{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Tutorial: Fast self-forced trajectories" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An essential component of the FastEMRIWaveforms (FEW) framework is the rapid evaluation of the inspiral trajectory of the secondary compact object. FEW provides the tools required for users to generate and visualise these trajectories. Users can also implement their own trajectory models to incorporate additional physics (such as environmental effects or modifications to gravity). We will demonstrate these capabilities in this tutorial." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### ODE classes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Parameter conventions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "FEW constructs trajectories by integrating the equations of motion of the compact binary; these are a system of ordinary differential equations (ODEs) that describe the evolution of the following parameters:\n", "\n", "| Parameter | Definition |\n", "| :--------: | ------- |\n", "| $p$ | (Dimensionless) semi-latus rectum|\n", "| $e$ | Eccentricity |\n", "| $x_I$ | Cosine of the inclination of the orbital plane|\n", "| $\\Phi_\\phi$ | Azimuthal GW phase |\n", "| $\\Phi_\\theta$ | Polar GW phase|\n", "| $\\Phi_r$ | Radial GW phase|\n", "\n", "The ODE system can be integrated efficiently with adaptive Runge-Kutta techniques. These solvers obtain trajectories by integrating the right-hand side (RHS) of the ODE with respect to a time parameter." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Stock trajectory models\n", "\n", "In order to handle the necessary information for evaluating the RHS of the ODE, FEW defines ODE classes. The following stock options are available:\n", "\n", "| Model | Features | Notes |\n", "| :--------: | ------- | ------- |\n", "| KerrEqEccFlux | Adiabatic; equatorial eccentric inspiral with spinning primary| Our most up-to-date model |\n", "| SchwarzEccFlux | Adiabatic; inspiral with non-spinning primary | An older model (currently outdated) |\n", "| PN5 | Post-Newtonian; eccentric inclined inspirals with spinning primary | Most complete model, but inaccurate for larger $e$ and/or lower $p$|\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Obtaining the right-hand side of the trajectory ODE" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As an example, let's examine the SchwarzEccFlux model:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:32.766149Z", "iopub.status.busy": "2026-07-11T10:48:32.765895Z", "iopub.status.idle": "2026-07-11T10:48:34.954499Z", "shell.execute_reply": "2026-07-11T10:48:34.953982Z" } }, "outputs": [], "source": [ "from few.trajectory.ode import SchwarzEccFlux\n", "\n", "rhs = SchwarzEccFlux()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before evaluating the RHS, we must first define the parameters of the system that remain fixed during an inspiral. At adiabatic order, these are the component masses ($m_1$ and $m_2$) and the dimensionless spin parameter of the primary ($a$):" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:34.955734Z", "iopub.status.busy": "2026-07-11T10:48:34.955670Z", "iopub.status.idle": "2026-07-11T10:48:34.957356Z", "shell.execute_reply": "2026-07-11T10:48:34.956977Z" } }, "outputs": [], "source": [ "m1 = 1e6 # Solar masses\n", "m2 = 1e1 # Solar masses\n", "a = 0.0 # For a Schwarzschild inspiral, the spin parameter is zero\n", "\n", "rhs.add_fixed_parameters(m1, m2, a)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can then access the ODE derivatives:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:34.958223Z", "iopub.status.busy": "2026-07-11T10:48:34.958156Z", "iopub.status.idle": "2026-07-11T10:48:36.769752Z", "shell.execute_reply": "2026-07-11T10:48:36.769387Z" } }, "outputs": [ { "data": { "text/plain": [ "(np.float64(-0.017771723696175704),\n", " np.float64(-0.000779281500397855),\n", " np.float64(0.0),\n", " np.float64(0.028647063536752972),\n", " np.float64(0.028647063536752972),\n", " np.float64(0.018040932375307846))" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p = 10.0\n", "e = 0.3\n", "x = 1.0 # Schwarzschild inspiral is equatorial by definition\n", "\n", "pdot, edot, xIdot, Omega_phi, Omega_theta, Omega_r = rhs([p, e, x])\n", "pdot, edot, xIdot, Omega_phi, Omega_theta, Omega_r" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "FEW integrates trajectories on the radiation-reaction timescale $t_\\mathrm{rr} = t \\nu$, where $\\nu = \\mu / M$ is the mass ratio of the system (for $\\mu$ and $M$ as the reduced and total mass respectively). The RHS of the ODE is therefore defined such that the $(\\dot{p}, \\dot{e}, \\dot{x}_I)$ are scaled by $\\nu^{-1}$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Checking the properties of an ODE system" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The ODE class also defines a number of properties that describe the physical and systematic assumptions of the model:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:36.783277Z", "iopub.status.busy": "2026-07-11T10:48:36.783189Z", "iopub.status.idle": "2026-07-11T10:48:36.785139Z", "shell.execute_reply": "2026-07-11T10:48:36.784833Z" } }, "outputs": [ { "data": { "text/plain": [ "{'convert_Y': False,\n", " 'equatorial': True,\n", " 'circular': False,\n", " 'supports_ELQ': True,\n", " 'background': 'Schwarzschild',\n", " 'separatrix_buffer_dist': 0.1,\n", " 'nparams': 6,\n", " 'flux_output_convention': 'pex'}" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from few.trajectory.ode.base import get_ode_properties\n", "\n", "get_ode_properties(rhs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Checking the model domain of validity\n", "\n", "ODE models that interpolate over pre-computed data can only be evaluated over a finite domain. The bounds of this domain can be verified with class methods. For instance, to check the maximum eccentricity at $p=10$ for this model, we write" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:36.786113Z", "iopub.status.busy": "2026-07-11T10:48:36.786062Z", "iopub.status.idle": "2026-07-11T10:48:36.787861Z", "shell.execute_reply": "2026-07-11T10:48:36.787490Z" } }, "outputs": [ { "data": { "text/plain": [ "0.755" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rhs.max_e(10.)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Some models, such as `KerrEccEqFlux`, perform eccentricity tapering at low $p$ as this pre-computing data is prohibitively expensive in this region. Examining it over a wide range of $p$ for a single value of $a$, we can observe the taper kicking in at $\\sim p=13$." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:36.788794Z", "iopub.status.busy": "2026-07-11T10:48:36.788735Z", "iopub.status.idle": "2026-07-11T10:48:40.475939Z", "shell.execute_reply": "2026-07-11T10:48:40.475492Z" } }, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Maximum eccentricity')" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from few.trajectory.ode import KerrEccEqFlux\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "rhs_kerr = KerrEccEqFlux()\n", "\n", "spin = 0.8\n", "\n", "p_lim_check = np.linspace(4., 20, 101)\n", "e_max = np.asarray([rhs_kerr.max_e(p_here, a=spin) for p_here in p_lim_check])\n", "plt.plot(p_lim_check, e_max)\n", "plt.xlabel(\"Semi-latus rectum\")\n", "plt.ylabel(\"Maximum eccentricity\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Trajectory evaluation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### The EMRIInspiral class" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Trajectories are evaluated using the `EMRIInspiral` class, which interfaces with the underlying integrator classes and methods in order to integrate the trajectory from its initial conditions until either the maximum alloted duration elapses or pre-determined stopping conditions are satisfied.\n", "\n", "The `EMRIInspiral` class offers a number of features that can be adjusted according to the desired output. We will demonstrate these below, working with the `KerrEccEqFlux` trajectory model as an example." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:40.477024Z", "iopub.status.busy": "2026-07-11T10:48:40.476922Z", "iopub.status.idle": "2026-07-11T10:48:40.478530Z", "shell.execute_reply": "2026-07-11T10:48:40.478227Z" } }, "outputs": [], "source": [ "from few.trajectory.inspiral import EMRIInspiral" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:40.479532Z", "iopub.status.busy": "2026-07-11T10:48:40.479471Z", "iopub.status.idle": "2026-07-11T10:48:41.713698Z", "shell.execute_reply": "2026-07-11T10:48:41.713294Z" } }, "outputs": [], "source": [ "# You can also instantiate this as EMRIInspiral(func=\"KerrEccEqFlux\") to save an import.\n", "traj_model = EMRIInspiral(func=KerrEccEqFlux)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:41.714809Z", "iopub.status.busy": "2026-07-11T10:48:41.714745Z", "iopub.status.idle": "2026-07-11T10:48:41.716387Z", "shell.execute_reply": "2026-07-11T10:48:41.716094Z" } }, "outputs": [], "source": [ "m1 = 1e6\n", "m2 = 1e2\n", "a = 0.9 # This model supports a spinning primary compact object\n", "p0 = 10.0\n", "e0 = 0.8\n", "xI0 = 1.0 # +1 for prograde, -1 for retrograde inspirals\n", "\n", "T = 4.0 # duration of trajectory in years (as defined by few.utils.constants.YRSID_SI)\n", "\n", "traj_pars = [m1, m2, a, p0, e0, xI0]" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:41.717207Z", "iopub.status.busy": "2026-07-11T10:48:41.717152Z", "iopub.status.idle": "2026-07-11T10:48:42.194712Z", "shell.execute_reply": "2026-07-11T10:48:42.194334Z" } }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAABKgAAAKwCAYAAAC8iEfpAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjksIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvJkbTWQAAAAlwSFlzAAAPYQAAD2EBqD+naQABAABJREFUeJzs3Qd4VcXWxvE3vUFCCYQWQu899CLYUEQUK4oiigWUq2KXq/d+dq69odiwICCoiBULFgSk995LAgRCKGmQfr5nJiQmEBA0yWn/3/NsT8lOGGcne85ee2YtH4fD4RAAAAAAAADgJL7O+ocBAAAAAAAAgwAVAAAAAAAAnIoAFQAAAAAAAJyKABUAAAAAAACcigAVAAAAAAAAnIoAFQAAAAAAAJyKABUAAAAAAACcigAVAAAAAAAAnMrfuf888vLytGfPHlWsWFE+Pj50CACncjgcSk1NVa1ateTryz0MV8J4AcCVMF64LsYLAO46XhCgcjITnIqOjnZ2MwCgmPj4eNWpU4decSGMFwBcEeOF62G8AOCu4wUBKiczM6cKDlZ4eLizmwPAy6WkpNigecG5Ca6D8QKAK2G8cF2MFwDcdbwgQOVkBcv6THCKABUAV8GSY9fDeAHAFTFeuB7GCwDuOl6QYAQAAAAAAABORYAKAAAAAAAATkWACgAAAAAAAE5FgAoAAAAAAABORYAKAAAAAAAATkWA6jhvvvmm6tevr+DgYMXGxmrOnDmn7MBJkyapbdu2Cg0NVc2aNXXTTTfpwIEDZXnMAAAuZvbs2RowYIBq1aplK5R8+eWXxb7ucDj02GOP2a+HhISoT58+Wrt2rdPaCwAoP1xfAMDpIUBVxNSpUzVq1Cg98sgjWr58uXr16qV+/fopLi6uxM6bO3eubrjhBt188832QuOzzz7T4sWLdcstt5xm9wMAPEF6erq9WTF27NgSv/7cc8/ppZdesl8340SNGjV0/vnnKzU1tdzbCgAoP1xfAMDpI0BVhLl4MMEmE2Bq3ry5XnnlFUVHR2vcuHEldt6CBQtUr1493XXXXXbWVc+ePTV8+HAtWbLkDA4BAJQNM2sH5cPczHjqqad0+eWXl3gczHhibn6Yr7dq1UofffSRjhw5osmTJ3OIAMCDcX0BAKePANUxWVlZWrp0qfr27Vusg8zrefPmldh53bt3165duzRjxgx7AbJv3z59/vnn6t+//0k7PDMzUykpKcU2ACht5pz0f1+v1Ru/bSFQ5WTbt2/X3r17i40vQUFB6t2790nHl9IaL8bN2qrHvl6rz5fu0oa9KcrJzfvb/x8AAM+9vnhmxnqNmbFeP67dq6S0zDP+fgAoDf6l8lM8QFJSknJzcxUVFVXsffPaXFicbAAxOagGDRqkjIwM5eTk6JJLLtHrr79+0n9nzJgxevzxx0u9/QBQ1Nhft2jC/J3y8ZF6N6mmVrUj6CAnKRhDShpfdu7cWabjxdcr92h9wp8XKsEBvmpeM1xt61RSmzoRalOnkhpEhsnX1+cf/TsAAPe9vsjLc+iTRXFKzcgpfK9e1VB1rFdFnc1Wv4piqobaHIsAUJYIUB3n+BOvuXNxspPxunXr7PK+//73v7rggguUkJCgBx54QCNGjND48eNL/J7Ro0fr3nvvLXxt7nCYZYQAUFqmLIrTizM32ef/d3ELglNuOL6U1ngxoncDrYg/rLW7U7R2T7LSs3K1PO6w3QpUDPK3vyNtoyuprQlaRVdSrYhgLkQAwEuuL3LyHPrvxS20LO6Qlu48pE370rTjwBG7mRm4RvWKQepUv4q61K+iTvWqqGlURW5uACh1BKiOiYyMlJ+f3wl3MxITE0+461H0bkWPHj3soGG0adNGYWFhNrm6yUViqvodzyzrMBsAlIWZ6/bp39NX2+cjz26oG3vUp6OdzCREN8z4UnRcONX4UlrjxaXtatut4A759gPpWr0rWSt3HdaqXck2aJWamaP52w7YrUBkhUA7u8rMsiqYbVW1AmMXAHji9UWgv6+u6hhtNyP5SLaWxR/S4u0HtXjHQa2MT1Ziaqa+W5VgNyMiJEAdYyrb2VVmMzc6AvzIHgPgnyFAdUxgYKBiY2M1c+ZMXXbZZYUdZF5feumlJXaeSXDr71+8C80gZJCcGEB5W7LjoP41eZnyHNLVHevo/r5NOQguwBTRMEEqM560b9++MC/J77//rmeffbbc2mGW8TWsVsFuA9vnB61MTipzp3zVrsNauSvZPm7cm6qktCz9uiHRbgVqVwpRu+hK6hBTWZ3qVVaLmuHy52IEADzu+iIiNEBnN61uNyMjO9fOxjUBq0U7DtpZVslHs/XLhkS7GSEBfuoQU8nOrjIBq/bRlRUSmN9uADhdBKiKMFNjhwwZoo4dO6pbt2565513FBcXZ6fUFkyf3b17tyZMmGBfDxgwQLfeequt8lcwBXfUqFHq3LmzatWqddoHAQD+qU37UnXzR0uUmZOn85pX1zOXtWaJVjlKS0vTli1biiVGX7FihapUqaK6devaseGZZ55R48aN7Waeh4aGavDgwXImE2BqUSvcbtd0VuGFyNo9KTZYterYbKtt+9O1+/BRu323Ov/ueWign9rXraTYGLPco7La162sCkF8rAAAT7u+CA7wU9cGVe1WcHPDjBNmdtXCY7OsDh/J1h9bDtjNCPDzUWxMZfVqXE29GkeqZa0I+ZHvEMBf4JNkESYZ4YEDB/TEE0/YwcCUAjcVNGJiYuzXzXtmQClw4403KjU1VWPHjtV9992nSpUq6ZxzzinXO+IAsOfwUQ19f5G9m2k+DL5+bQdmtpSzJUuW6Oyzzy58XZALZOjQofrwww/14IMP6ujRo7rjjjt06NAhdenSRT/99JMqVqzocr/A5kLE/B6ZrUBKRrbW7ErW8vjD9s65ma2XkpFT7GLEXHeYBOzm7nnHepXVMaaKakQEO/H/BACczxOvL8zNDZu3MLqSbunVwC4h37I/LT9YZWZZbT+ovSkZWrDtoN2e/3GjKoUGqEejSPVqFKmejSNVp3Kos/83ALggHwdr0ZzKJDGMiIhQcnKywsPDndsYAG7n8JEsXfnWfG1JTFOj6hX0+YhuqhQa+Ld/Huck1+VKx8ZcjGxOTNOSnQe1ZMche/d816GjJ+wXXSXEBqpMwMoErhpVq0BSXcBDuNI5Ca51bMzlpUmwPnfzfs3enKQFWw/YfIdFmQqyJlBlZlh1bVBFFYMDyr2dAFzvnESAyssHEADu62hWrq4fv9DOaKkRHqwv7uiuWpVC/tHP5Jzkulz92OxNzigWsFqfkGLzoRVlkuqamVkFAavWtSPsjC0A7sfVz0nezNWOjVkSaJaLz96UpLlbkmw+q9wiA4RZ+tehbiX1bFTNBq1MRVlyHAKegwCVG3G1AQSAezAf9kZMXKqf1ycqPNhfn9/eXU2i/vlyMc5Jrsvdjk1qRnZ+Ut0d+UsCl8cd1tHs3GL7BPr5qnWdiPyAVUwVG7yqHPb3ZwACKD/udk7yJq5+bMyy8flbD2ju5iTN2bzfzrYqqmKwv7o3rFqYvyqmapjT2grgnyNA5UZcfQAB4HrM1PnRX6zWlMXxCvL31cRbutjZKKWBc5Lrcvdjk52bZ2dVFQSszGNSWuYJ+zWuXqEwh5X5vTbLBH18fJzSZgCee07yZO52bOIPHtGczWZ21X4btDI5Dosy44ANVjWKVPeGkbbKIAD3QYDKjbjbAALA+V76aaNe+3WLTUr91vWx6tuyRqn9bM5JrsvTjo0JtMYdPFIkYHVQW/enn7BfVHiQTax7VuNq9rFaxSCntBeAZ5+TPIk7Hxuz9G/17uTC/FXLdh5STpHlgOazT5s6lXRWY5NsvZqtJhvg5+vUNgM4NQJUbsSdBxAA5e/jBTv1ny/X2OfPXNZag7vULdWfzznJdXnDsTmYnlVYJdAErMxFSnZu8URWplKgWfJhNjPDihxWgHN4wznJXXnSsUnLzNHCbQfsDCuzHPD4GxlhgX7q1rCqejaKVO+m1VU/kuWAgKshQOVGPGkAAVC2vl+doDsmL5PDIY06r7FGndek1P8NzkmuyxuPTUZ2rg1YFVyYrN2TUuzrZolr5/pV7IWJWf7RrEZFqgQC5cQbz0nuwpOPzZ7DR22idTMu/LElyd7YOH6Z+AUta9itVe1wlogDLoAAlRvx5AEEQOlZsO2Abhi/SFm5eXbW1NMDW5XJhy7OSa6LYyObs8pckOQn1k3S3pSMYn0UWSHQBqvMsg8zwyoqPNhpxwvwdJyTXJe3HJu8PIfWJaQU3sRYtP1gseWAtSKCbRqEvi2j1LleFSoDAk5CgMqNeMsAAuDv27A3RVe9NV+pGTnq2yJK466PtSWZywLnJNfFsTkxh9XW/WmFZctNEPdIVvEqgU2iKtiZVaZseZf6VRQa6F+uxwzwZJyTXJe3Hpvko9n6bUOifly7V7M27i9WObZyaIDObR5lZ1aZGxgsDwfKDwEqN+KtAwiA07Pr0BFdMW6e9qVkqlO9yvr45i5l+qGKc5Lr4ticWlZOnpbFmeWA+VWgVu1OtsthCwT6+So2prJ6NYlUr0bV1LJWOMsBAc5JHonxIn+JuJlZZYJVv6zfp0NHsgv7JzTQT72bVLPBqrObVVdECFUBgbJEgMqNMIAAOJlD6Vm68q15NiGomQny2fDuZV5amXOS6+LYnPnfzx9b/1wOuPvw0WJfrxIWqO4Nq9rqgH2aVVP1iiwHBDgneQbGi+JycvNsxVgTrPpp7V7tSf5zebi/r49Nsm6WAl7QIkrVWRoOlDoCVG6EAQRASY5m5eq69xZoWdxh1YwI1rTbu6tWpRDOSV6M8eKfLQfcnpR+LE9JkuZvTVJ6keWAJp1bh7qVdUHLKPVtUUP1qAIFcE5yY4wXpx4P1uxOscEqs21OTCv29fZ1KxUmWaciIFA6CFC5EQYQACXd6Rv+8VL9siHRTjv/fEQ3NY6qyDnJyzFelJ7s3DytiD9sg1W/b0zUyl3Jxb7eNKpifrCqZQ27FLAsChIA7o5zkuvi2Jy+bfvT9OPafTZYZcaFoszs9YJgFWMB8PcRoHIjDCAAjr+z9/C01Zq6JF5B/r6adEsXdaxXhXMSGC/KUELyUc1cl3+BsmDbQeUWqQJVp3KInVVlAlbmb7GsChQA7obPsK6LY/P37E3O0Mz1++wywPlbDxSrCFi7UojObxGlS9vVUrvoSty4AM4AASo3wgACoKiXftqo137dInMNbKr1mbt2nJPAeFF+Dh/J0i/rE/XTur36fdN+ZWTnFctbdV7z6vbvskcjqkDBu/EZ1nVxbP655CPZ+nXjPv24Zp8dC4pWBGxQLUxXdKijge1r28AVgFMjQOVGGEAAFPh4wU7958s19vnTl7XSdV1iOCeB8cLJueBmb95/rApUoi1hXiAs0E99mlZX35ZRtgpUeDBVoOBd+Azrujg2pV8RcPam/fpudYIdDwpuXJjV390aVNXlHeqoX6saCgvyL+V/GfAMBKjcCAMIAOOHNQm6fdIyORzS3ec21j3nN+GcBMYLF8tbtWj7wWNVoPZpb8qfVaAC/EwVqEi7DNAsAaEiILwBn2FdF8em7KRl5mjG6gR9sWyXXRJeICTAzwapTLDKVAVkOTjwJwJUboQBBIC56L1+/EJl5eTp2s7Reuay1k7LbcA5yXVxbFwrV9yqXcmFVaC27k8vsSKgWQoYUzXMqW0FygrnJNfFsSkfuw4d0ZfLd2vast22UmwBU33ZLP+7okNtNapePkVuAFdGgMqNMIAA3m3TvlRdOW6eUjJydF7zKL11fQf5+/k6rT2ck1wXx8Z1bUlMszmrTCWolcdVgTIVAfu1rqHL2tcmWAWPwjnJdXFsyv+mxfL4w3ZW1TcrE4otB29TJ8LmqxrQtpbNYwh4o5SUFEVERCg5OVnh4eGn3NfHYf6i4DQMIID32nP4qK4YN08JyRmKjamsiTd3UUign1PbxDnJdXFs3L8iYMeYynb5R//WNRURSs4quDfOSa6LY+M8mTm5+nV9op1VNWtjYmElQH9fH5uv0ASrzm5WTUH+zv28B5QnAlRuhAEE8N7qMFe+NU+bE9PUqHoFfT6imyqFOv/OGuck18Wxcd+KgF+t3KO5m/erIFYV6Oer81pU1+Xt66h302oKcOKsSeDv4pzkujg2ruFAWqa+XrlHXyzbrdW7kwvfrxQaoAFtaumK2DpqWyfCaWkdgPJCgMqNMIAA3lkNZsj4hVq845CiwoP0xR09XKZMMeck18WxcW/7UjL01YrdmrZ0tzbuSy183yz5uKRtLV3eobZa1+ZCBe6Dc5Lr4ti4ZkqHact22ZxV+1IyC99vUC3Mzqoyy8BruchnQaC0EaByIwwggHcxy33umLTU5qqpGOyvz0Z0U7Map16LXZ44J7kujo1nMJkV1iWkaPqy3fpyxR4lpf15odKwWphdAsiFCtwB5yTXxbFx7c+B87YmadrSXfph7V5lZOfZ980kqm4NqurqjtE2byFLAOFJCFC5EQYQwLsuTB/9co0mLYyzS3wm3NxZXRtUlSvhnOS6ODaeJyc3T3O2JNnlHz+t3avMnOIXKiZYdWGrGqoQ5O/spgIn4Jzkujg27iEtM0ffr06wY8D8bQcK34+sEKTBXerq+i51VT082KltBEoDASo3wgACeI/Xf9msF2dushefbwzuoIta15Sr4ZxUdlJTU/Wf//xH06dPV2Jiotq3b69XX31VnTp14thAKRnZ+mH1XrsEZOH2g4U9Ehzgqwtb1rDBqh6NIuXnS64SuAbGC9fFsXE/uw4dsYGqyQvjtDclozCxuvmseGOPemofXYlcVXBbBKjcCAMI4B2mLo7TQ9NW2+ePX9JSQ7vXkyvinFR2Bg0apDVr1mjcuHGqVauWJk6cqJdfflnr1q1T7dq1OTYoFH/wiM1XZS5WtiWlF75fvWKQBravbZeAmOIKgDMxXrgujo37ys7Ns1VgP5q3w+YqLdCmToSGdquni9vWZPkf3A4BKjfCAAJ4vl/W79NtHy/Nzz/Vp6EevLCZXBXnpLJx9OhRVaxYUV999ZX69+9f+H67du108cUX66mnnuLYoMRlwSviD9tA1Ter9ujwkezCr/VsFKkh3WJ0brPq8qcKIJyA8cJ1cWw8w5rdyTZQZSrBZh1bAh5ZIVCDO9fVdV1jFMXyP3jgOYm6xsd58803Vb9+fQUHBys2NlZz5sw5aefdeOONdqrl8VvLli1L50gCcHvL4g5p5ORlNjhlqrQ8cEFTZzcJTpCTk6Pc3Fw7thQVEhKiuXPnlvg9mZmZdkAvusG7mM8U7etW1pMDW2nRv8/T20NidV7z6naZ8NwtSRr+8VL1fn6W3vhtiy1nDsA1cX2Bv6NV7Qg9f1VbzX/4HPv5sWZEsJLSsvTar1vU43+/6s5PlmvpzoP2ZgbgKQhQFTF16lSNGjVKjzzyiJYvX65evXqpX79+iouLK7HzTO6QhISEwi0+Pl5VqlTRVVddVV7HD4AL27o/TTd/uNhWaOnTtJr+d0Vr8gd4KTN7qlu3bnryySe1Z88eG6wyS/wWLlxox4+SjBkzxt5tKtiio6PLvd1wHYH+vrqgZQ29N7STZj9wtkb0bqjKoQHaffionv9xo7qN+VX3Tl1hZ1wBcB1cX+CfqlohSCPPbqQ5D56tN6/roM71qignz6FvVu7RFePma8DYufp86S5lZOfS2XB7Pg5CroW6dOmiDh062PwgBZo3b66BAwfaC4W/8uWXX+ryyy/X9u3bFRMTc1oHgCm4gGfal5Khy9+cZy8e29aJ0ORbuyrMDSpxcU4qO1u3btWwYcM0e/Zs+fn52fGmSZMmWrZsmc1DVdIMKrMVPTYmSHU606PhHczFyLerEjRh/g6t2pVcLFfJDSZXSZuaCg7wc2ob4bkYL04P1xcoC2v3HFv+t2JPYQXYKmH5y/+u7xqjGhFU/4PrIAfV35CVlaXQ0FB99tlnuuyyywrfv/vuu7VixQr9/vvvf/kzBgwYYC8mfvrppzI5WADcpxrXoLcXaH1CiupVDdW027vbu1/ugHNS2UtPT7f9XLNmTZs4PS0tTd999x3HBv+ImTllAlXfrkxQVm7+xYqZYTWoU11d16WuoquE0sMoVYwXf43rC5S1g+lZmrI4Th/P36mE5Pzqf6ba64WtaujG7vXUMaYys/fhVuOF69/OLydJSUl2yUVUVFSx983rvXv3/uX3myUa33//vSZPnnzK/Uq6Iw7Ac2Tm5GrEx0ttcCqyQpAmDOviNsEplI+wsDC7HTp0SD/++KOee+45uh7/WLvoSmoX3U6PXNRcU5fEa9KCODuD863ft+rt2Vt1brMo3dAtxiZX9/X1oceBcsD1BcqamTV1R59Guq1XA81ct08fzNuhRdsP6rtVCXaLjamsO89ppN5NqhGoglsgB1UJCUmLMisgj3+vJB9++KEqVapklwOeCjlFAM+Vl+fQ/Z+t0rytBxQW6KcPb+qkulWZtYB8Jhj1ww8/2GXgM2fO1Nlnn62mTZvqpptuootQakxA3FyszH7wbL0zJNYGpEz+3J/X79MN7y/SuS/9rvfnblfy0T8rAgIoW1xfoKyZaq79WtfUp8O7acZdvXRNp2ibu3DpzkO68YPFGvjGH/p53T4SqsPlEaA6JjIy0uYEOX62VGJi4gmzqo5ngljvv/++hgwZosDAwFPuO3r0aDu1rWAzidUBeIanZ6y3CSv9fX301pBYW30FKGDO+SNHjlSzZs10ww03qGfPnnZJeEBAAJ2EUmeWePRtWUMTb+miX+7rbZd6VAzy1/akdD3x7Tp1G/OLnv5unRJT8peEACh9XF/AGVrUCtf/rmijuQ+erVt61ldwgK9W7krWLROW6OLX5+qHNQn2pirgikiSflwSw9jYWFsKtkCLFi106aWXnjJJ+qxZs+yd8NWrV6tVq1ZndABYvw94hndnb7MBKuOVQe00sH1tuSPOSa6LY4N/Kj0zR9OX77a5qjbtS7PvmTvsV3eso+FnNSRPFTgnlQGuL+BsSWmZenfONpun6khWfqW/plEV9a9zGumi1jXtDQ3AVT7DMoOqiHvvvVfvvfeenQ21fv163XPPPYqLi9OIESMKZz+Zu97HGz9+vB18zjQ4BcAzfLl8d2Fw6t8XNXPb4BQAz2YqiZrqTj+OOksf3NjJ5ibJysnTxAVx6vPCLN336UptScwPXAEoHVxfwNlMTtTR/Zpr7kPn6F9nN7KzaTfuS9WdnyxX35d/t59jc44V1wCcjSTpRZhqSgcOHNATTzxhk56bgNOMGTMUExNjv27eMwGrokwUcNq0aXr11VfL98gBcAlzNyfpgc9X2ufDetTXrb0aOLtJAPCX+XDOblZdfZpW04JtB/XGb1s0d0uSpi3bpS+W71K/VjVsHiuWKQP/HNcXcKWE6vdf0NR+Vv1g3nabj3Dr/nSNmrpCr/y8SSPPbmRvsgb4MYcFzsMSPydjyQbgvtbsTtagt+crPStXF7epqdeuae/21bE4J7kujg3K0or4wzZQZapAFTi7aTW7BCQ2pgqdD85JboTxAqf1e5KRbZf9meV/h4/kF86IrhJib1Bc0aGOXQIOlPc5iQCVkzGAAO4p7sARXT5unl3X361BVX04rJOC/P3k7jgnuS6ODcrDhr0pevO3rfp21R4V5NDtUr+KDVSZioCnU9kY3oFzkuvi2OBM8xNOXLBT78zepgPpWfa9WhHBur1PQ13VMVrBAe7/+RbORYDKjTCAAO7nQFqmrnxrvq2G1axGRX06opvCgz2jEhvnJNfFsUF5Mue3t2ZttUv+snPzI1VtoytpZJ+GOq95lNvPFsU/xznJdXFs8HcczcrVpIU79fbsbdqfmmnfiwoP0u29G2pwlxhmVOFvI0DlRhhAAPdyJCtH1767UCvjD6t2pRB9cUd3RYUHy1NwTnJdHBs4w57DR+1d9U8WxSkzJ69Y9af+rWsSqPJinJNcF8cG/0RGdq6mLo7XW79vVUJyhn2vXtVQPdyvuS5oGcVMWpwxqvgBQBnIzs3TyEnLbHCqUmiAPhrW2aOCUwBwvFqVQvTYJS31x8Pn2OUeFYpUf7r0jT80b2sSnQYAHsQs6RvavZ5mPdBHTw1sZasA7jhwRCMmLtWgdxZo1a7Dzm4iPBiZzwDgNDgcDj0yfbV+27hfwQG+Gj+0kxpVr0DfAfAK5gLloQub6Y+HztGo8xorLNBPq3cna/C7CzXsw8XauDfV2U0EAJQik1v1+q4xNlD1r7MbKcjfV4u2H9QlY//QvVNX2Bm2QGkjQAUAp+GlmZv06ZJdMmlXXr+2g2JjKtNvALxORGiARp3XRL8/eLZu6BYjf18f/bohUf1ena0HP1+pvceWgwAAPIOZOXv/BU312/19dFn72va9L5bv1tkvzNKLP220SdaB0kKACgD+wscLdur1X7fY509f1lrnt4iizwDI22dUPXFpK/10z1nq16qGrfhngvh9XvhNz/+4wZYvBwB41pLvlwe109f/6qHO9arYvITm83GfF2Zp6uI45RaUfgX+AQJUAHAKP6zZq/9+tcY+N8taru1cl/4CgGMaVKugcdfHatrt3dUxprIysvP0xm9b1ef5Wfrwj+3KOpZYHQDgGdrUqaSpw7vqres7KKZqqK3499C01er/2hzN2bzf2c2DmyNABQAnsXjHQd01ZbkcDtnA1N3nNqavAKAEZtnzZyO66Z0hsWpQLUwH07P02DfrdP7Lv+u7VQk2jx8AwDP4+PjowlY1NfOe3vrPxS0UERKgDXtTNWT8It30wSJt3kdeQvw9BKgAoASb9qXq5g8X27v/5zWP0pOXtqSsLgD8xQVL35Y19NOos/T0ZfmVn3YeOKKRk5dp4JvztHDbAfoPADxIoL+vbu5ZX78/0EfDetS3eQlNQaELX52j/3y5RgfSMp3dRLgZAlQAcJyE5KMa+v4ipWTk2FkBr1/bXv5+nC4B4HSY8+V1XWLsBYtZGh0a6KeV8YdtefJbJyzRrkNH6EgA8CCVQgP13wEtbF7Cvi2ibD4qk8PVLPd+d/Y25eSy3BunhysuACgi+Wi2bnx/sRKSM9SwWpjGD+2okEA/+ggAzlBYkL+t+GdKlF/Xpa78fH00c90+nf/SbL39+1Zlc8ECAB6Xl/CdGzpqym1d1ap2uFIzc/T0jPUa+OYfWrM72dnNgxsgQAUAx2Rk59q7+xv3pSoqPEgfDets7wgBAP6+6hWDbQXUH+7upc71q+hodq7GfL9BA16fq6U7D9G1AOBhujaoqq9H9tRzV7Sx+anW7E7RpW/8oTEz1utoVq6zmwcXRoAKACQ7FfmeqSu0aPtBVQzyt8GpOpVD6RsAKCWNoypq6m1d9dyVbVQ5ND+h7pVvzdO/p69W8pFs+hkAPIivr4+u7hStn+/trYvb1LSftd+evU0XvDJbczcnObt5cFEEqAB4PVNd6vFv1ur7NXsV6OdrpyY3qxHu9f0CAGWRSP3qjtH65b4+ujK2jq2SOnlhnM59aZa+WrGban8A4GGqVQzS2MEdbNqMmhHBijt4RNePX6j7P1upQ+lZzm4eXAwBKgBe781ZWzVh/k75+EgvDWqrbg2ren2fAEBZqhIWqBeuamvzlJh8f0lpWbp7ygrd8P4i7UhKp/MBwMOc2zxKM+/traHdYuxn7s+X7tJ5L/2ur1fu4eYEChGgAuDVzOD4/I8b7fP/XtxCF7ep5ewmAYBX5SmZcXcv3Xd+E1uufM7mJPV9ZbZe+2WzMnPIUwIAnqRCkL8ev7SVPh/RXU2iKuhAepbu+mS5hn24WLsPH3V28+ACCFAB8Fq/bUzUQ9NW2efDezfQTT3qO7tJAOB1gvz9dOe5jfXTqLPUq3GksnLy9NLMTer36hzN33rA2c0DAJSy2JjK+vbOXrrX3Jzw89VvG/fr/Jd+1wd/bLe5quC9CFAB8Eor4w/rjonL7CB4WfvaeuiCZs5uEgB4tXqRYZowrLNevaadIisEadv+dF377gKbRP1IVo6zmwcAKEVm1uxd5zbWjLt7qlO9yjqSlavHv1mnK8bN04a9KfS1lyJABcDrmPwmZiqxKXVu7tY/e0UbW2kEKCs5OTl69NFHVb9+fYWEhKhBgwZ64oknlJeXR6cDxyVRv7Rdbf1yX29d16Wufc8kUe//2lx7YwEA4FkaVTcVXrvpqYGtbCXtFfGHdfFrc+1M2uxcPid5GwJUALzK/tRMDXl/oV3z3rp2hMZdH2vv4ABl6dlnn9Vbb72lsWPHav369Xruuef0/PPP6/XXX6fjgRJEhATo6ctaa9ItXVQjPFjbk9LtXfWxv25m+QcAeBhzo/j6rjE2ifr5LaKUk+ewuQgHvT1f8QePOLt5KEdclQHwGmmZObrpw0WKP3hUdauE6v0bO9lkjUBZmz9/vi699FL1799f9erV05VXXqm+fftqyZIldD5wCj0aReqHUb3Uv01Ne8Hywk+buGABAA9VIyJY7wyJ1WvXtrezqZbFHdZFr87RNyv3OLtpKCcEqAB4BZN09/aJS7Vmd4qqhgXaPCfVKgY5u1nwEj179tQvv/yiTZs22dcrV67U3LlzddFFFzm7aYDLqxQaqLHXttfLg9raC5YlOw/ZBOqmCqvDQTJdAPC0pd6XtK1lK7x2qFtJqZk5uvOT5Xrw85XkI/QCBKgAeLy8PIcd1Ez58tBAPztzyiTjBcrLQw89pGuvvVbNmjVTQECA2rdvr1GjRtn3TiYzM1MpKSnFNsCbL1gua1/HXrB0rlfFzoi9/7OVGjl5mQ6lZzm7eQCAUhZdJVSfDu+mO89pJB8f6dMlu2xuqjW7k+lrD0aACoDH+98PG/Tlij3y9/XRm9d1UNvoSs5uErzM1KlTNXHiRE2ePFnLli3TRx99pBdeeME+nsyYMWMUERFRuEVHR5drmwFXvWD55LauevDCpvacPmP1Xl346mzN2bzf2U0DAJQyfz9f3de3qSbf0tXmI9yWlK7L35yn8XO3M4PWQ/k4mBvtVOaOuLnwSE5OVnh4uHMbA3ig9+Zs01PfrbfPX7yqra6IrePsJrk0zkllwwSXHn74YY0cObLwvaeeesoGrTZs2HDSGVRmK3pszM9hvADyrd6VrLunLte2/en29bAe9W3gKjjAjy4qB4wXrotjA09kZss+OG2VZq7bZ1/3aVpNL1zVVpEVSNnhSeckZlAB8Fhfr9xTGJx66MJmBKfgNEeOHJGvb/Eh18/PT3l5Jy+fHBQUZAfxohuAP7WuE6Hv7uylIV1j7Ov3/9iuK9+ap12HqPgEAJ6mcligTaD+5KUtbQXuWRv368JX5mj2JmbQehICVMd58803Vb9+fQUHBys2NlZz5sw5ZQeau9uPPPKIYmJi7MVEw4YN9f7775flMQNwGv7YkqT7Pl1hn9/YvZ5G9G5Av8FpBgwYoKefflrfffedduzYoenTp+ull17SZZddxlEB/oGQQD89ObCV3r+xo6qEBdpCGANen6t5W5LoV7gMri+A0stHOKRbPX39rx5qElVBSWmZuuH9RRozY70tiAT3R4DquBwhJmmtCTgtX75cvXr1Ur9+/RQXF3fSDrz66qttZabx48dr48aN+uSTT2wSXADOs3ZPsoZ/vFTZuQ71b11T/724hR3QAGd5/fXXdeWVV+qOO+5Q8+bNdf/992v48OF68sknOShAKTinWZS+ubOnWteO0KEj2bp+/EK9O3sbOUrgdFxfAKWvWY1wfTWyp67rUte+fnv2NjuDNv4gM2jdHTmoiujSpYs6dOigcePGFb5nLiQGDhxok9Ue74cfftA111yjbdu2qUqVKn/rALBGHChdZmC67M159o5K1wZV9OFNnclHwjnJIzBeAH8tIztXj365Rp8v3WVfD2hbS89e0Vqhgf50H+ckp+D6AihbP6zZq4emrVLy0WxVDg3Qm9fFqlvDqnS7CyEH1d+QlZWlpUuXqm/fvsXeN6/nzZtX4vd8/fXX6tixo5577jnVrl1bTZo0sXfFjx49etJ/h7LhQNk5cGyarwlONatRUW8P6UhwCgC8iEmQ/vyVbWyOElPl75uVe2zFp50H8hOpA+WJ6wug7F3Yqoa+v7tX4QzaIeMX6uMFO+l6N8USv2OSkpKUm5urqKioYh1kXu/du7fEzjMzp+bOnas1a9bYfCKvvPKKPv/882JVmo5H2XCgbKRn5mjYh4u1PSldtSuF6KNhnRUREkB3A4CX5iiZfGtXW91pw95Um5dq1sZEZzcNXobrC6B81KoUos9GdNMlbWspJ8+h/3y5Ro9MX01eKjdEgOo4x+epcTgcJ81dY6ovma9NmjRJnTt31kUXXWST3n744YcnnUU1evRoW16xYIuPjy+tYwl4rezcPI2cvEwrdyWrUmiADU5FhQc7u1kAACfqXL+Kvr2zp9pFV1JKRo5u+nCx3vhtC3mpUO64vgDKZwbtq9e004MXNpW5fJ+0MM7OpjIrLOA+CFAdExkZaUt+Hz9bKjEx8YRZVQVq1qxpl/ZFREQUy1llglq7duXnPjgeZcOB0mX+3h6ettqWmg0O8NX4oZ3UqHoFuhkAoBoRwZo6vKuu7VxXDof0/I8bNWLiUqVl5tA7KHNcXwDlHwy+o08jvXdDR1UI8tfC7Qd16Rt/aH1CCofCTRCgOiYwMFCxsbGaOXNmsQ4yr7t3715i5/Xo0UN79uxRWlpa4XubNm2Sr6+v6tSpU5bHDcAx5mJj2rJd8vP10RuDOyg2pjJ9AwAoFOTvpzGXt7ZboJ+vfly7T1e/NV+JqRn0EsoU1xeAc5zbPErT7+iumKqh2nXoqK4YN08/rEngcLgBAlRF3HvvvXrvvff0/vvva/369brnnnsUFxenESNGFC7Pu+GGGwr3Hzx4sKpWraqbbrpJ69at0+zZs/XAAw9o2LBhCgkJKf+jCXiZD//YrjdnbbXPx1zW2g5GAACUxMyimjK8q6qGBWpdQoq9YNm2/8+bjEBZ4PoCcI7GURX11cge6tGoqo5k5WrExGV69efNystzcEhcGAGqIgYNGmQTnT/xxBNq166dDTjNmDFDMTEx9usJCQk2YFWgQoUKdobV4cOHbTW/6667TgMGDNBrr71W/kcS8DLfrUrQ49+us8/v79tEV3eKdnaTAAAurkPdypp2e/5d9fiDR3XlW/O1PO6Qs5sFD8b1BeA8lUID9dFNnXVj93r29cs/b9K/PlmmI1ks83ZVPg6TwAVOk5KSYnNYmYTp4eHhHAngNMzfekBD31+krNw8DekaoycubXnSYgbgnOQpGC+A0pOUlqmbPlis1buTFRLgpzev66Czm1WnizkneQTGC+BEUxbF6T9frVF2rkPNa4brvaEdbeVvuNY5iRlUANzKuj0pum3CEhucurBlDT12CcEpAMCZiawQpCm3ddVZTarpaHaubpmwRJ8tobIyAHiqazrX1eRb85d5m6TpV46bpy2Jqc5uFo5DgAqA24g/eERDP1ik1MwcWz78lWva2eToAACcqbAgf40f2lGXt6+t3DyHHvh8ld74bYutDgsA8Dyd6lXRV//qYSt+JyRn6Kq35mtF/GFnNwtFEKAC4BYOpGXaZX37UzPVrEZFvXtDRwUH+Dm7WQAANxbg56sXr26rEb0bFlaG/b+v19qAFQDA89SpHKpPh3dT2zoROnQkW4PfXaC5m5Oc3SwcQ4AKgMsziQyHfbRE25LS7Vrxj4Z1VkRIgLObBQDwACaH4cP9mumxAS1k0hlOmL9T/5q8TJk5uc5uGgCgDFQJC9SkW7sWVvgb9uFifb86gb52AQSoALi07Nw83TFpmVbGH1al0AAbnIoKD3Z2swAAHubGHvU19toOCvTz1fdr9ur2iQSpAMBTVQjy1/s3dlK/VjVsbtuRk5fpk0Vxzm6W1yNABcBlmTwgD09brVkb9ys4wNcOImbNOAAAZaF/m5r64KZOdsz5dUOiRk5apqycPDobADxQkL+fxg7uoGs7R8us7B79xWqNm7XV2c3yagSoALisZ3/YqGnLdtlE6KYEeIe6lZ3dJACAh+vRKFLjh3ZSkL+vfl6faO+qE6QCAM9krjOeuay1bu+Tn4vw2R82aMyM9RTMcBICVABc0vtzt+ut3/PvYIy5vLXOaRbl7CYBALwoSPXe0I4K9PfVzHX7dOcny+yScwCAZ+YifOjCZvr3Rc3s67dnb9ND01Yph/N+uSNABcDlfL1yj574dp19/sAFTXV1x2hnNwkA4GV6Na5mK8aaINWPa/fprk+WE6QCAA9221kN9dyVbeTrI326ZJedQZuRTcGM8kSACoBLMWVe7/t0hX1+Y/d6uuPYdFsAAMpb7ybV9PaQ2MLE6XdPIUgFAJ7M3Bgfd31s4c0JU6yJZd7lhwAVAJexeleyhn+8RNm5Dpuo9r8Xm5LfPs5uFgDAi53dtLreGtJBAX4+mrF6r0ZNXcGyDwDwYBe0rKEPb8zPRWgKZpibEyz3Kx8EqAC4hB1J6brpw0VKz8pV94ZV9dLVbeVr5tcCAOBkJg/iuOtibZDqu1UJuvfTlcozJZ8AAB6pe6PI/GXex2bQ3v/ZSuVy3i9zBKgAOF1iaoZueH+RktKy1LJWuF1OYcq+AgDgKs5rEaU3jwWpTK7Ep2esd3aTAABl6Kwm1WwlcX9fH325Yo8emb6amxNljAAVAKdKzcjWje8vVtzBI6pbJVQf3tRZFYMDOCoAAJdzfosovXBVW/t8/Nztem/ONmc3CQBQxjcnXr2mvU2cPmVxvB7/Zq0cDmbQlhUCVACcJjMnV8M/Xqp1CSmKrBCoCcM6q1rFII4IAMBlXdquth7ul1+K3MyiMkv+AACey+TGNTcnTGrcj+bv1P++30CQqowQoALgFGYN971TV2re1gMKC/SzM6fqRYZxNOCR6tWrZxP+H7+NHDnS2U0D8DcMP6uBbugWI3MT/Z5PV2jxjoP0IwB4sMs71NHTA1vb52/P3qZXft7s7CZ5JAJUAMqdmRZrpsd+tzrB5vJ454aOalU7giMBj7V48WIlJCQUbjNnzrTvX3XVVc5uGoC/wQSY/29AS7vkz5Qfv+WjJdqSmEZfAoAHG9ylrq0ybrz6y2aNm7XV2U3yOASoAJS7N37bognzd9ppsi9d3U49GkVyFODRqlWrpho1ahRu3377rRo2bKjevXs7u2kA/iY/Xx+9dk17tYuupOSj2Rr6/iJb9AMA4LmG9ayvBy9sap8/+8MGvT93u7Ob5FEIUAEoV1MWxemFnzbZ5/93cQsNaFuLIwCvkpWVpYkTJ2rYsGF2FsbJZGZmKiUlpdgGwLWEBPpp/NCOqlc1VLsPH9WwDxcrLTPH2c0CAJShO/o00l3nNrbPn/h2nb5asZv+LiUEqACUmx/X7tW/p6+2z+/o01A39qhP78PrfPnllzp8+LBuvPHGU+43ZswYRUREFG7R0dHl1kYAp69qhSB9NKyzqoYFas3uFN05eRllyAHAw91zXmPd3DP/WuaBz1aRi7CUEKACUC4WbjugOz9ZrjyHNKhjtB64IH9qLOBtxo8fr379+qlWrVPPHhw9erSSk5MLt/j4+HJrI4AzE1M1TONv7KQgf1/9tnG/XvmF5LkA4MnMLPhHLmquC1pGKSs3T7dOWKLtSenObpbbI0AFoMytT0jRLROW2ESyJqHs05e1OuXSJsBT7dy5Uz///LNuueWWv9w3KChI4eHhxTYArsvkohpzeX6Fp9d+2axf1u9zdpMAAGXI19dHrwxqr7Z1InT4SLZu+mCRDqVn0ef/AAEqAGUq/uAR3fD+IqVm5KhzvSp6/dr28vfj1APv9MEHH6h69erq37+/s5sCoIzKkN/QLcY+HzV1hXZwNx0APD4X4btDO6p2pRDtOHBEt328RJk5uc5ultviKhFAmUlKy9SQ8Qu1PzVTzWpUtCfv4AA/ehxeKS8vzwaohg4dKn9/f2c3B0AZebR/C8XGVLY3ZoZ/vFRHskiaDgCerHrFYH1wUydVDPbX4h2H9ODnq+RwOJzdLLdEgApAmTBVjG76YLG9k1CncohNIBsREkBvw2uZpX1xcXG2eh8AzxXo76s3r+ugyApB2rgvVQ9PW82FCgB4uCZRFTXuulj5+/roqxV79PLM/KrlODMEqACUOjOtdcTHS7V6d7KqhAVqwrDOigoPpqfh1fr27WsvUps0aeLspgAoY2bMM0Eqc6Hy9co9+uCPHfQ5AHi4no0jba5d47Vft+jzpbuc3SS3Q4DqOG+++abq16+v4OBgxcbGas6cOSftvFmzZtlEz8dvGzZsKOvjBrisvDyH7vt0peZuSVJYoJ8+vKmTGlSr4OxmAQBQrjrXr6J/X9TcPn9mxnot2n6QI+CluL4AvMegTnV1R5+G9vnoL1Zp3tYkZzfJrRCgKmLq1KkaNWqUHnnkES1fvly9evWypcDNkoxT2bhxoxISEgq3xo0bl/VxA1ySmR3y2Ddr9e2qBAX4+ejtIR3Vpk4lZzcLAACnuKlHPV3arpZy8hz61+RlVHfyQlxfAN7n/r5NdXGbmsrOdej2icts0SicHgJURbz00ku6+eabbfnv5s2b65VXXlF0dLTGjRt3yk40FZlq1KhRuPn5kQQa3um1X7Zowvyd8vGRXry6nZ3mCgCAtzIz68dc3loNq4UpMTVT/55OPipvw/UF4H18fX30wlVt1bZOhJKPZmvk5GVU9jtNBKiOycrK0tKlS22OkKLM63nz5p2yE9u3b6+aNWvq3HPP1W+//XbKfTMzM5WSklJsAzzBxwt26uWf85MBPn5JS13StpazmwQAgNOFBvrrlUHtbT6q79fs1bRlu53dJJQTri8A72Uql79xXQdVCg3Qql3JeuKbdc5uklsgQHVMUlKScnNzFRUVVayDzOu9e/eW2HkmKPXOO+9o2rRp+uKLL9S0aVMbpJo9e/ZJO3zMmDGKiIgo3MwMLcDdfbtqj/771Rr7/O5zG+uGbvWc3SQAAFxG6zoRuuf8/AIJj329luUeXoLrC8C71akcqlcGtbOrSyYtjNMXy0ia/lf8/3IPL5yKfXxOnePfK2ACUmYr0K1bN8XHx+uFF17QWWedVeL3jB49Wvfee2/hazODiiAV3NnczUm6Z+oKORzS9V3ratR55GADAOB4I3o31KyNiVq845AdN6cO7yY/35I/Y8KzcH0BeK8+TavrrnMa69VfNttl3i1qhatZjXBnN8tlMYPqmMjISJs76vjZUomJiSfMqjqVrl27avPmzSf9elBQkMLDw4ttgLtaGX9Yt328xCYA7N+6ph6/pNVJA7oAAHgzE4x66ep2qhDkryU7D+mt37c6u0koY1xfADDuOrexejWOVEZ2nk2anpqRTcecBAGqYwIDAxUbG6uZM2cW6yDzunv37jpdpvqfWfoHeLotiWm66cPFOpKVq56NIvXSoLbcCQYA4BSiq4TqiUtb2ucvz9ykVbsO018ejOsLAAU3KF69pr1qRQRre1K6Hvx8lV2phROxxK8Is/RuyJAh6tixo12uZ/JLxcXFacSIEYXL83bv3q0JEybY16bKX7169dSyZUubBHHixIk2H5XZAE+WkHxUQ99fpIPpWWpTJ0JvDYlVkD/VKwEA+CuXta+tX9Yn6rvVCRo1ZYVm3N3LJtOFZ+L6AoBRJSxQb14fq6vemmcLZoyfu1239GpA5xyHAFURgwYN0oEDB/TEE08oISFBrVq10owZMxQTE2O/bt4zAasCJih1//3326BVSEiIDVR99913uuiii47vZ8BjHD6SpRvGL9Luw0fVIDJMH9zYyS5XAAAAf80shX/6slZasvOgtiWla+yvW3T/BX/mNIVn4foCQIF20ZX0n4tb6L9frdWY7zeobXQldapXhQ4qwsfB3DKnMknSTTW/5ORk8lHB5aVn5ui69xZqRfxh1QgP1ue3d7PVKeA5OCe5Lo4N4Fl+WLNXIyYulb+vj51F1SSqotwJ5yTXxbEBXJcJv4yaukJfrdhjl/z9cM9ZCg8OkCdLOYOYBzmoAJyWrJw8+0HaBKciQgI04ebOBKcAAPibLmxVQ+e3iFJOnkOjv1itvDzykQCAN8yifeay1oqpGqo9yRl67Ku1zm6SSyFABeAv5eY5dO+nKzRnc5JCAvz0wU2d3O5OLwAArubxS1oqLNBPS3ce0ieL/0wjAQDwXGFB/raqq6+P9MXy3fp+dYKzm+QyCFAB+MtpqP/39Rp9uypBAX4+NiF6h7qV6TUAAP6hWpVCdF/f/PxT//t+gxJTMuhTAPACsTGVdXufhvb5v6ev5vx/jFtlNp41a5a+/vpr7dmzR8HBwWrYsKH+85//OLtZgEd7+efNmrggTj4+spH+3k2qObtJwBkHWc2a9woVKsjf362GPQBeYGj3epq+fLdW707WE9+u09jBHZzdJK/BtQUAZ7r73CaatXG/1u5J0UPTVun9GzvZJYDezC2SpJsm3nTTTfr444/t8wLm4OXm5ha+TkxMVPXq1eVOSGIIV/bBH9v1+Dfr7PMnB7bSkK75FS3huTzpnDR//nw99thjmjNnjjIzM+17Zow455xzdM0112jAgAFyJ550bAAUt2Z3si4ZO1cmDZWpjnt2M9f/POvO5yRPvrZw92MDeJtN+1J18etzbb7fpy9rpeu6eN71lsclSX/99dc1YcIE+z/17LPP6ocfflCLFi1O2O/JJ59UtWrVtGrVKqe0E/AkXy7fXRicuu/8JgSn4FZ+/fVX9enTRz///LMyMjIKL0D27dunTz75RAMHDlRsbKzWriUxJQDna1U7QsN61LfPH/tmrb1QQdnh2gKAqzB5fR+8IH+p91PfrteOpHR5M7cIUL333nvy9fXVd999pwceeEB9+/ZV5con5sAxd0IOHDig6dOnO6WdgKf4dcM+3f/ZSvv8ph719K9zGjm7ScAZefTRR5Wdna327dvrt99+U1pamn29efNmvfnmm2rXrp2WL1+uLl262LEFAJxt1PlNFFkhSDsPHNGE+Tuc3RyPxrUFAFdiblB0a1BVR7NzbWGqnFzvvUnhFgEqc0FRr149devW7ZT7dejQQRUrVtTMmTPLrW2Ap1m846DumLTMlr2+rH1t/ad/C69fCw33s2LFCoWEhOj7779X7969FRoaam90mNyFI0aM0NKlS/XWW2/ZpRyDBg3S1q1bnd1kAF6uQpC/7u/bxD5//dctOnwky9lN8lhcWwBwJb6+Pnrh6raqGOSvZXGH9fbsbfJWbhGgMgnRzcXF6ahfv77i4+PLvE2AJ1q7J1nDPlysjOw8ndOsup67so09YQLuJjAwUE2bNrXLvk/mtttu09ixY3XkyBE99dRT5do+ACjJVR2j1axGRSUfzdarv2ymk8oI1xYAXE3tSiF67JKW9rk5/2/30qV+bhGgMvmmzJ0Os0TjdC5KTEJDAGfGnASHvr9IqRk56ly/it68roMC/NziFAGcoFmzZqc1Fpil4SaI9dNPP9GLAJzOz9dHj/bPz7P68fyd2rb/rz/74sxxbQHAFV3eobZ6NY60eQj/8+WaYkUcvIVbXH1eddVVtgLT008//Zf77ty50wapAJy+hOSjuv69hUpKy1LLWuF6b2hHBQf40YVwW4MHD9aePXv06aefnnI/s+wvOjpahw4dKre2AcCp9GwcqbObVrNL7cd8v4HOKgNcWwBwRT4+PnpqYCsF+ftq7pYkfbVij7yNWwSozDIMk4Pqueee0zPPPHPSSKLJNbJ//3575xzA6TmYnqUh4xdp9+GjahAZpo+GdVZ4cADdB7d26aWX2oIaZvwwlfxO5ujRo9qyZYsaNaIQAADX8e+LmtvZVDPX7dP8rQec3RyPw7UFAFcVUzVMdx4rUPXUd+u8Lh+hWwSoTP6pr7/+WrVq1dJ//vMfm1dk27b8xGHJyclKSEjQxIkTNXToUBt1NHdFAPy1tMwc3fjBIm1JTFPNiGB9fEsXW0EIcHcNGjTQggULlJKSogsuuEDXXHONfv31V2Vl/TnImyWAQ4YMsfvcc889Zd6m3bt36/rrr1fVqlXtuGYqCZpk7QBwvMZRFTW4c137fMz3671ymUdZ4toCgCu77ayGalS9gl3d8uwP3jWT1sfhRiPevn37NHz4cBusKmACUgXM/0qnTp00Z84ct1nmZy6MIiIibKAtPDzc2c2BF8nIztVNHyzW/G0HVCUsUJ8O72ZPhPBunnJOqlOnjl3iV5QZLwICAlSjRg3l5ORo79698vf315gxY8o8QGWWELZv315nn322br/9dlWvXt1WDjSzg01lQW86NgBOT1Japno9+5stO/7eDR11Xosol+o6TzgneeK1haccG8DbLdp+UFe/Pd8+/3xEN3WsV0Xu6kzOSW4VoCqwZMkSffLJJ/rtt9/sHWmTPL1u3bq68sor9fDDDyssLEzuggEEzpCTm6fbJy2zSwdMWetPbu2q1nUiOBjwqHOSCQqtWrVKK1euLHxct26dXdZXlLkYMQGt1q1bq1WrVoWbSaJbWhckZmz6448/7EXO3+VJxwbA6TGzp97+fZta1Q7XN//qWSx44myedE7ypGsLTzs2gDd76PNVmrokXk2iKujbO3sp0N8tFsB5X4DKkzCAoLzl5Tn0wOerNG3ZLnuSmzCss7o2qMqBgFeck/Ly8rRp06ZigSuzxcfHF+5TcAHo5+dXbEngP2GCXWap4a5du/T777+rdu3auuOOO3Trrbee9HtMcRCzFT02JqG7px4bACXniez57K86kpWrd2/oqPNdaBaVp48X7oxjA3iGQ+lZOvel3+1Y8OCFTXVHn0Yef05yzxAcgL/FxKOf+HadDU6Z5KtvDu5AcApexVTtM4U0rr76alsZ9ptvvrHVXw8ePKhZs2bp1Vdf1bBhw9ShQwe7HLC0mLyJ48aNU+PGjfXjjz9qxIgRuuuuuzRhwoSTfo9ZemgG84LNBKcAeBezBH9o93r2+Ss/byIXFQB4kcphgXq0f3P7/LVfNtvK656OGVROxh0OlKeXZm6yJzfj5UFtdVn7OhwAcE46RUC3tJbTmKWCHTt21Lx58wrfMwGqxYsXa/78/PwCx2MGFYCCO+hmFlV6Vq7eHhKrC1rWcImO4TOs6+LYAJ71efTqt+dr8Y5DurxDbb10dTu5G2ZQATjBe3O2FQannri0JcEp4C+UZq6XmjVr2mV+RTVv3lxxcXEn/Z6goCA7DbroBsA776Df2KNgFtVmu1QfAOA9n0cf7Z//GfKLZbu1atdheTKW+AFeYOriOD313Xr7/IELmuqGbvkfdAGUjx49emjjxo3F3jO5sGJiYjgEAP7SLT0b2KIm6xNS9PP6ffQYAHiRttGVdFn72va5uabz5DTiBKgAD/ftqj16+IvV9vnw3g10R5/TK2kPoPTcc889WrBggZ555hlt2bJFkydP1jvvvKORI0fSzQBOaxbVkG75Ae1352yjxwDAyzxwQVMFB/hq0faD+nGt596oIEAFeLDfNibqnqkrZILs13auq4cvbOZSJaoBb9GpUydNnz7dljFv1aqVnnzySb3yyiu67rrrnN00AG7ixu71FODnY/OQLI875OzmAADKUa1KIbqtVwP7fMz365WZk+uR/U+ACvBQJrp++8Slys51aEDbWnpqYCuCU4ATXXzxxVq9erUyMjK0fv163XrrrRwPAKctKjxYl7TNX+Lx3pzt9BwAeJnhvRuqWsUg7TxwRB/P3ylPRIAK8EBrdifr5g8XKyM7T+c0q66Xrm4rP19mTgEA4M5uPau+ffx+TYLiDx5xdnMAAOUoLMhfD/Rtap+/+stmHUzP8rj+J0AFeJjN+1J1w/uLlJqZoy71q+jN6zoowI8/dQAA3F2zGuHq1ThSppDf+LnMogIAb3NFbB01rxmu1Iwcvf5rfoV2T8JVK+BB4g4c0fXjF9poeps6EXpvaEcFB/g5u1kAAKCU3HZWfg6ST5fEK/lINv0KAF7Ez9dH/76omX0+aWGc9iZnyJMQoDrOm2++qfr16ys4OFixsbGaM2fOaXXkH3/8IX9/f7Vr164sjhPwlxKSj2rwewu0LyVTTaMq6qObOqticAA9BwCAB+nZKFLNalTUkaxcTVkc5+zm4DRwfQGgtMeBzvWqKCsnT2/8tsWjOpcAVRFTp07VqFGj9Mgjj2j58uXq1auX+vXrp7i4Uw/+ycnJuuGGG3TuueeW9fECSpSUlqnr3luoXYeOql7VUH18S2dbkhoAAHgWU433ph717PNPFsUpz6z3g8vi+gJAWYwD95zfxD43Nyp2Hz7qMZ1MgKqIl156STfffLNuueUWNW/e3JYAj46O1rhx407ZicOHD9fgwYPVrVu3sj5ewAnM9P4h4xdp2/501YoI1sRbuqh6xWB6CgAAD2Wq81YM8teOA0c0b+sBZzcHp8D1BYCy0K1hVXVvWNVWbB/rQbmoCFAdk5WVpaVLl6pv377FOsi8njdv3kk78IMPPtDWrVv1f//3f6fV4ZmZmUpJSSm2AX9XWmaObvxwkdYnpCiyQpAm3dpVdSqH0qEAAHiw0EB/Xdahtn0+aaFnlhr3BFxfAChL9xybRfXZkl02F7EnIEB1TFJSknJzcxUVFVWsg8zrvXv3lth5mzdv1sMPP6xJkybZ/FOnY8yYMYqIiCjczAwt4O/IyM7VrR8t0fK4w6oUGqCJt3RW/cgwOhMAAC8wuEtd+zhz3T4lpnhWklxPwfUFgLLUqV4VW9k1J8/hMRX9CFCVsJ6zKIfDccJ7hglmmWV9jz/+uJo0yY9cno7Ro0fbnFUFW3x8/N89dvBiJiHeHZOWaf62A6oQ5G8TopvS0wAAwDuYcT82prK9MDEV/eC6uL4AUFbuPTaL6ovlu7U9Kd3tO5oA1TGRkZHy8/M7YbZUYmLiCbOqjNTUVC1ZskT/+te/7Owpsz3xxBNauXKlff7rr7+W2OFBQUEKDw8vtgFnIic3T/dMXaFfNyQqOMBX44d2VNvoSnQiAABe5rpjs6g+WRSvXJKluxyuLwCUtfZ1K+ucZtXtGOAJs6gIUB0TGBio2NhYzZw5s1gHmdfdu3c/oeNMYGn16tVasWJF4TZixAg1bdrUPu/SpUv5HEF4FVOp58Fpq/Td6gQF+vnq7SEd1aVBVWc3CwAAOMFFrWsqIiTAVnCatzWJY+BiuL4AUB7uPrexffx6xR7tcfOKfqeXOMlL3HvvvRoyZIg6duxoK/K98847iouLs4GnguV5u3fv1oQJE+Tr66tWrVoV+/7q1asrODj4hPeB0mCWmz761Rp9sWy3/Hx9NHZwe/VuUo3OBQDASwUH+GlA25qauCBO05ftVq/GfC5wNVxfAChrbaMrqVuDqjb9y/tzt+vRi1u4bacToCpi0KBBOnDggF2ql5CQYANNM2bMUExMjP26ec8ErABnBKee/Ha9Ji+Mk0mJ9vKgdurbsgYHAgAAL3dZ+9o2QPXD2r16KivHVviD6+D6AkB5GN67gQ1QfbIoTnee01gRoQFu2fE+DnPlC6dJSUmx1fxMwnTyUeFkXvhxo8b+tsU+f+7KNrq6I9UfwTnJ2zBeACiJ+Sjf54VZ2nngiF4e1FaXta/DOcnLMV4A3jkW9Ht1jjbsTdUDFzTVyLMbyR3PSeSgAlzc2F83Fwannry0JcEpAABQrELcwHa17XOTBgAA4J1jwfDeDezzD/7YoYzsXLkjAlSAC3tvzja98NMm+/zfFzXTkG71nN0kAADggsv8jD+2JCkxJcPZzQEAOMHFbWqpdqUQJaVlavpy97xhQYAKcFGTFu7UU9+tt8/vOa+JbjurobObBAAAXFC9yDB1qFtJeQ7p65V7nN0cAIATBPj56uae9e3zd2dvU64ZFNwMASrABX22JF6PTF9jn4/o3VB3nes6a4gBAIDrufTYMr8ZqxOc3RQAgJMM6hStiJAAbUtK168bEt3uOBCgAlzMVyt268Fpq+zzG7vX00MXNrVrigEAAE7mwlb51X2XxR1WQvJROgoAvFBYkL+u6ZRfUGvC/B1yNwSoABdi7nre++lKmdqag7vU1f8NaEFwCgAA/KWo8GB1jKlsn/+4Zi89BgBe6vquMTLzG+ZsTtK2/WlyJwSoABfx09q9uuuT5Xat8FWxdfTUpa0ITgEAgDOeRTWDABUAeK3oKqE6p2l1+3zigji5EwJUgAv4bWOiRk5eppw8hwa2q6X/XdFGvr4s6wMAAKevX+ua9nHxjoPan5pJ1wGAlxrSLcY+frY0XkeycuQuCFABTjZ3c5KGf7xU2bkO9W9dUy9c1VZ+BKcAj/LYY4/ZGZFFtxo18mc6AEBpMeXF29aJsKkCflzLMj8A8FZnNa6melVDlZqRoy+Xu091VwJUgBMt2HZAt0xYrKycPJ3fIkqvXNNO/n78WQKeqGXLlkpISCjcVq9e7ewmAfBAFxxb5vfz+n3ObgoAwEl8fX1sLqqCZOkOc+fCDXAlDDjJkh0HNezDxcrIztPZTatp7OD2CiA4BXgsf39/O2uqYKtWrZqzmwTAA53bLMo+zt96QEezcp3dHACAk1wVG63gAF9t2JuqJTsPucVxIEAFOMHSnYc09P1FOpKVq56NIjXu+lgF+ftxLAAPtnnzZtWqVUv169fXNddco23btjm7SQA8UJOoCnapX2ZOnuZtTXJ2cwAAThIRGqBL2tayzz9dHO8Wx4EAFVDOVsQf1o3vL1J6Vq66N6yqd2/oqOAAglOAJ+vSpYsmTJigH3/8Ue+++6727t2r7t2768CBAyf9nszMTKWkpBTbAOCvmBx3ZzfLn6H564ZEOgwAvNjVHaPt43erE5Se6frJ0glQAeVo1a7DGjJ+oVIzc9S1QRW9N7SjQgIJTgGerl+/frriiivUunVrnXfeefruu+/s+x999NFJv2fMmDGKiIgo3KKj8z9gAMBfOadZfnnx3zYkuk3eEQBA6YuNqawGkWF25Y4JUrk6AlRAOVmzO1nXv7fQVlLoXK+Kxg/tpNBAf/of8EJhYWE2WGWW/Z3M6NGjlZycXLjFx7vH1GwAztetQaSC/H21JzlDG/elOrs5AAAnzqq9smMd+/yzJa7/WZIAFVAO1u5J1nXvLVRKRo46xlTW+zd1UlgQwSnAW5nle+vXr1fNmjVPuk9QUJDCw8OLbQBwOszs7G4Nq9rnszftp9MAwItd0aGOfH2kxTsOadv+NLkyAlRAGVufkGJnTiUfzVb7upX0wU2dVIHgFOBV7r//fv3+++/avn27Fi5cqCuvvNLmlBo6dKizmwbAQ5kiLMYfW06e6w4A4PmiwoPVu0l+bsLPl+6SKyNABZShDXtT7MypQ0ey1Ta6kj4a1lkVgwPoc8DL7Nq1S9dee62aNm2qyy+/XIGBgVqwYIFiYmKc3TQAHqrHsQDVou0HlZWT5+zmAABcIFn6tGW7lJvnurkJWWMElGFwavC7C3UwPUtt6kRowrDOCic4BXilKVOmOLsJALxM06iKiqwQqKS0LC2PO6QuDfKX/AEAvM+5zaNUKTRA+1IytXDbAXU/dhPD1TCDCiijZX1Fg1MfD+uiiBBmTgEAgPLh6+ujbg2PLfPbyjI/APBmgf6+6teqhn3+9co9clUEqIAyCE6ZZX3FglOhBKcAAED56tkof9bUH1uS6HoA8HID2tayj9+v2euyS78JUAGlPnNqwZ/BqZsJTgEAAOfofmwG1apdh3U0K5fDAABerEv9qqpeMcgW73LVCq8EqIBSDk6ZhOiFwSmW9QEAACepUzlENcKDlZ3r0Ir4wxwHAPBifr4+urhN/iyqr1x0mR8BKqCUg1NtCU4BAAAX4OPjo071q9jni3ccdHZzAABOdkm7/ADVz+v26UhWjlwNASrgH1q7J7lYcGoCM6cAAICL6FSvsn0kQAUAaFsnQnWrhOpodq5+Xp/och1CgAr4B1bvMsGphfnBqehKBKcAAIBL6VQvfwbVsp2HlJPrmklxAQDlw8ys7d+mpn3+45q9LtftBKiO8+abb6p+/foKDg5WbGys5syZc9LOmzt3rnr06KGqVasqJCREzZo108svv1zWxwwuYnncIQ1+b4FNMtehbiV9fHNnck4BAACX0jSqosKD/ZWelav1CanObo5X4voCgCu5oGUN+zhrY6Iysl2rgAYBqiKmTp2qUaNG6ZFHHtHy5cvVq1cv9evXT3FxcSV2XlhYmP71r39p9uzZWr9+vR599FG7vfPOO+V1/OAkS3ce1JDxi5SakWOnzptlfeHBARwPAADgUnx9fdSubv4yvxXxh5zdHK/D9QUAV9OmdoQtoGFuXPyxJUmuxMfhcDic3QhX0aVLF3Xo0EHjxo0rfK958+YaOHCgxowZc1o/4/LLL7eBq48//vi09k9JSVFERISSk5MVHh7+t9uO8rNo+0Hd9MEi+wfdtUEVjR/aSWFB/hwCeATOSa6LYwPg73pp5ia99stmXdGhjl68ui3npHLE9QUAV/Tfr9ZowvydurpjHT13ZemMC6XxGZYZVMdkZWVp6dKl6tu3b7EOMq/nzZt3Wh1vZl2ZfXv37n3SfTIzM+0BKrrBfczfekBD388PTvVoVFUf3NiZ4BQAAHBp7aIj7CMzqMoX1xcAXH2Z38/rE10qPyEBqmOSkpKUm5urqKioYh1kXu/de+rkYXXq1FFQUJA6duyokSNH6pZbbjnpvmYmlokeFmzR0dGlcRxRDuZuTtJNHy6yFQ/OalLNzpwKCfSj7wEAgEtrW6eSfdy6P93mzkT54PoCgKvqXL+KKoUG6GB6lhbvcJ3l3wSoSshqX5RZAXn8e8czidSXLFmit956S6+88oo++eSTk+47evRoO7WtYIuPj/8nxw/l5NcN+zTso8XKyM7T2U2r6Z0hsQoOIDgFAABcX9UKQYquEmKfr9p12NnN8TpcXwBwNQF+vjqnWXX7/Jf1++QqSJxzTGRkpPz8/E6YLZWYmHjCrKrjmap/RuvWrbVv3z499thjuvbaa0vc18y0Mhvcxw9rEnTnJ8uVnetQ3xZRen1wewX5E5wCAADuNYsq/uBRrd6drF6Nqzm7OV6B6wsAruzcZlH6Ytlu/bYxUY9e3EKugBlUxwQGBio2NlYzZ84s1kHmdffu3U+7Q82MK5NnCp7hqxW7NXJyfnBqQNtaeuO6DgSnAACA22lZKz8P1do95D8tL1xfAHBlPRtHys/Xxy7/jjtwRK6AGVRF3HvvvRoyZIjNJdWtWze98847iouL04gRIwqX5+3evVsTJkywr9944w3VrVtXzZo1s6/nzp2rF154QXfeeaczjiVK2adL4vXQtFUydS6vjK2jZ69oY/+AAQAA3E2r2vmVk9YRoCpXXF8AcFURIQGKjalsq9TP2pSoG7rVc3aTCFAVNWjQIB04cEBPPPGEEhIS1KpVK82YMUMxMTH26+Y9E7AqkJeXZ4NW27dvl7+/vxo2bKj//e9/Gj58eLkfSJSujxfs1H++XGOfX9elrp68tJV8CU4BAAA3n0G1PSldaZk5qhDEferywPUFAFd2TrPqNkD16wbXCFD5OMyaNDhNSkqKreZnEqaHh+ff2YJzvTdnm576br19PqxHff3n4uZ/mSgf8BSck1wXxwbAP9VtzC9KSM7QZyO6qVO9KpyTPBTjBYDTtXFvqi54ZbaC/H214r99y6RK/Zmck8hBBRxjYrWv/ry5MDg18uyGBKcAAIDHaFmLZX4AgD81iaqgWhHByszJ04LtB+RsBKiAY8GpZ2as18s/b7L9cX/fJnrggmbMnAIAAB6jaY2K9nHjvlRnNwUA4AJ8fHwKK7vO25Lk7OYQoAJy8xz69/Q1enfOdtsZ/zeghf51TmM6BgAAeJQmUfkBqk17CVABAPL1aBxpH+duYQYV4FTZuXm699MV+mRRnEwO9OeuaKObetTnqAAAAI+eQUUaWgCA0b1hVfu4PiFFSWmZciaW+MFrZWTn6vaJy/TVij3y9/XRa9e219Wdop3dLAAAgDLRILKC/cyTmpFjk6UDABBZIUjNa+bnKJy31bmzqAhQwSulZ+bo5o8W6+f1+xTo76t3bojVxW1qObtZALzEmDFj7Jr/UaNGObspALyI+cxTLzLMPt9EHioAwDE9G+XPopq7eb+ciQAVvM7hI1m67r2F+mPLAYUG+unDmzrpnGZRzm4WAC+xePFivfPOO2rTpo2zmwLACzWqVsE+btuf7uymAABcRPdG+XmoFmw76NR2EKCCV9mXkqGr356vFfGHVSk0QJNv7aruDfP/GAGgrKWlpem6667Tu+++q8qVK9PhAMpdw+r5M6i27k+j9wEAVseYyjYnc9zBI0pIPipnIUAFr7HzQLqufGueNu1LU1R4kD4d3k3tois5u1kAvMjIkSPVv39/nXfeeX+5b2ZmplJSUoptAPBPNTw2g4oAFQCgQMXgALWsFWGfL9ruvFlUBKjgFUxFgivfmq/4g0cVUzVUn4/oXlhqGQDKw5QpU7Rs2TKbf+p0mP0iIiIKt+hoijgAKM0AFUv8AAB/6ly/in1cSIAKKDtLdx7SoLfna39qpprVqKjPRnRTdJVQuhxAuYmPj9fdd9+tiRMnKjg4+LS+Z/To0UpOTi7czM8AgH+qfrX8JX7mc1FaZg4dCgCwuhQEqLY5r5Kfv9P+ZaAc/LYxUbdPXKqM7DzFxlTW+zd2UkRIAH0PoFwtXbpUiYmJio2NLXwvNzdXs2fP1tixY+1yPj8/v2LfExQUZDcAKE3hwQGqGhaoA+lZNv1BwZIOAIB361SvSuEM26S0TEVWKP/PoSzxg8f6Ytku3frREhuc6t2kmj6+uTPBKQBOce6552r16tVasWJF4daxY0ebMN08Pz44BQBlyaQ7MHYeOEJHAwCsymGBalQ9fxn48rjDcgZmUMEjvTt7m56esd4+v6x9bT13ZRsF+BGPBeAcFStWVKtWrYq9FxYWpqpVq57wPgCUtXpVw7Qs7rB2HCAPFQDgT7F1K2tLYppNk3N+iyiVN67Y4VEcDofGzFhfGJy6pWd9vXhVW4JTAAAAx8RUzc9DtTOJGVQAgD91iMmvcr8s7pCcgRlU8BjZuXl6eNpqTVu2y75+uF8zDT+rgXx8fJzdNAA4waxZs+gVAE4RXSXEPu46TIAKAPCnDnUr28dVuw7b6+vyXoXEDCp4hCNZObptwhIbnPLz9bFL+kb0bkhwCgAA4Dh1KufnoIo/eJS+AQAUalitgsKD/W0e5w0JqSpvBKjg9kyFgWvfWaDfNu5XcICv3r4+Vld3jHZ2swAAAFx6BtWew0eVm+dwdnMAAC7C19dHbaPzl/mt3FX+idIJUMGtmfLIV46bp5W7klU5NECTbumq85yQzA0AAMBdRFUMVoCfj3LyHNqbkuHs5gAAXEjbOpUKl/mVNwJUcFsr4w/r8jfnaceBI6pTOUSf395dsTH5a2YBAABw8jvkNSP+nEUFAECB1nUi7OOqXckqbwSo4JZ+25ioa95ZoAPpWWpZK1xf3NHdrpcFAADAX6sZEWwfCVABAEqaQbVpX6qOZuWqPBGggtv5ZFGcbvloiY5m56pX40hNHd5N1Svmf8gCAADAX6tVKX8GVUIyS/wAAH+qERGs6hWDZFIUrt1TvrOoCFDBbTgcDj3/4waN/mK1Teh5efvaGj+0kyoE+Tu7aQAAAG6lViVmUAEAStaqdv4yv7V7UlSeCFDBLWTm5GrU1BV647et9vVd5zbWi1e3VaA/v8IAAABnqkZ4foBqLzOoAADHMWl0jHXlHKBi6glc3uEjWbrt46VatP2g/H199MzlrXV1x2hnNwsAAMBtVT8WoNqXmunspgAAXEyLmvkBqrUJ5bvEjwAVXFrcgSO66cNF2ro/XRWD/DXu+lj1bBzp7GYBAAB4xAyqfcygAgAcp2Wt/CV+m/amKTs3TwF+5bNyifVRx3nzzTdVv359BQcHKzY2VnPmzDlp533xxRc6//zzVa1aNYWHh6tbt2768ccfy/qYeY0lOw5q4Jt/2OCUqTTz2e3dCE4BAACUgqhjAar9aZnKM5lwUWa4vgDgbqKrhNgJIlm5edq6P63c/l0CVEVMnTpVo0aN0iOPPKLly5erV69e6tevn+Li4krsvNmzZ9sA1YwZM7R06VKdffbZGjBggP1e/DNfrditwe8u1MH0LLWuHaEvR/ZQsxr50wwBAADwz1StECgfH9nCMwePZNGdZYTrCwDuyMfHR01qVLTPN+5NLb9/12FKo8Hq0qWLOnTooHHjxhX2SPPmzTVw4ECNGTPmtHqpZcuWGjRokP773/+e1v4pKSmKiIhQcnKynYXl7cyv46u/bNYrP2+2r/u2iNIr17RTaCCrUYHywDnJdXFsAJS22Cdn6kB6lr6/u5eaH8s3wjmpdHF9AcBd/Xv6ak1eGKfb+zTUQxc2K5fPsMygOiYrK8vOgurbt2+xDjKv582bd1odn5eXp9TUVFWpUuWk+2RmZtoDVHRDvozs/Ep9BcGp4Wc10FvXxxKcAgAAKAPVKgbZx/0kSi8TXF8AcGfNnDCDigDVMUlJScrNzVVUVFSxDjKv9+7de1qd+eKLLyo9PV1XX331SfcxM7FM9LBgi46mGp2RmJqha95ZoK9W7LGV+sZc3lqjL2ouX1+fv//bDQAAgJOKrJAfoDqQTiW/ssD1BQB31jSKAJVLrLU8fsnZ8e+V5JNPPtFjjz1m15lXr179pPuNHj3aTm0r2OLj4+Xt1uxO1qVj/9CK+MOKCAnQR8M669rOdZ3dLAAAAI/PQ2UcSCMHVVni+gKAO2pUvYJ93H34qI5k5ZTLv0lin2MiIyPl5+d3wmypxMTEE2ZVHc8EpW6++WZ99tlnOu+88065b1BQkN2Q7/vVCbr305U6mp2rBtXCNH5oJ9WPDKN7AAAAyljVsGNL/NKYQVUWuL4A4M6qVghSlbBAW7hs2/50taodUeb/Jkv8jgkMDFRsbKxmzpxZrIPM6+7du59y5tSNN96oyZMnq3///mV7tDyIKWf82i+bdfukZTY41atxpKbf0YPgFAAAQDnPoDqUzgyqssD1BQB316ha/iyqLYlp5fLvMYOqiHvvvVdDhgxRx44d1a1bN73zzjuKi4vTiBEjCpfn7d69WxMmTCgMTt1www169dVX1bVr18LZVyEhITa/FEqWnpmj+z5dqR/W5vfXjd3r6dH+zeXvR7wUAACgvFQOzQ9QHUzPptPLCNcXANxZw+oVtGjHQQJUzjBo0CAdOHBATzzxhBISEtSqVSvNmDFDMTEx9uvmPROwKvD2228rJydHI0eOtFuBoUOH6sMPP3TK/4OriztwRLdOWKKN+1IV4Oejpwa20qBO5JsCAAAob1XCAuzjQZKklxmuLwC4s4bV8tPvbE9KL5d/z8dhsoDDaVJSUuxsK5MwPTw83KOPxNzNSfrXJ8t0+Ei2LWv81vWxio2p7OxmAfDSc5K74dgAKG3ztx7Qte8usBcgv9zXh3OSh2C8AFBaflm/Tzd/tETNa4br+7t7lfk5iSV+KHMmBvrO7G169ocNynNIbaMr6e3rY1UjIpjeBwAAcJLKx2ZQJR9liR8A4EQNjuWg2p6UZvNI+/r6qCwRoEKZSsvM0UOfr9J3qxPs6ys61NHTl7VScIAfPQ8AAOBEESH5ASozu93cUPTxKdsLDwCAe6lTOUR+vj7KyM5TYmpmmU8yISs1yszW/Wm67I0/bHDK5Jt6cmArvXBVG4JTALzOuHHj1KZNGzut2WymEMf333/v7GYB8HIFAaqcPIeOZOU6uzkAABcT4Odrg1TGzgNln4eKABXKxA9rEjRw7B/anJim6hWDNOW2rhrSNYY7cwC8Up06dfS///1PS5Yssds555yjSy+9VGvXrnV20wB4sZAAP/kfW67BMj8AQEliquYnSt9RDgEqlvihVGXn5unZ7zfovbnb7evO9apo7HXtVb0i+aYAeK8BAwYUe/3000/bWVULFixQy5YtndYuAN7NLOkLDwnQwfQspWRkq5by75IDAFCgbpX8sSH+4FGVNQJUKDV7kzM0cvIyLd15yL4eflYD3X9BUzstEACQLzc3V5999pnS09PtUr+TyczMtFvRCigAUNrCg/1tgCotI4fOBQCcoG6VUPsYd/CIyhoBKpSKWRsTde+nK+0HnIpB/nrh6ra6oGUNehcAjlm9erUNSGVkZKhChQqaPn26WrRocdL+GTNmjB5//HH6D0CZqhCcfzmQSoAKAFCC6MrlF6Biagv+kRyzpO+HDbrxg8U2ONWiZri+vasnwSkAOE7Tpk21YsUKu6zv9ttv19ChQ7Vu3bqT9tPo0aOVnJxcuMXHx9OnAEpdhSD/wsrLAAAcr86xANXuwyzxgwvbc/io7vpkuZYcW9JnkqA/0r85VfoAoASBgYFq1KiRfd6xY0ctXrxYr776qt5+++0S+ysoKMhuAFAeASpmUAEASlL7WBW//amZysjOLdPrfZb44W+ZsTpBD09bpZSMHLuk739XtFH/NjXpTQA4TQ6Ho1iOKQBwhrBjAaojWcygAgCcqHJogEID/XQkK9dOUmlQrYLKCgEqnBHz4eWJb9ZpyuL8pSZt60To9Ws7qG7V/Gl/AIAT/fvf/1a/fv0UHR2t1NRUTZkyRbNmzdIPP/xAdwFwqtBAlvgBAE5d8bVWpRBtSUxTQnIGASq4hpXxh3XP1BXalpQuHx/p9t4Ndc/5TajSBwB/Yd++fRoyZIgSEhIUERGhNm3a2ODU+eefT98BcKqwwPylGkezcjkSAIAS1YwItgGqss5DxQwqnFYi9Dd+26rXft2s3DyHaoQH66VBbdW9YSS9BwCnYfz48fQTAJdklm0YR7MJUAEATh6gMvYlZ6gsEaDCKZko6f2frdSK+MP29cVtauqpga1UKTSQngMAAHBzwccCVCa3CAAAJakRkZ8oPSGFABWcwMyUem/ONr04c5OycvIUHuyvJwe20qXtanM8AAAAPESwf36AylRmAgCgJGYVlcEMKpS7jXtT9dC0VYWzpno3qab/XdFaNY9FTQEAAOAZCsqFZ2TnObspAAAXFRUeZB/3pTKDCuUkMyfX5poaN2uLsnMdqhDkr/9e3EJXdaxjM/cDAADAswQH+BZ+DgQAoCRRx2ZQJaZkqiyRgwrW3M1J+s9Xa7Q9Kd2+Pq95dbukj1lTAAAAnivo2BK/zBxmUAEASlatYv4MqqS0TJsOyM+3bCawEKDycqZM5JgZ6/XtqoTCX7zHBrTURa1rMGsKAADAwwX658+gMjlHAQAoSdWwQJlFVXkO6dCRLEVWyA9YlTYCVG5oWdwh/bxun67pVFd1q4b+rZ+Rnpmjt2dv0zuzt9qcAyYAekO3erq3bxOFBweUepsBAADgeghQAQD+ir+frxyO/Ocf/rFD91/QVGWBAJUbeuHHjZq39YCqhAXqll4Nzuh7zd2xqYvj9OovW+z0PKNz/Sr6vwEt1LJWRBm1GAAAAK4o4NgyjexcZlABAP7a2N+2EKDCny5sVcMGqKYujtdNPeqf1vpPUzr4syXxGjdrq/Yk52fej6kaqocubKZ+rVjOBwAA4K13xQ2TUwQAAGdiBpUbGti+tp7/caM2J6bp3TnbNKJ3w5PuG3fgiKYsjtOUxfE6mJ5l36teMUgjz26kazvXLZzWDQAAAO9TcKMzO48ZVACAkwvw81F2btnezCBA5YZMjqiH+zXTI9PX6H/fb9CuQ0dsPqroyqHKyMnVtv3pWrLjoH7ZkKgV8YcLv69O5RDd2quBBnWKVnBAfsUWAAAAeC//YwEq4lMAgFMxKYb2peSnCSorBKjc1ODOdbXr0FG7ZG/igji7lcR85ujRKFLXdamr85pHFU7jBgAAAHx9jgWoCrLfAgBQgrZ1KumndftUlghQuSkfHx+bP6pXo0i9/8d2Ldx+UKkZOTYgVatSiFrXjrCBqb4tolQ9PNjZzQUAAIALOhafAgDglO48p7EW7Tio20+RYuifYjrNcd58803Vr19fwcHBio2N1Zw5c07aeQkJCRo8eLCaNm0qX19fjRo1SuWte6NIvTe0k1Y/doE2PdVPW56+SHMfOkfjro/V9V1jCE4BAADgpFrUDNeGJy/Ub/f3oZfKiLtdXwBASVrXidCK//bVcAJU5WPq1Kl2EHjkkUe0fPly9erVS/369VNcXMnL5zIzM1WtWjW7f9u2beVsJuG572lU9AMAAAAM89nR5CYlP2nZcPfrCwAoTz4OBwvOC3Tp0kUdOnTQuHHjCt9r3ry5Bg4cqDFjxpyyI/v06aN27drplVdeOaMDkJKSooiICCUnJys8PPxvHEIAKD2ck1wXxwaAK+GcdHq4vgDg7VLOIObBEr9jsrKytHTpUvXt27dYB5nX8+bNK7WDY+6KmANUdAMAAADgWbi+AIAzQ4DqmKSkJOXm5ioqKqpYB5nXe/fuVWkxM7FM9LBgi46OLrWfDQAAAMA1cH0BAGeGAFUJ1fGKMisgj3/vnxg9erSd2lawxcfHl9rPBgAAAOBauL4AgNPjf5r7ebzIyEj5+fmdMFsqMTHxhFlV/0RQUJDdAAAAAHguri8A4Mwwg+qYwMBAW/Z15syZxTrIvO7evfsZdisAAAAAb8b1BQCcGWZQFXHvvfdqyJAh6tixo7p166Z33nnHloAdMWJE4fK83bt3a8KECYXfs2LFCvuYlpam/fv329dmMGrRosUZHgoAAAAAnoTrCwA4fQSoihg0aJAOHDigJ554QgkJCWrVqpVmzJihmJgY+3XznglYFdW+ffvC56YK4OTJk+3+O3bsOIPDAAAAAMDTcH0BAKfPx2GygMNpUlJSbDU/kzA9PDycIwHAqTgnuS6ODQBXwjnJdXFsALjrOYkZVE5WEB80Bw0AnK3gXMS9C9fDeAHAlTBeuC7GCwDuOl4QoHKy1NRU+xgdHe3spgBAsXOTudMB18F4AcAVMV64HsYLAO46XrDEz8ny8vK0Z88eVaxYUT4+Ps5ujstEWE3ALj4+nmWP9Au/M+X8t2TubJjBo1atWvL1pdCru48XnE/PHH1Gn5UHT/g9Y7xwXYwX5cMT/o7LG33mnf3lOIPrC2ZQOZk5QHXq1HF2M1yS+SN05z/EskK/0Ddl/TvDzCnPGy84b9Bn5YHfM+/rM8YL18R4Ub7c/e/YGegz7+uviNNcmcHtcQAAAAAAADgVASoAAAAAAAA4FQEquJygoCD93//9n30E/cLvDH9L4HeAMci1MW7TZ3B//B3TZ/yeuZ4gL7wuJkk6AAAAAAAAnIoZVAAAAAAAAHAqAlQAAAAAAABwKgJUAAAAAAAAcCoCVAAAAAAAAHAqAlRwSWPGjJGPj49GjRrl7Ka4hN27d+v6669X1apVFRoaqnbt2mnp0qXyZjk5OXr00UdVv359hYSEqEGDBnriiSeUl5cnbzN79mwNGDBAtWrVsn83X375ZbGvOxwOPfbYY/brpq/69OmjtWvXOq29KF1vvvmm/TsIDg5WbGys5syZc8r9f//9d7uf2d/83bz11lted0jOpM9mzZpl/66O3zZs2CBv8Ffnl5J4++/YmfaZt/+OofwwXpRtn3n73zLjRdn32Swv+B0jQAWXs3jxYr3zzjtq06aNs5viEg4dOqQePXooICBA33//vdatW6cXX3xRlSpVkjd79tln7UXP2LFjtX79ej333HN6/vnn9frrrzu7aeUuPT1dbdu2tX1REtM3L730kv26+fuqUaOGzj//fKWmppZ7W1G6pk6dagP5jzzyiJYvX65evXqpX79+iouLK3H/7du366KLLrL7mf3//e9/66677tK0adO85tCcaZ8V2LhxoxISEgq3xo0byxv81fnlePyOnXmfefvvGMoH40XZ95m3/y0zXpR9n3nF75gDcCGpqamOxo0bO2bOnOno3bu34+6773Z4u4ceesjRs2dPZzfD5fTv398xbNiwYu9dfvnljuuvv97hzcxpffr06YWv8/LyHDVq1HD873//K3wvIyPDERER4Xjrrbec1EqUls6dOztGjBhR7L1mzZo5Hn744RL3f/DBB+3Xixo+fLija9euXnNQzrTPfvvtN/t3dejQIYe3O/78UhJ+x868z/gdQ3lgvCj7PuNv+U+MF2eO8SIfM6jgUkaOHKn+/fvrvPPOc3ZTXMbXX3+tjh076qqrrlL16tXVvn17vfvuu/J2PXv21C+//KJNmzbZ1ytXrtTcuXPt7BAUn82wd+9e9e3bt/C9oKAg9e7dW/PmzaOr3FhWVpZd6lv02Brm9cmO7fz580/Y/4ILLtCSJUuUnZ0tT/d3+qyAOffWrFlT5557rn777bcybqn78vbfsX+C3zGUFcaL8umzAvwtnx7Gi7+vvQd/JiFABZcxZcoULVu2zOafwp+2bdumcePG2ambP/74o0aMGGGX5EyYMMGru+mhhx7Stddeq2bNmtnlj+ZEbaZhm/fwJxOcMqKioop1i3ld8DW4p6SkJOXm5p7RsTXvl7S/yelmfp6n+zt9Zj4AmmXnZhnkF198oaZNm9oPhCZvBE7k7b9jfwe/YyhrjBfl02f8LZ8ZxoszV9MLPpP4O7sBgBEfH6+7775bP/30k01CiD+ZpN9mBtUzzzxjX5tAjElwbYJWN9xwg9d2lckLMHHiRE2ePFktW7bUihUrbIDKJBkcOnSos5vnckwCxaLMTOLj34N3HNuS9i/pfU92Jn1mPvyZrUC3bt3smPXCCy/orLPOKvO2uiN+x84Mv2MoL4wXZdtn/C2XTv+W9D6853eMGVRwCWYKbWJioq2O4e/vbzdTBei1116zz80dDG+OlLdo0aLYe82bN//LBI2e7oEHHtDDDz+sa665Rq1bt9aQIUN0zz33MAPvOCYhunH83T7z93b8XUG4l8jISPn5+Z3RsTW/DyXtb86zpkqop/s7fVaSrl27avPmzWXQQvfn7b9jpYXfMZQmxovy6bOS8Ld8cowXpaOrh30mIUAFl2CmJq5evdrOginYzKyh6667zj43A4S3MhX8TKWGokzepZiYGHmzI0eOyNe3+CnM/J6YGWf4kymNbD4AzJw5s1heBRMA7t69O13lxgIDA21Qv+ixNczrkx1bc6ft+P3NzFVzvjVLZT3d3+mzkphqTubmAU7k7b9jpYXfMZQmxovy6bOS8Ld8cowXpWO5p30mOZYsHXA5VPHLt2jRIoe/v7/j6aefdmzevNkxadIkR2hoqGPixIkObzZ06FBH7dq1Hd9++61j+/btji+++MIRGRlpK0h5Y/XL5cuX282c1l966SX7fOfOnfbrpoKfqdpn+mj16tWOa6+91lGzZk1HSkqKs5uOf2jKlCmOgIAAx/jx4x3r1q1zjBo1yhEWFubYsWOH/bqpNDRkyJDC/bdt22bPH/fcc4/d33yf+f7PP//ca47FmfbZyy+/bKuwbdq0ybFmzRr7dfN3Nm3aNIc3+KvzC79j/7zPvP13DOWD8aLs+8zb/5YZL8q+z172gt8xAlRwWQSo/vTNN984WrVq5QgKCrLlbd955x2HtzPBlbvvvttRt25dR3BwsKNBgwaORx55xJGZmenwNgVljY/fTBDPyMvLc/zf//2fo0aNGvZ36KyzzrKBKniGN954wxETE+MIDAx0dOjQwfH7778Xfs38DphzaVGzZs1ytG/f3u5fr149x7hx4xze5kz67Nlnn3U0bNjQnmcqV67s6Nmzp+O7775zeIu/Or/wO/bP+8zbf8dQfhgvyrbPvP1vmfGi7PvsWS/4HfMx/3H2LC4AAAAAAAB4L3JQAQAAAAAAwKkIUAEAAAAAAMCpCFABAAAAAADAqQhQAQAAAAAAwKkIUAEAAAAAAMCpCFABAAAAAADAqQhQAQAAAAAAwKkIUAEAAAAeZvbs2RowYIBq1aolHx8fffnll2f0/Y899pj9vuO3sLCwMmszAMC7xwsCVAAAAF7kySef1OOPP668vDxnNwVlKD09XW3bttXYsWP/1vfff//9SkhIKLa1aNFCV111Vam3FYBrYrzwDukuNF74OBwOx99qBQAAANzK9u3b1aBBA9WrV88+h3cwd7KnT5+ugQMHFr6XlZWlRx99VJMmTdLhw4fVqlUrPfvss+rTp0+JP2PlypVq166dvdPeq1evcmw9AGdgvPBOPk4eL5hBBbixOnXq2JOIGUBee+01denSRREREQoJCVG3bt30yy+/OLuJAAAXsnz5cvtoPjjCu9100036448/NGXKFK1atcre6b7wwgu1efPmEvd/77331KRJE4JTgJdgvIAzxgsCVICbOnjwoHbv3q2KFStqxIgRuvvuuxUfH6/69evbry9YsMCeOMzJBAAAgwsOGFu3btUnn3yizz77zF5ANGzY0C7R6Nmzpz744IMTOikzM9PeOb/55pvpQMBLMF7AGeMFASrATZnotZGamqr58+dr8uTJNmC1YsUK7dixQx06dFBOTo5NWgcA8G7mw6KZcfvUU0+VmND0m2++cXYTUY6WLVsmk+XD3OGuUKFC4fb777/bi5HjffHFF/bzxg033MBxAjwc4wWcOV74/63vAuB0Zm1vARPRvuCCCwpfR0VF6cUXX9TZZ5+tOXPmKDc3V35+fk5qKQDA2Y4ePaoePXpo0aJFys7OVufOnRUQEFD4dZMcFd7DJMg3nwuWLl16wucDc+FR0nKNiy++WDVq1CjHVgJwBsYLOHO8IEAFuPkMqiuvvLJYcKpAp06dCqdZJicnq0qVKuXeRgCAa7jlllt03XXX2Q+TJk/hvHnzuHHhxdq3b29vXiUmJv5ljhCT5/K3337T119/XW7tA+A8jBdw5nhBgApw8xlUw4cPL/HrwcHBdtmGmZJZUnQbAOBd1qxZY++Emuo7zKr1fGlpadqyZUuxCweTBsDcsDJLNUzA0izBMDOuzQVIUlKSfv31V7Vu3VoXXXRR4fe9//77qlmzpvr16+ek/xMA5Y3xwrukudB4QYAKcEMmir1u3Tq7PMMkqCuJObGY4FT16tUVGBhY7m0EALjmjQ2W83mHJUuW2KX+Be699177OHToUH344Yc2ua3JSXbffffZHJZVq1a1FYCLXmyYgKbZ98YbbySoCXgRxgvvssSFxgsCVIAb2rRpk10fHh0dbWdKleTnn3+2j0VPNgAA78UFh3fp06ePvVF1MuYm1+OPP263k/H19bUVggF4F8YL79LHhcYLqvgBbpx/ylTpK4k5wbz77rv2+TXXXFOubQMAuCYuOAAAjBdwZQSoADe+yNi7d6/djmeCU6YkqFnGcemllzqhhQAAV7250aZNG2c3BQDgwhgv4CwEqAA3HjT8/f01cuRIHTlypDA31fjx43XXXXfZKk0TJkywidIBAN5tx44dtqJrTEyMIiIinN0cAICLYryAM5GDCnDjANWYMWN0//3323xTjRo1sut+9+/fb4NTU6ZM4S45AKAwd6HRtGlTegQAcFKMF3AmZlABbubQoUM2EFWnTh1bSeG9996zydLXrl1rKyYMGTLELgG85JJLnN1UAICLCA0NLazwmpmZ6ezmAABcFOMFnMnHcap07QBczu+//24rLfTr108zZsxwdnMAAG4gLS1NTZo0UUJCgqpVq2Zn3ZqKOw8//LAuvvhiZzcPAOAiGC/gTMygAtw0QXqrVq2c3RQAgJuoUKGCvalhbm6Ye5Pz58/XH3/8ocjISGc3DQDgQhgv4EzkoALcNP8UASoAwJlo164dM28BAIwXcFnMoALcDDOoAAAAAACehhxUgBvJy8uz025Ngtv09HQFBwc7u0kAAAAAAPxjBKgAAAAAAADgVCzxAwAAAAAAgFMRoAIAAAAAAIBTEaACAAAAAACAUxGgAgAAAAAAgFP5O/efh6nKtmfPHlWsWFE+Pj50CACncjgcSk1NVa1ateTryz0MV8J4AcCVMF64LsYLAO46XhCgcjITnIqOjnZ2MwCgmPj4eNWpU4decSGMFwBcEeOF62G8AOCu4wUBKiczM6cKDlZ4eLizmwPAy6WkpNigecG5Ca6D8QKAK2G8cF2MFwDcdbwgQOVkBcv6THCKABUAV8GSY9fDeAHAFTFeuB7GCwDuOl6QYAQAAAAAAABORYAKAAAAAAAATkWACgAAAAAAAE5FgAoAAAAAAABORYAKAAAAgFfbvXu3rr/+elWtWlWhoaFq166dli5dWvh1h8Ohxx57TLVq1VJISIj69OmjtWvXFvsZmZmZuvPOOxUZGamwsDBdcskl2rVrV7F9Dh06pCFDhigiIsJu5vnhw4eL7RMXF6cBAwbYn2F+1l133aWsrKwy7gEAcD4CVAAAAAC8lgka9ejRQwEBAfr++++1bt06vfjii6pUqVLhPs8995xeeukljR07VosXL1aNGjV0/vnnKzU1tXCfUaNGafr06ZoyZYrmzp2rtLQ0XXzxxcrNzS3cZ/DgwVqxYoV++OEHu5nnJkhVwOzbv39/paen259hfta0adN03333lWOPAIBz+DjM7QA4TUpKir17kpycrPDwcI4EAKfinOS6ODYAXIknnZMefvhh/fHHH5ozZ06JXzeXS2bmlAlAPfTQQ4WzpaKiovTss89q+PDhth+qVaumjz/+WIMGDbL77NmzR9HR0ZoxY4YuuOACrV+/Xi1atNCCBQvUpUsXu4953q1bN23YsEFNmza1ATIT1IqPj7f/pmGCVDfeeKMSExNPq6896dgAcH9nck5iBhUAAAAAr/X111+rY8eOuuqqq1S9enW1b99e7777buHXt2/frr1796pv376F7wUFBal3796aN2+efW2WA2ZnZxfbxwSYWrVqVbjP/Pnz7UVaQXDK6Nq1q32v6D7mewqCU4YJbpmAWNElh0WZr5kLwKIbAJSFsp7fRIAKADxQXp5Dd09ZrjEz1is9M8fZzQEAuKiUjGyNnLRML8/cZMcOb7Rt2zaNGzdOjRs31o8//qgRI0bYvE8TJkywXzfBKcPMmCrKvC74mnkMDAxU5cqVT7mPCYAdz7xXdJ/j/x3zM83PLtjneGPGjCnMaWU2M2sLAErb0axcDRm/SLM2JqqsEKACAA+UlJ6pr1bs0TtztinQn1M9AKBkm/el6bvVCZqyOE6+vj5e2U15eXnq0KGDnnnmGTt7yizZu/XWW23QqigfH58TZhIc/97xjt+npP3/zj5FjR492i6dKdjM8kAAKG1TF8dp7pYk3f/ZKhusKgtctQCAB4o/eMQ+1ooIUYCfd57qc3Jy9Oijj6p+/fq24lKDBg30xBNP2AuRAlRlAuDtNu7NT/LdtIb35iqqWbOmzQ1VVPPmzW01PcMkRDeOn8FkckIVzHYy+5hKeybh+qn22bdv3wn//v79+4vtc/y/Y36mWT54/MyqossNTV6XohsAlLavVu6xjyPPbqiQQD+VBe+8agEAD7c9KT9AFVM1VN7KJK596623bMUlk5jWVGB6/vnn9frrrxfuQ1UmAN5uXUKyfWxeo6K8langt3HjxmLvbdq0STExMfa5udFhAkczZ84s/LoJRv3+++/q3r27fR0bG2urABbdJyEhQWvWrCncxyRDNzOcFi1aVLjPwoUL7XtF9zHfY763wE8//WSDUObfAABn2JucoeVxh2UmcvZvXbPs/iFTxQ/Ok5ycbBb720cAKC3/+369I+ahbx2PTF/lteek/v37O4YNG1bsvcsvv9xx/fXX2+d5eXmOGjVqOP73v/8Vfj0jI8MRERHheOutt+zrw4cPOwICAhxTpkwp3Gf37t0OX19fxw8//GBfr1u3zvbZggULCveZP3++fW/Dhg329YwZM+z3mO8t8MknnziCgoJOu6896dgAcB0D35hrx4svl+86o+/zpHPSokWLHP7+/o6nn37asXnzZsekSZMcoaGhjokTJxbuY8YKMz588cUXjtWrVzuuvfZaR82aNR0pKSmF+4wYMcJRp04dx88//+xYtmyZ45xzznG0bdvWkZOTU7jPhRde6GjTpo0dJ8zWunVrx8UXX1z4dbNvq1atHOeee679GeZnmZ/5r3/9yyuPDQDXMGHedjtWXPbG3DP+3jM5JzGDCgA80NbENPvYsFoFeauePXvql19+sXfBjZUrV2ru3Lm66KKL7GuqMgHwdjm5eVqfkF/xrVXtCHmrTp06afr06frkk09sBb0nn3xSr7zyiq677rrCfR588EGNGjVKd9xxh634t3v3bjuzqWLFP2eevfzyyxo4cKCuvvpqOysrNDRU33zzjfz8/lwKM2nSJLVu3dpW+zNbmzZt9PHHHxd+3ez73XffKTg42P4M87PMz3zhhRfKsUcAoLif1uUvT76gZf6S57LiX6Y/HQDgFFuOBagaV/feJRsPPfSQXTbRrFkz+4E/NzdXTz/9tK699tq/rMq0c+dOl6jK9Pjjj/+DHgCAU9uyP00Z2XmqEOSv+lXDvLq7Lr74YrudjElQ/thjj9ntZExQySwjL7qU/HhVqlTRxIkTT9mWunXr6ttvvz3NlgNA2Uo+mq35Ww/Y533LOEDFDCoA8DAZ2bnacSDdPm8S5b0zqKZOnWovAiZPnqxly5bpo48+snegzWNRVGUC4K1Wxh+2j61qh3ttBT8AwKnN2pionDyHGlWvoPqRZXszgxlUAOCBJcPzHFLl0ABVqxgkb/XAAw/o4Ycf1jXXXGNfmyUVZmaUmZk0dOjQYlWZTAWnv6rKVHQWldmnIKHt6VZlMolwz7Qqk9kAoKysOBagahtdiU4GAJTox7X5s/37tij5M2tpYgYVAHiYgnwizWuGnzA7yJscOXJEvr7Fhzmz1C8vL88+pyoTAG9nKjIZ7aOLL2MGAKBgZcasjfvt8wtble3yPoMZVADgYdYdC1C1qBkubzZgwACbc8rk8mjZsqWWL1+ul156ScOGDbNfN8E7k/D2mWeeUePGje1mnpuktoMHD7b7RERE6Oabb9Z9992nqlWr2twh999/v52Ndd5559l9mjdvrgsvvFC33nqr3n77bfvebbfdZnOZNG3a1L42iXBbtGihIUOG6Pnnn9fBgwftzzHfEx7u3ccJgHOkZmRr475U+7xDDDOoAAAnmrs5SUeyclUzIlity6GYBgEqAPAwa3Yn28cWtbw78GGS1P7nP/+xFZfMkrxatWpp+PDh+u9//1usKtPRo0ftPmbJXZcuXUqsyuTv728rKZl9zz33XH344YcnVGW66667bCDKuOSSSzR27NgTqjKZf8dUZQoJCbFBMKoyAXDm7CmHQ4quEqLqFYM5EACAE3y/Zm9h9b7yWJnh43CYoQnOkpKSYu/Qm0pT3EUH8E/l5jnU+rEf7Z2OmfecpcZRZ1bFj3OS6+LYAChNL/20Ua/9ukWXta+tlwe145zkQRgvAJSG7Nw8dXzqZ1vFb8ptXdW1QdUyPyeRgwoAPMjW/Wk2OBUa6KcG1by3gh8A4NQW7ThoHzvVq0JXAQBOMG/rARuciqwQWG5jBQEqAPAgq3blL+9rVStCfpQMBwCUIDMntzBBeuf6JEgHAJxoxqoE+9i3ZY1yu64gQAUAHmRF/CH72Da67JMYAgDc08r4ZGXm5Nm74g2ZbQsAKGF530/r8vNP9W9dU+WFABUAeJAV8fl3xNtRMhwAcBILth2wj13qVy2XpLcAAPdb3nfoSLaqhgWqS/3yWwpOgAoAPMSRrBytT8gvGd6uLiXDAQAlm7c1yT52a/j3Et4CADzbtyv32Md+rWvI36/8wkYEqADAg5ZsmCp+NSOCVbtSiLObAwBwQRnZuVq2M3+2bY9Gkc5uDgDABfMU/rC2YHlfrXL9twlQAYCHWLozvyJTh7okvAUAlGzR9oPKys2zNzPqVQ2lmwAAxczelKTUjBxFhQepczku7zMIUAGAh1i8Iz9Beqd6BKgAACWbuyV/eV/PRpHknwIAnODrY8v7zOyp8q4KToAKADyAWdq3bOexAFU53+kAALiP2Zv228eejVneBwAoLi0zRzOPVe+7pF35Lu8zCFABgAdYtydFqZk5qhjsr2Y1wp3dHACAC9qXkqENe1NlCveRfwoAcLyf1u5VRnae6keGqW2dCJU3AlQA4EElwzvXq1LuU3EBAO41e6p17QhFVghydnMAAC5m+vLd9nFgu9pOWQZOgAoAPMD8YwGqrg0oGQ4AKNmsYwGqPk2q0UUAgBNm2f5xLE/hwPblv7zPLQNUOTk5evTRR1W/fn2FhISoQYMGeuKJJ5SXl1e4j8Ph0GOPPaZatWrZffr06aO1a9cW+zmZmZm68847FRkZqbCwMF1yySXatWtXsX0OHTqkIUOGKCIiwm7m+eHD+WV5C8TFxWnAgAH2Z5ifdddddykrK6uMewEA/pSdm6eFxwJU3RoSoAIAlDxWFMyg6t20Ol0EACjmy+W7leeQOsZUVkzVMDmD2wWonn32Wb311lsaO3as1q9fr+eee07PP/+8Xn/99cJ9zHsvvfSS3Wfx4sWqUaOGzj//fKWmphbuM2rUKE2fPl1TpkzR3LlzlZaWposvvli5ubmF+wwePFgrVqzQDz/8YDfz3ASpCph9+/fvr/T0dPszzM+aNm2a7rvvvnLsEQDebtWuw0rPylWl0AC1qEn+KQDAiZbuPGTLhlcJC1S76Ep0EQCg2CSfacvyJ+xc3qGOnMVfbmb+/Pm69NJLbWDIqFevnj755BMtWbKksGNfeeUVPfLII7r88svtex999JGioqI0efJkDR8+XMnJyRo/frw+/vhjnXfeeXafiRMnKjo6Wj///LMuuOACG/wyQakFCxaoS5cudp93331X3bp108aNG9W0aVP99NNPWrduneLj4+1sLePFF1/UjTfeqKefflrh4VwoAih7f2w5NnuqQVX5kn8KAFCCXzckFi7vI1chAKCotXtStGlfmgL9fdW/TU05i9vNoOrZs6d++eUXbdq0yb5euXKlnb100UUX2dfbt2/X3r171bdv38LvCQoKUu/evTVv3jz7eunSpcrOzi62jwkwtWrVqnAfEwgzy/oKglNG165d7XtF9zHfUxCcMkxwyywfNP9GSczXUlJSim0A8E/M2Zy/ZIOKTACAk/l53T77eE5zlvcBAIr7bEm8fTy/RZQiQgLkLG43g+qhhx6yM6CaNWsmPz8/u8zOzFa69tpr7ddNcMowM6aKMq937txZuE9gYKAqV658wj4F328eq1c/cQA37xXd5/h/x/xM87ML9jnemDFj9Pjjj/+DHgCAP6VmZGtZXH5uvN4kvQUAlGBLYpq2JaUrwM+HsQIAUExGdq6+XLHHPh/UMVrO5HYzqKZOnWqX45nlesuWLbPL91544QX7WNTxJRHN0r+/KpN4/D4l7f939ilq9OjRNsBWsJnlgQDwd83bekC5eQ7VjwxTdJVQOhIAcIKf1uXfOO3WMFIVg513ZxwA4Hpmrtun5KPZqhUR7PQVGW43g+qBBx7Qww8/rGuuuca+bt26tZ0ZZWYmDR061CZEN8wMppo1/1w7mZiYWDjbyexjKu2ZKn1FZ1GZfbp37164z759+VOhi9q/f3+xn7Nw4cJiXzc/0ywfPH5mVdHlhmYDgNJQUJGpV2PnDiYAANe++DD6tij58ykAwHt9emx535WxdZyeo9DtZlAdOXJEvr7Fm22W+uXl5dnn9evXt4GjmTNnFn7dBKN+//33wuBTbGysAgICiu2TkJCgNWvWFO5jkqGbGU6LFi0q3McEo8x7Rfcx32O+t4BJnG4CUObfAICyZGZr/nYs6e3ZlAwHAJQgIfmolh9bCm5yiwAAUCD+4BHN3ZJkn18Z69zlfW4ZoBowYIDNOfXdd99px44dmj59ul566SVddtll9utmad2oUaP0zDPP2K+ZAJKpqhcaGqrBgwfbfUyi85tvvln33XefTbi+fPlyXX/99XY2VkFVv+bNm+vCCy/Urbfeaiv5mc08v/jii20FP8MkWW/RooWGDBlif4b5Wffff7/djwp+AMraxn2p2pOcoeAAX3VrWJUOP46p8mrGhOO3kSNHFgb4HnvsMVvoIiQkRH369NHatWtPKGxx5513KjIyUmFhYbrkkku0a1d+Cd6iM2fNOGDGFrOZ54cP518MFoiLi7Pjl/kZ5mfddddd9uYJAJS1H9fkL++LjamsqPBgOhwAUGjq4ng5HPmrMepWdX66ELcLUL3++uu68sordccdd9ggkgkIDR8+XE8++WThPg8++KANUpl9OnbsqN27d9uZTRUrVizc5+WXX9bAgQN19dVXq0ePHjaA9c0339jZWAUmTZpkg1YmEGW2Nm3a6OOPPy78utnXBMqCg4PtzzA/y/xMkxMLAMqrZHj3hpEKDvjz3IV8ixcvtjNcC7aCWbNXXXWVfXzuuefsDY6xY8fafc3s2/PPP1+pqamFXWjGEnOzY8qUKbZibFpamr1RYQp0FDA3P1asWKEffvjBbua5CVIVMPv2799f6enp9meYnzVt2jR7kwQAytr3xwJU/Vrlp8EAAMDIyc0rXN53Tae6cgU+DnMLGU6TkpJi77ibpYPMugJwJq4cN09Ldh7SkwNbaUjXGM5Jf8EEm7799ltt3rzZvjYzp8x7pjpswWwpkz/w2WeftTc+zHm5WrVq9sbEoEGD7D579uxRdHS0ZsyYoQsuuEDr16+3M2nNLNsuXbrYfcxzswR8w4YNdsbt999/b4NapiiG+TcNE6Qys3tN7sPTPfczXgA4U/tTM9X5mZ/t3fG5D52tOpVL7+445yTXxbEBcDp+WrtXt328VFXDAjV/9LkK9Pd1+jnJ7WZQAQCkpLRMLY07ZLvivObV6ZK/YJbTmQqww4YNs8v8tm/fbotpmNmxBUz+wN69e2vevHn29dKlS23Ri6L7mABTq1atCveZP3++HXALglNG165d7XtF9zHfUxCcMkxwywTEzL9xMubrZkAvugHAmfh+TYINTrWtE1GqwSkAgPubtDCuMDl6WQWnzpRrtAIAcEZ+Wb/PXnS0rh2hmhEh9N5f+PLLL21eKDNryTDBKeP4iqvmdcHXzGNgYGCxaq8l7VO9+okBQvNe0X2O/3fMzzQ/u2CfkpjqtAV5rcxmZm4BwJn4dmV+IZ8Bbf8MkAMAsPNAumZvzq8GPriLayzvMwhQAYAblwynItPpGT9+vPr161dsFpNhZlMVZVa9H//e8Y7fp6T9/84+xxs9erSdCl2wmSWCAHAm1fsW7Tgoc5rp36YmHQcAKDZ7ytzs7t2kmmKqhslVEKACADdzJCtHczbnl4Pt25KS4X9l586d+vnnn3XLLbcUvmcSohvHz2AyOaEKZjuZfczSQFOl71T77NuXHywsav/+/cX2Of7fMT/TLB88fmZVUWbJoVmnX3QDgNP13ar82VOd6lVhpu1fMBVdj6/4WjBOGFR9BeBJMrJzC5Ojl1Ye29JCgAoA3MxvG/YrMydPdauEqmnUn9VJUbIPPvjALrkzlfQK1K9f3158FFT2M0ww6vfff1f37t3t69jYWAUEBBTbx1QDXLNmTeE+Jhm6md20aNGiwn0WLlxo3yu6j/ke870FTGVZE4Ay/wYAlIWvVuyxjwOYPXVaWrZsWazy6+rVqwu/RtVXAJ7k21UJOnwkW7UrhejsZq6Vy9bf2Q0AAJyZGavzAx0Xta75l8vRvF1eXp4NUA0dOlT+/n8OeabfTAW/Z555Ro0bN7abeR4aGqrBgwfbfUzep5tvvln33XefqlatqipVquj+++9X69atdd5559l9mjdvrgsvvFC33nqr3n77bfvebbfdZqv2mQp+hkmybir9DRkyRM8//7wOHjxof475HmZFASgLWxJTtXp3svx9fdS/DfmnTocZI4rOmio6e+qVV17RI488ossvv9y+99FHH9kZsJMnTy6s+mqWkpuqrwXjgynMYXIHmhm8BVVff/jhh2JVX9999117E2Pjxo12zDA3L9atW1es6uuLL75o8yc+/fTTjBkA/jFzTpswf0dh7ik/X9e6lmAGFQC4kaNZufp1Q6J9flHrEz9IozhzYRAXF2er9x3vwQcftEGqO+64Qx07dtTu3bvtxUHFin/OSnv55Zc1cOBAXX311erRo4cNYH3zzTfy8/Mr3GfSpEk2aGUCUWZr06aNvUgpYPb97rvvFBwcbH+G+VnmZ77wwgscLgBlYvry3faxT9NqqhIWSC+fhs2bN9ugkJlhe80112jbtm32faq+AvAky+IOadWuZFu175pOrleAhxlUAOBGft+UqKPZuapTOcRW8MOpmYCRuVNUEjOLyuQdMdvJmKDS66+/breTMTOrzJ3yU6lbt66+/fZbDheAMpeX59CXy/OX913Wvg49fhrMjKYJEyaoSZMmNq/gU089ZZdpr1279pRVX02OQ1ep+vr4449zrAH8pff/yJ89NbBdLVWtECRXwwwqAHCzNeNGv1Y1WN4HADiBqdy3+/BRVQzy17nNXSu3iKsyVV6vuOKKwiXcZtZrwVK+AlR9BeDu9hw+qh/W5Ae7b+pRX66IABUAuIn0zBz9vD6/YtyAtuQUAQCcaNrSXYV5CoMD/lyOjNMXFhZmg1Vm2R9VXwF4io8X7FRunkPdGlRV85quWR2aABUAuImZ6/YpIztP9SPDWN4HADhBWmaOvjtWSOOqjizv+7syMzNtUvOaNWtS9RWAx+Sx/WRRnH1+U496clXkoAIAN/HVit2Fs6eo3gcAON6MVQk6kpWrBpFhio0png8JJ2cqqw4YMMDmC0xMTLQ5qFJSUmwFWKq+AvAEny+N1+Ej2apbJVTnNi+e686VEKACADdwMD1LczYn2eeXsLwPAFCCT5fE28erOkZzI+MM7Nq1S9dee62SkpJUrVo1de3aVQsWLFBMTExh1dejR4/aqq+HDh2ySdVLqvrq7+9vK7Wafc8991x9+OGHJ1R9veuuu2wBDzueX3KJxo4de0LVV/PvmKqvISEhGjx4MFVfAfwjZlnfe3O32+e39KovP18fuSofx8nKG6FcmLszERERSk5OVni4a64DBeB8H8/fof98tVataofr2zt7ldm/wznJdXFsAJzK1v1pOvfF3+2Fx/yHz1H18GDOSV6K8QJAUd+vTtDtk5apUmiA5j18jkID/V32nEQOKgBwA58vy1/eN7BdbWc3BQDgwrOn+jSpVubBKQCAe3A4HHp79jb7/IauMeUenDpTBKgAwMVtSUzVyvjD9q74pQSoAADHyczJ1WdL8qv3Xd0pmv4BAFhLdh7SivjDCvT31ZBurpscvQABKgBwcZ8vzZ89dXbTaqpWMcjZzQEAuJgf1uy1uQprhAfr3GbVnd0cAICLePv3/NlTV3So7RbXEQSoAMDFkxpOX55/V/yKDpQMBwCcaNLC/NLh13SOlr8fH+8BANKGvSn6ef0++fiY5OgN3KJLGMEAwIXN3ZKkfSmZiggJ0DnNuSsOAChu075ULdp+0C4Dv6ZTXboHAGCNm7XVPl7UqqYaVqsgd0CACgBc2KeL85PeXtquloL8/yxVDQCAMfnY7CmztK9GBMnRAQDSzgPp+mblHtsVd5zd0G26hAAVALio/2/vPsCjqrY2AH/pjSSkkEYJAUJN6B0ElC4QERUURECkiIIoXBC9/hcscCmCSq6IDRQRLIiCdEVADDW0hN7TEyCk9/I/a8cZk9AhyczkfO/zjMyc2XPmeCaZnbP23mtdSc3GluNx6j5HxYmIqLT07DysOVS0DPzZ9r48QUREpHyy8zwKCoty2DbxcYapYICKiMhIyUVHXkEhmtWsisY+ToY+HCIiMsJ+IjUrD37uDuhcz93Qh0NEREYgLjkLP4YWDV689HA9mBIGqIiIjFBBQSFW7y9atjG0LUuGExHRjf3E8r8uqfsjOvjC3NyMp4iIiPDprgvIzS9EWz9XtK7talJnhAEqIiIjtPfCNVy6loEqNpbo39TH0IdDRERGZtfZK7hwNR2ONpZ4sjUHMoiICEhIzcK3+y+b5OwpwQAVEZER+vbv2VOSHN3BxtLQh0NEREZm2d+zp55qXVMNZhARES3deQFZuQVoXrMquvib3tJvBqiIiIxMfEoWNocXJUd/pi1LhhMRUUnnEtKw88wVmJkBIzvW5ukhIiIkpGThm71Fs6de61kfZtJJmBgGqIiIjLBkuCRHb+XrgoDqplN1g4iIKsZXIUWzp7o39EQtN3uediIiwsc7ziM7r0BdQzxkgrOnBANURERGJCevQL+8bwRHxYmIqJRradn4ITRS3X++M2dPERERVOU+3TXEqz1Mc/aUYICKiMiIbAqPxZXUbHg42qBvgJehD8fkRUdH49lnn4Wbmxvs7e3RvHlzhIaG6p8vLCzEzJkz4ePjAzs7O3Tr1g3Hjx8vsY/s7GxMnDgR7u7ucHBwQFBQEKKiikr36ly/fh3Dhw+Hs7Ozusn9pKSkEm0iIiIwYMAAtQ/Z16RJk5CTk1POZ4CIKpuv91xW+UWa1nBGhzpuhj4cIiIyAkt2nFMD3W1qu6BTPdPtGxigIiIyIsv/XrYxrJ0vrCz4Ff0gJGjUqVMnWFlZYdOmTThx4gTef/99VK1aVd9m3rx5WLhwIYKDg3HgwAF4eXmhZ8+eSE1N1beZPHky1q5di9WrV2P37t1IS0tD//79kZ+fr28zdOhQHDlyBJs3b1Y3uS9BKh1p269fP6Snp6t9yL7WrFmDKVOmPND/IxFpS0ZOHr7eU9RPjOtS12RHyImIqOzEJmdi1f5Ik589JVjyg4jISByLSsLhiCRYWZjhmXYsGf6g5s6di5o1a2LZsmX6bbVr1y4xe+qDDz7Am2++iUGDBqltX331FTw9PfHtt99i3LhxSE5OxhdffIEVK1agR48eqs0333yj9vvbb7+hd+/eOHnypApK7d27F+3atVNtPvvsM3To0AGnT59GgwYNsHXrVhUgi4yMVLO1hATLRo4ciffeew9OTk4P/P9LRJXfDwejcD0jF7Vc7dGHs2yJiAjAR7+fRU5+Adr6uaJDXdOdPSU4PE9EZCS+3H1R/dsv0BsejraGPhyTt27dOrRu3RpPPfUUPDw80KJFCxU40rl48SLi4uLQq1cv/TYbGxt07doVISEh6rEsB8zNzS3RRgJMAQEB+jZ79uxRy/p0wSnRvn17ta14G3mNLjglJLglyweLLzkkIrqVvPwCfPbnBXV/zEN+sDA33RFyIiIqG+evpOH7g0WpJ6b1bmDSs6cEA1REREYgJikT64/FqvujO9cx9OFUChcuXMCSJUvg7++PLVu2YPz48Srv09dff62el+CUkBlTxclj3XPyr7W1NVxcXG7bRgJgpcm24m1Kv4/sU/ata1OaBK9SUlJK3IhIuzaGxyHqeiZcHazxZCvOsiUiIuD9raeRX1CIHo080Lq2q8mfEi7xIyIyktlT0rlIwtvAGs6GPpxKoaCgQM2gmj17tnosM6gkAboErZ577jl9u9IjTbL0706jT6Xb3Kz9/bQpbs6cOZg1a9Ztj4OItKGgoBBLdpxX90d0qA07awtDHxIRERnY0cgkbAyLg/wp+a/eDVEZcAYVEZGBJWfmYtXfZWHHduXsqbLi7e2Nxo0bl9jWqFEjVU1PSEJ0UXoGU0JCgn62k7SRSnuScP12beLj4294/ytXrpRoU/p9ZJ+yfLD0zCqdGTNmqBxYupvkryIibfrtZDxOxqbAwdoCz3XwNfThEBGRgRUWFmLu5lPq/qAWNdDAyxGVAQNUREQGJsGp9Jx81Pesgm71qxn6cCoNqeAnScqLO3PmDHx9iy7u/Pz8VOBo27Zt+uclGLVz50507NhRPW7VqpWqAli8TWxsLMLDw/VtJBm6BJD279+vb7Nv3z61rXgbeY28VkcSp0vOK3mPm5HnJHl68RsRafMi5KPtZ9X9ER1rw8XB2tCHREREBrb73FWEnL8GawtzvNrTH5UFl/gRERlQTl4Blv1VlBx9zEN1TD6xoTF59dVXVYBIlvgNHjxYBZA+/fRTdRNyridPnqyelzxVcpP79vb2GDp0qGojic5Hjx6NKVOmwM3NDa6urpg6dSoCAwP1Vf1kVlafPn0wZswYLF26VG0bO3Ys+vfvryr4CUmyLrO5hg8fjvnz5yMxMVHtR17DwBMR3c4fpxMQHp0Ce2sLvPAQZ9kSEWldQcE/s6eebe+LGi72qCwYoCIiMqB1R2MQn5INTycbPNa8Oj+LMtSmTRusXbtWLZV7++231YypDz74AMOGDdO3mTZtGjIzMzFhwgS15E4q8cnMJkfHf6ZJL1q0CJaWlirIJW27d++O5cuXw8LinxwwK1euVAnYddX+goKCEBwcrH9e2m7YsEG9j8zssrOzU0GwBQsW8DMnotvPnvr9nLo/vL2vSpBORETa9mtYrBq4qGJjiZcfqYfKxKxQej4yGKnKJCP0shSEo+hE2iJJ0Xsu2okLV9IxvU9DvNitrqEPid9JRoz9BZH27DpzBc99uR+2Vub4c9ojqOZoA2PB7yTjxc+GqPLKys1H9/d3IjopE1N61sfE7v6V6juJOaiIiAxkY1isCk4521nh2fa1+DkQEZGejCF/+HtR7qlh7XyNKjhFRESG8cXuiyo45e1sWymXfTNARURkoLXjwduLlm2M6lQbjrZW/ByIiEjvr3PXEHr5OqwtzTGuS+W7CCEionuTkJKFj/8oun54vW9D2Fn/k26ismCAiojIALaeiMfp+FQ42lhiVEc/fgZERFRi9tT8LUUJcIe2rQUPJ1ueHSIijVuw9bSq/N28ZlUENfNBZcQAFRGRAS48FhcrGe5sz9lTRET0jy3H43A0KllV7qtsCXCJiOjehUcn44fQKHX//wY0rrSVvxmgIiKqYNtPJeB4TFHJ8Oc7c/YUERGVLKCxYOsZdX90Zz+4V2HuKSIirQ9uv/PrCUh5O5k51bKWCyorBqiIiCq6ZPjfuadYMpyIiEpbezga5xLSUNXeCmOYe4qISPO2HI/HvouJsLE0x/S+DSv1+TDJAFV0dDSeffZZuLm5wd7eHs2bN0doaGiJC8CZM2fCx8cHdnZ26NatG44fP15iH9nZ2Zg4cSLc3d3h4OCAoKAgREUVTZnTuX79OoYPH65KIspN7iclJZVoExERgQEDBqh9yL4mTZqEnJyccj4DRGSqdpy+gqORSapkeGWsvEFERPcvOy8fi7YVzZ56sWtdOLGARoWbM2eOWjozefJk/TZeWxCRoWTl5mP2xpPq/tgudVC9ql2l/jBMLkAlQaNOnTrBysoKmzZtwokTJ/D++++jatWq+jbz5s3DwoULERwcjAMHDsDLyws9e/ZEamqqvo10OmvXrsXq1auxe/dupKWloX///sjPz9e3GTp0KI4cOYLNmzerm9yXIJWOtO3Xrx/S09PVPmRfa9aswZQpUyrwjBCRKVXum7fltLr/XIfaLBlOREQlrNoXocqHezrZqByFVLHkuuHTTz9F06ZNS2zntQURGcqnuy4gIjEDHo42GN+1buX/IApNzPTp0ws7d+58y+cLCgoKvby8Cv/73//qt2VlZRU6OzsXfvLJJ+pxUlJSoZWVVeHq1av1baKjowvNzc0LN2/erB6fOHGiUE7P3r179W327Nmjtp06dUo93rhxo3qNvFZn1apVhTY2NoXJycl39f8j7WSfd9ueiEzXL0eiC32n/1oY8H+bCxPTsguNEb+TjBc/G6LKLS0rt7DVO1tVP/HN3kuFxq6yfSelpqYW+vv7F27btq2wa9euha+88opJXltUxs+GSKsirqUX1n9zo+oX5DrCVN3Ld5LJzaBat24dWrdujaeeegoeHh5o0aIFPvvsM/3zFy9eRFxcHHr16qXfZmNjg65duyIkJEQ9luWAubm5JdrIcsCAgAB9mz179qhlfe3atdO3ad++vdpWvI28Rl6r07t3b7V8sPiSQyKi3PwCLNxaNHtKcoq4OFjzpBARUYlR8qtpOfB1s8fg1jV5ZirYSy+9pFZG9OjRo8R2U7i2kOdTUlJK3IjI9M1cdxzZeQXoWNcNA5p6QwtMLkB14cIFLFmyBP7+/tiyZQvGjx+v8j59/fXX6nnpQISnp2eJ18lj3XPyr7W1NVxcXG7bRgJgpcm24m1Kv4/sU/ata1MaOxAibfoxNAqXrmXAzcGalfuIiKiE2ORMLN11Xt2f1rshrCxM7k90kyZpOg4dOqTyT5Vm7NcWQo5blzNXbjVrMsBJZOq2nYjH76cSYGVhhrcfC1C58bTA5Hq/goICtGzZErNnz1azp8aNG4cxY8aooFVxpT9ASW54pw+1dJubtb+fNsWxAyHSZnLDD387q+5PeLgeqthYGvqQiIjIiMzffBpZuQVoU9sFjwZ6GfpwNCUyMhKvvPIKvvnmG9ja2t6ynbFeW4gZM2YgOTlZf5P/JyIyXZk5+Wr2lJCiSvU8qkArTC5A5e3tjcaNG5fY1qhRI1VNT0hCdFF6lCEhIUE/IiFtpNKeJFy/XZv4+Pgb3v/KlSsl2pR+H9mnTPEtPfqhww6ESHtW7LmMuJQs+DjbYli7WoY+HCIiMiLHopLw0+Fodf/f/RprZpTcWMjSObkGaNWqFSwtLdVt586d+Oijj9R93d/0xnptoVty6OTkVOJGRKYr+I+zqmCGVOyb+Eg9aInJBaikgt/p00V5XHTOnDkDX19fdd/Pz099uW/btk3/vHQY0tF07NhRPZYOSKoAFm8TGxuL8PBwfZsOHTqoEYj9+/fr2+zbt09tK95GXiOv1dm6davqJOQ9boYdCJG2pGbl4uMd59T9yT3qw9bKwtCHRERERkJmxrzz6wl1f1CL6mhW85+q1FQxunfvjrCwMFWtW3eTfLfDhg1T9+vUqWPU1xZEVLmcv5KmchKKt/o3hr21tlZemNz/7auvvqq+xGWJ3+DBg9WXvJSDlZuQUafJkyer5yVPldzkvr29PYYOHarayNrs0aNHY8qUKXBzc4OrqyumTp2KwMBAfWJEmZXVp08ftXxw6dKlatvYsWPRv39/NGjQQD2WRIgym2v48OGYP38+EhMT1X7kNRy5ICLxvz/O43pGLupUc8CgltV5UoiISG9TeBwOXLoOWytz/KtP0d+XVLEcHR1VYvLiHBwc1DWCbjuvLYioogYt/vPLceTmF6Jbg2ro3eTWMycrK5MLULVp0wZr165VS+XefvttNWPqgw8+UKMcOtOmTUNmZiYmTJigpsVKtQwZfZAOSGfRokVq2q4EuaStjJ4sX74cFhb/zG5YuXKlSsCuq8gRFBSE4OBg/fPSdsOGDep9ZGaXnZ2dCoItWLCgws4HERmvyMQMfLn7orr/Rt9GsGTSWyIiKpafcM6mk+r+uC514e1sx3NjpHhtQUQVYd3RGOw+dxXWluaYFdREk0u+zQolTEcGI2VgZUaXTO/lrCuiymXCylBsDItD53ruWDG6rUl0MvxOMl78bIgql092nsd/N52Cp5MN/pjazeSWcfA7yXjxsyEyPYnpOeixcKf699Ue9fFKD39o8TvJ5HJQERGZgv0XE1VwytwM+Hf/RiYRnCIiooqRkJKF4O1F+Qn/1buhyQWniIiobL29/rgKTjXwdMSL3epq9vQyQEVEVMYKCv5JejukTS009GI1HSIi+sc7G04iLTtPJUWX5OhERKRd20/F4+cjMWpge+6TTdUSP63S7v85EVE5WXs4GmHRyahiY4kpverzPBMRkd7us1ex/mjRhch7AwNgLneIiEizFb/fXBuu7o/u7IfmGq/mygAVEVEZysjJw7wtp9T9lx+pB/cqNjy/RESkZOfl4/9+KboQea5DbQRUd+aZISLSsHmbTyM2OQu1XO3xWk9Wc2WAioioDH2y8wLiU7JR09UOozrV5rk1oJkzZ6rcX8VvXl5e+uelRoi08fHxUVVYu3XrhuPHj5fYR3Z2NiZOnAh3d3dVdlyquUZFRZVoI9Vihw8frpI/yk3uJyUllWgTERGBAQMGqH3IvqRCbE5OTjmfASIyNp/tuoALV9PV4MVrnGFLRASt56xdsfeyuv/fJwJhZ20BrWOAioiojFy+lq6qMokZfRvBxpKdjKE1adIEsbGx+ltYWJj+uXnz5mHhwoUIDg7GgQMHVPCqZ8+eSE1N1beZPHky1q5di9WrV2P37t1IS0tD//79kZ+fr28zdOhQHDlyBJs3b1Y3uS9BKh1p269fP6Snp6t9yL7WrFmDKVOmVOCZICJDi0zMwOK/E6O/1b8RnGytDH1IRERkIFm5+Zi+5pi6/0zbmuhY152fBQCWDCEiKgMyG+f/fjmOnLwCdK7njr4B/8zUIcOxtLQsMWuq+Of1wQcf4M0338SgQYPUtq+++gqenp749ttvMW7cOFUK94svvsCKFSvQo0cP1eabb75BzZo18dtvv6F37944efKkCkrt3bsX7dq1U20+++wzdOjQAadPn0aDBg2wdetWnDhxApGRkWq2lnj//fcxcuRIvPfee3cst0tEpk++c/6z7jiy8wrQsa4bgpoVfRcQEZE2ffj7WVy8mg5PJxu83reRoQ/HaHAGFRFRGdgUHoedZ67A2sIcbz/WRC0nI8M7e/asCgr5+fnh6aefxoULF9T2ixcvIi4uDr169dK3tbGxQdeuXRESEqIeh4aGIjc3t0Qb2VdAQIC+zZ49e9SyPl1wSrRv315tK95GXqMLTgkJbsnyQXmPW5HnU1JSStyIyDRtOxGP7acSYGVhhrcfC2AfQUSkYWFRyfh0V9HfpO8ODISzHWfU6jBARURUBtU3Zq0vyl00vltd1KlWhefUCEjQ6Ouvv8aWLVvUrCYJSHXs2BHXrl1T94XMmCpOHuuek3+tra3h4uJy2zYeHh43vLdsK96m9PvIPmXfujY3M2fOHH1eK7nJzC0iMs3iGbPWn1D3x3apg3oe7COIiLQqMycfk787jPyCQvRv6o2ejUv+jah1DFARET2gRdvOqsTovm72mNCtLs+nkejbty+eeOIJBAYGqiV6GzZs0C/l0yk9002W4dxp9lvpNjdrfz9tSpsxY4ZaZqi7yRJBIjLNCk3RSZmoXtUOLz/sb+jDISIiA/rvppM4fyUdHo42eHdgAD+LUhigIiJ6AMdjkrE85KK6/85jAbC1YmJ0YyUV9CRYJcv+dHmpSs9gSkhI0M92kjZSaU+q9N2uTXx8/A3vdeXKlRJtSr+P7FOWD5aeWVWcLDmU/FTFb0RkWg5cSsRXey6p+3MGsUITEZGWSTqQr/YUVe1b8FQzVLW3NvQhGR0GqIiI7lNBQSHeXBuOgkKgX1NvdKlfjefSiElOJ0lq7u3trXJSSeBo27Zt+uclGLVz5061DFC0atUKVlZWJdpIJcDw8HB9G0mGLrOb9u/fr2+zb98+ta14G3mNvFZHEqdLAEreg4gq7zKOaT8eQ2EhMLh1DfYRREQadj09B//64ai6P7JjbfYJt8AqfkRE92nVgQgciUxCFRtL/F//xjyPRmbq1KkYMGAAatWqpWY9vfvuuyrR+IgRI9TSusmTJ2P27Nnw9/dXN7lvb2+PoUOHqtdL3qfRo0djypQpcHNzg6urq9qnbsmgaNSoEfr06YMxY8Zg6dKlatvYsWPRv39/VcFPSJL1xo0bY/jw4Zg/fz4SExPVfuQ1nBVFVHkt3HZaX6HpzX7sI4iItErSOrz5cxgSUrNRt5oDpvdpaOhDMloMUBER3YeE1CyVV0RM6VUfnk62PI9GJioqCs888wyuXr2KatWqqep6e/fuha+vr3p+2rRpyMzMxIQJE9SSO0mqLjObHB0d9ftYtGgRLC0tMXjwYNW2e/fuWL58OSws/lnKuXLlSkyaNElf7S8oKAjBwcH656Wt5L+S9+nUqRPs7OxUEGzBggUVej6IqOIciriOL3Zf1C/tY4UmIiLtWns4GhvD4mBpboYPhrSAnTVTgtyKWaGE88hgZDRfRullOQhH0olMg3xtjl0RqsqGB1R3ws8TOsHSonKsmOZ3kvHiZ0NkGrJy89F/8W6cS0jDoBbVsXBIc1RG/E4yXvxsiIxH1PUM9P3gT6Rm52Fqr/p4+RHtFctIuYeYR+W4oiIiqkC/HIlRwSkrCzOV4LCyBKeIiOjBffT7WRWccq9ig/8bwKV9RERalV9QiCnfH1XBqZa1qmJ8V1b7vhNeVRER3YOElCz8Z91xdX/SI/5o6MXKakREVCQsKhlLd11Q96V8OCs0ERFp1xe7L2DfxUTYW1tg0ZDmHNS+CwxQERHdw9K+N9aGIzkzVy3tG9+NoyBERFQkJ68A//rxqBox79/UG30CvHhqiIg0Kjw6GQu2nFH3pZiSr5uDoQ/JJDBARUR0D0v7fjv5z9I+Ky7tIyKiv72/9TROxaXC1cEas4Ka8LwQEWlUSlYuJqw8hJz8AvRq7IkhbWoa+pBMBgNURER3gUv7iIjoVv46d1W/tE+q9rlVseHJIiLS6IqL6T8eQ0RiBmq42GH+k81gZmZm6MMyGQxQERHdAZf2ERHRrVxPz8Fr3x9R959pWwu9m3BpHxGRVn0VcgmbwuPUiovgoS3hbG9l6EMyKQxQERHdAZf2ERHRLUfK1xxDfEo26lRzwFv9G/FEERFp1LGoJLy38aS6P6NvIzSvWdXQh2RyGKAiIrqN2ORMVu0jIqKbWrU/EltPFOUm/OjpFrC3tuSZIiLSICmi9NK3h5CbX4g+TbwwqlNtQx+SSWKAiojoFqQS0+TVR1SHE1jdmVX7iIhI71xCGt7+9bi6/6/eDRBQ3Zlnh4hIo7Npp/14FJGJmajpaoe5TzZl3qn7xAAVEdEtfPzHOey7mAh7awt89EwLVu0jIiIlOy8fk1YdRlZuATrXc8cLnevwzBARadSyvy5hy/F4WFuY4+OhreBsx7xT96vc5iFHRkZi06ZNyMjIgJ+fH3r27Al7e/vyejsiojIVejkRH/x+Vt1/57EA+Lk78AyXk88//xzffvstLl++DCsrK/j6+qJVq1bo3bs3unbtyvNOREZnwZbTOBGbAhd7K7w/uBnMzVmhqaIUFBTg+vXrcHNzq7D3JCK6lSORSZizqSjv1Jv9GiGwBmfTGt0MqnXr1qF+/foYP348XnvtNTz++OOoVq2aeiwBKyIiYyZL+iatOqKW+A1s7oNBLasb+pAqrTfeeAPjxo1TgalHHnkELVu2xLZt2zB//nz1uG7duip4RURkLP48ewWf/XlR3Z/7RFN4Otka+pA0x9PTE7/++quhD4OINC4pIwcvrSzKO9Uv0BvPdfA19CGZvDILUJ05c0Z/f+rUqWjfvj2OHj2K1NRUnDx5ErNnz8bmzZvRpk0bJCYmltXbEhGV+RryN9aGITopE7Vc7fHOwACuIS9Hn332GebOnYstW7ao+19//bXavnPnTmzcuBEdOnTAiBEjMGbMmPI8DCKiu5KQmoUp3x9V94e2q4VeTbx45iqYubk5atSoof4lIjKUgoJCTP3hqLpm8HWzx5wnAnnNUAbK7Ju9YcOGcHFxQY8ePXDhwgV06tQJ1tbWallfgwYN8Morr+D48eNwcnLC66+/XlZvS0RUpn44GIUNx2JhaW6m8k452nINeXnKzs5G69at9Y/NzIqWydja2qolft988w327t2rZuZ+9NFH5XosRES3k5dfgInfHkZCajbqeVTBW/0a84QZiAxafPnllzz/RGQwi347g99OJsDa0hz/G9oSTrxmMK4A1Z9//olZs2ahevXqam24zJhq3LgxHB0d1Qj4iy++qC40+vXrh59++qms3paIqEwrMv1nXVFFpim9GqB5zao8u+VMlvGtWrXqtm0kH9WcOXMQHBzMz4OIDGbeltOqcIaDtQU+ebYV7Kwt+GkYSFpaGvbs2YPnnnsOcXFx/ByIqELJYPbi7efU/blPBLKKqzEmSZcZU3IT27dvx3/+8x80adIEhw8fVkv9QkND1dKNzMxMNULevHlzddEhtwkTJpTVYRAR3Zes3HxMXHUYmbn5qiLTuC6syFQRZHmfLAkXMrBRterNg4Iy+BEVFVUhx0REVNqmsFh8uuuCuj//qWZqBhUZjgx6x8bGqn8lT2GLFi3UbFy5vpD7TZs2VTNxiYjK2vGYZLW0T4ztUgePt6jBk2zsVfwkX8i7776rEt0WDz7JzKqlS5di0qRJqjLToUOH8MMPPzBARUQG999Np3AyNgWuDtZYyIpMFUaWgP/xxx94+umnVU6RPn36qEGMU6dOwcPDA5aWliqP4fTp09UFBxGRIWbX6i5Gxjzkh0cDvfkhGJhUC5ectjIIrrvt27cPy5YtQ05ODiwsLJCbm2vowySiSuZqWjbGfh2qBrS71q+G6X0aGvqQKp1yyS4os6cCAwPRrFkztUb8xx9/VEsAV65ciYULF6qRjQ8//FBtS05OLo9DICK6a78cicbykEvq/oKnmsKDFZkqlIx4h4eH43//+58qHS5BqWeffRa+vr5q5lT37t1VwQ1Jok5EVJHSs/Mw/ptQpOfko52fKy9GjIirqysefvhhTJ48WQWmZOBblv5JsGr58uX3tK8lS5aoQRDJlSs3SU+yadOmEgVUZs6cCR8fH9jZ2aFbt24qt27pnIoTJ06Eu7s7HBwcEBQUdMPMX+njhg8fDmdnZ3WT+0lJSSXaREREYMCAAWofsi8Z2JegGxEZVk5eASZ8c0glRfdzd1C5ai3Mi3KnkpHPoJJy4evXr1f5QmTG1BdffKFGxOXLvWbNmiUuMnQJcYmIDEFmTU1fc0zdf7FbXTzS0JMfhAFIUOr5559XN1kKHhYWhsuXLyMvLw+1a9dGu3btWLGJiCqU/N0q/YPMoPJwtMHioS1gacHKcRVNVmCcO3dOzZiSgkz16tVTM6Ru1ZfIILnc7oXM4P3vf/+r9i2++uorPPbYYypViaQsmTdvnhpkl8BX/fr11UqRnj174vTp0yrfrpBAmVz/rF69Gm5ubpgyZQr69++v0pzojnfo0KEqaCWVzcXYsWNVkEpeJ/Lz81W+3mrVqmH37t24du2aWpkiP4uLFy9+oPNIRA9m5vrj2H8pEY42lvjsudZwtmMhpfJgVijfeOXs0qVLOH/+PKpUqYKWLVuqABYVSUlJUSMoMpNMRmyIqOIkZeQgKPgvRCRm4CF/dywf1VbzIyEV9Z10LxccVIT9BVHF+nL3Rbz96wlV1XX12PZoXduVH0EFfidduXJFrcqQgE/xFRcSEJJl4TKjycvLq1xnaM2fP18NnMjMKQlAyXJz3WwpT09PlUdx3Lhx6vgkqLRixQoMGTJEtYmJiVED8xs3blRVaWW5uhSQksq0Mugi5L7M1pJl7bLkXWZtSVBLljDKewr5/x85ciQSEhLu+jyzvyAqWyv2XsZbP4dD5tZ8OaINHm7owVN8D+7lO8m8LC4yzpw5o75gZRRBIv+lyei3LNGQL2MGp4jIGOQXFOKV1UdUcKqGix0+eprTdCuCXHBIbkJZttCoUSNVXEP+YJfR5vHjx5drNSapBCizduUiQ4fLNojoZg5cSsTsjSfV/Tf7NWJwqoKdOHFCDWrLSgxZAiff1bqbXOjIagwptCSzbcuaXMtIUCg9PV0Fjy5evKj6pl69eunb2NjYqHy6ISEh6rHMkpKcV8XbSIApICBA30aqDsoFmi44JaRIiGwr3kZeowtOCQluSUBM3uNW5Hk5L8VvRFQ29l64hll/V/me1rshg1PlzNwULzKIiB7UB7+dwc4zV2BrZY6lw1vBxcGaJ7USX3AcOHAAn3766Q2J1nXLNmRJurSR0XhZtiE5r3QkoLV27Vp1wSJLLiTHiYxwFx+QkWUbR44cUcs25Cb3ZdmGjm7ZhlzwyD5kX2vWrFFLQIjIuCSkZuGllYeQV1CIoGY+GNmxtqEPSVPke1JyMEVHR6sZtrNmzVIBHBkQl3/ffvttdb0hVfykXVkFY6TvkdUeEnySaxn53pdrG901jcyYKk4e656Tf62trdXx3q6NFP8oTbYVb1P6fWSfsu/bXVvJAIwur5XcZOYWET24yMQMTPi7P3isuQ/Gd2WVb6MMUBnyIoOI6EFtOR6HxdvPqfv/HdQUTXyceVIr6QWHkIDSsGHDVN9U/OJB+qwPPvgAb775JgYNGqRGrSXvSEZGhipbLmQqsuRRfP/999GjRw9V5EPKmkv/9ttvv6k2smxDglKff/65Gm2Xm7zXr7/+qmYWi61bt6q+U14r+5B9yT6lHUe6iYxHdl6+SoKbkJqN+p5VMGdQIPOlVjAppCSzlmQFhgT733rrLTXTSJaCy7///ve/VW4oeV6Wwsl3aVmQJXbyfrIq5MUXX1S5n+R7+1Z5c6UPuVMu3dJtbtb+ftqUNmPGDNVf6W5yXojowYtkjPn6IBLTcxBY3Rlzn2jK/sAYA1SGvMggInpQkux2yvdF5cJHdaqNgS2q86RW4gsO8dJLL6nZSxIUKs7Yl21wyQaRAZKi/3gMBy9fh6OtJZY82woONuVST4huQwYKJBgjA+GSvPxmpMKrDArIZ3avFftuRWYpSZ/UunVrNSNJqpFL36XLc1V6BpPkhNLNdpI2UmlPqvTdrk18fPxNV6UUb1P6fWSf0g+VnllVnPRdugqEuhsR3b+8/AK8svowTsWlwr2KDT59rhVsrZgr1SgDVIa8yCAiehCpWbkYt+Ig0rLzVLnwNx5txBNayS84ZCmdlB6Xi43SjH3ZBpdsEFWsj34/h5+PxKik6J882wp1q1XhR1DBpGrd2bNnVTBfllvfziOPPIJatWqpqniSkLysSV8kAwV+fn4qcLRt2zb9cxKM2rlzJzp27Kgey8oRybNbvI0M1oeHh+vbyOxamd20f/9+fZt9+/apbcXbyGvktToyA1cCUPIeRFT+5Hf/rV+O47eTCbCxLEoF4u1sx1NfQSzL8yJDRqvlIkNmWRERGVJBQSGm/nAU56+kw8vJFsFDW8KK5cIr9IJD+oa7veCQAQ654Cg+4+heyT5eeeUV9ce9ra3tLdsZ67INWbLx2muv6R/LjGTmFSEqH78cicai386o++8MDECneu481RWsTp06aqaQkAqv8vhOZPaRaNu2rQriSNXw+/HGG2+gb9++6jtWchDK4MaOHTvU8m1dcY3Zs2fD399f3eS+vb29yj8oZMbs6NGjVV5BWUkiFQCnTp2KwMBA/exdydnbp08fjBkzRl1HibFjx6qchrK8UMhsXcl7JTkMpYKgnAfZj7yGs6KIKkbw9nNYtT9CVez78OkWaOVbcpCSjChAZaiLDCKiByU5p7Ycj4e1hTk+Gd4K1RxteFIr+QWHLJ2T5RXFR50lWfmuXbtUUnRdfiiZweTt7X3HZRvFZ1FJG92I990u25CR8ntZtiH/73IjovJ18FIi/vXDMXV/XJc6eKZtLZ5yA7h06ZL6VwJCmZmZ+sd3Iu3lWuNOAwu3I9/hEhSSmUsSbJKCGhKc0l3vTJs2TR2TFIiS725Z0i2DH46Ojvp9LFq0CJaWlhg8eLBqKxXMZaDewuKfZUErV67EpEmT9MvGg4KCVH+kI203bNig3kcKUNnZ2akg2IIFC+77/42I7t4PByPx/raiwYpZQU3QJ6BoiS9VHLNCGb69h4sMyT0lX5a3Wwdd/Ms+KytL/eH/IBcZlZmMiEtHKNN7OTJCVD7WHo7Cq98V5Z3676BAPM2Ljwr7TjI3L1pJLhcOd9ndlGgv/xavlncvZBT88uXLJbaNGjUKDRs2xPTp09GkSRM1ePLqq6+qiw8hwShZmjd37lyMGzdOnYdq1aqp5OZy0SHkAkZmEG/cuFHlkZIk6TLiLQEoCaoJuS/L3k+dOqVGxjdt2qRGyWUpii4Y9t1336kkvBLsuptzzf6CqOxFXMvAwI//UklwezX2VEv7zM3vP9ChJWX9nSSrNCSwL9/Hvr6+mDlz5h1fI7lvJZAlM5pkIEC+U4n9BdH92HE6AaO/Ooj8gkK82K0upvdpyBNpgP7irgNUhrzIqMx4wUFUvvacv4bnvtyH3PxCNTI+g3mnNH3B0a1bNzRv3lxV7xMSiJJcT8uWLdMv25BlHTK7SjcyLtWcpCKfjITrlm3IjGKZoaUbGZelITKCX3zZhvz/rl+/Xj2W/k/eVwZ3dMs2Ro4ciYEDB2Lx4sV3dezsL4jKVnJmLp5YEqKKZwRUd8L34zrA3ppJ0e9WeXwn5eXlqe/egoIC9T1bpUqV2xZukuV0umORnH5Ufp8NUWUWFpWMIZ/uQUZOPh5vUR0LBzdjxT4DfSfddS8sf7zf70WG/PGvq4BBRFRRziWkqqToEpzqF+jNkRADkOCSXHBIQQ0J4DzxxBN3vOCQmUuSbFZmNpX3BQeXbRBpU25+AV5aeUgFpyQv4Rcj2jA4ZQRkiZwsq5NlbpLDVgL6t/LOO++oWa8yQMDgFBE9yEzaUcv3q+BU53rumPtEUwanDOiuZ1AJjmqUPY5wEJWPhNQsPP6/EEQnZarkhitfaMfysAb8TpI8G3LBIUm/b3fB8frrr2PevHnqgkPaU/l/NkRaI3/6vrE2DKv2R8Le2gI/jO+AJj7Ohj4sk1Ne30m7d+9Gly5d1AxV6Q8kQXnp/FIfffSR6k/ks9y+fTu6du1aZu9fGbC/ILo7srxbZtJevJqOxt5O+G5cezjaWvH0GfA7qWjd3j2Oakig6k6V+XSjGpIgsDxHNWR2lq66ho50VjLDS3KLSL4sWdJx/PjxEq+TsrETJ06Eu7s7HBwc1MWT5AYpTpIgSsJEOZlyk/tJSUkl2kRERGDAgAFqH7IvSXwo/99EZDgZOXl44auDKjhV280enz3XmsEpA5OZSvLdLEvrJJHszcZG5IJDEsHKd7ouJxQRUVn7/M+LKjglqaYWP9OCwSkj07lzZ5UnUJZGy5JqWX4tS61lJq4kD5fHMsNWlgHK3/8MThHR/cjMycfzyw+o4FT1qnZYNqoNg1NG4J4X2stFg+TikIsMCQDdalSjIi4yDhw4gE8//VRV2ihORlsWLlyo8oXUr18f7777rgqsFc8pIsctuUGkjKysX5eysJLAtnhOEamaIUErqeKhyykiQariOUX69eunEujKaI+slZflLHLhdbc5RYiobEliw0mrjuBYVDJc7K2wfFRbuDowL4WxXHBIzie54Pjf//6nvpclsC/fndu2bcOFCxfU96dcePCCg4jKw6awWMzedFLd/3e/xuje6M5Ff6jiyQC0LAeXv+Glb5C/93Wkn5Bl4DLj9k4D5kREN5OXX4CJqw7jSGQSnO2s8NXzbeDpZMuTZWpL/HRmzJihLjIkAOXn53fbi4z333+/XA48LS0NLVu2xMcff6w6L13SW3lfXeBMLoZ0s6UkMW3pqkwrVqzAkCFDVBvJjVKzZs0bqjLt3btXlZIVcr9Dhw43VGWKjIxU7ykk4CWJb1mViajiye//rPUnsDzkEqwtzbFqTDu08nXlR2FEywLee+899Z0t38vFBzd4wWH4z4aosvvz7BWMXn4QOfkFGN7eF28/1oR5Roz8O0n+xpa/rWUAWVY2VK1aFS1atFB/v8s1CBnusyEy7WXe4Vi1PwI2luYqDUjr2rxeMLkk6cY2qvHSSy+p2Us9evRQx6Fz8eJFxMXFoVevXvptNjY2ajQ+JCREBaikk8vNzS3RRgJMAQEBqo0EqPbs2aNOoi44JaRkuGyTNhKgkjbyGl1wSshr5cJL3uPhhx++4bjlObkV/7CIqGx8+dclFZwSiwY3Z3DKCL355pt47rnneMFBRBUq9PJ1jP06VAWnpGjGzCAGp0yBDB7/61//MvRhEFElsnDbGRWcknHSD59uweCUkbE0xYsMec9Dhw6pJX6lSXBKyIyp4uTx5cuX9W0kL5aLi8sNbXSvl389PDxu2L9sK96m9PvIPmXfujY3C+5xOjJR2dscHot3N5xQ92f0bYh+Tb15mo0ULziIqCKdjE3BqGX7kZmbjy71q2HRkOawkARURESkKYt/P4vF28+p+28HNUGfAC9DHxKVVYDKUBcZMtX3lVdewdatW2Fre+t1oqXzYsnMrtLbSivd5mbt76dN6eWRUnWk+AwqOY9EdP8OXkrEK6uPQBYsP9u+FsZ2qcPTSUREuHQ1HcO/2I+UrDy09nXBJ8+2VEvAiYhIW5buPI/3t51R9994tCGGd6ht6EOimzC5Hlpma0l+p1atWqmqgnLbuXOnSswu93UzmkrPYJLX6J7z8vJSlfZk1tft2sTHx9/w/leuXCnRpvT7yD5l+WDpmVXFlxvKusviNyK6f8eikjBy2QFk5xXgkYYemDmAyzaIiAiIS87CsM/34WpaNhp5O+GLkW1gb/1AY7NERGSCvtx9EXM2nVL3p/aqj7Fd6hr6kKiyBKi6d++OsLAwHDlyRH9r3bo1hg0bpu7XqVNHBY4kWbuOBKMkiNWxY0f1WIJbkiereJvY2FiEh4fr20gydEnitX//fn2bffv2qW3F28hr5LU6MrNLglDyHkRUvk7FpeC5L/cjLTsPbf1c8b+hLWFpYXJfa0REVMYS03Pw7Bf7EJ2UCT93B3z9fFtVqYmIiLTlm72X8favRWlAJj1SDy8/4m/oQ6LbMLlhJEdHR5WYvDgHBwe4ubnpt0sFv9mzZ8Pf31/d5L69vT2GDh2qnpdE56NHj8aUKVPU61xdXVXZ88DAQJV0XTRq1Ah9+vTBmDFjsHTpUrVt7NixqmqfJEgXkmRdKv0NHz4c8+fPR2JiotqPvIYzo4jK14UraXj28/1IyshF85pV8eXINrCztuBpJyLSuNSsXIxcth/nEtLg7WyLFaPbopqjjaEPi4iIKtj3ByLx75/D1f1xXevg1Z71+RkYOZMLUN2NadOmITMzExMmTFBL7qQSn8xskuCWzqJFi9SSwMGDB6u2MjNr+fLlsLD45wJ35cqVmDRpkr7aX1BQEIKDg/XPS9sNGzao9+nUqRPs7OxUEGzBggUV/H9MpC2RiRn6ZRuNvZ3w1ai2qGJTKb/OiIjoHmTl5mPM1wdxLCoZrg7WWDG6HWq42PMcEhFpzNrDUZj+0zF1f1Sn2ni9T8M75qQmwzMrlIzeZDCSJF1mdMnSQc66Irq7nCJPLQ1BZGIm6nlUwXdj28OtCkfG+Z1U+bG/ILq93PwCvPhNKH47maAGLVaNaY/AGs48bfxO0hz2F6R1vx6LwaRVh1HwdwGldx4LYHDKRL6TmKyFiEyGzJga9vleFZzydbPHyhfaMThFREQoKCjEtB+PqeCUjaU5Ph/RmsEpIiIN2nI8TlX3luDUkNY18XYQg1OmhAEqIjIJSRk5ePbzfTh/JR0+zrYqOOXpZGvowyIiIgPLLyjEv348hrWHo2FpboaPh7VE+zpuhj4sIiKqYNtPxePlbw+pfmFQi+qYMygQ5uZc1mdKmLSFiEwi4e2IZQdwKi5VJbpdOaY9c4oQERHy8gvw2vdHse5oDCzMzbBwSHN0b+TJM0NEpDG7zlzB+G8OITe/EP2bemPek00ZnDJBDFARkVHLzMnH6OUHcTQyCS72VvhmdDtVMpyIiLQtJ68Ar6w+jE3hcWrm1OJnWqBvoLehD4uIiCrYX+euqgIZ0i/0buKJRUOaw9KCi8VMEQNURGTU1ZjGrjiI/ZcS4Whjia+fb4cGXv9U4yQiIm3KzsvHSysPqZxT1hbmallfj8acOUVEpDVbj8fh5VWHVXCqe0MPLH6mJawYnDJZDFARkVFKy87DmK8OYs+Fa7C3tsDy59sw4S0REanBi3ErQrHzzBWVEH3p8Fbo1sCDZ4aISGN+OhSlchBKzqlejT2xeGgLWFty5pQpY4CKiIwyIfrIZQdwJDJJlQr/YkRrtPJ1NfRhERGRgWXk5OGFrw4i5Pw12FlZqGp9neq5G/qwiIiogi3/6yJmrj+h7j/RsgbmPhHIZX2VAANURGRUrqRmY/gX+1RC9Kr2Vvj6+bZoWqOqoQ+LiIiMYGbt88sOqGXfDtYWWDaqLdr6cfCCiEhLCgsLsXj7OSzcdkY9HtWpNt7q15gJ0SsJBqiIyGhEJ2Xi2c/34eLVdFWtTxKiM+cUERElZ+Zi5LL9OByRBEdbS3z1fFu0rOXCE0NEpLHg1LsbTuKL3RfV48k9/PFKd3+YmZkZ+tCojHCBJhEZBQlKDf5kj/q3elU7/DCuA4NT9ECWLFmCpk2bwsnJSd06dOiATZs2lfgjZ+bMmfDx8YGdnR26deuG48ePl9hHdnY2Jk6cCHd3dzg4OCAoKAhRUVEl2ly/fh3Dhw+Hs7Ozusn9pKSkEm0iIiIwYMAAtQ/Z16RJk5CTk8NPmOgul33L4IUEp5ztrPDtC+0ZnCIi0hjJMzV9zTF9cOr/+jfG5B71GZyqZBigIiKDOxWXgqc+2aNmUNVxd8AP4zugtruDoQ+LTFyNGjXw3//+FwcPHlS3Rx55BI899pg+CDVv3jwsXLgQwcHBOHDgALy8vNCzZ0+kpqbq9zF58mSsXbsWq1evxu7du5GWlob+/fsjPz9f32bo0KE4cuQINm/erG5yX4JUOtK2X79+SE9PV/uQfa1ZswZTpkyp4DNCZHqupWXjmc/2ISw6Ga4O1lg1pj0LZhARabBy68vfHsL3B6NgbgbMf7Ipnu/sZ+jDonJgVihDyGQwKSkpasQ9OTlZjfATaY0kQh/x5X61fKORtxNWjG4L9yo2hj4szars30murq6YP38+nn/+eTVzSgJQ06dP18+W8vT0xNy5czFu3Dh1DqpVq4YVK1ZgyJAhqk1MTAxq1qyJjRs3onfv3jh58iQaN26MvXv3ol27dqqN3JfZWqdOnUKDBg3UrC0JakVGRqr3FBKkGjlyJBISEu76PFf2z4aotISULDz7xT6ciU9T/cK3Y9qhvqcjT5SR4HeS8eJnQ5WtOIZUbv3z7FVYW5jjo2eao0+At6EPi8rpO4kzqIjIYPZeuIZhn+1VwamWtapi9Zj2DE5RuZBZTBIUkllMEjy6ePEi4uLi0KtXL30bGxsbdO3aFSEhIepxaGgocnNzS7SRAFNAQIC+zZ49e1SHqwtOifbt26ttxdvIa3TBKSHBLQmIyXvcijwvHXrxG5FWnEtIxeMfh6jglJeTLb4f157BKSIijUnOyMXwL/ar4JS9tQW+HNmGwalKjgEqIjKIP04lqJlT6Tn56FjXDStGt4OzvRU/DSpTYWFhqFKligo+jR8/Xi3XkxlPEpwSMmOqOHmse07+tba2houLy23beHh43PC+sq14m9LvI/uUfeva3MycOXP0ea3kJjO3iLRg34VrGPRxiFr27efugO/HdUCdalUMfVhERFTBlb2HfLoHoZevw8nWUl0rdPZ352dQyTFARUQVbsOxWIz5+iCy8wrQo5GHGg1xsGFRUSp7ssROckLJsrsXX3wRI0aMwIkTJ/TPl676Iqve71QJpnSbm7W/nzalzZgxQ02F1t1kiSBRZbfuaIwaLU/JykMrXxesebEjarnZG/qwiIioAkVdz8BTn4TgVFyqWl3x3bgOqk+gyo8BKiKqUF/vuYSJqw4hr6AQQc18sOTZVrC1suCnQOVCZinVq1cPrVu3VjOSmjVrhg8//FAlRBelZzBJTijdbCdpI5X2pErf7drEx8ff8L5Xrlwp0ab0+8g+Zflg6ZlVxcmsL10FQt2NqLKSgO3SnecxadVh5OQXoG+AF1a+0E4lRiciIu04HpOMJ5fswaVrGaqy94/jO6g8taQNDFARUYWVhp257jj+75fjKCgEnmlbC4uGNIeVBb+GqGIvgiW3k5+fnwocbdu2Tf+cBKN27tyJjh07qsetWrWClZVViTaxsbEIDw/Xt5F8VjK7af/+/fo2+/btU9uKt5HXyGt1tm7dqgJQ8h5EWif9g/QNczadUo9Hd/bD/4a25OAFEZHGbDsRryp7x6VkoZ5HFfz4Iit7aw2vDImo3KVl56klfctDLqnH0/s0xOzHA2AhdWKJyskbb7yBP//8E5cuXVK5qN58803s2LEDw4YNU0vrpILf7NmzVV4qCSBJVT17e3sMHTpUvV7yPo0ePRpTpkzB77//jsOHD+PZZ59FYGAgevToodo0atQIffr0wZgxY9QyQrnJfanaJ8sLhSRZl7xXw4cPV/uQfU2dOlW146wo0rqi6kwHsWLvZciK17f6N1Y3c/YPVIFkhm2bNm3g6OiocggOHDgQp0+fvmGAY+bMmarghZ2dHbp164bjx4+XaCMDIBMnToS7uzscHBwQFBSEqKioG2bQSn+gyy8o95OSkkq0iYiIwIABA9Q+ZF+TJk1SgyhElZX8fn226wLGrjiIjJx8dKrnhjXjO8Lb2c7Qh0YVjAEqIipXMUmZeHJJCLafSoCNpTk+HtYSL3are8c8P0QPSpbeyR/+Eijq3r27mtm0efNm9OzZUz0/bdo0FaSaMGGCWgIYHR2tZjbJBYrOokWL1IXK4MGD0alTJxXAWr9+PSws/lmWunLlShW0kkCU3Jo2bYoVK1bon5e2GzZsgK2trdqH7Ev2uWDBAn7IpGlX07LxzKd78dvJv/uHoS3V7CmiiiazZ1966SU1yCCzZvPy8tT3uVR+1Zk3bx4WLlyI4OBgHDhwQM3Clf4kNTVV30b6FBn0kKqxu3fvRlpamhqwkEqyOjIIIrkRpT+Sm9yXvkpH2vbr10+9t+xD9rVmzRo1WEJUGeXmF+CNtWF4b+NJFBYCQ9vVwvJRbVk8SaPMCiVcSQYjZcNl9ESWg3AknSqbY1FJGP3VQVWFQxIcfj6iNZrXrGrow6Lb4HeS8eJnQ5XJhStpGLnsACISM+Bib6X6h1a+roY+LLoHlfk7SfIIykwqCVx16dJFze6QmVMSgJo+fbp+tpTkEZw7dy7GjRunzkO1atXUAMWQIUNUm5iYGFWBdePGjejduzdOnjypZtRKIKxdu3aqjdyXpeCnTp1SAyqbNm1SQS0pjCHvKSRIJbN8JQfi3ZzryvzZUOWSnJGLF1eGIuT8NTWL9t/9GuP5TrU5kF3J3Mt3EmdQEVG52HI8DoOX7lHBqQaejvj5pY4MThEREQ5eSsSgJSEqOFXL1V5V6mNwioyJXEQJV9eioOnFixdVsQuZVaUjeQS7du2KkJAQ9Tg0NFQVvyjeRgJMAQEB+jZ79uxRF2m64JRo37692la8jbxGF5wSEtySgJi8B1FlcelqOh7/+C8VnHKwtsDnz7VWs2i5ykLbWNediMp+DfmfF1SyW5mf2bV+NQQPbQFHWyueaSIijdsUFotXvjuCnLwCNKtZFV+MaK1m2BIZ098xr732Gjp37qwCRUJXibV05VV5fPnyZX0bqRzr4uJyQxvd6+VfmZlVmmwr3qb0+8g+Zd+lK8LqSPBKbsVnKxAZs70XrmH8N6FIysiFj7MtvhjZhpX6SGGAiojKdA35//0SjlX7I9Xj4e198Z8BjWHJSn1ERND6Rf8Xuy/qc4z0aOSJj55pDntr/ilKxuXll1/GsWPHVP6n0krP7JCf6zvN9ijd5mbt76dN6STvs2bNuu1xEBmL7w9G4s21YcjNL0SzGs747LnW8HCyNfRhkZHgEj8iKhPJmbkYteyACk5J8SUJTL39WBMGp4iINC4zJx+vfX8U724oCk4918EXS4e3YnCKjI5U4Fu3bh3++OMP1KhRQ79dEqKL0jOYJCeUbraTtJFKe1Kl73ZtpIDHzXJeFW9T+n1kn7J8sPTMKp0ZM2aoZYm6m+SvIjI2BQWF+O+mU5j24zEVnOoX6I3vxnVgcIpKYICKiB5YxLUMPLEkBLvPXYW9tYUaCRnViWvIiYi0TvoHyTe19nA0LMzN8Fb/xpgV1ETdJzIWMjtJZk799NNP2L59O/z8SlaTlMcSOJIKfzoSjJIk6h07dlSPW7VqBSsrqxJtYmNjER4erm8jydAlgLR//359G6kwK9uKt5HXyGt1pMKs5LyS97gZeU4SDxe/ERmTjJw8TFh5CJ/sPK8eT3ykHhY/0wK2Vv9URSYSnFdNRA8k9HIixn4dimvpOfBykjXkrdHEx5lnlYhI43acTsArq4+oGbbuVawRPLQl2tdxM/RhEd3gpZdewrfffotffvkFjo6O+hlMkrzczs5OLa2TCn6zZ8+Gv7+/usl9e3t7DB06VN929OjRmDJlCtzc3FSC9alTpyIwMBA9evRQbRo1aoQ+ffpgzJgxWLp0qdo2duxYVbVPKvgJSbIulf6GDx+O+fPnIzExUe1HXsPAE5mi+JQsvPDVQYRFJ8PawhxznwzE4y3+maFIVBwDVER036ONy0MuYfbGk2qabkB1J3wxog08uYaciAhaX8bx8Y5zeH/bGbWkr3nNqljybEt4O9sZ+tCIbmrJkiXq327dupXYvmzZMowcOVLdnzZtGjIzMzFhwgS15E4q8cnMJglo6SxatAiWlpYYPHiwatu9e3csX74cFhb/zBJZuXIlJk2apK/2FxQUhODgYP3z0nbDhg3qfTp16qQCZBIEW7BgAT89Mjnh0ckqOBWXkgVXB2t8OrwVWtcuqo5JdDNmhXKVSQYjVTZkxEWm9nJUhExFalYuXl8Thg1hRdPPZQ35/KeaMp9IJcDvJOPFz4ZMQUpWLqZ8fxTbThTl2XmmbS3MDGoMG0su46hs+J1kvPjZkDFYezgKb/wUjszcfNTzqIIvR7RBLTd7Qx8WGfl3EmdQEdE9ORWXggnfHMKFq+mwsjDDG482wsiOte9YxYaIiCq3s/GpGLciVPUPsoxDCmU83baWoQ+LiIgqUFZuPmatP4FV+yPU44f83dUSb2c7K34OdEcMUBHRXfsxNAr//jkMWbkF8HG2RfCwlmhZy4VnkIhI4zaGxWLqD0eRkZMPb2dbLHm2lVraR0RE2nH5Wjpe/OYQTsSmQMauJz3ij0nd/VkYg+4aA1REdFcjITPXHcfqA0Vli7vUr4YPhjRXa8mJiEi78vILMH/raSzdeUE97lDHDYuHtoB7FRtDHxoREVWgzeGx+NcPx5CanaeuEeRaQa4ZiO4FA1REdE8jIa/2qI+XH64Hc5YIJyLStMT0HExadRi7z11Vj8d2qYNpvRvA0sLc0IdGREQVJCevAHM3n8IXuy+qx619XdSSPi9nW34GdM8YoCKiW9ocHod//XBUjYS4OVjjw6dboLO/O88YEZHGhUUlY/w3oYhOyoSdlQXmPdkUA5r5GPqwiIioAsUkZeLlbw/hUESSfqDiX70bwIoDFXSfGKAiohvk5hdg7qZT+JwjIUREVIwUf/7hYBT+/Uu4GjWv7WaPpcNbo4GXI88TEZGG7DidgFe/O4LrGblwtLXE+081Q68mXoY+LDJxDFARUQlxyVlqJOTg5evq8ZiH/DCtT0OOhBARaVxyRi7e+DkMG47FqsfdG3pg4ZDmrMxERKQh+QWF+OC3Mwj+4xwKC4GA6k74eGgr1HKzN/ShUSXAABUR6e0+exWvrD6Ma+k5cLSxxPynmqJPgDfPEBGRxoWcv4op3x9FbHKWqsY0ubs/XmI+QiIiTbmSmq2uFULOX1OPh7Wrhbf6N4atlYWhD40qCQaoiEgt6Qvefg4fbT+rRkIaezvh42EtUdvdgWeHiEjDsvPysXDrGXz65wXVP8iSvkVDmqNFLRdDHxoREVWgfReuYeKqw0hIzYa9tQXmDArEY82r8zOgMsUAFZHGnUtIxWvfH8WxqGT1+Ok2NTEzqAlHQoiINE76h0mrjqgqrrr+QUbKHWz45yMRkVYUFBRi6a4LWLD1tFre5+9RBUuebYl6Hsw9SGWPf2EQabiz+fKvi5i35bRKdOtka4l3BgZwJISISOMkEfqKvZfx3oaTyM4rgIu9FeYMkiXfTH5LRKQlSRk5ann376cS1ONBLarj3ccDYG/NMAKVD/5kEWlQZGIGpvxwFPsvJqrHXepXw7wnmsLL2dbQh0ZERAbOLzLtx6P44/QV9fghf3cseKoZPJ3YPxARaS03rfQHMclZsLY0x6ygJmomrZmZmaEPjSoxc0MfABFV7Kj4qv0R6PPBLhWckvXj7z0egK9GtWFwiiqdOXPmoE2bNnB0dISHhwcGDhyI06dP3/A7MXPmTPj4+MDOzg7dunXD8ePHS7TJzs7GxIkT4e7uDgcHBwQFBSEqKqpEm+vXr2P48OFwdnZWN7mflJRUok1ERAQGDBig9iH7mjRpEnJycsrxDBDdm99OxKv+QYJTcjHynwGN8dWotgxOERFpSEZOHv7vl3A8+8U+FZyS3IM/vdgRz7StxeAUlTsGqIg0Ij4lC88vP4AZP4UhPScfbWq7YNMrD2FYO192NlQp7dy5Ey+99BL27t2Lbdu2IS8vD7169UJ6erq+zbx587Bw4UIEBwfjwIED8PLyQs+ePZGamqpvM3nyZKxduxarV6/G7t27kZaWhv79+yM/P1/fZujQoThy5Ag2b96sbnJfglQ60rZfv37qvWUfsq81a9ZgypQpFXhGiG59MfLG2jC88PVBVcW1oZcj1r/cGaM6+cHcnCPlRERaEXo5EY9++Ce+3nNZPR7e3hcbX3kIAdWdDX1opBFmhTJ8TAaTkpKiRtuTk5Ph5OTET4LKxbqjMXjr53AkZ+aqUfF/9WqA5zv7qVLhRFr5Trpy5YqaSSWBqy5duqjZUzJzSgJQ06dP18+W8vT0xNy5czFu3Dh1HqpVq4YVK1ZgyJAhqk1MTAxq1qyJjRs3onfv3jh58iQaN26sAmHt2rVTbeR+hw4dcOrUKTRo0ACbNm1SQa3IyEj1nkKCVCNHjkRCQsJdnevK/NmQ4YRFJeOV7w7jwpWiwO0Lnf0wtXcDFsqgO+J3kvHiZ0P3Kis3H4t+O4PPdl1AQSHg7WyLeU82xUP+1XgyqUK/kziDiqgSS0zPwUvfHsKkVYdVcCqguhN+ndgZY7rUYXCKNEc6ReHq6qr+vXjxIuLi4tSsKh0bGxt07doVISEh6nFoaChyc3NLtJEAU0BAgL7Nnj17VKerC06J9u3bq23F28hrdMEpIcEtCYjJexBVNKnE9L8/zuHxj/9SwSlPJxt8M7od/t2/MYNTREQaEh6djKDg3Vi6syg49UTLGtg8uQuDU2QQTJJOVEn9fjIe09eE4WpatgpGvfxwPbz8SD1YWTAuTdojs6Vee+01dO7cWQWKhASnhMyYKk4eX758Wd/G2toaLi4uN7TRvV7+lZlZpcm24m1Kv4/sU/ata1OaBK/kVnz0iagsRF3PwGvf/1Moo2+AF2Y/HggXB2ueYCIijcjNL8CSHefx0e9nkVdQCPcq1njv8UD0bsKKrWQ4DFARVTKpWbl459cT+P5gURJnf48qWDi4OQJrcO04adfLL7+MY8eOqfxPpZWuRiPBrDtVqCnd5mbt76dN6STvs2bNuu1xEN2LvPwCLA+5hIXbziAjJx8O1haYGdQET7aqwVyEREQacjY+VVX0PhaVrB+oeHdgANyq2Bj60EjjTG4qBasyEd1ayPmr6PPBnyo4Jde8Yx7yw/qJnRmcIk2TCnzr1q3DH3/8gRo1aui3S0J0UXoGk+SE0s12kjZSaU+q9N2uTXx8/E1zXhVvU/p9ZJ+yfLD0zCqdGTNmqGWJupvkryJ6kCUcAz/+C+9uOKmCU1IoQxLfPtWaJcOJiLSioKAQn/95Af0W71bBKSdbS3z4dHN8PKwlg1NkFEwuQMWqTEQ3Ss7IxZtrwzD0s32ITspETVc7rB7THm/2Yy4R0i6ZnSQzp3766Sds374dfn5+JZ6XxxI4kgp/OhKMkn6mY8eO6nGrVq1gZWVVok1sbCzCw8P1bSQZugSQ9u/fr2+zb98+ta14G3mNvFZn69atKueVvMfNyHOSSLL4jehepWfn4d1fT6j8IuHRKepiZM6gQHw3tgN83Rx4QomINCLiWgae/myvGqjIyStA1/rVsPXVrniseXXOoiWjYfJV/FiVibQ+CrLmUBT+u+mUKg0unmlbC2/2a4QqNlzBS9qu/DNhwgR8++23+OWXX1QlPR35/7Ozs1P3pVqfzMxdtmwZ/P39MXv2bOzYsQOnT5+Go6OjavPiiy/i119/xfLly1WC9alTp+LatWsqubmFhYVq07dvX1Xdb+nSperx2LFj4evri/Xr16vH+fn5aN68uZotNX/+fCQmJqoKfgMHDsTixYs199lQxdh+Kh5v/XxcDVyIAc188Fb/RvBwtOVHQA+M30nGi58NFSeX+9/uj8B7f8+gtbe2wL/7NcYzbTmDlozvO8lSa1WZpGz4naoySWWlO1VlkoudO1Vlevjhh284Xia9pbJyKi4Fb/0cjgOXrutzTb39WAA61HXjSSYCsGTJEnUeunXrVuJ8SDBKgkNi2rRpyMzMVMEsWXIn3/kys0kXnBKLFi2CpaUlBg8erNp2795dBat0wSmxcuVKTJo0Sd+vBAUFITg4WP+8tN2wYYN6n06dOqkA2dChQ7FgwQJ+VlTmElKyMGv9CWwIK5qxV72qHd59PAAPN7gxmT8REVVecclZmL7mGHaeuaIet/VzxYInm6GWm72hD42o8gWoTLEqE5Pe0oNKy87Dom1nVKJbKRNuZ2WBV3r44/lOfrC2NLlVu0Tl5m4mCEuC8pkzZ6rbrdja2qpZTreb6SSDJN98881t36tWrVpqJhZRec6qlVHyuZtPITUrT1VwHd3ZD5N7+MPe2qT/5CMionv8G+iXIzH4v1/CkZKVp64RpvVuoK4XzM1vXwiGyJBM+q8VU6zKJElvJahWfLpbzZo1b3tcRLqfq1+PxeLdDScQn5Ktr7jxVv/G8KlatFyJiIi06Ux8Kmb8FIbQy0WzapvWcFa5ppr4sIIrEZHWck39Z104/jh9Rd8fLBzcDPU8/pkdTmSsLE29KtOuXbtuWZXJ29v7jlWZis+ikja6hLZ3W5VJEuHeS1UmWW4oN6J7cf5KGv7zy3HsPndVPfZ1s8esoCboxuUaRESalpWbj+Dt57B013nk5hfCwdoCU3s3wHMdaqsZVEREpJ3+YOnOC/jfjnMqCbqVhRkmPuKPCd3qwtKCqyzINJjcT6qpV2UiuheZOfmYv+UU+nywSwWnZHruqz3qY8vkLgxOERFp3F/nrqr+IfiPcyo41aORJ7a91hWjOvkxOEVEpCE7Tieg9we7sOi3Myo41ameGza90gWTuvszOEUmxeRmUL300kv6qkySxFaX60lXlUmW1k2ePFlVYpKKTLqqTPb29iohra7t6NGjMWXKFLi5uemrMgUGBqJHjx6qTaNGjdCnTx+MGTOmRFWm/v3766tBSTLcxo0bY/jw4fqqTLIfeQ0rLNGD2nYiHjPX/VN96eEG1TAzqAnLghMRaVxieo5a7v3ToWj12NPJRs2q7d3Ei6XCiYg0JCYpE+/8egKbwouuiT0cbVT6j/5NvdkfkEkyuQAVqzJRZReZmKECU7+fStBXX/q/AY3Rq7EnOxoiIg2TWeRrDkXjvQ0ncD0jF5Lucnh7X7Wkz8nWytCHR0REFSQ3vwBf7r6ID38/i4ycfDVrdmTH2qoohiP7AzJhZoV3U+aIyo0kSZcZXbJ0kLOutC07Lx+f7ryglmpk/71u/IWH6mDiI/VYfYkqDL+TjBc/G20LvZyId349iSORSepxQy9HzB4UiJa1SlYkJqoo/E4yXvxsKre9F66p6nxn4tPU49a+LnhnYAAaeTsZ+tCIHvg7yeRmUBFVRn+evYL/++U4Ll5NV4871nXD248FoJ5HFUMfGhERGdDla+mYu/kUNoYVLd+wt7ZQSW9feMgPVkx6S0SkGVdSszFn40n8dLhoebergzVm9G2IJ1rWgDmLYlAlwQAVkQGdiElRFx47zxSVga3maIN/92uEoGY+XM5HRKRhSRk5WLz9HL7ec0klQJdrj8Gta+K1nvXh4WRr6MMjIqIKkl9QiG/2XsaCraeRmpWnlnc/07YWpvVugKr21vwcqFJhgIrIQHmm3t96Gr8cjYEssrU0N8PwDr54tWd95hEhItIwqb60Yu9lfPT7WSRn5qptD/m7481+jdDQi8s3iIi05HDEdbz1SzjCo1PU48Dqznh3YACa1axq6EMjKhfm5bNbIrqZa2nZKgH6I+/vwM9HioJTMlvq9yld8Z8BTRicIiLSKEkJuiksFj0X7VQVmSQ41cDTEV893xYrRrdjcIqoHO3atQsDBgyAj0/RDPaff/75ht/PmTNnquelani3bt1w/PjxEm2ys7MxceJEuLu7w8HBAUFBQYiKiirR5vr166r6t+RikZvcT0oqyiunExERoY5F9iH7mjRpEnJycsrx/56M0fX0HMz4KQyDloSo4JSjrSXeeawJfn6pE4NTVKlxBhVRBUjPzsPnf17Ep7vOIz0nXz8iPr1PQwRUd+ZnQESkYZL4XCrzHbh0Xb/ce0rP+niqdU1VmYmIyld6ejqaNWuGUaNG4Yknnrjh+Xnz5mHhwoVYvnw56tevj3fffRc9e/bE6dOn4ejoqNpMnjwZ69evx+rVq+Hm5oYpU6agf//+CA0NhYWFhWozdOhQFbTavHmzejx27FgVpJLXifz8fPTr1w/VqlXD7t27ce3aNYwYMUIFyBYvXswfAw0oKCjEj6FRmLPppKrWKga1rI4ZfRupvoGosmMVPwNjlY3Kv1Rj1f4ILN5+FlfTcvRTc1/v2xCd6rkb+vCIbsDvJOPFz6ZyLveet+U01h+NUY9trcwx9qE6GNe1LhxsOIZIxq2yfifJDKq1a9di4MCB6rEEh2TmlASgpk+frp8t5enpiblz52LcuHHqHEhQacWKFRgyZIhqExMTg5o1a2Ljxo3o3bs3Tp48icaNG2Pv3r1o166daiP3O3TogFOnTqFBgwbYtGmTCmpFRkaq9xQS8Bo5ciQSEhLu+jxX1s9GC7lpZTlf6OWiwYr6nlXwzmMBaFfHzdCHRvRAWMWPyAhGP9Yfi8H7W88gIjFDbavtZo+pvRvg0QBvVtogItKwlKxc/O+Pc1j21yU1kCEJb6UK05Re9eHtbGfowyOiYi5evIi4uDj06tVLv83GxgZdu3ZFSEiIClDJLKnc3NwSbSTAFBAQoNpIgGrPnj0qaKQLTon27durbdJGAlTSRl6jC04Jea0ExOQ9Hn744Zt+NvK83IpfDJLpiLqegYXbzmDt4WiV/kOqtb7aoz5GdqrNaq2kORyeIypDMsr259mrqjLf8ZiiPw7cq9jglR7+eLpNTXYyREQalptfNKv2g9/OIjG9aFZtx7pueOPRRlzuTWSkJDglZMZUcfL48uXL+jbW1tZwcXG5oY3u9fKvh4fHDfuXbcXblH4f2afsW9fmZubMmYNZs2bd9/8jGYb0A8Hbz6kKfTn5BWpbv6beqqI3BytIqxigIiojx6KSVGDqr3PX1OMqNpYY16UOnu/sx6UaREQaH7z47WSCyily4Uq62la3moMKTD3S0EMtKSIi41b691R+r+/0u1u6zc3a30+b0mbMmIHXXnutxAwqWV5Ixpub9ovdkpv2AtKy8/SDFZKbltX5SOsYoCJ6QBevpmPB1tPYcCxWPba2MMez7X3x8iP14OpgzfNLRKRhYVHJeG/jCey9kKgeuzlYY3LP+pxVS2QivLy81L8yg8nb21u/XXJC6WY7SRuptCdV+orPopI2HTt21LeJj4+/Yf9XrlwpsZ99+/aVeF72KcsHS8+sKk6WHMqNTC83bRMfJxWYkuJJHKwgYoCK6L4lpGThw9/P4rsDkcgrkJEt4PHm1fFqz/qo6WrPM0tEpGGHI65j8fZz2H4qQT22tjTH6M5+eLFbXTjZWhn68IjoLvn5+anA0bZt29CiRQu1TYJRO3fuVEnSRatWrWBlZaXaDB48WG2LjY1FeHi4qgAoJBm6JC3fv38/2rZtq7ZJMEq26YJY0ua9995Tr9UFw7Zu3aqCT/IeVHly0/q62WNKrwboH8jctETFcQYV0T1KSM3Cl7sv4auQS8jMzVfbHm5QDdP6NEQjb1ZKISLSsv0XE9XouOQjFOZmwGPNq6sE6DVcOHhBZIzS0tJw7ty5EonRjxw5AldXV9SqVUtV8Js9ezb8/f3VTe7b29tj6NChqr0kOh89ejSmTJkCNzc39bqpU6ciMDAQPXr0UG0aNWqEPn36YMyYMVi6dKnaNnbsWFW1TxKkC0myLpX+hg8fjvnz5yMxMVHtR17DanymR5Zm7jhzBfM2n8bJ2KLctNUcbTCpO3PTEt0KA1REdyniWgY+/fM8vj8YpaboiuY1q+L1vg3RnuVfiYg0fREScv4aPvr9LPZdLFrKZ2luhsdbVMeEh+vBz93B0IdIRLdx8ODBEhXydPmcRowYgeXLl2PatGnIzMzEhAkT1JI7qcQnM5scHR31r1m0aBEsLS3VDCpp2717d/VaCwsLfZuVK1di0qRJ+mp/QUFBCA4O1j8vbTds2KDep1OnTrCzs1NBsAULFvDzMzGHIq5j7qZT+j7B0cYS47vVxahOtWFvzUtwolsxK5S/qshgJImhjLrI9F6OjBinEzEp+GTnefx6LAYFf/+2SGDqpYfroUcjJrelyoXfScaLn43xkT+hdp65ogJThyKS1DYrCzM81bomXuxal8u9qVLjd5Lx4mdjOOcSUjF/y2lsOR6vX949ooMvJnSrBxfmpiWNSrmHmAfDt0S3uOiQZRpLdp7HjtNX9Nu71q+m8oe083NlIkMiIo1X5ZOlfMeikvUXIc+0qYlxXevCp6qdoQ+RiIgqUExSJj747Qx+DI1SA9qyvPuJljVUUYzq7BOI7pr53Tcl0kYSw99OxOPJT/ZgyKd7VXBKOpj+Tb3x68TO+Or5tmo5H6tsEBm/Xbt2YcCAAfDx8VG/sz///PMNQYaZM2eq52UZRbdu3XD8+PESbbKzszFx4kS4u7vDwcFBLceIiooq0UaWe0i+EBkZkpvcT0oqmk2jExERoY5F9iH7kiUekmSXTK+P2BgWi0c/2o0xXx9UwSk7Kwu80NkPu6c9jFmPBTA4RUSkIdfTczB740l0W7BDpQGR4FSvxp7YMrkL5j/VjMEponvEGVREAHLzC7D+aIxayncmPk2dE2sLczzZugbGPlQHtZk/hMjkpKeno1mzZhg1ahSeeOKJG56XykoLFy5UOULq16+Pd999Fz179sTp06f1eUUkMe769euxevVqlfhWEuBKQtvQ0FB9XhHJDyJBq82bN+uT3kqQSl4n8vPz0a9fP1SrVg27d+/GtWvXVF4TCZAtXry4Qs8J3Z/8gkK1zDt4+zmcTSjqIxysLfBcx9oqOOVWheXdiYi0JCMnD8v+uqSuHVKz8tS2tn6umN6nIVr5uhj68IhMFnNQGRjXiBtWZk4+vj8YiU93XUB0UqbaVsXGEs+298XznWrDw8nWwEdIVLEq63eSzKBau3YtBg4cqB5LcEhmTkkAavr06frZUp6enqps+Lhx49Q5kKDSihUrMGTIENUmJiYGNWvWxMaNG9G7d2+cPHlSVVzau3evSpor5L6UCj916pSqzLRp0yYV1IqMjFTvKSTgNXLkSCQkJNz1ea6sn42xD178fDgaH+84j4tX09U2R1tLjOrkp/qIqvbWhj5EIoPhd5Lx4mdTvv3Cdwci8eHvZ3ElNVttkyre0/o0QLf61bjKgugmmIOK6A6SM3Lx9Z5LWBZyCYnpRcts3KtYq4sOCU4521nxHBJVYlJCPC4uTl9JSdjY2KBr164ICQlRASqZJZWbm1uijQSYAgICVBsJUO3Zs0cFjXTBKdG+fXu1TdpIgErayGt0wSkhr5WAmLxH8cpRxcnzciveuVPFkEqtkkdkyc5ziEwsGryoam+F0Z38MKJTbTjZso8gItLcEu/wWLy/9Yx+wKKmqx2m9GyAoGY+MJecIET0wLjEjzQlPiULn/95Ad/ui0B6Tr6+cxnbpS6ealUDtlb/lAImospLglNCZkwVJ48vX76sb2NtbQ0XF5cb2uheL/96eHjcsH/ZVrxN6feRfcq+dW1uZs6cOZg1a9Z9/z/SvcvKLZpV+8mO84hJztIPXrzwUB01eCEzbImISFszpn45EoOlO8/rl3hLvzDxEX8807aWKpBBRGWHf2mRJly4kqaW8f10KBo5+QVqW0MvR1WRr1+gNywt2LkQaVHpggey9O9ORRBKt7lZ+/tpU9qMGTPw2muvlZhBJcsLqXyWe6/cd1n1Ewl/L9nwcLRRFfmGtq0FO2sOXhARaS3H1Or9kWpgWzdg4WhjqQYsRj/kxwELonLCABVVamFRyWqJxqbwOBQWFm1rW9tVBaa6NeA6cSKt8vLyUv/KDCZvb2/9dskJpZvtJG2k0p5U6Ss+i0radOzYUd8mPj7+hv1fuXKlxH727dtX4nnZpywfLD2zqjhZcig3Kj/JmblqRq1cgFz7e7m3j7Ot6iOeal2Ts2qJiDRGUn98FXIJX+25hKSMXLWtmqMNRnf2w9B2tbjEm6icMUBFlY7MSgg5fw1LdpzH7nNX9dt7NPLA+K510bq2q0GPj4gMz8/PTwWOtm3bhhYtWqhtEozauXOnSpIuWrVqBSsrK9Vm8ODBaltsbCzCw8NVBUAhydAlafn+/fvRtm1btU2CUbJNF8SSNu+99556rS4YtnXrVhV8kvegincmPhXLQy5h7aFoZOb+s9z7pW71MKhlDS7ZICLSGCmWJIMVMmtK1y/UdrNXaUAGtazOAQuiCsIAFVWqkfA1oVFqmcb5K0XJCy3MzVTiQglMNfAqKhtPRNqQlpaGc+fOlUiMfuTIEbi6uqJWrVqqgt/s2bPh7++vbnLf3t4eQ4cOVe0l0fno0aMxZcoUuLm5qddNnToVgYGB6NGjh2rTqFEj9OnTB2PGjMHSpUvVtrFjx6qqfZIgXUiSdan0N3z4cMyfPx+JiYlqP/IaVuOrOPkFhdh2Il6NjO+5cE2/vYGnI8Z0qYPHmvvAisu9iYg0N2Dxyc7zWHckBnkFRcstAqo74cWu9dAnwEtdSxBRxWGAikze0cgkfLP3MtYfi0FWblF+KXtrCzzZqgbGPFQHNV3tDX2IRGQABw8eLFEhT5fPacSIEVi+fDmmTZuGzMxMTJgwQS25k0p8MrPJ0fGfYPaiRYtgaWmpZlBJ2+7du6vXWlj8k5No5cqVmDRpkr7aX1BQEIKDg/XPS9sNGzao9+nUqRPs7OxUEGzBggUVdCa07Xp6DlYfiFT9hIyQC7ne6NXYCyM61kb7Oq4sC05EpDGhlxPVaovfTibot3Ws66aWeHeu585+gchAzAplPRQZjCS9lVF6WQ7CkfR7S1woIx0r90UgLDq5xEj4s+1rYWCL6nBkGXAifidVIuwv7s3xmGQ1W0qqL2XnFQ1euNhb4em2tVRFvupV7crlcyLSCn4nGS9+Njcnl71/nE7AJzsuYP+lRLVNapX0aeKlVls0q1m1Qj8nIq1IuYeYB2dQkclNw12597Kqxpeanae2WVuYo19TbwxrVwutfF044kFEpOFy4FuOx6nA1IFL1/Xbm/g4qdlSsuTb1ooV+YiItCQvvwC/HotVS/lOxaWqbVYWZniiZQ21xLtutSqGPkQi+hsDVGT0svPysTk8Ts2W2n+xaLRD+LrZq/LfUmnJ1cHaoMdIRESGczUtG6v2Rah+Ii6lqBy4pbmZyh8ysmNtDl4QEWlQZk4+fgiNxKe7LiDqetESbwdrCwxr74vnO/nBy9nW0IdIRKUwQEVGKzIxQ11s/HAwUl/+WxIVSjW+Ye181fpwcyYuJCLSdA5CmS0lI+M5+UXL+NyrWKvBC7kA8XTixQcRkdYkZ+Ti6z2XsCzkEhL/voZwc7DGqE61Mbx9bTjbWxn6EInoFhigIqOrsrT9VIKqxLfzzBXoMqR5Odni6bY18XSbWhztICLSsJy8AmwMi8XykEs4Epmk3y65Q0Z29MWjgd6wseQyPiIirYlNzsQXf17Eqv0RSM/JV9tquNhhXJc6asUFl3gTGT8GqMgoJKRkqSpLq/dHICa5aHmGeMjfXSWz7d7QA5Ys/01EpFnxKVlqVu23+yLUkj5dDpH+TX1UfqnmTG5LRKTJxOcyWPHN3gisOxqN3Pyi0e2GXo6qIl+/QG9eQxCZEAaoyKAdSsj5a6r097YT8cgrKNRXWRrcuiaGtqsFXzcHfkJERBruJw5FXMfykMvYFBar7yc8nWzUUu9n2tZCNUcbQx8mERFVsPTsPFWlVVZdHI9J0W9v6+eqAlPd6ldj4SQiE8QAFVU4WQv+06EoNQp+4Wq6fnub2i7qgkOS2nIKLhGRdiWkZuGXwzFYcyhKX3FJtPZ1UbOlpJ+w4qxaIiLNOR2Xqga31x6ORpquorelOfo39VarLlrWcjH0IRLRA2CAiipERk6emiX18+Fo/Hn2qn4UvIqNJQa1rK5mSzX0cuKnQUSkUVm5+fjtZDzWhEZh19mrKieh7sLjsWZFy/gCqjsb+jCJiMgAFb03hcWpwNTBy9f12/3cHTCsXS080bIGXFjRm6hSYICKyk1ufgF2n7uKXw5HY+uJeGT8naxQBFZ3VkszHmvuAwcb/hgSEWl5Cd+aQ9H49WgMUrKKRsNFi1pV1UWHjIpXtbc26HESEVHFu3wtXa24+CE0Sl+NTyp692rsqVZddKzrxoreRJUMIwNUDhcbSfjlSDQ2HIvFtb87E+HrZq9GwR9rUR11q1XhmSci0qio6xlYeygaPx2OxsViS719nG3xeMvqGNSyBvsJIiINyssvwO+qoncEdp25ot/u7WyrqnlLVW9PJ1uDHiMRlR8GqKhMnEtIU0EpSVYYkZih3+5exVpVWJKZUlJhyczMjGeciEijCW03hsXip0PR2HPhmn67vbWFyin1ZMsaaF+Ho+FERFoUlywVvSOwen8k4lKKKnrLZUMX/2pqGd8jrOhNpAkMUNEDlfxedyQGvxyNRnh0SomLjd5NvFRQqnM9d5Z2JSLSqIKCQhWMkrxSm8LjkJn7z1LvDnXc8ESrGugb4MWl3kREGu0j/jp/FSv3RmDbyXh97kFXB+uiit5ta6GWm72hD5OIKhADVHRPUrJysTksDj8fKRoBLyzqR2Bpboau9aup5Xs9G3nCztqCZ5aISKPOX0lTQSkpjBGTXDQSrkto+0TL6hjYojpquPCig4hIi66n5+DH0Cis3HcZl679s/KibW1XDGtfS82qtbHktQSRFjFARXdVOeOPUwlq+Z6sCc/JKyhR8luCUv0CvdVoBxERaVNSRg7WH4tVgakjkUn67U62lujfzEclPG9Zi0u9iYi0XBRDZkv9Gharv55w1Ff09kUDL0dDHyYRGRgDVHTLKbd7L17DL4djsDE8FqnFKivV96yCx5pXR1AzH9R05Qg4EZGWq7VKEts1h6Lw24kE5OQX6KssyaxaCUp1b+QBWyuOhBMRaVFadp6aTfvN3ss4FZeq3x5Q3QnPtvPFgGas6E1E/2CAikqMbByPScG6ozEqt5QuQaGucoYEpCQw1cjbkcnOiYg07HhMMtaERmPd0WhcTfunWmtDL0c82aoGgpr7wMORVZaIiLTqREyKWsInwan0nKL8gzaW5up6Ylh7XzSr4czrCSK6AQNUhMjEDFWB7+cjMaoaX/FlGf2aeiOoWXW083OFuTkr8BERabnC0q/HYlTekOKj4FKtVQYvZLZUYx8ngx4jEREZzrW0bKw/GoOfDkfjWFSyfnudag5qtpT0E872VvyIiOiWGKDS6EwpCURtOR6HLcfjERb9TwdibWmOHo081MVGtwbVmKCQiEjDYpMzsTEsDhvDYhF6+bp+u7WFOXo29lR5Q7rUrwYrC3ODHicRERkuV+32kwlYcygaO04nIO/vSnxSQKl3gBeGtaulqraamXGgm4jujAEqDQWljkYl/x2UisOFK+n652RiVIe6biooJVUznGw5skFEpFUxSRKUilW3QxH/JDvXFcaQCnwDmvpwFJyISNMJz5Pw06EoNWMqpViu2qY1nDFI+olmPnCrYmPQ4yQi08MAVSWWl0cYfacAAA+/SURBVF+A/RcTVUBq64l4xBYr9S2j353quamAVI9GnuxAiIg0LDopE5vCYrEhLBaHiwWlZMBbglKPBnqjb4A3vJyZV4qISMtpQX46FI21h6Nw6VpGiVy1MnghgSl/T1biI6L7xwBVGfj4448xf/58xMbGokmTJvjggw/w0EMPwRCycvPx59mrKij1+8l4XM/I1T/nYG2Bbg090KeJl1q+58iZUkREmu0voq5nYFNYnApKHYksGZRq4+uKRwO90DfQG55ODEoREWm1v0jJysXGY7EqMLX/UqJ+u721hRrolrxS7eu4qeqtREQPigGqB/Tdd99h8uTJqhPp1KkTli5dir59++LEiROoVasWKkJyZq5a8y1BqR2nryDj70oZwtXBWuWUkg6kY113lvomItJwfyGj35vCZaZUHI6WDkrVdkW/QG/VXzAoRUSk3f4iN78Af569ooJS207EIzuvQN9XdKrrrvIP9m7iBQcbXkoSUdkyK5RFxHTf2rVrh5YtW2LJkiX6bY0aNcLAgQMxZ86cO74+JSUFzs7OSE5OhpPT3Vc/iriWgd9OxqubLOPTJSQUPs626NXES11kyNIMSyavJaK7dL/fSWSc/YV08afjU7ElPF4NYpyITdE/JxcabSUo1dRbzaz14EwpIroH7C8qV39RUFCI0Ijr+PlwtMpBWHwVhr9HFQxqWQMDW/jA29nuPv+viEirUu7hO4lh7weQk5OD0NBQvP766yW29+rVCyEhITd9TXZ2troV/7Du1ejlB/D7qYQS2+p5VEHvJp5qNCOwujMrZRARaby/kOBU3w//xKm4VP02WYHR1q9oppRUV/Jw5PI9IiKt9xeyjK/Pol2IKZav1r2KDfo39VZL+AKqO/HagogqBANUD+Dq1avIz8+Hp6dnie3yOC4u7qavkVGPWbNmPcjbwtfNQa3zblPbRSU4l1ttd4cH2icREVWu/kJKetd2c8CFq+no4u+uZtZKfyFLv4mIyDgZor+QCt7ujjaqGp8MdstMqQ513LgKg4gqHANUZUAuAkqPWpfepjNjxgy89tprJUY4ataseU/vN75bHbzS3Z8lvomITExF9xf/N6Ax3h/cjHlCiIhMTEX3F4ufaaHyD9paWdznERMRPTgGqB6Au7s7LCwsbhjNSEhIuGHUQ8fGxkbdHgSXZBARmRZD9Rc+VZkrhIjIlBiqv5AVGkREhmZu6AMwZdbW1mjVqhW2bdtWYrs87tixo8GOi4iIjAv7CyIiYn9BRHR7nEH1gGQ67fDhw9G6dWt06NABn376KSIiIjB+/PgH3TUREVUi7C+IiIj9BRHRrTFA9YCGDBmCa9eu4e2330ZsbCwCAgKwceNG+Pr6PuiuiYioEmF/QURE7C+IiG7NrFAy7pHBSBJDZ2dnJCcnw8nJiZ8EERkUv5OMFz8bIjIm/E4yXvxsiMhUv5OYg4qIiIiIiIiIiAyKASoiIiIiIiIiIjIoBqiIiIiIiIiIiMigGKAiIiIiIiIiIiKDYoCKiIiIiIiIiIgMytKwb0+6IoqS2Z6IyNB030Us8Gp82F8QkTFhf2G82F8Qkan2FwxQGVhqaqr6t2bNmoY+FCKiEt9NUg6WjAf7CyIyRuwvjA/7CyIy1f7CrJDD5AZVUFCAmJgYODo6wszM7K4jkBLQioyMhJOTU7kfY2XAc8Zzxp+zuyNdgnQePj4+MDfnKnBjwv6iYrC/4Dnjz9ndYX9hvNhfVAz2Fzxn/Bkr+/6CM6gMTD6gGjVq3NdrJTjFABXPWXnjz5n2zhlnThkn9hcVy9R/jw2B50x754z9hXFif1GxTP332BB4zrR3vpzvcmUGh8eJiIiIiIiIiMigGKAiIiIiIiIiIiKDYoDKBNnY2OA///mP+pd4zvhzZjz4u0nGhj+TPGf8OTNO/N0kY8OfSZ4z/pwZHxsNXvczSToRERERERERERkUZ1AREREREREREZFBMUBFREREREREREQGxQAVEREREREREREZFANURERERERERERkUAxQGamPP/4Yfn5+sLW1RatWrfDnn3/etv3OnTtVO2lfp04dfPLJJ9CaezlnO3bsgJmZ2Q23U6dOQQt27dqFAQMGwMfHR/1///zzz3d8jdZ/xu71nGn9Z4wqDvuL8j1nWv9dZn9R/udM6z9jVHHYX5TvOdP67zL7i/I/Zzs08DPGAJUR+u677zB58mS8+eabOHz4MB566CH07dsXERERN21/8eJFPProo6qdtH/jjTcwadIkrFmzBlpxr+dM5/Tp04iNjdXf/P39oQXp6elo1qwZgoOD76o9f8bu/Zxp/WeMKgb7i/I/Z1r/XWZ/Uf7nTOs/Y1Qx2F+U/znT+u8y+4vyP2ea+BkrJKPTtm3bwvHjx5fY1rBhw8LXX3/9pu2nTZumni9u3Lhxhe3bty/Uins9Z3/88Ueh/Phfv369UOvkPKxdu/a2bfgzdu/njD9jVBHYX5T/OePv8j/YX9w79hdkLNhflP85Y3/xD/YX9479RRHOoDIyOTk5CA0NRa9evUpsl8chISE3fc2ePXtuaN+7d28cPHgQubm5qOzu55zptGjRAt7e3ujevTv++OOPcj5S06X1n7EHwZ8xKi/sLyrmnOnwd/nusL+4f/wZo/LC/qJizpkOf5fvDvuL+9eiEl/DMkBlZK5evYr8/Hx4enqW2C6P4+Libvoa2X6z9nl5eWp/ld39nDP5hf7000/VMsiffvoJDRo0UL/gsg6YbqT1n7H7wZ8xKm/sLyrmnPF3+d6wv7h3/Bmj8sb+omLOGX+X7w37i3vnrYFrWEtDHwDdnCQ7K05m/ZXedqf2N9temd3LOZNfZrnpdOjQAZGRkViwYAG6dOlS7sdqivgzdm/4M0YVhf1F+Z4z/i6Xzfm92XbizxhVLPYX5XvO2F+Uzfm92XbSzs8YZ1AZGXd3d1hYWNwQmU9ISLghgq/j5eV10/aWlpZwc3NDZXc/5+xm2rdvj7Nnz5bDEZo+rf+MlRX+jFFZYn9RMefsZvi7fGvsL8oGf8aoLLG/qJhzdjP8Xb419hdlo30lu4ZlgMrIWFtbqxKm27ZtK7FdHnfs2PGmr5HIaen2W7duRevWrWFlZYXK7n7O2c1IdQ6ZNkk30vrPWFnhzxiVJfYXFXPOboa/y7fG/qJs8GeMyhL7i4o5ZzfD3+VbY39RNg5XtmvYv5OlkxFZvXp1oZWVVeEXX3xReOLEicLJkycXOjg4FF66dEk9L5Ujhg8frm9/4cKFQnt7+8JXX31VtZfXyet//PHHQq2413O2aNEiVYXtzJkzheHh4ep5+XVYs2ZNoRakpqYWHj58WN3k/3vhwoXq/uXLl9Xz/Bl78HOm9Z8xqhjsL8r/nGn9d5n9RfmfM63/jFHFYH9R/udM67/L7C/K/5wt0sDPGANURup///tfoa+vb6G1tXVhy5YtC3fu3Kl/bsSIEYVdu3Yt0X7Hjh2FLVq0UO1r165duGTJkkKtuZdzNnfu3MK6desW2traFrq4uBR27ty5cMOGDYVaoSuDW/om50nwZ+zBz5nWf8ao4rC/KN9zpvXfZfYX5X/OtP4zRhWH/UX5njOt/y6zvyj/czZXAz9jZvIfQ8/iIiIiIiIiIiIi7WIOKiIiIiIiIiIiMigGqIiIiIiIiIiIyKAYoCIiIiIiIiIiIoNigIqIiIiIiIiIiAyKASoiIiIiIiIiIjIoBqiIiIiIiIiIiMigGKAiIiIiIiIiIiKDYoCKiMjE7Nq1CwMGDICPjw/MzMzw888/39PrZ86cqV5X+ubg4FBux0xERBWLfQUREZlaf8EAFVEl8c4772DWrFkoKCgw9KFQOUtPT0ezZs0QHBx8X6+fOnUqYmNjS9waN26Mp556qsyPlYiMD/sLbWBfQUQPiv2FNqQb0bWFWWFhYeF9HQURGY2LFy+iTp06qF27trpP2iGjE2vXrsXAgQP123JycvDvf/8bK1euRFJSEgICAjB37lx069btpvs4evQomjdvrkZPHnrooQo8eiKqaOwvtIl9BRHdK/YX2mRm4GsLywf+PyAigzt8+LD6V74IiEaNGoVLly5h9erVaqqudDJ9+vRBWFgY/P39bzhBn3/+OerXr8/gFJEGsL8gHfYVRMT+goytv+ASP6JKgBccpHP+/HmsWrUKP/zwg+oU6tatq6bddu7cGcuWLbvhRGVnZ6vRkNGjR/MkEmkA+wsS7CuIiP0FGWN/wQAVkQmTX36Zhvnuu+/eNEHd+vXrDX2IVMEOHToEWbktoxZVqlTR33bu3Kk6mNJ++uknpKam4rnnnuNnRVSJsb+g4thXEBH7CzLG/oJL/IhMWGZmJjp16oT9+/cjNzcXbdu2hZWVlf55SXZH2iJJ8i0sLBAaGqr+LU46k5tNwe3fvz+8vLwq8CiJqKKxv6Di2FcQEfsLMsb+ggEqIhP2wgsvYNiwYerLwc7ODiEhITd8cZC2tGjRAvn5+UhISLjjum9JfvnHH39g3bp1FXZ8RGQY7C+oOPYVRMT+goyxv2CAisjEhYeHq8i2VFNgcEob0tLScO7cuRKdwZEjR+Dq6qqm30rQUqbVvv/++6pTuXr1KrZv347AwEA8+uij+td9+eWX8Pb2Rt++fQ30f0JEFYn9hbawryCi+8X+QlvSjOjaggEqIhMnZTwFl/Npx8GDB/Hwww/rH7/22mvq3xEjRmD58uUqYaHkJZsyZQqio6Ph5uaGDh06lOhAJKgpbUeOHMnAJpFGsL/QFvYVRHS/2F9oy0EjurYwK5SMV0RksiZOnIjg4GAsXrwYL7/8sqEPh4iIjBT7CyIiYn9BxoxV/IhMHEc4iIiI/QUREfH6gkwdZ1ARmbiqVasiOTkZSUlJcHZ2NvThEBGRkWJ/QURE7C/ImHEGFZEJu3TpkgpO+fr6MjhFRETsL4iIiNcXZLIYoCIyYWfOnFH/NmjQwNCHQkRERoz9BRERsb8gY8cAFZEJs7e315cCzc7ONvThEBGRkWJ/QURE7C/I2DEHFZEJS0tLQ/369REbG4tq1aqhXr16MDc3x+uvv47+/fsb+vCIiMhIsL8gIiL2F2TsOIOKyIRVqVIFGzduRN++fVFYWIg9e/bgr7/+gru7u6EPjYiIjAj7CyIiYn9Bxo4zqIiIiIiIiIiIyKA4g4qIiIiIiIiIiAyKASoiIiIiIiIiIjIoBqiIiIiIiIiIiMigGKAiIiIiIiIiIiKDYoCKiIiIiIiIiIgMigEqIiIiIiIiIiIyKAaoiIiIiIiIiIjIoBigIiIiIiIiIiIig2KAioiIiIiIiIiIDIoBKiIiIiIiIiIiMigGqIiIiIiIiIiIyKAYoCIiIiIiIiIiIoNigIqIiIiIiIiIiAyKASoiIiIiIiIiIoIh/T/FAfLJzwTa+QAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "t, p, e, xI, Phi_phi, Phi_theta, Phi_r = traj_model(*traj_pars, T=T)\n", "\n", "fig, axes = plt.subplots(2, 3)\n", "plt.subplots_adjust(wspace=0.35)\n", "fig.set_size_inches(14, 8)\n", "axes = axes.ravel()\n", "\n", "ylabels = [r\"$e$\", r\"$p$\", r\"$e$\", r\"$\\Phi_\\phi$\", r\"$\\Phi_\\theta$\", r\"$\\Phi_r$\"]\n", "xlabels = [r\"$p$\", r\"$t$\", r\"$t$\", r\"$t$\", r\"$t$\", r\"$t$\"]\n", "ys = [e, p, e, Phi_phi, Phi_theta, Phi_r]\n", "xs = [p, t, t, t, t, t]\n", "\n", "for i, (ax, x, y, xlab, ylab) in enumerate(zip(axes, xs, ys, xlabels, ylabels)):\n", " ax.plot(x, y)\n", " ax.set_xlabel(xlab, fontsize=16)\n", " ax.set_ylabel(ylab, fontsize=16)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Trajectory stopping conditions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In principle, the inspiral trajectory continues until $p$ intersects with the separatrix, $p_\\mathrm{sep}(a, e, x_I)$. However, FEW truncates the inspiral at the buffer point $p_\\mathrm{stop} = p_\\mathrm{sep} + \\Delta p$ for numerical stability, performing a root-finding operation to place the last trajectory point within $\\sim 10^{-8}$ of $p_\\mathrm{stop}$. \n", "\n", "The size of $\\Delta p$ can vary based on the trajectory model, and can be obtained directly from the ODE object:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:42.195888Z", "iopub.status.busy": "2026-07-11T10:48:42.195805Z", "iopub.status.idle": "2026-07-11T10:48:43.356247Z", "shell.execute_reply": "2026-07-11T10:48:43.355868Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Delta_p: 0.002\n" ] }, { "data": { "text/plain": [ "np.float64(1.8074430840897548e-13)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from few.utils.geodesic import get_separatrix\n", "\n", "Delta_p = KerrEccEqFlux().separatrix_buffer_dist\n", "print(\"Delta_p:\", Delta_p)\n", "p_sep = get_separatrix(a, e[-1], xI[-1]) # the separatrix at the trajectory end-point.\n", "p[-1] - (p_sep + Delta_p)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Output for a requested time duration" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By using the keyword argument `T`, the trajectory to be computed until it reaches a desired time (in years)." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:43.357425Z", "iopub.status.busy": "2026-07-11T10:48:43.357361Z", "iopub.status.idle": "2026-07-11T10:48:43.361809Z", "shell.execute_reply": "2026-07-11T10:48:43.361507Z" } }, "outputs": [ { "data": { "text/plain": [ "(np.float64(17366327.48432057), np.float64(3155814.9763545603))" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "T = 0.1 # duration of trajectory in years (as defined by few.utils.constants.YRSID_SI)\n", "\n", "t_trunc, p_trunc, e_trunc, xI_trunc, Phi_phi_trunc, Phi_theta_trunc, Phi_r_trunc = traj_model(*traj_pars, T=T)\n", "\n", "t[-1], t_trunc[-1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Output on a requested time grid" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In addition to the sparse output of the adaptive solver, the user can also construct trajectories on pre-defined time grids. For uniform grids, the sampling cadence $\\mathrm{d}t$ can be supplied and the grid will be constructed automatically. Non-uniform grids can be supplied via the `new_t` keyword argument. In either case, the `fix_t` keyword argument can be used to truncate the returned trajectory at its end-point." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:43.362819Z", "iopub.status.busy": "2026-07-11T10:48:43.362769Z", "iopub.status.idle": "2026-07-11T10:48:43.424104Z", "shell.execute_reply": "2026-07-11T10:48:43.423828Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "t1 max: 19999900.0 t2 max: 4713600.0\n" ] }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dt = 100.0\n", "new_t = np.arange(0, 2e7, dt)\n", "\n", "# a warning will be thrown if the new_t array goes beyond the time array output from the trajectory\n", "t1, p1, e1, x1, Phi_phi1, Phi_theta1, Phi_r1 = traj_model(\n", " *traj_pars, T=T, new_t=new_t, upsample=True\n", ")\n", "\n", "# you can cut the excess on these arrays by setting fix_t to True\n", "t2, p2, e2, x2, Phi_phi2, Phi_theta2, Phi_r2 = traj_model(\n", " *traj_pars, T=T, new_t=new_t, upsample=True, fix_t=True\n", ")\n", "\n", "plt.plot(t1, Phi_phi1)\n", "plt.plot(t2, Phi_phi2, ls=\"--\")\n", "\n", "print(\"t1 max:\", t1.max(), \"t2 max:\", t2.max())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Return trajectory in dimensionless time coordinates" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Trajectories are returned in coordinate time by default, but may be obtained in dimensionless time units by passing `is_coordinate_time=False`:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:43.425309Z", "iopub.status.busy": "2026-07-11T10:48:43.425246Z", "iopub.status.idle": "2026-07-11T10:48:43.478580Z", "shell.execute_reply": "2026-07-11T10:48:43.478229Z" } }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjoAAAGvCAYAAABSC3+tAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjksIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvJkbTWQAAAAlwSFlzAAAPYQAAD2EBqD+naQAAV2pJREFUeJzt3Qd4FNXCBuAvvRdSSAgpEAgtoSMQutKr2Cty7QVBFEVRfxWvghUbKnblgsQCCCIiIE0gFEMNoQRCCklII530nf85Z8gmAcQESHZn9nufZ92d2bO7MzvAfp5qpSiKAiIiIiIdsjb1ARARERE1FgYdIiIi0i0GHSIiItItBh0iIiLSLQYdIiIi0i0GHSIiItItBh0iIiLSLQYdIiIi0i1bWDCDwYC0tDS4ubnBysrK1IdDRERE9SDmOi4sLERAQACsrS9dZ2PRQUeEnKCgIFMfBhEREV2GlJQUBAYGXrKMRQcdUZNT/UW5u7ub+nCIiIioHgoKCmRFRfXv+KVYdNCpbq4SIYdBh4iISFvq0+2EnZGJiIhItxh0iIiISLcYdIiIiEi3GHSIiIhItxh0iIiISLcYdIiIiEi3GHSIiIhItxh0iIiISLcYdIiIiEi3GHSIiIhItxh0iIiISLcYdHRu3759ci2QxMREUx8KERFRk2PQ0alDhw5h0qRJmDhxotwePnw4HnroIQYeIiJqEqsOpOHWz6Lx9daTMCUGHR1atmwZunXrhuLiYsyYMUPumzlzJk6ePInw8HBs27bN1IdIREQ6d/BUPnadPIPEnGKTHoetST9dYxRFQUlFVZN/rpOdTb2WohfKy8vx8MMPY+TIkTLwiKar6hqde++9F3379sVjjz2G/fv3N/JRExGRJTuaUSjvw/zcTHocDDoNIEJOp5f+QFOLe3UknO3rd6kOHjyI7Oxs2Wx1PltbW9xyyy147rnncObMGXh5eRmf++ijj1BRUYGnnnrqqh47ERFZpiPpatDp6G/aoMOmKx3WOgn/VANUvb+6XDVRw9OjR48mOEIiItK77KIynC4ohfjJ6dDC3aTHwhqdBjYhidoVU3xufXXp0gXe3t5YvHgxbr311jrPVVVV4eeff5b9dEQZITY2FlOnTsWOHTuwefNmvPPOO7j++uuv+jkQEZHliE3Nl/etvV3g6mDaqMGg0wCiNqS+TUimYm9vj08++QR33nmnDDpDhgyR+zdu3Igff/xRNm2tXbtW7ispKcHdd98t90+YMAE//PADJk+ezKBDRERX3BFZ6BzoAVNj05UOiYCzd+9eGXrefPNNue/VV19FixYtZA3OwIED5b41a9YgMjISlZWVCAsLk7eCggITHz0REWnd/lN58r5LoKepD4U1OnrVuXNnLFq0SI666t69u6zRadWq1QX9ckQ5UcsTEREht0XTFxER0eUSfUD3pahBp1sQgw41MjGfzvkdj6u5u7vj2LFjcHFxQceOHTFnzhxMmTKF14SIiC5b8pmzyC4qh52NFcIDTNsRWTDvDifUqO655x7ZH0c0Z/n7+2PatGkYNWoUv3UiIrpse5Jz5X14gAccGzCYprEw6FgwHx8fOUty+/bt5ZIRYp4dIiKiK7E7UQ0617RqBnPAzsgWLi8vD66urgw5RER0Vew+eUbe9wypmZTWlBh0LJynpydiYmJMfRhERKQDOUVliM8sko97t2bQISIiIh3Zda42p52fK7xc7GEOWKNDREREV0V0Qo68jwxVZ983Bww6REREdFVEn1CDTl8GHSIiItKTjIJS2T9HLOQZ2YY1OkRERKQj209ky3sxSaCns3n0zxHYdEVERERX7K9jatAZ0NYX5oRBh4iIiK6IWGpoS7wadAa184E5YdAhIiKiK3I4vRDZRWVwsrNBzxDzmBG5GoMOERERXZGNRzPlff+23nCwNf36VrUx6BAREdEV2XQu6Axp3xzmhkFH5/bt2wcrKyskJiaa+lCIiEiH8s6WIyZJXchzSHvz6ogsMOjolFiNfNKkSZg4caLcHj58OB566CEGHiIiuqo2Hc2CQQHa+7khsJkzzA2Djg4tW7YM3bp1Q3FxMWbMmCH3zZw5EydPnkR4eDi2bdtm6kMkIiKdWH84Q94P62R+zVaClSLGhFmogoICeHh4ID8/H+7u7v/+AvFVVZxFk7Nzhpxqsh7Ky8vRsmVL9OnTB6tWrZJNV927d5chJzAwEH379kVFRQX279/f6IdNRET6Vl5pQM//rkNhWSWWPdYPPYKbmd3vt22THJFeiJAzJ6DpP/f5NMDepV5FDx48iOzsbNlsdT5bW1vccssteO6553DmzBl4eXk1wsESEZGl2JGQI0OOj6sDugV6whyx6UpnqivoRAfki6nef7GKvKqqqkY+OiIi0pM1h07L+xHhfrC2rl/LQ1NjjU5Dm5BE7YopPreeunTpAm9vbyxevBi33nrrBUHm559/lv10RBlh9OjR6Ny5M3bs2IF7771X3oiIiP5NlUHB2kNq/5yR4f4wVww6DSFqQ+rZhGQq9vb2+OSTT3DnnXfKoDNkyBC5f+PGjfjxxx9l09batWuN5WNjYzFq1Chs2bLFhEdNRERaszc5V86G7OZoi8hQ81mt/HxsutIhEXD27t0rQ8+bb74p97366qto0aKFDDYDBw6U+0QnLtGU9cQTT5j4iImISGt+O5gu74d19IO9rfnGiQYdWWVlJV588UW0bt0aTk5OCA0NlT+gBoPBWEb0/XjllVcQEBAgy4gaBTGnS21lZWWYOnUqfHx84OLiggkTJuDUqVN1yuTm5soOtaJXtbiJx3l5eXXKJCcnY/z48fI9xHtNmzZNjjoiyOaoRYsWYcWKFcYana+//hpt2rQxfj0i9PTr149fFxERNYjBoGD1uaAztnMLmLMGBR1RO7BgwQLMnz8fhw8fxltvvYW3334bH330kbGM2Ddv3jxZZvfu3fD395eT1RUWFhrLTJ8+HcuXL0dUVBS2bt2KoqIijBs3rk5nWNH0IoZGr1mzRt7E49ojiUTZsWPHyrlixHuI91q6dKlx3hhSifl0RPhs1arVBV+JCDoiEBERETVETHIuMgrK4OZgi4Fmtlr5BZQGGDt2rHLffffV2XfjjTcqd999t3xsMBgUf39/5Y033jA+X1paqnh4eCgLFiyQ23l5eYqdnZ0SFRVlLJOamqpYW1sra9askdtxcXFiSJCyY8cOY5no6Gi578iRI3J79erV8jXitdWWLFmiODg4KPn5+fU6H1FOvGd9y+vN1KlTlRUrVpj6MIiISGNeXhGrhDy7Snnyh70m+fyG/H43qEZnwIAB+PPPP3Hs2DG5LSadE7UpY8aMkdtiUrrTp09jxIgRxtc4ODhg8ODB2L59u9yOiYmRE9bVLiOauSIiIoxloqOjZXOVmPSumpjoTuyrXUa8Rry22siRI2WzmPiMixHPiUmGat8s2YcffiibDYmIiBoy2uo3jTRbNXjU1bPPPis7sHbo0AE2Njay+ej111/HHXfcIZ8XIUfw8/Or8zqxnZSUZCwjOsk2a9bsgjLVrxf3zZtfOJW02Fe7zPmfI95TvHd1mfPNnTsXs2fPbsgpExERUS3bT2Qjq7AMns52GBhmfot4nq9BNTo//PCD7OD6/fffY8+ePfjuu+/wzjvvyPvazp+sTvQR+acJ7P6pzMXKX06Z2mbNmiWDWvUtJSXlksdEREREda3Yl2aszTHn0VaXVaPzzDPPyOUDbr/9drktOrKKmhpRUzJ58mTZ8VgQNSpiKHO1zMxMY+2LKCNGRolRVbVrdUSZ6hFAokxGhjoJUW1ZWVl13mfnzp11nhfvKZrFzq/pqd2MJm5ERETUcKUVVVgTq7aaTOzeElrQoCh29uxZWFvXfYlowqoeXi6GnYsAsm7dOuPzItRs3rzZGGJ69uwJOzu7OmXS09PrDHWOjIyUNS67du0ylhGhRuyrXUa8Rry2mpgITwQZ8RlERER0df15OBNFZZVo6emEnk20gGeT1uiIOWtEn5zg4GC5jICYlE4MJb/vvvvk86LJSAwdnzNnDsLCwuRNPHZ2dpbDxQXRofj++++Xw8DFMgRiYcmnn35a1g4NGzZMlunYsaOcrffBBx/EZ599Jvc99NBDcgh6+/bt5bbozNypUyc55FwMcReLVIr3Ea+p10rkRERE1CDL9qhz3l3fLcBs17a6QEOGcxUUFChPPPGEEhwcrDg6OiqhoaHKCy+8oJSVlRnLiCHmL7/8shxmLoZ6Dxo0SDl48GCd9ykpKVEef/xxxcvLS3FyclLGjRunJCcn1ymTk5Oj3HXXXYqbm5u8ice5ubl1yiQlJckh7+I9xHuJ9xTD2evL0oeXExER1VdGQYkSOus3Oaz8eGahYkoN+f22Ev+BhRLDy0UNk2gSYy0QERHRP/tiSwJeX30YPYI9seyx/tDK77f5d5cmIiIik1IUBT/FqCOVb+4ZpKmrwaBDREREl3QwNR/HMorgYGuNcV3Nf5LA2hh0iIiI6JJ+2K3W5owM94e7ox20hEGHiIiI/lFxWaVxksDbe2ur2Upg0CEiIqJ/9NuBdDl3TitvZ0SGekNrGHSIiIjoH32/K1ne39E7+F+XczJHDDpERER0UXFpBdiXkgc7Gyvc1DMQWsSgQ0RERBcVtVutzRnRyR8+rtpcK5JBh4iIiC4g+uUs25NqbLbSKgYdIiIiusDyPadk2An1dUH/ttrrhFyNQYeIiIgumAn5u+gk+XhyZCtNdkKuxqBDREREdUSfyMHxzCK42Nvgxh4toWUMOkRERFTHd9GJ8l6MtHLT2EzI52PQISIiIqPUvBKsi8uQj++JDIHWMegQERGR0bfbTsKgQHZAbtvcDVrHoENERERSYWkFonapC3jeP6A19IBBh4iIiIyrlBeWVaKNrwuGtGsOPWDQISIiIlRWGfDNNrUT8gMDQ2Ftrd0h5bUx6BARERF+jz0tOyJ7u9jjhu7aHlJeG4MOERGRhVMUBV/+lSAfT4oMgaOdDfSCQYeIiMjC7U7Mxf5T+bC3tcbdfbU/pLw2Bh0iIiIL9/HG4/L+ph6Bml2l/J8w6BAREVmw2NR8bD6WBdH3+NHBbaA3DDpEREQW7JNNam3OhK4BCPZ2ht4w6BAREVmo45mFcrSV8OiQttAjBh0iIiIL9emmBCgKMLyTH9r7a3+5h4th0CEiIrJAKWfO4pd9qfLxlGv1WZsjMOgQERFZoM+3JKDKoGBAWx90C/KEXjHoEBERWZi0vBK5rpXw2LX6G2lVG4MOERGRBc6bU15lQJ/WXogM9YaeMegQERFZWN+cH/9Wa3OeGt4OVlb6WLzznzDoEBERWZD5G46jokrtm9NH57U5AoMOERGRhUjMLsbPe07Jx08ObwdLwKBDRERkIT7cEC9HWg1p74ueIc1gCRh0iIiILMDxzCL8sledN+fJYZZRmyMw6BAREVmAD/6Mh0EBhnX0Q1cdz5tzPgYdIiIinTt4Kh+/7k+Tj58cHgZLwqBDRESkY4qiYO7vh+Xjid0CEB7gAUvCoENERKRjm49lYfuJHNjbWGPGiPawNAw6REREOlVlUPDG70fk43siQxDk5QxLw6BDRESkU8v3puLI6UK4O9ri8ev0u0L5pTDoEBER6VBpRRXmrT0qHz92bVt4OtvDEjHoEBER6dC32xORll+KAA9H/KdfK1gqBh0iIiKdyTtbLlcoF54a0R6OdjawVAw6REREOvP++ngUllaig78bbujeEpaMQYeIiEhHjp4uxP92JMnH/zeuE2ysrWDJGHSIiIh0NDng7F8PyWHlo8L90b+tDywdgw4REZFOrIk9rU4OaGuNF8Z2NPXhmAUGHSIiIp0MJ3/tN3Wph0cGhVrk5IAXw6BDRESkA59vSUBqXglaeDjikSFtTH04ZoNBh4iISONEwPlkkzqcfNaYjnC2tzX1IZkNBh0iIiKNm7v6MEorDOjdygvju7Qw9eGYFQYdIiIiDduZkINVB9IhRpG/PKETrKwsezj5+Rh0iIiINKq80oD/WxErH9/eOxjhAR6mPiSzw6BDRESkUV/8lYBjGUXwdrHHzJHtTX04ZolBh4iISIMSs4vx4Z/x8vGL4zpa7Ork/4ZBh4iISIMzIIsmq7JKA/q39cbEbpa9ntWlMOgQERFpzIp9afgrPlvOgPz6xM7sgHwJDDpEREQakne2HP9dFScfT7uuLVr5uJj6kMwagw4REZGGvPH7EeQUlyOsuSseGsQZkP8Ngw4REZFG7Dp5BlG7U+TjOTd2lk1XdGn8hoiIiDSgrLIKs5YdkI/v6B2Ma1p5mfqQNIFBh4iISAMWbErAiaxi+Lja47lRHUx9OJrBoENERGTmDqXl46MN6pw5L40Ph4eznakPSb9BJzU1FXfffTe8vb3h7OyMbt26ISYmps7Y/ldeeQUBAQFwcnLCkCFDcOjQoTrvUVZWhqlTp8LHxwcuLi6YMGECTp06VadMbm4uJk2aBA8PD3kTj/Py8uqUSU5Oxvjx4+V7iPeaNm0aysvLG/4tEBERmfEyDzN+3I9Kg4JR4f5ctLMxg44IH/3794ednR1+//13xMXF4d1334Wnp6exzFtvvYV58+Zh/vz52L17N/z9/TF8+HAUFhYay0yfPh3Lly9HVFQUtm7diqKiIowbNw5VVVXGMnfeeSf27duHNWvWyJt4LMJONVF27NixKC4ulu8h3mvp0qWYMWNGQ78DIiIisyVqco6cLoSXiz1euyGCc+Y0lNIAzz77rDJgwIB/fN5gMCj+/v7KG2+8YdxXWlqqeHh4KAsWLJDbeXl5ip2dnRIVFWUsk5qaqlhbWytr1qyR23FxcYo4tB07dhjLREdHy31HjhyR26tXr5avEa+ttmTJEsXBwUHJz8+v1/mIcuI961ueiIioKe1PyVVCZ/2mhDy7SvntQBq//Mv4/W5Qjc7KlSvRq1cv3HLLLWjevDm6d++OL774wvj8yZMncfr0aYwYMcK4z8HBAYMHD8b27dvltmjmqqioqFNGNHNFREQYy0RHR8vmqj59+hjL9O3bV+6rXUa8Rry22siRI2WzWO2mtNrEcwUFBXVuRERE5qi0oko2WVUZFIzvGoAxnVuY+pA0qUFBJyEhAZ9++inCwsLwxx9/4JFHHpH9YhYuXCifFyFH8PPzq/M6sV39nLi3t7dHs2bNLllGBKnziX21y5z/OeI9xXtXlznf3LlzjX1+xC0oKKghp09ERNRk3lt/DPGZRfBxdcCrE8K1982XFQJrngcyj2gn6BgMBvTo0QNz5syRtTkPP/wwHnzwQRl+arOysqqzLToon7/vfOeXuVj5yylT26xZs5Cfn2+8paSoky4RERGZk5ikXHyxJUE+nnNDBJq5aGxlckUBlj0E7PgY2PiadoJOixYt0KlTpzr7OnbsKEc/CaLjsXB+jUpmZqax9kWUESOjRMfmS5XJyMi44POzsrLqlDn/c8R7imax82t6ajejubu717kRERGZk5LyKjzz034YFODG7i0xIlz9bdWU2KXA0dWAjT3QvWYgkdkHHTHi6ujRo3X2HTt2DCEhIfJx69atZQBZt26d8XkRajZv3ox+/frJ7Z49e8pRW7XLpKenIzY21lgmMjJS1rjs2rXLWGbnzp1yX+0y4jXitdXWrl0rw4z4DCIiIi16+4+jSMguhp+7A14er8Emq9J8YM0s9fGgZ4B2I017PEoD7Nq1S7G1tVVef/11JT4+Xlm8eLHi7OysLFq0yFhGjLgSo6yWLVumHDx4ULnjjjuUFi1aKAUFBcYyjzzyiBIYGKisX79e2bNnj3LdddcpXbt2VSorK41lRo0apXTp0kWOthK3zp07K+PGjTM+L8pGREQoQ4cOle8h3ku85+OPP17v8+GoKyIiMifRJ7KVVs+tkqOsNhzJUDRp9UxFedldUT7soSgVpY3yEQ35/W5Q0BF+/fVXGTDEMO4OHToon3/++QVDzF9++WU5zFyUGTRokAw8tZWUlMhA4uXlpTg5OckAk5ycXKdMTk6Octdddylubm7yJh7n5ubWKZOUlKSMHTtWvod4L/GeYjh7fTHoEBGRucgtLlP6zlkvQ87Mn/YrmpR+UFFe8VSDzvENjfYxDfn9thL/gYUSw8vF6CvRJMb+OkREZCrip/iRRTH441AGWvu4YNXUAXBxsNXWBTEYgG9GAyk7gE7XA7eqI7JN/fvNta6IiIhMbNHOZBly7Gys8NEd3bUXcoQDUWrIsXMBRs6BuWDQISIiMqEjpwvw31Vx8vGzozogoqWH9q5HSS6w9v/Ux4NnAh6BMBcMOkRERCYcSj5tyV65cOeQ9r64r39rbV6L9bOBs9mAbwcgcgrMCYMOERGRibz2WxyOZRTB180B79zSFdbWl55c1yyl7AJivlEfj50H2NjBnDDoEBERmcDvB9OxeGcyxGT+793aTS71oDlVFcCvT6iPu90NtOoPc8OgQ0RE1MRS80rw7NID8vHDg9pgQJiPNq/Btg+AzDjAyQsY/irMEYMOERFRE6qsMmB61F4UlFaia5AnZoxop83vP/s4sPkt9fGoNwAXb5gjBh0iIqIm9NGG49idmAtXB1t8dHt32Nlo8KfYYABWPg5UlQFtrgO63ApzpcFvl4iISJu2H8/GRxvi5ePXb4hAsLczNOnvr4DkaHXOnHHvQ3Y0MlMMOkRERE0gLa8Ejy/ZK1clv6VnIK7v1lKb33tuIrDuZfXxsFeAZurC3uaKQYeIiKiRlVZU4dFFMThTXI7wAHf8d2KENr9zgwFY8ThQUQyE9AeueQDmjkGHiIiokc3+9RD2n8qHp7MdFtzdE452Ntptskr8C7BzBq6fD1ibf4ww/yMkIiLSsKhdyViyK0V2Y/nw9u4I8nLW7iirteeWeRg2G/AKhRYw6BARETWSfSl5eGnFIfn46RHtMaidrza/66pKYPlDQGUJEDpEE01W1Rh0iIiIGkFOURkeWxSD8ioDRnTyw6OD22j3e/7rXSA1BnDwAK7/WBNNVtW0c6REREQamhRw6pK9SMsvRaiPC969VaPrWAkpu4HNb8qHGPuOWa1MXh8MOkRERFfZ238cxfYTOXC2t8Fnk3rCzdG8Frqst7JCYNkDgFIFdL7FrCcG/CcMOkRERFfRbwfS8dmWBPlYrEge5uem3e939TPqvDkewcCYd6BFDDpERERXSXxGIZ75eb98/PCgUIzp3EK73+2+JcD+JYCVNXDj54CTJ7SIQYeIiOgqyC+pwMOLYnC2vAr92njjmZHttfu9ZscDv81QHw+ZBYREQqsYdIiIiK5QRZUBUxbvQUJWMQI8HPHRHd1hq8XFOoWKUuCne9XZj1sNBAaeCzwapdGrQEREZB4URcFLK2Kx9Xi27Hz8xeRe8HZ1gGateQ7IOAg4ewM3fgFYa3QW53MYdIiIiK7A51sS5MzHYvS4qMkJD/DQ7ve5PwqI+QaAldovx13DfYzOYdAhIiK6TGti0/HGmiPy8f+N64ShHf20+11mxAGrnlQfD34WaDsMesCgQ0REdBn2p+Rh+g/7oCjAPZEh+E+/Vtr9HssKgR/vASrOAqHXAoNnQi8YdIiIiBooNa8EDyz8G6UVBgxp74uXxnWClVi1U4sUBfjlUSAnHnALAG76UvP9cmpj0CEiImqAwtIK3P/tbmQVlqGDvxvm39lDuyOshK3zgMO/AtZ2wK0LARcf6ImGrwwREVHTr2H1+Pd7ceR0IXzdHPDVf66Bq4Otdi9D/Hrgz//WrGMVdA30hkGHiIionsPIZ/8ah83HsuBoZ42vJvdCS08n7X53OSeApfeJMwN6/ke96RCDDhERUT18sy0R/9uRBNEV5/3buqNLoDaXRJBKC4Cou4DSfCCwNzD6LegVgw4REdG/WB+Xgf/+FicfzxrdAaMi/LX7nRmqgKX3A1mHAVd/tV+OrYYnOPwXDDpERESXcOBUHqZF7ZWDk+7oHYwHB4Zq+/ta9xIQvxawdQTuWKKLSQEvhUGHiIjoHxzPLMTkr3fJhToHhvng1evDtTuMXNizEIieLx9i4qdAyx7QOwYdIiKiiziVexZ3f7kLuWcr0DXQA5/e3RN2Wh5GnrgVWPVUzYrkETfCEmj4ihERETUOMUfOpK924XRBKdo2d8U39/bW9jDy7Hi187GhAgi/QV3iwUIw6BAREdWSX1Ihm6tOZhfL4eP/u783vFzstfsdFWUCi24CSvOAlr2A6z+BHDpmIRh0iIiIzikpr8ID3+1GXHoBfFwdsOiBPmjhoeG5csqLge9vA/KSgGatgDuiAHtnWBIGHSIiIpEJKg14dHEMdifmws3RFgvv643WPi4aH0b+AJC2B3BqBty1FHD1haVh0CEiIotXZVAw46f92HRUnfX4m/9cg04B7tr9XsRY+DXPAUdXAzYOak2OT1tYIgYdIiKCpS/t8PLKWPy6Pw12NlZYcHdP9GrlBU3b9j6w63MAVsCNnwPBfWGpGHSIiMiivbv2GBbtSJb9c+fd2g1D2jeHpsV8B6x/RX088nUgfCIsGYMOERFZrC+2JGD+xuPy8WsTIzC+awA0LW4lsGq6+njAk0DkFFg6Bh0iIrJIP+xOxuurD8vHM0e1x119QqBpCZvVNawUA9DjHmDoy6Y+IrPAoENERBbn94PpmLXsoHz88KBQPDq4DTQtdQ8QdSdQVQ50HA+Me9+i5sq5FAYdIiKyuJAzdcleGBTgtl5BeG50B22vXyVmPV58M1BeBLQeBNz0FWBtY+qjMhsMOkREZDFWHUjD40v2otKg4PpuAZhzY2dth5wzCcB3E4CzOUBAd+D27wFbB1MflVnR8MIdRERE9bdiXyqe/GGfrMm5sXtLvH1LV9hYazjk5CWrIacwDfDtANz1M+DgZuqjMjus0SEiIt1btueUMeTc0jNQ+yGnIA34bjyQnwJ4twXuWQm4+Jj6qMwSa3SIiEjXfvo7BTOXHpCTBd9+TRDm3NAZ1loOOYUZasjJTVTXr5r8K+DmZ+qjMlus0SEiIt2K2pVsDDl39QnWfsgpzgYWTgByjgMeQWrIcdf43D+NjDU6RESkS4t3JuGF5bHy8eTIELwyIVzbHY/PngEWTgSyjgBuAcDklYBnsKmPyuwx6BARke4sjE7ESysOycf39m+Fl8Z10nbIKc4B/nc9kHEQcGmuhhyvUFMflSYw6BARka58vfUkXl0VJx8/OLA1nh/TUdshpygTWHg9kBkHuPiqIccnzNRHpRkMOkREpKu1q6qXdXh0SBvMHNle2yGnIF3tk5N9DHD1V/vk+LYz9VFpCoMOERHpwqebTuDNNUfk46nXtcVTw9tpO+Tkn1JHV4lJAd0D1Zocb40vVWECDDpERKR58zfE4521x+Tj6cPCMH2Yxms9xNBxEXLEpICeIWpNTjONLzpqIgw6RESkWYqi4P318fjgz3i5PWN4O0wdqvH+Kzkn1JBTkAp4tVFrcjwCTX1UmsWgQ0REmlRlUPDSilgs3pkst2eOao/HhrSFpmUeUTseF50GfNqdmwzQ39RHpWkMOkREpDmlFVV4Imov/jiUAdEN55Xx4ZjcrxU0LWU38P0tQEku0DwcuGcF4Opr6qPSPAYdIiLSlPyzFXhg4W7sTsyFvY013r+9G8Z0bgFNi18P/DgJqDgLtOwF3PUT4Oxl6qPSBQYdIiLSjLS8Evznm104llEEN0dbfD6pFyLbeEPTDv4MLH8YMFQCbYYCt/0PsHcx9VHpBoMOERFpwrGMQkz+ehfS80vh5+6A7+7rjQ7+7tC0HQuANc+qjyNuBiZ+Ctjam/qodIVBh4iIzN6uk2fwwHe7UVBaiTa+Llh4fx+09HSCZolVRje+Dmx5W93u/TAw6g3AmmttX20MOkREZNbWxJ7GtKi9KK80oEewJ76afA2auWi41sNQBfw2A4j5Rt2+7kVg4NOQvarpqrui6Dh37lw56+T06dPrzGnwyiuvICAgAE5OThgyZAgOHVIXVqtWVlaGqVOnwsfHBy4uLpgwYQJOnTpVp0xubi4mTZoEDw8PeROP8/Ly6pRJTk7G+PHj5XuI95o2bRrKy8uv5JSIiMiMLNqRhMcWx8iQM6yjHxY/0FfbIaeiFPj5XjXkWFkD494HBj3DkGOOQWf37t34/PPP0aVLlzr733rrLcybNw/z58+XZfz9/TF8+HAUFhYay4hgtHz5ckRFRWHr1q0oKirCuHHjUFVVZSxz5513Yt++fVizZo28icci7FQTZceOHYvi4mL5HuK9li5dihkzZlzuKRERkZkQ/9M8b+1RvPhLLAwKcEfvICy4uwec7G2gWcXZ6rpVcSsAG3vglm+BXvea+qj0T7kMhYWFSlhYmLJu3Tpl8ODByhNPPCH3GwwGxd/fX3njjTeMZUtLSxUPDw9lwYIFcjsvL0+xs7NToqKijGVSU1MVa2trZc2aNXI7Li5OEYe2Y8cOY5no6Gi578iRI3J79erV8jXitdWWLFmiODg4KPn5+fU6D1FOvGd9yxMRUeOrqKxSZv60Xwl5dpW8zVt7VP6+aFrWMUV5v4uivOyuKHODFCVhs6mPSNMa8vt9WTU6U6ZMkbUpw4YNq7P/5MmTOH36NEaMGGHc5+DggMGDB2P79u1yOyYmBhUVFXXKiGauiIgIY5no6GjZXNWnTx9jmb59+8p9tcuI14jXVhs5cqRsFhOfcTHiuYKCgjo3IiIyHyXlVXj4fzH44e8UWFsBr98QgSe1vjjnyb+AL4ep61eJdavuXw+0HmTqo7IYDe6MLJqI9uzZI5ulzidCjuDn51dnv9hOSkoylrG3t0ezZs0uKFP9enHfvHnzC95f7Ktd5vzPEe8p3ru6zMX6FM2ePbuBZ0xERE0ht7gc9323G3uT8+Bga42P7uiOEeEaX/5g3xJg5VTAUAEE9gbuWAK4+Jj6qCxKg2p0UlJS8MQTT2DRokVwdHT8x3LnJ2/R1vpvafz8Mhcrfzllaps1axby8/ONN3E+RERkeqdyz+KmBdtlyPFwssPiB/poO+SI4eMbXgd+eUQNOeE3qotzMuSYd9ARTUKZmZno2bMnbG1t5W3z5s348MMP5ePqGpbza1TEa6qfE52TxcgoMarqUmUyMjIu+PysrKw6Zc7/HPGeolns/Jqe2s1o7u7udW5ERGT6OXKun78NCVnFCPBwxM+PRKJXKy9tj6xa+gCw5S11e+AM4KavADsNz/tjKUFn6NChOHjwoBwBVX3r1asX7rrrLvk4NDRUBpB169YZXyNCjQhD/fr1k9siJNnZ2dUpk56ejtjYWGOZyMhIWeOya9cuY5mdO3fKfbXLiNeI11Zbu3atDDPiM4iIyPwt3pmEO7/YgZzicoQHuGPpY/0Q5ucGzSrOUVcfj/0ZsLYFJswHhr7EiQC10kfHzc1NdgCuTcxh4+3tbdwvho7PmTMHYWFh8iYeOzs7y+HiguhQfP/998th4OJ1Xl5eePrpp9G5c2dj5+aOHTti1KhRePDBB/HZZ5/JfQ899JAcgt6+fXu5LTozd+rUSQ45f/vtt3HmzBn5PuI1rKkhIjJvFVUGzP71EBbtSJbb47q0wNs3d9X28PHMw8CSO4Dck4CDB3DbQiB0iKmPyuJd9ZmRZ86ciZKSEjz22GOyKUmMnBI1LSIkVXvvvfdkU9ett94qy4qaom+//RY2NjV/wBcvXiwnAKwenSUmFRRz81QTZX/77Tf5Of3795eTE4ow9c4771j8RSUiMmc5RWV4bPEe7Dx5Rk4G/PSI9nhsSBttj6yKWwn88ihQXgR4BgN3/Qz4qv9jTqZlJcaYw0KJ4eWihkk0ibEWiIio8cWlFeDBhX8jNa8Erg62eP+2bhjW6eL9KjWznMPGOcBf5/4nWwwbv/lbwEXjK6rr6Peba10REVGT+P1gOp76cT9KKqrQytsZX9zTS9v9cUrygGUPAvFr1e2+U4DhrwI2/Gk1J7waRETUqAwGBe//GY8P/4yX2wPDfOQcOZ7OGl6zKvMIEHUncOYEYOsIjP8Q6HqbqY+KLoJBh4iIGk1RWSVm/LgPfxxSpwy5f0BrzBrdAbY2V7SmtGkd/hVY/ojaH8cjCLhtERDQzdRHRf+AQYeIiBpFcs5Z2R/naEYh7G2sMefGzri5Z6B2v22DAdg0t2Z+nFYD1YU5OQmgWWPQISKiq2778Ww89v0e5J2tQHM3B3w2qSe6B9dd+kd7/XEeAuL/ULf7PgYM/y/742gAgw4REV01YiDvd9sT8d/fDqPKoKBroAc+v6cX/Nz/edkgs5dxCPjxHiDn+Ln+OB8AXW839VFRPTHoEBHRVVFWWYWXfjkkVx4XbuzeUjZXOdppdBJAMfvKnoXA7zOBylLAPRC4XfTH6W7qI6MGYNAhIqIrllVYhkcWxSAmKRfWVsCs0R3xwMDW2p0EsKwQ+HW6upSD0HYYcMNn7I+jQQw6RER0RUS4efz7PUjPL4Wboy3m39kDg9v5avdbTT8A/PQfdei4lY26VlW/aVyvSqMYdIiI6LLnx/lsSwLeWXtU9sdp4+siJwEM9XXVblPV318Ba54HqsrUpqqbvwaC+5j6yOgKMOgQEVGDZReVyVmOtxzLktsTugbg9Rsi4OZop81vszQfWDkNiPtF3W43Gpj4CeDsZeojoyvEoENERA2y7Xg2pv+wT/bLcbSzxuwJ4bi1V5B2++Ok7gF+vhfITQSsbdVlHMTwca2eD9XBoENERPVSWWXA++vj8fGm47KVp52fq+yP006r61WJk9j5GbD2RcBQoa46LhbkDOxp6iOjq4hBh4iI/lVaXgmeiNqL3Ym5cvuO3sF4aVwnONlrdOh4SS6w4nHgyCp1u8M44PqPASdPUx8ZXWUMOkREdEnr4jLwzM/75SzHrg62mHtjZ4zvGqDdby1hE/DLFKDgFGBjD4x4Hej9IJuqdIpBh4iI/nECwDd+P4JvtiXK7S6BHnLV8RBvF21+YxUlwPrZwM5P1e1mrYFbvuEEgDrHoENERBdIzC7G1CV7cTA137jq+LOjOsDe1lq7HY6XPwxkH1O3e92nrlXloNGh8FRvDDpERFTHin2peGF5LIrKKtHM2Q7v3NIVQzv6afNbqqoE/npXXXHcUAm4+gPXzwfChpv6yKiJMOgQEZFUUl6FV1bWrFXVu7UXPri9G1p4OGnzG8qOV2txUmPU7fAbgLHzODeOhWHQISIiHD1dKJdxiM8sktPHTL0uDNOuawtbGw02VRkMwO4vgXUvAZUlgKMHMOZdoPPN7HBsgRh0iIgsmKIoiNqdImtyyioNaO7mgPdv74Z+bXygSfmpwIopQMJGdTv0WnXYuEdLUx8ZmQiDDhGRhSoorcDzyw5i1YF0uS0W4nz31q7wcXWAJif/O/gzsHqGupyDrZM6w/E1D3AxTgvHoENEZIF2JuTgmZ8PIPnMWdhaW2HmqPZ4YEAorK01uOzB2TPAb08Bh5ar2wE9gBs/B3zCTH1kZAYYdIiILMjZ8kq8teYovt2uzo0T2MxJzo3TPbgZNFmLI8LN788CxZmAlQ0w+Flg4AzAhj9vpOKfBCIiC7EjIQczz9XiCHf0DsLzYzpqc8Xx/FPAbzOAY2vUbZ/2wA0LgJY9TH1kZGYYdIiIdK64TNTiHMF30UlyO8DDEW/c1AWD2vlCcwxV6oiqP18FyosAazu1BmfgU4CtBvsWUaNj0CEi0rHoEzmYuXQ/Us6UGBfjfH5MB23W4mQcAlZOA1L/VreD+gLjPwCadzD1kZEZY9AhItJpLc6ba45g4blanJaeTnjzpi4YEKbBYeMVpcCWt4Ft76uzGzu4A8NeAXreyxFV9K8YdIiIdGb7iWzZF+dUrlqLc1efYMwa01GuPK45iVuBX58Aco6r2x3GAWPeBtw1vHo6NSkN/qknIqJ/qsWZ+/thLNqRbKzFeevmLujfVoO1OCW5wNr/A/b+T90Wa1SJgNNpgqmPjDSGQYeISAe2H8/GzKU1tTh39w3Gc6M1WItz/pBxQTRRiaYqJ09THx1pkMb+BhARUW1ihfG5qw9j8c5k47w4b93UBf20WItzwZDxdmpn45B+pj4y0jAGHSIijdomanF+PoDUPLUWZ1LfEDw3ugNctFaLU1UB7PoC2Ph6rSHjT6nDxjlknK6Qxv42EBFRYWkF5v5+BN/XrsW5uYs2F+I8sQH4/Tkg+6i6HdTn3JDxjqY+MtIJBh0iIg35Kz4Lzy09aKzFuScyBM+O0mAtzpmTwNoXgSOr1G1nH2DoS0D3SRwyTleVxv5mEBFZbi3OnNWHsWRXitwO8hJ9cboiso03NKW8GPhrHrD9I6CqTF2fqs/D6hpV7GxMjYBBh4jIjCmKgrVxGZi98hDS8kvlvsmRIZiptVocMZoqdqk6ZLwwTd0XOgQY9SZnNqZGpaG/JUREliUhqwizf43D5mNZcjvYy1n2xekbqrFanPT96nDx5Gh12zMYGDkX6DAWsLIy9dGRzjHoEBGZmbPllZi/4Ti+/OskyqsMsLexxoODWmPKtW3hbK+hf7aLc4AN/wVivhVVOoCdMzDgKaDf44Cdk6mPjiyEhv7GEBHpv5nq99jTeG1VnLGZanA7X7wyIRytfVygGVWVwN9fqcPFS/PVfRE3AcNfBTwCTX10ZGEYdIiIzMDxzEK8sjIOW49nG4eMvzSuE4Z38oOVlpp3EjYDa54DMuPUbb/OwOg3gVb9TX1kZKEYdIiITDyz8Ud/xuOrrSdRaVBgb2uNRwa3wWND2sDRzkY71yY3SR0ufniluu3kBVz3ItDzP4C1hs6DdIdBh4jIRM1UK/enySHjGQVlct+wjs3x0rhwBHs7a2vxza3vATs/AypLAStr4JoHgCGzAGcvUx8dEYMOEVFTO3q6EC+vjMWOhDNyO8TbGS+P74TrOvhp52KUnwV2LgC2vV/TD6fVQLWZyi/c1EdHZMQaHSKiJlJQWoEP1sfj2+2JqDIocLSzxpQhbfHgoFDtNFOJdan2LgI2vwkUpqv7mncChr4MtBvJ4eJkdhh0iIiaoJlq+d5UzFl9BNlFajPVyHA//N+4Tghs5qydCf/ifgE2vAbkHFf3eQQD170AdL6F/XDIbDHoEBE1ori0AtlMtTsxV26H+rjg5Qnhcti4ZiRsAta/AqTtVbedvYFBzwC97uPq4mT2GHSIiBpBfkkF3lt3DAujE2FQACc7G0wd2hb3D2gNB1uNNFOJYLN+NpCwUd22dwUiH1cn/HNwM/XREdULgw4R0VVkMCj4ec8pvPn7EeQUl8t9Y7u0wAtjOiLAUyOzAeecUGc0PrRc3ba2A665Hxj4NOCqoZooIgYdIqKrJzY1H/+3IhZ7k/Pkdtvmrpg9IRz92/po42suPA1segPYsxBQqgBYAV1uBa59HmjWytRHR3RZWKNDRHSFMgtL8f76eCzZlSz77LrY22D6sHaY3K+VnADQ7JXkAds+AHZ8ClSWqPvCRgJDXwL8I0x9dERXhEGHiOgKhot/vjlBzmpcUiFqQIDruwXg+TEd4efuaP7fa0UJsOsL4K93gVK1FgqBvYHhs4GQfqY+OqKrgkGHiKiBSiuq8L/oJHy86TjyzlbIfd2DPfHcqA7oE+qtjYAjmqe2vg8Upqn7fDuoc+G0H825cEhXGHSIiOqpssqAZXtS8d76Y0g/t7q46IfzzMj2GKGFxTfLCoG/vwa2zweKM9V97oFqH5yut3MuHNIlBh0ionpM+PfHodN4+4+jOJFVLPcFeDhi+vB2uKlHIGysrcy/D86uz4Edn6hrUwmewcCAJ4Fud3EuHNI1Bh0iokvYfiIbb645iv0pah+WZs52mHJtW9zdN8T8l20ozlHDjQg5ZQXqPu+2wMAZ6mzGNnamPkKiRsegQ0T0D0PF3/rjKLYcy5LbzvY2eGBAazwwKBTujmYeEAozgOiPgN1fAxVqDRR8OwKDngbCb2ATFVkUBh0ioloSs4vxztqjWHVAXbDSzsYKd/YOxuPXhcHXzcG8v6v8U8C2D4E93wGVah8itOiqLtfQfixgrYGh7kRXGYMOEZGYC6egFB/8GY8fdqeg0qBA9Cu+vmsAnhreHsHeZr7w5pmTwNb3gH3fAwZ1FBgCrwEGzQTChnMUFVk0Bh0igqWvSfXZ5hP4ettJlFYY5L5r2/vimZEd0CnAHWYt6xiwdR5w4MdzMxkDaDVQrcFpPYgBh4hBh4gseS6cb7cn4tNNJ2TYEXoEe+JZLcyFczoW+Osd4NAvYkyYuq/tMHUtqpBIUx8dkVlhjQ4RWdxcOD/FnMIH6+NxukDtx9LOT8yF0wHDOjY377lwUvcAW94Bjv5Ws0/0vRGdjFv2MOWREZktBh0ispi5cH6PPY13/jiKhGx1JFJLTyc8Obwdbuje0nznwhGLZyVsArZ/BJz489xOK3X0lBgmzrWoiC6JQYeIdG/bcTEXzhEcOJUvt71c7M/NhRMMB1sznQunohQ4+KO60GZmnLrPykZdTXzAU4BvO1MfIZEmNGis4dy5c3HNNdfAzc0NzZs3x8SJE3H06NEL/q/plVdeQUBAAJycnDBkyBAcOnSoTpmysjJMnToVPj4+cHFxwYQJE3Dq1Kk6ZXJzczFp0iR4eHjIm3icl3du0blzkpOTMX78ePke4r2mTZuG8vLyhn8LRKRLe5NzcfeXO3HXlztlyBFz4UwbGobNzwzB/QNam2fIEXPgbHgdeC8cWDlVDTl2LkDvh4CpMcANCxhyiBqrRmfz5s2YMmWKDDuVlZV44YUXMGLECMTFxcmwIbz11luYN28evv32W7Rr1w6vvfYahg8fLgORCEjC9OnT8euvvyIqKgre3t6YMWMGxo0bh5iYGNjYqP/w3HnnnTL8rFmzRm4/9NBDMuyI1wlVVVUYO3YsfH19sXXrVuTk5GDy5MkyaH300UcNOS0i0hHxb8DW49n4ZOMJRCfkGOfCuatPCB6/ri18XM10Lpz0/WrtzcGfa4aIewSpAafHPYCTp6mPkEiblCuQmZkpuvsrmzdvltsGg0Hx9/dX3njjDWOZ0tJSxcPDQ1mwYIHczsvLU+zs7JSoqChjmdTUVMXa2lpZs2aN3I6Li5Pvu2PHDmOZ6Ohoue/IkSNye/Xq1fI14rXVlixZojg4OCj5+fn1On5RTrxnfcsTkfmqqjIovx9MU8Z/9JcS8uwqeWsz6zdlxo/7lOScYsUsVVUqStyvivL1GEV52b3m9uVwRYldpiiVFaY+QiKz1JDf7yvqo5Off66928tL3p88eRKnT5+WtTzVHBwcMHjwYGzfvh0PP/ywrLWpqKioU0Y0c0VERMgyI0eORHR0tGyu6tOnj7FM37595T5Rpn379rKMeI14bTXxWtEsJj7j2muvveB4xXPiVq2g4NzaL0SkWRVVBvyyNxULNp8wLrjpaGeN268JxoODQmWHY7NcRXzvImDnAiA3Ud1nbQt0mgj0fQwI7GnqIyTSDdsrqR5+6qmnMGDAABk4BBFyBD8/vzplxXZSUpKxjL29PZo1a3ZBmerXi3vRB+h8Yl/tMud/jnhP8d7VZS7Wx2j27NmXe8pEZEZKyqvww+5kfPHXSaTmlch9bo62mBzZCvf2bwVvc2yiEqFm5+fA3v/VLLLp6An0uhe45kHAo6Wpj5BIdy476Dz++OM4cOCA7B9zvvPnoRCh6N/mpji/zMXKX06Z2mbNmiXDWe0anaCgoEseFxGZFzG53/+iE/HNtkTkFKuDD0S/G9G5WIyicjO3BTfF8PDkHcCOj4EjvwGKOvsyvMOAvo8CXW8H7NU+jkRkJkFHjJhauXIltmzZgsDAQON+f39/eS9qVFq0aGHcn5mZaax9EWXEyCgxqqp2rY4o069fP2OZjIyMCz43Kyurzvvs3LmzzvPiPUWz2Pk1PbWb0cSNiLQnq7AMX209iUU7klBUVin3BTZzwsOD2+CWnoFwtDOzEVSV5cCh5cCOT4D0fTX7Q68FIqcAbYZykU0icxteLmpLRE3OsmXLsGHDBrRu3brO82JbBJB169YZ94lQI0ZrVYeYnj17ws7Ork6Z9PR0xMbGGstERkbK/j+7du0ylhGhRuyrXUa8Rry22tq1a2WQEZ9BRPqQcuYsXvzlIPq/uUH2wxEhR8xk/N5tXbHp6SGY1DfEvEJOcQ6w5W3g/c7A8ofUkGPjoI6cejQauOcXdaFNriRO1CSsRI/k+hZ+7LHH8P3332PFihWyQ3A10UlYzJkjvPnmm7IvzDfffIOwsDDMmTMHmzZtqjO8/NFHH8WqVavkEHTRkfnpp5+Ww8NrDy8fPXo00tLS8NlnnxmHl4eEhNQZXt6tWzdZe/P222/jzJkz+M9//iPn9qnv8HLRdCWOXQQod3czX7yPyMIcyyiU61Ct3J+GKoP6z1S3IE850d/QDs1hbW4zGWceVjsX748CKtWlJeDqp/a9EX1wXHxMfYREutGQ3+8GBZ1/6vsiQo0IGYJ4O9HhVwQU0ZQkRk59/PHHxg7LQmlpKZ555hkZmkpKSjB06FB88skndfrLiOAiJgAUTWSCmFRw/vz58PT0rDNhoAhfonZJBC0x984777xT7+YpBh0i85zk75NNJ7Aurqb5emCYDx4d0gaRod7mtRZV+Vkg7hcg5jsgZUfNfv8uavNU+I2Arb0pj5BIlxot6OgNgw6R+U7yJ/LMqHB/GXC6BJrZZHmnD6rh5sCPQFl+zfIM7Uerw8ND+qknQEQm//3mWldEZDIGg4K1cadlDU71OlS21laY2L0lHhncBm2bu5rP1SkrAmKXAnu+A1JjavZ7Bqv9b7rdDbjXDMIgIvPAoENETU4zk/yJCu+0PWrtjQg55UU1k/t1GAv0mKyOomLHYiKzxaBDRE1GM5P8learzVKi9kY0U1XzanOu9uZOwPXCSU2JyPww6BBRo8s7W47FO5Px9daTdSb5e2Bga9zVx0wm+RO1Nym7gJhv1flvKtUgBht7oNP1au1NqwHse0OkMQw6RNRoYlPz8d32RDlEvKzSYJ6T/J09ow4JF7U3WUdq9vt2UMONmLnYWV3Pj4i0h0GHiK6qssoqrD6YjoXRSdibnGfc36mFOx4aFIpxXVrA1qZBc5U2Tu1N4lY13MStBKrOLfZr6wSE3wD0/A8Q1Ju1N0Q6wKBDRFeF6HPz/c4kRO1KMTZP2dlYYUznFrgnMgQ9gpuZfg6coixg32Jgz0LgzIma/f6d1dqbzrcATmY2lJ2IrgiDDhFd0fw320/kyOap9YczcG4CY/i7O8q+N7f3Doavm4k7GBsMQMJGtfbmyGrAUKHut3cFIm5Sa28CurP2hkinGHSIqMEKSyuwNOYU/rcjyTg8XBAzF0/uF4JhHf1M3zyVcwI4+BOw73sgL6lmf0APNdxE3Ag4qMvSEJF+MegQUYPWn1oYnYjle1JRXF4l97nY2+CmnoFycc0wPxMHh8IM4NAydWi4mP+mmoMH0OVWoOdktZmKiCwGgw4R/evkfmLdKdE8tfPkGeN+MWux6HtzQ/eWph0eXloAHFmlhpuTmwFFHd0FK2t1Mj8RcDpOAOydTXeMRGQyDDpEdFGZhaVYsjMF3+9KQkaBOirJxtoKIzr5YVJkiGkX2KwsB46vU8PNsTU1q4ULLXup4UaMnuKkfkQWj0GHiOp0Lv47KVcODV8Tm46KKrV3sY+rPe7oHYw7+wSjhYeT6ToVJ29Xw03cCqC0Zug6vMPUcCM6F3u3Mc3xEZFZYtAhIpwtr8SKfWky4BxOLzB+Iz1DmsnmqVER/nCwtTHNfDcZsWq4EWtNFaTWPOfqD3S+Wb216MZRU0R0UQw6RBbsZHYxFu1Iwo9/p6CwtNK4uOb1XVvK5qmIlh6mObDcJHXElLjVnq3YwR3oNEGd76bVQMDaDGZWJiKzxqBDZGGqDAo2HsnEwh1J2HIsy7g/xNtZjpy6pWcQPJxN0Lm4OEcdMXXwZyBlR81+sdZUu5FquAkbCdg5Nv2xEZFmMegQWYjc4nL88HeKrME5lasuWCn6El/bvrmsvRkc5gtr6ybuXFxerE7iJ2puTvwJGNRaJcAKaD1QDTdixBRnKyaiy8SgQ6TzzsV7knOxZFcKfq21sKansx1u7RWEu/uEINi7iYddV1UAJzaq4ebIb0BFzYSDaNFVDTeiU7F7QNMeFxHpEoMOkQ4l55zF8r2pWLb3FJJyzhr3R7R0xz2RrTCha0DTrhwuRkyl/q12Kj60HDibXfNcs1ZquBE33/ZNd0xEZBEYdIh0Ir+kQq4avmzPKexOzDXud7a3weiIFrirbzC6B3k23dw3ouZGrBAuJvMTzVOFaTXPOfuoSzB0vhUI7MURU0TUaBh0iDQ+a7HoULxsb6qcvbj8XNOU6GrTv60PbuzREiPD/eFsb9t0fW5ObAAOr1In8qs9141YRLPDWDXchA4BbPjPDxE1Pv5LQ6TBfjeH0gqwdM8prNyXhpzicuNz7fxccVOPQFzfrSX8PZpodNLZM2qoEeFGhJxKtaOzseam/Wig43ig9WCOmCKiJsegQ6QR6fkl+GVvmmyais8sMu4XsxaLYCPWnAoPcG+apqn8U2pHYtEslbgNUNQFPiXPYKDDeKDjOCCoD+e6ISKTYtAhMmPFZZX449BpLNuTim0nsuVEwYKDrTWGd/KTtTcDw3xga2PduAciPjjr6Ln+NquAtL11n/eLADqMU5umxOrgploDi4joPAw6RGY4oV/0iRxZc7Pm0GmcLa+pLend2gs39WiJ0Z1bwL2xVwwXI6XS9gCHf1XDTc7xWk9aAcF91WAjbl6hjXssRESXiUGHyEwcyyiUNTe/7E3F6YKa1bhbeTvjxh6BsmkqyMu5CUZK/aX2tzkqRkql152hWPSzEU1S7cdwZXAi0gQGHSITyi4qkx2KxXw3sak1i2l6ONlhfNcWMuA0+pBwMVLq+Hq1z40cKZVf85y9GxA2XA03bYcDju6NdxxERI2AQYeoiZVWVGH94QxZe7P5WJZsqpJ/Ga2tcG2H5rJpStw36mrhYqTU0d/VJik5UqqmBgkuvmqNjRwpNQiwdWi84yAiamQMOkRNNCT876Rc2e9m1YF040rhQtcgTxluxnUJgJeLfeMdRF5KzUippO3njZQKUYON6FAc1JsjpYhINxh0iBpRYnaxnMxv+d5TSDlTM79MgIcjbughhoQHom1z18b58KpKIDVGXSzz2B9A+r66z/t1VpukRLjxC+dIKSLSJQYdoqss72y5rLURa03FJNUsxeBib4MxndV+N31aezXOSuGi1kYEm+N/Aic31+1vI0dKRZ4LN2PVNaaIiHSOQYfoKhBLL4j+NqJp6s/DmSivqlmKYWCYr1yKYUQnfzjZX+V+N+Vn1Wao6nCTfbTu846eQJtrgTZDgXajAFffq/v5RERmjkGH6DIZDAr2ncqTo6ZW7k/DmVpLMXTwdzu3FEMAmrs7Xt2J+zIP1wQbEXKqymqet7IGWvYC2g4F2g4DArqzvw0RWTQGHaIGqKwyYNfJM3IiPzFjcUZBTcjwdXPA9V0DZNNUpwD3qztCKmEjcHyDOkKq9irggnsg0PY6tdYmdDDg1OzqfTYRkcYx6BDVYzj4X/HZMtiIYeF5Zyvq9LsZ2tFPNk0NaHuVlmKQnYj/VmtsRM1N6h5RlVPrb60j0GqAGmxEzY1PO3YkJiL6Bww6RBdRWFqBDUcyZbjZdDSrzjIMYgj4sI7NMSrCH/3a+MDRzuYqdiJeDyRsAcpqdyIG0LwT0OY6NdgE9+Mq4ERE9cSgQ1RrluL1cRmyWWr78Rxjh2KhhYcjRob7y9s1rZpdec2N7ES8rabWJvvYRToRnws24t49gNeJiOgyMOiQRUvNK8EfsadluPk78QzOTVIshfq6YNS5cNMl0OPKlmGQnYjjaoJNUvSFnYgDr6lpjmInYiKiq4JBhyzO8cxC/HEoA2tiT+Ngat0mos4tPTAy3E82S7Vt7nblnYhF5+HqW+0FMgWPoJpaG7FYppPnlX0eERFdgEGHLGL5BRFoRLARfW5OZBUbnxOVNNe08jrXLOWHwGbOV9aJ+NTumqHfaXvP60TspHYils1RohNxGDsRExE1MgYd0iWxUObuxDMy3Kw9dBpp+TWLVtrZWKF/Wx/ZLDWskx98XB0uvzkqLwk4sVENN+xETERkdhh0SDfKKquw7Xg2/ojNwLrDGXUm8HOys8G1HXxlzY1YGdzd0e7ygk12vNqJWN62AwWpdcuIOWxCr2UnYiIiM8GgQ5pWVFaJTUfFMPAMbDySKbereTjZYVhHtb/NwLDLGAZuqFI7ECfWCjZns+uWsbatmYlYNEcFdONMxEREZoRBhzRH1NSIifvEaKm/jmfLdaaq+bk7yDWlRLjp3doLdg0ZBl5VAaTvrwk1ydHnLYp5brI+MToqpD8Q0k99bH8F/XqIiKhRMeiQJqTnl2DtuZFSuxLPyD441Vp5O2NkhDoMvFugZ/1XBa8oBVJj1FAjwk3KLqCipqOyZO8KBPdVQ40IN2LYt+1l9ukhIqImx6BDZjtSKiG7WA03h05jf0penec7tnBX57iJ8EN7P7f6zXFTVgSc2nUu2GwHTv1ddy6b6j42YuZhGWz6Af5dABv+NSEi0ir+C05mo6C0Qs5I/Fd8FrbEZyHlTInxOZFjegQ3M07gF+xdj+aikjwgeUdNU1T6PsBQ04dHcmkOtOpf0xTl2xGwvgrrVRERkVlg0CGTMRjU+W22HFODzZ7kvDpNUmIYeN9QbxlsRnTyQ3N3x0u/YVEWkHyutkZ0IM6IrTuPjeARXFNbI8KNdxvOZUNEpGMMOtSkMgpKzwWbbGyNz0JurZXAhdY+LhgU5oOBYb6IbOMNF4dL/BHNT63pXyNu568XJXi3rQk14t4zuBHOioiIzBWDDjWq0ooqOXGfCDd/xWfjyOnCOs+7OtiiXxtvDGrni8HtfBHk5fzPc9jknqyprRHBRkzWd77m4WqgEc1Roq+Nm18jnRkREWkBgw5d9U7EJ7KKsPlYtgw3O0/moLTCUKevjVhPalCYrww33YM9Lz4E3GAAso/WqrHZfuFaUWIhzBZdz9XWiGDTF3D24hUlIiIjBh26YvlnK7DthBpsxK32cgtCczcHGWrEbUBbH3i52F/4JgVp6lBvcROjodL2AeV1a39gbQe07Hmu83A/IKgP4HCFC28SEZGuMehQg4kOw/tS8oydiMXQ71p9iGFva43erbwwqJ2PDDcXDP8uK1QXvKwONal7gMK0Cz/IzhkI7AWEDDg3OV8vwM6JV4yIiOqNQYfqJS2vxBhstsZno6C07jDtts1dZXPUwHY+6NvaG072NjWzDZ8+UBNoRLjJOnLhaCjRDNW8k1pjU33z7cA5bIiI6Iow6NBFlZRXyf41W0Rfm/gsHM8sqvO8u6MtBoT5nAs3vmjp6XSuw3AicHTLuVDzt7qkQmXdpizjMO+WPdRAI2pqRF8bexdeDSIiuqoYdMjYifhoRuG5fjbZcpmF2mtIiVUVugZ5GjsRdw30gG1Znhpo9n1f07/mbM6F36iDhxpqRKARwSagB0dDERFRk2DQsWC5xeVyUUx16HcWMgrqLocQ4OFo7ETcP8QVHvlHgNQ/gb9jgF/+Vod7n090GPbvXBNqxM2rDWcbJiIik2DQsSAVVYaaTsTHsnAgNV+2NlVztLNGn9beGBTmjWG++QguOQyrtNXA9r+B5bEXLp9QPSGfsV9NL8A/goteEhGR2WDQ0bmUM2ex+VywiT6Rg8KyumGlg78bRreywjD3FLSvPAbb9D3A1r1AWcGFb+bsc66mRtx6qCt5c94aIiIyYww6OpNVWCY7Ee9IyMG24zk4mV1c5/kAp0rcFpiDa11S0K7qGBwz9gL7Ui8+tLtFt7odhj2CuC4UERFpCoOODtaOEqFm58kz2JmQgxNZNcHGBlWIsDmF8d7pGOCUiNDyo3DMi4dVSk0nY+PQbrFqd+0Ow2Lbhn88iIhI2/hLpjHp+SXYmXDmXK3NGWONjQPKEWZ1CrfbJKG/axq62SYhoPQ4bKpKAdEKVbslyj2wbqgRNTcOriY7JyIiosbCoKOBifpkjU3CGew4mYOknLNww1l0skrCtdaJeNwuET3sUxBsSIGNUqW+SAyeqh5A5eBe0/xUfXPzN+UpERERNRkGHTPsPFzdDLUjIRtluekIt05EuFUinhP3DokItsqq+6Jz+QZOXkCLLurwbv+u6iR8YlSU9UUWzSQiIrIAmg86n3zyCd5++22kp6cjPDwc77//PgYOHAitTNJ3KrcE0Qk52HUiG6dOxMKn6KgMNuOskjDTOhG+jhcZ/VQ9s7AINDLYdFHv3VuyszAREZFegs4PP/yA6dOny7DTv39/fPbZZxg9ejTi4uIQHBwMcww2ok9NzInTSD6yB6Wn9qFlabwMNmOskuFqVQqct7C3YmUNK592NWFG3IuAw2HdRERE/8pKEb++GtWnTx/06NEDn376qXFfx44dMXHiRMydO/dfX19QUAAPDw/k5+fD3d39qh9fZZUBxxJOIjluJ4qT98HpzGG0rkpEG6tU2FtVtzfVqLJxAJqHwyZANDuJQNMV8OvEFbuJiIgu8/dbszU65eXliImJwXPPPVdn/4gRI7B9+/aLvqasrEzean9RjWHfuu9hHfMlAkqOo5NVPjrVfvJcd5kSW3eU+YTDJaQH7Fp2k7U0Nt5hHNJNRER0FWk26GRnZ6Oqqgp+fn519ovt06dPX/Q1opZn9uzZjX5s5YVZ6F0aA1gBBsUKmXYBKPLsAMegrmjethfsW3aGk0cQnKysGv1YiIiILJlmg041q/PCgmiJO39ftVmzZuGpp56qU6MTFBR01Y8ppOcoRFdWwr9dLwR36Al/R85RQ0REZAqaDTo+Pj6wsbG5oPYmMzPzglqeag4ODvLW2PxC2ssbERERmZZmJ1ixt7dHz549sW7dujr7xXa/fv1MdlxERERkPjRboyOIZqhJkyahV69eiIyMxOeff47k5GQ88sgjpj40IiIiMgOaDjq33XYbcnJy8Oqrr8oJAyMiIrB69WqEhISY+tCIiIjIDGh6Hp0r1djz6BAREZFpf78120eHiIiI6N8w6BAREZFuMegQERGRbjHoEBERkW4x6BAREZFuMegQERGRbjHoEBERkW4x6BAREZFuMegQERGRbml6CYgrVT0ptJhhkYiIiLSh+ne7Pos7WHTQKSwslPdBQUGmPhQiIiK6jN9xsRTEpVj0WlcGgwFpaWlwc3ODlZXVVU+bIkClpKRY5DpaPH/Lvf689pZ77QVef17/oCb48y+iiwg5AQEBsLa+dC8ci67REV9OYGBgo36GuNCW+I9dNZ6/5V5/XnvLvfYCrz+vv3sj//n/t5qcauyMTERERLrFoENERES6xaDTSBwcHPDyyy/Le0vE87fc689rb7nXXuD15/V/2cz+/Ft0Z2QiIiLSN9boEBERkW4x6BAREZFuMegQERGRbjHoEBERkW4x6FymTz75BK1bt4ajoyN69uyJv/7665LlN2/eLMuJ8qGhoViwYAEs5fw3bdokZ54+/3bkyBFo0ZYtWzB+/Hg5I6c4j19++eVfX6On69/Q89fT9Z87dy6uueYaOZt68+bNMXHiRBw9etRirv/lnL+erv+nn36KLl26GCdDjIyMxO+//24R1/5yzt9crj2DzmX44YcfMH36dLzwwgvYu3cvBg4ciNGjRyM5Ofmi5U+ePIkxY8bIcqL8888/j2nTpmHp0qWwhPOvJv5BTE9PN97CwsKgRcXFxejatSvmz59fr/J6u/4NPX89XX/xozVlyhTs2LED69atQ2VlJUaMGCG/E0u4/pdz/nq6/mIm/TfeeAN///23vF133XW4/vrrcejQId1f+8s5f7O59mJ4OTVM7969lUceeaTOvg4dOijPPffcRcvPnDlTPl/bww8/rPTt29cizn/jxo1iCgMlNzdX0RtxXsuXL79kGb1d/4aev56vf2Zmpjy3zZs3W+T1r8/56/n6C82aNVO+/PJLi7v29Tl/c7n2rNFpoPLycsTExMj/i6lNbG/fvv2ir4mOjr6g/MiRI2UirqiogN7Pv1r37t3RokULDB06FBs3boSl0NP1vxJ6vP75+fny3svLyyKvf33OX6/Xv6qqClFRUbI2SzThWNq1r6rH+ZvLtWfQaaDs7Gx5gf38/OrsF9unT5++6GvE/ouVF9W+4v30fv7iD/jnn38uq2uXLVuG9u3byz/woq+HJdDT9b8cer3+okLrqaeewoABAxAREWFx17++56+363/w4EG4urrKmX8feeQRLF++HJ06dbKYa3+wAedvLtfeolcvvxKiQ9X5f+nP3/dv5S+2X4/nL/5wi1s1kf5TUlLwzjvvYNCgQbAEerv+DaHX6//444/jwIED2Lp1q0Ve//qev96uvziXffv2IS8vT/6AT548WfZd+qcfe71d+/YNOH9zufas0WkgHx8f2NjYXFB7kZmZeUFyr+bv73/R8ra2tvD29obez/9i+vbti/j4eFgCPV3/q0Xr13/q1KlYuXKlrIYXHTQt7fo35Pz1dv3t7e3Rtm1b9OrVS45CEx3zP/jgA4u59vYNOH9zufYMOpdxkcVQQTHioDax3a9fv4u+RqTY88uvXbtW/kGxs7OD3s//YsQIBFGtaQn0dP2vFq1ef/F/46ImQ1TDb9iwQU6xYEnX/3LOX0/X/5++k7KyMt1f+8s5f7O59ibtCq1RUVFRip2dnfLVV18pcXFxyvTp0xUXFxclMTFRPi9GH02aNMlYPiEhQXF2dlaefPJJWV68Trz+559/Vizh/N977z05MufYsWNKbGysfF780Vu6dKmiRYWFhcrevXvlTZzHvHnz5OOkpCSLuP4NPX89Xf9HH31U8fDwUDZt2qSkp6cbb2fPnjWW0fP1v5zz19P1nzVrlrJlyxbl5MmTyoEDB5Tnn39esba2VtauXav7a385528u155B5zJ9/PHHSkhIiGJvb6/06NGjzvDKyZMnK4MHD65TXvzD0L17d1m+VatWyqeffqpYyvm/+eabSps2bRRHR0c5FHHAgAHKb7/9pmhV9ZDJ82/ivC3h+jf0/PV0/S923uL2zTffGMvo+fpfzvnr6frfd999xn/3fH19laFDhxp/5PV+7S/n/M3l2luJ/zRtHRIRERFR02AfHSIiItItBh0iIiLSLQYdIiIi0i0GHSIiItItBh0iIiLSLQYdIiIi0i0GHSIiItItBh0iIiK6qsQK5ePHj0dAQIBcwPSXX35p8HuIaf7EAqDt2rWTq6UHBQVhzpw5DX4frl5OREREV1VxcbFc8PPee+/FTTfddFnv8cQTT8i1wUTY6dy5M/Lz85Gdnd3g9+HMyERERNRoRI3O8uXLMXHiROO+8vJyvPjii1i8eDHy8vIQERGBN998E0OGDJHPHz58GF26dEFsbCzat29/RZ/PpisiIiJqUqKmZ9u2bYiKisKBAwdwyy23YNSoUYiPj5fP//rrrwgNDcWqVavQunVrtGrVCg888ADOnDnT4M9i0CEiIqImc+LECSxZsgQ//fQTBg4ciDZt2uDpp5/GgAED8M0338gyCQkJSEpKkmUWLlyIb7/9FjExMbj55psb/Hnso0NERERNZs+ePbKjsehkXFtZWRm8vb3lY4PBILdFyKku99VXX6Fnz544evRog5qzGHSIiIioyYgQY2NjI2toxH1trq6u8r5FixawtbWtE4Y6duwo75OTkxl0iIiIyDx1794dVVVVyMzMlE1XF9O/f39UVlbKZi7RtCUcO3ZM3oeEhDTo8zjqioiIiK6qoqIiHD9+3Bhs5s2bh2uvvRZeXl4IDg7G3XffLTsjv/vuu/J5MWx8w4YNchj5mDFjZK3PNddcI2t43n//fbk9ZcoUuLu7yyHnDcGgQ0RERFfVpk2bZLA53+TJk2XH4oqKCrz22muyD05qaqrsmxMZGYnZs2fLsCOkpaVh6tSpMti4uLhg9OjRMhiJsNQQDDpERESkWxxeTkRERLrFoENERES6xaBDREREusWgQ0RERLrFoENERES6xaBDREREusWgQ0RERLrFoENERES6xaBDREREusWgQ0RERLrFoENERES6xaBDREREuvX/7sHq61cNPdoAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Dimensionless time step: 454.856451460863\n" ] } ], "source": [ "t, p, e, x, Phi_phi, Phi_theta, Phi_r = traj_model(*traj_pars, in_coordinate_time=False)\n", "\n", "plt.plot(t, Phi_phi, label=r\"$\\Phi_\\phi$\")\n", "plt.plot(t, Phi_r, label=r\"$\\Phi_r$\")\n", "plt.legend(frameon=False)\n", "plt.show()\n", "print(\"Dimensionless time step:\", t[1] - t[0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Integrating trajectories with a fixed time-step" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The adaptive stepping of the solver can be disabled with the `DENSE_STEPPING` keyword argument, which switches to taking uniform steps of size `dt`. This is more expensive and memory-intensive than adaptive stepping." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:43.479644Z", "iopub.status.busy": "2026-07-11T10:48:43.479571Z", "iopub.status.idle": "2026-07-11T10:48:45.059226Z", "shell.execute_reply": "2026-07-11T10:48:45.058775Z" } }, "outputs": [ { "data": { "text/plain": [ "((15780,), (6,))" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "T_dense = 0.005\n", "\n", "t_dense, p, e, x, Phi_phi, Phi_theta, Phi_r = traj_model(\n", " *traj_pars, T=T_dense, DENSE_STEPPING=1\n", ")\n", "t_adaptive, p, e, x, Phi_phi, Phi_theta, Phi_r = traj_model(*traj_pars, T=T_dense)\n", "t_dense.shape, t_adaptive.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can directly verify the accuracy of the adaptive solution by evaluating its output on the densely-stepped trajectory's time grid. The phase errors will be larger than the error in the orbital elements by a factor of $M / \\mu$ due to conventions chosen during integration:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:45.060390Z", "iopub.status.busy": "2026-07-11T10:48:45.060319Z", "iopub.status.idle": "2026-07-11T10:48:46.714439Z", "shell.execute_reply": "2026-07-11T10:48:46.714006Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t_dense, p, e, x, Phi_phi, Phi_theta, Phi_r = traj_model(\n", " *traj_pars, T=T_dense, DENSE_STEPPING=1\n", ")\n", "t_adaptive, p_adaptive, e, x, Phi_phi_adaptive, Phi_theta, Phi_r = traj_model(\n", " *traj_pars, T=T_dense, new_t=t_dense, upsample=True\n", ")\n", "\n", "plt.semilogy(t_dense, abs(Phi_phi_adaptive - Phi_phi), label=\"Phase error\")\n", "plt.semilogy(t_dense, abs(p_adaptive - p), label=\"p error\")\n", "plt.legend(frameon=False)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also set a maximum time-step during adaptive integration:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:46.715578Z", "iopub.status.busy": "2026-07-11T10:48:46.715497Z", "iopub.status.idle": "2026-07-11T10:48:47.154366Z", "shell.execute_reply": "2026-07-11T10:48:47.154060Z" } }, "outputs": [ { "data": { "text/plain": [ "(np.float64(1869829.3562450137), np.float64(79645.72324508056))" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t_adaptive = traj_model(*traj_pars, T=1.)[0]\n", "t_adaptive_capped = traj_model(*traj_pars, T=1., max_step_size=86400)[0]\n", "np.max(np.diff(t_adaptive)), np.max(np.diff(t_adaptive_capped))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Evolving trajectories backwards in time" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Trajectories can also be evolved in reverse via the `integrate_backwards` keyword argument. Trajectories evolved in either direction will agree up to the numerical tolerance of the integrator:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:47.155620Z", "iopub.status.busy": "2026-07-11T10:48:47.155562Z", "iopub.status.idle": "2026-07-11T10:48:47.323200Z", "shell.execute_reply": "2026-07-11T10:48:47.322817Z" } }, "outputs": [ { "data": { "text/plain": [ "np.float64(-5.703348904262384e-11)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "traj_pars_back = traj_pars.copy()\n", "\n", "T = 0.55\n", "\n", "# forward\n", "t, p, e, xI, Phi_phi, Phi_theta, Phi_r = traj_model(*traj_pars, T=T)\n", "\n", "traj_pars_back[3] = p[-1]\n", "traj_pars_back[4] = e[-1]\n", "traj_pars_back[5] = xI[-1]\n", "\n", "# backward\n", "t_back, p_back, e_back, xI_back, Phi_phi_back, Phi_theta_back, Phi_r_back = traj_model(\n", " *traj_pars_back, T=T, integrate_backwards=True\n", ")\n", "\n", "plt.plot(p, e)\n", "plt.plot(p_back, e_back, ls=\"--\")\n", "p_back[-1] - p[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Setting the integrator error tolerance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The integrator tolerance (which is an absolute tolerance) can be adjusted by setting the `err` keyword argument. Higher error tolerances reduce the number of points in the trajectory, but at the cost of numerical accuracy. Note that `err` is a _local_ error tolerance, not a global one, and must therefore be set conservatively with respect to the desired global error tolerance. The default setting of $10^{-11}$ is a reasonable value and should not need to be changed for typical scenarios. " ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:47.324394Z", "iopub.status.busy": "2026-07-11T10:48:47.324329Z", "iopub.status.idle": "2026-07-11T10:48:47.352284Z", "shell.execute_reply": "2026-07-11T10:48:47.351899Z" } }, "outputs": [ { "data": { "text/plain": [ "(53, 32, 2.7758084719664566e-09)" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "p = traj_model(*traj_pars, T=T, err=1e-11)[1]\n", "p_hightol = traj_model(*traj_pars, T=T, err=1e-9)[1]\n", "\n", "p.size, p_hightol.size, (p[-1] - p_hightol[-1]).item()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Integrating trajectories in $(E, L, Q)$ coordinates" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Trajectories can also be solved in the constants of motion parameterisation $(E, L, Q)$ via the `integrate_constants_of_motion` keyword. This is supported for all stock trajectory models. Given input $(p_0, e_0, x_{I,0})$, the integrator converts these initial conditions to $(E, L, Q)$ and integrates these quantities alongside the inspiral phases. The output trajectory is converted back to $(p, e, x_I)$ coordinates if the keyword argument `convert_pex=True` (which it is by default).\n", "\n", "Integrating in $(E, L, Q)$ can offer some advantages, especially near the separatrix (see [Hughes 2024](https://arxiv.org/abs/2401.09577) for more information). Typically the trajectory also consists of fewer points than its $(p, e, x_I)$ counterpart, and is therefore faster to compute. However, it can also be numerically unstable for very small eccentricities, where small errors in the constants of motion can be amplified when transformed back to $(p, e, x_I)$. Usage of this method should be considered somewhat experimental, especially for eccentric and inclined (generic) inspirals." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:47.353312Z", "iopub.status.busy": "2026-07-11T10:48:47.353255Z", "iopub.status.idle": "2026-07-11T10:48:47.650530Z", "shell.execute_reply": "2026-07-11T10:48:47.650183Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "(ELQ, pex) trajectory lengths: [31, 44]\n", "(ELQ, pex) phase difference: -0.00011778558837249875\n" ] } ], "source": [ "m1 = 1e6\n", "m2 = 1e2\n", "a = 0.0\n", "p0 = 10.0\n", "e0 = 0.7\n", "xI0 = 1.0\n", "T = 1.0\n", "\n", "traj_model_ELQ = EMRIInspiral(func=SchwarzEccFlux, integrate_constants_of_motion=True)\n", "traj_model_pex = EMRIInspiral(func=SchwarzEccFlux, integrate_constants_of_motion=False)\n", "\n", "fig, axes = plt.subplots(2, 3, figsize=(14, 8))\n", "plt.subplots_adjust(wspace=0.35)\n", "axes = axes.ravel()\n", "ylabels = [r\"$e$\", r\"$p$\", r\"$e$\", r\"$\\Phi_\\phi$\", r\"$\\Phi_\\theta$\", r\"$\\Phi_r$\"]\n", "xlabels = [r\"$p$\", r\"$t$\", r\"$t$\", r\"$t$\", r\"$t$\", r\"$t$\"]\n", "\n", "lens = []\n", "phase_ends = []\n", "for traj_model, label, ls in zip(\n", " [traj_model_ELQ, traj_model_pex], [\"ELQ\", \"pex\"], [\"-\", \"--\"]\n", "):\n", " t, p, e, xI, Phi_phi, Phi_theta, Phi_r = traj_model(m1, m2, a, p0, e0, xI0, T=T)\n", "\n", " # Plot the results for comparison\n", " ys = [e, p, e, Phi_phi, Phi_theta, Phi_r]\n", " xs = [p, t, t, t, t, t]\n", "\n", " for i, (ax, x, y, xlab, ylab) in enumerate(zip(axes, xs, ys, xlabels, ylabels)):\n", " ax.plot(x, y, label=label, ls=ls)\n", " ax.set_xlabel(xlab, fontsize=16)\n", " ax.set_ylabel(ylab, fontsize=16)\n", "\n", " lens.append(len(t))\n", " phase_ends.append(Phi_phi[-1])\n", "axes[0].legend(frameon=False)\n", "\n", "plt.show()\n", "\n", "print(\"(ELQ, pex) trajectory lengths:\", lens)\n", "print(\"(ELQ, pex) phase difference:\", phase_ends[1] - phase_ends[0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Trajectory-related utilities" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Get $p_0$ based on desired duration of trajectory" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you have a desired length of trajectory to analyze, this function will give you the value of $p_0$ that corresponds to the proper evolution time." ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:47.651790Z", "iopub.status.busy": "2026-07-11T10:48:47.651718Z", "iopub.status.idle": "2026-07-11T10:48:48.047298Z", "shell.execute_reply": "2026-07-11T10:48:48.046965Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "p0_new = 13.05941726860424 will create a waveform that is 1.5 years long, given the other input parameters.\n" ] } ], "source": [ "from few.utils.utility import get_p_at_t\n", "\n", "traj = EMRIInspiral(func=SchwarzEccFlux)\n", "\n", "# Set initial parameters\n", "m1 = 1e6\n", "m2 = 5e1\n", "a=0.0\n", "e0 = 0.7\n", "xI0=1.0\n", "\n", "traj_args = [m1, m2, a, e0, xI0]\n", "traj_kwargs = {}\n", "\n", "t_out = 1.5\n", "# Run trajectory\n", "p0_new = get_p_at_t(\n", " traj,\n", " t_out,\n", " traj_args,\n", " #index_of_a=2, # specifies the position of the index as it appears in the argument of traj\n", " #index_of_p=3,\n", " #index_of_e=4,\n", " #index_of_x=5,\n", " traj_kwargs=traj_kwargs,\n", " xtol=1e-15,\n", " rtol=1e-15,\n", " bounds=None,\n", ")\n", "\n", "print(\n", " \"p0_new = {} will create a waveform that is {} years long, given the other input parameters.\".format(\n", " p0_new, t_out\n", " )\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Get $m_2$ based on desired duration of trajectory" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Similarly, if you have a desired length of trajectory to analyze, this function will give you the value of $m_2$ that corresponds to the proper evolution time." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:48.048390Z", "iopub.status.busy": "2026-07-11T10:48:48.048331Z", "iopub.status.idle": "2026-07-11T10:48:48.400217Z", "shell.execute_reply": "2026-07-11T10:48:48.399848Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "m2_new = 9.810595035183146 will create a waveform that is 1.5 years long, given the other input parameters.\n" ] } ], "source": [ "from few.utils.utility import get_m2_at_t\n", "\n", "traj = EMRIInspiral(func=SchwarzEccFlux)\n", "\n", "# Set initial parameters\n", "m1 = 1e6\n", "m2 = 5e1\n", "a=0.0\n", "e0 = 0.7\n", "xI0=1.0\n", "\n", "traj_args = [m1, 0.0, p0, e0, 1.0]\n", "traj_kwargs = {}\n", "index_of_m2 = 1\n", "\n", "t_out = 1.5\n", "# Run trajectory\n", "m2_new = get_m2_at_t(\n", " traj,\n", " t_out,\n", " traj_args,\n", " index_of_m2 = index_of_m2,\n", " traj_kwargs=traj_kwargs,\n", " xtol=1e-15,\n", " rtol=1e-15,\n", " bounds=None,\n", ")\n", "\n", "print(\n", " \"m2_new = {} will create a waveform that is {} years long, given the other input parameters.\".format(\n", " m2_new, t_out\n", " )\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### User-defined trajectory models" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In addition to FEW's built-in trajectory models, users can readily implement their own models in the same framework.\n", "They can achieve this by:\n", "\n", "- Subclassing the `ODEBase` base class,\n", " \n", "- Defining the `evaluate_rhs` method, and\n", " \n", "- Updating any relevant properties of the model (by default, they are set for generic Kerr inspirals).\n", " \n", "You do not need to handle any boundary checking in your modified class (e.g., ensuring quantities remain physical) as this is performed automatically by the base class. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Defining a new trajectory model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's implement a Post-Newtonian trajectory in Schwarzschild eccentric as an example:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:48.401330Z", "iopub.status.busy": "2026-07-11T10:48:48.401270Z", "iopub.status.idle": "2026-07-11T10:48:48.406446Z", "shell.execute_reply": "2026-07-11T10:48:48.406122Z" } }, "outputs": [], "source": [ "# Some elliptic functions for evaluating geodesic frequencies\n", "from few.utils.elliptic import EllipK, EllipE, EllipPi\n", "\n", "# base classes\n", "from few.trajectory.ode.base import ODEBase\n", "\n", "\n", "# for common interface with C/mathematica\n", "def Power(x, n):\n", " return x**n\n", "\n", "\n", "def Sqrt(x):\n", " return np.sqrt(x)\n", "\n", "\n", "# this class defines the right-hand side of the ODE\n", "# we define the method \"evaluate_rhs\" according to our derivatives\n", "# we set the \"equatorial\" and \"background\" properties accordingly\n", "class Schwarzschild_PN(ODEBase):\n", " @property\n", " def equatorial(self):\n", " return True\n", "\n", " @property\n", " def background(self):\n", " return \"Schwarzschild\"\n", "\n", " def evaluate_rhs(self, y):\n", " # guard against bad integration steps\n", " p, e, xI = y[:3]\n", "\n", " # perform elliptic calculations\n", " ellipE = EllipE(4 * e / (p - 6.0 + 2 * e))\n", " ellipK = EllipK(4 * e / (p - 6.0 + 2 * e))\n", " ellipPi1 = EllipPi(\n", " 16 * e / (12.0 + 8 * e - 4 * e * e - 8 * p + p * p),\n", " 4 * e / (p - 6.0 + 2 * e),\n", " )\n", " ellipPi2 = EllipPi(\n", " 2 * e * (p - 4) / ((1.0 + e) * (p - 6.0 + 2 * e)), 4 * e / (p - 6.0 + 2 * e)\n", " )\n", "\n", " # Azimuthal frequency\n", " Omega_phi = (2 * Power(p, 1.5)) / (\n", " Sqrt(-4 * Power(e, 2) + Power(-2 + p, 2))\n", " * (\n", " 8\n", " + (\n", " (\n", " -2\n", " * ellipPi2\n", " * (6 + 2 * e - p)\n", " * (3 + Power(e, 2) - p)\n", " * Power(p, 2)\n", " )\n", " / ((-1 + e) * Power(1 + e, 2))\n", " - (ellipE * (-4 + p) * Power(p, 2) * (-6 + 2 * e + p))\n", " / (-1 + Power(e, 2))\n", " + (\n", " ellipK\n", " * Power(p, 2)\n", " * (28 + 4 * Power(e, 2) - 12 * p + Power(p, 2))\n", " )\n", " / (-1 + Power(e, 2))\n", " + (\n", " 4\n", " * (-4 + p)\n", " * p\n", " * (2 * (1 + e) * ellipK + ellipPi2 * (-6 - 2 * e + p))\n", " )\n", " / (1 + e)\n", " + 2\n", " * Power(-4 + p, 2)\n", " * (\n", " ellipK * (-4 + p)\n", " + (ellipPi1 * p * (-6 - 2 * e + p)) / (2 + 2 * e - p)\n", " )\n", " )\n", " / (ellipK * Power(-4 + p, 2))\n", " )\n", " )\n", "\n", " # Post-Newtonian calculations\n", " yPN = pow(Omega_phi, 2.0 / 3.0)\n", "\n", " EdotPN = (\n", " (96 + 292 * Power(e, 2) + 37 * Power(e, 4))\n", " / (15.0 * Power(1 - Power(e, 2), 3.5))\n", " * pow(yPN, 5)\n", " )\n", " LdotPN = (\n", " (4 * (8 + 7 * Power(e, 2)))\n", " / (5.0 * Power(-1 + Power(e, 2), 2))\n", " * pow(yPN, 7.0 / 2.0)\n", " )\n", "\n", " # flux\n", " Edot = -EdotPN\n", " Ldot = -LdotPN\n", "\n", " # time derivatives\n", " pdot = (\n", " -2\n", " * (\n", " Edot\n", " * Sqrt((4 * Power(e, 2) - Power(-2 + p, 2)) / (3 + Power(e, 2) - p))\n", " * (3 + Power(e, 2) - p)\n", " * Power(p, 1.5)\n", " + Ldot * Power(-4 + p, 2) * Sqrt(-3 - Power(e, 2) + p)\n", " )\n", " ) / (4 * Power(e, 2) - Power(-6 + p, 2))\n", "\n", " edot = -(\n", " (\n", " Edot\n", " * Sqrt((4 * Power(e, 2) - Power(-2 + p, 2)) / (3 + Power(e, 2) - p))\n", " * Power(p, 1.5)\n", " * (\n", " 18\n", " + 2 * Power(e, 4)\n", " - 3 * Power(e, 2) * (-4 + p)\n", " - 9 * p\n", " + Power(p, 2)\n", " )\n", " + (-1 + Power(e, 2))\n", " * Ldot\n", " * Sqrt(-3 - Power(e, 2) + p)\n", " * (12 + 4 * Power(e, 2) - 8 * p + Power(p, 2))\n", " )\n", " / (e * (4 * Power(e, 2) - Power(-6 + p, 2)) * p)\n", " )\n", "\n", " xIdot = 0.0\n", "\n", " Phi_phi_dot = Omega_phi\n", " Phi_theta_dot = Omega_phi\n", "\n", " Phi_r_dot = (\n", " p * Sqrt((-6 + 2 * e + p) / (-4 * Power(e, 2) + Power(-2 + p, 2))) * np.pi\n", " ) / (\n", " 8 * ellipK\n", " + (\n", " (-2 * ellipPi2 * (6 + 2 * e - p) * (3 + Power(e, 2) - p) * Power(p, 2))\n", " / ((-1 + e) * Power(1 + e, 2))\n", " - (ellipE * (-4 + p) * Power(p, 2) * (-6 + 2 * e + p))\n", " / (-1 + Power(e, 2))\n", " + (ellipK * Power(p, 2) * (28 + 4 * Power(e, 2) - 12 * p + Power(p, 2)))\n", " / (-1 + Power(e, 2))\n", " + (\n", " 4\n", " * (-4 + p)\n", " * p\n", " * (2 * (1 + e) * ellipK + ellipPi2 * (-6 - 2 * e + p))\n", " )\n", " / (1 + e)\n", " + 2\n", " * Power(-4 + p, 2)\n", " * (\n", " ellipK * (-4 + p)\n", " + (ellipPi1 * p * (-6 - 2 * e + p)) / (2 + 2 * e - p)\n", " )\n", " )\n", " / Power(-4 + p, 2)\n", " )\n", "\n", " dydt = [pdot, edot, xIdot, Phi_phi_dot, Phi_theta_dot, Phi_r_dot]\n", "\n", " return dydt" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:48.407411Z", "iopub.status.busy": "2026-07-11T10:48:48.407350Z", "iopub.status.idle": "2026-07-11T10:48:48.502879Z", "shell.execute_reply": "2026-07-11T10:48:48.502552Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m1 = 1e6\n", "m2 = 1e2\n", "p0 = 10.0\n", "e0 = 0.7\n", "T = 1.0\n", "\n", "traj = EMRIInspiral(func=SchwarzEccFlux)\n", "flux = traj(m1, m2, 0.0, p0, e0, 1.0, T=T, dt=10.0)\n", "p,e = flux[1:3]\n", "\n", "traj_PN = EMRIInspiral(func=Schwarzschild_PN)\n", "flux_PN = traj_PN(m1, m2, a, p0, e0, xI0, T=T, dt=10.0)\n", "p_PN, e_PN = flux_PN[1:3]\n", "\n", "plt.plot(p, e, label=\"flux\")\n", "plt.plot(p_PN, e_PN, label=\"pn\")\n", "plt.ylabel(\"e\")\n", "plt.xlabel(\"p\")\n", "\n", "\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Modifying an existing trajectory model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In cases where the desired trajectory model can be expressed as a function of one that is supported out-of-the-box, the inbuilt model can be subclassed and supplemented as required by defining the `modify_rhs` method. This method takes as input the\n", "current system state and the corresponding derivatives produced by the model, which can then be modified as required. \n", "\n", "This method does not support a return argument for efficiency; the content of the first argument `derivs` should be modified in-place." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:48.504126Z", "iopub.status.busy": "2026-07-11T10:48:48.504065Z", "iopub.status.idle": "2026-07-11T10:48:50.814018Z", "shell.execute_reply": "2026-07-11T10:48:50.813612Z" } }, "outputs": [ { "data": { "text/plain": [ "(np.float64(-0.011514135697943613), np.float64(-0.011629277054923049))" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from few.trajectory.ode.flux import KerrEccEqFlux\n", "\n", "\n", "class ModifiedKerrEccEqFlux(KerrEccEqFlux):\n", " def modify_rhs(self, ydot, y):\n", " # in-place modification of the derivatives\n", " ydot[0] *= 1 + self.additional_args[0]\n", "\n", "\n", "m1 = 1e6\n", "m2 = 1e2\n", "a = 0.7\n", "p = 10.0\n", "e = 0.3\n", "xI = 1.0\n", "\n", "additional_args = [\n", " 0.01,\n", "]\n", "\n", "# Example usage\n", "# Example usage\n", "original_ode = KerrEccEqFlux()\n", "original_ode.add_fixed_parameters(m1, m2, a)\n", "\n", "modified_ode = ModifiedKerrEccEqFlux()\n", "modified_ode.add_fixed_parameters(m1, m2, a, additional_args)\n", "\n", "original_ode([p, e, xI])[0], modified_ode([p, e, xI])[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Passing additional arguments to a modified trajectory model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When calling a trajectory, the `additional_args` attribute of the ODE class will be populated with any positional arguments following $x_I$:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:50.815202Z", "iopub.status.busy": "2026-07-11T10:48:50.815136Z", "iopub.status.idle": "2026-07-11T10:48:53.209903Z", "shell.execute_reply": "2026-07-11T10:48:53.209448Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m1 = 1e6\n", "m2 = 1e2\n", "a = 0.7\n", "p0 = 10.0\n", "e0 = 0.3\n", "xI0 = 1.0\n", "\n", "traj_modified = EMRIInspiral(func=ModifiedKerrEccEqFlux)\n", "flux_modified = traj_modified(m1, m2, a, p0, e0, xI0, 0.01, T=T, dt=10.0)\n", "\n", "traj = EMRIInspiral(func=KerrEccEqFlux)\n", "flux = traj(m1, m2, a, p0, e0, xI0, T=T, dt=10.0)\n", "\n", "plt.plot(flux[1], flux[2], label=\"flux + mod\")\n", "plt.plot(flux_modified[1], flux_modified[2], label=\"flux\", ls=\"--\")\n", "plt.ylabel(\"e\")\n", "plt.xlabel(\"p\")\n", "\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The flux-based stock models perform interpolation to obtain the integral fluxes $\\dot{E}$, $\\dot{L}_{z}$, and then apply a Jacobian transformation in order to obtain $\\dot{p}$, $\\dot{e}$ if these are the variables of integration (and they are by default). In some cases, the user may wish to adjust $\\dot{E}$, $\\dot{L}_z$ directly if the modifications desired are more easily computed in this parameterisation. This can be achieved similarly to what was shown above, but with the `modify_rhs_before_Jacobian` method:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:53.211018Z", "iopub.status.busy": "2026-07-11T10:48:53.210951Z", "iopub.status.idle": "2026-07-11T10:48:55.590302Z", "shell.execute_reply": "2026-07-11T10:48:55.589975Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# A physically-motivated example: dissipation of energy and angular momentum due to dynamical friction with an accretion disk\n", "# Modify the angular momentum derivative according to Eq(2.2) of https://dx.doi.org/10.1103/PhysRevX.13.021035\n", "class KerrEccEqFluxAccretionDisk(KerrEccEqFlux):\n", " def modify_rhs(self, ydot, y):\n", " # in-place modification of the derivatives\n", " LdotAcc = (\n", " self.additional_args[0]\n", " * pow(y[0] / 10.0, self.additional_args[1])\n", " * 32.0\n", " / 5.0\n", " * pow(y[0], -7.0 / 2.0)\n", " )\n", " dL_dp = (\n", " -3 * pow(a, 3)\n", " + pow(a, 2) * (8 - 3 * y[0]) * np.sqrt(y[0])\n", " + (-6 + y[0]) * pow(y[0], 2.5)\n", " + 3 * a * y[0] * (-2 + 3 * y[0])\n", " ) / (2.0 * pow(2 * a + (-3 + y[0]) * np.sqrt(y[0]), 1.5) * pow(y[0], 1.75))\n", " # transform back to pdot from Ldot and add GW contribution\n", " ydot[0] = ydot[0] + LdotAcc / dL_dp\n", "\n", "\n", "m1 = 1e6\n", "m2 = 5e1\n", "a = 0.9\n", "p = 15.0\n", "# assume circular orbits, for extension to eccentricity see https://arxiv.org/pdf/2411.03436\n", "e = 0.0\n", "x = 1.0\n", "T = 4.0\n", "\n", "traj = EMRIInspiral(func=KerrEccEqFlux, integrate_constants_of_motion=False)\n", "flux = traj(m1, m2, a, p0, e0, xI0, T=T, dt=2.0)\n", "\n", "traj_accretionDisk = EMRIInspiral(func=KerrEccEqFluxAccretionDisk, integrate_constants_of_motion=False)\n", "flux_accretionDisk = traj_accretionDisk(m1, m2, a, p0, e0, xI0, 0.0, 8.0, T=T, dt=2.0)\n", "\n", "plt.plot(flux[0] / 86400, flux[4], label=\"flux\")\n", "plt.plot(flux_accretionDisk[0] / 86400, flux_accretionDisk[4], label=\"flux + mod\", ls=\"--\")\n", "plt.ylabel(r\"$\\Phi$\")\n", "plt.xlabel(\"t [days]\")\n", "\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:55.591457Z", "iopub.status.busy": "2026-07-11T10:48:55.591397Z", "iopub.status.idle": "2026-07-11T10:48:56.043865Z", "shell.execute_reply": "2026-07-11T10:48:56.043188Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Requirement already satisfied: pastamarkers in /Users/barry/miniforge3/envs/few_env/lib/python3.12/site-packages (1.0.2)\r\n", "Requirement already satisfied: matplotlib<4.0.0,>=3.4.3 in /Users/barry/miniforge3/envs/few_env/lib/python3.12/site-packages (from pastamarkers) (3.10.9)\r\n", "Requirement already satisfied: numpy<3.0.0,>=2.0.0 in /Users/barry/miniforge3/envs/few_env/lib/python3.12/site-packages (from pastamarkers) (2.2.0)\r\n", "Requirement already satisfied: svgpath2mpl==1.0.0 in /Users/barry/miniforge3/envs/few_env/lib/python3.12/site-packages (from pastamarkers) (1.0.0)\r\n", "Requirement already satisfied: contourpy>=1.0.1 in /Users/barry/miniforge3/envs/few_env/lib/python3.12/site-packages (from matplotlib<4.0.0,>=3.4.3->pastamarkers) (1.3.3)\r\n", "Requirement already satisfied: cycler>=0.10 in /Users/barry/miniforge3/envs/few_env/lib/python3.12/site-packages (from matplotlib<4.0.0,>=3.4.3->pastamarkers) (0.12.1)\r\n", "Requirement already satisfied: fonttools>=4.22.0 in /Users/barry/miniforge3/envs/few_env/lib/python3.12/site-packages (from matplotlib<4.0.0,>=3.4.3->pastamarkers) (4.62.1)\r\n", "Requirement already satisfied: kiwisolver>=1.3.1 in /Users/barry/miniforge3/envs/few_env/lib/python3.12/site-packages (from matplotlib<4.0.0,>=3.4.3->pastamarkers) (1.5.0)\r\n", "Requirement already satisfied: packaging>=20.0 in /Users/barry/miniforge3/envs/few_env/lib/python3.12/site-packages (from matplotlib<4.0.0,>=3.4.3->pastamarkers) (26.2)\r\n", "Requirement already satisfied: pillow>=8 in /Users/barry/miniforge3/envs/few_env/lib/python3.12/site-packages (from matplotlib<4.0.0,>=3.4.3->pastamarkers) (12.2.0)\r\n", "Requirement already satisfied: pyparsing>=3 in /Users/barry/miniforge3/envs/few_env/lib/python3.12/site-packages (from matplotlib<4.0.0,>=3.4.3->pastamarkers) (3.3.2)\r\n", "Requirement already satisfied: python-dateutil>=2.7 in /Users/barry/miniforge3/envs/few_env/lib/python3.12/site-packages (from matplotlib<4.0.0,>=3.4.3->pastamarkers) (2.9.0.post0)\r\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "Requirement already satisfied: six>=1.5 in /Users/barry/miniforge3/envs/few_env/lib/python3.12/site-packages (from python-dateutil>=2.7->matplotlib<4.0.0,>=3.4.3->pastamarkers) (1.17.0)\r\n" ] } ], "source": [ "# some nice italian-style plotting\n", "!pip install pastamarkers" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:48:56.045604Z", "iopub.status.busy": "2026-07-11T10:48:56.045469Z", "iopub.status.idle": "2026-07-11T10:49:00.202755Z", "shell.execute_reply": "2026-07-11T10:49:00.202389Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "p0_new = 12.876302296407138 will create a waveform that is 2.0 years long, given the other input parameters.\n", "4e-06\n", "Time taken for trajectory: 0.027784109115600586\n", "Time taken for flux_accretionDisk: 0.03368997573852539\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "p0_new = 14.288498631405439 will create a waveform that is 3.0 years long, given the other input parameters.