{ "cells": [ { "cell_type": "markdown", "id": "a14a85cf", "metadata": {}, "source": [ "## Battery Cathodes: Intercalation Potential and Volume Change\n", "\n", "Cathode materials are often judged by more than their voltage alone. A useful battery cathode should store lithium at a favorable potential, but it should also remain structurally stable during charge and discharge. Large changes in unit-cell volume can lead to mechanical stress, cracking, and capacity fade over repeated cycling.\n", "\n", "In this notebook we use the inorganic-materials UMA model, UMA-S-1.2-OMat, to optimize olivine LiFePO4 and its delithiated FePO4 counterpart. From these calculations we estimate two useful screening descriptors: the average lithium intercalation potential and the relative volume change upon delithiation." ] }, { "cell_type": "markdown", "id": "8e59638a", "metadata": {}, "source": [ "## Overview\n", "\n", "The workflow follows the reaction\n", "\n", "$$\\mathrm{LiFePO_4 \\rightarrow FePO_4 + Li}$$\n", "\n", "and evaluates it with a machine-learning potential. We will:\n", "\n", "- optimize bulk Li to obtain a consistent Li metal reference energy\n", "- optimize lithiated LiFePO4 and delithiated FePO4\n", "- compare the optimized structures visually and through their cell volumes\n", "- compute the average intercalation potential from the total energies\n", "- compute the relative volume change per formula unit and compare with experiment" ] }, { "cell_type": "code", "execution_count": 1, "id": "a6cd3909", "metadata": { "execution": { "iopub.execute_input": "2026-04-24T08:44:05.444595Z", "iopub.status.busy": "2026-04-24T08:44:05.444497Z", "iopub.status.idle": "2026-04-24T08:44:05.752459Z", "shell.execute_reply": "2026-04-24T08:44:05.752051Z" } }, "outputs": [], "source": [ "from math import gcd\n", "\n", "from ase.build import bulk\n", "from scm.plams import AMSJob, Settings, Units, fromASE, view, plot_image_grid" ] }, { "cell_type": "markdown", "id": "f246d97e", "metadata": {}, "source": [ "## Settings and Visualization Helpers\n", "\n", "We use the UMA-S-1.2-OMat machine-learning potential with a geometry optimization and lattice relaxation so that both atomic positions and unit-cell parameters can respond to lithiation state. The D4 dispersion add-on is also consistently included in all calculations.\n", "\n", "This section also defines a few small helper functions for structure handling, formula counting, and visualization." ] }, { "cell_type": "code", "execution_count": 2, "id": "d95fbecc", "metadata": { "execution": { "iopub.execute_input": "2026-04-24T08:44:05.754666Z", "iopub.status.busy": "2026-04-24T08:44:05.754585Z", "iopub.status.idle": "2026-04-24T08:44:05.758813Z", "shell.execute_reply": "2026-04-24T08:44:05.758503Z" } }, "outputs": [], "source": [ "def umat_settings(nproc=1):\n", " s = Settings()\n", " s.input.ams.Task = \"GeometryOptimization\"\n", " s.input.ams.GeometryOptimization.OptimizeLattice = \"Yes\"\n", " s.input.ams.EngineAddons.D4Dispersion.Enabled = \"Yes\"\n", " s.input.mlpotential.Model = \"UMA-S-1.2-OMat\"\n", " s.runscript.nproc = nproc\n", " s.runscript.preamble_lines = [\"export OMP_NUM_THREADS=1\"]\n", " return s\n", "\n", "\n", "def formula_units(system):\n", " counts = [count for count in system.get_formula(as_dict=True).values() if count > 0]\n", " nfu = counts[0]\n", " for count in counts[1:]:\n", " nfu = gcd(nfu, count)\n", " return nfu\n", "\n", "\n", "def render(system, supercell=(3, 3, 1), direction=\"along_y\", width=400, height=400, padding=-1):\n", " m = system.copy().supercell(*supercell)\n", " return view(\n", " m,\n", " direction=direction,\n", " width=width,\n", " height=height,\n", " padding=padding,\n", " fixed_atom_size=False,\n", " show_atom_labels=False,\n", " )\n", "\n", "\n", "def make_lifepo4():\n", " mol = AMSJob.from_input(\n", " \"\"\"\n", "System\n", " Atoms\n", " Li 0.0 0.0 0.0 \n", " Li 2.327458595 2.98537755 5.118098025 \n", " Li 2.327458595 0.0 5.118098025 \n", " Li 0.0 2.98537755 0.0 \n", " Fe 2.466481095 1.492688775 7.9960175444 \n", " Fe 0.1390225 4.478066325 7.3582765306 \n", " Fe 4.51589469 1.492688775 2.8779195194 \n", " Fe 2.188436095 4.478066325 2.2401785056 \n", " P 1.9486533972 1.492688775 0.9608338493 \n", " P 4.2761119922 4.478066325 4.1572641757 \n", " P 0.3788051978 1.492688775 6.0789318743 \n", " P 2.7062637928 4.478066325 9.2753622007 \n", " O 3.466919761 1.492688775 0.964563612 \n", " O 3.3223789033 3.25739339 8.5385692027 \n", " O 3.3223789033 5.69873926 8.5385692027 \n", " O 1.187997429 4.478066325 9.271632437999999 \n", " O 3.3043602309 4.478066325 0.4535511069 \n", " O 1.139461166 4.478066325 4.153534413 \n", " O 1.3325382867 0.27201584 1.6976268473 \n", " O 0.9949203083 2.71336171 6.8157248723 \n", " O 3.6599968817 3.25739339 3.4204711777 \n", " O 3.6599968817 5.69873926 3.4204711777 \n", " O 1.3505569591 1.492688775 9.782644943099999 \n", " O 0.9769016359 1.492688775 4.6645469181 \n", " O 3.6780155541 4.478066325 5.5716491319 \n", " O 3.515456024 1.492688775 6.082661637 \n", " O 0.9949203083 0.27201584 6.8157248723 \n", " O 1.3325382867 2.71336171 1.6976268473 \n", " End\n", " Lattice\n", " 4.65491719 0.0 0.0\n", " 0.0 5.9707551 0.0\n", " 0.0 0.0 10.23619605\n", " End\n", "End\n", " \"\"\"\n", " ).molecule \n", " \n", " if isinstance(mol, dict) and len(mol) == 1 and \"\" in mol:\n", " return mol[\"\"]\n", " else:\n", " return mol" ] }, { "cell_type": "markdown", "id": "35711d4d", "metadata": {}, "source": [ "## Lithium Metal Reference\n", "\n", "To convert total-energy differences into an intercalation voltage, we need a reference for metallic lithium. We therefore optimize bulk bcc Li and extract the energy per Li atom." ] }, { "cell_type": "code", "execution_count": 3, "id": "aeaaa2c1", "metadata": { "execution": { "iopub.execute_input": "2026-04-24T08:44:05.760113Z", "iopub.status.busy": "2026-04-24T08:44:05.760040Z", "iopub.status.idle": "2026-04-24T08:44:29.977640Z", "shell.execute_reply": "2026-04-24T08:44:29.977341Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[24.04|10:44:05] JOB Li_bcc_opt STARTED\n", "[24.04|10:44:05] JOB Li_bcc_opt RUNNING\n", "[24.04|10:44:29] JOB Li_bcc_opt FINISHED\n", "[24.04|10:44:29] JOB Li_bcc_opt SUCCESSFUL\n", "Li metal reference energy: -0.07082951 Ha/atom\n", "Li bcc cell volume: 40.53114 A^3\n" ] } ], "source": [ "li_bulk = fromASE(bulk(\"Li\", \"bcc\", a=3.49, cubic=True))\n", "li_job = AMSJob(name=\"Li_bcc_opt\", molecule=li_bulk, settings=umat_settings())\n", "li_result = li_job.run()\n", "\n", "li_bulk_opt = li_result.get_main_molecule()\n", "n_li = li_bulk_opt.get_formula(as_dict=True)[\"Li\"]\n", "e_li_metal = li_result.get_energy(unit=\"hartree\") / n_li\n", "v_li_bulk = li_bulk_opt.unit_cell_volume()\n", "\n", "print(f\"Li metal reference energy: {e_li_metal:.8f} Ha/atom\")\n", "print(f\"Li bcc cell volume: {v_li_bulk:.5f} A^3\")" ] }, { "cell_type": "code", "execution_count": 4, "id": "bb578599", "metadata": { "execution": { "iopub.execute_input": "2026-04-24T08:44:29.978902Z", "iopub.status.busy": "2026-04-24T08:44:29.978831Z", "iopub.status.idle": "2026-04-24T08:44:33.757553Z", "shell.execute_reply": "2026-04-24T08:44:33.757252Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[24.04|10:44:32] Starting Xvfb...\n", "[24.04|10:44:32] Xvfb started\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_image_grid(\n", " {\"optimized Li metal\": render(li_bulk_opt, direction=\"along_c\", width=420, height=420, padding=0)}, \n", " figsize=(4, 4)\n", ");" ] }, { "cell_type": "markdown", "id": "7c211669", "metadata": {}, "source": [ "## Lithiated LiFePO4 Optimization\n", "\n", "We define the olivine LiFePO4 unit cell directly in the notebook and optimize the fully lithiated cathode. The resulting total energy is one of the three quantities needed for the voltage calculation, and the relaxed cell volume provides the reference volume for the charged-state comparison." ] }, { "cell_type": "code", "execution_count": 5, "id": "f5b31b60", "metadata": { "execution": { "iopub.execute_input": "2026-04-24T08:44:33.758958Z", "iopub.status.busy": "2026-04-24T08:44:33.758879Z", "iopub.status.idle": "2026-04-24T08:44:33.795486Z", "shell.execute_reply": "2026-04-24T08:44:33.795207Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Fe4Li4O16P4\n" ] } ], "source": [ "lfp = make_lifepo4()\n", "print(lfp.get_formula(False))" ] }, { "cell_type": "code", "execution_count": 6, "id": "7033cde3", "metadata": { "execution": { "iopub.execute_input": "2026-04-24T08:44:33.796659Z", "iopub.status.busy": "2026-04-24T08:44:33.796591Z", "iopub.status.idle": "2026-04-24T08:52:38.918429Z", "shell.execute_reply": "2026-04-24T08:52:38.918124Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[24.04|10:44:33] JOB LiFePO4_opt STARTED\n", "[24.04|10:44:33] JOB LiFePO4_opt RUNNING\n", "[24.04|10:52:38] JOB LiFePO4_opt FINISHED\n", "[24.04|10:52:38] JOB LiFePO4_opt SUCCESSFUL\n", "LiFePO4 total energy: -7.21135335 Ha\n", "LiFePO4 cell volume: 293.76580 A^3\n", "Fe4Li4O16P4\n" ] } ], "source": [ "lfp_job = AMSJob(name=\"LiFePO4_opt\", molecule=lfp, settings=umat_settings())\n", "lfp_result = lfp_job.run()\n", "\n", "lfp_opt = lfp_result.get_main_molecule()\n", "e_lfp = lfp_result.get_energy(unit=\"hartree\")\n", "v_lfp = lfp_opt.unit_cell_volume()\n", "\n", "print(f\"LiFePO4 total energy: {e_lfp:.8f} Ha\")\n", "print(f\"LiFePO4 cell volume: {v_lfp:.5f} A^3\")\n", "print(lfp_opt.get_formula(False))" ] }, { "cell_type": "code", "execution_count": 7, "id": "3d56bf80", "metadata": { "execution": { "iopub.execute_input": "2026-04-24T08:52:38.919652Z", "iopub.status.busy": "2026-04-24T08:52:38.919580Z", "iopub.status.idle": "2026-04-24T08:52:40.726681Z", "shell.execute_reply": "2026-04-24T08:52:40.726362Z" } }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_image_grid({\n", " \"initial LiFePO4\": render(lfp),\n", " \"optimized LiFePO4\": render(lfp_opt),\n", "});" ] }, { "cell_type": "markdown", "id": "a6c7dabb", "metadata": {}, "source": [ "## Delithiated FePO4\n", "\n", "To represent delithiation, we remove all Li atoms from the optimized LiFePO4 structure and use the resulting FePO4 framework as the starting point for a second optimization.