Skip to content

Instantly share code, notes, and snippets.

@nipunbatra
Created January 20, 2017 08:42
Show Gist options
  • Save nipunbatra/261441fe84659311d76f15af733f505c to your computer and use it in GitHub Desktop.
Save nipunbatra/261441fe84659311d76f15af733f505c to your computer and use it in GitHub Desktop.
Display the source blob
Display the rendered blob
Raw
{
"metadata": {
"name": "",
"signature": "sha256:84284f6b47372c96a532e68dc8adaffa5c762cbd4b135d4c507259007af10fb3"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I took the Linear and Integer Programming course on coursera last year. It was a very well paced and structured course. In one of the modules, the instructors discussed least squares and unlike the conventional line fitting, they demonstrated the concept via signal denoising. Matlab code for the same was also provided. This is an attempt to do the same thing in an IPython notebook and leverage static widgets for a better understanding."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import seaborn\n",
"%matplotlib inline"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"True data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us create the `true` data, i.e. if there were no noise and the measuring system was perfect, how would our data look like. This is a modified sinusoid signal."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"n=400\n",
"t=np.array(xrange(n))\n",
"ex=0.5*np.sin(np.dot(2*np.pi/n,t))*np.sin(0.01*t)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.plot(ex);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAECCAYAAAAW+Nd4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n6P8BKaV0O4praiwAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x3c25ed0>"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"Noisy data"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, let us add some Gaussian noise about the true data"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"corr=ex+0.05*np.random.normal(0,1,n)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is how the corrupted signal looks like."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.plot(corr);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAECCAYAAAAW+Nd4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nBEEQeQiJP0EQRB7y/wGrOsQx1K5NXQAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x3ca6690>"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"The optimization problem"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Constraints\n",
"\n",
"1. We want the cleaned data to be as close to the corrupted data\n",
"2. We want the successive entries in the cleaned data to be as close as possible\n",
"\n",
"Mathematically, we can write this as follows:\n",
" \n",
">$\\min{ ||(x-x_{corr})||^2 + \\mu\\sum_{k=1}^{n-1} (x_{k+1}-x_{k})^{2}} $ \n",
"\n",
"Here,\n",
"$||(x-x_{corr})||^2$ corresponds to the first constraint and $\\mu\\sum_{k=1}^{n-1} (x_{k+1}-x_{k})^{2} $ corresponds to the second constraint."
]
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"Formulation as least squares problem"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For the least squares problem, we would like a form of $Ax=b$"
]
},
{
"cell_type": "heading",
"level": 5,
"metadata": {},
"source": [
"First constraint"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Looking at the first constraint,\n",
"$||(x-x_{corr})||^2$, this can be expanded as follows:\n",
"\n",
"$ (x_1 -x_{corr}(1))^2 + (x_2 -x_{corr}(2))^2 + ..(x_n -x_{corr}(n))^2$\n",
"\n",
"which we can rewrite as :\n",
"\n",
"$ ([1,0,0 ..0][x_1, x_2,..x_n]^T - x_{corr}(1))^2 + ([0,1,0 ..0][x_1, x_2,..x_n]^T - x_{corr}(2))^2 + ...([0,0,0 ..n][x_1, x_2,..x_n]^T - x_{corr}(n))^2$\n",
"\n",
"Comparing with the standard least squares, we get \n",
"\n",
"$A_{first} = I^{nxn}$ and $b_{first} = x_{corr}$"
]
},
{
"cell_type": "heading",
"level": 5,
"metadata": {},
"source": [
"Second constraint"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For the second constraint, \n",
"$\\mu\\sum_{k=1}^{n-1} (x_{k+1}-x_{k})^{2}$\n",
"\n",
"This can be written as:\n",
"$(\\sqrt{\\mu}(x_2-x_1))^2 + (\\sqrt{\\mu}(x_3-x_2))^2 + .. (\\sqrt{\\mu}(x_n-x_{n-1}))^2$ which we can write as:\n",
"\n",
"$(\\sqrt{\\mu}[-1,1,0,0,0,0..][x_1,x_2,..x_n]^T - 0)^2 + ...(\\sqrt{\\mu}[0,0,0,..,-1,1][x_1,x_2,..x_n]^T - 0)^2$\n",
"\n",
"From this formulation, we get for this constraint, $A_{second}$ as follows (we ignore $\\sqrt{\\mu}$ for now)\n",
"\n",
" [-1, 1, 0, ...., 0]\n",
"\n",
" [0, -1, 1, ......0]\n",
" \n",
" ..\n",
" \n",
" [0, 0, ..... -1, 1]\n",
" \n",
"and $b_{second}$ as a zeros matrix of size (n-1, n)"
]
},
{
"cell_type": "heading",
"level": 5,
"metadata": {},
"source": [
"Combining both constraints"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So, we combine the two sets of As and bs in a bigger matrix to get $A_{combined}$ and $b_{combined}$ as follows:\n",
"\n",
"$A_{combined}$\n",
"\n",
" [A_first\n",
" A_second]\n",
" \n",
"and $b_{combined}$ as :\n",
"\n",
" [b_first\n",
" b_second]"
]
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"Constructing $A_{second}$ matrix with parameter $n$ and $\\mu$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"root_mu=10"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"d1=np.eye(n-1,n)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"d1"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 8,
"text": [
"array([[ 1., 0., 0., ..., 0., 0., 0.],\n",
" [ 0., 1., 0., ..., 0., 0., 0.],\n",
" [ 0., 0., 1., ..., 0., 0., 0.],\n",
" ..., \n",
" [ 0., 0., 0., ..., 0., 0., 0.],\n",
" [ 0., 0., 0., ..., 1., 0., 0.],\n",
" [ 0., 0., 0., ..., 0., 1., 0.]])"
]
}
],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"d1=np.roll(d1,1)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 9
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"d1"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 10,
"text": [
"array([[ 0., 1., 0., ..., 0., 0., 0.],\n",
" [ 0., 0., 1., ..., 0., 0., 0.],\n",
" [ 0., 0., 0., ..., 0., 0., 0.],\n",
" ..., \n",
" [ 0., 0., 0., ..., 1., 0., 0.],\n",
" [ 0., 0., 0., ..., 0., 1., 0.],\n",
" [ 0., 0., 0., ..., 0., 0., 1.]])"
]
}
],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"d2=-np.eye(n-1,n)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"a_second= root_mu*(d1+d2)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 12
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"a_second"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 13,
"text": [
"array([[-10., 10., 0., ..., 0., 0., 0.],\n",
" [ 0., -10., 10., ..., 0., 0., 0.],\n",
" [ 0., 0., -10., ..., 0., 0., 0.],\n",
" ..., \n",
" [ 0., 0., 0., ..., 10., 0., 0.],\n",
" [ 0., 0., 0., ..., -10., 10., 0.],\n",
" [ 0., 0., 0., ..., 0., -10., 10.]])"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"Constructing $A_{first}$ matrix with parameter $n$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"a_first=np.eye(n)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"a_first"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 15,
"text": [
"array([[ 1., 0., 0., ..., 0., 0., 0.],\n",
" [ 0., 1., 0., ..., 0., 0., 0.],\n",
" [ 0., 0., 1., ..., 0., 0., 0.],\n",
" ..., \n",
" [ 0., 0., 0., ..., 1., 0., 0.],\n",
" [ 0., 0., 0., ..., 0., 1., 0.],\n",
" [ 0., 0., 0., ..., 0., 0., 1.]])"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"Constructing $A$ matrix"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"A=np.vstack((a_first,a_second))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"A"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 17,
"text": [
"array([[ 1., 0., 0., ..., 0., 0., 0.],\n",
" [ 0., 1., 0., ..., 0., 0., 0.],\n",
" [ 0., 0., 1., ..., 0., 0., 0.],\n",
" ..., \n",
" [ 0., 0., 0., ..., 10., 0., 0.],\n",
" [ 0., 0., 0., ..., -10., 10., 0.],\n",
" [ 0., 0., 0., ..., 0., -10., 10.]])"
]
}
],
"prompt_number": 17
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Similarly, we construct $b$ matrix"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"corr=corr.reshape((n,1))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 18
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"b_2=np.zeros((n-1,1))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 19
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"b=np.vstack((corr,b_2))"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 20
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us use least squares for our denoising for $\\mu=100$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy.linalg.linalg as LA"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 21
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ans = LA.lstsq(A,b)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 22
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"Comparing original, noisy and denoised signal"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.plot(corr,label='noisy',alpha=0.4)\n",
"plt.plot(ans[0],'r',linewidth=2, label='denoised')\n",
"plt.plot(ex,'g',linewidth=2, label='original')\n",
"plt.legend();"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAX8AAAECCAYAAAAW+Nd4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsnXdgFNX2xz8zW9N7gAChdwQEReCJ+rM9UfFheRQR7D6f\nXcGCCIqKgu1ZAPVZULGgolh4VhAsIEWREjoEEkjvyWb7zPz+2Oxmd7MJSQgkIffzT7Izd+7cLfOd\nM+eee46kaZqGQCAQCNoUcnMPQCAQCAQnHiH+AoFA0AYR4i8QCARtECH+AoFA0AYR4i8QCARtECH+\nAoFA0AbRN+YgVVV57LHH2Lt3LwaDgblz55Kamurbv23bNubPn4+mabRr14758+djNBqbbNACgUAg\nODYaZfmvXLkSl8vF0qVLmT59OvPmzfPt0zSN2bNnM2/ePD788ENGjhzJkSNHmmzAAoFAIDh2GmX5\nb968mdGjRwMwePBg0tLSfPsOHjxIbGwsixcvZt++fZx99tl07969aUYrEAgEgiahUZa/xWIhMjLS\n91qn06GqKgAlJSX89ddfXHPNNSxevJjff/+d9evXN81oBQKBQNAkNEr8IyMjqays9L1WVRVZ9nQV\nGxtLamoq3bt3R6/XM3r06IAnA4FAIBA0P40S/6FDh/LLL78AsGXLFvr06ePb17lzZ6xWK5mZmQD8\n+eef9OrVq87+RHohgUAgOLFIjUnspmkajz32GHv27AHg6aefZseOHVitVsaPH8/69et5/vnn0TSN\noUOH8vDDDx+1z4KCioaP/gSTlBQlxtmEtIZxtoYxghhnU9OaxtlYGiX+x4PW8kGLcTYdrWGcrWGM\nIMbZ1LSmcTYWschLIBAI2iBC/AUCgaANIsRfIBAI2iBC/AUCgaANIsRfIBAI2iBC/AUCgaANIsRf\nIBAI6qC4uIjnn5/f3MNocoT4CwQCQR3ExycwbdqDzT2MJqdRWT0FAoGgKTmQXUZBqa1J+0yKDaNH\nSkyt+7/55mt+/30tDoeD7OwjTJ58LT169OTFF5/DbDYCOh58cGZV/ZKZvP76Yl5/fSFbtvyJ261w\nzjnnMm7cldxwwzUsXbocSZJYtOhl+vbtz7nnnt+k7+V4IMS/DZFfYuVIQSWDeyagk8VDn0BQWVnJ\nCy+8wpEjh3nggXsID4/goYdmMXLkUJYvX8Err/yHO+64x9d+5crveeWV/5KQkMA333xNREQkgwYN\nYf36dQwfPoING37nlltua8Z3VH+E+LchdmaUAFBS4SAxJqyZRyMQVNMjJaZOK/14IEkSvXr1BiAp\nKRmn04nNZqNnT08iykGDTuW11xYEHDN79hO8+urLFBcXMWLEKADGjh3HsmUfo2kap59+Bnp965BV\nYf4JBII2iyRJAa8TExM5cGA/AFu2bKZz5y6+fS6Xi9WrVzJnzlO8/PJrfPvtCvLychk0aAhZWUdY\nseJLLr30Hyd0/MdC67hFCQQCwXHAX/wlSeaBBx7hP/95Br1eRtMkHnpoFpqmIUkSBoOB6OgYbrnl\nOkwmE8OHj6Bdu/YAXHjhRaxZs4quXbs111tpMCKrZwNoTZn+Qo1zzZYsALq0iyI5LowIs+FEDy2A\n1vB5toYxghhnU9PQcX744RJiY2O5+OKxx3FUNRFZPQWUVDjqHS2RkVfBpt35x3lEAkHbYO7cx/jj\nj41ceOGY5h5KgxBun5OErQcKAThnSMdmHolA0LaYOfOx5h5CoxCW/0mAW1EbdZyqabjcKsXl9hr9\nlVQ4mmJoAoGghSLE/ySg0uby/a+o9b8RuNwqW/cXsi29iPJKp2972sFith4oFDcAgeAkRoj/SYDF\nT/xVtf7z9y63isXuOdbhUnzbSy0e0fe/ITSU7MJKMnJb/sSeQNBWEeJ/ElBpd/v+Vxog/k4/wfcP\nd9ZVvXA10p0EsPdIKQdzyxt9vEAgOL4I8T8JcLqrRbwh4u9yV4u7RLX6G/Ryjf0CwcnO1KkTmqSf\nmTPvP6bjH3jgXnJzc5pkLHUhxP8kwK1UC36DLH8/cdeoPs6g13n2uxR+3ZrN3sOltfahaRpqy1gq\nIhC0CObOfbYJepGO3uQYEaGeJwGKn/g3xOfv/8SgaVBcbifMpMeb881qd6NoGtlFlfTuHBuyjx2H\niiksszN6UIeQyeJUTUOWjv8PWdC6ib76Kkwrf2jSPh3nX0j5h8tq3W+323n88VmUlZXSsWMnVFUl\nPX0/L774HHq9THh4JDNmzGbPnt188MF7GI0GsrOzOO+8C5k69QZycrJ5+unHUauCLO6553569uzF\nZZf9na+++p7PP/+U7777H7Is07dvf+65Zzp5ebk8++xTOBwOTCYTDzwwk+Tkdrz11uusW/cbCQmJ\n5OfnNennUBtC/E8C/CN8GiL+Dme1+DtdCvuyygCICvOs/HX43RxcbgWDXkdhqQ0NT7pcgMIyT5io\nW9HQhXiOVFUNWSfEX9Dy+OKLZXTr1p2bb/43mZmHuP/+e5g/fy4zZszm9NMHsXjx+3zwwXucfvoZ\n5OXl8t57S3E6nYwbdxFTp97AwoUvMn781Zx55lns27eXefOe4M033/PNn3377ddMmzaDvn378cUX\ny1AUhYULX+KqqyYyYsQo/vhjI6+9toCJEyezefMfvPXWEhwOR5O5n46GEP+TAP84f3cDxN8r3BDo\nArI5lBpt16bl0qdzLHuqXEDnDOlIQGYQv3/93UAtJHuIoIVTl4V+vMjMzGDkyL8BkJralZiYWDIy\nDvL88/MwGHTYbA46d04FoEePHsiyjNlsxmQyAZCRcYghQ4YC0KtX7xoW+4wZj7J06ftkZ2cxcOAg\nNE0jPX0/S5Ys5oMP3kXTNAwGAxkZh+jTpy8AJpOJvn37E3BBHSeE+J8ENMbtYzLoAsI7/Sd33bWs\nFcgqqPT973ApAcLuL/j+Y2jAsgOB4ITStWt3tm/fyujR55CVdYSyslJSU7vyyCNzGDiwFz/++DNl\nZWVVrWs+vXbp0o0tWzZXWf57SEhICNj/9ddfMH36DIxGI/fddydpadvo0qUrkyZNYeDAQaSn72fn\nzjS6du3OZ599gqqqKIrCvn17Qp6vqRHi38pRNQ1Fa/iEb2SYoVbxrw2rozqk1Gp3B4i/Vpv4C8tf\n0EIZN+5Knn76cf797xvp0CGF6OgYpk17iCeffBRZ9hhVDz00i4KC/KDUz57/77jjHubPf5KlS9/H\n7Xbz0EOzA/b36NGD22+/ifDwCJKSkhkw4BSSk9vx3HPzcDodOBwO7rnnfnr16s2ZZ57FzTdfS1xc\nHDExoefXmhqR1bMBtMSMhC63ytq0HGRJQtU0uneIZtjAlDqzegKkJESQXVRtycdGmCitrP+K3t6d\nYlE1jf1V8wSn9UkmsmquwOZws2GX5xF4eN9kwmvJHtoSP89gWsMYQYyzqWlN42wswvJv5Xj9/Ua9\njN2l1NvS9sbye/GP/KkPVoc7wC1ZqwuoRZgWAoEgGBHn38rxunmMBl3A66MRHH7Z0AVdNocbu6va\nDeR/zxFuH4Gg5SMs/1aOz/I3eO7jwRO+3ipEwZQ6i9haupHD1n2UOguxq1ZkZCL00cQb29E5vBdd\nI/pg1kWEPK/LrdbL568J018gaJEI8W/FuBXVz+1TZfn7Rf7sySyhpMLB8H7tkCQ4YEljfdH3bCj6\ngVx75lH710kGBkSfzmnx5zIy4SJijAkYdDKyJOFW1ICnBX+NV1Th9hEIWjpC/FspTpfCuh25PveN\nyev28bPAc4qtKJqbt/96n6Xpb7CtYItvX5gunK4R/UgN70O8sR1hughUVCyuUgoc2WRY95BRuYdt\nZevYVraOJYee4cykSxnf7SZSI3pjd7gDzuW1/F1ulezCyhrbBQJBy0KIfyvDandTaXf5fPxen3qw\n20fTNDYVr+S9g8+Q5zgMQLQ+nlGJYxgRdx4TnTFoq9YQdvgQprJMNFlGdrnQOezY45OwdD6L9B6T\n+a6Hytryn/ir5GdW53/OmvzlXJByJVel3EWsMck3Lu84dh4qpsRSHTXUkBXHAoHgxCHEv5Wxcbcn\nhLJfalzAdp/bR9XYW7SXm766hV+zfgYgJawr951+Lx0qR9Lj158Y+M5MIvKPnjWwL3BBWDhZfzuf\ndf/3JO/Gbeengs/4IXsZv+R+w6Qu93JZpym4FA1F0dieXhQg/CAmfAWtlw0bficvL5fLLrs85P5v\nv11BVFQ0Z555VoP69eb+aW6E+LdSbE53wOuYSCMy8GXGEt7+aR42t40IfQwTOt/JBe3G02HzFgYv\nvIbYg3sBcHZKxXHhRWSl9KTAHI2kqqh6I5jNmPKyiTlykKQ/15KwextdV35F15VfcXlCMpunXs+D\n3fawtvhnFh+cy/byX7ml25Pkl5opCioHCcLnL2i9nHHGyDr3jxlzaaP6bSl5DoX4tzB2HipGAkot\nTgZ0jyc63BiyndWvgEv/LnFYXGXM330bm4pXA3BFz/FcEnM3/TZspM/cq4nfmwaAJSWVXRNuJuKW\nG0lKiCQB2LE122ehhxn12Jxu9LLM9mvvIiIrgy4/rSB11VdEZWfyt//8l9UxsTx353U8ZV7OH0W/\nsLdsHI8MWkhX85Aa4xRuH0F9uHrFVazMbNqsnuenXsiHl9aeM8jtdvPUU3PIyclCUVQmTLia5cuX\nER+fgN1eyVlnnceRI4e59dY7eOedN/nllzXExsbhcNi56aZb2bz5DxISEunSpSvvv/9ujayf6en7\nWbDgRRRFpayslOnTH2LgwEFN+h6PhUaJv6qqPPbYY+zduxeDwcDcuXNJTU2t0W7WrFnExsYybdq0\nYx5oW8DlVsgvtfle5xRWEp1aLf7+lbdsVakW+nWJo1Q7zNTPJpJedoBIfQxvXbqIc3+zYnjkOmIO\n7QPAERPH/rFXs+ef16OERTCwyk0EVZaI5on9jzB7xN9k1OG2q1R27MLOKbez85rbGJC+hZ5LFmFc\n9xsznnyH8y48lzsuqWRTyQYe/msqt/R4nHOSxwW9J5XdGSV0aR9FmEnYGoKWw5dffkZcXDyzZz+B\n1WrlhhsmYzQamTDhaq64YizvvfcRAPv27WXDhnW89dYSnE4n1147ESAghDpU1s+DBw9yxx330L17\nT3788Tv+97+vW7/4r1y5EpfLxdKlS9m6dSvz5s1j0aJFAW2WLl3Kvn37GD58eJMM9GTE4VTYsCuP\nXp1i6JAQgcsdaCV7xbKg1IbZqAtwoXgt/99z13DfbzdjcVXQ15XM2+v6M2LR/UjZ2Z52SR3YNfFm\nDl14OarJ7Dvef5GXLEkoaOhkiT6pcYTlVZAQY2bL/sLqE0oSSVdeStkVl2Bb9Bop8x5j+A8/sXpP\nFybffilfWlewaP8M8u2H+WfnO3wXRmZ+BYqqUW51Mrxfuyb9/AQnD3VZ6MeLjIxDnHbaGQCEh4fT\ntWs3Nm3aQGpq14B2mZmH6NdvAJIkYTKZ6NOnX42+QmX9TExM4p133sJkMmG1VhIREXnc31NDaNQK\n382bNzN69GgABg8eTFpaWo3927ZtY8KECSLUrw4KymyomuZLkxxcM1fTPDeIHYeK+XNvAXa/xGqK\nprG28H/ctuYaLK4K/rkD/ngmn5E/rEHKzsbZrQd/3vUovy5dSfrYSQHCD4FWiyx7/tfJEga9TI+O\nMb4J5BpIEuWTruWH15ZT1qs/ERkZLJv9E/eYr0dGx7Iji1iS8azve/d+/f5J4QSClkCXLt3YuvUv\nAKzWStLTD5CS0rHGoshu3bqza9dONE3D6XRWZd0MpqYj/6WXnuPGG//FzJmP0b17zxanhY0Sf4vF\nQmRk9V1Mp9P5qtnk5+ezcOFCZs+e3eLebEsj+EfmCsqvo2oahWXVbiD/Sd4fcj/i5b3349bcTF8L\nS/8XRvmlV7Pp3iewrdvAgW9/I/3SiZiiQq/Qlf1O7f3X4Cf4Orn2WSmdTqKyYxc2vf4pZZeMQ2+3\n8szjnzBHvgmdZGBF9mLePvhkjRKP4vcgaEn84x9XUF5exm233cSdd97K9dffTFxcfEAbSZLo3r0n\nI0f+jVtuuY6ZM+9Hr9ej1+t9+/3/Vh0FwN//PoZZsx5k+vS70DSNoqLCgP3NTaOyes6bN4/Bgwcz\nZswYAM4++2x+/tkTVrhkyRKWL19OREQEhYWF2O127r77bsaNG1dXl22Sw3kV7EgvAuCikV05kl9B\n2oEiUttHkZlbQdeUaCxWF4VV8wCdkiM5km9hReYSFu72pI+d9yM8WDYQvviC3bo4DuWU0y0lmoPZ\n5QD06xrPwewy7M7AG8uIgR2IjfI8nn73+yEAOreLYkB3T05yl1th1abDAcdcNLIrACXldjbsyKVD\nYgQpcWG4Jl9Dyg9foskyr937T+6KXo5bc3JV11u4sfcM3/FnDunoy/wpELQWiouL+e6777j66qtx\nOp1ceumlvPfee7Rv3765h3ZMNMrnP3ToUFavXs2YMWPYsmULffr08e2bMmUKU6ZMAWD58uWkp6fX\nS/hbS/rUphxnaamVCosnPLKgoIK8/AoqLHZslUYqLHaKi3Xkl9h87qBsTeXrgx+zaL9H+Bf8D240\nnU3hF++jRcdgyfUcfzAbX78Wi51+nWL4ZVt2wLlLSipx2Z1AdVslzux7f4qq+rZ78e5zuVWcDheS\nolBSbmfrtKfp364zA5Ys4N/Pf4xp4t+4pd8Glh36L2Ytmss63gjAus2HGdIr0WcltYa0ua1hjCDG\n2dT4j1PT9GzatJlPPvkUkLj44svQ6SJaxPs44SmdL7jgAtauXcvEiZ5Z76effpoVK1ZgtVoZP358\nQNtQScUEHoI/GndVXh5vqganWw2YB/gu40te2z8TgOe/h0ti/kHJW2+gD/P48/UhauXqZcnn06/r\n3ABRfmGldRVdN+hlRg7wWD2lFgdIEjun3E55aneGPzuDG5auRZo0iBv6bOP9jOeIMybyj+7jKa5w\nYHcqIupH0KqQJImHH360uYfR5DTqKpQkiTlz5gRs69atW412l18eemWcwEOwvHp9/t7UDTa/WP7N\nJT/z8t7pqGg8/hNc0vEGNt08nbPNJl8bfYgK6qG2ec5dffb4KBPFFQ7CzdU/h/retP3bHTl7DJXt\nOnLWzFu4/qNtHPlnD2YPOMCr+2cxoF0v4umPS1EJq1fPAoHgeCLy+TcjwbMtXivfbPSIf6XdBUC2\nYw8v7bobBZUHf4Obut7MtpungyQFiG8ooQ9l9UOg5T+wewJnntKhTmu/fVz4UfsBKOk7iA0vvY8S\nn8CsTw8wpeQU3JqLGZtuId+eFZB1VCAQNB9C/JuR4Lw3LreKRHWVLQ0oduTx1ObrseFg8ja4M/E6\nih5+PKTfRh9UnatjYgQR5tAPd/43BVmSan1CABjZvz19UkPXFQ11wyjv0Zfi1xajyTJvvbKdUYZT\nKHEU8czu2yize/ykFVYnv2/PweFsWAUxgUDQNAjxb0aCMx+4FQ29TvaFWdqVSp7dch35WglnZsAM\n93hyZjyJ2RQ6Ysbg5/M36GR6dYqt1X1TRySnjyE9ExnSMxGTUdegfox6He7RZ7HjmtsxqPDFy4fp\nFt6VTOteZv0+HZvDxc5DJZRZHKTnlNd6fkVV2XWoGIvNdfTBCgSCBiHEvxnYnVHCr9uya1S5cisq\nep1cJbQaC9Pu4oByiJ5F8GrxZRy69wniY8yYDaEXYBn9tgfX6A2mPj792EgTsZGmOtv499OlXRQp\nCRH06xqHLEnsmvQvcoeOIimvlE+/jcYkh/H9kc95as1C35NHXbl/juRXkldqY6v/SmOBQNAkCPFv\nBnJLrCiqVmNFr6pqPqv/y0ML2FC5jlgbLN81jHaLFjN8QAeiwo2+3P3euQEvep2Mocp9U5cbB+qO\n5mkI/t0Y9TK9O8diMug823U6Nj74DEq79gxbvY05WSMAeDv9SQ5adgGeFNQ2hxuHq6b7x1spTKwN\nEwiaHiH+zYj/5Keqaaiqp97uTxk/8mHWIiQN3lqTTPsFy8BQ7eqRJIlRA9pzWp/kGn16Lf5QYZ/+\nNFUEbqg0Ef7bHXEJVLz+Npos8+Drq7lEdxYuzcm8tLuxKzYUVWXDrjx+35Fbo29viUq9XoQLCwRN\njRD/ZsTf8lcUDUXTyHcc4bavJ6NJMGutkbjb3kWLT6hxrNGgqzO082jWclOtv/D3+QdHFg3pmcjp\nfZNxjTqTinvuB2Dx6wfoZO7GEWs6i/fNr9Pt4xN/WfxMBYKmRlxVzYjbT/zdiopTdTBv7RSKZTsX\n74Vzzl2Ao3uvBvXptfjdQSGVXllOjg1jSM/EYxp3QL9+NxFd0A0lNtJEhNnzxGK7Zzql3fuQdCSL\nl7f1Qyfp+SrzXf4o/NXXPjj6yfsejubCEggEDUdcVc2Iv/i73Cof7n+KXVom3Ythduw9FJ42Gl0D\nhc/bXlED5xO8Im026o86idsQ5FrcPjXamU1smjYXVdYx7qNvuSn8CgBe3PUQFncZEFivAITbRyA4\nngjxb0a8E5oAP2R8yzeFn2BQ4IO0/hRedSuAbwK3vsRVCXuwwHs1uqkza/ob+3VlAgUo7TWAPRNu\nQtI05r2ykX5Rgyly5vF2+pMAOF2BNyyv+EstJAuiQHAyIcS/GfFO+BY785n5y20AzF0t03vOO6hV\nfu66rOlQpCRGMKxvO3p2jAnY7rXQmzpyprYJ39rYOfk2ylN7EJt5iIV/9cIkh/Fb4Qr+KP6pRsSP\n1+0jisALBE2PEP9mxKWoqJrCgj33U6JWcOF++Ge/O1D69EWrMoIbqP0AJMWF1RBir0YfTyE9muXf\nMTEC1Whk4/SnUHV6/u/9ZdzCWADeTH+cYmtpQHt3letK1AEWCJoeIf7NiKppfJX1NmkVG0mqhIXr\nO5F3452+fdBwy782qi3/4yekRxtrr06xdGsfTUnfQaRddxcAT7/wI73N/Sh25vHc5rls3JWH1e4O\ncIkJw18gaHqE+B9HKu0uMvMCc377W977K7azNPNFAN5dDkdufgIpzJPz0mvtNtViLK8bKCUxdGWv\npuBolj94qoAB7PnnjRSefiYRpSW89q2hKvpnCVsKN7E/qzRgMly4fQSCpkeI/3Hkzz0FpOeUU1Lh\n8G3zirpTsbNw/0OoqNy9Hvp3GUvBqSN8Yt/Uln9ibBjnDOkYkLO/qanPWH03CFlm2+wXsMfE838/\nb+O6sqFoaLy+fzaVDnvAGgjh9hEImh4h/scRr4B78/QXldl9Fu3Swy+TZUunbwE8sT6Krbc8AFQL\nqFfumsryPxHUZ6z+oavOhCQ23f8UAC8t/JMUuT2Hbfv59NCbuP3dPk0/VIGgzSPE/yhY7W7yS6zH\n1IeqQUmFg+0Hi9iyv5Dd5X/yv+x3kFV49wsoufUBHHGehVdewzi+qr5uRFjrqXpVn1XD+qCng9zh\nZ7P38qlEOBRe+9oj+J9mvsqRiiO+NsLyFwiaHiH+R2Hj7jx2ZpRgc7iP3rgWVL8kbqW2ChbufxgN\njYd+g96mPpRdc72vrdfy7981nkHdE0iMObnqXoVatLb9xmmU9OjH2E35jCnogEO18cyf1ZXihM9f\nIGh6hPjXk+AMnA1B0zTfMqUPMp4nz57JKXkw6xfYfPdjGEzVfnivT1yvk4mPNh/LkE8YPVNi6Nq+\nfoWk/SeFvUnoVKOR9Q8/j9sczqvv52DSDPxw5Et2lG307G+A5e8+hu9JIGhLCPGvJ/U1PjVNY09m\nCUVl9oBjVU1je+nvfJ/7IXoV3lsORy6aSGn/UwMqcLUmH7+XTsmRdG0fXa+2/iuW/esPWDp3Y/Md\nj9ClDGb86vmw3z74JIrmrvdnn11Yybq03GN6ShMI2gpC/OtJfePjK2wucoqtbD9Y5NumahrljnJe\n3T8TgFk/Q197Amk33IskSQHpl5squqelYvKrQeD/v06SyLhgHJnnjeXBX9x0rTBw2LqPVflL6+32\nsTndqJqGXZSGFAiOihD/elJ/y7/mNlXTeGnrXAqdOZyap2fGr7D9hntxRUYjSYFZK0928Qd8lcj8\nI3pMRh1IElvuehQppRsvrfCUblyasYByZ4mvnaKqtd6IvZuDk9oJBIKaCPGvJ/UVFH//tNeFs7lg\nI58ceBe9JvPO524qeg7k0IWX+9oY2pj4x0R45jj8Ndyor7ohhEeS98IiLt0ncV46WNxlfHbkNVRN\nw62o/Loth4278vl1WzblVmdAv96bgogOEgiOjhD/elJfQfGfGJYAl+pk3l+eGP7718KgPPjr9plQ\nlbhNkgMFvzX6/BtKz04xJMWGMbBHdZEar+tLA+QRI9g94Rae+wEkDb7P/YD0knQq7R5fvs3pRlE1\n0rMCi79XW/5C/AWCoyHEv57UV1D8XRmyLLH8yH85ZNlPD2s4s9eoHDr/Mor7Dak+IKjb+qRIaO0Y\n9DoGdI0nxi/ttP8N0GiQ2XnNbXSJ7Me1W8CtuXlq4xysdldAP1rQh+e9QQvxFwiOjhD/elJfy98/\n1PCwdR/Ls/4LwFsfW9EZwtl+47SA9v4JzKBtWP6h0AXV/+3dPZmi/yzi8Z9lwlywIv0L1mevDzgm\n2PUv3D4CQf0R4l9P6mtNet0+qqaycN8sFM3FjWlhnJ0BO6beiT3BU3TdVDXpqQQpWFvw+Yci+H13\nSIgg5oxhyBddx7R1nm0vbns8YLI3eOLXexsVlr9AcHSE+NeThrp9fsj9iD3lf5HsNPPcChvlp5zK\nvnFTfO3MfmGOgK/WbVtw+4QiOS4cgC7tAheLHb71Xu7eHkuyBXaV/cX6ou99+4TlLxA0HiH+9URV\nNTRNI6/YWucqUreiUejI4cOMFwB4dbmdKNXI7keeBV214JsNgeI/rHcSfxvYvs1Z/t6bXUyEkTNP\n6UCXoJXCWnQsh665l8dXe15/eOh53Konyic4/l9M+AoE9UeIfz1RVI/w78osIa/EVms7p1vhzfTH\nsatWLtun54pdsOvWB7F06RHQzhhk+cuyhEEfuK0tMHJAe0YOaA8ErnfwIklw8O9XckV5P/oWQJ7z\nCD/lfwbUbvkL8RcIjo4Q/3qiqhrllR6L0+2u3fJfnb2CzSVriHLpWPSVm5zhZ5H+j2tqCFJbde8E\no9fJvvmYm6KrAAAgAElEQVSPUMiyBDod2297hCeqrP/PMxbiUGw1LH/vUgzh9hEIjo4Q/3qiaBoW\nqyfUsLZ0AyX2Yl7d+zgAz36nkKBPZNO0p3BrGpqqBUTy6GTx0dcH72dWNGAoF/e9iqHZUKwU8X3u\nhzVuwtWWv1jhK6g/dqebNVuyyCmqbO6hnFCEAtUTVdV8K0q9/v9g5qybRZmriNEZcPNm2Hj/0zji\nElBUDXeV+A/sFk9MhJEOCeH07hTL0F5JJ/qttFpss5/g8V89q4O/yniVCld5gJWvCp+/oBHkV7lx\n9xwubeaRnFiE+NcTh1PBXpUt8nCBhV+35eDwSyD265Gf+XD3EowK/Pdr2HfFdeSddqZvf6XdhU6W\nSIwJ49ReSeh1MimJEURHHL+yiicDdqfnMzfoZNSUjpxy3t2MzoByKlmR9XbAimoR7SNoDPUpQnQy\nIsS/DvzdO5ag1aWqpnE43wKAzW1j2pq7AHjkZ2gf04+06++t0Z8kPu0G464S8sgwTyhs4bX/4pHN\nnrQQ3xx5m8MlOb4UzqqY8BU0grYp/UL86+RoaZwLSj2Pi89tmseh8oMMyIdpm0xse+xFVGNNi174\n+RtO9w7RJMaY6dslDgApPJyYix5kzD6wSk6e/nkuG3blVWX79BwjxF/QII6T+tudbvYfKQt4EnW6\nFDLzKlrEvFSj1EhVVWbPns3EiROZMmUKmZmZAftXrFjB+PHjmTRpEo8++mi9c+G3NI72/TjcClvy\ntrBoy8tIGrz5Fez818Ooffr42vgv5hIBPg0nzKRnYLeE6oggDTL/7xLu3+8Jnf0+fylFjlxyi23C\n7SNoUWzZV8iRQgtZhdUTybszS0jPKedIfvNPLjdK/FeuXInL5WLp0qVMnz6defPm+fbZ7XZeeukl\nlixZwkcffYTFYmH16tVNNuAThcutsOdwSZ1tVE1h+k93oGgKd2yETl0v4OCYfxJuqi66Hm4y+P5v\nawu4jhuyjHzFTP65A5ySwvL0FykotQnLX9AojtdVaXcpNfr3Zqb1zmU1J40S/82bNzN69GgABg8e\nTFpamm+fyWTi448/xmTyZGx0u92Yza2jFq0/B3MqKPQrxQiegiP+X+Q3We+xrWQbncvgoV2d+ePe\nJ0CSCDdXi79RLwfk6xc0DfmnjuSu3MHIKqwq/oqDJek+n7+qhY7GEghCcpwnfA2G6uu/JZl/jVIl\ni8VCZGSk77VOp0Ot8pFIkkR8fDwAS5YswWazMWrUqCYY6onFP9tm+7hweqTEcEqPRF/ceX7lQT49\n+DwAC1ZHsOOxN3BFxQAeV4UXSYJ2VXlryioDi48IGk5ctMeo6JQYieOqGVyzDRRJY9ne/wRE/gjr\nX1BfggX5SIGFjNzykG0bRQv9KTZK/CMjI6msrPZZqaqK7DeZqaoq8+fP5/fff+eVV1459lE2A/65\n4mVZonNyJImxYR7XjdPBp6umYNMp/HO3jtGPf0ZZShdf+zCjv/hLdGkfiUmvo1s9i5wLaifCbODM\nUzrQs1MMxf0Gc5NlJLIKq0u/Ic9+2NdOiL+gvgQ/Je7PKmPXweJj6tM/UjDUotDaHkxdbrXO3GFN\nif7oTWoydOhQVq9ezZgxY9iyZQt9/CY4AWbPno3JZGLhwoX1jqFNSoo6eqMTSEyRDUdVGH9cXLhv\nfPFmibSFk/h5UBGxdrj9kncIv+h8Iv84TFS4kf7d44mNNBF1yDNfEB8XQUqHWC7rEHtCx9/SPs/a\nOJZxRkWaka59lGs+u4j3hmh8m/4idw5fCEB8fAThZsNRejj+YzyRiHHWD0XVAtKrVLo1osocgGds\nUZFm3/+NxWp3+fqJi4vw9RUdXYbB4SY2Njxk/9/9fgiAi0Z2bfS560ujxP+CCy5g7dq1TJw4EYCn\nn36aFStWYLVaGThwIJ999hmnnXYaU6dOBeDaa6/l/PPPr7PPgoKKxgzluFFaZqXC4vH5l5XpKSio\nIClcpt20q7ly9C4Abmp3O9YuI8nOKaPCYifarMNtd1Fod2GtdKBoWtWxTSNC9SUpKarFfZ6hONZx\nJkebKOnZm3uMY/hA/ZbvS75lTOE+2pk7k5df4Vsb0JxjPFGIcdaPCquTP/cW0CMlhs7JHtd1UZHF\nd60XFFRQYbETFWk+pnGWWhy+PguLLJirHCPlFTbsToVSgxyyf/9x1IdjuUE1SvwlSWLOnDkB27p1\n6+b7f9euXY0eUEvB/7FMkgBFgUmTear9HxRGwLCwwYwechduRcVZNatv9MvKqdfJKG6lza4ePBF0\nTo6kc3IkzjufZPIL3/HeYI2vdz/DTUNeEW4fQUjyq9bmHMop94l/XbEBR/It7M8u44x+7QLm8o6G\n0+2/8rx6u0R1rermRoSh1Iqfz1+SiJgzix93fM17Q8CAgXuHv4hBp8OtaL7JYaPfrL6uqiC5WNd1\n/NG6dWeq7hJ0KqyyrCLPfljE+gtCoiie34V/2HVtiRpVVWN/dhkAReX2kG1qwz/pYH1/iyc6Qk1I\nUy34fw/xP66AtxZw61jP66tS76BLVHf0Ohm3qmKvyvFj0PuJf9WPS2pRwV0nJzqdhPXK+7k6TUaR\nNf6X9nSLWEEpaHl4hdhrnEHgte4vwP5Pj5LffovNdVSh9p+01ULZ+SGOr+0mdLxoM+JfUGqjsLT2\nIizBeL/48Nwsus55gMfOgfQ46BrRh7Ep1wOgr/oBWWyevD/+C7q8qRyE1+f4o5Ml7AnJTA6/Ep0K\nP9pXc6j8UHMPS9AC8V7Xer9H8sC60NVt/S127/bsIit/7MknM8/CwZxy9mSGXgjqVkL3WZcenGh7\npc2I/45DxaQdqn/4lltRQdM4/fmH2RJVzgujJCQkbu/1JHrZgCRJ6KoWb5VbnciShNlU7fP3uX2E\n+h93vPMqtnH3cfVOPYoMb695uJlHJWiJeJ8IvW6fjNwKDhdYfPvVWix/7xqSkir3T2GZjYy8CnKK\nrVQGJX2EQMs/lNsnlM4Ly7+FoKgaKWtXEpO2keuukFEkjXtG3EOv6EG+Nl7L3+FSMBt1AUKv97p9\nhPafMFzRsUyOmoBOheVlP3Go7GBzD0nQwvAKuk6W0DSNg0GLuZSA+hB+4h9UOMhfz3OLrDXOE+D2\nCaHpIW8IAU8ax/9GIMS/FhS7ncFvPsfjZ8OORJXuMT148twnfV+kJAXWnPVP6QD4ngpEPp8Tizbu\nLian6VBkjRdXzqCwzIbDpfhcc4K2jXfCV6eTAiJyqvdXb/MXcFfQwiv/3DyhVu4HWP6h/PuhxP8o\nC8OaGiH+IdA0jW5ffMBuMpl/pmfS9qVzXyXcEO5rIyEFLBTx9/eD34SvMP1PCL6nrvgErjGMRafC\nx7nfsmrXVn7fkcsfe/IDiu8ITm4UVWXt9hwO5tRi2Wv4ijP54/YTZf/fi8/yl4L6AV+od0A/Sk0r\nPq/EWqP2hD8BVelOgP9fiH8I1MIieixdxHXjQJHhmt63cEaHETXa1W35C7fPicQr/jpZxjH2LiZv\nl1AkjRW7n/W1sYe4SAUnJ3angktRycgLXCzlFVhVwxel54/iJ9r++4PrRfsT6gki2OdvsbnYlVHi\ni/sJbflX/y/cPk1EQz/IiOfmMW9YBTuSoYO5C/8e+IBfX1X/SNU+fyAgjTNURxOICd8Tgy94QwJb\ncgduCf+HJ+OnZSX59iyg7gtYcHJRW4i1u8qkVjUNW4i0yv5uH3/XTrDP34ssSaiaVmO/y636svmq\n1Hw6CBX6r9Yy33C8aBPi3xBfmm7fXnb/+KbP3fPvnk9hlsN8+3t09CRnax8fHmD5B6/+S4gx0yE+\nnNhIUaP3ROC9yXo9cer4B7g6TcYta/xv13zAMzEvaBv4x9b7ivxoms9do2kadkcIy99PgG3+bp+q\nm0LwTSUq3OPudboD+1JUDWNVASJN02roztEmfIXbp4nw/yDrfArQNHSPPcj1l6koMlzS4Vr6Rg8N\n+OI6JERw9uAUIsMMvkldk14XsMALPDeDPqlxGPxSPgiOH9UT656/uWFxTDZeiqzCj5UrKbBn1bhA\nBScfbkWlwuoMiLDxumUCV92GdgP6u2u8/nmvdR8q22ZUmMe4c7oCJ4pVTfNpgqqGiBY6yoRvyIVh\nTUyjcvu0NvwFX1Whttoqxv99zWPyKnYkQ4qxExNS76o6PrCddxLX6/YJM7eJj7FF47X8/b1sznHT\nGf/ZCpYOUPlm53wGd3wLm8PNtgNF9OsSR3SEeCo72fhzTwE2p5sBXeN92+xOBZNBF2DVa5qGy11T\nYP0nah0uBU3TsMr5bC/azs6tlRwuLqS4spwwXQSR+hgG6npgdqbidMX5jvPOG5iqxF8L4RY6+oSv\nEP+j4lZUJKnu4ui1Ld/2RyovY93CO3lxLOg1mTv6vIBJ53H3+Pv2/TEZdBh0MnGRpsa/AUGT4L0h\na5qfHzYhmWuM4/hY+5wfrCuZXJ6JS+mEzelmd2YJw/u1a+ZRC5oKp0thx6Finx/fX2ztTjcxEcYa\nMfyhLHlF1bC4StmYvY7fcn5gW+k6rEodGTbTPX+S0tpzYbcLGdNtLKfG/w0AvV5GqjpXcKjoUS3/\nE7Deq0WJv6ZpWB1uIhqQh/237TkYdDJ/O6VDrW3q4/O3PfUQN5zjWap984Bp9Iw6hd6dYnG5VTok\nRIQ8Rn+U8wpOHN57v+rnX42OMGL9xzTGL/uSj/srLNv4OLed9TpAQJiuoPWTXVQZEG+vhgjZVIIs\na38rHyDdsoN3D3/CD1lf4lIdvu3xpgQ6mnvTO6Enei0czW3ErlRiVcsp17LZXriVAnsuH+x6jw92\nvUe0Pp6LOlzNjbG3IEtGNA1crkDxV6p+o1a7G6NBRq+TT/iEb4sS//1ZZWQVVnJKtwQSYo5e99dr\nxQffVYM52h1V9/s67rR+QG4qDI8exOSet5NdaCMy3EB0uHANtAa8/lV/TU+KDWOfJZ7JYVfyifYJ\nKyw/coU1CyMJdT4pClofwROxgXH4VRE+/uka3KpPFw5advJR5otsKf3Vt/80wwDOLUrhH+l6Ts0p\no8KuYAw7hEvS4ayaKjXbLITHRXMwcTx7BrdnVYdCvipczWHbfj45vIAvs97kkpSpTO5xGwZ9TI0x\n2xxuNu7OIyrMwLA+yTVuTsebFiX+ucWeZdKlFke9xL++OdsDkjUFqb+Uk82n/xnPl+dApGLk2p4v\nkF3oSQAnCq+3Hnp1jEWSyujeIZoNu/IASI4NY9+RUpSx93Llss9Z1tfN8o2PM2HYSwFZHd2KyqGc\nCjomRTQoZ7ug5RDsU/d36Xgn+v3DOBVNo8xZxHsZ8/m14GsAIlQjkw+3595v8+ibuwPY4WtfHe9X\nk/5A/0/hcuBlWWLlgFieH6HwQ8cKPj/yX9bkLeem3jMYFn1RwKJP74RyRdXq80D3dAPefCNpUb90\nWZJQ0Or9xmuLvQ0mVHY+gJ17cjBNH8d953lWAd7Qaw5J5o6+/cERPIKWi8mo803yDeqegKJWR1u4\nomOZHH4Vy1jK19YfucCeS3xUV9+xWQWVHCm0UGpxcFrf5OYYvuAYcYQItfTitfz9wzx/LfiKdw49\njcVdhlGRuG2jxsxfnSRaMwEo6zOQou79kAYPIm7YILanFxOm09AUBafNAZpGWGI8PSIhZ/XvxO/Z\nTvT+XZiKC7hweykXbocNHeGuMbCxUwHP7LiPETEruLn3k0QZPJPDNmdw7H8bdvt4b4pHe+OFZTbi\nokw1Zu9rS6UQGO1THfOb+MwMJg7djdUI58X/nTPbjws4Ti8s/1ZJfHTNp0Zt7H1c8ckyPu/j5vut\nc+n6f6/79nkX/lhDLPcXtA6cVUKaFBNGQZktwMr3Wv5uVcPiLuO1/Y+wsXglAOcfgNdXaHSxGCm5\n8FI29j+dwgFDkXv3psJiZ2jvJFzhRizt8ilwuNHrZd96kaTYMJxd4znY4wx2Otwe3XK7CCvKJ6ww\nj/6OAr55922+MG/j3otgfdlPHFx7HtM6zaFrz7E+y99Lm17kVR2xUfsbzyu2knawmL2ZpQGWf/Dk\njT/By6YtNheFz7/Cc/LnpLWDVF1H7hn63LG/AUGLxR0RxdWREwD4xrmKvMps3z7v5O+JTqkraDoc\nLgWzQUd8tCfyzh3C8t9a8CcPbr2CjcUriXZILP4Cvv3YiPWyu1jx4Roy5r1CxgXjqExJ9R3rnfOL\njTShaFrAQkFv5l6jQUbRPJH5mt6AtV1HigYMxTZpCutfXUb/cYtYtWYwozIhz2hjZs4D7P78VmyW\n6voiLrcSZMw2+UdUgxYl/t5Y7bpc+RVWj3+soMwe4Nerq3JTgOWvQfaKVaxf9SjvnAomzcC9g17D\nJIWO6BGcHOhlGfmSexm3z4BDp/G/jdU1qEUKjtaNpmk43Somg8632M8/R49bVflw5xJuWnM5BY5s\nTsuCv17TuMQ9jC0ffc+uyf/GGRMXEAHWNSWakf3b+16HWqnvNVb9a3eHGaudKTpZQpZljoz8Pw7N\nWcrMM5ZzQ04vXDqY3f5nPn39LAxFnvmptIPFASkgTsSEb4sSf+81WJfl77/yLVD867D8/fbJuTkY\nXvoXd1zk+aBv7v04HcN6