{ "cells": [ { "cell_type": "markdown", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "# Tutorial 04: Dzyaloshinskii-Moriya energy term\n", "\n", "Dzyaloshinskii-Moriya energy density, depending on the crystallographic class, is computed as\n", "\n", "$$\\mathbf{w_\\text{dmi}} = \\left\\{\n", "\\begin{array}{ll}\n", "D \\mathbf{m} \\cdot (\\nabla \\times \\mathbf{m}), & \\text{for}\\,\\,T(O) \\\\\n", "D ( \\mathbf{m} \\cdot \\nabla m_{z} - m_{z} \\nabla \\cdot \\mathbf{m}), & \\text{for}\\,\\,C_{nv} \\\\\n", "D\\mathbf{m} \\cdot \\left( \\frac{\\partial \\mathbf{m}}{\\partial x} \\times \\hat{x} - \\frac{\\partial \\mathbf{m}}{\\partial y} \\times \\hat{y} \\right), & \\text{for}\\,\\,D_{2d} \\\\\n", "\\end{array}\n", "\\right. $$\n", "\n", "where $\\mathbf{m}$ is the normalised ($|\\mathbf{m}|=1$) magnetisation, and $D$ is the DM energy constant. DMI energy term tends to align neighbouring magnetic moments perpendicular to each other.\n", "\n", "In `oommfc`, $\\mathbf{m}$ is a part of the magnetisation field `system.m`. Therefore, only DMI energy constant $D$ should be provided as an input parameter to uniquely define the Exchange energy term. $D$ can be constant in space or spatially varying.\n", "\n", "## Spatially constant $D$\n", "\n", "Let us start by assembling a simple simple simulation where $D$ does not vary in space. The sample is a \"one-dimensional\" chain of magnetic moments. We are going to choose $C_{nv}$ as the crystallographic class." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import discretisedfield as df\n", "import micromagneticmodel as mm\n", "\n", "import oommfc as oc\n", "\n", "p1 = (-10e-9, 0, 0)\n", "p2 = (10e-9, 1e-9, 1e-9)\n", "cell = (1e-9, 1e-9, 1e-9)\n", "region = df.Region(p1=p1, p2=p2)\n", "mesh = df.Mesh(region=region, cell=cell)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The mesh is" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "nbval-ignore-output" ] }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "a3a228bd722546e981e1a9f48d51a246", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Output()" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mesh.k3d()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The system has a Hamiltonian, which consists of only DMI energy term." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "D = 1e-3 # Dzyaloshinksii-Moriya energy constant (J/m**2)\n", "system = mm.System(name=\"dmi_constant_D\")\n", "system.energy = mm.DMI(D=D, crystalclass=\"Cnv_z\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are going to minimise the system's energy using `oommfc.MinDriver` later. Therefore, we do not have to define the system's dynamics equation. Finally, we need to define the system's magnetisation (`system.m`). We are going to make it random with $M_\\text{s}=8\\times10^{5} \\,\\text{Am}^{-1}$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "import random\n", "\n", "import discretisedfield as df\n", "\n", "Ms = 8e5 # saturation magnetisation (A/m)\n", "\n", "\n", "def m_fun(pos):\n", " \"\"\"Return random 3d vectors for initial random magnetisation\"\"\"\n", " return [2 * random.random() - 1, 2 * random.random() - 1, 2 * random.random() - 1]\n", "\n", "\n", "system.m = df.Field(mesh, nvdim=3, value=m_fun, norm=Ms)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The magnetisation, we have set as initial values looks like:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "nbval-ignore-output" ] }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "201b74bda0e14d1ab94450b0a88cc1f0", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Output()" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "system.m.k3d.vector(color_field=system.m.z) # k3d plot" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "system.m.sel(\"y\").mpl() # matplotlib plot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, we can minimise the system's energy by using `oommfc.MinDriver`." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Running OOMMF (ExeOOMMFRunner)[2025-02-02T14:31:28]... (0.5 s)\n" ] } ], "source": [ "md = oc.MinDriver()\n", "md.drive(system)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We expect that now all magnetic moments are aligned orthogonally to each other." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "nbval-ignore-output" ] }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "d0bfc6f677034805aafed0f79169df0e", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Output()" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "system.m.k3d.vector(color_field=system.m.z) # k3d plot" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "system.m.sel(\"y\").mpl() # matplotlib plot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Spatially varying $D$\n", "\n", "In the case of DMI, there is only one way how a parameter can be made spatially varying - using a dictionary.