{
"cells": [
{
"cell_type": "markdown",
"id": "112fdc17",
"metadata": {},
"source": [
"# R$_{1ρ}$ Relaxation\n",
"Measurement of $R_{1\\rho}$ in solid-state NMR is a powerful means of characterizing μs to ms dynamics.$^{1-3}$ We may simulate it as the result of stochastic reorientation of anisotropic tensors, such as dipole and chemical shift anisotropies.\n",
"\n",
"[1] P. Ma, J.D. Haller, J. Zajakala, P. Macek, A.C. Sivertsen, D. Willbold, J. Boisbouvier, P. Schanda. [*Angew. Chem. Int. Ed.*](https://doi.org/10.1002/anie.201311275), **2014**, 53, 4312-4317.\n",
"\n",
"[2] J.R. Lewandowski, M.E. Halse, M. Blackledge, L. Emsley. [*Science*](https://doi.org/10.1126/science.aaa6111), **2015**, 348, 578.\n",
"\n",
"[3] A.A. Smith, E. Testori, R. Cadalbert, B.H. Meier, M. Ernst. [*J. Biomol. NMR*](https://doi.org/10.1007/s10858-016-0047-8), **2016**, 65, 171-191."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "25bae5ec",
"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": "c4639eb7",
"metadata": {},
"outputs": [],
"source": [
"import SLEEPY as sl\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"id": "a6b0651b",
"metadata": {},
"source": [
"## Build the system\n",
"We build an H–N system, with dipole coupling and $^{15}$N CSA. The system is constructed before (`ex0`) and after (`ex1`) a 25$^\\circ$ hop."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "1cb03062",
"metadata": {},
"outputs": [],
"source": [
"delta=sl.Tools.dipole_coupling(.102,'1H','15N')\n",
"ex0=sl.ExpSys(v0H=600,Nucs=['15N','1H'],vr=60000,LF=False)\n",
"ex0.set_inter('dipole',i0=0,i1=1,delta=delta)\n",
"# The 15N CSA is oriented about 23 degrees away from the H–N bond\n",
"ex0.set_inter('CSA',i=0,delta=113,euler_d=[0,23,0])\n",
"phi=25 #25 degree hop\n",
"ex1=ex0.copy()\n",
"ex1.set_inter('dipole',i0=0,i1=1,delta=delta,euler_d=[0,phi,0])\n",
"# We want the same hop amplitude on both interactions\n",
"_=ex1.set_inter('CSA',i=0,delta=113,euler_d=[[0,23,0],[0,phi,0]])\n",
"\n",
"L=sl.Liouvillian(ex0,ex1,kex=sl.Tools.twoSite_kex(3e-7))\n",
"\n",
"# Sequence with 45 kHz spin-lock\n",
"seq=L.Sequence().add_channel('15N',v1=45e3)\n",
"\n",
"rho=sl.Rho('15Nx','15Nx')"
]
},
{
"cell_type": "markdown",
"id": "4f5668c2",
"metadata": {},
"source": [
"### View the tensors\n",
"Below, we view the CSA before and after the hop, using the `ex.plot_inter()` function."
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "dd5bb7b8",
"metadata": {},
"outputs": [
{
"data": {
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KY1ix53jPXpcIO2gpJXOzc0wgoaLckoM23jvXz0SunVyuz5eq8bS4uNhcE7JtPLWCVL0myeDz+QpOOh+g6zr9/f3U1tbidDotzT6ns5NeWlrizJkz7Nu3L6lxP1OcdDaw2+1mfcuY31QUhenpabO+VVVVZRKvWHGaudxJ56IJJpuaZwHZIZPmsGROukFCMKQy5/FQUlJCU3EJxVq35evJd5teCzWt2MZTw2n39fXh9XopLS01G9GuBRtaNuvD8vIyzc3NOb2e9cQzzklH1qumpqaoqqqyPPtsxUlrmkZvby8+n4+bb7455bzhM0lPOleG5HA4qK6uNnmNg8Egs7OzpnCA0+mMqm/Fe998THcXsPYwekkef/xxbrzxxqxnn6WUtI2MstnvxdPWSqXTySs0mE3DRPPdSecKVrNZVtnQQqFQzno7snXShZ30OiG2OUxRFMviE1Z20ktLS3R0dFBbW4uU0hIhgFWDXm8Go2sZfTudThoaGmhoaACukrwMDw8nFA7Il8YxCEsKrsUcaQFXESuMAekFkfHsWVVVLl68iBCCP9u9G7vNDivLw+NpXFsqm56ZmWFpaYmamhrL44u5tP18YP2Lp+jn8XhypuinaVrGhCyFmvQ6IJEwRqbNYPEwOjpKf38/+/btw26309XVZem8Vnbouq4zNTVFaWlpRqmhfErDWjFst9tNU1NTUuEAn88XNV6TKXLhpA2ClwLWBuk0hyVCrD0vLCxw/vx5Nm/ezIYNG7K6vmS79MuXLzM/P09lZSW/7u/lgfoa/CXFHJUK77C7cK4D01emyJWzN6ZFnE4nhw4dilL0Gx0dRVXVKGIVK863sJO+irx30snqVblgEdM0jYsXL6LrOidOnMBut+P3+7PWkzYQCARob2/H5XIxPj6O3++nrKyM6urqtKLMbHfC6xV9J0qVXbhwgYGBAa5cuRJFrJJuqiwXjWMFJ712SEcYIxkMe5ZSMjQ0xMjICAcOHMgJBW48mzbsuKqqisOHD6OqKp8ostOrhO+pR9MI9Q/zvIlpKisrqa6uvmakIblCLrN7kUQmkYp+QNS0yODgIFJK8++J2NCyddLXkz3ntZNORWaQbbp7cXGRjo4OWlpaaG5ujkq7WXWKyY71eDx0dnayc+dOszar6zr9S0v8xL9MyZXLbPAum0a9nhKUVpGtYRupMrfbza5du3A4HCaxipEqi4y6UwUxuq5nlE6LxPUWeecjrMw+p/NsKYpCMBjk8uXLuFwuTpw4kTPbie0zMfgDDIU7TdPQgV4FEAKb3U6R3Y7c2sahpo2rSEMMNbu1aPhaj/NAcv6EZNMiidjQsgm+rzd7zksnbZXMINN0t5SSkZERBgcH2b9/P2VlZRmfN56TllLS39/P5OQkR48exeVymcHGZZvCX9VXMieqsLdu4C1+lS3Ts3g8Hnp7e02jzjWpQK4WiFyRmRiRsqIolJeXU15eTmtra1SqbHh4GE3TTAOOF3XnIt19vRl1viEV0RAk79aOh1AoxPnz59mxY4c5NpRLSCmj7PjIkSNR9WcF2CzD414AEmjT5CrSEGP+eGRkhOXlZTo6OsxJiPXWiL5WO+lUiJwWgfB3OTc3FzUtommayU2ern0btMfXC/LOSadTr8ok3R3ZXGKkt2ORzU7aWDzcbjfHjx83HzDjuP92CGaEwAaoCL7ttHNvxAMbDAbxeDwmqYDb7cblcpmLRra72GxxraP4yFRZW1sbmqZFRd2A6bArKysLNek8RqJekngwFuZUTtpwnPPz8+zateuaOGiD5//s2bOr7Biu2tFf+HU+7xR4hOCwJnlFnKRe5Pzx4uIiW7duxePx0NPTg8/no7S01AzK11puMtc76Uzt0OFwUFdXFzUt0tHRYQY3kdMixvhnMlxvQXdeOWm/34/f78flclmqV6Wb7g6FQjz11FO0trYmnaPLdCdtNK9s2bIl7uLxVbvg3x0KSwJqdGiTZvOpCafTaRq10XQ1NDTE3NwcTz31VFQ9e700ZNeyKzsyXQhXOYiNzEMwGMTn82Gz2TKKuuH6M+p8QLqzz1Zszli8S0pKaGpqumZyjKFQiIsXL6bcpW8CPhaUhPfRqRHZn7Fx48aormiDjjdZ1sjAMy3dnS6cTicul4stW7ZQXFwclY0wNi7GZxSPDa2wk74GMNLbHo+HiYkJ9uzZY+l1Vp2plJLh4WGWl5e56aabUn6B6eykjWsYHh5maGiIgwcPxl3wxwV83G1DX3mephQo0yRvVhNfv2HUdXV12Gw2tm7dmpFRG59BPhl2pueJTSdevHiR4uJiJicnuXz5Mg6Hw0wnWom6oeCkcw1VVfH7/aYMqJXvOVVWzOjv2L59O/X19Vy+fDml7WtIRpDUYP05Gx4eZmZmhp07d16TXXokhBBmqceg452fn8fj8dDf34+iKOYOsry8POd8AOuV7raCyKxKZDZCSmmOeCZiQ1NVNes+lXzCujvpyHpVOulrCBt2KvlJVVU5f/48DoeDkpISSxFWOg+uUd8uKSlJ2rwyBvgAm4QSASrwAk3ycmuJAPO61tOoIbeGnavxj5qaGrOvIFHUHTmjHYvrba5yvWAE2+Pj48zOzrJz507Lr02UFZNS0tvby8zMDEePHjW7/1MF6NPovN4OTyhQKyVvrK3ixiTPrjHlIaWkqalpXbJUsVkjQwRjfHyc7u5uXC4X1dXVqKqakx6TfEl3p3M+IcQqNrTl5WVmZ2fp7e3lox/9KAsLC3z5y1/mjjvuoLW1NaP3F0LYgFPAiJTyhdndTXZYNycdTxjDbrdbTl8br0lmqPPz81y4cIG2tjaampp4/PF0KA1Sw+v10tfXR1lZGfv370/6wO+TcFSTPG0TKBKaJbw2ZN3QJPAbBeYFbNHhp3aB027nFdXVbEth1FZZ2SxdxzqTssQi1pgTRd0DAwMsLS1RUlISpaMthLjuRjbWA5G9JOnaMcS3ZWPsqbKykmPHjq2Snk1m+5+2he0FYErA/2vbxPt0HXucINrr9dLe3s7GjRvZuHEjly9fzgvGMafTSX19PfX19cBVPu1AIMDp06ej6tmZsHzleiedy3UhHanKkpISSkpK2LhxI/fddx+33HILCwsLPPTQQ7z97W/P9BLeBXQC5ZmeIFdYFyedqF6VyU463vFSSgYHBxkbG0uYfs4WExMT9PT0mKNbqR5QB/Aln8Z/OBX8Au5VJbvSWAc+01TLD4psqITFA+ol2IDH7ZLP+3UcxDdqY5e9uLiIlJKxsbGMjRry30lHIlnU3dPTw/LyMlNTU5w+fZpDhw5Zfs/NmzdTVlaGzWbDbrdz6tSp2PcVwKeBu4Fl4A+klE9neo/5jHjNYenaMVxtHDMwPT1NV1cXu3btMpsqI5HKSS/G/Oy129A0uWrBGx8fp7e3l3379lFeXm7eQz446VgYz/Lo6CiHDx82n+XI0UVjlNNKvf6ZuJNOBcMm3/Oe92T83sPDwwD3AB8FMj9RjrDmTjrZ7HM6jWCJjje6q43ZyVynfHVdp7u7m+XlZY4fP87MzAxer9fSa6uB96WxezbQa1P4Xk0FNiAkwAs4JdQAFxTBWQHH45y2qKiI5uZmmpubWVpa4sqVKwSDQdOojXp2VVWVZVrMZ5KTjkVs1C2lpLu7m8XFRe6//37uu+8+fvWrX60ayYuHn/3sZ2ZdPA5eAGxf+e9ZwOdX/n9dIXZUMjLYznQnres6V65cYWFhgWPHjiVMO6di+rtXh+/YYIFwFurG2QVE6VUd+FgJ2kinlomTlpBG5Ts7GDYYqwlvTEEYhCFGb0Z5eXncMlw+O2nIrByWi3v6kz/5E4A/BVIvBGuANXPSVmaf0zXu2Gh6bm6OCxcusG3bNpNHOpfw+/20t7dTW1vLzp07zYUpV1H3rxWYVOA2NezQDagCdMJjW4LoxcAG1Fk8v9PppLW1ldbWVpMFyOPxMDAwgBDCdNjJuqRz2cWZC2QjaSeEYOfOnWzZsoW3vOUt3Hnnnbni8H4R8FUZfjCeEEJUCiGapJRjuTh5PiBZsJ2pk/b7/Zw8eZLa2lqOHj2a9DlTFAVVVRP+/XlS4b+COj9XoB441DeMvjesZuf3+zl37hz19fVxJWjTsWkJfMApeNiuUAz8WUDjpendekaIR+wUSRhizB5PTU1x5cqVVQ2Vxj3ma7o7U/h8Pst86vHw0EMPUV9fj5TytBDitpxdWBZYEydthcwA0jduI60WSTpw+PDha1JfnJmZ4dKlS6vSb7ly0h9xCv7RqaAKwT5V8g2/xiYZXgSqJdwyv8QT1RW4JJRLKCXsoN8Q1NmcwdvHsgAZRm10STudTrPeFTvmkA/GaCCXZCZWHbQQgjvvvBMhBG95y1v4oz/6o9hDmoGhiJ+HV373jHfSscIYuQi2Iby4joyMcPDgQfOZTAYr6nO3oHDLSgz/9IqdGmn03bt3mw1asUjHpr9sh//nVML61cD73TZu82rEP/PaIXb2OBAI4PF4GBoaYnFxkZKSElwuV9rfUyLkixpdtpwHjz32GA8++CCf//zn+wE3UC6EuE9K+dpcXWO6uOZO2mgoscLVm+7ib1ADPv3005SUlKwiHUh0Pel2b8frLo285myd9DLwhRUHDXDeLviKQ/DhoOQrdsEvK0tQA0FeGtI5rktuV8MLgovc5WNijdrv9+PxeMwxh5KSEqqrq80+gnxBLiL4dEewHnvsMTZs2MDk5CR33HEHu3bt4tnPfnbkIfEuKP+KnBkg0kHnItg20s4LCwu0tbVZctCQHpeBgf7+fpaWlpKm0SE9m76gCPPLFsCCgH4RDqxj4ReCL9sFowo0SnhNSJKpO0n3mXe5XFGiN8vLywwPD5v8C9mqVuXLTjrbSY2Pf/zjfPzjHwfYvLKTft96OmhYAydtGPO1+AIXFxeZmZnhwIEDZrNUqmtJ52EKhUK0t7dTWlq6qrvUQC70pOPRIUjgrAIn7QK7Bk4pWRKCfZpkdRuNhfdI04jcbjcbNmwwG668Xi8ej4fl5WVOnz5t8mtXVVWlTSqR66acbJ+tdA3bUFmqr6/nJS95CU899VSskx4mzHVhYCMwmtVF5hFS2bNVB7q8vEx7ezuNjY1s2rQpre8xHScdDAaZn5/H6XRy9OjRlIG8FSdtXOthXfJtCf6VS2/WYXeClz7aWMuMLXzguADhgD/MoEclWxi9GbW1tdjtdtra2kz+hZGREXRdj+JfsFJOyped9PXIebAm6e5cd0sau9vJyUkqKiosOWi4athWHiZN03jqqadS1rdTNbBYQQnhtPW/OBWkEOzQJK8PScZEmCP46nvBspFXA4YEjAk4pMO1HN0X4qp+rFFSMIx6aGjIbFKJJMhPhnyJug2kY9herxdd1ykrK8Pr9fLII4/w4Q9/OPawB4F3CCEeINwwNn+91KOtBNxWvtuxsTH6+vrYu3cvFRUVjIyMpOQ8iIRVJ230qZSUlNDa2mp5rMfqevUKFQaEzmM2gRN4T0AnUUXUE7N7H19nEzDsUFEUKioqqKiooK2tzRTASEdPIJdOOhtfsby8nFVNOuY6fg78PCcnywLrTmaSLgKBAB0dHZSXl3P48GE6Ojosv9aKYRvSd36/n5tuuinl4m3VoFMd95Gg5FZNY0rA7So0Ag0SfqRLRoBhp4MJRdDjUvijoM68EPy9S8EPHNUl/+7Tk9bBcskUFitFp6oqs7OzJkG+3W43SRni0fY9k530xMQEL3nJS4Dwfb/61a/m+c9/PkKItwJIKb8AfJ/w+NUVwtWMN1yTC18HZPu9aZrGpUuXCIVCUV3V6aavUx0fOYZ5+PBhent7cyY/Gwk38BchyVxIUkK4BJUIdf4AE1ythTRnF9tnjUR2GCuAEU9PwHDaxcXFOW9Cy6YZ9HokJsrLnXSiL9xo3tqxYwd1dXWoqppTwzbENxRFMeUUU8HqvYVCIRRFSfog3xVTxisB3huUfDGo8lBlMaoCkwje77bhkhAgbPBPK+EadibjXZkg9h7sdnvKJpVI5Z98SY0ZMIQOrGDLli2cO3du1e9XnLPxbwlkzKJwvWJpaYmOjg6am5tXpbezneyIhMEy6HQ6zTHMdNYgKwFAKBQya7cKWGoUu31imt62NkYUaNLhler6tilYdazx9AQMhq/l5WVzZDFXfNnZakkXnPQ1RryoTErJlStXmJubS4saMBbJjjcWkE2bNrFx40aefPLJnOyQIZzau3LlCoDZgFVdXW0pCKggvACEhGJG4AsCigl3dxsIWghi12r3Gq9JxePxcPnyZfx+PyUlJYRCIYLBYF5w7F5vXL/5iJGREQYGBuJKw0LubNnQiN+8ebPZO5Du+ZOVsILBIOfOnSMYDJpji9XV1ZbEXZxS8rp1dsyRyGT3K8RVkZDm5mZTJKSvr4+xsTEmJiaiSFUyGWksOOlo5J2TjhX89vv9dHR0mNSAseQn6ezQExmqUR+LZB2yatTJnLRBfOLz+cxrNxyWkfKz8kAfDKhUqirzjvDf6yTcGtJ5xKGY7GP/J8Uuer0YlCIJRDZt2oSu60xPT7O4uMj58+czalIxkG0vQAHXFsa41sWLFwESSsNCbpy0EQgcOHBg1a4unZ10omPn5+c5f/4827Zto7KyEk3TmJ2dNccWDRre6upqMw2cz8hFilqIsJ5ARUUFjY2N1NbWRknLRgYyVvUEskl3F5x0hkjnQTCctMPhSEkNmMl1RBqfMf7h9/tXsQ5ZXTR67AqPl5dQjU4zChLJt4XkpNRYnBzn94qLuHXnTjM1bzRgtbS0RAlk9PX1RRHsl5WVmZ/bdk3jw/2jPNK2CQH8YVDnOTp8Xdf4gU3QLEETMCjhPqdgScAtquTuNSBVSBdGKaG0tJR9+/atkp602+2mUUd+BvGQi7R5PtI/5jOs2rLNZmNubo7Ozs6U0rDG8VbT3WfR+VGRg8mGGl4qdG5QJZcuXUJV1YSBQKbyswZGRkYYHBzk8OHDFBUVEQwGV5V5DBre3t5efD4fZWVl1NTUZDQBsRa4FipYsSIhoVCI2dlZJiYmTD0Bw74TCd5kY9der5eKioqs7iXfkJc7aVVV6e7uTkkNmC4iDdXn89He3p4V69BDQudvS10suBv5pgP+PqTjFfAdLcjC3BwVtbV8z+Xi1gRrT+wDbSg4DQ8Ps7i4aBLo22w2blr08gf+q4uMBH5uU/iFIzyn+SM7tGkSjxJuZjnvFFQGdG5aeUk+NWtFXkus9GSsilVRUVFUPTvyHgzltFxeTwHZw+BG6OzsjLurjQerTnQKne/ZICQVlhXBD7QQ4+0XOF5Tm3SMK9OdtK7rUY1udrs94XkiaXh1XV81AREIBJibm7tmCnXpYi1oQR0OR1yREEPwprS01LRvo/yXbbo7VUD4TEPeOWkpJe3t7TQ0NKSkBkwXxkJg7ND37NmTkDzByqLxVRv4VyrFs8DXbLB9ZpZFqVJTXYPNbmOKMNe2lTAjVsHJmE0eHh7G7/cjhDBT43M2Gz+xXyVSmFJgRAjEytjWZk1ySRHcpOffTjGZEcZ+BsbupKenx9ydGEZd2EnnH0KhEBcuXEDXdQ4fPmy5mciqKMckKzzZQqCqKhPj41Tu2E5LSXJan0x20gZ9aENDA62trWnPcUeONYVCIU6ePGkq1Bkd0vGCz7XCetCCxgreGGtcV1cXgUCAioqKrLIO16OiXV456cnJSTweD9u3b6elpSXn5xdCMDQ0RCAQyAnrkM7KOMXKYZ5ZD5Uzs9Ts2IKy8sBukOEu7cQsw4nf30gLV1RUMD4+TnV1tZlO05wO3McPsuSwgRAEAV2Ev1AJDCuCTTJi551Hu8V0ZOiMJpWNGzei6zpLS0t4PB4uXLhgSiNOT09n3KTi9/tzNlf524Bkz5AhDbtly5aM2AOtpLtbAKcOo7MeVFWlbVMLe0XqbEq6O2mDtCdXpTaHw4HD4WDXrl1RweeVK1fw+/2Ul5ebY01rlRo3UtS5QCYBc+QaFykSMjIywvz8PIuLi2nxL0B4p16oSWeAVAZrNFh5vV4aGxuvyYccDAZN8pPYBrR4sNKU9moNPq6AH4lYXOTFvhAv27KNOl1yZqUD+/d0EDnSx4mcXQwEArzds8BnqkpZUhQaVJWAw4HPZkMKqJTw3DysSUPmAYOiKJSXl1NeXs7mzZuZn5+nt7eXubk5+vv7TZEBo55tZdHIluu3gPD3OTAwwPj4OIcOHaK4uJjp6emcasMbcPiD7OvsxN3cyGxQ41XCRiOpv2er55dSMjU1hcfj4YYbbshY0jUZ4gWfhtjN0FCY8r2qqoqamhrLz3EmuBY16Wxg2G8oFKK0tJSNGzcyNze3in/BIFWJd+2FOelrAIMasKGhgZ07d3LlypW0jNsYl0j2gBisQ5WVlTQ2Nlp6MK0wib1UKlRPzvCz0RFe3LqZww1NADxfCp5/jbOoLpeLt7tc/EEI5pH0+IK8r1SwoKpIKbl3doG5EGl3TK8FcjknXVxczLZt24BwIDY7O8vY2BhdXV243W7TaSfqtr0ejfpaI3JXGgwG6ejooKSkJEoaNlOxnGQweBJu3LWLe6qr+c2VPrZv25H2NSeCpmlmhqaxsfGaOOh4iCUHMpqtjOe4qKgoKjWeK+S6Jp3r+na8fhWj/Le0tGR+LlVVVWbJoNDdnWOMj4/T09PD3r17zQc0U1KDeIt+LOvQ+Pi45bqUFUKDgYEB3OPj3C0Eh8srLV9zLlEClCDYUFTCV3X4jU3QoGscDxHVMW2QiORD2jtX1xD7vTudThoaGkwaVyOl2NfXh9frjapnG6WO69Go1wqzs7NcvHiR7du3r6LmzcSOEx0vpaSvr4/p6em4IjdWz5/MnpeXlzl37hwbN26kuLiYqamptN8jV4hstopMjRs8A4FAgKmpqbR04OMhX/WkE41gxeNfmJ2dNUsGHR0deDweAoFAxu89NDTE61//en7+8593Eq5o/puU8tOZ3032WJd0t9ExGQgEOHHixKrRp1xE4AbrkMPhMCP8bMcwDGiaxvnz57Hb7Rw+fDguAxWAjuTDNsnPFai2KfylX+fQNdxh75SwU5WAAjU11K6kxv1+P0NDQ6biTVlZmRmZrweJR64MOtV5IrttDdIFw7GoqkpJSQk/+tGPLH8GhgGPj4+jKAp/9Ed/xLve9a6oY1aUc74L9K386ttSyr/N5P7yFVJKenp6mJmZ4ciRI3F3d1YbwQwkchZWRG6snj/R9RiNpMZmwePx5E1DYbzU+JNPPsnCwoKpAx85tpnO55OvetK6rqcMPiL5F4zPRUrJ1772Nd7znvewceNGvvGNb6T93na7nU996lMcOXJktxCiDDgthHhUSnkxw9vJGmu+k/Z6vXR0dNDU1MTu3btXfbHpGnc8p54L1qFExxoRt8FMpq6kl+Phi4rk07aV5jIbTLlt/Nynp12hTvbwLwAeAS2ShJU5o5NUCMHWrVvN0ZBIMhGDNWktUuO5So2l4+wN0oXy8nJaW1vRNI3h4WE6Ojp47LHHuPXWW/nsZz/LwYMHE54jwoBZXFzk6NGj3HHHHezZsyf20F9JKV+Y+Z3lN86dO0dRUVFSp5lusB0PkeQhyURurEBRlFUCHpE79MhG0lwLAhmYdjq4IGCXjGYLTAdGGnjr1q3A1RLP6OgoCwsLFBcXW06N5+tOOpNzKYrCs571LJxOJz/84Q8z7jMxduoAUspFIUQnYS343w4nHat8Ew82my2tdEWsMx0dHaW/vz8u/WA6C0c8Q52amqK7u5t9+/aZ15+swaxHRAsL9yuCZcIp6nQR7z3ut8NHXTYWgVs0yZf8etJzGwpGkc1XBpmI0ZzhcDhMI48lG8jVwpWrrtJsmIlsNhutra28/OUvZ+vWrfzpn/5pynn8SAMuKytj9+7djIyMxHPS1zX27t2bcqeTbro7EobIzcjICIcPH85JY1+sPauqSkdHB263e1Wwkcimp9HpFOEcaImARQWO6CRUvYrEF+yCfzi6D1w2btYkX/BHq2VpZOa4I0s8kRS83d3dBAIBMwA3px8CAURfH3IllZ6PTjobu/b5fBQVFeVksyGE2AwcBp7M+mRZYE2ctJEeVlV1FbNXLDJtONF1nc7OTkKhUFLWIatyeJHO35DG9Hg8HD9+PCo9mizqPrSyuzVCiL26zMhBx0MA+HunjcUVG/uVXfAlh+BP0hTZiG3O8Pv9eDwe+vv7zTqu4bRzNRqyVuluKzBGNgxCGavo7+/nzJkzPOtZz4r35xuFEOcIa0i/T0p5IauLzDM4nc6UGSmbzZaW9KSBSJGbEydO5CyzE2nPS0tLtLe3r8q0RSLWppfReUyALgS/EpL/LLXjFYL9quQ+v0ZbErPzAJ91KWghBQfwuE1wn13wZlUyB3zMJegUgnrg/UGdXemy3UqJGB0Fh4OS+vooCl6D0bC/vx/n4iLbHn6YkmAQp8tF0Y03Ip7znDTfLNEl5IfDl1LmykGXAt8C/kRKuZD1CbPAmjhpg6N648aNKb/ITBpOvF4vFy5coKmpiZaWloTvkUlNOhQKmd2riQTjEznp1+oK86rOTxWo1OGDfg1yNI7lB5YiTiUAb5JTWzUit9vNhg0bTLKBxcVFZmZmOH/+PJqmmYxgVgQFsr2WVMiFk86kcWxpaYmXvexl/PM//7PJ9R6Bp4FWKeWSEOJu4H+B7Vld5DMQNpsNv9+f1ms0TePkyZO0tLTknDXKsOeJiQl6enoSCn1A/HVimrCDBvhfG3hX/t1hF/yLU/CPgcReekmEg2rzWgD/yu/e4RacUxQqJISAzzoUPhtIw0tLieMf/gH7L38JikLo3ntR//APzfsw5owB5P33o/t8LPn9BOfmcHz/+3j276ekpCTrTvb1TndD7taVleDyW8B/SSm/nfUJs8SaOOmioiI2bdpk6dh0a9KBQIDu7m4OHDhgdognQro16eXlZXp7e9myZQuNjY1xj0v1ULxdV3i7Ht4hqLoEJfHxHuBvXIJuRVAu4R5VcrMmqYtzbAVwh6rz0IrIRrUOd+dYYScyNd7W1kYgEODMmTNZCwpYaQxZq/N4vd54jjYhQqEQL3vZy3jNa17DS1/60lV/j4y6pZTfF0J8TghRK6WczupC8whWvud0g+2xsTF8Ph833HBDWt+H1YVZCMHMzAwLCwsps3nxzlcBSCQCsUpxzofAZDSKg00ybKvfX/m5ccVW/8IleNym4BMwA2zRYDZNH6P8/OfYf/1rWLEDx0MPod18M3L37lXHOqTEttKEJoGZxUX0FX3vYDC4OjWeBnKd7s7mXNk4aiklb3rTmwA6pZT/mPGJcoh1n5OOhdW6sZSSy5cvs7i4yI4dO1I6aEivIWRpaYmZmRmOHj2aMOLONd7tVviuXSAJm/ycgH4FXrPyzJ1X4MMuhXEhOK7pfCogOabpzAm4Q5McuMaiUDabDafTyc6dO4H4ggJWUuO5ahzL1pghvJNOlPKMhWHAu3fv5j3veU/cY4QQjcCElFIKIU4QrnjMZHWRz0BYtePISQ+Dfcoq4snaAgyg80kbzAi4UcJbfKopFXvkyJGUz168TvAKFI7oOheE5FYN/tcmkUJQpUteEUpueAL4dEDSNDRIbVsbd2mSeglP2hRKAB9X7f3/WAy0lSeewPHNbyL6+2F+HiLojcXiYtyQQXvWs1DOn0eoKkLX8R08SENjo6noZUXsJ+l95jDdvV7cDo899hhf+9rXAJ4rhDi78us/l1J+P/Grri3ygnEsElYi8EAgQHt7O1VVVWzYsMHyQm1lJy2lpLu7m/n5eTZv3pwzBx0KhdA0Lem4z/mIXbYApoRABYYcdhqk5M9cCqds4WN6FYUmXeeDMTVoCfxSCafYbtagMuK+sjWi2HMkEhQYHh5GSplQazdXjWO5MOZ00t2GAe/fv59Dhw4B8LGPfYzBwUHe9ra3vVVK+QXg5cDbhBAq4fX3lTJf5nnWEFYyYj6fj3PnztHY2Mju3bs5efJkWoFXIo6EP7XD2ZVfndJ1Zob7+P2GBpP/PhUSBfObUdgs4QWqzjeCKkOKwq2a5KiF4NgBPH98iuObNgNhmuAyaezNww/KTZrOe1P1lCwusuFb38L9ox+BlFBWhhgbQ3e5oLgYfetW9JVnMxZy2zaC73gHtq4uZFUV4ic/ofIjH8HR1ARveENSsR+jb6OmpiZngkeJkOmuXFXVrNeDW265xfjuD2R1ohwi73bSqZy0Mee6c+dOamtr6e3tzRlBSTAYpL29ncrKypxyh3s8HrMZRlEU82EvLS2NWjS26JKeFUctgUop0YE6LXzNgyLaiQ8r4TRbhwI/s4WNvV/AE3YFBdikSz7j16nN0X0kc66xggKqqkZp7UYKCuRiBwxrX5OOMOBVeOtb3/oFACnlZ4HPZnVReY5cpLuNSYlIkZtcaEprSLpXLk9TVVRVZbl1M9WLPkZGRiydN1XGTSB4UUDDbs886LUDfxzU+YxTAQS3azofD8jkHd6Lizg/9SlqTp9GLC8DIBUF2diIduwY2uHDaHffDcnm/pub0ZqbsX3rW9T86Ec43G7sPT2I2VmCH/mIeVgisR+DYyAyNZ7rXW+mdn29sgeumZO2mmpOZNxSSvr7+5mcnIwiUEin9pVsETBmMg32pJGRkYy6U2OveWhoyGQ8M2Q4Z2ZmGBwcZGlpydScra6u5pPCwZ+j0KVAqYTbVclzNEmLLhkGDuuSH0Xsto9q4d9/xaGgEVbb+qld0LjSVT6kCB6yC/5AlTnbSVtFrNauMRpy5coVkzxf1/WsBAVy4aQL3N3XBsns2HgGYiclMmUbjHpfBFt0yRktiJQSp8vFXk2gKIGcEBlJKenq6mJyctLUPq+pqclIfvL5GjzPp+MDUlbhZ2Zw/v3fY3/8cYqmpyEQAJcLEQqhl5QQev3rkStlKCuw9fYSFAJW1gSlry/hsbFCGJqmrdKADwQCprxututMpiNYXq/3uhTLybuddDzDC4VCnD9/HrfbzfHjx1fNNGa7kzYE3Q8dOmRGYtkSGui6zsWLF5FScuzYMaSUqKqK0+mMorYzuqeHh4cB+OjKbrO8vNx82BdXzvlPfp1POgXjiuAGTfIHquRXSnjGEjDbV4Jc/WJzSQCajaOPZE3q7u6mqKiIpaWlKEEB476tLna5HMFaS6zMXz4kpdwX8bvbCI9rvTDid/9v5bhvrukF5gDxHK5RpqqsrIwrQ5uLnXQgEOB1XZ24t7URLCvjBh1+XxcsZagnHYlQKMS5c+eorKzkxIkT6LrO7OwsExMT5jNtZMmsdks7Vv5LBfvPfoYyO4t0ucL/2WzI0lJkfT2hd74ztYOWEtv3v4+YnUW75Rb0DRvC6XLjz2l009tstlViP6dOnTI3HqWlpWbWLJPUeKZ2vV4KWNfanvPOScca98LCAufPn6etrc0kkohEprPPcLVpJRgMmoLuiY5NB4FAgHPnzlFfX2/q0KrqarHK2O5pg1h/dHSUrq4uiouLqampMXcbVcDHgkZbWRjNEWtJMeGU+fLK4rdFl7w4hx3fuRpxkFJSXl5uEsIY9x1PazfZLjdXjWPpNCsVYA2xdmyUqXbs2GFmV2KRrs3FNngZQjq37NzJi4srrkavcY5Ndd5YJ23MVm/dupX6+nqCwWBUtiiSSOTSpUuEQiEqKyupqanJKZOfbGlB9fmQDgfBd78b7QUvwPbTn2J75BG022+HBPbg+MhHcH7rWyAE+n/+J/5Pf5rZri7qJycRDQ0E3/KWjK/J5XLhdDrZu3cvUkpTTjbT1Him60wh3Z0lrO5MI7+c4eFhhoaGOHDgQMKFNJ15zMhFwO/3097eTl1dXVx6UitSlfFgpM1jdWitPHSxxPper5eZmRlGRkbw+Xz09PSsasTaKuHlIZ1f2MM16U8EJD0iPEf9cg2MT+1aNI7l6jyJBAUM4vyKigrTyCNT47loHFtvwxZCbCE8k3l/kmOOAf++8qMN2CelXDeVFCvPgGFricpU8ZBJutuw0aGhIYaHhxMylKVjz7Fr1eTkJFeuXDFnq+OdJ5JLetOmTWZK2GDyczqdBINBlpeXrZVXpMT24x8jRkbQDx5E/Z3fQTl1CsXjwV9fj/sVr0C75x7cb3oT9p/8BIDQC15A4ItfNB21cu4coqcnPEv93e9eTW1PT2P//vcZf8UrKN6yJSflHuMzEUJQVlZGWVmZSb8bmxo3ynuxjIaxn2e6sPzZXkNcC3vOu500hL9wg1c6docbi0zS3UZUn0zQPZ3I28Do6CgDAwM5oTKMrAPV1NTQ399PRUVFVCOW8bA/u6iIZwfDTWZ/5xScXalbLyqSd4Tk6pT37CxiagrZ1gZp1IPXgoQkkdbuzMzMKkGBZ/pOWgixE3gAeAPhRvy/jBj7AGghnB47BRxaec0ngR+u6YVmAMPWzp49G7dMlew16byHIaSj63pShrJMiIwMbu+ZmRmOHTuWlhhNbErY5/Px9NNPm4Gnsbssqariit1Gs4RIzjv7v/87jm98I1zCeuABAh/8IMG/+AuU9nYGh4YofeUrsX/3u2EHvWKTjh/8APWRR9Ce/3zo7cX21FNhh61p4PNFN5Q5HGuiiBf7OSRjNMxW7CcPAu5rYs9556SXl5dZXl5m06ZNbNq0KeVDlK7xLS8v09XVlTKqT6cmbTSTLC8vpwwqMoWiKCZ9p7HbnJmZobu72yQi6Gqq52xtpSm08Wub4Nmq5KC86mCV3/wGx//8D2gasraW4NvfDhYpMa/VTjoZ4mntejweRkdHmZ+f59KlS2awkknTiN/vX69mkzrCalkvk1JeWKlhRQlzrNSwiPj5FcAR4M61u8zMsLCwgNfrZevWrQmJgGKRLpGRrutcuHCBlpaWlGtFOvZsBOjnzp3D5XIlZBpMB0VFRTidTg4cOGDSdXbOz/GxYjvjipsym413+1XuDekoU1PYH34Y4fWC3Y4A7D/9KcHbbkO/+Wa8J0+GTxov67DyO2Vq6mrq22ZDu+EGbGfPIjQNbdcuQq99LXJkZM3tOR6joSH2o2kaVVVVqKqaUfPYOsvOXjN7zisnPTExwZUrV3C73ZZHoKymyLQVZh1VVbn55ptTPgBWnX8oFMLn82Gz2Th06NA1j0wherdppNbm5+eZWfKyiIbbM4Nd1xHFJQQqa8G50sQiJfbvfS/cMKIoiJERHP/0T6hveQty48aU75sPdJ4Oh8MUFFhaWqKtrY25uTlTUMBIjVvV2l1H4oR5YAi4GUjJ7S2E2Av8DfBsKWV28lJZItUzYJSpioqKLDtoSE8AZ2ZmhqmpKbZu3WpprUgnM+b3+1laWjKV7nINg67zsfpqlhwKJbpOUFU58+NHufcv/xrH3BwiGISKijCTWEkJxAkk1XvuQX3gAeyPPx7++bbb0O66CwC9pgabrpuOWnvOcwj+2Z8hpqfDc9RuN3J4eF3tOZHYz9jYGKdPn8bpdCYU+4mHdd5JXzN7XtOadCLous7ly5dZWlri+PHjnDp1yrJDsOJMDdKEDRs2sLS0ZGlRthJ5G80kDoeDbdu2pTzntYJNCGrGxvi9gJ/zbjvDxUWouk5LVzc1j/8XXS9+MUIIXE4nrDTZiZERbE8/jbTZsP/iFwTf/360e+9N+j754KRjYdS/YgUFIlPjNTU1cVmT1pljJAi8GPiREGKJsBhHXAghKgin0V4vpZxam8tLH5qmmRMNJ06c4Mkn0xMPsko2ZNS4m5qaLC/KVmvSRinM5XIlddC5sAODXlQoCn6nk1d8/osUh0LhFLeUqAsLaMXF6BUVLL3kJRTH2p/Lhf9rXwsH3oqCeu+9Jj0o27ahLS4irlwBpxPtxhuhvh4ZsU7l0p5zcR6jXm2UR3w+H7Ozs5ZT4+s8TnnN7Hndd9JGA1dNTY1J2WcYqxVnmsqwYwXdjVGnbM9rkDEcOHCAjo6ONanvJII4fRplepoS4GM//CG/PLQfUVTM8670YmtsZKq+nsHBQaanp1Hq62m4eJHyri5QVSgvR4RCOP7939Fe+EKzvhUP65HuTgexggKG1u7IyAgLCwsma1JVVVVUinu9vjcppVcI8ULgUeAjSQ59MdAKfMm4VinloWt9fenA6/XS3t7Oxo0bo4R00vmuU6W7VVXlwoULOBwOjh8/nlMiI8CUxzx69ChPP/20pfNmgztUya9skj5FsIjEteTFIwQ1ioLiciH37yd0663M19czpGksPfUUZWVlhEIhgsFg2FG5XKgvf3nc8+uHD8PhwwnfP5f2nKugO/KaioqKKCoqiiv2Y3AsRDbS+ny+tDI3uca1sud1ddIzMzNcunRpVQOXYaxWnHQy0oR4gu5WkSjyjmwmMcgYEnEIW8WYCBORbFkhIYmHVdei62GHKgTKzFVq6JLycu7+zVPh9LWUaJs2UVVVhd/vR1VV6t/5TryPPILt8mXsqooiJTZVDafXpLzqpH2+cHep14u+Zw/6gQN5uZNOhlRauw8//DCKopiznanwwx/+kHe9611omsYf/uEf8sEPfjDq7yL84XwauBtYBv5ASrlqtZdS9gP7Vv49Bxxf+dN3Y477g4gf/9Piba85xsfH6e3tXaUTn65dJEt3Ly8vc+7cuSiFrEyaweLBGMU0pHTXqvxxQod3BXT+wq1QI+HMXXdQd/8D+FwuijUNfd8+bJs2UX7bbexdeYaNGm5HRwdAFJlKuraZj/ac6Fyx46qxjIb9/f2cPn2am2++Oav7Mmy8u7v7CvDvUsq/S/Waa23P65LujnSgR48eXTX4bxirFSaqeIZqdHy6XK5Vgu7pXO8qykFNo6OjY1UzSTpNKWPA/3MK5gUc0SQ2CY/aFaSArZrkT0KS2ERO1AMnJbYHH8R29izSbkd77nNZLi7iyxsaGCkuYvvmjbzxp79EKS9HNjWhPfe5ABT94he4Ozoo2boV1+teh83jwfmVryBXnPfQwYOMnjljpoer778f2wqNonL+PKqiIJub83onnQzxRmQmJib4zne+w+23387v//7v87a3vS3h6zVN4+1vfzuPPvooGzdu5Pjx4/yf//N/2LNnT+RhLyAsS7kdeBbw+ZX/X1cwvjtd1+nu7jYbJmPt1Qig0+Hijsd5YGSt9u3bFxUEpOuk4yEYDHLu3Dlqa2vZvHnzmj2XOuHAfLeERhlmPvjY33yIp3fv4q7hUW47dgJ9+3YoLzdT2IajMtafSF6FS5cuUVJSYjZRGpsS20MPYTt5EhwO1HvvRT940LyGfHXSVoKkWEbDhoYGvve97/Gtb32L+++/n9/85jdpMxlG2vjWrVv3ACeFEA9KKS9mci+5wprvpA195uLi4oQONBuqT6/Xy7lz55IKuls9b6Tj9fl8nD17Nm4zSTpO+pMuQe/KiFS7IhAynPcA6LMJfh5Uuev8RQiFwixADQ3R19Xeju3MmXDjl6Zhf+QR/vl97+LndgVF03m6rgZt717epF/9XG0/+AG1//IvICXOX/0KZWiI4Ic/jH/zZmwdHeg7d9J0xx3Uqmq4c3pgAPXJJ3G43bjdbtxFRSiXLyM3bMg7o84UNpuNZz/72WzatIlf/vKXKRf7p556im3btrFlyxYAXvnKV/Ld73431km/CPjqiqDGE0KISiFEk5Ry7Frdx3rB7/ebhD07d+6M+1wYdmx1sYy1eyklPT09zM7OrqIQhewIhyDcgd7R0ZGUYCURsnFwnQp8xKkwIgTbpOQGVfINp8Iy8OCrfpceHWxBnZtT3FoiXoWLFy+iaRobxsbY8MMfYnO7EUJgv/9+gtu2hRvRsryHSOQy6M50rLK1tZXGxkbe9a538ZznPCejc0TauJQyKIR4gLBN//Y46fn5eS5cuMDWrVtpiHE+kUjHSUcea6Q+9u/fn5YmbTxE7qQ9Hg+dnZ1RYgCRsNwJDgxEZhQIq1UZBGIC0DovoqxQZTIygnbDDeH5xpXzi8XFaFYhKbnsciLKypAr5+jWdYgQobc9+SS6EUQIgfL00yAE8rbbUG+7zTzO7Jyur8exfTvq/Dw+v5+ZqSlmxsbwjY6an0s2TnY96/eRiGw0SXU/IyMjUZroGzdujNcY1Uy4w9PA8MrvrisnLaWkvb2d7du3m6pJ8ZANF7cRzJeUlCQcgUqnGzwWRoo+kgp4rfA5h8LISqB+RQiadEmLJpkWUCLCu+zzNsHNuvXGxkhehdbWVlRVJdDXx3IgwNzCAja7nSKnE21wENeK1nS+7qQzPZcxgpXp62NtnLD9rnsmbM2c9PT0NJ2dnRw8eDClUaS7k9Y0jcuXL8cl7c8Uxu44spkkER+v1Z20gzCN56C4+vMuPaxLK4AyVaPaM8sv6mo45pmlRErs999P6cgImxYXsb3qVWg7d6L88peIFZpRWVVFk6soqpVwQ0y8IGMDiziBRswNof7u72L/9repuHCBqsFBGpaWGPd6uXLbbZw6dSojnuJcIhcdpenMVSZimYr9VbyXpn1heQ4hBCdOnEh5XKZOenFxkY6ODrZs2ZK0ESgdSmADhsDHwsJC3BS9eRzwU6EzTZjV72jCbpHVWAb+wSm4rAhadMn7g5JKQASDiO5uREMNNNUbF8SWb32b0slJfnTn8xjatZNZBV6oxg/6rWbs7HY7jqNHcZ48CbqOqqos2e1cXl4mcPIklZWVqKqakxHEXDaOZeOksx3BSvDZrrv9rpmTrqqqSsoIFIl0SA1UVcXn8yGljEvanw0WFhbMTtJk123FSRvHvCeo8xWHYF4IDmmS16uSX3kXCPn99NTV8KFjB9GEoMXr41PffZimri70sjKElNh+9CO0nTsJve512FfGp7RnP5t3aoLPeH2M2G1ss9v5wxhN2tCb3oTa2Ynz0iX05maCf/InKe9dbt+O+vrX43rnO6GyEsXno/anPyW4ZQv1L32pSaYSyVNslZ83X6L3dEY2Nm7caIqBQHgWOE45ZRiIDMU3kmQU45kMK898uk7aZrOZDjoZFbCBdNPdUkrOnDlDaWmpOUmSCD+pr2FOCUddvwH8ms7NFh31ZxyCH9jDynTnbIJhRecL47M0P/ggjpoa3hzw8YOd2/np776Ut/3V/+VVn/lXhJR8sKiIr73+NXz+kx+nRWS/0ZBbthB67WuxnTyJcDgouusuDjQ0mFSd4+PjPP300+Y8ck1NDUVFRWnbZ65GsCBzBSzInswk1sbJE/tdMydtt9stR4FW01iGQTscDnbs2GH5WlKleQyBDEVR2L9/f8oH0MqCNTs7y+zsLPW1tfxtcTFGgGb78Y+589FHURWFu9/3x2j1dYjlZYaK3fzPvt388ZWe8KgU4QVDzM4id+1CNdIyUtL8T//Ep370I1AUQi95Ceqb3xz95qWljP/lX6JIyYbodE5yjI4iQqGrHd9C4PB44pKpRPLzZmv0VpArBSyrTvr48eNcvnyZvr4+mpubeeCBB7j//lX0vA8C71ipZT0LmL8e69Fg3UlbdaK6rjM4OIjX6+Xmm2+2VMdOpxdkeXkZr9fLli1b4gr1xKK/pAgj36QAHQpmjTjVeNmATaADsyKs8XFeUfj5ySc47PcjR0Z41q9/zf5ggFd/93ts/vXjCCkRUlKyvMzLvv2/zO3fR9XvvyH1TXk8iMVF5KZNCYU19AMH0A8ciPqdQdUZOY8cy5VfU1NDZWWlZUKgfNhJZ6uCFWnjW7ZscQKvBF6d8QlzhHWfk44HKxH42NgYfX19HDhwgPb2dsvnTjWDbTSTbN++nd7eXksOJtViMTg4yOjoKHV1daYhVFVVUVtURP2jjyJsNqTNhh4KIvz+cHpaSkIHDiB/8CioKhL4r1tv4uzeHdQogle2X+Dr5SX0u520bKjjHeXlVHm9OP73f9FuvBG5b9/qC0m1w71yBdeHP4wYGEDfv5/Ahz+M3tiIMjEBgO5241+pZ0WfdjVPcTZGbwW54O1OJz1mt9v57Gc/y1133YWmabzxjW9k7969fOELXwDgrW99K8D3CY9fXSGc9bSw0l6/sBpsGx3WJSUlVFRUWG40s7qTNjI+RUVFlhw0QJEWfd7SGPNOZvNbNcljNmGKcFXqkiVdZ8Fhx376aUQwSDGC7Z45lGAQEXGeIq+Xex58iM2vi/PoaBr091M0MYHtwQdxfOELYenJffsI/su/QIZlp6KiIpqbm2lubjYJgWZmZujv7zdtOxnrVy57TLKtSWfDwx9p40An8BUpZUr2sGuNvGAci0UyJ22Mffh8Pk6cOJH2op/MSRuO/9ChQxQXF9PT02PpnIkMVtd1urq6CAaDHD16FE3TonaeM729MDaGzeWiqKiIe8528J3feTYA1RLuWfITuusu1L4+vllTybfvvhPsdqY9M3x660ZsUtIwN8/krp184SX38mdfvR+WllCeegqtrQ2KinD+5V9i/8lPaCkpYfo974EkHe+u//t/sZ06Ff6cfvpTZH09gb/+axzf+haEQswcOYJqgYIxntEbpPo2m41AIMDS0pIlqr9EyEUtLd302N13383dd98d9bsV5wzASlf327O6qOsIVoJtQzVux44dlJaW0tnZafn8qZy0lJKBgQEmJiY4duwYp0+ftnzu35mc5nxrC3PARgkvjDBvKSVTU1NmNin2Gf7jkGRC6PzSplApJcd1GDx2lEM//XnY0UoJZWWgKGhlZdi93vB5AUVVaV72hx135Hk1DeXHPwavl/LOTpzf+Aa2oSHQdWwXL6JMTuL/btRYbkaIJQQKBAKmw/Z6vZSXl1NTU0NVVZUZTOVyJ51N8G0SvGSBCBvfmtWJcoi83UnHMz5DNL6mpibh2EcqxDNsKaVJSxrp+DOVtoOrAvFVVVXs2rULee4c9Pcjiovh2LHwzrO6GvtznoPe2Yk/EOBV3/sBJXUNBFo2cddPf87O//4flOFhtKoquv/p7xF2O6O6xlBZGX6nEwXJXHkZIUXQMjGFmJlBVlSgaBp873soExM4P/c5EIJiKWn8sz8jePfdCVNjYnw8+rMaH4emJkLveAcAgbExs2HNKuIZ/alTp5IavRXkqiZ9PerPrgWs2F4qJz0yMsLg4KCpGhcIBNJWwUp0vCG+IYSwpMAViw3+IC/TBAHABYiVnkBN02hvbzeb1gxFKyNTZLPZcErJuz/zeV7x5BPYlrx03Hk7m+56Pku330Gwtg7nD34Q5uJWFALFxXhLSyn2+ZCA7nBwaecODsR+vgMDKMvL6JpG1Zkz2IaHrwpsCIHtyScRnZ3IOJmubOByuUxBDKOpb2ZmhqGhIZN2N5fINvhe79HOa4G8dNLxujYNQfedO3dSW1u76jWZcn2rqsq5c+coLy/n8OHDGTn+WCe9vLzM2bNnr3anXrqEcvYsUtcRs7OIpSWTglN9wxtQfvMbigIBnAcP8rrKSua7uii7779QOztxBALYxsbY853vcn5LG0slRYQcdkAiASkUphoaaC3rRzt6NFx/cjpRAgFsP/1p+IJW7tcxOkpwbi6h6pV26BBKb284gpcS9ejRqL/nIq1lCMTv27cPKSULCwt4PB6zYSMZ13YkCk46/5HISRsMX6FQKEo1LpuRrUgYM9xNTU2r1LHSeYYFgsgEst/v5+zZs2zcuNGcTZZShrNiMzNmP0bTE08gHvgGe6cmsQdDbO7rJTQ4zOQNNxJ673uRt92G0tuLaG/H2d0dVqay25DAfHk5nW9+EwdWXUzYJpWBARyLi0ibLTpgdjoR4+M5d9KRUBSFiooKk1AmGAzi8XhMvXufz5e17GSmdr3OPPzXFHnppGONNZWgezr0g5EkJQbxSapRj3TOacxU79u3j4qysvD1GbJxxqzzzEz434oCioJ+881X7x2ocbtxCYEtFArLzOk6r/3a/Yxu38boC+7AXlGBDRk2VKBRsfHGtu3oJ05c3SXrOnpJSTi1tgLpcERrysYg+JGPIOvrUQYH0Q4cQH3jG6P+ngsnHWlMQgjT6Nva2kwZyuHhYRYXFyktLTWddqzR58JJLy8vW65RFpA+bDYbwWAw6neGA21oaKC1tTXqecpETzr2eCN9Hk8rPl2a0shjjfPu3r2b6upq874URTEdE4T7MWa/8x2kGsLu94NQKFlcYiwYpKSnB8bGQFGQoRD2sTF6Dx2k+Ze/xB5QWSwt5fv33M2zdsRxtK2t6L29KKoaFtM4fBjHyZPh3bTdjrpvH0OHDnHZBo067FoDn+V0OmlsbETXdTRNo7KyMopbOzLgtmqruq5n3LeSL/wLuUZe16R1XefixYspBd3ToR80DNugGswV8YmUkuHhYYaHhzm6bRvFn/scor8fGhrQbrklqjlErtSjEkFu3ox+8CC2CxdA11EcDpxC8Odnz1M9O88X772