{ "cells": [ { "cell_type": "markdown", "id": "add8e12c", "metadata": {}, "source": [ "# Variational Circuit Preparation" ] }, { "cell_type": "markdown", "id": "29dc960e", "metadata": {}, "source": [ "## Approximate ground states via tensor-network circuit optimization\n", "\n", "We show how to represent an approximate ground state of an Hamiltonian expressed as Matrix-Product-Operator (MPO) as (i) a Matrix-Product-State (MPS), and as (ii) the wavefunction associated with a quantum circuit of finite depth. This reproduces (to some extent) the work of R. Haghshenas et al., *Variational Power of Quantum Circuit Tensor Networks*, [Phys. Rev. X 12, 011047](https://link.aps.org/doi/10.1103/PhysRevX.12.011047) (2022). This can be used to prepare an initial state for Quantum Phase Estimation ([arxiv:2409.11748](https://arxiv.org/abs/2409.11748)).\n", "\n", "We also used some syntax and advice from the [Tensor Network Training of Quantum Circuits](https://quimb.readthedocs.io/en/latest/examples/ex_tn_train_circuit.html) example in [$\\texttt{quimb}$](https://github.com/jcmgray/quimb)'s documentation." ] }, { "cell_type": "code", "execution_count": 1, "id": "6aa7eb00", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:11:14.403558Z", "iopub.status.busy": "2026-04-03T04:11:14.403398Z", "iopub.status.idle": "2026-04-03T04:11:16.326404Z", "shell.execute_reply": "2026-04-03T04:11:16.325613Z" } }, "outputs": [], "source": [ "import os\n", "\n", "os.environ[\"OPENBLAS_NUM_THREADS\"] = \"1\"\n", "os.environ[\"JAX_ENABLE_X64\"] = \"True\"\n", "\n", "import autoray\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import quimb.tensor as qtn\n", "\n", "from qpe_toolbox.circuit import ansatz_circuit\n", "from qpe_toolbox.estimation import qpe_sample, set_search_window\n", "from qpe_toolbox.hamiltonian import heisenberg_hamiltonian" ] }, { "cell_type": "code", "execution_count": 2, "id": "ecfb3b5d", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:11:16.328093Z", "iopub.status.busy": "2026-04-03T04:11:16.327771Z", "iopub.status.idle": "2026-04-03T04:11:16.330538Z", "shell.execute_reply": "2026-04-03T04:11:16.329895Z" } }, "outputs": [], "source": [ "plt.rcParams.update({\"font.size\": 12})" ] }, { "cell_type": "code", "execution_count": 3, "id": "614fb436", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:11:16.331836Z", "iopub.status.busy": "2026-04-03T04:11:16.331695Z", "iopub.status.idle": "2026-04-03T04:11:16.333917Z", "shell.execute_reply": "2026-04-03T04:11:16.333341Z" } }, "outputs": [], "source": [ "opt = \"auto-hq\"" ] }, { "cell_type": "markdown", "id": "fbc83315", "metadata": {}, "source": [ "## State preparation" ] }, { "cell_type": "markdown", "id": "fd714a40", "metadata": {}, "source": [ "### The DMRG algorithm to find an MPS ground state\n", "\n", "We first define our model Hamiltonian (Heisenberg chain) on $n=8$ qubits. We know that its ground state can be approximated as a MPS. We use first the DMRG algorithm as a black box to have a reference energy (using a very large bond dimension 100 to have essentially the exact GS energy)" ] }, { "cell_type": "code", "execution_count": 4, "id": "e2d3af5e", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:11:16.335277Z", "iopub.status.busy": "2026-04-03T04:11:16.335103Z", "iopub.status.idle": "2026-04-03T04:11:16.429837Z", "shell.execute_reply": "2026-04-03T04:11:16.429050Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "n_qubits = 8\n", "hamilt = heisenberg_hamiltonian(n_qubits)\n", "hamilt_mpo = hamilt.to_mpo()\n", "hamilt_mpo.draw(\n", " show_tags=True, show_inds=True, edge_scale=1, layout=\"kamada_kawai\", edge_color=True\n", ")" ] }, { "cell_type": "code", "execution_count": 5, "id": "8b3b5450", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:11:16.431369Z", "iopub.status.busy": "2026-04-03T04:11:16.431195Z", "iopub.status.idle": "2026-04-03T04:11:16.528554Z", "shell.execute_reply": "2026-04-03T04:11:16.527825Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1, R, max_bond=(10/10), cutoff:1e-13\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Energy: (-3.374931217799727+0j) ... not converged.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "2, R, max_bond=(10/20), cutoff:1e-13\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Energy: (-3.3749325986878667+1.1102230246251565e-16j) ... not converged.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "3, R, max_bond=(16/40), cutoff:1e-13\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Energy: (-3.3749325986878818-3.3306690738754696e-16j) ... converged!\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "DMRG reference energy: -3.3749325986878818\n" ] } ], "source": [ "dmrg = qtn.DMRG2(hamilt_mpo, bond_dims=[10, 20, 40, 100], cutoffs=1e-13)\n", "dmrg.solve(tol=1e-6, verbosity=1)\n", "dmrg_energy = np.real(dmrg.energy)\n", "print(\"DMRG reference energy:\", dmrg_energy)" ] }, { "cell_type": "markdown", "id": "6e392d36", "metadata": {}, "source": [ "### MPS search via tensor-network differentiation\n", "\n", "Let us now write a custom optimizer to find the ground state MPS, effectively performing the same task as in DMRG. The goal is simply to warm up for the circuit optimization that comes later.\n", "\n", "When one optimizes the energy $H$ with respect to a variational wave function, we need first to be able to evaluate $\\braket{\\psi|H|\\psi}$ as a tensor contraction" ] }, { "cell_type": "code", "execution_count": 6, "id": "42d4f60d", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:11:16.530038Z", "iopub.status.busy": "2026-04-03T04:11:16.529889Z", "iopub.status.idle": "2026-04-03T04:11:16.676879Z", "shell.execute_reply": "2026-04-03T04:11:16.675979Z" }, "lines_to_next_cell": 2 }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Contracted energy: (-0.7850974773699702+0j)\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "psi = qtn.MPS_rand_state(n_qubits, bond_dim=2)\n", "psiH = psi.H\n", "psi.align_(hamilt_mpo, psiH)\n", "energy_tn = psiH & hamilt_mpo & psi\n", "print(\"Contracted energy:\", energy_tn.contract(all, optimize=opt))\n", "energy_tn.draw()" ] }, { "cell_type": "markdown", "id": "8fc81a18", "metadata": { "lines_to_next_cell": 2 }, "source": [ "Now we can define a loss function, the energy, to be optimized w.r.t each tensor that makes the MPS $\\ket{\\psi}$. We use $\\texttt{jax}$ as automatic differentiation tools to evaluate the gradients." ] }, { "cell_type": "code", "execution_count": 7, "id": "0298458c", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:11:16.678335Z", "iopub.status.busy": "2026-04-03T04:11:16.678157Z", "iopub.status.idle": "2026-04-03T04:11:16.681742Z", "shell.execute_reply": "2026-04-03T04:11:16.681118Z" } }, "outputs": [], "source": [ "def loss(psi, mpo):\n", " psiH = psi.H\n", " norm_tn = psiH & psi\n", " psi.align_(mpo, psiH)\n", " energy_tn = psiH & mpo & psi\n", " energy = autoray.do(\"real\", energy_tn.contract(all, optimize=opt))\n", " norm = autoray.do(\"real\", norm_tn.contract(all, optimize=opt))\n", " return energy / norm\n", "\n", "\n", "def myoptimizer(chi, mpo):\n", " psi = qtn.MPS_rand_state(n_qubits, bond_dim=chi)\n", " return qtn.TNOptimizer(\n", " psi, # the tensor network we want to optimize\n", " loss, # the function we want to minimize\n", " loss_constants={\"mpo\": mpo},\n", " autodiff_backend=\"jax\", # use 'autograd' for non-compiled optimization\n", " optimizer=\"L-BFGS-B\", # the optimization algorithm\n", " )" ] }, { "cell_type": "markdown", "id": "ca0b130d", "metadata": {}, "source": [ "Let us optimize for a first bond dimension $\\chi=4$. This is already extremely fast and accurate." ] }, { "cell_type": "code", "execution_count": 8, "id": "5077d560", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:11:16.683286Z", "iopub.status.busy": "2026-04-03T04:11:16.683120Z", "iopub.status.idle": "2026-04-03T04:11:17.803652Z", "shell.execute_reply": "2026-04-03T04:11:17.802906Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimized energy -3.371801709452784\n", "Exact energy -3.3749325986878818\n" ] } ], "source": [ "tn_opt = myoptimizer(4, hamilt_mpo)\n", "psi_opt = tn_opt.optimize(n=200)\n", "print(\"Optimized energy \", tn_opt.loss)\n", "print(\"Exact energy \", dmrg_energy)" ] }, { "cell_type": "markdown", "id": "6cf1decb", "metadata": {}, "source": [ "Let us be more quantitative by relating the energy estimation to the number of variational parameters $d=2((n-2)\\chi^2+2\\chi)$ of an MPS, for various $\\chi$" ] }, { "cell_type": "code", "execution_count": 9, "id": "4f4274fc", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:11:17.805403Z", "iopub.status.busy": "2026-04-03T04:11:17.805020Z", "iopub.status.idle": "2026-04-03T04:11:20.593345Z", "shell.execute_reply": "2026-04-03T04:11:20.592603Z" } }, "outputs": [], "source": [ "bond_dimensions = [2, 4, 10, 20]\n", "n_values = len(bond_dimensions)\n", "n_parameters = np.zeros(n_values)\n", "optimized_energies = np.zeros(n_values)\n", "for i in range(n_values):\n", " tn_opt = myoptimizer(bond_dimensions[i], hamilt_mpo)\n", " psi_opt = tn_opt.optimize(n=200)\n", " n_parameters[i] = tn_opt.d\n", " optimized_energies[i] = tn_opt.loss" ] }, { "cell_type": "code", "execution_count": 10, "id": "36fe8a5c", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:11:20.595074Z", "iopub.status.busy": "2026-04-03T04:11:20.594744Z", "iopub.status.idle": "2026-04-03T04:11:20.874609Z", "shell.execute_reply": "2026-04-03T04:11:20.873900Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.loglog(n_parameters, optimized_energies - dmrg_energy, \"-o\")\n", "plt.xlabel(\"number of parameters\")\n", "plt.ylabel(\"energy error\");" ] }, { "cell_type": "markdown", "id": "1acf6050", "metadata": {}, "source": [ "### Finding a quantum circuit directly\n", "\n", "MPS are good candidates for the initial state of the QPE algorithm because they can be prepared efficiently in a quantum computer. One possibility would be to find variationally the circuit that best approximates an MPS (see e.g. [this recent proposal](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.132.040404)). Here, we take a shortcut, and directly find the circuit whose associated wavefunction minimizes the energy, in the spirit of R. Haghshenas et al., [*Variational Power of Quantum Circuit Tensor Networks*](https://link.aps.org/doi/10.1103/PhysRevX.12.011047). One practical advantage is that we may have less parameters to optimize using parametrized circuits compared to dense-tensors-based MPS.\n", "\n", "We consider finite-depth quantum circuits made of parametrized $U_3$ single qubit rotations and $R_{ZZ}$ two qubit gates." ] }, { "cell_type": "markdown", "id": "719ae843", "metadata": {}, "source": [ "Let us visualize the circuit wavefunction, and the tensor network contraction associated with the estimation of the energy." ] }, { "cell_type": "code", "execution_count": 11, "id": "a3b9800f", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:11:20.876353Z", "iopub.status.busy": "2026-04-03T04:11:20.876148Z", "iopub.status.idle": "2026-04-03T04:11:23.534361Z", "shell.execute_reply": "2026-04-03T04:11:23.533545Z" }, "lines_to_next_cell": 2 }, "outputs": [ { "data": { "image/png": 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", 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", 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0Fj8b6BsZHqp6EraSiMbi54C54Zz1n7jNLYrHo7xI/wR+E4pIs2y7Nai8qZC1TRq48fUbLhHAzW4XG3TT7flt3/9wy/p3qeah+SyFzJQJfGh0MDjc9Dfn4DAPnSaizhOCr67rw1sSPkUDdkzBlfv8jCe6TwDU8E5Dz/14dDB4VpX9XOF28YbVPXgqVVhLCWNT6EWTr4YiMtKo99NsUgmhAS9G9b96JuCeMfrHitLziX739q+HIrItw2LWAfwg1OL+JJSH9h7UAfzOlZ7b0kqsStanosTTGlTe2r9QQrZm/mEJS0wdjaq02w7cWanRZLOIxuJPQ40t+lQndPr+3Wf2OavXtfMbXi3X79bIAxRNfKgKxQtDEfmz8u2tTvHHA08H+s5c86UXrfZuP25NL56ZPDymb+BLB/8ToamqAUPPoU9PgJo+sOKLdRzai04TUfsDD67qRvjK+g5vn3bJWzxn8sv9viZKwzuR8p2jg8HLK+zDB0z0d+Hz1yiwz+ZhMssM0B+KyLbvnZJKCA+wGTjL50H6PaouSi9iZnVMVIPRF4Yico/2EO2E1Tj0yaj8qf1QOTj/Av45Mjw0r3fLYX6s+XJPQgmng1BtAf6DCgc90O4VlD/95NHHgnnp3r77vW5RmAH+AnwtFJF7jC9qd1IJcSrwq4AXrduPcFlp/oYJmTxk8pjAq0IR+aO5z43G4q79fbef9NxV3/vDgLUmGyZsmxR8Z/0mHuw/fde2+amdRbOgXzM6GBxs0ltzcFgQHSWiAFIJ8W1N8KrVvSqPCSCnw1jGzRcOupXJnLtoFvJjwMGjg8FMhefvCzy8phfcNcqrCwaMTQGwJhSRYw14K00llRBfEIILB3pUUn45hgk7p9ENk+tDEfnC1lhYf6xqsBCz42ceQ3mn0iPDQ3t8NxyqYzVpPAT1WR6F8vbdjxJO/1kJyf2Wp/aTQNSlUfR51IiYfIG8YeIF4sBHQ5GVseimEsIFPBzwsqGvi4pdT6ezMJNnAtgrFJF79MxLJcQLgV+s70crefV3zmjydvEsthz4/V37LOZmKGSm7xkdDB7ekDfj4LBEOi2xnMfyh7xzwPPEs+XUzD49ftw+D3jcoAmTJ237pvyLf+Mk8LxKAspiBsCcZxmczQSg7ZvOWVWNF/YF9hRQAC4N+rvxjk1xeiohjglF5K17btV+WOGk30Rj8etQ/XBCwAuB06Ox+B2ovI/72t1z0kiisfgGlHAKosaFbAf+gBKibe21rMAlwLtXdSO87tlQf48fX74AExk+jFoPPt06E+vKS4D1Pf7KAgqgyw8zebqBs4FkhU08gCxPi+j2meLQ6T/Rk3uQaf+B1r01hxM4OLSMjhJRKvdl48k+kfnWmWu/3CuzM2+ayrJKPSoNTOMG4C2jg8Gq40tCETmeSoibczrHe93Vf9nZAibwp1BEtr2IAl4tBLI8BDoXjws8LvSCwRuA9zTNsiZgjbK4E7jT6oPzVFS47/XApFWB5PSesojG4j3MtiXYC1WtlkZ5nR5biRWQqYRYC8T6u9SJWTlCgN8LpsQ1lSWeSoivhiJyqiWG1pdne9wUNY2qiQ2aAJ8HkS/wLCqLqHsAV9GY9ex7XCA0lwzt/Kb4096XAGAaRYlq7ungYCs6SkRhdR7Py64fPuM907emEuJ/UDkZHoH87wfe9rmF9iP5XFYnGfDi8lT4BPWiChECn6+P2S1nH7e2+9liJdwuvAWD/ZtjUmuwqsRutHrelPeeOiMaix8CfAgVnuqoZHSrLUEY1dX/YECi2hJcj2pL0PZ5gfPwBk1g1jrRCHhhOodLSl4L7JFv2Ya4xQJcRNY2FZMfQhF5RyohUjM5ntrXpUJ6QkCvryhOmLmav5gfoCg9GPmsCXy93m/AwWG5dIyIisbi+6Mqy/4+Mjx0K0AoIouoM6HFcg1w+tg0r+/x4w54QdNUblBWh5kcBmqR/End3kBrmZ4vfAlgmhio2WQrHsubUt576lyUoHoVMB2Nxf+B6nA/3jorG8+cYdxvBn4KfBfVlqCT8saO9Lhx1zrREEJ5WfQiRzXPrIby70JRVSNXe99SQr5IETVEvBrvyBX4g5ZD9PhVyxi/F7zZDIft/CH/0k4tosbofK/+b8HBYXl0hIiywguvRpXcXrvc/YUiUqYS4s1AajrH/0zn2AcwAQ3lcv4k8NWVkkAK/MQw+WShqPLHKmGakC8igB830zA7MDI8VIjG4o8DP0AJ7KehyrefHY3F7wZuAu5ZKWGsaCzuQVXXHQcciArX3Yqq3rx+ZHjophaa1yqKUu5aA6oiJZJlzuizEd+VcGlWx9Plq7xBrgBSIoBN1XYSisi/pBLizEye7+d0PD6PakHjEiZHT/+M271Pf2jf//7l41+MR1fK5+awgqj5g18JWA0hz0a5lLfUK6wQikgzFJFfAA4ATrozc8LH/jp5xqeBg0IR+ZUVJKAIReQdwPWTWQqVPFJSwmQWAyVSf9lk8+zCamBsZHho28jw0C+BzwI/A/qA1wEXR2PxZ1ljTNqSaCy+IRqLvxh4L/AK1InD94HPjQwPXYvyzPW30MRWcr1eRNTy2BomFAzcwO+bZlUDCUVkBnj/VBYzm1frQAkpVUrDZAYDuGS+CuVQRP4K2N+UxLI6v8zkucGQ4uod2gHnHHTvb9/q1WeeZc3qc3CwFZ3giToNNcfqWyPDQ3VP5rR6QN14tcoJOemCj/x0pVZqva5o8NexKTZ0+/H6PEqV5ouQyVEoGGSBM1ZCT6wlspqyMR9Wyf4tVlhvX1Te1CnAKdFY/HaUd+phu3unorG4F9U363hU36xp4GbgHyPDQ3MPjBN0roj6EbBzJsea3sCeeUJSwkwOE9UmY9necLsQisgvpxLCO5nl09M5TJ9HJZnnC+RNiRv4KLCgTuOhiNyJmnW4a97hcexqj7E/8KpoLH7ZyPCQM0vPwTas6D5R0Vg8CLwS+MXI8FBDO91GY/FjUGfnH680rHglYA1c/jBq6HLJo1JA5cDEQxG5lPyytsfqeP5B4Lcjw0N/rbFdFypv6mmoMTOPo8RU2m59kqKx+N4o4RQEvMC9qIaqd1Xz5kZj8RcCh48MD3XknLNUQpwO/CLgRev2IVxWKnXRUAIqV8AAXhCKyJaNSGoUqYRYt7Ow/oMgXrjK88RdQgntr4ci8rF67N9KyXgbajTTJqetiINdWLGeKKs/TRiVq7FbjkY4mT4UuAB4DbNNFC8HrhodDI4v8SVLs9b6UD/0FUcoIrcCF6USInbT5IveASJwQt8vv7gSmokuk17Ub6nm52AlWv85Gov/BTW4+QTgDFTfqRRw80JHnTQCq5N4ECWe9kZ9p/+K6tY+voBdTAD90Vhc2N3D1ghCEfnrVEKcltX5SlbnKE2gA9KU+FDz/N4Wisi/tNjMhhCKyG3RWPwnqCHen633/keGh6ajsfj3gTegPLq/q/drODgshRUpoqzZTOegxMzPyhf0cDL9euBbwuUy3L4uL0JDGsWBYj7zaaT8YDiZfsHoYDC9hJdd8SKqRCgip6+Oxe8HfG/9yC86XUCBCuUB7FzIxtb38R7gHmt23PGoyMWJ0Vj8AZTov6MZbQHKBv8ej+rt5Gb31gSLOeOfQDVPDKCSzTuOUET+PpUQTwKeeV/2yRe4MHL7++/4OnDTSsqTrMIAC/wNLIWR4aEHrca3p0Zj8YdGhofubtRrOTgslBUnoqyDwlmAH+X23RVaCyfTpwBXebp6NZcv4BJldbnuQLdXn55YbRby14WT6aNGB4OLFULlIqpTWOkHhYUygPosFn0AsTw8v4vG4tejhuiegCqEmI7G4reg2iRMVt8DbDzvgv2Bl6K8qo8AP9l05WU1RYx1ovFUlHjbAIwDN6CahtZ8vRqU2lv006EiClT1LvCXq2PxI4GJkQ80NpXARqxCfY8ayZ9RxTxnWflRHdFSxcG+rDgRBTwPNaLj2yPDQ3MPah9xef24/XsWSAkh8Pb0u3Lj2/uQ5nnAZxbzolaZe4bOEVECR0SVWA1MLqfBpuV1+jfw72gsvh4lpp4BPDcai9+J8k7dV+5V3XjeBWtRDQjDmqbpQmjSMA03UuY3nnfBZ4CPbbrysl2eJOsE4wCUcHoyqjr3DuA31Gd8TbmIqksuzAqgk34jA5QVVyyFcDJ9HPAO4JnWXX8GvjI6GPwnKC9uNBb/ESo/6uxoLP7NDmjk6mBjVpSIisbiRwAnA78bGR7aLck5nEzvDzyvkoAqIYTA7Q94i9mZC1mkiLKYxBFRHUEqIQQqN+OlL1m915MzZt9kKnHJd0MR+ehy9z0yPLQV+Hk0Fv8tKkfpBGAQ2BGNxW8GUlufeMwP/NXlcu/f29cnPB6vTwiBlJJcNuuempr4ELDfxvMuOH/9hr0DqGaYxwNrUblb16O8TnWrdHpq9+8z2wv7Dezju/tZqcQl+VBELuuAugLomIFvVu+wXpYYzgsn0y7ga8CbNbdH1zw+L4BZyB9qFgtvCSfTVwAXjg4GjZHhoWw0Ft+CKnA5nc5tq+JgA1aMiIrG4mtQYbw7UN1t57IvgHDVfsuaywMqqXYpNFVEhZPpHuBw1GJ99+hgsJnzuDpWRKUSIgj8EDjU46Kwt/txd8F4vGhKXplKiMuBi0MRuewKzZHhoTxwsxXW2x8lpk4FXuB2e55uSnP/gdVrvJo22+5NCEGgqwu32+3euXPHm7u6ex5G9XMC+A/wc+CBeiZ+W4LyrU/t4X0oL3Dp/puAj4Ui8qf1eq02o5N+I6XWFuNLfP5nQGz09q7C5fHOzuILdHuNgo4+Nf4mkBPA+wBGhoceicbi1wIvsfKjanVEd3BoGCtCRFm9bF4DzGB1zLYSdve2Lnvt3bvPsY/t/wyQJoiKY5wAkNIEKYvRWHxf4NFFHmwmscRaIwkn03ujSurPQyXxAuTCyfS3gP8bHQw+0mgb6KwDxC5SCXEk8Cefh+7eAMJlDV+VEq9ehIkMb5aSNamEeE29Eomt7+BDwEPRWPxXxWLhmcVi4cO9ff27CahyPF4vXq/P1PO5l9PT+3bg1kaMYbEE1DeAwW4fbr8XXBoUTcjmOT6r85NUQrw3FJErZY6kQ2UGrOtFe6LCyfQG4GJvT5/L5dlzlrHL48Xb0+fWpyci4WT606ODwVIF602ojvnhaCz+uDMA3KEVtL2IsvI8XgccifJAvRolnEriYgZ4rHv6iV8j5WAxn9vgCXRX3Z+Rzxb82bE7gLeiknvvAu5E5YzM512YRCUHN4xwMn0gcKPQXGvcgW6vy6PmLRiFvL+Yy7xZGsWzwsn0SaODwXsbaYdFx4ko4FMeF139XbjK54UJNa2egW48Y9O8Cngu8Id6v/jI8NDMxvMumAK8Pp+/5rZ+v981OTlx0Mjw0I31tqOMNwAbV/fsPozb4wJPF5rXDRMZPptKiL+EIvJvDbTDjjT1RCOcTPtQsxuPt173FuAHo4PBfBNefgAwgKV4wwcRmqF5fFXPbjWPD4RmIs1BrGacVn7UKHA+8OpoLP71ldqjz8G+rISxLy8HPoQShPsCOqq3zWbU6I2RkeGhqz/3iQ/9BiE+U8zOFEyjcv5vMZ/DLBbceX//BcC3gDTqTOe1wPujsfi50Vj8adFYvFrIbhLotibaN4ofaG7PWl//Gq/bF0BoGkLTcPsC+PpWezS3dzXwo3Ay3eh8jI7zRKUSYh/gzG5/9UGzHjd43RjARQ00xQ0qdFcT9Xh1t+sysbxQ7+vy7S6gyvF7weumSGM/DzvTlN9IOJk+F3gC+Jbm9r5Tc3svAq4CHg8n0+c0wYQBYGKJxQmHam6Pq9b3WQiB5vZowCHl91sh7++hijtesoTXdnBYFm3tibLm4h0IfAn42gLCFV8AeUp+cux0t7/b4/YFQAikaVDMZaSRzwK85ydvOPYW1ViaB4BrrUn1R6C8XS8BzojG4o+h+uncCTxmhVxKpeFLSrC0wpJvR4m3P8yt9gon0ycAx3u6+yoeQIUQeLp73fmJHUHgJFRlS6PoOBGFSs7GO8+vxufBrRd5RgPtuAcwC7queX1VJr8CBV2XqBzBRnEA8KTAnhGY3Qh48ehFzmqgHXalKYnl4WT6dUDSHegWbn8XQqhzYylNirnMqmJ2ZnM4mRajg8HvNNCMVSxyzYvG4n7gQO8hL9hQdK+dfy2RJt7cxIZoLP5kVA5WcWR46O8jw0NPRGPxnwMvj8biD44MD6UWb76Dw9JoaxEFhFA/pssWku8xOhgshpPplyNltJidfncxO70eJQQE8C8gPjoY/NHc540MD20HtgN/sfrrHIYSVCeiqgGnrLDfVpR3r48KC4oVetTmXObedzcqefiEaCz+a1SpuAZorsNfvNH09+Y1l7vqkVNzudHcHt0sFs7CEVErkk1XXvbExvMu+MlMZvpMj9frriSoTcMgm80YwBcbaEovgDaPVLAeD6QSQnRAw8lyGv4bCSfTAeCr7kCPmJumIISGJ9ADIIrZma+Gk+kfjQ4Gc5X2E43FXctsFTAAPFxrA6sj/gHAQcDBqLQL0Tvx3207/P0uaRoIrbLjVJoGZrHg6ht/aBz4P9S6n7KE2P2o9ftA4KXRWPyxkeGhJ5bxXhwcFkzbiigrZHYycNtifjCjg8Ei8MlwMj2Cyh3oBR4dHQzevpDnjwwPZVGeorTlCTuAWS/VicAbgQOjsfh/2FMoLfTMtBvVI+gFlAkhX37y6blA/7z/MyE0t6uQ2z8ai68GdjZoBEcniqhbAfSiyn+qRr5AERVSbiQfKej6i6emJrSenj6tPMG8WCwyMb5TR40a2dJAG54AZNFEeGskBhRVgGdHhwmoEo1+z68GEajVusXt76KYnelG5UtdXf6YdVJ4GnBsNBb/3FKGtFsnhwOoPmfl93vYXTTtg1oHp1Be/puBB/KBVePAiwuZ6X093X3a3JMCKSWFzLQBPJzrGngbYzwNeAuwDXgW8HwgjxJx/cCbo7H4Z61Qn4NDQ2lbEcWsALp+KU+2xNSyEl2tM7f7gfstr1EI1cjwWtQiYaIWUbPCpdr9h6EWhRuAX1n7NwEz71/lkmbxGCll1fwBKSWmUTC6s9vXAxcDejQWfwI17LZ0vbUOA287pgdOiVBEPppKiJ/O5Hip1105L6pQBL2IC7i0kbZsuvKyf28874IX5LLZn+ay2T6/P+DSNE0Ui4Wirutu4B/AmZuuvKxhB5JQRG5LJcS1mTyned2Vc6+khEweHTWbstNoxm/kaZrHWzM/TggNze3FPbP9ZVE1rqkAFFGem5OszW5AzT3sLnu8WLo9T66TH/ABk9FY/GBmRdO+qJy8GdR6mLKud8w9sQsn068y9Nz1UppeT6DHpbk9SCmRRpFCdtowC7oOvGrzO15swov/Ho3FH0Q1d9VR4uxg61JAjfxaB7x7vg/PwWG5tKWIss5wnoMq297eantgV6XIWuD3wHeW4v2xPFuvRpXu/sLyeu0inExfgWl+0CwWqFQKDGAWC0jT9BTdgYuALGqkx16oBfN41JmgjMbiY8yKqtL15CLt7kTPwvsLBqdMZOjuDeByWR4YKZWHaiJDAdVm44+NNmTTlZf9ZeN5F+wrhHhtsVj8H4n0C9UK4YPAnzddeVkz/j+fyBc4PZOHrjlBZilhKotpmBSAy5pgix2p2//A8visQgmEdcA6/0EnP1nv33t+sSYQrmJuL9S66bYuz0AJoDTq5O+4Gq9tMEdYld1ei1q3eoBp1LrzALMnk9vmW1dGB4N/DyfTJ5kF/fP5wtjzEEIHBFJ6UL+ld48OBm8tbT8n+vCwdbnBilDcCRwdjcVXLXBwtoPDkmlLEYVqOthFA0rIl8nhqKGtS1o4R4aHjGgs/plquQmjg8GHwsn0Nfr0xCt9fQNebU7jUNMwKMxM6MBPv/e256XVBBx2dW63Fph1KFFVElfPZLYdRNbyWpWLq61Vxpl0YjiPUETemUqIZ+cL/DBf4FCPi6IQuIoGBVPiQfVMurhZoatNV16Wi8bi30WJZFDfv0rNZhtCKCJvSCXEG6eyfDOrYwS8eF0aFA3I6ORNJaBeHIrIh5plk41Y0m8kGotrqGqzdXMua1ADnkGFr7a7C9nbcgX9OVLKqt4oKSVmoSCz3eu/MTI89C3rNYS1z7NRnpwbUZ4it/Ua7hq3597nQYmpW1AnkU8sZQ0cHQymgFPCyfQRSHks6rP75+hgcMGDhkeGh4rRWPwaIIISjJ3a6NWhSbSdiLKSE58N/KPCbLyWEY3F+4H1LFPYLSC5881Ic31+YsfzXF6/cHl9GoBR0E0jnzVRuThvqLLvIipRfddcM2sx7WNWVG1AhRSfjjoImNFYfAe7e6yeoMUiKpxMdwH7oXrTPGiFZ5tCKCLTqYQ4Anje9vza83Nm94EbvA/+GEiGIrLVM+Oa/j8JRWQylRA3FQ3eMZkVr5OSPk3IJ4ArgMvrMQqnTanpIbJOaqqJpVJ4NIvK/XkEJXK2WZepkeEhGU6mu4E3FXMZd7X+d8VcBpBZ4Lul+yyRszUai1+GOtt6CvDbpSaXW5XFkyPDQ48v5fnljA4G70JVPi+JkeEhPRqL/xl4QTQWv8HxRjk0krYTUajkbS9NCJcsksNRuUsNbXI5OhjMhpPpFwGvMPTcuww9dxxqsb4VSKCa6y244Zy1mE5Yl10Ll7Uormd3r9WRqM8e4KXAE9FY3ETNYitddo4MD1WsAKqG9VoHAvfMdwYbTqYPAN4PvIlZD9oT4WT6UiAxOhicWcxrLxXL0/R7K8xx4sjw0FJmLdaLluenhSLyDuCiaCx+KXAuqj9b3ebyLRRrBtsLUcUeeeC60cHgnc22owxppR+sYU+xtJrZXn3TqArgB1EJ1yWxNFPrNzE6GJwJJ9PvKmanrxAC4fJ17fJISSkp5jIUs9MSeNfoYDA79/mWaPqddVkO9wBHRGNx0aBClsVyEyrp3PFGOTSUthJRViXJScAtI8NDk/Nt32QOB/67WAGxFCyvyxYaWHllJZ6Xcg2A3apwNqB6Jm21bh+Nyq0obZfBElSUiSvrutJBYS9U1/lborH4z6slsYaT6ScDNwiXu8ft7/K4PF6klBh6fkMxl/kI0jw7nEyfPDoYnKjHZ7BA7BbWtJMtTSWcTG8EPgWsF5pLl1IKpOkLJ9N/BN48Ohi8p9bzo7F4D/Bk4KbFNI20fhcBVL7SKtRvZBXqO72DWa8uqF5y21CioySUti9nJM/oYPAb4WRaFDLTXyhkZjyaR9VKmgXdBKkDF48OBr+51P0vkHtQ73M16j23FMcb5dAs2kpEofJ3XKhKEttgueUPwX45WnXFEj9j0Vg8i/J8fX9keOjfsEvgrkYdQFaXXQ7C6idkoVtJ7XMF1u9QVYk90Vj8B3OrB8PJtBv4pebx9Xl7+ndVJwpAC7hx+wLe/OTY0dI0LkN1mG8WgtkBv62i3BPVahHVEq9YOJm+CPiCO9At3L4uhKb5QRVaFDJTJ5nFwt/DyfQJ1cYhRWPxdSjR40Ll9phzHvczK5JWMSuUSpfytPo8ahDvNOpEY5RZsdSQk6zRweDXw8n0d0Ceaxbyx6G+B/8AvtMk7+wDqND64dhARFk43iiHhtM2IsoqvX0G8PdWhAnm4UBUcuWCEyDbnA3W9a4KGauS8BHrshtWuG6A3QXWAPAk1AGodOBdBbweODkai/+EMg+WOOplz5Gaa19vhT4yAELT8HT3evWp8VeHk+n3jg4Gm5WHo9GhwsUuhJPp/YCEp7tPuH2B3R7T3B68vQNufWpnr1ksfBU4fe7zrbL8c1HJ0b8FjrMGmJcLpfIdF1AiaRwVfru17O+dQM6q1n0IOHBkeOif9XmntbHE0hXNeK25WJ6fB1H5lI3ukbYgHG+UQzNoGxGFOqOQNLYL91I5HOWm39pqQ5rEBtRZ54LOOC2vUqnqbzestg5rmT1jHEOdwR+CasngBvDmJ84q9u2NKGsqORfN7QWhFZDmy4CvLuYNLQMnnFeZZtrxVqG5Ci6vv2InfyEE7kCPW5/aeeobP7fllLXbbp9i1pu0HyqHSkN5LsKo7/a4dXkUuK3s73HmyVMqYytKkC23G3i7cDdKsHhsNAjY8UY5NJS2EFHRWLwX1dbgL8vJHWggy2pt0IZsQLU+qEcYywTOQiWx3wDcMDI8tA125Zr0AqsL3t4Xaru6MlVGCIHQNCkNc1Ud7FoodgvndSKnu7x+X62Gk5rbgwBDCu1i4J+oQopxVF+tP6HK/A1USP6GKm09Fss2VHhwtXV7pXMPSpAeSFlrlVbieKMcGk1biChUSwMD1cvEVkRj8TWoypvftNqWJrKBCl6lpWCFPX4DjI0MD43NfQzl4ZsMJ9P/wSg+jRrfWavDsbt34r8HRmM/PB5V7dfoJHO7hfPsZEuTkIH5XlUIgRRacXLVAdet2/rvL889AbAa5T7XuviBX9bBsJJwWkdniKjtKHF6ODYRURaON8qhYdheRFn9l54GXN+MyrclcBhK4N3XakOagdUIcD1z5mQth5HhoYUsuEmzoL/RNAw0V+UhpYaeB6Rcs+0//0a1YNCisfhWVJjhblT1ZL3DKnbwRJXTahHVcKxecQcBhwKH+g96rtTd3iKB6uuZaRggTZ/h9v+zkgfVmnzww2gs/ntUJ+5lMzI8NGNVqq6rx/7sjnVCdA9qTbQNjjfKoZHYXkShzgzzLHPOXQM5HHigDrPo2oUBVBJ9s6ekXw/8S58ef5Kvd8AzNzfKNIoUMpMFEF/9Yvy9X7KqBQ9B/X+OQZ2J5qOx+H0oQXVPndpk2M0TZRfqOe5EA/bGEk3A/qjPfSdwr1efGc4VC981iwU0d+XJ0KrhJPcwT05lAxr4bkWddHQK9wDHR2PxATs1Q2bWG/Vs4GcttsVhBWFrERWNxVcDx6I66dpOpFhVZwehKno6hT0q85rB6GBQhpPpl0ij+MfcxPb93b4ur+bxAhJDz5tGPitRs7reB7uqBW8DbrNyq/ZCCarDgTMBYY24KXmpHl6il8oOieUrLpxnVceVRNPBqOq4PMrj+wvgvlL4N5xMC+Cc/NT4S329q7zlQqrUcNLIZyTw3tHBYLM/n23MjuTpBO5jdpD6TS22ZRdl3qjnR2PxPzneKId6YWsRBZyMmgBumx/jHA5CfYad0toAlIiaHhkeakpn8HJGB4OPhpPp45DyTcXczLvIzRyMEg03obq1bxkdDO4hhKzcqtK4mz9aXqpDUYLqWNTZaT4ai9/LrJdqaoFmOeG8OjA3RIfKM5SoZq9/Q00CeKRSKM4S2OcizWR+cuxVmtuja26PVzVizemoMYZvGh0MtiIfZhuqQk+rUyGGrRkZHspbrR0Ox37rtuONcqg7thVRVqLnU4Ff2qhcdi6HM9swslOoW1L5UhgdDE4CXwC+YI34kKODwUUdnCwv1b+Bf1teqr2Z9VKFUV6qx9ndS1XtNZxw3hKoEaIbR4WEfgvcv9A8yNHBYA44O5xMh8xi4XyzWHgSynP1K+Bbo4PBVoWWyiv0trfIhmZzD6rXm7tOVY51wfFGOTQC24ioVEIcgyqP9QP3d2nvNjJm/ySq667tsA6+hwN3dlBrA1Ai6j+tNgKgktdpsVj/u0etyx+isXgXs16q41EVPbk5XqryZq92COeVYxdb9rDDKhIpiaZDmA3R3Y+qhrsXNXtxye9hdDCYAt6+1Oc3gPIKvU4SUacCB2C/ghvHG+VQV1ouolIJcTjwbeAEl0ZOE4iigfbytV9korj2awOeJwwYarWZlViLatjXMaE8K+QyQAs9UY3G6kOWBtJl3pKSl+plKC/VY1iCCuU9aXWYxk6eqF22lOUMloTTWpS4egT4O7MhupXciHIGyKCSy21x8tEEngCmUHlRthJRjjfKod60VESlEuIQ4K9eN329AXC71BBbKSGrG2jZJy4EssD/tNLOKhyBGv/wQIvtaCalKqMVK6LKsUJ4pVE211ujh0peqhNQlaPPAmQ0Fv8rykuVb4GptkgsL0vgPwE1vmcvVChrHCWYrkOF6LKtsrHZWGX/2+iQNgewR6uDX7fango43iiHutFqT9TnPS76VnXjLm82LAR0+cCl4Rqf4X2phNgUisi69SWqE4ejDgi2ifk3gQ0or0unhCV2w0qm/xfwL8tLtQ+q8mof4GzAsFoo3IEK87ZixmNTRZQ1fPsg4EjUicXx1uW7qHykZYfoVgDbUDlfncQ9wLHRWLy/CQ1vF4XjjXKoJy0TUamE2Bc4o9uPVm1ag88Dbhd60eAdwIXNtG8uqYR4NnARKm/L88p1PdNTxdVfTyUu6Q5FZNMr1VrEBtQk+k4SjhWxvFQPR2PxG1CeluuAo6zLGcAZ0Vj8YZSgumNkeKiRk+2bGs6zPHKHo0TTYYAX9RncAdyMEk4/b/B7bie2oQRFR1ToWdyHEvSHAbe02JZK7OaNSiWECzBDEdnJYt9hCbTSE/V0wPS6qTkPze/BO21wSpNs2oNUQgjgM8B7vW4Kfi8eAXQVp7u69On3SXh1KiGeF4rIR1plYxNpaWWeTelC5fWMo6bX/9VKTj8CJaieB5xmhXTusC6P1tkz09BwnhWmW8ust6nkVXkENe/wLtQsRRmNxTcAL0AljTsoShV6AyxwaHe7MzI8lLVOImwpokaGh/ThD781dUTXTe9OJS75Cuo7LVMJ8WdU9e8PQxHZKYLXYRm0UkS5BMgaM0MBFdpDLUCt4iIgsqobfB52dfHze6Hbj2fnDAcWDX6bSoinhCJyxSbIWgfSDagDpsMsXajE4V1YyekpIBWNxT2oPKqjmK32m4zG4neiBNUDdkysjsbiLlR1VUk4rUblAN4LjKIGblcKV5ZaEjgiapat1vV6OkREpRLCd3L/kQet9jwxmEpc8jlUbusPgK+FIrLlyeaphNj/xWu4XAixb5cPt9cNUiJyBU7K6TwT+FEqIV4bisiO97o71KaVIurfEjyFInhqWJEvUERNXW86qYTwAB/u8ePyVZgmoWmwqhvP9kmOQM1qG22yic2kH/DheKJ2YeVFBVAVWBWxepzdAdxhbX8As2G/E1DtE+62tllqYnpdPFFWE9LDUMLpMFS7kSngTlQLggcW0LOtlDTuX6odK5AZ1Oeyjg6o0EslxP7Adfv77zwo4MXldiFUsRARwySaSoi3hSLy6y20TwN+7XGxz6oe6dbKfj0+D1qXD3ZO8TIJ/wd8oFV2OrQHLRNRoYi8I5UQN87kObHfVTkvqmiAXsQFfKnpBipOBVYHvNU3cGng9yBzBd7CChVRqYQIHOA7+4iH80dqJm5HRM0SQAmYzHwbwq48qgeAB6Kx+LUoz15JUAVZZGL6xvMuEMCpQoiolPL5gCaE9tjG8y44ALhq05WXzdt13RqtdKR1OQDVsuExVGjyLuCxRYYeC6iB3I4nyqKTKvRSCeEHrvO4OHBVN+7yEZddPrxZHaayXJ5KiCdCEdmKDvKg8lqP6O9G0yocdzwu6O3CM5nh4lRC/F8oIltRIOLQJrS6Ou89+QJ/nM4huv2I8i+0XoSJGXRUiewNLbJvH02ga1rts2q3CxeFlTUfy8oFeynwXuB5z121BVNqBSHMNanEJYlQRHZMf6wadFvXiy4ssITJ49bl+mgsPoASMgtKTLcE1FeAt3m9PsPn97uFEBQKhX2zmZnPSinfs/G8C5636crLHip/nuUN24/ZMN06oIhqePkL4K7lDGa2BEMWR0TthovCjtWex45OJcSBwOOhiGxFK4xm8CrgoLkCCmarrosGZHU+BrRKRG30eZCuGtm4fg9MgVuqCQabm2aZQ9vRUhEVisi/phLixZk838/k6fF5cGkCUTDQiwZe4EfAG1tYMTEtJS4pd+VmVcRU1i35wGM3LAH1WeBdfo/K/9I0KBqmJ5PnLUWD81IJ8eJQRF7fYlNbTZd1vSBPVC2sifeVEtNPoUJiOmrQ8ltWDawRXq931+/Y5/PT1dXtnRgf269QKPx643kXPHn9hr3dqLysI1FVdV0o4XcXqqrw3joP+M7hhPMASCVEF3DRa9Zr79WEuQ4YBqZSCfE14HOhiHystRbWnQsDXlxzBVQ5XT5EVueYVEIEQxGZbp5pu9jPrdXOsxUCNA3DMHcNXHdwqEirPVGEIvJ3qYTYa6yw19vNgutNA+7HH3IJ4z/AN0IReUeLzfuNBPIFJSQqYcX6C8D3mmlYgzkPuHigG81blgvmcalqyaksMqvz81RCHBqKyMdbZmXrKXmili2iypmTmO5FjUg5Cnga8BzTNGdAfLint9ft9e75xdQ0jf5VA57t27YeHujq/gywE1WcsRVVKXUXVYb51gnHEwWkEqIPuF4IntznN72lvEq9SG8mz8WGycZUQjx7hXl1D/a4arfccCv5YqD6i7VCRG03TCQ1WoNICaZEA2zV48rBfrRcRAGEIjJvNT/rAT5ul14qoYgcSyVEcirL671uvHPPrqSE6RxSSgrAppYYWWcsL1Ss24fLWyGZXgjoDSDyBVym5M3Ax5tto43oQjUfXdCQ3KVgeYh2S0yfnp58A8guv7+6TtE0Fz6/Hz2ffx69XIgK0zVrCK8johRfd2k8eaAHb3noyO2CgBfv+Ayr9SK/TCXEESuonD5nzhM3sOIKGrNFCM3mu7kCZ/ZKXJVyokClk0gloloVcnRoE2r2aGoya4AxuwioMiKm5PYdU+iZPJimWgT0AozPYGTyFIFXhCJypZyxHAMcGvBV38DKbfABb2qWUTalC8g0qxv3yPCQOTI89EAum31M0zRdqxUzAdwut2YYBiPDQ39rooACJ5xXaib8yt7A7gKqhBDQ14Ub5WU8vcnmNZIfZHX0WgkYORU4zgB/aY5Je/BDYNtkBqOSnYYJkxl04NuhiNy25xYODrPYTUTZrodKKCKngOeYks9OZRnfNglbJ2DnDFIv8ivgpFBE2nE+1FJZA8hqZ2glrAPDmsabY2u6WUJSeR2YklK65DypgqZpArKZ4qmE44mCszRBwVvD1+/SwOfGBF7TNKsaz2WGiSdXJcPOMGE6hw5cHorIuobBF0ooInXgxfkCM2PT6Fld2VU0YCYHO6bQTcmtwDtbYZ9De+GIqAUQisjpUET+L7DXjRPh4Vunn/c+YL9QRJ4RisibW21fnRkDxHwueUP5C1txgLYTezTabBK/klLKfL56FFFKSS6XLaBm2DUbR0TBKk2bv5mwphKc1zbFoiYQish7gQsns8jJDLJotZGVErJ5GFMC5Tbgwy22MwUcWzT45mSG3PZJ2DEFUzmxVUqGgJOd1gYOC8EWIsoaYroKm4qoEqGIzN+bO+6x9Mzz/hWKyEdbbU+DuBV4IFujAFtKyOTRgauaZZRNaYknatOVl+0ENk1PTeqGsWezcykl01OTppQyS2vKs3M4Imq7YaLNV1dsmBRRfblWDKGI/BrwiqzObTum4IlxzK0TyMksM6bkK8Bz7TBvNBSR94Ui8gJgbcboefK1Y+d94Xtb3/+SUER+MhSRrcrXcmgzbCGiUCMlBLC91YYsAB+wUnu8YCW4fmomj6FXGHhQSqY3JSZwRbPtsxmt8kQBvNs0zX+NjW3XMzPTGIaBaZrk8znGd44Vs9mMDpy56crLWnE2nQXc1slRp/IDKdEq/YZKGOauZsLfbppVTSIUkT8BngqEbpt51pdvmzkpDmwIReS77ebhCUXkzEnvnbp9W+GAhwrS399qexzaC7uIqFJuja09URZeVrCIsvgacMXOaYzJDKZeVPkCOR12TlOwvFAvW8HeuIXSTYtElCWOTpam+YnpmenxHdu3sn3bE0yM7zQLBf2HwAmbrrzsj62wjdmqq471RoUicitw1WQGvVhhMqIpYXyGAvAvoFX/p4YSikgZishb/zl92s3/nD79djt4n+ZhDHVC7+CwYOxyprgGFQJo1Vn9grBKzL1APRsT2o5QRMpUQrwduC6r856szjOsh3TUWfNnQxF5W+ssbD3WQOZS08qWsOnKyzJA/D3vH7q+UNBfLaV0uV3ufydG/q9VY5JKlA8hnnf0zArmnabk4B1TPDfgxeX3qr5EehGyeXRT8jDw0hY2E24WBaBCwxTbMQbs1WojHNoLu4iotcCOZpWKL4NSZ8OV7onCWti3AFs+9qF3vMYt9ANevObrl4YismE9kdqFVEIc/pp1ntPuzx1zYkCbfjSVuOSWVvb50TTN9Pn8pVLslodK+lzbdE2YPft679o/lRDbV1APpEURishcKiFeBLwuq/PurM5TrYceBr4AXLGCWqPUosBsd387sxM4utVGOLQXdhFRa2iPfKiSiFrRnqi5TBjrdWB7pwuoVEIcisoDO8XnKuSP7L5Fk1K+GPhIKiHeF4rIVlTCwe6dl1t2IpJKiLXAxeG1vAMVFnkv8EgqIS4Fvmy3XJhmEIrIAvAt4Fsf+mD0ZFO6nvOJT3zq/1psVrNpJ09UIBqLB0aGh5zEcocFYaecqHbIhyq1oFzxnqg5eFALYcdiCaibPG6es7oH1vbhW98vPWv7EN0+9ge+k0qIt7bIvHkK6RtPKiH2B/6hCd7fG2D1ml5Y0ws9fvYVgo8Cf04lxECr7WwlObM3r8suu3vbG0GR9hFR4ORFOSyClosoa9hqF+0hojrSE4VaAGvUGXUEl3tc9A504/a4ZwdSuzToCahROMBXUwnRioGlLfVEWaOCfupxsdeaPrxdPjXaxO2Cbj+s7cXr0jgKpyWGAbUH365Q2sUTVep754gohwXTchHF7Be2HUSU44nqQFIJcRjw/J4A7mrNEwNe0AQG8OZm2mbR6nDes4Bj+rvwVOp0r2nQ14UXOCOVEIc02zgbYQCaVZTQSRSwT+pIVUaGh0rFTR3tMXVYHHYQUaVuvY6Isi9uOlhEASdrgrynhg9BCPB78QIvappVZS9fdrsVIuo1HjcFV43Px+MCl4YOvKppVtmPUrODTvNGtYsnCpw2Bw6LxA4iag0wMTI81A4H6U4O57XD/6dReGD+ER7Ww97aWzWEVouo1S6t9kFSCNA0BJ19gOpUEdUuOVHgiCiHRWIXEdUOXihQnihjZHio0/KDOj0n6k5T4jPmKdTXi+hAuikW7U6rRdR2w6gtsqUEw0DSHlW4jaJTRVQB8LRJGHMnjohyWASOiFocK77RZhU63RP1B+ChTI0gbqEIBQMvcFmzjCqj1SJqc8HAU6kzd4lCEUyJF/he06yyH50soqA93vcY0BONxVvhUXZoQ1qa7GedmawB/rnUfYST6QDwalSuxSrgAeBK4PrRwWC9Dygrem5eDTo6JyoUkWYqIaKZPN9zaYiAd7Y6D5RAGJ9BB34eishbWmaoohUi6u/A3yYyHDvQjVebc2pmmDCRQQdGQxH5UAvsswudLqLawaNdanMwADzRSkMc2oNWe6L6UQfoJbn4w8n0s4BHQHzd5Qu81O3vfrbm8Z4D/A64OZxM17vcvBPm5lWi0z1RhCLy+8Cbp7IUt0+iT2VhOgtjUxTGpsGU/Bx4XYvMa6knyupu//KiwUPbp9Cnc0pY6kWYysKOSQqmJAWc12zbbEaniqiScGqHvCinV5TDomi1iFry4OFwMv0U4LcuX6DfP7DO7e3uE56uHny9A25f/1ohXO4g8DvLU1UvfHRYOM/yFrqx/xlkwwlF5DeBfUzJR8ay3f/anu29r2DwLeD4UESeFYrIVnU5bnU4j1BEPg48TUo+NJPjkbFp2DkNmTx3S4gAJ4cispPn6EHniqhyT5TdyaDWeEdEOSyIVvfuWINaWJYyP+oSze1xe7p6NTGnbEpzufD1Dnhy49uPAHkO8M062AqdGc4rLXwd7YkqEYrIbcCnorH4bcA+I8NDl7faJmwgogCsOXCfSSXEyI+2vet8EFOvWJf4TgcM2F0onS6iGnK8CSfTBwNnAj3Ao8APRweDk0vZ18jwkIzG4mM4vaIcFkirRdRaYGxkeGhRA0rDyfQ64OVuf7drroAqITQNly/gNvKZi6mfiGpqOM9aHF6NOisaA743Ohi8v1mvb1H6jjgianc0WihY5mCrqqdQRMqrY/EcoDsCajc6XUTV1RNlHQeuBF6K0HShaVKahgspvxpOphPAh0YHgzXKHaritDlwWDCtFlH7AMVoLL4/6gfmLrt2V7jPA7jXrjniSds3PMWleWoXULg8HmHkOTIai2uLFWpV8AFLOsNZDOFkuh81tPRlQnPpQnMJaRpSmsZwOJkeBd4wOhhs1vR3xxNVGQHU4ztVD2zhiZqDXeywEy0VUda6si8qXHXf6GCwWd/fuudEhZPp1cCNwuU+wNPVKzS3xyeEQEqJoec8hZmpKMj9wsn0xiUUGI0BT6mXrQ4rm5aJKCvX5jxUPtTeFTaRqB9fwbredVszdNU5XMrdy6Tm7kBKhDQ14EPRWHwn6sdRui5dxhfR96nhLQ7CyXQX8HuhuZ7s6e7bbXEwiwUKM5Mvlqbx+3Ay/ezRwWCmkbZYlBa+js+JmoNdPVF2sclhT1oiosLJ9JOAGPAaZn/PD4eT6S8CXxwdDDbau94IT9QHheba39c74BFl5aBCCNy+AJrL7c5Pjp0LXA1cu8h97wT6o7G4a2R4aCmeLIcOopWeqNXAn4CfAf9hjlBCNbWseEAIJ9N+4D2Gnutz+7uqvoCh54rCNP4I/NJ6vdXAwcBxzL53GY3FJ6gssHaODA+Vi6Zl5URZwvGtwL3A9VV+oOcjxFN8fQMeoc2utUIIXB4vWt+ANzex48lIeT6QWKoti8DxRFXG8UQ5LJami6hwMv1s4Dea2+Ny+7s8mtuLlCaGnt+vmJv5OFKeGU6mTx8dDOYaaEZdc6KsE83z3YFur5jbT8NCc3vQPD7TLOQvZvEiagz1m1pF+/QwdGgRrRRRBwPTwN9GhocWJUxGB4O5cDL9tWJu5l0ur7/iD8ko6JgF3YXL86mR4aGbyh+zxEwvs8KqdNkXCFI2uiMai08xK65OBgxLdBVRi6JRdnvudaX70sBpwKHRWPyHI8NDu9o7hJNpAbzL7e/aTUCVIzQXbn+Xt5idiYST6S80oBfWXJycqMoI7CNY7CqibJWrZQOaKqLCyXQv8HOXL+AtL8ARaGgBNy6v35OfHDsRaX4SVUFZkWgsvhcqd3WpXvi6eaKisbjwHPbCYwve7h6Xx1dzW5fX7zYL+eeUPdcHnAjkRoaH/l7jqeVtDhwR5VCTVoqog4BHFyugyvi4NM0z85Njh3i6er2ax8uumHg+SyEzVUTlFV0394mWh2vSujxQ/pglsLrYU2DthfJgFVle0qG09n8W8IpoLP5HVFlt8SBvj++Bw04/aN7FweOjmJ05UBiFAWZ/8I3C8URVxgnn1cYudtiJZnuiXo8QgUoVzKCqmD1dPd7CzOT54WT6w6ODwd1aUERjcT9qoHYIuAa4Y4l2mKjvQ0URFY3FXag1sRtVYddd6/aarbfv//h+J9RM5QDrYWn6o7H4B1C/16ei1u+/RGNxE5hi9jiQKYt8TLL8dd6hQ2iJiLKEysHAP5a6j9HB4EQ4mT5JmsZl+vT4KxHCEEIzpWm4gRzwKeATi/XUWD+kGevy3zKb90EJqStQZbQa6vNzlV27Ktw397HVwHOBR4D7Ud2eBeA2XJ5Vi7H1wPt//55o7KePoVpETKB+/BPlf9dhzp+TE1UZJ5znsFiaLaJe6/IGPNUqmAFcXj+FmUlPYGbbm6Kx+K+Z/S7tD5yK+v3/CXBHY/Gg9ZiocF3pvvLHngJMRWPxdewpkCrlZOSZXYengYdLt4U03MCbzILucnmrn3AaBV0KKe8GbrDez5NRn/0A8BJ275NoWFGHSZS4OgzYBvyt6gs4ONA6T1Tph7Sscv3RweBO4DXhZHofpHyJlEYvSpz8dHQwWO/GhxtQB6itltAqhesWjDWPKYoKD149Mjx0T/nj4WRaAxJGQd+guat7vo2CDlLucBdzv0SFJftRyflHoT7X8tecprrImgBmquWeWbTcE2WVMr8G9R6ngB+PDgaXelZcL+zkiSrHTjbZJpwXTqZFE0Lf81FXEWWdjPpQa0AvSpjsuq0decYhQuupuQ8hBEII6cuNv4DdPS/HAX3A3agUh2Cl5y8AaV1OQImlHLPC6HF2F0ql2zMjw0M115twMv39Ym7mlZrH664kEqVpYOSzBprrUyPDQ38GsETiq4CbgRRqreyzLr1zbq8Fjl/ie3boIFolog5GLSj/nW/DhTA6GHwU+Ho99lWDvYAd8/24azEyPKRHY/HvAA9X2s/oYNAMJ9OXFnOZj7h9gYq5XtI0KeYyOkJ8/nMf/+Cf5z4ejcU9qIWgv+y6dDnMui5XaKUcr0oCawLwW9vVRURZC/8BwH/nazsRTqa9wOeB8xGaqblcUpomVquH3wOvGx0MPlYPu5aA44mqTcvtCCfTzwMuBl4M+MLJ9CPAV4ArRgeDSxo1tRxGhofMaCwumUdEWb8RP1XEUdntXvZcw3MoQTKlmcY2aRT3psZkCmmaSCm1qf79r1r/RPpaZv9v3ahQ3pHAncDPrX1Tto2cc3vX9dwTs2gs/gCQHxke+m6t974ILjGLhTMKM5Oap6tXK18rTaOIPjWuA7dRNvB6ZHhoDChvjjtlXR6Zu/NoLH43cIpToecwH60UURWFhI3ZQB0GUo4MD83nffsy0nxzfmrnft6efo/mmv0XmUYRfXqigDRLB4NK+y+gkiErJkRaC3SAyiKrVL3Yy+yBOYQ6K91uubunrcvUnOtpVMLmfAfPAPAG4IFoLP79keGhim0aLK/c9xDiJd7uPrfm8VE64zSLBfSZyWdLo/jXcDL9tNHB4LZ5XrMRaCzSE9lA7CiiWoZVoPFJ4H2ax2e4fX43QmAWi/sVc5lLkGYknEyfMjoYvL3WfqKx+AbgacC1dQiLl357LmBdNBY/jOriqIc91+Yss7+3nagT0JIIKN0/Vb6mhpPpHHru29LspVoVm6HnACYNt/9ncxLHM9FY/GpUGO50YN+R4aH/LOPtbwUOX8bzd2N0MHhHOJl+nqHnfmboubUur18gNE0ahYJZLHiAm4CXLaPq8EHUyebeqFCig0NFmi6iorG4hkoq/2uzX3upWIvfBuDGRr/W6GBwPJxMP1saxR/nJ3acoLk9BaG5PNI0SovDrajFYedS9m+JnIx1qejFsRI9S+7tM1FeqHtQi3sfqklqDyqUUE7RCh/OJ7aSwNnAW6Ox+HdGhoe2VjDjTOAMX99qV7mQBFW+7Osb8OQnxvaSphED3rOoD6E+OJ4o+/JW4L3e3lXC5fHt+vK4PD7c/i6vPj2+xizovwsn04eNDgZnKu0gGos/BXgZajh61f+z5fntnnPpqXBf6fIWVIVYaS3JMPv72IE6eM8VR9NLPOH8EfCwPj2xr7d31R5hL7OolwpwPjk6GNyj8s5aK9LWZblsA06MxuLueghSgNHB4M3hZHp/4OWGnjsL1ZLgIdSEir8tM3z7OGrdOwBHRDnUoBWeqA0oV3Wzx5csh16UB2XZnqiFMDoYfDScTJ8IPN0sFl4LhbWoxfw7wN8bndthua/HgfFoLP4o8KuR4aFfzd3OyvEqnUH3zLndi1qASgeUciTqwBQCTorG4r9ELX6zYuvol7/H5esScwVUCSE03IFub2Fm8q3hZPpDTWo8Wo6dcqJsk3s0h6bbZXkwP+QOdLsqVbkKIfD2rHLldm5bY83V/Eb549ZJ3ktRxR/3ohKLT4jG4tVEUqWxCRnK8ntQv93S7XUoL8lPUOKoYQUbo4NBPZxMn2oW9T/kxrevdfu7vJrbA1Ji6FnD0PMCJThGGmVDGdtQ34c11HEdHR0MFoAt1qVujAwPGdFY/GHUGvaXeu7bYWXRChF1MErh7xGHtjEbrOumiCgASyj9jdZXh/RTZUC05f4vNSatiuXZ6mZWYK0FnokKh0nUgWXAeqyUL/JMl9dXNZcDlGehoJ5zBCpRtJk4nqjatMqOZwL7uX2BqhsIIXD5/G4yE9FoLD7O7p6iI6zLTpQYejmqMrVcFG1DtUaZqXDJ1MqhsTxcMyPDQ+PLeI8LZnQweE84mQ4izTcXs9MXAfuhfnfXAV8AftmkhPtSyH09TVxHl8lDKAEtFpCm4NChtEpEPdTIM7AGsAGVVNmseXV2op9lCl7roDIJTEZj8SNRZ/kC5QW4sdQrrCxfqxehfWDeHVvSYd1jqRdGYz9chVqot6EKABqdr+Q027QZ0Vjc6z3k1KN0f19RaK6ajR01l1sYQtuAEvbl3qK/AceiUg6mUNMObq/jQXQKFRJvGqODwTHgM8BnLE+dbHal4sjwUNbKqVzXzNddJg+hGiyvZVYEOjjsRlNFlOWROBDVt6Od2At4otPORixR00d9xaNAhTNuHBke2i0fpTxfK5xM/9so6Me5vP6qISFTtXoodk8/MYkqoS6FDc1oLL6DWVFVLq7qJd7tGs6zi00NoawZ7lrUAXlt2e3+/p33HbJt75BbShMhqjsypWliau6HR4aHvlXh4RusvnCno3L3fgrcUqe3MImajNASmjh0uBLbaC8R9TDK23wAjohyqEKzPVH7oHII2ikfCpQnqt1srgel8FrdRNTI8NAdLKzz8ReNfPYbMtDtrjQCR0pJITtTQIhvf/Gj0a8CRGPxLtQivQ4VNliH6vVSapZjRmPxMWZF1VaWLq6ccN78LDknyhJLq6gslkqxOhMVdtuOSn7e7s+NTwFhI5/rrzZXU0pJMZ/VgW9Xe/2R4aFHo7H4VagmjUsq4qjCFNDXoSGibcChrTZioYwMD+WjsfjjKBFVLxHtsMJotog6GNWJ9tEmv+6SicbiblQyZNtUE9aRfuu6FWHM7wIX5Sd3PtXb0+8tbz4qTQN9ZqoojWIG+FjpfqtdwoPWZRdzxFXpciwqlANqCHVJXJWE1TZgew1x5XiiarMgO8p+X3PF0lp2n9u43brcU3Z7rNL/J5xMX1rITr9f83g9cwsTpJQUs9MSaZrAlbVss0TOQwt5H4tgCvW+/Ki2BZ3EVlSOUd0q9JrAQ6heWQ4OFWmFiHpwviaLNmMd6oDZLsmQ9aSUu9F0ETU6GMyHk+nTpGlsyU+OnSpcbl1ze7zSNAyzoAtUntYZo4PB++bbVw1xFWDh4qr8sh17eaLKsYuI2g3rsy73JpVuDzArAku5SQ+jCgW2oz7vyUV6bT6GlE/PT4yd4g50eVxeP0JomMUCxVymaBZ1CZzVov5ik9Z1L50norah1tK6Vug1mIeAZ0Rj8b6R4aHJebd26DiaJqKsM879gd816zXrxK5xL602pAX0AzqznYqbyuhgcBw4LZxMHyON4kbDKO6HEnQ/BH693PyOkeGhLGqR3M3bYA1enRsWPIZZUSmBM4B7o7F4BnVAeALlGWmFsLKNJ8pqBbAeeBYQsD7LtcyGVCWqfcZ2VFi35FXaXq3x6mKxSvvPAPnOYnYmUszOHGA9ZACjwMdHB4NLntu5TEpDfvvovDWlJFrX0V4iClRI79+tNMTBnjTTE7Wf9Xrtllu0Adg5p5tvp9APTLQ6d2N0MHgr8N5mvd7I8FAO1RF6t7FEZYJgPaqTdRbVzb0kEIrRWHwr6gBRun5ibgJ9vdH1/IBRLB6EEKbH4/HP/4zlU+bFW192Kc3EBJXor6Oq2x5gViwta3TSQrH6B30+nEx/ATXuyA88MjoYrNjJv4lMW9e9NbdagZRV6K1vtS0LZWR4aNoqUnFElENFmimiDkYddNrlDKTEXrSfzfWiao+oTsQSVw8DD0dj8T8AN40MD/2hzPuyoewSxPp9WV3cS96qkrjatty8kI3nXRAC/g81kb7kjTp343kXXAl8ZNOVly17Plw0Fvexu1gq3S6JABPVaXsrSixttS7/BrpHhofq2gRxsVjeyrtaaUM5I8NDRct72XEiyqLdKvRAeaMOmHcrh46k2SLqgVZ7NRZD2biXVje8bBX9VBkN44APVSSB5Wm6nzIvq9X5ejW7i6ujgZOsTUptGOaKqwV5/jaed8FzgN94vT53V3e38HhU4+x8LuebmZl6s2EYL9543gUnbrrysgWFjKzu8yUvW7loKhUXSFRT1W3AP5kVSxV7ckVjcR2V7+SwJ5N0tohqmwo9i4eAUDQW91snUg4Ou2iKiLIW6P2APUaH2JweVE+aTvZELaQdQUdh9TvzYImoSli5UaUQ1q5Bt5ZnpyRQSuKqFG4CyEdj8bnC6olSQ1KAjedd4Ad+Egh0eXp6+7TymWj+QACvz+cd37ljn2KxeCUqd6vcdjeVxdIqZr1Z49Zrp5mtVty+yDBcAfUZOexJ0xtu2oh2rdATqJzeu1tsi4PNaJYn6gBUVUY75kNBB4qossGqTjhvT0rz0hZ9VmqJod3yrcqampYLqwNRPa40a5txLEHl8XhOLBSKvT29vdrcobIAmqbR09vnHd859pK3X/y+U7u6ewxmRdMaZsXSJOqg9h/K2jvUKf/PEVHVmUKlCXQi7VihN4bKZTsAR0Q5zKFZIuog1Jdw2TkaTWYDytsw3mI7WkHpTNkp692T0mTbqp6oxWCF7yasy65Feo7XqCSujpWSjX6/31WrI7fH40XTNMMwjHcDv0cdvO4FbmRWLDUyNKHjiKhqTAKHt9qIFtF2FXojw0MyGos7eVEOFWmWiDoYuL+d8qEsNgBb29DuetDKRpt2Z1forZEvYoU7Hrcuu9j45gvP8Hq9R9V6rhACoWnFbC77p699+XMjjbSzCo4nqjpTQE80FtfarGfesrEq9KZpz+TyU9ssDOnQBKqfytYJqyx8H9ovlAdOZR44nqhK1NUTtWikvKdQLNTMT5JSYhiGGylb9bsrAB4rVOmwO1OokGrPfBuuULbSRm0OLB5COR32abUhDvai4SIKldshaDMRVRZKeXy+bVco/cC0c9ZVkdaKKLiyoOueYrH6vyaXzYKUOVRzyVZQQK0vzVhj2o1Sw81OrtBrN0/U46gQtRPSc9iNui9wqYQYGP3SMZe/88qrtoeT6eJdR7/i9nuPeOlb7zr6FS8LJ9N7TpK1L2vp3HEv4PSIqkWrRdRfgRsmxsd0w9ijuwC6rjM1NVEEPrnpysvq0gV8CZQ8Zd6aW3Um5aNfOpFtwGrrRLUtsMKu/8URUQ5zqKuISiXEAUDqgOK/3vqq6dgab3efy9s7oInuVfsgxBXAt9pISJUq8zptNEMJR0RVx4dqMtnwztuV2HTlZRJ4mWEY/9qxfWtxcnLczGWzZLMZxneOFcZ37gC4AvhEK+yzKH02Tl7UnmRQI2g6uc1BqY9aO/EQsL8TonYop24iKpUQbuDXHhd7r+mFfvNxDs7/GZfXh6e7D1/fajeIc4BP1+s1600qIfyphBhMJcQ3X7428bmT+7/z9NdvuKTd3M71og9HRFXDD+RbWXCw6crLdqLm071O1/X7pqYmctNTk5lisfBH4DnAOyyx1SocEVUF63szTWd7oqA986JK444cHID6Vue9AjhsVTcuTQOvR8gTxq/gob5TBYDm9uDt6XPr0xMXh5PpT7ZognpVUgnxEmAz0O3zoPm941qfe7xgSh5MJcSXgPeEInLP2MkKxDrTcjxR1dnVrbyVbLryMh34XjQW7wf2te7+1cjw0F9baFaJUq8pR0RVpmO7lrdxhd7DKA/0gXRuhMJhDvUM553l8yA0a489XlMcnv+D6M4/tGsDzeMDISTwwjq+7rJJJcTzgdEuH/3r+nGv6kbr74K1fXhWdaMJuBD4cqvtbCIB1MHPEVGVsYWIKsOO4QXHE1WbKTpURKUS4sgXDnzjBWet/ewXUgnx81RCvDeVELYP7Vkd+x/Ne3uPCifTA+FkOtBqmxxaTz1F1N4ubXZ/HjcIzSWP3fnNXRsIIRBCGKhRKrYglRACuDTgResNgFZ2OBICfB5Y1Y0HeFsqIY5ulZ3NIpUQfc/t/+4JGzz3rw5ok1PzP6MjsbOIsktPM0dE1abjRr+kEsKTSohvAHfs5f/vC9Z2TQUDXl4iBJ8AHkslxJtabWM1Ugkhbkl4XnfU/rd+6pFDn7MJ1cV8KpxMj4aT6VCLzXNoIfUUUWOmnF3AhYBeX1E8bfpqhKmON1JKpJQaLUrIrcKJwJO6fNXP5r0ecLvQUR6pFUkqIY5KJcQmYPsB/v9cf9rqqy565brP3ZRKiFgqIfzz7qCz8LGEkS8NxBFRbUQqIQZOG/jmaS9YddW5qYT4TCohXpRK1Gg/v3K4TMDgQI/y8vcGoK8L1vXh7Q3gBb6RSohXt9rIuVgn2l92UbzqOP0nq58q/4CvbzXenlUuzeN9MfDXcDJ9cqvtdGgN9fzh/jSvUzTLlnC/F3xymsPHVasas1gAKT3Ab+v4usvlGE2Qc89TM+hz4wVOaIpFTSaVEM8EbvG4OKe/C8+6PljbCz1+9hKCS4DfpxLCNt5DG+B4oubHaXEwh1RCiFRCXAI8vpfvwXce2H3/iR43FwO/AO63focrEsuLf96qHjzeOZm4QkCXD7rVieznUglhtwrutwHnD/Tg6vaaPGPq61Jze3B5fXh7VrldvoAHuDacTB/cakMdmk89RdR3JGyfzGBIaxnXBAS8Up44ebk0jSL69EQB+PboYPC/NffUXEwWnlOy4kY0WOLo534v/oEePH4vaBq4XNDthzW9eDXBccDnWm2rjfDjiKj5cDxRe/Jp4EN9XXjX9eEZ6MG1ugfv2j6E38t+qJOVp7XayAbxVrcLfa6AKieguq/tDZzWHJPmx/IQXtLjx+V1K7G3V/FOsWHmZkClqHi6ejXhcgvg3S011qEl1E1EhSIyB7woX2BqbJpCTgfDBL9biv0K/xL9Y38rIs0bgPPr9Zp14q+mxFeoUXcnJeQK5IE/Ns2q5vFaAT19ATRRQUq6NLBc7W9MJcSqZhtnUxxP1DxYZfzO/DyLVEIcAURXdeMKeJX3pYRLg74Ams+Dh5VbwHKM113bK+nSwKWhA3bKPX0KsMFvWe52gcvtksft/HpZ6orA7Qt4gZe3xEKHllLXOHwoIv8FhIoG10xk0LdPwkQGCsKfcclCAjhjdDCYredrLpdQRKaBv8/kMGWVw0++AIaJF7ismbY1idf6vbgrCagSPg8I9V15UdOssjeOiFoYjoia5QK3hu6r8mkIAd1+NODpqYR4alMtaw6FautrOdYmdsqZHYDdC456vIYIZn8qfIUds3eqBdQJXXcgdU9mDEXkg6GI3AgM/H7naz/w+52vfZtH5vq+9qZXv89uAqqMC/IF8hMZDKMsYCclZPIwkcEALglF5IMts7BxrNa02uFMIUAIDGBVc0yyPXYTUeU4IsqePNvnrX2Q9bhAE+SB45tkUzP5Xb6AXktIFQ0wTfzADU2zan52AJTn+vo8ak18yvi3d90nTRPsVWzi0CQaNrsoFJGZq2Pxx4FpuzepDEXkP1MJ8dx8gc35AodZlXiaYYBUTQM/Any+xWY2iocNg2OoIahNCabEQ+cOYyaVEAejEkzPee1693rgDanEJV8CrgpF5HhLjbOZJ8oa/3T+WWv7XusWhXwqccnvgK+GIvL2VtvWQhbTy8uOfb+WyzdNycezusormouUMJ3FAP4Zishbm25ddW4DHs7m2a/H6gplVZ5z4uSV3LzmHSA0jHxWB77fSkMdWkOjy2plE16jLoQi8mbgSOB5W3Mbvv1A5og/S3grsD4UkZ8LRRbijG5LvpkrlE6kKpNTvaengV81xyR7kUqI1wB3uzQiPX4OHOguBvr8xcOE4NPA3TYIv9hCRFnVZ/8LPODSiK7tmjxkIJA92u3ifOC2VEJ8zRoP1YncmC/s6uJekaIBpsQH/LNJNjWNUERuB94+lUVOZ6F8vSkaMDGDkS+SA85rlY2VsNb9D83kMfNlQcaAF/rMxzlw+joKM5OGNI0CkGiRmQ4tpNECZzGVby0nFJEyFJF//MXYhd+4fvzcX4ci8qpQRGZabVeD+SnwwPjM7u0pShSKMJWlCIxYxQMdRSohngNs7vHjWtOLr9uvFtCegOpv4/MwAFyXSoi1LTTTFiIKuAj4WH8XYk0vvt6A+pzW9OId6AEBb2LlenTn46tFA2++SraPlDCTwwT+EYrIFSeiAEIR+XXgdTN5Hts2ibltUujbJsjvmIJ8kRTwTCtH1W5sAj49PoM5kVFiyjTB7UIeP3YFhp7LAc8fHQw+3GpDHZpPM0RUW3ii5iBpI/G3HEIRWQROKxg8tn0SfTqnEulzBXV2ODaNCVwNfKLFpraKD/s8yG7/7hVVoP7u78KlCXqBt7TEOsuUststEVFWq4yP9wbQ/N49PyuvG/pV5/93pBJiv1bY2EpCEfkf4EvjMxRzuhJNJUwTprKYuQIG8M5W2dgMQhH5HWB/4My7Z475/VZ93y8Bx4Yi8mk2FVClk+sY8LKczt92zsDYNBQN9GltzW+B40YHg39vtZ0OrcEJ51WmXcXfkghF5P3AU6Xkf2dyPLhzBsZnMHIFfg+8DDgvFJErrkfWfKQSYm/g1C4fVZv/WY0CvbS2m33LRRTwSgGq0LsKXje4NArAm5tmlb14F/C5iQzF7ZPkx2cwd05T3DaJmdXZBpwWisgbW21kowlFpHH1E5f88sbJl//1V2Nv/XYoIlOttmkhhCLyZ6GIPOn7W9/3kh9te9f7BbLrLRf+4LTRweBdrbbNoXU0Oj/BbMJrNIKO8USVsJKjPwt8Nhobeidod40MD/26xWa1mn0BMV83e+vxvRtvTlXsIKKOdLswa7XKEAK8brxZnaOaZ5Z9sE5E3p9KiM+ako0PzRz46i5t8oFe987NwM8sr3CnUDou2LroqBJ52S3zsnu6E08sHfakGSKqHT067Wp3ndCgw0RkFWYApAnVfVG7yp9bmS9mh/9VQS5AwEk1X9Ou7SGaQigitwIj0Vg8APxqZHjoplbb1AJKv6h2FI5u2tNuhwbghPMq03GeqDms1ErExXIn8N/sPK3/sjoF4MdNsKcadvBEXVc08Bs1/Aqm6vxvANc1zSp7o9G5v7WSiGo7TxSOiHIow6nOq4wJEI3F29H2etDpIhLYFX75fCZHoVhlqc/pUCjiBi5tpm1zsIOI+hNw51RudnbmXDLKV5cBvtc0q2yKtbYIVuA8zgXStuE8HBHlUIZTnVeZ0mGgHW2vFx0voiwulXDt2BSFmZyqpJJS9baZysJEBgl8IBSRrQzJtFxEWf10XpcvoE9kMMpnURYNmMwgZ/KYwOs6sVVGBUprS6eKqHYP57Wj+HNoAE44rzKlA1GnColODTHsgZXs+woJQ9M5tm2bhK0TyB1TkMlzG3BOKCI/3WIzWy6iAEIReQtwUr7AzWNTsHUCfeuE0HdMQVbnTuBFoYj8Wavssxml/1mniqh29kS5aE/x59AAmpFY3o5CpLSwtaMArAdOOK8MS0gNpxLiMw/knnzWNv2AMw8L/OOLA54nbrZhJ/uW2mOVqz8jlRDB+zJPuUgIqR3kv+0bwF9t+Fm1ktLa0qmfSbvnRDneVAfACedVw/FEde57r0ooIot/mjg7dWf2xHt/Pnbhf2wkCmzhiSonFJHpP0++6g9/mjj7t6GIvNFGn5VdcMJ5inb06Dg5UQ67cMJ5lSktbJ0sJDr5vS8EO30+thNRFgJ72WMnOl1EtXM4zxFRDrtwqvMq0+mJ5c6Brzp2/GwcEdV+dHpOVLuH89rRbocG4ITzKtPpnignnNde2FVEaXSuSJiPTvdEtXM4z0ksd9iFE86rTKd7osARUfNhp8/HriLK8URVp9MTy51wnsOKwAnnVcZJLHeohh0/G7uKKMcTVR3HE6VwRJRDW+OE8yrjtDjoXAHZjthVRDmeqOp0uogqeaLaUYw4IsphF044rzKd7omCzn7vC8FOn48jotoPJ7Ec5MjwUDu+fyex3GEXbdVsM5xM9wCHohbmu0cHg9l67XsOTmK5QzXs+NnYVUQ54bzqdHpOVFsmZ0djcQ31v2s72x0aQzNE1LI9UeFkej/gg8AbAb9193Q4mb4CGB4dDG5b7mvModMTy51wXptg8yHZjieqOk44rz29Oe1cVejQAGwfzgsn04cD/xAu95s93X1+/6p1+Fetw9Pd1yM01zuAW8LJ9L51sXaWlnmiwsm0CCfTrvm3bCiOiJofu3w+c+2wk2hxPFHV6XQR5aI9RVQ753I5NABbh/PCybQARjW3d8Dbu8otxOyu3L4ALq/Pm5/cuZc0itcAz1m+ubtoqicqnExrwFnAu4CTAC2cTD8IfBH4xuhgcKIZdszBLiLBbthJpFTCTvY5nqjqODlR7SlEHBHlsBt2D+edDBzp6e4T5QKqhBAa3u4+T35y7NnhZDo4OhhML+O1ymlaYnk4mXYD1wAvd3n9wuX1awiBWdQPLOYyw0h5UTiZfu7oYPC/jbalDOfANz92EZl29kQJOlckzEfLcqLCyfQBwNuAc4Ae4FHgcuDq0cHgVJPMaFg4L5xMd6He2wXAgUAG2AJ8bXQweO8yd9/O/a0cGkCjRdQ64FnRWPxM1GI69yKr3G8CpvuwF77N7FplaC5XVTs1twehufLSKJ4F1EtE1SWcF43FNwD+keGhB2ts9nGECPt6B1ya27PrTpfHi9vf5dWnxvc1i4VfWSKxWQckW4TzrLDmoajv6cOjg8HJFpsE9hIpYG8RpWEve+xES8J54WT6NcDVQnMZLl/AJzQNaRTXF/PZLyDlR8LJ9AtGB4O3N8GUhoTzwsn0IcDvQezj8gVcmtstpGli6Nl3ScN4bziZPn90MPiNZbyEkxPlsBuNFlH9qDOdvVCLxqIu7mLu6IJWXUCVEJrmCkw8cXo0Fs8BeetS6fZ89+Wtktt6hfOOAk6JxuI3Ab8eGR4qlD8YTqZ7gYs9Xb2ecgG1630JDW9Pvyc3vv1o4DTg2mXasxhaJqLCyXQAeDdwEeq7A6CHk+nNwCdGB4N3t8o2G2JnEdXycJ4lxF+MCpU/zbLnJlSo/JdNPDGZS9NFVDiZfi6w2R3o0dz+rt3TIwI9Hn16fK1Z0K8LJ9NPGh0MjjXYnLr3Wgon093A7zW3Zx+V/jG7fLv9XV4jn6WQmboinEw/OjoY/OUSX8YJ5znsRqNF1CTw7ZHhoSuW8uTwpn/5hVE8GvBW20ZKiTQM03D7bgL+DPisi9+67kV5xMrvqyqOorG4DnQBrwdENBZ/GHXGtJRLHrgftYg/OxqL/wrYWnrcd8jzw3n/gMvl9VMNobnQPD7TLOQ30jwRVfcDXzQWXwVMztcXxmpjcR1CHOP2d3tdXj9ChTe9hWzmddIovCqcTD9/dDB4U71tXCQt99RZ2FlEtTSxPJxM+4EfAi90ef1S83hdAGYh/wJDz58K/DKcTL9qdDCYa4F5rfBEfcTl9UlPoHuPB4QQeHtWuXPj2waQ8o3A5+ZuY5X3Px2Vt/mNkeGh5eRqNsIT9VoQe88VUKDen9vfhWkUMfLZjwKOiHKoC40WUQPA+JKfLURSGsUPmMUClTw1AGZRR0rTnQ8MfHpkeOjR+XZplYS7mRVU5eKqdH0AKk/gXst+15yLr+y2VuHx8osHWAs8xdrvLi+KLzv+TL1rNZXyvcrRXC6XlsmcGI3F3wHoQMG6Lr/Mva/mNiPDQ7UWsLqG86zF923A9mgs/oOR4aHxGpt/QWjaMb6+1V6hzRYpurx+NI/PU5iZdBl67pfhZHq/Fh387CRSwN4iqtWeqK8htFN9fQPabg5tX8BlGkXyk2OnI+VlqNYpVYnG4gcBzwd+MjI8tKNOtjU1sdyqYH6By9dV3SAlNLzF7MzbmSOiorH4WuBlwP7A31AnyMuhESLqQrc/4JkroMpx+7qEkc8+LZxMHzU6GLwDIBqL+4BjgTtHhod2zvMajohy2I1Gi6hVwB1LffLoYPD2cDL9C3164lRf38BuB1UA0yiiT08WgM2jg8F5BRTAyPCQRImJAlAxiTIai08Avwa2jAwPLbmhZzQW3xdVdXcbKnHzRushF+Ca6dkwJqV8npSyppCSpmEKxGPAPSivXOnSjfqMvXMu8/5fo7G4QXWxdRagR2PxaWY/q9KlWOG+Spei9VkzMjxkRmPxzcArgQuisfhPR4aHbptrUziZXgMMerp6PXP/16AWeU93r2bouX7gbCA53/vsAOwuolriibKSpwe9Pf2iUkaA5nLj7en36FPjG8PJ9IdGB4MPz90mGou7gFOAZwEPAtP1sK3sRM4FBKKxONbfpfvqfnv9qoMP27rPsVVPRktoLg9IeWA0Fv+wdZdEnQieZN2+FSU4jrXslmXbMed2rcdeAXiisfga62+x3Gtx1MuOFvNkfwiXC0Cu2nH3a6KxH/4F2IAK8wpgSzQWvx/IotI8chU8505iucNuNExEWd6HfpbjiVKcK03j17nx7ce5fAGXy+MTAEYhbxr5rASuBy5c5mvMpQf1I1mup+NYlFC7ZmR4aI+GoOFk+hqk/JxZ0HF5fRV3oJIi8xJP4NKR4aEFhfOsz97DnuJqoff1ot7/gdbjbuu6dHtBRGPxSgLsQOD/orH4v1EL8q7Hu/d/5ikzvfugeSp/FqDyxFw+v8vI586htSKq5eG8jeddsD9wodC0d0hTBoQmckjZt/G8CxKbrrzsoVbbR2sTyweF5tI1d/Uvk+b2IjRN1/Izb4/G4l9hdwGyGngJyov8D5QH+URLWNVD2BwGvNC6T1/E+ypaF2MBt/Ol21KzzkqkCaJ6GzopTVDrXvlaI1Dr+JNRAuPvwEzZY9S4Xe2+/VHrzE1UF12LEWgSId6BlIHK72y3pwtPIdsFHA08E5V3eS9w6tyto7F4nllRlUWlhjwdxxPlYNFIT1QvaoGYzz1ak9HB4ISVEPkaI599l5HPBlG/hFuABPDD0cFgvb/QPcB0yZOyVEaGh35W6/HRweDWcDK9uZCZfI3mXr2Hp01KSSEzaQDbgB8v4nVNZpPlF000Fu8H/jsyPPTzCo9p7C6qKl2qPb4X6n+nW9fd5du7DP0oIYScL7wphEu4C5mnRmPxD5S9z6Ve9EXO77KFp2fjeRe8EPixy+XSAoEur8vlxjAMTzY78w7DMN6+8bwLztp05WW/aLGZyw7nWV4bLyqEXrouv1S8z3fwKc8v9O3lrvVdEkIgXG6PV586jT2FzIHAwcAOYB+UmFqIgMkvYJuitU8P8CPUGrkQUWQudU2yEuw/Uszn9qqUE1XCyGcLCPGDkeGhv8956G/RWPwQVEjv6cAXR4aHluyZi8biXuDokeGhPyx1H3MJJ9PXFPPZC93+rqo5tEY+BzC+ba+nfuQb73tdPhqLfw0IA08FNqHaIQRQqR2VrvdFHdtqu/QcOoZGiqgB63p8uTsaHQzmUV/wTcvd1wLpoU6u+wXwDmmaT8pN7AiqRGofQgiMgk4xlylIo5gFXjw6GFzM2epy8VPFC2cJjlLYb0FYwuslqIPSrcDPR4aH9gifhJPpx5HmmfOGN42igXDdBdzAngfQACrEOfdAW8s+nYWLrtXAIcC+0VjcjeX2R4mxpgisjeddcDQw2tXV7e3u6d3tswp0dXlnZqbIzMz8eON5Fxy36crL/t0Mm8qZk3fYE43F92GRImjO7VqquiRcdoliIC+QM0jTZLYkvTKmLOq+/r8DX2F30WKgwjwnozwQvwTuqNf/OBqLbwWOBx4cGR7aWo991mJ0MGiEk+lEMTfzMZfX56kU4jT0HGax4Aa+VGkfI8ND91keu6NRYmM5ZFAFPPXkq9IoXlzMZ3H79nRISdOgkJ3Rga9YxxRGhofy0Vj8+6iipMfm+/9GY/H1zHrrx+ts/y4uv/zy0omnQ3ORgH7++ecvOFzbSBG1yroeb+BrNIqmiajRweBUOJl+LlJGitnpi4rZ6VJJfw64Cvj06GDwvmbYUkaA5Ycyy+lBCahfATfV8Pz8HMgZ+WyP2195fZWmgVHIC9y+z40MD/15IS9uibhKB+v5Lj0V7tsXOAPYzu7JtbKsxUau7DL376rbzJPsX8573G4PcwUUKO9Kd3cvBV2nUCi8F3jTAvdZrehiIZdK22vA+ajebTeyO+We0l3CByVWxufcV2m7ci9iRS90OJl+iGLhTNMw0FyVdZRpFDGNghe3b3MVIfMnK+z8EuA1qKa4S87xnEPJS1xT4NeZzyHl8/OTY6d4Aj0el9eP0LRSxRrFXEYCHxgdDN5cbQcjw0N5IFUHWzKAPxqLuxbxva/J6GDwznAy/Y7CzOSXzWIBt79LaC43UpoY+ZwSUNK8BfhY+fMs4bSgnFpm82j76mFzOZdffrkA1qDWmEbnKzvU4PLLL99+/vnn1+rvuItGe6Km5/ZGahN6gMea9WKjg8EM8IlwMv0pZvOQHh4dDM7Ufmb9sQSHD3VAqwsjw0OTwKXzbTc6GMyEk+nPFTLT/6u5Pe65SbBSmujTEwXgPpQgW+jrm8wKliVjiYyjUCGeK1AHdX/ZxTfnbz/qd1D+d9WDppVDVlNomYZRADZ2dXV7q3nrhBAEuro9hYnx10Xe9+HL3G63YOGCqFZvtFKezW691VDhqEpeu72B3wN/YHchVGyC1+5PwH8KmcnDvT2r9gjrqVD5VBG4C/hLtZ2MDA+NR2Px7wD7ocLq9aLkya2eAFhnRgeDhXAyfQZS/m8hM3VxITO1GuVxc6HE4SWjg8HvNsmckicrQB1PWEcHg18NJ9OPGvnsR4189qnMvr9JlLfxo8us6s2hcjjrLqJQ1dtrgTHUb6qATdIHOgiB8jLue/nll7MQIdVoT9Sy8qFaSDPDebsYHQwaKIHQSkpNq1rRPgDgoyAPzU+Ovdbl9VM2BodiLqMj5WPA6dZn1VRGhodkNBaXKDHwxMjw0KJFbplIrSW+yv/uRp2d+gC/KeVqwOt21/7pupUA9SDl2VQXOTvZUxBVvSzWYxCNxe8BHh0ZHmraCUmJ0cGgDCfTrzAL+o35ybEeT6DbUypYMAt5CtmZgjSKU8ArRgeDNQ9UluCr99ilkohqpieK0cFgAYiHk+lh4ETUAeNR4Nb5Poc6U/rtdFPntXZ0MPgT4CfhZDqISmDPAH+tR0sUaw2YRH1udePyyy93o37nj5x//vmP13PfDotm5vLLLwclpB6eL7TXaE/UeAP33xAsb0Pdf9htRElE1c0TtRis3I1B4HuGnnuXoeeeizqTLA1kvrJFA5lLlH4zS/KwWl6xLEv8fN/wlrd3Ae83Ze1ceNNUv/uJifH/++YVXxpfymvVgeXOzlwWVnjnOGkUP6pPT5zDbI5JAfgOMDQ6GHygReaVwnlN80SVY+VY3tCK17YoeaLqnRe1C2uWar1GgZUzSf09UaXcv2bNLnSoTen/4GWetbrRnqgHGrj/RhFAHbQ7VUSVMjJb5YnCOiMeBUbDybQARAvHc8yldCBuSYnzVV//SmbjeRf8PpvNPNfr9VVNms5lsybw5xYKKGixiAKwRNLGcDIdQZXoS+D2Jow1qcnI8JBh9WprqifKRjRcRDWQSWYLp+qNE76zB6X/w7ytbBoioqyqpYZWLzSQHuu6U0VUSz1Rc7EElZ0WFjdgLLItQr35bD6XO1n35/H69nRk6HqeXC4LFUZ3NBkTG/TTArBEUys9L5XQ6VwRlUflK7WriDqw1UY42INGnSX2oxbPdsyJckSUomWeKJvjocWN9jZdednPgc+Oj4+Z01OTFItFpJQUi0WmpyYZ3zlmAF8AftJKO1Hit6WeKJuTp0XhvFZj5ZllUKkT7cYk0GelftiecDItwsn02nAyfZB13RZ2twuNCufVrUdUCyiJqKZXxtmEAOrgt6RGnR1A3afPL5H3A+lMZuZDmczMEWX33wUMA1dtuvKyVnvwWh7Oszmd7ImCxvSKagaTqO+1rXNnw8n0KuANwEXAoWUP3RtOpi8FrhodDI63wLSqnH3OudcDa7dcs/kpte4/+5xzXwhcDISwEvKBXwCXbLlmc73mWy6IRomoVagFtJUJwEulB1WJ1MzmlnbCj+pZ1OoDsF1xs8Sk8npiCaTke94/9KtCQb/ENM2ApmlZt9sT/fynP2qLUCyOiJoPR0S1p4gq7xVlSxEVTqZfCPwA6HJ5fbi8fhACpMTQc4cYev7zwMfDyfQrRweDCxonZjOOQa3DXwaeQFVhvgN4wdnnnHvclms2Ny2S0khP1GSL80aWSkvaG9iIADbJh7IpLQ/nlaNpmvD5/OX9i+wkfh0RVZuODedZtKuIKjXZ7WPhTTqbhiWgfq55vMLb3SfmjhNzef1Cmgb6zGTALOg/DyfTL203IbXlms2fnnvf2eecewuqIOkM4PvNsqVRC9wq2jMfChwRVXXkiwNgE09UGXPzG+wmopz8i+o4nqj2zImaQSXFN6Lh5rKwQng/0Dxe4e1Zpc0VUCWE5sLbs0rTPF4B/MB6XrtT6ke3vpkv2khP1BMN2nej6XQR5XiiamMrTxT2FlFOYnlt8rSniKgXM7ShJ8pquDmFDUUUKgeqy9vdJ+Yf5C7wdvdpufHtXcBGVB++tuLsc87tR534Hw6MoNacqhMIGoHjidqTThdRjieqNnZJLC8xd6W0UwjdCefVRscJ53W1S5XbHOretXy5WFV3F7m8Pqp5oOYiNBcurw/g4jat2rsWeBzVvuQI4O1brtmcaqYBdfdERWNxH+rsYrze+24SnS6iArSvAG4GTjhv4TgiqjZOOE81NvbSftXAjehavlzWAIe6vP55NyxH8/iFoecPBVaj5oK2Exeh5g0eA7yMFuSoNSKct8q6brsDcTQWd6EEYCeLKD9OOK8WHuy14NtdRLXj2W2zyOOIKFAhTTv9phbCJGrAtp1Q7XnmCePNRWi7tu/F3iJqj7VtyzWbb7Ju/vLsc869Afjj2eec+7wt12xuWmPdRpwllnpEtZ2IYjY/oZNFVAAnnFcLu3mi5v6G7SSinJyo2nR6OK/Ui6/t8qKwZ8NNddySi1sCpLlrezvM7as17LfmIOAt12z+MyoX+y11tWgeGrHArUIdZNqxWWVHdyu3FgQfjieqFrZOLLdZfy8nnFcbHXBHY/FO/YzaeX7eFGotWFzsrLHsAO419Nyi1gCzkJPAvUBL50laTFI5QuZhYSLPC2yoq0Xz0ChP1LjNFvOF0tEiCrUgCBxPVC3snFhut9+cI6JqUwphdWpIr51FVHmvKFtgzRm91NDzSLOm02YX0jQw9DzAF63nt5o7gIPPPufcdaU7zj7n3G7gKOux0n0Hz33i2eecezoqL+yOuY81kkblRI03YL/NoAd1IGpHL1o9sNXwYZtit3Ce3UXUwsqEOpPSVAQfHXjiMjI8ZERj8TztL6Ls1M7nKuDj+sxkwNuzSqvV5kBKiT4zaaLW+03NMnAergDeCVx39jnnXo46YX0TKl/rq2XbXXf2OefejarOmwCeApyP8qYlmmlwo8J57ZgPBUpEZdq003o9cIYPz4+dw3l2+946ieW1KYmoTvVEQfs23JxGnbTYxhMFYM3Ce6VZ0KU+PW5W80hJ00CfHjfNgi6Bs+wyQ2/LNZvvA56HqrL7CPBxlFPjtC3XbP5H2aZfQX1v3o8a/RIGvgscu+WazQ800eT6eKJSCeECXiolTz+5/8hnScRvUolLfhOKSDudsS8Ep72BwvFEVcfxRC0cJ7G8Np0ezoP2bbhpRGPxaWwmogBGB4PXhpPpl5oF/Qe58e1dLq8PzeMXQhNIU2IWctIK4WVRAurXLTZ5N7Zcs/kW4IXzbPMZ4DPNsag2y17gUgnxUuBh4EdeN9GDu+981gH+Oz4KPJZKiNcs28ImkUqIfQ/1//PotZ7/dnL4wfFEzY+dPVF2E1FOTlRtysN5nUq7zs8DGzbcLGHNwtsPiBh6/r7CzAT61DiFmQkMPX8fEAH2tZuAakeW5YlKJcQZwE+6fGjdPtA0tRiYJmR01szk+E4qIdyhiPx2XaxtAKmEOAvlEnz6M/t/Yt33jVcDnwxF5C9aaVszSSVE6NSBg8/cXtj3KUd3/WVfGLqn1TbZjZs/712/l/e1G9xC75l/66ZRLlJsJaI0ilIThqfVdtgY3SNybp+WacdwVr3IoJKB2xE7NtzchRWi+2I4mb4U1UizF1XhNmaTJPIVwZJFVCoh3MA3unxovYHdH9M06PGDADGd47JUQvwoFJGZijtqIamEiAMfCngh4AWXBoYSgM/K6fwslRDvC0XkZ1ttZyNJJcRzgC8Ax+7tu1/fy/uABvKVqYS4DnhnKCL/02ITW04qIV4CfMAteM6pA5sA3plKXPMH4FOhiPxla62zlycqlRAa8Cog8toNPFMAqcTwR4BLgctDETneSvvsQCoh+oG3vn4D70J5Cz6YSnwxjUqIvToUkXqt568UUgnhPbH3uCDwpFTikhng2lBEtlM+7SSwR5WY3bAE0w7s3UizbVmOq/1MYE13DUd0lw+EclW/dhmv0xAsL9qHVnWj9XWhedxK/Hnc0N+F1t+FAD6TSoiTW21ro0glxOnAdX4PoTW9sL4f7/p+6R7oAa+bk4G/pRLiKa22s5WkEuL9wM/8Xp410ANr+2CgB/weng38PJUQ0RabaBsRZZ1YfQ/YHPBy4kC3+qx6/OynCT4G3JpKiANbaWOrSSXE3sAtQvDxbj/7DfSoz6jLx1MEXAZcm0qIwHz7aWdSCSFSCfE/wOOHd/1j6Ijuf75SqOqwx1MJcXkqIdrFM2fXIcQOTWQ5IuoZHjeGVmMPQoDXgws4cRmv0yiifg/SVyXY4PeCz42Bih2vOFIJ4Qe+2+XD1d+NcFuZYEKA1w2runH53HQBm1OJRc4RWCGkEuJUYLi/C9HfheZ1K2+l1w393bgsof3pVEKc0kIzbSOigP8TEF7di6uvC83nUZ9Vtx/W9OH1uNgb+LVViNJxWL+jn7ldHLC2F2+PX30+Xjf0BhBrevFogpNQlUcrEusz+DLwid4AA+v6ca3vl551/Xj6u/BqgjcAv28HIXlcz7Ubju35zYk3f977xlRCHNVqexxaw3JE1GKOrLZKLk0lxCrg5ICvdg+bgA83ELbOsFcarwJ6uv2VS9CFgJ4ALiAInNBUy+zDe30eTH+V2im/F3weDOC9TbVqd2zR4iCVED3Axb1deDwVflWagP5uPMBhzFN5s4J5FnBcfxeeSiefLhf0deEFBlMJ0dSuy03kVOCCgR5cXT71vQC13vi9sLoXrxAcA7yvlUbWIpUQz0glxN+f1H3j95/c85czPFrha8B/Ugnxx1RCHNNq+xyay3LEzb/0IppZ49xXStCLFIFbl/E6jaAXZn/A1bAe12jPPibzcZrfg6vWZ+B2gVsjB5zeNKtsQiohuoAXBrzzCG0vbuAlLTxztosn6kwBbn+NNHKXBj4PEnhjs4yyGa/zuim6a3yjvG7QBEXg7KZZ1Vwu9nkwvFVOS10adPvwAhelEsJ2RQlWescffR6OX9MLG/qle30/3tUqBeIk4MZUQhzfajsdmsdyRNT3gUy2xuztrA5SIoHkMl6nEewEDGOe83brcZ2V2TsqIMT8jRCtbTqxBLsXEK55fiHW44LZkUHNxi4iar2mUZzPPe3WcAH7NMUi+7GXS6tdzCPEru/UulrbtTEv8HtqfwaW53ctcEQzDFoopZy/gBdXfxdauRj2lFIgPHiB73ZqCkQnsmQRFYrIHBCZziEz+d0HR0sJ2TxMZTGB/7VbRU4oIqeBn2Ty1fv9SAmZPDqQDEXkwgYRtRd36UX0WgO/pYSigQZ0YruDCcAoziO0i+qbUWR2DESzsYuImjAlrvkGyBsmJrC9KRbZj+2GWXsSvZS7Tt7aqUptMbjnkxdlD9utCenLgDU9frRK70EI6FUpEIcAK7YgyWF3lpWrFIrIbwJvm8qS2zaJPjGDnJiBbZPok1kKwP8An6+LpfXn03oRLVPBkyYlzOShoAREotmGNYkrDROPXqNtZFYHqTxxW5pmlU2wThK+n83X7k6e1SkA3w1FZA2fbEOxS5+on0mJyNf4PpkScgVM4JqmWWUvvqcX0Wp5wAtFMCVe4AdNs6q5PFCYp1VtQclMA3io8eYsitN8VhV3NVwaeFzowGlNs8qhpSw74TsUkVcAG6Tk3Rldu/q/M/vdOqav/zywIRSRnw1F5js3bQ2hiPwbsHEqizE2hZ7VQS8oD9rYNPpMjgLwqlBE/rvVtjaCUETeB3xzIkNh7qIm1cGOqSwGELdjj68mMaIXcc1U6d8+kwO9iAv4XFOt2h1beKJCEbkdSE5l0CuJBClhMoOB6lXzwyabZxd+B9w9maFYaVU0TZjMogM/DEXkf5ttXJP4UkanUC2X1jqBLaI+A7v1NfIKMf8x09qmE1MgOpK6VM2FInIyFJFf2bz1I2+4dudbvvfzsbePtkPTNKuT+rEFg6smM8zsnIGJjMgUDS4HgqGI/EmrbWwwF0rJ98emYWyKwkwOpnMwNoU+MQPAJ4GR1prYOkIReTMwOJ0rE9pF5aEbm0KfzmEArwtF5D/m21cDsYWIsrjYlPxzh/psKBoqNJXVYWyaQr7ANPCiTmkmOZdQRJrAS/Qi23dMoWfy6jMqGkqQb59CN0z+A7y51bY2kG9JySPj0xTMOWJbSpUCUlDFSB9riXW1uWchKRAFA0lnpkB0JHVtPTAyPCSxeSv8uYQiMh2KyPNDEdnz7Sc+fN63tw4NhiLyolBE3tlq2xpNKCL1UESeC5xQMLh6POu9b0em55GiyZeBI0IR+SG7ehKbRSgiNwPHFQw2TWbI7ZyGiQy5gsEm4NhQRLY6NGWLFgcAoYicAU6Rkg/P5HhkxxRsn4TJDLmiwddRn1eqlTa2mlBE3gsca5gkprJM7ZiCHVMwneNRKfkI8KxQRE602s5GEYrISeDkgsED2yYxx2cwZ3IwmYFtExSyOtPAC0MRmW61rRX4lilrp0DkCiAlJvCdplk1D1Zz07WphDjIunaS3utII/ofTdBGIqociastJ4ovF8vjcl40Fj8JeO7I8NAnW22TnQhF5L+At37wf9//bgP3+02pXf3p4Y/ZRWTbyRNFKCKzqAakI7/dOfgen8hmnrPq+9/q4JDwHoQi8nHg/Z/48Nu+LJDvPsB/e/LJ3X++dYUWsOxBKCIfSiXEk4AzxnL9/+sWhQ0+LXMfKlfu21bhj+0IReSjqYT48sQMF6zqwTO3TUO+AJMZiqi5qy0XwlY/xDcAFwGHlj10byohLgWuslvR19nnnPsAUJpqUAQeBK4HhrZcs/mRsu2+hXpv1ThlyzWbr1/odku3uDEiapL2Lc/NAKtabUQL0QFfNBYXllfRoYy87DJQCa92ah5rKxFVIhSR5tWx+CTw2EWRLY6AqsBYcR83MLFjet/7X/fBP3WEgCoRisgi8ONoLN4H5EaGh77XapsWyHskdO2c5s0eF7rPg1cC+QJ60cCLmkP60RbbSCohXogqTujyecDvUdWDVr7rIfkCnwc+nkqIV4Yi8toWmzuXFPBZwAMcA1wAvOTsc84NbrlmcylP7mvAbys8dxg10PqeRW63ZBolog5rwH6bQYYO9ESVkUcdlN1QuyqtQymFy+w0tsSWIsrCDdXbiDhQatCabakVraUX2NZqIxaKJf7ekkqIS3fqq+KuQvHpAW36CeAG4Kt2GNhuCaife92Ivq49e935vQjDhMkMAb3Iz1MJ8VKbCalHtlyz+erSH2efc+49qAHmb8Aq4tlyzeYbgRvLn3T2Oee+HGug95ZrNj+8mO2WQyPOqCeBnmgsbqcDzULpdBFVSvh1KksqUxJRdvJE2aXFQSU8OGK8FgHUd6pV7THsQC9qkG9bEYrIW3+8PXL5D7ZFPxaKyGNDEXmxTQTUKuAHXjdiVTdatWbBLg1WdaN53QjgB9bz7MrvreuqzVfPPudcH8p7dQc1iqEWut1iaJSIamUH5+WQAbzRWNx24waaRElE2a3JnV0ohVzsJKIcT1T7EkCFsuz2f2sK1jrrpw1FlMVq7NcU9Q1AV19X5Yag5QgBfV1oKMfBxibYtlT2ta5rtbx4H6rJ6Tu2XLO5VvXvQrdbMI1KLAeVXN7y5LpFUsrdCNCZZ9ClM2LHE1WZ0sHOTl5W21TnVcDxRNUmQGeH8kon2u0qogaAu1ptRAmr6u4in2fX6KB5seZZki9wcSohLrVJNbbn7HPOXYtaZ49GhfAMqlQ8nn3OufsDMeA7W67ZfF21nS50u8XSKE8UtGeFXmlB69SQnuOJqoHlMXASyxeO44mqTaeLqF7ruu1EVDQW11BFSHbyRK0BDvV75p+JWo61/aEoz5odOB2VJ/c4KpQ3DbxoyzWbqzW+HkGtM++ZZ78L3W5RNOJgkEcdjPsbsO9GU/JEdaqIcjxR82NiX0+UbURUNBZ3ChTmxxFRirYTUSjbXdhLRPWACtMthrLte2ts1kz+hhqbEwa+hwq/VZy3efY5554MvBr48JZrNj9ebYcL3W4p1F1EtWPDzTI6XUQ5nqj5MXE8UQuhlCrgeKKq44goJbLbMbF+wLq2k4iaBtXGYDGUbW8XMbt9yzWbf7vlms0/BV4L3A9sOvucc3dbd88+51wXqmrvn8CXq+1sodstlUYdDNq14aaOCtd0uohyPFHVccJ5C6NUnOF4oqrjB6pMZuwIeoGpNk2sH0D93sZbbEc5O4B7c4XFrQPW9vcCYw2xahlsuWazCcSBIHD2nIcvBJ4CXLjlms21+qwtdLsl0aiDQVt6oqwfc8e2ObDev47jiaqF3cJ5dm1x4Hii5sfxRNnH+7FYBlAC0Dbfbysp/NJ8Qc2sXAiGqTqtA1+0SVJ5JX4J3A28v3TH2eecuwbV1PSKLdds/lu1Jy50u+XQiOo8cBputjN5HE9ULZxw3sJwPFHz44io9hZRtvPcAFcBH5/MEFjVXbvNgZQwmcFEfQc3Ncm+RbPlms3y7HPO/TKQOPucc0/fcs3mXwOXoBL7bzv7nHNfX+Fp/9pyzeZ/LWK7JdNIT5TTcLM9cTxRtTGwlyfKri0OHE9UDaweSR4cEdWuIsqOPaKwZuG9Ui8ix2cwq3mkDBPGZzD1IhI4y24z9CrwTVTO1/9YfwdRa98XgGSFy1mL3G7JNNITVWq42Y69ojpZRDmeqNo4nqiF4XiiauO3rh0R1Z4MAHYZQr4boYi8NpUQL9WL/GD75K7ZeaJsdp60QnhZlID6dWstnmXLNZsPqnL/JGXVg1uu2fy8Be5vQdsth0YmlkMb5kXhiCjHE1UbWyWWF4uFQC6X3SeXze5bLBYD8z+jaTieqNp09Ny8aCzuQ52stZ2IsmzvwoaeqBLWLLz9gEi+wH0TGRifgYkM5AvcB0SAfe0koNqVRnqiQPWK+m+DXqNRdLqIcjxRtbFFYvnG8y7YC/gw8GZm/19v2njeBScB8U1XXvZAq2yzcDxRteloEUV7dyu3Y3uDPbBCdF9MJcSlqPBjyfM3ZuMk8rajUSKq1HCzbT1R0VhctGnp7XLRsU/TNTvS8nDexvMu2B+40eVyrevu7vV6fUpDFXTdNTMz/bpisfCyjedd8OxNV152ewvNdDxRtel0EdXOjTbbQkSVsATTDmrPnnNYIg05GKyAhptuZs+kOw3HE1UbOySWf9ft8axfvWad1x8IoGkamqbh8/sZ+P/2zju+kbPO/+9nZlRc197N7qb3DiJKQgqQhBJIA5QjoRMtsAdh4Si+QxzodxyKriCKANFD4HJHRCcXQDl6SYBAgCREiZKQ3utWe13UZub5/fGM1lqv5baSRrLn/XrNS7Yka76SRzOf51tXr/H5A4EBILdh4yY3xZ7niZqbmohaqX2iul1EVZhuzuyxgmmVJwq6t+Fmfdfypkx57jI6Iicqki0EgAtRrTLKwC9z0dBelaI2CVc9URs2bnoO8LzBgVUqU3QGQggGBlYZ28qbDwdeAvyq3TY6dJQnKpItrMMpS89FQ1vctgclosrpVKLpzf+6hAHU++/Gc+wwsGOFRio8ZtBKEbUTWNfC128V9SJq1EU73KKMiyIqki0I4N3AvwN9QjdMpETaVjqSLfwFiOaiITcnp7sdznuVbhhlw+dr6C3UdR2/329VKpVX4Z6I8gGm2xeaSLZwAfAh4My6+34LfDwXDf3UNcNUdd5KDeVB91fmdUUoz6P1tFpENa3hZiRbGALOQ335ngZ+nouGWrGKcWV+XiRbOBB4PbAWJd6uzkVD97XTBocK7obz/gVI+nr7NT3QgxCaAWCbVapTEyfZZuXPkWzhlFw0dL9L9i06nFc3jDewiC042/1+f+AciZx3/5qmG4bPd0Ysnvx/KGFccrbyjNt571uiEDJw2QsVyRY+BHxU9welHuhB03Vsy8IqF8+0KqWzItnCP+eiobRL5vWwckN50N0iajVwd4tee5Hjgz1aRO3/MO+5r9Uiqj8WT+p747KOZAt9wKeAt4IQQhOWtG0fsDOSLXwM+GQuGmrmaretIsp5f18FXic0rSo0Q0jbktK2PhrJFn4OXJKLhmadYN0iKoC/mYn1sXjyIGANcHs6lWjYEDKSLRwJ/Lu/fxW6P7jbY5rhwz8wZFTGd/TbZvXzwPnNsG0Om2vCxz9jOwQwYvHkiSxOFM3lvTJRomXmNjbzPtu2Bmzbfq6UctZw3q4XNKsVKeUtwHVMi7KaMOtDXQjq72sozGLx5EyRNZvYmvn4WtRxFAQqc/3fW0EkW3gp8FF//yqh+4O7Pihd09F9fs2qBKhMjH0iki3ckouGrpvrtZymwb50KtFM0eNat/JItrAeuAQ4CJgE/g/4U5PPo/MxQPf1ECQWT2qoDtjN9kRVUBfsAdT/xMNdajl78zpqWi2i9qrhZiRb6AGuE5p2gq93wK/5AgghfFLaWOXScHVq/D+BwyLZwruadQJIpxLVWDxZpQ0iKpIt+IGfIbRT/f2Dmmb4A0IIpJRIy6QyOfZiaVk3RLKF03LRULtOOLWJ6v66n/eWdcArgVNi8eS16VTi6QbP2yR0vaL5ArOGE4UQGD39RmV8x7mRbOHQXDT0MOwSPD72FDy1LTDHY3Nts6mUi1CCQzA9gX7mtqPu51KD59S2ymLmb23YuOlR4J8qlTKBQHDW51SrFUzT9AOfTKcSf5vvNWd4yuqFVbDBfUHUSWbtjPvqP68XA4fiiEfnO1Wr2p3tdq7HZj5nIWHCmO4P2Lo/OKs41P1BNF/Jsqvl96OEZqPP5hDgFaj/9RXz7HMxtF1ERbIFH5AB3oHQTM0wNGnbtrTM/wcUItnCq9sYKh8AHm/TvprJIOqYbqqIuvTSS80rrrhiG3DAFVdc0eO8fpXOaqC7EhCoY/MAYOull146rwOo1YnloHpFLVUAxBDihMDgar/Qps+FQmgYwV6EbhiV8R3vAK4Bfrl35u7GXveKisWT/cA5wB/nEA2XgDgtMLjap+n1708gDB+BgdX+0ti2w5D2+1BDFNtBTXkvSUQ5F2Td2Qxnexj4ESoc+4FYPHkb8BfUAVt7ji6OvTCi9/T55/KwaIYPwBradt9lsfg1dzAteObDdN7bbNvYLPeVGzz3cef2G+32rgBcdeXlT2/YuOm/do6NvnV49RqfYexeRGpZFmOjoxXgF1ddefm8Agp2VdNWnW1iKXbVCdma2HoQOAH4PrsL2cCMn2tescCM582FHYsnG4qwiq9PcNQ55+qBuXuPGoEeo1ItX/Dmz/zv0NrNd0wAVk2cxeLJXuBlwImo//m1C/80FkQPbcy5dHINv4EQr/L3DeqaL6DXvme2ZVKdGj/Orlb+FMkWTqotTlqFc6y0NJwXyRZ0lPfbBHY00cvWyvYGj6K8UAegvhMe7rH10ksvfWQhT2y1JyoERGLx5O0sYPVZH/aLZAsG8B4j2LebgKpH9/nRfAHLrpbfS4eJKNQFaT1waSye/C1wwyxhzRE90GPUC6h6hKbh6+n1V6cm3hPJFj6ai4Zm9VjUeRL0Bd7O9diBqIvHfbF4cmKW5y/k90bowHHAycCpQH2YUmq2OThfSoAQAoSwTV/vUygh1kgY7bY1S/A4oa2yGwKqjvdIKffdvm3rywPBoAgEgppAUK6U7FKxaAM3AW9sp0GO+Kh93sTiyaeAoXQqcediX8s5nmcKr7mEWP19/bbuWwuCRueNGs7jYtXow/8P9Z2XsXjSRK3+T0d5HAqog/IC57Eq6sI88+e5Hpvt51XAo23sR/cS4DWBgWGhzRDemm7g7x8yyju390vL/E/gTY1eJBZPHgiMp1OJvfGMB1CCu+kiKpItrAXeA/wD00LkgUi28Fngq7loaG9DssOo46PpkYFLL71Uos6JW6+44gof6lzq5Ui1FwlUFuKBqtFKEVVGhXGORa26/MzTe8k5SZWByn4D+w8/ddDpa40GIYsaRiBoVCqlc2Lx5AWok56GOvD25vYNqNXuAUy7U+UsP8/1GKhV/QGoarNLYvHk9ajEZGyhC467MKT7587h1nwBYGKfAx/+/Qdj8WvGmF387E3fIovpE7yFOvHsjwrFPF13v4m60NQ/35zn9/qfB1GeqNuA64E/1j+eTiXsSLZwpFatvI6evobHiW2ZIKV/YvCA76VTiVv34n0vFR3nf+gWV115eWXDxk0XAS+vVqr/XimXj5USoWniAdTU8muuuvLyTujPtCRx4IiK2iJr0ThpAP8hLVNHb3yKk7YJYIL8FsrWWn+42vfqKPX4LrFfe6y37mdjlp8X8n28FPVdON0JdVaY9gZWFng773PqFm7v0XwBSzN8s34gQgh8Pf2+ysToayPZwsjMNhCxeLIP9f0NAT8HblzAe2xES3pERbKFw4AbhKbtYwT7/JrhByRWpXyEWZ76FFK+IZItvCwXDe1NztEwsHMxIfilcOmll9b+vx4dTitFlA78GrgmnUrcDruS8uZbVQYAv+nrPU69zHxCXIB6H4egys9t1Alxrlub6XjzbI8/4fz8RN1OxBw/N3qsfiVRu6BogJBCLFD4qD83jcDTqLBCTXjMJlYa3TZ6zJq5Co7Fkwc7j38lnUo0JaHdySuJoFzg2XQq8VSDp37JNiuX2GaVmavlGmZxUgK356IhNwQUqP+fm14oAK668nILyMXiSQN4jnP3zelU4v9cNKsjyEVDxUi28L9mqXiR7g82PMeZpWIV+N7nkrH8LA/fEIsnnwO8HDgY+H46lXhyIfuv8wzPJrBqPx8I/AElpGoLzNlue1ALkNkem9dLEYsnLaAqjr3wJbo/MOf5XvP5AYyhbfe/JRa/5haccwQqAf35qOP+D8BELJ48vu7xxWw2LRBRkWxBA36qGb61/oFhX31KgGb40AM9vsr49pOlbX8Z2LAXu/LaG3jsRitF1B7N9pwQSJEFJFRGsoW/Ap+xzao+l7fGNqsgxIPpVOLLe2nvLmLx5Gpgcm8uSE5Oxd+j3msGuHFmCCiSLXzErlaO0H2NU0Dsahlg59MHnvqNK6J/36xE77moibtmelsqwO9Qn8Fcq6s/AT8oj+94hb9/yFf/uUgpMYuTWJWSBP6pibYtFtc9UTOov5C6Lu7qcDsMkbbNyqvN0iRGsG+PB6vFSWyzogOfbvgCqcTtsXjyMeBVqBD0gkTUjByzWc91sXjyfuCedCrx14W85ix/X8s9nCmuZhdjQiw8PFEtHoI6b9e83CcD+6ByG493tr3hOOAFwHgsnpxk+ppQRBVizPV7pUH486XAUf7+VdpsOZWaruPrHfRXJkbf6LS22JWn6lRfygWG6FcDzyz8rXosd9oqohZDLhrarlaTkxdpPr8x2xdDShuzPFUBPr8Xds5GM3rcaKiTzo1zeHQ+a5an0kaw1y+0PSvgpZSYpakKcHkuGmqHgIJpEdW0C7LjeWrkfdpFLhqSkWzhjUj535XxHa8XulHRDL8faWNVylWQFeANuWjoN82ybQl0hCeqjvoDp9MqeVyzJxcN3RTJFjZUpya+blXKth7o8QlNR9oWVrlYsc2qjmofMqeISacSO4Ar22P1wnGERM3LPC+RbOGPdrV8LoGehh5wu1oBsLbuG/qPKz/wxnqR4UeF8k4C7kW1RKgyLbIWuz2Oqtq+FeVpq21DqMKEHvas9txlZiye3ENo+Y542Sarf42cKw9O8/lBCAvbujgWT37Jufs5wLmoBdzvGv7xNMO0rkeURxfSShFVi8fsjRj5d9usRqpT45qvd2C3FYa0bSoTo1WkfAr4n73Yx2zstbchnUpMMH9Fz5VI+Y7y+Paj/f1DPq0uf8O2LKqTY1VpW9uYY7XcAlrhiVowTuLnGyLZwr9Jy3ybZZnHok6UPwO+vZf5DM3A80R1Cblo6JuRbKFgm9X32Gb1TUy3Ffgm8LlcNFRw18K28nmrUj7Ptky0WfLE1IJt0gR+WO+lAXBGs+Ri8eS9qHYPh6VTiduWaogTYjwQuL6R98fxtNVaZ/TM2GbeN4AQ+wrNmDNFQgiBJjTRt/PRi1GetYNQaSDPoMTZs9k9v3NmUYBAedCaWcTk0eV0rCcKIBcN3RHJFs61ysVrrUqpR/cH1WrSMm0nrPMI8NJcNLSzKRZP05Zuy7loaDKSLbxIWtY15bFtZ2qGryI03S9t23RCDfcAr8xFQ+10H9c8G64KhVw09Dfg/W7a0ACNzhJRneqJcjucB4Azb/HtkWzhUsDXoikH3cAvgJ+Wd24/x98/5NMM365mrdK2qEyOW7ZZLaImBsxKOpW4OxZP3tMEW2rHacNjxPG01TxN8+YgRbKFszTbPJY5rmlSSmxpy4q/748ob9r+qDY0fuAxVMXdzPy1YN19q1Diz+0B5B4dREeLKIBcNPS7SLZwAFK+ySoX34By+T4G/Bfwf43K/veStnkbnG7kZ0WyhZPVarm6HnXS+B7w+zZ3EQaXPVFdgE5neXw62RPVMaLO+R6tVAFFLhqyI9nCq5Hyisr4jkuEplc0w1dbsBmoHkV/N1+zzSa1Y5hXRC2Bb9vVylukbTVsbWFXKyClXu5Z/bl0KrEZuCUWT/4a1Rj2b+lU4sG5dhCLJ4dRYch2TpDw6HA6XkQB5KKhCeArztYO2j73KxcN3QLc0s59NqDpOVHLjE4L53WqJ8qjw3BC5Rsi2cJHpG1tsCrWwajmjtcCv8lFQ+36zrdCRP0auKcyMXbEzOo8UOkRlcmdFVRKwOba/elUYgr48QL3UV9h7eEBdImIcoFOu1C2E88TNTedlljeqZ6ojgjneeyJ05G8XRMQZqPpIsrxtJ1vm9Xfl8e2rjOCvU6fKLAqJaedhbwJeNde7KYV4s+jy2mloq6JqG5sGOb6BHoX0QC7TV2Uu5FOE9id7InqNHs8OoOWiBFHHJ4obfuj1amJreWd2ynv3I5ZmroP5PuAs3PR0NQ8LzMXtUWKJ6I8duF5oman0y6U7aTTcn46Dc8T5eGxd7TMo+PkmCYj2cK/o/JnLWBnk3JLPU+Uxx54Imp2VrInaiULyIXQaZ9Pp3qivAuNRyNaLkac/K7tTX5ZT0R57EE7wnmddMGZF2c0jWDliqhOK+HvNDrt8/E8UR7dRreKkW6126OFtFpEWS5Pu18KXSn+mkineVo6BqcBYKeF8zrVEwWdZ49HZ9CtYqRb7fZoIa0WUd3ozalVp3Wj7c3Ay4lqTEc0Ip1B/Qm9k0SLd6HxaES3ipFutdujhbRSRPnoTiHieaJW7nufj07soeWF8zy6jW4VI91qt0cL8TxRe9LNCfHNoNNyfjqJTvREeeE8j26jW8VIt9rt0UI8EbUnK73ZpBfOa4zniVo43oVmflbqZ9StYqRb7fZoIZ6I2pOV7onywnmN6USB3cmeKI/GrOT/VbeKkW6126OFeCJqTzrxQtlOPBE1C/mMWPfqtZ986/MHf/CCl6/+0qvyGTHstk0OHeeJymfEgc8b/OHzT+7/2Un5jDjebXs8Oo5uFSPdardHC2l1s81uFFEr3RPl5UTVkc+IfuCLwJt69EnryL7bhZTyLCn593xGfA34p/CILLtoYsd4ovIZcRjwWeDlR/TkpWPP2/MZ8Wfg/eER+Qc37fPoOLpNjHgiymMPPE/UnngtDjrEo+E2+YzoAX6lCV4/1Ie+dhD/2kHpWzuIf1UvfiF4O/DDfEa0cjEyHx3hicpnxJHAzT6d84f70NatQl8/hLF6AII+TgGuz2fEOW7Z59FRdKsY6Va7PVqIJ6L2xGtxsHLf+0zeJQQnrR7AH/CBcE6dQkDQD6v78QEvBd7koo2d4on6ht9gcLgfw1/3Wfl0GOxF6w2gA99zhKnHyqYrxUjdUPZWXjc9uoxWi6hqC1+/VXieKE9Ekc8IDXhfbwCf3uBbYujQ40cH3tdO22bguicqnxHPAU7r78EQs1wWhYD+IALoA17TZvM8Oo+uFFEOku6026NFeJ6oPVnpnqhOG2viFvsCBwV9cz8p6EcAJ+Yzwt8Oo2ahEzxR5+gaJZ/e+AlCQNCHDlzQNqs8OhVPRHksG7zE8j1ZkZ6ofEYcCrwtsmbNeSBL+cxlq4BvhUfkpMumucWCvht1Z1MDqLTIlgWa4Jr4Dc7mgZqJEAigt+XWdDD5jBDAKSf2v+CEfn2Hls9cdnd4RG5z264244koj2WDN/ZlTwxAduHg5CWRzwgjnxFfBh7UNT6wvnfbyet6tr9AqIq0Z/IZcZHbNrrEM8BEdZ4juKIefxoottyi2ekET9RDloUh59l71aIC3NcWizqQfEZcCNwF/PlZfX98zSHBu/4deCqfEV/PZ8Q+LpvXTjwR5bFsaKonKp8RvbcGXhn/eW/snNIxrzwEIUqRbOEa4PO5aOihZu6r2eQzYj/g7a9dF/y7qh1Yk89ctg64PDwiC27b1mIuF7BhVR/Cb+CveRSkxDdZxpgs8f18RrwiPCJ/6q6Z7SU8Isv5jPjqZJl/CPqnP5d6bAlTZSrA58Ij80mIltEJA4h/IOHyYoX+3sDsT6iYYFr4ga+11bIOIZ8Rfw98tTeA6PWDrktDSiib6BNF3mDZnJHPiNPCI3Kr27a2AU9EeSwbmuaJymfE4cBdJ5av/fBLi184VR8YXq/1DR0idOMfgHsj2cIrmrWvZpPPiPcAj2mCfxkKlk5c1zt2sE/nbcDt+YzI5jNinsyY7iSfEc8C/n6oH1999RlMJwP3+NGAzzlhiJXGpyybnaOTmPYMv6Rlw+gEVVvyNPAVV6xTuB7OC4/IKeDfxotY5VlKSUwLxiapAN8Lj8i/tds+t8lnxIHAVwZ6EAM9oDsJA06eGKsH8OkaBwKfcdPONuKJKI9lQ1NEVD4jBoDrfQYHDPRAuPQjenwmvp4+AoOr/UZPnw78MJItvLgZ+2sm+Yx4K/DZwR70fQbxD/RAfw+sHsA/3A9C8DrgCrftbBHvMHQq/jn8kX1BAI4AzmiPSZ1DeEQ+AZxZMXliy07s0Uns8SLsmMDauhO7avEAcFZ4RG530cxOCOcBpIFPjE7CtnEqkyWYKsOOCcxt42BLfgG82UX73ORSXcPqaVB6oAno78EPvG45h/XyGXFYPiM+ecn6y+5407rLPnLJ+sv+ls+ILzuLuW7BxhNRHnU0yxP1DiFYP9SH0eMHTdg8a/u3ARBC4OvpF7o/KIBMk/bXFBwP0yf6g4iewO6eGAC/AUN9+IC35DPiGDdsbDEnBwzmrCrTNdA0ysCz22RTRxEekXcDRwKvKlbE1U9PrnlwZ6X3J8D5wLPCI/IRdy103xMFEB6RMjwi/x/wbNPia9umejePThmPV0yuAV4IRMIjsuSWfS5zYaOQcI2AWsgI4Kz2mNRe8hlxLvA3XeO9Az2sHu5HDPYwaOhsBG7LZ4SbvdYWg+eJ8tiNZuVEvaXXj19zDq0Bv8lp41+Tt665VAhN6TQj2KdZldJzItnCEblo6IEm7XdveTkw3GiFCEpIGRoV0+btQKxdhrUJc0GuC/WkldrygfCINIFcLJ78CfBh4Jp0KnG7y2bV6BRPFADhEXlnLJ58Nyox/yfpVOJmt23qAILzXXWFACGwpSTYFovaSD4jjgJ+1Bsg0B/cfbHaE8A/WYKJElflM+LB8Ii80TVDF4Ynojx2o1ki6iCjrkdMTwCGy4+LgyZ+z+ODLwRA6LuesBroFBF1tKFR0TTm7KLs9+E3y3STy3mhXF+uclp/kECjVXLVAlud2Dv95NYOakLSzTEvM+kIT9QMfChxt1I9TzO5t2pxBNPtU/bAskBK/MCD7TOrbbzP0BEzBVSNviBUTeyyyYeAC9tu3TzkM0K7y3/23/+09wMXTxx9wbOlZvx9JFv4BfClXDS04nL8PHanWeG8kl23BtY18BlCPnf0q9P3Thcvub5arsOUC1hVOKa7OWS2VXzVsvGVGvSVlxImi1jAn1dAleK8OGMfTDpERMXiSUFnVOfNpOZN8USU4vJyFWHNIXGnVIex+4A/t8ek9uAUpLy1d55wZk8AA3hFPiOG2mTagshnxCBw3fGVX19x8eS/nCsG9jlA61t1tNCNS4E7I9nCpW7b6OEuzRJRvypXd+8J1R+wxTHlX4veypMAWNUywBRwR5P22Qyus2yC5hyBKimhVKUK/KptVrWJ8Ih8HPjgzinsyZIq2a9hWjA2hVU2qQDvcMvGDqRjRBR7LgA6xRNVE1HLceGxFH4G/HXHBJWZQkqqNhlMlZFA3MVWGa0iCPTqc3SzBzVCCXU96pjEekcA/kDTOH1VLxxavYW1PIavp5/gqjV+X9+gAC6PZAuXuG2rh3s0S0R9pmKil+r6NfsNEJrGCTu+jm2ZVKfGq6h+UR2zOg2PyFuBW8aLmI1OXVNlkBILyLbTtnYRHpFp4B8mSoxuGcPcNk55y05R3TYO5Sp3A88Pj8jb3Lazg+gkETXz+9spF2DPE1VHeERawHmWze1bVZWnNVWGiZKqZBwvYgObwiPyf922tQWUAWtmi5CZ1D2+s7XmLIrzgBcN9+EP+kHohjxx+5W7HjQCPRg9fQL4bCRbaNAhzWO50xQRFR6RNwMfGJtCThRVDx0hVIL5qeP/Q3XsmQpS/gZINGN/TebNFZPS6CRWfXdqy4bxIkyUkMBbwyNyzDULW0x4RF6OmhV3yfby6q8+MPns301agy8CQuERmXfVuM6jk0RUp3uiPBHl4Ix2OR2I7CgN/HX7VGDLZIk7LJtPAoeFR+SybKMSHpE28MNiZe7pFcUKNvCX8Ijc3B7LFsQlAR+ylu874DfFScXvYVgTu55gBHsBhoCOa9/j0R6adjEIj8hP5TPiycky6cky+wuo2mDooiL99uRXS9qq9+eioY5z74dH5J35jDi9YnLF9gmerwnKEiGklD7gYWAkPCJzLpvZcsIjsgx8NxZP3ghsBP7m5AB57E4niSjPE9VFOB6pH8fiySHATqcS33bZpHbxmYrJRaUKBGephK5UoaiiGOk22zUfRxn6dDFA0A9GqcpxO75LYZ+/B0AIDYRWRdprXbPSw1WaOjsvPCK/DRwEnCbhtYWJF37iJ5svffv33nzGuztRQNUIj8g7wyPyBcCzbMl7Hy4e9838xEv+EzhiJQioGdSWWf2uWtG5dJKI6mRPlEV3zs5sB0PAqMs2tI3wiPwDTqRibAq7aqrwnWnBeBG5YxIb+CxwtcumzmSqPs1DCOjzm5w2/l9SOvFHKSUgBZ2zgPFoM00fQBwekXZ4RP4lPCJ/ePvki386aQ+tc6qIOp7wiLwrPCKv+P3Ya79zx+RZW5dhkudCGHduPRE1O50kojrZE1XyPJl74pwLV7GCRBSoSAUQKVb4y/YJ2LITto3DVJkCsAF4fweeb39TqlKut6rXD2vNB8R+UzcBIC0TpPQDf3LHRA+3abqImsGjqBNqt7k6twJDsXiyUy6WbSOdSlRRyaCeiJqdjhBRGzZuOmrzM099bMvmp/958zNP/euWzU/Htmx++sMbNm461G3bgABeKK8RPYAfWLY5lo0Ij8j/++Yzl73+J9su/cyT5SNeChweHpEnhEfkNztQQAF81bYRU3UxFEMH3dDlyTu+KqVtU5ncWQV+kYuG7nfNSg9XabWIegIVYji4xftpNltRoZI1bhviEhPAgNtGdCiui6gNGzddDNxlGMY7+vsHelYNDWt9/QN9mqa/E7h7w8ZN57lpH44nymUbOpUh53bURRvcZP12c/8dvxmNXh8ekQ+5bcxchEfkU8CbJ0rYO6eQtfYU/QFLPKv0U6GPPVCVlvkoypPmsUJpqYhKpxIV4GlUnlQ3sdW57ZieJW1mHM8T1QhXRdSGjZtOBr7b1z9gDK/ex9/T20cgEKS3t4/Va/bx9/b2BYAfbdi46Vi3bESJqI7NgXSZIed21EUb3GQ9sCWdSnTFGKnwiPwO8PJihUe27ITNo1TGJjE1TAaqT/wOeEEuGnrGbTs93KPVniiAx+gyT1Q6lZhCNQZdqSJqAk9ENcJtT9QHfH6/3dfXj5jRAloIQV//AIbhA3ifK9YpPE9UY1YBFaDotiEusS9qrmLXEB6RP/vWM/8a+cPYxV8r2r2XAq8XcNAVb33tSz0B5dEOEfUoMByLJ7vtoryVlS2ivHDe7LgmojZs3NQHvLq3t8/X6DlCCHp7e/3Amzds3DRPn+iW4YmoxgwBoysx6T4WT2rAOrpMRAHY6Ic+XArlT/+nya+HR+T/OtMePDza5omCLvNGsbJFlBfOa4xrIsowfPsBuq7PvXtdeaJ6fD7fUBvMmg1PRDVmiBWYVO6wGjWc+mm3DVkChwEdncPl4Q4tvxikU4mdsXhyFJUXdVer99dEtgKhWDwpVuCqcQIIxuJJn1Ot5zFNy0VULJ70owT8uvpt1dDQum1bt2DPM0PDtlW6ydDwmvfG4sktwGbU6v8Z5+cdLT6mPRHVmCGUd34lst657SpPVCyeHEQJwIddNsWjA2nXivoxui+5fAtq1TTIyls51jfc3OGmIR1I00RULJ7UmUUsoS60tYSnHSjhc5uuG5uFEC8uFaee6/f7G3qRS8WiKYS4XgjxI9SFaz1q5EiP85RKLJ7czAxx5eQCNgNPRDVmCLjdbSNcYl9gPJ1KTLptyCI5zLl92E0jPDqTdomoR4Hju8yzUV+h54kojxqLFlFOLsgwe4qlNUyH1MdRouZu53YzqoqpUv9aGzZu+lipVLw6GOzBH9hz5mm5VKJcLunAx9KpxF/rbBCo/+d6Z9/rgf2BE0CNtojFk+NMe6tq4mprOpVYcOdxp7eajiei9iAWTwZRPbRGXTbFLdbTZV4oh0OBZ5q4yPBYRrTTE6WjTtqPtGmfe8sY6oK5D/CAy7a0G69reWMaiihHqAyyp1haW/c3RdSF5CHgzyiP5+Z0KrHQaq0fAp8ZHd3+jz29faKnp0fouo5lWhSLU7JYnJJA4qorL/91/R854btxZ9vVGNAReGvYXVwdDzzfeYodiye3sbu42kzj5Ghvbl5jhpzbURdtcJP1QMFtI5bAYajFjYfHHrRLRG1G9Y05mC4RUelUonbxWInJ5UXU7DOvQm9PTMCIxZN97CmW1qE8DaDK2DcDTwG3Me1dmtybfKSrrrxcbti46QPArcXi1L8UpyaPq3v4r0Dqqisv/9+Fvl46lbBRQm5L/f2xeDLAtKiq3R7BdEiwPFtIkGkR5fWJ2pMh53alebaJxZM9qPYOXeWJcoZFD+GF8jwa0BYR5QiSx+m+vKgVWaGXTiVkLJ6cpAM8UZFsQQP2Qx2rz+SiobZ5OOo8S/ugvEn7ABc4W20evYk6TjYD9zAtlsZalbx91ZWXS+Cb7//QZddVq5UP2bYd1DR9yu/3xxYTepuLdCpRRnmQa9W1tc9jgN2F1YFAGHZNuw8CrwTujcWTa1CfzZZFeNqWM0Oo46XbcoKaQVcmlaO8UJIuWfx7tJ92lmo/BpzWZdVuW4GT3DbCJVxtcxDJFgLAO1FNIw917p6KZAtXAulcNNS0k1pdzlJNKNXf1oulbSiBdD/wPefn7Y43p+0IIYTfH9hed1dL7XC+tzud7b7a/U6CfC0keArqonMocBROgnwsnpzAEVQzbsebfT6IZAsDQBR4F8r7XUaFQb+Yi4byzdzXIhlihfaIQiWV1xYc3cShwNPeIsCjEe0UUY8CL0JdnLbM/dSOYSswEIsng+lUYqXleLjWtTySLfQAv0CI04xgr0/3BwGBbVZ6zdLUpdIyL4lkCy/MRUOLqnKKxZM+1MV+plhaw7Qnpcx0eOsupi/2o45H9WSAdCrRCe06xIzfXbk4OyM8NgObHQ/mwcCXUUJ85ud9CGphsuvzdtowzBRYo0sRp5Fs4UjgOoRYbwR6fJrhQ9r2gFUpbbDN6tsi2cIHctFQeq/e8NJZxcrOh9ri1oJjKTie18OAO922xaNzaaeIegJ1kj+Y7hJRoC4ET7hpiAtMoAoB3OAzCO3UwOBqn6ZPN93W9B50f9BfmRjT7Wr5Z5Fs4dBcNFSZ+cdO/sVMj9I+7N46YAJ1HD4C3Mz0xXuiizwFu4moDrG7ZpN0Qou1fKld1Hn+av+b2nY8dZ4/JyexXlhtQXn+Zg1ZRrKFXuA3muHf1z8wZNSPxTGCvX6zXKI6OfaJSLbweC4a+k5z3u6iGGLlnUdq7Ev3NdkcRoXzvSabHg1pm4hKpxLlWDxZG0Z8S7v2u5dsc27XsvJOfk0P58XiyUOAp2aW7dcTyRaGgY3+voHdBFQNIQT+/kG9tGPLWt0svSkWT/6WPcVSzW6JWvlvAf5G3QV5mXgW63tFdYKAgmmbGnocHG/ENme7p3Z/Xc5V/f9zLcob0Oc8Tcbiye3MFho8/qLXgdjPP7DKmDlXEMAIBJFWVZilqWQkW/huLhpq92c2RHc1HG4Kjmheiyqw6CZq+VArtTmqxwJo9/iKx4Aj27zPJZNOJSqxeHKMFZhcjvLU9MXiSa0ZLngnlPZGoBqLJ68Dbm3wuq9ACDTfnj2QagihofuDul4a+yAqPGShLsg1z1Lt4rqtRX3JOkWw1CuFTgmT7PJELfYPZ+Rc7dZWJBZP9rK7sNoHCKFCZAAY1eJbZP9qXYjG06z0QC9maepoVEhx1sVcLJ5cB5yNEj2XN8PD51Q79rAyw3lrUNeabvNEHQo8uUwWXB4tot0i6lHg1Fg82ddFXWtdqdCLZAs66gJRykVDbjR5m0B5FXqZbr65ZNKpRDUWT34ZOB94HXBBLJ78C6qZZ19t6z/g1PMmhw+Ws3kS6hGaLqr+/ing86gxJp0iItpJ/YfUKcJuXk/UUnAaHT7KDK9A3YictZYR+AdDN+Y8cBzvpjUw+uh5sfg1AnVs1zYNOBNVbTgK/LyJIdKa2Btt0ut1E/s6t11TmVeXD9Vt3jOPNuOGJwpUSK9bmpdtRfXHaQuRbOEQ4L3ApThhqUi2cCOQAb7fxhBEfcPNWUWUc6LxUSeC5tl6UReqfuBU4HnAn1Al35PApCatZ6Rta1JK5hJS0jYtqekPpVOJbQ2ftPzpRBG1ZE/UUnBCw08CT0ayhR1SyjkXPFJKAC1YGj0QeDnT9mqoBqM26sL5KPDsWDx5KLsLrdo2tUjhPuTcji7ib5pCJFuoteoQwM5cNNTuBcd6YGeXVbitQZ2nvHwojzlpq4hKpxJjTnjsYLpLRJ0Siyd1pwqpZUSyhVOAXwtdDxjBPr+mG0gpsSql06xy8VvA+ZFs4e9beRJ0hFEPqt/PIaj3vpXGwsg3y8tMUSeMUKG22s9rUFWaPwO+CTxev9qPZAs/ADZZlZJhBHqYDWnbWJWyAL6+l2+32+nEnKiaKHHDM/hdq1z8ZyPY628kwK1yEWBiy77P+cfh7fdXUMd6v7M9ihL2RdSx2ocSAANMNxGtYTuViLMJrJlbBSWiLJrg1V0oTqL921BtQg537n4qki18DvhyLhpqV9PPbkwqPwx1DHv5UB5z0m5PFDRpGHEkW/ABFwKvQV2YHweuAq5rsrdmK+piNcxe9DhxcoKsRqvXSLYwCPxc9wf7fH2DWv1FQPf5NTvQQ3nn9ktQ5baLLtF2kjtrF4uBWX6uv09HXQxfgVrB3sLuouiZGb/Xb8VGYjMWT54InIYawHrNbLkGuWhoIpItfL46Nf6Pmu7zacbuh6iUksrEmInKffrxYj+HJjB3nLG9dGJOVE3YuSHqviJt60NmaQpfT98eD9qWRbU4WQG+pJq2hmD3Y/qBWDx5I/B3qO/7t9KpxDjsmgnYP8dWS4DvZ8/zahV13O8L/C0WT+5EdS2vv92rTvYzcc4nv0GI5xiBXp/uVzmGVrWyn1maSiLtt0WyhTNy0VA7xM16IN+G/TSTQ4En5iqC8fAAd0TUo8C5sXjSWGp35Ui2cALwE2C97g8KoWmabZmmXa1sAG6PZAsX5KKhJ5tkb/0g4r1pFPdGoCcWT/4wnUrMduKKIkT/TAFVQzN8GD39hlmc+OdItpDJRUMm7BJns4mhmUKplz3DP5OosN0EzkXE+bl2XxC4Op1K3LQX77seAfwK+OM8F4wPI+VR5Z3bXqkHejTdH9