+iKGIqvCTBsSbipo+Rj0Mu7wCCZFTwLgK8cq8iw5QKD455VYycitjuu2\nhijUIWhZeCN3jH41NbzaoGoqH2a8wD1rbsetubhjA/z8vomi655gzfNLoFdvXz/+bt64KDMmY7Wo\nx4RYy+M9lzeNAxCwcNCglwMWHVZ268tFV37FdMN16BV4rWcuy5b/nYRNv1BW6aTQr05wm3P7yH4L\ndWojZJpVPHf6cquT/VllNW4e3g9Sdjox3TOVSReVYDfAuUmXc0WPiYAnvatJr+O0vsmMHNCeU3sl\nNtXbEjQjKVVrNBJjPfMA+ovuZux+A3a9xqIv7wUCL7RdGSW+Ah8ZuRX88lcW+SU1i3UIWg7e7Jtm\ng85nvSuqhlt1sejAg3yR9QY6FV5dAc9sTGbzyx9zaMxVIEkBAu9v+Qc/DBr0MsagABCp6qX/IlD/\nKEWdLAUYFuaqcw0//UFmd3meMLfMB/0dvLrlX/R9Yx6Sq3qdgr+EudxqvYNbGkKLEv/aLH+3ovpK\npXlnyFVNC0i5qqgam/cWcKTAQpHfHdTTH6CqDHn+Qab230J6PPSL7M9rly7EXPWYpmiaL/zPZNCJ\nyd6ThJ6dYhjeN5nkWE+wnhIWztSEKQC8U/Qt+/Mzfa5Ef1RNI69K9IvK7DX2C1oO3uybZqPO54qp\ndFp5bs9d/JK/gigHfPc+jC8bwMoFn2Ltf4rvWJPBv/Rq9TUfahGgMShPl1fYvaIeH2Uiwi/ViyRJ\nSH799EiJoUu7KHp3iqVv6sXMGPQOkaqRZQPgUfldznzwOsxF+UCgt2JdWg5r03Ia+KkcnRalcN4v\nrrDczrYDRb7tW/cXsml3PjaHO6AAg/9FW1fNTFXTGPzfZ3g+/DvWdIN4OZZF539IbFhkQDinWPhz\n8iFLEuFmQ8D33P6qB7kk3YhNr7Fg6e0UlNlqHKeq1dFjIhF0y8Zn+Rv1yLKETankyR23sLlkDfFW\n+OldGNLtYtY8vwR7QrJv/Y4sSUHXv7/lX1P8/Z8SPG08f5NiwxjQNZ6B3RJqrA3yv4eEmfR06xBN\nZJjHpdw39nReGP05MbpIlveDh3r+xbm3X0HCjr8Cs5JW/Q2VjuJYaFFq5y/axRV23+O4dxFEudXp\nWxYNBBROrmumPPbzj1mV+S6vng4G9Dw0+A36degGBMby62rJ4SNo/fh/z/rIcMYn3QDAF9ovWCqy\narRXVc23ZvREFNYQNB5vyKTZpMOmWHhyx42klW2gQwX8/A70v+wOsl9+A8XszdXl+S0YdHKAOPtf\n/6FiAILdPt6aHZIkkRQbhixL6INdQ34deZ8y/H+LpyQO5sN/LCdcF8a7Q2Dm8CJGP3Q9EZvW1zh/\nqCfUY6FliX/QRRZcds+bHyNUaN7uzBLf/4fzLWQVVgJg+Hk1f70/jTsv9uz7V6+5jE4dUT1Z4y8K\nIt/LSYtOlmkXG0a39tHodTJh59/BmKworAaN3355oEZ7RdWqBUBo/wmn0u6qd91lr+WvSg5uXjmZ\nfZatpJbBr29D+6sfpPLxpzD5lVn1ib9eDhBnvd+Tf6gIMP+J3Q7x4XRIDK/RRpYkOiVG0qtTLBB4\nE/GKvr9L2WTUcXr7M3jn4o8wykZeGgELT3XQ+67r0P/1Z4BBXGGtWSv4WGhZ4h/krgmufuONyPEP\npwqFxe5i35FS9H9uYvvMiUy8QkGR4YpOt3JW0mUBX2Jtj32Ck49+XePp0j7KY53pdEw9dSYAH0ds\nxpmzO6Ct6rdo8ARE3QmC2LQ7nz/25Nerrd2pIMsKN/84lQ25a0kph5/eAfWsayi5cxoQKNxeQdbr\nZcJMejonRTKoe0KA5S+H0AKvb1+WJPqkxtXqJu7ZKYaOiZ5AgzKLR7Djo6ongvW66kxE3qeBczqf\ny4LzPAsP7/s7fNfRQszEK5D/2uw7rr43w/rSssQ/2PIPFv+qGW+zqe4CKfrKCvp8/AZHbh7DZZfb\nsBvgvOSrmNDZk5/ff3be7B+XKyZ52wTeG37y0An8X2EilUZYt2ZaQBt/y1+4fVoubkXF6nTwn733\n8VPmSpIq4cclUD5xBltuexipSqBNBj+rvkrYvb+DHh1jiI82H9Xn3y4+nJSECIY0IBIwosq/3ymp\neh2RJEk+699/HmFcryu5b+gMNAkmjtex3VhCwrgxdPnxC6hay9CUtCi1C16nFVxg2XszCFhI4csJ\noRK7bwfD/jObsZPOIeqzF7hovJPSMDi73YXc1ONR3xdqCHrs8vUlfP5tAu/3b7W7uXTwowC81z4d\n4+aVvjaa34Sv0P7m42iLnUrK7bxx4AnW5v9ArA1+WAKVU+ey//KpIEm+G7h/RT3fNl3t/vlQTgBZ\nkujdObZBmX77dYljcI/EGilHvDce/2gjgLtPnc6ZiWOp1CtcflMU5ZKd4c/OYNScO9HnZtOUtKjc\nPsGWvzMoB7bDN6uvQ3Y66bBhDV1//Y6ofTsJz89G5/I8Fh2Ig7NvNpId7mRkyt94fNgi8oqqH5mC\nJ2W8xT/ERd428F54Nqebzl3OZ9T+LqwLy+DX9bMYccpZaIaqwh8aIIm0Dyca/6gWt6JilGt/0n9l\ny4uszPsYkxv+9yH0+PdTfDfyct9+f999j5QY9DrJ50GoK3FjU636Nhl0NQTeu93pUmtMIutkmVt7\nPkGe8yD7ytOY9PApfDnvAB3XrSJ56kbsjz+F/eop1QUsjoEWY/n7Fzn2rrK1uwITHzlcCmH5OXSZ\nP5tLJ53FqCfuJmXNt0RlZaBzubDFJ/LjhH8w4r5EssKdnN7uDF45c0mA8EPNhG1eX15woiXByUmw\nxXfJqU8A8N9+pSR/8V/AY3F6I8jqmzpc0DQEpGaoI7xx+b5lvLZrHpIG738OwwZcjP3W2wOE21/D\nOydH0iEhotoDUIf4S8d5/q9351iG9Eqs4V7S62XC9GYe6PcyMaZYvlO3c+szU8ke8X8YLBVE3Xcn\ncWePwPz+u0gV5cc0hhYj/l7hT4g2c1rfZHSShMNZ/cXrbFZ6LX6Zi268mLj33sRUUUZp974cmjab\n3FVr+fzLP3nlzdcZP2gthUohfaOG8c6Fn5B+xFHjXMEXf/cO0QB0SKg5ey84+Qi+6HvFn85pUn8q\nTPBdxhsYy0pQ/IyRpo6vFtSNW609YeOh3HLyS6ysz17HnatuBeDZH+CKgmQqXlgQ4OqBmkVeoNrn\nH2x1B7Q5zh7gMJPeF+8feF6J+GgzMboOPDd6AQDvFr7Bm9OuZ8OM51BSOqLfs5uo++4k9tK/H9MY\nWo74V1lX3ru2yajzRPuoKqmrvuaiGy9mwPsL0TvsVF7yD35c9Bk/vracouv+hdpvAJsdf/Fo2hRK\nXYUMiD6Dh/u/Tpg+MuS5gn37ibFhjB7UgcSYuko2CE4WZFmqEdl12QBP5M/CoU46fvRCleXvESEh\n/icWtzvQ7eNFVTUO5Vawcvdmpn47Eafq5LZNMvf9DhUvL0JL9EzE1mb5e0mKMdO1fVTI1N/VxzXf\n/F9C1biGxZ7L9f1uR0Xhxb3T2HHmKArXb6H8lddwnnMurpGjjuk8Lcbn773Zy5qKftsWen75HeYd\n24nft5Wkw54CCyU9+7Pl3zPoM+lSStNyAU/kzpJdbzFv14Mompu/JV7CbT2fwiAbcSsqBp1co8xj\nqNQNYnVv28Kgl1H8Agr6Rg/lrLjT+KXkD74q+YxJ++9ECW+PAY/bp656EYKmxV2L28etqFjdFp7d\nfQeljlIuORLBy99Ukjv+WvTnXehrp5MlvIGCtcXrd20fHfLc3dpHU2JxNGt6F++EcqXdxe0DHmLd\nkd/ZU7GZN9LncOHgj5AnXI1jwtVA3RXGjkaLUTzFrdDxl+85bdKFxJ1/Fn1eeYouP32N7nAm1qQO\nbJo2l5ULPqXwlNN8IZkOxcbsTffw0K/TUDQ3l6XcwJ29nsEgez48t6KKalyCkIQShelnPwnAy2do\nhL/0aECkSV31IgRNh1tRKSi1+b32K8TudvPKvgfIsqUzwB7D0vcqqezcg+zpswL6kOtI0HY0urSP\nYkjP5k3qaDbqkACbQ0FGxx295mHWhbO+6HuW7fukyc7TMiz/efNov+QDuuxMA0Bp34HiM84io1t/\nks8ewQZzR9B5JmV1kidTXrplBwv3PcRh237C9eHc0v1xRiVeEtCtomoiV7sgJN6qXf5PhiNSRjEi\nfjjrizfyjmsNZ/+1HvuZZwPCkDhR7MooCUjM6G/5/+fP+fxZsppoxcSXr5cRrgtj5Yxn6RAd6N4N\ndPu0vutflj3ZRm0ON25VpZ25M7f2msWLu2cwa939nJ06mk5RnY/9PE0w1mNnxgxMO9OwJSRzcMZc\niv/YTtbTL3Lw4vGU9h3kE34ARXIyb8MTPLx9Aodt++ke3ZNvr/yJ0cmX1ujWrWgBk0cCgZekqvmd\nlFQhpv8AACAASURBVMTAIj53nO7x/b84ArotfsrnjxR+/xNDcEZer+W/4sBXLNj2HLIm8emHDrqX\nyeyfv4iyHv1qhFLWlZq5tRBm1ONwKxyqqi1xSeoETos/D4urgtt+/Beqduy/x0aJv6qqzJ49m4kT\nJzJlyhQyMzMD9v/0009cddVVTJw4kU8//fToHd59Nzkv/Zdv3vmegonXgtGIueoL9VpoqqbyS8FX\n3L7p77zw57NomsqNA/7NTxN+o19C/5AWvqKovrCxqBAz64K2S5/UWIb3bUdUeODvYlTKmQyIHEZp\nGLyXtJeU75YDcDCnnJyiyuYYapvBaq8Zau1yK6w9+Cd3rPoXAPNWSlx4AIrnPE3+qHOBmgul/Nfx\ntNYnf3NQBlGzUce/us8hxpDA+tzfWPDnwmM+R6PEf+XKlbhcLpYuXcr06dOZN2+eb5/L5WLevHks\nXryYJUuW8PHHH1NUVFRHb8CLL1J+yThUkzkg2geg1GphVd6n3L91HAv2PUiBI4f+CQP58vLvePrs\n+YQbPOGZIcW/KlY7JtzIsD7JDOqewBn92jXmLQtOMvQ6mXCzvkYooCxJXNnlTgCeHwWJi+ejs1kp\nrnCw53Bpcwy1zRAqcdm+/BxuXX0tVnclE3fqmL5WZc9V11My+Qbfiv9godSfBJZ/cACK0aAjxpjA\nLT085Uef+/NJDpUdPKZzNEr8N2/ezOjRowEYPHgwaWlpvn0HDhwgNTWVqKgoDAYDw4YNY9OmTUft\n0xtTrZMlrC4rP2f9wGv7ZzFh9ShePzCbw9Z9xBvbMWvoC6z656+M6DAysIMQX7LTpaBqmm+COD7a\nTJipZUxzCFoGweKgkyUGxpzBKTEjKTPDS/0K6LX8veYZXBvDXaMOh8qCfQ+RZ8/k1FyJt5YrZJ43\nlm03TcelqNidiicts1xzoZSX1ujzB0htF+mrQgfVTzenx5/H6KRLsCs2HvplWm2H14tGKaHFYiEy\nsnqSRafToaoqsixjsViIiory7YuIiKCioiJUNz4e+ekRDuRmk1GcQ17aAQ5VHAjwafWIGMiYlCmM\nSriIId3bo6tjubc/jqr0EHqRs0dQC8Hi4BWSSan3sn3777x8Btz65psYxk7CFRXTHEM8KXG5FdKz\ny3G5Vfp2iUOvk1Gq5lU6JUai00m8kbaAzSVriLXB50s1ysdezcZbZoIs43KrOJwK4eaaEnYyVOEz\nGnT07hxLdpWr0X8e495T5pD22yYOlh+b5d8o8Y+MjKSystr/6RV+gKioqIB9lZWVxMTUfdHM/XVu\nwGudpGNw0qn0CxvNsLhzSQ3v7btII8ND++5Dybv3sVCkahbURkyEkUizgY5VWRe9T9s9o07hjPgL\n2VD8A/NOr+TuZYvZcf09zTjSk4uCUjs5xZ4ymWUWJwkx5upV/jFm9lg2s3jfMwC8+wXIf7+B3ffN\ngqqSmnangqJpIfPmnAzi72VY7yTsfje5DvHhqFo4/xmyguF9j82F3SjxHzp0KKtXr2bMmDFs2bKF\nPn36+PZ1796djIwMysrKCAsLY9OmTdx444119jfnnDm47SZsFgN/H3gGZ/YYhllv5ufNRwLy7Rj0\nMp07xoXsIyq6DEOI3DxRkToSEyNJSooKcVTDaap+jjdinPVnTLvqBT+aphEV6SkMdGO/B9i0diVv\nDVW55813SZh8E/EJkS3WmGgJn2V9SEqKosyhEBXpWclqMBtISoqiyOoiyuJCF2nn3x9NQkHl/rUw\nYNRdHL77ASIMOuxVi7d0Rj1RkWbaJUfVeN8Ojf9v78wDoyqv/v+5d5ZMMpNkkpAEAiFAgBCWoIhL\nRRYXlFaqSFFkcamogAUX1BpAUXxF0Ne22OLaqlRwA/XViqjlV2upoCIqgqCssgcICSGTdbb7+2My\nw53JJJAFZpKczz/M3G0OT2a+99zznOccjpRWBz6rKXZGmlTd6/S0BCxmA1t+LqbClUpm+w5Nunaj\nxH/48OGsWbOG66+/HoD58+ezYsUKKioquO6668jPz2fSpEl4vV7GjBlDWlpavdebM3QOX31/gL1H\nHHSJScVxzIUDF5UV1YEWjl3bJ5DVPp7CwvAhJEdpJVW6+v/6/G1HqanO8xpCamrdnx9NiJ1Nw1Hm\n8y5HnXUeX1X8lpe+e4m5F1bx6MuLODxgYVB54GghWscyFL+dhYVlgXHeX3CchBgDRUXlHHdUcOsr\n4zjgLubCvTDrnJms+eUtuIvLMRkNgdatzioX1W4PleXmWv/v0uOVgWs3dkyidTzL8Gmdo6yKI0dK\nsWWlNPpajRJ/RVGYO3du0LauXbsGXl988cVcfPHFDbqmP49aH5/XL6oJ11kn2Kjgt3EWI8fLfdkD\nRindIDSAjBRr4Lv38NCHefW7V3mrr4t7X3qNbf++mcyze9VaHyA0DKf7hKNWXpPi6fVqrNy8gM+q\nNpJSAYttk3Ddk495RxEV1W6cbi8JcWZKK5xU15wf2lQdWlfYJxx+LWxqtdmoGSVPQPxPmKSvvtnQ\nJ+24GH2Hruh8TBeik56ZdrrWVHrNTMzkioyJADw01E3u68+zbb+kfDYVf039hDgzFVUuvF6Nb/f9\ni6UlS1A0eLngQuyz/wiKglnXhat9ctyJBk7UzvGH+ks1twYCPcxbi/i7ahZj6T1/Y0M8/xqS42MY\nmJMW1J5R0juFpjCl713EKXF80h32/LgcW8G+SJvUoigtd7JmU0FQD1qX24tRVbFajGjA3mMHmLd+\nKl4VZm5O4Rdz3w7k4Zp1YbZUuyWoH2+4ft7ROifTXPj/f6GpsQ0lKsT/eFk1Ho8XVVGCFjcYDae+\nUs+/WMdkNGCLNQV5C4nWU2+7JgihnNe9Gzfm/g6AmZd46bXUV2fd69X4bMMBNu8ujqR5Uc+OA8dx\nebzsOnii+YjL7cVsUrGYjXg1D/e8cSWF5mqG7lW5++6VoEslT7VbsNtiGNAjFZPxRGcsBYJ+535a\nu+evtibP/5ufjuD2arXu2A2K+Yfgb5ycao9tsQs9hOhhYs/bSTIks64TrD38AYZtWwOhC30VSqE2\nhkCM2jdemqbhqimUZ4kx8OH62axRfya9DO7LnAs9c4POT7TFcFb3diTUOHF+wVcVJexvu614/p4m\n1puKCvF3ujxUVrtrTdToY/6n/AetyRVOiDMzMCeN3KzwqaGC0BDiY2yM7TIDgJmXaihPzg3q7atp\nWqDHtBCMf87NX2fL7fF1STMZVb7Z9h5Lne+jeuGpYyPxDh170uv5daIup05RFCwmQ6ApSmvDHx1p\nNRO+Xk2rtRLXGmvytTWLt2CPj6n3/HDfA1vN+YLQVAyqwrC0UXSN6c6+RHimZAXGTd8H9m/YcZQv\nthyiyil9oEPxZ9v5K+z6n5iOV+7nvrXT0BTI35ZJ4rgnT+kJX6u56daXxHdBn/b069b4NMhoJhD2\n0VqJ+AOBGjx+bLEmBvVrT152ioi4EFEMqoqqGLih+4MALLgIKp+eE9jvTyv2lxQ5VVxuDz/sKgpb\n0bIlEq70dSA1scbzd3m8uL0u5n80hqMxbi7da2bYuGW4MZzSE77f840xtc1EjtAnqcYSVeIf2lgd\nGt5eUfotCacDv4D1TTyf8+MHU26Gx2P+S/r6NUHHNXQS7ucCB0dLq/jh55NUvm0BlFY4+XxTAXsO\nhV8c5Q9TeL0a/1ifz7rYw2SUwt3nPEu5LdlXhPEUxD+rfTzpSXH07tI2Q7qG1pbnD1KATYhe9GtF\nxnefhUkz8MrZYHhtFobKisA+rYGP4v4nWpe75TeLKaqpu/PzodKg7f4boj9M8e9t7/GmeyUGLyw2\nTSR2wCW4PN6aCrwn1wCTUSU3K6nNpnC3qjx/fz3u5CZM0HSoKX/azt6UlsaCEB69R9ohtgs39bkV\nTYEHBx6h95JFgX0N9cb8YtcaOoXpx6iiyk1Jma++jkd3Q9x9bDf5a31ps49sas9Zdz4dtFCroVl9\nbZFW5fkP6p/BRf06kNoE4c5Ms3Fhn/akifgLp4FQSZp+9u9JMiTwWVf4buti7Ns3Aw2fhPP/kFtD\nuFI/L7fup8Ns2HEUAK1GpNxeJ2NfvJwSg5NfbVf4zc2vg8kUVKLBIHN7J6VVZfuYjIZmqcdhDrPU\nWxCag9gYI8nxMYHMFasxkWln+yZ8771co+dfZqG4XU1+FG/JhNNtb003PYDlG2ezrmo7nUvg/oQ7\n8eT0BoJLNIQmfQi1UVXfklZPE/uTy0gLwimgKAp52e3onO5beVpSVs2F9qvpGdePgnh4OmsbPd9Z\n3GDxb2K2XkTYsf84+wvLam0P54l6vL6c/g27lvF/FSsweuDFg0MpHDU5EOIJFn/x/E8FVVVaR8xf\nEFoK/ifUXQWlOCrc3NL9YVQU/nw+eD/+C6bduxp0vabmakeC/UfL2HHgeK3t4cTf69U4VLiFRXt9\nVYDn7+hG6gOvgKLU6tcNtNqFWc2NUVVbR9hHEFoKSSGLDbvZ+jC8/Tg8Kky/3EXmw/dBAx7H9d5b\nS5j0rS/UEM4Trags44//GUep2cvI3XGMn/tvvCbfGIbz/O22+hdzCj4sMYYm1zAS8ReEBhAuvfCJ\nSx4jxZzC51mw3PMlltdOveG73vFvCeme7noWFoV6oorHzfyFF/F9YhldjqvcMGQp7nh74Di/+BsN\nKv2z23F+btPaErYl+me3o392uyZdQ8RfEBpIv67BZQPsFjuzL/D1ob73Cih+cibqoYJTupbek24J\n4l/fqlK956943Oz4+/UsTt2DxQW/z5yH0ik3UNcHglNDk+Jj2mzefmNQVaXJabEi/oLQQFISLfTo\nmBh4b1AVRmWPYYB9KMctcOfF5cQ9MIM9hxwnDeXoPf+WEPZx1xP28Xv0iseN6dnbmNPDl/46I+l3\ntOs7CoBte48FJoslpT+yiPgLQiMILTduUFVuy36EONXKP3rB+/s+xLlsObsL6u8Dq18A1RImf+vz\n/D1eDbxeshbO4I4eX+IywE3Jv2ZA/+lhyzZIqfXIIuIvCI1A38TdoPoyV1Ji2jOxy+8BmP5LyHrh\nQdj9c61zNU07UdteFyppCWsE9GGqUHu9Xo1eLz/FvRmrOJgA/Yy9uGv4s3g1LWy7xdZedz/aEfEX\nhEYQ6vn746+Xpl9Ln4TzOGqFe4aVkTvrDqiuDjr3xz3H+O/GAlxub5C3Hwntb2gfAr3nH/qk0nH5\nYv7qeIX/ZkG6msT0s16krMx3swiXmSKlHCKLiL8gNILQCrT+4rOKojCl+2NY1DiW94H3Y37AOmdm\n0LFHajp/lVW6grJCw3n+hSWVYRdUNRZHhZOCovLA++37j/PFlkOBktR1UVJWjVfTgvrGery+J5jK\najfmFf/gi/88yl/OBzNG/nTZUuzmVA4d8xW9Cyv+EvaJKCL+gtAIQsVML2Tplkxu6fYQANN+BQff\n/xvG5W/V8pSrXZ4Qz7+2+G/eXVxrQVVTJoa/2VbI1n0luNw+b/9gzY3geE0RNrfHW6syaUFRORt2\nHOXng6VBrQO/3HyINZsOceD5xayffzNTRvq2Lxj2JwaknRt0jXA1e8Tzjywi/oLQCEKFK3Tycmjq\n1QxO+xVlMTBxNFjuv5Mdq74M8u6rnZ6g9/XF/P03hp/2HOPzTQVUu5rWMjI0aUdRFJwuD59vKmDr\n3pKgfcWlvhtDsaM6KJdfA7LffoWkF2YwZrQbtwF+kzmJib1vqi3s4uVHHSL+gtBI0uyxZNSUEg9F\nURTyz1pAirk9X3WCx8+vpN+sO9i1/WAgZFRZ7T6p5x/YVyO6/jBKeaUraH9xaVVQOOdkaGHqiFbV\nxP79n+HHP8lrUJUTMX+vl7wXnqDjkie4cjyUxMJ5yZcyqWc+UDuk09SbldD8iPgLQiPp3SWZnpn2\nOvd3tKcyvccTKCjMGwJfmnaSMef+QMillvjXE805WR2XdZsPsXVfySlnDNXy/EP2V1SduLn4Bd+g\nKrjcHlSnk/Pn30fW+4u55nrYlQy9k/KY1uNJjAZfVk+o5y/N7aMPEX9BOE0kWM30TjyPMZm/Q1Ng\n3BjQvltB9gevAz5PW9NP+Nbj+YfLr9++v4Ti0qqgbae6SriW568EdyErKTsxAeyf5D1WVk3x/sMM\nnn0bHVd/xIQxBtZ0hhRze5664BUshrhA+mZoGqfZqHJOz1RSk6TfRrQg4i8Ipwl/h7rfdJrKhemX\nUBwLY66DXn9dQLuN6/BqvlIH/hDJqcT8/VRWuzlwtJyNu4J7/27eXUxhTTZRfYR+lkJwqqn/JlLt\n8gS89tjCQ1w8YyKp36/j1t/E8G4vD7EGG/m5z2NTfXVm/B6/3vNPtcfSu0sy8XFmOqXFn9Q24cwg\n4i8Ipwl/+WdVUfnzsBfItHXhmwy4/Uo3g+ZMJWHrJrzeE03L9Z730eOV/HfjwcD70LCP/q1eyEsr\nnGzeXQz40kR3HQzupxvufD/6z/eXcfhi8yHcXi8Ju7dzyV3jSNy9nRnXJLK4bzVm1cLM3OfJsuZQ\nWuF7UrDULObSe/7ZGQmBss1NrUQpNB/ylxCE00hOpp00eyyZyWk8c/FiYtRYXsuD+edWMGjmbcQe\n2BO4SehFfOvekiDBD/XU9emeTnf4ePrm3cXsPRK+vlDo9TQteJvHc2IVcruNX3PxjInEHT3EnNEZ\nLOx/HINiZEbOQnolnANARbUbAFusCQj2/PWC3xwd+4TmQf4SgnAa6ZBipXeXZBRFoW+7ftzT848o\nqDxyMSzLOsawGRPouPpj0LR6V/h6QgRcH9uvOslkarhwUmguv1fT0H+C2+PF7dHotPpjhsychLms\nlJnjs/mfvIMoKPyu+wIGJA2tdV2rX/x12T7+nrO+15LyGS2I+AvCGUJVYEDyMH7bdRYAk0Yp/Dvl\nKGfPmc45Cx9Gc53IsAlNi/8hJJav9+YdFcFpn6HU1WFLj6YF1xlyu71Yn3maC+bNwOBycdft/VjQ\ncycKCo9d8CcuSr0yzP9PIc5Sf1lmCftED1JAWxCaiYE5aVRUuSg8XhW2I5U/FDKiwwQKqw/ywcGX\nuWa8gRVvqAz/aDkWrwsWvwIGA0qt5EsCsXwIFv+yitqlGbSTrB8I3eaffAYwVFWSs/Ahkla+jQbc\n+cCF/CV2LQoq9/Z5kmt7TmDDjqO1rmmLNQV5/MnxMbUasptNBvp1TTnpTUI4/chfQBCaCVusCVus\nibSkuLD79cI4Mes+qjzlrDr8FldPMLFyicqwT96j6q5YHE89fdLPcrlPiPfhkkribcG9b/Udt8Kl\niXo12H+kTPdeQ9Mgfu8uLnz0ThL27sRpieH63w/k/9Q1qIqBad2fYESn0WFr8iTZYujRKTFoW14d\nnaZSEqVPbzQg4i8IZwj9JKiiKEzqNodqbyWrC//BiIlm3nnLxJXL3sC44Vsyxk6mOKMrle3ScSbY\na8WBTlbfR78/XNinsKSSIt0aAc0LcV9+ziV3++L7BV27cM3tqXxVvQazGsO9uX/g7MRLa3nyABkp\n1noXuwnRiYi/IJwhQle9qorK1O7zsFksrNy3jKvHGvj7f9sz4V9bGfg/MwLHueKslGTncqx7LiXZ\nuTgyu1Lesw8YTKTZY7HbYnArCo6yE2KunxAO13TdqSu3YKiqJHPhQjq+9jcUj4cvLrmQCVcU8XPl\n19iMiTw7bAl2dy+qnB5fgbYQxz9NFm61SET8BeEMES5cYlCMzD77Kcyajff2v8zEwYf4YdAw7vzE\nQ9yhAmKLjmAuKyV103pSN60PnOc1mqhIbY8x3oaSnU3MgP7EJHZma+/z8Zpjgjx//+SuFtI7QHVW\n0/Wjt8l980Vii46gqSp/vWUE93RdS3llKemWzszMfZ5z0weyfb+v2JuiQHysiY7trKTaY7HFmiR9\ns4XSYPGvqqri/vvvp7i4GKvVyoIFC0hOTg46ZvHixaxcuRKAIUOGMG3atOaxVhBaIaqqMKl7Pknm\nVP7+8/+yQP2MTydewtTs17AaE4g5dhT7jh9J2rGFxF1bSdyzg4Q9O7AV7IMCYNuP8NEK+gK58Qns\nuvRqPHffA/g88oNFFcTGGLFafGmYhqpKMle8RvbrfyPu6CEACnNz+f3kHP5e8j6aR2NA0jCm93gC\nqzEBo0EJ6jWsKAo9OkmYp6XTYPF/4403yMnJYdq0aaxcuZLnnnuO2bNnB/bv27ePDz74gLfffhtF\nURg3bhzDhw8nJyenWQ0XhNaCqvh6AF/V8Rau6H0+k1fdwrqiT9npuJop3R+jf9IgDp87mMPnDg6c\nY6woJ6akiD5JBpIO7SVhzw5cK1Zi2riBHu8twbviTZL7nE1JtxzK23eiMN5OUvd0znvrHTp+/v8w\nVvvSRku69uTtG37NXOt77C95DxUD12bewehOU1AVn0dvNKqBWkDSd7f10GDx//bbb7ntttsAGDx4\nMM8++2zQ/g4dOvDSSy8FviRutxuLRWb3BaEuFMXn/Xu9Gpd0vox/jvmMif+4ge2OTczbciuXpl/L\n9Zl3kWhOCZzjjrPijrPi6t6O6l+cB6nxlNydT/m6b1Cf+l8yV39M2vfrSPt+XdBnJdX8W9QrjzXX\nXcef0r/hP4V/RKvUyIjtyrTuC+genxd0jlFVA56/aH/roV7xX758Oa+++mrQtpSUFKxWXw1zq9WK\nw+EIvqDRiN1uR9M0nnzySXr37k1WVlYzmy0IrQdV8TWA9+fZd03sxuN5b/Luvr+xbN8i/nV4OWsK\nP+Sqjrfwqw43EWe0Bc5VQiaRvX378fWsP7Bv1mNoX3xBwp6dxBYdJqa0hFSjh5/bZbH+smG841nF\nPw89TlVhBQbFxJUdbuTazN8RY/BNIJeUneg7bNCFfcKtPxBaJooWus77JEyfPp3bbruNvLw8HA4H\n48eP54MPPgg6prq6mlmzZmGz2XjkkUfkUVEQavj4i921tuVkJVF0vIqjJZVcfn4WqqrwyZd70DSN\nPWXbeXnbAtYd/RQAiyGOSzqM4oqOY+mR0I/BZ3XEFmcOXKuiysXq7w6QnGih+PiJ7B+314XT/iN/\n+fxlPj/8EW7NtzDsvHaXcHvOg3S0dg0cO6h/BpoGa2sKy434RRd27Cthx/4Szu2dTkqiZPe0Bhoc\n9hkwYACrV68mLy+P1atXM3DgwKD9mqZxxx13cMEFFwTCQ6dCYaHj5AdFmNTUeLGzGWkJdja3jfp0\nTD8lJRU4HNU4yqo4fKQUVVEodfhi8slk8kjei+z3fM/TG55g8/F1rNz/Oiv3v47d1I7hu4dzdvrZ\nnNOlP1Z3MipGdh0tYltxGQfKDrCvYgdbHd+x1fEd5W5fL2AFhQtSruCqjEl0j+8HWrBdx4rLiY0x\nBrYVFjpItBjol2XH63Q3aTxawt8cWpadjaXB4j9u3DgeeOABxo8fj9ls5g9/+APgy/Dp3LkzXq+X\nr7/+GpfLxerVqwG49957OeussxptpCC0NvRhHlVRAuEbr1dDC3lQ7pFpZ6B1OLnxA/l6/0b+eehN\nvipexTHnEZZvf4Pl29+Az0/+mT3sOZyTMIKL2o0kzdKpbttqbLmgd3pQxy9zTblmoXXQYPG3WCw8\n/XTt5ec333xz4PXGjRubZJQgtHb0+q4oBPr6ujxejGr4vPkemXZS7eeTnZjDb52z2VexnbK4zew8\nvo095bvYX3IAt9dNWXUV8cYkks2ppFky6Rl/FjnxZzO8T3++31kU9tp6/NMIFrMsA2rNyF9XECKB\nAv5OiqqiEFPjVVc7PSjmENdf94SQnGDBoCooikJna0+G5A1DVZWgMMWaTQW4wpR/cIWp8RPWNJmj\naxPI0jxBiAD6rBlFOdHyscrpqVVxMzYm2EfTrxQOLRkBdTdMOdX+vuFWIgutD/H8BSEC6PVVURTM\nJp9gHz1eGRD0rPR4MtNstcQ80Ce3DpE2GsJvd4Xp+KWfewhnm9B6Ec9fECKAXmD1YZ9iRzU/7T0W\n2B7Oi/cfG65OPwR3ztLjdgcfnxwfw5D+GWFsE/VvC4j4C0IECA37+Buc6zHU4cHHx5nqvbbe80+3\nx5Jq9+Xlh/b6TbTWbjgjtB1E/AXhDOIXYr2AKzUrfEOpq99tgtUcdnvgPN3TQoo9lrSazwyN+UtT\nlbaNiL8gnEFyOycxoEdqkPD6Y/gZKdagY+uauD2Z56+/aRh0oaNQ8bfF1n8doXUjE76CcAZRVYUE\nq5mKandgm9/p75lpp7zSxfGanrx1ef4GVaVnJzvGOpqh628aqqoEmqZXOn2f2b1jIu2Tw7eaFNoO\nIv6CEAFCJ3z96OP89TVJyWhnrXOf/qahKhBnMWJQlEA7R6NBlQYsgoR9BCES6DNq9DcCfby+rgnf\nk6Gf8FVV33xCvK74W+j0Qm5WUqDRi9B2EPEXhAgQVN5B986o6l837ueZnGAhJcFCRooVa01cXz9J\nHJrKmZ4UR9+uwd34hNaPhH0EIQIEhX10Gq/P0W+s5x8bY6Rft5SgbfpJ4nBTCXXNLwitF/H8BSEC\nqEFhn/Ax/+YUZH1YJ2xaaSNvNELLRcRfECKAXvD1Gq8X/OZcaRsbc2IRWbjr+p847DZZ+NVWkLCP\nIESA0No+fk5X+KWuCWY9Q/IywhaKE1on4vkLQgQI9vxPLb2zuXDWUd1ThL9tIeIvCBEg2PM/8fp0\nTrzmdUsh0WomOV5CO4KEfQQhIgR38qq/Pn9zkZxgITlB6vkIPsTzF4QIIGWThUgj4i8IEaAuB19u\nCsKZQsI+ghAB6hJ5u81Muj2WdCm8JpxmRPwFIQLU5eArikJuFym1IJx+JOwjCBFAQcI7QmQR8ReE\nCCChfSHSiPgLQgSQiV0h0oj4C0IEEO0XIo2IvyBEgHCVNQXhTCLiLwgRQLRfiDQi/oIQAfwx/8Z2\n6xKEpiJ5/oIQIX7Rp7100BIihoi/IESIGJPh5AcJwmlCnjkFQRDaICL+giAIbRARf0EQhDaIiL8g\nCEIbRMRfEAShDdJg8a+qqmL69OlMmDCB22+/neLi4rDHeb1ebr31Vt58880mGykIgiA0Lw0WhgaW\nIgAABoJJREFU/zfeeIOcnBxee+01Ro0axXPPPRf2uIULF+JwOKSAlSAIQhTSYPH/9ttvGTJkCACD\nBw/miy++qHXMxx9/jKqqDB48GE3Tmm6lIAiC0KzUu8hr+fLlvPrqq0HbUlJSsFqtAFitVhwOR9D+\nbdu28eGHH/LnP/+ZRYsWNbO5giAIQnNQr/hfe+21XHvttUHbpk+fTnl5OQDl5eUkJCQE7X///fc5\nfPgwN954IwcOHMBkMtGpUycuuuiiZjZdEARBaCyK1sC4zCuvvEJ5eTnTpk3jww8/ZP369Tz88MNh\nj120aBGpqamMHTu2WYwVBEEQmocGx/zHjRvH9u3bGT9+PMuXL2fatGkALF68mE8//bTZDRQEQRCa\nnwZ7/oIgCELLRxZ5CYIgtEFE/AVBENogIv6CIAhtEBF/QRCENkhEO3l5vV4eeeQRtm3bhslkYt68\neXTu3DmSJgVxzTXXYLPZAMjMzGTy5Mnk5+ejqio9evTg4Ycfjlj5iu+//56nnnqKJUuWsGfPnrB2\nLVu2jLfeeguj0cjUqVMZNmxYRO3csmULU6ZMISsrC4Dx48fzy1/+MqJ2ulwuZs2axcGDB3E6nUyd\nOpXs7OyoG89wdrZv357JkyfTpUsXIDrG0+Px8OCDD7J7924URWHu3LmYzeaoG89wdrpcrqgbTz9F\nRUWMHj2axYsXo6pq84ynFkE++eQTLT8/X9M0TduwYYM2derUSJoTRFVVlTZq1KigbZMnT9bWrVun\naZqmzZkzR1u1alUkTNNefPFFbeTIkdrYsWPrtOvIkSPayJEjNafTqTkcDm3kyJFadXV1RO1ctmyZ\n9vLLLwcdE2k733nnHe3xxx/XNE3TSkpKtKFDh2pTpkyJuvEMZ2c0jueqVau0WbNmaZqmaV999ZU2\nZcqUqBzPUDunTp0aleOpaZrmdDq1O+64Q7viiiu0nTt3NtvvPaJhn2+//ZbBgwcD0L9/f3744YdI\nmhPETz/9RGVlJZMmTeKmm25iw4YNbNmyhXPPPReAIUOGsHbt2ojYlpWVxaJFiwJ1k8LZtWnTJgYM\nGIDJZMJms5GVlcXWrVsjaucPP/zAZ599xsSJE5k9ezbl5eVs3LgxonaOGDGCO++8E/A9iRqNxqgc\nz3B2bt68OerG87LLLuPRRx8F4MCBAyQmJrJ58+aoG89QOxMSEqJyPAGefPJJxo0bR2pqKtB8v/eI\nin9ZWVkgrAJgMBjwer0RtOgEsbGxTJo0iZdeeom5c+dy3333Be2Pi4urVdfoTHH55ZdjMJxo/q3p\nlmr46y2VlZURHx8ftL2srCyidvbv358HHniApUuXkpmZyaJFiygvL4+onXFxcYHPvOuuu7j77ruD\nvoPRMp6hdt5zzz3k5eVF3XiC73ecn5/PvHnz+PWvfx21389QO6NxPN99912Sk5MD5XE0TWu28Yyo\n+NtstkCdIPB5NKoaHXPQXbp04aqrrgq8ttvtFBUVBfaHq2sUKfRjVlZWRkJCQq2xjQZ7hw8fTu/e\nvQOvf/zxx6iws6CggJtuuolRo0YxcuTIqB1PvZ1XXnll1I4nwIIFC/j444958MEHcTqdge3RNJ56\nOx966CEGDRoUdeP57rvvsnbtWm644QZ++ukn8vPzOXbsWGB/U8Yzoko7YMAAVq9eDcCGDRvIycmJ\npDlBvPvuuyxYsACAw4cPU15ezqBBg1i3bh0Aq1evZuDAgZE0MUBubm4tu/Ly8li/fj1OpxOHw8HO\nnTvp0aNHRO289dZb2bhxIwBr166lb9++Ebfz6NGj3HLLLdx///2MHj0aiM7xDGdnNI7ne++9xwsv\nvACAxWJBVVX69u0bdeMZaqeiKEyfPj3qxnPp0qUsWbKEJUuW0KtXL5544gkuuuiiZhnPiGb7DB8+\nnDVr1nD99dcDMH/+/EiaE8SYMWOYOXMmEyZMAHy22e12HnroIVwuF9nZ2YwYMSKiNvozjfLz82vZ\npSgKN954I+PHj8fr9TJjxgzMZnNE7Zw7dy5z587FaDSSlpbGo48+itVqjaidzz//PA6Hg2eeeYZn\nnnkGgNmzZzNv3ryoGs9wds6aNYv58+dH1XiOGDGC/Px8Jk6ciNvtZvbs2XTr1i3qvp/h7MzIyIi6\n72coiqI02+9davsIgiC0QaIjwC4IgiCcUUT8BUEQ2iAi/oIgCG0QEX9BEIQ2iIi/IAhCG0TEXxAE\noQ0i4i8IgtAGEfEXBEFog/x/kP1aQDVAUYgAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x3cab650>"
]
}
],
"prompt_number": 23
},
{
"cell_type": "heading",
"level": 4,
"metadata": {},
"source": [
"Observing the variation with $\\mu$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us quickly create an interactive widget to see how denoising would be affected by different values of $\\mu$. We will view this on a log scale."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def create_A(n, mu):\n",
" \"\"\"\n",
" Create the A matrix\n",
" \"\"\"\n",
" d1=np.eye(n-1,n)\n",
" d1=np.roll(d1,1)\n",
" a_second= np.sqrt(mu)*(d1+d2)\n",
" a_first=np.eye(n)\n",
" A=np.vstack((a_first,a_second))\n",
" return A\n",
"\n",
"def create_b(n):\n",
" b_2=np.zeros((n-1,1))\n",
" b=np.vstack((corr,b_2))\n",
" \n",
" return b\n",
"\n",
"def denoise(mu):\n",
" \"\"\"\n",
" Return denoised signal\n",
" \"\"\"\n",
" n = len(corr)\n",
" A = create_A(n, mu)\n",
" b = create_b(n)\n",
" return LA.lstsq(A,b)[0]\n",
"\n",
"def comparison_plot(mu):\n",
" fig, ax = plt.subplots(figsize=(4,3)) \n",
" ax.plot(corr,label='noisy',alpha=0.4)\n",
" ax.plot(denoise(np.power(10,mu)),'r',linewidth=2, label='denoised')\n",
" ax.plot(ex,'g',linewidth=2, label='original')\n",
" plt.title(r\"$\\mu=%d$\" % np.power(10,mu))\n",
" plt.legend()\n",
" return fig\n",
"\n",
"from ipywidgets import StaticInteract, RangeWidget\n",
"StaticInteract(comparison_plot, mu = RangeWidget(0,5,1)) "
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
" <script type=\"text/javascript\">\n",
" var mergeNodes = function(a, b) {\n",
" return [].slice.call(a).concat([].slice.call(b));\n",
" }; // http://stackoverflow.com/questions/914783/javascript-nodelist/17262552#17262552\n",
" function interactUpdate(div){\n",
" var outputs = div.getElementsByTagName(\"div\");\n",
" //var controls = div.getElementsByTagName(\"input\");\n",
" var controls = mergeNodes(div.getElementsByTagName(\"input\"), div.getElementsByTagName(\"select\"));\n",
" function nameCompare(a,b) {\n",
" return a.getAttribute(\"name\").localeCompare(b.getAttribute(\"name\"));\n",
" }\n",
" controls.sort(nameCompare);\n",
"\n",
" var value = \"\";\n",
" for(i=0; i<controls.length; i++){\n",
" if((controls[i].type == \"range\") || controls[i].checked){\n",
" value = value + controls[i].getAttribute(\"name\") + controls[i].value;\n",
" }\n",
" if(controls[i].type == \"select-one\"){\n",
" value = value + controls[i].getAttribute(\"name\") + controls[i][controls[i].selectedIndex].value;\n",
" }\n",
" }\n",
"\n",
" for(i=0; i<outputs.length; i++){\n",
" var name = outputs[i].getAttribute(\"name\");\n",
" if(name == value){\n",
" outputs[i].style.display = 'block';\n",
" } else if(name != \"controls\"){\n",
" outputs[i].style.display = 'none';\n",
" }\n",
" }\n",
" }\n",
" </script>\n",
" \n",
" <div>\n",
" \n",
" <div name=\"mu0\" style=\"display:block\">\n",
" <img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQ8AAADVCAYAAABJ/XXDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
"AAALEgAACxIB0t1+/AAAIABJREFUeJzsnXdgFMXbgJ/rl+TSe0IaSSghFOlIlyL8bKg0FVAU9bMr\n",
"KAIqiIqAYkFRbIhdRFEUFFEUpUpvoYSSBuk9ubtcru33xyaXHAkEQkJC2Oef7O7Mzs5udt+beect\n",
"MkEQBCQkJCQuEnlTd0BCQuLKRBIeEhIS9UISHhISEvVCEh4SEhL1QhIeEhIS9UISHhISEvVCEh4S\n",
"EhL1QhIeEhIS9UISHhKNztGjR1m4cGFTd0OigVE2dQckWjbLly9nz549uLu7N3VXJBoYaeQh0ahM\n",
"njyZIUOGNHU3JBoBaeQhcdGcPn2alStXnrO8c+fODB061LEvuU+1TCThIVEDm83GhAkT+PbbbwGY\n",
"NWsWDz74IBEREQCEhYUxbdq0C25PJpM1Sj8lmhZp2iJRg3379hESEgKIo4b9+/c7BEd9kEYeLRNp\n",
"5CFRg82bN9O/f38Ajhw5Qps2bZzKL3baIo08WiaS8JCowZYtW7jhhhsA+Oeff+jTpw9//fWXQ/F5\n",
"sdMWaeTRMpGmLRJOFBQUkJmZyd9//82///6Li4sLBQUFuLi41Ku9r776ilWrVrFjxw6WLFmCXq9v\n",
"4B5LNBUyKZKYRHV+/vlnkpKSeOqpp5q6KxLNnHpNW+x2Oy+++CLHjx9HpVIxb948wsPDHeUHDx5k\n",
"4cKFCIJAYGAgCxcuRK1WN1inJRqPQ4cOMWrUqKbuhsQVQL1GHn/88QcbN25k/vz5HDhwgA8//JD3\n",
"338fEOe3t956K++++y5hYWGsXLmS7t2707p16wbvvISERNNRr5HH3r17Hdr4zp07k5CQ4ChLTk7G\n",
"y8uL5cuXc+LECQYOHCgJDgmJFki9FKZ6vR6dTufYVygU2O12AAoLC9m3bx8TJkxg+fLlbN++nf/+\n",
"+++87UlqFwmJK496jTx0Oh0Gg8Gxb7fbkctFOeTl5UV4eLhjtNG/f38SEhLo3bv3OduTyWTk5pbW\n",
"pyv1wt/fXbqedL1md62mul59qdfIo2vXrmzatAmA/fv307ZtW0dZWFgYRqORtLQ0APbs2UNsbGy9\n",
"OyghIdE8qdfIY9iwYWzdupXx48cDMH/+fNauXYvRaGTs2LHMmzePadOmIQgCXbt2ZeDAgQ3aaQkJ\n",
"iaan2dh5tPShoXS9K/N6LfneKq9XXyQLUwkJiXohCQ8JCYl6IQkPCQmJeiEJDwkJiXohCY8moLC0\n",
"HKPJ2tTdkJC4JCThcZkRBIEDp/LYeSy7qbsicZkoKMjnjTdaXuoJSXhcZprHwrjE5cTHx5dp055t\n",
"6m40OFIkscuMQJX0EARBCtHXQJzKKCa3qKxB2/T3cjmvHcRvv61h+/atlJeXk5Fxhrvuupvo6Bje\n",
"fnsRcrkctVrDs88+VxHC4jk+/HA5H374Hvv378FqtTFo0HWMGnU79947gRUrfkImk/H6668THh7D\n",
"ddcNPed1mwuS8GhE8otN6FxVTseqjzy2H87i2vjgy9wriYbEYDDw5pvvcubMaaZPfxJXVzdmzHiB\n",
"mJhYtmz5l3fffYtHH33SUX/DhvW8++5H+Pr68ttva3Bz09GpUxf++28bPXv2ZvPmzXz44ZQmvKML\n",
"RxIejUSxvpxDyfnotCpahXg5jlcXHmarvQl61jKJDvEkOsTzsl5TJpMRGysGh/b3D8BsNlNWVkZM\n",
"jOjL1anTNXzwwRKnc2bPfpmlS9+hoCCf3r2vBeCmm0bxww/fIQgCffv2Ram8Mj5LSefRSBQbzADo\n",
"TRan42d7A+QUGjmSUoAgCFisNg4l5WM86xyJ5svZ004/Pz9OnToJwP79ewkLq0pZYbFY2LhxA3Pn\n",
"vso773zAunVryc7OolOnLqSnn2Ht2p8ZPXr0Ze3/pXBliLgrkHKLDQCl3Fk+n60wPZJaCEBEkDuZ\n",
"+UbyS0wYTBZ6xwXVeY207FJ8PbW4aVV11pVoHKoLD5lMzvTpz/PWW68hCAJKpZIZM15w6LZUKhUe\n",
"Hp488MA9aDQaevbsTWCg+H8ePnwE//zzF9HR0ZfVt+VSkIRHI2Eyi8JDq1Y4Ha+uMK2ODJBXvIhm\n",
"S93TmSJ9OUmZJSRnljCwS+ildVaiXowceaNjW6PR8P33PwOwZMlHNep+8MGnANxzzxTuuaemTsNm\n",
"s3PTTbc2Uk8bB2na0kjY7KKQUCich7XnW6pVVtS1CwKZ+YZzVwQsFfoSaeX3ymfevBfZvXsnw4eP\n",
"bOquXBTSyKORsNnEz9p+1iDiXMKj1GhxCASAxNNFeLqpca2YkgiCwLHUQnw8tAT6uEpCowXx3HMv\n",
"NnUX6oUkPBoJm92Oa1Y6tHKeUlROW9wy0lDpSylq0wGAo2mFNdrILixDqzZjtwt46jRkF5WRXVRG\n",
"oI+rZG0m0eRI05ZGInr5u9wwaShxi15wOi4IILNZue6JOxj26GhiVn/lKPNIPs7w+28iYM9WAFKz\n",
"S0k8XcSJ9GJM5ZIvjETzQhIejUS7z94BwH/XFqfjgiCgLilGW1wAwDXvz8Pn6IGK7VfxTD3JwJk1\n",
"FWqlZWcv+TZGryUkLhxJeDQGlmof+llfuQB4nTrmdGzIE+OJ+m0lAQd2OI7JbOJIw/PUMbyPJ1BY\n",
"Wg5UrchIskOiqZGER2Nw5rRjU6V3XrOX5eUxYFbNkUX3t+c47btlnEZp0DP8oVsZ+ugYynLyANCo\n",
"xKXfZhJ6VqIakyaNa5B2nnvumUs6f/r0p8jKymyQvpwPSWHaGKRVCQ+lyYhQkeNGEARUp06I28Ch\n",
"EDWHfcyc8QC7DHRmiMuFrpkw8r7/YdVoHe0E7PuP9P7DUSpEeW+3S8KjpTJv3usN0ErjO1xKwqOB\n",
"EQQBU+IJp2O27ByOFSgoMpTjbcpkyVD4uhOke5hrbUNlg+Gn4P49Jm5OFF+Da19+gjIff3a+twLa\n",
"+mOzC3gdP4w+NKLWNq42PO4cjWbDHw3aZvnQ4fDn+nOWm0wmXnrpBYqLiwgNbYXdbicp6SRvv70I\n",
"QRDw9PRk5szZJCYe4+uvv0CtVpGRkc6QIcOZNOleMjMzmD//JUe2xSeffAZ//67cfPP1/PLLen78\n",
"8Xt+//1X5HI57drF8eSTT5OdncXrr79KeXk5Go2G6dOfIyAgkGXLPmTbti34+vqRk3N5YsVIwqMB\n",
"sdntpOca8NrmnF7TnpNDYr6Vlaff5e/s77H1E4/7m5TE05rO+46jskNSXBuOq/M57JLPr23g1zbQ\n",
"OQsWr4OBqeBSkEvsJ29hGfgl+rXrGDZzCjmdesCGv5rgbiVWr/6BqKjW3H//Q6SlpfDMM0+ycOE8\n",
"Zs6cTWRkFGvX/szXX39Bjx69yM7O4osvVmA2mxk1agSTJt3Le++9zdixd9Kv3wBOnDjOggUv8/PP\n",
"P1Fp8b5u3RqmTZtJu3btWb36B2w2G++9t5jRo8fTu/e17N69kw8+WML48Xexd+9uli37kvLy8gab\n",
"PtWFJDwaCLtdYOeRHMqtNq4/tBsAi6sbKqOBVYmreerMUvTWYhSCnAkH4eFd0E7dmmPjH6TP+mkA\n",
"7Gk3Hu9Dh3HbvIpvOsKia+FAEAyaDA/tgjfXg+7kMdYnZNFr/Y8ABBzcRW6T3XXzoeSbHxqlXf/z\n",
"lKWlpdKnT18AwsMj8fT0IjU1mTfeWACA1WolLCwcgOjoaORyOVqtFo1GA0BqagpdunQFIDa2TY0R\n",
"w8yZc1ix4isyMtKJj++EIAgkJZ3kyy+X8/XXn4vTYJWK1NQU2rZtB4hm8u3axXE5VOqS8KgHgiBg\n",
"tQlYrHZcteIjNJltlFtteJ04jMfpJMw6DzK792aRyx8sSRFfpn753sw52YGh68Tl2+NPjKPML9DR\n",
"bn5cF2waLa1/X8VT/8FDu2HiBw/zc+r7LO0BO0Ph6z+KANAW5l/mu5Y4m8jI1hw6dID+/QeRnn6G\n",
"4uIiwsMjef75uQQGBrF//16Ki4sratfUQURERLF//96KkUcivr6+TuVr1qzm6adnolarmTr1MRIS\n",
"DhIREckdd0wkPr4TSUknOXIkgcjI1qxatRK73Y7NZuPEicRar9fQ1Et4iJGRXuT48eOoVCrmzZtH\n",
"eHh4jXovvPACXl5eTJs27ZI72pw4mV5Mep6oBO3eNgCdi8rhRRu6dQMAR4eP4KnobWx0AzUK3vjN\n",
"xiM7C5EhCo68uC7k3DmZVt6uHN31IHlxXSiObk9xZBtkgkDEhp9JGX4rY8NHMX5bHtN8VrMnxMx1\n",
"t+cz5/gGp2XdUqMZd1f1ZX4KEqNG3c78+S/x0EP3ERwcgoeHJ9OmzeCVV+Zgs9mQy+XMmPECubk5\n",
"Z7nui9uPPvokCxe+wooVX2G1WpkxY7ZTeXR0NI88MgVXVzf8/QPo0KEjAQGBLFq0ALO5nPLycp58\n",
"8hliY9vQr98A7r//bry9vfH09OJyUK90k3/88QcbN25k/vz5HDhwgA8//JD333/fqc6KFStYvXo1\n",
"PXv2ZOrUqXW22dxT+hlNVpKzSogN9WTb4SzH8fgoHwDKy8y4vDSHmJ+/pERhYdCsMA7aT+NngBWF\n",
"IxnyyTqn9g5NfpLiR54iyMeVfSfzznndnu0C2HksB725gM9+6MumSPA2K9m4zErnilHuqrUHaN8m\n",
"CH8vl3rf36XQkq/Xku+t8nr1pV52Hnv37qV///4AdO7cmYSEhBrlBw8eZNy4cS3GHuFYWiG5RWUk\n",
"Z5agUlQ9tow8AwnJBRh/+JG2P3xKqcLC8Ilw0H6aSPz47xPovzmlRnsWVx0AMnnVL1LnaL8a0bAq\n",
"HeN0ah9+/knHyBNQqLYyYgKkVPzAqEuLyGvg+J0SEnVRL+Gh1+vR6XSOfYVC4VhuysnJ4b333mP2\n",
"7NktRnBAlV2F1SagUcqJ+HM1nqeOUlBh+Rm4ZxtGFYy8C3aHQoRrK771mUl0IagTjwJwpm9VUFtl\n",
"mRGoshgFMfaHXH7uuapa48FPK2BwMmS5w/UTIM8VBj5zD2RmNPQtS0icl3rpPHQ6HQZDVbwJu92O\n",
"vCJi1vr16yksLOT+++8nLy8Pk8lEdHQ0o0aNOm+blzJ8qg8Xez3PzFJkSgUeHi4ErVlJu9dnUu7l\n",
"y95FnxDz8Vv47tzEmDHwXxiEF8GGhzbiuyfVuZF27bHu3YayzIg1tg1eXq4E+Lvjnl4CQFioF2SX\n",
"4l5kcuqnu040FpMr5Ghs8NMKGHCfnIMBdm4bB399nkzcgll4/LsBdYUFanN/nlfS9VryvV0K9RIe\n",
"Xbt2ZePGjYwcOZL9+/fTtm1bR9nEiROZOHEiAD/99BNJSUl1Cg5o/jqP0lITpUYzajlE/PgNAJqi\n",
"fPpMEaM/zRgKP8aBu1XFYuN4PAigWFeCd7U28kbewr6ho/E7vJczXQcQXGQkT62gVC8Ki7w8PYWF\n",
"Rsc+iM8lLswTs8WGNvMMAJ7l8Pjg35h1cDSbI/TMHAqL/viHQ0dOExTie1XM0yWdR8Ndr77Ua9oy\n",
"bNgw1Go148ePZ8GCBcycOZO1a9eycuXKGnVbSl6Sytuw2uxo85zX47+Nh4X9QGGHJzp9gGX0LPG+\n",
"q61AlfkGUBgWjck3gDMDRoBMhkwmQ6tWoFbKCfPXcS5cNEo8dRrHvsnTBw/PCGb2+AilIOONa+GH\n",
"ONDs/O+cbUhINDT1GnnIZDLmzp3rdCwqKqpGvVtvvbJiMp4PWcXymcViw6WganUk0RceuEncftRj\n",
