{ "cells": [ { "cell_type": "markdown", "id": "e806dfaf", "metadata": {}, "source": [ "# How to use `vcdisk`" ] }, { "cell_type": "markdown", "id": "52579cad", "metadata": {}, "source": [ "This page demonstrates how to use `vcdisk` in typical use cases in Astronomy." ] }, { "cell_type": "markdown", "id": "e102a8f5", "metadata": {}, "source": [ "## What is `vcdisk`?" ] }, { "cell_type": "markdown", "id": "760d87a7", "metadata": {}, "source": [ "`vcdisk` is a handy toolbox which implements several essential routines for anyone working on galactic dynamics and, in particular, with galaxy rotation curves. `vcdisk` provides fast and efficient solutions of Poisson's equation (using results from [Casertano 1983](https://ui.adsabs.harvard.edu/abs/1983MNRAS.203..735C/), [Cuddeford 1993](https://ui.adsabs.harvard.edu/abs/1993MNRAS.262.1076C/), [Noordermeer 2008](https://ui.adsabs.harvard.edu/abs/2008MNRAS.385.1359N/) and [Binney & Tremaine 2008](https://ui.adsabs.harvard.edu/abs/2008gady.book.....B/)) in the context of thick galaxy disks and flattened oblate bulges of any observed surface density profile." ] }, { "cell_type": "markdown", "id": "843186ec", "metadata": {}, "source": [ "## Why do we need `vcdisk`?" ] }, { "cell_type": "markdown", "id": "6a5b1929", "metadata": {}, "source": [ "The most typical use case for `vcdisk` is in rotation curve modelling. Specifically, this module allows to compute *the contribution to the circular velocity of the observed baryonic components of a disk galaxy*, e.g. the stellar disk, the gas disk, the stellar bulge.\n", "\n", "If we have some kinematical observations that allowed us to measure the rotational velocities of some material in circular orbits in the disk of a spiral galaxy (e.g. cold gas), the observed rotation curve can be decomposed into several dynamically important components in the galaxy\n", "![Rotation curve decomposition](vrot.png)\n", "where $V_{\\rm DM}$ is the contribution from dark matter, $V_{\\star,\\rm disk}$ from the stellar disk, $V_{\\rm gas, disk}$ from the gas disk etc. \n", "While the left-hand side of this equation usually comes from observations, and the contribution of DM is the unknown that is often what we want to constrain, for all the other terms there is ``vcdisk``!\n", "\n", "``vcdisk`` calculates the contribution to the gravitational field of an axisymmetric component whose radial surface density distribution is known. For instance, the surface density profiles of stellar ($\\Sigma_{\\star, \\rm disk}$) and gaseous disks ($\\Sigma_{\\star, \\rm disk}$) can be directly obtained from galaxy images in appropriate wavebands and these can then be used as input for ``vcdisk.vcdisk`` to calculate $V_{\\rm disk}(R, \\Sigma_{\\rm disk}(R))$.\n", "\n", "The ``vcdisk`` module provides appropriate calculations for both disky (`vcdisk.vcdisk`) and spheroidal (`vcdisk.vcbulge`) galaxy components." ] }, { "cell_type": "markdown", "id": "5dedd674", "metadata": {}, "source": [ "## Example 1: analytic surface density" ] }, { "cell_type": "markdown", "id": "7ef6dbbf", "metadata": {}, "source": [ "### Import `vcdisk`" ] }, { "cell_type": "code", "execution_count": 1, "id": "5e702f02", "metadata": {}, "outputs": [], "source": [ "import vcdisk\n", "\n", "import numpy as np\n", "import matplotlib.pylab as plt\n", "\n", "# suppressing warnings in the scipy.integrate.quad calls in vcbulge\n", "import warnings\n", "from scipy.integrate import IntegrationWarning\n", "warnings.filterwarnings(\"ignore\", category=IntegrationWarning)" ] }, { "cell_type": "markdown", "id": "5ebce6af", "metadata": {}, "source": [ "### Exponential thick disk" ] }, { "cell_type": "markdown", "id": "566f9bf0", "metadata": {}, "source": [ "Let's start with the case of a thick disk with a classical exponential surface density." ] }, { "cell_type": "code", "execution_count": 2, "id": "c666c1a2", "metadata": {}, "outputs": [], "source": [ "md, rd = 1e10, 2.0 # mass, scalelength of the disk\n", "r = np.linspace(0.1, 30.0, 100) # radii samples\n", "\n", "def expdisk_sb(r, md, rd):\n", " # exponential disk surface density\n", " return md / (2*np.pi*rd**2) * np.exp(-r/rd)\n", "\n", "sb_exp = expdisk_sb(r, md, rd)\n", "\n", "# run vcdisk\n", "vdisk = vcdisk.vcdisk(r, sb_exp)" ] }, { "cell_type": "code", "execution_count": 3, "id": "57c4d80b", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def plot_sb_vdisk(ax, r, sb, vdisk, label=None):\n", " ax[0].plot(r, np.log10(sb), lw=2)\n", " ax[0].set_xlabel(\"radius / kpc\");\n", " ax[0].set_ylabel(\"log surface density / M_sun kpc\"+\"$^{2}$\");\n", "\n", " ax[1].plot(r, vdisk, lw=2, label=label)\n", " ax[1].set_xlabel(\"radius / kpc\");\n", " ax[1].set_ylabel(\"velocity / km s\"+\"$^{-1}$\");\n", " if label is not None: ax[1].legend()\n", "\n", "fig,ax = plt.subplots(figsize=(12,4), ncols=2)\n", "plot_sb_vdisk(ax, r, sb_exp, vdisk)" ] }, { "cell_type": "markdown", "id": "ab42a3c1", "metadata": {}, "source": [ "We can explore how does $V_{\\rm disk}$ change when changing the scaleheight of the disk $z_0$ for instance:" ] }, { "cell_type": "code", "execution_count": 4, "id": "40696380", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig,ax = plt.subplots(figsize=(12,4), ncols=2)\n", "plot_sb_vdisk(ax, r, sb_exp, vdisk, label='z0=0.3 kpc')\n", "plot_sb_vdisk(ax, r, sb_exp, vcdisk.vcdisk(r, sb_exp, z0=0.1), label='z0=0.1 kpc')\n", "plot_sb_vdisk(ax, r, sb_exp, vcdisk.vcdisk(r, sb_exp, z0=0.8), label='z0=0.8 kpc')" ] }, { "cell_type": "markdown", "id": "c5c8e1b5", "metadata": {}, "source": [ "### Sersic profile" ] }, { "cell_type": "markdown", "id": "435a02b8", "metadata": {}, "source": [ "Let's compare to other popular analytic surface density profiles. Probably the most used in Astronomy is the [Sersic (1968)](https://ui.adsabs.harvard.edu/abs/1968adga.book.....S) profile, which is often used to describe all sorts of stellar components, including disks and bulges. We can use the class `sersic` in the `vcdisk` package to get Sersic profiles" ] }, { "cell_type": "code", "execution_count": 5, "id": "7324c43e", "metadata": {}, "outputs": [], "source": [ "sers_n1 = vcdisk.sersic(md, 1.678*rd, 1.0)\n", "sers_n2 = vcdisk.sersic(md, 1.678*rd, 2.0)\n", "sers_n05 = vcdisk.sersic(md, 1.678*rd, 0.5)\n", "sers_n4 = vcdisk.sersic(md, 1.678*rd, 4.0)" ] }, { "cell_type": "markdown", "id": "71bcaed1", "metadata": {}, "source": [ "Here, we have taken the reference model `sers_n1` which is equivalent to the exponential disk above, since $R_e\\simeq 1.678 R_{\\rm d}$ for $n=1$ exponential profiles. Let's now compare the circular velocities of disks with Sersic surface brightnesses with different index $n$, while keeping the total luminosity fixed." ] }, { "cell_type": "code", "execution_count": 6, "id": "91b1ddfe", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig,ax = plt.subplots(figsize=(12,4), ncols=2)\n", "plot_sb_vdisk(ax, r, sers_n1(r), vcdisk.vcdisk(r, sers_n1(r)), label='Sersic: n=1')\n", "plot_sb_vdisk(ax, r, sers_n05(r), vcdisk.vcdisk(r, sers_n05(r)), label='Sersic: n=0.5')\n", "plot_sb_vdisk(ax, r, sers_n2(r), vcdisk.vcdisk(r, sers_n2(r)), label='Sersic: n=2')\n", "plot_sb_vdisk(ax, r, sers_n4(r), vcdisk.vcdisk(r, sers_n4(r)), label='Sersic: n=4')\n", "ax[0].set_ylim(2,10);\n", "ax[1].set_ylim(-1, 105);" ] }, { "cell_type": "markdown", "id": "d395897e", "metadata": {}, "source": [ "### Sersic bulges" ] }, { "cell_type": "markdown", "id": "fae4fffe", "metadata": {}, "source": [ "We have just computed the circular velocities of thick galaxy disks whose surface brightness profile is of the Sersic form with different $n$. However, we may also be interested in the circular velocity of a **spheroidal component**, *like a stellar bulge*, whose observed surface brightness is well approximated by a Sersic law.\n", "\n", "#### If for disky components we use `vcdisk`, for spheroidal components we use `vcbulge`!" ] }, { "cell_type": "markdown", "id": "537e718f", "metadata": {}, "source": [ "Let's now compute the circular velocity on the mid-plane of a nearly spherical Sersic bulges with different $n$." ] }, { "cell_type": "code", "execution_count": 7, "id": "a34eefe9", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/lposti/anaconda/envs/py37/lib/python3.7/site-packages/vcdisk.py:925: RuntimeWarning: invalid value encountered in double_scalars\n", " return -self.Ie*self.bn/(self.n*self.re) * np.exp(-self.bn*((R/self.re)**(1/self.n)-1)) * (R/self.re)**(1/self.n-1.0)\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig,ax = plt.subplots(figsize=(12,4), ncols=2)\n", "plot_sb_vdisk(ax, r, sers_n1(r), vcdisk.vcbulge_sersic(r, md, 1.678*rd, 1.0), label='Sersic: n=1')\n", "plot_sb_vdisk(ax, r, sers_n05(r), vcdisk.vcbulge_sersic(r, md, 1.678*rd, 0.5), label='Sersic: n=0.5')\n", "plot_sb_vdisk(ax, r, sers_n2(r), vcdisk.vcbulge_sersic(r, md, 1.678*rd, 2.0), label='Sersic: n=2')\n", "plot_sb_vdisk(ax, r, sers_n4(r), vcdisk.vcbulge_sersic(r, md, 1.678*rd, 4.0), label='Sersic: n=4')\n", "ax[0].set_ylim(2,10);\n", "ax[1].set_ylim(-1, 105);" ] }, { "cell_type": "markdown", "id": "dd88ec83", "metadata": {}, "source": [ "### Flattened Sersic bulges" ] }, { "cell_type": "markdown", "id": "32d4b1d5", "metadata": {}, "source": [ "We can compute the circular velocity also for flattened oblate bulges, thus for components whose 3D density is stratified as $\\rho=\\rho(m)$ where $m^2=R^2+z^2/q^2$ with axis ratio $0" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%%time\n", "plt.plot(rb, np.sqrt(4.301e-6*5e9/rb),'k:')\n", "plt.plot(rb, vcdisk.vcbulge(rb, sb_sers_bulge), c='C0', label='q=0.99')\n", "plt.plot(rb, vcdisk.vcbulge(rb, sb_sers_bulge, q=0.8), c='C1', label='q=0.8')\n", "plt.plot(rb, vcdisk.vcbulge(rb, sb_sers_bulge, q=0.6), c='C2', label='q=0.6')\n", "plt.plot(rb, vcdisk.vcbulge(rb, sb_sers_bulge, q=0.4), c='C3', label='q=0.4')\n", "plt.plot(rb, vcdisk.vcbulge(rb, sb_sers_bulge, q=0.2), c='C4', label='q=0.2')\n", "plt.legend()\n", "plt.ylim(0,160);\n", "plt.xlim(0,10);\n", "plt.xlabel(\"radius / kpc\");\n", "plt.ylabel(\"velocity / km s\"+\"$^{-1}$\");" ] }, { "cell_type": "markdown", "id": "74f01e6a", "metadata": {}, "source": [ "### User-defined vertical density profile" ] }, { "cell_type": "markdown", "id": "d76510dd", "metadata": {}, "source": [ "`vcdisk` allows us to specify our own vertical density profile, if we so choose. This can be easily done through the `rhoz` argument." ] }, { "cell_type": "code", "execution_count": 10, "id": "4333761f", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def rhoz_gauss(z, m, std): return np.exp(-0.5*(z-m)**2/std**2) / np.sqrt(2*np.pi*std**2)\n", "\n", "def plot_rhoz(ax, z, rhoz, label=None):\n", " ax.plot(z, rhoz, lw=2, label=label)\n", " ax.legend()\n", " ax.set_xlabel(\"radius / kpc\");\n", " ax.set_ylabel(\"vertical density / M_sun kpc\"+\"$^{2}$\");\n", "\n", "\n", "fig, ax = plt.subplots(figsize=(6,4))\n", "z = np.linspace(0,3)\n", "plot_rhoz(ax, z, np.exp(-z/0.3) / (2*0.3), label='exp')\n", "plot_rhoz(ax, z, rhoz_gauss(z, 0., 0.8), label='gauss')" ] }, { "cell_type": "code", "execution_count": 11, "id": "06f0b0e3", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig,ax = plt.subplots(figsize=(12,4), ncols=2)\n", "\n", "plot_sb_vdisk(ax, r, sb_exp, vdisk)\n", "plot_sb_vdisk(ax, r, sb_exp, vcdisk.vcdisk(r, sb_exp, rhoz=rhoz_gauss, rhoz_args={'m':0.0, 'std':0.8}))" ] }, { "cell_type": "markdown", "id": "5b7dd1c4", "metadata": {}, "source": [ "### Flaring disk" ] }, { "cell_type": "markdown", "id": "72f875b9", "metadata": {}, "source": [ "We can also have a flaring disk, i.e. one where the vertical density depends also on radius $\\rho_z=\\rho_z(z,R)$. We can work out this case as well with `vcdisk` by specifying how $\\rho_z$ depends on $R$." ] }, { "cell_type": "code", "execution_count": 12, "id": "44279f7d", "metadata": {}, "outputs": [ { "data": { "image/png": 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kfzWlIdhn7S7GmPyUaYN+f0XAXC8CGQoRWYGTXM5JOny2qu4VkYnAn0XkZbcmdBQ38dwOzvAvWQ84yeGaiyUXY0z+ybTNJXleFz9QA4zK0C8icjJwJ3ChqjYkjqvqXnd9UER+C5wGpEwuo6nGeowZY/JYpjWX5HldosABVY16GE9aRGQmcD/wXlXdknS8GPCpapu7/UZGKfkdi7W5GGPyWabJ5TTgT+4f788Dp4jI11T1OS+DEpGfA8uBahGpA74IFACo6g+BfweqgB+4wzIkuhxPAn7rHgsAP1PVP3kZm1dqSp0eYlZzMcbko0yTyxdU9Vcicg7wJuC/gNs4shvwsKnqlcc4fx1wXYrj24HFXsaSLfZYzBiTzzLtihxz128BblPVB4CgtyGND9agb4zJZ5kmlz0i8j/AO4GH3Pld7PXyIUiuuYznQfGMMfkp08TwTuAR4AJVbQYqgU8mTopIhXeh5bfiUIDioJ+eaJzW7hHvE2GMMVmVUXJR1U5VvV9Vt7r7+1T10aQif/U0ujxn7S7GmHzl9SOt8T2jToYmltqMlMaY/OR1crHGgwxYzcUYk6+sMX4UWXIxxuQreyw2iiy5GGPyldfJ5fUef15es+RijMlXab2hLyKDDquvqpe46wHnYDFHsxcpjTH5Kt3hX84EdgM/B57BHn95wmouxph8lW5ymQycD1wJvBv4I/BzVd2YrcDGA+uKbIzJV2m1uahqTFX/pKrXAGcA24C/ichHshpdrojHjl0mhcriID6Bps4IvdG4x0EZY8zoSbtBX0RCIvI24CfAh4CbceZUGb/2b4B7LoHHvzGky/0+obrEeTRW326Pxowx+SOt5CIi9wBPAacAX1bVU1X1q6q6J6vRjXWRLtjxd3j6Nmg/NKSPsHYXY0w+Srfm8l7gROCjwFMi0uoubSLS6nVQInKXiBwUkQ0DnBcRuVlEtonIehE5JencBSKy2T23yuvYjjDjVDjxAoh0wJP/b0gfYT3GjDH5KN02F5+qlrpLWdJSqqplWYjrbuCCQc5fCJzgLitxJixDRPzAre75hcCVIrIwC/EdtuJzzvrZO6B1b8aXW83FGJOPxuTwL6r6D2Cwd2YuBe5Vx9NAuYhMwZmGeZuqblfVXuA+t2z2TDkZFl4GsR74x39mfLklF2NMPhqTySUN03Deu0moc48NdDwlEVkpImtEZM2hQ0NrMwFgxWdBfPDcvdC0M6NLrTuyMSYfpdugf6aIjKUXJ1PFooMcT0lVb1fVWlWtrampGXo0NfPg5HdBPAp/+1Zml1rNxRiTh9KtuVwDrBWR+0TkfSIyOZtBpaEOmJG0Px3YO8jx7Hvdp8EXgPX3waEtaV9mDfrGmHyUboP+9ap6CvAloAK4W0T+JSLfEJHXug3pI+lB4Gq319gZQIuq7gNWAyeIyBwRCQJXuGWzr3IOnHI1aBz+lv57L1ZzMcbko0ynOX5ZVf9bVS8AzgP+CbwDZ7wxz4jIz4F/AfNEpE5EPiAi14vI9W6Rh4DtOCMF3AF80I0vCnwYeATYBPxyRIeoOfffwB+Cjb+FfevTuiQ5uajaXGvGmPyQ7thiR1HVLpw/8g95F07fZ195jPOKM0pAqnNZiSktE6bBqdfB07c6b+2/+75jXlIUDFASCtDeE6W1K8qEooIRCNQYY7IrV3uLjV3n3AQFxbDlYdi9Oq1LDre7WI8xY0x+sOTitZIaOMN9evfYVyCNR13V1u5ijMkzGSUXEfmwiFRkK5i8cdZHIDwBdvwDNj98zOJ97S42eKUxJk9kWnOZDKwWkV+6Y3iNpXdfxo7CClj+WWf7kc9AZPDHXX2PxVotuRhj8kOmvcU+jzOe14+A9wFb3e7Ix2Uhttx26nVQs8B5Y/9f3x+0qNVcjDH5JuM2F7en1n53ieK89/JrEfm2x7HlNn8A3uz+kzzxXWipG7Bo3xAwrdagb4zJD5m2udwoImuBbwNPAiep6g3AMuDtWYgvt815rTOoZaQTHv3CgMWs5mKMyTeZ1lyqgbep6ptU9VeqGgFQ1ThwkefR5YM3fg0ChbDxftjxRMoi1uZijMk3mSaXkKq+mnxARL4FoKqbPIsqn5TPgHM/7mw//GmIRY8qYjUXY0y+yTS5nJ/i2IVeBJLXzvoIlM+EgxthzV1Hna4sCuL3Cc2dEXqisVEI0BhjvJXukPs3iMiLOGN9rU9adgDpDaI1nhUUwpv+w9l+/GvQUX/EaZ9PqC4JAlDf3jvS0RljjOfSrbn8DLgYZ4Thi5OWZar6nizFll/mvwXmroDuFnjsq0edTvQYs7f0jTH5IN0h91tUdaeqXqmqryYtg01FbJKJwIXfduZ8WXsP7H72iNM1fY361h3ZGJP70n0s9k933SYire7SltjPboh5pOZEOPPDgMLvPgiRrr5TiR5jByy5GGPyQLo1l3PcdamqlrlLaWI/uyHmmeWfgep50LAVHv963+E51cUAbD3YPlqRGWOMZzJ9ifIdIlLqbn9eRO4XkaXZCMwdu2yziGwTkVUpzn9SRNa5ywYRiYlIpXtup4i86J5bk434hqwgDJfdBuKDp27pezw2f4qTo1/e3zaa0RljjCcy7Yr8BVVtE5FzgDcB9wA/9Dood9rkW3G6OS8ErhSRhcllVPU/VXWJqi4BPgP8vV8b0Ar3fK3X8Q3b9GVw1o04j8dugEgX8yeXAvDyvlabkdIYk/MyTS6JlzDeAtymqg8AQW9DAuA0YJuqblfVXuA+4NJByl8J/DwLcWTP8s9AzXxo2AaPfY2JpSHKiwpo7Y6y39pdjDE5LtPkskdE/gd4J/CQiISG8BnpmAbsTtqvc48dRUSKgAuA3yQdVuBREVkrIisH+hIRWSkia0RkzaFDhzwIOwMFYbj0B87jsX/diux+lnmT3NqLPRozxuS4TBPDO4FHgAtUtRmoBD7pdVBAqnliBnpWdDHwZL9HYmer6ik4j9U+JCKvTXWhqt6uqrWqWltTUzO8iIdi+jI4+2OAwgMfZNFEpxK42ZKLMSbHZTqfS6eq3q+qW939far6aBbiqgNmJO1PB/YOUPYK+j0SU9W97vog8Fucx2xj0/JVzrwvDdu4vOVuwJKLMSb3BTIp7D4GezswO/laVf2Kt2GxGjhBROYAe3ASyLtTxDMBeB3wnqRjxYDP7XhQDLwR8Do+7wRCcNkP4M43MH/njzlNZvHyfuvdbYzJbZk+FnsAp2E9CnQkLZ5S1SjwYZxHcJuAX6rqRhG5XkSuTyr6VuBRVU2OYRLwTxF5AXgW+KOq/snrGD017RQ45yYE5ebgLTQd3EMkFh/tqIwxZsgkk26vIrJBVRdlMZ5RU1tbq2vWjOIrMbEI3HMx7PoXT8QWMfmDf+SEKeWjF48xxhyDiKwd6HWPTGsuT4nISR7EZPrzF8Dld9HqK+dc/wZi//jP0Y7IGGOGLNPkcg7wnPvm/Hr3LXgbct8rZVN5ZN5Xiaswb9OtsP1vox2RMcYMSabJ5ULgeJxG8otxpja+2OugxrPw/Ddwc+ytCAq/uQ5a9412SMYYk7FMk8su4FzgGne6Y8VpQDcemT+5lJujb2ON72ToOAS/fn/KqZGNMWYsyzS5/AA4E2e4FYA2nDHAjEdmVxcT8Ae4vvMG4iWTYNdTzuyVxhiTQzJNLqer6oeAbgBVbSI7Y4uNWwV+H8dNLKGeCWw992ZneJh//jdsfni0QzPGmLRlmlwi7ojFCiAiNYC9kOGxxAjJa1kI533BOfib62D/i6MYlTHGpC/T5HIzznAqk0Tk68A/gW94HtU4N89NLpv3t8I5N8Giy6G3HX76TmgdaBQcY4wZOzIa/kVVfyoia4HXu4cuU9VN3oc1viWSy8v720DEGR6mdQ/s+hf87J1w7cMQKh3lKI0xZmBp1VxE5OOJBXgzEHKXC91jxkMLJjtji20+0OZMHBYIwRU/g8rjnEdj1oPMGDPGpftYrNRdaoEbcOZWmQZcjzNTpPHQpLIQEwoLaO6McLCtxzlYVAlX/QoKK2Hro/CnVWAzVhpjxqi0kouqfllVvwxUA6eo6idU9RPAMpzh8I2HRKTv0dimfa2HT1Qd59Rg/EFYfQc8fdsoRWiMMYPLtEF/JtCbtN+LM/y+8dj8vkb9fnO7zDoTLnOTyiOfhU2/H+HIjDHm2DJNLj8GnhWRL4nIF4FngHu8D8vMGyi5AJx0udtFWZ32l21/GdngjDHmGDKdifLrwLVAE9AMXKuq/5GFuMa9+ck9xlI59xNw2kqI9cJ9V9kgl8aYMSXTmguq+pyqfs9dns9GUAAicoE7+vI2EVmV4vxyEWkRkXXu8u/pXpsLTpzkJJdth9qJppo4TAQu/DYsuxai3fCzK2DnP0c4SmOMSS3j5DIS3FEAbsUZhXkhcKWIpOqV9oSqLnGXr2R47ZhWGi5gWnkhvdE4OxsGmOxTBN7yXVj6Hoh2OS9Z7np6ZAM1xpgUxmRyAU4DtqnqdlXtBe7DmV4529eOKcd8NAbg88HFN8PJV0CkA35yOexePUIRGmNMamM1uUwDdift17nH+jtTRF4QkYdF5DUZXouIrBSRNSKy5tChQ17E7an5UwZp1E/m8ztv8S96O/S2wU/eDnueG4EIjTEmtXTf0G8TkdYUS5uItB77EzImKY71f2PwOWCWqi4Gvg/8LoNrnYOqt6tqrarW1tTUDDXWrJnnvqk/aM0lweeHt94OCy6Bnhb48WXw6lPZDdAYYwaQ7kuUpapalmIpVdWyLMRVB8xI2p8OHDFio6q2qmq7u/0QUCAi1elcmysGfNdlIP4AXH4XLLgYulvgx2+FTX/IYoTGGJNaxo/FRKRCRE4TkdcmlizEtRo4QUTmiEgQuAJ4sF8ck0VE3O3TcO6lIZ1rc8Wc6mIK/MKuxk7ae9IcS8xfAO+453Avsl++F9bcld1AjTGmn4ySi4hcB/wDeAT4srv+ktdBqWoU+LD7+ZuAX6rqRhG5XkSud4tdDmwQkRdwpgK4Qh0pr/U6xpFQ4PdxXE0JAFsOpFl7AecR2UX/Dcs/CxqHP9wEj/+HjUVmjBkxGQ25D3wUOBV4WlVXiMh8nCTjOfdR10P9jv0wafsW4JZ0r81V8yeX8vL+Njbvb+OUmRXpXygCyz8NpZOc5PL3b0L7fnjzd5zHZ8YYk0WZPhbrVtVuABEJqerLwDzvwzIJiUb9IwawzMSy98G7fgKBMKy9G355NfQO8N6MMcZ4JNPkUici5Tg9s/4sIg+Qo43lueLU2U5t5bGXDzpzuwzF/LfA1Q9AuBw2/xHuPB8at3sXpDHG9JPp2GJvVdVmVf0S8AXgR8BlWYjLuE6ZWUFNaYi6pi427h1Gr++ZZ8AH/gxVJ8DBjXD7ctj6Z8/iNMaYZEN+iVJV/66qD7pvwZss8fmEC14zGYCHXtw3vA+rORH+z2Mw7y1OV+WfvgP+/m2Ipxi7zBhjhiHT3mL3uI/FEvsVImL9XLPswkVOcvnThv1DfzSWEC5z2mBWfN7Zf/zr8Iv3OMnGGGM8kmnN5WRVbU7sqGoTsNTTiHJIa28rb3vwbXzz2W/y+K7HaevNoLtwBk6bU0lFUQHb6zvYcqB9+B/o88HrPulMmxye4LTD3HEe7N8w/M82xhgyTy4+EenrDysilWTenTlvrN6/mq1NW/nppp9y4+M3cu5953LVQ1fx/ee/z+r9q+mNefPEMOD38caFTu3l4Q3DfDSW7ITzYeXfYOJroGEb3LECnrzZHpMZY4ZNMnnMIiJXA58FfuUeegfwDVW9Nwuxjaja2lpds2ZNRtdEYhHW16/n6X1P88y+Z1h/aD0xjfWdD/lDLKlZwqmTT+XUyadyUvVJFPgLhhTf45sPcu3/rmb+5FL+9DGPB0Xo7YBHPgdr/9fZn32uMxBm+Uxvv8cYk1dEZK2q1qY8l+kzfHdulBU4A0T+VVU3DT/E0TeU5NJfR6SDtQfW8q+9/+LpfU+zrXnbEefD/jBLJjrJZtmkZSyqXkTIH0rrs3ujcZZ97c+0dUd57BOvY6775r6ntjwCD3wIOg5BqAze/F9w8judFzKNMaafYScXEfmnqp4jIm04Iwwn/7XRLA1eOaK8SC79NXQ1sPbAWlbvX83q/at5peWVI84X+Ao4qfoklk1axrJJy1gycQnFBcUDft7Hf7GO+5/fwyffNI8PrTje01j7dNTDgzc67TAACy9zhpIpqszO9xljcpanNZd8lY3k0l99Vz1rDqxhzf41PHfwObY2bT3ivE98nFhxIktqlrB04lKWTlzK5OLJuONz8ujG/az88VpOmjaB33/knOwFqgrP/wT+tAp626GoCt74NVh8pdVijDF9PEsuIvItVf30sY7lopFILv219LTw/MHnee7Ac6w9sJaXGl4iqkeOfjyxaCJLJy5lcc1iFlScxNW31dHZKzzxqRXMqCzKboCNO+DBj8DOJ5z9WWfDW74DExdk93uNMTnBy+TynKqe0u/YelU9eZgxjrrRSC79dUW72FC/gXUH1/H8wedZd2jdUd2bhQDRzqksm7yYq5a+lpOrT2ZK8ZS+2o3nVGH9L5wG/8568AXgrI/Aaz8FwSwnN2PMmOZFm8sNwAeB44DkVupS4ElVfY8XgY6msZBc+otrnO3N21l3aB3rD61n/aH1R7XbAFSGK1lUvYhFVYucdfUiKsIZjKCcjq4m+MuXncEvUZgwEy74D2fcMntUZsy45EVymQBUAXcC1yadalPVRk+iHGVjMbmksr+tieXfv5d48FXOWdTBtuZNNPU0HVVuWsk0FlYtdJZKZ10eLh9+AHVr4A8fg/0vOvszzoDzvwIzTx/+ZxtjckpWH4tli4hcAHwP8AN3quo3+