\n", "4e-06\n", "Time taken for trajectory: 0.028750896453857422\n", "Time taken for flux_accretionDisk: 0.034442901611328125\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "p0_new = 15.382138511896606 will create a waveform that is 4.0 years long, given the other input parameters.\n", "4e-06\n", "Time taken for trajectory: 0.029779911041259766\n", "Time taken for flux_accretionDisk: 0.034941911697387695\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "p0_new = 16.28688761360239 will create a waveform that is 5.0 years long, given the other input parameters.\n", "4e-06\n", "Time taken for trajectory: 0.030762910842895508\n", "Time taken for flux_accretionDisk: 0.03621792793273926\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "p0_new = 17.06487324966146 will create a waveform that is 6.0 years long, given the other input parameters.\n", "4e-06\n", "Time taken for trajectory: 0.031939029693603516\n", "Time taken for flux_accretionDisk: 0.036682844161987305\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "p0_new = 12.876302296407138 will create a waveform that is 2.0 years long, given the other input parameters.\n", "1e-06\n", "Time taken for trajectory: 0.028837203979492188\n", "Time taken for flux_accretionDisk: 0.032525062561035156\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "p0_new = 14.288498631405439 will create a waveform that is 3.0 years long, given the other input parameters.\n", "1e-06\n", "Time taken for trajectory: 0.028856992721557617\n", "Time taken for flux_accretionDisk: 0.03400540351867676\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "p0_new = 15.382138511896606 will create a waveform that is 4.0 years long, given the other input parameters.\n", "1e-06\n", "Time taken for trajectory: 0.02993011474609375\n", "Time taken for flux_accretionDisk: 0.03564000129699707\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "p0_new = 16.28688761360239 will create a waveform that is 5.0 years long, given the other input parameters.\n", "1e-06\n", "Time taken for trajectory: 0.03020000457763672\n", "Time taken for flux_accretionDisk: 0.03581690788269043\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "p0_new = 17.06487324966146 will create a waveform that is 6.0 years long, given the other input parameters.\n", "1e-06\n", "Time taken for trajectory: 0.031208038330078125\n", "Time taken for flux_accretionDisk: 0.03644299507141113\n" ] } ], "source": [ "# Interpolate and compare the two trajectories\n", "from scipy.interpolate import interp1d\n", "from few.utils.utility import get_p_at_t\n", "from few.utils.constants import YRSID_SI\n", "from pastamarkers import markers\n", "import time\n", "\n", "traj_args = [m1, m2, a, e0, xI0]\n", "traj_kwargs = {}\n", "t_out = 1.5\n", "results = {\"orange\": [], \"blue\": []}\n", "for A, n, marker, col in zip(\n", " [0.4e-5, 0.1e-5],\n", " [59 / 10, 8.0],\n", " [markers.tortellini, markers.ravioli],\n", " [\"orange\", \"blue\"],\n", "):\n", " for t_out in [2.0, 3.0, 4.0, 5.0, 6.0]:\n", " # Obtain the initial p value for the desired trajectory duration, see below for futher explanations\n", " p0_new = get_p_at_t(\n", " traj,\n", " t_out,\n", " traj_args,\n", " index_of_a=2,\n", " index_of_p=3,\n", " index_of_e=4,\n", " index_of_x=5,\n", " traj_kwargs=traj_kwargs,\n", " xtol=1e-12,\n", " rtol=1e-12,\n", " )\n", " print(\n", " \"p0_new = {} will create a waveform that is {} years long, given the other input parameters.\".format(\n", " p0_new, t_out\n", " )\n", " )\n", "\n", " print(A)\n", "\n", " T = 10.0\n", " # T = t_out\n", " tic = time.time()\n", " flux = traj(m1, m2, a, p0_new, e0, xI0, T=T, dt=10.0)\n", " toc = time.time()\n", " print(\"Time taken for trajectory:\", toc - tic)\n", " tic = time.time()\n", " flux_accretionDisk = traj_accretionDisk(m1, m2, a, p0_new, e0, xI0, A, 8.0, T=T, dt=10.0)\n", " toc = time.time()\n", " print(\"Time taken for flux_accretionDisk:\", toc - tic)\n", "\n", " interp_flux_accretionDisk = interp1d(flux_accretionDisk[0], flux_accretionDisk[4])\n", " interp_flux = interp1d(flux[0], flux[4])\n", "\n", " # t = np.arange(len(flux[0]))*dt\n", " if t_out == 4.0:\n", " label = f\"A={A}, n={n}\"\n", " else:\n", " label = None\n", "\n", " # use the shortest trajectory as the reference\n", " t_f = flux[0][-1]\n", " delta_phi = interp_flux(t_f) - interp_flux_accretionDisk(t_f)\n", " results[col].append((t_f / YRSID_SI, delta_phi, marker, label, col, toc - tic))\n", "\n", "for A, n, marker, col in zip(\n", " [0.4e-5, 0.1e-5],\n", " [59 / 10, 8.0],\n", " [markers.tortellini, markers.ravioli],\n", " [\"orange\", \"blue\"],\n", "):\n", " results[col] = np.array(results[col])" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:49:00.203790Z", "iopub.status.busy": "2026-07-11T10:49:00.203730Z", "iopub.status.idle": "2026-07-11T10:49:00.297938Z", "shell.execute_reply": "2026-07-11T10:49:00.297565Z" } }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAm8AAAHNCAYAAABICpzwAAAAOnRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjEwLjksIGh0dHBzOi8vbWF0cGxvdGxpYi5vcmcvJkbTWQAAAAlwSFlzAAAPYQAAD2EBqD+naQAAialJREFUeJzt3Qd4U2X7BvC70JYO9t57yBRE2UvmhwIiKioiiKggiiLwqcj3F3CAoiAqiigoKAIuUFBBQLaoLJE9lI1saAu0dOZ/3e8hNS1tSUva5qT377oCzcnJyXnPOUmePO/yczgcDoiIiIiILeTK7h0QEREREfcpeBMRERGxEQVvIiIiIjai4E1ERETERhS8iYiIiNiIgjcRERERG1HwJiIiImIjCt5EREREbETBm4iIiIiNKHgTERERsREFbyIiIiI5PXibMWMG/Pz8Em9BQUEoWbIkbr31VowbNw6nTp1CZhs9erR57TNnziArOct+8OBB5ATr1q0zxzosLMzrj0Nq+5pVvPGYXC9OjfzSSy9h1apVHtneF198gdq1ayM4ONgcqy1btiCrOT87rnXuUttXbyiDXd4TWcVOn1PJr7+M7mN2fQf6gnU2eF9kaubtk08+wa+//oqlS5fivffeQ/369fH666+jZs2aWLZsGXzR7bffbspcqlQp5JSLfMyYMVdd5N54HFLbV8m4vXv3YtSoUTh+/Ph1H8bTp0/jwQcfRJUqVbB48WJz/VSvXt0rTk/y6zm1ffXmMuTk94SdPqeSs8M++pp1Nnhf+GfmxuvUqYObb7458f5dd92FZ555Bi1atECPHj2wb98+lChRAr6kWLFi5pbT6TjkDJs2bTL/N2zY0COBYGxsLHr37o3WrVt7YO+AyMhIhISEePx6Tm1f//jjD68tg6/w5PGww+eUHfYxI3LidR3pyTI7MsEnn3zi4KY3bNiQ4uNffvmleXzMmDGJy/bu3eu4//77HcWKFXMEBgY6brjhBsfkyZOveu6oUaPMczdv3uy48847Hfny5XPkz5/f8cADDzhOnTp11Xrbt2933HfffWad4sWLO/r16+cICwtLss19+/Y5HnroIUfVqlUdwcHBjtKlSzu6dOni2Lp1a5L1uP1HH33UUbZsWbOPRYsWdTRr1syxdOnSq8p+4MCBdO8Hffvtt466deua7VeqVMkxadKkxG2kZf78+WadZcuWXfXY+++/bx77888/3S6HO5z7lfy2YsWKq46D6/rcj7vvvtsci0KFCjmeeeYZR2xsrGP37t2OTp06OfLmzeuoUKGC4/XXX7/qNd29TtKzr7RmzRpH27ZtzWvzGmjatKnj+++/T9dxuNY1mdIx6du3rylrattMaZk711J6rqOMHtObbrrpquPJ45eQkOBILx6H5Ntq3bp14uPunB9n+TZt2uS46667HAULFnSULFkyzdflNm688UZT7ooVKzreeOONFI+T67lLbV+vVQZ3jvO1ypCebVzrOrnWeyIl7n5W0q5du8zr87W5r+XKlXM8+OCDjsuXL7u9jiePh7ufU+m93tz9bM/o9ZfSPrrzGe7czunTp5Mcb34eNGrUyHHy5Mnr/kxz93pI6zymdxvX8/3hzjVzrfdFemOVlMrsie/gTM28pea2225D7ty5sXr1anN/586daNasGcqXL48JEyaY9nE//fQTnnrqKVNfz2qZ5O6880707NkTAwcOxI4dO/B///d/Zju///47AgICkmT77r33XvTv3x/btm3DiBEjzPKPP/44cZ1//vkHRYoUwWuvvWZ+4Zw7dw4zZ85E48aNzS/pGjVqmPVYHbJ582a8+uqrpiqEKVXeP3v27DXL7M5+sJqFGclWrVqZdjNxcXF48803cfLkyWtuv0uXLihevLipqm7Xrl2Sx9hm4qabbkK9evWuuxyuHnnkEXOs3n33XcybNy8xrV+rVq0022fwvDEzMWDAAFOlPn78eJOtYFX6oEGDMHz4cMyePRvPPfccqlatao5JRq8Td/aV7bU6dOhgjs/06dORJ08evP/+++jatSvmzJljzps73L0mr9e1rqX0XEfXc0w//PBDU9aEhATTLIKc7bzSi8eqUaNGeOKJJzB27FjTPjZ//vzmsfSeH5b9vvvuM/t26dKlVF/z559/xh133IGmTZti7ty5iI+PN9fitd5vqe0r9yu1MqT3OKdUhvRu41rXSVrvidS4+1n5559/mhqWokWLmjaR1apVM1XrCxYsQExMjDlW7qzjieOR3s+p9F5v7ny2e/L6y+hnOMvFzyh+LvDz1Z0M0LU+09y9HtI6j+ndRka/P9y9ZtK6XjLyeZlSmT3yHezIhswblShRwlGzZk3zN6NlRqDh4eFJ1nnyyScdQUFBjnPnzl0VzTLadvX555+b5bNmzUqy3vjx45OsN2jQILPNtLIDcXFxjpiYGEe1atWSvA4j+iFDhrhV9uSZN3f245ZbbjG/PKOjoxOXXbhwwVGkSJFrZt5o6NCh5peL66++nTt3mue+++676SqHu/hLMaVfrmll3iZMmJBk3fr165vl8+bNS1zGX1L8ZdOjR4/EZem5TtKzr02aNDG/mHmsXa+BOnXqmNe7VibJ3WvSU5m3a11L6bmOrveY8rg99dRTDk/gL1vu31dffZWh8+M8Pi+++KJbr9e4cWPzKz8qKipxWUREhKNw4cJpZt7S2tfUlrt7nNMqQ3q34c5nTmrvCXel9lnJrBUzDa5ZmuTcWccTxyO9n1Ppvd4y8h2TnusvpX105zPcNfP22WefmQwP36vx8fFpPi89n2nuXg/peW9eaxsZ/f5IzzWT2vWSkVglpTJ74js4V3b2UqPLly+bXyCM8PlLgFkC540ZOj7+22+/XfX8Bx544Kpo3N/fHytWrEiyvFu3bknu89cUt+na45WvxV/KjKwDAwPNdvg/2+Tt2rUrcT3+qmYW65VXXjH7xGjfXdfaD0bkGzduRPfu3c1rO+XNm9f84nPHww8/jKioKJNtcWImjr8ce/Xq5ZFyeAKzhK7YgYXZms6dOycu4zngr6ZDhw5d13VyLTzu/BV59913m2PtxMwwfx0dPXoUe/bscWtb7l6T1yutayk919H1HtMjR46Y1/REezdPnh9mQtzZ7oYNG8yvYvaGd8qXL5/b7zd3ZeQ4Jy9DRrbhzmdfernzWcl2Pczy8PpPra2WO+t4+nhk1vWWkeN8vddfej7Dmd156KGHTGbr7bffRq5c7n/tX+szzd3vzrTem+ndRka+PzxxzWT0+SmV2RPfwdkSvPHCZXqwdOnS5n8WnilKpmFdbzwglFJXZ6YrXfFkMfWaPO3IZa6cqXgGOU5Dhw416WB+4S1cuNC8efnGuvHGG5Osx6Cob9++mDZtmkl1Fy5cGH369MGJEyeuWeZr7cf58+dNQJtSBw53O3VweIJbbrnFBGzENPysWbNMap776olyeILrvhDfqHwzuH6IOZfzDUEZvU6uxXncU+rJxevT+drucPeavF5pXUvpuY6u95im1Vlh6tSpaN++vflA5flm5yVWOWTF+XGnVx63y+re5OeMUlp2PTJynJOXISPbcOezL73c+azkseVnT9myZVPdjjvrePp4ZNb1lpHjfL3XX3o+w/kdUKZMGVN1l17X+kxz97vTKaXjmt5tZOT7wxPXTEafn1KZPfEdnC1t3n744Qfzxm3Tpg0KFSqU+KuGbUVSUqlSpauWsZC8IJ14UHlwk7+R3MGLmweO0b8rnoiCBQsm3mfbjEmTJpnb4cOHTduM559/3vzCYjuj68HjwF8PKbV3SM8J7devn6n35y+W/fv3mzYkXOYqM8uRWTJ6nbizXf4STWmoC7bFcB4vd2TkmuQHTnR09FXLMzo2U3quo+s9pgze+KF5ww03XPXY9u3bzQfwl19+ibZt25r2Hv/73/9MG5LMPj/utLlzHqeU3lue/hGTkeOcvAyZdf1nxmclv4i4r8xSpcaddbLjeHjy8yAzr7/0fIbzPtvktWzZ0mSOKlSo4PZ+Xuszzd3vzrTem+ndRkYVus5rJqPPT6nMnvgOzvLgjTvKBoUFChQwDQ754c+GvWyYyHSza1VPWj7//PMkv/j5JcELiwFhevHgujaOdQaYx44dM6nXlLDB4pNPPmneDL/88guuV2hoqBlW5dtvvzWNy53H4eLFi/j+++/d3s79999vfskwJcvgjW+8jh07prr+9ZbDE7/m3ZHR6+Ra+8rjzoaxDCp43NngnvirmB8qzAy4O05XRq7JihUrmjcsgy1nZoyNtdkINrOvo+s9plu3bjWBGz/QUgreGKx16tQpsfqFjXozUh5PnZ/k22XVBbf7xhtvJP5qv3Dhgvn1723Xrie24Yn3rzuflTxHHCblq6++MlV2KQU77qzjyePhbjkz63rLzOvvWp/hDNbWrFljMuHOAI6dQzzxmZaR787kPLENT18zKV0vmfUezOh3cKYGb/wAd9YJ8wuKFxCr9PhhP3/+/MS2DqyHZ68jXliPP/64+ULjRfzXX3+ZC3n58uVXbZsXPVO47BXk7AXDNCvr5NOLdegMdvhFxJPCjALfUK4p/fDwcHPi2HaM67FtAjMLzp59nsAeVxyQkV94Tz/9tMlOcj/Y9oK9X9zBXyqsk2d52IOFgbJrGwd3ysG2KOyx+uKLL5pbWurWrZt4DpkGZgo5ee8gT8nIdeLOvnLWD15HPC48XnxTsncZr1/2LnO392RGrkn+IuYxZpXGf//7X5Pmf+edd8y5z4rr6HqOKa81XivfffedCTxZPeD8Vc/ys6eeE9//Gc1YeOr8JPfyyy/jP//5j9n2sGHDzHHiIOL8YnX3/ZZV166ntuHue4KfCxn9rKSJEyeafWUgxIwCv4T5A4UZBlapc/vurOOp45Gez6nMut48df1l5LuI702+V/mZwN6m7KXJpgzX+5nm7vWQFk9sw13uXjOpXS+eeA96LJZwZAJn7xjnjb1c2HuHYx6NHTs2xd5F7NXx8MMPO8qUKeMICAgwPUU47skrr7yS6tgpXbt2Nb02OAYNx11xHbcmpTFuXPfNtRfJ+fPnHf379zf7GBIS4mjRooUZ54f76xynieMODRw40FGvXj0zvgx7ddaoUcO8zqVLl1Ldfnr2wzlem3N8rvLlyztee+0100OI49m4a8mSJYnHnmPSuHKnHM4ec1zmjhEjRpheU7ly5XJrnLfkx4I9LkNDQ6/aLo997dq1M3SdpGdfXcd14n7wmLDH2cKFC93aprvXZGrn/McffzQ9pvi6lStXNmMGpdXb1J1rKT3XUUaP6d9//23OEY+Zay8wlpn3XXvr9ezZ0+xDWlLrqenu+Unt+KRlwYIF5r3gepyuNc5bWvuaVhncOc7XKsP1bCO16y+190RK3PmsdO3pfs8995hezs7jy/G8XMd5u9Y6njgeaZXzWuO8ZeR6S22bGb3+km/P3e+ilPaPIxE0b97c9GhNazQIdz/T3L0e0jqP17uNvun4/kjPNZPa+yK9sUry/XX3/F2LH/+BjXC+MU5bwWloPNH2wNuxFwqnFWP155IlS7J7d8Sm12RWXkdM//MX/gcffGB+tX766acmy8BxvdhcQkS8mx0+03K6bOmwIKnjQI9MUTPNzcai/AJk5wOma0XscB2xeonD1nDgUba/ZJsZVtMocBMR8QwFb16G9edsZ8FfPKxn58wIP/74o2lsKmKH64jBGztNcAYGERHxPNtVm4qId+O4RRwQ1FMTs4uISFIK3kTEo1g9unfvXrcHlxYRkfRR8CYiIiJiI9k2t6mIiIiIpJ+CNxEREREbUW9TF5wChfPXccRjT42iLSIiIpnL4XCYXvalS5dOMquQr1Lw5oKBW7ly5bLvbIiIiEiGHTlyJFOm1vI2Ct5cOOfS48nPnz+/x0e458j2nCSe4275Gl8vX04oo8pnfzqH9ubr5y8zyxgREWGSL9eaE9dXKHhz4awqZeCWGcFbSEiI2a4vvil9vXw5oYwqn/3pHNqbr5+/rCijXw5p8uT7FcMiIiIiPkTBm4iIiIiNKHgTERERsRG1ecuA+Ph4U2+fHlzf398fly9fNs/3Nb5evpxQxvSWj+1VcufOnSX7JiIi/1Lwls5xZE6cOIGwsLAMPbdkyZKmJ6svNqj09fLlhDJmpHwFCxY0z/HF4yEiWcDhAE6uAPJXB0J8f4gPT1Hwlg7OwK148eKmt0x6vrA4APDFixeRN29enxxA0NfLlxPKmJ7yMdCLjIzEqVOnzP1SpUpl0V6KiM8EbUfmAbvfBgLyA5dPALVHAuW6Z/ee2YKCNzexGskZuBUpUiRDX4wxMTEICgry2S9+Xy5fTihjessXHBxs/mcAx/eFqlBF5JouHbL+X9kZyF8JaDYLCC0HxEUCKzoBeSsDherpQF6Dgjc3Odu4MeOWKZQ6Fhtyvh/4/lDwJiIpOrsJODADOLcFCGDyox/Qcj4Q7DKeqn8I0OgjYNPTQNufdCCvwffSB5nM4217nKnjZW2A3W8Bq+8Ejnzr2dcQySRq6yYiqbp4GFjRGdj2IlCsBdDuZ6DZHOux2DDr+89VgRuszNvBuTqo16DMW3a5eADY/4nVUDNfDaWORUTEd0SdBNbdD9R6FijVCdg9CVjRAYjjg0OBX+4H/GKB0IpA7eeBwjdZz6szCljTHah4XzYXwLspeMtCucL/APZ+DYRtBQLzA6W7ALf+ZKWLE8+IUsciImJjCbHAmh5AgwlA9ElgSTOgTFeg1QLALwT48Ueg/UrA3x84sQzYPBSocB9QbSAQUhIILQ+c/gUo1jy7S+K1VG2aVanjlbcheO+4f1PHrb4DSncGYs5nWep43bp1pl3Sf/7zH49u95dffkFgYCBatmzpke0dPnwYXbt2RWhoKIoWLYqnnnrKNKRP3tvxzTffRPXq1ZEnTx4zIfHYsWPhDdWIyW8ffPBBms/5+++/ceedd6JYsWJmvr+ePXvi5MmTWbbPIiIe9fcnQJnbgcsngR3jrKrSemOAwAJJ12MzpFIdrCTGwc+BXW9ZywvUUdXpNSjzllWp4xv+i0uhTZD/+CdW6jg+xrpw+QsFflmSOv74448xePBgTJs2zQRI5cuXv+5thoeHo0+fPmjbti2OHz/ukV69t99+uwlk1q5di7Nnz6Jv374mWHv33XcT13v66aexZMkSE8DVrVvX7MeZM2fgDT755JMkAXKBAsk+sFxcunQJHTt2xI033ojly5ebZf/3f/9ngtfffvvNJ3u1ioiPO/IV0OpbYGUXoNEUoECNtNfPnQdoNhtYcydQpT8QGwGc25hVe2tLCt6yKnUcdQJ5f+0ElOtmpY5df4Ew85bJqWMGCV9++SU2bNhgxqubMWMGXnzxxeve7oABA9CrVy8TZMybNy/FQGb8+PE4cOAAKlasaLJogwYNSnV7DMh27txpBootXbq0WTZhwgQ89NBDePXVV01mateuXZgyZQq2b9+OGjWu8aGQhjZt2qBevXpmaAwGtMweDhw4EKNHj8b1cA5c627W8uDBg/jjjz9M2ZzHrHDhwiaYa9++/XXti4hIloq9ACTEA9FngYB8QKEG1ndc+E7gxM9AQFEAoVc/j8OFlGgH7HsfyBUIRB62nqcBwFOkn/VZlDr22zkOl+pPA+pmT+r4iy++MIEOb7179zYBArNZrjg4a1q3zp07J1mf22CV36hRo1J8zY8++ggjR440QRcDLlZrMqs0c+bMVPfz119/RZ06dRIDN+rUqROio6OxadMmc3/hwoWoXLkyvv/+e1SqVMkEhY888gjOnTuX7uPCfWH17O+//26CzJdeeglLly5NfJxldpafwVXZsmXN/67HJbknn3zSVPfecsstpsqU46elhuVi1Sqrfp2c46wx8ygiYiux4YB/KBC2DShUH0iIA9b1Av4YBkT9A5z51Vrv4JVep67K9QDObbKCNz7P4XvTEHqKMm9ZlDp23DIFjtyVsy11PH36dBO0Eav0OJL+zz//nCSzs2XLFrcGZaV9+/bh+eefx5o1a8x8mCl5+eWXTdasR48e5j4DLWbVpk6daqpCU8KsYIkSJZIsK1SokMmK8THav38/Dh06hK+++gqffvqpqWp95plncPfddydWPbqLmTdn8FmtWjVMnjzZHJcOHTqYZczIRUVFuT0DAcvcrl07c6y4nWHDhpnq3P/9738prt+kSRMTPD733HMmuGVAzb/5Wp6ohhYRyVJxlwC/XED8ZSCgIHD8J2tUhQK1re+z4Cvfg/98D8SdBi7sA26eDOTyB4o0AuIjrbbg/D5MiLGWi3dm3uLi4syXG7/c+aXHrAozIK4ZC36psTqLGRmuwyqvHTt2XJXFYJsuZj34hditWzccPXrUS1LH9a0UcNgOYPc7wMHZQJwVFLiVOr4Oe/bswfr163HffVb7OQZb9957r2kD56pq1app3sqUKWPWY7DEqtIxY8aYDgMpOX36tKn67N+/f5Is1SuvvGKydcmzWrVr105z7DCef+dyXhc81wzc2EmC1wKD0xUrVpiypjd4c8VpnpxTPhHL7HoMeG0mPy6ueB03bdoU9evXN4Ebr+M33ngj1ddn2z4Gocwm8jiwfRzb7910000a9FZE7CcmDPDLbf0ddwFwJFi1SG2XAW2XACWtH8Yo3MT6HoyPAo798G9TI35vckSGoKQ/4iUprwhpX3/9dVO9xCosfolv3LgR/fr1M19kbJhOrNKaOHGiaavFgIFBALMj/LLOly+fWWfIkCHmS3Du3LlmCit+eXbp0sVUt2X56O8ppI5DtjwKOC5a9y/sBnZNAGo8DVTuc3XqeNeb1i8VZ+rYL+OnioENA2Rn8OUMhgICAnD+/HmT2aKUqgBdMVBatGgRLly4YM4R22mxitAZUHGbzJCx3ZozGGPVaePGjZNsx3kuXLNa3BdiWzFWYbriPnIEf2dGjgEWA1DXwLFmzZrmf3bESE87OOfrOjFAdP3RwACT2cW0MBuXGmbWIiIiTO/R5BlFJ3ZYYEDLDB3L5Wwzxx8zIiK2wgnmGZBxGqx/FgGRx4CI3cAfw4FS/wHK3gFsWwQcmw+ElLGSE8y0Eec3ZbaNwV/uECB3UHaXxmt5RfDGdk533HGH6WVIbMM0Z84cEyAQg4JJkyaZ9lPOKjgGevwynD17tmk0z2wFg5TPPvsssSpw1qxZZgiJZcuWmXZT2Z069j+7Bn4Fr6SO2Rnh5neBXW8A0ZmXOmbQxgwVqy8ZJLi666678PnnnycGYO5Wm7LN17Zt25I89t5775lqwq+//hpVqlQxmU8Gi6zifOCBB1Lcnmsw6cSsFdvIscrQOdk5g0G2CWvYsKG537x5c1MuBjx8Ldq7d6/5v0KFCvCk9FabJscAl23YGJBdCzPGxKpfZv+YORYRsZXAQlbwdvQ7oMwdVgataFMg5ixwYCbw58sAhgFBxYFTPwN5KwF1rnSe+2s6ELELaPAmsG+K9R0q3hu8tWjRwmTe+AXMbMqff/5pGmszYCP2VGR7J9fgg1/mrVu3NmOXMXhjdo3ZGdd1WMXKxu9cJ6XgjVVvvDkxQ0LcjnMuUyfeZxDJL/C0GqAnusxfErmslHFMOByOBCTkq4lcbZZYnWeOzIPf5mFwlL0Tfgdnw8Es27HvgTLdzDAifsy4nd8K5CkOB1/PnddMwYIFC0zmypnJTB68MeB19v5kleC1OMteq1atq6r/eE6YcXNmr9ibldlQZkbZzo7HmgF5WFiYaaOWEgbe3PaDDz5oMrLshDB8+HDTIYFBE7fLYUlYrfjwww+bbCyXsbqcz2U1plvn5wrnOXW977rMGUA6H2PWkeVxrdp1rsusL69TBqAMdFmNyx8cjz76qMnwcb1jx46ZjDEzyI0aNUrs+MHMIY8hf8jw2PC4sQ1eespyvZwdWJIfk7Q4M652mNvU+Z5O/t72Jb5eRpXPJvLWAU7+DBS4CSjZNslDsTGXgWXLEZu/PhBSFijSFAiuAJzcYHXQqzwIOPsnUOYennC3XzLWR695rw7e2ECbmbMbbrjBfAGwTRWzL/fff7953NlQPXm1E++z4bpzHVbZOasAXddxPj+5cePGmXZbyTHTk3wCelZnsSqLmZfkA8amxM+vJIJjLiLu7B4EHv8B8eEHEXBxL2LWP424Yu0RV7QDcFNT5F3fHQkM0GJiEBd2DLH5IuAXdQQhMZFXfnXkwaVLTCObOUXS7cMPPzRBLoMNZ3DqxICWx4DVghxn7Ho4jwmDGycONsvX5fhsPMc8pgzMHn/88av2xRWzqQzYWE3LrBU7IrCXqutzmFXlNtnejdtl4MaqdOc6rD5lmRhQ8cdBSpi94367bpfL+CGQ1v65ltEVn8cMJPedQQ2zgCNGjDCBp3N7DKRZ1c8qUucyZjFfeOEF8xjH3hs6dKgJqNPah8yUWvlSwuPHzOTq1avNsbMD197EvsrXy6jyeTu2a+sAbL4M4McU11h65Ep7Y/bL2u5cZzxgfaVb/kr5uSmJjIxETuLnSD5eRDZgG7X//ve/pmE3MzesvmPmgVkV9kpk5oxVZf/880+STAgzGmwUv3jxYvOFz+ySayaNmOVg1VpKo9ynlHljNSu/WJ1jbjldvnzZvBardBlQuMPv51uZx4CjVCc48pQw2wjKFQm/sK3wu7APDrZ9izoOv9OrzSC9juZfAvmqAttGw+/vj+CoPx5+f30AR/u021x5g9SyUtll5cqVJrP4119/XRXQ+0oZPS0j5eM1zXHq+L5x932RXRhc80ufnwnJ2zr6Cl8vo8pnI1EngO0vA+f/BJrPAoLLAFtHIfbMH1gaMxgdGhZGQPgW4Nh3VtVq3VFAQAFgbU9rSK3i6RvfNCIiwjQ9YSIo+fe3L/KKzBsDNw474ewNyRHzmVFjVojBm3PAU2bQXIM3tgtyZuO4DrMArg3wnes0a9YsxddlNZ/r+FpO/NBL/sHHbCC/0NjWye1R7wvUBI4vgV/hW5BQsj1iIyIQnD+/9fyEOPgdnQ+EbQfylgeKtoBfgerA2U3AwU+BqgPhF7YFKH8P/Gwwyr6zms15jLIbs6fMZrHjiq+W0dMyUj6ux/VTes94Kzvta0b5ehlVPhsIKAc0+xA4/DXw631Ak2nALW8AYfuBVdsQcHQuAoILAeW7WW27D04Dji8FbnwFKNMm/S8X4LvXu9cGb0x3Jv+yYPWp88uEve4YnPEXZYMGDcwyBmqrVq0y7aKIjdl58rgOq+uIjd45Cj97qmaLhm+bOU2xYSDQ/AvAvxpwdj3AoKzKoyYwMzdiAnTfVOCvD4G6LwPFWwK/3Ae0X509+25zr732WnbvgoiIlL8bCCkHbBlhDY/lx45vj1uJi4gEq8NCYEEgfw2g41prlAaxR/DGeRzZxo3tfVhtyh56rDJlg3TiL3tWo3IQUzbi5o1/s60TxxsjNsbnmGIcHoTZFk4vxLZHzOJl2xRD/DXR9DNg6//g9/sj8Ks/EyjRADj8JbC0OVCprzVsyNkNwJGvgeBSQIsvrd6pq7oA9V8Hcgdmz76LiIh4QtHGwK2LraGvLp0Elm8E2i4FAvX9ZuvgjQ3a2SCdjbRZzcleouxB6jr35rPPPmsaRnMdVo1y7DBWjTnHeKO33nrLdCxg5o3rcqR79urL1l5wIaWBJh/DcfArhP7xEND0Y6DhRODiIWD/DODADCBPMaDc3Vaw99fUf1PHJVpn336LiIh4Eoe84hAh5IPthnNc8MYAjMOCOIcGSQmzb5xhIa1Jw9lgmoEgb16n/F2IQmGE/vmCNQZOrtzWrxCOKM0BeJU6FhEREbsEbzlFfMGGQBt2fU6wps1ilSirSPULRERERNyk4C27UsfBmrdNRERE0s/3xjsQERER8WEK3jLJ2bPAyy8DU6dyxHprWVgYJ4m3ZrrauRPo3x84edJ67PRpDnj67/NXrgTGjuXYdpm1hyIiImJHqjbNJO+/D3zzDVC2LCdt52wQwPz5ofj1Vz+sXw9s2GBN29a5Mydj53RPQJ06wL33Ar//DrMO5zI/eJBTXGXWXoqIiIjdKPOWSThTEKdHXbiQ49gxA8dR6B2YONGB5csBjjW8fTtwzz1Wlo7r1awJsMMt54/fuJFzj3IAY8/tE6cZ47ApnCT+enEAZI6xV6NGDTPAcmoTzWcE5yXl2H+hoaFmupOnnnrqqvlkOZXTm2++ierVq5tZMjg9E8f+y24bNmwwQ9QULFjQzPTRsWNHM91bWjhF2+DBg01ZWeZu3brh6NGjWbbPIiJiLwreMknVqsDmzVYW7dVXga1bHZg7NxK33w588okVtP34I6cCA/r0sapMmZ3jc5i1YwB3+DAnMrcmX/CEjz/+2AQJa9euNQHS9WDAUaxYMYwcOfK6J7VPPg3Z7bffjkuXLpn95Ly333zzjRl82dXTTz+NadOmmQBu9+7dZgL6Ro0aITtxXtBOnTqZwaZ///13s/+cY4/LOCdjajgA9fz5801Z+ZyLFy+iS5cu5liIiIhchRPTiyU8PJxhkvk/uaioKMfOnTvN/9dy/rzDUb68wzF8uMMRH+9wHDrkcHTvnuCoVCnOUbZsgqNuXYejcWOHo2lTh6NZM+t2880OR+XKDkeZMg7Hxo3Wdt55h2Gbw7Fu3fWfoYsXLzry5cvn2L17t+Pee+91jBkzxmOnvXXr1o6nnnrKcf78eUc8C+zi448/dtxwww2OPHnyOGrUqOF477330tzWjz/+6MiVK5fj2LFjicvmzJljnu88LzwP/v7+pizXu9+DBw92/Pe//3UUKlTIUaJECceoUaNSXZ9lS6mMThs2bDDXz+HDhxOXbWXUDjj++uuvFJ8TFhbmCAgIcMydOzdxGcvOY7B48WJHVrpW+VKSnvdFdouJiXF8++235n9f5etlVPnsL7POYXga39++SJm3TMAsGid1YEaNU7bOmGF1Uli06CIOHHBg61bgt99YjQn88ot1Yxu4v/8GnnqK83IyAwUsXgy0amVVsV6vL774wlRx8ta7d2988sknpurRVd68edO8dWYDvXT46KOPTGaOU5/t2rXLVGtyJo2ZM2em+pxff/0VderUMbNsODFzxUzfpk2bzH1m2SpXrozvv//ezHtbsWJFPPLIIzh37ly6jwv3hVWVzJRxDtyXXnrJzI/rxDI7y88sWtmyZc3/rsfFiceWVZ/Tp0831byc5YN/c8q3ChUqpPj6LBOzcqxedWLZeQxYzS0iIpKcOixkgpIlrU4Ib77J4AA4dAho3NiBEiUcJphLyxNPALVrWz1TGeDNmWO1n7teDCIYtBHbvLFq7ueff04y7+u12mYFB3NCYfe9/PLLmDBhAnr06GHuM9DauXMnpk6dir59+6b4nBMnTqBEiaRj4LHtWGBgoHmM9u/fj0OHDuGrr77Cp59+aqoX2ebu7rvvxnI2KEyHevXqYdSoUeZvzpk7efJkc1w6dOhglrFqlkEYJSQkmOPGgI3t/FKaKWTlypW44447TNmJbfJ++uknM21bauVl2VhGVzwGzvKKiIi4UvCWCU6dsjocOOMTZuHcnV41NNTq6MD1H3kEGDECaNHCWpZRe/bswfr16zFv3jxzn4HEvffea9rAuQZvVdlQz0NOnz6NI0eOoH///niUjfmuiIuLQwE26LuS1VqzZo35m5mpHTt2JE6FlhyzhM7lDKKYiWPgxuDIGZw2bNjQlJUZsPQEb65KlSpl5td1KlOmTOLffN2IiAiTeUspeGOQ9/DDD6N58+aYM2eOCSrZJu+2224zHRnSE/y6lldERMSVgrdMwNpIju12JXkDJl3c/R5m9SqrTPPls8aBmz2bPTuBKlUyvj8MbBg0uQYiDA4CAgJw/vz5xKyPaxVgSlq2bIlFixa5WY6ExKrTxo0bJ3mMPV6TZ7W4L1SyZElThemK+8iqRWdGjgEWA1Bn4EY12VX3Sk/V9ARvztd1YsDk3PfkAWZqmI2j2bNn4+DBg6bq1xnccRmP73fffYf77rvvqueyvKxidT0PxACyWbNmbpdDRERyDgVvmYAxBtuusZby00+t4M1de/da2Td2TuzWDWCN4/UEbgzamKFi9aVruyq666678Pnnn+PJJ5/0eLUpAy0Gi6zifOCBB1JcxzWYdGratKlpI8ehSBik0ZIlS8xwIMysETNbLNfff/+NKlcOzl4euCsZPE9KT7VpZGSkWe6aMXPedw0IXbFMDCDZzq5nz55mGcu+fft20wZPREQkOQVvmYRVnRx4t3JlIE+epLMnpOX77602bxzfLTycWabr2w826mdWh9WXzupKJ7YRY1bOGbylt9rUGewxoGE16bZt20z2iI3tafTo0WaMNlYzMoPFqs6NGzea/Rk6dGiK22SAWatWLTz44IN44403TCeE4cOHm6pXbodY1XvTTTeZKspJkyaZwOiJJ54w7dRcs3GekJ5qU77+f//7X7MvHJKF67/22msmS3jrrbeadY4dO2bGgWNAzaFNeE54bjgUSpEiRVC4cGFT3rp16yap0hYREXFSb9NMwmmxOMhusWJAkSLWdFjOabJSwjFoOSXWtGlWxo01aOz0wMzd9WBwxiAgeeDmzLwxANvMweUyoEGDBubGHpNs49WqVSszPpkTe4AyczVjxgwTjLRu3dr8zY4LqWGV6g8//ICgoCCTYWM2qnv37qbtmBMDJ/Y4Zc9OvibHhWO1KcdJc2L1JTNe7ECQVW644QazX1u3bjUZRFYz//PPP1i8eHFiFpHVv2yXxyyd01tvvWXKyLKyzCEhIWY7zuplERERV8q8ZRKOdLFqlVX9yeE+OMPCLbfkR1CQn2n/xsQNb86/+V3ODN3dd1s3ThbAmOqFF65vPxgEpIbZq+TDhaSH63Nds1KuOAsDb+nBQW6ZMUwLh9Pg4L2pYfDGWQ7SGkA4pcDu22+/xfVg9s3ZUzUlHNYk+TFnoPruu++am4iIyLUoeMskgwYBkycDnOWI7c7/+suBw4cvIDo6HxwOtoGyAjfe2DmhcGFrSBB+r3MZs3QMAB96KLP20Lcx2/XCCy9cNQSHiIiI3Sl4y8Rq01tuAQIDAbbX37zZD3XrBpmq0O++swKzdu04eC5QvLhVVfrVV9aE9P/3f8Arr1hB34QJ1nAhkj5sayYiIuKL1OYtkxw4YGXdWra0Btzt3NmBX3/1x+TJfuDQYhx/9bnnrGzbmTPW4Lz79lkBHdvyc+SLPXuAZLWQIiIiksMp85ZJOMoDs2qcK51t3lhN+uyzF1C4cH4EBvqZ6tHo6H9nT+BoFBxShMOOPfwwsHv3vxk5EREREScFb5mkXDlg+PCkyxioOcd8Y7s212mvXIdQ4zAjvImIiIgkp2pTERERERtR8CYiIiJiIwreRERERGxEwZuX44CuZy5G45+wqOsaUFdERER8gzoseNCqPafxweq/ERufgNx+fqhTJj96N6mASkXzpntbpy9EY9qa/Vi++xQiLsea3qlViuXFnMeaeHKXzSwDnHeT841yRgIRERHxbsq8edDx8ChUKZoXnz7cCK90r4OCwYEY+sWfeOjj9fh510m3thEZE4dXf9iJO9//BYfORuLZ/9TAuufbYfHTLU32LSEh/dm3hx56yMzzyVtAQAAqV65sJj+/dOkSsoLztXnLmzevmbKKc5x60o8//ojAwMCr5mnlnKicA/UEB9ZLweXLl83x4dyrnECec4wmt3btWjPnaLFixcwcpbVq1TLzkV7L4cOH0bVrV4SGhpp9eOqppxDDSWxdAuc77rjDbJPr1K9fH59//nmSbRw/ftxML1ajRg0zp+uQIUNSfC1OFcb9ypMnj/l//vz5SR6fMmUK6tWrZ6Yv441zry5atCjJOv369TMzUnBOVef5atLEsz8WRETk+inz5kGX4+Kx83g4QgL9Ua1EPnN7sm1VLNt1Eu+v+AsFg3JjxG21Ub1UyiPv/rz7JN5YvAflCofgoz4NUbPUv5PJT1q2DxWLhiBXLr8M7dt//vMffPLJJ2Zi9DVr1phJ4xm83XvvvcgKfG3uA1/ziy++MIECg5ZOnTp5ZPu33XYb+vTpY26bNm0yQcyuXbvwf//3fyZQLFmyZIrPi4+PR3BwsAmsUpsrlYHVk08+iTp16piq6y1btuDxxx83yx977LFUt3v77bebgI/B39mzZ9G3b1/zfOccpuvWrTMB1XPPPYcSJUrghx9+MPvP4IpBH0VHR5ttjBw5MtWA8ddffzXn8eWXX8add95pAjdOcs/Xbdy4sVmnbNmyZtaJqlWrmvszZ840geMff/yB2rVrJ26rXbt2+PTTT02gSAyIRUTEyzgkUXh4ONNa5v/koqKiHDt37jT/p2ThlmOO9hNWOB7/bGOKj0fHxDpeW/ino+Xryx1jFmx3nAr/dzsHz1x0PP/Nn472E1Y6vtxw2JGQkHDV81/9YaejwUtLHE9+vindZ6xv376OO+64I8myRx55xFGyZEnHihUrTJmXLVvmaNiwoSM4ONjRtGlTx+7du816Bw4ccPj5+Tk2bNiQ5PnvvPOOo3z58mZfz50757j//vsdRYoUcQQFBTmqVq3q+PjjjxPX5fbnz5+f5PmFCxd2DB06NPF+WFiY49FHH3UUK1bMkS9fPsett97q2LJli3mM+8Jt7Nq1K8k2JkyY4KhQoULi8YqIiDD3n3vuOUdsbKzj5ptvdtxzzz3XdZxcxcfHO86fP2/+v/POOx29e/dOdd0ff/zRkStXLsexY8cSl82ZM8eRJ0+eFK8vp9tuu83Rr1+/FB9r3bq14+mnn75qec+ePR3/+c9/kizr1KmT47777nOkpVChQo5p06Yl3u/Tp495fZbPXdd6X3iTmJgYx7fffmv+91W+XkaVz/4y6xym9f3ti1Rt6iFr/jqNUxeicX+j8lc9tvav03h3+V/oVrcEPnrwJkTHJeDuqb+i67trcdvba/DE55tRKCQQXz/eFPfcXA67jkfg3MXoJNt44baa6NWoHH7df9ZUrV4vZpuYhXNiZmfChAnYuHGjqT58mNM8AKhYsSLat29vMmeueN9ZHcvsFrNcX331FXbs2GGq6FhNmFpG6ssvv8S5c+dMFS4xvmOWilWbrP5k5uymm24yWSCuxyrDhg0bXlWlOHv2bFOlyH2gfPny4eOPPzbleOCBB3DkyBG8//778DRmq5g1a926darrMBvGTF1pTmJ7BbOMzKSxfKkJDw9H4cKF07U/fK2OHTsmWcbX4j6mdg7mzp1rsqCsPnXFbB2zlNWrV8ejjz6KU6dOpWtfREQk86na1EPGdKuDw2ejMHnFX2hZvViSx8oVCsHMkwfx+e+HcUOpfKY6tEvdUoh3OBAUkNsEbmwv98K8bfjr1CXkDcqNCffUR+G8eRK3cTwsCrN+P4x+zSqaatnrsX79ehP4MDhyevXVVxODkeeff94EU2wPFhQUZKpYBw4ciIkTJ5rqyD///NNUHc6bNy+xbRfbazVo0MBU+bFNXXL333+/aUvFbTJ4YIDC7dKKFSuwbds2Eyhw+862at9++y2+/vprUzXJYGzy5MmmapD27t1rgiBW8blq27Yt7r77bhOcsHo2tSAyI8qXL4/Tp08jLi4Oo0ePTtz/lDAQZVWoK7YnYzVkau3vWNYNGzZg6tSp6dqvlF6L95O/Do8xgzWeA7Y9ZPUq28c5sVqb1c81a9bEoUOHTFDO4+mshhYREe/gFZk3ZndcG7U7b09wtvYrmRl+WTKLwYxRmzZtTIbHFTMagwcPNl/WbIvUrVs3HOXM8Fngcmw8Bn2+CScjLqN7/TJXPV6hSCim9m6I6b3qoH3NEqY8+89ewr6TF7Hx4Hks330SZy7EoEbJ/JjY80Z883hzVCwammQb+YIDUCA4AJsPh+HwufR3NPj+++/NFzaDMX6Bt2rVKrHtFbHtlRPbopEz68JG/MzGORvBM7vFHqo8b8T2XwyUWrZsadpvpZTxYXstBnxLly41gR7vO9tfMTi4ePEiihQpYvbReTtw4AD+/vtvs859991nAorffvvN3GcWjttxDT7on3/+weLFixESEmLa9nnSqlWrsHz5cpPNmzRpEubMmZPm+s6MoCue+5SWs/MCM5kfffRRkjZo7kq+zZRehxlMngMeQ54ztsHbuXNn4uNsN8eMHTOGbHPHDg0MktkWT0REvIdXBG/MNrBXnfPGL3i65557zP/jx483WR9mXrguq3U6dOiACxcuJG6DvfAYXDDjwqofBgNdunQxWZ7MdiL8MjYcPI9OtUvi/sZXV5tSXHwCTlyIRlhkDM5eikFALj8UzReIG8sWQOc6pTDo1ip48taqqF3m304KrvLm8cdrPerit/1n8cX69AelDLb4xb1nzx6TeWHWrDhnvr/CWYVJzi/9hIQE8z+zRQ8++KCpKmVvSWbtnNWq1LlzZxNoMSBg8MSMHnuzuuI5Y7DG/WD1KgNzZ+DA12HAyP1zvXFf//vf/5p1+Dify9cmBk69e/e+qpzMhrE3K6tfWX3LgMtTKlWqZAIrVic+88wz5gdFalje5JkvDsfCqurkWTLuI4MlXuPssJBeKb0WA+/kr8PzyHNw8803Y9y4ceY4vf3226lul8e8QoUK2LdvX7r3SUREfDx4Y286fgE5b8wSValSxVTjMYPALAfbZPXo0cNkBdhTLjIyMvGLnO2Epk+fbto6sX0Wq+9mzZplqomWLVuW6fvPLNmEe27Eyj2n8NHq/Vc9/sPWf9Bp0hq8vfIQjp6PQpmCwSiZPxihgf6mndyi7Sfw2Gcb0Wr8CvT66De8v/IvE+y5Co+KxfCv/kSzKkXQu0nKAWJamI3kFze/jF0DNXcxKOKxZNaJAQjPRfJzyPZnn332mTlfH374Yarb4n7cddddGDFihLnP9m0MPpjd42OuN9dqT1adMsPHNl7MyDEb52ratGkm28Ygk9cOe4gyyMyMIVF4XTLbmxpmN7dv325+jDgtWbLEVD+y/Z5rxo1V1OwJmlrP1Wvhazl/8Li+VrNmza6rDOwhy3aDzkysiIh4B69r88bMDgOvoUOHmgzQ/v37zRe7a4NsfgHyy5nVcwMGDDDVbgwoXNdhFSsDPa6T2nAU/OJy/fKKiIgw/3Nbro35ncv4ZccskTMj5SoqJg6XYuKQP8j/qsdbVC2CFlWbwREThZ1nYk3bt1/+OmOGY+Bgvq2qF8HIzjchNCg3Fv55HBsPnceuquGoXfrfLNzlmFjExCWgRP48KJY3MMV9SA3327nvyTmXuZYrpWWscuOYX6wW5TAfPAfOx0aNGmUCMAaGDMAWLlxo2k25vl7y48bMFYNstr9juyoGIKyeZUaIr8UMHqvtOJwFM0XEx5nd441ZOAYVzm2y3d2wYcNMlpb7weWvvPKKqfLjPr/zzjtmvffee8+0pXMNdpgB5HXHYIUZW+dYcayWJQas5cqVM/vFQJBZQbbJY3DofH1mffkDw5lN5I8IVukyY/n666+bjhfMRjIIZpUwn8fAjRk3DlPCIT5YZmeGzLXTAl+PuG/MqHH/uI6zypjNBdiUgAEgmwssWLDABNqrV69O3D/uG9u0sRzMWDMI5uszQ8l1uG1mErkOfzixivp///ufCZ55DlK73ric1xbfH2zT6M2c7+nk721f4utlVPnsL7POYayPXvO2Cd74xRoWFmba/5CzOiilBtn8gnGuwy8zNghPvk5qjcOJgcKYMWOuWs6sBdtMuWJQwqwgv+RcB1p1+vy3A6hWNBgtK4YmBoGuEhwOvL3iIL7ZchI3l8+P5ztWRrNKhXDyQjRmb/gHfT7+He1vKIIht1bCffWtbJPrdgIcDjQomw+Lth3H0y3LIjgwd7ouajayT2m/mMEkfqE7x/ZyZqpYVtfnsNMBg2GOIea6nF/ezKIxgHK2qWPmzXWdqKioJPcZYDHgYFDBalRmURls9e/fH2fOnDFVuswc8Ty4Po/BBa8RVqE7l/P1eb0wyOM+uq7PoI0BEqt2OdDusWPHTDWg6zpspM8Mk5MzM8ZqTucxYicOlo8BCqtPX3zxRRPEOrdz8uRJU83rul2WiQEb2wLyuLAjBTsBONdhppDbZtDFmxP3k9nn5PtD/KHCKmMGYVu3bjXL+COFmWd2OuF+cf/YLpEBtPO12P6TgST3k51KWP3LDhIcB47r8PywIwozp8xk873D/eZ55PFN6dohvhf4XAaKvMbsIHmW0hf5ehlVPvvz9DmMvPJdllP4cbwQeBFmyRiIMXtDDBb4ZcashGv1Ddsd8QuXjdP5Jckv0uRVQGwXxyzCBx984HbmjV+KDB74BeeK7cT4emykzy/i5H7ffxav/rgbgf658PXApMMvHDsfhZHfbcfhsxfx5K3V0OOmslc9f/Ph8xj13Q4UDAnEqK41UbV4viSPf/zLAcxcdwi9G5fHo62u7s2ZFcaOHWsyNvyST46XEQNADteRUoN8X+DrZcxI+fi+OHjwoHnfpPS+8Cb8EcMvDH4uZKTpgB34ehlVPvvLrHMYERFhagr44zP597cv8qrMGzNprO5xDkFBzpHxmUFzDd5cG2RzHWYAmClxzb5xnbTa/bDqL6UhEHhBJb+o2PGBX2jMTjkzVK6aVi2GJpVP4+j5yMTHD5+LxKfrDpoZFm6pWAgv31YZ5YoXSfH5N1csgi8HNsWL3+1Avxmb0L1+afRtVhHF81tfiIVDA83sCg82q5ji8zMTM3Acx805VEdKr++sVnMeI1/k62XMSPm4nnPaNbsEC3ba14zy9TKqfPbn6XMY4MPXe0q86huIDc1ZXcYG3E6sAmJw5ppiZaDGHnrOwIzVSjxxruuwoTgbjF+r0bYnnbxwGYVD8+CtpXsxaNYm3Dv1VzPB/Gs96uH1u+qhQFDaF1dongBM6Fkfb9xTDzuPR+C2d6wBfN/5eR/OXYpFVEy86dma1di2q0WLFqadoWsvUxEREcnBmTf+6mfwxrGn2L7Mib/qOQwIq+yqVatmbvybbaHYu5EKFChg2kqxwTrHCmNjb7Y14mTjbDieVYZ2qI5F206AFU4NyhfCC7fXRNlCVtu59HQwaFalqLn9tOM4lu48ZWZoCA7IbapLKyUb/y0rcG5QT08kLyIiIjYP3lhdygbhKWV2nn32WdMoetCgQaZqlI2s2amAbXOcOOgrgz42pue6HGuMAUdW9oCrVDQvBt1qDTzrCZ1qlzI3EREREa8L3jjMR2p9J5h94zAGaQ2KysbSnDHAddaAzOBl/TtEspXeDyIiObzNmzdzNobMad2RRdLifD/ktMbCIiLZyWsyb96O1a8FCxZMnO+Tbe7SM1wE27yxowWHVvDVnoq+XL6cUMb0lI8ZNwZufD/wfeHtA/SKiPgSBW/p4By2xBnApQe/7NgWLzg42GfHCPPl8uWEMmakfAzcnO8LERHJGgre0oFfaBxrjsOZpHcqDq7PUehbtWrlk1VMvl6+nFDG9JaP6yjjJiKS9RS8ZQC/sNL7pcX1OX0QO1b44he/r5cvJ5TR18snIuIrfK/hjoiIiIgPU/AmIiIiYiMK3kRERERsRMGbiIiIiI0oeBMRERGxEQVvIiIiIjai4E1ERETERhS8iYiIiNiIgjcRERERG1HwJiIiImIjCt5EREREbETBm4iIiIiNKHgTERERsREFbyIiIiI2ouBNRERExEYUvImIiIjYiII3ERERERtR8CYiIiJiIwreRERERGxEwZuIiIiIjSh4ExEREbERBW8iIiIiNqLgTURERMRGFLyJiIiI2IiCNxEREREb8Zrg7dixY+jduzeKFCmCkJAQ1K9fH5s2bUp83OFwYPTo0ShdujSCg4PRpk0b7NixI8k2oqOjMXjwYBQtWhShoaHo1q0bjh49mg2lEREREfHh4O38+fNo3rw5AgICsGjRIuzcuRMTJkxAwYIFE9cZP348Jk6ciMmTJ2PDhg0oWbIkOnTogAsXLiSuM2TIEMyfPx9z587F2rVrcfHiRXTp0gXx8fHZVDIRERERz/KHF3j99ddRrlw5fPLJJ4nLKlasmCTrNmnSJIwcORI9evQwy2bOnIkSJUpg9uzZGDBgAMLDwzF9+nR89tlnaN++vVln1qxZZrvLli1Dp06dsqFkIiIiIj6YeVuwYAFuvvlm3HPPPShevDgaNGiAjz76KPHxAwcO4MSJE+jYsWPisjx58qB169ZYt26duc8q1tjY2CTrsIq1Tp06ieuIiIiI2J1XZN7279+PKVOmYOjQoXjhhRewfv16PPXUUyZA69OnjwnciJk2V7x/6NAh8zfXCQwMRKFCha5ax/n85NhGjjeniIgI8z+DQN48ybk9T2/XW/h6+XJCGVU++9M5tDdfP3+ZWcZYHz5mXhu8JSQkmMzb2LFjzX1m3tgZgQEdgzcnPz+/JM9jdWryZcmltc64ceMwZsyYq5YvWbLEdJrIDEuXLoUv8/Xy5YQyqnz