{
"cells": [
{
"cell_type": "markdown",
"id": "c3c5437a",
"metadata": {},
"source": [
"# $T_1$ limits"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "c56d9f17",
"metadata": {},
"source": [
"Longitudinal relaxation occurs because a relative fast motion—on the timescale of the lab frame rotation—induces a slow evolution of the density matrix. In this notebook, we check the validity of this lab frame calculation against analytical formulas, and also investigate the range in which equilibrium of the system to thermal equilibrium (via `'DynamicThermal'`) is valid."
]
},
{
"cell_type": "markdown",
"id": "e7ff862d",
"metadata": {},
"source": [
"## SETUP"
]
}
,
{
"cell_type": "code",
"execution_count": 0,
"metadata": {"tags": [
"remove-cell"
]},
"outputs": [],
"source": [
"# SETUP SLEEPY\n",
"import sys\n",
"if 'google.colab' in sys.modules:\n",
" !pip install sleepy-nmr"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "93f81bd8",
"metadata": {},
"outputs": [],
"source": [
"import SLEEPY as sl\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"# !git clone https://github.com/alsinmr/pyDR #Uncomment on Google Colab to import pyDR.\n",
"#pyDR will also install MDAnalysis on Colab\n",
"import pyDR"
]
},
{
"cell_type": "markdown",
"id": "03d0f6b5",
"metadata": {},
"source": [
"## Range of $T_1$ validity"
]
},
{
"cell_type": "markdown",
"id": "3d81085b",
"metadata": {},
"source": [
"### Build the system"
]
},
{
"cell_type": "markdown",
"id": "903ef61b",
"metadata": {},
"source": [
"We mimick a tumbling motion by hopping around the 'rep10' power average. Note that tumbling is currently only implemented for colinear tensors without asymmetry (we don't include a gamma average, so this yields vector tumbling, not tensor tumbling)."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "e74838ec",
"metadata": {},
"outputs": [],
"source": [
"# Since we use a tumbling model, we only need a single angle in the powder average\n",
"ex0=sl.ExpSys(v0H=400,Nucs=['15N','1H'],vr=0,LF=True,pwdavg='alpha0beta0')\n",
"ex0.set_inter('dipole',i0=0,i1=1,delta=22954.8)\n",
"\n",
"# Set up tumbling\n",
"q=2\n",
"L=sl.Tools.SetupTumbling(ex0,q=q,tc=1e-9) #This hops around the rep10 powder average\n",
"\n",
"seq=L.Sequence(Dt=.1)"
]
},
{
"cell_type": "markdown",
"id": "78ab091d",
"metadata": {},
"source": [
"We plot the full Liouvillian below, just to give an idea what the exchange looks like."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "259556f5",
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
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dSxH5VEScInKNiKwQkaUislhEdt3O82zWX0TCReQuEXlcRO4Tkf28beeJyIiBjBsAVzSSOAUcoWjVMrRyORSuBASSh5P1zhHMeXcSlZctpumUp40n20V4GjLiQHCEoAUfmIjjLiwHEjMaiRmFNuRD3bq+/8G543D88yrCnzoZz5kP4Ln1BlNHeYgiseOJ++Q6rDN2puHQq7FfuiMwdlN2IWX+dVi7ZlG3/2Xoh38PjN2suaTMvw5JDqfhoD+hi/4bELtBAoDlwDrzYhI+vBT7iffxnH1V7++FQSQ40Q4+/Y467qMsHiIyhW5xgC5+r6rl3uOBk8lT23iZjhDj2Vrh4GgCbOPNdnYYTzc0DjLjICGTsIQV2B2KVi5HOuohMstbjCHEnKuuEo2pQzqbwfKe1xlm0noAtmdp3nJA3ATEciOWQGU7Wr0ciUiHqP4v/+ywOMOQhKlocwXa+QnUtKKVS5DwFP8um7ujkMTpaOY67I7v0apmqFpq7nNoov/shsQiIdPR1O+xO1ahZaVQtQyJHNa7rnaQXyZRI5DQRIh2QqMHrVmDqMdsIVmOQRtWUIVn8BlIes9WZfF6NlLVZZiJdGtssb+IzADuB47GVzJ5nc1o7VokbmL3Bz80AXHHoLYNTU0mujh6lHfwHiLfm4RWLqdwt8dIHBNGxHNnG5UegIZiqK2B6HzU04HEjoHQeHPM4TbCBLD9f2RRI3A8dwdaOp+KOXeTcGYmjsvuHdQ/Vn8i6XsS/fE4dMFLFE+7gfSHp2IddbP/7WYfTtwXs7E/eJziqdeT8eL+yJ4X+d/uTicT88lh2K8+RPnuN5L81vEmWCvILx9XJI5Lr0cbCuj8/QNYcS4cT9wBYUmDPbIgg8hAVgcOBd7ByNwNE5G1IvKIiOyznefZWv8umbxdMMo+/UJEzhGRBSKyoKK6GbGc0FHfLQjQVSowNBbi0ozX21XNxxkGkZlITBaJY8JwhFjo/M9g3ffQVm+WhCMiwRVhPGFPm9nv+0mIwNU/qTbLYfaCY7JI2DUGcVno+g+gZmV/b8OOjSPEpFpljiBtVjQ0daKFH/hfiMAZbn6/I4aTNisaraxA139o9tf8iSvS2B2eTOLMaChaj274xIhYBPnlE5aERGZh7R4LI8LQ4q/R8oWDEm8R3KPdMejXvewpi6eqjcBMjOZrBUbm7nd9PdfW+qvqP1X1Cu/rpP6M03v+J1R1lqrOSkpJgogMtGb15vsnMWOQrP3R1hq08LPee7KRWUQ8dzYh52bzn+NyKfv951BdYgpgZE5AEich8ZNNNHL1iu5JfIBIwjQc/3wA2Wcqa2b+C/vVp31y3h0VyT4Cx8sPg1NYudMT6OLXA2N3p9OM3ZIm1k5/DF0fmLKYsteFOJ65H/ubQkr2eBAt/zEgdoMEgPAUHFfegXX+SVQc/h/sW5/wfxrbVghOtINPv+7lQGXxtnC+wMjkYYTbJTTB7Kc2l3UXfRfLHAtLMNWj2mugodBEJIsFrjAkJZGDRrcSlR6C/fFiyF1jjollvFBXNBISazzm1sqBRx1aDuP9JI9izPmp4LLQhf8cukIElsvsn06ZyPhzU9CycvTHp8zvwZ843Mbu9GxGn5sKOWvRpc/437N1uMEVibV7Fql/GAZrFxpJwaDE3tDAGY5EpJF4fhYyKRpd8ixa8lVAhxD0aHcMBnIv+yWLtykBl8lzhhnR9pAYIwjQssmXadwEJG13tH4DWvIddPaI+s0aT8pLRxB6eDKv/7kC+5Xc3n0jMyFmLNpSjtbm9hITGAiSsTeOmx5AkiNZuNeH6Dev+eS8Oyoy4f9w3PogrG9g+Zx30I0/BMbubufhuPk+7I+Kydn/DbPy4XejFrL/5TguvwX7iRWUH/ESNBX7326QwBCdjXXRPcjcvcg5+F30hT76BD4kONEOPgO5l/2VxduUwMnk9cQZjkSmm4L/jUW95czEYYpRxGWjjRvMcnBDMbTWQlQM1tRUjjorHNwW9r3PmQn5p76ChCUj4UnGq20u883ejOWASbsx44ER0NyJ/eYNQ9ez9a4QyNyZTLonG128GP3gb/6fgLyrGtb/7cSo20ej336MzrvXSCX6264zDOu8qSRdOwb7y5fQ+Y/5bAsiyCAjFhI3mlH3joP0CPTtm9ENnwbMfHCiHXz6fS/7K4u3pfMETCavJ85wiM4GKwSty4P22u5jYkHsOLPvWpMHG5bA+nyoqTZRxZP3wLrxNAi1uPXeevTbH3r3jcgwe8FNpWhjkSl24QMkay7WWXdCYweLTlwFhYHx9AYLmXIq1hl/Rd8vJeeUH9D6ggAYtZDdzsM65WraH89j4xlfbr7q4Q8cIcicS7GOuYCG21bTdPnn/i+kESRwxE3EOvVvyIhMlp20FP3y48EeUZAAMqCHFlWdpqqdP9OkSxZvwLa2hIgkiMhjeBV+ttmhvR4t+753tSZ3FBI7ykyGdbm9PVvLjSRNgawZkJUNqSOR2FE/vaxzD+DaZ7LQshY8l51r9tfqcr2vHKgrgMZSn0cbyoEHMvPVqejyHOx//nnoRiODkdj784GMfmon9N03sF+8xv8i7gDOMELuPoDUB6Zhv/Ik9ps3BKaSkzuW6IfnEnHlBOzn7jUedV+qiwX5ZTBmD6a8OgucFvYTV/hdPD64R7tj4O97+RpwrIg8yjZk8TblZybRp+khk6eq56rqqG1q0QK0NUP5mt4i7q5I44EC2lTae7nOckDMKCRuPERlQmQahKf/5LHKmGOxTrsdNrbx8L316FcL0fpCtLEIbSw15RsbfF9GUbLmIgf9Bc1pYO2VuWhdwQ5R7s0vWA5k3AnI3PNpe7aIqpvWmIhwf1+vIwSZ9jtkn9OofiCf1nvXmYnW33bdUciss2HXwyn/Ww72f1ZAZ+vQLMX5K0QSpiIHXAUui1VX5kHuj35/kApOtIPPr0tUYHq2/vDR1aYWaXgSkrJrd0H5zmZT7rC93gQxRQ4zkzCYL9f2Om+ebA24ojeX2PtqIfpxBW2lbYRduxMMzzbnDok10ll+KJivxV9AeS76+VK0w8Zx7qVDs4IUgKcdXf8RbCzA/nAVkhWBdcp13b8jf9HRiBZ+DCUF2O+tRWYmYB1zPf3Kj94e2mrQ9Z/ChnzsT/Kw9huJ7H+Ff20GCRhatQzKlqILlqHrGrAuOAVJ3R3wrajAGAnVewcgKvCboKiAT/h1PbQ4QpHwNCgvhsYyb9F/r4fiDDfVW9SDttV6hQa6Ck84zN6sKwJtqzPqP7bnJy9DUmchBx5MW2kbC76y0cJKqK40OqshMSD+KYImGXsjk49Df6yj6l9FaFOJWfoeit6Pw42MPAyZeBD1b5Zjv1ZiPFt/Bwy5IpHRR8G42ZS/UIp+VmaCo/wtZRgSh4w5FkZNYeN/StAlxaagxSDlYgbxLZIwxUgotnoofbIYagp6F7vxIUGPdvD5dXm0sybqgvn/gtYqtGUjlK+E+NFIag8NhM4W82XWUoZ62pGY0d0i7rbH6/nWoy3lSFiyWUauyzVBT6vmo4WVlN60lo52GP7RsZAyEUmc6j8PyPagVUugbj32Pe9AohvHNTf5t2bvYNLZglb8CKWrsG/9Ajk8Fev02/B7ecr2BhPlnbuQzjsW4DhzJNbRN/vXJhjPtnIZrPwG+6GVWJfPRPa62P92gwSG2jVoQxH6ylvo8gasOy9h54Pu9KlH+/cBeLSHBz1an/Dre2jxSt2JOwYaGowH2FME3BlmPFG1zXuetu5jlsOIvDtCoLPrWBt4WsHTAcOzkcnZdLRDRb0bSop8l96zNSwHkjQDSdsVStrQxfVofT40b/SfzcHEGYakzYb0ydTnt6B5jVCf6/8UHHeU2QLIHE1NTjMUNUJ9nv+LS4TEIRl7Q1om1eua0Q1lpqpZz6C9IL9cYsch6XuhnUrzqiaoXw+2b1ctgh7t4ONTj1ZEPgUOBK4ETsKk9NjAH1R1voiEAzcB0UAz8Jaqfioi12zaHli2lbbzgN+pasH2jm/WrIm6YMF/zA92h9l/q8uBwkUwYufeYs3eSVYb8s21xU3o9kptj9nHba00AVR1BSbwKW2YmaTrSqGkiJKz5xOXHU74e/f7v6i47YGGArRqFc1nPEvofgk4rrmr2xsfanS2QON6dPWnVJ/zKXFXj8U68Vb/2+1ohMYN6PevU/mnhSTeNxM5aNsB7wOmvR6airE/fY66W9cQ+69DkOln+N9ukMDQaLZ+7OufYNZ/VvJjc5tPPNqxEqoPDMCjPSTo0fqEgaj39KKPsnmbSd8FVCavoxGtWuZV73EZb8EVibpDumXtunC4TfEJy7m51J3lACsMLLfp5wyH6BgjdRYSY2T2ohKIy16GM9xCS+dDVLqRQ/tpv9Yy/1cFbBNgtWnAlN1hPBdvacItXQ92hwkIslwmQtpuJzTRjUT77Fe7Y+IMg9hxkJpLWLwLQgKkbOSKhLgJkLGQ0PglaE0jbJyPxGT792HKHQ3uaCQthdDYXKgsM5KC0SPNsUBRuxZtr0Nix2/5MzmUsDvQmlWgah60/RDQ+BORmYgrEjJDEadvYzqCnung4zOPVkSuxpRebAHOUNUjttDmWeB0jPRdoqo+KiLHbKn9ltp6359HPz3aKS63Lj5mHI5/3wchcebNLu/Ucm55H7VnQNSmqG3yb9U2L3F0T6Rqm7zd0vmsnPkUGaOdxDx+ILi8f6wulxEl6GwHtZHhc35KM/qJlgq04GOISjPLh9L7T0bLvofGUiR9dveXvO0xkdHi/HVonHraTUS4IzSwX/ydLdDRiP3afRRcuoqR7xxq0nL8btdEx9uv3UfbvwoIffp3SNaB/rcLYHvw/O0Syv9ZROpXfzKfyaFMSwUdx11KZ7OHsDfv7JVp4BfUhvY6Zu1+PgsWrfWZR/vIADzaA4IerU/w5cNOX2TztiR9FzCZvPoQYHIkmvc+WvqN+WB3CbVvLVjJcmw90MZbsg9HiDmHw81P0niOEDP5RaWTMdqJI0SwP1uKLlsFba3Q0gJtLUbbNiLRTBZNxd37wWAm/4gkMyE3bthMRk3ckcZ7bq83e7J2hzdCOvHXMcmCuedhSYH3rpxhRg5tdBbDD4xDS4rQnNf9vzfujY6XUcNwH5QIpXlGYi9AVaRkXCzJByZA3o9owbuBKeIxWFhOHAcm4t41Fs37BC3+3L951GIZB8Aa4qtRv0J84tF6ZfM+V9VdvD87MJPjvpj91qtU9emf6d/n9gPbox2vP/zvTApmPUjWick47n3Qv8tBYLzSVW9if7aURy+v4MSJ7SQ8fYBX9UeQ7NkQM8bUPm2qRLIP6h0xrDbU56N5X0Da+J9y7X46ZncaRZCORiRzTmCXEYP8tCLiuedK1t1ZzLjvT0NGHRkYu54W7AevpfXNcsJeugxJnhkAux3QWk3nCZdTtaaZlPm3QNxE/9sdLDztaPVyynb7K0lTI3G8+LDfH+p8mUc7TkL10QF4tPsHPVqf4JNHJ1VtEREVkUhVbVRVDzAPmCciyzBLwE//TP/tat+FiBwFHAYkAw+r6oc/38NCojIZft1ICHWiXz0M2dOQYftt+yL7iwi43EhaBCdOLCYiLQT7tSXI5Fhk3EhAzJJzZLrJ020qRdrqICrLeMZimX3f5FHmSbdmFYSlmLxescByIpGpaEcTNJcazzg83f/pLkEM3v16a6+xjHEKumIRVG9EJh/j3z1bywGEIbPHEZoYCjnfonX5yPCD/DsRWC5wR2P9fiRJGxrQ79+AYT8iY48ZmoF3DjcSnkLyVaOgU9Fv/gHDxyEjDtlsK2dHZUBp/L+e7E+/4stPSr9k8wYok/e6Vxnod8AJfRpl7FisC+9F9pjOksO/Qf+3XZUh+42MHUnC0wfg3jmGl26vRd8s6XHQMgnsKTtDzTp044LehQlCE81+mCMUzf0KbdzQqy9xE5H4yWhNjsm5/Nny00H8gcy+EMfFt6Mvrif/8PdNipW/sRxGAOGEK7H/swTPpW9AW5X/7TrDsI6+GeuMi6m6dCGNZ701tAUQIjKwzr4LOexAVh/zNfZDb20eILkDY4n2+xXEN/hyou2vbJ4vZPKuBR7ertEmT2bqP8dCYhj2c1ej6/2lpmF5A5+cZkKdHMvxx7vRZg8d132Oli/tbipOJGE8xI1Ga9YY77XHnpCEJRuBA7sTLV/YO3fUciJxYyAqE61dY3I8h2KFqB0Zy4l1yW6MuG8C+snr6Pu3BUbE3RGKdfZuOM4fh371X/THpwJTQcodS8I9M4i4MBv79fvRHx4f0gIIEjOKcU9MRGbGY79wndmT38ERjEfb31cQ3+Cziba/snkDkckTwx3Ae6q6aHvGKwlTsE64FUmOZeFZOej3n29P9+0wJCaYyeUye7LjRmJdsQd2p3Lv+za6akV3W8thvNPYMVC1Fq1e21tiLzzF7MPZnbDhR2jrOdG6IHYsEpkFNTlGaOAX9NQ9JLBcyM5/wDrqYpoeyqPqskW95Rf9hTMMmXEmsucpdD68Bvuf3/q/RCSYOt4HX43sfxQFf1qF/ffvegt2DDViRmH99hZk0lh+PHsd+slXgz2iIL8QfBrepqrTttGkSzZvMb6Z5C8C5gIxIjJaVR/b7jPsdBCz3nejG8rx3HUx1v8dbYKKfIWqSeEJjUQyZmCeMcH192j+vGoFuqwaz6u/x7pwF8icYPrYncYb7WxFS78xIvLxk346pcRkQ0g02lIFTRuRhMndUcbOcCRlBlghwX3awcIdTeQ/jyByw3rsp+6HYVFYR/zF/3uYIQk47z0CKsuxX7wdGTsc2eUcv38OJHokI98+GC0twXP/VVi7j0FmX+hXm4OJDN+dGe/XoSXleO74I9Zxc5Hs32y74yARdEwHn0Dv5vdZNq+PMnkPqOpMr1Te9k+ygCROQ/a+BFRZcUsxbFhhlt18tuzqzbF1hUHMGFNkIW4CMu4ErKNuhrXNPPrfVuyvVsH65VCyGsq9+3sdHUadp7HULMl1jSksyRRN6GyBylzobOo+5nBD1AiISPPR+INsN84wZOLJyC5HUvHQeuwn870F4/28rOqOQsYeD6N3peVfhei3a8DT4n9pv7AkZOc/IJNmsO62Iuwv15rP5lCVbowdh+x1MRIdxvJbS2DFIh9/Z/gWEe33K4hv+PWJCnSVYNwErVoG1WvRT79FF9dh3XBWb7GB/uJph9YKaK9D6zdAZDqSMKXb7vzHsL9aRfP/ymir6ST+tklIRiZYFkTFIinTTURxQzESk9U7laK1Ejqa0PpCsDuR1F38LxsXpO90NBopww3rsP+7DDkgDeuYG/2/0tBWa/bwS9Zhz1uJNWcisuu5/rUJ0LwRLfkOXfkj+vIGrAt3CYzdwaJ2LVqxDP3mB3ReBdZNJ/ikeIgv03vGW6H6L+ewfvffsyMnmN7jA34Z8ekBQBKmIKOPhhYPpW9WQH2hmcgG+lTucJuKT+4YaKqEtrre8nyZE7Bmj6WtppO8PAsqWqCu1nizlhMiMhF3NDRUoK21vfuGJkJEpvEeWiq9ykPtWxtJkEDjikRGHArZ0yn/sAr9sQpayv1f5CEkFhm2P6SOpO29SjR3fWCk/cJTkdFHIemZFH5Yg+ash5aKwOwXDwaxY42UoSWsf7caSvPM9e5gAWHBYKjBJzjR9kQsrDMuIOP7S7GfmYfn5Mugbq1vzh2aZIpRhMSg+e9A3ZruY04n8bdNYtaDI8i5Koe1x39r9Gy7CE9Dxhxi8mzz3ob6nO5jlgNJ2x3J2AMtW2g8qKBm6Q6FJE0ndf7VWAeOofHgS7HfuyswdlN3JeyVK5FhKXguuAJd8WJg7E46ipFLrgKH0HDARejqVwNid7CwjjqXEYuvwP5qFW1HXYKWLxjsIf2EEEzv2REITrSbEjPa5LO6LVor29GaXKjL9Y1nG5qIOMPB04F2tHj37TrNZJmRiYxMQhUaWpxoaQPUlAPao2+o6dvZ3HvPzx0NIfGAbSbZ9nr/C6IH6TvuKCR5Z8gYTmttB5Q1Q81K/0v7hcQiidMgKQWqO6B8I9Tl+F9iLywJSd0ViYuktboTijeYVLWhWq4xajiSsisS6qSlutOIuNeuDa4uBfmJAU20IvKpiDhF5BoRWSEiS0VksYhs1+bmlvqLSLiI3CUij4vIfSKyn7ftPBEZMZBxbxNnGI4rriX85UvxXPwintNuMkt+viAqC8k+DADNfQcaNkJYmNmTjYxi7H9nMOOhkay8NJeWyz/rvewWnY2MOhw6203fpuJeY5bMOUjyDLToC7T026EbjPILRYYfSOI3d0NKOMXTrka/ezowdkcdjuM/t6ItLbSfeCO6/qPA2J1zHknf3YmuraBs12vRIj+l0O0IWA6sM/5MzPvXYt/5MU1H3gANASha0gdkAK8gvqHf6T19lMVDRKZgxAF68ntVLfceD5xM3vYQnopYTmSnaKhsN1J3MVlIwrTtC2axO0zRAsvpLRhuRAfEFY66w6Gz1ezHRsWaNolpSFI52TttICQjxNRAjkwzcmhddLZASzPaWo04wsx5HW5TcN7uBFfE0CyH90vHFWn2bYeNIHFCDlpZAxs+RRImQXiK/+2mZ+IYvxEqStHI+UjcOP+KT4TEmldmJPFjw6EoB3V/gSRNH5oSe+EpiDsKmRZNaKeipYugrc5c79ZESwJAcK918Ol31HFfZPH6eJ6AyeT9XNTxFlHbRPVWL6dizt0k7BqD458PbF9kb2s1mv8BRCSZmspd9VFtD6jHqAiV5yKj9zWBTcYwdLagGz5lwdQXGDtFiH70QHB4J3iH0/y/s9MrTDAXwlO7bdodgBXMo91R8bRBZwv2v28l5y+5jPnsaGTKqYGx62nD/s9fafn3BsKfOxfJ2Gfb/QZKp9km8Vx2LeXvV5L63V+QlF38b3ew6GiEhkLqD70Fd5SD0Dfu3a4HKV9GHU+wQvXfof2X99ulJTcYdewDBrJ03BdZvL4QMJm8ioqabXfo1dky+2sR6SScmYlMj0GXv2wCjvqK5YKoNJNHW59vIpnBTIIOtylGkTi8WxQAjMReSCxEpjF2iuCOcGC/sQhdtsZ4vx0d4PFARAzEpEFrFTQUdu/ZWq7gJLsj4/39yuQRjDo5CQpy0VXPQ3OZ/+26o5GJwwk7Lg2KVpnAPH/XKXaGQWg8sn8qySemweqvTfnCobpn64qEsGQiT0nHNTcBXfmmKfE6CFs5A8mhDebR+o5+TbReWTy3qtaqaiMwEzgHqABeFJHf9fVcW+uvqv9U1Su8r5P6M07v+Z9Q1VmqOispKa5/J4kajuOye5GjDmDN3LexH3ux73807igkY28kMhPN+wKtWtn7ePwkJHMfaChGC76Aju4vPYkeSfSjB+LeK457bq6h7r5c42V7OqGtFYkfj6Tvhdbmoxu+go6m/l1fkEFBdjsPx70PYH9Vxto9X0YrlwTMrnXOTdjvLqP17OeM1rG/sVxYx9yI47rrab7+e6qO