SEAKtaxSxNVZD2VuDcXDTUUs9gF9DJ4by2i7pcNPR4JFuImsWJb0rLxAj2akI3QHlzqRYnqkj5F+CyRq+RTiXudForvAY4BtX+AudcNco84TjHkxtgT5G1H+qz6QcOQC1O6stPTUdczSawarelRQit/xGaHgoMDvuEVtcmxPBhBHr85fEdB0vL/CFw+gJfb0k445EG6CJPlPM/PBQ1RsnDY07c8kTVhhEv2lUayRYOB36n+QJ9/r5BXWi7IhqGbVlUJkaPl5b520i2cFIuGhqf46UWyiRqdX24Myusxmweibnuuxk1LmQkFk/+GbiRuguNOO5Vb9eDvb658oCMQA9mcWKfNc/c+R+x+DWPo07IM8MMFtMiaBz1eU/MuG8CtfKd80IXiyenaOLFOZ1KLOiklIuGqpFs4TXAa61yccQqF091HnoG+BzwlVw0tJJzoWp0oohy0xNFLhr6TiRbeNqqlC6zKqUX1j20DVWE8LFcNDTnXD9nkfN552K6KByRU3K2XYuuWDx5ADCQTiX+x/ldoMKFg6ik8/rb1aiL+AC7h2wrDbxYu27TqUQlki0cCvydr29Q1AuoGkLT8Pev8pXHtp0WyRZOzUVDf5n5HKea8ExU09ObF/s51NGN417Wov43Xj6Ux7y4IaKeQTXVe08snvwVs1/g51pxxYVu9Pj7V+kzBYem6wQGhn2lsa0HI+VbUCfNPZhjtThzq3lw3oASQP+31DddMxF4Fmr1dw51JxZhm4fOdsKrxxGMlunv9aFGj8z83MZZ3Gp1Pmx2P4m3DcfL9G3g207o1shFQ92UmNoOOjknyjV7ctHQ9cCLHDFxMCrHKZ+LhhbV7qLJzUt9qLBe/WvXcqZm9ZrXheBniqxVqNmFR6Eu9qLub0r9B5526uTQQVXN8Pn3fFWFphtohq9qVytvBHYTUbF48ljU+a4H+NHi3+purEe97+3zPXGxRLKF41EpHf2oPn7fbdLi6jDUYvSx+Z7o4dF2EeWMzqj1Xjoa9QWY2RTIdGZt1bZxYKIUHLI4/CUbjGBfQ4+N0DSMQK/fKo7HYvHkH9kztFXbZstbqN/nY3U/ayg3/g+d5852cp3vvlXAuaiZY7cCN6BmSQFIqekXSdsKzfqmak+ybQB9bPiwH2ffG/nNXM9tEq6JqHqci18r+j11O52cE+W6Pblo6GHgYZfNqOFDjRRaMI6nuBbimxVnbuEgdSKr6ut9rtB0sYA2Ib5gcfuLY/HkR1DnIhOVr3okaozPrah5pyfXPb7Y7QyUIDFQCfZ7TSRbOBBVlHKW0PSS0DRhW6ZAykwkW/gyEFusYJ7BoaiCF++c4zEvbniiAH4KDKVTiSthV6+XmR6g+p8PAvotPXAo4Nd9sxWETaP5/JhFcbBEvFIg64XYFpSLdtYKmkYrz1g8eRxQTacSS3bvxuLJDSgh8Nl0KrHH8NxItvA1s1z8pNHT37iyqFIEtaL7/VLtWCQdIaI6kE7z+kCH2dQhI2g6CQOVGtBUnCKOHc4GQCRbeIGw7VfM3ybEqppG8A5UfqnhbAeiUgQk6py5re4xn/OYMc9Wv9NLHNuCTihyW9221bld8JzESLawHrhR6MZ6f98gmuELgio4satlKpM734mU+0eyhdctpYq5Lh9qjxCnh8dsuCWiRlEuU2BXr5ftzOPyvfDrtx4D/IOU85RISQlCWBOD+//bV+Jva8aK2GTvP6vvo4RYo2T6q5Dy36tT44avd2CP5HLbrFKdmjSB9F6ushaDJ6I6m04VUa57oTqQ3cJ5Leb70rZStllFbxDRsy0T26z6bH/f52fmPMXiyZ+gKhQPB25KpxILHvTtiBCNaUFVQnn170RVUa9BLYpPYLo9iu2M8tk2yzZzluVHhKavCwyu3i0aIYRA9wcJaLqvvHP7Rah0iZ8t1O461qPCmF4+lMeCcEtE7QAGFluhJzXjAWCLVSmt1WYpYa5hVUo2cGOTBBQoEdV4DskCmK/RXC4aGo1kC+db5eIvbbNqGMFev2b4QErMclFa5aIFXA18Ym/sWCQWnojqZDoxJ0qjc2zpJNomonLR0IORbOHa6uTO87TB1f664hsApLSpTIxVUa1G/jzz79OpxM5YPJlFdW5fVC6TI3gsZyvH4skqKjSWr3+eI7YGmRZWte1YVHuJmkKqONWS28qBwSmOOHuj0dPX0FuvGT50f0BalfJ7cURULJ4cRrVreTidSsznxT8Mdb5/fDHv22Pl4qaIAtWAbsFtA3LRkBnJFr5glqb+xQj07HFyALBNE6tSkqgO383CYvdy5JaQi4b+GMkWTpCW+Y/VyZ1vRa2IQPVYyQDfaHO3Yc8TtSed2ieqU4SL54maHYPpHMh28GZpW9eXxrYeZwR7/bovAAisarnWJuRJ4MJGPfUcMXRrE+wIMEsulPP6Y872YP1jTp7XMDMEVik4fCaIYK3nVSM0X1C3ysUXOSkUq1FVhiZwcyyefDbqnFa/6XU/vwx4dKntdzxWHm6G82BpDSw/jbQvKu/cfpyvd8Cv+fwIIWqdvalOjVeBa4EfNNHeZoTzFkQuGrof+IdItvCPqJNHKRcN7Zjnz1qFJ6I6m05NLO8UQddJtDOcV/NsvwApN5nFyfeZxclag+MtqKrlL7T6vOJ4m/wsPqHeQl0Xdrs2RLKFe4D3zreOUU4qAaoqczvqeuNH5aQ9gvqu2KjFsT1jOxgvH8pjEbglonaiDtihxf6h09H6hdK2vlKZGH01QjOFpklpWzpSWsAXgXiTPTZtE1E1ctFQBXiqnfucBZs2eOA8loznieoe2iqiAHLR0CTwqUi28BmUR0YA29vYpLaWkLUoETUH9wKmXa0Yc3mjrGrFRohb06nE9wFi8eR3gLOA7XP1qnM8YGcDdzTJXo8VgCsiqq7NwfBS/t6Z+fT6SLawH9KOSMteheq59INcNNSwHHgvaEs4rwPxPFEzEFho2J3ymXSqiOoUWzqJdofzduEsKPdm2sJSqSmdprQ2yEVD2yLZwvfM0uRrNJ9/1jY3tmVhlYsS1ZQX2FW49KsF7GIYdb7zGvl6LBi3PFGg8qKG9uYFctHQU8BXmmLN3LTdE9UheCLKIZ8R5wDve+N6zhOg5TP/+W7gy8CXwyOyWSOGFkvHJJbnMyIEvOsN64wLJVpvPnPZ2Siv8I/DI3JF55c4TTN1Vl6vs5qIapYnCuAy26y+ojIxps2YWIFtVqlMjFZQsz6vWcJrr3FuPRHlsWDcvEDuYImeKBfwRNQKJZ8RIp8RnwJ+FvBx7nAf2nA/DPSwRtf4Z+DOfEac5JJ5rudEOZ/PZcDths7GoV5zv+Heyqqgj5egLmQ35DOiW77nraJWyu+JqL0kFw3dB5xpV8tPlka32OXxHVZlcielsW2V8s7tSNv+FXDeEtvArEF5zZoxLsxjheDmBXKU7hJRXjhvZfJ2YGSoDzHUhx7wgd+A3gCsGcAf8DEA/DKfEatcsK0TwnnvBP51VZ/6PHoD6rNZ1Ye+zyCarnEikMtn5mmfvbypLcBWmkeu2TlRAOSiodtRrQgidrXy31a5+D1pmZ8HQrlo6OV7kdKxBtjmNYr1WAxuh/OCsXgymE4lSi7asRBqYwtWGiu6T1Q+IzTgX/qCaIFZmuQLAat60bfsZEBKLkGFr9qJqyIqnxE+INkfRAvO8vnoGgz14d82zhmo8R/t6rTfaax0T1RTcqLqcZLjf+xszWINXijPY5G47YmC7vBGmYCxlKnuXc5K90SdChzc03CMqxJSPX58wNvaZVQdbudEnQsMz/X5GDr4Daooj95KZaWLqKZ6olqIJ6I8Fo3bOVGwl8nlbaLmhl9pgmKli6h1gKnP8wkY6vH1rTdnD9zOiTpU16jO0vN2N3w6PuCotljUmazUcF4AMJ2+Tx1NLJ4MoOa0eiLKY1G4eYGcQrl5u8ETVTsJrLSQ3krvEzUG6PY88sRSPqDRlluzJ27nRBVtiSbn2bOtHm/68N0uYqV6ohbdaNNFvMo8jyXhmohykvdG6Q4RVVtBrkQRtZI9UX8EthfnyOiQEoplKkC2XUbV4baI+rmUGNU5/CtSQqlKFfhhu4zqQFaqiJp15EuH4okojyXh9gVyr3tFtYnaZWKleWVWtIgKj8gq8OnJEqY5S0BCSpgoIW2JDfxXu+3D5Zyo8Ih8HLh2vEjVbrD3yZKaoY07IrNTWMnhvG7yRE10QZGTR4fh9gVylO7wRK3kcJ7bx4jbfFzCtdvGMceLYFpg2VCuwo5JqlNlqsDfhUfkZhdsczsnCuAdps1T28eplipKWAJUTRibxJ4sYwGvC4/IMZfs6wRWsieqm0SU54XyWDRuXyB3AENdUPXmhfNWKOERaQGvAd49VeaebeOwdSeMTmJVTa4GTgmPyJ+7ZJ7b4TzCI/IZ4LmWzTfGpqhsHkM+M4q1fQJKVf4EvDg8Iq91w7YOoiaiVponyk93hfM8EeWxaNwWBTscG/rp7C6xKyac5zRFPAd475vWi7ORaPnMZTHU5PdvhkfklLsWth9HSH0lnxFXTFoDh/xx7FXvl+jf/ud/u/KPLpvmuogCCI/ILcDGn3/i0A89Vj720/v6H/zzgYH7fhEekfe4ZVMn4HyXnn/+6v1eu9Pc57jDegrn5TOX/cw5nlYCAbqgoMBZxK8B7nTbFo/uw20vw6hz2+khvRURznOaS14J/CTg45yhXhkY7pe+3gAhoRpJ3pzPCDdK+TuC8IiUL3j/zoefqR7+zObqIa5fCM1qtb9ULB5YLE4daFarvW7b88sdb63ePfW8+68ffdOPPQElngfcBdywLvDUO47su+OFQA54LJ8RF7trXdvolnBeP8pWzxPlsWjcFgX1vaIeddGO+VgpnqiEgEuG+9F8xrTADvigL4BvxyRHmhY/yWfEc8Mj8xW2L2uKQNCtnW/YuGk/IAG8lenRGm/ZsHHTGUDiqisvf8gl0/qc2473PrSSfEY8H7g+6EPvC4KhEwCJbcNUmf0my3w/nxHR8Ij8ptu2tphuaXHgVeZ5LBlXPVHpVKKC6hfVsZ6ofEboF67JnPHcgZ+edP7qr1ycz4gD3LapFeQzog94/0APhm8Waa2pER4+4ETgRe21ruMoAT1u7HjDxk2HAH/VdWPj4Koh/9p161m7bl9WrRrWDcP3euCvGzZuOt4N2/BEVC2E9/WgD32wF82oW3ZpGvT3QH8QAXw1nxEDbtnZJrqlxcEaVDh8x3xP9PCYidvhPOjgNgf5jHgz8OiAMfqD4/r+ct4+vqdSwKP5jLgmnxH7um1fk4kICATnGOGha+A3sFAekJVMCfc8Ud/z+fxrVq/ZxxcM9iCEhhCCQDDI8Oo1Pn8g0A/kNmzc5MZ3uw91MVpxeXN1nAUc0d+D1mjkcm8AhIoCXNJOw1ygW8J5a4Ad6VRipSX+ezQB18J5+YxYDWx8/Tp/TKe6Jp+5bAqVM/D58Ij8i1t21chnxPuBT/QF0Xr9oGlSkxIqJkyUeIVp8dx8RpziVCctB/bTNEwh5j4mDB2jYnJwu4zqUIq44InasHHTicCpA4ODiFmu0EIIBgZWGdvKmw8HXgL8qs0m9gPFdCrhVruFTuBMQ6esa41FthAQ8OMrVTgT+HIbbWsL+Yw4QUouevHQkef0auPr85nLngiPyE5O1/Aq8zyWjCueqHxGHA/cpQn+c1VPZf1wvzQGexn0GbwO+FM+I/6fG3bV2Xck8MnBXrT+oHLDg3Py88HqfnyGxr7Ap9y0s8mML3CER63T/ErGLU/UhYZhlA3D1/AJuq7j8/st4O/aZtU0fcCEC/vtJAyxe9XkrDhPaPyP7ELyGXFAPiNuAPI+nQ8e2nf/c9f4n9kEPJzPiG/lM8L14ocGeCLKY8m0XUTlM6If+LXfYM0+g/j7g0qY9PiVOFnViwD+PZ8Rb2y3bXVsMjSqwQanOCGgrwcf8Np8RuzTVstax4+lxKjM4dC2JZQqWMDVbbOqM3FLRPVrmjbvBVrX9FrbkHbTxwrOh3K4s2phNOrgDqohadmkAhTaZlWLyWfEWuBGQ+fUNQOwZpDA6n6MfQbxD/chNMHFwI/zGdFRwjEWT2rAajwR5bFE3PBEvUnAmqE+jNlyBoJ+6A2gAQknSdMNXh70459r7wEV9NKAF7THpNYSHpFPAv87XqQy28BdKWG8iI0ayrvSRVRbw3mxeHIwFk8+1x8IrDdNU5PzuAtNs2r6fL7BWDx5QiyebOfq3xNR8CNgrDhHJlC5CraNgTujglrFB3WN9cP9+OqT6YUAv/Le+4EzgNe6ZWADhlHncU9EeSwJN3KiLu0J4JtLoPT6YarM0cBJwC3tMqyOOQUUqJODUM6ZOVKxu453WDbP3jbOEX1B/EEfINQIj8kSZtWiArwiPCJX+nyplnqinOZ/+wFHA8c4P9t9ff0379i+7Q2VSplAYPbdVysVTNM0Vq0avhl4FWDH4slHgbuBu9OpxGir7EaJKDfG33QM4RFZyWfE+ydKXCkEosevzhWgFiIVE8amMIFPh0fkE64a2yTyGREELu0N4G/kJ9V16PGjFSu8D3C9tYNTjfzyV6xZ+6wnykeHNExLdQ3x8Fgcboio/Y15/F+6WslYwP64I6Luqpgc0hto3BfKtECqnIZ722hXSwmPyB35jDjdlsTHi7xzvMgqAAmWUN6nfwuPyL+5bGYnUAT8sXhST6cSTWm6GYsnfcBhKOF0NDCIEmv3AX8E7v9s+j+LGzZuOm7n2OjG4dVrfDNzoyzLZGxsRwX4yec/k/poLJ4ccF7rWOBlwHmxePJp4B6UqHo6nUo0s99XP15OFOER+T/5jOgZL/LZiRIEfSr3qWJSsWx8QAaIu2pkczkcGAjME6gL+NCKFU7MZ4Rwq89cPiMM4DJgBAis9m2xhoytBsiX5zPif4B/XIlTGTyWjhsiamKufAFQ7h2Ui9WtUTBfKle5wLJVWf9sTJWRwG3hEXlbWy1rMeERuROI5zPiMuDYW8bPeemT5SOtf/2PL2bctayjqHniguxF+CoWT/Yz7W06HCXKt6PGT9wLPDqLSHuvlHLf7du2vjIQCMpAMKgDVMplu1QqSuBGnNL5dCoxjlqE3BKLJwPAkc6+TgNeCIzF4sm7UYJqtn0t5r1oqBDnSg/nARAekV/OZ8T3nigd/on+6tjJg8a2x4Fbga92eKXaUlhM2oVrc1KdiQzfFPCqgR58QeUlNKSUlKvo40XeYktC+Yx4iedt91goboiobxcrfLA30DhkVlLt2UZRK3A3+Dnw5x0TnDzUh78+xi8lTJWhWEECH3TJvpYTHpFl4LZvqAv9WbF4UjTZa9HNLElEOWG69UwLpwNQfZUeA65HCaetc33OV115eWXDxk0XAedXq5V/rVTKYfWIuBNIAT+66srLqzP/Lp1KlFHi7M5YPKkDh6A8VMehRFUpFk/eixJU9zuNcBdDL+oC6Ykoh/CI3PaNePJPwLXpVOKHbtvTQh4CpiomvT1zJDeUq0jgDhenHVwEXDw8gO6bkbcV9IPPwL9tnOdKybuBtEs2enQZboioKyybD02VoW+WtA7TgokSVVS/KFe63YZHpJ3PiAssm2u3jfMCv4HlMzCkhGKFqlRl/hvCI/IXbtjXZraimuYNADtdtqVTKDq38yaXx+JJAziUaeG0CtWA8AHgL8B96VRiUeGDq6683AZ+HIsntwLnO3f/bzqVWFC1l+NxehB4MBZP/hTYFyWojgWeA5ixePJBVNjvnnQqsZAQ3YrvVj4Txzu3DrjDbVtaSXhETuUz4muTJTYFfbMvji17V2Vvpt321fG+oB/ha5CkoWvQG8A3WeJ9+Yz4dHhEruR+Zx4LpO0iKjwiH89nxBsnSny3aiF7A2pV4JTPM1miKtWq/D/bbdsMO0fzGXEW8MKKyTsqJkeX7R7/k+UjHj4wcM9bT/mnylY37WsjW5zbtXgiqka9J2oPYvFkH3AUSjQdgSo+GEV5ee4FHm5SLlV9sHlJq3vH6/WUs10XiyeHUWLqGOAVwCti8eTjTCemN6piqrVU8ETUNKtRIdrl0pB3Lj5m2bx2xyRrVvXg0+uESlUl01ck5IFvu2GcE8p7QdA3dzgx6IPJEgcCBwMPt8M2j+7GlY7l4RF5dT4jzipX+Ui5ystw4uSWNHY8Xj769z5Rec0FH7zP9ZlLjtv5emcjFk8eDmwA9FPcM6vdjKIGMO+D8p54zBBRTphuLdPepgOdx58Afo8STptbEA6tvyA0ZdWcTiV2oPKqbnTaI9QS018EvMzxftXyqJ6oe0+eJ2pP1ju3y15EhUfkU/mMeEHV5Edbx3m2oWMaGrppUTVt/Kju+W9w0gTcQIdZG/3vRt3jHdXPyqNzcW3sS3hE/gE4N58R+6MuOsUfbn3vjqI9+Dbg2Avgdrdsm4NHgSrKu7DsT4wA6VTCjsWT21AiwUNRQXl+jojFkweihNMw6ti4HzW+6L4FhsH2hr32RM2FE2bMA3mnevBwlKA6CdXzZzwWT96DCvsNApUl5FItZ9YD4+lUYkUIy/CIfPBzl732BL9W/MKxvX9eN2RsGQOeBr7hdlVveERW8xnxeNXkQP8cVz2n2XAJeLI9lnl0O66JqBpOk8cnAcJALJ68DzgzFk8WOi2ROZ1KmLF48hGUiHIr6d0NtuCJKGLx5GrU//4I1BDme4GfoUTEvcBDbR5i2nRPVCPSqUQVJ0fKyfU5CCUejwWe62zDsXjyZ6jEdC/0q3LNVsRiq8aj5WftD2y+v/jcj6VTiU6rQvzCVJl/62nQz8opGqoCXw+PyBUhfD32HtdF1Cz8FngbcDyqmqjTeAA4OxZPGito6vdWVA+jFYXTFuAwlGg6EuVtslHVdH8Cfgh810Wx31JPVCOcAcOPAI/E4slfogT2vwAnAK8ERCye3Izyyt2Pap+wUr4r9axnmSeVz8LRqMKLx902ZBa+akvePTrBvkN9GFrdt8eWMD6FZVoUgU+4ZqFH19FxIiqdSjzuVAadFYsn7+o0bxSqqulcVOLhgy7b0i62AH2xeLJ3sZVk3YTjYdkPJZiOQIWZNVTvpvtQAvrhdCpRjsWTa4HHXT4+60WUK5VEzvvf7Iipu4AsKux3JKrS7/lAJRZPPoQjqpy8q2VNLJ7sQVViPu22LW3mKNT/uOMq28Ijcns+I84qmcbvtuw0Dwj4sA0N3ZJIp3JwB3BeeESulPO6RxPoOBHl8FtUuOQYVAJrJ7EZ1ZX5CFaOiKpVIu6DygtbNsTiyVVMh+gOR7UtKKP+tz8BHmhw0Re00fvTgLaF8xaABtiOyL4DuKOuL9aRznY+oDk5djUv1cNOqHC5sc65XTHhPKdD/n50cKrDN5657BkN88unDv7YOJJbTyirXm3bgG8BV7uY+O7RpXSkiEqnEo/E4smHgRfG4sl7OskblU4lZCyefAB10f2l2/a0iW0owbAWl0RUJFsIoJrlvQYYcuz4OnB9Lhpa8PERiyf9qEaTNeG0FvXenkD1bXoAVXU2XwuCThBRroTzGiCYIeSc7+3TznZDXXj0SFQu1WmonlSPMC2q5mw22ohItiBQnq9hlOf0rsUcFy1gX9ToqpU02PYo1HF4v9uGzMEZNgZ/2nlh+tXxvy5br7pH++hIEeXwO1Q7gSNRoZRO4gHghFg82bcSKm+chPodKE9U24lkC6cAPwaGdX9QF5ombMs07WplA3BrJFt4eS4amjVsUucNqeU1HYwqdx5D/R+vBx5MpxLF2f5+DlwbX1FHx3mi5nqC0zX9buBu5/+yhmkv1dmoMPlYLJ6sCaoHnb9piCOe3gH8M7vn7f0tki38Zy4acmvY7XpgS7NmK3YJRwOPLeG71BZi8eQgcCpww3JOS/BoL50soh5CJfC+MBZP3t9J3iimw3iHAwvqEr0McKVCL5ItHANcp/uDPb6+AU2IXc4Xw7YsKhOjIWmZ10WyhefmoqFJ2DWTrj5E149qP/Aw8AuUeNq2l8eU54naHW0xNjif/VZn+5PTQuEQpkXVyYAdiycfY9pLtdvAZEdAXQG81Qj26XqgB6FpSNvCKhePM0tTV0WyhWNz0dC/NutNLoL1rKB8KKcz/+Govmidylmo9iQ3um2Ix/KhY0WUEzb7HfAm1AqzY/KP0qnERCyefAZ1kV4pImor8CwX9vthzfD5fX2D2sxOeZquExgY9pVGtx7hL429LxZP3oT6n+zrPOUpVJ+jB1Ar5GZWiHWCiOoqT9RcOHlRNbGE0zm9JqjORHmqJuq9VBx/0auAt/oHhnXdNz20TegGWu8AmuHXKhOj/xLJFn6bi4Z+tVTbFstKGfcyg0NQnfnvdduQ2XDak5wE/Go+76aHx2LoWBHlcD+qh9QL6SAR5fAAEFpBg3m3AEOxeNLfjIaKTn5M71yVWpFsYRh4nRHs9TVqNSw0DSPQ47PM0giqNPkBVGLrgy1udtkJIqrTPFFNE3LOcXETcJMzMPlgpkVVGJC6Wd5I35BWL6Dq0f0BNF/AsqvlEVTH7Haxksa91DgKNRZqs9uGNODFqIKgm9w2xGN50dEiyvFG/RZ4QyyePCSdSjzitk11PIgq396H6flyy5nae9yH5nTzfQ7w8lg8eTfw23Qq8VT9g7F4UviOPOfYqr/fpxlzjIYHNJ+fihEYAj7VRkHbaSLKbU/UHonlzcLJK3rI2X4ZiycHxwcOeK5lBC4LBOaeAW0EeoxKtXxBJFvQc9HQrPlJTtf5E4DfN6lJ6IoZ91LH0cC9nbigjMWT64FnA/+3TCtBPVyko0WUw72o3IIXAle5bEs9j6Bmyh3ByhBR9W0OmiGibkFddM8FXhCLJ7egwh8BVPXd0Nqnbz/oyYOfz/xaRQKYbT6Bd4KI6rRwXls+j3QqsTOSLTwEgNDmfK5QHRXFoff9/IJY/JonUb2AtqO8Jgeh8mSOQB3fzcrnWVHjXmLx5BqU9+3nbtvSgJeg/u95l+3wWIZ0vIiqy416bSyePCidSjzmtk2gcjhi8eSjqBPwn9y2p9U4DSZ3sojkcicMM+Rsw7Pc9qKEwCGofCs/8DdU+4Lb/JXxSeCNVqW8ygj2NtyPVSlZtD+htRNEVKeF89q5yt8CWNIydXS94ZNsywRpl3zVycNROTE14XkQqqfRM8CfUbM694vFk0Fgx156LNaz8rxQJspT2FHE4snaeKL/XWGVkh5touNFlMPfUCfNswC3SpZn4wHgRStoBMxW6tocOAm0AzQWSQNMX7Qkqq3AKCpv4l5gHDgdlZz/w3QqsUe+QiRb+GK1OBnT/UG/0Pb0OthmFatSFsDnmvD+FkMniKhO80S1zYZcNDQRyRauNktTF2k+/6w5c1JKzNJUBaF9+VOpxGfrRP0wKrxzIapaK4DKmfHV/jYWT46jPFbbmfZe7QC2L6CEf19WVlL5UaimqR01fNppo3E2StCupP+HRxvpChFV5426OBZP7p9OJTplwvaDwMtQ40EebvXOnJLu56FO+AZqIOwPctFQy6pNnBPRIMoDdThwutOwchg11qLeDTCBEkk7UN6kHXW/75y5EozFk5c4r3NVOpW4p4EJH0faF5Z3bj/K1zfg1ww/QgiklFiVEtXJ8SrwXVR38bbgfCbgvojqNE9Uu4Xcx22zcrFZnMTo6aNeSEkpqU6NS2mZJvAF2JVbtc3Z7neqOd/o2P0llDdlNeqYrN2uQzUG3ZV8FYsnS8wirpzbCito3ItTIHIInRnKOxw4FPh2J+ZqeSwPukJEOdwJvAjljfqOu6bs4mlgEhXSe7iVO4pkCycB3wCOE7pRApCWaQCTkWzhQ7lo6PK9eX1HGAyhxNLMrZbZ/RxUlVQFJeDqRdLoEkIg9wK/nplUXk8uGtoZyRbOlLb1lcr46MUIYQpNs6Vl6yCrQAb4SJu7U3eKiOokT1TLEssbkYuGbo1kCxebpcnvW5WSNII9AaHp2JaFVZ6qSNuuAhfkoqFZK3vTqcQTsXjyv1BtVM5IpxLXoryjexSwOGG+mQJrNWoBNcj0/2JfVJ7f47F4cgjlBXkGtYhoyfESyRYMVPf3VSgv7y1t/D4cjlpIdVRD5Dov1GN0aNsFj+VB14iodCphx+LJ3wN/F4sn16dTCddzDhwP2YMoEfXrVu0nki2EgRt0f8Bv9PSj6UYQQEobs1RcZRYnvhjJFvpz0VB6vtdyQnDD7CmU9mE6nFFBhU+3oIbK1n5+NvC8dCrx3Wa8r3Qq8ZeFPC8XDe0AXhvJFvZHyldIyxpE9YD6US4aamUbg/lwW0R1mieq7TbkoqFcJFs4WtrWO6pTE1GUkNgG/BfwtUad7GukU4ntsXjyS+z+Wc72vBKqoGIPL7jTaHLY2U4DQqhz6wuAoPO0otNbrn7bvDe5V5FsQQc+APwT6jtsoQTNA5Fs4T9y0dD/LPW1F8HRqM7snTZU+lhgf+B/PC+URysRUnbP8eXkNLwbeDKdSnzfbXsAYvFkGJVb8cmljhKIxZOvQ1UL/XK23KpItvAXzRc4yd+/Sp8t98MsF6lO7rSAg3PR0JPOa+qolfJMsbSGafFcYlog1W+zrppj8eRZwKnpVGJesbYcyWfEeuDtwKVSiv0RTArkd4Avhkfk7e22xzlujnN+/XSTyvMXRT4jjgXePmENnSuwp/r0nd8ArgqPyNF229IJxOLJ44DXoXqWFVFeqn1Ryea1bQ3TOXXb2F1YPc0CvFaOgPouiIjR0+cznG7tygtXxCxN2kAqFw19uCVvlF3envcDt6dTiV+0aj+LxVkovhP1OWbdtsdjedM1nihQOQ2xePIG4BWxeHJtOpVYVGsBx+39bFR+wyM1wbFUnPEiQdR0eiMWT/4ZVaFkOrdz/Vz/+6PAOcChsXjy6vr3FckWTgBO8fX006jhpO4PYhYnLP/kto/G4skfMy2WavlKRZSb/zHgr0yLpYlFrtJc8TZ0AvmMOAX4pSbo6Q3gN3SJbTNYrPCWqsXb8xnxrvCI3KuQ6hJwLZyXzwg/8FVgg6FTWRcY9UsJpSphKflEPiM2hkfkt9ppU4ewK9TrfLfGnG1Xzp8z4mYduwur5zPttSrVea2eZnav1duBCwODqw3NmD6Na7qO1tuPZvi0ysTo/4tkC7/ORUPXzWaoU7k2mk4lxpf4XvdDjVTqtHBZCHUO/IHbhngsf7pKRDnkUXlRLwa+t5A/iGQLAdSA0vcwXaIvI9nCL4BkLhpa0CylWDzZg0qiPAyVC7AWddIcQIXD9keFxGqb4dzO3cxGMeC8r4ucBqNFoDq4/8mnjw8fWtGMxh0nhRDo/qDfLvnPAK5D5WfdxLRYmmqSS7sTKtLajuOB+mXQx8BgL1q9lu0J4C+WYWeRL+Uz4uHwiPxZq+3ZsHGTBrxM1433gTxQCFGyLOvpDRs3XXXVlZe3a7DqfwnB64b6wG/sypljQOKbKsNEiW/kM2IyPCJ/1CZ7OoXa0dFQ1Dpi6AlnA3Yr4KgXVocDpzivKWPx5HbgGYl4Whx34Qf1nv7dBFQ9dd3a34c6J+zCye86H9Vg9FpUz7alcBTKm90RbWdglwf+xcDfOqgAyWMZ03UiyvFGPQZ8PBZPHoMSVQ+hSmwnQFWM1OYjRbKFIPBLhDjN19Pn0/1BEBq2WRVmaeqldrX80ki2cHEuGtrjZO9UoR2EOpkdhlp5CVQi9UPAb1GrTImqMJs1gdX5YtcElW+Wnw9BJUHei0qgv7X2mGkEjkGIBQgXQdXf91Q6lfj6/M9dMm5UYHUCb9MEPTMFVI2eAFQsZKnCh4GWiqgNGzfth6qEerZhGLZuGLpt21hW8fNAasPGTa+86srLb2ilDfmMCAGXOAJqN4SAviDYEjFV5jP5jMiFR7ooZ2DvqS2YFvWeZ3itdnl2HK/VWurEValn+HwptEP1ebu1B41KtfSK98f/7UyBFI5ta4CXos4vNwP7xOLJ81HnNa3BbaPH3oHysB0YiycfS6cSnXBuOBmVF9dJrXA8ljFdJ6IcfoBaRR2MqqY5GcDper0VODMWT37d6Tv0bwjt1MDgap9W15RP9/nRfX69WpyQZnHye5Fs4eCj77pmK6ra5jBnOxAVEptAtTO4CXgonUqM1l4nFk8e4fzYMLHSKa22gD1aETjx+4tRPac+NzNhPpItVLDtd9qWhTZHU0GrWq6w9BXlQlmRnijg0t4A/gbRVAB6/WilCi/IZ8Sh4RH5cCuM2LBxUx9wnWH4Dl81NCx0ffqAkAODxvj4zsFSceqXGzZuOuWqKy9vZV+cTT6dSr0Haia9AZgqcyhq0sD1LbSl02hq5abjtdotoT1y1W3HAx9qFN6ftkQDhI4Qz0dKG7UAOgB1btuO8nwd5dwv57id7b5aaHEV8FZgKhZP3osSVQ8stmdUJFs4CDgDJe7uBm5abIWhs+g9C7htsakeHh5LpStFlOON+iSwCRWu+hqqH8hhqK7ExwMfH/nwx3IcfcG7fX39/kYCxAj2CatUpGf8yc8Dt6G+xCWUp+nnzu3WOcJhw6gTy9gS34sdiye/ABQb7OP3wINmafIIf9/grK9hVStIy/QDrc7JaXsZe4ewzmisXwGoe3w/Wtfu4k1CiMOHhlf7tBmNR4UQDAwMapZpGtVq5SPAa1tkA0B4LgEFoGugaZRtm+NZWSKq9o9p3fdEaE8Clm2auu5vfGBKywTY8qmP/uvH6++PxZNHAa9A5Yb+NJ1KPLAUM5yw4CRqYsMxqIq4MGA6Vcv3oObpNcy5imQLh6D6eL0cIUzARsoAcFckW3h/LhpajGf3VOc9Xb+Et+PhsSS6UkSBmp8Viyd/gOrxEk6nEjcAdzihvoeBHdv3OeZkhAjq/mDD1xFCoAd6/CVzzenAZ1Gi6elFuKaHgbG9cWXPVdWXi4ZkJFt4r1UuXlvVNGEE+0RtBSqlxK5WqEyMVYH/zkVDdy/VhgWyUhPLpyybxgcRYE9/KktN0l0I7+3p6d1DQNUQQtDb12eMjVYu2rBx0z5XXXn51lmfuPdUF3QQSASqeGIl0fIeYrloaDSSLfzALE39nebzG3N0ay8DX575WDqVuM9p63AGuxcnLJZxYCidSjwOPA78OhZPrkYJqmNQQk3E4sknUN6le1DtECRAJFs4FLhJM3yrjJ5+oRk+nxAC2zIxS1PHW+XijyPZwhty0dC8ua9Okc8LgVvqIwUeHq2ma0UU7DoZ/B54SSyefDSdSjyaTiXyOIMmI9lCACFMIYRvrtcRmoat+6x0KvGHJZgxzByhvGaQi4Z+EskWXmMWJ68yi1N+3R/wIQR2tVKRtuVDVUm9r5U2OKzUcN73ihU29gYae1+KKnjxCKqvVqs4wuef0wGEz+cHFYI+jOmh0c3m16UKz+sPNg5xVk2wJQHaP9PQbZaUE7UEUrZZubBht/bJnba0rSINvNNOzuje9rarDXGuf93twI3AjbF4shcVLjwGOBOV97kjFk/eA9zN8RddqRm+Vf6B4d3G9mi6gb9vkKqma2ZxIhvJFn6Zi4Z2xOLJZ6HCh3ej8sPW1d2ehyrs+exevicPj0WxkKqxTuc6VHXIa2LxZN+Mx55ESkPac8+dtC1TsvQKk5aLKIBcNHQNsB7ku6xK6dtWuXiNtK2PA4floqF/yEVD7Vjxr9TE8i+alqo6m42qBZMlTOBT4RHZys/Hmr+v267HWzkM+Gu2RC81yHqREiZKWMAfwiPyby20oxMRTLc3aBm5aOivwEVmabJSHttaqRYnVb+4qQlKo1sqVqU0Bpydi4YaTgNoAuPAQN0YpN1IpxJT6VTitnQq8T1U36xvonI/nzXVu88/AS/29Q7MOvcQwAj2ghAEp7Z/JBZP/gOQAt4FvBfVi+t01BBzHZUz9v9qxUUeHu2i60WUE0a7GvVeXjXjC30j8KhZajwvVEobq1y0UN6cReHsazUqSbPl5KKhyVw09LVcNPTGXDR0cS4a+kguGtpjREULWZGeqPCIvAN4x3gROTaJXTWVULAsmCjC9nFM4Brgi63YfyyeHIjFk2fqhvFQuVScc0VQKpUQQhTX7LNuXSyenD2Jbi8Jj8ingJGdReRECew62WhaMDqJVTGZAi5txf47nLblDeaiof8DDpO2/Z9mceK+6uTOzWZpsoCUHwAOd4RWKxlHRTPmLhME0qmEmU4l7kunEv8HfPqZ/U96QghREXrjYMiu1i267xWoxeo2VA7Wd4BPoYTZdSjv1DXpVKLl7UU8PGbS1eG8GulUYjwWT14DXIKK8/8eIBcN2ZFsIWmWJr+mGT5N9wd2+zspJZXxMRO1illKB/Qe1AT4Tht50CpWamI54RH51XxGPFKq8uFSlTPrHnoYdUL/UjO9UE7V5hGoQoljACvgD3x/amrysmqlwmxhPdu2mJqcqOi6ca2u689FDYu+F1VV+mAzvSPhEfmFfEaMT5b45GSJNZomTIG0ndyxW4G3hEdkK0ObnUpb8wadhsH/5mztptYhfwBYcH+ydCohI9lCUQjNmq/CUAiNSmDg6XQq8R/OeJ3V6VRiM0AsnlyFKqB4BPjlkt6Bh8desixEFEA6lXigLj/qsXQq8TBALhr670i2cHBlYjShGX5TDwRV8qJpYpanqkj5DPCSXDRUWsJuh53blSKiVmpiOQDhEfkL4Bf5jDj47qnTXvJk+ciT9/E9/t4NH76+aZ+J4z06ESWeVqG6Vf8UKExNTZaBA3fs2PbW/oFBIxjsQdM0tRiolJkY31mxbfse27b/HhXOew7wXCAKbI/FkzcD+aWOJ5pJeER+PZ8R3/zb5OmpAWP7AQcG7v0LcH14ROab8fpdykpaaNSKKAZQx+lieEDaVkDaNqJBoQSAbVYqOHmGzkismoDyoUJ6VeBqp42Mh0fbWTYiyuF6VO+oi2Px5Fdq8fFcNJSMZAs/s83Ku22z8krAjxq18kXgqlw0tKT2BKw8EbUiw3kzCY/IR78RT94IHPpk5ah+9rIiz/E6HYnqd3Y06sJwB6rv15P1HqQNGzdtAh6eGN/5wYnxnb26rpu2bWtSSg3Vwf/dV115eS0v5CZHOB2E6nx9NmqRcSfKO/XE3nqnwiPS/EY8+TDwm3Qq8dO9ea1lwkpaaNSOs4El/O3Pga1meWqdr6d/1ifYZhXbrPqBK+rvd9IoXolqQvpf6VRicgn79/BoCstKRDk9l/4X1Un3olg8+Y1a64FcNPRn4M9N3uUwqr/TUrxY3chKTSyfjVooY5AliignHFHzOg0CTwE/Bgq1jvszuerKy23goxs2bvo0cIFlWfs7+//JVVdevkeDQUckPQo8Gosnf+bs72RUs9qnY/HkTc7+FtUcse49aKi8wJuW8vfLkBXjiXL69U2ijt1FkYuGzEi28CGzOPk1oema7g/uVmFoWybl8dEK8ItcNDSzifDpKC/r1elU4um9eQ8eHnvLshJRsFt+VBRVVvvbFu6uLZV5nUA+I/Z5Tt9Zzzalvy+fEfuER2Sryue7