{ "cells": [ { "cell_type": "markdown", "id": "823472ea", "metadata": {}, "source": [ "## Phonon-limited carrier mobility in semiconductors\n", "\n", "Author: S. Tiwari (v1, 06/01/2024)
\n", "Revision: F. Giustino (v1.2, 07/03/2024)
\n", "\n", "In this Noteboook, we compute the phonon-limited carrier mobility of silicon using the _ab initio_ Boltzmann Transport Equation (BTE). Electrons and phonons are computed with Quantum ESPRESSO (QE), maximally-localized Wannier functions are computed with Wannier90, and transport properties are computed with EPW. " ] }, { "cell_type": "markdown", "id": "886fe6bb", "metadata": {}, "source": [ "Below we define constants that will remail unchanged throughout the Notebook. The object `silicon` is created as an instance of the `EPWpy` class. This object will contain everything that we need to execute and analyze the calculations." ] }, { "cell_type": "code", "execution_count": 6, "id": "5b91a727", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " \n", " \n", " -*#*- ...............- \n", " .+*= .+%*-=%%: .=#*- -===============-:.\n", " :*%=*%%- *%* #%* :+%+-%%+ .:. -=. :==-. \n", " -%S -%%*: :#%. -%%-. -##: #%* -=. :==- \n", " .. .%S: +%%%%*. :*%%%#= %%= -=. :==- \n", " :=#%%*- .#S- .. .%%= :*#*: -=. :==- \n", " -%S:.=#%%*==%# *%%=::=##-+%%. . .=-. :==- .= \n", " :%%- .-+++: -+##*=. =%S :-::==: .==- --.\n", " *%# #%+ -=--:. .----:. \n", " :%%- -%S. \n", " .-=*####SS%#########: -###########*+: +#######= =%SS####+::. \n", " =+#**%SSSSSSSSSSSSSSSS= =SSSSSSSSSSSSSSS= #SSSSSSS*. +SSSSSSSS%%%%- \n", " *%% =SSS.. .SSS= SSS=. .:+SSS+ -SSS:. .-::. .SSS+. #%* \n", " #%#. =SSS. *S# *S%: SSS= %SS%. .SSS= #SSS%. :SSS: =%#. \n", " *%%: =SSS#*#SSS- SSS= .+SSS+. %SS*.=SSSSS+ +SS%.:+%+ \n", " +%%:=SSSSSSSSS- SSSSSSSSSSSSS=. +SSS:SSS%SSS:%SS*-#%= \n", " ....#S==SSS:..SSS: =+- SSS%######+=. -SSS%SS%.#SS%SSS==%%=. \n", " .:+##%%#*- =SSS. ::. :SSS. SSS=. SSSSSS:..SSSSSS: :*%%%*=- \n", " #%+. -+#SSS*+++++++*SSS: .=+SSS#++++: %SSSS+. =SSSS%. :-+#%%+ \n", " #%* .SSSSSSSSSSSSSSSSSS: *SSSSSSSSSSS. +SSS%. %SSS*. . .%%= \n", " =%S :::::::::::::::::. .:::::::::. :::. :::. =+=-.#%+ \n", " -%S: =+===#S: \n", " ==*------------------------------=========+++++++++++++++++++++++========++-+## \n", " =+++++++++++*******++++++++++++++++========------------------==========+++++++- \n", "-- -- -- -- -- -- -- -- -- -- -- -- Structure Info -- -- -- -- -- -- -- -- -- -- -- -- -- \n" ] }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "be361e45016a4a54988ca3504713bb70", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Retrieving SummaryDoc documents: 0%| | 0/1 [00:00" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from matplotlib import rc\n", "import time, sys, os\n", "import EPWpy\n", "from EPWpy import EPWpy\n", "from EPWpy.plotting import plot_bands\n", "import plotly.io\n", "plotly.io.renderers.default = \"sphinx_gallery\"\n", "\n", "silicon=EPWpy.EPWpy({'prefix':'si',\n", " 'calculation':'\\'scf\\'',\n", " 'structure_mp':\"mp-149\",\n", " 'ecutwfc':'40', \n", " 'celldm(1)':'10.262', \n", " 'pseudo_auto':True, \n", " },\n", " env='mpirun')\n", "silicon.run_serial=True\n", "\n", "\n", "# Summary\n", "\n", "pseudopot=silicon.__dict__['pw_atomic_species']['pseudo'][0]\n", "print('Pseudopotential:', silicon.__dict__['pw_atomic_species']['pseudo'][0])\n", "print('Pseudopotential directory:', silicon.__dict__['pw_control']['pseudo_dir'])\n", "print('Prefix:',silicon.__dict__['prefix'])\n", "app = silicon.display_lattice(supercell=[3,3,2],bond_length = 3.5,view={'in_notebook':True,'backend':'png'})\n", "app" ] }, { "cell_type": "markdown", "id": "f654aca0", "metadata": {}, "source": [ "### Self-consistent field (SCF) calculations\n", "\n", "Here we perform the self-consistent field calculation to obtain the electron charge density of silicon in the ground state. The calculation consists of three separate steps:\n", "1. Apply the method `scf` to the object `silicon`. This step specifies runtime parameters for an SCF calculation on siicon \n", "2. Based on the properties defined at step 1 as well as other properties that are set by default within EPWpy, the method `prepare` creates the input file needed by QE\n", "3. The method `run` applied to the object `silicon` instructs QE to perform the SCF calculation" ] }, { "cell_type": "code", "execution_count": 2, "id": "ba5f9cea", "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-- -- -- -- -- -- -- -- -- -- -- Calculation: scf -- -- -- -- -- -- -- -- -- -- -- \n", "Running scf |████████████████████████████████████████| in 3.9s (0.42/s) \n", "\n", "-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n" ] } ], "source": [ "silicon.scf(name='scf',kpoints={'kpoints':[[6,6,6]]})\n", "silicon.prepare(1,type_run='scf')\n", "silicon.run(4)\n", "silicon.pw_util = silicon.PW_utilities()\n" ] }, { "cell_type": "markdown", "id": "e3c8e276", "metadata": {}, "source": [ "### Band structure calculation\n", "\n", "In this step, we compute the band structure of silicon along some high-symmetry lines in the Brillouin zone.\n", "\n", "This calculation is not strictly necessary to compute the mobility, but it is useful to understand the electronic structure of the system under consideration.\n", "\n", "Also in this case, we use **three instructions** to specify runtime parameters, prepare the input file, and execute the QE calculation." ] }, { "cell_type": "code", "execution_count": 3, "id": "24a24c92", "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-- -- -- -- -- -- -- -- -- -- -- Calculation: bs -- -- -- -- -- -- -- -- -- -- -- \n", "Running bs |████████████████████████████████████████| in 4.7s (0.34/s) \n", "\n", "-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n" ] } ], "source": [ "silicon.scf(control={'calculation':'\\'bands\\''},\n", " system={'nbnd':12},\n", " kpoints={'kpoints':[\n", " ['0.5','0.50','0.50','20'],\n", " ['0.0','0.00','0.00','20'],\n", " ['0.5','0.25','0.75','20']\n", " ],\n", " 'kpoints_type':'{crystal_b}'\n", " },\n", " name='bs')\n", "silicon.prepare(type_run='bs')\n", "silicon.run(4,type_run='bs')" ] }, { "cell_type": "markdown", "id": "44de2907", "metadata": {}, "source": [ "### Band structure plot\n", "\n", "We now plot the electronic band structure computed at the previous step. The zero of the energy axis is set to the value specified manually via `ef0`.\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "9de61b52", "metadata": {}, "outputs": [ { "data": { "image/png": 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pqUFVVRVqampC0tTUhLa2NrS0tKCtrS2819LSgqamJjQ0NKRe1dXVQUQQiUQQi8UQiURCSktLQ0JCAhITE4WUkJCA+Ph4yaNsEVhZWaFFixZo2bIlWrRogRYtWsDMzAyMMblewxcvXuDrr7+GWCzGkiVLMGrUKLmWVxlgn6vIqoajoyN5e3sX69gnT55gwYIFyMzMREJCAl6+fCm0iPMZMGAAFi5cCCcnJ3mYq5RkZ2dj+/btWLlyJVJSUqCuro6ZM2di6dKl0NXVVbR5AlFRUfD29oa3tzd8fHzg7++P0NBQ5ObmKtq0YqGiooLatWvDysoK1tbWwqu1tTWaNGkCAwMDuZUdEhKCDx8+QFVVVUgqKirIysrCwIEDERoaiqFDh+L48eNQUVGRmx2Kws3NDS4uLiU6hzHmQ0SOhe7jIvz/lESE88mvkPT0dDx79gw+Pj7w8PDA6dOnkZWVBQDo2rUrFi1aBFdXV7m3RJSF6OhoLFq0CPv37wcRwcTEBOvWrcO4cePK/Y+ZkpKCR48ewcPDA15eXvD29kZ4ePgnxzHGUKdOHdSrVw/16tWDnZ0dateuDV1dXdSoUUMq+fj4oH379hCJRMjNzRVSTk4OsrOzkZGRgYyMDGRmZkq9z87ORnZ2NrKysoTXnJwcqKioQEVFRRC0/Nfq1atDX18f+vr6MDAwkHqvrq5eLtePiODr64szZ87g7Nmz8PPz++zxdnZ2ePz4MapXr14u9pU3XITlSFlE+GOioqKwdetW/P7770hJSQEAODs7Y9GiRejXr1+VEWNvb2/MnDkTDx48AABYWlpi9OjRGD16tFy6KYgIoaGhePDggZCeP38OsVgsdZyuri5atWoFR0dHODo6onHjxrC2toa2tnaxyinNH7EiQUTw8vIShDcoKEjYp6enB1tbW6HLRCwWIyEhAZGRkcIx1tbWmDZtGiZMmAB9fX0FfIMv4+npiZMnTyInJwcaGhqfpBYtWqBLly6f/FdlLcIK90hQpiSPGXMJCQm0Zs0aISIZAOrUqZNCArcrCrFYTEePHpVanhwAOTs7086dO0vtEiUWi+nt27d09uxZWrx4MfXq1UtqBYf8pKamRq1bt6YZM2bQkSNHyN/fv8zRu5TZO6IsiMViunr1qrDoZn4yNjamSZMm0X///fdJ7JD79+8LMbHHjh1Ltra2wnnVqlWjH374gQICAhT0jaTJysqiY8eOCavYfCm1atWKzpw5I/V7kbV3BG8JF0CWLeGPSUtLw549e/Dzzz8jLi4OKioq+Pbbb7Fq1SoYGRmV0uKKhVgshpubGw4fPozTp08jNTUVAKCuro527dqhTp06sLCwgLm5ufBqaGiI2NhYREREIDIyUkjh4eF49uwZ4uLiPinHyMgI7dq1E5KjoyN0dHRk+l0qW0uYiHD9+nWsWLECDx8+BCC5jiNGjMCgQYPQoUMHqKl9Oo4fEhICZ2dnxMbG4ocffsCOHTsgEolw6dIlbNu2Dbdu3RKOXbJkCVatWqWQp8DY2Fjs2rULv//+u9BiNzAwwIQJE1C3bl2hmyg/paam4sSJE4iJiQEAODg4YOHChRg+fDju37/PW8LySiVpCfv7+1PDhg1p7ty5JWpVxcfH08yZM4U5+YaGhrRz584qN/U3NTWVjh49Sj179hQCu5QmGRoaUvfu3WnBggV06tQpevPmTZmXOC8OlaUlLBaL6dq1a9SuXTvhmhoZGdH69eu/uMp3YmIiNWzYkABQjx49Cv0NP3/+nCZOnCj83seNG1euq3onJyfTrFmzSFNTU/h+DRs2pF27dlFqaupnz01PT6cdO3ZQ3bp1hXNr165NrVq1orS0tBLZgYo+WQNAbQDbATwEkJ53QawKOU4LwC8AIgFk5B3fqbjllESEBw0aJFSMhoYGffXVVyUKfO7n50ddu3YV8mjatKnc19lSViIjI+nq1au0b98+WrNmDX333Xf0v//9jxwdHcnW1pbatGlDAwcOpO+//55Wr15Nf/31F126dIlCQkLKRXALozKIsJ+fH7m6ukqJ77p1674ovkSSCSG9evUSRO1LsYEvXrwoLHPfq1evYpVRVs6dOycEnGKMUb9+/ej69esl/s1kZWXR3r17qVatWsK1GjFiRInyqAwi7AIgGsBlAFc/I8JHASQCmAygK4CzeWLcvDjllESEL1++TK1atZKac4+8SFPz5s0r1o9MLBbTmTNnyMrKSjh/3LhxFSLOcFWnIotwcnIyzZkzR5heb2hoSGvXri3RrLn8KcnGxsbFnpLs6ekpjI04OjrKbT3Fd+/eSc3idHJyoidPnpQ6v/j4eBo6dKiQn4GBAYWHh5coj8ogwioF3k8qTIQBNMvbPr7ANjUAAQD+LU45pRmY+++//2jRokVSd0nkTV1evXp1sfJIT0+n5cuXC4MbhoaGtGfPngq59EtVoSKKcP4AaX68D8YYfffdd/Thw4cS5VOWKcmBgYFkY2NDAMjW1pZev35dovM/R05ODm3ZsoWqVatGAKhGjRq0Y8eOMgXPun37NtWuXZsASTD6AwcO8CXvPyPCSwFkA9D5aPtKAFkANL+Ud1m9I/z8/Kh///6CmAIga2tr8vf3L1ZeAQEB1K1bN+Hctm3b8rXdlJSKJsK+vr7UuXNnKc8Ub2/vEudz/vx5oQ//0KFDpbIlKiqKWrVqRQCoZs2a9OjRo1LlU5Dnz58LeQKgwYMHU1hYWKnzy8rKkgpF6+zsTEFBQUTEA/h8ToSPAwgo5Phhecc3+lLesnJRS09Pl1r8kDFG06ZNK1bLViwW099//y20rFVVVWnOnDkyD7DCKRsVRYQzMjJo0aJFQteDsbEx7d27t1RPWffv3yctLS0CQEuXLi2TXSkpKdSzZ08CQHp6eqVubOTk5NDPP/8srPpSp04d+vfff8tk29u3b6l169YESELRLl26VGowkYtw0SJ8DYBHIcd3yzu+45fylrWf8PXr10lfX1+qv9jDw6NY+SYmJtK0adOEO7G5uTn9/fffChuI4khTEUT47t27VL9+famuh9JG9vPz8xN+y5MnT5bJ7zA7O5sGDx5MgGSlljdv3pTo/BcvXpCjo6Pw//r222/L3Fi5deuW0G9dt27dQgfLq7yfMGNsEoA9AKyJKLTA9msAdImozUfHdwNwHRIviXuF5DcFwBQAMDU1bXX8+PES2ZOamvrZ6ZlisRgbNmzAtWvXhG2urq5YtGhRoX6XHxMQEICtW7fC398fANCiRQvMmDEDVlZWJbKTI1u+VO+KJC0tDbt378a///4LQDJLce7cuWjcuHGp8ouJicG0adMQGxuL9u3bY+XKlVBVVZWJrdnZ2ViwYAGePHkCCwsLbN++/YtxL0QiEU6ePIn9+/cjJycHJiYmmDdvHhwdC3fDLQ5EhDNnzuCPP/6AWCyGo6NjkfFOSlP3rq6ulcdPGEW3hE9ASbojCuPJkydkbm4u3LX19fWLfa5IJKI9e/YI63SpqanR3LlzeReFAlHWlvC///4ruGWpq6vTsmXLKDMzs9T5xcXFCYt8dujQgdLT02VorYSkpCRq0aIFAaCWLVt+Nh61p6cntWnTRvgfTZo06YvucV8iLS2NRowYIeS5YMGCzw7m8e6IokV4GQofmFuBchqYKw6zZ8+WcmsbNGhQsSdqxMXF0dSpU6W6KP76668qN9FDGVA2EY6Ojqavv/5ayi2rpAtyfkxqaqogeI0bN5brIgVRUVHCdOcuXbp8cuPw9vaWWrHcwsKCLl++XOZy37x5Q82bNydAMsX65MmTXzyHi3DRItwib/vYAtvUALwCcKE4eZeHCBMRvXz5UmoWjq6uLl27dq3Y53t5eQkDBwDIwcGBzp07x/uLyxFlEWGxWEwHDx4kQ0NDAkA6Ojq0ZcuWMq9pmJ2dLYhe3bp1y+RpUFyCg4PJ1NSUANDQoUMpNzeXnjx5IuXzq6OjQz/99JNM1qu7ceOGcN3q1atX7JtWlRVhAEPy0h95FfJd3ufOBY45DiAhT6i7AjgNIBNAy+KUUV4inM+CBQukpux+9dVXlJGRUaxzRSIRHT16lKytraVc2qrqrLvyRhlEODQ0VPAwAEDdu3cv8eBWYWRnZwuTE4yMjOjVq1cysLZ4PHnyhHR1dYXWd/5309bWprlz58pkgodYLKatW7cKU6m/+uqrEol6VRZhKiK5FThGG8CvAKLyxNcTgEtxyyhvESYiCgoKEpzX839shw8fLvb5WVlZ9Ntvv0lFD+vTpw+5u7vzlrEcUaQI5+bm0rZt24RJCQYGBnTgwAGZ1HdmZqbQ8tTV1SVPT08ZWFwy3NzcBF97LS0tmjVrFkVGRsok74yMDBo3bpzwX1m0aFGJnxqqrAiXR1KECOezcuVK4c4MSELoleSun5ycTMuXLxf+mIBkTv+vv/5KsbGxMrGxtKSlpVFISAg9evSIvL29yd/fn96/f0/x8fGfhEWsKChKhH18fKTCMA4dOpSioqJkknd6eroQD8LAwIC8vLxkkm9JyMjIoMWLFwv/he+++05mjYnw8HDh2mlra9Px48dLlQ8X4UoqwkSSQDYFZ/2UZOpzPlFRUfTTTz8JfWv5o+TDhg2ja9euyXwqdFZWFgUEBNDly5dp+/btNGvWLBo4cCC1bduWbG1tqXr16kU9wQhJTU2NLC0t6euvv6atW7eSp6en0otzeYtwQkIC/fDDD0L3lbm5Of3zzz8yyz81NZW6dOlCyJvFpoh41zdv3qR69epJ/f4B0JIlS8qct4eHhzBdu27dumWKJcFFuBKLcD6HDx8mbW1t4cdYt25d8vHxKVEe2dnZdO7cOerTp49Uv7OBgQF16NCBpk6dSr/99hvduHGDIiMjpVobYrGYsrOzKTU1lT58+EAvXryg//77j3bt2kWLFy+m0aNHk4uLC1laWhYrDKWGhgbVrl2bWrRoQc2bNyc7OzsyMzMjXV1dqdZ/waSlpUXt27en+fPn04MHD5Sua6W8RDh/4M3ExEQQph9//FGm7olJSUnUoUMHQt6kiRcvXsgs7+IQFxcn1UXQsGFDunfvHp0+fVr4faxcubLU+R84cEDo3ujUqVOZA2RxEa4CIkwkeSwr6JKTP4BQmhCA79+/p9WrV0tFa/s46ejokLa2tjC9tbhJRUWFrKysqGvXrjR58mRav349nThxgu7evUsBAQGUkJDwWQEVi8WUmZlJvr6+tHv3bho/fjw1aNDgk3IsLS1p/vz59PjxY6UQ5PIQYV9fX+rYsaNwDTp06EDPnz+XaRkJCQnCI3rt2rUpMDBQpvl/DrFYTIcOHRJmqGlqatLq1aulnoL+/vtv4Ua/du3aEuWfnZ1NM2bMEK7f999/L5NYxlyEq4gI53Pv3j3hMSq/Vblu3bpS5SUWiyk8PJyuXbtGW7ZsocmTJ1O7du1IT0+v0C4CHR0d0tPTI3t7e+ratSuNHz+eli9fTnv37qXr169TYGCg3LoNPnz4QJcvX6bZs2cLkw/yk729PS1btqzYgZHkgTzr/e3btzRhwgRBfExMTOjgwYMyv/m8ePFCCMpuZWUlE8+K4uLj40Pt27cX6tTV1bXIJZAOHTok+MZv2rSpWPnHxsYKsZLV1dVp9+7dMrOdi3AVE+F8Vq9eLQQpASTO6g8ePJBJ3mKxmBITEyklJYWysrKUoqVZEJFIRHfv3qUffvhBeCzPT05OTrR9+/ZyH3yUR71HR0fTzJkzhUdnVVVV+uGHH2TiE/sxBw8eFIKsOzg40Lt372ReRmFER0fTpEmTBFE1MTGh/fv3f/E3t3fvXqHOf/vtt88e++TJE2E9w1q1apG7u7ssvwIXYXkmZRZhIknfXf7odX5q3749vX//vtxsUDQ5OTl0/fp1mjBhAtWoUUOq5d6/f386ffp0mabpFhdZ1ntiYiItWbJE8GxhjNGIESNkGms3n7S0NBo/frxw3UaPHl0uq1xkZ2fTr7/+Kjx1qamp0Zw5c0o05XjXrl2C3Z06daJ58+bRqVOn6N27d4KI//3338J4ipOTk1wmmXARrsIinM+jR4+oTp06wg+SMUaDBw8ulz+TMpGWlkZ///03ffXVV1IDfHp6ejR69Gj6559/ij35paTIot5DQkJo4cKFwqwtANS3b1+5xZB++fIlNWrUSBj43Lt3r9yfesRiMZ0/f16IPwFIljcqbVfSzp07Cx23qFWrllS85PHjxytV3XMRrmQinM+ff/75SWtw9uzZVXJFjsjISPr111+FOAD5qXr16vTNN9/Q6dOnv7iwY0kobb3n5ubShQsX6KuvvpKKIdK5c2eZPzbnIxKJaN++fUL3Q4MGDWQ+wFcYt2/flgq2U69ePbpw4UKZhT82NpYuXrxIy5Yto549e5KBgYHUf2DHjh1yvblwEeYiLIVIJKKFCxdKreZRrVo12rhxY5UUYyLJCiVr166V8rkGJA763bp1ozVr1pC7u3uZBhVLWu9v376lNWvWSMUM0dDQoJEjR9K