\n", "\n", "This mirrors the structural change associated with charge extraction and lets us compare the two end members on the same footing." ] }, { "cell_type": "code", "execution_count": 8, "id": "25bfdab6", "metadata": { "execution": { "iopub.execute_input": "2026-04-24T08:52:40.728026Z", "iopub.status.busy": "2026-04-24T08:52:40.727952Z", "iopub.status.idle": "2026-04-24T08:52:40.730254Z", "shell.execute_reply": "2026-04-24T08:52:40.729985Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Fe4O16P4\n" ] } ], "source": [ "fp = lfp_opt.copy()\n", "for atom in list(fp):\n", " if atom.symbol == \"Li\":\n", " fp.delete_atom(atom)\n", "\n", "print(fp.get_formula(False))" ] }, { "cell_type": "code", "execution_count": 9, "id": "a39108b3", "metadata": { "execution": { "iopub.execute_input": "2026-04-24T08:52:40.731326Z", "iopub.status.busy": "2026-04-24T08:52:40.731263Z", "iopub.status.idle": "2026-04-24T09:00:24.670312Z", "shell.execute_reply": "2026-04-24T09:00:24.670057Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[24.04|10:52:40] JOB FePO4_opt STARTED\n", "[24.04|10:52:40] JOB FePO4_opt RUNNING\n", "[24.04|11:00:24] JOB FePO4_opt FINISHED\n", "[24.04|11:00:24] JOB FePO4_opt SUCCESSFUL\n", "FePO4 total energy: -6.40276126 Ha\n", "FePO4 cell volume: 276.83401 A^3\n", "Fe4O16P4\n" ] } ], "source": [ "fp_job = AMSJob(name=\"FePO4_opt\", molecule=fp, settings=umat_settings())\n", "fp_result = fp_job.run()\n", "\n", "fp_opt = fp_result.get_main_molecule()\n", "e_fp = fp_result.get_energy(unit=\"hartree\")\n", "v_fp = fp_opt.unit_cell_volume()\n", "\n", "print(f\"FePO4 total energy: {e_fp:.8f} Ha\")\n", "print(f\"FePO4 cell volume: {v_fp:.5f} A^3\")\n", "print(fp_opt.get_formula(False))" ] }, { "cell_type": "code", "execution_count": 10, "id": "de9a2a44", "metadata": { "execution": { "iopub.execute_input": "2026-04-24T09:00:24.671509Z", "iopub.status.busy": "2026-04-24T09:00:24.671440Z", "iopub.status.idle": "2026-04-24T09:00:26.450355Z", "shell.execute_reply": "2026-04-24T09:00:26.450052Z" } }, "outputs": [ { "data": { "image/png": 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+2Uuo/bPLdn38RqVS6s5kXvsKTXuGzlh1Vb3+0wX1+l8we6G8v734eKKuPLf9aSo483RjUejX5+dEZXfHV0dHlalU6tQX2farTzaM3o2+f5PWbH4XwPa5HG9sbEwuXboU+Xx+X36M/eJpkTCJODc0/UJTQ5oxgqJqxOwMqNgBWAqBEVi5rR230HvF1Tdr38LsXaYQQtqMXVEuFP4rpeufWabr2sLOTlAcdw6Mj198Vbv9YgBT+yJG18315dPKv2gKGOccim4QMjmgWARYRBRE0pxqF44dtF6yZap5I4AAABzHCTtV9b9rpdIh3Zw/99BUiorFIs1rNs+2oujDH1OU938iivy9jY+IqFDInZy16AiFgxTOiZs2KFcAShmC3wK1PHQW3MM6+uyzXv5M+umlV80mdd+vVFqtd/vp9O8XMDZ/WbEIPZVi8yYn318OgvXnEV3+56f6pWXin+64Y5m+cih9wakLrdesHFKWd2aQtXVr6x2b/b+//036V2M12PCFrz18HpWIWFdX1znHKsr3nmcYpYFcjlZG0ZknVionLp+aeg2A0f0ZL2NEvR2pofOPK130L4cpZ83roP6CTW03MNf87k7nhy8/m19+6dWxs/NrerLZzFmFwldezdjzT8pkVMuy5MmGcc6PpPy39xL94ItS7teLy6EF3BrKZ88/f4n16hVn0/KuLKUsHSP3b4+uv/Ds1MXhdHvjz1c9XMYZIurO5c49z7K+d75hFObl87Qyis7aMj194ocM49Wf8byJ/Rnvk+1pMQ8zCHhOUZQhLwC1faDlApEjINsx4MWAD8iIwTZ4kZtK8byjHm6Ad4mEpmk9KSJFsyxQby9hYIAVbPu4tZb1jJfso5ELtk25SMhuxwe1PVDbBaQTA04MeBIyIJIRwVBwmFuBvvNrPUXx0kS9BmNQs1nC4CBYdzc7xDTP38p5z76Ij3NOqVTqmCCC5gRAywc8RzwyxpAQx8Q70vpRqXX8oXJJA9Dj2CwAKU1VwUslwrx50IrF3ErbfnVJVZ8W52HiH7dgflpPo/s9py9Of+e4xcqzDh1UBxcvsrODi1MrXnBG+qK3nFD82RF23+H/dcrD9bHGuZVi7G05opKdThObPx80NMS70ulTXNt+zg8Y22+jjjqI6MxS5ogXnJi+7BkrlHccNsgPO3SBmZ+/ONW3bHnqnHe/IPvtlx2f/8DLnsUfaqjqJCIh5SndUj4rpaqq3tUFLF5MWnd37nm53NunFKW4v+IFgAXzuDmYy73vOcfY31m5gJ27fFDrX7LQzs9bnFr+rFOst3zxtbnLXvWizJGffvHDZSwVRcno+psLjBVSmQzRggWghQvZYDZ75oJ8/pxzD7KRXU+LO0zGSAYxYbIpMVmXGCn7yA/X0cEI3OZAu4nWlI/JukQjAJo7XcMRwASQ2S4lbfQ85CcnYQKohyE1iNL76mxgTMqmB0w1gPFajOFJD6lUDekgAlMF4loD1WqEqQbko3slI86pQWRtEYK2NptYMjZGrN2WU3FstVVV3/URnxgpJXw/FJUWx2QdGKvE6Bh3oJllGE0XED6i6TbKtRjlZuz6qYcLsQbAVhR7HNA3RREWVqvoFIKidhstItvfj19ciQNfOk2Uy+Sev6SbPtCdo1RHVkO+M0PKYA6UUghOSy4wykf4vvPla+5WXwxgevaltk80fwrAVBRRvt0GB2QghAZd7167H7/Lg4xWjHtT/zO/A0d0ZDjrKNgw+3NEnTaBIqmXK9a5hPdUHDz4kfezn3zqc0JME6E7nR6qAtaElGh6HmVbLSAMpQcUCdiXvUCPkCHGUqXSCw45XH1vT46sUk5DvitDfCAHSisgp0WdRvnwwyP8z9i49xLMtqz5nGcizudPSUmTYUj5VgscQCgEU+K4pwMg7Jh1dhB4WiTMDkWp68Tv316ODu/JSUoZAYga6G/6SFuEOAxQrvm4azPGOwbY1C9/+nCTg5QycqPoqjtV9aU5x8nUtm+XeUAOh+HkKNHNd+2jGDXXrbYtY2TzFIaKaQFTdykWAt2VFgxVwnM9OV4J5T1b5D3bt8Hb+bWe43hTlvXXm1V1sVmvKyOOAy2OcXcUrSr7/vi+iK8ghITr3jbVTHlbpmDl7Aia0oYXRCiNK+AUo9XysG1KhOu3R6u3ikeUoTQMY/3mVGrT9VF0uJyawrxKBX4UBb913Ss3+P4/fwWIxFOWbqhm2jTemtKRVhWCpmvEMxlQRweQNUDtOsEN2Lzu4PiFHalnvuZo+tkP7pQSQLMq5ZpVQhzS0WhIb8sWykiJScfx1/n+li37qReAiCiby5+Zz+BkTQFTVU6aZQL5AtCVn+liIUi97pknLIzfsu5K+3cA6rNTsFY/qGmNO4Mgb0xMYKhWk7Hn4e4oGvWB/TZinIisfJa/OmXAUhWCrmvE07NlnDMITgPkhawzG5w03bCf8bbT6edfu1ZKTVHqDc7Xr4rj5R3NJvwtWygrpRx3nOhWYJgOomQJPA0S5kuIaAXn6kQY/WiygWetGUYeENLxPRqvBEgZM32V003p33h3+L3169v1nV8vhJC2bf/xQcP4gmsYb1kdBJYu5fhm1/34SL3+wMg+6Ht7K2P8cM4r9/vBz7ZOa+8zNahCRLLhCCpNejBUyCCMsa0sp6+4q/XzRlU+YoCDECLs6Oj44hrGestCnDrg+yyU8v4ttdoHJ6KosbfxnUdEZzCmbo2iO0c9ccu6MXaGyiULooAqzQj5FEFhUrY9IVZvl3ePTAZ/v+nBR5aL7/vj443Gv12XTn9uWxTNL0VRVFbV324Nw++vT/ovE7tBRKTpel9vkQ2FAvAjIj9kEBEDizggFQAqQCoxIm1+j3rcpjFcBiCO49itO87/3mXbxwVRNDjcaGAxAA40GGOTIZEOPPLic19gjJGpKydKCR5EgBcSwogBEQMEx8xCHRpJKDA0WjLmKZ0vfSk1pJRS07RbRguFH/2V8zdVXNdc7nnoBdCIoo0qkfpCIvr1fqgvoW4VGKPDowjkRyA/pJkyjjkgFECqkFBAxHhvXj2xi7HLAMh2ux1PEX3xznT6iDCKhkZmy1gDpjvCsOYCKmbHWxwMDuqEeaSmlU7O51/+JtM82QG2/DSWP71tml7hBMhNNiQ6MzEsDdKP4D84Fv16a6X2owcmHzuDvt1uu4yxz7mWdemDQOmwMNw6FQSTI3vZAX8IEStY1mEXlEqvfJmqzrsnitb/1Jc33z9CJzRcqKM1gWIKUDlkw0Vl9Xb3P0Yd59YttcdWmKmpqa2apr16UtOG7gG4HkVbTN9vjO5l5TpDUbR0NnvWcyzrX+YB/KYouvZHbd65aqtcVmmDD+cFshZAQDxRl+vv3V5930Tdm3z0+0gpJRH9LY7jZ40xNiAAJ+37WybDcK8HJCUObgSkvABmtQ1UWhKT9RAdkw7yVg3kuIDvQFY8NNsSLU927BjKKaWUnPObZRy/WE2nP3sq0TOO13XqN82O84PgJ3+Q8rNv4fx/vxnH+3T0KeecuKKW6g5YtQ2UmwJTFR/2eBMqEUgVkNU2gnqElifVIBDZiU0zrw2CwDNV9SNeOr1hwDQ/tYQoe5xlkcX5S5+n60O/qFbfCGDtvoyXiCiTyeSCiPSqA1RawGQ9QseUg7y9cxn7qDcFi5jaeesVCr0eD9XrWxtCvHRrOv25Uzk/6wRNo37L6nm2Zf3wl8Cn/5Pokg9LeVC0Ih20CXPIMDIn5vP/+3LDeNExuZyqKUp8QqWy9jXN5qdWx9qZ5Rat0LhgjLC10fJ/3JVilymhudu7MSFESESbAGy6dR9d4fmp1BFnp9O/eKFpzh/K5ejUKArPLJeveZ8XffK+cXr2SJUGVCZiKemOWiP89rKSct2WrWK3lTsIAoeI1gCAsw9iXMEYP6xUeuV5mvaFZ6dSuUI6jVNardahjcY33+OIa+4fprM3TSCjcFmPQn6lRv63li0yNty7zt3dMn4CwDQRlQHATe4sE3sgpZSmaY55IU2PVmVppCKQswMYWgODQYR0WgFEgGatLbdPxnJ4mtbU6w83A8ZxLAZyuS0DRNY8ztFZLEIdGCA0m4Vnbdr03vVheOUbiVZ/Zx+ei2EYSsdx759qmvFoBbyUjmEbM4NhO+ttaKpE6DiYqvjYMC7r3X1y+NKf7HT8KGppUk4vBbRe00Rq3jxQKqX2bt16/KFBcNEbOX/Xd+J4ny0SLaWUmUxmzAlkfbRK+ZGKQNYOoKszZZyZLeNWvYWR6VisHYkfmJwndu5yEQXT3FRUFGMeY+golaAMDJDabOZfIMR73uv7V51OdP+1B0F9P2gTZrtUOqFDyvNTuq5q/f2gdJp3rl9/yIXtdudHGs2Xu5aazahiqKTxFUsKelqR0XOq0G5dnE1ve7De3GVSkvvwD57hnHUXi68uMTY/lU4zNjQECkNtieedtLBc/tJoFF5Sj1hHl8kOSSk0f3EeC02Q+uJFfXfrjcmJn0yGu7y73Zcx1hjLT6vq/0tznjOLRaJ586BMTqaOcpxn95enzpqy5CfjON3TocsjutLohmCnYJw6XnW6du8dq8zmA7tZ2GFfxpg4uL2IiAZUdbodxdduL7MlOQtMVSIKYweVRoCsRWCI0XJjbJ6S5bvXBNf8cc0jW34qnOdCKZc3AHKIyOYcUFXJOc9PC3FkE1i9r+J9PhGdB6Dm+1cPO+a/PTiBgqkLCQTkeDFK0w4MVSKMIlluxOKWDeKaVavatZ3fwwO4ouvHOIDRJEJMRIqiSKkobEDTVjqcpwFU91XMLySilYw1R23rr9vL/LU5C1zlEUWxg2ozQMYicAjZciNsnZb1Ozc1/lKZih6qw0REmqb1CSkXNQG4s2UsVRWS8+6OTOaQbzrOmn0V7z/TQZkwiYg6OjsHJhXFGI5jLGg0KC0EgjCkAOj0ILuPKRgfPKrDeMG8lGLndcYthcVeJCbWV90fvv6I1MX/d09rn52Qu+IqCklVHRwD2EgQoFCrkSKEbAlhkkrdLuTKM/rTH12eU4/tsRQtqzPSCGEjiDfePtHxP6cO9l12/bYRd3/G2ACUppTpESkx6bo0UK0CjgMHyFuKauVN7exjuq13L86q8zsNrmY0ElLCn3Syt8b58sfeprFbvxYkK2wnnrjziPg2Ve08LZ3uPySKGg/4/rfazDj7/hEaimKg6cYYr8aUNkgSSdQd+Ldtir/vbm49dhye53njul59QIhMb7WK5VFEWhhi2PejcaJyZR/EqxDRMYpiDaTTQ/2AFgbByPYg/Pb2svpuAjQ3ELLcEijYIXQVCCOIbVNs07X3xpdsmhKP7pYQgZTT6wFxj+dxe3QUPdPTcBsN3BnHNUfKfdKNcTwRX2YYXZ3pdH9aynpHnX3zFmLHPTAilkcxWGOmjJE2CEQSDRfBHRvj726revdu2PaYi972OFFrjRCdPdWqXB5FpEURtvu+t97367sM4AB0UCZMKaUsFIt3rVWUqRt9v1OOjqKPMdR9P75DUUaW9ee/f2hRPbHPVnl3WkdX2kRaU5Q4Cge7LPV9eYMPvvXU/nd94/rh2v6KMQoCUfW86+80jOd1tFpKc8sWmZFSbve8yXUShZX9+U8sTCuD3bZKvVkTJduAwUkNfP+wDlO5ROOt0gWHLLzk8rUb91uHehtoTwAbb4njJXa5LA9ptcDDUNweRQ9Op/Q3ruy03jUvpZjdtka9GRN5S4MCqfW47jM6TGXx5b3Gaw8rFq9bXS4nd5SJOTuFSB3MZt/wWtt+z+ma1qkC/m2O86P3O977ytJ4/33b6YixOrSOFKSlSxlEqG+bCr9dC2qf3eiEj2kdcl13asI0f369rr8rcl1tk+dJXUpxvxA3jkXRzX/bBy0eR6dSS89Jpz/3QkU5ZUhVeTUM1xTa7U//wIOyZVp9bdVBbts0WNYCOENQa4s127a03pcqt++pxI85vmy3Wr9/IJd7nRlFC6vVKnUToSVl80+e93/bo2ivL5RXcK4P5vNveI5pvvtUTevQiLwrm+0fUK3+r3fJzOfv285WjNWgldKArUsZxqiNlIMf+Tz63IZN8SMGSkkppaqqw9NRdPkNnL8jdhxlk+dJHRD3h+GN61ut2/c23qeKgzJhAoDTbt83rutf+gvw3q2ely4S+WMivnyDQvMPM9mJKZXxtKFRKZfFQGceWdtEHHiYni5rsZQv2dAI7jhv0cKv/XnDxv1yhySllIqi/HSNopzkAeetcV1Fl7L2QBB818nqr16k0WBK45S1Teos5NFfysHSFHjtFrTJ6dSpsXifq5RveH0pc9v/TTf2S0KK47g1Wa9//JZstr8aRUvmxTF8ITbeHkV/7i4Z/57TmJXSFeTTNvV0FtCVS0MhiWa9DkbTg2f60afWGdEL8fC8uETicdlElM1kTj/dtj91mGEUOnp7iZkmzhkZecdIpTL+rVrtgk2ado4XGKeNVFhKhGJjEDhX+oFz+5G98S5HvAohAs75f63P591pTXt2EbB8Ka8Na7X/nfK82t7G3MO5eVip9MmjOH/2wkKBp7q6kG61jr9oZOTT91erL5ry3F9tCo1zqy11mUrU8DznNj/wrphvhCPSfOxayVJKyRh7YILodTelUu9dT3SIDUxUPe+7G1qt3/t7meAzRGRns6dcYJr/eahpZjp7e4kMI/PikZGLool49PZa7fluRnumH5onjVZZNo7Fushxr1GFc/sJmrLLZB2GYaSq6mdloVAvc/68YhzrQRzf2l+tfnZVGCZ3mE91nudFjLH/aVjWX7dwfpiQcpPOea03b1+uEjHOGFRNhW3byOQL0HNpwHeRi2KqtBzjkKzx+hsn/Z8C2BctNrsURdGkoihvbNn2sauBfi7EqpyqHNOnGMsVRsQ5I03TkUqnkS6WwE0datMg1/Nluu0V56mpV/ZQfBf20xqTsyPg7hyV8vwpVT3xFiBaGoT3ubnsB02OPCeCoihkGAYymSysUgHECUzh1Gi7KFnecQuK/ISTc7k/3lirPeFKvjwMsNkyoGE/jP1PPCU5ACua5mmMKB9rGiGbJcpmJWs2lWNarWf/Uohv+Lzxky1V949DBevko/vsFV1W4VWEwnnbGs6db8zp1zzAw+qNZfGI8y2O4zpj7LMVoi9PAkwB2lNxvE9aZyLO+3VFOTFmjEnLIhSLgKax/NTUsmPS6ZXliZHfrpXOnapiLj25p3BK70D2MEvJHl2N/fu3Tvk3HNnJ16yafGQsYma/u5sY56tGAT0DRMuEaO1tsgSANueUsaxnMaKMUFVCNkvIZCRvNIwj6vXnr6hWv7d22vtRxfR+O5C1TjllILcyp5mv4JR/1pap9h1nzrf+Pq14lfs2PLKMwzAsM8Y+2yS6JAZoWkrndvGY5uYD2kGbMIGHRrbeCeBOANTd2XkOgN5ISgqFpFAQAkmIJAEggDgk45DEkdJ4f0Z6vcd2d1dvn+OOKB0lxkoKtHxo6dyGMNKKf9Wa2uNWyiiKGkR0jQLA5pyF6Y63CAkllMBMfEAoCbEkcDBI4hBMIQkiXeHH/ta2U//+BAYALB0k5YS6ok2altbjx0E9I4JfbXV2O+JudoDONiLangbofsayBY7DYgmEEhQIIJAzcUowEDFIUiAZB2NM6TSN4zZ1Zf+EOU5gPscgEp2k6g1Dd0sGKxazyqAj4pv2TbdN4gAQAbRVSjzo++iYnESh2YTfaGBUSmVUURhp5uHP6k99anleO73XZFbBUMhUCKd2m95Ef+YeGml/bGVP9zV3jY0/YiqDECIEsM/vdhoATQG0UQhsqtexeHgY3PcxHgRsmwLFN7m1vJR/01Ed9tuH0spAh8mVrMagMSv2u0Xl3nL6h+cdYX7uz/e45Ue/t4hjB4Czi8PuHSL2UBlPTCBfr8NvNrFdSsUxTcZUdthZ/ZmPLy/oZ/ZaPF00GJmc4cRu0yu7uVVXj7gf+8zChdd8aOMjW+CEEBFmFvc6KB3UCRN4eEQmESESosuPwdoR0Aolal6I6aaDVKWOUhQBUYhK00HDj+DGkmIIAtvzRahCROdaaudRA90vWZFTz++1lXkWJzeI4lWvP7r489Gqd81fNrV3e5O0I0ZVVWWKMcuNJbVDiWYYo+YGmKy3YehVZBwdgeug0vbQCmJ4sTQl5JzWYT22QEwT5hFH9ve8cnBQO+VYSykxKSdrTnjtixYWf7xhzH3gHsfZbfPzbIzSsiwlkpRuRxKtUKARxKi0PUzUWuCcw1AY2s0maq6PZiAICvUZY3PatABLitzqzWefcWhX5mUDQ8oROZ2r01GrMpkNrhyYbo0AeMz8zsRBR/hheOO9nDfyvp9zJiZkN2Nwo0j8UoirR0196LiC9dMFaXVJp8lZV9pAV9pExlBBIjY7XPf4oqF8j1H7Dc+YP+/Kv27Zut/7z2MhRkfi+I6bgecqjYbc7jgwhZBro2jjta3m3WYu/5HjivZFfbZidtoaejIGijNjEpQwCDqLhvLOAVPpvmTF4EXvuG/bXi80sicijmXbcf52r2W9Ie/76fbEBHoYgxNFwW/D6M/3IjdwTK/yk6EsLes0OetOG+hKG5QxVElCmB2ue0JW59/9w6bgrW/p6/vLN0dGnjZjFA76hLmDlFJ2dHRsdmIZVQLB836MVNuHXmkgFgLlWh0kYrTabZRbPibcOKr4oT/pNB/3fZcyogW5zDHmQOZLx+e1YwbTitJpqZTRFXApDlteMp9/+7jztefM6/vPP24dedylrYQQCIJwrME1UQ0EK3sRrKYHhdfgBSHSuoI4DFBvtuSUE2LSE5ORmNpjRp83j3iplH7xodnCfy/NKL39KZWKpkoplS0QIj7usE7zZTcY0x/6bHf6sg+ONx93grHv+34s5GQtkIurgUDGCWHVHTAqo+m4MDgh8FxUmw6mvVhsrrlrKbPnMQoXKDzfO9jxiWO6zdcOpRW721apaKqouKEUKW3lylzXyW9bufwtnRu2b/p4Y//02Sb++WbnXf59lLHPXa1p79wQRcUc4ExG0a/iev3/Ojvz/9thsCUplbG0rlEhk0ZvRw6FjA0SERq1GoiqPc8YiD9tViqrAPxDu2Uc2kGk8xIAjqxfxt+ru99XNoqiVjab/ciqVCozLcTxfUFAAli3xnU/WObKkmNS5v/LqGSmNI6ZMQk59BayMHUFgePAKJe1SMoXX9GSt55TLHzjynLlH5rkf1S3RkABnEW4Y3T3+8zOjp/46wjnn79K19/+YBQVcoAzEUWX3gL5g8EivtJhYFlK5SxtaFTIpNDTkUcxbRHJGI1aHYwq/WcOiE9/y5WrsNNWfk/Esj4iI04jFAY6+/oOiFX0njYJEwCazeYGXSs+OOmJ5bYSQ2EhCdlG2w+R1jiYFAjCSNa9UK6rhXc09Pbw1uHH7zOIC8rAQD79vwO2cmzB4KyUsqi/mEYpZYJDoNlspQ2FvSsUjcbbB/o+99XtI7u9ixNCyDiOr3Fi+Y5xV1gGj8HJRxQLNBwPpsIAEcMLQpS9KL6v7F63vhk+bnNNmojyhdQzBzK5i7sN1l0wVXRmbeovZJA1NRJhIHP1xqCh0OcvXd/ctiKVuum+VuvxKls7jKJrayE7cdwVpLGIiFz4UYRyy4HOCCKOZMsPMO7E7e2e+/dbhx9/RaQS50qxq/Cek/LGm0sG14q2jp5CmnpzKaSdgKLAU5XQP51k65s3tIuvxD/4JZg4MLiu6zHGvig07TfDprmgK4rG4TgbIss+tkNTzlIZMc4YqZoKy7aQyeVhFjKAFGCMUcv1UWj7K4ol69kvKZW+f9njbFL+aMvyRGQpelpPLUip6FWZCKCZW5+3go/9/r7drwhUr9fv03X9xTXLWn4PoBque386jpuZzo4fmBy2wghc4aQbOtLpNNLFIripQ2u3EIYham1PX5YLXjthapfiCY6bOJOIGzmzkM2aSzUmDIXRxNGD6S0Nn1oPTuz64jKKIpcz9t+uYfxsRNMWxkEwkfG8DWTbx6ez+hkqA+OMSFVVWJaNbC4Hs5CdLWNOLddD0fFXLLLa55y7cOEPr9i4cc5lXNCItE6mz1dSQ7am9DLIONa1sjD7cQpTn8hHf9I9rRKm7/vjfhB8ownti8NtoUsZST8SVPcj2AoDJ8ggFrLii/KdFe8r1bZ43FsjlTHe0dHxmrTBjjY4MUNTKZOy0FEqoqOYAyOQXS7LMIr1ozrCN/5tuHYZgI27e7/Z4dm3KIpy+TSUl3CKeSwBJxJUdUMYnCRBwouFHHHi+5ut5k8mq+Jxr0YdZpg9VvbfUyrr0hVGpq4hl8mgq7MT6awNGfikKgrcIOo9quR/4P5K+l/wOGNshBCxZVnfVzXtBWOuWEYAIiHRCgWlnQAaIymFRCsS0bqaf1lZtPY4YVnqxrKCbbzOVKDpCodlGlTM59DZXULkBIDbJrXd4ENBdOq2RuvC9xUKX/p85R+7Ck8cGGb7wtYT0YN1KWWKiJmGcUwHyVQsQZEEIkmIwSAYB7gKQIAUFcQVIkYqpdjp5Uz6x5jjoLiVjHhHf/acJR2Zty7Oqsd2mdyyFRJCyMZoO/zrhcelv3jPGH/gvu27HsDm+36FiG4AAB9ATVF653E6TAKIJCiShAgM8exYCXBlJl5FJWIcOmdLHDOaf0KKqre05ja4pzNldh+/uOstyzvMlw6mlO68zrjG4NaCcPPdZe/rz1tm/+L3D7R3+T0Wz/TpbiKizQAQECFvWUcSZCqeLd8IMw9BfGaoFMkdZQwixueltXPTG8Z+DGBO9XHIZtpAqXDm0T3WOw9Jays7Z8pYOnG1eW9j1c1burXtJy/PrL1xTeMpOX/7aZUwpZRC1/Uf8nx+qBzwt/githqhlFlfkMUhAUI7lpVtVee/muPVv00+dn7UI1jptGEZ6rMZwCWIQAykaFB1E9xOAxzQPY80Q5e6ygdZgZ/83AULNv1h8+bdvm8Yhk1VVd9fKBQy41DOdeNYqQVCZlSCzkgKQFZ98eDWeu3tjdjZ+njxERHlcrmlhorlBJAAAZyDaxpU0wLZaZCmw2i2SdNU9Ke1IzO8Ne+wYnH9482dDIJgM2Ps35xYfHm7Ixa1I4lCIJBSCAoRQol4sh38UatOf3JDJX7cO+CZjamLz1AZugGCJCJiCrhmQLFsEGkgIhgyIk1pKKWUcs7NPV1fA7BfF21IPDXs6N9vAzAhF/kx4EYSTiTQDGJUHR/lRguMMSgk0Wq5aPoh3EgiEijEQsxpD69DlpKi9GVfv7Qr95+LM7zQa6vUZWvI6ioUkrnBTPjawZZ6kmi7b7+oq+tvX5mY2OMqVrlcLhMLdLoxyIkk2qFAww1QaTmwa02kggCx56HmBmiFMQIhlTaTWaUwt7LpKaaGjp9X+taKgnraoK0oPSkVRUuDqbC0iOPOBWljxV0T+jHnDA38x5Wbtu+2b3RHzIwxTox1eTHIjSScUKDpR6g5PqYbbTDOoT5UxhGcSBCBUmPx3K5dB4tML5QKbz2uM/XRRWkl15dSqNPWkdUVhHGcIdl+4WlHda7461bnLS/I5274TbX2lEuaT6uECQC+77c45x9JpVK3Sdt+nROLZaqHokI0GQhxR7nifsNy6zeOC7HHvkEhBBdClnwBcuOZStwKItRdH3bbhcoJjh/BjQRCAXIJR7Sl/DH20FgfhuGwqqpvyGQyF0ZSf2k9okGNoDKiMdcPr6w12982/fb6yejxmzqllLKnp2deLGTBjyW8eKYSNLwIDceDoqmgOEQ7iODFErGEDWJF8Mf/jomiSBDRlaZpviCVSr09EOpp5UAOaAyeBNY3He/yTK3xg3VhOJf5l0QkBwMBeLGEG0m0wxgNN0C77UF4EaQXwAljeEISES0UjbKBJGE+DdGWdiRRD6Ws+YLKjg+r1gIjQrPtQiUJ13FQabioejFqgWxI7HmEe4YRZUrp81Z2ZT5d1FkxqysopizqKWTQkbGgMaDdbsNQ60ueP4QvXsnofAB7HMnmOE4zZdvleiCy9YBR1Ytgtzxo5TrCKEZKVyGiAI1GE2UnQMUTcSNEa3oOY2INrqeX9nd8qcfiZ2Q1xnKWRh25NHrzaWQMDXEYoFqrW5zwxtBvbbygVPrK5dPTe8psgjFWni1j1IIYaTeAVW+BMULTcaAR4LoOKg0HVS+WkxF5d2X3PO4wT0RmLnvOYMb6REFnmayhoJieLeO0jTCO0JbTrEOJl5wu6X9+72svBLBtzyXx5HraJUwAiOPYJaJfOI7zZ85Y0TbNdKPdrgmJqTgK9zjl72QikgBWpNMYlpDNUKIRClS9CJMNB4ZWRRBE0BXAabUw2XRR82M4EeoSo3OKMQzDSSL6kqIoP8jlWL7iKYrnBbVcLMoNsefdFU4joiYAFIu+p+hRIxRKLRAoOwHGa02oCkez7YCJGPV6HeV2gFogEIoIwJ7XdZ5dSP1+zvm/KgorlUpaoeVHQbUqpuMoqo/tYb7YEUSUBTAPoJZE3IokGqFEzY8x1fZgV+sgApp+BEQBlMhD1Q1RCWJ3Km4nzbFPPzIMg7s9TfWmfWGllBgaD0FowwsjlBtNqASEYYiW58tpJ4o2Nv0b19bDPZ4rKlcs20hdZHMqapygqyqlbBvFQgHFUg5cYbAadYqFQI8fHTaQ9l5xUan0+a/soW9USlmTwNpqIIemfSFNJSKFeRBCoOV6sBQOiBiu78u6G8hhV2zxsmzL2k2PX3cUIsrnSmcVTDpL58Q0zskydOQyGXR0lGClLcjAh8I5uUFoLOqI3v63afe3R3YZ21ZNeI83PgHNZnM1S6edaV+kUgrNlrEDP4wx3WhBIyAKQzQ9H2UnFhsqzo2Av8c7wYDzbGfaeldKobTOCbqqUMp6uIzdWKDgxlSAj6YfHr4kG7zmOZ0dn/nj5NRTqq4/LRMm8FAzRHP2MWcvVpR0v2EsTgGSheHWqSheW/ZpYc4TsJSQFNZGFAtUm23onBAGPhqOhwknikY8/877yrsfbbeLGAWA8uxjTo6fWQi5Z0jXewE0lzrO9ht1vTzty76MF8NUAnDWghdGmDRUcAh4no9q28f2dlyu+O62hj/3m7d4ZteE8dnHnBzLudJjGPN6pSxqUo7eydiqVijllCeQUiPoTR9AHW3XRzuIwWUMHbGsOKEcbkWrddNNJmU+zczuFXmTZVk3Tvs4W2MCRBFFQqIVREipDCoBQgrphLEcbscPbvYbf5ioPn4rDBGRbduLNM5WYqaHjiRjIEWBoutglg2oHGoUQdcNKArn/Vn9eWvs6tcBPO4UkCiK2p7n/YAM46wxV5gKQQoJ8iKBmhvA4AQGiSASqAciWjXl/mRjZc9L20rGmKKz53GCKQGSRABTwFQNimEBVgqkqNDNNlRNg6XygaMs9dglW+PHvWObHT17o23bt0/77AyNCQC7KGMhpBPFctSRG9ZU6r/dOCH2+J3GbXtI4+wYzHQNkSQOUlQougFm2oAQUEwTuiRSFIV3ZPjZfsr6X+yHebN742mbMJ+oDsbo1Fxu2REdHf/9cl0/tk9V5VbXvXPK8264k/OzRl1hKSxGLAO4YYzpFofGZk+uMJabGuE924LGHeXm/tupYwkRW2rb5784m/3Us3S9J0XkXt5sXnpXHF1bDpSXGY5gjEKKhETTC5FSGRQCwjiWjSCO75n2/zQW+mNT9f0X42LOzaPz+X97i2m+YaWmpbw4nrguCL77UYk1455YoXEACMiPBOpuAC+MwAGpc0LZi9t3TDd+XuXyoNmQNjF3YRi2NE37eBhGS8dcMRAJCSeaaTq0OUFhQCwha4Esb2q7H28Jb2SOb70gljAf6hYIJdpBjIYXIOV40DQFgR/CjQT5Qgoi9E4gVcQeEuZskv+Toig/qUJ5nZAx92Ipm6FAWiXoDCAAnkC8vRn8eVs0/X+T048/iA8ANE1jiqIsDQTIjyW82W6Mlh+h5XrIqgoQhXCCCH4sEQqp+oay+IqeiN6wh+6gOI6bYRh+jHPjx6OuGAiFhBNL5AIBiwMqAyIB2QhlbV2t+elQ8/bYNE1ElM/n5z+ijGOBdhCh6c6UsZASQRDDIYEgBgnC4krkpJAkzAMTVxSralmfOIKxc/pKJW51d2PZ9PQzvzAy0rwgCH457SsvFzJWvUiiEcRIKQwqA2IpZS2QI+vGW/8xWY/228T7biJiuj7Umc3+9zJdHyr29xNPp/Gy7dvfPj019YXPxvKuEVccHc5+yVT9GBYncJIIBOSYE9+xfqr6panyHHvw/wFZIsoVChccrusfGEqlzMzAADJS5p+zefO//l+z+dX7oHxgW1tkg3hmYYmMFyGMIjAiEOPhxrr3w8mwddXWzcn2YE9Hs2us3prNZl8fG8anxiQ7th7GPK0QmQpJAoQTibXDdecTslr/7Xg85w3epR9LNCOJZiBQ80JMNR2Y5TriWMBUGXzXRbnhoO5FaIYyELIxp5G3QRA4qqp+qFAoTNahvNWNRW46kJRSiDSCjCRaZTf8TThZ/tAGP5yaa1kICdmOJJqhRD2IUZntauGcodB2QCJGvd5AxQnQCAVaAaLtc6jZO+7kfd9/dTqd+eS4J09ohEJNq4JMPlPGboy1U7XWp91m/dfj/px3Iwr9WMpmKNEMHy5jo1xDFMeQUmKy2oBUYtT8SLZC6R0j3adUcyyQJMw5K5tmiglxkqsoPNR1QjoNuC4zOT9ivuM8/x7DqE5De3UrirNpj2ArAowgnFCuHqm1P0i1+l8rYv990VcAFFOpYyTQ7zJGwjCIp9OSDMNcSHQoazbf7KdSnx6T7Mx6KIy0KqTJiYSEVw/EVbWp6ofajrtlf8UHAB5AjLEzIyLdUxSCbQNEYJrWd2wcN24LgjeTZX1kqyOWlQPJ0gpBxDEi0KTj+d+xpstf2hrE7f0ZY+KpbXaN1WtUVV2dsu0zPE07s60pA2EzmgyEuNVynD8XXXf76sfpQz+TiEqaxvuEEM8EsA7Y4Au0K76wsirBdEOodQdCSDTaDgyFIQ4DtBxXlp2INjtiWNbjOc+VDMNwWlGUT9i2/VtVVc9xQuXwKmOGHwRrXN+/SnHc26px9LhDfd7EOXNVleV8X/QQiVYYrq5z9eSKL5FSY9JbPhg14YUhpnQVTAp4noda28OkG/u1tvugMjW3lQGCIBAArtM07UWpVOrMkLHT27o+D8wvu468Rbbbf2n4/vZQ7j5ZLuCcFhgGK0gpzwLkfWG42ReGU/ZFNqsRLCeEyh3EUqLRdgEpMFxtwtdJlp0QY2686T7FfcrV9SRhzpEmhJgAnDVRhIFyWS4NAsBxsE7GQd/SuLppuPlh07Z/NdHkx9RdsQBAEIbR7e22c10URRNS7rmdf2+EANpBUNus6+F9QaAXx8Zkb7UKt16Xm4jqpxf91dtc8ZopzT522hGnVkApKWXFj+MbnWb7tigK9vuSXAEAF6itlRL3tNvS2LoVGQDjjhNXdUwuazcuryjRqoavHj/hsaMmAKVU6kCr1bomVa78+c5gz4OdEk8Ps4PifkFEv9A0hYVhLIQQqOxhsNlRqlo6ulR62/M07dSClK3OdvuyCd//y5QQN5UDdr7lCSgsJil9eFGMatuFzglSCHhhhIoXx/dOupc3lPAJjdKOoigEcAcR3ck5J4Ux8sNQ7Gkz9UVEtNKyTj2+o+PNJypKbzkMV1nt9jevJrp8MsYrxz2R1jhAFCASAk0vgK0ycEhEcYxmEMmtrWjtqkbrxg3+E7tgD4KgTES/UoBfcU1jEqEMAin3FHPBMAoXlEqvf4Gun2MTtR5otX7V22xe9dfYvrES0HmWK6BQREICXhij0nJBUmKq7cE1FFT8OLxjsvWrqiaShPlkO4qI7t4HK/y77XZt2rJ++nei9/utlra43QZJ6V5Pwd+UnPWq95ykPuOQXpYr18PpDVO48rc3e5dN1LypWi163CaLfRXf7JJit2yW8sYr4/jsarXK+4hkXcqJOy3c2rU8++nzF6vHdmSkMV2X6+/dFl1+/QP1K0RWejfc8PjHP5KIVu2bGIVt25et0vV/0Xx/3sjUFOUAOSzE7ZVelnnmkuKPjl2kzg+jyG04YtWvb/O/P4WCKqWMWp1zGLqbeFrZ6Yt7Tk13h+l6amGh8IUXadorTs1mFdu25QmNxjPmVSqf/kwUfanN9WNGXdEnJKQfS2qFM3OLNUaQkNKLpdjWCq8b9quXrS/H/1B92LEm81ye20dEacs6/chs9gcXGEb/gkKBmBCnr6zVTttQr7+qqaq/qobyVcwRPJIzcydrXgRToZmxCULKaiCb65vOF0Pdm/PAwV3EC8yxjE1VTZ9TKl38UlV9+SmZjGLbtjytXj83BfzHn133v4mnjh51RacE4McRtcIYKZWBpETVDWU9hNhS92+ouo1frB2Zc5P6k+agTZgvZUyRqtp/hKbhjao6+p0w3KuBIkKIUFWUi+Nstjqp68+yGYsVTd57/GHq6WevwNtWzFN4b6cK3bYgoujc56xUn/ujv4VvBbB5d+95nqpah2pa32t1vdmKoolfxv9YJdzBdd1aKpX6f3fY9rsfVJTlphAVK43J806gD560VJ93SJ9CxZIKVccJFzjBv1y/NvX1idH6xzEzL/wx+oloiaYVVmha8ZWaNr4xDJu37GXi9Dzv7q3V6oVuKvX2Ozjr0qTcPjSf0znHqF8+eoilhnpVSudsMIrPeNZx/ou+ek37R5deT7/knO/NYRNPcwoRdWWzx3QqygtTmqbonZ1EPT2kjo3ZZzrOmy5rNn98W6PxriCV/u9hR8xrRhIVX8BWaGagi0RU8eIbq2PliyaF/6RsAkCcq0Y6/Y485/1WOk1s3jwCY+hZu/aIcxuN59xYLn+Y5XLatM9e5MaxXgsEMirB4AQCpBNjeqTmftadrPxi6x7mbO8rhm0f28nYi2xFeaiMlbEx85mu+4ZFk5M/29pu/5tr258adsS8ZiiR82e6rwgSdT+Kw6a4LjdRe/c9reApuYfuQZkwF5pm9zml0kfeYBjnDnGOdUFwzXsM46P/43lznvqwK2EU1Yjoyw1V/UqsaakTlmR+sriHjuvOK6yrMwVjfg6U18G8trLULJ/94oA+++Zz1Td864rwEQlpKed0imEc/qyOjk8+V1WPzDBWvbbV+t6/cv6tL8fxXk3Ib7VaWxTG3j2pacww9BXnL7N/M1jCQFdeo1JPBspgFmQSGY26dYZafdtPRpV1L30Wfffnf3lkIhzQNG1Rb+9L38HYO07gvDuScuN/R9FnT2LsrzeJPY/k2504jgWAmwzOb+EZlZfs1OvP7uf/05sns6doINufA/WkQBRRKV8ZeEG9+tbb73Wva0ZPaPZP4gD3GiISAH60D1o2gJnbo7aUi2uANi4EGq6LfLMJBAH5RHkLUn223vzNnyTf5PjKGyOpnlIPWadC0hcinmg50WVBq/nTWuDtcqHx44hoOUDjgPzzPoq5YhhqjvMlk1LSRBhSqdWCyjkiISgEus6OvYkbefmtfpD6Wy3SXubGfNGkD5OTrPhheJdotr8hHfeWkZmpX4/xIiLKA/jOPoqXiKhYLM6rAsa4lA+Xse8DROkhIqNHNH9+fTu6N9TMt4dCO6kWokMh6TPGKnam8+9b1q//XNXznrJrRR90CbOfMb6go+P9Z2jam5YUCjzd2YnjK5XXx0T0el1/2//5/l71g0kpZZoo5rpxcleaTtVVMF1TSE2lQJ2dQEcK8JpgfoQl/cGzi2nrSAA37vweLV3vDgqFrx+rKMfP6+4GT6X6LxgZ+UxVysqbiX78rb08gSMhhKIoVErnXpOzqV+bWUOWeC4L6u4GUipg6lJp+uaZh4dvvWFd6zfYaa7nPCKiVOqUM4kuPtw08929vQDQ94lt2wY+ahjPO5Fo7c17GaMvhMxKmStljDfbujQ0lUO3TKJCEdRTBHgMECGVaedfdSouuO5O72+Yy4oKiQPa0Yxpy03zyEOKxdMKgPsfhnHVtO9v+Ibc+zukKI7vexBw7gxDzZycxFC9LuH78p4w3LZduI7eq6YPNSla2IVLH9ja/vl0Q8QTjXAcXjxZ9aLW7vruztX1zqMKhbOXES1ZEce3/Bdj131AiL3ew9J33aCaSt19D+fLOlstFmzZQgUiVBxH3Etyc7tIyrxOFHpTYk1XLvrU9WvbbMtkXOPExssNdzreTaKcz7l6jG0ffWSxeHpWytZ7bPuKLY6z8dd7Wadnd4S6fwPQvDMMs+bkpFxYr5P0fbkqDKdHS7IBUlOLjBRWLo1+HFHz0hvvldGWiXDs8OVDcWf34CFb1q59Sm/hd1AlTCIibhiFRYpybsyYIm2b0NEBAsQh5fIzAmDgGKLNd+zlidECsU7TOjEWsLwQcEJCFDJoIQPFCiAVSChgxKxCWjnpdWfSzd/728MVvmpZC9U4XhnpOslMhlAqSaXZ1IcqlWfdBFyKfZAYTNNUNE05Lowl80KQGxJEyMBCBsQKIFWCVKSpsMHQY4MnL6XKjetmymWKMeq0rGczIBfrOslCgYhzaU9PD/al08+Qnrd2b+OTUkrTsvoYk4N+BPJCIj9gQEhAxAEiACpJcKZwnDg8pmr7olwST10LOVcGCoV3P9cw/v0sw8jldR1OJrPx0krlre9l7O9fFP/4wDkppeScr5pMpb5zDedvK3ue2e/7MpKycqPvfi3usU59zgnmRSuHaEVvHpm0ZbSrLXHfr29rfTUwGpd/8pu7/s4YMoxFLykUvv1KXT95qWUxEsK/S1W/9VvGPvJ8IR53O789EUJEjVbry6symWPCOF68udWiDCC2Svm3243otqOWFT9/4dHacxZ2Um8pQ/SBF5mjN631//jnO7yL79yw61agwzlXjyuV3v4SVf3wmaaZz2uabLrupq9OTf3rmURX/m0vL0yazea908Xid/4q5dvLnqcNeB4FRNM3xMHX/Zx+1gtPsN9+7EKs6M0rqaxlNmvnitW/u9X7+t/Wp69z3ABzXHP+n+agSphSSmlblqwSifVxjEXVKpYCYO02bY5j2QZ2OQ76jDPOIMzMIYYQQl533XWP+1cjAnGF7GobVG4Ck7UYk5MO+tNVKK4PRC7iKRe1pkTTQ/rRnacWY3IbINeGIXonJ9HTapFXr2OblGJXS9icfvrpRES04zM++OCDGB0d3dMEZPihVCstYLopMV4N0THWQlEvgzIq0GrArwSoNCVFMR6xeKwggkqkbJCSHnAcZIaHkWEM064r21LGu4px+fLl1NHRQQCg67q84oor9njmp1Mpre1DLbeAqYbAWNlHZqQBmwjQJGSlBa8eoelBjwPMaaPsxIEpT0TSNBedrusX9ahqPtvTQ6yrC6nx8UXPE+ITm1z3AgDVvTlGHMeeqigfd2z79hFdP1sj8h0/+tNgt7r0Bccrnz98PmUX96rU2W1ASfFctwhP+fcB5cg/3pTt+/M7zK+ed4n7iKq80LJYqqPjovlSntqRTjN1/nwAMFdu2PDmb0bRHW8m+unetBZJKSUR3SWBF7Yt6yX3AguFlHeHMrz1GUdaF5+1gp24tJezBb06rKIGUuXQ83vVtx++QDn6O38KXwtgw87vx4kob9tLj1OU93drWiHT00PU2YnM+PiiC+P4IzXGbsZeLhTgeZ7LGPuYk8vdOaqqZ+lSui3Pu7y7Sz38ZcfaX1y5gFJL+lTq6DKgpFihMw5PfUe/cuTgjdYXf7RK3klzWir/n+egSpgA0Mu51xvHG+Zxvky2WnRPuy0nhIhvDYIra1E0fNfsCXz00UdTX19fVkp5aC6XO8GyrJyiKD4R3fHa1772Xsdxxi+77LLdnexxHIv7Jxss2laGWkhFMLQWgjBGMauCIUSj4WDrRCwmxtg91Z3mP6WJqCedbs1Pp8s9cdxbrVSwuVKRo0K0riD6/YadRqMtXLiQLVy4sEfTtOMymczhpmlyznnNsqzbjjnmmHuEEK277rprd1sNxX4QPThcUVZunZaUtQKovI5Bx0fa5ohDH5Wqi7VjsjFZRqVZe/i13XHMOsPwnvmcR9kgULdOTMhJKeWmON60vtW6+oGdvgOWL1+uqqq6oL+//6RcLjdf13Uiok3PfOYzbyOizVdeeeVu1+at1+vjplGa2DaNdGc2RspwiVBBT60NQ5PwXRcjk6HcOi1Xa717N2gr8dTmAUhZ1soA6GgQUcAYKZwDqipVogUTUhaxlwkTAMIocojol3XgV5oGso3cMQt7lQ91ZpArpBUUSmlSBvKgogWELrSJ6fQ5xzY+csnv9Dt+cQLd8H+3PHzyb43j9HIhTmoRsRYROjknYkySouh9qrr4zpmL8L1u5gSwlog+DYBsm5QFPR1fGepkJxbTjBVzBlk9ebC+LGAAVKuxIVY+8cVHxx959+nsTRdf+/AmEgJArCiH+UC+AVBAtKOMoTC2ZIyohH2wso4QwiGin1eBy1SArHTm+OWDxoe6skgXMiryxTQpAwVQ0QRCF/r4dOa0wze9//s3nPavcazt7eH3q4MqYfYypgzNm/eO10XROeem05RJp2WrVpNfdZzrrnXdT9w+26bf29ur5PP5s0zTfN+iRYtO6OzsNLLZLEzThJQyajaba2+77bYvnH322b+++uqrH9MXIYSQtm1foyq5rWtHsVBXBCLhU7UVIW8TFCZkyxPy/u14YNNm79artj5cyYq6Xjzesj79BkXpObpQgMK5HKlUgp943n83y+Xf7mguHhoaSpdKpZfNnz//Xf39/YtLpRJLp9PQNA1xHHu1Wu3v11133RfOPPPM6//2t789pvlFCBFLiV9P1HH+AyOwFBaTF7qYrAVIm4AUQlZbIr5hXfTXZjMcuXfi4RjVdPqIcw3jY680TWV+Pg8ZBLimUqn+ut3+14rrbrxv5sqXcrlc78qVK9+1YsWKl/b09PQUCgWybRucc0RRNLVly5bfv+pVr/r0j370o12uYRlF0ajnR3/aPKVcZBvghBAtT2Bk2oWhSoSRkPdvl966es/lWyfmtrJK4sDkAUgFwdRmXfdXh6FWmpzEglYL0nGwNorcsZlpvPvEjqkdjDE13WG8ImWgqHCCoqjETRuULwKlDBA5RH4orYqbPWG5/tqtAb8ZO3ULaESeQzT9gJRyfqtFfMsWZIhQabVwL2ONfbmmm5RSEBEJYSzNp5Xn6ioY54xUzQCls0CxAzA5wBVidRcLFwbnhncZy17yHLr3sj8+4i63vBmIV4chirNlLBwH94WhMy7lPpv3uKOMU6TytG2/IqWjwDlBURRSLBuULzxUxvBDaafaxmlDVx03WfN+hH34t97XDpqESUSkGUbXMUHwupSqGnpHB6G/X6ZGRujCrVuVzVHUAoCenh7Ftu0XLV++/JIFCxYUOzo6qFQqoVAoYPbLXvN9f0VHR8c3br/99iVnnXXW56655prHnEiO42zmnH+MKP3lOEax5kiMViJkLIAR5FQDk1Nro09OtN2RnWPMd3aeVuL8XNswSOnrA6XT6F+3jl/oOOyvswk9n89n5s+f/5nDDjvsdT09PcaOGHO5HEzTBACro6PjvEKhcNS6deve9epXv/rXP/zhDx+RNGcXUv5jIZ//9oZx7a1+CL3cEujOClg6EAvE26bF9Xdsan1m9baHFwSwFYX1lUqvyhP1W6kUsfnzCWEoz/A8fmu1Gt4+e8WcyWQWHHXUUd9ZtmzZqZ2dnbxUKqFYLCKTyUDTNAghuorF4uuz2eyid7zjHW+65JJLHrNxdhzHkWVZl3CePWn1drbS8cEnGzFKqRiaArR96W+u52+4Z4u31vU799WpkngK6gKQC4J1UogNW4Cjrmk20dFqSUgZXOd5v9kSRbscnbqXdMbkEWEEckOQEwBhAKieBAUABIOMOUTMUNTVQxqTLAWgtuPFK4SQbeAvFeAZq3xfHS2XkQXkaBxv/IPjXHH7PhiotDMppezs7BwSQha9kOAGgOsD0pcgH4BCQDwTcyyosKgntfArX3Pu2fn1fba9UUr54BYhVohmk1a3WlJK6a2Koh+Xms05r140V75CKU2nI4II5AWAGwChDyj+w2WMmJOUjDpz0fLDOqSOJGE+OQgo1oH0sBCYarfRU6mQcBxZi+NcJY7NU1IpR6ZSx/b391+cz+dLqVQKmUyGCoUCurq6kMvloCgKHMeBaZrWscce+94gCIYvvPDC7/74xz9+dEISRHQZEbXj2Hp31WHLHhyHYahwvTC+1w1bnzemnL/fW3/kQAUex8VJRWHbogjz6nVKhSH8IKBRKQe3A9Td0aHYtv2agYGB12ezWSOdTiOTyVCxWERnZydSqRQAoNVqQdO0biHE5++6666NRx999N133nnnI44VRZGrKMpHJXKbN03pb5hoUH/GkIxzNOrt+MqG0/zUyFj7EXd/LhGFnOdHATYcBMhXq1DiGK04VoeBDBijwcHBVH9//392d3efmk6neTqdRi6Xo46ODhSLRViWhSiKZL1eZ5zz04Ig+OIrXvGK1/70pz+tPfpv5rruZgCvECLzvjXD/NxtZWRTOqQERqfr4be7uu1VjLXAWDIP82DVTUSdhnHov+TzF5+vKIf0qSpGokj+OIpGbvf9b3dUqxevFWK/tDBEMfFKGyg3JaZqESanHPTbNSh+ACCEnG5Tsx7JmgPedB/u6z8qldKXd3S8/WVE7zpK0xQG4OogiH4QRX8dbbU+1Wq3798f8RIRa3qgSguYbgiMV3xkx5pIcw6yOdBqIKj4qLYkTU6zR/T7z8tklr89m/3ic1V1ca+i0EgUyR9E0ehVYfiNVq325c1z2AP4iccrKRJglTZQbkmarMWYnHLRZ9egeA+VMdr1GC0PVHmKtyMdNAlTSikN09w6DGy8OY479elpLKnXIcNQXun792yNotqoYWimaf5rOp3u0nUdmqaRYRhIp9MoFosolUpQVRXtdpuISHqeZyxduvSdq1at+j2Ax1zhSiljIvq96zhXq5q2cEzKDikxoev+piVLhHfbhkd2+EsppW3b996v67UbfD8fj4yglzHUgiC8Q8pr24BsO86CBT0977IsS1dVFZqmkWVZyGaz6OjoQDabBQA0Gg2K4xiu6w4ceeSRb/N9/yLMtGw9QhRFTSL6imEYl1YYLYGEGglsywX+9sld7asZx7Ll+/fcoesvKzabamPLFpmRUm72/fJ6YG1FCDQajWcPDg4+T9d1rqoq6boO27aRz+cfSuphGJKqqgiCgC1YsODc7du3n/OqV73qFz/60Y8eUyYANnLOL9J1vW8KmAcg5qp8sKdgTbMwWom97AdKPLUFlmV1Z7MXr1CUs4aKRZbq7kax0ZAfGB4e+9j09Le/Esf7axJuFAkMj1aB4Qpkzo5I19oIQ4HilAqFxXBbjhyvRFi1RYyzLdIFAJuIitnsuYuJPrrYMNI9fX1EhoGXbd8uRkdHf399u33zH/bR3Madzcz2So01jExjuIJ8R0YgZfpgrIbelg/bJMSBh2rdxZYp2V496k49p5voj+NSLtK0zLJS6bOHKcrZQ8Uis7u6qNhoyHcPD1eq1er3vhcE+6WMpYQThGJ4rMYwXIbM2SHpWgthFKMwpUKhGE7bkVsnI2ycxPDUdjylU+ZBkzABwPe8xmSj8ZEb0ulLJqNoYCCKZEOI+9a1Wp+vCxG5irIopeunMsYeulJkjEFVVRiGAcMwwBiDbdswTZM0TUMmk5mfSqVOOP3003977bXXPqYSzH7hO0S0esf/ue7uK4vneXeN+P7n/qLr79wcBNm8lMFYGP5iY7X6u+0AVF1/pqZpA7OjYgkAOOfQNA2GYUDXdQB4KEZVVdng4OCzNmzY0AVg666OObuv5hQRPbR6xuRuKrQQQpim+cMHVPUoF3j2as9TNSlrDzD2mUnX3biJSO9KpV6gKIpJRNjx4JxD13VYlgVVVaEoCmzbhmEY0DRNy+VyL77pppsuB7DLvSzjOA6JaOuOzyAdKQ899FByZvbqThykiIgM2+7XiVZEjDFpmoR8HuAcxuTkESnbPvItROPf3A8JSErp+77/23LLfO6DY7B1RSAWPhrtCPkUQeUSXhBjvCr8q+91f7PNiHwAyAPEFeWZEkhFqkrIZAipFJRKRTnesp53l+N8CzNjbPZ1vNKyrPvDmO7dNClPSxkAo4i8wMFk1YdtAFLEstaO5aotWO1sDlZdPT5Tbtttu3cZcFrIGBM7lXHH5OT8LOcrXkw0+sv9UMZRFIWu61861TSfu34cpqYKxLGPentmvMeOMt46JaP7xMk33zV59VN6r9uDKmHODsP++3AcP3uC6BADiCIh7i54Xm0jgE5FWSyl7IzjGFEUURiGCIIAQRDA932EYQhVVRFFEeI4hhACcRwbAwMDywcGBi7H49zp7GlB4h3iOA4Vzi9uG8aftwH9BDRKvn/3uihyVVVlnaZ5lBCCR1GEKIrw6BijKAJjDGEYPhQjYyzfbDbnnX766dt2ldSfaIyu605zzt9cNYyV9wMpknKb9Lz1FSHibDab5ZwvF0IgiiIKguChGH3fh+/7UFUVs79HHMckhJDFYnGxYRhZALudmDzX+BIHF4aZk2JDHGOoXsfi7duheB5Gw1BOSSnX7afjSimlruu/1zT9t5um2EtjAaXpCUzWBbIWoDCg7SNauwm/2zDZ/s39m2bOz1EAXUTYIiXWeR4VxsaQNwy4zSbGGZOkqvspYsB13Ua92fo4KPWD1dvlgBdIVFsxSpkYpgYIATlWo/HrHmh9ZgLeQxsqGESYBOTGOMZQrYbFjIHPlDEq2A/ZfdbM/Ffrr5qW/8XmSe9lsYDWdAUmdirjlo9oQy39Vz0KN0E8tadaH1QJE3joS3ebQbTdxsN3UkREcRx3RlFEruvCdV04joNWq4VarQbbtkFE0HV9ZlucWg3tdhue5xERda1evZpj9rw6m4g6AJgA/u8