hZr3cpC6GWjz4YiOo1FC5kiU1+l24K+LmfV11ZWXl1DJ7AvGWbHfEIsn/+Ds+7moXj7nxOLJ24Cba/kmi2AVqjpq2yL/brmykjxRoBYTS/FE1VIthquTO9NmcbKqB4J+ENhmpWpXKz5UC4bX1f9NLJ48HDWs/Q/pVKKVXfk9PBbEshNRAOlU4kFniO+LnP5RD7VoV6tZ5iIqnxGHA/8OvPY5/b+rHS/vz2fE94APh0dkqz7bTqeIaiS5aiFPjsWTQyiP04moi84TqOGvdyzVC7RUHO/UfcB9jl0nO7adGosnH0F5lf62wDyTNc5tWypUO5V8RmjAy16+el20aA8cmM9cth34TnhELveS+3GWKKIActHQpyPZwjXSti41i5PnoSZGFIAvAX+oH/0SiyeHgdeg2iTsbY8rD4+mIObvO9OdOCv+S1CN2C5vVv+QfEYEgFcDz99cOShsSd9f9ws8+K/hETnajNfvJPIZcRzwR59OX18QX23YbMWEiRJV02ICeF54RN7jpp1uEYsn3wvcnU4lftHgcZ1pr9MRQAXldbql08IQjq3HobxTh6JKyf/KPB2gY/HkqcC5wH92yADatpPPiBcA3wIOMnSqQqCZJlIqkf2vwKeX6xDmWDz5SmD/dCrxlRbvxw/8PUpkfTWdSjTuW+Ph0UaWpScKduVHXYOar3dxLJ7M7u1JPp8RrwKuBPoDBuIg32OiYnKKlLw9nxEfRjVbXBYny3xGCOAav0H/UB9GfSVywAd+A9/oJAMVkx/kM+JZy+V9L5KdzJIP4oy+OAk1R6wfNRIjB9zZbq/TQnG8TnegRietRYmpU4EzYvHkfSjv1AOzfIfWANtXsIB6HnBd0I/eH0TomupqLyUUK/jGi3wc1QrlP1w1tHXsRLXgaBlOIvmFqPSJr3kCyqOTWLYiCiCdSkzE4smrgTcDL3z3lVfd9KjvxFeihsSC6mfz21w0NO8FIJ8RrwSu7gug9QZBc0SFlGilCuws8jHU5/mxVrwXFzgLOGawl1lbuQgBgz0YW8c5DngBcEOb7esExlAh3Zon51iU1+lw1BDr21C5Tost/3aVdCqxBfhpLJ78NRBCCao3AaNOtd+tdRVRa1jZ+VCXB33ogz1o9d8TIaA3AJpAH5vi3/IZ8T/hEfm4e2Y2n3xGBF86fNiZVdt/zl8/kxzShPwd8KsWdO0/A3gW8N0l5Ox5eLSUZRvOqycWT5713IGfvv/I3r+ef1PgNcbPVv1LCYmQthUA7gcuykVDDZMU8xmhA4/2Bth/oEFv3mIFdk5hAgeER2TXf9HzGZH26bxn9UDjeXEA28epVC0+Gx6R/9wu2zqFWDx5NqpS6C8or1MfqhLuFuCudCrRytErbcPxBByAElPPRlWg3YXyTr0KlT81a0hzOZPPiFOAv6wZAEOf/TlSwrZxKpbNx8Mj8iNtNbCF5DPiHcAngR5DFxKkbVr4UF7XaHhE/q4Z+4nFk0cBbwR+l04lrmvGa3p4NJNl7Ymq8aZ1l50oBK8M+hCnlr/Hjb0f7in71iBti8rk+OF2tXxDJFs4Yw4hdS6wb1+gwaNA0AcTAtuWbGR5eKP6NI0Gl4ZpNA0di952GNQpxOLJIGpl/HLgfFTuy22o/KE92gx0O04i+uPA47F48hcowfhcVJn5ecCVsXiyt1lNPLuIUzWNkqETbPQEISDgwz9V5ox2GtZK8hnxPuDT/UG0ngBoQi3ELRsmSxxYrPCrfEacHR6RezV8OhZPrgEuBu5F9QD08Og4lr2IymfEYULwqcFeRNAHUzvh2Tu+wS3r3ofQdPz9q/TKxGi/Xa18O5ItPKe+GqSOkwydiqbNf7IsVjilhW+nnTxmWphSojeazCAlVE1M1AV2WVM3huUEVNhOR+UQ/Qk1t6sdA6BdxxFKf4ypZqOHo5LQDwXe74yYyQP3r5AO0vMMLdn9ua0zo33kM2IdkB7sUQKqHl2DgR40CZQqfDWfEcctJFcyki3oqCbJAhjNRUPbY/FkAHg9qqHnNa0e6OzhsVSWvYgC3qZrmEGfEgMDAZPTxq/k5n3ejdB0hBD4egf18tjWZ6O6Ov9lltdYzBd4uVw8spbNf1RMlUg+GxUTbIkPyLbVsjYSiyfXozwvIVSS+BbU0NNCOpXYOcefLmuci9oDwJtj8WQv6vMJA28AJmLx5O2oETNdH9qeg7xlE7Qs0OcI55WrVJj9vNKNbNQEdrBBkF8I6A+glSocQ90c09nIZ4SvJPo+/Cr/2bEf9iV7pdABZCRb+OW6oUOvGxp9WKAq8WZtPOvh0QmsBBH1vICPQG3J2OOHwdIzHDrxGx4ZfBkAmq6D0MpIO8TsJ7ubTYuAZavV1mwst5NleEQ+ls+Ir49N8abV/fhm5nyYFoxNUQWy4RG54GaT3UAsnuxHiYITgH1Rw1ULqJDdU96qeHcc79SfgT/H4sl9UWIqDDw/Fk8+ifJOFZZhVdUfgHsnyxw12Du7p6ligmXjY8boki7mBQEf/rlccLoOukbJsjmNBiLKaRXzkx4mzwyX/893z8AreWDw5UjbEmZx8uzN+4VfMtW37pJvvfv8ld7U16PDWQkiarf3qGsQ8Al5yuhXeGTwZfWngrkujL8EHpsscVCjk2WpArZEAP+99yZ3DJukZO22cc4P+JABn8qRKlexylUEajDuu9w1sTk4E+KPQQmnI1HHwz0or9NKCU/tNU7/q5/F4slfAkehmoueB5wbiyfvRgmq2VoldB3hESnzGfGuYoWfC4HWF0TUVe1SrsKYKjb5XHhEPuCqsc2j8bTgOsT8z/2oEJy5uh/feEnKU3f+Fw8NRwS6jmb49OrkTnti1YFXRrKF63LR0HL2Znp0OStBRN1eNTkNpqvM+gK2OHLiBvrLjzAROARp2yDtQKC4Y9bwTHhE2vmMuLRY4SdCQF9gevC40w+G8SI28MHwiFw25d7hEVnOZ0QEOKdc5b3lKqdKhDZm7rPNL4qxXn3i2haUM7cNp+rsIJRwehYQROV3/RTVSXy5eU7ahiM67wburvPsnYhqlTDujJnJp1OJrvY0hEfkr/MZ8cqpMt+cKrPKb4AmEBWTqi3RgU+gGm4uF26pmLxUysbeKMsG0yaA8tzuQT4jBoB3D/QoD3dfQIrDJ/7EYOl+dgaPVCkWfYOabVYMadvvBJItezceHnvJsm9xkM+Ik4Gbh/uh1nFbStg8bsjf910qbtg3QWVyJ3ZxfOcR9/zfZzVp3w/ciPI+yBmvdT7wP8Aav6GGjFZMhC01WbT7P/KC948th6q8OYnFk4PAPwHfT6cSd7ppSyRb2A/VgG97LhpacAdwZ3zEc1DiaTWq39NtwO3dflHvZBzRuh/TOWY9KNGaR4nWrh3k/fGPbNxvf/8Dnz+y55Zqjz45hRKQX18O7U7qyWfEQcAjq3oRjfKixoswVeYx4NDZFln5jLgAyK1bpfJUa+fjP/a8Wfx2/4/uel51agKzNHlzLhpaLsU6HsuQZS+iAPIZcYWAtwz14fM7SdJTZdhSGiC931+olKuWsK0Lj7r7R4+i+v4cAGxFVV7dVt/vJ58RBhABng/othR3XrP1n4ZK9sAT6VTi2+1+b24QiyffDTySTiWudWP/kWzhQuCDwPPq7v498LFcNPST2f7GqfZ5Fko4HYIawXIXSjw97OU5tRcnfHo0yjt1JKog428oQfXQXOG+SLbgA/4O1WJiEJXg/t+5aOiu1lrdmFg8+TzgbODjy6U/WCPyGfFR4AOrejECvukSRSlhsgyTJSRwYXhEznp+yGfE64Xg6+tWTUcHpsqwtdTHZw+7A0tXHVOqxUnM4sRtuWgo3Or35OGxVFaKiDKAzwHvNHQqPh2/7eQsfHXwqvJjvvBrctHQtbBbiOd01CyxEnAzcFOjaqxYPPkc4CJUJcmySrKejVg8eQFwVDqV+Gy79x3JFj4CXKYHeqQR6NGEpiNtE7NUtK1KSQD/nIuG0o6dGqoM/wTU/1IHHkJdqO/u1BEsK41YPDmA8gyeCOzDtGcwn04ldhtsHMkWng/8EFit+wMCoWm2Wa1Iy/QDPwAuyUVDbe9XFYsnNwB2OpX4Rrv33W7yGSGKVl8mqE2+R9eo+n34pURWqpgSysBbwyPy6kZ///v06pcPGDuuXbtq9xyyp8d0rl39ce5aEwWgMjmOVZ66IRcNndmO9+XhsRRWhIiqkc+IZ6OGEh8DVMbFmtsuH/ruV7755rNnzWNywj6noU7uPpy+QOlU4skZz9NQCdY70qnEN1v5HjqBWDx5HPA6IDPXcNpmE8kWzgN+4u8fErp/z86nVqVEZWJMBoo7LjrkoeumUCGjAZRXMY8K163YtgSdTl1n9DCqM3oQ1QH+VuCue4+/6DjgRj3Q4/f19Gu7EhMB26xSHh+tIO3fAuctZJRTE+32ozyjv0inEn9u137dJBZPbhg2ntrvgtVfQQiehWo4ewPwnfCI3EPEOufIo4CTDFE57jVrP/6BVT1WsK+u897OKXjIPkb+92G/E1LalEa3VpDy/blo6AttelseHotmJSSW7yI8Iu8APlR/31xLnHQqsQNVaXQdaqDsacBzYvHkI6i8qXvTqYTtDDu+Hnh1LJ48KJ1KPNaad9AxPIyqXjsc+Gsb9xvT/UFb9wdm7cqj+4NovpItS9rHUIOi70CJJ68tQRcwozP6z1GLnRNR4fMLjGrx1XbPKp+vd0CbOdBRM3wEBof95bFtZwPnAD9ro+mHo7yc97Vxn64RiycPAw7fYe73nRP/Ud49z3OHmR7GPQA8aUp/TqLtmChZn/Tp6LUUi94A7Dt+j1g3cROP2UdUkfIZ1PfYw6NjWVEiaqk4zd5ujMWTf0Z1qz4d1U13Ryye/BPqQn0nSpO9GLjKJVPbQjqVKMbiyaeAw2iCiHLyYyKoOYZ3zJYPE8kWBoCz9UCD4YUORqBHr1RXHf3EQc/7/LffdY5XXdelOHlFdwB3xOLJwZ2rDj7HNIJhf0/f7BOxAU030P0BaVXK72EOEeV4vEQT2ywcBWybGXpcjjif3UuAJ1AtQGZ7joE6T56EEphl4HbUMO6nAPKZy24BDtoxyUhQtU/RhAChCU7YfiWP9F/2DHCGG6FZD4/F4ImoReCcdO8C7orFkwegxNS5qJPKLc52QSyePDSdSjzsmqHt4UEgHIsnRRO8PBJ1LF4EnBWLJ3+HOkEPAkPA0P79+x7x5MHPpz6EMxvO42JyYL8ewBNRy4B0KrEzki1MArZm+OY8ADRfQLcq5RNnOy6dkNKzgLNQhQVf3VvbHFFxFOq8sBI4CpUzmp3l812LEk4nAL2oUOwPmGUYtzMO5p/yGfHLUpVYqcoZgM9G2zKurfsxKrfRq5T16Hg8EbVEnATy/3WaCp6KGsjqR5VwvzYWT6aXQ0PBOXgQNdZhLbDoMm6nWm4VjkgCRoGnUJ/lhajxKvc6T7eCxR1TSGlLy9LQGx+20rZAXSDHF2uTR0ezsGanUqLZ1T7gQ7F4cgdQ21YxnWd1B/DrJtm1DiX2753vid1OnRfqEdT3v5YPdjxwMkpcTaE887cuZBh3eET+FNWXjXxGiJNGTHkS8I+teAMeHi3AE1F7iZOo/CvHe3ICqvT6ncCqWDz5IEoYPOncbmmmsIpkCwKVp3UCYAN/ykVDhWa9/jw8hkomPZxZRFQsngyyu0iaudXH5SxURVbJ2R5EVWDdiRJXE5n/+JAdyRZOM8tTr9L9gYbHrVmaqgLfzkVDy7rMfAXyV8C2qxVttqKCGlalVBW2/Vvgd6geYsOoysxzUd6RO1Bh6NfMEFnbaz8vsl/VUSjR/uii31H3cTxqDNKVwH6xePIkVPFGANVm4vvAPUsdxr2QYcUeHp3GiqrOawfOau1kpr1S+wFrUJMQTOBplKCqiastM0eKxOLJF6NCXL9tFCqLZAtnA58HjhOaVpISgbQDqNl9m3LR0K2teH+OfQK1or8UlSz6K/YUSXV1N5gokTTaYJtAlbZHned/M51KPDNzv5Fs4RTgT77efs0I9u32mJQSszSFWZwwgZNz0dDte/MePTqPSLbwTaEbrwkMrvbNlhdlVStUxncAnJ6LhnarkovFk+uAt6GE1O9Q36+ayFqNEgI1itSJKnYXWeP1C6FYPPlWoJhOJb7TrPfZiTih0Peivu+bUee1cVTl5K1OEY6Hx4rDE1FtwAld7Ys68ezv3O6DElYW8AzT3qqnUGXeL0dVAP5ippCKZAsXADk90KMZwV6hOeEt26xSLU5adrVcAc7KRUM3L9FegfIUDdHYm1RrXnkUcDWNBdIoMDlf3lQsnjwdtdK9eq42BJFs4Y3AVZrhs/RAj1/1ibIwS1MVaZka8LpcNHTNot6wR1cQyRYOAm7WDN+wr3fApxmqrEtKiVUpUZ3caQL/BbwzFw3tcbw5/ajehBJOX66156g73utF1XDdNsiucXBYqGN6Oyp09XrgO6hmrztaOWMxki2sATYC72B6MPbVwBdz0dCc0wOc98hC8xdj8WQvKlS/zrk9Czgf+DlKON2CmuqwnFMWPDzmxRNRLuHkEswUVmuZFla9qM7af0CFtp5JpxJmJFsIAk8bwd5Vvt6BPV5XSkl1csyyKuUHgWMaXEyE8/pDNBZK9UMdKjT2JE0Bo+1sIRDJFp6NWhW/EehDebKuAr6Qi4b+1i47PNpPJFs4FPgW8Dyh6SWhadiWqSGlDXwSuGyuHlHOguZ5qOa5kwvZp1NtNsSeIusQ4A2onJ4SKqQ+ihJY25yt9vPY3giOSLYQBn6N0PqNYI9f0w2kbWOWixVpmT6U9/mKBvbvg/qu/CadStwx47EedhdLtdt+5ym2Y38VdZ64PJ1KePmGHh4OnojqIGLxpA8lpk5FjZU5GiWqbkKdzDY/dcApx4yvOug9weG1uhCzFyrZlkV5bCs9k1tefdAjv7+H2UWSr+5PykyLotnEUrFT+yxFsgU9Fw21bPXv0ZlEsuANmC4AAAOZSURBVIUQylvbi0p0/l4uGmr7xd1ZkAygQvZrUAKr9vMwqn8UqIXRDnYXVrWfd871/XI8UPfo/sCQr2+VPjOUaZaLVCd3SuCCXDS0W2uHWDy5H6rBcBnlRepjd8FUW4nZji2bUUUdtdttrfSueXh0O56I6jBi8eTJwCtRfVhuQpX6r8bxVj1y2Is/ZA7ue7p/YKjBDHVFeWxrtXfHI3/c//G/XI9aJY/SWCiVOlUkeXh0K04e0Sp2F1a1n4eA2iqoyrTAmimyJu89/qIYQvuP4NA+/kY9sioTY7ZVKf356LuueTFKIK0FjgBejfIq/83Zj3Rev14obUaJpSUlhHt4rGS86rzO4w7g0RnlwU84G5Fs4XW6EM+b9S/rEZpd7F2bBz62yGojDw+PJuCE72qJ6Q/UPxaLJ3WUkJrpvXo2SnjV1FJFs6ojWv9QQwEFYAR7NatSel6xZ/XHe4rbR1FiqYryQFVQyfK/Am5Z7gOSPTzaiSeiOgynO/pc/VXusc1qWUoZaHRSlVJim6aGEbjVE1AeHp2HEyKreZt2w8nBWu1sa2zN+IgxR280AOE8PjZ82K09xe2/RFX9Vh1v2LGoPLCXohLCPTw8moQXzusyItnCgcAj/v6hhv1yzNIU1anxSWCdNzbBw6O7iWQLm329A2uNYG/D50jbojS6FeDEXDSUn+05sXjS53mhPDyay9wzNDw6jlw09DjwxcrEWNWqVnZ7bFep99S4BfyrJ6A8PJYFV5vlYmWuJ5jlEqiQf8Nmu56A8vBoPp6I6k7+EeSVlfEdlMa2VapTE1SnJiiPbatUJsYkkAQyLtvo4eHRHL4gLdNnlmcfBWlbJmZxsgpkvEpVD4/24oXzuphItnA8sAk4BVWi/FvgK7lo6BFXDfPw8GgqkWzhUuBy3R+URrBXE7oB0sYslxwBJX8KXJyLhrwKOw+PNuKJKA8PD48uIJItnAd8BJUkXuMJlNc54wkoD4/244koDw8Pjy4iki0chhoNNQEUvBCeh4d7eCLKw8PDw8PDw2MJeInlHh4eHh4eHh5LwBNRHh4eHh4eHh5LwBNRHh4eHh4eHh5LwBNRHh4eHh4eHh5LwBNRHh4eHh4eHh5LwBNRHh4eHh4eHh5LwBNRHh4eHh4eHh5LwBNRHh4eHh4eHh5LwBNRHh4eHh4eHh5LwBNRHh4eHh4eHh5LwBNRHh4eHh4eHh5LwBNRHh4eHh4eHh5L4P8D/eukBgXkePsAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "depth = 4\n", "circ = ansatz_circuit(n_qubits, depth)\n", "psi = circ.psi\n", "psi.draw(color=[\"U3\", \"RZZ\"], show_inds=True)\n", "psiH = psi.H\n", "psi.align_(hamilt_mpo, psiH)\n", "energy_tn = psiH & hamilt_mpo & psi\n", "print(len(energy_tn.tensors))\n", "energy_tn.draw(color=[\"U3\", \"RZZ\"], show_inds=True)\n", "simplified_tn = energy_tn.full_simplify()\n", "print(len(simplified_tn.tensors))\n", "simplified_tn.draw(color=[\"U3\", \"RZZ\"], show_inds=True)" ] }, { "cell_type": "markdown", "id": "a463a8b3", "metadata": { "lines_to_next_cell": 2 }, "source": [ "We can then define our optimizer on the angles that parametrize the gates." ] }, { "cell_type": "code", "execution_count": 12, "id": "09cfccdd", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:11:23.535898Z", "iopub.status.busy": "2026-04-03T04:11:23.535743Z", "iopub.status.idle": "2026-04-03T04:11:23.539276Z", "shell.execute_reply": "2026-04-03T04:11:23.538604Z" } }, "outputs": [], "source": [ "def loss_circ(circ, mpo):\n", " psi = circ.psi\n", " psiH = psi.H\n", " norm_tn = psiH & psi\n", " psi.align_(mpo, psiH)\n", " energy_tn = psiH & mpo & psi\n", " energy = autoray.do(\"real\", energy_tn.contract(all, optimize=opt))\n", " norm = autoray.do(\"real\", norm_tn.contract(all, optimize=opt))\n", " return energy / norm\n", "\n", "\n", "def make_circuit_optimizer(circ, mpo):\n", " return qtn.TNOptimizer(\n", " circ, # the tensor network we want to optimize\n", " loss_circ, # the function we want to minimize\n", " loss_constants={\"mpo\": mpo}, # supply U to the loss function as a constant TN\n", " autodiff_backend=\"jax\", # use 'autograd' for non-compiled optimization\n", " optimizer=\"L-BFGS-B\",\n", " )" ] }, { "cell_type": "markdown", "id": "c67a8c34", "metadata": {}, "source": [ "Let us make a first test. Since the contraction is a bit more involved than for straightforward MPS optimization, the simulation becomes a bit more tedious." ] }, { "cell_type": "code", "execution_count": 13, "id": "3566ef79", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:11:23.540667Z", "iopub.status.busy": "2026-04-03T04:11:23.540525Z", "iopub.status.idle": "2026-04-03T04:11:37.635574Z", "shell.execute_reply": "2026-04-03T04:11:37.634839Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimized energy -3.191441136862914\n", "Exact energy -3.3749325986878818\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "depth = 4\n", "circ = ansatz_circuit(n_qubits, depth)\n", "circ_optimizer = make_circuit_optimizer(circ, hamilt_mpo)\n", "optimal_circuit = circ_optimizer.optimize(n=100)\n", "print(\"Optimized energy \", circ_optimizer.loss)\n", "print(\"Exact energy \", dmrg_energy)\n", "circ_optimizer.plot();" ] }, { "cell_type": "markdown", "id": "6b6a2845", "metadata": {}, "source": [ "It can be also interesting to optimize a circuit of large depth using the optimized parameters from a circuit of smaller depth. However as shown below, we don't observe an improvement. So we will not use that in the following." ] }, { "cell_type": "code", "execution_count": 14, "id": "912d14f9", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:11:37.637282Z", "iopub.status.busy": "2026-04-03T04:11:37.637107Z", "iopub.status.idle": "2026-04-03T04:11:55.989039Z", "shell.execute_reply": "2026-04-03T04:11:55.988245Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimized energy -3.0615528098434437\n", "Exact energy -3.3749325986878818\n" ] } ], "source": [ "# optimize a shallow circuit\n", "circ = ansatz_circuit(n_qubits, 2)\n", "circ_optimizer = make_circuit_optimizer(circ, hamilt_mpo)\n", "optimal_circuit = circ_optimizer.optimize(n=100)\n", "\n", "# initialize a deeper circuit with previously optimized parameters\n", "circ = ansatz_circuit(n_qubits, 4, param_scaling=1e-4)\n", "circ.set_params(optimal_circuit.get_params())\n", "\n", "# optimize the deeper circuit\n", "circ_optimizer = make_circuit_optimizer(circ, hamilt_mpo)\n", "optimal_circuit = circ_optimizer.optimize(n=100)\n", "print(\"Optimized energy \", circ_optimizer.loss)\n", "print(\"Exact energy \", dmrg_energy)" ] }, { "cell_type": "markdown", "id": "f08592eb", "metadata": {}, "source": [ "Let us analyze how things improve increasing the depth" ] }, { "cell_type": "code", "execution_count": 15, "id": "eec00770", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:11:55.990590Z", "iopub.status.busy": "2026-04-03T04:11:55.990430Z", "iopub.status.idle": "2026-04-03T04:12:26.968175Z", "shell.execute_reply": "2026-04-03T04:12:26.967271Z" }, "lines_to_next_cell": 2 }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Depth 1\n", "Current energy -1.2499999999880975\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Depth 2\n", "Current energy -3.03077640499415\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Depth 3\n", "Current energy -3.2152133183266898\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Depth 4\n", "Current energy -3.260072334394258\n" ] } ], "source": [ "max_depth = 4\n", "depths = np.arange(1, max_depth + 1)\n", "n_values = len(depths)\n", "depth_parameters = np.zeros(n_values)\n", "depth_energies = np.zeros(n_values)\n", "for i in range(n_values):\n", " circ = ansatz_circuit(n_qubits, depths[i])\n", " circ_optimizer = make_circuit_optimizer(circ, hamilt_mpo)\n", " optimal_circuit = circ_optimizer.optimize(n=100)\n", " depth_parameters[i] = circ_optimizer.d\n", " depth_energies[i] = circ_optimizer.loss\n", " print(\"Depth \", depths[i])\n", " print(\"Current energy \", depth_energies[i])" ] }, { "cell_type": "code", "execution_count": 16, "id": "bfd19e51", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:12:26.969701Z", "iopub.status.busy": "2026-04-03T04:12:26.969525Z", "iopub.status.idle": "2026-04-03T04:12:27.175441Z", "shell.execute_reply": "2026-04-03T04:12:27.174781Z" } }, "outputs": [ { "data": { 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dXcMkIpIBKU0EeubMGaZMmYKLiwsdOnSwIJWI5BRdwyQikgFdu3bl9u3b1K1bFx8fH4KDg1m/fj03b95k6tSpKc57JSK5hwqTiEgG9O/fn8WLF7Ny5UrCw8Px9PQkMDCQZ599li5dulgdT0Syma5hEhEREUmHrmESERERSYcKk4iIiEg6dA1TFomPj+f8+fMULFgQm81mdRwRERHJAMMwuH79OiVKlEhzAloVpixy/vx5SpcubXUMERERyYSQkBBKlSqV6v0qTFmkYMGCgPmCJ6xuLiIiIvYtIiKC0qVLJ/4dT40KUxZJ+BjOy8tLhUlERMTBpHc5jS76FhEREUmHCpOIiIhIOlSYRERERNKhwiQiIiKSDhUmERERkXSoMImIiIikQ4VJREREJB0qTCIiIiLpUGESERERSYdm+rZH10Lg5pXU7/coDD5at05ERCSnqDDZm2shMKsuxMakvo+LKzz7g0qTiIhIDtFHcvbm5pW0yxKY96c1AiUiIiJZSoVJREREJB0qTCIiIiLpUGESERERSYcKk4iIiEg6VJgcVdxtqxOIiIjkGSpMjmrTOLh1w+oUIiIieYIKk73xKGzOs5SeswdgUWeIuprtkURERPI6TVxpb3xKm5NSpjXPUsQ5WD0Czu6HoPbQfxUU9Mu5jCIiInmMzTAMw+oQuUFERATe3t6Eh4fj5eWV/Se8eBQWPw6Rf0GhctB/NfiWz/7zioiI5CIZ/futj+Tu0ezZs6lWrRr169fP2RMXrwZDNppl6WowzG9rligRERHJchphyiI5PsKU4Ppf5kjTpaPg5gP9VkKpejl3fhEREQemEaa8oqAfDPoKStWH6GuwsCOc2GF1KhERkVxFhSk38PCFAWugQgu4fQM+6wFH11qdSkREJNdQYcot8heAPp9DtU4Qdwu+GAiHFludSkREJFdQYcpNXFyhWxA8MACMeFj7LOx53+pUIiIiDk+FKbdxcoYO78FDo8zbm1+FbZNB1/aLiIhkmgpTbmSzwSNToPUk8/Z378BX/wfx8ZbGEhERcVQqTLlZ4zHw2AzABgc/gVVPQOwtq1OJiIg4HBWm3K7eYOj2CTjlgyMrYVkfuHXT6lQiIiIORYUpL6jRFXovAxd3+HMLLOkCUdesTiUiIuIwVJjyikqtYcBqcPWGM9/Dwscg8pLVqURERByCClNeUqYhDP4KChSDv36B+W3g2hmrU4mIiNg9Faa8xq+muWivTxkIOwmftIHLf1idSkRExK6pMOVFhSvCkE1QtCpcPw/z28K5Q1anEhERsVsqTHmVVwkYvAFKPABRYbCwA5zaaXUqERERu6TClJd5+MLAtVC+KdyKhCXd4PevrE4lIiJid1SY8jrXgtDnC6j6GMTFwOf94fBSq1OJiIjYFRUmgXxu0H0h1OkLRhysfgr2fmh1KhEREbuhwiQmZxfoOAsaPmPe3vgy7JiqRXtFRERQYZI7OTlBmzeg5avm7W/fgg1jtWiviIjkeSpMkpTNBk1fhEffNm/v/8j8iC7utrW5RERELKTCJClrMAy6zAMnF/j5c/Ni8NtRVqcSERGxhAqTpK5Wd+j1Gbi4wbEN5rQD0RFWpxIREclxKkyStsptoN8qcPWC07vMCS5vhFqdSkREJEepMEn6yjWCgevAowhcOGwupRJ+1upUIiIiOUaFSTKmRB1z/TmvUnDluLlob+ifVqcSERHJESpMknFFAmDoJihcCSLOwvw2cP6w1alERESynQqT3B3vUjBkI/jXhpuh5jVNwbutTiUiIpKtVJjk7hUoAgPXQ9nGEBMBS7rAsU1WpxIREck2KkySOW5e0G8FVG4HsdGwrA/8/IXVqURERLKFCpNkXj536LkYavWE+FhYNQz2f2x1KhERkSynwiT3xjkfdJ4DDZ4EDPj6Bfh2mhbtFRGRXEWFSe6dkxO0+y80e9m8veN12PQfLdorIiK5hgqTZA2bDVqMg7Zvmbf3zoa1z0JcrLW5REREsoAKk2Sthk+bH9HZnOHwp/DFQLgdbXUqERGRe6LCJFmvTm/zYnBnV/h9PXzWHWKuW51KREQk01SYJHtUbW9OO5DfE07thIUd4WaY1alEREQyRYVJsk/5pjBwLbj7wvlDENQOIs5bnUpEROSuqTBJ9ipZ11xKpWAJuPy7uf7clRNWpxIREbkrKkyS/YpWMRft9a0A187A/Lbw1y9WpxIREckwFSbJGT5lYMgm8KsJNy7BgvZwZp/VqURERDJEhUlyjmcxc9HeMg9CdDgs6gTHt1qdSkREJF0qTJKz3H2g3yoIeBhio2BpLziy0upUIiIiaVJhkpyX3wN6fQY1ukL8bVgxFA4GWZ1KREQkVSpMYg2X/NDlY6g3BDBg/WjY9a7VqURERFKkwiTWcXKG9tOhyf+Zt7dOgi0TwDAsjSUiIvJvKkxiLZsNWk2AR143b++eCetGQXyctblERETuoMIk9uGhkdBxFtic4NAiWDEEYmOsTiUiIgKoMIk9eaA/dF8Azvnh6GrzG3S3blidSkRERIVJ7Ey1TtBnOeQrACe2w6LOEHXV6lQiIpLHqTCJ/anYwly0180Hzu6HoPZw/S+rU4mISB6mwiT2qVQ9GLwBPP3g0q/mor1hp6xOJSIieZQKk9iv4tVgyEYoVA6uBpuL9l48anUqERHJg1SYxL75ljcX7S1WHSL/gqB2EHLA6lQiIpLHqDCJ/SvoB4PWQ6n6EH3NXLT3xA6rU4mISB6iwiSOwcMXBqyBCi3g9g34rAccXWt1KhERySNUmMRx5C8AfT43px6IuwVfDIRDi61OJSIieYAKkzgWF1foFgQPDAAjHtY+C3vetzqViIjkcipM4nicnKHDe/DQKPP25ldh22Qt2isiItlGhUkck80Gj0yB1pPM29+9A189r0V7RUQkW6gwiWNrPAYemwHY4OB8WDUMYm9ZnUpERHIZFSZxfPUGQ7dPwCkfHFkJy/rArZtWpxIRkVxEhUlyhxpdofcycHGHP7fAki4Qdc3qVCIikkuoMEnuUak1DFgNrt5w5ntY8BhEXrI6lYiI5AIqTJK7lGkIg7+CAsXg4i/mor3XzlidSkREHJwKk+Q+fjXNRXt9ykDYSfikDVz63epUIiLiwFSYJHcqXNFctLdoVbh+3ly099wPVqcSEREHpcIkuZdXCRi8AUo8AFFhsLAjnNppdSoREXFAKkySu3n4wsC1UL4p3IqEJd3g96+sTiUiIg5GhUlyP9eC0OcLqPoYxMXA5/3h8FKrU4mIiANRYfrb5cuXad++PQUKFKBKlSps27bN6kiSlfK5QfeFUKcvGHGw+inY+6HVqURExEGoMP3tmWeewc/Pj8uXLzNt2jR69OhBWFiY1bEkKzm7QMdZ0PAZ8/bGl2HHVC3aKyIi6VJhAiIjI1m9ejWvvfYaHh4edOzYkZo1a7JmzRqro0lWc3KCNm9Ay1fN29++BRvGQny8tblERMSuOWRhioyMZOLEibRt2xZfX19sNhsLFixIcd+YmBjGjh1LiRIlcHd3JzAwkC1btiTZ5/jx43h6elKqVKnEbTVr1uTXX3/NzqchVrHZoOmL8Ojb5u39H5kf0cXdtjaXiIjYLYcsTKGhoUyePJnffvuN2rVrp7nvoEGDmD59On379mXmzJk4Ozvz6KOPsmvXrsR9IiMj8fLySvI4Ly8vIiMjsyW/2IkGw6DLPHBygZ8/Ny8Gvx1ldSoREbFDDlmY/P39uXDhAqdPn2batGmp7rd//36WLVvG1KlTmTZtGsOHD2f79u2ULVuWl156KXE/T09PIiIikjw2IiICT0/PbHsOYidqdYden4GLGxzbYE47EB2R/uNERCRPccjC5Orqip+fX7r7rVixAmdnZ4YPH564zc3NjaFDh/L9998TEhICQKVKlYiMjOTcuXOJ+x05coTq1atnfXixP5XbQL9V4OoFp3fBwsfgRqjVqURExI44ZGHKqB9//JHKlSsn+7itQYMGABw+fBgwR5g6derExIkTiYqKYv369fz888906tQppyOLVco1goHrwKMIXPgJ5reF8LNWpxIRETuRqwvThQsX8Pf3T7Y9Ydv58+cTt33wwQecP3+ewoUL8/zzz/P555/j6+ub6rFjYmKIiIhI8iMOrkQdc/05r1Jw5bi5aG/ocatTiYiIHcjVhSkqKgpXV9dk293c3BLvT1C0aFG+/vprbt68ybFjx2jdunWax546dSre3t6JP6VLl87a8GKNIgEwdBMUrgQRZ82RpvOHrU4lIiIWy9WFyd3dnZiYmGTbo6OjE+/PrHHjxhEeHp74k3A9lOQC3qVgyEbwrw03Q2FhBwjebXUqERGxUK4uTAnfpvu3hG0lSpTI9LFdXV3x8vJK8iO5SIEiMHA9lG0MMRGwpAsc22R1KhERsUiuLkx16tTh2LFjya4v2rdvX+L9Iqly84J+K6ByO4iNhmV94OcvrE4lIiIWyNWFqVu3bsTFxTF37tzEbTExMQQFBREYGKjrjiR9+dyh52Ko1RPiY2HVMNj/sdWpREQkh7lYHSCzZs2axbVr1xK/6bZu3TrOnjW/Bj5y5Ei8vb0JDAyke/fujBs3jkuXLhEQEMDChQsJDg7mk08+sTK+OBLnfNB5Drj5mMuofP0CRF2Dpi+Yy6yIiEiuZzMMx1yqvVy5cpw+fTrF+06dOkW5cuUA8wLv8ePHs2TJEq5evUqtWrWYMmUKbdq0ydI8EREReHt7Ex4eruuZcivDgG/eMhfsBWj4DDzyurmgr4iIOKSM/v122MJkb1SY8pC9H8LGl81/1+kLHd4DZ4cdrBURydMy+vdb/2kscrcaPm1+RGdzhsOfwhcD4Xa01alERCQbqTCJZEad3ubF4M6u8Pt6+Kw7xFy3OpWIiGQTFSaRzKra3px2IL8nnNoJCzvCzTCrU4mISDZQYRK5F+WbwsC14O4L5w9BUDuIOJ/+40RExKGoMN2j2bNnU61aNerXr291FLFKybrmUioFS8Dl381Fe6+csDqViIhkIX1LLovoW3LCtTOwqBOEnYQCxaD/KvCraXUqERFJg74lJ5LTfMrAkE1mSbpxCYLaw5m9VqcSEZEsoMIkkpU8i5mL9pZ5EGLCYVFnOL7V6lQiInKPVJhEspq7D/RbBQEPQ2wULO0FR1ZanUpERO6BCpNIdsjvAb0+gxpdIf42rBgKB4OsTiUiIpmkwiSSXVzyQ5ePod4QwID1o+G76VanEhGRTFBhEslOTs7Qfjo0+T/z9rbXYMsEcyFfERFxGCpMItnNZoNWE+CR183bu2fCulEQH2dtLhERyTAVJpGc8tBI6DgLbE5waBGsGAyxMVanEhGRDFBhEslJD/SH7gvAOT8cXWN+g+7WDatTiYhIOlSYRHJatU7QZznkKwAntptzNWnRXhERu6bCJGKFii3MRXvdfODsfljQHq7/ZXUqERFJhQrTPdLiu5JpperB4A3g6QeXjsL8NhB2yupUIiKSAi2+m0W0+K5kWtgpWNwZrgab5an/l1C8mtWpRETyBC2+K+IofMubi/YWqw6Rf0FQOwg5YHUqERG5gwqTiD0o6AeD1kOp+hB9DRZ1ghM7rE4lIiJ/U2ESsRcevjBgDVRoAbdvwGc9zKkHRETEcnddmKKionj++edZt25dduQRydvyF4A+n5tTD8Tdgi8GwaHFVqcSEcnz7rowubu789FHH3Hx4sXsyCMiLq7QLQgeGABGPKx9Fva8b3UqEZE8LVMfydWtW5cjR45kdRYRSeDkDB3eg4dGmbc3vwrbJmvRXhERi2SqMM2YMYNly5Yxb948YmNjszqTiIC5aO8jU6D1JPP2d+/AV89r0V4REQtkah6mWrVqERoaysWLF3F1daVkyZK4u7snPbDNxk8//ZRlQe2d5mGSbHUwCNaPAQyo0RU6zwGX/FanEhFxeBn9++2SmYP7+vpSuHBhqlSpkumAInIX6g0GNy9Y9SQcWQnREdBjEeT3sDqZiEieoJm+s4hGmCRHHN8Kn/eD2Cgo3dD8Rp27j9WpREQclmb6FsmNKrWGAavB1RtC9sKCxyDyktWpRERyvUwXpri4OBYuXEiPHj0IDAwkMDCQHj16sGjRIuLidFGqSLYp0xAGfwUFisHFX8xFe6+dsTqViEiulqmP5MLDw2nTpg0HDhygYMGCVKhQAYBTp04RERFBgwYN2LRpU576aEofyUmOu3LCXLT32hkoWMJctLdYVatTiYg4lGz9SO4///kPP/zwA++//z6XL1/m0KFDHDp0iEuXLjFr1iwOHjzIf/7zn0yHF5EMKFzRXLS3aFW4ft5ctPfcD1anEhHJlTI1wlSyZEm6devGzJkzU7x/1KhRrFixgvPnz99zQHs3e/ZsZs+eTVxcHMeOHdMIk+S8m2GwpCucPwT5PaH3Uijf1OpUIiIOIVtHmK5cuZLmlAJVq1YlLCwsM4d2OM888wxHjx7lwIEDVkeRvMrDFwauNUvSrUhY0g1+/8rqVCIiuUqmClNAQABr165N9f61a9dSsWLFTIcSkbvkWhD6fAFVH4O4GPi8PxxeanUqEZFcI1OFacSIEWzevJlHH32UzZs3ExwcTHBwMJs2baJ9+/Zs2bKFZ599Nquzikha8rlB94VQpy8YcbD6Kdj7odWpRERyhUzN9D1ixAguXbrEW2+9xaZNm5Lcly9fPiZMmMDTTz+dJQFF5C44u0DHWeDmA3tnw8aXIeoqNB9nrk0nIiKZck8zfYeGhrJ161ZOnz4NQNmyZWndujVFihTJsoCOQtMKiF0xDPjubdj+unm7wZPQ9i1w0ly1IiJ3yujf77suTDdv3qR06dK8/PLLvPjii/ccNLdQYRK7tP9j+PoF89+1ekKn2eCcz9pMIiJ2JNu+Jefh4YGLiwsFChS4p4AikgMaDIMu88DJBX7+3LwY/HaU1alERBxOpsbnu3btyooVK9C6vSIOoFZ36PUZuLjBsQ3mtAPREVanEhFxKJm6hmnnzp2MGDGCIkWKMGzYMMqVK4e7u3uy/R544IEsCekI9JGc2L3g3bC0F8REgH9t6LcKCuS96w1FRO6UbdcwATjdceGoLYVv3hiGgc1my1OL8KowiUM4f9icFfxmKBSuBANWg3cpq1OJiFgmo3+/MzWtQFBQUKaDiYiFStQx159b1AmuHIdP2pilqUglq5OJiNi1uy5MMTExFCpUiHLlylGrVq3syCQi2alIAAzdBIs6m6Vpflvot9IsUyIikqK7vug7f/78dO/enT179mRHHhHJCd6lYMhG81qmm6GwsIN5jZOIiKTorguTzWajUqVKhIaGZkceEckpBYrAwPVQtrF5IfiSLnBsU/qPExHJgzI1rcArr7zCrFmz+OOPP7I6j4jkJDcv6LcCKreD2GhY1gd+/sLqVCIididTF33v3buXwoULU6NGDZo3b57itAI2m42ZM2dmSUgRyUb53KHnYljzjDm55aphEH3NnPRSRESALJhWINUD55FpBWbPns3s2bOJi4vj2LFjmlZAHFd8vLlY7/6PzNstXoWmL2jRXhHJ1bJ1HiZJTvMwSa5gGPDNW/DtW+bths/AI69r0V4RybWybS05EcnFbDZoMQ7a/l2Y9s6Gtc9CXKy1uURELHZPhWnv3r1MnTqVMWPGcPz4cQBu3rzJoUOHiIyMzJKAImKBhk9D5zlgc4bDn8IXA+F2tNWpREQsk6nCdOvWLbp06UKjRo34z3/+w3vvvUdISIh5QCcnHnnkEV3wLeLo6vQ2LwZ3doXf18Nn3SHmutWpREQskanCNH78eNavX8+HH37IH3/8wZ2XQbm5udG9e3fWrFmTZSFFxCJV25vTDuT3hFM7YWFHuBlmdSoRkRyXqcK0dOlSnn76aYYPH46vr2+y+++77z5Onjx5z+FExA6UbwoD14K7L5w/BEHtIOK81alERHJUpgrTpUuXqFmzZqr3Ozs7c/PmzUyHEhE7U7KuuZRKwRJw+Xdz0d4rJ6xOJSKSYzJVmEqXLs3vv/+e6v27d+8mICAg06FExA4VrWIu2utbAcLPmIv2/vWL1alERHJEpgpTnz59+Oijj/j+++8Tt9n+ntzu448/Zvny5QwYMCBrEoqI/fApA0M2gV9NuHEJgtrDmb1WpxIRyXaZmrjy1q1bdOjQge3bt3Pffffx66+/UrNmTcLCwjh79iyPPvooa9aswdnZOTsy2yVNXCl5StQ1WNoLznwPLu7QcwlUam11KhGRu5atE1fmz5+fjRs3EhQURIUKFahatSoxMTHUqlWLBQsWsG7dujxVlkTyHHcf6LcKAh6G2CizPB1ZaXUqEZFso6VRsohGmCRPir0Fq5/6uyzZ4LHpUG+I1alERDJMS6OISPZzyQ9dPv67JBmwfgx8N93qVCIiWU6FSUTujZMztJ8OTf7PvL3tNdg83lzIV0Qkl1BhEpF7Z7NBqwnwyOvm7T3vwdqREB9nbS4RkSyiwiQiWeehkdBxFtic4MfFsGIwxMZYnUpE5J6pMIlI1nqgP3RfAM754ega+KwnxERanUpE5J5kqjB9/vnnREdHZ3UWEcktqnWCPsshXwE4uQMWd9aivSLi0DJVmHr37o2fnx9Dhw5lx44dWZ1JRHKDii3MRXvdfODsAVjQHq7/ZXUqEZFMyVRh2rVrF3379mXdunW0bt2aMmXK8PLLL3PkyJGszicijqxUPRi8ATz94NJRmN8Gwk5ZnUpE5K7d08SVsbGxbNy4kU8//ZR169YRFRVFzZo16d+/P3369MHf3z8rs9ql2bNnM3v2bOLi4jh27JgmrhRJSdgp82O5q8Fmeer/JRSvZnUqEZEMT1yZZTN9R0ZG8uWXX7JgwQK++eYbnJycaN68OQMHDqRHjx7kz58/K05jtzTTt0g6rv8Fi7vApV/Nj+n6roDS9a1OJSJ5XI7P9H3kyBH279/PL7/8gmEYVK1alStXrjBgwAAqVqzIrl27supUIuKICvrBoPVQqj5EX4NFneDEdqtTiYhkyD0VpmPHjjFx4kQqVapEo0aNWL58OX369OHgwYP88ssvHDp0iP379+Pr68tTTz2VVZlFxFF5+MKANVCxJdy+AZ/2MKceEBGxc5n6SG7mzJl8+umn/PDDD7i6utKhQwcGDBhA27ZtcXZ2Trb/woULGTp0KLGxsVkS2h7pIzmRuxAbA6uGw9HV5iSXHd4z528SEclh2fqR3JgxY3B1dWXOnDlcuHCBzz//nPbt26dYlgDq1avH+PHjM3MqEcmNXFyh23x4YAAY8bD2Wdj9ntWpRERS5ZKZB504cYLy5ctneP/q1atTvXr1zJxKRHIrJ2dzZMnNx1x7bst4iLpqrklns1mdTkQkiUyNMN1NWRIRSZXNBo9MgdaTzNu7psNXz2vRXhGxO5kaYRoyZEia99tsNtzc3ChVqhTNmzfnwQcfzFQ4EckjGo8xR5rWj4GD8yE6HDrPAZfcPR2JiDiOTBWm7du3ExUVxeXLlwEoVKgQAFevXgWgaNGixMfHc+XKFWw2G23atGHFihV4eHhkUWwRyXXqDQY3L1j1JBxZCdER0GMR5Nf/3xAR62XqI7kNGzbg6urKpEmTuHLlSuJPaGgoEydOxN3dnd27d3P16lXGjx/Pxo0bddG3iKSvRlfovQxc3OHPLbD4cYi6ZnUqEZHMTSvQqlUrKlWqxJw5c1K8/6mnnuLkyZNs3rwZgD59+rB7925Onz59b2ntmKYVEMlCZ/aaczTFhEPxmtB/FXgWszqViORC2TqtwN69e6ldu3aq99euXZs9e/Yk3m7SpAkXL17MzKlEJC8q0xAGfwUFisHFX8xFe6/m3v/gEhH7l6nC5OPjkzh6lJKNGzfi7e2deDsyMlKjLiJyd/xqwpCN4FMGwk7C/LZw6XerU4lIHpWpwjRs2DDWrFlDt27d2LZtG6dPn+b06dNs27aNbt26sX79eoYNG5a4/9dff02dOnWyKrOI5BWFK8KQTVC0Klw/D0Ht4NwPVqcSkTwoU9cwGYbByy+/zLvvvktcXNL5UpydnXnuuef43//+h81mIzo6ms8//5xatWpx//33Z1lwe6NrmESy0c0wWNIVzh+C/J7QeymUb2p1KhHJBTL69ztThSnBpUuXEkeYAMqWLUurVq0oVizvXZypwiSSzWKuw7I+cGonOLtC9yCo2t7qVCLi4LKtMN28eZMmTZowbNgwnnrqqXsOmluoMInkgNvRsHIo/L4ebM7QaTbU6W11KhFxYNn2LTkPDw9OnTqFTWs9iUhOy+cG3RdCnb5gxMHqp2Dvh1anEpE8IFMXfbdt25ZNmzZldRYRkfQ5u0DHWdDwGfP2xpdhx5uQ+asLRETSlanCNH78eI4dO0b//v3ZtWsX586dIywsLNmPiEi2cHKCNm9Ay1fN29/+FzaMhfh4a3OJSK6VqYu+nZz+6VlpfTT372/Q5Wa6hknEIvs/hq9fMP9dq6d5XZNzPmsziYjDyOjf70wtvjthwgRdwyQi9qHBMHDzMa9n+vlziA6H7gsgn7vVyUQkF7mnaQXkHxphErHYsU2wfADERkPZxuZcTW7636KIpC1b15L7t/Dw8Dz18ZuI2KHKbaDfKnD1gtO7YOFjcCPU6lQikktkujAdPHiQtm3b4uHhQeHChfn2228BCA0NpVOnTnzzzTdZlVFEJGPKNYKB68CjCFz4yVx/7lqI1alEJBfIVGHas2cPjRs35vjx4/Tr14/4O76ZUqRIEcLDw/noo4+yLKQ9mz17NtWqVaN+/fpWRxERgBJ1zPXnvErBleNmaQo9bnUqEXFwmSpMr7zyCvfddx9Hjx7lzTffTHZ/ixYt2Ldv3z2HcwTPPPMMR48e5cCBA1ZHEZEERQJg6CYoXAkizpql6fxhq1OJiAPLVGE6cOAAgwcPxtXVNcVvy5UsWZK//vrrnsOJiGSadykYshH8a8PNUFjwGATvtjqViDioTBWmfPnyJfkY7t/OnTuHp6dnpkOJiGSJAkVg4HrzW3O3rsOSLua36URE7lKmClPDhg1ZsWJFivfduHGDoKAgmjVrdk/BRESyhJsX9FsBlduZUw4s6wM/L7c6lYg4mEwVptdee42DBw/Svn17NmzYAMBPP/3EvHnzqFu3LpcvX2b8+PFZGlREJNPyuUPPxeZM4PGxsGqYOUO4iEgGZXriyu3bt/P0009z/HjSb59UrFiRefPm5bkRJk1cKeIA4uPNxXr3//0t3havQtMXQCsXiORZGf37fc8zfR8+fJjjx48THx9PxYoVqVu3bp5cNkWFScRBGAZ88xZ8+5Z5u+EIeOQNc0FfEclzcqwwiUmFScTB7P3QHG0CqNMXOrwHzplaXlNEHFi2Lr6b4OjRo5w8eZKrV6+SUu8aMGDAvRxeRCT7NHzaXLR3zTNw+FNz0d6un0A+N6uTiYgdytQI04kTJ+jXrx/79+9PsSgB2Gy2PLW+nEaYRBzU71/BF4MhLgbKN4Ven4FrQatTiUgOydYRpieffJJffvmFGTNm0KRJEwoVKpTpoCIilqra3px2YGlvOLUTFnaEfivBw9fqZCJiRzI1wuTu7s4rr7yiqQPuoBEmEQd37gdY0g2iwqBoVeg0G5zS+G9Kj8LgUzrn8olItsjWEaYiRYrg7e2d6XAiInanZF1zKZVFneHy7zCvVdr7u7jCsz+oNInkEZn6Hu1TTz3FkiVL8tQ1SiKSBxStYi7a61Uy/X1jY+DmlezPJCJ2IVMjTJUrVyYuLo7atWszZMgQSpcujbOzc7L9unTpcs8BRURylE8Z8+O4xZ2tTiIidiRThalnz56J/37hhRdS3CevfUtORHIRd32RRUSSylRh2rFjR1bnEBEREbFbmSpMeW2dOBEREcnb7mmm75iYGA4dOsSlS5do1KgRRYoUyapcIiL271ak1QlEJIdkerXJ9957D39/fxo3bkyXLl34+eefAQgNDaVIkSLMnz8/y0KKiNilLwbDie1WpxCRHJCpwhQUFMTo0aNp27Ytn3zySZLlUYoUKULLli1ZtmxZloUUEclRHoXNeZbSc+MSLH4c1j0HMdezP5eIWCZTH8m98847dOrUic8++4wrV5LPQ1K3bl3ee++9ew4nImIJn9LmpJRpzbOUzx0OfAL7P4IfFsCf26HT+1CheU6lFJEclKnC9OeffzJq1KhU7/f19U2xSImIOAyf0unP4v3o/+C+DrBmBFw7A4s6Qb2h8PBkcPXMmZwikiMy9ZGcj48PoaGhqd5/9OhR/Pz8Mh1KRMRhlG8CT38P9Z8wbx/8BD580FzIV0RyjUwVpkcffZS5c+dy7dq1ZPf9+uuvfPzxx3Ts2PFes4mIOAZXT2j/DgxYC95lzNGmhR3g6xfh1g2r04lIFrAZd16xnUHnz58nMDAQwzDo0KEDc+fOpV+/fsTFxbFy5Ur8/f3Zv39/nppmIKOrHYtILhdzHTaPhx+CzNuFykGnD6BcI0tjiUjKMvr3O1OFCeDSpUu88sorrFq1KnGkqWDBgnTt2pW33nqLYsWKZSq4o1JhEpEkTmyHNSMh4qx5O/ApaDUB8hewNpeIJJHthelOly9fJj4+nqJFi+LklOmpnRyaCpOIJBMdAZv/A4cWmbd9K5ijTWUftDaXiCTK6N/vLGk3RYsWpXjx4nm2LImIpMjNCzq+D/1WgldJCDsJQe1g4ytwO8rqdCJyF9RwRESyW0BrGPE93N8PMGDvbJjTGEL2W51MRDJIhUlEJCe4eUOn2dDnCyjoD1f+hPltYPOrGm0ScQAqTCIiOanyI+ZoU+3eYMTDnvfho6Zw9qDVyUQkDSpM92j27NlUq1aN+vXrWx1FRByFeyF4fA70XgaexSH0GHzyMGyZCLejrU4nIinIkm/Jib4lJyKZdDMMNr4MP39u3i5aFTp/ACXrWptLJI/I0W/JiYhIJnn4Qpe50OszKFAMLv8O8x6GbZMhNsbqdCLyNxUmERF7ULU9PLMPanQDIw6+ewfmNofzP1qdTERQYRIRsR8evtDtE+ixGDyKwKWj8HEr2P46xN6yOp1InqbCJCJib6p1NEebqj9ujjbtnAYft4ALP1mdTCTPUmESEbFHBYpA9wXmj0dhuHgEPm4JO6ZqtEnEAipMIiL2rPrjMGIf3NcR4mPh27dgXkv46xerk4nkKSpMIiL2zrMo9FgE3eaDu69Zlua2gG//B3G3rU4nkieoMImIOAKbDWp0Na9tqvoYxN+GHW/AvFZw8ajV6URyPRUmERFH4lkMei6BLvPAzce8EPyjprDzbYiLtTqdSK6lwiQi4mhsNqjV3RxtqtzOHG3aPgU+aQ2Xfrc6nUiupMIkIuKoCvpB76Xw+Efg5m1OcvlRE9j1rkabRLKYCpOIiCOz2aB2L/ObdJXaQNwt2DoJ5j8Cl/+wOp1IrqHCJCKSG3j5Q5/PodMH4OoN536AOU1g90yIj7M6nYjDU2ESEcktbDa4vy+M+B4CWkNcDGyZAPPbQuhxq9OJODQVJhGR3Ma7JPRdAR1ngasXnN0PcxrDnlkabRLJJBUmEZHcyGaDB/qbo00VW0JsNGz+DwQ9CldOWJ1OxOGoMImI5GbepaDfKugwE/IXhJC98GEj2PshxMdbnU7EYagwiYjkdjYb1B0EI/ZA+WYQGwUbX4aFj0HYSavTiTgEFSYRkbzCpwwMWAPtp0O+AnB6tznatG+uRptE0qHCJCKSl9hsUH+oOdpUrgncvgkbXoRFHeFqsNXpROyWCpOISF5UqBwMWAuPvg35PCD4O/jgITgwT6NNIilQYRIRyaucnKDBMHh6N5RtBLdvwFf/B4s7wdXTVqcTsSsqTCIieZ1vBRi4Htr+F1zc4dRO+PAhODgfDMPqdCJ2QYVJRETM0aaGT5mjTWUehFuRsH4MLH4croVYnU7EcipMIiLyj8IVYdBX0GYquLjByR3wwYPww0KNNkmepsIkIiJJOTnDgyPgqd1QOhBuXYd1o2BJVwg/Z3U6EUuoMImISMqKBMDgDfDI6+DsCie2wQcN4cclGm2SPEeFSUREUufkDA+NhKd2Qcl6EBMBa56Bz3pAxHmr04nkGBUmERFJX9HKMHQztH7NHG06vtkcbTq8VKNNkieoMImISMY4OUPj0fDkTijxAESHw+qnYGlvuP6X1elEspUKk4iI3J1iVWHoFmg1EZzzw7ENMDsQfl6u0SbJtVSYRETk7jm7QJPnYfi34F8Hoq/BqmGwrC9cv2h1OpEsp8IkIiKZV7waPLEVWrwKTvngj6/gg0D4ZYVGmyRXUWESEZF745wPmr0Iw78Bv5oQdRVWDoXl/SHystXpRLKECpOIiGQNvxowbAc0fwWcXOC3deZo05FVVicTuWcqTCIiknWc80HzsWZxKl4Dbl6BFYNh+UC4EWp1OpFMU2ESEZGs51/LLE3NxoLNGY6uNr9Jd3SN1clEMkWFSUREsodLfmjxCgzbDsWqw81QWD4AVgyBm2FWpxO5KypMIiKSvUrUgeE7oMkL5mjTkZXmaNNv661OJpJhKkwiIpL9XFyh1XhzCoKiVeHGJfi8L6wcptEmcQgqTCIiknNKPmAurdL4ebA5wS/LzTXpfv/a6mQiaVJhEhGRnOXiCq0nwtCtUKQyRF6EZb1h1ZPmHE4idkiFSURErFGqLjz5HTR6zhxt+nkZfPAgHNtkdTKRZFSYRETEOvnc4OHJMGQTFA6A6xfgsx6wegREXbM6nUgiFSYREbFe6Qbw1C548FnABoc/NUebjm+1OpkIoMJ0z2bPnk21atWoX7++1VFERBxbPndo8wYM2Qi+FeD6efi0K6x5FqLDrU4neZzNMLScdFaIiIjA29ub8PBwvLy8rI4jIuLYbt2E7VNg74eAAV4loeP7ENDK6mSSy2T077dGmERExP7k94C2U2Hw11CoPEScgyVdYN1zEHPd6nSSB6kwiYiI/Sr7EDy9Gxo8ad7+YQF88BCc/MbKVJIHqTCJiIh9y18AHv0fDFwPPmUh/Aws6gTrn4eYSKvTSR6hwiQiIo6hfBN4eg/UH2bePvgJfPggnNppbS7JE1SYRETEcbh6Qvu3YcBa8C4D187Awg7w9Ytw64bV6SQXU2ESERHHU6EZjNgD9YaYt/fPhQ8fguDd1uaSXEuFSUREHJNrQXjsXej/JXiVgqvBsOBR2DBWo02S5VSYRETEsVVsCSO+hwcGmLf3zYE5jeH099bmklxFhUlERByfm5c5sWW/leYkl2EnIagdbHzFnART5B6pMImISO4R0Nocbbq/H2DA3tnmaNOZfVYnEwenwiQiIrmLmzd0mg19voCC/hB2Aua3gc2vwu0oq9OJg1JhEhGR3KnyI+ZoU+0+gAF73oePmsLZg1YnEwekwiQiIrmXeyF4/EPo/Tl4+kHoMfjkYdgyEW5HW51OHIgKk4iI5H5V2pqjTbV6ghEPu2fA3GZw7gerk4mDUGESEZG8wcMXusyFXp9BgWJw+XeY9zBsmwyxMVanEzunwiQiInlL1fbwzD6o2R2MOPjuHZjbHM7/aHUysWMqTCIikvd4+ELXedBzCRQoCpeOwsetYPvrEHvL6nRih1SYREQk77qvA4zYB9W7mKNNO6fBxy3gwk9WJxM7o8IkIiJ5W4HC0D0Iui8Ej8Jw8Qh83BJ2TNVokySyGYZhWB0iN4iIiMDb25vw8HC8vLysjiMiIpkReRm+eh5+W2ve9qsJnT8ENx+4eSX1x3kUBp/SORJRslZG/36rMGURFSYRkVzCMODXVfDVCxAVBjZnsAHxcak/xsUVnv1BpckBZfTvtz6SExERuZPNBjW6mt+kq/qYeW1TWmUJzGkJ0hqBEoenwiQiIpISz2Lmt+hajLc6idgBFSYREZHU2GxQqbXVKcQOqDCJiIhkBSPe6gSSjVSYREREssLS3rDzbbh+0eokkg1UmERERLJC5F+wfQq8Ww2WD4ST35rfuJNcQYVJREQkKzR/BUo1gPhYOLoaFnWEWfVgz/twM8zqdHKPVJhERETS4lHYnGcpLS6uUKcPPLEFntoN9Z+A/AXhyp+w+VV4pyqsGg5n9mrUyUFp4sosookrRURysWshdz/Td0wkHFkBBz6Bv37+Z3uxalBvCNTqAW7e2ZNXMkwzfecwFSYREUmRYcD5Q3BwPvyyEmKjzO35PMwJMusNgZIPWJsxD1NhymEqTCIikq6oa/Dz52Z5uvz7P9v965jFqWY3yF/AqnR5kgpTDlNhEhGRDDMM83qmg/PNC8TjbpnbXb2gVk+oNxiKV7c0Yl6hwpTDVJhERCRTblyBw5/CD0EQdvKf7aUDzVGnap0hn5tl8XI7FaYcpsIkIiL3JD4eTn1rjjr98bU5PQGAeyGo0xfqDoYiAdZmzIVUmHKYCpOIiGSZ63/Bj4vhh4UQHvLP9vJNzVGnKu3BJb91+XIRFaYcpsIkIiJZLj4O/txqjjod2wT8/Se7QDF4oD88MBAKlbU0oqNTYcphKkwiIpKtrp2BQ4vg0GJzGRYAbBDQ2hx1qvQIOLtYGtERqTDlMBUmERHJEXG34Y8N5qjTyR3/bPcqaY44PdAfvEpYl8/BqDDlMBUmERHJcVdOwA8L4MclEPX3enU2Z6jSzhx1qtACnLQKWlpUmHKYCpOIiFgmNgaOrjWnJji9+5/thcpB3UFQpx94FrUqnV1TYcphKkwiImIXLv1uFqfDSyEm3NzmlA+qdTRHnco2ApvN2ox2RIUph6kwiYiIXbl1E35dZV7rdO6Hf7YXqWwWp9q9zDme8jgVphymwiQiInbr/GFz1OnnL+D2DXObixtU72KWp1L18uyokwpTDlNhEhERuxcdAb98YY46XTzyz/biNc3162r1ANeC1uWzgApTDlNhEhERh2EYcPagWZx+XQWx0eb2/J5Qs7s56uRfy9qMOUSFKYepMImIiEO6GQY/LTPL05Xj/2wvWc8sTtUfh/we1uXLZipMOUyFSUREHJphQPAuszj9tg7ib5vb3byhdm9z8d9iVa3NmA1UmHKYCpOIiOQakZfh8BI4GATXTv+zvWwjc9Tpvg7g4mpdviykwpTDVJhERCTXiY+Hk9vN4vTHBjDizO0eheH+fuakmL4VLI14r1SYcpgKk4iI5Grh5+DHxfDDQrh+/p/tFVqYo05V2oFzPuvyZZIKUw5TYRIRkTwhLhaObzavdfpzK/B3jfD0gwcGmD8+pS2NeDdUmHKYCpOIiOQ5V4PNEacfF8ONy+Y2mxNUamOOOgW0AidnSyOmR4Uph6kwiYhInhV7C35fb84mfmrnP9u9S0PdgXD/AChY3Lp8aVBhymEqTCIiIkDocfhhAfy4BKKvmducXKBqe3PUqVxTcHKyMmESKkw5TIVJRETkDrej4Oga81qnkH3/bPetaC7DUqcvePhal+9vKkw5TIVJREQkFRd/Nacm+GkZ3LpubnN2heqdzVGn0oGWLf6rwpTDVJhERETSERMJR1bCwU/gwk//bC96n1mcavc0ZxYHuBYCN6+kfiyPwlnybTwVphymwiQiInIXzh0yP677ZQXERpnb8nlAja7m9U5fDITYmNQf7+IKz/5wz6VJhSmHqTCJiIhkQtQ1+Hm5WZ4u/3Z3jx3+LZSoc0+nz+jfb/u5TF1ERETyHncfCBwOI76HwRuhVk/zW3V2RoVJRERErGezQdkHoctc6LfK6jTJqDCJiIiIfUm48NuOqDCJiIiIpEOFSURERCQdKkwiIiIi6VBhEhEREfviUdicZyktLq7mfjnE/r63JyIiInmbT2lzUsocmOk7o1SYRERExP74lM7RQpQefSR3hw8//JAHHniAfPnyMWnSJKvjiIiIiJ1QYbqDv78/kyZNomvXrlZHERERETuij+Tu0LlzZwC+/vpra4OIiIiIXbG7EabIyEgmTpxI27Zt8fX1xWazsWDBghT3jYmJYezYsZQoUQJ3d3cCAwPZsmVLzgYWERGRXM/uClNoaCiTJ0/mt99+o3bt2mnuO2jQIKZPn07fvn2ZOXMmzs7OPProo+zatSuH0oqIiEheYHeFyd/fnwsXLnD69GmmTZuW6n779+9n2bJlTJ06lWnTpjF8+HC2b99O2bJleemll5Ls27hxY2w2W4o/r776anY/JREREXFwdncNk6urK35+funut2LFCpydnRk+fHjiNjc3N4YOHcorr7xCSEgIpUubX0fUiJOIiIjcC7sbYcqoH3/8kcqVK+Pl5ZVke4MGDQA4fPjwXR8zNjaW6Oho4uLikvxbRERE8jaHLUwXLlzA398/2faEbefPn7/rY77++uu4u7szb9483njjDdzd3Vm8eHGK+8bExBAREZHkR0RERHInu/tILqOioqJwdU2+zoybm1vi/Xdr0qRJGZ6wcurUqbz22mvJtqs4iYiIOI6Ev9uGYaS5n8MWJnd3d2JiYpJtj46OTrw/O40bN47nn38+8fa5c+eoVq1a4nVTIiIi4jiuX7+Ot7d3qvc7bGHy9/fn3LlzybZfuHABgBIlSmTr+V1dXZOMcHl6ehISEkLBggWx2WwZOkb9+vU5cOBAdkWUFOg1T19eeo1yy3N1tOdhr3ntIVdERASlS5cmJCQk2TW6kj0Mw+D69evp9gaHLUx16tRhx44dREREJHlT7du3L/H+nOTk5ESpUqXu6jHOzs76H0QO02uevrz0GuWW5+poz8Ne89pTLi8vL7vJkhekNbKUwGEv+u7WrRtxcXHMnTs3cVtMTAxBQUEEBgY6xEdjzzzzjNUR8hy95unLS69RbnmujvY87DWvveYS+2Az0rvKyQKzZs3i2rVrnD9/ng8//JAuXbpw//33AzBy5MjEJtijRw++/PJLxowZQ0BAAAsXLmT//v1s27aNpk2bWvkURERE7lpERATe3t6Eh4drhMnO2GVhKleuHKdPn07xvlOnTlGuXDnAvMB7/PjxLFmyhKtXr1KrVi2mTJlCmzZtcjCtiIhI1oiJiWHq1KmMGzcuxW+Ci3XssjCJiIiI2BOHvYZJ0vbhhx/ywAMPkC9fvgzPLSX3Tq+73EnvB5HcQ4Upl/L392fSpEl07drV6ih5il53uZPeDyK5hwpTLtW5c2c6duyIj4+P1VHyFL3ucie9HySrxcTEMGTIEMqUKYOXlxcNGzbk+++/tzpWnqDC9Ldff/2V7t27U6FCBTw8PChSpAhNmzZl3bp12XreyMhIJk6cSNu2bfH19cVms7FgwYJU94+JiWHs2LGUKFECd3d3AgMD2bJlS7ZmzElvvPEGNpuNGjVqZOt59Lrbt0OHDtGxY0d8fX3x8PCgRo0avPfee9l2Pr0fxFHExsZSrlw5du3axbVr1xg9ejQdOnQgMjLS6mi5ngrT306fPs3169cZOHAgM2fOZPz48QB07NgxyVxPWS00NJTJkyfz22+/Ubt27XT3HzRoENOnT6dv377MnDkTZ2dnHn30UXbt2pVtGXPK2bNnefPNNylQoEC2n0uvu/3avHkzDz74IJcuXWL8+PHMnDmTxx57jLNnz2bbOfV+EEdRoEABJkyYQJkyZXBycqJXr17kz5+fP/74w+pouZ8hqYqNjTVq165tVKlSJdV9wsLCjJUrV6Z6/2effWZERkamen90dLRx4cIFwzAM48CBAwZgBAUFpbjvvn37DMCYNm1a4raoqCijYsWKxoMPPpjiY5588klj4sSJqZ7fnvTs2dNo2bKl0axZM6N69epp7qvXPXcKDw83ihcvbjz++ONGXFxchh+n94PYq+vXrxsTJkww2rRpYxQqVCjN91Z0dLTx0ksvGf7+/oabm5vRoEEDY/PmzWke/9ixY4arq6tx7dq1bEgvd9IIUxqcnZ0pXbo0165dS3WfDz74IHECzX/75JNP6NOnDwsXLkz18a6urvj5+WUoz4oVK3B2dmb48OGJ29zc3Bg6dCjff/89ISEhGTqOPdq5cycrVqxgxowZGdpfr3vu9Nlnn3Hx4kXeeOMNnJycuHHjBvHx8ek+Tu8HsVd3M3p5tyOXUVFR9OvXj3HjxmVoaQ+5NypM/3Ljxg1CQ0M5ceIE7777Lhs2bKBVq1ap7j927Fjat29P79692bZtW+L2VatW8eSTT9KvXz+efvrpLMn2448/Urly5WSzvzZo0ACAw4cPJ26LjY0lOjqauLi4JP+2R3FxcYwcOZInnniCmjVrZugxet1zp61bt+Ll5cW5c+eoUqUKnp6eeHl58fTTTxMdHZ3q4/R+EHvl7+/PhQsXOH36NNOmTUt1v/3797Ns2TKmTp3KtGnTGD58ONu3b6ds2bK89NJLyfa/ffs23bt3JyAggAkTJmTnU5AEVg9x2Zsnn3zSAAzAcHJyMrp162aEhYWl+ZioqCijWbNmhqenp7F3715j69athqurq/HYY48Zt2/fzvC50/sooHr16kbLli2Tbf/1118NwJgzZ07itokTJyY+j4Sf1I5rtVmzZhne3t7GpUuXDMMwMvSRnGHodc+NatWqZXh4eBgeHh7GyJEjjZUrVxojR440AKNXr15pPlbvB7F3ab23XnzxRcPZ2dkIDw9Psv3NN980AOPMmTOJ2+Li4oyePXve9Xtb7o1LDnYzhzB69Gi6devG+fPnWb58OXFxcdy6dSvNx7i5ubF27VpatGjBo48+yq1btwgMDGT58uW4uGTdSxwVFZXiVPlubm6J9yeYNGmSQ0yUd+XKFSZMmMD48eMpWrToXT1Wr