbDJDfGJOSaNF1X4DfJn9mpJPzYQXKMhZndGKymjrvnCsT0yff+vroIICiz5BWva/JruoDgmIR3WOOvXYa+ylmtLjXIJH5QbfWyqmuzQmGE9EPUnKdXBPihwEqKst1oUoV0rhxCIiavR8hyvFogUYFChQEEAWGoiENJHPohuGE9IEwChCorqXlGcWWd7NxZ6p1Z9jUl8XIDm9fQtQhbhDTRNF0XjH/Dq6EiQklEFECcEK4uo44ex3R36Z1+jGLtAoE27EscyUqDwkh6g22ytfPQqBEtzqDiGBknqGYTEUTI2TmKuRWKsA4yJXKbSKtpdhrM1kOEtazEBUvhABUYhCo8Qz+SRPN1bD6LaXdoLDbRc3V6wavYC3nDrmnXOYBNiJ/XBLNKQbUErjHvy00gqVoz0Znw2ypdeq+hX4WQ1T6+SicEPtletQyNaQyCyZ4Tr6Y6z1i2sOKxiSrsLacduQmwScoBH9IP7XXOYWWAGafp/BQjfyKLLFJ/HSooK6+OwGmE9Ul/IxRWJuTCoF1OYYyvMFo79sSs9W1UeVH4fj8JTvu8li0M2hZonWMCyOuaXFtkbhjuZAwuD7G1Ea1RjrSasF6jftMthM0motGm/9TTDE6fp5eN2Mha5CphNt1lcXiF0BZjoLdSsdtYYLe2gFYJwyuSUbpFpDNWW6vMv+Y+EAHdU+fYfmET6XLC5jy119wLRYoZbGO2e4gwRQ0yCAK29QwXgiGjSHBxG6KdBtJqGsUuzeHTKFNgL52mt76GqDVQ8ylqWWJHhuzMFsXT5xh2Cs7ZdXa3mwwHryYT38FUmP8trf8utOscwNQUPeKqzNaYueyBYsy5smVPYTW+TEoqPpkae2ZVGFiJ4IixhlbpE038K2d9bspZUMF4wvZ03dK4ydSkQFhUdSxrqCZwS1Xy8yuli5JB78oRcE6E2PK1agvaVbuU07ixCF0gTd+vi+o4qZDOIW1OaHJfhZQxRihSmZPZglxbtHFk2gOZsY7CWiQwShWuSBFKYPOcItPYVJOLjJwhJtRktYxRzWCGBb31ATund9Gqy3x/iDQZUafFzOvfiM1zBs8+x5VPfZbRhYuc33ecr99yP/1mh5vzZ7h34zStvO+9LiUpVMxzyXGeqd3CkJCzZ3IubF9goR7wf955M4fvfR3ZhUtc+p3fY/Phr9A6fohDP/YuWnfeQn7ueQYP/RHF2iZCSITy/LpL/RZPuR12Y8fuDmxtzhCYgjerS7xFfY1EZ6Tn1ti4dAXRniU4cDfBUYXuGnqPX2T0J09yeXaHz+8c4vRqRPFqJvFvVCGvadc5gF0riV/ZVLJ+7NFM8k4V52lvHqtK2U88MzHZ5SXOVIWkL1WlnD5iVeqbXuu8a+dc6XxcGyh9cUCVVUEfZo2PWrYPCTwoOjH9bV3SMpwpaSZevtoKWdInJtJD1jmMtRTGA5g2Blf1c9qqMd7hrMFa7Yf4VrkZa7HaoQswhcMVGgrPbhftGaQQuHOXKHZ3ydbWGdSX2XIxPdWi62JGuSXKdBmeCjSOgYvYkk16NmBtlHNhc4jWCcOgjphbxm0PyXf7DM+cJWw3sWENMbcE25sUTpJnpYChNCAF+ShjMMro24zt1LKeBQTGMiQjYIuwSEl7XYreCGQNlxusFRQahv2cwfaILiM2doasN4bo9NUTNLxh17brGsDsFGZMslLTf/ttAjdOYjrhh76O5ah1KUo3BYZiT5g5RXwVfnr3dG4NIX1Dsas4UyVACsYzGr13N+GH2alMmxDVnEYxOZ+QuCrpPxVOVq8psLr0+hxKeQ/Dn1ZMwmpnodzHygACf94Ah3QFoTMlCRYaUcBCQ6KEYKOXcWZzSKE1g/UuqR6ilKM2iFmdTbC5oLEjMLspQhv22y5RuEUwWzD/+ttoH5knSCKy9ctc+YM/op80OT93kG7SopklLN19PwsnTqLnDzA8uMwgaaLMCl/ZOUkQDVnu1Fidr2NVyLZa5nJfU+iM/cNLHCsuUk9rpJsNHr1QR2wNEY2Q2cMziIU6Z1PN+fUBvR3JmtvPMFLsa8Dtc4JWJFgsJEcvPMHABRwOQtI4JMBybLiDGwzRtiBsJrQPL2KaMwyTiEGmGYqQc6sn2LgjwzYb3LKiuKmzRRoPeeQVuZP/YrtRhby2Xd8Ahgex6XL/iyb0OKYS92BkiFERAucreLbKGUW4EgiwXqYHIRCV4iuMM+Njf83hPQwZjnNc1UmdE5gSzJSzBE6XQBVghe+qrEaiUVVASwASlbvnKEMHxuAnwIeEelh6bzHIeHJ9VUhtDULnvjghQ6yKfS+kyZHWEKNRwuff2knAwZkajVDxhHE8cX6X7iBlp3uB0cXnCaSm1b6JY0u3Y01MZygpekPiUHHCbnF7vI5o11EnH0A0F8guXGDjf/4eVx77Ghdm9/PHN7+Fs/OHeM1ig//HW9/O6kxMwylaNmRkBY9ZzZ9sSgZpzt2HZ4lOzCOl5PL5ARfODQiyAW/un+G+7Ely0eTZS7P8kerQ7g24cybh4M0L7Cy0eLpfcOVsj61NxSl3lN14mdcvwK03CTpNx+ozpxGPPELWH9A8sEjr2AoykLjBFWyvR4Ejme+QzLbJa2269YTNVLNLzBPHXsvp2iH2hynvaG9wc7JGb5jyq6/0Tf1SdiOEvKZd1wD2zdmkZjj2lKrtbvr5Kc16J3w4tid4vEYgOW4kH//PV/MQTIem4hqPpsuYV0eXVz2YLCm/jf34OLd3SNx0tXOaujHlTU7Gz/mtSgqScgJRqDwnTBuHMTk27+OkRjUK4lBileeYYSwoSNC0pEaEDjfTxM0vYgd9bJGTb26RiSbDYUa/aRgh0c02draByjT1YY5yBqUUo7jBwCUMkzajWodACowqEK5H4AxNlzPPkNRJZD5iNEqJiwIbBohWHZfEjJygnxu6RrAjauwEkkHocDUI6o44VNRdTmgyOi5lVmZIqRhKy6AC/ijG1eu4pIZRCm0thZDk9Qb5jMCpPq36DouRI7HTX1o37Dth1zWASTfxlPaOyLiWlc+LCUHTeysBVZN3tVvZYbi3srmHACvLXBTjvsW9RFkfBsrx+sqLE1ASTcWYYzUJW8eKq+O2pqlWqamihJMKF9X9ZclgTKmQ5cRvf8BSwsc5pCkQLh+Hr1ZFGCkQskBKO+Z8VdI6UaiII0UkAgIilJSIQE2cWTcBYhGEiChBhHHZN2qQwhI1AmqzMStLdd58osNrD8wRBIrHL3Z5cr1Pp7/B8sZZomLEYjjH3csrDGVELQ54fmOAxDEvR/zAPk1cWI4HEXXVJgoibgp2mNPPI6TBrBzgzOwCw3oHZuZpxgFZLaTdirAS6jWNxLcSBcv7aDz4NnRWELo+Ru9idUGwtErz4K1oobgiY7ZkhA5iRqpNbjzAH5mvM9+IWFZ1ZuohMhoh+q9mEn8SRXzL678L7boHMInFOfXSyDV2QMT4VwUsQqpxL+KEKV/mkcZO2rQHVIKU8INXPd44cGaSoK9S62W458NO5UmzTDlcrnzOVcNGjH/srB+T5iwIhVCB9+Sc9TwwnJ85GXki66Sr01+XdBUQl2dyBpmPECbHioAibGBkhJUCIVOUqEameQZ8oARxpIhjRSRCAhF5dn9YAVhVPCjPEYSIOEFEsc/nGY2SjrgZoudqtPc1uPlmHxY+vj7i409uc3o747bNZ/mec59nId1h5c7X03jjUfLWLM9tDHhqvY+wmrfODHnzgYJEG5yIsXRAQDvchmLIbtji6/tv4UyyAlIho5iWCiiMpdNJIJQ06inKjcBown37adxyECtDOPVl9Nc/j9A50eGD1G+5h1RFXL6c89XNHIekrWo0rJe5PrHYJAkkzQBm60uI0CFeVUFDU/77v4z134V2XQPYtF0d6E1MvKhaOR53NvaQrrHyL/jCmgSB057XS+/74oOXq6tiwlXbJ3tea3XlMU6HrlUSfypkLAHy2ud+8fWOCyKCPSTW6kk3wegpV2zvcfYUU4RAOUuiM5J8RKwzhLUe9K1B6hxlMkKdUtcpoU5JTE5gC4Q1xCanoVMikzMUgiz02vUxlshmpLaGkYpRWCfAUXeG0Ggio8fj5fz74K9Fq4A0rGFUiAgShIwQEoyK0UFCKiNGSpKVVJg9yrm81P316piz1ld8X8b670a7vgFM+PYbC2W7D4yrdVNpJicUBLIMwxxCp4AoJwD5m3SqyxE55mFVVb1q+m1VFRTjIRDS2ZLP5XwLkFAldky4YxMALblf1jAGGKlKL26iuO9jwbKqKaq8nUKUml1WSHTFVhfjV4wTAu3UJEQVgBS4sIZQIc6BshppC5T2FIlq7mNhfN5LW/+3sQ5tfAWwEAU6KvwMSeMoMk0+KJCFxYxSXDoEocBZnJRYJ9CpIe9l6LPrFJ/8LKrzGMHMEm8+dCt3H1pieXPAwdmT1Ee7DGSBe+SzSBlxfGaGlbkFBI6VK+fYeeo8xsH5+jxrtVuIXcHxYp19+TZpmNINMzZtRscMOJxdZEH3kFnM490Ou3nEMLJYFUPsuDCwfHFri75VzAzrzC/diXSG7XSO7Sd20TIgl4owCLwiRtlYXhjHc1cG9LOCJZnRSrZoBwPs4AaN4jtt1zmAlbLLpWdghUCJMWpNHBRRyuM4iyhSpM68FxMmOBGO0/ZAqapqPYgJ6SuTU3moSvF0vGI6tKvAR4hyn5K6MZanBoxG2KI8duTzcJ4CD873Wfrc3ARQx6+1PIZFYsrXrCiT6kKUtBIx1tQaA3kgEcRgClQ+QOgMpSs+1wS0tLV7AMwUGp2maAp0XWNNuV9mKAY5SivMKMNlI1Ch/5YXCucEOtXk/QK7e5nu8+tYA6177+ENr72V+k0LyM0M1TmOGOwinjnH6EufR6Y5y3fdyvyBuxBKsvP0GXa/+BgDGfPUrW/m6eMnabqURtZjYbhGFkwALM53md95hqPpRXp6Hp2dZNfOMGwrXBAhYsmlXcvnzm5zJRMcmq1xYuE2lBQ8uz7gmTM9hIBjK20OL0VEgSQKfHP8KC94fnPAmc0hR2SXW8PnOaQ2McP023Zrv8jsywwhX87av8R2fQPYVU79i4mi03ZVyCRe/OefHwS6yeNKqmePNI+46udaR7vWNVT7TtcFr7FvuWA8Pq7Mx41zbdOXQXlte0LAScA7yQeWg03EdK107+VWbVACN84fCin8z9Vh5nRoXF2OlMgkRKAIAkWQDQn6u+gsIyXEyhp5EKEihTCSEEOYjTwjXwhsrYEVMTZKsEGEcZYsrDEM6uRBTGANTT2koUfENid0xk+Vkl4CXE69nYGAmoJ64LX/CxlghECogDj0yqs1CurFgNApgrBGqQ9LIAWhEgRSIcMQVAzhq5gYvwFg17TrGsCqeYhSTEFAlZepFCME/sNcMcmF7ykE/+GqgsfKcxkn98fNjpNPaCV5I67O/1QTu0tlC38sMQY3T6StvLRy/6m8XJXT8sn6qmpYXmupYzZRwPBN2yHGA5mtCgYCJ+WUoKOZ0ur3Ia5zoGWEFRE61ARBShxoQuXnQFZWVWqnG8IDJUlChVWSpBYStWKiSKGSCIJoTObF+PyVUiBDSbiwROPOewiXVhC2YPjE1xg+/mUuJy2eaywxVIsc6MCJe0JqJkNg6Z96DickWXsB+7abQcXUGyvM1WqELmQjOsETMwugNYdGXQ72rtAkYzHMCYOEGjVmXZ1FV6fdNCinQWsON2u881idgQ3YMZINY7HOVxhvW2oQ2oK53XPMrF/EBRHdpWMMw/1ek3++wUIzZilsMtNoI+Mc+WpWIW/YNe0VBzBjDL/0S7/Ef/yP/5G1tTVWV1f5W3/rb/HzP//zE5ka5/jFX/xF/t2/+3fs7Ozwxje+kd/8zd/k5MmT39S5qqT12O9xMG7rQY0ZrlUFT1BK4YiwXCAnSefKGyq3Twskjs81dd49I91kBWBTDKtp58SWJMTqNAgmWqv48A+JpaysVt+2UiFE4EHJCWyJKNI6VKnIWp7YA7bzvZg+iq5yc+VrtwYjFFolGBFgghwVFMSBJVRyL1e3SuJPvWYlBXEocdYR1QKiRkQYKlQUIoLA9xtC+T4bhBSoUBIvzjH3ptfTuPU2Bl9/jI3/+7+SnjnN6ZVbefjmVXaaczzYinjNwSZzIqP/3PN0n3oG4yTZ605g734LIohJejkzwwLrInbqB9lxB+iMtrh99AgHhi8glSSqRagwIREJHZkwKxIa9QxJBlqzWquxspSgZciXNy2XL2syKzgx3+Q1yy1iPSJ44gmC00+SBQmnW7MMOvsIlWL/TIKSgnakaM3GyJpCdrvf1P36cswZgzPfuhf1ctb+ZbZXHMB+7dd+jd/8zd/kt37rt7j99tt59NFH+Ymf+Ak6nQ7/4B/8AwD+2T/7Z/zrf/2v+a3f+i2OHj3KBz7wAb7/+7+fJ554giRJvrkTOhjLOE/FUXtCIufKqpTzOZrK0yqf8y7YVGg4vb2Moyb+VPWcGPNEJ0O+J/D0UhUrf+6p5DyUSfypdePiQZXEq3JvdlwGHEef1euutu/hq5U7VTy3cc+kN1vmvZxzRBISJQiEwFmHNRZTGHRaYCiInKUTKZwQ1NttwoVllHQYK8g2dzGJZhgMyciwI4dutolW9uFm5tm2Ad2hxdgA15ohnF+gPjvDTDNBNiJEEHHFhGTOQdhEdOaRSEaqxlZqfRFht0u828NJiWy1kLUaNR2gCo0djBBJDDMz0KgTiTazssZAxMShZSuXSCupBdByjhBLUgxp9PuEFuozkBAToaHIcGkKyhH0d4m7m4gwImo2CcIaSSBQWERFeXm17IYe2DXtFQewz3/+8/zQD/0QP/iDPwjAkSNH+M//+T/zhS98AfAf1g9/+MP8/M//PD/0Qz8EwH/4D/+B5eVlPv7xj/M3/+bf/IbPVdI6Jx9ax/hD7yhVRsvKG9qPwLLKEzkBr9RQJtonPC5Kb6lEp3FP5BReCDGpNuJw1YxGMV36vEZ+RIAj8PI0CCbcMx8WVnkrpyKfnS9JspUIo6o+MOPcU1lYqM5vmfRQCnyF1ZXnLLukAsoPoDUMMs3OsKATKuYTyXwt4FwIJjeMRgXD7QG99S2UyJk9UDCzmCCThGb7LhonD+KGA0ZPPsH2px+lFzV57IjkzKJgXmnuv+Vejt5xO2s24fNbigublzgkI+6//20sypyo1mGutUSqItY3JL9/MUfnIa+ZuZXXvfl2pJSc6yY89NQmLss4cu4J9l86RdRu0n7Tm2gcvR1xpUewM2DnuXWilX3I229CHTnKvIh5UHToE7G10+PTF3PSUcYdy4I31TLaYc7Clee59emnMNqwX91CZ+FWpNEMtjcZXtrCAM3hlwkvnUW2Zwhvex3BwlFiYajrPrJfIF9NOZ0bdk17xQHswQcf5KMf/SjPPPMMN910E1/96lf53Oc+x6//+q8D8MILL7C2tsbb3/728ZpOp8MDDzzAQw89dE0Ay7KMLMvGf3dL192noSqPY1KtG4d940Kh9RI6eClmgyj/K/NSpffC+FelHXbtJK2jlPERpRjg+JmrJx5d/bjMdU3LS1eelysJIcLPh3RC+HDMVCPYzJiu4WTg9b4Q4PTUt2uZxxOivMZS2kdInFcWQ1qDwCKsJSs0g8xgraUdSeZrkoYSWG3IM0PaSxlu9EhEzrzRLHYiVKuBW2zhxAmKzS12vvIUW197lo2wxZeGB/jK6jxHFxrccf8JOkc7XFgf8tgja3z10hb3HuzwujvuoL3YoO0cB5zBWMcnBwWP7vTYGSmaq0s8cPsqgZJc+dIlvvrUJWR3l/lnn6Jz+hHqiwss33s7szMJ+SBgY5DSv7SNaSzS7KzCodtoC2iX3u3DxvJYN+LctkEmcG+umRGW9u4aB88/jityZldr1LN9OGPp93qkW12whmQ0orl5DrmwQnjyJKoWElpLlI6QxQCVvopDPax9mUn8Gx7YN2Tve9/76Ha73HLLLSilMMbwK7/yK7z73e8GYG1tDYDl5eU965aXl8fPXW0f+tCH+Cf/5J+8aPvUPKDxFm/eCxF7Nrvxw0nx7+pgrwonr/3arkUq/fPAavK7Ko3u7Y0cJ8oqWsaY6e8m28YXK31fZglIkwKGH8025T6Ow+rxlVhL5a9Wr2NPGP2ia75qU8kp81XLSXFjnNO01WAQN1HdERKkIo4CVtoxu6mmlSg2+gWBGlHLR7RGXYQpiHuWA62Adi1EScn5bo4qz3FwtoaKDfPDZeriCHGriUtT8jOn0dtbBPUayaHDsLDE5VziNkfUQ8lcIyAJJKKUCjIWernjXN+SFg6rmrjFVYTOMSiyKxtgLUJK4qUlT3dBe7AXDmU1oc2QpYxQIWNyWVz7Rvk2mLMG9zIA7OWs/ctsrziA/c7v/A7/6T/9Jz72sY9x++2385WvfIX3vve9rK6u8p73vOdbOub73/9+fuZnfmb8d7fb5eDBgyhsOZVnCoim6AVVCX3POA1RzVH0/YpjBJk0+I0jM/9w8qEfn0fIvZ/1F3lqZQg3ruypUqOrBF1nxscZZ9fKXkeHK0eqTYDPVTmxUnlVOz99yAFh2f4joCy1a7wnVnphziJ1BkbjhEIHMVYG6LI/80XANO1PSoGU0r9fUk1+qL48psfTTTxiBzihsDJksQXvuGWeBw+3uDwo+Pzz2+yOCg5vneXu81+lk/VYPHk7f+OuBygaLc7tZPx/H1vHOsfh2Ro/eu9+Eixz/Tk6w9fBcEj6wnNc+c//EVWv0zx2hNnX3c0lHfLZbcHph85yfCHh+26a4dBMjDQ5zhiMsZzasXz8tKEZCY7XjnHHmw9RcwWj88+T/+nnEUCyssLC296KzXOyM8+Rr19AKUFiBsTpFlYoMpWggwa9/FUcbHvDrmmvOID97M/+LO973/vGoeBrXvMazpw5w4c+9CHe8573sLKyAsD6+jr79u0br1tfX+euu+665jHjOCaO4xdtl+NkdvnBcxMvQ5QgNqn8UW6f5MYnlTafa/I2lUvboyhRrp7OP+0xN7WtkiIsPRQBzlWj3ipdJ1G2EU15jVU4Wo53m0jsUIKmL0BYC7rUlJaiJLI6h8B4b0vsLTgIUyB0hpEhTkYYOX7nrmaKvPi1lQ3iQk4ay6eltV/8HpQBfRkqN5OQ21YaYBMeOdfjE09s8vTlIf2L51h9+isw3GK+M8NNSzHMd7jc3+BrF7to6zgyX+d1h2aoRwrrFrAO8svrDB/7Cv1HHiHZv8rcvXfTed09XLyScurhNR49v0VRNHnjwRqyrUpispfJvjKy9DYtUSgJjy5wy/FFhNAUFy8weu4FlITagQM0Tp7EZSmut4XeXENKCGxOVAwoVEKhGqRBnVHwKno17mUm8W/I6XxjNhwOkVLu2aaUwpZv/tGjR1lZWeFTn/rUGLC63S4PP/wwP/VTP/VNnq38wIyxYxoQxOSXlCD9TCH/ASw/5BXXy1Vrp47rJqB19Qi1CZuUqwoIk72ujkQnBcPy2NeKRqtdplFlKjq0k9OixCRQtq6axi3HuTE3njcpypyZA6HKcMh4ukbpjU6AXIzBSkp/TGccTtjxoI3SJ2SiTzUhzIoyB1flAQUOOxqSrV3EDvoEfcGRpiJUTY5GS8yKm2imuwSNGumZM7iNTVo9wU1zEcYJZtNd8ud2MUqxHbXYDRvQzYlmFqnfcgtudo4LOuL82pDLA81CM+KOfU2OzNWIo9Arz0690a04YN9sjVqsiJTkYjdl22maSZvm4RM4HJfDGS5tO2RuSVJLZBzSCYwMKYIEI0ICZ4hNSm4medlvt90IIa9trziA/bW/9tf4lV/5FQ4dOsTtt9/Ol7/8ZX7913+dv/23/zbgvZ73vve9/PIv/zInT54c0yhWV1f54R/+4W/uZCV4jKFGUCar2QMQToa4cAJs0hmvliokFt+2I8C7MyXpVThb5nEmsjST6qSdpNXG2xgfv7q2q4fTVmGisIaKKuFKAcMJ/aEM14Qsj+1vPIvDTOl7hbI6pO9/BEegpBedFgLPevPX78I6MvTXqaxB2ZTQFYQSQiX9ZCJRKsVKSRBKgkghhCgH2ZrxoFoQYLUvipgqRyT2sPOF9H2gwlmKy5fZ/MM/ZPTcc9QOH+cHHngrdmkfjXyO2eExQp2TvvA8m3/wvzFZzoE77uZHX/d6UAHR44+y+9kvMXKSRxdv57G5k7QiyV85cSd33X0bG7ngjzckT3xhnYVGxD0HW7zj1ph6HDLbrpEJRSGCMcAfnKnxtpsX6NRCzu2kfP6FLayxvLZzmNe+fT/WOr60Y/nas5okz3hgU3NbYRAWUtVAx/NIZ4j1kHrRRWSvZhL/BhP/WvaKA9hv/MZv8IEPfIC///f/PpcvX2Z1dZW/9/f+Hr/wC78w3ufnfu7nGAwG/ORP/iQ7Ozu86U1v4hOf+MQ3zwFj4n25MuwTL/Js3FT+yPlEbZmDcsixWIMYL6w8KocQbpJ/ouJgVTaZbLQnT3a1K7bnr6pTwDJpPZ+6zrFnVp1zb2K+gjhVhY344R5VVdUKkGXir2qvnDD08QoQVoM1KOeHi0gpxjnByn0SUk6OYz1NxDtb0+GunfDS9jhwk0qswGGHA0YvnKb/9a/TjmMOtQT1A22gDazgjKG4vM7o+RfQuzssHDrI8nyMDEM2RjtsPvMkXS0425/h8dES8506rz++QvOmOba2U86vX+KrF7e5ZQnecWvEXatNtJDk+GpzmSUFoJUEHJmrM9eIuNzPOb+TkmnLofl5xJF5nHWsfX2dx7Y3aGaGEyODsxbrQMsQGySEJiexmtiMiM3o6pvthr3K9ooDWKvV4sMf/jAf/vCHX3IfIQQf/OAH+eAHP/iyzuXGhNAq2V59dPacDc+lqip8+OS2v5BrRHLVB9lTD67K1k+BzEQ/bG82aPpDPrUOqJq1hVTj/NbYq5mq6vm15irPzo0VMIS1iKqVSCiUCManqgbUVsNtJ6DpQUcjfTJfWM/s33PVE0Kwdy6dDyGdK7sJSmY/ngfnZNntIKrwscrXCarmc9lsUb/5ZkQUEy4tkp49h+526UVNrtTnyEVATJ36rbdTGw2QcczgySfLNi9B4/bXIAg4MbeffKZBHEd0hwVfONOllxlmGxGvOzzL/kgTXDhNd0MjWm3Uvv0EjaYv9FS3ye4W5tldbCyYzyR3tBQ5ktgVvLA5xDiIAsUty03qqWW2CKHvwBoCkxPoEdJZChFgVJ2hukFk/U7bdd0L6aQah2B+A2NAc0w+/2KsZgqTid3T+ZopE1P7vCj3VVUK5d5qAJM82mT3q6kN1cWUJFiq/sbqCBIq+epKbmfKu/MhmR+kKkyBNJ6Yq4IEglJV1oEpCwFSVJr7DmE1whmME+ROoUWA7zqcqCkISkiuLtv5yUdWW4yzOOPH0Y1H0gWRn0cpVRk2eqdRlqEkQmKFJFxaZvb7vp/OaER65gw7Dz9Efvkyz84d4aH9r2OnPsN98/P81Xf+dWaUYfDE42z+/u/jrKF5193M//W/wVwUM4PifqHYSS1/enbIHz69xWw94oHj83zPrcvIS+cJ/uTTXDr9LPUTJ5j/q99HVDtEiEZJgVICd/EM+aknKUg5euIkJ26/kyKu8Xh3xJ++UOCE5MhsnR+4fZlokDA7qMG6QxhNVPSp5TtoETCQCZlq0QtfvSrkjVaia9v1DWDs9SCuJjNM1Q73PjtFJH3xuqnK3zg2onTe3FV7T62+ZlJ+4nmJcWWyOn/ZNzkVNVYHuZY2xNjPq/JuJalVKDtuZh+D9lT9wv9UJEif8zMozHSl8ur3hwnejnF4anxa1TTuxqjlwV6KMvkvKugVkNSI9h8AQO/uUmxsMHruOTZ7IS+oE2y0Io4tLKAO7ieJYfjs06Tnz+G0pnnXPcSHjqCShFY+QBQj1roFo6zg2fUhB+YczTjg5FKDdFewsbnO8PnnUfUabjREWe0196Xz3uiwj7l0Dqv7dFbmWKwZdB2e2tWsdzVIxcmFBgdmaoRhhozV+E1QVhOaHCtBBwG5jCnkq5fEv2HXtusawMat01UrTZW4FozzNe5FyhHXOs5UKcBxFapZqqrjWAV1LHJYrb7a8yoPNO11XQ1eYgqmqsi0pG1UFcQ9Qea4WOD3qdqhEHJcFBiHcVMv1JcSfNuThbIJ3BJYjTWWQltMlkLPILRApSNC6YgjRa1To31glpZNCRmizzxNUW9wKZhhXc3AcEC71WHm9pMEUYM7Dy3RXmxRSyIud0d87rm973ktC5i5+XZmlhY5Wl/k9TMJvcgwpzKeWu9xJhA0VI3mTUcRxnA5avD8+R4qHLJfb7JidghGBSeyLv1gyLyLWdzRiAubBLsXqLcUcv8ccU2gL77ASA9p9eHuGA7NOeZVk015E0Nb4OYPMRs3cEFMGDkasQUpaShLkwyhHN25fQwO3UFcT0hURH24iwxqxM0mBAKtrvmt9e2xG0z8a9r1D2DT1UFRqio4MfFGKMHJ2RKXLGWN7Krkuv9dHXkMYuNEtdgrNPgi8pSboBFc5XVVoFcdW0yS8tMoVu5vhMQikTgUZkKqLyV5rAgwKvFej7Moq8u0XOCVW8WeV+bpBFL6sWo2QzpDYAu01qTaUAyHsDlARpqwr6ipiHoS0llus9BcZcaOkG6X7KufI5URX4pP8FB8jEQ63r6wzOu/9/WsRAkrC0fI2gusDQx/dLrH/3pyY5wfQ8CtMxHvevP3sNqUzGdDbu7vUOiCJ9Ihf/z8JiMjeSBs8bY33IPC8bWswx8/sUHgNN/DaWY4T2w0D/RzbosKIhcwd+kcqhsj0oz2fEijdgBnIXvyy6RPwMLsHO/afxi7UOeF+TkeW97PyAWI/U0O1jqEgSRJDDMNjRAwG2hm3QAdWC4cOMm51mEaFLSjHWa21xG1NvXGHEkkENGrCWA3qpDXsuscwGCcmyoT3JNc/lQstTcXPrV2+smrA9BrgBLTntfVa64VxE4/vdczmj783o/BRJJnkuCfug7nvEx0WQgYy1aX1zM+y3R6rvIAnS8EKGeRzpatPw5rDOQjcDnCJEgRopQkiEMikRA5iy0K7O4mhYjYiZe4mIxoRIqsFRMvzBJGMfW5OjQjCpczzDTnd1IQXopHCMG+VhM7t0AwXyPqb9BhF5sZXkgLdgY5XSMZzgbI2RmkcAwuh6z1c0Kb02NAIboEVtPRBW2hkVYRjjTChghrUZFEqDp6OMLs7mBGObVI0g5WCGoxGyoiVfN0XcSwFqJlUIa9lkj59zJCExrr6SlJg6Fro8wIXXRxWQpB7GXExaQSfMO+c3ZdA9gesulk49hjmrQSlVr0MBn8+iJwesmTjBP3dnob0yBxDW+suqY97Tmlt2hdGfLJUvrZp9Cr6dzePzTjjBh4HXwrQ3AOOzXhCGf8lG48zsmS4Vp5YQKHMh6wqrVOSYycwJ0QlGRf6dnuhSXLHYXWmEJjnacTVBQJB15y2lis1rgix6myahvE2FJmRxeG2UbIrStNFhohtVDy9Ys9Tq33Wehe4PD6M9SyHu1kkftrqwxVhHKWz234Zva+rHPTcgvlNMPRCl9OBXExYjG7wEx/F6kk1hhUHDGQMeeCRbpRnXiwwUx3m6g7QHUKUBEirhGKmJoNyK1ifWj443OaEIvu73Kyv0toNc1eSveFjFxFFJ0jiMY+bFGQXrpMd+c0ur1AL9hHZjv0e/lfcO+8cnZjqMe17foGsHHyCPbmojwBwlWtRG6SPxDW4tT0+pLP9aKemvL5SqsehxWMh4eIae2wsVdWxYPiKjb9VAK+FBdECKSKSi1CAS6AMiRW1xgqYq2kkNVmMVVh9BO4wSEDNzUmrnw/nCUwBViDFQoTxF7QUDGliuHPI6TCOEGaG4YZZFqj8wLrCqiqi3jtfWMcRnrPzOUpTvmKMEGCUxZjQeeG2dmE7zk+w+37Wjyx1ud/PHaZs5sj7th5jrdf/BKL2Q7zN53g++5JMI0Wn9sM+R+XIjIUtx5ocdf+WQDOXwn5zNYcDXa5Z7RBtNElCAQmK1BxxJVknkfn9nMm2ccyz3HH9lPMX+kSLhQ4FSPrTSJVo0lEYRRnuikPnx0idc6bxXneIs6R6JT84gbb61vk9RbZ3QHi5AouyxmcPsv2C48xnN/P+eQYu26BYf9VHOpxI4S8pl3nAPbn23TKaWp64lVh5p4NL2F7E/wv7bNd7YlN/1223VTN5tPHhb3gueciyz3L1qeq+2k6b1YdZ0KSrdZUL7PsAJgqIFRvjKh+i0nJYNyUXYG3cwg3WTO5zPLc4yKJf3560EogoK0cC6GlLixZbuimmv6oIBvlFHlGQ2d0yHEiQzlFzyhSfEtUS5VnUSE9VcfKgpTQ89mcAOtbqTLn6Q1d1aApErQVOF22QJVfAlJAiCFyYLWhn1uEdjiZ05ADakVKNxuQDodoQqzW5Qt12EJj0hyd5eSFJdWOTH93ejXXk13fALZn9l9V1fMftOmMkx+r5pvBvcZ8WVm8GoncVQ8cVIoRE+WGCh6qEPGqfJoz5To1hikx1RI0uSrvHY1D27EXOfnATbcvCaQHICeQtvBeFdZ7mkEy9WL9u2BFMB6m6xQ4EfizmoLAFoS2IJYQh376jlAKlEUFfip3