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@brandondube
Created April 3, 2019 01:33
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{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import inspect\n",
"\n",
"import numpy as np\n",
"\n",
"from prysm import NollZernike, MTF\n",
"\n",
"from matplotlib import pyplot as plt\n",
"plt.style.use('bmh')\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, we will show that the area under the MTF can be used as a proxy for the Strehl ratio, and that through the Strehl ratio it is related to the RMS wavefront error. The Strehl ratio is defined as the ratio of the peak of the diffraction pattern to that of a diffraction limited system with the same pupil and first order properties.\n",
"\n",
"First, let's see how the Strehl ratio is related to the RMS wavefront error by Welford in Aberrations of Optical Systems (this is an implementation of that)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" @property\n",
" def strehl(self):\n",
" \"\"\"Strehl ratio of the pupil.\"\"\"\n",
" phase = self.change_phase_unit(to='um', inplace=False)\n",
" return m.exp(-4 * m.pi / self.wavelength / self.wavelength * std(phase) ** 2)\n",
"\n"
]
}
],
"source": [
"print(inspect.getsource(NollZernike.strehl.fget))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"the `std` function calculates the standard deviation of the phase, ignoring NaN values. The use of microns for the unit brings everything into compatible units. We can see that, excepting for the coefficient of $\\frac{-4 \\pi}{\\lambda^2}$, this is a function of the standard deviation of the wavefront, squared. I.e., its variance. The full equation is\n",
"\n",
"$$ \\text{SR} \\approx \\exp{}\\left({\\frac{-4\\pi}{\\lambda^2} \\sigma^2}\\right) $$\n",
"\n",
"where $\\text{SR}$ is the Strehl ratio. For a zero-mean signal, the standard deviation and RMS are equivalent, and piston (a constant or bias) has no consequence in a wavefront. Consequently, std(wavefront) == rms(wavefront) for all reasonable intents and purposes.\n",
"\n",
"There is an equivalent equation,\n",
"\n",
"$$ \\text{SR} = \\frac{\\iint \\text{MTF}_{\\text{actual}}}{\\iint \\text{MTF}_{\\text{diffraction}}} $$\n",
"\n",
"which allows us to connect the area under the (2D) MTF to the RMS wavefront error. If the pupil is rotationally symmetric (and most pupils are circles) and the wavefront errors also rotationally symmetric (this is the case on-axis for any nominal camera lens design, but is (hopefully minorly) violated by the reality of sample-to-sample as-built performance.\n",
"\n",
"Let's test the connection. `NollZernike` is a class that lets us generate wavefront errors with Noll-ordered Zernike coefficients. These are orthogonal (and orthonormal as we will use them) over the unit circle. This means that when we put in spherical aberration, the required defocus to maintain \"best\" focus is maintained. In this instance, the definition of \"best\" focus is the one that minimizes the wavefront variance (which, from above, means we maximize Strehl). This is a good choice! Use of $W_{040}$, Hopkins' spherical aberration, on its own does not provide this for us, and is a bad choice.\n",
"\n",
"The below makes a pupil of diameter 10mm with RMS wavefront error, $\\sigma$, of 0.02 waves."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"rms normalized Noll Zernike description with:\n",
"\t+0.020 Z11 - Primary Spherical\n",
"\t0.067 PV, 0.020 RMS [λ]\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"pupil = NollZernike(Z11=0.02, dia=10, norm=True)\n",
"pupil.plot2d()\n",
"plt.grid(False)\n",
"print(pupil)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we will calculate its Strehl using the function defined above, and via the MTF equation"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.9469344297567935, 0.9691028612720589, 0.9771247899462738)"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"efl = 28 # F/2.8, arbitrary and meaningless here\n",
"pupil_diffraction = NollZernike(dia=10)\n",
"mtf_diffraction = MTF.from_pupil(pupil_diffraction, efl)\n",
"mtf_real = MTF.from_pupil(pupil, efl)\n",
"\n",
"# convenience function, needed since the samples are log-spaced\n",
"def integrate_mtf(mtf):\n",
" return np.trapz(np.trapz(mtf.data, x=mtf.unit_x, axis=1), x=mtf.unit_y, axis=0)\n",
"\n",
"int_real = integrate_mtf(mtf_real)\n",
"int_diff = integrate_mtf(mtf_diffraction)\n",
"strehl_mtf = int_real / int_diff\n",
"\n",
"pupil.strehl, strehl_mtf**2, pupil.strehl / strehl_mtf**2"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The ratio of the two is .977, a good fit. Especially considering Welford's equation is only approximate. We can see (perhaps) how the area under the MTF might make a good metric, given how much is known about RMS wavefront error as an indicator of imaging or focusing equality. \n",
"\n",
"Let's check if the two move together when we increase wavefront error by adding focus"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"def make_mtf(focus, return_p=False):\n",
" p = NollZernike(dia=10, Z11=0.05, Z4=focus, norm=True)\n",
" m = MTF.from_pupil(p, efl=28)\n",
" if return_p:\n",
" return p, m\n",
" else:\n",
" return m\n",
"\n",
"def make_rmswfe_area_under_mtf_tuple(focus):\n",
" p, m = make_mtf(focus, return_p=True)\n",
" m_strehl_proxy = integrate_mtf(m)\n",
" rmswfe = p.rms\n",
" return rmswfe, m_strehl_proxy\n",
"\n",
"def plot_ratio_of_metrics(values):\n",
" plt.plot(*values.swapaxes(0,1))\n",
" ax = plt.gca()\n",
" ax.set(xlabel='RMS WFE, λ', ylabel='Area Under MTF')\n",
"\n",
"focuses = np.linspace(-2, 2, 50) # +/- 2 waves RMS of focus error is a pretty big range, but this is no problem.\n",
"values = np.asarray([make_rmswfe_area_under_mtf_tuple(f) for f in focuses])\n",
"plot_ratio_of_metrics(values)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see two lines because there are both postiive-valued and negative-valued focus contributions, but the RMS is always positive. The curve looks a lot like $1/x^2$, what if we manipulate things to undo that?"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"vals2 = values.copy()\n",
"vals2[:,1] = 1 / np.sqrt(vals2[:, 1])\n",
"plot_ratio_of_metrics(vals2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now things are proportional, less some wiggles. We can conclude (with perhaps a lack of some mathematical rigor in how easily we were convinced) that the area under the (entire) MTF curve is inversely proportional to the square of the RMS wavefront error. This makes sense, given our bridge through the Strehl ratio, and knowledge that a high MTF needs low wavefront error.\n",
"\n",
"If we maximize the area under the MTF, or minimize this manipulation of it, we achieve minimum RMS wavefront error focus.\n",
"\n",
"Now, there may be ripples in the MTF as a function of focus. Let's plot an image to see them."
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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DgRNQxBIo+h7c9ZpLoT0poO4n76SaLDmxFLp+XPeJzP1UJNeZSylmS0DGu9wzuw6XLVumAgO+ggrSXIZXIbCDD2nZDTVVolyeFniLuS54dv6hJL1j5S5upQ0kNtnkLHIxFgURfTeAzwTwCUT0CoCvA9ACADN/O4AvBPDHiagH8BzAW3lUtnUsTkuNO2Ihsj0loEAIYABOLQEBC8gdutdSHlb3qe/AfZNAxXiKFNqqZUGiupRS/ScUBQQdASyAIS6dkF1QS1FQ8GJUJKJaLYToJPpJQYUdpt1QzADK5LrKFTWwLFBZJIWrbc7CqDLFR3LbaKdDcm5gOHVY7wZkm7ygcjFAwcx/+MDxt0PCZ1eJg4CEh9R6cj4ieEZsCNFyJYAUfUTFf5gdgaySrCv6a1uV2MhIJ2hOBWufCrMUOAQBEI5IYBEdyGu0lSMNb83cw5QLSohy5RMWwCK/8RnOogAL2Z4GCzk0wSFU2dyzUvMPU8pxLgv6UMHDU8p953ZsILHJCywXAxTnEkcRjdN2qFZBtlEQ0PIaOVQVyVJgBQCp6eTAPZR3CNnNoaU6RLEXhQItOqrrwGhBVlYjgYUXchpQXkEzsAMSiV2WEQGAUX4FkK0DswRKywU+cxaD8h0xWQ6Jt5CNdDxZF8ZBHMNd2Fym5Jd4h1rOCQwmm5WwySZHy6MGCisK2GjfbLgcIgvNk+C+FyUchHxmEo6CvPEUDdC2oL6XSaOGylKbGR4FFDSNuLO0thMAkAtaW8p4Bk6lPYgIPIqCqsACUBLc5zExK2lzYZHLJDcRSRhtXRcqn6RPBUdhyr+IihqARS2HMrJrsDiHDLLSpzibO153A4FNNgHwSIHCFwpLyoxb32zhKWID8K4B7XZZGVjSndZ8AqlVYYl3jX5UmidBPmaS2UEsiaYBpZLj6n5yBIpNDpV1BASI4odcahAFVfEVpOuQgoMSMZVDWy2/gsHwut8X52HohpKT8gdVAMYALIAEMoDxKZg4v9hvbik9d/Bcnzcnd4l42kBhk03OJi9M1NOx4oUChkdESxFey3iw06S7VkJdSQHALArZUMK7ceDGg652AipOek8Mku9MNPQVbZPzIrRQYOpVUURAlVndKQrKMrCLbnhckslmuZQJfkVxv6W6UKnRUp1kV55ra07vKVscsx3x6rnm5C5Jd+dU4lu01CabHJRHCxQmniIaF9D4OHA9xZ0X5d+qpRClN4Vx1Gxg4T3QtjKOKLVH5fpu2kqKO7FA6jaobDkWQC7q50z5+4ECFddVxKh9quVtlOBS5zFY6GzVP2Myi7vkD2qwmAiJPQgWJmush/tsejQnG0BssskqeZSuJxNHLH2ziYvmRVoccOfBVy1w7TWU1Wo+WT4B5LnxAhJNA+AmlfOg0kKQiwGsCXXeg9om5y/0mthHQjIPiG1i5UTcgGgekNuaV5EjtWLiNwTZsmJOBDcABGRAsjXWEVGVy6bOxB6U8Ci2ByT5VBTTbYjpuxQOPFY2kNhkk9XyqIECADwxGgoKFACXhLblPwBaSTYCO8UKSE0oblwmvp0T1w7CsJmRKTOzKkquIvZqVYiFQBqRlLgNJnGSMct6UJDhat4QkEueA8NmR5ZjUYgR6eJyqj6QGizSSdNJdYm/qGSQd0E4XcTSXYBhU/6bbHIWedRAYRyFI4YnBvmYLYpWy3RoOCv1Aeg1QxukzeKU0NbMa/JOKn1Y69MQNOGuTKhTq6IVsDCOggOAXnkJ5UsA6B1/VJCAzq8RVlqyI5HbVtoDyJFQCFKCvAiZlRdqaVQlP9I6NadjEAE1yLkwiYtgka45R1yvjUa6izvrrgDxovXL2ABxk3uWC3AUn1ccRbRqUZCWGueGEHdKaDsnd/NdD/Qh8xREqZERey8uKGt4pKQz9/0wWgoYWhVaLwpA4g7YuuBVfAV5l7gNKqyHQUlyA4uCsyCzikqCO51cdb2b4S1mS3+UU02VDFExsns1hzGe4Ljxg4XdUmmequTIQ8iLuu5NXlh5tBaFI4Le/8MRo3GxKDWune5avdO2ftZa9ynFsiaSWpsZNVoo0CyKfZdLfXjK7iRotnbTAF6KCbK5onr5g1Pb5Dt9c0ch5IS9Mg/BenIzI/e2oKF1weoSK5sZacjqoCjgJG9R5VxMFQjEYf6iOjjkQOaaHun7S+eU26eWTblussmt5NEChYkHi0Wh9Z6CZ7CnFPmU/P39HuiuhKdgSYpjFs+NRSZR2wK7XY5i6nvQvhOi25V3qMo3MKfxQI6ASjkaXlaYSFwtR574iFCQDxwlN4NcJrhNinIfKdsbQ3KiVPIpm3uQyY2Ku5iq2RSrzSJhL809446amu/A/KtkRKLz/LFzyuYO2uQRy6MGCk/SCtVrGY+ygmxQi4K9JLNx14O6LvXPTuLUSrDop10L7PeAVZ71XgCj5ioisgtqt5P9vRLbNp5oyFcoxzHkK3gYugrN+AaGVoWBBWlBQ+Ihb8HZRVbWiZrnLgqFX0rFX8iYecBIp8UZ99JUTak5uY/EuznZgGCTV7E8aqAAAAfhKBqK8D6iM/dTC4SdS3fv3EuDIooRZW8K1lLi3GgyneZU8L6TpkNdB/St5FoMLjwktlMIrtV2UsuiLL0h11RFbdaJEeEIhSuqIrhLMUuGJMMbRWkQOVdI7gFY2HrtubAGBlngtVSFAiU0d1pRl/tn+Y5LUsaXtJa7yKSr75G8t03uTR41UHiIReHAaFzQwoCsHIVEPlnPCVgIay+hr2XoJxOAxgmv0DZAuwP5G+UdokQ39b3UdDIFb0pUCwBSZKAN2TqwRDyn7qYyvwISGZWsCisImPoXaac7hMxZACNCPQFGQM63KJTEIOeivONPrihOXMNig6NCDAQW+YtS1hYQvC830mNToo/t/WzyIPJogcJraT0PRut6NC7mpLtGy423EvmUcilYIoooFmUdSIhsYhQ5FR5cFArkrgca7YDX+AwWRmwrAW65FaTWgSTUKSGuq4WtxRXvIlWaLcNfM2cxILnLfIuiU17Ot6h5huzSooKrGEhdKLDOm5iIWlqKkhrJoPT55jraZJNLk0cLFCYO0pOiIQWKMvKpAbj1cE2TwIKCJN5RZAmPBWB9tKFFArFrQbtWyohbqY06AgoYJtVZbgVzPq/IvmboXTjTEGgqzmLEPVikk5HcU7zFIN9ignuw+TQiatDYqBQqcy/8jDtqIociWToHwmCPCZM9RHxvwLDJJieTRw0UmSOOaF2Ad5yAItV8ah182+Y78Rgl8S4q8UtQlwikmZHmOVgEFN8UZT36fhgBZVK5oNhyIrQRUQIL57R3RfEmVDkLSBScRRk6a9FKU4l5en1rgJR4C2/nlgl6wIC/qBX3DH8hy1ggvYu57T2VsuSmmrVM6gZJU9c9hbwo3fjOKWs/gxf5PW6yKI8aKAApCmhkduMDyEqNt7k4IF+1WnI8Aso5UB/FokiJWcY5kFgGV7tU84n3ndyxdz246UWhN0UuRumCArI7KUUjqZLX1qzSVnWYY0HkUutWAjLBDWSwKHmL0d18xVswj8NhUyXVKvfCFHuttEfNjjKncUzDoiUS/N7k3BzIi1oGfQOJTfDIgcJTLuPRuoDWRTgvHAU7ErDYOeBqp2GvnZDSXQ/qGlDjCvcTDdxPbBFQWnKcQ5SoqX2nXEFBbAPZBaWJeGS5FV1uiMQIoBjB0bKzfbZOjLNwlMEGGNZ5YoliYigxr02MkrWkrqia6J7LnUgKvL5zn3ERDQsGYjTf0rlHcRpLcu5mRg8lc+u+bwX9ogHCETcsm8zLxQAFEb0DwOcB+GfM/GkTxwnAtwD4XADPAHw5M//IoXmdJtpZYUDnInrP4CZnaMddA9+2EiIbIuimA652Us5D3frmgqLGyd12L1wFug7w0iUv9aroXCa2SzEehFmARndbDwruWMNqy8ihyjLRVqolWAx5gexOIlZXWVlipKhACye8BjMp90EjhT3qU0EOA+I77cvXz8dmeIwpOSbZbqox0tQcLyooHCOH3uNaJTkHsC+qkn01fPdLcmKAvBigAPBXAbwdwDtnjn8OgDfp49MBfJs+T4pTR79HTIUBGxfhfASsd7aXXIr4pIHftcD1dVL06HpBkkpRW0Mj0tpPtVUhwOG0XSrlKCb74XqnF1dlrusVN1SXS4tb9rZxFknRa34GFCysmRIwrCXFLAAA5Te8H+dcWDOkGMWllgCjLjBYhMRqaZBBocCqM97gEm4MAKs65tXrHE4wS7afTO6jf/d9yG0U5ot8F76Uqb/JreVigIKZv5+IfvPCkLcAeCdLx6AfJKKPI6JPZOZfmDvB1EZLPVoKaF1A00TceEZsGLElhB0hXokrCd5L9FLXgboeFMxnXySLuSoBL7RAH8TVw/tcYNB34vZBk8ECyMq5aZAS+gDpZhccELUmlPeiwEPQSKgiMY6cpFokcpk0hDYM8i2MBzmYc6H7BKCGiXpA5d5KH0ScB4tSJuo3JT7Djj8WpbzJw8iWVDiU8r99os/hYoBihbwewMvF9iu6bwAUv/TBgDe/7WVEMHqO+Jy3fiw+7Q+9Tghty6VoIrjxmnQHhCsHvmrgiBBZiwP22l2OkT5sJkifijJU1nsJlU1WhZYf7/qU1W2d7JI4gsGYuH5Ye2JHsClcS8gzt5GVOx+U3dDEPEfiMoPerVfNjAbchVkyU6ABJHdUHSGViHeTohvfACxuI0sEeK0ETt0ZbwOpF1MuhbO5NDmTy+1FAoqpT2D0q3jdaz1+6H1vxLO4x4fiHi+HK/zsXsjsnevR+CAhsi7XfIqtA++0i12M4qrpxaKgEAGnZT6Mq3CZq0DbyJ3/rhWCOkZxQe33orjJiVIuie0iEkomZtBOlbhZCYDmaIgiI++E5G7VHVaS5LEIoU2fDE0rcQuUqhP1yrUBQ8AI5kKa5hzW8BBTnfIG5yXXVbHWO5Uff8EA4NWu4NbKkiK8hM/wUDDFfV37xPIiAcUrAN5YbL8BwM+vOdGlMh4R3rGEyDZaRbYFwhUhth6+0WqyXSe5Dl0PCo0UDiyjnwquAm2j3fHabE0wZ7Dwmm1dcxUTJcmJIxB86pXNIRacgx/nWpSJeRVYcAiSK1HwDAOrgHiYqDflktL9RnjL7orcxgThDaBuj1oWBTTQmA+JrdvyVdeZPrhw7Jgs8QciQR9SwbwIcirS/lzy0NzImX+3J7bjzyrvAfClJPIZAD60xE+YSHgsp1yK1ocUIpuintrMU6RyHn0vPEUX4Kz0OJAUNDvrUeFSZVlqJR+DtFAehwje76XBUeIxivwGIgGgphE31