9e/fkIhrZ2dl06NAhYfANAI0aNUruT0ze3t7Uo0cPocyaNWvS1q1b5dZNJBaLKTAwkI4fP05+fn5yKaMgXIS5CBdKRkYGjRgxQspvt3r16rRixYoqK8ZEkihZv/zyi1SLrKBbXo8ePWjt2rV07do1qb7FL/Gleo+JiaETJ07QlClTpCYgAJK11TZu3Ci3wcT09HTauXOnlEtinTp1ZDa1uShevHhBQ4YMEcrU1dWlVatWVbqQq1U+qLs8cXR0JG9v7xKd4+bmBhcXF/kYVAqioqIwZswY3LhxA/l1q6OjgxkzZmD16tXFCiRfWYmJicGdO3fg5uaG27dv49WrV58cU716ddSvXx8ODg5o0KABrKysoKenB11dXank5eUFBwcHREdHS6WIiAi4u7vj+fPnUvnq6uqie/fumDJlCrp16wYVFRWZfjciQnBwMM6cOYMtW7YgOjoaAFC/fn0sWLAAI0aMgIaGhkzLzMfDwwMbNmzAP//8AwDQ0tLC9OnT8dNPP8HIyEguZSqS0vznGWNFBnXnIlwAZRTh3NxcJCcnCykpKUl4n5qaCpFIBLFYLPVKRFBXV8fx48fh4eEhiLGWlhYmTJiADRs2KO2qEOVJdHQ03NzccOfOHfj5+cHf3x+xsbEyyVtLSwsdOnRAly5d0LVrV7Rs2VKmN0AiwqtXr3Dnzh3cvXsXd+/eRUREhLC/RYsWWLRoEQYOHCizVTA+Lv/atWtYv3493NzcAACampqYMGECFi9eDAsLC5mXCQBhYWHYv38/jIyM0LJlSzRt2hQ6OjpyKasouAjLkZKIsFgsRm5uLm7fvo327dtDJBJJpZycHGRkZCAjIwOZmZnCa3p6OlJSUpCcnPzJa1JSEhITE6VSSkqKzL8nYwxt27bF1q1b0bp1a5nnX5H58OED/P394e/vj1evXiEsLOyTesq/AdasWROmpqZSycTEBM2bN0fbtm2hpaVVorJzc3ORmZkppIyMDMTExCAiIgLh4eGIiIgQ3vv5+SEuLk7qfGNjY3Tq1AlTpkxBjx49wBiT5aUBIFmO6MyZM9i4cSOePn0KQNLK/+GHHzBz5kyYmprKvMx8rl+/jhEjRkh9bxUVFTg4OKBly5Zo2bIlBg0ahLp168rNBoCLsFwpiQgfOHAA48ePl7NFEsHU1dWVeiTOf1+tWjWoqalBVVUVKioqwisgaeW9f/8e7969Q3h4OEQiUaH5GxgY4Mcff8SiRYtk/ohcUcjNzcXLly/h5eWFFy9eIDAwEO/fv0dMTAxSU1ORm5uL3NxciMViiMXiYuWpoqLySWKMFSqMYrEYWVlZRdZRUZibm6Nz587o1KkTOnXqBAcHB7kILwBERERg9+7d2LVrF6KiogAAtWrVwuzZszF16lTo6enJpVxAcn3WrFmDFStWgIjg6uqKunXr4vHjx3j58qXUdTMwMICHhwfs7e3lZo+sRbjqdhCWETU1NaipqYExBnV1daiqqkolDQ0NaGlpQVtbW3jNTzVq1ICurq7Ua40aNaCvr/9JqlGjRpnFUSQSITIyEm/fvsWtW7ewe/duhIWFAQASEhKwdOlSLFu2DM2bN8e6devQs2dPWVwipUMsFsPLywtXr16Fp6cn/P39ERUVhfT0dLmUVVzBzkdFRQXa2trQ1NSElpYWtLS0YGxsDHNzc1hYWMDCwkJ4b2trCysrK7mJLiDpcrh37x527tyJs2fPIjc3FwDQsGFDzJgxA2PHji1xa7+kxMXFYdSoUbh69SoYY1ixYgWWLFkidLFkZGTA19cXjx8/xrFjx3Dv3j307dsXHh4eMDQ0lKttsoK3hAugjH3C8iI0NBQ7duzAX3/9haSkJKl9Ghoa6NSpExYsWICuXbsqyMKykZ6ejosXL+LatWvw9vZGSEgIkpOTizyeMQYtLS3o6+vDxMQElpaWqFevHmxtbWFkZARDQ0MYGRnB2NgYJiYmcHd3h42NDYKDg6XSq1evpAb8LCwsMGzYMHz99ddo2LDhZ8tWlkHTpKQkHD16FH/++Sd8fX0BAKqqqhgwYACmTZuGzp07y1X88/Hw8MDQoUMRFhYGY2NjHDt2DN27dy/y+NTUVHTo0AHPnj2Dq6srrly5IpfBSFm3hBXuFqZMqSK7qJWFN2/eUJcuXQoNS6mtrU0dOnSgDRs2KDw4fFGEhobS1q1badCgQWRnZycVBvTjxBgjfX19atKkCY0YMYJ+//13Cg0NLXGZn6v3Fy9e0KJFi4T4BfmpRYsWdOzYMaVcmFUsFpOHhweNHz9emNSBvNgOS5YsKdep8WKxmLZt2ybESmnbtm2xY1u8e/dOCHg1ceJEubjkcT9hLsJyIykpiZYuXUpaWlpFiliNGjWobdu2tGbNGnr79m252vf+/Xs6cOAAffvtt9ShQweqVatWkfGIkRc9q3bt2tSjRw9avXq1TKcDF6feRSIR3bt3j7799lupWV3W1ta0Y8cOSktLk5k9pSUxMZF27NhBTZs2lbp2rq6u9Pfff5dLHI6CfPjwQWphz1mzZpV4Uo2Xl5dwI/7ll19kbiMXYS7Ccic5OZnWrVsnJRxFiZ2Kigrp6+uTg4MD/e9//6MVK1bQlStXyN/fv0Qik5OTQ35+fnT8+HFauXIljRs3jrp27UoNGjQgPT29LwaP19HRofr169OQIUNo+/btcm+5lbTeMzMz6a+//iJ7e3upmWSrV6+W61LyRfH8+XOaOnWq1HJYxsbGNG/evCJDSsqbBw8eCDMK9fT06MyZM6XO69SpU8KTz7lz52RnJHER5iJcjqSkpNCqVauEVoWmpia5uLhQq1atpP68X0oqKiqkoaFB1apVo2rVqpGWlhZpaGiQmpoaqaioSMVQ+FLS0tIiCwsLat++PU2fPp0uXLggt0Atn6MssSNOnz5Njo6OUjMbZ86cSSEhITK18WOys7PpxIkT1KlTJ6lr6uLiQsePHy/3Vm8+IpGI1q9fL9zonZ2dZXItfv75Z+EG/fjx47IbmgcXYS7C5c7bt2+FJdABkI2NDZ0/f54yMzPpzp07tHr1aho4cCA1atSIDAwMSE1NrUTCWrC/VlNTkwwNDcnGxoacnZ1p8ODBtHr1arpz545SrTtX1noXi8V08+ZN6t69u9TNatiwYTJf4fjt27e0fPlyqcUBqlevTj/88EO5L2X0MdHR0dSzZ0/Brnnz5slk9QsiyTUeM2YMAZL427IKa8lFmIuwwrh586YQChEA9e7d+7MtFpFIRJGRkeTl5UX//PMP7dq1i/766y86fvw4XbhwgW7fvk1eXl7k7+8vl8Dl8kSW9f7kyRMaNWqUVIjGDh060Llz50q8HHs+mZmZdPLkSerZs6fUDdHBwYF27NhBSUlJMrO/tFy7dk24MRgZGdGlS5dkXkZmZqawRFSzZs1k8r25CHMRVig5OTm0bds2ITi3jo4Obdq0SSlH/OWJPOr9/fv3NH/+fKnlpoyNjWnYsGG0e/fuLy4/JBKJ6Pnz5zR79mxh3TZAEq3tm2++oZs3byrFqimZmZk0Z84cwb5OnTrJtQ8/Li5O6Ivv2bNnmVvaXIS5CCsFUVFR9M033wh/pJYtW5Z4ReiKjDzrPTk5mbZs2UI2NjafdNnY2NjQlClTaPPmzTR37lz6+uuvqX379mRpaflJsPOmTZvStm3bKC4uTm62lpRXr14JMZ9VVVVp9erVpW7tl4SgoCCqWbMmycJ1jYswF2Gl4tKlS8KItoqKCs2ZM0emwdOVlfKo9/w4ub///jsNGjSI9PX1v9ivbmpqSlOnTiUvLy+laPXmIxaL6c8//xQGea2trenhw4flaoOHh4dQ/po1a0qdDxdhLsJKR0pKCs2ePVtwI7OysqJr164p2iy5ooh6z83NpUePHtHatWtp2rRptG7dOjp8+DC5ublRUFCQQrxEikNsbKyU7+/o0aMV1id97tw5oY/88OHDpcqDizAXYaXFy8tLanmhCRMmVLgBt+LC6714XLhwgUxNTQmQBHk/duyYok2ibdu2ESCZzHPr1q0Sny9rEa6aYbM4csHR0RFeXl5Yt24dNDU1sW/fPjRq1AgXLlxQtGmcciY5ORmTJk1Cv379EB0djU6dOuHZs2cYPny4ok3DjBkzMGvWLOTk5GDgwIF48eKFQu3hIsyRKWpqaliwYAGePn2Ktm3bIiIiAv3798fIkSM/iX/LqZzcvXsXzZo1w969e6GhoYFNmzbh9u3bsLKyUrRpAps2bcKgQYOQlJSEHj16ICQkRGG2cBHmyIUGDRrg3r172Lp1K7S1tXHs2DE0bNgQp06dUrRpHDmRmZmJuXPnwsXFBaGhoWjRogUeP36MOXPmKF2salVVVRw5cgSdO3dGREQEunXrJrUySXlSrCvDGNNkjLkwxhYwxn5jjO1hjK1jjI1jjNnI20hOxURVVRUzZ86Er68vXFxcEBsbi2HDhmHYsGEyW0aIoxx4enqiVatW2Lx5M1RUVLB06VJ4eHigUaNGijatSLS1tfHvv//C0dERb968QY8ePfDhw4fyN6SozmJJXzLqAdgBIAGAGEAugA8AwgCk520TAXgEYBwAlc/lp+yJD8zJD5FIRH/88QdVr15dmIRw8uRJRZtVani9S0hPT6e5c+cKnjH29vbk4eGhaLNKRFxcHDVs2JAAUOvWrb+4OnS5DcwxxnYCeAmgNYBVea9aRGRERLWJSAeAGYBBAJ4C+BXAC8aYs2xvE5zKgIqKCr799lv4+vqiS5cuiIuLw7BhwzB06FDExMQo2jxOKXB3d0fz5s2xadMmAMC8efPw9OlTODtXLAkwMjLC9evXYW1tDS8vL/Tv3x8ZGRnlVv7nuiPMATgRkTMRbSEiHyLKLXgAEUUT0XkimgKJIP8BoJkc7eVUcKysrHDjxg388ccfqF69Ok6fPo1GjRrh5MmTijaNU0zS0tIwa9YsdOzYEYGBgWjYsCEePHiAjRs3QltbW9HmlQpzc3PcuHEDZmZmcHNzw7Bhw5CTk1M+hRfVRK6ICYALCp9JlFic83l3RPkSEhJCXbp0EeppyJAhFBMTo2izikVVrffr168L06lVVVVp0aJFCguBKQ/8/PzIyMiIANCgQYMK7Zooz+6IMYwxHfneAuTGDABtC6RuijWHUxiFtYq5B4VyEhsbi9GjR6N79+548+YNmjZtCk9PT/z888/Q1NRUtHkyo1GjRrhy5Qpq1KiBs2fPomXLlnj8+LFcy/xcd8QBAFGMsQOMMVe5WiF7XhGRR4FUstU7OeUGY6zQvuKvv/6ae1AoAUSE/fv3o0GDBjhy5Ai0tLSwbt06eHt7o1WrVoo2Ty44OjrC09MTTZs2RVBQENq0aYNt27blP23LnM+JcHcA5yAZeLvBGHvLGFvDGLOXiyWcKo2VlRWuX7+O33//HdWqVcPJkyfRqFEjnD59WtGmVVkCAwPRtWtXTJgwAfHx8ejWrRv8/PywYMECqKurK9o8ueLg4AAPDw98//33yMnJwaxZs9C/f3/5TDgqqp+C/r+fVQfAaADXIHFREwF4COBbAPpfOr88E/6/Tzg6z84PAI4BqFuc83mfsHLw5s0bcnV1FfqKhw4dStHR0Yo2SwplrPf4+Hh68eJFmQP5pKen0/Lly0lTU1NwJzx8+LBSRWUrT86ePStEsDMzM6PvvvuuxPGzIasAPpB4QMwH8BwSH+EMAKcA9C1JPvJKAFoA2ASgH4DOAGYBiAEQDsDkS+dzEVYeRCIR7dy5U1jLzsjIiI4dO6Y0QqDIeg8LC6MjR47Q8uXLaeTIkeTs7CwMJiEvMI2joyN9//33dODAAXr58iWJRKJi5X3hwgWytrYW8ho3bpxSxSMub3Jzc8nLy4t++uknqWD7y5cvL1E+nxNhRqXs52CMNc9rDU+WNKhJrVQZyRnGWEtIJpOsJ6IlheyfAmAKAJiamrY6fvx4ifJPTU1F9erVZWEqpxCioqKwadMm+Pj4AADat2+P2bNnw8jISKF2KaLeExMTcfToUZw/f75Q9yktLS0YGBggKirqk/7LatWqoXHjxnB0dESrVq1gZWUFxpiwPyIiAjt37sSDBw8AADY2NpgxYwaaNataHqcikQghISHw9fXF06dP8eTJE6SkpEgdo6qqikWLFqFLly7FztfV1dWHiBwL3VmUOn8uAegCYD+AJEhaxAGlyae8EiSTTq5+6TjeElZOxGIx7d69m2rUqEEASF9fnw4cOKDQVnF51ntSUhItX75cmG2IvPX9Fi5cSHv37qW7d+9SRESEcD2Sk5Pp9u3btH79eho0aBDVrl37E7dNc3NzGjt2LB09epRWrlxJWlpaBIBq1KhBW7durTLLVSUkJNB///1HS5cupa5du0pd4/xkZWVFkydPphMnTlBMTAxduHChxOVAFt0RABwArAPwDpL+1gQAfwJoW9w8FJXyRPjKl47jIqzcvHv3jnr37i38OXr16vXFddfkRXnUe0ZGBm3evFmqq6F3796lWr49LCyMDh06RKNGjRLi+36chg8fThEREXL4JopHLBZTWFgYXbhwgVavXk2DBw8udPko5C0hNWrUKNq1axcFBwd/kle5BnUHUBPATADeecKbA+ASgGEAND93rrIkAI55tq/60rFchJUfsVhMBw8eJAMDA0LeQqO//PJLubfc5F3vV65cEZaNAkDt27enu3fvyiTvxMREmjZtmrDUT36qXr06DR8+nM6ePUvp6ekyKau8EYlEFBoaSleuXKGtW7fSt99+Sy4uLsL6ch8nDQ0NateuHc2dO5fOnj1LkZGRXyyj3EQYwEUA2XndDc8BzAFQq6jjlSEBOApgDSRudV3ybI7La70bf+l8LsIVh6ioKBo+fLjwZ2rRogV5eXmVW/nyqvfk5GSaMmWK8L2aNm1Kly5dkknXS3JyMv38889kaGgo5N+pUydavXo1tW7dulBBPnToEIWFhcngm8mOxMREevr0Kf3zzz+0ZcsWmjlzJvXv35+aNm36yY2lYNLX1ycXFxeaPXs2HTx4kJ4/f16qlZfLU4RjAGwF0KKoY5QtAViYd8NIymu1vwewG4BZcc7nIlzxuHz5MllaWhLyFhqdNWsWpaSkyL1cedT77du3ycrKSmihrVu3TiYt/LS0NFq/fr1Ut0bHjh3p1q1bUuL+5s0b2rBhAzk6On4iYPXr16fvv/+ezpw5Q/Hx8WW26WNEIhHFxcXRy5cv6fbt23TixAnatm0bzZ8/n0aNGkWurq5kb29faJ/tx6lWrVrUuXNnmjp1Km3ZsoX+++8/Cg0NLdWNTCwWU0xMDN28eZN++ukn6tSpExkYGJCnp2eJ8vmcCBfpHcEYU6OPAvZUdhwdHcnbu2ST69zc3ODi4iIfgzjFIi0tDStWrMCvv/4KsViM2rVrY+PGjfjmm2+kPABkiSzrPT09HQsXLsRvv/0GAGjRogUOHTqExo0blynf3Nxc7Nu3DytWrEBkZCQAiXfJypUr0aVLl89emzdv3uCff/7BzZs3cffuXaSmpgr7GGOwsrJC7dq1UadOHdSuXVtIBgYGyMnJQVZWFrKyspCdnY2srCxkZmYiISEBCQkJiI+Pl0qxsbGIjY2FSCQq1vfS1taGlZUVrKysYG1tDWtra+G9ra0t9PX1S33NUlNTcePGDZw/fx4PHz7E27dvkZmZ+clxCxYswLp164qdL2Os7N4RACwgCVfpDeANgMZ522cBcC5uPsqceEu4YuPj40OtWrUSWkRt27alR48eyaUsWdX73bt3yc7OjgCQmpoarVixolSPyAURi8V0+vRpsre3F65Fq1at6Nq1a6VqDWZnZ5O7uzutWrWKOnfuTBoaGl9sjZYm6evrk729PXXo0IEGDRpE3333Ha1Zs4b27dtHV69eJT8/P0pISJC5V0xQUBBt27aNOnbsSKqqqp+1z8nJiQYOHEi+vr4lKgOfaQkXy7eXMdYIwD38/2y5FgA08nZbAnACMKI4eXE48qJly5bw9PTEwYMHsWjRIjx8+BBOTk4YM2YM1q5dCwsLC0WbKPDhwwfMnz8f+/btAwA0btwYBw8eRMuWLcuU7+3bt7FgwQI8evQIAFCvXj38/PPPGDJkSKmXGFJXV0e7du3Qrl07LF26FJmZmXj//j3CwsKElP85ISEBmpqahSYDAwMYGBjA0NAQhoaGwueaNWuiZs2acg8ElJubi+DgYLx48UJIDx8+xLt37z45ljGGhg0bwtXVFT179kT79u1hYGAAQPIUVNanlIIUd4LFZgCvAPQEkAnJgF0+DwBskJlFHE4ZUFVVxYQJEzBkyBCsXbsWW7ZswaFDh3D69GksXLgQM2fORI0aNRRmHxHh8OHDmDNnDuLi4qChoYFFixZhwYIFZRKh+/fvY8WKFbh58yYAwNTUFMuXL8ekSZNKFechNTUVQUFBCA8PR2RkpJCioqIQFRWF7OxsqKmpQV1dXerV1NQU5ubmMDc3h4WFhfDe3Nwcurq6cuseKmh3aGjoJ+n169fw9/dHdnZ2kedqaWmhR48eGDZsGHr37g1DQ0O52ppPcUW4A4DhRJTKGFP9aF80gFqyNYvDKRu6urpYv349Jk+ejPnz5+Ps2bNYunQpNm/ejO+++w4zZsxArVrl+7MNDAzEd999h1u3bgEAXF1d8ccff6B+/fqlztPd3R0rVqzAjRs3AEi+97x58zBr1qxizehLSEiAr68vXr16JZXev39fapuKQlNTEzVr1oSJiYnQ+jUxMYGuri60tLSkkra2NlRVVZGdnS30K+e/z8zMRHx8POLi4j5JSUlJn7VBR0cHmZmZEIvFAABDQ0MMGzYMAwcOROfOnRUSlrO4Iiz+zD5jSGJIcDhKh62tLc6cOYPbt29j2bJluH//PtatW4fNmzdjzJgxmDt3bplEsDi8ffsWO3fuxLZt25CdnQ0jIyP8+uuvGD16dKlbhoWJ76xZszBr1izhsflj4uPj4ePjI5WKWupdXV0ddnZ2qF27NszMzD5JWlpayMnJQW5uLnJzc4X3KSkpiIyMRHh4OCIiIhARESG8T0tLE7ov5IWmpqYwaGdlZQVDQ0O8ffsW9+/fx7t375Ceng7GGHr27IkpU6agX79+Co8IV1wRfgRgPIALhewbBsBdZhZxSkVycjIiIyMRGxuL6OhoYSQ6MTERKSkpSE5ORkpKCjIyMoQWRXZ2NnJycoQESPrCVFRUwBgTBEJTUxPVqlUTkq6uLnR1dVGzZk3Y2NjAzs4O9vb2Sh1Dw9XVFffu3YOHhwd++eUXnDt3Dn/99Rf27t2L/v37Y9KkSXB1dUW1atVkUh4R4ebNm9ixYwcuXLggtLwmTJiAjRs3lir2BRHh2rVr2Lhxo9CarlGjhiC+BR+fc3Nz4efnhwcPHuDBgwd4+PAh3rx580meWlpaaNKkCRo2bAgHBwchWVtbQ01NtuFg0tPTBU+ImJgY4TU1NRWZmZlCysjIQGZmJnJzc6GhoQFNTU1oaGgISVNTE4aGhjA2NpZKRkZGMDAwQGZmJv755x8cOnQIe/bsEa69mZkZJk6ciIkTJ8LKykqm360sFPcqr4YkpvA1SEJDEoBujLGZAAYC6CQn+yoNYrEY6enpSE5OFsQxOTkZycnJSEpKQkpKChITE5GUlISkpCQkJycjNTUVqampSEtLQ3p6uvDjzBfP3NxciMXifO8VhcMYg5qaGrS1tWFkZITatWujXr16aNq0KVq3bo3WrVtDQ0PjyxnJkTZt2uDMmTMIDAzE5s2bcfDgQZw/fx7nz5+HhoYGOnbsiJ49e6JXr15o3LhxiVuqKSkpOHjwIHbu3Al/f38Aklbl8OHDMXPmTLRu3brENufk5OD48ePYtGkTnj9/DuBT8U1JScHVq1dx//59PHjwAI8ePZJyKwMkrl3NmjVDq1athNSwYUOZi21R6OjowNLSEpaWljLPWyQS4f79+zh06BBOnTolBN1RV1fHgAEDMHbsWHz11Vfl9l1LQrGjqDHG+kAyecO2wOZQAD8Q0X8yt0wBlMRP+KeffsKWLVsgFouFP2q+y0n++4Kv5UF+K1ZNTU0YLMlvOeT3teV/zm9d5L/mP5LlfweRSAQiglgsRkZGBtLT05GWlia0VLKysoQbQ3Z2ttDa+BIaGhowNjaGra0tmjdvjk6dOqFbt25l8u0sC9HR0dizZw8uXboET09PqfoyNzdH+/btUatWLZiamsLU1BQmJiYwNTXFy5cvYWpqitevXyMoKEh4DQ0NFfxdzc3N8d1332Hy5MkwNTUtsW0pKSnYs2cPtmzZIjzC16pVC7NmzcLgwYPh6+uLe/fu4e7du3jy5MkndWBjY4N27dqhbdu2aNeuHRo3bqyUIlRaRCIR3N3dcfLkSZw5cwZRUVHCPmdnZ4wZMwZff/21zCPulcZH/HN+wiUOZckYqwfABMAHIgoo0clKTklEeMqUKdizZ0+pyskXSxUVFaiqqkJVVVVKMLW1taGtrS08/teoUQN6enrQ19eHoaEhjIyMULNmTRgbG8PU1BRmZmbQ1dUttQuSLMjNzUVISAgCAgIQEBAAPz8/BAUFISwsDB8+fEBaWtpnhVpDQwO1atVCw4YN0alTJwwYMAAODg7l+A0kbmM3btzAlStXcOXKFak/dXFhjKFjx46YNm0aBgwYUKr+Rl9fX+zatQuHDx9GcnIyAMDOzg6urq4gIri7u+Ply5dS56iqqqJVq1bo2LEj2rdvj7Zt25b7wGN5kJubiwcPHuDUqVM4ffq0VB1ZW1vjm2++wZgxY9CgQQO52aBwEa7MlESE3717J/gatmzZEmpqalBVVRVetbS0BBHV0dGBjo6OQkVSGYiLi8P169dx7949PHv2DG/evMGHDx+KXFpcRUUFxsbGcHBwQMeOHTFw4MAy+9EWFyKCr68vfH19ERMTg5iYGERHRwvvo6KiYG9vDzs7O9jZ2aFevXqws7ODtbU1tLS0SlxeRkYGTp06hV27dgkxfQEILejo6Gip47W0tNCmTRt06tQJHTt2RJs2bZS6T74sxMfH48qVK7h06RKuXLmC+Ph4YZ+1tTWGDRuGoUOHomXLlnJ3gQNkL8KfmyE3qKh9nznHDECbkp6nLInPmFMMCQkJdPjwYRo7diw1adJEiBtcWFJRUSETExNycXGhpUuXko+PT7FXjZAlsqh3sVhMnp6eNGPGDNLV1RW+I2Psk+9do0YN6t27N61bt47c3d0pKyur7F9CSRGJRPT48WNat24ddejQgVRUVKSuRb169einn34ib29vhcSUlnUAn891EG1njC2DJGbwSSKKL+pAxlhHSNahGwlgNgCPYt0eOBwA+vr6GDVqFEaNGiVsy87Oxu3bt3Hp0iU8fPgQQUFBSExMhFgsFlqjbm5uWL16NRhjMDIygr29Pdq1a4fevXujU6dOStn/mZOTg5s3b2LPnj24ceOG0N1QECJCzZo10aFDB3Ts2BGdO3dG06ZNlfL7yAIiwosXL3Dr1i3cvn0bd+7cQUJCgrBfTU0Nrq6u6NOnD/r06QN7+8q11vDnatUOwFwAqyAR5FcAngGIBZAFwACADSTxevUA3AXQnYgeFJ4dh1N8NDQ00LNnT/Ts2VPYlpubi9u3b+PChQt4+PAhgoODkZiYCCISnPUfPHiATZs2AZAs6WNubo6GDRuibdu26NWrF5o0aVKu3UJEhOfPn+PEiRO4fPkyXrx4gdzcT+NiWVhYoFu3bujYsSM6dOgAe3v7cnm0VgRpaWnw8fGBp6cnPD09cffuXcTGxkodU7duXXTt2hV9+vRB9+7doaurqyBr5c8X+4QZYxqQuKH1BNAGgDkALUhWMvaHRHxPEJG/fE2VPzyKWsVDLBbj/v37gjAHBAQgPj7+s4OAWlpaMDQ0hIWFBezt7dGsWTM0bNgQ9evXh7W1NVRVP54U+imF1TsRISYmBhcvXsSlS5fg4+OD8PDwQqODGRkZwcXFBYMHD0anTp2UKq6FLElPT8fLly/x7NkzPHr0CJ6envDz8/vkmpibm8PV1VVI1tbWSnsTknWf8Befb4goG8CJvMThKBUqKipwdnZGnTp10K9fP7x//x7R0dEIDAyEr68v3r17h/j4eKmpqpmZmcJsLi8vLxw9erTQfPMHWgsmdXV1aGpqCjEI0tPTkZmZKfhtF4Wuri4aNWqE4cOH45tvvkHNmjXlc0EURHJysuAd4+fnB19fX/j5+SE4OPgTN01VVVU0b94czs7OcHZ2Rvv27WFnZ6e0oitvKmcnE6dSkZmZibdv3+LNmzdCCgkJwbt37xAWFvaJ54AsEIvFEIvFRXpulJTk5GQ8fPgQfn5+2Lx5sxBNrGBUsXz3w4Kv+ZHGtLW1FSZSWVlZiI6OFoL3REVFfVIfcXFxhZ6rpqaGBg0aCCs9Ozs7o2XLltDR0Snnb6G8cBHmKAXp6ekIDg6Wmvzw+vVrBAcHIzw8/LOTXlRVVWFubi4EGTczM4ORkdEnSV9fH5qamp+0blVUVJCZmYmUlBRERETgxYsXCAwMxLt37xAXFyc1WzE/kExaWhp0dXWlpnPr6OhAU1MTOTk5wmzHlJQU4bVgevv2bYmuj7q6OvT19WFgYAB9ff1Pyi5oQ35Es49T/k0lv9We/z7/u+fP4MxPiYmJiI6ORmJi4hft09LSgo2NDWxtbdG4cWM0adIEjRs3Rv369RU+S1LZ4SLMKTeys7MREhKCwMBAvH79Wur1c0FdVFVVYWlpCWtra9jY2MDGxgbW1tawtLREnTp1UKtWrWL1434OLS0t6Ovro06dOnB2dv7i8aXpFxSLxcK09fwVJgquNPHhwwfhNT8lJiYiMTERmZmZQtyF8iY/RGXBmYN169YVRNfGxgampqZV3g++tHAR5siU3NxcIX7rxyk0NLTIATN1dXXY2NgIkx4KvtatW7dSuGepqKhAX18f+vr6sLa2LtG5mZmZSEpKkoo7kpaWVmjKj2wmEomkopypqKhAXV1dKgZwfh93flCmj5OpqSkMDQ25wMqRiv/L5pQ76enpCA0NRXBwMIKCgoTXoKAgvH37tsgBKhUVFVhbWwszzQq+VhahlRf5sT9KE4OCo9zwXz3nE7KysvD+/Xu8ffsWb9++RUhICEJCQoQBsS/FVKhdu7aUyOYnGxsbhQTN5nCUmeKuMfcAwB+QzJzLkq9JHHmSm5uLqKgohIeHf7JGWL7oRkVFfXYgTF1dXVjdtl69ekKytbWFtbU1tLW1y/EbcTgVm+K2hLMBHASwlTF2EMDuyjA5o7IgFoullg6PjY1FVFSUsCZYwdfo6Ogvhp1UVVWFhYWFEPs1f0As/9Xc3LzMA2EcDkdCsUSYiFwYYw0ATAEwBsBMxtg9SFrHZ4lINs6UVZT8mL357kv5LkL57xMTE4scUY+NjcWHDx+KHc+XMYZatWqhdu3aqF27NiwsLIT3+aJrbm7O+2c5nHKi2P+0vJbvj4yxhZAsaTQFklU24hhj+yFpHX+6fkol5cGDB9i3bx/Cw8Nx4MABwbk/P+Xm5gorYBRcTqhgMPT09HRhxlVZ0dfXFxZPrFmzJmrVqgUzM7NPXk1NTbnfJoejRJS4uZPXJ3yYMfYCwK+QLG00H8Bcxtg5ANOJqOTRsCsYQUFB2Lt3r8zy09LSQo0aNQTXoILv9fT0hJlTBWdRGRoaCsHdFb1YIYfDKR0lEmHGmDaA4QC+BdAKQACAmQBOAegHYAWAowC6ytRKJaRt27bYs2cPAgMD0bBhQ2GljPxFMvNXyshfOqjgQoX5Qd51dHSgra0NLS0t7ofJ4VRRiusd0QTAVEjiBVcDcB7AT0R0u8BhexhjUZAIcqUn3+2KR1HjcDhlobgt4WcAIiBZ6HM3EUUWcVwQgIcysIvD4XCqBMUV4SEAzhPRp4FRC0BErwC4ltkqDofDqSIU10XtrLwN4XA4nKpIcfuEl31mtxhAEoDHROQuE6s4HA6nilDc7ogVkKx0WlhU6fztxBh7CKAPESXJxjwOh8Op3BTXL8oBkkG3OQAsIVljzhLAvLzt7QB8nXfcWtmbyeFwOJWT4orwTgB7iWgLEb0nouy8180A9gL4mYhOA9gAoL+8jC0OjLE6jLHTjLEkxlgyY+wsY6yuIm3icDicoiiuCLcF4FPEvseQrMIMAN4ATMpqVGlhjOkAuAWgAYCxAEYDsANwmzFWTVF2cTgcTlEUt084CZJZcDcL2dctbz8g6aZIloFdpWUyABsA9YkoCAAYY88BvIZkssmvCrSNw+FwPqG4IrwPwELGWA0ApwHEQNLiHQrJFOZ1ecc5A/CTtZEloD8Aj3wBBgAiCmGMuQP4H7gIczgcJaO4IpzvojYTwPd57xmANEgEOH//JQAnZGZdyWkEyZTqj3kByQ2Dw/kEsViMxMREvHv3DhEREYiIiEB0dDRiYmKQnJwsRL9LSUlBUlISkpKSkJiYKKzuXKdOHRgbG8PY2FhYur5mzZowMTGBsbExj1rH+SzFnawhBrCEMbYJQBMAZgAiAfgSUWKB4x7Jw8gSYAggoZDt8QAMCjuBMTYFkrCcMDU1hZubW4kKTE1NLfE5nPIjNjYWr169QnBwMMLCwoQVjFNSUpCeno7s7Oxix2L+mKioKHh7e3/xuGrVqkFfXx9GRkYwMzODmZkZzM3NhfeGhoZgrDDvT44yIuv//BdFmDGmASAKwDgi+hfAPZmVrgQQ0W4AuwHA0dGRShqMhwfwUSxRUVFwd3eHt7c3Xr58iZCQEERHRyM5ObnEcZoZY1BVVQURQST6dIa+qqoqtLS0oK2tDSJCdnY20tLSviji+asgh4eH4/nz55/s19HRgYODA5o0aYLGjRsLr2ZmZlyclRBZ/+e/KMJElM0YywVQ9sjj8icBhbd4i2ohcyoAISEhuHv3Lh49eoRXr17h7du3iImJQVpa2mfXwstHQ0MDNWrUgJGREUxNTWFubo46derAxsYG9evXh4GBAS5duoR9+/YhJCQEgESQu3Xrhq+//hoODg6ws7ODsbGxIIr5f0QiQkREBJ48eYLHjx/Dzc0Nt29LggvmhzYtuPq0hoYG6tWrB2NjY6SnpyMkJAQfPnyAj48PfHykHZAMDQ3RokULODk5oXXr1nBycoKFhYWsLitHSShun/A/kATxuSY/U2TCC0j6hT+mIYCX5WwLpwS8e/cObm5u8PLywosXLxAaGoqYmBikp6d/UWg1NDSgp6eHWrVqCcLatGlTODk5wdbWtshYzTExMVi1ahV27dolCGXdunUxfvx4jB8/HpaWll+0mzEGCwsLWFhYoG/fvli2bBkeP36MVatW4fz58xCLxVBXV4eTkxOysrKEFjsAGBsb4+uvv0a/fv1QrVo1+Pn5wdfXV3iNj4/HzZs3cfPm/zslmZubo3Xr1nB2dkanTp3g6OjIV7Cu6BDRFxOAgQDeQ+IZMQoSd7UuBVNx8pF3AjALQC4AmwLbrADkAJjzpfNbtWpFJeX27dslPqeq8vbtWzp8+DBNnz6dunTpQjY2NlS9enVijBEk09+LTFpaWmRhYUHOzs40duxY2rp1K3l5eVFOTk6J7UhJSaEVK1ZQ9erVCQCpqKjQkCFD6OrVq5Sbm1usPIpT70+ePKFBgwYJ30FbW5sWL15Mq1atIgcHB6nv17hxY9q9ezelpaUREZFYLKb379/TuXPnaNGiRdStWzfS09Mr9Lp07tyZli5dStevX6fU1NQSXw9OySjNfx6ANxWlW0XtIGlxExeRRPmvxclH3gmSgPNBAHwhcUnrD0ks5DcAqn/pfC7CZSMnJ4e8vLxo+/btNHHiROrQoQNZWlpStWrVii205ubmUkLr4+NDIpFIJvZlZ2fTzp07ycTERCizb9++5OvrW+K8SlLvz58/lxLjNm3akJ+fHz158oTmzp1Lpqamwj4DAwOaN28ehYSEfJKPSCSigIAAOnz4MH333XfUuHHjT66hmpoatW/fnlauXEkPHjwo1U2K83kUJcKdv5SKk095JAB1AZyBZNJICiRdKVbFOZeL8OcRiUT07Nkz2rdvH82ePZu++uoratSoERkZGZG6uvoXRTZfaM3MzMjJyYlGjx5NW7ZsoUePHsldLC5evEh2dnaCHc7OznTnzp1S51eaev/333/J3NycAJCGhgb9/PPPlJ2dTVlZWXT06FFydnYW7FNRUaEBAwbQnTt3SCwWF5lnXFwc/fPPP/Tjjz+So6MjqaqqSl1vPT09GjBgAO3cuZOCg4NL/X05/49CRLiqpKoswiKRiIKCgujUqVO0YsUKGjlyJHXq1Ins7OzIwMCg2CLLGKNq1aqRpaUldejQgSZOnEjbt2+XaYu2JISHh9OQIUME++zs7Oj06dOfFbbiUNp6T0hIoEmTJgn2NG/enB4/fizs9/T0pFGjRkld73bt2tG///5brOuXmJhI586do++//17qppOfHBwcaN68eXTnzh3eSi4lChVhAMYA+kISl8Ewb5sWAJWS5KOsqTKKcEJCAnl4eNDhw4dp9erVNHHiROrRowc1bdqULCwsqEaNGqSmplYsgc0XWW1tbTIzM6PmzZvToEGDaMmSJXT27FmKjIxU9NcVyM3NpZ07d5Kuri4BIB0dHdq8eTNlZ2fLJP+y1vv169fJysqKAJCqqiqtWrVKqj86MjKSli1bRoaGhlL9xocPHy6ReIaGhtKePXto6NChn/QpGxgY0IgRI+jYsWOUlJRUpu9TlZC1CDPJ/s/DJH45GwFMB6CRV4mtiegxY+wqgPtEtPqLGSk5jo6OVBzn+4KUh5+wWCxGXFwcwsLCEBERgaioKGFGV0xMDGJjY5GQkIDExESkpqYiPT0dWVlZyMnJKXFZmpqaqF69OgwNDWFmZoY6deqgQYMGaN68ORwdHVGrVi05fEPZ8vz5c0yZMgWenp4AgL59+2LHjh3F8nYoLrKo99TUVCxevBi//fYbAKBz5844fPgw6tSpI3XMnj17sHnzZoSHhwMArKysMG/ePEyYMAFaWlrFLi8nJwfu7u64ePEiLly4gMDAQGGfhoYGunfvjsGDB6N///4wMjIq03erzJSm7hljPkTkWOi+YorwIgBLAawGcB2AJwDHPBGeBmA0ETmXyColpCQi/PjxY1y9ehVBQUGoW7cuiCQO/vkpJycHWVlZyM7OlkpZWVnIzMxERkaG8D5/e37KyclBTk4ORCIRxGIxilNHn0NFRQUaGhrQ0dGBnp4ejI2NYW5ujrp168LW1hYNGjRAkyZNYG5uXqZyFE1mZiZWrlyJX375BSKRCObm5ti+fTsGDhwo80kPsrz5Xr9+HWPGjEFUVBQMDAzw119/YdCgQVLHZGVl4ejRo9iwYYMgnubm5vjpp58wefJkaGtrl7jcwMBAXLx4EefPn8e9e/eE35mqqipcXV0xaNAgDB48GCYmCguMqJTIWoSL2w3xBsDCvPeqkHhEtMz73AtAXHHyUfZUku6IiRMnFvsRXlZJRUWF1NXVqVq1amRoaEgWFhbk4OBAbdu2pb59+9L48eNp0aJFtHPnTrpy5Qq9efNGIf2wiuDRo0eC2xdjjKZNmybXR2xZd0NFR0dTnz59hLqeMmWK4K5WkNzcXDp16hQ1a9ZMONbU1JQ2b95cJve0qKgo+vPPP6l79+5Sg3uqqqrUs2dPOnDgAO+yyENR3RFZAHoR0W3GmCokfrf5LeEuAC4RUclvxUpGSVrC69evxy+//ILc3FxoaGiAMQbGmDAxQFVVFaqqqlBTUxNe1dTUoK6uLkx91dLSgo6OjpD09fVhYGAAQ0NDISCMiYkJTE1NoaurK8+vXmHJysrCqlWrsGHDBohEItSvXx/79+9H27Zt5VquPLqhiAjbt2/HvHnzkJ2djQYNGuD48eNo1qxZocf++++/WLVqFR4/fgwAqFmzJubOnYvvv/8e1atXL7Ud8fHx+Pfff3Hq1Clcu3ZNmMiiqamJPn36YPjw4ejTp0+pWt+VAUW2hKdT4S3h2QBeFicfZU+VcWCuMuPt7S34yjLGaM6cOZSenl4uZcuz3p8+fSq06jU1NemPP/4o0ptDLBbTxYsXqXXr1kLr1djYmNavX08pKSlltiU2Npb+/PNP6ty5s5Svt66uLk2aNInu3r1bZk+Tioai/IQ3AIgF0L6ACLcAYA8gDMCy4uSj7ImLcMUgKyuLli5dKjw229nZ0f3798vVBnnXe1paGk2ePFkQvWHDhn22O0AsFtOVK1eoTZs2wjlGRka0bt06Sk5OlolNYWFhtHnzZmrVqpVUN5m1tTUtX76cgoKCZFKOsqMoEdaGJHqaKK9VLIZkZloWgNsANIqTj7InLsLKj5+fH7Vo0UJo/c6aNavQvlN5U171fuzYMWF6ta2tLXl7e3/2eLFYTFevXqW2bdsKImloaEhr166VmRgTEb148YIWLFhAtWvXlhLk9u3b0969e2ValrKhMD/hvBbwaABHIAnk8zck/sJqxc1D2RMXYeVFJBLR5s2bSVNTU2h9lWXGW1kpz3oPCAig5s2bE/Jm2v32229f7AIQi8V07do1ateunZQYr169mhITE2VmW25uLt24cYPGjBlD1apVE8qqVq0ajRs3rlJ2V/AZc1yEqxyhoaHk4uIi/MEnTZqk8JZWedd7RkYGff/998I1GDRoECUkJHzxPLFYTNevX6f27dsL5+rr69Py5cspPj5epjampKTQ/v37qWPHjlKtYzs7O1q7di2Fh4fLtDxFwUWYi3CVQSwW04EDB4RZbyYmJvTvv/8q2iwiUly9nzp1SrgeVlZW5OnpWazzxGIx3bp1izp37iw1uLZkyRKKi4uTuZ0BAQG0cOFCMjMzk3J369+/P/37778Vesq0ovqENQAsB+APID2vb7hgyi1OPsqeuAgrDzExMTRw4EDhDzxw4ECKiYlRtFkCiqz34OBgcnR0JEASNW3z5s0leuS/c+cOdevWTarrYO7cuRQRESFzW3NycujSpUs0cOBAqenx5ubmtHjxYnrz5o3My5Q3ihLhbZDE6b0AYG2eIEul4uSj7ImLsHJw8eJFIbxjjRo16MCBA0rXr6joes/MzKSZM2cKotavXz/68OFDifJwd3ennj17CnloaGjQt99+K7doa1FRUbRx40ayt7eX6q7o1q0bHT9+nDIzM+VSrqxRlAiHA1hcnGMrcuIirFhSU1Pp22+/Ff6cnTp1otDQUEWbVSjKUu/nzp0jfX19AkB16tQhd3f3Eufh7e0tFe9YVVWVRo0aRX5+fnKwWNI1cufOHRo9ejRpaWlJudTNnj2bXrx4IZdyZYWiRDgJSrJ6hjwTF2HF4eHhIYRe1NDQoF9++aXYq1woAmWq99DQUCEWsaqqKq1fv75U09VfvHhBY8aMkZq23Ldv3y/GNC4LCQkJtGPHDqlp2IAkfOf+/fuVcqUQRYnwEQArinNsRU5chMuf7OxsWr58ufDHb9y4MT179kzRZn0RZav37Oxsmjt3riBi3bt3L3Vo0ZCQEPr+++8Fd0AA1Lp1azpx4oTcBtTEYjF5eXnRlClTBL/o/O6oKVOmkKenp9J0SSlKhJ0BBABYBsARgM3HqTj5KHviIly++Pv7CwNMjDGaO3cuZWRkKNqsYqGs9X7p0iUyNjYWvEmuXr1a6ryio6Np2bJlZGRkJIiilZUVbdu2TSZToosiJSWF9u7dK+XjnH+D3rp1q1y8OUqCMqwx97FnhAhKssZcWRMX4fJBLBbT9u3bSVtbW+jLvHXrlqLNKhHKXO/h4eHk6uoqiNf8+fPLFMw+LS2Nfv/9d6pXr56Qp56eHs2aNYsCAwNlaPmnvHjxgubMmUM1a9aUGkAcMmQIXbx4USGubooS4XGQzI4rMhUnH2VPXITlT3h4OPXo0UP4Q40ZM0amM7jKC2Wv99zcXFqzZo3QzePk5FRmr4fc3Fw6e/as1MQPANS7d2+6dOmSXMOmZmVl0ZkzZ6h3796koqIilF2rVi2aO3eu3AYRC4NP1uAiXGE5ceIEGRgYCCPhp0+fVrRJpaai1Pv9+/epTp06wuSMI0eOyCRfHx8fGj9+vFS/sa2tLW3evJliY2NlUkZRvH//ntatW0f169eXuhk4OjrSb7/9RtHR0XItX+lEGIAK8tabq+iJi7B8+PDhA33zzTfCn+Wrr76Sy8SA8qQi1fuHDx+kXNBGjBghs6eP2NhYWr9+PdWtW1equ2Do0KF09epVubaOxWIxPXz4kKZOnSq1fp6qqir17t2bjhw5IhfvinITYQDxyIsZnPeZAfj340G4vEE73ifMKZTLly8LU1erVav22di4FYmKVu9isZj27NlDOjo6BIAsLS1lGv4zNzeXzp0790l3Qd26dWn58uVy9/dOT0+nv//+m/r27Ss1M09HR4dGjhxJly5doqysLJmUVZ4iLAbgVOCzVDD3Atu5CHM+ITk5maZMmSL8Gdq3b1+p4s1W1HoPCAgQ4gGrqKjQsmXLZD649e7dO1q1apWwmnS+90vnzp3pjz/+kPv089jYWNq5c+cn3hUGBgY0btw4unz5cpkEmYswF2Gl5+7du2RtbS08mm7cuFGpJ16Uhopc71lZWbRgwQJhpYy2bdvS69evZV6OSCSiGzdu0PDhw6X6jguuWyfvQdng4GBavXo1NWrUSEqQ9fX1ady4cXTp0qUST5fmIsxFWGlJT0+nH3/8Ufhzt2jRgnx9fRVtllyoDPV+69YtsrCwEB7b5dlVlJiYSAcPHqTevXtLzcjT0NCgvn370p9//knv37+XS9n5vHz5klauXCksiZWfqlevTkOGDKGDBw8Wa1CRizAXYaXkwYMHQmAWVVVVWrJkicz64JSRylLv8fHxNGLECCl3M3kPmuavW+fi4iK1bh0AatasGS1evJgePHgg16enV69e0apVq6hp06ZS5auoqFDHjh3pl19+oZcvXxZ6UypvER6I/58VZ5e3rR+kZ8sN5iJcdUlPT6e5c+cKgzENGzakR48eKdosuVPZ6r2g+6ChoSGdOHGiXMqNiIigv/76iwYMGCC1Mke+Hf3796dffvmFPDw8yjTh5HOEhobS9u3bqXv37qSuri5lQ+3atWn8+PH0999/C33Z5S3CH8+MK3JbUflUpMRFuGR4eHhQgwYNhBbEggULKsy047JSGes9PDycevXqJQjQ8OHDSxwesyxkZmbS1atXafr06cKYQsGko6NDXbp0oeXLl9M///xDQUFBMneBS0pKopMnT9KoUaPIxMTkExtq165N1tbWdPfu3RLl+zkRZpL9n8IYG1vojiIgooMlOV4ZcXR0JG9v7xKd4+bmBhcXF/kYpKRkZGRg5cqV+OWXXyAWi9GgQQMcOHAAzs7Oijat3Kis9U5E2LVrF+bMmYP09HSYmZnhzz//RP/+/cvdjpCQENy7dw/37t3D/fv3ERAQ8MlxOjo6aNiwIZo0aYLGjRvD1tYWtWrVgpmZGUxNTaGpqVmiMhMSEhAVFYWoqCj4+vri5s2bePToEaKjo6WOXbZsGVauXFnsvBljPkTkWOi+okS4KsJF+Mvcu3cPkyZNQmBgIFRUVDBnzhysWrUKWlpaijatXKns9f769WuMHz8e7u7uAICRI0di27ZtMDIyUphNMTExuH//Ph48eABfX1/4+fkhIiLis+cYGhrCzMwMRkZGUFVVhYqKipAYYyAifPjwAVFRUYiOjkZOTk6h+aiqqsLBwQHm5uaIi4vDkSNH4ODgUGzbuQgXEy7CRZOSkoKFCxdi586dAAAHBwfs27cPbdq0UbBliqEq1LtIJMKOHTuwcOFCZGRkwNTUFH/++ScGDBigaNME4uPj8eLFC/j5+cHX1xfv3r1DVFQUIiMjER0dDZFIVKL89PT0YGpqilq1asHW1hatWrWCo6MjmjZtCm1tbQClq/vPibBaiXLiVEmuXr2KKVOm4N27d1BTU8PChQuxePHiEj3qcSoeqqqqmDlzJvr06YOJEyfi7t27GDhwIL755hts374dxsbGijYRhoaG6NixIzp27PjJPrFYjLi4OERGRiIhIQFisfiTBABGRkYwNTWFqampILTlSlGdxVUx8YE5aeLi4mjs2LHCoESrVq3o6dOnijZLKajM9V4YIpGItm/fLkx7NjY2piNHjlSKKeglRdbeESrlL/scZYeIcOTIETRo0AAHDx6EpqYmNmzYAA8PDzRr1kzR5nEUgIqKCqZNmwZfX1906dIFcXFxGDVqFHr37o2QkBBFm1ehqVQizBgLZYxRIWmAom2rKAQFBaFHjx4YPXo04uLi4OLigufPn2P+/PlQU+O9V1UdGxsb3LhxA/v374eBgQGuXr2KRo0aYdOmTcjNzVW0eRWSSiXCeVwF0PajdEehFlUAsrOzsXbtWjRp0gQ3btyAoaEh9u/fj1u3bsHe3l7R5nGUCMYYxo0bB39/fwwfPhwZGRmYN28enJyc4OPjo2jzKhyVUYTjiMjjo5SgaKOUGXd3d7Rq1QqLFy9GZmYmRo8eDX9/f4wbNw6MMUWbx1FSTExMcOzYMVy+fBmWlpZ48uQJnJycMH36dCQmJiravApDZRRhTjGJjo7GuHHj0KFDB/j5+cHW1hbXr1/HoUOHULNmTUWbx6kg9O7dG35+fvjxxx/BGMOOHTvQoEEDHD58GMRdYL9IZRThfoyxdMZYFmPMg/cHf0pubi62b9+O+vXrCwNvS5cuha+vL7p166Zo8zgVkOrVq2Pz5s14/Pgx2rdvj+joaIwZMwYuLi7w8/NTtHlKTaWarMEY2w7AC0AIAFMA0wB0BjCaiI4Ucc4UAFMAwNTUtNXx48dLVGZqaiqqV69eFrPLFV9fX2zbtg3BwcEAAGdnZ0yfPh0WFhYKtqxiUdHqvTwRi8W4du0adu3ahcTERKioqGDIkCEYO3YsdHR0FG1emSlN3bu6uhY5WUPhvrlFJQDd8FHwjCKS22fyUIVElN8Xp8zK7CccHh5OY8aMEa6bpaUlnT9/vkr6ecqCilLviiQ+Pp6+++47IVxlrVq1aN++fXJdd648qEp+wg8AOBQjjSkqAyISATgFoDZjzEzeBisj6enpWL16Nezs7HDo0CFoaGhg6dKlePnyJfr3788H3jhyw8DAAL///jsePXoEZ2dnREVFYcKECXBycsL9+/cVbZ7SoLQiTETpRORfjPSuuFnK1WAlQywW4+jRo6hfvz6WLVuG9PR0DBo0CC9fvsSqVasqxWMhp2Lg6OiIBw8e4MiRI7CwsICPjw86duyIb775Bu/eFffvW3lRWhGWBYwxNQBfA3hHRFGKtqe8ePjwIdq2bYtRo0YhLCwMLVq0gJubG86cOQNbW1tFm8epgqioqGDkyJEICAjAsmXLoKWlhRMnTqB+/fpYunQpkpOTFW2iwqg0IswYG84YO84YG8MYc2WMfQPgNoCWAH5SsHnlwsuXLzFo0CC0a9cOjx49Qq1atbBv3z54eXmhc+fOijaPw0G1atWwcuVK+Pv74+uvv0ZmZibWrFmDevXqYceOHcjOzla0ieVOpRFhSDwiTAD8AuAagD8BZAHoRUQlc3moYISGhmLcuHFo0qQJzp07B21tbSxevFiICauqqqpoEzkcKSwtLXH8+HG4u7ujXbt2iI2NxfTp09GwYUOcPHmySvkXVxoRJsnMuC5EZEpE6kSkT0TdiOiqom2TFzExMZg5cybs7e1x8OBBqKio4Pvvv0dwcDDWrFnDXag4Sk+7du1w//59nDt3DvXr10dwcDC+/vprODs7w83NTdHmlQuVRoSrEtHR0ViwYAFsbGzw22+/ITc3FyNHjoS/vz927twJM7Mq6QjCqaAwxjBgwAD4+fnhzz//RK1ateDl5QVXV1f06NEDnp6eijZRrnARrkC8ffsW06dPh5WVFTZs2IC0tDT069cPz549w5EjR/igG6dCo6amhqlTp+L169dYuXIldHV1cf36dbRp0wb9+vXDkydPFG2iXOAiXAHw9/fH+PHjhcGLzMxMDBgwAJ6envj333/RpEkTRZvI4ciM6tWrY9myZQgJCcHChQuho6ODixcvomXLlhg8eHClmwbNRVhJISLcvHkTgwYNQsOGDXHgwAGIxWKMHDkSvr6+OHfuHJycnBRtJocjNwwNDbF27VqEhITgxx9/hJaWFs6ePYumTZti2LBhePr0qaJNlAlchJWMhIQEbN26FQ0aNEC3bt1w7tw5qKurY+rUqQgMDMSRI0fQuHFjRZvJ4ZQbJiYm2Lx5M4KDgzFt2jSoq6vj1KlTaNGiBfr16wcPDw9Fm1gmuAgrAUQELy8vTJw4ERYWFpg9ezYCAwNhYWGBlStXIjQ0FH/++Sfv8+VUaczNzbF9+3a8efMGs2fPhra2Ni5evIi2bduia9euuHXrVoV0beMirCCICI8ePcJPP/2EevXqwcnJCfv27UNGRga6d++Os2fPIjQ0FMuWLePeDhxOASwsLPDrr7/i7du3WLRoEXR1dXHr1i107doVbdu2xalTpyrUUktchMuR3NxcuLu748cff4SVlRWcnZ2xceNGvHnzBiYmJvjxxx8RGBiIa9euYeDAgXxNNw7nM9SsWRM///wz3r59i9WrV8PIyAienp4YNmwY7O3t8dtvvyE1NVXRZn4R/i+XE0SE9+/f49GjR/D09MSjR4/g4+ODtLQ04Rhzc3MMHjwYgwcPRocOHfjMNg6nFOjr62PJkiWYPXs2Dhw4gC1btiA4OBgzZ87E8uXLMXXqVKWOmV2pgrqXFUdHR/L29i7WsREREXj69Cnu378PExMTfPjwQUhxcXF4+fIloqI+jRlka2uL//3vfxgyZAicnZ2hosIfRioibm5ucHFxUbQZnEIQiUT4999/sXnzZri7uwOQ+CAPHjwYP/zwAzp06FCmEK6lqXvGWJFB3XlLuJRcvnwZkydP/uwxBgYGcHJygpOTE5ydneHk5MTXbuNw5IyqqioGDhyIgQMHwtPTE5s3b8bZs2dx4sQJnDhxAk2aNMEPP/yAkSNHKsXUfi7CpaRevXro2bMncnNz0bBhQxgZGcHIyAjGxsYwMjKClZUV6tWrx4OmczgKxNnZGSdPnkRYWBh27dqF3bt3w9fXF99++y3mz5+PcePGYcqUKWjUqJHijCxqyY2qmCrz8kYc2cLrvWKSlZVFx44do3bt2kktk9amTRvas2cPJScnfzGPqrS8EYfD4cgUDQ0NDB8+HO7u7njy5AmmTp0KXV1deHh4YPLkyTAzM8OECRPg7u5ebj7HXIQ5HE6VpHnz5vjzzz8RGRmJgwcPolOnTkhLS8P+/fvRoUMH1K9fHytWrMDr16/lagcXYQ6HU6XR0dHBmDFjcOfOHQQGBmLBggWoVauWEM3N3t4eTk5O2LZtG6KiomTeQuYizOFwOHnY2dlh3bp1eP/+Pa5evYoxY8agevXq8PLywqxZs2Bubo7evXvj8uXLMiuTizCHw+F8hJqaGnr06IFffvkFy5Ytg7W1NQCJI0NWVhbu3Lkju7JklhOHw+FUAnJycnD+/HkcPHgQ//33H0QiEQBAT08P/fv3R25uLn7++WeZlcdFmMPhcACEhYVhz5492LNnDyIjIwFIJn707dsXo0ePRr9+/aCtrQ03NzeZxnXhIszhcKosRIRbt27h999/x/nz54VWr4ODA6ZMmYIRI0bAxMRErjZwEeZwOFWO9PR0HDp0CNu2bYO/vz8AST/w0KFD8f3336Nz587lNtuVizCHw6kyREdHY+fOnfj999/x4cMHAJJohlOnTsWkSZNgbm5e7jZxEeZwOJWely9f4tdff8WRI0eQlZUFAGjdujXmzJmDwYMHKzR2NxdhDodTaXF3d8f69etx8eJFAABjDP/73/8wZ86cMoe0lBVchDkcTqWCiHDlyhWsW7cO9+7dAwBoaWlh/PjxmDVrFuzt7RVsoTRchDkcTqVAJBLh1KlTWL9+PZ49ewZAsurGtGnTMGPGDKWN5c1FmMPhVGiys7Nx6NAhbNiwAUFBQQCAWrVq4ccffxSipCkzXIQ5HE6FJD09HXv27MGmTZsQFhYGALCxscH8+fMxduxYaGlpKdjC4sFFmMPhVCiSkpLw+++/Y8uWLYiNjQUANGrUCIsWLcKwYcMq3CrlFctaDodTZYmNjcVvv/2G7du3IykpCYDEzWzx4sXo169fhV00l4swh8NRasLCwrBp0ybs3r0bGRkZAIDOnTtj8eLF6Natm1K4mZUFLsIcDkcpef36NTZu3IiDBw8iJycHANCnTx8sXLgQ7du3V7B1soOLMIfDUSoeP36MDRs24PTp0xCLxVBRUcHXX3+NBQsWoHnz5oo2T+ZUCBFmjP0IwBWAI4BaAFYS0Yoijh0AYDkABwDRAPYAWEdEIlnaFBYWhmfPniEoKAj6+vqoUaMGdHV1UaNGDWhqalb4RyQOpzwhIty8eRMbNmzAjRs3AADq6uqYMGEC5s+fDzs7OwVbKD8qhAgDmAwgGcA/AL4t6iDGWE8AZwDsBfAjgBYA1gKoAeAnWRp0+/ZtjBkzptB9ampqMDU1hZ2d3SfJ1ta2wrjOcDjyJjc3F2fOnMHGjRvx+PFjAED16tUxdepUzJo1C7Vr11awhfKnoohwIyISM8bU8BkRBrAewH0impL3+TZjrDqAJYyxLUQUJSuDTE1N0atXL4SFhYExhpSUFKSkpCA5ORk5OTkIDw9HeHg43NzcpM5TVVVFkyZN4OzsDCcnJzg5OcHBwQGqqqqyMo3DUXpSU1Oxf/9+bN26FW/evAEAmJiYYObMmfjuu+9gYGCgYAvLjwohwkQk/tIxjLE6AJoDmPLRrsMAVgLoDWC/rGzq0aMHevToATc3N7i4uEjty8rKQlhYGF6/fi2VgoKC8ObNGzx9+hRPnz7Frl27AEju/I6OjujQoQNcXV3Rtm1baGtry8pUDkdpCAsLw/bt27Fr1y7BzczW1hZz587F2LFjq+TvvkKIcDFplPfqV3AjEYUwxtIBNCwvQzQ1NWFrawtbW1v06tVLal9aWhoeP36MR48e4dGjR/D09MTbt2/h5uYGNzc3rFmzBpqammjTpg1cXV3h6uoKZ2dnaGpqlpf5HI7M8fHxwa+//oqTJ08iNzcXANChQwf8+OOP6N+/f5V+EmREpGgbik1ed0QOChmYY4yNAHAUgAMR+X+0LwzAVSKaWEieU5DXejY1NW11/PjxEtmUmpqK6tWrl+icj4mPj8fLly/x7NkzPH36FMHBwShYL1paWmjWrBkcHR3h6OgIS0tLPvCnYGRR75WdnJwc3L17F+fOncOLFy8AACoqKnBxccGQIUPg4OCgYAtLR2nq3tXV1YeIHAvdSUTlmgB0A0DFSG6FnKuWt29FIftG5O1rUMi+MAB7v2Rbq1atqKTcvn27xOd8iQ8fPtDZs2dpxowZ1Lhx40+ujYWFBY0fP57+/vtviouLk3n5nC8jj3qvLISFhdHSpUvJ1NRU+M3q6enR3Llz6e3bt4o2r8yUpu4BeFMRuqOI7ogHkLiPfYn0EuabkPdaWI++AYD4EuanMAwNDTFw4EAMHDgQABAZGYkbN27g2rVruHbtGsLDw7F//37s378fjDE4OTmhZ8+e6NWrF5ycnKr0ox1HMYjFYty5cwd//PEHzp49KyyY2bhxY0yfPh0jR45EtWrVFGylclLuIkxE6QD8v3hgyXmR99oIwMP8jYwxKwA6AF7KocxywczMDKNHj8bo0aMhFovh6+uLa9eu4erVq7h37x48PT3h6emJVatWwcDAAN26dUPPnj3Rs2fPKuHiw1EcUVFROHDgAP766y8EBwcDkHgADR06FNOmTUPHjh1519kXqDQDc0T0jjH2DMBIAH8V2DUKkn7k/xRimIxRUVFBs2bN0KxZM8ybNw9paWlwc3PDlStXcOXKFQQFBeHUqVM4deoUAKBhw4bo2bMnevTogc6dO1fJ0WeObBGJRLh69Sr27NmDCxcuCK3e2rVrY8KECZgyZQosLCwUbGXFoUKIMGPMEYAVgPwwSQ0ZY0Py3l/Oa10DwCIAFxljuwD8DclkjSUAtpEMfYSViWrVqqFPnz7o06cPACA4OBhXr17F1atXcevWLbx8+RIvX77Eli1boKmpiY4dO6J79+7o1q0bmjdvXmEjT3HKHz8/Pxw+fBhHjx5FeHg4AEmrd8CAAZg8eTJ69uzJu8JKQ1GdxcqUABxA0QN4Vh8dOwjAMwBZAN4BWAZAtTjlKMvAnKzIysoiNzc3WrhwIbVs2fKTa2dkZETDhg2j3bt3U0hIiKLNrVAoc73LkvDwcNq0aRM1a9ZM6rdja2tL69ato8jISEWbWO7IemCuQrmoyRtHR0fy9vYu0TmFTdZQVmJiYnDz5k3cuHED169fx/v376X2W1lZCb7Jrq6uvD/5M1Skei8pcXFx+Oeff3Dy5EncvHkTYrFkrpSBgQGGDRuG0aNHo127dlW2r7c0dc8YK9JFrUJ0R3Bkg4mJCYYPH47hw4eDiPD69WvcuHEDN27cwK1btxAaGip4XQBAvXr14Orqik6dOqFjx46wtLRU8DfgyIvo6GicO3cOp0+fhpubm9DPq6Ghgb59+2LUqFH46quv+KQhOcBFuIrCGIO9vT3s7e3x/fffQyQS4enTp3Bzc8Pt27dx9+5dBAUFISgoCHv27AEA1KlTBx06dEDHjh3RoUMHNGrUiPcpV2CCgoJw6dIl/PPPP7h7967Q4lVTU0OvXr0wePBgDBo0CIaGhgq2tHLDRZgDQDLA0qpVK7Rq1Qpz5sxBbm4uHj9+DDc3N9y7dw/u7u54//49/v77b/z9998AAD09PTg7O8PZ2Rlt2rSBs7MzjIyMFPxNOEWRnZ2Nu3fv4tKlS7h8+TICAwOFfRoaGujRoweGDBmC/v37V6kAOoqGizCnUNTU1IQob/Pnz4dYLMbLly9x//593Lt3D/fu3cP79++FCST52NnZwdnZWRD05s2bo0aNGgr8JlUXIsLLly9x69Yt3Lp1Czdu3EBqaqqwX19fH7169ULfvn3Rt29f6OnpKdDaqgsXYU6xUFFRQePGjdG4cWN8+60kmmh4eDg8PT3h4eEBDw8PeHt7CxHjjhw5AuD/uz1atmyJVq1aoVmzZmjSpAlMTU0V+XUqJfn9/Ldv3xZSTEyM1DFNmjQRXBrbtGlT4VYmrozwGuCUGgsLCwwaNAiDBg0CIAnY4uvri0ePHuHx48fw8fGBr68vAgICEBAQIHRjAEDNmjXRpEkTITVu3Bj169eHvr6+gr5NxSMpKQleXl7w8PAQboZxcXFSx5ibm8PV1RVdunRBt27dULduXQVZyykKLsIcmaGuro6WLVuiZcuWwrbs7Gz4+flJibKvry9iY2OFx+SCmJqaon79+mjQoAHq16+P+vXrw8bGBlZWVlV6tl90dDSeP38uJG9vb7x69Qofu5iamJigc+fO6NKlC1xdXWFvb19lXckqClyEOXJFQ0NDEOZJkyYBkDw2v3v3ThBkX19fvHr1CgEBAYiOjkZ0dDTu3r37SV5mZmawsbGBjY0NrK2tUbduXVhYWKB27dqwsLCAvr5+hRacnJwcvHv3TvBKef36NV68eIHnz59/0q0A/P9NL39gtE2bNrCysqrQ16AqwkWYU+4wxmBpaQlLS0v07dtX2C4WixEWFgZ/f38EBATA398fgYGBCAkJwdu3bxEZGYnIyEi4u7sXmq+Ojg4sLCxgbm4OExMT1KxZ85NXfX196OnpQV9fH7q6uuXmYpeZmYm4uDhEREQgIiICkZGRwvuwsDAEBwcjNDRU8M/9GF1dXTRt2lRIzZo1Q/Pmzfl6hZUALsIcpUFFRQV169ZF3bp10aNHD6l9ubm5CAsLQ0hICN68eYOQkBC8f/8e4eHhCAsLQ1hYGNLS0oSBweKiq6sLPT09VKtWDTo6OtDW1pZKmpqaUFVVhZqaGlRVVYUUERGB06dPIzs7Gzk5OULKzs5GamoqEhMTkZSUJLxmZ2cXy546deqgXr16qFevHmxtbdGwYUM0bdoUdevW5S3cSgoXYU6FQE1NDVZWVsLU6o8hIiQnJyMsLAxRUVGIjY1FTEyM1GtsbKyUMCYnJwtJ3mhoaMDQ0BDm5uYwNzeHmZmZ1KutrS2sra2rdL93VYWLMKdSwBiDnp4e9PT00KhRoy+fAElIxpSUFCQlJSEtLQ0ZGRlIT09HRkaGkLKysiASiZCbmwuRSCSkwMBAODg4QF1d/ZNUo0YNocsj/5V3G3CKgoswp8qiqqoKfX39UrnFVeYAPpzyhU/853A4HAXCRZjD4XAUCBdhDofDUSBchDkcDkeBcBHmcDgcBcJFmMPhcBQIF2EOh8NRIFyEORwOR4FwEeZwOBwFwkWYw+FwFAj7OCh0VYYxFgvgbQlPMwYQ98WjOJUNXu9Vl9LUvSUR1SxsBxfhMsIY8yYiR0XbwSlfeL1XXWRd97w7gsPhcBQIF2EOh8NRIFyEy85uRRvAUQi83qsuMq173ifM4XA4CoS3hDkcDkeBcBEuIYyxE4yxeMZYrY+2qzLGvBhjrxljfKEwDqcSwRgbxxgjxlg9WefNRbjkTAdAAH7/aPtcAK0ATCKijHK3iiN3CvwRC0t+iraPUzHha8yVECKKYYzNBnCQMTaUiE4xxuwBrACwi4juKNZCTjkwFEDYR9vSFWEIp+LDRbgUENEhxthwADsYY7cB7AUQC2C+Yi3jlBNPiShI0UZwKgdchEvPVAAvAHgCsAHQh4hSFGsSh8OpaPA+4VJCRO8A7IBEgM8S0WUFm8ThcCogXIRLCWNMF8BoSAbpWjPGaijYJA6HUwHhIlx6fgFgAKAPABMA6xRrDofDqYhwES4FjDEXAJMBLCGi/wCsAfAdY6ydIu3icDgVDy7CJSRvIsYeAF4AtuVt3gDJIN1fjDENRdnG4XAqHtw7ouSsAmAJYBARiQGAiHIYY5MAPASwGMByBdrH4XDkRy/GWNRH25KI6HppM+QiXAIYY44AZgNYS0S+BfcR0SPG2DYACxhjJ4nohUKM5HA48mR7IdteAGhc2gx5FDUOp5gwxsYB2A/Ajk/W4MgKLsIcDoejQPjAHIfD4SgQLsIcDoejQLgIczgcjgLhIszhcDgKhIswh8PhKBAuwhwOh6NAuAhzFAZjbHje0kCdPtpumrc9upBzfsjbV2rn+IoCY6w5Y2wFY8xQ0bZw5AcXYY4iuZv32umj7Z0gWS7IhDHWoJB9HyCZpVTZaQ7JFHguwpUYLsIchUFE4QCCUbgI3ypiX0cA94nPMioVjDFNRdvAkYaLMEfR3AXQljFWMI5JJwD3ANxHARFmjNkBMANwhzHWmjF2mjEWxhjLYIwFMMbW5kW5yz9+J2Ms+qO8wRjTZIwl5MX6yN9WkzH2J2MsnDGWxRjzZ4xNKbC/dV43SP+PvwBj7HfGWCxjTL3AtimMsWeMsUzGWBxjbO/H3QqMMTXG2E+MsZd5x8Uyxq4wxhoUmCINAK8LrOpslXeuLmNsB2MsIs/eAMbYbMYYK5C/S945gxhjexhjsQA+6eLhKBYuwhxFcxdAdQAtAYAxpg9JMJR7ealjgWM7FTinLoCnAL4F0AuSsKIT8P/CBQCHIQm43+OjMvsC0AdwKK9MXUgE/ytIVs3uA+ACgD8YY9MBgIi8AAQAGFUwo7zQpV8DOE5EOXnb1gPYCeAGgP4A5uXZ+B9jTLXA6ccB/AzgMoABkMSofgnJjeYSJHGqAcnqzm3zUiRjTCVv/3gAmwH0A3AFwK95+X3MdgAMkpVgxhWyn6NIiIgnnhSWAFhDskTU3LzP/SDpD9YAYJ+3zypv30EASQBUP8qDQRIRcBQAMQCjAvsCAfz90fH/AHhZ4PNSAJmQBOYpeNweAHEA1PI+LwaQAUCvwDED8mx0yvtsBUAEYNlHebXPO25A3ucueZ9nfObajMs7pt5H2/vmbR/30fa/AGQBMM777JJ33DlF1zNPRSfeEuYoFCIKARCG/2/ldgLgSUTZRBQIIOajfe5EJMp7HN/AGAuGRHhyIGn5MgB2BYo4DOB/+WsAMsaMIGnxHi5wTC9IVs0OyesiUMvrwrgKwAhAw7zjjgDQhKRlms9oAAFE9Cjvc3dInjCPfpSXJ4CUAt+lByQCuaeElyz/OogBHPto+xFIbl5tP9p+rhRlcMoJLsIcZeAugA55/Zn5/cH53AfQiTFWG5JWZr5HxX5IuiJ+g0T4WgP4IW+fVoHzj+R9HpL3+WtIWs1HChxjklduzkfpVN5+IwAgord55Y8GhK6TPpAWdJO816BC8quRn1feazwRZRR9WYrEMO/c7I+2RxXYX5DIUpTBKSd4UHeOMnAHwAgAbSDpG15SYN89AN8D6Jz3+S5jTAvA/wCsIKKCg2tNPs6YiEIYY+6QdFXsz3t1I6L3BQ77AEmLe2YR9gUUeH8YwB7GmCWAnpC0PAsK+oe81x4AEgrJK39/HABDxph2KYQ4Pu9cjY+EuFaB/QXhniRKDG8Jc5SB/NbtAki6Ex4W2Hcfku6FYZD0FXtB0iWgCknrsiDjisj/EACXvAVa20K65QpIBrUaAHhHRN6FpJQCx56CpPtjJCQt4nt5LeR8rkPSVVC3iLxC8o67lvddJxVhM/LKAQDtj7bfgeS/O/Sj7SMBZEP6+nGUHN4S5igcIvJnjMVAMijnQ0SpBXY/AZCat+82STwQkhhjHgDmMMYiIWlVTgBgUUQRpyDxEDgCycDa6Y/2b4Gkm+IeY2wLJC3fapAIc0ci+l8BW5MZY+ch6fowg8SjoeB3CWaMbQCwgzFWHxLBzARQB5Juk7+I6DYR3WaMnQHwK2OsDiR+0eqQdItcIiI3SDwlAOAHxthBSG46zwH8B8nN6U/GWE1IJq58BYmgryOiuCKuA0cZUfTIIE88EREgEUoC8Gsh+67l7VteYJsVJGKUAklXwg5I+mcJgMtn8j9WRPkGkIhxCCStyRhIukJmFXJsfjlSnhIfHTMagAeANEhuIq/ybKxd4Bg1SDwuAvPKjIXEXa1+gWOWAwiHxOOioKeIbl5+kXnnBkKy/iErcK5L3jndFF2/PBWd+PJGHA6Ho0B4nzCHw+EoEC7CHA6Ho0C4CHM4HI4C4SLM4XA4CoSLMIfD4SgQLsIcDoejQLgIczgcjgLhIszhcDgKhIswh8PhKJD/A18NOSITaJbwAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ef_from_file = silicon.pw_util.efermi \n", "\n", "Band=plot_bands.plot_band_scf(f'./{silicon.prefix}/bs/bs.out') \n", "plot_bands.plot_band_prod(Band,\n", " ef0=ef_from_file,\n", " xticks=['X','$\\Gamma$','L'], \n", " xlabel = 'Wavevector',\n", " ylabel = 'Energy (eV)' \n", " )\n" ] }, { "cell_type": "markdown", "id": "36be241b", "metadata": {}, "source": [ "### Phonon dispersion relations\n", "\n", "To compute phonon-limited mobilities, we need to determine vibrational frequencies and eigenmodes. This operation consists of three steps\n", "1. We compute these properties on a uniform and centered Brillouin zone grid\n", "2. We perform a Fourier transform of the results in order to obtain the interatomic force constants (IFCs)\n", "3. We interpolate the IFCs along specified Brillouin zone paths to obtain phonon dispersions.\n", "\n", "This plot of phonon dispersions is only meant for us to develop a qualitative understanding of the vibrational properties of the system under consideration. The phonon interpolation needed for transport calculations is performed once again later by EPW." ] }, { "cell_type": "markdown", "id": "9a87ccb1", "metadata": {}, "source": [ "#### Step 1: Calculations of phonons on uniform Brillouin zone grid" ] }, { "cell_type": "code", "execution_count": 5, "id": "c1068ea4", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-- -- -- -- -- -- -- -- -- -- -- Calculation: ph -- -- -- -- -- -- -- -- -- -- -- \n", "Running ph |████████████████████████████████████████| in 5:28.7 (0.00/s) \n", "\n", "-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n" ] } ], "source": [ "silicon.ph(phonons={'fildyn':'\\'si.dyn\\'',\n", " 'nq1':3,\n", " 'nq2':3,\n", " 'nq3':3,\n", " 'fildvscf':'\\'dvscf\\''}\n", " )\n", "silicon.prepare(type_run='ph')\n", "silicon.run(16,type_run='ph') " ] }, { "cell_type": "markdown", "id": "6576c175", "metadata": {}, "source": [ "#### Step 2: Generation of IFCs" ] }, { "cell_type": "code", "execution_count": 6, "id": "dea16d30", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-- -- -- -- -- -- -- -- -- -- -- Calculation: q2r -- -- -- -- -- -- -- -- -- -- -- \n", "Running q2r |████████████████████████████████████████| in 2.1s (1.08/s) \n", "\n", "-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n" ] } ], "source": [ "silicon.q2r(name='q2r')\n", "silicon.prepare(type_run='q2r')\n", "silicon.run(1,type_run='q2r')" ] }, { "cell_type": "markdown", "id": "c50f001b", "metadata": {}, "source": [ "#### Step 3: Interpolation of IFCs and generation of phonon dispersions plot\n", "\n", "The logic and syntax of this operation are the same as for the band structure plot above: three instructions to execute `matdyn.x` and then plotting." ] }, { "cell_type": "code", "execution_count": 7, "id": "b8f11a12", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-- -- -- -- -- -- -- -- -- -- -- Calculation: matdyn -- -- -- -- -- -- -- -- -- -- -- \n", "Running matdyn |████████████████████████████████████████| in 1.3s (3.28/s) \n", "\n", "-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n" ] } ], "source": [ "silicon.matdyn(name='matdyn',\n", " kpoints={'kpoints':[\n", " ['0.5','0.50','0.50','20'],\n", " ['0.0','0.00','0.00','20'],\n", " ['0.5','0.25','0.75','20']\n", " ],\n", " 'kpoints_type':'{crystal_b}'\n", " },\n", "\n", " )\n", "silicon.prepare(type_run='matdyn')\n", "silicon.run(1,type_run='matdyn') \n" ] }, { "cell_type": "code", "execution_count": 8, "id": "1820db3d-e524-48e1-b601-6a093e59a96a", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "Band=plot_bands.plot_band_eig(f'./{silicon.prefix}/ph/si.freq')\n", "plot_bands.plot_band_freq(Band,ylabel='E (meV)',ef0=0,xticks=['L','$\\Gamma$','X'],color='royalblue')" ] }, { "cell_type": "markdown", "id": "17f5061f", "metadata": {}, "source": [ "### Transformation of electrons and phonons to Wannier basis with EPW\n", "\n", "Now we have Kohn-Sham wavefunctions and variations of the self-consistent Kohn-Sham potential on coarse Brillouin zone grid. We will generate the electron Hamiltonian, the IFCs, and the electron-phonon matrix elements in the Wannier representation using [EPW](https://epw-code.org/). Details on the underlying formalism can be found [here](https://arxiv.org/abs/1603.06965) (free version) or [here](https://doi.org/10.1103/RevModPhys.89.015003) (journal version).\n", "\n", "This operation involves four logicals steps:\n", "1. Compute Kohn-Sham states on a uniform centered Brillouin zone grid (QE)\n", "2. Use EPW to load these states and call Wannier90 to generate Wannier functions\n", "3. Use EPW to load IFCs and potential variations, and combine with 2. to compute electron-phonon matrix elements in the Bloch representation\n", "4. Use EPW to perform the transformation to the Wannier basis and write to file" ] }, { "cell_type": "markdown", "id": "19f5dc5e", "metadata": {}, "source": [ "#### Step 1: Calculations of Kohn-Sham states on uniform Brillouin zone grid" ] }, { "cell_type": "code", "execution_count": 9, "id": "8ae0cdcb", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-- -- -- -- -- -- -- -- -- -- -- Calculation: nscf -- -- -- -- -- -- -- -- -- -- -- \n", "Running nscf |████████████████████████████████████████| in 11.0s (0.13/s) \n", "\n", "-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n" ] } ], "source": [ "silicon.nscf(system={'nbnd':8},\n", " kpoints={'grid':[6,6,6],'kpoints_type': 'crystal'})\n", "silicon.prepare(type_run='nscf')\n", "silicon.run(4,type_run='nscf') " ] }, { "cell_type": "markdown", "id": "d9be08fa", "metadata": {}, "source": [ "#### Steps 2-4: Load Bloch representation, Wannierize, write to file quantities in Wannier representation" ] }, { "cell_type": "code", "execution_count": 18, "id": "5f16f45e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(4, 3)\n", "[51, 51, 51]\n", "-- -- -- -- -- -- -- -- -- -- -- Calculation: epw1 -- -- -- -- -- -- -- -- -- -- -- \n", "Running epw1 |████████████████████████████████████████| in 1:00.7 (0.02/s) \n", "\n", "-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n" ] } ], "source": [ "# File with k-path for sanity checks\n", "\n", "\n", "\n", "\n", "silicon.epw(epwin={'wdata':['guiding_centres = .true.',\n", " 'dis_num_iter = 500',\n", " 'num_print_cycles = 10',\n", " 'dis_mix_ratio = 1',\n", " 'use_ws_distance = T'],\n", " 'proj':['\\'Si : sp3\\''],\n", " 'band_plot':'.true.',\n", " 'filkf':silicon.filkf_file,\n", " 'filqf':silicon.filkf_file,\n", " 'etf_mem':0, \n", " 'fsthick':12.0,\n", " 'wannierize':'.true.', \n", " 'elph':'.true.', \n", " 'num_iter':500\n", " },\n", " name='epw1')\n", "silicon.filkf_file = 'LGX.txt'\n", "silicon.filkf(path=[[0.5,0.5,0.5],\n", " [0.0,0.0,0.0],\n", " [0.5,0.25,0.75]],\n", " length=[51,51], \n", " )\n", "silicon.prepare(type_run='epw1') \n", "silicon.run(8,type_run='epw1')" ] }, { "cell_type": "markdown", "id": "811e49cf", "metadata": {}, "source": [ "#### Sanity check: Interpolated bands and phonons from EPW\n", "\n", "At this point we have all necessary quantities in the Wannier representation on file. As a sanity check, we perform a simple interpolation of bands and phonons to make sure that we reproduce the results found above _without_ Wannier interpolation.