YhyhkwgjEFYgAokKA5QICKQiUMK3LoU+PBNR7HNz1iBxhJEkTgLkqMfgy+fZejKjHrR508oqt+9fYa4riQ8HZPmAUajpnb+EUIL52lHuO7iPQgQcy6/QefIJjJDMREvM1+eJohbDQzdzbqaNlAIVh8hAsRs0CRrzzEURs52E1lKLppohma0hhQWd0+r2OLx+moXCstRY4siRfQgBR69cgI0cbS3y4HHiYzMQ1QlWDnpp7DiifnCVTjyk1llCrM6yOF9nEL2azdw3Bttey65rABNjmehpiWYPLHIMYg5UMJ7/OPYYXhq99j5fVg+rsK3ceI2rqfJb1Si1UsPegZoGquqYMAanyXnK1yDKUW7WIKwf8CGEb9Z2ApQuUMXA5+aiGi6s+0OYAmyBz6fJEsTAorDCz7uM9BBlC0JrSJSjFimiMECqAKEcQeA1vGrWEVqFKLzXJpVChgFKhgRCEUpJGPhp2DIBESeeVFxOS49CP/xD9K7Qe/rzbHTP0bjlDr73nYcJDu6nN1rkSvcoWV4wPPUVgq9+BpUOWLhjngfvmAEV0HjscRqPf45cBMydeAP9wys4GdNv387I3jLlEPqMYUjAApK52TqdfR1atT7JbB0hDK7IaO9e4ti55yiyHHHbfXDiFggjwiKGcymFEMibbia55V6ECAmGFpk6VBLTPHyA2X0xrjHDzIEFTKdOL9bf+M36Mu1GDuzadl0D2NU2CaiqxqJrhGgvlbh/qShy7BlREuUrxtj0zm5q90lz+SRC3Vut3KtuMbXznxvJTr8yNx4qUhUKJgNOplzCiq4xXUOAUsX2pU2UgF2Fn9cEfDfZtwJeIZjw7qZ3tRaMRVlDzWTEJmOEIwsSRi5EqZiaUDgkylnqJgMMsckITIETltjk1GyGIUCrgCK4Sl7JWZQuvOyNzUuduCrc9rlMZTWRSVE6R+oUaTOwDoPvdXRSYcIEGzXIhMJkOZCXt0CpsVa+xy9q1Ph22w0e2DXtugawqiXH/+E/NNaV7KuXuLn8B15OkvtMtLmmIa/iiVWA4PNLpqwgyskYtClQqTwwAQhpJh7bmMgqyrXT9UWoJKN9r6Qs+7ircNKLIQrnCEwOzk2G7lINufWfJikDL6kDvsWnfCWB8w3czjmMDH0rkShIjSYtDLnSWF3gROFfog0wFow2Pu9j8rKpG7SAQhVk0hAIvEpFOXWpAkZrHXmmGQ0LbK1N874HmYszrNbsPvpl7MNf5HRtgS82D7Mb1Dhq2tx264PUXY5NC+yffBqBJY4K2jedxCBYdT3C5x9mFCScbR1kq744RRqBZtbj4PZpOqNtkp0NzJkL9Ho7uKhFI/f8ORlIwnqClFCsnyf97B9gZUhfhfRWX0uhQi5nbTaf2QSlqMchSaQgLxievcD25VNknSW23RLDosWgd6OZ+ztt1zWAjbt0xwx1iXWeqipwL8HTqbwVN05uV8BSaUdVlNfxN2159GrWom9kLr+NS3kdoJw96b8lpRM4Jgn16dmRVpTgUk1TshZMAc4gKh0vMQE8hA8Ppc1LgHQg/RgzKyS6TLAHIkBMv2g36aGUVmOEJJOhl1AWgtQMSAtLroxPWMsCawTWhhgrysncOdpkY89KS8gDTR4YQuHH6GFNCWJlocQ5r6k/zDGdFo17b2XuYIvul7/K2m//NsPnnue55Vt45DhsNhfIDnfYf+sRRAjioc8g/vTTBDojesPdNO94rf93euYZmqe/xq5qcG5fwNZ8u8wAegv62yycfYyDO2cpeiNGF7bpDTJUZx5TaA/8ShHUE6R0ZGsXGJ7/GgUBG3e9mct3vYVhkPD05SGnLmwRh5I7D8xwYrEBRe4B7JknGSx0Odu+mW21zOhGFfI7bvIv3uX6s5fy7F8cCImpn3ENbhKAXuNA7hp/vaimOGZYTMdue8PMqZ0mVzbVLnT1WjGuGExGpFWKGdOh87WvdxK2jjsOyuqiKYmsNs8waYrQBUpCqAQqjpGNFrLRxsmQItXoUQHGEkiBVIIcSc8G9AsYdQdkVzYxO13qwjJXj6jHISMUW4Wij8JFMTJJCJUg0Sm1fIDUBSMUQxFQOJBl03juBD0i+jLGhjFRkhBFIVGeEe7uEA161NE0I0VdgsoyxGCAzQpGKqYfNxnJkCLN0cMho9ywa0O2XMIuEX1CBgT0rK989rUkNQLjXClF5Em4IBgYxWYRsJNB3h/C7jZ0d158g3ybrGrmfjk/3y7b2tri3e9+N+12m5mZGf7O3/k79Pt/vlbaRz/6Ud72trfRbrcRQrCzs/Mtnfv69sCuys9IIPDRIXK61/AqG4eXUk5CNecnFwkktpw4xJ71AmQwBiKBHYNK5blJqoqjX1FtF85PA/J/2KlcVfV8SUY12lcMVVSGuQapCx+eCem3l95l9dosClNyH5Qqr5Nx2sdfnwi8PI2zBCYjsBalc3RRkBWGUdpjsHmGge0iglUWkhmCep355ePUkyVim9L/6mP0vvhlhhbUyeMsLsWoOOICCX8ysMSjIbPPPULz0iWy1gz333IXt77hIGlh+crpbR56ZoP9RnD369/E6v33IHsjwo1L9NPz6N2jnFmrIcKIwxZOrHRQVnMmaLG2VScIA06s3M7h1ePQT9n/lTMUjzxOOD/H/JvfQPP4CvLsFtGfjdg6tcl2a4EXDt1BtzHLoTgjOX2BmfNnec61+QpL9AkJmweJTmqckFwJV7hyroeRI5wSLLUS6rFivhExk4QM4gZfDA9xXmW0R4KbnniS1ReeZphN1Dz+/9ne/e53c+nSJT75yU9SFAU/8RM/wU/+5E/ysY997CXXDIdD3vGOd/COd7yD97///d/yua9zAJto4ANle8cEGCou0rRNcmOVN+N3FDZHWF3K8+wdezbxYspZkM76PBTOT9Qu+VXjpHf5qwpxVJU/g5KPNRVWltVGr3JajMmlVigPeiZHWIMLYv9Thp9lfh5rHMZU+b+pyy69CChzhUIhjadPKJMTmAKjNbm2ZIMB6dYFRtkWYj5m9uDNBPUancV5avubRKZAn7rMztkdRrlBrubMNiNsnLCOYHMEtY0Rh/70MRYffYjmTce4885bmbtrH1+/0OX//ekrfPn0Dq8/2ubuN97D0kqd1tOPsfQnnyTrb/J4L+ChK6uMwjodC/FiC+UMF1WTP9tNiGoJ7WP7uelQk2D9Miuf/QrukT+mfuQQR952JwuH2vR6CWe7Gdtndrh8dIVTK7dyZf9R9NazHDz7J4jhBqeaN/HpmZNshh1m2zGLMzWkFGx0M66sDZBCcGCpyb75Os04YLYW0ooCBlHC48E+HlaOw+kWR577Cov5RfrFq1eF/MuqB/bkk0/yiU98gkceeYR7770X8KKm73znO/kX/+JfsLq6es11733vewH4zGc+87LOf30D2NjE1KMyPJoKDfeYc9PBWbmLG68eA9E1fbepw4z3vPocVfL9qirolDLF5Eqr81X0iYpK4a6iiLhJpa86e1UscNPSilORqqtIs+X+DrwwdalSKhRKScJA+qlGUoz1vKQUKCmQSiJUgBAOoRRSSaSyqEAQKYlRpXKrECAlUoEKvCcYKogU1ELJbCNisR1Tr4UMnWSrEDgnUYEiiSQNZZhxQyILSglGtY6Xo45qiMBPQhoY2EgdTktsq0VjZYlkroMyBexuIrMhYadJsrpCvDBP0KgTxBGq+rExtVgxF1lEaGjFgkY9QghJI3ekmZclmolgPtA0AkEjcMSBIA4V9XpMo12noTNqcYe4GKHzV2+s2iuVA6tmqlb2UgNzvlF76KGHmJmZGYMXwNvf/naklDz88MP8jb/xN77lY38j9l0AYJPKnm8ZKr8Vyyk+TMGRx6pqGMVV0CMkLpgosE7Gxk+D28ScUOz1/6DSoPd7Txqtx0NphR+w4aqhtFP0B1yEsP6aq2IB4EUDVTQWDnQCpM4ROgPnCEWArBRenaKwyhcwTE5YDfMtQ22LICPEqAgd5jTrlgVTMCMT6kWDOM+IGglxpCgCOdbLVwjCWkAym0ChabViOvUIE4elNyioNSNm9jWZOz5L7UCTqCYQJmelqXjXXSu8/uQ8hXU8vat5YmeX/Tua2zotmonheKhpuhfITETaTHi2czdaBAyTORbjJk5ITm1nnNvJaFjNLXffz6Hbbka6AjnaoP/p/4klYPENr2X+Da8jClusJ/sIgoSlaIa56BCzRZs7wzazcZ9UFeQzEelCEyNDunN1docFAYbj8ZDD0S5RFNJu1GnUJaGLueumBeJmzIpc4li0wIoa0BsO4bf/28u7fV9lO3jw4J6/f/EXf5Ff+qVf+paPt7a2xtLS0p5tQRAwNzf3knNeX0m7/gFMTDwX5yq5Zesn8Qi1Z1eHG9Mh9rK4yvyWnKZXVIn1KQArOWGOSs9r0jIjSq/Lh6CVo1W1D1WgWXpYcqLICuV0JFmpsPqcGBZfaQyiMWVjLIFtDaJIfTgaxCjp9ymcRJevUVmNMtnkNTiLFgGFrJOLCKMEtaSgraHhIqJ6TBAkhElEEHimvZITvlMQK6JmiCskST2knihMGIzfx3oS0Jir0dzXJF6oEUQCYTSzieK+Y7M4IXnq8oDff3qDczsjcme5pV6jVjPEzrBk1tFW8UTjJM+1T5CqhEBJOkpSGMv5rSFruylztZAjt9/M4uEZ3MYl+p/5n4ye/DLhykE6b/l+oqMnyfuG+fWcfGiYiZo0k0WaJqEhBEfECCtzNmaXuDSXkAcJg1wzyA2h05y0I465ISoIcbHGxRJByLHVDrKRMB859s2sMltzqF7vlb6bX9JeqalE586do91uj7e/lPf1vve9j1/7tV/7c4/55JNPfsvX80rZdQ5gYs8voOzDm/KkuFblUY7T4BXL3TkL9ur98Ml9ypC0as2ZAq6q9jeRLBR7tvpNZcWwBCJXNSlOVQT98+Ns2+SqrQFhS3pF6d3tAdiS4Cic7xagmmMpStWK6lilxpizBBRlw7gfpFtN1XbWYqylMJZCO4yt2pgA68bzFQttSXOLwZQAJwi0RRcGkxlsYcbMb5ulFDsb6KxAjGBOwf+PvT8Pkuw6z7vB31nukmtl7dXVewONbiwEQADEwp0EJJGUZGuZz8MZesJaQgw7hl7CinDYEZItyXZ400TY1B/DiC9ibCsse+YbK6RPXj7alLhTIIiNBIi9gUYDvVR37bnf5Zwzf5x7b2Z1NymBIFtsTr8RVZl5865ZeZ96l+d93rwVEmc1tsdtrJHE2YhaNsA5Qx7lpMaRYomzIS2bYJwjVQGyFdGIFP3E8NrGCN3LieM2weIqeXueC4nEbKVcHBl2Rjmj1DJOMrLhiDwf+nxhZn3e0mwQBheRKsaMUswoRTuDUjs42cVGMaadYQ0kuWN3kLKxM0LqnGE2JA0z0v7gLXxX3559v5j47XZ7D4B9J/vVX/1VfuEXfuG7rnPs2DFWVla4dOnSnuV5nrO1tVXNgP1B2vUNYOX4scKckBihC0aY8CPGKisARcpizJbXii9DSkFZJZQ4FfhkuTOFN2QQUuMoj1cCmCcxSDc1fbAcGltRHRzOadAe1MpZhaIgpJZQaoTCKVXBa3l+Mht5oJEB6LAIN4sBts4iSP35CYFWIVIWeS6pMFJX5+k9S0NkUmKTExuLMzmZceS5xSQZJslIgozeMGU3TxkloZfRweByQz7OyRLDbj9lbXeECR1B0ROZ9hJ6W2MG6wNcbYxJ/OeZrF3i0h9/ieHpM4jDR7n/offijq6wva341nlBMhpxaPgmJ7c3CU1K3w3YDhIyaVjtnuZ49zQ6CLA3vQNzy0mGmeP5N3f40rMXWYgcH165ndtO3Ma5IXxhDV47dZ5cSBKtMUJQH+yws3meMN0m2RkxuDTAGoc+eJH2zRcgCAg3egTrPaRwiNmAYUdDo0UaLpI3Vlnrpjz76hZPvLbFIddjVbxKkw164x9dSenFxUUWFxf/zPUeeughdnZ2ePLJJ7n33nsB+PznP4+1lgceeOAHfZrXOYAVIFGCh+fVy0KxYdqb2cuwn5JzqJL+FQerGIKL9J6SsD5hjpgaCuIK/82Ve3RVCFml1Kd6G312vAwbZcUx8sDntcacUFghixaYKe/LZB5olSsAW3jwKq4W6xDCE2bLIbVOSAwhudSFx+dZ9MpmBG5IYMcEBrBe9sYa639yQ5YZRqlhJAxZXoKkwxmLzbyXNRrn7A4zTK6qZnCZ5IwHKUkvJRhk2EKpIe926X3rWXaffobZBxOOfeAhGitNvgV8fcOxnoyR+RaHhxkiHzGOvRiiEY5o9xLL669QiyNqJ28mXm2y1jd8+bmLfOWlDQ4t1Ln3lmNEJxdJLvR47uXTPH56myjWdDoxYajY7Q4Zbu4wHm0xuNhj58w2JjXMpiNmohEyVLhz27hzW/7/2/450mQG1xozPjAkzR27Y8PZ9QGnzuxizAab6cv087MMsmuXxPcTot6OB/bdi1Lfq91666185CMf4Vd+5Vf4zGc+Q5ZlfOpTn+LjH/94VYE8d+4cDz/8ML/7u7/L/fffD/jc2draGqdOnQLg2WefpdVqcejQIebm5v7cx7++Aawc87VHNLC0CUhdQaW4nPbpFf2qHNa0Jr2TRTq+zENN7d1TKqZAcGp/ZXRYvXYTT7HysMCHaKKoDTqmdMYK4FVB4RX6yUO+EKA8J2xPZdNfQ6mdL5VFFl0CJUteOONHqskQIy2IHCkKWkcRCiopCLUkKquTZfVTSVQgUU4Rhop6qMhDVXlgWklUqNCRRoWqGIsGqlGnfuwI1lii5UXMzjrJaYkbSmIUjSiAZptuZ5XUjAhqEfvtDiCYUylhLUAFCtfbInvjVUQqWNUpd+xvMteKGBnDa1sjtkYZyzMRd+xvgZIQaVCCpgmJWnXCYMSIGk4t+Ih7fxM930YpQZwUM1KERCwtky4uQKONrDeJlaARShZnYvYvNVhxOW23n9gF5Mk1FDQ09u0B2NvY9s+y3/u93+NTn/oUDz/8MFJKfv7nf55Pf/rT1ftZlvHSSy8xHE46Fz7zmc/wm7/5m9Xr97///QD823/7b//M0HXarm8AM77Hj4p4KgowuBLObAEKctpjAqpqYCnIV9IZKL7Q0oeTk/yV30oVQHMFeAGVAGK1YHJDl7x5UQ2GLQBHQjk8t8yiOSEhqE8BcAHIKsLKcHK8op1KmQRhUgQCLTytAWc9l8zkWCHJZIhVNdIgAzVAyaygTkiEkkShpl0LEHFILdIIqcBZVKQJmyEmM8y0IxbbMXkQVd5oLdbUWhG12ZhoJkKF/nqj5WWWfvonmRsMsTvrJC8/w+ipXez8UeYP3kM0O4NoHObMXIfAZLRHm7x/+CqBzehEQ1oLbYRzJK+/xOjUKxA3ec+xu3nn+25iYARn+hn/5flLtELJu452+PFbF9gaG051U3ZTw/5Gh060RDMLGYfL2PgwuYoR0YhaPCQkJ1repbG7gxWa3vJN9BYOo8KI9sI8zVjibMCdN88Rt2OW1CJH6ksshmOiwQD+H//rW/7afi/2w6xGMTc3911Jq0eOHLlCQOA3fuM33lb1s7TrGsDKPBBMJJZLnvqeKuMed+gy0Ckri0JV/YXlNoICxCqZG1F5ZpNK4xSQldvu+SkqhxW/q2z+mZyHKMixl3egOyGLaqpgoh3mqn7KPR6hs35WZKn26gzCqWK7DGFTchFgVY1MRRgJQsjJKLRCt15Jz3vKAk+jKK9dlh6WgChSNGJNrhWZ8e1IgZIEkULXNCpShXor6GaDxolZkIrRC99i5+kvk7zxGi4PqR+8C+IAG82w25xB2pz5zQGH+9tEZowKFDKIsFnOaH2d5MImqjPHoZO30jjU5sLQ8MLONi+tDzkyG/OewzPculTnXC9lIIbIQUZLxtRsgzAzqNl9uKXbsGETYTYIzEUCm6LiwIOzDBgsHCCdP4bSGlWTxErQiiQrczUSpZgLHZ3OLPWaI7+GVcgbdnW7rgEMPAg4N4ELWXgEVZqrSHmVFNBqwk9JZadQOS32I/AtQB7zpigQolAYmy4gFmcgxFRlsVpaVian5KQLK0Gt4qYV51MIYRfAhj8T55PyE1Kq57tJa/wVlxOyy2sqcm+mGCwrEAgZIgsKh3I5GIeyRYuSc5jMkA3GpMMhspHRDhVBHGAdnO8lhCYDJ9DtOrXcsFAD9JCxMlzMJZuZJJQavXqQRs2gm01Mr8vo5ecZ6Rrr9UUGQYNorGjtO0K9ViNpzzI3uETdDDD1NnlrHiE0sQCbZhiTk9c70FnAWEc/a9NTC+h6nZpz1LfXkKmgKR1zjZC2duj+Bk4IglwxoyNMPUBTZ200zw4xuW7S1JaGzpBOsmHqaEJqoaXmAKnIVcA4t2iXY6TvyQwyy5xJyERGUyi0iEllQDrtBf+A7Yc5hPyLtOscwKYS8FAMrvA3pRBywusSgooRViavHJSSNCUkebDwgaaFoocx956PVKBKeuokCBVTwFbtu9hWVVQH73l50YgyHLVMyg8ll01NaBGFt+ZMVkTHk4lIwmTobAw4jK5hhFdk9V6kH4iRi4Ac7WlngS4Gm+SE2QhhUqLMq2tYB/k4YbS+w7C7SdAasb8RkHfq7I4znrrQhyzlkBEc2zdH4Awzc3A83qIvQr42qvP6OEYFMdE7H2B+5gHs7jbj559m+PSjnK8t8tXFd3K2vsLxpuaRd76H5dgRXbxA7dQLZMMB2eHbSJbmIYppXgQzGJGYjGz/CumRd5LLgPXFIVu9MbHLaLgdZl5/hkDUWFIHGS7Ms2h7xJdO4y5sEzcWObhwkvl2m51wkW8ngnGScDgKuS0y1IMR607zSr6AFY7D9QaHmy2kECTU2U0NIRnZeBspetSs5WiasyosQtaRah9D1WQkrx0o3ACwq9v1DWDTrTLTuaWCmlAKyE/hCpXExMQVm+yiWOaKViThJgApXDlRw69spzJte5yvaa2vKb6WKGSsvZJ12T40bWV1tDyf6SrqdPXUh4vCZh4YVbhnF05MSLa2HPJbJOkleOqGyVDFqTl8FTIfp+TDMTLPaWiJCRU7o4zNYUaepiw4garHRCInihyRToidI3IBWR6QhyFqfoHoQIv8/JsMhgOSN1+n20g5545yqtWmFTYw80uEsxFu1MeNt8l3N0mT/YyVwwaKUIDLjOej6TpJc4lMhwxlyiBKsfmQrLuN7W0hgia11irtWFFPLGp3Fze6hBYhDenQsaabxGzpNt08Y1E56tLSlpYNEdElIhewpCwu9JVck2uy3IEzWDcG10fhaFlDC0uOYiAEidCk4vq+fX4U7Lr+CxipJn5MSYOYUqewZWL/8r7A6tkEMKbzYtKZAmJsQYHQXku/qkS6Yq7ipKLodzIZjQaeWOrRrQS86dpnSd3wlVSBA1MUFISEgs9WpeqcRebj4hoNqICSP5ZXl6Q8oDmHNClBnvh8mPLJeGcNYzRWxAwwpDYjyy1ZZsjGOdkow6bGj0xzjsxYkoKgmoxT0v4ILXJ0koIxOGcYJTm9QUaA8LQLwOaW8faI3oU+aiXl5k6N2f0dOpHk5Usjzm+P6ewa9rXniEJFPh6Rf/MpchmSJbsMFo5iheSSabD+ZpdMaga5YZhbQptihjFrySykiny8xoLcopF0sdvnGIy2GGcNeotjkihnq59wYWPAdj9l5sIWrz9/kRmRkcwtsrS8ilEB67tjzg3H3jOeqSFaApnlDN48z/ql11DCoSOJDCTdYIZXZiI24pzh4Boy8Y3x8zvfxvY/inZdA1guQ4xQXnOe6ZYdV/QqenhRruwt3Ets9ZQJz1aXxToCV6hHOMq2Hyd0tb5Xj7BIm1/mJQmsxNMlCkpCmTBzbuL4VfDqXZ9qpmOJQk4FENZxMsA6h3HeI9T5GJn1fe5LR7jAa9Abp0hNca5C++Zrm6PTHWTS9+cf1EBHXl/LhYxFzI5LGeQ5SWYYj3OSXkrSTbCDzLPVjWOcW4ZJTjbOGfVGjLe6SJETLI1weY6xkn4/YX0bMI5x6vtQ8ySnd67H5kubhHqZd+9rEd25wqvrfb700joXdsbc18z5maX9zOsFkpfOknzxKZJRRnLnPYzuf4hxWOO59Yznn71E5iCMNGGkkFhesE0CGzGf9bi/9zLHRmuIJCHb3WZrNGbUj9ja12ccpZzdHPLi6ztsbA+x556n8cqfMpv12P+eOzn2kfux9Qb/xxnLf3vV4ZTmXXe0uLstUGnKztMvMvj6V1EaGos1onbEm3qO/1ZzPBf2yMfXkInv3mYV0t0IIX/orOxJ3EtncFVotNfnmqZOTL0nKEaGTe2jzKuVlb49KqnlhqViBFdwNpzbu64Tk2j3ilplcc6enOqKSmjhiSGmSLM+Z0VViSxzabLYhcPJoqld2CLR71VenQ58N4BTGCSZ0GQYjBNYV7QIGYvNLda6QorHFQDqqiG2JsuxIvf5FOdwzpIbS1oQYG1BlnTWkSc52SAlzgxzkWKmFbC2I9kZ5pzbTTgWOExUQ8Tae3PrF7H9hPSWlGGtwyhusnNpi/Ven9xaGo2QuisqsmgcGpePcMMBjf46Js1J+kOycUY6SkkzQ2oc48wyGGX0hym97R7dc5dQ4y4rt27RyIZYIxmNBG/uCqwSnBxbFCCtJe/2yS9uojVo2UTaiKHSrI/6nA2GmOSGpPRftF3XAFYyz8tADiknYCQksmLj4wFhjwPmCRfSTjwzR9H6I8A5NakMujJHX6hYuKpOOaWOWuzW5j6/JT0F4XKV1Mm2zoemgSi0mjzYTGqcvqJaFiWklN6Tcg6jAnwTkkTgCMtShAPjvEa+1TVU6HwhQ0egArCOmvWDLwYipxXCIA6o10LiZkSUxuS1gEz5fwyRljSjAIOh0aoRd5pEwqBbDUStjjIBtXpIuxHQbIToQPk2La2IOjWa+xrEcY5740XSMKGThzyw3OSmhXkWVMLrbsClcUY8u5/WPXfQSjLGq8tsJZbUJuyPcxb3O7CWkB4BObnU7IQd+rrFQpYyIzrEtTkSArr7GgxdiFvaT312ljjWLLQi9i81iWPFgeZx9u8XdOyImeMLSO3bxY4ttfmQnsFJyR2djJXhWXTWRxzuwLvf4XmxLU1Qk6yE89zfPsBSvI9k1OeV7+s3+jvbjST+1e06BzA/amzi7TgPPAVsVKTRKot/GZjg9eL9C1EBlqUYiVbtyVcVdQk+055XyZJH+JYfm3m5fQJQ+irHs76/EgE69PsvJICEpSLRioI5L10RqkqJ002cEBgnyJwHZI0hFjkgSB1kxl95rhsIVfMN3tLzvYTJaOZdhEtIpGA2kiRO0m6F1GdrxNTJmiFOKZCCWqCYbQSYwNHuNGgks8TCEHZmkPUWygY024r5saJTDwkCjUEgAkVjqQ6HZ9D1FPvyEyTnn2fxwDE+cu8HYWEfr2+PeOrcLr1Rxu3LIQ8dnKcuDOezWS6ODfl4zD2NjLsXHKEzuO42brDDUNZ4pd3ibL3JTOZYqC3QGI6xYYdR5wQ78QJxLabTaRNFAYPZGjcdnGF+WON4e4mb5u5jRkNrfBE5PItwGXccaLF422FwjoXu68x130Bagzi5hLhlyecobQo2p16bpbV8M4PWCv1ej//n9+m7/GfZDQC7ul3XAFbZdIWxoknsDRkn604n0YvHyn2aBq0pTYiy+DiV6K8OXB5PTIBuz/7FHrYXZShbZc+kbzuf9E1eGY8K5/wQkSK8tFA1aXvIneTiqrMrWqJ8EVJUE70lDoVFIVCy0PuSXphQKEE1xaTYTgm/TCmJ1MoDoVL+B4ks9iGlmNJq9INwZagQ0kEywgpDlI5oSIMO4aKWjAnoOsE4qOHaBqTF9SJcYsAZ6mQs6IzIpliZYBkRA22R05SWmnLIIMBEMSaqkzZnSOtzBIFCBgFaSgItiALfYRA06sj5FiKUuO0hdqwQ1hFrwVwkEA5aIiMyI/+ZRnUIIu8hZwqXZwS1iGY9JGiEKBtc+f26YdfUrmsAk4VahCiHyYrJ7ez9kMJsoSoBFeOeksslJHv6EvHCM5NBHf6G9sfJCz5XKVVTth1NgVc5SbsEkBI5hPR9k+XwW1EMj7A+B6dk4HX8hc9TeRyURQHBYa3ETJF0/aBdEHbCX1NCEAoHWESeIgoOmShDbefIRECqNUNh6KcZ3bGhNkgY7o4JtkekvYRRkpNnhkGa0x3n2CxjOErJhglaGvRojB0PMUYz6Gu2dxXSOLKsUNfIDcPNEbtne8T7lqi983biA6vYzLH9+Dex5pukzUWWFo5Qn63RTw1fuDhCWYe0A+5wuyibM3PmEpu7F9EuR4sUJVJSGdLYtKyE57BS8lqgOKX2MabB5i4MR0NmawGBlJgYtvsZ59eHbPQTelt9Lry5QU3B0UbGifYKIYbeyxfonn0OhUPs0zSXAmye0XvlLKP1Xa+HFjqkgu14jmfPt7jQyBkPv/vgiu+nOeveZivRVf6Z/wjYdQ1gFahUiW2NLRLZRTejB5NC1QHwXNFSALEYpSZwlTIEUHk0THliomzlcQZkgJWqaDMqz6VMtBc8tELixiEQUuNHqE0EFV0hPpgLh0IgVIBA48VrvOSPc2DxdIrcQW681xUpQayhUn21OQJ8Q7X0lVhphoi0aJ6t2PmakW6SyYi+GLObpuwMU2q9hOHWkHBjQLI7ZpTkZJmhN87ZHWXYNGMwSEgHI7QwBMMBbjTA5Jp+N2BjWyONnwUphcOlOYNLA7Ze32WmvZ+l4/dSv+8uet98ho3/939m+Opp8nvexepP7yefX+Cl8zlfOqdJEsMHmz0+1t6gacbsnDrF+jOvgTXUF+rU5mogBC15jjqKrdosj6/ex6udg7hc4TKHE32WWxHt2JN4N3sJb1zssbY9IhuNyHp9pHO8+x2ryPsP0xSW3W9/i90//K8EwtL6qXex78fuxiSG7RdeZ/2JF5FKUJ+PCZshZ4IFPtds8UyUYJJrN1atVAx5O9v/KNp1DWC4MmQraQ9l0FcFfBOAqRL1l5kAnJja6sr3r7q83LY6VhmyToWZ1U4nldHJFtXigmIhpvL3l9UqC+/JlROPimlKQpSAWLLTpooWU/uZ8NTKfRYaZNaRG/9jcuuH1JrSC/WAnGYGkxkMstAjy7G5Ix+MMCZAGUmsAgIpyI1lMM4ZZX6Aroxr2KjGWNcYqjpjEZIbi8syRJoSJGNk4smzOZIMhTCGKBkS5SNUlvmqqBWMc0Ge+lFuoXJEyqCcZWQEu7lGSkEsBVqCMAY7HJHbFDceo/G6ZXmWM+72EcaQjhexMsBKR5ZkjLd2sNKSpzmoEKcMo9Sy20vQgUTNRARCYYwj6Y8YDXuY9NoB2I0c2NXtugYwP826oBaU4Z/wEoGT6iQgp0kVvlLoEEWlspgChK/gCeFbw8tWybJtqKCE+QZpIX2YOTWl2+94wv2iYMQjBLkTFIODCIREyUITn7KKOsXsdwZlUlQxQFepQlLaZoQ2wY9G02jp5ZylSREmBbyHlRfSPVbGOOWvJ9ISLSXCWuJ8QGB6hOMck6UkuSVNTTHzMSd2lvm6hKbm4obhwsU+4yTleGeB8M4HiGzG4I1zbDz/JImOueXIXbTuOoARirMbA37v4oDWeMSxe9/FkeNH2K13+NMt2H70DItDwcmH3svqPXfSTyzbj/4pmYFD+w/RuekkNgjY98pZNr/xCr08QS3uY/En38HYCZ7bHPPy9phGpLn3yAy3rDSJsoDeRosLa32W2hH33DzHwfk68uIa6iuPMd7cZHlhhY8cO0laX+TSN5/jjedeIO8NuONkzOH6bcRBwChQDI0lRZDUZ7GLRxj0xzzdOMOjwTqz7TofuOskKyf2s7Ax5JbHziLeeJk0T/mLF1X+/2+7rgHMx1jFwIyyH1IW4SSFkgMl8jAJJ4uQSwjluVMILIoc6TW5ZCGXg/ChXLFuNQ4NW4SKhdczTZeo6Bolf0yQO8isr4ZK4RPmDgGu7IYUlfSOLGRxpMlwOsIGQZHbzxF26EesiRCM1zIXJkXkqa9OSk9WtU6Qihq5jtBCIEKJ0gKRjYjGO4ikT5QIbCpJckGaTQBsxjn21RSqqfimyVm72KM3zunvWyR6x+1E2ZiNb5/j/OefRtZr3HLoZt591wJrA8vv/ul5vvDiFkfnY37p3fdy9KYOz10Y8Oij5/nms29y/6EWtz/0HlaXYta/9HV2/l//CXd2jUM/9ePs//C9BHMdNl7OuPjEKVyasfpX3sHKxz5Kl4DTj57jvz+9xlw95NCJg9zzjiXCzRH9L53jwtoWHSW4bb7Gu26aZWv9NV796pfZfeZ5lj70Xh744N3Uj+3ntfPP8sz6S4wurnOif5jDNYGqhZwNJUPjkEKS1maxC4cZxmOebuznj/R5DrbnuOPOd9N83ztYeOEVbvnC0zReeIyxNfx/fvDfcuCGB/ad7PoGMKDs8ysreGUYdyVldarSWPVDTqK2qTWu8mp6rb1PLzuZvVVE5/vrxJRG//QeS9ibDEsrg71y4MfUpRXeWplXmwoWJ6x/ilwdvg2q2r8owtBKV784qvRVxnKEmlSTkWpa+oJkJc6oFCKIvOCi9NQP4QyhEtRDReydQFJjyRGIKEI3GwR1SxQGxIFEBZo0CBnpiDyM0HFMWIuIlCDKxwTpkECCqjewYU4e1RnqiBEB1GrEzQZRIyAPYgYiIJWGKAro1ALagSA2CeG4T5ANCWxCQEYoDLVQUg8VrUbETKdBmI5oxBptUpQRRJGmvtDxXQy1GinK9znGNYJ2m6DdQjcaqFqNoFaj2YqZadcIbQ7b3+m78P21G0z8q9t1DWBOBV6ZVKoi31OGYaUkjWUP+BRVPi4L+QR++KzEFPmfqcpilaQvJncXU7In+5ik/J1UWCLAIUzuJwcBWkUI6T0pVTaHAwrpqagVuPiBtqmKQAZIqVBFr6dvMWp49juKTChwEEiH1v4aNBZhRuAcofGDNYRSBLaGcL7tahS2MSImyS3NRsq8s3TaMc25GnVbI2qFlOo8YaRpd2JETVOrBcXsSEHcqTFzqIOs14jaNVAaFUhmOjVWVloszNWIYv/VWmpHfPSuZe452kFryeu9jDeHOZ3mEis/+1PE4wFhTZK98DhGQtwQ7P/4z5ILxYWFA3z77BAjFPvmG/zf3nsIIQW5knzhdBdnHe84OsttB2bo5H3mzn6b/us7uLV15lYjmuFBWjctoGOvatu59Tgn/9pfIRsMmF1uojdOIaXg0PElwk/+nzFKE5w8weleTj91HD5+hI8GNRZmahzYN4fG0lpoc/wj72H11gP0x2P4rad+IN/tG/bns+sawFDaNzW7AsAK8meVvZoWCaw8IznFryjMgcJMAd6UR1OsIpyv9uGsb4wuBoqUeTK/UjGYw1lPYcjHgEBLhZRBkVyfEFlV5eEIzBStw6jIa9jLotsA4Vn7oe8KyC2kRT5fKFBSABZtcrTJitA68+EmGucCHCFWKMa6RSIcWZxSqw2YdaknsnYiYhMTNAqgwhGGkmYrgkgT1XTBBhFEMxGt1RYirhG0IpAaqS2tdszCQoPOTEgU+q/WfDPkfScWsA5e3Rrxhdd2uNBLuH1hjlseOcRiLBk/9ySDr/8Jdjig9s53M/uhD5OEdZ4/0+Ubb3QJlOADR2d54GCbfmL44ukdnjzXZ6ER8KFjs9y22CC/cIbRF19hePpFEILOYoBYXiE8NIuKA5wQtI8doXX4IJgcceFlxBvPgslYPXwz+x58gFQGnB7CmUFO7hyrh/ezfHAfrVCybyEmwBLMNmm8752IB07Q7fXht37j+/ud/g52I4S8ul3XAGZLrmi15PJXZVhVvlc8VjFjQacot5uW36lskpSfVBynKbITDdjpZdMh3gRY955X6Sm6ghAxGUQi9lQ/yxKEc5Nao5g6SklY9bQOB8L6RD5FQm8KjKUzKGeQRd7QzyxxWON/nJ18Pq58z7oqr+eg6p2UpihkFJ+pyR1Zbshziy10+F2a4Xp9bJIiR46GsLQijZCSrdRhnUU4jaq3kFIxlBH9sSMxlsxBM1QEwhEMeti1IRiIc0srUjSkQ3V3sbaH295BSoVstnFZTjYe4XKDGGfEBQdqmBq6wzEmz2mm0A5ihNL0jaTfT8mEY2w1kdII4xgkKf1RCrEia2twGptlpLs9TK/LYHANm7lvANhV7boGsNyCsRZlcy9mKKSXvSkyQLboY5TOFBI5rqhYeg/I6QirQp8AtxScMNBMBBAnDlxRDHAF2dRNwk+fhnNYR1FtdGikl7Fxzks6p8Z7WirEygDhLMp6CWgppRdLLHJVUpSFAyhBI7eQGq+zr50lKsJdIQVWBH4OrtRIZ7HOMcaS4HsoYxkQCIF0GfVsl1o6opdAljgGCTSGGaOdMcHWiLjvqQsCQZ5bhsOUYWJIU1s1j6eDnOH6AFlzNIYpWEueG3Z2Rly40CNOc8ajGXCG5MIal/7kKwxPv4E5dJg7738Qe2CZte0R/+Pb6wzHObfXGzx413upS8vTvZivP7ZGiuToUp0PHGoSpCPCp57ijeeewzUaHLz/QVZO3orc2YavfJXTr50imm0ye/sRWiduo/vqGS597isM3rzAnN5P/J4MheOFM+v8z8dfZbc/4qHDTR45cZJQCR47tcuXvvZtUIr77jjMXScO0B+lPPPNN/j6c2+wb7bOvvce51h7heHaJU79ty+y8fwrDNNrN9Tjhl3drm8Ac57LpMoqpAKE9kDmmFQQ8eRRnPPyNSYDIbFS4xRFCOeJpdIxAS+mfboiTzXVL+kcKDEhvjr8Mf1z4eM74YrRaGmhcR9gRDH/0RY69k4jpaYcXFtRMJjQuXIHifUekZSWQBiv7CMCjCxbWpQHUusYWxji2flaKAIE0lmCfIBMu4SpwmQR40ySjHOSfkraTcnHeeVt5bkjSbzcTpa7qgCQj3PGO2NUKjGJ79W0xtLvJ2xtDplVgizNwVqyzS22v/YY249/i7n33s9N776X5r4mX+qOefz0Dme3xsg7FnjgnTcR1gLOPnmBP37hLJlx/F8f3MedS/OE/ZTXT5/i3H/9n4QL8xw+eZzlfS1G4y3OPPssa5/7Iu07TjD7wL3U7ryHXl+yvf55Nl+8iDi8w2qSg4Mzazt89rFXWNsaUAtv570P3oGMAl584pv874+dRivJweVZVu7RbJuUi+cv8Y0nX+LIcpsfP7kAZp7x1g5v/Om3OP2lbzB2105jy9rCq30b2/8o2nUNYOVg2El4Nwn+JiFWmRvDP68IXR6QqjnWwqs/SDGpCl5hJTmMsvLHZP84hCv35td1UuGc9Uz8CgD3DuL1QzuKZYXiq63C3Ml5SOHBUshCe8Oa4rLVJIQtgM46L68dOIsSAul8ycAhCtCOcEoilR/cobUf2KEihdSydCkR0hNHlfLUj9LdlOX6oUIoWX0eQaCI44AoUn59QMYR0b5l6scOE87NwKiLXb9APB6xr6mRxNRjzXZiyTAIpdg/V8Maw4xLYOsidjggqEXUjxwkmGmjRY7bXEMMdwk7TerHDqFWlumKkGxo6BqQ9ZB6p0bUCH2fJo5WPeTQcod6HDLTqjGy4IyjXo85utJBS5gNHXK0i0oSZmqa5aVZFuabxLUIpELFEc19C8wd3c/I5PDcq9/Td/et2o0Q8up2XQNYaFO0y33f4dRoNfBVQ1WOLHMGCqaVUwHoyOedlAbhuVcBDi1skY0CLgcx4bliZXO217zw24pCTcJ3RxbbSYnBc7UKf63Ik+kCm6QPYQmq8xU2956g8GoYUjh00fMYCJC6UKDIMmQ29PsMqdRZEwuZAZwjMGNikyCcQrk6woZYIRlHHYxqkmKIaxltZ2g1QxpFFTJsRUjtCxQ6UNTqAUZJgrDgwUlJ0AipLzaQcQ1dD0BKVACzszVWV1ssdiLiWgBCEK2usO/nfpr5D38AkfYxb7xI/9Wn2ddZ5f90662Moxa93PHE+QEGaNUCPvHQAQKbsXjpZcZffRnpoH1smebtv4BwBpXuMPrqf8fJgMX7b2f+3e9iR9d4Luiw8WqXdt+wenSexfoBWjfNE8YKieOOI4v8yk/dwzDNiZs1zg8tYpxx85El/u9zdQKXczTood94ljgX3HV4Bjd7P7ONiP0HlkHHNPatcNvPPMzRB2+nPxrBp77yg/hq37A/p11ej/sz7ctf/jI//dM/zerqKkII/vAP/3DP+845/uE//Ifs27ePWq3GI488wiuv7FVN2tra4hOf+ATtdptOp8Mv//Iv0++/9cbY6dwXRVWwKgjiUEXCWpQtOOAFA3VYtMUUoRyeuKqFQ4nLFbyK6wIqfbCCj6WK3FcpkSOdRTuLKqSordS+XUVFOB17JVU5qVxW75UhYBEKG+fIratmWQp8RTKUEMmSLpFCniJtXqqhYRyMrSfNKptRd2NqLkHbHPDj2FJdZxy2MWGTIAyoBYo41kQNP1pM13yCHSFRShKGmjDUKD25bh1pwlZI2AxRofcglZTUGyGdTky7HREEHs6DmRlm7r2bxUc+SOuWI9jN84xf/Cad3fPcty/i/cdnWZyJOL2b8Pz6EB0oHrx5lvfd3OGA65K98hzpmZeJF2ZY/PB7mHvwnWiZkr3yLG79LM2jqyw+8n6id97FOdng2Usjzo4t4UKDhSOztJca6MB7YPsXmrz/7sP82Ltu4vDqPDuZY2NkWF5o8+F7jvDw3Qc52ga1dZawt8ahhRp333GM204cojM3Ayog6syw/55bufnHHuTYh971lr+z36t5D8y8jZ8bHhgAg8GAu+66i1/6pV/i537u5654/1/+y3/Jpz/9af79v//3HD16lF//9V/nJ37iJ3j++eeJYz895xOf+AQXLlzgc5/7HFmW8Yu/+It88pOf/K7DMb+rieoXV3pOU8suExh0e1abDkHdFK/MVu+XLUXltj7iK+K6Ktsm9uyx4E5UG8lSu5+CmDoJYquKgQdlkG5KLMeVl+JDU1NO5hZ6Um3F0y4oQsWc0A+mFaKgb4C2FqyftuSsB0sLIAVCSq+PlgwQ4x6hy2gVMx6dEGyNDWNrcHGdaHERoQNIRmTnz4BRLAjB0bkaM5Gml1he2x4XhRUFSHSqiGeXCQFZq2O21jFJQr3nOBBYRhI62S5uo4+1GRJDuLAAOiQJY5LE4nJBUpslmzuAnJkllzFBYhnkDq0kzUgTN5uIxVVsK8LWWpjdLV8FjmrIehOEJE4HdJIexjpqWQ2V1f2gFJt7zxpouJQ5hoQuwOSKbiqRzhGi0TIik9mf7/v5fbAf5sG2f5H2lgHsox/9KB/96Eev+p5zjn/9r/81v/Zrv8Zf/st/GYDf/d3fZXl5mT/8wz/k4x//OC+88AKf/exnefzxx7nvvvsA+J3f+R0+9rGP8du//dusrq6+tRMqclkTELnsvVIjrPrZ63S6qXVFMZeRymObgrtyuEeRa5oQHvz0bqbyUH53PvQrSRfClo85qpDTQWgoVFVL71E6CFzucVMqnAsoufUUfZNGxeShJ7IqrVEFH823Knkpn1zUGBMhRSHAbHOktcR5gjM5UeawuSHNHcaC0D6npfIxcuccihEdE3JkLqJvJEZInt8YUSPnwOwS+++9B5mlpLsXGXzpdai3uev4vdxy2810E8PL632+frbLBJgFhyPNQ7ffz6zOybfWGX37Sex4xNLCCh/edwQbhNR2LuLOnGdsDbpRp3P33WQ64mxzgbWtFGclcukEsrkfdICTc7CZMsottTjggJTMz6+iDs+SiwzZ32J86ll0OiJYXkUfuRkVxSx0N4h3LuKspaEWCIIFhLPYbIwTEAjLKrvMW0GWx3QHi7yWSUIJnbBOLajTC6phfT9wc/Zt5sBuANifbadPn2ZtbY1HHnmkWjYzM8MDDzzAo48+ysc//nEeffRROp1OBV4AjzzyCFJKHnvsMX72Z3/2iv0mSUKSJNXrbrd72RoT72V64rYrFBumR5JNt/rs8aKKbaocPBMQ83rz/nnVrFRy0ISo5ju6yealwCt7tfpd4YEVNA4nK1BCgENO5e4szgkM7jJYFlipyFXZqC5KCPQAWPZwyoCcUsDQexbCGk/dMCnaCJwBY4VXP5MCoSTCZYhRFxFJYjdDp9ZAO40VgvVhTiwMS7UmcXMfcjQgXb9E+vopZGeelRN3EC01OLub8I03d3n+0l7NeLVUwxw9QNQJcMmI/NJ58q11Gtqx7/AKqiYYXdxieP40ubWEN58g3reCUDGjvM6lkcEJSVxfJGgt4Rxk1mJGBoufDj5Tk9SjGrK9hA0l5o0XMK9cwu1cQikQS4socurJLtF4HaxBJRqV1v3f2Xp1W4Wj5RJmXJ+BNWxlM2w7Q6QVQRAgpGIsb9Ao/qLt+wpga2trACwvL+9Zvry8XL23trbG0tLS3pPQmrm5uWqdy+2f/bN/xm/+5m9esdxJXVT1Sq9pCkIKl6RUk5i2UoLnirCxeCxnKlYAJIqK4R4Pq3DonJ2aeDSRt/bvlbucgJgVZSdA2dBdho3+fSfwYV8Bbl7rzFYiiiV4KuGfKJsjjZ/SrVG+Vco5ZMHElz6uxAjf0J6JECcFIyyJ8VOJKjWKcYZJ8iJnkmNyQ5obUicx1o9ZM8KSaoMT3iOwaUY2SlFRhs08SFpjGA5Sut0xrVhzaL5Ou6bpxIrTGyM2dsdEA01j/hC61kGIOrx2DqkEjHqoRhMrBBfykO2LllykjLKLtPOLGKUZNOboRi0s+HNyjjBP6Iy2ifMxcatFrvcxFA30IMVs9JGbXS6pLt24h607Fk3KfiQax+75DYand3BSErYiwuYiGIvb6OJ6l+iHDS7O1zjfqiGBi86h4ZqOVeNtViG5kQP7i7N/8A/+AX/37/7d6nW32+XgwYPYwCfAq3FqVQ8knsJQ0BdcmefB55dKVnw1XnYSJ+KAvJjMLctEvSi4YpXX5TFICDydIU+8UqvSPiEvpobiApOcmu91tGXeqiCsSudBVVKQRZV/X9gcmXsJnUwEJDLEIj0zXfprVekQmQ78McMGKqj7iUTJAJGNfL4sbJEFNQyWsdTkzrJDQjcrlCaGGaPumNrOmLg/xiZjZFojTVP645yunXxENWkZ1jKsyBFZRtYfMd7qo6lhxwnC5uRJytZGn/NnuxxfaXL/HYvctr/Fa+sDvvjyJms7CTfPRjx487uZi6D//LNsffFR5LDPzM2rzN1+mDSIeXq7xefPG6QZ8670DHdlZ0nCOpdW7uL1uZswiArAFoebHLj0TVb7F8iWDzMI30NPhOiNPuHLa4gL53j2XI2vnF2mH7f4sf0ZP3dY08Rx7qmXeeXRV3BByPLHHmHx4ffDcEj62OfInniC3cYsz90Z8frhOuNxzvalHsN+ck3Hqt0QNLy6fV8BbGVlBYCLFy+yb9++avnFixe5++67q3UuXbq0Z7s8z9na2qq2v9yiKCKKoiuWl6PFvLTNZR5Y5Q2JKc9pAiiToM8/lNLRJYjZIlfmJx+VIaMfOSYQVcGzVGqt+i5l8ZHu8QYnLUNeBbbSi6WkwLpym8LbQ0ioJLMNCInBYYVDFwAqhUO6AuQEoL1aRJlrkybBOu23Q2KEIBOCVDhSDKnxHkyeW0xqMEmOzYz/b114UrmxZNYWxGAH0pIHBoqkss0MZpwj0swPT3UWazz5td9PcZlhua45NhuxvjPm/E7Ci2sDwniWd3RWaLZC3AuvYM5dQu5uUV/uIGt1RFRnYz3ghS2LzjJuTbdoZG8ioyZZ4yi7tbQAMD/2rTEYEGxdpLn7BsMopjseM84tepRhd0awOeBiNuA5O2A3VtzaFGRF/ba/scOlF05jwxrRezIa8Swi14y2x6Snz7PbTtja32V9PmEwSDm71mN3e4i9hoKGN+zq9n0FsKNHj7KyssKf/MmfVIDV7XZ57LHH+Bt/428A8NBDD7Gzs8OTTz7JvffeC8DnP/95rLU88MADb+l4VXBYTswW016PqJ5PZGvK+E9eAWVlhc9XCh34+TpYJwt2vVc/9bQLi5j+hyZVQa+QUwWAyfEcsghB/Vt7WsZFWeGU2LLI4PxaDlF4dAqEJig8Nu1ypMmrASJOF+DuHCLz07utUBhdLyqAwvPlrCW2OdpaGiKjGQqasaYea8J6SDAOUXGA0AqUQmlFFChiq3zPpHNEQqCCABGEiDBE1SKCZoSuR8jAUyqkUtQaIa2ZmFim5G+eYjSUNEaau5dilmdqzM/EDDLDWi+h3p6nffe9qNGA7QP72DazpFmEate480iNME840J+jPphDBxGH6ylKbRby2wYjHHNhj/nZiFo0j5udoVGPUKFCt2KilRmE6HNkcZEHD+xnUG+zugy7TUfmcjhxB4sP13A6JDp0gMR63bbawSVa77yFsN7hyOEl1FKTNDEciDTjYUo6GvDGW/rGfu92owp5dXvLANbv9zl16lT1+vTp03zzm99kbm6OQ4cO8Xf+zt/hn/yTf8Lx48crGsXq6io/8zM/A8Ctt97KRz7yEX7lV36Fz3zmM2RZxqc+9Sk+/vGPv+UKpCyncMuyYdlNJKYpc12F1mkJZsKz0ineqaqJVZHPoUyOchaLIDUai0QJS4DzVT5bwFCZZ1NBdTyfs6I6BxCgfDjr8PM8bEGJ0IXahMdaRe484VK6yaAOU4CTgIIWa5F5hsxGHiylwkUND3omQ457Bd+rRhY0EfiKWmBTtDWEdgw2ZyRgLpYkLmKmHdHoxNRcjbAZI8MQoUNCAhporNNYC8Y5YmEJowgZ15DWErQaxHNN1EwdGXlpIxUGtDs1FlaaNPNN0meeYzdfZ3b/TfzUPR/AzK9yoZ/y4taIs13DwaWDzP/UPkIcrw1yXuxm5EawstjiI8db1GzCgUvbzGz2cQga0Zjbgzf90F/h6SBB3dCIWoSuRjC7hJupk9QDgsUm8YkV5JIgPnyMw7fdStacBZdz0fl/AtH7jnH0gQ+CkAxrDfoWQqWYv+NmFg+EjMMG8cJRDrfnkUCAL44M+j3+01v6xn7vdoOJf3V7ywD2xBNP8KEPfah6Xeam/tpf+2v8u3/37/h7f+/vMRgM+OQnP8nOzg7vfe97+exnP1txwAB+7/d+j0996lM8/PDDSCn5+Z//eT796U9/D6dfaMFPMfC9ld7X3hCuek8w5ZMVHpiY3tqn8T0Hy/lnjio8mwZK73kVQ3CtuSz3NXVaYkpq0bkqvC39P4sffeYo8nnFvsvigffxbDXZqFShdVJ7L8vhya02pxQuNDLwLDKXVmRb/5MTIAiVItSCQCtUoJCBQmhZDeUVwo9M086Hr8L53kopPXFYKOVHrZXbFv9IhBToQBFFCm0MtrtNPlgjml1goSYIZiPG1pKvG4ZpTtqsw0oboSTDtR7r3R2MdaxGESszETULrVENNWp4EUVpEAyKv2+Ow4CSuECDDFG1mEArrBSEoSJsRsg8ptOpUV9oYJoNthPDxijHOgjamlrs/8EkRSHDItCtOrVoDqVrzLTruHqIloJGIAmVpBf/aILC9WRvGcA++MEP4qZv0MtMCMFv/dZv8Vu/9VvfcZ25ubnvnbQ6fSyTFTdsMEWBcJPHvWvvee5XL8LCywDQSYXz8Ryq6JdUhSSOKJUtPVuhgDpfTfRzEtWk77IAqunqpaq2EF7OUIgpvCspH76yKpxF5bmHMmd9S1RZzQz8P4QMRe40OEcgAgLtA1RlM6KsDwicUmRC46TESHBOM8AyMoZxZkiSnHSYkQ1SzCjFpSkuT30SP8npFZdincNKSxakuGCMTUZk/SHj7SGaGrXETxe3ec5okNDdGTMKItSx26iFh7EyYuepb+O++RIEEcdqDfYpTd5v8OwbGVYo+pllth4ijaF24U3Ma5uMMGzJnETOE9qUfaNN5tJd76UWwo0DXedsY4XdoEkYtmkmkiA0qJ0Ro9MbiPWLJBvPMzhrMLUmZvUAweEjGB3w5tou39weoLAcaMFqE3Q6In/tFBfPn2EYt3n1UMzFxQhnHDbJcblhNLiGY9WMw5nvfN/9ebb/UbTrogr5naycfVi1EnGZ91OteJl3VlhFXXA+s1XGkQ6fAwIvrQMgrEOaQoqnJM+6SdUS4eWZxRStQ1hbeFVF3sv5obJamKnzKMmQrnLMynFtIjfIfFTp/gvrmd8urGOjFlZIktwxyv11NGSEVp5LFmRjgrSHlQFp1CYLYox1RRXSsUtKP+szSHJGo4xxd0y0OyYqqpAiiRgnCTvDhB1rK9pILi1jOcbKIQwHJNt9hhe7BCakNRyDyTFpRm93xNb6gMG+BsGdD9E80KT7zHNc+s9/xPC1M7ROHuKuD9yJXpjh0e0mf7I1YMdoji03uWVfm5pJaT3/Ivk3vsRQSJ6/5V2cOnonDTPioUvnuG3nzQrAsI5ztUU+v3gTrzVXWdEN7hpJFnWGuNhDPHse3jxD377JjnkcE4R0fuLHmF9dJQ9DXnh9ky88cZoQw8dvD3nwlgDR73Px8adYe/w5dtoLPPmuFq/d1CQZ52yudRn0EvJrOVbNvs0q5I0c2A+jTVcdudLp+jO39VZKGk4WiKqTqPLNClb95W9M1zNdmZWneLGXo+EpE+yVPuTyY0+tW1Y5KcmvtggtXVmpVFhhMUU+zs/EVJPguJg/6ffnB4f4ZnGHQWKclyMypWihcT7Xkuf+xxjvbTvfl+kcZM6SW1+ZVMZhjMXmBptbbJZ57y3LEMZ671Yq387TniXXMWmvT7qxiei1aeZDIhuhU8VgENIzAXkaEQtLTViCUR+3uY6RmtE4Y1fEGCyDXDAa516YsSisJDls55pLeUiYa4Y5JMZCZmFsYGgYJgmDYY7Rmka3i8xTlM0ZjRIu7QyJyEmHOVEeINIhbjgk6Y4YMWTQHdLvDRkNM7a2+/S74xtVyB8Cu64BzOvhBxPQ8AmxyQp7JG+mNyyrg0DVPmQQdkJ1cELu2UwUFUE/nag8WCFzU1QM96pYTMirCFXQL7hskref0i2YeIATbw0QEqtj3+JiLUZ6XSspg6JJvdAvK6gessJOidU1nPQj2aQQBC7zuv8uxzrLrk3Js4xRZsilIJypU6eJ0o5kfR05HDDfDrlv8QADGfPadsIrmwkDLKdkSE13iExAvTlLfd8sMtKMTr1E3uvjRMy72ous3LdMEGhevtDl9c0hna7g4LvexerJm6g1BWY8YnxhzMIg5KFBzNBKVrcaHNAtQpuj0w10JyQMYk7un2Hx2CwmabA1Osyf9AztSHHHSp39MxFxViPvNRn2U3aU5Nz2iHFusbqFOXEPbvEI/SRnd5jjBETNJkdffxbCkHovp9GseY21bEi6voMyluDkLTQXj+Eyx5Fel/DJL2OsI8lzcmNJs4TX3u6X+M9pfjL32wghb0zm/uEzp0NfAZwiopbP97QPOVfINV+WH6um9FhPSygT4DKgaqKmlHCWSBVSkCKKfJQ/hJ7QZKdOzlFq7LuS34XACumBppDh8WPSJklzcFNS2dpTGvDqFKl0nsogHTVrEBgUCi2Vz6m5EsMFeVDHCI3AK9aGzuenYpeCy9mwhjzLGCaGXEqiuQb1uI3UjmRtDaE1SyfmWF0JSKIaSZLx5BspY2N5Qcf0wzZNU+Md7XmOH1zAjVN6zz3D+GvfQK/u530f+ynid5zg5fUR/9uTl3h+bci9+yL+6gfex+HZgOzsqyTffoz04jYrmePh1GKB8FJE3I8QOPJ0m3wuRtSb7DvSITq5yPow5/fXb+YrFxsc6ETsv3OFW491qF0ak39jg/76AA2cqQ/ZHmdkeobkzvdgspxRmtMb+g6FJXGO6JXHCZ2llR+m2T7sxSnTLdK18+hanfAd99Hed5Lo/BruP/0+S1/7OjpS1BbrhM2AQZbxv37/v9ZXNWvAyu8dhOy10168pnZdA1ipaf9nr0eBWdUTYBKA7hEwdHseJnhXAJBPuhdMLnG1L9TeY1DBYPnuRECx9NLKdqXpOkS1daFY4YTzPwCUyXxK363YedloPuVFFsuxk2B3mhPnHT2BDDz9ARzO5DjniLC+4hYqQimqSd6JlQzRaDRWB6hIY/Mclybk3V2C2Q5NDTPNkFbP5+3SzJKiyOsN8nZMXquTCo2xAuUMLVLAoaxF5f5us1Jg4xhZqxEGkqbIGUqLDEPyuEkeR2RxiyxuYiJJEGpqWhJK/08js45cabJGE2sdeWqwQYYwOaQbiLFF2oxIWpqhQAsIFFXxRdbrBHOzuMGQugabjwgCTVNHRGFA+Of46n2/zBmLkzdoFJfb9Q1ge+xy4GDScM2k7lgm2EsocVXYpar+IFF6SeAT/GJCrRBucvNX7t5Uo/iEGDuV+ypySKJw2XwLEv48bA5S+a686hImXQXCTrw7T1PwmvjCeo1/JSWB0sVxFKkt+XAW7XyzsXGCXHhwEkqCdJggJQwtjQhqWUjUrBHquudWWQtSIsMQlMYp7c9R+rmRoZbUQ03daqJaSNCoYQXEMzVsmhLO1CAKyVXIXNvx4duWuHX/DGEgeGkn59Ven3hQp7l8B3p2xMxgnYXuOQKTIkONCr3sdq9zkIuig1QK0x+hn/oKipD7WgvM37eK0pLdHL7weo8sM9x1sM3J5TqpkAyEIhOy+uyd83k+YyzSOZYR5K6DdDnHx4J4nKKw3B7VqUf7kXEd1W6Qh2BaAeHJZTqjm1HNBrUjhwnmZolHY/jf/8fb+dLesLdpPxoAVnlhgun8lq2Weg9GUJQEq9yUnGxXcJiKRqErdl2SYaclo/euJPaGrZc5dbaga6ji0bf7FG1CCKQqGrmLfFwJYv59h5QarQJ/NcbreYFDSV3pdeVWkBbgFbmUwOUYBKkIyfDqs6IIg02gicKMRuSoGw9gQVgvkvg+rFVRCCrw7VFSVnMhw0BSj9QEwJIYJx3RTA2bp+h2DFFELgNmZzQfui3GWctLG0M++/IWb+4mLDbqHFm6g2YgOLj1Ckt6SJgNkFqhAk2mQvrtmznbvgWZ50Rnn6J56nF0s809932Id91ykvWR4Yunt3nxQo/VZsCHD7c41gm5OLJ8aytjc+yrp7r4p6GEIFASJWA2nCePjiMw3LJzhvu2z6CcIYwaBGEHwhpRu4ENBK4d0Dy5gqndhGzPEdxyN2phlbB3jWkUbyOEvEGj+GG20s36Dvy0MkwsE+nT7+ypCBZekg/brixqXj1imA7IrlxePt/7arp66qqf6S6CSbA5OfJ0COiKtie/X0vF17ji2D7SnYxsK4552WflpoDdUT5COWDE4QeKuGrM2qQy6b02V2hWFc/LazCGIBkisowwSb10t5KgNIkMkUIwUjFDXQdnEVohlCZXASMVM1YRCkmuAg+mQqCzhGDYIxw7AmvQUqKxBMmIcJCgEgG5wFivyWak/wwClxNluRf1FjXGcR2DpGUdYTZGuRwTBKQiRIgAjaKMKK21mNyDu8pyZJ7jTH7Vb8QPwqxxbzMHdgPAfuisnNxDRfAsPSAPP67Ie/l7s7yligEVZf7J5VUeqpy6LcS0PPW0HI+r8iOegQ/TsDABIX9uZYuRFBJd1RqLXqJpBQ1nwJqpffnrsEJ6Hf7iLGThjTmE738sEmYyG+EQKBngRFC0dGpy5/sqtTUom008OmcJshyTZSSZJUkzsuGYLBlDyTeSCpXbomFekaWOYS9hlFm6zYjtZoqxCYPeiLQ7wA5HDC71Gax1iYIBtbG/udP1DXqPPkpy9hxicR/vOv4O7ji4yM4o53w/YatvGWUNduObCaIMi2/xMkJ5Da5BTiQg3XcTav8ipCm7L79J8qfPkjZnuPnEney76SDh1jr5V77BGxfPcaG9xNn9t7HenPMwXIDzvq2zdM6/Qi0b0z14E2eP3orQiiNnzsKZFwHH2v6TXNy3jyCucagVspwJ8m7K9rMXGDzxEkGzTvv0DtHcLL3x+Pv7hb5hb9muawArwanU5PJJa3VF+FZW9hAgC+DxgJUVA17LvFgRZvr+Z/wMyCtpET5JPgG28n+b5yQVw0OKEWwgikolBVj5YwlrJxwvixccLMJaP6lIeEFD6a9RudxrfOGwUmNkCIDKxsg88etogQuC4nPxtVFhDdqOkNa3E/kRbzk6d5g8J8ltoQeWko98I7izDqTC5oW8j1BkuWPUzxhmhv4gZXeYgc0YDcak/RG2P2K0OWBwsY9pjuiUALa1xdZX/pTe09+iff993PXOO6jdNMeza31e3RxyqZ+yo+tcjI8gBWTGkea+D5RcwtDQDBXpvsOo1RZ2/RLdr/xHdv74C0SHDnD46GE6h9/BYLDG2cef4NxjT3Dh6EnWPjDH+v66ny9gPF2l9trrhN/6MrVRlwt3DHg1WsGEIer0Gu0XTuGk5EUO8WKzQc3UcOOQWg5pP2Pt5YtsPfoqUT1g4c0LNDox/ezaeWA3kvhXt+sbwKb6Dsvamn9O9bwkqZY6YXuLltM696IsyV1R2RQlv0xMh2lcvWxYndvEQ5TucqjzhQHv7ckq/zbtyZUZfbFnl5Mgsnou9oKstGbq9dT6xaxMgSy8KouQAiXLDoKp/J30lcmpmNfn75RA2mIbKVD4vsgyNya19D/KvwaQWqNbLYK5WXQcIUd95M4m4WBEywxIyJEiRKq4yEkWPphzRDYjNBm1XGGyGtupQxiJiesEsx2CZgNtUmRvC5UOCeoxwfwc4UybIAoJtEDZ4vqsIA4VUayInKIeQEvlGKXQUUjWmMFKBXGdQAdordHST5/SUhDUQqJ2jageErSa6FYdnV07TXxbFCHezvY/inZdA5iwWaHDpSoW/HRWS1X3ddkgDXvqg0KAKlhc0zI8ZasQe7HMTYWVCDGBh7Ji6KZKB1PKrHuOL3zBwDkBWoAKC+ychL6ecV+ohk3ROkyhNWbwCql+fxoZ1Dyp1Rpk2vebKO0/F8AIRSYVTjqsiMBZsiAnjke085x6FhDGIdr5QSHOeQ9M6gmrP4oUzU6MyiyddsxcM6JtDfVhTJjWsVJQX2h4vf3FOmFNo6SgtrLE0k9+hNkH3wXpiOTFbzH+9jdoBRHvrjVIlWYrWGKtfoBUhWTGkuYWaXP2D9bYPzwHiWLj/CH+uJtRszkn7ryHg8ePeC20/iWGX/pvWKeZf8+9dN7zEGHQZKuxTKzrSCHQUiCxHNVLrAbHaKQ9WqszHJofkgeG9MRhussLGKFoLqxyfK5NHGpWGoqONth2QHTPIVbiu1CNJvVDhwlm56gPR/Cf/uAtf29v2PfPrnMAKxUZfM7KV/uK9+AyTfpC9tmVQOGn+5RcqTKHXeHT9HGAyxUv9r5fgmMRyiKY0pMuPMWi/7GYHO4TYqpw4CbhKaXSROExquLRSIURvhXcOMiLC1VSFXJCFpGkXmZHgHOe5GuFxIjQN3NDIW4IuU4Jg5x6CHGo0KFGmaBqHULIYj6kh9YglNQaISK3NBsBrVjTsgFxLUTXQhyWaCbG5SlBJ0aHyhNDZ2cJH3wXOMfw+WfY/qP/jeSN16ivzHPHiYOoZoPTKiKLDzJQAZmxJMYSGMeRYZfb0jcYW8kbWcST23Vm6hFHThxn8WALu7FG/8v/B+MXnyFYPczMh/4SwbGT2EHG4sUBDDNCJYm1RAtY1bMshPuo520WZ5rImQSj4JX2Mq8cXCAXinqomQ0UsRLMx4KGMoiGonl8Cdu6CdHsoA7fhpxdQV3DKiTG8wDfzvY/inZdA9gkab9nSVWUvMraVwv29ixzl603qQxeeayrHXXPGLSpL1zpYe0NCcttp+uYZbjnCvmecrGcgGvRFE65R98BzgR5xUTVtdhOYqt8YClf7V85UBpZqyFFA5skZP2hP/9uF7W5jo2H6GRMM/SzIgFGqUE5x1jXSBrziCBBJIogaKLaHUy/T3L2TVKpGYQNUhVCLhEzc4RLA4LZNjquo8KQyObUe5sgB1gdYIIQLTM/QWk0BidoMWBJ9mi4HJc32UkdIgcrFSrUOK0YOhC5I0lS4uEO7f4IFdfQuoVSmlyFbKkmQyep6ybNsIFTIXkeMMrBCKgjiAsybGod3dQhjEAGDUR9DllrEYc1hA4Q+trdPtZYrPje81g3JKV/CM0VYZKACUVC7KUseBNMGrQnVT6YAFVJei2fgwcKUXCyRFkRnA4NiycTiWhXpPgLH69oN7KAFboAEoF05eCQAvZcwaHFA50pQj8p/E8JfeXMR4kB5/Mv0mdpJqFpqU2mAj9IFz8LUrm8KBgYnLNE1tMAcuNwUY1w30FiN8fw7HmGr1/CDIaE2fOYwQAT12mG+zk2d4ghmlFqOL0xoC4dc52DdFZWiXC0TqQ0XY7pDRi+/DLbX3uU9cY839x3B2vNJY5oxbvveQ/LKkWTEogRwhnaG10OvvZVsswRHdhPfPgwUjn0cJPxhXWsgxNLIatxhrENRruSb8iQ+jDlSFxjYd88/VaTM4Oc3bU+4fYaC689w0p3g2zxIOOb7iaPYrbDWV7Xx7Bk3FSf4da5eaRSbG3knO+mIASzsWK+5km/G+OMN3oZymoa9cNE0TJxGLDYmKER1rDBj2h/znVk1zWAlQTLac35y0O/PXYV8CrBao8XVoCZLCuGpfcifO5qT+/4VHq+5EtN9LtKL0ftnXJULHXOg9j0pEonBLasfpbpuLIYUF2GF1MujjR1paIqQrhiKrhwFoUp6CK2eDQEhUSxsQ7CENWYJ9BNxPoOaX9MutXFWYvKBtgoJj4QsnT4GAMZcWZzyHovoRYotpfn6S62qQeSmbqkEQnGZ86w/ejX6T7xOGudA3zr5llenQ1I9jd44JbjNOdjxGAbsXUWlwypXVhn/sIrmNGYVsvQEbMgJTtJj92dHjjLykyNmxD0XYsnh8u8RkInN+wLQsKZJi6K2UgsF3YTFrZ2WF4/zezOOYaRZNvdTqoV66rOKbnIWFriqM3RxiyBEgw2d9ke7SKF/9s3Q4VxjvO9lHN9zzObqy3QCBTNQNCJpE+w6uAtfFnfnrm3GULeILL+UNreP4rA7cnFVwGYKIbWTimhVitNPZsK4qofn0+a5M3Kw1a80YpfVubXqkNWr73nNb3e5KjlcT2QiSIPV6x72fMyBMS5qdydqPJ+SkiEKvT5oRr3Zgtg88NIHMIJrDAYl5Ebi3GiYNoXuUQ7TUz1QJcbS5IbEmnJcosxFlP0R5aCjWW1s6rWWkesJAdmYtRSg04t5EI3wxiHGKXInoBMEboa0cwsYc3TOMYX13FCkBCQLR1CYLG1EGcsIk2p97eYzUJqNqFvFef1LLuyTc+oiUDjICHrjzGjgv8moCEyVuiTuhw5lpzbjhBK0U3yoqpqYXuTPFvHCIm1NXAhxkJ3nDNKDaNAUpMKYyW98bULy24A2NXt+gawKuEsqtflyDTnRDFZqBydtpcfBiUdwZuAiUqE88WBsi9yDxgy7bl58qt0Xl3fleoWZQ6/QCdZ5rJckSEr24lKCoTzYagtPElVcdJcNdHbn5e/YaxUPkREYJyoKpKBDNCyJL4KhPOSyTkSU3iAWgeeb6USxmbMMDWkITgdQihxQmNz56cUZQabG0xuGI4ztvopfSnojTLGiUE6yHKvD5Y7Vcy89MRXa33eZaEe8GMnFnC37OfC9oivvrbDVj9BkqMRKCLuDpd4/wlNm5TRhXU2Hn0S4wSjo7cyfvBelLBEW68S776BNCmrm8/RzF9iHNZ5c/4w324eIJUhO2nEOE9RuyO6a7sE69uYmT7kBiVgPz2OuDM4O+L05iJf2MkYiwApJVEgifIMXnqW0doLmLCGueU+xMGTpLnjwu6Y3jinGSp25mJm6wGD/rUbbHsjB3Z1u74BbI8VaFGSTacmD4G4Iv9+OX2rVBz1axea+E4UwDfVM8kEwBygnPd0CkotQk6XEESVV6/ah0qwc6VXVEKV92RKwUNZNnS7yWOZU0NIP+RWeDpFXihN+IqkKsiyhfy180N6cyF9sFkMujTSkNlirJrDb6f8vp2hGCIx8cKy3DJMDSNpSDLjgUuJQgyRPR6Y84iPc9AIFPsW6zQPzPBYZnl9a8yLa32UlgShIlCaheUmYjEgVinD8+sM3jjnz+3oXWSHTqCExaRbmM3XEWlCq7tFbTRmq77ASzM3czpYxjowxnk561HGuDcm2R3iBilYhxQwQ8Iy2wg74I1xwKtJiz4RyzMxy+2YEAvrF8heeBZTb2IXjyIOOHIL28OUS92EZqyJQ0XiBKPBtSOy3rCr248GgFWVwukQUXznciRuSre+XFYiWLmvqeWV2WI7UXlZlQ9XHWtPguyy84M9ihXVMF6BLTwyUcFdoYtf7UtM1FULUmrZcVjCYBG1TS3zXpe01itYgBc1FKBsRiAgUBIt7ERcUYDUpbyOQoYBhAFCySnRDU9q9UoYovpRhUcqhEMGAh0pRD4meeM0QgqiPtwyo6iHM1ghMMV/DR0rTieODSFx9WXssZNYJ9itz7LVTZA4Etdg1FhFh2NqZoMQCGoRYagJtUTnKbVslyAbM2u2aUYQNCNsHJAVBRyT5+TDMXI8ohMaTswGjIRmxvWZ6W0Q5Qmz7ZjG8ZvJowZBp+PFIJVgth6ihKAZaZabIXP1gKG7hjmwskPibWz/o2jXP4BV/CkPXqXiqfeSRIVpFb44u5d4WpG/JJWeTRVXlu6TmIxMK/NPBXlWQIEaFUmhOKAt8mB4b8iaKrnupwg5pEm90pyQSB0WctCF11fs7fIvnqOQx3GiOnWvsuNzYWkBiFpItPTXGLiUwHj1Ct9PaQkyQ6wctVARKn9+zmQIYdE1ja0HBI2IsFnDRDEqmijfaiUIA0UUKmqhohlqalp4IDQOKQxhXRPNRIjxLt2vfp7e44/SOngTP3nfBzCL++inlo2xITGWne6AP9nWWGM4stThlqN3IYTgzFDx3Js9HLAaLrO8PEcjH3JL9CIHem9Si1o0mhGtOKA96nHT4BTz/YuopEcwAyqcIZmtk2mJcY5smDDe2EaPuhw5vI/lY3WsDrGvv4F9/UWkc8wcOED7vo8xliFbap5NqahrwU3zDZSARqg40A7oxJpe7Ro3c/O9g9CNZu4fZruCqyWYdoyudMQmoFeFilgmQ2Uv98CK96texyLwqxQh3N7V9zwpM20FMFYs/wJIraGk3Isqzp1sezkwOnxUad0kl1aIYntaRgXYJZAan6Mrq5DWP0rnUIUHpmThDRYaY1IJVCD9uLRQ4wKNKIac+NP3umBKCXThhfm2mzJExu8jVLg8IT1/FmcsjXqd1aYk3tdie2xo9FOGmaWXGM6mI0aZoTk/w7GDsygh6J7ZZu3itg/VZ2uI2ixtMyAdn0PmEToMCQJNqAR1YVjMdlgZX8KajDQEK0LyqOwrBZsb8nGCGI1pS8NKWyMCxUgOGfXXQErqzWPEhw8DAbonkUPfNtWONfVA0dCShbqmEynC7Efj9rme7br+C0zAacqTqoqBk45BwUTjy4dkwq8kbFWxq7TqBYjKEysARtjLgK3MtRWvCo/KTlUEpZsAlxOyAKli/qMrqoqirPwJ7wFdoahRnTAOh7GTfJkqPUOmKpxTnqassFBUQ3W996jBWayyCJkihZkAqcl90j4zmNRgU4NNM89hs5ZAes9OQCEO6PNvmXFoWTRRCYmzkI1ykm6CajSJbzqIarVQ7Vn6L73C8M0LDC1gHdoJOtQ52GwzJsI5eOVSH4kjzIbc3Ur8NQcBubEMjeANMUOi9mEI0YNd9uev0RxuEwy6mHFCPs5Iu2PyNCMfpkjn0FKQ1mfYXDiKHPVpZQp76mWUALO1jlSSXGre6Bu2z43IlKEnIhyS1FjWdscY62iFCmtjhnVNb3DtkvjO+Amlb2f7H0W7zgFMlk8ow62SyeAHXpREw4KVfgU4CH9TUyag/Ws5Pc3b5UxgoYgZncPLOhf7K3oUrYPcN1aimbDdEVOTuZ3w1Ubnl6tScMpk/nhCFCPiCklo6aunxkJqfapfS+/x+DOahMSuOs1Jc7ZD4bTwrUXOYYpexyzNEMqipPUAmGc4k2DTFDPOycc52SglGyZYK5FNQ6QlmfR0jLxI7Ke5YWwsUkhM5NuajIHxbspgbUD95hXmH/wAzZMn6b/0Cpf+xxcYvXkOWdfodkQcBuw7cTf1ez5I0pjh1KU+X31lA6zhvXNjHllKsELyTBrwYhoxtIotsQ+CWTp2wN3bZ7gl20AkCXp3i3Q8Ih0kDC91yYYZYnGIsg6pFf3OCttHHyBPxiyeewnztS8TZGOiRkDUCBjLgKfWM76200WFIcdWZtg/FzDOLKcu9bmwO6JTD9lNWqzMxAz7yQ/ke3018wD2NnJgP6IAJv/sVX54rQQe2Bsils5YmQ6feGKXAREUMdFeeZxJBFpUAe1kWvaVZ0CVe6v4UGVDdLmXMmycXmdqO3/AIsdWlvQqnn51JhROC47LWfqu8rqkKEe3MXVuvjrp82+e4Foy9kXZlO6sP+dCD8xWI9YMLvdemiqAU019fMZBbgoqhfWyRdaByR0mczgZouaXCPYfRDRaJBubjF4/Q/bGm4i1c6j189SGXTohzMa+gro5SNnqJ2iTshpm7A8zmsKPecuNY5cal9QMO9RQ6ZiZwSbN0Q4qS/y559bTQFKDzQzC+pDZBBHD5hyD5gJDKxlvbpKsX8QMBwgpcUqxnTje2M04283pJ55OY62hP87YHKRsD1J2xzm9xNBLbjDxAba2tvjEJz5Bu92m0+nwy7/8y/T737lPdGtri7/5N/8mJ06coFarcejQIf7W3/pb7O7uvuVjX9ceWBGQFfd/wauicLKmk9/Fjek3moCGvwndntX8XgvSZyFDLcTeAkG5H791GTYWVAZRVgap1q1IEm4S2vlTLI4lBEIFhec17SVOoFcKR1BEvmWDN0XVrxo5M6WiURUxSjBzE1Argc45PxfSRhG2uYALcmztItZKTGpI+ykyGEBs6KwYbpuLSMMah5oBOws1D6qZ4enXtwmkYK6uaUWScNcwe/w25htNxvOLPNNXjF7aoDYKmH3nPSwePoiONWE7QmrFMG5hXngGp0MOhx3EoQVwluXea3S/dRprDbWswcG8jo1ixP5DiOUlmv0xjc2M0WYXGdfR+48RNVvocQ67CVlica025vWXcBfO0JqZJZhfxjYUo84cp5ZOIrOEw8sNWisNAhkQdjsEPUVEzsz2WRbTlI7QqLjJkf0xjUhxqJkzG44YhNdO0PCHOYn/iU98ggsXLvC5z32OLMv4xV/8RT75yU/yH//jf7zq+ufPn+f8+fP89m//Nrfddhtnzpzhr//1v8758+f5z//5P7+lY1/XAFYSSKdveDGNL1XKqgwFRRWSwd7k/nRLkStIr9Ok0gk47C0HWCaN/hKvkHOFTziV6JcU4IFXHvUA5rx4sShyayX3awo0pYCwkBQWZQUV54UQS2ljpSvVDOfAlh5a1bwtCgD1CXfn/FBbE9Swc/O4msI2zmOMxCSGxI7Ixykyjlk6mXNsXw3RbJI7iXGSnVHGZ7+9zpdObWFxxLEmDBQHmpqfvvchjv/EB3l1J+VLr/R46bVz3DEf8jMPP8Khtva0DK3BOXaeepL0819ADgbc/u73c9/DxxFKkfzxU2x86RvY8YhGEHBSafT8PLOHf5LW8ROYS2PG307on9sk2l+jccs7qN10nMxKAqPInSA59RLDr30es7nB7Dvewcz7349od3hyaYWn+zWy3KJXFTfvU8ROEJ0VRKmkng9ZvPgKB5PX0a02t996N+rAUaR0RCJFi4RuNvievrffizlrp3TevrftfxD2wgsv8NnPfpbHH3+c++67D4Df+Z3f4WMf+xi//du/zerq6hXb3HHHHfz+7/9+9fqmm27in/7Tf8pf/at/lTzP0W+hSf66BrCJVbHUFV4VxetS2PDK96bXKvZVPSu9oXL5VOxUoaCbPBSri6sexk1tNdlnFdxWhyrBaxIeX5GYL7yvSuG1Krm6vai85/oneyrpH5X6vZCgY1yg/axNhNe+zwtZH5ET4piJFDouaCBSoYvxZVv9hNxBmBpUoKgFCtPuEK12EKJPzw7Y6Kd0Z2NsZxa1VPfhtFCeexZEyEEP3d2lkY9YCAEt2LAZg/4QOxoSRIo4UARJRIeUmdCRBbAJJMY3y9taC9ua87lFGYGQmHNvIPpd2LyE7u9QN74LQOqAYb1DYhxJDfJYYJxDhoZIGyLjiLIh0WCbKHC0dE7c8DM6RaHwat6GQupflHW73T2voygiiqLveX+PPvoonU6nAi+ARx55BCkljz32GD/7sz/759rP7u4u7Xb7LYEXXO8AZsuWn4lKxAQ4So+pyB5N88WmxA3LW1tOg19FUZjaFw5KJjyiUlH1VcBi0bTTVdE5XEUS9bsqFV8vR5kJIHqNfFs0qhcJ+emcWnneQiCKobZVJ4A1BRgqJBNyq6muzrt/noXvilYgR+4cxk2IsEyBpXNF03iZRxOiakT3H7Mfqlue/3TubrYR8ODROQ7O1oi14JkLA168NCzOXSKcY0G02f/ge4iyETKK6D76Vf83kYK5D30InPXiiloglCLf2WHnC3+MNQa5uELjgz/GIJ7h8V5E98Vt5hsRNy9Dpx5gihmazlqyzQ0G3/4Wot2mE+/j7uWDpCIgcWO+tDYGZwmF40MrgigRHEhB9Py1ZypGBE1fDZYGZy294NqlkL9fIeTBgwf3LP9H/+gf8Ru/8Rvf837X1tZYWlras0xrzdzcHGtra3+ufWxsbPCP//E/5pOf/ORbPv51DWATQUNdgVU5VAMoAMA/dW6qYaecmC2ockYVpDifBaOc9FOKDzoKDpUraBMFgDDJe/kQdsq7coBwfgK3KeSHpS4ECIsKIVMHLg9kTaGRX15XAcRltRWJKciuUgiUKq7L5MV2FIVXT+3wIZ+YghVIrCPNHamxZMZTNMxUccH3alIIHHpArooAeKArm8SlEh6fS57a1IEWmiEfPrlAbhzPXejyX761xuubQy9DLTzH6v2HOtz84R9nXlt2v/4oW3/8P3B5Tuf9H2Tup38KGcdVVTXf3mL7T/4nO08/gVpcovXwR2ncdiebOwlfeWGL509tcMe+BsutgJW6IMMXIJx1pBfX6D45QMYxc3c+xEPHT5JGTR57fYsvvTlAYfnwPsGHD0r0WJJtQlZcZ6pqmLCNdZBIH3r3gmt3+zj7NquQxX+mN998k3a7XS3/Tt7X3//7f59/8S/+xXfd5wsvvPA9n09p3W6Xn/zJn+S22277noD0ugawPSJe38mmc2HT24nyzelVp700fE5qGljKu7MCyctbvMu97AULV4Z6l8WWldd0teuafqw2u9rFFiFhFT2W+3TVmV+xZXmZRR7sio+xQvPpgLyMj8XUuYhisZiIN+59QONoCoMTlpozGGMY59ZvI73efCI0aa1JGvhJ2jZNIc8xUpHVW8harTp+PkrIEZg0gcyQ6hBRa5EMFWO3yzj3vDTnXNVXWoX5xmKzHFRGYDJCl6FdhnSWsRVoJ9DO0nI52qX0MGTV51P8XYXACVs8XsMivikJ19+jFRFAu93eA2DfyX71V3+VX/iFX/iu6xw7doyVlRUuXbq0Z3me52xtbbGysvJdt+/1enzkIx+h1WrxB3/wBwTBW2/Nur4BrAjHSs/q8rvwahQLP+m6uPmkomgvZCJzM6VG4WTxvpxKrluEkxPSaaV373xOpwAUV4Rj4grQKcJTvEpFKdk8gTHh9extMexjD39tAiaygitXFBEEUqoqFHZVE7pDWVOIKJbH9zMSpwmwqviRUiCVH9BRfWbTne7FUX0l06GVIAgVGD90wppCasd6ry7f2mL03LNkG5eoRzO8b+kgdx5Y9ldc7FMK+PKpbZSzHIgWOfqBDyGc40xrH2+8tE0muwWbxVEzCTftu4V9P9ahH9T45jBm7VsXADi+2OD4UoPVdshcs1YJXvo/nUMs7kPfeSey2cI5SJ74KrlQ7G+s8r5Dq0hnWNh6hd0zryHTMfnmRVyeI/KMIBsSZr6tKTQWay0i6/2ZX9Hr1RYXF1lcXPwz13vooYfY2dnhySef5N577wXg85//PNZaHnjgge+4Xbfb5Sd+4ieIoog/+qM/Io7j7+k8r3MAK/NMVwLFVR0zR5HH8iHktGbXnhxZlVtzE89mao7jHo5W2Z4DODmZ/uNDLFeprU6fgxAeTLz4TtmaJKpr8iGxm3g85dWV4e4Uy984yItr0EIhhSwuqQhxnUXjQ9Jp0+RVuF0WCJQAVU4XUrIKH0XhZU3/QxD4bgCtJTpUuNySJZ6nZY0PsXLnSDY32X30q4xffI7G7e/ggz99mPDwSnW91jm+fGqLP3jmEt1xxkduWuSODx0nkILTL+/yX1/YYpgWoJhblpoh/8vdJzhx84P0dxOe+uZFvv7ieW5abPBX7tvPHfvbBFIQFYwUV3QGOAtiYRV93wdQs3OkT36N9Cv/E5smHHzoEQ7ffhKswZy+yM7XH0PkGbqm0aFC5jlBNiROe4Cr2rFEfu008a1xb2uy0NuZaPTd7NZbb+UjH/kIv/Irv8JnPvMZsizjU5/6FB//+MerCuS5c+d4+OGH+d3f/V3uv/9+ut0uP/7jP85wOOQ//If/QLfbrYoLi4uLKKW+2yH32HUNYK7yDKb/ONP+1mV/tGnA+k7r7HlryqubRIiXHaPa8XfZ28SDujJe/HOey9XC3UkCbRIqilIksfTriseCVzJ9Dwjhc2gTB8tVWyKmruoqp/6dnk8vExThpfSUCYUjTMfE40G1knUQmtQPaJKSXGkGMkRLQS79ZCOlBDhRjG+TpDKgL0KG0g90CaQgwBJlY+Kxn6YkoxDUVA4UyIViKAKkDH33RAHa2qToZADWkliLKQYST2swlf8yROXZTxGfr4E5c2Vj/1va/gcEYAC/93u/x6c+9SkefvhhpJT8/M//PJ/+9Ker97Ms46WXXmI4HALw1FNP8dhjjwFw880379nX6dOnOXLkyJ/72Nc1gFH0EVbDYas2nKIqV1b+Sk4VAqRAlLI0iMkXXAiqZLmY9jUmQoJly9BeQqvEqfJWnyhhCAGqzBEhceiiBfOylqbqJnEeXKuG60LTTAZX8H98VdN7VFIodMmqp/ILK/PX7Bubyn5K6xy5gEBr4sASKoF0BmEFWLtHusWfZpkDtJPPovSgrCPPLcb4HJ8sG72FH60r5mbpvPf95Lfehh0n7D7+JNtf+zpCCZSWOCVZmj3AT958nHFQI8lyPvuSb+COA8VfumPJA53105isdWwMUn7/6fMoAUfma5xYqtMa7lJ75jE2vrZJvG+F9t13Ei0s+AKKd9G50Es4//o22bbkqJ7h1vvuJ8oTRumY8Rc+i0MiajHhBz+KyMbI86cQG+dAByS6htHt4ivhPfF+eH3fPt8vm5ub+46kVYAjR47sAd8PfvCD3zd5n+v7L1D0DArnZYMdhespKGK4ksc0RV0QXJYvK3NJshg0axGUncnlSl7w2cm9+/HHElVoN+2wlfe9KHJtZYVusu1l+7k8hLXWE1OZKhUUOxdTo9f8ENliPTcZ8DZxTItWIqUwzsvtGOfIhUNrz60KlZ+bWIXOZb9ScRH+OtwkjJ6aj+msDxlLxU8PYGVOzaFmOwTvegCso/v002z+x//E8JVTyFASxBoZaObf90Fuvv+d2M48//PFdf7HS5tkxvLTty/xyIl56qHCFCn5S/2U/++T5/jyK5vsn4n5v9y7jwePzpC82mP9i0+z9ewztG6/ncbBfTA7Ay6vruPSIOXJs7sMdhXRUot77ryLlk3J/vQxkj99FKsC4oc/RvjghxDJEPGNFHYv4rQm0TVS3aBUtnBAP7h2Hph1bzOE/D4Bxg+bXdcAdhk9k70lsEl+Z/KstDI+mvxRpzlflRQNokq4T+ZCisv2tfdIokiWT0e3V+bn9oZ9V7Xv8uaku7NcYEufs6pUlcef4HSZj7NXfF7WeV5YWuStyhEAftK2QkYaYTNsf9fLVBc4ZsaGwKS0Yo2xXpFCCS89M0oNl7pJsSMP8InTuHoTPTMDWmJChdUKi0D0dpBAkIyIlEAJSZCOkDtbiECilQfhcJBST3q0sj7NLCNKGgQjiUn7KJshhSUzOVuDjF43IckkeXMGNztGRyFxOsCNFCKvkYg6WuEVafMM5/xzpAYVIKMGoj6DCOuoJEXubHsPXiuklMjxtWPim+Ifz9vZ/kfRrmsA84nyUn209FKKAbKVzPNlNp2MLlt3mNz0vgXHe3bgynuvAo1pcBJMNLhcAV7CmWqitpg6ZnXOxX5K6BWuhJNy396jK/NYUzXTqTyXl34BL9sjTYYvLaiKHyYoyLnO+XCzaNaW1gNsROYrk84xNo71sSOzjjwTWClRgSRs14lnm6goQA3XGT/1JZCatDci7SUMVcTq/M08dOwwSikWa5KZUDLKLC9d6PH4a9uAQCifg1t1Ae98/8Msv2/MyDh2M0tqHb1RD/e5z4FzzCwe48EDJzBCMnf+ZTaeepnAGcJ2TNCMwMDd3ZQVl9McKZZOvcb4YoTp7lKrGfTRRS7Uanzx5V02LqyxTI1b3vlBWmQs7uzwwMaLmC1DM7qZ15buQMmAwEaEgQIp2Upy+tsjAMKFmwmCDjpPaL95hviV59FxSG2xQ9CsYQbDt/iNvWHfb7uuAWxPvqdi4k+FYlfdZjrkcxV/qSKgipLGWggFiuldl5Do9oBjNQ28GqW2xyfzz6abrKe8tSKgnVLDKJn3Yk+4Mh1tWiGxxUkJm4HLq2MZISe6YAJ/JS4H40POshE8KAQOHZAYx07qK5oq99wsqSVBM6K+1EaFGpvskr70LayxDC/tMlrvkjdmmH//HNFtd1CLAo61A5britc2hjz+6jZfe3W7SEv6hvX7Ds/wzgfvZX65wdbYsN1LyZIM942vkH/xc4h+l8Z7Nbe9426c0gTfPsful76EyhPqS01q8w2kVhxv1DgZh5CAPCtIi082ihzhSoeBifj6mwNetJvcebjD8j3vpN6JmH3+G+w78ySit8PGQpvzY4nVIQsuYFEpkIJuZljrJRCE1Gf2E80dINq+hD79IsErTyNbdfSxVaL5GZLhtWvmNu7tDdf+EVXTub4BTJQKC8WNvvfNy5YVRFI/UGPaPZp6vwQet4eVVbwPpdroJHAt61JT+a2pHU8FqFecewlkk/0XPl5FlPWPl+f4y+eTZnWfm3IORKntVb3vitxgCaCu+hzcdN7OFd6sKxTWhKiY8pNUncOVuvmFdyuEDxtDJb22vqQIIymOAaFWzDYC4kDRiAO2E8ObvYxeYtgcG9LM0tAxen4JVauhtCLsboBUBCInmG0hTEzWbpM3miglaIUQ6YkX6wAjAsZhTC41o2wGISKCXKG0Dz2dVMi4RjQ7hwwVcaiIhztY5RvQ9dKKn/ZUa5JZB8aSK40WXmZHxTFBq0nQrCObM4hGByFGV/xdf1B2I4S8ul3XACZdoSZaJZWnbTpBbid3qihDR38Tl2PNPHm1JJhepuHqmAgklqBZritVleMRYqLENaE5QPmkfDlpBCi8LmeRNqMiypbFByn2bGuL8E8KUdAfHNIYRJ4i8H9M36UkkCW9DB8SO1WqsvpfuRQYEpzLfVLf+hBSClChQkUaGcip1igKSoRARZqgESLrISbWiFARBRItqGSpg1ASxgH7OzEfPD7Hkbka26Ocx8/s0H9lEysErmgePdJa4baHf5LIZgS9TcQ3v4S0hkYoaLz/HjKpeF3PcVbPELmM48lZ2vmGzzcWN+YoaHGmdYytaJa1VFPvx6xmmtlODal8BVOvrNJ+6P0E2Qi12yU684Qnx84uUH/kp0hlgHFtuqmDPPdtWlIQhSG1I4eYnQVZb6EPHkN2FpDfRfPqhl0bu64BrNIDo6wOXr5CeQe7Kifm3BRxtKwGCu+CCGcKr0hetjsPJLISNoRJwaBgxVdj3KYKC2UWvyLAlp7XJI1eelLClmTTiRfmK6IUtQQ3JWboPIA5LymE9aRUJaQHVDc5RU/FmOTGyn/EVtgqEHaOgjnvvASPFshAIqe70wtSrSjCSxVpRKQJQwVaEiqJErYi2Srlx6bNtUPeeWiGu1ZbPPHGLp9/ZZOXLw2IQk2jrgm1ornawR47htQO/eQXCb71Aiob077jVtq3nmQc1BlnC5zP56jlAw7ujlH9XjXVyTmHiVuszx7kXH2VQWKIgjGzqaFRDxBFWkB25qgtNYldhnzuKfRLT2HzDHVgFX3HPTgVYc93Ga31AeOrn9bhlCZamKcxC9TauNWbob2IuEzZ4QdpN0LIq9t1DWB7zTHlYhQZ+dKDcZVHVPbGec9LVqtcUVcs0WWS4y9IotO5Nqae20nlsjxqxXTfG5LuhTpRhXSi0NZ33uWbTLku1p3QGUDYUkoa3xJVXfPUeZTbFkM8mDonbI6xhqxo+5nsvzj5cjq3sb7DwLqKH2aNwxZDb7Fucn1CYoX/nIx1mNySD0Yk584xGml013GgLnBLDUJhqSmDloaaS1jvjelLmLOSxXYLbSJ2VJ2NUcgoU6xbwdBZnBFsigZrwSxYh7EWZx07okXfajLjG9TT3P+Y0qsUglHuOJ8ZlDHoDIJAI4Wjm1p6OyNSaTCDLovZDghJzc2gZIDMLHm/TzLYQjQyVO0Swlpc79q1Etm3GULeoFH8UJujciWmpmRX47Gn80qFF+X/K3tBQZhkr7yXVuwTwWTEmc8jlbr5E0ByuEJmRwhVKU3YwmMCf/OoomdTVueC92hKzoLSOKfKq/GPQlaqEDABPmkzZJ4WsajEBfViA1MMIRGevFpMWZImKbzHiTcokpwkSRkkOc2CkKllUbiYAql8nCKNqvJhzjjMOCPtJzhSbFbkBYXESolVkpyMNHWMhxmD/jobr73CmtmifuAIP3HPe8kXVlCjHXT3AmQJr4xzvnEqI7HwgAs5dMvNaAzP2iUeX2swFgFZAFmQEAqHkft4szGHtY5xakiNxaiIJI/Jxzm9ccbOMGOY5IyaEVoKIi1Z27V8fWNMlqSc6AnuajVQNuflbspj374IQnJ7fpYHzRouCNlunqSn2qhRyuj0G2y9+Ry62aCxtUE4N4sdXMMcGG/TA/u+nckPl/0IAFj5Vy0re74KWFUAy2R2uWqRY/LyMHYyJM1VkFWl5D3DoQQymMDcdBBIxU73HpqssHQyZBZcOYTDFVI97CkVVnk8D7Ny71vFr6p/wBkvz+PwAoRF64swzlccKbQoxNQ8S+PJvmWjusgteW4KL8VO2orKC3eu0Jf3+TghJUJJnLV+alFicKEBY6c+GomVCov0E4syQ9LrMjj7Et3uG7SBEx98P/XDM7A7RgqDGY9ZGzre2HTsZJLjc5JgaZ5AwKXNNk9vRCQo2jVoxAYtBTZus1OEdwOXk2BRUlC3miA3JJlllBpGqfcwlRAEUtDNHK/s5AxHGR0DRBHSKTbGlud6fRSOk+EGh/QFnKvh3CHGEqQxZNvbDM+eJ2zViWIIsh3c6NpVIW/Y1e36BrBqIAZMRAuhCLT806qNyHtkAl1RFoSQE1AQQEGTqAbflrtmIqlShps+YX9Z2FoiFw6JmExIujw9Nw2MU/ueRKuF/KArvT4mo88oCxCqCjNtGYwKiZC6iAVLZYxCx6s8T1uEqTon0IY4oMhfeblpWfQbCiWL6dwaqScDQCzC0yJK+QoxUXgVzg/OlVjPxteSoNWkdtNNNPNZgqVFsosXGOYJcrSD3L2Azca0xi1urUl6sSYOJK9ndaQAGzU4PN/AOGjnfZrZViGbPYvTLV+Zs/5Tq5GzZHZo2owNK+lr79GGSvppUc7RCBWHOzFJXREnHS6OllA2J67PcKuI0c6wMBa4JMOIgLwQe5RSoTsdaqsrBI0GenEVMddBXEsPzDnMpCr0PW3/o2hvGcC+/OUv86/+1b/iySef5MKFC/zBH/wBP/MzPwP4ps1f+7Vf47//9//Oa6+9xszMDI888gj//J//8z3a2OVUkv/yX/5L1fz5b/7Nv6HZbL6lc6kkY2x+RY9esUaxqGgDApwsQkmmxAgdRbWtpBqUyXpZPToEpmjVkWIymUeUYVlp1nhvBoko1SMqz4ZJKDsFfA5B7gpSrrMENvM+lFRYGfjzsMZP8i6/iEr7cxIaU4bBMkRK7415WR0PYAaJlWHhWPntbZhSr0HHpDTjgFBLtJQoJVGBQoUKHQcEzRoy0D4n5hwiN6hI+6G1ge8DLYFXuhxpQWEItCCINPXlFeZvOcrynCa7eIHBM09gtjeR0qJljhBwYGk/P3dAkYU1TqcRnx82yYRicbbDBw/PEJiE9ptnaa69RKpj3py5nfX6LJkTBEqSZIb5fMRdwzOsZJucER2S+DA6btGINQYv3rjcDNnfmgPn2NgOeXa9hTWG5Zka/8tMnTBPaLwqsJtD0gCScco4t6ggpH70MHNLAbLeRK0eRbTnUL1rV4U07u2FgTeS+IUNBgPuuusufumXfomf+7mf2/PecDjkqaee4td//de566672N7e5m//7b/NX/pLf4knnniiWu+tTjH5jibKm8dVnpZffsWKlETSvfhW+D2VZo6YCjdLoCvXpSK4lhQIv3iK1DoFTqLKoV9ZHRXFVtPn4fsYRQWIouwokG7iFZZVUFkAd+FJlh6YFKJq/K7OywmsAFO4k75zwIFyBFoRFb2Qqsi1lXpgvtqoUIHvV3TFuDXpnB/I4cXDKkWQksPmf+xkcnezQXz4EPX9bYZ5Qm/jEsnpU56KUQuRgaLZbrE/TrB1zYVuzJtZTCIC5sM6+2fr1HJoXxzTyjYYUqcvUnqBRFlBbvzfteEMS7bLwXyDsZK0QktNKQLt5Y2Mc7QixWI9QEnoZ5aNrh8Jd7iluGVeEaaWYQDjLMe4DFMUAaxS6Jk2cTNH1Fq4+RVozSP0tatC3rCr21sGsI9+9KN89KMf/f+1d2Yxcl33mf+dc9fau6tXbi1RFLVYomRZEiVZceQtMZBgBoltGBMEg7zMBElowI5fguTFzpPynAWBn5J5GMCBMeNBrNmgkWSOZUuxREWWtZCiFqpJcWk22UttdznLPJx7q6opamxJFOmW6wOaXX3vrVvnNKu+/q/f/7LnWq0Wjz766JZjf/u3f8vBgwdZXl5maWnpfU0xeTeMeo5LV6Ykqq2+mx02Um+FGH80rAwtMpNFCYETQDTO3RR+YV1RKF0U1gyuaHakRQHDhIEY3d8OaaXU0xfDtZfrEYX2/FCyeqxUQBUWpxDSJQwK8jJ2ZFGOyKQUZQTPlCoSZbO3wLe5a7YWgtxY1gY5g0zQ1FCpVYhMg2B+AX/PdYggIFs5S3bmNCbPkZ5HZaaJrVSw+Trm7Gt4QqB0Sl/nyNxjfxzD9S2mayErnZTn3t4kygIa199MtTVNAlywzlmerdepZinSGkIT06z45MKjqTZprK0T25w4jvD37CMykmbaYfbky+gwpj29gG62aHUCgtWcbLNPHHXY61+g4WtqpolVMf1cUhM5nugRCkM77bBXbaCNpp1GyH4IKsXzcKQbVGg3QkTdxzeW3qDOstEE1GgQEllJXqphXgVMLLDL40OPgW1sbCCEYGpqCrhyU0ygJLDS6igGx5azFcdgGWvJKVBSxrBNCIp72CJ+VAS/VercQs93Vd1Cun7HomZLF/2HFjevcfgLHRuNNtK1B4XTpxdFZtITJW0W6xICJ8Ts7iELaR2NJBdOWqcsZIXx+iA7CsKDW7NRbqirysDkgBj+fkJtCQpF1VQbTm0mCGtZ0rCj3aRaFwQ33ER420HwQ5Knn6T302PYNKG6MEVtRxsRBJjBGcyxDWyuyM6v0d/o4rXn+dQ9D/HggT2c6ymeOdPlzIk1bqjFPHTwM8xWBL1OxvLFPt1UkekVprvLRCiqlQaLzQgtPBbTZeZOLTv3dm4P/t4H8Xo9Fp47QuW1HyOn54gf+CzBniXEuQ3ksYT+yhr1hubeaoiNLrJmFziVNlm3Hs2sS5BsUCFnqbdOO7uINYZar4Yvawhj8H2LmGsThRWi2To72yF95XPCzHA0c+S1z1aYsR6p/cWF9z4oJjGwy+NDJbAkSfizP/szfu/3fm+ow/1+ppikaUqajsa4l+qNIyevDEiV1swlBHYJeZXPLUls67lRxtGKomWmLD1gzFCzZau1LKbzXKoQMdJjL7Oh5TpMYXnJS1572OZdurt2VNRqheuBHPVLju3NvmMHQ5fTWWKqUI0dZSelHRXE5tqQ5E4mOTUWEYX4XoTXaOJNz7tMZ1BFJTk2TUEIgloF4QmM6mPTLirJ0OdWSS9sEFrLfKCozVTQIqGbKk6tJ7TiBro9j9euoNcTurbLZpLR7/ZRA0WgU7xYUfWd21sZDIj6FwkDH+Ffj5iaRYqAWKWY9XN4gaBOThx7qEDQN5o8U4Qqo2V6BBaMaXJSK1JtUDYHM0CSUsm7RHoTjEEqi0jLRIjbvwwjgshHRE7aOxEhFxAo6zOwHrl1Az8muLb40Agsz3O+8pWvYK3l7//+7z/QvR5++GH+8i//8t0vGKULRzGssfhTGZ/ZEi/DxXlsEbgXRXzJDWvwKMszbWHZIUaCgcNbF+m3raE3d9VwYrYQWCmH7i64bJ9zRY1LRjKq8h8G/IsXM2VlvZCU6qoSjdRmGOMqX1cisXhFltJlE60VCB8njAguoI8gE5pMZ6TKkClNN3UDN/qpQqU5WuV4ee7KL4RADTKSjRSbpFR6qasP8yRGKYzSqEFGuj6gvzrAVFNU5jKkjSjgtoUa05WAyJO8tLzOq6c26WjD+UyTG8NpFROIHUQyJenlzPaO4mGo5Sto1aPnhZx8u8Pp/hqBStnZ2kn7zntABPReX6azfAFhc4LGHOGBJp5JUXkXc2GdzaTBWdvnYhhifIMIQ6pWUFvJaJw6i6dz1+PYapILj5N5yGnVwo+r7BpEzOWCi33FibNdXj7TpR779Dop7XpIv3s1C1k/mAv5IQqyXlN8KARWktdbb73F448/vmUKyvuZYvLnf/7nfOMb3xj+vLm5OTbfrnAfZRE8L6viGfVHCsZagIauHVgbDImCcvSZkBgvxAjfteqIseEaYnhLSstN4Ny5URSqIFNrEDrHClHI3IzIThZxNGnL5msDOncua1kCIYRTnZCBq4RHlFvEMxpfp8P2obJi39gAY8sastHAEutHxXmnPKEtJCJjoLOiXkqx3s/JlabTS8n6CUon+GkKeYqwoLoD+ud7mMGAyuyA6vzAEVjuCCzrpfRWumye6qCjPip1yYaZmuTX93rk2vDiqQ7/7chZTpzv02hGzM7XiEKfDVPnhLePQOTcePE1bl15nlgn1GKJjiQdEfGjC6v8gDrT1ZAv3noT13/i46Snz7L6vf/N2rMvUL3hOha/8m+pHbgV/fabpM/+ALNyjtVahdeTDc6GkrOx5FS1Soxmz/KAfS+8QZz2qMw0iGcb9P2Yp/0beTLYRaVa4aFelbsywbmO4oXXL/L00RWiOODF+Tq1ekQ+uMp6YBMX8h244gRWktfx48d54oknmJmZ2XL+/UwxeffpwZdaW+OZw5GTuKVWa5idc4/LQoYtMjwWrCiFDCkkqMXovuXDobe6RVeiuGxruUS5hGG7zvh6hplHw0hMcTxrupU2y0xfOaqtfO13DD7dUiTr6tascNdpRDELshjAYYxrKyqmC1njhsGWJSVGG3RusLnGKONajARu5L02WOXO60yjcz2UpA48mA4FWElFWjr9jJXNBOMJprKIQEIiJANZwScgV4Z4sEFVDfBEBeVXyYRlM9ecz3O08EmCGky3ses916p0dgV/po0OKtjWLGZtFWNApxkqyEkyRSIMXV8SaZ8EwXQKST9HpBleNcVPQjJfshkJVkREVUf0jIcykGlLP1F0ehmpNni9kEQIVJJd5j05wdXEeyawbrfLa6+9Nvz5zTff5Pnnn6fdbrNjxw6+/OUv89xzz/HII4+gtR7GtdrtNmEY/kJTTH5ReFYX+lvjGI9DFd+EALyxoLo7bpCFx+lGkpXXCiGcOLUAKzy0LGu6ROHyiSJT6EjOM6qwesqyAjFy+cTW4bfDrCYlv4hLCFFihD+UuxFaDQlPlu5mIetcFtIKq5yFVlh/jlfLzKMFmwEWz0JgcN917prXrUVKQSX0CT1JRQUEcYivQ2QQDEs2/MgnaoTYQBPUQ/xKVJRTeAhfEViotCuYNKMyU8GPXCLEdDZIl99Ab6zTVBU+tTTFTTtb1EyXaX2GIM3YjKa5WJkDEVGvx0T1Cr722JjawUZrkdSL2R0t8lvBHEHgM7Dw5HKXsCtpHLiDndNN0pl5XrcxgxNrNFcH7ApCaq06rWaNPbM1KlGNVsVnthYRCksj3UtffJIsT9HNCnaqQiZDZuQCH5PTVOKQXc2QqRBUzeOm3U362lCJA3bP12nVQ5JehcPv6R37/jHJQl4e75nAnn32WT7zmc8Mfy5duz/4gz/gW9/6Fv/8z/8MwMc//vEtz3viiSf49Kc/Dfz8KSa/KByBFfVSwwbm8mxpkRUeYuECyrFTFjGKDUjfVbFTBtOL2qxCb76gwOE9nZsHwuSFqKDFegFWhu700LUrW3QKAisC6rboV6SMUxXN51ZItPSdfpVWeDotasIYi++Vbq0Yqlg4m80i5fi1RSxOZcVkcFFG/IiUy7Ja63og65EPWGomJExjfKXwosDF0aTErwTE0zE2tUSNmKAWI0oXMldIz6M2X8fzDOFCDT/2wBjU+kX6//o06Vuv077uZn7rk1+A+d1w+jXEK29he2ssRzdyrLZA5ke0BhXiXh1pFBfm9nJ89mN4Ucz+2TqfbVfppoYnlzf5yWsbzEaS37j/fq6fepBTfcOTp3NeO7bKvrzHdBAy227Snmqyb6HJXKXBVCVgoRYSSEGneSvru3a7oSSxj6kEWAQLShIpQewL9rYjZiII8Dmwr02tXaMVB9wyX2OhHtLpbPKt9/yufX9wBPZBXMgruJhfIrxnAvv0pz/9jqzXOH6RaSM/b4rJL47SZRxz7y77eJSZHK5OlHxQktzWnKQo/b0tY9jG9jZ2eKisardeWWppibGjpRa9sOMZSMGINi8l41E2cyjJc0nGc7hLe5nRW0XGdOjSDkstRuQ+JHYYJhjE8EHphrppQ1bK4tzYixfXCilcC5I3dt4YTJ5j0pRQZdSEJvANRuYYM8DoATWdULEZ0np4UqD8EGE8Ej+mH1Tx/Qjfk7SEBqERxpAoQxr65HEV3YxdA7nYJFXKCRIKAZ5ASumG73qSSFgqaAIEPd8nrTTQFsLIJ4rdR8EbpNRURowkFK7V3xOCwJeEgRM/rBRfyr+aZRQTC+xy2Na9kM7V8sZE92zRLwiXWmUjG2g8UWmHH+ZSZbR45vB+kpGG/RbSGI+rlVnQsZCbEEVBanmksKKskOA5K00LD2OLggoZIIQ/JBineOqutcW+ynFrWngo/IJUPIQIcEoXGjnMfPruy7MY4YPn/n7rIiyXSoUmwVrlrJCiVSjNFPkgQ6kUmesiYSuxxqJzg8kUeS8l3ei54bfGkWM+yBhc6NM710VFA+qpWyetGeID9+Dvuh6dWzaf+1esOoKXrhP0VkClVPJT7B5YMi8kA35a2YsSHmeYZqXryitOvXKCysVTmChmz96badywG6Utr57t8eKJdfzAY2ctYmm6Qnu9Q/VETtbps2F7vBX2WItCjNlgpzlPQM66aXHUtEkIaNdD2rWQQOc0Tr1O/cxbRHFE9vEDrN94A6t9zSvLm7x4apNa7HN6tUa7HjHofXQnc28XbG8Ckx5GekWnonXaVEWFvC2LR8fIaxjmL2NJwtVCuSC6HmO20nIq663KCvqi3ae0osYXs6Vj28XArPBGpGicq1uOuzdQBNHdMzzpDfW+yhp7hAA/dHfQhWIrrng2E64X0pNlX6bBVwmyyKRa38P6ERZQ0g7lfZRx3xMvRZENj6XKBerTVKEGKUoleJkaWoTGgM40JlXkvYRsvYvwpWv8FgLVcwTWPdNF1wZkqXGZ3NYM0R33ERlD92cvsPlf/ivJm28QtyLqCzX8yKfSHbBn9Qy55/PKzK38dP4O+n6FgRYMuoqwu0nzh8/gPfNDqvNtlv7DFPc8eICT6yn/+UcX+PHxC9y0UOffP7ibu65roZdXyV/PyTa6rKsub4ku5wKfev8EYuMFQtVjPbiBl8Nb6XgV5lsV5qdiKlmf/S+8wPyLPyJoNsnaLdb27OVcV/HKiXX+5eh5otjn6HydaiOcZCF/CbCtCWzkkAGM6rS2XoMLtotRJrBEqR46ukNRdDrsq7SlOTV6zmVXMvKn7KWHx0QVKdZSmG/D9b/znpfuorQkx3Y4TrbjWUsX8bvsGi/bUGUduSntClm1BTwPrI9CMFAGiyE3uKC972GDEB1WnMuocoRWaGUgiJD1BiKK0UlGtr6BkRLlh2gZkhJgpIvf5cKjawOk9QktxMIgMRgLXePTNz7CaiIUIQpjDH1tkcog8ow46xNkGXme08sMaa7w8pQ465PrFC3AeL7rROj38DwPkSVO6wyBzXJIuwhPQSzARs4FT1NMp4tGoDY2Eesb6M0MOegRpX1862E6BqV8VHL1phK92//qe3n+RxHbmsCMcZOmrSgdPCeDLCialil6FK1BUmbzRh/jSz/QQ5tqvJpfjD1rPOMpZDEM3Csmc7usZtnWg7V4W/7qFfcxygXdhcQTfpGttHjWtf0Mrb6SNMsJ2YV4IQg8q4m0KtYcgozc6k2hEyYEQmXuuwXfOtVSi8UrJm+HWmG1ixcluRnWgSVeRLBjJxWR8nbQ4I3TAzKb0VYwu9jC0zXM/lvp7rsZshz70gvYN19FRhXqd93N1OIejNJ0XznOxr++xHp9muM7b+JiY4ZFJTlw/6+zcO89LHcyfnphQCfT3NzU3DOdU/EFWdbgzIUBiVDc0cy4vZUjw4zzB/ZxqtGkFgraaxdoPPbf6auQuD/DzEydmkjIXnyGjeN9pM0JqhHh9UssrCpuO36EnX3D4u4Z+jcdQMUB8Stn2P/8j8k0zN7/CeZuuQc/F4QGVs/38ddSaj/4MZW3TuNZuGeQc73UqL5mcCYhTxRpnrK183eCq41tTWDajmZDlgWloigqdRK8OOvLGpctpCCB8T6cEtIbli6MrJ0xDFuHXByrdCKdpI+LdY2rsI7afEsbq7CejAarEcJDeNJZBsbgGTUqZC37ObdI9QjKYlpPZfg6BcrhHGHxUnpYOS9kRjmJyDN6VOBb1HaFWmO1RmlDkms2BzlprklaIcH8AlGoWU1qPHs2oafgrhx2zTUIPUH3hpvo3/oApttDv3QCc3KNaM5n5+130P7MQ/ReO8GJb/8nLhx+ipOze3j8TsWb8zdwcG+L2x+8n9mFOkdfu8BTT5/k9Fofmin37h5QCSzZ2zHnzibkNmWmkvBgJcHUJIdvvo6X9xygMuiw+60fM/vqSwwqbcKdn2RqepZqf4Ps2Atsbr5FPD/L1G03E80sMLvxFje98QK9lQ1E49dIdn+WZHqa6Oj/Yu/Lz2KThJlbFphtPYjVHhcsrF0cIPMcvfEs5qcvEFQD7tw7TXW+Rm+QcPL4CutnuwzMBwmrvzdMXMjLY1sTmNjy/VJnrHCZhm7c2DNKL+xdHMIt8fnxN40ddzVNkTzYmt3cesdLM5jFl2XkRpZrEeUYszK1IN5xjy2Tjob7KmjVFgkCWQoZjinvl6octtA7K84LKfCkLIi/uK2UCM9H+AI8r3BzLRQCh9ITiCCAIIQgc2KHXjnBO0TGsfsuQaLwpaEWerSqPmHoM8Bj3UhSLyCqVqjlIGJJRxR/IHyfduz00RpSEagEI3x8X+BXKnhCoeMKaVRFBxG1wDLrZ0x5OZF0QorSk8gwQIQRfuAThxITgg48lO9jvBCvWqXanoIkoRoHVGyCtZpqNSCdazs3NZJEoSSohlRrEbVaBAoaUzVMJvC1gvOXfQtdcUyykJfHtiYwXwoCJ+I+jCa5iUJlF2PxEZYShMvmiaFYofsQm8J6KisDLKCsROPqqnwsXqn2OqYwIUtiKIP1ohDHKYQTpfVG8bTSuhqyokswGNxfRolAyMDVhcHQhbVjZRGyaHUqq/WtHwECJTxSXVCejPAi95tQInDyOxSJCoogPgZtLamXU4mhpZ2qRifx8YQgCn28MEQEhoqNmCYkVtAYRATVmMAThJETQLShh2xXkbtbBO0GftX1W8rQo76jjt3fprprjpn7djG4bgklBMdW+7x8oY81cO8NbayFQPV4VnWQuSZoWr58KwRWs9Tvoc+eJpcB9alpdk/FSOOThXdxetcehLAckIbbxTI10WP3zhrN2Z0E7Vn89iyyOUW82GH65h1U5yt0d02x5nnkCKq33cpU7d/hqZzWXIXWxusIa5g5sINs/t8gtCa0OYHJkYEkakYEFZ+aElTuhCyFbpLAX/zLh/kWn+DnYJsTmKtwH1acjzluYvgPw9iRC2OpggQsRniYYfFqOXYNFKCswCvJqyQwo8essALSoyzbF8IbeZ4FSVlri/IHPTpeaJfZwv11cs3+O6L5VjA2RUgjtbuP8AKsF2ERKCPJi1pe3wuK/QhyI8gLy7NQfkYbSK0LyOeeRxhq6sqJ+lVC1wQeBj7SDxC+ISKgKQJCDZVKSFCJ3PDawCeQAut7BM2YYL6ON1XFi5x0tQwk1dkqYk+T2eunuO22OaIbF3n5fI9Hjl5geT1l/1yNT+5tM10JeHUl5rlTHmmu+GRb8dm5jJrNSF5LSE6tomRItZkz34gwsopq1Vk1N9LMN7l1/SV29t9GBAYRV8BGeM02fnMKWWsStqdoXjeLmg5Qc3WMJ1BC0LjhemZv20doNfVzR2mce8Wpc+zbhbz3Nvc7H3QgG4xq6AD8kKnqFIQxm50u/MX7e+++V0xcyMtjWxPYsLBzi5s19uBd/s9GxaKXebZgOJl7NN52zJ0TlziLYuxcGeO6pBCVd9yjvHupSFFee8maygLUIltaVvaXahlO118M25TKZxZOopuAJBjuQhaE7CxR7YL2uRuCobQbUebGlDkrVRt3PNcWXQz4MBK0dlrxGJcVlLlG5GOzL41FpZq8nyM2++TnVpBxA9m3tDzLbC2gaXO88ytYXyAHlkgKCDxk2kOdv0hmMtLMkFRaZDLAM5pq7yK59Nkkoi8CRKbJBim21yeXHn0/JpcBsY2Y0oZQ5ZgsI++l5J0E0R8Q5z28PCRTHmcTH88odiQ59SJ2upYYuus50hhqvS6VZNP9Ln2J9FztYb6Zo2VIp3c1yygmLuTlsK0JzGX0jLOdhHQf0qErKEYcMzaZ2wrPlQngPuReoWFP2foDeLJUVwVhPWyhje9IRWwlLTlWsGpKoUOccODQJWSre1hkBz0MspTwsT4aN9NIFtagE1Qs6r+kRPvxMEZmihiXxFKRZaDfqYSWWU3fKrBjsTVrCIzCGs3FPOfiZp9TGzn9VLPezciVZhBl6DTBoEnSiLUkpa+gszkg2ehipKDfT+hmCpKccGNAeL5LaGJqSY7EYlNF9/Qma8cu4J/J6ax8H781BUvXc//BT6JvWEAcP474nz+iu75OdMMtXHfgbnRUITx+lNMvPo2vc5J9+0n23QdCEG6eZ+nVH9IREW+F13EsmGc2XWNh5QytzZOsxVO8NPcxVmpz7E4t93USFvMBg7fPsfriKZLVNWJVY8/iAla1eOas4fBJQ64tv7GYMrcjxlr4v290+eHZAWGacM/F17hl822CUFCdrRI1QgYDzdkzCZubOf180sx9rbG9CayQTbbSd9NyLs0cjof3y2xeEfdyBKEQaMoexJKYvLIUbIwEC3+uuMfIwrKleyrca7ieQws2GLP0CqJj3PqzeAWxGiRKFINjKctli/XpDKxGixjjBy5uZ8vqCksgNIFwMb0cyHFGYmi1IzABbjiJKEg4AzRS5XQHGRe7OUle6IBpQ5YpjMqxnnY1VomipyyDJCPvpwhPkKU5SW4g19h+ht1MIUqxuXaxNqVJLg7onukizvfpn15F+h7TDxxk/0P3U9/V5MKxLsvPHyFZPkUgfGbvuhtbD/EvrrF25CVQOencPtK5/fjSsHjxNDNnjiKI6VZjluMaSdJl7dw6/Y1VLjRCXmnUeCNeoKf6fCw5z7wZkK1t0Dl1gf7ZNaLZ88x0zyKDHptvK576aUZfCW68q4reXUMbeOVcn//xswHVfpf43OtMXTxOXPFoXdeiNldlcy3h5EvnWT3TZWAnWchrjW1NYMCQdLZ2+BWPSr6x7orhU7Y8V449Lp45zFKW9y1cI1E6YoyIqXDj3HlJKUftrKxiyjalcGL54qWZOLq3KIptx0tbbSmRXRDsuLKsLO4jzKjUwokkulcziGJa0WiNLpLjspRGGgLfIw6dCE8aaKSAwHcTwl1C0w3FCLEEgY8fhfiei4F5bgYbfujjV3z8yEd4RQLDkwS1kKgV41ViwvlZ/GqVaK4NnXXUmWVE2qU6N4WHIm8EBP1VrEjwIol33RLWGLLGFJu5IUAzKyV+HBETsBDm7PW6TIU5fqtFP9hDVpsjrNVpxAGVOMSPYkQIXq1KPF3H5hlhLURK13kxU/O5eTEgMYKpqRq9wBFYYzpg364KlSRiPl6g0eoRRZLKYo1wKqYS5UwNYphK6SsFR17/uW/RK4GJoOHlsa0JbNiAPdY0XX7IhbWFUkWBodUkxrhKbjk+uu8w2Th8rkVipNhCbuCUJmRpgUkfG4ii9mykEmG9wCmrIhjvv0S4oRuufaiQBhIFWQnnTFrfK4o2nJa+xVmIvhRFsaxGKjdg1Rc+slDPyJGkIioEFJ11arBkwkcLQ+b7NGqaeSPpp25gbK40tarFjxUi1EQioklIoCyNVpWKahFKQVKvkIU+aJ+4VSGcbxBM1/ErAQiBFwc097SQH5sjWNxF/eCvEexagt46+Zsvkr/yL0jPY8ev3Y6QklRr+qeewyBQ07PoL32JTAZ0RJ3X1zNCkzHvR8SLc4QWPiV63C6WUTIk2XErb/v3MPAjZuI2sV9hVxRSqfvIIKO6J2PuzrPka02qizN4vkBYzSf2tJhfapPJAL9a41SthkGw/4Bg/iZBpBL2bbTZ2b0RT1r8UOIFgpaVTH0qIjM+nf4A/uP/uXJv6P8PJhbY5bGtCWw8GF5iGGIvRQIp4l7Da0urZ0Ral/uvLWvBrBg1chvKkrJx5QkxlBizUrqAvLUu5VdI/Vgo+iLLOxfxuLEUgShajCwSUxCmlYUOfuEymqKsohxCWyYBMApsId1lXUeAwSPHQ+B6JT0hXPkEkhyLlhCHAfXYIoQgVZpMCsJQIX1nTfm+Txx4ICGqhIS1mEC6MorAl+BLgkpA2IjxaxEycCQtfUk8FWMX60TXzdG86wDxjbeQvPoSnePPkJ96i8p1S7Q+fid+o8ng5DLBq0fReU566wLpgQPYoEry9gYX3t4g0jmZ9AkadXyr2asz9poBm2GLl2cWWK0tYYGqtVQstEKPoCYQgSKYblHfOY2ug9+oOssSw+6pkOvmp9BexBt5ldfzGkZIZqdD9ld8QpMx3RU0Bg2XtdbKJWj8iGajjYiqLgs5wTXFtiSwsrSg0+kUH3Rv3K4BcBOirRoRmBy5U1szflsJzMIwxiRw1o4UhQk/dOFGBCaFwBuqV4+GcAiduap4BMZPMV5UvHopj2MKhYnx0WvObXQaZLJYi91KYDjrK/SciyrzASLvuYV5Plb4GCQDfDJ8l6WUbp3GWAbakhtLr5cz6HVIezlZpsj6KVluGAQpnV6P0Dd0lccgDUk19Pp9OoMEXwo6vR7dTgeSPmowIEsz/CTF9nrkm5vknS6dQUKS5WRJCr0u2WaHpNulm6TkaYZKUmSvjy99Bv0B/SRF54q0PyDrdEgCxaDXIet3Qaf0ZZ9NL8G3ekgmHRXSi3sM6AxnP1oL/VDRsSlRoMh7fQaDBJOkeH5I2E+Q2iDDPl6nh/ZyusrSzw1GePRUQKA8AqPwel3soFcQmC4ITCEIITNsdntb3o8fJgaYD5RJzD5QJ+UvL4S9Gr/9K4xTp06NaeJPMMG1xcmTJ9m9e/eHcu8kSdi7d++7Tux6L1hcXOTNN98kjuMrsLJfDmxLAjPGcPr0aay1LC0tcfLkyS2DQz5KKAeYfJT3CNtzn9ZaOp0OO3fuRMoPb8htkiRk2Qcv2QjD8CNFXrBNXUgpJbt37x7Oh2w2m9vmTf9+8auwR9h++2y1Wh/6a8Rx/JEjniuFqzcbfYIJJpjgCmNCYBNMMMG2xbYmsCiK+OY3v/kuMyM/GvhV2CP86uxzgiuLbRnEn2CCCSaAbW6BTTDBBL/amBDYBBNMsG0xIbAJJphg22JCYBNMMMG2xbYlsL/7u7/j+uuvJ45j7rvvPn7yk59c6yV9IDz88MPce++9NBoN5ufn+Z3f+R2OHTu25ZokSTh06BAzMzPU63W+9KUvce7cuWu04g+Ov/qrv0IIwde//vXhsY/aHif4cLEtCeyf/umf+MY3vsE3v/lNnnvuOe68806+8IUvsLKycq2X9r5x+PBhDh06xNNPP82jjz5Knuf85m/+Jr0x2eI//dM/5fvf/z7f/e53OXz4MKdPn+aLX/ziNVz1+8czzzzDt7/9be64444txz9Ke5zgKsBuQxw8eNAeOnRo+LPW2u7cudM+/PDD13BVVxYrKysWsIcPH7bWWru+vm6DILDf/e53h9e88sorFrBPPfXUtVrm+0Kn07H79++3jz76qH3ooYfs1772NWvtR2uPE1wdbDsLLMsyjhw5wuc///nhMSkln//853nqqaeu4cquLDY2NgBot9sAHDlyhDzPt+z7lltuYWlpadvt+9ChQ/z2b//2lr3AR2uPE1wdbLtm7tXVVbTWLCwsbDm+sLDA0aNHr9GqriyMMXz961/nwQcf5Pbbbwfg7NmzhGHI1NTUlmsXFhauiNTK1cJ3vvMdnnvuOZ555pl3nPuo7HGCq4dtR2C/Cjh06BAvvvgiTz755LVeyhXFyZMn+drXvsajjz46UVeY4Ipg27mQs7OzeJ73jszUuXPnWFxcvEarunL46le/yiOPPMITTzyxRSRvcXGRLMtYX1/fcv122veRI0dYWVnhE5/4BL7v4/s+hw8f5q//+q/xfZ+FhYVtv8cJri62HYGFYcjdd9/NY489NjxmjOGxxx7jgQceuIYr+2Cw1vLVr36V733vezz++OPs3bt3y/m7776bIAi27PvYsWMsLy9vm31/7nOf42c/+xnPP//88Ouee+7h93//94ePt/seJ7jKuNZZhPeD73znOzaKIvuP//iP9uWXX7Z/+Id/aKempuzZs2ev9dLeN/74j//Ytlot+4Mf/MCeOXNm+NXv94fX/NEf/ZFdWlqyjz/+uH322WftAw88YB944IFruOoPjvEspLUfzT1O8OFhWxKYtdb+zd/8jV1aWrJhGNqDBw/ap59++lov6QOB4biirV//8A//MLxmMBjYP/mTP7HT09O2Wq3a3/3d37Vnzpy5dou+AriUwD6Ke5zgw8NETmeCCSbYtth2MbAJJphgghITAptgggm2LSYENsEEE2xbTAhsggkm2LaYENgEE0ywbTEhsAkmmGDbYkJgE0wwwbbFhMAmmGCCbYsJgU0wwQTbFhMCm2CCCbYtJgQ2wQQTbFtMCGyCCSbYtvh/DsONrbuYQPMAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(det_state.model.U_full, \"RdBu\")\n", "plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "d1929b30", "metadata": {}, "source": [ "The mean-field states support quick measurement without Monte Carlo noise.