\n", "\n", "In order to define a parameter using a dictionary, regions must be defined in the mesh. Regions are defined as a dictionary, whose keys are the strings and values are `discretisedfield.Region` objects, which take two corner points of the region as input parameters. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "p1 = (-10e-9, 0, 0)\n", "p2 = (10e-9, 1e-9, 1e-9)\n", "cell = (1e-9, 1e-9, 1e-9)\n", "subregions = {\n", " \"region1\": df.Region(p1=(-10e-9, 0, 0), p2=(0, 1e-9, 1e-9)),\n", " \"region2\": df.Region(p1=(0, 0, 0), p2=(10e-9, 1e-9, 1e-9)),\n", "}\n", "region = df.Region(p1=p1, p2=p2)\n", "mesh = df.Mesh(region=region, cell=cell, subregions=subregions)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The regions we have defined are:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "nbval-ignore-output" ] }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "ab524a0d4d6d4a1db2b4013c6beb2d67", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Output()" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mesh.k3d.subregions()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let us say there is no DMI energy ($D=0$) in region 1, whereas in region 2 $D=10^{-3} \\,\\text{Jm}^{-2}$. Unlike Zeeman and anisotropy energy terms, the DMI energy constant is defined between cells. Therefore, it is necessary to also define the value of $D$ between the two regions. This is achieved by adding another item to the dictionary with key `'region1:region2'`. The object `D` is now defined as a dictionary:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "D = {\"region1\": 0, \"region2\": 1e-3, \"region1:region2\": 0.5e-3}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The system object is" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "system = mm.System(name=\"dmi_dict_D\")\n", "system.energy = mm.DMI(D=D, crystalclass=\"Cnv_z\")\n", "system.m = df.Field(mesh, nvdim=3, value=m_fun, norm=Ms)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Its initial (and random) magnetisation is" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "nbval-ignore-output" ] }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "f4cb13dec1444544985da21370410a54", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Output()" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "system.m.k3d.vector(color_field=system.m.z)\n", "system.m.sel(\"y\").mpl()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "After we minimise the energy" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Running OOMMF (ExeOOMMFRunner)[2025-02-02T14:31:29]... (0.3 s)\n" ] } ], "source": [ "md.drive(system)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The magnetisation is as we expected. The magnetisation remains random in region 1, and it is orthogonally aligned in region 2." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [ "nbval-ignore-output" ] }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "a126b930c30b479ba45c3dec480609e9", "version_major": 2, "version_minor": 0 }, "text/plain": [ "Output()" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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7CgoK4O/vb/J6dA4+tm7dirVr16KsrAwBAQHo2bMnunfvDk9PT1hbWyvKFRcXIyEhARcvXsSFCxdw6tQpnDt3DgsWLMCECRNM8RgIIYQQQkg1oGFXdYeXlxdSUlJMXo9OK5wvWrQIR44cQa9evRASEgIfHx+dK3jw4AHWrFmD8+fPY+jQofj2228NajAhhBBCCKkZfA8uN3ud94d/afY6XwV//PEHvvvuOxw6dAj29vYmq0en4KNjx45Yvnw5hgwZwrmi33//HV999RWuXbvG+RyEEEIIIaTmaFkNwUccBR8mER0djd9//x2nT5/G8OHD4enpCaFQqLasIbNd6RR83L9/H76+vpwrMfZ5CCGEEEJI9fPZ/39mr/PByC/MXuerwNfXFwzDKHK6GUZ1MgH5VLuxsbGc69Ep58NYAYM+57l//z7mzZuH+Ph4nDhxAl5eXlUeEx0djR9//BF3794Fj8dDp06d8PHHH+s1TIwQQgghhOiGZruqO6ZOnQqhUKg26DAmTlPtFhcXY82aNTh79izS0tIglUrVlmMYBvfu3dP7/Dt37sS3336r13iz69evY+LEiejatSvCwsIgkUgQHh6OcePG4cCBAyZbIp4QQggh5FVFCed1R0hIiFnq4RR8rFq1Cnv27AHDMKhXrx5EIpHRGhQVFYVVq1Zh6dKlSE5ORlhYmE7HrV27Fi4uLggPD1eMT2vbti169+6NDRs24JtvvjFaGwkhhBBCCMDSVLt1VkFBAYqKiiASiYx6rc8p+Dh37hw6deqEH374Aa6urkZrDAA4ODhgz5498PPzw/r163U6JicnBzExMRg/frxSYoyTkxOCgoIQGRmJr7/+2uTdSIQQQgghrxLq+ahb0tPTsX79epw9exaZmZmK7W5ubhg4cCBmzZoFW1tbg+rgFHzk5eVh7ty5Rg88AHDKz3j06BFkMhm8vb1V9nl7e+PMmTNITU1FgwYNjNFEQgghhBACgJXRjd26IjU1FaNGjUJaWhoEAgHc3d1hY2ODoqIivHjxAlu3bsX58+exZ88e1KtXj3M9nIKPli1bIi8vj3OlxpaWlgYAcHR0VNkn35aenk7BByGEEEKIMVHPR53x888/Iz09HUuWLMGoUaNgZWWl2FdYWIg9e/Zg7dq12LhxIxYuXMi5Hk7Bx0cffYTFixejV69eaN68OefKjUUsFgMABAKByj75ttLS0irPM6DNEuM2rAr3Z6kGS3KSnFy8+Oxr8Oxs0fCz+bCw5x5hym3o/z+Dz6Gv3RlddS4rk8iwp+9OBH3RHZ59mnGqL22oDafjuErc4GTW+hoO5T61HReJ+9sAAKSFxUj5+SgK/imfQMJhQADcpg4ySZ33gn41yXk18fpthsZ9aVsjUHTzFhzfGQL7N3qZsVWml75zDwqjYxT/5js4oMmXn4Hh1a3x208//RxsWRkafjQblu51Z+IRVibD82XfQJqbq9hmG+iP+u+NqcZWGV9pwlMk/7AeFi710ShkHngVLoZqO3FyMpJWrVHaVn98MGw7dzT43PEfmSdxGKDZruqSixcvYtSoURg/frzKPpFIhMmTJ+Pp06c4ffq0+YOPbt26YfLkyRgyZAjat2+PRo0aqb3wZxgGK1as4Nw4XVlaWgIAysrKVPbJt1nVsi8sno01AECWX4CM/+2E29xpYPj8am6VaWXGZkBSLEHCn084Bx/ENJJCf0PRnQTFv3NORsOmTTPYdfOrvkaZgfxzmH30OCw9PWDVzLN6G2REtoH+SsGHNCcHJY8ew9pHdfhqbcaztoa0pATp2yLQcOF88G3Me4PCVBgeD7YBnZEbeVaxrfDGLTiNGAbef7+JdQHvv9dLkp6BjN/2w+X94DqTvyls2BDCpk0gTnyu2FYQHWOU4MOsKPioM9LS0tChQwetZfz9/XH48GGD6uF0i2vfvn1YsWIFpFIprl27hmPHjuHQoUNq/8xBnnuSlZWlsk+eLGOs/JSMgnijnKcqjEAAWJQHG6UPnyDn+Gmz1FudUq4mAwCeX34BcYG4mltDKqof3AfgK39dpIQfQVladjW1yDx41uXBB2QypG/fAWlBYfU2yIisvJrDwkm597UgKrqaWmM6/P8CSElWNjJ2/QYd1tWtNWwD/JX+zYrFKLp5u5paYxryGwAAUHT9BvL/vlyNrTE+20Dl17Ak7gEkObkaStdQbDX8EZMQCoUoKSnRWqakpERth4M+OPV8bN68Gba2tpg6dSq8vb2NOv0WFz4+PrCwsEBcXJzKvtjYWLi4uBgt+EjJjUWZtAgN7Vsb5XyaMAwDno01ZHkFAIC8k2dg5eUJ69bmWSE+9UUZ3Bob9ubSV8rVFACATCzFs7+eosXgunUH1hAsy0KSVVBt9Vv7NEX993ojY0ekYpusqBRJ3x+A+/9NBGNRN3vleBXukktzcpH+6y64TZtcJ4YmMTweRAH+yD318sZG0c3bkI0sqVNDWypevBbfuYu8v87D/o3Xq609xiRwc4WlhwdKnz5VbCuIjlG5oK3NFDcA/pN16HdYurvXmSF0ok4dkXX4KCBfL41lURBzFQ59e1dvw/RBCed1hre3Nw4fPox3330XFhaqIYJEIsHBgwcNXryb0y9ocnIypk+fjmnTpuGNN95AYGCgxj9zsLOzQ1BQEE6dOoXi4mLF9tTUVPz7778YMGCA0eoS8C1xN+kPFJZmVl3YQJW/dDO27YYkK8eodRQXynDxD9XJA7aGpuHGZfPd5ZWKpUi7mar4d/yfT8xWd01XkpCKp1/uxJOPt0DKSqqtHU5vB8Gmg5fStpIHz5Gx+6yGI2o/fqXPYMn9OKVhLrWdbUBnpX+zZWUovHGrmlpjGjxr5WFW2UdPoOSJeXqwzUHlzvnDR5CoGQVQWzF8PpiKw8ikUqRvi4C0qKj6GmVEfJEINq2Vh68WRsXUqh46ljX/HzGNUaNG4datWxgzZgz27duHGzdu4P79+/jnn3+wY8cODBs2DDdv3sSYMYbllnEKPurXr6/X6uP6eP78OW7fvo3bt28rZrF69OiRYptYLMbhw4fh5+eHS5cuKY4LCQlBfn4+PvzwQ/z99984d+4cpk+fDnt7e0ybNs1o7bPgW0IqE+NG4iFIZao5JsZU8Y4dAMgKi5Cx5VewGlaU15dUwmLFnOdYMfsFIr5PV3zZyWQsblwuRNiXKRCXyoxSV1Uy7qZDWvrycaXEJKM4q1jLEXWfJLcQST+fwOP5m1B4Kx6SzHwkQLV3z1wYHg8N5w4D31F5fu+sw3+j8PrDamqVaVX+DAJAzh+nUPzwUTW0xvgE9evD0kt50pDaOPRK23eiymsokyF9+6+QFlRfT6Ix2XTsAFS6Q1kQfbV6GmMAra9hpZsAdW0IXeUAsiwtDeKnz6qpNRzQsKs6Y8SIERg3bhzu3LmDL7/8EmPHjsWwYcMwadIkfPPNN3j06BGmTJmCd955x6B6OAUfI0aMwPHjx03ywQ8LC8PIkSMxcuRI7N27FwAwd+5cxba0tDTIZDJIpVLIZC8vjH19fREREQGJRIJZs2bh448/RqNGjbBr1y6jrkdiwSsfjlBQmob7KabNw+CpSYwsjX+KnCN/GHxulmUR9kUKYs6X927sDsvAmo+TUSZm8fRBKXKzpHgRL8beDabv4QFeDrlStE/K4umZBLPUbW6SPO137GRlUmQc+RcPZ/6E7JNXAdnLz9lTxKGErb47fhb2tmj40XCgUi978rpDkGTVnOm3jUXdZxAsi/SInZDUoOnGDVH5wqf0STzKMjLM3g59f09YmQzFDx8hfeduJH65HNIi9TcrKl+4AoA0Nxfpv+4GKzPPzRVT4ttYQ9S2jdK2gujquXOub50ysRgFMdeQEv4LUjds1FhO3U0A+RC6usC6lS94lRZtK4iK0VC65mFkjNn/iOl8/vnnOHDgAKZOnYrevXuja9eu6NOnD2bOnIkjR44gJMTwmdQ45XwMHjwYCQkJGD16NEaOHIkmTZpoTD4JCAjQ69zffvstvv32W61lmjRpguHDh6tsb9++PXbs2KFXffoS8F+OhX6efQOONh5o5GCa/A91X7gAkBd5HpZenrBp30btfl1E/1WAk3tzlLadOZSLrDQJ/Dq/rPe3DZnoNbgemnqZdvaU1GvJKtvi/3wC31GtOJ9TIiuDBc+8eStVkeQU4OnyPfBaO0VlH8uyKIh5iJT/nYY4Sf2wCT4sUIg8WKH6ZuwRtW0O5xE9kbn/gmKbNK8IyT8eRJMv3wdTITG96G4CrH3dlbbVJuouXAFAlp+PjIidcJtZ82ehYyUSyIqLwROJ1OaqiNq3Q9aBQ2DFL3tyC6KvwnFgf7O1UZKTi7wLF+H09uAqy5ZlZKAgKgYF0VchzX454UHRjZuwC1Kd2lttAImXQ+gc3uzLveFmwLIs2LIysGIx+BpWFRYF+qPw+g3FvyUZmSiNT4BVc/PNGljy+DHKUtJg91o3reVYlkVpfAIKoqJReP0m2ArT4JdlZkLg7KxyjKbPYfbRE7D08DDr4+SCZVmw/yXxqnssDJ8P286dkHf+5Xdq4fUbcBz2NngGJvaaBfVE1DmtW7dG69amy23mFHz0798fDMOAZVncvq19Zo3YWP3XJYiLi8OaNWtw7do1SKVS+Pn5Yd68eVoDmfHjxyMqKkrtvhkzZmD+/Pl6t0MdC77yRfi95D9gb90AIkvVL0xD8aw1J31mRuyFYHEjCOpzW2ci4HVbvL/ABRFr05W2X/+7ENf/fpnrIRGzWP9FClbtdDfZ9IbSUgnSbqerbE+/lYaClALYNlD/g1uVxwXRyBYnw8XKAy6WHrCzqF+tUzRK8ouR8OVOlD5NAyuVKV2QlzxLR8qWP1F4Q0OuC4+B01sBaHusAQSM0Ewt1sz53V4oupuA4tiXQwOK7iQg8+BF1B9Vvh4GK5UhdeNxuE4eCFE7864HdOd+KW7cEWPcSDuDzqPpBgAAlDx6jJyTf8Jx0ECD6tAFK5FAWlQEWVExZMXFkBUV/fffl/8vVbevuAhgAaeRw2DXRX0OHs/KCjbt2qEw5uVQnYKoGDj076cUrMhKS00yhWvx/Tik79gFqxaa3yOykhIU3riFgqholGrI1yiIjlEffGi4cAXKh9BZenqYfHphlmXBisVKr4usSPNrVv66FkP63z4L+3pwmfC+xuDDuqUP+Pb1IM192RtXEBWtdFEub4OxX0NWJkPu2b+Qc/wPOI8aobGcJCsLBTHXUBAVDUmG+h71wuircBjwpsp2jdMj/zeErtHH8zU+N8bCymSQlZS+fH1UPofFkGraV1wMq5Y+cBk3VuP5bbv4KwUfsuJiFN+5C1HHDi+3megzaLAa2hPB5VqSlEtKSkJUVBRevHiB0tJSWFtbw93dHV26dEH9+vUNPj+n4OOtt96CUCg0yYVcYmIigoOD4enpidDQUFhbW2Pr1q2YOHEidu3ahXbt2mk8tnXr1li2bJnKdmMOuxLwlD/45fkfB9G1+QTwjXyXXdMdO6D8iylj8w40CJkFRqD/y8gwDMbOqg/XRgJ8/2kSpFrymG9fKULkgVz0G+mgdz26SL+TDplY/XjfhNPxaDO+Lafzeoo64FnRbeTkp+Bh/hVY8kRwsfSAi5UHnIVNYMEz30W8tKgUz5btQunT8jwmWbEYfFsrSPKKkL7nArL+iFEaXlWRbScvNJjUD5ZNXSA4btgigyzLIgkJqAdH2DEOnM/D8PloOH8EnoZsgDT/5XCXzL1/wcbPAzatPZF/+S7Ez9ORd+GW2YKPsjIWq9Zn4+sfsvDTt4Z/7isnK1eWe/oMLJt5wsaPew9dZQVXryH/73+ULl5YNWsY6cLCxQWuE8dD2KiR1nK2gf5KwYc0Oxslj5/A2rsFAKDoXixKnz4zam8IK5Mh59Rp5P4ZCbAs+JXyCFmZDCWPHqMgKhpFN29X+RyUxidAkp0NC0fl6YO1BZBgWaTv2IVGC42zkCtQ3u7so8dR+iRB6WIUHHP1rNu0Rv33Rmtdn4Th8SDy74y8M+cU2wqv34TT8KHgCcu/57KPHod1K1/Fa2oM0sJCZOzcjeJ79wEA/ErPoay0FEW37qAgKholOuRJFV67Afv+/VSuLbQFkNLcXKTv2AW36VOMNgudtKAQmXv3QZKd8zIgLC7hlunMMHAY2B/2fXtrbZ+wUSMImzSG+PkLxbaCqBhF8CErLUXapv/BbdaMmrfOSQ3s+TDkWvJVVlZWhi+//FKxjkfFoZQMw4DH42Hs2LH47LPPwDPg88Yp+Fi7di3nCqsSHh4OqVSKjRs3wsmp/K5+586d0b9/f6xduxbbtm3TeKxIJELbttwuVHVlwVftjSgoTcf9lNNo3egto9bF1/ajCUD87DmyDx6D0+ihnOvoM8weTq4W+L8Pn6O4QPP4583fpiGwty3snTi9ZbSqnO9RUfyfTzgHH5Z8G7jbtEN84TUAQKmsEM+L7+F58T0w4MFJ2FjRKyKycOBUhy5kpWV49s1