/K/v4h52RMKSsM6/C+v0/2P9Ee9gX/Mc2MHgqF8r/dqjHags3hbOFyCZvAFgOZCYEYy9YxS4LPSDv8Gk3ZCsudvuK5aJDE4bD5YTrVpmBAK6lpPEgcRkoSHRaGMx0loF0dnmmMOBjInm7BkVRCS7sZ9eiMxORMZn/ySTR8xwCG9EGwqR1kqIGhn0aH8JiGUmoKMmM2ZEBLrwKyhchex8cm9NYn/YdYZiHTqFkMlF6LIPIWkxMuZI/xY8sRzgiiTs0rGElTWjn/8bskYgk//PeNtDDcuBRKQz7Pbx4FH0w7th/LSAl2u0gnu0g85Alo77JYu3KQGXyRsIcROxzroTmTyahccuRT/cjnk9JA5J3R1xRUL+d2hjUfexLqm75JlGEGDjj71yYWV8NrGP7Y8jO5yXHmlE55X36isJU0waR/UatHxx8Mn5l4RYyO4XYJ15A55/5VN84mdoU8m2+w0Uy4Xsei7WYRdhP7EU+4YP/Z/2A+CKxDryJqzjfk/pRUtou/yjoVvQAiBqONbptyP7zGbZiUuwnw9MxHdPggUrBp+BBEPNBP4E3Ac8CMQCnUAOcI6qVorIqUCtqr4lIi+q6maTofc8W+zvPf6Kqv62R/t5bBIMJSL3AM9uS8Fnu4OhtoJWLkG/eQ2aO6GxAznwwL55tmCCoxo3mOhgu9MIBHQJhNseqM8xebKd7eYLqLbIuyfbia7JR+eVY5e20VrbQeTTxyOjj/H27YD6vJ/6SkgUxI7nlyJO/avH044u+Q9aWAg1bUhSGHLQZf6Pzu1sRle+DBXlaEMDkpGBzDjDRLH7k9Zq9Jsn0eo6qGtDJo1Edv3D0P281uWgXz6HNrVBQwcyZzYy+qgtNvVlMNRER4g+F57R7/7TG/ODwVA+oN+f6v7K4m3pPIMhkzcQJHEa1m9ugnAni/5YACu+6/uebWi88T4Bipd1B0eBWVqLHYdEj4KaPCjPNdHFXRJ747Oxzt2N1toOHv/agvy13uhl2yuTNw6JHA6V69Da/KBM3i8JhxuZcSbWAWdT+0Ae9X9dZfbr/V2o3hmOTD0dmfkbOh7NxX5lMXha/W83NB7Z73Jk97nkXJmD/eyPvYUzhhoxo5HDr0eGpfHjxfnot/MDEhwVCD1aEfmTtw7CchF5XkRCNzkeJyL/89ZJ+F5EJvc4ViAiy7z1E3xSUktETheRdd7X6T3e/9JrZ7GIlIjI676w16cx+VNUwOvR1qjq2yLygqqe2I9zbNWjFZE/YvZzfwAWb0vBx1cebRdauQQKf0CX56A5DVjnnoBk7N27UUcjWr0ScUf29jBbq6Gt2kjddbYgiZO79+XsDmgqRlurYeMKiIhB4rv7asVSyF+L/el6WNmIdfVsSPeuvtudpqZyZBKSuX9wr/aXRmczmv8uFK/H/jIPmRCHdfR1/vcw2+vRDZ9BRQm6JBeZOhLZ7Tz/e5jNZWjO+1CYj/1dOdbhk5DdL/CvzcGkdg2a+yW6Lh9dUoN1zmHIyMN6NfGlRzvJEaLPRfTfo92p4ec9WhHJAL4CJnpjd14C3lXVp3u0uQtoVNWbRGQ8Jp5mf++xAmBWX52rTWzPY/PVzXhgATALUGAhMFNVazbp+yrwhqr+e3vt9gd/r9P0WRZvUwIlkzcQJHEaMvMs6LBZ98hG44F2NPZ+UrU7oLEUba7s1pkFCI2HmNHmeHWhiRju6me5IGoEEpFhHitdEUb6LjrbPBmPPgbZ/wpY2ch/3+xEf1gLhSthYw5Uefd+xadSw0EChTMcGfNbmDSH8ieL0beKob3O//Wr3dHIqCNh+FRanitGF+ebz6S/ywiGpyBTT4cx48l5bCO6KM/sFQ/V8oWx48x3RoiDVY+WQ97Kzb8zfEwA9midQJiIOIFwYNMgg4nAJwCquhoYISI/m1gsIqNE5H0RWej1RMf3cSwHAR+parV3cv0IOHiTc0cB+wGv9/GcA8avE62qNqnqGap6nqo+u519q7wT6ChV/VuP959W1VqfD3YAWMf+jnELz0Q/X4rnrD+iVT3SNFyRSPpsJDIDLfkKalf36isJk5FRc9H6QnTDx71zGkPikOy5SEQqWvghWr2iR0fBuno2pz6YSt2TRZT/fh5sLAXbhtbWoftF9StBYsaQ+sVFWGdPx3Pa5div/zUwduMnEf7ChciM0XhuuBJd9FRg7Gbty9hFf4CMCDqPPR9dHBBHY9Cw9judSYvPQnPL8Zx0AVrypX8MiX9FBVS1GLgbU8GvFKjbQvbHEuAYABHZBRiO2VYE43V+6J1Qz+nR5wngIlWdCVwOPNLHK86ge7sSoMj7Xk+OBj5RVT8nkHczRCMPAkzcRCTrILTDpmp+HdSth6ZS85RquUywkyvCLCN3NHlFsb3FJUJiITzNeLttddDR0B2F6XCbik+uSGitM0++nc2mr1iQPgbZaSTtjR5KSy20ogWqKk3wlAbrHP+icUeZSmJZ46hY1IAW1Jt8V38XlwiJRdL2gKR0OhbUoUXF5rPsb5GK8BRk+EFIQgKlCxvQgkJoLBq64hgxo5ARB4MllP1QDxX5pna5Hx6QB+jRJnYV/PG+zul9bokDjgRGAulAhIicsskQbgfiRGQxcBHwIybwFWAPVZ0BHAJcICJ7i0gkMBt42dvncSDNa++Mrn1WzPLwu96f/9c1pC3cgk2fGP4PeL7vd3DgBCdaX2E5cJx7KUnzLse+5x08J10JDQXdx0MTTNF/d7SpX1zfo+C4WEjqLsiwfY2QdNFnvb9gItKRUYeBM9wrk5fXfSzETfI9U5h6fzbLL8ll3ck/QEPAHtSC+BlJ3Z2U72/CmpZB9Z6Xop88EBi7mXMIfelaJCYaz+//gq5+LTB2dz6ZzKU3QX07NXtfaj7vQxjrxD+S9v212K8toOWIK9Dq5T49/0AEBbwzVmVXwR/v64lNTMwF8lW1QlU7MNuFs3s2UNV678rmTsBpQBKQ7z1W4v23HPgfphKghclW2anHa4K33VNd72H2Yg/1/ny011wR0FPpPpMeS9kikuC18c723MeB4tOJVrah5iNbV+TZsdR7+kvUcCR+MiS6UVvRqlVGHqzLs3VHm8L/Iqin1YgNdD3BuiKNOLzlNNHCbXXd3ovlMp6GKwLEMik8rdXGC3Y4IS0DyYgl1G3jsQVdXwVVJcAQjeD8NeGOQhKmQGYWlstCK5vQikVGYNyvdqMhboKR2HMKVJZD9Qr/e9ShiSb2ISkCcQgUrUcrfwxMju9gEJlp8uCTvMFuVWuh07cV3vxcgnE9sJv3+1qA/YFVve1LrIh0RfOdBXyhqvXeOgtR3jYRwIHAcu+Sbr6IHOc9JiIyrY+X+wFwoDfSOc57zg96HD8OeFtVW/t4Pp/gs4lWtqzmMxXzxNO1Zt6lyHMXsJOqfiq91Xt6tt+sra/G6ldcETiuuQnHv/5I8xnP4jnrdmjvEfAWno4M2x/AeLbNPeIGHG4kYy8kdRe05Bu05JvuJWaAqJEmQrGzHc1510QXh4Yaib3YOMa8sBvj7h7N4j/m0XH95737BvlFI6OPJHbe3yHEQeGUm9HFLwXG7oRjcfzjdrSimpbjb0OLtqPO90DsHngJsZ/dg/1tIWW73oKWfR8Qu4OCw411znWEvXot9pXv0r6idLBH1GdUdT7wCrAIWIaZU54QkXNF5FxvswnAChFZjVkivtj7fgrwlYgsAb4H3lHV973HTgbO9B5bgVme7st4qoFbMJkoPwA3e9/r4kQCvGwMA5DJ2wJHYqK40jDLDW0Am4RtzwDux2xGd31TbLG9iGyp7Y6PWOap3O4kdL8EJNrZOwLYcgAOxBWJhsSCtUnpOUeI2c8NjfVK3Vm9+1phSEgUGhEHDpc5d3i72ZNNBoktYfLexTjGRKDr3oDodCRmVI8QQsv8Xz3m/6EJm6eOdLZAWzU4I7Yso9ZWY7zpkNjN5b+aitHyxUjsSIibuP33r780FKAVy5GE8Saae6jhDDOaw9nDGbbXBrS8HPLfQVJm9lZu8rndcBMJPWIY7j1qoKIIDfnc5IL7U2LPHW0CCcfFkjS7CQpXoupBUncfmhJ7ofFgOZF9E3B/kbft9tuBvys8qeoNwA2bvP1Yj+PfAmM2OY6q5gFb9FRVNZ9NooW30GbOVt5/Enhye/r4G5/l0YrIVxjPtBOTVxUOfAy8qKqfe9ucBYzzdslQ1ZO8G9+btd9SW+855hEombyB0hXUtCVtWLXNEvHW8lx/SvXZwvGuvlvuCHYHuu4NvpzyBjN2FyLun9udDxniBqcL2tpABBl1UHdlqi4aCtG8zyB5jAmM2WRcWvoVtNYaMYRNvmx16TOs3OdNJtwzGuv3d2xljL5HP72b5Ud/x6T/TDLFRIYqdgfYHdiPXMPam9Yz7rv/M+lAgbDracN+4gZaXioh/MU/mknP33jaob0Oz++uoGJBPSnf34gkTPW/3cGis4VZu57FgoWrfTI9TnaG6Guxaf3uP66qMFgZygf4xKOVHmo+3p9nYqTt9sWo8VzlTcv556Z9VbVxK+03a9vPsZ2DUQYiK8uPT/5b4ufE18XacnxcFz9XaOJn+zqMlxmdzozdBXekA/vZH5BpscjEUdAGeGyISjCec0u5iXSOHNbtnboiIHGk+bl2rSmkERrvtS1IeBLqCPX2bTRR013jTRjB+EvTjPDCd4/C6NndlbD8yYjxTLwkH5o70fmPIeP2hdhx2+73S8NymTrFO49mzCUdsHo52lCHjD/cv+LxlgvEgcwcTVioA/IXoY2lSNYB/vUwHW6T43v8MJJm1cPiD9CMlcjo3xhve6jhDPNpkRATPRysEDfY+OQ3qqotgHq9U1TVo6rzvEsKFwLHbqP/drXvQkQmiMhjIvKKiJy3lXMPXCbvF4jEjCLi/rk4JkZyx731tPyrsFtir6MdSZiIpO6GVq9DS76Hzh6xAaGJSMY+iDsSzf0C7Rk93SWAkLQTWpuDVizpJWIgGfvguPYBiHGzYL/P4Ps3A3O92YfjuPFBaO5k0X6foOvmBcTuYCG7X4Dj6nuw3ywi56B30LqcABi1jMTeqddiv7KMjotegxY/a+gCOEKwjrkJx3mXU3vFD9Se/JrZvgjSJwYYdRzEB/gy6rhfaj5bay99U+9ZparnAsdjcqqCdCFivhinxXLx3oo7yon9wHx0Tc+0IicSPwbistG6dVC7pneFmpAEyJwKqibys7W6d9/YURCVadKNGgq6q16Jhey0FzMfzUZrW7BfvQ6tWhqAa7aQvXdn+iOj0Nz12G/cAIGYgAYLcWKdOZNRd49Fv3wP/fjOwExAjlCsk2bhPG8U+v0r6JKn/a/AIxa4Y4j96xRiLs7GfvdRdME/ggF/QX4R+HKifQM4CogEnhGRlSKyFFN+60Zvm2OAV9RI23WJMm6xvarmqeqZ2zIqIr/B7PF+4sNrGTLIxFGE3z0HK87FS/9tRRdUde/vWg4jPB83AarWopWrehe6CE9BUnYx7xUuhNYeKSU/CSCMNF5xTU6vvpI1F+v026GunR9PWw3FPwbmekcfhXXabeiKWlactgKtXhMQu4OC5TAe5gl/puXhXMrO+w5aq/xv1+FGZp6Ftd/Z2I+sxP77lz5PSdki7mjk0OuQQ09gwx+XY9/6pf9LUw4BgjJ5g49PRQW8odgzVbVzK8f/glHaWSwiz3UFOG3jnNuUyfO+/46qHsbPEPBgqMGkqRQt/BTa2rsl9hZU4VndRHNlBzEvndZdzNzugPp8k9vb3oCExvWOGG4ug9ZKU9XK7kTiJ3YHQXnaoakIPK1oRxMSEg8xo37qqhs+gdU/oEU10O7BOv5Mk5/pZzTvbchdjhZWgyVYx19o9qGHIp42dMULJue0oBbSI7AOv8r/e5gdjWju21BRhm4oQ7KHIbuctXkkuq9prUQXvYBWVMD6BmTWqCElROBLUYEpLre+Ed//2JRR5RuCwVA+wKcFK1R12tYmWS9FdNe4HLBtEZkjIg+IyOPAuwM935BCxEQXO51gWciEUVin7ExzZQfPL3BAab6ZJG0PiMOIFYSlQEUOWr+h95JceArETzLLg+VrTfBU1zKxw23EDkKToG492tx7z06G7Y/sfwW6up7ca/PQhg0BWe6T7MORff+IflROyQ1r0OaNQ3eZ0RFipO5mn0DlAwW0P5xrCjz4W4bNFYmMPxEmzKHtnwXYn60yHqa/7YYmIrMvRKbtytobC7HfXxkYu79ABLCk/68gvsGvMnmbGTPVPx4CWoGvfk5owFsq61bgAOCfXcICIvI74PX+CAv8ujzaYjTvU4hKQBK6vVOtXAGl+djPLqVtRSNht+8FadnmoN0JLbWm2lRIDBI9zEywXbRWGjm1xhLj2SbP7I449bSbpWVHWHeEcg+05CuozMX+aBG0K44LL4Oo4X68AZhUpOLPoSIf+50fkVg31tnXbnF8Q4KORlMEpSgP+3+rkNlJWMfe5H+pxPZ6tPRb2JiPfrMa2X2ckdjzN80bTQGNNSux3y7COmNmYOz6GV96tFNdbn0rsf8e7YiNQY/WFwRUS01Vm4Az+ti2Cjh3C+8/7eNhDVG8hSlcESb9RpxmTy9qBGS103b173jnczh2SS7S1grh4WaCDQ01ogStG1F3JOJpNx6v5TBpPu44qM2B5mqIbwZnqFkqdLjhZ3QvJX1PSJwKd8yjdlkj8WeUICFxpvSkvzRPLYcpzB9fSvufP8XusIk4ZaO3HOYQLHrgikSyf4OGfUP565+TDHBYpblWfy4ju6OR4Qeh1qe0vvEFofGhyPQaY9MRsu3+/SU8FRl7PNr0FHmvLWXUbgXITtXmM+9Pu0GCbCcB9WgHm1+VR+tN9KelHK1eZ6KLu7xT24N+/wS6JJeq+wvwdNikPDDD1LW1LIhNQVJnmWXg2nwkcULvnNS2WuhsQqtWABaSvsfP5wx3YXtM0fS6Auzb3oTUEBzX/dX/HqanHa1aBtXrsK97D9kjHuvC2/o25l8i7Q3metd9T9stP+C+YBTWUTf7325brYlez5mP/exSrDN3RWZsM55x4DSXobXr0K/fp/XhPMIeOMho3P5C8alH63br2wPwaIeXBj1aXxBU7xmqONym4pMzDDpNoJLZt+swnm5aNjI+A0+HTV01aGkDlG80ebYOF4QlI84w6GhB2xu7+4IJhApNNEvNnc3d8n3bwnKYgvEpM6G6A1Y3mfzPpmK/3gocbiR5JpIyldbydnRNo5kQmjf61+5g4Y5C0mZDZjb1G1qhpMmkOfk79SckFkneGZJSsQtbYGOJSfvytyBAeAqSvicSH2Oud32hud6ORv/a/YUgaL9fQXxDcKId6kQOQ7IPA8uJ5r3TW54vPJyUB2Yw5q4xzD+vgLWn/ghNPdI0okYgow4H9Zi+jT30lB0hSMbeSMrOaPHXZo+ur8Eo4Sk4/n0z1l3H0XDkvXju/ltg0jSiRxPx5l+xLppD9b63YD9zd3dQ1xBEhu1H8nd/Q0bEsnHWn9Ev/xEYu8MPwvX8LWA56DzpOrTgvcDY3fMsUhfejm6op2L3q9D1wYw/CKb37AgMaKLdlizedpxnaMjk7Yh49yPFFQHOUJPC01LRLbGXlIKkRhIf2YHbqWjORqhYb3JtHe4efd3GK26p6C3t54o0+7RggqH6IqNmucwkHpdNxHDTV0u+NuUe/YnDbVKP4kYSlRkCHR4TpNWz8tVQwhUJsWMhM4uo9BC0uh4t/dqka/kTdxREjYCUNCQzFMrL0PKFZsvBn4TEmetNCycy1Q3F+ejGb4euxF4fEEAs6fcriG/o90TbR1k8RGSKiLy9ySu5x/GhJZO3oxI9Ghl5qNm/y3nfRBd3SewlJTP21T0ZfusYvju/EPtvX/UuXBE73uTctlajuR/0LlzhjkKG7YfEjUMLPkErtqMwRcw4HP++D+vEvVi/ywPY/37UZ5f7c0jKzrhfewDZeTQ5O/0d+81NtayHFjLpRCI+eBhaOsmZeg+6OjBi6jL1JBx/vxPNL6Hl+HvQsgUBsWsd9mfC3r4X+43VbNz9zsBUJdtREW9p9H6+gviGgUQd90UWD1VdhplIt8bQksnbUehsMUX/XRFmP7VLni80Do1JhdZaE10cm2L2ZAGJjGLXI8pgYiS65D+QOAyJ6wqCUuhoMsUvmssQVQhLNl6iw23sRKZsn3Sa5TBeSMwIMn+bDGFOdPULkDTRvwotlssEYKWPJvuYH8FWdM2LSMp04xENNRwhZql/3HCyj6qE4g1o1CtIxp7+ldjrsjt2OKG/aYHSHK/U3a7+ldhzRYIjDNktkeROhZwFaEsNMmyOORYkSIAZyDPLocA7wIfAMBFZKyKPiMg+23merfX/DPgbsAtG2SfI9tBWjeZ95o0M7kHcRJPyEhIDnk4kdRaSdYB5zfg9jpf+gXX0DD6Y+Qmtv38GXfsRuu5jdN0n0FAF7hAoWYqu/7x3sElInPFsE6Zs91AlZWccf38ImZDFkp1fRd9/YYAX30e7WQfgeOQRiHSxZNYr6A+vBcTuYCG7nIPjsYexF1eyZrfn0bKFgbG789lYF/0V+4tVtJz+DNqQv+1OA8VyYB17A46/3Uz7X7+n4tCnoKnE/3Z3QIJ7tINPvzzavsri9eVcQ1ombzBxRkDyGOO91aw0AgFdMmqWC4kehrojjXfaXm/21BxuwAGJw9hnf8EZamE/8i2ydxIyaRR0eot+xaWDKwJtKkLaqk3hCcvV/7UmsYztEVOYeosRvdZP7oJpc5HE6QO+FduyK1NnMvXmerSmEebdi+x0+ND0bL2rGtbcCYyNcaFLv4eNBchOx2+uSexzu2FYe08gND0CVn2BJq0xgXb+9DC98Qmu80aRWNyEfvsSZA5HJh7/K8qzDZZ42hHo1zfjQGXxtnC+oEyerwmJRdL2QEJi0bxv0IbC3sfjJxnBgNp8tHRhr6hfiRtH6B37YqW4+euTLXS+WNQtsddpah1L0gyoXoeWLfJZaUPJnIN1yX3gFBYc8QMs/8wn592m3VFHYv3p71DezI+Hf4sWfR8Qu4OF7H4B1vm3ov8toPDoj9Ce0eT+wnIgu56Ldezl2P9ehn3lu4FRGnKGYx11M9Yp51F+8Y80nf+uKSH6ayG4R7tDMJBb2S9ZvE0JyuT5mdBEyJoB4kDLvu8dcSoOU4wiYSxaswqqV3Sn6Iggeyfxl0MsLIdg3/Y1urbHkp/lRBInQtxotHoF1KzyWaqM7L4vM58ZixZXYv/3L6b4QgCQQ/Zhp6fGoYtXYL94jZH/G6pYLqwr9yTrgcno+y+j797i/6hgAGcY1oV7Yp0/Af3sX+jCfwYmtSs0geSHdyb8wmzsl+5G5z/2q6mNLCL9fgXxDQOZaPsri7cpQZk8fxIab7xPy4KipaZecRddUnexY6Emz0jKaSd4E9Vl0ihcN+2FOIXXXu9E19R1T6aWC+ImINHZULkWrcntHak8ACRrLtZxf4XyZpadvw6qfDeJ/6zdUUdiHXsDOr+KdeevQusKhm6ereVCZp2NddgF1D+QR/VVS00lMX/jDEOm/Q7Z7Xg6Hs3B/vcP/teyBRNDcMBVyN6HkX/5GuwnfgC73f92gwRhgCUY/SGLt4VzBGXyfEFrNbRWoG110NmCJEwy3i6Ypd/GDSZPtrXaRBc3VJk9WU8nujYfXVNH2+c1NFe0k/DeuUjWXNPX0276djZDazUSlthbiGAAaNE8WL8cXV4IrZ1Yp53n/71TtdHC92HDOnTpenAK1imXQUSaf+0OFp0taM4bULwBe3ERMjwa66ir/V+esr0BXf8RVJSiq9YjE7KMIIC/1yuby9BVb0FJEfbSKqx9xyGzL/Svze3ElyUYdwoN0Q+H9/+zm7K2MFiC0QcM6FMdaFm8TQnK5G0D29PtkYXGm3rFdidU5pvCEl1LZ5YLorOR8FSo2QB15UZez+kEhxOZMAbryBk0V7Tzzko3VG0wJRftDiM4EDXCCARU5qNNvitrKJlzkF3PQZfUUXx7vlEN8rf3IxYy4lBkl9Ox3y+n6v4CtKV86AqMO8OM1N1OB1Px2Ab0+fXms+Hxs7fnjkJGHwPZO9PyzHp0Qa55wPO3lGF4CjLzLBg/hXX3lqDzc7o/y0OVYNjxoONXUYHtkcXbQt+gTN5AaKtBK5ci4Um9RdzbaqGjAa0vhM5mExDVU8S9tcKICZQshbh0I/LuRatXQ9UG7Lu/oCm3hai/7wMpWeag3QktDRCXhWTs7bvrUBst+8EIEfz3C7DA8edr/e9h2h3oxvlQlY/95FfI8HCs827wb/7nYNLRiJZ+A+vXYP/jR+TwdKzf3ux/D7OtFq1YDMWrsT9cjnXgZGTXzUS7fE/zRnTjAnTZD+hzhViX747s/Af/2+0DPvVow0L0o5Hp/e6fvKog6NH6AL/K5G2PLN4W+gZl8gaC3QmttagjFPG00SWTR0gsuKOhNtdI3XU2mWVCR8hPUneiirpc3mIXCWA5zZ5eZCakN9OU+wHfzbeYuzwfaW6CqKhuiT1fa5+KZQocxI6B1e/SXNpG5PkbEIcLQuL9NxFYLiPtFzWMth/fw53TjHV6CaCmyMZQwxWJZB2IWm4qvvqMpOxwaC4FV7R/JQVDYpHMOWhnM+2ff0nIuCJkaoX57PlT2i88Fck+HMo3UDhvKcOPWY9M2gjumCGn6hQspTj4BAO4hyohsUjmPqYS1IZPoD6n+5hYRs0ma1+0aoU53rP4RFgykn0IuKPQ/HeNEkoXlouov+/D3H9kUnrzWjae+TXU1oBtQ2srdPppidUdg+OJK4n89ynY5z6E55brA6POEp5G2Kt/wXHXYbQefyv24zf7f1l1EJHkmaR8dy3WPtnU738Z9vt3B8Zu+p6EvngVkpqI55wr0ZUvB8butN8yYtm10GFTt+/F6LrXA2I3yK+L4EQ7VLFcxnt1hoMq2tnae+/NHeXVgbWM99ve0F183eE20crOcKPc09lilpw97aZ9ShaSnYzlENpaFF1fjZYUmTxbf0lrWQ5T1SrRu5Rd3m7SijbND/Y1DrepdpU4DvUoWtZmNHUbi/xrd7BwR5ko9YzhdLZ6oLLV1AruGa3uF7vR5j4npUCrByrKoXZN30QqBkJYknnoTIigs8U25Smrlg0pIYLgFu3gE5xohzrhaaY0ouVE138KTT0mCMuFpO+BpO2Ols43Cjo9vbWo4WZ5TT1o7iYyeVFRpD6xK1m3juWLszeQf9ZS49H6m8jhOP77N6yrjqBq/3vwPHRPQAJZJG4SYW/eiXX8Lmzc5RbsFx7wu83BREYeQvxX90J8CMVTr0fnBya2QUYfgePp29GGBtpOuNl8ZgNhd78LSfj6bnRpCWW73WD2q4cCwYIVOwQ+vZXbks37Gem7oEyev7AcZs/JFQHuSOiSyeuaULuOhUQZcYGW8u6KPZYLnOGIKxJCY0wKT3Npt8ReXAIkhTEssZXwCNCVG6Asz7+5p5YDIjIgJou4GdFIiGV0R2tW+s8mGC8/MhMSRpA8Ixo8Nlr4AdTl+tfuYOEMN1rGw0eSMj0KraxG138Izb6LKt8irkiISEMyh+HcKRoqS420n98l9mJNKdHhUSRNjoT1q0162VDwbC3p/yuIT/DZRNtH2bzNpO+CMnkBIjILydwH7WhCi77oLXXnDEcy5iAJk9D1n5ti8z0ny9hxyIiDvDJ5H5voYq/EnqSlk/3qHFKuGsUX5xVjP/qd0bL1MxI/Fce/7kfmTmftzCewX3rS7zYBJH0vHM8/hIxJZeVOT2B//HRA7A4WMvVkXK89ApUtrJn+OFoQmLowMv10HLfciS7No/nEh9Cq5QGxax15NY7n7sF+cikb97of9bdGsp8RgkvHOwK+jDrui2zelqTvAieT11yJ5r2JDD/YW0B/CNNUbCbFhBFIxj4/rQVJSDwa2QGOTSIrLYfxYmIyN09h6eoblojGdxpP13J4A5+8VaTCwtnrjBoYH4l+8wikj0QSxm95bJYTwtM3/x201xuPOiTeu3/cA7WhqdhUn4rI+KlgPImjGH1uKoQ60SVPQ+YMP0vsOYzdkRMYf04uMnZwxAe09BuozEVGzoHIYf4z5JVBlGmjGHNOs/l8BAKH25T5nJpNmICExW+7jy9whpnSpIelkzwiDFZ+jtblGy1nf0ZBBxnS+CyPVkS+wnimnZiSiOHAx8CLqvq5t81ZQJfAaYaqnuQVJtis/Zbaes8xjy1UhuoLEx0humi/kYS+9eDmX+RDDM1/h5UznmT8pWk4rn3A/xsuapugq28e4Y29vuXQQyxcN+y55bYRkciYwzef0GtWoTlfQNZ0k9/bE08bmvcWdLQho3/TO+XE9qCf3cuKY+cz8d+TsH5zk08vbavYHu+jf+A3s+yHL2Pd9fmM/e4kZMxvt91hoHh/vz5P3+qLXQj8PVYbmktpOOAyOpo9xH95t1laDgC+zKOdHhGqn03o/8NR3MLcYB6tD/DJROuVzftcVXfx/uygW/buD8DPyuZtT/vtnWh7yeTFh8zMv3tPiA9Fxo5Hxp8wdHf8a1Zi/+8ZcFkQ40Z22qu7bKIf0by36bjwBcQSrBALOTodmTYR2lrNl1fKSLMP5wxFXBEQPbr7y7u5DK3LNR6vw4VEDutRJtJjon07mrx9IyF61E99tWge+uF7EOVCIkNhl9/417MdZHTls+h3SyEuBImOQnY7yXj6QXxHewP6wT1oRQvEhyBZw5Fpp/p9NczXE+28Sf2faGN/CE60vsAns8xAZfMGIrPnVQhaKCKHb+Xc3TJ5I7ORAw8j58xl2H//xAT1DFXiJmL9/g5kTBYLT1yFfvZxQMxKwnhcN+yJFWJx62sd6LdVEBZhgqcsB5IwBUmcCpVr0PIlvQu7h6cgabONl5jzXW+lIcuBJE5DEibDxhVoxbJeIgaSOQfr93dAq4flJy6GgiEudTfxZKzTb0E/3cj6U742lb6C+BZ3FHLEjciRp1By0VI6rv3MBBP+wgiq9ww+vnTn+iWbNxCZPC9Xsh17uBI7ijEv7o4ckIb9z6vRZUO8JOPo2cx6ZQq4LOxHLzfFKQKAHJ3ONedHQn0n9pVvoGt7FL1whCCpOxmJvYpFRp6vR/CVRGbB6Nlou7csYGt1j76hSOZMiB2Jlv+wWbSxzDmAyS/OQFfnYT9zlf+jkQcTy4l10VyynpyFfvgm9ivX+T/f9VeIRKSR8ewcnGdnYz91M/rtw78cVSfBfMv39xXEJ/jyVvZXNq/fMnkiMhdYCZT9XLteRGQg+1+BTJnMij8XoJ95hct/KX8424kkTkMOvQ5CHPx4eSGs/iEgOpwybSLWnw6GZg+vv9aB5jX0FjGIm4BEZUFFDlqb31tiLzwFSZxmvIfiFdDRo2iBw20KV0RkwMa1aN36Xtcjw/ZDDroKLWqk4M9rzLmHqu6oWMjY45F9z6fzxSJq/7oaWquG7vUOFqGJyN6XILP2IeeaPOzXlv1ivjOCUcc7Bj6LOlbVhSIyBViiqrO30iwT6FLx9nT1A7bWflvsC0RgJucWEXlXtW+ffsmYzeSv2tG1a/FcdiHW2XsjE7eoTT8kkDnHMePbH9GFK7H/ciHWxSebWr7+oq0VOjuR4zM5alYDTW+U0/xkESnzJiBdggCuaGTkPmh7PVr0mcmfTJjSPeb4iRCZgTYUQW0ekjLL1GkGU2Jy1D5oewO64WMkeli3eIJYWKedwMiD16HvfYq2f4x15sUQNcJ/1zuYuCJxPXIScWXr8fzjESQ1HOvEa8xeeBCfIQmTGfPFsZCXi+fPF2MdN81I+wUJsg18ujgQaNk8Vb1GVS8BngP+0ddJFjDJ+FNORZISWPfvSnTlaq903NCUy5KEqcjU06HdQ96TZVCZ21sqz9eoDbYHGT0Sa+4kmqvaWZATCg0l3nKObeaROSLDBDaVF0JzeW9PISwJorNNAFRtcW8ZNUeIkfYLiYGqIrS1pvf1pu2BTDoeXdFAzZNFaFNpYGojDwYOt5H2G38Azf8rQ18vMZ5tZ/Ngj2xoEZ5iHsZHZJP7TDm6LC8wkoIDRCzp9yuIb/CrTN5mxrZDNi9gMnmNRWjNGnTex3Q+vwHXA79FRh+1vaf+5VCzCm3YgP3yO7CoHuv+S8wyra+oy0FXfwxp2b28U61dBw0ldPzpbeqLWkl4fA4ke5+5OluhrhaiYyA6HYke3tv7bKsxMm7VqwCMJ96V0+hpM8ed4d3e7k9GbbRqCdStx37sPYh14bj0ejOBD0U6W9CKH6F8LfbdXyAHJGOdcotZqg/iO5rLjBjH95/R+c98XLftj0zvl0jZFvFl1PGMqFD9cnpWv/tHfrkuGHXsA/wqk7cp2yObFzCZvMhMJDITjfycypVNpBXnQ0ohhCUPObkswOyNxoyG9repXdZIfF2BkcILT/HNF7LlhIhIs2zpjjKep+Uyy8VttdQXvcLKVU72XFGI1NdDXLwp9aYKHg90tBhPrLMFLLdX2i8OnBHgWWom5Y4mQLrl/cJTtzwWsZDE6aY4RsnrkNeCNhQgapvrHWo4w5C02ajlpGnd+0SMboSG9eb+DfG88YASnoKEp0DeEipWLCNtfQEyusD7nbEDFrUIbrYOOsG4Mi/WQReQtvBmdFEhtfv9GS39drCH5D8sF46LriD+w8ux//omnpOvNlWXfEFEhilG4QxFc97qLbHnDCPhiX3Z87EsCq7NoeyiBeB0QmS0+TKITkbS9wDECBw0l3b3dbiRjL2R9Nlo8Zdo8Rd9X+YPTcTxyLVY95xAx+/ux3P/rUN6WVUSphD9/k1Yh02j7sCrsd+8d7CHNCSRXU8nY/GtUNlC1R5XoPnvDfaQtkhQVGDwCd7KLsJTkPhJkBCKK9yC8jy08kfjWQ1FIoch8RMgPQScglYsN6kwA92z9crziSsCHA4jsddaafaxxIKkDCQzlogYC8shaE4+rC8wHq04jRfsDDNtPa29983dUeZluU371qq+FX23HBAzCokdjSPOBa0es8Ranzewa91RcYZB7DhIysId5YSGdpMK1VS67b5B+k5oPMRPgqQw3JEOKFmPli8cGkIEQXxKcKLtiVhYJ15NxNt/w37sO2rm3obWrRvsUfkPVySO6/6K9cgFNJz0Xzzn3tk7lWYgRI9Gso8w+4Zr34Hmku5jcfEkP38IiTeN58MT8yk47Xto7yEYHzEMSd/TCCCUbJJH64pEhh+AJE5GCz5By77ve5pF9Cgc/7wT69T9qdj3Xux/P/SLSNHoL5I5h7A370WGJ1I881b0q6cHe0hDEuvgy4n66B7sT3Mo2/1Wkxu+oyDBYKgdgQFNtNuSxduO8+w4MnnuaKPhunsCMXvEQf58U+TB07btvr80xDIC75EZRBySCBMj0YIP0Y3zBz4BeeX5JCQWIhPQ9nqjZ9vZavZkwyOQ2EjGJbcQEWehiwuhLLe7r8NtopFDoqGzyUj79Yw4dkVAeILxoBs3dEv7bWtMYUkQPYyEAxLA7UDz3x66RS0cIWYveng2aXMT0IZmNO/toStaP1i4o8x3xuQ4kubEQf5SI6G4A0S5B/Nodwz6PdH2URYPEZkiIm9v8krucXzHk8lzhGCdfguOv11F4yWf0HDcP8wX/VAlIgPHtfdg/f4Y1s95HvvWf/muPGXcBCOx17QRXfuJiS722FBfBzGxjHh5HxLPz+LDi8uw/7Og9wQfPRJJ2RltLjPSfR1N3cdC4pCsA5DIDHTtR2h13ydLSZqJ4777kRljWbfL09jv/tc317qDIqOOxvGPh6C1k3W7PImu/WCwhzT0EAvrmOtxPHgb9j0/UH7AE9CwI5TF7L83G/RofcdAoo77IouHqi7DTKRbI3AyeduDww0h8UT8YSTUtKILXoLMEWY5dCimSzhCkKhMhv1lJIQ50W8fhxFTkMw523ee9noTWBUSb7yprqiKiDRIcUBjuYkujkr66T5KeAQH/LEZGRmOfnwnjByLJEzwnlChpRraG9G6XOMhR2V1S/W5oyFlNBKW2PcximX2MdPGMfrqFeAQ9LtHYcweQ1OIwHKAFYbMmMyovzSjRevB/gcy/hAjZh/ENzjc4I5GThlO0voGdNE7kLkMGX3k4GUwiPcVZFDpdx5tX2Tx+niegMnkbTGPtg9o5RKKp91A2qxoHC8/3FuibQiiq19gyc6vMvWWTKxL7tu+znU5xnPNnGIEAnpid5jaxR0tJrq4531UG/34Tl46cCm/PcqJdVWPvl2fURGIitpcJm+A2G/ewPJTVjDlf7si+1/hs/PukNgePHf8idx7ihiz4CxkxKGDPaKhSUMBlbMvxx3hJPrTv289BW0L+DKPdmZMmH6z24h+9w/9cHUwj9YH9GuiHags3hbOFxiZvKzUmYWFb/d1WN00b8T+8BFo6gSnIFMmIhP+b8jGv2vVUvT9F8wPTkF237fvEnut1WhXSo+IEQjoyllVGxrXe1NrvHmwEcO6pe5yXsO+4nU8bTbqUVynDUemTjDlHAFSx4Ar3JzXFQkxY32ij6obPkG//AScFrgsZO/jehXbGGroymfRxSvMtUaGIvuctV0TQZA+0FaLfvoQWtVk7vOoEciM3/VpNczXE+23s0f0u3/I+8GJ1hf0a6YYqCzeFs4XGJm8pLjtGVY34alYR92M7LkPq85djf2fr7u9rCGIJEzFOvk2JDWOhWesQ+fP63vn0Hgj2u5wQd4CtHljjxNbpuJT1Ei0oRitzestdZcwAeuq2ahHuf1DRZfXdkvsOZxIwiQkbjyUr0ErV/YWIhjI9Q7bH+uk26CmlVW/XwHly31y3h0VmXgy1vHXom+WUHreQrSpZNudgmwfIbHIIdciBx5D4R9XYt/zzaCVdw3u0Q4+A3HJ+iWLtymBlskbCJIwkYlvzUFmJWDff9nQl9ibNpdZ7+4G7Tb2fZegRfP63FUihyFj94bOVrT4897BZJYbiR+PRGehNaugLrdXEJTrtOFce1UsFLTQ8cfX0HW53X0doUjmLkZib+N3aNUyfIUcdjgTX98T/WEJ9j+ugNq1Pjv3DocVgnX9YaT9azb6+vPYL17Tt8jtINuFRI1gxBsHIidmYT90jZHYC+gAglHHOwIDmWj7K4u3KYGVyRsIkcOQPS9CsrNZcWMROn+ZKcQwRGXJJHE6MudSUGXZDUWwfrm53r6k/oQmmmR+9UDpWmiv6+5nOUwQTlgyNJaizWVe79SsEsjUCVhnzsVT18GH79lQ3AidXrsON8SORcJToTIPGkt8JlkmmXOQvS5E19RTcuM6oxq0gxeM7zeWAxlzLLL7qbQ9X0zTg7kmX3mIimoMGmFJyG7nIVNmsvaW9djz1phUwQB9ZwhBj3ZHoN9Rx/2VxdvSeRgEmbyBIKP3Y/KCKHTxYjznnIf15wORcSf42+ygIYecxNQFq9B5P2A/eyHWdWciqX1LlZa48RCZ7pW6y0VSdzG1d8Hk2SZPh84mtHyBiS5W/Uliz/m7ERx6QCM1TxXTdn8had/tZGrMglcmb3+0rQZd/5ERIoif5IOLdWBddCoZpxSgr7yJbb+B4w9XDN3o3JA4Qp/+PVQU4LnzHmRcNNZJNwzNOt+DiKTuwrjvOmD1MjznnI917i7Izn8IjPGhGUryi2JAv4JAy+JtwX7/ZfIGQtRwZMxvkegI8t6sgXVrussMDkEkYQoy5rfQ2knJ/8qhrsDr/Wzh2Unt3k/sofFmX9bTDvXlJom/6z5ZLhMo5YqC1jpo753gL2NGIXtOoK2+kzWFodBQZJagu8pihiUjjhCo2IC2VPnoYi0kdXdk1GHo0gaaXy1Dm0uNtN9QxBGCZM1Fsveg6ZNq9PMKaCkPlhH0NeGpyJhjIS2Dgreq0TUF3u+MIVgIJ8hm+FUmb3tk8bbQNzAyeQOhqRitL0DffYO2Z4sI/dfJyMjDfHf+HY3atWhjCfbjL8PqRhxPXNkttt5F4wa0dD7Ejektv9deDx1NZk/V04Fk7N2domN3mGN1uZD/A2SMRxK83qnaaH0BNBTReMbLtFR2kPTUfpDo9Ww72qC+HoZNMuf0FbYHrVkJdYXYf3sdRoThuPwWCIn1nY0dic4WU/SjdBn29Z8ix2VgnXzrkI2sHzSay9C6XPSLd2h5JI/whw9DJp/Sq4kvo45nxYXp/H1H9bu/838rglHHPsCvMnnbI4u3hb6BkckbCBEZSEQGGvkujRvbCd1YAPE5EJExNJfeYscikcPAepnm0jYia/IQRyhEDu9Os1GPmfw6mszk6gj9KZH/p3vS2WpqKosYOb0uIYKQWDQqyqTwOEJ+6ivhKRCTTUvlcxSud5C4ohBJrYKkZFPO0R9YDpPiExILja9CXjNatw6JSDe/36GGMwxJnol6Wmmuep+I8haoXWP22oeqfu9g0CWxF/8FjaXthBeth8y1EJFu/hb8QfBZadAJ/gp8gHXkn0j65lbsD1dRs9/VRhlmqOIMw/Hna4l89VLsy17Cc/qN0NIjhSciwxSUcIaia96A+h4yeZYLSd8TydwbLf0B3TCv99JZVJbpK4KufRMaCrqPuSJJemo/Zj4wgjV/zqXi8iUQGmq0b/0ZHhmejuMfN2NdczRNx96L57E7h+wWAYAkzSDq3duQ3cdQufd12O8+MNhDGpLI3n8g5Yc70JxKKmZfjRb1ucbPdhrCPIz297Wt04sME5HPRGSVt179xVtoc4W3hv1iEVkuIh4Rifce+5O333IReV5EQgd8ySKni8g67+v0Hu+LiNwqImu94/3jQG31leBE6wtCE41aTVYEUekhULrKFOYfqhJ7EWlITDZMjIREN7pxgZEUtD3GO3VHmYISoeFoZys0l3VPqM5wryh8uBGJb6noTivp2TckzEjsdfUVCxJTkNRIEpLBFe5Al6+FvFz/5jRbDhNtHjuSsNHhiIipbjVUU3+cYRCdDakjiB0RBs2dRvvXV3rFQQwhcRAzGjIiiRkeCkU5aOnX/tkbtwbw2jadwGWqOgHYDbhARHrtJ6nqXaq6k6ruBPwFU+yoWkQygD8Cs1R1MuAATuzrZW1JYMY7gd8A7ArsAtwgIl0FFH4HDAPGe8f7Ql9tDZTgROsrLAfWKdfhfO6v2Ld+Qe2h95gqSEOVkHgcN9yOdcuZVP3mP9h/erC3mHr0qG6ZvDXv9v6idoYhmfsiyTuh6z83e7o9A6tixpq+bXXouvdMcE4XSckkvXgEMZeN5n+nFFD8h0XQ6SMBhJ8jdjyOx+5BDt2N4t3/jv3SP/xvcxCRrANwvvIAEhdGwYz70B9eHOwhDUmsI67C/eo92C+toGzPe7ZLHGNHQFVLVXWR9/8NwCrg5/ZW/g94vsfPTiBMRJyYMrwlACIySkTe9xYj+lJExvdxSAcBH6lqtarWAB8BB3uPnQfc3BU0q6rlWzmHz/HpRLst2byfkb7bcWTyBoIr0uTNHZ5K9GFJ6OpP0YJ3h+ZSo1imgHpEOnGnpCPTo9HVr6ElX5njXVJ3oXEQl4a2N5il4C7P1nKBMwKiUs2ebENBd1ELb19C4yA2DW2rMcc72sxylsuFxISya3ozEalu7Pk5UOZn3WDLYfZrY4eTdko6hDjQ1S/4tGDGDoXDbbyuMePIOikZra1F17xoJAmD+A5nuKmmtncyScckw7rveusvDxQZwLLxdsY/eL+XpwPzt3I8HDPpvQqgqsXA3cB6oBSoU9UPvc2fAC5S1ZnA5cAjfRxGBj3U4zCZL10T/yjgBBFZICLvbVIoya/4bKLto2zeZtJ3O6RM3kBwhmOdfhuOyy6m+pxPafndf02xhqFK1HAcV96DHHMwa/d9A/vh53p7p3ETkawDjEzeuk96Vx9yRxnPNno4mvMZWrWi16klYQoybD9oKELXzTPRxR4bGhogMYmMF/cn+qQ03rq8AvutwOyLS8quOG69H8lOY/Xsl9F5gReWCiQy9jgc9zwEla2snf0iuv6LwR7S0MNyYR17E46bbqT1hvk0r/Jxha6BTbSJ3omp63XOlkx4y/G+ClyiqvVbGckRwNeqWu3tE4dRgRsJpAMRInKK91yzgZdFZDHwOEblDRE5o2u/F5gFvOv9+X9dQ9mC3a69pRCg1RtF/Q/gyb7ewoHiy6jjvsjmbUn6LnAyefUb0aXPIJNONFGt/sJyQGgicVePhRCHiZ4NNA0F6A+vwIjxSPbPqRT6AMuFxGQx5rZsCHWin90L43bultizHEj0MNQdaZ7ge+L1jEmfsGWpO3GYiXgrEZlWeDhH3PgjkhSC/b/rkUmT4SeJPej+GxOTcxs9cvPC7i0VaPNGJCLN7Lf3xO6AuhwQB0SPMr9bsWDkNMbdugE6bfSj22H6Ib3TmYYKXplDmT2NMbfZkBAwJ6AbuwNd+yrU1iA7Hbf572goYDnAFUnIH0cTnuPj2tMDc6cqt5XeIyIuzCT7rKq+9jNNT6T3svFcIF9VK7zneQ0zwb4J1Hr3dHuhqk8BT3nbz2NzgZkiYE6PnzOBeT2Over9//+6zhMIfJZHK32QzZMtSN9JAGXyJlghumjOCMLefcgUUhjCaN7bLJ/+NBMvScFx44MBy4fUJU+zYp+3mXjvKKzf3xEQmwD2/67nxWNyOP60UKzzd/EORrtLM4oFsXHeiOjek71WLIK872H07M31aNsb0LVvmOXq0Udt9oBmP3s1i87OYeaHeyF7XuSnq/uV09GI57SLKP+ultQfbhyaDzQ98GkebWK4zj98bL/7O59Z8rN5tCIiwDNAtbd40NbaxQD5wDBv2ifeLcUnMaugLcDTwAJVfVBEvgHuU9WXvTamquqSTc45j03mAm8w1EKMUwewCJjpDb66HVirqk+KyBzgLlXdua/3YiD4ZKKVAcrmbU/77Z1opadMXlLozPyH50BjBzJhBLLLOT6RWdshqcvB/vw/0NwJzZ3I3rubicLPaNVS9OtXoc0DrR5kzgFm+dffdte+hH3r+3gq2mlv8BB+0Shk6mRo9EZxZkw0Kwt2JxISBbHjux8+msvQpmKwO0EViR3T/SDmaUdr14Cn1RTaCI3t1VfXf4wu/MLcZ1uxDjvFN6Ugg3Rjd6BL/osW5kNTJ5IQiex3oVkJGYL8wibaPYEvMaV2uyrzXQ1kAajqY952vwMOVtUTN+l/E3ACxkH7EThLVdtEZCTwKGbF0wW8oKo3b9J3HluYC0Tk994xANzq9YIRkVjgWe/YGoFzN528/YVP3JyByub1VyZPROZ4I9Ie8z6hbOnc3TJ5WSORPQ4m98/rsJ9ZBD9bPfIXTsxorN/chIwcxo8X5aFff+eTwvvbQhKmGruRoay4cB2sCIxdEiZgnb8L7Q0eHvpKjBBBSJSR2HO7kbgJJiWpfDVak9NbYi88BUmaYYLWNizuvY/scJu94qgRJm2rJq9XOpFkzcU6+ma0qJEVF65Dq9cE5np/TVguZPoZWAf8gaZH82j861JTDCV4n/uGH9N7VPUrVRVVndqVwqOq76rqY12TrLfd05tOst73b1DV8ao6WVVP7bGFmK+qB3vL/E7cdJL1tpmzJYdLVZ9U1dHe11M93q9V1cNUdYqq7h6oSRZ8G3XcL9m8rbWXvsnkKebJJBSz/r5NJHYMoz88AuvQDDx/vSzwslUBRsbty4x5cyHEgef6i9C8fgjf94ddfsPkTw9Gqxrx3HmJyREMAOEXjeLP9yaj39fRevZzaG5e90FnBDJ8T4gZgRZ/sVnEsMSOQcbMQZvLjCRgz/rG7mhk1D4QnYEWfQY1vdMwrJOPYfIH+6MffYN9/2VG+i+IbwmJI/Kp3xJ5667YT9yN/caNwVrB28LPBSuC9A1fTrT9lc3rt0we8KWqHoLRpL2pT6MMT0GmnwHjJpLzQAm6INcUuh+q8mCx44xKSJiTlQ+UQe5yk+/qZ5kuSZiKzDwLOm0K790A5euMXX96IarI1MnIUQfQXtHO158obGwyakB4JfZiRiGhCVC5HprLe0vshadAzBjzeagqMAVHuu6TIwRiRiMh8VCejzb17iuZc5Cdf48urqX03ny0qXToFiwZLJzhRtxi8v5U/6sIfavYeLbByfbnkQG8gvgEn020auTufpLN87r7U1X1mB6Rx5l0p/p4uvr9TPtt2ez61q7BhG73Gcncm7ELz4KsKDwnXoD++Mz2dP/FYc05lcmLz0ALq/GcfL4RYw+E3d+cxsjvzkK/Xobn4kvQKn+t1ngDnxoboLackHOz2e/BVCoeKKT0uPfRnvmfoYnI2AMhPAkteA9qVnUfEwtJnoVk74tWr0SLPuldiCMsGRl/CIREo3nvmHrAP12sC+vmc0j/+CTsB5/Dc+sV0NyjPGUQnyBRI0l4/3yss2bgufAq7LduDS4j/xxBj3bQ8WkoqgZYNk9EjhGRx4H/YFSC+k54KjLiUCQpiaJv6tC8AlO9qOeX6lAiZrRRFrKE0m9qoSIfmkr9X0wjbiIy/GBot6n9sgbq1puyiv70qB0WMnY0sus4PO02JeUuY7exyHir6vFq4gpUlKCtNeY+9JT2i0g34gettUYg4acSkmEQmYm4IqChBvW0dtsVC0nZBRm2L6xtov3zajPBt/bpuTFIX3FHmQC7zAnUfFcHefXQVGK82yC9CWDBiiBbx68yeZsZ2w7ZPAmUTF5rJdq4AX3vJeofyCPmv8cMaRF3GjegzRuxH3+G9s9rCH3uUiR5pv/tNhSgTaXY9zwDJW04HrkWYvov37UpWrUM1n0Fw6cicV15tLaZ6OrWU3HYv/G02aQ+fyDEeSOK21qhqRESkiAyHYkZBRFp3Sdtr4eOBrRsodFtzdzXLD+DmXg7mszEu6lSk+2BurVoTS6df3wRa2Y0jmvv8J86y6+V9ga0IR+Wf0LjNfOJvHYqcvDV2+63g+PTqOPkCJ1/bF+rF26O87FFQZk8H+BXmbxN0e2QzdNAyeSFJiKhiZDwNmorFK1HE5ciUSO79VKHEpHDkPBUJPZ57A4bqteBKwyiR3dPIv4gaoS5z7EuyGtBq1cj6ukuAjFAxBGCxsaZFB4RU97R4TY2Q5PwtD1NZbWDlOX5kLwRSc/cfLnR02I8XkeYGZM7GiwnYBkvuK3G5OC6o7wyflvZrbAcEDcBsVxYLoHqDrRyKRKZDlEjBnytQby4o5CEqWj6WmA+WtUIlUuQyIyhWdSivwQr2g86wV+BF5l7MXGf34O9qIiy3W406jtDFcuFdfa1RLx+HfZ179F01C2BqWHrisRx6fVYj15IxwXP47ngb9Dmo7qu0SNNMQq7E13zZu/rCYkl9fkDmXRPNkv/lE/t9SshJs68xDLebMrO4GlDyxb0HpMzHMnaH0mahhZ+aj4Xfd0PjBqJ49k7sS4+mIp978HzxH1+D0L7NSIjDyXqg3sgwsnGnW9EF7882EPasQguHQ86wYm2C3e00VLNjiZpRjSsX4Vu+MQ/slU7AqHxEDEM2SOe0ImRaPF3Rv7N39HXYUlIZBaOveJhdDha/CVa/sPAg1ksl5kUQ6IgMg7tbDJ77l0Se3HxkBxG1igIjXWh8xfCGm+KjuUw3qkz3AgceFqN99p1L5xhxkMOizEeblNJ79SfrY7JAeGpEDOChN1jEZeFFr6/WWpQkAHiDDd/u8NHkrxbLFSUoes/NLEAv3bkpyqa/XoF8Q3BW9kTsbCOuhbH03dhP/4jZXMeRnsKlw813FFYF96G9deLqD7xdTrOfCQwDxbhKTiuuB3r3JOoOPxZ7Fv+4bsUjdjxyIhDoLkCXfthr0AkSc8k7uUTCD1rOE+dWsjGPy7pPcFHDkOSZqKtlWj5j2YPtouQWCTrICQ6C137AVq5tM9DkoRpOJ64H9lzMmtmPYn92tM+uNAgmyLTTsHx7wfRkkYKdn4ULf5ysIe0YxD0aAedAU2025LF247z7DgyeY4QcMcgR2aQdFYmLP0EXfvS0I1GdoYhYcnEnTcc58FJ6I/Po4Uf+D9dwhmORKSReOFwZEoMuvi/RmB8oIhlvNvwZEjMQlur0LpcE/ikNqiNxIRw6IgWItNCsD9cBaWre/R1ICFxEJ5oVJd6Rkh37dsmjQCHy4i/90XSzFswnpQxjLkwFVwWuuAfaGXACtP8OrBc4IpEdhpN1h8zIWc1uuw/3fKLQYIMEv2eaPsoi4eITBGRtzd5Jfc4vuPJ5DncRrbqoj9T/5cfqD3xFd