"Cp28rnWUVQ+hb1Nr8PN0Ia+4alQBIJfLnHK3VJe17SO8neqaPb1RFxeS3V00TOoc2IcJUTP4LGU+\n",
"990Mf+77A8XwYeQm5+PnpmoxgluieSJ51V4ARpMFe4XyV1aQj9wqutwbVTBmLOg1cK3f/7jx2plO\n",
"5ykUMo6NuReA5IenE+TjWue1Ar1d8fd0oUuMH4HezvV3vfEZJ28cz75Hngeg3GxnZPBEBlrbU6KF\n",
"qeo17E7MJi2rtIaQKjWa2XciF5NZCip0udixYzu//PLTOcvXrVvLli2bLrrdm2++/lK61WBIFqZ1\n",
"YLbY2Hksx7GvrGZC/MQIOBQI4bIApnV4lVB/HYX6gqq6CjkJ9zxB7qjxqDvEXdD15HIZHSpsR86m\n",
"KDaOjMdF1/2YEE+SM0uQyWS8EPQEh1P/j63eebTN+pYx7vc5xUMFSEguoNxi43SOnthWl8eI6Gqn\n",
"V68+5y2vHn39YmguA0pJeNTB2VndtAWiJ8l3Pb34pFsRWgssGfQBvTu0BiDMX+dY8QAQVGoMUbG4\n",
"Ki79P1658h3o5UKrAB2nMkTT58C2XfnwPbh9HHyVuoh+ocMo1QeQX2KiY2vR5NlacR/y5vLmNTB3\n",
"rh3NhrSG9aodGj6cPyef26vWarXy6qtzycxMx2azM27cnfz00w/4+PhSUlLM0KHXc+bMaf7v/x7l\n",
"s88+YdOmf/Dy8qa83MSUKf/H3r278fX1IyIikq+++hy1WkV2diaDBg1l0qR7SUo6yZIlb2Oz2Sku\n",
"LuLpp2cQH9+pQe/xUpCEx0WiKcon1xUeHSraaTx/LIL2UwY4yqNDa095WNtH66K5uMdfGTy5UpfR\n",
"OcaP7AIjfsEBxJ1QcedBC990MvH+sTk8E/s++SVVUxdbheRRKqSZakPx88+r8Pb2YfbslzEajdx7\n",
"712o1WrGjbuT/v0HsW7dWgBOnDjOjh3bWLbsS8xmM3ffPR5wXkyo9Lr18FDTr18/Jk26l+TkZB59\n",
"9Elat47hzz9/59df10jC40rE+9hB4r94l9KgUB66EfLUZjp49CLmvo8d+VbOh+2s4D3+ni6E+rtd\n",
"XCcqmqh857x0GrwqVmGyr+nNm+s3s6aDmt15/7DD9096+w53ZCurRHEeI7QrmW9ubByv2vORmppC\n",
"9+69AHB1dSUyMopdu3YQHh7pVC8tLYX27Tsgk8nQaDS0bdu+RluVXrcuLi4Or1s/P38++2wZGo0G\n",
"o9GAm9u5V+SaAulnqA4qFaW9FzxD0O4t7E75jlVx4GZX8VDMPORKVY2UktXRVkxhzh54BHq7XPQU\n",
"QnAIj5rnJY8YTaABXtgveul+lvwqZTZDDd1HC521NAkREVEcOLAPAKPRQFLSKUJCQmv8f6KiWnP0\n",
"6BEEQcBsNld4vZ5NzX/M4sWLuO++B3nuuRdp3Tqm2VlsSyOPOqj8f6mLC8Xpyv/E/edt/yNAK+Zk\n",
"OTsrXHU6x/hRarbj6+b8qOvzGjhWfGq5nCFI7MvUtaf5IRB2tsrmxzMf0D9uobMOpnm9f1c0t9xy\n",
"GwsXvsLDD0+hvLycyZPvd0xVKpHJZLRuHUOfPn154IF78PLyQqlUOpbxKwVNbV63118/khdeeJaA\n",
"gEDatYsjPz/PqbypkYRHHVT6tOhDI3gmLoECVxiSBOM6DGN3RZ3zTQVcNErCW9W0GryUXxFZLS+P\n",
"f7xo5asQYMlv0PMB+C39c+5KvYe+MfFV9yNJjwZDqVTWyPZWfQWlcruwsBB3dw8+/vhzzGYzkyaN\n",
"IzAwiHvvfcBR95prujm2f/75dwDGjbuLcePuqnHdyvKmRhIetVBQYkKjVuCmVTk+8s3BZXzeBTRW\n",
"WLoWZAP8HPUvxhjLVaPEWG51REG/GM438ghtF45NrUFhLqdHBtx5EL7pZGHx/ldwY0lFA3Zp5NEE\n",
"eHl5cfToYX777RdAxk03jSIgILDO85o7kvA4C0EQOJgkRuka1CUUu8VKm+WLGNfxFACzNkNsAST7\n",
"1m6LURfXxPpRbDA7mZtfeOcq/tYmq2Qy7Co1CrPo5Tv/L/ixPWwt+J39ubu5ae1/tFvxESff+wJu\n",
"HF6vvkvUD5lMxqxZc+queIVxVSlMrTZ7ndOF6sUZeQZKf1jNzxnLSPSDtnnwbEUCOHtwSL36oFIq\n",
"8PN0qde5lV07l6I1e0CVUAgvhqcqXF2+Ofw88cvfRlVmxP2/LbWeKyFxsVw1wsNuF9hyKJP954na\n",
"Bc46geNnijhTcopXxbhHfLAWtrz5LZtf+QAhIBAvnYYQ34tcbr0E6tJXJD41h5M33eHYn7EFAvRw\n",
"2H6Sn8X4uMgr4ohISFwqV43wsNrEJctiQ+25Uio52x5jiWIN5UqYeAAGpUBB+y5k9RyITC6jS4wf\n",
"bcIun6l3+3DRUe5cPjJ2nY59j82mKK4zAB7l8HyF68TswWJiKUVJca3nWqx2ivXlDd9piRbLVSM8\n",
"LoSEpHy2V4tPmlC8g43a47iaYcEG0a2+kqYw8w70cWVQl9BzWqZWrvrseX0Zex8Vnefu3wutikUf\n",
"nO/jQFFSVOu5e4/nsu9kHkaT5DgncWFcNQrTC1lkyKtmzm0XbHyeLKZMmLkFPF1D2ffgdEd5c/QR\n",
"cdUqyS8Bi7cvp26+C7O7F665mdzeysDi0g+YMxiGbC9CEERD9+r3UFbhbVtusTnSSUhInI+r5i25\n",
"WLuKjTk/kmo8RlgxTNsGu+c8T1avQY7y5mjm7e6icto/PfgGAHrZLQTv/IlEv2x+9EmjXWoh2RUB\n",
"k3vHBaJVV70Gzc2KUaL5ctVMWy7mmzBa9axIWwzAa3+CixVKImOd6pzHIr3J8PNyqVWBq5SrGO97\n",
"NwAL4nPIKKwyWMstco77IRmRSVwozfATaBwu5hf1p/QPKbbk0/uMjHEJsO7T3zAGhjrVaY5RuuQy\n",
"GW3CvGo46gX7uHJt8Chi8yHZ08bW3F8dZWc/F0l2SFwoV43wsF/gR5FtOs2vGZ8DsHidgE3rir5V\n",
"zRCL50uR0PQ4961NmBd9erbjmZ2iYdpvRxYS9fNXIAg1hIU0bZG4UK4a4VH9oxAEocZHYrcLyCxm\n",
"vjkxD6tg4Y5EF3qmg8nL2ZLUx12LjOapMK2kuqOeWilHJpOhUikY5D6UsGJIUheS9vc8/A7tdsQI\n",
"qUSSHRIXylUkPKq2N+9PZ1tCllO51WZHWHov20v/xdUMr/0qKhTLPZ2FR6doXwZ0rp916eWia9sA\n",
"vHQa+nQIok+HIECcZiXfPoWpu8UcMPP6w6CnJ6HKSHc6V9J5SFwoV5HwqPoojCYrFptznItys4X5\n",
"oXsAeHYrtCqpOO5V04elOeo7quOp09Alxg+NSuHU1+LodgQ8vRFfqwt7Q2B9DAQuX+p0rv1C53cS\n",
"DYbFar8iA1NfNcLDbrNzzTtzifhzda3lq3a+x75g0aDq6W1Vx2sTHlcyKhcv7taIPjCv9gdFsbPR\n",
"2NkWthKNz/bDWfx3JLvuis2Mq0Z4aPfsIGbtCnq+PhMq8uoeTSlAEAT05lJeT3wbgIUbwNVSdZ6t\n",
"VTixoZ50beNPr/ZXvhs1wO3D5uJlgs0RsE+/36lMmrZcfiqf+ZWmrL5qhAfmKonQZ8qthGzdQHZR\n",
"GfklJhbvfZNcezG9T8Mdh5xPKx57F6H+Ojxc1RcdsLi54ucfytBwMZ/Me+GpFBboUelL8D6eUClX\n",
"JZqAK01wXzXCQ15S4tj2PHaQvnMfQ2nQczjrJB8cEIPlvLW+apEzvc8QNiz5HltQcC2tXZnEhnoS\n",
"E+qJQiFjePhkNFZYGyuwZf33DH7qLoY+Oga33VLKyqbiYgW30WTln/3p5BSKntKHkwtITCtshJ7V\n",
"Tr2Eh91uZ/bs2YwfP56JEyeSlpbmVL527VrGjh3LHXfcwZw5c5rFcKw4I6fGsaj1q1hy+FXKbeWM\n",
"PeFG7zNVZQVt4ylsE9+sl2QvllB/Ha38dchlMrzUftyWFYIgg51/PoFn6kkAvP45d54SicblYr+T\n",
"9Dw9ACfOiJ7SucVlZBZcvpAL9RIeGzZswGKxsGLFCp5++mkWLFjgKDOZTCxevJgvv/ySb7/9Fr1e\n",
"z8aNGxusw/WhsLQcS4EokZNG3E5hp+4A6H9bwL9Zv6KVqVm0xoDZvSrniqC4+DCBVxq3u4hJdj/v\n",
"DLkVXv7ysrIm7NHVjb0W+6PzUZmQTKVsmglEva66d+9e+vcXI+R07tyZhIQER5lGo+G7775z5J6w\n",
"Wq1otdoG6Gr9sVhtqPSiP4c9MBhzUAh2GTw5Qix/qKgLYSWQMvQWNr36CWkDR5J0wzigKg5IS8JV\n",
"o0Quk2G/8QkGGiIxqeD9HmKZTAoW1GSkZpWy/r9UysovbNnWYmla4VEvDaBer0enq0pAo1AosNvt\n",
"yOWiNaOPj7i8+eWXX1JWVsa11157rqYc+Pu716crF4RFJsNsEX9R/VuHoEhL5MtOsCcEQktg6iHx\n",
"2kKPHhgHDeHIoCF0ifTBUGYhOtQTbQMoShvz/upzvdsDPdhyIJ1RHZ7k35QnWdITpm8FF30xXvXo\n",
"a3O7v+Z+LZtdcHhmu+vEH1e9WRQGdoXigq6pTS/BXSbD38cVf393RzvVzz14Mhe5TEZ8tN+5mqk3\n",
"9foqdDodBoPBsV8pOKrvv/7666SmpvLuu+9eUJtnpyZoSAoKjLgVitMWvUKLpXMcMxV/AmKQn9AE\n",
"cVrl160jB/Wil6mhtIwAb1dKS8q41J75+9dMvdCYXOj1vF2UhAQNo9s2UZB+2RnuyMi46L421/tr\n",
"rteyWO1sTcgk2MeVtuHelOqrPJvddVry8/XYzBZ0Lqrz6tzyCwxYbHZ0ajnZOSWOdqr3NzFZDOYd\n",
"6FF7wO1LEYz1Gu907dqVTZvE+Hb79++nbdu2TuWzZ8/GbDbz3nvvOaYvTYkgCPgeEe0Z7J6eLOhr\n",
"J9MduuVqufMQyCrU3EJsldt9c7cibQgCvF0Z2KUVjx8Wwxu+0QcUxQVN3KuWj75MNBs4l3Izp7CM\n",
"vcdzScooqbW8kuoGfdUtgy/XAkW9Rh7Dhg1j69atjB8vJuydP38+a9euxWg0Eh8fz6pVq+jevTuT\n",
"Jk0C4O6772bo0KEN1+uLRLtzOx5nkgE45S3w6dEPAZhROAi5ICbQMQaGIujcAfEfdhXIDkD0Dh5h\n",
"jye8aDPH/eAP/3z6NnWnWjh1uQDoTaJwyS0sIzrEA5PZVquNUaVdiF1w9t0ShMvz/tZLeMhkMubO\n",
"net0LCqqym396NGjl9ari6TUaCYjz0BsK69aXeVVKUkA5LftxCumVVjsZgb430JMVntAFB6l7Ts6\n",
"DcNa0hJtXaROn8cj747k2QEG3upppa/RCK61B1mWuHRswgWOEmTiMmxGvgF3FzWuGgXtI2u6SwiC\n",
"4GRgZhfmrvtYAAAgAElEQVQE5JchJWWLMBLbdyKPzAIj2YW1DwOVWZkArO4Xxl9n1uGm1HFXxFQM\n",
"Qa0cdco6dLosfW2OmMMjCXrmXzzKZWyKhIPJm5u6Sy0aW7UVvG0JWXRd/CLXPTYOmdXiVE8GZOSL\n",
"usXSMjPZRWWOANV2QcA9LYm2332MOjPdaTRTud3YFqstQng4hm/nGA6qsjOxymF+8E4AHuo8FW91\n",
"AKWhEY46JTeMqrXNqwG5TIaLwo1JJ8U0EksPf4S+zHJFenpeCVR/Ty02O9G/fodv4kF8EhPOc5ZI\n",
"QUWQbpvNzogpN9Bp2ZuEL1/iNG2p63toKFqE8KgLVXYmH3SHU8pcwnSR3NPhIQBKI2I48MB0Nr+8\n",
"FEVMtNM5V5HsQFbxFtxzOgK5HVbn/c0fBw/x35FsyUW/ARAEgf8OZ3EsVVzxs9qqnqnMUpVHSGES\n",
"R85+h3Zz+4h4Wv3+o6PM9/A+AvZuo9xiA8BWXKVMVRfkcSZXT8dPFtH+66UOM/ezA2A1NFeF8Cgt\n",
"OsPsweL2rB4voVZWrQAdHz2ZrF6DcFE7W5RebSMPgABVIKOPgA0bv2d9DYDZamvKrrUIBAFMFhtZ\n",
"FdNqazUnFk21PDraQnFZNWzjr8jtNkL++Q0Amc3KgJlTGDjjPlx2VMSLqOYSIteXkpd0hnYrlxH/\n",
"+TvYrRVTm2r2jY3xOl8VwmNu+zQKXaCza3eGhI3EVSumKKieqb5Smx3oLSoKz05j0JKpFB4lkbGO\n",
"/LZ/ZXyDyWZ0mEBL1J+zf4hs1UYeHT99y7Hdet33dH98Aq22iDZInifEhQeP1FMoK0YlAau/BUB+\n",
"ukp4KEpLccmrFhmvsKDGdRvjx7DFC4//Uv5heXw5aitMjn0RgBA/N9qHe9Mp2tdRT6kQH0W7cC+u\n",
"7RDkEDBXA5ULSxm9B9H7DPQ5DaWCgc3pKzFbbJLu4xIwmCzkFlX5C9ntAkJBAdc9Po5OH71GZLXg\n",
"VP6HduO3eyvaInEEoi3IRZufg/fxKl2Ia7LowKg4c9pxTKkvwTWnSngockQnUHsjT1taRoCKc2C2\n",
"mZm+6SkApu3TETIgWgx0LJMR6ONaq9+KTCZDrWr5TnHVqVzeLoqJ4/CER3hq+3tsD4N/DizkRr/b\n",
"KXd1p0uMH166pjf4u5IwmqzsOubszV1usRH22fv4HjuI77GDNc4p0sLqdrApAvYFQcbh/2FWGfB+\n",
"AiKLoGfmMfpnbKfHmaqRh7q0mH5zHnbsy/LEZO5OStRGGEA2G+EhCAJmix2NuvYP12K1cygpn6hg\n",
"D7zdL+wl/uDAexzTnyK6AB5Obc12QFdtOqJUyIkMckd3FY0yasNh0yKTcWTSo/ROPEBE0RZO+MKx\n",
"PR8T1X8qRfpySXhcJDuP1QwtaDLb8Dl5rMbxI/6woB981wHMTl+lAZRQ5ALJ3rAxysrC1dcT6ePK\n",
"rK5wz35Q68+yRM3Nodxiw24XaP/VewgKJfaXZjfszdGMpi2HkwvYfiTrnB6FmfkGSoxmDpzKu6D2\n",
"0kpSeX3nfACWrgWlXygDOoXUGFVEBnng5+VyaZ2/wjk7SZTFL4jHd4jbq0xrAVA0xxR5VyAWqw1t\n",
"doZjP98FHrxZTvzDom+RRQHXJcGs7D5sXQZpb0LeQjj+Dvzwi46p28BP8CTF1cgDN0OHR8RRSnXy\n",
"TqSy/XAW1oJC4r9YQsflbyNYGn7q2WzeiMok04YyS63lF6PwOZ1TyuMbHqPcbuLWdH+GJYGxTbtm\n",
"nqip6fDzciHI2xV3FzUAx+6byj2HlLiXw063TJL1R5DLxPAE/+5PJyXr/D4XEhU6Bru9huGXxWpH\n",
"VSwu2W5oLX78H3W1oxDg/3bBqcXw2Kgd3NR3DteehrAS8C2D2ALoHXQ9b/wBWS8V8+0P0CYPTvjC\n",
"wMkwbTiYVeKQRVtQMW05darqwmcFum4Imo3wqOTsqZldECgxmB3zt/N9/oIAJQYzH+1bxrasf3CX\n",
"u/P+t7lYNS6cuX1SY3X5ikcuk9Euwpsusb5cE+OHT3QY299bx317xfJ1aZ9gswuUGi0IQErW5fOg\n",
"vVIxW+0MfHYyo27tSciWP4lc9wM3j+6DetcOlEX5PH8dDJ8I2Tpo796NP7b3YumvEFUEFp0Hmo5x\n",
"2OVVo+Tk62+jvF0HABQCjE+AQ0th5h4PlDZ481oY+Ign+S7gfiYZbV42spRkx/myooYPT9jshMfZ\n",
"WuGk9BL2nsglp1DUWJ/P27XcamPr+jV8c3QOAK8kxBCkh/S+QzG6Xt54E1ciCrkczwq9hjEwhMd3\n",
"gNwOW/PXUbptrTRyuwisRcUEHNiJstxE98Vz6PHWC2hKivB/80XGjYF5A0AmwNyNMCf+c1q5tXE6\n",
"PzjQwyntx+5p8zDHO7tQnBr7II/ndGXj5xCoh/+88hk4GeQHN/C/u4fjufEPR11ZUXGD32MzFB7O\n",
"+5X+KmUVy4W1yY6QbX8xaNpEincd4LO9j1CqFrjtCDy2ch8AiWMmX3CuWokK5HK8fdpy6zFxHv7D\n",
"yeVOxUX68mYRm7a5IktMdGxrKqYpRVq4vdsBVsWBpwn+/BKmmAYhlynI6iYGzBJkMnq0C0Ahl3N0\n",
"+isIMhkZvUULR+u1fflv5iIOTX6KH9YdImHyk+T17Ee/NNj9EYSrwjkcAP0nQ7bWTNC6nxx9kBc1\n",
"fKiFZrPaUsk5X0hBwP/ATvRt48kpKkOrVuDhKs7R+774KAAnP7qRjTeArxHe/1Wc4uTFdcEe35m2\n",
"YZ61tytRg8qwdocnPsrUTx9jVRx8o9nLA5aqAFD7T+YRE+JJep6BHh0Vze9XqImRJTqvqJRo4PoJ\n",
"sLOVGL3u96/AL6wvO6e+DEBWr0HsePY1zJ260K5i9a9s2Eh+bfUXZg/R50itUnJ68A1O7abfNgGK\n",
"i8nu1pe5EUEs+W0Qe0JgxATYtBy8KuIMyYuKEQQBq82OStkwpgjN7n9eGSjFWGFcI7OY8Tx1lMjf\n",
"VzFo+j10WzidIykF7D2e63Te/iCYer24/fqxdgRWvOdCVGu6tfV3CBqJugn1dyM8wJ2MvkOx3v8+\n",
"Pc9AodLMJ3u/cKp3MqOYMrOVfYk1I9Nf7ahOHnds69Uw8i5RcISVubB6Rzfyp33K5vmfUO5dFR4w\n",
"bchNGKKqAlJp1QrKAoKxacXVQI2qls9VpeLohIcpaN8ZL/dgvt8YSbtcOBQI/V9oz4kBQwCQFxeS\n",
"klXK1oQsSozmmu3Ug2YnPNLzDBSWlrPzWA6HUwqI+Wopwx+6jR5vvQBA8La/a5xTqoaxY8T18fv3\n",
"qxk6ep6jzBLSqkZ9ifOjkMtpHeIBQFlgKFO3i8d/SFlGwH9/o83Pqagn6UDOhfrkCQDKvDy4bRxs\n",
"C4dQk5aZ/daQPOcrcq7pU2cbZ9s8uWpVxEV40ycuqEZdb52Gnu0DSJj7GTM6f0aANpgEy1GmdzuN\n",
"gKgwPZ0jpmrILWyYCPnNTniAOJ+upMNX75+zXl5xGYIg8NCN4pJVpyyYzY1Y+/ajzMcfgLL4zo3e\n",
"35aKp5saY2Aotx+FsGLINKWg//IRRt4jhp1XXuW2H6VG8zmj62uTTyAA/zfWnT+jIUAPq5KH0jE4\n",
"ttb6taGuNr1QVDovers6CRVLtfQLSoUck18grpG9+Oi6b3BRurDa8zhLe4CisMDhv3Wh0dnrotn8\n",
"91uv+ZahD9+Ga3a6Qyl69hp5JUqjOCdJSC7gk4Mf8HUncDPDdz8AI29FpVHz+7Jf2fzyUvRDRlym\n",
"O2h5dGztS6cukdh1Xg6jsTf7gLK8DG1eNgrF1TvyKDWa2XM8l4TkWhSRZjMu6Wm81he+CElHa4Ff\n",
"voUIdTAKhfMn5+WmQaWQE+rnVqMZdbVpyrUdnUcbfeKCuLZDkGMhQeeiclqJ7BjQkbcGi5kQnxgB\n",
"e0sT0FYIHZO5YTylm43w6PbuS3ifPMoNE4eiOi5qqnUZabXW1Z1JAWB/4RZe2DYTgE9+gWijG+aB\n",
"g1Gr5Fjd3MnqNQhFAymHrkaUCjkermrKgkKZslcU0H+3hgOB0PnDhY3jMHGFUBnRq/oo2UFqCr/E\n",
"2pgxTNz96kfolQ52nXuNqZ6Hm5q+HYPx9aiZ28hNqyIi0J3O0X41LHw1agVqlQI/T/G8QB/nsJEa\n",
"lYLbYscw2WcUVgU80Ho3Rqton2NroKXHZiM8rJoqE3HPDesAcM3JrLWu77H9nDGe5O3jU7ELdp7/\n",
"VzSa2TbnXRSuLk4SWLJNuHRMQaF4mXAYjb3VB8L/XUfA3781bceaKccO/svdFYHpZniM5/aKkL52\n",
"d48aQqJSmJzLfqkuX672Ed706RDkFF4CqlbMnuw6m64ZkKKzsHzd3dw4fgAeiYdqa+qiaT7Cw6VK\n",
"cmpPiZpq11xReOTGdyOj1yBO3nwnAMZTW3n5yH0YbaUM1/Vh7j9QGBNHzjV9agwLLVI8ikvGHBoG\n",
"wOM7RMOmbzpCpg7ckk8QtOMfVCUNb/p8pWK0GHkw8zVKtHBzaQRTuj7tKLO7uuHhpnZSeFYKj/r+\n",
"xinkcifBERfpQ0yIp0MYaYNa8dlaNVoL/Kjax7rAXPo+dkf9LnYWzUN4CALq0ioLONdkUVPtkivG\n",
"KMjt1IOtLy8le+StpLvDpDYbKTTnEOfRg9mpg5ALUBIhhhGsdPJqF+6NUi7H17NpU122BAqHjMTs\n",
"5k50IYyqMBp7vwe0W/Ex/V94iGtmPNjUXbzsnD3015dZ2LjvDI//+QRH5dm0yYPFLnchhIU76qgK\n",
"RPMCjVrh8FDWuYo2HbIGGiEHeLnQKqAqm6OHTk2YNorXxPhCPHQDlMjLGyS0WLMQHkJJCXJblQZY\n",
"l5aE56ljtPlRtCsw+gcDkKQz0/9e0TW5Rzq87DKVkAr9SEGbjkCV92eQjyv9OgXXGM5JXDzGbr34\n",
"ZeUW1i37jUGdRR3T0h5QjqjQ9tm/sym71yQIBfn0e+4BQreIJuDZBUY25qzil5TvcLHJ+WEleER3\n",
"QKaQkzj6XmwqNcU33uY4Pz7Kh87RVTFSNBW6uXOFpKgvCrkcY0w7HtkF/VMhRwczhoIsO6vuk+ug\n",
"WQgPe54YOaksKASzty8KcznDH7oVlVFclzYEt+Jk6SEeS32UZG/ong7rvoLbHroDr5PihLIwNq7J\n",
"+t/SUShkCCo1+rAogrpNpKMmhnxX0YW8EuEqUp7aBQG3t14neNdmrn3pCQBO65NZnvwqAIs3e9Mx\n",
"B4iOQS6TcXDKNH76ZQ+W8EhHG0qF3EmXoVEruCbWn76dQhq8v+Vt45AL8OEaUNngo+7w36FfL7nd\n",
"ZiI8RBdiq4cXplbhTmUC8F3AKeYkTKDYWsiIE7Dxc9FNGcD7lCg8jIGhl7PLVxXV9UYymYx7I0UP\n",
"5bd6g71itG3PzW+KrjUJadmluGaecezbLGZe3jeVcnsZA3xv4L7N4hTcFhEpBlqSyxEUyjqzuHm6\n",
"qRslip1hwGAEmYz2eTBji3js6aTXMdsuzdK0XsLDbrcze/Zsxo8fz8SJE0lLc15S/fvvvxk9ejTj\n",
"x4/n+++/r7M9IV988aye3pjDIh3H0zzhf1N0LE17FYtg5s629/DLt6A7654FuRyTT8NnAZcQCfXT\n",
"OWJ9AIzoeBehJXDMH9ZXZKzI3d0wGvwrgdL8UrxPHHHsv/3HbA4V7MZbHcAjrpOR26yYAoLBxcVp\n",
"abap8h/b4zuy8Y0vOfDAdMb4TCAmHxJtmby54626Tz4P9RIeGzZswGKxsGLFCp5++mkWLFjgKLNY\n",
"LCxYsIDly5fz5Zdf8t1335Gff/5fJSG3YuTh6Y01Iop0dzG4SftH4PdWenQqHe8P/Zi3h7yDqpbR\n",
"scnbjyB/D9qFe9fndiTqwFWrpFtbf8e+i4cX48p7AaLRGEDZ4aOOhEQtHb91PzlWAhMC4M0UMffx\n",
"p6ss9Fj5DQCmMDG8V3VDuqYa5mtUCvLju3F89GSSxj/MO3+JK5tLD7xxSe3W63727t1L//79Aejc\n",
"uTMJCVXRnU+dOkV4eDju7u6oVCq6devGrl27ztvevtyDrI+Gt2LOMCZ4LeFPicFNjGro7TuCrXfs\n",
"ZnSbcQAUtBUVowWxHRznmwOCaRvuTZCPlF/1cqCQy4m/YTEamZYN0XAoAHTpKQ1mfNQc0ZdZKDaI\n",
"Q16PY+IoK7NDZybdChaZjXuOuTNqTyFR68VETeZwMXezsrrpQBOZHHm5a3BRi6bpZk9vWseN49aj\n",
"UCZcmrCvl/DQ6/XodFXLQQqFAnuFwkyv1+PuXhV4x83NjdLS80ee6mNYxIiJMD9oP1vsx1HaYfRh\n",
"+OOfjkxt+xbBuiol0qZXP+bfBcs4eP8zjmPlQcH1uQ2Ji6QyULJCIUOn9GRw4O2AaDTmfialxSYH\n",
"Lyu3sjsxh30ncik323BPElf4Xr07in3BEFkI7/zo/I5bIqNqtNNUz0cuk9G1TdXIMbtrXxavg4HZ\n",
"lxYgq17xPHQ6HQZDVWwHu92OvGKJ1N3d3anMYDDg6Xn+WBqdLH74nc4jMqoXvfuOZ/TNT+FtgvTr\n",
"o8ls5Y2/f9VNaoMDKQsORGGsuobpumGE+1/cg/C/yPqXSku43g0DojGV2/By1+CeXMiYmCmsz/qG\n",
"rzsKvLT0X3xMxfjH+NfdUANwOZ+nm7sWd51oL6Rx1eCRcoI9wbC0bA0An60G97P0cK4d2+Nd0cfK\n",
"c/38dPh61h1su7HubUywJxarjXR/BWGzYMPndji332md1Et4dO3alY0bNzJy5Ej2799P27ZtHWWt\n",
"W7cmNTWV4uJiXFxc2LVrF/fdd99529txfCja71eQOu8OZO0m4m0Sc63kDr+JMB8XcnOrpHqpvnKo\n",
"pSBl6C14phzn9ICRuOReeFxNf393pzYbm5Z2vVyTmVK9CXeCuK7VCP46s47FXU1M+O5nhID7G/0X\n",
"9nI+T39/d7KyS7CfOIFn8nHSlSNwN5Uy6W4ZNsHGlFbjGZi6osZ5xbEdsFb0sfKdLSgwYK8jgdbl\n",
"uDe30CDK/QLQ5F1aHJZ6CY9hw4axdetWxo8fD8D8+fNZu3YtRqORsWPHMmPGDO677z7sdjujR48m\n",
"ICDg/A0WVKTH8/ZBo1Tw78JPURcXYh807Ly+Kbumi4raUPeaHokSjUt8lA9ymYxHvKfy15l1LO0B\n",
"N2WexJKtJyKoZcWLtVjtXPf4eLTFBZwoe4XZg+GIv0CMVywzhr3J0XHuBO7bjk2twT9hDwCKyIga\n",
"7TSnSZ05MKRphIdMJmPu3LlOx6KiquZ4gwcPZvDgwRfeXoG4GiP4+KBUyByBUlqd5xdMIZc5FHRq\n",
"yXP2suNXMfzu6dKdfpZotqhPsUKxiTvNVixWG2XlNjzcrtzobRl5Bk6mF3ND/2g0+/agLRZ/4FL+\n",
"ep9FN4iBod8d8gHuWjf+vW8qCYB3fhZ9HxnLqRvH46+q+Wk1J32yxb+OH/QLoFkYiakOHhA3AgKc\n",
"1sJl5+ldbCsvx7bkv9J0qFUKngufCMBX/onorSXsScxlb4Vy8Url+Jki7IJAdoERdaJoiGhQwUPX\n",
"ZiDI4ImUCLoF9kAmkxEWoCMi0B3fjm1Zu2ITRyc8XOuI2daMrHCtfi1EeFT6tdgjIp2P1zF3bh3s\n",
"QaCXi1MKSYnLT992w7kuCUpVNlYnLMFkEYWGwWRplOzslxOrzY6iIon09GFwykeMWPdkUTdHnegQ\n",
"T6KCPZyC91Sncpm0oQIPNwQW/8BLbqNZCA+AlKE3OwL3VDoL+dQSIKUSQRAID3SnfaTPOetIXCba\n",
"t+OFTeLmd2mfU2YTV8IOJuVzNLXuZEPnCuXXlFT+cNnsAsqcbP5sDe/3FH1DvvgJlD41P75z6eeu\n",
"ifWjQ6QPns1oGmdrKdOWo0/MJmHyUw5T3g6RPvSJC2pWD1vi3CjcdXhf9xR906BIbuL3zK8dZblF\n",
"5w+2m5ZdypZDmZQYGiaid30xma2cSi92CLLKd9FmEzAVpnPvLWK9Of9A52ywBNa0Lar0S9Ge5Z+i\n",
"Vinwb2b5kMtj29ZdqQ6ahfBIHTeZMv8ghzWeSilvcNdkicZDLpdR0rotc/4R93/J+BSDVcxnW1eQ\n",
"5NRscVmyLiHT2BxNLeR0rt4RYbxSeFjtduZEHOCMJ3Qx+fPsVrG+vk//Gm14uKqJj/ThmjaXx9bl\n",
"UjB178Xfb31zSW00C+EB4jDx7GztteFT4cbsppX0HM0FpUKOISiMoUkwIEODwVrMyUW9GPrQbbgV\n",
"553/3Arh0tSm7eUVepqsfCPZBUbHFOSv1N/4JqoQrQXmd3wVu5snRVFtMMe0qbUdPy+XKyKGjFwh\n",
"J7/DNZfWRgP15ZLo0zGYa+ODLsjrsEOUD93a+F/Ry4AtDYVchiEoFGQyXv1dDBD0dm8wZx0l6ofP\n",
"znuu3DE9aFq9R6WOo9xq42haIRpDKaoDG3l5lxhG8NW/oHWHIaz/6Bf+WfRFjXCXVxqKBjDkaxZP\n",
"wFOncXYgOg8KuRx3Kftbs0ImkxHdOpCi6Pb0TbNzUyIY1PBqf/DfteW85zp0C5d55JFVYHSaKp29\n",
"stfh9ef4dsfDFJhyGZACj+2Uo/LywOQbgMXd84oPrN0Q/W8WwkPiyifUz42Crr0BeOVvMVDyB90h\n",
"tzT5vOdVuqxbL7PwOJZWyOGUqpwrcrkMpaGUdt9+iKYwj41561gZL6abWP4z2Dy80KirDL+udPOA\n",
"hsj2JwkPiQYj67a7AOiUDXceEtN/zu5nAtO5Xb8rY87am1jnoTaWcuNdg+m4/G3CFz3MwxX5pN/6\n",
"HVoXgsXDy5HOQCGXXfE6NxeNAtUlTr0k4SHRYHh06UDy9WKQ35mJkbhYYEVH+HXnL+c8p3Ix5nJO\n",
"W2oTVJFff4TKaMAug2ntD1GshZsSYUpFrhqrh+gZfm2HIPp0qJkr9kpDpVTQt+OlhbKQhIdEgxHk\n",
"48qJZ14iYdKj5Ex9j8eP+ALw6rH5HD9dSGkt2dkrDVAvp+l2bYLKLS0JgHd6iVnx/A3w8S9VzmwW\n",
"D9EdQq1SXLB+rqUjPQWJBsXdx5OjEx6hKCKGR9OjCS2BE9ZTfHP0aw6eqhmOUmgC8/XaBJUqP4+E\n",
"ADEtAYjpSwMN1Sq00EBHl4IkPCQalEotvl0QULv7s2CDeHzFyQWYsquUpxl5Bo6mFFSlu21gGWKx\n",
"ntspr/rIo1J42YtzmHAblCthyh64OdH5HGPrC89uf7VQL5d8CYlzoagmPCxe3tz5t5hdbntYCX/8\n",
"cS9Dhh4DRK9VAFdLGQEH91Lco5+jDX2ZhdTsUtq0qlJSXgjJmSUOv6gDp/KICvKoEVsku8CITAbe\n",
"xxOwqdSUxPhhF+DNLhkcCIIIsztvrhetXhMmPYalTTvkKckYbhuLJD6ckYSHRINSfXSfPfwWQld9\n",
"xYdroOuD8FlEBgO3/ECP+BscdToueoHwjb9y6P9mQKdZACQk5WOy2HBRK/H11FKsLyc88PwBhsrK\n",
"raRml5KaXUqonxgcKj1Pj0Ihw91FhadOQ7G+nKNphSgNpdz66BgAvl9/hP8yf+bDa6yorbDUNBp3\n",
"83IAjt9+N67+vpTqTbVmsb/akaYtEg1Kpf2Dl05DYafuFEfG0jEHpm8FQQbzNz9C2q/rHfXDN4qZ\n",
"y9p8vdRxzGqrmErYBfadyCUps8QRG8RgstSa4qG67sShhLUJnEwvZt9J0UTeVNGGZ/JxR938nAMs\n",
"TX0ZgIVbPQj738MUR8ayY/oCbC5u1dq8skMLNAaS8JBoUHw8tHRq7Ut8lA92QeD0gBEAPL8JMdmQ\n",
"ZxmbfpuMS46Y98SmrsjVWi3ReeXoRaimCKmMC7LrWA47D9eWZ7WmQrN6LBGL1e7QdXidEqdOJiUs\n",
"SppOmWBkzGGYUByHLaQVf3z0C2lDb3Fuq/lFDWhyJOEh0eD4eGhRKuQIgsCx8fez8+n5bPxkPUu2\n",
"BiATYGEfG4Ub3wHAEFCVVuPsX/fquzuOZnPgZJWTXWFpeZ39qN6avsziEB5+h/ciAFNuhlPCaWLy\n",
"xdUVY1Ssk+WlplrwHmnkURNJeEg0GoIAglJF6vBRGELCKVnwLxMYhl0Oz/n8htFaisxetSpiN5sp\n",
"0pdjOYeTXKG+SmAcOJWHvsxCWnYpNrvdaZRS24duLLeSuecwN43pS/g/v7GgH3zdSTQ/X7USPMpF\n",
"4VFdZ9O9nT/+3mIcjis9IlpjIAkPiUaj+keskMnQqhX8X795dM2A025mPk6YitKorzqhqIT9J8/v\n",
"wu93aDeBf4t6ksPJBSRllpCapaeubzunwMg1S19FW1zAT+1g1lDR/+abVaI5PYCpVx+nZVyVUuFw\n",
"mJNkR00k4SHRaFT/4BQKGb3jgojt3I7P/vTCvRy2GrewOL7KOU0oqdJ7YLeTf5ZiVGYxM3jaRK55\n",
"/lF06SmUVeRAMZmt5xwZaArziPp1JarCfAL3bOW/VjBBtKDnHp/7GKyPwK5QsmP6AmQd4mtEOK9u\n",
"tyLhjCQ8JBqN6jYW1cPwRapC+EpM6cqsIbAupqKgWBQeUeu+5/b/dcLtwG6n9oJ3bXZsB+7Z6tgW\n",
"cBZUjm1BYPiDo+i+eA5dnpnCYR8zI+8ScyCPzolkRLtp/L78d1atO0Ta0Ftw1SodIQQrQ2BGBnsA\n",
"0DrEo76PocUiCQ+JRsPfy4WBnUO4Jtaf6NCqlKOCWs3NiTB3o7h8O3YM7AwFWcXIo/tbs5HbbQx5\n",
"8k6Ct/9N+6/ep/Wab+k1vyo/cfzyxaj0JRUNOk+RsgqNAOjOpKAtEk3ic3IPMnwiFLnALYky7u76\n",
"rlPwKS+dBk83Nb6eWuIjfYiPEv1yPHUaBnUJdeSpkahCMhKTaFRkMlmNQNYym6gkfX4THPcVFZcj\n",
"74JV+UfAxzkwb785jzjtn+k3nJDtf6M2lOJz7CDZ3fshIDiNPDySj9P71alk9RgIwL4guH4i5LpB\n",
"d6ENd4xZTpmuKuq+QiajS4yfY9+vmQUrbq5IIw+Jy47MKuoq5AIsXy26vhe4wti8+aQYjp7zvJK4\n",
"TpxY9CGZ14s2GC65FfYeZ408eiyahWfqKdr+8Cn/RsDge0TBcf1JmNVqAXKdD94VZuzAFRGwuDly\n",
"0UD+hY0AAA2DSURBVMLDZDLx2GOPcdddd/HAAw9QUFBQo85nn33G2LFjGTt2LEuWLGmQjkq0HDLH\n",
"3ePYVtlh5fcw9BTkCqXM3X8nG1rXfp4tMJj41r64RkcC4JonLpPklZgoq5adzi0nAwFY3AuG3A3F\n",
"WrjtmIKvNkdhayV6qAT7utInLohBXUKv+KhgTcVFC49vv/2Wtm3b8vXXXzNq1CiWLl3qVH769GnW\n",
"rFnDd999x8qVK9m6dSuJiYnnaE3iaiT7lnFsf/4tx77WCmu/gVvM7TDITFw/AV4ZAL9+7BxEyOor\n",
"Ti1cY8S8yK45GXgkHwe7neTEM1x/3w30eO1Ziq2FjBsDT44Emxym5HRg7KS9bPxgDYKiYqYuk0np\n",
"PS6RixYee/fuZcCAAQD079+f7du3O5UHBwezbNkyhzLKarWi1UpORRLVkMnI6dTT6ZDGBstSe/Ps\n",
"Lh12ObxwHTxRNIvPn37QUacyv6o8vBUAUet/5PoHbyHml28I2f432owk1hX9Qtwj8H0H0QDs+5Xw\n",
"ZOlg5Eo1KKqEhRSd49I5r8L0+++/54svvnA65uvri5ub6DDk5uZGaWmpc4NKJV5eXgiCwGuvvUZc\n",
"XBwRERF1dsTf//xekw2NdL2mu152STmGwCoFpckvEG1eNm5F+czdpmFQop5JkwM4ZUjgHl0CK+6C\n",
"/9sN3Vv54+/vji0szKk9j+/m89YTNzDuMUityH8+9BR8tAaiiiDl5gDcdeIPmLe7hsLScsJDvdBd\n",
"YBT+5vwsm5LzCo8xY8YwZswYp2OPPfYYBoMYYslgMODhUXP9u7y8nFmzZqHT6XjxxRcvqCO5uaV1\n",
"V2og/P3dpes14fWKi8soKa8yQTcEBKPNy8Z++gwuxYWMKIQ3Ov3Mj1nLWJf5Fb/Hmvg9FjTWObR/\n",
"/3tiPcJQ3QZ5rnDMD9K87GBfA17QPhde/htuO1o1upB7eWEqM2Ox2ekc5U2Ah4YyQzllhrr9Y5r7\n",
"s2yI69WXi16q7dq1K5s2baJTp05s2rSJ7t27O5ULgsDDDz/M/7d37zFNZXkcwL+3L6At5WVVVB4r\n",
"QXwQMKhZHR6OMz6YFV0k44PiK4ICMzK+h8pDxSy+Vjc6qZnRXQ0RjI5myJisCcbEGBIxoquIggrD\n",
"qpuo4wjqpK1giz37R6W00FEp91KY+X3+sd7X7/7S+vPce889Z/LkyVi5cqXLJ0b+ONoCrJNGezTe\n",
"A2exwOTtA08PX+j+8necq1mBysZ/ovpZBe5In6Dm2Q3UPLsBRHXu79cKTL8vQvp/LJj+X0DMgFZ/\n",
"NbyePwNgnZNl8rghYMw6u53Six4y8qHHxSM1NRW5ubnQaDSQyWTYt28fAOsTluDgYFgsFly9ehVm\n",
"sxmVldap0zds2IDx48fze+bkd8P8dsZ2cau1c1ebj7UPhkwqxrTICHhLv8ZsfI3hgRya39xHq/hX\n",
"6Fd/icDHLQh9CYxuBsSssyXz01wNfpqbhgn7t0D+7AkMCdMQ8J45c0nP9bh4eHp64sCBA92WL1++\n",
"3Pa5tra2VydF/lg4uRyvvX1sY3q89vVHoL8cgONMbn6efgj3GQa12hsvf/4bfBu7D6h8f1YKbnxZ\n",
"AHAcLv6jDAAwLsC/23ak96gckz7XUQ/MciUA4NWESXg+Jtq2ng0NRESwHwDHmc3sC8nzmCnWP0dF\n",
"Ohy7OXJCt5HOaeBzYVD3dNLnuLe3Miv+9W/4NdbD85NEmOvuILDaeplrHhKIjucg9n0x7OdXbfoy\n",
"Fw2f/hWGwCDMXjLddn/DpFRB7iHBq9ftnftR9RAEtTxInwvwsT42bRs0BE+mTAMn4vAifJxtvTlw\n",
"mNP97N9fkUjE0AeHQeblhV/Hdd5PM6l84eft4bAfR8VDEFQ8SJ/z8/ZAbGTnVIccx8H3zxNsf28f\n",
"6jgNYsf9Dy+PzlaI/RQPLR9Nsy3XR47HnwIduw8M8Ant+y26bCFuYT8fC8cBg8KDO1fKFQ7bjgry\n",
"xchhPg77iN9O+WhhDC/nLUBtczMeT/kEY0cFdpsOkloewqCWB3E7juMgEnG4mbERP0+Mw6uP4rut\n",
"7zr5U0eB8JJJoFApcG/hSuiDw2w3R8e8veEK8D4ZHXmLWh7E7USc9TKkYUE6GhakY8wHvAs1XK2A\n",
"TCKCv8rDNs+L9VjW6jHEX447/3sBgEY+FwoVD+J2HMc5XFqIP+AmhYdUjBGDrY962+1GW3d2hUK1\n",
"Qxh02ULcrus/eLG4Zz9L+3scnN37siMDVRCLOHjLabwOIVDLg7hd1xuaH9Ly+G2dzYzgId7vneOW\n",
"uI5aHsTtupYKsbjnxaPjca5MSgP89BVqeRC361oqXOkRGhHsZ+vSTvoGtTxIvyOiXl0DAhUP4n5v\n",
"a0WQWgkPiRgyCf0sBwK6bCH9RthwH4fJoUj/RiWeEOISKh7E7Tgay3xAouJBCHEJFQ9CiEuoeBC3\n",
"UXpau417elDHroGInrYQtxkfPgjGtnYoPOndk4GIWh7EbSRiEXwUHzZrG+l/qHgQQlxCxYMQ4hIq\n",
"HoQQl/S4eLS1tSEnJwdpaWlYtWoVnj9/7nQ7i8WCjIwMnDx5stcnSQjpf3pcPE6cOIGIiAgcP34c\n",
"ycnJ+Pbbb51ut3//fuj1ehq5mpDfqR4Xj+vXryMhIQEAEB8fj8uXL3fbpqKiAiKRCPHx8TT4LCG/\n",
"U+/s53H69GkcO3bMYVlAQAAUCuu8GgqFAnq93mF9Q0MDzp49i2+++QY6nY7n0yWE9BfvLB7z58/H\n",
"/PnzHZbl5OTAaDQCAIxGI1Qqx9m5zpw5g6dPn2Lp0qV49OgRpFIpRowYgbi4uHeeiFrdt2NNUjyK\n",
"1x9juSOeq3rcwzQmJgaVlZWIiopCZWUlJk6c6LB+06ZNts86nQ5qtfq9hYMQMvD0+J5HamoqGhsb\n",
"odFocPr0aaxevRoAUFJSggsXLvB+goSQ/oljdEeTEOIC6iRGCHEJFQ9CiEuoeBBCXELFgxDiErcO\n",
"BmSxWLBt2zY0NDRAKpWiuLgYwcHBvMeZN28elErrjOpBQUHIzMyEVquFSCRCeHg4tm7d2utu9Ddv\n",
"3sTevXtRWlqKhw8fOj3+qVOn8P3330MikSA7Oxsff/wxL/Hq6+uRlZWFkJAQAIBGo8Fnn33GWzyz\n",
"2Yy8vDw8fvwYJpMJ2dnZCAsLEyxHZ/GGDh2KzMxMhIaG8p7jmzdvUFBQgAcPHoDjOBQVFUEmkwmS\n",
"n7NYZrNZsNw6tLS0ICUlBSUlJRCJRPzkxtzo3LlzTKvVMsYYq6mpYdnZ2bzHaGtrY8nJyQ7LMjMz\n",
"WXV1NWOMsS1btrDz58/3Ksbhw4dZUlISW7hw4W8e/5dffmFJSUnMZDIxvV7PkpKS2OvXr3mJd+rU\n",
"KXb06FGHbfiM98MPP7AdO3Ywxhh7+fIlmzp1KsvKyhIsR2fxhMzx/PnzLC8vjzHG2JUrV1hWVpZg\n",
"+XWNlZ2dLfj3ZzKZ2BdffMFmzZrFmpqaePt9uvWy5fr164iPjwcAREdH4/bt27zHuHv3LlpbW5Ge\n",
"no5ly5ahpqYG9fX1mDRpEgAgISEBVVVVvYoREhICnU5ne4/H2fFv3bqFmJgYSKVSKJVKhISE4N69\n",
"e7zEu337Ni5evIjFixcjPz8fRqMRtbW1vMVLTEzEV199BcDaWpRIJILm6CxeXV2dYDlOnz4d27dv\n",
"BwA8evQIPj4+qKurEyS/rrFUKpWguQHAnj17kJqaCrVaDYC/36dbi4fBYLBdTgCAWCyGxWLhNYaX\n",
"lxfS09Nx5MgRFBUVYePGjQ7r5XJ5t/dzemrmzJkQizsH8WV2XWc63v8xGAzw9vZ2WG4wGHiJFx0d\n",
"jdzcXJSVlSEoKAg6nQ5Go5G3eHK53Lb/mjVrsHbtWofvie8cu8Zbt24doqKiBM1RLBZDq9WiuLgY\n",
"c+bMEfQ77BpLyNzKy8vh7+9v6+XNGOMtN7cWD6VSaXtPBrD+LyMS8XtKoaGhmDt3ru2zr68vWlpa\n",
"bOudvZ/TW/Y5GAwGqFSqbrnyGXfGjBkYO3as7fOdO3d4j/fkyRMsW7YMycnJSEpKEjxH+3izZ8/u\n",
"kxx37dqFiooKFBQUwGQy2ZYLkV9HrMLCQsTGxgqWW3l5OaqqqrBkyRLcvXsXWq0WL1684CU3txaP\n",
"jvdkAKCmpgYRERG8xygvL8euXbsAAE+fPoXRaERsbCyqq6sBwOn7Ob01ZsyYbsePiorCtWvXYDKZ\n",
"oNfr0dTUhPDwcF7iZWRkoLa2FgBQVVWFyMhIXuM1NzdjxYoV2LRpE1JSUgTP0Vk8IXP88ccfcejQ\n",
"IQCAp6cnRCIRIiMjBcmvayyO45CTkyNYbmVlZSgtLUVpaSlGjx6N3bt3Iy4ujpfc3Pq0ZcaMGbh0\n",
"6RIWLVoEANi5cyfvMT7//HNs3rwZaWlpthi+vr4oLCyE2WxGWFgYEhMTeYnV8cRGq9V2Oz7HcVi6\n",
"dCk0Gg0sFgvWr18Pmax3I4d3xCsqKkJRUREkEgkGDx6M7du3Q6FQ8Bbvu+++g16vx8GDB3Hw4EEA\n",
"QH5+PoqLiwXJ0Vm8vLw87Ny5U5AcExMTodVqsXjxYrS3tyM/Px8jR44U5Dt0FmvYsGGCfn/2OI7j\n",
"7fdJ77YQQlxCncQIIS6h4kEIcQkVD0KIS6h4EEJcQsWDEOISKh6EEJdQ8SCEuOT/uaeorBvJBZoA\n",
"AAAASUVORK5CYII=\n",
"\">\n",
" </div>\n",
" \n",
" <div name=\"mu1\" style=\"display:none\">\n",
" <img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQ8AAADVCAYAAABJ/XXDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
"AAALEgAACxIB0t1+/AAAIABJREFUeJzsnXd4FFXbh+/ZmrKbXgiQUAKEDiIgvSio+FrgVQRREFFE\n",
"/exYEJXiK4K9oqAiKqKIlWJDBEQQkRZ6T0ggpNfNJtk63x+b3eymkGRJSAjnvi4vMzszZ84sO785\n",
"5zlPkWRZlhEIBIJaomjoDggEgosTIR4CgcArhHgIBAKvEOIhEAi8QoiHQCDwCiEeAoHAK4R4CAQC\n",
"rxDiIRAIvELV0B0QNE0OHz7M6tWrefrpp12frV+/nhMnTqBQKIiIiGD06NEN2EPB+SLEQ1DnLF26\n",
"lF27dqHX612fGQwG3n//fb7//nsAxo0bx5AhQwgJCWmobgrOEzFtEdQ5d911F1dddZXHZzt27CA2\n",
"Nta1HRcXx/bt2y901wR1iBh5CGrE6dOnWblyZZX7e/TowYgRI1zb5UOm0tLSCAgIcG0HBASQlJRU\n",
"9x0VXDCEeAgAsNls3HHHHXz11VcAzJw5k2nTptGqVSsAoqOjmT59eo3bkyTJY9tgMKDRaFzbarWa\n",
"oqKiOui5oKEQ0xYBAHv27KF58+aAY9QQHx/vEg5vKD/y8Pf399guKSkhMDDQ6/YFDY8YeQgA+Ouv\n",
"vxg8eDAAhw4dokOHDh77azttKT/yiI6O5sCBA67tvLw8unTpUhddFzQQQjwEAGzZsoX//Oc/AGza\n",
"tIn+/fvzxx9/uAyftZ22lB959OnTh9dee821ffDgQZ544ok66LmgoVDOmTNnTkN3QtCw5OTk8OGH\n",
"HxIQEIDRaMRgMFBYWEjLli2Jjo6udXtffPEFq1ev5siRIxgMBjp37oy/vz9+fn5s2LCB7du3M3z4\n",
"cC677LJ6uBvBhUISmcQEq1atIiEhgccee6yhuyK4iPBq2mK325kzZw7Hjh1DrVYzb948YmJiXPv3\n",
"7dvHyy+/jCzLREZG8vLLL3tY2gWNi/379wtvT0Gt8WrksW7dOjZu3Mj8+fPZu3cvixcv5v333wcc\n",
"c90xY8bw7rvvEh0dzcqVK+nduzdt27at884LBIKGw6uRx+7du12W+R49enhY0RMTEwkKCmLp0qUc\n",
"P36coUOHCuEQCJogXvl5FBYWotPpXNtKpRK73Q5Abm4ue/bs4Y477mDp0qVs27aNf/7555ztCbOL\n",
"QHDx4dXIQ6fTYTQaXdt2ux2FwqFDQUFBxMTEuEYbgwcP5sCBA/Tr16/K9iRJIjPT4E1XvCI8XC+u\n",
"J67X6K7VUNfzFq9GHr169WLz5s0AxMfHExcX59oXHR1NUVERycnJAOzatYv27dt73UGBQNA48Wrk\n",
"MXLkSLZu3cr48eMBmD9/PmvXrqWoqIhbb72VefPmMX36dGRZplevXgwdOrROOy0QCBqeRuPn0dSH\n",
"huJ6F+f1mvK9Oa/nLSIwTiAQeIUQD4FA4BVCPAQCgVcI8RAIBF4hxKMByDWYKCqxNnQ3BILzQojH\n",
"BUaWZfaezOLfI+kN3RXBBSInJ5vXX3+5obtR5wjxuMA0joVxwYUkJCSU6dOfrv7AiwyRSewCI1Om\n",
"HrIsV0jXJ/COk2fzycwrrtM2w4N8z+kH8fPPa9i2bSsmk4mzZ89w++13Ehvbjrfeeg2FQoFGo+Xp\n",
"p58tTWHxLIsXL2Xx4oXEx+/CarUxbNiVjB59M1Om3MGKFT8gSRKvvvoqMTHtuPLKEVVet7EgxKMe\n",
"yc4vQeen9vjMfeSx7WAaA7pGXeBeCeoSo9HIG2+8y5kzp3nqqUfx8/NnxoznadeuPVu2/Mm7777J\n",
"gw8+6jp+/frfePfdDwkNDeXnn9fg76+je/ee/PPP3/Tt24+//vqLxYvvacA7qjlCPOqJ/EIT+xOz\n",
"0fmoadk8yPW5u3iYrfYG6FnTJLZ5ILHNL2w2dkmSaN/ekSg6PDwCs9lMcXEx7do5Yrm6d7+MRYve\n",
"8zhn1qz/8cEH75CTk02/fgMAuOGG0Xz77dfIsszAgQNRqS6Ox1LYPOqJfKMZgMISi8fn5aMBMnKL\n",
"OHQqB1mWsVht7E/IpqjcOYLGS/lpZ1hYGCdPngAgPn430dFl5SssFgsbN65n7tyXeOedRfzyy1rS\n",
"09Po3r0nKSlnWLt2FbfccssF7f/5cHFI3EWIyWIDQKXw1OfyBtNDSbkAtGqmJzW7iOyCEowlFvp1\n",
"blbtNZLTDYQG+uDvo672WEH94C4ekqTgqaee4803X0GWZVQqFTNmPO+ybanVagICArn33slotVr6\n",
"9u1HZKTj3/nqq69l06Y/iI2NvaCxLeeDEI96osTsEA8fjdLjc3eDqTsSoCj9IZot1U9n8gpNJKQW\n",
"kJhawNCeLc6vswKvGDXqetffWq2Wb75ZBcB7731Y4dhFiz4BYPLke5g8uaJNw2azc8MNY+qpp/WD\n",
"mLbUEza7QySUSs9h7bmWalWlx9plmdRsY9UHApZSe4lY+b34mTdvDjt3/svVV49q6K7UCjHyqCds\n",
"NsdjbS83iKhKPAxFFpcgABw9nUegvwa/0imJLMscScolJMCHyBA/IRpNiGefndPQXfAKIR71hK1U\n",
"NcobSKuathxOzq3wWXpuMT4aM3a7TKBOS3peMel5xUSG+AlvM0GDI8SjnnBOW5z/d1KbZz4pvcxw\n",
"1rV1SJ30SyCoK4TNo54om7aUFw/vRgyG4vJLvt71SyCoK4R41BPOaUuFkYeX7eUaTEDZiozQDkFD\n",
"I8SjHrDZ7a6H217e5lG66Ztxlh4fvES3Ja8TsWcbvplpxK7+kh4fvERA4rEKbRYUOZzOtGplaTtC\n",
"PhobkyaNq5N2nn32yfM6/6mnHiMtLbVO+nIuhM2jHnBOWcAhHs4HXS79W7JaGPrEJE7bUtgbCWdO\n",
"f4xdgiQzdM6Efj8vY9f8L8juenmFtlVKh96Xnw4Jmg7z5r1aB63Uf8ClEI86RpblCtGdNrtjmTXP\n",
"aMIvKJ8fts/g0QkppARU3obaBlfvvIO7P1IwxNaJrO5XsO/ux0GpdAlR+enQpU7AhFvQrl9Xp22a\n",
"RlwNv/9W5f6SkhJeeOF58vPzaNGiJXa7nYSEE7z11mvIskxgYCDPPDOLo0ePsHz552g0as6eTeGq\n",
"q65m0qQppKaeZf78F1zVFh999EnCw3tx443XsHr1b3z//Tf8+utPKBQKOnbszKOPPkF6ehqvvvoS\n",
"JpMJrVbLU089S0REJEuWLObvv7cQGhpGRsaFyRUjxKMOsdntpGQaSUgtIGL334Tv20HiNTdjs7fn\n",
"aPppVp5+lw3p32KTbBAAoVZfYsMH0O5MAUqFipToZpwuOMTJkqP81AF+6mCnR9pB3v7lIF00Gg5O\n",
"fgQZsFhtJKQWNPTtXvL8+OO3tGnTlqlT7yc5+RRPPvkoL788j2eemUXr1m1Yu3YVy5d/Tp8+V5Ce\n",
"nsbnn6/AbDYzevS1TJo0hYUL3+LWWycwaNAQjh8/xoIF/2PVqh9werz/8ssapk9/ho4dO/Hjj99i\n",
"s9lYuPBtbrllPP36DWDnzn9ZtOg9xo+/nd27d7JkyTJMJlOdTZ+qQ4hHHWG3y/x7KAOT1YZvZhoD\n",
"Zz+IylRM+L4dfNfjSR6Ln0ahNR+lrOCOfXD30SByXlyHTaeHTp5t5Zky2bvvfb42/8LeZvkMuwvu\n",
"27GY+z4pIXHKU2w9kNYwN9mIKfjy23ppN/wc+5KTk+jffyAAMTGtCQwMIikpkddfXwCA1WolOjoG\n",
"gNjYWBQKBT4+Pmi1WgCSkk7Rs2cvANq371BhxPDMM7NZseILzp5NoWvX7siyTELCCZYtW8ry5Z8h\n",
"yzJqtZqkpFPExXUEHG7yHTt25kKY1IV4eIEsy1htMharHT8fx1dYYrZhsjriWbp/+AoqUzFWBbwQ\n",
"vYv3fnRU1uvh24uFPxQz8J/D7Lt7CraocHIMJRXaD9KGM7TPbPrbZ/DjmY/48fQHLOpjZ8fZT/nf\n",
"D75Yxjx84W5WUCWtW7dl//69DB48jJSUM+Tn5xET05rnnptLZGQz4uN3k5+fX3p0RRtEq1ZtiI/f\n",
"XTryOEpoaKjH/jVrfuSJJ55Bo9Hw+OMPceDAPlq1as1tt02ka9fuJCSc4NChA7Ru3ZbvvluJ3W7H\n",