\n", "For example, the energy is given by" ] }, { "cell_type": "code", "execution_count": 6, "id": "52b2bb26", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Mean-field energy: -67.80696117575033\n" ] } ], "source": [ "E0 = det_state.expectation(H)\n", "print(f\"Mean-field energy: {E0}\")" ] }, { "cell_type": "markdown", "id": "7870f83f", "metadata": {}, "source": [ "The obtained energy is the final result in the training curve. We can also measure some other quantities, for example, charge and spin densities." ] }, { "cell_type": "code", "execution_count": 7, "id": "df9335b6", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def charge(i):\n", " return number_u(i) + number_d(i)\n", "\n", "\n", "def spin(i):\n", " return number_u(i) - number_d(i)\n", "\n", "\n", "i = lattice.index_from_xyz[0, 4, 2]\n", "C = [det_state.expectation(charge(i)) for i in range(N)]\n", "C = jnp.asarray(C).reshape(lattice.shape[1:]).real\n", "S = [det_state.expectation(spin(i)) for i in range(N)]\n", "S = jnp.asarray(S).reshape(lattice.shape[1:]).real\n", "\n", "fig, axes = plt.subplots(1, 2, figsize=(5, 5))\n", "\n", "axes[0].set_title(\"Charge density\")\n", "im = axes[0].imshow(C, cmap=\"RdBu\")\n", "fig.colorbar(im, ax=axes[0])\n", "axes[1].set_title(\"Spin density\")\n", "im = axes[1].imshow(S, cmap=\"RdBu\")\n", "fig.colorbar(im, ax=axes[1])\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "1fdd9808", "metadata": {}, "source": [ "## BCS state\n", "\n", "The BCS state contains pairing between spin-up and spin-down orbitals, i.e.\n", "\n", "$$\n", "\\ket{\\psi_0} = \\exp\\left( \\sum_{ij} F_{ij} c_{i \\uparrow}^\\dagger c_{j \\downarrow}^\\dagger \\right) \\ket{0},\n", "$$\n", "\n", "where $F_{ij}$ denotes trainable pairing coefficients, and $i$ and $j$ iterate over spinful degrees of freedom.\n", "As the BCS state doesn't have a fixed amount of particles, the `Nparticles` argument defined in the lattice doesn't apply here.\n", "\n", "The pairing appears when there are attractive interactions in the system. For illustration, here we show the result in an attractive Hubbard model. To enforce half-filling, we set $\\mu = U/2$." ] }, { "cell_type": "code", "execution_count": 8, "id": "f508aba9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-50.99276841959967\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "bcs_state = qtx.state.SingletPairState()\n", "\n", "H_attractive = qtx.operator.Hubbard(U=-4)\n", "mu = -2\n", "opN = sum(number_u(i) + number_d(i) for i in range(N))\n", "H_attractive -= mu * opN\n", "\n", "energy = qtx.utils.DataTracer()\n", "\n", "for i in range(1000):\n", " step = bcs_state.get_step(H_attractive)\n", " bcs_state.update(step * 0.1)\n", " energy.append(bcs_state.energy)\n", "\n", "print(energy[-1])\n", "energy.plot()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 9, "id": "021995b9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Particle number: 63.99999999321078\n", "Mean-field energy: -50.99616092421499\n" ] } ], "source": [ "params, static = eqx.partition(bcs_state.model, eqx.is_inexact_array)\n", "loss_fn = bcs_state.get_loss_fn(H_attractive)\n", "solver = optx.BFGS(1e-8, 1e-12)\n", "out = optx.minimise(loss_fn, solver, params, max_steps=10000)\n", "E = loss_fn(out.value)\n", "model = eqx.combine(out.value, static)\n", "bcs_state = qtx.state.SingletPairState(model)\n", "\n", "print(\"Particle number:\", bcs_state.expectation(opN))\n", "print(\"Mean-field energy:\", E)" ] }, { "cell_type": "markdown", "id": "4ed6b280", "metadata": {}, "source": [ "The matrix $F$ in the definition can be obtained by" ] }, { "cell_type": "code", "execution_count": 10, "id": "d60f04fe", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "max_val = jnp.max(jnp.abs(bcs_state.model.F_full))\n", "plt.imshow(bcs_state.model.F_full, \"RdBu\", vmin=-max_val, vmax=max_val)\n", "plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "fd2b3d7a", "metadata": {}, "source": [ "The observables can be measured similarly." ] }, { "cell_type": "code", "execution_count": 11, "id": "278afb9b", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def charge(i):\n", " return number_u(i) + number_d(i)\n", "\n", "\n", "def spin(i):\n", " return number_u(i) - number_d(i)\n", "\n", "\n", "def Delta_s(i):\n", " _, x, y = lattice.xyz_from_index[i]\n", " return (\n", " annihilate_u(x, y) @ annihilate_d(x, y)\n", " - annihilate_d(x, y) @ annihilate_u(x, y)\n", " ) / 2\n", "\n", "\n", "C = [bcs_state.expectation(charge(i)) for i in range(N)]\n", "C = jnp.asarray(C).reshape(lattice.shape[1:]).real\n", "S = [bcs_state.expectation(spin(i)) for i in range(N)]\n", "S = jnp.asarray(S).reshape(lattice.shape[1:]).real\n", "Ps = [bcs_state.expectation(Delta_s(i)) for i in range(N)]\n", "Ps = jnp.asarray(Ps).reshape(lattice.shape[1:]).real\n", "\n", "fig, axes = plt.subplots(1, 3, figsize=(12, 5))\n", "\n", "axes[0].set_title(\"Charge density\", pad=20)\n", "im = axes[0].imshow(C, cmap=\"RdBu\", vmin=-2, vmax=2)\n", "fig.colorbar(im, ax=axes[0])\n", "axes[1].set_title(\"Spin density\", pad=20)\n", "im = axes[1].imshow(S, cmap=\"RdBu\", vmin=-1, vmax=1)\n", "fig.colorbar(im, ax=axes[1])\n", "axes[2].set_title(\"s-wave pairing density\", pad=20)\n", "im = axes[2].imshow(Ps, cmap=\"RdBu\", vmin=-0.5, vmax=0.5)\n", "fig.colorbar(im, ax=axes[2])\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "7ae58503", "metadata": {}, "source": [ "There is nearly homogeneous charge and pairing density in this system." ] }, { "cell_type": "markdown", "id": "0f880c99", "metadata": {}, "source": [ "## Pfaffian state\n", "\n", "The Pfaffian state is a generalization of the BCS state to allow general orbitals not restricted by spin species. Its expression is\n", "\n", "$$\n", "\\ket{\\psi_0} = \\exp\\left( \\frac{1}{2} \\sum_{ij} F_{ij} c_i^\\dagger c_j^\\dagger \\right) \\ket{0},\n", "$$\n", "\n", "where $i$ and $j$ iterate over spatial and spinful degrees of freedom. It can be defined and trained as shown below. We don't have orbitals with mixed spins in the solution, so the optimization will give equivalent results compared with the BCS state." ] }, { "cell_type": "code", "execution_count": 12, "id": "e8be842c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-50.97335331035188\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pf_state = qtx.state.GeneralPfState()\n", "\n", "energy = qtx.utils.DataTracer()\n", "\n", "for i in range(1000):\n", " step = pf_state.get_step(H_attractive)\n", " pf_state.update(step * 0.1)\n", " energy.append(pf_state.energy)\n", "\n", "print(energy[-1])\n", "energy.plot()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 13, "id": "620b8b04", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Particle number: 64.00000000320587\n", "Mean-field energy: -50.996160924215246\n" ] } ], "source": [ "params, static = eqx.partition(pf_state.model, eqx.is_inexact_array)\n", "loss_fn = pf_state.get_loss_fn(H_attractive)\n", "solver = optx.BFGS(1e-8, 1e-12)\n", "out = optx.minimise(loss_fn, solver, params, max_steps=10000)\n", "E = loss_fn(out.value)\n", "model = eqx.combine(out.value, static)\n", "pf_state = qtx.state.GeneralPfState(model)\n", "\n", "print(\"Particle number:\", pf_state.expectation(opN))\n", "print(\"Mean-field energy:\", E)" ] }, { "cell_type": "markdown", "id": "22d39b77", "metadata": {}, "source": [ "The side length of $F$ in the Pfaffian state is double the length in the BCS state to include 2 spin species." ] }, { "cell_type": "code", "execution_count": 14, "id": "4521e43f", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "max_val = jnp.max(jnp.abs(pf_state.model.F_full))\n", "plt.imshow(pf_state.model.F_full, \"RdBu\", vmin=-max_val, vmax=max_val)\n", "plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "284d63b7", "metadata": {}, "source": [ "The measurement gives similar results." ] }, { "cell_type": "code", "execution_count": 15, "id": "2c4afb4e", "metadata": {}, "outputs": [ { "data": { "image/png": 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z2d+K1Lssv75OLUt5+Xzo0CH9/PPPpa5xpdLXvd5w7ep/fDr1TEREhBISEvT1119Xaj+7GcusXz28unTpUk2cOFGpqamKjIyUw+HQ8OHDPab5LHFmj1xluVwudenSRU888YTX7xMTE6tcdnWOU5G/0/XXX6++fftq9erVeu+99/TYY49pzpw5ev311yt0l+XXgoODdeONN+r555/XM888o08++UQHDx7U73//+0qXBaDqQkJCdOGFF+rCCy/UeeedpzFjxujVV191N3aqqyL5Uh0lOf2nP/3JdvKOX19YlFcnh8Oh1157TZ999pneeustvfvuu7r55pv1+OOP67PPPivViKyI9PR0xcbG6uWXX9Yll1yil19+WXFxcUpLS6t0WUBdU941xNy5c91TqUtSq1at3I2YPn366Pnnn9f//d//6aOPPlLfvn3lcDjUp08fffTRR0pISJDL5fJosL388ssaPXq0hgwZonvuuUcxMTEKDg7W7NmztXv3bo+6DR8+XM8++6z+9re/aciQIXrllVfUoUMHj4mCaur6rTL1tlOZ61Rf53NlcO1aM3w+V+iVV16p5557TtnZ2UpNTTVW7muvvaZRo0bp8ccfd6/75ZdfKvzi01atWkk6fZf3sssuc68/deqU9u7dq65du7rXtW3bVl9++aX69+9f6TfOlxxn586d7u5h6fQwzj179ngES3WOU5b4+HjdcccduuOOO3To0CFdcMEFeuihh2z/pS/v2CNHjtTjjz+ut956S3/729/UokULZksDalFycrIk6fvvv/dYXzLs6Ez/+te/1KhRI/eMWqa1atVK69evV0FBgUcDaceOHR7bldylbdiwofHGz0UXXaSLLrpIDz30kFasWKERI0Zo5cqVuvXWW71uX1bmlfyHPisrS3PmzNGaNWtKDbEHAllZ1xAjR450z2goeTY6Shpi69at0+eff+5+n9gll1yiRYsWuXuuzhy2/dprr6lNmzZ6/fXXPX6X3m5EXXLJJYqPj9eqVavUp08fbdiwQf/zP//jsY2J66qDBw+Weh3Uv/71L0lyj8iqTL1rQkxMjMLCwrRr165S33lb92tcu/ofn0/rP2nSJDVu3Fi33nqr8vLySn2/e/duPfXUU5UuNzg4uNSdhAULFpT7XEaJ5ORkNWvWTM8//7xOnTrlXr98+fJSQ36uv/56HThwQM8//3ypcn7++WcVFhaWeZwWLVpo8eLFKi4udq/Pysoq1bisznG8cTqdpbriY2JilJCQUOYQoUaNGkmSbeO3a9eu6tq1q1544QX97//+r4YPH857QoAa8MEHH3i9g/rXv/5VUulhh9nZ2R7PT+zfv19vvPGGBgwY4LMGxxVXXKFTp065p+mWTmfRggULPLaLiYlRv3799Oyzz5ZqaEoqd8imNz/99FOpv0/37t0lqczMK7kQs8u8m266ST/99JP+8Ic/qKCgoE7dlQWqqiLXEG3atFFaWpp7ufjii93bJiUl6eyzz9aTTz6pkydPur/r27evdu/erddee00XXXSRx/VDSS6d+TvevHmzsrOzS9UvKChI1157rd566y39+c9/1qlTpzyGQ0pmrqtOnTqlZ5991v25uLhYzz77rFq0aOFubFam3jUhODhYaWlpWrNmjcdzYLt27dLf/va3cvfn2tX/+Lymbdu21YoVKzRs2DB17NhRI0eOVOfOnVVcXKxPP/1Ur776qkaPHl3pcq+88kr9+c9/VmRkpDp16qTs7Gy9//77atasWYX2DwkJ0fTp0zVhwgRdfvnluv7667V3715lZWWpbdu2Hi31m266Sa+88opuu+02ffDBB7r44ovldDr1z3/+U6+88oreffdd9x3uX2vYsKEefPBB/eEPf9Dll1+uYcOGac+ePVq6dGmpccDVOY43x48f1znnnKNrr71W3bp101lnnaX3339fn3/+uUfP5K+Fh4erU6dOWrVqlc477zxFR0erc+fO6ty5s3ubkSNHut9zwsULUDMmTJigEydO6JprrlGHDh3cObpq1Sq1bt261HuJOnfurPT0dN15550KDQ3VM888I0keQ5hMu+qqq3TxxRdr8uTJ2rt3rzp16qTXX3/d63McCxcuVJ8+fdSlSxeNHTtWbdq0UV5enrKzs/Xvf/9bX375ZaWOvWzZMj3zzDO65ppr1LZtWx0/flzPP/+8IiIidMUVV9juV3LR9T//8z8aPny4GjZsqKuuusrdkOvRo4c6d+7sfrj+ggsuqFS9gLqoqtcQZ+rbt69WrlypLl26uJ85veCCC9S4cWP961//0o033uix/ZVXXqnXX39d11xzjQYPHqw9e/Zo8eLF6tSpkwoKCkqVP2zYMC1YsEDTpk1Tly5d1LFjR4/vTVxXJSQkaM6cOdq7d6/OO+88rVq1Sjk5OXruuefcL2+ubL1rwvTp0/Xee+/p4osv1u233y6n06mnn35anTt3Vk5OTpn7cu3qh2pqOsp//etf1tixY63WrVtbISEhVpMmTayLL77YWrBggceUzpK8TuXZqlUra9SoUe7PP/30kzVmzBirefPm1llnnWWlp6db//znP0ttVzIdtN00z/Pnz7datWplhYaGWr169bI++eQTq2fPntbAgQM9tisuLrbmzJljnX/++VZoaKjVtGlTq2fPntaMGTOsY8eOlXv+zzzzjJWUlGSFhoZaycnJ1qZNm6xLL73UY2rUyhynIn+noqIi65577rG6detmNWnSxGrcuLHVrVs39zS7JX49NaplWdann35q9ezZ0woJCfE6Ter3339vBQcHW+edd1655w7AjL/97W/WzTffbHXo0ME666yzrJCQEKtdu3bWhAkTrLy8PI9tSzLi5Zdfts4991wrNDTU6tGjh/XBBx94bGc3rf/gwYNLHd9bZnnz448/WjfddJMVERFhRUZGWjfddJP1xRdfeJ1Ceffu3dbIkSOtuLg4q2HDhtbZZ59tXXnlldZrr71Wqo6/zvEPPvjAkuQ+p+3bt1s33HCD1bJlSys0NNSKiYmxrrzySo9XG5T8bX6dabNmzbLOPvtsKygoyOsU/48++qglyXr44YfLPX8gEFT0GqIsCxcutCRZt99+u8f6tLQ0S5K1fv16j/Uul8t6+OGH3ddlPXr0sN5++22v1ykl2ycmJlqSrAcffNBrHapz/XbppZda559/vrV161YrNTXVCgsLs1q1amU9/fTTVa73r/OnZOr+w4cPlzq+3bT+FblOtizLWr9+vdWjRw8rJCTEatu2rfXCCy9Yd999txUWFlbmeZfg2tV/OCyrFp5Q9GMul0stWrTQ7373O6/duzjthx9+UHx8vKZOnaoHHnigtqsD4FccDofGjx+vp59+urarEhCeeuop3XXXXdq7d6/XWc4ABJ5+/frphx9+qPTkef5syJAh+uabb7w+4xzo6vK1q8+fYfNnv/zyS6nnHV566SUdOXJE/fr1q51K1RFZWVlyOp1MbQ0g4FmWpSVLlujSSy+lsQagzvj55589Pu/cuVN//etf6+01bl2+dq07T9v5wGeffaa77rpL1113nZo1a6bt27dryZIl6ty5s6677rrarp5f2rBhg/7xj3/ooYce0pAhQ0q9sw4AAkVhYaHefPNNffDBB/rqq6/0xhtv1HaVAKDC2rRpo9GjR6tNmzb67rvvtGjRIoWEhGjSpEm1XbUaFQjXrvW6wda6dWslJiZq/vz5OnLkiKKjozVy5Eg98sgjHm92x3/NnDlTn376qS6++OJSs74BQCA5fPiwbrzxRkVFRem+++7Tb3/729quEgBU2MCBA/WXv/xFubm5Cg0NVWpqqh5++OFSL8QOdIFw7cozbAAAAADgp+r1M2wAAAAA4M9osAEAAACAn6LBBgAAAAB+igYbAAAAAPgpGmwAAAAA4KdosAEAAACAn6LBBgAAAAB+igYbAAAAAPgpGmwAAAAA4KdosAEAAACAn6LBBgAAAAB+igYbAAAAAPgpGmwAAAAA4KdosAEAAACAn6LBBgAAAAB+igYbAAAAAPgpGmwAAAAA4KdosAEAAACAn6LBhjpv9uzZuvDCC9WkSRPFxMRoyJAh2rFjR7n7vfrqq+rQoYPCwsLUpUsX/fWvf62B2gJAzdq0aZOuuuoqJSQkyOFwaM2aNeXus3HjRl1wwQUKDQ1Vu3btlJWVVWqbhQsXqnXr1goLC1NKSoq2bNlivvIAABpsqPs+/PBDjR8/Xp999pnWrVunkydPasCAASosLLTd59NPP9UNN9ygW265RV988YWGDBmiIUOG6Ouvv67BmgOA7xUWFqpbt25auHBhhbbfs2ePBg8erMsuu0w5OTmaOHGibr31Vr377rvubVatWqXMzExNmzZN27dvV7du3ZSenq5Dhw756jQAoN5yWJZl1XYlAJMOHz6smJgYffjhh7rkkku8bjNs2DAVFhbq7bffdq+76KKL1L17dy1evLimqgoANcrhcGj16tUaMmSI7Tb33nuv3nnnHY8bWMOHD9fRo0e1du1aSVJKSoouvPBCPf3005Ikl8ulxMRETZgwQZMnT/bpOQBAfdOgtivway6XSwcPHlSTJk3kcDhquzr1kmVZOn78uBISEhQUVPFO2F9++UXFxcVG6/HrfwdCQ0MVGhpa5n7Hjh2TJEVHR9tuk52drczMTI916enpFRoqBNQmMrJ2VTUfJbMZWdV8rIjs7GylpaV5rEtPT9fEiRMlScXFxdq2bZumTJni/j4oKEhpaWnKzs6u9vGBqiIfa5e/5GNISIjCwsKMlOUv/K7BdvDgQSUmJtZ2NSBp//79Oueccyq07S+//KLwJtHSqZ+NHf+ss85SQUGBx7pp06Zp+vTptvu4XC5NnDhRF198sTp37my7XW5urmJjYz3WxcbGKjc3t1p1BnyNjPQPlclHyXxGViUfK8ouH/Pz8/Xzzz/rp59+ktPp9LrNP//5z2ofH6gq8tE/1HY+xsXFac+ePQHVaPO7BluTJk0kSb9ftFYh4Y19cozgIN/edXG6fD/K1JfnUPxzoZb9Id39/0WF9ikulk79rAadrpeCG1a/Es6TKvjHK9q/f78iIiLcq8u7ezx+/Hh9/fXX+vjjj6tfB8APlfwud+7cWanfKMw4fvy4zj333Er/7Y1mZBXzEQh0Jb/Lrne9rODQRrVcm/rHWXRCf3/y97Wej7n/eEXFxcU02HyppAs7JLyxQhqd5ZNj0GCrmKoMJ3A0DJMjOKTax7aCgiVJERERHhckZcnIyNDbb7+tTZs2lXtnJy4uTnl5eR7r8vLyFBcXV7UKAzWk5HfZpEmTCv82YF5Vh1uZyMiq5GNl2OVjRESEwsPDFRwcrODgYDIUfqfkdxkc2kjBob656Y/y+UM+BhpmiYRRjqBgY0tFWZaljIwMrV69Whs2bFBSUlK5+6Smpmr9+vUe69atW6fU1NRKnzMAVFRN52NVlJePISEh6tmzp8c2LpdL69evJ0MBVFldyMfa4nc9bEBljR8/XitWrNAbb7yhJk2auJ9Di4yMVHh4uCRp5MiROvvsszV79mxJ0h//+EddeumlevzxxzV48GCtXLlSW7du1XPPPVdr5wEAvlBQUKBdu3a5P+/Zs0c5OTmKjo5Wy5YtNWXKFB04cEAvvfSSJOm2227T008/rUmTJunmm2/Whg0b9Morr+idd95xl5GZmalRo0YpOTlZvXr10rx581RYWKgxY8bU+PkBQKCjwQajjN3dsCpexqJFiyRJ/fr181i/dOlSjR49WpK0b98+jxmLevfurRUrVuj+++/Xfffdp3PPPVdr1qwpc6ISAKguIxlZiXyUpK1bt+qyyy5zfy6ZIXfUqFHKysrS999/r3379rm/T0pK0jvvvKO77rpLTz31lM455xy98MILSk9Pd28zbNgwHT58WFOnTlVubq66d++utWvXlpqIBAAqqjbysa6gwQajHA5DDTZX5YZElmfjxo2l1l133XW67rrrKlMrAKgWIxlZiXyUTt/MKisns7KyvO7zxRdflFluRkaGMjIyKlUXALBTG/lYV/AMGwAAAAD4KZ812BYuXKjWrVsrLCxMKSkp2rJli68OBT/iCA6SIzjYwMK9BAQu8rH+MpOR5CMCF/lYf5GP9nxyVqtWrVJmZqamTZum7du3q1u3bkpPT9ehQ4d8cTj4kaCgYGMLEIjIx/qNfATskY/1G/lozycNtieeeEJjx47VmDFj1KlTJy1evFiNGjXSiy++6IvDAUCdQT4CgHfkI+Cd8UlHiouLtW3bNk2ZMsW9LigoSGlpacrOzi61fVFRkYqKityf8/PzTVcJNcjYLJEBeocE9Vtl81EiIwONkYwkHxGAyEeQj/aM97D98MMPcjqdpab2jY2Ndb8f60yzZ89WZGSke0lMTDRdJdSg2nhxNlBXVDYfJTIy0JCPgHfkI8hHe7X+ZN6UKVN07Ngx97J///7arhIA+A0yEgC8Ix9RXxgfEtm8eXMFBwcrLy/PY31eXp7i4uJKbR8aGqrQ0FDT1UAtcQQFyRFk4D6AiTIAP1PZfJTIyEBjJCPJRwQg8hHkoz3jZxUSEqKePXtq/fr17nUul0vr169Xamqq6cPBzzAkErBHPoJ8BLwjH0E+2jPewyZJmZmZGjVqlJKTk9WrVy/NmzdPhYWFGjNmjC8OBwB1BvkIAN6Rj4B3PmmwDRs2TIcPH9bUqVOVm5ur7t27a+3ataUeJEXgOd2dbWKWyMDs0gbIx/rNSEaSjwhQ5GP9Rj7a80mDTZIyMjKUkZHhq+LhpxwOQ93RjsDs0gYk8rE+M5KR5CMCGPlYf5GP9gKzGQoAAAAAAcBnPWyop4KD5Qiu/t0NyxWYd0gA1HMGMpJ8BBCQyEdbNNhglKkZegJ1lh8A9ZuJjCQfAQQi8tEeQyIBAAAAwE/Rwwaj6GEDAHvcQQYA78hHe37bYAsOcig4yOGTsp0uyyfllvBVvc/ky3OoTtlBQcEKMjKtf2D+4ABIvk9I36lu3Y1kJPkIIACRj/YYEgkAAAAAfspve9hQN5l6cbYjQF98CKB+M5GR5COAQEQ+2qPBBqN4hg0A7PGMBgB4Rz7aC8xmKAAAAAAEAHrYYBQ9bABgjzvIAOAd+WiPBhuMosEGAPa4IAEA78hHewyJBAAAAAA/RQ8bjHI4DPWwOQLzDgmA+s1ERpKPAAIR+WiPBhuMcgQHyxFsoMFmoAwA8DcmMpJ8BBCIyEd7DIkEAAAAAD9Fgw1Glbz0sPoL/2oCCDxmMpJ8BBB4ajMfFy5cqNatWyssLEwpKSnasmVLhfZbuXKlHA6HhgwZUqXjVhRDImEUs0QCgD1mQQMA72orH1etWqXMzEwtXrxYKSkpmjdvntLT07Vjxw7FxMTY7rd371796U9/Ut++fatT5QrhNh0AAACAeumJJ57Q2LFjNWbMGHXq1EmLFy9Wo0aN9OKLL9ru43Q6NWLECM2YMUNt2rTxeR3pYYNR9LABgD162ADAO5P5mJ+f77E+NDRUoaGhpbYvLi7Wtm3bNGXKFPe6oKAgpaWlKTs72/Y4M2fOVExMjG655RZ99NFH1apzRdBgg1FBQQ4FBTkMFGSgDADwM0YyknwEEIBM5mNiYqLH6mnTpmn69OmlNv/hhx/kdDoVGxvrsT42Nlb//Oc/vR7i448/1pIlS5STk1O9ulYCDTYAAAAAAWP//v2KiIhwf/bWu1YVx48f10033aTnn39ezZs3N1JmRdBgg1GOIIccBu7+migDAPyNiYwkHwEEIpP5GBER4dFgs9O8eXMFBwcrLy/PY31eXp7i4uJKbb97927t3btXV111lXudy+WSJDVo0EA7duxQ27Ztq3MKXtFgg1EOh0MOh4EGm4EyAMDfmMhI8hFAIKqNfAwJCVHPnj21fv1699T8LpdL69evV0ZGRqntO3TooK+++spj3f3336/jx4/rqaeeKjUU0xQabAAAAADqpczMTI0aNUrJycnq1auX5s2bp8LCQo0ZM0aSNHLkSJ199tmaPXu2wsLC1LlzZ4/9o6KiJKnUepOY1h9GOf7zwGh1l8p2iW/atElXXXWVEhIS5HA4tGbNmjK337hxo/tOzplLbm5uNc4eAMpmIiOrMmSoMi+F7devn9d8HDx4sHub0aNHl/p+4MCBVfqbAIBUe/k4bNgwzZ07V1OnTlX37t2Vk5OjtWvXuici2bdvn77//nvTp1sp9LDBKIfD0DNslezSLiwsVLdu3XTzzTfrd7/7XYX327Fjh8cY57JekAgA1WUiIyubj5V9Kezrr7+u4uJi9+cff/xR3bp103XXXeex3cCBA7V06VL3Z1MP9QOon2ojH0tkZGR4HQIpnb7JX5asrKwqHbMyaLAhIAwaNEiDBg2q9H4xMTHurmwACERnvhRWkhYvXqx33nlHL774oiZPnlxq++joaI/PK1euVKNGjUo12EJDQ70+lA8AMIshkTCqZIYfE4t0+sWHZy5FRUVG69u9e3fFx8frN7/5jT755BOjZQPAr9V0Ppa8FDYtLc29riIvhT3TkiVLNHz4cDVu3Nhj/caNGxUTE6P27dvr9ttv148//liNvwyA+s5kPgYav+1hc7osOV2WT8oO9vH/mb6q95l8eQ7VKTvI4VCQgRnMLEflXnxYWfHx8Vq8eLGSk5NVVFSkF154Qf369dPmzZt1wQUXVLt8wNcc/1l8wfcJVn+ZyMjK5GNVXgp7pi1btujrr7/WkiVLPNYPHDhQv/vd75SUlKTdu3frvvvu06BBg5Sdna3g4OAqnBWA+s5kPgYav22wAZLvXnzYvn17tW/f3v25d+/e2r17t5588kn9+c9/NnIMAPAlX+XjmZYsWaIuXbqoV69eHuuHDx/u/ucuXbqoa9euatu2rTZu3Kj+/fsbrwcA1Gc02GCU6RdnV/TFhyb06tVLH3/8cY0cC0D9VNMvhq3sS2HPVFhYqJUrV2rmzJnl1qlNmzZq3ry5du3aRYMNQJWYzMdAwzNsMMr0M2w1KScnR/Hx8TV+XAD1R03n45kvhS1R8lLY1NTUMvd99dVXVVRUpN///vflHuff//63fvzxRzIUQJXV1evHmkAPGwJCQUGBdu3a5f68Z88e5eTkKDo6Wi1bttSUKVN04MABvfTSS5KkefPmKSkpSeeff75++eUXvfDCC9qwYYPee++92joFAPCJyrwU9kxLlizRkCFD1KxZM4/1BQUFmjFjhoYOHaq4uDjt3r1bkyZNUrt27ZSenl5j5wUA9QUNNhhV8uLC6rIqWcbWrVt12WWXuT9nZmZKkkaNGqWsrCx9//332rdvn/v74uJi3X333Tpw4IAaNWqkrl276v333/coAwBMM5GRlc3HYcOG6fDhw5o6dapyc3PVvXv3Ui+FDQryHHCzY8cOffzxx15vYgUHB+vvf/+7li1bpqNHjyohIUEDBgzQrFmzeBcbgCqrjXysK2iwwShH0OnFRDmV0a9fP1mW/dx2v36p4aRJkzRp0qQq1AwAqs5ERlZl/8q+FLZ9+/a2mRoeHq5333238pUAgDLUVj7WBQF6WgAAAABQ9xlvsM2ePVsXXnihmjRpopiYGA0ZMkQ7duwwfRj4KYfDYWwBAg35CPIR8I58BPloz3iD7cMPP9T48eP12Wefad26dTp58qQGDBigwsJC04eCHwoK+u8Y5OottX0mgHnkI8xkZG2fBWAe+Qjy0Z7xZ9jWrl3r8TkrK0sxMTHatm2bLrnkEtOHA4A6g3wEAO/IR8CezycdOXbsmCQpOjra6/dFRUUqKipyf87Pz/d1leBDpl+cDQSy8vJRIiMDDS+GBSqGfKx/yEd7Pu04dLlcmjhxoi6++GJ17tzZ6zazZ89WZGSke0lMTPRlleBjDoehF2cH6BhkoERF8lEiIwONkYwkHxHgyMf6iXy059MG2/jx4/X1119r5cqVtttMmTJFx44dcy/79+/3ZZUAwC9UJB8lMhJA/UM+Ap58NiQyIyNDb7/9tjZt2qRzzjnHdrvQ0FBetBlAghwOBRm4u2EF6B0SQKp4PkpkZKAxkZHkIwIZ+Vh/kY/2jDfYLMvShAkTtHr1am3cuFFJSUmmDwF/ZugZNgXoGGTUb+QjjGQk+YgARD6CfLRnvME2fvx4rVixQm+88YaaNGmi3NxcSVJkZKTCw8NNHw4A6gzyEQC8Ix8Be8YbbIsWLZIk9evXz2P90qVLNXr0aNOHg59hlkjAHvkIZkEDvCMfQT7a88mQSNRfJS8uNFEOEGjIR5jISPIRgYh8BPloL0DfBw4AAAAAdZ/PX5yN+sXhMPMOjEB9jwaA+s1ERpKPAAIR+WiPBhuMcgSdXkyUAwCBxkRGko8AAhH5aC9ATwsAAAAA6j562GAUk44AgD0eqgcA78hHe37bYAsOcijYR390p8u3MxH5qt5n8uU5VKdspvUHUJ6amAvOXxOEaasBwDvy0R5DIgEAAADAT/ltDxvqJmaJBAB7zIIGAN6Rj/ZosMEonmEDAHs8owEA3pGP9hgSCQAAAAB+ih42GOVwGJp0JEC7tAHUbyYyknwEEIjIR3s02GCUqdk9rQDt0gZQv5nISPIRQCAiH+0xJBIAAAAA/BQ9bDAqyFAPmytA75AAqN9MZCT5CCAQkY/2aLDBKFNDIgP1BwegfjORkeQjgEBEPtpjSCQAAAAA+Cl62GAUPWwAYI87yADgHflojwYbjKLBBgD2uCABAO/IR3sMiQQAAAAAP0UPG4xqECQ1MPIeNgOVAQA/YyIjyUcAgYh8tBegpwUAAAAAdR89bDCKZ9gAwB7PaACAd+SjPRpsMMrUi7OdAfqDA1C/mchI8hFAICIf7TEkEgAAAAD8FD1sMCrYEaTgoOrfBwh2cC8BQOAxkZHkI4BARD7ao8EGo0w9w2aiDADwNyYyknwEEIjIR3uB2QxFvbNp0yZdddVVSkhIkMPh0Jo1a8rdZ+PGjbrgggsUGhqqdu3aKSsry+f1BIDasHDhQrVu3VphYWFKSUnRli1bbLfNysqSw+HwWMLCwjy2sSxLU6dOVXx8vMLDw5WWlqadO3f6+jQAoF6iwQajSu6OmFgqo7CwUN26ddPChQsrtP2ePXs0ePBgXXbZZcrJydHEiRN166236t13363KaQNAhdRGPq5atUqZmZmaNm2atm/frm7duik9PV2HDh2y3SciIkLff/+9e/nuu+88vn/00Uc1f/58LV68WJs3b1bjxo2Vnp6uX375pUp/FwCojXysKxgSCaNqa0jkoEGDNGjQoApvv3jxYiUlJenxxx+XJHXs2FEff/yxnnzySaWnp1fq2ABQUbUx5OeJJ57Q2LFjNWbMGEmn8++dd97Riy++qMmTJ3vdx+FwKC4uzut3lmVp3rx5uv/++3X11VdLkl566SXFxsZqzZo1Gj58eKXqBwASQyLL4rcNNqfLktNl+aRsX/+f6at6n8mX5+BP/7Ln5+d7fA4NDVVoaGi1y83OzlZaWprHuvT0dE2cOLHaZQM1wfrPAu989bfxp795RfKxuLhY27Zt05QpU9zrgoKClJaWpuzsbNuyCwoK1KpVK7lcLl1wwQV6+OGHdf7550s6PUIhNzfXI0MjIyOVkpKi7OxsGmwAYBhDImFUsMNhbJGkxMRERUZGupfZs2cbqWdubq5iY2M91sXGxio/P18///yzkWMAwK/VdD7+8MMPcjqdXvMuNzfXax3bt2+vF198UW+88YZefvlluVwu9e7dW//+978lyb1fZcoEgPKYzMdA47c9bKibTL04O+g/Zezfv18RERHu9SZ61wCgtpjISF/nY2pqqlJTU92fe/furY4dO+rZZ5/VrFmzjBwDAH7NZD4GGhps8GsREREeFySmxMXFKS8vz2NdXl6eIiIiFB4ebvx4AGBaRfKxefPmCg4O9pp3ds+o/VrDhg3Vo0cP7dq1S5Lc++Xl5Sk+Pt6jzO7du1fiDAAAFcGQSBhVW7NEVlZqaqrWr1/vsW7dunUed5UBwLSazseQkBD17NnTI+9cLpfWr19f4bxzOp366quv3I2zpKQkxcXFeZSZn5+vzZs3k6EAqqwuXD/WFnrYYFSDIIcaGPixOCtZRkFBgfvur3T6oficnBxFR0erZcuWmjJlig4cOKCXXnpJknTbbbfp6aef1qRJk3TzzTdrw4YNeuWVV/TOO+9Uu+4AYMdERlY2HzMzMzVq1CglJyerV69emjdvngoLC92zRo4cOVJnn322+xm4mTNn6qKLLlK7du109OhRPfbYY/ruu+906623Sjo9g+TEiRP14IMP6txzz1VSUpIeeOABJSQkaMiQIdU6NwD1V23kY11Bgw0BYevWrbrsssvcnzMzMyVJo0aNUlZWlr7//nvt27fP/X1SUpLeeecd3XXXXXrqqad0zjnn6IUXXmBKfwABZ9iwYTp8+LCmTp2q3Nxcde/eXWvXrnVPGrJv3z4FBf13wM1PP/2ksWPHKjc3V02bNlXPnj316aefqlOnTu5tJk2apMLCQo0bN05Hjx5Vnz59tHbt2lIv2AYAVB8NNhhVW+9h69evnyzLfsLtrKwsr/t88cUXla0aAFRZbb1nKCMjQxkZGV6/27hxo8fnJ598Uk8++WSZ5TkcDs2cOVMzZ86sdF0AwBvew2aPBhuMqq0GGwDUBVyQAIB35KM9n0868sgjj7jHuwMA/ot8BADvyEfgv3zaw/b555/r2WefVdeuXX15GPiRYIehHrYAffEhUIJ8rJ9MZCT5iEBHPtZP5KM9n/WwFRQUaMSIEXr++efVtGlTXx0GfqbkpYfVXQL1xYeARD7WZyYyknxEICMf6y/y0Z7PGmzjx4/X4MGDlZaWVuZ2RUVFys/P91gAIJBVNB8lMhJA/UI+AqX5ZEjkypUrtX37dn3++eflbjt79mzNmDHDF9VALWDSEaBslclHiYwMNDxUD9gjH+s38tGe8R62/fv3649//KOWL19eofexTJkyRceOHXMv+/fvN10l1CBTb6kP1B8c6rfK5qNERgYa8hHwjnwE+WjPeA/btm3bdOjQIV1wwQXudU6nU5s2bdLTTz+toqIiBQcHu78LDQ1VaGio6WoAgN+pbD5KZCSA+oF8BOwZ72Hr37+/vvrqK+Xk5LiX5ORkjRgxQjk5OaV+bAgswUGm7pDU9pkA5pGPMJORtX0WgHnkI2ozHxcuXKjWrVsrLCxMKSkp2rJli+22zz//vPr27aumTZuqadOmSktLK3N7E4z3sDVp0kSdO3f2WNe4cWM1a9as1HoEHp5hA+yRj+AZDcA78hG1lY+rVq1SZmamFi9erJSUFM2bN0/p6enasWOHYmJiSm2/ceNG3XDDDerdu7fCwsI0Z84cDRgwQN98843OPvvsatXfDvfpAAAAANRLTzzxhMaOHasxY8aoU6dOWrx4sRo1aqQXX3zR6/bLly/XHXfcoe7du6tDhw564YUX5HK5tH79ep/V0acvzi6xcePGmjgM/AA9bEDlkI/1Cz1sQMWRj/WLyXz89Sse7J53LC4u1rZt2zRlyhT3uqCgIKWlpSk7O7tCxzxx4oROnjyp6OjoatS8bPSwwShenA0A9ngxLAB4ZzIfExMTFRkZ6V5mz57t9Zg//PCDnE6nYmNjPdbHxsYqNze3QvW+9957lZCQUKF3B1ZVjfSwAQAAAEBN2L9/vyIiItyffTWb6COPPKKVK1dq48aNFX4dRVXQYINRwQ6Hgh0GhkQaKAMA/I2JjCQfAQQik/kYERHh0WCz07x5cwUHBysvL89jfV5enuLi4srcd+7cuXrkkUf0/vvvq2vXrlWvdAUwJBJGBTkcxhYACDTkIwB4Vxv5GBISop49e3pMGFIygUhqaqrtfo8++qhmzZqltWvXKjk5ucrnXFF+28Pmy7eVO12WT8otURMPhPvyHHz99wFQfY7/LHVRTSSMr/42dfVvDgDwLjMzU6NGjVJycrJ69eqlefPmqbCwUGPGjJEkjRw5Umeffbb7Obg5c+Zo6tSpWrFihVq3bu1+1u2ss87SWWed5ZM6+m2DDXVTsKRgA1c0vB4TQCAykZHkI4BAVFv5OGzYMB0+fFhTp05Vbm6uunfvrrVr17onItm3b5+Cgv47KHHRokUqLi7Wtdde61HOtGnTNH369GrU3h4NNhgVZGgGM2ZBAxCITGQk+QggENVmPmZkZCgjI8Prd79+vcTevXurdIzq4Bk2AAAAAPBT9LDBKGaJBAB7zBIJAN6Rj/ZosMEoUzOYMQsagEBkIiPJRwCBiHy0x5BIAAAAAPBT9LDBqCCHmVkieaYeQCAykZHkI4BARD7ao8EGo5glEgDsMUskAHhHPtpjSCQAAAAA+Cl62GAUk44AgD0eqgcA78hHezTYYFSwoWfYTJQBAP7GREaSjwACEflojyGRAAAAAOCn6GGDUQyJBAB7DPkBAO/IR3s02GBUcJBDwQZm6DFRBgD4GxMZST4CCETkoz2GRAIAAACAn6KHDUYxJBIA7DHkBwC8Ix/t0WCDUcwSCQD2mAUNALwjH+0xJBIAAAAA/BQ9bDDKYWhIpCNAu7QB1G8mMpJ8BBCIyEd7NNhgFLNEAoA9ZkEDAO/IR3sMiUTAWLhwoVq3bq2wsDClpKRoy5YttttmZWXJ4XB4LGFhYTVYWwCoOZXJx+eff159+/ZV06ZN1bRpU6WlpZXafvTo0aUydODAgb4+DQCol2iwwaggSUEOA0slj7tq1SplZmZq2rRp2r59u7p166b09HQdOnTIdp+IiAh9//337uW7776r1rkDQHmMZGQlj1nZfNy4caNuuOEGffDBB8rOzlZiYqIGDBigAwcOeGw3cOBAjwz9y1/+UrU/CgCodvKxrgjU80ItCXY4jC2V8cQTT2js2LEaM2aMOnXqpMWLF6tRo0Z68cUXbfdxOByKi4tzL7GxsdU9fQAoU13Ix+XLl+uOO+5Q9+7d1aFDB73wwgtyuVxav369x3ahoaEeGdq0adMq/10AoDbysa7w22fYnC5LTpflk7J9Pb7VV/U+ky/PwZ/G/+bn53t8Dg0NVWhoqMe64uJibdu2TVOmTHGvCwoKUlpamrKzs23LLigoUKtWreRyuXTBBRfo4Ycf1vnnn2/2BAAfsf6z+IL/JEDV+epv4/t0rzhf5uOZTpw4oZMnTyo6Otpj/caNGxUTE6OmTZvq8ssv14MPPqhmzZpV8WwAAHboYYNRJS89NLFIUmJioiIjI93L7NmzSx3zhx9+kNPpLNVDFhsbq9zcXK/1bN++vV588UW98cYbevnll+VyudS7d2/9+9//Nv9HAYD/qAv5+Gv33nuvEhISlJaW5l43cOBAvfTSS1q/fr3mzJmjDz/8UIMGDZLT6azGXwdAfWYyHwON3/awoW4KDjq9mChHkvbv36+IiAj3+l/fPa6q1NRUpaamuj/37t1bHTt21LPPPqtZs2YZOQYA/JqJjPR1Pp7pkUce0cqVK7Vx40aPiZmGDx/u/ucuXbqoa9euatu2rTZu3Kj+/fsbrweAwGcyHwMNDTb4tYiICI8LEm+aN2+u4OBg5eXleazPy8tTXFxchY7TsGFD9ejRQ7t27apyXQGgJvk6H+fOnatHHnlE77//vrp27Vrmtm3atFHz5s21a9cuGmwAYFiAtkNRW07P0mOiS7vixwwJCVHPnj09HogveUD+zF60sjidTn311VeKj4+v7CkDQIWZyciKH6+q+fjoo49q1qxZWrt2rZKTk8s9zr///W/9+OOPZCiAKqvpfKxL6GGDUUGGZuip7BjkzMxMjRo1SsnJyerVq5fmzZunwsJCjRkzRpI0cuRInX322e5nPGbOnKmLLrpI7dq109GjR/XYY4/pu+++06233lrtugOAHRMZ6et8nDNnjqZOnaoVK1aodevW7mfdzjrrLJ111lkqKCjQjBkzNHToUMXFxWn37t2aNGmS2rVrp/T09GqdG4D6qzbysa6gwYaAMGzYMB0+fFhTp05Vbm6uunfvrrVr17oftN+3b5+Cgv7bofzTTz9p7Nixys3NVdOmTdWzZ099+umn6tSpU22dAgD4RGXzcdGiRSouLta1117rUc60adM0ffp0BQcH6+9//7uWLVumo0ePKiEhQQMGDNCsWbN88hwdANR3NNhglKkZeqpSRkZGhjIyMrx+t3HjRo/PTz75pJ588smqVA0AqsxERvo6H/fu3VtmWeHh4Xr33XcrXQcAKEtt5WNdQIMNRpmeJRIAAgmzoAGAd+SjPZ+c1oEDB/T73/9ezZo1U3h4uLp06aKtW7f64lAAUKeQjwDgHfkIeGe8h+2nn37SxRdfrMsuu0x/+9vf1KJFC+3cuVNNmzY1fSj4odocEgn4O/IRDPkBvCMfQT7aM95gmzNnjhITE7V06VL3uqSkJNOHgZ9yOE4vJsoBAg35CBMZST4iEJGPIB/tGR8S+eabbyo5OVnXXXedYmJi1KNHDz3//PO22xcVFSk/P99jAYBAVNl8lMhIAPUD+QjYM95g+7//+z8tWrRI5557rt59913dfvvtuvPOO7Vs2TKv28+ePVuRkZHuJTEx0XSVUIOC5DC2AIGmsvkokZGBhnwEvCMfQT7aM95gc7lcuuCCC/Twww+rR48eGjdunMaOHavFixd73X7KlCk6duyYe9m/f7/pKqEGlXRnm1iAQFPZfJTIyEBDPgLekY8gH+0Zb7DFx8eXevlwx44dtW/fPq/bh4aGKiIiwmMBgEBU2XyUyEgA9QP5CNgzPunIxRdfrB07dnis+9e//qVWrVqZPhT8UJDj9GKiHCDQkI8wkZHkIwIR+Qjy0Z7xHra77rpLn332mR5++GHt2rVLK1as0HPPPafx48ebPhT8EEMiAXvkI8hHwDvyEeSjPeMNtgsvvFCrV6/WX/7yF3Xu3FmzZs3SvHnzNGLECNOHAoA6hXwEAO/IR8Ce8SGRknTllVfqyiuv9EXR8HOmZugJ1Fl+APKxfjORkeQjAhX5WL+Rj/Z80mBDPWaqOzowf28A6jsTGUk+AghE5KMt40MiAQAAAABm0MMGo5glEgDsMQsaAHhHPtqjwQajHDLTGx2gvzcA9ZyJjCQfAQQi8tGe3zbYgoMcCvZRM9npsnxSbglf1ftMvjwHX/99ANRvdfk/qHW57gCAuslvG2yom4IcDgUZmHXERBkA4G9MZCT5CCAQkY/2aLDBKIfMzBIZmD83APWdiYwkHwEEIvLRHrNEAgAAAICfoocNRgXJzF0A7iQACEQmMpJ8BBCIyEd7NNhglMPhkMPAmEgTZQCAvzGRkeQjgEBEPtoL1IYoAAAAANR59LDBKF6cDQD2eDEsAHhHPtqjwQajHA5Ds0QG6A8OQP1mIiPJRwCBiHy0x5BIAAAAAPBT9LDBKGaJBAB7zIIGAN6Rj/ZosMEoZokEAHvMggYA3pGP9gK1IQoAAAAAdR49bDCKWSIBwB6zoAGAd+SjPRpsMC5AfysAYAQZCQDekY/eMSQSAAAAAPwUPWwwiiGRAGCPIT8A4B35aI8GG4xilkgAsMcsaADgHflojyGRAAAAAOCn6GGDUQyJBAB7DPkBAO/IR3s02GCUQ2Zm+AnQ3xuAes5ERpKPAAIR+WiPIZEIGAsXLlTr1q0VFhamlJQUbdmypcztX331VXXo0EFhYWHq0qWL/vrXv9ZQTQGgZpnOR8uyNHXqVMXHxys8PFxpaWnauXOnL08BAHzG368habDBqCCHw9hSGatWrVJmZqamTZum7du3q1u3bkpPT9ehQ4e8bv/pp5/qhhtu0C233KIvvvhCQ4YM0ZAhQ/T111+b+DMAgFeBko+PPvqo5s+fr8WLF2vz5s1q3Lix0tPT9csvv1Tr7wOg/qqNfJTqxjWkw7Isy2elV0F+fr4iIyM19qWPFdLoLJ8cw+ny7SkH18AAWl+eQ/GJAr04uq+OHTumiIiICu1T8v9bbl5ehfcpr7y42NgK1yElJUUXXnihnn76aUmSy+VSYmKiJkyYoMmTJ5faftiwYSosLNTbb7/tXnfRRRepe/fuWrx4cbXrD/iK+7eWm2vkt+ZNoA4pMSE/P1+xcXGVyseS/UxlZG3no2VZSkhI0N13360//elPkqRjx44pNjZWWVlZGj58eLXOD6iqkt9Zj8mvKzi0cW1Xp95xFhXqi0d+V6fyUaob15B+28PmdFk+W4KDHD5dfFn3mjoHf5Gfn++xFBUVldqmuLhY27ZtU1pamntdUFCQ0tLSlJ2d7bXc7Oxsj+0lKT093XZ7oD6xfLzAjNrKxz179ig3N9djm8jISKWkpJChAPxCRfJRqjvXkH7bYEPd5LAsY4skJSYmKjIy0r3Mnj271DF/+OEHOZ1OxcbGeqyPjY1Vbm6u13rm5uZWansAMCEQ8rHkf8lQACbVdD5KdecaklkiYZblOr2YKEfS/v37Pbq0Q0NDq182ANQWExlJPgIIROSjLRps8GsRERHljkFu3ry5goODlZeX57E+Ly9PcXFxXveJi4ur1PYA4G9qKx9L/jcvL0/x8fEe23Tv3r2ypwEAxlUkH6W6cw3JkEgY5bBcxpaKCgkJUc+ePbV+/Xr3OpfLpfXr1ys1NdXrPqmpqR7bS9K6detstwcAEwIhH5OSkhQXF+exTX5+vjZv3kyGAqiyms5Hqe5cQ9LDBrMMD4msqMzMTI0aNUrJycnq1auX5s2bp8LCQo0ZM0aSNHLkSJ199tnuMcx//OMfdemll+rxxx/X4MGDtXLlSm3dulXPPfdc9esOAHYMDvmpKNP56HA4NHHiRD344IM699xzlZSUpAceeEAJCQkaMmRI9c4NQP1VC/ko1Y1rSBpsCAjDhg3T4cOHNXXqVOXm5qp79+5au3at+6HQffv2KSjovx3KvXv31ooVK3T//ffrvvvu07nnnqs1a9aoc+fOtXUKAOATvsjHSZMmqbCwUOPGjdPRo0fVp08frV27VmFhYTV+fgBQHXXhGtJv38N2c9ZHPnsPm6+nrff1e94k355D8YkCPT+yT5Xew3bo398Zew9bzDmtKv0uDyDQ1cR72HzNf14cUnnVfQ+biYwkHwHveA9b7arue9jIR3v0sMGsWhoSCQB1Qi0N+QEAv0c+2jI+6YjT6dQDDzygpKQkhYeHq23btpo1a5b8rCMPAGoc+QgA3pGPgD3jPWxz5szRokWLtGzZMp1//vnaunWrxowZo8jISN15552mDwc/c/qlhdW/u+EgoBGAyEeYyEjyEYGIfAT5aM94g+3TTz/V1VdfrcGDB0uSWrdurb/85S/asmWL6UPBHzEkErBFPoIhP4B35CPIR3vGh0T27t1b69ev17/+9S9J0pdffqmPP/5YgwYN8rp9UVGR8vPzPRYACESVzUeJjARQP5CPgD3jPWyTJ09Wfn6+OnTooODgYDmdTj300EMaMWKE1+1nz56tGTNmmK4Gags9bICtyuajREYGHO4gA16RjyAf7RnvYXvllVe0fPlyrVixQtu3b9eyZcs0d+5cLVu2zOv2U6ZM0bFjx9zL/v37TVcJNankx2ZiAQJMZfNRIiMDDvkIeEU+gny0Z7yH7Z577tHkyZM1fPhwSVKXLl303Xffafbs2Ro1alSp7UNDQxUaGmq6GgDgdyqbjxIZCaB+IB8Be8YbbCdOnPB4G7gkBQcHy+UKzBYvfsVySSb+vw7QOySo38hHGMlI8hEBiHwE+WjPeIPtqquu0kMPPaSWLVvq/PPP1xdffKEnnnhCN998s+lDwQ85LJehaf0D8weH+o18hImMJB8RiMhHkI/2jDfYFixYoAceeEB33HGHDh06pISEBP3hD3/Q1KlTTR8KAOoU8hEAvCMfAXvGG2xNmjTRvHnzNG/ePNNFoy5glkjAFvkIZkEDvCMfQT7aM95gQz1nWacXE+UAQKAxkZHkI4BARD7aMj6tPwAAAADADHrYYBZDIgHAHkN+AMA78tEWDTYY5bAsQ7NEBmaXNoD6zURGko8AAhH5aI8hkQAAAADgp/y2hy04yKHgIIdPyna6fNv69lW9z+TLc6hW2QyJBGqE4z+LL/j6/mRN3P/0fQpXEUN+AMA78tGW3zbYUEfRYAMAe1yQAIB35KMthkQCAAAAgJ+ihw1m0cMGAPa4gwwA3pGPtmiwwSiH5TI0S2Rg/uAA1G8mMpJ8BBCIyEd7DIkEAAAAAD9FDxvMcrlOLybKAYBAYyIjyUcAgYh8tEWDDWZZ1unFRDkAEGhMZCT5CCAQkY+2GBIJAAAAAH6KHjaYxSyRAGCPWdAAwDvy0RYNNhjFLJEAYI9Z0ADAO/LRHkMiAQAAAMBP0cMGsxgSCQD2GPIDAN6Rj7ZosMEsyzLUYAvMWX4A1HMmMpJ8BBCIyEdbDIkEAAAAAD9FDxvMspySy2mmHAAINCYyknwEEIjIR1s02GCU5XLJMvCWeRNlAIC/MZGR5COAQEQ+2mNIJAAAAAD4KXrYYJbL0JBIE2UAgL8xkZHkI4BARD7aosEGs2iwAYA9LkgAwDvy0RZDIlHvHDlyRCNGjFBERISioqJ0yy23qKCgoMx9+vXrJ4fD4bHcdtttNVRjAKgZlc3HI0eOaMKECWrfvr3Cw8PVsmVL3XnnnTp27JjHdr/OT4fDoZUrV/r6dAAgINDDBqMsp1OWs/p3N0yUYWfEiBH6/vvvtW7dOp08eVJjxozRuHHjtGLFijL3Gzt2rGbOnOn+3KhRI5/VEUBgMpGR/pSPBw8e1MGDBzV37lx16tRJ3333nW677TYdPHhQr732mse2S5cu1cCBA92fo6KifHYeAOoef8/H2kSDDWa5XKcXE+X4wLfffqu1a9fq888/V3JysiRpwYIFuuKKKzR37lwlJCTY7tuoUSPFxcX5pF4A6gkTGelH+di5c2f97//+r/tz27Zt9dBDD+n3v/+9Tp06pQYN/nuZERUVRYYCsOfH+VjbGBIJv5afn++xFBUVVau87OxsRUVFuS9GJCktLU1BQUHavHlzmfsuX75czZs3V+fOnTVlyhSdOHGiWnUBgOrwp3w807FjxxQREeHRWJOk8ePHq3nz5urVq5defPFFWZZVrfoCQH3htz1sTpclp8s3YR4c5PBJuSV8Ve8z+fIcqlW2y2Vo0pHTd0gSExM9Vk+bNk3Tp0+vcrG5ubmKiYnxWNegQQNFR0crNzfXdr8bb7xRrVq1UkJCgv7+97/r3nvv1Y4dO/T6669XuS5AdVj/Weoi3ybwab7621S7XBMZ6Wf5eKYffvhBs2bN0rhx4zzWz5w5U5dffrkaNWqk9957T3fccYcKCgp05513Vrm+AAKMwXwMNH7bYEPdZLmcsgw02ErK2L9/vyIiItzrQ0NDvW4/efJkzZkzp8wyv/322yrX58yLjy5duig+Pl79+/fX7t271bZt2yqXC6B+MZGR/paPJfLz8zV48GB16tSpVMPxgQcecP9zjx49VFhYqMcee4wGGwA3k/kYaGiwwa9FRER4XJDYufvuuzV69Ogyt2nTpo3i4uJ06NAhj/WnTp3SkSNHKvVsRUpKiiRp165dNNgA1Ap/ysfjx49r4MCBatKkiVavXq2GDRuWuX1KSopmzZqloqIi24YmAOA0GmwwyzI06YhVuTJatGihFi1alLtdamqqjh49qm3btqlnz56SpA0bNsjlcrkbYRWRk5MjSYqPj69UPQHUcyYy0s/yMT8/X+np6QoNDdWbb76psLCwco+Vk5Ojpk