vKH6YpNgmzS9CzrlbSN9zHtIC9XNqCxs7o8HkN2HX2TgXC7lsJu7jBhgwaARPg88ncLZHg9lD8WLl7pcbZSySfzgAj++mI2PvXwCAgn/vQTZ1EHiWph0+cP12KSbPT8XNu+VrxLTyFiAjU4r6ztyHRWnrfZTL2LkbjRYugIWjA+d6KhJ17IDSJ/HI//sfg85j07ED6o8eqdO0uVYtvMB3dIA0O0exrSAqGtbeLVDyJB7pWyNU1pQwhDQ/H+k7dqHkwcuJCiz+Cz7K0tNfDqvKydFwhpf4Dg6wDegM20B/lcADAPhVBJCy/HykR/yKBh9ON8oQOobHg32f3kh9vBmSNNUeXZ3xeHAc8hbqvd5Lp4tN2wB/peCD/e/C39a/E3IjzyLv7F+w9PDg3p5KShOeIm37DqX3DN/eHqxMhtL4eBRciUHhzVtKw6o0Ebo3hW1gAEQdO6h9rFoDSJSvjWHMIXR8WxHse7+B1I1bIDNgVi2enR1cxr+nc8+abYA/sioEH8X34yDJzQVfJEL61giUPHoMVixWnv2rJqiBwYch15KvsnXr1uHQoUNo1KgR+vXrB3d3d1hZWaG4uBhPnz5FZGQkdu7cCQcHB8yePZtzPca/kjQAy7I4c+YMgoKCFG8WoHzRk759+2Lnzp3Izc012UxburDgqf/Ql+d/uKORA/c8jMqq+sIFgPzzf8OyRTOIOrfnVIekjEVRgRQNmwrwJFbzj0RethRbvk3DglDtd1C5kC8uqE72gyzkJuTA3tOB07mb2XbEs6LbkLLKd01ZyJApTkSmOBH3cQk2fHu4WHnCxdIDTsJG4DHGGccvK5MicdV+FN15qrQ9fvF2SLLVz7bDE1nBdWxPOA30N8r6GaVsCR7hNpJR3oYOeM1od85s/VvCcXBXZB/7V7FNkpWPp4s2QZJRvlCWrFiMgpg41HvNeJ+NikpLWXz9fRZWhWUr3VweMCYJQwfaIiLMjfO5GR4PjJWVYry2OrLCIqRv34EGcz402sWr08jh4NnYIPf0Gf1PwOfDadjbsHstSOfXuXy1bP/yXoj/FN28jZJuXZG6cQvYsjJIi40z+1zJ48dI374T0koJ+6WJiUj+MQyl8QlVt1cggE37trANDIBVCy+td5R1+R4tffzEqEPo+LYiNPhwOtK2bEXJw8f6H29vD5cPxumVyyBs4Aahe1OInyUqthVEx4AtLUX2sRMAUD4Mz0AsyyL/wiVk/X5MpTenMDoG6XfuQZJZ9UQl/Hr1IAroDNsAfwgbaP+MahsFIGfsIXSWnh5oMOdDpG7YqDScTefjvZrD5f1xevWoiTp3RNaRo4B8IgSWRUH0VYifv0Dx/fKZDmVFxTVu6FVNSwCvDdeSNdWxY8fQpk0b7NixA9Zqehznz5+P4OBgHDx4sHqCj+zsbJw/fx6pqako09AdzjAMZs2apfM5U1JSkJubixYtVO/0ent7QyqV4uHDh/D3r74FlARqej7kyvM/Ghot/0NbV3NFmTv3Qdi0EQSuLjqfOy2pDCd/y8GpvTnIStNt7YjTB3LRd7g92nU13qKSkhIJMu5ovzsY/2c8OkzrqNd5nxXeQVz+ZQCsTmtjFElz8bTwJp4W3gSfEcBZ2EQRjFjxuT1eVirDi+8PoeCq6nADtYEHj4Fj/85wfa8XLOoZnlAuY2VIxCM8wT1IUf4c2MERzmhg8LkrchnXF8Wxz1Dy+GXPjjzwkMu7cMskwceVayWYMj8N9x6IVfYVFrH442whpFIWfD73H0e+jTUkVaz4WprwFNlHj8Np6Nuc66mIYRjUe6MXSh4/0ZjjoI6FkyNcJrzPaQG2ysEHKxYjJexnxYWQIXeAgfLhSHln/0L2iZMvL64qKNJhfRHL5s3K75B3aKfzQoi6BB+A8YfQ8ays4DR8KFLW/6zXc2fl2xIu48ZyymGwDQxAVoXgo+TBQ6XeJZmGGcF0JSsuRsaevRpXUc87f1H7CSwsIGrbBqJAf1j7eOscrOv0W/jfLHSNPl5gtCF0ggZucBz0FjJ27dHrOPt+feAw4E29b0bwbW1h09oPRbfvKLblVPq8yIqLACP1shpNDev5qA3XkjVVRkYGpk6dqjbwAAAbGxuMGDECoaGhBtXDKfi4e/cuPvjgAxQWFmqdWk/f4CM9vfwitGKkKifflqFlCsjs7GwsXrwYly5dQnZ2Ntzd3REcHIzg4GCd21AVPk+I8nlGVR+3VFZm1PwPXX802ZJSpG/egQYL54An1K1eSRmLglwpCvP0G4e87vMUhB9vBqGlccbWpt1Kg0yifbrL+D+foP1U9d3xmrBgVXo7dCVly5BWGo+00vKLPjuL+v8Nz/KEg8AVDFP1Y2dlLJJ+Ooa8v3XL0RC1b4YGk9+ElYdx8pMy2RTE4SaKkK+0vRlaGX28MCOwQMMFI5EQsgFsiWoQAACF1x9BklcIi3rGCVyLi2X4MjQLP2zMUXcdW94uBujXywY5uTI4Oxkw9MrGBsjKrrJc3l8XYNm8GUTtuA/9ZKVSFMc9QEFUTPkFiB55ArrkBlQkyc1Fxu694NvYgG9fD3x7e5WkZeWLHu4XruW5AXtQfE//nCULJ0eIAvxhG9AZAg6JjlXl7VSU8evu8otXAy7uZCUlKLx+szw5XodeHAUdcwMqKoq9j7y/LsDCvh74Dg5gKs+MVOn32ZDXsPT5C6Rvi9CYLK6NpacHbAP8YdOxQ5XDidXR9bdQVlBglCF0ZZlZKIwuH/qnSy+OHM/GBvXHjdUrgM05dRqlzxJhYW8PvoM9mMpBdaUvOEMDSFNgaljwYei15KvMxcVF4+y1FRmadM4p+Fi9ejVKSkowcuRI+Pn5wUrHO1BVEYvLL1zUPXD5tlIt40cTExPRr18/hIaGQiwWY9euXVi+fDkyMjLw0UcfGaWNDMPAgmcJiUz9ndCC0nTEJp9Gm8aG539U9YVr2aIZ+Ha2kGTnQpqTi+wDv8N5rObZRipq5CHEh181QPDc+jj2azZ+j8hGXnbVFzov4sXY90smgufq3suijbopdivLT8xD1v1MOLfS/c3OVF6IwgASthRSWRlkrAQs2CrPzLIsUjafQs6Zm1WeW9jQCQ0m9YNtgLdRgoJithAPcBPpSFLZZwt7uKChwXUA5Tkr+f/GovRZGsSJaSh9mqox8Cg/QIb8y3fhOED9jEv6uPhvMaaGpOHhE+3BJcsC3s0EBgUegPa7royVFUQd2kGakwtJbh6yjxyDsFEjCOrr1/spTk5BQXQMCmOuQpqXX/UBSg3ULzdAzsLeHqIO7ZC5Z59O5ble9KjLDagKIxTCpn072Ab6w8qruUGJxFXl7QgaNoSwcUNIc3MhyclFxu7f4DZtMhgL3X8eWZkMJQ8flQeNt6pOjldpo565AXLWvi1RGBWj85oQXHqvWJZFwT9XkHnwMCDRrZccAPgO9rAN8Ietf2cI3Ay7qVJVz4d1K18wQmH5a5iVhZw/I/WeHEFWWoqim7dQEB3DaaicpYcHXCaMU5t3pI1dj+4oWPM9iu/e06m8pvVsqhVbs4ZdGXot+SobMmQIjh07hpEjR6r9PZHJZDh58iSGDBliUD2cgo/Y2FhMmjQJCxYsMKjyyoT/zcqhbhiX/M2kKdBZv349+Hw+7OxeTq3Zo0cPjB07Fps2bcLkyZNha6Sp+AR8zcEHALzIuQEnkeH5H1WNc+WJRHCZ+r7i36xUCpZl9boAsXeyQPBcF4yY6ozIAzk4sCULKc+0/3Du+TkTvYbUQ5Nmho871ZZsXlH8n0/0Cj4MVU/gAlfLZnCzagZbC2e9ntO0nX8h67huq0QzQgtYONkZHHhIWQkSEIeniIMM6rsCjNnrwbO1Bltahpw/o4Eqeq7k8i7cMij4KCiU4bMVmfjpf7lVF/7P199nw74eDwtm6HdBUJG2mwBsSQns+/SGwOXle1PXheukhUUovHYdBVHRECc+59Q2LrkBFdl2CUTJ43gURld98apvvoC23ACNeDw4jxoOUaeORhvXzvD5YCwtNSY+s2Vi1A8eq/hs6LNQXllaOgqiY1AQHQNpju7vy4q45AbIMQwD59EjUfr8BSTpVSe36xtAykpLkbnvAApjrul8jIWzE5zfHQkr7xZGm32qqt9CCydHpWl+df0MsjIZSp/El685cuMWWLGWGyha1OvVE45D3tIrYJXj21jDZcL7SP5hvU6fE2Pk7RhdDev5MORa8lU3YcIELFmyBMHBwRg7diy8vb0hEolQWlqKx48fY+/eveDz+Rg2bBiSkpRvcjaqYlbFijgFH2KxGD4+PlwO1crNrTzpLCtLdYG1zP+6PjVNm+vg4KCyjcfjoU+fPrhx4wYePXqEDh06GKWdFnwroEz7D8295D9Qz7oBbC25XzDzbF5+OCzcXGHTthXyIl+u6Fp8JxbSgkLwbcuHshjSzWxlzcPgcU4YONYRl0/lY/+mTDy4pT7AkohZhH2egpW/Grb2R1lRGTLu6jYbTEJkPDrPCQDD060+FysPdLYoj8xv5ZxGmZZgEQAY8OBs2QSulp5wtWoGKz63QDX9wN/I2HdJ5/KlT9Pw5OMtqD/iNbiM7gEeh2mTASAdSchGmsbAQ4R6cEVjTudWh2EYOA7uCquWTZC0Zh8k6VVfeJXEPYc4JQvCBtzWpuHzgKUhTvhywcvj5deJbIVfP8W2Cj+I+gblFVUctuM0chiyfz9WaUG+GDi+NUDxb20XXKxUiuL7ceV3yO/crfpig2Fg5d0CJY+fqJQ1JDfg5ekZOI8cBnFiIspSUrWWlRWX6Pw8lucG7EPRzarzOJQPlKHo5m2IOnfS77gq8GysIS0tBU9kA/t+fZF9+HfFvsoL8lX1+KRFxSi68d+wqoSnWssCACMUwNLDQ+1Us1xzAyriWVnBdeL7SP7+R7Bl2nsm9Jk0QJySgvStEShLTdOrPZLMLJQ+fQYrI66dwq/Q82Hp6QFBo4YouPxykovCazfgOPTlgnxVBT1lGZnlPY3RMZDoMKSSb18PfDs7pWlwgfKez/rvjTZoqCUAWDZtAqdh7yBr/8Eqy9bIYVe6xXpmY8i15KsuKCgIQPlv5vXr11X2y38DBg5UnpyDYRjcu6db7x3AMfho1aoVnj6t+ktXX25ubnB2dkZcXJzKvtjYWAgEAnh7q/9Ck8lkkMlksKh056Hkv0RRSyPODqFpxquKpLIy3Ew8ZFD+B2NpCTAM+I72cJs7FWAY5J258PKqSipFYcwN1Hv9NU7nV4fPZ9DjrXroPtAOt68UYf+mTET/VahS7ua/RThzKBd9hztwrivtVhpYafljsWtS3mOV//zlkJPGQU3A8Bk8v5iIorQipN1MhVtH3ZKlrfl2sObbIaX4scbAw4IRwsXSA65WzeBi6WHwuh9ZJ2KQFnFW/wNlLDIOXoYkuwANZ7wFnkD/C5EGjDsawB0pbCLu4IrK/mbwNcnc8NbeTeC5egZSwg6jIFr1c1tZ3sXbikUI9a7Lmgcd52AwKnnPh9Owd1Cv+2soTXimvCBfdEz5BaSWCx5xUnL5HfKYa5DlVz2syqJ+fdgGluc58O3s8HThpy93csgN0IZnaVl+53Xtj9rv/MpkYEtLVcekV1KeG7ADEo5jqovvxyH1541wnTqZU36AOjxrG8iKiuE2fQqETZog79xfWhfkq4yVyVAS9xAF0TEoun27yot8oLxHwzbQH6L27VDyJF4p+OCSG6CNsFFDOI0cjszde7WW03XYVUHMVWTu3a8UZOsj58RJyIqK4PjOEKN878g/g4JGDeE6bTKkOTlKwYe6Bfkqk5WUoPDmLRRExaD0sYbFXCtgBBawadOmfEa1lt7IPnJUKfgQNmkMlwnjOeUhqWP3WjeUPn6itFK9Oobk7ZhMDev5MORa8lXXtm1bo14va8Ip+JgzZw5CQkIwePBgeBhx3nAAePPNN3Hw4EGkp6fDxaU8r6CoqAiRkZHo3r272qFTiYmJGDhwoMpQMKlUitOnT8PBwUHtrAdcaZvxqqLy/I8/0abxIE71MDweBG4ucJkxQZEAadXKGyX3HijKFP4bY9TgQ1E3w6BdVxHadRUhIa4EBzZn4a+juZBU+C3atCINAa9zX/sj5WoyhPUs0X5KB/gMb4lLX15QCj7smtghMKQrcp/mInbPXSReeKZz8AGUR+iPC5SHk1jxbRXDqRyNOKVuztmbSP7lD53L86yFsPFtChu/prDxbQprn0bgWRm+6GEuVJMjbWALN+g/+5Gu+LbWaLRoDHKOX0Hajj+1DsPKu3ALziN71rxFsrTgWVvDYcCbqNerBwB1C/LlKC3IV1nGrt9QEFX1MDzGygqiju1hGxgAS08PxXMkqXD3jmtuQFWEDdzgPHokMnbs0lpOVlSkcZYplmVR8O8VZB44rFdugDri58+RsWMnXCa+r1gkzxAW9ezgNOxtWLq7A0CVC/JVxEokeLFilU53yF8mx/sr5f1Ic1/2DHLNDaiKXZdAlD5+ojX/o6oLV5m4DFmHDqPgH9UbGPrK/+cKGEvL8sDcwM87z8YGFvXrw23G1PIJEmxsVBfki47RGHyUPn2GlJ9+1imYsvT0gG1gAGw6tFcKfiUVXkO7oG5wHPayp8UYFEPoXrzQuj6MobPOmUJN6/kAuF1LEmDvXu03MIyF01VjSkoKevbsiSFDhuCNN96Ap6en2sQefWe7AoCZM2fi1KlTmD59OubMmQOhUIiNGzeiqKhIEVhERUVhwoQJWLp0KUaPHo2mTZuib9++2LRpExiGQVBQEPLz8/Hrr7/iwYMH+Prrr3XK3teVBV9zVMgwPLRtPARiSRFKyvJRIslDXnEK6llzm97UdfYUWDi9/JGy7RqgFHyInz2HOCkFwkbGnT61Is+WVgj5rhHeX+CCI9uycGJPDooLZOVrf6xKw4JV3Nb+cPRyxLADI2BZr/z5tLBWfjtKissvYOw97NF1URAkJfpd0KSXJiBfkoF6Fi5wtWoGV6tmsNMzf0MXeZdj8WL9Ua1lLJztYOPnDptWTWHTqimsPFzB8I0zHroiH7QHD3wUowDFKEI+suFpghmuKtN1GFZZUiZKHifBuoXxhoCZmm1AZ6XVt7UtyKeO0L0poCn4YBhY+XiXX+y0baN2tjrJf3foDckN0IVt504ofRyP/MuaFzeUFhXDQs2oufLcgINKQRkjsADP2gY8G2vwrK3/+68NeDY24Cu2qdtvbdSLOgBwHjMKFhWG5mpbkK8yxsICwsaNNQYfjFAIUYd25UFj82Zqe6Mk/+WD1OvVA45DBnHKDdCF08jhKE18jrJk9bl02obslKVnIH1bBMQvXo7jZiwtFa8L36bSa1TpNeNXej2NseaNoh18PhrMngGLei/f+yoL8sXGQZKbp/bzIWjUEIyFhcbgQ5fkeGluHhihEM6jR8LWyMMC5XhWVnCd8D6Sv1+ncdKCmtnzUfNuJulyLUmqD6dvwE8//RQMw4BlWZw6dUpjOS7Bh5ubG3bu3InQ0FAsXLgQMpkM7du3R0REhCLPhGVZSKVSyCoklYWGhqJVq1Y4evQotm/fDoZh0Lp1a/z888/o3bs3l4epUcVhV3yeEFLZy6EKLCsDw/Dh4RxgnLqclO+OWbdrDcbaCmzxy6FEhf/GQDh8sFHq08aloQBTFrth7Oz6OLErB0e2Z+H0/v/W/uii/xSqzQd4Kf3bwkp98KFpf1UsGCF6ub4Pa75d1YU5yr/2CM/XHARkFfqdGcDS3VXRq2Hj1xQCF3uz3O1nGAbeaAuWZfEcT/AMYjQwYa9HZboMw8o7f6tWBR8WlfLJ1C/IdwuyEcPU9gqIOnVA1qEjSjkbFq4u5Rc7AZ1Vzl+ZNDfXKLkBunAc9jZKnz1TGdsup+nCR5qTC7ugrrDv+4bJAghDVH6O1S7IFxWtNvgAynu7Kq69AABW3l7l08e2b1dlcjwrFsNl4gcQtTcsN6AqPKEQrhPeR9LaH9Um2MuKi9Xm7bAsC2lhIZzfHfkyoLC2Mvn7TR+VX0NR507KkxmwLAqvXoV97zdUjuUJBBB16oj8S5cV2xiBBWza/Tejmg7J8TxrKzRc8FGVCyIa6uUQut/U7qecD93oci1J1EtLS8OlS5eQnp6ucR0/AOZfZHDZsmUQCAQmu5hq3rw5NmzYoHF/ly5dVMbyCYVCTJ8+HdOnTzdJmyqSD7vi84QI8AzG3aTjyC95mZSXlHMbDer5mqRunlAAUaf2KPj7Zbd4YdQ1OLwz0Gw/FCI7PkZNd8bQiU746/dc/B6RDd8O1gav/aHS86FnT0dlTpamvcDNKk1C4sqjAMOU92r4lfdq2Pg2Ad+2GpITKmAYBg3YprCAADwd1iUxpqqGYeX/fQeuE0x/IW1KqgvylaHw5i3YdVGdzYtvYwObtq1RfP8BRJ06lN8h99B9sgabNq0h6tDeaG3XhicQwGXCeCSt/kHtqu6aLnwEbq6oOaGGblQW5Hv4CJLsHLVrfFi38gVPJALPygq2AZ0hCvCHwFn3iRMcBw00WW9HZQI31/IhdBE7VXdqyNthGAZWnsYdQm1qfFsRbPxaKQWFBVExqPfG62o/W7YB/si/dLl8ocoA//KFKvVIInOdNMFsr6Fdl4D/htCp9pjWxOCjpuV8yFV1LUlU/fPPP5gxYwbEYnGV6/iZPfgYPXo05wp1ERcXhzVr1uDatWuQSqXw8/PDvHnzEBCgvTeB63H6suBZgcdYoJP7KNhbN0Qj+7aIKzmj2J+R/xhiSSGEFsZbCbwiUVd/peBDmpePkvsPYd3aNAGPJgIhg34jHdBnuD0kZYZ/+6gOu+KW7GgOUlaCAkkWPP9vPKy8GnCepcqUBIwQDeFeLXVXHIaVvHY/ytJyFPukuYUouvUEoo61N+FP4FIfls2bKa0+XhAVozb4AMqT1XnWNjovAlqRuS545AT166P+e6OR/r/tKvtq5DSfHKn0SLEsCmKuwqFfH5WyjIUFGi6YCwsnJ0433cz9Gtp26ojSJ/FKd/rlZMXFOq8OX9NV7pEqS0mFOPE5LN1Ve3uF7k3R+PPFeq/BI2fu19Bp5LD/htApr4UlrYGfwZq2yCDhbvXq1WBZFqNGjYKPjw9EItNcx+p0S3TdunVGqezHH3+sskxiYiKCg4ORlZWF0NBQhIeHQyQSYeLEibh1S/O0jVyP40JoYYMOTYfDSVR+p6ihfWugwtJzLGRIztV9yjF9WTb3gIWr8gwbBf/otsiUKfB4jFFWPFcZdmVgz4cp8RkLuIvawMa3SY0MPGoKa+8m8PhuOmwDlQPj3AvG/UxWB9sAf6V/lz5+gjINqz9b2NtzCjyqi6hdW9Tr1VNle42868qRvEeqooKoaI13+wTOxs8XMyWnoW9D2LSJyva69Bpa+7UCz1b54kjT5A4Mw3AOPKpD+RC68eWzXlZQI18/WTX8EZN48uQJpkyZguXLl2PcuHEYNmyYxj9D6HTFuHHjRkyZMgWpqdrngdckNTUVkydPxqZNm6osGx4eDqlUio0bN6J3797o1q0bwsLC4OLigrVr1xr9OC4a2vvBxe5lcqmlwBb1bZsrlUnKuVP5MKNhGAaiLp2VthXdugtpDZwFQx8W1soXZ5VzPkjtxLe1RqNPRsN14gDAovwrp+DKfciKa/cKs6IO7cBUymso0GGxvtrCcchbsKw0m2GNTHY1gG2gcq+4JD1Dp7U7agPGwgIuH4xXGWJV238nKmL4fIg6KefpFF67DtbA2dZqCoGbK+qPHqW0TZ63U5MwrPn/iGnY2tqiaVPT54nqFHxs2bIFd+/exYABA7B69WqVVQ01SUlJwZo1azBgwADcuHED4eHhWsuzLIszZ84gKCgITk4vx9MKhUL07dsXUVFRyM1VnUWH63FcMWrG0DdyeJlIKLQQwVHUFDJWx1V9ObDt0hmoeBdOIkHR1Zsmq88cNM12RWo/+TAs968nQeDqALa0DPlR96u7WQbhWVvDptLiYoUxV3VeXbmmYyws4DJhPHiil4ss1sRpPg1h3dIH/HrKE1Jom6q2thHUd4ZL8BilbXUvgFTugZQVFaPorulGHpibqFMH2HUPerlBKuW8ErvJsNXwR0yif//+uHjxosnr0Wm8SJcuXbB//34sWbIEmzdvxpYtW9C8eXO89tpraNasGZydnWFnZ4f8/HxkZmYiPj4e//zzDx49egSWZdG5c2esXLkS7u7ax5+npKQgNzdX7Zoc3t7ekEqlePjwIfz9/Y1ynDG52nmjkX1bNLD3g7NtM5Mn+Vo4OcLKxwslcS8Xrir4NwZ2PbqZtF5Tqk3Drgg38mFYKT8dQd6FW7DvZZ5EalOxDfRH4dVrin9LMrNQ+iQeVi28tBxVe1g4OqB+8FikbdwCoIYO+TAAw+eXr/lx9i/FtsLrN8pzdGrRMDltbNq2Qb03eiHv3HkAde81tGzSGIJGjVBW4aZoQVQ0RO3bVWOrjMtp6NsoffoM4sTnAP7L2zHDQnC6op6IumPhwoWYN28eQkJCMHLkSDRq1EjjUhWNGnFbZgHQI+G8cePG2LZtG/7++2/88ssvuHbtGh4/fqx2DCzLsrCwsEBgYCDGjx+Pvn376lRHenr5wjoVey/k5Nsy1Kyay/U4Y+LzBGjbZIhJ66hM1NVfKfgQxz9DWWqaxnnKazoLGxp29SqQD8PK+SMK0vwi8O1sqj6ohrLybgG+gwOkOTmKbQVR0XUm+AAAG79WsO/XB7mnz0Bax+6aA/+t+VEh+GBLSlB0+w5sO3esvkYZmePgt1Ca8BSl8Ql1atIAOdtAf2Qf/l3x7+LYOEjy8pTWBanN5L2Qyat/gKy4uDyArGKKbrOi4KPOKCwsBMuyOHHiBE6cOKGxHMMwuHePew+j3pmyr732Gl577TUUFBTg33//RUJCArKyspCfnw87Ozs4OzvDw8MDXbt21XsFSfF/XYnqoiz5tlI1c5dzPa6yk3e+0b2xNcFMANt263HAQlO1RKMBzasuoxAIYK6BFeo2IrD2qhsjesqN0LRjqTlbgfiPDDzB/I+N0o4a7aOQ6m6BaX37XXW3wPQWfFLdLTCduv7+lFu+orpboFZNXOeDcPPFF1/g/PnzsLOzQ9OmTU022xXnaXpsbW117tHQlVAoBAC1i5rIAwwrNVMEcj2OEEIIIYQYgHo+6ozo6Gi8/vrrWLduneLa2hRq1Byhbm7lK4dmZWWp7MvMLJ/C0tVVdUgR1+MIIYQQQgh31PNRd0gkEvTv39+kgQdQA4MPZ2dnldXLASA2NhYCgQDe3qoLk3E9jhBCCCGEGIB6PuqM9u3b48WLFyavx7RTMnHw5ptv4vLly4okcgAoKipCZGQkunfvrjGPhOtxhBBCCCGEG1rno+5YsmQJDh06hPPnz5u0HoatYavVpKamYujQoWjYsCHmzJkDoVCIjRs34tatW/jtt9/g4+ODqKgoTJgwAUuXLsXo0aN1Po4QQgghhBhP60Xfm73Ou6vmm73OV8Enn3yCzMxMXL58GS4uLmjcuLHayZwYhsH27ds511Ojhl0B5UOodu7cidDQUCxcuBAymQzt27dHRESEIoBgWRZSqRSyCot56XIcIYQQQggxHuqJqDt+//3llNVpaWlIS0tTW07dMhv6qHE9H4QQQgghpHZou9D8PR+3V1PPhynEx8dDIBDoFFw0btyYcz2cej6io6PRtGlTNGjQQGOZpKQkREVFYejQoVzbZjQSiQTr1q3Dxo0bMXDgQHz/veoHRSKRYMuWLThw4ACSkpLg7OyMQYMGYe7cuVVO02vIsTXFp59+ikOHDmncP3v2bMyZM0ftvvXr1yMsLEztvk6dOmH3bn3WIql5rly5gvfff1/j/rt378LCQvNHqbi4GOvXr8eJEyeQkZGBhg0bYuTIkZgyZQr4fL4pmmw2+fn5+OWXX3D69GmkpKTA1dUVPXv2xOzZs+Ho6KjxuIMHD2Lx4sVq97m5ueHChQumarLJxMXFYc2aNbh27RqkUin8/Pwwb948BAQEmOS42uKff/7Bzz//jLi4OLAsCy8vL0yfPh2vv/66xmN69+6tMenx66+/xqhRo0zUWvMZP348oqKi1O6bMWMG5s/XfHEVHR2NH3/8EXfv3gWPx0OnTp3w8ccf1/pe/ufPn6NPnz5ay6ibWAYAWrZsqfGYrVu3IigoyKC2VYf79+9j3rx5iI+Px4kTJ+Dlpbx4qSHfHUb93qFb2HVGs2bNzFIPp+Bj/PjxEIlEWLp0Kd5++221ZW7fvo3FixdXe/CRnJyMBQsWIDExEdo6eVauXIk9e/Zg1qxZCAwMxIMHD7B69WokJCQgPDxcax2GHFtTzJ49G8HBwSrbb9++jWXLlqFDhw5VnmP//v0q20y1QE11WLZsGVq3bq2yXVvgAQDz58/HlStXEBISAl9fX1y7dg3r1q1DRkYGlixZYqrmmpxYLMa0adPw8OFDzJkzB35+foiNjcUPP/yA6OhoHDp0qMrg6ueff4aLi4vSNnXjS2u6xMREBAcHw9PTE6GhobC2tsbWrVsxceJE7Nq1C+3atTPqcbXF2bNnMWvWLHTv3h3ffVe+kN/27dsxffp0/PDDDxg4cKDGY9944w3MmjVLZbshd9tqmtatW2PZsmUq27VNDX/9+nVMnDgRXbt2RVhYGCQSCcLDwzFu3DgcOHAATZs2NWWTTcrV1VXt7whQvviZpaWl1uPfffddvPvuuyrbzXVBZUw7d+7Et99+C3t7e7X7DfnuMPr3DgUfdU5paSmioqIQHx+P4uJiiEQieHl5ISAgoMprHl1wPkNRUREWLVqEf/75B0uXLq2xd/g/+eQT8Pl8HDp0CN27d1dbJjExEbt27cKkSZPw4YcfAgD8/f0BlF9wxsTEKP5tzGNrkiZNmqBJkyZK22QyGZYuXYq+ffuiR48eVZ6jbdu2pmpejdCsWTO9H2NUVBTOnTuHpUuX4r333gNQ/v7Izc3F1q1b8cEHH6g877XF+fPnce3aNaxatUpxkyEgIAClpaVYvXo1rly5UuXdRh8fn1r7+CsKDw+HVCrFxo0b4eTkBADo3Lkz+vfvj7Vr12Lbtm1GPa62+OGHH+Dh4YHw8HBFUBkYGIhevXohIiJCa/Dh4OBQ579TRCKR3o9x7dq1cHFxQXh4uGIu/rZt26J3797YsGEDvvnmG1M01SyEQqHa5yMyMhJxcXEaAxM5V1fXOvGeiYqKwqpVq7B06VIkJyerHVlgyHeHsb93KOejbjl06BBWrlyJ/Px8AOV51vJhWC4uLli+fLnWnmtdcJ5qd9GiRWjfvj0OHTqEESNG4OHDhwY1xFRGjx6Nbdu2qdxdrejs2bOQyWQYMmSI0vZBgwaBYRhERkaa5Niabv/+/Xjw4AEWLVpU3U2ptSIjI8EwDAYNGqS0ffDgwZBKpTh37lw1tcxwzZs3xzfffIO+ffsqbZcPf0hOTq6OZpkdy7I4c+YMgoKCFD/kQPmFVN++fREVFYXc3FyjHVdbsCyLmTNn4quvvlLqzbKysoKHhwdSUlKqsXW1U05ODmJiYtCvXz+lRcCcnJwQFBSEyMhIrT38tZFYLMbKlSsxfPhwtT3PdZGDgwP27NmDkSNHqt1vyHeHKb53aKrduuPSpUv47LPPIJPJMHjwYMybNw+fffYZPvroIwwYMAD5+fmYPXs2bt26ZVA9nHs+GjVqhJ07d2Lt2rX43//+h1GjRuGzzz5T2+VZnQYPHlxlmbi4ODAMg+bNmyttt7e3h4uLC+7fv2+SY2uy4uJirFu3DmPHjoW7u3t1N6fWiouLg6urq0rXuZeXFxiGqbXvD6D8MVQegwwAT548AYA60aOhi5SUFOTm5qJFixYq+7y9vSGVSvHw4UOVHlCux9UWDMOo7dkoKyvD06dPa31+QnV49OgRZDKZ2kVzvb29cebMGaSmpmrNx6xtdu3ahYyMDMydO7e6m2I2VX02DPnuMMn3Dq1wXmds3boVLi4u2LdvH9zc3FT2v3jxAsHBwdi0aRPWr1/PuR6DFhnk8/n4+OOP8csvv8Da2hpLly7FggULUFBQYMhpzS49PR12dnZql5N3cnJCRkaGSY6tyfbs2YO8vDxMnz5d52PWrVuHfv36oW3btujVqxdWrFiBoqIiE7bSvE6ePInhw4ejY8eOCAwMxNy5c/Hs2TOtx6SnpyvdXZITCoWwtbWtte8PTVJTU7Fhwwb4+PjolLi4a9cuDBo0CO3atUNQUBAWL16MzMxMM7TUeOQLm6p7neXb1L3OXI+r7davX4+cnBzFMERNEhMTMWfOHAQFBaFt27YYPnw4Tpw4YaZWmkd2djYWL16MHj16oE2bNnjrrbewc+dOjeXl016qm8xBvq3iQru1XUlJCTZt2oTRo0ervRCq7N69e5g8eTK6dOmC9u3bIzg4GP/8848ZWmpehnx3mOJ7h3o+6o47d+5g7NixGj9vjRs3xnvvvYerV68aVI9R1vno2bMnjhw5gpCQEJw4cQJ37txB//79jXFqtcrKyqq86LOzs9OatFeRWCzWmOQqEAi0XkAbcqw5cHmupFIptm3bhrfeegv169fXua7nz5/j008/ha2tLc6ePYsdO3YgNjYWERERBs8JbQq6PjdysbGxmDhxIho1aoQ7d+4gLCwMY8aMweHDhzW+18Riscake4FAgNLSUu4PwES4fr4yMzMxY8YMlJaW4rvvvgOPV/W9jcePH2Pu3LlwdnbGlStX8Msvv+DGjRs4ePAgrK2tDXoc5iIWiwGoT5SXb1P3OnM9rjbbs2cPNm7ciHfeeUdrvgdQfpd/ypQpGD9+PHJzc7FlyxbMnz8fRUVFGoej1DaJiYno168fQkNDIRaLsWvXLixfvhwZGRn46KOPVMq/au+Zw4cPIzMzE+PHj9epfGxsLKZOnYqZM2ciJSUF4eHhmDRpEjZv3ozXXnvNxK01H0PeByZ5D1EwUGcUFhZWOWlF48aNkZeXZ1A9Rltk0NXVFREREVi/fj02bNiAzZs3G+vUKlJTU/HWW29pLTNs2DB8++23Op3P0tISZWVlaveJxWKtyfSGHGsOXJ6r8+fPIyUlBcOHD9epjkmTJiE4OFjpTkqXLl1gYWGBzZs349KlSzolrJubrs/N8uXLcenSJTg5OSlmb+rcuTM8PT0xbdo07NixAyEhIWqPr+nvD3W4vGeePXuGKVOmIDs7G5s3b4avr6/W49966y307NlTKbj19/eHo6Mjli1bhiNHjmDMmDGGPRAzkfd6qnud5T/06l5nrsfVVmFhYVi/fj0GDx6MFStWaC27f/9+WFpaKgXu3bt3x6BBg/DDDz9gxIgRNfKGhj7Wr18PPp+vdIOjR48eGDt2LDZt2oTJkyfD1tZW6Rj5bE/q3jPybXXpPbN3714EBAToNIPXpUuXYGdnp/T4u3TpggEDBmDdunV1Kvgw5LvDFN87DA27qjMcHByQkJCgtUxCQgIcHBwMqodT8BEQEKC2y45hGMydOxeBgYFYuHChyYZPNGnSRONc31y4uroiPz8fYrFYZfhUVlaW1vnDDTnWHLg8V2fOnIGDg4POYz5FIpHau/v9+vXD5s2bERsbWyODD32eG3UTFvTo0QNWVla4d++exuNcXV3x6NEjle2lpaUoKCjQuXfOnPR9z9y/fx+TJk2ClZUVdu3apXY8emVWVlZqf+D69euHZcuWaX1Oaxp593RWVpbKPvl3oLrXmetxtdHSpUuxZ88eTJ48GR9//HGVgYO63xdra2t0794dv/32GzIyMrROIlIbqPvx5vF46NOnD27cuIFHjx6pTHEufz+8Cu+ZlJQU3L17V+N6QJWpez+4uLigQ4cOGtdTqa0M+e4wxfcODYOqOwICArBjxw68/vrraNOmjcr+69evIyIiQuPssbriFHzs2LFD6/6uXbvizz//RHZ2NqdGmVurVq3AsiwePHig9GRnZGQgPT0dw4YNM8mxNdXly5fRpUsXnYbNyKkLvkpKSgBAbT5MbaPu8UmlUkgkEq1zz7dq1QqXL19GVlaW0gWVPNHcz8/PNA02kxcvXmDKlClwdnbG5s2bdRqXLaftPVPVfP41iZubG5ydndUGbLGxsRAIBGoDMq7H1Tbff/899uzZgyVLlmhdrLMiqVQKhmFUvoPkw0Fq0/tDE5lMBplMpjJnvrbPgI+PDywsLDS+Z1xcXOpM8HHp0iUA0HlxQHXfJ0D5e6YuvF8qMuS7wyTfO9TzUWfMnDkT586dw7vvvot27drBx8cH1tbWyM7OxqNHjxAbGwsbGxvF0hJcGZRwro2NjU2tWQyqb9++EAgEOHLkiNJ2+b8HDBhgkmNrohcvXiApKUnnmWhYlkX//v3x/vvvq0zxePLkSQCo9Ss1L1myBF26dFEJpk+fPg2JRKL18clf/99//11p+5EjRyAQCNC7d2/jN9hMpFIp5s6dC6FQiK1bt+oVeEyYMAEDBgxQdPPL1db3zJtvvonLly8rJfsWFRUhMjIS3bt3Vxk+Y+hxtUVkZCQ2bNiAkJAQnQOPqKgotG3bFvv27VPaXlBQgEuXLsHHxwf16tUzRXPNJjExEe3atcO6deuUtkulUpw+fRoODg5qZyOys7NDUFAQTp06heLiYsX21NRU/Pvvv7Xu90abq1evQiAQqMwkqc7hw4fRrl07RcAi9+LFC9y+fbvWzhinjSHfHcb+3qGE87rDx8cHW7ZsgZeXF27cuIG9e/di+/bt+P3333Hv3j34+flh+/btame61IfRcj5qIrFYrBLd5+Xl4fbt2wDKZwdp0qQJ3NzcMHnyZGzatAn29vbo1q0b7t69i3Xr1mHo0KFKc4t/8MEHiI+Px4ULFwBAr2NrA/nc+9rG2Pr5+WHgwIFYs2YNGIbBBx98gGXLlmHu3LkYNWoU+Hw+IiMjsWfPHrz99tu17jmobOzYsTh+/DgmTpyIadOmwcXFBTdu3EB4eDi8vLyUppfu168f6tevj927dwMA2rVrh8GDB+OHH34An8+Hn58fLl++jN27d2PmzJm1+i7loUOHcOfOHSxcuBDJyckq63rIP1+A6vPywQcfYNasWZg8eTImTJgAkUiEf/75B1u2bEFgYKDK2iE13cyZM3Hq1ClMnz4dc+bMgVAoxMaNG1FUVIQFCxYAKL+onjBhApYuXYrRo0frfFxtJZFI8O2338LDwwPdunVTfO9W1LJlS5w4cQKfffYZNm7ciO7du6Nz585o164dVqxYgby8PHTs2BFpaWnYvHkzsrOzdc7lq8maNm2Kvn37YtOmTWAYBkFBQcjPz8evv/6KBw8e4Ouvv4ZAIMDhw4eVnhsACAkJwejRo/Hhhx9iypQpEIvF+PHHH2Fvb49p06ZV8yMznpSUFDRs2FDtasphYWEIDw/HsWPH0Lx5c/Tt2xceHh5YuHAh5syZg5YtWyIxMRHh4eHg8XiYN2+e+R+AAZ4/f6642SWf4ezRo0eKCWxatmyp83eHOb53GBlFA3VJ586dcfToUSQkJCjedyKRCD4+PjrlX+miTgcfaWlpKrOiXLp0SXF3pGLS7EcffQQHBwfs3r0bGzZsgKurKyZPnowZM2YoHS+TySCVSpW26XpsbSC/E6LtzodUKoVM9rKf9b333oODgwMiIiIQEhKC4uJiNGvWDJ988gk++OADk7fZ1Nq0aYOIiAhs2LABK1asQE5ODlxcXDBixAjMnj1bKd9FKpWqvD9WrlyJn376CVu2bEFGRgYaN26MxYsX6zyDS00VExMDAFi9erXa/RU/X5WflzfeeAObNm3C5s2bsWTJEhQUFKBRo0aYMmUKZsyYodeQv5rAzc0NO3fuRGhoKBYuXAiZTIb27dsjIiJC0YvIsqzKZ0eX42qrlJQUJCYmAoDG2anOnDmj+E6VPy98Ph+bNm3CL7/8gv3792P9+vUQCoXo0KEDduzYgc6dO5vtMZhSaGgoWrVqhaNHj2L79u1gGAatW7fGzz//rOgRrfzcAICvry8iIiKwevVqzJo1CxYWFggMDMSPP/5Yq29mVJaenq7xd0j+WZL3ttva2iIiIgI///wztmzZgrS0NNja2iIwMBCzZ8+udZ+lsLAwHDp0SGlbxXVOzpw5gyZNmuj03WGW7x2KPeqcsrIyNGnSBJ6enoptOTk5KCsr0zjDqz4Ytq4th0oIIYQQQswiYNJas9cZ/b/a3TNck+3btw+rV6/G9u3blWau3LdvH1atWoXFixdjxIgRBtVRu24vEkIIIYSQGoORmf+PmMb58+fxxRdfgMfjKZYWkHN3d4etrS0+//xzXLx40aB6KPgghBBCCCHcsNXwR0xi8+bN8PPzw+nTp1VmPevSpQv++OMP+Pn5YePGjQbVQ8EHIYQQQgjhhHo+6o4HDx7g3Xff1ZhvZW1tjVGjRuHBgwcG1VOnE84JIYQQQojp0NS3dUfl6e/VEQqFOpXThno+CCGEEEIINyxr/j9iEl5eXvjzzz817pfJZDh06BCt80EIIYQQQqoHDYOqO0aPHo0vvvgCkydPxtChQ+Hh4QErKysUFhbi4cOH2LdvH+7cuYPly5cbVA8FH4QQQgghhBMKPuqOUaNG4eHDh4iIiMDly5dV9rMsiw8++ACjRo0yqB4KPgghhBBCCCcUfNQtn332GYYPH44//vhDscK5jY0NWrRogYEDByqt/cEVBR+EEGIEjx8/xqhRo9C3b1+Ehoaavf7k5GSMGjUKzZs3x+bNmyEUCs3eBkLIK4hyMOocX19fowQZmlDCOSGEGCgvLw8ffvghGjdujP/7v/+rljY0bNgQa9euRXR0NL799ttqaQMh5NXDsOb/I+ZRUlKCsLAwJCUlGfW8FHwQQoiBVq1ahadPn+Kbb76BpaVltbUjMDAQY8aMwc6dO/HPP/9UWzsIIa8OWuej7iouLsZPP/2EFy9eGPW8FHwQQogBHj9+jEOHDuHNN99Eu3btqrs5mDNnDiwtLbFq1arqbgoh5FVAU+3WaawJnm8KPgghr6SYmBi0atUKY8eOVfly3b9/P1q2bIlFixZVeZ7NmzdDKpUiODhYafvFixfRsmVLrF+/HrGxsZg8eTL8/f3h7++PMWPGqMwksmbNGrRs2RKXL1/G7t270b9/f7Rt2xZvvPEGNmzYAAC4d+8eJkyYgI4dOyIoKAgLFixAZmam0nmcnJwwcOBAxMbGIiYmhstTQwghOqOeD6IvCj4IIa8kf39/TJ48GdeuXcOuXbsU2zMyMhAaGorGjRvjiy++0HoOlmVx/vx5iEQidO7cWWmfQCAAAMTHx2PSpEnw9fXFF198gUmTJiEuLg5Tp07Fw4cPVcofPHgQe/fuxfvvv4+PP/4YUqkU33//PTZu3Ijp06fD398fn3/+Odq2bYvjx4/js88+U2lXr169AAB//fUXp+eGEEJ0RTkfRF802xUh5JU1d+5cXLp0CWvXrkWfPn3QoEEDfP3118jPz0d4eDhsbW21Hh8bG4vMzEz07t0bFhbKX6cMwwAAjh8/jm3btqFbt25K+3744QecOnUK3t7eSuWjo6Nx8uRJWFtbAyjvyQgJCcGaNWuwadMm9OzZEwAwePBgvPbaa7h06RLEYrHS7FbdunUDwzC4ePEiFi5caOCzRAghWsgoGqgrnj17Bnd3d8W/LS0tMWzYMNSvX9+o9VDPByHklSUUCvHdd9+hrKwMX331Fc6ePYs//vgD06ZNg7+/f5XHJyQkAACaNWumsUzr1q2VAg8A8PPzAwCkpKSolH/77bcVgQcARXDi6uqqCDyA8h8Fd3d3SCQSZGdnK53D0dERDg4OePbsWZWPgRBCDEHDruqON998ExMmTMCJEydQVlYGGxsbrFy5UutvHBfU80EIeaV5e3sjJCQEK1aswJUrV9C6dWvMnj1bp2PlF/3Ozs4ay3h6eqpss7KyAgBIJBKVfU2aNFH6t0gkAgA0btxYpax8X1lZmco+Z2dnPHr0CMXFxUrBDCGEGBUlgNcZHTp0wL///osrV67A3t4eQ4cOxahRo+Dl5WXUeqjngxDyyhs6dCgsLS1RVFSEYcOGKfIvqpKXlwcAsLOz01hG38X+NNWta5vk5G2St5EQQkyBej7qjj179uDMmTP46KOP4OLigm3btmHw4MEYO3YsDh8+jJKSEqPUQ8EHIeSVt3z5ckgkEnh5eWHdunVITk7W6bh69eoBAPLz803ZPE7kQYe8jYQQYgoMy5r9j5hO48aNMWPGDBw9ehRHjhzB5MmTkZqaik8//RQ9evTA8uXLERsba1AdFHwQQl5pJ06cwLFjxzB58mSsX78eJSUl+OSTTyCTVX17zcnJCQBUprutCbKysmBjY0NDrgghJsVIWbP/EfNo2bIlFi5ciLNnz2LHjh3w8fHB7t27MXz4cLz33nucZ1Sk4IMQ8spKTU3FsmXL4OXlhTlz5sDLywuzZ89GVFQUtmzZUuXx8nyO+Ph4E7dUP9nZ2cjJyYGHh0d1N4UQUtex1fBnBFeuXEHLli01/lXMyZNIJPjll1/w5ptvok2bNujVqxdCQ0PVDkP67bffMGTIELRt2xavvfYavvjiC+Tk5KiU+/PPPzFixAi0b98eXbp0wbx585CUlKRSLjo6GuPGjUPHjh3RuXNnTJ06FQ8ePFApFxcXp5gspWPHjggODkZ0dLRhTxLKfye3bNmCb775BlevXgXLsmjfvj3i4+Mxc+ZMzJs3D2KxWK9zUsI5IeSVxLIsPvvsM+Tl5eGXX35R5GZMnjwZp06dwo8//oju3bujVatWGs/h6+uL+vXrIyoqChKJRGW63epy+fJlsCyLHj16VHdTCCF1XS0fBrVs2TK0bt1aZXvF7/OVK1diz549mDVrFgIDA/HgwQOsXr0aCQkJCA8PV5T73//+h1WrVuGDDz7A0qVL8eLFC3z33Xe4d+8efvvtN8U5T506hblz52LIkCH45JNPkJOTg++//x7jxo3D4cOHFcNlr1+/jokTJ6Jr164ICwuDRCJBeHg4xo0bhwMHDqBp06YAgMTERAQHB8PT0xOhoaGwtrbG1q1bMXHiROzatQvt2rXT6zmRyWQ4e/Ys9u/fj0uXLkEikaBevXoYP348xowZAy8vLxQXF2PdunXYunUrGjZsqNOivIrnVq/WEEJIHbFr1y5cunQJkyZNQocOHRTbLSwssGLFCowcORILFy7EwYMHYWlpqfYcDMOgZ8+eOHjwIK5fv46AgAAztV67CxcuAABef/316m0IIaTOY2r5Oh/NmjVD27ZtNe5PTEzErl27MGnSJHz44YcAoJiKfdmyZYiJiYG/vz8KCgoQFhaGgQMHKhZ/9ff3h4ODA6ZNm4bjx4/jnXfeAcuyCA0NRfv27fHdd98p1njy8vLCoEGD8OuvvyrqWbt2LVxcXBAeHq64Qda2bVv07t0bGzZswDfffAMACA8Ph1QqxcaNGxXDgTt37oz+/ftj7dq12LZtm07PxdOnT7F//34cOnQImZmZYFkW7dq1w5gxYzBo0CCl30Jra2ssWrQImZmZOHLkCAUfhBBSleDgYAQHB6vd5+vrizt37uh0nnHjxuHgwYPYuXOnUvDRpUsXxMXFqT1G3b45c+Zgzpw5KmWbNGmi8Tw7duxQ2ZaVlYWTJ0+idevWKquuE0KIsdX12afOnj0LmUyGIUOGKG0fNGgQli9fjsjISPj7++Pff/9FYWEhBg8erFSuZ8+esLe3R2RkJN555x3ExcXh+fPneP/99xWBBwC0aNECvr6+iIyMxIcffoicnBzExMRg/PjxSrMmOjk5ISgoCJGRkfj6668BAGfOnEFQUJAi8ADKZ1rs27cvdu7cidzcXNjb21f5WPv37w+GYWBtbY1Ro0Zh7NixWnv/AaB79+44depUleeuiIIPQggxQOvWrfH222/j6NGjuHXrlt7d28YWFhaGkpISve5CEUIIZ7W856MqcXFxYBgGzZs3V9pub28PFxcX3L9/X1EOeLkwrJz8WHk5+X8rlwPKA5BTp05BKpXi0aNHkMlkast5e3vjzJkzSE1NBcuyyM3NRYsWLdSWk0qlePjwoU4L57Zs2RJjxozB22+/rVhHqiodOnTAypUrdSorR8EHIYQYaMmSJYiKisKSJUuwf/9+jcO0TC06Ohq7d+/GuHHj0KVLl2ppAyHk1VLbp749efIkVq1ahfj4eAgEAnTt2hULFy6Eu7s7ACA9PR12dnZq12xycnJCRkaGopx8m7py8uCkqnJlZWXIzc1FWloaAMDR0VGlnHxbeno62P+ef03nA6BoY1WOHDmiU7mK3N3dFc+Vrij4IIQQAzk4OCiSAD///HN89913Zm9DSkoK5s+fj4CAAOr1IISYTw0LPsrKyvDs2TOtZSouDBsbG4uJEyeiUaNGuHPnDsLCwjBmzBgcPnwYrq6uEIvFWhd/LSoqAgDFjE/qygoEApSWlupUTl5Gl3Lyc+pTriag4IMQQoygdevWuH79erXV36BBA1y6dKna6ieEvJpq2robqampeOutt7SWGTZsGJYvX45Lly7ByckJfD4fQHmStqenJ6ZNm4YdO3YgJCQElpaWKCsrU3sesVgMKysrAFD0eJeVlSm2VSwn31+xnLrzyctoKyffZmVlpViTStv5KrenulHwQQghhBBCuKlhPR/aJumozMXFRWVbjx49YGVlhXv37gEAXF1dkZ+fD7FYrDL0KisrCy1btlSUA8oXna3YsyIvJ99fsVxlWVlZsLKygr29vaJcVlaWSjn5sa6urophV1WVq0lokUFCCCGEEMKNlDX/n5GoWxxPKpVCIpEoeh5atWoFlmVVFvbLyMhAeno6/Pz8AEDx38qBj0QiwYMHDxRriWgqB5QPAfP19QWPx4OPjw8sLCw0lnNxcYGrqyvc3Nzg7OyssZxAIFCbtF6dKPgghBBCCCGcMCxr9j9jWLJkCbp06YLs7Gyl7adPn4ZEIlFMnd63b18IBAKVZGz5vwcMGACgfAp1BwcHlXKRkZEoKipSlGvRogW8vLxw9OhRxZApALh9+zaePHmiKGdnZ4egoCCcOnUKxcXFinKpqan4999/FeUA4M0338Tly5cVyewAUFRUhMjISHTv3h22trbcniQTYVi2hvWXEUIIIYSQWmFA+y/MXufJm/9n8Dnu3LmDcePGKXI8XFxccOPGDYSHh6Nhw4bYt2+fYrrZ77//Hps2bcKHH36Ibt264e7du1izZg0GDBiAVatWKc65d+9efPHFFxg/fjwGDBiAZ8+eYdWqVfDx8UFERIRiXY8LFy5g+vTpGDhwIMaMGYPMzEx89913sLKywoEDB2BtbQ2gfFre0aNHo1OnTpgyZQrEYjF+/PFHpKen49ChQ4rhVKmpqRg6dCgaNmyIOXPmQCgUYuPGjbh16xZ+++03+Pj4GPx8GRMFH4QQQgghhJMBbZeYvc6Tt78xynlu3bqFDRs24NatW8jJyYGLiwv69OmD2bNnw8HBQVFOJpNh+/bt2L17N5KSkuDq6oqhQ4dixowZKnkghw8fxpYtW5CQkAB7e3sMGDAA8+bNU+l9OH/+PNavX48HDx7A2toar7/+Oj7++GPUr19fqdzNmzexevVq3L59GxYWFggMDMSiRYvg4eGhVO7JkycIDQ1FdHQ0ZDIZ2rdvj5CQEK2rt1cXCj4IIYQQQggnA1pXQ/Bx1zjBB6keNNsVIYQQQgjhhKmQt0CILij4IIQQQggh3MhoAA3RDwUfhBBCCCGEGxq9T/REwQchhBBCCOGGhl0RPVHwQQghhBBCuKFhV0RPFHwQQgghhBBuZNLqbgGpZSj4IIQQQggh3FDPB9ETBR+EEEIIIYQbSjgneqLggxBCCCGEcEMJ50RPFHwQQgghhBBuKPggeqLggxBCCCGEcEPBB9ETBR+EEEIIIYQbSjgneqLggxBCCCGEcMJKaapdoh8KPgghhBBCCDc02xXREwUfhBBCCCGEG8r5IHqi4IMQQgghhHBCw66Ivij4IIQQQggh3NCwK6InCj4IIYQQQgg31PNB9ETBByGEEEII4YSlqXaJnij4IIQQQggh3LCUcE70Q8EHIYQQQgjhhBLOib4YlqVMIUIIIYQQQojp8aq7AYQQQgghhJBXAwUfhBBCCCGEELOg4IMQQgghhBBiFhR8EEIIIYQQQsyCgg9CCCGEEEKIWVDwQQghhBBCCDELCj4IIYQQQgghZkHBByGEEEIIIcQsKPgghBBCCCGEmMX/A+Svpf/6gT6yAAAAAElFTkSuQmCC", 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