f+JKP4jgiojU6sIYBWLfTexCRGgQBeZ4Hx3HQbrfRaDRQqVRgGAaiKALnHK1WC41GA47jwPd9JoQwxU6zTF9MRCqAS//BJBTHsUtENymYGRbYnn0fxpghhOjwPI88z4Prug/FUi6XoaoqPM+DEAL1eh3NZhOu68L3/YIQIoXZhHkOERVnC/TnSaJ82prdf3F4JI7vvgl4Jms0+LZ2G4YQcm0U3X9Xq3XPvticYHd833d0XX+fzGUrGyfVl0+3kCumJEsZJIRAo1YJfuEOtz55v/Pwbj4SkCFwxT3AK7O+n2tOTqKLCK049q/zvN/c327vt30cpZSSDON6OPwtUuj/6fh0yHAFRs4CNAV+05PrplvuJ9qBd8X2kYfLzWk2R8YN47obhXgONRpsW7sNTUrxQBiu3xoEq67dj2Ucx07TMMz3SZma3jSpvXq6OVvGOolYojZRj3+u9xe/kWbRwD4eJ7XPHXQJcwdvFycA53wkDEPRarVYs9lEo9GAaZoPNXO2223ouo4wDNFsNlGpVNBoNGSlUtl2x+23R/OJSDeMwvGZzBkLiAp1Ke97naKs+l4U7Xau4e7s6m5KSgkhhOu6rmw2m7RzIpqdToJ6vQ7OOXzfR71eR7VaRa1Wi4MgaIxu24YuxlhnKjV0eiZzcgcR/3AqddOmdnv9pf/AmbirGKMocoQQo61Wq6PZbFKz2US9XodpmuCcIwxD2Lb9UHnWajXUajXU6/XJIAga83t6SJ+cVI+z7WN6OT/MBCqv1fXrvu8/OQtaJ556wjB0JiuVd91VKFwyDRzTKwQJKdeM1WofLUfRXq3/PBe+748xxv7NsswfgfSVNce0gyBwWm131QrbvWeVEz+ifksppaqqV/Jc7lNXadq718dxJiNlazwILp2qVn9+/37+1peeJ4joqtg072wrysmubw8Nl4G2097mONENluVO1euPjCGKotZUtfrhVblcago4qldKioRYfa/n/Uc6CPZ73fM8d5Jz/mHTNH/ieuaxNUezXddtc8+/e17g3hOnsmnkrP79HcfeOoATpgSDxNGLiOZ1znyQy27a/VWSlFKmUqmtiqJM1+v17nQ6DcMwoCgKiAi+76NWq+2YEgHP89BoNDA9Pe2sW7du9fKODpoMgv5n5/Pfe72mnXCIbfM4ilpX12pffhNjn/+22OUiPQCA044j6lEAHcAPHyfGOI6l53m3cs7fUKvVVNu2oWkaOOeQUsJxHNi2DUVREEURHMdBvV6XExMTW/P5/KZ5nkf1bPa011rWt15kGINdpomm4wx/e2rqTa8i+vvjLWR9/klEJoBaHbhize6f5ziOk0qlVrXb7SOq1aqc7UcFYwxRFKHVasE0TTDGEAQBWq2WrNVqWL9+/f1TExP1jlpNWdjV9Z6XcP7eMywrbSqK2OC6130onX7jZ5rN4d0dN3Hwmr0wW69p2ktqur70Xim5FkVr875f2/YktT4IIUIiutNxnDuBGoQQkojo1vaujx+GYcCI/rdpmpdv43ywM463z3PdbfdL+aQMWpkdlzBNRL9rtFo7/m+33Rqz3VVrJqrVF5YV5ZB7iFQ7CNaUg6AWP0llHMexT0SrWq3W3YwxklKCMNMKuHTpUuRyT0YUe+eATJicczrttFPhtSrWwlLqmI4MW2KqsvaO51prqro3/ONf7boh3PO8DbZtX9Vuty+cmpqCoigE4KHkY1kWNE2DlBJhGMpWqyW3bdu2plwu39bcto0VstlXDzF2akcmoyhDQ1CCIH/6+vVvv6XV+i2A+x59vPPOIZZLqaVeK31YwUK/odKWd79SW33/PWHtitWPvQqdTerXmKb5YK1WW6brOjjnJKVEEARot9sP3clJKeF5nmw0GmL16tV/2r5tW6Xabpsr0un/GFCUoVxHB2MDA8hOTi54aRR9mHveXdjFKh7HH8v0+R1mf97MHJE1ofb1igf+3xvZhq9/Z9eLRwshgna7/UvG2IvK5XJa0zQwxiClhO/7aDab0HUdjDHEcQzHcVCpVJwNGzb8jDUa8WgqddhKoou6Na1gDQwQy+WwZNOms45pNl/9WqLPfj9pnn3aCoKgTkS3A0Drn3AePDrZ7KlPXcyMkt8MYPM2AJueAjHP4bl1IroNeLib5cm0I16xF+sC/zMdkAnTImKq9AZffCL/9OmHZA5d0suNfIpiNxATt2/w/+/dz1e+cvFvo8ckhyiKglQq9T+c81Or1eo8IkIUReR53kN3RupMh72cveOsrlu37lO6rlc3C6HmNG1xDeBVKakjjsEAMM6zUtP6X0G0+qc7nYBHziNlXkfmFScN2e8+9iS2aF4HUywd4XQ9te73SvPzl79V+c0F34gek9gdxxkxTfMSABdPTU0ZUkoZhiF5nodmswnDMHYkTOm6rpyYmFizadOmr23fvj3mqtoVMLa0ArCmlGTEMYhIcsYWr5rpMnxEmZx7ttaxJFv64HnL1ZcdPsiy3QUignQ2TdjXfOxfUp8oLHHu/9f/FI/5EuGc/z2VSv3Sdd0LJyYmVCEEhWH40EWHrusgIhnHMdrtdrRp06bLms3mdRsqFZHt6hpoAZ1lgHwhyBQCkjGe1fVDhwxjr5cSSxzYDrSBXwdavMCBGfNTxQGXMDvzRGcUOo815OaPLu/l8xb36qxvwIJS0JCR0YLzuloftTR0vPwFyocv/U30mBV62u326kwm8544ji8ul8sDnuexVquFVCr10N2bEEK2Wq3KyMjIx3zfv3rLli2Ccy58xsY2SCnuazYp3rSJUkJgu+u6RDSd3ukY8+YRL9mZNx57aOozhw1QdqjHoFKfBUpzPeN7K9/Uzb/251VFdvHJ9It33/jIO00hhOCc/zifzw8CeMfExITtui6azSZs237o7i2KIlGtVh/Udf3dvu9vDYJAHKVp054Qo+ujqK9vehoLHUeS7+PuKBofeVSyXLQwnV/a1ffVU44Onn9IH1fm95uwu0xAh1EYcF7YV9SWfP9G9hIA6x9dhnEcO4ZhfCiXy6Vbrdb5URRp7XYbmUwGtm1DVVUQkfR9P5qYmPhNvV7/0MaNG9uMiJam09Nb0+nmuiDIZ0dG0DM1JZ12W9wQhlvv8p/SI8oTB7ELiEgB8KsDJJmcPjtobhLADQdIzOcSkQ7gdwdIvLtywCVMyTV7rEP58PHZcF7G4iyXs0np7QD1ZQEZSD42rp7siTetr2X/+v630h8+943HNLPEiqL8zjTN4VQq9e/NZvNsx3EsTdNo9ove9X3/9unp6c8R0fW1Wi0AgOM0zR4EOi9kDMsZg9Nqyb/GcXAd0c82tFprbtzpJGg2jaUr+lMfKKaRy6ZUyhQzYAMdQMmEdJpk8fHCKQvqH/72QuMGACOP+oiI47jNOf90KpVaZVnWO6vV6hHNZlPTNA2KoggpZaPVal0eBMElmqbdPzw8LPJEtFxVe84C5PMVRfZKibF6HVfHceVvjcbFG8LwoYWrGSPq7ii+aGBZcH7OIiWX1snqLIDmFwGbQ1bKrDueOOyE7eZ733o6u+gb1z52lRXP8yYMw3hbKpW6B8DrgyDortVqfDahx0KIbc1m89LJycmvhmFYBoAFAOWBoVcR4WzOYQaBXNNuy6ukXHOr7//4yeqvSjx1LF1KVBwFznwV4T+/JuR5pxD9+YYn7zzQieg0Tct3p1KHpaUMLzCM+1u+3/jr45yLL1hOtMwj4ASg8oDEN+56cs/bsxlT51nWfIux/nlxvPWDRFs/K+VuR+aeeiTR9auk/PBzGV1XBlQpcc0tT17Mi4lI1fX80bZ9SIYofqemrfvfIKg9Wcfflw6ohElEZJn2IbaOEwhgkhgR1wAzBaTyAIVEjbbUzIYxlLdffM/69p+w0+4fO0RRJGY7+F9nGMYiRVFWYGaWSCylvK/dbq8TQjy0YWyJiA8VCm88m+jlR+VyvNjbS7LVEv7w8Oap8fH/+kEQPNTfxzmxQrF0tqGiDyBIUkCqAdgZIJUGKQpgNShlt5aqqn3yW99Iv/jGdx578s5O6/hlu92+yrbtQwAcipkpa40gCFb5vr9V7DTQiKmqmcnn/+dETTvm0M5O0otFlCYm5INjY1e+wnF+feFOI/eIdNXUjecrXGoSBDAV0CwglQVSGiiKCEaNLe1Tz4mY2X3BChq+/L7Hxuh53jRj7HOapv1A1/WjMLMkKABMhmF4h+d5k0I83J/sZrPLj7Htz56g6/n5fX1guo70tm3R7yqVLyyt19ftz6HtiaeWTAZ00glMX1CwjhxaqK9cxE3rK/+vo70wb9/2rpfxNV/62S53kdunVhKxQ/P5M55nGJ96jqYt71YUMer7qy6bnn7nCURrbnnU+djXR8xkZudxSzKndi6wBnMWsHFRe+PLTrZunPTc8jV37v85EUtUNXdsqfTR1+j6S4/WtJQQonFzu33xB1T1K/8VPnZHnzNP44bO7aM+/MqOIxcO9Vi5HtbeXqne+aH3sns+88V9vxTeow0S0aBlnfWybPaTz9a0Q7sVRW523Tt+omkX/SoMH9zbTaufbAdUwgQAItnnhzAdH2g4EvVWjHTVB0s7IBZDtmIELkiFyIn07v8WO63Qcx8eNWDn0W38Fcasebr+vJhIi3WdkMuBVJUGJib6K4bR+0ai7d95qDMb4MSyrg/W9EC1tkC7EUKreCBVAfwA0hEUBuC2wgadDbvfAmg2jhoR3Qrg1t3FR0Sk23avqihHhowxYduEQkFy18VJ5fK8z3FuXbjTgsacyyxxOdDygIYLqrUEgnoAveKBohiyEUK4ElFMOR8YChTsdvTqbEIcJqJH3CnvKsaOzs4TCeiLFAU7VkdJlcv8xGr12CuBn+7uGImDDSOdl7qH0vW3nXsEf8nyfsr2FTmzLVVEkVm7fq37o8+/zfzc+77m7tfpDtOa1nWyYXxhuaoe3tfZyYxSCYump097iZSfHhkffxWAh5aLmz/f5PM78uc/63DjYyctYUuGuphWzBBURfUmqvG6395gfvhNpxlXfvs6b78lzSwRK5VKLz9a0/7fYtvWs319AGPpc7Zt+49QynUvIPrTb3aqd8Wc2fe8Ewsfe+bx2ouW91O6r8CZbZEIwnz9zgftn/77+fp//ffv/P2xqP1DFEXpGchmv3DoTBmTVirh0HL5TAFcfOXU1L8A2OXgwqeqAy5hgsitOYinm8BYNcaWMQe6XkGh7YErAmG9jonpEMNlER7a3PPFyxw7wGVdSnedEFjdaMgjtmwhLQyxOQzFWiK/8KgnCyCcakKOVaUcKUeUH2mB8SmkKg0g9uGW23JkWmCkIp2R4T0PcplLjCQlxgD5QBRhcHoaC3wfcaOBB4R4TJsv58wPY+aM1wXGa0Jum/IpbdfRJwR0m0N4DuqTHkYq0q+3USnPYdOfucQohHA3AVjt+yiMjqKkabLVbGK7lO3Gnl6cOCgQEQyd64Zf/uIxQ/ys+Z1MGew2kOu1QBmVIfJL5xWUt3c/kC186TnWO9/1R2e/rHFKRJROpY5SGFsccs6kZZEsFIAoYvmpqdO9TKYHswmz1yIyStlnHT3f+uqhfbJrsEOlvj4TaocJUqU1r9U+8nVZ5Rtf/338muecSNf98eb9c9dk2zY3df35AtAiTSNksyBNk8r0dMatVM7JAX/G7MX3/Hla9vAFHV86ej4uWNDBlMEuA7leG5RRmBX5xTPyrf9n6Sz/qTfqb/3Id/z9krQYEeVzuSMVokNDzklaFmGmjPnA1NRRuqb1X0D04OUH0F3mAZUwpZTSNM1VLU+Obi9j6eZJIdOWT35YRddUE7oq4XkBxqtxvGG1fxt3wn3zh5DSaQrxi5sYO1VxHGOb50lTSnGHENfc325v2PDIP7gMfP+e6abibpyEnTZjMHLQciMU0wycYjTaATZPiHKwtn1rx/Ruj/oEwpOScT48EsdX/B24MKzVlKFmE7EQ3vWe96tyGD46H7WExK3DZRy7cRzM1CJI2US14SFjEuI4lJVGKO/cGG/URqMttw3v/QktpZSWZV23TtMeuCoMD61PTVEXEaaEmLopji9fnYyOfVrgigLGlUV5s3lm1oaSsVVKFTJgfSWgNLNpM6kT2mFO5SW3LzQuf/cz6fKLr9o/X6gSwIiU2BBFmFepYDCOgXYbw3GMjJQPrTddDczsirT94c6M7EpbnLIZk9TOImiwMLNpc6WMTDw5cMEJqY81bP8F2AebMO9KJQxhxjG2MIZ1joPM6ChSnKPdbmMMwI5KnmFEdkfuhQu68dyMCSVja5QqZED9pZmNsQMXXB1XVnriBbdstP/wppfSL7798/2wVi9mLpBGAWyIIgxWKpgXx5CtFoajCA3sYreIp7gDKmECgOd5ZdfzvzMh+KfWjMAAxbLaEiimfegKEIRSPDBN99y4Tv6mq2aZb+Q8+E68i105noDZkas/E4WCXtO0V9wcx5k4DK+vtttf2BCGj7gCnl3q6wbTMK5YP8afz0gyN4gw1YiRswBOQMOV4pYt7HflaXNjwRXmB4m8z+7l6iAijj3TMD54Xz7fGGHs7FwUBdUoujSo17+17lHv7bqu6Ojo+JaU2nNXD2OBgEDLCzBWCWHrMxOgJ+toXXdP9I2wqcp3apq+PgzDv+xljJ7nbZtotd56vWm+dx2wzAC2lNvtbwzX63c2DqCrzMQ/znNd47ZbbzrhOStVRYIDpACqAVhpIJUBIh2w21CMhnFIn/7SWyf4n7Af9keUUsq0ad47LOWWW+N4uahWMdRsSh7H8R1RdO2DrdYoMHMnmslkjrRNHEoEkmBEXAUMe6bP32BAGBGMBrpz7hGspSz7t5Po1i88zgIl/6j+IBCx5/3+Hss6I+N5anV8HCVAlqOoeU0YXrV29qIzYIrRYZgvUDk0gADGQZoBWDPjKBDpQL0FRW9aRw7qz1+9hX6H/ZC7pJTyNMNYtc2y7r01jleKWg0Lmk2wOBY3R9E924QYuekAq/cHXMKUUsaapn17xYknLty8acOrmh6sbdOSCjbAGeJqG6vSE/KWf4P9vcOzqWzZjm77gG1/8r/a7V3u5DFXcRy3GWPfqDJ26SigHSJEde1u9o8LgqBpGvq/ERW0+7azZ043oXVnJaVNSCHhjldw7ZHTkr9Js6/tLlrhWs/7xYWK8vUfR9FetUy6njepKMr7x4E8ABFLWZFxvMvRc+Xp6bXZbPbdE9L+rBtg6VgVvDMjYWoQToByMI3fnjOtvuCMjPk+lhZT1zSbXzmf6PLfPc5ovD2Znax8E+d81QhRRgLtDiFaSbJ8WlEI6HN9oOWBGq6E14qg1gOQ4QMihHQFRT5kSuUD/gRZ2A8Jc0jTMi/J5d7wbMYKA4xhSgj5xyBwhqW89t5W64NbZi+EpZSyu7u7Mwil3fYJTU+i0RYoNEOwug8KOdCOIX0JL0DGYFb3p2+aQ1/QEzRIRP2p1EkvNIzzj2aMmUS4KQzlH4DtG4EvDUfRlSOz9SgmMkGs0wkkWj6o4Ui4zRjpug8YGhDNlHEcQBLQH/vYL5vNvojzzJJ8/i3/CvQMck4TQuAPceyMSHnDtmr1PeOed0D1XwIHYMIEgHw+bulq/AvG2LXbxtsnTdWNxYzJlucFN2YExEWG+cmTU3amu6uLFrvuId2cd31T0179liDYqx3Fxczq5tU9PhHAsqLcvr1Rf50I9eetb/PThyt6j0A87La9K1eoxrmnaNqFxxQKqpXPY+H09GFCUYxXGManf+p5e7VwcxRFAYCJPX4WKcVi2/7zSLm82retF5Vb2nGWrqSC0L8nDqPbL9Csj5+s6Yce2tXFuKbJBWNjyxqcTz+H6Po/7mWCi+PYwQHW2Z/Yd2IBOdUEphoSY+UQ+bE25qllmE0HJANE1aYsVyKMVaWou/u+qd7mXD+io+PDZ6vqO89Ip/VCsUjCcUTv1NSDvy+XL/pdu7155+cLIeK6w+RkA5isCYxMeUjZdRRjAW4SpNNCe8rHZF2KdrR/RsqKTOaw4237u8/Q9YUrSiXGDUMum5yM1EbjC5ly+Zu3BsFDrWhEEGEs46kGMFmXcrQSUn68hUGVw2y0QTJEVG1huhJhsiGj1n64XO1lTBsqFD76EtO86KxMRssVCiQcRxYmJh54W7n8JuH7wxMH4IXyAZUwM0Rk5o3Skq7sOV3V4QsO72VGRk1thhQ/+OHa2t+6BuO6N5b/tUKUYbbN0NMDuC7vqFZPL6dShwK4YX/H2ElEC9PGkkMGiued3q8clVLIslW29sbR9mX3jzvXxjF6U6b9OeJcYbkcoa8PHNBWNJsv+oWifBlAbX/HuKjEjfk8dfypSwrPLBm0xOLwYsjr/rCx8feJZuuBXj37LybRUtI0xkolQiYDo93uOMFxnndPrXYTZjYwSSSeMCLyiSlrRqs4busUZMqIiPM2XD9CcUKBwmI4joeJaiyvXyvv7jsErX0dg0ynCznOX64ypmvZLGFgAKzVokObzSVXqOrCNxNt+ZZ8eJcjyzI3NvV8Zes0OgspAUMLIGQdPXUXtgHEUYhKw8OGMVlevbm16dnLif70OOsxP1FExPq6us5JEQ1puk6sqwvI5ZCJIuUk1z3vNsa+vfPzhRCtIIjWjlaVE7ZOA2kjgsLbcL0IhQllZtNm15djlVhuGKZ74o37/g4+VJTurK5foDKmqpnMjjLGymZz8XM17ZDI9w/IdaMPmIQ5n4j1FjNnHD2Y+8/DsspRELG6KG+iZCoQsXjjvIxx46+mKh95ANLcLCUebLelNTJCahhiIgyVTbq+3z9rb4+i9Q92vHZlt/X+xRllsMdSWN7gUIlwZMls3NHl/GjNveUfbpHgG6MIi6tVOQiQqNUwHMfqtBD7pWlkZ51pnj2yq/Spo7vtV81P8UyXpSCtcTDIlx/dYW2+Y7T931ePBNF2SHowCNAzOYlCswmn3aYxISxtdlPrROIfYZpm+MxnPvP2a6/9+8vXjgqLMyn9MKRqK0bOIihcSC8Q2D6N8vp72pdatQivI+IpQFyyj+5IFMCuA+aIEBh1HAxNT4P5PppxzMeA4s7j8KSUkjF2vxdEV2yZUl5pqmBSRtTyYoxVfNg6IISU1ZYQNzwQ/b6x1lu/vAX2ZiL5rX23awnFUmYmAGwLQ/TVashEEULXJUfKYk1KAzttzB7Hcey4/verqvKCtaPIcSalH4VUaUbIWQSVQ7pBjG1TmPrjbd5Pl0xL+Voi3gbEL/ZRGbcArQ6Yw0JgzHEwf3oazPPQiCLD17SSti8O8k9wQCRMRkSlbObIQ7sy/zfP5gMdlkoSGvWXcujNGFKEoZlvtp5hKyz3lVr7L7e05fFWq2VMeJ60