\n" ] }, { "cell_type": "code", "execution_count": 30, "id": "a1060918", "metadata": {}, "outputs": [ { "data": { "image/png": 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MRL9+/XD//n0MGDAAmzZtgkqlKjE/yhOCIFwk6fvMY4oIP6YwIvwkaWlp+O+//3Dx4kX4+flhy5YtyMzMBAB07twZ06ZNQ8eOHUt8JFJWiIyMxLRp0/DLL7+AJJydnbFgwQIMGzas1D+YycnJOHfuHPz8/HD+/HlcuHABoaGhT7UTBAGVKlVCtWrVUK1aNfj4+KBixYqwtrZGhQoV8piFhYU8atVoNLJlZ2cjKysL6enpSE9PR0ZGRp7fs7KykJWVhczMTPlndnY2VCoVVCqVLGiPflpZWcHW1ha2traws7PL87uxsXGpvH4k4e/vj61bt2Lbtm0ICAgosL2Pjw8uXboEKyurUvGvPKCIsI4UR4SfJCIiAsuWLcP333+P5ORkAEDz5s0xbdo0vPrqqy+NGF+4cAGffPIJTp8+DQCoXLky3n33Xbz77rslEqYgifv37+P06dOyXb16FaIo5mlnbW2NJk2awNfXF76+vqhbty6qVKkCc3NzvftUHiGJ8+fPy8IbGBgoH7OxsYG3t7ccMhFFEfHx8QgPD5fbVKlSBePGjcOIESNga2trgGfwfM6ePYs///wT2dnZMDExecoaNWqETp066eWzWpAIG3wyrCxZSayYi4+P57x58+SKZADYrl07gxRuNxSiKPK3337Lsz05ADZv3pzfffddkVOiRFFkcHAwt23bxunTp7NHjx55dnB4ZGq1mk2bNuXHH3/MX3/9lTdv3nxpqncVFlEUuW/fPnnTzUfm6OjIUaNG8d9//32qdsjJkyflmthDhw6lt7e3fJ6lpSU//PBD3rp1y0DPKC+ZmZn8/fff5V1snmdNmjTh1q1bi/1+QQETc8pIOBf6HAk/SWpqKtauXYv//e9/iImJgUqlwtixY/Hll1/CwcGhRK5Z1hBFEUePHsXGjRuxZcsWpKSkAACMjY3RqlUrVKpUCR4eHnB3d5d/2tvbIzo6GmFhYQgPD5ctNDQU//33H2JiYp66joODA1q1aiWbr68vLCwsSvvplitI4sCBA5g9ezbOnDkDQHodBw0ahP79+6NNmzZQq5+exw8KCkLz5s0RHR2NDz/8ECtXroRWq8Xu3buxfPlyHD58WG47Y8YMfPnllwa5C4yOjsbq1avx/fffyyN2Ozs7jBgxAp6ennKY6JGlpKRg8+bNiIqKAgDUqlULU6dOxcCBA5/5OjwPZSRcAiPhmzdvsnbt2vzxxx8L9S0ZFxfHTz75RF6Tb29vz+++++6lW/qbkpLC3377jd27d5fTmYpi9vb27Nq1K6dMmcK//vqL9+7dK/YW5y8Toihy//79bNWqlfyaOjg4cOHChc/d5TshIYG1a9cmgHy3gb969SpHjhwpv9+HDRtWqrt6JyUlcfz48TQ1NZWfX+3atbl69WqmpKQUeG5aWhpXrlxJT09P+dyKFSuya9euTE1NLZQfKO95wgAqAlgB4AyAtJwXxOsZ7cwAfAUgHEB6Tvt2ul6nMCLcv39/+R9jYmLCV155pVCFzwMCAti5c2e5j/r165f4PltllfDwcO7bt48///wz582bx/fff5+vvfYafX196e3tzRYtWrBfv3784IMPOHfuXP7444/cvXs3g4KCFMEtBgEBAezYsWMe8V2wYMFzxZeUFoT06NFDFrXn1QbetWuXvM19jx49dLpGcfn777/lglOCIPDVV1/lgQMHCv2eyczM5E8//URXV1f5tRo0aFCh+ngRRLgDgEgAewDsK0CEfwOQAOA9AJ0BbMsR44a6XKcwIrxnzx42adIkz5p75FSa+uyzz3R6k4miyK1bt9LLy0s+f9iwYeWizrBC+SUpKYkTJ06Ul9fb29tz/vz5hVo192hJsqOjo85Lks+ePSvPjfj6+pbYfooPHjzIs4qzWbNmvHz5cpH7i4uL44ABA+T+XFxcGBoaWqg+XgQRVuX6fdSzRBhAg5zHh+d6TA3gFoB/dLlOUSbmUlNTOW3atDzfkshZujx37lyd+khLS+OsWbPkyQ17e3uuXbtWmTxS0CuPJkgf1fsQBIHvv/8+Y2NjC9VPcZYk3759m1WrViUAent7886dO4U6vyCys7O5dOlSWlpaEgArVKjAlStXFqt41pEjR1ixYkUCUjH6devWKVveFyDCMwFkAbB44vE5ADIBmD6v7+JmRwQEBLBPnz6ymCJnCe/Nmzd1Ov/WrVvs0qWLfG7Lli2Vvd0U9IK/vz/bt2+fJzPlwoULhe5nx44dcgx/w4YNRfIlIiKCTZo0IQA6OTnx3LlzReonN1evXpX7BMDXX3+dISEhRe4vMzMzTyna5s2bMzAwsMj9vSwivAnArWe0fzOnfZ3n9a2vFLW0tLQ8mx8KgsBx48bpNLIVRZF//PGHPLI2MjLixIkT9V5gReHlID09ndOmTZNDD46Ojvzpp5+KdJd18uRJuS7FzJkzi+VXcnIyu3fvTgC0sbEp8mAjOzub//vf/+QaLpUqVeI///xTLN+Cg4PZtGlTAlIp2pkzZxZ7MvFlEeH9APye0b5LTvu2z+tb33nCBw4coK2tbZ54sZ+fn07nJiQkcNy4cfI3sbu7O//44w9lIkpBZ44fP84aNWrkCT0UtbJfQECA/F5+77339PI+zMrK4uuvv05A2qnl3r17hTr/2rVr9PX1lT9fY8eOLfZg5fDhw3Lc2tPTU2+T5YoIFyDCAEYDuADggqenpz5e7zxotVoOGTIkT7z47bff1jkl7cKFC3KBeADs2LHjS7dJokLhSExM5NixY+X3TK1atXjq1Kki9/fgwQM5Lvraa6/pNZ0yIyNDztCoVq2aTpN1Go2GixYtksN+lSpV4v79+4vlhyiKXLp0qZxK161bt0LHygtCLyIMwARACwD9AbwDoPuTQlgaVoAIby4r4YhncfnyZbq7u8sfDFtbWx45ckSnc7VaLdeuXSvv06VWqzlp0iQlRKHwFP/884+clmVsbMwvvviCGRkZRe4vJiZG3uSzTZs2TEtL06O3EomJiWzUqBEBsHHjxgXWoz579ixbtGghf45GjRr13PS455GamspBgwbJfU6ZMkXvO+EUWYQBGAF4A8BeSKleWgBiLtMCeABgEYBqBfWlLytAhL/AsyfmZqOUJuZ0YcKECXnS2vr376/zyCImJoZjxozJE6L48ccfX7qFHgpPExkZybfeeitPWlZhN+R8kpSUFFnw6tatW6KbFERERMjLnTt16vTUF8eFCxfy7Fju4eGhl5rV9+7dY8OGDQlIS6z//PPPYvf5LIokwjniewdABoAdACYC6ASgHoBqAJoBeAvANwBuA8gGsBaAS3596sMKEOFGOY8PzfWYGsANADt16bs0RJgkr1+/nmcVjrW1daFup86fPy9PHDy63fz777+VePFLiCiKXL9+Pe3t7QmAFhYWXLp0abFHcllZWbLoeXp6FivTQFfu3r1LFxcXAuCAAQOo0Wh4+fLlPDm/FhYWnDx5sl72qzt48KD8ulWrVq3YX1oFUVQRDgMwHoBtfm2eaN8c0uKImbq0L6zlfCm8AWBVzj/k/Zy/2+dqswlAfI5QdwawJedLpLEu1ygtEX7ElClT8izZfeWVV5ienq7TuVqtlr/99hurVKmSJ6XtZV119zJy//59OcMAALt27Vroya1nkZWVJS9OcHBw4I0bN/TgrW5cvnyZ1tbW8uj70XMzNzfnpEmT9LLAQxRFLlu2TI7/vvLKKyW+CWlRRdgsv2MFWVHP06Ff5mNHc7UxzxmZR+SI71kAHXS9RmmLMEkGBgbKyeuP3myF2RImMzOT3377bZ7qYb169eKpU6eUkfELikaj4fLly+VFCXZ2dkVeRPAkGRkZ8sjT2tqaZ8+e1YPHhePo0aPypJuZmRnHjx/P8PBwvfSdnp7OYcOGyZ+VadOmlcpO6EUV4cr5HXtRzRAi/Ig5c+bI38yAVEKvMN/6SUlJnDVrlvzBBKQ1/d988w2jo6NL0PPnk5qayqCgIJ47d44XLlzgzZs3+fDhQ8bFxT1VFlGhYC5evJinDOOAAQMYERGhl77T0tLkehB2dnY8f/68XvotDOnp6Zw+fbr8WXj//ff1NpgIDQ2VXztzc3Nu2rRJL/3qQlFFWAvgMIBhAKzya/cimSFFmJQK2eRe9VOYpc+PiIiI4OTJk+XYGnJmyd98803u379f70uhMzMzeevWLe7Zs4crVqzg+PHj2a9fP7Zs2ZLe3t60srLK7w5GNrVazcqVK/Ott97ismXLePbsWUWcnyA+Pp4ffvihHL5yd3fn9u3b9dZ/SkoKO3XqREBaxWaIeteHDh1itWrV8rz/AXDGjBnF7tvPz09eru3p6VmsWhJFoagiPBfAPUhZECkANkDKuRXyO6e8m6FF+BEbN26Udy5+9Ka5ePFiofrIysri33//zV69euWJO9vZ2bFNmzYcM2YMv/32Wx48eJDh4eF5RhuiKDIrK4spKSmMjY3ltWvX+O+//3L16tWcPn063333XXbo0IGVK1fWqQyliYkJK1asyEaNGrFhw4b08fGhm5sbra2t84z+c5uZmRlbt27Nzz//nKdPn35pQyuPJt6cnZ1lYfr000/1mp6YmJjINm3aEJAWTZR2HnpMTEyeEEHt2rV54sQJbtmyRX5/zJkzp8j9r1u3Tg5vtGvXziAFsookwnIDoD2AnyBVJ9MCeAhgPoBazzu3vFlZEWFSui3LnZLzaAKhKCUAHz58yLlz5+ap1vakWVhY0NzcXF7eqqupVCp6eXmxc+fOfO+997hw4UJu3ryZx48f561btxgfH1+ggIqiyIyMDPr7+3PNmjUcPnw4a9as+dR1KleuzM8//5yXLl16aQTZ39+fbdu2lV+DNm3a8OrVq3q9Rnx8vHyLXrFiRd6+fVuv/ReEKIrcsGGDvELN1NSUc+fOzXMX9Mcff8hf9PPnzy9U/1lZWfz444/l1++DDz4o1VrGuSmWCMsNAVMAb0MqJ5mdI8jnAHwAwF7XfsqylSURfsSJEyfk26hHo8oFCxYUqS9RFBkaGsr9+/dz6dKlfO+999iqVSva2Ng8M0RgYWFBGxsbVq9enZ07d+bw4cM5a9Ys/vTTTzxw4ABv375dYmGD2NhY7tmzhxMmTJAXHzyy6tWr84svvtC5MFJ5Izg4mCNGjJDFx9nZmevXr9f7l8+1a9fkouxeXl56yazQlYsXL7J169by/7Rjx475boG0YcMGOTf+66+/1qn/6OhoeSWesbEx16xZo0/3C41eRDjPSYAzgAkALuWIcXpR+ilrVhZF+BFz586Vi5QAUrL66dOn9dK3KIpMSEhgcnIyMzMzy9xIU6vV8vjx4/zwww/l2/JH1qxZM65YscLgk4/6IDIykp988ol862xkZMQPP/ywRNKn1q9fLxdZr1WrFh88eKD3azyLyMhIjho1ShZVZ2dn/vLLL899z/3000/y//zbb78tsO3ly5fl/QxdXV2LtWRbX5SECFsCGArgUI4IZxeln7JmZVmESSl292j2+pG1bt2aDx8+NLRrpUZ2djYPHDjAESNGsEKFCnlG7n369OGWLVuKtUzXECQkJHDGjBlyZosgCBw0aJBea+0+IjU1lcOHD5dft3fffbdUdrnIysriN998I991qdVqTpw4sVBLjlevXi373a5dO3722Wf866+/+ODBA1nE//jjD3k+pVmzZqWyyEQX9BWOECDVi/gV0kSdFsBNAFMBVNS1n7JsZV2EH3Hu3DlWqlRJfkMKgsDXX3+9VD5MZYnU1FT+8ccffOWVV/JM8NnY2PDdd9/l9u3bdV78YgiCgoI4depUedUWAPbu3bvEakhfv36dderUkSc+f/rppxK/6xFFkTt27JDrTwDS9kZFDSV99913z5y3cHV1zVMvefjw4WXqf1/cibkGAL4GEJojvLEAvgfQ/HnnljcrLyL8iB9++OGp0eCECRNeyh05wsPD+c0338h1AB6ZlZUV3377bW7ZsuW5GzuWBhqNhjt37uQrr7ySp4ZI+/btS+y2WavV8ueff5bDDzVr1tT7BN+zOHLkSJ5iO9WqVePOnTuLLfzR0dHctWsXv/jiC3bv3p12dnZ5PgMrV64scyG1IokwgEkA/ssR3iwAOyEtEzbJ75zybuVNhEnpAzZ16tQ8u3lYWlpy8eLFL6UYk9IOJfPnz8+Tcw1ICfpdunThvHnzeOrUqVLNRQ4ODua8efPy1AwxMTHhO++8wxMnTpSIaGRlZXHDhg3y5BsADh48uMTvmC5cuMBu3brJ13RycuKyZctKLEwkiiJv377NTZs2MSAgoESuUVyKKsIigCs5E3DO+bV7kawsiLBWSwYHk4cOkb/8Qs6fT378MTl8ODlyZN62ixaRX3xBfv89uXt3Ovv2HZQnb9fKyoqzZ89+acWYlKpkffXVV3lGZI/MwsKC3bp14/z587l///48scXiEhUVxc2bN3P06NF5FiAA0t5qixcvLrHJxLS0NH733Xd5UhIrVaqkt6XN+XHt2jW+8cYb8jWtra355ZdfKiVXWbAIC9LxpxEEoQHJ/5558AXF19eXFy5cKLXrxcQAly8DNWsClSpJj82bB8yc+ez25uZAWtrjv729gXv38raxs4uAkdEQxMYefPRlCgsLC3z88ceYO3cu1Gp1CTyT8kFUVBSOHTuGo0eP4siRI7hx48ZTbaysrFCjRg3UqlULNWvWhJeXF2xsbGBtbZ3HzMzMEBMTg8jIyDwWFhaGU6dO4erVq3n6tba2RteuXTF69Gh06dIFKpVKr8+NJO7evYutW7di6dKliIyMBADUqFEDU6ZMwaBBg2BiYqLXaz7Cz88PixYtwvbt2wEAZmZm+OijjzB58mQ4ODiUyDXLG4IgXCTp+8xj+YnwMzoRALwKoB0ABwCzSQYLgtAewB2SYfpy2FCUlAiTwP37wNWrwJUrkvBeugQ8fCgdX7ECGDdO+n3TJmD8eMDHB6hcGXB11cDWNgnGxkkQhCS0bJmIpKQkJCUl4d9/UxAbq0V8vIiICC0iI0WkpWkBEH36GCM6ehP8/PxkMTYzM8OIESOwaNEiWFlZ6f15ljciIyNx9OhRHDt2DAEBAbh58yaio6P10reZmRnatGmDTp06oXPnzmjcuLFevwBJ4saNGzh27BiOHz+O48ePIyzs8UewUaNGmDZtGvr16wcjIyO9XTf39ffv34+FCxfi6NGjAABTU1OMGDEC06dPh4eHh96vCQAhISH45Zdf4ODggMaNG6N+/fqwsLAokWvpk2KLsCAIdpAWaTQHkAzACkBTkpcEQfgVQBzJj/Xos0EojAiLoojMTA1SUrRIT9ciOVmL6GjJQkK0iInJxtCh6UhPT0d6ega6d09HUlIGgDRIL2ESjI2T4eychFq1kuHqmoTExEQkJCTkseTkZL0/T0EQ0LJlSyxbtgxNmzbVe//lmdjYWNy8eRM3b97EjRs3EBISguTkZCQlJck/k5KSkJ6eDnt7e7i4uOQxZ2dnNGzYEC1btoSZmVmhrq3RaJCRkSFbeno6oqKiEBYWhtDQUISFhcm/BwQEICYmJs/5jo6OaNeuHUaPHo1u3bpBGjfpl6ysLGzduhWLFy/GlStXAEij/A8//BCffPIJXFxc9H7NRxw4cACDBg3K87xVKhVq1aqFxo0bo3Hjxujfvz88PT1LzIeiog8R/hFADwADAJyHNFHnmyPCwwB8RrKO/lw2DIUR4XXr1mH48OEl7JEkmNbW1nluiR/9bmlpCbVaDSMjI6hUKvknII3yHj58iAcPHiAkJBSiqH1m/3Z2dvj0008xbdo0vd8ilxc0Gg2uX7+O8+fP49q1a7h9+zYePnyIqKgopKSkQKPRQKPRQBRFiKKoU58qleopEwThmcIofaFnQqt99v8oP9zd3dG+fXu0a9cO7dq1Q61atUpEeAEgLCwMa9aswerVqxEREQEAcHV1xYQJEzBmzBjY2NiUyHUB6fWZN28eZs+eDZLo2LEjPD09cenSJVy/fj3P62ZnZwc/Pz9Ur169xPwpCgWJsK73R68BmETyjCAIT97bPABQqTgOlkck8VNDqzUCYARBMIJKJZmRkRGMjU3g7GwGCwtzmJmZwdzcXLYKFSrA2to6z88KFSrA1tb2KatQoUKxxVGr1SI0NBzbtgVj1arDuH17DYAQAEB8fDxmzpyJL774Ag0bNsSCBQvQvXv34r9AZRBRFHH+/Hns27cPZ8+exc2bNxEREYG03IF2PV5LV8F+hEqlgrm5OUxNTWFmZgYzMzM4OjrC3d0dHh4e8PDwkH/39vaGl5dXiYkuIIUcTpw4ge+++w7btm2DRqMBANSuXRsff/wxhg4dWujRfmGJiYnB4MGDsW/fPgiCgNmzZ2PGjBlyiCU9PR3+/v64dOkSfv/9d5w4cQK9e/eGn58f7O3tS9Q3faHrSDgdwKskD+aIcDYej4RfAbCZZIUS9rXEKe2JOUNx/z4wZ859bNy4EmZmPyI1NTHPcRMTE7Rr1w5TpkxB586dDeNkMUlLS8OuXbuwf/9+XLhwAUFBQUhKSsq3vSAIMDMzg62tLZydnVG5cmVUq1YN3t7ecHBwgL29PRwcHODo6AhnZ2eo1Wo8fPgQd+/ezWM3btzIM+Hn4eGBN998E2+99RZq165d4LXLyqRpYmIifvvtN/zwww/w9/cHABgZGaFv374YN24c2rdvX6Li/wg/Pz8MGDAAISEhcHR0xO+//46uXbvm2z4lJQVt2rTBf//9h44dO2Lv3r0lNhlZWAoaCeuUugUpVW1xzu9GkNLXGuf8vQjAaV36KetWFlLUSpPYWFIUpTQuqZbs02Upzc3N2aZNGy5atKjM1me4f/8+ly1bxv79+9PHxydPGdAnTRAE2trasl69ehw0aBC///573r9/X6/+XLt2jdOmTZPrFzyyRo0a8ffffy+TG7OKokg/Pz8OHz5cXtSBnNoOM2bMKNWl8aIocvny5XKtlJYtW+pc2+LBgwdywauRI0eWmUUbKO6yZQCjIcWBpwOokiPCnQAMB5AK4B1d+inr9rKJcG5CQ0lj40QCMwmY5StiFSpUYMuWLTlv3jwGBweXqo8PHz7kunXrOHbsWLZp04aurq751iNGTvWsihUrslu3bpw7d26JLQfOD61WyxMnTnDs2LF5VnVVqVKFK1euZGpqaqn68ywSEhK4cuVK1q9fP89r17FjR/7xxx+lXocjNjY2z8ae48ePf2pRTVgYee4cefQouWcPefgweeUKGRIiDSrOnz8vfxF/9dVXpep/fhRbhKU+sBCABo+3vddCCkv8T9c+yrq9zCJMknfvkm+9RQJJBBYQeCwc+YmdSqWira0ta9Wqxddee42zZ8/m3r17efPmzUKJTHZ2NgMCArhp0ybOmTOHw4YNY+fOnVmzZk3a2Ng8t3i8hYUFa9SowTfeeIMrVqwoc0WNMjIy+OOPP7J69ep5VpLNnTu3RLeSz4+rV69yzJgxebbDcnR05GeffZZvScmS5vTp0/KKQhsbG27dupUJCeTOnZK4PqJlS0m5nmXduklt/vrrL/nO5++//zbI88mNXkRY6geVIe1kPA3AGABVC3N+WbeXXYQfcfo06etLAskEvqRKJY0qTE1N2aFDBzZp0iTPh/d5plKpaGJiQktLS1paWtLMzIwmJiZUq9VUqVR5aig8z8zMzOjh4cHWrVvzo48+4s6dO8tUoZbnodFouGXLFvr6+srPycrKip988gmDgoJK9NpZWVncvHkz27Vrl+c17dChAzdt2mSw6nNarZYLFy6Uv+ibNWvO1auD+PrrpKmppFK5a81/8gnZuDHZrp0kuu3akXXrko6O5Nixj9tNmPC/nPefBb/44hILUbBN7+hNhF90U0T4MVot+fPPpLMzOWRIsLwFOgBWrVqVO3bsYEZGBo8dO8a5c+eyX79+rFOnDu3s7KhWqwslrLnjtaamprS3t2fVqlXZvHlzvv7665w7dy6PHTv2Qu07J4oiDx06xK5du+b5snrzzTf1vsNxcHAwZ82alWdzACsrK3744YelvpXRk0RGRrJ79+6yX506fcZKlbLkka0gkG3akBcu6NZf7rfI1q0iBWFITt8eNDML4fvvk4bYC6BIIgzALb9jBRkA16KcVxZMEeGniY+nPII4dOgQvbzqyB+Ynj17Fjh602q1DA8P5/nz57l9+3auXr2aP/74Izdt2sSdO3fyyJEjPH/+PG/evFkihcvLC5cvX+bgwYPzlGhs06YN//777yJvx56RkcE///yT3bt3z/OFWKtWLa5cuZKJiYl6fhaFZ//+/fIXg729A+3sdsviW706uXgxWdyoUnh4Bn18Hm0R1YBAIgHy9dfJ0pwfLaoIpwJYDqBmfm1ytTUHMAhSFsWM57Uvq6aIcMGkpZFeXtkEllOttpFjsV9//XWZnPEvbzx8+JCff/55nu2mHB0d+eabb3LNmjXP3X5Iq9Xy6tWrnDBhgrxvGyBVa3v77bd56NChMpEtkJGRwYkTJ8r+tWvXjg8fPuQHH5AtWpDbt0t3YvoiJiZGjsVXrNidpqZZHDhQf/3rQlFFuAke75xxGcC3AEYC6AOpuPvbObHh7QCSIG0EOg2AWX59lnVTRLhgtFryp59IBwcSiKAgvC1/kBo3blzoHaEVnk1SUhKXLl3KqlWrPhWyqVq1KkePHs0lS5Zw0qRJfOutt9i6dWtWrlz5qWLn9evX5/LlyxkTE2PopyRz48YNueazIBhx8OC58mg/IyPvBJw+CQwMpJOTEwFw4MCRfPDg8YVOn5YqEpZktKtYMeEcMV4F4B6krIjclgbgCICxACo8r6+ybooI60ZMDPnee1K8DthNIyNPOaY5ceLEMlE8/UXgUZ3c77//nv3796etre1z4+ouLi4cM2YMz58/XyZGvY8QRZE//PCDnDomCFUInGG9eiUnvE/i5+cnX3/evHkkpYFFw4aSEtauTeo5HC+jt4k5SBt8NgTQAoAPAOPCnF/WTRHhwuHnRzZpQgLJtLScIKeReXl5cf/+/YZ274VDo9Hw3LlznD9/PseNG8cFCxZw48aNPHr0KAMDA8tslkh0dHSe3F/gXQKJHDBAyk8vTf7++285Rr5x40aS5L59pI+PpIYqFTl5Mqnvl1LJjlBEuMTQaMhVq8i//5aS5HNvLzRixIiXesJNgdy5cyddXFxy3hPWBH6ngwP511+G82n58uUEpMU8hw8fJinNd0ya9Ojujqxfn9TnJh2KCCsiXGpkZ2ezXbsFBEwJgO7u7vznn38M7ZZCKZOYmMiRI0fmmhxsRyCIvXuTERGG9o4cP348kbMoJPeWSKdPk9WqScro7CyJsz5QRFgR4VJDq5US6IEbBFrKH8JBgwaV2doTCvrl2LFj8tZKJiYm/Prrr3nggJYrVpRe/Pd5aDQa9u/fXx4o5M48SU4mR4wgN2zQ3/UUEVZEuFQRRSk84e2tIbCMgDQZYmvrxD///NPQ7imUEOnp6Zw4caIcc3Vza1RmN94kpb342rdvL2edhBYQoF63jjxwoOjXUkRYEWGDkJlJfvstaWcXSKCDPCoeMGAAo6KiDO2egh7x8/OTd3UWBCNKhaAyWco1kwpNYmKivIS8Tp06z0znu3nz8fLpsWPJouxbqoiwIsIGJTGRnDFDy0aNVtHKykpehLBypTIqLu+kpaVx0qRJcmaMiUl1An40M5NyystK+KEgYmJi5C+Qpk2bPrU7dHY2+b//kcbGkmKOGVP4axRbhAHMB+CpS9vybIoIlyyiSAYFBeXULkZOPO4N7t8faWjXFIrAyZMn5ZVogqCisfFnBNJYvTrL/Aj4SUJDQ1mlShUip6BR2jNm5K5eJbt2JcPDC9+/PkQ4GVIZyz05K+ZUupxX3kwR4dJBFEW+++4qAlY5YuzIBg028/jx8jFyetlJSUnhJ598Isd+XV1rE/AjQL79dtFu18sCd+/elWtZ9O7dm1lZWXrrWx8ibAWpdOXFnJVyDwHMAuChy/mlZQA65LOSKEGX8xURLl3Ong2ip2enXP+nN9i0aRT//dfQninkx4EDB+Tl1EZGRpw2bRqDgzNYpQq5enX5/xINCAigg4MDAbB///5PhSaKil5jwgCaAvgJQAqk3Tb+BtCjsP2UhOUS4Y9yVvU9Ml9dzldEuPQRRZFffbWKJiaPR8U9eyqx4rJGVFQUBw8eLH9hVq5cn35+j+tLGqgUcYlw/vx5VqhQgQBYrVo1Xrx4kdnZ5PHj5NSpLFJd4hKZmAPgBOAoHu+ycQ/Ah4YMVeQS4S5FOV8RYcMRFBTE9u0fj4rffPNNRkVFcds28quvpMk9hdJHFEX+/PPPtLe3JyAV1a9dewGBLM6YYWjvSo7r16+zbt36OTVRjGluvoyASIDcsqXw/el7JOwNYDGAKEjbG22FVFHtt5y/1xS2T32ZIsLlG61Wy++//17etcPJyYkVK/5FgLSxIadMKdqkiELRuHXrFjt27Ch/MTZs2IWOjoEESGtr8vffDe1hyfLee2kEPpCfv6Vlb44ZE82rVwvflz5iwkYA3gBwIGeCLhTAHADuT7QbCyBRlz5LwnKJcGTO6DwWwO+6ZnYoIlw2uHfvXp4Pv5PTAAKRBKR8zTFjyOeU1n0piYuL47Vr14pdyCctLY2zZs2iqam09NzBwZFt2myUR4Lt2pF63qDaoCQnk5s2kf37Sz8fcfAg2bw5OXjwNlpb2+YsQHHjkiVLCl0/Wx8iHJEjakcADACgzqddcwCiLn2WhAFoBOBrAK8CaA9gfM6IPRSA8/POV0S47KDVavndd9/Jo2IbGwf6+v4uC4GRUfFWMJVnQkJC+Ouvv3LmzFns1esdNmjQXJ5MksyYKpUvVaoPaGa2jm5u19mggZb9+5PP28Nz586dcqoWAA4YMIyurjEESDMzcskSqWhTeScpifzjD0l4zcwkJQTI3r3zttNoNDx//jwnT56cp9j+rFmzCnU9fYjwtwBq6dK2rBmAxjmj93n5HB8N4AKAC56enoV6YRVKnqCgIHbp0kV+83fq9BoHDAhjpUp5yw0achPH0iIqKooffzyearXJszKAaGlpSQ+PKgSetb+fNYGenD59KQMCAiiKIidNkkRn2TLy33/v8tVXX5Xb16tXj8eOHaMokp07SzscG2JvtpJgxoy8wguQrVqRS5eSQUHZvHz5MleuXMnXX3+ddnZ2T72WarWam3IPmXWgRCbmypMBuA5g3/PaKSPhsokoilyzZo08Y21ra8s1a9bJRcvj40l7e3LIEPLuXcP6WhIkJiZywoRZuTJIQKAngam0t/+JgwcfZ1hYGEVRZHY2GRSUxD17jnDevIV89dX+dHOr+JSQuLu7085uKIHfCMwhYJYjMBXo4rKMBw48vt2OjdXvdkOlSXCwtHQ+dwmLpUsfbyA6f348N2z4lzNnzmTnzp3lFZ25zcvLi++99x43b97MqKgoJhThG18fI+F2BVgbAPVQhgu854jw3ue1U0S4bPPgwQP27NlT/nD06NGD9+7d486dpFotvZvVavLDD8nIF2ARXnp6OpcsWfJEqKEnvbwu8csvSX9/3fNyQ0JCuGHDBg4ePDhXfd8nbSCBMAKkr2/JPreSIjOTPHZMmsStV4/ySHfqVJEhISHcuXMnp02by1deef2Z20chp5jP4MGDuXr1at7V07e6PkT4URpaQZYM4H+69FeaBsA3x78vn9dWEeGyjyiKXL9+vXybaGFhwa+++oq3bmVzyBBpZwSAtLIi584lU1MN7XHR2LJlL93dPWVhaNKkNTt0OM4jR4q/ICIhIYHjxo2Tt/p5bFY5QryNFSvmXbb799/SiLgs8/77pKWllsB9AnsJLKNaPZZOTh1oY+P0TME1MTFhq1atOGnSJG7bto3hJZR+ow8RfhXAfQA7ALwLoFvOz50AggEMAbASUoraJF36LAmDlCY3D0B/AJ0ATAQQA+ABAMfnna+IcPkhIiKCAwcOlD9MjRo14vnz5+nvT/bq9XgE1KuXoT0tHAkJSWzbdrT8vOrXr8/du3frZb+4pKQk/u9//5NzfgHQxaUdBWEugaZ5xMnU1IoDBw7khg0beP58CAVBKmDTp4+UQWCobQSTksh//knguHFX2KTJds6evZSffPIJ+/TpQ3v7+nxUNvVZZmtryw4dOnDChAlcv349r169qtelyQWhDxH+CcAP+RxbDeCXnN+/BXBDlz5LwgBMBXAVQGLOF8JDAGsAuOlyviLC5Y89e/awcuXKBKSNRsePH8/k5GQeOUI2akTm7F5DsuzHNdetO0JTU68c0TChl9cChoUVLhXqWaSmpnLhwoV5whpt27blli2HaW4uUq2W0v5OnrzHRYsWyaUdc5uFRQ1KObNbCcTRwoJ86y1JkPWxH5tWq2VMTAyvX7/OI0eOcPPmzVy+fDnHj/+cTZoMpotLx5wKbU/HbJ80V1dXtm/fnmPGjOHSpUv577//8v79+0X6IhNFkVFRUTx06BA//HAyq1dvRycnZ54t5I6gBYmwIB0vGEEQ4gC8RfLAM451BbCZpL0gCK8A2EbS7LmdlkF8fX154cIFQ7uhUEhSU1Mxe/ZsfPPNNxBFERUrVsTixYvx5ptvw8hIkNsNHw6YmADz5wMODgZ0+AkSE9PQo8dU+Pl9CwBQqxthwYINmDixLgThOScXgEajwc8//4zZs2cjPDwcAODq2hrr1s1Bt26dIAgCtmwBGjcGqlbNe+69e/ewfft2HDp0CMePH0dKSkquowIALwAVIQiV8PHHFeHtXREVK1ZEWpodbG2zQWYiMzMTWVlZyMzMREZGBuLj4xEfH4+4uLg8FhERjdjYaIiiVqfnpVKZw8bGC56eXmjcuApq164CLy8vVKlSBd7e3rC1tS3ya5aSkoKDBw9i+/YdOHLkDCIigpGVlfFUuylTpmDBggU69ysIwkWSvs88mJ86M+8IMxHA2HyOvY+cBRoAOsOAizWKa8pIuHxz8eJFNmnSRB4RtWzZkufOnSNJPnjwuB6svb1UbKYsjIyPHTtOc3OfHJ/VbNx4NqOiineLLIoit2zZIpeZBEArqyYE9hMQ+csvhesvKyuLp06d4pdffsn27dvTxOTZKXLFN1sC1Wls3Ib9+/fn+++/z3nz5rF375/50Uf7+PvvAQwPj9dLaCY3gYGBXL58OZs3b0uVyihf/2xsbGln14wDBnxMf3//Ql0DehgJ/wGgO4D3AGwnqRUEwQhAP0i3+3tJDhIE4WMAw0g2fm6nZRBlJFz+0Wq1WL9+PaZNm4bIyEgAwJAhQzB//nwkJXlg3Djg8GGpbdOmwHffST9Lm9jYWHz++ef4+eefAQDGxnXx7bfrMXZs8T46R44cwZQpU3Du3DkAgFpdDRrN/wC8gQoVVBg7FvjkE8DDo+jXyMjIwMOHDxESEiLbw4cPcedOCE6dikd6uimAp61PHzu0amUHe3t7nDxpjw0b7ADYwcnJCdWrO6F6dVPUqAHUqQP06oVi3QU8C41Gg7t37+LatWsICLiG69ev4cyZM3jw4MEzWgswMamN+vU7Ytas7qhXrzWiouwQHQ20aAHY2xfu2gWNhHUVYUdI1dJaQ1r4EA/ADoAawCkAfUnGCoIwFEAqyS2Fc7FsoIjwi0NSUhLmz5+PpUuXIisrCxYWFpg6dSo+/vgT7N1bARMmAGFh0gd9zBjg++/1/6F/FiSxZMlGzJ07EUlJMTAxMcHUqdPw0UdT4OBgWuR+T548idmzZ+PQoUMAALXaBRrNLACjUKWKMcaNA0aOBGxsdOsvJSUFgYGBCA0NRXh4uGwRERGIiIhAVlYW1Go11GpjSDJgDFINNzcLODm5Q6VyR2ysB7Rad5iYuMPZ2R1DhlijUSPpRY6MBJKSgEqVALNiBC+1WiA2VuqPBKpWTcH9+/dx69Z9fPvtfURH30d8/H0kJd1BevpNkFkF9GYGlaobTEzehJFRT0yfbo+pU6UjW7YAAwZIvx8+DHTsWDg/CxJhtS4dkIwB0FYQhG6Qlia7AQgH4MdccWKS6wvnmoJCyWBtbY2FCxfivffew+eff45t27Zh5syZWLJkCd5//30cO/Yx1qxxxdKl0ge5NAT4xo3beO2193HnjjQUb9GiI9atW4UaNWoUuc9Tp05h5szZOHLkIADpeX/22WewtByPPXusMG4c0Ls3YGT07PPj4+Ph7++PGzdu5LGHDx8W2af8WLbMFILgBBMTZ7i7O6F1ayc4OzvD2NgaV66YwcLCDGZmZjAxMYOxsTlE0QgZGVlo0SILpqZSfPngwSz8918GkpPjkJISg8zMGEgJUDEwMoqBVpv4HC8sAGRAyroFVCp7iOKbkG7q20MUTZGREwJOTn58VqVKQKNGgLMzYG6u39fluSNhQRBMAGwGsJTkcf1evmyhjIRfXI4cOYIvvvgCJ0+eBACYmJhgyJAh6NdvEnx9a8DZWWq3fz8QEwO89Vb+wlVYgoOD8cUX32HjxuU5IzEHtGjxDXbufBeOjkVT/5MnT2HixNk4d+5gziPWaNVqPHbtGg87OzuQT3+xxMXF4eLFi7hw4SLOnr2Iq1cvIigoKJ8rGAPwAVARjRq5oXt3N7i5uSE01A2LF7sBMIOUgKSBlZUGVlbZsLDQYOrUZKSkhCM0NBQ7d4YhPDwMGRmhyM4OA5lapOdaGExNTeHl5QUvLy/ExXkhJcUeISHBSE4+CSlTFRAEAd26dcPo0aNhafkqsrON4eAg3SWYmUkia24OWFoCxsb68Usf4YhkAK+SPKofl8omZUGERRFISADi44HERMmSkoCUFMkGDHgcj/rpJ+DMGSAjA0hPT0JKSjgyMqKRmRkJS8t49OgRj4SEBCQlJWPfviRotckg0yHV4n9k2TAxyYYgZOdcX4BWq4JKJcDISIBKBZibm8LKyhKWlpJZW1vD2toaTk5OqFq1Knx8fFC9enVYWVkZ5kUrBH5+fvjqq6/w999/S5MigoA+ffpg1KhRaNeuI1q2tMT161JccupU6fU2MSn8dUji0KFD+OqrlThwYCdIaeRlYTECa9cuxqBBhU/PIIktW/Zj+vTF8mgaqABgPJo1G4/PP7fH669Lj2o0Gly9GoCdO0/jyJHT8Pc/g7i4e0/1aWZmhnr16uHmzdpITq4FQDIzsyqoVEkNDw/g3XeBESOk9jExwH//AS4u0qjQ3h5Q63Q/DaSmpuHOnWjcuhWNlJQoqNXRiIqKQlhYCs6cyUBGRgaysjKg0aRDo8mAIGhgbGyCWrVM4ehoAhMTEyQnmyAryxSurvbw9HSEl5cjXF0d4ejoCAcHB9jZ2eH69QwMHLgdAQEbIBV+FHOeqxt69BiJefNGok4dr0K//sVBHyK8F8BRkgv17VxZQh8iTAKZmZJgOjo+fnzfPhE3b6YhJCQJISHxiIpKQFxcEhISkuDjk4ju3ZORkJCACxcSsXdvIoAkSJuXpABIBZAGIB1WVhkAspCdnY3MTA2kN9jz/4elgwC1Wg1TU3M4ODigcuWKqFatGurXr4+mTZuiadOmMCmKopUAt2/fxpIlS7B+/XpkZmYCkEbH3t5tER7eHQkJPQDUhYuLgFGjJDGuX//5YYvk5GSsX78e3333HW7evJnzqDEE4U0MHPgJVq1qCmvrwvmanZ2NTZs24euvv8bVq1dzHq0Ac/PxGDZsPMaNs4e7ezI2bz6N69dPIiDgNM6dO/dEWhkAmANoAKAJzMya4MiRJvD1rQ21Wo0dO6SRf6VKgKcnYGtbOiEafRETo8W1ayexYcMG/PXXX0jOiSUIgjGaNXsVEycORb9+r0Ct6zeGntGHCNcBsB3A8pyf4Xjik89HX/XlmMKI8OTJk/H110shisDjl4J5fhcEQJfXV38IAFQQBDVUKjUqVDCGiYkJTExMERFhBkEwA2kCUpqtFkXp95o1TdCokXTfdfo0ERxMSCu9CUnk0yF9CaSidu0MZGSkIzMzE6GhaTnHsvBotPE8VCoTWFo6wtXVG7VrN0T79u0weHAXODnZ6vvF0InIyEisXbsWu3fvxtmzZ/P8v9Rqd2g0rQG4AnDBJ5+4oFMnZ7i4uCA62gp37gQjOvoOgoMDERgo/YyKug9Synd1d3dHz57vIyrqPSxd6gJv78L55u+fjIkT1+Ly5aWIiQkBANjbu8LRcTxGjXodCQn+OHToBK5fP47k5Mt48n/g5lYVCQmtULlySzRp0gpt2tRFnTpqVK8ujWLLk8g+i8xMLRYvPoUffvgTERFbIYoR8rGaNZtjxIghGDHiLTiUgaRwfYjwo/9ufo1J0jBfMXqkMCI8evRorF27tohXksRSEkwjqNVGsLSUBNPY2BRZWeYwMzOHhYV0+29jUwF2djZwcLCFh4c9nJ0d4OTkBEdHR7i4uMDNzQ3W1tZQqVSF9kQUJXs0QAgIAE6dAqKjpRnnyEggKkr6CQA3bjw+19FRmpmW0AAIAnALwC24uQXA2zsQISEhCAuLRVZWKgoSahMTE7i6uiIrqzYEoR28vfuidu1a8PYGateWRmceHiW7yCI2NhYHDx7E3r17sXfvXkRERDz/pKcQ4OTUFt99Nw59+/aFcSGDiunpwPLl/li5cjVCQzdCuiMCfHx80LFjR5DEH3+cQkrK9SfONIKJSRM0b94WEya0RsuWLeHi4lruhfZJNBoN9u07jfnz/4Kf35Y8wuvuXgVDh76NIUOGoGbNmgb08mn0IcKz8Zx7XpJziuRdGaIwIvzgwQMcO3YNYWFqqNVGMDFRw9LSCBYWalhYGMHCwgxVqliiQgVLWFhYwMLCokgiWZY5c0YS5/h4SYwTEh7Hs/v2fZzSs3UrMGoUkJISA43mAIATAP6DtC1hLKQJnmehAuAIKU7ZFu7u/RAaKuXRhodLcco6dQBvb6BaNaBGDaBiRUAfLzNJ+Pv7w9/fH1FRUYiMjEJUVCSioqIQFRWFmzcTAVSCSuUDExMfODpWg7u7D1q3roLevc0KnXt89mw6pk79C8ePr4ZWe1p+3MjIBQCg1UY+cYYZrK1boE6ddujWrS3efbcFvL3Lfky+KMTFxWHv3r3YsWM3duzYi8zMOPmYWl0FHTq8iRkzBqBdu8YQyui3TrFF+GWhLEzMvehotVK8PDVVSgFKTQU8PROwd+8uHDx4EP/+ewmxsfeh1SY/83yVSgVHR0c4OdXGtWttAfQF0BCSYEuTaD4+wMaNUkoRAGRlFW1yraQRReLChfP47bffsHr1OmRmJuUcEfDkmMfcvAI6dGiDdu3aoXbtdmjb1hd2dmXwSekBURTx33//Yd++fdi9ezdOnz4NUcx9F1UNXl6vY/z4ARg3rnGepellFb2KsCAIVgAcAISRzG8IUy5RRLjskJWVhSNHjuR8CM/gzp1AJCUl5NNagPSWrA6gFYCe2L69HV57TYqx9OgBXLwI+PoCrVpJK+SaNjVM/Yi4uGwsXHgI69evRULCQWRlJeXT0gnW1m3QqFFb9O/fHkOG1IetbbmP+D0Tkrh27RoOHz6MI0eO4NixY4iPj5ePq9VqtG/fHr169YKLSy80aFAddeoY0OEioBcRFgShN4AvIU2vAkBTkpcEQfgRwGGSv+vFWwOiiHDZRqPR4MiRI9i5cyfOnDmDu3fvIj4+AflFyiwtLeHu7o5792pDq20JoAek/QekUbOjIzBoELB8ecn5TBJnzlzF4sWbcejQHqSkXIMUP8+Lh4cHBKELvLzaom/fNnjnnepwdS37I7yikJqaiosXL+Ls2bM4e/Ysjh8/jujo6DxtBMETZGcAvTBpUld89VUhU0rKGPqICfeFtLX9IQD7IW1575sjwtMBtCPZXX8uGwZFhMsfoiji5MmTsjDfunULcXFxT9y+PokZAHsAHrC1rY5p0xqgdu3auHmzBmbOrIJKlYxQowZQr540em7eHHBze342AUlERUVh165d2L17Ny5evIiHD0PlbIm8OMDUtAOWL38dvXu3g0dxijmUYdLS0nD9+nX8999/OHfuHM6ePYuAgABotXlfE1tbd6hUHREX1xFARwBV0KaNgHHjgH79ymY4qTDoQ4QvA7hIcpQgCGpIOUmPRPg1AN+TLPfvIkWEyyeZmZm4cycMFy8+xLVrDxEfHwkjo9vw9/dHcPADhIfHQRQfL1XVDRUAI0gr+yWzs1PD3NwYpqamCAszQna2lLpHZkCKzD09wn2MNVSqOvD0HIhevd5Gp05OqF0b8PIqXu2EskJSUhKCgoJw69YtBAQEwN/fHwEBAbh79+5TaZpGRkaoXbsemjVrjtatm6N169aYO9cHv/4qwMZGWhzy3ntSXvaLgj5EOAPSirkDOdXTsvFYhNsB2M9yWkM4N4oIl00yMjIQFBSMu3fvITj4Hu7du4cTJ4IQGPgAyckh0GiezBwoy1SANAq3A2CPTp3s4O1tD3t7e5w5Y4+AAAdUqGAPOzsHODjYw8XFDm5udqhTxxzDhz8eit+7J8W0ra1LPt83MzMTkZGRcvGeiIgIBAcH4969e7LFxMQ881y1Wo2aNWuiVq26cHHxRXp6cwQENMb58xb4/XdpeTggxexv3ZKyaiwsSvb5GIJiF/CBlKzomM8xLwDR+RxTUNCJtLQ03L17F5cv38G5c4EICLiDoKA7iI6+i/T0UBScIWkEwB1mZhVhbV0Jrq5ueOMNBzg4SBYV5QB3dwdUqmQLJydTWFqqcyqASaZSqZCRkYHk5GSEhYXh2rVruHXrNgIDHyA8PAZJSWlISkpHhQoZcqHyiAgNRNEUgCUEwRJGRpZQqy1gamoKV9dsuLikICUlBbGxyYiISEF2djKys5MhbcWYDGlXMKki16PSmo+IiwOCg/M+JgjGmDzZFnZ2drCxscX589bytc3MLGFuLuWUW1lZoH17Y1SvLj236Gg1wsPVsLZWw8xMhIlJNoyNs2FsrAGZjezsbPm5JyUl5bGEhARERkYiISHhuf8/MzMzVK1aFd7e3qhbty7q1auHunXr4vffa+DUKRPs3Am5MA4g5aXfufP47yZNJHsZ0XUk/BukGY12kN5B2QCaQNrF+ASAKyRHl6CfpYIyEi5ZsrKyEBQUBH//2/Dzu4OrV28jPPwOEhJuIyQkpIAzjQBURq1aVdCmTVVUrVoVKlUVpKdXRqNGldCkiSvc3Y3K/MIEURSRlJSUZ4eJ3DtNhIXFIiIiDtHRsYiJiUVCQiySkxOQlpYAjebp3R1KC5VKDQcHF3h6usLFxQVmZi6Ii/OElVVVmJh4QxCqIjnZBZGRKkREAA8fPi5807o1cDon7bl2baBdOylbpWNHFHr5dnlGHyPh6QDOQVoOtQfSsGQKgPoAbCAlayooQKPR4P79+7h9+w4CA+/gzp07OH1a+pmcfB/5xWWNjY1RtWpVBAdXQ4UKPqhUqRpq1vSBr281tGjhiVq11CjGrjVlApVKBVtbW9ja2qJKlSqFOjcjIwOJiYmIj39UlCkJqampSEhIRVRUKqKjUxEXl4r4+FS4uGhgZqaBVqvF7dsa3LmjQUZGNrKyVMjONkZWljEyM9WwsjLGuHFSjNva2hpffGGNlBRrALnNBaJojw8/VGHWLMmXf/4BXnstf1+Dg6XFMwAwc6a0IrMohdBfFnStJ3xfEITGAOZA2mFDC2lUvBfAFyTDSs5FhbKGFDq4j2PH7uLKlUDcvn0XDx8GIjo6EKmpwch/gkoFoAoEoTpsbHzg7l4dtWv7YNGi6vD09IRarX5mCUYF6XbfzMwMLi4ueumPlMIDuWvjNmgghUJSUx9bZqa0lLpNm8ftatQApk+XJhRtbIAKFaRaFK6ugLu7VGHtET166MXdFxplxVwulHCEREZGJq5ceYiLF4Nx7Vow7twJwsOHQUhNvQeNJkiHmgoVUb26Dzp2rA4fHx8Igg8SEnzQrFlV1K5tCk9P3csfKii8COgjHKHwgqDRaHDvXgQuXw5FQEAIAgNDYGsbgvj4hwgODkZAQDBSUiJQ0ESYsbExvLy8EBVVBdbW1VCxYjX4+FRDvXreaNq0CmrVMoeTkzKiVVDQBZ1FWBCE9gAGAvCElO2eG1Ja3qJgAERRRFxcHKKiohEUFI07d6IRHR0BQQjPSScKx7lzEUhLC89J53pevqwRVCoPmJtXhp1dZbi5VUHVqlVRt24VDB1aFe7u7jDS17YTCgovOTqJsCAIYwCsAhAH4DaAzCeb6NmvlwpRFJGeno7k5OQ8qUKJicmIjk5CREQCIiLiERUVD1PTOCQnSzPqd+/GIS4uGpmZsdB9IYIAwBWmphVRoUJFODh4oHPnimjZsiIqV64Me/vK8PBwf2HrFCgolDV0/aRNBPA7gBEseLvSl4bTp09jwYKfceuWCEDM2b5G+imZBrVrZ0GrzUZWVhbu3s1CamoWtNpMaDRp0GjSodWmQaNJy1nNVVxsAThBpXKChYUT3N1dMWiQG1xdXeHm5obAQFfUqOGGBg1c4OFhooQKFBTKCLqKsAeAXxQBfkxgYCB27fqpwDb57qH4DMzMzFChQgWYm1vjwQNrSCurrGFkZA0zMxtYWNihQgU7DB5sj4YN7WBnZ4eQEHukpjqhWjVHVKpkDDc3aaZaQUGh/KCrCF8EUBVSAR8FAC1btsS8eWtx+7Yqp1i7CoLwyASoVMbo2dME5uYmMDY2xvnzJkhJMYGxsYlc5N3CwgIVKpjD29sMjRpJlb2ys6WC5VZWkqDqa7dXBQWFsomuK+YaAvgNwPsv8rb3SoqagoJCSaCPFLWdkJbPHBEEIQ1A/BPHSbJyMXxUUFBQeCnRVYQPoezsq66goKDwwqDrsuVhJeyHgoKCwkvJi7X9r4KCgkI5Q2cRFgShkSAI2wRBiBEEQZNT0AeCIMwXBEEp06GgoKBQBHQSYUEQ2gA4A6AmpEUbuc8TAYzVv2sKCgoKLz66joQXAtgHoA6AT584dglAY306VRwEQagkCMIWQRASBUFIyhm9exraLwUFBYVnoWt2RGMA/UlSEIQnsyRiADjp162iIQiCBYDDkGpbDIWU0TEPUmpdfZKphvRPQUFB4Ul0FeEMAPltv+cGIFE/7hSb9yCt7KtBMhAABEG4CuAOgDEAvjGgbwoKCgpPoWs44iSA8Tk7LT/i0Yh4JKTRZ1mgDwC/RwIMACSDAJwCUMCGLAoKCgqGQdeR8ExIQvYfgC2QBHioIAjfQNrws2nJuFdo6gDY8YzHrwEYUMq+KJQTRFFEQkICHjx4gLCwsByLRHBwFCIjkxAXl4WUlEy4uSUjMTERiYmJuH8/E4LgAAuLSjAzqwRzc0cYGzvC09MerVrZo08fJzg7O8POzhFqtYlSA0QhX3Te3ignJe0rSHvLGUHKijgB4FOSl0vMw0IgCEIWgG9ITnni8XkAppB86ktHEITRAEYDgKenZ5PgJ/caVyjXhISE4OzZs/D398ft27cRFhaGyMgoxMbGIzk5GdnZGdBqtSXshQ3UaidYWLjByakqvLyqok6dqmjevCratq2CihVdISi1RV9o9LK9EclLADoLgmAGwB5AAsk0PfloMEiuAbAGkAr4GNgdhUISERGBU6dO4cKFC7h+/TqCgoIQGRmJpKQkZGQUtk6zAGl8QUh72T6JEaRNZcwBmABIBpCK5xfUT4RGk4ikpEAkJZ3A3bvAoVz1CC0sLFCrVi3Y29eDu3tdtG9fD1261EXFim6KOL8EFHr7BJIZAMrq7srxAOye8bg9ni46pFBOCAoKwvHjx3Hu3DncuHEDwcHBiIyMQlpaKnS7kzOBVJ/ZAYALAHcAlQBURbNmNfDDD3bYvXs3Vq36GWFhUhFoQRDQpk0XuLm9hT//rAXABw0bOmLUKAG9egFeXlLPJBEWFobLly/j4sVL2LHjKC5fPpJzXVWOafL4YmxcDaamjsjKSkOFCkGIjY3FxYsXIVWMBdavl1oaGdnD2bkRatVqhm7dmmLw4Gbw8PAo+gupUCZ5oXZbFgThMAATkm2eePwopOfavqDzlVKWpc+jLe4fPHiAQ4eOYtOm8wgMvIaYmPtITY2CVpuG59eOMgFgA8AVOckxWL++Plq2bAZvb29UrqxCdDTg4QFUqyZt7V6rFuDoGIUdO77E+vWrodFIQunp6Yk+fYZj0qThqFy5MjIzgQ8+AIYOBdq21W3z0kuXLmHatC+xb9+j6Qlj+Pg0Q1RUJhITH7+/1GpHjB79Jl599VVYWlriq68CcOWKPyIjA5CV5Q8g4am+3d3dUbt2UyQkNEfLlu3QrZsvGjUyhbu7srFqWaagcARIvjAGYDykYUfVXI95AcgGMPF55zdp0oQKxSMri7x/n0xPf/zYb7+Rb79NNm8eTHf3jbSw+IhGRp0IVCVg9Sj3/DlmRjMzDzZv3pxDhw5l+/bLCJwnkE1jY9LJiaxTh+zenRw3Lu/1k5NJUcz9dzJnz55NKysrAqBKpeIbb7zBVav2sXVrDe3syKio4r8Wly9fZvfu/eXnYG5uzvfem842bb6ksXGtPM+vVq26nDx5DVNSUkmSsbEit259yNGj/2aTJtNYv34X2tjYPPN1AdrT1HQm69Q5wBEjUhgXV3zfFfQLgAvMT7fyO1AeDYAlgEAA/pBS0vpAyui4B8DqeecrIqw78fHkmjXk55+TvXuTtWqR1tbZOcK4gu3bj2SbNm1YuXJlqlSWBJ4vtGZmZhQEdxoZNae5+VA6Oy9jvXoX2auXliNHkvv3P75+YiIZHEympenuc1ZWFr/77js6OzvL1+zduzfPn/fnlCmkWi19IpydyZMn9fdaXb16lf37PxZjlaoFJ08O4OnTlzlp0iS6uLjIx4yM7Nit22e8di3oqX60Wi1v3brFJUs2sk2b92lvX/cZr6OarVq15pw5c3j69GkOGpTNvn3JL78k9+4lY2P197wUdOelEWHpucITwFYASZBmTrYD8NLlXEWEH5OWRl6+TP7+OzlpEtm5Mzl4sJb//fcff/75Zw4aNIHAKwTqEHAgYKzDaBYUBDOam7vRza0ZW7R4lx9+uJTnzp1jdnZ2iT6fXbt20cfHR/ajefPmPHbsGA8fJr29pU+CIJAffih9wZQEW7f+Q3Nz9xwfTFilyv94504WMzMz+e67v1Gtbp7rtVKxatW+XLfuGMXcw/gniImJ4d9/b+eYMZ+yenVfqlRGT7zeNgT6EviOwF0CZPXq5IgR5JEjJfM8FZ7mpRLh4tjLKMIpKVIIQavVMjAwkO3b/0VT09kE3iHQjoAPATudRRYQaGJiSQ+PymzTpg1HjhzJFStW8OLFi9RqtaX+/EJDQ/nGG2/I/vn4+HDLli0URZFz50qfAEAKZZw+XfL+xMfHs0uXUblGxQ05c+YliiKZkUHOnn2Wjo6D87ze7u6t+M8//+j0+iUkJPDvv//mBx98kOdL57Eo1yLwGYFjXL788RfftWvkX3+V3BfQy05BIlyYPGFrAK/kjDTNnjhMknN16qgM8yJOzCUkJODatVs4ePAOzp27jzt37iMq6iHS0iKQnR0LIAkqVTpEUfPcvgApa8DMzAy2trawtXVB9epVUa9ebTRu3BgtW7aEq6tryT4hHdFqtVi9ejWmTp2KpKQkWFhYYO7cufjoo49gnLNy4vRpoHNnYNo0YPJkwMSk9PzbsuUghg59D2lp9wEYwcdnFvz9p8HUVFqUevBgBCZPXoVLl1YCiAMA1K1bFwMHTkaTJm+jSxc1jIzy7V4mODgYBw4cwP79+7F//34kJj6uMGBjY4devXqid+/eOHu2F5Yvt4aREdCmDfDaa5JVrar/5/4yUtDEnK4bfbaGtM+cbT5NSFKHt0TZpqyKsCiKiImJQUhICMLCwhAREYHIyEg8eBCFhw+jEBERjZiYeCQnJyA9PQXZ2WkgM0FmF/paarUp1Gor2NjYw83NDd7eldCgQU00atQQvr6+ZUZkC+Lq1asYPXo0zp49CwDo3bs3Vq5cCZWqMnbsAMaNe9w2OhpwMlD5qeTkFAwYMB379n0LAGjfvj02btyISpUqyW0iI1OwceNaLFu2BKGhoTmPesHG5jMMHToCQ4aYoXFj3TIjsrOzcerUKezatQs7d+7E7du35WNqtQmsrbsiPv51kH0gpfMBDRsCo0YBH36opyf9kqIPET4PKVP9PQD+JLP062LZoDAifOnSJfz88z7cvKkFqc25tdBCFKW/tdps1K+fCY0mC1lZWbhxIwvJyVnQajORnZ2B7Ox0ZGdnQqPJgFqdBTOzTGRmZiI9PROpqdkQxWyQWkgLAXS7W8kPlUoFUTQBYAEjIxuYmzvC3t4dVat6omlTb7RpUxO+vvXg7u5erOsYmoyMDMyZMwdfffUVtFot3N3dsWLFCrz6aj+sWCHgiy+A1FTgwAGgSxdDe/uYTZsOYPz4IYiMjICdnR0mT/4Rb7/dH5UrP26TmZmJ3377DZMnL0JMzCPxdAcwGd7e72HQIHO88w5Qo4bu1719+zZ27dqFHTt24MSJE4/mVKBSGcHJqSMSEvojM/N1jB3rjFWrpHPS0oC4OKBiRb089ZeGYqeoAUgB8IoubcuzFSYmPHLkSB1jpPo0FY2MjGlpaUl7e3saG3sQqEWgJQWhN01MhtPObhq9vb9j7957ee/ePYPEYQ3BuXPnWKtWrZy4p8Bx48YxMTGRJ06QDRo8jv3270+GhBja26eJjIxkr1695P+1Wj2aixenUqPJ206j0fDPP/+ij0+DXO8LFwJLOHlyityugLm8ZxIREcEffviBXbt2pZHR48k9lcqIrVp157p165iYmMgNG6QJzE6dyJ9/JpOS9PDkXwJQ3Ik5ANcB9NOlbXm2wojwggULaG5uT0FwoCA4UhCcKAjOFATXHPNgpUqerFq1Kn18fGhqWosqVT2qVI2pUrWikVFnqtW9aGw8gJUqDeX777/PqVOncsKExXR2/pGVKm1nzZon2bTpbXbrlsjBg8lPPiFv3HjsQ2QkGRpKZmbq7PYLR0ZGBqdNmyYLR40aNXj69GmGhZGDBz8WXy8vcvduQ3tbMKIocv785VSpTHJEsCbr1r3Cy5ef3Xb79u1s1KixLJj29k5ctGgRk5OT+fXXZMuW5MqVZExM4fyIjY3lL7/8wldeeYVqtVru39TUlHXq9Kda/ReBNAKkuTn5zjtS+uCTXxgKj9GHCL8F4CwAa13al1d7GbMjyjMXLlxg3bp15dHvxIkTmZaTOPzpp9K729SUnDmTTE01sLOF4MqVK6xY8dFiDlMKwipOmCAyOfnptqIocteuXWzatKkslo6OjqxceSGBZAKksTHZty/5zz9kYTMBo6Oj+cMPP7B9+/Z5FtWYm1vT1XUUgeMERALkq6/q5/m/iOhDhDcCuA8gFsAuABuesPW69FPWTRHh8kFmZiZnzpwpj359fHx4/PhJPnjwuE1srDRCCww0nJ/FITU1lUOHvpcr5PAmmzdPzLe9KIrcu3cvW7RoIZ9jZeXA6tUXUBCS5DsCd3fyl1+K5lNISAiXLFnCJk2a5AmT2dpWoa3tLM6e/fjFvn1bClc864vjZUQfIhz0HLunSz9l3RQRLvsEBASwUaNG8uh3/Pjx3LMnlb6+ZJUqUq7ti8Tvv/9OCwtpebWrqzcvXLhQYHtRFLlv3z62bNlSFkk7O3v26DGf3t6SGG/a9Lh9Wlrh48ckee3aNU6ZMoUVK1bMI8itW7fmTz/9xI8+kq5lZUWOHEmeOlW067woFFuEXxZTRLjsotVquWTJEpqamhIAq1SpwtWrj7FrV8qjPDc30t/f0J7qn1u3brFhw4YEQBMTE3777becNk1abJLfl44oity/fz9btWqVK2ZszxEj5jIqKkFuN3Ik6etL/vFH4UMVpDRRePDgQQ4ZMoSWlpa54seWdHYelidcUbMm+dVX0lzGy4YiwooIl2vu37/PDh06yB/w118fxT59Ht9iW1uT8+ZJq/9eVNLT0/nBBx/Ir4Eg9CcQzxo1yEOH8j9PFEUeOHCArVu3zhU+sOWsWbMYERHHihUff4l5e0v1QIp6N5GcnMxffvmFbdu2zTM6trPzoZXVfAKhBMjhw4vWf3lGLyIMaaPPcQD+AnAo5+cHAMx17aOsmyLCZQtRFLlu3TpaW1sTAJ2dnbl9+z+sVk1655qZkZ99VvjZ//LMX3/9Jb8exsZeBM4SkDJBIiLyP08URR4+fJjt27eXxdHa2pqTJ8/g11/HyPUzALJSJXLVquKFdm7dusWpU6fSzc0tT7qbq2sfLl78j1wrZM8ecvZs8uHDol+rPKCPmLArgJuQVg4EATiT81MEcAOAiy79lHVTRLjsEBUVxX79+skf4F69+jEqp77kb79JhXZCQw3spIG4e/cuc3aBoUqlplq9hIBIOzty7drnx16PHTvGLl26yK+tpaUlP/10Er/7Lox16z4W4ytXiu9rdnY2d+/ezX79+uVJd3N3d+f06dPZuvU9AqRKJWVX7Nr1Yqa66UOENwCIBND6icdbAQgHsE6Xfsq6KSJcNti1a5dc3tHYuAJVqnX89NOXeFbnGWRkZPCTTz6RRc3J6VUCsXztNd37OHXqFLt37y73YWJiwjFjxnLlyrv87LO8bQ8cIIu77iciIoKLFy9m9erV84QrXFy60MhoE4EMAqSnpxReCg8v3vXKEvoQ4WgAI/I5NhJAtC79lHVTRNiwpKSkcOzYsbninu0I3KdKRY4ZY2jvyiZ///03bW1tCYAODpW4bdsp+Vh4uFQh73lcuHAhT71jIyMjDh48mAEBASSlkpcA2bAh+e+/xc9yEEWRx44d47vvvkszMzP5uhYWDrSxmUDgGgFyyZLiXacsoQ8RTgfQI59j3QGk69JPWTdFhA2Hn58fq1Z9VHrRhMBXBDQcOJC8edPQ3pVt7t+/z+bNm8sCunDhQmZladmsGdmoEfnff7r1c+3aNQ4ZMiTPsuXevXtz4cJj9PAQ5TBFhw6kn59+fI+Pj+fKlSvZoEGDPKNjB4dWXLHiF6bkzLauWUOuXl1+J1/1IcJXAPyWz7GNAC7r0k9ZN0WES5+srCzOmjUr1we/LoH/2L//i5luVlJkZWVx0qRJsoi1adOVFSuG89GKuS+/1G1UTJJBQUH84IMP5HRAAGzSpCkHD95MW9tsWYz798+7jL44iKLI8+fPc/To0fK2UwBYoUIFjhw5mvb2ZwmItLWVNhkICtLPdUsLfYjw4JxJuIMARgDoCWA4gH2Q9gYfpEs/Zd0UES5d/P1vsnp1Xz5aeDFp0iROn57O56xHUCiA3bt309HRMSdO7MzevffJotmkiVS8XVciIyP5xRdf0MHBQRZFT08vdumynGZm0pLoSZP0/xySk5P5008/5clxBkBz87oElhGIoUolLcU+erR8LALRV4raaAAROWL8yMIBvKdrH2XdFBEuHbRakWPGrKAgmOdMzFTi4cOHDe3WC0NoaCg7duwoi9dbb31OT88sAlItjRUrCtdfamoqv//+e1arVi1XepsNGzYcz7Nnb8vtTp8mw8L0+1yuXbvGiRMn0snJKVeqmwkF4Q0Cuwhk89gx/V6zJCiWCEOqI9wAgBMAFYBaAFrn/FQ97/zyZIoIlzyHDoXS3r5brtvNIdy5M8HQbr1waDQazps3Tw7zNGnSjG+8Ie0x9803Re9z27ZteRZ+AGDPnj25fftuVqqkpbk5OX68/tMHMzMzuXXrVvbs2ZMqlSpXRocrJ06cJE8ibtpUcL60oSiuCKsgbRnf7Xlty7spIlxyxMWRPXpsprRfHSgIDhw2bMtLXYazNDh58iQrVaqUM3q15owZv+ZJNStqbeWLFy9y+PDheeLGlpbeBJYQiKapKTl2rFTIR988fPiQCxYsYI0aNfJ8GdSv70tB+JbGxpEcNozPLAFqKPQRE74HpZ6wQhGJjY2lj8/b8oelcuVXGBCg5/tWhXyJjY3Nk4I2aNAgJiQk8P590sZGWkZc1Gpn0dHRXLhwIT09PfOEC4ABBPYR0LJ/f+lLWN+IosgzZ85wzJgxtLGxySXIRgR6EviVbdqkcNs2wy8A0YcITwZwDICJLu3LqykirF+ys8k9e/bIS1eNjCw5ffqqArdwVygZRFHk2rVraWFhkfNFWJnz55+kmZmkAtWqkefPF71/jUbDv//++6lwAeBJW9tZvHfvvty2JHbjSEtL4x9//MHevXvnWZkHWBB4h25uu5mUZLjbLn2I8DwAITn2I4C5AL7MZXN06aesmyLC+iE9nZw0KYkODqPlD0Pr1q0ZWF6L+75A3Lp1S64HrFKpOHbsF6xXL1tOZfv66+KvjHvw4AG//PJLenl5yf9/QRDYvn17LliwiqamUezbl9y8uWTqDUdHR/O7775j8+Z5syvs7Ow4bNgw7tq1h+fPl64g60OExeeYVpd+yropIlx8jh0jK1Y8TqAKAVCtNuHixYupMfT9oIJMZmYmp0yZIu+U0bx5Sw4efEdOZeveXT/lJrVaLQ8ePMiBAwfmiR1L4YLuBNbRxCSBr74qFQy6d6/413ySu3fv8ssv57JmzTp5BBmwpaPjMI4fv5txcSVfhFovKWovgykiXHSSksjRo9MIfEpA+nBXr96I/sqKizLL4cOH6eHhQQC0sLDg2LGraG8vUq0mz57V77USEhK4fv169uzZM8+KPGl1ZG8CP9DU9CHT0x+fc++efmO5169f55w5c+jhUfcJQbait/cb/PLL9YyOjtbfBXOhj5GwJwDjfI6pAXjq0k9ZN0WEi8bhw6Sr62kC1XNuPY04ZcoMZiqpD2WeuLg4Dho0SBakjh178ocf8k6a6nvD7kf71nXo0CHPvnUA2KBBA06fPp3Hj5+mqamGlpZkmzbkBx9Iy5ZPntTPJN+lSzfYt++XtLCo/4Qgq9i2bVt+9dVXvH79ut7mL/QhwloAzfI51kQJR7y8pKWlsVu3SQSkyZiqVWvz3LlzhnZLoZBs3ryZdnZS+qC9vT03b95Mkty2jWzRomRCBSQZFhbGH3/8kX379s2zM4cUs7Yn0IdSHRE/AllyyGTbtsd9XLpE7twppcMVZXeQf/+9z3btVlCt7kojI+Mn4sgVOWjQcP7xxx9yKdWioK+YcH4i3AJAti79lHVTRFh3oqOlojs1a9bMGf2q+NlnU5ie+35SoVwRGhrKHj16yAL09tsDWadOLAFp95I//ijZ62dkZHDfvn386KOPWKVKlSdGqKCRkQUrVOhEtXoWly7dzsDAQGq1Wn7wAWVxNjaWtlF67TXy88+lyT/dr0+Ghibyzz//5ODBg2lp6fyUD66uFVm3bl0eP368UM+tSCIMwBZA1RwTAfTL9fcjqwNgFYCH+fVTnkwR4eeTkUF++mkaTUwmy6lINWvWpJ++ymopGBRRFLlq1So5lc3FxY0tWuyQRW7o0JJJMXuWH3fv3uW6des4cuTIpxZmPDILCwt6evrS3X04bW2XENieM2oOJpDBdu0e95mRIVWAGz1aygL55x+pANGjcYMoioyNjeW1a9d46NAhjhixjI6OrxJweeq6X3zxRaGeT1FFeNajzIfnmAhgZn79lCdTRLhg/P1Jb+/juWK/Kn722WfK6PcF5Pbt23mWJzdr9g7NzGIISHvRnTlT+j5FRkZy69atnDhxIrt160Z3d/dnCnNus7S0Z506ddiuXTs2a9aRQGcCXXOyM3rk/PSlSlWRarVxvv0IghHNzetSperGJk068/r164XyvSARFqTjTyMIQgMADQEIAH6GlCt894lmmQCuk7z6zE7KGb6+vrxw4YKh3ShziCKwcGEyZs6cClH8DgDg5VULf/zxM1q0aGFg7xRKCq1Wi5UrV2Lq1KlIT0+Hg4MLKlT4Affv94WPD3D9OqBWG9bHuLg4XLt2DQEBAfD398eDBw8QERGB8PBwREZGQqvVFqo/GxsbuLi4ICnJFRER3pCmvHwB1AdgDgDYvx/o2rVwfgqCcJGk7zOP5SfCT3QwFMAukrGFu3T5QhHhp3n4EOjdex+uXh0N4AEEQY3PP5+KOXOmw9TU1NDuKZQCgYGBGDlyJI4fPw4AqFHjbSxZsgK9ejka2LOCEUURMTExCA8PR3x8PERRfMoAwMbGAaQL6tVzgY2NJLR//gmcPAmkpADZ2ZIZGwOmpsD48UDduoXzpSAR1uk2HUB1AO3zOdYOgI8u/ZR1U8IReYmJiWGfPkPlW7Jq1Zrwij52f1Qod2i1Wq5YsUKOFTs6OvLXX3+lKIqcOJFcvlz/qWwvEtBDdsQeAF/nc2wxpFGywUW0uKaIsERyssgNGzbKxcGNjU05Y8YieZtyhZeXu3fvslOnTvIXc6tW3QlIOya3bUveuWNoD8sm+hDhKAB98jnWG0CkLv2UtAG4j2cH1vvqcr4iwuSGDXdoavp4O/QOHTrw1q1bhnZLoQwhiiJ/+eUXOa/YxMScVlZfEcimuTn51VdFy9d9kSlIhFU6hjQqAMjI51g2ABsd+ykN9gFo+YQdM6hH5YCkpCy0aTMfQ4bUQ2bmQRgb2+Pnn3/B4cOHUb16dUO7p1CGEAQBw4YNw82bNzFw4EBkZaUjJeUz2Nk1Q3r6RXz2GdC8OXDpkqE9LR/oKsL3AHTO51gnSCPQskIMSb8nLN7QTpVlfvrpFJydm+DUqekAMtCgwbsIDr6J4cOHQRAEQ7unUEZxdnbG77//jj179qBy5cqIj78MlaoZrKw+wqVLCfj+e0N7WD7QVYQ3AJggCMKHgiCYAoAgCKaCIHwIYDyA9SXkn0IJEhISiYYNh2HUqDbIzAyAsbE3Vq48gCtXNsDNzcnQ7imUE3r27ImAgAB8+umnEAQBKSkrYWlZE40bb3wUJkRoqJTqqPAM8otTMG+s1QjAFkgLMzSQYsSanL//QhnZaw7SiDwRQBqkHGY/6BgP5ksUE87Ozua3336bazcCUzZvPpOxsWmGdk2hnPPff//lWeTRrl07Xrrkzxo1yGbNDLPIoywAfZWyhBR6WAhgDYD5ADoU5vySNgArAAwB0BbAGwCO5rwZBhdwzmgAFwBc8PT01NdrXmY5cuQk69VrIH9IWrd+hb/+qkxpK+gPrVbLX375Rd4h2cjIiJaWEwkkESDffJO8e9fQXpYuehPh0jQAXfDsTIcn7WgBfRgBOA8da1u8yCPh0NBQvvLKEPl1q1y5Mnfs2KFsNaRQYsTFxfH999+Xy1VaWrpSrf6ZgJbGxuQnn+ineHx5oCAR1mnFHAAI0gzNq5AWZzgAmE0yWBCE9gDukAzTqSMdEQTBAlId4+eRRvJBAf18DmARAHeS4QV19CKumEtLS8P8+UuwaNFCaDRpAExgZzcZ169PgaurhaHdU3gJuHDhAsaNG4ezZ88CAOztmyAubhmANqhVC7h2DXjR53/1sWLODsAZSDHgREiFexrnHPsVwLe69GMIA/A5pNGf6/PavkgjYa1Wy40bf6WDQ8Vcdw39OWpUIFNTDe2dwsuGVqvlr7/+Ku/kAYDu7m9x4cJguU1CAhkfbzgfSxLoYbHGj5A2+WwJaScNMZcIDwNwTZd+SttyfL0IIFiX9i+KCJ8+fZpNmzbLJb6NWKPGUV66ZGjPFF52UlJS+MUXX9DMzIwAaGZmxhkzZjAxMZFTpkh1i2fMkOpVv0joQ4SjAQzN+d3oCRHuBCBJl35K0gAMBLAJ0sRcRwBvAziRI0Rv69JHeRfha9eusV+/frL4mpu70tz8Zy5frtHrXl0KCsXl/v37fOutt+T3qpOTE+vVW0EgkwBpaUlOmEA+fGhoT/WDPkQ4HUAXPluEXwGQrEs/JWmQdvg4DCAS0iq+BAAHAXTXtY/yKsJBQUEcMmQoBUGVI77mnD59OoODkxkRYWjvFBTy59SpU2zV6vHW9B4e3mzYcDMBkY92yhg+nAwMNLSnxUMfInwFwGI+W4QXATitSz9l3cqbCEdGRvKjjz7OVYxaTVvbDxgcHPb8kxUUygiiKPLvv//Os3tGnTpN2bHjEapUkkoVcjehMoc+RHg0gCwA0wFUyRHhTgCGA0gF8I4u/ZR1Ky8iHBERwcmTJ9PM7NHGiAKBd+jhEcjffiOVrDOF8kh2djZ/+OEHurq65spj78oPPvDL856eNEna7648FQkqtghLfWAhpFVyj7Y00ubc9v9P1z7KupV1Eb5//z7HjRtHU1OzXJNur9LG5iq/+UbaQ0tBobyTnJzMOXPm0NraWn6f9+7dm5cuXeK1a5JqAaSnp7RXXEKCoT1+PnoRYakfVAYwCsA0AGMAVC3M+WXdyqoI37hxg8OGDaNarZbflKamfWlldZZz55KJiYb2UEFB/8TGxnLq1KlyIXkAfO21/pw505/Vqz8WYysrcvx48t49Q3ucP3oT4RfdypIIi6LIgwcP8tVX+8krjlQqFd955x36+/vz1KkXN6dSQSE3kZGR/PTTT+W0NkEQ+MYbA7h8+WV26PBYjC0sSmcn6KJQkAgXtNGnLqvVZFjAqrXyQllYMRcfH4/169dj2bJVCA6+nfOoCYDh+OKLzzBnjrch3VNQMBhhYWFYsGAB1qxZg6ysLABA79698cYb03HoUAtYWUEun6nRANu3A6+9Ju0NZ2iKtGIOum13L1t+/ZQnM9RIWBRFnjt3jsOHj6CxsXmueK8HgTls1iyMf/1VviYiFBRKipCQEE6YMIHm5o8/K506deLBg4fkWih//imNjitWJBcuJOPiDOszijgSHpbzBHWCZLmvKVyaI2GSOH/+PDZu3Io9e7bg3r17uY52hYXF+3j33Vfx4Ydq1KtXKi4pKJQroqOjsWzZMqxcuRJJSUkAgObNm2PixIlQq/th2jQ1bt6U2lpYAMOGAR9/DNSoUfq+FnvL+5eFkhZhjUaDU6fO4ocftmLv3q1ISHgcwXF2dsbgwYPRoMFYmJj44LXXAHPzEnNFQeGFISEhAStXrsSyZcsQGxsLAKhSpQo++WQ8KlUagR9+sMKBA4/bv/8+Sn3XjxIVYUEQVABsScYVq6MygD5FmCQePnyIc+fO4cyZs9i69RxCQi5Cq03N1codKtXrmDDhdSxa1AZGRkZ6ubaCwstIamoq1q1bh6VLl+Lu3bsAAFtbW4wZMwZdu36EzZs9sHEjsHAh8Mkn0jmJiYBaDVhalqxvRRJhQRDiIC1VvpTztwBgB4DxJO/latcc0oq5cq8ghRHhsLAw7N9/BZcuxSIhIRbx8bGIiYlFXFwsEhJikJBwHVlZEc840xu2tq+hffs38M47zdGjhwoVKuj3eSgovMxotVr8888/WLJkCU6dOgUAUKvVeP311/HOOx+iY8c2sLKSamfOmAF89x0wYgTw4YdA1aol41NxJuaa5fo7z3LlXI83x0s4Mbd27drnFpy3tbVj9+7dOXPmTE6cuIs//hj1whQkUVAoD/j5+XHAgAE0MjKSP5f16tXjDz/8wOTkZL72GuUUN0EgX3mF3L2b1Gr16weKODEnAmhB8lzO30aQVsj5Mmd0nPP4SzkSPnr0KD7/fCHCwx1gbu4AS0sHODg4wNnZEZ6eDmjUyAv9+lWDickLXq1aQaEcEBISgtWrV2PNmjWIiooCAFhbW2PYsGFo1Wo09uypg82bgcxMqX2VKsCyZUCfPvq5flHDEYoIKygovFBkZWVh69atWLlyJU6fPi0/3qJFC7z55kgkJ7+FX36pgPv3gSNHgA4dpOMxMYCdHVDUaZuCRFjXLe8VFBQUyj0mJiYYOHAgTp06hcuXL2PMmDGwtraGn58fPv30PSxe7IYOHUZg2bJTaNfu8QB16FBpdDxzJhAUpF+fnjcSfh3AfzkPGQG4BeA1ANdyNW0E4E9lJKygoFAeSUtLw5YtW/DTTz/h+PHj8uM+Pj4YNGgQ3njjHfTr54PAQOnx1auB0aMLd43ihCOePCjk95giwgoKCuWdO3fu4Oeff8a6desQEfE4u6lp06Zo1uwdxMS8hR9+cIGtbeHmeooqwkMLcxEqK+YUFBReEDQaDQ4fPozffvsN27ZtQ0pKCgBAEASYmZlhy5YteOWVV3TuryARVud30osgqgoKCgpFQa1Wo1u3bmjYsCHq1q2LVatWISgoCCSRnp6OY8eOFUqEC7yWXnpRUFBQeEHIzs7Gjh07sH79evz777/QarUAABsbG/Tp0wceHh6YO3eu3q6niLCCgoICpFzitWvXYu3atQgPDwcAGBkZoVev3mjS5F3cu/cqhg41R+fO+r2uIsIKCgovLSRx+PBhfP/999ixY4c86q1Vqxbeems0MjMHYfNmZ+zeLbXXaKCIsIKCgkJxSUtLw4YNG7B8+XLczKl3qVarMWDAALRq9QGOHm2PuXMF5GgyKlaUcoWHDNG/L4oIKygovDRERkbiu+++w/fffy+XvXR3d8eYMWMwatQouLu744svgB07pOpqr78OjBoFdO1a9NVyz0MRYQUFhRee69ev45tvvsGvv/6KzJwCEU2bNkWfPhNx48brcHBQw91dajtqlFTLe/hwwNW15H1TirrnQskTVlB4sTh16hQWLlyIXbt2AZDyfHv16oN69SZi3742uHRJWnRRowZw4wYglFC9rSLlCSsoKCiUR0hi7969WLBgAU6cOAEAMDMzw5tvDoeFxXhs2VIdOZoMBwdg5Ehg7NiSE+DnoYiwgoLCC4FWq8Vff/2FhQsX4r//pJI3tra2GDduHD7++GMcO+aEAQOkto0aAR99BLz9tuG3EVNEWEFBoVyTlZWFDRs2YNGiRQjMqbLj6uqKTp0+RY0aY/DFF9YAgL59gTFjgHffBVq1MtzI90mUmHAulJiwgkL5IS0tDWvXrsXXX3+NkJAQAICXV1U0avQ5zp0bitBQM5iaAg8fAk5OhvVViQkrKCi8MCQmJuL777/H0qVLER0dDQDw8amDqlWn4cSJN/H335Ks1awpbehpZWVIb5+PIsIKCgrlgujoaHz77bdYsWIFEhMTAUhpZmPGTMfo0a/izh1pj4ouXYAJE4AePQBVOdi2QhFhBQWFMk1ISAi+/vprrFmzBunp6QCABg3a46uvpqNLly4QBAE7dwI2NsDEiUD9+gZ2uJAoIqygoFAmuXPnDhYvXoz169cjOzsbAFCvXi8kJEzFf/+1hoXF48m1bdvKx6j3WSgirKCgUKa4dOkSFi1ahC1btkAURahUKtSr9xZCQ6fA378hAKByZSA+/vE55VWAgXIiwoIgfAqgIwBfAK4A5pCcnU/bvgBmAagFIBLAWgALSGr16VNISAgOH/4PMTEVYGNjDXv7CvDwsEalShXg4mIKlaqM5L8oKJQDSOLQoUNYtGgRDh48CAAwNjZGgwYjcPPm5/D39wEg5fd+9hkwYIBU2+FFoLw8jfcAJAHYDmBsfo0EQegOYCuAnwB8CmkT0vkAKgCYrE+Hjhw5gqFD8yuppIZa7YIWLXxQq5YPfHx8YGnpg4YNfdC4sTfMzMz06YqCQrlFo9Fg69atWLx4MS5dugQAsLKywpgxYzB+/Hh8+21FXL4MdOsmiW/nzmUnv1dvkCzzBkCV81MNaaPR2fm0uwzg2BOPfQEgC4Dr867TpEkT6sq+ffvo69uDNjataWFRjyYmXlSpHAgYM8fHfMyItrYN2aLFGE6d+hMvXvSnRqPR+boKCi8CycnJ/Pbbb1m1alX5s2Fr68wqVf7Hr7+