3vuExkZyc2bN3nqqacSvxXXpUsXbt26xUcffcTkyZOpVKlSio/V+0EcWUZGLhMWlX/yySe5cOECmzZtytL3tqRNH8n9S9WqVWndujUDBgxg/fr1REZG0qFDB4x0VpDx8vLi7bffJiwsjMjISGbMmIG7u3uWZnN3dycmJibZ9oSPKrL6fDnh1VdfxdfXl5EjR2bq8Xrdc5eE17J3795Jtvfp0wcg3flm9H4QR3XhwgX8/f2TbU/Ydv78ecD8Rve8efPYv38/RYoUwdPTE09PT7777rsczZsXqTClo1u3bhw4cIBjx46lud/Jkyfp27cvVatWpWzZsnTt2pULFy5kaZaEz8L/LWFbiRIlsvR82e348ePMnTuXUaNGcf78eYKDgwkODiY6Oprbt28THBxMWFhYmsfQ6567JLyWxYsXT7K9WLFiAFy9ejXNx+v9II4qoyOXZcuWxTAMoqKiiIyMTPxp0qRJjubNi1SY0pHwJg0PD091nwsXLvDwww+TL18+tmzZwpYtW7hx4waPPPJIun/w70adOnU4duwYERERSbbv27cv8X5Hcu7cOeLj4xk1ahTly5dP/Nm3bx/Hjh2jfPnyTJ48OdXH63XPferWrQuY7407JfzXdVof2+r9II5MI5f2T4Xpb5cuXUq27fbt2yxatAh3d3eqVauW4uOuXr1KmzZtiIyMZOvWrZQqVYpKlSqxadMmQkJCaN++PTdu3MiSjN26dSMuLi7JRJoxMTEEBQURGBiY+Pm2o6hRowZffvllsp/q1atTpkwZvvzyS4YOHZriY/W65049evQAzKkA7jRv3jxcXFxo3rx5io/T+0EcnUYu7Z+uFvvbk08+SUREBE2bNqVkyZL89ddffPrpp/z++++88847eHp6pvi4Dz74gJCQEL755pskF6PWqVOH9evX88gjj7Bw4UJGjBiR6rlnzZrFtWvXEv8ret26dYmzGo8cOTJxfo3AwEC6d+/OuHHjuHTpEgEBASxcuJDg4OBkf2AcQZEiRejcuXOy7QlzMaV0XwK97rnT/fffz5AhQ5g/fz6xsbE0a9aMb775hi+++IJx48al+kdD7wdxdHXq1GHHjh1EREQkufBbI5d2xOqv6dmLpUuXGq1btzaKFy9uuLi4GIUKFTJat25trFmzJs3H3b592zhy5Eiq9//0009GfHx8mscoW7Zssq8eJ/ycOnUqyb5RUVHGCy+8YPj5+Rmurq5G/fr1jY0bN2b4eTqCjEwroNc997p165YxadIko2zZska+fPmMgIAA4913303zMXo/iCNIa1qBvXv3JptBPjo62ggICDACAwNzMKWkxmYY6Xz9S0RERDLtztHLDz/8kC5dunD//fcDSUcvE2arHzNmTOLI5f79+9m2bRtNmza18ikIoMIkIiKSjcqVK8fp06dTvO/UqVOUK1cOMC/wHj9+PEuWLOHq1avUqlWLKVOm0KZNmxxMK6lRYRIRERFJh74lJyIiIpIOFSYRERGRdKgwiYiIiKRDhUlEREQkHSpMIiIiIulQYRIRERFJhwqTiIiISDpUmERERETSocIkIiIikg4VJhHJEt988w02m40VK1ZYHSVDLl68SLdu3ShcuDA2m40ZM2ZYHUlE7JiL1QFERKwwZswYNm3axMSJE/Hz86NevXpWR7Jbb775JtWqVaNz585WRxGxjAqTiORJ27dvp1OnTrzwwgtWR7F7b775Jt26dVNhkjxNH8mJiEO5ceNGlhzn0qVL+Pj4ZMmxskJWPS9HER0dTXx8vNUxRDJMhUnEAU2aNAmbzcaff/7JoEGD8PHxwdvbm8GDB3Pz5s3E/YKDg7HZbCxYsCDZMWw2G5MmTUp2zGPHjtGvXz+8vb0pWrQo48ePxzAMQkJC6NSpE15eXvj5+fHOO++kmC0uLo5XXnkFPz8/ChQoQMeOHQkJCUm23759+2jbti3e3t54eHjQrFkzdu/eneLzPHr0KH369KFQoUI0btw4zdfm5MmTdO/eHV9fXzw8PGjYsCFfffVV4v0LFizAZrNhGAazZ8/GZrNhs9lSPV7Ca/j222/z7rvvUrZsWdzd3WnWrBlHjhxJsu/PP//MoEGDqFChAm5ubvj5+TFkyBCuXLmS4ed1t8e4l99XTEwMEydOJCAgAFdXV0qXLs1LL71ETExM4j42m40bN26wcOHCxNdq0KBBifefO3eOIUOGULx4cVxdXalevTrz589Pcp6E69uWLVvGq6++SsmSJfHw8CAiIoLbt2/z2muvUalSJdzc3ChcuDCNGzdmy5Ytqf5ORKygj+REHFiPHj0oX748U6dO5dChQ8ybN49ixYrx3//+N9PH7NmzJ/fddx9vvfUWX331Fa+//jq+vr589NFHtGzZkv/+9798+umnvPDCC9SvX5+mTZsmefwbb7yBzWZj7NixXLp0iRkzZtC6dWsOHz6Mu7s7YH4c1q5dO+rWrcvEiRNxcnIiKCiIli1b8t1339GgQYMkx+zevTuVKlXizTffxDCMVLNfvHiRhx56iJs3bzJq1CgKFy7MwoUL6dixIytWrODxxx+nadOmLF68mP79+/Pwww8zYMCADL0uixYt4vr16zzzzDNER0czc+ZMWrZsyS+//ELx4sUB2LJlCydPnmTw4MH4+fnx66+/MnfuXH799Vf27t2brJil9Lzu9hiZ/X3Fx8fTsWNHdu3axfDhw7nvvvv45ZdfePfddzl27BirV68GYPHixTzxxBM0aNCA4cOHA1CxYsXE17thw4bYbDaeffZZihYtyoYNGxg6dCgRERGMHj06SdYpU6aQP39+XnjhBWJiYsifPz+TJk1i6tSpieeIiIjg4MGDHDp0iIcffjhDvxuRHGGIiMOZOHGiARhDhgxJsv3xxx83ChcunHj71KlTBmAEBQUlOwZgTJw4Mdkxhw8fnrgtNjbWKFWqlGGz2Yy33norcfvVq1cNd3d3Y+DAgYnbduzYYQBGyZIljYiIiMTty5cvNwBj5syZhmEYRnx8vFGpUiWjTZs2Rnx8fOJ+N2/eNMqXL288/PDDyTL17t07Q6/L6NGjDcD47rvvErddv37dKF++vFGuXDkjLi4uyfN/5pln0j1mwmvo7u5unD17NnH7vn37DMAYM2ZMkufwb0uXLjUAY+fOnRl6Xnd7jMz+vhYvXmw4OTklea0MwzDmzJljAMbu3bsTtxUoUCDJYxMMHTrU8Pf3N0JDQ5Ns79Wrl+Ht7Z34XBLeGxUqVEj2/GrXrm20b98+2bFF7I0+khNxYE899VSS202aNOHKlStERERk+phPPPFE4r+dnZ2pV68ehmEwdOjQxO0+Pj5UqVKFkydPJnv8gAEDKFiwYOLtbt264e/vz9dffw3A4cOHOX78OH369OHKlSuEhoYSGhrKjRs3aNWqFTt37kx2bcu/n2dqvv76axo0aJDkYztPT0+GDx9OcHAwR48ezdiLkILOnTtTsmTJxNsNGjQgMDAw8XkBiSNoYF6jExoaSsOGDQE4dOhQsmOm9Lzu9hiZ/X198cUX3HfffVStWjXxdxAaGkrLli0B2LFjRxqvBhiGwcqVK+nQoQOGYSQ5Rps2bQgPD0+Wd+DAgUmeX0K2X3/9lePHj6d5PhGr6SM5EQdWpkyZJLcLFSoEwNWrV/Hy8sqSY3p7e+Pm5kaRIkWSbf/3dTUAlSpVSnLbZrMREBBAcHAwQOIfxoEDB6aaITw8PPG5AJQvXz5D2U+fPk1gYGCy7ffdd1/i/TVq1MjQsf7t388LoHLlyixfvjzxdlhYGK+99hrLli3j0qVLSfYNDw9P9viUntfdHiOzv6/jx4/z22+/UbRo0WTHBJKd+98uX77MtWvXmDt3LnPnzs3QMVJ6vpMnT6ZTp05UrlyZGjVq0LZtW/r370+tWrXSPL9ITlNhEnFgzs7OKW43/r4eJrWLmePi4u7qmOmd524kjB5NmzaNOnXqpLiPp6dnktv/HpWwVz169GDPnj28+OKL1KlTB09PT+Lj42nbtm2K3whL6Xnd7TEy+/uKj4+nZs2aTJ8+PcV9S5cunerzTHg8QL9+/VItv/8uPSk936ZNm3LixAnWrFnD5s2bmTdvHu+++y5z5sxJMnomYjUVJpFcLGGU5tq1a0m2nz59OtvO+e+PVgzD4M8//0z845lwwbCXlxetW7fO0nOXLVuWP/74I9n233//PfH+zErpI6Njx45Rrlw5wBzV27ZtG6+99hoTJkxI83GpyYpjZFTFihX56aefaNWqVZrfEoSUi3fRokUpWLAgcXFx9/x79PX1ZfDgwQwePJjIyEiaNm3KpEmTVJjErugaJpFczMvLiyJFirBz584k2z/44INsO2fCt8kSrFixggsXLtCuXTsA6tatS8WKFXn77beJjIxM9vjLly9n+tyPPvoo+/fv5/vvv0/cduPGDebOnUu5cuWoVq1apo+9evVqzp07l3h7//797Nu3L/F5JYzq/HvU7W6WXMmKY2RUjx49OHfuHB9//HGy+6KiopLMC1WgQIFkpdvZ2ZmuXbuycuXKZNMrQMZ/j//+WNfT05OAgIAkUxuI2AONMInkck888QRvvfUWTzzxBPXq1WPnzp0cO3Ys287n6+tL48aNGTx4MBcvXmTGjBkEBAQwbNgwAJycnJg3bx7t2rWjevXqDB48mJIlS3Lu3Dl27NiBl5cX69aty9S5X375ZZYuXUq7du0YNWoUvr6+LFy4kFOnTrFy5UqcnDL/34gBAQE0btyYp59+mpiYGGbMmEHhwoV56aWXALOcNm3alP/973/cvn2bkiVLsnnzZk6dOpXhc2TFMTKqf//+LF++nKeeeoodO3bQqFEj4uLi+P3331m+fDmbNm1KXC6mbt26bN26lenTp1OiRAnKly9PYGAgb731Fjt27CAwMJBhw4ZRrVo1wsLCOHToEFu3biUsLCzdHNWqVaN58+bUrVsXX19fDh48yIoVK3j22Wez/DmL3AsVJpFcbsKECVy+fJkVK1awfPly2rVrx4YNGyhWrFi2nO+VV17h559/ZurUqVy/fp1WrVrxwQcf4OHhkbhP8+bN+f7775kyZQqzZs0iMjISPz8/AgMDefLJJzN97uLFi7Nnzx7Gjh3L+++/T3R0NLVq1WLdunW0b9/+np7XgAEDcHJyYsaMGVy6dIkGDRowa9Ys/P39E/f57LPPGDlyJLNnz8YwDB555BE2bNhAiRIlMnyerDhGRjg5ObF69WreffddFi1axJdffomHhwcVKlTgueeeo3Llyon7Tp8+neHDh/Pqq68SFRXFwIEDCQwMpHjx4uzfv5/JkyezatUqPvjgAwoXLkz16tUzPBfYqFGjWLt2LZs3byYmJoayZcvy+uuv8+KLL2bp8xW5VzYjM1dtiojkEcHBwZQvX55p06Zp3TmRPEzXMImIiIikQ4VJREREJB0qTCIiIiLp0DVMIiIiIunQCJOIiIhIOlSYRERERNKhwiQiIiKSDhUmERERkXSoMImIiIikQ4VJREREJB0qTCIiIiLpUGESERERSYcKk4iIiEg6/h+qJ3MbmM0FzAAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.loglog(depth_parameters, depth_energies - dmrg_energy, \"-s\", color=\"tab:orange\")\n", "plt.xlabel(\"number of parameters\")\n", "plt.ylabel(\"energy error\")\n", "plt.title(f\"Optimizing {n_qubits} qubits\");" ] }, { "cell_type": "code", "execution_count": 17, "id": "f7075e94", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:12:27.177043Z", "iopub.status.busy": "2026-04-03T04:12:27.176885Z", "iopub.status.idle": "2026-04-03T04:12:27.189614Z", "shell.execute_reply": "2026-04-03T04:12:27.188704Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "fidelity 0.9170002040282711\n" ] } ], "source": [ "psi_exact = dmrg.state\n", "overlap = (psi_exact.H & optimal_circuit.psi).contract()\n", "print(\"fidelity \", abs(overlap) ** 2)" ] }, { "cell_type": "markdown", "id": "2bfdae22", "metadata": {}, "source": [ "## Quantum Phase Estimation\n", "\n", "Let us know use a guess state the circuit optimization to initialize the QPE algorithm. For simplicity we will take a Hamiltonian defined on $n=4$ qubits." ] }, { "cell_type": "code", "execution_count": 18, "id": "63baccdc", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:12:27.190997Z", "iopub.status.busy": "2026-04-03T04:12:27.190848Z", "iopub.status.idle": "2026-04-03T04:12:27.210126Z", "shell.execute_reply": "2026-04-03T04:12:27.209427Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1, R, max_bond=(10/10), cutoff:1e-13\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Energy: (-1.616025403784439-8.326672684688674e-17j) ... not converged.\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "2, R, max_bond=(4/20), cutoff:1e-13\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Energy: (-1.61602540378444+5.551115123125783e-17j) ... converged!\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", "Stored reference energy -1.61602540378444\n" ] } ], "source": [ "n_qubits = 4\n", "hamilt = heisenberg_hamiltonian(n_qubits)\n", "hamilt_mpo = hamilt.to_mpo()\n", "\n", "dmrg = qtn.DMRG2(hamilt_mpo, bond_dims=[10, 20, 40, 100], cutoffs=1e-13)\n", "dmrg.solve(tol=1e-6, verbosity=1)\n", "dmrg_energy = np.real(dmrg.energy)\n", "psi_exact = dmrg.state\n", "\n", "print(\"\\nStored reference energy \", dmrg_energy)" ] }, { "cell_type": "markdown", "id": "28c3e100", "metadata": {}, "source": [ "We take the shallowest circuit" ] }, { "cell_type": "code", "execution_count": 19, "id": "756c4354", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:12:27.211616Z", "iopub.status.busy": "2026-04-03T04:12:27.211451Z", "iopub.status.idle": "2026-04-03T04:12:28.723375Z", "shell.execute_reply": "2026-04-03T04:12:28.722584Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Optimized energy -0.49999999996946454\n", "Exact energy -1.61602540378444\n" ] } ], "source": [ "depth = 1\n", "circ = ansatz_circuit(n_qubits, depth)\n", "circ_optimizer = make_circuit_optimizer(circ, hamilt_mpo)\n", "optimal_circuit = circ_optimizer.optimize(n=100)\n", "\n", "print(\"Optimized energy \", circ_optimizer.loss)\n", "print(\"Exact energy \", dmrg_energy)" ] }, { "cell_type": "markdown", "id": "b140a3f0", "metadata": {}, "source": [ "With this depth, we should be able to reach around 30% fidelity. If it isn't the case, try to rerun the optimization" ] }, { "cell_type": "code", "execution_count": 20, "id": "75a7c517", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:12:28.724999Z", "iopub.status.busy": "2026-04-03T04:12:28.724709Z", "iopub.status.idle": "2026-04-03T04:12:28.729716Z", "shell.execute_reply": "2026-04-03T04:12:28.729115Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "fidelity 0.3110042339501942\n" ] } ], "source": [ "overlap = (psi_exact.H & optimal_circuit.psi).contract()\n", "fidelity = abs(overlap) ** 2\n", "print(\"fidelity \", fidelity)" ] }, { "cell_type": "markdown", "id": "fa9d1a9c", "metadata": {}, "source": [ "Running QPE on a state with 30% overlap should increase the fidelity.\n", "Let us initialize a circuit with a physical register and a phase register. We take $m=3$ phase qubits." ] }, { "cell_type": "code", "execution_count": 21, "id": "7cae665c", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:12:28.731043Z", "iopub.status.busy": "2026-04-03T04:12:28.730903Z", "iopub.status.idle": "2026-04-03T04:12:30.825561Z", "shell.execute_reply": "2026-04-03T04:12:30.824674Z" } }, "outputs": [], "source": [ "n_phase_qubits = 3\n", "\n", "# circuit from optimized gates\n", "circ_qpe = qtn.CircuitMPS(n_phase_qubits + n_qubits)\n", "\n", "for gate in optimal_circuit.gates:\n", " label, params, qubits = gate.label, gate.params, gate.qubits\n", " qubits = tuple(qb + n_phase_qubits for qb in qubits)\n", " circ_qpe.apply_gate(label, *params, *qubits)" ] }, { "cell_type": "markdown", "id": "79cbc519", "metadata": {}, "source": [ "Set QPE parameters: first define the size of the search interval $\\Delta$ which sets the evolution time $t$" ] }, { "cell_type": "code", "execution_count": 22, "id": "6b0e0ee9", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:12:30.827141Z", "iopub.status.busy": "2026-04-03T04:12:30.826979Z", "iopub.status.idle": "2026-04-03T04:12:30.829866Z", "shell.execute_reply": "2026-04-03T04:12:30.829158Z" } }, "outputs": [], "source": [ "E_target = circ_optimizer.loss\n", "size_interval = 3\n", "E_const, Emax, evolution_time, global_phase = set_search_window(\n", " hamilt, E_target, size_interval\n", ")" ] }, { "cell_type": "markdown", "id": "81c16d85", "metadata": {}, "source": [ "and the Trotter parameters" ] }, { "cell_type": "code", "execution_count": 23, "id": "a98ac4da", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:12:30.831221Z", "iopub.status.busy": "2026-04-03T04:12:30.831048Z", "iopub.status.idle": "2026-04-03T04:12:30.833632Z", "shell.execute_reply": "2026-04-03T04:12:30.832927Z" } }, "outputs": [], "source": [ "trotter_order = 2\n", "n_steps = 4\n", "dt = evolution_time / n_steps" ] }, { "cell_type": "markdown", "id": "285ce47e", "metadata": {}, "source": [ "then run textbook QPE (this can take a minute or two). Since `n_qubits` is small, for faster execution you can always use exact time evolution instead of a Trotterization." ] }, { "cell_type": "code", "execution_count": 24, "id": "f5ac6c1e", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:12:30.834937Z", "iopub.status.busy": "2026-04-03T04:12:30.834792Z", "iopub.status.idle": "2026-04-03T04:13:14.968582Z", "shell.execute_reply": "2026-04-03T04:13:14.967943Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 45.7 s, sys: 723 ms, total: 46.4 s\n", "Wall time: 44.1 s\n" ] } ], "source": [ "%%time\n", "traces, res = qpe_sample(\n", " hamilt, circ_qpe, evolution_time, dt, global_phase, trotter_order=trotter_order\n", ")" ] }, { "cell_type": "markdown", "id": "44fd044c", "metadata": {}, "source": [ "NB: the energy minimum can be $< E_{\\rm exact}$\n", " when $E_{\\rm target} - \\Delta/2 < E_{\\rm exact}$. We only consider the bitstrings with probability $> 4/\\pi^2 F$ where $F = |\\langle{\\psi}|\\psi_{\\rm exact}\\rangle|^2$. The $4/\\pi^2$ factor gives a lower bound on the QPE success probability depending on the initial overlap as explained in the [Textbook QPE](./textbook_qpe.ipynb) example.\n", "\n", "NB: in practice one will not have access to the overlap. An approximation of the fidelity is sufficient. The following quantity can be used as a proxy, see [arxiv:2306.02620](https://arxiv.org/abs/2306.02620):\n", "\n", "$$ F \\approx \\exp\\Big(- \\frac{(E-E_0)^2}{2\\sigma^2}\\Big ),$$\n", "where $\\sigma = \\langle H^2 \\rangle - E^2$ is the energy variance on guess state $\\ket{\\psi}$, and $E_0$ is an estimate of the exact ground state energy that doesn't need to be very accurate." ] }, { "cell_type": "code", "execution_count": 25, "id": "f0fa849a", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:13:14.970127Z", "iopub.status.busy": "2026-04-03T04:13:14.969960Z", "iopub.status.idle": "2026-04-03T04:13:14.974908Z", "shell.execute_reply": "2026-04-03T04:13:14.974224Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Most probable energy = -0.12500 w prob = 0.33323\n", "First 5 energies = [-0.125 -1.625 0.625 -0.5 0.25 ]\n", "Minimal \"significant\" energy = -1.62500 with probability 0.32249\n", "error = 0.00897 (theoretical error bound = 0.37500)\n" ] } ], "source": [ "k_probs_list = sorted(enumerate(np.ravel(res)), key=lambda x: x[1], reverse=True)\n", "\n", "kmin = 2 ** (n_phase_qubits - 1)\n", "prob_min = 0\n", "emin = E_target\n", "energies = []\n", "\n", "for k, prob in k_probs_list:\n", " energy = E_target + size_interval * (1 / 2 - k / 2**n_phase_qubits)\n", " energies.append(energy)\n", " if energy < emin and prob > fidelity * 4 / np.pi**2:\n", " emin = energy\n", " kmin = k\n", " prob_min = prob\n", "\n", "print(f\"Most probable energy = {energies[0]:.5f} w prob = {k_probs_list[0][1]:.5f}\")\n", "print(f\"First 5 energies = {np.round(energies[:5], 5)}\")\n", "print(f'Minimal \"significant\" energy = {emin:.5f} with probability {prob_min:.5f}')\n", "print(\n", " f\"error = {abs(dmrg_energy - emin):.5f} (theoretical error bound = {size_interval / 2**n_phase_qubits:.5f})\"\n", ")" ] }, { "cell_type": "markdown", "id": "3ee5a97c", "metadata": {}, "source": [ "When the GS energy is measured, the physical register contains the GS wavefunction.\n", "We thus project the phase register of the final circuit wavefunction on the previously found bitstring that\n", "gives the minimal energy while satisfying the probability criterion" ] }, { "cell_type": "code", "execution_count": 26, "id": "a15ab6e8", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:13:14.976405Z", "iopub.status.busy": "2026-04-03T04:13:14.976128Z", "iopub.status.idle": "2026-04-03T04:13:17.877889Z", "shell.execute_reply": "2026-04-03T04:13:17.877113Z" } }, "outputs": [], "source": [ "psi_final = traces[\"circuit\"].psi\n", "# change psi_final.backend from 'jax' to numpy as a workaround for\n", "# https://github.com/jcmgray/quimb/issues/340\n", "psi_final.apply_to_arrays(np.asarray)\n", "\n", "bin_kmin = f\"{kmin:b}\".zfill(n_phase_qubits)\n", "for i in range(n_phase_qubits):\n", " psi_final.measure_(0, outcome=int(bin_kmin[i]), remove=True)" ] }, { "cell_type": "markdown", "id": "9a7bf0f4", "metadata": {}, "source": [ "The fidelity should improve" ] }, { "cell_type": "code", "execution_count": 27, "id": "0e964ef9", "metadata": { "execution": { "iopub.execute_input": "2026-04-03T04:13:17.879414Z", "iopub.status.busy": "2026-04-03T04:13:17.879253Z", "iopub.status.idle": "2026-04-03T04:13:17.883416Z", "shell.execute_reply": "2026-04-03T04:13:17.882784Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Fidelity before QPE = 0.31100\n", "Fidelity after QPE = 0.96258\n" ] } ], "source": [ "overlap_qpe = psi_final.overlap(psi_exact)\n", "fidelity_qpe = abs(overlap_qpe) ** 2\n", "print(f\"Fidelity before QPE = {fidelity:.5f}\")\n", "print(f\"Fidelity after QPE = {fidelity_qpe:.5f}\")" ] }, { "cell_type": "markdown", "id": "775e4ee6", "metadata": {}, "source": [ "We observe that even with a moderate overlap, Quantum Phase Estimation projects on the ground state. As an exercise, you can try to reproduce the following figure:\n", "\n", "\n", "\n", "it shows the infidelity as a function of circuit depth (orange curve) or bond dimension (blue curve) for a guess state prepared with either circuit optimization or DMRG. The colored stars then show how the fidelity quickly improves (error drops to $\\sim 10^{-5}$) when running QPE with even a few phase qubits upon the trial state from circuit optimization." ] }, { "cell_type": "code", "execution_count": null, "id": "c0747d6c", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "jupytext": { "formats": "ipynb,py:percent" }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.12" } }, "nbformat": 4, "nbformat_minor": 5 }