tUVyLK+LaTViGkjy423CDpfGLqDUgOk3S43NZpqSlQAB5cNkZjHP3Irs06U57NGSVTwFJQtpPTMC8BypMwCy1zi3dR7OSQPrXCA/Nu4pMidck314z6uNye3+Y5PLZf0PZ1JLsaiIKLvBvCZAD6BiF4B8HUAWgBg5m8H8F5IaOwHIOGxX3FoTk+kINGjdT2uXK+5FAGhYcRWCe2WEHcOfLUDXV0JGa1lOeim1Q53df0jAQpuGIgeCE3Oiu4lXBbaBY/2ndy5Nx4DcrtM5oO6sEqCOwSAfY5q0n0MiAvJqVurJLuN6LY1staY0hIek1ndxMJfaBMnqjiL+jVp9BSndImcnDfIx6isirvKyXItpuRS/+yXQtTe1zXXfA8PDQwml8KT3MNv92KAgpn/8IHjDOBPrJ3Pa9kNZz0ptIJs6wO8Zyk3nnIptOPdkwbuyRVwcyN37zc30s70qgEFBzifdSypn13vrqllUcp9C1yp60irxLLxFdwqh9Dk4oGpymzhmoES3G0rPMLwcxAgghDSrIUApTR5SXQDcE3O9tbyH7b4QZXXmr8ABtZBAo6yhhQyYFhobS4NYlna4+9lyiq4EwDMuZzmXAF3+VNdSoTWpYDHqeRFzP6+lBuLe1rHIlAQrWYTWRX5RYq5nlqt+dQ0AWiKcuONRD7FqwbuaiekdncNvtmLG+dqB9o1oqTtXRLJXXijlWXZD0ltdTNxJ30umFmTs4WTQKwioSqwMIAgotybGwoU5jIChgUDPXJUVMrb8Nm6APTa6mKa4BYyjyHtWI3HgKMMDBVgAChyMRhScmQmVwLlbq53zH6Hs7KPTouyAAAgAElEQVTmJ1pWpb1r1NTa8+8bUF408DhGwV3a+7h0Qv0Mcsii6FbMQQCeA3jN3ZdzWnEQkHCIcBTROAmRbVwENVFKeWhb1NASwhMP/3QHd3UFfn4t/ELTCFfRR1Dj1DWkF1BiOzYOjtUFFRkUd1rPScho7hiIGi5r5HZJGpc/PMveLvMstI82hyAWAofkjkogYc+pt0XxQZADXBTXk1owg5pP8Al8ABS8grRUtQZH5moaAUbxmgAtE2KggTy/ySSnUF17Sm4bKnvqkNo5uQRro5SHVmh3vdu9NKV7aYT6ms/3RLkUh4DiOYBPPbQUAD9655WcSZw2LxKLwkJkI1ziKIC4A8KOEJ44hJd2cFc7kHWxU46BugBqPdjyFggabSRRR+aCQovsLopRwmuDdLVLbiMt00HBifVS14Xy2SqQ1qYRCA7Uk/ITUXgNJaSJROkDAOsPg4woBxLpLGkXUebX9ZBZF2XdJy5+XEV1WutTMQKMGSm5jsxncHLhjPprLxUTPBIk5ojvO/MclwYGt5VzR1k9JpC4RN7knl1fh4Dim5j55w5NQkTffKL1nEU8GDvNzt65gF3TjwntHdA/cWiupJqsdbGTGkydENutFz1GDgBlzpaQXFAShaFVYkNMiXiw4n8hAJ3wBRISK+MHDY9K7iLd/avrKDLQcnFhfWlKX6/Bdrdv/bMt8skUrIGGEt5QAj2V/SgU6igXwwCjTmMpe2bP/ZAnmiPlMh8+cxsHGiNNyap2q3NyXwBwaoVyCoVxqtDO267lkkChlEvlTh6AH1kECmb++jWTMPM3nGQ1ZxBPrHkUyk9oFdlEaPshoS1Z2i3c1Q583Ypit6qwbaM9KVzV2IgENxqXPD6i6yIoPhmU2QAA3u/FVaM8hnEIgyKCpXXBGhWF7GZCQU6bi6fkL2QOqeMkHfQ8UPeYKK0MJcZJe3kPOIxStCx63izGBFXW5HIU1ZwMjlkvECXDgQEIHiMHAWIOEC5VWR2SQ+u+jVK5D0V06Z/3pYLEA8nBqCcieg0AMPNHdJsA/HsAPg3ADzDzu866wjuI0bweEZ6E0L7SyCchtGOyKCRMVvpoxycN6MkOdL0DP7+WchzXNwIUjYNzTvptCykAQFxPhIKvYAbFRvpbRHX3qCuLmYH9Pitt4yF6jN1QJWAYWJADxZAKESb3UYxgFH0uIOG1BjBgN7QuTBKHQcnCKOcEMhghuuTykgNDboGZYGVFoB3zAIxAY9LiqHkNkznlv9YKuI8GR5cq5ft86Eidc7m4TjnvpZPsD/QdrrHp3wXgC4rtbwLwjQA+CcC3EtGfOcfCTiU54S4XBmwVLFwbwa26n3ZA2EmWdnjSgF+6Aj15IlwFs7iervegLqQOeMnV5JB5CkfgRooGcuvBuxZ4+gT05Ikk1DWCzWyVXjvpgcHWC6MPuc6UiQGHd0DbalLeLifoWUFDqysFXZcWBUztWpUQT9tmHZSKVHtYCOnuJUTXuvoZ76FJdlQDTrruBJDU5ctn/mSkvMwwl4OKJk7l4BcpX/RVLqdSqudI9rvNfK8ikADW5VH8bgB/FACIaAfg3wfwFmb+XiJ6M6Qs+F863xLvJg5SwsNCZHeuV54iwPuITgntsCtJbQ//pAU9vQK6DvT8WkJUb/aSV+G93P3WLU+BVAtqEOqq1oZwAFFrQqlCZRarA3tw9IDTbGquSG57OAgzzFqHigjsPMgr9wFoEyQMXUQlh8F6vMqPSEBgJTZAMldR3iNHS1GqMDtqelRma5diYGEk9rF/tinLosptGBDk5RiT5Jab+dMdKkp4H3JKpfrY5KGsh3Nc/xh54O9yDVC8xMz/n77+3QB6Zv5eAGDmHyKiTzzb6u4gDg5OP9yBRUEBO99L3acmomsiuHXZ/aRWRXzawF3v4K53cre/3wPdHti3kmHdqDJsPTjw0FVEkPIeJmSKF0pe64/NEuBCSLWl4DQSihnEzahbHjsSQrvIeiYK4JivIR8AzSvmMtPblui9Rky5IsGONH9CB3kNr7US6OaamuMz5mSqNtQhmbMeZuaYj3o6YIXc9/9xav2PUcGf2kV0F7lv0t2ud99BAieUNUDx80T0O5j5xwH8WwDebweI6OMA3JxrcacQby5+imhJynjsCp6CUuQTS28KtSr6Jx7+qpUIqOsG2O+lbenNjQCFEttmPaQIIFPmsOgoDL5oKslr7ahnpT6SAm1DJq7VVWVgQZGHc6b9MVkJ5L3mW5SKfCJhr1TukdWSYQEM5zJAACMrYxY0ChlYDHPJfdW+gQzAIcwq//HYhWF+4XpnkkWC/dzus1O911MouWMV3iVFiL1KLQmTNUDxTQD+VyL6ewA+G0O+4rMB/Pg5FnZKKQsDCqHd48r3iacILYOtN8WOxKLYOYQnDejJFdxNB3QKFPsO7G9EGZflua2cByB8BUg0feOAPsozewBSNJC0Si26DrxH7mVRuEZSf2yn5/ocMpvE3FFw0m3POaARXkKq0QoHYQUFKQTJabCaT0ZC23yWg1ECBtHQYlBrxSyPMhQXhXuLACHYmbOFU5fBWEy0G5YbH5QdKeVYZXtX5Xyk8l0EuMnpT+leOc4SG4+7a94JP4yyO+U17/IZ3MWauBCQAFYABTN/JxF9AOJ2+mZm/rvF4ecA/ty5FncKEY7CXE/ifrryPZ74XniKJiC0HmHn4HeEcAX0VwT/1MHfePjrFnyzA/ZXEhLLLKGyzT4rgCcNuPXQttP5wlEyt0cd7pSYJl+4eRLZjKzANfeCibSUOWnVVhpnd5vp1HiNuOJUaZZDFA5D8yus/pMof6sYG2XxmoE94DMqLgNh4UdvJUKKc6aKCAIo+A1gwHGUUii6OwPEbeWMFshZCx0uydq6VadwGd0nWDw0QNxHTsqhXvFnkFVFAZn5+wB838T+95x8RScUrXKULApPjCeuE0Lb99ip+6nT6KdwxXB7sSj6PQQsnjegl67gul5KaGiIK66vswvJQbrjtZqIZ2J37o7AFmBmSXSk5TnIWqGO+YMUbUUEoJMqtt6JuyfI84jwTtdm0czOgTSzm50HUT9cQyiinoqigiWfMQCzWkqrakrUKoF9MrM1ofxKF9QJZOUf68GU+H3IUfxQ8f3eVvGd23Uz9xuc+u2cqnfJmuufcp65/8E9FKtck0fxjkNjmPnfOc1yTi8eUsbDKUeRS3kEXDW5nEdotZpsKumhXMVLHq5rQfsrUK9+/+sbyauInJv+OFdYmYXSJikeSAYWTl09FgKqQEFKWpNyFSW/wGVtJe0xwe1OiHE0A+siub9AEhVVlDQnCnI8OJA1SNJGS0v8Aoehq2jgArKCgQUg2PUmX3uf3VL2BaVru9G1D8qRORa3bn60icilhJAeWsexNxencC/ddc7bgER5/Iy/3zUWxZcD+IeQxkH7s63kzOIRsaOQCG3pTSFhstdNQGg84s4JSFwR3J7QP3Hwe0bYN6BuB9drUb59J9nVIYiSbEVZExGIJekOTt1QFq0EFvdQhERMkdLf4huT8xuvSXlBEuqKyrPpbt57aXQEgLnR4oNeAMhLtdeBmJvKynTEOMtjlABlvTUGSput416VXGcVZjnzFpP9uMs1Db6cYUc7qv9gSyR5Gd1VrDO/nPizPrbs7Cm5BP/2KdxWa9/H2irCk/vPYEWcCiQuJFdoDVB8ASSP4ksBvBvAO5n5B866qhOKJ4InTlVkWwp44jrlKTpcNT3aNqDbRcRdRNx5xB0Qr4DQAX3n4HoP6nephzYZCR2iJuLdgJyU7+Do4aIk28G7XDxQa0OxgwAHsfw2dJuck1Ib3oO6XiKiAOUbJKKJI4MQNLLKgdCnIoHkHdBTdgVZTkQpjgDnM0fQcLImOApQ1AQ4Gc/BLOdRyWvoa3MbHaowe1vlZbzHGjl0V/VqydKeek8PRSrf5511LQd/Dydc223mvHCAMFlDZr8bwLuJ6OMBvBXANxPRayGJdm8vciwuVry6nsyiaCngqdvjie9x1fTYNT32bYOu9Yg7RrgCqCe4TrgK1ztQ70GhBXVXQmb3PXCtRQNv9mJNaD8K7Np0bSsgyEQgx/I6QsNf8103OyfhttpfmzqX3DNyFoY/QCOMtYkR90WpDOfF0lGX2CBjuyS+0yI552aEINVqIycCHFrmHBa9pNVwgcL9hHpKtS7WKvgFmXVFreAQyBHunHx3nwr2nKB1CgV2G1kT+XNKhXlqDuLU4LA0710A4ozup9Ud7pj5VwF8GxH9DQD/MYCvB/B/Avjes6zsBOKUTXbIfSl2ylE0LuLKS5jsVdvjug3odwGxI8TWS6jsFeA6oA8E1zu4vgH1O/j+aXKPWGMiPI9AH0Cp/MZVJoyBbD2opA55ylsQcbI2EtEN5S6aBtg3OTfC5mCWCCTLYzAxHqOR0h5DwMCQ+E6uIs7uKbMWgs4RgiT/hQAEP3BNzQkzr1fwSz/uu4a+FuXMx+KLYVN34Mdd+k5yCLSOnu8EkUpLcpt1rjnn1KHL9+H6OoVVcmEWRC2rgEI73X02gC8D8HsB/M8APkujoU4iRPQHAHwL5N/7Hcz8jdXxLwfwFwH8E931dmb+jkPz2scvpcYDHEVcuQ5PXIenvhP3k9+hbQL2mlMRrxixB4JaFRTMqoBYFSHCGSH77Lk0OEpd7WKOhgLgmKXmkyMJly0DSAws7HdGVQSTd0DjQX0jNZf6Xq4RixIgRSe91J/Ca0JgZMBHyRI3wLDw2onyI/JBKZ8RC9BwmojXCFil40Udp1w0MGayelRQUJ/1vLnCgkMiPP8JbxUee0wi3jFywju31I/jlNc+FcE6u4bSSjshj3BbOaVL8VyE/QsIECZrop6+CcAXAfgHEHfTlzPz9SkXQUQewF8B8PsBvALgh4noPcz8k9XQ/4aZv2rNnK64HZQE6tL9FHBFPXZO8imeNB2u2hb7tkG8cog9IfTSKIgCQJHQ9wBFB4oexDuACCkYNgQht9UdxJTzI4hbcGApEmg1oFwGjJLwhmOtrUTihrIQ2JitFQpSNJC1zwWhT1FRnMCj+CCYQVobKuVjpOsVwJQ+uIIcrsJuS9CQqTNg0Bx4lMR4mUexdOdXxt1zPO7PdGRy20GZc2/dhTwdTTW/5mlL5w7XPkWo69Rco2Prv7Oj3/940MS+M3APt73GEQCxJjnzIcK211gUfxrAPwLw0QDeBuBtdYloZv49d1zHmwF8gJl/FgCI6F0A3gKgBoqjxYOky52WG2+pxxPa44nr8JLbq1XR40nT46btEXqHbmdgwaAgtY4MMETbNWAiNBCLgawvhLqGJGKpEwXZB7EKWknK49aDG5czuS2sVcwQuYN2LD0vgrRf5cCg1kuGdx+kNatzQniTG/AXbD0hHGXgAsS6cASEOCxmWJQBHwCIfBHDD5NoEKFElRWRgAMYg4dxIFM1ohQ16z/A4E8z9cc6NSiUciGNj0Ycy/oTp/cPGkIdYXXcERSOyU6/dU+RY+Wc4DA1/x3AoR5/32CxBii+4uyrAF4P4OVi+xUAnz4x7g8S0e8B8NMA/hQzv1wP+KUPBrz5bS9LXwYAf+SLn+ILv+QpnJXwQMCOAq5chyvXC1A0HZ42Ha7bBn1wCL0ARewJMQAhElxvdZa0kx2JtYDwNLuhuk4UTGTpitf3wI2GvRrJfbUDWg9qHGLjpKpHQS6n0h8A4KTjGzUM9AXhbeG0nQN5yY0gskS8wpywH2qMUmYjWJRSIRouS0S5nasCwiRwTOVHlBaHzQk/BI8l4ABSdNcpZHUexm3vVieHvSCRU6vcdcdOeTfAPktuy5TldG5gmLv+xGd+18/svsFiTdTTdy0dJ6J26fhKmfrU6k/hfwLw3cx8Q0RfCeC7APy++qTXvdbjh973RgSO6BHwLHa4Zmlc5HnYP/uJ63ClXMWzRqyKrvHo2iA5FYEQggMiQIH0zpcB1rDX2CS965wD3eyBm724hazgnypp2rXSk4IZFFsJo2UPZiePiR/OgMMocy8snNY5oAlapLAF2TW5vFsf5kfIxOoKKrKymaSkiPWegOslE3wKNGoifO4ZKEjvCjgACcWtrJCDfStqMJk4PujVPfVHPya3Ih2+bCC4q+J5CFmd47JGWS9aPPdsOaT9rtq8h+/oTJFPq6OeaiGiKwB/DMCfBfDGO67jlWqONwD4+XIAM3+w2PyvAfyFNRM7kjv0YWHAPvXQfuo7PI0dXmr2uGkadDuHLnjE6BACIQYCRUJOTib9EallgUYY88bBPZNeFXSzFwVlEVExK+lUYC80QGBxLdmDKENm7d4jkralcGBW66JxMo9yGFL0L2qNp5jLl4cgCrtoWsRsfIZZININz0JkpSps4a7yDqkTXmlZHMqTKC0SQBP+kD7DOaLb/qhUH7NM81jwJCYxpszvwfXsM7T9qW93Sci64fXrt/EA5v7cOm554mkXskYWFNYqkHio/JYTcg+z39cJghfu8ze5hsz+FADfCeB3AvgZSOLdpwD4VkgE0ik63P0wgDcR0W/ROd8K4IurdXwiM/+Cbn4+gJ9aO7kngmOGI8aOxfX0hDq85G7wzO3w1O3x1Le4bjrso8e+7RAj4SYSIhMCoNxE0uLCJZBYAtwQmsbBtw6+9aCPuKzgmMEISQFz10nYqypwOHFNiXXgwF4UqzVA4vLumORaAEANg6OAlSTLtZKYF9SFY8DRazRWL6Q39b2Q5B2l/Iy63Dg7sQQkC1vbpxak8hzHUX1fq76bNK6o/2TryIMMPAoFr8Oo7KCn/MkAPGrrJr3POHT5pWNV+FOxjsXIqPss/3EupV8rtdsooRWfw2rltjZZ774TCRe4h5MAw9y5D1hiZo1F8a0QgPjzEOX9tyFVY7+Mmf+3UyyCmXsi+ioA74P8U9/BzD9BRN8A4O9r8cH/gIg+H9JZ+lcgpUVWiyfA87jmk7meXhPFoug5WxQxEvZRXD9SMNUpVoiiZJIIpegdYkNoWgf2ToDJynMX9ZtATsCBSO7yrZOHgUXbCOntPchnTiK1WDWLg0i4DI/UCxssipACKyB4UB/BrUVMad+IvgH3PahpxFXV9UNeQ9eTxPpcsEPNbyyBgXxcNAaSGmAG16Vp5WTmdLJiyoN+ABwSnjzBo9hhUzxGypulN3oDNm68nOn8kWlFcHQXv1PJbZT8Meccay2skSm3yVKy3rkAYg6gZniHo8O2l6zCQ71LHggs1gDFvwzg85Ub+H4AHwbwycz8yikXwszvBfDeat/XFq+/BsDXHDuvRD2J5OgnKTv+xHV4EnvcFFxFzw5d6xGYEJgQI6FX3jVILGtiT5gI7IWqYA+wd2DXgL1YGK7xoF0r5cK7Lvnn2XIhzBUUo9SLuroC7XYCFo0X8Gg0RFZJbOmcxwpU+sZIakwxtDRIkH2sJb7JOXDjtdRHkGv1mnXdhpyXAeQfYvGDHfEbtn/KrVP/0MuCgfo86KBXAkn5H1jrc7Zs8eIbT1ICiJ2aF6/Dqz/1wh91BDK1TADILAAdkiOI/UkwmlNGJwCDWSA4ReLkVOY8cD6eYZZfWHYrHQSH27oIy/NuU3ngTLIGKHbMfAMAzPwRIvrQqUHiPsQBidAWjsIKBHZ4iT2ufYuOb9Cxw14tC2YCqzbuWVw1gRwAqWnEjtIzyLYJ7EksjJ2He9qCrnvQzV5rOIn7CRGS1X1zI+XLrcbT0wCKV1LdtfcSWttEcOO0HpREKbEv3T/6JtWqgFMw8xCXFhEQSQsKCmCgFT4jkc1hGLaaChGylfeoSPGJXArL46iTsdh6aJuCrYBDdhXgAQz/eIud7RaO+SXXxYyLac69VFsqk+dOn7xoVcwBgs214twpy+5WlsxaYDiWcCaaB5ElALlt34U754cciFI6MlR70fJeWuuUhf1AVsUaoLhSF5DJ02p7cOd/ieJBhSURE1g8oQ5PaI/Oebzk9ui8R88effSIEH4iFqnUvWvABAQC2JNaEQRuoODAiA0htA7NFSE88fDXHv6mhb9uQTcd6LoD7b3Uiep6rboqvS7Q9+IOIm3246Uon7iSnLixnNO6UUhKVjrR6SInwgIFVDzIsQBfa6S1mkqm7C2r2gDEwEMBY6prnrVB5RAkKisAoxBcEyPHgRSWm7K3DTDsVFfMUfe5duP3eGeZc3uZLP1Bp8jx8lTLlZm88x+6+SZOzq/r8xfOnb3mgbXWcmeQKI9PKcyRq+kEwLGG21gIX10EhQlAWMvHTS9jxjVaXu8CgijWAMXfxDAi6V3V9sO/i5WitsAgn+KJ69Bxg87foGOP6AmhHX55jqQW0w0BPTGi8whe+Ag4BQsHxIakn0Urpcr9FcM/JTTXLN3ynnn4XQO6bkGNhKE678E3GrnUtpkwtoxmZiGkB30lsr+frfgfkRYEdBk4iugkJuM4CgLXFwSvXSuo1VAABdmzVphFjPlhVkcI6lbL/S1SYUBgOomvjIZa+rMNXBDuZL70kayYd32OxpF3fbcFvAPXWQSMFXerk0UVp3iENeufCTIYjpkCyxnwWCJ5DynvOTfSjCU7+/t0C8B2SKZclUTrf2P3KGvyKL7iPhZyDnFwcGAAUcqNG0fBjB0COnVBCVh4dP4GESSAwS5ZFaUQMTqSm9zo5E7YeVG6LgEFwXUKGHtC2DGaa0LTEuKVh79q4J40cLtW8iv2Xe43Ud9BWihrp/tK9w6Jj9/yH6TPhHa9M/CwpkbmqiqAA1BrAxDXFJCLA7JEEREXwFEkyVFU4KisDhR5HHTq7ObIkJaBE6fO/bnmFOmhP+NdOYIXVWbAAiisi0MVeI8Fjcl1lPMdsDpuWy5kLSjMgcGxlsRKi3AEFjWoP4D76dZ5FC+SOL3jcUByP+0R0SKoC8qhcx4dN4huj6B37zVIAMJzEAG9YwTnwY41w5rgGsD1ADcE6hUw9kDcy+uwI/gnDs21g+sa+Kct3M0V3D6AujDOhTDC2RRxiKnGExeRStQ0qRAgmiZXnFXAYJ8jsBJYmNVhADEK+SPLkQO0lwYlEHHKR+SH9eimElASwT0kwudzJybcIhW5PsqbSOOm948T9iYU1DkieO4oR+dLnCpkduGzGAFGfd21ZdtXrWPBXbWwtmrneN9aQDiFBVHfbBxyIy6BxYLcB6H9qgAKAEXkk7ifdoiIkHyKQE6e9UcQ2FXnSg5G4yIaF+FcxI1v0fmIvvGIey8RTy1JmfJGypNzQ6AdEPeEsAP8FaTHxVOxOPxrPPy+gesYbh/huphAg7ogTZG0thOIwKxmhTUTioXC9Zl4Zi8/OqsWSwYQzqUciJxpXQHFoguovstBcjswcao8m3pb2DklMDCPakSlxLt0x1oQ4lZAUO+q0h9oIgprtlotMFCAJ80IPocQDQs7Lo613+ryCafMCi7nmgWNPKA4ruet/VxvE456WyCYAYDb8A85sXNizliB6eA/5cbgko49LFfxqgEKQNszk/Wm0I53ChbROe1cAYQquqVxQYCCAjwJWLQ+4sY32DceXeMRWgWMrgCMViyMuBPLIgQBCLcnuJ7hOoLrHFzP8Ht5uH2E30cBjptWQGPfA10vZHjbgW/2QnyHkElhAwSTyGDEXDCQCCDdHiTMlX/GiljTP92cC6kuOzIYZ37r8g9Rh8AWfwwChtVlU20U/eYiJ4KbIgDvC0CIeT4gZWMP8D6WimYCNNbcGd8XcBx15z0BEFNRUFM4srYE+1JEzwEA4joQAUCO0jscCXXIVTRQ5HNAcIgLO2VpjciT1xiBRwkYM2BxSXzFqwIoPEj4BgICa/QTouxDQCSHCLEs4JAAI58vtaKcgoQAhTQ/anyDGx/ReUbvGaF1AhYFYLgeoCsBDdeJW8r1ur8X68N1BL8H/N4paES4rhHA2IdsaewVMLRd6iqCEMh39kf47NP/eepYSarXRPWSiV0r95lrD5LsDGTK5DoLV53KyNbrUzm3L6+ZS4ekbOsBGPpZJXayAnbnVABr5+YJXsykUMrlez5omdQRRIvZ7LewDI4JijgU0lqPOSRrqtrOZLePeQc3DxYXKHep9fTbIKU2voiZf8fplnR+sZyKbFX0CCA80TveUIabAvAU4QJrxFREQxHXrpECgz5g13hc+yD5F71H33gBjN6BO60X1bkMDD2k1aptq6UR9gVodOqe6hhu36gFIpYG9RHO3FOBcy5EzRsY0VzyBvYD1XBXAEBUhVHnSwDZPVQq9hRZpdyHJc6Vbqy1seZrzOnaKpFvJYOGDSuT6KaKC5Yl0lcUF6yFmceKrwaYwQkLYDOln07dwnOtTN1sTPQBuU2S2aLrxk2on7sCwGiNM9dfsqbmvgdf/A5rscoL9RxFOPIoAu0FAoujgIKIPhnAvw0BiN8O6XT3n5xhXScTT6Th+1LvydxPkbNVARIrIrBDoD4BBpyS39wUPEXQR4vGRVyHFvvg0bqImyZg33t0rRfA6B1C7wUw+ijNkAJJ57yeQR3BhQo0enVP9QTqOVkermO44AUweobrJAObegEx6oUboBBBgYFechyotzDWOCTKQwSRFg1k/ZFax7wiNyJ30gtDglGT6FgBYlX2tW2XcowPuB47+uMWitpjoMTTmVMZ2QdARcbE6SzrEXAMfGt5vvJtVGvL81Wuv4Err1p/uYa7yCiI4Q5ho7dx/ay4xqF1To4fnHr4Nzb8jubrfcmEGH8PAzdnARolYMxZF7VcoPtpTVHAT4KAwxdBCgO+D9KS9D3M/Oy8yzu9eCIEi4AiAYvAhB2CRgHpOKdlyRHhOKbKszeu0RpRPZ67gCe+wz42uPY9rkODrvW46Rvsg0fXe3TBIwSHvvOIkRQ0aAwa1k0vKEgEgIICSLHP9azPSNsu7TcA4bRNfYTrC/AIQcBDq8iOIqyK8iLWH1vqU4kriCNnBTIFElMy16XugMtjtcwp0aLo3ySYACOrBCgsk8HOBb/z4Jp+ZI0MXGBpHCasFjeYc9YtBoze66rEuNuCwAEAOLHOWLUAACAASURBVHi3P9hHw2P18Xq++prVte8sc9nt5fflJ5R1rKyHERdXcF8TYJFkicCuZW7ee5BFoCCi/xTS4e5/B/DLuvsjAP7xiwQSDg4BQbkK+aC9WhVB3UkAAAai/oA9xWxVcBTAoIiWezgwrpwUFryJLW5ikLaqUQDi2rfoogBGFx364LFvvTRFCmJlxECIvQOCgIb1vJCHdtZT4Bi8jmqFhOy2MsvDAGQNeMi2Whl9FBeWAgWNSpaHcZ+LqT9/2l53t3dsRMnhOyu/4MqaiyZZOU8JJmwE/Jxb4wDBm3iTsQM/nXlIedRWSrkxde6xd/uHgGQmImmSZF5jdSxZGqeQSQtuwnKcCbOmwZDi92/WQxkAsQQWNt+UpXDB7qdDFsVXA/hdzPz/Asn19JUA/jYRvQzgLwN4l9WCehFEcikSBsATIzIjghFI+AoAAAOSBCFkNhzgmNGxhwfjOrYKFD1uYpMAo/cOuxDQRyeAETx6drjpG/TRoQsuWRkhOMTgpFJtT+BI4EBaI4