52/Cki09bQDN6jqC+65nUAbEAOiA918slxJLgAr713Doy8d4MuXvIarz5zFnvY9bKjfwIv1L7KhfgObGjfRFe066rqpxVNZWLWQ+ZXzWVC1gPmV86kprMn8kVosCmt+BH//FnQ2OMfmXwSv/6IzfpkxZlzwMrncCtytqqu9Cm6A7/EDW4DzgTqcqYuvVNWXksqcBWxS1SYRuRD4kqqe7p7bCdSqan2635lLyeW3z9dx0y9e4Iy5ldy38syjzkfjUXa07OClhpfY2LCRlxpeYnPjZrpj3UeVrQxXsqByAfMq5zG/cj4nVpzIrLJZBHxpDLzQ3QpP3Qz/uhUinSA+WPpeWP4ZKJvixa0aY8YwL5PLS8CJwKtAB877Lup1g76InImTLN7k7n8G54v+Y4DyFcAGVZ3m7u8kj5NLS1eE2q/9mVhcefZzb6C65NgvYiYSzqbGTWxq2MTLjS+zuXEzbZGjx0ML+UMcV34c8yrmcWLFiZxYcSLHVxxPZXiAd13a9sPfvgnP3QsacyYmW/oeOOtGqJg13Ns1xoxRXiaXlH8pVPXVIcY20PdcDlygqte5++8FTlfVDw9Q/t+A+UnldwBNOC98/o+q3j7AdSuBlQAzZ85c9uqrmd1GZM8e9n72cxRMnkxg8mQKJk8iMMldT56Mv6Iia724rv3fZ3l88yG+8daTePfpQxumRVWpa69jc+NmNjVuYkvTFrY0bmFvR+r536rCVZxQcQLHlx/vJJzy45lbPvfwi5/1W+GvX4FNDzr74nfe8D/nJqixCUuNyTc59xKliLwDeFO/5HKaqn4kRdkVwA+Ac1S1wT02VVX3ishE4M/AR1T1H4N951BqLh3PPMuua64Z+D4KCghMnOgknkkTCUycRGDSJGd70iTn3MSJ+ELpDQGT7Jerd/Op36wf8NHYcLT2trK1aSubGzezpWkLW5u3sq1pG53RzpTlpxRPYW75XI6fcDzHlR/H3LiPuRseoHTD75yaDAILLoJzPg7TRqTJzhgzArysuQhwFTBXVb8iIjOByar6rDeh9n1PWo/FRORk4LfAhaq6ZYDP+hLQrqr/Ndh3DiW5xFpb6Vr/ItED+4ns3090/wEiB9z1/v3EW9ObOdI/YYKTaBIJp6aGwMQaAjU1FLj7/poafMFg3zXNnb2c863Hae+J8qNrann9gkkZxZ6puMbZ17GPrU1b2da8jS1NW3il+RV2tOwgEo+kvKYmVMmcmDKnqY65PT3MiUSYU3MyE0/9v/gWXgqBYMrrjDG5wcvkchsQB85T1QVuW8ejqnqqN6H2fU8Ap0H/9cAenAb9d6vqxqQyM4HHgKtV9amk48WAT1Xb3O0/A19R1T8N9p3ZaHOJd3URPXCAyIGDRA8ecLb3O+vowYNEDh0kevAQRKPH/jASSchJOoGaGl7qCfKHul581VV84epzKZo8mUBNNb6Skuy9VNlPNB6lrq2OV5pf4ZWWV9jWvI0dLTvY0bKDnlhPymsK43FmxWB22WxmzTyH2RNPYnbZbGaWzaQsmPPD1BkzbnjeFVlEnlfVpe6xF1R1sUexJn/Xm4H/h9MV+S5V/bqIXA+gqj8UkTuBt+N0LgC3y7GIzMWpzYAz18zPVPXrx/q+0WrQ13icWFOTk2wOHCB66BDRg07SObx9kGhDA8Rix/5AQEIhAtXV+KurCFTXEKiqOrxfVU2guopAVRX+6mp8xcVZSURxjbO3fS/bW7b3JZsdTdvY2bSFxtjR3aQTKkIVzCybyayyWcwsncnMspnMKJ3BjNIZTAhN8DxOY8zQeZlcngHOAla7SaYGp+aS87NRjvXeYhqLOUno0CGi9fV9yaduex3PrNlCdU8brymMIo0NxDtTt42kIqEQ/qpKJ+lUVjoJqLLKPVaFv9JdV1QSqKxACoY2H02ylu4WXt3ye3ZuuI+d9RvYGfCzKxBgV7CArkESXVmwrC/RzCidwfTS6Uwvmc700ulMKpqE3+cfdmzGmPR5mVyuAt4FLAPuBi4HPq+qvxrsulww1pPLYD523/P8bt1e3rBgIndecyrxjg4nATU0OOv6emL1SdsNDc65xkY0g0QE4Csrc5JQZSX+ygoCFe52RblzvCJxvAJ/RQW+wsLBP7B1nzMC8ws/Rxtf4aDfz66CAK9Wz2HXxBPZVVjC7q6D7G7bnfLF0ISAL8DU4qlMK5nG1JKpTC+dztTiqUwtcY5VFVbhk0wnXjXGDMbL5HITsAY4GZssbMw42NrNed/5+5Aa9+OdnX1JKNbU5KwbG4k2NPYloVhjI9HGRmJNTRlPgSyFhU7iKXeSTd9SPgF/hZuEysvxT5iAv+tV/Lsexrf5d9DdkvgEmHkmuuASGuaew26Jsqt1F3Xtdexp20Ndex11bXUc6jo0aBxBX5ApJVOYUjyFqSVTj1hPKZ7CpKJJQ54l1Jjxysvk8kXgnUAjcB/wa1U94EmUoyyXkwvAnU9s52t/3MTMyiIevem1hAu8f0Sk8TixlhZijY1uwmki1uQmnsYm51iTu93kLBpJ3ZNsMBIO4y8O4Q/04KcNfzCKPxh3lonT8M89Bf+8c/HPmOckpQkT6C0Jsa/nEHva97CnfQ972/cesd3c0zz4dyJUF1YzuXjy4aVoMpOKJzGpaBKTiydTXVid3sgFxowTnr/n4nYBfhdOg3qdqr5heCGOvlxPLpFYnLfc/ARbDrRz0xtO5KNvOGG0Q0JViXd0Emt2Ek+sqYlYczPRpiZiTc3Empv7klCsublvGUpCApCiIifZlJW5SacMX1kZ/gnlxErCtIWU5mCE+kA3B/0d7JFmdmsjO7We/T2HiOvgtTKf+KgOVzOxaGLfMql40hH7NYU1lBSMXG89Y0ZTNpLLZOAdwBVAqc3nMjY8vb2BK25/mlDAx18+/rrsTyaWBaqKdnY6Sai5mXhLy+HtxnpiO18kVreZWP1+Yt0xYr1CrMdHrNcHOvQ/6FJUBKXFxIrD9BYV0Bn20R5WWgoiNAZ6OOTv5JC/k/aQ0hmGzpDQEYLOEHSGIe47/N2FgUJqCmuoLnQSUXVhNTVFzn5iqSmsYUJogrUDmZzm5WOxG3BqLDXAr4FfJA8mmcvyIbkAfPS+53lg3V5WzKvhR9ecis+Xp/8FHYvCnrWw7c+w9VF07wvEo0K81+ckHCknNmEBsaI5xIJTiMdCxFpbibW2Em9tIdbSeni/rS3jtqT+eoM+usJCe1BpD8XpDImTePoWZ78r6VhvOEBwQjmFZVWUlE+koqyGqnAV1YXVVBVWURmupCpcRWVhJROCE6w3nBlzvEwu3wTuU9V1HsU2ZuRLcklu3H/LyVP47jsXEwqMgz9KbQfglb/C9r/Bjiegrd/4aMU1MP00mHGqs566tG8mTY3HiXd0EG9NJJw2Yq0txFvbiLW1uus24m1tfcmob7+tjXh7+7CTE0DED11B+pJQVxC6QtK31qIwvuIifMWlFJSWEiwrp7C0kuLyaorLqymbMIkJFZMpr5hCeUmVtQ+ZrMu5scVGQ74kF4CnXqln5b1rae+JctZxVfzPe5dRGh5HPaFUoXE77HzCSTQ7n4D2fv1OfAGYtAimn+qMdzZlMVTPA3/mf5A1Hife2XlEsnESURvx9jZibe3OseTttjaiba1E29uItbdDewcSG36CSuj1Q09I6A35iYYLiBcG0cIwUlSIr7iYQEkpwZIygqUTKCytoKi0kuIJ1QRLy/AVFR21SGEh4rNHeOZIllzSkE/JBWDj3hbe97+rOdTWw2umlvG/157KxNLwaIc1OhLJpm417H4W6p6FAxuhfwN+IAyTXuMkmimLYdJJzmjOoZIRCFHR3t7Diamjg3h7B/EOJxlFWltob6mnq6WB7tYmIu1OYoq3d0BnJ9LZQ6A7QkF3lFBPHF8W/m8dCwXQcAgtDOErLMRXVEygqJiC4hIKisvwFxXhKypEiorwFRa5ZQrxFRYi4aTtwkInaYXDffuWuHKTJZc05FtyAdjd2Ml7f/QMOxs6mVlZxL3vP43Z1cWjHdbY0NMOe59zEs6+9bBvHTTtTF22fBZMXAgTFzjrmnlQdXzfY7WxRlWJdLbT0nyAlsZ9tLYcoqPlEJ2tjXS1NtLT3kJvW4uTwDo70c4upKsbX1cvoV4lHFHCvThL5PA6myQUOpx4CgvxhcOHtwvDTnIKh5HCML5w0rHCMBIOO+fC7rlwyLk2lLQOh5FQyHrxecySSxryMbkA1Lf38P67V7O+roXqkiB3X3sai6bZGF0pdTXB/hdh3wvOcuAlqN8CA4z6TNl0qD4eqk5wkk3V8VA5BybMyMkRn1WVjkgHrb2ttPS00NLbQmtPKy29LbR0NdPR1khnWxPd7U30tLUS6Wgl2tFOtLMD7eom5CalUATCESXUt+2sQ+6xcASCUSdpBaPZT1zJJBw+nGzCIXyh8BHHfOEQEnLPBY885qz7b4eca0NhJBQ8/NlBdzsUQvz52+ZpySUN+ZpcANp7otzwk7U8sbWewgI/7z9nNh84Zy6Vxbn3B3DExSLQ8AocfAkObnLW9VugccfASUd8TuKpmAUVs52lfCZMmO4spVMgz0YDiGucjkgHbb1ttPa29q3be9tp622jLdJGW2/bEfvtve10RDpo726lt6sdunsIRhOJyFmCESUUhZCbiEIRCEXd44ky0cPnghEIRpVwRAhHpe94QVQJREfpb10ggC8Y7EtGEgo6iasvOQWRAvd8MIiEgk5yCib2Q26yco5L4ngwiAQLnCTWt5+0FLjn3X0CAc9rbpZc0pDPyQWgNxpn1f3ruf+5PQAUBf2894xZXHfuXGpKM5+sbNyLRaH5VWf2zYZt0LDVSUJNr0Jr3dHtOcnE5ySYRKIpnQJlUw5vl06B0kkQLIFx9BgnEovQHmmnPeImnUTycfcT252RziOOJZbOSCed0U46Ih0p5xiSuPYlomA0kYgOJ6QjziWfjyoFUSiIQigqFMb9hGN+wlEhFPf1lXfKKIFIHH8kjj8ax98bRcbKn1gRN+kU9EtEBcy47TaCM2YM4SMtuRxTvieXhLWvNvH9x7byt83OWFzhAh/vPm0W//d1c5lUNk4b/L0W7YWW3dC0w2nHadoJLXugpc5Z2vbhzMB9DIFCKJnoLpOc7tTFNVBcDUVVzlJcDUXVUFQJAfuPhITeWC9d0S46I06y6YweTjyJ413RLjqjnXRFuvqOp1o6o51929F4enMv9VHFHz+csAJRKIg5iSjYt+0ktkCMI9aF8QCFMT+huJ9w3Eco5nOSWUwIxoSCmDjXxyAQVfxRJRCN448q/mgcXySGLxrDF4khkRgySHf5WQ//kaI5czP+d7bkkobxklwSXtjdzPcf28ZfNjlddIN+H6fNqeTs46s594RqFk4py98XMEdbtNdJMC27oW0/tO511m17D++3H4RBRoFOqaAYCivcpfzI7VAZhCdAuNxdT4BwGYRKnSVYAvaS5jFF4hG6o919ySax3R3rpjvanXo/1kVPtKfveE+0p+98T6zHKRdztnuiPfTEeuiN93oeu8S1L7EF4kmJLga3vO9+5lafmPln5mJyEZELgO/hTBZ2p6p+s995cc+/GegE3qeqz6VzbSrjLbkkbNzbwi2PbeNPG/eT/D+F8qICzj6umrOOr+I1Uycwp6qYCUX51U4wpqlCb7uTZNoPQkdiXQ+d9e664cgl0/+q7i9YcjjRBIvd/cS2u19Q5PSSK3CXYLG7XXh4CSRvh521Ja6MxDV+RLI5akkcj/fQG+t1ElKsl+5oN73xXnpjvUcc74n1EIlH+vb7FrfsHW+8g8nFkzOOM+eSi4j4caY5Ph+ow5nm+MrkoWbcmSo/gpNcTge+p6qnp3NtKuM1uSQ0tPfw1CsNPLmtnie21rOn+ej/aq4oKmB2dTGzq5xlSnmYyqIgFcVBKouDVBYFKQ0HrMYzGhLJqKvJWTobD293tzhLT+vh7a5mp3xP2+ElnUd1Q+ULOEknEHKSjT/oJJ6Au07e9/dbAiGnA4Q/6Kx9SdtHHAu46wLn+xJrX4GT3Pr2A85+33bSMfH327b3bwYzWHIZq+NDnAZsU9XtACJyH3ApkJwgLgXuVSc7Pi0i5SIyBZidxrWmn6qSEBcvnsrFi6eiquxq7OSJrfU8vb2BVw51sLO+g6bOCE27mnl+V/OAn+P3CWXhAEXBAOECH0XBAIVBP0VBP4UFfgr8Pgr8PoIB6dsu8Pvw+8Avgs8nh9futgiICD4Bn7tGhEQKE3GGzHfWh9vA+0ocuXKvObw3UCocSlv66Le/+4Aqd8H5f3iJuwxG4wSiXQSibRREO/BHOwlEOwlEOwjEEtud+GNdBKJdzjrWhT/WjT/aiT/W42zHuvq2A7EufPFe/LFuJB6F3jZnySGKoOJHxZd6jbNG+pVzr+s7jg8VAfGjIig+EN+R2wgqPkCOPIc41ybOi8/5zwD3GvCBOLEePnb4GkSOPgZJ+zD5os9TUjnF03+7sZpcpgG7k/brcGonxyozLc1rzSBEhFlVxcyqKuY9Z8wCnHcgDrb1sKPeSTQ7Gjo41NZDU0cvjZ0Rmjp6aeropa0n6iShzhF8ecFkSdhdqob5OUoBMUL0EiJCmF5CEiFIlBC9zloihOilgBhBIgQlSpAoBe4SJEIBMQoksZ84FyMg7pqYu3bOBSSOnxgB4gSIuusYPnftF3fdVyaGn7i7xAhIHEERjWa1UjcW7G68ftwkl1T//df/5x2oTDrXOh8gshJYCTBz5sxM4ht3RIRJZWEmlYU5Y+7Af2x6o3HauiN09sboisScdW+MrkiUrt44kVic3pizjkTjRGJKbyxOPK7EVPvWsTjE3f24OtvgrGNx7ftBncOKqrOdOJN42ntkucSxI3ZSGsrfkrH4iDlXRd1ltInG8RHDp3HEXfuI9zseP7xO2hZVfMTcBOVe5247dQmnTOI6Z9vZB3Wvd8rSdy75uqTF7fouifKQ9F0kfSZ959x6GQDnTJjo+b/dWE0udUByp+vpwN40ywTTuBYAVb0duB2cNpfhhWwAggEfVSWhYf+3rjEmt43V1qrVwAkiMkdEgjiTkj3Yr8yDwNXiOANoUdV9aV5rjDEmi8ZkzUVVoyLyYeARnO7Ed6nqRhG53j3/Q+AhnJ5i23C6Il872LWjcBvGGDNujcmuyKNhvHdFNsaYTA3WFXmsPhYzxhiTwyy5GGOM8ZwlF2OMMZ6z5GKMMcZzllyMMcZ4zpKLMcYYz1lyMcYY4zlLLsYYYzxnycUYY4znLLkYY4zxnCUXY4wxnrPkYowxxnOWXIwxxnjOkosxxhjPWXIxxhjjOUsuxhhjPDfmkouIVIrIn0Vkq7uuSFFmhog8LiKbRGSjiHw06dyXRGSPiKxzlzeP7B0YY4wZc8kFWAX8VVVPAP7q7vcXBT6hqguAM4APicjCpPP/rapL3OWh7IdsjDEm2VhMLpcC97jb9wCX9S+gqvtU9Tl3uw3YBEwbqQCNMcYMLjDaAaQwSVX3gZNERGTiYIVFZDawFHgm6fCHReRqYA1ODadpgGtXAivd3XYR2TzEmKuB+iFeO9bky73ky32A3ctYlC/3AcO7l1kDnRBVHeJnDp2I/AWYnOLU54B7VLU8qWyTqh7V7uKeKwH+DnxdVe93j03C+YdS4KvAFFV9v7d3cFQca1S1NpvfMVLy5V7y5T7A7mUsypf7gOzdy6jUXFT1DQOdE5EDIjLFrbVMAQ4OUK4A+A3w00RicT/7QFKZO4A/eBe5McaYdIzFNpcHgWvc7WuAB/oXEBEBfgRsUtXv9js3JWn3rcCGLMVpjDFmAGMxuXwTOF9EtgLnu/uIyFQRSfT8Oht4L3Beii7H3xaRF0VkPbACuGkEYr59BL5jpOTLveTLfYDdy1iUL/cBWbqXUWlzMcYYk9/GYs3FGGNMjrPkYowxxnOWXNIkIheIyGYR2SYiR40aII6b3fPrReSU0YgzHWncy3IRaUlqz/r30YjzWETkLhE5KCIpO23k2G9yrHvJld9kwKGZksrkxO+S5r3kyu8SFpFnReQF916+nKKMt7+LqtpyjAXwA68Ac4Eg8AKwsF+ZNwMPA4IzJM0zox33MO5lOfCH0Y41jXt5LXAKsGGA8znxm6R5L7nym0wBTnG3S4EtOfz/lXTuJVd+FwFK3O0CnJfOz8jm72I1l/ScBmxT1e2q2gvchzNMTbJLgXvV8TRQ3q9b9FiRzr3kBFX9B9A4SJFc+U3SuZecoOkNzZQTv0ua95IT3H/rdne3wF369+by9Hex5JKeacDupP06jv4fWTplxoJ04zzTrUI/LCKvGZnQPJcrv0m6cuo3GWBoJsjB32WQe4Ec+V1ExC8i63BeTP+zqmb1dxmLY4uNRZLiWP+sn06ZsSCdOJ8DZqlqu/v+0O+AE7IdWBbkym+Sjpz6TdyhmX4DfExVW/ufTnHJmP1djnEvOfO7qGoMWCIi5cBvRWSRqia38Xn6u1jNJT11wIyk/enA3iGUGQuOGaeqtiaq0OpMWVAgItUjF6JncuU3OaZc+k0GGpopSc78Lse6l1z6XRJUtRn4G3BBv1Oe/i6WXNKzGjhBROaISBC4AmeYmmQPAle7PS7OAFrUHd15jDnmvYjIZBERd/s0nP+dNIx4pMOXK7/JMeXKb+LGmHJopiQ58bukcy859LvUuDUWRKQQeAPwcr9inv4u9lgsDaoaFZEPA4/g9La6S1U3isj17vkfAg/h9LbYBnQC145WvINJ814uB24QkSjQBVyhbneSsUREfo7TW6daROqAL+I0VObUbwJp3UtO/CYcHprpRff5PsBngZmQc79LOveSK7/LFOAeEfHjJMBfquofsvk3zIZ/McYY4zl7LGaMMcZzllyMMcZ4zpKLMcYYz1lyMcYY4zlLLsYYYzxnycWYEeCOnvsHd/sSSTEa9RA/90oR+Vy/Y+8TkVu8+HxjhsreczFmiNyX50RV45lcp6oPcvRLuEN1AXCzR59ljGes5mJMBkRktju/xw9wxpWaISK3icia/vNkiDNvzssi8k/gbUnH+2oWInK3iFyedK7dXU8RkX+IM0fIBhE5N0UsAixx4xgo3reIyL9EpNr9rh+KyBMiskVELnLL+EXkv0TkRXHm8fjIcP+djLGaizGZmwdcq6ofBBCRz6lqo/v2819F5GScuT/uAM7DeeP5Fxl+x7uBR1T16+7nFqUosxR4YaA3wkXkrcDHgTerapM7Ssls4HXAccDjInI8zpvYc4Cl7ggOlRnGasxRLLkYk7lX3fkuEt4pIitx/v80BViI81Rgh6puBRCRnwArM/iO1cBd7sCJv1PVdSnKXIAzuVMqK4Ba4I39RvL9pfsYb6uIbAfm44wz9UNVjQKoas7PK2NGnz0WMyZzHYkNEZkD/BvwelU9GfgjEHZPpzO2UhT3/4fuY64g9E0e9lpgD/BjEbk6xbVvBB4d4HO348yeeGK/4/1jUpyh1m0cKOMpSy7GDE8ZTrJpEZFJwIXu8ZeBOSJynLt/5QDX7wSWuduX4g5WKSKzgIOqegfOyLxHzGcuIhOAgKoONALvqzjtPPfKkRNYvUNEfG5cc4HNOAnqehEJuJ9tj8XMsFlyMWYYVPUF4HlgI3AX8KR7vBvnMdgf3Qb9Vwf4iDuA14nIs8DpHK4VLQfWicjzwNuB7/W77nzgL8eIbTNwFfCrpCS3Gfg7zuO069047wR2AetF5AWc9h5jhsVGRTYmB4nIncCd/dp+jnXN3cAfVPXXWQvMGJc16BuTg1T1utGOwZjBWM3FGGOM56zNxRhjjOcsuRhjjPGcJRdjjDGes+RijDHGc5ZcjDHGeO7/A3Lj/4w3nvAbAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def