2p3Nob75+/jKjjJGRkchJvCJ4K1WqFGrVqpVkWc2aNfHNN9+Yv9k5gZhB47pOp06dSszGcZ2YmBjT+cE1+8Z1mjVrluLrjhgxwmT7XDNvbCPHqtf8+fN7/FcBL1Z2smDHDF/j6+XLCWVU+exP59DefP38ZWYZI67UnOUUXhG8safpnj17kizbu3cvKlSoYP6uVKmSCc54wpmVIwZqq1atMp0dqGHDhuZC4Do9e/Y0y44fP47t27ebnqopYbUsb8lxO5n1xsnMbXsDXy9fTiijymd/Oof25uvnLzPKGODjx8srg7dnnnnGZMdYbcrAi23ePvzwQ3MjVntyGBA+Xq1aNXPj36za7NWrl1mnQIEC6N+/P4YNG2bGiitcuDCGDx+OunXrJvY+FREREbE7rwjebrnlFjM+G6sxX3rpJZNp49AgDzzwQOI6zz77LKKiojBo0CBTNdq4cWPTNi1fvnyJ67z11lvw9/c3ASDXbdeuHWbMmIHcuXNnU8lEREREfDB4Iw6my1tqmH3jDAu8pSYoKAjvvvuuuYmIiIj4Iq8Y501ERERE3KPgTURERMRGFLyJiIiI2IiCNxEREREbUfAmIiIiYiMK3kRERERsRMGbiIiIiI0oeBMRERGxEQVvIiIiIjai4E1ERETERhS8iYiIiNiIgjcRERERG1HwJiIiImIjCt5EREREbETBm4iIiIiNKHgTERERsREFbyIiIiI2ouBNRERExEYUvImIiIjYiII3ERERERtR8CYiIiJiIwreRERERGxEwZuIiIiIjSh4ExEREbERBW8iIiIiNqLgTURERMRGFLyJiIiI2IiCNxEREREbUfAmIiIiYiMK3kRERERsRMGbiIiIiI14RfA2evRo+Pn5JbmVLFky8XGHw2HWKV26NIKDg9GmTRvs2LEjyTaio6MxePBgFC1aFKGhoejWrRuOHj2aDaURERER8fHgjWrXro3jx48n3rZt25b42Pjx4zFx4kRMnjwZGzZsMIFdhw4dcOHChcR1hgwZgvnz52Pu3LlYu3YtLl68iC5duiA+Pj6bSiQiIiLiw8Gbv7+/Ccqct2LFiiVm3SZNmoSRI0eiR48eqFOnDmbOnInIyEjMnj3brBMeHo7p06djwoQJaN++PRo0aIBZs2aZAHDZsmXZXDIREckUDgdwYjkQqVoWyVn84SX27dtnqkXz5MmDxo0bY+zYsahcuTIOHDiAEydOoGPHjonrcp3WrVtj3bp1GDBgADZt2oTY2Ngk63BbDPS4TqdOnVJ8TVa18uYUERFh/ue2ePMk5/Y8vV1v4evlywllVPnsL8ecw5gY4NhCYO8UICAfcPkkUPO/QJnbYWe+fv4ys4yxPnzMUuLnYGormy1atMhk0qpXr46TJ0/ilVdewe7du027tj179qB58+Y4duyYCcicHnvsMRw6dAg//fSTycD169cvSSBGDOYqVaqEqVOnpvi6bEc3ZsyYq5ZzeyEhIZlQUhEREfG0yMhI9OrVy9TE5c+f3+cPsFdk3jp37pz4d926ddG0aVNUqVLFVI82adLELGcnBleMOZMvS+5a64wYMQJDhw5NknkrV66cCfo8ffL5q2Dp0qWmrV5AQAB8ja+XLyeUUeWzP588h+e2AIc+B85vQ2xAYSy90Bsd2rZEQFC+pOtF7AW2PAe0mg+78snzl0VljLhSc5ZTeEXwlhx7izKIY1Vq9+7dzTJWnZYqVSpxnVOnTqFEiRLmb7aRi4mJwfnz51GoUKEk6zRr1izV12H1K2/J8YLKrDdOZm7bG/h6+XJCGVU++/OJc3jxMLBhAOCXC6jUB2g4HoiLBxYvQYDjIgL8C/FX/b/rF6kN5CsHHPsGqHgf7Mwnzl8WlzHAx4+X13ZYcMXqz127dplgjdWeDM4YqTsxUFu1alViYNawYUNz4lzXYY/V7du3pxm8iYiIF4o6Cay7H6g2EGj5DXDxALCiA7DiP9bjv9wP/NQYWNMTOLf53+fVGQXsmZRtuy2SozJvw4cPR9euXVG+fHmTLWObN6ZA+/bta6o9OQwIOzBUq1bN3Pg326SxfpsKFCiA/v37Y9iwYShSpAgKFy5stsnsHXufioiITSTEAmt6AA0mANEngSXNgDJdgVYLAL8Q4McfgfYrOUQBcGIZsHkoUOE+K9ALKQmElgdO/wIUa57dJRHx7eCNg+nef//9OHPmjBkihO3cfvvtN1SoUME8/uyzzyIqKgqDBg0yVaPsjbpkyRLky/dvm4e33nrLDDfSs2dPs267du0wY8YM5M6dOxtLJiIi6fL3J1avUfYg3TkOaDYHKFDDesy1RyGrTEt1AIq3Apa3B+KigJrPAAXqAAfnKngTn+YVwRsH1k0Ls2/sGcpbaoKCgvDuu++am4iI2NSRr4BW3wIruwCNpvwbuKUmdx6g2WxgzZ1Alf5AbARwbmNW7a1Izg3eREREEHsBSIgHos9a47cVamANxBu+EzjxMxBQlF3arj5QoeWAEu2Afe8DuQKByMPW864xIoGIXXllhwUREcmBYsMB/1AgbBtQqD6QEAes6wX8MQyI+gc486u13sE5Vz+3XA/g3CYreOPzHJoaUXyXgjcREfEOcZesoUHiLwMBBYHjPwEnV1idGFgVGn9lIPZ/vgd2TQDWD7QCNSrSCIiPBGLOW1WpCTHZWhSRzKTgTUREvENMGOB3pZNZ3AXAkWB1QGi7DGi7BCjZwXqscBPg4GwgPgo49oO1jAEeq1zDtgJB1higIr5KwZuIiHiH/NWtgOzSIeCfRdb8pRG7gT+GW23eyt5hrXdsPhBSxmrXxkwbXT5hZdsY/OUOAXIHZWtRRDKTgjcREfEOgYWs4O3od0CZO4AiTYB6LwPBpYADM60hQSioOHBqNRC+DSjWwlr213QgYhdQuZ/V3o3VryI+Sr1NRUTEe+S/ATi+BCjcECjdMelj0VFmeiwUrAfkLQUUbQHkrwqc3QQcnAlUHQic3wyUvzu79l4kS+iniYiIeI+GbwN5KwEbBlpBGZ1dD+z7gKN+WvdrvwDcPBmocC+wbyqw/jGg7stA5b7W7ArVBmVrEUQym4I3ERHxHuwp2vQzoEQb4Pf+wMX91nhvEXuBFVcycWfWA7vfAZa1Bk4uB1p8CZS+zZrztP7rQO7A7C6FSKZStamIiHiXkNJAk4+Bw18Da+4BmkwDGk4EwvYDq7YBh2YDwYWAcndbwd5fU4HjS4EbXwFKtM7uvRfJdAreRETEO7HtWkg5YMsIa+5Sv2AAjwNh24GIBKt6NbAgkL8G0HGtNcCvSA6g4E1ERLxX0cbArYutwXgvnQSWbwTaLgUCVTUqOZfavImIiPfL5W8NEUKas1RyOAVvIiIiIjai4E1ERETERhS8iYiIiNiIgjcRERERG1HwJiIiIpJTgrewsDA8/PDDKFmypLn17dsX586d89zeiYiIiIjngrc+ffqgVKlS2LFjh7mVL18e99133/VsUkREREQyI3hbvHgx/vjjD3Tq1CkxeGvfvj12796NRYsWZXSzIiIiIpIZMyy89957iIyMxOTJk+FwOBKXc9n777+Pzp07Z3TTIiIiIuLp4G3BggWoXLky3njjDVSoUMEsO3LkCFq0aGEeExEREREvCt78/Pzw5ptvmmCte/fu5v78+fPNMv4tIiIiIl42Mf1dd92FG2+8EcuWLTNVp08++SSqV6/uub0TEREREc8EbxwmhAFb1apVzU1EREREvLC36a+//ooGDRqgSJEiKFq0qMm8rVu3LnP2TkREREQyHrwdOnQIHTp0gL+/P8aNG4fXXnsNefLkMcsOHDiQnk2JiIiISGZXm44dOxbNmjUz47jlzp3bLBs2bBhuv/12vPrqq5g2bVpG9kFEREREPJ15O3z4MFauXIl7770Xx44dM/d5O3r0qFm2YsUKM1SIiIiIiHhB5q1ixYpmCJDHHnssxcfZeYHrxMfHe3L/RERERCQjmbfNmzebuUvfeecd87frjbMs8DH+7QlsT8dAcciQIUmCw9GjR6N06dIIDg5GmzZtzJRcrqKjozF48GDTkSI0NBTdunUzmUERERGRHBe81a9fHy1btjRVp+xh6npbtWoVWrVqZf6+Xhs2bMCHH36IevXqJVk+fvx4TJw40QSKXKdkyZKmo8SFCxcS12Gwx4GC586di7Vr1+LixYvo0qWLsoEiIiKSMzssPPfcc2aYkDvuuAO9e/c22bHPP/8cP/zwg5mk/nox2HrggQfw0Ucf4ZVXXkmSdZs0aRJGjhyJHj16mGUzZ85EiRIlMHv2bAwYMADh4eGYPn06PvvsM7Rv396sM2vWLJQrV84MItypU6fr3j8RERERWwVvtWvXNlmtgQMHYuHChWYZx3tjAMfHrtcTTzxheq4y+HIN3jgMyYkTJ9CxY8fEZRyipHXr1maMOQZvmzZtQmxsbJJ1WMVap04ds05KwRurWXlzioiIMP9zO7x5knN7nt6ut/D18uWEMqp89qdzaG++fv4ys4yxPnzMPDLDAjNfXbt2xbZt20xGjNWbAQEB5rEtW7aY6tWMYFDINnOsEk2OgRsx0+aK9zn2nHOdwMBAFCpU6Kp1nM9PqW3dmDFjrlq+ZMkShISEIDMsXboUvszXy5cTyqjy2Z/Oob35+vnLjDJGRkYiJ8nQ9FgM1m666SbzN6srmXljleWff/6JuLi4dG+PQ4w8/fTTJmgKCgpKdb3kE94zeEy+LLm01hkxYgSGDh2aJPPGalZm7/Lnzw9P/yrgxcp2es5g15f4evlyQhlVPvvTObQ3Xz9/mVnGiCs1ZzlFhuc2Xb58OT7++GPMmzcPefPmNZ0ZmHnLCFZ5njp1Cg0bNkxcxiFHVq9ebToo7NmzxyxjBq1UqVKJ6/A5zmwcOzDExMTg/PnzSbJvXIcDC6eEVa+8JccLKrPeOJm5bW/g6+XLCWVU+exP59DefP38ZUYZA3z8eF3X9FgcdoNt0apUqWKG4WBW6+uvv8bx48dTrH50V7t27Uw1LIM/5+3mm282nRf4d+XKlU1w5ppmZaDGXq7OwIyBH0+e6zrcr+3bt6cavImIiIj4bObttttuM7MotG3bFi+99BK6d+9uxlJzulb1ZVry5ctnOha44rbZGcK5nMOAcHquatWqmRv/Zru0Xr16mccLFCiA/v37m+m6+LzChQtj+PDhqFu3bmLvUxEREZEcE7wtXrzYBEoMopgVy2rPPvssoqKiMGjQIFM12rhxY9NGjoGf01tvvQV/f3/07NnTrMuM3owZMxLnYRURERHJMcHbL7/8Ytq4MfPGdmes0mQwV7Vq1UzZMQ4G7IqZPc6wwFtq2Nnh3XffNTcRERGRHN3mrWnTpmbwXHYa4GC9zHrVqFEDTZo0McHSyZMnM3dPRURERCR9HRaI7cwefvhhM/3Uzp07zbRYbH+mdmUiIiIiXhi8uWLmjXOOshcqhwzh7AgiIiIi4qXBmxM7BLD36YIFCzyxORERERHJzOBNRERERLKGgjcRERERG1HwJiIiImIjCt5EREREbETBm4iIiIiNKHgTERERsREFbyIiIiI2ouBNRERExEYUvImIiIjYiII3ERERERtR8CYiIiJiIwreRERERGxEwZuIiIiIjSh4ExEREbERBW8iIiIiNqLgTURERMRGFLyJiIiI2IiCNxEREREbUfAmIiIiYiMK3kRERERsRMGbiIiIiI0oeBMRERGxEQVvIiIiIjai4E1ERETERhS8iYiIiNiIgjcRERERG/GK4G3KlCmoV68e8ufPb25NmzbFokWLEh93OBwYPXo0SpcujeDgYLRp0wY7duxIso3o6GgMHjwYRYsWRWhoKLp164ajR49mQ2lEREREfDx4K1u2LF577TVs3LjR3Nq2bYs77rgjMUAbP348Jk6ciMmTJ2PDhg0oWbIkOnTogAsXLiRuY8iQIZg/fz7mzp2LtWvX4uLFi+jSpQvi4+OzsWQiIiIiPhi8de3aFbfddhuqV69ubq+++iry5s2L3377zWTdJk2ahJEjR6JHjx6oU6cOZs6cicjISMyePds8Pzw8HNOnT8eECRPQvn17NGjQALNmzcK2bduwbNmy7C6eiIiIiMf4w8swU/bVV1/h0qVLpvr0wIEDOHHiBDp27Ji4Tp48edC6dWusW7cOAwYMwKZNmxAbG5tkHVaxMtDjOp06dUrxtVjVyptTRESE+Z/b4s2TnNvz9Ha9ha+XLyeUUeWzP51De/P185eZZYz14WPm1cEbs2QM1i5fvmyybqwCrVWrlgm+qESJEknW5/1Dhw6ZvxncBQYGolChQletw8dSM27cOIwZM+aq5UuWLEFISAgyw9KlS+HLfL18OaGMKp/96Rzam6+fv8woY2RkJHISrwneatSogS1btiAsLAzffPMN+vbti1WrViU+7ufnl2R9VqcmX5bctdYZMWIEhg4dmiTzVq5cOZPBY8cJT/8q4MXKtnoBAQHwNb5evpxQRpXP/nQO7c3Xz19mljHiSs1ZTuE1wRszZ1WrVjV/33zzzaZjwttvv43nnnvOLGMGrVSpUonrnzp1KjEbxw4MMTExOH/+fJLsG9dp1qxZqq/J6lfekuMFlVlvnMzctjfw9fLlhDKqfPanc2hvvn7+MqOMAT5+vLyyw0JqWTO2R6tUqZIJzlxTrAzUmJVzBmYNGzY0J851nePHj2P79u1pBm8iIiIiduMVmbcXXngBnTt3NlWWHP6Dw32sXLkSixcvNtWeHAZk7NixqFatmrnxb7ZJ69Wrl3l+gQIF0L9/fwwbNgxFihRB4cKFMXz4cNStW9f0PhURERHxFV4RvJ08eRIPPvigyZYxEOOAvQzcWCdOzz77LKKiojBo0CBTNdq4cWPTqSBfvnyJ23jrrbfg7++Pnj17mnXbtWuHGTNmIHfu3NlYMhEREREfDN44RltamH3jDAu8pSYoKAjvvvuuuYmIiIj4Kq9t8yYiIiIiV1PwJiIiImIjCt5EREREbETBm4iIiIiNKHgTkZzJ4QBOLAcij2b3noiI2K+3qYhIlgZtR+YBu98GAvIDl08AtUcC5brrJIiILSh4E5Gc4dIh6/+VnYH8lYBms4DQckBcJLCiE5C3MlCoXnbvpYjINSl4ExHfdXYTcGAGcG4LEFAEQD+g5XwgOP+/6/iHAI0+AjY9DbT9KTv3VkTELWrzJiK+5+JhYEVnYNuLQLEWQLufgWZzrMdiw6yqU1cFbrAybwfnZsvuioikh4I3EfEtUSeBdfcD1QYCLb8BLh4AVnQAVvzHevyX+4GfGgNregLnNv/7vDqjgD2Tsm23RUTcpeBNRHxHQiywpgfQYIJ1f0kzID4KaLUAaLfMWtZ+JdDpd6Dqo8DmocC+D6zlISWB0PLA6V+yb/9FRNygNm8i4jv+/gQocztw+SSwc5xVVVqghvVYbOy/6/n5AaU6AMVbAcvbA3FRQM1ngAJ1rKrTYs2zrQgiIteizJuI+I4jXwE1nraqPxtN+TdwS03uPECz2cChz4GYCCA2Aji3Mav2VkQkQ5R5ExHfEHsBSIgHos8CAfmAQg2sjgnhO4ETPwMBRQGEXv08DhdSoh2w730gVyAQedh6HrNzIiJeSJk3EfENseGAfygQtg0oVB9IiAPW9QL+GAZE/QOc+dVa7+CVXqeuyvUAzm2ygjc+zxGf5bsvIuIuBW8i4hviLgF+uYD4y0BAQeD4T8DJFVYnBlaFxkdb6/3zPbBrArB+oBWoUZFGQHwkEHPeqkpNiMnWooiIpEXBm4j4hpgwwC+39XfcBcCRYHVAaLsMaLsEKNnBeqxwE+DgbKsX6rEfrGUM8FjlGrYVCCqRfWUQEXGDgjcR8Q35q1sBGafB+mcRcGwhELEb+GO41eat7B3WesfmAyFlrHZtzLQR5zdlto3BX+4QIHdQthZFRCQtCt5ExDcEFrKCt6PfAWXuAIo0Aeq9DASXAg7MtIYEoaDiwKnVQPg2a/YF+ms6ELELqNzPau/G6lcRES+l3qYi4jvy3wAcXwIUbgiU7pj0segoYPESoGA9IG8poGgLIH9Va/7TgzOBqgOB85uB8ndn196LiLhFPy9FxHc0fBvIWwnYMNAKyujs+iuzKFwZ+qP2C8DNk4EK9wL7pgLrHwPqvgxU7mvNrlBtULYWQcTOzp4FXn4ZmDoVuHDBWnb+PDB9OpCQAOzebS07dcr6//Rp4PLlf5+/ciUwdixw4kQ27LyNKPMmIr6DPUWbfgZs/R/we3+g1TxrvDfOmrCCmbhhwJn1QPgm4MjXVpVqiy+t3qmrugD1XwdyB2Z3KURs6/33gW++AcqWBd57DxgwAFiwAFi9GvjtN2DrVuCFF4C77gIaNgRmzQLq1AHuvRf4/Xdg/XqgYEHg4EHgww+zuzTeS5k3EfEtIaWBJh8Ddf4HrLkHCN8ONJwINJlhPX5oNhB9Cih3N1CiLfDXVKs9HNcv0Tq7917E1oKCgJAQYOFCoGtXYMoUIDAQmDQJWL4cqFfPWu/OO60sHderWdN6vEABYONGoFMnIDIyu0vi3ZR5ExHfxLZrIeWALSOsuUv9ggE8DoRtByISrOrVwIJA/hpAx7XWAL8icl2qVgU2b7ayaK++at3YsfvYMStIY1VqXBxQqxZQt65VZfroo8Cbb1oZNzp82Kpq1UQnqVPwJiK+q2hj4NbF1mC8l04CyzcCbZdaqQAR8aiwMGDIEGDwYKBRIysI4/1t26wgrVAhK0AbNgyYOBGIibFu584B0dHAd99ZVam33AI89ZRVzdq0qU5SShS8iYjvy+VvDRFCmrNUJFMwQMudG+jTB8iVC5gxw+qksGYNULy4tSw2FvjxR2DJEiAg4N/njh8PvPYaMHcusHgx0KoV0KCBTlRq1OZNRERErlvJklamjFWgdOgQ0LixtZyBW1qeeALYsMHK3jHjNnKk1X5OUqbgTURERK4bh/9gh4MaNaz7zMLx5o7QUKujA9d/5BFgxAh1WkiLgjcRERG5buxgwA4JHa5MI+zvf+2MmxOrV+PjgXz5gP79rUDw+HGdlNQoeBMREZHrVqKE1dGgd2+rtymDNwZ07ti718q+sU1ct25Ajx5AlSo6KalR8CYiIiIe0aKF1RGhcmUgT56ksyek5fvvgdq1rarS8HCgVCmdEK8P3saNG4dbbrkF+fLlQ/HixdG9e3fs2bMnyToOhwOjR49G6dKlERwcjDZt2mDHjh1J1omOjsbgwYNRtGhRhIaGolu3bjh69GgWl0ZERCRn4rRYHGS3WDGgSBFg585/p8lKCYcK4ZRY06ZZGTcOJ8JOD59+mpV7bT9eEbytWrUKTzzxBH777TcsXboUcXFx6NixIy5dupS4zvjx4zFx4kRMnjwZGzZsQMmSJdGhQwdccLkqhgwZgvnz52Pu3LlYu3YtLl68iC5duiCeFekiIiKSqUqXBn75xar+5HAf7DlavTpQsSJQqRJw443WejfdBNxwgzWoLwfp5YwLd99tzWvKQX45Ppx4+Thvizmoi4tPPvnEZOA2bdqEVq1amazbpEmTMHLkSPRgRTiAmTNnokSJEpg9ezYGDBiA8PBwTJ8+HZ999hnat29v1pk1axbKlSuHZcuWoRN/CoiIiEimGTQImDwZYKVXs2bA/v3WbAlnzlgdEji7ApfNmWMN2Fu4sDUkiHM2BeZjGAA+9JBOktcHb8kxEKPCPKsADhw4gBMnTphsnFOePHnQunVrrFu3zgRvDPRiY2OTrMMq1jp16ph1UgreWM3Km1NERIT5n9vhzZOc2/P0dr2Fr5cvJ5RR5bM/nUN784Xzx+rP5s2tIT/69gX+/BOoX9/KtLFdW9mysbjjDuB//4s1wdtttwHffgts2gQ8+ywwapTVW/Wtt4ChQ91/3VgbH7OM8HMwreVFuDt33HEHzp8/jzUclhkwwVfz5s1x7NgxE5A5PfbYYzh06BB++uknk4Hr169fkmCMGMxVqlQJU1kRnwzb0I0ZM+aq5dxWCAecEREREa8XGRmJXr16meRP/vz54eu8LvP25JNPYuvWrabNWnJ+yaa1YaCXfFlyaa0zYsQIDHUJ7Zl5YzUrAz5Pn3z+KmB7PrbTC3CdE8RH+Hr5ckIZVT770zm0N184f5yAft48a45SVpsScyrMxHHokJiYWCxb9m8ZnVNqsbi//grs2wcULWpl5NIj4krNWU7hVcEbe4ouWLAAq1evRtmyZROXs3MCseq0lEv/4VOnTpl2b851YmJiTMauELuruKzTzHkFJcOqV96S4wWVWW+czNy2N/D18uWEMqp89qdzaG92Pn/smJC8ujOlojjL6PoYOzjwlhEBNj1etu5tyuwYM27z5s3D8uXLTTWnK95ncMZfJE4M1NhL1RmYNWzY0Jw813WOHz+O7du3pxq8iYiIiNiNV2TeOEwI25l99913Zqw3ZtioQIECZkw3VntyGJCxY8eiWrVq5sa/2S6NddzOdfv3749hw4ahSJEiprPD8OHDUbdu3cTepyIiIiJ25xXB25QpU8z/HHg3+ZAhD13pL/zss88iKioKgwYNMlWjjRs3xpIlS0yw5/TWW2/B398fPXv2NOu2a9cOM2bMQG53Z8YVERER8XJeEby50+GV2Tf2DuUtNUFBQXj33XfNTURERMQXeUWbNxERERFxj4I3ERERERtR8CYiIiJiIwreRERERGxEwZuIiIiIjSh4ExEREbERBW8iIiIiNqLgTURERMRGFLyJiIiI2IiCNxEREREbUfAmIiIiYiMK3kRERERsRMGbiIiIiI0oeBMRERGxEQVvIiIiIjai4E1ERETERhS8iYiIVzh7Fnj5ZWDqVODCBWvZ+fPA9OlAQgKwe7e17NQp6//Tp4HLl/99/sqVwNixwIkT2bDzIlnIPytfTEREJDXvvw988w1Qtizw3nvAgAHAggXA6tXAb78BW7cCL7wA3HUX0LAhMGsWUKcOcO+9wO+/A+vXAwULAgcPAh9+qOMsvkuZNxER8QpBQUBICLBwIdC1KzBlChAYCEyaBCxfDtSrZ613551Wlo7r1axpPV6gALBxI9CpExAZmd0lEclcyryJiIhXqFoV2LzZyqK9+qp1cziAY8esII1VqXFxQK1aQN26VpXpo48Cb75pZdzo8GGrqpXP8/PL7hKJZA4FbyIiku3CwoAhQ4DBg4FGjawgjPe3bbOCtEKFrABt2DBg4kQgJsa6nTsHREcD331nVaXecgvw1FNWNWvTptldKpHMoeBNRESyHQO03LmBPn2AXLmAGTOsTgpr1gDFi1vLYmOBH38EliwBAgL+fe748cBrrwFz5wKLFwOtWgENGmRnaUQyl9q8iWQU62VOLAcij+oYilynkiWtTBmrQOnQIaBxY2s5A7e0PPEEsGGDlb1jxm3kSKv9nIivUvAmkpGg7cg8YFkbYPdbwOo7gSPf6jiKXAcO/8EOBzVqWPeZhePNHaGhVkcHrv/II8CIEeq0IL5N1aYi7rp0yPp/ZWcgfyWg2SwgtBwQFwms6ATkrQwUutIdTkTS/ZuIHRI6dLjy5eR/7YybE6tX4+OBfPmA/v2B2bOB48eBKlV0EsQ3KXgTScvZTcCBGcC5LUBAEQD9gJbzgeD8Lu+iEKDRR8Cmp4G2P+l4imRAiRJWR4PevYFPP7WCNwZ07ti718q+sU1ct25Ajx4K3MS3qdpUJCUXDwMrOgPbXgSKtQDa/Qw0m2M9Fht29bdKgRuszNvBuTqeNudwOHDmYjT+CYsyf0vWadHC6ohQuTKQJ0/S2RPS8v33QO3aVlVpeDhQqlRm76lI9lLmTSS5qJPAuvuBWs8CpToBuycBKzoAcXxwKPDL/YBfLBBaEaj9PFD4Jut5dUYBa7oDFe/TMc0iq/acxger/0ZsfAJy+/mhTpn86N2kAioVzZvubZ2+EI1pa/Zj+e5TiLgca+LzKsXyYs5jTTJl3+VqnBaLg+wWKwYUKQL8+adVlcrq0JRwqJB164Bp06xptTicCDs9MHP3/PM6wuK7FLyJuEqIBdb0ABpMAKJPAkuaAWW6Aq0WAH4h1jgF7VdadTonlgGbhwIV7gOqDQRCSgKh5YHTvwDFmuu4ZoHj4VGoUjQvXrj9Bhw7H4XF209g6Bd/okBwAHo3rYD2NUtccxuRMXF4a+leLNp+AnVKF8Cz/6mBtjeUQHhkDO58fx0SEhzIlUujvWaF0qWBVaus6k8O98Fgrnp1KwvHAXeDg4Fx44CbbrLWYaaNj919t3XjvKYc5JdTaIn4MgVvIq7+/gQocztw+SSwc5xVVVrgSvc3fls48ZukVAegeCtgeXsgLgqo+QxQoI5VdargLUtcjovHzuPhCAn0R7US+cztybZVsWzXSby3/C98ueEInu1UA1VLpJy6+Xn3SbyxeA/KFQ7BR30aomapAomPTVq2DxWLhihwy0KDBgGTJwNHjwLNmgH791uzJZw5Y3VI4OwKXDZnjjVgb+HC1pAgztkUmKVjAPjQQ1m51yI5uM3b6tWr0bVrV5QuXRp+fn749tukQy+w7cno0aPN48HBwWjTpg127NiRZJ3o6GgMHjwYRYsWRWhoKLp164aj/BQQcdeRr4AaTwN7JgGNpvwbuKUmdx6g2Wzg0OdATAQQGwGc26jjnQW+//MffP7bIZTMn3RAL35+dKhVEl8NbIrapfOj/8yNeGnhDpy5EJ24zqGzlzBi3la89uNu9G9RCR8+mDRwo6DA3Nh2LAKDZ2/W+cwizLRxhgTOZ/rAA9Y0WOzEsGgR8PjjwBtvWOs995xVLcq2bpyUnm3kWHX6yitWgDdhgk6Z+DavCd4uXbqEG2+8EZP5sysF48ePx8SJE83jGzZsQMmSJdGhQwdc4E+tK4YMGYL58+dj7ty5WLt2LS5evIguXbognj/ZRK4l9gKQEA9EnwUC8gGFGlg/6cN2ALvfAQ5/lfLzOFxIiXbAvveBXIFA5GH3u8lJhq356zROXYjG/Y3KX/XY2r9O452f9+HuhmUxre/NiI5LQJ9P1pvH7p7yK574fDMKhQTi68eb4p6by2HX8Qicu/hvcEcv3FYTvRqVw6/7z5qqVcl8Bw5YWbeWLa0Bd2+/3Zph4Z13rEnpORYcMdvGbBwH5923D2jXDhg61Jr/dM8eIL9LZ3ARX+Q11aadO3c2t5Qw6zZp0iSMHDkSPdgHHMDMmTNRokQJzJ49GwMGDEB4eDimT5+Ozz77DO3btzfrzJo1C+XKlcOyZcvQia1gRdISGw74hwJh24BC9YGEOODXB4GY80DB+kD4PgDtgYNzgGp9kj63XA9g15tAgdrW8xzxgJ/XvL180phudXD4bBQmr/gLLasXS/JYuUIh+PTEIdwx+RdUL5kPNUvlx39qlQBiLqBtzWIoGBps2su9MG8b/jp1CXmDcmPCPfVROG+exG0cD4vCrN8Po1+ziqZaVjIfp7n64gtrblO2eSNm09jElDd2UGAWjtNgsVdqVJS1nH8//DCwe7c1lRaHCxHxZbb4RDpw4ABOnDiBjh07Ji7LkycPWrdujXXr1pngbdOmTYiNjU2yDqtY69SpY9ZJKXhjNStvThEREeZ/boc3T3Juz9Pb9RY+Ub7LPP95gJjLQK5CwNHFwMlfgfw1gbN/Ijaoklkt9thiIPoMcHE/0OANIJc/kL8BEBdrbSN3ASA6EvAPhp3Y6RxGx8Zj6JdbcP5iFPo2rXjVPpfOH4j37r8R+09fxLq/z5rODIfDI1E1L7DtyDk4/HKhaGgQbigRioEtK+KGUlaqxnU7wQFAsVB/bD1yDgdOhaNsoRB4Ozudw5RwKqynn7b+dhaBsyYwkc37cXFJy8fAzbkup9LizfW5dmP385edZYz14WOWEj+HFw5kxDYrrP7s3r27uc/gq3nz5jh27JgJyJwee+wxHDp0CD/99JPJwPXr1y9JMEYM5ipVqoSpbEyRDNvQjRkz5qrl3FYI51oRERERrxcZGYlevXqZWrj8OaDe3BaZN9egzhXjzuTLkktrnREjRmAoG0q4ZN5YzcqAz9Mnn78Kli5datrpBTDH72N8onwxYcDv/YHitwJH51s9R08ssapES7ZHbKHmWLpsGToEvoOA4IKAfwGrt2mlB6zJ6dc/bnV5Y7Vpm+8BP69pUuqT53D5bvYo/Rvd6pdG32YVkzz2044TeHf5PoQE+KNq8bwokT8PEuLiUSPhANbHlMWJi7FmEN7o2ASULRyMplWK4KGmFeGf+99zxrHe7p6yDlWL5cWorrVRooD3z3Rut3OYXiqf/WXWOYy4UnOWU9gieGPnBGLVaSmXobNPnTpl2r0514mJicH58+dRiCM1uqzTjH3OU8CqV96S4wWVWR98mbltb2Dr8gUUAxIigOPfAmU7A0ElgOK3ADFngcOfAttfATDMBG4Bp38G8lYC6r1gNbg5OAO48CfQ4E1g3xQg8Orryi7scg6j4/0QFp2A/KF5rtrf1jeURJuapZA3jz9+238Wn/12CBv/PoUX6gEr951Dk6rFMOK22gjN44+FW//BhoPn0arGZdQu/W+P0/ioeFyMAYoWCEXpwnltNWSIXc5hRql89ufpcxjgw9d7SmyRGmC1J4MzRutODNRWrVqVGJg1bNjQnDzXdY4fP47t27enGryJXCX/DUDkEaBwQ6Dqw0CVfkDN4dYk9Ldembe0YD2gUm+g5nNA/qrW/KcHZwJVBwLnNwPl79aBzQJfbDiCWqXy4fa6/zalcMoXFICQgNwY9+MuPPrpRsTExmNkl9rmsQ/7NIR/Lj88+PF6fLR2Px5uXgkf9bk5SeBGRfPmQaPKhbFo23EznpyIiLfwmuCNw3ps2bLF3JydFPj34cOHTbUnhwEZO3asaQvHgOyhhx4y7dJYx00FChRA//79MWzYMPz888/4448/0Lt3b9StWzex96nINTV828qobRhoBWV0dj2w7wNW3Fv3a78A3DwZqHAvsG8qsP4xoO7LQOW+1uwK1QbpQGeBwW2r4ljYZfT52BoCxBU7KPSbsd4M1vtSt9r4qO8t6FzHyuBXL5EPr999Iybf3wC/7z+Hvh+vx75T/w455PTJugPYeiQMj7epot6mIuJVvKbadOPGjbj11lsT7zvbovXt2xczZszAs88+i6ioKAwaNMhUjTZu3BhLlixBPpdJ79566y34+/ujZ8+eZt127dqZ5+ZmdyURd3DQ3aafAVv/Z7V/azXPGu+NsyasYE/mYcCZ9UD4JuDI10BwKaDFl0BAQWBVF6D+60DuQB3rLNCkSlE0rlQYR89HJi47fC4Sn647aIK2RhUL4+37GqBgSMrno2HFwvhyQBO8+N0OPPTxBnS/0nau+JVBfwuFBJiq0gebVtD5FBGv4jXBG2dMSKvjK7Nv7B3KW2qCgoLw7rvvmptIhoWUBpp8DBz+GlhzD9BkGtBwIhC2H1i1DTg0GwguBJS72wr2/poKHF8K3PgKUKK1DnwWOnnhMgqH5jFzk+47eQF/HAkzQdtrPeqhSZUi13x+aJ4ATOhZH+v+PoOPVu/Hbe+sQeNKRVCjZD6EBOZGVEw8ToRfRuVi6Z/oXkTE54M3Ea/Dtmsh5YAtI6y5S/04btvjQNh2ICLBql4NLAjkrwF0XGsN8CtZamiH6li07YSp0K5RtBDy/VUTlSNCULu49TjnxZw3D+jXzxrAlThKf5kywOnTABP3HK2/WZWiiDlSFJ8fPg7EnTIzNAQH5MajrSqjUlGdVxHxLgreRNJStDFw62Jr+I9LJ4HlG4G2S63JFyXbVSqaF4NurWr+fvll4Cd2FC4LvPceMGAAsGAB500GfvsN2LoVeOEF4K672MGJM7AAdepYc2P+/juwfj0nOy+FBg1K4csPs7tkIiI26LAg4tU4i0LQlXTONcYWlOzBDBrH1l64EOjaFZjCEVsCgUmTgOXLrbkx6c47gbNnrfU4FyYfL1CA7W4BTsQS+W8TOhERr6TMm4j4hKpVgc2brSzaq69aNzajPXbMCtIuXOD0SkCtWkDdusDly8CjjwJvvsmMm7WNw4etqlY+TzG6iHgrBW8iYnthYcCQIcDgwdak5gzCeH/bNitI47jdDNCGDQMmTrQmOOft3DnOcQx8951VlXrLLcBTT1nVrE2bZnepRERSpuBNRGyPARpHBOrTB8iVC5gxA0hIANasAYoXt5Zx3uoffwSWLLEmxXAaPx547TVg7lxg8WKgVSugQYPsLI2ISNrU5k1EbI8z6DFTxipQOnQIaNzYWs7ALS1PPAFs2GBl75hxGznSaj8nIuKtFLyJiO1x+A92OKhRw7rPLJy7Y3OHhlodHbj+I48AI0ao04KIeDcFbyJie+xgwA4JHTpY9/39r51xc2L1any8NeZb//5WIHj8eKburojIdVHwJiK2V6KE1dGgd2+rtymDtzQmbEli714r+8Y2cd26AT16AFWqZPYei4hknII3EfEJLVpYHREqVwby5LE6Mbjj+++B2rWtqtLwcKBUqczeUxGR66PgTUR8wtSp1iC7xYoBRYoAO3daVamp4VAhK1cC06ZZGTcOJ8JOD59+mpV7LSKSfhoqJLuwTufkCiB/dSCkbLbthoivKF0aWLXKqv7kcB8M5qpXt7JwHHA3OBgYNw646SZrHWba+Njdd1u3sWOtQX45hZaIiDdT8JYdQduRecDut4GA/MDlE0DtkUC57lm+KyK+ZNAgYPJk4OhRoFkzYP9+a7aEM2esDgmcXYHL5syxBuwtXNgaEsQ5mwKzdAwAH3oou0siIpI2BW9Z5dIh6/+VnYH8lYBms4DQckBcJLCiE5C3MlDoyuSLIpJuzLRxhgTOZ/rAA1YWzTlrwvz5QPny1qT0zz1nVZGyqvSrr6wJ6f/v/4BXXrGCvgkTrOFCRES8ldq8Zaazm4CNg4ElLYE/hlvLWs4HmkyzAjfyDwEafQT88d9M3RURX3fggJV1a9nSGnD39tutGRbeecealJ5DgBCzbczGcXDeffuAdu2AoUOt+U/37AHy58/ukoiIpE2Zt8xw8TCwYQDglwuo1AdoMAGIiwcWLwFiw4CgfElnvS5wg5V5OzgXqHhfpuySXNvZs8D771vTKfXqZY37xWq3efOAfv2A3but9RgElCkDnD5treMcjZ+N39etAx5+2BrZX7IWp7n64gtrblO2eSNm0zhsCG/soLBokTUNFnulRkVZy/k3zxnPL889M3IiIt5MwZunRZ0E1t0P1HoWKNUJ2D0JWNEBiOODQ4Ff7gf8YoHQikDt54HCN1nPqzMKWNNdwVs2YuD2zTdA2bLAe+8BAwYACxYAq1db0yZt3Wo1ZmfVG6vjZs0C6tQB7r3XGluM1W9sS3XwIPDhh9lZkpypXDlg+JUEt5PrNFeuv5eIHRhchxnhTUTEDlRt6kkJscCaHlamjZY0A+KjgFYLgHbLrGXtVwKdfgeqPgpsHgrs+8BaHlISCC0PnP7Fo7sk7uMXPadJWrgQ6NoVmDLFaj81aRKwfLlV9UZ33mll6bgeq9r4eIEC1vRMHKqCvRhFREQyizJvnvT3J0CZ24HLJ4Gd44Bmc4ACVyZb5NgErimAUh2A4q2A5e2BuCig5jNAgTpW1Wmx5h7dLXFP1apWI3dm0V591bqxJ+KxY1aQxt6I7LFYqxZQt641COyjj1qToTPjRocPW1Wtzh6MIiIinqbgzZOOfAW0+hZY2QVoNOXfwC01ufMAzWYDa+4EqvQHYiOAcxs9ukviHjZwHzIEGDzYajPFIIz3t22zgjT2TmSANmwYMHGi1X6Kt3PngOho4Lvv/u3ZyGmaWM3KAV9FREQ8TcGbp8ReABLigeizQEA+oFADK/0SvhM48TMQUBRA6NXPY6/TEu2Afe8DuQKByMNK22QDBmi5cwN9+lgTms+YYU1Yzt6KbMTOZUye/vgjsGSJ1cjdtaH8a69ZDeEXL7YayzdokB2lEBGRnEBt3jwlNhzwDwXCtgGF6gMJccC6XsAfw4Cof4Azv1rrHZxz9XPL9QDObbKCNz7PEe+x3RL3sHcoM2WsAqVDh4DGja3lDNzSwiEnNmywsnfMuI0cmbShvIiIiCcpePOUuEvW0CDxl4GAgsDxn6zpr9iJgVWh8dHWev98D+yaAKwfaAVqVKQREB8JxJy3qlITYjy2W+IeDv/BDgc1rtR0MwvHmztCQ62ODlz/kUesAV7VaUFERDKLgjcPOXviAl7+9F5M/bwiLoRfBhwJOJ+rMaYfWIaENkuw+5I1/dUptAEOzsbpM/64/Pci68kJsVi5uRbGvl8HJyJremqXJB1Yw80OCR06WPc5/te1Mm5OrF7l9Esc861/fysQPH5ch19ERDKH2rx5yPuza+GbVYVQ9m/gvQ/vwYC7NmDBsmewelcsfltxClv/ao8XXliEuwa1RsNqFTBr6a2oc8MF3NsX+P2XWKxf+zQK5r2IgydL4MP7VeeW1UqUsDoa9O4NfPqpFbwxoHPH3r1W9o1t4jjAa48eQJUqmb3HIiKSUynz5iFBoSEIyROFhS88jK7tT2HKd/9BYOHKmDRiJZav8ke9oovNene23oizpy9j4agnUbN2kDVGmGMHNr52Kzp1iEXk5UCr+lWyHAdpZUeEypWBPHmsTgzu+P57oHZtq6o0PBwoVSqz91RERHIyZd48OUbYvur4/Y8ieHXMJbxaujAcjsI4dqw8arYFLkR0QFz8EtSq5Y+6NU7icqEH8WjrAnhz9BYU3NYTqNQPh+dexvm46hojLBsnNucgu8WKAUWKAH/+aVWlsjo0JRwqhNNhTZsGvPyyNZwIOz0wc/f881m99yIiklMoePPkGGFP5UKjmyJw+IcxGPLdLdi2pxAuR0ajUN6LKFg8H4YNByZ+0xMxMQGIiXHg3MlwREeWwnfT30PDyrVxS4Wv8dSUYRojLJuULg2sWmVVf3K4DwZz1atbWTgOuMvplMaNA266yVqHmTY+dvfd1m3sWGuQX06hJSIiklkUvHlyjLC+/shV5VPM+PJ3JJz9A2sWV0HxCqWR689XEXt6I36MHoYls9cjIHwTcORrILgUxq94D6/NbI+5AW2xeO8CtGrlpzHCssmgQcDkycDRo0CzZsD+/dZsCWfOWB0SOLsCl82ZYw3YW7iwNSSIczYFZukYAD70UHaVQEREcgI1rvL0GGEhpXEo4U40blUMJff2QK4L24GGE4EmM6yVD80Gok8B5e4GSrTFE+3ewoZfziCs/Cj89kcRjRGWjZhp4wwJnM/0gQesabDYiWHRIuDxx4E33rDWe+45q1qUbd04KT3byLHq9JVXrABvwpWpbUVERDKDTwZv77//PipVqoSgoCA0bNgQazhMflaPEVakLnDL+8CWEcDS1sDGQdaDYduBk6ussd/CdyC0aGmEFC6F3GU7aoywbHbggJV1a9nSqgq//XZrhoV33rEmped5JmbbmI3j4Lz79gHt2gFDh1rzn+7ZA+TPn90lERERX+Zz1aZffPEFhgwZYgK45s2bY+rUqejcuTN27tyJ8uXLZ+0YYUUbA7cutgbjvXQSWL4RaLvUSu24jhGW8O8YYbNnW2OEaaiJrMdprr74wprblG3eiNk0nk/e2EGBWThOg8VeqVFR1nL+/fDDwO7d1lRaHC5EREQks/hc5m3ixIno378/HnnkEdSsWROTJk1CuXLlMGXKlCwZI+z331MYIyyXPxBU3PqbjaNcaIww71GuHDB8+L+BmzPLxvOZwqkzHRicc5xymBHOrqDATUREMptPZd5iYmKwadMmPJ9snIaOHTtiHcd0SCY6OtrcnCIiIsz/sbGx5pYebOD+1VcAk3ucKolZGtdNOLeXfLuc6PzGG/na3B+gTJmkz7OL1MrnS3y9jCqf/ekc2puvn7/MLGOsDx+zlPg5HO6OI+/9/vnnH5QpUwa//PILmjGaumLs2LGYOXMm9rBBkovRo0djzJgxV21n9uzZCGEEJiIiIl4vMjISvXr1Qnh4OPLngIbHPpV5c/JLVr/F+DT5MhoxYgSGsqW5S+aNVazM1KX35I8aBaxdCyxebI31xSo0ZtLYvM0aIywWo0cvxcsvd0BsbIBpL8XHuncHXnzR6qE4Y4ZVbWfHoSb4q2fp0qXo0KEDApx1iT7G18uo8tmfzqG9+fr5y8wyRlypOcspfCp4K1q0KHLnzo0TJ04kWX7q1CmUYMO0ZPLkyWNuyfGCSu9FNWAA8PbbwMmTVvunXbtSHiNsxowAFCwYkGSMMPZO5bRKHNW/b99/21HZUUaOnd34ehlVPvvTObQ3Xz9/mVHGAB8/Xj7dYSEwMNAMDcKo3hXvu1ajZgaNESYiIiJZwaeCN2I16LRp0/Dxxx9j165deOaZZ3D48GEMHDgwU19XY4SJiIhIVvCpalO69957cfbsWbz00ks4fvw46tSpgx9//BEVKlTI1NfVGGEiIiKSFXwueKNBgwaZW3aMEeaKbdqcUhojzIlt5HgTERERyXHVpiIiIiK+TMGbiIiIiI0oeBMRERGxEQVvIiIiIjai4E1ERETERnyyt2lGOad5zYxpNjglCOde47Z9cSRoXy9fTiijymd/Oof25uvnLzPLGHHle9uHpmtPk4I3FxcuXDD/c35TERERsd/3eIECBeDr/Bw5JUx1Q0JCAv755x/ky5cvxYnsr4dz0vsjR46ke9J7O/D18uWEMqp89qdzaG++fv4ys4wOh8MEbqVLl0auXL7fIkyZNxc84WXLls3UA86L1VfflDmhfDmhjCqf/ekc2puvn7/MKmOBHJBxc/L98FRERETEhyh4ExEREbERBW9ZJE+ePBg1apT53xf5evlyQhlVPvvTObQ3Xz9/OaWMWUEdFkRERERsRJk3ERERERtR8CYiIiJiIwreRERERGxEwZuIiIiIjSh4ExEREbERBW8eMG7cONxyyy1mWq3ixYuje/fu2LNnzzWft2rVKjRs2BBBQUGoXLkyPvjgA/hK+VauXGmmGEt+2717N7zRlClTUK9evcRRv5s2bYpFixb5xPnLSPnsdv5Suma5v0OGDPGZc5je8tntHI4ePfqqfS1ZsqTPnL/0ls9u58/p2LFj6N27N4oUKYKQkBDUr18fmzZt8pnz6C00PZYH8MJ74oknTIATFxeHkSNHomPHjti5cydCQ0NTfM6BAwdw22234dFHH8WsWbPwyy+/YNCgQShWrBjuuusu2L18TgzyXKdAYfm8EadFe+2111C1alVzf+bMmbjjjjvwxx9/oHbt2rY+fxkpn93On6sNGzbgww8/NMFqWux2DtNbPjueQ16Ly5YtS7yfO3dunzp/6SmfHc/f+fPn0bx5c9x6663mxyF/7P/9998oWLCgT51Hr8CJ6cWzTp065eChXbVqVarrPPvss44bbrghybIBAwY4mjRp4hPlW7FihVnn/PnzDrsqVKiQY9q0aT53/twpn13P34ULFxzVqlVzLF261NG6dWvH008/neq6djyH6Smf3c7hqFGjHDfeeKPb69vt/KW3fHY7f/Tcc885WrRoka7n2O08egtVm2aC8PBw83/hwoVTXefXX3812StXnTp1wsaNGxEbGwu7l8+pQYMGKFWqFNq1a4cVK1bADuLj4zF37lxcunTJVC/62vlzp3x2PX/MEN9+++1o3779Nde14zlMT/nseA737duH0qVLo1KlSrjvvvuwf/9+nzp/6SmfHc/fggULcPPNN+Oee+4xWTfu+0cffZTmc+x4Hr2BgjcPczgcGDp0KFq0aIE6deqkut6JEydQokSJJMt4n9WSZ86cgd3Lxw8bVu188803mDdvHmrUqGE+fFavXg1vtW3bNuTNm9dM2zJw4EDMnz8ftWrV8pnzl57y2fH8MSDdvHmzaQ/mDrudw/SWz27nsHHjxvj000/x008/mS98np9mzZrh7NmzPnH+0ls+u50/YjDK9rXVqlUz5eTnzFNPPWXKnRq7nUdvoTZvHvbkk09i69atWLt27TXXZePT5IFRSsvtWD5+0PDmxAzPkSNH8Oabb6JVq1bwRtzfLVu2ICwszHxg9u3b17T3Sy3Asdv5S0/57Hb+uG9PP/00lixZYho9u8su5zAj5bPbOezcuXPi33Xr1jX7W6VKFdM+kz8Y7Xz+MlI+u50/SkhIMJm3sWPHmvvMvO3YscMEdH369En1eXY6j95CmTcPGjx4sEkbM7XNBuJpYS8j/uJwderUKfj7+5teOnYvX0qaNGliqg28VWBgoGnQzw8fZjduvPFGvP322z5z/tJTPrudP/Zm4/FnjzWeA94YmL7zzjvmb1YV2/kcZqR8djuHybEzFIOc1PbXTucvI+Wz4/ljtjD5j8GaNWvi8OHDqT7H7ucxuyjz5gH8lcDAhtVQ7N7N9gzXwl9RCxcuTLKMv6r5xRoQEAC7ly8l7NnIN7ddsNzR0dG2P38ZKZ/dzh+rk1gt7Kpfv3644YYb8Nxzz6XYq89O5zAj5bPbOUyO1+auXbvQsmXLFB+30/nLSPnseP7Y0zT5MFJ79+5FhQoVUn2O3c9jtsnuHhO+4PHHH3cUKFDAsXLlSsfx48cTb5GRkYnrPP/8844HH3ww8f7+/fsdISEhjmeeecaxc+dOx/Tp0x0BAQGOr7/+2uEL5Xvrrbcc8+fPd+zdu9exfft28zgvt2+++cbhjUaMGOFYvXq148CBA46tW7c6XnjhBUeuXLkcS5Yssf35y0j57Hb+UpK8N6bdz2F6y2e3czhs2DDzGcPz8ttvvzm6dOniyJcvn+PgwYM+cf7SWz67nT9av369w9/f3/Hqq6869u3b5/j888/NOZo1a1biOnY/j95CwZsnDiKQ4u2TTz5JXKdv377mw9YV38gNGjRwBAYGOipWrOiYMmWKw1fK9/rrrzuqVKniCAoKMkNSsPv4Dz/84PBWDz/8sKNChQrmXBQrVszRrl27xMDG7ucvI+Wz2/lzJ7ix+zlMb/nsdg7vvfdeR6lSpcwXd+nSpR09evRw7Nixw2fOX3rLZ7fz57Rw4UJHnTp1HHny5DFDgHz44YdJHrf7efQWfvwn+/J+IiIiIpIe6rAgIiIiYiMK3kRERERsRMGbiIiIiI0oeBMRERGxEQVvIiIiIjai4E1ERETERhS8iYiIiNiIgjcRERERG1HwJiK20qZNG/j5+Znbli1b4O0eeuihxP399ttvs3t3RMQHKHgTkSw3ZMgQdO/ePcPPf/TRR3H8+HHUqVMH3u7tt982+yoi4ikK3kQky23YsAGNGjXK8PNDQkJQsmRJ+Pv7IzvFxMRcc50CBQqYfRUR8RQFbyKSZWJjYxEYGIh169Zh5MiRpiqxcePG17XNTz/9FEWKFEF0dHSS5XfddRf69OmTeJ/TOI8fPx6VK1dGcHAwbrzxRnz99deJjy9evBgtWrRAwYIFzfa6dOmCv//++6oq2yeffBJDhw5F0aJF0aFDB7ONunXrmm3yee3bt8elS5euq0wiImlR8CYiWSZ37txYu3at+Zvt1Vid+NNPP13XNu+55x7Ex8djwYIFicvOnDmD77//Hv369Utc9r///Q+ffPIJpkyZgh07duCZZ55B7969sWrVKvM4Ay4GZcwK/vzzz8iVKxfuvPNOJCQkJHm9mTNnmozfL7/8gtdeew33338/Hn74YezatQsrV65Ejx49TKAoIpJZsrfOQURyFAZE//zzj8lQMfPlCcx49erVywRmDOTo888/R9myZU2mzBmYTZw4EcuXL0fTpk3NMmbgGEhOnToVrVu3Npk6V9OnT0fx4sWxc+fOJG3rqlatajJ4tHnzZsTFxZmArUKFCmYZs3AiIplJmTcRyVJ//PGHxwI31w4MS5YswbFjx8x9BnLOXp7EAOzy5cummjNv3ryJN1a5OqtG+T+DQAZ1+fPnR6VKlczyw4cPJ3mtm2++OfFvlqNdu3YmYGPg+NFHH+H8+fMeLZuISHLKvIlIlmJ1afLgjT1P8+TJg/379yMsLMy0I0tPgNegQQOzPoOxTp06Ydu2bVi4cGHi486qzx9++AFlypRJ8ly+LnXt2hXlypUzAVjp0qXNc5hxS94pITQ0NEk18NKlS00bPgaP7777rmnL9/vvvycGfyIinqbMm4hkKQZW9erVS7Js69atJqPF9mZsmzZp0qR0b/eRRx4xGbePP/7YdBpgIOZUq1YtE6Qxi8ZqT9cb1zt79qxps8bXZiatZs2abmfQmN1r3rw5xowZY7KK7JAxf/78dO+/iIi7lHkTkSzFjBaDNbZ9YxaL2Sv2FGVnAWLglJHg54EHHsDw4cNN5owZOFf58uUzj7GTAl+fvUojIiJMxozVpw8++KBph/fhhx+iVKlSJsh7/vnnr/mazLCxc0PHjh1N+zjeP336tCmDiEhmUeZNRLLUK6+8gi+++MJUX7700ksmkKtdu7YJ4pydADLS6J/t1NjpgMFYSgMAv/zyy3jxxRcxbtw4E1yxepVVq6zeZEeKuXPnYtOmTaaqlEHeG2+84dZrrl69GrfddhuqV69uMncTJkxA586d073/IiLu8nOoT7uIZKMPPvgAb731FrZv327au7HKk8N+OHtvJscepPXr10+xapUdEhiYvfPOO/A2rF5lRvF6ZpYQESFl3kQkWzHzxvHU2G6sbdu2JuOVWuDm9P7775sMG9vP0blz50zmjEOBPPHEE/AmAwcONPsqIuIpyryJSLZi+7M5c+Yk6WCQFg4HEhUVZf4uX7686SBQsWJF08Hg//7v/0zbNm9y6tQp076O2J7OtbeqiEhGKHgTkWzFNmcHDhzQWRARcZOCNxEREREbUZs3ERERERtR8CYiIiJiIwreRERERGxEwZuIiIiIjSh4ExEREbERBW8iIiIiNqLgTURERMRGFLyJiIiI2IiCNxEREREbUfAmIiIiYiMK3kRERERsRMGbiIiICOzj/wFeiMi22K2RTwAAAABJRU5ErkJggg==", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.title(\"Dephasing vs. time to plunge $t_p$ for different accretion disk parameters\")\n", "plt.scatter(\n", " results[\"orange\"][:, 0],\n", " results[\"orange\"][:, 1],\n", " color=\"orange\",\n", " marker=markers.tortellini,\n", " label=results[\"orange\"][:, 3][2],\n", " s=200,\n", " linewidth=0.2,\n", ")\n", "plt.scatter(\n", " results[\"blue\"][:, 0],\n", " results[\"blue\"][:, 1],\n", " color=\"blue\",\n", " marker=markers.ravioli,\n", " label=results[\"blue\"][:, 3][2],\n", " s=200,\n", " linewidth=0.2,\n", ")\n", "# plt.ylim(1e-3, 1e6)\n", "plt.ylabel(r\"$\\Delta \\Phi_{\\Phi}$\")\n", "plt.xlabel(\"$t_p$ [years]\")\n", "plt.grid()\n", "# import values from https://dx.doi.org/10.1103/PhysRevX.13.021035 fig 1\n", "plt.scatter(\n", " 4,\n", " 1e2,\n", " marker=markers.farfalle,\n", " label=\"PhysRevX.13.021035\",\n", " s=400,\n", " linewidth=0.2,\n", ")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The dephasing $\\Delta \\Phi_{\\Phi}$ obtained from the difference between the final orbital phase of an evolution with and without migration torques in $\\alpha-$ or $\\beta-$ accretion disks. For $\\alpha-$disks, the slope is expected to be $n=8$, for $\\beta-$ disks, $n=59/10$. The obtained value in previous work for $t_p=4 yr$ is shown in the Figure as a tortellino (see fig 1 of [PhysRevX.13.021035](https://dx.doi.org/10.1103/PhysRevX.13.021035))" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "execution": { "iopub.execute_input": "2026-07-11T10:49:00.299104Z", "iopub.status.busy": "2026-07-11T10:49:00.299045Z", "iopub.status.idle": "2026-07-11T10:49:00.360281Z", "shell.execute_reply": "2026-07-11T10:49:00.359863Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.scatter(\n", " results[\"orange\"][:, 0],\n", " results[\"orange\"][:, -1],\n", " color=\"orange\",\n", " marker=markers.tortellini,\n", " label=results[\"orange\"][:, 3][2],\n", " s=200,\n", " linewidth=0.2,\n", ")\n", "plt.scatter(\n", " results[\"blue\"][:, 0],\n", " results[\"blue\"][:, -1],\n", " color=\"blue\",\n", " marker=markers.ravioli,\n", " label=results[\"blue\"][:, 3][2],\n", " s=200,\n", " linewidth=0.2,\n", ")\n", "# plt.ylim(1e-3, 1e6)\n", "plt.ylabel(\"Timing [s]\")\n", "plt.xlabel(\"$t_p$ [years]\")\n", "plt.grid()\n", "plt.legend()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "few2.0rc1", "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": "3.12.13" } }, "nbformat": 4, "nbformat_minor": 2 }