RAPRUAgqotKwY9vZ1xH+bKKsDG9dDt4jm5qsR9RRGy3cfBM6xsuT2XYazlj5rH+0bRUlPjp7bj9LjJO/NRrPr4jzYoX15fY44r8EuKytwKM3/qJQJ35pJnlwOKXYYcqdxH45ZuHpa3pxp3rZXJqLxRngImfn/FNdPvoVDWUwlxXHENBgiHwCKtY2LfCyAHgcJAAgCY+ecAfA0RfR3EHfXHIW6o33i+JZ5GSmsCkN9NgHAQAdarIla3DgDcHp4bOI5wMcKjgXfSJe+axQ3VuoArBYyOPXauRx89nvge++jRRyk02AWPfVR3FBP6IFZGHxU0IiXg4AhwcOAgAIKQQQOxtDaQwMNVlkd5LIOMWBuIEMtE9wlQKJAYaAT9E6ZtljYckZEKEEbIn4ehPAdS0l3ep3PUuRX2vyoIeABDIKoAiKZAZAKkRvzEEjCVYt34zi1rXCdLlskiSbzC0jlWca9xB91mTWtltmItD8OgZ25GKPLQPVTnMQw4hvE1kouoOC9ZBVNg8chkESiY+R0z+/cA/jqAv05EL0zEk1N+wqdndVGrVQGSnhURLH4dAKm7D6BuKIbnKI2QOKKjgJZ7dNTgyglYXLkeHXs8jR43USrR3oQGfSOgsI9qXUSPEB266ORZQaLXXhgJPGIGDNbWrGxWxwBAVMkHKTtOCggUS0uERJmXlokdj8igEDF6gKtjxfbwGKdrJBCxYwMw0eMJGOZBBkAuJwKMgcb2lc8zlslq0FA5uhQJVt4hz0bkrNw/mY28bh9PjVvCrlsknq2SWcCutsu6ZPV5h6xRZilVk8bR/Hc6UPyUQaUEi9vICw4ihziKp8z8fGkMM//4mnGXJnbPqHEpCGptCEhoW9AKLByi1ouKcIjYkcOexYroKKBjj1afO/bonMdVlDpST71HF30GDRZAkGq1Ahq9AkZgEqtDQcKAw9qzctQS6BECHvqQcC5I9IwCwPC5eC1vtgCCPAZMBRDouPSainMYYOFMEvjE8jXn83him7V3hgEE22sMAYaHY3JmN7KlwSgUA3TfEDAGXqkl4Fj4P9MBUJmTScVcy7GKembOicoz1XVOqPQXQHTCC3jA5Vic68bfD6NQ9jG/h8GNQgkIc98jS8MxmgKD2m1U77+tnAIkZioN3Icccj39UwAfs2KefwLgN9x9OeeX2gWV9hMjMsERIzDBUQTYIVDEDigsCwEPRxEdNzpn1AfDO0aLHl00APG44j4BRx+za6pjl0qa74MUItyrldE3Ahq9AkeILgGHNFQS8GBtrsT6OgEIC3CwdugbgAhnyyIBCXMGAttvCjop+srySHNNgQQy4CQLg8ZzVsCRgaJ+5on9hSVi/5tqfwaN4ssuwQUYKbvh2PFvaBVY3EGnTMq5iY2F9U6+3yn3TBpfTDkA5Ik5SxA3oGSeBAUqFbbPc7Mdr9foMK3s9TmBxRo5Fcm8mLB56h/N6eQQUDwhoneumKc9xWIeQsz9BAAOjKC9KwD5L3hERDiJgirBgptkcbjiXyMA4jW8NsJzRGAHx4yWAzryaNgjuh49i5URmbBzAho7dohM6NX66NV66DkDBwMKHE6rfrvUOyMBR3qGWCDQPxTbM1XbkD9kUuTj16XCr62SARAYyCSwoaGSL0FoZtwYOIpjKM7lQrEX+4DCSsFwzOI2MAaSYtxof3UsXbeWGR1ASzeGB/TGImDNHRqttT4+VvgAhpxP9dkN1qIfeV4bZVApPtd8uOIKVLETo7i7XwAE5hTWzkTjz+S25PFUwMYJZW1uxCXkUACHgeLPr5znG++6ECL6AwC+BXKv8B3M/I3V8SsA74S0Zv0gJCP8H9/1ukAmtgEhty21ylFEYJ+tCxj5reGz7BClrKo8A1rWHMlqcRTRRcni7tgrt6HWC0v9qMgODTtEFwQQCqAwAOjZK4Bk4IhqaURt28ppG+k1Q4CEdZ+BSLJAMAEgJXiohZIru2ZLwiyUrOw5nZPAAygUf/E61qAw8Ro0DQJz4FAq/fL8wdis0NLYch4U73UKHGaAZrBvMI5H++bGjvYvnsMwlTl93bk5eLwvluOysuXyPfr8XXANpFEsgPIzYZuHUfALAhqMEgyQLQhAArIigwkZLGwxRZ7TalkIfhgVrxy86Yl9q6sgz+yfXN/EsdvyIGeUQ2T2n7uPRRCRB/BXAPx+AK8A+GEieg8z/2Qx7N8F8KvM/M8T0VsB/AVIEuCdZc3XUhcKrMUhphpRZoUYwER9bilXZjMwiiAEYiACkYQg76OH9wyn1kYEoeGIPjo0JH0yvAIEuwwabEACJBBhJkQOyeqogaO0PMCF+0oVLPMQRGD/Lc4WB5eKlQsgSY8pUOC8vzwX9bh8fGBZHByXv5shGAzXmo7PAQCP902PmQMgmj1nav+i0h+AD61aW9425Z7ff1L8Vj4pKUCqwEOOcfGeiPWtcU7AZOOTSM5jIpCaGIO7/dLfP7BgytfFugvOYRQ5t7h/Ggiothbqc+pjwGlAIlbnlnIhlsOcXEpRwDcD+AAz/ywAENG7ALwFQAkUbwHw9fr6vwfwdiIiPtI2CxgOD8VmBCVACCBE/QfFIv6uBIzydYSNpQQYkd1w/GCeeebSJb4kAnAAy9qc3bqzQ+MEOCKABhGRcpOlyJIK5nxAiA6kc5mlwcrDGCg4l0EjAwgq4OAJUMjjSsXLA6AQrVHenWYg4UJxToBJcZ2szHkIKCjGT4AKcABIJpRtfc6h8eW15o+X50+AyszYqeNcvC/7SEoroAZSeV0pd1uyfZZAtgJIwGPRLWYXMxncuQ/fY4pw03OGIFCMjfWxCghK5V1GvA32z4PAACBGQHBHgJic6wBInMhyuI+eKZcCFK8H8HKx/QqAT58bw8w9EX0IwGuRM8aPlvJrCoWSLcEiQJR9YIcOHoEdIhz22gVvzxIDFdihY48Ah5heU36tHfNsnLmUym56gWW8uZ+iuZ6K/t1znffq/t4mRJwsdldmpkPcbUSMGB0ATq+JOP+XmEGc3VTJv5yUtt4dGmjo7tEj7SdxPRTjSOfgYh8PlDyPFCBXlgUXCi9tly6U4vzJc6u123u116i2S1AbbJfvv/4sMFT0piSTwrZrUfVeKQNj+XpRqvdUKuApYBoFBqTjXHxP1RwlEb0GHEbHy/MXQKAAjMH+NH4eABbdS4fAodh3FEDUxw+BxMz+4fjzg8GSXApQTPl16k9mzRj80gcD3vy2l5My+oo/8lH48i/5KACQXAkVcwJFqPWg1oQ9TOmbkjeQ6LjR442EsXKTxpkFYa9LgOiigQgVQJGPGSAYPzEEhzy2j9nNVI7hYqz8h/M+eUZ2NRk3MbIiqPjPVFYF7HXx4SfLoPhqKuti8E0Nxs2NKb7wuTF32l5Yw4QCnVrLHCcy6RJD8XqwzSvGzFyjUuLz42pFPnH9OlpsdP3iLr8OVS7POwQKg/MXQOHQfp1nTvkfZTUMjsXRscUGWLPW1BggBnOV1xrNc3nchMmlAMUrAN5YbL8BwM/PjHmFiBoAHwvgV+qJXvdajx963xsROCKCERERmAcup6BfTmC1GtSKMGuiBIkSGGorwnIoSguiiw2s73ZpPZTg0LGbtBxK8tqOD4DA1lhGOeFuoGB3t7OgUIxJFoEp/YFirABikguouAsdt+wamjiOpfEzbqcDSt5kDhCOVehrlPncvJMKfXEcL587BQaDtTwQGABjfiGdMw0Ek4Aw9bwGFKrjhzojHgsOgznr647mi9Wh4TzDg/cPKKuBgoj+NID/g5l/lIg+A8B/C0kq+BJm/oE7ruOHAbyJiH4LJCfjrQC+uBrzHgBfBuAHAHyhrmXh05wWsSDkOUJcTqaA93AjkNjrc7k/JdkVIFECQwkOZh2Y1VCChEUx1aAQytclCc3jyKY5MBgS1hiCAGwbGQi43Deh9JNyqyKCeAUAjBTkmJAGCgCoFN5wewZY5s7FtJKd2l5vKfDx54/2jecYr5Mn1z7lJjrGGpB1cKXg6+vxcOwh/sD223MJDqNjy0p+VZmWNVn3hwBhNM8MKCyNq4/V89frmJz7AEhcQG2oYyyKPwXgO/X1fwbgmwH8GoD/AmM+4ShRzuGrICXMPYB3MPNPENE3APj7zPwevfZfI6IPQCyJt66d30JXh1bF2OUkrqNpkLjmNgHBNbcDgOg0H8Je18l0XRHqatnY9tpAoQxzHUYsYTZiKYW6lkCwFgDmlH+t+JHHjO6Ep5Q3Fz7CybHzd/xHK/yZsbe54y+PrZ17SelPz3dafmDKekjnLWStr+YHbN8hUABubwFMzTF3HJh322CFgj3Uy2OyuOAyKExet17n7PXGYy4RJIDjgOJjmflDRPTRkL4U/yYzByL6S6dYCDO/F8B7q31fW7y+BvCH7nqdwDywJsStpJYCfAKCEiiuY5vAo2NfbBswONzENoGDPddlOkLMPIOV6kgAoVnXdeLcKO+hBIIi7wFF3sMUGKwLWYUk06HYj/GYg8p+SjFjXuHO3VUfBoBlBb0EAPNKdum8aUUvr4s5yrv84r3kcybu9CfXkhX3KnePjptV7KX1gLljt1T4U3fp96HsJ+aYPO/QHAvnLDoulniFufNmzlnlIDnUh+RMcgxQvExE/yqATwXw/QoSH4PMC1+kGB8RFSAChtaEuYhqkLiOLfbscc07dOxxE9sEEFYlVgr+iTVxE30Ch31Ry8kK/x0qxVECQuRh1nTKYbDEN3sulfvka8wDwoTSn1P4s8pzSZkvKv+xYj77Xfzk2LFyr/fnczjPX0X7jOaaUvD6ejAGWFTyed5K8R4iesvtUyv6Y905wFgx3+ZOfmnsYOojFOdtyeMTXmN2vcd8JvcgxwDFn4XkL+wB/EHd93kAfujUizq3lNbEHjlS6ZpbXMedgoVYDtfcjkDCHvvYoItSOtzAwfpPWClxK+7XByWzYwEOYVzcD3VxP1P+dpdq5TMYGNRl0jeWtk35p7tbOx/TSjVW24vAwgeAYOIZE+dibtxKF00152C+cp5TKfa6uOAat8y5fPXl62NcNkt38Et++CUgmBq/1kVTrm1O1irmC44aAlaC2IW4mmpZDRTqGvqkavd/p4+LlgCJejK3k1kTHbvCpdQMXEslQNyohWHg8Dy0uAmNAIR2teuKPhNd0Wciaq8Jq/oaC0DgUIBCpAwIg+J7uZJrUpARw7pKsTgGjMeXz/X+WunX40bPEyCRnocKuT7H1jar3Ku79qNcMvp6VrEfUt4HFf68Uj86Aqe+O9ftWmmPVMZd3C5H3KHfSqHf1j2zdL3BHEcq0DV338e23T111z2TNe9t4v1Mup3OZHUcE/X0WxcO/+wJ1nIvEjhbE5ZQt0/WhACEgcSzuMN1bAUY0nOD69AkgLgJ0pDIutdZM6IYHUKvJHSg1IQIBTiQNiQa9IpQJV/2ijAwGFVctf0GGOV+5qHSr8CjVOLT4DBTrXUCZEbnzCj5yQibgQspK9ZF5b5mv86zygWzpNgPKfVSod+2jMOCz/4kcoI77aMDDI9R7CuV21H++ENzUlnhrT40AwghDVi/jrvKhfSwOMb19AGIWsgZ/1nuoSXY3WQYFputiQQO+vyReIVncSdAEXZ4Fnd4HgQk9rHBdd/iOjQJIPbBo+sFKPreIwRCDNITOwFD6kqnwFD2wS5BQUGjBIZBCe/BNg+shcFrBsrmQQlAeNwPIp9/QOnXCn9J2c8o+sU7+Lm79ykFv3TnvvKunWslPuVasWNrlfuarNolMnJOKRxQTLOK7Vg5RgGeUIGtBoA111wLaKxaf6qp00FACMd95scCy4WAQynHuJ4G75aIfhOArwPw/lMv6pQSEWEZ2eZ2Mk6i4wYdfLIiDCSehasEEB/pr3ATGzzrW1yry+mmbxJAdMGj7x1Cb+DgwH0GCAqUe1uX1sOgbWnxCPVrngEKDBoBJSBIVoYq9ZAVewkAFAqlP6f8pxT/nNKf3Det8Gfv5pdcNBN38rLjFnfxdy2fUMw9UnKHiNvbCC/Hi3DEpMJLslpRHakA7ygnj9i5zWddn1N+jgvAvWbt6bM8g+K/r2gnk1tnZjPzLxLRnwTw0wD+5umWdDqJyF9QYE5up05LbewLfkI4iOxy+kh/JUARdrjuWzzvBSSu+wY3XTMCiNh5QAFCgIFA/RAQXF+BQ8Cwf7X1qx6BB6O2JMxqSB3ikoWRe1un/SUImKWxBABz20C+a68V/6S1sHyHf7TSnyqJMEXSTin8tXf1wwMz++/3T7pKmOfBguP9uktWylpQSt/P3Huw72nq/R/7XS19jvX1lmQGTE4BxPcNEsDdS3h8CoCXTrGQ+xBzO1lJjg7qelK3k1gT2dX0kbDDs36H532L512Lm77BTe/RdQ1CrxxE74DOZYDoSAAhAtQBLgGGgcHw4QIPwMMNwKICiME+VfSxAIOQFX86bkAQeBkEJpT9agCYcu+c+o7/1G6dS1T2x8hsX+11gHArhfUQYMNxxVr9vPIknM+VM/UbohkrQj+7JSW/9D4fAhxKOYbMfj8w4CVeguRUfMOpF3VqkagnDDKwzZowItsinMyaMJD4SLfDdd/gumtw07XoOi9WROfAnQP6CiB6wPUA9STPwbaz1WD7E1DE+vUYFMSqUOVtgKAAIW6kGTAwt82SJbBkMdzFAij2Tfr317h9ynnrubHC9VNf59yypjf2UfOtV853vlu9QKvj4Jr0+15WsifmXpZ+T+WxOTfWzHt6aDBYkmMsiu+otj8C4MeY+WdOuJ6Ti5XtiEAqj7GHz9YE75K76dfDVQKJX++u8Lxv8axrcb1vcdM16DuPvvMCEJ0DdQoQHWVw6DI4uE5BogCHtB2q557VBTUBCvp6BAgxZssgxqGSnwKCmhs4JwiU504dq88rrzEYNP7jHu0qOlYOKfsjFepZ/P6XqNQfQuxzWPjuj7pTLz/Xu/6e1oBGfc07Xe98JPgxZPZ3nW0VZ5aYnnPhP7MmkiURjLzO7qZnXYtnNzt0vcd+3yDuDSQIbu8UJCBA0RWWg752PScLw/UCCq5nBQwFBH04A4ReXUYhFtZDAQpmIYS4DAgnBgMZNgMI5Rxzx6fmWCMTf9z5P/6MC+JWXpYVJ93mD35usvgS7kovMGpnTsrveRY0Rord3EtHfNZzoFHOf8Hgf4zr6W8B+M+Z+f3Fvn8dwFcz8xeeY3GnlFS2Q3tKWHmOa240HFYS6a5Dg+d9K+6mfYt914i76cYDewfqHGhPcHuxItzewKKwIjpWcFCA6DMwuI6TBZGBImaLIcbRs1YGHIOCgQWQQeEEgCBD1yn+2T+Lc5Pn0MLdOh/8nxyIwo4MOmWg9h2V+tJ7vY2sAtmlNd8VRO4AAPfhVrmr5UaOZm40FgDjrpFWR7qnHkqOcT39XoyL8v0AgHefbjnnkVQIUN1OicxWi0JAYofr0Io10bV4ru6mrvOIewWJvRNgMHAoQMLvFSASYPAQJHqxGlwXQb25kiKoj+peKp9jBobCchhZCgYKxwBCuR82fObHviZRa+nuyh3pornN9Uvx9xfaeZ9yi2r6WW6joI8EhJMmwg3GLtyF17IyZPVOQm7eujA5VZTVsaBxZivuGKC4BvAaAB8u9n0UgO6kKzqhBOaUQ1ES2SVISOa1uJ2e9RoK22kI7L7JlsSNg7txAgo3BLevAGIP+C4DhO/UeugNMBQgSnAIIVsNCg4JGAYAUYFCCQi3sQ5qOUWNnLvcPS9ZJXeVe6r/cydlvkZOpQRvqVCOVsJrr7P2c1saR7T+ene9U58Ci3otJse+t6Xw5vL6c8fOKMcAxfsA/FdE9MeY+cNaOfbtAL7nPEs7nUjFWEq5EykkVstyCEi0yeV007UCEnsP3HjQ/9/emUfdUpVn/veec1GjgMgko8EBTdA2SitDNFkqahSDRpcTGhoSaRNtlzFtd4sxK22yEpem0y0rrVFbo+IQEW1pFFAGidoOgENUIGAERLlc5DIooYX7nVNVb/+x967aVafGc+qMdz9rffc7p2rXrr3PPd/71DuPhOGugSGHkTDcsgQxguFILWFoanIajgwpGA3DCP/BOIEoycghijNiKPod4jhPCrmIpJqcgiL6FpKzCu6q9TTGrU8pJKfc/9RCf8nCvJ9bL9A81Re5NpFIbuyUn60voFs40NN7T+PHqPt7WNJ3owtRvBH4GPAzEbkT2Bf4PHDKPBbWF2I0zZ8wfaddc6JtbOm2tIbTrtjmSVhzUzQeos5hvWVIwmkSwy1LElvKcATDsWZEMVYGo4RBnCCjhEHkEUSUTBJEHTmUEEPrJilVmEHYT2tzT9fcdO86ImnzB9fhc2hNBvN6ku4JKxdS2ZQUlxtb9QTd4546B0+0eKpPxzZoF26+vsxRS0SXqKefAc+zpTsOB25W1Z/ObWUzIinU3jQlxYeZRpGrCDvMSnNEPkkMGGxJztw03LIEsWW0CGd6Gm4lhiAiZTAypCDjPEGIJYnUB+GTQ2LLNDhyaAo9rUNLMujb2drmPp21n7o/sprPo9eKpCvuxF0LtDX5aNKPkJyWbLr4RVqbu9afLDplZovIQ4BnA4cCt4jI+ap611xW1iNiNY7son8ii3SyJqdoyHi0jcTlSWyJNTV5JLErI4ltW8pwy9MiRrHxRWzFhiDGsSGI2JAC9remkUxxOTE0tVGs+wJVkMSiSAGm9Il0JJD6rmPzIYAg9A36ygupjTBqP0n58VmdzP41ffztzBJSuwKE0SU89njgAuA64MeYpkVnisjzVPUb0y5ARPYFPgkcAdwEvNRqL8VxMXCVffsTVX1+m/kT+5PVdsram45syfD7oj3YNd7GaGSS6tgaMtgaMLQkYQjCaBLbdjmTk7JtV2K1idiYmcaGHGQcwzgyGkSqRcRonEyQQ0oMTeGoPgFUfYFKSKJPguikDUzhN2kmmP4JIAj/7lipz6ytc3faUFaYvG6Wv6k11S66aBRnAq9V1bPdARF5GfC3wJNnWMMZwBdV9e0icoZ9/6aScfep6hO6TJwrCoiQpL0njFbh+yZG0TaiyCTUydiGwDqHtW9u2nKaRMJwlzU3jWOjRYxjZBwh48hoEFGcJ4g4LieHaZyu/henQBCV5ND0JFgiAFon2U2Tdd0WPdv9V0rQBfSLuszqaSKSylB2bRdBvoZk0YUoHg2cUzj2aeC9M67hBcDT7OuzgC9RThRTIVZNw2IdWYxdO1Ovp0Rk6ze50hwuTyKLbsIQxEgZ7kqMT2IrNuamUYyMokyLsEShUVxNEFawFgXqhJD3SaArOXQxEVSF1PZQoG8awTzPctfzmHu3I595Oe37TDSrczZPYwqqQ1cz0ZqRRRei+CHwcvIlxV8C3DDjGh6qqrcCqOqtInJgxbgHiMi3gAh4u6q2TvRzobEmI9toEyPfiW3rOOW1CUMSmTah1vSUkYQxOUUZSYwjiGI0chpFZAgijmvJoRKODCoIYpJUeiAGyJX9KB4rJYYqUtASknFo6J/QVvAusn9CHea9joUSUZ81jtqiqupq6dgOZNIl78GhD21jXgJ9SWTRhSjeAJwvIq/H+CiOAI7E+CpqISKXAgeVnHpLh/s/TFV32Jasl4nIVao6QVK33xlzzGtvRlESlJe94pc46eQ905anxpFttAnnxI5iUzKcaOBlXbsfY3JyjuvhroThLqtFbI2RLUsQozFEkSUJ55PICCKXQV2GoqApksS0BNGlNEcfGkPbct51zvkOWan+vVeFNPrAwoihD82gj6fyLuaceYcg92GiahN8MksJkLZk0ZPGVEsUIvIQ51hW1a+LyCOB5wGHAJ8DLmwT9aSqz6y5x20icrDVJg4GdlbMscP+vlFEvgQ8kRJt5oD9hlx50eGMNeZeHXFPEnN3YnModJBGOzmyGEVDxk6bGJlKsMMtp014YbBbaghiK2awZbQI2TU2JDGO0LEhCsZRShBqTU5mA1UqcAkBzEoSTWakOk2hZQVXc7jFl7Duj6HnKq27nfmnDeYtVOeZkT6rL6APzOIEd5iHlrFgzaJJo/gxsDcYrcAK/I/1vIbPAqcCb7e/zysOsGG596rqlojsDzwF+Os2k7uIp3zU05BRYtqYjuMhSTyE8YDBWEyzoSjTKEyuhAl/HW4lmbnJ0yQ0p03EGUHYP9LKp14ZpII+RxKzaBFlGdsljvMcMZSsc2qUCfeq5jErVvhsnaqergxqs4jnQCJt5+xTiPZBFtD/57FAsmgiintF5HHAtcAxYqTVxMpUZ/oLeztwjoi8CvgJtvCgiDwJ+ENVPR34VUz5kAQYYHwU/9z2BolK2vLUmZ5G8Ta2PCe2az40dNFOY5t1PbIRTls2usmRxGicJ4nRKEugi03yXK3gLZKEr0XY160c1E2+Bo8gasmhhcaTP9z1C9qurOtCS0i0mm/NtZRlhlWuSuJcH2vp2/ndFxZEFk1E8efAlcD97fuocF4ACePltgAAIABJREFUpa0UKIGq3gmcUHL8W8Dp9vXXgX8zzfyuvLj5GaSO7F3xNqJ4SByZTnWup4REWILwTE4uwmmXNTn5JDEeoS7KKU5AEyPs6pqTFM1NbUjCF8wdyCF3voog6lT8kn7LtSQxY6XLsrlbk8c0JLFqf/h9o2l/K5DMVYu+BHSXjOs26ynOueGoJQpVfY+IvB/jiL4O0/rUkcNKIyHJV45V27DIRjqNkyGjaGid2LZL3diFw2qaVDccFUhiy5LE1pb5HVmfRBxnBNHmaWYg3UmiyqxkDqTvS/0NZealptDBLgRRhxmf8iv7BEwO7H6/3ekPf9VJoQ59mX+gP9/HqmgZC9AqGqOeVDUCtovIE1X1x3NdzRyQQKF0xzYiHbBlo52SyJqdXNMhp02MSX0Sg5HNth6VkMQ4qtYiCpCBpCanlCQK/ohSc1OZBuETRIVZCVqYv8pq6/gaT1dy6OD4nlsz+TqtpmuoZBfMU2Css5DvC/MUzLNoHH2S2LSYM1l0CY/9iYj8FXAysJ+qPlhEng08WlXfNZ/l9QeTR2Ed2fE2omRAFA0hGuT6XqcVYG39JrE1nGRkIpxcdJMjCbX+iNqncxlUk0QdQRQw4ZwuIYhGs9fE+vrRGqbpY63x5P3njnn2Jw7C3GCWPIppxs7DSVx2n1XHHMmiC1G8E1MM8JWY8uIA19jjK0sUuYZFyTaiNOJpQBwPIBYGkZc7Mfa0iXHCYJT3S+AIIg2DbX5CnZUkqqKX/LLkOYIoPh0V/AyVZNDxSXyCHMo+i7o/4rqGMz0J9Kq9zuw0X7WIrSbMK6JrFcxB8yKOLoSxCloFzI0suhDFC4FHqeovbPQRqnqLiBza+6p6QozzUXjJdtY/MY6Hxuw09sxOY+fEtjWctkwNJ0Zjkx8xGqG+X8KVBm/IMgamIokyDSI97jmja0nCW8NEaG4TuuRPtE20K46pS6rqQRjvtrkViwj1nbdgnNYc1DdxtF3HqvkselxHF6IYFceLyAHAnb2tZg6INWtY5HwU43hIHA/QaJA6sV2XuuFYrTM7MUX+RmNky/glTJTT2IS/VtXN959CPJPTVCRRNDG18T+U+Bs6EURBwLQStHVmmGmeFNftaX1eWPW8jkU+Rc8SvdWnAG+jZayCdtHz/bsQxaeAs0TkjwFsFvWZwNm1Vy0ZSZpsZ5zZkQ4Yp/4Ja3aKyH6cb8L1lRhHJuM6ykJgc8KzrFplkSSGg9YkUemHcDWj3H2KwrREuLYmiLblOKrmqRXsC0y0W3XBOi8sMwS2UiNcsKCcZ8mMuvutmx9jSnQhij/BZENfBTwQUyTw/Zhci5WEExuxDkhUjAM7GdhsbOOfkBhrelKbZKe2S12UK88x4ZcoPKlXNWHpTBJl0Uylobct8htmIYeqP7yUDFsK+5bO8s4moq6ksOwnvGViWdnMbTEvZ3TZWvp+2q8yn66CVtEjurRCHWEKA77Bmpzu0Km70C8OaWlxr2rsOBqSxII4J/Y4c2IPxpr6JmQ0NlFOvl/CJwk/br9MmxgUQmApJ4k6LSLng6j4uFPh29Hv0EgQ2QILf2wN2ssUcNf36lNY/a/naqGvpLSumHcuyyJ9KRuKLh3ujgJ+A9gXuAv4v0DrMhqLRmz/8xI1NZ5ixEQ8xUOixORPDKIiWWjWiMhqE34Np6qqplmWsxGoOb+Ew2DQniRiJ7STCk0lI6kcYUFpcl6tX6NVWef+SWImQphnr+KA5WLRDuHwHWmFRqKw9Z3+HlOwbzuwAxMme4iIfBT4/VXVLFKyIMvKjjULi5Wcf8JmYY8TEw7rciasuUkTzWsSTjg6vwFkAtyd90xObUjCLyZY66j2zV5eVFWKAkm0ysYu3iN3bLpci1oy6GrCKq6nC1lUrmElv7bLwSwaRJfPcZqQ13n+P4XvQCu00ShejelAd5yqftMdFJEnA58A/oDZu9zNDa58R6ID48i2EU9EAwYxSGxJYgwSadr3OqdNWIE3QRIOzizktImBIMPhVCRRmpvhyCd9216LKA2dbUEG+VMzEENjbsUUDujC59GwqJp5FmRemZcwWqR5aJ75Eg51Tui+1xHQCW2I4hTg9T5JAKjqN0XkDcCbWXWicFnZyZBxMiCJB0icz58wjuwkIwlPm0CTiaS5NBIp0cyGbwWYiOSc10XUhr76Qr1oYjIvJiesq+lU5nvwfQ6zlOtIbzlDXkWbulhVc7chiz4IZVasc2TMIgVz28ilqmsC5oY2RHEU8OWKc18GPtrfcvqFMwolOsj1oEhiyUJjPaKQsc2dcJFOzjfh4JLmHHzBjhG0aZRTRYRTHUnkw24lN2+pJtOGIMxN89fVJeK1RKeSHfP6Y+6zbWbZuN0t3HaVhG7XJLfiNQG9og1RDFX1nrITqnqPyGpnRyU6MOXFE+PEjhNB40EWFhvZcNhxwiCyGkUU27DYCE3UCNLh0JiTwAh6v9Wpe/IfDnNRTqUkYV5Mhr5CqcmpkiTSSVv0lago+lcbTts28a6LM7zqD3meT9y7m7Cvw7oK0rZa56pkRm8g2hDFHiLydJhsWNRhjqXB+ChML4pIh0TxEI2FYSTWP2HJYqwpSehonPcV+OYkVVQ9k5M7PxzmTE6VJJEk5fkRDnW+CB9FLaTj03VpMl5dPac+BO5cCWEODtV1wu4kHJu0jRDJ1DvaCPmdwAcbzq8cEpLUTTrWbWmyXZzYiKfEkISkGdme2cllYTshaTWKbHJPuHsO7FqfBGSO65x/I08Spb6IsoimIknU1HgyL2sc2G0JootGMIui2ZaUphUGy0hAmxZB4NVjN8uQXhba9KM4YgHrmBtiBmlnu3Ey9EJjs7Idw7RkRwRbI5tcZ4SVFP0SSTIpyKxGURfl1Cq6yc4FVPsjmjrUdSkE2GReakMSZZjVGtkl/HWeWAShBCLoB+FznCuW7l8QkZeIyDUiktg+2VXjniMiPxCR60XkjDZzx2p8FImaZLsoGRDHgtjS4s5HkYXFutyJcRbpNBzmtIkysxODBpOTTxLOtzGxQU+bKCMJTdJ8Di1GSGUfUm6u1HRVFk7qEU46pzteNncZnKmtsI9O8O/X5d5V918GVKf/CQhYA6yCf+Fq4EXA+6oGiMgQeDfwLEzS3zdF5LOq2pgZ7nplxyom4inxNQpNf3K5Ey4z2jmwBwMvUimv6qa+CZqd1xPmpjJ/RF0tpJatS2tDaYtZ2n0krk3bUa4vhKS6gIC5YulEoarXwqSQLeAY4HpVvdGOPRt4AS1KiLhe2VEyJFZBE5ONnTqyY0y0U5TAeJw6slOTkyUChQmzkyERyYXDevsyL5zzOk4yc5OXx9BYp6kozIs22SYHdW5RLXIs/Llzx6bQFCaONQjteWgHi9A41pmMAskGtMDSiaIlDgVu9t5vB45tusiJKpNHYRzZGguDWExWdpTlT2Cd2Fnhvz1SkgAyJ7RDMbmudAGe8zo1q3iRUn5UU1MJjrKigB39EK2KAM5qSircMzvWQuisq2Ny3dbbFiHcNMBiIUQhIpcCB5WceouqntdmipJjpd/e2++MOea1NxOTEKnytJcJh73wYUTJkMg2K8pyKFx58cT4J+IkE9KppiDZMc+Wn4t0KvgmJvwSvg/AfCD2d31+RHV+RUkyXsn12csSgjALLb+3W1sX9GVi2lShu6oIJBDQAgshClV95oxTbAcO994fhilOOIED9hty5UWHc3dyH7fFCT8c78f37t1GZDUKEtuDInaO7ASixCTZOSez1RRKo51c06AmbcJdU4xw8suQl16jeS3CR6GKa22eBRUhrlXz5Y5P3ya1ElVPp4EY+kcQ/gE9Y11MT98EjhSRhwO3AC8HXtHmwlgHJEg+h8KangaOLMZxlgQHmQPb9UiwxyfCR5u0iaLJySeJqpIcRVNT26zqdAE1xQChX3KYRuj3SQzTCsR1I6cg+AOWjFUIj32hiGwHjgcuEJGL7PFDRORCAFWNgNcBFwHXAueo6jVNc8dqmhbFarKyk0RMY7gYExIbeWan0dgIeFevKS3XoTkSAc/sVNA6qqOcSvwSTXWb/LnstaVhr7lrCs5q//oyVIXOlqFosiqbt9FZPaj+6YJZQ0tXJVw1hNAGrAmWrlGo6rnAuSXHdwAneu8vBC7sOn8W9WT6UKQ9KGKQ2GgTYjvYoWoEv6clqPtjTTyBDem4CfglOoqd79z1Ncl0E1pL0VTVxlnd5KjuIpjbVoH15y89t+QQ2rboEpkVhHjAboKlE8UikKgQu/LiiSnfkYt4imLbdyIxwt+FvUIq+J0wS5PwKsp1pCYnP7HOF/ZepneuvDhM+iVaRiC1qsfUhSSmEdxN5pw+yWCZtXwCOQTshthYokhUSWwvClMQcICq58j2NArGYyPYrUYhQ2sOURe55D3pe07sUt+Eb3JyKHE8F5sClpJEVbvT7KJyLSIlhY6hrnX5Gv66+sIsju2ysUGIBwTMBRtLFA6JZsUANYFB7MjCZmTHcZY/4ZuXBmIaWhSjnSoS7IBKB3bRL5El49VFONWYm2CSJCoL9k3hfyjsaSoHeJUGUSfM2zjd69DlmkAqAQGtsdFEkZbvwJCFxoO0aqz5sWGxrkGRDLJoJ8nyJ8r8Bq20Ca/rXWOEk5motU+inblpRpJwe+gyZ916ugjnOoLqA6FTWkBAa2w0UYCJfErLd8S+6ckUA5QoK7QnQ6rrNUFW1qONNuFdU+WXKHVc597XkESVgK+o+1SZdFc2R9v11M3XB+ZNFj6CkzogoBIbTRSJDY9NkEKynVcIMCqp5uo1KKLga6jMm8gl12lemyhBlbnJ/CqU9vDW0JiIV5xn8sbe6xp/Rsl8tXO1wTQlIaYR2rOSS9X1gUACdlNsJFHEmhDbCh+xmjaocZpDIVabAImtgMdqC8OCiSjxncueSQomBbh6JGHHp/kW3hjzokTAVjmui6GzxdDXQrZ29rJGk/AFXlcfRJc6TpXzztmXMG0IbxPaXNs3mQTSClgBbCRRODgfRaJiyos7jSLtQ5HkynaYftdWOBZ8ABMNjBz88uPFrndezoXvwK7KvG6MbqrMj5i8prIJUV2kUVf/wzoKq1kd5k2YZs5piiGGgn0BC8RGEwUY89NYTT8KsT6KQZy1Pk17T6TNh2yMvhdJlDcFZUTikvEqu9VNdMcrMRuZG5STRJVPIr2uEEKbXlbhj5i2COAyE+LmmTOxakJ21dYTEGCx0USR5lAktmFRAqJWm4jVRDw5jcE1KXJw/gYHvyd2rqJsdaRTGUloQfNoKu7XxidRShJd6jJN44OYl3mnbr4gSAMCloKNJgqwrVARkkRMVraLehonJuLJ62aH63vtmgyl0VDDfJKdRxJa1ChqfBMTJqeGp/jSPhRtMqzbFgPsOoc/17Rk0EbY9+Hb6HK/gICAWmwsUSQYkoht5dgkKYTGxtY/oUkWyeSEuxPO/hN1IckuVwOqmFxX6LGdzTmZGNdUKnxC2BfGTjit6wR8dlHN/VqaqqZB2/mmsdlXIeRLBATMjI0lCjCmp0StMzvO96LIQmM9jcIJYlcx1m9iVOxPAROtUf1w2FIHdjquxuTU5JeghT9immKAbR3V89QkAgICVhJLLzM+b8SIKTGuniPbj3hyIbANtZgm+lMkk36DYnIdUO3Ahm4k0dTwqKk5UZ0fYt4kERAQsNbYcI1ikGoUmggDxeZSGKJwpcWBLOLJFgdMBXxZtzvAJeT5xQJLUefALh3ekCtRHGvvkRtfvKbJWd2ltHYd6gimzgRUN3/QRAIClo6NJYpYs4S7KBmgiXj+CU1rPGkcp9FOImLS9IompSK8TGxzYYUZqVi0r8HkVFr3yc5vflVkWs8S0dSmdEcT5pU9HUgiIGAlsLFEAVnEU6zWP5GQ9so2/SLywj5Fob5T6sSWARCn2sQEmRRrOjGZ+NbovC7cvzZPoiq3orififlbahJtEIR5QMDGY6OJAmzPbGt6Mgl3ak1PMToel9vnnf/Br9U0kGxsYvwbTmBX9poo6ZddirJS48WM7XRoC3PTLLWZgh8iICCggKU7s0XkJSJyjYgkIvKkmnE3ichVIvJdEflWm7ljxCsIiNEoEowjO4pTH0MuNDYpahN5+/pkTkTmDC86sXNJeNmkNnkvC8WtJIkqX8a0JOFCet2Pjza5EcXrm5Lu6uYsm6vt3AEBAQvFKmgUVwMvAt7XYuzTVfWONpO6nGqnUVD0UcRxVufJIiUBv7Bfsay464dtBmZ+h6ZIp6LQL9ZiKqKqftMsJDFxjxmd1F3maDNXl3sEIgkIWBiWThSqei1QXnBvRjiSiB1RWB+FxAXB6Qtw9fwW1j+Rri3NyPajmDzhPBikZT+0MCZnniqrCNvgvM7nS/RgbppHMlsT+nR6h0S6gICFYemmpw5Q4GIR+baIvLrNBYntbpeantJe2ZlWUHzKTxPwsOTlsqy9IoDegMIN3dN+hyJ6dT0p0iE1zmvvmol5+3Ba95VTMe0a2l4XfCsBAXPDQjQKEbkUOKjk1FtU9byW0zxFVXeIyIHAJSJynap+pTjo9jtjjnvtdsaacJ/+nCN+5wEkv35kWucpLQiYaOYvcIJWk3xobLEIYFI4X1LXKUWxy527V1GbyD6k/Ph0moIZq6KkhwykfRmPNr6IOsx6fVcEbSEgYKlYCFGo6jN7mGOH/b1TRM4FjgEmiOKA/YZc/oXDuCW+l6tG+3PZ3Y/kK7dK5syOs6gm06hoAENHFEZjcIUAoWASc2GxUJs7kSeAFv0l6sZ697YLKj/dhiTWjSACAgJWAmthehKRB4nIXu418GyME7wWsTrTk0xqFOBVjPV8B7mudjJZtiMpZGMXcyequtdVld7wx9CgTRTHV/olpoxoKr1PQ/RS0/V189X9BAQErAyWThQi8kIR2Q4cD1wgIhfZ44eIyIV22EOBr4rI94ArgQtU9Qtt5k9UUPVJAq++0yBrf5poVr6jQjiXncuRhN+9DsojnarKh9PCed1HnkTpdTP6IYIfISBgo7EKUU/nAueWHN8BnGhf3wj8Wpd5YzXO7MR2t8vaoCYQe6anYqKcL6Bda1Tnu/CIQIbDrJmR78Qu801AfThsgVByZqQJ7aChj3VT5dg+CwB2MTUFs1VAwNpi6UQxT8S2hIeqpMl2A89HgRj/hCkJHmeO6jKh5bQJnwiqEuxUYTBkAmUFAqtQ1bDIvfWd1+6eRUxbbK9PoR7CWAMC1h4bTRQAsdrudmpzKCK14bEleRDYp3kr3DrndkwId883UaVRlGVft+hqV691FOZzWlF68ZTJd31VmQ0ICFgrLN1HMU+kjYuSQS6HwmgOWki0K+RIFH0LSTGctbyXRCVKS3VUZF+XocnklI6rD9VdKkkEbSIgYC2xsUSRYKrHRjow8snrQ+F8FH5Uk4PzK9RqE0UtpOSJPpdfUeOfKI1yqsiVyN+0KVeiJCpqXklvbWtEBQQErCV2G9PTIBEkUcRGNznkynO4/ArnpLYVY7UsfyIlgWLIbLlgL9MmWpFEGdr2oGjT/3rWpkGhDlNAwMZjo4nCdbjDOrMHLurJRTdt8xzORZ9FzlGd5LWCupapZXWdpg1bLdyreswUzudZCKKuImxAQMDGYWOJIsYUA0zszzaXlR0lWT0nW0JcfSJwT/kDX9Bnwr60L3ax73RZSGwLH0Zrk1Odual4ryZHdxf06awO0VABAWuDjfVROCS4pkW2xHiSQGJMT0U/RFoocDjMHVO/HHmx9HghUzs1JxX7TfioyptoQpuOdm3MTbX3mFN9qFnHBwQELA0bq1GAS7gTUMCGxxInk0l1Xo8JsSUkMt9FwQdRRJk2UeV78Html51P58iPq+xD4d9zYl0LyKuYVdgHsggIWAtsNFHk2qAmZI7sOC4Nf83BlfXwE+3S7nRGME/4J/pAweRUm1Q3Yb6ZoiDgNP6IIOADAnYrbKzpKVYj4KJkmBGF60XhTEmSmYdSBzdMdrRzhFGCWrOR3zPbolGbKJu7i8lplk52xWumJYlQ6C8gYKOwsUQBNuoJSaOeXK9s4ngyt8EvFNhGqBUjociTQGnuRFMEU5UDG+oztesc5dOYm2YxNYWIqICAjcNGE4WLeEp7USRAFKFehzuAtM9EQeDm8iea0JRlXXSc12gTOcKZ6FlRU0G2S4RTF5JomzA3y7UBAQEri431USSIzaMwGgUJDOLEhMKWPYHnHNwlAs9mW0/0nvDDZv0udr7ZqcSJXTb/xJgqc5JPEpVjpniynyVkNYS7BgRsLDaWKBx8jYLYOLM1jk2YbDbIS7grJNo5+CUxyhoYFZDL1C4752sTbR3YbZ3XXUliGl9EMDEFBOw22EjTU4IRVqYXhc3Mjl3UU4k2YXMdSgW/PVbZG9vBD4stOrGbtIncUioc2FUmp1kT6qZ1dAcEBOw22EiiAJuZje+jsHWeigK4xCmdQj2SyB0uMTul87V4os7lXbR0YNfN0QZdnvSn7VURtImAgI3ExhIFWI0iGSCx2BLjhUQ7qHRkp7kVfltTT0hOhMWWZVq7vhal3es0J3Q7ObDnZXKa1vEcHNYBARuN3cRHYbQK3xSUH+TMREkuhyIX8dRWa5gQ8hVcXGlKKpDAIkmiCcFhHRCwW2LpGoWI/DcRuU5Evi8i54rIPhXjniMiPxCR60XkjKr5br8zq8vkTE9paKyf+JaLXpoUeI1hsQUfRBtMlBovnstunr7crjeWDJ6BJMqS3+rIpCphbgqSKN3LGmOT9rNJe4HN2s8q7GXpRAFcAjxOVR8P/Avw5uIAERkC7waeCxwFnCwiR5VNdsddce692n/EDx5q6VhOI5uKhQBrxpubzlBWvIBb9MZ2RFTWqGhiTE9O6Na5JXmSuYUfTXe/Fc3ynno/K4hN2gts1n5WYS9LJwpVvVhVI/v2cuCwkmHHANer6o2qOgLOBl7QZv5EJSMJX363JYtZ0Jg7McePf1PMQlWksCJkERCwO0DmUthuSojI54BPqurHCsdfDDxHVU+3708BjlXV1xXn+NznPrdr586dqVqx9957377vvvveMeelzw133XXX/uu8fh+btBfYrP1s0l5gs/azwL388gknnHBA2YmFOLNF5FLgoJJTb1HV8+yYtwAR8PGyKUqOlTLcSSed9IBp1xkQEBAQMImFEIWqPrPuvIicCvw2cIKWqzjbgcO994cBO/pbYUBAQEBAFZbuoxCR5wBvAp6vqvdWDPsmcKSIPFxE7ge8HPjsotYYEBAQsDtj6UQBvAvYC7hERL4rIu8FEJFDRORCAOvsfh1wEXAtcI6qXlOcqG0I7apARD4oIjtF5Grv2L4icomI/ND+fog9LiLyt3Zv3xeRo5e38nKIyOEi8o8icq2IXCMif2SPr92eROQBInKliHzP7uXP7fGHi8gVdi+ftA8uiMj97fvr7fkjlrn+MojIUET+SUTOt+/XeS83ichVVmZ8yx5bu++Zg4jsIyKftqkC14rI8Su1H1dKe91/gCFwA/AI4H7A94Cjlr2uhjX/JnA0cLV37K+BM+zrM4B32NcnAp/H+GuOA65Y9vpL9nMwcLR9vRcm3PmoddyTXdOe9vUewBV2jecAL7fH3wu8xr5+LfBe+/rlmKCMpe+jsKf/CPwDcL59v857uQnYv3Bs7b5n3trPAk63r+8H7LNK+1n6B9TjB308cJH3/s3Am5e9rhbrPqJAFD8ADravDwZ+YF+/Dzi5bNyq/gDnAc9a9z0BDwS+AxwL3AFsK37nMNru8fb1NjtOlr12bw+HAV8EngGcb4XMWu7FrquMKNbyewbsDfyo+Bmv0n5WwfTUFw4Fbvbeb7fH1g0PVdVbAezvA+3xtdqfNVc8EfMkvpZ7sqaa7wI7MYmhNwA/1yzvx19vuhd7/m5gv8WuuBZnAv+FLJtoP9Z3L2CiHi8WkW+LyKvtsbX8nmGsILcDH7KmwQ+IyINYof1sElG0DqFdU6zN/kRkT+B/A29Q1X+tG1pybGX2pKqxqj4B8zR+DPCrZcPs75Xdi4j8NrBTVb/tHy4ZuvJ78fAUVT0aU63hP4jIb9aMXfX9bMOYoN+jqk8EfoExNVVh4fvZJKLYlBDa20TkYAD7e6c9vhb7E5E9MCTxcVX9jD281ntS1Z8DX8LYg/cRERdW7q833Ys9/2DgrsWutBJPAZ4vIjdhqho8A6NhrONeAFDVHfb3TuBcDJGv6/dsO7BdVa+w7z+NIY6V2c8mEcWmhNB+FjjVvj4VY+d3x/+djXg4DrjbqaWrAhER4O+Ba1X1f3in1m5PInKA2AKVIvJLwDMxEXf/CLzYDivuxe3xxcBlag3Iy4aqvllVD1PVIzB/F5ep6itZw70AiMiDRGQv9xp4NnA1a/g9A1DVnwI3i8hj7KETgH9mlfazbEdOz06hEzGRNjdgsr6XvqaG9X4CuBUYY54SXoWxBX8R+KH9va8dK5jCiDcAVwFPWvb6S/bzVIwK/H3gu/bnxHXcE/B44J/sXq4G/swefwRwJXA98Cng/vb4A+z76+35Ryx7DxX7ehpZ1NNa7sWu+3v25xr3t76O3zNvT08AvmW/b/8HeMgq7Welaj0FBAQEBKweNsn0FBAQEBAwBwSiCAgICAioRSCKgICAgIBaBKIICAgICKhFIIqAgICAgFoEoghYKYjIn4jIB1qO/bCI/OW817RpsJVX7xORjy57LV0gIpeJyC4R+eqy17K7IRBFQCNE5Kki8nURuVtE7hKRr4nIk3uY92kist0/pqpvU9vydsa5TxORWET+n/fzrlnn3SCcpKqn9DGRiPwvr97S3KCqzwD+cN73CZjEQjrcBawvRGRvTLXR12DKUt8P+A1ga5nraolvqOpTmwaJyFBV46ZxAZV4DvAXy15EwPwQNIqAJjwaQFU/oaZI3n2qerGqfh/SJ/evicj/tBrHdSJygrtYRH7PNmK5R0RuFJE/sMcfhKmpf4j3xH+IiLxVRD75klAhAAAFmklEQVTmXf8pEfmpnfsrIvLYWTdkTVbvEZELReQXwNPFNOv5GxH5iYjcJiLvtaU73DX/WURuFZEdIvL7IqIi8ih77ksicro39jTfPCIivyKm8cxdYhprvbSwlneLyAX2M7pCRB7pnX+sd+1t1jR3kIjcKyL7eeP+rYjcLqbW1jSfyVT3EZHHY6rQbve+C+8UkZ/b/+9ft8dvFtOk61Rvrg+LyN+JyOft///X7D3PFJGf2e/SE6fZT0C/CEQR0IR/AWIROUtEniu2y1YBxwI3AvsD/xX4jIjsa8/txPRD3xv4PeCdInK0qv4CU/lzh6ruaX/KCpt9HjgSU2L5O8DHe9rXK4C/wjRY+irwDgwpPgF4FKZs859B2q73P2F6axyJqfvUCpYQL8E0DDoQOBn4uwLhnQz8OaZsw/V2XYipZ3Qp8AXgELuuL6qpDfQl4KXeHL8LnK2q47Zr89Y4y31OBC7wzh+LKUOxn93z2cCT7Zy/C7xLTHVhh5cCf4r57mwB38D8P++PKY7n1wwLWBICUQTUQk2ZcFfD6f3A7SLyWRF5qDdsJ3Cmqo5V9ZOYRirPs9dfoKo3qMGXgYsxpqu29/+gqt6jqlvAW4FfE5EHt7z8OPtk636O886dp6pfU9UEI6D+PfDHqnqXqt4DvA1TQA+MMPuQql5tCe6tbdePIcmbVPVDqhqp6ncw1XVf7I35jKpeqab3w8cxZOWu/amq/ndV3WU/B1dh9CyM4EVEhhiymdY5Pct9ngdc6L3/kd1rDHwSU+X0L1R1S1UvBkYY0nA4V1W/raq7MFVgd6nqR7zrg0axAghEEdAIVb1WVU9T1cOAx2GeOs/0htyi+aJhP7ZjsFrI5dak8XPME+j+be4rpnHQ20XkBhH5V0xXM9peD1yuqvt4P5d75/zGLwdguth925EK5un6AHv+kML4H7e8P8AvA8f6hAW8EjjIG/NT7/W9gHviPhxT+K0M5wFHicgjMJrO3ap6ZYd1+ZjqPmKq6/4K8HVv/G3e6/sAVLV4bM+a8XVjA5aEQBQBnaCq1wEfxhCGw6Ei4jdTeRiwQ0Tuj3l6/htMt659ME+fbmxTRcpXAC/AmHoejGkbi3f9LPDvfQdGKD3WI5UHq6oTUreSr///sMJcv8AQjYNPAjcDXy4Q1p6q+poWa7wZeGTZCfsEfg6GdE5hem1ilvv8FsZEFQIBNhyBKAJqYR2xbxSRw+z7wzHmB//p/EDg9SKyh4i8BNMJ7kJMhNT9MW0eIxF5LqZ3gMNtwH41pqS9MGahOzGC+G397SyDNT+9H+M/ORBARA4Vkd+yQ84BThORo0TkgRg/jI/vAi8SkQdaB/ervHPnA48WkVPs57OHiDxZRMq65RVxPnCQiLxBjLN9LxE51jv/EeA04PmAHwBwhHW2H9HyI5jqPkyanQI2FIEoAppwD8ZBeYWYCKHLMf0Z3uiNuQLj5L0D44h9sareaW39r8cI2p9hNIS0mZTVTj4B3GjNMocU7v0RjJnnFkwjl8uZH96EcSRfbs1clwKPsev8PMbUdpkdc1nh2ndibO+3YWz6qcPdfgbPxvg7dmDMTO/AEGgt7LXPAk6y1/0QeLp3/muYHtjfUdWbvEsPJ/vcGjHNfawG+SyMiS5gwxH6UQTMBBE5DTi9Tb7CJkFEFDhSVa9f8jouA/5BVT/gHftT4HZVfV/FNT8ADsY4kk8tG9N0HxE5BniXqh4z6x7aQkQuwbSjvVJVT2gaH9AfQsJdQMCaQkx2/NEYP04KVa0ta6Kqj6k73/Y+TJrg5gpVfdYi7xeQIRBFQMAaQkTOAn4H+CNrOlrofWaIsApYQwTTU0BAQEBALYIzOyAgICCgFoEoAgICAgJqEYgiICAgIKAWgSgCAgICAmoRiCIgICAgoBaBKAICAgICavH/AZiRDovRZP98AAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# make_mtf returns a prysm.otf.MTF object, tan returns (abscissa, coordinate) arrays, we just take the values for now\n",
"source_of_units = make_mtf(0)\n",
"mtf_values = [make_mtf(f).tan[1] for f in focuses]\n",
"\n",
"mtf_im = np.asarray(mtf_values)\n",
"plt.imshow(mtf_im, extent=[0, 1e3 / pupil.wavelength / 2.8, -2, 2], aspect='auto', interpolation='lanczos')\n",
"plt.gca().set(xlabel='Spatial Frequency, [cy/mm]', ylabel='Defocus [λ RMS]')\n",
"plt.grid(False)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Plenty of ripples. What if we plot the MTF at a single spatial frequency, say 75 lp/mm?"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[Text(0, 0.5, 'MTF, [Rel. 1.0]'), Text(0.5, 0, 'Defocus [λ RMS]')]"
]
},
"execution_count": 53,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"idx_75 = np.searchsorted(source_of_units.tan[0], 75)\n",
"plt.plot(focuses, mtf_im[:, idx_75])\n",
"plt.gca().set(ylabel='MTF, [Rel. 1.0]', xlabel='Defocus [λ RMS]')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Clear ripples. What about the area under the curve overlaid with this? Our wavefronts are rotationally symmetric, so the area under the tangential MTF (or any other radial slice) is proportional to the area under the entire thing."