rhoz_exp_flaring(z, R, z00, Rs):\n", " z0R = z00+np.arcsinh(R**2/Rs**2)\n", " return np.exp(-z/z0R) / (2*z0R)\n", "\n", "fig, ax = plt.subplots(figsize=(6,4))\n", "z = np.linspace(0,3)\n", "plot_rhoz(ax, z, rhoz_exp_flaring(z, 0.0, 0.1, 0.8), label='R=0')\n", "plot_rhoz(ax, z, rhoz_exp_flaring(z, 0.5, 0.1, 0.8), label='R=0.5')\n", "plot_rhoz(ax, z, rhoz_exp_flaring(z, 1.0, 0.1, 0.8), label='R=1')\n", "plot_rhoz(ax, z, rhoz_exp_flaring(z, 1.5, 0.1, 0.8), label='R=1.5')\n", "plt.ylim(None,2);" ] }, { "cell_type": "code", "execution_count": 13, "id": "745345ef", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig,ax = plt.subplots(figsize=(12,4), ncols=2)\n", "\n", "plot_sb_vdisk(ax, r, sb_exp, vdisk)\n", "plot_sb_vdisk(ax, r, sb_exp, vcdisk.vcdisk(r, sb_exp, rhoz=rhoz_exp_flaring, rhoz_args={'z00':0.1, 'Rs':0.8}, flaring=True))\n" ] }, { "cell_type": "markdown", "id": "fcfda35e", "metadata": {}, "source": [ "## Example 2: observed surface brightness" ] }, { "cell_type": "markdown", "id": "8ab4c0f2", "metadata": {}, "source": [ "### NGC2403: a late (Sc) bulgeless disk galaxy" ] }, { "cell_type": "markdown", "id": "fb9c3c48", "metadata": {}, "source": [ "Let's say that, instead of having just simple galaxy images from which we can derive an analytic approximation for the galaxy surface brightness, we have a detailed galaxy image from which we can measure the intensity in elliptical annuli. This is for instance the case of nearby galaxies such as [NGC 2403](http://cdsportal.u-strasbg.fr/?target=ngc2403), that I use here as an example.\n", "\n", "I use data taken from the [SPARC](http://astroweb.cwru.edu/SPARC/) database for this galaxy, which I include in this package as the `NGC2403_rotmod.dat` file. Here are reported measurements of the intensity at 3.6$\\mu$m taken with the *SPITZER* space telescope in elliptical annuli for this target." ] }, { "cell_type": "code", "execution_count": 14, "id": "7060aac6", "metadata": {}, "outputs": [], "source": [ "rad, _, _, _, _, _, sb_n2403, _ = np.genfromtxt('NGC2403_rotmod.dat', unpack=True)\n", "# convert SB to Msun / kpc^2\n", "sb_n2403 *= 1e6" ] }, { "cell_type": "markdown", "id": "f39e2ff5", "metadata": {}, "source": [ "Now we can very easily use `vcdisk` to calculate $V_{\\star, \\rm disk}$ for this galaxy, and we can evena compare it to some analytic profiles." ] }, { "cell_type": "code", "execution_count": 15, "id": "84d306ee", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/lposti/anaconda/envs/py37/lib/python3.7/site-packages/ipykernel_launcher.py:2: RuntimeWarning: divide by zero encountered in log10\n", " \n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "vd_n2403 = vcdisk.vcdisk(rad, sb_n2403, z0=0.4)# z0=0.4 kpc from Fraternali et al. (2002): https://ui.adsabs.harvard.edu/abs/2002AJ....123.3124F\n", "sb_exp_n2403 = expdisk_sb(rad, 1.004e10, 1.39) # numbers taken from http://astroweb.cwru.edu/SPARC/\n", "\n", "fig,ax = plt.subplots(figsize=(12,4), ncols=2)\n", "\n", "plot_sb_vdisk(ax, rad, sb_exp_n2403, vcdisk.vcdisk(rad, sb_exp_n2403), label='exp-disk')\n", "plot_sb_vdisk(ax, rad, sb_n2403, vd_n2403, label='observed')\n" ] }, { "cell_type": "markdown", "id": "2503de91", "metadata": {}, "source": [ "The $V_{\\star, \\rm disk}$ curve obtained with `vcdisk` directly from the ellipse photometry of NGC 2403 is much more structured between $1-5\\rm \\,kpc$, which is where the surface brightness has dips and peaks. \n", "*Capturing this rich structure is* **essential** *to rotation curve modelling*." ] }, { "cell_type": "markdown", "id": "d9c2392b", "metadata": {}, "source": [ "### UGC 2953: an early (Sa) spiral galaxy" ] }, { "cell_type": "markdown", "id": "c1380446", "metadata": {}, "source": [ "Let's take a different case now of an early spiral galaxy, i.e. a disk galaxy with redder colors and a prominent central bulge: UGC 2953.\n", "\n", "I use again the data taken from the [SPARC](http://astroweb.cwru.edu/SPARC/) database and I include them here as the `UGC02953_rotmod.dat` file. There are measurements of the near-infrared intensities of both the disk and bulge components separated." ] }, { "cell_type": "code", "execution_count": 16, "id": "7b43b94d", "metadata": {}, "outputs": [], "source": [ "rad, _, _, _, _, _, sbd_u2953, sbb_u2953 = np.genfromtxt('UGC02953_rotmod.dat', unpack=True)\n", "# convert SB to Msun / kpc^2\n", "sbd_u2953 *= 1e6\n", "sbb_u2953 *= 1e6" ] }, { "cell_type": "markdown", "id": "05cd0512", "metadata": {}, "source": [ "With the two different surface brightness arrays, we can use `vcdisk` and `vcbulge` to get the corresponding circular velocities." ] }, { "cell_type": "code", "execution_count": 17, "id": "29abfbcf", "metadata": {}, "outputs": [], "source": [ "vd_u2953 = vcdisk.vcdisk(rad, sbd_u2953, z0=0.6)\n", "vb_u2953 = vcdisk.vcbulge(rad, sbb_u2953)" ] }, { "cell_type": "markdown", "id": "12a96665", "metadata": {}, "source": [ "And we can finally plot them together." ] }, { "cell_type": "code", "execution_count": 18, "id": "305d2ce0", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/lposti/anaconda/envs/py37/lib/python3.7/site-packages/ipykernel_launcher.py:2: RuntimeWarning: divide by zero encountered in log10\n", " \n", "/Users/lposti/anaconda/envs/py37/lib/python3.7/site-packages/ipykernel_launcher.py:2: RuntimeWarning: divide by zero encountered in log10\n", " \n", "/Users/lposti/anaconda/envs/py37/lib/python3.7/site-packages/ipykernel_launcher.py:2: RuntimeWarning: divide by zero encountered in log10\n", " \n" ] }, { "data": { "image/png": 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rY4Bpaw8y5IsltHllFveNW8XPy/dzKOHCXTzaVGzDhz0+xNPmyfgt4/ll2y+F/mxKlQX79u1jyZIlAIwfP57OnTsTFRXFypUrAfjtt9/yfV3Hjh1zn5swYULu8T59+jB69GiSk5MBOHDgADEx55y2V2AFSahjjTHxxphHgd5AuyK/a2kgAhWb0TMlBSB3IQCllFLuYcIW65fkkPpDqBJQ5aKu8dLvm1i6+xgVg7yZck8nLm9csUgxiQhtaobw6fWtmf/4ZdzZrTbVQnyJT8lg+rpDPP7bOi55fS6Xv/cvX/y7k8TzTGa8tMqlvNLpFQDeWfEOexL2FCk2pdxRo0aNGDNmDM2bN+fYsWPcfffdPP/88zzwwAN06dIFuz3/OQYffPAB7733Hu3bt+fQoUMEB1t14L179+b666/nkksuoVmzZgwZMoSkpKQixynGnL+vpogMNsZMzfP4fmPMx0V+Zydp27atWbFixcW9+M8niV3xJZfXqI7NZmfWkFmE+4Y7N0CllDoHEVlpjGnr6jhKUpHu2XlkZGfQbWI3ktKTmDJ4CnUq1Cn0NeZtieGW75fjZbfx292X0qxa8Uy8MsawJy6FBdtjmb/tKEt2HuVEehYAAd4eXN+hBrd0iqJysG++r39ywZP8sesPmoY15Yf+P+Bp8yyWOJXKa/PmzTRq1MjVYVy0lJQUfH19EREmTJjA+PHjmTq14P0u8vv857tnX3CEOm8y7XhcapLpIqvSkoisbLraAsnMzmTS9kmujkgppVxCRHxEZJmIrBWRjSLyouN4qIjMEpHtjn1Intc8JSI7RGSriPQpyXjXxKwhKT2J2sG1LyqZTs3I4v+mbQDg0T71iy2ZBmvUula4PzddEsU3I9uy5vnejL65LZfUDiM5LZOv5luTIR/+eQ07Y5PPev3THZ6msn9lNsRt4Mu1XxZbnEqVJStXrqRly5Y0b96czz77jHfffbdY369QXT5EZIyIVMjzOERERjs9qpJSuSUAw+PjAZi4ZaL2/VRKlVdpQA9jTAusuTJ9RaQj8CQwxxhTD5jjeIyINAaGAU2AvsBnIlJi/d2WHV4GWGURF+Ozf3ay/9hJGlYK5NZOJbtEuafdRo+GFRl/R0em3deJAc0rk20Mk1YdYODHC1m84+hp5wd5BfFq51cRhK/Xf82amDUlGq9S7qhLly6sXbuWdevWMX/+fOrWrVus71fYtnnNjTHxOQ+MMceBVk6NqCSF1wOvAC6Ji6Z2YA1iTsYwZ+8cV0ellFIlzlhyhkc9HZsBBgNjHMfHAFc6fh4MTDDGpBljdgM7gPYlFe/qI6sBaFup8BUze+NO8MW/OwF4aXBTPOyuW+OsebUKfHp9a/559DIGNKtMSnoWN3+/nNmbjpx2XrtK7bi56c1km2yeWvAUJzJOuChipVR+CnsXsZ3xdV8opWtxmMKx2aFySwQYHtYGgAlbJ5z/NUopVUaJiF1E1mCtVDvLGLMUqGiMOQTg2Ec6Tq8K7M/z8mjHsfyue4eIrBCRFbGxsUWOM9tksyHOKtdoHt680K9/5+9tpGdmc3WrqrSvFVrkeJyhRpgfHw9vxU2X1CQ9M5s7f1zJ1DUHTjvnvpb30TC0IdHJ0by1/C0XRaqUyk9hE+p3gSUi8rKIvAwsBtz7/9VVWwNwRbrBz8OPlUdWsuP4DhcHpZRSJc8Yk2WMaQlUA9qLSNPznJ5fU+R8Z7kbY74yxrQ1xrSNiIgocpz7EvdxIuMEkX6RRPgV7nqbDyXy+9qDeNltPNqnQZFjcSabTXhxUBPu6V6HrGzDgxPXMG7pvtznvexevN75dbxsXkzaPkm/UVWqFClUQm2M+QG4Gjji2K42xowtjsBKTPUOAAQcWM0Vta8AYOLWia6MSCmlXMpR2vcPVm30ERGpDODY5zRsjQaq53lZNeBgScS35fgWABqFFr4DwXuztgFwQ8caVKmQf1cNVxIRHu/bkMf7NsAYeHryer50lKcA1A2py8NtHwbgxSUvcvTk0XNdSilVggo7KdEH6wbbE7gM6OM45jaysw0JJ/NMPKzuKPk7sJLr6l4NwLSd00hOP3umtVJKlVUiEpEz6VxEfIHLgS3ANGCk47SRQE7np2nAMBHxFpFaQD1gWUnEuu2YlRTXD6lfqNdtP5LErE1H8PawcXf3wncGKUn3dK/Ly4ObAPD6n1uYvDo697nhDYdzSeVLOJ52nOcWPceF2t8q5Y7i4+P57LPPznvOnj17GDdu3AWvtWfPHpo2Pd8XbkVX2JKPH7BmdH8EfAI0AtxqhPqXlfvp8c4/TFl9wLoJBURCREPISKF+SgJtK7YlJTOFyTsmuzpUpZQqSZWBeSKyDliOVUM9HXgD6CUi24FejscYYzYCPwObgL+Ae40xWSUR6I54qyyvsAn1d4v3ADCkTTUiA0v/WNCIS6Jyk+pnJm9gl6Olnk1svNzpZYK8glh4YCE/b/3ZlWEqVSycmVCXhMIm1A2MMaOMMfMc2x1A4e5oLjZ3SwxxJ9J5cOIabhq9jL1xJ6B2d+vJnfMY0XgEAD9u+lFb6Cmlyg1jzDpjTCtjTHNjTFNjzEuO43HGmJ7GmHqO/bE8r3nVGFPHGNPAGPNnScWak1AXpv90akYWU1dbk/xuvjSqOMIqFjd2rMkVza3uH/ePX01apvU3S0X/ivzfJf8HWKso7k7Y7cowlXK6J598kp07d9KyZUsee+wxHnvsMZo2bUqzZs2YOHFi7jkLFiygZcuWvP/+++zZs4cuXbrQunVrWrduzeLFi0ss3sJ26FgtIh2NMf8BiEgHYJHzwyo+X9zYhl9WRPPan5tZsP0ovd+fz3stGjAAYPe/dL/sKWoF12J3wm6m7pjKkPpDXB2yUkoph5SMFKKTovGweRAVFFXg1y3fc4wT6Vk0qRJEvYqBxRegk4kIr13djLXR8Ww8mMibf27l/wY2BqBPVB/+3f8vv+/6nacWPMXY/mN1FUVVLJqNaVYs110/cv05n3vjjTfYsGEDa9as4bfffuOLL75g7dq1HD16lHbt2tG1a1feeOMN3nnnHaZPnw5YqyPOmjULHx8ftm/fzvDhw3HGyqwFUdgR6g7AYhHZIyJ7gCVANxFZ7/iasNQTEa5tV505D3fjqlZVScvM5omVgWRhw0SvwJZ+grua3wXA52s+JyUjxcURK6WUyrE7YTcGQ1RQFJ72giePCx2LpXSuF15coRWbIB9PPh7eGg+bMHrR7tN6VD/V4Smq+FdhY9xGvlj7hQujVKr4LFy4kOHDh2O326lYsSLdunVj+fLlZ52XkZHB7bffTrNmzRg6dCibNm0qsRgLO0Ldt1iicIGwAG/ev64lV7euyrNTNrAuqTatbDv4fsIEBg+9iUahjdh8bDNfrvuSh9o85OpwlVJKAduOWxMS61WoV6jXLd4RB0CnOu6XUAO0rF6Bx/s24LUZW3js17XMeKALlYN9CfQK5NXOr3LrzFv5Zv03dKnahZaRLV0dripjzjeSXBIKOvH2/fffp2LFiqxdu5bs7Gx8fEpurkRhR6jDjTF7825Yqyfm/Ox2utSLYOaDXUmvZi1fm7J9Pr3fX0D38LsQhDEbx7Au1i0G35VSqszLqZ+uG1LwZYTjU9LZcDABL7uNdlGlYyGXi3Fb59p0qx/B8ZQMHpiwhqxsK8loW6lt7iqKTy54kuOpx10cqVJFFxgYSFJSEgBdu3Zl4sSJZGVlERsby/z582nfvv1p5wAkJCRQuXJlbDYbY8eOJSurROZJA4VPqL8WkdxCGhEZDjzr3JBKno+nnQ7d+gPQ1Xc3sUlpvDX1JJGmF1kmi0f/fVR7fSqlVCmQk1AXZoR6yc44jIHWNSvg62UvrtCKnc0mvHttCyICvVm2+xgfz92e+9x9Le+jSVgTDiQf4MF5D5Kele7CSJUqurCwMDp16kTTpk1ZsmQJzZs3p0WLFvTo0YO33nqLSpUq0bx5czw8PGjRogXvv/8+99xzD2PGjKFjx45s27YNf3//EotXCtO/UkRqA78CNwCdgZuAK4wxCcUT3oW1bdvWOKXg/EQcvF0b4+HL+J6LeH3mDpLSUgmM+hp89tIgpAFf9/6aEJ+QC19LKaUKQERWGmPaujqOklTUe3bPn3sSczKGGVfPoHpg9Qu/AHhm8np+WrqPR3vX574ehSsVKY0W7TjKjd8uRYCJd16SO+oekxLD8D+GE5MSw6A6g3il0yuI5LegpVIXtnnzZho1KvziSWVFfp//fPfswq6UuAsYBvwGDAF6uzKZdir/MAiphWSe5PpaKcx5uBuXN6xK8r4RZKeFs/X4VoZOG86amDWujlQppcql5PRkYk7G4G33pmpA1QK/bvFOR/10Xfesnz5Tp7rh3NWtDtkGHhi/moQUq8VrpF8kn/T4BF8PX6btnMa3G751caRKlR8FSqhzung4Onn8CoQCUcBSd+nuUSBVW1v76BVEBvnw9U1tePeaTnjG3kvWyaocOXmAEX+O4KbfHyQ6qURW2FVKKeWwJ3EPADWDamKTgo0HHYg/ye6jJwj09qBZ1eBijK5kPdyrPi2qV+BgQipPTV6XO2mrUVgjXu/yOoLw4aoPmbV3losjVap8KOgI9RXAwDxbB6B3nsdlQxVHQn1oLWC12Lu6dTX+eWgQQ6q8TtaxHphsO6uPzaH/b4MYvXqaC4NVSqnyJW9CXVCLHO3yOtYJw8Ne2GlDpZen3cZHw1oS4O3BjPWHmbh8f+5zPWv0zO1O9fSCp9l4dKOrwlRurrwua38xn7tAd5czO3vk0+mjbKjS0to7EuocFfy8eGlQK5bc+Q63Rn2OZ2pzjKTx3tpn+b+5X5V8nEopVQ5FJ0UDUC2wWoFfk5NQd6oTViwxuVLNMH9eubIpAC/+vokdMcm5z93c5GauqnsVqVmp3D/3fg4kH3BVmMpN+fj4EBcXV+6SamMMcXFxhW65V9g+1MVORB4AbgcE+NoY80GJvXklRwOTIxshKwPOWDQg2M+Thy+7hLs7tePGX19nW8bPTN7/MUf/iOfT/o/p5A+llCpGOUlhtYCCJdTGGBY5+k+744IuBXFlq6rM3xbLpNUHuH/8aibfcyk+nnZEhOc6Pkd0cjTLDy9n1MxRfNfnOyoHVHZ1yMpNVKtWjejoaGJjY10dSonz8fGhWrWC/+EOpSyhFpGmWMl0eyAd+EtE/jDGbD//K53EJxhCasHx3XB0G1Rsku9pvl4e/Dr8We77PYx/j33BgqNjGTwxmnFXv0mAl2+JhKqUUuXNoROHAKgSUKVA5287kszR5DQiA72pExFQnKG51EtXNmXlvuNsPpTIG39u4YVB1u8uT7snH172IXfOupP1R9cz6u9RjO4zmkr+lVwcsXIHnp6e1KpVy9VhuI1CFZSJiLeIXC8iT4vI/+VsToynEfCfMSbFGJMJ/Atc5cTrX1jOKPXhDec9TUT4dNA9XFXtCUy2J7vT5nHZT9eyKWb/eV+nlFLq4hw5YS25XdGvYoHOzyn36Fw3vEx/gxjg7cFHw1rhYRO+X7yHcUv35T4X6BXIF72+oHFYY/Yn7ee2v28jJiXGhdEqVTYVdobGVGAwkAmcyLM5ywagq4iEiYgf0B84q9GoiNwhIitEZIXTv4rILfso2DKbL19+Ay+2/QzJDCHVtodh069jwrp/nRuTUkqp3EQw0i+yQOev2R8PQPta7rs6YkG1qF4ht5762SnrmbvlSO5zQV5BfNXrKxqGNmRv4l5GzRyli5Up5WSFTairGWOuM8a8ZYx5N2dzVjDGmM3Am8As4C9gLVbyfuZ5Xxlj2hpj2kZERDjr7S2Rja39kU0Ffsk1zTry26Cf8ctqgLEn8cqq//HgjI/Jzs52bmxKKVVOJacnk5KZgo/dhyCPANi3FBKiz/uaDQetZRKalqF2eeczrH0N7u9Rl2wD9/60mnXR8bnPBXsH83Wvr6kXUo89iXsYNXMUcSfjXBesUmVMYRPqxXmXHi8OxphvjTGtjTFdgWNAydRP56iYk1AXrs1QvYhKzLtxHPW8ByCSzZzYr+g+diQ7jh4qhiCVUqp8yRlRDfcJRcYNgdG94aPWsHdxvuefTM9i99ETeNiEehXLbv30mR7uVZ+rW1flZEYWt36/nP3HUnKfq+BTgW96f0PdCnXZlbCL2/6+TZNqpZyksAl1Z2CliGx1LPSy3tkLu4hIpGNfA7gaGO/M619QhSjw9Ifkw9Zy5IXg5+XFpGFvMCzqGcjy4ThruGraVbz+7wQdrVZKqSI4lnoMgLDkWNg51zqYlQYzn8n3/G1HkjAGakf44+1hL6kwXU5EeOPq5nSuG87R5HRGfreM4yfSc58P9Qnl695fUzu4Njvid+hItVJOUtiEuh9Qj1OLuuQs+OJMv4nIJuB34F5jzHEnX//8bDaIdKzdHnNxzfCf6TaM73tPxD+7EdhPMG7Pq3T9YQT/7dvqxECVUqr8yEmoQ1ISwD8S7lsBPhXg4Kp8v1HcdiQJgAaVgkoyzFLBy8PGZze2pmGlQHbFnuD2H1aQmpGV+3y4bzjf9vmWOsF12JmwU2uqlXKCQiXUJbGwizGmizGmsTGmhTFmjjOvXWA57fIKWfaRV5tqtVl00wR6V7wHsnxIkHXcNmcYIye9yom0NCcFqpRS5UPuCHV2NrQbBeH1oJFjPGfLjLPO3+5Y5KR+ZPkp98gryMeT725pR6UgH1bsPc4t3y3nRNqpKUnhvuF80+eb3KT6tpm3aVKtVBEUtm3e/+W3FVdwLpOTUMcUfGJifux2G+/2vZtfB06lsq0TYstkVdIEuvx0FbN3rL3wBZRSSgEQl2qVJYRkZUGtbtbBer2s/a55Z52fs2pgeaqfPlPlYF9+vK09kYHeLNkVx8jRy0hMzch9Pmekum6FujpSrVQRFbbkI2+rvCysEpAoJ8fkehENrX3MFqdcrkFEFf4e8QWPNH0fW2YYGfb9PLhgJLdPfZvUjPQLX0AppYqZiFQXkXkisllENjpWrUVEXhCRAyKyxrH1z/Oap0Rkh2NeTZ/ijC8x1ar+q5CVDZWs9nBEdbH20cshI/W083fGWgl1WV7QpSDqRgYy8c5LqBxsjVSP+GYpCSmnkuow37DcpHpXwi5u+esWDp847MKIlXJPhS35eDfP9irQHahaLJG5Uk4NdewWcOIa9je3uZy/r5tKdY/uiC2L/+J/oPPYq5m5fbXT3kMppS5SJvCIMaYR0BG4V0QcbY943xjT0rHNAHA8NwxoAvQFPhORYpv9l5hsJXlB3iHgHWgd9Au1Wp1mpcOhNbnnpmVmsf9YCjaBGmF+xRWS26gV7s/Pd15C9VBf1kYnMPzr/4hLPlV6GOoTyrd9vqV+SH32JO5h5J8j2Ze47zxXVEqdqbAj1GfyA2o7I5BSxT8C/MIgLRESDzj10hUDgplxw8fc0+hNJKsCafa9PLLoZgaOf0gnLSqlXMYYc8gYs8rxcxKwmfMPmAwGJhhj0owxu4EdQPviii8xxVrEK8j/jLUHqrW19tErcg/tP5ZCtoFqIX7lqsPH+VQP9WPiHZdQK9yfTYcSGfbVf8QknRrVD/UJZXSf0TQPb87BEwcZ+ddIth3f5sKIlXIvha2hXu9ol7dORDYCW4EPiyc0FxI5tcCLk8o+znR3+/78NWQqtbx6AYY96bO5fd4Q2o++iudmf09mVtYFr6GUUsVBRKKAVsBSx6H7HPf90SIS4jhWFdif52XRnCMBd8bqtjklH0EBlU9/oqojoT6wMvfQ7qNW7+WocP+Leq+yqkoFXybe0ZF6kQFsj0nmui//42D8ydzng72D+br313So1IGjJ49yy1+3sD62YKsGK1XeFXaEOqdN3kCs1nlVjDGfOD2q0qCIrfMKokpQKNOGv8dHXX6kir0LJtuDk/YdTDnwLp1+uJaNR/Zf+CJKKeVEIhIA/AY8aIxJBD4H6gAtgUNAzuq4ks/L862Rc8bqtokZVk10UOAZOXvV1tb+4KnSuT1HTwBQS8s9zhIZ5MOEOzrSqHIQu4+e4Novl7Av7tTiL36efnx6+ad0r96dxPREbvv7NpYdWubCiJVyD4VNqNsDxxyt8m4BfhaR1s4PqxRw8sTE8+lRpzkzb/yM2UPmMrDyg5AVQIptG8P+GMbvm5cX+/srpRSAiHhiJdM/GWMmARhjjhhjsowx2cDXnCrriAaq53l5NeBgccV2IssqTwgIqHT6ExGNwMMHju+Gk9Yo9t5jVkJdI0xHqPMTFuDNhNs70qJ6BaKPn+TaL5fkTuIE8LZ781739xhQewApmSncPftuZu+d7cKIlSr9CptQP2eMSRKRzkAfYAzW6EXZk1PyEbu5xN6yUmAIr/UexaRBk/DLrg/2RJ5eci8/r19YYjEopconERHgW2CzMea9PMfz1lhcBWxw/DwNGCYi3iJSC2vRr2IbykzNtnoo+56ZUNs9oKKj68cha+HevY4R15qhOkJ9LsF+nvw4qj3to0I5nJjKdV8uYcvhxNznPW2evNb5Na5rcB3p2ek8/M/D/LT5JxdGrFTpVtiEOqewdwDwuTFmKuDl3JBKiUjHCHXsVijhZcPrhVdm7vXjCKU12E/y0sp7GTDuf6w+uLtE41BKuRcReaIIL+8EjAB6nNEi762c+TPAZcBDAMaYjcDPwCbgL6yVbYtt8keqse7DPmcm1ACVW1h7R6ePfcccCbWWfJxXoI8nY25tT5d61jLlw776j/XRCbnP28TGMx2e4X+t/ofB8MayN3h3xbtkm5L9naiUOyhsQn1ARL4ErgVmiIj3RVzDPfiGQGBlyEiB+D0l/vb+3t78ef1X1PHuCxj2ZcxjxN9XMWDcA3y7YibZJZzkK6VKHxH5Oc/2C3DbxV7LGLPQGCPGmOZ5W+QZY0YYY5o5jg8yxhzK85pXjTF1jDENjDF/OuVD5SPbZHNSrPJsn8DKZ5+Qm1CvIzMrmwPHrYl21XWE+oJ8vex8fVNbLm8USXxKBsO//o/FO08t7iIi3N78dl7t/Coe4sH3G7/niflPkJ6laygolVdhk+FrgZlAX2NMPBAKPJbzZJ7Z32VDCdZR58fP05spw97ms27jibR1BLLZlzGXDzY+Svvvr2T82n9dEpdSqtRINMZc69iGAmWy0DUty+qZ7JOdjc2nwtknVG5u7Q+t5VBCKpnZhkpBPvh4asu8gvDxtPP5jW0Y2KIKyWmZ3Dx6OTPWHzrtnEF1BvHp5Z/i7+nPX3v+4o5Zd5CQlnCOKypV/hR2YZcUY8wkY8x2x+NDxpi/85wyx6nRuVpu67yiLUFeVF1rNWHOiK/5qMuPNPG7ErICSbPv5rU199Fr7J1sOKwN+JUqp1494/EzLomimKVmWhMSfYwBr3xGnSMbg80D4nYQfcRqy1dDR6cLxdNu48PrWnLzpVGkZ2Vz77hVjP1v72nnXFrlUsb0HUOkbyQrj6zkxhk3sjtBSxGVAueXa+TXRsl95bbOK7mJiefTo05zJgx9mbnX/kXzgGsw2R4czl7MsD+v4rapb5KUdvLCF1FKlRmOBVUQkXDH42Oujah4nMywaqJ9jQHPfDp3eHg7vlE0JO9bC+gKiRfDZhOeH9iYx/o0wBh4bsoG3pu1DZNnxeAGoQ34acBPuasq3vDHDSw6sMiFUStVOjg7oXbeOt2lQd4lyEuRiIAgfrrmBb7r9QuhtEZs6SyN/5HOP/bng8VTtL5aqfJntKsDKE6pjtICH4PV1SM/jjpqc8hKqKuHaEJ9MUSEey+ry5vXNMMm8NGc7TwzZQNZ2ad+vVfyr8TYfmPpWaMnSRlJ3DPnHsZsHHNa4q1UeVM2JxQ6S0QDa390G2RlujaWfLSrVpd/R47hf43fwSOzEtkeR/l2+3N0+eEG/ti64sIXUEqVFWXr28EznHSskuhzvo9ZyaqjDjhmLcalHT6K5rp2NfhyRFu8PWyMW7qP239YQXLaqd+Dfp5+vNf9Pe5qcRfZJpt3VrzDc4ue08mKqtzSko/z8Q6E4BqQlQ7Hdro6mnO6vV0fFt00nW5ht0GWD4mygSf/u4X2o6/kpXk/ciItzdUhKqWKV5keGsxJqH05zyRDx8TEiie2Atrhwxl6Na7Ij7d1IMTPk7lbYhjy+eLTliq3iY17W97LO93ewcfuw9SdU7ll5i0cPnHYhVEr5RrOTqh7Ovl6rlfK6qjPxc/Tm0+ueIApg3+nnnd/yPbhpH0nv+x7k44/XcaNv72okxeVKrvK1mDGGdLTkgDwlvP8yqrUDBBqZO3FiwydlOgk7aJCmXxPJ2qH+7PlcBKDP13Euuj4087pE9WHH/r9QCX/SqyLXcfQ34ey8IAuSKbKlwIl1CIy7XxbznllckJMxdLR6aOg6oRVYtKwN5k7dA69K96DR2YVsCexNvlXhv01kMt+uEXb7SlV9jzl6gCKU2a6tZS4h+0c9dMA3oFkhdbBkyyaex0kPKBsrjnmClHh/ky651IuqR1GbFIa1365hJkbTx+FbhTWiJ+v+JlOVTsRnxbPPbPv4ePVH5OVXWxr/ShVqhR0hPoSoBqwAHgHePeMreyKyBmhdo+EOkdEQBDv9r2blbf8yaPNPiBc2gFw1KzgtTX30eG7a/hu5SydwKhUGWCM2SAiQ0UkEEBEnhWRSSLS2tWxOUNGhpVQe8r5+0onhTQBoLP/AayV1JWzVPDzYsyt7RnaphqpGdnc9eNKPvtnx2kTEUN8Qvis52fc3+p+RISv1n3FHbPu4OjJo+e5slJlQ0ET6krA00BT4EOgF3DUGPOvMaZsD3fmXYLcDdlsNka27sm8m0Yzoe/vNPO/BrJ8SLFt470ND9Px+6v5fNkMTayVcn/PGWOSRKQz0AcYA3zu4picIsOxsIun7fwJ9UE/ayJ5Kw/tjVwcvDxsvDWkOY/3tdrqvfXXVu4dt4oTeSYr2sTGHc3v4OteXxPmE8ayw8sY+vtQFh9Y7MLIlSp+BUqojTFZxpi/jDEjgY7ADuAfEbm/WKMrDcLrg9ggbidkuvfkvqaVajBuyAv8ec1M2gYNhyw/Ttp38tnmJ2j//SBtuaeUe8v5bn0A8LkxZipQJuoeMhydIy40Qr3VVheAelmldxK5uxMR7ulel69vakugtwcz1h/mqs8WsfvoidPOa1+5Pb8M/IV2ldpx9ORR7px9J28seyN3kR6lypoCT0oUEW8RuRr4EbgX+AiY5OyAROQhEdkoIhtEZLyI+Dj7PQrF0xdCaoHJgrgdLg3FWaoFh/LdVU8z+9q/uSTkJsgKIM2+l2+3P0e77wcyY+tKV4eolCq8AyLyJXAtMENEvCkjrVEzc0ao5Tw11MCq9JpkG6HiyR2QoYlbcerVuCJT7utEnQh/th1JZtAnC5m75chp50T4RfB1r695oPUDeIgHP23+iWHTh7HlWOla20EpZyjopMQxwGKgNfCiMaadMeZlY8wBZwYjIlWB/wFtjTFNATswzJnvcVHcpNNHYVUMCOarQY8xf9gsuoaNgqwg0u37eHzJKEZNeYPUDO0nqpQbuRaYCfQ1xsQDocBjLo3ISXJGqD0uMEK9PcGww1TBbjLhyMaSCK1cqxMRwJR7O9GnSUWSUjMZNWYFH87eftoiMHabndua3caPA34kKiiKnQk7Gf7HcEZvGK0TFlWZUtDRixFAfeABYLGIJDq2JBFJdHJMHoCviHgAfsBBJ1+/8HIS6jJ6gw7xC+DTKx5k7rV/EuV1OSJZLEv4ic5jr+GfXRtcHZ5SqgCMMSnGmEnGmO2Ox4eMMX+7Oi5nOFVDff4R6n1xKazNrmM9OKCLW5WEQB9PPr+hDY/1serX35+9jRHfLiUm8fRvCJqENeHngT9zXYPryMzO5P2V73PrzFvZm7jXFWEr5XQFraG2GWMCHVtQni3QGBPkrGAcI97vAPuAQ0BCfr8QROQOEVkhIitiY2Od9fbnVkqXIHe2iIAgfh/+Pvc1ehPJqkCafQ/3/TuCe6d/QGaWjiQopVwjt4b6PAl1WmYWhxJTWYdVR020JtQlxWazliv//pb2hPl7sXhnHP0+XMC8rTGnnefr4cuzHZ/l056fEu4bzqqYVVwz7RrGbByjo9XK7ZWq+joRCQEGA7WAKoC/iNx45nnGmK+MMW2NMW0jIiKKP7BI9+pFXVR3tu/PjGumUsXeBbFlMj/uWzr9cC3Lo8tGDblSyr1kZmcA56+hjj5+EmPgYIDjfh29vCRCU3l0qx/Bnw90oVPdMOJOpHPLd8t5bcZm0jNPn+zetVpXpgyewsDaA0nLSuOdFe9w0183sSt+l4siV6roSlVCDVwO7DbGxBpjMrAmPV7q4pggtA7YPOH4Xkg/ceHzy4BqwaHMvPEzbqnzImQFkGLbxi2zhvHV8j9dHZpSqpwpyAj1vrgUADLDGoOHLxzfDSe0/3FJiwzyYeytHXisTwPsNuGr+bsY+sVidsUmn3ZesHcwr3V5jU97fkqkb2TuCovfrP+GjKwMF0Wv1MUr6KTES6RkuuTvAzqKiJ/j/XoCrp8J6OEFYXUB47b9qC/Ww52vZuqVUwilNWJL46ONT/Hav+NdHZZS6gwi0lZEJovIKhFZJyLrRWSdq+NyhpwEy9Puec5z9h2zEuqq4UFQtY11UEepXSKnBOTnOztStYIva6MT6P/RAr5btJvsPBMWwRqtnnzlZK6qexXp2el8uOpDhvw+hGWHlrkoeqUuTkFHqEcCK0VkgojcLCKViiMYY8xS4FdgFbDeEd9XxfFehZa7wEvZrqPOT+3Qisy5cTT1vPsjksW43a/z4J+fujospdTpfgK+A64BBgJXOPZuLyPbWjjEw3buhHqvY4S6eogfVG9vHdz3X7HHps6tTc1QZvyvC1e3qkpqRjYv/r6J67/5j/2OP35yBHkF8VKnl/iy15fUDKrJroRdjPp7FI/Pf5zYlBKYJ6WUExR0UuJdxpjWwAtACPC9iCwRkddEpKvIBXoZFYIx5nljTENjTFNjzAhjTOlYTcVNlyB3Fg+7nV+vfZ0OFW5ExDAn5gtG/PaSLgSjVOkRa4yZZozZbYzZm7O5OihnyMipoT5PQp0zQl0zzA9qdLQO7l9a7LGp8wv28+S961ryxY1tCPP34r9dx+j7wXwmLNt32rLlAJdWuZRJgyZxX8v78LZ78+fuPxk4ZSBjN43N/TegVGlVqBpqY8wWY8z7xpi+QA9gITAUKPt3rdxe1OVvhDqHzWbjm8FPMKDy/zBGWJP8C4MmPEx6ZuaFX6yUKm7Pi8g3IjJcRK7O2VwdlDNkOkaoPe3e5zwnZ9SzRmjOCLXAgZW6wEsp0bdpJf5+qCv9mlbiRHoWT05az02jl501Wu1l9+LOFncyZfAUulfrzomME7y1/C2GTBvCwgMLXRS9Uhd20ZMSjTEnjTEzjDH3G2PaOjOoUim304frS7pd7Y3et3NL3ecx2R7szZhDn3G3k5R20tVhKVXe3QK0BPpilXrklH0UiIhUF5F5IrLZsVrtA47joSIyS0S2O/YheV7zlIjsEJGtItLHuR/nlAzjKPk4Rw21MSZ3hLp6iB/4hkDFJpCVrv2oS5GwAG8+u6E1Hw5rSbCvJwu2H6X3+/P5ZsEuMrNO/7azWmA1Pu75MR/3+JjqgdXZlbCLu2ffzd2z79ZuIKpUKm1dPkqv0Frg4QOJ0ZCa4OpoXO6RztfwWIt3INuHo2YFvcbdxOGk464OS6nyrIWjnehIY8wtju3WQrw+E3jEGNMI6AjcKyKNgSeBOcaYesAcx2Mczw0DmmAl8Z85s/zvtMAcPYrt5yj5iDuRzsmMLAJ9PAj2c5xTs5O137OoOEJSF0lEGNyyKrMf7sbAFlU4mZHFK39s5qrPFrPx4Nm/W7tX786UwVN4tO2jBHgGsPDAQq6edjWvL32d+NT4kv8ASp2DJtQFZbNDhLUSVHku+8hrZOuevHnpF5AVyAnbFvr/cgNbY12/sKVS5dR/jiT3ojhWVlzl+DkJq8NSVay1AcY4ThsDXOn4eTAwwRiTZozZDewA2l/s+59PtslJqPNvmxd93PqGrHqI36mDUZ2t/Z4FxRGSKqKIQG8+Ht6K0Te3pUqwD+sPJDDok0W8PmMzJ9JOLyP0snsxsslIpl81nWvrX4vBMG7LOPpN6scXa7/gREb5aGerSrdCJdQicl/er/vKnZyJibFa9pGjf4M2fHP5GGyZEWTY93PttBv4b1/5ai2oVCnRGVjjKL8oUts8EYkCWmHNj6lojDkEVtINRDpOqwrsz/OyaMex/K5XpNVts4xVDnCuEeqcOtzqob6nDkZ1BgT2L4MMLUkrrXo0rMjfD3fj5kujyDaGL+fvose7/zB5dfRZkxbDfMN47pLn+GXgL1xa5VKSM5L5dM2n9J/Un7GbxpKWVTp6GKjyqbAj1JWA5SLys4j0LaHe1KWHjlDnq0ONevw6+Ce8smqQ7XGU22ffzO+btYeoUiWsL1AP6E0R2uaJSADwG/CgMSbxfKfmc8zkc6zIq9tmkZNQF2KE2i8UKjWDrDTYt6TQ76lKToC3By8MasLkezrRonoFjiSm8dDEtQz5Ygnro88uA6kfUp8ve33J6D6jaR7RnGOpx3hr+VtcMfkKJm2fpB1BlEsUtsvHs1g37G+Bm4HtjtZ5dYohttKnnC1BXhj1wisz49pxBGY3BnsyT/13D9+umOnqsJQqT8LztstztMxrXpgLiIgnVjL9kzFmkuPwERGp7Hi+MhDjOB4NVM/z8mpAsdR8nRqhzr9EO/q4Y1GXEN/Tn6jTw9pvn1UcYSkna1m9ApPvvpS3hzQnPMCblXuPM+jThTzx6zpiks7u1tKuUjt+7PcjH/f4mHoh9Th84jDPL36egZMH8uu2X3XFRVWiCl1DbazvYA47tkysvtS/ishbTo6t9CnHi7sURMWAYGZd/wORto6ILY33NzzBq/+Mc3VYSpUXX4tIs5wHIjIceLagL3Z84/gtsNkY816ep6ZhLe6FYz81z/FhIuItIrWwBluK5aupUwl1/iPUB+KtEeqqFc5IqBv0s/Zb/gCT7+C5KmVsNmFo2+rMfbQbt3ephV2EiSv20/3tf/hw9nZS0k+vrxYRulfvzq8Df+WNLm8QFRTFgeQDvLjkRQZMHsDPW38m3bF0vVLFqbA11P8TkZXAW8AioJkx5m6gDdbqXGVbcA3w9IfkI5ByzNXRlEr+3t7MvP6L3FUVx+95g//98bGrw1KqPBgCjBGRRiJyO3APVvlHQXUCRgA9RGSNY+sPvAH0EpHtQC/HY4wxG4GfgU3AX8C9xjhmDzpZliMZPlcN9QFHycdZI9TV2oF/JMTvhSMbiyM0VUyCfDx5ZkBj/nqwK5c3iiQlPYv3Z2+j+9v/MGHZPrLOWMLcJjYG1B7AlMFTeKvrW9QJrsOhE4d4+b+X6fdbP77f8D3J6cku+jSqPCjsCHU4cLUxpo8x5hdjTAaAMSabQvQ7dVs226lRau1HfU45qypeEnITIoZ5R7+ixw+3sebQHleHplSZZYzZhdXG7jes5Lq3MabAPT6NMQuNMWKMaW6MaenYZhhj4owxPY0x9Rz7Y3le86oxpo4xpoEx5k/nfypLtqOG2pbPCLUxhoOOEepqFfxOf9JmP32UWrmdupEBfDOyHRPu6EjzasHEJKXx5KT19PtwPrM2HTlr4qLdZqdfrX5MGjyJd7q9Q72QesScjOHdle/S+9fefLjqQ46ePOqiT6PKssIm1N5nLmUrIm8CGGPKR4YZWb6XIC8om83GV4MeY3DVhzHZHsSapdz419XcPPlV4k9qiyOlnCWnm4ejo8evQCgQBSy92C4fpU3meUaoE09mciI9iwBvD4J88ykJaegY69nye3GGqIpZx9phTLmnEx8Oa0m1EF+2HUnm9h9WMPjTRczbGnNWYm0TG32i+vDbwN/4tOentI5sTVJGEt+s/4Y+v/bhpSUv6QIxyqkKm1D3yudYP2cE4jZyJibq14cF8srltzCm96+ESzvElsHKxAl0Hdeft+b/THZ29oUvoJS6kJxuHjlbB051+ih0l4/SKGeE2p7PujE59dOVg33It/FUra7gFQCH18PxvWc/r9yGzWYtCjPnkW48d0VjwgO8WRedwC3fLefqzxezYHvsWYm1iNC1WlfG9BvD2H5juaz6ZaRnp/PLtl8YPHUwd826i4UHFpJt9PeRKpoCJdQicreIrAca5IyEOLbdQJkYASmwnBFqnZhYYG2q1mHeTaN5pOn7eGRWxXgcY+zul7l0zLXM3L7a1eEp5dbO7OyRT6cPt5dbQ53P0uM55R5VzpyQmMPTB+pebv28dUaxxKdKlreHnVGda7Hg8ct4un9DQv29WL0vnhHfLmPoF0vyHbEGaBnZko96fMTUwVMZUn8IPnYfFh1cxN2z72bwlMFM2DKBlIwUF3wiVRYUdIR6HNZIxzROHwlpY4y5sZhiK51yFneJ2ayzxgvp5jaXs+SmafSKvAey/Dhh28oji0bSdcxNvPLPOOJSklwdolKqFMri3CUfhxJyEmqfc18gt+xD66jLEl8vO3d0rcOCxy/j8b4NqODnyYq9x7nlu+UM+Ggh09cdPGvyIkDtCrV5/pLnmTVkFg+2fpCKfhXZk7iHV5e+So9fevDKf6+w9ZguUKYKp0AJtTEmwRizxxgz/IzRj/LX6iKwEvhUgNR4q9uHKhQfTy/e63c3f1w9nTrefQHhOKuZuPd1uk3sRo8fRvH2gl9JSNVRAqUKQkQuKeuLbOUm1PmMUB9KsPoTVw4+xwg1QL1eYPOAvYu0Q1MZ5O/twT3d67LwiR483b8hEYHebDqUyH3jVnP5e/8yYdk+UjPObkBTwacCo5qN4s9r/uTtbm/TOrI1JzJOMHHrRIb8PoQRM0bw+87fSc08uwe2UmcqaMnHQsc+SUQSHVtSzuPiDbGUEckzMbF8zMMsDjUqRDBl2Nv80v8PLgu/A5+sOogtg1izjB92vUin8V3pPfYuft+83NWhKlXajQRWisgEEblZRCq5OiBnyyn5sOU7Qm0lO5WCzzNC7VsBorqAyYZtfxVHiKoUCPD2yB2xfuXKplQL8WX30RM8OWk9nd+cy4eztxOXfPby5J42T/pG9WVMvzFMGjSJ4Q2HE+AZwJrYNTy98Gl6/NKDV/97lU1x2oxAnVtBR6g7O/aBxpggxxaY87h4QyyFInSBF2dpFFmNjwbcz/Jbp/D95VO4NGQkXlk1EFsah7IX8dTS2xg56VVSMs6+CSqlwBhzlzGmNfAC1kJb34vIEscqtl1F8pnJ52ZyRqg98mmbl1PyUfl8CTVAIy37KC98PO3c2LEm/zzanQ+ua0mTKkEcTU7n/dnbuPSNuTw1aT07YvLvSV0vpB5Pd3iaOUPn8OKlL9IkrAlJ6UlM2DqB66Zfx9Dfh/LT5p9ISCtwR0pVThR2YZehIhLo+PlZEZkkIq2KJ7RSTFvnFYs2Vevw5aBHWXnrH3zR/Wdqe/VGJJtVSRPoMvYa/tm1wdUhKlVqGWO2GGPeN8b0BXoAC4GhwFLXRlZ02Zx7hPpwbsnHBRLqBv2t/Y7ZkFq+vlgtrzzsNq5sVZXp93dm3O0d6NkwkrTMbMYv28fl7/3LiG+X8vfGw2Rmnd3hw8/Tj6vrXc2EKybw68BfuaHRDQR7B7Pl2BbeWPYGl/18GQ/Ne4g5++boEucKKHzbvOeMMUki0hnoA4wBvnB+WKVcbkKtI9TFpVPNRkwd/i4PNXkXyQwh3b6X+/4dwX3TPyQzq1gWY1OqzDDGnHQsynK/Maatq+Mpqsxz1FAbYzicmFPycZ4aaoCgKlCzM2Smwqap5z9XlSkiwqV1wvn25nbMfrgbw9vXwMfTxoLtR7lj7Eq6vf0Pn87bkW85CECD0AY82f5J5g6dyzvd3qFTlU5kmSxm75vNg/Me5LJfLuOV/15hTcyafLuLqPKhsAl1TiYzAPjcGDMV8HJuSG4gpxe1dvoodre27c1fQ6dQxd4FsWXyb9w3dP7hOlYf3O3q0JRSJSRn/NBuP/3XTcLJDFIzsgnw9iDAO59FXc7UYpi1X/OTcwNUbqNuZACvX92MpU9dzrMDGhEV5seB+JO8PXMrl7w+l/vHr2bRjqNk59MdxMvuRZ+oPnzR6wtmDZnFI20eoX5IfRLSEpi4dSIj/hxBv0n9eH/l+2yO26zJdTlT2IT6gIh8CVwHzBAR74u4hvvzDwf/CEhPgoT9ro6mzKsSFMrMGz/jljovQlYAJ2xbuWnmtTz599e6OIxS5cC52ubljE5XDPIu2IWaXAme/rBvCcRuc2aIys0E+3lyW5fazH2kO2NubU/PhpFkZGfz+9qD3PDNUrq/Y41aH0nMv8NHpF8kNze9md8G/cavA3/l5iY3E+kbyYHkA4zeMJprp1/LwCkD+WT1J2w/vl2T63KgsMnwtcBMoI8xJh5rAsxjzg7KLWjZR4l7uPPVTBo0iVBagy2VPw59xCVjhjBv13pXh6aUy4nIfSIS4uo4ikPOV6NnJtRHEq2v6M/b4SMv70Bodo3184rRTopOuTObTehWP4Jvb27Hwid68EDPelQJ9mHfsRTHqPUcbv1+OX+sO5Rv6z2wSkIeafsIs4bO4rs+33Fdg+sI9Qllb+Jevlz3JVdPu5pBUwbx4aoP2Ri3UZPrMupiSj58gKEi8n/AHUBHZwUjIg1EZE2eLVFEHnTW9Z0qt+xDJyaWpHrhlZk34juG1ngCsgJIsW3n/vkjuPG3F7V3tSrvKgHLReRnEelblnpT54xQ2+ynl3UccUxIrBhYwIQaoO0oa792HKTrPUOdUrWCLw/1qs+CJ3rw/S3t6Ne0EjYR5m6J4d5xq2j/6myenryelXuP5ZsU28RG20ptebbjs8wZOoeven3FNfWuIcQ7hD2Je/hm/TcMmz6MfpP68fbyt1lxeAWZ2Zku+KSqOBSg6Ow0U4F4YBXg9D5mxpitQEsAR6unA8BkZ7+PU2inD5ex2Wz832U3cnOrPtw942X2ZcxjbfKvdP3pX/7X4glGte3j6hCVKnHGmGdF5DmgN3AL8ImI/Ax8a4zZ6droiiZ3hNp+emlHbslHQUeoAaq0hKpt4cAK2PArtL7JOUGqMsNuE7o3iKR7g0iOJqcxbc1BJq2OZsOBRMYt3ce4pfuoGebHoBZVGNSiCvUqBp51DQ+bB5dUuYRLqlzCsx2fZeWRlczaO4u5++ZyIPkAP2z6gR82/UAF7wp0rdaVy6pfxqVVLsXP088Fn1g5Q2ET6mqOlkwloSew0xizt4Ter3AidHEXV6tRIYI/rv+In9b+wzsrXiXT4zAfbHyUCZsn81m/56kXXtnVISpVoowxRkQOA4eBTKyyvF9FZJYx5nHXRnfxTiXUp09KzKlvjQwsYA11jva3w+QVsOQzaHkj2MrfVCBVMOEB3tzauRa3dq7F1sNJTFoVzeTVB9gbl8LHc3fw8dwdNKwUyKCWVRjYvArVQ89OiD1sHnSo3IEOlTvwdIenWRu7lrn75jJv/zz2Ju5l2s5pTNs5DS+bF+0qt6NL1S50rdaV6oHVXfCJ1cWSwtTyiMhXwMfGmGIvWhWR0cAqY8wn+Tx3B1a5CTVq1Gizd68Lcu6T8fBmTfDwgacPgs3t105wayfS0vjfnx+w9PgExJYJWb4MqHY7r/S8FQ+7/m+jSicRWemstnYi8j+sVROPAt8AU4wxGSJiA7YbY+o4432Kqm3btmbFihWFes2l3zUlySYsGvQ7QSFRucdv/2EFszYd4fMbWtOvWSH+gM5Mhw9bQNJBuP5nqK/faqmCy8o2/LcrjmlrDvLnhkMkpp4q22hRLZh+zSrTr2klaob5n/c6xhh2J+xm7n4ruV4fux7DqZysVnAtulbtSpdqXWgV2Qove/lrqlbanO+eXdiEehNQF9iNVfIhWIMizZ0RaJ738QIOAk2MMUfOd+7F3Jyd5t1G1g35/lUQVip+V5V7/+3bysNznifJthEA36x6vNn9RS6r3czFkSl1Nicn1C9hlXecNcIgIo2MMaXi67SLuWe3/64pJ23Cf1fNxD+oSu7xwZ8sZG10Ar/dfQltaoYWLpDFH8Pfz0KNS+HWPwv3WqUc0jKzmL/tKL+vPcisTUc4mWfiYpMqQfRvVpk+TSpRNzLggtc6evIoiw4sYn70fBYfXExyxqnVHH09fGlXqR2XVrmUS6tcSlRQFGVomoTbON89u7AlH/2cEE9B32fVhZJpl4tsaCXUMZs1oS4lOtZowMKR43ht/gQm7vqYk3Zr0mLL1Vfx6YDHCPbR+jRVZnmfmUyLyJvGmCdKSzJ9sbIdecOZJR8xSdZUnsjCTErM0Xok/Ps27FsM+5dB9fZFDVOVQ94edno1rkivxhU5mZ7Fv9ti+XPDIeZsjmHjwUQ2Hkzk7ZlbqR3hT+/GlejVuCKtqlfAZjs7GQ73DWdw3cEMrjuYjOwM1sSsYUH0AhYeXMj249uZHz2f+dHzAajiX4WOVTrSoVIH2lduT7hveEl/dHWGQo1QlxQRmQDMNMZ8d6FzXTpCPfMZWPIJ9HgWupbP7oGl2f74OO6a8RL7MuYCYMuM0EmLqlRx8gj1KmNM6zOOrXP2N4hFdTH37FbfNyVThFXXLcLTJwiA7GxD/Wf/JDPbsOXlvvh4XkRp1+wXYeF7UK8P3PBz4V+v1DmkZmSxcPtRZjiS64STp5Ynjwj05vJGkfRoWJFOdcPw87rw2GZMSgyLDy5m8YHFLDm0hPi0+NOerxdSjw6VrDrtNhXbEOh19kRJVXTOLPkQ4AagtjHmJRGpAVQyxixzTqggIn7Afsd7JFzofJcm1KvGwrT7oOk1MER7mpZW49f+y1srXiHT4zAAlW2d+GLAi9QOrejiyFR554yEWkTuBu4BagN5u3kEAouMMTcW5frOdjH37ObfN8WIsPb65dg8rdHouOQ02rwymyAfD9a9cJF/JCfHwofNISMFbpsD1dx+lXZVCmVmZbNszzFmbTrC3xuPcCD+ZO5zXh42OtYOo0eDCHo0rEiNsAt/i5qVncWW41v47+B/LD20lNUxq0nNOrUAjU1sNAptRPvK7WlfqT2tI1tr9xAncWZC/TnWKrA9jDGNHIsI/G2MaeecUAvPpQl19Er4pgdENoF7FrsmBlUg1qTF91l6fKJj0qIfV9e8h+cvG4FNZ/grF3FSQh2M1c3jdeDJPE8lGWOOFeXaxaGw9+xsk02LH1oAsH7E2tyOHJsPJdLvwwXUjQxg9sPdLj6g2S/AwvehVle4aRpoXaoqRsYYNh1KZM7mGOZuiWFtdDx507Da4f50rR9Bt/oRdKgdWqDR6/SsdNbGruW/Q/+x/PBy1seuJ9OcmihpFzuNwxrTpmIb2lRsQ6vIVgR7BxfHxyvznJlQrzLGtBaR1caYVo5ja40xLZwUa6G5NKFOPwGvVQGbJzxzCOyeF36NcqnFe7fw8NznOGGzVrgMzG7Ch71eoV21ui6OTJVHziz5cAZHd6UrgBhjTFPHsReA24FYx2lPG2NmOJ57ChiF1dnuf8aYmRd6j8LeszMy02j9U1vsxrDm5g25x+dvi+Wm0cu4tE4Y424vwvpiJ49bHT9SE+CG36De5Rd/LaUK6WhyGv9ujWXulhjmb48lKU/HEC+7jXa1QuhaL4JOdcNpXDko39rrM6VkpLA6ZjXLDi9j+eHlbIrbRJY5NVlSEOqG1KV1ZGtaRrakdWRrKvtX1kmOBeDMSYkZjgVXjOPCEVgj1uWTlz+ERMHxPRC349RiL6rUurRmQxaPnMhzc75n2v4vSLJv5JZZ19I5/AY+6Hs/Pp7alki5FxFZaIzpLCJJQN4RkpwuTEGFuNz3wCfAD2ccf98Y884Z79sYGAY0AaoAs0WkvjEm//WZL5JxrCR35vdIsbkTEgvZg/pMviHQ5VGY9Rz8/QzU7qaDI6rEhAd4c02balzTphqZWdms2R/Pv9timb8tlnUHEli0I45FO+IACPHz5NI64XSqG06numHUCPXLNwn28/SjU9VOdKraCbAS7DWxa1h5ZCUrj6xkfex6th/fzvbj25m4dSIAkX6RtIpsRcuIlrSIaEHD0IZ46v8PCqWwCfVHWCsXVhSRV4EhwLNOj8qdRDa2EuqYzZpQuwmbzcarvW7l5qP9uOvP/yOG/1h07Hs6jZ3DC5e8wMBGOttfuQ9jTGfHvsizkIwx80UkqoCnDwYmGGPSgN0isgNoDywpahx5Zeck1Gd8mRqbbCXUEUVNqAE63AkrRkPsFlj+LXS8q+jXVKqQPOw22kaF0jYqlEd6N+DYiXQWbI9l0Y6jLNoRx4H4k/yx/hB/rD8EQJVgHzrWCeOS2mFcUieMaiH510n7efrlttsDSMtKY8PRDayOWc3qmNWsiVlDTEoMM/fMZOYe60smb7s3jcMa0zKiJc0jmtMsvBkV/XXe0fkUKqE2xvwkIiuxVjEEuNLd2zEVWWQj2DpDV0x0Q/XCKzNnxNd88t/vfLXxbdI99vPU0tsZs74/X17xNGF+OktaKYf7ROQmYAXwiDHmOFAV+C/POdGOY2c5YzGuQr1xdpbVHeFcI9ROSag9vKHv6zB+GMx7FZpcCYGVin5dpYog1N+LwS2rMrhlVYwx7I1LYeGOoyzacZQlu+I4mJDKpFUHmLTqAADVQ31pHxVGh1qhtKsVSlRY/iPY3nbv3HpqsOYp7IrfxerY1ayNWcva2LXsSdyTm3DniPSLpFl4M5qFN6N5RHMahTYiwOvC/bXLiwIl1CLy8Dme6ici/Ywx7zkxJveSuwT5JtfGoS7afR0Hcl3Tbtwx/RW2p/7F1pPTuWz8Yu5o8ij3dRzo6vCUKhARGQM8YIyJdzwOAd41xtxaxEt/DryMVU7yMvAucCtWScmZ8p2UY4z5CvgKrBrqwrx5tqOCxHbGpXMS6vAAJyTUAPX7Wu3zts+Ev56CoRfs2qpUiRERosL9iQr358aONcnONmw5nMSSXXEs2RnH0t1x7D92kv3HovltVTRg/bHZPiqUdlEhtI0KpWGlQDzsZ0/Ct4mNuiF1qRtSl6H1hwIQnxrPuqPrWBu7lvWx69lwdAMxKTHM2TeHOfvmWDEhRAVH0SSsCU3Dm9IkrAkNQhvg6+Fbcv9hSpGCjlDnDNU1ANoB0xyPBwLznR2UW8kp84jd4to4VJFEBAQxedhbTNl0NS8teZEMj2i+3Po0k7ZN4bN+L9IwopqrQ1TqQprnJNMAxpjjItKqqBfNu8CWiHwNTHc8jAaq5zm1GtYKt06VfYEaaqeMUIPV3aP/2/DZAtg4CZoNhYb9nXNtpZzMZhMaVwmicZUgRnWuRVa2YfOhRJbtPsay3cdYvucYsUlpp5WI+HnZaVm9Am1rhtAmKpSW1SsQ7Jt/nXQFnwp0rdaVrtW6AtYo9p7EPayPXc/6o1aCvfX4VnYn7GZ3wm6m77JuCzaxUTu4No3DGtM4rDGNQhvRMLRhuWjbV6CE2hjzIoCI/A20NsYkOR6/APxSbNG5g/B6IHY4tgsyToJn+fzLrKy4snFH+tabykN/fcKCoz8Sa1vG0N+vok+VUbzR63Y87BexeIRSJcMmIiGOcgxEJJTCz5M5i4hUNsYccjy8CshptTENGCci72FNSqwHOG1NghzZ2VbJx5nD4UeTnTxCDRBSE3o8BzOfgukPQo2O4FfIJc2VcgG7TWhaNZimVYO5tXMtjDHsjD3B8j1Wcr1y73H2xqWweGcci3fG5b6uXmQArWpUoHWNEFrXDKFuREC+nURyEuXawbUZXHcwYLXr2358OxvjNrLh6AY2xG1gV/wudsTvYEf8DqbttMZeBaFmUE0ahjakQWiD3CQ7zDesZP7jlJDC3mxrAOl5HqcDUU6Lxh15eFvLjh/dZm2VXdZBUDmJj6cXnw98mBXRg3hw9v+RYF/PzCOfMn/MX7zW9UUur6v/G6tS6V1gsYj86ng8FHi1MBcQkfFAdyBcRKKB54HuItISq5xjD3AngDFmo4j8DGwCMoF7nd3hA6yRMYAz/5QtloQarAmKm6fBviVWUj10jPamVm5HRKgbGUDdyACGt7fmLcQkpbJq73FW7DnOyn3H2Xggke0xyWyPSebnFVaZSIC3B82qBtOyRgVaVKtAy+oVqBTsk+97eNm9aBLehCbhTbi2wbUApGamsu34NjbHbWbTsU1sitvEjvgd7Encw57EPfy156/c14f5hFE/pL61hdanQUgDagXXwsvunt22CtuH+hngWqxOHwZrtGKiMeb14gnvwlzahzrHzzfBpqlw1VfQ4jrXxqKcKjs7mzcWTGT8zo/BnoQxNpoHDOazAU9Qwdff1eEpN+fsPtSOVnY9HA/nGmNK3eSOwt6zj8Zt47Lp1xCaZfj3VmtwPCMrm3rP/IlNYPur/bEXoDdvoRzbDV90hvRkGPQxtL7JuddXqhRIy8xi48FEVu+LZ9W+46zZF3/aKo45KgZ506xqBZpXC6ZZtWCaVQ0u1B+yGVkZ7EzYyea4zWw5toUtx7aw9fhWTmScOOtcD/EgKjjqVKIdUp96IfWo6FexVPTJdlofamPMqyLyJ9DFcegWY8zq872mXIhsbCXUOjGxzLHZbDzdbTg3tezDXX+8xN6MOaw/MZlu4+Zzb/MnuKNdP1eHqFRenjj6Tzt+dnv5dfk4dsL6ojTU38v5yTRAaC3o/w5MuQtmPA5V20LFxs5/H6VcyNvDbpV61AhhFLUAaxR77f4E1u6PZ210PGv2x3MkMY0jiUeYvTl3OgVVgn1yS0yaVg2iaZVgIoPyH8n2tHvSMLQhDUMb5h4zxnDwxEG2HtvKtuPb2HZ8G9uPb2dv4t7ckpEZu2fknh/oGUjtCrWpW6EudSrUoW6FutStUJdw3/BSkWjDRdTXGWNWAauKIRb3FeH4R6Kt88qsasGhTL/+Ayasm8+by18l0+MgH296nJ+3TObTvi/QIKKKq0NU5ZyIPIC1ouFvWEn1jyLylTHmY9dGVjSnunycUmzlHnm1HA6758PacTDxRrhjHvjocs2qbIsM9KFXYx96NbZ6TmdnG/YeS2FddDzroxNYdyCBDQcSOJiQysGEVP7edCrJjgj0pnFla6Jkzj4qzD/fP3pFhKoBVakaUJUeNXrkHk/JSGFn/M7cJHvr8a3siN9BQloCa2Otln55BXkF5SbZdSrUya3zjvSLLPFEu8gTVhTWCDVArCbUZd2w5l0Z1KgDD8z4iCXHxnOEJQz5/Ur6Vb2N1y4fpZMWlSuNAjoYY04AiMibWIusuHVCbbLzS6itEeqwgGKutRzwLhxeB0c2wG+3w/DxYNP/j6vyw2YTaoX7Uyvcn8EtrTbzWdmG3UeT2XgwkQ0HEthwIJENBxOITUrj36RY/t0Wm/t6X087DSoF0qhyII0qB9GwUhANKgWes7uIn6cfzSKa0SyiWe4xYwxxqXHsiN/Bzvidp+0T0xNZFbOKVTGnj/P6e/pTK6gWtYKtrXZwbWoF16J6YPViWwFSE2pnCK0Ndi+I3wdpyeCtjc7LMj9Pb74e/BhL913JQ3P/jyT7Bv48/DH/jPmTN7q9SI86zV0doiqfBMg7KTCL/HtFu5Ws7LNLPuJKYoQawMsPhv0EX3W3+lPPfAb6vVG876lUKWe3CXUjA6kbGZibZBtj2H/sJJsOJbDpYCKbDiWy6WAiBxNSWbPfKh3Jq2oFX+pXDKB+pUAaVAykfsVA6kYG4ON59h+sIkK4bzjhvuF0rNwx97gxhtiTsbkJ9s74nblt/I6nHWdDnNV5JC8P8aBaYDVqBddiROMRtKvUzmn/XQqVUIs1fn4DUNsY85KI1AAqGWOc3irJrdg9ILy+NYoRuxWqtXF1RKoEdKhRj4U3/cRr8ycwcdcnnLTv4H8LbqLFmiv5bMDjBPuU/b6bqlT5DlgqIpOxEukrgdEujcgJTG7Jx6m/DXJKPsL8izmhBgiJgmvHwtirYOnnUKE6XHJv8b+vUm5ERKgR5keNMD/6Nq2ce/z4iXQ2H05ky6EkthxOZMvhJLYeTuJA/EkOxJ9k3tZTo9k2gZph/lai7UiyG1QKpFa4P575LEgjIkT6RRLpF5m7rHru+6YeZ3fCbnYl7MpNsncl7OJg8sHcjiNX1r3Sqf8NCjtC/RmQjTWL/CUgCatez3kpvruKbGQl1DGbNKEuR2w2G892v56RLftw94yX2Zsxh3XJv9H1p/n8r8UTjGrbx9UhqnLCGPOeiPwDdMJKqEcaY9a4NCgnyM6n5CPuRAmVfOSo1QWu/Bwm3WaNUgdWhqZXl8x7K+XGQvy9uLROOJfWCc89lpVt2BN3gu1Hkth6OJltR5LYeiSJ3UdP5G4zN56qzfawWcl63YiA3FaAdSICqBMZQIB3/mlsiE8IIT4htK7Y+rTjqZmp7E3cy+6E3bSIcG4L3MIm1B2MMa1FZDXkrsTlng0DnU0nJpZr1SuEMf36Dxi/9l/eWvEKmR6H+WDjo0zcMoXP+z1PnbBKrg5RlVEiksTpS35LnueMMSao5KNynqx8VkqMc9RQh5dUQg3QfCgkHoDZz8OkO8ArAOr3Lrn3V6qMsNvESogjAujb9NTxtMwsdh89wdbDSVaS7Ui29x9PYVfsCXbFnjhtEiRA5WCf0xLsOuH+1I4IoGKQd76TEn08fGgQ2oAGoQ2c/rkKm1BniIgdx81bRCKwRqyVTkxUwPAW3RjUsCP/+/N9lh6fyCEWcuXUwQyqficv97wZm+3sr62UKgpjTKCrYyhOpyYlnvrlGFeSJR95dXoATsTCkk+szh/DfoJ6vUo2BqXKKG8POw0rWRMX80rNyGJX7Al2xCazIyaZnTHJ7IxNZlfsCQ4lpHIoIZUF24+e9hpfT7s1mTLCn9qOSZW1wv2pHR5AsF/pmJT4EdaiLpEi8iowBHjW6VG5o8hG1l5HqMs9f29vvr3ySRbvvZJH5v4fyfbNTDv4PnPGzODt7i/RpZb2s1WqoLLN2SPUuX2oS3KEGqwVE3u/AhknYcW3MH4YDP4UWgwr2TiUKkd8PO1WK74qpyfaWdmG/cdSrCTbkWznlIzEnUi3JkYeSjzremH+XtQK9+f+nvXoVj/CaXEWdmGXn0RkJdATx6QXY4xmkAAVaoKnHyQdgpPHwTfE1REpF7u0ZkMWjZzAS//8yG97PuOEfSt3/3MD7dYM5ZP+j+DvXcKja6pMK6uTxnNqqPN+eZvbNs/fBRWHIlY7PZ8gWPg+TL4TkmOg0/9KPhalyjG7TYgK9ycq3J/LqXjac/Ep6afVZO86apWM7D6aTNyJdOJOpJOZ5dwCi4tZ2GULsMWpUZQFNhtENICDqyFmC9S8xNURqVLAZrPxQo+buPlYX+6a8SIHmM+KxPF0/nEej7Z9hhtadHd1iKrsKJOTxnMWdrHnqYfMu1KiS4jA5S+AfyTMfApmPQfJR6DXy9bvAqWUS1Xw86JVDS9a1Th9cDM723AkKZXdsSfOGvEuqkL9P19ExohIhTyPQ0TE7dsyOU1ETtmHLkGuThcVGslfN37Kw03fw5YZQabHYd5Ycz8Dxj1AdMIxV4enyoYOxph7gVSwJo0Dbj9pPNsxKTEnnT6ZnsXJjCy87LZzzvAvMZfcA1d/AzZPq656yl3gWCpdKVX62GxC5WBfLq0bTgU/594eC/undHNjTHzOA8cNu5UzAxKRCiLyq4hsEZHNIuI+Q71aR60u4JY2vZh/w3RaBAzBGDv7MubS77creGnej2Rn6/xeVSRlctJ4dm6XDyuljjthTUgM9fcq8aWF89V8KFw/ETz9Yd1Eq191coyro1JKlbDCJtQ2EckdPxeRUJy/2uKHwF/GmIZAC8B9stPcTh9aEaPOLdjHjx+veZ6PuvyAb1ZdsCfxy7436TRmGIv2us8/d1Xq5Ewar+iYNL4QeM21IRVdtrH+JrA7EurjJ6wRYJeVe+Snbk+4eTr4R8CeBfBFZ9j1r6ujUkqVoMIm1O8Ci0XkZRF5GVgMvOWsYEQkCOgKfAtgjEnPOyJe6kXm9KLWkg91YT3qNGfxyF8ZWPlByPIj2baZO+cO56ZJr5CQmuLq8JT7iQTexkqiD2FNGv/FtSEVXc5KiTlj0Tkj1CW2qEtBVW0Ndy6Amp2teuofBsM/b0B21oVfq5Rye4VKqI0xPwDXAEeAGOBqY8xYJ8ZTG4gFvhOR1SLyjYj4n3mSiNwhIitEZEVsbOzZV3GVoKrgHQQpcZBciuJSpZaH3c5rvUcx9cppVLF3QWxZrE6aSNefruDr5TNdHZ5yL0HAF8AwrLKPMlGcn7uwi6O843iKNSExxMn1j04RVBlumgpdH7ce//M6jL0Sko6c92VKKfd3MdORDwHLgLVAuIh0dWI8HkBr4HNjTCvgBPDkmScZY74yxrQ1xrSNiHBeD8EiE8lTR62j1KrgaodWZOaNn/Fosw+wZ1Yi2yOWjzY9Sq+xd7Iz7rCrw1NuwBjzojGmCXAvUAX4V0RmuzisIssp+RDHGPWx0ljykZfdA3o8AyMmgV847J4PX3SCjZPBmAu/Xinllgrb5eM2YD4wE3jRsX/BifFEA9HGmKWOx79iJdjuQ5cgV0UwsnVPFt04nfbBN2KyPTicvZgrpw7m2dnf6aRFVVAxwGEgDqsMxK0Zxwi1PTehPjUpsVSr0wPuXgRRXazVFX+52VoIJiHa1ZEppYpBYUeoH8DqabrXGHMZVocPp9U2GGMOA/tFJGeR9Z6Aew316hLkqoislRaf4JueEwjIbgT2FKYeeI9OY4axdN92V4enSikRuVtE/gHmAOHA7caY5q6Nquiyzlh6PGeEOqSYlg92qsBKcNM0GPCeVQ647S/4tAP897nWVitVxhQ2oU41xqQCiIi3Y5GXBhd4TWHdD/wkIuuAlrjbLPVIHaFWztGxRgMWjZzA4KoP505aHDXnOu6c9g6pGemuDk+VPjWBB40xTYwxzxtj3Gsw4hxyJyU6ZiXGp+Qs6uImK43abNBuFNy7DBoNgvRk+OtJ+OZyOLDS1dEppZyksAl1tGNhlynALBGZChx0ZkDGmDWO+ujmxpgrHb2u3UfO4i6xW7ReThWZzWbjlctvYdKgKVS0XYLYMlh8fAyXjr2S3ze79YrSysmMMU8aY9YU5RoiMlpEYkRkQ55joSIyS0S2O/Z5W6c+JSI7RGSriPQpynufS+5Kibkj1DmTEt1ghDqvoMpw3VgYNh4Cq8DBVfB1D/jlFji2y9XRKaWKqEAJtYjkdPL4xxgTb4x5AXgOq73dlcUTmpsKiASfYEhN0Ob+ymnqhVdm9oivuKvBa0hmKBn2/Ty19Hau++VZ4k+ecHV4quz4Huh7xrEngTnGmHpY5SRPAohIY6yOIk0cr/nMsbCMU+XMHciZlJjb5aO011CfS8P+cN8y6PQA2L1h4yT4pD3MeBxOHHV1dEqpi1TQEeo2IlITuNWx3HgosB5r4YCAYovOHYlAuKMKRhd4UU52b8eBzLnud+p59wcMm1Km0m3cQMaunuvq0FQZYIyZz9nt9gYDYxw/j+HUIMpgYIIxJs0YsxvYAbR3dkw5I9Q5bfNKfZePgvAOhF4vwf9WQcsbIDsTln0JH7a0elenlImOh0qVKwVNqL8A/gIaAisd24o8e5VXhCbUqvhEBAQxadib/F+bz/BwtNh7a90DDBz/EIeT3KtCSrmFisaYQwCOfU7nkKrA/jznRTuOOVV2nkmJxpjcGupgXzcr+chPcDW48jOrG0i93pCeZPWu/qAZ/P0cJGnLTKXcRYESamPMR8aYRsBoY0xtY0ytvPtijtH9ROapo1aqmFzbrDPzb5xGy4BrMcbGnvTZ9P5lEB8vmerq0FT5IPkcy3fiSFEW48odocZGclommdkGPy87Pp5Ory5xnYpN4IZf4OYZVru99GRY/BF80BymPwTHdrs6QqXUBRR2UqJ7ddxwFe1FrUpIoLcvY695jnc7fY93Vk2MPZ6vtj1Lz7G3syVW+90qpzgiIpUBHPucySHRQPU851XjHJPUi7IY16mSD4hPsco9KpSF0en8RHWCEZPh9nnQaCBkpcGK0fBxaxh/Peycq5PdlSqlCptQTymOIMqcnF7UMZv05qdKRJ96rVh80xQ6h96CyfYkJvs/hk6/ivv/+Ehb7KmimgaMdPw8Epia5/gwEfEWkVpAPaxVdJ0qZ6VEm9hyJyRWKI3LjjtT1dZw3Y9Wq70Ww0HssPUPGHsVfNLW6mOdmuDqKJVSeRQ2of5PRNoVSyRlSWAl8A2xbniJTu0qqNQ5eXl48PnAh/mm53iCTTOwpfLP0a+5dOxgxq/919XhKTcgIuOBJUADEYkWkVHAG0AvEdkO9HI8xhizEfgZa/Gtv4B7TU7TaCcy5lQN9XHHCHWIfxkdoT5TRAO46gt4aCNc9ozVbi9uh9XH+t2GMOVe2LNIB26UKgUKm1BfhpVU7xSRdSKy3rEAi8pLBCKbWD/HlIm1FZQb6VijAfNv+pFb6rzoaLEXzWtr7qPPj/ew/eghV4enSjFjzHBjTGVjjKcxppox5ltjTJwxpqcxpp5jfyzP+a8aY+oYYxoYY/4sjpiy8rTNiy8vI9RnCqwI3R6HB9fDtT9Yy5lnpMCaH+H7/vBRS6s7yPE9ro5UqXKrsAl1P6A20AMYCFzh2KszVXSUfRzZ6No4VLlks9l4uPPV/Dv8D5oHXIPJtnMwawFXTxvMw39+TnpmpqtDVKpAckao7WLLraF2u0VdnMXuAY0Hw83T4b4V0PlhCKpqJdL/vA4ftoDR/WDpl/rtqFIlrLAJ9chzbOpMeeuolXKREL8AfrrmBb7sMZ5A0xTsJ5kV8xmX/HAlkzYucXV4Sl1Qbg01kmdSYjkboc5PeD24/Hlr1HrEZGh2LXj4wr7F8Ofj8F4j+LaPVW+dcMDV0SpV5nkU8vy8S7L5YI1QayuL/FTUkg9VenSq2YiFN/3EOwt/5ccdH5Nu38v/Lb+T0Wt78Hn/56heIczVISqVr0GNb+AKjzBMZENe2ZZT8lFOR6jzY7Nbrfbq9IDURNg2EzZNgR2zYf9/1vbXk1C1DTQcAA0HQkR9V0etVJlTqITaGPNu3sci8g7WTG91ptxe1NsgK9P6qk4pF7LZbDze9Vpuad2Xe2e8yaaU6ezNmEP/SUsZVP12Xu55MzZbYb+0Uqp4SaWm2Cs1BSBh7RqgHNZQF5RPEDQfam1pSY7keipsnwUHVlrbnJcgrB40usJaTKZqW/DQ/55KFVVRf3v6YdVUqzN5B0KFGlYf0WM7XR2NUrkiAoL4+dpX+aDzD/hl1wN7MtMOvk/H769h9o61rg5PqXPKnZRYVvtQO5N3IDQbAteNhcd3wXU/QYvrrQ5Ucdth4fvwXT94qxb8dK1VGhKzWTuGKHWRCjVsKiLrObUSlh2IAF5ydlBlRmRjiN9nTUzMWY5cqVLi8rot6FH7V16cN5ZJe7/gpH0HDy4YSceNw/mk/0P4eOqolSpd4k86aqi15KNwvPysEelGV1jfmO5dBFv/hF3zrBV9t8+0NoCAihDV2bF1hbA6VucqpdR5FbYO4Yo8P2cCR4wx2i7gXCIbw7a/dMVEVWrZbDZe7DmS2xMGcucfL7AvYx