"ZrNx/PjRSq9X13glHo7MSHM4duwYarWaefPmERMTU+G4559/nqCgIKZPn37eHW1MnEjJJyXLEXvS\n",
"Oy4Cna/aFUUbHr+dmD9/IUevZdztWtY3K0CDksdzhzLvhY0o7DJmfSCnh11HoFpBj9gw9p7MqvQ6\n",
"GoWWW2MepG/oVbwVP5VdzbO5u3AxTxpH0dK/rP6vociM3k9T/zcu8GD06JuZP/8F7r//bqKimhMQ\n",
"EMj06TN48cXZ2Gw2FAoFM2Y8T2ZmRrnQfcffDz74KC+//CIrVnyB1WplxoxZHvtjY2P5v/+7Bz8/\n",
"f8LDI+jSpRsREZG89toCzGYTJpOJRx99kvbtOzBo0BCmTr2T4OBgAgODuBB4VW5y3bp1bNy4kfnz\n",
"57N3714WL17M+++/73HMihUr+PHHH+nbty+PP/54tW029pJ+RSVWEtMKaN8ikL8Plk0burZxeH6a\n",
"LHaOn8lj8Iy70R76m+FPRrJXmU6YEX5cAQNPO45P6X8Ve/5vJsURzYkK8aNZiB97TlQuHgB9O0bw\n",
"75EMCs25fLJqKFtaWAi2qHmv+B6Cu91IYfNWIEl0aR1CeJCv1/d3PjTl6zXle3Nez1u88vPYvXs3\n",
"gwcPBqBHjx4cOHCgwv59+/Yxbty4JuOPcCQ5l8y8YhJTC1Ary762s1lGDiTmcPx0Ll2WvoXPob8Z\n",
"eafEXmU60f6t+WN1lEs4Dk58kL/nvkdxRHPX+ZKi7I3UIzasQjYsZ2CcThPMB+k3Muo45KotTJc+\n",
"oNNjo+ixyDG/zqrj/J0CQXV4JR6FhYXodDrXtlKpdC03ZWRksHDhQmbNmtVkhAPK/CqsNtnlqAWQ\n",
"U+r5GbNhLa2/Xcyo22FXlEyMvjWfjPiejIfeIf3a0fwz41UO3fFAhXYVbsNZH40ShaLquWrC1Od4\n",
"NnIOA3KCSdPDNXeAfvO3KMwmTCKloeAC45XNQ6fTYTSW5Zuw2+0oSjNm/fbbb+Tm5jJ16lSysrIo\n",
"KSkhNjaW0aNHn7PN8xk+eUNtrxeYakBSKQkI8EU2mpBUZQKizs+l+0cvc8cY+CcaInya88edGwhQ\n",
"RLK7OJg9vXoD0FKnJb/Q5DovKMiPiHA9+hTHsmt0iyBIN6DPKzOihofr0et8ANBHBGC45U4et4wh\n",
"bed4jnGYcTcW8fZfa8j+7yQCg/zQlApbY/8+L6brNeV7Ox+8Eo9evXqxceNGRo0aRXx8PHFxca59\n",
"EydOZOLEiQD88MMPJCQkVCsc0PhtHgZDCYYiMxoF5BlM2EpHVbqUU/R9dhpze2XzfWfwU+qZ0XEx\n",
"AbZQCgzFGApL0Ot8MBSWEOirwlBYJgx5GgVZGqXrs6ysQnJzizyOycw00Dk6ELPFxsmzBRiKzICG\n",
"p+MW8dyOG/mrVT6f73yRK3sO4UiAhqhQ/0tini5sHnV3PW/xatoycuRINBoN48ePZ8GCBTzzzDOs\n",
"XbuWlStXVji2qdQlcd6G1WZ3CYdkMdNv3nTWhiTz8iBQoODxuLdo6dcOSZJcmcGclJit5dqU8NEo\n",
"0agURIfrqApfrYpAndYjkjZYE8HMvh+isku81dvEqV+f80gmJBDUN16NPCRJYu7cuR6ftWnTpsJx\n",
"Y8ZcXDkZz4VUunzmfEAj9u9k6PSJHA2Fe6dJgMw9sc/RPWiA65zyyY/DAn3Jyvf061AoJI/aLe5a\n",
"26lVcLleeNqQeoT15Z7AKSwyLOG5qL9YnnmcIH1XMhOzCfNXNxnhFjRORFRtDSgqsbiiYy1WO/rk\n",
"BAbNmEKRGsbeCoUamQFh1zE29k6P89zzl4bofWgW4lfttSKD/QgP9KVnuzAigz2PL29/NpntDO86\n",
"nVEpgRT4wAsb72Hn0XSS0wwVRMpQZGbP8cwKox9B/bF9+zZWr/6hyv2//LKWLVs217rdG2+85ny6\n",
"VWcI8agGs8XGv0cyXCHxFpudjis+RGmx8PB1CvZHQgu/1kzv8hItyk09VG5LujrfmpVHUCgkurQJ\n",
"IUinrbDPPby/XfNAikosSJLE80H3EmaEHcoTrEv7ytHPclOYA4k55BvNnM4orNmNC86bK67oz403\n",
"Vj36HjXqegYNGlLrdhvLgFK4p1dDhapudjtR2zfxQ0dYcpkdtULLwuGfMKBVWwCiw3WuFQ93yts/\n",
"vMGpHZFBvrSM0HHyrMP1WT9yLIsfeZWbx8EXSa8xqMVIDIURZBeU0K2tw+XZWnofisbyy6tjJqy9\n",
"hfXJdRtVOyLman6/q+qoWqvVyksvzSU1NQWbzc64cRP44YdvCQkJpaAgnxEjruHMmdPcd9+DfPrp\n",
"x2zevImgoGBMphLuuec+du/eSWhoGK1ateaLLz5Do1GTnp7KsGEjmDRpCgkJJ3jvvbew2ezk5+fx\n",
"xBMz6Nq1e53e4/kgxKOWBCYeo8CWz7SbFICd21tNp0tY2T9obIvKSx5W9tD6amv39TuTJzttGT3a\n",
"hZGeU0RYyyhamDsxYd9hvuxewvtHZvNk+/fJLiibujiNvO6jIcH5sWrVdwQHhzBr1v8oKipiypTb\n",
"0Wg0jBs3gcGDh/HLL2sBOH78GNu3/82SJcswm83ceacj1sndJuWMug0I0DBo0CAmTZpCYmIiDz74\n",
"KG3btuP333/lp5/WCPG4mAnf+w/3Xw+Zvna6BFzBtc1ur9Goonz+jfBAX1qE+9fu4qVNOH9zQTqt\n",
"a3pz6urRvPH5YdZ2UrIzaxPbQ3+nX+jVrmplTpTncEK7mPny+vqJqj0XSUmn6N37CgD8/Pxo3boN\n",
"O3ZsJyamtcdxycmn6NSpC5IkodVqiYvrVKEtZ9Str6+vK+o2LCycTz9dglarpajIiL9/1StyDYF4\n",
"DVVD+TSCf6ev4bvO4I+W+9vNQyEpKqyquONTOoUpP/CIDPat9RRCdolHxfOSr7yBcJOa+esc05NP\n",
"E1+i2GasYPtoorOWBqFVqzbs3bsHgKIiIwkJJ2nevEWFf582bdpy+PAhZFnGbDaXRr2Wp+I/zNtv\n",
"v8bdd0/j2Wfn0LZtu0bnsS3Eoxo8qtqnHmJW+0MAPB47nQgfR5nH8lXh3OnRLozoSH2FUYY3PwOn\n",
"kFUmAObAYM5eMZRpO2V6FIWRY07n+zOLKthsGtnv76Lmppv+S0FBPg88cA8PPXQfd901leBgzxIZ\n",
"kiTRtm07+vcfyL33TubZZ59EpVKhUqlc+93/X3oWANdcM4rnn3+aJ554GFmWyc7O8tjf0HgVVVsf\n",
"NFYvvlyDyREyL8t8u3IYK6MzGJgbyrtT93HirMOtfGiP5uf0qXC/3qb4FAA6twomIrj6pVt3tu5P\n",
"xWKz0zJMR7uWnraVpDQDxavXMPi5+9jRHPreC2pJw/LhGxjYritbDzgS4raNCiAmsm7dn5uyF2Zd\n",
"XCs3N5dNm/5gzJhbMJvNTJo0jnfeWURERGS9XK82nI+HqbB5VEJOQQlajRJ/H7VrqJi14U1WRmeg\n",
"tcLEXu+gdottqY0zlp9WRZHJ6hFcV1PONfJo1UzP3wOGc2TsFPp88wm3HvNlZYdi3tr3Ev684zqu\n",
"cbwqLi2CgoI4fPggP/+8GpC44YbRlQrHxYYQj3LIssy+hGwAhvVsgd0uY7Gbed32BQCTzcMIiep1\n",
"zqnKubisfRj5RjOBlfhxVN+50v9XcWmlQsGByY8Qs/V3Xv3pNKvbSvyd9TPxmZNor+8BVLThCOof\n",
"SZKYOXN2Q3ejzrmkbB5Wm71ao5P77rNZRo6fyWfV6Q85qSsmLguu6TYDcDyo3qBWKQkL9PXqXGfX\n",
"qjK0KhUSslrD/mdfpaVRzWPbHGd8fuplt/IPXl1aIKjAJSMedrvMlv2pxJ8jaxd4vpmPnckjqTCR\n",
"H88sBuCN7ZFYI1sBoJAcS6XNQ2u53HoeVDdqcC7D5l52BRtf+4ynt0BEIRw17GFH1u81akMgqCmX\n",
"jHhYbY5Vh3yj+ZzHlffHWH5yPmbJysS9EDGgLJmPpJDo2S6MDtEXJl8kQKcYR6BcVTEy7lnJcjpf\n",
"xolpc3jmb8fMdE38c0jFxipHXhar3SPXiEBQHZeMeNSEAwnZbHPLT3ogfzvb8zfhZ4anE+I4de1/\n",
"Xfsaws07MsSPYT1bVOmZWt4BLOH6cXT672JaFkgc9TeQ//ZNUFR5usLdxzLZcyKLohIROCeoGZeM\n",
"eNRksJ7l5s5tl218lujID/rMFjBePRlZWfbQNsYYEWcZCHcKug9gbOQUAF7tnELoj18gy3KF6Utx\n",
"abStMwu8QFAdl4541HKuvzHje5KKjhCdD4/s8uHMoJEe+xujm7e+isjdPj0eoYU9hKNh8EfSdxxJ\n",
"ymXz3rNsik+pEKLfSNx+BBcBl5B41PzYImshK5LfBuCV3yGn7whsvp6GUS8XW+qVsCDfSg24KoWa\n",
"sVFTAXi9+WHSUzNc+zLzPPN+CIOqoKY0wkegfqjNG/WHlMXkW7Lpm65l3AFIGnFjhWMaY5YuhSTR\n",
"ITqoQqBeVIgfV7S9g7YFGhKCZQ5vWeDaV/57EdohqCmXjHjUtKh8eslpfjr7GQDvrjZh9dOR0at/\n",
"hePOVSKh4fHsW4foIAZ3bcl435sA+KpkFYpCRy6Q8mIhpi2CmnLJiIf7QyHLcoWHxFmX5YtTr2GV\n",
"LVxn7kHfFMjo0dfDUBqi90GicRpMnbh7v2pUCiRJQq1S0HXgTFoY1RwJtZH641NAWY4QJ0I7BDXl\n",
"EhKPsr//ik/h73KV5q02O4fy/2V7zjq0Ch9e/dHxZj7b/0qP47rHhjKkR3MaM73iIgjSaenfpRn9\n",
"uzQDHNMslcqHm5pNBmCpz2Z0p45XEAth8xDUlEtIPMoeiqISKxabZ6i6yWLls1MOW8Aj+4PpfOgU\n",
"ReFRJF95fYW2GqO9w51AnZae7cLQqpUV+jqg8wOEWrTsbg5nN79ZwSnOXtP5naDOsFjtF2Vi6ktG\n",
"PKp7JlYe/5JE42HCCWb2j6kUh4Tx58tLsGu8CGBrxGiUPtweNQGAz9Qb0Rw94rG/vJgI6p9tB9P4\n",
"51B6Q3ej1lwy4lGZIfDwqRxkWabQbOD1XS8C8MpvNvwskHjtLRS2bEOgn4b2LQLp1SGcKzpd/GHU\n",
"ALcOfoYAq5q/WsGpX1/32CemLRceuyto8eL67i8h8aj4WXpeMdkFJby9+w2ySjK5IkXBndsKMOkD\n",
"SbzmZgAC/DW0CNcR4KepdcLixkq4LpjrAxzLz5/a/iA3uyz5jF0UnWswLjbhvoTEo/J/mINpJ1i0\n",
"9z0A3vrFjrF5DL98+htFUS2Bxr4kWzvatwikXYtAlEqJYZ0eQWuV+KmthV1fve86Rtg8Go7aCndR\n",
"iZVN8Slk5BYBcDAxh6PJufXQs8rxSjzsdjuzZs1i/PjxTJw4keTkZI/9a9eu5dZbb+W2225j9uzZ\n",
"jWI4dibLWOnn7x18CZPNxLijPvQ7A7sffB6LvizFX2Nekq0tLcJ1tAzXoZAkgrThXGfuhizBb4mL\n",
"XEMzmxh6NBi1fU5SshwFvI6fcawMZuYXk5pTVOf9qgqvxGP9+vVYLBZWrFjBE088wYIFZR6LJSUl\n",
"vP322yxbtoyvvvqKwsJCNm7cWGcd9oZcg4m80nBzTX4ubZYtInrjTxwp2MWfaT/hg5pXfyqhILot\n",
"6ZcPbNC+XkiG93oegK9jslHv/QMQI4+GxF6J/9G5cCa3VqsaZgLh1SR+9+7dDB48GIAePXpw4MAB\n",
"1z6tVsvXX3/tqj1htVrx8fGpg656j8XqiBT1zUxj2DN3o0tOwC7B/01TQDN49HAY0QWp7LrzjgoJ\n",
"Qq22pvcm9tOqUEgSzUK6MtTYmj/9T7Fl7+tc0XOEqziU4MKTlGbgYHI+naMDa2Rfs1guQvEoLCxE\n",
"pysrQKNUKrHb7SgUDm/GkBBH+vlly5ZRXFzMgAEDqmrKxflkca4OiyShzzRyxfzp6JITHH3rDrub\n",
"2WlRAM99n4pZH4hpwh3oZUdkasfWIRiLLcS2CMSnDgyl9Xl/3lzv5sgAtuxN4cbLZvDnsfv4rPkp\n",
"RhpS0bfs7FVfG9v9NfZr2eyyKzJbr3O8XAvNDjGwK5U1uqZPSgF6SSI8xI/wcL2rHfdz953IRCFJ\n",
"dI0Nq+tb8E48dDodRmOZDcEpHO7br776KklJSbz77rs1arM+083n5BSh2bGd4AO7sYaGcfC39Tz+\n",
"y5Vgy2HBevC3wJ57HiC2TSSb950FwGgoJiLYD0NBMefbs8ZamiDYV0XL0CF0Kwhgf0ABhz+cQLen\n",
"N5IZVruSEI31/hrrtSxWO1sPpBIV4kdcTDCGwrLIZr3Oh+zsQmxmCzpf9Tltbtk5Riw2OzqNgvSM\n",
"Alc77v09muhI5h0ZULm/0vkIo1fjnV69erF582YA4uPjiYuL89g/a9YszGYzCxcudE1fGhIZCDu4\n",
"C4CCkdfxQfKn5NhyaO/fjR7dH2DnI3NJ/O8kj5WVxu5FWhdEBPsxtEcLxrW5B4AP2qcR8ufPDdyr\n",
"pk9hsQWgSuNmRm4xu49lklBaF6gq3B363G1VF2qBwquRx8iRI9m6dSvjxzsK9s6fP5+1a9dSVFRE\n",
"165d+e677+jduzeTJk0C4M4772TEiBF11+taYrPZCT/oKAt4+LI2fHJgPgCT2z7LkR6OkgQ+5eqo\n",
"XALaATiWovv1eYCoNR9yLKyQ+CMracnUhu5Wk6Y6o3RhiUNcMnOLiW0eQInZVqkNxOkXYpc9/Zhk\n",
"+cL8fr0SD0mSmDt3rsdnbdq0cf19+PDh8+tVLTEUmTmbZaR9y6BK/TJsNjthhxziMddvE5ZiM0PC\n",
"b3LVMgHwUXt+FU1pibY6NEo1N4SO48OCJXyi303FaB5BXWKTazhKkBzLsGezjeh9NfhplXRqHVLh\n",
"sPJpJe2yjOIClKRsEk5ie45nkZpTRHpu5cNAdeJJtPm5/Nw9gN+z/8RfpeP2Vo97HOOrrX0Ft6aC\n",
"QiExMG4aASbY0sLCvoO/NXSXmjQ2txW88tHd7kjA2WyHbdFQbCY9r9iVoNruIUCeoxnn3/Xtsdok\n",
"xMM1fKsbLwLdAAAgAElEQVRiOOi3+1+sCnjsaseS7f09HidYE+FxjI/Gc+RxsbkKnw8KScJXree2\n",
"FEfh7kXbXqWw2HJRRnpeDLj/TstHd1dHTmmSbncBcuSncWu/muehrmgS4lEduj07WNQbjumMROta\n",
"M7nL/RWO8S2XefwS0g6k0l/BDfqbUNjhx5IdrNu3n38OpQunsTpAlmX+OZjGkSSH67jVVsPvtJKZ\n",
"hzO7vXsbdhnOZBaWbdvLruveh7rmkhAPy5HtzBru+HtmnxfQqCquAPlqPKctl9rIA0Dufwu3HAKr\n",
"Qub3Ux8DYLaKUgzniyxDicVGWum02noeIQBOr1J350Wrze6a3oD7yMOzD3VNkxcPKTubuR2TyPWF\n",
"bgH9uCp6FH4+Dkcw90r1Tmt2ZLDDx6GqMgZNEad4FEdEcYfhMgB+z/iGEluR68cq8J7yLyJbDUce\n",
"lR3n9JZ2X6Y1l6u1U7YKI1f4rC5p8uKx86/PWNILNDaJu2NnAdA8zJ9OMcF0jw11HadSOr6KjjFB\n",
"DOjSzCUwlwLuC0sBw/6P/qehQGlic9p3mC02Yfs4D4wlFjLzyqr02e1yBTuHPjmBsH07XNsKUwkR\n",
"e7ZhL65Y3c/iNvJQGQ34ZpytIPByJQbT+pi2NI0EFVVgtpmZnvgmaGFK/uU0922D3S4jSRKRIX6V\n",
"xq1IkoRGfWmtvLgvb2f0GsC0XyLZFp3Ob4kfMip6IjY79GwXRpCu4R3+LiaKSqzsOJLh8ZnJYvOw\n",
"IwWdOMRVD49HYbVweNxU7MUZbMnZyE+hBexI9SMlXIfZVkyowUyrAiWt2o7EFvAgrc2tGXn/f9Gl\n",
"nWHfPdM5eus9rjadzXsYUethANloxEOWZcwWO1pN5Q+uxWpnf0I2baICCNbX7Ee8aOebHNLmE5sD\n",
"13Z/DjOgc5uOqJQKWjfTo7uERhmV4eHTIkl07HkvrfL+R1JQFtuzNtI7ZDh5hSYhHrXk3yMVUwuW\n",
"mG2uKUdA4jGufOQ2FFYLh8Jhgfkjvu4OZtdTWQQWh53E6A/J/vBX8Sq++GEVrYr9eba5kckZELvm\n",
"K06NHI2qyIg5MBiLLaSCSNXHtKXRiMfBxByyCkq4olNkpd50qdlGCorM7D2ZxbCeLaptL7kgidd2\n",
"vQLAy3tb43NrN/q1C6vgRNa6WUDd3MBFTPkiUSlXjeaBN17h6eEmfjuxkN59h6NsjCXyLkIsVsdD\n",
"HZB4jCtefpo8lZknxgbxWfs8ZAkkGfqYWzNQczljl3xHdD74WSAtxJ9DLbX8E5jDiq6QFGDk3hvh\n",
"1YHw8eqz3DjOEeVeGBXNrx+vRVZr6OrmUNakDabOItPGUr//8tRGOU9nGHh4/UOUYOG2/dC28wTU\n",
"KkWTygpWl4QF+dIs2A+9rwYAhU7HlZFj0Ztgr/UgiYWHUEiOefaf8SmcSjt3zIWgahuDxWonfNNv\n",
"XDPtJnZyhC4PSnzaIQ+FQsUN6qtY1v1Hnhz2C9df8xqq8fPRh8VR1PdaTry5jmZPrWL24bYkvQUf\n",
"/tOaaDmC46Ew9C6YfjVYFaBLPU2Lvx25WUrMZYbUJj3ycFJ+amaXZQqLLC7lPNfjL8tQYDTz4Z4l\n",
"/J22iZAieG2dgp0fj0J3jvMudRSSRMdWwdjsdgqLLGTll5Bx3UTu/uoL3uoPP5/5hKva98NQZEEG\n",
"TqUZxIitGqpapTKbLHT84CWeuxJeGgyyJNMp4HKmtp1DS7926HU+GApLCAnQcmLkaJJGjnadK4X4\n",
"8dtHa1BYLQRptLxsN/P9mQ/54cwi3hhg48/erfjtzSRi167gzNBRlLitwlwSfh7lbzIhpYDdxzPJ\n",
"yHVYns8V7Wqy2lh3YC+fn3oZgPd+BiluIKbgsArLWYKKKBUKAkvtGsbmMUzM7IjCDluzfyW1MFWM\n",
"3GqBpQrxCPz0PaYMPMO8ISBJCm6NfpDZXT6jpV87j+OiQv0qxFf5aFSgULjKgagUGia0fpjZXT8j\n",
"UB3GLk0SQ6dIWBP+pe/LT2HOLxsh1oevXyMUD89tZ7xKcely4bni1c5kFLL42EyKbUb+ewjGH4Ck\n",
"kY76rMJRsvaYr7mHMUfAKtn45sQSj315haZGkZu2seJ8WTkFwDfjLJ0WPMhUw6t81xl0sg/PdVnC\n",
"LdH/h0LyXCTo0zECpULhYdwH8Kkk/kqlkugYcDkLun9DS99YDobLDJ4C6n/X0PmhO1EVOZzHLsmR\n",
"R3kUkkRGXjEFReYK+35JXc5ew3ZCi2DhLxInRk/k9NBR6H01xMUE1VeXmxzOtHanh1zLtJOO0pqr\n",
"Tn5GkaXMizH+RBYpmUa2H0on/QIm3b1YcLqR+2iUSFYL3V+4l7vb/sFfrSDcHsCcnl/TNbBfpef6\n",
"l67+lRcPjaqieKhL/ZNCtc2Y23UZbf27kBAM19ypRH18J0OfmoxPdgay7Hi2LHXoMdzoxMOZKKWo\n",
"nHONE0mCQ6dy2H0s0+PzU8bDLEtw5OlYuM6Hva+vIv6BmUQ3C+DyuHAC/DT13/kmQotwf2Ii9KBU\n",
"EtLvLvqegXyK+Hj35x7HnTibT7HZyp6jGVW0dOlisthQFhvptPwDLp95J7cNOsm/LSFS1Yy5fX4g\n",
"xr9DtW34lHNb0KorPq7u0/gQn1Bmdv6IFr5tORBm47o7NfgmHGDY9InIViun0gxsPZBW6YvXGxqd\n",
"eKRkGck1mPj3SAYHT+VU8MarbGBSbDPy5pFHsUg27tsBQya9SUHr9gCuPJGCmqNUKGjb3GEQTe1/\n",
"FY9vc3z+XeLH2GW723Hiu60Kk9lG31dmEP3xG0zrtoe/Y6C5RcfsHl8Qpq1ZofTyPk9+Pmo6twqm\n",
"f+dmFY4N1mnp2ymCAHUwz3b+iAifKLZFmZk2WoXubDKag/s5neEInsvMrfhS9oZGJx6Aq0xCZbiL\n",
"SVZ+MbIs89HJuaSakumeBi8md6VkzC2uY4R/gvcE+msojohiuKUz0flw1pREfO5m137VJf7dGorM\n",
"VWbXl1NTabF1PQ/8B36PhYhC+KjTu3SLal/j9t2nKcrSEUZEsJ+HqFjcyi84QyzCtM358Mov8VX5\n",
"sqyrlQ/6gO+2v1z+U8Wmugk3aJT/+jVN4nUgMYeP9y9iS9Ya/M3w9bdQ9MRs1G5ZwcTb0Xu6tQ2l\n",
"V4dwsoaO4uHtjs9+OlNmOFUqL93v1lBkZtexTA4k5lS6P+CvDQ4HrstBI2l4ottHRHS/GqXS85EL\n",
"8teiVipoEeZfoQ2N2zRlQDfP0Ub/zs0Y0KWZayFB56v2mMJ0i+jGm8MdlRAfuRYOHFzrmga5+3+c\n",
"D41SPDzyHcgyoQf30O6Hz+n+4asEnDru2hWfu4Xntz4DwMerQd/+SsxDhnt86UI8vEelVBDgp+HM\n",
"zROZcCoCfzPsL9yJ4d8VDd21BseZ0auyUbLNbmfn8a95eqRj+8EOr9I6ahCSVPH3GOCvYWC3KEID\n",
"KtY28vdR0ypST4/YsAojaK1GiUatJCzQcV5kiGfGe61ayX/bj+XOmIlYlXBvh3hKjNml/aublZdG\n",
"KR7uPhldPn+XKx+bwGUfzCfu20/o99J0sNk4U3SCt449jl2289yfMPaYlu3PvIZKKXkosPBNOH8k\n",
"fQDx8z5n8gGH0XlT/Etoc7OaZEGsumBf8n4e77gXgCfaPkS/0KsBx0pheZFwiklV/kvVxXJ1ahVM\n",
"/y7NPNJLQNmK2aP95tEj24fEIJkP/34YAJkmJh7uDjHm0kpYPtkZxK10JKXJbxULQOCp46g2fc7/\n",
"Dt1Nkc3AKHsX5m6C1D6Dsfn4VhgWVuWsI6g5KpWEsUUrLr/2XSQZVnSyELX0hZpnxLqEKLIU8fC6\n",
"2ynQwphkPfcMeN61T5IcIw13g6dTPLx9xykVCg/h6Nw6hHbNA11i5Kf1ZY5pHD4WWGX7m+3Z6+os\n",
"O1yjEQ+AAD8NGpXClb2q1fpVKC0WUgZcxbqP1rJ3xgJS9PC4+XVyzRl0DujDwp91KGQ4O+AqoCzI\n",
"q2NMMCqFgtDAhi112RRw+hLo2g2hn/9ALEpYbfqdELccFJca5Yf+hcUWNu45w8O/P8JRazIdsuBt\n",
"7QSPaYrzgdZqlK4IZZ2fw5dDqqMRckSQLy0jyoIxAvzVqK66h/mbHNdZenAG+UXZdXKtRiEeztTx\n",
"2oJcmsdvw1RiRmUspP2PXwCQMMqxerJzcA8G3aPgVKCN3qkKXlI+QKs9u7ArlKReMRQoW11pFuLH\n",
"oO5RFYZzgtqjchvNXdv2PgA+6AOR679rqC41OOWnbOk5RWzM+I7Vp77G1yrx7UrwG3mjhyi4z0y6\n",
"tgmhR2xZjhRt6cpKVSkpvEWpUKBp2ZyhXR5lcBLkqIpZs2FqnXicNorAOLsMgScPM/CpyagNBUQM\n",
"vx51kQHf7AxyYzuR1mcIJwz7WXBkGgWBdnqnwK9f2AktvguAjB5XYA4IbuC7aLq4r6p01F9ON784\n",
"9nOUjfm/EVX8POh8kGX5kqiyB45gzaQ0zxKUpwsTWZr4EgCL1sjEGfXk9+uPwlL2kLp/PyqlwsOW\n",
"odUouax9ODEtgsjPq1uPXV+NihM338Vjq3L4x7aEbwMOcseJDQxof9V5tdsoRh52u50eH76C2uAI\n",
"5Gm1cS3Nt/+JVevDtpmv8UfmN8w+cAcFllx6Bg3muZ7LUUWUBRIdnjCtobp+SeBuN5IkiUk9HwHg\n",
"vcuKiVuxGKhFRvAmQHK6waNwk81u4397HsdkL+a6ki5M2gtZfQeDSuVhy6tOWwP9NfWSxc5HqwRJ\n",
"wjr6CR4+4rC3PL3+fsy28/M09Uo87HY7s2bNYvz48UycOJHk5GSP/Rs2bOCWW25h/PjxfPPNN9W3\n",
"V1RM2IFdyJJEwtzXXZ9vvfE6ZhW+xuKTc7DIZibETeapjgsxt+/Fug9X8+fLn7Dx9WVkXNbfm9sQ\n",
"1JAWYTpXrg+A/8SOIUwK5kg4JO/4kOY/f1fhTdyUyS/0fOje+PdN9ufsJFgTwZvrHaOJnEFXAlRq\n",
"87jQuE/db2zzIO2y4aicxhvbXj/HWdXjlXisX78ei8XCihUreOKJJ1iwYIFrn8ViYcGCBSxdupRl\n",
"y5bx9ddfk519bgON/PffKC0WjB06UzB2Aquem8PEJ/tyTbef2ZW7EZ1ax/sjPuKtq95BpSgNFpIk\n",
"Mi7rT1a33gBEhfjRMUZMXeoDPx8Vl8eFl22rNVwTMwWAN/pDmy8/4kxWoasgUVPHGfSmKcjldMEh\n",
"3tzjiKmaf+oKOuzcjVXrS/5wx/Ks+5SvoYb57uKRMfwmXv/HUfDsg70NIB67d+9m8GBH2rMePXpw\n",
"4MAB176TJ08SExODXq9HrVZz+eWXs2PHua3yezd9xW+xMG+kH/f/eStjVC/whf+/mOwl9Au9lq23\n",
"7eSWDuOqPD/QT0NcTDDNyjnKCOoHpULBVZFj0Sp8WB8LpwqP4p+SVGfOR42RwmIL+UbHiMNmlwnf\n",
"8w/X3jaYZX+MxSpbmJgQxrQP1wBwfPQdqEIcKQDdjc0XoHxspQTptfiWVkSUlSqaDXuMMYehWDq/\n",
"aYtXBtPCwkJ0urLlIKVSid1uR6FQUFhYiF6vd+3z9/fHYDj3kLaf76cwEWAHpINKUtM7ZCSjW0yl\n",
"ra4LUbpzBxJdym7SFxKFJGGXZZRKCZ0qkOERN/Nr2nLe7A+P/P0HikG9GrqL9UKxycrO0sjh/p2b\n",
"QYmJy9+dy/yBNuIjoXUuLFyRhcXXj12PzOX08P/QrpII2IYqnq6QJHp1CGfrgVQAkq+8npcefheD\n",
"5ux5teuVeOh0OoxGtwpVpcIBoNfrPfYZjUYCAwPP2V7PVAg2K2kx4g4GtxtKcEkv9GrHOWFBvoSH\n",
"l4mRXlfRbyMk2M/jmJpQ2+PPl6Zwvf8MiaXEZCNIr0WfmMvYdvfwW9qXLO8m89SvvxEUPJvw0Iox\n",
"GvXBhfw+/fU+rt+d1k9Lu42rOGY7xYtDHPvn54/CMEzD3on3Uxgbhx6IigxwfRfOc8PCdIQG+lZ7\n",
"vfq6t7FRgVisNpLTDKjHPcjvL86Ez6s/ryq8Eo9evXqxceNGRo0aRXx8PHFxca59bdu2JSkpifz8\n",
"fHx9fdmxYwd33333Odvbsxj23f0Ith5PEBrow/bD6RhMJYTotUSH+JKZWTZyMRRWnFf7qxUex1RH\n",
"eLi+VsefL03tepklZgyFJehpxlVRI1mfuo6PQ/Yx6q/9SAM61/sb9kJ+n+HhetLSC1y/u9Nn84hc\n",
"u4KxY8CmgCld7kM54BG2Ok8oPa7QUEJmabEU57k5OUbs1RTQuhD3FqBVcvj68WQYLPQ+j3a8Eo+R\n",
"I0eydetWxo8fD8D8+fNZu3YtRUVF3HrrrcyYMYO7774bu93OLbfcQkRExDnby/pmNUcD2hGnlDzm\n",
"iD4aVY1iU8S05cLTtU0ICknigeAnWf/TOhb1hmu2ruF0bAytml3YUVZ9Y3FbhjYnnebtFgc4FAHt\n",
"Atox84rZ7D6SV+GcShP31Gsva4dSrSLxP7deePGQJIm5c+d6fNamTRvX38OHD2f48OE1bs84aCjs\n",
"P4tSIXnUEDnXG0ypkFwGusrSswnql7DS4Xdf394MssSyRXOSVWnfMt48DYvVRrHJRoD/xZu97WyW\n",
"kRMp+fxncCxWNz+Xo1uW8toAUMjw7sjF6LV+gEM8fNRKV8byyn6TjcmeXBcBo43CSexwaU4ElVLh\n",
"sRYunaN37VuW5SQV8SsNh0at5Jm+TwGwLPI4haY8dh3NZPfxTEx1lDeiITh2Jg+7LJOeU+RKQFVi\n",
"NjDX/AmyBPfahnJ5ZB8kSSI6QkerSD0tw8sWESp7OG31UfPRS+oiVUWjEA8n5W+ourlz26gAIoN8\n",
"KySKFVxYBgybxNAzWgq0Mmv/med6+xpLLPVSbOhCYrXZsVjt+J9NZvOykSTqzXTLUDB+5DuuY2Kb\n",
"B9ImKsAjj4w7zmVSdSMaIdeFXapxiUepvcMZLBRSSYIUJ7IsExOpp5NbST1Bw6BUKZhic8RJLM9b\n",
"RbHNsdq2LyGbw0m51Z7fGPOCOB8um13GarVRvPQ+Pu6Uj9oGD7d6AW1Axd9dVVOBy9qH0aV1CIGN\n",
"aBrXZKYtTpwjjy6tQ+jfuVmj+rIFVaNUSLTsMp6ByZCnNPFr6nLXvsoy4LuTnG5gy/5UCox1k9Hb\n",
"W0rMVk6m5LuEzPlbtNlk5L1beLRXIgBjW9xH4GU3V/rwOeNSfMrFp2jUSsKDql+ivZA0OfFwrrSo\n",
"VYo6D00W1B8KhURO557M/Nfh4bvm9EcYrY4gx+qSJCelO5YlqxOZ+uZwUi6nMwtdGcad4mG123n/\n",
"xHzOBELPkjBuaPN/HvvdCfBzFJe+rEN4hX2NjSZl81BIUoVq7ZURUhrG7CyMI2h4VEoFskpNh1bX\n",
"MywRCuVC1pz9pHTfuf9NneLS0K7tzniVtOwi0nOKXG/mP5J+5nvdYXws8Fqzx1BKDvtFVW/usCDf\n",
"iyKHTJMZefTvFsWArs1qFHXYpU0Il3cIv6iXAZsazrfYyZvuYN5Gx9+/nF5Knjmr2nMVrulBw9o9\n",
"nDYOk9XG4eRclAoFBZZcXvx3OgDzNkDMIPeSHo3Ja6P2KJuKwTRQp/UMIDoHSoUCvaj+1qiQJIn2\n",
"LYMoaN2eqO63csNRR9DV79tnVrva4rItXOCRR1pOkcdUqeLqg8yShBfINmUx5BTclRGHKjys7PiL\n",
"XDyazMhDcPHTIswfH7WSvZMf5bEz3ZBkWCX/Rf7Jf855ntM72HqBxeNIci4HT5XVXCn/MP2Ruopt\n",
"2b/iZ1OydBXkXT7AYzpysbsHNCmbh+Dix0ejwhIQRNZzX3NTRnPMKvhm73PnPMeZc7auMnp7i7t4\n",
"ZJlS+eDwLADe+slGq0INybfc6SpnoFRIF73NzVerdCW29hYhHoI6o1loaT4VSeLWPi/ja4G1YadZ\n",
"vfe3Ks9xLsZcyGlLZULlnLbYZTvvn5iJUTZyw1G4ew/su/8ZTM2jARjQpRn9u1SsFXuxoVYpGdgt\n",
"6rzaEOIhqDOahfihLx3O+7e+gkcOORypXtn2JMdO52KopDq70yRyIV23KxcqGYWphB3rHuVA/j+E\n",
"G+H9db5sWbGBE9ePd2VB16iVNbbPNXXEtyCoUwL9HUvpNrvMJN1oWhTAMfspvjy8nH0nK6ajrIsS\n",
"ALWlMqGy2ewEvvcA7/n+DjjKl+aMeYCiaEfAZ0Ml8mnMCPEQ1ClO24Fdlsm7ZQovbXD8xL5KfJV8\n",
"U4HruLNZRg6fysH1HNexhlisVQfluY88nOIVuvoLnmizDZMKJh/0od3l93F0bFkemmp83S5JxFci\n",
"qFOUbuJhataSAVFj6H8acm25fHPsJddxx87kkZ5X7Kry7j4AKSy2cPBUTq1LhSamFpBrMJFrMLH1\n",
"QFqlGd3Tc4owFltc2wVGM7kGE++ffZe9zSCGUIZP2cLByY941EqQGlU2jsaBEA9BneI+updlmUN3\n",
"PsLrO1qissHPuT+wet/vHv4VTs9Od3+QAwnZZOYVczqjkHyjmeT06jNrFZusJKUb2Hsyi6x8R/sp\n",
"WYWcySwkv7SSfX6hicPJuRxyC9bbcyKLJeve4pN22Wis8NLAJfgqK6ZSvNijg+sDIR6COsXp/xCk\n",
"02KXwRQSTsaslTy2xx9Zgvkbp7E3Ia3Cee4rIM4CUna7zJ7jmSSkFrhygxhLLJWWeHC3nbiMsDaZ\n",
"Eyn57Dnh8HQtqSS/SGrxKRaefQWA2ae60rl530rvqyFsM40dIR6COiUkwIfubUPp2ibE9bY2BwRz\n",
"9RXzaZcNJ9VZrD74UoXz3N/sztGL7GYIce7fcSSDfw9WFJ/Kkvy5t2mx2j1XWWw2LBYjC/+9E6PS\n",
"wtiDMLzfs1UaRhtRHp9GgxAPQZ0TEuDjCJZze3hzrxjJvLODkGRYmf81R/L+9ThHpuLb3X1z++F0\n",
"9p4oi5XJNZiq7Yd7a4XFlrK0lfm5XHPPdfy8pDfH1Bm0y4ZnbOMwXNbXw/NS65a8R4w8KiLEQ1Bv\n",
"lH/eVJPe4vE9euwK+ODAIxRZPW0Zdlkmr9DkSvtXntzCMsHYezKLwmKLo26s3e4xSqnsQS8yWTl5\n",
"Nh+AXu++wMI2ySzvDv5m+J/qPk7cNwelQuFhs+ndMZzwYF9X3wSeCPEQ1BvuD7FSklAHBnBX37n0\n",
"OgupijwWnXjO4xi7HeJPVB+J6+RgYg4JqQUkpRVWEKryZOQUgc1G16VvsTPjV2aOcKyg/F/Xd1GO\n",
"chTu9vNReUxt1CqlaxojtKMiQjwE9Yb7A6dUSvTr3IyIu+7k0z+C0Zvgn5x1rEr52HVM+bd7djW1\n",
"b53LvCVma41GBp2+Wkz+X4u547+O7QmtHqd32AjXfj+tqkKGc3e/FYEnQjwE9YZ7/RZXGj61msA+\n",
"Y/jie8fmV8lvsj/lZ6BizIlzGbc6HPYSt+1KnnOfA/FY1y1k1O1QpIFh4WO4sblnMTI/H5UrhaAz\n",
"BWbrqAAA2jYPqFFfLiWEeAjqjfAgX4b2aM5l7cOJbVFWcvTMxGmMyI5k7kbHisqbx6aTt/Vj742S\n",
"sucUKS23yGO3wmxG/eksrr3DTp4v9Am5imntXvBIPhWk0xLoryE00IeurUPo2iYUcOSaGdazhatO\n",
"jaAMIR6CekWSJAL9NR5LoNaIZvz75AKe2wy374NCLcwoeYPD2YeqbEdTkEvnZQvpP/ch4t55EWxl\n",
"oxIZuUqbRNDxg4TPvoGbBh8kXQfd/XvzSIfXXekEwWGP6dkuzCUmYUG+rvB7QdV4VTFOIDgfJCCz\n",
"R18UMiz9EQq0sCZOZtLPN/Fk54+JVbSi5V/raLbzL5SmEiS7jYj47ahMZTYQgy6Io7fe49iQK19h\n",
"URYXYV98Lzdel0O+D1yu6cmjXT9Eo9ASrNO6Vm8uhoTFjZFai0dJSQlPPvkkOTk5+Pv7s2DBAkJC\n",
"PGtYfPrpp/z8s2MeO2TIEB588MG66a2gSSBJgELBrofnELNhDQsP2ilW7WF9bA6zD0xi8f6e9F25\n",
"pcJ5xs7dUVzRF9+lH9Pls3c4PWQURc1akFVQQnC5Gj+yLLN55/94b3QONgX0D7iShzq/iUrhsGVE\n",
"hfrRMSZYZOk/D2o9Nvvqq6+Ii4tj+fLljB49mg8++MBj/+nTp1mzZg1ff/01K1euZOvWrRw9erTO\n",
"OixoOiRcP45Nb3xB+pWjWfsl/DcrimJbIZM7buHFIXDkpgmc/M847Co1RWGRJM5/l8KX38D635tR\n",
"WizEbFjjauv4mbJi08acBJb+eh1vK3/EpoDJhj480uUdl3AAIElCOM6TWovH7t27GTJkCACDBw9m\n",
"27ZtHvujoqJYsmSJa/5otVrx8RG1ZAVVk3FZf7Q2WLGsiOn7Q7Er4Pkr4fpB+1g55Wa++3kfP325\n",
"CXNsewDkO+8EoNWGtR5LK1a7md/PfM7j+27i18BT+Jvhq9W+3NzrFRSSp1CIGNnz55zTlm+++YbP\n",
"P//c47PQ0FD8/R1Rh/7+/hgMnl6CKpWKoKAgZFnmlVdeoXPnzrRq1arajoSH66s9pi4R12u466UX\n",
"mCg0u3mRtm+PoU179InHee07GHbEl7tuD+Sk8QAz999K79ChXBc9ge6BNxEersd29dWYA4MJSD5J\n",
"/7dnseH/prIh93d+OfMVGSUpoIERJ+Htf5uTNXcZmi5x5JW6swfrteQaTMS0CEJXwyz8jfm7bEgk\n",
"uZbrYw899BBTp06le/fuGAwGJkyYwJo1azyOMZlMzJw5E51Ox5w5c2pUjyUzs/qw67oiPFwvrteA\n",
"1zt2Oo+z2UbXtgS03LCWfguedOwfM4l/7n2YH84s4pfU5ZjsjhB7rdKHTiGdaB/ejuK/d2HOSuBI\n",
"GCQHlbXdKRPmblIQdO+X5HXqAUBcdBAJZwuw2OwM6hZFidlW4+znjf27rIvreUutDaa9evVi8+bN\n",
"dO/enc2bN9O7d2+P/bIs88ADD9CvXz+mTp3qdccElw5KhYLTw/9D29QTsGc3h+54AF+lP+9d9yq/\n",
"xU/hj/Rv+Sf7NxKMB4nP3EN85h4IwvEfEFwMI0/ClD0wIgH2PjCTk6XCAY4Ugv26RCLLjup2Ol+x\n",
"DELnMq4AAAmASURBVFsX1Fo8brvtNp5++mkmTJiARqPh9ddfBxwrLDExMdjtdnbs2IHFYmHz5s0A\n",
"TJ8+nZ49e9ZtzwVNBh+NksISO4mPPU9yRtlbV6NWMrxrHHr1VEa3nEqLKIksWyLFynz+OZiMD3ra\n",
"nylg4rxnUVscruq7Hp5NwvXjPdqXpLISD4K6o9bi4ePjw9tvv13h88mTJ7v+3rdv33l1SnBp4RAP\n",
"C8Umq+uzqBBHGQd357Jgn2DaBzYnPFyPLucERSYrhMDux6DH4pdJ6zOIxFG3VGi/JtNmQe0RTmKC\n",
"C075Z9m5ZJpZmj4wMtiPuJhgwLOymbuQuI8kkkfcSPKIG2t8PUHdIMZyggtO+WTCGpXnMqpHQh43\n",
"Xwz3qm7OMpWV4af1fCeKsgn1gxAPwQUnNNDT76f8s11VHVX3dUFV6TFalRJdudKPwXptufaFeNQH\n",
"QjwEF5xgvZaBXctKHUqSRNuospD38qMKp/3DV1s2CnEv8eB+vEaloE2UZ/j8RV7QvtEixEPQILhH\n",
"rUqSo1Slk/IrIx2igxjYNQofjVskbGnJR7sse0xTurQJrVAOUow86gchHoIGR5IkT3tGuaGCJEkV\n",
"QuSdAuGrUXl4ijp1olOpwRXqvBidoBSx2iJocBSSp2BUZfNwp0W4PxqVgpAAravOi6Mtx7mRIX4c\n",
"TnYUdxKZz+sHIR6CBkeSJI+pRU3EQ6tW0jJCB4DVLdt6ZTMUoR31g5i2CBqcCqstytr9LN1tHO7L\n",
"wG2jAlAqJPR+NYtjEdQOMfIQNDjlDZo1GXlUTdkwIyZST0zkxRGhejEiRh6CBqe8VJzLAawqnMu5\n",
"GrVI8HOhECMPQYNTXiq88QiNiwl2ubQLLgxi5CFodCiEV9dFgRAPQcNTqhXR4Tq0KiUaUfbgokBM\n",
"WwSNhtgWgR7FoQSNGyHxAoHAK4R4CBqc8iH6gosDIR4CgcArhHgIBAKvEOIhaDCcSXx8tMKx62JE\n",
"rLYIGoye7cMwlljx9xGxJxcjYuQhaDBUSgWB/jWr2iZofAjxEAgEXiHEQyAQeIUQD4FA4BW1Fo+S\n",
"khIeeughbr/9du69915ycnIqPc5ut3PPPfewYsWK8+6kQCBofNRaPL766ivi4uJYvnw5o0eP5oMP\n",
"Pqj0uLfeeguDwSAyVwsETZRai8fu3bsZMmQIAIMHD2bbtm0Vjvn1119RKBQMHjxYJJ8VCJoo5/Tz\n",
"+Oabb/j88889PgsNDcXf3x8Af39/DAaDx/5jx47x008/8c477/Dee+/VcXcFAkFj4ZziMXbsWMaO\n",
"Hevx2UMPPYTRaATAaDQSEOBZnWvVqlWkp6czadIkUlJSUKvVtGzZkkGDBp2zI+HhFzbXpLieuF5j\n",
"vFZDXM9bau1h2qtXLzZv3kz37t3ZvHkzvXv39tj/5JNPuv5+7733CA8Pr1Y4BALBxUetbR633XYb\n",
"x48fZ8KECXzzzTc8+OCDAHz66ads2LChzjsoEAgaJ5IsLJoCgcALhJOYQCDwCiEeAoHAK4R4CAQC\n",
"rxDiIRAIvKJBkwHZ7XbmzJnDsWPHUKvVzJs3j5iYmDq/zpgxY9DpHBXVo6OjmTZtGjNmzEChUNC+\n",
"fXtmz5593m70e/fu5bXXXvv/ds4lJKovjuOfeSRlZhIYEsRIEj0QhaCV9lioTTSJSFA+SlDBmaDU\n",
"KLrOqDCCj1orVKAE40ahoWXhpk0DicTgK10ItrBIkoKZobqTnhbh/H3Mf/Efz/m7OZ/V5d6Z87lf\n",
"zuU3c7nndwkEAnz8+DHp+KOjo4yMjGC32/F4PFy8eFGKb3Z2FrfbjcPhAKC6uprLly9L88Xjcbxe\n",
"L58+fcI0TTweD3l5ecoyJvPl5OTQ1NREbm6u9Iyrq6u0t7ezuLiIxWLB7/eTlpamJF8yVzweV5Zt\n",
"nZWVFSorK3n+/DlWq1VONrGLvH79WhiGIYQQIhwOC4/HI93x8+dPUVFRsWlfU1OTGB8fF0II0dnZ\n",
"KcbGxnbkePbsmXC5XOL69ev/Ov7y8rJwuVzCNE0RiUSEy+USv379kuIbHR0VQ0NDmz4j0/fixQvR\n",
"09MjhBDi+/fv4sKFC8LtdivLmMynMuPY2Jjwer1CCCHevXsn3G63snxbXR6PR/n8maYpbt++LS5d\n",
"uiQWFhakXZ+7etvy/v17zp07B0BhYSHT09PSHXNzc/z48YOGhgbq6uoIh8PMzs5y9uxZAM6fP08o\n",
"FNqRw+Fw0N/fn+jjSTb+1NQUZ86cYc+ePWRkZOBwOJifn5fim56e5s2bN9TW1uLz+YjFYkxOTkrz\n",
"OZ1O7t69C/z9t2i325VmTOabmZlRlrGkpISuri4AlpaWOHjwIDMzM0rybXVlZmYqzQbw+PFjqqqq\n",
"yM7OBuRdn7taPKLRaOJ2AsBms7G2tibVsW/fPhoaGhgcHMTv93P//v1Nx9PT07f15/xXysrKsNn+\n",
"eYmv2LB0Zr3/JxqNcuDAgU37o9GoFF9hYSEPHz5keHiYo0eP0t/fTywWk+ZLT09PfL+5uZmWlpZN\n",
"8yQ741Zfa2srBQUFSjPabDYMw6C7u5urV68qncOtLpXZgsEghw4dSqzyFkJIy7arxSMjIyPRJwN/\n",
"f2WsVrmnlJubS3l5eWI7KyuLlZWVxPFk/Tk7ZWOGaDRKZmbmtqwyvaWlpZw+fTqx/eHDB+m+z58/\n",
"U1dXR0VFBS6XS3nGjb4rV678Lxn7+vp49eoV7e3tmKaZ2K8i37qro6ODoqIiZdmCwSChUIibN28y\n",
"NzeHYRh8+/ZNSrZdLR7rfTIA4XCYEydOSHcEg0H6+voA+PLlC7FYjKKiIsbHxwGS9ufslFOnTm0b\n",
"v6CggImJCUzTJBKJsLCwwPHjx6X4GhsbmZycBCAUCpGfny/V9/XrV+rr63nw4AGVlZXKMybzqcz4\n",
"8uVLnj59CsDevXuxWq3k5+crybfVZbFYuHPnjrJsw8PDBAIBAoEAJ0+e5NGjRxQXF0vJtqtPW0pL\n",
"S3n79i03btwAoLe3V7rj2rVrtLW1UVNTk3BkZWXR0dFBPB4nLy8Pp9MpxbX+xMYwjG3jWywWbt26\n",
"RXV1NWtra9y7d4+0tJ29OXzd5/f78fv92O12Dh8+TFdXF/v375fme/LkCZFIhIGBAQYGBgDw+Xx0\n",
"d3cryZjM5/V66e3tVZLR6XRiGAa1tbX8/v0bn8/HsWPHlMxhMteRI0eUzt9GLBaLtOtT97ZoNJqU\n",
"0IvENBpNSujiodFoUkIXD41GkxK6eGg0mpTQxUOj0aSELh4ajSYldPHQaDQp8QcCpDemCLH80gAA\n",
"AABJRU5ErkJggg==\n",
"\">\n",
" </div>\n",
" \n",
" <div name=\"mu2\" style=\"display:none\">\n",
" <img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQ8AAADVCAYAAABJ/XXDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
"AAALEgAACxIB0t1+/AAAIABJREFUeJzsnWdgVNXWhp8zNZnMpDdKEiCE0EEEBJGigspnQ0WqYkEE\n",
"FBQFkXJFvIpgR1EUy8UrFgS9iqIooiiCdAgQOgQCJBDSM5NkMu18PyYzmUkCISGd/fyBOW3vM5nz\n",
"nrXXXnstSZZlGYFAIKgkirrugEAgaJgI8RAIBFVCiIdAIKgSQjwEAkGVEOIhEAiqhBAPgUBQJYR4\n",
"CASCKiHEQyAQVAlVXXdA0Hg4ePAgP/zwA88++6x727p16zh27BgKhYLw8HCGDBly0e2ChoMQD0G1\n",
"sHTpUnbu3InBYHBvMxqNLF68mP/9738ADB8+nP79+6NSqcps79evH8HBwXXSd0HVEMMWQbXw0EMP\n",
"ceONN3pt2759O7Gxse7P8fHxbNmypdztW7durbW+CqoHYXkILsjp06dZsWLFBfd36dKFgQMHuj+X\n",
"XiZ17tw5/P393Z/9/f1JTk4mICCg3O2ChoUQjysYu93Offfdx1dffQXArFmzGD9+PDExMQBERUUx\n",
"derUS76eJElen41GIxqNxv1ZrVZTUFCAJEnlbhc0LMSw5Qpm9+7dNG3aFHBaDQkJCW7hqAqlLQ8/\n",
"Pz+vz2azmYCAgAtuFzQshOVxBfP333/Tt29fAA4cOECbNm289ld22FLa8oiKiiIxMdH9OScnhw4d\n",
"OmAwGMrdLmhYCPG4gtm4cSO33norAH/++Se9e/fm999/dzs+KztsKW159OjRg9dff939ef/+/Uyb\n",
"Ng1fX99ytwsaFsq5c+fOretOCGqfrKwsPvzwQ/z9/cnPz8doNGIymWjevDlRUVGVvt7nn3/ODz/8\n",
"wKFDhzAajbRv3x4/Pz90Oh1//PEHW7du5frrr+eqq65CrVaXu13QsJBEJrErk1WrVpGUlMRTTz1V\n",
"110RNFCqNGxxOBzMnTuXI0eOoFarmTdvHtHR0e79e/fu5ZVXXkGWZSIiInjllVe8vOuCumffvn0i\n",
"qlNwWVTJ8li7di3r169n/vz57NmzhyVLlrB48WLAOe696667WLRoEVFRUaxYsYLu3bvTqlWrau+8\n",
"QCCoO6pkeezatcvtpe/SpYuX5/zEiRMEBgaydOlSjh49Sv/+/YVwCASNkCrFeZhMJvR6vfuzUqnE\n",
"4XAAkJ2dze7du7nvvvtYunQpmzdvZsuWLRe9nnC7CAQNjypZHnq9nvz8fPdnh8OBQuHUocDAQKKj\n",
"o93WRt++fUlMTKRXr14XvJ4kSaSnG6vSlSoRFmYQ7Yn26l1bddVeVamS5dGtWzc2bNgAQEJCAvHx\n",
"8e59UVFRFBQUcOrUKQB27txJXFxclTsoEAjqJ1WyPAYNGsSmTZsYMWIEAPPnz2f16tUUFBQwbNgw\n",
"5s2bx9SpU5FlmW7dutG/f/9q7bRAIKh76k2cR2M3DUV7DbO9xnxvrvaqilgYJxAIqoQQD4FAUCWE\n",
"eAgEgiohxEMgEFQJIR51QLaxiAKzra67IRBcFkI8ahlZltlzPINth9LquiuCWiIrK5M33nilrrtR\n",
"7QjxqGXqx8S4oDYJDg5h6tRnKz6wgSEyidUyMiXqIctymdR9gqpxPDWX9JzCar1mWKDvReMgfv75\n",
"RzZv3kRRURGpqWcYPfoBYmNbs3Dh6ygUCjQaLc8+O7s4hcVslixZypIl75GQsBObzc6AATcwZMg9\n",
"PPzwfSxf/h2SJPHaa68RHd2aG24YeMF26wtCPGqQzFwzep3aa5un5bF5/zmu7diklnslqE7y8/N5\n",
"881FnDlzmunTp6DT+TFjxnO0bh3Hxo1/sWjRW0yaNMV9/Lp1v7Jo0YeEhITw888/4uenp3PnrmzZ\n",
"8g89e/bi77//ZsmSR+rwji4dIR41RK6piH0nMtH7qGneNNC93VM8LDZHHfSscRLbNIDYprWbgV2S\n",
"JOLinEmjw8LCsVgsFBYW0rq1cy1X585X8cEH73qdM2fOi7z//jtkZWXSq9e1ANx++xC++eZrZFmm\n",
"T58+qFQN47EUPo8aIjffAoDJbPXaXno1wPnsAg6czEKWZaw2O/uSMikodY6g/lJ62BkaGsrx48cA\n",
"SEjYRVRUSSkLq9XK+vXreOGFl3nnnQ9Ys2Y1aWnn6Ny5KykpZ1i9ehVDhw6t1f5fDg1D4hogRVY7\n",
"ACqFtz6XdpgeSM4GICbSwNnMAjLzzOSbrfRqH1lhG6fSjIQE+ODno67wWEHN4CkekqRg+vR/8dZb\n",
"ryLLMiqVihkznnP7ttRqNf7+ATz66INotVp69uxFRITz73zTTbfw55+/ExsbW6trWy4HIR41hNni\n",
"FA8fjdJru6fD1BMJUBT/EC3WioczOaYiks7mceJsHv27Nru8zgqqxODBt7n/r9VqWblyFQDvvvth\n",
"mWM/+OA/ADz44CM8+GBZn4bd7uD22++qoZ7WDGLYUkPYHU6RUCq9zdqLTdWqio91yDJnM/MvfCBg\n",
"LfaXiJnfhs+8eXPZsWMbN900uK67UimE5VFD2O3Ox9pRyoi4kHgYC6xuQQA4fDqHAD8NuuIhiSzL\n",
"HErOJtjfh4hgnRCNRsTs2XPrugtVQohHDWEvVo3SDtILDVsOnsousy0tuxAfjQWHQyZAryUtp5C0\n",
"nEIignUi2kxQ5wjxqCFcwxbXvy4q88wnp5U4zjq2CK6WfgkE1YXwedQQJcOW0uJRNYvBWFh6yrdq\n",
"/RIIqgshHjWEa9hSxvKo4vWyjUVAyYyM0A5BXSPEowawOxzuh9tR2udRxac+r8AZdKZVK4uvI+Sj\n",
"vjFmzPBquc7s2c9c1vnTpz/FuXNnq6UvF0P4PGoA15AFnOLhetDlUv9PKTzOyfzDZFnO4ZAd+Ch1\n",
"NNe1ppVfe3Sq8hdkqZROvS89HBI0HubNe60arlLzCy6FeFQzsiyXWd1pdzinWXPyi9AF5vL5yQ/Y\n",
"mLGaLEv5OT2UkpougddyY8S9dA+6wSuK0SU+pYdDVzr+o4aiXbe2Wq9ZNPAm+O3XC+43m838+9/P\n",
"kZubQ7NmzXE4HCQlHWPhwteRZZmAgABmzpzD4cOH+OKLz9Bo1KSmpnDjjTcxZszDnD2byvz5/3ZX\n",
"W5wy5RnCwrpxxx0388MPv/K//63kl19+QqFQ0LZte6ZMmUZa2jlee+1lioqK0Gq1TJ8+m/DwCD75\n",
"ZAn//LORkJBQzp+vnVwxQjyqEbvDQUp6Pkln80ptlzmcdpoVpxfxx/lvsMvO6NNAVTCdHC1oatWj\n",
"khXkYeKINouj9pPsyv6LXdl/EaNry0MtZ9I+oCfg9HVYbfYybQhqn++//4aWLVsxbtxETp06yTPP\n",
"TOGVV+Yxc+YcWrRoyerVq/jii8/o0eMa0tLO8dlny7FYLAwZcgtjxjzMe+8tZNiwUVx3XT+OHj3C\n",
"ggUvsmrVd7jeFWvW/MjUqTNp27Yd33//DXa7nffee5uhQ0fQq9e17NixjQ8+eJcRI0aza9cOPvlk\n",
"GUVFRdU2fKoIIR7VhMMhs+3AeYps9jL7vj3wDU8ljMdky0UhKRlgGMiT643cvmYHSvuuMsenBml4\n",
"//Y2vB+bQnLBIebuf4CbIkYwpuUM1FYFmxLP1cYtNSjyvvymRq4bdpF9p04l07t3HwCio1sQEBBI\n",
"cvIJ3nhjAQA2m42oqGgAYmNjUSgU+Pj4oNVqAUhOPknXrt0AiItrU8ZimDnzeZYv/5zU1BQ6duyM\n",
"LMskJR1j2bKlfPHFf5FlGbVaTXLySeLj2wLOMPm2bdtTGy51IR5VQJZlbHYZq82Bzsf5FZot9jLC\n",
"oVA4+PjYy/zyzxcAdNb35KV9Lfi/r1ahtBThUCrJaN+VwpAIkCRkhQL/U0k0TTrEi58lMlsFz98Z\n",