9qRO5ohKdinXsncuzR5PzmE+zbXjZ1f/1NdDbWBXcjc/di3cHvoS/+nPDH9iEJU5CMvaGuAHK+NtHFnZ1QXQVJKaQ+N5fwgxJ57cZqdN4mE17UCCRuAtpUgtasBruHtx2aiAzbH3FHo2s+Rev7XgFKMvbGceODSGIEC/f+CL7937Y7BdluZJdzcFx1N/bHRaw/8FW0Zs22Ow1VBL+WYAzSNwYSddwXWTxUdRlmIt0agZPJ2x688m3R101Cq5qxP3gcGTEc2ek0/0bnDhZiIdFZjPr7eLAV+82/IlNnIqOO9L/duNGMvn88OAT7zRuQ6Xsjw/bfvvO0VKCNG5CIDFPhCYzEXuwoNDQeGr3SY5HpP0U5W78J59joJRDuxP7PX5CZkyHJmxqkCo1loJ1o5TIkJBpixnZHSIcmwvBpSHga24VYMHl3ZjzYgDZ1oG/cgOx57OaqQUH6j1ggTqwTpzNsWj46/0OI/wHZ7Xfe/OlfGcEl4EFnIM8shwLvAB8Cw0RkrYg8IiL7bOd5ttb/M+BvwC4YZZ/A445GDr8eOfwkSv64DPvmL4Z2ubeoEVgn34bsshNLT1uFvvlZYOzGTTR2R2Sy/JQV6JefbPcptHkj5H1vVHi6EAviJyEpu5gJ1htdLKm7m9f0M7D+9HcId/H8aYXYD38OufPNK+97qCiGyjIoWIRWrugtQhGegqTuDpGZm41lW0jWXKwz74SGdn48aSUU/rDd5wiyDSwHsvMfsE64ks5/5FF53te/3iXk4B7toNOvghUDlcXbwvkCI5OXlTqzsLAfRfVbK9EFz6OVFVDShEzPRnY7b+iG5dWuRX94Da1phPJm5JB9/O/ZYiT2WPwBWlUHNa3IYYd3i8dvi9ZKtKnEVHPytBupuy7P1vZAS7nJk/W0mSjVyGHdUncrn8V++HM61jbRXNFO7LXjkSmToaEeLAsyppg92Y5mJCQW4ib45HevGz6BFfPRsnpo92D99vfm3EF8h6cNXfkSFBWiJfVISiRy0KU7dPEQnxasSIvQ7383ud/9Hbd/HyxY4QP69W0xUFm8LZwvMDJ5Sf1cNgpNRPa8CJmxJ+uuy8d+e0XvYvRDjdixyAFXIcnxLL5qA7roh4BcryRMRfa/AlwWq67Kh9wf+243NNEsv6pC8Qpor+3uZzlMxaewZLSpDG0u6yV1R9IErFOn01zRzpNLXFDRYop4WBa4Q5C48UhEJpSvQ+sLe0vsDeR6h+2PHHgluraenL/konWFQ1fcYrBwhCBTTkX2OIm6RwroeHitV0QkmM8cJHAM5LG8X7J4mxJombyBIInTGPv18Vi7p+K59I/o/Mf9bXJQkZ0OZ/p3R0KbB8/FF5gc0EDY3fs4Jn7zW7SwDM91F6NlfS8eIrFjkLFz0ZYqdMPHvYPYHGFIwiQkIg2tXgoNBb36xl47nksfSUc/LKfxtOfQ/B7H3TFI9hyIykQ3fLqZxF6/sRxYF5zEmE9+g/7vfTz3XA4Nhb45d5BuwpKJffkUXNfsiueOW7DfuOlX8lATrHW8IzCQifYN+ieLtymBlckbCOEpyPgTIWs4ec9VoCvyTeGCobpvGzsWmXwKuCxynquEDevM9fr5C0oSpiAT/g/aPJQ+XQI1BabucF+8kNB4U0PZ0w41JdDR0D1eywFhSWbZsKUGba/3eszGu5Upk5GD9qa5op0fvwMqW0y0snpMAFzUCJP6U1tqJvCeQgQDud70PZEJx6KL6ql5utgsgbc3DN0Vk8HAFYlk/wbG7Er1y2XoN+XmszzUpQyDUcfbjYhk9fEV3ddz9jvqWFUXishPsnhbaZYJdD36b/EbySuvt7X+2xpDv2XyBoKMPpjRi0eg335M6+EXEHL3Aci03wXKfMCxDjmTsYsL0DffwXPnRTge/wOSvqf/7R53NhkHF6GvvIm99GOsuy9BEqb0qa8k7QRx49DqlVC5HMnYy+TAgvnSTZ4B7XVo+QJvdLHt3ZNtJOJPY9izsoXim3IQRw6ZS/fpjlYNS0bGHII2b0Tz30YSJvhmX9UZjnXfRSTUFmLf8C9IDsFxzS3mwSGIz5C4CSR+cinkL8Jz0mXIGSOxfuP/Z/RBJeiZbi/PYFZLf+7GKfA08O++nHBAogKqOm0bTbpk8Rbjh+cjETkGOAiIZXtl8gZCeAoSngKJC6nJaSZ1fQGMzIOw5B06yKLfRGcjUSNQ57vU5LaQWJUPUcMgPM2/qU6xY5GoEdj2GzSvaSKyrhBCYiG8O0XnJ+wOEwjlCDFjCokFVxToMlPhqaPBlE90hpvCBiGxZiXC094dTdy1JztuHGQ2Io4cGpsdaE0uYrmNN4yYc6gHKsvQ6GG+0ce2HEjidPMZKn8NytvR+lzE09ZbUSjIwHBHIWmz0bZa6vI/J7a4CerzICTefCaGIr9Sz7S/qOq+vj6nX2XytkcWbwt9AyOTNxBaq6GlDPuVJ6l+IJ+E/52CjD7Kd+ff0WgqRVvKsW99hLYfGwh79S999jAHRGMR2lyKfc3j0OjB8Y+bTdRwT2pWocULIW1a7zF1NkNHE1r6LWAhWft3y9rZHrDb0MplULAIRs5E4rySYuqB5o1oTS5Fe/4Th1tIe/EgiPIqOrW1Q2szZO9s0od8hd1hpAwrV9J0+rOEzU3Acc1dm0vxBRkYHY3QVIIueJ2ay38g7p5dTCDeDoBPo47TI/X7P/T/b9Rx43fBqGMf4FeZvO2RxdtC38DI5A2E0HjzSgknPMENJQVo1PdGD3UoSuxFpCGh8cjwcNw5zVCxAtVOJG6Sfz3byEzEFQkjwiCvGS1fgrTXQ+z4bs9WHOByGUGAlgqzTNwlFCBe0QD1GGUeT4TxXiwHWOFISDSakGRSeDxt4I7xesVxiOXG4RZamkGX5EJyGDIsq3fUsi+xXGYFwdNKWKobOhUt+95Iv8WM9o/NXyOuSIgdCxnDCEtcglbXwcb5SEy2d+ViiCAEl459gIi8AHQFp5Sq6p+3p39wUcEHWIdcQfi792K/t5aNu/1taNewdYRgnXcDzn//hbaL3qL1+LtMjqq/CYnFcfktWH87l6bTn8Vz2b1mObiL6FFmNcHTga7aRCbPK9ouyTPR9V94VYp6hAzEjEWyj4COZnTtO9Bc0n0sLIm0Fw9i5F9HM/+i9dTfugZiEiEq2luByE9fYjHjcPznPqxT9qZ4l/uwn3k4GBzlB2TsMYS9fT94lOKZf0NX9yPPfkcnGAzlC75V1VNV9VTgju3tHFDh9yGLK9KkjsxMILm+E3IXom11SOY+Q3PPNiQWUNxHJKNlbWjux5AwAknfa/O9Ux/blYh0wo5KRkTQ/PchdjiSsqvXrgMJjUVjU9COBqSh0Ox5OsOMh+oMh4gks1fbWGi83tDE7r4hsWhMMtpejzRuMH0Rs1ycHMaEqRCe5EK/+BbiQ5BUP+6dWg5vBPUI0o5KhlAnmvMaxI8LzHL9rwVHiHkQGz2CtN+UQ2kRGv0GkrZbd8GTXzJBj9ZXHCkiNvCBqq7d3s7BZxZfYTmwjrkex1230HnHAioOeTIwYuqDRUgc1gV3YF1yFhuPegP74qcCo3AUkYHjkruQ44+i+IAXsO//T+8CEj/J5FWhaz6E1qruY+4oZNh+SOxoNOcztGKTlYe4CUjWAdBYiuZ+0ktzVoZlEfP8/+H8bQaPnbmB6msCoykrKTvjeOBBZPJwls18AX3/+YDY/bUhM36P48EH0NVVFMx+Gi1bMNhD8h3BPFpfcCqQCxwrIv/c3s4+9WhF5FPgQExe60mYlB4b+IOqzheRcEy+azTQDLylqp+KyDWbtsekBW2p7Ty2owRjQLFc4I7GceZIEosa0e9fh4yFyPhjh2Ywi8ONhCWTcs0Y8NjoV4/DyAnIyMP8bzcynfTrxkCIA/36ERg5zZRrFMuIXUelo5YTbSlHOpsgaoTxXsT6SbIOhwuqVxivNjylW+06Mh2coaZ+snpM4JOq2b+ND+H4ie1EpLixX12CdVokJO/sv2sVy4w7azKTbzTayPr5fTBpPyRxW0H/QfqM5QArDNljPMOvtWDVIrSqBJl01C9/zzboTg0YVS0GioF3+9PfZ7+CPsrmbSZ9t0PK5A0EZxjW0TdjnX4hlX9aSOO5b5sIx6FKZCbWWXciBx/AymO/xX7s7cCUt4sdi3XOXciuO7H6yC/QtzbZW4ubiKTvAXXr0fxvNhdxz9gbCU1A132J1uf16ioJU4xgQG2uERhobYaOdqipRlLTSPjX/rhnRvPK3fXod30XgB8IkjkH69K/g9tiwSHfwtKPAmL314bsei7Webdiv1pA8dHvoA3rB3tIQXYwROSMrZX83Rq+9Gj7Ipu3Jem7wMnk1RSjX96P7H6O/z3MkHgS75uJ1jRiv3YfMjoL2fls/+5hDiISO5oJ/5yIjB3rvwChLZE0iXH/WAGdNvazVyN77YdkzfUOyoEkjENjW7f8+w5NNCk9W5K6EweSMAGNHtYdYdzjuqzTIjlu7FJQsB+/HNljJ0juUbiiq1qYIwRxR0LMmM2FCBqLjMcdPXJz+bbOZrRqOeKK6CViILvOYeZTChP6VeNlYKiNLvsPmpuLtf/vIDo7MHY97ej8J9CKCqwDzoPwVP/as5xY5+9OxtElSES6f235GwkuAfuBd4Dp29PBlxPtoRjPtBO4XkTWAh8DL6rq5942XdJ3ABnAoxiZvC2131LbAdFS0ErH337A/dqpAZhoY5GD/gIb55M/7XaGH7gRx1OngzUEl5ABYkZhHXtLwM1KwhTk2CnoR7ez8MhFzHjW2WOitcy+69Y6h8YjW6u8ZDl+vm/yzsgUM8m+fG4Jv72+BetI7+Sq6i3dqBAZhcalItHZm0202lgMpSshO2bzibajCfIXoglJSOzY7ok2a2739QUaVewX57P+n6WMWFBgrikQ2O3Yd31Pyfx6MpeWIn6faF3IzLP8ayOQBJeOfYqqlmNq/fcZnxSsGKhsXsBk8lIiZhb85xB0VRkyMQ3Z7zL/e5gtFeiK19GSInRVDdZeY5HZF/rX5q8QrVwCq79AC0vRokask4/pu8TeQOwu/y/2y9/S/nUtTaVtxP91oqks1dQIIaGQMR0QaKtDwuIhbmJ355YKaKtG2+rA7jDRxF1lIj1tUJ+LdjRBSzVEpg2+OLzaaOGHsGENuroIHBbWCZf4v3KV3YHmvgkb8tGVJRAbgnXclUO2kpNPC1YMi9LvL9su56sXjj99GSxYwQ6SRztQ2bwByORZInKriDwoIqdv5dzdMnmZWTB5bzbeW4D9QZ6JkvW3gkdYEjLrbGTidNbdWYz97TpTyPxXoRwSOCRxGrLnRWArK28rgaJVZrLyd+5p8gSsI2fQVNrGyyvdUO6NvHa6ISwCic5GwpKhthBt3Nhb9i8sCWLHmc9DVb7xYruOOULMPnNYMhSvg4YSs/c9mLm0YiEjDkZ2PQP9tJKav+ehLeWmjKU/sVzImGORXf+PpudKaHok31t4xM92hwIywFeQLgaUR+vLRYV+yeYNUCbvSMyycgd9lMmT+AmkzTsb65DReC76E/rZ3/t6fQNC0ndj3PenIWNi8Zx+PrrwyYDY/bVhHXYKkxeehP6Yi+f8C4xoQACI/+tE/vBYOm0vllBz0utQ3CO1KyQOGT4HiUhBN3wKtWt69ZWEKcjwvdC6XLT4i97Bc2HJyJTDITwBzX0drV4RkOv5WZwRWPecSfxzR2I/+AT2Y3/plQrlN0ITiXzxbCIf2B/PNbdjP3Pd0FXOCrKjcaSIXCQiY71VC7cLX060/ZXNG4hM3jjMk8almCjlbRMSh4w4FIaPofzDKjSnDJrL/J8DGp6KjDoSSUun8ONadF2h1+4Ql+kKNPGTkFFHQZuHje9VQl2BWaL1ZyS0KjJuHLLXdFqqO8hZI2hFE9TXmn1ahxsiMkxaUXM12lZvJoiuMYXGQ0S6+Qy2VJnPRJe35gwz8nyuSKjcCG113hWRQRQutxxG2u//2zvv8Diqqw+/Z1a76r1YtiVbtuXesA2Y3nsPIUAooYUWIARCIPTeS0KooQTyUQIECL1jTMe4gXuXVSzbkqzepZ3z/XFXlmQElrU7K1ua93nmsXdn75yZ1e7eOfeUX85++L+vQj8phfr1zk+2nkgk+0AYNp2qLyvQr8uM3eZqZ+3u6Ij0fHNpo62O9vie1NGGbKINyN1tls1T1XGqOklVj++QeZxFe6mPv23cL7x+axRhJPI2H6+7SNa+ZM66BhmSRP0Rl6Hfh8fDlAnHM2zB1QDUHHQpuuL1sNjtV4iFddbFDPruCuxnZuI/7Qqo2uZmLt3D32TisXW10NRM8m0T2fnRYeRdtYINJ7wLjaXtr40ZiAw7FLzRaN77UJPXvs/yIpm7IYP2QEvmocVfdfbW4nOQySeAWOjSV6F6lTPXsy1EZ+B9/kqsu4/Cf/ad2E/dGpblXEkcSfLHV2P9YXcajr0G+6U73PaUv4S7dBw0qrpOVd8DjlbVbc6UC2k+mqpOVm3THOuSNtm8UNl+HThURB4CvtimkZFJSMYuMGAgTTWt6MYSqFji/F15dDoyYFckJY6mqlYoLDB2+3KtbW+QOALJmAZRFs0VLWjFaqha5YwnqGoSn+LiYfQ4ZNJIYmLB9itatsQ0xWiqMIIHVoSR86ssRZsqzN+9LV7vS2hP8PE3G0+tbaUlIto01fBGm5pe7UWPtg2PzyRopY7B32ijJY1oxVKoW++s3YhoJH0qDMiluc4PZY1mSb1+o7N2d1RcjzaU9Cjzz1GZvJ8Y2wbZvLDJ5DXXQFM59lv/pOzW5aS/fjwy7tRtPfS201QJzZXYzzxI6cMFZHx0jlnSdgkt9RvQ2kJaz/4HllfwvHBPSOswtWQuFM6HnF3by11UobEULVvC4qnPkpzQyqA3joaY2MA51RmR+dR0iEtB0qd0ztxtbYCmSiPtF5XSuYe0v9l4uhFRphPZ9oC/GRpK0LUzKT/lTZL/NBzr7G3OF9l2WhuM3fn/Y/3vPifz/gm9UmIWakKadTw0Xr+/alqPx3su+rzfZR0HHLeFgW2RqtZ02LdGVbe5ri2sogLbIpsXNpk8X3ygB24GqWOLoHgdmvg5kjbpp7WNoSQyyWzZ8aSOjoHClaj3C/Oj2xcl9nqLmEzEisCalgDlLWjxN5CYg6RODklpl/ji0ORMQEzWcGSyicn64pHWBpITWhFL0LnLICMGyRkG/lbjLfgCQget9Ubb2BdvJs+IaOPl+uJM/WxDCXhjA9J/PmclCXuCxwdxWZCSQ9L4ONOOs3AGkpjjbFOLiGiIHwqDh5E2bg7Ut6KFnyLJo835uLj0jIXAJOBUYIKIVNM+8fbox9ktZQ4ge16I56V/YP+4juLd/4ZunB0Wu9bRVxPx8n3Yzy9kw15/QyuXhcVuvyIqDc91d2NdcyalR72AfeUj4A9RElriSCTnUGiqQtd+0jkmGzuIQW8cTea1uXx5QRF1dy+HqGiIjTPLzCkjkUF7oo2bzA1Ac1X7WF+CkfZLHIbmz0A3LQzN+TqIZO6O598PImOyWLvzQ9ifPhseu8OOwPfGoxATwfKdHkXn/jcsdncY3KXjbSJQEnqxqu6rqqmYHg+PA9VsY6OKNlyZvDYCclnWTllkntUKK39Em6pNFx4nC+MjosGKQA4eSEaaD5Z+hVYXIkMP6ZsSe72FNw6JG0TquVmI10IXvgwDRiKD9wnuuAEhAolOQf3NJiRgt0LMQBCPWS7OiGHqdCU61Yu++y1kxSG5w8x+y2vk+VRNRrG/BaLTjGdreSEiFhIGm/9XrzEes5MrLcFgeYzXnT2aIb9fDs1+dNHzSNauRmTdMbte8HmRceMY+bsStKwcFj6H5OxjPN7+Tv+cL3uMiAzp4ulFge0/HfZXqmq3Ut5dj3YL5IA/47n2Tuz/W8rGw15EO2aGOoXlxTr+JjzXXE/ddd+z6VcvQmN3E69duk18Dp7LHkCOPojlB7+H/cTLoctWTR6HDN4brSlCi77plNwmOcOIe+ZXWPunct+fS6i5f2XnsUmjkIypaG0RWjrfJEu1EZWCZO1nJuO8L9CqzgII2yMy9BA8tz4ElrBk7/+hi3rkBGy73TEn4bn/YVhfx8I930TXfRsWu9s3QXiz/dSjBf79M9uzga3t/8d194BBebRbk8XbhuNsPzJ5YoEnCuusCWTsswG+fRPN/B7Z6VRnPUzLA754Yv4yipiN9difPYNk5yCTTjHetktosDxI0jBG3TMCvBb6/u0wYffQ9A8WD5IwBI1MQuuKzIRZX2disl4vZMVx/q7riU71Yj8zC+uiWGhrqygeJG6wablYXwxNURCb1R5HjkyGAWNBBN20EIkdbOpvt0fapAqn7crYe5pMRv8n9yC7HA+JuQ7btZB9pzDhXgtdtBjW3YtM/23/jtn22/myZ6jq/qE+Zo892m7K4iEiE0XknS22jA77tz+ZPI8P2e9yrJMvo/buZVRfPCM8nW+8cVjH3Ix1wlmsv/hHmv/6idvQwgmSx2Gdcw8ybgRzT1iIfvxRaI7bJmKQvhNUrIHCH012cUMDNDYiucNIeOwQPCNieOnhWnTegs5jE3ORpFFo1Vq0YiV0rJSLTkcypxsvI/97aNj+S1lk+DFY594LhbUsP2kWWhomScGJp2Odeyf62UZWnPgtWrU6LHa3SwTXo90OCMaj7Y4sHqq6EDOR/hzhk8nbVnzxxN2/H7pxPfZrDyNDM5C9L3Y+6zM6k0H/tw9aVoH9f7cjE3KQ3S7kJzJrLsGRsyvTXl6H1rVgP/kX5LDDTOehbaG2CK1dhyQObxcIlwgkfQKaUAEly012ccpIE5MFrIti+e3uC6CqGf/9l2IdNMV4q2Am1+oS81/vHKMulDR6899eYrPQoR6IHhCStyAcyDEHMnrUfHTWHHTOXKwjz3M+dioerEsOYOQhS9GP3kPjPsY66tIdX8TdZYckmF/uIzC6fB8B2SKyQkQeFZF9t/E4Pze+TSZvV0zWV/jxxiHTL0D2PIHS21di/3OhaTrgdBeaqBRkv8uR6fuz6urV2C8t6NyM3iUkSNpk5OibIDqC+X9aC4tnbXNDC20oMVJ3TeXtT1oe450mj4W4FIjJQFImIKmTzDbmZKxT7kDrW3jjilLsD+ZB0QIoXgTFS6G8DCo2wfplaFV+5+YU0emmScT2umzcBTL8KOTQK9Fvyij+y2IjD+j0Z1ks8z4f9idaXiqi5JolJiO8P36HrCA2l5DQo4YVwcridXG88MjkDcmclp//TndPq52mSnTth1BUgP1NPtbuQ5ADr3Dew6zfiK7+CNauxv5qI9ZxE5DdL3LWZj9ENy2A/NnowpXoimqsi05BBu3VvcFNFdBYjjaaHsWSOrF9ErRboKHMiLg3bkIikzpl3+qPz2J/MI/6t0uoXdfEgAcnIbmjoL4eoqKRwdOMNF19KRKb0Vlib0dDTW0tJXnot0sh0oN1+pXOe5j+ZjT/AyjOx/56JZIZg/Xba7frWvWQNqzISdDvb9i1x+M953za7xpWOEGPZopgZfG6OF54ZPLSe1gWEZmEjD4JRk1lw5NF2LMKTXs8p5VDYgYgE0+H3NGsemoj+kOe6WTlyoOFFEmdhEw9B5r9rP7nBihdZd7n7ni3kcmQOMJMqhWF0FLT3lLR8pqOT5HJUFeCNlZ0XpkYMBbrwInUrmvig7XRsKkRWlvBEwFRMRCfA5EpUL0OrS/bsVc1xDKi9RN+hc4oo+7/Ck0jDqfFPDw+ZPgxyKQjqX5lAy0vFprVh/6U++D2Ou51gnHJeiSLtyXhlskLBsmYyqCv/4i12xD8v/sT+uUjTps0docewKj5F0BmDC3H/wH98bmtD3LZZqwTzmbknPPQGT/gP+dStLz7yTuSOhEZdiBaU4gWfdZZUcYXjwzaDYlOQ9d/Y+phNxu1GPDgJM74Vza1/8xn02/fho0degVHpSI5ByLRqUZ0vWqL0qAdDV8i1mMXEffUcfhvfBD78evC0+c7ZiBJb/8R350H4L/gJuz/u6l/aEK7yVDbBcFMtG/SM1m8LQmvTF4wRCYj2QdA1hDK5tegBSVQW2i8HyeJGYAMOQRJS2Xj/Bo0P9/Yddob6G8kj0WGHIi2KhXzqqEyH+rWde8H2Zdgmv7brdBUY9oxtnlNlhei0ky7xZY6U8LT2mASn1SR3FHItHE017RSXAi6sRoqNwEBib2YTNPYpKkGba41f/cddZKwvEjmdGTgLrSuqEPnV0FtgfN14xHRJhyQNYmqxbXo0iqoKTBL/y4uDtPjibansnhdHac3ZPKCQXIOZcB3t0BiJFUHXoEueCk8dnc5lcELboGKJsr3uhzNey8sdvsVlhfPBZeT+umfse99B/9pV5ubmu4gFjJgZyRrH7RsgRFx77hEGZ2GDNobiYgy+8rWQG2Nicn6bVLvn8qEh3JZdMkqNp70fudJIDYLGXYYWFZAYq8gtNcdbuKyiXz5BqyrDqXh17dhP3NXWDR2JWUCKZ/djHXiFCoOuBr71Xsdt9nbuA5t7xNUNk8vyOJtSc9l8oIhMskIjGcOxOOzYMN6tHSe83fHUWkmnpgejSfSgnUFxq7THnV/I34okjIBMkyjEC1bYqQMu5oIWuuNsHxbvN4bB75E48WqBlSaAsvIltck4XiiNpf6IGL6H8cnQu4YZPwIMtJtImIsdMMc8/dtLDPLq2pDSz1UlYPtcH6A03h8pmwpaQTeWA80tKKlc7t/U9NTIqJNUllGDt4YD1Q3oyWznZf2603cmbbXcVQmb1tk8boYGx6ZvGBorYfmauwXH6DkzlUM+OBUZOQ25YH1jOYaaKnG/8CdlPxrHZlfXGKWtF1Ch9om27x6NXW/foDoTB+e5/72k7Ia3fg95M1FRu/bOSvY3wTN1ei6L8EXh2Tt3y5rZ/tBW9GSObB+GTJsD5P4ZI4ITRXohjnMGv8iQwc2k/n6MRAZqN2urzci8+MPQNImO/42OI7dYrK2l7/HxhPeJuPm0Vin3em8XX+TeZ+/fpb8079j6JM7mVKv7YCQZh0PS9DZt+zW4/HW7z52s45DgKOiAtsii9fF2PDI5AVDRAxExCC5maTvtwkK81Dfh0jmrs42fvfFgzcWGZtMxj71kL8Y1VYkc/ftumxhh0IsU8/sbyL6oFRoVTT/YyOxN2CX9gYS3lg0NR1tqUNq8iE6w3hNnkgjbReVYl5bv8EIBESlBNoqepCoFDRl8OZJnahU4+lFxEDCRoYObMYb40G/XQQDY5ERI8xrLavveBuW18S204aSfkAK2IrmvYukjDHZ3E7hiTSx75xcsvddhta1wJq3kIwpEJftnN1wIwJWH/ms7MC4JckhQPa5BM9jf8f+dA3Fez+GloVB0kwsrF9dj+fxu7EfnMPG/R9Ha9Y6b7e/ETsQz7X3Yl1wIusO+A/2rU93TkRKHouMOBYaytGFb3dujRgRY2KySSPRgi/Qsi2ymJNGm+Sr+lI0f0anphcSP4TM148h5aKhfHLRehofXNUusRcbh1h9S3hLBu+L57GHkIFJrNj5afSb/4TH7ohf4XnhUWi1WTz1/9DF74bFrkv/wp1oQ4HlBW8s1gHDGPinHFjyDbro+c4lHk7g8Rnd0pOHkP6HbJj/Prrspf5VIxgOIqKRuMEMumoYMjkRnfUkWjTT7BPL/P3jBsKgXLShFCqWdsg49hjPNjkHvDFQucLEdDuMldgMSMyGxk2m9MffDFhmuXhgLHvtC5GpXuyXv0AXLgmcVB/zUiyPWQnInUjuX7PRuiZ09j/N++W43Rhkp/GM/XMmWlxs7DodKw4nbh1tr+NOtKFCLOTAv2BddCP2w0soO/ENUxriNJ5IrF/fiuf8K6i4YjZVp/8vPAII/Y3EXKxL7kf2n87Cw2air7zRabekTkKGHAxVBeiyGVvU0SYgA/c0dbT53/xU6i55HDJwdyMmUPx9p7ItGTGC6CeOg53iufuGcpqeXOvYJW4PyLAj8VzxN6hrYfHBH6NrvgyP3Qmn4bn2QXRZJYsO+hjdOC8sdsOCmwzV64R0ohWRGSISISLXishiEVkgIj+IyPTA/hgRuVdE/ikifxORAwLP/+T1v/DamSKSE8rzDikRMVhXTCP1ulHYM15Ev3k4PPWuvkSS75xMwh+HY7/7CDrnyR231nJ7RSxIGc2Ex0bBgBjs/16HFnzSYb9AyigYOhmtWo2Wze/cxSsyGQZOBI/X7GvzbAHEgyTnQspItCYPrVhqEp+aGqG1BRmVyGUHCr5YD/aDX5tM6L6KWMjeezDukVHo6jz07ZsgHAo8lgfr6F0Z/1AuOud79J1b+kY2suvR9johm2i7KZv3E+m77VImLxg8kcjel2IdfR5Vty+n8bpvTPMCp/ElIIdfhxz2Gwr+uAj77q/cidYBJHUi1ql3IFnpzD1jBfrtZx12WqZDVMY0KFsNBfM6t+mMTDb7LC8UzEPr13caS9JoJGWskdhbt8RkFzc2Gom9kcOJuucASIrglf9rRJeGR3Kut5Dhx2Cdchu6rJJVZy9AK1eFx+6E07BOuRF9o5i158xHd/Ql5DB0hhKRywKO0iIR+Y+IRHXxmv0CTtRiEfk88FyUiHwvIj8Gnr85JJcscoaIrAxsP2nNG2jZG4Z2ZO2EMqOiO7J5XUnfbb8yecEQmUrS04dD2Ubs1/+GjMhGdj2vXcjbISQum6H/OxgtKcF+9Fpkl9ywChHo+m/Q119D9p+KjOuy62bfYPwB7PyOH8bu8dN9lg/J3tWo7kT85DfHiLYP26NrqTvLi2TsBGlNqL8FRAKJT+ZHz7ouiZN+vQAKa/Ff+wesM/ZD0icAoHYr1Jca7zgm3dTzdiV4XrfOLG3HDzUZzh1pqkA3zoWY9J+WD6mNfvEgumQd1snnQPLYbrxRQSAW1ulHkLvnEnTGDNTzGdbxFzsv4m75sG4+nJwzV6NvvILGv4F1/BU7lGJSJxz0TEVkMPBHYJyqNojIK8DJwLMdXpMEPAocpqoFHfTIm4ADVLVWRLzAVyLyvqp+103bM9lCYEZEUoAbgZ0BBeaKyFuqWhHYvzOQ1PMr7hmhXDrujmxeV9J3269MXjD44pEpZ8GUw2l6ei3250vB3+B895vodGT3i5BJu7Li5gLsT5YaryoMXXcAKFvNyhvy0O8WmGXTHbUJ/laQtMnIAVcgA7uaaD2mGUPyuPba2Y5EpZhJqqsfbstrylqSxxkbqZPMcZLHmgznkb/GOuZmtLiB9++oRL+fj1bmodWFUFUAeQuhcDFaU2QUhbr6uzdVorXrTUhjy79PSy3kL4bq/EC9b4f9qtjvrSDvxtVoTWFYxC0k5whk7wvQmaWU3bESrd/o/EqN5UFGnYjsfTb1z6+j6r5VJiPcXSH6OSKAaBGJAGKA4i32nwK8rqoFAKpaEvhXVbXNs/QGNgUQkREi8oGIzBWRL0VkTDfP5VDgY1UtD0yuHwOHBY7pwayQXtnTC+0pIWlYEaxs3nYvkxcMzdXohu9g/Rr062XIHqONiLvT1G9A130FyxZhv1WEdc608NitLUTXz0IXLUBnbMC65CBk1InO2+1n6IpX0O/n0/RsAdUFjWT8YxoMG2EmeV88kjbJNMVoLEOi0jt7gc01ZpJt2oTafiQx12T8gsmWritGm8rNxJ0y0kz2bXbXfw2b8rA/nA2NNp5Lr3S+7tT2o+u/gk1rsd+fi8R7sc6+1nkP099ksss35GG//iMyOgHrdzf+dBUgxIS0YcWIRJ199549Hm/95v18oOOq5BOq+kTH14jIpZjmQg3AR6p66hb7/46ZRMcD8cCDqvp/gX0eYC6QCzyiqlcFnv8UuEBVVwZyfO5U1QO2OO5MfurRXgFEqeptgcfXAw2qel/gPC1V/ZuI1KpqXI/fmG0kJB5tsLJ5Qcjk7S0ij4vIUyLyzc8cO3iZvGDwJSBDDoFBI2l8qwRdkW9aNTpdghOTiYw8AQZns+aNcnR5PjSWOy/tF5eNjDwBSYin6NUSWL0iYNeV9gslkj4B2XMvqgsa+WplJFpUCRXlpoQoMgmi0wJCBNXt0n1t3qkvHqLT0UD3qk4rHhHRkDgC8SXAhiKoL+u0XwbuiYw6Bn6ooeq/G9DaYpPl7uTKheVBBu+LjDgE+8sKWt/eaOqVnW496olEhh6KjNqH6o83oR+XmAS2Ha3laXDJUGVtv5+BbctJNhkTNhwGDAJiReS0Lc4gApgGHInxOK8XkVGw+bd/J0yr3l1FZEJgHtkD+K+I/AD8ExNiRETOCsR6f8AsD78XePy/Dle7JSoig4DfAA9twzsXMkK5dNwj2bxgZPJU9UtVvQB4B/h3CK8l5MiAXYh+5c9Ibhb+P12JLngxPHbHHEXugj9DdAR1h16ELg6TAMJupzBk3pVoSS3Nx/8RLfxk64Nctg0rgox/TONXT2ZRdt9qSs/8BKo7ZDL7EpH0KRARg5bMgy2SryRpNJI81mQ5ly/qfDMUNwSZeiJ4o81npmp5+76IWKy//4nk10/HvvoJ/LdcE56SsqhUIp69HO+Dx+C/+B7sJ28KT814/DCS3r8C6y970XzStdj/uT18oZhgcT4Z6iAgT1VLVbUF039+y3hKEfCBqtYFcnC+ADolAARa6s7ELPNaQKWq7tRhGxt43TNtzwFzgCMCj3/VwVbHJZYszFL2FIzXvEpE1gIxIhKeDDtCO9G+Sc9k84KRyWvjFCA8rWR6ii/BZJymZ6JFjUZztGZteCT2Bu6JpCRQU9wERQWmCYDTGqCxg038MtZLbXETbCwwJRpuM42QoHYr+Ftg2AhkwjAA6ipsKMiH2nVG0MDyGvk+y2c8Wn+Tef83e68xxrtVBbsZ/I3tKx4R0Ua0PiIGGhrQphozmdotxsNMnYRkTIXKFlhVj1atcr5u3OND0qYg6RPwl7ega+uM3foNztqNiEYG7AqZo6nb2IwW1UHVis7lWdszzpb3FAC7BcoxBTgQWLrFa94E9g6UfsYA04GlIpIeSJRqCz8eBCxT1WogT0R+E9gnItLdxt4fAoeISHLA2z4E+FBV31XVTFXNUdUcoF5Vc7t5zKAJ2UTbU9m8IGXyEJEhQFXgj7PdI0MPJeLFWwFo+e316Nr3w2N373PJnHMPuraSkt2uRgvDUy1lHXUpKTNvw/5iKTWHX4uWzg+L3T5PfSkUrTIx2cyhpL9yDDlPT+HH3y6k/Pj/QEuHr0N0hrnJUxstmdtZ+9XyIinjkcRctHwpWrm8k7cmyWOQnU42OroLXu4szxczEM//3Yp15wnUHPsA/gfudD40AZCQi++V27DO3peqw27DfvGBsCTdScY0kmfcibX/aDZOvw777Qcdt7m9o6qzgFeBecBCzJzyhIhcICIXBF6zFPgAWAB8jxGJWYRZDv4s4GDNxiQxtSXRnAqcIyI/Aosxy9PdOZ9y4NbA8WYDtwSe61VC2jBVVbd219Emm/cDoZvkzwGeCdGxnMcXb7bMwVhDC6CsBE2ajSSONLE1p4hMNtugWBKyo6BoDRr9DZI60Vkhgqg08CUjmTHEDIyEkhWoFWHstiXguGw74gFvQHYvMskIEsTEkz1sIdEpXrRgBiQMRZJH0yaAoM3V0LAJopIDrSETTBtPT6SZqDyBDOmWavNcRIz51xMJvjiIju1cnmZ5jKRgSy2xw8zfUou/RuKzIGmUc9fu8Rm1o6Ri4nOioNmPrv/G2N2sguQAgfg1mTkkDo2C2hZ03RdI4nDnS456jPMdngK5NTdu8fTjW7zmXkzGb8fnFmCWdLs6Zh6BbOFfsLvfzzz/L+BfWxkbtkQoCFHWcbeNbYNsnuwIMnnBEFjGs1++i4an84l5/vdI9oHO222th+Ya/NfeQMkbJWR+85euS1RCTUstNG7C/4ebqVtZT8L7Nzpfh9mXKTclPJI2ySQ+gVkCbqlGC2bw8eg3mDaxhZR3zjVLxwCVRVCyARKTIC4eyd7XKNi0YfuhuQLdtASJToWU8R32BZKpLO/mibvTuJZqNO9D8vd7iSHXDce6+AFHL3/zObXUovNfouj4Dxn89wlYJ97mvF1/M7TUYn/0IKvOXsjIl3ZDDgpdxUhIs45zk3T2/Xv1eLx13LuuTF4ICKsEyLbI5u0QMnnBEPAUZNRQoo9rhOKVqN2KZE531rONiAErEtkjnQyAld+jDWVGz9br4E2eN84k4BycQWxuLbr6K0gvQLL2M++Fy7bhS4TYVtBWaK4yjz0+8KRBwlCmTWwhdoAP/fwzZFAKDBtt5NLi4yExDSITTPa73Wpk6iyv8VA9URCVBFaEiUFGRJu/XVf1wG1YHrNakjSU7N8OgKgII26RPq5TaVDIsbyBVZoRDDppALTa6IpXkAFTIdHB8JvHB54UZNRYRvx6HVpZA8tfRgbtZpqAbE8IrkzedoArKtDLyK7nYV18G/bMJTSc8W+0Jt95o5YH69c347n9FppunU3pEf+Gui1rzB0gIgbrtFvx/Okyai7+lMZz/s8VQOgpcVlIygS0sQzdtLhTkpkkjyblnXPx/W4I7/wun6a7foCacvBGwYBhyMBdkMF7o9UF6LqvOyfGeePM5OhLNLJ+2/C5kAHT8dz3EDJ6MAt2fRX9+OUQXvAv2M0+CM99D0Gsl2W7vYzOfys8dkefiOfRR6G8kYW7/BfNmxkWu9uMKyrQ67gTbW9jecATjbXfOKLOy4GlM4034HRWcKCxge+iEaT9MQf95mV0wb+dT2YJeCFxl+cS+dvB6Df/Rle+uuOUS2xPWB4kKh2JyTDead168z6KZdpADkrhkIMEb4wH++Gv0CULMF95y7RpTMiGxBwzmVat7tz5KCIGiRtkYsG1hd3LjhfLeHvDJjPxtmwj4v7JPWjZjw69AZ3tysRdGH1rDrqpAv38b1DlcPVGm93dJzHhtmx05Sr0i79DbZGzdl12ONyJdnvA8iDTL8A6/grsZxdgX/2e+eF0mogYrONuwTr1QjZeOp/6Sz4IjwBCVArWibchR/+GdWd9g33H+6a8xGXbicuCxFy0bgNatbrz+zhsNJH3HQwZPm57qh59p0P5jViBNo+T0PKVaOmPnSdaX4KJoVsetHx5J1H6rSFZ+2H98W9gCXOOmQOLw5PhLsOPwrrofihpYMlxX6Hr54TH7sTTsS6+D/2ulGXHfYmWLwuL3W7jerS9TlDJUCIyA1OndBWmltUP2MD5gbTv7h7n2i3HY1LFbwYSgHrg7YDaz0y2oQVjR7arZKiuaG1AF78MJRvQhgZkUBYy5XfOxzCbKtAvn0TLq6GhFRk9NCwCCNStR796Fq2ph8ZWZOqEvi1E4BRqm2YU/iZTwtNcDRuXmNicNwpdsqB9krXAuvp4JOcI89j2Q/UqtLUR7FbEFweJI9sTnpqrTTmQKqAmeaqbsXwt/BSdNROa/KCKHH6KyTZ3GF3zFrpgDjT6wSNYh/3e2WxkMO/70v+gS5ZBQyvEebEOvcjEv7eRkCZDjUzS2Q/u1+Px1pFvuslQIaDHHq10TxYPEZkoIu9ssWV02N+3ZPKCISIamXwmsusJtD62GvuFOeGpS4xMRg66Etn7cFZfsQL76bkmycZpYgcih16NTJ3Oqj8tx37/e3cJuSeIBbGDIWYgWrcBqgtNdnFdLUTGI1P2xrr+ZLDg1SfqYfXi9rrTgACCxA+FilVo5WqjOtSGLwEShpu+yVVrt2nFQ7IPxDrhVthYz6I/rITy5eGpdx1+DNYx16OzN1H4x0VodYHzdsVCxp2Kdcxf8L9cxPpLF6ANG7cDUQ0xn4+ebi4hoccerYhcg2mt2ACcpapH9/A4x3c1XkReAM7AyOSlqepjgedn0lc92jaaa9CCj6F0PbokHxk31AgCOP3Br9+ILnsH1hVi/1CGddDY8Ejs1RahKz5EiwrQxRVYx053PdutUbfOJJLFDWmvg7b9xvtsLEPzvoXENGTgLrTdT2vpfFi9GF2wDl1Vj3XpQZAaKLFqqYf8+RAdDYN2QqJSOosFNFebSTYyaZvrn7VoplEUWpAHDX6ssy5yNisYjIdZ8DEUr0J/yAOvhXXK5Z3LmZzAbkHXvAvr8tB5+ZAahXXyNeaGpZuE1KMdlayzHzpg6y/8GazDXnc92hAQzC93d2TxukPflMkLBl88kns8DNuZhv8rROeuNj9yTst0xQxApp4DYyaw8u/r0dmrTN2t03bjspCp5yCDslh9fxH6w+KAXde7/Vmaq9G6jZ2l7iyPWaqMGQBx8aaEJzrDPI4daCTnDvgzuqqezx6tRX9YAFV5UFsM9RuhqRHq66G+FG2q7CyT50sItGTc9iYjkrUfsuvv0QXVFN+bh9auc74Vp1hGEGDqqeiMUqoeW4s2lIQl2U9yj0OmnUDNS+tpeDrfxLfDsTLlst3SI482WFm8Lo7Xd2XygqGp0mRsFi3Ffm8h1hETkek/KS0OPfUb0I1z0QXfo8+vxbpqL2Tnc523W1uEli1AZ3+DvlWMdcORyMhuCTn1P1rrzdZQgvqbkKTR7fJt/mbz495UgVYXmOzi5HGbh+qKV9AfFlBz/0pq1zcx6OndIDvHdIaKSjJNMPyNaH0JEjMgNF2P1EZL5kDVWuznPocIwXPFtWbydhK7Bd04GyrzsZ/9AhkSg3XujdvkYfYIfxO6/lvYuAr78e+Q3VOxzrjVZGVvhZB7tA/3vBGOdehrrkcbAnrk0QYri9fF8fquTF4wRCYhg/eFjGyav65EC4qM59Fa76zdmExk2JFIRgaFX1aha/JN6YjTXkhclvG64qLY+GUFFKwxDeNdb+CnRMRAZApq+82yb2tj+8qDxxdIWoqHxkojCNBRTCB1LLLzrtSub2JhYQxaVAHlZeCNNl5wZIppXNFSaz5r/ubgY41iIQN2RYYcBCvqaJyxCa0tDCRaOSmx50UG7oFk7YF/QQ36VXlg2d3hrH5PpGnGMnQaVbOr0LkVUFfUC3Xjbox2eyCYd7JHsnhb0l9k8oJBBu9N9CvXIBmp+M/9K7rkv+Gxu9OJDF14AzT5qdzvT+iqN8Njd9/fM3D29eiaEhqOuhxd92VY7O5wiIUk5iIp49HafHTTws43JTEDkJxDEF8cuvZDqO5QV+qJZNDTu3HIv7JZf+NySs/+DOo7TD6RSUaIwOMznmj9xtCcsy8Rz+NXEfPMqdjnPYz/9hvDU1IWMxDfC1dj3Xw4zafejv30bWHRSJakMSR/ej3WWbtQc8Q12K/c7bjNn56EW97T2wQz0fZUFm9L+odMXjD4Ekzf2fQMaLahtAQql5sEFSeJTkfSpyKpMfibbFhXaH7MnW6mEZOJpE+FBB+tzTaUroWKpa7EXldERBvPFctkC7fWt79PbS0KPVGAbUp4miqNB+xvguwcZHQ23hgPrY02rF4JVflAoKfx5taLCnZTaOLmlgeSxyJp48yvT0mT0cJ1uiOax2e+QykjQUErmtGKxc5L+0VEm05bA4ZjtyhUNKKbFoTuxmVrtLVg7OnmEhJ6PNH2VBavq+P0J5m8YJCRx+J59i60poamk25BCz8Lj90DLyH16/uwfyhi4243ouu7XKUPOdZxVxD/7u3Yr8+j+vCb0fIlYbG7w2F5kOSxSNJotGIFWrG084QYPwTJOQzsVuPZ5s+HojUmJjtoOOmvH8/AhybzzfHLqDzplc43NNGZSMbO4G9GN87ZpsYVv0hcNp7n78T6y1FsOvB+/I8/4HzSHSDJ4/G9ejfW0TtTts/t2K8+5LhNABm0F4mf3odMymbdTjdgf/xoWOy6S8fbB0G9k6o6WfUXCy7bZPGCtvUL7FgyecHgjTPZo4MHE7FTApQWo+u/dj7uE5lk5NCGJpA+KR4KlpuSDadF6yOTzSQxOoHY8bGwfqG5XtezNTHG2sL296JN7s4bbQQBmivaVx4sr2mp6IuDyHhTwuOLNOIBMemQNgrGTGDcRJv4wZHoqrfR4q+MjZZqaK03WcgN5aHr4GV5Te1v0lCSpyYgEYIWfGpWLpzE4zN2U3NImRIPfkULPoHqNQ7bjTTlUlk5ZO4UbyT2Cj5y2zX2E5y+ZXkd+LWIPAa8vS0DRSRVRB4HpojI1R12PQtUtj1Q1RtVNTwu1naCTD0Lz613oz+upv7kh9HyxWGxax13DZ7n7sF+cj4b9/0HWrUyDEa9WKfciOfvN2DfMIPa3zxkuiD1c3TjXHT+652b/nsikeTxSFw2umkJuuXkkTgSGXIwDNoJBo1E0iYhaVPNNuJYkr97Cs/dh/G/8e9SdexDxkbJfLRkPmxcarzgEIcNJGUSnqcfRA7YiZU7P4H96i/KiIbO7sC98DzzD2T4ANbs/Aj2zPCkeMjwo4l47VGIEJbt9E/0h/+Fwagbo+1tHJXJ2xZZvC7G9m2ZvGDw+MCKQCYNI9oGChaiDZtMlqOTZQsR0SAe5KhBpA+PgcUz0cF5yLDD20tLnLIbmYL8ZjCxJQ3o4vchM8dMGt0ol+iTxKTD4GFoUzlS2WoaV0REB0QqIo2erBVhsrYjYsznIrAcKFEpqFjgbzRLwZFJxsP0eSFpKAfs7Ccu04d+9BEyNAWGjw2IvCeAhPgnIyBuQXouI87PBJ8Hnfc0DN3FYYm9gN2cMeRcuBqa/OiCfyND93S2mUbgfZbxYxl1bjlaWgo/PouMOLBzg5BQ4k6YvY67CL+jIhay24VY59yI/cYCms5/2fnEDgCPD+uEW/BccTU1f/2eit+8BI2bnLfri8c69Xass85n03mf4f/jS9AahmzV7RRJm4zkHAlVBejCDzqHDyJiTOJPZIqR0NvycxGXjSSPQ+tLTNy7Q6aypI4n8bVzsY4dyGvnFtH64GKorYCoGEjPAW+sM9czaC88tz6EDEhg3t4foF+95oidn9jNOQLPjf+AFpsl+76FLvskPHbHn4LnzodhbTWL9nkHXd/t1vDbaAg3Rrsd4L6TOzJigScS6/jJ+P4wAp3/LrrwOefrbMUCbwJx14wm6Y/DsT95Ep3/jPPlEmJBVBopN43FOjEL/fghdPnL20E/2V5CxGTR5kxEa9aa5iYdy3siopH4bLB8ULO2c5a6CBIzAIkdaGpZ69a1J1CJhQxN4bgjPVhewb7rc3RJm9Sdg96R5YHx05ny9xxoaEXfvsl5ib2AXZk+nbH356KF69AP7zSygU4ilrF70DTG3zcM/eEH9OO7HLhZDiLj2M06DhnuRLuj4/Ehu5yPdciF2P9chH3XDOeTlMB4mMfcjBx7KsUXLaD1+hnhaSwRnY7161uRAw5n7TnzsR+f0bkJfn9CLCR1EjJoTyhZAau/7Zwo5o2DpFGmFrZilZlQO4wlLgvic9DaYrR6bWchieFjibj9QIjycPtLTeiX4SlHkewDsc69F+pamHvSElj7fXjsjjgW6+y70fxqVpwy26wEhMPuxNOxzr4d/WA9q0753vwdXPocQcnk/eRgW5HNE5EYupa+c2XygqW1Hl32OpSVoKXlSE42Mu3sQB2kgzSWobOeQ8vKoawBmTwCmX6+88tOdevQ2S+jlZVQ1ojsMbn/ChHYfqhabjpAtdSBLw5Jn9L+t2+uMbFYu9VMpjED22P5apuaTrvJlPA0VZrEJ8sDUTHokh/NJFvZCo021u0nI0MOcfyStOATWPQtWlYHLTbW8Wd2aiPpmN0178CKBWhpjZHYO+ZC52Knbdh+dMV/YeUytKSeXW/5njn5NaFpwTgmTWc/fVSPx1t7/dttwRgCQvZr2E3ZvJ9I3/ULmTzb73yD/IgYZMJpyKRDafpnHvY7CzbrkzpKVBqy72XILnuz4po87DcXBrRLHSZ2MLLf5cjY8ay8ahX65XznbXaF2p2b74fbLgSaQIxDkkfDhpVQuqLz+fjiIX4ooGh1YedOTGKZfsPRGUZir6YYyjcZgQFfArLT3liXnACNNu8+3wjrVpp6V7U7b23nFKL3QYYchBx+Lbq6hhVXrkYr88IiMiHDj0IOugz9opQN1yxF69Y7b9fyIGNORg6+mKYXiqgvCnEIxo3R9jqhTCE8FngDGAiUqWoTwBbNJ6YCD2Kk714JPNfl60Wkq9fueFSuwP/IQ8joJKzjb3Dew4zLJuqJ30JpEfYTNyLTco3EnsNI2iRGf3k8JGY5Lxjf0e7gPRj1ZSukjtz6ix1AFz6H/fIsrHOPMU0hwmX3iwex31uB9afTkIF7mie9sciog8z739XnLCYT8cZ3nZluRSIpY02dbNpYk13sjaUtJmvdfjJH/2El9szl8Oj5WH+cDgOGtY+XCEzLJT8SN9gkY3U6YRst+wEaK5EBO//0HBpK0U2LkbhBZrkbQCys805i9LEr0bc/wW75CM95lzkv4m75sG74LQMvyEP/8x805r9Yv7sKotKctetNIOqpU4g5OoTNLAQ363g7IJS3LN2RzetK+q5Py+RpcxUlTxWhH6+HxnLnmy34EpDhR0HWWBpeKUYX55kkGKcTlWIykXGnGhGEcBKXbewO2DW8dgPo6tUUPLUeCgMtMcMk7adL1rH2mQ2wKa/druWFxBFmIurKG/HGGcm8rqTuLA9EpweaSIw2x4nJ3Cy7J0MOQaafB0tq+fKFBnTOSlizCIpXw8Y8KM0zrTLLCtGGsq6FCOpLoaq4a+nF1nqoLEIbN7V7zIAM3geZeBI6v5pNTxahtcXOtwC1PEj2gci4Y7E/LaPxxXXQUOK8XY/PfHejU0N4UDcZansgJDHaYGXz+rRMXnONEdxeMx//PXOwzh6G9atbnLfbVGla8eXNw351IdYpOyPTfu+83f5G9Rq0ai36wfvojDKs+89BBu3lvN2KpWhNIfZ/34UfarD+/idn607BeKVznkTnrKT4jlU0NQnDn50KmYPA3wrJ6cjA6WayrFiDpI7qHFdtqoCWus2tNGXQ3u2Tvr/JfGYbNkJ1IZIyxkz2YGKYm340EnsPfgApXjxX3+y8h2m3mO9uZR72Ax8jkxKxzr/V2ZpxQiyTNzZdZz97bI/HW7s97cZoQ0BIPNpgZfOCkMkbIiJvici/ROSvP3Ps3pXJ88Ujg/eB7JFsWl4PhTWm1CIMbRMlc3dIH4h/SS26rtC0e3P6rry/kTAcyT4APBaVi2uhfK15n51eQUgeiwzeDxptqhbWQFXArtMe9YBhyNhBNDUJ6ysiTbJSZQX4bdNmMDoTiYiBxlq0udZ83tq818hkI0Tvb4G2fZtbSEYaz9kTBc21aJtEn+03Hmb6VGTQHlDUiD23Gq3OM804nMTyGmm/AVNoXduALqo2392GUmfthho3RtvrhPKd7JFsXjAyecAo4F1VPRuj+rPdIoP3YcCsW5HRGZTtdgX6WXiaisuQg/G9dBMSHY3/9GvQ1TuQ8P0OhHXSn0iZcR32f7+l+Td/RSuXOW/U48Nz6ZUkf3AF9q1v4j/9GqN56jRR0Qx/dip7PJ1D/l+Ws+Gcr6Guww1c3BBk5FEgYj5vHZV5PD6zHDxwd3Td12jxl52XkeNzTKcxuxnNe7/z9USl43n2BiL+cRKNJ/8N/723hafvdXwOkS/fiHXpgdQddyv2c/eELUQQEtwWjL1OKCfansrmBSOTNx84OVBWFB4pm57ijTPLaNlDiEyMQMtr0Y3fO3937Is3LeUyMiHJC6UbTRMApyX2+huxA42CTkYUnigLNi0zcmhOe7Zx2SbbeFAk+Cy0dCGUL3Z2IvBYkDkIyUojKsYkmevqEtiwFrBNW8zIJOPZeiLQ1npTw9v2XvjizebxmsGNm9prvz0+k2cQEWNaSLbWm9wGu8XEkRNzkeQR+JK90GijJXOdby7h8ZkEraRhRCZEQGOr0eitLdz62N6mLRnKnWh7lZBNtD2VzQtSJu8s4EZVPQA4MlTX4iQy6njiP3kQgLxJd6KLXg+P3fEn4XnsbrRwI40n3o2u/zYsdvsVHh/W76/H86+rsa96h5bT7jFJNE7jS8Bz/W1Y//gDNac8j/+i+4zqTqgRy2QXeyJMTDYmlsyn9iDzmlw+OH8dtX/ewjtNGoMMOxIaK9GV73d+L7xxpoQndTy69lN04+zOyVNJo5Chh6D1pWj+x53bfCaOwvP8fVhn7UfxbvdhP/NwWMqrJGMqEa88gOwxjvW73YX91mOO2wyeICZZd6INGSHtEK6qk7fykjbZvB8IzST/AXCTiJwCrA3B8ZwnItq0xhs5lKEHrUfXF8PqN5GB002Wp9N2h2fjO7gWNuSh1gwkY6ppKu8SGgLvpRyUjqekEV07E1JyTLzcqbInsSAqBfEPJvZIkyCkeR9C0lBkwPTQxdrUBgLJk8npJq4KSEwMe+9eSMzIGPTHFyEtG0ntEMlpqYXmJrShBBEPRKeZDGlPpCkhik0zXmNtoSn7iUw2+y2vkfLzN5s2km20ZUgn5pB5eBpEetDVbyApo39aVhRKLK+xmzGMAYemgq3o6jeRtAntiVvbI5Yba+1tQtoZaqvGRGKBh4FG4CtVfeEXXpsK3A4cDDylqncGnj8TeENVK7fV/nbVGcpuAbsV/4N/ZeUdRYyedTqSe1x47PqbsB++jsY3S4h+5TIkYxfn7fY3/M1oxVLKD7iNpPFxeP79oLPKSpvtNqHFX5O/yz/I/u0APPc9FDqFI7XRwk+grBAZfRhEt90Y2iZD98cX+dfOMzh2XDOp/z60fZwVSKzxWBAVjQw5CKJS2vfbfqhZi676DAaNba8LDthEteubFA3Ynf0vFh36KeMfHol1+p2hudZfwvaDtqIf3cvy0+Yz+qVdkIO7zMXsESHNOh6XobNf+E2Px1tTH3WzjkOAozJ5W7Itsnl9XiYvcMdu7T6SkVcqumQ+VJYi448zd81O2sVCdh9NVEoUrJqFVuUjQw81cTOX0ODxIdEZJP9pOPhtdNYzkD0aGXqIs9mcnkgkPosh1w2HqAj0m8dg2GQjoRgsYiFxg1FPJNq4CWltMPJ8Hp/5XKVlc+y4ZmLSfdivzUcmJCFjhgc6hdmQOMh8xho2mKXt2MGB74HH3IRkjjRL0xVLIXqAmYzF4md1DAKiGmSNZdw1S8ES9KuHYMw+SNrWFteCwPIAHhi9E6OuLUOr6+C7x5CxBzsrsddT3CXgXsddU+hlZI+L8fz5bvS/heQd+R5atWbrg4LF8hiJvZOvwn5hAa2XvQlNYZC662/EDsQ6+27ksMNZe8JM7CffCk97yqRRWBc/gOw1lQVHfom+/mbojp0y3iyDV6xBC7/rpBQlqeNI/fehRO6exCt3VaLvrAdvoEOVbSMpY5CMaWjFGnTjvM4iFNHpptmJNxpd8Tlam093kaz98Fz1D4iJYO4hX8L890N1tb9sd/hRWJf/HSqbWHL4J2jBdpj34CZDbRe4E+32gOXDunhXch4Yi858y8h0OV1nCxARg3XOdCL+MAr9+sWA1F0YFHj6GZKYw9DHJyKTkrFfuxFd81Z4DKePY+IToyEtGvula9HCT0NzXCvCNKNIH4VWrfxJlrNMSOLEkyOh0U/LXz9GF61qHysRSMpISBpmxlZ27sss0QMgZyrYrSajuLG826cl0/Zh6pO5aGk19ivXmazvMCD77cnYx8egS5djv3kjVIfhZrnbiFtHux3gvpPbA5YHmX4B1vGXUffwasoum2vUVpzGE4lMPQfZ+3T8jyzFfuIb57Vs+yMJw7F+dQsyfixLz1uKfvplWMxK6iSsk29HMpKYe/ZKdNbMEB3YMiIGKeOgfDW6aanpkdy2e8xwrKv3w99kc+f7NvpVhyICywNJo5GEXKhYjVasNKpCbcQMMO007VbIn9NZ2m9rpzXkIKxT74BNjSw4ZzlsXBiKq9263RHHYv3mFnRhBWvPW4BW5YXFbrdxWzD2OkElQ21NFm8bjuPK5AG0NqDLXoN1heiKUsiKwzr66q5704aS5hp07ftQshHNK0ZGDUV2OTes4gD9gsoV6KIP0Y0lUFiLHHOg6W3rMFr2IyyegRaVwsZ65MTjQhOztVugJj9QJ1tpsovL129eHtdFq9CvyvAXNdJS7yfmuXNMIlTb2NpC85lvrkYikyB5bPux6zdC0ya0qQpsP5I6odvZ8Vo4A1b/gK7eAE1+rFPObxcqcBBd+x7kL0dXrYcIC+uES40y0jYS0mSo8QN09su/7fF4a+KDbjJUCOixR9tNWTxEZKKIvLPFltFhf9+XyesuEdFG6m7X4yh9KB//020N41u2PjYYfPHIqBNh1B40Pp2Pfr0M/A07VvebHYGkUchelyCJ8ay4tQCWzQ+LlKGkTUb2vQxUWXRTERQu7rndjlJ4ltc0kIgdBOX5sKk4sOQooIqMH4F1/nRa6v18/YVARZGxa/tBPEb8ICoVytegtes7iQkQM8A0eGlpgI0robXuZ0/pJ9ebfQCyzyXooiryb16D1hQ63zgEkJwjkN1/j84opfyeVWhDSVjsbv3E3Bhtb9Njj1ZErsG0VmwAzlLVo3t4nOO7Gi8iLwBnYGTy0lT1scDzM+mrHm0bLbVo0edQtAr7xUXIgZlYx9/kvIfZVIlunAPrV2F/sRRrn7HI9J8kfrsES9UqtHQBOmsO+k0Z1lUntnt6DqKbFkL5cnTGd+iCaqwbfr/NqkdaOg/qS5HMXU29K5jJpKHETCzrF0JiphEFaBtTsRIqirBfnAXL6rCu2QMGDAmMbYHaCvBFQlQCkpjTuRa2scy0WYzO2Fy3270TtdEN30FFHvabs8BWPJdeBXFZ23S924ztR9d/BeUF2G/MQtKisM6+bptq1UPq0U7I1NmvnNrj8db4B1yPNgQEE6Ptjixed+jTMnk9whtnOuoMn0LJB2Xo3E3QWOq8IEBkkvnBzxxG07ul6KqC8Ej79TcSc5Hc48EjrH+rBEryzITi8MqFpE40dhv8rH+jxAgRNJZv28pFYyXUlBrx+DZvzeODuCwkZiBERZsSnphMiM2C+KGmA9SE38KyOma934QuWA2rFsGGfCjfAH4/NDZCZQnaVNnu9YJR6InL3rZJFkwp0sA9kBFHwoIaat4oQeuKjYKQkysIlgcZvC8ybH/831SiH5RA/frebXnqerS9To882mBl8bo4Xt+VyQuG5hojdbfsa+pv+J7oy0dhHXuz83abKtGaPFj6Bfb/LcS6eC9k8pnO2+1v1OSjtevQV181EnuPXYRkTnfebtUqtHYd9uOvwIo6PI9f1Tk++ks0V0NrPVq2APwtRpmqrf7abjE9ixs2oBVrAtnFowP7/OjsJ9EFq1l9zWpsG0a9tCukppt2jqmDkcxd0PpiqFiNpE9sHxsMth+tWAJVedjX/w+Gx+C57nbnu6EFGpZQvhz72neR/dOwzr+jWzcMIfdoXz29x+Otsfe5Hm0I6JFHG6wsXhfH67syecHgizdLe4OH0VDWAhvrTTH/NpQ89IjIJCRtCqQPgJJm2LDeNG5va/zuEhrihyKZu0Gkh/rSZqjMM++z03G9xFzzuYoQGjc0oRWrTUlKdzxqX4KJq4LxPFtq21daLK9pMhERY9R3WuvNZ8ZuMd7RgCHIsHRsG2oaItANVVBaEpDYM+0NJSIGWlvQlrrQ5CdYHuPJp0+Gej+sbUArVxhJQSfx+EzTjNSxtFa3ousa0Mrlzkv7uWyXBLN03CNZvC3pLzJ5wSBDDyLt23uQgbEUT7kG/eZf4bE74ig8L9wOzU00//ZGtODjsNjtV4iFdfqVxL91PfYjM2g68QaoCUN5SEQ0niuuJeaVy7AvewX/GTd1XwDB8iKD9kYG742un2XyCTrWX8cONh2wAM3/sLPKTVw8o17alan/HMHyS1ew8eLZ0NghNJEwHBlxFPhb0FVvh04hJ3YQnudux7r5OCqPuA//Q/eEJ0EqaTSRr96BdeqeVB58G/ZLf3Pc5k+wrJ5vLiEhmHfyTXomi7cl/UMmLxi8cZAwHIbkkDIyBi2vQtd9bkognLYblw2DsvCMjIXS9UbaLxzNNPoT0emQMAwZHUdEVhRa8qNp1uB0tnnsQCRxOEyKhwwfun42Wja/ezHbiGjz+fAF5OwaSk38E4xn641DImLN61obzCTubzH9jlPTkYwEklMVj9dCF6+D4lXtY33x4I0BX6zxbOs3Bj8pWl7zWU7MIWFULFig676AyuXBHXdreHwQPxSShpIwIhpabfPdrVnrrN3NSJCbSyjo8UTbU1m8ro7Tn2TygkEm/Jaodx6BqiZWTn4QXfVBeOzudDqee+5GlxZQf+Lf0NIfwmK3XxERg3X+LXju+zONF7yB/5y/Ox8iAIhMwXP9XVg3n8OmY5/Hvuyh7jctiYhGsvZH0iejBZ+jG77vPEkn5iJDDkabq9G1n5rs4jaJvcQkBjy5F6kXDeXli9fTeP03nRpXSPI4ZNgRUF9qPucdZfKCQJLH43n2b1hH7kreLo9gv/hESI67VbuZ0/E8/yAybgj50/6G/dHTYbHrtmDcPghKVKAXZPG2ZMeTyQsGT6Tp5jR+GCN+Wwn5eajvJWTI/qbu0Gm7Y4cQfUILrFuGttYjg/YKjyJNf8EbB9EZRP5mEDS0osvfg7ShpgewkxJ7vngkdhDJZw5GIgRd+hqk55q/75Y0lJqJOCbTfC4sL0TEQvxA473VrDWfieh0c2yPD4lMQuMHQu1Gk12cOtjEZAGJjOS4AzfgGx9nBBAGDzOyc2AaX7TUmhguIcoUtjwmESp1GENPG2CEFxY9DwMnIamTQmOjS7teYzdrJNmnLzae7dL/IIN2cV6IwG2l2Os4/Rd4Hfi1iDwGvL0tA0UkVUQeB6aIyNUddj0LVAKo6iJVPUFVL1DVK0J0zts9Mv18PH9/CPu7Elbs+UrYPEzZ7UKs82/G/mgRjb9/Aa3pfuN3l24SlYZ1/t3Iqaew8YS3sW95sVN7Q8eIH4rnz/chvzqMlQe+hf3Ii10uIeumxWj+l53DB754JGs/JD4bXfUZWr6k86DkscjgvSHK3JRJ5i7IkIPNttuFRH/4DNYJ43hsn1lUnfQCuvxjs634BCpKzHJziH+qJHN3PPc+hOSk8+Pub6IzXgnp8X/W7tBD8Nz9EHgsluzxKrrg3XBYDWJzCQWOyuRtiyxeF2P7tkxeMIhlJPaOGs/IQdHo/K+hYBmyy6mm7tBJuxFRWIdMIHJ0ESz+FE1fhOQebbwxl9BgeZDYgWTcPNqIi3/2IORONLXVjtr1IolDyb1zBPg86Ed3w/jpSPaBm18icYPQiEi0YSPSXGW6O3l8Ac84AQaNBYlANy0wAgFtKy3iQRJz0KgktL4Yaa40eQeW14wfPIxTdv6G6JQI7GfnInukGYk9cEbxqK1p/sgpTLprPbTYRsxj2hHOSuwF7MrUXRh7VwNaUgYz7kOmHbd9Suy5hAR3TWFHRSxk94uwzr0J++k8ik76DK1d57xdy2sEEI6+FPvJBdg3fOCW/ThBXDbWaXcie+/NipO/x371I8dbNQKQPBbr3HuRiSOZ9+v56Adb5AEkjUIydobqQnTjfPA3tu+LTEYG7olEJsCqbzqveIhlJPYydjZiAuvnQWv7WEmbQOKjBxCRG8tLj9aiX5QYiT1VaG0lZEvHWyDZB2JddD/4lbm/mg8rwiT4MPwYrPPvg+I6lp3wLVryo1OW3BjtdkBQogI7GjtMC8Ztwd+M/vB/6Np8qG5G0mORQ/7kfOy0tR5d8l8oLUFrapCsbGTKGcY7cQkdVavRb/6D1jVBXQuy9x7I8J9L4A8dumkB+tVr0NBq7B58SHubSLWhOg9tqQW72dS+Jo0y3ilAY7nRk7VbwW5FEoa3e7a2H6pXmWxifwt4Y5DkcVCbH1guzjeT7IZmmqpaiTp7CDI+FxlzuBGKd+p6Cz5B530BtS1gK9ZRp3duBemU3TVvoYvmGrsRFtbh57Lz/teFrmHFxEE6+81zezzeGnGL27AiBLge7Y6Ox4dM+z3WoedT9VAeVTcvNoX+Tns/ETHIpDOQacfQ8thq7P/OC0uD/H5H4gjk8OuQoVksuXQV+u13YXmPJXUS1rE3I7Fe5l2yFhZ9225XLHNeSSOhqgCtWNVZ6i4qxTQ8wYLCBdDUIWO4TSYvMRfKV0HFalD/5uVhGTMc66K9aapq5R+fgy6sdGbpeMvrHXIQ1nG3oIV1LPnjKrR8ZXje5+HHYB15LfptGcWXLQqsSoX6et0YbW8TUo92a7J5IhJD19J3rkxesLTWo2vegaIC7G/zkdFJWL+63nkPs7kaLZgBZevRBWuQScOR6ee7mY6hpnIFuuZLdHUeuqwS6/QjkJwjHDerZT/C2u/RJavR1TVY551k2i6C8U7risxnr74UopKQlAntf/vGcmgsQxs3QUsDkj6pPYcgIJNn6mQDfbwrAg0zVI29hZW0/FBDS52fuP/+od2uk9e77nMoWorOXWkk9s6+BBJHOGzURgs/gfVr0Dkr2fWOOcxZVxs6j/at83s83hp+k+vRhoCQ/Rp2UzbvJ9J3rkxeiIiIMVJ3kw6k9F/r0DfXQXNV5449TuBLQHKPg6GTaHihCF24xll7P4fdYn6snW7ysCX+5vDYTRqFTD0HiYpgzT+KYc2SgF1npQwlbTKy87nQYrPy4Q1Gsq7NruUxzRiiB0Dteqgr6ex9RqWYJWXbD2X5ncUpLK/pAhWdARWFULXJxGQjIkAEGZ+LddI0Wur8LJiNOX7b+9wm1Wf7zWPb/8veZ0dpv672dZDnk8H7ItPOQOdXsfEf+UbkwGnEQoYcgkw+Ef2klKaSMH+GXRwnlFnHxwJvAAOBMlVtAtii+cRU4EGM9F1bPn2XrxeRrl7rshUkIZcBMy+C/CX4z/wLcmI21vE3O+5hSsp4Yv5zERKd0iverK54DfvmD7Gu3AeZ0qNE957ZnfUE9r3fY91zLDJym1p89wjZ53Ry56xCZ8zA/vcfse44w9TZOox1/JmMPiAPffsT7Ie+wbrnIiR9qtnpi0ey9wXL12W9r6ROgMRhXWfERyYjIw7BLGS1fW7aJ8W4/45mj9r12H//BH/+23gf+a2R0gO0udYoEEUmQvxgM2lvWU+utqnttVvbM6Q7Ur0GLZ4NGROQ1InmOU8k1m3nkXlDDRIGwfjN+OKxHruQyNV3hvCgghsh7H1C+RfojmxeV9J3jsrkich5IjJHROaUllb09DA7Dr54U44xZDSlc6rRNdVQt855ma7IJNPgILmXWk5XVlDyXSWan2eut7vdjYJES0spnlUNhQG7Tq8gJI5Ahh4KHmHTrCrYtBbq1jvftzd5HDL0MLTFZtO3lWaCq98Q8Gy9poFFVErXYyOTTCJTV8o1Hh/EDjT7Ywd2+L/ZZPA+yPAj8ec3sPq7Bli9GC1faZaqG8qgZAPUbzLZz/5G8z509F5Vwd+ItjaYeuQtVh60tQEqNpnvR5vHLBYyYFfzPWpTJgoHlhfJ3B18iaE7ptsZarsgJBNtQDbPp6qVqloLTMNI05UCL4vImQCq+pSq/iWwnRJ4rsvXd/XanrBDq/cEgWTuzoDvb8KamkXFPn9GP3mwt0/JUWSn35A5+yaoa6Xm0D+jee+Fxa518IVkLbgRXVJMzcF/Rou/Co/d4y8m/YtrsN+fS8tJV6IVi8Ng1IPnvMtI/+zP2A9+gP/UK8MjgOCJxPvIbxnzynTWnvot+Xs9CwWLzFL00PHGG00ZD+Ix70NTh9aVlgcSRiAJw6AmP6BS1L7cLkmjkKknGzm9hS+b/X0NBydaEckWkc9EZKmILBaRS3/mdfuJyA+B13ze4fnLAs8tEpH/iEhU8JcrZ4jIysB2RofnnxaRH0VkgYi82qY+Fw5CMtEGK5sXhEzeOBF5RUQeE5ETgryMvoUv3rSUG5wNAlpWZxrGN3a3jfQORlSaiSemBr47xYXopgXO1/jGZJoM26SAt7ZxjbHbMR7pBHFZSNokJN6L+hXKV0LFEuc92/gcJG0SpHixWxTdtMxINzoZKw40uyBnFCJKQ7MHXVUExYUQEYVERBtpvrbyIn+TWdFoOydPJHiizMShttnXtvLgiTRL2t5YILAc3VgWFmWf8OFo1nEr8GdVHQvsBlwkIp2WtUQkCXgUOEZVxwO/CTw/GPgjsLOqTgA8wMndviqRmSKSs8VzKcCNwHTMauiNItLmYV2mqpMDuUAFmLkmLIRy6bhHsnlByuQdDjykqhcCvwvhtfQZJPcYkr/4G0RHUDDxZnTeS719So4iB1xM/Af3oXPz2bTPLejG2WGxa/3mKuI/uAP737OpOPBWI/rtuFEv1tnX4nvxWuyb36f5lDugvth5u944PFffTMS//kjj71/E//u7OnuRThGVxNDXD2L030fywx9WU3XFd52X6qPTTdazvwktXwwtHcIlHh8kjoTYwWjVSuPddkBSJyITTzIiBj/8F+rXO389fQBVXa+q8wL/rwGWAlsWPJ8CvK6qBYHXddRjjACiRSQCiAGKAURkhIh8ICJzReRLERnTzVM6FPhYVctVtQL4GDgsYLc6cGwBogl9HdXPEsqJ9k16JpsXjEzecxiZvHuB1BBeS98hIsbEuoYNJWu3BLS0FF37Xt8VoPYlQOwgGJ5A8m6JplSjcIbznm1kEsRmIVOSSZyWAAXz0KKZznu2USnG7h4peCbEoUXfouu/cT4LOioNicvGt28KjIpFCz8zEopO1J6qGk+zpQ7SM5GhAxg+1iImzYt+PxMtXWBeF2hNiifaNNHwNwXE4wOereU1cdCIaBCP6dfc9vfx+Ewb0ahkSE4x2ca1hX3AsxU2t5vsybYtlox3OQWYtcWuUUBywAOdKyK/A1DVdcB9GO9yPVClqh8FxjwBXKKq04ArMB5xdxhMe5ULGGGbzRO/iDwDbADGAA91/+qCI2RZx6o6V0Q2y+b9zMuyMPWxEJDNC8jt/dzrt2azBLNU4cEIGLj8DDL1TDyv/Bb78RtYfvbTjP621pQD9UXEwjr6Wji0Gv/Ff6Xiu89I/eIGZ9VZADw+rDNugd+sp+HYa2iu+5jET4aZEhgn8cVjnX8bWrWKqsNuIz4nCs/zYyHS4ZyEmEw8196LlsyleLf7yDw8Dc+jk7tOegoK2yRflWwwMdmRmSS+Pgn9fiYvnLCaU04owPPK8e0TQ+xAiM4wHahqC5HksWAFQgoR0ZA0Gpoq0YrlSEy66bkcQDJ2hvSd0DVvo5tKkcknGCWiHZngkprSRGROh8dPqOpPtAUDYcPXgD+1eY4diMDk4RyI8SS/FZHvMDk5xwLDMEIx/xWR0zDVK3sEHrcdIzJg5yygLQ6cC7wnIs1Anqr+iq7Xuzd7rqp6VmC+eAg4CXimG+9B0IRUVCDcsnmBO6hrgFhMva3Lz9F2N7/zCEZe3ATLl6B1zyCjj3BWYq+38ESaGt+jB5MyPh4WfYoOWmE0TiNinLUbmULkmUOILGtE5//PSL8NO6I9hugEEdFIdDoJ5w+FZj86/yUYNALJPsjZcquIaCR2IAMvHwaRHnT2vyBrLJK1XwiNWKaEJ7UVYtKNRwowaTKnnFAAY+LQD+6AMVOQzF3NPrXRuo1mQvVEIr5Es9Jhedks3xedajzbhlITo42IMclTKhA/2GQch/ymoTcIaqIt21rDChHxYibZF1S1K4enKHCcOqBORL4A2uaKPFUtDRzndcwE+xZQqao7bXkgVX2GwOT4M82LioD9OjzOAmZucQy/iLwM/IUwTbThLrDqtmxeN2Xy1qrqeap6qqqGJ91zB0d2vwjPDQ9gv1PEqkPeRitX9vYpOYcnEuvYm7DOu4Laa2dRe9ar0BSGEi9fAtbpdyBnnMP6331OyyX/dX4JGSAmE+ucu5DjfkXR8R9i/+21zq0RnSJxBNal9yMH78GiQz/FfiHEi0sSmPjSRpm2j0mjTAOPkSfgeeUZrD0Gcu8RS7CvexWtXGm2qlWmuUbecsibhW6Y3UnEAG+cUcvxRJrvQGOHGLNYSObupoxqh9dbdnbpOBDvfBpYqqoP/MzL3gT2FpGIQHfA6ZhYbgGwm4jEBI5zYOA41UCeiLQlTYmIdFdS6UPgEBFJDiRBHQJ8GDhGbodzPhpY1s1jBo2jMnlbsi2yea5MnoNIBNZZ0xix21r06w8g5Vtkr987v9TYGwTk2+Kum4RuqsX++J/I0GHI5NOc9TDFQqIzyLx/AtS3Yr99LzJuHDLmJGc9TLGQ+CwG/30CtNrY79yOTNwFGX6Uczbb7KaMZvzDI8ES7P/dgEzbp12IINhjR2eYOtnGcrBq2oXlxYIxU/jzKatNJvRTL2LtPgSGj4O4eIiJhYQsiIhGq9cg3liIH9beWCMiFokbDKipg45MdnbFo++xJ3A6sFBEfgg8dw0wBEBVH1fVpSLyAbAA043kKVVdBBBIdp2HyV6ej4nNApwKPCYi1wFe4CXgx62djKqWi8itQFsW5C2B5yxMLlACxsX/EdN9MCy46j39mcZy6g+7mOrCRjLn3mU8hT6Mlv3Ihl1uImO3JDz/91DYNHS18FOW7/QoI3+Xhuf+h52d4DvaXfEKy3Z7mdG35hgpuDChXz3E3EO+ZOqTuVin3hG6A/ubN9cLS8qE9vexoRStXIn91Iu8ckM5J16RgHXabpA8CHyJSMo4EEHXfmCWjIce9tMOUbWFaE0hkjii10MpO+98eujUeyZn65z3/tTj8ZJ1hdvrOAS4vbn6M95Yov9xKAMe3An7P09gv3GD6Y7TR5G4wWT+5xCsU4Zi/+smdNbj4VFoSR7N6Nf3QvbKwH70KnRheG72ZMBUxry+J2TGYD92BbrmrbDYZcw+THtzKgjYD11usr5DgRWBxGUb77a20HTE6rh79yGceEUC/sW1VJ79HqxZ1L7TE4lk7ASJw9DS+ab2tyO+JCRxuPGaa9aGZ6k/bLjqPb2NO9H2ZzyRRupu71PY9NBamv6xKiyN6nuNqDRktwth8h7k37Aa+5PF7U3pnSQuC9n3MmTUKBZdU4B+82OnRvaOkZiL7Hc5kpbC0mvy0AVzwmJX0iYjB/8VIiwWXFMIq38IjV2xTHOJyGSjCNRU3kFQQGH4OKzTdqNuYzPPzItAC0pAW80+y2vej9iBUJmH1hZ3/rv74k0bSbvFJFF1FLTf0QlTeY/LzxPUOykiMwIB7msDbbQWBNpsTd/G4/xkfCBAfq+I/FNE/iYiBwRe+5NuIC5BEpNJ2tunE3XTrvivvwn7tRvDr4ITRiRtMjlfnYo1dQD+Ky9F5z4VHrs5+zDx+xMgNRr/JRehy8OjlSE7Hc24b38DjX78f7kELfg4PHYPPJHJs45DV2/A/+eL0Q3fhebAVqTRs41KNSU8Fcth/TLT8Sl5EEn378af/j0EfX8jTb97FK1c3j7Wm4Bk7YnEDTSSeFt6tjGZJuGqqQKqVjnfu9pxgvFmXY82VPR4opXuyeIhIhNF5J0ttowO+12ZvN7GG4eMOBZGTafk9Y3oV6Um6SRMjfnDTswAZOQJkDWUohc3oEvzzA+r0z+q8UORMScjyQmseqkMXb40YNfhpgiJuciYk8EjFL24AYpXmWYNDt9MSeokZNyp0OSn4MUSqMgL2O3BCkKbLB6YRKZA0pI2V5tjVpSDbZuG/GP2RA4+mpayZhZ/0wzV69rfZ/FAzCCT8FRegDZs6iyz540zzUf8TebY2gdWd1xRgV4nGI/2Z2XxVHVzHzhVXaiqR22xdWzB9XPjpwJfYDqNuDJ5YUBSJpD5zRVYJ4yj6VeXY79zV2+fkqNI7mEMmXsFxPto/tUl6JIweZjTf8uoBZdCeSNNx1yM5n8QFrvWYb9nyJzL0R/y8J92afjaU55yPjlzLsZ+cxb+My9DK5Zs2wHapO6qlne+GYqINc0oEnMgMQkSspCUcWZLnUjkC39i6o+nYl/9PxqOvBgtnIFWLDZb5RqoqoSadSbBqqG0/bhimZ7OSaNMj2QXlyAJZqLtjixed3Bl8rYXfPHIwD1h8Aiq8hthXZ1ZPgtH7WlvEJ2ODNoLSUmmam0jFAXUXZxOCIvLMhqycV4q1jRAccCu0wk48TlGytBrUb2mASrzTc9fpz3qpFHIoL3BVmpW1UNVnrG7LR613Yr6W8xE23a+lsesxvgSITHZdH0SgYgo06wkYxcke1+aK1rZsLAeVi+EsqXQUG7+xm0em7/FnIu/qd2zjYg23m1fiFO6Mdpep0fvpHRTFq87uDJ52x+SvR8Z392JDE9m4y5XoV/8s7dPyVFktzNJ/+YOtLiaiv3/Gros2a1gHXUpmd/fhv31SmO3ZK7zRsXCOuVykj66DvvZL2g+8VqoCkPTEo