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x1d117e2ff98>"
]
},
"execution_count": 58,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"mtf_im_auc = np.trapz(mtf_im, x=source_of_units.tan[0], axis=1)\n",
"plt.plot(focuses, mtf_im[:, idx_75], label='MTF @ 75 cy/mm')\n",
"plt.plot(focuses, mtf_im_auc/mtf_im_auc.max() * mtf_im[:, idx_75].max(), label='AUC') # arbitrary normalization\n",
"plt.gca().set(ylabel='metric', xlabel='Defocus [λ RMS]')\n",
"plt.legend(title='metric')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It misses a little bit at this frequency, but does a nice job of smoothing out the ripples. It also looks similar to a Lorentzian or other curve-fittable form. To demonstrate the bad idea-ness of using a single frequency as a focus metric, let's crank up the amount of spherical aberration and put a bend in the MTF vs Frequency."
]
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {},
"outputs": [],
"source": [
"def make_mtf(focus, return_p=False):\n",
" p = NollZernike(dia=10, Z11=0.15, Z4=focus, norm=True)\n",
" m = MTF.from_pupil(p, efl=28)\n",
" if return_p:\n",
" return p, m\n",
" else:\n",
" return m\n",
"\n",
"def make_rmswfe_area_under_mtf_tuple(focus):\n",
" p, m = make_mtf(focus, return_p=True)\n",
" m_strehl_proxy = integrate_mtf(m)\n",
" rmswfe = p.rms\n",
" return rmswfe, m_strehl_proxy"
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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irsKAy9RT6aUAmojCdZ+Cr9i3w5R+AnfAYmWyJaoIwctfp56KajH4fpvaYV1mWtQ0UTluZ2mvoi4L1Oa6mlpq+Ar63uXP25LZSaywlsK2PRbL9FbLP6zxFmv9E43Q32oZbNOgt8NfHGq4WznO7LmtHXPOTyXr8Vivc9WWutozsGcDFCLyjSLyj0Tk/9yz/eeLyCdF5Lv973ccOl4UMfkO76WQoGhXUk/+tj1KkLTopYiC9tHST0G8UW5r+xbxv3Khlua7oh8FMyddJTtKBZQDQJnloJ6q0pK6Aqq6bCG3i5P1FNiMrxBPay0kye1EPHIZhnmPRUNwzx3/LlhUUnyN5N6n46Tz81u1p3JyjxU5PFXfxTVKudozsOeUevrjwDcAHzmwz19S1V926gENJKzySQLkTk1BtjjecUQGL1W1fEytfMp9IPQdEgI5JUgg7TQ78C5tI6vFieXaJJe9US80pG5pqvM/3Q41qhAJ6KY3kAjBtZkaIppUHb/gpxupUYTEgOZcByaVZjfBOAuBylHUklzY4Syg4S3KY213dZA5bzEbaDR3ajP+Aio4ntRHcQ6P8RiltM/JQT+nc7naZ6Q9G6BQ1W8TkZ906eNGlC4kykyKUvkEoAUospreEzKrfNLO5cCLrtI4WroqKepNfGiparJUlWy39sJF1qM08NVehWBRReml0GyAERptqNKn4RIg5GyZsVLOSgMWEipxLrUJT+d9EzjHAVPqCSo3stNnAfV54r0VS7CYeIs4B4g9k/CKzYcrnVBGe4pw4CWihqszvtrV9tqzST2daP+CiPx1EfmfROSnH9s5yNRwJ673lDvIcYoorKPaIwqPKoqUx6pAYFv6KgVYwpRa6nuASYJjsX+JKmTjvAZM6aFxnKUzpOxfeI1CGLdigDqV95aS1qovVQjgdoiRLlJKiz6LvdPvlhzEgrdYHXDUHmPFdviLpS15jGPO/NyeilOPe7WrfYbbs4koTrDvAr5IVX9MRH4p8E3AFy93+qFPJH7u17xPQrlT4Wf9ylvCL/wpxKgMnZK7UMls9UqltvIJADEw0Rim7mvfX5wA166s/DFS2xvr6LqJbxhHTzPF5tgWLUjfV1kP8ugkeIRurCv/IvWhkhEHhJnjTsmwrcyrkAAhI2W2n+oMLGr3djl+e04lulCxVFSZ7tp0ca9GFmCP75MRb3SmDgkE1rTUuXYIDI6lr64AcbWrnWTvDFCo6o82t79ZRP4zEfkJqvrD7X6f+zmRv/rnvpAfya/5/rHnO1//RL7tR5QQvOqp9/RTIanHEbzpTkoRT5DaoW3if92s98II8IhWWQ2pqaeSVmIYzFl3o0cDbfpJKk8hnfVMaDaZD9na8wpBDbgD72p3eHHimrJvMz2nSYZcawOg9Vg0H5Cnruy0ZYezEO/DkLjLOdSy22KheT9FEmTZOzF7+nS8g6qyh4YeHbJTeY3HtKtk+dVeoL0zQCEiPxH4h6qqIvJhbC3/ibV9Y7PKDGIcRQiTgmzuptLCGiW45pOG8td0aN9s5txDSgYuEi2aEMzZ9h0y9tAN6DBMQJRSlQ2p/AN4VJFn++l2a6vrMoOilkJaykrzBA6UqqnS6AbWY1F4hT09Fjro9Br1g5rSbG1kYU9pVWBLT4fMye5DvEVrRTfK+y/2f+GnpI32dGK3DvkcbmOfI79U5dS+41wB5GrP3J4NUIjInwZ+PvATROR94HcCPYCq/hHgVwK/UURG4DXw5arrV1jSTPQETMRmZoeZ1PjkrG1CXZ4GGGmp93eeoo8GFMONzZJwAtxGqgaUKf1E71PtPILQwXsq+oR0eV77Xlbznc3wVteAYhxh6yCR4yQVEhVV4yvsHAaU4sDTNIQoa3XcEoN1cwfXfypltXWSne0rs2FGDhbJxqfSjEdtq5zK86WIIhawwJ/jwoLFZhVS9fV2S2j3RRonpaXWfg6ngsYp2x/LzukUv9rV3oI9G6BQ1V9zZPs3YOWzR62NKHaEAUt3dlnhA+RMSNnSSd5MbaS2kDcOFHfbaUDRdrAUU+nSroS2ughgNCdbmunGEcboznRRLrvpUc2Iz9ZWH24k3YiGiLTfkPMQpVIJ3doCvyjX1jnaEydSJEJqWW0CKAR7np6zdJIx+uQ/U5ilqZ5quYfajd1ay12UfWBKKRVrj3PEZuKH75pdQeBq77g9G6B4DAtOOnQh0cUMTepJ+4j03dQYN07zswFUpO6nm97SRHdbS/Vst8h4gya1mEfEQCJODXjGMQyWItpufTRqwweUFFRQ14HqkWFER1/xj+Mkt1FmfIuAKEpn5HaMXgHlDjRNjnzWUR2dLPZt5rAn4qJ+BrIAskJyp1R1n+xpTRqrJbrnH/50u87bbqq/9oDEIdJ7tfv7FF7iMSOFKwhc7TPAXjRQgM2k6Ive0xIobm6QuzsXBsxIoqZhNIImsfTTTZHzECtjFbFVfyvnDRZVxFh5jQIqOo5wt51EAOO04icG0G6S7YAaVSDi0YNN05txCDlCzJMcCEw9Fjl7j4TPsahzJuJEcLcfkpoooII59Z1ztOjC+jfWRQJ3HPYSOGTBXxzifJd9GadwGfchv8+xKyBc7V2yC6czXzRQRNT5CeMpxAnt3EHeRGIR/VO1EtnR0k+587y9QI6B0Eebo10mx5Vpdq48q5Uc96giRrjZ2D7D4KWvA4w9pH5atbcpqEJse/+BiQbaZqtgWkhn+KCj0lBe+YdEJam1PNen48E08c7Ao5R5Nf0SHoVJG1n4axq5XoYdNXxFcxx/MrVZb2Wy3bJje3aM9jhLLqM5xo6dM8vilCjkCgxXe1etzQhc6Hf8YoEi+IcVyfSS6EJuZlJA3niH9DAAIGMmJCUpFSQ0eESx00+RKqmtN91EgAdstd1bN7Vse7S3clkt3EZphlumeLoOufEvNVu3tnEigqTO+IqyLzhR7TpQIvYawzgjqwWLcux5oXmel8ZqGbYEtXFPjRjXlKaqq2KlByRnq/Zy7mKWVircB7A6Ea85F9/JH1pEKWuigSLHI4xT7FjK6qWCxLV092r3tBcLFIDNonD12BgyIWrtzk43Eb3pkbsyqjRXnkJdyoOoE1j0kdAb91CE/BhGZEhW4RTNYWvE5lH3nUUV2y263Zqe0zDAtptkPBbENjqNTZUiL5510oLC0l9Sm/Eimh04wABmbPgDFeMXwCKAMIEMMVhEITLJg+hUDiviqaamnHenvDfnKkNeie59QoGHIoHVGduL1dBVKfVqVztuj3SdvGigAEs/9ZLoJLvek3Vn517QjYn+gZWDWurJCW2vfqo9FS47LpuNr8Szkdp33ownzge0FVC+v2wGb3zLc2J7KRndeTTTRDpA7eAuBLZ2XXXgEsLk6BsOAn+schZFO6odiepd3DPeYjHTQlEXNxR2yO4iXniIuyh2QrpnJhq4xjk8NJJ4yMCkl7Difgnv4Wr77REXUy8aKKJoHYUaQ0ZCNrWJDtLGgIIYzBGOieBAIdnJ7FJlFLxLe9NPJHXOlkrqB+Smn3oqYOqr6JyrGCaV2CIAWIYJ7fRWFInx2xvYhjqDQoYBzU36qXHYEgIag82kAHutAhgeUVSJDgzTqhZSyHVb5S3a5rwy90JtoJKU8arNee/jLoqt8g/L0amwuH+gaW/NHrsr+6kjmqtTv9ozshcNFFCqnoyjCEEZowsDdiYlHkPwFNKIbEdC6utsIjCw0CjkLhBue+Tuxpz26zfodmvNdbcb6CMzjUUpk+o65PYWmhGoNQXVdfg4ufqcQmybRDiwZSboZ7sFNGZ37v6adexpqD0VJnnuqSRSJb4NaHIFC4lMvEVKU9/EDDDCXLJ8ybFULsT7LmB+DD/OkqA2HmPFCdcqqV3bp1b7oM7qh0QrjwFSp5zzFUyuVuyRFzIvGiis6snGoXaSiN5LkT2iyJtoK3F3rPLqxngKlxxvG++0D+imQ282yJsefXNn6aCiKJtckdVX2iogpVs7ZRh6ZNtZVFE4ju1gzrljkYKKCJtJ8C9nSwGVCGEcLU0TIhLtNcUJcRVPE7nWU+ncLmBRmu/QsMtbeNpMcq79GVOT3dQzoSqTNEhYONjyfJiNUd0tp536KHZ6J5YT7R4zWnhoOmvfMZ5Cd6o2PV4B4zPaniDafbFAUaZQV47CI4qq99R75VMZX5oy8mZrkuMZZpLjwdRkrUvbR5/6kKIq6TEmZJyUaQmgBOgmroLN4GW1LiseAxqsV2KmBVX5CuvatpLWocqDS0roFiQmEwuMceJaWoK700mK3K1trtM2BVZkP3zGd40+gJmoIDifoXX6nzScRfu/JbtN0mN32BHspp8OOdmD6ai1csC1i+ipuI6nsitgXO2R7cUCRWtBMp1zFdSRqDYWtXAU+vo18t4rwpCm8aXluhNcTXYiteuQopwnsCi9FmXeRYAy2EhvemSw3grdbr1je7BU0YLU1iBWORV8Il6ywUVS5mYXaZCi7bSBqh1lp4t2XSW4BSbOAiZHrzpvzit9D41U+T7uApiCDXACuunuhkUprc4AY5+tNvKdKh54KQL8KYDgVKd+zmrxChj77ak/m6d6vSfizl40UASMoyhT7qreU6fkXqzyKVjqKW8H69KuhLbWkakaxHWiAiG69HjvPRJl7sR28F4LoajKgvvEKEY0397YVDswsEjJqqBqRZFMzt/5CrJLggSBwY+Ztug2NWNQIxp1IppDsE7qrjNHX3Sgat+Ey5on5iQ3ceIuClj457PGPcyiA1Hfn3laqukmt2MoRTiw2r7GvXKRaZouiIcqzu6z5zq74j6A0t5+W+f9nEDrqQsRnlMp94Wa7l40UICJAvaSrAIqqPVGeESRerGZ10FsxrXPppCMDTLyLmX1AiENmPbTjUuPD4NVMQ0j2g3I4EOKwqICSoPNrtj0BhTZUk9lCp4M0fkGl81oq4q6qTpKq0ZSAB2r0zeOxRvpmh9FacojBiTFqgXVjkfVNI1JVX+zM+6ikPLi3eolnVQHGzXktIqV1BaKoQBXsYa/qFEG1MFHB4cXFU5jJcI4ONuiPP0+ZbvPwcmdam/zXA85xgtLSZxlbyuKeCp7wtd70UARxTiKknrqYkJiNgVZTz3lTSR2nX3o2fL/piRrjRRFTbYOMwoLocBSybQdbAxq31kFVEvWihixXVJQ48bA5e7OtqdkKakgiHb2rbSzs0uDHRgxHgc0Re91sChBtkDMHv3ESUiwiwZUTnKXdFNb+to256HqgOSRQCHKY6xkvek+YVVQTRpJiyS56zwZoDQcxsJEHCya2RZ1+FFJI7Vd2bbD/BgHQOIgn/FcI4h3zfY5q7cNDk99Hk/de/PEoPSigQKMn+gl0QeLKiR6010UkgNF1/dGNgcxUntwDafGCdXGu8JTbHq42RgpXSqZBo8q+m5quoMZsS1qHduMyVbow2DOeRxd7M9jkd6jiBgazsQrqPrenlvUYkvfRErOa+iukKAIOjLThyI1zjJrdexlf+s4j9XRt4BR01WH5DD8vGcShCXN5jYDC9glvncoh3ml1IPA4JC9zZXwc7fnBg7F3lbK5zmlmh7JXixQhKanIWLlsX20SXcp4gOMTByQV7eEmxtbreZMGDJhMEBBTG5cUOcpBOkCsukIm956IbgzB1uiimFEoqBE7/AWA42SgnJ1WdRI6lIFpSkhalHBJMpXVtLGWUhp4qtlrp4OcrmPmjJaCgmW4Ud0TeNdnkAG5txD4UtgBhZ2KjI9luZRxY7Q4MJEbbJeK0M+izhqSipaCmxpjTbUql2qr+Kc/c6xt+1M99l93+tzeD9vE7jexmu/BWB6sUAB3iBNrjxFFzIhZlJX5MYh3QT01Q28urU0yZis8W7ojOyO05dSmu+0DyY9fmekNjEaOd1GFaUvgTBJe7Q6UCn7RD1F3+QpItj6Kj0EL1elSbuIdW2DNb6V8amuO1UE/pacRu0AB8q8bikzw32mBT5zQgcHi0R1+gUs7BQa7qIQ5zlPgBVYJaqnu838ihIdlHOEemxgzmPgx130VsyiilNAomx7V1afL6Rq5lHs0LlfQeKi9qKBApyjINOFTB8SXZfYRp0qn26E/N6GeHuDfvqNRQOvt4SbjrAJ5L4hiMXKZHMUq37adFbNtDGuosp6dE43ulNMAAAgAElEQVQghwC9TMQ2mAPvAtxY+khy9pW8VyR5uS2Ddzp3E+gUctvGnEbrw/DUFcNYX0J9DreMMnEOvoq39JFULoOcvHkvWMd4EAOJogKb1Zl9P3dYbbIj5/lUvLTgG5amu2BhLzG/EGpqCubS6Gspr1MGGR270J5bOe1j5tzfVZB4rgDxUl+XzwCgANd8crCIs0l3kDaBdNsRbjbw5g7dDkgIhFcb5L2+qslWK2DR+5yKTY/c3JjM99ZnT9zdTeNQu7BLbIemCspX4lL4hpwtDQXGIWyyRS1tQ14r/60+ma+fOqiBSeNpGD3tZBpS6s15dVqey5SL5HmT3YLonpHSzoVUsh0msPDHBBrtpwNcwuLxxUil+aS8pa3Mt9AyMEnY78Av0Y39tuwhpOmlHM1zIaqX9hxA4jmk4h7Bng1QiMg3Ar8M+Eeq+jNWtgvwB4FfCnwa+CpV/a5Dx7ThbtlmUoTEJow2l8Llxk0c0NJPfW+KrHr3xhzm9hVhyEiOSCpkNoAYOR0MLOTWGunYDi7V4RPwuq2t+ksTnlAaO9BsPAca0dwhaTORs2UOxXZrzrlU/5RoArybO0A0clyz2n5gztrNxAt1SjeBOUnRqZKqRAmA0PmwI9eLWjrxMhypHKdENgUwCmgsogt707pzPDto6+Tn2y09xnHH3mw3IrwcM67uPn/5e1zYz7Uz+zHsuTi+5+Cg32YE9pajv2cDFMAfB74B+Mie7b8E+GL/+xLgD/v/g1bKYwNKFzJdzEjMaKfkziufboKNRoVafSR3g41H9TnakiewkEAdaKSbDr3dWHnssEUHGq5iigSkCyat0YAFXUCyCwdSAAD0ddN9DQuZjVAzQXX13kWUDUUQUEs1VW4GE2X1yCJNc7jrYWTiIEIPKUCKLv/h3IM2RLdmIDUzveMMoGapqcJpVNCY0kwtcNTjNhe8qqXMZuKAS9BYjTjiOihNL9YcThabjjic5wYSj2XPASBOdY7PBSQe6zyeQYrw2QCFqn6biPykA7t8GfARNS/zV0Xks0Tk81X1B48deyOpzqToY7Lqn85VZD2iyJtIcIen262pyQ7JRAKjujCs9VWo+H9XoJWNK8jeWWShpQKq205ie3h/BTRVUO6gb6jEtWa1yXlD01A3jNOEO+cm6o8nBgj9xFmkbD0ZOftoVXe+7bzvqA5ace5oY6zDjCRqjSrUm/rUR5yWC0JTaspkZUpHtY12bUrK52UsRQP3Ol/nSWYKs6dOuGvf19L5HxAbPFpyewoP8q7bc23eW7PnQhy/YJCAZwQUJ9gXAB9v7r/vj82A4oc+kfjw13ycjJJQ/pUv/yA/51d9Fn0YuQkjvfMUY6eoN92Vfgp6E9gr6q4yJMKQDRCKmiwYTyFeKtsbyESfVcGwtVnXhdgufEAoJPLk5EojntLIaOQMQ4eM3dxRD1s0R2umK2NZl0KCIhYtgaWiShRQOrJVrfu8EMcxmeMrw4yCeKQRvLdhQXZjw5QU5g7bezCkjSraC2f5Y3fwEAfcg6KBskeGvNh9Ukfl/PfYSWBxwnGudoY9J4CAdwMknvB3+C4BxdqntvMNfe7nRL7jWz7EnQ58Mm/5Byny8XGu9xRq6kl9LoX1U1i3tY0j1ZxtjvaQLM0kwRvnSpmpk9o5WFqpRBXDjRHgLv5H6YkoVVBeJluPgUlmtE1wkm4JfoyS/tFhrMQ0pSu88BYtWGSTAFftqkQ5bd9CzjVNpCk4lxBcN6poVZVxq9rwF6D0SEjz6qP2y2h5iNLM10iBLOU8Cljs9E4sRQP3RRB7Lo7WyZ8i77FmR8Fi2vFexweuIFPsOTjl1p7D+Rw6h7Xf3CNHuu8SULwPfKi5/4XAD5zyxCI13ouR2jHmmYps6sX6KW57wu2tkbZZTd31rke6QAhCClL5AZVCaqtxFX00/acx1ZQRKZkWVKl0cqAQQn1+OZZ0PtK075C8MdAoXd/lWD6StKRyjBtoUj5QUzw1QvFu8xnf0JLSMU5Ed3lObB26ALFWRpna7py/gAYklgJ/yZ1uqy4Lc/Ib6sxvE1MM8/6JYnv6M1b7KMq2ViL9iFPfP21vv92LDD/xfB584d+3Gsr7bx7N7pNOeal6TefYW6zWe5eA4mPAbxaRj2Ik9ieP8RPWcGd9FEEyXUhsogPFMqK4EfJtT7i1CXZoRu4GwmawBrs+IOq/V5leoMiP5z7ApiOMG59P4Q7e504wDDO+YkZu45VQPuio5PwlRjSYqm0ep4Y6wHiIOsLUOYiWtwAvw40uGpibqXfNiFOffAdYBBIVLYx9cZRFi6mzVcuMvyjlvWrzucnBO8bnJaulyc4G+i14jPqFrQBHOUbVhFpUYu1TnG2tlhI3FVsXskcFk3MHN93XmT63VfrSnlOaqbXHOK995/KWS7qfDVCIyJ8Gfj7wE0TkfeB3Aj2Aqv4R4Jux0tjvw8pjv/qU4wafctc7ob0JoxHaXZ7NpUibQHqvJ753i7y5Q++26Bvrh5Cb3kjtXl1V1iMKO3EXDLRubU3dTrmsDiNEm2ZXVtQaOnPkM5VZ6/wWutpvYQ1nuU7hK05HU0YKcS7eJxFj7ehuwYI8gUR1wK3ERjtbWxVJzqm0/EX9ooJ58cJfFNmPlD2KSSY3nlh3cEVTigWn0YJGvsdKuoTey9Vwe+Htudjum556MnuXCfSHrtA/00HiHIB4xN/JswEKVf01R7Yr8Jvuc+yINdwVGY8+ZkKXyb0aV9GL9VPcRvKrnnizgbst3N1BFwnbW3LqkBTMDwVBgnc8B52iCrUKKBtSdAPZnW/OloKCMl3VOqA34qkjf48lRVX6HLCyUkm9VzDp1PhWOrhHpvLWTW+DjggVKIhSow3BV+Yu6ld7G4qjrFIexZOXDnCvjlpWSQUfjpQTswFM7er/wCp+ll5KaWf7jrUr82PNdiv2mIDwoBTUpeyxU0bn2HOOIIo9pxTYQ0Hike0gUIicfKaqq0nlt2sRIYq6guxoEh4ydWgnn5+dO+cpbj391He2St5urRJqOxCGDXmjtvCPkDGwAAOOHIWYhdzHWi5by0C3gzngN8Z9zMjtzgjtYlqql8igsc6YKOAiw1jTPXWmBSB9Z4KCYGBRUlFtOkrjBBI+2a866JZrGMapqikmU6uNFc1201JEaGd1+2S9VR6j2KHBRW7VsZ84rEhKkcCiauqgnbgCexQgeIzVX9Ox/yj2Epr7nlMUAc8eJOB4RDGccAwBXgMfePjpPI6ZMKAR2jeeejKewsaAWtWTy3ncRLqNC/2lDG/uCG+2yPaG4KWw4AQtUEpl8QqoENUqoJJ6w15uGt+SgY+DhJWcduAqtbPSWQcRiwL6ibPofO62k9yVD9CJ4K40ikwpKIA6WlXEByUlR8lGpryQ55opg5uEAc0+eS/G2gNSf8yFwxDqqrakpGY8BkyEemCuVgvMGu7ENafahrv24jkYHezpyF5z9gfC9Xe6+a51PpdycOc42DVH9zaHRJ1aRfTU3+lOIcHzAohix4DiNfDTj+wjwHdf5nQub5Z2UosoJBmh7eKA0im5L6knIW2UdBvINz1xs7FVtDt3eb0ldJZeyV7BQ5Ypl+TlpEQhd64DVaKKMi7VuQK2g2suWVmo+PwKEZ2qobIds+UsiM5FbL1CanQhQFVr1HNHD1SpcElhtyqq64yQztEb8wJSIpPCXxSOQc1hlyqqWrlU52sXpGzMS15R8WBjARoiK+KBE0A8itM4Ih8yPXTgtc91Ivd9H5detT8UNM4t1VyztwUSlyKHL32O94gi2lksT23HgOJrVfX7jx1ERL7uQufzaFZKZEtE0cdE6LMDRQMWN4H8qiO+ukVe35Bfv0Fev0G6jtBFG1qkAUnNyrdE+85fEMWIbVUYffxp7ZZ2Uvn1G3fuuQELr1TK/oNYcBZWZmqEuACkRMgZHafVvap1dsNoPEj0Jr1Cdrc9Fz5bmxBQSTVKsmikkMPNccsEPH/fwLyhsABHC0owgYYUbsRLdP391RTVbFTrkdTTORfLjtT5ic89Bxgu6Ugu7cwP7bfvtS4BDnD8M3xKkLhPGvIpSOsziyxO7vG5oB0EClX9XaccRFV/z0XO5oIWCAQRk1YSm0lRpt1Z5VMmhEzqvUN701RA3XbE924Jr18h24F8d0cIYjzAjfVVSDDROzXlQX9Rsd9VF6wpukzCyxnJt4DzFcNgKShP8QhUANDOwUIasACIWAe3TM7cVuVhilbA0jowcQPRZnGrNxIaP1KE/MQil9J3kZv5F81QpGLaOHN7rYmjKaS3NF3e84ojjzLsTVEn43mUIX6uFTQO2X2ig+ecJrqEHeqEP2TndP+edT6HZFke2e6T839GIHFK0cVesHikyqejVU8i8gEAVf2U3xfg3wB+BvDtqvrRi5/Vha30UpSqp030foouM8S2n6JJP31wg7x5hbx+jf7Ylvyp14SbG8J7t2hfOqzF8jGdRxMlDeUjU3O2FJTk3khsPx8tXEVJHXl5qwGARxZxcrRzsAgWffhLSYx2HFeK1TLMqBDSKRsh7byBbnonxoOv8v2vgIVzGKLdbq9E4TJabqFEHdmcvWYDph3Sew00VlJT9obnAFUv2FYjCpr9jzTfHbvgL5HqOXSM51fn8Xi58KdyuK09NL30NkDingDxtuyU8tiPAn8G+C/8/tcCXwX8BeDrReQLVPU/eZzTe7hFMaAowoBtL0XXJaTP5D6SN+o8hZBuA+N7PeEDt4Qfu4VPvUbHAV6/QT79htBbmWhWa0LTzLRaDpZj15Iq6gOqvprHOYDB5D00JdeU2sI21vJVc7TRgMgJ7lWwCAG6aLpQPrfbIgPv4HaewXiAZD/ULainoerku0bAr0QUVetJs6XONBuPkpI11lUOQ0Gbpj1/D3Z8nfiLxfjTmdXKKU85qXeAl4ilIbhr1VYhxMGIdLjfSuopOnGfCkQukC7a56zuRey/DYC4BAA+Jh9xQYB4yhTUKUDxc4BfByAiG+DfBL5MVb9VRD6MyYI/W6AACGIRRSRzGwZuQqIPE0+RNgUsbD7FeCPEV4H03obw3ivkU59GP5UsBfX6DdJ3BBG47cgOCKBzR1j5ioB2CmoftXhZq2z9o89q+frt1lbtY7LubO19PkSuqagZWJQxpNGrp/yvcgw4+Zyn1XhRey2RhtqHU/sjZBFdWBoo2OzwlEzCo+U4WOETyvPK61cgyrXZkPK6yyqmegxXsfXZEoLUklttU2oVQPJcKwoqQGlW9g4xelsVJrPy3ROcxLlppTOlSh5kbyPFdMlKoeX5PyZwL85z7/ewfD/PIG16ClC8p6r/r9/+OcCoqt8KoKrfISKf/2hndwErH3ksvRRiILGJiU2XCDGRuq72U+SNkG5gvA10t5H83i3hA+8ZrzCO6I99ykCikMpBLIujsvsbC5hwIHHqlEgZub21lNDdnT3mDXkyuCzHzWbSamrAolp11urVUhOIVI4hCDJEL3WdTqyVAamHc36hRhr1/MMk3CfigBGQFOuUOymzKmAOBG3qqJDUs88mTIS6CLPIY3ZyJdqx4wlz7qNGL4XbiOW1g0dnOFgeH2K0ahe6SGcrv3Md2z38+iXAYO9q9W0Q1GdEDydVBz12BLQnijgZHNa23UcW/0J2ClD8gIj8TFX9HuBfBv5S2SAinwXcPdbJPdSKyyslsqWXopNp2l3XZYYuo716RCETqX0Tie/1yAffQ4YB/dEfQ+/uyCEQus4a87pALiWtEVp5DyOoMcDwkahlxrboK0uvjGOdcZ1L17Wac67EtUZLs0RZ/AD9dSImmwG16c16LsZJ56lUGhU12maCnYYR6bpJObdEGF7KWl5LwKqoiiR57b6ecwi1V6I+3nAaNBeLp790Bhr+nLC40NoLqWmsE6bzs5dWV8JlkghZOoADEiG7faMLgDn3ovSL+znnn5e26nieMnK4Rwpt7fPd60SfKoo4FkGcvWB4e1IupwDF1wL/s4j8FeAXAb+i2faLgO95jBO7lEVM7yk0EcVNGNmExE030nVeJrvJ5I2nn26E9AbSrZDe6wnbV4S7AXlzR/7Up+D1a/RmY93XXfBubecsokxhjNjjAKiXuvYR1CIGCcF6NO7u0GGY9Ja2vrKvs6e9Wkmj91M0znEBFvjsCPps3MXojX5jQmSchAFLE+BiEFARBiQGl1aXWaRQZ0gQJw6jIbgr+Q2zaKOdM1EUXQXmqrJa+kiCNSzWEtw9ndaz1FUTccDUHe42A4DlRD7boZ5TtTVAqZLoJ1jWt5feWrMDTuZkcHhq3uEB+lxPBhLnpJie0+/hDDsKFKr6x0Tk+7C009ep6l9uNr8GfvdjndylLIppPRmhbQOMXsWBm+hd2l0idx25VwOJDaQbSHeB8b2IjBv6O6uAkrs7q1q62xJe31WnRh+9T85Xx8vfca2SMocPG2ugw3/QRXHWBfpkGFG5Q3Kus7c1dza0SMMEQH5sAO2kApJFBoXsTtaFHQM6DLNTqzLcB4QBddYb0XRjQ9ORbc15iFYpkdJYV4QCZ4OJFhdMLZEt87o9mqqfLyW1taIJteY0QgMY9bnN6y2Va9dAYbmP77c81ppVtdunsFOinHO6zx9zxb1mR9JK94nG3gpIHDrnNYA49r6esPz1mJ0kCqiqfxH4iyuPf+ziZ3RhiyKg8xLZXhI30aKKTZcs/dRn8iZY9dONVT+NNxDGQBg74psb4usPIHdbeHPn2k1vKAJ9knvzmc4dEDz11PIDtVfCfjQ1WsgZ8g2zprOUkC11BoX01rinN73zCNHS+jV6maIMdT30Kh4YpqFJlc8oQoHJc/lt9VPtxSgt4uXQE3hMWlIL7iQAPsyplrx6tDBpP83TSzvchgMdMOvbWL2sRSbsWHPsD7FyXq1D2fcaC6A5BUzs0A9wVveoRDqLd3islEyb0pztcyLZe8R23uPbAoj7gMNy3+cgNslpfRTfeGwfVf3XLnM6j2PRU0/R/ypPEUduvEy2dmkX6fEbSFtIgxA2gfSqJ3zgFeFuaxVI44i+ubP+Ac/3S7AmvwzuSHe/ZJPkCFYEper9Crnm06VoLUEdyQpYxPHKS0N7rQOGlGDaSzADC3stQGIFhzLqtPZedKNP1GuccevQU5pxDYo7QG/iq7pPxWq57fTJIzpdPIXP2JP2qbbYPuM69tkiRbbj0B+7DPahMunH7B7SIvcmo+FyILEKCOuFC2cTvacA4SVB4kCK6SBAPCSyXAOLtxBVnBJRfBXwf2GDg7aPejYXNmMPzAlGlB7vpfD52RsvkZ3ST9GjCuMpwlYYBwijkLaR8IENcfygOetPfdp6IbxySbxUFSCoegVRmKegBJs/IdMK3rJQ/cRZdOMk+rfdGlhgEUYI865s7SJFidbKZRcrNRGTQWeS2ajpqNRZKW6RFXHCW8qAoyLX4YBRwUsCEjP0niIrEuT2IexeFKVHAmglPIDdPokCUF5ttSTD7am6e5FIsK+5Lbkt0wDrR7E8r0fKFZ8IEgcjiTNB4a1FCYfsBK5hFRge0CR3sBP/qQFijVy/b5R5JLJ4isqnU4DiV2B9FL8e+CbgI6r67Y96Vhe0QClI0loie7vgKW77kTd9YtxkdDBSO91AGOwvDaYBJR/cWFapCP0VRdhxhLu7SshK6tBNZymmYHyCtrxFsHSYRkFUqHLiIjVFZKJ+9sMr/Q+6HRDxXonsjr6LM8CoXAhMK/zo14nEib9I2STUvXdDvCLKOrsDMooNI8rZCGdKma1xEeoVWgrupMPUYLfkMWjed0vwFgI6NxdHSVOt2AwkZvsY56FZaedT1Ea8MCeg64S9nR/LPcHjoeBw5sr/2RDPSzvVoS62XcIuDhIXAIdTgWH3pc8omHgiO4XM/ibgm0Tks4EvB75ORD4Ha7T7hqbH4llZaJbyNrtHd5Rkb8LIbRzYxA1dzMQuMzpXkUYIWyHclKgigIJoTz/cEkbrqi4DiRhH4yzGEW42Jga46auIoAn07aZDZnLiNAGIWkqrNslBdeSi7tBDtAl8XVcBw4T+ViKMAhhIXbWL6kR6F8AIXrIrwQhwEUtTBZn4AgnTRdBEA1qrlQq/cNp3tXpRtD0aLmNuIBDnTXR1gNEFLt4LpYyOXuSXiBieGhguwTHcJyVzJJV00VTTgfd0yu9r9bd16uJjheOa/Y7eMl9x8oQ7Vf0R4A+LyJ8C/kPgdwH/G/Ctj3Nql7W4KJFtJcdv4simS9x1idQH8iYjQzSeYoAwwpgEyYLkSNhukCHZij7cmSP1Sii92yLDgNzeGkmsvZEFnc/cXv6WAkwjUKM/x56nKdnmIvrnFUGWBhqMI+g62GSLMLxjWTWajLiGifBe8Bc1ysiC9A3pPVp1lHTZAKPrkHF00MrTD7ohvqu1Hdntj7wZXFRJ81NWW0VSJGcvSy3kdzl20+NwodXc0s5e2T2gAmnafCYf8dS9DGG3efEiVT5LOwACjwoQx6KHfeDwkHRmUVF+pnYSUPiku18EfCXwLwH/I/ClXg11ERORXwz8Qezq/6Oq+vsW278K+APA3/eHvkFV/+ix40ajjm12NhOhbVIeo4FEtJ6KN33HOEZSp2ivpA2EjZBGIYzqQBEYtxEZNkRVK1d9c2fE9uvX5tSHwcjt2jCnkCJ0OvVAFCu/DTG5conBHL0qcnNjndoFiFr+wGdlEwdz4pvexAc7AxpVI5olBgOiAhjzD9U5DCPYKaS3E87Secdz6iuxXfmCtiqpEQ6cRRhNf0VJG1mkMvEaU6/EAfI5NpP54Pwm6yMX4NkpofrE8y7se+WRn7IL+j68wpmAsFOmfMpnfyiKuC9wPhY4nLtAWVbUNb/V55SCOqXq6WuBXw38DSzd9FWq+uaSJyEiEfhDwC8E3ge+U0Q+pqp/a7Hrf6Wqv/m+r9NLmghtSdyGgVdx4DYO3HQjm25k6KI13iVBxkC6xQAiiaXCE4RXEckbCELorNKJbJIcmhXdDgRf7QsYsdpFA4sYpxX+vvLLoGjfTZxFCGjOyDiiWwwssoIOFq00jXlWqtvVngSN9nyJARu0VCqg5p+NRrHtbUpKtc7qllQa6xwsCgnemcqstN3frRS55rmMiAsIinMZRdiv9lDss1MvwFMrqOr2IytTTnTwb0uP5wCnc9JzZ/fPaBR7AFm7fM7B7+ScKAIOfxaXAIellM6aHfodLxcty+/vmUYWp0QUvxX4O8CPA74G+JqVVcHPe+B5fBj4PlX9uwAi8lHgy4AlUJxlUw+FN92pNppPIzcysnGeopDa27Fj3CTSKOQbiyYk4X9CSDCm4t38NYDgk+tKqSyqlroJgpTqoM7/vPJozWmrWAkrQWZT7WR0B+uNcQYWE9mNeE9ykRrvOq/Eml6zgkYQioeevb7/16Ialaniey1omOR4hhztfwhozJNwYAxGhHsDn9EJWjkFaXsxuECaaCXNZQ+3j5/ofBbb977OU9kpn825n98DuIRL5uHhwHcE+7+nQ6B87LNYA4cVzmFv1PDQVNNayvYhYP9EdgpQfPWjnwV8AfDx5v77wJes7PevisjPA/5v4N9V1Y8vd/ihTyQ+/DUfR7Feg1/3Fe/xq37t7aT31EqOe5nsTUjcxoHXsZ+iij6gozfgZZACGNkijNa7iyoymvMMQbw6SewHvR1mKq3SOa/Qd1attFzpQ8MjuDN3srs4XCkXymzlrlPfhYiVa8VggNF1Pv40TOJ/QafeA20Aa5byqYe2Vy/RRs5omCKNChglynAinpSNeC+9Gkt+A853cnsihtVei7akdvHY3uO9a3ZG9dA5EcLZ5cRr0fERuxeQnxu57QPFQ+BwAjDcZ3GjhyKHFiyabXvTT0/cS3FK1dOfOLRdRPoLnMfap778dP574E+r6p2I/AbgTwC/YPmkz/2cyHd8y4dImhlJvNGRT+fJoQbJ3qE9kdo3wXmKOLLpOrZ9Io2RcczoRshJyDdKyoXQLutkq4RCQZKan+0icrdFxwTZZljX1Is3q7HpkXxjKqzVcU99GPNPxlNUIUA0TkTZIO1kuyUvUHoeoldEbTbmtLsI0f+XCKNELRUwYK3b2z489T6QWEuBtXRR52yfS/YUVRN9TOmq3el4dqJ557FZb4U9ML/PCjgsgeGc4UXPyU6oKLKH9jirE3iDk4DgPpHePsB4aKR3jlN8SEppBRh2P6szPpfmfZTj6AognGRvsfLp5KqnpYnIDfBvAf8e8KEHnsf7i2N8IfAD7Q6q+onm7n8O/P5TDx5FCKoEUTaa2EiqUYWR2sZVvIk9d93IXewY+2QAMYovlAOSTXbIIgovYVJBNCDaE6PYRLvXPbIdjOTOnoIavMM6Tvl6SR30PZKdh0iye8E6X2BPkJpSUu+yJk2reGAOTI1CrKhNn6PrbHXfdfa6IpbCKhIfQZoIx89h6UMC1hEOSCjnV2ZF6HTOLbex3NYAXEt6l/2kyH+0MyiaZrxq7ypI7HPCFygxPQoCD0kfLW3N0V0yFXgKQJzCreyLGo4Bw337P8p5LzTHyvHvDRZvyU4hs38a8MeAnwX8P1jj3U8Dvh6rQPptFziP7wS+WER+sh/zy4FfuziPz1fVH/S7vxz43nNeIApE1SaiSNyKgYR1aY/cdgNvUsdNPzLmQEqC3gRUhZzU2gJUPNYpOk5Trj9HIXaB2EfC665pwHMpjJSntMw4TgJ8ZQhRjR5kTnb7foD/8ALS9w03EEwHCiOFNQWq2p86kITgK37vGs95et3SrBcaAcDCZYhzFW1qjPq253wGuGqH7oJAeQ8l8liASQseS+BoR6VqU8NvMugl9VQcQXktX72Vnov6OT7hRXmO8uklooATooSH8kG7XcMLR7enLHp67AyuCOYpllM+z3OihiUwXEKGo7yP5QyJU6KBZ8xVnBJRfD0GEL8Xc95/FlON/UpV/V8ucRKqOorIbwa+BcuMf6Oq/k0R+T3AX3PxwX9bRH45MAL/GHvODl8AACAASURBVJMWOckmrlZrh3ZcyI6/igOvU89tHLnrRsYUraciB1K2qAINVvmUxQRN1SMLCWhQtAPtAtoFYpAynmJKObX9EHlKz8x+GmJEb+ETZumf0P6gzYlLzu7E89S0pwppkYtNyRx9GTgkYrMlyrCiJWiITKkp/5MGwDSXc1l8yDTgAU6I+6msVFOh6j0fDXCUqqoV4BD7wUxAAlOkAjupKmkfY8XRnWqnhvxHHMpeR31q6udU538p5dpD7/sxAaK1U6uxjkUN+4DhkPTGudV2ywiiBboGLB5c+voMtZ7+eeCXOzfwbcCPAl+kqu9f8kRU9ZuBb1489jua278d+O3nHjciDJgfK5VPvcuNl0FGE1eRalQxdJExBVIKaG88hWa1NFRmFlmo2BwFDQ4YjZ8MUYy36HsbfjSOc0c3THpK9cKL0eQ1um4CjcJTLCONNgqJASlfaXu8Yo3YoOIXjAv87YBGjDU1VSONvAIa2kQaawu+JYDkxUAkVa+IWgBFE5VM8y4WgNBELbJMOe0ht+snd8BBPUXt+sGV/SEnf2rq49AxTm3oW+OMYB0gDnFHy+NyIkBwJPX2UGAIi+to7TWOWY12pt9zPfYaWDzEnnln9kZV7wBU9VMi8slLg8RTWyTPpDym6qeRuxC5jVb5tE2RMQdyFjQFy37kMHEU7XQ1cecnAIEy6S52gdBHwqa38tnBBf+qMmyCIaHDiI4mByLRR432Gek6W70Xp74ECmg4DKtmkq6zVf8BLkBzUaDNxptURdhskcSYpqimTUMdAg1PUQGraap6uuV5BTBqusjPM8/vz0CjjR5aIIF5iqv9v+LYDtXu1zM/dHFfCkweWhp8qs0qbnbz5rbPLkisAsSp4LA8JscB4mLAsA8U9gHCfbvGlymmWfXSSrrpGUmHn2OnAMWNp4CKvVrcn638n7OZjIdFFcEHGW1cJPAuDLyKWwYNbLuObY4MXfS0k1gKSi0XnrSAhP93UCiRBWDRRRRyL8RNJGw6wrYjvBkNMLYDbH2QUFY0ONmtPnlOAhLStPIP9gOcSmiX3re5IF2xtQ4QaiujFg1wWp5bnHHp+YjRAKrMwwgN4b1ISVVeowGxCh4wAxCYQGRZDlwdfvvWWkdV0nRLQGhvt4ByYJ/VyGLp/NfA4Bjx+IjRyNkaUu1vYpn/3rfaXwLE2jjZM1JLSzs4Y+KYhlILDKdEC2ugcKwn5ASbDaVaixruyzWsPOed6cwG/kvmFUkfXdx/Hu/kgMVponTVfNpI4o3mmoaalcp6E17qAkkNJHIOoEJSk+UwFSYHi1Ih1EQWOQo5KrEXtBNCJ8SNjUINb6wJTpq0T4A652KWbqKkVoA87n+Tp66IJNg5tmQ30Yhi0pQ7rVzGaKBRLrwYkXGKLtaAA5iDB0zpMZoLdHGh6tqF2zy2AyT7HHtWk29f7rNyW84BClVW9UP2qr+ecGkc2mdtGNIhZ3JotXooHbQPHGbPOwIO7fFOsT1k8VlppLVo4RggnED4V9s3Lre5Ls9OMb2D0QSc1kfx1U9xIk9hgYnQroOM2ql3YeQud9yExDYmtjmxyYnUjw4YMtELis3ILoR2k4ZSgRgVDYJGyDEQOyFvAzHaX+isa1r6Dtl29oPd9KbrtPJj2pnZUG7P3uDuimuaKjftK0HQpcPTDDlYm2JzQWg5rohrNJmyrBHewaKNBXAsie9TwKOmosrjp9i+/eqc8uZ7gdXoQddAZ+GMZcchLtMJK4+t7bc8B1hffVbH33yHK7bqtNfKgpfbTulXaR47CA7L11yzUzq9V4BhNVpYppDWOvxnac/mtc+JIFTnz/Wikbpt+X7OBIDD80jO4zMeexYFPKCP4l23iadIdepdAYvCVWxCZAiRFANDDNatraANYFBmZFMIbfNTGoUYFI1CiIIGJUa1HoQAsROkj4RtRO46A4xhBJcvtxRUtouwyGGU9NCa4B4l3ePOe291jTBJdi+sdnz73XabBOMyChiUCzl49ZQsXrsFDjgOHr7P7H8536Udu+BPWckvL/r2/jLSWVahLj+65XPWjlls6VQORTErzvsgUfwYwLB8reVrtnakxPfe3MIpoLDWF3HoGii2+t5097tb6Xe4iGjfO9BDAS8cKGYT7kQmGQ//cgO5AYmRPoz02nlvRccYR0aNZIQhWz+FAUUgAapCJkNJQ8n0A9NoTjAGRQM1utAQCJ2Qh0DoM3ETkJtM2HYmAzJYN7cNE0oGHD4cSZKXwqbkOkqlYqiUkYq93zrTOqw7WucwgFWHM2taa5yeJteOKseoYDDOgWM5U3sJHn68Ch7l/sp/XSMh1+4/xE6MBo5GFged/uEU2FHCfV9V19q2M1JJO6+zPNd9dioowHFu4RRQ2AcIy6hjOoHj7wF2K/XyAiQO8A37lAGOAfYquBzjJ95yyupFAwUUsJijdmgEAoPO0082pyJzE0bGGNjmyBgCNzEZkZ0DuTfwSYqJl4vJZ1tE4SmnLZb1qADhjwcInRB6JfQOGKMShogMmTBmZOhs3sVgQCHDiIydNemNo0l/eNNeGSjUhp+HCMMdQcfAfMW5BhJgtzWhRdjPuZoWCLSNIBrgwKfyLcGjns8BJyDlee3jy9tr9y9hp1zQh5zsvnTWQyOFdtspoLB4/F7A0Nq+RsBlmucSoLAPEI5FDsvHTuWLLl2VdCgttxZNnBJhvAWl4hcPFIDJgPsPpZDaQfIEFpWvUNqhRl3ObEJiDIkUrVt70yVyiSzAbhNQzeQZwQ2Fr7A/QaOnogYIHYQohE4NKHqTNQ+Dg8aYCdvRwKLvPMrw8afjWGXHy0AhWeubOMdmue28/8KqgFEuWN2dV12AA+YX+zLv3AIITCDSPHZW3vmUVMMpdrDP4BhQrDvqoxVCx/iGU8pVF6+/unK9NCicSjYvQGH2vS6izNnrHkhL6lnfq6wXLhyIGFZtGe2d0r/T3D8K6M/UHqL19FMwqY1frao/83Kn9Hi2jDIrWKCNUGCcoovgU/DiyKiBG7VGtZTF01BW0QSgGlBasABKRZTzEhr9dlTyKATjhgk+GCmMamDSCWGwqXehj56SijDmmoqSlCc+w1VbJ6Y9n1XmeC8rx9HkaSmoaa8CHLDj+FdXiwdKHevZnlkHf7T0cd/2IxftSc73kM7Ugahg5/gnRAer53SfFfGhz+9UTmEP4B+MEmbP2ZN2bF97eXufrQC6hgYsjgFE/X0fSNXdN+V0btT3DCqlzgIKEfki4FdhAPFTsUl3/9EjnNejWuEqYOIpoliPRZCJt+i8W3vMkU4ynWT6kBliRjVRuGXjK+xoFSxqRKGEICCFtzDAkAg06agKJFHRQcmdEPqADhkZFdnEKmUuYzbQyAYWk8S3/y/SFy7zvQSQ2ogXfC51AHy2hYRsIoHC+mp3zWarM+c5Eu4sLE0nRXsJfzz5sZvIYQKFFWJyn8Tzngat2RmfG1Hss72lp/ngfruOfL3scm3bRaKCpZ3CJTT37x0lnAAIOxzUMUBY+y7XuKMlGe3AMAOLdnvr5NdA4pRI4pRI8D6pwdl7O6+B8VJ2iijgP4WBw6/GhAG/BRtJ+jFV/fTjnt7jWnTuIpC9Cip7dGGg0UviTrKloUKij4FRA33hK7zHwlI1loYCGrCwIaME++HKiAFG8GtQBIlaiW9N9kPOEUKSChiSlDAGJPncizz/rzkjSXeAo4rtpYQ2Ut9LkT2ZldCG5kdfBlIsSO5iR8d0Nj/+3MZzDh5B5hVWVZdqDiLFav16eeAUVdR9+97H7tNsd0ppa933whf9qVxC89jRKOEQl3AqIKymE8+MGGbvs7ldyOg9KcJZI+YxkFhE4boGBucQ10/BHz2SHQQKEfmPsQl3/yvww/7wp4C/966DxD6rfIVkB4vMKJkuZLqc6UMihUCOybq2Y3a/Kt4JHUAnsAgoWYy3sIvLrwP/k9EiCkTRZLcl2Yq8AIYkRUeFDCEFizBasPDbJHf6JdpoAEPKfU9RldLbSUcpNz/23YuEnKdxq7AKJMVOXeXs7jfNq2hBpO4/bfTd9zjuS0UQ59o5F/V9CMl9GkSnRgj+2NH+hLW00ZJHWDr+Nl0kK6BwhIRebbZcmOxx/nttAQQ78i+PCBD1eXCYjzgHJE75zTwS0X0sovgtwM9W1b8NNfX0G4A/KyIfB/5T4KNFC+pdtCi5eqBy26TIp1RUkBJl2O0YMjEHYrDbGiFngShk9dSNCnRKRgws1P8jUx2WX5MWaTggBJBkOf8CGJKF3CkhKToK0qlFF50QkgvidR5xpIz0DhweaegCNNBG2rtcGDqptNZ0FZwMInbXL8jIei6e9qHDF/nh7enAtt3NB2UjnqudOoHuWHRQnvuQlNHC8e+NDvakkQ7pfs32h/3OP9txdsBits86EDx3gJg9p30vR+yp0k5wAlAUkABQ1e8HfruI/E4sHfUbsTTU5z3eKT6NhQYwgNq1XbaFymFMfzFkYhADgWA9DeJkNeqiewqqFgpX0EBqVCHluhRzaBowQEgtYBjPocGccPBtBgJYZBHxyMJysOLAMUtLZaZIwy+MVqm1TqaDVQCpEQhMAOK3VXUu6T27WJw3aC6GOjei2J6V0CUuhqe8oJZ23yl0R2c2nyNpcW66aBkdHOEadtSDzyWeW1umjfYBw9Lht4+dChBLh15+67Nj5pXXObEabe3878tBvYWS2NYOAoWqfuOex7fAnwT+pIi8ExVP+ywt224XFtyhzcDCow1p/kJQcsiIRiSogwWmOaRQpD4KWNisH5/D3YJGwFZ5Qa1FIlBBIpS0VLkd7b6E4LO8FYlS01GWipoGFklWNGmde01mAoRy8awNFmrvt+ABE4BQjrW70qqRBhyovtoFE1gBlPbYB+wxwOGkyOTcAUT7Sn0Pid7trNxPAINyjIeAwRIIDqWOTqGEmq9xNVKov7Fmn1kEcAQglvs+k+hh9rzZfvtA8e2CBBznKF6p6utD+6jq95yy33O3fAQwipWCTamRBV7gpPOoopBqgvHDUQ0sYhO4tL6y8+tTcAVvAxbJVEVvDRa5SCqRh4NLAYwMFKBIao9rAxqKp5Zsu3EVOl2Afns5WGgHLMp9mAOI398LIuUx2HvRVXfzwAtPVrT7lq+3105MVa0PDDpAsK9Vbh0rI17yBe22+6SJlqDh21ajgmOpo3OjBViNEGYgMVvpN9sPRQTt77M9xoHfqP07HxzuGznsPLfud+D3eAAgnjpKPpZ6+ofAP3HCcf4+8E8+/HQex7J/Qe3HnhBXgMV7H+bRRdJAItRKpnosdi8Oiy7striMhzl2tdxqwGZYBMyRlttR8XU2ok5et79DjzhKBEKC7McWByKLJBwwskccatVUJcogz0FDM3WqnN0vIJJtWxNxzKbSLcAC2AGQ2WOw/wK1L8Yft+2rgNJs33m8bG4Bpu53wVXYnoqp3dGkbcplT4/HCgDMjrUkjutju6v8o3zBuUBwQupIdz7oXdsJAtvfAswBYLn9UPTwQHBYLmDm5/REUcPi2Kt2JIJ4G6nUY0BxKyIfOeE4/SVO5jEsL+Q7DCCk2e4gQQEG/2v38cdaU223r1w94iDgUYLNrPCHmseKPpS6o5/ksakRh3Ea6lLk7geSkKWAwRIwTPepRhlaogxPn6inqWpE4c42i19EGLqpg0rr6BvwsO2LC3MfWNTn6xwQ1lZounKR2gfdfAHT9yrTzrvfw9pzD9mhaGIJDMekstvnHNMoWj5+Jmk8c/b7yOQ9qaPZz/c+xP/elMkuQOwDh9nje9JKO1HsvghjT3p0fi4PiBguCQr1AKctbN4W33YMKH7vicf5fQ89ERH5xcAfxGou/6iq/r7F9hvgI9ho1k9gHeF/79AxlyAx2+bOPyEWPfjVMt23aCLX/82fuya7b8ebfud7LrQCCkgFjJKWqqCgi8cWB8hoBZlsn4n7EPX/BigSDDiQCTDw1JV49KAFYIKiildcTaCBlshCK2jUFd/Oam/3Qlf7gNbBAnYHC60Ch+4HgdUw/sK53FPmWM/SMrL72NIpH5OmWKaP4DIgsACAHU7hED4sPmpZfEf2WNn3CDisRQ2HgGENQJbR6r5U0qmgcN8O+MVncNAeyDOcBBCPyGUcI7N/96O9cmMiEoE/BPxC4H3gO0XkY6r6t5rd/nXgR1T1nxGRLwd+P9YEeJIlVZJiTXJLUEDIBAaNNZrIKgwaGcp9hDHHChZjVZO1juJyG2Airxsr33MDGPXibMeoLgEkMFVP1al67bHw5+p0O4OK9W1IeXKSCkSqHlmUNJQ6iKiDhqorHopxKjvAwQ5Q7FzQcDDFUIGkffzQbRpw2bN9x45th13Hf2TbSbISy2ihfexkB394u+3DzuvMAGDtrR3jFXYAuXnqwvGugsMqCKw9tgsCO2nMtTTSEhQOdUbvA4Q9YHByieoTkctvs1pvac9FFPDDwPep6t8FEJGPAl8GtEDxZcDv8tv/NfANIiJ6D0H4kn5KGsiebkoeYRg4RAcNiyiGbLOzRw2kbH8K9XYuoNFqQCnzSAHsyl4DkWIy7SZlN19glpTTWiqrqNTOruoyUEntwCpUXsPVDK0uPZimviiuReJ/Io3D99sq4BEINMBRK7t2V5Oz+/u2AztVLyv3d77oS19Ia2mXQxEErBO9K6Bx+n7r57MXAA44/r0Z0dWd299O2fcAMCwjhrUIc/bYHATWuK3ZPvvSR2vppNzut1aeXR5qAWL5+3q88uyXYM8FKL4A+Hhz/33gS/bto6qjiHwS+BymjvGTrKSNEgYShbS2PwOPwSOHUSOjGkCMDViMuQCGRRM5l+l3DhBZpr8CDr5yL387AEJzf80qOEzRQwschge+rfAdRTK5vS8TeJQIopyjls0lylBvcGqf5qBRI5ygFY92HIs7RG0dxvRF1MZuWYLAGvafvx44z/Y53FOAYW3ftZU/nL76vweJfMj2EsywCgwHQaF9fB+/sACK1WjhWKSwjBLaCOFI0+ehhs+9zv8xI4V9XfWXskeOcp4LUKxdBstv85R9+KFPJD78NR+3oT7AV37Fe/yar3hFYlrAJmTiJ5BZFDFoJHkaasiRu9RN0YQGhhRJKgzJwSIFA4kCFMluT2CBkcQqnqKxv5qBaoGD5v4pn1gTVUj7GKyCBQ5igs+UzkJJKbWAUTNcWScQYQ00/EVb4FA1Z6jTW1oCCMyvG4W3Aw5wMkDAirM+N+9/qvM/t+x05XOa/Yaqw263T074XpHCWhSgR3iFC4LCsTGwJ+uSPcZvbO37O+TIHxtELmDPBSjeBz7U3P9C4Af27PO+iHTAjwf+8fJAn/s5ke/4lg+RNDOSGDTxRn3QkANDS2KXtJMBQ8egkbvc+Z9FFNvcMaRYQWJMkTHFCSiSpZ9yBQkqKEgFC6YKJV1sX4LFMWuzTDLdN9BwIPBtwgQWdpsGENybJ3tO8fOrgMH0eAsasA4c5XForsUg9bx3QKT1qnnlsUvbgeqeVd2hM5z6xQBg58DzH8j+MtSyfQ7QF4sSyvd7LErw5+8AQjmnM1JHe1VbOREUnmLRcei1Dn33+0DkFAB5Ir7kZKAQkd8K/AVV/W4R+bnAnwFG4CtU9dsfeB7fCXyxiPxkrCfjy4Ffu9jnY8BXAt8O/Eo/l6PffvKrpnycWef8xHYRTdzlztNMkW3u2KaObYpsc2TIFlGMbTTRgkQSI42TRROSHCSSVJAoIFKBowBEc18KiLQAMlsh7r7PkjayiGJy5AUPEIOP4vvt/0p04Qe3faYKLUtJaRNRiN/+/9s782hbrrrOf37nvgd0yAAJCRk1gIAGGoGWJIjYQACRsaWBDiANCo1KsxDbtgVxobBaGmyVLBsVGkTCIBBsYiAJhCEykwEQSGJAkhjI40FeBoaYkPfuqfr1H3vvql1Vu8ZTZ7z7u9ZZ91TVrl27zj3n963fbHwdKLDlBIxYh3p1vZXKHaH/oEcoo6NNVrcI804moBE0AuhvLiqcU9IEsrEhDcFtDzUb2XFtGkLvft0NBBA0H61ABnMt6kTVEAJZAvpoFL8F/LV9/7+APwNuAc6g6k/oBetzeDGmhPkW8FZVvUJEXg18QVU/YK/9DhG5CqNJnN51/szk5EgCnyR2mZfVInyNYppOLEFsZRrF9tRqFsmEJJHuJOG2S9qFTxDmw8BqGmHCyH/YFP82IVMQcrLInuydBuJMVXaUP3Wmo2xJlTAkm7yGNOwCnGzIyMNJuvyHUhCMdb+frk+GA5/eZ/UFmEna19hIAlAi1w5kAGHB7+8vkERHQvDnCtT+Ks4XIASPTIL+gxCGJpyVn8D9eUbW5kZD4HewiuhDFIep6g9E5BBMX4pHq2oiIn86xkJU9Xzg/NK+V3rvbweePnT+RI0j25meDthQ2MwfYV/TzNxkNApHEtN0wjSxjmxHEslWThLTSRaCKpYwXMKbS4irmKBslFFGCB451L4okQqlfdmO4vEyXGSVb8KqkIUzaYExaSlVwiCX6VnWQ5k0oEQcdlBJHphArZYfpP1BdfLjNGAUQuiyjqDvxT+/+gTdRASFc1pNSKVtRwalfXW5CcGIo5DJqJCQmVYJQdNB0UN1tbW6VgMu9kAZCHevfQT5EFLxz1lB0uhDFNeJyM8C9wM+ZUniUFprPq8WMpIomZ1yv8QufpTs5kCyi/1T45s4kGxxwGoS0+kWydSam6aCJhNPk7AaRMXkhEcUUto26yqMK5OHr01k772bqvleZmG2+H/DJiigqFlI0RSVXSZEGOaDzbQMc+2iplHY51AhD4wJrA7e2K6Cvk6Q9yaaph9/4FD1vkok4M/ZRASl42GSaNEO3Pi+hAD1WoJ9X+c70NJ2J7t9SSPIHkQGlokfel6B1Jr8BLW+Be+6s5DGChFGH6L4HUz+wgHgP9p9TwQuGXtRYyJVJVElxXNme2an/elubk93e2RhiOH2ZBcH0i32J1tsJ5MCSSTJxEQ3OS3CmZqy8t8ls1LI1OSblQLkUEcSZYIY9GQd8FeY6XIzFOTahS/s7WVzwnBaQJk0/Hl9gqjMVfwxyKR0Q/5vsccPsNPnMqvwh2IkV4gE/PdlInDHOmkMJSFv3zcSQkC4d3YsN0UaNTmUy8Kz8TPWVmHYKOxnjRaqEfShawY1okLoXgNpDDVbrRBhdCYKaxo6trT7ffa1kkhK/yDjyJ5k5qeQE/tAuiszOYU0iSSZoNOJNTf5JGEJYoAWUSEFj0TMtha37d/OKAUx5U/9pX3OEe58FJN8rbWEgdFSzHbxCTBEGtlc2bm+0CSLOMquU2hz6d9T+AcYJIi6H2ppd50WEJw7RATeGpu0gtrjZbOQfV/bvrNvOYsh4ad1moKPIaGnLdrEXAmiPE8Hp3H2nW7yj7RpGLMQxpLJok/U0z0bDl8zwlrmhoRiaOy27vIc2dY3YcniQOI5rpMakpjmjmvJXrQ7rMtaRBM5qDteQxLlfTXIoqEcPMc2qgWysIeLpqgtb33umCMM58PI2KakZTCcNAr7y6Thfo9dntYKAr14KOQfMPvrzi8K+8IcQwnB/S1rCKX9g2sc1YWg+u/dHP7nUGdC6oPG8ig1FXm7mIuGhpPOu95SE1nA7NrFELIYer0S+pieriJ/MIXiz66u+v/KII94stnXHknsT3ex35qabk92m/c2wmk63WJaJonppGpq8jWJgOmp1syUEYK3nb2vJ4kKQvtKDKD4mkNRE/D/qWXntE8YQG6SoqQRMAfS0BotowtZ1JBEMAFQQ+d0EPqdjoeFf6OmUN4/oM5RMBy1T16CL/TqPuPahMXuT/2jtaodSAQLLdMxi3axRFNUH9NT4T8vIkcDfwB8euxFjYHUSoYEtakLuTbhm5xuT3dzwDqwHUnstyanA44kpluk25MsskmsRjGZegRhU79dNNOYBAFVkghpE13s8r6GkedeZCl6Fe0CqqRQ8GEEnNbZtbJ5JLtehTR8Ye2dmJFDHWF0JQtvITNHGLUdrwjfIgEEK+Y2aQz2fW257K7k4G2P7mcIoQNJyESy6619PaWh2tYamaIGZ2ar6ndF5KXAPwN/O96S5genUTiz0+3p7oI24cxOvl8iTbaM09ojCfMqkkRZo2h1VLcRBKXj/nbgfYbAd69ifoKC2ciRhW+K8qfqQhih4+UlZdeBij/DFCnMNR53ooqXBZ4RnFTJonLTOcGYaxdJYhBBLJAczJ8SGdQJ+Q4Ekc3nn1+HsgklJNRm1CQGk8MKJaHNjDUii1lLeNwXOGiMhcwTieYd7VxGtp83sd86sDOTk/NLJDYE1moQGUlse1pDYpoI5RqFRxBtPog2giAfA80k0bk+VIEcytseWQSPu+2i8M6c3qHjHiqE4V/LlT0Xf0z4ejOhK0kEjg12QJeP9yWIwjq0QBDZeCiQQmd4pOA/5VcietqE0pj1isYggzFs84sQxGtCFn2c2Z+m+DM9CJNT8eqxFzUWUq91UVYyXHdxoOSfKGsTSTIxuRLTCWpNTrKdE8UkcVoEno+iShB+8lyhXIdHDlBjYqK0r9d2+Wm6ZvwYaCOLxnPDZDF4KRUCcPtzIds5q9n9bSSP0j7f99CVVOpMTBAmib6YTLJriJiS8nhanDng9fKeVIX0KIlrIYylHYxBCl3mXYEw1QoWRBZ9NIq3lLZvBb6iqt8YcT1zQQqZycmvFpvnTRS1ie1tE+WUkYQjCKdJTHMtwpmZJiWNIkgWAXKomI86kkF4jHYY0zSPNp8TghuTlrYDa6meW7pexW8Qnks84V5dc2BsyB/RpkW0mZkCRNBLi4BhJNEkXD1SKDyplsjCTKvFwoghTcJer8nZ3MuENC+z0SxP5X0QusYYQnrW9S+ALPo4s8+c50LmCT/RzjmznRP7QLrLJNd5UU5pskU6nYBnaiqQxNTTIgqRThS1h3J4K1TJoQcRhPYVk7dKY0L7hhBE4ZySIG4jiC7X60AQUhLsTQQRrI00K3WkEAAAIABJREFURINw+yrCuir0O2kRheuXiGAGZJoCNJOFd12/r3eFNHzUaROeuap6qOae5hm+WhaUiyCOpuusovYxA/qYnt4PvF5VP+3tezjwm6r6tHksbgyYpDu/tLjXf8KZnLyif8bkJFXndQKTbWtqmhoBOfHIoqpNeATh/QWoE8SNAr6wbz3IYRZiKGyHyKHBvFQdM0dyKM8VOq+whoA/ojA+EJLa1+RUJgt/Lr8PeIA0CmuCMIGkGhb6DeRhDrfcxxA/R5cyGoXxSyCQRZCGu96crtXH9PTvqRbl+zzw9+MtZz7IcihceKytDLvfFf6z2oQp9jfJSnPItvFNTBxJOMLwfRTlSCdnB/fJoY0YQoK8sl/rx3YiixZiwK05QEKLJIYOGkPh3Fn9DpVjNQK+zrRUuN5AcgAqpqa646X91T7PAcEZEo5DHN8Odb6kpuqt1BNIHTqZtfrWYuoiSMcmkzkL8cq1Zs0ED6APUdwO3Bn4obfvYGB7tNXMAcZ1ILZKrO/E3p2RxAFXHXbbhsI6gphaUrAkYfImMH99c1NqCaLisKbj072/ryqou54fShrr5PheICH0MSEVzp0hWqm4Bm/MppFCT0Lo1G5+iAN9JF9EmVh6h9TWkUjb+uZlxlqkNjMyKfUhiguAN4nIr6nqD23l2DcAHx51RSMi8aSqMz05snDlOvYnu0zRv21bMnxqS3JsuxdMtoXJtqdJFIhCK8l13UiihRDq9rcJ6yZC8LfT+mOha6yCdlC8jjYfK5wbIJAm81H53OD+GU1IpRDXwhwOaWCOuuOh8wtjOwqpBecpLCXZrsFsFh4//hP63DHyWvsQxW8D7wS+JyI3AYcDHwKeM+qKRoaLeCqTRNbi1HatS5OJdWAbJ/bEhsFOpp5mUdAoPILw/RPaLkTNvtJCu5ACFIVuB1IIagl9CWEoGQSIoDLG/1tnKrLHimvwiaJZ2C9UO+hDBnVE0IUA6gTs0KY/Ox1tdZpgPQljJPSJevoe8ARbuuME4DpV/e7cVjYiUjX+Ceer2FanSfjd6iZZDSdnYsozsLHRTs43oQXTU1mLqM1j8PZ12t+kLbSQQkhLqCOERnNUHRkM1ArWgggK5zSYiQImor5EUNUiAkIoIMAaBf6q5CcsO/JnzCTAwrw7jzB6ZWaLyF2BxwLHAd8WkXNV9ea5rGxkZKGxrie27WI3TSZMp1ueA9u+psaBPZnmL5M/oUUndmZy0hptwltE6XtVqymEzteOpFAgE2/OkoZQ6zdoI4MhOQmtx+oF/VgkYN6Wz+lHAoU5aq7RqA10IIFaAugi/FdNcI29nt69yOdsRttBhNEnPPahwHnA14BvYpoWnSEiT1DVzw9dgIgcDrwXOBG4FniG1V7K4xLgMrv5LVV9ctO8KSmmaVFuenJtT41/oqhRqFfDyUQ5SWZmMhFPMJlqHvWU5UyUopyghiSKX6Yu4awVR3MLKVS0hNI8jYRQRwZtWsFQjWDeZqEmH8E6awI7QCjVosu9L0OL2QGE0UejOAN4kaq+x+0Qkf8E/DnwkBnW8DLg46r6WhF5md3+3cC4H6nqA4dcwPdPmN4TVptIjTbhfBN+BravRVRIIskJouDEhsKXpZ8fopu2ENIUaknBMxmVNYRGQqh7+l+FfIPCOd39A61E0JUEGoT5QrKUF5WFvK6Y5bOZlWQ2+H/ThyjuA5xV2vd3wBtnXMNTgEfY92cCnyBMFIOQYiOe/I52qUuym5AkgrrmQwGn9cQzN02yRDvNBHrlab70PemaF1GnMVT8CgUNpqwJeOMCpFAxF3UhhML++qf/uWsGHcigeH6zVtBoEgqV3g4cWxqWbftfJBYpeP1rDf2MN5Qs+hDFN4DTKZYUfzpw9YxruLuqfgdAVb8jIkfVjLuTiHwBmAKvVdXOiX5+d7tparSJ7WSLabJFmuaRToUsbF+T8AnDObF9gigI9OK1OyeweecX5g4QQ9mE5JuPOpNC2ZTURggrpB0U5uhrJmrQDlpJISQABguUOTlaVxFjluaozD0noTwLaWwgWfQhipcC54rISzA+ihOBe2N8FY0QkY8BRwcOvaLH9X9MVffalqwXishlqlohqRtuSjj5RdeRoqQoT33mQfz86QfjemTvT3cb/0Q6YepCYpM8BNY5sCskMdW8bEfqhDJFwQ1VovB/I12IAerJoY0YmkihlihKJLFoQggd8/bN5DuYVVPo8mMvj1mRp/3WHs+LRFdSnLXd6iJIo3zNOmwYWTQShYjc1TmWVfVzInIv4AnAscAHgfO7RD2p6qMbrnG9iBxjtYljgH01c+y1f68RkU8ADyKgzRx5xBaXXHAC+3WbW9ID3JAI1ycT26xoi22dMNWJ58SuVoedlCOeErW+iTz72pEFhMkgu7+SiSnogB6BGBo1hS6kMJbJqHBOAyn4x8fMM2ghgM6mpKE/ctVugsRdd06axUoQxKKxCNIIzV3bxGlzyKJNo/gmcCgYrcAK/HeOvIYPAM8FXmv/nlMeYMNyb1PV/SJyN+BhwB93vUBeOdY0KjJmJ9PilMQ2JUoompwSLYbDOpJIyZLtumRa1ya1DSWHNO1GDDXO5do+zTBbqCl0J4bS/lpyqMzVkog2xJ9Ql2g1NJJlXiGcsxDKKvhVFo1FkYY//4pok/NAG1HcJiL3B64EThZTZrLyaajO9E18LXCWiDwf+Ba28KCI/Azw66r6AuCnMOVDUkwDzNeq6j+1TZwCqV1ukjm0jUYxTSekqXi9r30ntuaObRvp5ExOeZvTsKbgUA6NbTUrJTXk4J72K0TQQgx12kJXUvD2dbLx9ySH6rwt/oA+5SocAiQQNMk0FbNblR//2MJ+EU+6q/LZLUvT2CC0EcWrgEuAO9rtaem4a065NXQBqnoTcFpg/xeAF9j3nwP+7dBr+BFPrhBgkkxMtJMzO2UlOzxymGr2V5xm4fwLZU3BLLRw3dpEt5D2kGq75hAiB297rtoCdCOG8rgmcsjG9CMJoNiDwSFU1dSRQEsl00biKA6sPzYWNkXgzFsbG4Jl9a1YczQShar+lYi8GeOI/hqm9ekYnYvnjsR+AZzZKcFoEdN0wnaalxOf+L0mMie2lzfhk4RzYntCpZIrUT7mkQMYE1bFtJSk+XaiBTJw43sRwxBSKK29NeKnLbdgCEGErtOAWrIIXH9oCeyKrX+ezXeya2yObbsXht7zLASzSBPVGqM16klVp8AeEXmQqn5zAWsaDYmqqfPktT+dpjYsNplkvoksP8ISxKRAFp6PwgpzX1NwCGda12gPTsiHtIfK+wA5lE1JiyCG8vjQOaEx5WsOQak7m49Ca8/COSXh0UXgB+6ndxvQsYikj/Db6QKu7f67fpY7laA7oE947LdE5I+AZwJHqOphIvJY4D6q+ob5LG8cJDoxORS6xYF0iyQVkz+R2kQ717XOL/rn50wkmpfqKOQoVK9VqaHUhSDSNDctZe9LBJF4Qt8/7vZBP2KAYeQQOq9uXPn6hfHjmnCC2oWPumY7hUnCZqr64QP6JcwjVHRVfAFdsWhhXL5e0+cVySKIPkTxekwxwGdjyosDXGH3ryxR5KYnYTvdIrHmpzTJk+v8hLosn8I3O6XqaRSlCCcHX4uAXgRRMC8laVV7qCOHWTSG0nkFdCWHmrG9yaHphzlL451FlNTwIBMZLyx17LDZ8v0t0w+zSm1KIzqhD1H8EvATqnqrjT5CVb8tIsfNZ2mzI8EQxQHdMlVjbY2ngn/CEYOXZJebnNSGx3ompDIh+MgyrnsShE8O3vuKZoGdw76fGyk0zdNHc+jjg6ghhJmb8cwo9DYmH6EP8SzCDxO8bvQXrCr6EMWB8ngRORK4adQVzQEuK9tpFEnBP+F6TuTaRNGJrbkT25mSyrBf6nLTnqCTOk2rBJGmRe2hYmYKkENf/0L+YdQf66E1FNZSGNuBHAJjejXngVZhtTECvi82JWciksZKoQ9RvA84U0R+C8BmUZ8BvKfxrCXDtECdkCJMbfOi3JEthYqwTnuYTK2/wJmd0tzXUEYlPDYjlNx0lBOD5j6IxGkVaZEgfHKwczaW0HbXrf8A2j+ksTWHFmLoRAqzVGndFGG5TKiuju8jhrQuHX2I4vcw2dCXAQdhigS+GZNrsXJISfM2qGr8E1PX9jSdkLUv9TOyM9JQW7YjJwkJ2u39p/pSBnWTFpGWSKJMEG3kMMSMVFj3jP6GWYmhAynM1LdhbEGyKgLTYV1t+WN9jqF5InnMFX1aoR7AFAZ8qTU53agzxz0uBnkehSndkQbKihfDYRWZWpIoZUyHEKq/VKtFpGk7QXStldSGNoHahRjGLKlRs6bBXd3WVWDuVHT5HGcp7933WhGd0afD3UnAw4HDgZuBTwOtZTSWjQRTumOamtIdSWoysic2G1s8gsiysX2S8P0TIRQyr5u1CPF8EqTub4kgmsptw2xmlS7mpI7E0CvsNts9kskoCoHNxVhkEn0co6KVKGx9p7/GFOzbA+zFhMkeKyLvAH51VTWLRHMfxbbatqdp7sj2X1l12Kymk+efgKCQDfV8KEQ0pWnRF+FtkyRVgujiqO6LWbSGMXo6BMbMjGULgRhrv1yUP/s24oj/r5nRRaN4IaYD3amqeqnbKSIPAd4N/Bqzd7mbK1K1TYvUFgJMi47sAklM04wgCqGtIbgvXxNJOE2ipEVolnUdIIh5aw1QJIc2raGGGFai+9uy/Aer5rdYFlZBAPcljoje6EIUzwFe4pMEgKpeKiIvBV7OChNF3i97UgyNdc7sQi9szfbhSKLRqWoJIotays1OFZLwNAn1NAqgaHJy2yOgLzl00Rq0SdvpKzTiD3r90fQ/XBaJrAJ5bRi6EMVJwCdrjn0SeMd4yxkXKba8OGIc2emENJlk2kSebKdepJN50pfEy21wk01Kk1Oqz9RGEGUtwicITwD7Alt6CNPWCKUmk9IsWsPQH2Z8EtxcRGG9UehCFFuqekvogKreIrKazX8TG6KUMrEJdyaHQtU1KpJiv4mpiXQi8UgiKT+R528r5b/rSMI3NTktwhFEDTn4KO+vLYJXWGdHzSFg6uptThpTIDTNFUlkeYhCf8ejC1HsFpFHQrVhUY85loIEyV6pNT2lzuxUcGZ7TuzUD4u1RFAXt10mCT/UNSOLkqnJI4khMQCd6yh10R4sCTSak1YFbZ9VJJJmRGEfMQO6CPl9wFtbjq80XJ2naeIqxvrRTjaxbppmjmy02BMiiJID2xGEJDUkkaRhgqgrejfpqKiNoT10Sebz4QvloS1Dx8ZO10aW/flHbDS69KM4cQHrmAsSFVNiHGGa5jkUzuzkek+I7UchqSUMF7UE1jcRNkEFE+mmSU4SjhzKJNGlxLYbEyKMeWgPfQRNyLewik7NWa6/6uSy7M80Ykdh6f4FEXm6iFwhIqntk1037nEi8nURuUpEXtZ1/jRLuNsidf6JtGx2Mk7svD+1cU7nDYQovERrsq2zfZYk0lyT0CTNScLXVto0F5eU578cfFNXauZXVXttZ+5K0SRBUzUkoWn+8ueZBU3rh5xI/Neqo+5/tCqviIgFYhX8C5cDTwXeVDdARLaAvwAeg0n6u1REPqCqrZnhrl/2VG1obMn05DQJXOmORHOCcNcv/zAzAW3NVC4/IvHMTZoL64IWMcaPvM7EVKc9NPkdxnZG9+kmtmpYdQEcy1RELAlLJwpVvRJaw0BPBq5S1Wvs2PcAT6GhhEiqSpo5su0rFUMChWS7vP+EezKX8lNbORPYCeVyMp0LgXU+CZ8kAuYhoLsvwl07u8GAD6KOIBYpUPqQxaphlc1nobXF4ngRC8LSiaIjjgOu87b3AKd0OdGV8EhSk5VdLC2u1j9hQ2ITZ2ZqeQJPPeHvRTg1kkQXv0RThFV2Q/VO6sHO6TGxriTRhmU9zff9PJfx+Udy2ngshChE5GPA0YFDr1DVc7pMEdgX/HbecFPCyS+6jikpBxROffodOOyJ97DlO7xkO1sEsFApNk2N76GcS1BItMvtxIUif0litQrrkwiQhBPuBe0pTYtaRZOvghYNwmy0zzUPbCpB1GGs+3X/o1X+/CIR7HgshChU9dEzTrEHOMHbPh5TnLCCI4/Y4pILTuB7yW1cl0y4bP9RXPqvNuLJmZ4yZ7bXcyJrearhH2/2tO75JTxndua8Vvc+J4ly7oOq5mTRxfRUQxKNPohZf9xNYa+rLNTWDfP+LKOQjxgB62J6uhS4t4jcA/g2cDrwrLaTUjVNi1I14bGaChMvI9sQhjElZVFMjgD8ipNODvuahJdkp2ke/lo2S81UWLcc7lo2MzX5IGapmBnKk1gUxhZsm0hqUfhHLBirEB77SyKyB3gocJ6IXGD3Hysi5wOo6hR4MXABcCVwlqpe0TSvX8JjqlumfIcNjSXNHdmm9WlqynX42dW+ZtEUpuibnJIEzTKw01y4p56Q7wpPiyiWIu9AEm7/PENRZVL/6ot5hn1uQqjpuq03YuOwdI1CVc8Gzg7s3ws83ts+Hzi/y5yJFaKmDaqp8ZSkNjQ2zdueypQs2kk8LUBSRSfkT+Xub9nk5OdLOL9EmST6ok2LsO/tgOa5hgiVJmKpI4FZyn6sguDruoZFaCer8HlERJSwdKKYN1wL1CTrQ+FlYSdetJNHEhnqSKLw8ggjSTqRRNCZHWorWmdqmgfqhOA8yCGbY82E4rqtNyJiJGw0UWQ5FAhp6vWhcOGxaTFZTjyHtaSgk5KdPzM3eQ5sP1y2TBJOmLaZY1pKb3QyNfVFa1ewngTRZ13u2m1riII5ImIlsNFEAa5ntnFqoy7ZTgsvUoL2X2OCkuy9r0lkDuwsEzvQ97onGkmia/RRm3AdYlqyawnvn6MwH2LqieQSETE6NpYoUkyyXerqPHk5FBNrfpp4/oksJ8KHSEHL8LWJzIHtair5TYkGoDY/om6+IUI0mN07gByy4ysolGO2ckTE6NhYonBIEK9XtjE7YUlCXOkOP9rJoa5sh69N2IJ7mcmplAAnk6rQCpUqac2P6CromsaVrzvU9zBWfsYisSql0CMi1hQbTRSuYZGr8ySpIGo1Clu6o1DNNVWY1AgVL6KpoE34JidykqggQBpm2qomYSeqF2x9y0kU8iJ6aBCLJIVZrjWPQoSRVCIiMmw0UYDn0C5EPDmS8IoB+gK7LNT9RDynOXjaREUT8NEgmEP9qmt9EnVCriuZNK1lKEHMqh2MJYz7aFJdMQ/NJ5JPxJpiY4kiUSWx/bKnuoWmfolxtdFPaR4S62dkpwpbXsSTnx+RdbDztIk6kmhAL8f1rCTRx8y0biTR9TqrkKFdNmdGRKwJNpYowFaO1Ykp36F5HwpjerIE4ddl8oWKn0PRpk041IXDehpKsQ1qTQhsF3QhiXmFuK6C0O2LruQ7j2tFRKw5NpooAJNDoYKmpqNpbnrClO3oWhoh9TOvA9pESfiGHNlBtOVJ9Ini6UsSfQVaV+G6DoJyHdYYEbEi2GiicCU8VAVN/RaoapPtXOMhzZPetrbyCXxtArKaTVkJcb+9aAhNjuM0QDKLIol5aA5R8EZEbCw2mijAaBRT9UuMW/+EKwQY0iZUKbTAKJmdyuGwjQhpFiF/Rl1obt2YurEhkuhj0uprklmVcNlIVBERc8PGEkUCtiDgJCsIOLFZ2ZNprlFU/BO+Q9tte07svKaTVp3PIh3KdbQ4r4eSRFeCGDNCaAzh7D7vWTFLWfWIiIhGbCxROLh+2fhNi1yNJ8/sVGgm5KNJm6jJdZBJC2GMQRLFCwav0fn8pmv3WcdQRAEfEbHS2GiiSJlktZ7I/BPY9x0c2XZ/2YmdaRO9F2TnW5QmseoEERERsRbYaKIAT6NQyaKdXI0n1+s6y6zeCmRluxBY34nt0CZAff9EU9vSPqaX1oqrHfwR84pe2qSoqIiIiAwbSxQpeVa28VFgy3f4lWOLT/WqSkHUtZmdfFj/RKPZqa0abGV8kz+hdI2u2dXz0CDWMa8iIiKiMzaWKMA6s5mQuDpPXtMi58SuNBlyjYScE3sMs1OX8U7wt/XB9sc6dPVHjN3/IWoQERE7AqvQM/vpInKFiKQi8jMN464VkctE5Msi8oWu86cqqPqObLLudnkpjoCGkE8AkJudGpzYjejiwG4yG82TJLokHJbn6jJf33kjIiJWEqugUVwOPBV4U4exj1TVG7tOnNpaT0k6MRqFc2L7hQCbhHMh0c5oF+HCfwGh6fwT5RIfIZKoCP8OiXduvrpz2s5tO2/ec0VERKwNlk4UqnolhPs0zALDBxNSBIU86ikji0B9J4eCw9rTIFr8CxX/RDlnojC4RBJt2dl9NYkxfBGLzMyOWeARESuLpZueekCBj4jIF0XkhV1PStT0y/ZrPGVO7CRpvqDvn0hrzFN1grwyWagqbIkk6jDU3FS7lg4moT7+h7ES78YcFxERMRoWolGIyMeAowOHXqGq53Sc5mGquldEjgI+KiJfU9VPlQfdcFPCqS/awwFNuVV/yNFPvCPpQ+6F2IS7LCs7SXNHdqjMRkYQxuGtfQTURLppE6Frto3rkiMxNHGv7fy+8/RFJIGIiJXEQohCVR89whx77d99InI2cDJQIYojj9jiog8fz7emt3Hp/uP40M0/yUXX+XWeNK/x5ExJ6SSsW3lhsWazzg/Q0JyotsdER79EMKFugD9ijOS7KMgjInYk1sL0JCJ3FpFD3HvgsRgneC1SXD8K291ObWnxFK/GU31fhmKLUm0NcS34J9qS63zh38ec1SUqKoQ27aNrFFNf+HO3XSMiImJlsXSiEJFfEpE9wEOB80TkArv/WBE53w67O/AZEfkKcAlwnqp+uG1u1+FO07xpUaZR1BGALxAtYWiSNIfQNqFcNLB8rHzNpnnqxs5CEq3XHahF9CmRHhERsdJYhains4GzA/v3Ao+3768BfnrI/C6PYpI5shVxORFNWoJrj+r3nXDoUql0QA/tbO7yuEEENYOzepHO6YiIiJXH0jWKecE0LRITHquS51Gk5HWeNA06qbN9Thvook10JYDqxapj6kiiqzYxi5COAj4iIqKEjSUKcAl3YmSfl5VNqcZTuG+D3ZfWEIQnoCttT7v0wO6rJQzNlQidM2tUVERExI7CRhMFWNOT1SZcQUBUTQOismnIbft1nVw2dsihWxa4dWG2XTKwm7SJPiTRFBE1lrkpOqcjInYUNpYoEjX9sqfpFnhmJ5dDkZmdShqDH+1UMEHVIZCJHa7p1MHn0NUvMYQk6jAkoinWcYqI2FHYWKIAG/WENT1l4bEuy7pBO/DNTmUndhu6mpTqCgM2jWsaOzRDOyIiIqIFG00UQNYGtahNeBFNdehSIdZpAE2O7LqQ2Lq5/DGzksRY/ohoYoqI2NFYenjsPOH3y5aKM7ulamy5vlONsKw4sqHZ7OTmz47NUM4jNK5tfNM5defPonlEx3lExNpjY4kiRWzCnZQinvzyHVoVZH7/CQeZVImlplf1oF7aQ3Mm+pLEkDIeMeEuImLHYyOJIjWFxW0JjwlZv+wkL9/RWOTP6z9RgUcuwbanvqAPleto0ib6mJzmQRKzjK9bQySHiIi1x0YShY9UBbI8Chsam3rO6skkLOxdeKzTEHytQhXK8tjXJkKaSh2GJur1GdtHWI+hQURyiIjYKGwsUSQICZIRRVYQ0NV5qnNk+xFPs5bOaNMmuuZMNF3Dn6/r2Lrz+gr46OSOiNgR2FiiAGN6Kpbv8BzULaanPNEubX/qdxhCLIXzOzqwy1g0SUQHdUTEjsJGEwXgObM11yZaBFrW0KhHfadBTuz85MDcMwrjriQxhhYRCSIiYqOx0XkUuenJNz+lRWd1U5SPl30cdFzXoYsTu61xUQhjFwWclSRidnZExI7AxmoUJofCNC4ql+/QmqqxnfwTTe1Ju6BLAl5X4T+EJMbQJCI5RETsKGwsUQAkmY8i70WRFQSsQxYZ1SwMQxVjzYEuRDCCItfXkTy00mwZkSQiInYcNtb0lNj41Swz23W3c70o6oigpuR4sXHRpHS47ISuMSt1yZuYhylpSBJdJImIiAiLjdYoUoSk0LCoxpk9KZljmmpA9elj3eX8wrEZwk3n5ZcYek5ERMTGYKOJwpmenCM7b4FaI9wdkTjU9ZEo73PO6rrciCa0tlTt4JtommOoT2LoORERERuHpZueROR/i8jXROSrInK2iNylZtzjROTrInKViLysbr4bbkoAG/Hk2qCqIQkTHuvMPfbvpGRGUpND0RTl5PsnOofFdq0iW1wMe/SalnkGVI5tGu9ecyCJyr2sOTbpfjbpXmCz7mcV7mXpRAF8FLi/qj4A+Gfg5eUBIrIF/AXwi8BJwDNF5KTQZDfenBS2sxIeShbO2VjnqXLxDh9R03xdj9UI9W/zL/VjxvJJLCjDunAvG4BNup9NuhfYrPtZhXtZOlGo6kdUdWo3LwKODww7GbhKVa9R1QPAe4Cn9LmOOKJoXEyDWWpTMQZJxNaoEREbDen1dD1niMgHgfeq6jtL+58GPE5VX2C3nwOcoqovLs/xwQ9+8PZ9+/ZlasWhhx56w+GHH37jnJc+N9x88813W+f1+9ike4HNup9NuhfYrPtZ4L38+GmnnXZk6MBCnNki8jHg6MChV6jqOXbMK4Ap8K7QFIF9QYZ70pOedKeh64yIiIiIqGIhRKGqj246LiLPBZ4InKZhFWcPcIK3fTywd7wVRkRERETUYek+ChF5HPC7wJNV9baaYZcC9xaRe4jIHYDTgQ8sao0REREROxlLJwrgDcAhwEdF5Msi8kYAETlWRM4HsM7uFwMXAFcCZ6nqFeWJuobQrgpE5K0isk9ELvf2HS4iHxWRb9i/d7X7RUT+3N7bV0XkwctbeRgicoKI/IOIXCkiV4jIb9r9a3dPInInEblERL5i7+VVdv89RORiey/vtQ8uiMgd7fZV9viJy1x/CCJ/YSlDAAAKIklEQVSyJSL/KCLn2u11vpdrReQyKzO+YPet3ffMQUTuIiJ/Z1MFrhSRh67U/bi8gXV/AVvA1cA9gTsAXwFOWva6Wtb888CDgcu9fX8MvMy+fxnwOvv+8cCHMP6aU4GLl73+wP0cAzzYvj8EE+580jrek13Twfb9buBiu8azgNPt/jcCv2Hfvwh4o31/OiYoY+n3Ubqn/wb8LXCu3V7ne7kWuFtp39p9z7y1nwm8wL6/A3CXVbqfpX9AI37QDwUu8LZfDrx82evqsO4TS0TxdeAY+/4Y4Ov2/ZuAZ4bGreoLOAd4zLrfE3AQ8CXgFOBGYFf5O4fRdh9q3++y42TZa/fu4Xjg48CjgHOtkFnLe7HrChHFWn7PgEOBfyl/xqt0P6tgehoLxwHXedt77L51w91V9TsA9u9Rdv9a3Z81VzwI8yS+lvdkTTVfBvZhEkOvBr6ved6Pv97sXuzxHwBHLHbFjTgD+B+ASxQ6gvW9FzBRjx8RkS+KyAvtvrX8nmGsIDcAf2NNg28RkTuzQvezSUTROYR2TbE29yciBwP/D3ipqv6waWhg38rck6omqvpAzNP4ycBPhYbZvyt7LyLyRGCfqn7R3x0YuvL34uFhqvpgTLWG/yoiP98wdtXvZxfGBP1Xqvog4FaMqakOC7+fTSKKTQmhvV5EjgGwf/fZ/WtxfyKyG0MS71LV99vda31Pqvp94BMYe/BdRMSFlfvrze7FHj8MuHmxK63Fw4Ani8i1mKoGj8JoGOt4LwCo6l77dx9wNobI1/V7tgfYo6oX2+2/wxDHytzPJhHFpoTQfgB4rn3/XIyd3+3/zzbi4VTgB04tXRWIiAB/DVypqn/mHVq7exKRI8UWqBSRfwM8GhNx9w/A0+yw8r24e3wacKFaA/KyoaovV9XjVfVEzO/iQlV9Nmt4LwAicmcROcS9Bx4LXM4afs8AVPW7wHUicl+76zTgn1il+1m2I2dkp9DjMZE2V2Oyvpe+ppb1vhv4DrCNeUp4PsYW/HHgG/bv4XasYAojXg1cBvzMstcfuJ+fw6jAXwW+bF+PX8d7Ah4A/KO9l8uBV9r99wQuAa4C3gfc0e6/k92+yh6/57Lvoea+HkEe9bSW92LX/RX7usL91tfxe+bd0wOBL9jv298Dd12l+1mpWk8REREREauHTTI9RURERETMAZEoIiIiIiIaEYkiIiIiIqIRkSgiIiIiIhoRiSIiIiIiohGRKCJWCiLyeyLylo5j3yYi/3Pea9o02MqrPxKRdyx7LX0gIheKyO0i8pllr2WnIRJFRCtE5OdE5HMi8gMRuVlEPisiDxlh3keIyB5/n6q+Rm3L2xnnfp6IJCLyr97rDbPOu0F4kqo+Z4yJROT/evWW5gZVfRTw6/O+TkQVC+lwF7G+EJFDMdVGfwNTlvoOwMOB/ctcV0d8XlV/rm2QiGypatI2LqIWjwNevexFRMwPUaOIaMN9AFT13WqK5P1IVT+iql+F7Mn9syLyf6zG8TUROc2dLCK/Yhux3CIi14jIr9n9d8bU1D/We+I/VkT+UETe6Z3/PhH5rp37UyJyv1lvyJqs/kpEzheRW4FHimnW8yci8i0RuV5E3mhLd7hzfkdEviMie0XkV0VEReQn7LFPiMgLvLHP880jIvKTYhrP3CymsdYzSmv5CxE5z35GF4vIvbzj9/POvd6a5o4WkdtE5Ahv3L8TkRvE1Noa8pkMuo6IPABThXaP9114vYh83/6/f9buv05Mk67nenO9TUT+UkQ+ZP//n7XXPENEvme/Sw8acj8R4yISRUQb/hlIRORMEflFsV22SjgFuAa4G/AHwPtF5HB7bB+mH/qhwK8ArxeRB6vqrZjKn3tV9WD7ChU2+xBwb0yJ5S8B7xrpvp4F/BGmwdJngNdhSPGBwE9gyja/ErJ2vf8d01vj3pi6T51gCfGjmIZBRwHPBP6yRHjPBF6FKdtwlV0XYuoZfQz4MHCsXdfH1dQG+gTwDG+OXwbeo6rbXdfmrXGW6zweOM87fgqmDMUR9p7fAzzEzvnLwBvEVBd2eAbw+5jvzn7g85j/890wxfH8mmERS0IkiohGqCkT7mo4vRm4QUQ+ICJ394btA85Q1W1VfS+mkcoT7PnnqerVavBJ4CMY01XX679VVW9R1f3AHwI/LSKHdTz9VPtk616nesfOUdXPqmqKEVD/BfgtVb1ZVW8BXoMpoAdGmP2Nql5uCe4Pu64fQ5LXqurfqOpUVb+Eqa77NG/M+1X1EjW9H96FISt37ndV9U9V9Xb7ObgKo2diBC8isoUhm6HO6Vmu8wTgfG/7X+y9JsB7MVVOX62q+1X1I8ABDGk4nK2qX1TV2zFVYG9X1bd750eNYgUQiSKiFap6pao+T1WPB+6Peeo8wxvybS0WDfumHYPVQi6yJo3vY55A79blumIaB71WRK4WkR9iuprR9XzgIlW9i/e6yDvmN345EtPF7ouOVDBP10fa48eWxn+z4/UBfhw4xScs4NnA0d6Y73rvbwPcE/cJmMJvIZwDnCQi98RoOj9Q1Ut6rMvHoOuIqa77k8DnvPHXe+9/BKCq5X0HN4xvGhuxJESiiOgFVf0a8DYMYTgcJyJ+M5UfA/aKyB0xT89/gunWdRfM06cb21aR8lnAUzCmnsMwbWPxzp8F/rVvxAil+3mkcpiqOiH1HYr1/3+sNNetGKJx8EngOuCTJcI6WFV/o8MarwPuFTpgn8DPwpDOcxiuTcxynV/AmKhiIMCGIxJFRCOsI/a3ReR4u30CxvzgP50fBbxERHaLyNMxneDOx0RI3RHT5nEqIr+I6R3gcD1wRIMp6RCMWegmjCB+zXh3lsOan96M8Z8cBSAix4nIL9ghZwHPE5GTROQgjB/Gx5eBp4rIQdbB/Xzv2LnAfUTkOfbz2S0iDxGRULe8Ms4FjhaRl4pxth8iIqd4x98OPA94MuAHAJxone0ndvwIBl2HqtkpYkMRiSKiDbdgHJQXi4kQugjTn+G3vTEXY5y8N2IcsU9T1Zusrf8lGEH7PYyGkDWTstrJu4FrrFnm2NK1344x83wb08jlIuaH38U4ki+yZq6PAfe16/wQxtR2oR1zYenc12Ns79djbPqZw91+Bo/F+Dv2YsxMr8MQaCPsuY8BnmTP+wbwSO/4ZzE9sL+kqtd6p55A/rm1Ysh1rAb5GIyJLmLDEftRRMwEEXke8IIu+QqbBBFR4N6qetWS13Eh8Leq+hZv3+8DN6jqm2rO+TpwDMaR/NzQmLbriMjJwBtU9eRZ76ErROSjmHa0l6jqaW3jI8ZDTLiLiFhTiMmOfzDGj5NBVRvLmqjqfZuOd70OVRPcXKGqj1nk9SJyRKKIiFhDiMiZwH8AftOajhZ6nRkirCLWENH0FBERERHRiOjMjoiIiIhoRCSKiIiIiIhGRKKIiIiIiGhEJIqIiIiIiEZEooiIiIiIaEQkioiIiIiIRvx/jRSNr11AY6cAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"mtf_values = [make_mtf(f).tan[1] for f in focuses]\n",
"\n",
"mtf_im = np.asarray(mtf_values)\n",
"plt.imshow(mtf_im, extent=[0, 1e3 / pupil.wavelength / 2.8, -2, 2], aspect='auto', interpolation='lanczos')\n",
"plt.gca().set(xlabel='Spatial Frequency, [cy/mm]', ylabel='Defocus [λ RMS]')\n",
"plt.grid(False)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see a characteristic curvature now. What is best focus? Depending on the frequency we look at, we will give a different answer."
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[Text(0, 0.5, 'AUC'), Text(0.5, 0, 'Defocus [λ RMS]')]"
]
},
"execution_count": 67,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"mtf_im_auc = np.trapz(mtf_im, x=source_of_units.tan[0], axis=1)\n",
"plt.plot(focuses, mtf_im_auc)\n",
"plt.gca().set(ylabel='AUC', xlabel='Defocus [λ RMS]')#, xlim=(-0.25, 0.25))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The area under the curve gives a single answer (and a smooth function!), and it's very close to zero (the \"right\" one, as chosen by minimum RMS wavefront)."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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