"xpudslibtpxjpn1Ma/sOodqmtX7PgrK0aNGKffv20LfvAFJSzpCbm0N0dAv+9a8XiIiIJCFhF7m5\n",
"ucVHl/VBxMS0JCFhV7HlcZiQkBCv/T/++D3Tps1Eo9Hw9NOTSUzcS0xMC0aOvJ+OHTuTlHSMAwcS\n",
"adGiFd9+uwKHw4Hdbufo0cPltlfdVEk8nJmR5nLkyBHUajXz5s0jOjq6zHHPPfccgYGBTJ069bI7\n",
"Wp84lpJLSoZz7Un3+HD0vmr3KloXVrmARUemsuX8n2gUGp403sgLC7fim7MNgNP9buHs9OcJbNea\n",
"PcczvM71Sz1FqzUrafHL/3jl23RGboLbHzaQxH5m7xvJc+0/obmutft4Y4EFg05Tw3ctKM2QIfcw\n",
"f/6/mThxLE2aNMXfP4CpU2fw0kvPY7fbUSgUzJjxHOnp50st3Xf+f9KkKbzyykssX/45NpuNGTPm\n",
"eO2PjY3l8ccfQafzIywsnA4dOhEeHsHrry/AYimiqKiIKVOeIS6uDddd149x4x4gKCiIgIBAaoMq\n",
"lZtcu3Yt69evZ/78+ezZs4clS5awePFir2OWL1/O999/T8+ePXn66acrvGZ9L+lXYLZx4lwecc0C\n",
"+Gd/ybChY0tn5GeR1cHRMzkAmGy5vHn8URIz9xJk8+G730LovzUFgIz2Xdnz6HSy2l9Fk2AdkcE6\n",
"dh/LKNsgoDQXcsOGlfi/+So5Wju3PuLPlpA8DKpAnuuwlBZ+bd3HdmgRTFigb5Xv73JozO015ntz\n",
"tVdVqhTnsWvXLvr27QtAly5dSExMLLN/7969DB8+vNHEIxw6lU16TiEnzuahVpZ8bakZ+SSeyHIL\n",
"R74tj5f3PURi5l5aZ8L298z035qCsVkM//xrIevf+pKs9le5z5cUJW+kLrGhXtmw7D6+WKfP5K9X\n",
"l6LTBPP7B3kMTDVgtOXw8oFxnDenuI/NqOb8nQJBRVRJPEwmE3q93v1ZqVS6p5vOnz/Pe++9x5w5\n",
"cxqNcEBJXIXNLrsDtQCyiiM/AYrshSzY9zDHCg/SKgt+WxWEdeDDJL7+Eb9+9CMp/W6GUpmnFB6f\n",
"fTRKFIqyY9WMzj34Y+GXyMHNWP2JkevOG8ixZjDvwCPkWZ0L6opESkNBLVMln4deryc/vyTfhMPh\n",
"QFGcMevXX38lOzubcePGkZGRgdlsJjY2liFDhlz0mpdjPlWFyrYXcNaIpFLi7++LnF+EpPJO8uOQ\n",
"Hbyz43EOF+4nOgd+3xyHfvVqDpmcvgg9EKDXkmsqEZvAQB3hYQYMKc5p16hmgZBmxJBj9uqnQe8D\n",
"8fEc+ngFHR66m9WfpHHdRB8SA0+y8OiTzO/+BZJSSUCgDk2xsNX377MhtdeY7+1yqJJ4dOvWjfXr\n",
"1zN48GASEhKIj49377v//vu5//77Afjuu+9ISkqqUDig/vs8jEYzxgILGgXkGIuwl7Kqvjo6n43Z\n",
"fxBghpV/ROH35Rpy/AIxnkvHoPfBaDIT4KvCaCoRhhyNggyN0r0tI8NEdnaB1zHp6UbaRwVgsdo5\n",
"7ojkj9c/o/+zD7H241SufkxNIttZcmA+Y1pM59DxdJqE+F0R43Th86i+9qpKlYYtgwYNQqPRMGLE\n",
"CBYsWMDMmTNZvXo1K1asKHNsY6lL4roNm91RRjg2pa3iu/TPUDpg2e/hpM38HMLD3ZnBXJgt3iUm\n",
"JUnCR6NEo1IQFabnQvhqVQTotcgy5DeNZv0bn+Pv15SVX1lROSRWpy5lS8avXsmEBIKapkqWhyRJ\n",
"vPDCC17bWrZsWea4u+5qWDkZL4ZUPH3mekAVkoRDlkktSOLjI/8CJbzxlx7F5C8pCAkHyiY/Dg3w\n",
"JSPX7LVNoZC8ard4am27mKBSvXCKVmF4EzbM/5hBk4bx+q8mpgyG94//i/4texNoiCX9RCahfupG\n",
"I9yC+olYVXsJFJit7tWxLvHQqBUU2Qt5d8dD5CttDN+voPd9/6UgsiQZsWf+0mCDD5HBugrbigjS\n",
"ERbgS9fWoUQEeR/vafCYmrfk0OMzeGIr3H5MRaHdxL+2PMmOw2mcOmcsI1LGAgu7j6aXsX4ENcfW\n",
"rZv54YfvLrh/zZrVbNy4odLXveOOmy+nW9WGEI8KsFjtbDt03r0k3mp3iodaqeTL3dM4pjpPXCY8\n",
"0fZFDAOu8zpX5TGlq/e9tPIICoVEh5bBBOq1ZfZ5Lu9v3TSAI4PuIa3btXz8nY1gi5p9uVtYe+4r\n",
"Zz9LDWEST2SRm2/h9HnTJfVDcPlcc01v7rjjwtb34MG3cd11/Sp93fpiUIrw9Aq4UFW37SmrWGP5\n",
"Ax8rfGy+h7jJkwGICtO7Zzw8Ke3/qAou7YgI9KV5uJ7jqbnsePpFBo+/k4++M3HPcPg8+XWuazYI\n",
"oymczDwznVo5Q55tHsOtxsio1UNZd6p6V9UOjL6J3x668Kpam83Gyy+/wNmzKdjtDoYPH8V3331D\n",
"cHAIeXm5DBx4M2fOnGbChEl8+unHbNjwJ4GBQRQVmXnkkQns2rWDkJBQYmJa8Pnn/0WjUZOWdpYB\n",
"AwYyZszDJCUd4913F2K3O8jNzWHatBl07Ni5Wu/xchDiUQXyLJm8vXcGaOD5hAiavvGOe19ss/JL\n",
"Hpb30PpqK/f1u5Inu3wZXVqHkhaswzT3Je5+ZgrDDvuwIt7M4kPP80zcYjLzSoYuLievpzUkuDxW\n",
"rfqWoKBg5sx5kYKCAh5+eDQajYbhw0fRt+8A1qxZDcDRo0fYuvUfPvlkGRaLhQceGAF4Tya4Vt36\n",
"+2u47rrrGDPmYU6cOMGkSVNo1ao1v/32Cz/99KMQj4aMLMss2zGJTI2FAckKOt3zH1Q6nwrPK51/\n",
"IyzAl2ZhfpVs3PmP6zcXqNcSqNdiuf9Bsj76mHd+SGTN0xp2ZPzJ1pDf6BVyk7tamQtlOUFojYEv\n",
"b6uZVbUXIzn5JN27XwOATqejRYuWbN++lejoFl7HnTp1knbtOiBJElqtlvj4dmWu5Vp16+vr6151\n",
"GxoaxqeffoJWq6WgIB8/vwvPyNUF4jVUAaXTCP5z/gf+IgF9EUzTTaCgeasysyqe+BQPYUobHhFB\n",
"vpUeQshu8Sh1nkLB7sdmEZEP89c6HaKfnniZQnt+Gd9HIx211AkxMS3Zs2c3AAUF+SQlHadp02Zl\n",
"/j4tW7bi4MEDyLKMxWIpXvVamrJ/mLfffp2xY8cze/ZcWrVqXe8itoV4VIDn3yvPmsWnR51T1K9s\n",
"D6Hw/8YDZavCedKldShREYYyVkZVfgYuIStPALLaX8XJgXcwYZuDq3L9ybKk8b8zH5Tx2dSz31+D\n",
"5s477yYvL5fHHnuEyZMn8NBD4wgK8i6RIUkSrVq1pnfvPjz66IPMnv0MKpUKlUrl3u/5b/FZANx8\n",
"82Cee+5Zpk17AlmWyczM8Npf11RpVW1NUF+j+LKNRe4l8+8fnMb67J+4MQk+7PohOzs6Fwf279L0\n",
"ojEVnu39meBczNY+JojwoIqnbj3ZtO8sVruD5qF6Wjf39q0knzNydv8xbn7kNvYEGOn5KKglDV9c\n",
"/wd9WndkU6IzIW6rJv5ER1Rv+HNjjsKsjrays7P588/fueuuoVgsFsaMGc4773xAeHhEjbRXGWo9\n",
"wrSxk1VcqR5Kcobuz93G+uyf0Npg3qF2FAy+3X18ZYKxdMVOUm05MzIVcTHLIybSgCMikr2PPkOP\n",
"VBh+UINVtrBw78skeCz5rx+viiuLwMBADh7cz7hxY3j88XHcfvuQcoWjoSEcpqWQZZm9SZkADOja\n",
"DIdDxuqwOKNIgVl/g2nUc/irqqa7V8WFkptvIaCcOI6KO1f87wW0SqlQcOKWobT4+1de/WUT37dR\n",
"8E/GzySkjyHO0AUo68MR1DySJDFr1vN13Y1q54qyPGx2R4VOJ8/dqRn5HD2Ty6qUj0ixniY+A0Zx\n",
"E1ntr0J5ESfpxVCrlIQG+FbpXFfXLuRoVSokkCT2P/syTc2+PP2P09/x2clXPEo+VKlpgaAMV4x4\n",
"OBwyG/ed9TLhyz3O4+k6ciaHZNMJvju9BIDFa5QceciZUlEhOadKm4ZUcrr1MqjIanBNwxY2iybx\n",
"oSeZsRHCChQcNu5me9bvl3QNgeBSuWLEw1YcVp6bb7nocaXjMT4/+RpWrNy/B5p3Hk1+U2euVkkh\n",
"0bV1KG2iaidfJEC7aOdCuQutkfHMSnbsztHYo9rx3J/O+15xehEO+cKWl9Xm8Mo1IhBUxBUjHpdC\n",
"YlImmz3ykybmbmVb1jp0Fnhxky8HR01w76uLMO+IYB0Duja7YGSqZwCYrFSxa/LzPLILmufCqYIj\n",
"bMn85YKV5nYdSWf3sQwKzGLhnODSuGLE41KM9QyPcG6HbOe/J+YDMHMjGG8ZiyWgZIl8fVwj4ioD\n",
"4SKrXRdSbxrGc8ULN1eceher3YYsy2WGL4XFq21LZ4EXCC7ElSMelRzrrz//P5ILDhOVC48nBnH0\n",
"7ge99tfHMG9DOSt39z38FKOSAmmVBanmE/yW8j2HkrPZsCeVPxNSyizRrydhP4IGwBUkHpd+bIHN\n",
"xPJTbwPw6m+QPGw8Np23Y7SKky01SmigbxkHrtU/kANjpzPnL+fn/x55i9TskiCk9BzvvB/CoSq4\n",
"VOrhI1AzVOaN+l3KEnKtmfQ+DbenRXL8thFljqmPWboUkkSbqMAyy/8tw0Zyk6MbcZmQaj7DpvSf\n",
"3PtKfy9COwSXyhUjHpdaVD7NfJqfUv8LwMJfYP8DT+LQlA3oKq9EQv3Bu29tYoJRvPUO0zc5t686\n",
"+R4O2TkLU1osxLBFcKlcMeLh+VDIslzmIXHNQnx+8nVssnNqtmVwd5IH3el1XLDBB4n66TB14blQ\n",
"T6NSIEkSUqdO9GlyN1G5cNp2mu1Z64CSHCEuhHYILpUrSDxK/v93Qgr/lKo0b7M7OJC7ja1Za9FZ\n",
"4KU/Vex8cm6ZhSSdY0Po16V+F5ruFh9OoF5L7w6R9O4QCTiHWcdHPs60Lc4/+arjbxeLqPe5wuch\n",
"uFSuIPEoeSgKzDZ3LlIXRVabe2r22U1gumUsxujYcq9VH/0dngTotXRtHYpWrfTqa2F4E66PHE64\n",
"CY7ZktiTs7FMUNyF4kAENYfV5miQiamvGPGo6JlYcfRLThQconkuTEhq7hUQ1pg4MXwiU7Y740F+\n",
"PPqWO7epi9JiIqh5Nu8/x5YDaXXdjUpzxYhHeY7AgyezkGUZk8XIG9uKk/ysg0MT5+LQOlMLBug0\n",
"xDULoFubMK5p1/CXURcFhzGs9YMEFsI+20F2ZWzx2i+GLbWPw71osWF991eQeJTdlpZTSGaembd3\n",
"vkGGNYtep6FPyGDSuvdxH+Pvp6FZmB5/nabSCYvrK/KEaUzc7byXFTtfJdujWLdDFJ2rMxqacF9B\n",
"4lH+H2b/uWN8sNuZ/fzVv3TsmTDTa3/9npKtHHHNAmjdLAApLJRbIkejtcFm607WJG53HyN8HnVH\n",
"ZYW7wGzjz4QUzmcXALD/RBaHT2XXQM/Kp0ri4XA4mDNnDiNGjOD+++/n1KlTXvtXr17NsGHDGDly\n",
"JM8//3y9MMfOZOSXu/39nXMowsbovaAd8hxFwWFe++vzlGxlaRamp3mYHoUkkTXkMUbvVyFL8NuB\n",
"N93H2IXpUWdU9jlJyXAW8Dp6JheA9NxCzmYVVHu/LkSVxGPdunVYrVaWL1/OtGnTWLBggXuf2Wzm\n",
"7bffZtmyZXz11VeYTCbWr19fbR2uCtnGInLKWW5+JH0Tf+T8jq8Vnsy8pkxMR2PGqvfnbj/n/a4r\n",
"+IM8axYgLI+6xFFO/NHFcCW3Vlcxq93lUqVWd+3aRd++zuS/Xbp0ITEx0b1Pq9Xy9ddfu2tP2Gw2\n",
"fHwqrmtSk1htJStF9T5qfDRKZGsRK3ZMAeDpPQbOTnyt3OSgNnvjexPrtCpnoe5bn+DWIxJFSgfr\n",
"j34AlBSHEtQ+yeeM/LolmcKiS5u2tVrrVjyq5AE0mUzo9SUFaJRKJQ6HA4XCGc0YHOxMP79s2TIK\n",
"Cwu59tprK7zm5WRxrgirJGHILASgc+tQ8vKL2P3OPextZaKZUeL2cd+SHRZFsE6NqcCZ+Lhti2Dy\n",
"C63ENgvApxocpTV5f1Vp754Ifzbu0fPA9335iQ2syVjBvb6zMBh8q9TX+nZ/9b0tu0N2r8w26J0v\n",
"V5PFKQYOpfKS2vRJycMgSYQF6wgLM7iv43nu3mPpKCSJjrGh1X0LVRMPvV5Pfn6JD8ElHJ6fX3vt\n",
"NZKTk1m0aNElXbMm081nZRVgNDlXj2Zn5+P38eu8FuZ0Et4X+TjnDDFYTGauahXMhr2pAOQbCwkP\n",
"0mHMK+Rye1ZfSxME+aow3TCVq3duYGfTIn49sJS7Ok6odF/r6/3V17asNgebEs/SJFhHfHSQ+7cJ\n",
"TiHJzDRht1jR+6ov6nPLzMrHaneg1yhIO5/nvo5nfw+fcCbzjvAvP+F2rZde6NatGxs2ODPMJCQk\n",
"EB8f77V/zpw5WCwW3nvvPffwpS7xNMT9161hya7XOWuA9rTgqs4TsdgcKBWS18xKfY8irQ7Cg3Rc\n",
"decAxmd0AGBN8odY7SIZUE1jKnRatxdybp7PLmTXkXSSUvMueh3PgD5PX1VtTVBUSTwGDRqERqNh\n",
"xIgRLFiwgJkzZ7J69WpWrFjBgQMH+Pbbbzly5Ahjxozh/vvvZ926ddXd70phL/ZbaLMzKXjtKd7s\n",
"7dw+utMCFJLzKyg9brwCtANwTkV3HTSb6Bw4qclhW+ovdd2lRk9FTmlTcc2g9OxCZFm+oA/EFRfi\n",
"kL3jmGrLbVWlYYskSbzwwgte21q2bOn+/8GDBy+vV5XEWGAhNSOfuOaB5cZl2Iu/3W6L/s3ka3Kw\n",
"qKBf6B3uWiYAPmrvr6IxTdFWhPnqaxm3pgnPdTvL6n2v8fgND9R1lxo1dvkSrQTJOQ2bmpmPwVeD\n",
"TqukXYvgMoeVTivpkGUUtVCSslEEie0+msHZrALSsss3A+0OmbCErRxKXcv37cBPqWN0i6lex/hq\n",
"K1/BrbGgUCq4pssU/M2wU32KPed21nWXGjV2jxm80qu7PZGA1Eynb9FYaCEtp9CdoNrhJUDe1ozr\n",
"/zUdsdooxMNtvl3AHLTbHcR/vogptzg/T+w6jSBNuNcxPhpvy6OhhQpfDgpJIufaW3ngsNN5tuTn\n",
"mZgKrQ1ypWdDwPN3Wnp1d0VkFSfp9hSg0qkVKnoeqotGIR4Vod+2iW99d7E/HKL8onmww8Qyx/iW\n",
"yjx+BWlwdEcZAAAgAElEQVQHkgJQKrkp+iEUDvi+YAtr9+xly4E0ETRWDciyzJb95ziU7Awdt9kv\n",
"8TstZ+Thym7veQ2HDGfSTSWfHSXtevahurkixMNv6WvMud75/1k9X0KjKjsD5KvxHrZcaZYHgOXG\n",
"B7n7qBqbAv7a7wxZt9jE7MvlIstgtto5Vzystl3GEgBXVKln8KLN7nAPb8DT8vDuQ3XT6MVDvelv\n",
"Xo7YRbYvdNb35Maoweh8nCUKPCvVu1bMRgQ5q7GVV8agseISD7uPL3f73ArAz6Y1mO0F7h+roOqU\n",
"fhHZL9HyKO84V7S05zStpVStnZJZGLnMtuqkcYuHw0HCu0/xSTdQywoejpsLQNNQP9pFB9E5NsR9\n",
"qErp/CraRgdybYdIt8BcCXhOLOlveopeZyRy1TY2H12KxWoXvo/LIN9sJT2n0P3Z4ZAv2c9R3tII\n",
"azmWR2mBl8txmNbEsKVxJKi4ANL3K5gUfwSAIU3G0tS3JQ6HjCRJRATryv3jSJKERn1lzbx4Tm+b\n",
"Q8K5L78HW9jGmtT/MjD5cewO6No6lEB93Qf8NSQKzDa2Hzrvta3Iar+oH8lkzePP8z9xIG8HJ/MP\n",
"kmvNxGI346fyJ0zbjHYBXbH7DyVa09F9TmmrwnV5LydqDRiQ9UY8ZFnGYnWg1ZT/4FptDvYlZdKy\n",
"iT9Bhkv4ERcV8dGP09nfA6IcwdzZ4nEA9B7DEZVSQYtIA/oryMooj9IxLS37zyDm0N2cDDSy8/Rq\n",
"uja7jRxTkRCPSrLtUNnUgmaLvdxUj2cKjvF9ykf8k/ELNrlsMfZ8ex7ni86wP28r35xeQqRPNHc0\n",
"G8uAsLtQKbx/v1a7o4xI1cSwpd6Ix/4TWWTkmbmmXUS5GbvOZuaTV2Bhz/EMBnRtVuH1zn/4Mi92\n",
"zQHggfYLCNUb6No6tEwQWYtI/+q5gQZM6SJR+a3a8eC6FrwQeJK1h9+ma7PbUNbHEnkNEKvN+6E2\n",
"WrP56tTb/J62AhkZSYbeeeHcelJLjzMyEXIguiIHJlsOhyIU/N7Glx8iz3HOfIoPjz/Pjyn/YXzs\n",
"i7QP6OG+5oGTzvQKHT0CymrCYVpvxMNVZDq/0FqueFRGOdM3buPpkwspjIUbFT3pHNwXtUrRqLKC\n",
"VSehgb5E5hWRb7ZhLLSgViroedVTGExPssPnDCdz9hDXrB82u4NN+84SE2kQolsBF/IxWG0Ot3js\n",
"zfmHd49MJ8eWicoBj+yE6ZugZY7nUOeM+39XHYSRf4JdgpUd4PkBcCQ0mbn7x3B7+H2Min0WpVTy\n",
"7JgtJY7URm15uCg9NHPIMqYCq1s5L/b4yzIYs/L4/f1RrO0jE2jVMLz36zXV1UaDQpJoGxOE3eHA\n",
"VGAlI9fM6e6DuO+TQN5vn8P6PQu4oV1fjAVWZODkOaMQjwq40CyVxeagyG5l+amFfHfmQ2Rk+ibD\n",
"B6shLl9Pep8b2N26I4ZunUiy+aDON+JQq7H6+dNEMsPWrQQf3sstp5K486MkXultY15f+PH855w9\n",
"9ReTeixFZ3Ba5maPWZgrwmFa+iaTUvI4k2HCtzgC9GKrXYtsdk79+0lmd3cq94OtnydQ40wrWHo6\n",
"S1AWpUJBgF5LRq4ZJImbWoxjieM11ikSeMyYSoC+ZcUXEQAlsyKlMRUV8Grik2zOXIvCAXP/golp\n",
"HTk8+TG+79EPQ4AfRpOZvp2bYNx3zstiCI3050RU+5KL2e3cmLiDa759noeuS2aH/jSv/HULz8V/\n",
"iCqut9csWU3E+tW7gWxpgXStVyks/iIutl7N+tMaXtb+D6MWrtP0pHfTu9z7RKBk5bH1v487krRY\n",
"lfDjBu+FkDmmonqRm7a+4npZeTqj8215TP57BJsz1xJghrWfSwxtNoG/3vqKs72uB6VzsqBH23CU\n",
"CoWXcx/Ap/T6K6WSnB7XYnphDe8FLCA+R8PBYBv/OjIW9T//c74EirkiIkwrukmFJHE+p5C8Am+P\n",
"tE9GGrt+fZLfYiHQ7sOYzm+4rRSDr4b46MAa63Njw5WeQFZrGOJ/NwAr836hwFoSxZhwLIOU9Hy2\n",
"HkgjrRaT7jYUXGHkPsWzhwU2E/MSx3LAuItmebD+S1+UEz9l/4NPIiu9BwB+xbN/pcVDoyo7E6lW\n",
"KkCScFxzJzMGrKWTMYCkIJk5abOJ/Gax+20sy85ny1qNEcP1TjxciVIKSgXXuJAkpzd515H0km12\n",
"G37vTWR6P+fxT3R9lUCNM+1aVLieq+PD8NdpaqH3jYNmYX5EhzsXyRkGTqFHqoJsjY3Pf37Z67hj\n",
"qbkUWmzsPny+vMtc0bjEw1erwmzPZ37iWI4VJNIyG9avCCDj2WWkd+l50Wv4lApb0KrLPq6ew/hA\n",
"QxOevP5nWlqD2BcBs6yLaLd4LtjtyLLMyXNGNiWeK/PirSr1TjxSMvLJNhax7dB59p/MKhONV55h\n",
"0mLZm0zodhCLCm4PvZvRXUe69ynFDEulUSoUtGrqdIja9f6MtPUD4NuUZThkh8dx4ru9EEXFMx1q\n",
"lczrBydzuGAvUbnw86oQjj//OTlxHSq8RumYJ52PmvYxQfRuH1nm2CC9lp7twvHXBPNMr2+IJJCN\n",
"MfC6tIJe86bgsFg5fd65eC49u+xLuSrUO/EAyi2T4MJTTDJyC1H9vpaF5qUcDYFWiihm9nvNKyuY\n",
"iE+oOgF+TmutxaA5ROVCkl8Bx/Yvc+9XXeHfrbHAcsHs+kVW59v+rcTZ7M3bTLgJfvk+ENPC7zDG\n",
"tL6k63sOU5TFFkZ4kM5LVKwe5RdcSyxCtU354P++w1fS8t+u8GPROsJfmesOgbjU7OwVUS//+pea\n",
"xOvMbxv5bPFovugMvg41kzt/QLDO4BwHFiPejlWnU6sQurUJQxnZnBGFziCkX5Led+9XKq/c79ZY\n",
"YGHnkXQST2SVu99ssfPT2f/w3cmv8LHCd9+oUcz9FGuM94xVoJ8WtVJBs1C/MtfQeAxTru3kbW30\n",
"bh/JtR0i3RMJel+11xCmU3gn3hq4GIAnb4Ejv39E3LefuvtWHdRL8ago34E2O5MOn76N5d1RPH29\n",
"00p5tM3LNNO1QqVUeH3pQjyqjkqpwF+nQa1U0GXAS/hZYGNoLjl7v6vrrtU5roxe5VnJdoeDDWd/\n",
"5bOTzhij//6owfL4x+R361Hm9+jvp6FPpyaE+JetbeTnoyYmwkCX2NAyFrRWo0SjVhIa4DwvIljn\n",
"vV+t5O64e7k/fjw2JYy+ByI+eImui19GLqgeB3e9i/OAcmIyZJnQfTuI/mM1/qeOE3x4H4cDLYwe\n",
"Cw4F3NNkHH3CbwOcodaeCiyiSi8flVKBJjiau/I78blmH78nvsE9nYY0yoJY1cHes4d49/B0AOav\n",
"g6b3LORsl54ESBKB/lqS00pKI7jE5ELxSy2bXDwYr11MEDa77JVeAkpmzJ7uMpuNZ/7mBAd4crDE\n",
"0u+X0WT7BmzvL8Haq+J6Shej3lgenvPhFmvJjzJy65/c9OgdXD9tDLE/ryAscSen/CzcMFZDrg/c\n",
"0Oz/uLfFFPfxSqX3LV0oWEdw6ahUzr/Ntb1fQJLhf1GZqLatvvSMWFcQBdYCJq1/iAK5gKH74dE2\n",
"4znb25mJSpKcloanw9MlHlV9xykVCi/haN8imNZNA9xipNP6MjnuVbQKLZ92lVnWLxJ9SjIBdw5G\n",
"P/XJKt6lk3ojHgD+Og0alQKLzY5P5nl6LphO3+cmEpB8DHNQKEfvn8jKBW/S+5kmpPlYaO/fg4eb\n",
"z3OXT4CSRV5to4NQKRSEBNRtqcvGgMuHFBrcjuvNcViVsCnhFRxXcFHs0itjTYVW1u8+wxO/PcnR\n",
"vIO0yYAl25qQ/dQM9zGuB1qrUbpXKOt1zlgOqZos5PBAX5qHl1Rz9PdTE+3XmodaPwvA5JssbLn/\n",
"YVAq8V229LLaqhfDFlfqeK0xh4gtf2PYvY2Ytd+jMhdgV2tIfGgKR+8cTY4yndm7H+S89Syx+k5M\n",
"b7sYjdJbHFxjw8hgHZGlxoGCqqHysOYGdJnBH0fG8mlsJoO3rCWr98112LO6o/SQLS2rgPXnv+WH\n",
"k1/ja4VvVgCvvQkGA5x1Rnp6jkw6tgzGWGB1i4i2eGblQikpqopSocCgU3N9yHA2BPzMgdwdPHet\n",
"ieVj/8Zn9SrKumkvnXpheTjyC2j/2SL63nktXV+YQuwPX6IyF3Cmz0B+/Xg1R4Y+xFHzYabuvJfz\n",
"RWeI9evIrHZL0Kn0FV9ccNl4zqrEh/Smi6MpmTrYs/U1jwjGK2cI45Blks95l6A8bTrB0hPOILoP\n",
"VkNw/E3YB9/qNRz39GuolAqvvDRajZKr4sLo07lptffXV6NCkhQ80nIuSknNurQVbPTPpWD6rMu6\n",
"br0QD0WzpnT4fDFKSxE53Xuz76EprFu0gs3PL8IU2Zzf077m+cT7yLNm0zWwL893/BSDOqiuu33F\n",
"4Ok3kiSJ+69xOgM/aplC2I6NQCUygjcCTqUZvQo32R12Xtz9NEWOQkbvhRFJgRx88jmAUuJx8esG\n",
"+GlqJIuda01Mc10sQ5o9AsAzG57EYr+8SNMqiYfD4WDOnDmMGDGC+++/n1OnTnnt/+OPPxg6dCgj\n",
"Roxg5cqVFV5Pyssjs21ndn+4kiOfrOTQyPFkx3cioyiVVw89zpLjc7HKFkbFP8j0tu/ho7wcY0tQ\n",
"WZqF6jH4loT3/1/b4YTb9BwKg3PrX4Vy3sSNmVyT90P35ra32Je1g6Z5sOhn2D71JeSmzmXxynpQ\n",
"/9jToXpX8/FE+kRzNOcwb25967KuWyXxWLduHVarleXLlzNt2jQWLFjg3me1WlmwYAFLly5l2bJl\n",
"fP3112RmZl70egVJyfzxzteYruqJRq0kqyiNz068wlO7b2Nn9nr0aj2LB37EwhvfKZNyzUWTYB1t\n",
"o4U1UhPofFRcHR9W8lmt4eaohwD4pMkxgndv5UyGyV2QqLFT5BFKcCr/CAt3OYcrn/wAKcMmkXrt\n",
"je4H1nPIV1dmvqd4aBRaHmn1PACL99WBeOzatYu+ffsC0KVLFxITE937jh8/TnR0NAaDAbVazdVX\n",
"X8327dsvfj3OkZC9kS+OL2biX8OYuPMGVp/9lCJHIb1CbmHTyB0MbTP8gucH6DTERwcJB2ktoVQo\n",
"uD5qNL4OFetioWjlfKDsDERjwlRoJTffaXG47tPmsPL+/qewYuPRHRDXdjgHRz8GlDywns7mWigf\n",
"Wy6BBq07Hw5A58Br6Rk8ELP98oLFqjTbYjKZ0OtLnJVKpRKHw4FCocBkMmEwGNz7/Pz8MBovbtL2\n",
"/ewa705JaroHD2JIs3G00negif7iTqQrOUy6NlFIEg5ZRqmU0KsCuD7sLn7OXMnSwL2MPrAbRcuB\n",
"dd3FGqGwyMaO4pXDvdtH4nDIKCWJ30+/zXFbEi2y4am8Aeya+ZzbsaEpZwVsXRVPV0gS3dqEsSnx\n",
"rHvbgy1nUWjPv8hZFVMl8dDr9eTne1SoKhYOAIPB4LUvPz+fgICAi16vU1hnFHY9nSLa07fFtQSZ\n",
"u2FQO88JDfQlLKxEjAz6snEbwUE6r2Muhcoef7k0hvZu7ReLuchOoEGL4UQ297R7jDV/r+SLTjDl\n",
"548IvO8OwkJqxx9Vm9+nn8HH/bvT6rTo/LSczdrOx6c/AQW8sy+eUy98gEFbMnvSJMLf/V24zg0N\n",
"1RMS4FthezV1b/c2CcBqs3PqnJEcUxAtQ768rOtVSTy6devG+vXrGTx4MAkJCcTHx7v3tWrViuTk\n",
"ZHJzc/H19WX79u2MHTv2otdbN2Izf+08ReumAYQE+LD1YBrGIjPBBi1Rwb6kp5dYLkZT2XG1n1rh\n",
"dUxFhIUZKnX85dLY2ks3WzCazBiI5MbwG1iX/gefsZ7b125BurFHjb9ha/P7DAszcC4tz/27O52a\n",
"Q3p2Ni+vfwi7H0w+FIx90mfkWmWwlvw2TUYz6cVBdK5zs7LycVRQQKs27s1fqyTlXFG5z1JlqJJ4\n",
"DBo0iE2bNjFixAgA5s+fz+rVqykoKGDYsGHMmDGDsWPH4nA4GDp0KOHh4Re9nivgRqmUvMaIPhrV\n",
"Ja1NEcOW2qdjy2AUksRjQTNZ99MffNAdhq1YzOmOi4iJrF0rq6axekxDmwos/PL3kxzxMxGfKfH0\n",
"4z+xvbDs+pNyE/fUaC8rR3UsGK2SeEiSxAsveOe0bNmyZKnx9ddfz/XXX3/J13Pl6FAqJK8aIhd7\n",
"gykVkttxVV56NkHNElpsfvf07c41uu5sZQff56/ijvPPYQ3VUVhkx9+v4WZvS83I51hKLrf2jcXm\n",
"EeeyJ/EHvlBvQOGAxS2fQdemPexJBcBHrXRnLC/vN1mf/MnVsWC0XgSJHSzOiaBSKrzmwqWL9C6u\n",
"eUlOUrF+pe7QqJXMHuycqn/vajt+33zEzsPp7Dqa7s6m1RA5ciYHhyyTllXgfrmZLUbePPAMsgRP\n",
"pMTSafRsJEkiKlxPTISB5mElkwjlPZz2erQWqDosj3ohHi5K31BFY+dWTfyJCPQtkyhWULv0jbmO\n",
"qxTtyPOBb08sxWJyOszzzdYaKTZUm9jsDneE7c/rx3FSX0SndCV3j/zaPbMS2zSAlk38y51hAdzT\n",
"pOp6ZCFXh1+qfolHsb/DtVgouJwEKS5kWSY6wkA7j5J6grpBqZS4o61z1eaiLoWErV0OwN6kTA4m\n",
"Z1d4fn3MC+J6uOwOGZvdwfEDX7HcsAe1HaY0mY06JKLsORd4m18VF0qHFsHutI71gUYzbHHhsjw6\n",
"tAimd/vIevVlCy6MUiHRPqAnnR0tydLBn4ffRVnoDEAqLwO+J6fSjGzcd5a8/OrJ6F1VzBYbx1Ny\n",
"S5z3xb9Fu10mLz+DRSnOKNJJaV0w9BxZ7sPnWpfiU2p9ikatJCyw4ina2qTRiYdrpkWtUlT70mRB\n",
"zaFQOLO33dHeuUpz4VX5RKz6CKg4SbIrq1ZFIlPTHEzO5nS6yZ1h3CUeNoeDz9Y+TKqfjavPa+h9\n",
"60de+z3x12no2CKYq9qEldlX32hUPg+FJJWp1l4ewcXLmF2FcQR1j0v0OwX1obu6Pdm+sPrMJ2iz\n",
"Myv8m7rEpa5D213rVc5lFpCWVeB+M/+1679857sPHyvM7zAPfJ3T0Bd6c4cG+pZJCVgfaTSWR+9O\n",
"Tbi2Y+QlrTrs0DKYq9uENehpwMaGZx7O+7r+G4BF3a1EfPlahecq3MODuvV7uHwcRTY7B09lo1Qo\n",
"yLNk8eJupzX1bHJbom9+wH18Q0+srWwsDtMAvdZ7AdFFcGZGEsJRn5AkyT11Hq3txDU+PcnXwBeW\n",
"VeiPHbzouW7fQi1bHueyCryGSmVnH2RWbHiY81oLfU8r6T3kI69cGw09sXajsTwEDZ9moX74qJXY\n",
"HA6Gxs9CkmHJ1WBYOrf8Mn/FuKKDbbUsHodOZbP/ZEnNldIP09Ytb7JWdxg/C0yJmoM9vInXcKSh\n",
"hwc0Kp+HoOHjUxzPEOMXT9/Am7Go4I0mu9H8uuaC57hyzjrq2OfhKR7Gs/t4K8tZ3Oq5vP5I141A\n",
"IZWUM1AqpAbvc/PVKr2Ko1UFIR6CaiMypCSfygPtZuIjq1jeCXa+MwWKyi8h6pqMqc1hS3lC5Rq2\n",
"KEy5/PefB8jVytycGkD3kZ/gkGX3/ms7RNK7Q9lasQ0NtUpJn05NLusaQjwE1UZksA5DsTkfqmnK\n",
"va3GAzC92zmMby7EWE51dteIpjZDt8sXKhmFxcKBz4exoUkhoYUKRt7wBVZJiUOW3aURNGrlJfvn\n",
"GjviWxBUKwF+zql0u0NmROxjhBHIzqawftPrHNl6oMzxdZF1vTyhsjtkdP+Zxrz2zny8E1vMRRcc\n",
"695fV4l86jNCPATVist34JBldBo/hsfNBOBffYtotfBZt6mRmpHPwZNZuJ/jatYQq+3Ci/I8LQ+X\n",
"eIV8/xkzw3+jSAWDtTfSKfZer3MqiHW7IhFfiaBaUXqIBzJcF3obbX06cM4A7wRtxufz/wLOVatp\n",
"OYXuKu+eBoip0Mr+k1mVLhV64mwe2cYiso1FbEo8V25G97SsAvILre7PefkWCjdu5uNDL7InEqIJ\n",
"YUTXV8qcJ9WrbBz1AyEegmrF07qXZRmFpOCR+JdRygoW94A9708nZ98h9zGuyE7P1beJSZmk5xRy\n",
"+ryJ3HwLp9IqzqxVWGQjOc3InuMZZOQ64zdSMkycSTeRW1zJPtdUxMFT2RzwWKx39K8d/LXgHj64\n",
"2oHGoeDlG77At5zSHg19dXBNIMRDUK244h8C9Vp38ptovzbc0fwRZAkm3GRG99QEKOV38JwBcRWQ\n",
"cjhkdh9NJ+lsnjs3SL7ZWm6JB0/fidsJa5c5lpLL7mMZAJhL5RfxPX+WpvMf5PEbnetZxsbNon1I\n",
"53Lv60qqiHepCPEQVCvB/j50bhVCx5bBXm/re5pPpImmOfvD4f3QXcR995nXeZ7HuqwX2cMR4tq/\n",
"/dB5tu0/V07LZYcVnte02hxevg7DqeNcO3UkD9yQhlELvQMHcnvMAxd0jNajPD71BiEegmon2N8H\n",
"lVLh9bbWKH2Y0GY+EhLzr4PctW9gSD7m3i9T9u3u+XHrwTT2FFsQANnG8uNGvM73+L+p0OoWj4Ck\n",
"wwx4ejRP9EljTyQ00TRnfJv5KJUKr8hLrUfyHmF5lEWIh6DGKP28tfPvzp3NxuFQwAN32uj40kS0\n",
"2SXVBB2yTI6pyJ32rzTZphLB2HM8A1Oh1Vk31uHwslLKe9ALimwcT80lIOkw/ac/yFudc/miM/go\n",
"fHm63bvoVHqUCoWXz6Z72zDCgnzdfRN4I8RDUGN4PsRKScJHo+Spbs8S59eO5EB4qucZ+jw3HmWh\n",
"M22hwwEJHtZFRew/kUXS2TySz5kutnwGgPNZBfifOEL/Zx/i56Y5zBronEF5os3rxPg5S4fofFRe\n",
"Qxu1SukexgjtKIsQD0GN4fnAKZUSvdpH0i4qjJldF+Gr0PFNB/gofD/9Zj6CNiu9zNs9s4Lat65p\n",
"XrPFVqFloD9+mAHTH2S3IZvRQ50/+1ExT9M9+Ab3MTqtqkyGc8+4FYE3QjwENYZn/RbPNHwxhlgm\n",
"t3Hm+ph1I2y3JHD9tDFIKSle53sWlL4YTn+Jx+dSz3no3u10nzyKwz7Z3DJGRaHKwYDwu7mjqXcx\n",
"Mp2Pyp1C0JUCs0UTZ02WVk3L1ma50hHiIagxwgJ96d+lKVfFhRHbrKTkqEIh0T34BoZFTUKWYNhw\n",
"BQflk4QPvQ1dWspFrngBZO8h0rnskgLOUet/ov+MsZxQ5zDwYQ25Ghs9gm9kfOwLXsmnAvVaAvw0\n",
"hAT40LFFMB1bhgDOXDMDujZz16kRlFClok8CwaUiSVKZRNYuP8LdzSeSWpjMxowfuWWMkg2fnGTg\n",
"40NJ79Sd7LgO5LRuT3Zce4qCQi/ahoxc1idhtxP33TK6fPQqCREyA8dqyVIX0SmgF0+2eQOlVPLT\n",
"V0oSXVuXtBFaz5IV11eEeAhqHdf7XiEpeKz1PArtJnZmr+fGsWp+XZpD103raL5pnfv4gtAI8mJa\n",
"Q0gIBS3jSO/cA2Przp4BIV6WR8Dxg3Rf+DzBh/fxVwzc/oAGo6KILoHXMS3+HTQKLUF6rXv2piEk\n",
"LK6PVFo8zGYzzzzzDFlZWfj5+bFgwQKCg71rp3z66af8/PPPAPTr149JkyZVT28FjQLP6VCVQs1T\n",
"8W/xysGJ7MvdTJ+JOhYUjuTmIzaCju4n8PhBdBlp6DLS3Oe0AtrEtuPIPQ+Q0mcQGUCQvw/6Mydo\n",
"vepLYn/8Cslh57UbDMzsl48dC71CbuaJuFdRKZxWUJMQHW2jg0SW/sug0uLx1VdfER8fz6RJk/j5\n",
"5595//33mT17tnv/6dOn+fHHH/nmm2+QJImRI0cyaNAg4uPjq7XjgsaDRqFlRrsP+PzsHNYkr+JJ\n",
"n6UMu3USdzX/FIUsoU9NxnDmJM0wE3HmKD7f/4+g4we55tUZwAzMAcEUBYXQJfkYkiyTppd48JEY\n",
"fglMBuCOpmMZFfMUCslDKCRJCMdlUmmH6a5du+jXrx8Affv2ZfPmzV77mzRpwieffOJ2RtlsNnx8\n",
"RC1ZwcVRKzS83mcJdzefgIyDr0+/w+y9IziWvx9T85ac7XU92XePIP+lV7AeO872p18iq01H7Go1\n",
"PrlZBJw8SpFayYtjutLmGT2/BCajVeh4us1C7msxzVs4qF8V6xsqF7U8Vq5cyWefea9BCAkJwc/P\n",
"uerQz88Po9F7xaNKpSIwMBBZlnn11Vdp3749MTExFXYkLMxQ4THViWiv7tpLyyvCZCkbRRocrGdc\n",
"+2e5KrwXb++fyfH8RGbtG0b3kP78X9QoOgfcSViYAbvdQebQ0WQOHQ0OB1mpe9hw5lu+N/9BmiUB\n",
"ZLgquA9PtJ9PpC6KQIOWnOJw9iCDlmxjEdHNAtFfYhb++vxd1iWSXMmg/cmTJzNu3Dg6d+6M0Whk\n",
"1KhR/Pjjj17HFBUVMWvWLPR6PXPnzr2keizp6RUvu64uwsIMor06bO/I6RxSM/PdnyWcsRrtY4Lc\n",
"y+UL7fl8d+YD1pz9giKHc4m9VulDu+B2xIW15uz5Qoy2bFIKksiwnHVfq5lvLMOjn+Ca4EHu3118\n",
"VCBJqXlY7Q6u69QEs8V+ydnP6/t3WR3tVZVK+zy6devGhg0b6Ny5Mxs2bKB79+5e+2VZ5rHHHqNX\n",
"r16MGzeuyh0TXDkoFQpsDod7KT6Ar9KPd//vNX5NeJjf075hS+avJOXvJyF9Nwnpu73O91MF0Dmg\n",
"N9eH30PnwN5lhigKSaJXhwhk2VndTu8rwpuqg0qLx8iRI3n22WcZNWoUGo2GN954A3DOsERHR+Nw\n",
"ONi+fTtWq5UNGzYAMHXqVLp27Vq9PRc0Gnw0SkxmR5l8Gxq1kus7xmNQj2NI83E0ayKRYT9BoTKX\n",
"LftP4YOBMJ9mNPNtVUYwPJGkkhIPguqj0uLh4+PD22+/XWb7gw8+6P7/3r17L6tTgisLp3hYKSyy\n",
"ubc1CXaWcfDMrxHkE0RcQFPCwgzos45R4HH8xbiUYbOg8gg5FtQ6pZ9l15RpenH6wIggHfHRQYB3\n",
"ZQSCud0AAAiXSURBVDNPIamMJSG0o2YQ4iGodUonE9aovIccXgl5NOXXh3WVqSwPndbboBZlE2oG\n",
"IR6CWickwDvup/SzfaE6qp7zgqriY7QqJfpSpR+DDNpS1xfiURMI8RDUOkEGLX06lpQ6lCSJVk1K\n",
"lryXtipc/g9fbYkV4lniwfN4jUpByybey+cbeEH7eosQD0Gd4CoaDU7LIzK4pM5taX9Gm6hA+nRs\n",
"4i6kDaAsLvnokGWvYUqHliFlykEKy6NmEOIhqHMkSfL2Z5QyFSRJ8hIbwC0QvhqVV6SoSyfaFTtc\n",
"odqL0QmKEUvyBXWOQvIWjAv5PDxpFuaHRqUg2F/rFVzmco5GBOs4eMoZrSoyn9cMQjwEdY4kSV5D\n",
"i0sRD61aSfNwPQA2j2zr5Y1QhHbUDGLYIqhzysy2KCv3s/T0cXhOA7dq4o9SIWHQXdo6FkHlEJaH\n",
"oM4p7dC8FMvjwpSYGdERBqIjGsYK1YaIsDwEdU5pqbhYANiFcE3natQiwU9tISwPQZ1TWiqqEhEa\n",
"Hx3kDmkX1A7C8hDUOxQiqqtBIMRDUPcUa0VUmB6tSolGJX6WDQExbBHUG2KbBXgVhxLUb4TECwSC\n",
"KiHEQ1DnlF6iL2gYCPEQCARVQoiHQCCoEkI8BHWGK4mPj1YEdjVExGyLoM7oGhdKvtmGn49Ye9IQ\n",
"EZaHoM5QKRUE+F1a1TZB/UOIh0AgqBJCPAQCQZUQ4iEQCKpEpcXDbDYzefJkRo8ezaOPPkpWVla5\n",
"xzkcDh555BGWL19+2Z0UCAT1j0qLx1dffUV8fDxffPEFQ4YM4f333y/3uIULF2I0GkXmaoGgkVJp\n",
"8di1axf9+vUDoG/fvmzevLnMMb/88gsKhYK+ffuK5LMCQSPlonEeK1eu5LPPPvPaFhISgp+fHwB+\n",
"fn4YjUav/UeOHOGnn37inXfe4d13363m7goEgvrCRcXj3nvv5d577/XaNnnyZPLz8wHIz8/H39+7\n",
"OteqVatIS0tjzJgxpKSkoFarad68Odddd91FOxIWVru5JkV7or362FZdtFdVKh1h2q1bNzZs2EDn\n",
"zp3ZsGED3bt399r/zDPPuP//7rvvEhYWVqFwCASChkelfR4jR47k6NGjjBo1ipUrVzJp0iQAPv30\n",
"U/74449q76BAIKifSLLwaAoEgioggsQEAkGVEOIhEAiqhBAPgUBQJYR4CASCKlGnyYAcDgdz587l\n",
"yJEjqNVq5s2bR3R0dLW3c9ddd6HXOyuqR0VFMX78eGbMmIFCoSAuLo7nn3/+ssPo9+zZw+uvv86y\n",
"ZctITk4u9/orVqzg66+/RqVSMXHiRAYMGFAt7R04cIAJEyYQExMDwKhRoxg8eHC1tWe1Wpk1axap\n",
"qalYLBYmTpxIbGxsjd1jee1FRkYyfvx4WrRoUe33aLfb+de//sXJkyeRJIkXXngBjUZTI/dXXltW\n",
"q7XG7s1FZmYmd999N59++ikKhaJ67k2uQ3799Vd5xowZsizLckJCgjxx4sRqb8NsNstDhgzx2jZ+\n",
"/Hh527ZtsizL8pw5c+Tffvvtstr48MMP5dtuu00ePnz4Ba9//vx5+bbbbpMtFotsNBrl2267TS4q\n",
"KqqW9lasWCH/5z//8TqmOtv79ttv5ZdfflmWZVnOycmR+/fvL0+YMKHG7rG89mryHn/77Td51qxZ\n",
"sizL8tatW+UJEybU2P2VbmvixIk1/vezWCzyY489Jt98883y8ePHq+33WafDll27dtG3b18AunTp\n",
"QmJiYrW3cejQIQoLCxk7diwPPPAACQkJHDhwgB49egDQr18//vnnn8tqIyYmhnfffde9jqe86+/b\n",
"t49u3bqhVqvR6/XExMRw+PDhamkvMTGRP//8k/vuu4/Zs2eTn5/P3r17q629W265hSeeeAJwWosq\n",
"lapG77G89vbv319j9zhw4ED+/e9/A5CSkkJAQAD79++vkfsr3Za/v3+N3hvAq6++ysiRIwkLC+P/\n",
"2zl3l9bBMA4/aeSg9UJxcBAEUcQLpf4Bda0UvCDiIF5BXcULitHaIUJp3S3o4NTOwdF/wA7iIC66\n",
"OIugODRdqrRnODSn2i4nfjku7zOFfCRPfnzhDSHfG1B3f/5o8bBt23mdANB1nVKppNTR1NTE6uoq\n",
"5+fnmKbJzs7Op3G/31/Tn/OvjI6Oout/f+Jbrlo6U+n/sW2b1tbWT/tt21biGx4eZm9vj2w2S1dX\n",
"FycnJxQKBWU+v9/vHL+xscHm5uaneVKd8atva2uLUCjkaUZd1zEMg0QiwcTEhKdz+NXlZTbLsmhv\n",
"b3dWeZfLZWXZfrR4tLS0OH0y8Ocp4/OpvaTu7m4mJyed7UAgwOvrqzNerz/nu1RnsG2btra2mqwq\n",
"vZFIhKGhIWf7/v5eue/p6Ynl5WWmpqYYHx/3PGO1b2xs7L9kTKVSXF5ecnh4SLFYdPZ7ka/iisfj\n",
"hMNhz7JZlkUul2NxcZGHhwcMw+Dt7U1Jth8tHpU+GYDb21v6+/uVOyzLIpVKAfD8/EyhUCAcDnN9\n",
"fQ1Qtz/nuwwODtacPxQKcXNzQ7FYJJ/P8/j4SF9fnxLf2toad3d3AORyOYLBoFLfy8sLKysr7O7u\n",
"Mj097XnGej4vM15cXHB2dgZAY2MjPp+PYDDoSb6vLk3TWF9f9yxbNpslk8mQyWQYGBjg+PiYkZER\n",
"Jdl+9GtLJBLh6uqK2dlZAJLJpHLHzMwM+/v7zM/PO45AIEA8Huf9/Z3e3l6i0agSV+WLjWEYNefX\n",
"NI2lpSXm5uYolUpsb2/z69f3/hxe8ZmmiWmaNDQ00NHRwdHREc3Nzcp8p6en5PN50uk06XQagFgs\n",
"RiKR8CRjPd/BwQHJZNKTjNFoFMMwWFhY4OPjg1gsRk9PjydzWM/V2dnp6fxVo2masvtTelsEQXCF\n",
"LBITBMEVUjwEQXCFFA9BEFwhxUMQBFdI8RAEwRVSPARBcIUUD0EQXPEbBjQlxe5Z1zsAAAAASUVO\n",
"RK5CYII=\n",
"\">\n",
" </div>\n",
" \n",
" <div name=\"mu3\" style=\"display:none\">\n",
" <img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQ8AAADVCAYAAABJ/XXDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
"AAALEgAACxIB0t1+/AAAIABJREFUeJzsnWdgFNUahp/Zns1uNr0QElLoXUSagCiiF0VFRUAURAWx\n",
"XlGQYqGoCIgFRRD0KioiiAVUFEUURHrvnYQEUknP7mb73B+bbLJJaCEhIczzB3bKmTObnXfO+c5X\n",
"BFEURSQkJCQuEVltd0BCQuLqRBIPCQmJKiGJh4SERJWQxENCQqJKSOIhISFRJSTxkJCQqBKSeEhI\n",
"SFQJSTwkJCSqhKK2OyBxdXP48GF+/vlnxo8f79m2Zs0aTpw4gUwmIzQ0lP79+1dpu0TdRhIPiSqz\n",
"cOFCdu7ciV6v92wrLCxk3rx5/PjjjwAMGjSIm266CYVCcdHbe/bsSWBg4JW/IYlLQhIPiSrz6KOP\n",
"4u/vz7Zt2zzbtm/fTnx8vOdzs2bN2LJlC2q1+qK3b926lb59+16Zm5CoMpJ4SHhx+vRpli1bds79\n",
"7dq149Zbb/V8Lh8alZ6ejp+fn+ezn58fSUlJGAyGS9ouUfeRxOMaw+l08vDDD7NkyRIAXn75ZUaN\n",
"GkWjRo0AiIqKYsyYMRfdniAIXp8LCwtRqVSez0qlErPZjCAIl7Rdou4jrbZcY+zevZsGDRoA7lHD\n",
"nj17PMJRFcqPPHx9fb0+WywWDAbDJW+XqPtII49rjH///ZcePXoAcOjQIZo2beq1/1KnLeVHHlFR\n",
"URw4cMDzOS8vj1atWqHX6y9pu0TdRxKPa4wNGzZw5513ArBu3Tq6du3KX3/9Re/evYFLn7aUH3nc\n",
"cMMNvPPOO57PBw8eZOzYsfj4+FzSdom6jyAlA7p2yMnJoV+/fgwbNowWLVpw8uRJrFYr7dq1o1u3\n",
"bpfc3tdff82qVatIS0vjvvvuY/jw4eh0OlasWEFqaioul4vo6GjuvvtugEveLlG3kcTjGuKnn34i\n",
"ISGBF154oba7IlEPqNK0xeVyMWXKFI4dO4ZSqWTatGlER0d79u/bt4+ZM2ciiiJhYWHMnDnTy6Iu\n",
"UTvs379f8t6UqDaqNPJYvXo1a9euZfr06ezdu5cFCxYwb948wD0Hvvfee5kzZw5RUVEsW7aMjh07\n",
"EhcXV+2dl5CQqD2qNPLYtWuXx2Lfrl07L2t5YmIi/v7+LFy4kOPHj3PTTTdJwiEhUQ+pkp+H0WhE\n",
"p9N5PsvlclwuFwC5ubns3r2bhx9+mIULF7J582a2bNly3vYks4uExNVHlUYeOp0Ok8nk+exyuZDJ\n",
"3Drk7+9PdHS0Z7TRo0cPDhw4QJcuXc7ZniAInD1bWJWuVImQEL10Pel6de5atXW9qlKlkUeHDh1Y\n",
"v349AHv27KFZs2aefVFRUZjNZpKTkwHYuXMnTZo0qXIHJSQk6iZVGnn06dOHjRs3MnjwYACmT5/O\n",
"ypUrMZvNDBw4kGnTpjFmzBhEUaRDhw7cdNNN1dppCQmJ2qfO+HnU96GhdL2r83r1+d5KrldVpMA4\n",
"CQmJKiGJh4SERJWQxENCQqJKSOIhISFRJSTxqAVyC62YLY7a7oaExGUhiccVRhRF9p7MYtuRjNru\n",
"isQVIicnm3ffnVnb3ah2JPG4wtSNhXGJK0lgYBBjxoy/8IFXGVImsSuMSKl6iKJYIY2fRNU4mZrP\n",
"2byiam0zxN/nvH4Qv/32C5s3b8RqtZKaeoaHHnqE+PjGzJ79DjKZDJVKzfjxrxSnsHiFBQsWsmDB\n",
"XPbs2YnD4aRXr1vo3/9+HnvsYZYuXY4gCMyaNYvo6Mbccsut57xuXUESjxokO9+CTqv02lZ25LH5\n",
"YDrdWkdc4V5JVCcmk4n33pvDmTOnGTduNFqtLxMmvEbjxk3YsOEf5sx5n2efHe05fs2aP5gz5xOC\n",
"goL47bdf8PXV0bZte7Zs2USnTl34999/WbBgRC3e0cUjiUcNkW+0sj8xG51GScMG/p7tZcXD5nDV\n",
"Qs/qJ/ENDMQ3uLJZ1wVBoEkTdwLpkJBQbDYbRUVFNG7sjuVq2/Y65s//yOucSZPe4OOPPyQnJ5su\n",
"XdypH++6qz/ff/8toihy4403olBcHY+lZPOoIfJNNgCMFrvX9vLRAJm5Zg6dykEURewOJ/sTsjGX\n",
"O0ei7lJ+2hkcHMzJkycA2LNnF1FRpWUt7HY7a9euYerUt/jww/msWrWSjIx02rZtT0rKGVau/IkB\n",
"AwZc0f5fDleHxF2FWO1OABQyb30ubzA9lJQLQKNwPWnZZrILLJgsdrq0DL/gNZIzCgkyaPDVKC94\n",
"rETNUFY8BEHGuHGv8v77byOKIgqFggkTXvPYtpRKJX5+Bp54YjhqtZpOnboQFub+O992239Yt+4v\n",
"4uPjr2hsy+UgiUcNYbG5xUOjknttL2swLYsAyIp/iDb7haczeUYrCWkFJKYVcFP7yMvrrESV6Nu3\n",
"n+f/arWa7777CYCPPvqkwrHz538OwPDhIxg+vKJNw+l0cddd99ZQT2sGadpSQzhdbpGQy72Htedb\n",
"qlUUH+sSRdKyTec+ELAX20ukld+rn2nTprBjxzZuu+3qKu4tjTxqCKfT/Vi7yg0iziUehWa7RxAA\n",
"jp7Ow+CrQls8JRFFkSNJuQT6aQgL1EqiUY945ZUptd2FKiGJRw3hLFaN8gbSc01bDifnVtiWkVuE\n",
"RmXD5RIx6NRk5BWRkVdEWKBW8jaTqHUk8aghSqYtJf+WcCnPfFJGqeGsdUxgtfRLQqK6kGweNUTp\n",
"tKW8eFRtxFBYVH7Jt2r9kpCoLiTxqCFKpi0VRh5VbC+30AqUrshI2iFR20jiUQM4XS7Pw+0qb/Oo\n",
"4lNfYHY7namV8uJ2JPmoawwbNqha2nnllZcu6/xx414gPT2tWvpyPiSbRw1QMmUBt3iUPOhiuf+n\n",
"FJ3klOkoObZ0XKILjVxLQ21j4nxbolVUHpClkLv1vvx0SKL+MG3arGpopeYDLiXxqGZEUawQ3el0\n",
"uZdZ80xWtP75fH1qPhuyVpJjqzynh1xQ0s6/G73DHqBjwC1eXowl4lN+OnSt4zdkAOo1q6u1Teut\n",
"t8Gff5xzv8Vi4fXXXyM/P4/IyIa4XC4SEk4we/Y7iKKIwWBg4sRJHD16hMWLv0KlUpKamkLv3rcx\n",
"bNhjpKWlMn36655qi6NHv0RISAfuvvt2fv75D3788Tt+//1XZDIZzZu3ZPTosWRkpDNr1ltYrVbU\n",
"ajXjxr1CaGgYn322gE2bNhAUFExm5pXJFSOJRzXidLlIOWsiIa2g3HaRoxmnWXZ6Dn9nfo9TdHuf\n",
"GpTBNNO3J1jdAIWgwOjIJ8l8jATjQXbl/sOu3H9opG3Oo7ETaWnoBLhtHXaHs8I1JK48K1Z8T2xs\n",
"HCNHPkVy8ileemk0M2dOY+LEScTExLJy5U8sXvwVN9zQmYyMdL76aik2m43+/f/DsGGPMXfubAYO\n",
"HEL37j05fvwYM2a8wU8/LafkXbFq1S+MGTOR5s1bsGLF9zidTubO/YABAwbTpUs3duzYxvz5HzF4\n",
"8EPs2rWDzz5bhNVqrbbp04WQxKOacLlEth3KxOpwVtj3w6HveWHPKIyOfGSCnB4hd3F7+IM00bWv\n",
"NJ9Hni2LDVkr+SV1IUnmI0w5+Ai3hQ1mWOwElHYZGw+kX4lbuqoo+Ob7Gmk35Dz7kpOT6Nr1RgCi\n",
"o2MwGPxJSkrk3XdnAOBwOIiKigYgPj4emUyGRqNBrVYDkJR0ivbtOwDQpEnTCiOGiRMns3Tp16Sm\n",
"ptC6dVtEUSQh4QSLFi1k8eIvEUURpVJJUtIpmjVrDrjd5Js3b8mVMKlL4lEFRFHE4RSxO1xoNe6v\n",
"0GJzVhAOmczF/068xe+bFgPQxtCFR2NfoaG2MQCBeg05hZYK7furgunXYDi3hT/IijOfsjzlE1Zn\n",
"LOWEcT9jm39IsLpBDd+hxMUQExPH/v176dGjFykpZ8jPzyM6OoZXX51KWFg4e/bsIj8/v/joii+J\n",