pcT9Ut71YLu9dn/GuIiIpbuKrzu0aH6u1+KZDktDT96mrowFU2HSd91s3lTerHFurNoU3HFtLHpRqWBRoyFFHMdXBMFVo55X258xLpzH7fmdpc8tKVqv7TS51pky0JdPUdE2oJCgZstZlNP555u8/T9XbI1GrwmCAWdiQvYQoRpF7Uvb7SvHpUzuLhP/MN/3MTExMbJw4aL/2rhh/b8FMdLVtsRoNUbWBBiDrDlo3rXe/U9lEqkz9c4vDXXCGI+ia97N2OUXi11vCvBEkJTTY8D6/9/efcbZddT34/98Z04/t9+7u1pppVWXZVuuuAAGG0wxplfTCeUXkn8IBEJIAgScUBIIBEIwJZhQkhBIKAGbxAVcMAZccJFk2epttdp299bTz8z8H2jlGNuS1lgGS8z79doHkq7umZ29Zz/nnJn5zm1Snuu325gJQ7hSql1JMrs9zzdc+aDQkFKmjuN8iLHqinvH2bn9BDTVVdQoCrgmVCqgdk3Jm+/dnHz1KUbjbedV6XQL2PanhcK39gTB5qMQQjLJsi3rDSNZkCSuGB9XCzlHlKbyGqKbW4w9ZOIhkXsLY8UPjZO8NM1RaPUVhisKpYN9HKCzfmf+UW+WDZxWHvz0MiJrLI5/9G7DuPITef6o+1gSNSeIdt4m5bDfbqvpMIQjpdqZppObw/COzQA+8mgP8ltwTAQmyHIrpcJf1m024hmMfMciZlpYMDSIRY0yyTSGMzWNTMgznrEgueOLm8PPfN+wXnF7lllKynt5p/OeqSQ54rjer908Iirb9rI1BefdJZMVXZNT0XMxUKti0WANrmNR0uuBT0xaZy8Ql9Ca/l9cdgUT+xWdPZimoi3ldePd7ke3SvmYbTxrEFGtWn/u6mH7dZ5BlmcZVC76GGo0MFQvgzNF/dkWFFTpwiHx6runux+/IWRv2JrnC4tAZzxNvxoHwdUbjsFxB+3xg4hARIJl2ZfjKNk6raw/bId0sj+hiq5FvSTD3VOz/c81yKq/o+B947mOU19QLKo8jl/zC9c9472O84GPxnH0aNrQ7Xa7UsoP3Vos/mMnz5evz3PiwOx4nv/dRBQ9pHYyAJhJsp0HwWs7uf0naW49b18LCws2FGPY1+6nV7aD9BsvNv2/e4NrPvW0YpFZhqHOb7cv+RzwumcR3XHNozhvlFKqWql8fx9w5tVKvXVPktgNQDSl/Olts7Of25gkD7PzUZTWq8bnZFIZm4X9tnaAddsmle+YrJNmasP+megzC4ChN7je157rONWhYpFEHL/6l+325z7P+Qf+UIhHNWs2y7L2bBh+4BbX/UI7z1fcnedgQGtjkvxTO0m2bT5Gf4887gOTiMh1i8s9TuczAiNixLkJw3LgFIrg1Sp4mqAQJ+S0e7Sm6lzYMHsX7Z5tfWEsz81BpaY3ZdkR10UtqXHaMyvU2gGf7p0OHvEPk3uFCx1OS+jAkAO4acJxPTilMrjvwDE4/H5AdjcosO2Fp+bR5JvuCbLBnYBoK7U/zrIjlgJbXXVoSytWJ1QrdF+r/YjayCyLe571KpPgEBExzmFaNtyCD6tSAXGCLyW8bo9cM1y+usSjDftbz5tKs7IJhEyIiQkhjviIae0A0b3TSq2qFWjr7GMxnUA7lvk+wDghD7tWSUa/dPLs/UwQ68aG6JDRmZpp761xMkdq/rV1xurFep1hdFQZ/b5zxpYtb7muWPwvALc+mjYopSQRXbNPyufOOs6zbiPykaY3UhDcsV+Ih32C8jyD8XtsxLGMvmZl2X9LZot2JJMgCfejFU1Y9epbRxh7asV1DWvJEkKxqBrbt6++IEnezqLoLQAe1dK2VrvdZ4y9v18uX72TsXMUsGVFv//jjUky/XCvHxwkKpmO7SO9i/LsfQ4Y46mR70tEt9fv7+Uus0b82rUNzmvFep1o6VIyul1v3datb/me637n2US3Xv0oQk1KqRjRjVEYPn/W959xG5EzGoY/SeJ4/V2P4Y3BY+1xH5gAwLk6URL8VAKJVIiEhJlLxKmATHMgE0iFQgaiXGFkSdGpP2V/57Z/FGJeP/DFw5a9oOCMPn1NuTBassWLlpanBkR34kt75/2BYaZpLM8VjFQqSiQQ5wpBJpGkOZgpIHKFVAKZAhU4P2FZURlNynZsmj3yMdZViDqGXVpWcEZe3Sh4S8teeM6iwu5qGgZXTc9vXznGWIUYW5EpUCIVYgGEuUSYCmRpDoMzZLlCpoiEIr7A4StPqNZaN+/d+7An5IO9iBHNLLQXLCy4g884ocxHy3b/pSPWru+MpY95vUrt2LGM2BCaY895ghf97cueMFwrmczmhOkd7fhn1+7uXrZogQrWt/iSmLF6E6COEPDTlCCEkkRFodSJLyS67dFWh5nbgHkbEW2f+/PDvt+ow41G0X/SiScN/8Gra/YZDZtVHE5xmMltG2fib94yFmyaMQwRSyxrA2xGKSzNMlhZRhJgBuen7XJdE48yMAFAShkS0TUArgWgpg/R5hUNd+G66tBrTm84L19aNIdKJtm2UpPTnfjm69vRl8Yj3ptpu0tCYHFTKeoKQX6aAlJCEXkJ5yfXHuVFCXBgJj6ALUS0FQAmjtG7ygc6JgITAMUC1M8UuqlEO8rAMoV9My2YECCRo93uoRWl6GWSolxgPmE5wphRGqic8/RFC959UtU6c8hhXsEkmQo1eV+n+B+vW+l86V+3xfMJDAKBglyhlyl0EoFmmGB/qwuDM5RcC3kcY7oXohPn6OeKBRnYfMKybBnukweqL3v64vJbV5b48qrFXM+gqJdWt27cNXv5havMb/94a3bYR1RERLZtMyEV62cKvVShE+eY6UUYa3YglYLDCUG/j5l+hG4qEOSKTD49rw/4Cs8ZWrti8P87f4H/0iU+H6xYjBkM4URQvv2SMxofn+3N3nbt1mP3qlI7OhoF/9QnjjY+PZS2z1tWdvjioo2KY8LhGFxetteeOeg964qd3fetK3VuuL0le+uVQqPVUiclCew8x544jjbk+a6jWUrtcCUdfY+ba4brbz97wP/zFUVeX+gb1PDMA5PklFqyumI9eV3DetqPNjbfvTeh/ZuUUsuiCNbYmFpgGAiDQN2W55vvi+OjNu4/196HbXOlQrSg7px48oLG50+pmucuLhjGkGei6pqwGQZHqs7Ji0Pvoh9sNd5zZzf4+QSc2fVCVBqtFk5MEjh5jj1JkjSJtm4/Wg3G/MpmHiuOlcDcGgsVNRPplGMBL0hAlGLHxAyiMABXEmEUYbafqKlITrey/hHXSg4xxvyBymvOWVz62AklY2CkYNKCgo2yY4JDNkZL9qXrbfsJ71+07o8+vG/DkQoUyzzLxnoZl81EUTHKyelGYESIkhS+xaHyDL0gQjPM1O5utuO0MG8fqY2LKqa/dvHApasGnT9YUTT8RQULgwUbBYuXpRALlpWMM5ZOF07+hxPql77rvuYhQ3Ou+lAry8XYbEonNhOBQpTB6oRQCugEIRwOZEmCdhCqySiX+3O+c3PnoWMjD2TbRLbpjJ6zdODLp9TNpy4tGHxh0Ubds+EaVBstZ4tWlq2zr9rN3/2qBbX/+o+JWR2av6NWm+bAysWNTy8pmE+xSbCqZ9NQrYShkg/fMpAlMSt2ukteSPjEd+9OXtVM08t/atsfjuLY2ZIkZAHZBiH+KwiC238T7R0lYgsbjUuWl9wPNGwqVhyDGiUfi6oF1DwHDBL9Xt92DPaK7ESWfOru1t83GbvkaiHOmOj1aBBQbaX2/rjX++yuR1lpbL4k7KEK1S4b8Y0nVx1ONc+mBbUChko+PMtAGscodrpLX3YCfWpGJK+9u5N/6acw3x/FsX9fkpAN5Pdk2Xe2RtEvbz2OQu5oetwHplJKmaa5JS8Wb5tO8EzXEOAE4krCJKAbRuBQyHKhukmu7plNr13WTfYc7j2JiLxy6bR1Nf8jdZsGSo5B9aJPiwYqGCj5MCDR6XQMk9PzDN5rvnHZyB9/ZefY4QbBVRhF1zmOMzERy0U2B4hSZFKiE8ZwDQZSEnGWq2YskvWt4HvTjeywYbSQiBfqtTcsLlh/VLGYU3EtGqgUsbhRQcV3oLIUM62WD8IfXZWbm16+eODf/mvv9CEDKcuyPEnT7/UMfsH+SFomy0kpIM4EZvohbE6QQiBMc4wFct/moH9zfoRPR9UwvEat/DejPn9KxeK84js0VCtjUa2Egm0iiQK4zdbwsxQ+cl/e2QRg/eHfUTseDRAxVq28YqVrPtHhxCzi5LsuapUKFgzWYLs2ZBQSZwxRJoZOX1Z+9823TLxpDJjqcv7in3JezNL06qjf/8q+LDvsuswLBon2RURrhEk7vKJsLEzwk/WPvPJOy3IGlhbsPy0YVLANRq5toVwoYLDRQK1aAkHCn21RLiVfmYqXvmKB882b9vRee7tl/f4W0zzVzPP99X7/C/vC8Gf7jhA+z1pF1Juw2elCqslBV31nV+cRt5c4p0ajfknN5k92OZFtcPI9F7VKFUODNdiuBRGGZHCm4kwsvGhx9R23ju1/8ySZe672vFf4jBWyLLvRbLe/sCnLDrvdwklLiU6cYgiZyUbA5YaqwM/2xr8TAfu4D0wAyPM86Pf7H6Ni8dSxQA4KBdhKkESCTpKDASqTSk3Favcvm+lnts7mh51AQ2TyilV4a8GkYYsxsgyDfN9DrVpFZaAGYgqmZVKUZMaiQvaiIutdfnGjcev/zMwcchsuzvl9cZp+oQ3r/QRpZxIIc0WzZg6HkyIAkZBidy+/suN0v3/PxsOfRFOmWa8WnLe6HLbJGGzLRLFYRK3RQKFSBNIERIR+lLgnF7M/2GfiCgCHrGSklFK2bX/LcZxnT8Z4gYJgiVToZYIKBoPFAAmluqmKN83Gn97V6dzXbB66jURElUr1CWXHfL7FYJgGI8exUS6XUB8chOk78Po9yoREN0pHp2z+xrOWLX33bTt36bvM3zGzjBWWeO5LDYIJAIoIzDBgOS5MvwDmeyDDgNsPyDa7GPLMJ6+ru4N37579xh6i/4g5p3KWydZhgmexxZjTcJacUBt8zgWuce6SglU/IUl3hblx44uXOtd9b1fcnG97iYjqtdqTbY41BBCIQIyDWzYs1wMrFAEGOFkOp92FbQQFo8RfOOLab980Of1nuyyLPSnL5A1HmCS3pm74q63COY3G8DPPOtU5ySQR2XG+/pUnVa/ZmPTu2rgtn/edqWGYrm/ZL+QErggAMXDDhOU4MAsFMM890MdBQJbVxaBnPum0AX94pov/vLPZ/E/GGCunqTjUuCgArCMie9BbMlIeuri+1jjntKI90I/TvWuT5Ppnn2LfcPX6x24lwuPFMRGYB9YV0U8A/DGKxY/sDuQKSwnWl4RirABC3k3kxh2t4C+9VueIdzGco+w4dIZSQK5AAgRJHIqbINMCOIFbDphhgjOqqKp77sL9zcMOggshBOf8H1Gtegr270dC1GZTiaJBsDkpIZFMh+L70czsu+4L0sPO2iUi8svl5ZxohQSRACgHg2Qc4CZg2gARmGUTMwzYBjuxyLEEhwlMAEiSpO267juqlQpNxOzZ/VzaM4mCzwUMRioRmNnfiz8XiOblzebhT3bGGIpF/1wCCkIRckWQYFDMAAwLsGyQnYGbFogxWlNzz/75nlYRv4FKRtrji+M4PoiWpRKUSpCCQpRLBGmOOMnhGSlkJpAIhVQBCuQzz1g2NKA23Tcpjzgze3gBM4eGKy8/d6j0vhVFvmbYM6hic/IMXwkp39KMSre87pyhD6yf8W66e/vO+RQTIMu2VwkJK5UKsTjwFWYCQZrDjzMwDqSZQCoVZQooWuZJC4NpNiNlBuCIxzjbNhetWDb4t6cMOC9a7HO/4RhUspgyGF4aZcV3rm+Wv/iytc6nvn1vPK/9jEipOoNalElSqQCL5QP6OM7gcQMyzZEIhbk9nHzG2ErY5r15lqkjtXl4ATfKC6ovOXdR8YOryubqYZezqsPJMxwlhHrTRFi6/Y2nN/6qK1rXf2f9kWfTH6uOicAEDhRdJ6Lvpml6V6lYfCkrFS/eF2e+7KdToRBXruz2vj8Rxw/e+vFhEaEslRqMhEKYK/RTgXaUYqYXwrJNWIwh6IfopRnCXDGXMc9LjrwsSQjR55xf6rrulannXRIJ4/QpIkPk+bY0zf+30+5dmch0XqW+DEI1U+BhrhBkCr0kx2wQY6bbBzECiQydIEY/FUilssY5hp4ySnTT7sPfuUZRtNe27d8rFArPSQzjOd3MWMkJeZZld/bC6JvFILx9XD781PoHUkoZeZYviU1O0dyM4G6So9mPUOz0UM4z5FGETpRSkEuVKgwqk5WgA/N3jmEYXEjY/Vyhl0vYpNAKU0y0ezAYQ8mzIbMUrU4f7ThDP5cUSxi5f+T3HrEZ8wfKl6ytFT8z7LLKgGtisOhiqOSiYBmkRG7Vg/C8gkFfM3r916wbGvzZhsmp+exBa0RCoZ8r9DKJdpxhuhfCa7aR5wIWA8J+D80gRjcRiISiO+fZH8tK5sDCxY0vrK7aFw04nA/4NoZLHmq+TRYDxXFcK9vGe1w+3HjZ8to7v71j9oiFBIhg5kpZB/u4mwg0gxjFdg+c8QN9nCZotftoRxn6maJMSsynrv1SIuYP1F562qLCZxf5Rm3ANWio5GKw6KJoG6REbtSD8Jy6Y3x50z561dpK5Rf3th/ZsrdjxTETmMD/TQU3DOPvTz3ttFtbs7PbN9x993gqhJh5ZIPUQa7QbqdqpJ1KNKMMfieAwRmCKILNCXEYotmN0IyFmsqU2AfQm4nIAdRlhzmWODDA/3Mi+oVt25wTUZwkwlBKJY+kjQq9KFeynUq0UoGZMIXX6oFAaHf74Eqg1+9jup9gJhZiNpH9wR7Y7xHJKQD/c5hjJUnSIaJvEdF/2rbNlVIqSRLxSGazEZHgBt/XzxVaqcRsIlDsxbDNDoSQKDkmRJ6i0+liJszQjGWzGnX6b3GIJQnUv+pJBb8z+v1+z/f9be1UDrUSRg4JTPYjODMMcZLCtwyQFAjCELP9BJORiKIk2XXzjiN/RgKylyxy/fdXTCp7JkfBtaleKWPhQBXlgnMgiJuzkEotPm9J/te74L0E/7d15KGoPM+3hNzKZlNllxMJL0hh8j6klGj3AliMkCYxukGImShXu3vp5moxPeJwQ5ExozTUePMCz3qWZxD3bZPKBR9DjSoWVEuwDIao31PGdJOfIuRrp7Pomr9YUP3u3020DtsXRDQjQePtVI22EqkKZk5OLwZjHURJioJlQM31cStIMBGJsJenu8LsyPtz9yx7ZGXJ/WDFpJpvMjrQxyUsGqii7LuQeYr2bAtKNRdPVEofXOi2X465zbePN8dUYB6U57l82tOehjhJ8iTPf50p27NS4e5Wqk6eiqVyeE6chUhzgWY3gM2APM/Qj1LsD/Pe9pnonmqp/PTljJ3rAfe+1zCu+2ieH3Ym7lz4/FrTyefGG7f7nrdnOlGri5Egmx24EozSHEWbw4BCkqboRqna0xfbm5Hqrabqq9bWaEGaprd90DB+8df5ocdyHzA9/dd6fCKlVGEY3UauE0zFsugbOUyWQCqFfpTANzmgBKI4UbNRho0z8V1OaAwP+IXXDfsQlzrOVZNJsuPzR6/epvb41YdSP+rl9MTJWFKRBE30UxCAbpTANRiYkkjzXHUTobZ1s1sz6u880ptyzqler7/Y47SCMyLOGJmmBc/3UKxUYJYLQJ6iLCS1gxALC+nZC1TrSa8eHr76G/v3HzaA+r3ebZZZG5uO5QqPEzhlUDhw/s3YHBY7OEkuUzOxCJNOdsXO3pHXRNv1eq1sW68xGQxGBM45bMdBoViCW6uDLI6CZVEpTpTXD52VfuEN91J+FYDDTsTJ87yXZdkVPRhnT8aSW1yAkCITEt1wro8hkWa56iS52trJbu8m0bZ7pg5/UUJErFatPd8zaCUnIjbXx67no1CpwCwXgTxFSUhq9QMM++l5C2vmE19ZKFz7zf7xV7jkmAxM4P4SW7/W/82yLA+C4Evw/Yv3hbLGCCpXivqpQNGcmwCjlAozKbb18hsWZuw5by0W33Cu77sWY/l6x/nB1yuVt72+3Z46yt/WA9s4naTpVzvMvnQslDYhp1QeeDTrGQwGKeRSqk4q0w0t8aOLDPeyNzjmOScUCiTzPLir0/nkhwzjY391YLuvo04ppSzbvsX0/RumE/Fck0mmkFGcS7TjFC5nICiV5ALTiZreF2DfK8uVK17ououHXBdhGP7xT2Zm/uATRDe8W99tHteEEMK27a826o0XTsbytJAk3CCnVAItM4fLAQaoVCo0E9m9far/6T09ccS9YS3LYp5jP1kBPD9QFGTui5CDYIMB4FCMQxGHAnnLC/zkgS37rz7c+87Nmdib5fllfTI/OhZKRwKUigy9NIdvMJjswOuCTIkdPfHjsan29Xf2jhg+VKpWlwIYFQqUK1CmgGyu7RIETgfba5AipgxGazfbVgVHDkzled6/80rlkskYpxAkcplTlEu04xwOB4igMiExm6jmnbPdy8bifD4lBrllGU+WAM8VKHtAPwtFABhA/MDcBWYARE7D56ff1Wj8CIdYL3osO2YD89FQSinG+S8453/XgfMB0Rd+kCm0bImCQTAZIVNKTsXyrh2d7JoXc+Pjg47jO0uXgjzPOnXbthfsILrh3Ybx+U/k+WPyoZBS5o7jfNEwjDXT4K/OpLR6uUIlEThwxUuIhYr3h9k3WyEZS0DnNkolzlesAE/T0olbtrz9P/r9KwDc9Vi0DwCyLOv1s+wDnLGl+yJ5YiwU72QK5ZjgcAIA1ctUb3sv/4cFKV48zPloZWCAaPFi+JOTK5cnyfuvCILbgKO/hZP2+JJl2VgYhe+C531hOler0Zfo5TmKJsFmBAJUP1etva3g0k6vfW3rCOEDAEopCKmcKD8wxhJkEp34wDh6odVDXQgwmaPdC9FLcoS5RGKY9Z/Uwf4EOOzjU6WUMAzjX6rV6vIOrDdmfeH3M4VKSvAMCYOAVCJrxuLG6Yn2O+/tJfP6DJOUhUyCh0IheMD8ieluAMs04dkGkjBAO4rRzySFAnUTWWE+7x1F0RiAP61UKpeNR3J1KBQ6qby/jxWgglw1p6a67w3TztWdzrwuVEkpFOP8wHyPIJfoxhlm+wfGR+tSggmBdj9EN84oEhKJwOhRKGz0uPQ7GZgAIIXIGGOfRbU6Jm37TyKhVk0lquBw5ABmkyy9xiv2PppK62k9XjRnAKRZRrYQSgAmB1aoA1tdPWZXUXEct23bfle5XN4yq8zX93K1yOVwbU5RLmhMifBf2knwryWz8q8tMtisUtTIMnAplSIqe5a16g1Ed3/tMbqDU1IqIlovXfflhULh/Zk0n97OZNXhMEyGXpLJ+zpx+ukaj++KeOWtMwB1pSQ7ywClVInzwR7n/hlEwR36LvO4JqWURHSTEOKlIyMjl7a63XO7gSraTBEnhEmW/3K2m36mGLRv2HNgpul83hNCiF4v56qTSWolAn4Qw57tQUqFVtcGVwJBEGC2H6GVCDUZpZOzHcgziehkAIc7N/I87xqG8Z5KpXKbMIw/jCWWTyfkmgy5UmoijtP/aLZ7X+ol8SNZTtFOpMo76YEwm40yuN0AnB8ocuKZHHmaoNPtoxmmqp3KyQkZdy/2DHIjgQaALx6izXN3xtcDeEmpVHpXU/FndDKUbaYYIwRpLm7t9cIvULf7o0ml5ru8Symg2c0U2qlEKxbwgwR2qwupJFpz8ymCIMBsL0IzluhmahtTB2q9vISIvnscndu/s4EJAFLKmIi+Zdv21ZZlneC6xjKLcvaMC+oTVrO/r9XJ+zmsmU0dld0aRZa5d68aNgx0gyC/Lo737pLzq+P6aCRJ0maM/b3rul83OD+x5JZGAtZLljes3avr6eT+hOS9+9W9d2fq6Yu6XUp37EBJSuyO46DH2M7HKiwPmhsL3UJEby74/rLctdZGzKhZPO48eY25c9Ne1aoMIN63RzbvEGppfWYGa4MAlCT4ZZ63dgGRDsvfDUop6XnevWefffa/3H333R/avHlzHUQMSo3HcbxLKZUcbq3lg2VZJuM4vrrPvZdOx9LwuIDBUij0EaUHJrpwSGRZhl6cYjKUvftmgruGyvAo8FYusKyh93ne9iSO93ziECGd53lMRP/GOf9v27ZHlVJDAEVSii1Gksz2H8EYvFJK+b6/W0i1pZnIM4omwWI5EcXIhUSnH8ExGJTIESWpakU5dnSzDaIdd3MyF9QrxRN9IHunbW/8VJI87BKyufPxXs75/2fb9jARLVGAqZTan2bZzkKep51Hdr7lRHRjIPDK6URaniHI5CmUAsIkQ9E2DhSOyVL0olRNRKI/PRvc3o6Y+6ZicdWqSmXBxY6zYyhNd3xFymN+a8DjPjBfRUQegC8f5qrM96ldqxibThhSJ7/siYXXn7g4O2moVGCMFfbcdG96xWVXq6v/ty0v3tfv2wNE2YQQN/2s3//2HUcpMF9DRPsBXHeINkopxcAA2190yvyZ67ILLzyl8IIVg1hUL9pJlqtN/3pjft0Vt9K9P0jyE7Z2u9wDwvXAV7d0u/ccjfadT0RLABxuZqtSKvM8d8dAOa289Fz7krNWFJ+ybIDKnk2dXdP2TT+8U171o18Yw704XrgsSSCV2neXaX5sW5oel7PptIeX5zn27duHIAjGoyjaePDvf516o3MlH692XHfDVILTTCahkFMqFHpxDtckGACElKqfSbGlnV+/K3O2rSPnE2+oWZecatsepJy9sdf77LsN41OfyB9+TG+ubT0iugfAPb9uewEgiqK267pf7ZF98ngkbQZAKCDKBGatBDYnQCmV5BIzsej/Yn/wL8wsXfB7JfcjzzbNNQOGofYnyS3/UC6//V2dzoZDHUcIkRHRXgB7H/R9PCJKKeV53v9UKtWN07E6/WAfJ0Khl2TwTQZOgBBS9TMp72sl18pWuvP0YuMzb/Csl5xi266ScvbGfv8f/5/rfvpLUXTEXZkez47bwDyDiK2zrIVD5fJqB0hfaVkbv5mm7Yd7baPBC8sb3t8+/yzzjacuZdaqEZtKAzbIUictGY3XrBtNfvKx76n3fm+zHHGTdLMIgiu2JcnEo23jyYxZZ3neqiXl8vCIlM0PMHbP30j5sJN08tRf8pQz3MsvOJkuOGWJwUYXOeTUTAD5U9+3JD7t7NPzL3/0m/jGnfvzhgyCn68Ow6vWC/Go9g0EgNcaRmlJuXzyMsD5K9fd3k2Svf8oH7qYfGSEaKhWf8ZzzrA/f85KWnLyqEkLhh0YRV4YzdJXnLk6HvfM5J++eoP0r8uZSvv9qxdH0S+Ohx0MtEeOiNTRKMqdZdlEp9N5P5XLXxgL5Ugyt3aybApyOSlGQCYhJ2Nx7617gw/UHfP3zrTMN64sFKzy4sUAMHTR7t3vSfP87lcT/c83Dn9R+KjbK6UUruv+q2ma58ym7BVCCisUCt2UoWASLHbgGWiQq3BrO7xsR5DteKFf/MEazlcNDw6SNTCAFdPTT3mGEH/zNsN43Wfz/JBjp0er6HkURVOGab4fvn/5vlAOJ+LA2vCWRfA44WAfT8Xivk0z8YfsSu3NLyR6/fJikZdGRgBgwUW7d/95U4i7/p7omj87hs/54zIwTySicrn8zPN8/x+e5zjLqoYhtwTBDR+zrLf9eZrueuBrKxUix66+YPVC8w0DJbLrZRvF4RrRaBXkEPjsrHkKZp568a7ez+7ZPft+c0Ymd2SP/gd+gWG4qwYG/uwSy3r7kxzHM4DwetP81BcZ++RbpfyVKgkDA4YzMjj8l0sH5Pn1IuONmkfOSB20sARQBmtiqnyhaL/5rtOjV3yzP3PDrkmVH+pu9ZG42DAG19Zqn3yd677oBMfhUZaN/bDTed97iL778QeNgcSRXT9hufXXIzUsqRUNqjeKZIw2QHUXiPusYE8t+sPnyJfduH7mRfdNJpNTwbzHUDTtkObG7a4G8OZyufzX+2Oc2s6E6xukbEYKhF6Q5T+e6vX/moQc9wznoozIzCwLKBaJOIcxOVk0ff9pQ73e/+I3MLMziqKu4zjvLJfLE21lvC4Qsj4dK+4ZgMEoV0ztme7G/2T1W192qsPP57lamnBO0vMIlQqQJLTYss4KGBsGsPWxbu9cH18Lpd6ofP+v9yt2aicTjm8Q5vo46Cbihtlu9FdOnu12Kt4zcqVYbppAsUjgXBmTk6Uh03zyz4Ef4QgTrh7PjsvAFLY9sND3P7zSNE+oDw+T2Whg3djYs1vAO/7Bcf70XXF8/x1SEBruYN25xDHhMEYwDIuYXwRVG4BnEIjAmn3jvBOTl98+bn7mMzvjR7UTOQA4RDRUKDzpSYbxp0tdt1hcuhSwLOcZO3b82ael3PgGoh88cOyRyFxY9MTzTU4GY5y45QDFMlBrACwnilNlTwWls1aIl/cSfsPHtmaP+qQvcc5HarU/frFtv2JRpWLao6Owg2DFM3fs+Mj6ILgFwP0F7omIarXq04ouncwZiHODmOOBylWgXgISl9CLUC6Epz7rdO+sk/LkB4+2fdrvjjMYc4pEXg1QuVK9Kx40Fja3IfSPhRB32LZ1Qeb5Z/ZS1EjJMYb4DoX4ZycuTXv37GTFPsrZDilxXxDAHxuDzxi6YYi9Somjtf7qQiKqMFZcARhTQPJVIR6yJCSO4yZj7H2e533DsazzEsta22KUQET3VSvpT1edlGy1pqXgXWRjOeTWPMfimRksyTKg38ceIWR8FMP9FM6tKlBYA8hMqeArDxrTnau09qMoin7ped7TMtc9o5dRg0PthIw2RFH08+eemLev32N7MZBvVwr3hiG8sTEUGEMnDLELkO2j1eDfkuMuMD0iMmx7yYnA0i4RpZyTaduAbfMqY6fdQ8TwgMX6SqFMoBVxCgQxqBcDeSBh9HMQCIgUVEZEYEOzTWvReefR7E9/+uju3hIAiWU9OSLye4xBGAZx21bMMArLbPsJm4ArMXcVRkRULJZGhKRymAD9GAgiiXIgQEEOcAGVgEROquGq0Ykx5eAozOkOiDxuWWf3ASNkDMo0iRwHvmEM90xz3UuJ9n7n/lAnZhjWKWkOO0yAXqwQhxJ2PwcV8gMLzVJACuKWQWeFY7gC8zjZbduGYRgwTZPiR3+doh2DXm5Zy587OPjeiw3j7GHGkvvS9Io3meZl/5Jlv1JMfe7x46zn0feSKLp69ULv7Gef4Tx93Yj/RsfyXnLHjvDmRYX02pu2iP++HcbZbhy7MxMTqgqoaSE6PwiCq4J5bjh/OJZp2hdWKq94leu++STOhxIp7/2LYvETQRD84p8eNJQhpcyI6G7LCtY7zBk5dalz0cVnemcvrHrPaPazTb/YnFzt2f1f3jHu33eTEKfk7TZb1uuBpJS3JMnN40LMqxTo4QwT0Yjrrn7u4OA7XsD5UxYwFq2Poivfy/k/flSIX6l5fbCPi0X6btAL/uekJd45zznTe9bJS/zXu6b74o27k5vacXL1xunsytvBn+hFkTkzMaFqgJoSYva7UfQT9WsWSnm8OO4CMwJgA8EeILo7z1VjcpKWdbsQQaA2StnlD8o6ApBkUFNdYLKjMDadoDLWwSAAXuBA0ENvOsVEWyHJINPdhz/+okWLqFKpmI1GwwagyuVyallW9u1vf/tXDpwptfc+pdSdUQR3zx40DAPtXk/dDcyoB4UJYyR78YE2TrQF9k7G8PwWymkGMhRku4vZZo6JDtCaR1TWajW2Zs0ay7IsC4BYtWpVfPnll//KYxIC0q5SzY1SqtFOh8T27XDnNpidUGrigQO4RFCGyeNmD5jsAvtbOQYmQphOE24vAESCbCbAdFuiFUC25vFAZu3atbzRaDie5zlCiOSEE054TJfwaI8/y0yz8oR6/fNPtaynn1arMadUwuJW61SDqPRx0/yL92TZQ2Zdrl5Zra+sGB947hnma04ZZeUlA4yKBYZnPcF+7e792Ya//ybe87/3ic/+L+Ov35Dnjq3U9L44/mTS6/3s7kc5jFEiogW12guf7bqfPct1C0sGBgApVy2dmjrpMilf8jSiTdc/6Bicc1b1/Ke/8inex55yAj9x1TAzh6oclmO/5CVPct927R3xVzZ9K37fbZH9vnEpT2pIKQKlbtoVhpduOQpzFAY8r7qsXP7shYZxwcE+XtJqrTMB59WMXfqNh5lTUfDM8pNWV9938RnGm08dZaXRwQN9/IwznNe+4in53Z/6fvh337vd+MxVMF63IVeOo9TkeBh+Yke3e9PUMTx+CRyHgTm3f+a2/UJ863rgjwv9vmWFIS1kDFUpQyFlGcADr06bucDde5pYO1RWyndSAnUw0o1RdAkiS1WzE6v1u+W2wkKx99YbH/4HPjg4SKeffvrA6OjoM9euXXv+wMDAGtd18zzPt23btu26d7zjHdds2rSpfe2116q50nfXbnbdW36c5+d47TZ/AudwgHQwTZMmcP9dsFJKDQ0N7ewnNLNzWvn1goRjxchFCwuafTimQhzHamI2UzdsTDeNj8lDnkSFQoGPjo6uWrdu3XNPPfXUJ5RKpVHLsmaDIFj/ohe96Iput/vL6667LgUAIUQq2u0v3VKpPLGQJKNus6nWMgZPqWil61qz4f/Vg1ZKqTAI750xvHjnFLyKJ2DyAFGco1Hm4CTQ78fYPS1TaePn07OHDr56ve40Go0z165d+/zly5efAmCRYRh7ut3u9RdccMGVUsodP/nJT4756enakXUKhbPLnD/JMk3O63WihQsVtyx+Zr//wm8x9k9PINpz+wN+Adfr3FmxYOC9Zy7nbx1tMHNkwEF9cQFUt0HI7ZXV7hmXvin+zOQX5Bt/ek/38h2Syiek6dj+JJneN/91iYcUmqa7wrbfZAMFy/cJixYRiFQhDJevCcPnjYfhvXjARV+5TLRgcMFp551ofH7tQrlsUd2ghcMenGEf5HEyo7D2fL/7x1KF+d/9z+zLNu6xhmOBtBBFO2cOMaP3kSAiqpVKTzqHsSdapsmNuT5mlmWd0eu98r/C8LMAxn/1/5jW6Wvq7z9jOX/b6ACzRgZt1BcXiOqOIuTWaK37hL98OT7ejsJXXH17/5+3C6OEOB47N8tmpo5CH/+2HXeBCQBZlmULPO8jolp9wlKip66t1civ1Wh4dvYlcZZtfTnRpf81t34qz/MsjMKvTnPv4nvGUAZJFcQJTc5m8B0oKSRmeiq6dn329S2booedkVYsFo0FCxZc4Pv+h0877bRTBgcH7VqtBt/3YRjGBaeccsrrpqamfjo5OXnpKaec8ov169dLlab7gl7vXX6x+P3Vpjm0cmgI3HHc3x8f/+C/KXXfe4lu/OjcL4NmszlVq1W/vnva+nPHhCVkjm4oqDHN4JhKpZlSe2bU/l/sCL92+56HX+tUKpXcxYsXv/Wss8565+jo6PDAwAAvl8twXReMsYtOPfXU39+2bdu/X3TRRR+96qqrJpVSqkT0E3Kczwx63sfWuq6xZHgYlGUL/2T//n/8cK/3YgD7gAOB6TjODaHj3bJlP863uGJpntJsL0e1QMpgCkEs5V271c0b9/RvufkQe4HWarXhk08++YPr1q172aJFiyqNRoPiOIbruifXarVnP/GJT3zbrbfe+g9vectbLr/88sv1M9rjHLPt8hRg7xUCq7pdDJkmqV5PtaT0A8B/4LM9xyGqlL3TFtb47xU9mJ5roFDyiYYaoIVlgDKQY7IF8dTat1+UvVVS+Paf/lJuuz0+enc8BNgpY+VxAHuTBNVmExZjiNKUYqL65AMuhAEgDJk9XMcfD5blUs9hVPRtsmsV0KIBoGyB+h3FlbIuPE285aoN/Dt+uXfHjTdBRUfxLi1Xqj6tFN8z18eDB/oYbaUqgW07D3695xbPHGnw15c8WL7DqVDyQUMDoIVlAuUgZxJDsVj26ifLt/Jy/21f/+9I5PmxfVf5QMdlYBIRubZdLgAjjHNipRKwcCERkXlmq/X8H1jWpzG3d6RSShmGcaPBjUt3zVgfCFNUpjpKDZYEHAuIM0TbJ7IvTETyaxub8iFXSOVymYrF4nNWrVr1z0uWLBms1+vUaDTQaDSoXC7DsiwlhHAqlcqFpVJppWmar3/a0552s+IcuWkudIE6mSaoXieUy8ru9weWd7svuR34KeaKt+d5npVKpc8Yhrn2vnF6XjeCPd5Sql4UMBjQiTB5x470g5003vjg9gHA6OioPTQ09Oennnrqu4eHh716vY5Go0H1eh2FQgGcc5Wmaa1SqfxhoVBYcNFFF73tqquumg44Vw3HWW4BnLkuaHCQICUGW62TCqZ5zsuIvvftuZM3SdLWbEv9KUh9+a497JRmALaoKlH2AAByoq3u3DrVf2e2L33YovXVanVg5cqVl69evfqZg4ODRr1ex8DAAJIkoUKhoAYGBowoipaWy+WPbtq0qXz++ed/4sYbbzym13Rph0ZE5Lruvdur1clbsmyhMTODFZ0OVJbhTim35kTjDyx4IYRBplF6jslRUoogFSPFTMDyAKcIMAG4AZFl8sUNfuFTT/MLV/y0e1QvuqQQvdksu+MOw3hCrd/n/T17VBXAdJIk03F8m/+g2aGmU6i6Nns6AUwqIgkOGDbg+IDjAlIS7LbynF5ldcO+MO2FdxytpSIHEWN3bgNat2bZAnNmRi3rdIA0VZvyfONiIdq/8loiNjg4+HSToyYVIBWHIgswf7WPYbXYmkXJU+WtvJ7n6XG1qfRxGZgAIAA2A/BtQmBVq4VlRJCdDsaltGaJjLOI6La5D1+e56lhGJ8rFAqbhfTeMN3DGscAAZiIouTfSrXW9zbeIx92T7ooikaWL1/+kXq9Puj7PhUKBSqXyxgYGECj0YDrupRlGdrtNoho9KlPfeqHN27c+PJOp9PctXu3sxegLWmK4clJNHo9REGAPYDx4DIe3W63aRjG/6tUKi+LM+uSfbMYsAzITGD90FDnn3dORLd1Og+9uyQiajQaz1y+fPk7yuWyN9dGVKtVDA4OolarwTAMiqIIjuMYSqkXN5vNXeeee+77TMuSgoh2KoXNYYjCvn1wAcymKTpE/IFnrlJSEdHds03rFWlaeGM/ti/YMQnfNBDHibhxcrb/z6ViuHOi9dAT3jAMc2Rk5D0LFy58ZrFYNHzfp2KxiFqthjzPUa1WaWhoCP1+H6ZpFlavXv2uvXv33v1Hf/RHP7zsssuOm6tX7f/MLWW4b9yyPnmD77+/mabVc9OU1hChJEQyyPmKpxHdef3ckyLGGBHnJwSJYr1IoRNKdHs5vFYMeCGIC6huDhEpSInyHffQ8LMupOY1Pz56ASSEyIvF4j/dUyyeEkt59kQUmWcCqBOlBmNDg4ZRwNy2V3OT+RZnAqVeDHRDhXZfIm6ncJshSEogSoBAIIrAGyX3RG9z/9fbbeIQlFKKc37vpGF88gbb/stmmlbPSVNaA6CmVKykXPZVztu/J+7fEJoRqZPCFNSLQe25PvZbMcgLAUNCdVOISCHN0Uj7avjJa2jq5s36DvNxTSmlDNPct1+In/8EWEztNl/Z6wFCiGuT5H93Jklz/YOu1PI8z4jo6l6vdyMAFwAUkFWV6u/Z//AVfYiIDw4OvqJUKq2xLItM0yTLsuB5Hg6Gpuu6yPMcnHOK4xiNRuOJcRy/oFAofCXo93+x2XG2XZdlq8OpKSxkTHWE6H83Sa4WD7NWKc/zDmPsK0T0nwDMA98sgu27xCHvtBhjru/7b/M8r2SaJhmGAdu24fs+arUaBgYGYBgGoiiClJKCIDDWrFnz6r179349SZJ7d+/ade3tnveaQhSVpsfHUVZK7cqy3Ruz7PafPagP565+tzNGHyRiBQAcgPR9FYTBoeuD2rZ9QqlUeq3jOMbcrFi4rotSqQQpJSqVCgYHB+E4DvI8RxAElTVr1vzBD3/4w+sAHHFzXe3YpJTKLaLPTRJtOdXz/vlUzheeVSqRY5oXXuy63/zMzMzrn0L0i5uUUnmeqyRJJ2d6pprsgPa3BCoTIUxzFpUgBjck8l4PrekUe2dV0m6J1jV3Hf1f5P1+f7MXxy+frtU+Pmqar3mi49DCYrF8fpp+bJdlrfylZf3FmWkaK6VUtVpthwmyqS4w0VEYm0lR8HoYUYBdMoE8RtwMMNkScs9MNrPi6Y9+Fu+DCSGyIueXTdXrG8k0v3Yq54NnlUpkm+aFT3Xdb9/YbL72PUQ/+/iBc1spRVMzPWCqA0y0BPZMhLCsuT42/6+Px1sIeyl60XETlQccl4EJAHmWpQst66/uqNUwAVw4KGXazfMrw3b7E+sPMfg89ws/mvs6ItM0bcuyXsA5NwDQwfxgjB1cDgHOORhjcBwHc6FqjI6OPm/Pnj1fW7BgwZ79s7Nvv7FYfP82IU4qCjHdj6IvWp3OVdccukyexDw3ZyUichxnuW3bpzDGaO57BM3tw3ewjQfbN9dGOI4zVC6Xn5wkyaZ+EFy12zDe90PLesedWVa3lLrTabc/NBPHh5wvLKUSADqH+vcHt7FWq51nGMbA3HZtNPf34Jzf33+GYcB1XViWRYZhoFwun6WUWnLGGWdsvuOOO46z01I7KAcybpq1xcBAzXHgjIwQVSoo7dq1/PlSvmtSylcByKWUKs/Fz2f65lt3TsMsuQIGi5GkAgPNPhxDIU1TNdPJ1L3j8u7Kguiw+9n+upRSqmqa+RDnKwcYQ6VWA1u6lBCG7kiWve5bef7fHya68XsHQn4yzbFl9wzOrRcVXCsjhR66QYKyx0DI0QtS7J2W+Z2785/PbpPq3Y9Bm7lSCUm5YAlQemAfl3ftWrwiSd5+db9/Jw5cmMosy25t9ox05xTsoivI4DGSTGKg2YdrKCRzfXzLNrFjYkaO37Ht+Lm7BI7jwASA8TTdwTn/fz3XHdyU57mXZTNTQhy1cQvLshwiWpTnOWVZhjRNkSQJ4jhGFEWIogiccwghkCQJsixDnufkOM7yNE3Lu3fvbhLRj9Ioum3GdatGmkZWls2MH6UixXMzbFdIKesH2/fgNsZxDNu2kSQJ0jRFlmUkpeSu6y4dHh5mmzZtShhj/5xw/t29ruuNhGFzU57PKwzniYhopRDiYdtHRPB9H3meI47jg30IxljBMIwTTdPcfBTboj3OzO0INNIB+IxSlKQpnDQlpRQMKVdP5nkZQHNu5vmPXMf5+bYJnGdysDTP0Q4E1QopbFOpLFeYaKvw6jvF16Z2qkc9y/RQQsCPiRbOAmjnOflJAspzZEApt6yTlhHdCABBEPRs2/7CdNc+9d598KCkCpOMpts5ii4pBol+rOTGvbhpXxBcf9vkYxM+HSK4lrW0Ddgz6sDG9E6akpKSiOikHlAEEM7V7r3Gtp1btk3SeSYHy/OcOoFArUCwTagsV5jsoHft3fHnZ0R23E3MO6YD0/d9GhkZIcM49LexePHiCMBuNvfnpUuXHrVxgHq9bkspjSiKEIYhgiBAr9dDu93G9PQ0OOcoFAqQUqLT6aDT6SAIAqRpanLOzbPPPpuNjo4qHLgb65g4UHHgaLTx4J2k7/tGlmXsYIAHQYBut4vZ2Vm4rgspJRzHQZIkaLVa6PV6CMMQQghyHIeWL19OS5YsEQAmCYCq1Y5qHw4PD8OyLJamKR7Yj51OB81mE0opKKVgWRbCMES73UYQBIiiiIQQ5tFqh/a4pRRj4/cC8pdxzOx9+7BoehpJGKpb03QnHrC4Pk3TmV6//04F/8sb9tIprQA03lKo+kIZHOjHCO/bF398vNv+/rbmQ+shHy0SCCeAmbuEWNxot9XJaQpXCIzFcbi+19sezOWelFJyzr8DVFftnrHfFSZwp7pKDZUV+TaUkFD72+pOc6L/rvZE+rC7kxwNpBSyJNl/n+Okv4xj2x4fV3N9jFuk3LnvAfvVZlnWbLXYOwjiXzaOsVPbIWi8pajqK2VyoJegv22H+ttdU/kPds4cX3eXwDEcmIZhUK/Xa/i+D8bYkf/DYyDPczcMw6Tb7aLdbsNxHJimCSJCmqZot9vwvAPTRKMouj8EJiYmuu122+n1esOu6/7Kex7NH4hSClmWyTzPo06nU2i1WrAsC4ZhQEqJKIowMzMDy7IghEC/30e73VbNZlM1m021e/fuBbZtP+RD7z7cwX5NlmWREEIcDEPP8+5/TCylvL+dB+8+u90uWq0WWq1WGobhvjDUQ5jHM6WUcl336u3l8nXXAs+Y7vfZAiLVU6p5Yxx/sZfn4oGvJaK7hBAvz33/nVFqnLe3iRHbRF8ItaHVC79uO70rd+85ek+ZHk6e582pXu+zPysWP5kkSWVLmpIDZBuAH+4muvmBa0eFECHn/O/yvLhJCO+1swGd7BgocI69/Sj/0fRM8LlFMti1NXnswkdKqVzXvXK7Zb38WuCC6V6PLyBSfWDqeiEue2CBhLk+Xt+ctV6ZFot/GGX2BXubWOqY6GS52GhY4Vcdp3fljhl1XM5gP2YDs1gsbjVNc51t2wt/W21QSrEkSTZ0u92VExMTEEJQFEVot9uYnJyE7/uwbRtEhDzPEUWR6nQ6as+ePZvyPF/74LB8LGRZhn6/P95sNldzzpFlGcIwxOzsLPbv339wrejBcEUQBGi1WuG2bdtmLcta95g3EEC/39/X7/ejqakpHwDSNEWv18PMzAwKhcL9k5KEEAf7EGNjY+MTExNbtm/fftxdxWq/KoqiSce235IUi2/eZVlPYkLsS8Lw60av99Mth5h4xjl/J2Os6nl2mSiJez01K0T+kJquj4W52rb/tlupZt/zXnkL59U4jn80HkVfj6LoIfMPhBAhEX2r3+9fWSxSTUrbDoKkXZByNpDiN7LYP47j/TOdzpvW+/5bdpnmOWaej1WD4N+6afrTsQft+TnXx1sZY+/hnFeLRasWRnmUpXnTtmUYhsffneVBx2xgfuc739l74oknjv22jn9wgkq32531ff+8KIoG0zRVUsqHPK4kIjDGFBEhy7KJHTt2fMY0zfV5nj+mHyzbtjExMUEAVimlPhxFkTE3Rnn/ax44UYmIFBGpdrv9s1ar9UUA/ce6klWe5zAM42eMsWdlWfasJEmQ5zk98LiTk5P33xUnSYJut5tt3rz5a7Ozs83DvLX2OFYsFml4eJj2798/rw/YwODgPqXUh5px7BVNM/XL5Swslw/5+oULF+YApue+UCwCixcvpr179/5GfpmPjIwIAq5Mhbi6m+fmiOdFme+rQ7Vh5MA2WMHcF0ql30QrH3L8MSXE38xmmXuuaSasWs0PV6x20aJFAsAMgBnf//WPPTw8TIsWLfr13+A3iB7rX4jHO865Wa1W/9K27b9wXddpNBqoVqtULpfheR4sy1KMMeR5jl6vF27evPlvpqam/mFsbOw3Vt7NcZx6tVr9d875M4vFIg0MDKBarVKxWDz4GFkBQJqmqtlsjsdx/Ko77rjj5qmpqd/Ih4MObMd2ju/7/845X1qr1aher6NSqVChUIBt2+CcK6UUoiiSExMT14+Pj796w4YN07+J9mlHj2VZdP755188NjY2JYToP5LhFKUU0jQlzrk63LyFxxMhBIQQZFnWMfGLVkqJPM+Jc64457+xY3LOiyMjI40bb7zxf9M0fdz2lQ7Mo6BUKpV83/8zxtjbDMMoFYtFlEol8jwPhmEoAIiiqDc2NvYJzvknt2zZ8pjN0DsUx3FWViqVT3HOn+04jlEsFlEsFuG6LjjnSkqJbre7dceOHe/hnP9wfHz8N1r3kYhYqVQ6v1AofJ4xtsrzPCqVSvc/1maMIcuybHZ29sf79u17m2EYO/ft26c/vMeg5cuXD9dqteVzT2k0DUopzM7O7tixY8f+33ZbDkcH5lHCOXeKxeL5nue9mTF2NmNswDAMMMYm0zS9JYqif+n1ejfGcXy0tt17xBzHqfq+/2rLsi4xDGMVY6xmGEYfwHgURdfkef7l6enpe492+a35IiJm2/aKYrH4RsuynssYW8w59wzDaEkpN/d6vf/sdDrfStNUP4o9xq1bt47kYzdRVTvGMMawYcOGx30Y6cA8ioiIDMOwiWjYdd0GY0wFQTAjhBhnjGVZ9ug3dj4abeSclwzDGC4UCtUwDHtZljWFEFNSPrRW7m8DEXHTNBuMscFyuezHcdwKw3B/nue931aYa5qm6cDUNE3TtHn47Sxg1DRN07RjjA5MTdM0TZsHHZiapmmaNg86MDVN0zRtHnRgapqmado86MDUNE3TtHnQgalpmqZp86ADU9M0TdPmQQempmmaps2DDkxN0zRNmwcdmJqmaZo2DzowNU3TNG0edGBqmqZp2jzowNQ0TdO0edCBqWmapmnzoANT0zRN0+ZBB6amaZqmzYMOTE3TNE2bBx2YmqZpmjYPOjA1TdM0bR50YGqapmnaPOjA1DRN07R50IGpaZqmafOgA1PTNE3T5kEHpqZpmqbNgw5MTdM0TZsHHZiapmmaNg86MDVN0zRtHnRgapqmado86MDUNE3TtHnQgalpmqZp86ADU9M0TdPmQQempmmaps2DDkxN0zRNmwcdmJqmaZo2DzowNU3TNG0edGBqmqZp2jzowNQ0TdO0edCBqWmapmnzoANT0zRN0+ZBB6amaZqmzYMOTE3TNE2bBx2YmqZpmjYPOjA1TdM0bR50YGqapmnaPOjA1DRN07R50IGpaZqmafOgA1PTNE3T5kEHpqZpmqbNgw5MTdM0TZsHHZiapmmaNg86MDVN0zRtHnRgapqmado86MDUNE3TtHnQgalpmqZp86ADU9M0TdPmQQempmmaps2DDkxN0zRNmwcdmJqmaZo2D/8/NJK25U6c0WoAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_image_grid({\n", " \"optimized LiFePO4\": render(lfp_opt),\n", " \"optimized FePO4\": render(fp_opt),\n", "});" ] }, { "cell_type": "markdown", "id": "caad2145", "metadata": {}, "source": [ "## Analysis\n", "\n", "With optimized energies and cell volumes for Li, LiFePO4, and FePO4 in hand, we can evaluate two useful cathode descriptors.\n", "\n", "The average intercalation potential is obtained from the reaction energy, while the relative volume change measures how strongly the crystal expands or contracts on delithiation. For meaningful comparison across cells, both quantities are reduced to a per-formula-unit basis where needed." ] }, { "cell_type": "code", "execution_count": 11, "id": "4818c11e", "metadata": { "execution": { "iopub.execute_input": "2026-04-24T09:00:26.451666Z", "iopub.status.busy": "2026-04-24T09:00:26.451596Z", "iopub.status.idle": "2026-04-24T09:00:26.454291Z", "shell.execute_reply": "2026-04-24T09:00:26.454073Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "LiFePO4 energy per formula unit: -1.80283834 Ha\n", "FePO4 energy per formula unit: -1.60069031 Ha\n", "LiFePO4 volume per formula unit: 73.44145 A^3\n", "FePO4 volume per formula unit: 69.20850 A^3\n", "Average intercalation potential: 3.573 V\n", "Relative volume change: -5.764 %\n" ] } ], "source": [ "n_formula_units = formula_units(lfp_opt)\n", "\n", "e_lfp_fu = e_lfp / n_formula_units\n", "e_fp_fu = e_fp / n_formula_units\n", "v_lfp_fu = v_lfp / n_formula_units\n", "v_fp_fu = v_fp / n_formula_units\n", "\n", "voltage = Units.convert(e_fp_fu + e_li_metal - e_lfp_fu, \"hartree\", \"eV\")\n", "delta_v_percent = 100.0 * (v_fp_fu - v_lfp_fu) / v_lfp_fu\n", "\n", "print(f\"LiFePO4 energy per formula unit: {e_lfp_fu:.8f} Ha\")\n", "print(f\"FePO4 energy per formula unit: {e_fp_fu:.8f} Ha\")\n", "print(f\"LiFePO4 volume per formula unit: {v_lfp_fu:.5f} A^3\")\n", "print(f\"FePO4 volume per formula unit: {v_fp_fu:.5f} A^3\")\n", "print(f\"Average intercalation potential: {voltage:.3f} V\")\n", "print(f\"Relative volume change: {delta_v_percent:.3f} %\")" ] }, { "cell_type": "markdown", "id": "e032c500", "metadata": {}, "source": [ "## Comparison to Experiment\n", "\n", "A quick comparison to representative literature values helps place the calculation in context. Agreement at this level is useful as a sanity check before extending the same workflow to doped olivines, sodium analogues, or larger screening studies." ] }, { "cell_type": "code", "execution_count": 12, "id": "b9e1b94a", "metadata": { "execution": { "iopub.execute_input": "2026-04-24T09:00:26.455409Z", "iopub.status.busy": "2026-04-24T09:00:26.455349Z", "iopub.status.idle": "2026-04-24T09:00:26.574941Z", "shell.execute_reply": "2026-04-24T09:00:26.574517Z" } }, "outputs": [], "source": [ "import pandas as pd\n", "\n", "experimental = {\n", " \"LiFePO4 volume (A^3/f.u.)\": 72.85,\n", " \"FePO4 volume (A^3/f.u.)\": 68.09,\n", " \"Volume change (%)\": -6.534,\n", " \"Intercalation potential (V)\": 3.5,\n", "}\n", "\n", "calculated = {\n", " \"LiFePO4 volume (A^3/f.u.)\": v_lfp_fu,\n", " \"FePO4 volume (A^3/f.u.)\": v_fp_fu,\n", " \"Volume change (%)\": delta_v_percent,\n", " \"Intercalation potential (V)\": voltage,\n", "}\n", "\n", "df = pd.DataFrame([experimental, calculated], index=[\"Experimental\", \"Calculated\"])\n", "df.loc[\"Delta\"] = df.loc[\"Calculated\"] - df.loc[\"Experimental\"]\n", "df = df.round(3)" ] }, { "cell_type": "code", "execution_count": 13, "id": "19b54fc6-00d4-468d-85fb-3dc6db8b8bb8", "metadata": { "execution": { "iopub.execute_input": "2026-04-24T09:00:26.576512Z", "iopub.status.busy": "2026-04-24T09:00:26.576441Z", "iopub.status.idle": "2026-04-24T09:00:26.580933Z", "shell.execute_reply": "2026-04-24T09:00:26.580680Z" } }, "outputs": [ { "data": { "text/html": [ "
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LiFePO4 volume (A^3/f.u.)FePO4 volume (A^3/f.u.)Volume change (%)Intercalation potential (V)
Experimental72.85068.090-6.5343.500
Calculated73.44169.209-5.7643.573
Delta0.5911.1190.7700.073
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" ], "text/plain": [ " LiFePO4 volume (A^3/f.u.) FePO4 volume (A^3/f.u.) \\\n", "Experimental 72.850 68.090 \n", "Calculated 73.441 69.209 \n", "Delta 0.591 1.119 \n", "\n", " Volume change (%) Intercalation potential (V) \n", "Experimental -6.534 3.500 \n", "Calculated -5.764 3.573 \n", "Delta 0.770 0.073 " ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df" ] }, { "cell_type": "markdown", "id": "1443642e", "metadata": {}, "source": [ "## Extensions\n", "\n", "The same workflow can be generalized in several directions:\n", "\n", "- replace Fe with a dopant and examine the trade-off between voltage and structural change\n", "- adapt the workflow to a sodium analogue and compare Na insertion with Li insertion\n", "- loop over multiple cathode materials and collect a benchmark table automatically" ] } ], "metadata": { "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": "3.8.16" } }, "nbformat": 4, "nbformat_minor": 5 }