LwY3NuAJBav0BdpeV89ctG7jh2Tfz8p/9EgXQt2yB5z0P/dw5hMeDDATQFQXHP/8zoT//8/jv73AQeu97E19XDuYhkznXSBlKKSVLS0urCPUNnuJcNI4tLy+vp2rOdY/YYNtQmIrnQCG9bm1Y7aRHR0cZGBhIGMwbx6f73BjEJ4nOG4mioiLcx44x/YufIxQbEslCWTnMzhKsrGLhJz+horIS58gIYnoaTWpoNjsBtwtfURG7u7ooevppOH48+sSKgv7c5xLauJGloSHKa2sJtrSg9PWh/c7vcPENv8+XGmpQRbi2fY+qc/saCZoan6mhSLd58+YoytLFxUWKi4tNp51MR0HTtLR1FqCwk15zGM1FJ0+epLGxkZaWlqROPl0O36GhIRYXF3NGfALQ19cHhNv4HV/5CsrKz4yPo5w+jfac5yAHBqCoCO1ZKUhsFIXgX/0VsrQU+yOPoLndzJeV8fMbT/CU20GJz0/j5DSlqka93w/BEJPAj5qbqH/pi7nJ7kSUl6OcPYt2+DC2J54gWFqKze3GduEC+qOPmrqz6SAXkarVmUohRJTRG4T64+PjdHd3oygKTqcTv9+fMZlKtiMbv81Ip7QkpWRwcJDx8fGUpEDpIPL8XV1d+Hy+qPR5vPOn02ei6zr9/f0mLanVngnxwhfiXlpi4qEHKRkbx7lrN00nTnDWZkNTVQYHB5FCsEnTqJyewh4KYVdVKhcWOHj2HIyOYnvoIYTPh75/P/quXcZFIbduZeg1r6FeiLDjPnoU7HZ+5hCoxqQk8LgiuF1bG8clpVy1gYpHWerxeLh48SKqqpoBt6FgZSDTDFkgEFgXUqW1wJo6aatGsri4yNTUFEeOHIlLwxkLq/OYmqYxOztLWVlZxsIbsVBVlenpaaqrq9m3b194oZmfjzpGzM8jb7gB9ciR1O+5vIzS3490uQh94AOEPvAB/MPDTP70pzxSWsyvjx3CW1REsc+PKv1MtWxiu7sYoev4/X56lj3YR3oQFeX8dNc2ev/+I0xPjLOtt5/945O86YmTiIWFjO41V+nuTD73SEJ9Y9Gfn5+PIlMxjN5q40m25AcFJIfNZjPpPRVFyaiBKxkURUFVVU6fPk1lZSWHDh3KaTBviOkcsWK3MSh75Sspe+Urw+loVUV1uRD/+7/U2mzUNzSgaxqemmrOdLTznOER401xCgXlvvvM2rLS0UHota9FRvBASLcb/ciRqPeLfeKVNcz6pnKskZSlLS0tqKrK3NycSePsdrvNMa9MnfQ6a0lfU+TVTtoYmRgdHY3qCE4FK/OYRtOH2+2mtbU1J4uFIZ9XWlrKhgjxCbl3L1y6FE4pSxmOhL3e8IhTVxeytZXABz4AsaT+i4vYv/tdRCAQrin396NcvEjJxz7GmWcd49H//DLzFZVIJIt2O5W6xFFcjK6DQ1GoLCriro2t1De38Hd6kJPodG3cgK2shJC7CFFays/Gx7nt4kVsDz+MdvfdSfWjY5GrnXS2n70QAofDQXV1NRs3bjRH2qanp7ly5Qoul8s0+mSGW3DS1xahUIiJiQl27NgRy4mcE/h8Pubn5zlw4EBSLQADVjcJxohgY2MjmzdvXn3A9DSOr34V/H60u+5C378/8clsNpOfwL9xI1LXYWoKxelk7oUv5OEX3c2h3zxJ+cwMUkoCNdUUDw4S3LCB4ulpHD4ftp/8BHXFSSeywTtCkn4nLAmBXcILVIkGTIvwOGd6elDpIV3GMbvdTm1tLbW1tUgpTfbC7u5uFhYW8Pv9SCktsRcauJ6bQPPGSWuaxvnz57Hb7Rw8eJCuri7Lr00VIRu1sD179jA5OZmVck7sOfft28f4+HiU8cvnPx/N7Ub09CDr65EvfCH2v/1blB/+MHxAXx8uKQl86lPR99HZGXbQi4uwuIgyNobrc59jqLqKf3vLm7AHAtjVEL6iIooCARpcLu4ISZqRaAhOqJIGACGYLirCrYBDEQink7mQhjo6xtziIvovf4jt4YeRg4PoSeQZY5GrnXSuaUEzJVO5ng37WiPVdzg9PU1XVxdlZWXXxEEbu7Di4mJLDhqs7aQXFxdpb2+nqKgovopeKITtfe9DXLmCBOy/+AX+T30qaqebEEKgHT1qOu1GQHMq/PjNb+TE/3wT1eViY2k5LocDe1cXjs7OcAd5Tw8Lra0U33lnwlO3AB8ISnqFZIOEBQGvdSv0KoINuuRvgjoHsl/24iKbXpVY9sKLFy9SXl5ushc6HI6ogDvRc3c9B9x5ke42dqSGDGQwGEyb8zeR8RnNXEeOHKGoqIjp6emsnfTIyAhDQ0NmfW1iYiL6voRAPvvZyEOHwnqwigLDw1HnEIODq0+8cpzt3DkEIJeWEMvL9B85RPniEkU+H8qyDxVBDYLXFZXzMlWuMApHf64bpWQaQQmSZcVGUXUVTpuNo8Oj2B0ONFXF++CDXLrhBtPBJTMCyJ+dNISDukS1RysMSk6nE6/XmxFD0fvf/36+973v4XQ62bp1K//xH/9BZWXlquOEEP3AImF2SFVKeSztN3uGIVIr/uDBg1y+fPmanH9mZoajR49y5swZy69NtZOenJzkypUrHDx4kEuXLq06VvzqV4gf/xjlySfDrICKgvB6sZ08ae50477v0BDOf/xHdg0OYnvd6+DFLwagCHh7SOeDb38rp3duZ8fQKJU7tvMydwnFr3kNwm4HlwtRVIT9hz/kbH09QgiCwaCZ3o20x1LgwMol/4NTMKAIbMCEIvi8Q+HzgavrXi4brXJJZiKlpKqqypQDNgLu3t5efD4fFRUVVFdXU1VVFWX/13MT6LrvpOMJuqfD+Qvx092xs5hG2iQTUv5Irt5IkXvjnKuMf3QU5etfD9eiKyrQX/1q5M6d8OSTZnpZ37lz1Xvp+/Zh/9d/DdMmSAktLWiLi7QMDeMKBjl4+Qq9ra1QVMSfB3Sem+g2Jid52yc/yX8e2sum/ftYOnacrTML3Pmbp9gyOgY2GzabjarWVvbs2WPOeBpGYJCLxKaa1rJxzMp5rKTC4pGpeDwePv/5z3P69Gn+/M//nFe/+tXcc889lt/7jjvu4OMf/zh2u50PfOADfPzjH+cTn/hEosN/R0o5bfnkz2CoqkpHRwdut5tjx46ZExrpIJkUqpFtczqdpnxlNt3gBqSU9Pf3Mz09zbFjx3A6natt+oknUB58EAIBCAQQU1PIhoYwZe/8PKKjI2zjsY2oqor7938f+6lTNALy8cdZrqxEX5GI9QrYjEC7/XY6CYfabSGdm3bvDkvWirCjrayr49ixYywuLnLx4sWU9upBML/S6e2QK5K4Mfecq3Gla6knnYi9cGBgAJvNZo6/LS4u5mwn/f73v59/+Id/uAQEgR7gDVLKuZycPAOsm5OWUtLb24vH41nVZZ2uTmys8RlcwDU1NezevTvjWczIuUpVVWlvb6esrGxVg0rsYqE88gjC5wsTDPh8KI8+ivqud6HpOvbubrRNmwi9612r39DtRu7diz48HJ5pLi1FvfFGaufnuWN2kdP3voitTjd3BnQOJ7kF9zvfSdkPfsD7Vn72f/zjdN99NxV3Ph+9/TxKXx96UxPBt751FaOQQczQ19eH0+k0d9lFRUXr2jgWi0yjd5fLRVNTE3/zN3/Dr371K/7oj/6IqamptM5xZ0Ta8YYbbuCb3/xm2tdxvWFpaYn29nY2b94clSZOV+850ZiUz+fj3LlzbNy40dxlpYt4O2ljzBOI0q2OPVb09obT1MXF6EeOIM6dQzoc6K2tiOpqbBcvIgcGwn0eEdcuBgawr1DtAuGd92OPmU4aAClpungRhz/A5JY2KK0g9KY34fz7v0csL6Nv3Ejo9a8Hws+vy+Vi//79UVmiVfbqLEZFIAFVwLYYbep84duOd65EwXeigPvUqVP88R//MRUVFfz3f/8399xzT1YO+4477uAf/uEf9kkpVSHEJ4A/Az6Q8QmzxJqnuyG1oHu6D0/kztuoKe3YsYO62MYs0nPSxrGBQICzZ8/S2toat061yvj9/ugD/H6w2wn9yZ+gprg37eabET/8YdjQbTa0W2/F19JCQ3c3t1fV8HUh+HeH4NmazqtOncXx5S8jfD5Cz38+2stfHv48zp2LOqft7Fm4+260lhb8992HmJ5GVldDzEhJPGIGo6EjEAgghMBut1NVVZWxUebKoHNxnlAoxC233JIVDeFXvvIVfu/3fi/RnyXwiBBCAl+UUv5bxm+UZ4i00YmJCXp6eti/fz9lKwQ+xjHp7qTj2WdkT4nVZlIr5zaC+bq6ulXEKqtsurY2nN0SArZtQz18mOALXoD9wlX9BbG0BOPjUfz4srERvakJZSxCDC2iRn9Ah+f94EeoAwOgKBx6+iyH7n4h2h134Dt0CDEwgNyzByJSucZ1xjotw14vdnfjaKjh5ooy5ktKaLDbuSmGzTefnbTVcxkBd1NTE3/1V3/Fb37zGzo7O7nxxhuzctJ33nknUkrjE3sCeHnGJ8sB1nwnbUTc2bJ8RcLYeRukAwcPHkxYa0x3Jz03N0dXVxd79+6NW3c0jos8p9y/H/GTn5gsY/qKIpWRykn2EOo33kioqQkxMYG+eTM0NIDfz5Ki8EWHQmDFrr4tdLY+cD/PPnkSAFdnJ/6mJvSbb0bfsgVl9KoMqt7WdtUobbZwms4CioqKzJ2LpmlcuHCBhYUFTp06ZY5NGJJ3VpHLxrFsBTaEEAm/i9tvv53xGC5zgI9+9KO86EUvMv9tt9t5zWtek+gtbpZSjgoh6oFHhRCXpJS/zOqi8wgG573BORA7R5zJ9xxb6hoaGmJkZCTpfLVVRDpeYx3atm0b9fX1SY8FkLffjj4zg9LTg15aSuDee5GBAFLTEMZzqOurlahKSvD/4z/i/NjHCE1Pw4tfjH70KI5/+zew2Qg9+9nsv9zDRZcTp4Sbgir27m702lqoq0PGbDSklASFoF2EhT8iCX4j7fW8TTLp9+P1zOH1+Zjz+hktLjHJRPI13Z2pw/f7/ezYsYP3ve99qQ9OD28EvpHrk6aDNXXS4+PjXL58eVXEnS2EEIytRKqpSAfi8YInQjAYpLu722w6S/b+UVH34iJcvIjw+1Ff8hLkjTeir6T9NE2DkyexP/44wulEveceRMyYh9y8GbnyOwn8yGXn261NtNsEDVJSKUF4lxl1RdS/NA2lqwv95pvx/9M/4f7Lv4TRUbRnPYvg+98P0WLmacNms+F2u6mvr6eiosKM2js7O5OSE8Qil41j2ZwnVS3zxz/+cdK//+d//icPPfQQP/nJTxIuUFLK0ZX/TwohvgOcAK4LJ62qKk8//TTl5eUcOXIkZ4u0EXAbPSWqqkb1f2R7bl3Xzc7zAwcOJFyHVtm0oiBf9SpUKcMEKqEQmqoihoYQg4Ph4/fti8uLr91zD7577uHMmTPsr6yk+ItfNHm3Z/t66WxsQHU7UYEnbYJbk9zrkIA/3bON0WIb5RL+PKDxkjgVhRdqgl+6i1kuKmazrnNocTm8y14hE6moqEBV1ZzYY64bxzKdk05n92wlCBdC/AWgAv+V9gXlEGvqpIuKitJi7rECVVUZGRnB6XRy7NixlIuFlWYTY4cQDAY5ceJEUgcNMQbd2YntM58xjdD+rW/hu/VWREtLOILt6sLx1a8iVyTrlN5elv/qr1CKi3F+/evYTp1C374d9W1vA5uNCwqcRaFM1SiRMLmiaFVUXMyemdmrF2Gzmc1ocudOfP/zP1fvB2h3uyh1OXgekOlyakTMsWMTBhvYxMQE3d3dlJSUmGMTsRR/uWwcy8XCkMm1/PCHP+QTn/gEv/jFLxJ2lAohSgBFSrm48u87gb/N6mLzCDabjba2tpyrICmKQiAQ4OLFi9TW1rJ58+acBQBCCCYmJlhcXOTYsWNJ6ScVVUXG8I7LFQdt8Es7HA705z4XbXERXVHCfSQrG4DIRtWo8/b1RQljLAYCzDc3UeKZAwFjFZV0HzzIL+2CILBLSm6LcMJfKXIwZHMggXEBf+OyURrQuF2Ltusa4CUm45iAkhJKSkpMMpHJyUmmpqY4efKkaa/xOPKtIFc2nQ2Wl5ctj+JB6iBcCPH7wAuB58l15hxdUyddWVmJmobUYao0ijG6VVlZmXJ8yECqdLfRoVpSUkJlZaUlRxDppMWVKwhVNQeipM+Hra8P2doKgK2nB0XKcGQuJXi92AcHcXz727g//ekwQ5EQqI88gv9b32LB5UARYUahmzXJRQW265IX6Qo7/vDNaEJBBgJ0vfQlaLfczBYJkVesAx9xCn6xoRaH3c6vFcGHg5JM3Fui7yOWDczr9TIzM8OFCxeiiPbLy8vXvXHMQDZ29453vINAIMAdd9wBhJvHvvCFLyCE2AD8u5TybqAB+M7K52UH7pdS/jDjN80zGP0LuYbRwb179+64PSWZQtd1ZmZmsNvtKZnPlH/7N7Y98ABFxcWI3/s95Oteh5QSTdOiAlUIfw7KylSK4cANwQnjfhRFQQSD1D36KI7FRURfXzhTJgQum42u5z4X1e3CteRFb6hnWCjIFTM7haBWSvatLFl+wjatEi6PaxKGFEGXLi2Latjtdmpqapienmb//v1RHPlSSstKdAZyZdPZIJcjWD8M81l8AHiOlHI5JyfNAus+gpUIhjNNlOYyUlb79u3D5/PhXRFOT4VkzSw+n4+zZ8/S0tJCc3MzZ8+etbSYRzppuWsX0uWCQCD8u9JSpMG9C8gNG8wGFCEE0unE3taG8+GHr+rDShlu/vre92i594UoDgUpoQK4U5O8JSRxAvqhQ/j+5V94yA4dQlAsYRuSe9SrjvpxBU7awmq4AjhtEzyuSG7JYFTcSu0pkgKwtbUVVVXxeDyMjo5y6dIl7HY7brebUCiUVUYlWycdCAQyIvIHuHLlStzfr6S37175dy9wMNPreybAKoOX1e9qfHyc2dlZdu7cmZaDTvVcGtrudrudlpaW5Ndy8iS2734Xoeugqti+8Q1Chw6h7d6d0hlF9psYnOKGw3b99V/T9ItfYC8tDa9BU1OwezcNd93F9ppaugW4y8r4naDkEedVhjAb4Im4tecHVL7vFqgifMQ+PRxwByx+VgaM3W8sR36sEl1ZWRm1tbVUV1cn5CXIZbo7U2TKeRAP73jHOwDKCPeRADwhpXxrTk6eAfLWSRsKOvFmdQcGBpiYmDBTVsFgMO2O7VgYetWRHaRWm8wiHb/cto3Q+96H8t3vhruzX/EKiGiQk4cOob7oRSiPPQYOB9qLXxwmPIlNqdvt2HSdJsXGXRNTPBEK0hIIcpMGdkUxxzy6BHzBrjCuhB3xCU1njybZurJ2RperVrrrgQ4BlxWBAziqSeJwK61CJg0idrs9imi/r6/P7MCHsH50bW0tpSuLl1XEezbSgdfrTVnGKCB7GI1gyRZxKSVXrlxhYWGBpqamtFKuqYL5SDna5eXllEGF8HjCAXTE7wyHmo4jimTDsw0MoJ48iW1FWlbqOuru3QTe9z4UReF3gxpCURgUEBRQroNv5a2khI0RRnxrSONvBkf42e7tFBHuDrdJaEszMZTIlmOV6BYWFpiZmWFwcBBFUcy0eElJifn6fEl352onvRKE554mL0OsywiWFcQjNDE6jGPJ+tOZq47neMfGxujv71/VIGZ1p2AQ/ZspsZtuQtx8c8L71e+5Bz2GPCP0sY/hfPWrEXNzUFKCdvw43HUXExMT2Ccneeu+fShSQSccmRv3+6jbzphydef8pE1hIcI136zDw7rkNOHa9E5dslGHx+3CJOX/mV3wClWm5PfNtotTCGHOeTY3N5ui8YODgywtLVFeXm7WslNpymYbvV/PNIL5BCPYTvR9GvwDpaWlHDlyhJ6enow0peM5aUPb3ZCj7evrS92PcvQosqYGlpbC9lxfj0wh3GFichJx/jxy/36Tl19dWmLqS1+i0evFvaJcJaXEVlx8VcUL+K4iuWi3AYJaCW26RJWCPVKyJeZt9nh9vCQgaVdAl7BDQrpiu1azYobe+5YtWwgGgyZz3/LyskmkkquddDYlqOtZ0S5vd9KxjtcQi29qaqKlpWXVsZnspI0I3hghiV1I0t1JGzWrTB5Y/dZb8Xd1oXzrW4iiItTnPY8rU1P4/X4OHz68Ss7N+K9clzilJASwUruObJ+wAx8NSO6b8FBRVsa9xaWcF9GqORowC6weRIlGrslMDNH4xsZGy1F7JLK5loKTzh5WgthYTelIGD0lmzdvpqmpCUifETDR8aa2e8TolqW57dpaQh/9KPNf+QqalBS/+tWUOJ0o3/kOYmIizCB4112ruriVX/wC53veg5iaQm9sJPSZz+A7fJixz3yGRlXF1dwMAwNInw+5cyf6m95kZgz6pM5FGyua8zrTwLGgxnHij2sKIXACx7JgN87Elp1OpzmXHEmk4vV6aW9vj6IXzgTZ7MivZ3vOWycdadxGKnr37t1xm1XSoRE1jFrTNDo6OigqKuLw4cMJnYDV6G5ubo7a2trsHpTiYvTXvQ5d17lw4QJut/uq/GXMPRjGe5eu8xNdMKKArktuC+nUBlXUlRlgRVFwALcsLFHrdOMohnoJHVzdfTuInrdMhFzRgsbbVcVG7QabUH9/P16vN4r+MNUu2wquZ67ffEIiJz0zM8OlS5ei6ICTHZ8Iq+aZZVhb2u/3rxrdsjrZoTc1Ufb+9zM9PU3v9DSuL32J2pkZSktLKdY0lB//GP0Vr4h6nf1zn0NMT4MQKBMTyM98hjN//Mcc0XWKGxrQi4oQDQ3oGzagvfvdEHHPulCw2cL2GK5jS3Sho6maGfjbbLa01qNUyNaWI4lUPB4Pu3btYmZmxhS1qayspLa21nLzLWTHfZDLmnS+Ie+d9MjICIODg0lnldNNd4dCIU6ePJmSYjBVVG80hlRVVREMBrl8+TJ+v5/q6mrq6upSzgzHQygUor29nfr6ekvqQRsVhX9W4Vc2KJaCO3SQNpuZejeM3GhkAWgGbtAkV5RwPeuobu1BWEuBjUg2oViRDLvdTjAYZHl5maKiooyuaWlp6bqNvPMJsQF0vJ6SSGSzk1ZVlXPnzlFeXs7BgwfjBrfJ1onIDm6Hw2HS5YrLl/EHAni9XianprBPTyNHR6mtrb1aP48Y19J1ncXpafbt20dRZydMTUF5ObK8HP3w4SgHDbARWJQwpkAdgi1CcNTuxKno5jUZ9xgKhUx7zna6IZejbW632+TYjpWOtUp8lM09LS8vF5x0LpDOQ6EoCn19fWb9OdnuKR3D9nq9eDwejh49mpJiMFnkGjszGcnM5fF4GBsb49KlS5SWllJXV0dNTU3Kbmafz0d7ezttbW1xWZAgPH4hiU5X1wMvM9aeiKYywzH7/X7m5+dpbGwkFAqhKArbhGCHTG0Q/cB3HYJFwF1TyfYcpLvTXRxi6Q/9fj+nT5+OitoNKUqrkfj1nB7LJ0Q6RiNDJIRIOAaVDtmQcbyu6+ZkRmTqPBap7DlhuWrjRkrGxigpKUFKyfKGDYwFg7S3tyOlpLa2lo333ktZRwfS7ydkt1P8xjeilJai3Xsvtu9/H+bmkJs2IZ/73FXvfZ8NXAKKZVgy7Xe0sEKWYcfGMx0MBunt7aW+vj6qLyXRTHYq5JJxLBKx0rHLy8tm5iQUCiUkPsrWSV+vmbG83EkHg0EmJiaoqqpi//79KR8mq+nu8fFxenp6KC8vt8QBnEw1x3DQkTOTxrVEzgwvLi4yNTXF4OAgNpuN2tpa6urqVj1Qi4uLnD9/nj179kSl/yJxXsBJJTwjuUOH56TIfCmKgt/v5/z582zbto3KykozKtd1HVVVzZR4POOQwANOweLK/fWXFvNrh407kr9tUuSiycTtduN0Ojlw4ECUKEhvb+8qUZBEKDjp7GFlkTcyYkZPSWNjIy0tLQlfa7PZ8Mdy3yeBoijMz8/T39+flLrXODaePRs2IRYXcfzv/8LCAnL/flMEQz7rWWh2O2JsDFlRgeumm9hss7F582aCwSDT09NcPHoU92tfS3VnJ+7nPY8SIx1eW4u2Io4RD0HgihJeiI0ZkB4FZiV0K+AEbtVgQyDAuXPnaGlpobGxMflMdhK6WwO53EmnghXio5qamqwmNhKV0a4H5N1dGeM5VVVV1NXVWSYoSZXG6unpYX5+nsOHD3MhghQ/GeJF3olIDRK9vry8nPLycrZu3Yrf7zfnuwOBADU1NdTW1qKqKj09PRw8eDBhNLgAPLFizA7ChtykQTKp+aWlJTo6Oti9e7e5eEXOcRoGHpkWN2pfiqKsNJQJ8yEREjzK2u+k453DQDJRkGAwGLXLjly4rufIO59gs9lYXFyku7ubXbt2mburREg33e3z+ejr6+Po0aPpMQOyOth2fPGLKH194T+eP4/qdKLfdFP42KNHWRUTS0nRt75Fy9mzlI2PY5+epsjtJvDQQ3QHgwRuvZW6urrotHgMgsCEBF2Ey1ACmAIGbeFsWQB4UA9y9OxZdm/bZn5+yWayIeywDTuO57BzOTaVznkSER+dP3+eUCiEEIKFhQXLRCq/DcirdLehpnPw4EFmZmayGqsyYDSIud1ujhw5kpbGbex5k6bELMDtdkelxY1Gi4WFBerq6lhcXMTpdMaNCL1EM4kpgE/A6pUjjLm5OXP8JF6txjBeu91uGnnkZ2MY+Sa7nTHbymKApE2PoTRLE7nYSSdz9LGiIJG1saKiInPEK9Od9F//9V/zpS99ySTb+NjHPsbdd9+96jghxPOBTxNea/9dSvl3ab/ZdYClpSXm5uY4fvy4paDIalbMoO71+Xzs2bPH0sx77GRHVDZM08JylMZzpSiIy5dhxUlHYWwM2//8D8qvfoWto4PloiKqZ2ZQKiuR+/bhdLnYNzTE3NatTE1NcW5Flc7IohnTCsvAR+0wq4Q5uYclvFKD7RLOr7yV3+9neGKCl+zZTU1Z/EGryJlsh8MRNWmSKADPtcBGJoglPpqenja78g0iFcNek5UKTbbH69Sp58VO2tjpGsbscDiYm5vL2kn7/X7Onj1Lc3Oz2YSVrgqW8QCYKTELqSSr12w45ec85zl4vV6mpqbMxigj2jQWn3qgVMLyynMogE0JbGNqaore3l4OHz5sSTko0sgB08h1XedVvhA/cigsCdg2OcPhksp1d9JWzxFZG5NSmrWxBx54gM997nPs3buXAwcOcOONN6Z1Te9+97uTqu0IIWzAvwJ3AMPASSHEg1LKi5bf5BmAZIui0WXt9XppbW21nLWw0gSqaRrt7e0UFxfT0NBgeXE27DluucpmQ9bUhMlMwjcQnpeOA9u3v40yPQ3j44S8XlyAzeEIp8nNg2ymA2prazPT4r29vXi9XqqqqriwcQPjVWVUIqiU4VHIG/WwnXcAvuVlJicn2dXUxEabdXa8eLvs2AA8XZ1vK1gGPucQ9CuCFl3ytpAkHRklg/1s69atZqlwZmaG4eFhhBAm8VG8kczr1UHDOjjp2JSTwZVdVFTE0aNHzQ/bZrNZbiCJ9wUtLCzQ0dGxKsWWzhhD5LhWvPpzptB1nc7OTmw2GwcOHIgaP9q2bRt+v5+pqSk6OzsJBoPU1NRQV1fHPRUVtCsCjTCBQbyxqdHRUUZGRjhy5EjGtJuRRl6r67xK11mYX6DTM4feqpvNZ5kELLmI4DOpXQkhKFkRGfiDP/gDMxh64IEHeNaznpVrWsMTwJUValCEEA8ALwKuKyedCMaEQkVFBa2trQRjhCqSIVUQbQTeRrbk8uXLGY1fripXCYH6xjdiv/9+WFxE7tqFHidDAiAWFgiFQvh0ncoVO5CVlRBYIed0u9Fe+tKo1zidTrNbXNd1ZmdnWZqbY0oP4rDZcLndOFwu7Ci0AofGp3hyYZZbWjfzHJsz47g4XgCuqipTU1OUlpYSDAYRQmCz2TKygUh7/qJD8At7+N8DK2WxPw1Z32VHBt+RpUIjyDGmO2JHMiPvM1cQQrwP+CRQJ6WczunJ08S67qQNMoPW1lY2bIgmpkx3XjIShq704cOHV0Xw6TgIIUTOHbTBsFRdXb1KaN6A2+1m06ZNiE2bGJIaS55ZgiMjLHR2UlZWRl1dHdU1NRCRFpdS0t/fz9zcHEeOHMmJtB+EH/6FhQW6u7s5ePAgLpcrrdpXLPJFGi8UCnHnnXdy1113pf3az372s3z1q1/l2LFjfOpTn4rXhNgMRGqDDgPPyvxqnzkwdJq3bt1KQ0MD4+PjadWYk6W75+fnTfENowch3czY4uJi4lLH1q2oH/pQyvMsNjSwePkydTfcACdPIgF9925Cf/iHCF0Pi2ckUWQyiHpeTQ2DdkmXHm6s2zIwxPzoJGfsdpyhEH98+DAOW+4UAw10d3dTVFRES0tLVErcsOl0AvDI2vZgTL/KkJKkHpfgXIneM5ZIxSA+6u/v