5L43+k89iFvN39NS6r3czVISqVKyFFE+ois3tA7W7WBpB4CHb949jmQfIR2PCbtQEEVraS6xodocYlENEItDRMqbMUNqFuD/xljEkSkWeB1iLyijFmVTHE5v50YqJyE9WCQ/nj+o/4fNkMPt/wOmn2Pdz/70102TiCD/v9Dy8PnQOgXC/BMUIdrF0+nCeoMrQcbm3GwNFtsGcB7F4AexZC0iFY/4u1AXgHQ/X2UKMDVGsPVVpZtdtKlXOF/S35nDHmFxHpDPQB3gE+Bzo4PbKyIFJ7USv3cnf7/gxs0JHbfn+OA8xn4bHv6PzDfN7v+TqdajZydXiqHDPG5JZ8BGsNdfEQscoTIxpAu9usBDt2i5VY7/sP9i+FhP2wY5a1WS+yzq/aFqq1sbqJRDTSiY6q3ClsQp2zrOwA4HNjzFQRecG5IZUhYXXB5mE13U8/AV7+ro5IqQuqFhzKXzd+ysdLpvLV5rc4ad/JnXNv4NKw4bzd+16CffxcHaIqh5LTMsnKNvh72fHy0JKDEiFidayKbATtb7eOJUSfSq6jV8Dh9VbSHbvFWrkRwO5lfUNbuSVUaWntIxuBh7eLPohSxa+wCfUBEfkSuBx4U0S8KXqnkLLLwwvC61slH7FbrL/clXIT918ymCsbdebW35/hMItYcvwHuoybxhXVbub/LhuhkxZViUrQ0enSIbia1T2k2RDrcUaqlVQfWGEl2AdXW52tDq62tpWO14ndGsmu2BQqNbX2FZtCQKROelRlQmET6muBvsA7xph4EakMPOb8sMqQyEZWQh2jCbVyP9UrhDFrxBd8tnQ632z8lAx7NL8f+oAZP0zghvp38kinq7V3tSoROaskBmlCXbp4+kD1dtaWIzUBDq2DQ2vg4Bo4tBbidjh+F26C9T+fOtc31BrNjmxklUlGNrYWnvENKelPolSRFHZhlxRgUp7Hh4BDzg6qTAmrZ+3jtrs2DqWK4J4OV3BH2368Nn88v+36hiyPw/yw60Umbv+B+1s+wMjWPV0doirjEnWE2n34BEOtLtaWIz3F6nh1ZD0c3mCNasdshpPHrEmQexacfo2AitY3vBENrZHtsLrWcutBVXVEW5VKpW7qvojsAZKw6rUzjTFtXRtREYU7EuqjmlAr9+Zht/N/l93II5cO5ek5XzP38E+k2XfzzvoH+XZ9K74f+Da1Qyu6OkxVRmnJh5vz8rMmLVbL802tMZB4wJFobzxVHnl0u9W+L/nI2Ym2p9+p5Dq0jtUnO7QOhNYGv1BNtpXLlLqE2uEyY8xRVwfhFDkJddwO18ahlJP4e3vzYf/7iE2+icdnfcLy+Ekct63myilDeKrNKwxv0c3VIaoyKEEXdSl7RKya7OBqUK/XqePZ2VY3kditcHSrtY/bYSXaKUfh8DprO5NPsJVYh9SCkCgIrXXq56AqYLOX1CdT5VBpTajLjrC61v7YLmuFKrv+J1dlQ0RAEN9d9TSrDw7njr8eJNW+i1dX/49/9o7g0wEP4WHXX17KebRlXjlis0FITWur3/v0504eh6M7rDLKuJ3W79ZjOyFul1W7nTMZ8qxrelqJe0hNqFATKtRw7KtDcHUIrKQJtyqSwi49/nA+hxOAlcaYNU6JyFra/G8RMcCXxpivnHRd1/Dyt2q+Eg9A/F7r6ymlypBWVWrx74ifuXnyS2w+OY3Fx8fQfexqfhz0PlGhka4OT5UROSPUQT6aUJdrviFnT4IEq3zkRCwc2w3Hd5++j99rlY8cdxzLj83D+l0dXN0azQ6u6nhc7dTeN0RLStQ5FXa4tK1j+93xeACwHLhLRH4xxrzlhJg6GWMOikgkMEtEthhj5uc9QUTuAO4AqFGjhhPespiF1bUS6rgdmlCrMsnP05ufr32VDxa349str5FgX8egydfwTLvXuK55lwtfQKkLyJ2UqCUfKj8iVgu+gEhrFcczZZyE+H1wfK+VYMfvhfj9VmlJ/D4rGc85fi6efo7kuioEVbMS76Aq1rGcnzXpLrcKm1CHAa2NMckAIvI88CvQFavbZJETamPMQcc+RkQmYy13Pv+Mc74CvgJo27atKep7FrvwerD7X6v+q34fV0ejVLF58NIr6VKzGXfOfIg0j928vOo+Zu2+nvf7/o9Ab19Xh6fcmE5KVEXi6XtqFcj8ZJy0Fq1JiLYGwBIOQGK0Y+94nJ7kKDU5T5MBu5fVoSR3i7TKSQIiIaASBDqO+0fqapJlTGET6hpAep7HGUBNY8xJEUkrajAi4g/YjDFJjp97Ay8V9bouF17f2mvrPFUOtKlah39v+IWbpjzPttQ/WBr/I51+nMHVtUbxbLcbtLZaXZTE1ExASz5UMfH0tQa/choJ5Cc18fRkO/GQ9TjxACQetLa0RGvUO2H/hd/TN8RKrHNG1v0jISAC/COsn/0jTj321AGJ0q6wCfU44D8RmQoIcAUw3pH8bnJCPBWByWJ9XeIBjDPG/OWE67pWzsTEo9rpQ5UP/t7e/HbdG3z6Xye+3vgRWR6H+W3/20z9fhy3Nr6bezsM1AVhVKHk1lDrCLVyFZ8ga4tsdO5z0lMcLf9iIPkwJB051QIwd4uxtpPHHZMst174vb0CwC/MkWyHg184+IVYC+P4hlgtA31DHM9HWD/rJMsSVdiFXV4WkRlAZ6yE+i5jzArH0zcUNRhjzC6gRVGvU+rk9qLe5to4lCph93YcyO1t+/HCvDFM3/c9mR4H+Grbs4zdPIZH2j6k9dVuJL81AkQkFJgIRAF7gGuNMceL4/2Tcks+tFOSKsW8/Kx2faG1zn9edra1qE1yjJVkn4jNs4+19idirJ9TjkJ6srWdr8Y7L7GdSsD9wk4l3X5hVhKek4D75knKfSuAXf9gvVgXc2fKBLKxunFkODecMiqoGnj4Wv/nSE2wemUqVU54eXjwWq9RPJE6nKdmfcmC2AmctG/nldX38Nnq1nzV/3UaRFRxdZiqYM5cI+BJYI4x5g0RedLx+InieOPEVB2hVmWIzWaNNPuHQ8XG5z/XGKuU5MRRa0tx7E8es0a4U/LsU+KsZPzkMUdSHlu4uLwCTyXXvhWsn30qnDrmU+GMfbD1s09wuR8RL2zbvAeA24HfsEaofxSRr4wxHxdHcGWGzWZ19ziywSr7yLtSlFLlRLCPH58NfIiDiSN5bNZHrE2cxjHbKob8PoSHmr/ArW17X/giqrQZDHR3/DwG+IdiSKiNMSSe1BpqVU6JOBLX4IJ3CsvKsBLsEzFWkp1yzEqyU4479o4kPG9SnhpvTbxMT4KEfYWP0zvoVJx5t9OOB+U5FgTeweAdaP3s4ePWHVIKO0I9CuhgjDkBICJvAksATagvJKyulVDHbdeEWpVrVYJC+emaF9hw+FZG/fkQKfZtvLfhUebtHcK3g5/Gy0O/0i+l8lsjoKIx5hCAMeaQo93pWYra6jQtM5v0rGy8PGz4eJbvUTClCsTuaXUUCaxY8NdkZ1sj4anxp+q7cxLtk/H57BOsn1MTrAmbaYmnJmVeDJvnqeTaOyhP0h14xhZk1ZSfeczbcczTzyWJeWF/cwlW/VyOLMcxdSE5nT6OaqcPpQCaVqrBvzeO57Zpr7Mm6TfWJP9Cl7Fr+X7AhzSKrObq8NTZzlojoKAvLGqr00Rd1EWp4meznSr1CIkq3GuzsxzJeKIjwU7Ik3A7Eu3TjidAWtKp16QlQVaaY8T8WNE+h9is0pWcBDs3+Q5wHHf83PQaqNikaO+VR2ET6u+ApY7+0AJcCYx2WjRlmU5MVOosPp5e/HjN83y9vCMfrX+RFPs2rp0+lPub/R93tOvn6vBUHudYI+CIiFR2jE5XBmKK471P1U/rtxdKlUo2+6lJjhcrM+30ke7cn5NPJd9pSae29DOOpyZaxzJTIS3B2s6nUnPXJdTGmPdE5B+gE1ZCPdKJS46XbTmt8zZPg6xMsOsvBqVy3N6uD12imnDL9IdJtm/mo41P8M/epXw58AldEKYUOM8aAdOAkcAbjv3U4nj/BK2fVqrs8/C2+m4HRBTtOlkZeZJtxz4978/J1s9OTKahgAm1iCRh1c/lHsrznDHGBDk1qrIob7P4TVOg2RCXhaJUadQwohr/jhjHHb+/yYqEiaw/8RudfpzH4Jq38Fz3G7W22rXyXSNARJYDP4vIKGAfMLQ43jxnhDrQR/8NKKUuwO5Z9NHyi1CglRWMMYHGmKA8W2CeTZPpgvAOhAhHM/gjG1wbi1KllJeHB99f9QyPNX8fj8zKGI9jTDnwLh3GDOCjxVPJzs52dYjlkjFmlzGmhWNrYox51XE8zhjT0xhTz7EvYvFj/pJyVknUlnlKqVJKlyorSV0esfbHdrk2DqVKuZGte7J05AwGV30YyQwh0+MgX29/lo7fX8P4tf+6OjxVwnRSolKqtNOEuiSF1rb2cZpQK3UhXh4evHL5LSy6cSZdw0ZBlj8n7Tt4bc19dBkzghXRO1wdoiohuSPUWvKhlCqlNKEuSTlLkR7f49IwlHIngd6+fHrFg8wa+ictA4Zisr2IZw23/H097y2c5OrwVAnQVRKVUqWdJtQlyTcE7N6nZpsqpQqsUmAIY6/5P3674ncq0BLsJ/lu5/NcM/FJTqSluTo8VYySdFKiUqqU04S6JImcWrUo+YhrY1HKTTWIqMK/I8bQJfRWjLGxLfUPuv00lJUHdro6NFVMcpYd14RaKVVaaUJd0gIrW/ukw66NQyk3ZrPZ+GzgQzzX+hMkswJp9t3cPHM4Hyye4urQVDHIHaH21pIPpVTppH/ul7QAxwj10W0Q1cm1sSjl5q5r3oUO1X7jxmkPkWBfx7fbn2Nh9FKuadA33/O9PDwZ3LADHnZ7CUeqiiJnUqKOUCulSiu9O5W0wErWfvqD0PYWl4aiVFkQFRrJPyN+4N4/3mfRsbFsPTmd19ZMP+f57y5rzNwbx+Lj6VWCUaqiOJVQ6wi1Uqp00pKPktZiuLUXOxhz/nOVUgXiYbfz5aBHeabVRwSZpvhk1cl3I8uXJNsmbp7ysqtDVoWgkxKVUqWd3p1KWtXW4OEDmamQkQJe/q6OSKkyY3iLbgxv0e2cz3+/cjbvrH+EjSlTeHdhSx7pfE0JRqcu1qk+1DpCrZQqnXSE2hW8Hau1pya6Ng6lypmb21xOp9ARAHy//Q0W7d3s4ojUhWRnG5LTrYQ6QEeolVKllCbUruDjSKjTNKFWqqR9fsXDhNEGbKncN/tB4lKSXB2SOo/k9EyMAX8vO3abuDocpZTKlybUrqAj1Eq5jM1mY8LV72PPjCTT4yDDfnuU7OxsV4elzkEnJCql3IEm1K7gHWjt0xJcG4dS5VSlwBDe6fYeJtuTw9mLeXjm564OSZ1DsrbMU0q5gVKZUIuIXURWi8i5e1+5Mx8doVbK1S6v24JhtR4FYPaRr/l5/UIXR6Tyox0+lFLuoLTeoR4ANgNBrg6kWHgHW/tju+DEUfD0Ay8/18akVDn0bPfrWTFhNTvT/uKV5U9SLegbKgZUuKhr1awQoQvGFAMt+VBKuYNSl1CLSDVgAPAq8LCLwykeOSPUc1+2tr5vQse7XBuTUuXUT1e9QveftpNq38md/wy96Ov82n8mDSKqODEyBZDoGKHWDh9KqdKsNJZ8fAA8DpxzlpCI3CEiK0RkRWxsbIkF5jQNB0BwDfALszZPH1dHpFS55e/tzfcDPsY3qy5k+V/0ZhPtQFFcwgO8CPPXlS2VUqWXmFK0Wp+IXAH0N8bcIyLdgUeNMVec7zVt27Y1K1asKInwlFLKqURkpTGmravjKEl6z1ZKuavz3bNL2wh1J2CQiOwBJgA9RORH14aklFJKKaXUuZWqhNoY85QxppoxJgoYBsw1xtzo4rCUUkoppZQ6p1KVUCullHIvItJXRLaKyA4RedLV8SillCuU2oTaGPPPheqnlVJKuY6I2IFPgX5AY2C4iDR2bVRKKVXySm1CrZRSqtRrD+wwxuwyxqRjzX0Z7OKYlFKqxGlCrZRS6mJVBfbneRztOHYat291qpRSF6AJtVJKqYuVX/Pts3qxGmO+Msa0Nca0jYiIKIGwlFKqZGlCrZRS6mJFA9XzPK4GHHRRLEop5TKlamGXiyEiscDeQr4sHDhaDOGURvpZy67y9HnL6metaYxx2yFbEfEAtgE9gQPAcuB6Y8zG87ymvNyz3S1mjbf4uVvM7hYvFH/M57xnexTjm5aIi/llJCIrysvqZPpZy67y9HnL02d1J8aYTBG5D5gJ2IHR50umHa8pF/dsd4tZ4y1+7hazu8ULro3Z7RNqpZRSrmOMmQHMcHUcSinlSlpDrZRSSimlVBGU14T6K1cHUIL0s5Zd5enzlqfPqs7mjv/7u1vMGm/xc7eY3S1ecGHMbj8pUSmllFJKKVcqryPUSimllFJKOYUm1EoppZRSShVBuUqoRaSviGwVkR0i8qSr43E2ERktIjEisiHPsVARmSUi2x37EFfG6CwiUl1E5onIZhHZKCIPOI6Xuc8rIj4iskxE1jo+64uO42Xus+YQEbuIrBaR6Y7HZfazqvMr7fdtd7vvuuO9013vge52HxORPSKyXkTWiMgKx7FSG7OIVBCRX0Vki+Pf8yWujLfcJNQiYgc+BfoBjYHhItLYtVE53fdA3zOOPQnMMcbUA+Y4HpcFmcAjxphGQEfgXsf/nmXx86YBPYwxLYCWQF8R6UjZ/Kw5HgA253lclj+rOgc3uW9/j3vdd93x3umu90B3vI9dZoxpmaeXc2mO+UPgL2NMQ6AF1n9r18VrjCkXG3AJMDPP46eAp1wdVzF8zihgQ57HW4HKjp8rA1tdHWMxfe6pQK+y/nkBP2AV0KGsflas5avnAD2A6Y5jZfKz6nbBfwtucd925/uuu9073eUe6I73MWAPEH7GsVIZMxAE7MbRXKM0xFtuRqiBqsD+PI+jHcfKuorGmEMAjn2ki+NxOhGJAloBSymjn9fx1eEaIAaYZYwps58V+AB4HMjOc6ysflZ1fu5633aLf6/udO90w3vgB7jffcwAf4vIShG5w3GstMZcG4gFvnOU1XwjIv64MN7ylFBLPse0Z6CbE5EA4DfgQWNMoqvjKS7GmCxjTEusUY/2ItLUxSEVCxG5Aogxxqx0dSyqVND7djFxt3unO90D3fg+1skY0xqrxOpeEenq6oDOwwNoDXxujGkFnMDF5SjlKaGOBqrneVwNOOiiWErSERGpDODYx7g4HqcREU+sXwg/GWMmOQ6X2c8LYIyJB/7Bqtksi5+1EzBIRPYAE4AeIvIjZfOzqgtz1/t2qf736s73Tje5B7rlfcwYc9CxjwEmA+0pvTFHA9GObyoAfsVKsF0Wb3lKqJcD9USkloh4AcOAaS6OqSRMA0Y6fh6JVS/n9kREgG+BzcaY9/I8VeY+r4hEiEgFx8++wOXAFsrgZzXGPGWMqWaMicL6/+hcY8yNlMHPqgrEXe/bpfbfqzveO93tHuiO9zER8ReRwJyfgd7ABkppzMaYw8B+EWngONQT2IQL4y1XKyWKSH+suiY7MNoY86prI3IuERkPdAfCgSPA88AU4GegBrAPGGqMOeaiEJ1GRDoDC4D1nKpRexqrFrBMfV4RaQ6Mwfp3awN+Nsa8JCJhlLHPmpeIdAceNcZcUdY/qzq30n7fdrf7rjveO935Hugu9zERqY01Kg1WOcU4Y8yrpTzmlsA3gBewC7gFx78PXBBvuUqolVJKKaWUcrbyVPKhlFJKKaWU02lCrZRSSimlVBFoQq2UUkoppVQRaEKtlFJKKaVUEWhCrZRSSimlVBFoQq3KPBHpLiLTHT8PEhGnrKYkIsNF5Jkzjt0sIp844/pKKVUe6T1buSMPVweg1MVwLE4gxpjsC56chzFmGs5bGKIv8JGTrqWUUmWW3rNVWacj1MptiEiUiGwWkc+AVUB1EflcRFaIyEYReTHPuX1FZIuILASuznM8dzRCRL4XkSF5nkt27CuLyHwRWSMiG0SkSz6xCNDSEce54h0gIktEJNzxXl+IyAIR2SYiVzjOsYvIOyKyXkTWicj9Rf3vpJRSpYHes1V5oiPUyt00AG4xxtwDICLPGGOOiYgdmONYUWsb8DXQA9gBTCzke1wPzHSsEmUH/PI5pxWw1pxjZSQRuQp4GOhvjDlu3cuJAroBdYB5IlIXa2WnWkArY0ymiIQWMlallCrN9J6tygVNqJW72WuM+S/P42tF5A6sf8uVgcZY37zsNsZs///27p41qiCKw/jzl0Rs1NJSoiCCYKGCnS/4glYWYiGClUg+gF/ETkgMolZqYWEQxEbBRoskgmAQghFsBAsFwSJwLPaKy5pLElaju3l+1d3ZndnT7NnDzLlcgCR3gatr+I5XwFSSUeBhVc0u85kzwOOW+ceBQ8DpqvraNX6vOe58l2QB2AucBG5U1RLA//JIV0n6Q8zZ2hBs+dCg+fbzIskYcA04UVX7gWlgS/P2srsQPZZofgPNceBmgKp6DhwBPgJ3klxeZu5p4EnLugvAVmBPz3hvTAVklbFK0iAyZ2tDsKDWINtGJ1l/SbIDONuMvwXGkuxuXl9smf8eONhcnwNGAZLsBD5V1QRwEzjQPSnJdmCkqj63rLtIpwfwdpJ9XeMXkmxq4toFzNNJ8ONJRpq1PT6UNKzM2RpaFtQaWFU1B8wAb4Ap4EUz/p3OceF0c4PLYssSE8DRJC+Bw/zaSTkGzCaZAc4D13vmnQKerhDbPHAJuN/1JzEPPKNz7DjexDkJfABeJ5mj0wsoSUPHnK1hlpb+fEktkkwCkz19gSvNuQU8qqoHfy0wSdJvzNlaD96UKK1RVV351zFIklbHnK314A61JEmS1Ad7qCVJkqQ+WFBLkiRJfbCgliRJkvpgQS1JkiT1wYJakiRJ6sMPcFRzC1T89v0AAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig,ax = plt.subplots(figsize=(12,4), ncols=2)\n", "\n", "plot_sb_vdisk(ax, rad, sbd_u2953, vd_u2953, label='disk')\n", "plot_sb_vdisk(ax, rad, sbb_u2953, vb_u2953, label='bulge')\n", "plot_sb_vdisk(ax, rad, sbd_u2953+sbb_u2953, np.sqrt(vd_u2953**2+vb_u2953**2), label='total')" ] }, { "cell_type": "code", "execution_count": null, "id": "3db9d50e", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.7.13" } }, "nbformat": 4, "nbformat_minor": 5 }