2b0lgD8F+1kI91BQ02GGV6SKRpHTt21MCBAzV27FgtXrxYJ0+eVEZGhoYPH+6eAe3AgQPq37+/XnrpJfXq1Uu7d+/WihUrdMUVV6hZs2b6+9//rrvuukuXXHKJunbt6pN6AghM/jzkpyr5mJ+frwEDBujEiRN6+eWX3ROgSKcbisHBwXrrrbeUl5eniy66SGFhYVq3bp0efvhh/elPf/LJeQCom/w5H2sbDTbUO8uXL1dGRob69++voKAgDR06VPPnz3d/f/LkSe3YscM9C2RISIjef/99zZs3T4WFhUpMTNTQoUN1//3319YpAIBPVDYft2/f7p5Bsl27dh5l7dmzR61bt1bDhg21cOFC3XXXXbIsS+3atdMTTzyhsWPH1tyJAUAdRoMNZrmchmaJ9N0dkujo6DJfkt26dWuP6aYTExP14Ycf+qw+AOoRExnpR/nYr1+/cqfnHzhwoMcLswHAKz/Px9pEgw1m+fmLswGgVvFiWADwjny0VekXZ2/atElXXXWVEhIS5HA4tGbNGo/vLcvS1KlTFR8fr/DwcKWlpWnnzp2m6gsAfot8BADvyEeg6irdYCssLFS3bt20cOFCr98/+uijmj9/vhYvXqzNmzercePGSk9P1y+//FLtysL/WU6nsQWoa8hHlId8RH1FPqI85KO9Sg+JHDRokAYNGuT1O8uyNG/ePN1///26+uqrJUkvvfSSYmNjtWbNGg0fPrx6tYX/M/GW+pJygDqGfES5TGQk+Yg6iHxEuchHW5XuYSvLnj17lJubq7S0NPe6yMhIpaSkKDs72+s+RUVF7mmAz5wOGAACSVXyUSIjAQQ+8hEom9EGW25uriQpNjbWY31sbKz7u1+bPXu2IiMj3UtiYqLJKqGmlczwY2IBAkhV8lEiIwMO+QiUQj5CEvlYBqMNtqqYMmWKjh075l72799f21VCNVgul7EFABkZaMhHwBzyMbCQj/aMNtji4uIkSXl5eR7r8/Ly3N/9WmhoqCIiIjwWAAg0VclHiYwEEPjIR6BsRhtsSUlJiouL0/r1693r8vPztXnzZqWmppo8FPwVQyIBr8hHSCIfAS/IR0giH8tQ6VkiCwoKtGvXLvfnPXv2KCcnR9HR0WrZsqUmTpyoBx98UOeee66SkpL0wAMPKCEhQUOGDDFZb/gry9CPxQrMHxwCG/mIcpnISPIRdRD5iHKRj7Yq3WDbunWrLrvsMvfnzMxMSdKoUaOUlZWlSZMmqbCwUOPGjdPRo0fVp08frV27VmFhYeZqDQB+iHwEAO/IR6DqKt1g69evnyzLsv3e4XBo5syZmjlzZrUqhrrJ1AOfgfrQKAIb+YjymMhI8hF1EfmI8pCP9irdYAPKxIuzAcAeL4YFAO/IR1u1Pq0/AAAAAMA7ethglqkZegJ0lh8A9ZyJjCQfAQQi8tEWDTYYZTmdspzV/7GYKAMA/I2JjCQfAQQi8tEeQyIBAAAAwE/5bQ9bcJBDwUEOn5TtdNnPUmSCr+p9Jl+eQ7XKdrnMPPAZoA+NAnWB7xOsHjORkeQjgEBEPtqihw1mmXpLfYCOQQZQz5GPAOCdn+fjkSNHNGLECEVERCgqKkq33HKLCgoKytx+woQJat++vcLDw9WyZUvdeeedOnbsWKWPTYMNAAAAAMowYsQIffPNN1q3bp3efvttbdq0SePGjbPd/uDBgzp48KDmzp2rr7/+WllZWVq7dq1uueWWSh/bb4dEom6yXE5ZBu5umCgDAPyNiYwkHwEEIn/Ox2+//VZr167V559/ruTkZEnSggULdMUVV2ju3LlKSEgotU/nzp31v//7v+7Pbdu21UMPPaTf//73OnXqlBo0qHgzjAYbjDLxlvqScgAg0JjISPIRQCAymY/5+fke60NDQxUaGlrlcrOzsxUVFeVurElSWlqagoKCtHnzZl1zzTUVKufYsWOKiIioVGNNYkgkAAAAgACSmJioyMhI9zJ79uxqlZebm6uYmBiPdQ0aNFB0dLRyc3MrVMYPP/ygWbNmlTmM0g49bDDKclmynCZ62Hw7kycA1AYTGUk+AghEJvNx//79ioiIcK+3612bPHmy5syZU2aZ3377bbXqJJ3u8Rs8eLA6deqk6dOnV3p/GmwwynK6zDTYDJQBAP7GREaSjwACkcl8jIiI8Giw2bn77rs1evToMrdp06aN4uLidOjQIY/1p06d0pEjRxQXF1fm/sePH9fAgQPVpEkTrV69Wg0bNiy3Xr9Ggw0AAABAvdOiRQu1aNGi3O1SU1N19OhRbdu2TT179pQkbdiwQS6XSykpKbb75efnKz09XaGhoXrzzTcVFhZWpXryDBuMKnlg1MQCAIGGfAQA7/w5Hzt27KiBAwdq7Nix2rJliz755BNlZGRo+PDh7hkiDxw4oA4dOmjLli2STjfWBgwYoMLCQi1ZskT5+fnKzc1Vbm6unM7KzWZJDxuMYkgkANhjSCQAeOfv+bh8+XJlZGSof//+CgoK0tChQzV//nz39ydPntSOHTt04sQJSdL27du1efNmSVK7du08ytqzZ49at25d4WPTYAMAAACAMkRHR2vFihW237du3VqW9d9Jofr16+fxuTposMEoetgAwJ6/30EGgNpCPtrjGTYAAAAA8FP0sMEoy+mUq5IPUtqVAwCBxkRGko8AAhH5aI8GG4yyLDMz9FhWYHZpA6jfTGQk+QggEJGP9hgSCQAAAAB+ih42GMWkIwBgj4fqAcA78tEeDTYYRYMNAOxxQQIA3pGP9hgSCQAAAAB+igYbjLJcliyXy8Bi5kWD3jz00EPq3bu3GjVqpKioqIqdl2Vp6tSpio+PV3h4uNLS0rRz506f1RFAYDKTkb7LxyNHjmjEiBGKiIhQVFSUbrnlFhUUFJS5T79+/eRwODyW2267zWObffv2afDgwWrUqJFiYmJ0zz336NSpUz47DwB1j7/nY21iSCSMcjldchnojjZRhp3i4mJdd911Sk1N1ZIlSyq0z6OPPqr58+dr2bJlSkpK0gMPPKD09HT94x//UFhYmM/qCiCwmMhIX+bjiBEj9P3332vdunU6efKkxowZo3HjxmnFihVl7jd27FjNnDnT/blRo0buf3Y6nRo8eLDi4uL06aef6vvvv9fIkSPVsGFDPfzwwz47FwB1i7/nY22iwYZ6Z8aMGZKkrKysCm1vWZbmzZun+++/X1dffbUk6aWXXlJsbKzWrFmj4cOH+6qqAFBjvv32W61du1aff/65kpOTJUkLFizQFVdcoblz5yohIcF230aNGikuLs7rd++9957+8Y9/6P3331dsbKy6d++uWbNm6d5779X06dMVEhLik/MBgEDBkEgYVfLAqIlFkvLz8z2WoqKiGj+nPXv2KDc3V2lpae51kZGRSklJUXZ2do3XB0Dd5c/5mJ2draioKHdjTZLS0tIUFBSkzZs3l7nv8uXL1bx5c3Xu3FlTpkzRiRMnPMrt0qWLYmNj3evS09OVn5+vb775plp1BhA4TOZjoPHbHjany5LTR+NQg4McPim3hK/qfSZfnkN1yjY9S2RiYqLH+mnTpmn69OnVLr8ycnNzJcnjYqPkc8l3QE1z/GepiwLzCYOKMTkLmul8zM3NVUxMjMe6Bg0aKDo6usysu/HGG9WqVSslJCTo73//u+69917t2LFDr7/+urtcb/lZ8h0ASMwSWRa/bbABkrR//35FRES4P4eGhnrdbvLkyZozZ06ZZX377bfq0KGD0foBQG0xnY9VNW7cOPc/d+nSRfHx8erfv792796ttm3bVrlcAMBpNNhglGWdnqXHRDmSFBER4XFBYufuu+/W6NGjy9ymTZs2VapLyXMZeXl5io+Pd6/Py8tT9+7dq1QmgPrJREb6Kh/j4uJ06NAhj/WnTp3SkSNHbJ9P8yYlJUWStGvXLrVt21ZxcXHasmWLxzZ5eXmSVKlyAQQ2k/kYaGiwwajaenF2ixYt1KJFi2of15ukpCTFxcVp/fr17gZafn6+Nm/erNtvv90nxwQQmGpjyE9F8zE1NVVHjx7Vtm3b1LNnT0nShg0b5HK53I2wisjJyZEk9w2u1NRUPfTQQzp06JB7yOW6desUERGhTp06VepcAAQuhkTaY9IR1Dv79u1TTk6O9u3bJ6fTqZycHOXk5Hi8a6hDhw5avXq1JMnhcGjixIl68MEH9eabb+qrr77SyJEjlZCQoCFDhtTSWQCAWR07dtTAgQM1duxYbdmyRZ988okyMjI0fPhw9wyRBw4cUIcOHdw9Zrt379asWbO0bds27d27V2+++aZGjhypSy65RF27dpUkDRgwQJ06ddJNN92kL7/8Uu+++67uv/9+jR8/3nYYJwDgv+hhg1G11cNWGVOnTtWyZcvcn3v06CFJ+uCDD9SvXz9J0o4dO3Ts2DH3NpMmTVJhYaHGjRuno0ePqk+fPlq7di3vYANQKf5+B3n58uXKyMhQ//79FRQUpKFDh2r+/Pnu70+ePKkdO3a4Z4EMCQnR+++/r3nz5qmwsFCJiYkaOnSo7r//fvc+wcHBevvtt3X77bcrNTVVjRs31qhRozze2wYA/p6PtYkGG4xyuVxyGXiGzUQZdrKyssp9B5tlec5j53A4NHPmTC4wAFSLiYz0ZT5GR0eX+ZLs1q1be+RjYmKiPvzww3LLbdWqlf76178aqSOAwOTv+VibGBIJAAAAAH6q0g22TZs26aqrrlJCQoIcDofWrFnj/u7kyZO699571aVLFzVu3FgJCQkaOXKkDh48aLLO8GOmX5wN1CXkI8pDPqK+Ih9RHvLRXqUbbIWFherWrZsWLlxY6rsTJ05o+/bteuCBB7R9+3a9/vrr2rFjh377298aqSz83+kfi9PAEpg/OAQ28hHlMZOR5CPqHvIR5SEf7VX6GbZBgwZp0KBBXr+LjIzUunXrPNY9/fTT6tWrl/bt26eWLVtWrZYAUAeQjwDgHfkIVJ3PJx05duyYHA6HoqKivH5fVFSkoqIi9+f8/HxfVwk+ZLkMvTg7QB8aBc5UXj5KZGSgMZGR5CPqA/Kx/iEf7fl00pFffvlF9957r2644QZFRER43Wb27NmKjIx0L4mJib6sEnzMchl6hi1Af3BAiYrko0RGBhojGUk+IsCRj/UT+WjPZw22kydP6vrrr5dlWVq0aJHtdlOmTNGxY8fcy/79+31VJQDwCxXNR4mMBFC/kI9AaT4ZElnyY/vuu++0YcOGMu+OhIaGKjQ01BfVQG0wNUNPgD40ClQmHyUyMuCYyEjyEQGKfKznyEdbxhtsJT+2nTt36oMPPlCzZs1MHwJ+zOV0yWXgx2KiDMDfkI8wkZHkIwIR+Qjy0V6lG2wFBQXatWuX+/OePXuUk5Oj6OhoxcfH69prr9X27dv19ttvy+l0Kjc3V5IUHR2tkJAQczUHAD9DPgKAd+QjUHWVbrBt3bpVl112mftzZmamJGnUqFGaPn263nzzTUlS9+7dPfb74IMP1K9fv6rXFHUCs0SiPiMfUR5mQUN9RT6iPOSjvUo32Pr16yfLsmy/L+s7BD5Tb5kP1BcfIrCRjyiPiYwkH1EXkY8oD/loz6fT+gMAAAAAqs7nL85G/WI5LVnO6t8lM1EGAPgbExlJPgIIROSjPRpsMMrlMjRLZICOQQZQv5nISPIRQCAiH+0xJBIAAAAA/BQ9bDDKclmyXAaGRBooAwD8jYmMJB8BBCLy0Z7fNtiCgxwKDnL4pGynj//P9FW9z+TLc6hO2S6n5Aqqft1czmoXAQQ06z8L6hYTGUk+AghE5KM9hkQCAAAAgJ/y2x421E2W0yUriPewAYA3JjKSfAQQiMhHezTYYJTltGQZGBIZqNOyAqjfTGQk+QggEJGP9hgSCQAAAAB+ih42GOVyWoYmHQnMOyQA6jcTGUk+AghE5KM9GmwwimfYAMAez2gAgHfkoz2GRAIAAACAn6KHDUa5LEsuA++Ic1mB2aUNoH4zkZHkI4BARD7ao8EGs5yWLIeBH0uAjkEGUM+ZyEjyEUAgIh9tMSQSAAAAAPwUPWwwyuV0yeWo/gOfrgB9aBRA/WYiI8lHAIGIfLRHgw1GWYaGRAbqiw8B1G8mMpJ8BBCIyEd7DIkEAAAAAD9FDxuMoocNAOxxBxkAvCMf7dFgg1E8wwYA9nhGAwC8Ix/tMSQSAAAAAPwUPWwwyrIsWQZenG0F6IsPAdRvJjKSfAQQiMhHezTYYJTLacml6v9YXAE6BhlA/WYiI8lHAIGIfLTHkEgAAAAA8FM02GCU5bRkOV0GFt/dIXnooYfUu3dvNWrUSFFRURXaZ/To0XI4HB7LwIEDfVZHAIHJTEb6Lh+PHDmiESNGKCIiQlFRUbrllltUUFBgu/3evXtLZWPJ8uqrr7q38/b9ypUrfXYeAOoef8/H2sSQSBhlOS1ZBoZE+vIHV1xcrOuuu06pqalasmRJhfcbOHCgli5d6v4cGhrqi+oBCGAmMtKX+ThixAh9//33WrdunU6ePKkxY8Zo3LhxWrFihdftExMT9f3333use+655/TYY49p0KBBHuuXLl3qcaOrojfMANQP/p6PtYkGG+qdGTNmSJKysrIqtV9oaKji4uJ8UCMAqH3ffvut1q5dq88//1zJycmSpAULFuiKK67Q3LlzlZCQUGqf4ODgUrm4evVqXX/99TrrrLM81kdFRZGhAFAFDImEUS6nZWyRpPz8fI+lqKio1s5t48aNiomJUfv27XX77bfrxx9/rLW6AKib/Dkfs7OzFRUV5W6sSVJaWpqCgoK0efPmCpWxbds25eTk6JZbbin13fjx49W8eXP16tVLL774YsDO5gagakzmY6Dx2x42p8uS08D08N4EBzl8Um4JX9X7TL48h+qUbblcshzVr5vlOv3iw8TERI/106ZN0/Tp06tdfmUNHDhQv/vd75SUlKTdu3frvvvu06BBg5Sdna3g4OAarw/g+M+CmlXdv7mJjPRVPubm5iomJsZjXYMGDRQdHa3c3NwKlbFkyRJ17NhRvXv39lg/c+ZMXX755WrUqJHee+893XHHHSooKNCdd95Z5foCCCwm8zHQ+G2DDZCk/fv3KyIiwv3Z7rmxyZMna86cOWWW9e2336pDhw5Vqsfw4cPd/9ylSxd17dpVbdu21caNG9W/f/8qlQkA1WE6H6vr559/1ooVK/TAAw+U+u7MdT169FBhYaEee+wxGmwAUAE02GCU6fewRUREeFyQ2Ln77rs1evToMrdp06ZNtet1ZlnNmzfXrl27aLABqDCT7xkynY9xcXE6dOiQx/pTp07pyJEjFXr27LXXXtOJEyc0cuTIcrdNSUnRrFmzVFRUxAROACTxHray0GCDUZbL0CyRlRxW2qJFC7Vo0aLax62of//73/rxxx8VHx9fY8cEUPeZyEhf5WNqaqqOHj2qbdu2qWfPnpKkDRs2yOVyKSUlpdz9lyxZot/+9rcVOlZOTo6aNm1KYw2AW23kY13BpCOod/bt26ecnBzt27dPTqdTOTk5ysnJ8XjXUIcOHbR69WpJUkFBge655x599tln2rt3r9avX6+rr75a7dq1U3p6em2dBgAY1bFjRw0cOFBjx47Vli1b9MknnygjI0PDhw93zxB54MABdejQQVu2bPHYd9euXdq0aZNuvfXWUuW+9dZbeuGFF/T1119r165dWrRokR5++GFNmDChRs4LAOo6ethgltMlyzIwFYIPHxqdOnWqli1b5v7co0cPSdIHH3ygfv36SZJ27NihY8eOSTo9bfXf//53LVu2TEePHlVCQoIGDBigWbNmcXcYQOWYyEgf5uPy5cuVkZGh/v37KygoSEOHDtX8+fPd3588eVI7duzQiRMnPPZ78cUXdc4552jAgAGlymzYsKEWLlyou+66S5ZlqV27dnriiSc0duxYn50HgDrIz/OxNtFgg1EupyWXgamaXT7s0s7Kyir3HWxnTjcdHh6ud99912f1AVB/mMhIX+ZjdHS07UuyJal169Zep+N/+OGH9fDDD3vdZ+DAgR4vzAYAb/w9H48cOaIJEyborbfect/Qeuqpp0q9c9Iby7J0xRVXaO3atVq9erWGDBlSqWMzJBIAAAAAyjBixAh98803Wrdund5++21t2rRJ48aNq9C+8+bNk6MaryyodINt06ZNuuqqq5SQkCCHw6E1a9bYbnvbbbfJ4XBo3rx5Va4g6hbLaRlbgLqGfER5yEfUV+QjyuPP+fjtt99q7dq1euGFF5SSkqI+ffpowYIFWrlypQ4ePFjmvjk5OXr88cf14osvVvn4lW6wFRYWqlu3blq4cGGZ261evVqfffaZ+0Fl1A8uyzK2AHUN+YjykI+or8hHlMdkPubn53ssRUVF1apbdna2oqKilJyc7F6XlpamoKAgbd682Xa/EydO6MYbb9TChQsr9HoUO5V+hm3QoEEaNGhQmdscOHBAEyZM0LvvvqvBgwdXuXIAUJeQjwDgHfmImpSYmOjxedq0aZo+fXqVy8vNzVVMTIzHugYNGig6Olq5ubm2+911113q3bu3rr766iofW/LBpCMul0s33XST7rnnHp1//vnlbl9UVOTR6s3PzzddJdQgp2XJaeDur4kyAH9T2XyUyMhAYyIjyUcEIvIRJvNx//79ioiIcK+3m9V78uTJmjNnTpllfvvtt1Wqy5tvvqkNGzboiy++qNL+ZzLeYJszZ44aNGigO++8s0Lbz549WzNmzDBdDdQSp3V6MVEOEGgqm48SGRloTGQk+YhARD7CZD5GRER4NNjs3H333Ro9enSZ27Rp00ZxcXE6dOiQx/pTp07pyJEjtkMdN2zYoN27dysqKspj/dChQ9W3b19t3Lix3PqVMNpg27Ztm5566ilt3769wjOhTJkyRZmZme7P+fn5pboxAaCuq0o+SmQkgMBHPqK2tGjRQi1atCh3u9TUVB09elTbtm1Tz549JZ1ukLlcLqWkpHjdZ/Lkybr11ls91nXp0kVPPvmkrrrqqkrV02iD7aOPPtKhQ4fUsmVL9zqn06m7775b8+bN0969e0vtExoaysuHAwhDIgHvqpKPEhkZaBgSCZRGPkLy73zs2LGjBg4cqLFjx2rx4sU6efKkMjIyNHz4cPcEOQcOHFD//v310ksvqVevXoqLi/Pa+9ayZUslJSVV6vhGG2w33XST0tLSPNalp6frpptu0pgxY0weCn6KIZGAd+QjJIZEAt6Qj5D8Px+XL1+ujIwM9e/f3/3i7Pnz57u/P3nypHbs2KETJ04YP3alG2wFBQXatWuX+/OePXuUk5Oj6OhotWzZUs2aNfPYvmHDhoqLi1P79u2rX1sA8GPkIwB4Rz6irouOjtaKFStsv2/durWscnr4yvveTqUbbFu3btVll13m/lwydnjUqFHKysqqUiUQOFyGhkTyniHUReQjymMiI8lH1EXkI8pDPtqrdIOtX79+lWod2o07RmByytCQyOoXAdQ48hHlMZGR5CPqIvIR5SEf7QXVdgUAAAAAAN4Zfw8b6jenZckpZokEAG9MZCT5CCAQkY/2aLDBKKdlpjuaWdAABCITGUk+AghE5KM9hkQCAAAAgJ+ihw1G0cMGAPa4gwwA3pGP9vy2wRYc5FBwkMMnZTtdvv1/01f1PpMvz6E6ZfMMGwDY4xkNAPCOfLTHkEgAAAAA8FN+28OGusllaEikjztBAaBWmMhI8hFAICIf7dFgg1EMiQQAewz5AQDvyEd7DIkEAAAAAD9FDxuMYpZIALDHLGgA4B35aI8GG4w6/WMzMSTSQGUAwM+YyEjyEUAgIh/tMSQSAAAAAPwUPWwwiiGRAGCPIT8A4B35aI8GG4xilkgAsMcsaADgHflojyGRAAAAAOCn6GGDUZYkl6FyACDQmMhI8hFAICIf7dFgg1EMiQQAewz5AQDvyEd7DIkEAAAAAD9FDxuMYpZIALDHLGgA4B35aI8GG4xiSCQA2GPIDwB4Rz7aY0gkAAAAAPgpethgFEMiAcAeQ34AwDvy0R4NNhjFkEgAsMeQHwDwjny0x5BIAAAAAPBTNNhglMv6T5d2NReXj26Q7N27V7fccouSkpIUHh6utm3batq0aSouLi5zv19++UXjx49Xs2bNdNZZZ2no0KHKy8vzTSUBBCwTGemrfJSkhx56SL1791ajRo0UFRVVoX0sy9LUqVMVHx+v8PBwpaWlaefOnR7bHDlyRCNGjFBERISioqJ0yy23qKCgwAdnAKCu8vd8rE002GCU07KMLb7wz3/+Uy6XS88++6y++eYbPfnkk1q8eLHuu+++Mve766679NZbb+nVV1/Vhx9+qIMHD+p3v/udT+oIIHD5cz5KUnFxsa677jrdfvvtFd7n0Ucf1fz587V48WJt3rxZjRs3Vnp6un755Rf3NiNGjNA333yjdevW6e2339amTZs0btw4X5wCgDrK3/OxNvEMG+qVgQMHauDAge7Pbdq00Y4dO7Ro0SLNnTvX6z7Hjh3TkiVLtGLFCl1++eWSpKVLl6pjx4767LPPdNFFF9VI3QHA12bMmCFJysrKqtD2lmVp3rx5uv/++3X11VdLkl566SXFxsZqzZo1Gj58uL799lutXbtWn3/+uZKTkyVJCxYs0BVXXKG5c+cqISHBJ+cCAIHC7xps1n9axsU/F/rsGE4f95cGBzl8Wr7k23Mo+dtbVbhL8bNcRmboKZZLkpSfn++xPjQ0VKGhodU/wBmOHTum6Oho2++3bdumkydPKi0tzb2uQ4cOatmypbKzs2mwoUaV/C6PHz9eyzWpn0r+7lXJR8lMRtZkPpZnz549ys3N9cjHyMhIpaSkKDs7W8OHD1d2draioqLcjTVJSktLU1BQkDZv3qxrrrmmRuuMwFXyu3QWnajlmtRPJX93f8jHQON3DbaS/xgu+0N6LdcEx48fV2RkZIW2DQkJUVxcnJbnHjB2/LPOOkuJiYke66ZNm6bp06cbO8auXbu0YMEC2941ScrNzVVISEip5zliY2OVm5trrC5ARZRkZLtzz63lmtRvlclHyXxG1kQ+VkRJBsbGxnqsPzMfc3NzFRMT4/F9gwYNFB0dTYbCqJJ8/PuTv6/lmtRvtZ2PcXFxCgkJMVKWv/C7BltCQoL279+vJk2ayOEov6cqPz9fiYmJ2r9/vyIiImqghub52zlYlqXjx49XaphKWFiY9uzZU+7kHZWtx6//HbC7ezx58mTNmTOnzPK+/fZbdejQwf35wIEDGjhwoK677jqNHTu2+hUGakB9y0h/q39V8lEyn5G+zkegLiIfa5e/5GNISIjCwsKMlOUv/K7BFhQUpHPOOafS+0VERPjFv6zV4U/nUJk7IyXCwsJq7Qdy9913a/To0WVu06ZNG/c/Hzx4UJdddpl69+6t5557rsz94uLiVFxcrKNHj3r0suXl5SkuLq461QYqrb5mpD/Vvyr5KNVeRlY2HyujJAPz8vIUHx/vXp+Xl6fu3bu7tzl06JDHfqdOndKRI0fIUBhFPta+upaPdYXfNdiAqmjRooVatGhRoW0PHDigyy67TD179tTSpUsVFFT2ZKk9e/ZUw4YNtX79eg0dOlSStGPHDu3bt0+pqanVrjsA+FJl8rGykpKSFBcXp/Xr17sbaPn5+dq8ebN7psnU1FQdPXpU27ZtU8+ePSVJGzZskMvlUkpKik/qBQCBhGn9Ua8cOHBA/fr1U8uWLTV37lwdPnxYubm5Hs9RHDhwQB06dNCWLVsknb5bdMsttygzM1MffPCBtm3bpjFjxig1NZUJRwAElH379iknJ0f79u2T0+lUTk6OcnJyPN6Z1qFDB61evVqS5HA4NHHiRD344IN688039dVXX2nkyJFKSEjQkCFDJEkdO3bUwIEDNXbsWG3ZskWffPKJMjIyNHz4cGaIBIAKqPM9bKGhoZo2bVqNz4xlUiCcQ12xbt067dq1S7t27So1bKJkVqOTJ09qx44dOnHiv7NMPfnkkwoKCtLQoUNVVFSk9PR0PfPMMzVad6Aq6nq+1PX61zVTp07VsmXL3J979OghSfrggw/Ur18/SadHGBw7dsy9zaRJk1RYWKhx48bp6NGj6tOnj9auXesxvGn58uXKyMhQ//793Vk6f/78mjkpwEZdz5e6Xn9UnMOq6tybAAAAAACfYkgkAAAAAPgpGmwAAAAA4KdosAEAAACAn6LBBgAAAAB+igYbAAAAAPipOt9gW7hwoVq3bq2wsDClpKS4353l72bPnq0LL7xQTZo0UUxMjIYMGaIdO3bUdrUABBDyEQC8q6v5KJGR9VGdbrCtWrVKmZmZmjZtmrZv365u3bopPT1dhw4dqu2qlevDDz/U+PHj9dlnn2ndunU6efKkBgwYoMLCwtquGoAAQD4CgHd1OR8lMrI+qtPvYUtJSdGFF16op59+WpLkcrmUmJioCRMmaPLkybVcu8o5fPiwYmJi9OGHH+qSSy6p7eoAqOPIRwDwLpDyUSIj64M628NWXFysbdu2KS0tzb0uKChIaWlpys7OrsWaVc2xY8ckSdHR0bVcEwB1HfkIAN4FWj5KZGR9UGcbbD/88IOcTqdiY2M91sfGxio3N7eWalU1LpdLEydO1MUXX6zOnTvXdnUA1HHkIwB4F0j5KJGR9UWD2q4ApPHjx+vrr7/Wxx9/XNtVAQC/Qj4CgD0ysn6osw225s2bKzg4WHl5eR7r8/LyFBcXV0u1qryMjAy9/fbb2rRpk84555zarg6AAEA+AoB3gZKPEhlZn9TZIZEhISHq2bOn1q9f717ncrm0fv16paam1mLNKsayLGVkZGj16tXasGGDkpKSartKAAIE+QgA3tX1fJTIyPqozvawSVJmZqZGjRql5ORk9erVS/PmzVNhYaHGjBlT21Ur1/jx47VixQq98cYbatKkiXvcdGRkpMLDw2u5dgDqOvIRALyry/kokZH1UZ2e1l+Snn76aT322GPKzc1V9+7dNX/+fKWkpNR2tcrlcDi8rl+6dKlGjx5ds5UBEJDIRwDwrq7mo0RG1kd1vsEGAAAAAIGqzj7DBgAAAACBjgYbAAAAAPgpGmwAAAAA4KdosAEAAACAn6LBBgAAAAB+igYbAAAAAPgpGmwAAAAA4KdosAEAAACAn6LBBgAAAAB+igYbAAAAAPgpGmwAAAAA4Kf+HxVZXMnPjCihAAAAAElFTkSuQmCC", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def charge(i):\n", " return number_u(i) + number_d(i)\n", "\n", "\n", "def spin(i):\n", " return number_u(i) - number_d(i)\n", "\n", "\n", "def Delta_s(i):\n", " _, x, y = lattice.xyz_from_index[i]\n", " return (\n", " annihilate_u(x, y) @ annihilate_d(x, y)\n", " - annihilate_d(x, y) @ annihilate_u(x, y)\n", " ) / 2\n", "\n", "\n", "C = [pf_state.expectation(charge(i)) for i in range(N)]\n", "C = jnp.asarray(C).reshape(lattice.shape[1:]).real\n", "S = [pf_state.expectation(spin(i)) for i in range(N)]\n", "S = jnp.asarray(S).reshape(lattice.shape[1:]).real\n", "Ps = [pf_state.expectation(Delta_s(i)) for i in range(N)]\n", "Ps = jnp.asarray(Ps).reshape(lattice.shape[1:]).real\n", "\n", "fig, axes = plt.subplots(1, 3, figsize=(12, 5))\n", "\n", "axes[0].set_title(\"Charge density\", pad=20)\n", "im = axes[0].imshow(C, cmap=\"RdBu\", vmin=-2, vmax=2)\n", "fig.colorbar(im, ax=axes[0])\n", "axes[1].set_title(\"Spin density\", pad=20)\n", "im = axes[1].imshow(S, cmap=\"RdBu\", vmin=-1, vmax=1)\n", "fig.colorbar(im, ax=axes[1])\n", "axes[2].set_title(\"s-wave pairing density\", pad=20)\n", "im = axes[2].imshow(Ps, cmap=\"RdBu\", vmin=-0.5, vmax=0.5)\n", "fig.colorbar(im, ax=axes[2])\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "quantax_env", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.11" } }, "nbformat": 4, "nbformat_minor": 5 }