5+/+7u/QNI3u7m62b9+e9To9FJb1vQMYzOpEOcK6OelEZAYG0pl9NiClpLe3l9nZ2awlMaWUuN1ukxihrq6O8vLyrB4Av99Pe3u72aGZDB3A9+wgsKE31HJPbS036GFWLiMt7nA4zPGuoaEhVFXl4MGDOY0qZ2ZmuHz5MocOHTJT5+nUvmKxlrPWyZCsJp1Ma/Ztb3sbH/rQhxBC8KEPfYj3vve9fOUrX4k9NN4Nrqvc3VpgampqlV58usF2IrtPFHhbddKaplFSUkJtbS1dXV2EQiFqamqor69Pq0lpfHycwd27OVJTg21pieDLXoa88Uazlp3Ol+wA/lwVnBN2XK5Sdm8o4fKSn7m5OdxuN6dOnTIbaKuqqrJ+5o3+nMrKSjZHaNin6ktJFoBH9ue06ZLLylXe8zY9vUfeqka8oihUVlZSWVnJ1q1b+cAHPsB73vMePvCBD/Ca17yGl7/85Wm9byze/e53A/wp8N2sTpQjrIuTHhgYYHx8PKmma7rGLaWkvb0dp9PJkSNHsh701zSNqqoqjh8/HsUvXVlZGd7JVlen9R5LS0ucP3+enTt3Whr/Omm7utIrhEevDsnotLjP52NycpKTJ08CsGHDBhYXF81gYhEYFOHXb5XhcY50MDk5aXKax+tOTVX7UlV1lcPOl510su7uVFqzBt785jfzwhe+MN6fhokm6N8IjKZ5iXkPw7EZwikzMzMcO3Ys6lnJxEnHNmsmC7ytEg4ZbFYtLS2mprJBQbu4uJjSrg0SFo/Hw5EV3oYsWDlN2IAjMroEduLECZPCdHZ2lqmpKbq7uykuLk7ZLZ4IBtFLQ0NDXAKnZH0pyXbZkbb4llBYkatvpSb9ljRS3ca5MskA1tTU0NbWxne+8520XxuLBx98kObmZqSU5/Klzr3mTvrixYuoqppS0zUdqs9AIMDy8jKbNm1axeudLmI7uBVFMVVhjJlcY8dg1Wg8Hg/d3d3s27fPMiuOQlitagpYEGAX4cj7uAZ7V45xOBzMzMywefNmmpubzSaLhYUF7BUV9GxqorSsAsWmMCbhNt16z9fo6Cijo6McPnzYUkYimZFHpsdz5aSzTednylA0NjZmkmV85zvfYd++ffEOOwlsF0K0ASPAK4FXZ361+QtD/9npdHL06NFV3226TjrS7iPPnSjwTuakk/EZ2O12y3ZtNMFpmsahQ4dyXv80drgVFRVs3rz5avCjKHyjvobhxhoOaJJ7FrxMJ+kWT4RgMGjOWDckScNHIjYAj/zPyIYZWQ/jvV3AO0KSTJNGmc46e73etMYpk2XKPvaxj/HII4+kfQ3XEmvupFtbWy1ROVpNdxsNYi6XyxKNZjKk6uCOnMk1ZvympqY4e/YsiqKYHdmRD8z4+DiDg4McPnw4Lf3iwxr8txPmBMwKOKKBX4TpPxs0KF8xvI0bN5pOI1Ji7szSIkvLS4xNTGK32ykrr2C4pJQWV+pu78HBQWZmZjh8+HDGzjCekXu9Xnw+H7qeXfOZ1bRYMmQ6gvWnf/qnnD17FiEEmzdv5otf/CIAQogNhEet7pZSqkKIdwA/IrxZ+oqU0tpw/jMIPp+PU6dOJaXXzTTdHQgEOHv2bFxBnUgYfSOxSOag471nPLs2nKGRGt+zZ0/Ou4gNreumpiaam5uj/va3dvhvezij9r82ga+ilDfEdIv39PSwvLycMC1ukMhs3bqV2trajK4x2Uz28vIyQogoYqRMkWkAn64CVqJMWUdHB319fRw8eJCBgYF+whmwp4UQJ6SUq736GmHNnXRpaamlHbIV456cnOTKlSscOnSIjo6OjHdY6Ri0gcgZv7a2NgKBAFNTU1FEJaqq4vP5OHLkSNoR4rAC22Q4b1oETCoQ0sAhYDzg46nzF2DXDoLlFbglRCbQhRDUlZXTWFnOBiAQCOKZn6e/s5PxYMjkFo+tsRupRa/Xm9PatsF81tnZyd69e3G73WnXviKRq3R3Jjvpr33ta3F/L6UcBe6O+Pn7wPczvb5nAux2O7t27UrK8pVORgyu0oKeOnWKnTt3pnQsxsxvJNIhHIpFpF03Nzdz5swZKioqWF5e5sknnzQnLSoqKrJ22IYD3bJlizl3H4mTSnRzw5MKvGFlSYzXLR6bFi8pKaGzs9Nyic0KIjNmgUCAnp4edu3aZQZLqqqaf083AM+Ucczr9eaEPXD//v1MTk4aP24WQvQDx37rurutPtjJnHRkDcyoUxlpL6tfsmHAmTjoeHC5XOaOwujgXl5eRlEUurq6zAYvy9dHuIa8QYbnDzUR/p3m99HbcR7Pvj0Ul5SwRJix6G4dIvfIG4EJHYYFKE4nN9fUsaumzqzFDQ0Nsbi4SEVFBbW1tVRXV9PT04OmaZaoWNOBIWW3d+9eysvDhAzp1r4ikQsn7fP5CoxjWcLpdCZ10JD+Tnpqagqfz8dNN91kKYjKNeGQAa/XS0dHB9u3bzdHOA0CopGRETo7OykvL0/brg3EYwOMRZ0Mc+cbSMTVZnSLG3wAXq/XvMaSkhLm5uZwOBwp0+LpwKAxjiRLstqXkgiZ2nWunHS+Ii/ITOIhkXHrus758+ex2+1RNTDjeCv108hZ6Vw46EgYdbTKykoOHz4MhEdHJicn6e3txe12m/WuZOnvG3U4rQACWiXUaLBhcYmSzks07d2Lv+Sqg1EFTAKRSUEBHJNwYIUgzPiiI2txUkrz2i5evIjdbqe1tZVAIGCJBMUK4hlzJJI1n0XWviKNPBfp7uuZ6zefYLVsZYwQTk9PU1JSYr13I8JJ54pwyGDr27dvn9mlDuE1pr6+nvr6etN2DOIgl8tFfX19SruOPH8imzDwwRB8SISbP/dK+BMLtBHGjtbj8XDDDTfgcDgspcXTwfz8PBcvXlxFY2y1LyXRTHamTvpa8fBLKTfn/KQZIG9XqXgNIcFgkDNnztDY2Ehra2vK45Od20ixZpISSwSjQaO5uTlq7tsYFwDMeld7ezuQuPmjBni3ChcUKJNQNzFJ/0q9ZNbt5hJXm8AkEJ8wMHlHt0EYMDAwQGtrK/X19czMzHDhwoWwcdXX46qtZVtJCWUZfD4LCwtcuHCBAwcOWDKiSCOPrH1FGrmxCGXbOJYrXd4CksPKTlrXdS5eDPO8HD16lCeeeMLy+Q1bzhWfwcTEBP39/SnZ+oQQpl1v377dtOuOjg5TGSueXafDBrgb+GYwrHxn1XUZTaqHDh0y2QoTpcWNkbR0usXn5ua4dOlS1PkTIV5fSrKZ7Ezt+noXy8lbJx1raIuLi3R0dLBjx464dap0nbSqqtjt9pzVXZeXl2lvb49Kj8WDwXoVqaBjSC7G6lCXE95RDw8PMzQ+brKINQF7degS4R3zAR0qM7hmTdM4d+4cdXV1ZtNdSUkJLS0tnNFC/GbZy9LiHA9PjHGbqrGzOsyja8WQDGNOJhqSDMmi8vn5eVPDO5Pa1/XO9btWsNq7kQzBYJCzZ89SX1+fkNwnGQy7z9ZBSynNhsmjR4+mnWWJZ9c9PT34fD5z9+rz+RgdHU2bDdDqk22MTCZqUo2XFk/GLR6LyAAg3Uyb4bCTzWRnSl7l9Xrj1vSvF+RtTToSRoPYgQMHEqaHrNa+NE2jsrKS06dPm04xViEpXSRKj6VCZPNHrA61wSy2uLiI1+uN6rSeJ6yOs13CPhmtLW0VoVDIpFeMp7/b7XRQ6QzvFKSULC4sMTs6Rk9PDy6Xy+xkj7cYzM7O0tXVlZExJ4IRcV+5cgW73W4yD2VS+yogP2Cwk23fvj2jRVZKicvlYm5uznT0iZ7JVOfJ5YhVPLu+fPkyXq+X2tpaPB4PNTU1KQOBJeAXCviAXTrEHfZbgdWRyTnCPS51MY2v8QKL2tpaMy1uiAGlO6USD/EC8Lm5OZaXl6PooK1OfxR20usIo0Fsenp6FUlCLNIhNWhra2Pz5s14PB7Gx8fp6urKuAlkcnKSvr4+S+mfZIjVoZ6fn+fSpUv4/X7Ky8sZGxujpraW/y5x89+2cHR9QoM+Cf8njflnCM+Vnzt3jra2toSLow6cEzApoFwKXlJWxo4d4QBkeXmZqakpzp8/j6ZpZsdrWVkZHo8nZ8YcCSklV65cQVVVdu/eHRXsrVXtq4DVSIcLPxKGZOuBAwfiBrapmOmMnZjT6eTEiRP4fL6odLNhS6kWb6OHpLS0lJ07d+Y8u6IoCh6Ph9LSUo4dO8bS0tIqxsC6urq4wew3bDCzcjmXFXCq8aVpBwcHmZ6eTjkyeWnlPDYBDgm36OHJEUjeLW632wkEAjm3aQNerzcqqLfSlxKJdEewnmnIWyet6zp+vx+v1xuXJCEW6ZIaCCHMekxsE4jb7TabQJIFBkNDQ0xOTmYlZpHoegcHB6mrq2PLli3mAvT1wT6+trEJf3ERDrudX9hs1GkwTbiGHWuey4Sj8CquOnGfz8e5c+fYsWOHyX8cD7PAEyvBgAC2SLhtJVFRXFxMa2srra2thEIhZmZmGBgYYG5uDl3X2bFjR06bsgxZQk3TzHGPSKRb+ypoSa8vUjEOpprUkFKaoz7G9x75TAaDQZOYxO/3m/SfsSOHRg/Jhg0bVs0o5wK6rnPhwgXcbrc5Yx3LGDg1NWX2gBjXWVpail8IxsTVnhIb0KfAjoglztjELC4upswA6EC3EiZFAggJuCJgf5z4KjItPj4+Tn9/P42NjWbfQKK0+BBwWYQd/wmLGT6jsTS2LJaqLyXS5gs76RzDSqRq1KkURWHPnj2Wdj2J0t1WRqziNYFMTk5y7ty58MxxXR319fXmTtlwGkZ0mctdmUHfV19fb9aJjQWoygbVis64puEPBFjSNJ72BQg53VQUF9OCwnNk2Kl2A+dXqEVLJTxHh9DKWMnu3bvj8qVHYglolmHWsyJgUCGspRcDh8NBY2Oj6fy2bNnC7OwsAwMDljvZkyGVg46FldrXwsLCNdkRFJAYhkTkpUuXUjIOGgt0PCdtpUHM6XTS3NxMc3OzOTYVOXJYX1+Py+XiwoULKXtIMoUxhllbW5uQjMUQuWhpaTGD3f7+fpaWlqioqoK2Tcji4nC2AqiIcKiGXYRCIVNJLxVi/XGq/MfY2BgjIyMcPXrU3ITEkqgY8pFLVVU85Lz6fY7o8PIULUKJHLSBRH0phk0bgdr8/HzBSa8lIutUPT09actKRiJTUoOSkhLa2tqiSEo6OztN5qH5+XnKysrYt29fTtNjRhq6tbU1Ln3fTg2qbArLDoVlh4NiXVIjBcG5BQbGxxhzuVFcbk6UV9Lhcphf7rKA095FaE88ChWLShGm+TNcWXWSr2FsbIzh4WEzo2Ck0CM7XnVdNyPw0tJSa4tKmg46FomM/Bvf+AYzMzNpnauA+LCS7lYUhUAgwPnz56murqatrS0lA1jsOGWmfAaRY1NG7XN4eJipqSmqqqoIhUKEQqGcZsKMTYYVIR0DRrDb2NhopptvGBnjUbsNvcjFfqebI8Vl4HAgpTRHJq2yoClAmwzLOikChAz/nAijo6OMjY1x6NChqKxYorT4TybHGa2pCo/PlZQybLcR0K+uH7FYXFzkwoULaTWWxhvXnJyc5Kc//SlvectbLJ3jmYi8ctJGispoEOvv77fcln+tSA0iSUp8Ph9nzpzBZrMxMzODruvU19dn3XgGV7vDk6Wh9wBvUeHxFWKTuzTByeJSHMWlICU+v5+5qWlO95yhp6GG6rJyKioqCAaDLPT28bI0DOKVKszaoU9Ag4TfV+MfZxjz4cOHV6W4IzteQ6EQ09PT9PX14fV6LQkaZOOg40FRFO677z4ee+wxfvOb32R9vgKs4/Tp02zbts0Sd3Q8W85FB7cx1WGQpaiqyuTkJAMDAynrw1Zhdcoj1XXW1NRwe00Nz5PSrGOf7bpiMrJVV1ezY8eOtD6LAxLqZbgE1gAkWgmGh4eZnJzk0KFDSdfeyLT4LJKAGmTJu8TI6AhCwkhIp762dlVa3HDQBw4cyLjsZDSzvepVr+LLX/4yz372szM6zzMBIkUUnPNhUinlKhF4Q2HGeDCMOvDTTz/N7t27LTVkDQ4OIoRg06ZNOdeAhnAtt729nba2NjMqn52dZXJykrm5ObMbu7a2Nu1ZP2OeOJKRKxWWgCcE/EYJj18ZQ2nP06Ae+EXQT7d3iVmPhys2wR53CS8sKWVrqXVZvlQYGhpiamqKgwcPpnXPkYIGs7OzFBUVmbtsQ9Ag1w4a4Otf/zr33XcfDz300LVIjz0T5rlybs+hUChpw6bH4+Hpp5/mwIED1NfXWzpne3s7W7ZsobS0NGcOGsJrxNTUFAcOHFi1czbqw1NTU2iaFtV4ZvU9jfRtOnacDjRN48yZMzidTjRNIxgMmk2b2croGhgcHMTj8bB///60bFoDvquEy2JOCc8OBKmenDYZ5IxucbvdzsWLFy1zJyTC3NwcL3vZy/jABz7Ai1/84ozPkwR5Y8/r7qQNIgMpJXv37o3aVZ09e5Zt27ZZSs8ODw+jqiqbNm3KuYM2nOiePXvi1nKlvKrzPD09bbIPGU4nGQy95nSiSh24zwZLImwco8BNWrhZw9inSODk9CRf0UKMbWhEqCoO7zKv6e5lZ1FxRnKbkRgYGGB2dpYDBw5klUUw5jWnp8MGbZQmXC4X+/bty1m9/9vf/jb/9m//xsMPP5zWmFwayBujToKc27OqqglHH4eHhxkeHsbpdLJjxw7LLGLnz59n06ZNlJeXZ8zBHQkpJd3d3YRCIUs9Lkbd1XAwVvi6jRnibHaHyWAIcRipZsCk+J2amjLr7YZdZ0IK0tfXx8LCQpjDWlH4ji1MNfxaLazAZ+k6CadnIz8lXdfxeDyMjo6aZYampiZqamrSltyEcDD0spe9jHe+85383u/9Xtqvt4i8sed1ddJGd2VtbW2URJuBjo4OWltbLUWlo6Oj+Hw+WlpacuqgDbKRdIzPqMVOTU0BmI1nsa83FLIOHjyYViPTNHC/PbpWcUSDGyK+reHhYYYmJ/mnE4dRlKufxZ2qzounw7tYj8dDSUmJmQGwWpczOkpz6UQBs7HI6/XicDhyRmP40EMP8c///M88/PDDORMaiIO8MeokWBMnbcwd+/1+9u/fT2dnJy0tLZZ3lxcvXqSxsdEMprJ5xowRq5KSErZu3Zr2umA0nk1NTbGwsBDXEU5MTDAwMJC2HVuF0auyefPmhNkIKaWZnfJ4PBQVFVnWnjaEdZaXl9m7dy+TisJLXNCphB+YF2jwX8HM+BgMRNIDSymZnp5meno6asrGStbC6/Xyile8gje+8Y287nWvy+KKUiJv7HndatJGg9i2bdsSPnhWCUqklBQVFZkdhw0NDVkt6gZGRkZMhqB0Ir7IWmykOpaRnqqvr2d2dpaZmZmMFLLKAZvEfIx0wh3cBvr7+5mbm+PwwYM4FBHVlO0Q0bJ8Rr3rzJkzCeU2DRjG7PP5romDvnz5MhCmhhQiN6L3jzzyCJ/61Kf4/ve/fy0ddAErMKYTysvLOXjwYBTlo1UIIczmzGyeMWMT0NTUlFBKMxVi+brn5uZMcqXi4mJsNlvGSndWYHVkUghBVVWV+YzHsoklmhs3+AeCwaDZCPttW9hBQ3iJ+YENnhJwY4Yh3tLSEufPn49KcZeVlZmNufHY2eL1+fh8Pl71qlfx2te+9lo76LzCmu+kIez8khEZGOjq6qKmpiapXF1kg1ikYMTs7CxlZWXU19enTVBiOKOlpSX27duXNU+0AVVVmZ6epre3l0AgQGNjI/X19RkFFF3AL23h9NIOHW6XVw0uEAiYab3v2MKkCJKwotaHQ9GylpHw+/1mmi8QCJh1YmMHdOXKFUKh0CoykWxhpQYdSWM4PR1WjktFY/jzn/+cD3/4w3z/+9+3XA/NAnkTeSfBNd1J+3w+zp49y+bNm6NY7KzYMVxtEFtaWmJwcJD5+XnKy8tNG07HRowGrm3btmWso5wMuq5z6dIl5ubmsNls2O12s8SVK5Y9Qz0uUZnNKoy58ampqVX0w5cvX0bX9Si7+7IN3uO8+kDbgF/4w+yG6cJQ+7JSg9Y0jdnZWaanp5mdnTWzfEZw8upXv5p7772Xt73tbWtB6Zs39rzmTlrTNE6dOsXu3btTpoauXLliGmnci4tDahD5t4WFBSYnJ5mZmTEJSurq6pKmdXVdp7OzE5vNlnMGIsOwFUVh+/btUc1TpaWl5mKUSURupIqFEKuuewCYXlHSSbR8+LhKfCKIrnctLCwA4bnO/fv3rylRSSJE1g3jpcV//etf88EPfpCHH344Lu3pNUDeGHUSXBN7VlWV2dlZLl68yN69e1dJL165coWysrKknd3xGsQid65GacYgGUr2DBoqTdeqgSvSjg1bi208q62tpb6+PmN5SKMPxurIpIFZ4GcKLIpwJ/fz9GiRHYOmdGpqisnJSZxOJ1u3bo1qeA0Cr3HCI7ZwqvX/C8H/TTDdkQzpOOhYRGb5PvOZz/Doo4+yb98+PvnJT7Jr1670LyZ95I09r8tOOhgMWpp/7uvrw+12x11k0+3gNr7wqakpM4UVG/UaBAQ1NTVmbTtX0DSNjo4OKioqVtXfpZQsLi4yOTlpNp4l48aOhcFsVFRUZNbddMIzkSVAKlbkswJ+ZQunzRt0eGmEYRszmZqm4Xa78Xg8lhnZUsFo6ImN5NNFZFr89OnTfPWrX2VoaIgHH3yQAwcOZHx9aSJvjDoJromTHhwcZGBgICE1bl9fHy6XK0oZLuqiLHRwG4v2xMQEMzMzOJ3OuM2ZBk3vgQMHsqLpTYRkdmzAGDecnJxkeXnZbDyrrKy09Iwb3PeZNKF9R4HZiLfYqsNzYr51w6YdDgf19fVMT0+bn6mx7thdLp4QUEZ4dCtdZOOgI6GqKm984xvZsWMH27ZtY3Z2lve+970Zny8N5I0957WTHhgYwGazRdWTcjGSYUS9k5OTJs+vkfpJh4DAKozOzMbGRku1MYMb2+h2TsZDrGka7e3tVFdXm/KdQeABG0ytzFMf11YbqgEV+IItTHBg4LAWrj8Znfdut9t0/lJKlpeXzYACEte7ksFw0FLKnGYsTp06xfvf/35uvfVWnnzySR566KGsUoVpIG+MOglybs/Dw8MMDQ1x4MCBhLvbyPHIVReUIeFQZHOmEIL6+npCoRBzc3NxR6xyAcOOm5qaLNOIRu5cI9P3iTqwjfrswYMHU6bNI9pSTHxtpQRmoEHCPRETckZAX1xczJYtW6I+b2PdmZ6eNrMB6ZAPGciVg9Y0jbe+9a1s376dv/qrv1pr1bq8see8dtLDw8NommY6n1zOTEZey/DwMP39/bhcLrNOnO6DmQh+v98Us8ikLmrUkyYnJwkEAlE8xIbUZGNjY9Si8YSA30TYvwq8TYV4STM/8AV7dEpsnwa3aDrnz583GzxSXV9kvau+vj7puMq1ctAdHR28+c1v5pvf/CY7dsSTIrimyBujToJrUpNWVTXpd2iMR27evDn6YpKUq9KBz+fj4sWLLC0tmV3NRqo5V8jWjoGonpnIDmyjBDcxMWFOeyTLUM0A/+gIEw016fDHKrSu/O0RBYYjGkqP6nB45VvXdZ2Ojg7Ky8uT2jRczQZMTU3h9XotKwbmykHrus473/lOGhoa+PjHP74esrJ5Y8/r4qRTESAYGBsbw+fzsWXLlmvioOHqfOO+fftwu91mmsp4MA1GsUzez7vClb1z586cdBYb4yCTk5MsLCwQCoVobm5my5YtUYbzmICnIpx0CHizmrhh7EEFhpTwUykkvDSkM9beTlVVlRkgWb2+2F1DrLLYtXLQnZ2dvOENb+CBBx5gz549OTlnmsgbo06CnNuzruumtGAiRNqxgVwRDmmaZu4Mt27diqqqZlDr9/ujmh8zfR/Djnft2rWq3p4pIhshp6amzM/w4MGDKWvQ/2SHxyLse7d2tWasAk8KWBDQJOHQyjduZNyMUl46iCwnGf0zhl1HZixy6aDf97734Xa7+cd//Mf1UqzLG3vOayc9OTnJ/Pw827ZtywmpQSzGxsYYGhqKO9+o67rZODU/P28S81slADGaV9Jt/LACv9/P2bNnaWhoIBAImJ2QRp3Ya7fzXzYIiHA03bZSZ04EHWgX4V31ZlVjbEUYIF560ioilcVmZmbMOvvCwkJUw00ucPnyZV73utdx3333rWUNOhZ5Y9RJsC5O2rDj7du35zTYDgaDtLe3JywjaZpmBt1LS0tUVVWZ0xRW3/da2rGB/v5+ZmZmqK2tZWZmhlAoZDaexcvofdgOFyOcdKMOn03yFRgZt7q6uqxsGq72zxh2bUjslpSU0N3dnfXnpOs6f/EXf0EwGORf//Vf11NSNm/sOa+dtDHwvnXrViC7lFgkpJTmLLGVbuXYLtNUndgGAcrBgwdz3rxijJZERvVGU41RJ3Y4HBQ1NDDbUEep3cl+rD1xmqZx9uzZVenzXMDr9XLx4kV8Pp+pjpUu7WI89Pf386pXvYr/+I//4MiRIzm84rSRN0adBOvipI1gd+fOnTlz0IYdbN26NaEmeux1ejweM2BIVRuGq/Xha9WEJqU054Mj2RZTpZq/aYOv20Cs9JzcocFbE3RfG3PrTU1NCRv3soHf72d4eJjBwUGKiorMZr6ysvTph6WU/M3f/A3T09N86Utfytnoa4bIG3vOayft8Xi4dOkSW7ZsSXtOMhGMUSUpJbt27Ur7nLGd2LGdzoYiVKq6UiYwWHv27duXdL7c5/MxOTnJ1NQUuq5bqtGpqsrZs2dpbm7O+chSbIo7chEy5O6s1LtiMTw8zO/+7u/yxS9+kRtuuCGn15wB8saok2BNuPhjMTc3x8jICLt27cqJg852xMrI8kxMTCQc7RodHWVkZOSa2LFxDV1dXeY6lOjziBdc1NbV8WR9Db12GxskvFy7qhcfCaPR7VrYtAFjlnv//v243e4omtJUIjqRkFLyd3/3d/T29vLVr351vR005JE9r4uTTsb3C1cbxDRNM1OmHo8nY3ISA8b4hNE4kYt0q6E9PTU1RTAYRFEUDh48mHMBh7m5OS5dusT+/fvTOrcxT2zU6OLxEIdCIVNaz4pKUTpIVYM2CAz+//bOPS6qOv//rw8MmAQCKowCFV5S8QJ41zJS0byhDGB4ac21Na3NQDf9pbmZa2llZrbqxmY/Uit3c0AEZbylYmIqeUFEURNF5DYDKCJ3Zubz/QPP7DDMfc6BA5zn4zEPYeZwzmeE17w/5/N5v1/v4uJilJWVmV0vXlhYiJkzZ+Lrr7/mSwcc3ojaCC0SpMvLy3Hjxg0MGDAAHTp0sEl3xcXFmuxnNu5udVehHB0dNd2yTHWBshZ9VRPmjlV7C8lYKSSXmmbQDtC6S9z6muhoJ8npvq8tW7YgPT0de/bs4SQz3wp4o2feBWlDe1a65iROTk5mGRswMBaB3t7erC/7MIYc1dXVcHNz05QwsJVlyjThsPWDSZ8Psbu7O3Jzc9GzZ0+zlg0twdIkMe1VitLSUoPtAxUKBcLDw/HFF18gODiY1THbAG9EbYRmD9KUUtTX12s6pjHlUp6enhY7c92/fx9yuRwBAQGcfJBTSnHt2jVUVlZq7EyZ5Vu2lruZGwU3N7cm2e6WwtwgMB7YzOeNvb090tPT0aNHD9Y1rX1tQwFaF123QGasXbt2hZOTE2JiYnD69Gns3buXk1ULK+GNnnkVpM1NKtGd/Wp3ndInXiY705Yer4ZgZsWOjo54/vnnNWPWvYNlEkEs3atRKBTIyclp1MKTrXEXFxfjxo0bsLe312RiW9JowxhsZHHrujjV1taiuroan3zyCT755BNMnjzZ5nGyCG9EbQRO9FxbW6v3eX0Z3DU1NU22YsRisdEgyNjdcuEZz8DUDz/11FPo3bs3CCGoqanRZIprt6+0NjGK2R8Wi8VWe4kbgukRUFRUhEePHsHT0xPPPfecVXvDprAkQBsb64kTJ/DFF18AAGJjY/HSSy+1ZKKYLrzRc4sEacZKsNGFrDQ1ABovOTMeup6ennB0dERZWRmysrJM7uNa+z4ynpQqGZsV62aZMnuwprJMCwoKUFBQwMmdA5Mh3qdPH7i7u2smPUzGpi0+xFyUWdXX1+Po0aNYu3YtqqqqMH36dGzZskUQtWU0S5A2d7JdV1cHhUIBhUIBpVKpd+VJrW6o1+/YsaMmeLIN4zTYtWtXg+VJ9fX1jUq7tP0KzBkTs5L3zDPPsG6WxMBoulevXlCpVCguLm6U1W5pzoc+bA3Q2uzevRtSqRSLFy/GL7/8gn/+85+s+Z6zAG/0zIsgzZapAdBw9yWXy1FcXKwxWvD392fddcra5XNDWaa6iXG5ubkoLS2Fv78/6/tiTGcdQ3WftvgQc1UHXV5ejoiICCxduhShoaG4fPkyRo4cycq5WYI3ojYC5+ZE1pZY6QZBJuEoOzsbYrHY5tIhY2O3NHgaKu0yFAQZIxTGI5sLDGmaqXFWKBQoKyuDi4uLZsXM0s8VNgP0zz//jF27diE5OZn1/B2W4I2eWzxIs2VqoEtubi7kcjk8PDxQWlpq9tKaOTCCsLXDjrYDUWlpqabrS2VlJaqqqjhZ2rO0sw7z4VlcXIzq6mqjjmJcBeiKigpERkbizTffxGuvvcbKOTmAN6I2AqdBmq0aaKVSiYKCAmRnZ8PBwQFisdiiu1ZzYXRsyzYYEwTlcrne0i6mVIwtQyN9MNfw8/Mzqmkmr4fZG9beJjS2lVYMYL+yFrl5eZjlIcbAp20L0AkJCYiJiYFMJmN9dZNFeKPnFgnSarUadXV1nDiIMUlctbW1jWoPdZfWtM0CLIFx1fHz82PNfYgZ9+PHj5GVlYXq6mqNeYopAVkCM3Zrl/4ZRzHG8Uz7A8nOzo6TAF1VVYXIyEjMmzcPCxYsYOWcHMEbURuBsyDNVGOwYTjEdIDq378/nJ2dUVpaCrlcrtkqEovFRm1nzYEpZ2SzU5bupLtDhw6adrfGekHbAjPptkbT2o5nADTbDdpNPaoBrEQd7pSXw83VDZ1EIqypB6zNF09OTsbmzZtbQ3933ui5xe6ka2trWQ/QjEWgqf0rpk5XLpdrkrrEYrFJv26mDGrgwIGsuw8xLTIdHBzw/PPPN6p1ZjJibckyZT6U2HJOYgxemHIQlUoFJycnDBw4kLVJRU1NDebOnYvQ0FC89dZbLeHfawm8HtwTONuTZgxNbF35MVZixbgAMpNENzc3iMVii/daGStgS8sZLaGsrAyZmZno0qULysvLDXbtsgU2Nc0kczGlpMyee4ajCJ/VVcHd1Q0ih4YqmjlK4BXTNhdNOHbsGNavXw+ZTMbZsj+L8EbPLRKk161bh7y8PISFheHFF19kpT8xU7hv6f4V0zdZLpejsrJS88epO1MvLi7GnTt3zOpOYynaxvf62t/V1tZqArb2KoC5bl2M+UNAQIDFre9MwZjDKJVKPP300ygpKdFYBVpTZsNQV1eHefPmYcKECYiKiuJ7gAZ4JGojsK5nhUKB2bNnIyQkBBKJBGKx2OrfVV5eHoqKiuDv728ykOnutXbq1AlisdikcYZcLse9e/f0WgGzBTMJ0J5oMJ3j2Jp0M6sNtvpk64P5TCwsLERWZQX2Bg6Ek1NHODo6Qk0IopQNjTss4dSpU/jwww+RnJzMWd02g0qlwrBhw+Dt7Y2DBw9aexre6LnFumCdPHkScXFxOHv2LEaPHg2JRIIxY8ZYlcVcXV2NjIwMm2t9tRtYPH78WJMQUlVVhaKiIk6yrC311dXuVVtdXW0yy5S5++fCopRxTSKEoE+fPo3KbLRLVyxteVdfX4833ngDI0eOxIoVK1gL0L6+vnBxcYG9vT1EIhEuXLjQ5P1ER0dDJpPByckJO3futMRqlDeiNgInes7NzYVUKkVCQgLs7e0xY8YMSCQSdOvWzazfnXaJ1YABAyxOaNK17TVkenT//n0oFAoEBASwcmOgD6Zk0tgkQJ8+LNl6e/ToEbKysqzqN20u2vvcR0QECUSN6rp6jKqqwQJ7R5NmQ9qcOXMG77//Pg4ePMiJNakumzdvxoULF1BeXi4EaTaor6/HqVOnEBcXh9TUVIwYMQISiQRBQUFmLQtp71+xmcHNZGFnZ2ejsrISYrEY3bp1g7u7O2vJXIwrkI+Pj1W2fYYmFczyHzOjDwwMZP3u31CA1kWfD7GxzmJKpRKLFi1C//798eGHH7J6B+3r64sLFy4YXGqTyWTYunUrZDIZzp8/j+joaJw/f97c0/NG1EbgVM+UUuTn5yMuLg4JCQlQq9WYPn06JBIJvL299f4umfrkDh06NPIZsGUMjOlRSUmJJhmzoqKC0zpr4H9WooGBgWZP5nUTM01Nuh8+fIibN29yMulmqKqqwpUrVxrtc1MAKkpRpWU25OjoqKkdNzQhSUtLw9KlS3HgwAHOMvS1ycvLw/z587F69Wps3rxZCNJso1QqNc4zp0+fxtChQyGRSDBu3Di9AZtpZMHFjJLJVFYqlejXr58mIeThw4c225MCDUvYV65cga+vr9X9abXRXf5zdHREdXU1hgwZwsn/jTkBWhdTrSxVKhXeffddeHl5Yf369awvcZsK0osXL8bYsWMxZ84cAEDfvn2RkpJi7gSKN6I2QrPpmVKKwsJCxMfHY9++fairq8P06dMRGhqKZ599FoQQ1NfXIyMjAx4eHha3TzR3DI8fP8b169dRU1MDV1dXiMVig6ZHtpCbm4uSkhIEBARY/ZlgatLNOA9yMelm0BegjR3LTDAopY2a5gBAeno63nrrLSQmJprsX80WM2fOxKpVq/D48WNs2rRJCNJcolKpkJqaCqlUilOnTiEgIAASiQTjx4/HU089hTt37qC0tJQTA3xmdt+xY8cm3rr6yqbEYrFFyz9M6UefPn04yfqUy+XIzs5G586dUVZWpulOw4abmLUBWt95tH2I9+zZg8LCQjz77LOctajr0aOHxkBm8eLFWLRoUaPXQ0JCsHLlSowZMwYAEBwcjM8//xzDhg0z5/S8EbURWkTPlFLI5XLs27cP+/btQ0VFBcaOHYtLly4hJiaGM3MPlUqFzMxMuLi4oEePHqiqqoJcLkdJSUkT0yNroZTi7t27ePz4MQYNGsTa362hSfewYcM4DdBMeaalGe91dXWaJfyrV6/i119/xe+//44DBw6gX79+nIxXl4MHD0Imk+Ff//oXUlJShCDdnKhUKpw9exZSqRTHjx+Hi4sLvLy88M0337CeZW2O+xADY0/KCJ8xvDc2U2csSk3VNFqLXC5Hbm6uZsmN8c1lklYcHBw0Y7Q0cYatAK2LSqXCsmXLcOvWLajVakgkEixfvpyVc2tTUFAALy8vKBQKTJw4EVu3bm3UnGPatGlYtWpVoyC9ceNGDB061JzT80bURuCFnk+cOIH58+drVqiYpDNLmk2YgkkkNdRrWjuRS9uj25IAyJR71tfXw8/Pj7NldGbS7e7ujrKyMr1du2zFlgCty8WLF7F8+XJ0794dOTk5OHPmTLMYlqxatQo//PADRCIRampqUF5ejvDwcPz444/WnI43em4VQVqbJUuWQKFQwMvLCydOnEC/fv0gkUjwyiuv2LysW1dXp+kcY83snrHW1A6G2jN1Zv+cqwbyhYWFmj0xQ+LVLu2ilGrGaGp/i6sArVarsXbtWpSVleHbb7+FnZ0dVCoV563q1q5dC2dn50aTAWG5u3lITU1F9+7d0atXL5SUlGD//v2Ii4tDaWkppk6dColEYtPfWE1NDTIyMszeSmL8xBUKhdmaoJTi+vXrEIlErOpBl6KiIty/f7/RpFu3axdTSWHtigCzssdGgM7OzsZrr72GH374AQEBAc2iZX0Id9ItyL179/Dcc88BaPiAv3jxIvbu3YujR4+id+/eCAsLw6RJkyyeubHhPqSN7kydMWUIDAzkJCMzLy8PcrncovZ6TG2kQqFAfX19oyxT3SV+LgI0pRSffvop7t27h507d3Iq5srKSqjVari4uKCyshITJ07EmjVrGjXpSE5OxrZt2zSJY1FRUUhLSzP3ErwRtRF4p2dtHjx4gMTERMTFxUEul2Py5MmQSCTw8/Mz+2+OWamy1uFLWxOm/MSdnZ1Za3mrD8a739ik29bSLjYD9L179zBr1izExsaau0XEGUKQ5iFqtRrp6enYu3cvDh8+jB49eiA0NBRTpkwxmQDBhfuQNozFIdNLly17Uob79++jpKTEJp9v3dIuJgu7U6dOuHXrFicBevPmzcjMzMRPP/3EWUkMw507dxAWFgagYUtj7ty5WL16NWJiYgAAb731FiilWLJkCQ4fPgwnJyd8//33lnzY8EbURmg1ei4rK0NSUhLi4uKQl5eHSZMmISwsDP379ze4rMz4AbC1UsVkXsvlctTV1aFr167o2rUrbt++zVmyG4O1k25L/BTYDND5+fl49dVX8c0332D06NE2nYsn8EbPbSZIa8OYg+zduxeHDh2Cj48PQkNDMXXq1Cb7wFy7DzHLVUyCmzmdfywhJycHjx49YjVphcnCZvbamfIYU0YR5kIpxfbt23H27Fns3buXL03ebYU3ojZCq9Tzo0ePcPDgQcTFxSEnJwcTJ05EWFhYo7/5kpISZGdnw9/fn5PSJKVSiaKiIty+fRv29vbo1q0bxGIxJ60guZh065Z2sRmgi4qKEBERgS1btuDll1+26Vw8gjd6bpNBWhtKKTIzMyGVSiGTySAWixEaGoqQkBBcvHgRzs7OCAwM5MR9iJkNGzJP0O78U1tba3C52RB37tzReAOznbTCLHEDDZ6+xcXFrJSfUUrx3Xff4ejRo9i3bx9nrk8tAG9EbYRWr+fHjx8jOTkZcXFxuH37NiZMmACRSAQPDw/85S9/Yb3Sg4HJV/H19UWXLl2atJ5lw08caJh0l5WVwd/fn9VJt3Zpl4uLC8rKyjBw4ECb+w8oFAqEh4dj48aNmDBhAivj1cf9+/fx+uuvo6ioCHZ2dli0aBGio6M5ux54pOc2H6S1oZQiKysLUqkUO3fuhEgkQlRUFMLCwlgvhWLENmjQILOCmVKp1Ai/qqrKqKkBpRTZ2dmoqanBgAEDWJ/JG9qD1jaKKC0tRceOHTW1kebeDe/atQsJCQlITExkdbnflIBTUlIQGhqqqdcMDw/HmjVrWLn+E3gjaiO0KT1XVFTg7bffxunTp+Hm5oZx48ZBIpFg6NChrE5ajeWr6PqJ29K7mctJN0NlZSUuX74MFxcXVFVVNenaZQmlpaUIDw/HP/7xD0ydOpWT8TIUFhaisLAQQ4YMwePHjzF06FDs378f/fv35+qSvNFzuwrSDKdOncLWrVvx4Ycf4sCBAzhw4ABcXV0RGhqK6dOn29x+8vbt26itrTW6f2YM3ZmvtksXANy6dQsqlcqihBpLxn/z5k3Y2dmZdICqqKjQmBnY29trsmIN3R3/5z//wU8//YQDBw6wurVgjoBZSCQxBW9EbYQ2pef6+np8+eWXeO+996BUKnHo0CHExcUhMzMTY8eOhUQiwYgRI2wKeJa0dtVtW8l0sjO1TcT1pJuBmWww5Z/ang8PHjyAk5OTZtJtKkekrKwMEREReP/99yGRSDgZrzFCQ0OxZMkSTJw4katL8EbP7TJIM31vmZkjE1jj4uKQlJQEJycnSCQSTJ8+HR4eHmaLhmk2QQhhrV0jY0+qUCjw6NEjUErh5ORk9h26JTDjt7e3t9iisbq6WrN0z7gPabe927dvH7799lskJydz3kNWn4CFIA2gjepZl5qaGhw9ehRSqRTp6ekICgqCRCLBqFGjLNIMUzJpTRtIxk9cLpcb3SZiaq2VSiUnk24G3QCtb7zapV36SkgZysvLMXPmTERFRSEyMpKT8RojJycHQUFByMzM5CTR9wm80XO7DNLGYByE4uLisH//fnTo0AGhoaGYMWOG0Q4/xlzK2BrXtWvXoFar4eDgoOn8wwjf1uUxWwK0LtruQ0ePHkVWVhZu3ryJlJQUznvIGhJwSkoKIiIi4OPjAy8vL2zatAkDBgxg89K8EbUR2p2ea2tr8csvv2Dv3r24ePEixowZA4lEghdeeMHo3SLjkc2G5TCzTSSXyxu5FHbu3BnZ2dkAwGoPdl1MBWh96JZ2eXh4wM3NDSKRCK+++ioWLlyIP/3pT5yM1xgVFRV4+eWXsXr1aoSHh3N5Kd7oWQjSRqCU4t69e4iPjzfa4UelUuHq1atwc3ODr68v6+NgJgBOTk7o2bMnCCFN7EmdnZ01LkTWdBFiK0DrkpiYiK+++gre3t4oKyvDiRMnOPswMibg8vJyTb26TCZDdHQ0/vjjDzYvzxtRG6Fd67murg7Hjx+HVCpFWloaRo8ejfDw8CbtcplMcS7a0mq7FObl5UEkEmm693FR5WBNgNaFqR3fuHEjDh8+jOHDh2P9+vVc7gfrpb6+HiEhIZg0aRL+9re/cX053uhZCNJmYqjDz/jx45GcnIy5c+fC29ub9esy5WSurq4GJwBMIwFmqcoSr24uA3RKSgrWrFkDmUwGT09PqNVqzhJiLBWwqWYbVsAbURtB0PMT6uvrNe1yf/vtN4wcORJhYWHIz8+Hh4cHxo8fz1mmuFqtxvXr1/HUU09BLBZr8jocHBw0DUDYuHZNTQ3S09NZsSCura3F3LlzERwcjG7duiEvLw8rV660eYzmQinF/Pnz0blzZ2zZsqU5LskbPQtB2gqYDj+7du3Cpk2b4O/vj0mTJjXq8MMGKpUKGRkZ6NKli9nGCbpe3Y6OjhoXIl3hcxmgU1NTsXLlSiQnJ1vVhtMSzBFwUVGRZrsiLS0NM2fOxL1799h8z7wRtREEPetBqVTi1KlT+Pjjj3H79m2MHz8eERERePnllzlp3sO4lfXs2bPRa8wSs0KhMCsR0xhsBui6ujrMnz8fY8eOxdKlSzlbCTNGamoqXnrppUa18Rs2bOAyq5w3ehaCtA188sknGDp0KAYPHox9+/YhPj4eVVVVCAkJ0ZT7WPsHrVKpcOXKFXh6euptEGAuhoTv6OjIWYA+f/48li1b1mw9ZA0JODc3F0CDm9i2bdvwzTffQCQSoWPHjti8eTNeeOEFNofBG1EbQdCzARQKBZYtW4aYmBhcvHhR031v8ODBCAsLw7hx42yu6Ver1cjIyDBrW0zbTxyAJhHTnLJFJkD369fP5jpopVKJBQsWYPjw4Xj//fdbJEC3ELx5o0KQZhmFQqEJ2OXl5Zg2bZrFHX6USiWuXLmC7t27w8vLi7WxaQu/srISTz/9NPr378+ql/ilS5fwzjvvIDExkZP9eR7DG1EbQdCzBahUKpw5cwZxcXE4efIk/P39IZFIEBwcbPFeNbMq1rVrV4snrozdp0KhgEql0tgK69MtmwFapVJh8eLF6NOnDz766KP2FKABHulZCNIcUlJSgoSEBMTHx5vd4ae+vh7p6el45plnOOmzyyxxA4Czs7PG59dWe1IAuHr1Kt58803Ex8fj+eefZ2vIrQXeiNoIgp6tRKVS4dy5c4iLi8Px48fRv39/SCQSTJw40eTdrUqlQnp6OsRisU2rYkDjygnGT1wsFsPZ2ZnVAK1Wq/Huu++iW7du2LBhQ3sL0ACP9CwE6WbiwYMH2L9/P+Lj4w12+NG2HjSnxZ6lGNqD1tdIwBJ7UgDIysrCggUL8PPPP8PPz4+1MR8+fBjR0dFQqVRYuHBhk2QVSimio6Mhk8ng5OSEnTt3YsiQIaxd3wJ4I2ojCHpmAbVajd9//x1SqRTHjh1Dnz59NO1ydSe5SqUS6enp8Pb2Zj03Q9ufu6qqCnV1dejduze8vLxsCqpqtRrvvfcenJyc8OWXX3KW7MlgSuMtBG/0LATpFqCsrAyJiYmIj4/XdPgZM2YMTp48iaioKDYzjjUwAVokEqF3794GRaxUKjUzdX3G/Pr4448/MG/ePPz444/w9/dnbcwqlQp9+vTBsWPH4OPjg+HDh+M///lPo9IPmUyGrVu3atpLRkdH4/z586yNwQJ4I2ojCHpmGbVajUuXLkEqleLIkSPo1asXQkNDMXnyZFRXVyMrKwt9+/aFWCzmbAw1NTW4fPkyxGIxKioqUFlZqdGtpX7iarUaH3zwAerr67F9+3bOA7Q5Gm8heKNnbn8DAnpxc3PD/PnzkZSUhJMnT8LLywvz58/HuXPnsG3bNmRkZECtVrN2PXMDNACIRCJ0794dAQEBGD58OFxdXZGbm4tz587h5s2bePjwIbQndjk5OZg3bx527tzJaoAGgLS0NPTu3Rs9e/aEo6MjZs+ejcTExEbHJCYm4vXXXwchBKNGjUJZWRkKCwtZHYcAO2zatAmEEJSUlLT0UFjDzs4Ow4YNw+eff45Lly7h73//O27cuIHg4GC89NJLSE1N5aQrF4N2FnfPnj3h7++PESNGwN3dHXl5eTh37hxu3LiBBw8ewMQNGSilWLduHSoqKrBt2zbOAzRgnsbbO7wK0mvXroW3tzcCAwMRGBgImUym97jDhw+jb9++6N27Nz777LNmHiW7uLq6ora2Fvv378ehQ4cwePBgbNq0CWPGjMGaNWtw+fJlmwK2JQFaFyYbfNCgQRg5ciQ6d+6MgoICnDt3DklJSdi9ezfmzJmDHTt2cLLEnJ+f3yjJxsfHB/n5+RYfI9Dy3L9/H8eOHeO0B3NLY2dnh8GDB2PdunXo1KmTZtl22rRpmDVrFvbs2YNHjx6xdj1De9D29vbw8PDAwIEDMXLkSHh4eKCoqAjnzp3D9evXUVpa2uQzhVKKzz77DIWFhdixYwfrlsOGEPRrGuMu6i3AsmXLsHz5coOvq1QqvPPOO42WR2bMmMGH5RGr0X6/c+bMwZw5c1BRUQGZTIavv/5aMzMPCwvDkCFDzJ7hMl2/HBwcLA7QutjZ2WnM99VqNY4cOYLt27ejqqoKO3bswLBhwzjxEtdFX0cwU8cItDzLli3Dxo0bERoa2tJD4RyRSITExETNttXHH3+Ma9euQSqVYvr06fD09NS0y7XWJpcJ0H379jWaJGZnZ4cuXbqgS5cuoJTi4cOHUCgUuHXrFlxcXODu7g5XV1fs2LEDN2/exJ49e5otQAOCfs2Bd0HaFNrLIwA0yyOtOUjrw9nZGZGRkYiMjER1dTVkMhliYmI0HX7CwsIwfPhwgwGbzQCtS3FxMdavX48tW7Zg3LhxyMjI4ETYPj4+uH//vub7vLy8JiVp5hwj0LIkJSXB29sbAQEBLT2UZkM7r4QQgoEDB2LgwIFYu3Ytbty4AalUirCwMLi7u0MikSAkJKRJG0xDaAdoS4I8IQSdO3dG586dNbbCZ86cwYoVK6BSqbBp0yYolUqTHbDYRNCvaXi13A0A27Ztg7+/P9544w08fPiwyevtcXmkY8eOiIiIwJ49e5CWlobg4GDExsZi9OjRWLFiBX777TeoVCrN8VwG6NLSUkRGRmLDhg0IDg6GnZ0dAgMDWTu/NsOHD8cff/yBu3fvoq6uDv/9738xY8aMRsfMmDEDu3fvBqUU586dg6urK+cOZwJNmTBhgiYQaT8SExOxfv16rFu3rqWHyAsIIfDz88OaNWtw/vx5bN26FQ8ePMCrr76K0NBQxMbGori42OD+cW1trVUBWt84XF1dUVhYCD8/P0ilUmRkZKCsrMzqc1qDORpv7zR7dveECRNQVFTU5Pn169dj1KhR6Nq1Kwgh+PDDD1FYWIjY2NhGxzFZlN999x0A4IcffkBaWhq2bt3K9lB5T21tLY4dOwapVKrp8DNjxgycOHECs2fPZr31XVlZGcLDw/HBBx80m5BkMhmWLl0KlUqFN954A6tXr0ZMTAyABicxSimWLFmCw4cPw8nJCd9//z2GDRvWLGPToTWs0TV7dvfVq1cRHBysMd5g7pTS0tI48QForVBKcefOHUilUiQlJeGpp57SdN/z9PQEIQS1tbW4fPmyzQGaYffu3YiPj0dSUhKnyW2m0KdxHsAbPfO2BCsnJwchISHIzMxs9PzZs2exdu1aHDlyBADw6aefAgBWrVrV7GPkE3V1dTh27Bjee+89ODg4YOTIkYiIiGjS4cdaysvLERERgWXLlmHmzJksjLjNwRtRG6HFS7A4aGzS5qCUIicnR9Mu18HBAePGjUNaWhpiYmLMXhY3xs8//4xdu3YhOTnZJgOjNgxv9Myr5W7t0pmEhAQMHDiwyTGmlkdWrFiBfv36wd/fH2FhYQaXb3x9fTFo0CAEBga21J0Xqzg6OsLDwwPh4eG4ePEiIiMjkZCQgBdeeAFRUVE4ceIE6uvrrTp3RUUFZs2ahb/+9a9CgBZoMczVdmuHEIIePXpgxYoVSE1NxZdffonvvvsO5eXleO2117B9+3YUFBSYLKkyREJCAmJjY3HgwAEhQLcCeHUnPW/ePKSnp4MQAl9fX/z73/9G9+7dUVBQgIULF2pKsowtjxw9ehTjx4+HSCTC+++/DwD4/PPPm1yrvczomQ4/UqkUqampGD58OCQSidkdfqqqqhAZGYl58+ZhwYIFnIxxxYoVOHDgABwdHdGrVy98//33ejNWfX194eLiAnt7e4hEIly4cIGT8VgJb2beRmjxO2lbMFfbbY2UlBQQQhAUFISCggJNu1ylUonp06dDIpHAx8fHrK2t5ORkfPXVV0hOTmZlydwczNU3z+CNnnkVpNkmISEBcXFx+Omnn5q81l6CtDZKpRKpqamQSqX49ddfMXjwYEgkEoMdfmpqajB37lxIJBIsXryYs9KINjKx4o2ojdCq9ayNMW23ByilKCoqQnx8PPbt24eamhpMnz4doaGheO655/Rq9dixY9iwYQNkMhkrS+bm0konV7zRM6+Wu9kmNjYWU6ZM0fsaIQSvvPIKhg4dim+//baZR9YyiEQijB07Ftu3b0d6ejoWLlyIlJQUBAUF4c0330RycjJqamoA/K+H7JQpUzgN0ADwyiuvaPbNR40ahby8PKvPlZOT02SbJCUlBSEhIY2e+/Of/4y4uDirryPQshjTdnuAEILu3btjyZIlOH78OBISEuDm5oaoqCgEBwdj8+bNyM7O1iyJM/2yk5KSmjVAA9brW9ByA62uThowniHOmCWsX78eIpEIr732mt5znDlzBl5eXlAoFJg4cSL69euHoKAgTsfNJ+zt7REUFISgoCBNhx+pVIp169bBz88P+fn5CA0NRVRUVLOaC8TGxmLWrFl6X2MmVoQQLF68GIsWLWq2cQk0D2xou71BCIFYLMbbb7+Nt99+G8XFxUhISMDy5cvx8OFDDBo0CGlpaThy5AinHuLmYEzfAvpplUH6l19+Mfr6rl27cPDgQRw/ftxggGEK5j09PREWFoa0tLR2FaS1sbe3x4svvogXX3wRarUap0+fxt69e7FixQrWAnRLTKzu3LmDiIgIzJ071+AxFy5cwMKFCwE0uNllZmZanZAjYDtsaLu94+HhgUWLFmHRokUoLS3Fxx9/jNjYWE5NQrieXLVrLVNKjT1aHYcOHaJ+fn5UoVAYPKaiooKWl5drvh49ejQ9dOiQ5uf79OlDe/XqRT/99NMmP6tWq+m7775Le/XqRQcNGkQvXrzIzRtpZ+zcuZOOGjWKVlZWmnX8Rx99RL/44osmz9+9e5cOGDCA3rhxgwYGBtLLly/TkydP0k6dOtGAgADNw93dnUql0kY/u3z5crp8+XJr34IpLfHh0aoxR9vmnMOYvgW4wVJ9U9qiWqa05bWqebQ5Uffq1Yv6+PhofoGLFy+mlFKan59Pp0yZQimlNDs7m/r7+1N/f3/av39/+sknn1BKKVUqlbRnz540Ozub1tbWUn9/f3rt2rVG509OTqaTJ0+marWanj17lo4YMaJ532AbxNaJlTZ3796lnp6etG/fvjQzM5NSSunJkyfptGnTGh03f/78RsL++eef6fjx46lSqbT2bbS4mM14tGoMadtczNG3APtYO7lqQS1T2vJa1Txa5XK3MW7fvq33eS8vL00JV8+ePXHlypUmx5jjC26oNaJgRWk9S5YsQW1tLSZOnAigIbkkJiamUemdXC5HWFgYgIYs9blz52Ly5Ml6z+fq6opnnnkGZ86cwYABA0xe/9q1a/joo4/w66+/NmtzAQHLMKRtc2kvvv98w5C+zUHQcivdk+YKfb7g58+fN3lMfn6+EKRtwJaJlT4cHR2xf/9+TJo0Cc7Ozkb34h49eoTZs2dj9+7d8PDwsHzwAq0Gc/QtwD62TK4ELbfxEixLoVRojdhWePrpp3Hw4EF89dVXRnv47t+/H/fu3cObb76p6WMu0DYRtNs6ae9aFu6ktRBaI7LL2rVrsWPHDs2sdsOGDZg6dWqT4w4fPozo6GioVCosXLgQK1eutPqavr6+Gr93Nzc3/P777wDQpI/xzp07NV/Pnz/f6usJtB4E7bYuBC03YMpxrF1BCBEBuAUgGEA+gN8BzKWUXtM6ZhqAJQCmAhgJ4J+U0hE653kGwG4A3QCoAXxLKf1a55ixABIB3H3y1D5KaZvq50cIWQugglK6ycgx9mj4P58IIA8N/+dzKKXXm2WQAu0Gc/RtwblMalxAgA2EO2ktKKVKQsgSAEcA2AOIpZReI4S89eT1GAAyNATo2wCqAOgztFYCeI9SeokQ4gLgIiHkmJ7Ac5pSGqLn59sTIwDcppTeAQBCyH8BhAIQgrQAqxjSt5WnM1fjbRpCyHIAXwDwoJSWtPR42iJCkNaBUipDQyDWfi5G62sK4B0T5ygEUPjk68eEkCwA3mifgWcJIeR1ABfQ8KH2UOd1bwD3tb7PQ8MKhYAA6+jTt5Xnafcaf7KaMBFAbkuPpS0jJI5xDCHEF8BgAPrSSEcTQq4QQg4RQkzXF/AQQsgvhJBMPY9QAN8A6AUgEA0faF/qO4We54Q9GIFWgwmNt2W+AvD/IOiVU4Q7aQ4hhDgDiAewlFJarvPyJQDPUUorCCFTAewH8HwzD9FmKKUTzDmOELIDwEE9L+UBeEbrex8ABSwMTUCAc0xovM1CCJkBIJ9SekXIkOcWIUhzBCHEAQ3i/YlSuk/3dW1BU0plhJB/EUK6tqV9HUJI9yfLggAQBiBTz2G/A3ieENIDDck8swEYNugVEOAJpjTe2iGE/IKGxDhdVgP4AMArzTui9okQpDmANEwt/z+ALErpZgPHdAMgp5RSQsgINGw9lOo5LgfAYwAqAEpK6TA91/oaDclsVQD+TCm9xOLbsYWNhJBANCyH5QBYDACEEC8A31FKp7KczCMg0CyYo/HWjqFVMkLIIAA9ADB30T4ALhFCRlBKm3bZELAJoQSLAwghYwCcBnAVDeUZQMPM81mgIRHtSWB6Gw1ZotUA/kYp/U3PuXIADDN0h/1kqfxd/K8k7GtKqZB4JSDAIYY0/iQxzdpz2qMhwTK/NVV9mPqMErAN4U6aAyilqdCfEKV9zDYA21i4XCiA3U+yzs8RQtx0lpkFBARYxhyNW0E0gCwAnVg+r0ArRsju5j8UwFFCyEVCyCI9r+srYfJulpEJCAiwAiHEB8A0AN+19FgshVLqK9xFc0e7CdKEEF9CSKbOc2MJIQd1nttJCJnZvKMzyouU0iEApgB4hxASpPO6UMIk0K5oxVo2xhY0lDOpTRwn0M5oN0G6tUIpLXjyrwJAAhocurQRSpgEBFoxhJAQAApK6cWWHosA/2iXQZoQ0pMQchnAcCPHDCOEpD95XCWENPvdKSHk6SeWgyCEPI2GkgfdMqYkAK+TBkYBeCTsRwu0F1qLlk3wIoAZTxKw/gtgPCHkx5YdkgBfaHeJY4SQvmgQwgIAbgD+TghJ1zrkWQAHKaUX0OCUBULIFwAON+tAGxADSHhS5iACsIdSetgKL3EBgTZHK9OyQSilqwCsAjSNd5ZTSv/UkmMS4A/tLUh7oKHzVMSTxhljodPkghCyU/sHCCGRAIagBQr3nzSdCNDzvEVe4gICbZBWpWUBAWtpb8vdj9CQCf2iOQc/8dP+B4DZlFIVlwMTEBCwiDapZUppSmuqkRbgnvZ2J10HQALgCCGkAkYSrAghrmhYSnudUlrcPMMTEBAwE0HLAu2C9nYnDUppJYAQAMsAuBo5VALgOQA7mKQT7kcnICBgLoKWBdoDgi2ogICAgIAAT2l3d9ICAgICAgKtBSFICwgICAgI8BQhSAsICAgICPAUIUgLCAgICAjwFCFICwgICAgI8BQhSAsICAgICPAUIUgLCAgICAjwlP8DWP5CQII5JX8AAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig=plt.figure(figsize=[8,4])\n",
"ax=[fig.add_subplot(1,2,k+1,projection='3d') for k in range(2)]\n",
"ex0.plot_inter(-1,ax=ax[0])\n",
"_=ex1.plot_inter(-1,ax=ax[1])"
]
},
{
"cell_type": "markdown",
"id": "866080a6",
"metadata": {},
"source": [
"### Run the sequence and plot\n",
"We run the sequence, and plot the results."
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "568be350",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"State-space reduction: 32->16\n"
]
}
],
"source": [
"_=rho.DetProp(seq,n=6000)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "34eefdd9",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax=rho.plot()\n",
"_=ax.set_ylim([0,1])"
]
},
{
"cell_type": "markdown",
"id": "cc3423c6",
"metadata": {},
"source": [
"### Origin of multi-exponentiality\n",
"Note that the signal decay is multi-exponential. This is always the case in solid-state NMR, where different orientations give rise to different decay rates. However, this curve is particularly multiexponential, due to TROSY-like effects resulting from relaxation due to both the dipole and CSA (see [TROSY](../Chapter2/Ch2_TROSY.ipynb) in chapter 2).\n",
"\n",
"We may investigate this by actively separating components when the $^1$H is in the α and β states. Here, we must construct our detection operators explicitly from the spin-matrices found in `ex0.Op`."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "d63ce04e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"State-space reduction: 32->16\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"rho=sl.Rho('15Nx',[ex0.Op[0].x@ex0.Op[1].alpha,ex0.Op[0].x@ex0.Op[1].beta])\n",
"rho.DetProp(seq,n=6000)\n",
"ax=rho.plot()\n",
"_=ax.legend((r'H$^\\alpha$',r'H$^\\beta$'))"
]
},
{
"cell_type": "markdown",
"id": "2e50e91a",
"metadata": {},
"source": [
"Indeed, we see two very different decay curves, corresponding to the two different components. However, this is somewhat unrealistic in solid-state NMR, where $^1$H spin-diffusion periodically inverts the $^1$H spins. We may add this effect by flipping the $^1$H with a rate of 50 s$^{-1}$, to see how the two curves re-converge. Here, we plot the average curve plus the two $^1$H states separately."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "d465851c",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"State-space reduction: 32->16\n"
]
},
{
"data": {
"image/png": 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HVHX9PulXI6EppZQ3aSI44/y/lLsqLjLYXp6/qeS4eaV9M+Ebezm/OL96cSmllJdpIjjDr+I/xcybrDOR3T1rQ6VddWrSyV5O+LTMazNKKVVnaCJwNvJpR/m46yTUF3Z1zEX6y84TlXb16zWO5xHS89MraKmUUrVLE4GzoXc6yu+cU26zm2ZWPitZdIjjieXhs4dX0FIppWqXJgJnAcEVrl7+8Ah7edexzEq7c568JjE9scphKaWUN2kiKKnVYEe50PUuoRaNQ+3lUa8vrbSrQP9A+sRa7yIaP3d8zcSnlFI1TBNBSVc7jRW08u1Sq++5uLO9nJ1fVGl3n451TLGgU1oqpeoiTQQlNWrhKC9+ptTqe0c6EkHPpxZW2p2I8MTQJwCd0lIpVTdpIvBQyfGD3Bmr6equV9vLH23T0UmVUnWLJoKyTHSaYMY2j7Gz7X8dZS9PeHOZW11+Me4LAP6+VucrUErVLZoIytL/ekf544mlVocFOSa933LEvWcEusc4hrB+YtkTVY9NKaVqmCaCyqTtLXPxj/edby/f//lGt7pacvUSAObunUthcWF1I1NKqRqhiaA8A29ylMu4DtC5aaS9/PWGI25dK4gJjSE2NBaAS+dcWv0YlVKqBmgiKM+4fzjKa2eU2eTZy3vZy4/P3epWtz9O/hGA1NxUUnNTqx6fUkrVEE0E5XG+O+i7+8tscsPQtvbyZ6sOudVtgF8At/ax3kZ60RcXVT0+pZSqIZoIKnLpc5U2aR7lmCR6zrrSdxiV5e7+d9vLq5NXex6XUkrVIE0EFRk23VFO3lRmkxWPXGwvP/Bl2W3K8u3EbwG4edHNVYtNKaVqiCaCijifHvr3+eW3c3Iis/JZzAA6NO7AiNbWQez+t/9/HoemlFI1RRNBZa6q/EngAy86Jrgf/Pxit7t+brj11NN7m9/DYiyex6aUUjVAE0FlujuNGnpoVZlNRIQLusTZ6+7cSgoQGRTJAwMfYH/6ft7a+FblGyillBdoIqiMn7+jPKP8e/8/+j/H8NWX/qPyIarPuLHnjcSGxvL5rs/JKMioUohKKVUdmgjc4TzkRAW/9hfZnjbecyILi8W9owIR4e2L3yazIJO3NuhRgVLq7PNqIhCR0SKyS0T2isjD5bS5UEQ2isg2Efm1rDa1bvwbjvLmz8tt1sXpaeN+f13kdvfdY7pzVZer+O/O/7LxxMaqRKiUUlXmtUQgIv7AW8AYoAdwrYj0KNGmMfA2MMEY0xO4ylvxVIuf05/pm9sqbPrLny8EICOviKJi9y8A393/bhoHN+bR3x+l2FJclSiVUqpKvHlEMBjYa4zZb4wpAGYDJYfyvA742hhzCMAYc8KL8VRPb6ccVcHpofax4fbyxa+5f4ATFRzFzb1u5nDmYd7f8n6VQlRKqarwZiJoCRx2qifZljnrAjQRkSUisk5EppbVkYjcKiJrRWRtSkqKl8KtxCSnL+cfKx5Get3jIwE4mJbj9rUCsF44jguN482Nb3I062iVwlRKKU95MxFIGctKfisGAAOBy4BRwBMi0qXURsb8xxiTYIxJiIuLK7n67Fv+RoWrYyKCmTSgFQBDX3T/uQIR4e2R1nmSr/vuuqrHp5RSHvBmIkgCWjvVWwElf+YmAT8YY7KNManAUqCvF2OqnmnfOcqpZc9TcMbLk3oDcCIznw2HTrn9Ed2iuzEgfgBpeWl8s+ebKoWplFKe8GYiWAN0FpH2IhIETAHmlWjzLXCeiASISBgwBNjhxZiqp91wR/nNgRU2DfB3/GmveHu5Rx9z5qjgyeVP6rMFSimv81oiMMYUAdOBhVi/3L8wxmwTkdtF5HZbmx3AD8BmYDXwvjHGvYH964KU3RWu3vSU4wG0Oz5d53a34YHhXN3FOuH9ubPOrVpsSinlJq8+R2CM+d4Y08UY09EY87xt2bvGmHed2rxijOlhjOlljHndm/HUiD/+7Ci/NajCplGhgfbygq3HPPqYJ4Y5LkjP21fyQEoppWqOPlnsqZYlTgllHq+w+bZnRtnLfZ5e6NFHfT7O+vDaY78/RqFF5zhWSnmHR4lARO4VkVhvBVMvvVrqJicX4cEB9nJGXpHbA9IB9IjpwbktrKeGBnwyoGrxKaVUJdxOBCLSB3gJmOa1aOqLiW+71iv5ck986TJ7uf0j33v0Ue+MfMdePpx5uIKWSilVNZ4cEdwM/AUo86Evn9KvxD3+q/5d6SYfO41OejqnwO2PEhF+nPwjoQGhPLviWY+OKJRSyh1uJQIRCQbGAv8G9orI8Eo2adikxLNyPzxU6SbnO81X0O+vP3r0cc3Cm3FXv7tYkbyCgZ9WfNuqUkp5yt0jgknAQmNMPvAh1qMD3zb5Q9d6zslKN1n/xCX28i+7PBtW6Q/d/wBAoaWQpUnuz3eglFKVcTcR3Ax8YCt/D5wvIhHeCame6HWla/0fPSvdJDo8iAjbxeObPlzj0ccF+AXwwMAHALhr8V16ikgpVWMqTQS2oaKPGmM2ABhjioE3sY4u6tviujnKhTmVXjQG2Op0O+kbi/d49HHTek2zl/t83MejbZVSqjyVJgJjzGljzA0llv3DGPNzedv4jDtXutbXflB2uxLm3mW9JfSNn/dS7MHopADrrnc8obz4oPsD2imlVHncvVgcIiL3i8jXIjJHRO4TkRBvB1fnlbxo/N0Dbm3Wr3Vj/jqxJwXFFh6es9mjjwzyD+LZc58F4N4l9+qDZkqpanP3GsHHQE/gDaynhboDn3grqHrlyRIXifPS3drshqFtAfhyXZJHo5MCXN7pcntZHzRTSlWXu4mgqzHmZmPML7bXrVgnlVF+/q71l9q4tZmI8K9r+wNw6yfuD0h3xqapm+zldza+U0FLpZSqmLuJYIOIDD1TEZEhwDLvhFQPPV61WdMm9G3B1QmtSMnM59fdnvXhJ378e6T1Qba3N71Ner57RyJKKVWSu4lgCLBcRBJFJBFYAVwgIltExLOT3A1RQJBrfd1Hbm/614m9aBwWyI0zVrMvJcujjz2n5Tn28vDZvv2Mn1Kq6txNBKOB9sAFtld7rE8ajwPGeye0euaJVEd5/p/c3iwk0J+XrrTOZnbxq+5Pdn/G5qmOPKzTWyqlqsLdRNAB6xf+OKCDMeag88t74dUj/oEQGu2o52e6venoXs3t5XYPf1dBy9JEhO+usG6zJXUL21K3ebS9UkpVmAhEpKWIrAKexpoMOgFPi8hqEWl5FuKrXx464Ci/2MqjTZf8+UJ72dO7iNo0asO0ntMAmPLdFIotxR5tr5TybZUdEbwJvGOMucAYc78x5j5jzAW25W9Xsq1vustp6Ihi9+/xbxcbTtNGwYDncxwDPJDgeIah3yf9PN5eKeW7KksEPYwxM0suNMZ8DHQr3VwR53RX7bOezeGz6tGR9rKnp4jA9ZbS51Y+5/H2SinfVFki8C9roYj4lbdOAY8mO8pF+R5tuvrRi+3lz1Z5dvnFT/z4avxXAHy+63P2nPJsLCOllG+qLBHMF5H3RCT8zAJb+V2so5CqsgSFOcrPxXu0aXyjEAa3s150fuybreQWeHa+v2t0V0a3Gw3AlfOuxGIsHm2vlPI9lSWCvwDpwEERWScia4FEIAP4s5djq98ec5rUft7dHm36xe3D7OXuT/7g8Ue/csEr9nLfj/t6vL1SyrdUmAiMMYXGmD8DrbHOVfx/QFtjzJ+NMe7Pt+iLAp3G5Fv/sVsT1zhb85jjesENH6zy+OM33rDRXp6ze47H2yulfIc78xGEAV2MMVuMMZuNMTki0kZvH3XDPU4PXf+tvUebxkUGc/Nw6za/7Unl8Mkcj7b39/Nn0aRFADy94ml2n9rt0fZKKd/hzgNlhcDXztcJgPeB5uW0V2c0aeta3/CZR5s/Ma6HvXze337xeFay5hHN+WSMdZDYSfMmkV/s2YVrpZRvcGdimkLgG+AaABFpA8QZY9Z6ObaGYZrTNfVv7/R488SXLrOX2z/i+fX5fvH9uK3PbQAkfJqgU1wqpUpxd4iJ94GbbOWpWCewV+5od65rffFfPe5i01OX2sv//nWfx9tP7z/dXh746UCPt1dKNWxuJQJjzE4AEekCXItOSuOZP21wlH971ePNo0IDeeEK68B0Ly7YSVZ+kcd9rL9+PQCFlkLm75vv8fZKqYbL3SMCgA+wHhlsNsZ4NhiOr4vu4Fqfda3HXVw3pI394nGvpxZ6PNdxoH8g319pPbX06O+Psj99v8cxKKUaJk8SwRdAX6wJQXnqqdOO8q7voQrn6p0vHnd81PPrBa0jWzNj1AwAJs6dSGaB+yOkKqUaLrcTgTEmxxgTZYz5yZsBNVgiMN1pSspnGlepm53PjraXqzIe0aBmg3j23GcBOGfWORRZPD/NpJRqWDw5IvCYiIwWkV0isldEHq6g3SARKRaRyd6Mp9bFdoKYzo567mmPuwgJ9OfVqxxPC1flYbPLO13OmHZjALji2yv0TiKlfJzXEoGI+ANvAWOAHsC1ItKjnHYvAwu9FUudcrfTXbcvty2/XQUmDWxFaKB1zL/f9qSy9Yjn8xX/7YK/0SK8BYkZiczYOqNKcSilGgZvHhEMBvYaY/bbhqOYDUwso93dwBzghBdjqVucRydd+W6VutjhdIpo3Bu/U1js+eByCyYtYETrEby+/nW9k0gpH+bNRNASOOxUT7Its7MNU3EF1tFMyyUit4rIWhFZm5KSUuOBnnVBYXDFf6zlHx7yeKjqM5wfNuv82AKPT/H4iR+vXPAKg5sN5sllT7L8qOcT4iil6j9vJgIpY1nJb6rXgYeMMRWOtWyM+Y8xJsEYkxAXF1dT8dWuvtc4yh4OVe3swItj7eWqPHkc5B/E6xe9TvvG7bnvl/vYkbajyrEopeonbyaCJKyjlp7RCjhaok0CMFtEEoHJwNsicrkXY6pbnG8p9XAcojNEhFVOk9lU5U6iyKBI3rn4HRoFN+LOxXdyJOtIlWJRStVP3kwEa4DOItJeRIKAKcA85wbGmPbGmHbGmHbAV8Cdxpi5XoypbhGBO1ZYy9/eCUlVG76paaMQ/jmln71+44zVnvcR3pR3Ln6H/OJ8bv/xdk7nna5SLEqp+sdricAYUwRMx3o30A7gC2PMNhG5XURu99bn1jtNnW6kev9iyMuoUjcT+7Xk7hGdAPh1dwoHUrM97qNTk068MeINjmYdZfrP08ktyq1SLEqp+kXq2z3kCQkJZu3aBjbwqTGuD5g97fntoGe89cteXlm4C4D/3T2cXi2jPO7jx4M/8sCSBzinxTn8a8S/CPIPqnI8Sqm6QUTWGWMSylrn1QfKlJtEYJrTuf2nPf/yPuOuizrx0f8NBqy3le457vkwEpe0vYQnhz3JsqPLuH/J/fr0sVINnCaCuqLdcNf6qv9UuasLusTROjoUgEv+sZSUTM9vT53cZTKPDXmMX5N+5dHfHtVkoFQDpomgLnE+JbTgQUjzfO6BM377ywh7edDzP5FT4PkX+ZRuU7h/4P0sSFzAw789rMlAqQZKE0Fd80Sqo/zGACjwbK5iZ4kvXUZ8ZDAAPZ5cSEZeocd93NTrJh4Y+AALExdqMlCqgdJEUNf4B8Iff3HUX2hepSGrz1j92Eh7uc/TiziRmedxH9N6TdNkoFQDpomgLmo5AJr1cdSrOGT1Gc5PHw9+fjHHM6qWDO4feD8LExfy4K8PUmjx/OhCKVU3aSKoq27/zbX+Rpl3fblFRNj/giMZDHlhMSeqkAxu6nUTfxn0F3469BP3/3I/+cVVGyNJKVW3aCKoy5yHoEjbAzs9Hz7iDD8/12Qw+IXFpGV5/kV+Q48beGzIYyxJWsLFX15Men7Vn3lQStUNmgjqMhF40ml66NnXQc7JKnfn5ycup4kGPvcTuQUVjvdXpindpvDC8BdIz09n5JcjdTgKpeo5TQR1nZ+f65HB39pDdlqVuxMRl+Grb/5oDZlVuJtofMfxvHjei+QV53He5+exOWVzlWNSStUuTQT1gYhrMnilAyRvqlaXiS9dxt+v6svyfWn0fnoRh096fpvquA7jeGDgAwD84fs/8P6W96sVk1KqdmgiqC9E4LHjjvq/z4fEZdXqcvLAVvzdNv/xeX/7hW83ej789LRe03h8yOMA/HP9P7l87uXVikkpdfZpIqhPAkPgDqdZxGaOhWNbq9Xl5IGt+OK2YQDcM3sjn6xI9LiPa7pdw/PDnwdgX/o+en/Uu1oxKaXOLk0E9U3TnjD27476u+fC6UPV6nJw+2geHtMNgCe+3ValyW0mdJzAJ2M+sdd7f9Qbi/F8HmWl1NmniaA+GvxHuPBRR/313pC6t1pd3n5BR/77xyH2eruHv6PY4tkTzf3i+/HrNb/a630/7ktabtUvbCulzg5NBPXVhQ/Ble856m8OrPIMZ2ec0zGWb+86117v+Oj3pOd6dkdRdEg0m6Y6LmRf+MWFrE72fMY0pdTZo4mgPutzNVz/taP+/sXVvoDct3VjNjxxiaP+zCL2nvBsTgM/8WPLjVvs9ZsX3czdi++uVlxKKe/RRFDfdboYbvyfoz5zLCT+Xq0um4QHuTx4NvK1pTwx1/OL0ltu3MLApgMBWJK0RC8iK1VHaSJoCNqfB3/a4KjPvAw2f1mtLs88eBYbYR3G+pOVB+ny2AKP+5k5eibvXeo4hdX7o97kFXk+zpFSyns0ETQU0R3g8RRH/etbYP491e527eMjefyy7gAUFFt4eM5mjy8iD20+lBXXrrDXB302iKVJS6sdm1KqZujk9Q1RyTmPn67+wHDpOYUMf/lnMvOLOL9LHK9f04/ocM8ntXc+PdSlSRfmTJhT7diUUpXTyet9zdPp0PlSp3oUFFVvyOiosEC2PDOKF6/szcp9aQx49kc+XHbA43623LiFO/reAcDuU7sZ+/VYCot1bgOlapMeETRkW+fAV//nqF/xb+g7pdrdbklKZ/ybjgvSe58fQ4C/Z78pUnNTueiLiwDoHt2dl89/mfZR7asdm1KqbHpE4Kt6TXIdkuKb20qfNqqC3q2iWPHICHu902MLOJTm2aB1saGxbLlxC69c8ArJ2clcPf9qvtj1BfXth4lSDYEmgoauaU94YJfrsqejwFK94R+aR4Vy4MWx9ruKxv7rtyoNWje63WjmTJjDgKYDeHbls/zplz9xMq/qcy4opTynp4Z8RXERPBvjuuyB3RDZtNpdJ53K4Z7ZG1l38BRX9G/Jo2O7ExcZ7FEfFmPhsx2f8Y91/yAqOIpnz32W4S2HVzs2pZRVRaeGNBH4ms9vgB3zHPVLn4dzple726JiC//6eS//WrzHvuzAi2MREY/62XVyFw//9jB7T+/lmq7XcN/A+wgPDK92fEr5Ok0EylVeBrzU2nXZU6etcx5U0ycrD7o8hfzV7cNIaBftWXhFefxrw7/4dPuntIxoyZPDnmRYi2HVjk0pX6YXi5WrkEbWW0x7TXIse6YxbJpd7a5vGNqWpQ9eZK9PfncFb/3i2cioIQEh/GXQX/hw9If4iR+3/ngrTyx7QkcyVcpL9IjA12WnwisdXZc9cgSCI6rd9SWv/cqeE1n2+vtTExjZw7NrEnlFebyx4Q0+3v4xANd1u46HBj+En+hvGKU8oaeGVOVK3lbaMgH+uLja3RYVW3hy3jb+u8o6ec4T43pw47C2Hj93sP74eu5bcp/9jqIXhr/A+I7jqx2fUr6i1hKBiIwG/gn4A+8bY14qsf4PwEO2ahZwhzGmwlnZNRF40c7vYfa1rsvu2w5RLavd9fpDp3jx+x2sSTwFwOX9WvD6lP4e9WExFr7e8zXPrHjGvmz+5fNpF9Wu2vEp1dDVSiIQEX9gN3AJkASsAa41xmx3anMOsMMYc0pExgBPG2OGlNmhjSYCLzPGer2gpBq4mGyM4bstyUz/r2Ok1GUPj6Bl41CP+tlwYgNTF0y11+PD4lk0aRH+fv7Vik+phqy2LhYPBvYaY/YbYwqA2cBE5wbGmOXGmFO26kqglRfjUe4QsV5InjrPdfkzjWHfL9XsWhjXp4XLxDcjX/2V137cTV5hsdv99I/vz5Ybt3BN12sAOJFzgku+uoSlSUv1yWSlqsCbRwSTgdHGmFts9RuAIcaYMm9aF5E/A93OtC+x7lbgVoA2bdoMPHjwoFdiVmX4dBLs/cl1WQ3danooLYeXf9jJd1uSaREVwr0ju3DlgJYeXT8oshTx6tpXWXRwESdyTjCk2RDuT7ifHjE9qh2fUg1JbZ0augoYVSIRDDbGlJqzUEQuAt4GhhtjKrxHUE8N1QJLMfy1xLMALfrDrUtqpPuV+9N4ccFONh0+DUDXppH8cO95Hj2MVlhcyBe7v+Dfm/7NqfxTXNbhMv7U/0+0iGhRIzEqVd/VViIYhvWc/yhb/REAY8yLJdr1Ab4BxhhjdlfWryaCWlRcBCvehJ+ecixrey7c9H21uzbG8MPWY9zx2Xr7ssHto/n81qEeJYTMgkxmbJ3BJ9s/wWIs/KH7H7il9y1EBVd/sD2l6rPaSgQBWC8WXwwcwXqx+DpjzDanNm2An4GpxpjlZXZUgiaCOqCsZw/OvRcueabM5p7ILyqm6+M/2Ouhgf78bXIfxvf17Jf9sexjvLnhTebtm4fBcGe/O5naY6oOV6F8Vm3ePjoWeB3r7aMzjDHPi8jtAMaYd0XkfWAScOakf1F5gZ6hiaAO2fo1fHWT67JRL8Cwu6rddXpuIX2fWWSvn9c5lntHdmFg2yYe9bPr5C6eWv4U29K20Ti4Mdd3v55ru19Lo6BG1Y5RqfpEHyhT3rXkJVjyouuyVoPhlh+r3fWp7AL+89t+Zq8+xKmcQs7pGMMdF3ZkeKdYj04ZbTyxkXc3v8uyI8sIDQhlStcpTO05ldjQ2GrHqFR9oIlAnR2//wN+etp1WVAkPJpU7a6z84v4bNVBPvj9AMcz8undMopbz+/A2N7N8fdzPyHsPLmTD7d+yA+JPxAgAVzR+Qqm9ZxGq0i9c1k1bJoI1Nn1xY2wfa7rsqjWcO+Wat92mldYzJdrD/Ph8kT2p2TTPCqE7s0b8crkPsREuD8HQmJ6IjO3zeTbfd9SbClmZNuRTO0xlX7x/aoVn1J1lSYCVTsWPma9y6ikP++BiPhqdW2xGBZuO8YLC3Zw+GQuALed34Hrh7aldXSY2/0czz7OrJ2z+GLXF2QWZtI7tjc39LiBkW1GEugfWK0YlapLNBGo2pV+BH77O6yd4br8+jnQaWS1ujbG8PGKgzz//Q6Kii1YnP4573thrNunjXIKc5i3bx6f7viUgxkHiQ+N56quVzG5y2S9jqAaBE0Eqm4oyofnShwJhDaBy16DnldU+7TR0dO5XPH2Mo5n5NuXPTymG2N7NadNjHtHCcWWYpYdXcZnOz5j+dHl+Is/F7W+iKu6XsXQ5kN1+GtVb2kiUHXP8jdg0eOll1/1EfS8vFpdp2XlM/C5n0otT2jbhM9vG+b2UUJieiJz9sxh7t65nM4/TauIVlze6XImdppIs/Bm1YpRqbNNE4Gqu/LSrbefrnoXjMV13Z/3QkRctbpfd/AUN324moy8IvuyczvF8OjY7vRo3sitW1ALigtYmLiQuXvnsvrYavzFn2EthjGx40QuanMRwf7uX6RWqrZoIlD1w+c3wI55pZd3vhSu+6Jap47Scwp5eeFOftp+nBOZ1lNHneMjuLx/Syb0beH2BebDGYf5eu/XzN83n+M5x4kMimRUu1GM6zCO/vH99dSRqrM0Eaj65fg2eOcc12UxnaHPNdbTRrGdq9X9qewCvtuSzLcbj9gnyhnYtgmX92vBZX1aEB0eVGkfFmNhVfIq5u2bx08HfyKvOI8W4S0Y3X40o9uNplt0N48eeFPK2zQRqPrr8GqYdzeERMHhVdZlcd2hxwToPgGa9qzWkULSqRzmbTrKtxuOsut4JgF+wnmdY7m8f0tGdIsnMqTyW0hzCnNYfGgx3x/4npVHV1JkimjbqC2Xtr2US9tdStcmXTUpqFqniUA1DOlHYMd86+vQcus1hegO1oTQYwK0GFCtpLAjOYO5G48wf+NRjqbnEegvdIqPZFTPplwzqDXNoyqfSe103ml+OvQTPxz4gTXH12AxFlpHtmZE6xGMbDuSPnF99PSRqhWaCFTDk3UCdn4H27+FxN/AUgSNWkGGbTiLezZDk7ZV6tpiMaw9eIr/bT7KV+uSyCmwzp6W0LYJo3o2o2/rxgxq16TSX/kn807y86Gf+enQT6xOXk2hpZCYkBgubH0hF7a+kCHNhxAa4Nk0nUpVlSYC1bDlnIRdC6wXmnf/UHr9eX+GEY9X6WjBGMPGw6f5al0SaxNPset4JgBNGwVzaY9mXNQtjnM6xhISWPF8yZkFmfyW9BuLDy1m2dFlZBdmE+QXREKzBC5odQHDWw6ndWRrPYWkvEYTgfIdx7bAu8MrbnPrr9CiX5W6P3I6l/+uOsiO5EyW70slr9BCgJ8wqF00I7rFM7xzLN2aRVb4hV5QXMC64+tYmrSU3478xsEM6yjsrSNbc06LczinxTkMbjaYiKCIKsWoVFk0ESjfZLHAZ5Ng38/ltxn5NCTcDCGez0+QX1TM8n1p/L4nlV93p7D3RBYAsRFBDOkQw9AOMQzvFEu7mLAKE8PBjIMsP7qcZUeWsfrYanKLcvEXf3rG9GRI8yEkNE2gb3xfnVRHVYsmAqWg7NtSy3LPJmjSzuPuk9Nz+W1PKiv2pbFiXxrHMvIA62mkIe1jGNIhmmEdYmgfG15uYigsLmRjykZWJq9kVfIqtqZupdgU4y/+dIvuxoCmAxjYdCAD4gfQJMSzSXqUb9NEoFRZUnbD3DvgSCX/nsb/E/pPBT/37/YxxnAwLYff9qay+sBJVu1Psz/IFh0eRP/WjRnUPpr+rRvTt3Xjcq8x5BTmsDFlI+uPr2fd8XVsTtlMgaUAgA5RHaxJoekAEpom6LAXqkKaCJSqjDFwfGvl1xcAxA/uWgOxnTzo3rAvJZs1iSdZf/AU6w6dYn9KNgBB/n50b9GIfq2i6N+mCX1bN6ZtdBh+ZYyJVFBcwLa0baw7vo51x9ex4cQGsgut/TQPb07fuL70ietD79jedI/prsNfKDtNBEpVRX4WzLkFdi+ouN3FT0K78yG+OwS7f4E3NSufDYdOs/bgSTYeOs2WI+n2W1UjQwLo3TKKPq0a07tlFD1aNCozORRbitl9arc9KWxO3cyx7GMABEgAnZt0pkdMD3rE9KBnTE86NemkycFHaSJQqqYcXAEfji5/fZN2EN8DYjpB23OheV+IbObWratFxRZ2H89ic9JpNh9JZ0tSOtuTMyi2TbIQHuRP9+aN6NmiET1bWJNDp/iIUqeVTuScYEvKFrakbmF72na2pW0joyADsCaHjo070j2mO92iu9GlSRc6RHUgOiRab11t4DQRKOUtFgukH7JeiD7zOroeTh9ytAmKtI6PZH91sY6dFN0BAkMq7D6/qJidyZnsPJbBtqMZbD+awY7kDLJtRw7+fkKnuAi6Nouka7NIOsdH0LlpJG2iw+zDbRtjSMpKYkfaDnactL3SdnAy76T9c6KCo2jfqD0dGndwvEe1p0V4C/z9Kn5GQtUPmgiUOtvyMyF5E5zYAam7ba+9jiefwXqtoXEba2KI7WI9ijhTDo8t9yjCYjEkpmWzPTmDncmZ7EjOYOexTI6czrW3CQrwo1NcBB3iwukYF0Gn+Ag6xkXQPjac0CB/jDGk5Kaw+9RuDqQf4ED6Afan7+dA+gGXBBHsH0zbRm3pEGVNDGfe2zZqS0hAxUlM1S2aCJSqK/KzIG2v9ZW6G1L3WF9pe6Aoz9EuJKqMBNEZmrSHgLJHR83MK2TviSz2nMhi74ksdh3LZH9qFkmncnH+37xl41A6xIXTNiaMdjHhtIkOo63tPTTIn9N5pzmQYUsOp/dzIMP6fiTrCAZrR4LQMqKlS3Lo0LgDHaI6EBUc5c2/oKoiTQRK1XUWi/VowTk5pO62JozMZEc78bdehzjzatwaolpbjyyiWkNE01K3ueYVFrM/JZv9qVnW95Qs9qdmk5ia7TJhD0B8ZDBtY8JoEx1uew+jVZNQ2kSHERkKhzIPWpPEaccRRGJGIvnFjulBo0OiaRPZhpaRLWkZ0ZLWka1pGdGSVhGtiA+L11NNtUQTgVL1WV6G9Yghda8jOZw6YL0OkXvKta1/EDRqaUsQbSCqFTRqYa03amW9cB0caT/tdDqngINpORw8mcOhtGx7+WBatsvcz2C9zbVF4xBaNA61vqKs5aZRQQQGpZPDUZJzDnEg/QCHMg+RlJnE8ZzjWJxmnvMXf5qGNaVZeDNaRbaiaVhTmkc0p1lYM5qFW18RgRF64doLNBEo1VDlZ0J6Epw+bL1offqQrXzY+p51rPQ2QZHQqDlE2l5nyhHxENHMmiwim5FrgjhyOofDp3I5fDKHI6dzOXIqlyOnczl6OpcTmfmU/PqIDA6gaVQIzaNCaNoohJgIP0JCMpCgUxRJKnnmJOmFxzmRe4wjWUdIyU1xSRQAYQFhxIfF0zS8KU3DmhIfFk9caJz1PSyO2NBY4kLjCPKvfAIh5aCJQClfVZRvPbV0+rD1PTPZmjgykyHzmO2VbB3Gu6SgCGtyCI+3JYl4CI+DsBiIaEpRSBNSTSOSC8M5lBtMckYBx9LzSE7P5Vh6Hscz8knNyqfIUvo7JjI4gLhGwcRFBhAZnktoaCYBQekY/9MUymlyLSfJLErjZN4JTualUWRKx9coqBGxobHEhsYSExJDTKjtFRJDk5Am9vfokGjCAt2birQh00SglCqfxQI5aZB13HoEcSZB2JedsL6yT5Q+FXWG+EFoE2uSCIuB0GgIa4IJiSYnoBEZEslJSzgpRWEcKwwlOT+Yw7nBHM4SUrMLScnMJyu/jGQEBAVAk4hCIiNyCA3NIig4G/+ATIx/JkWSTr5JJ6f4NFmFJ8m35JXZR7B/MFHBUdZXUBSNgxsTFRxFo+BGLvWo4CgaBTWy1xvSnVEVJYKAsx2MUqqO8fODiDjri14Vty0utCaI7BTbK81az0m1LU+1JotTB+DoeiTnJOHF+YQDzcv87ADrHVIxjbGERFEQGEWuXwQ5fmFkEUa6JYxTllDSikJILQzmRGYQx1KjSM6N4Vh+IFkmhHwCAds1BSlAArIQ/2wCArMIDckjOCSHwMBcigrzOJmbQ5pkUSzHKSSLfEsmxWUcbZwR7B9MVFAUUSHWBBIVbE0ajYIaEREUQURgBJFBkUQGRRIeGO54D4wkPCicQL/KpzqtCzQRKKXc5x9ov4bgFmOgMMeaHHJPWScRyjsNeemQe9patr375Z4iJPcUIXmHaJKfCfkZrrfUlmQbKcP4BVAcGE5RQDiF/uHk+4WS6xdGDqFkE0pmUQiZ+UGkFweRXhTDyaLmnCwIIKM4iGyCyCaAbH9Djr8h36+YfP9CCv0LwT8PS2AuhYG5nArIRfxPg/9RLJJNseRgKKx09wP9ggj1DycsMIzwwHDCA8OIDIog3FYPCwwjLCDMvj4sIIzQgFDCAq3vzq8zbQP8av5rWxOBUsp7RCAo3PqKauX59kX51rum8tKtiSEvHQqyrM9j5GdCQSaSn0VAQRYB+VmEFGQSaV+XbG1XkAkF2a7XQfxtr5IstlchFEkghX4hFPiFkC/B5BNEPkHkmiByTWMyTAAnCeAUcFr8yBR/sv2EHD/I8YNcP8j3M+T7WSjwKybFL5tkyaDYrwiLfxEWvyKMXyEWKQBx7xT96FZTeOXixzz/O1bCq4lAREYD/8T6J3/fGPNSifViWz8WyAGmGWPWezMmpVQ9EhDsdNqqmooKoDDbmhwKc6zJoTAHCnKsywtzrfXCXCjMJaAgm4DCXELt6/KgyPZemANFOfa6KcqDojwkv4IjmHIYIE+EHBFy/PzIESHTL4AMCSRLAsj08ycbf7L8/ImwHKn+36EMXksEIuIPvAVcAiQBa0RknjFmu1OzMUBn22sI8I7tXSmlalZAkPUVWvMT+tiferBYoDjfmjiK8qxHNMUFjrL93VYuLkCK8gktLiC0uIAYe3vXd0uR7dXlghqPHbx7RDAY2GuM2Q8gIrOBiYBzIpgIfGysty6tFJHGItLcGJNcujullKrj/PzALxQCQ2u2W9vLW7zZd0vgsFM9ybbM0zaIyK0islZE1qakpNR4oEop5cu8mQjKeka85BURd9pgjPmPMSbBGJMQF1cD5wqVUkrZeTMRJAGtneqtgKNVaKOUUsqLvJkI1gCdRaS9iAQBU4B5JdrMA6aK1VAgXa8PKKXU2eW1i8XGmCIRmQ4sxHr76AxjzDYRud22/l3ge6y3ju7FevvoTd6KRymlVNm8+hyBMeZ7rF/2zsvedSob4C5vxqCUUqpi3jw1pJRSqh7QRKCUUj6u3g1DLSIpwMEqbh4LpNZgOPWB7rNv0H32DdXZ57bGmDLvv693iaA6RGRteeNxN1S6z75B99k3eGuf9dSQUkr5OE0ESinl43wtEfyntgOoBbrPvkH32Td4ZZ996hqBUkqp0nztiEAppVQJmgiUUsrH+UwiEJHRIrJLRPaKyMO1HY83iEhrEflFRHaIyDYRuce2PFpEfhSRPbb3mp+iqRaJiL+IbBCR/9nqDX1/G4vIVyKy0/bfepgP7PN9tn/TW0VkloiENLR9FpEZInJCRLY6LSt3H0XkEdv32S4RGVWdz/aJROA0beYYoAdwrYj0qN2ovKIIeMAY0x0YCtxl28+HgcXGmM7AYlu9IbkH2OFUb+j7+0/gB2NMN6Av1n1vsPssIi2BPwEJxpheWAexnELD2+eZwOgSy8rcR9v/11OAnrZt3rZ9z1WJTyQCnKbNNMYUAGemzWxQjDHJxpj1tnIm1i+Illj39SNbs4+Ay2slQC8QkVbAZcD7Tosb8v42As4HPgAwxhQYY07TgPfZJgAIFZEAIAzrvCUNap+NMUuBkyUWl7ePE4HZxph8Y8wBrCM4D67qZ/tKInBrSsyGRETaAf2BVUDTM/M82N7jazG0mvY68BfA4rSsIe9vByAF+NB2Oux9EQmnAe+zMeYI8HfgEJCMdd6SRTTgfXZS3j7W6HearyQCt6bEbChEJAKYA9xrjMmo7Xi8RUTGASeMMetqO5azKAAYALxjjOkPZFP/T4lUyHZefCLQHmgBhIvI9bUbVa2r0e80X0kEPjMlpogEYk0CnxljvrYtPi4izW3rmwMnaiu+GnYuMEFEErGe7hshIp/ScPcXrP+Wk4wxq2z1r7Amhoa8zyOBA8aYFGNMIfA1cA4Ne5/PKG8fa/Q7zVcSgTvTZtZ7IiJYzx3vMMa85rRqHnCjrXwj8O3Zjs0bjDGPGGNaGWPaYf1v+rMx5noa6P4CGGOOAYdFpKtt0cXAdhrwPmM9JTRURMJs/8Yvxnr9qyHv8xnl7eM8YIqIBItIe6AzsLrKn2KM8YkX1ikxdwP7gMdqOx4v7eNwrIeHm4GNttdYIAbrHQd7bO/RtR2rF/b9QuB/tnKD3l+gH7DW9t95LtDEB/b5GWAnsBX4BAhuaPsMzMJ6DaQQ6y/+myvaR+Ax2/fZLmBMdT5bh5hQSikf5yunhpRSSpVDE4FSSvk4TQRKKeXjNBEopZSP00SglFI+ThOBUiXYRve8s5I2/xaRc89WTEp5kyYCpUprDFSYCIAhwErvh6KU92kiUKq0l4COIrJRRF4puVJEugO7jTHFJZbPFJF3bHNC7BeRC2xjzO8QkZm2Nv62dltFZIuI3HdW9kipCgTUdgBK1UEPA72MMf3KWT8G+KGcdU2AEcAEYD7W8ZBuAdaISD+sY+m3NNZx9RGRxjUWtVJVpEcESnluFOUngvnG+rj+FuC4MWaLMcYCbAPaAfuBDiLyhoiMBhrs6LCq/tBEoJQHRCQMaGyMKW+kx3zbu8WpfKYeYIw5hXVWsSXAXbhOqKNUrdBTQ0qVlglElrPuIuCXqnYsIrFAgTFmjojswzo9oVK1ShOBUiUYY9JEZJltEvEFxpgHnVaPwToHQFW1xDq72Jmj8Ueq0ZdSNUJHH1XKAyKyHhhirBOkKNUgaCJQSikfpxeLlVLKx2kiUEopH6eJQCmlfJwmAqWU8nGaCJRSysdpIlBKKR/3/yn2OaowraKUAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"L.add_relax('SpinDiffusion',i=1,k=50)\n",
"\n",
"rho=sl.Rho('15Nx',['15Nx',ex0.Op[0].x@ex0.Op[1].alpha,ex0.Op[0].x@ex0.Op[1].beta])\n",
"rho.DetProp(seq,n=6000)\n",
"ax=rho.plot()\n",
"_=ax.legend(('Average',r'H$^\\alpha$',r'H$^\\beta$'))"
]
},
{
"cell_type": "markdown",
"id": "2adea70c",
"metadata": {},
"source": [
"### Field-strength dependence\n",
"We may also observe how the decay rates depend on the applied field strength. Below, we apply field strengths of 10, 20, 30, 40, and 50 kHz, where we expect faster relaxation as we get closer to the MAS frequency (60 kHz)."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "8c27f907",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"State-space reduction: 32->16\n",
"State-space reduction: 32->16\n",
"State-space reduction: 32->16\n",
"State-space reduction: 32->16\n"
]
}
],
"source": [
"rho=[]\n",
"for v1 in np.linspace(10e3,50e3,4):\n",
" rho.append(sl.Rho('15Nx','15Nx'))\n",
" seq.add_channel('15N',v1=v1)\n",
" rho[-1].DetProp(seq,n=6000)"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "699a9bb2",
"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]\n",
"for rho0 in rho:rho0.plot(ax=ax)"
]
},
{
"cell_type": "markdown",
"id": "825d49ef",
"metadata": {},
"source": [
"The curves are fairly similar, indicating a relatively fast motion (300 ns was input). We may slow down this motion to obtain faster relaxation, but also more dispersion among the curves."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "9a5f23b6",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"State-space reduction: 32->16\n",
"State-space reduction: 32->16\n",
"State-space reduction: 32->16\n",
"State-space reduction: 32->16\n"
]
}
],
"source": [
"L.kex=sl.Tools.twoSite_kex(1e-5)\n",
"rho=[]\n",
"for v1 in np.linspace(10e3,50e3,4):\n",
" rho.append(sl.Rho('15Nx','15Nx'))\n",
" seq.add_channel('15N',v1=v1)\n",
" rho[-1].DetProp(seq,n=1000)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "979b16f5",
"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]\n",
"for rho0 in rho:rho0.plot(ax=ax)"
]
},
{
"cell_type": "markdown",
"id": "0fc82611",
"metadata": {},
"source": [
"We may also investigate correlation time dependence for several field strengths. In this case, we use a special feature of SLEEPY, the `rho.extract_decay_rates(...)` function, which extracts non-oscillating terms from the propagator or sequence directly, without actually propagating the system. This is achieved by finding the eigenvalues and eigenvectors of the propagator. The real parts of the logarithm of the eigenvalues yield the decay rates, where we may filter for non-oscillating terms by finding eigenvalues that are strictly real.\n",
"\n",
"Note that various modes for this function exist, yielding different averaging and different weightings. Type `help(rho.extract_decay_rates)` for more details.\n",
"\n",
"This mode of the function only works where oscillating terms should be neglected (so, for example, we cannot get $T_2$ this way, because peaks in a spectrum both oscillate and decay)."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "3d9fa0b6",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"log10(tc)=-8.0, 21 seconds elapsed\n",
"log10(tc)=-7.0, 176 seconds elapsed\n",
"log10(tc)=-6.0, 303 seconds elapsed\n",
"log10(tc)=-5.0, 419 seconds elapsed\n",
"log10(tc)=-4.0, 535 seconds elapsed\n"
]
}
],
"source": [
"# ~ 10 minutes calculation time (164 simulations with powder average)\n",
"from time import time\n",
"sl.Defaults['verbose']=False\n",
"tc0=np.logspace(-8,-4,41)\n",
"v10=[10e3,25e3,40e3,50e3]\n",
"R1p={v1:np.zeros(tc0.shape) for v1 in v10}\n",
"rho=sl.Rho('15Nx','15Nx')\n",
"\n",
"t0=time()\n",
"for k,tc in enumerate(tc0):\n",
" L.kex=sl.Tools.twoSite_kex(tc=tc)\n",
" for v1 in v10:\n",
" seq.add_channel('15N',v1=v1)\n",
" R1p[v1][k]=rho.extract_decay_rates(seq)\n",
" if np.mod(k,10)==0:\n",
" print(f'log10(tc)={np.log10(tc):.1f}, {time()-t0:.0f} seconds elapsed')"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "5a7e03b4",
"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]\n",
"for v1 in v10:\n",
" ax.semilogx(tc0,R1p[v1],label=fr'$\\nu_1$ = {v1/1e3:.0f} kHz')\n",
"ax.legend()\n",
"ax.set_xlabel(r'$\\tau_c$ / s')\n",
"_=ax.set_ylabel(r'$R_{1\\rho}$ / s$^{-1}$')"
]
},
{
"cell_type": "markdown",
"id": "31512ae3",
"metadata": {},
"source": [
"## Combined decay from reorientation and chemical shift modulation"
]
},
{
"cell_type": "markdown",
"id": "fdd4150a",
"metadata": {},
"source": [
"It is also possible that we have both reorientational motion *and* chemical shift modulation, induced by the same motion. To investigate this the results, we add chemical shifts to the $^{15}$N, and observe the field-strength dependence of the relaxation."
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "f7067c57",
"metadata": {},
"outputs": [],
"source": [
"ex0.set_inter('CS',i=0,ppm=-5)\n",
"ex1.set_inter('CS',i=0,ppm=5)\n",
"\n",
"L=sl.Liouvillian(ex0,ex1,kex=sl.Tools.twoSite_kex(tc=1e-4))\n",
"seq=L.Sequence()\n",
"rho=sl.Rho('15Nx','15Nx')\n",
"\n",
"R1p=[]\n",
"v10=np.linspace(1,51,21)*1e3\n",
"for v1 in v10:\n",
" seq.add_channel('15N',v1=v1)\n",
" R1p.append(rho.extract_decay_rates(seq,mode='pwdavg'))"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "ef8ab7ca",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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eXtm0O7S9UlCYpqR/5ihd0RfJLc+tb6ard+RHPSVSmKZAQ0pFctPDrzcwobyYU2dMCK0GhWkKtGcqkntWbt3D8vomrjtzFkUhTtyuME3BBE3DJ5JT3J1/fHItNRUlXLt0Vqi1KExTUFxYwPjSIna3aXy+SC54dkMLr2zezZc+cQzRkiNahemIhRKmZna3mTWZ2eqEtpiZLTOzDcHthITnbjazjWa2zswuCKPmftUVGlIqkgv6+pxvP7WWaRPKuHLJ0WGXE9qe6T3AhQPabgJWuPtcYEXwGDNbAFwBHB+85wdmlv1FsIegyU5EcsN/r36f1dv383/Om0ekKPyD7FAqcPdngYETSl8M3Bvcvxe4JKH9AXfvdPfNwEZgyUjUORiFqUj4enr7uO3pdcybVMElJ08Nuxwgt86ZTnL3nQDBbX/v26nAtoTXNQRtoaiORnSYLxKyh1Y2sKmljT/75LEUFozc0iTDyaUwHcpg/1KDDo43s+vNrM7M6pqbm7NSTCwaYU9bF30any8SioPdvfzTig2cfHQV5y8Ir5P+QLkUpo1mNhkguG0K2huA6QmvmwbsGOwD3P1Od1/s7otra7Mzn2EsGqGnz9l/sDsrny8iw7v/5a3s3HeQr11w7IgumHc4uRSmjwP9C/ZdDTyW0H6FmZWY2SxgLvBqCPUBWqVUJEwHDnbz/Wc2ctbcGs6YUxN2Ob8mrK5RPwNeAo4NVj29DvgH4Hwz2wCcHzzG3dcADwLvAE8CN7h7bxh1A8SimuxEJCw/em4ze9q7+fMLjgu7lA8JpZeru185xFPnDvH6W4BbsldR8g4NKdUoKJERtau1k7ue28RFC49i4bTKsMv5kFw6zM8L/Yf52jMVGVnff+ZdOrp7+er5x4ZdyqAUpin6YOYoDSkVGSkNe9q5/+WtXH7qdI6ZGM7kz4ejME1RSVEhFSVFugAlMoL+afkGMPjyeXPDLmVICtM0aBSUyMjZ2HSAh19v4KrTZjClqizscoakME2DwlRk5HznqfWUFRfyJ2fPCbuUYSlM01AdjehqvsgIWLVtL0+ueZ8/+thsqoM12HKVwjQN2jMVGRnffmodsWiEz501O+xSDkthmoZYRTxM3TU+XyRbXtjYwvMbW/iTs+dQEfLEz8lQmKahOhqhq7eP1s6esEsRGZXcnX98ah1TKkv5/dNmhF1OUhSmadCQUpHsempNI6u27eUr582jtDi0ueBTojBNg1YpFcme3j7ntqfXMac2ym+fkhsTPydDYZqGmFYpFcma7y1fz4amVm785LGhLt2cqvypNId8MKRUYSqSSQ+tbOBffrmR31k8nU+dcFTY5aREYZoGzWkqknkvvbuLmx95izPmVPOtz5yQUxM/J0NhmobySBGlxQWa7EQkQzY1t/KF+1dydKycO37vVIrz6PC+X/5VnCNqx5WwuaU97DJE8t7uti7+8J7XKCowfnzNEirLi8MuKS0K0zRdePxRPLOuiZ37OsIuRSRvdfb08vn76tix7yB3/sFijq4uD7uktClM0/QHp8/E3bnvpa1hlyKSl9ydmx5+m9e27OG2y0/i1BkTwi7piChM0zQ9Vs75Cybxs1ff42B3aEtSieStf16xkUff2M6N58/j0ydNCbucI6YwPQLXLp3FnvZu/uuN7WGXIpJXHntzO99dvp5LT5nGFz9xTNjlZITC9Ah8dFaM+ZPH8+MXtmjSE5EkvbZlN1/7+Vt8dFaMv//thXnXBWooCtMjYGZcu3Qm6xoP8NK7u8IuRyTnbWlp4/r/qGPqhDJ+eNWpRIpGTwSNni0JyW+dNIVYNMLdL2wJuxSRnLavvZs/vOc1HLj7mo9QVR4Ju6SMUpgeodLiQn53ydGsWNvI1l1tYZcjkpO6evr4/P11NOzp4M6rFjOrJhp2SRmnMM2Aq06fQaEZ976oblIiA7k7f/no27y8aTe3XraQJbNiYZeUFQrTDJg0vpSLFk7m53XbNGG0yAD/+suNPLSygS+fO5fPnDwt7HKyRmGaIdcuncmBzh4eXtkQdikiOeFgdy9//tAqblu2nksWTeErObzmfSYoTDPk5KMnsGh6Ffe8uIW+PnWTkrFtS0sbn/nBizxY18CXPnEMt3120ajpAjUUhWkGXbt0Jptb2vif9c1hlyISmqfWvM+n/+V5du7r4MfXfoQbP3kshQWjO0hBYZpRFy2czKTxJdz9wuawSxEZcT29ffzdE/V8/r6VzKqN8osvnck5x04Mu6wRk3NhamZbzOxtM3vTzOqCtpiZLTOzDcFtTs6IUFxYwFWnzeC5DS1sbDoQdjkiI6Zp/0F+90evcOezm/j9047m5184nWkT8ncGqHTkXJgGznH3Re6+OHh8E7DC3ecCK4LHOenKJUcTKSrgx+rEL2PES+/u4qJ/fp63t+/je7+ziG9dspCSovxYUTSTcjVMB7oYuDe4fy9wSXilDK+6ooRLFk3hkde3s6+9O+xyRLKmr8+541fv8nv//jLjy4p47ItLueTk/FlNNNNyMUwdeNrMVprZ9UHbJHffCRDcDnoixsyuN7M6M6trbg7vItC1S2fR0d3LA6+9F1oNItm0r72b6++r49Yn13LRwsk8/sUzmTdpXNhlhaoo7AIGsdTdd5jZRGCZma1N9o3ufidwJ8DixYtD6580f/J4Tpsd4z9e2sp1Z87Kq+VqRQ5n9fZ9/PFPVvL+voP8zacXcPUZM0d9t6dk5NxvubvvCG6bgEeBJUCjmU0GCG6bwqswOdcuncX2vR0se6cx7FJEMuJgdy93Pvsuv33Hi/T0Ov/5+dO5ZuksBWkgp8LUzKJmNq7/PvBJYDXwOHB18LKrgcfCqTB5582fxPRYmS5ESd7r6e3jgVff45zv/Iq/e2ItZx1Twy++dCanHJ2TnWpCk2uH+ZOAR4O/dEXAT939STN7DXjQzK4D3gMuD7HGpBQWGFefPpNv/f96Vm/fxwlTK8MuSSQlfX3Of69+n9ueXsemljYWTa/its+exBlzasIuLSflVJi6+ybgpEHadwHnjnxFR+byxdO5fdl67nlxC9+5/EObJZKT3J1nN7Tw7afWsnr7fuZOrOCHV53KJxdM0iH9MHIqTEebyrJiLj1lGv/52jZu+tRx1FSUhF2SyLBWbt3DPz65llc272bahDJuu/wkLjl56pgYDnqkFKZZds3Smdz38lZ++sp7/Om5o3vWHMlfa9/fz3eeWsfy+iZqKkr45m8dzxVLpo/JzvfpUphm2ZzaCj4+r5b7Xt7KFz4+Z1SteSP5771d7dy+bB2PrdpBRUkRX7vgWK5dOpPyiKIhVfoXGwHXLp3JNT9+jSfe3jmmR4hIbuju7eN/1jXz0MoGltc3UlhgXP+x2fzxx+eMunWZRpLCdAR8bG4ts2uj/PiFzVy8aIpO4kso1r6/n4fqGvivN7fT0tpFdTTCNWfM5I8+NptJ40vDLi/vKUxHQEGBce0ZM/mrx9Zw38tbueq0GQpUGRF72rp4fNUOHlrZwNvb91FUYJw7fyKXnTqds4+tpVij8zJGYTpCLjt1Ok+taeQbj63hmbVN3HrpiUzU3oBkQU9vH/+z/oPD+O5eZ8Hk8XzjNxdw8aIpVKtXSVaY++hcYmPx4sVeV1cXdhm/pq/Pue/lrfz9f9dTWlzI3158Ap8+aUrYZcko4O6sff8Aj76xnUde305LayexaIRLFk3l0lOncvwUDRrJFDNbmTA96CHaMx1BBQXG1WfM5Ky5NXz1wVV86Wdv8PQ7jfztxcfrxL+kbHdbF89taOa5DS08t6GZxv2dFBUY5xw3kctOncY5x05U75ERpDANwezaCh76wun88NlNfG/5el7ZtItbLztxTC3xIKnr6ulj5dY9hwJ09Y59uMcHh5w5t4azjqnhvAWTNDgkJDrMD9maHfv46n+uYl3jAa5cMp2v/8YCKkr0N07ih+6bW9p4dn08PF/atIv2rl4KC4xTjq7iY3NrOWteLQunVmqE0gjSYX6OOn5KJY9/aSm3L1vPnc9u4vmNLdx2+SKWzIqFXZqMsIPdvbyzcz9vbdvLW9v38cqm3Wzf2wHAjOpyLj1lGmfNreH0OdWMKy0OuVoZSHumOaRuy25u/Pkq3tvdzh+dNZuvnj+P0mIN5xuNunr6WPf+Ad7avpe3tu3jre37WN94gN6++O9jTUVJfO9zXi1nza1hRnU05Iql31B7pgrTHNPW2cPfPVHPT155j3mTKrj10hNZNL1K/VLzWGdPL5ua23i7YR9vbd/L2w37qN95gK7ePgCqyotZOLWSk6ZVsXBaJSdOq+So8aX6P89RCtM886t1TfzFw2/RuL+TqVVlnDW3hrPm1rL0mGpd+c9B7k5zayebmtvY1NzGu82tbGpuZVNLG9t2txPscDKupIgTpsYD88RpVZw4rZJpE8oUnHlEYZqH9rV38/hbO3h+QzMvbtzFgc4ezGDh1ErOmlvDmcfUcuqMCer+MkLcnf0dPezY18HmlrZ4WB4KzjYOdPYcem1pcQGzaiqYXRtlTk2UORMrWDi1kpnVUQp0sSivKUzzXE9vH6sa9vF80KfwjW176e1zyiOFfHRWjDPn1vKxuTUcM7FCezlp6ujqZce+DnbuPfjB7d6O+P19B9m5t4O2rt5fe8+UylJm18ZDc3ZN9ND9KZVlCs1RSmE6yhw42M3Lm3bz3IZmnt/QwqaWNgAmjS/hxGlVTK0qY2pVGVOqyphSVcrUCWXUREvG1C+4u9Pe1cvuti52tXWxu62TltYudrfFf3a1xtsa93eyc18He9q7P/QZteNKmFJZyuTKD/4tJ1eWMaO6nNm1UU1VNwapa9QoM660mPMXTOL8BZMAaNjTHt9r3djCxsZWXnp3F60Jh50AkcICJleVJoRsGdOqyphcVcr40mKiJYWURYqIRgopixQSKSwIdS/X3eno7qX1YA8HOns4cLCH1oM9tHZ2x+/3tyXc7u/oDoKyk11tXXT29A362SVFBVRHI8QqIhxVWcrJR1f9WlhOqSxjUmWJJkeWpGnPdJRyd/Yf7GHH3g6274kfqm7vv7+3gx17D9J44CDD/fcXFRjlkULKI0WUlxQSjRRRFikkGimktLgQMzCCsDUwOBS+8fsk3Dd6+pyunl66evro7Omjq6ePrt6+X3scv+2N3/b2DVtfv5KiAsaVFjOutIiKkiKqKyLEopF4WEZLqK7ovx+hOnhcHinU6RBJi/ZMxxgzo7KsmMqyYuZPHj/oa7p6+mjcHz8v2NrZQ3tXL+1dPbR19tLR3UtbYltXLx1d8baW1i4OdvfSn3PuHr8fNHjQ9sF9cJyiggIihQVEigooKYrfVpQWESksoKS48EPPlRQVEC2JB2R/UI4rLf61x9GSIl2Ak5ygMB3DIkUFTI+VMz1WHnYpInlPf9JFRDJAYSoikgEKUxGRDFCYiohkgMJURCQDFKYiIhmgMBURyQCFqYhIBoza4aRm1gxsHeLpGqBlBMvJJm1L7hkt2wHalsHMcPfagY2jNkyHY2Z1g42tzUfaltwzWrYDtC2p0GG+iEgGKExFRDJgrIbpnWEXkEHaltwzWrYDtC1JG5PnTEVEMm2s7pmKiGSUwlREJAPGXJia2YVmts7MNprZTWHXkwozu9vMmsxsdUJbzMyWmdmG4HZCmDUmw8ymm9kzZlZvZmvM7MtBez5uS6mZvWpmq4Jt+WbQnnfbAmBmhWb2hpn9Inicr9uxxczeNrM3zawuaMvqtoypMDWzQuD7wKeABcCVZrYg3KpScg9w4YC2m4AV7j4XWBE8znU9wI3uPh84Dbgh+H/Ix23pBD7h7icBi4ALzew08nNbAL4M1Cc8ztftADjH3Rcl9C3N6raMqTAFlgAb3X2Tu3cBDwAXh1xT0tz9WWD3gOaLgXuD+/cCl4xkTelw953u/npw/wDxX96p5Oe2uLu3Bg+Lgx8nD7fFzKYBvwH8e0Jz3m3HMLK6LWMtTKcC2xIeNwRt+WySu++EeEgBE0OuJyVmNhM4GXiFPN2W4ND4TaAJWObu+bot3wP+HEhcHzsftwPif9CeNrOVZnZ90JbVbRlrC+oNtrav+oaFxMwqgIeBr7j7/nxdetnde4FFZlYFPGpmJ4RcUsrM7DeBJndfaWZnh1xOJix19x1mNhFYZmZrs/2FY23PtAGYnvB4GrAjpFoypdHMJgMEt00h15MUMysmHqQ/cfdHgua83JZ+7r4X+BXx89r5ti1Lgd8ysy3ET399wszuJ/+2AwB33xHcNgGPEj/Fl9VtGWth+how18xmmVkEuAJ4POSajtTjwNXB/auBx0KsJSkW3wW9C6h399sTnsrHbakN9kgxszLgPGAtebYt7n6zu09z95nEfy9+6e6/T55tB4CZRc1sXP994JPAarK9Le4+pn6Ai4D1wLvA18OuJ8XafwbsBLqJ72VfB1QTvzK5IbiNhV1nEttxJvHTK28BbwY/F+XptpwIvBFsy2rgG0F73m1LwjadDfwiX7cDmA2sCn7W9P+eZ3tbNJxURCQDxtphvohIVihMRUQyQGEqIpIBClMRkQxQmIqIZIDCVEQkAxSmMuaY2Q/NbOmAtpmJUxsmtLcOeHyNmf1rtmuU/KMwlbHoo8DLYRcho4vCVPKSmVWZ2fsJj1eaWWUS75sPrPf45CRDvWZ2MEHyRw7zWV8IJh9+08w2m9kzKW2EjCpjbdYoGSXcfW8wBrvY3buJDx08EXjuMG/9FPDkUE+a2bHEJ/q41t3fNLOyYHq9fjGC+Rzc/d+AfwsmbfklcPvAz5OxQ2Eq+awROIr4HLXHEZ8V6C6g0t0vG+I9FwDXDvFcLfHJLy519zVBW4e7L+p/gZldAywe8L5/Ij4xyP9LZyNkdNBhvuSzHcAUM/sdoMXd17v7dUO92MzKgSoPpmcbxD7iwbx0iOcH+8xrgBnAN5OuWkYl7ZlKPttBfOmJC4Hzk3j9OcBw5zW7gs97ysxa3f2nw32YmZ0K/Blwlrv3DfdaGf0UppLPtgOXEV/QriWJ138KeGi4F7h7WzDr/DIzazvM532R+DnUZ4JVAurc/XNJ1CGjkKbgk1HDzKqBW4jvpf67u//9gOdfBz4aXLASySiFqYhIBugClIhIBihMRUQyQGEqIpIBClMRkQxQmIqIZIDCVEQkAxSmIiIZoDAVEckAhamISAb8LxGc0h86h7QoAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"ax=plt.subplots(figsize=[5,4])[1]\n",
"ax.plot(v10/1e3,R1p)\n",
"ax.set_xlabel(r'$\\nu_1$ / kHz')\n",
"_=ax.set_ylabel(r'$R_{1\\rho}$ / s$^{-1}$')"
]
},
{
"cell_type": "markdown",
"id": "58680df4",
"metadata": {},
"source": [
"We see increased relaxation rate constants at low RF-fields, due to chemical shift modulation, and at high RF-fields due to reorientational motion of the $^{15}$N CSA and H–N dipole coupling. Note that the timescale dependence of the two relaxation mechanisms is different. This experiment is particularly interesting because while being essentially the same experiment, we investigate two different mechanisms of relaxation just based on the field-strength setting.$^{4-5}$\n",
"\n",
"[4] J.D. Haller, P. Schanda. [*J. Biomol. NMR*](https://doi.org/10.1007/s10858-013-9787-x), **2013**, 57, 263-280.\n",
"\n",
"[5] P. Rovó. [*Solid-State NMR*](https://doi.org/10.1016/j.ssnmr.2020.101665), **2020**, 108, 101665."
]
}
],
"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
}