"Ro1i2bNnV/HI4yhBQUFe+3/5ZQVjx05EpVLx4ovPceDAPho1iuHBB4fSunVbEhJOcOjQAWJi4vjh\n",
"h2W4XC6cTifHjx+t9HrVTZXEw50ZaQrHjh1DqVQybdo0oqOjKxz32muv4e/vz5gxYy67o3WJEyn5\n",
"pGS5Y086NgtF56P0RNGWYBfNzDk2hi2Z61DJVTwcPY7bw4d4jTTUShnt4oPZezKr0uuoZGoGRj9L\n",
"p6DevHPkvySYDvLK/gd5reVnHgECKDTb0GtVNXCnEuejf//7mT79dZ566nEiIhrg52dgzJgJvPnm\n",
"ZJxOJzKZjAkTXuPs2cxyI0z3/599djQzZ77J0qVf43A4mDBhktf++Ph4nnlmBFqtLyEhobRq1YbQ\n",
"0DDeeWcGNpsVq9XK6NEv0aRJU7p378nIkY8QEBCAweDPlaBK5SZXr17N2rVrmT59Onv37mXBggXM\n",
"mzfP65ilS5eyYsUKOnXqxIsvvnjBNut6ST+zxUFiegFNIg1sOlg6bWgd6/b8tNpdHD+TB4DRkc97\n",
"J0dxIHsvekUAX9+zDGtawwptRgRqCQ/UsvtE5eIB0Kl5KNuOZGK05zHr6HMcLtiBXuHPa60WEuPb\n",
"3HNcq5hAQvx9qnx/l0N9vl59vreS61WVKvl57Nq1ix49egDQrl07Dhw4UGH/vn37GDRoUL3xRziS\n",
"nMvZvCIS0wpQyku/ttQsEwcSczzCYXIUMO3gCA5k7yVKF8u0tktpG9TpnO0KstI3Urv44ArZsEoC\n",
"43RKf15u8QnX+feg0JHHW4dGkmlJ8RyXVc35OyUkLkSVxMNoNKLT6Tyf5XK5Z7kpMzOTuXPnMmnS\n",
"pHojHFDqV+Fwih5HLYCcYs9PAKuziLcOPcFJ0wGi9TF83vsHwjXRJJ1nZURWZjirUcmRyc49V/VV\n",
"+jK2+Ue08utMnj2LaYdGUGB3B9RZpZSGEleYKtk8dDodJlNpvgmXy4WsOGPWH3/8QW5uLiNHjiQr\n",
"KwuLxUJ8fDz9+/c/b5uXM3yqCpd6PUNaIYJCjp+fD6LJiqDwTvLjEl18sPcFjhv3EqppwF+P/I2f\n",
"LIxdRZkUWR3odRoMOjX5xlKx8ffXEhqiR5/iFpeoSH/IKESfV2pEDQnRo9dpANBrVRSaVUy9/hPG\n",
"7RhMQuFhZh9/nukdFyPI5Rj8taiKha2uf59X0/Xq871dDlUSjw4dOrB27Vr69u3Lnj17aNasmWff\n",
"0KFDGTp0KADLly8nISHhgsIBdd/mUVhoodBsQyWDvEIrznKjqsVJ77Ix83e0cj0Tmi/AzxlEQWER\n",
"hUYLep2GQqMFg4+CQmOpMOSpZGSp5J5tWVlGcnPNXsecPVtIyygDNruTk6kFFJptgIrxzeYzcd9A\n",
"DuRtZ8Gh6QyLGceRk2eJCPK9Jubpks2j+q5XVao0benTpw8qlYrBgwczY8YMJk6cyMqVK1m2bFmF\n",
"Y+tLXZKS23A4XRWEY8PZX/kp5X/IkPNis9k01DZGEARPZrASLDbvEpOCIKBRyVEpZESF6DgXPmoF\n",
"Bp3aKy4mQBXKa+3mIBcUrExdyJasP7ySCUlI1DRVGnkIgsDUqVO9tsXGxlY47t57r66cjOdDKF4+\n",
"K3lAZYKASxRJLUrkk5PuJbYR8a/Q1r+b55zyyY+DDT5k5Xv7dchkglftlrJa26JRQLleeItWu+Ab\n",
"GNroJb44NZ2PT77KTbFd8dfHczYxm2BfZb0Rbom6iRRVexGYLXZPdGyJeKiUMqzOIt47OhqLy0y3\n",
"4Dt4IP4Rr/PK5i8N1GsID9Re8FphAVpCDD60bxxMWID38eXtz1abi74RQ+kU1Jsip5FXtzzPjqMZ\n",
"JKcXVhCpQrON3cfPVhj9SNQcW7du5uefl59z/6pVK9mwYf0lt3v33bdfTreqDUk8LoDN7mTbkUxP\n",
"SLzd6RYPpVzOwsS3SDYfI1Ibw5hWbxFZbuqhKLOkq/O5uPIIMplAq9hA/HXqCvvKhvc3bmDAbLEj\n",
"CALj285Arwhgf/4WVqcvcfez3BTmQGIO+SYbpzONF9UPicunc+eu3H33uUffffv2o3v3npfcbl0Z\n",
"UEru6RfgXFXdtmav5u/M71HK1My9+XO6NYoDICpE51nxKEt5+0dVKNGOMH8fGobqOJnqdn2ODYrk\n",
"ifgpvHv0eb5OeofukX0oNIaSXWChTZzb5dlRZrpVHxmycgBrkqs3qvbW6Nv489FzR9U6HA7eemsq\n",
"aWkpOJ0uBg0awvLl3xMYGERBQT633no7Z86c5sknn+WLL/7H+vXr8PcPwGq1MGLEk+zatYOgoGAa\n",
"NYrh66+/RKVSkpGRRq9etzJs2GMkJJzgo49m43S6yM/PY+zYCbRu3bZa7/FykMSjChTYc5h96FUA\n",
"Hmo0hlbBpX/Q+MjKSx5W9tD6qC/t6y9Jnlxiy2jXOJiMHDMRwVo6B91G9+B+bMhaybwjk3mpyTyy\n",
"C0qnLiVG3rKjIYnL46effiAgIJBJk97AbDbz2GMPoVKpGDRoCD169GLVqpUAHD9+jK1bN/HZZ4uw\n",
"2Ww88shgwHsxoSTq1s9PRffu3Rk27DESExN59tnRxMU15s8/f+fXX3+RxONqRhRFPj05lTxbNq38\n",
"OvOf8IcualThlX/D6SSqKIeYxGRkhy2IWi2iwR9nVDT4+Jzn4u5/Sn5z/jq11/RmWMx4duX+w46s\n",
"dWwN+pMuQbd5qpWVID+PE9rVzDf9aiaq9nwkJZ2iY8fOAGi1WmJiYtm+fSvR0TFexyUnn6JFi1YI\n",
"goBaraZZsxYV2iqJuvXx8fFE3QYHh/DFF5+hVqsxm034+p57Ra42kMTjApRPI7gx6ze25qxGK/fl\n",
"qcbTkAmyCqsqZdEo5QgOB/rt2/Hd8S+9/t1EwInDKCzmCseKgoAzLh77jT2x9b0D2023QJmix6JH\n",
"PCoXAH9VMEMavcD/El7ni8S3aOd/I3aHy2saVU9nLbVCo0ax7N27m549e2E2m0hIOEmDBpEV/j6x\n",
"sXGeQtZ2u7046rU8Ff8wH3zwDpMnv0mjRjF89tmCK5Ja8FKQxOMClNWOAnsOnye+AcDotpMJ1bjL\n",
"PJavCldyomLrFm5e/BWaP35Dked2Iy9ZP7GHRUDDSESND0KRGSE3F/npZBQnT6A4eQKfrz7HFRyC\n",
"ZfBDFI16GldYuEfIzicAt4YN5N+snzhasJcfz8ynR8uZXuJRjyIGap177rmPmTPf5OmnR2C1Wnn0\n",
"0ZGeqUoJgiAQF9eYrl1v5IknhuPv749CoUBR/FIoEZrKom5vv70vr702ntDQMJo3b0l2dpbX/tqm\n",
"SlG1NUFd9eLLLbR6QubnHp/IP2dX0MbQhS/7/MCJVLdb+U3tGpT+8UUR5dq/8J02FeX+vZ52HI2b\n",
"YOvbjx3hLcht0orG7eIJLbcUi92OYt8eVGv/Qv3DMhTF1dZFtZqiJ57mr9uHYlH50DBYR+OG3raV\n",
"pPRCEtPd/Ul1HmX01v4oBRWLb/6bGxu3ZuMB91srLsKP6LDqdX+uz16Y1XGt3Nxc1q37i3vvHYDN\n",
"ZmPYsEF8+OF8QkPDauR6l8LleJhKI49KyCmwoFbJ8dUoPcF9B/O38c/ZFSgFFSPiJqNUlJ0KuIVD\n",
"fvI4uvFjUa1fC4AzNAzrgw+jHfU4ucHukPzCwxnYrA6v4DoPSiWO62/Acf0NmMeMR7FzO9q5H6L+\n",
"9We0c96n99Il7H76FYRK3P0bhetJyTJic7hoZmjnMZ7O3vcWvnzoOa5uvCquLfz9/Tl8+CC//fYz\n",
"IHDXXf0rFY6rDUk8yiGKIvsSsgHo1T4Sl0vE7rLxacIUAO5t+AQRPjHeUxWHA+2c99G+9zaC1YrL\n",
"3x/zf8dQ9PgT4OODNkQPxW+T65oEk2+yYajEj8MLQcDRsRMFC79GsWsHuolj0e7exY1TnyPj4FZ4\n",
"990KxlW5TAa4l2SHNHqBrTl/sinrN/acHUYTfTugog1HouYRBIGXX55c292odq6pdTuH03XBNAFl\n",
"d6dmmTh+Jp+fUj4ltSiRBj6x3BM5Eih5UEGTlYHhvn74Tn8DwWrFMvghcrbspujZ5ytdOVEq5AQb\n",
"zrOiUlm/O3Qkb9Xf7Hn6ZZxKJWHff03A7b2QH/M2vJVdSQlWN+DOCLfH61enZpYp+XBJl5aQOCfX\n",
"jHi4XCIb9qex5zxZu8D7zXzsTB5JxkSWn/kEgJFxU1DK3On+ZALEH9jCf56+D9WWTTjDwsn77icK\n",
"P/wYMTCo0rYvC5mM4/2H8teHyyiKiUdx5DD+d9yK8t9/PIeUX4btHzkSgzKIo4W72Z7zV4X7k5C4\n",
"HK4Z8XAUu5Xnm2znPa58PZSvT83CLtroGXI3rYrLHyCKBMx9jw4vPooyLwfbTTeT+/dG7DfdXCN9\n",
"L6FFdAD58c3J+mMd1jvvRlaQj2HQvai/Wwp4ZyUD0Cp03NfwSQCWnZ6DSzz3yMvucHnlGpGQuBDX\n",
"jHhcDAcSstlcJj/pgfytbMtZg1rmw5BG7iTOgtPB9bMnE/TudERBwDThVfK/XY4Ycr4k/dVDWKCW\n",
"Xu0j0QQYKPjfl5iffNbtQ/LsKDTfLKrUAax32AMEqcJJNh9jS/bv56w0t+vYWXafyMJskQLnJC6O\n",
"a0Y8LmawnlXGndslOvky0V1/o3/kSAJVocgtRXSb8hxxq77DpdZQ8PnXmF8cB+dxEqsx5HJMr7+F\n",
"8dWpCKKIfvQzNPrtuwqHqWRq7m/4FADLTn+E3elAFMUK05ei4mjb8lngJSTOxbUjHpc411+b+SNJ\n",
"5iMEqSK4q8GjyIvMdH/tSRpsXYdVbyDr2xXY7ryrhnp78RT99wWMk9yOa3FvjKfhut8qHNMr9F7C\n",
"1FGkFiXyZ8oKjiTlsn5vKuv2pFQI0a8jbj8SVwHXkHhc/LFmh5GlyR8A8HDMGHxsTnq8OorQvdso\n",
"Cgxh7fuLcXTqXEM9vXSKnn0e4yuTEUSRzm9PIGjbv177FTIl90c9DcCXxz8gNbfUCelsnnfeD8mg\n",
"KnGxXEPicfEPxfKUBeTbs2mqb09Pn5vo8cooQvbvoCgolHXvfElhdHydy9JV9N8XMY96BpnDznUT\n",
"nyTg6H7PvohALT1C+hGhaURqUTIbz/7q2Vf+e5G0Q+JiuWbE42KLymdYTvNr6pcAPB4+mp6vjiLk\n",
"wE7MwWGse+dLjA3d6RbPVyKhVhAETFOnYRkwCEWRmR6vjkKXcgqAplH+9Gjd0OOjsjzlU1yie/Wp\n",
"vFhI0xaJi+WaEY+yD4UoihUekpJViK9PvYNDtHNTwB08Nm02wQd3YQ6JYN07X2GMjCFQr0GgjibV\n",
"kcko/GAe2d16oc7PpftrT+FrLkAQBJQKGT1D7iJIFUFK0Um256wBSnOElCBph8TFcg2JR+n//92T\n",
"wqZyleYdTheH8rexNWc1apmGOV8mEnxoD6bQCNa98yWmBu5avG3jg+jZrg4XmlYqUfzwPYVNWqA/\n",
"c4pbZ40FuztdoUKm4p7IxwH48cyCYhH1Pl2yeUhcLNeQeJQ+FGaLw5OLtASr3cGXp9xLs6P3GGiz\n",
"6zCmsAasm/UVpogor2Prmr2jPIbwIGzLfsAZGoZq47/oxr/oUc9bQu/HoAwi0XSIvXkbKjjFncsP\n",
"RKLmsDtcV2Vi6mtGPC70TCw7/g2JpsM0MCmY9EsGprBI1s36CnNExQLVVwOuyIYUfLUEUaPB5+sv\n",
"0Sz8HwAquYYH40tsHws8uU1LKC8mEjXP5oPpbDmUUdvduGSuGfGozBB4+FQOoihitBXy7g63r8Ss\n",
"3x24gqNY++5XmMMjMWhVNIk00KFpCJ1bXF1h1I4OHSmcPRcA3WsTCDy8B4CHWzyGr9yPwwU72ZW1\n",
"xescadpy5Sn5zq82Y/U1JB4Vt2XkFZFdYOGDjdPIsmbR5TTclR3FullfUhTqtmv4+aqIDNHhp1Vd\n",
"csLiuoD1vgcwj3wSwW6n6xujUedmE6IL4PaIIQB8fXwBuWWKdbukonO1xtUm3NeQeFT+hzl6eBvz\n",
"D3wMwJu7wvln1lcUhZZWcKtzS7JVwDRlGvZOXdBmZXDzu+OR4+I/4Q+hFFTszFnLqgPbPcdKNo/a\n",
"41KF22xxsG5PCpm57ny4BxNzOJqcWwM9q5wqiYfL5WLSpEkMHjyYoUOHkpyc7LV/5cqVDBw4kAcf\n",
"fJDJkyfXieHYmSxThW2a7EwW/TAYq1xk4Ekd5nHfUhQS7nVMnVySvVSUSgo++wpXSCj6bRsJmP8h\n",
"/qpgeoTcjYjIymK/FgCnNPSoNS71OUnJchfwOn7GXb/nbH4RaTkVE2vXFFUSjzVr1mC321m6dClj\n",
"x45lxowZnn0Wi4UPPviARYsWsWTJEoxGI2vXrq22DleF3EIreeXCzX3OpqOeNZAfY034OARuu/1L\n",
"LEGhtdTDmscVFk7BRwsACHhvBoGH99CvwXAA/jm7ggJ7jvs4aeRRa7gq8T86HyUFyZSK2plAVOmq\n",
"u3btokePHgC0a9eOAwcOePap1Wq+/fZbT+0Jh8OBRqOphq5WHbujNFJUp1Hin5VKzzEP83JHt4X7\n",
"obhR+IW2rPRch7P+vIntN/fG/NRzCE4nXaa/RIwYRoeAXthdVv4oLlPprAOjxGuVpPRC/tiSRJH1\n",
"4pZt7fbaFY8qWQCNRiM6XWkBGrlcjsvlQiaTIQgCgYGBACxatIiioiK6det2rqY8XE4W5wthFwT0\n",
"2UUAXCcvIPCpQXwTlsLOBhCsCmXo9S9hNsnQaZUYzXYAmscEYiqyEx9pQFMNhtKavL9Lut7sd2Dr\n",
"Rnx37eLGT99i0NOj2LVjHX+kf8NDTZ9Br/epUl/rzP1dJddyukRP/hW9zv1yNdrcYuCSyy/qmpqU\n",
"AvSCQEiglpAQvaedsufuO3EWmSDQOj64um+hauKh0+kwmUptCCXCUfbzrFmzSEpKYs6cORfVZk2m\n",
"m8/JMVNotKA7nUjgxMew5KUz/mEF4GBwozHkZjuwOVxcFxfI+n2pAJgKiwgN0FJYUMTl9qyulSaQ\n",
"f/QpAbf2IPS35fRs3Ym4kFYkmA7yW+IyBsiGXnJf69r91fVr2R0uNh5IIyJQS7PoAAqNpZHNep2G\n",
"7GwjTpsdnY/yvDa37BwTdqcLnUpGRmaBp52y/T2a6E7mHeZXecLtyxHGKo13OnTowPr16wHYs2cP\n",
"zZo189qACWhfAAAgAElEQVQ/adIkbDYbc+fO9UxfahMR8Es8xs1jh6HMTGfq4IZk+DhoomtL9+B+\n",
"2Bwu5DLBa2WlrnuRXg7Oxk0wTnsbgE7z3mJY8AMA/JK6ELtTSgZU0xiL3KPbcxk3M3OL2HXsLAnF\n",
"dYHORVmHvrK2qiu1QFEl8ejTpw8qlYrBgwczY8YMJk6cyMqVK1m2bBmHDh3ihx9+4NixYwwbNoyh\n",
"Q4eyZs2a6u73JaE8uJ9e44ajyc1i362dmNM4E4DhsS8jE9xfQfl5Yz3WDgAsQ4ZiveMuZMZCnpr/\n",
"J8GqCNIsp9ia9Xdtd63ecyGjtNHiFpezuUWIonhOG0iJX4hL9PZjulJmqypNWwRBYOrUqV7bYmNj\n",
"Pf8/fPjw5fXqEik020jNMtGkoX8FvwzF7p00fvQBFAV5pHXqyZiBPthSbfQMucdTywRAo/T+KurF\n",
"Eu35EAQK334f5ZaNhG7dyNCet/O+bxo/JP2PZ7s/WNu9q9c4xYscJQjuZdjUbBN6HxVatZwWMYEV\n",
"DiufVtIlisiuQEnKeuEktvt4Fmk5ZjJyvYeByg3rMdx3F4qCPFK69mb+6IdYk/oHvgodDzV60etY\n",
"H3UlFdzqOWJoKMaZ7wHw2oL1aAUtB/O3szdzdy33rH7jLLOCVz66uywCkJrtti0WFtnIyCvyJKh2\n",
"eQmQ92im5P817bFaL8TDM3wr8wWq/liF4cH7kZmMnL3jXja8OouFp2cB8FS7FwlQeft0aFTeI4+r\n",
"zVW4qljvuY+sPv0IKCjikWN+AMzb/RHGIvtVGel5NVD2d1o+uvtC5BQn6S4rQOVTK1T2PNQE9UI8\n",
"yqP5/FP8hg9BsFopGv44R6e8x+qsHzlddIIoXQzDWz1V4Rwfjbd4XCPaAcCpl6dh8Q9i/Mp0ZKLA\n",
"zwnLWb1vP1sOZUhOY9WAKIpsOZjOkSS367jDeZHfaSUzj5Ls9mXbcIlw5qyx9LOr9Lpl+1Dd1C/x\n",
"sNvRjXsB/YQxCE4nphfGYpz5Hjm2PL497V4yfvmG11EpKq4A+ai8py3XysgDwBUYxM7/TqZRPtx/\n",
"WIZTdPB7+mIAbA5p9eVyEUWw2J2kF0+rHZcRAlDiVVrWedHhdHmmN1B25OHdh+qm3oiHqiCX+CeG\n",
"4PPFZ4hqNQVzP8E8cRIIAvOPTMfkyKeNoSu9o/qi1SgBvCrVl0TMhgVoAdD7KK/8TdQSMkEgtXsf\n",
"km7ux4ub3GLxZ/q3WJxmz49VouqUfxE5L3LkUdlxJd7SZZdpbeVq7ZSuwogVtlUn9UI8gvdto8+T\n",
"96LfthFXSCh5y3/F+sBgALakbWbVmWUoBCWPx70GQINgX1pEB9A2vrSmrELu/iqaR/vTrVW4R2Cu\n",
"BUoWlnY/8wrtzMF0PQ0mZwH/ZK7AZndKto/LwGSxczavyPPZ5RIv2s5RWWiEvZKRR3mBFysxmNbE\n",
"tOXqS1BRFrsd7Xtv0+v9WQguF8b2HbEu/ApXpDv7l81pY9w/owF31bcGPrG4XCKCIBAWqK30jyMI\n",
"AirltbXyUrK8bffzZ+fzU3nh22fYHAWrTn/OHUlDcLqgfeNg/HW17/B3NWG2ONh+JNNrm9XuPK8d\n",
"yWgvYF3mrxwq2MEp02Hy7dnYnBZ8FX6EqCNpYWiP028A0arWnnPKjypKmvcyotbAALLOiIcoitjs\n",
"LtSqyh9cu8PF/oRsYiP8CNCrUa5fh+6VcSiOHkEUBA49OArbhFeIjPD3nDN/71yO5BwmXBNN/4ZP\n",
"AKArMx1RyGXEhOvRXUOjjMoo69OS1vUWOqy/k0Z5v5Lkn8LWzL/oGNybPKNVEo9LZNuRiqkFLTZn\n",
"pakez5hPsCLlUzZl/Y5DrFiM3eQsINN6hoMFW/n+9ALCNdHcHfk4vULuRSHz/v3ana4KIlUT05Y6\n",
"Ix4HE3PIKrDQuUVYpRm70rJNFJispH3/CzErPkO1eSMAzphY/n1qEmev60ITRel5yQVJzNo2HYAR\n",
"cZMI1ulp3zi4ghNZTLhfDd7V1YFC7v2d7H/qVZ76eB0Tepj4e//bdLy5N/LaqMdbD7E7vB/qQnsu\n",
"S5I/4K+MZYiICAi0NnShU+AtxPq2JkgdjlqmwejIJ8N2in05W9mY/RvplmQ+OTmZX1I+Z1T8G7Q0\n",
"3OBp89Apd3qF1mUcymrCYFpnxKOkyLSpyF5BPITcHEK+WkiTpYvwO50AgMvgT9HTz2F+6jnOHsn2\n",
"Ov50ZiH/3fAcVpeFG4PvpK3/jSgVsnqRFawmCPb3IbzAisnioLDIBgGBtOsxFb11LDvUyWQkrqFJ\n",
"5P04nC427k+jUbheEt0LcC4bg93h8ojHvrxNzDk+nnx7FnJBwS2h9zOkyTP4ukII1GvIKSwTMKcM\n",
"oEVwM9obevFwzFg2Z//OsuSPSLOcYsrBYfSLGM5DMWOQC6XPjsVWakit1yOPEkqmZoKxENXq31H9\n",
"vBzVmj8JtrmT+RQFBuN64kmKRoxC9DN4nSuKUGCy8cnuz9iUvg6dwsAjMeOv8B1cfcgEgeaNAnC6\n",
"XBjNdrLyLZzudicPfDeXzyMT+XfzZLp2vodCsx0ROJVeKInHBTjXKpXN4cLqtLM0eTbLz3yCiEgL\n",
"v+sZGTeFhtrG6LUaCo0WAv3UXuIBbi/oPBPIBDk3Bt9J58A+/HjmE5anLGBl2hckmg7xYrPZ6JUB\n",
"gHt5uIT6azDds4ew7dsxJJ2gQUYC+uNHkB8/imB3BwiJgkBmp54c/88AMrreTI/rG1XajNXhZPWB\n",
"vXx1aiYAj8W+hr8qBKi4nCVREblMhkGnJivf/aPtdPM7fHHkfpZH5TDm69nInnm5lnt49WA/h3gY\n",
"rWbePjiazVl/ICBjYNQz3NfwSWSCt60vIkhLQmqB14ihvBe0QqZiSMx/aevflXePjuZgwTamHBjG\n",
"K60+I1AV6rVKVhO+fnVDPK67jp7lNomCgL1zVw53vIXkbrd6covKzzP1OJNpZP6J1yhymugU2Icb\n",
"g+/w7JMcJS+dwOCW9JBdxz/sZvneD3gycRDgHnHkGa0YfFX1OnXB5VDyspIJgkcATI4Cpmx4hkMF\n",
"O9DK9Yxt/iGtDV0qnHtD81DkMhk6HyUF5lLjqaaS+CuFQqC53/XMaPsd0w6N4HTRCSbvf5ipbb6G\n",
"/NIQjPrrYdqmDRntu3Cy3yDOTJlJ7m9ryDqZQt4vf5Bw3zCvpMQyQSAzr8jrSy1hVdpi9uVvQq/w\n",
"Z0TcJM8PW++jolm0f4XjJSqnbHqCW1u/BMAn1znRTXgaivN97DmRRcpZE1sPZZBxBZPuXi2UuJFr\n",
"ilcPzQ4j0w6N5FDBDgJVYbze+utKhQPAt3j1T1fOUVGlqCgeymL/pCB1OFNbLyLOtxUZ1tO8dWgk\n",
"JkdpPhBRdAuIvRo9huuGeOzbx/q3F7Lrv1NIvvtBHB07YVaovZxrShAEtzV517GzXttPmQ57pisv\n",
"tHoTf5U77VpUqI7rm4Xgp1XV/H3UEyJDfIkOdWeYaqpvTxOfluRo4TvXTpqsWOQ57kRqPkU2B7uP\n",
"Zp6rqWuWEvHwUSuwOE1MP/wEJ4z7CFU35M023xDt2/SCbWjKuS2olaWPq+B0oDQWoMnORFmQh+Cw\n",
"E6gJ4uWWnxLpE0ey+RgzDz+NzemegoqiyKn0QjYeSK/0xVsV6sa0pQwpWSaCDT7sPZlV6f7KRl9F\n",
"ThPvH30Bh2jnjsghPNR2kOf8801zJCpHLpMR18CP5MxCBEHgzqjHmX1sDO93gQOfvE9a55swNoxF\n",
"LhOk8pTnwFq80qFUiLxz5L8cLdxNiCaCKa2+IFh9cYXSNQ4LQQd343/iEAEnDhFRmMndqakoMzOQ\n",
"mSuWEhHVaqw+Om6ICaJvXw1H2MmS9Y8y1u9Z5Ip2nLZpQSbjbG5RtbxM65x4ABXKJJSlrGtvVn4R\n",
"QX4aPj05lTRLEo20zXi18xtew27JP6HqGHxV5JtsdA66jSBVBMeC01jdyEbnd15h7buLUChUOF3X\n",
"riG60GzDR63whDaUxWp3Iooi7x98lX35mzAog5jfcxmhqujz1lbRnTyK9sd1qP5ZS/CuHbQ6R1pI\n",
"USbDodHiVGuQ2awoi0wIVisaq5W2e7JZlQZdRsCv6j3c8eMIek2EOIUSU3gkjvAG+ESG4woJgU/n\n",
"V/n+66R4XKwN7kBiDsdlP7Mh6xfUMi2jm75HoFbvmQeCNPK4HNrEBWG2OjiYmEPfiIf5OmkW7/RU\n",
"svaz3TRZsYiUISPgGg17KTTb2HnsLP46Ne0bV8xMbrE5+TXtc5af+galTM245nOJ1sVViGvx91Xj\n",
"SE2jxaZV+P/0Pf4JRzz7RLmcvLjm5DZpSVCPzriaNccV0QBXWBgWjQ5BJrDpoDuZUFy4nmg/BVs2\n",
"HcE3I5XW5DE38w8e4yee7wttLIH02J+D/swpOHMKdhRfpL6Jx8XmO9iTu4EZRyYC8GTj14nUxqGQ\n",
"y1ApJfGoDhRyGX5aFUq5jN5hA/ju9FzWRZnZGwZtFs4mr0dvzKFRtd3NWqEko1dlo2Sny8X6tD/4\n",
"6tQ7ADzX5G2a6NshCN6/R5/MVNr88hVhK5YiWN3t2PV+OPrfh63Pf7Df2J0EI/jr1Fj13qEBJZ+C\n",
"DRqy8i2EBfmCUo4lOAxLcBj2VuH0Uz7M0L9eYtHRBTw4TMcn1/2O/GQahsIcWupcCCYTl1NUok6K\n",
"x8X4ZJwxn2D2sRdxiS7ua/gkNwbfCbhdrcsuH0pepZePQi7DV+HHLWH3syptEW/cF8X3H5+mzfTx\n",
"/P3Oogs3cI2xL+0Ic45PAODF9q/SRXsb4F4p9PdTk3Y8mZaL5hK/8ltkTrcIGXvfzt4b78R4y210\n",
"aFlqE4m9wNPdolEADqfolV4CSlfMXmz3ChvO/Eui6RAfJrzN47FvYFPJsbZ0r2BejnjUGYNA2eAs\n",
"m/38IYCZljO8cehxzM5Cbom8g4FRz3n2ycvNP8/lrCNx8SgU7r9N34iHERD4KTyNhKgggg7upvm3\n",
"n9Zy7+oWZruZZ9c9SpHTyG3Rd/FE6/969glOB6FLPueux++gyU+LEUQXOXfeS84/W0j/9GtSu/dB\n",
"VF1a8KFcJvMSjpYxgTRuYPC8QLVqH55r8jZqmZo/Ur9na/bqassOV2fEA8BPq0KlkJ0ze5VWrSDH\n",
"msHrBx8l15ZJS78beKzhNE/5BCgN8moeHYBCJiPIULulLusDJTakcE00NwT2xiE6mPJEVwBaLZqL\n",
"36G9tdm9WqH8KpOxyM7a3Wf475/Pczz/MBGaGN7p+aFnmmI4eYSmD96J/uVxyPLzyO7YjdUfLyd7\n",
"zic4W7REqKYRcqi/Dw1DS6s5+vkqifZtzKON3WEa/0t4nXxrXrVcq06IR0nqeJlMQK2Ue9bIy5NW\n",
"lMSkAw+TaT1DvK4N45rPQyX3FoeS1ZXwQC3d20ZUGM5JXDplVxPubPAIACuEDey7bwgyp4N2r78A\n",
"popLh/WZ8rlgMnLMrM38gZ9PfYtapmFMsw8I9g1AQKT5kgXc+uwDaA/tx9kwivwvvsH286/E3trN\n",
"k+ZAXewAdq6UFFVFLpOh1yq5OWgQLQ0dybdns+jUu9XicVonxKNExGXFiXgq8x04UbifMTsfcAuH\n",
"b2tebrEArUJX4TiJ6kdeJmS/uf56WgW2o9CRx7y74siPaYJvciK6yddO3ItLFElK9y5BedqYyMLE\n",
"twB4tvkbxOqboczPJeKxIbRZOBuZ00H2kOHkrt+C7Y5+KBRyAsoYQdUqOdc1CeHGthfnA3Ip+KgU\n",
"CIKMEbFTkAtK1mQsY3PK5stut26IR3GaI5kMVOUqt4miyF8Z3zL5wMMU2HNp79+Dya2/8EQOStQ8\n",
"Ze1GgiAwvMWTAKzM/IbN42fiUqrw+Wohqj9W1VYXryjJGYVehZucLidv7H4Rq6uIniF30T3obsKO\n",
"7yegdw+069Zg1Rv4980FpE2egag7t4nS4KuqkSx2JTExDbXx9I8cAcBL65/H5rw8T9MqiYfL5WLS\n",
"pEkMHjyYoUOHkpyc7LX/77//ZsCAAQwePJjvvvvuwu2VG3mUkGVN5e0jz7Dg5BTsoo0hzYYzrvlc\n",
"NHLfqnRboopEBuvQ+5R6JN4Z159AVRgpRQmsDzzLsSfd8S/6F55ByKz/rur5Ru+H7r1t77M/ZwcB\n",
"qlAejXmZRt9/SdfnhiBPOYP1uo78+fGPpHfqWWtBhGWn7vc2HEW4JprjeUd5b+v7l9VulcRjzZo1\n",
"2O12li5dytixY5kxY4Znn91uZ8aMGSxcuJBFixbx7bffkp2dfZ7WSgvYlIhHjjWDrxJn8sLufuzM\n",
"XYtOqWPerZ8yu/eHFVKulRARqKV5tDQaqQm0GgXXNwsp/axU0TfiYQBWpn7BqUGPkXFdF2RZWehH\n",
"P13vi96Utcklm47x/m53xrpnIl+h98ypXPfxW8gcdsxPPEXOit8oCnVPRWprmF9WPFQyNSPiJgMw\n",
"b38tiMeuXbvo0aMHAO3atePAgQOefSdPniQ6Ohq9Xo9SqeT6669n+/bt528vbTd7cjew+OQ8nvpn\n",
"IE/tvIWVaV9gdRXRJeg/bHxwBwOaDjrn+QatimbRAYQHaqtyOxKXiFwmo3fYA6hlPuzP30yi6Rjb\n",
"x07HafBHvWY1ms8W1HYXqx1jkZ18k3vEUWKTc7jszD0xAYdop6/2dsa9/B5R63/HrvXl+NvzMb05\n",
"E4VPGYN+Lbkc+evV+JTJBdLWvxudAm/F4ry8aOgqOYkZjUZ0ulJjpVwux+VyIZPJMBqN6PWl8zpf\n",
"X18KCwsra8ZDj686e3dKUNIxsA/9I0cSp2tFhO78RiS5XHIEuxKU5KaQywV0CgM3h97H7+mLWZ70\n",
"OSNjXif9jXeJ/O/j6Ca/gqPddThu6HzhRq8CiqwOdhRHDndtGY7LJSIXBFbnLSTRdJgIVwCL31iH\n",
"vtBKXlwzNr/6PuGd21M+CURtFU+XCQIdmoaw8UCaZ9vw2Jcpcl7eClmVxEOn02EqszRXIhwAer3e\n",
"a5/JZMJgMFRooyxtQtoic+poE9aSHjHdCLB0QK90nxPs70NISKkY6XUV/TYCA7Rex1wMl3r85VIf\n",
"rndnz3gsVif+ejX6xFweaDyCP9K/YW3aTwxv8hLyIYMgYT/C7NkEjHwEdu2CsLBq7wdc2e/TV6/x\n",
"/O7UWjVaXzUp1iMsPPohAEu+zCWgEM70G8ihMVMR1BoiwvwICXLb5krODQ7WEWTwueD1aureHogw\n",
"YHc4SU4vJM8YQGzQN5fVXpXEo0OHDqxdu5a+ffuyZ88emjVr5tkXFxdHUlIS+fn5+Pj4sH37dh5/\n",
"/PHztrdm8Gb+2ZlM4wYGggwath7OoNBqIVCvJirQh7NnS0cuhUZLhfN9lTKvYy5ESIj+ko6/XOrb\n",
"9c5abBQaLegJ55aG/+GvM6tYenw+AfKX6TD2VQI3b0W5dTO2+x8g/7ufQFG9URBX8vsMCdGTnlHg\n",
"+d2dTs3jbF4eU/c+jVN0MnozdE9Vsv2FSZzqOwDsgN2CsdDC2eJVxJJzc3JMuC5QQOtK3JufWk5K\n",
"urXSZ+lSqJLNo0+fPqhUKgYPHsyMGTOYOHEiK1euZNmyZSiVSiZMmMDjjz/O4MGDGTBgAKGhoedt\n",
"r8ThRi4XvBySNCrFRcWmSNOWK0/r2EDaxgXxTLsXAVidvpTUwkxO51gp+N+XOEPDUG38F983Jtdy\n",
"Ty8fe5lATaPZxk/7ppBUlECzLHhjXyjrZn3pFo4ylE3cU0Jd+pVWR8BolV4JgiAwdepUr22xsbGe\n",
"/998883cfPPNF91eSZiyXCZ41RA53xyxbCKaytKzSdQswcXD704+HekYdBM7sv/ht7QvaRb2MtYG\n",
"IaTP+R8NhvRH+/EcnM2aYxkytJZ7fGmkZpk4kZLPnT3icZTxczn522y+F1cgE+GzQ82xrFpOTvHq\n",
"tEYp92Qsr+w3WZfyJlVHwGidcBI7nOguUqOQy7zWwoXz9K5Jw1JzlBS/UnuolHIm9XLXAF6Vthij\n",
"o4CdR8+yKaAxedPcIem6sc+j/Pef2uzmJXPsTB4uUSQjx+x+ublcxH4xi2k5sxEFeC69OU2/WI/Y\n",
"IJKoUB2NwvQ0DCldRKjs4XTWRM3HKlIdI486IR4llL+hC1mn4yL8CPP3qZAoVuLK0qNRd1obulDk\n",
"NPJD4heet2/mgIcwPf0cgsOB32NDkR8/Vss9vXQcTheuvHxunPIsC/M+52QgNLGHcM/jP4PG/dKK\n",
"b2AgNsLPK49MWUqWSZV1aIRcHSs/dUs8iu0dJcFCgX7nHlGIokh0mJ4WZUrqSdQOcrnA/Q2fAmBZ\n",
"wmeeJcB9CdlsHzoaa99+yPLzMAzsj+x0coXzKys4XtuUPFyyE8dpP/weDmauZV4nUCBnZMdP8FFV\n",
"XDU511TguibBtIoJxOBbd5Jw15tpSwklI49WMYF0bRlep75siXMjlwm09LuBZvoOFNjz+D1tsWff\n",
"2UIbBfM+xX5DZ+QpZzAMuBtZRrpnf3JGIRv2p1Fgqp6M3lXFYnNwMiW/1HgvEwjftp7ou2/FkX6S\n",
"R+93jx4GRD9LjG/zSh++ktAKTbn4FJVSToj/hZdoryT1TjxKVlqUClm1hyZL1BwymTt72wNRTwPw\n",
"c+rnnpohCpkMfH3J/+Y77G3bo0hMwDDgboQsd3b7pAz3smRlZTauJIeTcjl91sjpTCM4HLRcOJvu\n",
"rz2JvLCAUcMbkOLroGVAO+4pDiyrzGbgp1XROiaQ65qGVNhX16hXNg+ZIFSo1l4ZgcVhzCWFcSRq\n",
"nxLRb2PoRvvALpgc+fyS+nnxPvffVDT4k//tchzNmqM4egT//n2RpaW6xYWKyXWuNCXxKnlHEtDe\n",
"fQdNv/4YBIEvxt7HtxGpqGRq3uoyx1NI+lxv7mB/n6sih0y9GXl0bRNBt9bhFxV12Co2kOubhuAn\n",
"TWnqDCVvMUEQGB4/FoBfUxeRZ/OuvSMGBZH3/S84WrREcewo/nfdji7VbQNx1rLdQyYINFz/OzeN\n",
"uAvfHVuwBIXy84wPGRP8LwAPx75I86DmnuOv9sTa8vpiMDXo1JXWvqgMd2YkSTjqEoIgeJbOo9Vt\n",
"uD7gZqwuM8tTPvEq1AwghoWRt+I37B2uR56cRPenBxCye8sVH3mk55g9UyUhP4/2b46h65svoC7M\n",
"J61jDzYt/JmZPivJsZylleEG7mk43CtdxNWeWLvejDwkrn4ig33RKOU4XC4GRz+PgMCf6UtJN5+p\n",
"cKwYEEj+9z9jvfU2VAV59Jw4goZffgxX0A/iSHIuBxOzUa38mYCbuhL558841D7sfG4SG6YtYJVl\n",
"I5uzf8dHruXZJtNRyOVe05Gr3T2gXtk8JK5+NMX+DI18m3FjcD8cop1Fp96t9FhRp6dg0becGvoU\n",
"MpeTJh+/jeHB+xEyMq5IX/XJCfSYOALDYw8jT00hv2U7/vz4BxLuepAsWzrzjk4B4OlWkwnTRCET\n",
"SssZyGXCVW9z81HLvYqjVQVJPCSqjfCg0nwqjzYeg1qmYWPWb/x88O/KT5DLSXx2HP++8TE2QwCq\n",
"tX8R2LUDPnM/hKKaWX2RZaTjO2Est426h/Bdm3D5+1M48z12fPIDxoaxuEQX8068jNlZyPUBN/Of\n",
"yEHu5NzFNoJurcLp2iq8Rvp2JVEq5NzYJuKy2pDEQ6LaCA/Uoi8ezgerGjAwdiQAb+14hWOncyms\n",
"pDq7KEJ651788+lPWPvcjsxYiG7qqwRd3xqfD99HyMutlr7JUlPwnfQygTe0Rfv5JwguJwl9HyBn\n",
"824sj46A4rfwqrRFHMjfgp8ikFHxr+NwujP7l5RGUCnlF22fq+9I34JEtWLwdS+lO10ig2OfJFAV\n",
"RoLpIN8cXsy+kxXTUZaUALCEhlOw+Dvyl3yPvW17ZFln0b05maA2TdE/NQLVmj/AfImZr+x2lH//\n",
"iX7EIwRe3xrt/I8QLBbMffuxev4Kdr7wOmJQkKe/yaZjfJP0HgBPNn4Df1VpDdraSuRTl6mT5SYl\n",
"rl5KrPguUUSr8mVIoxf56Ph4vkl6j06BfQD3UDk1y0S+0VpqIy1ebLH1vg3bLX1Qrl2D9uOPUP2z\n",
"Fs0Py9D8sAxRo8HeqSv06IaqRVscTZvjahAJKhWIIkJeLvLkJBR7diPfsgnN2jXIctxBl6JCgaX/\n",
"fRQ9O5r8pq0oOOIOhRVFEUEQsNgtzDk+Hrto45bQAXQMvKXcfdX4V3fVIYmHRLUiLyMeiNA9uB+r\n",
"05dwrHAPS5Pf546O7qrsx864q5aVrGCUXdE1WhwkxV1P0yXLUacko1m2BNXq31Hu3Y1q/VpYv5ay\n",
"uelEmQzkcgS7vUJ/HE2aYr13AJaHhuGKaEBGjhmhqPS4ApMNlwgLjk8jyXyESN9GPBI7oUI7Qp3K\n",
"xlE3kMRDolopO7oXRRGZIOOJuKmM33c/f6Qv4eeDg+ga2cVzTIlnZ1l/kAMJ2VjsTnxUCoKCG5A/\n",
"7FmiX5qIkJmJctsWDEf2Ydu4GfmpRGRpqQgud8i83UeLOSwSe9PmJDdpR16HzgR07oBeq8KgU5Nv\n",
"tHI42duGsvtEFpuyfuO3lG9QCEpmdl6AylKxtEd5fxUJSTwkqpkS/wd/ndqT/Cbatyl3N3ic5SkL\n",
"mLptDDPb/YBC5u3oV7b4sqM4c5fLJbL7+FkAwgK0qENDyb21L87778dpLR49iCI4nZiNRWxLzAdB\n",
"oEGQL6nZJuSCQHaqO8amV/tILLaKZUzTik6x4OQkAEY2eYWWQW05kZJf4bjqKM9Y35BmchLVSqCf\n",
"hrZxQbSODfR6W9/f8EnCNdGcLjrB92fmVTiv7LEloxcRscL+7Ucy2XawNCoXQXDnSNX4eA97yrVp\n",
"d7gqeLHaXFbeO/oCRU4TXYL+w10NHzqnYbQO5fGpM0jiIVHtBPppUMhlXm9rlVzDU42nISCw4syn\n",
"HCnY6XWOSMW3e9mPWw9nsPdEaaxMbqH1gv0o25qxyO4lHqIoMv/EaySZjxCuiebJ+DeQy2Venpfq\n",
"Msl7pJFHRSTxkKgxyj9vLfw6ck/kSFy4mHN8HGaHd5ZwlyiSZ7R6ctqWJ9dYKhh7T2ZhLLK768a6\n",
"XPmQvdcAAA7HSURBVF6jlMoedLPVwcnU0unIipRP2ZD1C2qZljHNPkSr0CGXybwGLx2bhxAS4OPp\n",
"m4Q3knhI1BhlH2K5IKBRyXmhw3ga61tx1prK/JOveR3jcsGeE1mVNVUpBxNzSEgrICndeMEKl5k5\n",
"pT4i27L/ZEny+wgIPN90Fo183aVDtBqF1+hEqZB7pjGSdlREEg+JGqPsAyeXC3RpGU6LqBBebvsB\n",
"PnJftmT/wU8p//McU/7tnl1w/roiRcU1UCw2x0WPDI4V7mHO8fEADGn0opc/h1atqJDhvKzfioQ3\n",
"knhI1BiNwksrn5VNw9dIH89zTd4GYEny++zOXQ94r7iAd0Hp8+G2l5T5XMlzbrU7STIdZfqhUVhd\n",
"RfQKvY+7G3gXI9NqFJ4UgiUpMGMi/ACIa+B3UX25lpDEQ6LGCPH34aZ2DbiuSQjxkaVuXTKZQMfA\n",
"WxgY9SwiIu8ffYEThfuqbpQUvadI6bkV3dgTCk7w5qERmJwF3BDYm1HxU72ST/nr1Bh8VQQZNLSO\n",
"CaR1rNtt3aBT06t9pKdOjUQpknhI1CiCIGDwVXktgZb8/76GT9E9+C4sLjNvHX6CwzmHq3QNEfG8\n",
"NolE4yEm7X+YfHsWbQxdeL7pu550guC2x7RvHOwRk2B/H0/4vcS5kb4hiStOiYzIBBlPN57G9QE3\n",
"Y3TkM/T3+zhlOreABPlpCK6sHId47qXUQ/nbmHpwOAWOHNr5d2dc83moZGoCist7AFdFwuK6yCWL\n",
"h8Vi4bnnnuOhhx7iiSeeIKc48KgsX3zxBQMHDmTgwIF89NFH1dJRifpD2eVQhUzJC83ep42hK1mW\n",
"TCYfGMa+vE2VnqfzUdI6LogmUf5e27MKLBSV8x4VRZHfUr/i9YOPYXYW0iXodsY3n4ta7p5+RARp\n",
"6doynF7tI6/6rGC1xSWLx5IlS2jWrBmLFy+mf//+fPzxx177T58+zS+//MK3337LsmXL2Ljx/+2d\n",
"fVBU9RrHv2ffWNhdXu+qiLwklwjirsbQXBterJkoLDLi5lVW0kYkwAkz02EFLXGGMK/NVQdHbcaG\n",
"ER1Trty6TRNe5zYOM2JZQ4RAitHVa2ioqLW7AQvs7/6x7rpnWRSWc1iw5/PXcs7hfM/DLt/9vT2/\n",
"5xTOnz8v2AMTDx4KiQ8McXuxIPJF9A6ZUNGej2OX98DK+IZg7+7MCBmee3LhTqIdAPxi6cHfO9ai\n",
"+mIlrBjCwpl5WPPw+/wl8RxH5T3GyZjNo6mpCWlpaQCA1NRUnD59mnc+NDQU+/fvd/QfBwcHoVRS\n",
"LVni3sglCmxP3ofsWYVgsOLI5V0oa1mCH4xnHdfYp01lI4xHDFot+PfPh7G2ORNf9tTDR+KHtQ/v\n",
"QG7UOkg4vlFQjuz4uWdiXG1tLQ4cOMA7FhISApXK5vwqlQpGI3+VoEwmQ2BgIBhj2LZtG+Lj4xEZ\n",
"GXnfB9FqNfe9RkhIz3t63b/2w2QZvoo0OFiN/PgSPDZtHna2bUCnuRWlZ/+KpJD5eC5cD13Ai9Bq\n",
"NRgaskKjvvuF9PNvl3Hy53/h858O41pfFwDgseBkrI6vxAy/cARqfHD7znL2II0Pbhn7EREWCPUo\n",
"d+GfzH9Lb8KxMc6PFRcXIz8/HzqdDkajEXq9Hp9++invmv7+fpSWlkKtVmPz5s2jqsdy/brxvtcI\n",
"hVarIT0v6nVcvo0rPWbHzxxsazXiI4PQfsmWMt87ZMY/f9qLz68eQr/Vtp+pj1SJuOA4xGj/iKvX\n",
"emEcvIWu337EDctVx73CfKOxOGI1/hyc7vjcxYYH4scrv2JgyIqUP4WizzI06nGOyf63FELPU8ac\n",
"kp+YmIiGhgbodDo0NDQgKSmJd54xhlWrVmHevHnIz8/3+MGI3w9SiQSDVqsjFR8AfKUqVD33Nxxv\n",
"XoH/dP8DX/Ycx4/mNjRf/xbN17/l/b5KFgBdwBN4atpfoAt8YlgXRcJxmPfodDBmq26n9qVJRiEY\n",
"s3nk5OSgpKQEer0eCoUC779v21q/uroaERERsFqt+PrrrzEwMICGBtvKwbfeegtz584V9smJBwal\n",
"QgpTn3XYfhsKuRRPJcRCI89H1qx8hIVyuDH0X/RKf8GXbf+DEhpolWEI8509zDCc4TibQRHCMmbz\n",
"UCqV2Llz57Djr776quN1S0vLuB6K+H1hM48B9PYPOo6FBtvKODgvLgtSBiEmYCa0Wg3UN3/Ab07X\n",
"34vRdJuJsUN2TEw4rv/L9inT67/YxjamB/khNiIIAL+ymbORjKUlQd4hDmQexITjupmwQsbvcvA2\n",
"5FG4rw8rlY7sCH4+/AY1lU0QBzIPYsIJCeCv+3H93x6pjqrzvKDszjU+MinULqUfgzQ+vJ+p2yIO\n",
"ZB7EhBOk8UFywt1ShxzHYXbo3ZR311aFffzD1+duK8S5xIPz9QqZBA+F8tPnp3hB+0kLmQfhFZyz\n",
"VjnOVqrSjut4xsPhgUhOCHUU0gYA6Z2Sj1bGeN2URx8KGVYOkloe4kDmQXgdjuP44xkuTQWO44al\n",
"yNsNwlch460UtftE3J0BV4C/ETIhHFS3hfA6Eo5vGCONeTgTplVBIZMg2N+Ht7jMPjg6PdjPUeCJ\n",
"dj4XBzIPwutwHMfrWozGPHzkUsyapgYADDrttu6uh0LeIQ7UbSG8zrDZFunYPpbOYxzO08CzQ/0h\n",
"lXDQ+NF+HWJALQ/C67gOaI6m5TEyd5sZEdM1iJg+NTJUpyLU8iC8jqtV3GsB2EjYp3MVctrgZ6Kg\n",
"lgfhdVytwpMVobERQY4l7cTEQC0PYtIhoVVdUwIyD8L73PGKcK0aPjIpFFT2YEpA3RZi0hAdFsAr\n",
"DkVMbsjiCYLwCDIPwuu4pugTUwMyD4IgPILMgyAIjyDzILyGfRMfpQ8t7JqK0GwL4TXmxvwB5r5B\n",
"qJSUezIVoZYH4TVkUgkCVKOr2kZMPsg8CILwCDIPgiA8gsyDIAiPGLN59PX1obi4GEuXLsVrr72G\n",
"mzdvur3OarVi5cqV+Oijj8b9kARBTD7GbB6HDx9GbGwsDh06hKysLOzZs8ftdTt27IDRaKSdqwni\n",
"AWXM5tHU1IS0tDQAQGpqKk6fPj3smvr6ekgkEqSmptLmswTxgHLPdR61tbU4cOAA71hISAhUKhUA\n",
"QKVSwWg08s53dHTgs88+w65du1BVVSXw4xIEMVm4p3ksWrQIixYt4h0rLi6G2WwGAJjNZvj786tz\n",
"ffLJJ+ju7sayZcvQ1dUFuVyOWbNmISUl5Z4PotVO7F6TpEd6k1HLG3qeMuYVpomJiWhoaIBOp0ND\n",
"QwOSkpJ459evX+94XVVVBa1We1/jIAhi6jHmMY+cnBxcuHABer0etbW1eP311wEA1dXV+OKLLwR/\n",
"QIIgJiccoxFNgiA8gBaJEQThEWQeBEF4BJkHQRAeQeZBEIRHeHUzIKvVis2bN6OjowNyuRwVFRWI\n",
"iIgQXOell16CWm2rqB4eHo6CggIYDAZIJBLExMTgnXfeGfcy+u+++w7bt29HTU0NLl265Pb+R48e\n",
"xZEjRyCTyVBUVIQnn3xSEL329nYUFhYiMjISAKDX67FgwQLB9AYGBlBaWoorV67AYrGgqKgI0dHR\n",
"osXoTm/GjBkoKChAVFSU4DEODQ1h48aNuHjxIjiOQ3l5ORQKhSjxudMaGBgQLTY7PT09yM7ORnV1\n",
"NSQSiTCxMS9y/PhxZjAYGGOMNTc3s6KiIsE1+vr6WFZWFu9YQUEBO3PmDGOMsbfffpudOHFiXBof\n",
"fPABy8zMZIsXLx7x/teuXWOZmZnMYrEwo9HIMjMzWX9/vyB6R48eZR9++CHvGiH1jh07xt59913G\n",
"GGO3b99m8+fPZ4WFhaLF6E5PzBhPnDjBSktLGWOMffXVV6ywsFC0+Fy1ioqKRH//LBYLW7VqFXv2\n",
"2WdZZ2enYJ9Pr3ZbmpqakJqaCgCYM2cOWltbBdc4d+4cent7kZeXh+XLl6O5uRnt7e14/PHHAQBp\n",
"aWlobGwcl0ZkZCSqqqoceTzu7n/27FkkJiZCLpdDrVYjMjIS58+fF0SvtbUVJ0+eRG5uLsrKymA2\n",
"m9HS0iKYXkZGBlavXg3A1lqUyWSixuhOr62tTbQYn376aWzZsgUA0NXVhYCAALS1tYkSn6uWv7+/\n",
"qLEBwLZt25CTkwOtVgtAuM+nV83DZDI5uhMAIJVKYbVaBdXw9fVFXl4e9u/fj/Lycqxbt4533s/P\n",
"b1h+zlh55plnIJXe3cSXOS2dsef/mEwmaDQa3nGTySSI3pw5c1BSUoKDBw8iPDwcVVVVMJvNgun5\n",
"+fk5fv+NN97AmjVreO+T0DG66r355pvQ6XSixiiVSmEwGFBRUYEXXnhB1PfQVUvM2Orq6hAcHOxY\n",
"5c0YEyw2r5qHWq125MkAtm8ZiUTYR4qKisLChQsdrwMDA9HT0+M47y4/Z7w4x2AymeDv7z8sViF1\n",
"09PTER8f73j9/fffC6539epVLF++HFlZWcjMzBQ9Rme9559/fkJi3Lp1K+rr67Fx40ZYLBbHcTHi\n",
"s2tt2rQJycnJosVWV1eHxsZGvPLKKzh37hwMBgNu3bolSGxeNQ97ngwANDc3IzY2VnCNuro6bN26\n",
"FQDQ3d0Ns9mM5ORknDlzBgDc5ueMl7i4uGH31+l0+Oabb2CxWGA0GtHZ2YmYmBhB9FauXImWlhYA\n",
"QGNjIxISEgTVu3HjBlasWIH169cjOztb9Bjd6YkZ48cff4x9+/YBAJRKJSQSCRISEkSJz1WL4zgU\n",
"FxeLFtvBgwdRU1ODmpoaPPLII3jvvfeQkpIiSGxenW1JT0/HqVOnsGTJEgBAZWWl4Bovv/wyNmzY\n",
"gKVLlzo0AgMDsWnTJgwMDCA6OhoZGRmCaNlnbAwGw7D7cxyHZcuWQa/Xw2q1Yu3atVAoxrdzuF2v\n",
"vLwc5eXlkMlkmDZtGrZs2QKVSiWY3t69e2E0GrF7927s3r0bAFBWVoaKigpRYnSnV1paisrKSlFi\n",
"zMjIgMFgQG5uLgYHB1FWVobZs2eL8h6605o5c6ao758zHMcJ9vmk3BaCIDyCFokRBOERZB4EQXgE\n",
"mQdBEB5B5kEQhEeQeRAE4RFkHgRBeASZB0EQHvF/R9DiBzJiopkAAAAASUVORK5CYII=\n",
"\">\n",
" </div>\n",
" \n",
" <div name=\"mu4\" style=\"display:none\">\n",
" <img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQ8AAADVCAYAAABJ/XXDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
"AAALEgAACxIB0t1+/AAAIABJREFUeJzsnXd4FNX6xz+zPZvdbHqvJBA6iKhYULBjxYaIiliwe6+K\n",
"BfWK6BXRaxcL6LU35IqiYkMU5QfSlN5LQkJ6b7vZOvP7Y7Ob3Ww6acB8nidPsjNnzpyZ7HznnPe8\n",
"530FSZIkZGRkZDqIorcbICMjc2Qii4eMjEynkMVDRkamU8jiISMj0ylk8ZCRkekUsnjIyMh0Clk8\n",
"ZGRkOoUsHjIyMp1C1dsNkDny2LVrF99++y0PP/ywd9vy5cvZv38/CoWC6OhoJk6c2KXbZfogkoxM\n",
"B3jvvfeku+66S5o5c6Z3W01NjXTZZZd5P0+aNEmqqKjoku3l5eXdfEUynUXuech0iBtvvJHQ0FDW\n",
"r1/v3bZhwwbS09O9nzMzM1m7di1arfawt69bt44JEyZ081XJdAZZPGQ4dOgQixYtanH/iBEjOPvs\n",
"s72fpSbLoYqKiggJCfF+DgkJIScnB5PJ1CXbZfomsngcA7hcLq677jo+//xzAB599FFuu+02UlJS\n",
"AEhKSmLGjBntrk8QBL/PtbW1aDQa72e1Wo3FYkEQhC7ZLtM3kWdbjgE2bdpEfHw84O41bN682Ssc\n",
"naFpzyM4ONjvs9VqxWQyddl2mb6J3PM4Bvi///s/xo4dC8DOnTsZMGCA3/6ODlua9jySkpLYvn27\n",
"93NVVRVDhgzBaDR2yXaZPkovG2xleoDLL79c2rNnjyRJkvT6669LCxculJYvX97p+hYvXuw322I2\n",
"m6WLLrrI+/niiy+WysrKumy7TN9EkCQ5GNDRTEVFBRdddBFTp05l0KBBHDhwAJvNxogRIzjllFM6\n",
"XN8nn3zCjz/+SGFhIZdffjnTpk3DYDCwZMkSCgoKEEWR5ORkLrnkEoAu2y7T95DF4yjnm2++ISsr\n",
"i/vuu6+3myJzlNEpm4coisyePZu9e/eiVquZM2cOycnJ3v1bt27lueeeQ5IkYmJieO655/ys6DI9\n",
"x7Zt22QvTZluoVM9j2XLlrFixQrmzp3Lli1bWLBgAW+++SbgtsRfdtllzJs3j6SkJBYtWsTo0aPp\n",
"169flzdeRkam9+hUz2Pjxo1e6/2IESP8LOTZ2dmEhoby/vvvs2/fPs444wxZOGRkjkI65edRV1eH\n",
"wWDwflYqlYiiCEBlZSWbNm3iuuuu4/3332fNmjWsXbu21fpks4uMzJFHp3oeBoMBs9ns/SyKIgqF\n",
"W4dCQ0NJTk729jbGjh3L9u3bGTNmTIv1CYJAaWltZ5rSKaKijPL55PP1uXP11vk6S6d6HqNGjWLl\n",
"ypUAbN68mczMTO++pKQkLBYLubm5APz999/079+/0w2UkZHpm3Sq53HOOeewevVqJk+eDMDcuXNZ\n",
"unQpFouFSZMmMWfOHGbMmIEkSYwaNYozzjijSxstIyPT+/QZP4+jvWson+/IPN/RfG2e83UWeWGc\n",
"jIxMp5DFQ0ZGplPI4iEjI9MpZPGQkZHpFLJ49AKVtTYsVmdvN0NG5rCQxaOHkSSJLQfKWL+7uLeb\n",
"ItNDVFSU8+KLz/V2M7ocWTx6mL4xMS7Tk4SHRzBjxsNtFzzCkMMQ9jASjeohSVJASD+ZznGgoJrS\n",
"qvourTMqNKhVP4gffviONWtWY7PZKCjI49prbyA9PYNXXnkBhUKBRqPl4Ycfawhh8RgLFrzPggVv\n",
"sHnz3zidLsaNO5OJE6/gppuuY+HCrxEEgeeff57k5AzOPPPsFs/bV5DFoxspr7Zi0Kv9tvn2PNbs\n",
"KOKUoXE93CqZrsRsNvPSS/PIyzvEQw/di14fzMyZj5OR0Z9Vq/5g3ryXufvue73lly//mXnz3iYi\n",