8Pz6VXkfjOn7Gv/x/+313f/X7bbR5m4giTbVy9qvMkHTvINJewIkwJT0fBgIhYop46nZwX92Dhr2axdp+XoGipmaxzJiDpE4wwPWqECJoqQ3nV2wlujLa36dFEG6wsXhfHc2Xytie8caamNmsosQN8aHmNaVRfv7G3z8wZIpON1zUgjtgMHxTnmwb5TgsRRKdD0hgkM4aYNC9sWI6WzHbes43JRJJGI0Ni8CR50bLFRkLRac82LsskGg2PgbgItGS+kRTsTszW4zPtEK0IQMx71PY+WV6zGuONBY/PiLm3Sd2JB+IHQdYQ4qONHV26FgrXtsvneSIDLUojjFfbpzLvg4jPujHakBHM2kCPZPG25OfGiyuT1+vIuBOJ+/ghaPKzZvK96NJf7Jq5wyOHXo7vtfuwP15G2f73oJsWbn1Q0EYtrN9eS+Srd2Df/xUVh9wTNjF169wb8Tx6JS1/eouW0++HxtKtjwsWXyKe627Huu8CKn/zPPbFf4OWbt7QWF5IyIXYLNNisWZt55Kh+GGmGUVLPbr2E2jocGMYO4CcNw9h6F2jmHXBWupunNs50Sk6w8R7W+uNxGFrXUgut9cR3KXj7YBgWjC+CVwG5AEPiRH3bQVWYZaBoV0W7+1AE+cXujhOXFfjVbUMOGcrE+1zGGHfY3Bl8kKPJ9LU2o7OIefoUiguQhNeQwbvaWoO+xreOCOxtlMqKfV+yJuHNlUig/dxtouUL940Yzgwg8RBkeiqLyGj0DTmd7KpvS8B1E/EUQPQimZ09SeQmoMM3Ku9RWGoEQsik5DYQSSckAkW6Mp3IHUYkrn71n/cLY/p7uSNY7PUXZvEneUBPEhkAhqbbibwukKoLzNeamo6MrSOibsWEJ3pQ2d+CLvsZJak2yaWiBjEbjYZ92qDN96598Kl39DjibansnhdHQdXJm+7RnY5F8+0M/DffSUrz3yR0bMjne+d21tYHqxjr4fDKvGf8meq8j4nZWau8+0pI6KxzrwNagqoOOBqvDEe4j6c7PwNTWQy1vl3ohWLKdvndlKmxON5ZqqZ/J0kLgvPlfeh674gb5dHGHraADz37to9L8oTaf4ebVJ30alGIKCN5LFI4ihTJ1teYLKLRSBnAozJJPalXdCZH/L4aWs5/+yNeJ7uIBfZJrFXtRxtqUNSxoO1o/c+dpeAe5ugRAXCLYu3Ja5MXpiwPGBFY+0/mlExHnThbCgp7BtanV1heU0261nDSFpXh855AwZnI6OOd9bDtLwQlULi5blQ3Yx+/Szk5CIjfuWsV+XxIdEZpF6VC35Fv3kScsYgOUc4Z7PNbkI2OTcOh6gIdOaDMHIKkn1g59epDdVr0NaGQMlN4G/giTR6suIxiVURse03CJbHNKXw+CBqHQASm9lerrPLTpx/9kbIjcV+9Xpkys7IwECfHVW0dj20NEDiyB1fZMCNtfY6Ti/Cd1sWb0tcmbztD9njYqxL7kBfzGftsR+hNQW9fUrOERGNdczNWKf+gYorZtN4yTvdjyUGQ2Qy1ql3IL8+ifzTv8O+7h2ww9CdKHYw1hl3IQcdzJoTv8R+5t3wJAQljcb6w/3IrhP58dhZ6Fvv/fQ16keLZ8Pyzzv/DSKijWh7RAxatca0ZOxI8lizHJ02FpJzjdebOAISRyCjTsTz9NPIyETu+s1q7AfeRavWBLbVsGEVFOf1kc5QVhCbSyhw1Xtctg27BZ37L3RNAbTYSGoscsDFpptOX6SpEv3qSbS8CvyK5OYgU892Pm5Xtx6d8U+0rgVabWSn8ciE05y1CVC9Bnvmv6HJb/6+06ebrmEOo5sWoDNegRbbvM/7Htgusae2Kb1prjaTvzcWSZ3YrsDTWh/Qkw38lvmS2j1btU0zCruFzT2PozM2L1Hr6jexH3gXIgQiBOuwHBgxzmjXWj4ke7+wf7ZDqt6zU47O+eT6Ho+X9N+76j0hwL1lcdk2LC+yy/lYR19CzUNrKL/qR2iu6u2zco7IJOTAvyB7H03xnxdjP/092A6XwQDEDkSOvgnZdTpLLl6J/b/vwuNhJgzHOuZmZPRIll60HP38G+dtApI6Ces3tyGp8cw7fzU674sOOy0kdSKSNtmIuRf90PlvEBEDcVkgFlpT2DljWCwjexedjjaUog0lnbKNZeB0rOvOhAjh1Qeqsb8pgppyiEoxZUFbyum5uPQAd6J16Rm+RBKePY6UB3bBfvJv2K9d38ekxTojicMZ/M6xWEcPwf7H1UZiLxx2M6Yw/sODkAkp+O++DF30fHjsDt2TcR8cDAk+/Pdfiq55Jyx2mXYE0z7ZB2pb8N/5R5PQ1IYnEhm+F2TthK77Ct0wq/PNR2SyySD2N5mOZh07fFleJD4HiUqHmoKfSuwdlsMJN6XQ/GUFm057Bwq2EBvYkXHraHsdd6J16RkR0cjY38KUwyl5rAB9Pt/8sDnd9KC3iE5HppwFoyeRf3c++v0Kc2PhtMpRXDYy/QIkazBL7ipG5y0K2HXYu03MNXbjY1h1RyGsWBAWu5I2GdnjYrCVpXcXmy5OrQ1mCdjyQtJoJGEobMiDqrVGBm9z28SYgGi7GrEAf3P7PrGMl+qLR5vKobkyICag5jUjxmEdtzN1G5v43yIfWryx8/gdFjdGuz0QjHrPL0rk/YLMnSuJ14eQ+BwGfHI+1uXT8P/hr9j/u7UP/Dj9PDJwN3K++z0yIhn/+Rej8/8dHrtjj2DCvNMh0oP/9D+gq14Lj93dTmTU7DPR0hr8F16CrpsZFrvWUaczfs5p6NyVxm7JnPad3gRk/BGQOgZd8za6cVbnwdEDkORRZjKtXN55pcUTjSSNNt3Aqpaj5Utg3WITk03OIvWxfTnn5eHYz+XTeNqjaPWasFyvo7geba/T017H3ZHI+4nMXa9L4tktJmkinBOB3WKSMfpqY35fvOkzO2wyJTPL0cUVUL/e+faFvUXMAGTYkZCRyfqPNsH64q2PCQVx2ciIY5HYSApmVELeatMS0+ms2MQRyPBjwCNs/HgTlOR1SC5ykJTxyIhjoMlPySebOn+ePD4jORiVAptKoam689iIaDORqm3aMXbsAGV5TKMOTxTaUmdKeJqawfJBZAKMnI7sdRgtdX4KfmyE6kJTOtRaHxA0aAq0f6w3//qbft7L9zf//AqP3WKOEZZWj26v496mR1nHInINps1iA3CWqh7dxWteAM4AfgWkqepjInJ8V6/v6rWB52cCZ6rq2m0+yS6YGh+ls6+cgueqO8yXLQzopgW0nnEvnkPSsC66u+8mVzTXoJUrYMnn1F7zPXFXj0GOvqm3z8o5GkrRmgIkdpBpchAu6tajtYXoG69Q//w6Yp8/09zoOE1tIVq3Hv3Pf7A/LcPz1CXIgF2dt1u12nTnShr10yYa/maTiOeJ7Pr77G8yk6wn6qeNMGy/KZvyN5vXeSLbv5tqG0+2upCm816kpc5P3COHQkJKYGwLNNSBLxK80Uja+M4NMwBaG0x/cPEgA/f4yfdey36E4h+QIbtB0uhO+0KadTxluM6ZcUuPx0vK6W7WcQjo6dJxdyTyupK5c1QSrys6yeQ1+2FDM1q+1KiAhANVWuv96PomtHwR1K0Lj91w44tHMqbB4CG01PvR0gbTK7ixrLfPzBmi0831hnOSBZONPGBXiPfRUuc3scqKJc4nosVlI+nTICaC5ho/VOZB5YowiNaPMO9zV52qPD7TMOXnbpo9kSZu21W3Kctj9kUmmbhuZJJ5HBFjmpWkTkIGTKOlzs+mNY3oguWwYiHUVkBVhRGar68zNb6t9YHSoy28fPWb7OiWauO9dsKG1la0udasdjm9QuDSq2yzRxuQyPtcVXcNPPZgJsf9gfOBv6rqs78wvtuvD7VHu/PUXJ396ulUnfQc8Sdn4rnsPpNg4ST+ZmgoQdd8ysZfvUnGX0dgnduHm1i11kNDKfanT1N8yQIGv7Afss+fevus+h6N5dBUjv+O+6n+eBNJ718RHg+zsQwaSvD/9QFa1zYQ+fKNzren7C1a69GFL6MLlvPVOWsZktbI0PeONp5scxNkjkYyppoa38o8ZNDuEJfdYXwDNFehxd9BdHLnHtIBT1o3zIKSPGT0wRCfAzjg0X52a4/HS/JprkcbArbZow1WIi8ISbxOaj7dUQb6CZYPEocQv1M84rXQos9MsoSTeHymxi81h/RJcdCqaMFHULXaWbu9RUSMiZ8NGUrGxDh0Uzla+GnfldjrLaJSzPs8OoGE0bGwbiFa/JXznm1UGsQNQSYlEjE8Bt0wL1Bm0wc9MvFAQgqSEceQtEaiEzzoopWwdo3xkj0+I0LgjQVfnMm6r9/Y7uVHRAfaQgYEEBpKjOcLZqwv3sSF4+LRpiqz2uXICoEbo+1terp03COJvGAk8VR1jaqe0+GpNmWgc4FjunvikjwezyN/Qw7amYLpj2K/+nR3hwaFDNwLz8uPIGMHsWynf2J//GxY7PYWMvl0fG88CiX1rJzyiJEtcwktlhfrdzfieeImWq77jMqj/wF1YUjO8sZhnX8rnjsuo/78N/Gf+3AfFUwPMCiLoe8dTfp1I/nyrHyqbl7cOaEyaQySfRBaX4IWzuyc+OiLR7L2RRKGogUz0U2LOh1a0qchucdCZR666G1nkiZdmbxep6fv5JvAcRiJu3+LyBIRWQCMA24KvKaribDL13cxiXaHLNoznLufumd5zJ1k8jCyLsiCSA+68DkjQO0kbXaHjmbUWenQ7Ed/fNZ5j7q38PjAl4BMGsaIszJgzWrTbMH1bENLRAxEphBxUhYJxw9AF79vmks4HTuNiIGodKJPzcI6OA1d/AZa8EkfEkzHTKZ2C7S0gC8SSYlh8lSb6JQI7Hfnw7qAMFnAu5XoNIjLND2XawvbvXzLazzbhMHg8UL1mvYJ1fKYWHLcQMjIRuuLwd8YwosIxpt1PdpQ0aOJNiBtt1kiT1XHqeokVT0+oCMLXUyEqjr3F16/rbQpA/XoOmTgHniufxAZnMrivd9EvwpTXWLO4XjufQSAeXu8iy78ICx2ewvZ7UI8dz2I/VkxK/d7Hd20uLdPqe/hi8c6/XY8f/gDJWd+RtP5/+ncFckpotOxfn8XcuLJrD/hPezbXzINJPoMarKL62pNTHZwNon/PISIvZJ58IZy7JfndH55yngkc3e0Kg8t/rbzMn5UCjJ4H8SXiK79Eq3Oa98nFpI5Hck+ADYshvo+3NK0nxKMHm1YJfJEJBW4nXY1n38AD4vIkWyjMtBmLA+M2plx95dAkx/94A7Y5SgkdVKwp/vziAUCsuuuTHmgGS0ugfdvQ3Y/sW8mlYhlljh/M5ncMWvQ7z+DNT8i00838T6X0GB5ICqN9NvGQm0L9kcPIqPGIqNPdHYJ0PIgcYPIvGMs2Ip+dC+M3qmP6BWLSXyKT4DM0ZtLdKwj4dLaOZDhw/7XVciuE5FBUwBQuxXqK6CxEa1aZWp9Y7Pbk6Aik2HAWNMMonwxxA4yzwFYEZAxGiKjQ3wZrmfa2zi5CN9tibxuSuJtUtULVHWEqt6pqnWqepaqXqiqL/T0JCVrP6xz7oFmP4tOmgdrvu3pobbNbu5xWOffh66tYcFJP6ClC8Nit1cQC9ntQqwzrqf1qTyKT/8c3aLXrEsIiE7HOvE25NAjWXX2Quy/fQJ2GDzMuGysU+5Adt+N5afNR9/oI/F4scAbDQnJSMZUZMCuZpt6Dp67H0OSo7jtnELsOz9FC2ejhbOhcB6UlUJNNWxcgm5a1tnLj04PZIdb5vUNJe37LC+SsYsDNf5uC8bexpXJC6CFM2DRN2hFPbTaWEf/DpLHOX5OuuYtWDwPLW8ES7COuwDihzput1fwN6MLXkAL1kJZA6RHYx12Rdc1ki49p7YI/e5FtLIGyhuR3SchE0933m7VavT7/6LVdVDZhOy3Z1gk9hzD9kNNnqmT9TeZ7OKkMZtXCHTR89h3fgr1fuwWxXPOMGTkKGhsAMuC7ClIRBTqb0K88UY7t211oaHUlP0FmmpI4sjNcnwhLe+ZOkLnfH5Pj8dLwglueU8IcG9ZAkj2Achh16Dr6si7YjlamReWxA4ZfgxyxNXozFLyr1iG1q7rWwklHfH4kClnYR1wFpUP5VF313JTzN+HeyP3CnFZyEFXIhMnsOiKPPSzeYEG+g6/z4kjkIP/igwexNIrVqNzvt+xP8uWx4grxOeYrOCqtZ1WCGTQFKwr98VuUd5+1w9FtWAJ+HwQG4ck5kLMIKjMN9/rjk5NdDqkjDc9ljcu6yxoH1LEzTreDnA92i3Q4q9g40r0u8XQ5Mc659LNheSOoTZa+AmsX4P91VIkKgLrrCsDSiR9kNZ6dO0HsC4fe8YqZEIy1vE39N32lL1FTT6aNxNduQr9rhTrrL2Rcd0rOQ+KqlVowbfo0uXowgqsc45Eco5w3q5T2C2m33FLLVpfYrKLU8ZD+WKzZLxmDRTV0vjaBqrXNZJx13hkwgRk2OGm/WNDifnMN5QhMRmd2zU2lkFzNVpv+kdL2mR23uMPIfRoc3XOFz1vkCPxx7sebQhwb1m2QAbthUw8CV1UTfnThWhtsfMZnGIhQw5BJv2a1o/KqH62yAhU/6RtWx8hIgbJPR7G7kPp8+vRD9abcoc+rGfbK8QPRSadgaSnsuLpUnTJsq5bBYaaxFyzVB3pIf+JYshfbkQBdlTv1vKajk+RKVC7AW0oM2EQuxVsRUaOQg6cRvW6Rt5fFQUlDWb5WO32hjW+BKgrQRvLzfvftroQlWZu5FsboLY48J0PtfPjlvf0Nt32aEVkBnAIcBVwCqZkxwbOV9VZvzR2i+Ncu+V4YCFwM5AA1ANvB9R+ZhLKFozd8GgB42GW/QDVhdhPfAAJEXguv8Es9ziJ3WLkwCrWYt/zCTI5AeuiW8Eb56zd3qK5Bi2dB3kLsO+fjZw2FOvXPW8X5/Iz1Bah5cvQzz/F/3IREX//NZJ7nPN2q9eYUpePPkRnlGLdcyYyeN+tj9te8TebG8KmcrQqz2QXl5VCTCz4fOjKVVDSQNWTBSCQ/MnNkDy2fWxLNTRuQmuKkIQcSBzRfuymSmitQytXscvh9zNnwbrQebRf3t/j8RJ3nOvRhoBulff8jCxek4ikAb4Or5uIEQfoyNmqWhLYv/vPjG+TySsAnlTVy4K7rCARC0mfCrGDoegNqPWjNWsRtZ1dzrW8SObuEJVK45q3iGpVqMmH6AznJ/newBePDN4XbW2kbPFM0gtqoGYt+JI2J4a4hIC4LCQuC437gpIFNQxalweZheZz5Yl0zm7CcCRhOBrxMRU/1JBaXgCJRQG7O0iYoG2VJSLanHPMACMU0FwLjY0m7mpZEBmFTJhgPNmnCqjb0ExSVT7ijTPlO2KZJh9aAjUb0MgEpHWg8ZYtb7uogX9xiD3/NuF3l96ku3W0xwJvAAOBMlVtAtiy2YSqLsRMpD9Hl+NFZCrwIEYm75VtOH9niUrD8+h1aMVyWs/+B9buSXiuutt8IZwkPofYN29C18+j+ohbiTttENYf7m2vxetjyKA9GfBdFjrvXcr2uILUe3ZCDr+ut0+rz2EdehGD5m9E/+9fVF95BQmvXYhk7ee83RMuJfXIEuzHnsT/zYd4n/sLkra1MvztAH+zkbpTPzJobzPZAsRkIjmHoVWrYOMSGDDOJD4BqE3yJ9NJqsqn6jfPAJD4xGEQn2j2N9RBxSZoakarC5GMnUw2MphkwYF7QOSzob0Ot4621+nurU53ZPG6Q+/K5JVuYx9Ry2MyKZNysZK90GijpfNNCzUn8fiMRmXKCHzxHrSuFS353ni3fRFvnEkuyRqCLzYC3VSHlsw2JRAuoSNmAJIyAVKjiIiyYOMqtGy+87Hx2IFI8lgkLQqPz4Ly5UZC0ek2kaFAAje3zVXt4vOW17QXjUqBuDQkIioQj40ynmnyWKNRCzSUNaPzl8HSBVBXDU2B9oqWmGO3NnSWyfPGtdsMGW4dbW+z1XcyIIvnU9VKVa0FpgHnAaXAyyJyZneN/dx4VX1KVf8S2E7pyYX8gs0nVHVnVd05PT25ZwdJGIHnibuxzjiY0v0fwH72obCUpEj6FKLefADrwIkUTLkb+/XHHLfZm0jusSTM+Dt4LdZOvAP98Wc1Jlx6ilhYJ19D7Dt3Yj/+HRUH3YFWrXTerseHdfZ1eJ69Gvvad2k+5S6o386blgQ8TMmYihZ/91OVothsJHt/1N9kxAQ6Np+ITCbxicMYcP0o3junkKLzfzDPR0Ub73bAWOMVN1ejaz/qPNalz7HViTZYWbwujtd7Mnk9xfKYGGlCNqmHpkFUBJr3jhHcdtSu18SEMoaRdVAK+BVd/SZUrXLWbm8REW2W5UbkMOSAJHTjBtPQo35Db59Z38KXADEDkd1TSdwzGfJmGSlDf5OzdiOTIHYwsn8aETsnooVfmXK67VliLyCFR3QyRESZz2JjudkXEAQQb7zZ31pv9vubTUw2PhFJj2bywHpiM7zonCXompXGm/V4zVhfghnbXA116515L0R6vrmEhO6uDfRIFm9LtgeZvGCQ9Cl47v87Mm00q6Y/i/1ONzKYQ2E3a388zzyCZMaxcMpz6JcvhsVubyFTz8Tz3COQV83yXf6Nrvu6t0+p7+GJxDrjVjx3/pXaP31K9QlPhMer8iVgnX8H1uUXUHnam9iXPgktdc7bDYaIGGTgXkjiCHNzsIXUHQnDkYF7oQ1lRuS9pbp935Acst4/jqRLhvHJ74uov3cF2B0qPZLHIln7o7XFaNEXZok6lAQzyboTbcjo7kTbU1m8Lel9mbxgEMt4XQPHMOLqIeC10O8eC4/EXkQ0jJnM+KsGonVN6DcP912JPctrftym5zLyisGwbCE650lXYi/UeHwQmULs+cOIP3UQOue/6KrXnfcwPZFIdAaJFw9DDs5AZz9nGphszx3CLA94YyFpqOl/XLmiPYdALCOuEJMB8YOgcZPJnm+oMxJ7nghIj2aPvZTIxAjs52dB0Y/tY8WDxGZCQpa52QmpTB64Mdrep1vvZE9l8bo6zvYikxcMMmgvrMv/jsRFsvCQT2Hee+GxO/wYPNc+BDUtzDv4c3T1l2Gx21vI7hfhufJe7DcKWXPEe2jV6t4+pb5HZBLW6Xcip57FutO/wH/Z/0xbQKeJycQ6+27kyKPIP+FT7EfeAN3OG1r4EkzMNirVdL7qKHUHplFH+hS0pghdP99kF9ebyVaGDiP2H4dgjY7l7geqsT/5oX2cWEZiL2NntGKNKR0KJa5H2+t0WyYv3LJ4W+KITF6wTN6LCY83ohW16P9uQPb5DZI60XGzst8eTHncg67MQwtuwDrgjM7F730JicC6YFeG7b8W/eJdSPkC2ef8dmkxl5Ag0QMY9PBkI7H3v7uQ8WOR8ac43u9WEoYy5JGJ0Gpjv34LMnUXZHhYIkFbx25By5cANpI8vr32NzIZBk4EEbTsRyR2UHudu3iQhBw0MgGamk08dsBYE5MFrNPgqswfEI9gP3Q5su9kGLRTwF4r1G4Cezv27F16RCi/Rd2WxduS3pTJCwbJPgDrlDugsomlZy+GjQ4vIbfZzT0O69Tb0B8rWHLWErQiDFmjvYXlQXY5H+uEP9Pw6BpKLpptluZcQkvMAKxjb0b23o/lFy7Dfu7rzk3wnSI+B+vXtyKTJrD03CXox184b7O72C1Q/AMUzOucKBaZjKRPRSwfrJvfObYtlikJTBlvsovjkpH0nczr06ciU87C85cHwWtx1x83YD/5tTnGuvmwbgFUVjgw0botGHsbV1QgBGjRTFg9H83fCI1+rBN/b+pgHUbz3oU1S9DVJUZi7+Q/mr6qfRF/E7r0v1BUgK4qg8FxWEf/1fnmIf2N2iL0h/+hpaWwtho5aFqYJPZWoQveRUvKoLgOOXK/3vdsbT9Ur0Kba6GxAiITkPRp7Y1jmiqM1F1LHbQ2IsmjTO9iMJN0bSG0NqDN1Sa7OHns5hUCXfBvM8kWNNJc00rkH3ORXCOxt8vprzFnaWloWjBOG61zvu15WaBEHui2YAwBbrQ7BEjWfsjeF6Mrayi+eSVaUxSWYnwZdiSyz4XoxyVsuG0lWr9xx2gC0BM8kciE05DdTmDTowW0PrEm0Kh+Oy4N2RGJy0L2ugQZPpzFNxWh3y0wnymnBQESc5G9L0WSE1l+Yz66aK6x25sJUpYHkkYjicOhJA8q1pj2i23nFJlsbqjVD2WrTYlO2z7Lazo+xQ6CqoKATF4HqcJBO2H9fg+aa1r59DOMEIEqeL1muTmkuB5tb+N6tCFEN3wLFWvRD2ahrYrnwr8472HafrT4SyjNw359DpLuwzrveohKcdZub9FSixZ9DkWrsF9ZjOyTgfXrm/tse8peo7YQXT8L/eEH9IP1WH85GBlzsvN2q1ahJT+is+ei35Zh/eUEZMghztv9JewWqFuHNlVBZR7EDUQyp7fvb6qElhqj9NXagKTv1N6r224xS8vN1WhtsckuThmPlv0I6+ajeWugpIHafxVSU9zIwIcms+s13zNncUnoPNrvnujxePHt53q0IcD1aEOIZO6OjDgSXVRD/f82onXF5kvo5F255TEe9ahDaP66gqY3NkLDBnN33RfxxiHDjoTcnSl9rwz9vgwaS52XMuxvxGUjI09AkuJY81YFrFxmtFOdXjFJzEVG/hoiLNa/XgLr15gGEb25cmF5IT7H6NBu2gANZaZ1Yts5RSYZGT27BepLoLWu/X2yvEacxJcE9WVoU6WJ97ZJ7OWOQnafRE1xI7MKY6CsAfzbefa1yzbjerShxvajFUugugD7rv9BVhSeK291PkvW34yWL4JNK7Cveg/ZPxXr4jvaG6H3NZprTEboyu9ovHEWkX/MxTrult4+q75H3Tq0ei363ps0vVBE1FOnIMN/STckRNTko7Xr0NdfQz8pxXrsQqNs1ZsEZPK0vhg2LIaM0UjGLu37m2uMwHvFMvA3GYGANolLu8U0o2goMSU8tZtM4lNMLHi96No8KGug7N7VHLBqPYtam0Lk0Y4J0qPd1/VoQ4Dr0YYay4OkTkTSxlM9u5rmz8rN3avTeHxG2i9lJIWzqtEvywm9gPR2hC/eLN+lZbB8dgsUuh6tI8QORgbuCc02S79vMRNEOIgfimTuhpY3searWmjaDlZoAjJ54omCshJoqum83xdvQjYtddBQ0Xkly/KaRCmJgJoyqKuF1tbN3qvkDENGDWZTCdT7Qxwbdetoe51+5dGKSClQB/S0SUZaL4ztDZvuWHesOzb4sT0dN1RVQyJAvfPOY3TOrKd7PF4i9nI92hDQ7YYVfQFVTReROT394PTG2B3tfN2x7lh3bPA2Q4vrmfY2/WqidXFxcelfuEvA2wNujNbFxcXFxcVB+qNH2/MUvN4Zu6OdrzvWHeuODd5mCHH9qd6mXyVDubi4uPQndt55rM6Z/e8ejxdr+laToUTkMOBBwAM8pap39dhgH6U/erQuLi4u/QTBSY9WRDzAI8DBGAW32SLylqoucczoDoi7puDi4uLSl3G2jnZXYJWqrlHVZuAl4FhHr2cHxJ1oXVxcXFx6ymCgsMPjosBzLh1wl45dXFxc+ihz5y79UGTntCAOESUiczo8fkJVOyZ5deX2uok/W9DnJ1oR+R1wJr9cta2YxLD93bE7ztgd7Xzdse7YXxrrBKp6mMMmioDsDo+zgGKHbe5w9PmsYxFJAJK681pVLXDH7jhjd7Tzdce6Y39p7I6IiEQAK4ADgXXAbOAUVV3cqye2ndHnJ9qOiMhUoFZVVwQexwKHAOtV9Tt37I47dkc7X3esO/aXxu5IiMgRwN8x5T3/UtXbe/eMtkNUtd9swNdAbuD/AswH3gw8f607dscdu6OdrzvWHftLY92tb229fgJhvVhY1OH/+wDLAv+P6LjPHbvjjd3Rztcd6479pbHu1re2/lbe01EY9gDgUwBVbQX87tgdeuyOdr7uWHesSz+hz2cdb8EqEbkV+AE4DzgZQERS2PoH3x27fY/d0c7XHeuOdekv9LZLHc4NSAH+gYmT/K7D8wOBXXo4NjOIsa7dENntT9fq2u37dt2tb219PutYRGKAX2FqvYqA11W1PrDvbGB/TJLCY6ra0N2xrt3et9ufrtW12/ftuvRd+kOM9mGgAngv8O+jHfaNwRSXzwNu3saxrt3et9ufrtW12/ftuvRR+sNE26Cq76nqAlV9F2jqsE8xd5+FQMI2jgVARCa4dnvNbn+6Vtdu37fr0kfpD8lQX4nIi5gviAd4q8O+wcAajEDzj9s4to07gaNdu71itz9dq2u379t16av0dpB4e9mA/Xo47i3X7vZttz9dq2u379t1tx1v6w8e7Wa20hJtZk8P69rtfbv96Vpdu33frkvfoj/EaDvyEGADiIgAX2ESG+4XkWt7eMzupG27dp2325+u1bXb9+269CV626UO54YDLdGANNdu79vtT9fq2u37dt2tb239zaMNeUs0VS1z7W4XdvvTtbp2+75dlz5Ev4rREkRLtK3EarYmeeXadd5uf7pW127ft+vSl+htlzqcG8G1YgtGLsu167Dd/nStrt2+b9fd+tbW6yewo2z0kuSVa9d5u/3pWl27fd+uu21/W5+P0QaWeDo+Htbh/2eLyHMicrmIRG/lUNsUq3HtOm+3P12ra7fv23Xpu/T5iRa4fYvHHVPyt9a3tCOrRORWEfk1JlbzMvxirMa167zd/nStrt2+b9elj9IfkqEOEpH/0nXtmmL6ls6n676lHTkPuAn4HfBXVf0i8LwPON+12yt2+9O1unb7vl2XPkp/mGifUtW7f2bf1vqWbkZVy4E/dvH8BmCDa7dX7Pana3Xt9n27Ln2V3g4Sby8bXfQtBVK2eDysw//PBp4DLgeiXbvbr93+dK2u3b5v1912vK0/xGgBEJGkrbzkhy6eCzpW49p13m5/ulbXbt+369L36A9Lx228ISLNwNvAm6paICKjgGOAf6ZZigAABGVJREFUIzEizcdvMSYUsRrXrvN2+9O1unb7vl2XPka/mWhVdT8RGYD5kjwaSNlfAfwPOF5VK7oYFnSsxrXrvN3+dK2u3b5v16XvIapd3Xi5bAsisp/2XDLLtbsd2+1P1+ra7ft2XXqHfhGj/aUC9G6OT9rKS374mXGXbPH42DDZ3XeLx2PCYTcw9jYROXBb7AVjV0R+1eH/+2x57U7YDIyLFpFTROQqETlORCQcdrs4zl7hsCsi40XkzyKSIiIHikh2mOwODfybLqZJxNgw2e2V3wyXvkm/mGj55QSF7vCGiHwkIpeIyBAAERklIleIyGfAv35m3O9E5K4Oj48Mk93jA689OvD40jDZBYgB0kTkZhGJCYPdQzv8/yrg1jDYBKNT2gyUA8eGy66I3LTFJHdqOOxi6kFnAa8Cw4GHw2T3msC/NwTs3xQmu731m+HSB+kvMdpfSlDYKj2M1QDMBj4SkfuA24D0MNmNDPx7lYi8A6SGw66I/A4Yj4k/1QJfADs7bDdRRHxAErARKOiuvSBsAtSp6qsAIjKabUxuCcLuB8B1AY/pRbbxOxyE3TJV/UpEbFV9UkSmh8lujIhYQIOqfi0ip4TJbm/9Zrj0QfpFjFZErvqFBAUn7Z6nqk+IyE7ARcArqvpxGOxeiPGenwcOBOaq6uNhsHsEcC7wFIEfKFV9z2Gb+wAXY7zLG4Asbe/A46TdCzGN4iOARwN2n3Pabgf7ccBvgTNUdZuWj3to7x5gGPAOsD+wNBzfKRHZA/gLkIZZPfg/VX0tDHZ75TfDpW/SLybaYBCRFDUdXtoeD1PVvDDYvURVH+rw+FhVfTMMdvdV1c87PB6jqsucthuwdRvwmap+GiZ7v1LV/wX+vw/m+/D5VoaFwm40pswjG1iOKR0J+xdRRPZS1a/CYGc8cBjwDDAFWKGqhWGwO1RV80UkHTgdeF9Vl3ZzbDTwayALKAJeV9X6bo7tld8Ml+2X/hKjDYZgYzU9Jdj4bk8JNr4bDMHEd3tCsPHdnhJsfLdHhCC+21NuIrj4bk8JJr77CObv8x6mXvbRbRjbW78ZLtsp/SVGGwxBxWqCIKj4bhAEFd/tKcHGd3tIUPHdIAgqvhsEQcV3gyCo+G4QBBPfbegQ9lggIsdsw9je+s1w2U5xJ9qt80sF6E7yg6rOEJFy4F627Y46GH4MTLAPYwrrZ4TJbhlQH/i3FOOFOM1jmDj25vhuGGwCLBOR/9AhvhsOo6r6HfBdh/juNpXKBEFNYOJ5TkSeBbq1fBsCHgNew6ySvAn83zaM/UpEXsRMlh7grW0Y21u/GS7bKW6M1sXFxSWEBBPfdembuDFaFxcXl9ASTHzXpQ/iLh27uLi4hJZg4rsufRB3onVxcXEJLcHEd136IG6M1sXFxcXFxUHcGK2Li4uLi4uDuBOti4uLi4uLg7gTrYuLi4uLi4O4E62Li4uLi4uDuBOti4uLi4uLg7gTrYuLi4uLi4O4E62Li4uLi4uD/D9MCwEsvuZpRQAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax=L.plot()\n",
"ax.figure.set_size_inches([6,6])"
]
},
{
"cell_type": "markdown",
"id": "dbc4f548",
"metadata": {},
"source": [
"### Sweep the correlation time\n",
"We don't use explicit propagation. Instead, we extract the decay rates using `rho.extract_decay_rates` to find the $T_1$ decay. We also calculate the signal at equilibrium. This is done by raising the density matrix to an infinite power (internally, we don't really use infinity- this just triggers an algorithm to calculate the equilibrium density matrix)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "e20bca43",
"metadata": {},
"outputs": [],
"source": [
"tc0=np.logspace(-5,-13,80)\n",
"rho=sl.Rho('15Nz','15Nz')\n",
"R1=[]\n",
"for tc in tc0:\n",
" rho.clear()\n",
" L.kex=sl.Tools.SetupTumbling(ex0,q=q,tc=tc,returnL=False)[1]\n",
" R1.append(rho.extract_decay_rates(seq))"
]
},
{
"cell_type": "markdown",
"id": "d34fa496",
"metadata": {},
"source": [
"### Plot the results"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "a99ede23",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax=plt.subplots(1,1,figsize=[4,4])[1]\n",
"ax.semilogx(tc0,R1,color='red')\n",
"nmr=pyDR.Sens.NMR(v0=400,Nuc='15N',CSA=0,Type='R1')\n",
"ax.semilogx(nmr.tc,nmr.rhoz.T,color='black',linestyle=':',linewidth=3)\n",
"ax.set_xlabel(r'$\\tau_c$ / s')\n",
"ax.set_ylabel(r'$R_1$ / s')\n",
"_=ax.legend(('Simulation','Analytic'))"
]
},
{
"cell_type": "markdown",
"id": "e035725a",
"metadata": {},
"source": [
"We see extremely good agreement between the simulation and the analytical formulas implemented in [pyDR](https://alsinmr.github.io/pyDR)."
]
},
{
"cell_type": "markdown",
"id": "6242aabc",
"metadata": {},
"source": [
"## Dynamic Thermal performance\n",
"The method `L.add_relax('DynamicThermal)` gives us the ability to add recovery to thermal equilibrium to systems where longitudinal relaxation is introduced by an exchange process (necessarily in the lab frame). This is not a fully accurate approach, as it does not properly introduce non-adiabatic contributions to the coherences. A good discussion is found in Bengs and Levitt.$^1$. We do not expect this particular limitation to present problems in the applications presented here. We will not be able to introduce electron effects like the contact and pseudocontact shift via exchange-induced relaxation of the electrons: we'll have to use explicitly defined relaxation of the electron instead. To the best of our knowledge, no approach exists to induce contact shift via exchange-induced electron relaxation.\n",
"\n",
"A second limitation occurs, which is numerical stability of the approach. Essentially, when fast dynamics ($\\tau_c<10^{-10}$) is present, numerical error between the fast dynamics and slow recovery fails to stably reach equilibrium. We demonstrate below, where we evaluate the relaxation rate constants and thermal equilibrium.\n",
"\n",
"[1] C. Bengs, M.H. Levitt. [*J. Magn. Reson*](https://doi.org/10.1016/j.jmr.2019.106645), **2020**, 310, 106645."
]
},
{
"cell_type": "markdown",
"id": "dd04ea27",
"metadata": {},
"source": [
"### Thermalize the system"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "2d21d6ea",
"metadata": {},
"outputs": [],
"source": [
"_=L.add_relax('DynamicThermal')"
]
},
{
"cell_type": "markdown",
"id": "dfb90037",
"metadata": {},
"source": [
"### Sweep the correlation time"
]
},
{
"cell_type": "markdown",
"id": "5a738a38",
"metadata": {},
"source": [
"We just have to add the recovery mechanism (above), and repeat the calculation. Note we initialize at thermal equilibrium, and invert the $^{15}$N magnetization at the beginning, to be able to observe decay. This is because the function `rho.extract_decay_rates` always assumes decay towards zero. Therefore, we can't start at zero, and we can't start at thermal equilibrium. This also means that the decay is twice as fast as if it were going towards zero, thus we divide by two."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "1de4c343",
"metadata": {},
"outputs": [],
"source": [
"tc0=np.logspace(-5,-13,80)\n",
"rho=sl.Rho('Thermal',['15Nz','1Hz'])\n",
"R1=[]\n",
"Ieq=[]\n",
"for tc in tc0:\n",
" rho.clear()\n",
" L.kex=sl.Tools.SetupTumbling(ex0,q=q,tc=tc,returnL=False)[1]\n",
" U=seq.U()\n",
" L.Udelta('15N')*rho\n",
" R1.append(rho.extract_decay_rates(U)/2) #Divide by 2\n",
" L.Udelta('15N')*rho\n",
" Ieq.append((U**np.inf*rho)().I[:,0].real)"
]
},
{
"cell_type": "markdown",
"id": "50ddd147",
"metadata": {},
"source": [
"### Plot the results"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "6c6cb675",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax=plt.subplots(1,2,figsize=[9,4])[1]\n",
"ax[0].semilogx(tc0,R1,color='red')\n",
"nmr=pyDR.Sens.NMR(v0=400,Nuc='15N',CSA=0,Type='R1')\n",
"ax[0].semilogx(nmr.tc,nmr.rhoz.T,color='black',linestyle=':',linewidth=3)\n",
"ax[1].semilogx(tc0,np.array(Ieq))\n",
"ax[1].semilogx([tc0[0],tc0[-1]],ex0.Peq[0]*np.ones(2),linestyle=':',color='black')\n",
"ax[1].semilogx([tc0[0],tc0[-1]],ex0.Peq[1]*np.ones(2),linestyle='--',color='grey')\n",
"ax[1].set_ylim([ex0.Peq[0]*2,ex0.Peq[1]*2])\n",
"\n",
"for a in ax:a.set_xlabel(r'$\\tau_c$ / s')\n",
"ax[0].set_ylabel(r'$R_1$ / s')\n",
"ax[0].legend(('Simulation','Analytic'))\n",
"ax[0].set_ylim([-1,4])\n",
"ax[1].set_ylabel('Polarization')\n",
"\n",
"_=ax[1].legend(('Simulation','Theoretical'))"
]
},
{
"cell_type": "markdown",
"id": "d331e02b",
"metadata": {},
"source": [
"Below, we plot a simulation below and above the failure threshold."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "813c6fe1",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax=plt.subplots(1,2,figsize=[9,4])[1]\n",
"\n",
"tc=5e-11\n",
"rho=sl.Rho('zero',['15Nz','1Hz'])\n",
"L.kex=sl.Tools.SetupTumbling(ex0,q=q,tc=5e-11,returnL=False)[1]\n",
"rho.DetProp(L.Sequence(Dt=0.1),n=500)\n",
"rho.plot(axis='s',ax=ax[0])\n",
"ax[0].plot(rho.t_axis[[0,-1]],ex0.Peq[0]*np.ones(2),color='black',linestyle=':')\n",
"ax[0].plot(rho.t_axis[[0,-1]],ex0.Peq[1]*np.ones(2),color='grey',linestyle='--')\n",
"ax[0].set_title(fr'$\\tau_c$ = {tc*1e12:.0f} ps')\n",
"\n",
"tc=5e-10\n",
"rho=sl.Rho('zero',['15Nz','1Hz'])\n",
"L.kex=sl.Tools.SetupTumbling(ex0,q=q,tc=5e-10,returnL=False)[1]\n",
"rho.DetProp(L.Sequence(Dt=0.1),n=100)\n",
"rho.plot(axis='s',ax=ax[1])\n",
"ax[1].plot(rho.t_axis[[0,-1]],ex0.Peq[0]*np.ones(2),color='black',linestyle=':')\n",
"ax[1].plot(rho.t_axis[[0,-1]],ex0.Peq[1]*np.ones(2),color='grey',linestyle='--')\n",
"_=ax[1].set_title(fr'$\\tau_c$ = {tc*1e12:.0f} ps')"
]
},
{
"cell_type": "markdown",
"id": "b269f5c1",
"metadata": {},
"source": [
"We see that for the shorter correlation time, thermal equilibrium is not achieved (dashed/dotted lines indicate the thermal equilibrium for the two spins)."
]
},
{
"cell_type": "markdown",
"id": "6d1877e8",
"metadata": {},
"source": [
"## Better \"DynamicThermal\" performance for smaller systems\n",
"The validity of `'DynamicThermal'` is better for smaller exchange systems, due to less numerical error buildup. Here, we consider a system in two-site exchange. We need to include a powder average to compare to the analytical formulas (since these are valid only for orientationally averaged relaxation). We also need to include a scaling factor, $1-S^2$, for the relaxation, where $S^2$ can be calculated from the angle of the two-site hop:\n",
"\n",
"$$\n",
"\\begin{equation}\n",
"S^2=\\frac14+\\frac34\\cos^2\\phi\n",
"\\end{equation}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "b54be680",
"metadata": {},
"outputs": [],
"source": [
"phi=np.pi/4\n",
"S2=1/4+3/4*np.cos(phi)**2\n",
"\n",
"ex0=sl.ExpSys(v0H=400,Nucs=['15N','1H'],vr=0,LF=True,pwdavg=2)\n",
"delta=sl.Tools.dipole_coupling(.102,'1H','15N')\n",
"ex0.set_inter('dipole',i0=0,i1=1,delta=22954.8)\n",
"ex1=ex0.copy().set_inter('dipole',i0=0,i1=1,delta=22954.8,euler=[0,phi,0])\n",
"\n",
"L=sl.Liouvillian(ex0,ex1,kex=sl.Tools.twoSite_kex(1e-8))\n",
"L.add_relax('DynamicThermal')\n",
"\n",
"seq=L.Sequence(Dt=.1)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "b53ce038",
"metadata": {},
"outputs": [],
"source": [
"tc0=np.logspace(-5,-13,80)\n",
"rho=sl.Rho('Thermal',['15Nz','1Hz'])\n",
"R1=[]\n",
"Ieq=[]\n",
"for tc in tc0:\n",
" rho.clear()\n",
" L.kex=sl.Tools.twoSite_kex(tc=tc)\n",
" U=seq.U()\n",
" L.Udelta('15N')*rho\n",
" R1.append(rho.extract_decay_rates(U)/2) #Divide by 2\n",
" L.Udelta('15N')*rho\n",
" Ieq.append((U**np.inf*rho)().I[:,0].real)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "16a37433",
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax=plt.subplots(1,2,figsize=[9,4])[1]\n",
"ax[0].semilogx(tc0,R1,color='red')\n",
"nmr=pyDR.Sens.NMR(v0=400,Nuc='15N',CSA=0,Type='R1')\n",
"ax[0].semilogx(nmr.tc,nmr.rhoz.T*(1-S2),color='black',linestyle=':',linewidth=3)\n",
"ax[1].semilogx(tc0,np.array(Ieq))\n",
"ax[1].semilogx([tc0[0],tc0[-1]],ex0.Peq[0]*np.ones(2),linestyle=':',color='black')\n",
"ax[1].semilogx([tc0[0],tc0[-1]],ex0.Peq[1]*np.ones(2),linestyle='--',color='grey')\n",
"ax[1].set_ylim([ex0.Peq[0]*2,ex0.Peq[1]*1.2])\n",
"\n",
"for a in ax:a.set_xlabel(r'$\\tau_c$ / s')\n",
"ax[0].set_ylabel(r'$R_1$ / s')\n",
"ax[0].legend(('Simulation','Analytic'))\n",
"ax[1].set_ylabel('Polarization')\n",
"\n",
"_=ax[1].legend(('Simulation','Theoretical'))"
]
},
{
"cell_type": "markdown",
"id": "da8e4af5",
"metadata": {},
"source": [
"We see that the correct thermal equilibrium is maintained at correlation times almost two orders of magnitude shorter."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 5
}