Ok9uFh5OXLxvOT30B4ALz0Z1ytVhDEAQ1gGw8IxwhCEIlAA8AjCa5NtfjVQDcAzCC5C8F9a+vxRoxMZn4778QZGffwZ07d3D79h389tsdJCQEgrwHQMzT3tTUCi1b+qJNmzbo2LEjWrZsCXNDr6VUUCgBQkJCsGLFCqxevVpOM3Ny8oZKNQmRkUMBmKNxY+DiRcP6qW8KWqxh8FFuYQwFjIQB9Mg51vIZx1IBfPW8/gszEi4K2dnk2bMpnDz5OJs3/5rW1m8SqPzUaFkQTFm5cnsOGzabBw4cY0ZGRon6paBQ0ly4cIGDBg2iWq2W3+cVK7ahpeU2AhoCZKVK5FdfkQkJhvZW/6CAkbDBhbUw9hwRHpRzrOYzjoUA+CmfPkcDuADggqenpz5e70IRE0PevRvB7du3c8KECbS3b0hAyCPKKpUFq1fvyU8/Xcpr165RFMVS91NBobBkZmby999/Z6tWreT3spGREd9++23OmXOWgKRAzZqRmzaRWVmG9rjkKFMiDKDLkyO/fOzoM87VuwjntpIeCetCXBy5cWMse/XaRgeHjwnUfeq18fDw4LBhw7lw4R+MiooxtMsKCnkICQnhzJkz6eLiIr9nzcxs2KrVJAYHB5MkMzPJMWNIPz8DO1tKFCTCpR4TFgTBAoCnDk3TSD544tyCYsI9AewB0IrkmSeOpQL4nuRnBV2wLBbwiYwEtm0Lx59/HkRKyn48eLAfUVFRuVoIsLNrhmbNuuOdd3rg7bebwdi4hPZhUVDIB1EUcezYMaxatQrbtm3LtU18XaSmfgSN5h1YWFgiNBSwtTWsr4bgZYkJe+YcG/XE4145jw9/Xv9lYST8PLRaLa9cucKRIxfT1LQzAZMn4sl2dHcfwGXLfuTDhw8N7a7CC054eDgXLFhAb2/vXO9BI1paDiBwjIBIQSB79iS3b5fmRV5GUJbCEcWxgkQ45/gVAEeeeGwGSiBFrSwgiqS/fwo//ngXa9QYR7W62lOhi9q1a7Nx4wkcPPhf7tmTxpQUQ3utUN7RaDTcvXs3+/btSyMjo1wTbRX5wQdfEAghQHp6krNnk/fvG9pjw1OQCJeLFDVBEHwhjWhVADYD+AvAnzmH95BMy2n3CoBdkFbJ/QFpscYCACv4nFAEUDbDEYWBBI4fv4utW/chOHgfDh8+jJSUlFwtTCEIbVGxYle0a9cFffs2RMeOKjg4GMxlhXJEQEAANm7ciN9++w2hoaEAAEEwgq3tq/j11/fQvXt3GBkZYfZsoG1boGPH8r2cWJ8UFI4oLyK8DsDQfA5XIXk/V9v+kJYt14S0bPlHAP+jDsuWy7sIP0lWVhaOHTuDVav24dSpfYiKuvRECwc0a9YZo0Z1QdeuXaHReCE7W6rD+sKtSlIoEmFhYfjjjz+wceNGecsgABAEb5CjAAyDILgiMBCoWtVwfpZ1yr0IlxYvmgg/SVRUFHbtOoQ//zyIM2cOICnpYZ7jFSp4ITm5IywtO6Jly47o0qUi2rQBmjQBlJXWLw8xMTHYvn07/vzzTxw6dAiiKC0uEgQ7kG8CeBdAKzRpImDQIOCttwAPD4O6XOZRRFhHXnQRzg1J3LlzBwcPHsTBgwdx+PBheQXTY6oB6Agjo3Z48822+P33yoZwVaEUiIyMxN9//40tW7bg6NGjcnaDiYkJevfujTffHIxRo16Bp6cpBg6UhNfHx8BOlyMUEdaRl0mEn0Sr1eLKlSs4cuQo9uw5gjNnjiMjIzlPm0qVKqFNmzaoVq0t1q9vg44d66BNGxVatZJCGEr8r3wRGBiI3bt3Y/v27Th+/Lg84pXmv7vAxOR13LvXHx4e9gCA8HDAzc1g7pZrFBHWkZdZhJ9Eo9Hg0qVLOHr0KA4fPoGzZ08hISH+iVY2AJoDaA5LyxZo0aI52rd3wKefApaWBnBaoUCysrJw/Phx7N69G3v27MHt27dzHTUB0A3AGwD6oG5dO7z+urRNkI2NYfx9kVBEWEcUEc4fURRx/fp1nDx5EseOncCRIycQGfnwqXaC4IOBA5ujadMmaNKkCY4ebQg3twpo3hyoXRswUtaRlBokcf36dRw+fBiHDx/GwYMH82TL2NraonXrHti9uzeA3mja1Ab9+wP9+gE1ahjO7xcRRYR1RBHhwhEaGoqzZ8/izBk/HD/uhytXLiArK/2JVgKA6gAaw8SkCWrUaIDWreuhfXsXtG+v3N7qk0dx/iNHjsiWd3UlANSDs3MvbN3aCy1atIBarcaGDVI6WaVKBnH7pUARYR1RRLh4ZGdnw9/fH+fOncOlS5dw/vxF+Pv7Q6vNfkZrJ9SqVQ/dutVDvXr1IAh1kZ5eAy1b2qJ2bSUbQxcSExNx/vx5+Pn54ezZs/Dz80NMTMwTrdwhbUrTCUAXODh4omdP4OefAWPj0vf5ZUURYR1RRFj/ZGVlISAgAJcuXcLJkxdx/rw/7t71R2ZmUj5nuACoARubmvD0rIHatWugdeuqGDXK66WusRwZGYmrV6/KduHCBdy4cQNPfn6dnZ3Rvn172Nt3wurVHSEI1dG8uYCuXYFXXgGaNlVCQoZAEWEdUUS4dCCJBw8ewN/fX7bTp28gJOQWtNonwxmPcXNzQ5UqVREYWBVublVQubInfHw8UKdORTRs6IFatWxhZlZ+V5lkZ2fjwYMHCAwMRGBgIO7cuYNr167h6tWrzwgrAIAxgMaQJkdboG/fFti2zQuCICAxEThyBGjfHrCzK93nofA0igjriCLChkUURYSEhODq1Zs4ceIWLl68ibt3byMlJQgJCcHQaDTP6cEC7u4e8PFxh7OzM5KTnZCY6AwnJye4uzvDzc0J7u62cHOzgaenLerUsYaqlPLqMjIyEBMTg7CwMISFhSE8PFz+/cGDENy6dRdhYffl/Nwnsba2Rv369fHggWRAAwANYWNjhqZNgWbNgK5dgQ4dSuXpKBQSRYR1RBHhsotGo0FISAiuXw/C4cP3cONGEB48eIjo6FAkJoYgMzMEZGqh+7W2toaNjQ3CwiyhUlnAyMgcarU5jI0f/TRFrVpGqFJFDSMjI0RFGeHWLSMYGakAaCCKWRDFbGi1ktWrl4WUlBQkJCTg7t1EpKYmIDs7EWSWjh5VgrRIphoAbwC18c8/9dG7tycEQcDGjcCdO0CDBkDDhkCVKkp+dnlAEWEdUUS4/EIS8fFJCA0NQVRUBKKjo3H6dBSuX49GdHQUEhOjkZISjYyMRGRlJYBMhEaTX1y6JDABYA9poswd1au7YeBAd7i5uYF0x6JF3nBxqQJ3d3O4uEjLgCtVAjw9AV9foEKFUnRVQe8oIqwjigi/XGi1WiQnJyMhIRFhYamIj09HfHwakpLSkZSUjpSUdKSnZ8LVVQsbGw20Wi1CQ7W4c0cLrVaEIBhDEIyhUhnD2Fiynj2NYWNTATY2Nrh50xaiaAMHB1tYW5vBzAywsJAWstjZAfb2hn4FFEqLgkRYXdrOKCiUFYyMjGBrawtbW1t4eem//+bN9d+nwouHEk1SUFBQMCCKCCsoKCgYEEWEFRQUFAyIIsIKCgoKBkQRYQUFBQUDooiwgoKCggFRRFhBQUHBgCgirKCgoGBAFBFWUFBQMCCKCCsoKCgYEKV2RC4EQYgGEFzI0xwBPLmdgcKLj/J/f3kpyv++MkmnZx1QRLiYCIJwIb/CHAovLsr//eVF3/97JRyhoKCgYEAUEVZQUFAwIIoIF581hnZAwSAo//eXF73+75WYsIKCgoIBUUbCCgoKCgZEEeEiIAjCMEEQKAhCNUP7oqCgULIIgrBZEIQ4QRBcn3jcSBCE84Ig3BEEwbyo/SsirKCgI7m+fJ9lAYb2T6HE+AgAAXz/xOOTADQBMIpkelE7V/aYU1AoPAMAhDzxWJohHFEoeUhGCYIwAcB6QRAGkPxLEITqAGYDWE3yWHH6V0RYQaHwXCEZaGgnFEoPkhsEQRgIYKUgCEcA/AQgGsDnxe1bEWEFBQUF3RgD4BqAswCqAuhFMrm4nSoxYQUFBQUdIPkAwEpIAryN5B599KuIsIKCgoIOCIJgDeBdSJN0TQVBqPD/9s4+Rq+iCuO/x5YWolZopUrkoyZWGqMJMdZYtevGaG0o0IaoRKHJSpCojR9EjSSgJUbBxliCFCXZmga6ILEYNAaLYCzdLeGjGr9CZavNRqUW+gGpxbS0occ/zrwye9234rb0bprnl0zenTkzZ+a9m33u7LlzZ46FX4uwMca8NL4NnAYsAmYCNxwLpxZhY4z5H0jqBT4JXBsR64FvAJ+W9O6j9W0RNsaYI1BexOgHNgM3leIV5EO61ZKmHI1/r444OhZKeqpRtjciHmhlNMaYl4OvA+cAF0fEYYCIOCTpCuBh4Bpg+XidW4SPjpvHKHsceOvxHogx5tgj6R3AVcD1EfHH2hYRj0m6Cbha0o8i4vFx9eFd1Ix5aUjqA9YAs/2yhjlWWISNMaZF/GDOGGNaxCJsjDEtYhE2xpgWsQgbY0yLWISNMaZFLMLGGNMiFmHTGpI+Vo4G6mmUv66UPz1Gm2XFdsK/ECPpPEnXSZre9ljMy4dF2LTJYPnsaZT3kMcFzZQ0ZwzbHvLNxBOd88jXYS3CJzAWYdMaEbEd2MbYIvyrLrb5wKbwW0bjQtLUtsdgRmMRNm0zCMyTVO9j0gMMAZuoRFjSbOAMYKOkuZLulvSkpP2ShiVdXx89LukWSU83fCNpqqRny3v/nbLTJd0qabuk5yU9IenKyj63hEEuan4BSd+TtEvSSVXZlZJ+L+mApN2SftAMK0iaLOkrkraUersk3SdpTvWKNMCfq1OdZ5W20yStkvSPMt5hSVdJUuW/t7S5WFK/pF3Af4V4TLtYhE3bDAKvAt4OIOlUcgOkoZLmV3V7qjZnA78DPgUsJLcYvJwXhQtgLbn59oJGnxcApwK3lz6nkYJ/PnmC7iLgZ8D3JX0WICI2A8PAZbWjso3hJcBdEXGolH0LuAX4JXAR8OUyxvWSJlXN7wK+CfwcWELuV7uFvNHcS+5ZC3m687ySdkh6RbF/AvgOcCFwH7Cy+GtyMyDyVIi+MeymTSLCyam1BLyRPC7mSyV/IRkPngK8udhmFdttwF5gUsOHyB0BLwMOAzMq21bgh436PwG2VPmvAgfIjXnqev3AbmByyV8D7AdeU9VZUsb4zpKfBbwAfK3h6z2l3pKSf3/Jf+4I16av1HlTo/yCUt7XKF8NPA+8tuR7S7172v49O3VPngmbVomIEeBJXpzl9gCPRsTBiNgK7GzYHoqIF8q/4yskbSOF5xA58xUwu+piLbC4cx6YpBnkjHdtVWcheYLuSAkRTC4hjF8AM4C3lHoDwFRyZtphKTAcEY+V/AfJ/zDvaPh6FNhXfZcFpED2/5+XrHMdDgN3NsoHyJvXvEb5PePowxwnLMJmIjAIvLfEMzvx4A6bgB5JZ5KzzM6KijVkKOK7pPDNBZYV28lV+4GS/3DJX0LOmgeqOjNLv4caaV2xzwCIiL+W/pfCf0Inixgt6DPL51/G8Pfqjq/y+UxE7O9+WboyvbQ92Ch/qrLX7BhHH+Y44U3dzURgI/Bx4F1kbPjayjYEfAZ4X8kPSjoZWAxcFxH1w7W3NR1HxIikh8hQxZry+WBE/L2qtoeccX++y/iGq5/XAv2SzgE+RM48a0HfUz4XAM+O4atj3w1Ml3TKOIT4mdJ2SkOIX1/Za7ySZALjmbCZCHRmt1eT4YSHK9smMrzwUTJWvJkMCUwiZ5c1fV383w70lsMa5zF65gr5UGsO8LeI+PUYaV9Vdx0Z/riUnBEPlRlyhwfIUMHZXXyNlHr3l+96RZcxU/oBOKVRvpH82/1Io/xS4CCjr5+Z4HgmbFonIp6QtJN8KPebiHiuMv8WeK7YNkSuQNgr6RHgi5J2kLPKy4E3dOliHblCYIB8sHZ3w34jGaYYknQjOfN9JSnM8yNicTXWf0r6KRn6OINc0VB/l22SVgCrJJ1LCuYB4CwybLI6IjZExAZJPwZWSjqLXBd9EhkWuTciHiRXSgAsk3QbedP5A7CevDndKul08sWV80lBvyEidne5DmYi0vaTQSeniIAUygBWjmG7v9iWV2WzSDHaR4YSVpHx2QB6j+D/zi79n0aK8Qg5m9xJhkK+MEbdTj+jVko06iwFHgH+Rd5E/lTGeGZVZzK54mJr6XMXuVzt3KrOcmA7ueKiXikyrfjbUdpuJc9CU9W2t7T5QNu/X6fuyccbGWNMizgmbIwxLWIRNsaYFrEIG2NMi1iEjTGmRSzCxhjTIhZhY4xpEYuwMca0iEXYGGNaxCJsjDEt8m+fo/NXDRoy2gAAAABJRU5ErkJggg==\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Electrons\n", "\n", "Band_EPW=plot_bands.plot_band_eig(f'./{silicon.prefix}/epw/band.eig')\n", "Band_QE=plot_bands.plot_band_scf(f'./{silicon.prefix}/bs/bs.out')\n", "\n", "plot_bands.plot_band_prod(Band_EPW,\n", " ef0=ef_from_file,\n", " xlabel='Wavevector', \n", " ylabel='Electron energy (eV)',\n", " xticks=['L','$\\Gamma$','X'],linestyle='--',color_c='b',color_v='b',first = True)\n", "plot_bands.plot_band_prod(Band_QE,\n", " ef0=ef_from_file,\n", " xlabel='Wavevector', \n", " ylabel='Electron energy (eV)',\n", " xticks=['L','$\\Gamma$','X'],first = False) # False controls if this is the first set of plots \n", "\n", "# Phonons\n", "\n", "PH_epw=plot_bands.plot_band_eig(f'./{silicon.prefix}/epw/phband.freq')\n", "PH_matdyn=plot_bands.plot_band_eig(f'./{silicon.prefix}/ph/si.freq')\n", "PH_matdyn=PH_matdyn*0.124\n", "\n", "\n", "plot_bands.plot_band_freq(PH_epw,\n", " xlabel='Wavevector', \n", " ylabel='Phonon energy (meV)',\n", " ef0=0,\n", " xticks=['L','$\\Gamma$','X'],linestyle='--',first = True,color='blue')\n", "\n", "plot_bands.plot_band_freq(PH_matdyn,\n", " xlabel='Wavevector', \n", " ylabel='Phonon energy (meV)',\n", " ef0=0,\n", " xticks=['L','$\\Gamma$','X'],first = False)\n" ] }, { "cell_type": "markdown", "id": "3cb07363", "metadata": {}, "source": [ "### Calculation of carrier mobility\n", "\n", "In order to compute the carrier mobility, we perform the following operations:\n", "1. We interpolate the electrons, phonons, and electron-phonon couplings onto a fine Brillouin zone grid (60 x 60 x 60 for electrons and phonons in this example)\n", "2. We use these data to solve the BTE within EPW\n", "\n", "Both steps are performed within a single call of EPW. Note the keyword `temps` which is used to perform calculations for multiple temperatures (300 K, ..., 100 K in this example)." ] }, { "cell_type": "code", "execution_count": 33, "id": "90f85efc", "metadata": { "scrolled": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "rm: cannot remove './epw/si.epmatkq1': No such file or directory\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "-- -- -- -- -- -- -- -- -- -- -- -- -- Warning -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n", "Refreshing EPW input (remove refresh from epw_save.json if not needed)\n", "-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n", "-- -- -- -- -- -- -- -- -- -- -- Calculation: epw2 -- -- -- -- -- -- -- -- -- -- -- \n", "Running epw2 |████████████████████████████████████████| in 6:26.9 (0.00/s) \n", "\n", "-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- \n" ] } ], "source": [ "#silicon.reset()\n", "silicon.epw(epwin={'elph':'.true.', \n", " 'etf_mem': '3',\n", " 'nkf1':40, \n", " 'nkf2':40, \n", " 'nkf3':40,\n", " 'nqf1':40,\n", " 'nqf2':40,\n", " 'nqf3':40, \n", " 'mp_mesh_k':'.true.',\n", " 'efermi_read':'.true.',\n", " 'fsthick': 0.3,\n", " 'fermi_energy':6.5,\n", " 'temps':'300 250 200 150 100',\n", " 'degaussw':0.0, \n", " 'scattering':'.true.',\n", " 'int_mob':'.false.',\n", " 'carrier':'.true.',\n", " 'ncarrier' :'1E13',\n", " 'iterative_bte':'.true.',\n", " 'nstemp': 5,\n", " 'clean_transport':None},\n", " name='epw2')\n", "silicon.prepare(type_run='epw2')\n", "silicon.run(16,type_run='epw2')\n", "\n" ] }, { "cell_type": "code", "execution_count": 53, "id": "2647d4c2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "/mnt/storage/sabya/For_video/epwpy/notebooks_basic/si\n", "obtaining nscf and ph attributes\n", "916.544 300\n", "1411.82 250\n", "2516.74 200\n", "5680.29 150\n", "18524.0 100\n", "[1106.83, 1612.69, 2532.93, 4305.52, 7503.36]\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "print(os.getcwd())\n", "silicon.reset()\n", "silicon.epw_fold = 'epw'\n", "silicon.epw_file = 'epw2'\n", "temps=[300, 250, 200, 150, 100] \n", "mob=[]\n", "font=16\n", "for T in temps:\n", " silicon.epw_params['temps']=T \n", " print(silicon.ibte_mobility_e[0,0],T) \n", " mob.append(silicon.ibte_mobility_e[1,1])\n", " plt.scatter(T,silicon.ibte_mobility_e[1,1], color = 'crimson')\n", " plt.scatter(T,silicon.serta_mobility_e[1,1], color = 'royalblue')\n", "print(mob)\n", "plt.plot(temps[::-1],mob[::-1], color = 'crimson')\n", "plt.xticks([100,150,200,250,300],fontsize=font)\n", "plt.yticks([1000,3000,5000,8000],fontsize=font)\n", "plt.xlabel('Temperature (K)',fontsize=16)\n", "plt.ylabel('$\\mu$ (cm$^2$V$^{-1}$s$^{-1}$)',fontsize=16)\n", "plt.xticks(fontsize=16)\n", "plt.yticks(fontsize=16)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "05fd32cd", "metadata": {}, "source": [ "\n", "$\\underline{\\large \\rm We\\, now\\, calculate\\, the\\, drift\\, current\\, in\\, linear\\, regime}$\n", "\n", "\n", "$J_{\\rm drift} = e n \\mu E$" ] }, { "cell_type": "code", "execution_count": 37, "id": "08d4bd45", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "300\n", "250\n", "200\n", "150\n", "100\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "E=np.linspace(0,1,50)*1e6 # V/cm\n", "n=1e15 # cm^-3\n", "e = 1.6*10**-19 # Coulomb\n", "J = []\n", "\n", "for mu in mob:\n", " J.append(e*n*mu*E) # Ampere/cm^2\n", "for i,T in enumerate(temps):\n", " print(T)\n", " plt.plot(E,J[i])\n", " plt.text(E[-15],J[i][-15],str(T)+' K')\n", "plt.xlabel('$F \\\\rm (V/cm)$',fontsize=20)\n", "plt.ylabel('$J \\\\rm (A/cm^2)$',fontsize=20)\n", "\n", "\n", "\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "acfc6e66", "metadata": {}, "source": [ "$\\newcommand{\\mrm}[1]{\\mathrm{#1}}$\n", "$\\newcommand{\\vec}[1]{{\\mathbf{\\mathrm{#1}}}}$\n", "$\\newcommand{\\Ver}[1]{$V_\\mathrm{er}$}$\n", "$\\def\\>{\\rangle} $\n", "$\\def\\<{\\langle} $\n", "$\\def\\bk{{\\bf k}}$\n", "$\\def\\bq{{\\bf q}}$\n", "$\\def\\be{{\\bf e}}$\n", "$\\def\\bv{{\\bf v}}$\n", "$\\def\\a{\\alpha}$\n", "$\\def\\d{\\delta}$\n", "$\\def\\w{\\omega}$\n", "$\\def\\ve{\\varepsilon}$\n", "$\\def\\hc{{\\hat{c}^{\\phantom{\\dagger}}}}$\n", "$\\def\\hcd{{\\hat{c}^\\dagger}}$\n", "$\\def\\hH{{\\hat{H}}}$\n", "$\\def\\hp{{\\hat{\\bf p}}}$\n", "$\\def\\ha{{\\hat{a}^{\\phantom{\\dagger}}}}$\n", "$\\def\\had{{\\hat{a}^\\dagger}}$\n", "$\\def\\Vep{\\hat{V}_{\\rm ep}}$\n", "$\\def\\Ver{\\hat{V}_{\\rm er}}$\n", "\n", "$\\underline{\\large{\\rm Plotting\\,inverse\\,relaxation\\,time}}$\n", "\n", "We next obtain the relaxation time as a function of energy which is defined as,\n", "\n", "$\\frac{1}{\\tau_{k}}$=$\\big|\\frac{1}{N_\\bq}\\sum_{\\bq}\\langle \\psi_{\\bk+\\bq}|\\hat{V}_{\\rm ep}|\\psi_{bk}\\rangle\\big|^2$\n" ] }, { "cell_type": "code", "execution_count": 44, "id": "9f0f79b7", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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