"IoIffviO4GADw4ePZO3aPznxxDH83//9HwsW3NKLV9R+ZPHoJqrrbGzLLsegU5MYH+rd7isedqfY\n",
"Cy07OkmPN5Ee37OR1gVBoH9/dzDpqKho7HY79fX1ZGS413INH34c8+e/7nfMrFn/5q23XqOiopwx\n",
"Y9xhIC++eCJffvkFkiRx6qmnolIdGY+lbPPoJqrNdgDqrA6/7U1XA5RUWth5sAJJknA4XWzLKsfS\n",
"5BiZvkvTYWdkZCQHDuwHYPPmjSQlNaa4cDgcrFixnCeffIbXXpvPjz8upbi4iOHDR5Kfn8fSpd9w\n",
"5ZVX9mj7D4cjQ+KOQGwOFwAqhb8+NzWY7sypBCAl1khhuYXyGitmq4Mxg2PbPEducS0RJh3BOnWb\n",
"ZWW6B1/xEAQFDz30L15++T9IkoRKpWLmzMe9ti21Wk1IiIlbb52GVqvlxBPHEBPj/j+fe+75/P77\n",
"r6Snp/fo2pbDQRaPbsJqd4uHTqP02+5rMPVFABQNX0S7o+3hTFWdjazCGrILazhjZMLhNVamU0yY\n",
"cJH3b61Wy//+9w0Ar7/+dkDZ+fPfA2DatFuYNi3QpuFyiVx88WXd1NLuQR62dBMu0S0SSqV/t7a1\n",
"qVpVQ1lRkigsN7dcEHA02Evkmd8jnzlzZvPXX+s599wjK6G33PPoJlwu92MtNulEtCQetRaHVxAA\n",
"9hyqwhSsQd8wJJEkid05lYSH6IgJ18uicRTx2GOze7sJnUIWj27C1aAaTQ2kLQ1bduVWBmwrrqxH\n",
"p7EjihImg5biqnqKq+qJCdfL3mYyvY4sHt2EZ9ji+e2hI898TnGj4WxoaniXtEtGpquQbR7dROOw\n",
"pal4dK7HUFvfdMq3c+2SkekqZPHoJjzDloCeRyfrq6y1AY0zMrJ2yPQ2snh0Ay5R9D7cYlObRyef\n",
"+hqL2+lMq1Y21CPLR19j6tSru6Sexx578LCOf+ih+ygqKuyStrSGbPPoBjxDFnCLh+dBl5r8nV9/\n",
"gIPmPVTYixAlEZ1ST6I+g37Bg9Grml+QpVK69b7pcEjm6GHOnOe7oJbuX3Api0cXI0lSwOpOl+ie\n",
"Zq0y29CHVvPJwfmsKltKhb35mB5KQc2I0FM4K+YqRoed6efF6BGfpsOhY52QKVeiXb6sS+u0nX0u\n",
"/PJzi/utVitPPfU41dVVJCQkIooiWVn7eeWVF5AkCZPJxCOPzGLPnt18+ulHaDRqCgryOeusc5k6\n",
"9SYKCwuYO/cpb7bFe+99kKioUVxyyXl8++3PfPXV//jpp+9RKBQMHDiYe+99gOLiIp5//hlsNhta\n",
"rZaHHnqM6OgY3n13AX/+uYqIiEhKSnomVowsHl2ISxTJLzWTVVjTZLvEnuJDLDo0j99KvsQlub1P\n",
"TepIMo0jidTGoxJU1DmrybHsJatuBxsr/2Bj5R+k6AdyY9ojDDadCLhtHQ6nK+AcMj3PkiVfkpbW\n",
"j+nT7yA39yAPPngvzz03h0cemUVqahpLl37Dp59+xAknnERxcREffbQQu93OxInnM3XqTbzxxitM\n",
"mjSF0047nX379vLss//mm2++xvOu+PHH75gx4xEGDhzEkiVf4nK5eOONV7nyysmMGXMKf/21nvnz\n",
"X2fy5GvZuPEv3n33Y2w2W5cNn9pCFo8uQhQl1u8sweZ0BexbvPNL7tt8G3XOahSCkrFRF3Ne7DX0\n",
"N4xsNp5Hlb2MVWVL+a7gfXIsu5m94wbOjZnM1LSZqB0KVm8v6olLOqKo+ezLbqk3qpV9ubk5nHzy\n",
"qQAkJ6diMoWSk5PNiy8+C4DT6SQpKRmA9PR0FAoFOp0OrVYLQE7OQUaOHAVA//4DAnoMjzzyBAsX\n",
"fkJBQT5Dhw5HkiSysvbz8cfv8+mnHyJJEmq1mpycg2RmDgTcbvIDBw6mJ0zqsnh0AkmScLokHE4R\n",
"vc59C612V4BwKBQi/93/DD/9+SkAw0xjuDHtMRL1GQCEG3VU1FoD6g/VRHJR/DTOjb2GJXnv8HX+\n",
"2ywrXsj+um08MPA1IrXx3XyFMu0hNbUf27ZtYezYceTn51FdXUVycir/+teTxMTEsnnzRqqrqxtK\n",
"B74kUlLS2Lx5Y0PPYw8RERF++7/7bgkPPPAIGo2G+++/h+3bt5KSkso111zP0KHDycraz86d20lN\n",
"7cfixYsQRRGXy8W+fXuaPV9X0ynxcEdGms3evXtRq9XMmTOH5OTkgHKPP/44oaGhzJgx47Ab2pfY\n",
"n19Nfpl77cnozGgMQWrvKloPDsnCvL0zWFvyOxqlhuuSH+K82Cl+PQ2tWsGI9Ei2HChr9jwahZZJ\n",
"yXdzYsRZvLD7H2SZd/DYtmt4fPC7XgECqLXYMeo13XClMq0xceIVzJ37FHfccTNxcfGEhJiYMWMm\n",
"Tz/9BC6XC4VCwcyZj1NaWtKkh+n+++677+W5555m4cJPcDqdzJw5y29/eno6d911C3p9MFFR0QwZ\n",
"Mozo6BheeOFZ7HYbNpuNe+99kP79B3DaaaczffoNhIWFYTKF0hN0Kt3ksmXLWLFiBXPnzmXLli0s\n",
"WLCAN99806/MwoULWbJkCSeeeCL3339/m3X29ZR+FquT7KIa+ieY+HNH47BhaJrb89PmENmXVwVA\n",
"nbOalw7cxvbyLRhVYXxy6SJshYkBdcaF64kN17Npf/PiAXDiwGjW7y6hzlHF83vuYVfNXxhVoTw+\n",
"5H1Sgwd6yw1JDScqNKjT13c4HM3nO5qvzXO+ztIpP4+NGzcyduxYAEaMGMH27dsD9m/dupWrr776\n",
"qPFH2J1bSWlVPdmFNaiVjbetoMzM9uwKr3CYnTXM2XEL28u3kGRIY87whQyPOLHFegVF4xtpRHpk\n",
"QDQsz8I4gzqURwe9zXGhY6l1VvHMzumUWPO95cq6OH6njExbdEo86urqMBgM3s9KpdI73VRSUsIb\n",
"b7zBrFmzjhrhgEa/CqdL8jpqAVQ0eH4C2Fz1PLPzVg6Yt5NsTOW9sxYTq0smp5WZEYVPd1anUaJQ\n",
"tDxWDVYH88DA1xkSchJVjjLm7LyFGod7QZ1NDmko08N0yuZhMBgwmxvjTYiiiKIhYtbPP/9MZWUl\n",
"06dPp6ysDKvVSnp6OhMnTmy1zsPpPnWGjp7PVFiLoFISEhKEZLYhqPyD/IiSyKtb7mNf3RaidfH8\n",
"esNvhChi2FhfQr3NidGgw2TQUl3XKDahoXqio4wY893ikpQQCsW1GKsajahRUUaMBh0ARr2GWouG\n",
"J49/m4f+mkxW7S5e2fdP5o7+FEGpxBSqR9MgbH39fh5J5zuar+1w6JR4jBo1ihUrVjBhwgQ2b95M\n",
"Zmamd9/111/P9ddfD8DXX39NVlZWm8IBfd/mUVtrpdZiR6OAqlobria9qk9zXmR1yU/olUZmDlxA\n",
"iCuCmtp6auusGA06auusmIJU1NY1CkOVRkGZRundVlZWR2Wlxa9MaWktg5NM2B0uDhTUUGuxAxoe\n",
"zpzPI1snsb1qAwt2zmVq6kPsPlBKXETwMTFOl20eXXe+ztKpYcs555yDRqNh8uTJPPvsszzyyCMs\n",
"XbqURYsWBZQ9WvKSeC7D6RIDhGNV6fd8k/9fFCi5P/MVEvUZCILgjQzmwWr3TzEpCAI6jRKNSkFS\n",
"lIGWCNKqMBm0futiwjTRPD5iHkpBxdKC91lb9rNfMCEZme6mUz0PQRB48skn/balpaUFlLvssiMr\n",
"JmNrCA3TZ54HVCEIiJJEQX02bx9wT7Hdkv4Yw0NP8R7TNPhxpCmIsmp/vw6FQvDL3eKrtYNSwpq0\n",
"wl+0RkSewPUpD/LBwbm8deBfnJF2MqHGdEqzy4kMVh81wi3TN5FX1bYDi9XhXR3rEQ+NWoHNVc9L\n",
"e+7FKlo4JfICrkq/we843/il4UYdseH6Ns8VE6YnyhTEyIxIYsL8yze1P9vsIhPirufEiLOod9Xx\n",
"r7X/5K89xeQW1QaIVK3FzqZ9pQG9H5nuY926NXz77dct7v/xx6WsWrWyw/Vecsl5h9OsLkMWjzaw\n",
"O1ys313iXRLvcLnFQ61U8n72M+Ra9pKgT2XGkGdIaDL0UPlM6RqC2pceQaEQGJIWTqhBG7DPd3l/\n",
"RrwJi9WBIAg8PPxZjKowtlWvZVnR5+52NhnCbM+uoNps51BJXbvaIXP4nHTSyVxyScu97wkTLuK0\n",
"007vcL19pUMpu6e3QUtZ3daVL+O3ki9RK7S8Mf49TknpB0BSlME74+FLU/tHZ/BoR0xoEInRBg4U\n",
"uF2f0yISuDV9Ni/u+Sef5LzAaQnnUFsXTXmNlWH93C7PTp/h1tHIlKVXsjy3a1fVnp18Lr/c2PKq\n",
"WqfTyTPPPElhYT4ul8jVV0/h66+/JDw8gpqaas4++zzy8g5x++1388EH/2Xlyt8JDQ3DZrNyyy23\n",
"s3HjX0RERJKSksonn3yIRqOmuLiQcePOZurUm8jK2s/rr7+CyyVSXV3FAw/MZOjQ4V16jYeDLB6d\n",
"oMZRwSs7/wXAtSkzGBLZ+A9NT2g+5WFzD22QtmO33xM82WPLGJERSXGFhbhIPSdFnMtpkRexqmwp\n",
"b+5+ggf7v0l5TePQxWPk9e0NyRwe33yzmLCwcGbN+jcWi4WbbroWjUbD1VdPYezYcfz441IA9u3b\n",
"y7p1f/Luux9jt9u54YbJgP9kgmfVbUiIhtNOO42pU28iOzubu+++l379Mvjll5/4/vvvZPE4kpEk\n",
"iXcOPEmVvZwhISdxfuy17epVNI2/EWUKIiEquIMnd//yfOdCDVq/4c3U1IfZWPkHf5X9zrqIXxgT\n",
"ca43W5kHZStOaEcyn13UPatqWyMn5yCjR58EgF6vJzU1jQ0b1pGcnOpXLjf3IIMGDUEQBLRaLZmZ\n",
"gwLq8qy6DQoK8q66jYyM4oMP3kWr1WKxmAkObnlGrjeQX0Nt0DSM4OqyH1hXsQy9Mpg7MuagEBQB\n",
"syq+6BqGME07HjFhQR0eQkhe8Wj+uFBNJFNS7gPgg+xnqHeZA2wfR+mopVdISUljy5ZNAFgsZrKy\n",
"DhAfnxDw/0lL68euXTuRJAm73d6w6rUpgf+YV199gZtvvo3HHptNv34Zfc5jW+55tIHv/6vGUcF7\n",
"2f8G4N7hTxCtc6d5bJoVzpcRGZHU2kUigv1vdWe+Bh4ha00Azo6ZxP+VfcOemi18lTefsYOf87PB\n",
"9LHv3xHNpZdeznPPPc2dd96CzWbjxhune4cqHgRBoF+/DE4++VRuvXUaoaGhqFQqVCqVd7/v74aj\n",
"ADjvvAk8/vjDREfHMHDgYMrLy/z29zadWlXbHfRVL77KWpt3yfwb+x7hj9IlDDON4cNzFrO/wO1W\n",
"fsaI+FZ9KnzP9/tm92K2wSlhRIe1PXXry+pthThcIomRBjIS/W0rOUW1ZBe521Pg2sO96yaiFjR8\n",
"Ov43Ts0Yyurt7oC4/eJCSI7pWvfno9kLsyvOVVlZye+//8pll12J3W5n6tSree21+URHx3TL+TrC\n",
"4XiYyj2PZqiosaLVKAnWqb1dxR3V6/mjdAlqQcMt/Z5A7bO2pSPOWHqtCovN6be4rr201vNIiTWS\n",
"X1aH3SmSaRrhNZ6+svUZgnnNW65vvCqOLUJDQ9m1awc//PAtIHDxxRObFY4jDVk8miBJEluzygEY\n",
"NzIBUZRwiHbeyZoNwGWJtxIXlNrqUKU1jusfSbXZjqkZP462G9fwu4VTKxUKwG3jmJJyH+sqfuHP\n",
"sh/YXDqV/sYRQKANR6b7EQSBRx99oreb0eUcUwZTp0ts0+jku7ugzMy+vGq+yX+Hgvps4oPSuDRh\n",
"OuB5UDuOWqUk0hTUqWM9TWvJ0Oo7kxKpjefCOLfH60cHn/NJ+dCpU8vIBHDMiIcoSqzaVsjmVqJ2\n",
"gf+beW9eFTl12Xyd9zYA0/vNRq1wh/tTCO6p0viIDk63HgZt9RqaTsNOTJiOSR3BntpNbKj4tV11\n",
"yMi0l2NGPJwNbuXVZnur5Zr6Y3xy8Hkckp3Toy5hiKkxIpigEBiZEcmApJ6JFwkwKNm9UK6lNTJC\n",
"E/HQqwxcnng7AIsOzUOUWu55OZyiX6wRGZm2OGbEoz1szypnjU980u3V61hfsRytIogpKf5BnHvD\n",
"zTsmXM+4kQkteqY25wB2VsxVRGhiybXsZW35Ty1mmtu4t5RN+8uwWOWFczLt45gRj/Z01st83LlF\n",
"ycWH2e78GxMTphOuifYr2xfXiHjSQPiiUWi5IvEOABYdeh2Hy4kkSQHDl/qG1bZNo8DLyLTEsSMe\n",
"HRzrryj5ihzLbiI0cVwcf2PA/r7o5m1sYeXuuOjLiNEmUVCfzS/5S9idU8nKLQX8vjk/YIl+H3H7\n",
"kTkCOIbEo/1lLc46Fua+CsB1qTPQKHUBZTo52dKtRIYGNWvAVSnUXJF0JwAf7nuVgspGJ6TSKv+4\n",
"H7JBVaa99MFHoHvoyBv16/wFVDvKGWAcySkRFzRbpi9G6VIIAgOSQgMW6sWF6xkbdRFxuhQK6nNZ\n",
"Xfq9d1/T+yJrh0x7OWbEo71J5Yuth/i+4EMApqU+0qJItJYioffxb9uApFDGDk30+qh8nf8OouSe\n",
"fWoqFvKwRaa9HDPi4ftQSJIU8JB4ZiE+OfgCTsnB6VGXkGEMjJ0QbtQh0DcNph58vV81KgWCIKBW\n",
"KTg96mIiNHHk1x9gQ8VyoDFGiAdZO2TayzEkHo1//9/mfP5skmne6RLZWb2edRXL0CqCuCb5vmbr\n",
"GZ4ewekj+nai6VGZ0YQatJw8JJaTh8QC7mGWSqHh0oSbAfgqb0GDiPofK9s8ZNrLMSQejQ+Fxer0\n",
"xiL1YHM4+fCge2r20oSbidDGtlhXX7R3+GIyaBmZEYlWrQxo65nRV2BSR5Bt3smWqlUBTnEt+YHI\n",
"dB8Op3hEBqY+ZsSjrWdi0b7PyDbvIkITy8XxN/VMo3oBjVLHNeke28cCb2xTD03FRKb7WbOjiLU7\n",
"i3u7GR3mmBGP5gyBuw5WIEkSdfZaXvz7acAdk1SrbFy4ZtJr6J9gYtSAKE4adOQvowa4btBNBCtD\n",
"2FXzNxvL1vrtk4ctPY/oXbR4ZN37Y0g8ArcVV9VTXmPl1Y0vUWYtpb9hBKdGXuhXJiRYQ0KUgRC9\n",
"psMBi/sqUYYwzoubAsAn+xZQ6ZOsW5STzvUaR5pwH0Pi0fw/ZkfRfuZveR2AG9JmBtgI+vaUbMfo\n",
"n2AiI8GEUilwfuy1qAUNf1es4MftG7xlZJtH79FR4bZYnfy+OZ+SSgsAO7Ir2JNb2Q0ta55OiYco\n",
"isyaNYvJkydz/fXXk5ub67d/6dKlTJo0iWuuuYYnnniiT3TH8srMzW5/fccz2Fw2Tou8mAHGkQH7\n",
"+/KUbEdJiDKQGGVAIQiEaiIZG3UJEhJLG/xaAFxy16PX6Ohzkl/mTuC1L8+dv6e0up7CCkuXt6sl\n",
"OiUey5cvx+FwsHDhQh544AGeffZZ7z6r1cqrr77Kxx9/zOeff05dXR0rVqzosgZ3hspaG1XNLDff\n",
"XfM3fxR9j1ap80YdP5a4KH4aAH+ULqHGUQHIPY/eRGzG/6g1PAnJ1KreGUB06qwbN25k7NixAIwY\n",
"MYLt27d792m1Wr744gtv7gmn04lOF7g2pCdxOBtXihp0anQaJaIk8kH2XACuTb+DSG1cs8c6XUff\n",
"m1ivVaEQBBL16YwKG4dDtPFzQ5pKVx/oJR6r5BTV8vPaHOpt7Zu2dTh6Vzw6ZQGsq6vDYGhMQKNU\n",
"KhFFEYXC7c0YHh4OwMcff0x9fT2nnHJKS1V5OZwozm3hEASM5fUADM+IpMZi57vsRWSZdxChjeWG\n",
"IXdjMSsw6NXUWRwADEwNx1zvID3BhE6rApsNCgoaf/Lz3b/Ly6GmBqqr3b/r6tyDV0lq/NFqiTIa\n",
"wWBw/5hMEBcH8fHun6QkGDAAQkK67Jrbup9XxISwaks+V9tvY+Nfv/Nz0WdcO+AujMagTv0vuvP/\n",
"19vn645zuUTJuzLbaHC/XOvsbjEQlcp2nVOXX4NREIgK1xMVZfTW43vs1v2lKASBoemRXX0JnRMP\n",
"g8GA2dxoQ/AIh+/n559/npycHObNm9euOrsz3HxFhYXaOvfq0cpKM3aVjff3PgfANcn3UVnuxO4U\n",
"OS41lL9+/RtD3kG0P5UQXZiL4sB+XAf2oziUi9DN9gBXTCyu/gNwZQ7EMXIUzuOOx5XRv8NLeNsb\n",
"vj8sSEWqegT9goeQZd7BD9mLuFJxfYf/F3LqhY7hcIqs3l5IXLiezOQw73cT3EJSXl6Hy+7AEKRu\n",
"1eZWXmHG4RIxaBQUl9R46/Ft755sdzDvmJDmA273eOqFUaNGsWLFCiZMmMDmzZvJzMz02z9r1iy0\n",
"Wi1vvPFGn/DG9O2IC8Dba5+h0lHKUFcSt3+7D1P+3RjzDhJSmMuFtuZD8UkKBa74BMS4OMTYeMTY\n",
"WFyxcUgRkUhGI6IxBMloRAo2uB92QfA+9OHBKipzixEsdQh1dSiqq1EUF6EoKkJRXIgyNxdl9gGU\n",
"xUUoi4tg1Uo8niaiMQTnqOOxjx2H44xxOIcOB2XH0zY0R3SYnkhTENdYbmPOln/wXcH7XJo6pUvq\n",
"lmmZunp377awwkJmQ2hJX0oq68kqrCExykBGC7mPwd+hz9dW1TTFaHfRKfE455xzWL16NZMnuxP2\n",
"zp07l6VLl2KxWBg6dCiLFy9m9OjRTJ06FYAbbriBs88+u+ta3Q6EmmqUB7NRZh0gcutOTty1G0Ne\n",
"DuWWLN67oQ5U8N/3DjEk/79+x9WHR1GbmIp6UCbqgQNxpWe4f1JSQaPpXGOijDjj23h7uVwo8g6h\n",
"2r8X5Y7tqDdtRLXpb5QF+Wj+WIHmjxXwNIihodjHnYn9gouxn3UOkvHwhjoKhcD4uAtYsGsuhdaD\n",
"rCv7jRO45rDqlGmdtozSdVa3uJRW1pMeH4LV7mrWx8jjFyJK/n5MktQzaUU7JR6CIPDkk0/6bUtL\n",
"S/P+vWvXrsNrVVtIEkJ1FYriYhTFRdizc7Du3ktURSGqnGyUB7NRVFR4i/s+XrdcDXYVXJ0dSmzm\n",
"WLaflUJdQir0H0DGuONZsd+ddW14vwjCQ3rQ0KtUIqakYk9JhbPOpb5hs6KoEPWa1ahX/o5m5e8o\n",
"D+WiW/IVuiVfIWk02E8fh/2Ci7FddAlSaOBbrD1olGouiJ/KRwefY3HOf7n7NFk8uhNXkxXeLSK4\n",
"p2ELys0YgzTotUoGpYYHFGsaVlKUJBQ9kJKyb7hMfvkl2rJqcDgQ7HZw2BHMFhQ11QjV1Qg1VSiq\n",
"q92CUVI1tbkcAAAgAElEQVSCoqQYoYXhhQcpKAhXahqu1H6UxyaTHxbP77F1LLE8S7DKwJlXfcN6\n",
"n7ikceF6JIMRqOnmi+0YYmwctsuuxHbZlSBJKLKz0P78I9ofvkO1fi3a5cvQLl+G4ZEHsJ1/Ibar\n",
"r4GrJnboHAqFwFkxV/G/Q2+wo3oDW0o2MSL6uG66IhmXzwxe09XdvghAQbnbtlhbb6e2HlKsTvQ6\n",
"lZ9YSJJ/b0YUJVB2v8dq3xCPq66io51v0WBEjIlBjI6hSBdKXVwShsGZhAwfhCutH2J0jLfvlpNf\n",
"TU5JFfM2XwbAHSPuJ6xJQGOdxv9W9ElXYUFA7JdO/R13U3/H3QglJWh//gHtkq9Qr/oD3Tdfofvm\n",
"K7gvhuDLJ2G9fprb4NoGCkEgSBnMWTFXsbTgfd7c9Dovnj4flVIIuC8yh4/vg950dXdbVNRY0esM\n",
"fgLUNLSCdzjTzT47feObcfnlWCUB1BokrRbUaiRdEFJoKGKICcnk/hGNJsSoKMSYWAhujNW5riF5\n",
"dP8EE0FRhoDqXS6RX4q+4FD9fpIMqUwbcgc791f5lQlqEnm8L2pHU6ToaKzXT8N6/TQUeYfQffkF\n",
"2i8+Q3VgP/q35qF/ax7208dTf+Mt2M+bAKrm/91Cw2TOhNhr+aHgQ77N+przQu8iXBvD6cPjjyoX\n",
"/d5AkiTW7Swm1KBlYEoYTlc7v1zN3HZPdHvfOkQJ8krrGj+Ljef1bUNXG1H7hngsXkxtd07VWiv4\n",
"4pB7yvjRE55CowqctgrS+M9g9MmeRyuIiUlY7n0Ayz9nEJW1k/rX30L31f/QrFyBZuUKXHHxWKfe\n",
"SP3Um5CiovyO9UwHRukSOCniXNaU/8RPRZ8yJeV+7E6X3Ps4TCQJrA4XRZUWt3gcxpS/x6vU13nR\n",
"6RIpKPdNG+Lpefi3oauNqMfEwrj5u+didlYzzHQyZyVNQK9zpyjwzVTvsWbHhLmzsbWUxqDPIwgw\n",
"Zgx1L79O+Zbd1D39LM70DJSFBQQ/N4eI44dgePA+lFn7vYf4+hJcGO/Ob/tL8SKsLov3yyrTeZq+\n",
"iFzt7Hk0V87jLe07TWtvkmuncRZGCtjWlRz14rG2cA0/5i1CJai5ud/jAMRHBjMoOYzh6RHeciql\n",
"+1YMTA7llCGxXoE5kpFCw6i/9U4q//ybqi+/xXbu+QhWK0EfvkvYyccTMu1aVBvW+b2RBhhHMsA4\n",
"ErOzmj9KlmB3uI7IKFd9BbPVQWlVvfezKErttnM0tzTC0UzPo6nAS2KgeHTH4tSjuj9qd9l56I97\n",
"AXfWt/igNETRPfaLCdc3+88RBAGNumucsPoMgoDj9HE4Th+Hcs9ugt6a57aP/PAd2h++I/O4E7Be\n",
"egMFY8aDQsGFcTewt3YzPxR+xAU5U3CJMDIjklBD816KMs1jsTrZsLvEb5vN4WrVkFnnqOH3ku/Z\n",
"WfMXB827qHaUY3dZCVaFEKVNYJBpJK6QK0nWDPUe07RX4anez4jaDR3IPiMekiRhd4hoNc0/uA6n\n",
"yLasctLiQggztu9LPH/LG+yu2EWsLpmJibcCYPAZjqiUClJjjRiOgl5Ge3FlDqTulTewPPI4Qe/M\n",
"R/fBuxg2beDUTRuoSU5n96RbEMefR5Q2nkJrDuvKVjA6fDxVdTZZPDrI+t2BoQWtdlezoR7zLPtZ\n",
"kv8Of5b9hFMKTMZudtVQYstjR806vjy0gFhdMpck3My4qMtQKfy/vw6XGCBS3TFs6TPisSO7grIa\n",
"KycNimnWm66w3EyNxc6WA2WMG5nQZn25NTk8v969avaWfrOINBgZmREZMHOQGtt1i9GOJMSYWMz/\n",
"mo3l3hk43nkX0ztvEpJ7gBNfeIShH77G+qmDeclYwPcFHzA6fDzKvpgi7wjE4fR/qGsdlXye+yq/\n",
"Fi9CQkJAYKhpDCeGn0la8FAitLFoFTrqnNUU2w+ytWIdq8t/oMiay9sHnuC7/Pe4Lf3fDDad4K1z\n",
"50G3g+RQH4ey7rD/9xnx8CSZNtc7WnXFbQ+HSmr5x6p7sIlWTo28kOGhp6JWKeQpx2aQDEYU9/6T\n",
"jRdfQ8jSr0n9ZAEhuQeY9Xoh79wPO2rWk1e8lv4J5+F0iazeVkhKrPGYFd320pKNweEUveKxtepP\n",
"5u17mGpHGUpBxZnRVzCl/10Ei1GEG3VU1PosmFOHMSgyk5GmcVyX+gBryn9iUe7rFFoPMnvHVC6K\n",
"m8a1qTNQCo3PjtXeaEg9JgymTYdmoiRRY7Z7lbO1x1+SoMZs5+1N7/Jn0e8YVCZuSH24u5p61KAQ\n",
"BDIzYoj+x62U/PYne176L8604dy80b3/7yW3EDd3FvX7DyIBB4t6bgXtkUpLs1R2p4jN5WBh7ivM\n",
"2XkL1Y4yBoUcz/MjvmZ6+mxi9UkAhDezCjZI6x7SKwQlp0ZeyIsjv+HKxLtQCiqWFn7A0ztuptbR\n",
"GIbQ6jML0x0G0z4nHk0vMiu/ho37SimpdFusW3N0sTldLNu+hY8Oupfb35T2OKEat09D0+ksmUCU\n",
"CgWmkCAqx5/Hb68u5ISzXkAhwaLBLlzf/Je08aMZ/cKjGHMP9HZT+zyOFsSjzmbhPzvu5au8BYDA\n",
"pKS7eWLIhyTqM/zKxUXoA5bjN/W3USk0TEn9B08M+QCTOpIdNeuZvX0qFXa3kdZ3lqw7nE37oHj4\n",
"fy5uCO5a33AjWnN0ySupY/7+x6l3mTkx/BxOjWxMUi1H1+sggoB65IWcEHEuDiU8f3V/EEXSln3N\n",
"edMvJui6a1D+taHteo5RPC8rXwEwO2u4Z9UU1pT9jF5p5PEh73Jl0l0oBP9JghMGRqNUKPyM+wA6\n",
"beBkgkolMDDkeJ4d/j8Sg9I5VL+fJ7ZdR4W9hLLqxmHPMdnzaIpCECipqqfGEmiR/rHwU7ZW/4lR\n",
"Fcot/WZ5eynGIA2ZyaHd0t6jEd+wdp44p++llbJ72e8cuOhqRJUaw7LvCb/gLITzzqVy8bdHhj9/\n",
"D+JxI9c1zB5anHXM2TmdnTV/Ea6J4amhnzDUNKbZY4MbZv+aiodGFSge6gb/pAhtLE8O/Zh+wUMo\n",
"th3imZ3TMTsbF3m6g9pJfiE5D5c+Jx6eQCmWJs41HgTBbU3euLfUb/tB8y7vcOW+IU8TqnGHXUuK\n",
"NnB8ZhQh+k7G4jgGSYgKJjnaHWFqgHEkGYbh1DiqeKvsDzb+Yzbff7ycXVdPx6E3ELlpLWFXXkro\n",
"2aej/eYrcMnDQ2gUjyCtCqvLzNxdt7K/bivR2kSeHvYZycED2qxD18RtQasOfFx9h/HhuggeHfwO\n",
"CUH9yLXs5bldd2J3uXsfkiRxsKiW1duLmn3xdoY+Jx75ZWYqa22s313CjoMVAd54zb3g6l1mXt5z\n",
"H07JwQUJU7h2+NXefUp5hqXDKBUK+sW7Z1MEQeCiBpf1Lw++iyiJ2MKj2H7z/fz42Qq23nQ/tvBI\n",
"1Nu2EDJ9GmGnHI/uo/fBam3tFEc9toaZDrVK4oXd/2BP7SaidHHMHvoBkdr2JUpv6vOk16kZnBLG\n",
"yYMD8yiHGbScOCiaEHUYjw1+h2hdHLtr/+adrCfd8T5EiUMl7sVzpZWBL+XO0OfEA2g2TYIHXzEp\n",
"q65HkiTeOfAkhdYcUvSZ/Oukf/t1u2X/hM5jCnb31k6KOJcITRyF1oNsrlzZWCDExJ7J0/lj8f9R\n",
"+5+XcaWkosrOwvjAPwkfPYyg115GqCjvpdZ3P7UWe4vR9W0OF5Ik8fKOf7G1+k9M6gjmn76IYXFt\n",
"h0jw4DtMUTb0MKLD9H6i4vBJv+BZYhGpjeftMz8jSBXEH6VLWFb0OSKN67faG529Lfrkk9Xe1X/b\n",
"syv477b5rCr7Dq1Cz70DXiJcb/SOA0HueRwOw/pFMGpAFHqNlglx1wGwtLAxQZRS6b63olaHddrN\n",
"VKzZSM2C93AOGYaypBjD008QMTwT4+03o16z+qiyi9Ra7Py9t5Tt2RXN7rfaXXxf+B5fZ3+GWqHl\n",
"oYFvkGzoh1Lp/8iFBmtRKxUkRAYH1KHxGaacMsy/t3Hy4FhOGRLrnUgwBKn9hjDDoofx8nh3JsQP\n",
"Ds5lU8kG7zDI1//jcOiT4tHeeAebK1fx+OpHALg94ykS9P1QKRV+N10Wj86jUioI0WtQKxWcFXMl\n",
"WoWe7dVrOWje3cIBKmyXXUnlb6uoWrgY21nngMOB7qv/EXrpBMJOO4Gg+a8jFB95GeGbYrG6H9rm\n",
"eskuUWRl4c98dPAFAO7p/x/6G0cgCIHfx5BgDacOiyOimZCXwTo1KTFGRqRHBvSgtRolGrWSSJP7\n",
"uJhwvf9+tZLL+1/F9Zm34ZKczFxzJxZnbUP7ukbE+6R4tMcnI8+yn1f23o8oiVyeeLs3QbVKKfgp\n",
"sOxVeviolAqCVSGcGXMFAN83pKdsMSGWIOA48xxqPl9MxYatmO97AFd0DKp9ezHMepSIEZmYrroU\n",
"7cJPEWqqe+oyeoythbuZt28mAPeP/BdjIs4F3DOFTUXCIyYt+S+1tZZrUEoYJw+J9QsvAY0zZveP\n",
"eIy04MHkm3N5fedTAEh0jXj0Gfd0hSB4XWjtjtaXAJZY8/j3zpuxuGo5M+ECJiXd493XtFvYkrOO\n",
"TPtRqdxf7Alx1/FT4SesKvueKSn3ESHEtHmsmJyC5ZFZWB54BM2yn9At/ATNb8u9EeGlB+/FPv4s\n",
"7OdOwH7Oee4ocUcwFoeFu3+/kXpXHecmX8ytQ//B1iy33UcQ3D2NkwfHsmanO3apRzwUAijrLQTV\n",
"lqGqPYiiohyhthbBbEaoq0Woc6ftEMwNv202cDjA6UBwOMDpRHA4uNBqQ3KJaDRKEAQMInyiFTnr\n",
"XIGfC77k6i83Mr4wnBCjDtRq+P23Tl9rnxEPgBC9Bqvdib2FuWi9VkVeTT5P7biRSnsJg0NO4KbE\n",
"OSiERsFQNYzDByaHsT+vmghT76a6PBrw2JBidcmcEH4W6yuW83PR50xO/mcHKlFjv/Bi7BdejFBR\n",
"jnbpt2i/+h+aP1eh/ekHtD/9AIBj5HHYzz4Px6ljcYwaDUFBbVTcOzTt+tfVO9iwu5hPC59kX/Uu\n",
"4nSpvHD6aygVAoLTQVB5CYai3WjryggqyGfMjn0oC/IJt1ShrqogoqyMjPrDT1LddH24GjgF+I8E\n",
"/7gAZg7PYuLKLDRdMBnWJ8TDEzpeoRDQqpVYWrAGF9bnMGv7NEpseaQbhvHQwDfRKJt2Axu+6OF6\n",
"YpuMA2U6h8qnN3dh/A2sr1jOL0ULuTzhtoD73x6k8AisU2/EOvVGFIUFaJb9hGbZj2j+7w/Umzeh\n",
"3rwJXngWSaPBedzx2E8+Fedxx+McNhwxIbErL63TeIdskoRQVkbt5t1s2vMJ3wpfoBOVfLgygcwv\n",
"r0aRd4j0kuKAbIOBkXbBpdbgCI9AGR2NFB6OFGJCNBiQDAakYJ/fwcGg0yGp1O54v2oVeP5WqdzJ\n",
"xrzpTmHfoQoGW2yMqJ/DFsMepv5rHB8NmoGgVnM4rpN9Qjw8Iq4QBJRqJbUNjmK+7K/dxrO7b6PG\n",
"UUl68FAeHbQAvaq5f4FMV+OZVQEYaDyeIeEj2FGxhZWl33J27CSg8wF2xbh4rDfchPWGm8BiQbPq\n",
"DzQrfkW9dg3KndtRr1uDet2axvLh4XDccQT3H4SrX7r7Jz0DMS6+w2k528TlgpISlLuzURQVoizI\n",
"R5F3CEV+Hkl7shhQUoC+tAil3UZlOLx2O6CBBd+4OGfLam81kiBgiYyBhEQUqSmICYm4EhMR4xPd\n",
"GQAiIpEiI6lCQ3JiGFVVh98D8cUWU0lFpYUbLC/y4JbLWOr8nZVpMzklse0c0q3RN8SjQZUVCvym\n",
"WcH9pfytZBHvZT2DQ7IzMnQs92e+jE4ZOLUl0z342o0EQWDaoNt5cPUdfF/4IWfGXAm4Z8jUqsM0\n",
"Tuv1btvHuRPc56quQr1+Leq1a1Bt2Yxq+xZ3Mq9ff0X/669+h0oqFWJUNGJ0DGJUFFJoGJI+GEmv\n",
"R9IHIQW5e6GCbxJyl8ttU/DYFcx1CLW1KCrKUZSVIpSXgyQRmGYJfAdTjlATU6+xY9HUc2l5CseP\n",
"voJNF8eTduJQ6iJiWVutQFKpGZQS5o2R2xwm6JYodp41MYn6dCYm3MLivLd4cOU/WXH16jaObJ1O\n",
"iYcoisyePZu9e/eiVquZM2cOycnJ3v2//fYbb775JiqViiuuuIKrrrqq9fp8eh6+N6/MVsC7WU/z\n",
"d+UKAKZkTuOisPsDIifJdC8JkQZqzA5q691uzRf2m8jcDbPJr89iS9UqTjeeS05RLRmJLedV7QyS\n",
"KRT7OedjP+f8hg0SioJ8InL3YV73N4rsLFRZB1BmHUBRWoKysABlYUGXtoGICJwRkW5haugx5KpC\n",
"KTVFYYmOoz4qjjWKb1m78SnCNNFMnPAFO1UmQg1aEjMiwe5CajCO9lbeZt+ZmMsSb2N12ffsq9rD\n",
"S+te5sVLn+50vZ0Sj+XLl+NwOFi4cCFbtmzh2Wef5c033wTA4XDw7LPPsnjxYnQ6Hddccw1nnnkm\n",
"ERERLdbnSWDjEY8KWzFLCz7gl+IvsIn1GNQG/nPGy1w54Gp+b8jR0pS4cD0mOUxet6DXqTg+M8p7\n",
"7/VqDRPiruPTnBdZWvABpyedS15ZHeEh2u5N0SkIbpvHyEFYTh7vv89qRVFWiqKkGEVJCUJVJUJ9\n",
"PYLFglBvQaivd093CAKSILinNwSFu3fisSsYjEgGA2JEJGJkFFJ4OFFxYVQ2SQuStavYa5fLNe/l\n",
"5U3uiHV3pD9NsMotoJ4H1nfI11t+Eb7ioVFouaXfEzy982be3NYL4rFx40bGjh0LwIgRI9i+fbt3\n",
"34EDB0hOTsZodC+sOv7449mwYQPnn39+y/UVbmJz5VbKK/azpfJP1hWvRmoICzQm4nwWXPgKcYaW\n",
"1wOY9Jpms43LdA9KhYKzYq7iy0Nvsq16Ddm1u4kUUrvM+ahT6HSIiUmIiUndUn1dvQOXKGEK1niv\n",
"0yk6eGP/TJySg7NjJjEybKy3vOeB9TU290D62GYJNWoJ0qi83qjDQ0/hxPCzWV+x/LDq7ZR41NXV\n",
"YTA0GiuVSiWiKKJQKKirq/MKB0BwcDC1ta1Hnhr70Un+jRLUjA4/h4kJ0+lnGNKqcLjPLzuC9QQe\n",
"XxylUsCgMjE++nJ+KvqUr3PeY3rqUwHBa44W6m1O/trjDrBz8uBYRFFCKQgsq3qfbPMuorQJXJ/6\n",
"kN8xmmZWwPbW/VEIAqMGRLF6e6F327S0R6l3mQ+r3k6Jh8FgwGxuPLFHOACMRqPfPrPZjMnU+lh4\n",
"WNRwFC4Dw2IGMzb1FMKsozCq3cdEhgYRFdUoRkZDYLc4PEzvV6Y9dLT84XI0nO/C09Ox2lyEGrUY\n",
"syu5KuMWfi76jBWF3zCt/4OEhiURFdEzhuyevJ/BRp33e6fVa9EHa8m37eb9Pa8B8MCwF4g2+Q/L\n",
"42JCvPfCc2xkpIEIU9t+K911bVfFmXA4XeQW1VJVF0ZaxGeHVV+nxGPUqFGsWLGCCRMmsHnzZjIz\n",
"M737+vXrR05ODtXV1QQFBbFhwwZuvvnmVutbPnkNf/ydS0a8iQiTjnW7iqm1WQk3akkKD6LUZ8xZ\n",
"Wxfo3RKsVviVaYuoKGOHyh8uR9v5Sq12auusGInlzMTz+TXvRxbum0+Y8lFGZUZ1+xu2J+9nVJSR\n",
"ouIa7/fuUEEVpVVVPLntHlySi5uG3E6aZmTA97Ku1kppwyyiZ19FhRmxjQRaPXFtIVol+UW2Zp+l\n",
"jtAp8TjnnHNYvXo1kydPBmDu3LksXboUi8XCpEmTmDlzJjfffDOiKHLllVcSHR3dan0ehxulUvAb\n",
"I+o0qnatTZGHLT3P0LRwFILAXWH382vejywrWsilCbcQVRxESmzP9rK6G4fPQs06i51Fua+RY95H\n",
"Rmh/Hj3pCTburgo4ptnAPd3ayo7RFQtGOyUegiDw5JNP+m1LS0vz/j1+/HjGjx/f9LAW8cToUCoE\n",
"r3s5tD5GVCoEr+GqufBsMt1LZEP3+8Sg0YyOOIO/yv/gh8IPyYx5FIfTRb3NRUjwkRu9raDMzP78\n",
"ai4cm47Tx89lfdE6vit4HwUK5p01H6NWD7jFQ6dWeiOWN/ed7EtxdLtiwWifWFW7qyEmgkqp8JsL\n",
"F1ppXf/ERsdaef1K76FRK5k1zp0D+MfCT6lz1vD3nlI27iv1RtM6EtmbV4UoSRRXWLwvN6vLwos7\n",
"H0RC4tr0Ozg+5gQEQSAp2kBKjJHEqMZJhOYeTld35HzsJF3R8+gT4uGh6QW1NXbuFxdCTGhQQKBY\n",
"mZ5lbMppDDWNod5Vx+LsD7xvX7PV0S3JhnoSp0v0eth+lvsiRdZcUvSZ3Jh5r7dMeryJtLiQZmdY\n",
"AIIaUiao+1APuSvsUn1LPBrsHZ6cqK05HEmSRHKMkUGpzTkPy/QkSqXAFYl3ALAo613vFODWrHJ2\n",
"5VS2dijQSlyQXsTzcLlECadLZGvVan4q/AyloOau/s8SpA78brY0FDiufyRDUsO9YR37AkfNsMWD\n",
"p+cxJDWckwfH9qmbLdMySoXA4JATyDSOosZRxU+Fn3r3NRcB35fc4lpWbSukxtw1Eb07i9Xu5EB+\n",
"daPxvuG76HJJVFureWv/vwC4KulOUoMHNvvweZZW6JqsT9GolUSF9q3QAkedeHhmWtQqRUDkaJm+\n",
"i0Lhjt52VdKdAHxb8J43Z4iqjZWuOcXuacm2RKa72ZVTyaHSOm+EcY94OEWRt/b8m3J7EYPDRnBp\n",
"wi1++30J0WsYmhrOcQOieq7hneSosnkoBP+ZlpYIbwjJ5kmMI9P7eER/mOkURoaPweys5ruC9xr2\n",
"tf4/9YhLr7q205hnpajcQnGFxftm/jXnB34pXIxGoeWZMfO8iaRbenNHhgYFhATsixw1PY+Th8Vx\n",
"ytDYdq06HJIWzvEDoo7oacCjDd84nNPSHwDg+4KPqbKXtXmswjs86F27h8fGYXO62JVbiVKhoMZR\n",
"yb83uK/nurT7GRgx0Fv+SA+srTxaDKYmg9Z/AVErKBUKjHL2tz6FIAjeqfNk7TCODxuPTbTwdf7b\n",
"bc62eG0LPdzzKKqw+A2VAmcfJN7NeooKaylDTCdwaeI0v3ARR3pg7aOm5yFz5JMQGYxOrcQpikxO\n",
"/icCAr8ULaTIktfqcR7vYGcPi8fu3Ep2HGzMudL0Yfq18BvWlP9EkFLP3f3nolIq/YYjR7p7wFFl\n",
"85A58tE1+DOkBGdyauRFOCUHHx98sdVjPDFnxV62efiKR5mtkDf3zAbgziFPEKNLQiE0pjNQKoQj\n",
"3uYWpFUGRO3rKLJ4yHQZsRGNIfZuzJiBVqFjddkPfLuj5fD+nsmYnhy2NCdUnmGLKIm8uf9RLK5a\n",
"jg8bz/kJV7uDczfsP2VILCcPObLTQ4DbYe3UYXGHVYcsHjJdRmy4HmNDdz5SE8+ktOkAPPPXY+w9\n",
"VEltM9nZPSaRnnTdbl6o3Nt+LPyY7dVrCVGFc1v6Uzhd7sj+QkPPRKNWtts+d7Qj3wWZLsUU7J5K\n",
"d4kSk9NuJ1wTQ5Z5B5/t+pStBwKTXku94L7enFC5RIlc814+y3kJgNsz/k2oJtK7/2gNdHQ4yOIh\n",
"06V4bAeiJKHXBDMl5X4APst5iWpbjbdcQZmZXQcr8D7HXawhjhYSh4F/z8MjXlaHlXn7HsYh2Tkz\n",
"+kpGh5/pd0xXZ3U4GpBviUyXovQRDyQ4LfIiBhhHUuUoY2Huy95ye/OqKK6q98bV9O2A1NU72HGw\n",
"osOpQrMLa6istVFZa2P19iJyigKD6hRXWDD75AWqMduprLWxYN8cciy7SQhO4Ya0mQHHCX0qGkff\n",
"QBYPmS7Ft3cvSRIKQcGt/Z5EKaj4uehzvt2xws+/wuPZ6esPsj2rnNKqeg6V1FFttpNb3HZkrXqb\n",
"k5ziWrYcKKOs2l1/flkdeaV1VDdksq+us7Ert5KdPov1Nu0v4611H/FD/meoBDXPnbSAoGZyAh3p\n",
"q4O7A1k8ZLoUj/9DqEHrDX6THDyAS+JvRkLiyfUz2JJVFHCc7wyIsyFylyhKbNpXSlZhjTc2iNnq\n",
"oKImMHyer+3Ea4R1SezPr2bTfrenq7WZ+CKF9QdZcGAWANP7P8bgiOHNXldv2Gb6OrJ4yHQp4SE6\n",
"hveLYGhauN/b+orE24nVJXOofj9f5r0ZcJxvWU/vRfIxhHj2b9hdwvodgeLTXJA/3zodTjFglsUu\n",
"2nhpz33Uu8yMiTifixOvbdEw2ofi+PQZZPGQ6XLCQ3SolAq/t7VGqeOOjDkICCzJe4fdNX/7HSMR\n",
"+Hb3/bhuVzFb9jeulamstbXZDt/aPHlXGuuWmL//cXIsu4nVJXN7+r9RKhV+npdan+A9cs8jEFk8\n",
"ZLqNps/boJDRXJowHRGRefsewuL0t2WIkkRVnc0b9q8plXWNgrHlQBl19Q5yi2txiaJfL6W5B91i\n",
"c3KgoNr7eUn+O6wq+w6tQs+MzNfQqwwoFQo/m83ogVFEhQV52ybjjyweMt2G70OsFAR0GiX3jXqY\n",
"DOMQSm0FzD/wuF8ZUYTN+9teiethR3YFWYU15BTVBQhVU0oqGjPPry//hc9zX0ZA4J8Dnicl2J06\n",
"RK9T+fVO1Cqldxgja0cgsnjIdBu+D5xSKTBmcCyDkqJ4dPirBCmDWVv+M9/k/9dbpunbvbwZw6gv\n",
"nmleq93Z7p7B3trNzNv3MABTUu738+fQa1UBEc59/VZk/JHFQ6bb8M3f4huGL8WYzj39/wPA57kv\n",
"s6lyJRC45sQzjdsWbnuJz+dmnnObw0WOeQ9zd96GTaxnXPTlXBLvn4xMr1N5Qwh6QmCmxoUA0C8+\n",
"pF1tOZaQxUOm24gKDeKMEfEc1z+K9ITGlKMKhcDo8DOZlHQ3EhIv77mP/bVbO2+UlPyHSEWVloAi\n",
"WTX7eXrnLZhdNZwQfha3pT/pF3wq1KDFFKwhwqRjaGo4Q9Pc6SNNBi3jRiZ489TINCKLh0y3IggC\n",
"pmCN3xSo5+/LE+/gtMiLsYoWntl1K7sqdnXqHBJSqzaJ7LqdzNp2HdWOMoaZxvDPAS96wwmC2x4z\n",
"MovtehMAAAzUSURBVCPSKyaRoUHe5fcyLSPfIZkexyMjCkHBnRlzOD5sPHXOaq7/6XIOmlsWkIgQ\n",
"HZHNpeOQWp5K3Vm9nid3TKPGWcGI0NN4aOCbaBRawhrSewBHRMDivkiHxcNqtXLPPfdw7bXXcuut\n",
"t1JRURFQ5oMPPmDSpElMmjSJ119/vUsaKnP04DsdqlKouS/zZYaZTqbMWsIT26eyterPZo8zBKkZ\n",
"2i+C/kmhftvLaqzUN/EelSSJHwo+4qkdN2Fx1TIm4jweHvgGWqV7+BEXoefkwbGMG5lwxEcF6y06\n",
"LB6ff/45mZmZfPrpp0ycOJG33nrLb/+hQ4f47rvv+OKLL1i0aBGrV69mz549XdZgmaMPjULLzEHz\n",
"mZByKfWuOubsnM7iQ28hSv6C4BnuxEYErj3Zl9eYbLraXs7Le+/ng4NzEXFxSfzN3DvgRVQKn9i3\n",
"giCn9zhMOiweGzdu5PTTTwdg7NixrFmzxm9/XFwc7777rnf86HQ60enkXLIyraNWaHjh1AVcnng7\n",
"EiJfHHqNx7ZOZn/tNm8Zz7SpqgV7hFO0s6zoc+7ffBFry39Cq9Bz/4BXuC71ARSCv1DIa2QPH1Vr\n",
"O//3v//x0Ucf+W2LiIggONit/MHBwdTW+nsJqlQqQkNDkSSJ//znPwwePJiUlJQ2GxIVZWyzTFci\n",
"n6/3zldcY6POHuhFGh5uYPrghzkuegyv7niEA+btPLptEqMjzuCCpCkMN11KVJQRl0vEaGh8IRVZ\n",
"DvF70bf8mPc5JdZ8AI4LP5V/DJ5LrD6JUKOWqgZ39jCjlspaG8kJoRjaGYW/L9/L3kSQOjg/ds89\n",
"9zB9+nSGDx9ObW0tU6ZM4bvvvvMrY7PZePTRRzEYDMyePbtd+VhKS9tedt1VREUZ5fP14vn2Hqqi\n",
"oNzs/Szg9tUYnBLmXS5f7zLzdd58fiz8FJvoXmKvVeoYFD6I/lEZFJbUU+usJN+SRZm90FtXQlA6\n",
"Vyf/g5PCz/F+7zKTQskqqMHhEjltWBxWu6vddo6+fi+74nydpdWeR3OMGjWKlStXMnz4cFauXMno\n",
"0aP99kuSxJ133smYMWOYPn16pxsmc+ygVChwiqJ3KT5AkDKY1y94np8338SvxV+ytvxnssw72Fy6\n",
"ic2lm/yOD1aZGG46mfHRVzA89OSAIYpCEBgzJAZJcme3MwTJk4xdQYfF45prruHhhx9mypQpaDQa\n",
"XnzRHVr/gw8+IDk5GVEU2bBhAw6Hg5Ur3Z6DM2bMYOTIkV3bcpmjBp1GSZ1VDIi3oVErGT80E6N6\n",
"OhMTp5MQJ1DmyqZeWc3aHbnoMBKlSyAhqF+AYPgiCI0pHmS6jg6Lh06n49VXXw3YPm3aNO/fW7du\n",
"PaxGyRxbuMXDQb3N6d0WF+5O4+DrXBamC6O/KZ6oKCOGiv1YfMq3RnuGzTIdR5ZjmR6n6bPsmTIt\n",
"bQgfGBOmJzM5DPDPbOYrJB3pScja0T3I4iHT4zQNJqxR+Q85/ALyaJrPD+tJU9kceq1/h1pOm9A9\n",
"yOIh0+NEmPz9fpo+2y3lUfWdF1Q1lNGqlBiapH4MM2r9PsvDlu5BFg+ZHifs/9u715Am+z4O4N/r\n",
"2sHD5vSxZ53uPNyKj9Ut+iD1ykO9yDJaYZKUhxRS0kV2Iml5qCaYFr2ImHSAQtKolKReBIYQIWQk\n",
"IWZqZgh1g4WRFWwjm7b/88K2trl68vK6mt78Pq9kW/vux8av/3Vd///1D/JDUtz3rQ45jkPUku9L\n",
"3j1HFY7zHwF+30chrls8uL5eKefx5xL35fPzfEP7OYuaB/EJ11WrHDe1VaWD5/mM/4SFICluiXMj\n",
"bQCQfdvy0c6Y22HKX38umLYdJI08pEHNg/gcx3Hu5zM8hgocx01bIu9oEAFKudtMUUefWPHthCsg\n",
"+mZ05JsZX6olRGw8594wfnTOw9UfWhWUch6hGj+3yWWOk6OLQgPx/O+p2ap053NpUPMgPsdxnNuh\n",
"xa80Dz+FDMsWqgEAky53W/d2hEK9Qxp02EJ8btrVFtnMfpau5zhcLwNHLdFAxnMICqT7dUiBRh7E\n",
"5zxPaP7KyOPHvg8zwhcFIXzR/FihOh/RyIP4nGer+NkEsB9xXM5VKugGP78LjTyIz3m2CiEzQmPD\n",
"/+Wc0k5+Dxp5kDmHp1ld8wI1D+J733pFmFYNP7kMStr2YF6gwxYyZ0T/Eey2ORSZ26jFE0IEoeZB\n",
"fM5ziT6ZH6h5EEIEoeZBCBGEmgfxGcdNfPz9aGLXfERXW4jP/Dfm37COT0LlT2tP5iMaeRCfkct4\n",
"BKt+bdc2MvdQ8yCECELNgxAiCDUPQoggM24e4+PjKC0tRW5uLnbv3o0PHz54fZ3dbkdRURFu3Lgx\n",
"6w9JCJl7Ztw8rl+/jtjYWFy7dg0ZGRk4f/6819edPXsWZrOZ7lxNyD/UjJtHd3c3UlNTAQApKSl4\n",
"9OjRtNe0tbWB53mkpKTQzWcJ+Yf66TyPlpYWXL161e2xBQsWQKVSAQBUKhXMZrPb80NDQ7h79y7O\n",
"nTsHk8kk8sclhMwVP20eWVlZyMrKcnustLQUVqsVAGC1WqHRuO/OdefOHYyOjiI/Px8jIyNQKBRY\n",
"tmwZkpOTf/pBtNrfe69JyqO8uZjlizyhZjzDNDExER0dHYiPj0dHRwdWrVrl9nxZWZnzb5PJBK1W\n",
"+38bByFk/pnxOY/s7Gy8fPkSOTk5aGlpwd69ewEADQ0NuH//vugfkBAyN3GMzmgSQgSgSWKEEEGo\n",
"eRBCBKHmQQgRhJoHIUQQn94MyG6348SJExgaGoJCoUBNTQ3Cw8NFz9m6dSvU6qkd1cPCwlBcXAyD\n",
"wQCe5xETE4Pjx4/Pehr906dPcebMGTQ2NuL169de37+5uRk3b96EXC6HXq/H2rVrRckbGBhASUkJ\n",
"IiIiAAA5OTnYuHGjaHkTExMoLy/HmzdvYLPZoNfrER0dLVmN3vIWL16M4uJiREZGil7j169fUVlZ\n",
"iVevXoHjOBiNRiiVSknq85Y1MTEhWW0OY2NjyMzMRENDA3ieF6c25kP37t1jBoOBMcZYT08P0+v1\n",
"omeMj4+zjIwMt8eKi4tZV1cXY4yxY8eOsfb29lllXLp0iel0OrZ9+/Yfvv+7d++YTqdjNpuNmc1m\n",
"ptPp2JcvX0TJa25uZleuXHF7jZh5t27dYidPnmSMMfbp0ye2Zs0aVlJSIlmN3vKkrLG9vZ2Vl5cz\n",
"xhh7/PgxKykpkaw+zyy9Xi/592ez2diePXvYhg0b2PDwsGi/T58etnR3dyMlJQUAkJCQgL6+PtEz\n",
"BgcH8fnzZxQWFqKgoAA9PT0YGBjA6tWrAQCpqano7OycVUZERARMJpNzHY+393/27BkSExOhUCig\n",
"VqsRERGBFy9eiJLX19eHBw8eIC8vDxUVFbBarejt7RUtLz09Hfv27QMwNVqUy+WS1ugtr7+/X7Ia\n",
"161bh+rqagDAyMgIgoOD0d/fL0l9nlkajUbS2gDg9OnTyM7OhlarBSDe79OnzcNisTgPJwBAJpPB\n",
"breLmhEQEIDCwkJcvnwZRqMRhw8fdns+MDBw2vqcmVq/fj1ksu838WUuU2cc638sFguCgoLcHrdY\n",
"LKLkJSQk4MiRI2hqakJYWBhMJhOsVqtoeYGBgc5/v3//fhw4cMDtexK7Rs+8gwcPIj4+XtIaZTIZ\n",
"DAYDampqsHnzZkm/Q88sKWtrbW1FaGioc5Y3Y0y02nzaPNRqtXOdDDD1vwzPi/uRIiMjsWXLFuff\n",
"ISEhGBsbcz7vbX3ObLnWYLFYoNFoptUqZm5aWhpWrlzp/Pv58+ei5719+xYFBQXIyMiATqeTvEbX\n",
"vE2bNv2WGuvq6tDW1obKykrYbDbn41LU58iqqqpCUlKSZLW1trais7MTO3fuxODgIAwGAz5+/ChK\n",
"bT5tHo51MgDQ09OD2NhY0TNaW1tRV1cHABgdHYXVakVSUhK6uroAwOv6nNlasWLFtPePj4/HkydP\n",
"YLPZYDabMTw8jJiYGFHyioqK0NvbCwDo7OxEXFycqHnv37/Hrl27UFZWhszMTMlr9JYnZY23b9/G\n",
"xYsXAQD+/v7geR5xcXGS1OeZxXEcSktLJautqakJjY2NaGxsxPLly3Hq1CkkJyeLUptPr7akpaXh\n",
"4cOH2LFjBwCgtrZW9Ixt27bh6NGjyM3NdWaEhISgqqoKExMTiI6ORnp6uihZjis2BoNh2vtzHIf8\n",
"/Hzk5OTAbrfj0KFDUCpnd+dwR57RaITRaIRcLsfChQtRXV0NlUolWt6FCxdgNptRX1+P+vp6AEBF\n",
"RQVqamokqdFbXnl5OWprayWpMT09HQaDAXl5eZicnERFRQWioqIk+Q69ZS1dulTS788Vx3Gi/T5p\n",
"bQshRBCaJEYIEYSaByFEEGoehBBBqHkQQgSh5kEIEYSaByFEEGoehBBB/gcOf0RF2EELzwAAAABJ\n",
"RU5ErkJggg==\n",
"\">\n",
" </div>\n",
" \n",
" <div name=\"mu5\" style=\"display:none\">\n",
" <img src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQ8AAADVCAYAAABJ/XXDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n",
"AAALEgAACxIB0t1+/AAAIABJREFUeJzsnXdgVFX2xz/vTc2UTHohpBEgNAmLqKhgr7uo2BBREQt2\n",
"d1UsiCuCLmJdGxbcVbEj6s+GHUVZUUClhl5CAuk9UzL9/f6YzGQmPUNCCu/zT2Zeu/dN5n3n3HPP\n",
"PUeQJElCRkZGppOIPd0BGRmZvoksHjIyMmEhi4eMjExYyOIhIyMTFrJ4yMjIhIUsHjIyMmEhi4eM\n",
"jExYyOIhIyMTFsqe7oBM32D79u18/vnn3HfffYFtK1asYM+ePYiiSEJCApMnTz4s22V6CZKMTDu8\n",
"/vrr0q233irNnj07sK2urk668MILA++nTJkiVVVVdev2ysrK7rpFmTCQLQ+ZdrnmmmuIiopi3bp1\n",
"gW2///47WVlZgffZ2dmsWbMGjUbTbdvXrl3Lueee2123KdNJZPE4Qjlw4ADLli1rdX9OTg5nnHFG\n",
