{
"cells": [
{
"cell_type": "markdown",
"id": "152ee532",
"metadata": {},
"source": [
"# Bloch-McConnell Relaxation Dispersion"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
""
]
},
{
"cell_type": "markdown",
"id": "d6fab419",
"metadata": {},
"source": [
"In solution NMR (and also sometimes in solids), if a two-site exchange process leads to modulation of chemical shift, it is in some cases possible to calculate the rate of exchange ($k_{ex}=k_{1\\rightarrow2}+k_{2\\rightarrow1}$), the change in chemical shift ($\\Delta\\omega=\\Omega_1-\\Omega_2$) and also the populations of the two sites ($p_1/p_2=k_{2\\rightarrow1}/k_{1\\rightarrow2}$), based on a series of $R_{1\\rho}$ measurements. However, this depends on the rate of exchange and also the strength of the spin-lock. If the exchange is too fast, it is impossible to separate the populations from the change in chemical shift, obtaining only the product $p_1p_2\\Delta\\omega_{12}^2$.\n",
" \n",
"Furthermore, if only on-resonance $R_{1\\rho}$ experiments are applied, it is impossible to determine whether the larger population has the larger or smaller chemical shift, whereas this can be resolved using off-resonant $R_{1\\rho}$ experiments. We will investigate this with simulation, and also compare to the formula provided by Miloushev and Palmer.$^1$\n",
" \n",
"Note that we also use [$R_{1\\rho}$ in solids](../Chapter3/Ch3_R1p.ipynb), but then we must also consider reorientational dynamics.\n",
" \n",
"[1] V.Z. Miloushev, A.G. Palmer. [*J. Magn. Reson.*](https://doi.org/10.1016/j.jmr.2005.07.023), **2015**, 177, 221-227"
]
},
{
"cell_type": "markdown",
"id": "b2f7e9a9",
"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": "99b4cf3d",
"metadata": {},
"outputs": [],
"source": [
"import SLEEPY as sl\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"id": "af8f1a62",
"metadata": {},
"source": [
"## Theoretical Background\n",
"Miloushev and Palmer provide us with the relevant formula:\n",
"\n",
"$$\n",
"\\begin{equation}\n",
"R_{1\\rho}^{ex}=\\frac{\\sin^2\\beta_ep_1p_2\\Delta\\omega_{12}^2k_{ex}}{\\frac{\\omega_{e1}^2\\omega_{e2}^2}{\\omega_e^2}+k_{ex}^2-\\sin^2\\beta_ep_1p_2\\Delta\\omega_{12}^2\\left(1+\\frac{2k_{ex}^2(p_1\\omega_{e1}^2+p_2\\omega_{e2}^2)}{\\omega_{e1}^2\\omega_{e2}^2+\\omega_e^2k_{ex}^2}\\right)}\n",
"\\end{equation}\n",
"$$\n",
"\n",
"with the following definitions:\n",
"\n",
"$$\n",
"\\begin{eqnarray}\n",
"k_{ex}&=&k_{1\\rightarrow2}+k_{2\\rightarrow1} \\\\\n",
"\\Omega&=&p_1\\Omega_1+p_2\\Omega_2 \\\\\n",
"\\Delta\\omega_{12}&=&\\Omega_1-\\Omega_2 \\\\\n",
"\\omega_e^2&=&\\omega_1^2+\\Omega^2 \\\\\n",
"\\omega_{e1}^2&=&\\omega_1^2+\\Omega_1^2 \\\\\n",
"\\omega_{e2}^2&=&\\omega_1^2+\\Omega_2^2 \\\\\n",
"\\sin^2\\beta_e&=&\\frac{\\omega_1^2}{\\omega_1^2+\\Omega^2}\n",
"\\end{eqnarray}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "3516b730",
"metadata": {},
"source": [
"In the above formula, the relative sizes of the three terms in the denominator determine the availability of information from $R_{1\\rho}$ experiments. For example, if either the field strength is set too high, or $k_{ex}$ is \n",
"too large, the third term can be neglected, yielding\n",
"\n",
"$$\n",
"\\begin{equation}\n",
"R_{1\\rho}^{ex}=\\frac{\\sin^2\\beta_ep_1p_2\\Delta\\omega_{12}^2k_{ex}}{\\frac{\\omega_{e1}^2\\omega_{e2}^2}{\\omega_e^2}+k_{ex}^2}\n",
"\\end{equation}\n",
"$$\n",
"\n",
"In this case, $p_1$ and $p_2$ never appear separately from $\\Delta\\omega_{12}$, so that we cannot separate their contributions based on experiment. We may control the applied field strength, which modifies $\\omega_{e1}^2\\omega_{e2}^2/\\omega_e^2$, but cannot control $k_{ex}$. \n",
"\n",
"Note that if the applied field strength is significantly larger than $\\Delta\\omega_{12}$, then the last term of the denominator drops out, and the first term simplifies to $\\omega_e^2$, yielding\n",
"\n",
"$$\n",
"\\begin{equation}\n",
"R_{1\\rho}^{ex}=\\frac{\\sin^2\\beta_ep_1p_2\\Delta\\omega_{12}^2k_{ex}}{\\omega_e^2+k_{ex}^2}\n",
"\\end{equation}\n",
"$$\n",
"\n",
"In the simulations below, we will test some of these behaviors. First, we define a function that calculates the above formula, which we can use to compare to simulated results."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "2c7bcc8c",
"metadata": {},
"outputs": [],
"source": [
"def R1p_fun(kex,v1,CS1,CS2,p1):\n",
" p2=1-p1 #Population 2\n",
" #Convert to rad/s\n",
" omega1=v1*2*np.pi \n",
" Omega1=CS1*2*np.pi\n",
" Omega2=CS2*2*np.pi\n",
" \n",
" Omega=p1*Omega1+p2*Omega2 #Average shift\n",
" D_Omega=Omega1-Omega2 #Change in shift\n",
" sin2beta=omega1**2/(omega1**2+Omega**2) #Sine of offset angle\n",
" \n",
" #Effective fields\n",
" omega_e2=omega1**2+Omega**2\n",
" omega_e2_1=omega1**2+Omega1**2\n",
" omega_e2_2=omega1**2+Omega2**2\n",
" \n",
" x=sin2beta*p1*p2*D_Omega**2\n",
" num=x*kex #Numerator\n",
" den1=omega_e2_1*omega_e2_2/omega_e2 #Denominator (1st term)\n",
" den2=kex**2 #Denominator (2nd term)\n",
" den3=x*(1+2*kex**2*(p1*omega_e2_1+p2*omega_e2_2)/(omega_e2_1*omega_e2_2+omega_e2*kex**2))\n",
" return num/(den1+den2-den3)"
]
},
{
"cell_type": "markdown",
"id": "7c12570d",
"metadata": {},
"source": [
"## Define parameters, define the spin-system"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "724323ac",
"metadata": {},
"outputs": [],
"source": [
"p1=0.75 #Population 1\n",
"p2=1-p1 #Population 2\n",
"kex=30000\n",
"tc=1/kex #Correlation time\n",
"DelOmega12=500 #Change in Chemical Shift in Hz\n",
"\n",
"ex0=sl.ExpSys(v0H=600,Nucs='13C',T_K=298) #We need a description of the experiment for both states (ex0, ex1)\n",
"ex1=ex0.copy()\n",
"ex0.set_inter(Type='CS',i=0,Hz=DelOmega12*p2)\n",
"_=ex1.set_inter(Type='CS',i=0,Hz=-DelOmega12*p1)"
]
},
{
"cell_type": "markdown",
"id": "70b267eb",
"metadata": {},
"source": [
"## Build the Liouvillian, add the exchange matrix"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "04d968e1",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The average chemical shift is 0.00 Hz\n"
]
}
],
"source": [
"L=sl.Liouvillian((ex0,ex1)) #Builds the two different Hamiltonians and exports them to Liouville space\n",
"L.kex=sl.Tools.twoSite_kex(tc=tc,p1=p1) #Add exchange to the Liouvillian\n",
"\n",
"print(f'The average chemical shift is {ex0.CS[0][\"Hz\"]*p1+ex1.CS[0][\"Hz\"]*p2:.2f} Hz')\n",
"#ex0.CS lists all chemical shifts and their parameters in the system"
]
},
{
"cell_type": "markdown",
"id": "e8cfb577",
"metadata": {},
"source": [
"## Create a propagator with on-resonant spin-lock, calculate $R_{1\\rho}$ relaxation"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "3a2f4ba0",
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
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EShcVhxPQICqCyOQfeOqR+zWdhoiUKioOJ6gWO9iyegnz1273OoqISJFRcThB7458iXoD/49JSUc+yyciUnKpOJygyIiy9G5Rg8kJa0hNO2nmBxQROSEqDkXg1OBNLH3hX7z6wedeRxERKRIqDkXg0rNPJ/LU0/hp3V6vo4iIFAkVhyJQsUJ57n36FRbtq8imXXrmQURKPhWHInJJXB3SdqfwwgdfeR1FROSEWWm5Pz8uLs4lJCR4miGybhPSXDA71ywmJFh1V0ROfmaW6JyLO3K/foIVoQeefI6Kfe5g5nL/rEonIlJcVByK0JDL+lGrXgPen7vO6ygiIidExaEI+YKD6FY9nU9e+ze/b9rhdRwRkUJTcShibatmsufX6bz8oS5Mi0jJ5ffFfkq7/uf1ZcpLn/PLTkf6wUx8ujAtIiWQfnIVMTPj6m4t2LLnANN/2+h1HBGRQlFxKAbxTaqy5/PnGHLLjV5HEREpFBWHYuALCSaudUu2+6qyNkVTaohIyaPiUEzeHf48kaddzDs/r/U6iohIgak4FJPqFcLo27IGYyZ+wa59B7yOIyJSICoOxajxgZX8MeZuHn3tPa+jiIgUiIpDMbrxsn/S9soHmZ8RTWZm6ZjDSkQCg4pDMfL5fDx6582s232QmSu2eB1HRCTfVByKWZ8WNQhdN5d7HhnmdRQRkXxTcShmvuAgonYtY9H3n7Nsw06v44iI5IuKgx+8/+Z/ibnuFd6ds97rKCIi+aLi4Af1alThgjZ1+CRhLVt36aE4ETn5qTj4ybmNy/L7a9dy2xMveR1FROS4/F4czKy3mS03s1VmNvQobeLNLMnMFpvZ9/7OWBxOj21Eg9ankbjdR2raQa/jiIgck1+Lg5kFA8OBPkAz4FIza3ZEm0rAf4F+zrnmwMX+zFhczIyxY94irXpzJiTq2oOInNz8febQAVjlnFvtnEsDPgTOO6LNv4CJzrl1AM65UvOAQPuYysRWC+Wp194m42Cm13FERI7K38WhNpDz1+bk7H05NQEqm9lMM0s0syv9lq6YmRm1Ns9m+ftPMPLTWV7HERE5Kn+vBGd57DtyXokQoB3QAygLzDazX5xzK3K9mdkgYBBA3bp1izhq8Xjm/iEk7qvC1HVB3OIcZnl1iYiIt/x95pAM1MmxHQ1syKPNl865vc65bcAsoFVeb+acG+Wci3POxUVFRRVL4KJWqVJF7rvqPJZt2sPMFVu9jiMikqdCFQczizOz0EK8dB7Q2MzqZ79+ADDliDafAmeYWYiZhQMdgaWFyXmy6teqFplJk7l+kFaKE5GTU4GLg5nVBH4GLinoa51zGcBg4CuyfuB/5JxbbGY3mtmN2W2WAl8CC4G5wGjn3G8F/ayTWWhIEC2qhrBxyzbmrtbZg4icfMy5gk0lnf1sQkOgsXMuvjhCFUZcXJxLSEjwOka+7T2QzhnPzaRF7Yq8e00Hr+OISIAys0TnXNyR+wszrHQFcD8QamYNTzhZgCpXxscNXRvw3fzlfDVvmddxREQOU6DiYGbdgGXZF4rfBq4tllQB4oKWVdg4+kZuvecBr6OIiBymoGcO1wJvZn89HrjYzDQ/UyFVi6zEwLufYG/TviSs2e51HBGRQ/L9gz17WotOwBcAzrndwC9A32JJFiBee2QINevU46VvVnodRUTkkHwXB+fcTudcI5fjCrZz7grn3NTiiRYYwkND6N8sgsmvPMTkWfO9jiMiApzgQ3DZE+nJCfpn22j2r5rD8+OmeR1FRAQ48SekR2U/qIaZdS2CPAGpYUwdXp78M8mV2zBndYrXcURETrg4PAK8aWbvAe2LIE/Auib+VKpXKMMj42ZQ0GdPRESK2okWh38Dy8maPO+jE48TuMqGBtOJFUx/5BKGT5judRwRCXAnOivrvc65bWZWDngZuK4IMgWsR2/6F5/NSmDCinRuPJhJSLDuEhYRb+Trp4+ZPWxmdx25P/thOJxze4EbijhbwImsXIkRLzzF2r+MCYnJXscRkQCW319NrwBGHLnTzK4zs/sBnHNaGLkI9GpWnQa2mSG3Dmbv/nSv44hIgMpvcUh1zu3LY/97wOVFmCfgmRlnVE0lZfEPPP/JD17HEZEAld9rDqlmVtM5tzHnTufcATPLKIZcAe3RO27ij3It+HjFfm7dm0ZkucIsnSEiUnj5PXN4AfjUzOrl3Glm1YDMIk8V4IKCgnj4grb8dSCdh9/5yus4IhKA8nXm4JybkP2wW6KZ/QIkkVVYLgYeK7Z0Aaxx9fLUWvUpI14cx7/OWESXlpodXUT8pyBzK70DNCDreQYfsB+41Dk3rpiyBbyXH76dWmffwGuzN+nBOBHxqwI955A9E+u7xZRFjhDXqjnDhg7h0SmL+WrxZnq3qOF1JBEJEMc9c8he3/kNMxtgZlPN7CZ/BJMsl3WsS+S2RVx55RWkpunav4j4R36GlboDg4DBzrlzgVbFG0lyCgkOomdMKDuTV/Hy54lexxGRAJGfYaUU55wzs2eztw8UZyDJ7ZkHbmdHdGfeXbCDq7rvp0bFMK8jiUgpl58zh5cBnHOfZW9PLL44kpegoCAe6RdLWtoBrn96tNdxRCQAHLc4OOeWHbGrUzFlkWOoExlOw+TpTH1uCB98m+B1HBEp5Y47rGRmOafiNqA18GzeraU4vfPi4/QpV5/hCbs574wMwkNPdFJdEZG85WdYabdz7pLsPxcD3xR3KMlbjaiqjLzvapJ3pPLCl4u9jiMipVh+isOwI7YfLI4gkj8dG1ShzcHlPH7FWcz6daXXcUSklMrPNYc/AMws3MxaOee2/33MzOqaWe3iDCi5PXDZWUTUasSwqYvJzNST0yJS9Aqy1Fg6MDF71be/jQZqFm0kOZ72rVvy9vsfsXyPj7Fz1nodR0RKoYLMrZQOTAL6Q9ZZAxDlnNOtMx44v3VtOtT0cfttt7FwlVaNE5GiVdBFikcDV2d/fSXwdtHGkfwyM65tU56dSdO5+YWxGl4SkSJVoOLw9zMPZtYEuJSsleDEI2d3PY1R0+aQXLEl785e43UcESlFCnrmAPAmWWcQC51zOwr6YjPrbWbLzWyVmQ09Rrv2ZnbQzC4qRMaAcW3PWOKbRvHom5NJ0vCSiBSRwhSHj8iafO/Ngr7QzIKB4UAfoBlwqZk1O0q7ZwEtg3YcZsZdp1dn/XtDuej6Ozio4SURKQIFLg7OuX3OuYrOucI8DNcBWOWcW+2cSwM+BM7Lo92twCfAlkJ8RsBp2bge9/3fSNJaX8ybP672Oo6IlAKFOXM4EbWB9Tm2k7P3HZL93MQFwMjjvZmZDTKzBDNL2Lp1a5EGLWmeGnIVvds04Lkvl/LzEt3eKiInxt/FwfLYd+Q4yEvAfc65g8d7M+fcKOdcnHMuLioqqijylVhmxtP/bEnKpKc4p98F7ElN8zqSiJRg/i4OyUCdHNvRwIYj2sQBH5rZGuAi4L9mdr5f0pVwVSLKcNt1VxDc5AyemLrE6zgiUoL5e1rPeUBjM6sP/AkMAP6Vs4Fzrv7fX5vZGGCqc26yHzOWaI/fdRMRLZYxfMbvdG0SxT9aaXYTESk4v545OOcygMFk3YW0FPjIObc4e53qG/2ZpTS7vWcTau/7nUv6dGPR77q9VUQKzt/DSjjnpjnnmjjnGjrnhmXvG+mcy3UB2jl3lXPuY39nLOl8wUHc368NZnDn2NmkZWR6HUlEShi/Fwfxj3N7nsGEL2ayMjWcJz/X9QcRKRgVh1LsnNhaXN2pNi89+RBPj5nsdRwRKUFUHEq5wV3rkblmHv95ZzJLN+72Oo6IlBAqDqVclcjKJC2YT/2el3PT2ER2paZ7HUlESgAVhwDQKLo6/72sLat/X0X3y24l46AuUIvIsak4BIi4mEjiDi4l6csPeOj9WV7HEZGTnIpDAJkw8v8Y/NpEPly8lwkJ64//AhEJWCoOASQ4OJjnB3bj9EZVGfzo83z83TyvI4nISUrFIcD4goN4sncMO2aO4aah/2Zdyj6vI4nISUjFIQDFRFfny+9mUbP3TVw9Zi4792kGVxE5nIpDgOresRWjrurAmo0pnH7pbezdr1tcReR/VBwCWKcGVehXcR2Lp47mX0+P0y2uInKIikOA+89Dt/P02C/59UAUD076Dee0BrWIqDgEPDNj6KU9ubV7I96ZOI1L7njS60gichJQcRAA7jyrCZXWzODTcaN5efpir+OIiMf8vRKcnKTMjISvJ3HHuDm8+N0aIsLDufb0+sd/oYiUSjpzkEMiyoUz4toz6d28OnfccQd3vzjG60gi4hEVBzlMSHAQw85tTOjW5bwx4QvGz1vndSQR8YCGlSSXKpUrsuLXOQz5eClDJy4iLS2DK7o08DqWiPiRzhwkT5EVK/DGlXG0j3Jce148tz472utIIuJHKg5yVGG+YF67sjPVa9bi49928dp3K72OJCJ+ouIgx1StaiR/JP3MgHN78Pz0Fdz1+lQ9KCcSAFQc5LhCgoN44eJWdCm3hf/cdB7n3fmcptoQKeVUHCRfgoKMMUMvp+/Vt5MU1IhB7yWyLy3D61giUkxUHCTffD4fn7/5Ak9dHMeMxX/S5vxBrNu83etYIlIMVBykwC7vVI9Bjfez4st3OOf+1/l9619eRxKRIqbiIIVy/6ABTJ45D1/9OC4Y/hPfLk72OpKIFCEVBym087q25dNbulA+dSNnn9aa+159X3cyiZQSKg5yQupEhvPWoHhqNTiVcUvTeWDSb6Rl6E4mkZJOxUFOWNOGMayZP4vb+nXk/Tlribv0Lpau3eh1LBE5ASoOUiSCgox7e5/CfR3LsWjiq/S84XG+X7HV61giUkh+Lw5m1tvMlpvZKjMbmsfxy8xsYfafn82slb8zSuHd/M9ufP7tjzQ/awBXvT2XJz76WQ/MiZRAfi0OZhYMDAf6AM2AS82s2RHN/gDOdM7FAv8GRvkzo5y4vvGd+PTWMzjnlEr8+4YLObVnf/7cmep1LBEpAH+fOXQAVjnnVjvn0oAPgfNyNnDO/eyc25G9+QsQ7eeMUgTKhgbz8uWduHTgdWTEnEbvl2bx2a8bvI4lIvnk7+JQG1ifYzs5e9/RXAt8cbSDZjbIzBLMLGHrVo1vn2yCg4N596V/M/P5G2hULYKBdzxCx39ez659B7yOJiLH4e/iYHnsy/PGeDPrRlZxuO9ob+acG+Wci3POxUVFRRVRRClq9aqU46NBnWgatpvfliyh7ys/Mvv3FK9jicgx+Ls4JAN1cmxHA7nGGswsFhgNnOec00+RUsAXEszsaR/x3dRJhAQHcfGL0+j6r1vZtnuv19FEJA/+Lg7zgMZmVt/MQoEBwJScDcysLjARuMI5t8LP+aSYdWxUjS+HdKVNxjJ+nDCKHo9N4Oslm72OJSJH8GtxcM5lAIOBr4ClwEfOucVmdqOZ3Zjd7BGgCvBfM0syswR/ZpTiVzY0mM9GDmPq9/OoWbcB17+bQK9bhrFqvYqEyMnCSstcOHFxcS4hQXWkpEnLyOTpj2bx2OU9iDrjUp568gkGdo7BF6znM0X8wcwSnXNxufarOMjJ4LPvfuKDZen8vG4vNTO3cXO3hlzR53SvY4mUeioOctJzzvHN0i30v6Afuzes4ppXp/Fwv5bUiQz3OppIqaXiICXGn5u28Pz47/hiW0UOHnQ025PI8EduJTqqktfRREqdoxUHDezKSad2jWq8OGQAM+6Op0P4Vqa89gidrn+S175bqXWrRfxEZw5y0psw7Vu+3BLBt8u24ftzAd3rh/Pig7cSXsbndTSREu9oZw4hXoQRKYiL+/bgYiBx7XbO++cLvD19DQtCW3BjfGMu7VCXsqHBXkcUKXU0rCQlRrt6kayd+zWfTP6M+lHleXxyEtWbdWDI82+z94CGm0SKkoqDlCjBwcH847TmjL/hNF7oG01I2l98mLCBLs9+x5OTE/k9eYvXEUVKBRUHKbEu6t6elLXL+PyZm+hYP5IXXnqFJo0acNPoGSzbtNvreCIlmq45SIlmZsTFRBIXE0m/2jfwwluVmLn2AF+89APVN/zI+We04e5rLtIT1yIFpOIgpcY53TtzTvfO7NyXxns//8G9A25g8fw5TNwSyYD2dTivZRSNakZ6HVOkRNCvU1LqVAoP5daeTUlZv4p3Xn+VlrUr8tLkn2kSE033wc/y9ZLNpGtda5Fj0pmDlFrhZcO4sEtzLuwCv7Qtz53rz2dbmVpc/24CYTtWU23nYoY9NJTTW9TDLK91qEQCl4qDBIROsafw82fvk34wk++Xb+Wxp77jp0/Hclnts2hUew2nVd7HBZ2aEtesoddRRU4KekJaAlbylu38uOYvJi74k8+evomMPSn0ffwDereoSfdGlWgaXcXriCLFThPviRzDd7PnM2X2Ev4IjSFp/U42jLqeeh3O5rZ7H6RPixo0qhahoScplVQcRPJp5YYU7nzgMbaFRbOxUgsyD+xj+0cP0O/aO7n+XxfSqUEVTdkhpYbmVhLJp8a1qvDZmFcB2LRrP+9N/4UXv6zIj+v28vOYebB9LUELP+WmOx+gf4/21K2i9Sak9NGZg0g+7U8/yJw/tjPy3Y+Y+MojVLvyZYIjKlNuy0LKbPiVux58lB6x9alRMczrqCL5pmElkSLknGNNyj6+X76F14e/SuLn71HzhjexoGDKrPqOyhnbuf+xJ+lQP5KaFct6HVfkqFQcRIpResZBlm/+i19Wp/DSkw/yx7LFRF36NABpP75NzSoVuPmeh2lXrzLNalYgNETPn8rJQdccRIqRLySYFrUr0qJ2Ra776gPSMw6ydNMeEtfu4P/mZLBh6w7+PXUJAJvH3kO95u247Nb7aVG7AlFB++jUohEhmv9JTiIqDiLFwBcSTGx0JWKjK3H1jMlA1sXtxLXbeXJJO/ZXiGbcnLWkHkhn/YuXULn9Pzjz8ttpXqsCuxfP4h+94una5lSdYYhnNKwk4pGMg5ksTU5h+Kg3OVipHrsqxJC0dBUrX76SyF43U6ndOdQOS2fTVyM559Jr6dm1C42iwompWo4yPv1eJ0VDw0oiJ5mQ4CBa1oti5LChh/alpcXx3YVN2ZIRxua0UGbPm8/cJfP54McuTEouy/7kpWwZ/xDtbvg/OpzWhUpuN3v+WMj5/c4ltmFtqpQL1cN6UiRUHEROIqGhPnqf0eF/O84+BR76F6lpGfy+dS8z50bw4d4BRDeoz+INu1jyw+ds/ewFPlkbiq9qHVibyJ55E+l353O0bFSPsge2w95t9Io/g3pRFXRdQ/JNw0oiJdhf+1KZvWAxVKxJ8q40vpo2le8+Gk3jK59m4z7Hjtkfs/P7MdS5YwIhZcoStGIGe5Z8zyUPDqdeVEUyt68j5MAu/tHnbGpWKktEGf2+GGh0K6tIgEnLyCRp+Rp+TkiiZrM4/tyRypcT3+fX76fRaOCzbNq9n61f/Ze9i2dS5/bxAOyZNYaMP5dw9gOjqV4hjO2LfyIkYy//HHA5UeXLEJK2h+iqFalZtbKGr0oJXXMQCTChIUF0aN6ADs0bHNp3Z6/HgceBrAviSZc3YdGKP6hcrxlb9uzni9RW/FGpDACLkneS+PH7HEjZwPe0AGDLJ0+QsXsrMdcPp0q5UDZ99TplguHs6+8nslwo6xK+I7JiBD169SayXBnS96QQXbUS0TWqEhykYlKSqDiIBKiQ4CDimjUirlmjQ/sGdX3osDYH7/yBDdt2cMDC2LJ7P19ED2Zzyk5i2sewfW8aX8wMJvVABvPX7WDH3nRWvv4yweUqM2FLNQA2vH0rIRWqUf2ih4koE0Ly+w9TOboBHQfcToWyISz69A1qxzSka58LqFDWx8qEWdSrV4e2rVtRPszHrm2bqBVVlepVKup6iZ+pOIjIUQUHB1OnelUAGlWLoPPgKw47/vzFHxy2vXVIApt37IawiuzYl8bnUfeTZmWIbtmY3anpfDqnEWFVapGRmcmabftI+nE6y9a1ZF5IcwDWvzyYcs26EnnWTQCse/FiImJ7EdnjekJDgljz2lXU7tyPpr2uoFxoMHPfuJ9TT+9Lq659KBsCv3zyBrGdziS2XXtCLJP5339Fi9jWNGzUCJ85klcvJ6ZePWpUq0posBHsDlIxIlyFJw9+Lw5m1ht4GQgGRjvnnjniuGUf7wvsA65yzs33d04RKbioyEpERVY6tH3GXdcfdvyxfu8f/oI7/gCyro/s2Z/OvHO+xfnCCI+swZ796Xwe+gSVa9WnZuMm7N6fxifzzqT2qadSIzKc3X/tY8+2zazftI09q7axa/culo4bTsKGVCokh3MwdTfJr9xM5Z43UKHdP8j4azt/Ds96hqR8m75k7N7CnyOuIbL3bVRp2xvbu4U179xHo/MGE92qKwd3beLXcU/R5oIbqNMsjv3bN5LwyQg69BtInSbN2bdtI/O/+ojT+lxE7ZiG7N2+md9+/pYO3XpTs2Yt9u7axurFSbTp0JnIyMqk7tnJhrW/07xFSypWqMD+fXtI2bKZmJj6RISXJe3AftL376NKlUjCQn0YDl9wEEFB3hQuvxYHMwsGhgNnAcnAPDOb4pxbkqNZH6Bx9p+OwIjsv0WklAoNCaJKRBl6n9H+sP3nxt592PaD53x0+AtvXn7YZuawg+w7kMH+g46/Ug+won8i4RUqUyaiIjt37+HHxm9Su9GpVKoWTcr27UzPuIsmcWcSWbc+WzaGMb11B5o1rEPlquXYvD8YCw4mNd2xafd+UjZsZd3yRYSs+pOl6VXYvvo31kx+l5W+BpSpd5DUPxaw5aPH+HZrWcKim5P6+zy2fPw4Na54gTK1mrJvxWy2ThpGzateIbR6A/YuncW2Kc9R89r/Elq1Ln/99h0pn/+HWoNG4atciz2/Tmf7l69Q9+a3Catcnb8WTmfz16NpPuRNylaowrb5X7Fh5vu0v30kHwzuQa1KRTvBo1/vVjKz04DHnHNnZ2/fD+CcezpHm9eBmc65D7K3lwPxzrmNx3pv3a0kIl7JOJjJvv1pbN22nTIRERAUwvadu1i1chW1YxoSUqYsmzZvZulvC2nSsh2+sHA2/JnM4gVziD2tO2XCI1i/eiUL5/5I+57n4wsvx5plv/HrT99y+gUDCQkrx6qF81j0w5d0vWwIwaFlWZH4PUtmTSP+uocZdnE7qkaUKVT2k+JWVjO7COjtnLsue/sKoKNzbnCONlOBZ5xzP2Zvfwvc55zL9ZPfzAYBgwDq1q3bbu3atX74LkRESo+jFQd/D2bldS/bkdUpP22ydjo3yjkX55yLi4qKOuFwIiKSxd/FIRmok2M7GthQiDYiIlKM/F0c5gGNzay+mYUCA4ApR7SZAlxpWToBu453vUFERIqWX+9Wcs5lmNlg4CuybmV9yzm32MxuzD4+EphG1m2sq8i6lfVqf2YUEREPnnNwzk0jqwDk3Dcyx9cOuMXfuURE5H/0WKCIiOSi4iAiIrmoOIiISC6lZj0HM9sKFPYpuKrAtiKMU9KpPw6n/jic+uN/SkNf1HPO5XpQrNQUhxNhZgl5PSEYqNQfh1N/HE798T+luS80rCQiIrmoOIiISC4qDllGeR3gJKP+OJz643Dqj/8ptX2haw4iIpKLzhxERCQXFQcREckloIuDmfU2s+VmtsrMhnqdx9/MrI6ZzTCzpWa22MyGZO+PNLOvzWxl9t+Vvc7qT2YWbGYLsheeCuj+MLNKZvaxmS3L/ndyWoD3xx3Z/1d+M7MPzCystPZHwBaHHOtZ9wGaAZeaWTNvU/ldBnCXc+5UoBNwS3YfDAW+dc41Br7N3g4kQ4ClObYDuT9eBr50zp0CtCKrXwKyP8ysNnAbEOeca0HWzNIDKKX9EbDFAegArHLOrXbOpQEfAud5nMmvnHMbnXPzs7/eQ9Z//Npk9cM72c3eAc73JKAHzCwaOAcYnWN3QPaHmVUAugJvAjjn0pxzOwnQ/sgWApQ1sxAgnKyFyEplfwRycagNrM+xnZy9LyCZWQzQBpgDVP97gaXsv6t5GM3fXgLuBTJz7AvU/mgAbAXezh5mG21m5QjQ/nDO/Qk8D6wDNpK1ENl0Sml/BHJxyPda1aWdmUUAnwC3O+d2e53HK2Z2LrDFOZfodZaTRAjQFhjhnGsD7KWUDJkURva1hPOA+kAtoJyZXe5tquITyMVBa1UDZuYjqzCMc85NzN692cxqZh+vCWzxKp+fdQH6mdkasoYZu5vZWAK3P5KBZOfcnOztj8kqFoHaHz2BP5xzW51z6cBEoDOltD8CuTjkZz3rUs3MjKzx5KXOuf/kODQFGJj99UDgU39n84Jz7n7nXLRzLoasfw/fOecuJ3D7YxOw3syaZu/qASwhQPuDrOGkTmYWnv1/pwdZ1+lKZX8E9BPSZtaXrDHmv9ezHuZtIv8ys9OBH4BF/G+M/QGyrjt8BNQl6z/Exc657Z6E9IiZxQN3O+fONbMqBGh/mFlrsi7OhwKryVrTPYjA7Y/Hgf5k3em3ALgOiKAU9kdAFwcREclbIA8riYjIUag4iIhILioOIiKSi4qDiIjkouIgIiK5qDiI5FP2DKU3H6fN62bWxV+ZRIqLioNI/lUCjlkcgI7AL8UfRaR4qTiI5N8zQEMzSzKz/zvyoJmdCqxwzh08Yv8YMxuRvXbGajM708zeyl4fYUx2m+Dsdr+Z2SIzu8Mv35HIUYR4HUCkBBkKtHDOtT7K8T7Al0c5VhnoDvQDPiNrHqfrgHnZTyEHA7Wz1wnAzCoVWWqRQtCZg0jROZujF4fPXNZ0BIuAzc65Rc65TGAxEEPW1BQNzOxVM+sNBOzsuHJyUHEQKQJmFg5Ucs4dbWbfA9l/Z+b4+u/tEOfcDrJWWpsJ3MLhiw2J+J2GlUTybw9Q/ijHugEzCvvGZlYVSHPOfWJmvwNjCvteIkVBxUEkn5xzKWb2k5n9BnzhnLsnx+E+ZK13UFi1yVpx7e+z+ftP4L1ETphmZRUpAmY2H+iYvQiMSImn4iAiIrnogrSIiOSi4iAiIrmoOIiISC4qDiIikouKg4iI5KLiICIiufw/5PnIp+HehWAAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"seq=L.Sequence(Dt=.0003)\n",
"v1=500\n",
"seq.add_channel('13C',v1=v1) #Spin lock at -3.5 ppm (on-resonance)\n",
"U=seq.U() #Propagator (10 ms)\n",
"\n",
"rho=sl.Rho(rho0='13Cx',detect='13Cx')\n",
"n=300\n",
"rho.DetProp(U,n=n)\n",
"\n",
"ax=rho.plot(axis='ms')\n",
"R1p=R1p_fun(kex=kex,v1=v1,CS1=ex0.CS[0]['Hz'],CS2=ex1.CS[0]['Hz'],p1=p1)\n",
"ax.plot(rho.t_axis*1e3,np.exp(-R1p*rho.t_axis),color='black',linestyle=':')\n",
"_=ax.legend(('Simulated','Calculated'))"
]
},
{
"cell_type": "markdown",
"id": "7cb1b92d",
"metadata": {},
"source": [
"### What happens if we vary the populations and $\\Delta\\omega_{12}^2$, but leave $p_1p_2\\Delta\\Omega^2$ fixed?\n",
"We start out with fast exchange, i.e. $k_{ex}>>\\Delta\\Omega_{12}$ ($k_{ex}=$30000 s$^{-1}$, $\\Delta\\Omega_{12}$=500x2$\\pi$ Hz).\n",
"\n",
"We claim above that for fast exchange, we cannot separate $p_1$ and $p_2$ from $\\Delta\\Omega_{12}$ experimentally. We verify this by fixing the product $p_1p_2\\Delta\\Omega_{12}^2$, but varying $p_1$."
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "9cde21a9",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"kex=30000\n",
"tc=1/kex\n",
"ax=plt.subplots(figsize=[8,6])[1]\n",
"p1p2Delv12=p1*p2*500**2 #p1*p2*DeltaOmega**2 is fixed below\n",
"p10=np.linspace(0.1,.9,9) #Sweep from p1=0.1 to p1=0.9\n",
"for p1 in p10:\n",
" p2=1-p1 #Calculate p2\n",
" Delv12=np.sqrt(p1p2Delv12/p1/p2) #Adjust DeltaOmega to keep product fixed\n",
" \n",
" ex0.set_inter(Type='CS',i=0,Hz=Delv12/2)\n",
" ex1.set_inter(Type='CS',i=0,Hz=-Delv12/2)\n",
" L=sl.Liouvillian((ex0,ex1)) #Builds the two different Hamiltonians and exports them to Liouville space\n",
" L.kex=sl.Tools.twoSite_kex(tc=tc,p1=p1) #Add exchange to the Liouvillian\n",
" \n",
" seq=L.Sequence()\n",
" v0=Delv12/2*p1-Delv12/2*p2\n",
" seq.add_channel('13C',v1=500,voff=v0) #On-resonant spin-lock\n",
" U=seq.U(.0003) #Propagator (10 ms)\n",
" rho=sl.Rho(rho0='13Cx',detect='13Cx')\n",
" rho.DetProp(U,n=n)\n",
" rho.plot(axis='ms',ax=ax)\n",
"ax.legend([r'$p_1$ = '+f'{p1:.1f}' for p1 in p10])\n",
"_=ax.set_title(r'$\\tau_c$ = '+f'{tc:.1e} s'+r', '+'$p_1p_2(\\Delta\\Omega_{12})^2$ fixed')"
]
},
{
"cell_type": "markdown",
"id": "b41080b5",
"metadata": {},
"source": [
"As we can see above, all relaxation curves are nearly identical, preventing us from separating the populations from the change in chemical shift. \n",
"\n",
"On the other hand, if exchange is slower, the curves will separate as we vary the populations. In order to demonstrate this, we reduce $k_{ex}$ to 800 s$^{-1}$."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "f75284a1",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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272LWzEVjHI0QQowzG/4Zaj8LbZups+CavqfAT1ZcXMyNN97I888/zwcffMB9993H8uXLh6y3aNEiOjo6+mx/7LHHWLJkSe/n6upqsrKyej9nZmaydevWAds9fPgwO3fuZP78+UPGMFyS3AfiswDQ1STLvgohxHjhdDppbGxk9erVABQUFNDS0kJZWRkPPvggbW1tvPjii/3W3bRp07D6CK5cfiKlVL9lOzs7ueWWW/jxj39MTEzMMI9iaJLcB6C0DQCfu++3NCGEECM0jBH2aNi9eze5ubnY7cGlvXfs2EFhYSHZ2dk8/fTTrFixYsC6wx25Z2ZmUllZ2fu5qqqK9PT0PvW8Xi+33HILq1at4uabbx7JYfUhyX0AimBy1zjHOBIhhBChUlxcTEVFBS6XC7/fz+rVq3n00UeHVXe4I/eioiIOHjxIeXk5GRkZrFmzhmefffaEMlpr7rzzTvLz87nvvvtO+TiGIjfUDcCiIoJvDHnWXQghxovi4mJWrVrF4sWLKSoq4p577mHhwoUh7cNsNvP444+zdOlS8vPzufXWW5kxY0bv/mXLlrFp0yaeeeYZ3n77bebMmcOcOXNYv3596GIIWUvjjNUeDYAyycpwQggxXhQXF/PUU0/xyCOPnLC9qamJBx54gJ07d/LQQw9x//33j6ifZcuWsWzZsn73HUvi/V2bDxVJ7gOIiIjC4zehTN6xDkUIIUSIlJaWkpub22d7QkICTz755BhENDrktPwAHDEx+P0WDLMkdyGEGC+qq6sxjPGf+sb/EZ6mqKQEfD4LyiLJXQghxNlFkvsAYpJT8PutGGa55i6EEOLsIsl9ADFpKfh9FpSclhdCCHGWkeQ+gKgJ8QR8VgyLjNyFEEKcXSS5D8BkNhHw2eS0vBBCiLOOJPdBaLnmLoQQ4iwkyX0Q2mfDMHvx+/1jHYoQQggxbJLcBxHw2lAKOpztYx2KEEIIMWyS3AfjC67p3tbdMsaBCCGEOJts3LiRvLw8cnJyePjh/lfAc7lcXHDBBRQWFjJjxozeZWhDQZL7ILQvuDJcp7NtjCMRQghxtvD7/dx7771s2LCBkpISnnvuOUpKSvqUs9lsvP322xQXF7Nr1y42btzIli1bQhKDJPfBeHuSu6sVgNKa/WMYjBBCiFBYuXIlt912G/Pnz2fSpEmsW7cupO1v27aNnJwcsrOzsVqtrFy5krVr1/Ypp5QiKioKCK7t7vV6UUqFJAZZOGYQ2hs8Ld/lamfzvrfprvkmta1PsrDgyjGOTAghzm6PbHuEfc37Qtrm9AnT+f4F3x+yXHFxMTfeeCPPP/88H3zwAffddx/Lly8fst6iRYvo6Ojos/2xxx5jyZIlvZ+rq6vJysrq/ZyZmcnWrVv7bdPv93P++edz6NAh7r33XubPnz9kHMMhyX0wPcnd6W6juvZ90i1QWbcNJLkLIcRZyel00tjY2Ht9u6CggJaWFsrKynjwwQdpa2vjxRdf7Lfupk2bhtVHf0u5DjQiN5lM7Nq1i9bWVm666SZ2797NzJkzh3k0A5PkPpie5O7xdGDxbQMLuLtD+01TCCHORcMZYY+G3bt3k5ubi91uB2DHjh0UFhaSnZ3N008/zYoVKwasO9yRe2ZmJpWVlb2fq6qqSE9PHzSuuLg4Fi9ezMaNGyW5j7Zjp+U7O/aS7qghoBV2VTbGUQkhhDhdxcXFVFRU4HK58Pv9rF69mkcffXRYdYc7ci8qKuLgwYOUl5eTkZHBmjVrePbZZ/uUa2howGKxEBcXh9Pp5M033+T73w/Nlx65oW4wPjNaK2LV+wDUuC9igq2O9m65e14IIc5GxcXFrFq1isWLF1NUVMQ999zDwoULQ9qH2Wzm8ccfZ+nSpeTn53PrrbcyY8aM3v3Lli2jpqaGo0ePctlllzF79myKioq48sorufbaa0MTQ0haGadMGjo7JxAd3USdcxJpqddhtH3I3spdzM+7dKzDE0IIcYqKi4t56qmneOSRR07Y3tTUxAMPPMDOnTt56KGHuP/++0fUz7Jly1i2bFm/+9avXw9Aeno6O3fuHFE/A5HkPhit2bXzGu66/Vouyz2fisbDlLZBVX2xJHchhDgLlZaWkpub22d7QkICTz755BhENDrktPwgDA2g6GptwTAMJiZOptsbQWfn3rEOTQghxGmorq7GMMZ/6pOR+yAUwccZ2uoaATAMg1bvZMzq4FiGJYQQQgxq/H99GYFjjyV2thy3cIxlGhOsVXh9shSsEEKIM5Mk90EcO3Pj6nL1bouLLcBq8nKwuu88wUIIIcSZQJL7IEw92d3Z/fkofXLqHADKa3eNQURCCCHE0CS5D8JkCp6X97p9vdumZczEGzDT0rZnrMISQgghBiXJfRBmmwUAnzfQu81msdHszsDwfsIf3rifLfveGavwhBBCiH5Jch+ExR6cftbnP3ERAK+RQ4rjCGmmF+iq+QZ/eu+xsQhPCCGE6Jck90FYIyIA8PtP3D572p0c9a1gYt6r1Dkn4+l8bQyiE0IIIfonyX0Q9phIDK04aeDO3Knz+dJVj5CbkY/PNJ1oc93YBCiEEOKMtHHjRvLy8sjJyeHhhx8etKzf72fu3Lkhm1ceJLkPyh4ThQUTvr5L835exj6JSEsXje314QtMCCHEGcvv93PvvfeyYcMGSkpKeO655ygpGfjx6Z/85Cfk5+eHNIawJ3el1NVKqf1KqUNKqX/uZ3+sUuoVpVSxUmqPUupr4Y7xGHtsFHZtxacGLhMfkw3A4TqZtU4IIc4GK1eu5LbbbmP+/PlMmjSJdevWhbT9bdu2kZOTQ3Z2NlarlZUrV7J27dp+y1ZVVbFu3Tq+8Y1vhDSGsE4/q5QyAU8AVwJVwMdKqZe11sd/pbkXKNFaX6eUSgL2K6X+qLUO+5Rw0RPicWDFabgHLJORkMPRVqhrPgSEdtlAIYQYr2r/8z9x790X0jZt+dNJ/cEPhixXXFzMjTfeyPPPP88HH3zAfffdx/Lly4est2jRIjo6Ovpsf+yxx1iyZEnv5+rqarKysno/Z2ZmsnXr1n7b/O53v8ujjz7ab7sjEe655S8ADmmtywCUUmuAG4Djk7sGopVSCogCmgHfyQ2FQ2RiPHZtoV0NfF5+cuo0qg8p2jvLwxiZEEKI0+F0OmlsbGT16tUAFBQU0NLSQllZGQ8++CBtbW28+OKL/dbdtGnTsPrQum/OUKrvKeBXX32V5ORkzj//fN59993hH8QwhDu5ZwCVx32uAuafVOZx4GWgBogGbtNaBxgDjvg4bAEzHtPAyT3CFkG7Jw6PrhywjBBCiBMNZ4Q9Gnbv3k1ubi52ux2AHTt2UFhYSHZ2Nk8//TQrVqwYsO5wR+6ZmZlUVn6eE6qqqkhPT+9T78MPP+Tll19m/fr1uFwu2tvb+dKXvsQf/vCHkRwiEP7k3t/V65Mz51JgF3A5MBV4Qym1SWvdfnJFpdRdwF0AEydODG2kgDXSji1g4LNo/B4XJqsdn9uJYTJjmC295br9aZhUdcj7F0IIEVrFxcVUVFTgcrnw+/2sXr2aRx99dFh1hztyLyoq4uDBg5SXl5ORkcGaNWt49tln+5R76KGHeOihhwB49913eeyxx0KS2CH8N9RVAVnHfc4kOEI/3teAl3TQIaAcmN5fY1rrX2mt52mt5yUlJYU8WKUU5kDw+0hXQyU6EOCp//oXXv/1v55QLmDKINpUG/L+hRBChFZxcTGrVq1i8eLFFBUVcc8997BwYWjvlzKbzTz++OMsXbqU/Px8br31VmbMmNG7f9myZdTUnJz6QivcI/ePgVyl1BSgGlgJfPGkMhXAFcAmpVQKkAeUhTXK4/Qm9+YaXB1N1Pmi8dZ3cvVxZez2SUTpN2jubGZC1ISxCVQIIcSQiouLeeqpp3jkkUdO2N7U1MQDDzzAzp07eeihh7j//vtH1M+yZctYtmxZv/vWr1/fZ9vixYtZvHjxiPo8XliTu9bap5T6DvAaYAL+T2u9Ryl1d8/+J4F/B36rlPqM4Gn872utG8MZ5/HMPTPYdDbXU1txCIDmQBQdR0uJTpsKQFz0FGiHI3UHmBC1YKxCFUIIMYTS0lJyc3P7bE9ISODJJ58cg4hGR7hH7mit1wPrT9r25HHva4Crwh3XQIye5N7V1siBygZs2HBj48iu95jZk9zTEnJoaIfa5kMwVZK7EEKcqaqrz437o2SGuiEY/uCN+vW1R6n0RHNBlh0LXirKS3vLTEmdBkBbhzwOJ4QQYuxJch+CDvgxaYNPj7oBRf68S8hyODnS7OotE+2Iod0Ti9tVMXaBCiGEED0kuQ8hoP04sNKpHUSrbtJmXUpmUhx1vih8rq7ecl2+VEyBc+N0jxBCiDObJPch+PDj0MF13aclmFCGwYTEZEDRVn2gt5zfyCDSLI/DCSGEGHuS3Ifgx4/9WHIvmA1AfErwUf2W6kO95Wz2icRY2+hw9plrRwghhAgrSe5D0CZNpLZhwk/2guDCAvGZwRvoWuo/n4QgNnoKAOW1B/o2IoQQQoSRJPchaLNirm8K87MysETEABCVmo0JHy3NTb3lUifkAFDTJEu/CiGEGFuS3IegrAaR2HAYcb3bDJOJOMNFa0d377ac9ALcfit1dRvHIEohhBDic5Lch2BxBK+3+1pdJ2yPt2taXJ8vVhftiKFJX0e6/UN+v/G7vLRhHu999mpYYxVCCHFm2LhxI3l5eeTk5PDwww8PWG7y5MnMmjWLOXPmMG/evJD1H/YZ6s421hgHNIDuCi4p/+aTazB1gd/koKXbf0LZJUXfZef2V8iwvoLT58Bd9z3eAy6dde0YRC6EEGIs+P1+7r33Xt544w0yMzMpKiri+uuvp6CgoN/y77zzDomJiSGNQUbuQ4iIiwVAucDjdjP1SApTG9KIb8nBhQ1ny+ePv6XFpxOI/keajLu48ML36PTFcLgiNMv3CSGECI2VK1dy2223MX/+fCZNmsS6detC2v62bdvIyckhOzsbq9XKypUrWbt2bUj7GIqM3IcQOSEOT8CNyas4XH6ICG2mNL6G+LZoAFqr9uOIT+0tf+2Cr/e+79ALSLK+Tbe7mwhbRNhjF0KIM9WmFw7QWNkZ0jYTs6JYdOu0IcsVFxdz44038vzzz/PBBx9w3333sXz58iHrLVq0iI6Ojj7bH3vsMZYsWdL7ubq6mqysz1c3z8zMZOvWrf22qZTiqquuQinFt771Le66664h4xgOSe5DiJwQhzdQi1mbqD9cyWQi0XkRRG81AdBcU07arEv7rZuVfhW6aSNb9r3B5YU3hDNsIYQQ/XA6nTQ2NrJ69WoACgoKaGlpoaysjAcffJC2tjZefPHFfutu2rRpWH1orftsU0r1W/bDDz8kPT2d+vp6rrzySqZPn84ll1wyzKMZmCT3IUSmJNIQOIIZC+017XiUlew5BQS2VAKa+ppKZgxQd8H0K3n3fSuNR18HSe5CCNFrOCPs0bB7925yc3Ox2+0A7Nixg8LCQrKzs3n66adZsWLFgHWHO3LPzMyksrKy93NVVRXp6en9tnlse3JyMjfddBPbtm2T5B4OUckJ1ATcmA0LlkZNXUQL0zzpdGlwKKhtahuwboQtggZPIZHGx2GMWAghxECKi4upqKjA5XLh9/tZvXo1jz766LDqDnfkXlRUxMGDBykvLycjI4M1a9bw7LPP9inX1dVFIBAgOjqarq4uXn/9dX74wx+e0vEMRG6oG4I9JgJvwI0FCwnt0XTHelj7L/9Et6+DKGzUdfd/quWYiKgLiLc1UV53aNByQgghRl9xcTGrVq1i8eLFFBUVcc8997Bw4cKQ9mE2m3n88cdZunQp+fn53HrrrcyY8fk53mXLllFTU0NdXR0XX3wxhYWFXHDBBSxfvpyrr746NDGEpJVxzGQ28Aa8JJqjsfpsNJYV06ICdPlameCLZr/Jg7Ol9oSb6o43LWsRjYefYHf5e0xJyQlz9EIIIY5XXFzMU089xSOPPHLC9qamJh544AF27tzJQw89xP333z+ifpYtW8ayZcv63bd+/foT4hkNktyHocvXhdWwAVDZUIqhounytZHqS2C/qYm6/duZvKD/Z9lnTJrLhoMOmlu2AXeGMWohhBAnKy0tJTc3t8/2hIQEnnzyyTGIaHTIaflhKGnbyZs1f8a7wka9rxZlm0Gnt5V0nQxA3ZGBF4sxm8w0+wpw6M/CFa4QQogBVFdXYxjjP/WN/yMMAUOZ6fS14ikNXjePjMqky99NBFbseDhaVzdofUfk+STY66hurBy0nBBCCBEKktyHwTAsBLSP2pJ9AEwryqPLH0ChiLHC4dYAOhAYsH52xsUAFJe9G45whRBCnOMkuQ+DyTAT0D7qqmtA2UmfOQVvzxwFcZFxtAYiaTy4fcD6hVOKcPlsNDZvCVPEQgghzmWS3IfBbLIR0C6aOlpRpgQSM6Mx2awEdIAYSwIAB7a/M2B9i9lKkzcPq1+uuwshhBh9ktyHIWHS+Wh8dOPCZEogNslB7IQkXP4uYppNJJs6OFg5+HV3i+N8khzV1LcOXk4IIYQYKUnuw5BVdCGGeSIAEY54DJNB8uSJOH0dODqs5KZGUeGKxN3eNGAb2RnBSRJ2lr4bjpCFEEKcwyS5D0Pe/FTMjotB2UiaGJwPOTU/G6e/gwh/JJNzZxDARM3uDwZso3DKhXj8FuoaN4crbCGEEOcoSe7DEJPoIGtGPrbYb5N5XiEASfmTcfo6cRiRZMwKjsqrSksGbMNutdPonobZ92lYYhZCCHHukuQ+TAUL01BKkZgRBUB0fCTdATdWw4a2xzDB6KSqbuDT8gAm+1yS7BU0dQxeTgghxNlt48aN5OXlkZOTw8MPPzxgudbWVlasWMH06dPJz89n8+bQnN2V5D5MufNSuOZbs5g4M3h3vMli4PJ7AGioqyUzxqC6yzTo8+4T0xZiKM2u0vfCErMQQojw8/v93HvvvWzYsIGSkhKee+45Skr6P7P7d3/3d1x99dXs27eP4uJi8vPzQxKDJPdhUoYie24ShvH5KnDugBeA1sYmMtPT6NQO2qr2D9jG3KkL8QbMHK2X6+5CCDFWVq5cyW233cb8+fOZNGkS69atC2n727ZtIycnh+zsbKxWKytXrmTt2rV9yrW3t/P+++9z553BdUesVitxcXEhiUEWjhkBr/YB0NncypRphVDyPlV7NhM3sf9vXpH2SBpd2Si1M5xhCiHEGeed3/6K+iNlIW0zeVI2l331riHLFRcXc+ONN/L888/zwQcfcN9997F8+fIh6y1atIiOjo4+2x977DGWLFnS+7m6upqsrKzez5mZmWzdurVPvbKyMpKSkvja175GcXEx559/Pj/5yU+IjIwcMpahyMh9BHTPKN7d0kVK/oUY+KmrqRi0jjnyYlId5ew4JKN3IYQIN6fTSWNjI6tXrwagoKCAlpYWysrKuPPOO1mxYsWAdTdt2sSuXbv6vI5P7ABa6z51lVJ9tvl8Pnbs2ME999zDzp07iYyMHPT6/KmQkfsIWCMceAJuVKMTs81Bgqmb+pbB61xd9G02fbiG6n2PcV7On8MTqBBCnGGGM8IeDbt37yY3Nxe73Q7Ajh07KCwsJDs7m6effnrQ5D7ckXtmZiaVlZ8vFFZVVUV6enqfepmZmWRmZjJ//nwAVqxYIcn9TBARHY3T1YG1JfgtLTnSoKaz7ze248VFxdNpuY0My2/43bqV5GZ/k4vyrwhHuEIIcc4rLi6moqICl8uF3+9n9erVPProo8Oqu2nTpmGVKyoq4uDBg5SXl5ORkcGaNWt49tln+5RLTU0lKyuL/fv3k5eXx1tvvUVBQcEpHc9A5LT8CEQnJtDpbSG6O/h4XHJCHC2BKDydgw/fr7/oe9R4byTGtJ+umm/x/DsPhSNcIYQ45xUXF7Nq1SoWL15MUVER99xzDwsXLgxpH2azmccff5ylS5eSn5/PrbfeyowZM3r3L1u2jJqaGgB+9rOfsWrVKmbPns2uXbv4wQ9+EJoYQtLKOSouPYWWA8Wk6Cn4fD6S07OgvIyGQzvImDPwaDzSHskdS/+b9u42/vLOt8h0/Jryui8wJSUnjNELIcS5p7i4mKeeeopHHnnkhO1NTU088MAD7Ny5k4ceeoj7779/RP0sW7aMZcuW9btv/fr1ve/nzJnD9u0Dryp6umTkPgITsifR4W3GrMwcrakgOXsWAPVHDgyrfkxELAvn/giAbSV/Gq0whRBC9CgtLSU3N7fP9oSEBJ588klKS0tHnNjPBJLcR2DClEzavcFT8HWV1cRPmokZH/W1NcNuIyd9OrXObPzdb4xWmEIIIXpUV1djGOM/9Y3/IxxFkXE2OnxOADqONmOYLSSZu6lr7TqldqxRS0lxHGFf1e7RCFMIIcQ5RpL7CJgtJrwYePwu/I3BJJ8eZ6PaaSfg8w67naL8mwH4rPS1UYlTCCHEuUWS+wiZjQg6vC3YWoO/ysnZU3Fjpbbkw2G3MTk5m1Z3PN2du0YpSiGEEOcSSe4jZLVE0e5tIq4zOF3gpMJLATiy5+NTaqczMJ0oY1/I4xNCCHHukeQ+Qo6IaNq9jcT7YmhpbiQmI5d4o5PD1XWn1E5E1BzibM1UNQ4+fa0QQggxFEnuIxQdP4EGVxUA+3buAmBynImKTjMBv3/Y7UxOC04/uPvw8E/nCyGEEP2R5D5CcWmpNLtrcGsXXfsbAZiaOw0ndj589pEhan9u1uQivH4zDU2hn8xACCHEuUWS+wgl52Sj0TT5akisjSQQCDBj6deYFdvNW6UePnnp8WG1Y7faaXRnY/g+G+WIhRBCjHeS3EcoYdpkwESrq45ETxwVh0tRhsEN96xmqqODVz5t5IM/DHOVH9sckmzltHe3jWbIQgghRtnGjRvJy8sjJyen35Xe9u/fz5w5c3pfMTEx/PjHPw5Z/5LcRygmwYEyomnsCl53L99ZAoDZHskXv/cguREdvH+oHb/XM2RbGSkXYTIC7Cwd3spDQgghzjx+v597772XDRs2UFJSwnPPPUdJSckJZfLy8nrXg//kk0+IiIjgpptuClkMktxHyBFlQRnRtLobOepoxHzQ3bvPZLUzp3AWHqzUFL8zZFvnTV2EP2BQVfvRaIYshBDntJUrV3Lbbbcxf/58Jk2axLp160La/rZt28jJySE7Oxur1crKlStZu3btgOXfeustpk6dyqRJk0IWg6wKN0LKUJhNkXh89bRN9pG7N4XmpgYmJCQBMGXelbD5V5Tt2U7WvKWDthUbGUeDexJa7wxH6EIIMWZaXynFU3NqU3UPxZoeSdx1U4csV1xczI033sjzzz/PBx98wH333cfy5cuHrLdo0SI6Ojr6bH/sscdYsmRJ7+fq6mqysrJ6P2dmZrJ169YB212zZg233377kP2fCknuIWCzRtLhdpM+axKmvW72bPmYRcuDS/1FJGSQau6g/ChcOoy2Apa5JBkv09bVSmxk3KjGLYQQ5xqn00ljYyOrV68GoKCggJaWFsrKynjwwQdpa2vjxRdf7Lfupk3Du2Sqte6zTSnVb1mPx8PLL7/MQw89NMwjGJ6wJ3el1NXATwAT8GutdZ87DZRSi4EfAxagUWs9nLw4ZqLjUujoAEdtPY1WjW9fFxz3JXBKUiTbjoKnqw1rZOygbeVNvo6Oqpd4c8dvuWXRd0c3cCGEGCPDGWGPht27d5Obm4vdbgdgx44dFBYWkp2dzdNPP82KFSsGrDvckXtmZiaVlZW9n6uqqkhPT++3zQ0bNnDeeeeRkpJyuofUr7Amd6WUCXgCuBKoAj5WSr2stS45rkwc8HPgaq11hVIqOZwxno7kvNnUVK6nYstHeNNnM6kiAY/XjdViA2BybgGbj+7n6J4PmXTBskHbmpdzMc8dnILZ9SKBwN+eE0sTCiFEuBQXF1NRUYHL5cLv97N69WoeffTRYdUd7si9qKiIgwcPUl5eTkZGBmvWrOHZZ5/tt+xzzz0X8lPyEP4b6i4ADmmty7TWHmANcMNJZb4IvKS1rgDQWteHOcZTlpQzGWXEUlVeRlReMo6Anf2ffdq7Pzl7JgCNVWVDtmUYBjEJt5NoP8qrW/9v1GIWQohzUXFxMatWrWLx4sUUFRVxzz33sHDhwpD2YTabefzxx1m6dCn5+fnceuutzJgxo3f/smXLqKmpobu7mzfeeIObb745pP1D+JN7BlB53Oeqnm3HmwbEK6XeVUp9opT68kCNKaXuUkptV0ptb2hoGIVwhyd5cjTKnEGjq4tphbMJEKB+z5He/bFZBZjx0dgwvPnml5z3RWqdU4l0PsTvX/su9a2nNk+9EEKI/hUXF/P1r3+dLVu2UFJSwpe+9CUAmpqauPvuu9m5c2dIrn8vW7aMAwcOUFpaygMPPHDCvvXr15Oenk5ERARNTU3Exg5+ufZ0hPuae393FJx854EZOB+4AnAAm5VSW7TWB/pU1PpXwK8A5s2b1/cOhjBJyozGbE7HY5TgOXCQqqgGbJWfh2OYTCSYnTQOc24ah9XBTUv+yovv/CNpllfZuvVNps/8E7kZ+aN0BEIIcW4oLS0lNze3z/aEhASefPLJMYhodIR75F4FZB33OROo6afMRq11l9a6EXgfKAxTfKfFZDFISM8G4OBr6+jO1GS1J9HR/nk2T4wwaHT1f7dkfyJsEXz56idIm/onlNJs2fl9AoFAyGMXQohzSXV19TlxL1O4j/BjIFcpNUUpZQVWAi+fVGYtsEgpZVZKRQDzgb1hjvOUZRVOxzCl8elnO5kwNQUTJvYV7+rdnxgfQ0sgEq+z85TanTl5Lm7HXaRH7OG1T/q/IUMIIYQ4XliTu9baB3wHeI1gwn5Ba71HKXW3UurunjJ7gY3Ap8A2go/L7Q5nnKcjbWocJseFuEwK56b3cCsPbftqe/cnpqQBiubyTwduZAA3XvQdWtyJNNT/JYQRCyGEGK/C/py71no9sP6kbU+e9Pm/gP8KZ1wjlZodi2GehF3FsHvHFnxF04itsfbuT8yaBtuqaKzYT0rBRafUtslkwmlcTLLlVVo7W4iLig91+EIIIcaR8X/hIUyi4m1MX5BGIGI+nSYFqo00ZyJ1dcFbChKyCwFNQ231abWfM2k5FsPHhyWvhDBqIYQQ45Ek9xBacGM2Fsd0lDboLA1eSTi4M3ga3hoZS5zRTWPL6S3nWpR7CR2eaBobXg9ZvEIIIcYnSe4hFBVvp3DJVJRtGoeaS+kwdeE+1Nq7P9EeoLHLf1ptm01m2gLzSbDsxOsbevlYIYQQ5y5J7iE2a3EmZmsePkPRYjpKcl107yNsiTEOmnwOAv7TS/CJCRfhMLsoLv84lCELIYQYZyS5h1hUvJ3swgIAXB1HiffGcLgsOP9OYlISXiy0V/eZj2dY5uReDkBp1fuhCVYIIcS4JMl9FMy6YjrKmEBt02EAKj7dD0BiRnCim8bDe06r3YwJWTQ403F3bwtJnEIIIUbHxo0bycvLIycnh4cf7rP4aa///d//ZcaMGcycOZPbb78dl8sVkv5PK7krpeb1TEIj+hF8LC6Nelcd9bZmKHMCkDhlFgCNNUcGqz4oj2kuidZ9uDyh+QMQQggRWn6/n3vvvZcNGzZQUlLCc889R0lJSZ9y1dXV/PSnP2X79u3s3r0bv9/PmjVrQhLDKSd3pVQa8BFwa0giGIesDjORkan4lZ8OezMZzcElYCOTJmLHTWNT42m3nZp0MTaTh48Pvhu6gIUQ4hyycuVKbrvtNubPn8+kSZNYt25dSNvftm0bOTk5ZGdnY7VaWblyJWvXru23rM/nw+l04vP56O7uHnDd91N1OpPYfAX4HfAN4A8hiWIcysidTvu2twh01uEI5LC3eBeF8+aTaHXT2HH67V5YcDUffPBDqis3smjG1aELWAghwmjDhg3U1tYOXfAUpKamcs011wxZrri4mBtvvJHnn3+eDz74gPvuu4/ly5cPWW/RokV0dPT9B/yxxx5jyZIlvZ+rq6vJyvp8GZXMzEy2bt3ap15GRgb/8A//wMSJE3E4HFx11VVcddVVQ8YxHKdzWv4O4H7AqpSaGpIoxqHshYWgbDTVH8aPn4Y9FQAkRVmoc1nxe0/vcbZoRwz1nkKi9AeykIwQQpwip9NJY2Mjq1evBqCgoICWlhbKysq48847WbFixYB1N23axK5du/q8jk/sAFr3XaRUqb4Lh7W0tLB27VrKy8upqamhq6uLP/whNGPmUxq5K6UuA/ZprRuVUr8B7gR+EJJIxpn0nHgMUwoN7Y1UTmkgojL4P2zu9AJ2flTO4a2vMvXim0+r7fgJVxLp3M6O0s3My10YyrCFECIshjPCHg27d+8mNzcXu90OwI4dOygsLCQ7O5unn3560OQ+3JF7ZmYmlZWVvZ+rqqr6Pd3+5ptvMmXKFJKSkgC4+eab+eijj3rXmB+JUx253wk83fP+eeALSim5474f0Ql2zJZEurUTV3qAzM4kmpsayL34Jmx4+GxH31M0w3XRjOvxBwz2HJJV4oQQ4lQUFxdTUVGBy+Wiq6uL1atX873vfW9YdYc7ci8qKuLgwYOUl5fj8XhYs2YN119/fZ/2Jk6cyJYtW+ju7kZrzVtvvUV+fn5IjnPYiVkpFQcsADYAaK3bgS3AspBEMs4opYiNSwOlicGNgcHB3buxRMSQP8HP3mYT7TWHTqvtxJhkan1Xk259jS373glx5EIIMX4VFxezatUqFi9eTFFREffccw8LF4b2DKjZbObxxx9n6dKl5Ofnc+uttzJjxoze/cuWLaOmpob58+ezYsUKzjvvPGbNmkUgEOCuu+4KSQyqv2sDZ6N58+bp7du3j3UYJ3jjibf59P3/Yf7s+WR0XkzptAaWfO1WDm95hd9u/ASASbZ2rrn+ZlJnXHxKbbd3t/H6e1diVl5cti9w3YV/R6Q9cjQOQwghQmLv3r0hG5merksuuYSnnnqKvLy8E7Y3NTXxwAMP8MYbb/CNb3yD+++/f4wi7F9/vzul1Cda63n9lR/RKXWllGkk9ce7jLnTQdmpKT/M0agmbD03hk5ecB133XQpV0y1Ue+28ps/rcfT2XJKbcdExDJ12s/o8GWSpJ/mlbeuYW/lZ6NwFEIIMX6UlpaSm5vbZ3tCQgJPPvkkpaWlZ1xiPx0jvV7+K6VUBIBS6pIQxDOuJE+MxjCl0NTRRleKn/T24PPuAOmFl7Hojvv5wpULcGOldPOpL+U6d+p87rj2FYzEH+Mwt7Hz0+/JHfRCCDGI6upqDGP83yo20iP8IfC0UuoZoCgE8Ywr8amRGOZkurWLiPRobNpK2f59J5SZVHQ1dtzsKzm9KWkBLpt9HTrqblIc5bz3maz3LoQQ57qRJvd/B/YDGnhh5OGMLyazQVR0CiiI6eoEoPbA4RPLWO1Mi/NzoEWd9rPvAFcXfY1W9wSqq34xkpCFEEKMAyNN7v+ktf4RcA+weuThjD8p2TkAdBzcS7OlHX+Vs0+ZvPwCnNip/OT10+7HbrXjd3yBNMdBDlbvPe12hBBCnP2GldyVUv9PKfX3J2/XWjf2/OwCvhXi2MaF9Jk5oBzUlJXTFN9BbLO9T5nsC5YCUHVo94j6mpd3EwA7D8qpeSGEOJcNd+R+B9DnfK9S6htKqfsBtNb+UAY2XiRNjMEwJdPY3k4g1UKqK4GO9rYTyjji04hVXRytbxpRX9lpudQ7s3B3vjeidoQQQpzdhpvcnVrr7n62PwOMfJ68cSwxMwplTqULD7GpsQCU7e972jwtUlPbOfI5BwK2haQ69lPfWjfitoQQQpydhp3ce5Z6PYHW2g34QhvS+OKIsmJ3JIMCR0NwZN5UfrRPudTEOJoCkbg7mkfU3/TJyzGUZsteOTUvhBDnquEm9/8G1iqlJh2/USmVDMiD1UNImTIdgLqdH9NgbUUfdfcpkzYxG1DU7Tv9OecB5mYvoM0TR0vzWyNqRwghxNlrWMlda/0n4AngE6XUq0qp/1BK/SfwIfDYaAY4HqROy0QZCVQfKaMlvov45oh+ypwPwNHyfX32nQrDMOjQC0iy7qLb3d+VFCGEEKNt48aN5OXlkZOTw8MPPzxguZ/85CfMnDmTGTNm8OMf/zhk/Q/7UTit9e+AbILPs1sAF3C71vqPIYtmnErMisKwZNHo80CqhWR3PHV1NSeUiUnPJQIXtbW1I+5vYvpV2EweNu/dOOK2hBBCnBq/38+9997Lhg0bKCkp4bnnnqOkpKRPud27d/PUU0+xbds2iouLefXVVzl48GBIYjil59y11u1a699rrb+vtf43rfWZtVLLGSptaiyGOYuAAVFdwTvlS4tPfOxNGQapDg9H270j7m9B/lW4fDaqal4bcVtCCDHerFy5kttuu4358+czadIk1q1bF9L2t23bRk5ODtnZ2VitVlauXMnatWv7lNu7dy8LFiwgIiICs9nMpZdeyl/+8peQxGAeqoBS6m7gfOAtgnfGr9NayzRopyAq3k5scjaN5dB+4DPizJl0l/W9cS5tQjSbqwP43E7MNsdp9+ewOmj0LSTJ8j4NrXUkxaWMJHwhhAi5Awf+nY7O0E64FR2Vz7Rp/2/IcsXFxdx44408//zzfPDBB9x3330sX758yHqLFi2io6Ojz/bHHnvshDXdq6urycrK6v2cmZnJ1q1976eaOXMmDzzwAE1NTTgcDtavX8+8ef0u8nbKhkzuwOXAbcAmrfXFSqknQ9LzOWbizCyaK5KoPFKGeV4zcbV9J7NJzcgiUF1Fw4GPSZs1snV45s34NrWlb/PmJ7/g9it+NKK2hBBivHA6nTQ2NrJ6dXBS1YKCAlpaWigrK+PBBx+kra2NF198sd+6mzZtGlYf/S2lrpTqsy0/P5/vf//7XHnllURFRVFYWIjZPJy0PLThtNKktdZKqUd6Pve91VsMKWNaHMVvTKXZV8/kCZrUpgQaGmpJSkrtLZOWOxe2VVFbunvEyX3GpLl88tkcYi1/obTmdqam5w1dSQghwmQ4I+zRsHv3bnJzc7HbgwOsHTt2UFhYSHZ2Nk8//TQrVqwYsO5wR+6ZmZlUVlb2fq6qqiI9Pb3fNu+8807uvPNOAH7wgx+QmZl5Wsd1suEk958AaK2PPTj9Ukh6Psdk5MVjskzB79qCua4SyKRk83Yuvf7a3jITsudg4SWOHq1mbgj6nDPjfg4f+Dq7P72Nz8q/xRXnrSLaEROCloUQ4uxUXFxMRUUFLpcLv9/P6tWrefTRR4dVd7gj96KiIg4ePEh5eTkZGRmsWbOGZ599tt+y9fX1JCcnU1FRwUsvvcTmzZuHfSyDGfKGOq31yc9mLQhJz+eYyFgbCVlTMbBRd3AX1REN2IrdJ6y/bphMpFqdHG3pu7jM6Zg9ZR7TZjxLtz+OaPdjrH/nGupa+k6gI4QQ54ri4mJWrVrF4sWLKSoq4p577mHhwoUh7cNsNvP444+zdOlS8vPzufXWW5kxY0bv/mXLllFTE3xi6pZbbqGgoIDrrruOJ554gvj4+NDEMFQBpdTxS7kqYA7wSP+lxWBy56VQdyibmo4SEmeYyPl4Avv3fEr+rDm9ZVLj7BTXQ8DvxzCZRtzn9MyZTEt/m3c/fZmYhn/mzY/u4OYrX8FhPf0b9oQQ4mxVXFzMU089xSOPnJjGmpqaeOCBB9i5cycPPfQQ999//4j6WbZsGcuWLet33/r163vfD/dswKkazqNw7VrrW3teXwDeHJVIzgFTz0vGZMnGa1IkB9w4DTdH3zrxxMjEydl4sFL5SegeYzMMg8vn3Ahx/0Kqo5w3d/R/ekgIIca70tJScnNz+2xPSEjgySefpLS0dMSJ/UwwnOT+4EmfHxiNQM4FE9IimZCeBygqP3qfivxWptVmsHPb59dYpl18E2Z87Nn+Ycj7X3r+F2l0pdHR9OwJlwOEEOJcUV1djWGc0hQvZ6XhXHMvB1BKRSilCrXWvQ9oK6UmKqUyRjPA8WbagikoUwZHqiu4aMUyGmwt+DbU4fcHV8y1xSSQG+2ipMFHwDfyCW2OZxgG5uhbSXEcZtsBWRZWCCHGq1P5+uIFXlJKRR637ddAn9XixMByzkvGZJ1ChwrgPHIY50I7ac4Edm39qLfMjIICOrWDg+/3/6zlSFx5/ldw+ezsL1sT8raFEEKcGU5lbnkv8BeCE9qglJoIJMkUtKdmQnokcUnTANj/lxeZd+mltJk7ad9c3Vtm2iW3EG908uL7u9n35h9C2n9MRCyNvnnEmzbj9sqUBUIIMR6d6oWHXwNf63n/ZeA3oQ3n3JC3aDbKiOPQ7s+w2mwczekkuyGNmuoKAKyRsXz9rntJNDtZ88Eh/vQ//4jPHZrH4wDSUq4l0tLF5r1vhKxNIYQYjv5mbxODO53f2akuHLMPQCk1DbgdeOaUexTknp+CYZlKg9eJs6GRvMvOx4TB/i07e8tEp07hzn/4dy6dZLCnPZJdrz4Vsv4vnrkcl8/OkepXhi4shBAhYrfbaWpqkgR/CrTWNDU19c6oN1ynM4nt0wRH8J9qrVtOo/45b0J6JJExObS7P2H/n59nzt33stO2G33kxNG52R7J4q/8C4ce+gc27e5izrUjW1DmmAhbBI2+IiaYPqTb3U2Ere/68kIIEWqZmZlUVVXR0NAw1qGcVex2+ylPS3s6yf0FglPS/ttp1BUEFxDImT+XHevWcmjbZubcfS9Nyd1k1MTj9/sxHTd5jTIMLr1oPs++t5fPNv6WuTfcE5IYpky8DW/9Jt7Z9SeWz/9KSNoUQojBWCwWpkyZMtZhnBNO+WE/rXW31jpWay2T2YzAlDmpGJZsqjva8Lvd2LPjiPZHUHrw5Nl+IffSLxCruth/sDRk/S/Mv4oWdyLNDX8OWZtCCCHODOP/Sf4zVEZePBZrNj5DU/bqWqbMygegpuRQn7LKMJg6wUR5pwW/1xOS/k0mE17rNaRH7GH34Z1DVxBCCHHWkOQ+RixWE5kFswGDA++8SUbmJBqsrQQO939XfHZOLm5s1Hz6bshiWHzeXXR6o/hsz324PK6QtSuEEGJsSXIfQ5MLMzHMkzhSd5RAIEBzYhdJLdH9lp0ybymgKdv9ccj6T4tPx5H4LyQ7Knjh9dvYWbo1ZG0LIYQYO5Lcx9DEggQM61Schqb2ow8wZTqI98ZQe7SqT9nIpEzSzB2U1TSFNIarzv8CLea/Id5SRvORL/K7dato6ghtH0IIIcJLkvsYik+LIDo+uDrRvldfJiknC4DD+w70W35KchRV7ki8zs6QxrHiku+ycOF71AVWkWbbxqubvhfS9oUQQoSXJPcxpJRi0pxsDFMyh8sPkJNXgFf56Dzc2G/5idnT8GOi5rP3Qx7LhKgJfHHJv9FsfJlM+4es2/b7kPchhBAiPCS5j7GJBRMwLLm0EMBZUcHRyCZstf2XzSpcDEDF/uJRi+eWS75PvXMiHQ1PybKwQghxlgp7cldKXa2U2q+UOqSU+udByhUppfxKqRXhjC/cMqfHY1inArDvpRfoTvaT2jEBr7fvcq+RSZkkmjqoONr/yD4ULGYrEfErSXLUyLKwQghxlgprcldKmYAngGuAAuB2pVTBAOUeAV4LZ3xjwRFlJXnKZEwqkrJPdxExZQKOgI2De3f3W35inIXKbiuBnvXfR8Plc2/vWRY2tCvSCSGECI9wj9wvAA5prcu01h5gDXBDP+X+BvgzUB/O4MbKpBkJYJ1GncfJ5CkTATi6u6zfshMnTcaFjbqSD0ctnmhHDE2BxSRbPqSpffTOEgghhBgd4U7uGUDlcZ+rerb1UkplADcBTw7VmFLqLqXUdqXU9rN5IYLgdfccAoai4Z23qYqsx3qk/5H51AuCz7sf2LFpVGOaPe0rWE1e3tklN9YJIcTZJtzJXfWz7eS1/34MfF9rPeR5Z631r7TW87TW85KSkkIR35hIyY7FETMJQ5sp3fIhnZl+MtuT6Ors6FM2OnUKmdYO9lWO7rPoc7IvoNY5BV/HX+XGOiGEOMuEO7lXAVnHfc4Eak4qMw9Yo5Q6DKwAfq6UujEs0Y0Rk8lgyuxkDNtUqtqaiZ+WhkWbKdm5o9/y0ycmc9QXQ2vF3lGNKzLuFpIc1WzZ/86o9iOEECK0wp3cPwZylVJTlFJWYCXw8vEFtNZTtNaTtdaTgReBb2ut/xrmOMNuypxElCUXr8kg8mgNbeZOuj/q/5m46fOvAmDvh+tGNaYrzltFpyea0tKfjGo/QgghQiusyV1r7QO+Q/Au+L3AC1rrPUqpu5VSd4czljPNxIIELPYpoBVl771DfaGbqS3pfPrJtj5lE3PPI8vazqb9jXQ19J2qNlSiHTF4HHeQHrGH9z9bP2r9CCGECK2wP+eutV6vtZ6mtZ6qtX6wZ9uTWus+N9Bprb+qtX4x3DGOBYvNxOTZ6ZgtmVQcraTomitoNXfQtb6y32vv1964AhcWXv39j0M+He0J/Vz4bVrcCTRW/z92lfX9oiGEEOLMIzPUnUGmzU8B6zS6TIr2XTvpviqC9K4EPnliPR6v+4SyKQUXcXlOJHs7onjyv35EU+norMnusDqYnv9L0Irasjv43bovsa+q/2fwhRBCnBkkuZ9BJs1MwB6VCxr2vvIXLrhkMRWLusluSeejVzb2KX/xl/6ZO5bMxhkw84c//pHOuiOjEtfMyXOZX/QX6n1XM8G8i9KSW3ljxzlxQkUIIc5KktzPIGaLiWnzczDMaZSVHQJg4TVXUxpfQ+ondpqb+j7LP/Xim/ni9VfQEbCx4Y+Pj1psGYlZfPnqn1B43iu0edPwNP6QqsaKUetPCCHE6ZPkfobJm5+CYZ1Gu6Fp2LUDwzDIuqUQh9/OjnXv9lsn87wrKUoz2Ntup6O2fFTjm5g0haI5j2My/Ly17Yej2pcQQojTI8n9DJM2NY7o+DwAdr/wHADZOdOpiKsjptw8YL3zL7+JACZ2vv7cqMeYm5FPEyvItG9iZ+mWUe9PCCHEqZHkfoZRhiL/0hkYpnT2H9zXOzucf5qNdGciRw4f6rdeYu55TLG380l5CzoMM8pds+DvcfnsfLr/F6PelxBCiFMjyf0MlHdBKoZtBl2GpuK1DQDkXjAHgNKtnw1Yr7BgGm06kqOfjf5SrROiJtCsrybN+hGH6/tf5EYIIcTYkOR+BpqQHknypELARPFfg3elZ2ROCi4oU+obsN60hdehCLB/lBeVOWbR3HsB2LTzibD0J4QQYngkuZ+h8i/OxrBOo7y5nu6G4Mq3nRMDZLUn0dnZ3m+diIQMsmyd7K9uC0uMk5OzOeq5iAlqA00do7uQjRBCiOGT5H6Gyp2XgsU+F7+h2PHznwEwIS8dEyb27to1YL28iSnU+qJHfVGZY2bn3YPd7ObN7b8KS39CCCGGJsn9DBUZZ2PizHxMpmR2f7aDgM/H9NmFeJWPtgP9LygDkHfBlQAc2NJ30pvRMHfqAmq6Z+DwPMcRufYuhBBnBEnuZ7C8+akY9nl0mRT7nn2GiIgoqmIaiKwZ+H+2xNzzSDA62V8+egvKnKxozn9iUn4++PhuGlrrwtavEEKI/klyP4NNmZOENTIPE1Z2bHwFAHeGIr0zifb21gHr5aVGUO6MwNXWd0a70TA9cyamCf9Csr2Mbdsu55nX/0nuoBdCiDEkyf0MZrWbyTkvDZPjfOr8Ho5u/pCkgomYMNjz8fYB6+UVzieAidIto7ve+/Gunnc76Tl/otE7h1TTS+zZdR0fHwjPXftCCCFOJMn9DJe3IBVlLURp+OQPvyW/cA6dpm669zYOWCfzvCtx4KJkz54wRgozJs3lK8v/yJT8V+n2RVN3+G72ywpyQggRdpLcz3AZefFExcfhsGZRXleN4QtQndJC+tE4fL7+n3k3WazMSbNQ0u6g8eAnYY4YctKnUzTvWQC2FP9b2PsXQohznST3M5xhKKZdkIrPdh4ek8G+5/+IoyCBaH8kez8deA33i2++CzN+3nllTRij/dzk5Gy6LF8i0/EJ7+/eMCYxCCHEuUqS+1kgb0EqyjwZkzZR8s6bzLygCK/yUfdx6YB1IpOyuHCilT3tkbz+qx/i93rCGHHQdRf9HS3uBCqP/E/vHPlCCCFGnyT3s0BCRhQpk+OwRuRT3d2BqbOb0kl15JSnUnF44AR/6Ze+T1Gyh49qDH7zX/9MU+nAI/3REGGLwBT9FVIdZby/e31Y+xZCiHOZJPezxIxLMvCbZxMwFJ/+/v8ovGUxXsNH6Z8/Hvjau9XO8m//JzcXZdDosfH7PzyLu6M5rHFffcHXaXPHU1XxhIzehRAiTCS5nyVy56Vgi8rAQiT7d35MUlIqlXM6yG3I4P2fvojL5Ryw7uzl3+SLyy+hTUfyzh//N4xRg8PqgKivkBZxgA0fPxPWvoUQ4lwlyf0sYbGZmH5hGjjm0oSf+k8+5vJbb+LgvGam1Wfw4VNrBx0ZTyy6hnlJbrbWqrCfnr/+onuoc07B2/JjmcFOCCHCQJL7WWTGonQMaz5oKH42OAq+bMUN7JtVR151Bu+vfXXQ+pfcdCcAO99ZO+qxHs9sMpM//UEc5i7e/ugWdh8O75cLIYQ410hyP4skpEeRPi0TsyWDg0cOEei51n7ZypsojzvKhB0mvF7vgPVj0nPIjexiV3V32O+enzt1PlHpT+AwtVNXtoI/vHoNH5a8EdYYhBDiXCHJ/Swz85IMlG02TpPBob/8GQCTyYTtwmQmeGP4ZNP7g9afO2cOnTqCQ5v+HI5wT7Cw4ErmFW2gUX2DCFMDrtq7ef6dh8IehxBCjHeS3M8yU89LJjohH4WZ4nV/7d1+3sKLabS24t3WNGj9aZd+gQhcFO8K/8x1AOkTMrjtsvtZetl7VDkvZELgad7Y8eKYxCKEEOOVJPezjMlsMPuKbAxbIRXd7TR+WgyA2WymabqHKa1pHK2pHLi+1c6MZIMD7fawrRrXn0h7JCuu+CUNrkk4G/6NpvaB58oXQghxaiS5n4VmLMrAFnUeYLD1V4/3bs9eMAuA/VsGv2Ft9gWX4sPMvvfGdsQcaY+kIP8hHOZu1m9+cExjEUKI8USS+1nIHmlhxiX5mGx5HKiroeXAfgCmZE+j1t6EcXDgZ94huGpcnNFFccnBcIQ7qDnZF1DjuZIU06vsrSge63CEEGJckOR+liq8IhOT/SK0Mnj30c9Hva2TPUxqSaG1deBr78owOG9yHOWuGI5+NvgNeOFw9YIf4gnY+PizH8ksdkIIEQKS3M9SsUkR5Jyfi8Uxh7L2JirffhOA9PNyMWHis4+2DVq/6Lo7seFh0xsvhyPcQaXEp9Ft/QoZjk95Y8cLYx2OEEKc9SS5n8UKl2ShbBdiwsQ7TwXnbp8+s5AGayv+Pe2D1nXEp1KUaaWkPZLyj8I7qU1/blj4t9Q5J+Fr/jd2lQ3+xUQIIcTgJLmfxdKmxpKSnYwjdhENAS8lv/0/DMOgKdvJlKYUmprqB62/8JZvkWTq5NnXt3HwvT+FKer+2Sw2Lpn/W9z+CGpKv8If37ifsqMHxjQmIYQ4W0lyP4sppZizJAuvMQe7trB5w18J+HxMXDAjeGp+09ZB6zvi0/jyN75NrMnNH9/Zw/P//Q94uwcf8Y+mzMSJzJnzHA2eeaSaXqB87zX8bv1Xae4M70p2QghxtpPkfpabOjeJ2OQo7ImX0W7Ant//hpxp+dQ4Goks9g06HS1AdNpUvvUPP+LybCt7OyJ59qc/GtMEn52Wy1eWP8OU/I3U+m8lzfohb7x/vSR4IYQ4BZLcz3KGyeD8pZNw+guwB0xs2xi8QU5fEkuaM5EPX90wZBsWRxSXfPkH3HheGuWuGDa/+LPRDntI2Wm5rLryIeypPyXeWscr790rd9ILIcQwSXIfB/IWpBI9wYEj6RJalabsry9RdOliyuKOkrrdxt7Pdg2rnTnX3830qE4+KOuiq2HgWe7C6ZKZ19Bq/gaZjm28vPmXYx2OEEKcFSS5jwMms8HcqybS7Z+JOaDY/tcXMAyDySvPx2nyYH22ic1vvTmstq64/ja8mPngpV+NctTDt+KSf6Smezqmzp9ztKVmrMMRQogzniT3caJgYToRMRFExBRS7eqiYdcOJk6eStbfXsDR6Gay3rDx7ktDP/KWNK2ImXEuPjnqx90++CI04WIYBvNm/ydWk5vXP/oHOT0vhBBDkOQ+TpitJuZcORG3qQiFYtuvnwQgMTGFefddy8GkaiZ9HMORw4eGbGv+JVfhwcqujb8f7bCHLX9iIa2mr5Hp2MpfPnx86ApCCHEOk+Q+jsxanElkfAJ2WzaH6qrobgg+5263O5j55cX4lI+yP28fsp3M85aQYWln275qAn7/aIc9bCsu+SeqnXOIdv+MF959FP8ZFJsQQpxJJLmPIxariaJlk/Hb5uMzDD75+U979yUlpVIxu4Pchoxh3WB34XkzaApEsffNZ0Yx4lNjMpm4/tJfc9R9PgmBX/KX1y/k2Td/xOH6srEOTQghziiS3MeZ/IXpxKVOwWJK5tPPduBube3dV7TsclzKTfWmfUO2U3Dll0kwOnn/48/OqNF7XFQ8d1zzLJ7of6Xbn0aK8Qz7Pr2GddvOnEsIQggx1iS5jzMms8EF12WjHItxmQw+Om7FuJiYOA5nNjK5MpH29tZB2zHMFhbNyaHOF03xK2fWI2iGYXBN0Zf48rVrmZK/kQZXDvbOf+Xlzb8e69CEEOKMIMl9HMotSiFxUh4Wy0Q+Pbind713gPRFedi1jR1vbxqynVnXfJ1JtnZe3VVD1Y7hPUoXbtlpuay46kVquvOxdD7GniM7xzokIYQYc5LcxyHDUCy8JQfluAK/MrH+X3/Q+/jY9JmFVEU24PjUO+QjZSaLlVu/8T2ilJvfvPwu7/3uQXyurnAcwilxWB1cvuAXuP12Ptv9t3Q4x276XCGEOBNIch+nJs5IYPLsqVijLqXW52bbYw8BwVPa7tlWMrqT2PvZ0KPcyKQsvnHX3UyPcfNOuZcn/+uHNOw/85ZkzUjMIj7jP0iwH+Wld/5+rMMRQogxJcl9HLvolhyUdS4Rpgls+fhDGop3AXD+FZfgNFwc3XRwWO1Ep03lC/f9F6sWF+AMmHn2+RfobjrzZoq7dNa11OvbyLS/zR/f/H8y2Y0Q4pwlyX0cS0iPYsYlmfijbgYU6x/6EQGfj6ioGI5Mbia3KpVDB0qG3V7u4ltZufxy2gIO1v7mf0Yv8BFYedm/UeW+glTjWZ7Z8CV2HNosSV4Icc6R5D7OXXDtFGyRE4hLWUKj9vHhf6wG4PwVV9BtclH74p5Tmgwma95SLpsawf7OKMo3vzxaYZ82k8nEl676BfX6DhItxbRUfImXXlvAnzf9GJfHNdbhCSFEWIQ9uSulrlZK7VdKHVJK/XM/+1cppT7teX2klCoMd4zjSUSMlfnXT6HTO5t4Sxzb9+yi8dNi4ick0nhRgMntqbz/v38a8tG44y245V5iVDdvvP0u+gwcFZtMJm6/4kfMX/AOnfbv4/InEuf9GX96/RbaulrHOjwhhBh1YU3uSikT8ARwDVAA3K6UKjipWDlwqdZ6NvDvwJmzPNlZauYlGSRNjEYn3w7Aez9+FICF11zNoQtamNKYSvl/fcAnH30wrPYsETFcPncKNd4Y9rz229EKe8QSY5K54aK7+OKyV+ly3E+K/QCvvLuSTmfnWIcmhBCjKtwj9wuAQ1rrMq21B1gD3HB8Aa31R1rrlp6PW4DMMMc47hgmg0tvz8PV7SAhvoDDna1Uv/8uhmGw+Obr6fpiDB6zl4SXfRRv3zqsNmcv+wbJpg7e+rgEn9s5ykcwMoZhcP2F3yAQ96+k2A/x57fvknnphRDjWriTewZQedznqp5tA7kT2DCqEZ0jUrNjyb8ojU5jMWateO9Xn6+sNmP2eUz77mKa7G2Y/9pMfd3RIdszzBauvGQBLYEotvzpJ6MZeshcPe+LtJi+SaZjK8+99YOxDkcIIUZNuJO76meb7regUpcRTO7fH7Axpe5SSm1XSm1vaGgIUYjj14U3T8UeHYMjbgFHvS5K177Uuy82Np74L00n0ufg07XvD6u9nEW3kB/dyduHuqj85PXRCjukVlzyj1S5l5JmfpHn33lI7qQXQoxL4U7uVUDWcZ8zgT4PTCulZgO/Bm7QWjcN1JjW+lda63la63lJSUkhD3a8cURZWXTbNDxGEWZt5v1nf0vA5+vdn52Tx6FJtUwtT6b2aNWQ7SnD4Pqv/wMxhotnX3mbvW+cOSvIDcQwDL545Y+pchaRqH/NH9dfxytbnqa5s3msQxNCiJAJd3L/GMhVSk1RSlmBlcAJz1MppSYCLwF3aK0PhDm+cS/n/GSy56RhRF9BMwE2P/IfJ+yfft0ClFbsfuXDYbXniE/ljlVfJM7s4fkPS/ndw/dRu3voeevHksVs5Y5rnqXN8l0iTXVEdP8n27ZcyO/Wf4O6lqEvSQghxJkurMlda+0DvgO8BuwFXtBa71FK3a2Uurun2A+BBODnSqldSqnt4YxxvFNKcentediiZ2Mzp/Hxrm3Ubvv8JrrMzMmnNHoHSJg6lzv/8UGW5kVS77Lw6xc3ntF30UNwBH/zor/hhqu2Ep35G+p9V5NqfZ8t265mZ+mWsQ5PCCFGRGnd7yXvs868efP09u3yPWC49m0+ypv/txVf22+wB3ys+t9fEJ01EYCqqsP4Hj/Moew6ltx12ym121l3mDVP/5QaTyRfu24RWedfNRrhj4o9R3ayt+Rb2E3dpEz+BUXTFo11SEIIMSCl1Cda63n97ZMZ6s5ReQtSmTpvKubYL9BtwJ//4W/wdHQAJ47eSw/sPaV2o1Ims+qefyLGcPHiq2/gPItOc8+YNJd556/B6Yui/vC3+GjvW2MdkhBCnBZJ7ucopRSLV+UROWEyMUnX0oSfv37nm7032M35wmU4DTd1L+zB6/WeUtuO+FS+cP3VtGsHr//h7HhM7pjJydlceMELdPom0Fr1HTbt3jjWIQkhxCmT5H4Oc0RZueLL+bj9eaQmXUClq5PX/+HvAEhMTKF1sYmJnSl88NM/n9L0tAAZc67gogzFzib7GTkH/WAyEyeyaMHztHuS6Kr9O3634dts3f8Obq97rEMTQohhkeR+jps4I4HCK7Jo8S4kPXoie44eYdeTTwCw4IorOFjUTHZDKhWPfsR7f33llJ4Lv/SL9xFvdPLX1zfR3VQ9WocwKtInZHDFwj9R572cFMtbdFZ/g41vX8Azr/09Te2NYx2eEEIMSpK74MKbppIyJZaOyC8Qo81senMdHZUVGIbBZbfcQNcXY2mJ7GTqljje+fkLeNzDG8FaI2NZcf0yOrWdl57+H7xn2ZzuSXEpfOWaXzDvgk14Y/6dVt9MUkwv896HV7N539tjHZ4QQgxIkrvAZDZY+s0ZGCYT9ilfxmsoXvvh/b37C2bPZeH3V7B/Vj15VRm8//u/DrvtjDmXs2x2Moe6o/nN//yQ+n3Dm7v+TJIYk8zV877IV5b/kYTJv8OnLbRWfps3drw41qEJIUS/JLkLAGISHFzx1QLa2+JIiD+PI91t7P7tr3v3G4bBFatuYV92DdNL09m5bfOw2z7/5r9h5cU5NHnt/HzNev7843+iqXTnaBzGqDs/5yIWX/RXmj2Z6Ob7eXnzr4euJIQQYSbJXfSaMjuRecsn08El2LHz3qsv0X7k8AllLvrScurszbCuAaeze9htT1/yJf723m+zMAP2tlr4+TN/Zt9bfwzxEYRHclwK1y5+kTpXPpHOh/jdhm9R3Vw5dEUhhAgTSe7iBBcsn0L2nBR0zArchsHL/3wffq+nd39ERBTGNUkkueP56KVTW7AvMimTK7/5r/zdt75OqqWb5zftP2sTfGxkHCuuep4a742kWd6mZOdl/H7djaz96Jc0dQy4HIIQQoSFJHdxAmUolny1gAmZU7DFLKEu4GHtPXeekODnzr+IAynVTN4dx5HDh065j+i0qXz5bx4gzdLJS5v2nJXX4QEcVgd3LP1vJk7/C/WBW3GoWqJcj7J964X8bsM9dDjbxzpEIcQ5SpK76MPqMLP827Oxx52HI6KI8o4WXrzzDtwtn6+clr9yIV7DR80fiod99/zxbDEJ3PaVb2FRfta88CecLbWhPISwmp45k1VX/ie3XP0RsVm/p853FenWN1j/zjIOVJeMdXhCiHOQJHfRr9gkB9d+Zw6m6EuJjllIlauTZ771FdrKSgFIS8ui7UoLWZ3JfPSzv9DaeuqnomMz87ht2WJaAw7+/NR/4fe4Qn0YYWUYBvNyF/Llqx/HnvI4dlMH+3av5J1PXxnr0IQQ5xhJ7mJAKZNjWPrNmfgsC0jNuolO7WfNP/0tLfv3ATB/8eWULmhlUlMK1Y9t461nXqSz89RORU8suoblPY/K/eF/fkB3U81oHErYLZp5NTNmPU+3L45A43f53fpvUlz28SlNAiSEEKdLVoUTQyr5sIZ3ntlHWlodFbufIUqZuOOXv8MWPwGAvXuKqduwl5zGDJosbXBDEoXz5p9SH7te/gUv76jBio+FU6OZf9M9WKPiR+NwwqrL1cVL7/2QRGMdVpOXNnc8HXoOaSlLuWLOzZhMprEOUQhxlhpsVThJ7mJYtr1azsevlpOWWE75gZfIsEVy62+exTCbe8vsKf4E518qifVE4V2ZQMHsuafUR+2eD3h7/V840BVNpHJySX4q599wN2abI9SHE3YNrXVs2v0nOto2E2/+jEhLF3XOSeRPf4i5U0/ti5AQQoAkdxECWms2v1TKzjcqiLdu5mjdZmakTeLqHz9xQrn6uqNU//xjrH4LSX8zh+SUtFPuq+Ljjbz15usccccwydbOF+99AFtMQqgOZcz5/D42fPw7vK0/J8LcSbv5G9yy6D4ZxQshToms5y5GTCnFhTdPpXBJFs3uBcRHZLPn6BE+/p9HTyiXnJJG7B152P1W9v32ffx+/yn3NbHoar76/ce46fx0KtxR/P5nD55V68IPxWwyc92CO7l4wXrq3HNICDzJsxtuYmfp2flIoBDizCPJXQybUoqFt+Qw54qJdFuvI8KUwKYt77H3D78/oVx2Th7VF7nIbknnnT+8dHp9GQaF193FbRdPo9Ybye+eeIyuhvE1C1xyXAp3XPMcbdbvEWcpp/nIF1mz7hKeee3vef+z9XS7hz8DoBBCHE9Oy4tTprXmgxcOUvzWIXT77/EEOpg3bSaLfvRg7zX4QCDA20++wPSKDEovbOPSG6497f4Ovf8n1rxdTLzJyR1fv5uYjNxQHcoZo6mjibc+eRp35wck2fdjMXy4/Vaa9LUsW/B9EmISxzpEIcQZRq65i5DTWrPtlXI+XncAU9daur2VJCkzy37wryTOLgTA43az+Sd/ZWpzOvvTqph8zRymTss/rf7KN7/Ms69tRaG5aHIEc5d8gdjMvFAe0hmjw9nOtv1vUlXzCum2TXR7ozDi/oblF3wNw5CTbUKIIEnuYtR89m4V763ZT4TpU9rr30ShWbzkWgq/9W0AvF4v761ZS3bJBKzaQlncUWKXTDrlR+UAGg9+whtrn2N/ZxSgmR7VxaVLrydt1iUhPqozx66ybezZ+y+kOkqp6S5gavbfsmD6FZLkhRCS3MXoOvRJPW/8Zg+RUV14y5+mVXu49KLLmPfdf+gt09zUwK43NpFQYiXOE03p3GYWf+GG00pSzWXF7HznL3xc6caDmcXZDi5e9X2McXq3ud/vZ+1HP8fS/UsiLE46PDG0+fOwRcymcOpy8icWjnWIQogxIMldjLqqfc1s+OVuFB5U7VO0+ju5uGgh8//xByeU6+rqYOtT65hWm8H+WfVcseqW0+7T2XKUV3/zP+xpjyQ/upObvvXAuJj4ZiAdznbeLf4Tzc0f4mAfCfY6AI525zEl+3ssLLhyjCMUQoSTJHcRFq113az/xae01rVjbX+GNl8LC2bPY+EDPzqhnN/v591f/Im8qgwOFjVz2S03nHafOhBgy/P/zev7O0g1d7Lyq98at9fiT1bdXMmHnz6L2fUCsdZWqp2zKJj2j8zLXTjWoQkhwkCSuwgbt9PHG/+3h8Of1mHueoEuby2zs6Zy+YOPYrLZest5vV42/ezPTKsP3k2/6LplI7qOfOCdNbz43qcoNJfkxjH36i8RkZARikM643W5uli35Qns7j8QaemiunsWjuhFTElfwMxJ52O32sc6RCHEKJDkLsIqENBse7mM7RvKUN3rcHkOEasVl6z4ItNuvb23nNvtYvNP15LTlM6BlGqSL8ulYPbc007yjQd3sPEvf+RQdzQGfqZGdDN3zmymX/GlcXs9/nhtXa2s3/JjTO7XSLDXA+D1m2lw5xCbcBNXnf8lSfRCjCOS3MWYKP+0kbd/txdn224C7a/hVT6SDQuXfetvyFx8OQA+n4/3/vQykz+NxaatNNhaaM7zcuGNS4mIiDqtfo9+9j6fbX6T3UddtOsIkk0dLL/qcibNXx7KwzujHakvo+TIZhqbd2DzbybBXkerOx6i7uCaC75JhC1irEMUQoyQJHcxZjpb3Lz52z1U7WskxvwxrXUf4TOgaMZcFv6/f+sdpXe0t1H84Wb8n7YxtSWdJmsblhUZp7z4zPECPi97Xv8db23fT2sgkqJkD0u+9Pfjap764QgEAry3ex3VFT8nLeIAHZ5o2llESuJCCiZdSFbSpLEOUQhxGiS5izEVCGh2vHaEba+UY7N7MOr/QLO3hUkRsVz/k59jjYk9ofynn2zD/3ItMZ5IGq5SLLjs8hH17+5o5u0//g9ba03Eqm6uu+wCci75wojaPBsFAgE+LHmdsiO/J9m6A6vJC0CbO46OQB4JCVdyxXkrcVjP/lX4hDgXSHIXZ4T6I+28/ft9NFZ1EMX7NLV+QpxW3Pzv/0V83vQTyjY21rH/l++T1ZHMwTlNXLrieszHLS97Oio+3sjLG9+k0R9FkqmDgsw4Zlx4JcnTF4yo3bOR0+Nk9+HtHD66je7OT4ky9hBna6HTE02HsZSLZt1Jdtq0sQ5TCDEISe7ijOH3Bdjx2hG2rz8M3gO4Wl/FCPiZM30WRX/390QkJfeWdTq72fzLl5lWm8GR6FpMFyVQuGABDsfpXy/2OjvZ+cpT7Cmt5Ig7GlCkmDtYdH4BM5Z+DXWOzvzm9/vZtGcDRyr/QLo9+P+jRlcWHjWNqOgCMpPnMGtykVyrF+IMIsldnHGaajp59w/7qDl4GLrfwOOrxhQIMGVCCkV3fI30i4NTygYCAT56/XViP/QT743Bo7xUxjdgm5dI0aWLR7QGekdtOSXv/5VP9ldR748mw9LOVUuuOKduvOvPkfoyPvz09/hcu4izlBFp6QLA7bfS4JlDRtoKLp19HRazdYwjFeLcJsldnJF0QHNgWy0f/aWUzqYK7N7NdHaXEVAwNS6RK3/0EJHp6UDwufjPPtlG854qEo9EkOiJ43BMLekrZ5OdPbJJawI+L8Xrfs3bu8rp0BFMi+zgokWLmXTB8nN2JH9MIBCgovEwByq3U9vwPjF8QLS1g3ZPLJ3qUjJSLmVa5nmkT8iU+e6FCDNJ7uKM5nH5+GTDYXa9VQkBJxGet2hq34c1oLn8+i9Q8OWvnVDe5/Ox+fU3SPzQwB6wUja7hUUrlmO12AboYZhxdLWx9aUn+KC0Azc2olU32XGKqVNzyF14LY74tBG1Px64vW7e+3QtR2tfJMVajMXkA6DLG0mbNwttziUzdTHzp19JpD1yjKMVYnyT5C7OCm0NTj5eV87+rbUYuh5/y59x42RyZCyX/O3fkzTnvBPKNzTU8tkf32VabQZVkQ3oi2IovHDBaT8ff4yns4W977zA/oMHKW8348SOCR8z4jwsvOomUgouHFH740Wns5NdZR9R21RCV9d+TP4yJtgqsJk8ePwWGjwziYq5lPPzljMpOXuswxVi3JHkLs4qTTWdbHulnNIdR9Huj/B2f4ImQKJhYWr+LApuu50J0wt6y299523sb3eT4I3Fq3xUxTTgnmiQd/F5ZE0aWVIJ+P3UFL9D8Za32VWv8GIhL6qDBRddwqT5154TM9+dCqfHydZ9b1FR8waOwFYm2BsAaPfE0uVLxW/KJC52HrOnXs6UlJwxjlaIs5skd3FWqj/Szo6NRzi0o5yAqxjl2o2HLtCaTHskC++8h8xLLwOCp+o/2/ExTbsriaw2kdGViAYOZh6l4KaLSM+YOOJ4uptq2PbK/7H1cCdO7ESrbibHwuSJE5kyZxHxk2ed89fojxcIBNhfvYfPSjfg7D6IKVBNtKWaKEsnAM2uJJzG+aQmXUph9iJS5LKHEKdEkrs4q7XUdrHzjQr2b6nF52nCEdhBZ/tn+FWA7JgEFv/TA8RPO/Gmurq6Gj57dRPZh5IAKJvWyJzrLiUxMWXE8Xi729n7zvPs33+Awx0GXTo46Uus6mJGmoNZF15B6oxFkuj7EQgEKKkoZu+Rt3F2biHRuhubyQNApzeKdm8m2jyZiIhcUhMKOC/nYnn8TogBSHIX40JXq5vdm6rZs6mG7tZ2DM+HuLqLUVozMTqe6ZdeRs71N2GLn9Bbp6a6gr0vfURudRoaqIqppzs5QERWHLlzZpOcMrLRog4EaDy4ncOffcT+skrKuiMIYCLB6GTWxDhmLryGxNzzR3jk45fL4+KTQ5uort+F03kIU+AIseYqIixO4NjCN3kY9kLioqeSmjCNKanTmRA1YYiWhRj/JLmLccXvC1C6s57d71ZTfeAIftd2Ap49aPyogCbRbGXi1GnMum0VCbNmA1B2aB9lH32GvQrSOiZg01b8BChPqCVmUSZzLrgwJI9ydTVUsff9P7P74BEOu4KT5ESrbtIj/WQkTyBnzkLSZl4io/pBBAIBjjZXs6/qY2rqPsTi206CvRpDff5vVac3ik5fCn5TPgnx55E/8SImp0yVx/HEOUWSuxi3Wmq72L+lln0fVdLeVA6+cpT7AB7dCVqTbovgvOU3knvr7b3/8Hu9XsoO7qPy432kHowkzhdNdUQDrkIrufNmh+T6PEB79UH2fvgq1TVHqenw0+iPAhQxqptpiSZy82cx5YJrsEbFh6S/8azb3c3h2gNUNu6ntb0Ml6sSw3+EBFtZ72n9dk8Mnb4stDkLh2MKE2KzyUqazqTkqdhG+JikEGciSe5i3NMBTfWBFvZtqaV0ZwPe7ha0dxe+7mICyktUACZnTiZ9ViETF19ObPZUILim/LY338a23U26MxGAVnMHjXHt+FPNxGWnMOv8C7DaRp4cuhoqOfDRq+w/WEpppw0vFkz4SbV0kRprIzU1hdTJ+aQWXIglImbE/Z0LvD4Pu4/spKxmC50dn2LWlcSYa3pP6wP4AwYtnmRcehIW2zTiY3OIj84gOTaT9IQsWeNenLUkuYtzis/jp3JfC2U76ynbVYuztQS/u5iArxZ6Tu06/AHS45MouGoZU2+8CWUyU35oP5W7D+CvcRLTZCPFOQEDg3ZTFzWT2kibn0PejMIRL2AD4HN1UfHJ6xzas5Oa5k5qXTZcBL9AmPCTZe9iSloCUwrOI33WJZhlQphhCwQCNLY3UF5XQm3TQTq7yvF5ynGoCuJt9Sec3ofgY3qdvgy0eTKRkVNJjp9OduoMUuPTRzS9sRCjTZK7OGf5/QFqDrZStrOBw8VHaW+sJOA7ivJV4vMcQasANr9mSmo6ORcvJnPRpURmZALQ1dlBya6ddGyvYXJdMlZtoctw0hDVhivOjynJTmxmEnmzZhMZFT2iOHUgQFvVfmoPfMKR0v2UN3RR6wteszfwk2DqJjnSIDkhjuT0LJKzZxE/aSaG2RKC39K5o8PZzuG6gzS2VdHWWUO3sw6vpwqzriDOUo3d7Oot6wuY6PTG4grE4yMBkyWTqMhsUhLyyE7JJyk2Ra7xizElyV0IQGtNW72TipJmKkuaqNxXj6frEH7PPgLeciAAgN0PCRERJKVlkjarkKnX3oBLafZs2053aRO2FoPEzhii/cHRtFf5qIxtwDfFQlZhLpOn5mGxjDzpdjfVcPiTNzhaeZj6lg7qu6ElEAkoAMz4SDJ3kxxtITlxAskZU0jOKSQmPVdu2DsNgUCA6qZKymv3UN9yAJe7Fr+3ARVoxGY0EWttwGL4est7/Ba6fMHk7yceZUrEYk0hJjKLpPgpZCZOJTUuTb4AiFEjyV2Ifvi9AeqOtHP0UCsVn1Vz9NABvO56Ar568NUS0G1A8Ex+ksVB5uQpxGdNIn5qDokzZuGymTly8CDNJdVEV5nJ6A4+U+9VPppsbXTEuPDHG9hSokmanMHU3PwRJ31PZwsNh3ZQf3g/9XVHqW/tpt5lokN//iy4DTfJVjfJMTaSk5NJzppKcs5cIhIyJOmPgM/v43DdISrq99HUdgiX6ygBfxNGoBmr0UyEqfWEa/0QfJSv2xeFOxCDV8egjThM5mTs9jSiIzNIiMkkLX4iyXEpssqeOGWS3IUYhkBA01TVydHSVuoPd1B7qI7m2nIC3uBLB1pPKG8JwASrjdT0LNJnz8FRMIPqhiZcte0YzQGiO+wkumKx6OA1+m7DxdG4ZrzxYIqzYZ8QRVxqEumZE4mNHdkd891NNTQc2kl95UHq6+upb3NR5/78Oj6AFQ+xJjexNoiLtBIbE03shCRikzKITZ1CdNpUTBZJMCPR3t1GZUMZtc3ltHQcxuU6it/XCroNk27DZrQRbWnpXXDneN3eCJz+aDyBaPwqHmVKwmpNxmFPIToimeiIBGIjE4iPTCA+OgGzaeT3foizmyR3IU6Tx+mjobKD+iMdHN1fQ21pBV1tLQQC7Wh/IwFfLTrQ1Fveps04DAsRVjPR0VEkTpyCY0oOHRGROKs7iKmzMsEVjSNw4h3abeZOGmPa8SYb2JKjiIyPITZhAokpqURHx57WqV0dCNBRW0b9oV00VJfT2tZGW6eLNleAVp8VJyfGoAgQo5zEWv3EOszERUcQGxdPbGI6sSkTic3IxRYtk8eMVCAQoKGtjprmCpraqmjrqsLtbsbna0H721C6FatqIdLcQoSlu/82tMLpi8Dpj8ETiCWg4lCmOEymWCyWWGzWeBy2OKIc8URHTCAuMpEJ0YmyUt84I8ldiBDyefy01HXTXNNFc00XDeX11JcfpKvjKAFfPVp3QsCJDrQDPSM0DTYsRFkjiHI4iIyKwh4Rh2GLBns0fnMEEV0RpHZNwMyJd2i7lYdWWycdkS58cWBOdBCdEk90fDxxExKImzDhtJa79XS20FZ9kLa6I7Q2HKWttYW2ji7anD5aPSbatQPNiV8qHLiINXuJtkKU3UxUpIOo6FiiYuOJjE0kMj6ZiAlpOOJT5Wa/EOhydXG0uZLmzno6u5vpcjXhcrfi8bbg97Wi/a0YugWr0YbD1I7D3N3naYDjef1mnP4IPIFIvIFIAkShjWiUEY1hisJkisRqicJqicZmicZui8ZhiybKFk2UI45oRwzRjhh5iuAMIcldiDDwef20N7poa3DS3uCkpa6DhkPltBw9grO7iYC/BR1oRge6QDv71DdpExFGJDH2eBzWSBzWCKxmByZbBCZLFFYVTZwvDrvum8g7TF10Wl102914ozUqxowpwool0oY10oEjKpKIqEiiomOJjonF4Rh6vvaAz0tHbSltR8tpa6imtamBtvYO2rrcdHo0nX4zndre5wtAkMaBmwjDR4Q5gMOicFjNRNitOBwOIiIjcUTFEhEdjyM2gYi4FBwT0rA4RrZc77nO7/fT5myjtaOJtu5mOpzNdLtacLpacHtb8Xlb8fvbIdCJoTswqS4sqgubqRu7yYnJCAyrH7ffittvxxtw4NN2/NqBVhFoFQEqEsMUicmIxGw+9mUhCps1EpslCoctighrJA57NJHWSCId0dgtdrnx8DScUcldKXU18BPABPxaa/3wSftVz/5lQDfwVa31jqHaleQuzmQBf4DOFnfPy0VHYxfNlbW01zXQ3thAd1czXk8rgUALBLrR2g3aTe/I/xgNEaY4oi3xOExROMwR2E0R2MwRWCwObOZI7EYkkWrwR/M8yku3yYXL7MFt8eK1BvBbAwTsCmU3YTjMmB1WrJF2bJEOHNFRREVHExUdQ3R0XO/ILeDz0t1UQ2dDBV2tDXS3N9Pd0U53dyfdThddLg9OT4Bun8LpN+HUFrwMPKK34MWmvNiNADYjgM0MNrOB3WLCZrVgs9mw2ezYHQ5sjkgstggsdkfPz0gsjkisETFYHNFYImLk7MEpCAQCuLwuOrrb6HAGX053O05PBy53Bx5vJ15fJz5fF35/F4FAF+huVKALAycm5cSsnFgMFzaTC6vJO+y+/QEDT8CKN2DDG7Dh1zYCWAloO1rZ0NhA2VGGDaXsGCY7huHAbLJjGFbMJhsmw4rZbMNs2DCbbViOvUw2bGYbVosdq8WGzWzHZrFjs9qxmW1n9ZeKwZJ7WO/IUEqZgCeAK4Eq4GOl1Mta65Ljil0D5Pa85gO/6PkpxFnLMBnEJDqISXQct3XqCWX8vgDODi/ODg/dHR6c7R46mtppq6yhraaaztZGnF0teH0uGgMetL8D7W4E7UZrF+jPr88aGFgMOxbDhtVkx2rYsRh2bEYkNiMCq6lnn2HDYdiIMVmxGFYshg2LsmGo4//B8wNtQBudQDsBXMqN0+zCbfbisfjwWTQBiyZgjkJbolAWA3u0gSPBhGExYbKZMVktmKxmDAIEfE60txufp5uA24nP3Y3P7cTr8ePzGrh9Adxehduvafdo3AGNWwfw4Ae6el6NQ/7eTfix4MOi/FhUAIuhe15gMSksJgOr2cBiNmOxmLFYLD0vKxabHYvVhsVmx2S2YDJbMVl6XmYrJost+LLaMFnsn/+0RWKYzGfdkwmGYRBhiyDCFhGS5Xe9Pg/t3e10uNrpcrbR7e7E5enC7enC7evC6+3C6+vG7+/Gr7vxayc64AScgBuFGwM3JjoxKQ9m5caMF4vhxqK8GOjgn6YfOOl7xLHNrpOD6i/OgBl/wIxPB3/6tYUAZgLaQgALAW1BKwtgQWMBZQGsoKwow4JSVgxlDv40WTCUGcOwYCgLJpMVk2HBMILvE2OzOD/nohH/bocj3LdbXgAc0lqXASil1gA3AMcn9xuA3+vgKYUtSqk4pVSa1vpomGMVIqxMZoOoeBtR8cefdk8D8vot7/cFcHf7cHd7cXf76G7ppKWiio6jdbg6unF2deNxufC6XXg8bro83fi8nfj9jfi1D639aLygvWgd/HnsX0mzsmLt+WJgMY59ObD1fkmwHntvshNp2DErMyZlwWRYMCsLJmXGbAw2arYCsQPu9Wsffu3Dp/0ECKAJECCAHz9ufHiUFw8+fIYfHz0vFXz5lR8fAfwqgF/58fe8DxDARwA3moDSBND4Cc5ucOxnQPkIni1xEvxCc5q0xlABTGgMAhhoTCr43qQ0JgWGEfzZ+zIUJgMMpTBUz08DTEphGApDKUyGgWEolFIYhtH7s+/7np+GwjBMPe+DPw2TKbi/96cZwzChevYFv5iYercFv6So4HulUMoApVDKhDL6fgZQhgmlFCbDRByKeFMEKjIKFW2ACsbXt+1gjCjVW5+ebapnW7CuQgNun5tuVxcunxOP143H68Ljc+PxufEee/nd+HxufP7gyx/w4Pd7CATcBAIe/AEPOuBB654XXsDT+/8FpT0ovJjoRuHDwIsJLybl63l5MSsfJsMfvNdBE3wdu7px0peO3bUXjdvkngFUHve5ir6j8v7KZACS3IU4jslsEBFjJSLm2ONrsXB+xim1EQhofG4/Hpcfr9uHu9uDq7WN7uYWPJ3deJ0uvC4PXqcLj9OJu6sLp9NJu9vZc3o2QMCjCegAfr8Pv99LIBB8ae3HQGEoEwYGJmVgKFPPT4WJ4M/gF4PP95mUqedlDo56CO4zlIHqeW9TJhyYMJQlmKAI7jeUqbfM5+V7PtOTMAb7faDxE/xy4FPHvjj0fLFQx75iaPw97wLoni8OuufLR08Zddz7Y+XVsTInlveq4BcOf2/pYBxaaY79J9D7juPe9/xHHRunnls+v29QoXrfnfj5hPLHv9PH3lkJftHsp8xx7/QJWwbqI4BhBFCq52UEMFQAQ2mU8qNUgEinHZYP7/hGKtzJvb/f+ckX/YdTJlhQqbuAuwAmTgzNSl5CnEsMQ2F1mLE6zIANiATigclhiyEQ0AT8AQJ+TcCn8fsDeF0efC4XPqeLgNuNz+3B53bj93jxezz4vV78Xh8Bnw+f14/2+/D7/AR8rp62/Ph9frTfT8DvJxDwB7f7gj91IIAOaAJao3RwxKWPjbqO3YekAa0+f9/zs/efda2CddVJZQBDq8+feeito4L/PSEpKdQJ/wyrPgnqWKng++Dn45ON7um4N0SljwtXo5U67qsBPblNo1FodVL9nrq693N///gG69JTnp54OK6t3o44Ppbgr+r4z73x6OPeH9dPcJvqc4wnleiN++R2+1InxXhSnQG29Ol3gO+IfWI/aZ/JE74vYeFO7lVA1nGfM4Ga0ygDgNb6V8CvIHhDXejCFEKEi9Fz6viE++xibcDI5usX4lwW7js+PgZylVJTlFJWYCXw8kllXga+rIIWAG1yvV0IIYQYvrCO3LXWPqXUd4DXCD4K939a6z1Kqbt79j8JrCf4GNwhgo/CfS2cMQohhBBnu7BPTqy1Xk8wgR+/7cnj3mvg3nDHJYQQQowXZ9eDmEIIIYQYkiR3IYQQYpyR5C6EEEKMM5LchRBCiHFGkrsQQggxzkhyF0IIIcYZSe5CCCHEOCPJXQghhBhnJLkLIYQQ44wkdyGEEGKcUVqPj8XUlFINwJEQNpkINIawPTEw+V2Hh/yew0d+1+Fxrv+eJ2mtk/rbMW6Se6gppbZrreeNdRznAvldh4f8nsNHftfhIb/ngclpeSGEEGKckeQuhBBCjDOS3Af2q7EO4Bwiv+vwkN9z+MjvOjzk9zwAueYuhBBCjDMychf/v727C7GijsM4/n3YTUot1orCVkMNKUVQI9IyetEgLdFuogJBAq8SMumFtbsugqCIIkIC8wWKIlRIg6QwgwgSSYPV7MUsdMtUepUu0vLpYmbr4O5pYz3ryPh8bs6Z/384/PbH7nn2zH/OTERE1EzCvR+S5kr6QtI+SV1V11MXksZK2iZpr6Q9kpaV4xdLek/SV+XjqKprrQNJbZJ2SXq73E6fh4CkDknrJX1e/m7fkF63nqTl5fvGbkmvSzo/fW4u4X4KSW3AS8A8YDJwv6TJ1VZVG38Cj9ieBMwElpa97QK22p4IbC234/QtA/Y2bKfPQ+MFYIvta4CpFD1Pr1tIUifwEHCd7SlAG3Af6XNTCfe+rgf22d5v+zjwBrCw4ppqwfYh2zvL58co3gQ7Kfq7rtxtHXB3JQXWiKQxwF3Aqobh9LnFJF0E3Ay8AmD7uO1fSK+HQjtwgaR2YDjwPelzUwn3vjqBgw3bPeVYtJCkccB0YDtwue1DUPwDAFxWYWl18TzwOHCyYSx9br0JwFFgTbkEskrSCNLrlrL9HfAscAA4BPxq+13S56YS7n2pn7F8paCFJI0ENgAP2/6t6nrqRtJ84IjtT6qu5RzQDlwLrLQ9HfidHBpuuXItfSEwHrgCGCFpUbVVnd0S7n31AGMbtsdQHP6JFpB0HkWwv2Z7Yzl8WNLocn40cKSq+mpiFrBA0rcUy0qzJb1K+jwUeoAe29vL7fUUYZ9et9btwDe2j9o+AWwEbiR9birh3tcOYKKk8ZKGUZy0sanimmpBkijWJvfafq5hahOwuHy+GHjrTNdWJ7ZX2B5jexzF7+/7theRPrec7R+Ag5KuLofmAJ+RXrfaAWCmpOHl+8gcinN20ucmchGbfki6k2LNsg1YbfupaiuqB0k3AR8C3fy7FvwExbr7m8CVFH/E99j+qZIia0bSrcCjtudLuoT0ueUkTaM4cXEYsB94gOKDU3rdQpKeBO6l+NbNLmAJMJL0uV8J94iIiJrJYfmIiIiaSbhHRETUTMI9IiKiZhLuERERNZNwj4iIqJmEe0QA/9zd7MEB9nlZ0qwzVVNEDE7CPSJ6dQD/Ge7ADODjoS8lIk5Hwj0iej0NXCXpU0nPnDopaRLwpe2/ThlfK2mlpG2S9ku6RdLq8t7ma8t92sr9dkvqlrT8jPxEEeeo9qoLiIizRhcwxfa0JvPzgC1N5kYBs4EFwGaK69svAXaUV3BrAzrLe3EjqaNlVUdEH/nkHhH/1x00D/fNLi532Q0ctt1t+ySwBxhHcVnWCZJelDQXyN0AI4ZQwj0iBiRpONBhu9kdEv8oH082PO/dbrf9MzAV+ABYSnEt9ogYIjksHxG9jgEXNpm7Ddg22BeWdClw3PYGSV8Dawf7WhExsIR7RABg+0dJH0naDbxj+7GG6XkU9yofrE5gjaTeo4UrTuO1ImIAuStcRAxI0k5ghu0TVdcSEQNLuEdERNRMTqiLiIiomYR7REREzSTcIyIiaibhHhERUTMJ94iIiJpJuEdERNRMwj0iIqJm/gbHowd+5zk6LwAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"kex=800\n",
"tc=1/kex\n",
"ax=plt.subplots(figsize=[8,6])[1]\n",
"for p1 in p10:\n",
" p2=1-p1 #Calculate p2\n",
" Delv12=np.sqrt(p1p2Delv12/p1/p2) #Adjust DeltaOmega to keep product fixed\n",
" ex0.set_inter(Type='CS',i=0,Hz=Delv12/2)\n",
" ex1.set_inter(Type='CS',i=0,Hz=-Delv12/2)\n",
" L=sl.Liouvillian((ex0,ex1)) #Builds the two different Hamiltonians and exports them to Liouville space\n",
" L.kex=sl.Tools.twoSite_kex(tc=tc,p1=p1) #Add exchange to the Liouvillian\n",
" seq=L.Sequence()\n",
" v0=Delv12/2*p1-Delv12/2*p2\n",
" seq.add_channel('13C',v1=v1,voff=v0) #On-resonant spin-lock\n",
" U=seq.U(.0003) #Propagator (10 ms)\n",
" rho=sl.Rho(rho0='13Cx',detect='13Cx')\n",
" rho.DetProp(U,n=n)\n",
" rho.plot(axis='ms',ax=ax)\n",
"ax.legend([r'$p_1$ = '+f'{p1:.1f}' for p1 in p10])\n",
"_=ax.set_title(r'$\\tau_c$ = '+f'{tc:.1e} s'+r', '+'$p_1p_2(\\Delta\\Omega_{12})^2$ fixed')"
]
},
{
"cell_type": "markdown",
"id": "27b9bf3f",
"metadata": {},
"source": [
"For slower exchange, the third term in the denominator becomes important, yielding differences in relaxation depending on the population.\n",
"\n",
"In the last example, we increase $\\nu_1$ to 5 kHz, but leave the exchange rate fixed. Relaxation also slows down, so we acquire longer."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "5a1c4b60",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"v1=5000\n",
"ax=plt.subplots(figsize=[8,6])[1]\n",
"for p1 in p10:\n",
" p2=1-p1 #Calculate p2\n",
" Delv12=np.sqrt(p1p2Delv12/p1/p2) #Adjust DeltaOmega to keep product fixed\n",
" ex0.set_inter(Type='CS',i=0,Hz=Delv12/2)\n",
" ex1.set_inter(Type='CS',i=0,Hz=-Delv12/2)\n",
" L=sl.Liouvillian((ex0,ex1)) #Builds the two different Hamiltonians and exports them to Liouville space\n",
" L.kex=sl.Tools.twoSite_kex(tc=tc,p1=p1) #Add exchange to the Liouvillian\n",
" seq=L.Sequence()\n",
" v0=Delv12/2*p1-Delv12/2*p2\n",
" seq.add_channel('13C',v1=v1,voff=v0) #On-resonant spin-lock\n",
" U=seq.U(.0003) #Propagator (10 ms)\n",
" rho=sl.Rho(rho0='13Cx',detect='13Cx')\n",
" rho.DetProp(U,n=n*20)\n",
" rho.plot(axis='ms',ax=ax)\n",
"ax.legend([r'$p_1$ = '+f'{p1:.1f}' for p1 in p10])\n",
"_=ax.set_title(r'$\\tau_c$ = '+f'{tc:.1e} s'+r', '+'$p_1p_2(\\Delta\\Omega_{12})^2$ fixed')"
]
},
{
"cell_type": "markdown",
"id": "a4025fa2",
"metadata": {},
"source": [
"The stronger field slows down the relaxation considerably, but furthermore, we again cannot separate $p_1p_2$ from $\\Delta\\Omega_{12}$. This can present challenges using BMRD in solid-state NMR, where we need to be able to apply low fields while retaining a spin-lock. Since other large, anisotropic interactions may be present in solids, a larger spin-lock may be required unless we can spin quickly and decrease the $^1$H concentration to avoid higher order effects."
]
},
{
"cell_type": "markdown",
"id": "dc5e87f6",
"metadata": {},
"source": [
"In the case of slow exchange, with a sufficiently low spin-lock field strength, we can separate the population from $\\Delta\\Omega_{12}$. However, we cannot say with an on-resonant spin-lock whether the larger population corresponds to the larger or smaller chemical shift. Then, we must apply an off-resonant spin-lock.\n",
"\n",
"Therefore, we simulate the behavior of relaxation as a function of offset frequency. First, we calculate a spectrum to see where the peak actually appears (and also mark where the original two peaks would be in the absence of exchange)."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "92f5d572",
"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",
"kex=2000\n",
"tc=1/kex\n",
"p1=0.75\n",
"p2=1-p1\n",
"Delv12=np.sqrt(p1p2Delv12/p1/p2)\n",
"\n",
"ex0.set_inter(Type='CS',i=0,Hz=Delv12*p2)\n",
"ex1.set_inter(Type='CS',i=0,Hz=-Delv12*p1)\n",
"\n",
"L=sl.Liouvillian((ex0,ex1)) #Builds the two different Hamiltonians and exports them to Liouville space\n",
"L.kex=sl.Tools.twoSite_kex(tc=tc,p1=p1) #Add exchange to the Liouvillian\n",
"U=L.U(.0003) #Propagator (10 ms)\n",
"rho0=sl.Rho(rho0='13Cx',detect='13Cp')\n",
"rho0.DetProp(U,n=1000)\n",
"rho0.plot(axis='Hz',ax=ax,FT=True)\n",
"ax.set_ylim(ax.get_ylim())\n",
"ax.plot(ex0.CS[0]['Hz']*np.ones(2),ax.get_ylim(),color='black',linestyle=':')\n",
"_=ax.plot(ex1.CS[0]['Hz']*np.ones(2),ax.get_ylim(),color='black',linestyle=':')"
]
},
{
"cell_type": "markdown",
"id": "95dd5786",
"metadata": {},
"source": [
"Application of off-resonance fields results in an effective field that is larger than the applied field ($\\omega_{e}^2=\\omega_1^2+\\Delta\\Omega^2$). The larger effective field results in slower relaxation. However, if the exchange is sufficiently slow, it also matters how large the effective field is relative to each of the two resonance frequencies, resulting in different relaxation behavior depending on if the off-resonance field is above or below the mean frequency ($\\Omega=p_1\\Omega_1+p_2\\Omega_2$)."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "e3d5a5df",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"v1=500\n",
"voff0=np.linspace(0,750,5)\n",
"\n",
"fig,ax=plt.subplots(2,len(voff0),figsize=[10,5])\n",
"rho=sl.Rho(rho0='13Cz',detect='13Cp')\n",
"Dt=.0003\n",
"for voff,a in zip(voff0,ax.T):\n",
"\n",
" # Here we just plot a spectrum plus mark where the offsets are placed\n",
" rho0.plot(FT=True,ax=a[0],axis='Hz',color='black')\n",
" yl=a[0].get_ylim()\n",
" a[0].plot(voff*np.ones(2),yl,color='red')\n",
" a[0].plot(-voff*np.ones(2),yl,color='dodgerblue',linestyle=':')\n",
" a[0].set_ylim(yl)\n",
" \n",
" # If we flip the right amount for the off-resonant field, we reduce oscillation\n",
" flip=np.arcsin(500/np.sqrt(500**2+voff**2)) #Flip angle\n",
" # Flip from z\n",
" Uflip0=L.Sequence().add_channel('13C',v1=100000,t=[0,flip/100000/2/np.pi],phase=np.pi/2).U()\n",
" Uflip1=L.Sequence().add_channel('13C',v1=100000,t=[0,(np.pi/2-flip)/100000/2/np.pi+1e-10],phase=np.pi/2).U()\n",
" rho.clear()\n",
" \n",
" seq=L.Sequence().add_channel('13C',v1=v1,phase=-np.pi,voff=voff)\n",
" U=seq.U(Dt)\n",
" for n in range(100):\n",
" rho.reset()\n",
" #Partial flip down, off-resonance spin-lock, finish flip, detect\n",
" (Uflip1*(U**n)*Uflip0*rho)() \n",
" rho.plot(axis='ms',ax=a[1],color='red')\n",
" \n",
" seq=L.Sequence().add_channel('13C',v1=v1,voff=-voff)\n",
" U=seq.U(Dt)\n",
" \n",
" rho.clear()\n",
" for n in range(100):\n",
" rho.reset()\n",
" #Partial flip down, off-resonance spin-lock, finish flip, detect\n",
" (Uflip1*(U**n)*Uflip0*rho)()\n",
" rho.plot(axis='ms',ax=a[1],color='dodgerblue',linestyle=':')\n",
" \n",
" # Make the plots nicer\n",
" if not(a[0].is_first_col()):\n",
" a[0].set_ylabel('')\n",
" a[0].set_yticklabels('')\n",
" a[1].set_ylabel('')\n",
" a[1].set_yticklabels('')\n",
"fig.tight_layout()"
]
},
{
"cell_type": "markdown",
"id": "4fe39a50",
"metadata": {},
"source": [
"Then, we see that relaxation is faster when the off-resonant field is applied towards the chemical shift corresponding to the smaller population. In this case, we are less off-resonant relative to the two chemical shifts, resulting in smaller effective fields and less relaxation.\n",
"\n",
"In the final example, we go back to the fast-exchange regime, and observe that going off-resonance no longer helps distinguish which population corresponds to the higher or lower chemical shift."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "cb9560bd",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"kex=20000\n",
"tc=1/kex\n",
"L.kex=sl.Tools.twoSite_kex(tc=tc,p1=p1) #Add exchange to the Liouvillian\n",
"\n",
"voff0=np.linspace(0,750,5)\n",
"fig,ax=plt.subplots(2,len(voff0),figsize=[10,5])\n",
"rho=sl.Rho(rho0='13Cz',detect='13Cp')\n",
"Dt=.001\n",
"for voff,a in zip(voff0,ax.T):\n",
" a[1].set_ylim([0,.51])\n",
" rho0.plot(FT=True,ax=a[0],axis='Hz',color='black')\n",
" yl=a[0].get_ylim()\n",
" a[0].plot(voff*np.ones(2),yl,color='red')\n",
" a[0].plot(-voff*np.ones(2),yl,color='dodgerblue',linestyle=':')\n",
" a[0].set_ylim(yl)\n",
" flip=np.arcsin(500/np.sqrt(500**2+voff**2))\n",
" Uflip0=L.Sequence().add_channel('13C',v1=100000,t=[0,flip/100000/2/np.pi],phase=np.pi/2).U()\n",
" Uflip1=L.Sequence().add_channel('13C',v1=100000,t=[0,(np.pi/2-flip)/100000/2/np.pi+1e-10],phase=np.pi/2).U()\n",
" rho.clear()\n",
" \n",
" \n",
" seq=L.Sequence().add_channel('13C',v1=-500,voff=voff)\n",
" U=seq.U(Dt)\n",
" for n in range(100):\n",
" rho.reset()\n",
" (Uflip1*(U**n)*Uflip0*rho)()\n",
" rho.plot(axis='ms',ax=a[1],color='red')\n",
" \n",
" seq=L.Sequence().add_channel('13C',v1=500,voff=-voff)\n",
" U=seq.U(Dt)\n",
" \n",
" rho.clear()\n",
" for n in range(100):\n",
" rho.reset()\n",
" (Uflip1*(U**n)*Uflip0*rho)()\n",
" rho.plot(axis='ms',ax=a[1],color='dodgerblue',linestyle=':')\n",
" \n",
" if not(a[0].is_first_col()):\n",
" a[0].set_ylabel('')\n",
" a[0].set_yticklabels('')\n",
" a[1].set_ylabel('')\n",
" a[1].set_yticklabels('')\n",
"fig.tight_layout() "
]
}
],
"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
}