"4L3UZAlUSUkJkZGRgfeRkZHk5+djMpm6dbtM70EWj36Kx+Phyiuv5P333wdgzpw53HjjjaSnpwOQ\n",
"mprKrFmzOnw9QRBC3pvNZtRqdeC9SqXCZrMhCEK3bpfpPcizLf2UDRs2MGDAAMBnNWzcuDEgHOHQ\n",
"1PLQ6/Uh7+12OyaTqdu3y/QeZMujn/K///2PiRMnArBt2zaGDh0asr+zw5amlkdqaiq5ubmB9zU1\n",
"NYwcORKj0dit22V6ET3ssJXpJi666CJp586dkiRJ0qJFi6SlS5dKK1asCPt6H3/8cchsi9VqlSZN\n",
"mhR4f95550kVFRXdvl2m9yBIkpwMqL9RVVXFpEmTmD59OsOHD2fv3r04HA5ycnI44YQTOn29d955\n",
"h6+//pri4mIuuugiZsyYgcFg4NNPP6WoqAiv10taWhrnn38+QLdvl+kdyOLRD/nss8/Yt28fd955\n",
"Z093RaYfE5bPw+v1Mm/ePHbt2oVKpWLBggWkpaUF9m/evJnHH38cSZJITEzk8ccfD/Gcy3QvW7Zs\n",
"kaMxZbqdsCyP7777jpUrV7Jw4UI2bdrE4sWLeemllwCfV/7CCy/khRdeIDU1lWXLljFu3DgGDRrU\n",
"5Z2XkZHpOcKyPNavXx/w5Ofk5IR4xfPy8oiKiuKNN95g9+7dnHzyybJwyMj0Q8KK87BYLBgMhsB7\n",
"hUKB1+sFoLq6mg0bNnDllVfyxhtv8Ntvv7FmzZo2rye7XWRk+h5hWR4GgwGr1Rp47/V6EUWfDkVF\n",
"RZGWlhawNiZOnEhubi7jx49v9XqCIFBebg6nK2ERH2+U25Pb63Vt9VR74RKW5TF27FhWrVoFwMaN\n",
"G8nOzg7sS01NxWazUVBQAMCff/7JkCFDwu6gjIxM7yQsy+PMM89k9erVTJ06FYCFCxeyfPlybDYb\n",
"U6ZMYcGCBcyaNQtJkhg7diwnn3xyl3ZaRkam5+k1cR793TSU2+ub7fXne/O3Fy7ywjgZGZmwkMVD\n",
"RkYmLGTxkJGRCQtZPGRkZMJCFo8eoNrswGZ393Q3ZGQOCVk8DjOSJLFpbwXrdpT2dFdkDhNVVZU8\n",
"/fTjPd2NLkcWj8NM75gYlzmcxMTEMmvWfe0f2MeQ0xAeZiQa1UOSpGbp/WTCY29RLeU19V16zfio\n",
"iDbjIL766gt++201DoeDoqKDXHHF1WRlDebZZ59CFEXUag333fdAQwqLB1i8+A0WL36RjRv/xO32\n",
"cMoppzF58sVce+2VLF36CYIg8OSTT5KWNpjTTjuj1XZ7C7J4dCOVtXYMOlXItmDL47etJZwwKvkw\n",
"90qmK7Farfz73y9w8OAB7r33DnQ6PbNnP8jgwUP45ZefeeGFZ7jttjsCx69Y8S0vvPAqsbGxfPXV\n",
"F+j1BkaPHsOaNb9y7LHj+d///sfixdf34B11HFk8uolai4MteZUYtCoGDogKbA8WD6fb2wM9659k\n",
"DTCRNeDwZlcXBIEhQ3yJpePjE3A6ndTX1zN4sG8t1+jRf+GVVxaFnDN37iO8/PLzVFVVMn68LyXk\n",
"eedN5qOPPkCSJE488USUyr7xWMo+j26i1uoEwGJ3hWxvuhqgrNrGtv1VSJKEy+1hy75KbE3Okem9\n",
"NB12xsXFsXfvHgA2blxPampjuQuXy8XKlSuYP/9Rnn/+Fb7+ejmlpSWMHj2GwsKDLF/+GZdccslh\n",
"7f+h0Dckrg/icHkAUIqh+tzUYbotvxqA9CQjxZU2KuvsWO0uxo9IareNglIzsSYteq2q3WNluodg\n",
"8RAEkXvv/SfPPPMEkiShVCqZPfvBgG9LpVIRGWnihhtmoNFoOPbY8SQm+v7PZ511Dj/99ANZWVmH\n",
"dW3LoSCLRzdhd/rEQ6tWhGwPdpgGIwBiwxfR6Wp/OFNjcbCvuI684jpOHpNyaJ2VCYtzz50UeK3R\n",
"aPjww88AWLTo1WbHvvLK6wDMmHE9M2Y092l4PF7OO+/Cbupp9yAPW7oJj9cnEgpFqFnb1lStsuFY\n",
"ryRRXGlt/UDA1eAvkWd++z4LFszjjz/WcdZZfauIt2x5dBMej++x9jYxIloTD7PNFRAEgJ0HajDp\n",
"1egahiSSJLEjv5qYSC2JMTpZNPoRDzwwr6e7EBayeHQTngbVaOogbW3Ysr2gutm20up6tGonXq+E\n",
"yaChtKae0pp6EmN0crSZTI8ji0c34R+2+P/66cwzn1/a6DgblRHTJf2SkekqZJ9HN9E4bGkqHuFZ\n",
"DOb6plO+4fVLRqarkMWjm/APW5pZHmFer9rsABpnZGTtkOlpZPHoBjxeb+Dh9jb1eYT51NfZfEFn\n",
"GpWi4TqyfPQ2pk+/rEuu88AD9xzS+ffeeyclJcVd0pe2kH0e3YB/yAI+8fA/6FKT14X1e9lv3UmV\n",
"swSv5EWr0DFQN5hB+hHolC0vyFIqfHrfdDgk039YsODJLrhK9y+4lMWji5EkqdnqTo/XN81aY3Wg\n",
"i6rlnf2v8EvFcqqcLef0UAgqcqJO4PTESxkXfVpIFKNffJoOh450IqddgmbFd116TccZZ8H337a6\n",
"32638/DDD1JbW0NKykC8Xi/79u3h2WefQpIkTCYT998/l507d/Duu2+hVqsoKirk9NPPYvr0ayku\n",
"LmLhwocD1RbvuOMe4uPHcv75Z/P559/yf//3Id988yWiKDJs2AjuuONuSktLePLJR3E4HGg0Gu69\n",
"9wESEhJ57bXF/PrrL8TGxlFWdnhyxcji0YV4vF4Ky63sK65rsl1iZ+kBlh14gR/LPsIj+aJPTao4\n",
"so1jiNMMQCkosbhrybftYp9lK+urf2Z99c+k64ZxTeb9jDAdC/h8HS63p1kbMoefTz/9iMzMQcyc\n",
"eTMFBfu55547ePzxBdx//1wyMjJZvvwz3n33LY455jhKS0t4662lOJ1OJk8+h+nTr+XFF59lypRp\n",
"TJhwErt37+Kxxx7hs88+wf9b8fXXXzBr1v0MGzacTz/9CI/Hw4svPscll0xl/PgT+OOPdbzyyiKm\n",
"Tr2C9ev/4LXX3sbhcHTZ8Kk9ZPHoIrxeiXXbynC4Pc32fbztI+7ceCMWdy2ioGBi/HmcnXQ5Qwxj\n",
"WsznUeOs4JeK5XxR9Ab5th3M23o1ZyVOZXrmbFQukdW5JYfjlvoUde991C3XjW9jX0FBPscffyIA\n",
"aWkZmExR5Ofn8fTTjwHgdrtJTU0DICsrC1EU0Wq1aDQaAPLz9zNmzFgAhgwZ2sxiuP/+h1i69B2K\n",
"igoZNWo0kiSxb98e3n77Dd59900kSUKlUpGfv5/s7GGAL0x+2LARHA6XuiweYSBJEm6PhMvtRaf1\n",
"fYR2p6eZcIiil//ueZRvfn0XgKNM47km8wEG6gYDEGPUUmW2N7t+lDqOSQNmcFbS5Xx68D98Uvgq\n",
"35UuZY9lC3cPe544zYBuvkOZjpCRMYgtWzYxceIpFBYepLa2hrS0DP75z/kkJiaxceN6amtrG45u\n",
"/iORnp7Jxo3rGyyPncTGxobs/+KLT7n77vtRq9Xcddft5OZuJj09g8svv4pRo0azb98etm3LJSNj\n",
"EB9/vAyv14vH42H37p0tttfVhCUevsxI89i1axcqlYoFCxaQlpbW7LgHH3yQqKgoZs2adcgd7U3s\n",
"KaylsMK39mRcdgKGCFVgFa0fl2TjhV2zWFP2E2qFmivT7uXspGkhloZGJZKTFcemvRUttqMWNUxJ\n",
"u41jY0/nqR1/Z591Kw9suZwHR7wWECAAs82JUafuhjuVaYvJky9m4cKHufnm60hOHkBkpIlZs2bz\n",
"r389hMfjQRRFZs9+kPLysiYWpu/1bbfdweOP/4ulS9/B7XYze/bckP1ZWVnceuv16HR64uMTGDny\n",
"KBISEnnqqcdwOh04HA7uuOMehgwZyoQJJzFz5tVER0djMkVxOAir3OR3333HypUrWbhwIZs2bWLx\n",
"4sW89NJLIccsXbqUTz/9lGOPPZa77rqr3Wv29pJ+NrubvJI6hqSY+HVr47BhVKYv8tPh8rL7YA0A\n",
"Fnct/957I7mVmzAqo3nngmU4igc2u2ZyjI6kGB0b9rQsHgDHDktg3Y4yLK4antx5O9vr/sCojOLB\n",
"kW+QoR8WOG5kRgzxURFh39+h0J/b68/35m8vXMKK81i/fj0TJ04EICcnh9zc3Gb7N2/ezGWXXdZv\n",
"4hF2FFRTXlNPXnEdKkXjx1ZUYSU3ryogHFZ3HQu2Xk9u5SZSDZksGL2U0bHHtnpdQWz8RcrJimuW\n",
"Dcu/MM6gimLO8Ff5S9REzO4aHt02kzJ7YeC4ii7O3ykj0x5hiYfFYsFgMATeKxSKwHRTWVkZL774\n",
"InPnzu03wgGNcRVujxQI1AKoaoj8BHB46nl02w3steaSZszg9dM/JkmbRn4bMyNikDmrVSsQxdbH\n",
"qnqVnruHLWJk5HHUuCpYsO166ly+BXUOOaWhzGEmLJ+HwWDAam3MN+H1ehEbMmZ9++23VFdXM3Pm\n",
"TCoqKrDb7WRlZTF58uQ2r3ko5lM4dLY9U7EZQakgMjICyepAUIYm+fFKXp7bdCe7LZtI0A7gh6t/\n",
"JFJMZH19GfUON0aDFpNBQ62lUWyionQkxBsxFvrEJTUlCkrNGGsanajx8UaMBi0ARp0as03N/KNf\n",
"5d4/prLPvJ1nd/+DhePeRVAoMEXpUDcIW2//PPtSe/353g6FsMRj7NixrFy5knPPPZeNGzeSnZ0d\n",
"2HfVVVdx1VVXAfDJJ5+wb9++doUDer/Pw2y2Y7Y5UYtQY3bgaWJVvZv/NKvLvkGnMDJ72GIiPbHU\n",
"mesxW+wYDVrMFjumCCVmS6Mw1KhFKtSKwLaKCgvV1baQY8rLzYxINeF0edhbVIfZ5gTU3Jf9Cvdv\n",
"nkJuze8s3raQ6Rn3smNvOcmx+iNinC77PLquvXAJa9hy5plnolarmTp1Ko899hj3338/y5cvZ9my\n",
"Zc2O7S91Sfy34fZ4mwnHL+Vf8lnhfxFRcFf2swzUDUYQhEBmMD92Z2iJSUEQ0KoVqJUiqfEGWiNC\n",
"o8Rk0ISsi4lWJ/BgzgsoBCXLi95gTcW3IcmEZGS6m7AsD0EQmD9/fsi2zMzMZsddeGHfysnYFkLD\n",
"9Jn/ARUFAa8kUVSfx6t7fVNs12c9wOioEwLnNE1+HGeKoKI2NK5DFIWQ2i3BWjs8PbpJL0JFKyfu\n",
"GK5Kv4cl+xfy8t5/cnLm8UQZsyjPqyROr+o3wi3TO5FX1XYAm90VWB3rFw+1SsThqeffO+/A7rVx\n",
"QtxfuTTr6pDzgvOXxhi1JMXo2m0rMVpHvCmCMYPjSIwOPb6p/9nh9HJu8lUcG3s69R4L/1zzD/7Y\n",
"WUpBibmZSJltTjbsLm9m/ch0H2vX/sbnn3/S6v6vv17OL7+s6vR1zz//7EPpVpchi0c7OF0e1u0o\n",
"CyyJd3l84qFSKHgj71EKbLtI0WUwa+SjpDQZeiiDpnQNER0rjyCKAiMzY4gyaJrtC17eP3iACZvd\n",
"hSAI3Df6MYzKaLbUruG7kvd9/WwyhMnNq6LW6uRAmaVD/ZA5dI477njOP7916/vccycxYcJJnb5u\n",
"bzEo5fD0dmitqtvayu/4sewjVKKGF099nRPSBwGQGm8IzHgE09T/EQ5+7UiMimBggoG9Rb7Q58zY\n",
"FG7ImsfTO//BO/lPMSHlTMyWBCrr7Bw1yBfy7A4abvVHpi2/hBUFXbuq9oy0s/j+mtZX1brdbh59\n",
"dD7FxYV4PF4uu2wan3zyETExsdTV1XLGGWdz8OABbrrpNpYs+S+rVv1EVFQ0Doed66+/ifXr/yA2\n",
"No709AzeeedN1GoVpaXFnHLKGUyffi379u1h0aJn8Xi81NbWcPfdsxk1anSX3uOhIItHGNS5qnh2\n",
"2z8BuCJ9FiPjGv+hWSktlzxs6aGN0HTu4/cnT/b7MnIGx1FaZSM5TsdxsWcxIW4Sv1Qs56UdD3HP\n",
"kJeorGscuvidvMHWkMyh8dlnHxMdHcPcuY9gs9m49torUKvVXHbZNCZOPIWvv14OwO7du1i79lde\n",
"e+1tnE4nV189FQidTPCvuo2MVDNhwgSmT7+WvLw8brvtDgYNGsz333/Dl19+IYtHX0aSJP6zdz41\n",
"zkpGRh7HOUlXdMiqaJp/I94UQUq8vpON+/74v3NRBk3I8GZ6xn2sr/6ZPyp+Ym3s94yPPStQrcyP\n",
"oo0gtL7Me5O6Z1VtW+Tn72fcuOMA0Ol0ZGRk8vvva0lLywg5rqBgP8OHj0QQBDQaDdnZw5tdy7/q\n",
"NiIiIrDqNi4uniVLXkOj0WCzWdHrW5+R6wnkn6F2aJpGcHXFV6yt+g6dQs/NgxcgCmKzWZVgtA1D\n",
"mKaGR2J0RKeHEFJAPFo+L0odx7T0OwFYkvco9R5rM99HPx219Ajp6Zls2rQBAJvNyr59exkwIKXZ\n",
"/yczcxDbt29DkiScTmfDqtemNP/HPPfcU1x33Y088MA8Bg0a3OsitmXLox2C/191ripez3sEgDtG\n",
"P0SC1lfmsWlVuGByBsdhdnqJ1Yd+1OF8DfxC1pYAnJE4hf9VfMbOuk3838FXmDji8RAfTC/7/vVp\n",
"LrjgIh5//F/ccsv1OBwOrrlmZmCo4kcQBAYNGszxx5/IDTfMICoqCqVSiVKpDOwP/ttwFgBnn30u\n",
"Dz54HwkJiQwbNoLKyoqQ/T1NWKtqu4PeGsVXbXYElsy/uPt+fi7/lKNM43nzzI/ZU+QLKz85Z0Cb\n",
"MRXB7f200beYbUR6NAnR7U/dBrN6SzEuj5eBcQYGDwz1reSXmMkr8fWnyLOTO9ZORiWoeffUHzlx\n",
"8ChW5/oS4g5KjiQtsWvDn/tzFGZXtFVdXc1PP/3AhRdegtPpZPr0y3j++VdISEjslvY6w6FEmMqW\n",
"RwtU1dnRqBXotaqAqbi1dh0/l3+KSlBz/aCHUAWtbelMMJZOo8TmcIcsrusobVke6UlGCissON1e\n",
"sk05Aefps5sfRc/zgeN6x0/FkUVUVBTbt2/lq68+BwTOO29yi8LR15DFowmSJLF5XyUAp4xJweuV\n",
"cHmd/GffPAAuHHgDyREZbQ5V2uIvQ+KotToxtRDH0X7nGv620rRCFAGfj2Na+p2srfqeXyu+YmP5\n",
"dIYYc4DmPhyZ7kcQBObMeainu9HlHFEOU7fH267TKXh3UYWV3Qdr+azwPxTV5zEgIpMLUmYC/ge1\n",
"86iUCuJMEWGd6+9aa47W4JmUOM0A/pbsi3h9a//jQSUfwmpaRqYZR4x4eL0Sv2wpZmMbWbsg9Jd5\n",
"18Ea8i15fHLwVQBmDpqHSvSl+xMF31TpgNhOTrceAu1ZDU2nYSenzMSkimWneQO/V/3QoWvIyHSU\n",
"I0Y83A1h5bVWZ5vHNY3HeGf/k7gkJyfFn89IU2NGMEEUGDM4jqGphydfJMDwNN9CudbWyAhNxEOn\n",
"NHDRwJsAWHbgBbxS65aXy+0NyTUiI9MeR4x4dITcfZX8FpSfNLd2LeuqVqARI5iWHprEuSfCvBNj\n",
"dJwyJqXVyNSWAsBOT7yUWHUSBbZdrKn8ptVKc+t3lbNhTwU2u7xwTqZjHDHi0RFjvSIonNsreXgz\n",
"z1d/Y3LKTGLUCSHH9sY1Iv4yEMGoRQ0XD7wZgGUHFuHyuJEkqdnwpb5htW3TLPAyMq1x5IhHJ8f6\n",
"K8v+j3zbDmLVyZw34Jpm+3tjmLexlZW7pyRcSKImlaL6PL4v/JQd+dWs2lTETxsLmy3R7yVhPzJ9\n",
"gCNIPDp+rM1tYWnBcwBcmTELtULb7JgwJ1u6lbioiBYduEpRxcWptwDw5u7nKKpuDEIqrwnN+yE7\n",
"VGU6Si98BLqHzvyiflK4mFpXJUONYzgh9q8tHtMbs3SJgsDQ1KhmC/WSY3RMjJ9EsjadovoCVpd/\n",
"GdjX9HORtUOmoxwx4tHRovKl9gN8WfQmADMy7m9VJNoqkdDzhPZtaGoUE0cNDMSofFL4H7ySb/ap\n",
"qVjIwxaZjnLEiEfwQyFJUrOHxD8L8c7+p3BLLk6KP5/Bxua5E2KMWgR6p8PUT3D0q1opIggCKqXI\n",
"SfHnEatOprB+L79XrQAac4T4kbVDpqMcQeLR+Pp/Gwv5tUmlebfHy7badayt+g6NGMHlaXe2eJ3R\n",
"WbGclNO7C02PzU4gyqDh+JFJHD8yCfANs5SimgtSrgPg/w4ubhDR0HNln4dMRzmCxKPxobDZ3YFc\n",
"pH4cLjdv7vdNzV6Qch2xmqRWr9Ub/R3BmAwaxgyOQ6NSNOvraQkXY1LFkmfdxqaaX5oFxbUWByLT\n",
"fbjc3j6ZmPqIEY/2nollu98jz7qdWHUS5w249vB0qgdQK7RcnuX3fSwO5Db101RMZLqf37aWsGZb\n",
"aU93o9McMeLRkiNw+/4qJEnC4jTz9J//Anw5STWKxoVrJp2aISkmxg6N57jhfX8ZNcCVw69Fr4hk\n",
"e92frK9YE7JPHrYcfryBRYt967M/gsSj+bbSmnoq6+w8t/7fVNjLGWLI4cS4v4UcE6lXkxJvIFKn\n",
"7nTC4t5KvCGas5OnAfDO7sVUBxXr9spF53qMvibcR5B4tPyP2Vqyh1c2LQLg6szZzXwEvXtKtnMM\n",
"STExOMWEQiFwTtIVqAQ1f1at5Ovc3wPHyD6PnqOzwm2zu/lpYyFl1TYAtuZVsbOguht61jJhiYfX\n",
"62Xu3LlMnTqVq666ioKCgpD9y5cvZ8qUKVx++eU89NBDvcIcO1hhbXH7oq2P4vA4mBB3HkONY5rt\n",
"781Tsp0lJd7AwHgDoiAQpY5jYvz5SEgsb4hrAfDIpkeP0dnnpLDCV8Br90Ff/Z7y2nqKq2xd3q/W\n",
"CEs8VqxYgcvlYunSpdx999089thjgX12u53nnnuOt99+m/fffx+LxcLKlSu7rMPhUG12UNPCcvMd\n",
"dX/yc8mXaBTaQNbxI4lJA2YA8HP5p9S5qgDZ8uhJvC3EH7WFvyCZStkzA4iwWl2/fj0TJ04EICcn\n",
"h9zc3MA+jUbDBx98EKg94Xa70Wqbrw05nLjcjStFDVoVWrUCr+RlSd5CAK7Iupk4TXKL57o9/e+X\n",
"WKdRIgoCA3VZjI0+BZfXwbcNZSo9vcBKPFLJLzHz7Zp86h0dm7Z1uXpWPMLyAFosFgyGxgI0CoUC\n",
"r9eLKPqiGWNiYgB4++23qa+v54QTTmjtUgEOJYtze7gEAWNlPQCjB8dRZ3PyRd4y9lm3EqtJ4uqR\n",
"t2Gzihh0Kiw2FwDDMmKw1rvISjGh7QJHaXfeXzjtXZwYyS+bCrnMeSPr//iJb0ve44qht2I0RoTV\n",
"1952f729LY9XCqzMNhp8P64Wp08MvApFh9rUFtZhFATiY3TExxsD1wk+d/OeckRBYFRWXFffQnji\n",
"YTAYsFobfQh+4Qh+/+STT5Kfn88LL7zQoWt2Z7r5qiobZotv9Wh1tRWn0sEbux4H4PK0O6mudON0\n",
"e/nLoBhWbS4CwGquJyFah7munkPtWW8tTRAdoSRDlcMg/Uj2WbfyVd4yLhGv6nRfe+v99da2XG4v\n",
"q3OLSY7RkZ0WHfhugk9IKisteJwuDBGqNn1ulVVWXB4vBrVIaVld4DrB/d2Z50vmnRjZcsLtQxHG\n",
"sOydsWPHsmrVKgA2btxIdnZ2yP65c+fidDp58cUXA8OXniTYEBcEgcWbnqHaVc4Qw2gmxE3C6fai\n",
"EIWQmZXeHkXaFSRE6zg5J4XLB98IwBdFb+DyyMmAuhtLvc+6bc25WVZdz/pd5exrqAvUGsEBfcG+\n",
"qsM1QRGWeJx55pmo1WqmTp3KY489xv3338/y5ctZtmwZ27Zt4+OPP2bXrl1Mnz6dq666ihUrVnR1\n",
"vzuFJ8hvccCyn9dzXwJgRuYcRMH3ETQdNx4B2gH4pqJPTf4rcepkiu37WVvxY093qd/TnlPaYveJ\n",
"S3l1PZIkteoD8ceFeKXQOKbD5bYKa9giCALz588P2ZaZmRl4vX379kPrVScx25wUVVgZMjCqxbiM\n",
"YIV+cv08XF4nJ8VfEKhlAqBVhX4U/WmKtj3UChV/HTCdt/Y/zsf5/+W2CZf3dJf6NR6pg1aC4JuG\n",
"Laq0YoxQo9MoGJ4R0+ywpmklvZKEeBhKUvaLILENuysorrJRWt2yGegXj801v/LDwa/RKw1ckX5X\n",
"yDERms5XcOsviKLA6YmXEqEwsLX2dzaVbejpLvVrgi3hpqu7gxGAokqfb9Fc76S0pj6QoNobIkCh\n",
"1oz/dXdHrPYL8QiYb62Ygx6vhEdy82bD1OzNOXcR3SShsVYdann0tVDhQ0EUBCIUek5PvBSAlzYs\n",
"wlLv6pMrPfsCwd/Tpqu726OqIUl3sAA1Ta3Q3vPQVfQL8WgPj8fL9yUfcKB+D6mGDGaMvLnZMRFN\n",
"Mo8fQdpBg9uHc5OuQETk832f8N3mLazZVioHjXUBkiSxZmsJO/J9oeNuTwc/0xZGHv7s9sHX8Epw\n",
"sNzS+N7b2G5wH7qaI0I8quxVfHDAN2U855iHUSubzwBFqEOHLUea5QEQr03huNiz8Ehuvil5FwCn\n",
"W559OVQkCewuDyUNw2r3ISwB8EeVBgcvuj3ewPAGgi2P0D50NUeEeLyyYyFWdy1HmY7n9NRz0Wl9\n",
"JQqCK9X7V8wmRvuqsbVWxqA/Euwc/tsAX33b70uXYffYAl9WmfBp+kPk6aDl0dJx/mjp4EkAZ5Na\n",
"O42zMFJkvAuHAAAgAElEQVSzbV1JvxePNcW/8fXBZSgFFdcNehCAAXF6hqdFMzorNnCcUuH7KIal\n",
"RXHCyKSAwBwJBE8sDTWOYahxDFZ3LT+XfYrT5ZF9H4eA1e6ivKY+8N7rlTrs52hpaYSrBcujqcBL\n",
"LThMu2PY0j8SVLSC0+Pk3p/vAHxV3wZEZOL1SgiCQGKMrsV/jiAIqFVH1sxL0+ntvyVfzS7zRr4q\n",
"fou/5k/D44Uxg+OIMvR8wF9fwmZ38/uOspBtDpenTT+SxVXHT2Vfsq3uD/Zbt1PrqsTpsaNXRhKv\n",
"SWG4aQyeyEtIU48KnNPUqvBfPsSJ2g0GZO8Qj/x8hLJaXC4vagUISI2RL755KNxuD7sLqkmJ02GK\n",
"UIbsi95ZhiB50ZXrUUZqQZIQkHix+AN2VG0nRUhgZsUYNBW/ElsZDXv1qKqtqJDIqbQQoVSgLtvs\n",
"C0VtuGbg+pIESAhNt0kSiCKSQgEKJSgUoFQgiQpQ+t5LCiUoRIg3oayzI6nUSBoNaLVIWi2SRgta\n",
"re/cHqRpTMuxsWcQrxlAsT2ftRUrGRdzKjUWhywenWTdjuapBe1OT4upHg/a9vBp4X/4teIb3FLz\n",
"YuxWTx1ljoNsrVvLRwcWk6RN4/yU6zgl/kKUYqiV7PJ4m4lUdwxbeod4ZGTQkWU7Ca1sP6OFbfuj\n",
"4IlbARW88WYZZ+67IWR/VJO/3U10G/sklQpJGwEajU9UtFokbQSS0YhkMPj+6o2N7w0GJGMkksGA\n",
"17/PZEKKjsYbFQ10br1C0yJRCkHJuclX8db+x/myaAnjYk5F0RtL5PVBXO7Qh9rsqub9guf4oXQZ\n",
"EhICAqNM4zk25jQy9aOI1SShEbVY3LWUOvezuWotqyu/osRewKt7H+KLwte5MesRRpiOCVxz235f\n",
"eoVRQQFl3eEw7R3ikZaG1eFGEkTUKgWiUuEbiAuCr66jIOD0+BRVEkUMEWqkoH1muxsJAa1GiVqt\n",
"xO72MPOE3dSr6rioIIYcQxbVRyvR69SAgFqj9DmZGs6X/G0FXROabwscJzb89XoR3B7weMDjBo8H\n",
"we32WS5uN0LDdpUALrsTweVEsNvB4UBw2H2v7XYElwvB5eKQV+D50emIiYpGiorGGx2NZIry/fW/\n",
"D/4bFU1CVBQ1WgVmVJjtLlQKkdMSLubDA4vYWreOPMs2hgjH4/Z4Wb2lmPQkIxlJkV3U2f5Jaz4G\n",
"l9sbEI/NNb/ywu77qHVVoBCUnJZwMdOG3IreG0+MUUuVOWjBnCqa4XHZjDGdwpUZd/Nb5TcsK1hE\n",
"sX0/87ZOZ1LyDK7ImIVCaHyk7c5GR2r/tTzy8/nq+x0AjMiIISGqMQGxV5Kw2FxU1tnJLzUjACeP\n",
"SQk5/aeNhQAMHmAiUq/myV9eYsXeuRiUJs656FN+nhpPbKSWowb5HKTx8UZqD/Mq0JrW2pMkcDoR\n",
"HHawOxDs9QgOB0K9DcFiQTCbESzmhr8WBEtdYLtosSCY63z7zHWI1dUI1VUINhsKmw2KCjveR0DS\n",
"aPBEReOIjMIaYWTauFheS7OyetV9TFt9OUJCHMn1CsyRUSiOzcYbHYMU3ZZNdeTS2iyV0+3F4XGx\n",
"tOBZPjn4KhISwyOPZuageQzUDcao02K22ImJ1ISIB/iioGusIAoKToz7G8fFnMn/HXyVTwoXs7x4\n",
"CXnWbdyV/SxGle9/Yg+ahTkiHKZNb3JfYR0HKyxENESAtrXa1eH28F3uJt7a71tuf23mg0Sp44Hm\n",
"01m9BkHwDVc0GoiEQ/4XSxLxOpHK3QUI1dWINdUINdU+YWntb3UVYnUVgsOBsrQEZWkJeuCBAnjj\n",
"7/C1cQ/is4+QZIYWq9lERhITFYM3JhopOgZvdAzemBifZRMTE9gmxcQEBEcyRvbr1YeuVsTD4rDx\n",
"xNY7+K3iWwREpqTeykUDb0IUQv1eybE69hXVhVgMTaOglaKaaRl/Z3TU8Ty98w621q1jXu50Hhj5\n",
"GjHqhJBZsu6I9euF4hH63r9epb7hg2jr+3awzMIrex6k3mPl2JgzOTGusUj1ERMoKQhgMOAdmAoD\n",
"U+mwZEoS2GyINdUU7iygOr8IdV0Np7j+w4+a7Tx2TQ7/OjgMS2EJmroajPVmlLXVCDU1CHV1KOrq\n",
"UBTs73A3JaUyVFwiIxv8OUYkvQFJr/e99vt49IbAa9KSEG2eBoezxvdXpepVYuT/sRIFISAAVncd\n",
"8365lW11f6BTGLl72POMMo1vdu4xwxJQiCKGCBV1tkbnqbaF9VdKpcCwyKN5bPSHLNh2PQfq9/DQ\n",
"liuZf9Q7UNvoJTwiLY+miIJAWU09WrWCSJ06ZN/Xxe+yufZXjMoorh80N2ClGCPUDEk1dVuf+wWC\n",
"AHo9Xr0el9JEWUw6AKfWJfFj7jTeTMzn+ts+Z+f+xsWHgweYKCwzc2yaDmVFOUJVgwXj/1tTjVhV\n",
"5bOAqqoCFo5YXY1gsyJUlCNWlIfV3dgm7yVR9M1iaRrExO981mhBrUZSKn2zYGLDrFjgtbJhxizo\n",
"tX+fKECEGkN989mPdj9Ou5u/WBwoFSJujxez6GLG0JVs01eS6Izg9d0TGLruO+C7kPNUKgUJJl9G\n",
"sNEWJ9aG5fkAcSYt2trQoYxKKQasnKMVOVw7pJpcDvDMqvN5b9cZRHrUgXPVKgWSVwpMzUsqFSx+\n",
"qdP35qfXiYc/UYrN7sJqbx6cJAiN3uRTgnwf+63bA8OVO0f+iyi1b/4mNcFA1gBZODpDSrwet0ei\n",
"oMzMUOMYBhtGs8eymf+uf4uJMZcEjttT5Mvavb7MzdGDB8OgTjRit/uGVH6hqatDsFp8/hyr1efn\n",
"sVh8ImMxN2zz7VfVW/HY6hv9RA6f0xmbDcHW9dnDI9o/pMVz/DOIFjVcfSVs1kNmNfy0pJ602q/D\n",
"are92cGVOph4DeyIr+Uf0R/z3dsQ0VaMX38Sj8IKK3GmCDbtrWhxf0uGSb3HyjM778QtufhryjSu\n",
"GH1Z4HxFP6q7crhQiCKDBkRSUGZGEAQmDbiaZ3fN4qP9r3Fi9EWBBEoKUQi/PKVWizcpGZKSOz60\n",
"aiA+3khVUwe02904i+Vw+GaxHD4HNHYHgrdhVsztRvC4weObEcPbMEMW2Nd4HJKE0ajF3MRx2RHK\n",
"qm3U2pzo9UquVrzJWnUeyd5IXpCupuIqEy1/u0GrUZEapwd8y/BLgrKNDUmJwlLvRKtWklfiyzKm\n",
"VSmxu9zoNEqSYnQUFNfxlFjL9d43+SW9jil3j2ae5TxSYgwUV9mQkIg2aIgzRYBK1clJ/VB6nXgA\n",
"LZZJ8BMc2ltRW09spJb/7J1PsT2fdF02/zzukZCsYHJ8QviY9GpqrU6Oiz2L2IZMYxurVzE25hQA\n",
"lKKIx9tLHNENwxJJrz90p3MQxngj9lZmysw2JxEaZWBpQzD791ZQWWdnacm/WJuXh0kVy6JTP8Wk\n",
"TmNvG7VVjAYt8YN9gzKL2cFe/4+gIJCaMwAl4Ab2NswwRqiV1DvdJERFEJMezd5Nvhy8r0RdxOXf\n",
"/ZXl2s0kDr+AO4+/luISM1a7i7hILYaGmcdDEY9e+WR11O+Vm1fFf7e8wi8VX6ARddwx9N/E6Iyo\n",
"FMHiIVse4XLUoFjGDo1Hp9ZwbvKVACwvbiwQpVAcuZ+t2ebkz13l5OZVtbjf7vTwZfHrfJL3HipR\n",
"w73DXiTNMAhFE6GJ0mtQKURSGqyNYNSqxmNPOCp0nuv4EUmcMDIpMJFgiFCFzEQelXAUz5zqq4S4\n",
"ZP9CNpT9jrZh5Xhw/Meh0CvFo6P5DjZW/8KDq+8H4KbBD5OiG4RSIYZ86LJ4hI9SIRKpU6NSiJye\n",
"eAkaUUdu7Rr2W3f0dNd6HH9Gr5asZI/Xy6rib3lr/1MA3D7kCYYYcxCE5t/HSL2aE49KJjayeW0j\n",
"vVZFeqKRnKy4Zha0Rq1ArVIQ1+BcTYzRhe5XKbhoyKVclX0jHsnN7N9uweY2N/Sva2yzXikeHYnJ\n",
"OGjbw7O77sIreblo4E2BAtVKhRCiwP2p1mxPoVSI6JWRnJZ4MQBfNpSn7I8FsbqCzcU7eGH3bADu\n",
"GvNPxseeBfhmCpuKhF9MWotfykyOJNrY+pqi4enRHD8yKSS9BDQm9L4r5wEy9SMotBawaNvDAEhd\n",
"NLDrNeIRvDjL6Wr7S1lmP8gj267D5jFzWspfmZJ6e2BfU7OwtWAdmY6jVPr+N+cmX4mAwC8VX1Lt\n",
"LOt4RqwjCJvLxm0/XUO9x8JZaedxw6i/B/YJgs/SOH5E4xDELx7h/sYpRDFEOEZkxDB4gCkgRjpN\n",
"BLcPeQKNqOHboo9YW/ldl2WH6zXiARCpU6NWiq1mr9JplFQ5Snl46zVUO8sYEXkM1w5cEPD+Q+Mi\n",
"r2Fp0ShFkVhTz5a67A/4fUhJ2jSOiTkdj+Ti25L3j6hsa01pavpb6l2s3HCQv3//D3bXbidZm8FT\n",
"Jz0fMkzxP9AatSKwQtmg862IFbrIQk6IimBgQmM1x0i9ijT9YK4ZfB8A/933MLWOmi5pq1eIhz91\n",
"vCgKaFSKQJ7GphTX5zM390rKHAfJMhzFvcNeQq1oagY2fNFjdEwYndzMnJPpPMGzCYFMYyVLcXo6\n",
"P4XZX2g6ZCutsrGy7GM+3/8BGlHLrOzniNNHh4hC8MhkVGYMOVmNOVI0St/3VKPu2u+rQhQx6lSc\n",
"GnsZI0zjqHVV8vb+p7sk4rRXiIdfxMWGRDwtOXT2mLcw689LfcKhH8Wc4YvRKQ3NjpPpeoJnVYYZ\n",
"j2ZkTA5mdw2ryj8PbD9cVcp6A15JIr8kdPr2gCWPN/IeBeC2YY+QacxGqRBDhuPBfg2lQgzxZWjU\n",
"Cv4yJJ4TRw/o8v5GqJUIgsj1mfNQCCpWlC7jt8LfDvm6vUM8GtIciSKom1RukySJH0o/4KHcK6lz\n",
"VTMmaiIPjVoSWDko0/0E+40EQWDG8JsA+LL4TbySPy3ekSMeBaXmkMJNHq+HRzbchcNbz0nx5zEh\n",
"9vyAxRsqHm1f16RXd0sWO/+amIG6LCanXA/APav+gdPT+bD7YMISD6/Xy9y5c5k6dSpXXXUVBQUF\n",
"Ift//PFHLrnkEqZOncqHH37Y/vWaWB5+KhxFPLHjVhbvnYdLcjItewb3DnsRraL5nLhM95ESZ8AY\n",
"0biO6G+DJhOjTqSwfh+ban4BaPZL3J+ptYQ+dP9e9wxbqv4gWp3ANZkP4PJ4A9/jlnweh5vgofuF\n",
"A28kSZvG7pqd/HvtM4d03bDEY8WKFbhcLpYuXcrdd9/NY489Ftjncrl47LHHeOONN3j77bf54IMP\n",
"qKysbPN6/gI2fvGocpTyVt7j3LlhEn9Wr8SgMvDSGf/h2dOfb5ZyzU9yjI5habI10h3otEqOzo5v\n",
"fK9SNwaNFS0B4GCFJVCQqL8T7JMrsO7imQ0NxcSy/oVe6VtH5X9gg4d8PWXmB4uHWtRw/aCHAHhp\n",
"y6GJR1jh6evXr2fixIkA5OTkkJubG9i3d+9e0tLSMBp9ga9HH300v//+O+ecc07r1yvewMbqzVRW\n",
"7WFT9a+sLV2NhE9Qxseew+K/PUuyofWxoEmnJlsWjsOGQhQ5PfFSPjrwEltqfyPPvIM4IaPLgo96\n",
"I5Z6Fx6vhEmvDtyn2+vixT2zcUsuzkicwpjoiYHj/Q9sSOh6D4UcRRk1gTB2gNFRJ3BszBmsqzq0\n",
"AvRhiYfFYsFgaHRWKhQKvF4voihisVgCwgGg1+sxm9s2aSe+dVxopwQV42LOZHLKTAYZRrYpHL72\n",
"5UCww4E/N4VCIWBQmjg14SK+KXmXT/JfZ2bGw/22OHi9w80fO31Z0I8fkYTXK6EQBL6reYM863bi\n",
"NSlclXFvyDnBUc5+eurzEQWBsUPjWZ1bHNg2I3MO9R5rG2e1T1jiYTAYsFqDKlQ1CAeA0WgM2We1\n",
"WjGZ2l4Sf1T8aESPgaMSRzAx4wSi7WMxqnznxEVFEB/fKEZGQ/O4jZhoXcgxHaGzxx8q/aG9v52U\n",
"hd3hIcqowZhXzaWDr+fbkvdYWfwZM4bcQ1R0KvGxh8cfdTg/T71RG/jeaXQadHoNhY4dvLHzeQDu\n",
"PuopEkyhGUaSEyMDn4X/3Lg4A7Gm9hf4d9e9XZpswuX2UFBipsYSTWbse4d0vbDEY+zYsaxcuZJz\n",
"zz2XjRs3kp2dHdg3aNAg8vPzqa2tJSIigt9//53rrruuzeutmPobP/9ZwOABJmJNWtZuL8XssBNj\n",
"1JAaE0F50KpGs6X5uFqvEkOOaY/4eGOnjj9U+lt75XYnZosdI0mcNvAcfjj4NUt3v0K0Yg5js+O7\n",
"/Rf2cH6e8fFGSkrrAt+7A0U1lNfUMH/L7XgkD9eOvIlM9Zhm30uL2U55wyyif19VlRVvOwW0Dse9\n",
"RWoUFJY4WnyWOkNY4nHmmWeyevVqpk6dCsDChQtZvnw5NpuNKVOmMHv2bK677jq8Xi+XXHIJCQmt\n",
"FU3w4Q+4USiEkDGiVq3s0NoUedhy+BmVGYMoCNwafRc/HPya70qWckHK9cSXRpCedHitrO7GFTQN\n",
"bbE5WVbwPPnW3QyOGsKc4x5i/Y7mEZuaFoYtvelb2hULRsMSD0EQmD9/fsi2zMzMwOtTTz2VU089\n",
"tcPX8+foUIhCSA2Rtn7BghPRqJVyFOnhJq7B/D42YhzjYk/mj8qf+ar4TbIT5+Bye6h3eIjUq9u5\n",
"Su+lqMLKnsJa/jYxC3dQnMu6krV8UfQGIiIvnP4KRo0O8ImHVqUIZCxv6TvZm/zJXbFgtFcEiW1v\n",
"yImgVIghc+FCG70bMrAxIZu8fqXnUKsUzD3FVwP46+J3sbjr+HNnOet3l+PoorwRPcGugzV4JYnS\n",
"Klvgx83usfH0tnuQkLgi62aOTjwGQRBITTCQnmhkYHzjJEJLD6enO2o+hklXWB69Qjz8NL2h9sbO\n",
"g5IjSYyKwHAEVbTvjUxMn8Ao03jqPRY+zlsS+PW12l19fvGc2+MNRNi+V/A0JfYC0nXZXJN9R+CY\n",
"rAEmMpMjW5xhAQJlQ1S9yELuCr9U7xKPBn+Hf7FQTAsJUvxIkkRaopHhQSX1ZHoGhULg4oE3A7Bs\n",
"32uBKcDN+yrZnl/d7vm9MS+I/+HyeCXcHi+ba1bzTfF7KAQVtw55jAhV8+9ma0OBvwyJY2RGDKZe\n",
"NIzrN8MWP37LY2RGDMePSOpVH7ZM6yhEgRGRx5BtHEudq4Zvit8N7CuvqW/z3IJSM79sKabOemjr\n",
"LA4Vu9PN3sLaRud9w3fR45Gotdfy8p5/AnBp6i1k6Ie1+PD5Q9K1TdanqFUK4qPCycHeffQ78fDP\n",
"tKiUYpcvTZbpPkTRl73t0tRbAPi86HWsbl92b2U7CajzS33Tku2JTHezPb+aA+UWDpRZgEbxcHu9\n",
"vLzzESqdJYyIzuGChoVlLfkMInVqRmXE8Jeh8c329Tb6lc9DFIRm1dpbIqZhGbNeK/s5egt+0T/K\n",
"dAJjYsZjddfyRdHrDfva/p/6xaWnQ9v961VKKm2UVtkCv8w/5H/F98UfoxY1PDr+hUAh6dZ+ueOi\n",
"IvpEDpl+Y3kcf1QyJ4xK6tCqw5GZMRw9NL5PTwP2N4LzcM7IuhuAL4vepsbZWnWSRsTA8KBn/R5+\n",
"H4fD7WF7QTUKUaTOVc0jv/vu58rMuxgWOyxwfF9PrK3oLw5Tk0HTYu2LlvBlRpKFozchCEJg6jxN\n",
"cxRHR5+Kw2vjk8JX251tCfgWDrPlUVJlCxkqNZ99kHht38NU2csZaTqGCwbOCEkX0dcTa/cby0Om\n",
"75MSp0erUuD2epma9g8EBL4vWUqJ7WCb5/mjg92HWTx2FFSzdX9jzZWmD9MPxZ/xW+U3RCh03DZk\n",
"IUqFImQ40tfDA/qVz0Om76NtiGdI12dzYtwk3JKLt/c/3eY5/pyzXZXRO1yCxaPCUcxLO+cBcMvI\n",
"h0jUpiIKjeUMFKLQ531uERpFSHG0cJDFQ6bLSIptLDx0zeBZaEQtqyu+4vOtP7Z6jn8y5nAOW1oS\n",
"Kv+wxSt5eWnPHGweM0dHn8o5KZf5knM37D9hZBLHj0xqdn5fQ6VUcOJRyYd0DVk8ZLqMpBgdxgZz\n",
"Pk49gCmZMwF49I8H2HWgGrOteSyH3yVyOEO3WxYq37avi98mt3YNkcoYbsx6GLfHl9nfnwVdrVJ0\n",
"2D/X35E/BZkuxaT3TaV7vBJTM28iRp3IPutW3tv+Lpv3Nk9H2RNZ11sSKo9XosC6i/fy/w3ATYMf\n",
"IUodF9jfXxMdHQqyeMh0KX7fgVeS0Kn1TEu/C4D38v9NraMucFxRhZXt+6sIPMddrCGuVgqHQajl\n",
"4Rcvu8vOC7vvwyU5OS3hEsbFnBZyTjuxbkck8kci06UogsQDCSbETWKocQw1rgqWFjQm3N11sIbS\n",
"mvpAXs1gA8RS72Lr/qpOlwrNK66j2uyg2uxgdW5JixndS6tsWOtdgfd1VifVZgeLdy8g37aDFH06\n",
"V2fObnae0KuycfQOZPGQ6VKCrXtJkhAFkRsGzUchKPm25H0+37oyJL7CH9kZHA+Su6+S8pp6DpRZ\n",
"qLU6KShtP7NWvcNNfqmZTXsrqKj1Xb+wwsLBcgu1DZXsay0OthdUsy1osd6GPRW8vPYtvip8D6Wg\n",
"4vHjFhPRQmmPvr46uDuQxUOmS/HHP0QZNIHkN2n6oZw/4DokJOavm8WmfSXNzgueAfEXkPJ6JTbs\n",
"LmdfcV0gN4jV7mqxxEOw7yTghPVI7CmsZcMeX6SrvYX8IsX1+1m8dy4AM4c8wIjY0S3e15FUEa+j\n",
"yOIh06XERGoZPSiWUZkxIb/WFw+8iSRtGgfq9/DRwZeanRd8rN96kYIcIf79v+8oY93W5uLTUpK/\n",
"4Gu63N5msyxOr4N/77yTeo+V8bHncN7AK1p1jPaiPD69Blk8ZLqcmEgtSoUY8mutVmi5efACBAQ+\n",
"PfgfdtT9GXKORPNf9+C3a7eXsmlP41qZarOj3X4EX81fd6Xx2hKv7HmQfNsOkrRp3JT1CAqFGBJ5\n",
"qQlK3iNbHs2RxUOm22j6vA2PHMcFKTPx4uWF3fdic4f6MrySRI3FEUj715RqS6NgbNpbgaXe5asb\n",
"6/WGWCktPeg2h5u9RbWB958W/odfKr5AI+qYlf08OqUBhSiG+GzGDYsnPjoi0DeZUGTxkOk2gh9i\n",
"hSCgVSu4c+x9DDaOpNxRxCt7Hww5xuuFjXvaX4nrZ2teFfuK68gvsTQTqqaUVdkCr9dVfs/7Bc8g\n",
"IPCPoU+SrveVDtFplSHWiUqpCAxjZO1ojiweMt1G8AOnUAiMH5HE8NR45ox+jgiFnjWV3/JZ4X8D\n",
"xzT9da9sp/atf5rX7nR32DLYZd7IC7vvA2Ba+l0h8Rw6jbJZhvPguBWZUGTxkOk2guu3BKfhSzdm\n",
"cfuQJwB4v+AZNlSvApqvOQkuKN0WPn9J0PsWnnOHy0O+dScLt92Iw1vPKQkXcf6A0GJkOq0ykELQ\n",
"nwIzIzkSgEEDIjvUlyMJWTxkuo34qAhOzhnAX4bEk5XSWHJUFAXGxZzGlNTbkJB4Zued7DFvDt8p\n",
"KYUOkUqqbc0O2Ve3h39tux6rp45jYk7nxqz5IcmnogwaTHo1sSYtozJiGJXpKx9pMmg4ZUxKoE6N\n",
"TCOyeMh0K4IgYNKrQ6ZA/a8vGngzE+LOw+618ej2G9hetT2sNiSkNn0SeZZtzN1yJbWuCo4yjecf\n",
"Q58OpBMEnz9mzOC4gJjERUUElt/LtI78CckcdvwyIgoitwxewNHRp2Jx13LVNxex39q6gMRGaolr\n",
"qRyH1PpU6rbadczfOoM6dxU5URO4d9hLqEUN0Q3lPYA+kbC4N9Jp8bDb7dx+++1cccUV3HDDDVRV\n",
"VTU7ZsmSJUyZMoUpU6awaNGiLumoTP8heDpUKaq4M/sZjjIdT4W9jIdyp7O55tcWzzNEqBg1KJYh\n",
"qVEh2yvq7NQ3iR6VJImvit7i4a3XYvOYGR97NvcNexGNwjf8SI7VcfyIJE4Zk9Lns4L1FJ0Wj/ff\n",
"f5/s7GzeffddJk+ezMsvvxyy/8CBA3zxxRd88MEHLFu2jNWrV7Nz584u67BM/0Mtapg9/BXOTb+A\n",
"eo+FBdtm8vGBl/FKoYLgH+4kxTZfe7L7YGOx6VpnJc/suosl+xfixcP5A67jjqFPoxSDct8Kglze\n",
"4xDptHisX7+ek046CYCJEyfy22+/hexPTk7mtddeC4wf3W43Wq1cS1ambVSimqdOXMxFA29CwssH\n",
"B57ngc1T2WPeEjjGP22qbMUf4fY6+a7kfe7aOIk1ld+gEXXcNfRZrsy4G1EIFQp5jeyho2xr54cf\n",
"fshbb70Vsi02Nha93qf8er0eszk0SlCpVBIVFYUkSTzxxBOMGDGC9PT0djsSH29s95iuRG6v59or\n",
"rXNgcTaPIo2JMTBzxH38JWE8z229n73WXOZsmcK42JP5a+o0RpsuID7eiMfjxWho/EEqsR3gp5LP\n",
"+frg+5TZCwH4S8yJ/H3EQpJ0qUQZNdQ0hLNHGzVUmx2kpURh6GAW/t78WfYkgtTJ+bHbb7+dmTNn\n",
"Mnr0aMxmM9OmTeOLL74IOcbhcDBnzhwMBgPz5s3rUD2W8vL2l113FfHxRrm9Hmxv14EaiiqtgfcC\n",
"vliNEenRgeXy9R4rnxx8ha+L38Xh9S2x1yi0DI8ZzpD4wRSX1WN2V1No20eFszhwrZSILC5L+zvH\n",
"xZwZ+N5lp0axr6gOl8fLhKOSsTs9HfZz9PbPsivaC5c2LY+WGDt2LKtWrWL06NGsWrWKcePGheyX\n",
"JIlbbrmF8ePHM3PmzLA7JnPkoBBF3F5vYCk+QIRCz6K/Psm3G6/lh9KPWFP5LfusW9lYvoGN5RtC\n",
"ztcrTYw2Hc+pCRczOur4ZkMUURAYPzIRSfJVtzNEyJOMXUGnxePyyy/nvvvuY9q0aajVap5+2pda\n",
"f8mSJaSlpeH1evn9999xuVysWuWLHJw1axZjxozp2p7L9Bu0agUWu7dZvg21SsGpo7IxqmYyeeBM\n",
"UpIFKjx51CtqWbO1AC1G4rUppEQMaiYYwQhCY4kHma6j0+Kh1Wp57rnnmm2fMWNG4PXmzZsPqVMy\n",
"R1MibQsAAAjiSURBVBY+8XBR73AHtiXH+Mo4BAeXRWujGWIaQHy8EUPVHmxBx7dFR4bNMp1HlmOZ\n",
"w07TZ9k/ZVrekD4wMVpHdlo0EFrZLFhIOmNJyNrRPcjiIXPYaZpMWK0MHXKEJORRt1wf1l+msiV0\n",
"mlCDWi6b0D3I4iFz2Ik1hcb9NH22W6ujGjwvqGw4RqNUYGhS+jHaqAl5Lw9bugdZPGQOO9FGDSeO\n",
"aix1KAgCg5Ibl7w3tSr8/o8ITaMVElziIfh4tVIkMzl0+XwfL2jfa5HFQ6ZHCF61Kgi+UpV+mvoz\n",
"hqZGceKo5EAhbQBFQ8lHrySFDFNGZsY2KwcpWx7dgyweMj2OIAih/owmpoIgCM2WyPsFIkKtDIkU\n",
"9evE8AaHK3R5MTqZBjo9VSsj09WIQqhgtObzCCYlXo9aKRITqQkJLvM7RxNjdGwv8EWrypnPuwdZ\n",
"PGR6HEEQQoYWHREPjUrBwAQDAO6gbOstjVBk7ege5GGLTI/TbLZF0bmvZbCPI3gaeFByJApRwKiT\n",
"83V0B7LlIdPjNHVodsTyaJ1GMyMt0UhaYt9YodoXkS0PmR6nqVS0FQDWGv7pXLVKTvBzuJAtD5ke\n",
"p6lUhBMRmp0WHQhplzk8yJaHTK9DlKO6+gSyeMj0PA1akRpvQKNUoJbLHvQJ5GGLTK8hK8UUUhxK\n",
"pncjS7yMjExYyOIh0+M0XaIv0zeQxUNGRiYsZPGQkZEJC1k8ZHoMfxIfrUYO7OqLyLMtMj3GmCFx\n",
"WO1u9Fp57UlfRLY8ZHoMpULEpO9Y1TaZ3ocsHjIyMmEhi4eMjExYyOIhIyMTFp0WD7vdzu23384V\n",
"V1zBDTfcQFVVVYvHeb1err/+epYuXXrInZSRkel9dFo83n//fbKzs3n33XeZPHkyL7/8covHPfvs\n",
"s5jNZjlztYxMP6XT4rF+/XpOOukkACZOnMhvv/3W7JhvvvkGURSZOHGinHxWRqaf0macx4cffshb\n",
"b70Vsi02Nha9Xg+AXq/HbDaH7N+1axdffvklzz//PIsWLeri7srIyPQW2hSPSy+9lEsvvTRk2+23\n",
"347VagXAarUSGRlaneuzzz6jtLSU6dOnU1hYiEqlYuDAgUyYMKHNjsTHH95ck3J7cnu9sa2eaC9c\n",
"Oh1hOnbsWFatWsXo0aNZtWoV48aNC9l/zz33BF4vWrSI+Pj4doVDRkam79Fpn8fll1/O7t27mTZt\n",
"Gh9++CG33XYbAEuWLOHHH3/s8g7KyMj0TgRJ9mjKyMiEgRwkJiMjExayeMjIyISFLB4yMjJhIYuH\n",
"jIxMWPRoMiCv18u8efPYtWsXKpWKBQsWkJaW1uXtXHjhhRgMvorqqamp3HjjjcyePRtRFBkyZAgP\n",
"PfTQIYfRb9q0iaeeeoq3336b/Pz8Fq+/bNkyPvjgA5RKJTfffDOnnHJKl7S3bds2brrpJtLT0wGY\n",
"Nm0a5557bpe153K5mDNnDkVFRTidTm6++WaysrK67R5bai8pKYkbb7yRjIyMLr9Hj8fDP//5T/bv\n",
"348gCMyfPx+1Wt0t99dSWy6Xq9vuzU9lZSUXXXQRS5YsQRTFrrk3qQf59ttvpdmzZ0uSJEkbN26U\n",
"br755i5vw263S5MnTw7ZduONN0rr1q2TJEmS5s6dK33//feH1Marr74qTZo0SbrssstavX5ZWZk0\n",
"adIkyel0SmazWZo0aZLkcDi6pL1ly5ZJr7/+esgxXdnexx9/LD366KOSJElSTU2NdPLJJ0s33XRT\n",
"t91jS+115z1+//330pw5cyRJkqS1a9dKN910U7fdX9O2br755m7//zmdTumWW26Rzj77bGnv3r1d\n",
"9v3s0WHL+vXrmThxIgA5OTnk5uZ2eRs7duygvr6e6667jquvvpqNGzeybds2jjnmGABOOukkfv31\n",
"10NqIz09nUWLFgXW8bR0/S1btjB27FhUKhUGg4H09HR27tzZJe3l5uby008/ceWVV/LAAw9gtVrZ\n",
"vHlzl7V3zjnn8Pe//x3wWYtKpbJb77Gl9rZu3dpt93jGGWfw8MMPA1BYWIjJZGLr1q3dcn9N24qM\n",
"jOzWewN44oknuPzyy4mPj4f/b+fcXVoHwzj8pJGD1gvFwUEQRBEvlPoH1LVS8IKIg3gFdRUvKEZr\n",
"hwildbegg1M7B0f/ATuIg7jo4iyC4tB0qdKe4dCcaruc+OW4vM8U8pE8+fGFN4R8b1B3f/5o8bBt\n",
"23mdANB1nVKppNTR1NTE6uoq5+fnmKbJzs7Op3G/31/Tn/OvjI6Oout/f+Jbrlo6U+n/sW2b1tbW\n",
"T/tt21biGx4eZm9vj2w2S1dXFycnJxQKBWU+v9/vHL+xscHm5uaneVKd8atva2uLUCjkaUZd1zEM\n",
"g0QiwcTEhKdz+NXlZTbLsmhvb3dWeZfLZWXZfrR4tLS0OH0y8Ocp4/OpvaTu7m4mJyed7UAgwOvr\n",
"qzNerz/nu1RnsG2btra2mqwqvZFIhKGhIWf7/v5eue/p6Ynl5WWmpqYYHx/3PGO1b2xs7L9kTKVS\n",
"XF5ecnh4SLFYdPZ7ka/iisfjhMNhz7JZlkUul2NxcZGHhwcMw+Dt7U1Jth8tHpU+GYDb21v6+/uV\n",
"OyzLIpVKAfD8/EyhUCAcDnN9fQ1Qtz/nuwwODtacPxQKcXNzQ7FYJJ/P8/j4SF9fnxLf2toad3d3\n",
"AORyOYLBoFLfy8sLKysr7O7uMj097XnGej4vM15cXHB2dgZAY2MjPp+PYDDoSb6vLk3TWF9f9yxb\n",
"Npslk8mQyWQYGBjg+PiYkZERJdl+9GtLJBLh6uqK2dlZAJLJpHLHzMwM+/v7zM/PO45AIEA8Huf9\n",
"/Z3e3l6i0agSV+WLjWEYNefXNI2lpSXm5uYolUpsb2/z69f3/hxe8ZmmiWmaNDQ00NHRwdHREc3N\n",
"zcp8p6en5PN50uk06XQagFgsRiKR8CRjPd/BwQHJZNKTjNFoFMMwWFhY4OPjg1gsRk9PjydzWM/V\n",
"2dnp6fxVo2masvtTelsEQXCFLBITBMEVUjwEQXCFFA9BEFwhxUMQBFdI8RAEwRVSPARBcIUUD0EQ\n",
"XPEb+xcbgROah84AAAAASUVORK5CYII=\n",
"\">\n",
" </div>\n",
" \n",
" <b>mu:</b> <input type=\"range\" name=\"mu\" min=\"0\" max=\"5\" step=\"1\" value=\"0\" style=\"width:350px\" onchange=\"interactUpdate(this.parentNode);\">\n",
" </div>\n",
" "
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 24,
"text": [
"<ipywidgets.interact.StaticInteract at 0x3edab10>"
]
}
],
"prompt_number": 24
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For smaller values of $\\mu$, the first constraints is the dominant one and tries to keep the denoised signal close to the noisy one. For higher values of $\\mu$, the second constraint dominates."
]
}
],
"metadata": {}
}
]
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment