{ "cells": [ { "cell_type": "markdown", "id": "e6f395d2-35c2-47f0-b0cb-55a7a832c3b2", "metadata": {}, "source": [ "# Setup\n", "\n", "Install missing packages\n", "\n", "```bash\n", "mamba install -c conda-forge -y ipykernel ipywidgets matplotlib numba numpy plotly pythreejs streamlit\n", "```\n", "\n", "or create new conda environment\n", "\n", "```bash\n", "mamba env create -f ../streamlit-plotly.yaml\n", "```\n", "\n", "Activate the newly created environment:\n", "\n", "```bash\n", "mamba activate streamlit-plotly\n", "```\n", "\n", "```bash\n", "python -m ipykernel install --user --name=streamlit-plotly --display-name \"Python (Streamlit-Plotly)\"\n", "```\n", "\n" ] }, { "cell_type": "code", "execution_count": 13, "id": "e5ad694e-16d8-4b44-837b-3b1c167afd78", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "/home/codespace/.python/current/bin/python\n" ] } ], "source": [ "!which python" ] }, { "cell_type": "code", "execution_count": 14, "id": "56498654-4c67-4394-bd75-f4f5ea7597af", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from ipywidgets import interact, widgets" ] }, { "cell_type": "code", "execution_count": 15, "id": "45f8b434-28cc-4a6c-8741-7ba6dfa3a27e", "metadata": {}, "outputs": [], "source": [ "def draw_tree(x1, y1, angle, depth, angle_change, length_factor, linewidth_factor):\n", " if depth > 0:\n", " x2 = x1 + np.cos(angle) * depth * length_factor\n", " y2 = y1 + np.sin(angle) * depth * length_factor\n", " plt.plot([x1, x2], [y1, y2], color='green', linewidth=depth * linewidth_factor)\n", " draw_tree(x2, y2, angle - angle_change, depth - 1, angle_change, length_factor, linewidth_factor)\n", " draw_tree(x2, y2, angle + angle_change, depth - 1, angle_change, length_factor, linewidth_factor)\n" ] }, { "cell_type": "code", "execution_count": 16, "id": "2792510f-bc33-4c10-b277-b6d75787de4b", "metadata": {}, "outputs": [], "source": [ "def plot_tree(depth, angle_deg, length_factor, linewidth_factor):\n", " plt.figure(figsize=(8, 8))\n", " plt.axis('off')\n", " draw_tree(0, -100, np.pi/2, depth, np.deg2rad(angle_deg), length_factor, linewidth_factor)\n", " plt.show()\n" ] }, { "cell_type": "code", "execution_count": 17, "id": "0a9af2d2-36fd-41a0-8b2b-be5296f77b59", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "107d086b8188422489fa20b86f2d3c75", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(IntSlider(value=9, description='Depth', max=15, min=1), FloatSlider(value=30.0, descript…" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "interact(\n", " plot_tree,\n", " depth=widgets.IntSlider(min=1, max=15, step=1, value=9, description='Depth'),\n", " angle_deg=widgets.FloatSlider(min=0, max=90, step=1, value=30, description='Branch Angle'),\n", " length_factor=widgets.FloatSlider(min=5, max=20, step=0.5, value=10, description='Branch Length'),\n", " linewidth_factor=widgets.FloatSlider(min=0.1, max=2, step=0.1, value=0.5, description='Branch Width')\n", ")\n" ] }, { "cell_type": "code", "execution_count": 18, "id": "8b0baf67-f84f-4f58-a67b-06e2cbd0efd8", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "e60cd18cf0374459b7ead8a609efe529", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(IntSlider(value=9, description='Depth', max=15, min=1), FloatSlider(value=60.0, descript…" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from ipywidgets import interact, widgets\n", "\n", "def draw_tree(x1, y1, angle, depth, angle_range_deg, length_factor, linewidth_factor, length_scale, width_scale, branching_factor, branching_scale, initial_depth):\n", " if depth > 0:\n", " scale_exponent = initial_depth - depth\n", " scaled_length = length_factor * (length_scale ** scale_exponent)\n", " scaled_width = linewidth_factor * (width_scale ** scale_exponent)\n", " \n", " x2 = x1 + np.cos(angle) * scaled_length\n", " y2 = y1 + np.sin(angle) * scaled_length\n", " plt.plot([x1, x2], [y1, y2], color='green', linewidth=scaled_width)\n", " \n", " # Compute current branching factor\n", " current_branching_factor = max(1, int(branching_factor * (branching_scale ** scale_exponent)))\n", " \n", " angle_range = np.deg2rad(angle_range_deg)\n", " angles = np.linspace(angle - angle_range / 2, angle + angle_range / 2, current_branching_factor)\n", " for branch_angle in angles:\n", " draw_tree(x2, y2, branch_angle, depth - 1, angle_range_deg, length_factor, linewidth_factor, length_scale, width_scale, branching_factor, branching_scale, initial_depth)\n", "\n", "def plot_tree(depth, angle_range_deg, length_factor, linewidth_factor, length_scale, width_scale, branching_factor, branching_scale):\n", " plt.figure(figsize=(8, 8))\n", " plt.axis('off')\n", " draw_tree(0, -100, np.pi/2, depth, angle_range_deg, length_factor, linewidth_factor, length_scale, width_scale, branching_factor, branching_scale, depth)\n", " plt.show()\n", " \n", "interact(\n", " plot_tree,\n", " depth=widgets.IntSlider(min=1, max=15, step=1, value=9, description='Depth'),\n", " angle_range_deg=widgets.FloatSlider(min=0, max=180, step=1, value=60, description='Angle Range'),\n", " length_factor=widgets.FloatSlider(min=1, max=100, step=1, value=10, description='Base Length'),\n", " linewidth_factor=widgets.FloatSlider(min=0.1, max=10, step=0.1, value=1, description='Base Width'),\n", " length_scale=widgets.FloatSlider(min=0.5, max=1.5, step=0.1, value=0.7, description='Length Scale'),\n", " width_scale=widgets.FloatSlider(min=0.5, max=1.5, step=0.1, value=0.7, description='Width Scale'),\n", " branching_factor=widgets.IntSlider(min=1, max=5, step=1, value=2, description='Branches'),\n", " branching_scale=widgets.FloatSlider(min=0.5, max=2.0, step=0.1, value=1.0, description='Branching Scale')\n", ")\n" ] }, { "cell_type": "code", "execution_count": 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" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "debf37c3e35142759ab6c2949e552db4", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(IntSlider(value=4, description='Depth', max=8, min=1), FloatSlider(value=30.0, descripti…" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "import plotly.graph_objects as go\n", "from ipywidgets import interact, widgets\n", "\n", "def cylinder_between_points(p0, p1, radius, n=8):\n", " \"\"\"\n", " Generate the mesh data for a cylinder between two points p0 and p1.\n", " \"\"\"\n", " # Vector from p0 to p1\n", " v = np.array(p1) - np.array(p0)\n", " # Length of the cylinder\n", " length = np.linalg.norm(v)\n", " if length == 0:\n", " return None # Avoid division by zero\n", " # Unit vector in direction of cylinder axis\n", " v = v / length\n", "\n", " # Create arbitrary vectors orthogonal to v\n", " not_v = np.array([1, 0, 0])\n", " if (v == not_v).all():\n", " not_v = np.array([0, 1, 0])\n", " n1 = np.cross(v, not_v)\n", " n1 /= np.linalg.norm(n1)\n", " n2 = np.cross(v, n1)\n", "\n", " # Generate circle points in the plane orthogonal to v\n", " t = np.linspace(0, 2 * np.pi, n)\n", " circle = np.array([np.cos(t), np.sin(t)])\n", " circle_pts = radius * (np.outer(n1, circle[0]) + np.outer(n2, circle[1]))\n", "\n", " # Points at base and top of cylinder\n", " x_base = p0[0] + circle_pts[0]\n", " y_base = p0[1] + circle_pts[1]\n", " z_base = p0[2] + circle_pts[2]\n", "\n", " x_top = x_base + v[0] * length\n", " y_top = y_base + v[1] * length\n", " z_top = z_base + v[2] * length\n", "\n", " # Combine base and top points\n", " x = np.concatenate([x_base, x_top])\n", " y = np.concatenate([y_base, y_top])\n", " z = np.concatenate([z_base, z_top])\n", "\n", " # Define faces of the cylinder\n", " faces = []\n", " n_points = n\n", " for i in range(n_points):\n", " next_i = (i + 1) % n_points\n", " # Side faces\n", " faces.append([i, next_i, n_points + next_i])\n", " faces.append([i, n_points + next_i, n_points + i])\n", " return x, y, z, faces\n", "\n", "def draw_tree_3d(x1, y1, z1, theta, phi, depth, angle_range_deg, length_factor,\n", " linewidth_factor, length_scale, width_scale, branching_factor,\n", " branching_scale, initial_depth, cylinders):\n", " if depth > 0:\n", " scale_exponent = initial_depth - depth\n", " scaled_length = length_factor * (length_scale ** scale_exponent)\n", " scaled_width = linewidth_factor * (width_scale ** scale_exponent)\n", "\n", " # Compute the direction vector\n", " direction = np.array([\n", " np.sin(theta) * np.cos(phi),\n", " np.sin(theta) * np.sin(phi),\n", " np.cos(theta)\n", " ])\n", "\n", " # Compute the new point\n", " x2 = x1 + direction[0] * scaled_length\n", " y2 = y1 + direction[1] * scaled_length\n", " z2 = z1 + direction[2] * scaled_length\n", "\n", " # Store the cylinder data\n", " cylinder_data = cylinder_between_points(\n", " [x1, y1, z1],\n", " [x2, y2, z2],\n", " scaled_width\n", " )\n", " if cylinder_data:\n", " x_cyl, y_cyl, z_cyl, faces = cylinder_data\n", " cylinders.append({\n", " 'x': x_cyl,\n", " 'y': y_cyl,\n", " 'z': z_cyl,\n", " 'faces': faces,\n", " 'color': 'green'\n", " })\n", "\n", " # Compute current branching factor\n", " current_branching_factor = max(1, int(branching_factor * (branching_scale ** scale_exponent)))\n", "\n", " # Generate new branches\n", " angle_range_rad = np.deg2rad(angle_range_deg)\n", "\n", " for _ in range(current_branching_factor):\n", " # Random angles within the specified range\n", " delta_theta = angle_range_rad * (np.random.rand() - 0.5)\n", " delta_phi = angle_range_rad * (np.random.rand() - 0.5)\n", " new_theta = theta + delta_theta\n", " new_phi = phi + delta_phi\n", " # Recursive call\n", " draw_tree_3d(\n", " x2, y2, z2, new_theta, new_phi, depth - 1, angle_range_deg,\n", " length_factor, linewidth_factor, length_scale, width_scale,\n", " branching_factor, branching_scale, initial_depth, cylinders\n", " )\n", "\n", "def plot_tree_3d(depth, angle_range_deg, length_factor, linewidth_factor,\n", " length_scale, width_scale, branching_factor, branching_scale):\n", " cylinders = []\n", " initial_theta = 0 # Initial angle from z-axis\n", " initial_phi = 0 # Initial angle in x-y plane\n", " initial_depth = depth\n", " draw_tree_3d(\n", " 0, 0, 0, initial_theta, initial_phi, depth, angle_range_deg,\n", " length_factor, linewidth_factor, length_scale, width_scale,\n", " branching_factor, branching_scale, initial_depth, cylinders\n", " )\n", "\n", " # Prepare data for plotting\n", " fig = go.Figure()\n", " for cyl in cylinders:\n", " fig.add_trace(go.Mesh3d(\n", " x=cyl['x'],\n", " y=cyl['y'],\n", " z=cyl['z'],\n", " color=cyl['color'],\n", " opacity=1.0,\n", " i=[face[0] for face in cyl['faces']],\n", " j=[face[1] for face in cyl['faces']],\n", " k=[face[2] for face in cyl['faces']],\n", " flatshading=True,\n", " showscale=False\n", " ))\n", "\n", " fig.update_layout(\n", " scene=dict(\n", " xaxis=dict(visible=False),\n", " yaxis=dict(visible=False),\n", " zaxis=dict(visible=False),\n", " aspectmode='data'\n", " ),\n", " showlegend=False\n", " )\n", " fig.show()\n", "\n", "interact(\n", " plot_tree_3d,\n", " depth=widgets.IntSlider(min=1, max=8, step=1, value=4, description='Depth'),\n", " angle_range_deg=widgets.FloatSlider(min=0, max=180, step=1, value=30, description='Angle Range'),\n", " length_factor=widgets.FloatSlider(min=1, max=10, step=1, value=5, description='Base Length'),\n", " linewidth_factor=widgets.FloatSlider(min=0.1, max=2, step=0.1, value=0.5, description='Base Width'),\n", " length_scale=widgets.FloatSlider(min=0.5, max=1.5, step=0.05, value=0.7, description='Length Scale'),\n", " width_scale=widgets.FloatSlider(min=0.5, max=1.0, step=0.05, value=0.7, description='Width Scale'),\n", " branching_factor=widgets.IntSlider(min=1, max=5, step=1, value=2, description='Branches'),\n", " branching_scale=widgets.FloatSlider(min=0.5, max=1.0, step=0.1, value=1.0, description='Branching Scale')\n", ")\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "9b007b29-7b72-466b-83ca-d03efb7c725e", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "color": "green", "flatshading": true, "i": [ 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7 ], "j": [ 1, 9, 2, 10, 3, 11, 4, 12, 5, 13, 6, 14, 7, 15, 0, 8 ], "k": [ 9, 8, 10, 9, 11, 10, 12, 11, 13, 12, 14, 13, 15, 14, 8, 15 ], "opacity": 1, "showscale": false, "type": "mesh3d", "x": [ 0, -0.35355339059327373, -0.5, -0.3535533905932738, -6.123233995736766e-17, 0.35355339059327373, 0.5, 0.35355339059327384, 0, -0.2474873734152916, -0.35, -0.24748737341529164, -4.286263797015736e-17, 0.2474873734152916, 0.35, 0.24748737341529167 ], "y": [ 0.5, 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" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "5cd7e54d631c4b7b8171d7fc10ebf8f2", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(IntSlider(value=8, description='Depth', max=16, min=1), FloatSlider(value=30.0, descript…" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "import plotly.graph_objects as go\n", "from ipywidgets import interact, widgets\n", "\n", "def cylinder_between_points(p0, p1, radius_base, radius_top, n=8):\n", " \"\"\"\n", " Generate the mesh data for a tapered cylinder (frustum) between two points p0 and p1.\n", " \"\"\"\n", " # Vector from p0 to p1\n", " v = np.array(p1) - np.array(p0)\n", " # Length of the cylinder\n", " length = np.linalg.norm(v)\n", " if length == 0:\n", " return None # Avoid division by zero\n", " # Unit vector in direction of cylinder axis\n", " v = v / length\n", "\n", " # Create arbitrary vectors orthogonal to v\n", " not_v = np.array([1, 0, 0])\n", " if (v == not_v).all():\n", " not_v = np.array([0, 1, 0])\n", " n1 = np.cross(v, not_v)\n", " n1 /= np.linalg.norm(n1)\n", " n2 = np.cross(v, n1)\n", "\n", " # Generate circle points in the plane orthogonal to v\n", " t = np.linspace(0, 2 * np.pi, n, endpoint=False)\n", " circle_base = np.array([np.cos(t), np.sin(t)]) * radius_base\n", " circle_top = np.array([np.cos(t), np.sin(t)]) * radius_top\n", "\n", " # Base circle points\n", " x_base = p0[0] + n1[0] * circle_base[0] + n2[0] * circle_base[1]\n", " y_base = p0[1] + n1[1] * circle_base[0] + n2[1] * circle_base[1]\n", " z_base = p0[2] + n1[2] * circle_base[0] + n2[2] * circle_base[1]\n", "\n", " # Top circle points\n", " x_top = p1[0] + n1[0] * circle_top[0] + n2[0] * circle_top[1]\n", " y_top = p1[1] + n1[1] * circle_top[0] + n2[1] * circle_top[1]\n", " z_top = p1[2] + n1[2] * circle_top[0] + n2[2] * circle_top[1]\n", "\n", " # Combine base and top points\n", " x = np.concatenate([x_base, x_top])\n", " y = np.concatenate([y_base, y_top])\n", " z = np.concatenate([z_base, z_top])\n", "\n", " # Define faces of the cylinder\n", " faces = []\n", " n_points = n\n", " for i in range(n_points):\n", " next_i = (i + 1) % n_points\n", " # Side faces (two triangles per side)\n", " faces.append([i, next_i, n_points + next_i])\n", " faces.append([i, n_points + next_i, n_points + i])\n", " return x, y, z, faces\n", "\n", "def draw_tree_3d(x1, y1, z1, theta, phi, depth, angle_range_deg, length_factor,\n", " linewidth_factor, length_scale, width_scale, branching_factor,\n", " branching_scale, initial_depth, cylinders):\n", " if depth > 0:\n", " scale_exponent = initial_depth - depth\n", " scaled_length = length_factor * (length_scale ** scale_exponent)\n", " scaled_width_base = linewidth_factor * (width_scale ** scale_exponent)\n", " # Calculate the top width\n", " scaled_width_top = linewidth_factor * (width_scale ** (scale_exponent + 1))\n", "\n", " # Compute the direction vector\n", " direction = np.array([\n", " np.sin(theta) * np.cos(phi),\n", " np.sin(theta) * np.sin(phi),\n", " np.cos(theta)\n", " ])\n", "\n", " # Compute the new point\n", " x2 = x1 + direction[0] * scaled_length\n", " y2 = y1 + direction[1] * scaled_length\n", " z2 = z1 + direction[2] * scaled_length\n", "\n", " # Store the cylinder data\n", " cylinder_data = cylinder_between_points(\n", " [x1, y1, z1],\n", " [x2, y2, z2],\n", " scaled_width_base,\n", " scaled_width_top\n", " )\n", " if cylinder_data:\n", " x_cyl, y_cyl, z_cyl, faces = cylinder_data\n", " cylinders.append({\n", " 'x': x_cyl,\n", " 'y': y_cyl,\n", " 'z': z_cyl,\n", " 'faces': faces,\n", " 'color': 'green'\n", " })\n", "\n", " # Compute current branching factor\n", " current_branching_factor = max(1, int(branching_factor * (branching_scale ** scale_exponent)))\n", "\n", " # Generate new branches\n", " angle_range_rad = np.deg2rad(angle_range_deg)\n", "\n", " for _ in range(current_branching_factor):\n", " # Random angles within the specified range\n", " delta_theta = angle_range_rad * (np.random.rand() - 0.5)\n", " delta_phi = angle_range_rad * (np.random.rand() - 0.5)\n", " new_theta = theta + delta_theta\n", " new_phi = phi + delta_phi\n", " # Recursive call\n", " draw_tree_3d(\n", " x2, y2, z2, new_theta, new_phi, depth - 1, angle_range_deg,\n", " length_factor, linewidth_factor, length_scale, width_scale,\n", " branching_factor, branching_scale, initial_depth, cylinders\n", " )\n", "\n", "def plot_tree_3d(depth, angle_range_deg, length_factor, linewidth_factor,\n", " length_scale, width_scale, branching_factor, branching_scale):\n", " cylinders = []\n", " initial_theta = 0 # Initial angle from z-axis\n", " initial_phi = 0 # Initial angle in x-y plane\n", " initial_depth = depth\n", " draw_tree_3d(\n", " 0, 0, 0, initial_theta, initial_phi, depth, angle_range_deg,\n", " length_factor, linewidth_factor, length_scale, width_scale,\n", " branching_factor, branching_scale, initial_depth, cylinders\n", " )\n", "\n", " # Prepare data for plotting\n", " fig = go.Figure()\n", " for cyl in cylinders:\n", " fig.add_trace(go.Mesh3d(\n", " x=cyl['x'],\n", " y=cyl['y'],\n", " z=cyl['z'],\n", " color=cyl['color'],\n", " opacity=1.0,\n", " i=[face[0] for face in cyl['faces']],\n", " j=[face[1] for face in cyl['faces']],\n", " k=[face[2] for face in cyl['faces']],\n", " flatshading=True,\n", " showscale=False\n", " ))\n", "\n", " fig.update_layout(\n", " scene=dict(\n", " xaxis=dict(visible=False),\n", " yaxis=dict(visible=False),\n", " zaxis=dict(visible=False),\n", " aspectmode='data'\n", " ),\n", " showlegend=False\n", " )\n", " fig.show()\n", "\n", "interact(\n", " plot_tree_3d,\n", " depth=widgets.IntSlider(min=1, max=16, step=1, value=8, description='Depth'),\n", " angle_range_deg=widgets.FloatSlider(min=0, max=180, step=1, value=30, description='Angle Range'),\n", " length_factor=widgets.FloatSlider(min=1, max=10, step=1, value=5, description='Base Length'),\n", " linewidth_factor=widgets.FloatSlider(min=0.1, max=2, step=0.1, value=0.5, description='Base Width'),\n", " length_scale=widgets.FloatSlider(min=0.5, max=2, step=0.05, value=0.7, description='Length Scale'),\n", " width_scale=widgets.FloatSlider(min=0.5, max=2, step=0.05, value=0.7, description='Width Scale'),\n", " branching_factor=widgets.IntSlider(min=1, max=10, step=1, value=2, description='Branches'),\n", " branching_scale=widgets.FloatSlider(min=0.5, max=1.0, step=0.1, value=1.0, description='Branching Scale')\n", ")\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "6188cb7b-7268-49a6-b37c-dbcec9993169", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "color": "saddlebrown", "flatshading": true, "i": [ 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7 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hchYJrhOA7LccdowfC+T6WVdau5y0KttXLc6e60OG1dDQ6hE0fOS42NYjUWZu0OYD2jRn0RJCmxrqb8gYU4zb3WuejdzGKEEyJwzpne5Kw1MvKu9WXRFn62eSPuFhden1o14OuGZrF5PcLhJ84y/e8SIzQHygDP23+MDTW2Or86PMFclbOgjY5hF6F+dETOmg0nE9MYlu3ojoaj7gcQlwPNObN67PeD/AXIbqe3Tt5MjPqY6bCadqxtivW7lc3evVJuuEySpOCX67+IvPk9z4LYY+SxsEAUFAEBAE8oOAkOD5wVVKFQQEAUFAEOhkCPh6RTMBDcuHC6uHU1lZGb379lv02wNvKsIbC1AfgjwIHqiL6xbemSYCfb2ZddIG18COwofIMb1XuW35VtXavF1duLDPOgfdBPb5Un2BDL977jXWcQQhM2F6ndo40RXIaB82MKCA9k08Rj5462M0f2kDTb1+gboMbTBJeb3+uAS9rQ++RDjmjXlKQS+PVe9TP3N2FsZR7ExsViiN2/blbV74jqvk61wI2PzAMQ8lEGbhx9Ekulnp/d6Bt9SpDz3FPYVT+F5FrzFI9ewqzXaiqTMFjNQJbX6ngn0dhAeuU1qMBZ5zIMH5BBKIcdjBSRIEBAFBQBAQBEwEhASXOSEICAKCgCBQ0giw9QmCYPoQp8j/wOK5GYEuscBCQhm7d27PCPbHpDgCP46unaTyrX9oeRYJiDLgL+5LkrMvOers038A9e1XZbWXMAdPt9Vg0jKMzA6yu2DVcb4miS+xaqufg4rmQy0eZgECAoaoTfm4m8SMvoERhpvZf5f6XldHmuSPGbDVrDMpn3BbEEpb/9jDXicodBKD56OubtfzwvfeJ4kVig9KkicIAVdcAAQkZnsqQbAwCNhsUDAOsOqqnzkx6/QN4g7kayO0MD221xKFAEfeV9qDXZqWJ7XTZqsTQ8WUcBoMpDbiqnxwOKXi1slvV1v5dBjGG+9EiNOCGC0qZst5g9Vl5m853+8uxYSrtEUQEAQEAUHAHwEhwf2xkpyCgCAgCAgCnRAB0+4DBF3NqHEE0nr4yEuc3sM2hS0WYhOurqOadluU1/ftoZebNltJcQSvhIpJX5jCmgTHkc0Fvc0aJS7UJuHJARjDfJb1QI163SgPC88zz0sFBVWEfP8qtQhFsEgsRPE9L0TjtFu3BTGvZyUbSFTgyUefbfUkrRZ3YcJ1c33mxkZU9bVPkMzVyxYr33Ikl0+xnseGT5g1js/YuU4NBF0L5frGJx5O/xbYY33axedkXRa2YcMX2CwsggLB+vRN8nQ9BFy/cf20RddDpWN6bG5q4T6BDbGu5APuS4Cz37d+4gbPSpDeHen3rRPaeGbjdBzaCmU3gnsHJbyb8XsG29OxDVlq09me8PzFOwS/awEH2JP5xpXomNkutQoCgoAgIAh0FAJCgncU8lKvICAICAKCQMEQwCJs767tBNJ6z85tGUdrg/ynsaBrfOj+NPmoNxhEJDw2cfyWy9+9a1uWUtzsJBb2WNA1rlyWXrShDfPvalDtanq+MdBOxVTZukBkJTn6gMUhFoZzFi2lC6qHK8LaVNCFKZ99BisuYR5m98KkKbfZ11scbeZND9iooO9RFsY2D1obDrYx8Vm8c1km9rYgmVCcr15Wry5hcsjWliArF+Q3rXZ8xlXPE0a028qDuh2BPBEMlBM2ZfRgn/y5L/loWlgAb7FCiTqaXTt/0MmG+hWPKQWypMIgYLvXrtmyk3Y0b84KRhwURLgwrc1PLT4EOJ4VphUXbxSPqZ1UEGW8ruZmGzgmu4Os4PidBOptpeBut5TDZjqey+g/fpP3zpuRfmcJCgRqbgR0JuuX/MwgKVUQEAQEAUHABwEhwX1QkjyCgCAgCAgCJYUAFlo4jgtVcYq4zvTxNhXFyL/xiVXKf9lU/+LfIMPh0cwkrU6KuwJugsjULSLYuxtAw8vblVAfkr7YjKMkZ8IaR4uh7IYynklWW92sxDpy6P20sgu4xPU/NwlzKOd1ktRsg0mE69+jHRib3bu2e6nF0WcEuISiH5sZriP1YeS8z4/CNzjlPfNmpPtv83E3TzQ07T/qrD7MHiWqUl2vCGOEtvomJux1Eh/Xzl3yPVq7/I6sYnzJR/P0gEsd79tOydf1EDA9+RmBMiJa0R58tuuhUvgeu2xQoGruKj7gQQQ4BxnWN84xShyfAs+YJFNKuf0mwYcdJLevZQnaYNqW4P6vf2ZrJ+rb9OQjGWKDoCCXNvIbJ/RgnSNJEBAEBAFBQBAIQ0BI8DCE5HtBQBAQBASBToEAiNBc/EF1tbjNdgNqXyZ9mfgGMCDHmQjGohRqa/zVU8q3c4tScAUFeGLyEx6fUNxCZQ7FVJg6PAoJrvcjysBiMYvFtu1YMiu4sGiG3yerw1B+agF9MI1dlDrNvHzcG5YsUJGBvHdZssRRi9sscoKsWnz7gnbfu/Y5urDdW95FBOibH6bvN/qjK6fD7G1QR5Bq26dNtnb6+oLzteytbJL4+I3ogUU5v8sTXW+LzQrFlzz3HTPJV/oImHOSewwS/G9+f3ohF4un0kcvuR6adidsZ1E/88qMTdagjdDkWlP4knQCnAOBYu4x2WtupOM5nIvlCe6fKBvP66gBKIGOIraxcT6sRj2HYWECWzTbCbMwNE0f77BA3oihgfch3WZObLDCUJbvBQFBQBAQBHQEhASX+SAICAKCgCBQEgjA2xWEsY2EjtJBJvk4kCX+wsvSDIiJMkHkYSF45OD7SlHOCzObOhz5UTYW9kFEOAfaBEED8hieqCB7oaTVCXffPtmU42zlgoXrrxGgSiOuwwJ35mKngf6jLlaZKXL88Pvq3/w5Fudx1eXABCS/+qt5mGOhjrR/3+52FXuqPlc9ukVOUEBSHiuX2t8cozBPbpO0NglhPZCk78I/zB4lrE22eWaSVkFzkdtpkueujZuNv3gndDNLrFB8f/2SLwiB5g3rqWHxjVlZQIJv8JiHgm7uCNhsUB54eiutvq8+y7YMz8JS25gwCfAHn9lKhw++T80bYXuyPg0wyGGcOENMER8M4gagRIW6bYk6KdZvgAoqzrYluY86qecwbE/0d6GgdwtXANu4m7lJ9EHKEAQEAUFAEOicCAgJ3jnHTVotCAgCgoAgYCDQuHJ5miQGyQvfUJ/FogkkyDrYPegqVZQ3tnYKja6dRG/s26MW6LoSyTUYTJJOmF6XVoejfPgj6wvcoMHkMlilvP6h+wNtQ2xlKauWfgOySHSbcl33p8b3E6fX0aP31Wcp8hB4Kg6+YRPXtCBxkaVMdocF2wqrL9fvsQjHXMNx7iA7F64HmIIYtp1aMPuOkwDIy0kPShl0XNzsk41w0POYqvMwTKDGw+/NJwGf1EbOAAoLqokxha93WBIrlDCE5HsfBEyLHr6mf9UAev7n7/gUIXlyQMBmg8InjTgIMBfvu+mXQ3MKfqlJgMPS4+WmFzLeLVw+17kEoERH9SCUEA/42JYkAZAroGfdoqXqpJmZzKCX/D0LDeDbr07oHTqYcWnK5m1AEk2WMgQBQUAQEARKDAEhwUtsQKU7goAgIAh0ZQTMBVYux4axsAJJAoW3SYhD/c0WJS5bB3McmEivnT5LLc58bDZcARehDPch4fU2QPELGxHUa2sbiHoOrAVVPcrHQnPTq79RxP/dc6/JqBPf1Tc8pixbkk6mV68NB4wtyGckmx2LUnon5F8e1j8QFZgTwML0bbVdi/z1DY9n2eYgb1CQTN033CTIw9qI74PsUaL4hLtsJFxtYJI9LKimb5+mfubsjE0Z32CaPhhJnq6DgGs+YnMPpzAk5RcB/X6GmpjwNZ9RUTfp8tvqZEoPizeB59sFF6UCOSN+SZQAlNxC07Ykjpob7dSTjXDGiSqdhOYTXpnXpZ7HeHaY7y4YdxDxSLBn0VPcTe5S3DRJZuZJKYKAICAICAJCgsscEAQEAUFAECg5BEDaQr3MgSzNwJVRO4yFII7Om4Q4ytHtS7C442BVsPhAfnhim0EsOTDjnp3b1HFgm2UJkwJYHKIfvKA1y4vSFywMWcXOqivdyoPVVSDZQRAhNbQHiLMp5PF9vggK85j81Otupk1Prsrork6E++Lg8i9nO5Zc/MvZyxb+7z7WNS41N29C8BxgJbVO2sUNBAm1ekP9jVYrmChHy00iOgx/bFhgXgUF1fSZS6YVCur1sVAJa5983/UQcG1Efn7seFq27sWuB0gBe2wLsIt7BJ5P+vOSA+sWsGl5rYq9uE27lyQqZXU3Ntlxr9WTSWbju6QI5yTaHrUMPgnG18H+TE+u01ZR65H8goAgIAgIAqWHgJDgpTem0iNBQBAQBASBdgRAmK1buSwxMhzFMiGORbzuZ4nFOvtZg0yes2hJOoikHnTz5abNymPcTDa1s5mHPaLRL5DhO5pfyCLZgwYf7cLisH7WlUp11/D0VqvfuG5BYhLNNiuMXOxngtqrk1RoL9TqqF9PcYhwnx+Izb989bL6jEtdSv35dzWozRC03xb8US/Ehp2phGeyXLdvYJW+T1/MPEH2KObcdZVvqjjD2oHxm7d0Bd07/6vOrD6KblO9G3czIKy98n3pI+Cy5/nSH9fRrX++tvQB6KAe2gLb4j6OZ5r+TNWDRHZQUxOr1mYDkljhBSwIY6LbjHBwar0JbJOGPtuef3gWIHYLJ8QmQcKz3ZY/lxN9BYRGqhIEBAFBQBDoJAgICd5JBkqaKQgIAoKAIBAfAR8yHOrxrRvWU83IcYrA9PGTRLk43gsLCxux7SKH9fZE6ZXur8zXgVDAcWm0w0d9jDLQN5ANuvIW5bzcvIWaNjRmLESVOvxPbqa6hUvSTbUFWwyy+IjSRz0v2gSiio9PA8+aUeOz/KjzRYSb7TYDQkK5iHG3+WMzcY25YaobzXKB8b1rn8uwRzFVqtgAwekCbGBwylUBHWRPEqbKdvkpc9vOHTSYTra0ZRx91zeKbHPC5wi7WKHE/TXJdSYCdeOrs+7bCIo54xu30J98+3sCWJ4QsNmg4L5uxslAgEzc8ztzUpvmG9fTxr9elVPA5yjkM+PFFiP8b8QF0RXiCHTJp9Bc18SN+4GTXHgfMa1PbKefXEEv0bYxEyard4+47ejMc0faLggIAoKAIJAfBIQEzw+uUqogIAgIAoJAESKgL7bMgFOmF7MiXEeOV6Srz0I8KFggFnEqOKURqIl9x33Ia4ZTDwhlLgxR3gOL53oFaOTyWF2uD5eNpDcXry41MbzHObhZElPApopGuSbxXAgi3PTCxhxq3PYrMq1buN9oE9TPqr0P3a/yBSWdeDY9Y7msaRefky6CrWpywTmIpA9S+L/+2m66afJoZ9U9u5XRzfevtXrQuy6yzUVzXmIjQk+5bgTkgp1c27kRmDCkd1YHysuIbvlOA315zoLO3bkibb3NzgixAMygwmGbcEXavYxm4Z0AsUNs8Ttwb9U3lk3CurOSvnogS/1EmW2T3BX00hxbbDbbgmZ2hjkgbRQEBAFBQBAoPgSEBC++MZEWCQKCgCAgCOQZAZCR61YuV8osfXGm24zox3LZ93tIdQ1xYEtbE3UyFIs23W8b+c3gmFwGyGvUBzI8zD5Drxd2HPAXB1mPvwh8haSrp32gZIJVJ+ltgbtMIhzttpG7tvJ82uHKY5LMUAxDyW4S4S6P7VzqNq/V/brxHS/Qbep4fK8HnPQ5AaDnN/tteub62If49D3IHiXIJ9zEguuCmraNiB5+div9rxc3h5L/uM7H3kWsUHxGU/L4IGBurvE1leX4TT9OX5w6y6cYyRMBAfNkD98f2UaMi+rsFkcuZTP3rxTtPXS7Fz5txuNq9tfHGoZFCpgLOAGF9xuf03kRpqNkFQQEAUFAEOiiCAgJ3kUHXrotCAgCgkBXR8BUYWOxBZ9KVn0zMb1713YyfbxBPuOY7tjayYp41hdnrKzFsWN4br934C3a0bxZKcL0gF8uQtxFpvqOFwfQdJHpUN3tf22M5t7fAAAgAElEQVR3ljoN1zU8/WJGX2ARc9u1EzPabSOa9U0Fbid7jielaDP9wYEtjpkXmgg3TwywGhz9tm0c4HOTSLbhpY8vCGH4ioM8MINkspUN8ieplnRtaDBBze3R2+kKLAgSHIraubffRVfMnO+1KeMTAE+sUHzvApIvDAHXSYbuFUTfW/8iffrz48OKkO8jImCzX9LVwnyvxL09qedGxCbmlL2rkd+8eaoHk8b7Bb876c8xfj6uhzp+w3orziw2GH3FJCorK1OnA1hIkMSpp5wGVy4WBAQBQUAQKBkEhAQvmaGUjggCgoAgIAjEQSCMDOcyseB7pXlLVjBKLNygUhpbO4WGj7yEhg6rISaPmQjHgj6IZDQJcZ1MNUmCOH00rwGRbfMotRHXNiLcZnmCfHfPvSaDXDcXwbm03VQRMvlss6HJtyLcVEDrC3S0E563tk0IHTcf6xqQ3CCHQTbbUj4Uk0H2KCbpbm4I6G3sXlFGF48aR/ete1FtDsy5tDpw+MPsbGw2CmH2KbnMN7m2tBEAwYbfqZmgBP/B/97XKUnYYh4x2+/X9mzrjD7gXY38xjwzn8d4TkEYwPYv5ruEyyMcZXGsD4gL8LtkaxyUMWbCFKqdNku9V0kSBAQBQUAQEASSQEBI8CRQlDIEAUFAEBAEOj0C5hHdID9kDkYJhfeenduUNQcnVjNhQQd7E6QHn9lKF1aPUP8dZonBhDgI9XvnzSCorKZdfzPt3rUti1iF6gqLT91THP8GofjbA29ltc1nkGxEuI0wsvl0uojdpBTLGCNYvbCinsstNBFu848HeaMnl0e8iQXmQ0P9DVbfWJSH8YBfrI1U91FP+4y5mSfIHgXzE3Y0UKS7iESU16OijKCq3bDviCre5ZvOdYdtXIgVSpyRlGtcCDRvWE8Nls2lyooy2vDzd6hn3yoBLyEEbDYotqLD7gEJNSexYroi+Q3w9OcDnk94P8H7Bse80MfRhRGuQ7wVPNvgDc7Pt9T7Sx2Nrp0kG1GJzVQpSBAQBAQBQUBHQEhwmQ+CgCAgCAgCgoCGABZ4UN7yoszHvxOLfKjEQVSbPuAo2qaIZksMfA8lOdTi5rUg0t898KZqHUhn5DEJU5CSKZJ8e4b3MshWKKhApNsCcwUNus0H2qb6BRkKIt5MNgJY97rOZcKZZCqrqwtNhJtq8Ec3v5KlVnMRvzqRDCziBEhlDJv2H80FTue1QScXeKNkLwh8h0odJPixljZa83wTXXjxJaoel30Kvqtf8RjVTp/tbI9phYKgciBbJAkCcRBwbVKdcfoAWv+zd+IUKdc4ELDZoJhZ83GqJV8DEhbQkYNeguQttaT/bvBeg3cA3NfxjqFvoMNuyPbugTxDhtWkLVPU+48Q36U2TaQ/goAgIAgUNQJCghf18EjjBAFBQBAQBDoKAV2xjcUeiOap1y/wCs6Ea7FQNtXbunUKlE5MDCI/K6NANiMfku4hjn+D+MN1Dy6em6E+x3e4BotuBJFiZTo+A3GuK9V98cS19659Lu2RjutM4gh5dJW7XrbN29xWpm979Hw6qYIyV2/ZqfpZSCLc3BRw2XnYbGLQF5vi3tyA8cHGRr77XOebx+VfHja3YIfS0tqmfMG/Mu/bqjqXZzq+C+qHWKH4jpbk80XAtSEz5ILzafVPXvMtRvKFIGD77ZqX4F6Ie3ixBz4Muz+jH4idYNsY7uwTxVR08/sGW5dg071u4Z3q5FqQ7zfjwCfeRPHd2WeGtF8QEAQEgc6HgJDgnW/MpMWCgCAgCAgCBUQgFzIczeQgUVhE8oKRm88BNo8cej8rWBTUUVhY7rGoy/EdFuQmSZ4PWEzbkyhEuMtWI9dj7zZ/cCZRCkWE2whdl0e1CwfXpgDmyer76r0U/C41fpJzIYi8DqqnV7cy+uyY8XT3E/+QzoZNgXmTRmVdFuQJbipJ82UDkyRmUlZxIwA/cPN+jICu47/wBVryg78v7sZ3ktb52qAUuw+4aZVmI/HrFi1VNmSlltD3NcsWZ/1WTr3DDCL0HRsACFTtCnqJ/CC+YXWCv50x8Gmpja30RxAQBASBroqAkOBddeSl34KAICAICAKRENCJyajKcK6IyTxWhO9/bU8gkY18cxYtUTYRb+zbS+tWLrN6Q/MCE8E5dzS/4MxjdhiL9qBFK+c3SWuTaLapmvW6bMfhTUuQSIPRrirW/cF1EtWm8syVeLe1z6wniMgFIQQywYa3rW1BdiR6W/LRL1tffdujXwsSvGe3Mnr2lx+kPw7yEXdtItSNr07bAqEgsUKJ+muR/CYCuHeYJ2TKy4gmXVNHN9+/VgBLAAEfGxRbkOUEqk6kiK5MfiuLricfocaVy51YYjMSVm449eayXItDfHN5+H3iZNvtK9YW/SmBRCacFCIICAKCgCBQEASEBC8IzFKJICAICAKCQKkgoNtD2Ly+w/rJBDIH3nzvwFuEAJsvN23OIPr0cnC8mheCphWIrgbnI8ZnnjdIBcu0BVPUywV5DRVX48ploarjXIlwkL9QN+vttXmPh+Gnf+/yB0eeQhDhIEnmXFqd0WQXkcuZggJm4ji5aQkQFkgVc2P2wjuz/Mij4Bglr8sexVZG78oyOnqijf5qYxMNqkn5goPgqJ91JUF122Zc1PDUi8rSR082O4ViV45GwVPydgwC5sYKWoFArjO+fgvV3fG9jmlUCdXqY4NSrD7gXZn8xhTUrU/wjB4xajwhkKxv8iW+QbRDCIANfljH6VZuqIst4uYtXZETCY7xFOW57+hJPkFAEBAESh8BIcFLf4ylh4KAICAICAIJI2AGMsRirb7h8Qz/7KAqmbw1FdRYrHGATZCFOmEMwn3C1XU0tnayUntveuIR5T1aM3K8Vf2NhSi+g0dn04ZGp+Ic6mUsMl0qZb0fsGeBco+TqfQLU4S7bDVyUQOabdBJ6EIQ4VHU4IybbUMA3wUFDw0in7uVl9Ff/+/XCrbQR9CzmyaPDv1VITjmydY2unnxd+jLN/6pyu+6FqT4zXc30OQ5CzLKhRIRGwecYCHUuG1faN2SQRAIQmDCkN5ZX+PkwjeWrMiag4JkdATMwMFmCcXoA+5DfuMZjJMopZh02y7eIEdg7iA1uI5DUBBx3Pex4Q91N4jv/a/tzth454CZUJaP+Pw4pTCP6xHPFnQ4dYT3KLwDbXr1N6U4ZNInQUAQEAQEgRgICAkeAzS5RBAQBAQBQUAQAAImGQ7iec6ipV5kOBOhfftXUcPTW60EpksFDEKcCXIQpw1Pv0gvN29R6mdbQruwoDSVVpyXg1pB7bVu5fJAixYmzXmBapLAYUQ4MHtg8dwsj1Gz3CgzTCdczPrzTYSbanA9UGdQH4ICZiIg6YXVI7IuD7JUQb8bt/0qCmw55XWRXN3KiU62poquKIO6toxGXnIp3dnus4w+TLv4nKy6QYLPXrQki2ASK5SchkkutiBgO8GBbDi5cNuKx2jclFmCWw4ImBtXtqLWbNlpvcflUG3sSzEf4GcdRPbiJFTttNkF22iM3ZkYF5rkP5PZYZhwVSb5zYT37l3bFdlt2r7hneXM3weyToLw5jagzr27XnIKAhA7Iy6pHgNSuUQQEAQEAUGgiBEQEryIB0eaJggIAoKAIJAMAlBNwx4Eiy4svoZWj6ALqoerBa3Pwgj+sVBdT71+gTW/6ZfsS4aDCL3t2omqkw8+s1WRAiBtZy9ckrHYDrOgAPE6dsJkFSwzzALFhSj7nI+unUQPLp6b5ZerX8fEO2N3+8yJGfWGEeEoy7QywWc+19naj37r/uAYKyx6OZntw+e5qM/NNphEu69Pd1DAzPl3NTgDrU39zNnWjQrfepP4VaHP2DQxLU1AgiMxEQ5iEYpw3Rfc1n6Q4Jd9aQrdsepv080TK5QkRkrKMBFwnUaAEhwbip/63DgBLSYCrsC3enFJ3ntjNlNdxr7XTc83Ou3AgtTNudRdLNea1icIhA1/bzyfTc98s814Z8A7Ub/+p9H+fSmy27yGCW+cSruwenhOCm+9flPtrXuSs40K3gNYAFAseEs7BAFBQBAQBDoeASHBO34MpAWCgCAgCAgCeUYAx2Kx2MMiDcd79YSFHMhwEORDqmsIftogo6HQZpIXCjGQ6EjTrr/ZSYaD1AQ5yEQ0FmA33dUQqHjTLUJSC9A3CYtyUx1uU1BjsQdSP4j4xiIUi0F4bvoQ5HwMGotZLIRdSSes0bb6mVdmLIBNotxWDtrTUH9DBgERx2cdZWN8dSW8Tgjb2odrgDdIjlyTqSyNqsp2BZBzkdo2dTt7bD/yd830yc+OzbVLodfbAlxyG3Q1eL/u5fThyVZa8/wpX3BXUMKLR42nP1v/YrpuU1GKuSHH2kOHRjKEIIDNmwbLqRls2PzNP+6jqrMGCYYxEbD9tvWizA3KmNXkfJlO/toKK3XyW3/v4PcIvO/gvh435Yvw5vaEqb0RGHz4yEsKFh8jLk5ynSAgCAgCgkDHIiAkeMfiL7ULAoKAICAI5IgAW0T4FgOPSF01FHQd/IdT3pRVyldSXyBiMY/PbcmsIygvrtcV3MiLeljNZJZvlg2iHTYnQX0CeYg0YXqdarMPIY5ykYKIc5MIBwGit8OHCHepoU3/cZ/xNclkPYBivolwU20elWC3KePRZz0oKmPg8lavLC+jgWd/gkCE9z/zEz6Qxc5jszUBCY5UoVmigFg8drKNvvmn36GJ30j5gt8zb0YW2VJeRjRo8Pn02P/3WrpNJqEWZ07E7qBcWLII4GTQ6mX1Wf2r6lFOjT87QD372u/rJQtIQh0Ls0EpBh9wIb/fpPUPLVebxrmkfBPeaJuP2nvEyPFK7S2BL3MZTblWEBAEBIGuhYCQ4F1rvKW3goAgIAiUJAIue4iS7GyOnWKl95jaSdS84Smrh2aUKlAee1jbyFlf5Z9NDY3FLcjkKAvcIH/wfBLh2Jyon3VlGrqoanBciA2Hu+dek2V1YrOJsSmxUQbI5Mkz5tCC5WuiDGOsvDabGRDhOgkOVTjI+bHjL6XFj/+9qsc21siHAJ8v/NsRlcfm26xvasRqsFwkCDjmH+btJ84cSH/18tuCUQwETEsqswhsxLLlV4zic74kjPyO86zJuVEFLgAbrTjR5isC0JvHQbiTtDSxdT9M7V0zarwKnIm/kgQBQUAQEAQEgTgICAkeBzW5RhAQBAQBQaBDEOCFtrIuGVaT9vZGY3y8vZFv05OPWG0+oPrWEwhTlMkqcP4On3NQyg4BIaFKdd/yxoeWBwYFC6sSBAeIcJRpI8JxtBxkdljiYKE6viCA6xse9wo2ivJNMgaKtdVbdqarzicRbgaLjKoG5/bXz5yYRVToGHNnbGQySPDWNqI7lj1Il187PwzynL43LWhQGIJhtrQR9exWRh+dTDmGwxIF/35q72H1b5sSl6/7ux2/UnYUYoWS09DIxQEI2OyE8LsZ9skL6C/+4ZeCXQwEbBtiejEd5QMeRn7j+YL7dKmSqiCVke6dNyMW+Z1vW5ggtTeeeRgX9vaOshkeYwrLJYKAICAICAJdBAEhwbvIQEs3BQFBQBAoBQRAcOIoL7y98d+ZZGnKuoQDX55x7ilfV+Q7cuggvb5vj/LbLiYSGws9tIftR959+y01VKZ3eT7Hj9uQax1M+tqIcF8rC5fVRxQSJcgfHH101YFgmlhwx01mvXHU4KgbxAAsQ2xWNDoOyGda0OD67hVl1LtfFa3evJNOPyd//sY2tTaT8P26l9Hh4ykSHDYTx1raaNVzW2lQzSXKCgX90xOT4MiDwIQmqeY7f+KOnVzXdRCwEbbdK4hGXXIpLf3rf+g6QCTUU5eVExfvuwmaUHNUMTiZg80Ol+qZT0QlERMiyXYnURbuy/C9b9rgDviJeoKe+/kkv4PU3ti0HgHi+4pJJbsxkcQYSxmCgCAgCAgC8REQEjw+dnKlICAICAKCQAcjgMXeG/v2EIhjLPgQzDGfiYNogmjf366wYgUZPMNBSqItuRDYqAMKdLMMLNqhfmeFOvoJYh+BPIEDVFJR/M7zhRMHc7QRza5Aj2Zb2Ofd9C21+WO7+mGq201Vtq19SRzZT0INzn1yBczUCWEbEQ1rh7IyoouGXkh/+eK/5muoVbm2QHggtOEFziQ4lOBHT7SmfcFN6xiUg2ugYF/6/cfpk5+9hOZcWp3RbrFCyeswdqnC68ZXZ91fcVLhqj+uo3nL8m8jVEpgh9mgFNoHHPcW3PtdsSxKmfxG35s3gvzO9vtm32wE/4alyZ6fbbee/gIJfduKtYkGl+SYJ3t2bct6RxG1dyndDaQvgoAgIAh0DgSEBO8c4yStFAQEAUFAEAhBAOqiNcsWpy1MkL0PyOS331TKcRsxrVRHI8fTWecNIijH9+x6SZHJvz3wJh059L4il0FqB1mgwEYFlikgxvnvu//xJjVtPLUQharqK9ctUKQ1q9LRvmJUprtgxmIVSvugQJl8LZPd2KC47dqJGcp7XyIcZdkUhroHediPIsgfHNfmgwg31eAgH0Dgxk0ulSXKhXIdGyY2O5ueFWX0UUsb3Xj7XXT1/G/HrT70OhtRX1lOBA04PL5hiQJlOkjuS7/wBfrW2h+r39O0i8/JKBsKcpD3c2+/iw4fa1V94oS5t+nV34S2RTIIAj4I2GJI9OleRnMWLqWpefyt+LSts+UJskHB7xZWVIWwseBTYq6Aj6VKfjPB3LhymVX1jn5Pu/5mwsap65mHz5PGB4Q8iHb1d9f2jGktau/O9iuX9goCgoAgUFoICAleWuMpvREEBAFBQBBwIADi7Y19exUhvn/fbqulCi8Gx0yYQmedm7JXgWoKRCOuh9obpPp7B96i3bu2pRVXLvW23hRdRc5kOeoAWQgVu75QhOIZpHoQgW/rJhaXffpXqa9yVaTbymc12Y6mzaGWMqxWzpUIBy4N9TdkLPCB5ZxFS9ILe9ekN0lumz1JPohwUw3e8NSLOR3t9gmYadYJTHpUlFF5OdHDP9pJg/5geF7uDTZVN6wljrfACzylBge53b9HOYFofPLVlC/4hCG9s9oD8nzKjDn0f974dcbvoSPsFPIClhTa4QjYNmDQqH49yukbd66gL82+qcPb2FkaEGaDEsXCKm6fuyr5jU3/Hz75iFX1ze8xdYuWEgJgc7wUV+yPJDYrRO0ddwbLdYKAICAICAKFRkBI8EIjLvUJAoKAICAIFA0CIEQaH7o/HSgTJCn0qNlWJJl+4xdUD1fqNijPoTzTF5FYDKJcEOVKRX4YFilvKtUxCHhfP3IQzrA/AWF+5OBB2vjkqjRuTKibvuicgdXpyp7lQMpjPKmEuusbHlN92/jEw4Hlg7yct3QFvdy8Rfmz6imKIhz9xPWmogxEe93COwODoprKbJu3dNJEuFlnEiSuy8cc4zH/rgblKQ9rEn1+QV2N/31qyIX03b/5B+p/5ieSmgaZYzn+oox5ANU3Nnf6aJYoA3qWU0trG33/b1O+4DYbFSjGR9TU0D///NWM8sUKJS/D1iULtdkHAYj+Pcro9hWP06hJM7skLlE7HWaDkm8Pfx/ye8LVdVQ7bXZBlOhR8YubH88Wc9NcLwvPGvRZD/Tpen7iujgWYCgPCe81LrU3lz12wmSqGTle5VeWcYffz+g6PsOpOz1x+fpnOEWHvHqaf9eKnGJ4oCxbXXjn8g20Hncc5TpBQBAQBASBjkNASPCOw15qFgQEAUFAECgSBPRFYop8HkFNz69XhCJ7VtosVfTAUiDQ717zbKCXJkjpTU88QhufWKXKhnIb/4NUFuUrpfmB1AIzLOk2LEoxnmc/dLM9THKAmF63cpnTJgUY4Tg2FpawztCT6dMd1meb9QbwA+5BR+5NBZxNoZgkEW4ra91P9+VMxmD+PLB4rgosaSZsKvSF/YCBMdTgJ1rb6JrZ19Gf3PNoGMSxvscGhWlDADV4qm5SligIjvnB8Vb69l130/iv3ZEV+BIVgwQ/3pIKpskJ86dx2z4hJWKNjFxkImA7uYA8IMFX/nAnnfup/JyYKLWRCLJBwT254ekX8/KbDSO/gXM+gzp2xDhyn10xP/DugdNrU69bkH7G8DVhp7ZwLU6dIXFQbr2Pvu8jHYFLvurEuw1O6eG0H95dOGh5vuqTcgUBQUAQEAQKi4CQ4IXFW2oTBAQBQUAQKGIEdAUvFvJMLGMRBMIWRK5uqWLzH2VrFL2bQZ7iRQxHaNMYFxDQIMN3NG+mpucbvdXuqCAqEQ7MV99Xn1EHq9NhI+NKuvLYdfzbRYTH8bU1ieEk1ODcN9exdtSBjRSTJO9dWU5t1Ebf+f4P6HNf+mrouEbNgPrumTcj47IeFUTHWohO61lOv/uolXp1gykK0RWXfYFuWf1jpew3fz8gzY8ZJHiSuEXtl+QvPQSaf39yp8E4lYKZCTuUH/yv16jqLJwGkhSEQJANShLWGra6cW/e9OQj6VNbtjylRn7jvooNc1ccDjx/J0yvU6Q/pzCblI6a2bb3oqC2IOB3lBTFdx6xYvAup4QNIQKC+hWPUa2Gb5Q2SV5BQBAQBASB4kRASPDiHBdplSAgCAgCgkAHIWCqtbkZrGgeXTsprfYGGcBEua7Sgko7SEHFCnDYnaA+HG+GbUmmsjy4DB2eU/YnqePChSTdTQLahV/QcEa1u3BZgwQdwbf5g4PcNo8928qGWq7h6a2RlNw224Uk1OCMo20zAN/pc4jzwhKlsqKMzv598FZgnQ9bFNPjG0rwk61Ep/eqoP882kLdymGPUk5VPctp1bb/oL/761XUuPJU8Eu01aYER/DPoM2NDrpNSLWdFAGcxFm9rD6j9fh9fKx3Ba3fk/Krl+RGIMwGJeqmZhjWqK9543q1ueqy9iol8jss0CXw4kDbQ4fVpOELIszx/MK4YPOUCXWcHBrx+XEZ8COeCGxHkAfl2U6XMfGOWCl6/WHj2JHf450EhDcEDFB3BxHfeDeDMh4WLugjTgWKNUpHjp7ULQgIAoJA8ggICZ48plKiICAICAKCQAkgEHTsGkQjvC6HVNcQSHGokPQAkOyFjTL27nqJdjS/EMkPnOFj72/8O8juxEZ84hq+Hotb9hfHMV/Yl+TDKxwerGNrJ6vjw+j7vfNmeNm0xPElxcKWPdn16aar081paCqWXSrjpIjwfKrB0TfMubvnXuM1lmyLMuqPPkv3PPNS4r9QKMF1Bboi3svLqHdlmVKCI4EQb21rU1YJ//b6v2cpcnFNq+aGIlYoiQ9Tly/QZqmEDZtPnDGQVr/0dpfHJwwA83eu50/aBxwbfY0Bz6pSIr+xia7I/g3rrUMAIhuBLjk4NWcKwoivAU766SEzHgfqfvknW2jPzm1Zz2uUAX9xbESibiaE9fbWLVxCKLMYEpTwqcDl22n/a6kA6D5xWNDP+obHxfqkGAZR2iAICAKCQJ4REBI8zwBL8YKAICAICAKdGwHd8xoqIZtvN5TYNaNSxC8rrfBZkCIb3+PIL5RXrgCXIAGRfBZxWKSCgD7j96plkN5BKq04au0oo4h2MyEOixQo5sMSrrl37XORF6G2o/lBC1rTSsQVoFPf1OC2R1WE56oGx4IeGyxBSrQomw39upfTYfhyf+de+uLXMtWwYeMT9r0ZDBT5e3cro+OtbYR6QYQP7FVBBz9qoVtvvZXO/NxEqp91ZWCxIF2gXJckCCSFgM2Gp2e3MqoeegF978f/mlQ1JVmOzfaIO4pnI07WJJHCyG/cF0C86sEfk6i30GXgOYyg0UFEP/oKX2r9NEyYWlwnv9EnkwBH4ExWe4PMNt8vUOfY2ik0fOQlGe8RrnptMTbyjWUUdbdLJIA22gKJ5rvtUr4gIAgIAoJAxyIgJHjH4i+1CwKCgCAgCBQxAlj04egslEWsno5CTDMZTG1Effr3pyOHDqkgmEcOvZ8ivg8d9FJKmxCBcDCJ87hqaj1QZz6GIgpeqB8L8Dntijff9mBB31B/Q5Yi2rU41/3BUceaLTvpQgQoNVISRLhJurlId7Nu9AnB50BoNG77VSAULlW8eRGU1j27pfzBG3/6q0RtUWyEP0jwoyfb6Jy+FfTOBy3Ut3s5tbS20ZVXfJFqFyynmyaPDuyX+LH6/gIkny8C5m8f1/XpXkbjJ06hW//yGd9iulw+3GPqxldbN2ST8gEPI79NcrezDkJY0EpWX89euCTDgssnQCYIcyjyOekEOJ8MM0+VudTeXIZNpe5SpudjTHzV3egf7Etw6g0n3nr360+v/GSLUoTrJ99c+Oaj7VKmICAICAKCQPEhICR48Y2JtEgQEAQEAUGgSBDQ1a1B1iT4bv5dDYowRyCrIOW2y6JEV3DrhCKUSrrCPAgaJpyhwp563QJvD+t8K8PjDCd7sE+9foGXJycwAuFsBhFjaxpdTW3zB3d5fudKhJvkMBbgNi9yEyMQD6yUbnjqRS/Voytgpl42gmR+dLKVLq4eSvc8s5169E2dNkgigbTX8a8sT5U6oGfKFxye3wiQCf/l7//jWzSl5mxntWKFksSISBkmAiByzXgNCIp51dV19PXvrhbAHAgE2aDk6tvfVchv9BPxP1yBLl0kf5A1Gw8XNleh8OYAkbjmlebNBPsfW3KpvTmvS/WdT+V0FHU3e3cr0rt6hDoBx6ff8OxEEFUzQHSpbKLITUoQEAQEAUEgNwSEBM8NP7laEBAEBAFBoMQRwGKQF5bcVRCjj95Xb13MYqGFwEpIvNjV1dCsVsJxY9ihIClLlANvqv8GkY60o2mzItOjKqn14Yiqqi5WMhykfu20WV6BuGyevzYbE/Nof5D1Rq5EuEkO+waP42CT85c2EDYDfBL61VB/Y+BGTFXPCjoEW5JvfYuuXLDMp1ivPLagg327l+Hwg0ofHG9TBPjJ1pQv+JJboN5PzXcziRWKF+SSKSICZgBXXH5az3L66s1LaOr8b0csrWtk51Mptt7m4gPeFcjvMPU2MNZbA8kAACAASURBVHURyy4yVx8H3Rc9jre3OaaFUn3HVXcHBat0zad8Evdd4w4gvRQEBAFBoLQQEBK8tMZTeiMICAKCgCBQAARAFsMbvHnD+izlNx+1xfesRMqFyEZ3mDjHfzMhzyQ5PoMSat7SFcr706YyY9VX7fRZXqrqpMlwYAI8fLzNg4bPl9S3EcGs1seCmJOvPzjy24ggX49wXdWNsnwsTpCPyfOohLAtsKeOK2xRelWWqyCVf77qCaq+4ppEfjUgNkyLE5DgIL8/3julBkdwzA+Ot9K3bv0m/Xj7PztVkVGI/0QaL4WUPAI2yx50emCvcvrmnz9GoybNLHkMonYQzwJYyNgCKUe9L3HduB+6nlV8f0QQSP1eHbXdHZ0fzyCQsqYamduFZwCsS0bXTs7aZA/bHEAZTOxiXFCHzdub3w1uW7E2cAM5n6rvKOpuFhDA6x3vNG1tbbTnZy9R335VzsCbrk0GsTzp6F+A1C8ICAKCQPEiICR48Y6NtEwQEAQEAUEgzwjwAg3VgKA1FdkgbpEH6d233woMdGlrqkl+gzQAic1KcfhWvr5vD73ctDlDEctBLlE3H2de99N9GYtlk6hmgnj3rm3UuHK5FbmoFiNJkuFYtKNfsIvZ/9qenAhxLHAnTK9T6mhX0EgXEWwqF02VdtDRflvwR18ivG78RRlEko8aXFdWb/zFO14bGDzwGDtYGLiO3sMWpaWtjf7Hp4bQt//qx4n5g5v9RNDBEy1tdGaflC94VY9yOt6S8gV/t6WPkySK2t883yqk+BJAwLZJwyT4kkefpeHjv1wCvUy2C7aTNaghjg94mK2Huq+3W3kFBQNOtofJlRYWsBI14TmNZ5eN4Pchv5nYxl+btzdw489BJOPEjQvLpFXfKA+kPOqHD3fQc57tTGpGjidT3W2bJ+bzwNZ2YCKWJ8nNZylJEBAEBIFSRUBI8FIdWemXICAICAKCQCgCJgHKF2CBj4Vj3/5V1Kd/yjMZ5HWf9s/Uv89NWZ7Ai5KT6UOZCow5u53kfkst0Fx+0CAtX2neQiCxdZU3lw0C+fYVa7MWtDYyHIS9y2aCCYyxEyarxTgW5WEpKTKcSfja6bNVXzc+8bBVYRjWHn2coKZDeaZlDfK4AkZiAX73mmfVNVH8wVFmXCLcvM5HDa6TdnF9d10kFvrSr3s5HTnRStOuqqUbH/qRL+yB+cxAoBVlRJUVZaquw8dblTUKvMHP6ltBNV+ZS8/9YFVWef26l9FT//QO9UzQrzyRzkkhnRoB0wIJncGpCGzMPPyjV+iMocM7df+SbnyQDcoDT2/1enagTWHkN/KYntZJ9yWf5bkIWf05heetGeiSsWneuJ6anm+M9SzE8xvK6RGfH6c216Hax4a+613DRdTj/QJxRFBWWOKA4Xt+tl0R3bBwMwl5ve8crLJm5LgM726zHpQLLPRNfN3uhZ+/m7CRvm9PxuVieRI2avK9ICAICAKCACMgJLjMBUFAEBAEBIEuiwArwUF0g/S2EalRwQFxsG7lsgwF7pnnDk6T0iBgQYSHJRCge3e9RDuaX8goC4veIcNqaGztZKWgYpWXS/mMxfCY2ikqIJfNjsTXYgTtTZIMRyBR1F0/c2Ksxb+JX1A/sGg2A4SBkL937XOqDSbZEzZGcYnwOGpwviYX711b/4EfCMCe3cqpjdrom9++h774tfqwaRn6vWn9ggtgifLRyTY6o08FvXekhU7rWaHK+fzlk+jHm7PJd3g0CykZCrVkiIgA7KsaFt+YcVX3CniCV9Cqpl9S1VmnNjQjFl1y2YNsUHzvRT7kt0lydiYgw5TbrErmE2B633ywsWGB5xaIapDWern68992Osml+sZGuGsTGfUnpe4OGlcmv/WNAH1e2L5HeWJ50pl+LdJWQUAQEASKBwEhwYtnLKQlgoAgIAgIAp0IASwOoXByHTUG8bhu5XIr8exLIjAcTISyN7gecBNtQJBN/AUpbrPAYOUz1Ncmqc51pDxKbyEf33AQJM0bnspZyY12QQEI5ZdLSRZ1Srj8zxHc8u6512QR7qi/buES5VGrK9D4c1f9LiLcpfRHOeY1YWQ7rsF4QsHqkzcIK8wZ9N/cCAERXlFWRmf260Z/+Q//mogtytTPnJ1RD0jwoyfa6Lz+3eitgycVGX7wo1a6fMxn6e+3/0tWs2Ghsuq5rTSo5pKowy/5BQEnAuZvHBkx1+AJ/uSrhwU5DQHXCRIfH3Afgrezkt9xAl2ycvq9A2+pANhQT7u8wm2TEPf+ESC+r5hkVWq7CPAg1Tfbk3F9cdXdaBveO4YOq4n8+wkjvyEE+OGTj6jnpp7E8iQy1HKBICAICAKCgIaAkOAyHQQBQUAQEAQEgRgIgOhDgocpVNk2WxGQxY0P3U8gxM0URrLq+XVbDHhJj6mdRG/s20s7mjdn+ImzSoyDZGGBCpU7CFDdDxzXmmp1ri+qb3iYGs4HWrQzKRI8qB8un2yMHexGzA2EMN9uG6kW5sNqqsEbnnox8Ai6TpybvvA+2Op5XKcFYFHSRkSX1HyKvrPx1ajFZuVn4p6/6AFPFCJFgu//3Qka2KuCPjzRSsM+8TH6l1//Z8b13cqJWtuIljd8nz43dW7ObZECBAFGwLTqwee9K8vokxdeQA1//68CVDsCLhuUsPgHpUx+4z6M01SuGAuADs9O2J4gAQvEGMnluTZ/6Qpr4EzXPZ192mFPoixWNPJYV03j+6je3dhkZ8uVXE/MhZHfLqzF8kRuUYKAICAICAJJICAkeBIoShmCgCAgCAgCXQ4Bmxc3/KlBqJrqcKiQH72vPmsBHYUIZwLH5iUd5CfOdh88QCYZjoW9qbTivFGsUpIgw/M1icx+2Mhr4AqLltX31afV4j7B36IS4aYaPExZCcJgzqXVCpowUt4HP8yV+plXWsmZXpVlNP+WW+nKBct8ilL2OFA1wosW/vk8780+Qm3ep7KcQHB3Ky+jD0+2EXjx03uX0xu/O5lRVy8E0mxto9vuvJsuv/4Or3ZIJkHABwFzcwbX9OtRTp8eXkPffXaHTxElnyfIBsXlA+6yq9DBwn0O969cCdRCDoDqVzv5DdK40ClM8Wzey3HC7OWmF7JOO6EcWKj5encj3okZrDKJvtvmCWxd5i1doYrHBkPjymUZ7RfLkySQlzIEAUFAEBAEdASEBJf5IAgIAoKAICAI5IiA7gMepKTGEWidZEW1UHth8RqWopChyMvWJyApbV7gqI+PpIPA3PTEI7TxiVVO33AQ/FiwhqVCkeHA2dUvVxtBxMADFUp6jFlD/Y1ZZQATU0EXZHGCuqIQ4TY1dpjCG8HOoCgE/lCs55pcinCUO7B3Bd354F/RiAkzQqsxA8vC+56DyZqKSQQfPHislYacVkn/ceikCkb4u49a6GRrZjUgwU+2ttHV06bS9d97KrQNkkEQ8EWAf0d6fvjPj5s4mW7+i2d8iynpfC4bFNeGLU454bnhIolBYoL89gm42JHA5mpZErXtbG2GjUOorEE8X1A9nI4ePmSJKTKI6hYtVc9rTjgd9uDiubGU5jithI1LFbCyekRgsMqo/bLlt5HfeBbDhgztWP/Q8qyNeLQL70V6n5Noi5QhCAgCgoAgIAgICS5zQBAQBAQBQUAQiIEAiFKo2vTglFiYgnxmMtmmpLYFl8SCjwNFBjVFV4M3PL3VS1UXRHhyXWgnSO53335LHflWR7kPH8xqShSrlHyT4Vgcg3TdvWtb4BF1G57cj9G1k7yIBB8P9yhEuGnLgL6AKHKloFMAMaauusRleYDvwmwPuE6bsjasPfBgPnayjaA6h0+4mbpXlCmV+BWXfYFuWf3jsOLke0HAG4G68dXpAMV8EfzAv3R1HX3tntXe5ZRqRtc9wXZaJez+HqZiLjSGfGoFzzU851Le3LtztiyJ0g/GBJuwrlgiXJ49wPYgtZnAwSp96ubgmUOqa/Ki7g5qQxD5jU0Tm72MWJ74jKrkEQQEAUFAEMgFASHBc0FPrhUEBAFBQBDosggwAcg+3PAFB6mKxS0HjuQglDbyGAvEe+fNyFBygWytW3inc4GsE9pRrFSCLDDiDCD6Ay/0mpHj6MLqEaoI1zF3Hy/VOG3ANRzwE+pjBOp0Bf10lc9jF3RMnK/1Uez7EuG6qp/LD1KD4wQB5hvSo5tfiRWEzIaBrb2cD9jcu/Y5q9c958G8AlnDpNKRdnuUDw4dzCIbfccY7uFlZURnnH4aTZ2H30KVUkjid4U5Buz27tquFIQ2H37feiRf10NgwpDeWZ3+eJ8K+uqCO2ny3G93PUCMHpvxCvA1iFv9JEwxk9/YhIYPN2JegORW3tdvv+nc1M11wFnNHeb9zSeQoqqacX9ds2yx067Mp/3YKFbjeN4gdQ9NndRJ/e3bj/9dpfzMcU8Nepb71Ic8LvK7dtpsKisrs1qejJkwhaZet8BrY9+3HZJPEBAEBAFBQBCwISAkuMwLQUAQEAQEAUEgJgIm2Y1isOAdWztFEeIg7UxFl64Ot6m0sRitb0DwS7v1CI6f48g6EoIqIrG67YPD75MiIN9+UxHxWJy7VN0xuxx4GdthsEe0+tu+0EY7oPxK2lsVeM1ZtCRtKXPKx3V9bCLW1ckw2xJcZyOWbUrvKGpwjOW0i89RzZq/tIGmXr8gseGzEV964T7kv60xejBX/h4BMo+1tClvcNMGJU6HkvBIj1OvXNP5ELBtPMGr/vTeFXTrnz9Gf3jVtZ2vUwm2uHHlcnXvMhP7gBcD+a2ruWEPxQQ3NuHePfBmgmicKoqDS8NTG5YlIJPPOHeQerbDamzTk48QNiltKY6qGfMU7wxhQTi5Pp2Ix7MfKSksohLoKjbJT7ZQ0/OnnvN43wH5vfdn22lH0+aME2ZieZKXKSuFCgKCgCAgCIQgICS4TBFBQBAQBAQBQSABBFyEeM3I8eoIM2xTdN9tKOzgTw2yHIpwkxzG4hHXYWELha0isw8dTJHcAQt+LIqxQO/Tv0r1KvXfKcUXFvEox/T+5mPaijQ/gHpS9YFcUGS6xRolAcgSLQJ4wS9bP2YOMmFH82a1KE+iD742IT5EeFQ1OPtvhwXSjAqqrR1mGT52MLZ6TYIdPuAfHG+loQMr6d/+64SzqSAnW7OdUqz52crHFpA2KhaSv3QRsG3KdK8g6tu9nO5Z8xxddMlVpdv5kJ4hcPO8SaOycmEDDM8OM1ihnhH3RFhp+cS1CAMYzxrcj9478FaHW5awjYitzWEbAhxrwzcIKObm3l0vKeIb5H5YAnms57NZzwDLNCnebm/G7w+8WY7nPPLwhnn6vxN83puBudE3vKOMnTCZ8G6EDQW8q7BKPcwmJgwb+V4QEAQEAUFAEAhDQEjwMITke0FAEBAEBAFBICICShHVvIW2YlHbHpiSLURgm4LvQUSDpMXnIKiDFNK8IGcyGwo4Dt542/fWKrJcHW/uPyCwpSAYbEGoQB4HBb3kBTXqBUFhI9IjQpSX7CAD6hset9pkJEWIh/l3c8d8iPAoanC9vKb9RxPFL8gWhSuybTKENcLsH/zAQXB/rHcFvXXwpPPyAT3LCbYoOBFxvLIfQaUaRg7pvy+xSQkbma73ffOG9dSw+MaMjmM+9utRTt/f+DKdMXR41wOlvce2gKGsgDYD3DJIyuLrT25WKl9fshfX6pYlIGPxfNQV3h01CD6q7STJb/h6N29c7+3vjecz/sfvAjbPcFsMkrh48jOfCXI895EUUX74faXCRzLV3XHr069jBToHWeb5pZ8sQ34h0JNAW8oQBAQBQaDrISAkeNcbc+mxICAICAKCQAERwCISHqVQefGCkZVQffoNoCOH37ceE4Y6igkIG7nLKluQFfBsDUom+Z1S792SVp6hPQ8+szXt7+0LD46BM5nvugZ14Sh5yqIlvle0b5uQD5gMGTZCqRihfufFNBbNSEcPH6J1K5elNyiilI28vn7sYUS4qcIOUpqDNKmfdaVqKmxwsPGRZGKleVCZvkp4LkNvMz5DwEuQjlCDB9mhgASHEvyelY/TL/a9oUhwM6EtIEVsJB1bEtVOnxW6MZQkhlJW8SKAUzirl9VnNLB3ZZlSgj/S9EuqOit1b+hqyWWDEoRDkNK5IyxL2BIEm8C47+Oe39rWRm/8ag+93LTZucGMe0iYF7XN31rHRp3ouroudDOA4yfgmekT2BLl4h7PxLdrgzvfZLhrHrg2BNBufUOfLU+wqYmEk2ZITKLrJ9zU5zna2qREBae8znUCHeVjbiAJgd7V7nTSX0FAEBAETiEgJLjMBkFAEBAEBAFBoEAIMCGuW3SwfQkWg0hs2wGiAST5y80vpBeVeuBMnWB0eSObC3jz2LQeeCsuEY422xbiOqSmQg3tQt187J2VZeyHWojhYLVZ3EX3mi071UI6TH1vqqHRN11NbpLPQT7XUz9ztpofce1JgnC1+dPb8od51pvXcJv584G9yun9j1oD7U769yinYyfb6FNDzqe9//+vrc0GOYQTDJhHus2QnpkDn8KuQdThhfhVFW8dtg0pbMgM6FFOP/jFoeJteB5bht88VOC+VlG4b33lulQ8Aj0A5f72gJT5jD+he3NjU1P9u1+VIr31ezArrPmklA0+n0CVrlNTXJ7NgsSsi59nIL5dvuH6NUx8Q10fdZOzUGR4mBqe+8NzZeiwmsgzuKOsXNRpoul1NP+uFenTCRxklQOWo21hz/zIHZYLBAFBQBAQBAqKgJDgBYVbKhMEBAFBQBAQBE4h4GPRgcW+Ti5goTb/rgZFpDLBisVz47ZfZUAL0ocDVIUt2JkgQr45i5Yqj84Lq0dEOuaOytFOBApzeXCzDzoCO0ZRthXjnEFf0AdgBeI6yBLARoQzkW2qpW1jyf2/Z94MRab4qP/jYAaCA23VExR8NntuXzU8t5nL7Nc9pQQPsvzu272MPjzRRi2WTJj/IO1stjRBmzHKvkF5F7vnXhzM5JrOgYDtN3haz3K68MIL6M827+0cnUiolbhPwwfcx2aIq8R9ScWnSNAvWu+OqeZGQGXE0cD9NYxIZbI5yLscdfl4dcOu5Yd4hm1Yb0U77FmKtsAKbUfzC9ZTKmahuJePGDWeaqfNCu2nz/Dniwz3Ib/ZH3507eTI7w4+ffPN42vlgvmM568+p13zvG7hEvXshS1XPk5i+fZN8gkCgoAgIAjkjoCQ4LljKCUIAoKAICAIdAACWKyChIziR9oBzfSukgnx1PHtlCo8KEHNhoUZW2SwglhfrIJYGDNhMk2YNlst9IICY7F3uVknFNNQ28F6AkeJzzxvUChBHqTORfk+hGSYujwMn0J+362clL3MV2/+tpPct5FwTCSbASRdanDd0mHdT/flZe6b7ewBH28i+vBkNiMNUmne0hWByjiTWIclio3c9hkv4NX0/Hr1+wgi4cPmnwTT9EG7tPLY7H5wKmHY8Br6zjM7Squzjt6EqZvzDYKvmtu3HdyfIF9qJq2DAl2iPtynYFnm8kDn561NoQ0i9eWfbKE9O7eFxi5AXaxED2uTLw62fEmR4T7kt4+yPpe+JHEt3hdx8gwkNt51YMfiijPhitPCSv3ZC5fk5dmbRD+lDEFAEBAEBIFwBIQED8dIcggCgoAgIAgUIQIczIsVZPCdHlo9goaPHNfpFyhQHPmo9NB3JBDc+n9HGS62BQG5DZI8LAChXraLIOcgnSAjX27eEkouQH3usqtIigwHPnMWLVFkPvoJb9K0T3lCfuWoY8Y3blGWAT37psZGTy4iHDjqCmyXGhwL+Zsmj1ZFhgUzjTIH9Lw2WxSot0FcHz3RmlUsiK271zzr/M2ZvudmAVCaV1aU0fEQZpxJb7ZXmb+0Qam6w1KYOhx+vghWK3YpYUh27u/rxldnbS5+vE8FjZswmeY98HTn7lxI6wtFfrO1F+6xyqYkgpo7ygCEEdYoC3ZJ2KQLCviMfGEkr8vWI9fAllH6m0veuGR4GC5oUy6WJ7n0yXUt+9GzhQnb9LjeafRNGbw7wkceRDkrvlFPLhY1+eijlCkICAKCgCCQOwJCgueOoZQgCAgCgoAg0AEIgDTcvXO7VTVtEuMXVA9P5KixTzfNo7i4BgsrJFtQKHzOCm0fBXhQG5Sn5dV1KhAkkh4ECv/G0XIOGhVkRwJy+PV97WopqKY8lOlmu5ggT/m31iirFN3f3MzP6lwXaZEUGR7mp81+5b/et1cd/9f9yt99+y3lFRpmCXD++ecrW5lLpszMGi6bIjWlcG7MCCjmUoOzatxmB+IzP33ygASAjQmn8jKiAT0r6MiJVuXVnT3Wg+jetc85A6sGBd1EcMK2NrvSnOvRsZgwpLf6uH7FY1Q7fbZPd1QeH3X42NopJME0vSHtVBlNb3rM6dN7V6iAhtfds7pT9cW3sfkgv3Ffx4YpTmApstvhze3bRt983JegoJK+Sl0f+xTTOoU3dPfs2pYVyNrWBz2wZRgR74tBLvl8yfAw8rsYLE+wGWx60rtOsgEzzFHemMF/I5YHW+ywfQ1OATBZLsR3LjNNrhUEBAFBoPgREBK8+MdIWigICAKCgCAQgAAHm8QiaP++3YHEOBbuUKiBlB0+8hK1kI8a5AgKbZDC6UCWIErV/8LJUXQDJAKIYRDSSGzngkUaEtRz+ver76tX5CgI7oanX6S9u14K9BuFXyWT3UlaxbCPLIhg4Ay88xEILcwqJQkyPEy9HPaDMwk1V34zICiTsfUzr8xS3GPhjXHm5FKDB/nAh7U7yverly2mTU+sSl8CW5Q+lQhq2eIMajl/6QoVtNNMuo2L+d1pvcrpRAspn3AzwWbmgaebaNgfXaK+0lXlufiyhqnDYXkgwTSjzJbizot787SLz8loZPcKoqqeFfS1RUtowtf/tLg7ELF1IIoR58Fl7RFUnK7mZgssX2/uiM30yo4NORCzQYElw3y6uaIwIt0k0ZksD7JJ0TvRGchTFxmODcCNTzyc8QzS+9YRlidRLUzSGzPqHS+T7Nb7IsS3109PMgkCgoAgULIICAleskMrHRMEBAFBoOsi4EuMAyGQ0jWjxiliHAQ5FvxBxPjqZfUEIjhFVKcIaySX6hrfoT1sYxGmRDZHDQs2WL9AfcyLfQ4AxsEZgyxMmHQHoYG2MrEBohyKqFx91dE3tBHK6VzV43rfWdWOY8pQ8psbFiBo161cHqrKdv0K2B7FRtqG/XKiEvFMIIypnaTwBmY2Itys12Z5ontsP7r5lbydcEAbMe90Yh62KGVlRL0qy+lEaxv999GWLKhs89tliQKSe3BVJb3xuxNZgTKh1D2vfzf6zhN/T4NqUiS4bgeThCd6mDo8bEMmbJ7I98WBgG3+9cSmTvcyuu17j9MfXnVtcTQ0x1bEJb/Z71pZmPQfkGMrcr/cR6mNWqDWhpLf5tOttyJMEa/7huOeELbRrJcNshVxN0ZfMSlv9+LcEc0uwfcZlm/LE7YwwWk5vD+EWZjop/zwzuW7QYNnB8ZVFN/5mE1SpiAgCAgCnQsBIcE713hJawUBQUAQEARiIhCXGMfRb5AEuZIDurIWC+f6hsec9hFmF9/Yt4fmTRqV/hiLdtiegAAAOYy+NT50f4ZyNypM+SDLk1aPs0qRA3WCOd34xKrYRDgwwlH121esjTW+IBIa6m9wqufMMdBJVXwXRoRj3j3w9NaMYnRCz9cXO+pc4Pwmeci2KB+eaKVPfrwn9f/kSHpp2z9mFY92g8DXfzNm8M+gNsEnvH+PcupeUUb3rn2Who65SmXXbVo2/uKdWGPmqjeMFEKfJk6vo9HtGxlxMZXrCo8AyGEOIMy1w4YHRPiyx55Lz6/CtyyZGsMsLIJqwbMkyMoomRbaS2EClMl39tlGf1wpih0Hytv05CNOFTmT3/iLwJYvN73gdS8vRGDLfOKOssPmjGkHk2t78CyBzZru1x1kYWIju6Nu0oD4bt74VMa4dga1fq5Yy/WCgCAgCAgCwQgICS4zRBAQBAQBQaDLIsAqZiiE2OLDparWg0DWjBynCOyodiMmaeqyj9AHBAu5NcsWZxxtd/lB60Qj2hvHyztsMiRBludLPR7W9iBipb7h8djBEWGRE5WM56BtYQFQbbYfHBQWBD7I5nwm2CqgjZxgi9K/R4UKknn5Z/+A+g6/gp5+/OGsJoBsaHh6a/o3YtqrBLWZyXb8vXnxXTSmbrHK3rxhPTUsvlH9d9P+o3npto86XIJp5gX6vBWqzxuupF+PcupTWUYPbHiZzhg6PG9157PgMCIzqG5fC5Gk2w9ies/PtpP6u2u7Kh73MSiA9VMnZr1R7DjCcEHfEUgbJ6OCPMb1NqCN+B/aEfW5nzSGuZQXhA025/X3H5udV1jdpoUJb3S44mjowSnxXsXkd1zRgRDfYSMk3wsCgoAgIAgICS5zQBAQBAQBQUAQ0BDQiXEEstyzc5vT+xoLNhzFhsUIbDuGeyyQUf4Di+em1WlYaCLwn7mw1o9ws/Ib3uPs04xginULl2SMna545GCCHOgRx40RTAp9giIrpczyC/QYZ4LEJctZPR7mAxunTWHXsJXHa/+0nQb9QbAtjllWXDV+2GaFbcODCWXMv02v/iasWzl/b6q4YYtSWVGmbFGurbuOzhp7Nd0995osRT7aB5Up5ngUEhwNHtirgk60tNLNC79JX5yfIuHZWxyYNW7bl3O/wgrwUYdLMM0wFDv+e5snfVXPFAm+8sVfUtVZgzq+kRFaEEbyBhVVaPKbbSh2NL+g4kiEBRW2tZ2JZ7YfY+sxWHrhHsPxNPB7ZaswFwbIjxTWjmILbBlhelizBs0ZXfXtE0BTJ7ZBmmNc8U4RZMsWFJwy174J8Z0rgnK9ICAICAJdCwEhwbvWeEtvBQFBQBAQBGIigIUW+16HEeMq+OawmkBiHItSBL3EYlz3p7aR32x7gqbrylybkjxO4EQsakGww3ZFJ8rxGRa4vkE/40AbjjdiLAAAIABJREFURJYDl+aN62lH0+ZQ0iJO3bZrsFhnPC69cgpdNnV2JIU4xg9jECconasPpv+1vtmRS4BIX8x0X3pcw0rtj0620eABlTR32RoaeNEoqp850armxDyN6t8+oGc5HT3RRnVTrqAZD/xINZXnPsZo9Zadvs3POZ+POhy/+TmLlkaaKzk3TArwQsC2ATOwVzmBCF/7z4e8yiiGTLmQ3yCSEewVauZ8JvbzhnVRmLo7n+2IU3YpWmW45ozug25TtuP5hfcTndjGfTcoGLau4k4FIHcHp4wzPvo1QnzniqBcLwgIAoJA10VASPCuO/bSc0FAEBAEBIEcEcCCcO+u7emATi6lG3tZjxg1XhHjHOgRJLNOmOrHkaH01slvvalMdOMzM3hipmf0CooT+NEGCxPDUHxBVc6KcvQBn6m/B97MEdHcLgfBgyPuGIcgVVrUWqqqBtCEq2fTZV/6nzTk4rFel9tIBK8LLZlMNTjGYtrF56icrOILKhuYxD1ezuXiBALIRE5si/LB8Raq/dxFVPcXm6iiV/+MUw6+/R1U1Y3eO9JCINU5wRP8REsbfWnc52jeX21TH/O8L4QNjOs3gHGF9Y1rk4N932unp/z6JXU8Avr9klvz8T4V9IlBg+nPt/xrxzcwpAW5kt84MRQWPDIuCLgX4beQIr2Tve/GbVOu1+E3zPdLxATBf+uBsPv2OxUQG8GloUjn/MXym3fNGZutDFuY4GTY7l3b1CZwmGqfA1dHCU6Z67gI8Z0rgnK9ICAICAKCABAQElzmgSAgCAgCgoAgkCACvsQ4qgTpDcWU6UvKthyuZmGRykEVsRh98JmtGUE2dTW47sucYDedRXEALBDlIMZBlh9pX1QXgijnDYcgxVoUHGD7cbK1jbqVlylSdvDg8+myabOpdtos+tg54SQnyOOoKmhb+6CYB+E99foFinC5febERNXmqFMnf2xtMDc5KspTubqXlylLgv5nfkL9O4xA0cvuXkF0wYBKOny8ld453JL+CpYrrW1Enzn/Y3T3i/+uPr9n3gxFtrk88aOMa655Qci80rwl0AsehJPYpeSKdO7Xs4c+l4STDKf3rqBPD6+hO596KfcK8lAC7l84BdP0fKNXsEazCUkHNtTLx/MKgSSh9E7qxAvub/k8cZSHIXIW6SLRcQFbt7ClC0j0jM9z3Dhzkd/YOBx9xSTqVzVAbRD7WJiYwSlhaaOPdxzP8KjjIMR3VMQkvyAgCAgCgkAYAkKChyEk3wsCgoAgIAgIAjkiEIUY56qwaMXx9Qur7d7UKJPtJ8wghPp3xUAYmvCxTznsZXSinH3KO1pRbhvusrLUp90ryuh4SxtVlBF9dvSlNP7KKTR+ykzq2TflNWtLYXYaUaYXExNJkU9R6k46b2U5UVXPCmpta6Oz+3ajX/7n8XQVfbuXEyAfMrAbfXfrmwpfJjNtfvhJt823PFbChqnDJZimL6LJ56sbX51xSgXzbkCvCvrCxCl0Q8NTyVeYQ4nFSH6D9H5j314ySdAcupm+lO9nHBcjzrMyiXYUWxnYFECCEh2JFeYmic6+6Agq6vJDB8ZBHujs142yw4JT+niG54qljfhGH8ZOSAUnzbelT67tl+sFAUFAEBAEihsBIcGLe3ykdYKAICAICAIlhgCTHI0rU8H+eEEHosG1UMWCGIrxmpEIwjlIqb6xKA4iwnXvcNNTujNA6groWQifchOfbuWklOCV5WVKsQxCHGQ4Pjt6olUR4mPGfUEpxD/7hS87CfF8+IV3hrG0tRGYQumNAJiHj7XS8DO70z+/cyydtXdlmQq+eVafCrrr6ZfojKHDicnM+UsblCK+2JKPOty0Lyq2PpRieyYM6Z3RrZ7dyqhfj3L60tV1NPs7jxZFl/VYEHEalKTyG/MYpDdOXQQ9l+K0E9dAQYyYGWOumBRq06LHzohbn+s6Jn/xPZ6tSB8cTsXHwOklJHWi6NBB9RlSMW7Q+uKSZHBKFxluC/Lt0z7MM5x80E/FCfHtg5zkEQQEAUFAEIiKgJDgURGT/IKAICAICAJFhQAW6jhSDFI4V9/jfHcMxDQfb7eRFlhwIzjlbnisNr0QeAweC0T4vLISFW3HIrfh6RfTONSNv0iVUYxq8DhYMzmTOs6d3FH8oLbAOgFkLf/VCfEPT4IQLyP4Yx872aZsU844/TT63OhLafLXFjj9w20EQhw8SuGa03qW04nWNho6sJJe/e0pJXivbmXUq7Kc8P1tDz1DQ8dcRVM/c7baKKpf8RjBc7tYE36TzRuesipn8RuF3dGY2klFf78qVnyjtEv3z+frsMHSp3s5fePWpfTF6++IUlzieYuB/ObnDpPeeGYkmTjgJDZ8QYCHPac5uKZL2Zxk2/Sy+JkKRTRidwwfOc7p6482IiEeBhLsv5Bg/6V/DvJc2by0E+n5tnwpZHBK9NP2LPPdkBHiO18zWcoVBAQBQUAQCEJASHCZH4KAICAICAKdGgEmxtAJKKZrRo2jIdU1SjntshLpqA7Dxxlk/eyFS0KD5mGx3PjQ/QRPaU7sNRqkRgPJxgE4sVAH8Y7U8NSLoaq7jsLFVq++IQDCO4rPdD76ARK8ot0TpaWtTRHjIMR7dSunbhUgwVOEOKw98F1LaxudPvA0mjJjDo28fDINqhmTbhb6tunJR9SGSNAxdZ9+oA1IUE3/z69+jS7/6jzq0bcqTbyElYH6QdD4JEXoHE4pJE2vYmwEAJ+2tjYa9qkhdHr1KJVPV/bB3uRU6MsUflDlQlWPv1CEHz6eyoHPYIkCwnLBdxroDy6fkQ4G2pnmMkiiHc2bs8aaA2iOrp1EQ4fV+MAveWIggI2zmyaPzrgSKnB40d/R8Dh95sprY5Sa+yW5kN9MKvs8R2wt5Y1TbLbu2bkt0SDCqI/JZCa9bcEiOfgiFOccjBEBPE01cBjSeN5NmF5Hw0deosh1n0DVYWXq33OMCbxPJPlewYGmUReIdP0+7CLSEbgSySTSgcG8pSuU33hHBeb0JcOF+I4y+ySvICAICAKCQD4QEBI8H6hKmYKAICAICAIFQwAkB7ylX29XB5tkqU6Mw0rER4lWsMY7KsIil9VyWFw21N+QVoVDRTr1ugVKMY5F8f59u2n3zu2hx7RBnMxZtJQuqB5edKQbEyJ7frZdkd0gvaOqEdE/HLEHWTHi8zhuP0Id6V+3clmk4G0gFKA0D0o9KsqoorxMqcNhh8KE+Gm9KuhkKyllOH+OYJogxAefdTp9/ssz6Wcv/TS0/LD5B/uVFo1NBqkHq5ZDx1ro46cPpBlfv4UuvzZFhucrgcSbc2l1unj0uX+PCjpyvJU+/4ne9JU7HqZhV6QCWSKgJZJJgoP4xqYBrsMmQs9u5fSfR1PBMUGQ4/NuZURfv2kh/dGsemWHArKoM9r7BKnDCxFgLl/zoNjL1ecft7WqZznhNwxrGpwwKGTKlfyGt3zttNmRyU6Qj7i/qr+7tifeZQ4Ci41nnFDSE1uqgHRPYkMTdYH4xt8w0jdfHuMui7LEgQ0okIn0vv2rQtX1hWqXiwxH/UlbnfB7A54JneG9rlBjIPUIAoKAICAIBCMgJLjMEEFAEBAEBIGSQyBs4csLWA4ExR7bxQDEA4tvJPigMqlQO32WapauCgfhe+/a55Q3OCcVfPHJR4i9xoP6YqrboKIrpJ0MB1qDAhAquDDS2ewLH/kG2cKEd9ARew605au8Bva+RFHvynJFhoMUP3ysJU2In9GnG73/UQudaCUCEV6IdGbfbsqn/N0PTigy/Lp5i2jM1TfmjQzXfefRv37dy6lnZbnaALjyjy6irzZspKozBxHb8ugYMCE+sBfwK6OPTrYqVb1JgkM7/tWrp9FX7lmn/HlhO4Dx6cwpTB0Ov/Mwy4jO3P9Ctr15w3pqWHxjRpWYczhp8PDWX1LVWanAg/lOuZLfdYuWepG+3A/c8/bueklZ8uTjFA2fOIKvNzYcMV9RJ36fKbsqbNJGv7eHPbdwzx9bO5kQEBLPvzgEcNj7Qdy5wM8lbMbCTgUbzoV8rsZtdz6uw3sIn0LTy8fpANil+Aa3xJzCSSVsaEMhjzmF/ymv9sOnTjAVu0VWPjCWMgUBQUAQEATiISAkeDzc5CpBQBAQBASBToZA2MLXXMAG+YHms+urly3OsEBBXUyIQ8neUH9jevGH4+N1i5ZkNEe/Ht+DNNj4xCqlyA1LvDmAvEmpU3P18dbHpWbkuHRQ0LC+2L5XGwVPPKLwCLIhQZ3692w5ApV3UAIhDjIXyvA4iQOBsSeuTxlm2/Dv86oq1aVvHzxBnxpyIf3Jt+6iERNSauykk05wYzNgQM8KVUVVzwqqvfwyuvp7G9WmDjZ3bAlqcKhycS3S7z5KgcxlYQPhmi9fTjMe+FHSTe/w8oLU4QgwB7JIUm4ImBs1KO3jfSoInvOrtv2HM4htbrWeuhobfmiD76aaXi82O0F++8wDvmfg3h3nJE1Yf9mCZcTI8cpmTCcmk1B3h9Uf9D2eWyDDQcYrS5BzB6dJ8jClOJcb9n6QS/uwYZC0nUou7cnXtS6rE4yBvtGte4bjHsibmzjZBqIb8wnzK2hz3PQ+x+k42TjM18hKuYKAICAIlBYCQoKX1nhKbwQBQUAQEAQiIKAvfKEu4mPbXIRN2VUI/14mxzY+8XCWLYhp18GKvCOHUl7NJoEKgiDIQzwMLt8gV1w3B/aMQ4yYhDcCnuYDb8a3aUOjtwodpBkCOCJBbf3RyZhMtwVwWI1DmTr285+lmbd/j84Y8mn6+SvbaPV99V62MOCPYUcCwTmrzpkMR1sPHDpBwz45hK69ZUniZLhpiwJblgG9KpQafMjA7nT1TXfSqFm3Z6nBWQkOEnxwVTf6rw9b6YPjrRm4DuxVoTYVxv/BGfStH/06bKp26u9NdfgDT2/t9Ir3YhgQPlnDbcHmyum9K1TA1VU/8/PCj9OPfJPf7Oudr2CWp4JEDqK+/QYoL6N8qLvjYBv1GhtJjmdLmId2Polx/TRaWBDOqP0tZH4fj2/giBMZpjLc3Gx2tVsXAXSWIOiFHAOpSxAQBAQBQSAaAkKCR8NLcgsCgoAgIAiUOAJ6QEZ1nBvHug+8me41W4kg+CQUZ6aVCB/fxQU4Go6kBxREmenP2olrqJ6QBykXwjru0HDATVf9HMRPt2lIwscbi1scHYfCO1+EdxgmNg9T8xoQZ3HV3UH1g6g+f0B3RWD/9oOTigQGaX3eGQPpqj+uo8E1Y+lffv6LUOU614HycP3xllRwTiSQ99Vn9KT//rBFKcNrLkqeDEfwVpxA4NRHBbQsp5MtbVRzTi9asP6faddL27LU4Izrx3qVE5WVZZHgA3qWU0sr0afP6E7f/el/hw1lSXzPvyvTV7kkOtcBnYAfvX4KprKc1CbNJy88n+754d7EW4RTD40rl3ltXpmVhym/QTi+/JMteQlmmf7t9oO/dJUiiPNhoxIEODZ0YXNS6HpBSOOUFRTLrCR3keT5JMbD3i0Sn6wxC7QR3ygK8xf44Znuo+YOq543xW+6qyHD+i3sOvleEBAEBAFBQBAIQkBIcJkfgoAgIAgIAoJAAAJ8XLd543oViNJUi/OlvICPc+w9yQFgSw2UqQeigjUK24DAj3Pe0hVWP1UQmutWLrfahbA6MI7XKxPewAnH6fOh8M4FR4wblOEgsfKdTu/dTVUBtfSHJxAQsozgIQ6bhuMtRG8fOqG+w+fnI6Dm5ZMVGf7zX/zCq2mVCNxZRhlkOFTVsEn5r6Mt9O4HJ+kPPz2U5t63hs4dPtqrzLBMOtkIlTeChCL17V5OY0Z8iq5a9jzVz5yYQQ6CsD/Z2qZUuUzeHzx2ynOmf49yVcanTq+kbz6xjc4YOjysGfK9IJCBwPxJozJOe+A3hUCyNTU1tLjxpcTQygf5zbET4Ovd0c+VxIDSCuLAlkOqa9Qzgb3Fg2yCgtrhqyyO2hdWbfPmADa/4fcN+w0Q5/kkxtFWM7h3R8QwcRHfYVjqtiUYVyRs+pue3lwO+4V31KZ4WH/ke0FAEBAEBIHOj4CQ4J1/DKUHgoAgIAgIAhEQwOILiRXZ8H5Wi7J2tTcU2bAWUYu0EF/KCNU6s2KBqxa656UCtGFhzYtt9e9+qX9DIYcFZSrvYKUy39G8mWzBHlHmmAmTCYQzLDXQR6i0oF7HsWSkdT/dpxbwtoQF75pli72tQswydA9UkBvFrmpl9X++rAVsGEMFfVqvbkoFDsX04eMpQhzksfpfz3KljP6/R1vo0LFWOqNPBQ0YcBq9/d5/0cF23+yw+QfCDwE7US4rw0GGf/JjPZQq/L8/PElf/OJl9Mc33ZkzGQ4MdZKbbVGgSh88oJImf20B/dPr72ZsMoAshxUM2vbJgZXKDxyKdW4rAm1WlBOd278b3bpmCw2quSSsy/K9IJCBQN346ozTNb0rywgnFSb9cR1de9ejOaOVC/kNEpjjNqAhHD+B70NBcQtybngBC9ADGePZEIXg5DgOwDnslJTaaK2uIQSTxvMRz+/X9+1Rz3Ooy/FsDysjDiw2krx3v/4qmOMHhw8qVXTS6vZ8WLX5BqE0MWIlPRTg6t3l3MF0+ODv6OjhQ+odwtw0N9u+dUNjepPHduoszpjINYKAICAICAKCgAsBIcFlbggCgoAgIAh0CQSwmAYhkiSx4CKw+/QfoBbeu3duty66QQQwSZ2Eqsv0E3YNKOplBRYUVwi+p9u/xFmsszq8pj1gWrET3sCGfdP37NqmyImgAFy5/jigOu3fvZx6VpbT4WMgeU+qIvUgm70qU/YhfXuU04fHW7MI8Y/3rlCf/fbwSfW3ra0t4/qgNoJo7t29HJa+dATXtmceenp3OqtvJf36d8fpw5OtdNkXL6Mv3/CnOZHhZgBMtkVpbWuj4Wf1otGzbqc/u++ejOayGvycfhVKDf7uBy10DObm7SpyeKUP7FVON92/hv5H7bW5Dodc38UQmDCkd0aP8XvE5tC137iFJi28PzYaSZDf2MzEvRv3If3UTuxGFcGFeMagX/w8YHV3Ek3zfc6hLhDiE6fX0ejaSVkBE3H/BzELohyb3/hvEOQpovz9RN8R2GoMOKiy21XQaGOS7yIoj+1UXEE42WoJ9TI5ncLirdDNAR5XtovB5jY25lXQy9f2KMJ/965tgYR3kO2ZaUsmZHgSvxgpQxAQBAQBQcCGgJDgMi8EAUFAEBAEugwCdeMvStsx8OKUVdaswAaBjc+QcOzZVGCrzx0KahuQWHhigZgiW3dbifFTQcgGU65BshpXLs8KQKW3Sz8yntTxcRAOcxYtLdpAfrrCEkT/u+1e7fma+FBB9+sJK48yOnysJR2sEv7cA3t3Uz7doHlBih881kLHtCCbIMShgO7bo4I+ONaiSO9jJ1upqmeFUoODLP/le8eU1UmUBBK8VyX+n+jDE22qfuVJflp36t+jgv79d8dV8LtcyXA9ECHbokCNjj7DFuXXbR+jXS/9NN102LZA+Q1F/NCBlfTm+ymiHwmq3Z7dyqmqRxl97ZtLaUzdKd/xKH2XvF0TATNoK1CAxQ7m2jduXUpfvP6OyMDkQn7DhgpE4G8PvJVXX+/InYpxQaGCGLuaxqRpmMIa7ZxwdR2NrZ3s/XxiCzSQ5CCIQZTnW00eYwi8L8FmfRxyH/M19b/URgKeo8AEBLratAGBbjxLc43zIWS497BKRkFAEBAEBIGYCAgJHhM4uUwQEAQEAUGg4xFg71AmrblFOG6tJ6iXkJCfyW787ahkEuM2NbJ5ZHj4yHHe5DsWkg31N+RE9sI+JRW0cnzarxVk/rqVy5z+tFgAQ10eZZMgH2OAxfreXS8pZZrLwx31oo/5JMRheQI1NIhcpBMtbXToWMruAx+BfIY9CVTi+O69IycVac4qcZ0Qh0c4SHH8ZbuQCwd2JwT6e+9IC/3uwxYrlLAbQWpr58zRJhDp+OfRdmU4CGpYpKC+//N/jykyfOLll9OEr98RWRnuskVpaW2jM/t2o8+NuZTW/6gpo62sBh9yWqUiwNEfJLQLberVjWjG7Ovoytsfzsd0kTJLFAHcB26anOl5j1MF+E0s+YvHvU8WYE4jJgSsp+LeL/J9r8nnEOZT3Z1ru6P4h7O6GOrwXGJSoE4ox99QVispKzUQwr6q6lz7nNT1tk1wdUqtfcMAivHdu7Y77VzyGedDyPCkRlnKEQQEAUFAEDAREBJc5oQgIAgIAoJAp0UABGf9rCsTaT9bm3BhrBA/9e9TCnH+jMl1/jeU42bSCXmoyk3yHfXgM1afgbyFYhzEuBk8io87w9sbinEE5wLhjOvZ4gMqLaid4wRSw6J26nULlId30CaBuUA1+zz1+pupbuGdgWUkMmjthegB5IKUgexVrrxh20mLuEfSQWoBJ+AepkbkvoJ8BimOBHX0oY9a6KOTKVIbhO8ZfbspYhw+2CC1EcSSv+/RrVx5hVeUldF/HDyehg+fQSGOwJpvvn+C3jp4IgtaqK1V4MnWtjQZjuCZUFqDcGcynP3CUQDIcNiowDP8susWRyLDMT9unzkx3Q7uNxTtnz23tyr7wKFT7YRyHgEyB/QsV/97+9BJOtFKBCsUBNbsUUF0Ve1lNOOBHyU5baSsEkcA3toI2KonBJ/FvFryyN/S/2vvbqCkqs983z/10lXV77y/C44d5wAJEHOOETGimSNgctBjTJQ1YHticoOAGV2JNDMRE/QImZE261xIMpjkrgXLZszKTJBzossEmHXvjI4GJ3PPDGQmZM2NydJoIiZm5E1BoPvObze73L27qveurl3du6q+ey2XSu296///7KK76lfPfv7vWfTRIQWiCL+riXi0q7vLtSq1f/hVS250+odX4gtxvXY0nl+oL7gnKC/39065RlEd732/5H+vpOdwiw28z+e9yy7/vurCmicD93t3/RP9LnEX9Nbrs/vxH+Svl/veKao5cR4EEEAAgfoQIASvj+vMLBFAAIGaFXAXutQE3Z6b7mR1665304fRkyfezP+Ruzim+wfO48e9jw88vhKLavkvjNumxf3zMM+pcFdbFL2t9fxXLdVt+4sL9lP1jneo1gCV7Omp0Pvw3z/rVHkHhd76wkAtCE4ce9N+fOGY4VZzau76omDpxztNPdW9mz6sazyqPg/zBYQqssc0pq1ZpdzqD3u21956R6F3n1MlrkBa/7RmU051uBbH1D8Kxd1K8VljM9bba3bynfN27PR5p2WKWqkoQHdbinjHmE1poUyzt86+20qlWBg+f2qjs6Cm2qS05VJ29eIP29W3d4UOw3u2bzG15nE3zUXBv9q4zJ6YtRd++Vb+MRWrK6Q/29tn/2la1n7ym3ecMbrV8mZ99geXXWqre/6xZn+OMbHoBfbu/Lrt2NyVP7H+zo1vSpn+HvyP7/+ztU8ZeMeQu6N+p+zevmXAIq7Rj250z+hWd6t/9PwPXu308R7tO3iiFCm1f7jaeanPdSUC8ULz8leTj8QCnlH6xvVc/vdP7jjdhcfVFkdf0rMhgAACCNSvACF4/V57Zo4AAgggUKaAN4DXqbyhuiqMdau0d9Nt0+6mwF19Rgc8/sq7j+tY7fPu/qUv2OWt7NN59u78WsEZq6rZXaTNu4N7fLEFxrSvW33nVmv5n6DcMNxdzOv5v34qsMLdvT170XXLTeGOAnK1MSh30Tn53HzHHzlfCoQJijTmHx54yhRsPL//ycBFxxTOqWWKwmaF3grDtYil2zrl3UC8f3HNn/2uvxJcFdbqb9ySSTlV26roViCuY4v1DFcrCFWdq/pcgbu7abFAnU+LUrqV4eoXfun4rDOO4YTh3h78/QFk2tQWZWJz2n514qwzF3dzq8GntvaH///8+jv5EFxzWXRRztbv/22Zf2M5vJ4E/F/E6Asgvba0UO3/+JuXLdfSv/aDu9Vi+O39HaA7lRT0RrlYZTW8nirZP7yS8x/JBTwrOY+w5+68e2PB36/e903ecxV6D+V9f+UtaHD/nBA87NVgPwQQQKB2BQjBa/faMjMEEEAAgRoVKFSB7bbn0C3HqnxWGxZ/31O1B+juWm3+FiAKSnY8ddBZEFTh7b49PQUrrBUyF7uFPCgM1/g677l/UAW1/xLpPE5V9YVepMWqqt1wRy1JVMmof2tT4B1F8O1WxC+5+bb8uYf7clKYIdfnDnwvVOsUBdIKw9U6JZlIOH3Ava1T3HFcc3GTE1r/+sQ5p/pb/bMzqeSAQPzkmV6nwtq/qUWKQne1KHErw1WRrTBdIfnb5/rDcAWHCsN/b2zpYbh/YUK3Lcrps702pbXB/r83zuSHpfFoU2X65dOy9v/+6oydPq8WKSmnX/r7p2Ts7m//U9Hq3eFeG46rXQHvIq2aZf/fq6TNmDTWHv7rd+/yqZXw21vdrf8u9Dugdq928MxK6R+udh+62+djd9w1YtXhwTMYuMdoLuBZ6qLaboW2KrI75iywKTNmOq9Pffkeh3VaSrVnfwQQQACB6hUgBK/ea8fIEUAAAQSqSEBh7qY7b3Wq8IazeKTb87tn2+ZBi7MpYO5+fF+oKmWdR+GQP1zWB36Ny93cama193hu/5ODgvNigXhQoKTjdOu5/u1uWmBs357ddljtTY4cLnhV9SFaQbe7UKcbemvnqIJvncttd7JoyfKKhR/urfphererglp9whWIN2VS9tqJdwZUULtV4v2tU5L2hlqhnOk1FXmr7UNCIfo7Crp77Y23zg2y1T5tuaRTPe4Pw9UzXH/mhuFzJ+VsRnvGOc8rx87a+Oa0Xfmha23hqvVF26QUa4uiinC1W1HYrk0ZuHo1K9R/78SM/UrB/ulep3K3t6/P3jOuwdZ87UmbueBDVfS3nqGOpoD6geuLP3fT61l/jy695GJ74H/+2OnnX41tT6juLv9VFaf+4eXPpvAZCn0xrS9Hbrv7PnvrxPH8gp6HDj7b30ruxMA714Yal/v6lJXzAAAgAElEQVT7WOfT3QU6n9v7XHe46S4sZ+0Nz91vxc7nDch1p5W+yNddC/pSXuueKCQPcwdWpRw5LwIIIIBAbQkQgtfW9WQ2CCCAAAIxFfAuFqjQ+sFv/KVdcqGX91BDdoMabxCtwFofMhUYlxKAe59HrVEe27ZlwAdfnVf9rv29UfUB+edHfmz79/SEDsSDFs/0huH+oFTj1Lw65i6wRUtucMbjr2r/2U8O2YEn/sKe3/+9QV8KFPLU+fShXB+s/T3B9diipTc6i4KO9IftoC8bir02FHhPb8s4/cIVJOvffX19Nrkl7QTHWijz7XOqAjc7fbbPCcXPnFPV+FknfPZvbdmk5RqSFyrO+4NpBfB6HoXTbhjekk2awnC1NlEYfvTkOaeq++obV9kVK++1tskXDTq3Fsl0v3Rx26Io2FY7FoXv7qaWKPpzjWVaa9r+5TfvOAtlqhp+ZnvKVnc/HriYYUz/+jOsURDoXDxnQAin17Kqwd87b4Flps+tip7fbqsqfelHdXdlXkRh+4e7dwfpd6T3S9zKjCq6s+o9xKObNwz4QqjQ4tXaT19IH33lZWdxboXjYUJsjdRddFoBthbtdqu89fvUXSRUa7SozZvam6h1nLtAddiwXNX5+v3dXz3e/2+F5e9WlA9eeDw6Rc6EAAIIIFArAoTgtXIlmQcCCCCAQOwF9AFT1eAKYfWB+vZ7NhZdpMmtblbrEzcUVhBy290b89WLww3AdT43RC7UJ9z7Yb/QYmFDhQYKB1StveTjtzmBclAYruBdLUf0Id1ZpO2KxU7AUCiMHk7wrQ/Kbq92f/jtPre3qny0X0SltE5R6xC1TVFo3JxJOX3AFYafutAXXK1EnEC8JWWN6aTTXuSdc33227fO20tvvuP0BfdubosULUh5/HSvU5WtTc/Tkkk6PbrdMHxsY8ounZDNh+G/e+u8UxleKAzXnLpWLst/+eC2RVE1+O/ePp8fggJyBeF63qtn5py+4BqCFs2c0pKyW++6zxZ1bhjtS8TzV4nAx94/dcCXfPp7cq63b8DCsHGaivtzT+0i6rF3dxyuRSn9w2++47PO3UnVEoj7fxcHvQfR9Sj2+ztsOxS3ylu/293QWi1RVADg/x3vhuW/OPJjJyDXIub63d3fG/3lUNXq3ufzBuXNbe1OWE5VeRz+ljEGBBBAYHQFCMFH159nRwABBBCoMwF/OxJVZK29f2tewd/v299L2+1zW2oA7lZ5qT1AKQtFBlW/hQnEtaCkqsB2PNRVtGpbi2IV6r/qhsJP7Pxq6IpvVZDrQ68+QPvbvqhiTebFgvY4vRzdCvznDjwZuCiot22KgvFUMpEPw/sXyuy16W0NTiiufxQsa3HKV4+fGxBEa/5uixT9tz8Mb88mTYtrumH4tLYGJwxXsK3K8GJhuF7Xeu26m8bQP8b+Vi3upudWD3OF3jPbG+xfXn/HCeEnNiVNodOH126J0yViLDEU0N/7v/rzP7XvfeexAaNz2/uM9pC97UyKrd8w2mOs9+cvpX/4UGtlxNFR7wG8v4v1XqKr+1tDhvn6ParFr73thdzWYWplpdBa1eO6Q02/s8O2VlF1d/9Cre1Or/D+L8LfbZXm99N1cSvI9Z7C24LFDcvDVK+7VeV6Pm/7FW8FexyvHWNCAAEEEChfgBC8fEPOgAACCCCAQMkCOzZvMLcKW8GsbrH2Br1qA6L2HN4q5VIDcIXdz//1U0V7bbstR/RBUPsWW4TSnZzCm6Wf6LSrltxQ8IOqs6DlwWecNgP+D6LuQmPqMa4PyoU+JOv8CjoVmv/4hb9z2q8U6xHuBXcXBdUHWH0w9vcwdx9XFf1Itzsp+YUxxAGy7Vp1vbNHUCWeW22tHsiqElfVtQLnU2d77fTZ85ZLJ21Sc8ppn6Jq7J+98U6+P7c7BFV/q1+4Fqb0huFub+W+PrOT7/Q61bXu4pkKrF859o4dP9Nrvzcua//pI39oiz/zoGVb2p0Q3L2zwW2L4q8GVzW6wnE9rgUyXzt53t54u9fasgn7zx/+sK145H9FScq5akxAQdgXbrvejr/+ywG980drmu5ile5aBv2B35jRGg7POwyBUvuH63eYgtw4X+dC/cI15qD1Sood51/nw30voN/3Qe8rvJdEf1/u3foN5/d0OX5uWK6774bTgqVr6zedu9nYEEAAAQRqT4AQvPauKTNCAAEEEKgSAW8Q7g5ZLToKhbVhAnC1C1F4/NyB7xX94OlWrc274kOD+myXUv0WNhAv9CE4KMANc/ncYHveB692Fn8stGCovkiQp/5dC5uq8LTYn7bH/vaIc3u4e72LfbGgfRUoj2lMO21TFH4rZHZbp5w+q77hfU7v7bfPDmxPomNV9a3jVF1+5lxvPgxX9V+TFutsSJg3DL90fNYJv7UpDD/Xa9YxbYJ98OY7bcp/XGL3r+5vB6TNDeqPnznv9Ct3nk+V6Omk81xzJ2acgP03b/U6vZw/fOUH7L/t+JtauJTMoQICbtud3732S6ePvbfffAWebsApqe6utHA8zl9K//ChvjCOx2xUwf2m9Wz/cv4LeY2rUL9w/3iLheH6Mt+/qLS77sXPjhy25/c/GbrPuH8B2GJtVMqxLNavfM39W8sK4csZE8cigAACCFRWgBC8sr6cHQEEEEAgYgF3ochqW5zKy6CK3r27vj7g1mL3cbVG0YdQ71YsAJeFPpQffuGZoi1OVFk1f+FiW3Td8gFV5UGXJcpAXOM8sGe3lVoV5h+jG3yrh7iCVIXC3tuztb/bPqYa2p0EXQP/43t3ft12bO5yqsD3/tOvBzzsbZ1y+OAzRSvoFYgrCG/LpUw9wxWIa1MfcS1Uefy0/t07qF+42yLFDajdynAd3V9tnnSqzVUZrj+bP7XR6Reu7eiJs84CnbOmjLezrVPtr5/7Byfc1qa2KNq8vcHVF1xbSyZh75uUscNH37HGhoRdfslE+6O9Py+Vjf3rQECv/66V1+df93oJ+XveR8VAdXdUktV9nlL7h7vrZMRx1qqY/vOHuvJfnrt3ZXXeszFwuLq7R3dtuRXf7rGF2pvpZKWse1HoyXV+VYrrrgq1UKlEOB44aXZAAAEEEKhaAULwqr10DBwBBBCoTwGFnt1dq512Gu6HrTh/uPReJX+/b7enpiqnVOHrfohU9bJbieQNwDc9+h3n1t6gFidqoaLq50KLTw3nVeNWfYUJsYMqxPUFQM/2LSXdIq0xq2e4rvPu7VsGBf5uOH7TJ+8aVN0+nPnG9Rj3zgG1lul55siQw3Sr73TN/O1hvAf626boMYXZCsJfO3HWCcYH7p+wMY0pSyYSAyrDFTq251JOBa4bhuvc7uKZOodbGT65tcH571/8Totz9jlhubcaXOfKpPqrwa+YkXN6hv/y2Dm7fHrOPvvEi5ZraY/rJWJcoySgn5/+L8TKHYq3EtUJvqfPLOmLxHKfn+OrQ6CUL4zj3j9c70G6uz6Tv1snTL9w9yoVWnhTrWGKheHe4/S+IMz7i6BXhH43Llh4tdPn+z1z5tvvzZlXdmuVoOfkcQQQQACB6hIgBK+u68VoEUAAAQScRZjetAN7/mJA24+4frh0qqCf2G37v9uT/2BZrOWJv0/45Bmz8sGOPoy6bSS8LwIFNW7oPRLVz6VUdbuB+KnjbzrVX0O17BjOC9v9EkGe9bC5QZ++4Hjg0e+UNGVvq5xi18FdXFOtT1TZrSrxN06ds9dPnR1QVasWKa1Ov/D+Km5vmxT1BFcvcYXharmiynBVe8+ZlHPan6i/+CvHtdhl0qa0NNgv/u2MvX7inKWSA6vBVXmuSt6JzUl736Ss/dNrZ+z9U7J2+5//PzbpPfNKmjs717ZAobZSpc7Yre7ury6db1pf4D1zF5R6Gvavc4Gw/cPdL1j8vbTjwqf1Sh7btiW/dod+1677YrfzxXrQpt81B574C+c9j7v2h35Hh7l7L6h1iv5uqle4qr9LWYTTXYBT76kIx4OuII8jgAACtS1ACF7b15fZIYAAAjUvoA9cPzzwlD2x82v56vA49OJ027a4CwGGbdPRs22LUyk91OYG/pfMmTeqlYluIB40Xv9c3ADg6CsvDag4W7T0RltwYUGxTXfeWnDxTJ1LxysE9i4aWvMvdFXDL57j9FNVuxy1zRnuFrZ1ikJrBd3qx/3GW+cGLTSoRSzHNaWcHt7a1INZ7VTO95kpDG/Pvtt/XEH5tLYG+72xWecxheFHT561pkzKOUZV5yfO9Pcn16aWKP0tLfrsQzMbnQUy23NJu/1Pd9t7Fn10uFPnuBoT0M8e/cwsdVMop1YK+hnKYpWl6rF/GIFq7x/uBvre3+9h+oW7NmEX0RzKcqjWKQq2Fy29wfnSyl388sWfHCrpy3Z/axUtyl3Ni2eHeV2yDwIIIFDvAoTg9f4KYP4IIIBADQkM93bcKAn87T6CqpX1QVHj1q38OrZYtbeCffX1Hs3ARl84vP7qy07fXVVhKcTWf5e6uR9eVW2mTV8QdD++L//hM0ywFdR3tNQxVcP+SzuanGGuvb/bucU8qi1M6xQF1wq9/e1RNAZVbY9tSlk6qertPjt5ptdOvNPrLJiphTNVVa72KaoMLxSGqxXKy2+edfqSHz/T60zLXSDz7Plemz0hY82ZhNPL/CN/9GX7jx+7M6qpc54qFgjzc6LQ9MK0E6piFoYeQ4Gw/cP1fmHBFYsDW4iM5BQVRKstm7/nd5h+4Rqne+feEzu/mn9/o3kOpwpeYyjUOsX9Yv2qJTeaFv1Wtbj6nB964dn+9yl6v/LqS0Oy6RxqM6Zj2RBAAAEEaleAELx2ry0zQwABBOpWYDTapfj7favSsFiPan2IO/z3/R/m3A+W/oulYFi37hbqE17pCys/fWj8+ZEf22uv6gNkcHWVt53AlOmznPYnbnV+0Hj9t0rr2LXLFzqBv26h1ofYYueqlzBcJrdfM8ehVBW8WqJUagvTOsX/3G6LlJZsf+CtMPzY6V6nOlyBdlMm6QTibhje29tnHeOzNqW1wTmVKsNf+OUpp32Ku6ChWqro2EzK7MqLGu3ts732oVvX2ofXll75Wykrzjs6Avp5q2Au7KbXnvrM9/X12Sf/ZKv9l9vXhT2U/RCITKDU/uHLPt5pqk6OQzDrLzIopV+4C1joHPodH9Q3vNAFGKp1it4XXLX0BucLBdfPLTg4+oq+yD9khw4+mw/GS6lwj+zFwIkQQAABBEZFgBB8VNh5UgQQQACBkRLw35IctHBjKeNSMLl319ft+f3fcyqc9KFQLT0+9sm7BtxSq1BRgbJb7e32yXSfy+3rrVBcj3kro73Vjv6K6VLGWmxft7pbFVMKu70tSgod410sTq1L3P8v9iE97C3hei63Cq7QQqf6ANuz/cvmVo/7x+a2m6nV/uC6TutuuNKZ9mN/e2TEbtkO2zrFvR5ui5TMhRYp53r7K8PdMLw1m7TGhv72KaoMVxX5rLEZZ3HMgy+fcirNtRCmNp1LvcNVDa5FMXXYzNnz7b/t+JsoXvqco0oFVOG5ZvnC0KNXOx/dRaDtlrvus1vWfSH0seyIQKUESukfHocWb66DvoDa8VDXgH7hpVZ1632Bvth2F7ON4svsoVqn6L1Fx9wFdtWSG5z3Ge7m/n5TW6Q4fNFQqdca50UAAQQQeFeAEJxXAwIIIIBAXQi4VUD64OVWV+u2eIWm3iokfSg7efyYLRqi+qpYv283gA3T4sQJfBcutvkf7P+3qhr14bJQ0O390KkPi13d3yy5ElhjVsCtMP7QC88EtjLxht2q7I6id67ch+r17X0hFgvENY9HN2/If3j2v3iHe5t13P8SHNiz27ovVL7uf/GtURtumNYpGpyquN0WKfr/8719TiW3wnBtWnxT+2hzw/BTnsfdanCF5NrGN/UvkKnt79/I2COP77OZ/4EFMkfthTBKT+zeJeL/IrHYcLwB+Ec719kn/+ThURo5T4tAcYGwXxa7YbGqm0dz4dZC/b6HU03tP49bpOAvJBjOaydM6xR6gA9HlmMQQACB6hYgBK/u68foEUAAAQSGIVBswSbdevzcgSedgLVQZZLC6P17ega0KFly821OiK0q7uf/+ik7fPCZgn2y1S5E7T3UxkJBrbfqaKgA3J2ewp+ulcvyPTXVj7Pz7o0FZ++2sxhOKxONc9L0mRX5gL1j84Z8Jbc+MGvb/92eogtgupMr1CfVf1u1H6LWwnD3joC49TMOap2iym+3RYoTeJ/rdaq/U8mE/ebUOWdRTTcM/93b5522KP0LYvZfUS2QqX3VXuWqi3LOopr/+OszdjbTatu+s9+mvud9w/gJwCHVKOD/GRg0B72utLirtmtvWmXrtjwadAiPIzDqAqX0D1cP7CUfXzVqVcz+goDhVnRHsYjmUBduqNYp7holurOtkm3GRv2FxQAQQAABBBwBQnBeCAgggAACdS1QqF3KlBmznGpwfXBSxaECVbdNiCq1FXpfed1ye/3VX9pzB77n9M/2VyZqP91+64beOmehLUwA7h6n8Tyy4c58FbTGpf7Q/tt4OxfPKbgIlALu5rZ2Z1z6wFepsLvQPNXGRCG4Nplo3O4WtgpO+2vO3g/+Ola3ZhdboFP7r9/6zRFrH1Kpv0zu68RvV6nnG855+/vd7rbHtm0Z8PdB/cLbcylngUxtCrQzyYRNaUk7i2ee7e2z37513l47ec4Jwb2bu0Cmjrl0XIONa0zaqyfO2dimjM2aMt5u+OIumz6vv00MW+0K6LWldQIKLRxcaNa6gUB3G2i7ePY827TzaWtmwbvafYHU4MzC9g9379pSS5LRausRRb9w9xL6iw0q8YV2odYpeh7dYcSGAAIIIFDbAoTgtX19mR0CCCCAQEiBQh849eHSH24rhHR6Z7/68qAzuwHtvCs+FKqSupQA3Ptk/j7hD37jL+2SOfPzuyhwVkW7wu6oWpmEZCy4mz4gr1+5zHlMQXz34z8oWLnm9udUtf1z+58MVSHuBuLPH3jKerZtLhqSDedW7XLmHPWxCgAV9KvljkL9OG+Fqvo0XlXmtuWSTvW3NgXbLQ1Jm9aadh775bGz9rPfvWPn+jum5Dc9pgU1E9ZnV89qNFWMj2vOOlXh2pZ+bpvNue7WOJMwtjIE9HrqWnl90S+6/KfWnQStmaQlEgmbOG2mbd3zHAF4Gf4cOvoC7s9U3aVW7AtfjXK0g1z9ru/u+kz+93A5AbY/WNd7B/0eH6pV3XCvlJ5LRQHFihWGe16OQwABBBCInwAhePyuCSNCAAEEEBhFAbV3UM9pt2/4UENx+1cuum65Ux1eyjbcANx9Dn0Y7u5a7QTFGsfaL3Y7AWncNm8P31IW9hxOIL7gisVOBb9C9EI9g4d7q3YcTN3q/rX3dzs97KthK9a/XRXhCsMVbGtTv/BxjSmb2pI2LaT5v3992k6ceTcJdxfI1H4LpmScfdPptBNyuhtBeDW8IoY3RvdnZZijFYC3ZPpfWwrAN+162iZNL3wXTpjzsQ8CcRMIunNq7f1bnbB4tLZCX4Lqvcma+7cOq21Lobv1br7jswPWchmtufK8CCCAAALVJ0AIXn3XjBEjgAACCFRA4OdHDtufP9TlhN8KS69aeoPddvdG++GBJ/NtPAo9rb89R5ihlRuAu8/h75GrD776AByXzTs+mX7l2/sGVKyHHafbz3Pfnp6CrWf851HFmJ672OJ5Gsvt92wc1aAg7Ny1n+Z/82XTnEO6tn7TlsTwy46h5lOof7vy6zanX3h/ywptqg+f3JKy9mzKfvqbM07bE21uSxT99/jGpL13UsYJwBWEezeC8FJeVdWxr3cdgaAR63WiHvQKwJta250KcALwIDUer2YB/WzVYt9ak8T7+y4ObcD0e6tn+5fz64CU+yV0oUU0CcOr+dXL2BFAAIHRESAEHx13nhUBBBBAoIIC+rDk75Md9HSqrO7ZtsUJRvUB0ntbrKrDtf34hb9zeoAXqhIP+wEvqgDcnY/mqsp19dHUFocPv+7Y3BYe+n+18IiiUr3UQHyo667KdFXQx30xLAX6t18zx5nKnz/5w1CtdoJe76PxuF6j/pY1WviyvfHdFikal1qHT2pO2xtvnXfao2hzF8hUNfjCGVlLJxN2+nzCxjU3DJgKQfhoXNnKPKe37VPQMygAVwW4FlHV1r3neZs1e17QYTyOQE0IuOsxuOtuaFJx+bJXv7/0vsd931Tu7123dd0TO7+ab7ui9xZLP97pvP9hQwABBBBAYCgBQnBeHwgggAACNSWgD0hqHaFNLUomz5hl75kz3+b5gu1yJh10O3KxPphuqFNKW5Cw4wzqEx72PFHt521h0HnPRuu8e2NUp86fJ+zCYUFPXE7f0qBzR/G4vqB5YM0K51RP/OOvSv6CJ4oxRHWOYv3Cc2mF4Skn3NamfuETGlP2m1P9C2bqjzOppPVpgczxDU4f8TdP91qvJW1y68AgfOGq9XbFynujGjLnGQUB70K6YZ6+qSHhvD60rdvyqF1706owh7EPAjUlUOjOiWILaI/0xP2LWEfxe9d/l1EU5xxpF54PAQQQQGBkBQjBR9abZ0MAAQQQqLCAG4IX6wmtCu/5Cxc7wfjvzZnnVHyXWjXuTkHP5d6OHFQdvnfX151K80oE4O54NIZNd96avy16tHqDegP5kWrREkUgHtcP0Ht3ft12bO5yKvv2/tOvK/w3aGRO77+DQc+qFimq5m250NJCf3bmXK/99tR5Z1DZVMJpg6Ie4VfNzNnxM7328rFzNqG5wS4akxkwcILwkbmOlXgW3TGgL9HCbo3pRH6x1Vvuus9uWfeFsIeyHwI1J9C5ePagBaL1u0MLaMehUlpfcD22bUv+fUo5/cK9730e27Y5X22ueapVStzv8qq5Fx8TQgABBKpAgBC8Ci4SQ0QAAQQQKF1At+D++IVn7WdHDtvRV14a1DPTe8bJ02fZgoVXW8ecBdYxd75dMmdeycF4sQpXPY8+gLoLWO546uCAViulz2zoIzTvB9essBePHHZ2HKkQ2h2VN8DSB9FHHt8X9RQDz1duIK4P5eoH722JE/ikFdzBre5Tr3O9fmppK9QvXCH32KZUPth8/cRZO9trTvjdcKEafN7k/gUy//n1M/arE+ftqoubbUxuYI9wgvDqe6VobYZ7/3BZ0X7+/hnpDoJcur8CnAC8+q43I45ewLsYtf/sej/Qefd9Jb+/iXqUlerv7T9vVG3Yop4/50MAAQQQGD0BQvDRs+eZEUAAAQRGWEAfDhWyHH3lZTv0wjPOIotHX32p4CgUjCsQX3CFWqrMdBZ0DBuKDtUuZTgLaZbK5K+yVXi66dHvhB5/qc/n7u8NsFTxrsB2uFX2wx2D/7jhBuJhe7yXOs5/+/XLoQ55++QxO33ymLPvNx7ZbP948Bm7fNE19unPF24r8+bRX4Y67+mTx03nDrOdPnHM3j55PMyu1r9vyPN65uaeXH83/ZvbGuX1U+fs1eNnByyQObEpaXMmZuzts7327MunrbEhYZfPaLZWz0KbOh9BeKjLF4udhgrvCg1QdwY0NvQH4Gp/ojYobAggYM5ilG5/cPdLeNdFv5u7ur8Vi6pw/Z3XmiZq+aVNY+u85/6y1w9x79KjEpy/DQgggAACfgFCcF4TCCCAAAJ1LaAPSz8/8mMnEH/xyCE7dPDZosG4PkwqGO+YuyBUn3G3gtf/IVTgbsi65OO3VSyc9n4QrvQHX32Y7Vq5zLkNu5ItX8p5sbpVYvoCpFD7mkLndq+TAumj//uAZdP9Pau925uvDQ6g+6xvyKFeaH0dajq/On7WXjl21i4dn7HxzQOrnQudQCMs5fxJ9SEJuWnPgrsXmW4p49B5iw3luZfestPn+vILZKo3+AenZ50Q9J9eO2OvnzpvH+5otaYLoah3OgThIS/uKO7m/fkRZhhaKLVZK6ia2dzLr7YHdj0d5jD2QaBuBLzrcjzw6Hdsx0NdA9qkjPRdYkPB09u7bl6WTBQBBBAYdQFC8FG/BAwAAQQQQCBuAgpL+9up/J0TjCsg1/8H9RmfMn2WzbviQ06o7fYAVxV29+M/cI7/4YGn7ImdXxt0nkr2otaHy+6uz+Q//FaiT7i8ulZe77RgUWj8lW/vcyrn47zpehzYs9u5IyBsIK52HClPqqsgLq0/VDBcJBxWhXLQ5pwnIC1Wtus+11Dna7zQGmLIfbxj8oTX3hzbrbANGvtIPa5K8H95/Ux+gUw976Xj0ja1NW2/OnHO/vWNs7bk0raiwyEIH6krVfrz6OfH2uULB/UxLnYm/ZVT73j1h7949jzbtPNpa24bU/oTcwQCNSxQ6ItpBePe33cjdZdYWGa1U+vZtjn/syBurcnCzoP9EEAAAQTiK0AIHt9rw8gQQAABBGIm8LOfHLJfHPmx02f8xZ/0h+OFgnHvsDvv3mgLFi4e0Ge8UB9kHVOpFhz+PuFRLETlnaO34my0e3C6bTXUB17b66++bCePH7OTJ950/l9/7vz/vwf3p5x/Hyta+R+zl9+IDCdzIdQP82Tqx6xtqGO8XxT4z6l2FtqU24cJ+F984x17+1xffoHMTMps4YycnT3fZ2+c7rOLxmSHHDZBeJirOrL7eL9AC/PM+q5IAbjuXpg4baZt2vW0TZo+K8yh7INA3QmoRdma5QudebuV3947xNz3Hbffs9F5PA5bpfqFx2FujAEBBBBAYPQFCMFH/xowAgQQQACBKhbwL8Dp9rYsNCW3z/jkf68UX3DF1TZp+kyn2vy5A98bUJ2lMFzB+c13fDayvp36YNmz/ctOr1BtUVWA9WzfYj3btjjn7Lxnoyn0L3eTqRtS61zeIFuh9akLlfp6bDSDbG/4668SL2SgfRovtHAo9ri30ty7TzbV3/ohzPO4x2UKtG4p+doM3dWl5NP1HzC8k57v7bNXjp+zE2d68xX58yY12Lk+s1xD2sY1BbeKIQgf5i+BHGYAACAASURBVCWr0GHeL9CCnoIAPEiIxxEYLOD9He1+Se2/Q0xH6Y40PR527ZNKW/vfs0TVL7zS4+b8CCCAAALxFiAEj/f1YXQIIIAAAlUk4H7YVMCsQDjMApxun3GFuYVarkS9kKZ/wawHv/GXww7avedSdbk+QGvTh1dvtbWq5d2wWhXZ/iBbTtqKLVJaRS+BWAw1qJo7KEhX3p4K6BOusD6oaDxoHMIK2qdQD/bXTpyzk+/0WkMqYeMa1Rajv03NxWNz+YUSh7oQBOGxeJk6C/e5X8oFjUj3DKgCXNe5qbXdHtz1fZs1e17QYTyOAAL//jt5/cplzhft3vU69H7D3x5F70e6ur9pcVpQkn7hvIQRQAABBKIUIASPUpNzIYAAAgjUrYA3AFcP8BZfj9pSFuAshOi2SrlyyXJ7z9wFZTnrFulNd96a77tZqILbDbLdtiJukP3aq/1tRtQKxlv1rip3p3r7xLGyxhaXg72LoKrX+2PbNtuZU8fsXG9cRlib45C7/++OO9Pjr7+7AKlaqcxob7ATZ85bb19/ZbkqhRWEt2RTgThzr1thSz73fwbuxw6VEfBWp4Z5BgXgbt/8rq9+2y7/g+VhDmMfBBAwc75g9y5c3fPMT/Muhf4uRt0yLYqL4K9eV1C/5v6tsalcj2KOnAMBBBBAoPIChOCVN+YZEEAAAQRqXCAoAC82/VIW4PSeQ9XhbquUYoGh9i/UH9v581dfcnpjaxEqd1P1er56u0aC7KCXnRt06/ZvtaiRgVrU6P/9rvriQIuaFtt0fDlbS+sYa2lrL+cUztjL2ZrbigfQYc9byVvpd97xQVMQrh7gb53ttTffPmfHTp8bNLQZ7Rkb19QQOGSC8ECiiuzg70kc9CRNDQnLXGgH9Mk/edg+2rku6BAeRwABn4B+36vyW5v/i28FzPpi3PsltqrGu7q/New7xSp1AfTz47FtW5yxVmodlUqNnfMigAACCIy+ACH46F8DRoAAAgggUMUCww3Ah5pyKQtwqgJ78oz+8HM0+2OXcgn1wdUZ7wiE7aUE3aXMgX1HXuCNX71sXauW2Ssv99+NoHYsk1pS+Qph74gmtzTY5NZM4CAJwgOJIt3BG8SFObEWX81p5VQzu+Wu++yWdV8Icxj7IIBAAQFvC6JHHt83IOD2L6DtHq4FMzvvvq/oHTqjAe0unqn3X9r0e37tF7tNFexsCCCAAAIIDCVACM7rAwEEEEAAgWEKVCIALzYU/wKchw4+MyIh8lA0qkhXxbQqmJsv/NutaFZVcV9fn7145LAlLOH0+1aluSrQC/U+H+YlyH8A7pg73xmL/j1URXc5z8Oxoy/gD2oIwkf/moQdge6muPcPl4X+ueUNwFX9rSpwNgQQKE+gc/FspxWatz+494yFevVrX60fcsmc+eU9ecRH+/ua6z3J7ffcH7vq9YinzekQQAABBMoQIAQvA49DEUAAAQTqV2AkA3C/sqope7Ztzvf0Hs5VUOXUgoWLnQDbbeWx/7s9+XOq3+bHPnmX85j2UcDs/XC89v6tpgoxVWSpP7iquhV467+9fzacsRU6xq3o9gbd3j+L6nk4T/wF9Pp6YM0KZ6E3bVoYc1JzquAim2Mb03bRmGzgpFQRvvgzD1q2pbyWNIFPVKc7KKxau3xh6ABcC6Y2NfRXgF970ypbt+XROpVj2ghEK+D9u+hd0Nr7LFrvo7tr9aC/r+7v/WhHVP7Z/Itndt690Wn5woYAAggggIBfgBCc1wQCCCCAAAIlCoxWAF4o/FbV89KPd+b7SasvtALpo6+8bC8eOWSHDj7rVGEX29ROZcHCq61jjhbb7HP6hCvM1qaqqgce/Y7z33t3fd16tvXfeuw+5obfJfIV3Z2gOyrJ+jiP+tu6fe0VhI/NJa050x+ceje10+gYn7OUVs4cYpt4yXvt43+6hyA84pePd1G+MKdW95OWTP/iphfPnmebdj7t3GnChgAC0Qh4+/IXC7aLtUfR+4L1W78ZywUp9ftAc9v06HdiOb5orh5nQQABBBAoR4AQvBw9jkUAAQQQqDuB0QjAi1V++xe3KnYxhrsAp86nYDrK3t0E3XX3V6aiE3b/PrpPMiaXtNbs4CC8IZWwjnE5y1zoL11sUATh0V4u/exRBbjaL4TZ1N6mJZO0RCJhE6fNtK17niMADwPHPgiUKOB+iajfyTueOlgwNNbf357tX3aCZe+mY26/Z6NzNxgbAggggAAC1SRACF5NV4uxIoAAAgiMqsBIBuCqwtItvoXanqg/pxaBUsuScrZSFuAs5XkIukvRYt9yBfxBeFs2ae05gvByXcs9XgFa18rr83eWBJ1PhfoKwJMXAvBNu562SdNnBR3G4wggMAwB7x0aek/R88xPi55FIfhj27YM+kJc70HWb/1GrBbNHAYFhyCAAAII1JEAIXgdXWymigACCCAwfIGRCsD1wfTAE7vN25/bW42t9ieVuNVXz/vDA0/ZY9s2h6r81pimzJjl9Ax3F6OkR/fwX18cWZ6A7pZQZaO7tWQSNraxv6WGd1NF+MVjc9Z4od90sWelIry866Gjve1qgs7mDcCbWtudCnAC8CA1HkegPAEtVrtm+ULnJKrqVmuUYluxtkYK0Lu6v8VilOVdCo5GAAEEEBghAULwEYLmaRBAAAEEqldgJAJwfcDcvX1LvsextLRoVZ+ZHdiz28EL2/4krLQbfO/f01O0WtNdQFNB95Tps0w9x/XfWqCSDYE4CejOiU133pr/EqepQUF4f2Wxd1PgqsUy23PpIYevIHz5/TutbfJFcZpmVYzFu4hu0IB1dVQB7vZs797zvM2aPS/oMB5HAIEIBLx30qjXt953FNt0d8ejmzcMeJ/i7qsQvfPu+3hvEME14RQIIIAAApUTIASvnC1nRgABBBCoAYFDB5+xrlXXmyqwux//QeQf8IqF30tuvs304VTBniqtOu+5f8gPp2Gphwq+9TwdcxfY8weezJ8u6ENx2OdlPwRGQkCVjQrC3R7UKvie1JIaFIRrLFPbMjaxuWHIYbVNusg+/md7CMJLuHj+9jRBhzY3JE0V+trWbXnUrr1pVdAhPI4AAhEKrF+5LP9eo/vxfYGLSnoX1vQOg6rwCC8Kp0IAAQQQqIgAIXhFWDkpAggggEAtCah39nvmLoh0Sv7wWxXXVy29wW67e6O9deJYPsjTh8owH0qHGpzbX1wV3wrV/R9aFyxcbArdVeHt7eEbdeV5pICcDIEiAv7b9pWvKghPqwTct01uabDJrZkhLQnCw7/UioVjxc7QmE5Y9sJipbfcdZ/dsu4L4Z+MPRFAIBIB78/M+VdcbY88vi/wvP4vHL0HBLVWCTw5OyCAAAIIIFAhAULwCsFyWgQQQAABBAoJ+MNvhdxLP9HphNDqse2toiwnhA4bfCsAdzdvD99ynpsrj8BoC+j1/+CaFfk2P0MF4ROa0jatPUsQXuZF8/dlDzpdLp2wHAF4EBOPIzAiAt6/v2F//6s9yiMb7hxw95g72EqtXzIiGDwJAggggEDNChCC1+ylZWIIIIAAAnESUFsVt72JxuVvceLttTnc9ifDCb5dI2/4rp6gaoPChkA1C/gDGrUGn9ScssyF1hveuY1tTNu0tky+L3WheVMRXvzVoKrQe/9wWahFdXWWbCqRX5xU7U/UBoUNAQRGV8Dby/+xvz0S2BbFHW2xO0B0h9vt92x0Ft1kQwABBBBAIA4ChOBxuAqMAQEEEECgZgXUX/uJnV/LtyEpFHB7b0Uutf1JOcF3oQ+wlep9XrMXmInFXsAb7CgIH5tLWnMmOWjcqkruGJ8jCC/xiupn0NrlC0MH4PoSoknN2s1s7uVX2wO7ni7xGdkdAQQqJdC5eLazpoLei+x46mDodVDUaq276zP59Ri841OLFX2xrrvd2BBAAAEEEBhNAULw0dTnuRFAAAEEalZAtxb3bNuc/0BYrLpbFVSPbdviBEhh+2hGEXy78N5boEv90FuzF4+J1ZyAf7HGtmzS2nODg3At0NgxLmeZC206CkFQEf6uir//etALR0X4LZmkJRIJu3j2PNu082lrbhsTdBiPI4DACAl4v9Qq9a4wHau2au7aI/pSXX+m9zeqCu/q/qYtWnLDCM2Ep0EAAQQQQGCwACE4rwoEEEAAAQQiFPCH36qAuvmOzxb84OdWqOrD4dovdps+cBbbogy+3efwtjAotQI9QjJOhcCICBCER8usdjOqAFfVaJhN65K2XgjAJ06baZt2PW2TplMZGsaOfRAYSQFvexNVcA/13qTQuLw/a/XeomPugnzfcH3Z33n3faErzEdy3jwXAggggEDtCxCC1/41ZoYIIIAAAiMg4A+/9aFRi116F550h1FK+xN/ZZV7Dn2w1LmLPUfQlL1jUAj/lW/vs0vmzA86jMcRqGoB/+KNLZmEjW1MDZqTAtuO8Y35vtWFJl3PFeEKwLtWXp9feDToRSFPVYAnEwkjAA/S4nEERl/AXShb7w/UFqXUViaqBt905635KvCrlt5gz+1/0vl/vX/p6v6WqUiADQEEEEAAgZEUIAQfSW2eCwEEEECgpgQUBD1/4KkBbU8Uft9298aiHxjVI3zHQ11O9WSY9if+diXlBN8uvr+C84FHv8MtyjX1ymQyQwn4F3FsTCdsXFN/QOvdFNxqscxxTQ1FT6cg/IYv7rQJl7y3rtDdgCzMpKXamu33bWpttwd3fd9mzZ4X5lD2QQCBURLwf1nf88xPSx6J/0t8vT9y72rTyagKL5mUAxBAAAEEyhQgBC8TkMMRQAABBOpPQB/iDjyx2/Z/tyffCiAo/JaSe4twmPYnXtUDe3bbpAuV31Foq4XBi0cOO6dae/9W54MoGwL1JODvZa11Gic0pyyt5Nu3TW3L2MTm4kF4trnNPvFnT9RNEO5daDTMa0YtUFIXXLu++m27/A+WhzmMfRBAYJQF9IXhmuULnVF03rPROu/eOKwReX9mqPq7Y+582//d3U5VuPqGq1c4d6INi5aDEEAAAQRKFCAELxGM3RFAAAEE6ldAwdnu7Vvs0MFnnPDbbUkyVOW3tLzVUKPde9tbwVnOh9r6fRUw81oR8AfhWrRxUkvhIHxyS4NNbs0UnXq9BOH+vupBr4WmhoRlUv0LkH7yTx62j3auCzqExxFAIEYC3r/zjzy+b9gtTHQXXHfX6nw7lM577rf9e3qcRTRVGHD7PRv5Qj5G152hIIAAArUqQAheq1eWeSGAAAIIRCbght9qTaJNQfbST3Q6/biD+mSqkkp9Md32J6O5IJT3w6wq17XgFRsC9Szg722tIFwV4Rn9h2+b0JS2ae3Zug3CvYvlhXnN5NIJy6X7A/Bb7rrPbln3hTCHsQ8CCMRMYP3KZU5YXe6X+Hov9eCaFfk70fRFfEtruz22bYsTjqtKXO9Lgt5XxYyH4SCAAAIIVJEAIXgVXSyGigACCCAwsgKFwm9VLylADrN525+MdpWTN8DSB01VdLEhgICZgvBHN28w90sutQaf0JQyhbj+bWxj2ukT7rb38D9eqxXh/gVFg1433gBc1d+qAmdDAIHqFPDeNVPuF+j6eduz/cum9yTa3FZybjhOVXh1vkYYNQIIIFAtAoTg1XKlGCcCCCCAwIgJlBt+e0O1ciunopi0bkN+YM0K51Qaz46nDlpL25goTs05EKgZAX+v63GNSWvO9FcyezdVN3eMzw0ZhF+z+iGbc92tNWHjX0g0aFKqom9Sk3Uzu/amVbZuy6NBh/A4AgjEXMD7RVgUa4koBNc5FYK765J4fwYvWnKDrd/6Dd6rxPx1wfAQQACBahMgBK+2K8Z4EUAAAQQqJqBe386Cl562J6VUfmtg3oopfbAbzfYnGo83wIpDIF+xi8eJEYhAwN/zui2btPbc4CC8IZWwjnE5y1xo91HoqZd+blvVB+H6eaaFdNWqIMwmjpZMytn14tnzbNPOp62ZL9zC0LEPArEX8IbUj/3tkYq0LVHble6uz+TXXenq/taw+5DHHpQBIoAAAgiMuAAh+IiT84QIIIAAAnETUPit8EsfvrSpXUjn3RttwcLFJQ1VlU1ub8soKqVKevICO3sDed1irApwem2Wq8rxtS7g731dNAhPJpyK8FoNwv0LhwZdd7VRb8kkLZFI2MRpM23rnucIwIPQeByBKhPoXDw7H1D3PPPTioze3zIlDgUFFZkoJ0UAAQQQGHEBQvARJ+cJEUAAAQTiIqCK755tm50PdNp0W64Wuyw1/NaxboVUXKqt9SFSFZzu3NQDXOE+GwIIBAvoZ8OOh7ryFdBNDQkb39Rf4Zzf+sySCbOOCY3WeKH9R6EzV2NFuP/nR5CYHBSAJy8E4Jt2PW2Tps8KOozHEUCgygS8d4conNYX/pXa/FXhD37jL+2SOfMr9XScFwEEEECgDgQIwevgIjNFBBBAAIGBAoXC79vu3jisKmn/glFr7t8aix6W61cuy1e2r9/6zdCLefJaQQCBfgF/L+xsKmETmvuDXn8QPq09Y+OaGorSXbP6v9v7/+tnqoJWAXjXyuvtxSOHQ43XG4A3tbY7FeAE4KHo2AmBqhTw3i1T6fcX/oWLdZde5z0bq9KNQSOAAAIIjL4AIfjoXwNGgAACCCAwQgJRht8ashacVLWoqq3j0P7EZXxkw+p8X3N9WNSHRjYEEChdwN8SRAXfE5pTllbyq63v3XNObcvYxJbiQfjCVevtipX3lj6IET7C+/Mj6KmloArw1AWP7j3P26zZ84IO43EEEKhyAffnxEjd/ab3W91dq527c3RXm8J32rtV+YuI4SOAAAKjIEAIPgroPCUCCCCAwMgKeMNvfWBTu5PhVn67I3cX0BupD4BhxbwL+1X6VuWwY2I/BKpZwB+Eq/f1pJbCQfjk1gab3JoZNN2+vv60XEG4/onr5l34LswYFYC7Xwis2/KoXXvTqjCHsQ8CCFS5gPfnokJptVyr9KbnVPiuNila56T78R/Ye+YuqPTTcn4EEEAAgRoSIASvoYvJVBBAAAEE3hXQh6UDT+y2/d/tyS/idPMdn7Url9xQVvWQzvvgmhVOqwD1EC83TI/ymnlvUV605AZ74NHvRHl6zoVA3Qr4W4QoCFdFeEb/4akGF9CE5rRNa88Osop7EO79Ai3MhVaf9Ewq6ex6y1332S3rvhDmMPZBAIEaEVDLqDXLFzqzGcm7zvRep7ltDG3eauR1xDQQQACBkRQgBB9JbZ4LAQQQQKDiAgqp9+76uj2//3v58Lvznvsj+bCkD3yb7rzVOe9IfuALg6bKKPUB19YxZ75TIdXSNibMoeyDAAIhBPy9adUafEJTynIKwn3b2EYF4Zl8mxD34bgG4d4v0EJQWC6dsFyaADyMFfsgUMsC3i/PHvvbI2UVGdSyE3NDAAEEEIiHACF4PK4Do0AAAQQQKFNA4ffu7VvyvbDVpiSq8FtDi2v7E43Nu4Bf3NqzlHlZORyB2An4W4aMa0xas5qF+zaFxB0TcrEPwtUuSi0Gwm7eAFztT9QGhQ0BBOpXwF2IW+8/djx1kC/g6/elwMwRQACB2AsQgsf+EjFABBBAAIEwAlo06YE1Kyzq8Nsbrset/YlcvH051SNTH0BZLCrMK4Z9EBi+gL91SFs2ae3ZwUF4QyphHeNzlrlQNe0+Y1wqwr1foIXRUPuXpguB/9zLr7YHdj0d5jD2QQCBGhbwvg/R+yQtWsmGAAIIIIBAHAUIweN4VRgTAggggMCwBH72k0ORLpLk/WAXt/YnAlJ7hrXLFzrtWRSAf+Xb++ySOfOHZcdBCCBQmoC/hUi1BeH6+aafH6dOHAs1cXV90UKYiUTCLp49zzbtfNrpy8uGAAIIeO8oWXv/VtPC3GwIIIAAAgjETYAQPG5XhPEggAACCMRGQCGR2gSs+2J3LMNl9xZkganyShVYbAggMHICCn52PNSVD5K1WOT4xtSgASQTZh0TGq2xQNsUVYUvXLXe+WekNu8XfGGeU+NvvRCAT5w20zbtetomTZ8V5lD2QQCBOhFwW0VxV1qdXHCmiQACCFShACF4FV40howAAggggIC3L3Ecq9S5QgjUi4B3wVzNOZtK2ISmpCW1cqZvmzEmY+OaGgb9uYLwy25abdes/u8VZ/PeQRLmyRSAqwJc8yEADyPGPgjUr0Dn4tn5Rcl7nvlp/UIwcwQQQACBWAoQgsfysjAoBBBAAAEEigt4+xETgPNKQWD0BfyV1Sr4ntCUsrQSZN82ubXBJrdmCgbhc6671ZZ9fnvFJqQAvGvl9fbikcOhnkOjb832B+BNre324K7v26zZ80Idy04IIFB/At42S7w/qb/rz4wRQACBuAsQgsf9CjE+BBBAAAEEPALePsQsQMVLA4H4CPiDcPXQntQcryBc7Z3UwiXMpgBcFeCpC0F+11e/bZf/wfIwh7IPAgjUsYD3fcojj++z+VdcXccaTB0BBBBAIE4ChOBxuhqMBQEEEEAAgSEEDr/wrKkPuLaOOfOt+/EfWAsL0/GaQSA2Av5KawXhqgjP6D9824TmtE1rzw76c7VGqURFuLeFUhgw9TfPpJLOrp/8k4fto53rwhzGPggggICznoq+cJs8faZ1P77PpsxgDQFeFggggAACoy9ACD7614ARIIAAAgggECjgvcWYD5WBXOyAwKgKeCuuFX8rCM+lBwfhbbmUXTQmm6+2dgcddRDubaEUBqYxnbBsuj8Av+Wu++yWdV8Icxj7IIAAAo6A984YFu7mRYEAAgggEBcBQvC4XAnGgQACCCCAQBEB74dJAnBeJghUh4A/eB6TTTr9tf1bLp20i8dlLXMhdPYG4TPmLbIbvrjTsi3tw560tzVBmJMorNeYtKn6W1XgbAgggECpAlo0WGsJUAVeqhz7I4AAAghUSoAQvFKynBcBBBBAAIEIBNReYe3yhXb01ZetubXdvvLtfXbJnPkRnJlTIIBApQX8QXhbNmntBYLwhlTCOsbnCgbhEy95r33iz54YVhCudgSqSg+7ZVMJa9SqnmZ27U2rbN2WR8Meyn4IIIAAAggggAACCMRagBA81peHwSGAAAII1LuAeoCrF7g2bimu91cD869GAX8QPVQQfvG4XD6Edueq1ijDCcJVhXnvHy6zUyeOhWJrSCasOdMfgF88e55t2vm0NbPmQCg7dkIAAQQQQAABBBCIvwAhePyvESNEAAEEEKhTAe9Cdmvv32ofu+OzdSrBtBGobgF9kbXpzlvzgbQWnRzfmBo0qWTCTEF4S3bgY6UG4d41BMLIad3OlkzSEomETZw207bueY4APAwc+yCAAAIIIIAAAghUjQAheNVcKgaKAAIIIFBPAt42Cp33bLTOuzfW0/SZKwI1J6DKbAXham2kTV1HJjWnLJkYvGDmjDEZG9fUMMAgbBDuXUMgDKKCdwXgGocC8E27nrZJ02eFOZR9EEAAAQQQQAABBBCoGgFC8Kq5VAwUAQQQQKBeBLztE5Z+/DanDQobAghUv4A/oFYFtoLwtJJo3za5tcEmt2YGBeFtky9yeoTr3/7Nu4ZAGC1vAK4F7FQBTgAeRo59EEAAAQQQQAABBKpNgBC82q4Y40UAAQQQqGkBtU1QH3BtHXPm246nDtb0fJkcAvUmoCD8wTUr7MUjh52pRxWEKwDvWnl9/rxBrordVQGeuhDAd+953mbNnhd0GI8jgAACCCCAAAIIIFCVAoTgVXnZGDQCCCCAQC0KePv4Tp4+0wnAW1iYrhYvNXOqcwEF1g+sWZFf9FaBtCrCM0rEfdvYxrRdNDab/9O+C//VNmnGgIrwRzasNt1FEnZTAO5WoK/b8qhde9OqsIeyHwIIIIAAAggggAACVSdACF51l4wBI4AAAgjUooC3TYIC8O7H99mUGfTlrcVrzZwQcAW8wbXi77G5pDVnkoOA9GdaMFNV204I3tcfhbutUf7iW1+1vTu/FhpWC3NmUv3Pc8td99kt674Q+lh2RAABBBBAAAEEEECgGgUIwavxqjFmBBBAAIGaEvC2MWhubbevfHufXTJnfk3NkckggEBhAe8iuNpjTDZprdnBQXgurSA8aw3pZD4E1/7Jxlb7weFX7VxvOOFcOmE6FwF4OC/2QgABBBBAAAEEEKgNAULw2riOzAIBBBBAoIoF1ANcvcC1PfL4Ppt/xdVVPBuGjgACpQr4g/C2bNLaCwThDamEXTI+N6htyqFfv22vHj8b+LTeAFztT9QGhQ0BBBBAAAEEEEAAgXoQIASvh6vMHBFAAAEEYiuwY/OGfBuDtfdvtY/d8dnYjpWBIYBA5QTUz1vtUdytJZOwsbnUoCdUED5rbNYaG96tFn/jrXP2wi/fGnJw6jfedOGYuZdfbQ/serpyk+HMCCCAAAIIIIAAAgjETIAQPGYXhOEggAACCNSPgLf6s/OejdZ598b6mTwzRQCBQQK6I2TTnbfaqRPHnMfUu1t9wpOJgQtmJhPmBOEt2f6QPCgEV/eTlkz/vhfPnmebdj5tzSy6yysQAQQQQAABBBBAoI4ECMHr6GIzVQQQQACB+Ah4qz5V/a0qcDYEEEDg50cOO0H40VdfdjBUvD2pOTUoCNdjM9ozNrYpbcdPn7e/e+lUQbxUQgF40hKJhE2cNtM27XraJk1n0V1eaQgggAACCCCAAAL1JUAIXl/Xm9kigAACCMRAQCHXmuULnZGo/7f6gLMhgAACrsBrr7xkXSuX5YNwBdkKwtMqAfdtk1oarDWXsr/5+clBj2l3BeCqJCcA5/WFAAIIIIAAAgggUM8ChOD1fPWZOwIIIIDAiAso3Fq7fKHT7qBjznzrfvwH1kJbghG/DjwhAnEX0M+KB9essBePHHaGGhSE/+T10/b2ub78tLwBeFNruz246/s2a/a8uE+b8SGAAAIIIIAAAgggUBEBQvCKsHJSBBBAAAEECgu4bVAmT59p3Y/vsykzaEvAawUBBAoLvPGraqNF4AAAIABJREFUl2zdkvfav53udXZQHbgqwrXIpX87+U7vgP1UAZ66UDl+6t8fu+fPvmFLP34b1AgggAACCCCAAAII1KUAIXhdXnYmjQACCCAwmgJa/G7S9JkE4KN5EXhuBKpA4Nnv/YW98LV77J9fP2O/OnE+H4RrsczmTHLADH739nk7dba/ElwLamZS/Y+/fbbXzpzvsxtXdNpnv/yNKpg1Q0QAAQQQQAABBBBAIHoBQvDoTTkjAggggAACCCCAAAJlCxzYs9ue+NO77KL2tP3o1dP5kFsnHpNNWmv23SD8tZPn7GyvWWM6Ydl0/5+fPtdrp8/1mf537f/xKbvhj79W9pg4AQIIIIAAAggggAAC1ShACF6NV40xI4AAAggggAACCNS8gELw7g2r7YrpWfvFm+dMbU3cam9Nvi2btPYLQfgrx89ZNp2w3IUA/My53nyP8EvGpm3Fp//IPrx2S82bMUEEEEAAAQQQQAABBAoJEILzukAAAQQQQAABBBBAIIYCPdu3WM+2LdaQNBvbmHJGqPYmJ955dwHMlkzCCcJ/+1avNWpHM3vnfK+9daE1ijLxxbOa7JpP/rFdeVtXDGfJkBBAAAEEEEAAAQQQqLwAIXjljXkGBBBAAAEEEEAAAQRKFnBDcB3Y3JDI9wE/29tnb77da24UrhYo6WTC9Oe9fWZnz/c5j2n5zEvHZ6xjfNYJwBeuWl/yGDgAAQQQQAABBBBAAIFaECAEr4WryBwQQAABBBBAAAEEak5gx+YNtnfnu328kwmzbEqLXiasIWWWTCTst2+dd4Jvd9M+elz7qTXKJeMyNqYxZdfe+ZBddtPqmjNiQggggAACCCCAAAIIhBEgBA+jxD4IIIAAAggggAACCIywwCMbVtv+PbuLPqu6n5zr7X9Y/cAb00knAPdul07IWGs2Zcvu3W5zr1sxwjPg6RBAAAEEEEAAAQQQiIcAIXg8rgOjQAABBBBAAAEEEEBggEBQCO7unEurL3h/z3D/RgjOiwoBBBBAAAEEEEAAATNCcF4FCCCAAAIIIIAAAgjEUCCKEPy9k3NOlfiNX9plHVd+JIazZEgIIIAAAggggAACCFRegBC88sY8AwIIIIAAAggggAACJQusX7nMDr/wbOBxQ1WCuyH4Jx5+wi6af1XgudgBAQQQQAABBBBAAIFaFCAEr8WrypwQQAABBBBAAAEEql4gbAje3JC0lkyy4HwJwav+ZcAEEEAAAQQQQAABBCIQIASPAJFTIIAAAggggAACCCAQtcDa5QvtxSOHA087VAg+f2rO0smEfWrXj6x98szAc7EDAggggAACCCCAAAK1KEAIXotXlTkhgAACCCCAAAIIVL1A5+I5dvTVlwLnMVQI/oHpjc7xhOCBjOyAAAIIIIAAAgggUMMChOA1fHGZGgIIIIAAAggggED1CoQNwduySWtMF26HQghevdefkSOAAAIIIIAAAghEJ0AIHp0lZ0IAAQQQQAABBBBAIDKBckPwTCph75uSc8bzue8fjWxcnAgBBBBAAAEEEEAAgWoTIASvtivGeBFAAAEEEEAAAQTqQmBpR1OoeRarBCcED8XHTggggAACCCCAAAJ1IEAIXgcXmSkigAACCCCAAAIIVJ9A2BB8bC5lCrz9GyF49V1zRowAAggggAACCCBQGQFC8Mq4clYEEEAAAQQQQAABBIYtcPL4m3bzZdNCHV8sBG/JJO33J2atbfJF9uld/xDqXOyEAAIIIIAAAggggEAtChCC1+JVZU4IIIAAAggggAACVS3w2isv2e3XzAk1B0LwUEzshAACCCCAAAIIIFDHAoTgdXzxmToCCCCAAAIIIIBAPAVKCcEnNKYslRzcDqU9l7SO8VSCx/MKMyoEEEAAAQQQQACBkRQgBB9JbZ4LAQQQQAABBBBAAIEQAlGE4OOaUnbx2IzNmL/Ibnl4b4hnZRcEEEAAAQQQQAABBGpTgBC8Nq8rs0IAAQQQQAABBBCoYoFDB5+xrlXXh5pBsUpwQvBQfOyEAAIIIIAAAgggUAcChOB1cJGZIgIIIIAAAggggEB1CZQSgk9uThecnBuCd1z5EbvxS7uqC4DRIoAAAggggAACCCAQoQAheISYnAoBBBBAAAEEEEAAgSgEnj/wpD2wZkWoUxULwae2pm1qW4PNXbLCln1+e6hzsRMCCCCAAAIIIIAAArUoQAhei1eVOSGAAAIIIIAAAghUtcCBPbute8PqwDloOcxJRSrBCcED+dgBAQQQQAABBBBAoE4ECMHr5EIzTQQQQAABBBBAAIHqEQgbgqcSZhOaCrdDmdHeYJNa0nbZTavt2jsfqp7JM1IEEEAAAQQQQAABBCIWIASPGJTTIYAAAggggAACCCBQrkAUIfissQ02viltV97WZQtXrS93SByPAAIIIIAAAggggEDVChCCV+2lY+AIIIAAAggggAACtSrQs32L9WzbEji9oSrBCcED+dgBAQQQQAABBBBAoE4ECMHr5EIzTQQQQAABBBBAAIHqEQgbgjckEzauMVVwYm4IrlYoaonChgACCCCAAAIIIIBAvQoQgtfrlWfeCCCAAAIIIIAAArEV2LF5g+3d+bXA8Q0Vgl86IWOt2ZQtu3e7zb1uReC52AEBBBBAAAEEEEAAgVoVIASv1SvLvBBAAAEEEEAAAQSqVuCRDatt/57dgePPphI2Jle4EpwQPJCPHRBAAAEEEEAAAQTqRIAQvE4uNNNEAAEEEEAAAQQQqB6BsCF4Lp2w9mzhEHz2xKw1ZZJ245d2WceVH6meyTNSBBBAAAEEEEAAAQQiFiAEjxiU0yGAAAIIIIAAAgggUK5AFCH4eyfnLJtO2CcefsIumn9VuUPieAQQQAABBBBAAAEEqlaAELxqLx0DRwABBBBAAAEEEKhVgfUrl9nhF54NnF5TOuH0/S60EYIH8rEDAggggAACCCCAQJ0IEILXyYVmmggggAACCCCAAALVIxA2BG9uSFpLJllwYvOn5iydTNindv3I2ifPrJ7JM1IEEEAAAQQQQAABBCIWIASPGJTTIYAAAggggAACCCBQrsDa5QvtxSOHA08zVAj+gemNzvGE4IGM7IAAAggggAACCCBQ4wKE4DV+gZkeAggggAACCCCAQPUJdC6eY0dffSlw4K2ZpDU1FK4EJwQP5GMHBBBAAAEEEEAAgToRIASvkwvNNBFAAAEEEEAAAQSqRyBsCN6WTVpjenAInkkl7H1Tcs6EP/f9o9UzcUaKAAIIIIAAAggggEAFBAjBK4DKKRFAAAEEEEAAAQQQKEfgY++faqdOHAs8BSF4IBE7IIAAAggggAACCCBghOC8CBBAAAEEEEAAAQQQiJnA0o6mUCNqzyYtRyV4KCt2QgABBBBAAAEEEKhfAULw+r32zBwBBBBAAAEEEEAgpgJhQ/CxuZSp9Yl/a2xI2JxJOWubfJF9etc/xHSWDAsBBBBAAAEEEEAAgZERIAQfGWeeBQEEEEAAAQQQQACBUAInj79pN182LdS+xULwlkzSfn9ilhA8lCI7IYAAAggggAACCNS6ACF4rV9h5ocAAggggAACCCBQVQKvvfKS3X7NnFBjntCYslRycCU4IXgoPnZCAAEEEEAAAQQQqBMBQvA6udBMEwEEEEAAAQQQQKA6BKIIwcc1pezisRmbMX+R3fLw3uqYOKNEAAEEEEAAAQQQQKBCAoTgFYLltAgggAACCCCAAAIIDEeAEHw4ahyDAAIIIIAAAggggEBxAUJwXh0IIIAAAggggAACCMRI4NDBZ6xr1fWhRjSxKWXJxOB2KG4leMeVH7Ebv7Qr1LnYCQEEEEAAAQQQQACBWhUgBK/VK8u8EEAAAQQQQAABBKpSoJQQfHJzuuAcp7ambWpbg81dssKWfX57VTowaAQQQAABBBBAAAEEohIgBI9KkvMggAACCCCAAAIIIBCBwPMHnrQH1qwIdSZC8FBM7IQAAggggAACCCBQ5wKE4HX+AmD6CCCAAAIIIIAAAvESOLBnt3VvWB04qFTCbEJT4UrwGe0NNqklbZfdtNquvfOhwHOxAwIIIIAAAggggAACtSxACF7LV5e5IYAAAggggAACCFSdQBQh+KyxDTa+KW1X3tZlC1etrzoDBowAAggggAACCCCAQJQChOBRanIuBBBAAAEEEEAAAQTKFNi78+u2Y3NX4FmGqgQnBA/kYwcEEEAAAQQQQACBOhIgBK+ji81UEUAAAQQQQAABBOIv0LN9i/Vs2xI40HTSbHxj4XYobgiuVihqicKGAAIIIIAAAggggEA9CxCC1/PVZ+4IIIAAAgg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" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "f15446a2ef7d4d248e9be0af18ab21ab", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(IntSlider(value=5, description='Levels', max=8, min=1), FloatSlider(value=7.0, descripti…" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "import plotly.graph_objects as go\n", "from ipywidgets import interact, widgets\n", "\n", "def cylinder_mesh(p0, p1, radius_base, radius_top, sections=8):\n", " \"\"\"\n", " Generate mesh data for a tapered cylinder (frustum) between two points.\n", " \"\"\"\n", " # Vector from p0 to p1\n", " v = np.array(p1) - np.array(p0)\n", " # Length of the cylinder\n", " length = np.linalg.norm(v)\n", " if length == 0:\n", " return None\n", " # Unit vector in direction of the cylinder\n", " v = v / length\n", "\n", " # Create arbitrary vectors orthogonal to v\n", " not_v = np.array([1, 0, 0])\n", " if np.allclose(v, not_v):\n", " not_v = np.array([0, 1, 0])\n", " n1 = np.cross(v, not_v)\n", " n1 /= np.linalg.norm(n1)\n", " n2 = np.cross(v, n1)\n", "\n", " # Create circle points in the plane orthogonal to v\n", " t = np.linspace(0, 2 * np.pi, sections, endpoint=False)\n", " circle_base = n1[:, None] * np.cos(t)[None, :] + n2[:, None] * np.sin(t)[None, :]\n", " circle_top = circle_base.copy()\n", "\n", " # Scale circles by radii\n", " circle_base *= radius_base\n", " circle_top *= radius_top\n", "\n", " # Points at base and top\n", " base_points = p0[:, None] + circle_base\n", " top_points = p1[:, None] + circle_top\n", "\n", " # Combine points\n", " x = np.hstack([base_points[0], top_points[0]])\n", " y = np.hstack([base_points[1], top_points[1]])\n", " z = np.hstack([base_points[2], top_points[2]])\n", "\n", " # Create faces\n", " faces = []\n", " n = sections\n", " for i in range(n):\n", " next_i = (i + 1) % n\n", " faces.append([i, next_i, n + next_i])\n", " faces.append([i, n + next_i, n + i])\n", " return x, y, z, faces\n", "\n", "def rotate_vector(v, k, theta):\n", " \"\"\"\n", " Rotate vector v around axis k by angle theta using Rodrigues' rotation formula.\n", " \"\"\"\n", " v_rot = v * np.cos(theta) + np.cross(k, v) * np.sin(theta) + k * np.dot(k, v) * (1 - np.cos(theta))\n", " return v_rot\n", "\n", "def grow_tree(p0, direction, length, radius_base, levels, angle, length_reduction, branches_per_level, tree_elements):\n", " \"\"\"\n", " Recursively grow the tree from point p0 in a given direction.\n", " \"\"\"\n", " if levels == 0:\n", " return\n", "\n", " p1 = p0 + direction * length\n", "\n", " # Calculate the top radius (tapering)\n", " radius_top = radius_base * 0.8 # Simple tapering factor\n", "\n", " # Add the cylinder representing the trunk or branch\n", " cylinder = cylinder_mesh(p0, p1, radius_base, radius_top)\n", " if cylinder:\n", " x, y, z, faces = cylinder\n", " tree_elements.append({\n", " 'x': x,\n", " 'y': y,\n", " 'z': z,\n", " 'faces': faces,\n", " 'color': 'saddlebrown'\n", " })\n", "\n", " # Calculate child branch parameters\n", " length_child = length * length_reduction\n", " N = branches_per_level\n", " radius_child = radius_base * np.sqrt((radius_top / radius_base)**2 * length / (N * length_child))\n", "\n", " # Generate branches at this level\n", " for _ in range(N):\n", " # Random rotation for natural appearance\n", " theta = angle + (np.random.rand() - 0.5) * np.deg2rad(10)\n", " phi = np.random.rand() * 2 * np.pi\n", "\n", " # Spherical to Cartesian coordinates\n", " new_direction = np.array([\n", " np.sin(theta) * np.cos(phi),\n", " np.sin(theta) * np.sin(phi),\n", " np.cos(theta)\n", " ])\n", " new_direction = new_direction / np.linalg.norm(new_direction)\n", "\n", " # Rotate new_direction to align with the parent branch direction\n", " rotation_axis = np.cross([0, 0, 1], direction)\n", " rotation_angle = np.arccos(np.clip(np.dot(direction, [0, 0, 1]), -1.0, 1.0))\n", " if np.linalg.norm(rotation_axis) > 1e-6:\n", " rotation_axis /= np.linalg.norm(rotation_axis)\n", " new_direction = rotate_vector(new_direction, rotation_axis, rotation_angle)\n", "\n", " # Recursive call to grow the branch\n", " grow_tree(\n", " p1,\n", " new_direction,\n", " length_child,\n", " radius_child,\n", " levels - 1,\n", " angle,\n", " length_reduction,\n", " branches_per_level,\n", " tree_elements\n", " )\n", "\n", "def plot_tree(levels, trunk_length, trunk_radius, angle_deg, length_reduction, branches_per_level):\n", " tree_elements = []\n", " # Start with the main trunk\n", " p0 = np.array([0, 0, 0])\n", " direction = np.array([0, 0, 1]) # Grow along z-axis\n", " angle_rad = np.deg2rad(angle_deg)\n", " grow_tree(\n", " p0,\n", " direction,\n", " trunk_length,\n", " trunk_radius,\n", " levels,\n", " angle_rad,\n", " length_reduction,\n", " branches_per_level,\n", " tree_elements\n", " )\n", "\n", " # Plotting\n", " fig = go.Figure()\n", " for elem in tree_elements:\n", " fig.add_trace(go.Mesh3d(\n", " x=elem['x'],\n", " y=elem['y'],\n", " z=elem['z'],\n", " i=[face[0] for face in elem['faces']],\n", " j=[face[1] for face in elem['faces']],\n", " k=[face[2] for face in elem['faces']],\n", " color=elem['color'],\n", " flatshading=True,\n", " lighting=dict(ambient=0.5, diffuse=0.8, roughness=0.9),\n", " showscale=False\n", " ))\n", " fig.update_layout(\n", " scene=dict(\n", " xaxis=dict(visible=False),\n", " yaxis=dict(visible=False),\n", " zaxis=dict(visible=False),\n", " aspectmode='data'\n", " ),\n", " showlegend=False,\n", " margin=dict(l=0, r=0, t=0, b=0)\n", " )\n", " fig.show()\n", "\n", "# Interactive widgets\n", "interact(\n", " plot_tree,\n", " levels=widgets.IntSlider(min=1, max=8, step=1, value=5, description='Levels'),\n", " trunk_length=widgets.FloatSlider(min=1, max=15, step=0.5, value=7, description='Trunk Length'),\n", " trunk_radius=widgets.FloatSlider(min=0.1, max=1.5, step=0.1, value=0.5, description='Trunk Radius'),\n", " angle_deg=widgets.FloatSlider(min=10, max=80, step=5, value=30, description='Branch Angle'),\n", " length_reduction=widgets.FloatSlider(min=0.4, max=0.9, step=0.05, value=0.7, description='Length Reduction'),\n", " branches_per_level=widgets.IntSlider(min=1, max=8, step=1, value=4, description='Branches/Level')\n", ")\n" ] }, { "cell_type": "code", "execution_count": 4, "id": "842fb3c7-4b5a-493b-a4db-62967f51d7f9", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "color": "saddlebrown", "flatshading": true, "i": [ 0, 0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7 ], "j": [ 1, 9, 2, 10, 3, 11, 4, 12, 5, 13, 6, 14, 7, 15, 0, 8 ], "k": [ 9, 8, 10, 9, 11, 10, 12, 11, 13, 12, 14, 13, 15, 14, 8, 15 ], "lighting": { "ambient": 0.5, "diffuse": 0.8, "roughness": 0.9 }, "showscale": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "8397589db2d74253bf040c17a844ce59", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(IntSlider(value=5, description='Levels', max=8, min=1), FloatSlider(value=7.0, descripti…" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "import plotly.graph_objects as go\n", "from ipywidgets import interact, widgets\n", "\n", "def cylinder_mesh(p0, p1, radius_base, radius_top, sections=8):\n", " \"\"\"\n", " Generate mesh data for a tapered cylinder (frustum) between two points.\n", " \"\"\"\n", " # Vector from p0 to p1\n", " v = np.array(p1) - np.array(p0)\n", " # Length of the cylinder\n", " length = np.linalg.norm(v)\n", " if length == 0:\n", " return None\n", " # Unit vector in direction of the cylinder\n", " v = v / length\n", "\n", " # Create arbitrary vectors orthogonal to v\n", " not_v = np.array([1, 0, 0])\n", " if np.allclose(v, not_v):\n", " not_v = np.array([0, 1, 0])\n", " n1 = np.cross(v, not_v)\n", " n1 /= np.linalg.norm(n1)\n", " n2 = np.cross(v, n1)\n", "\n", " # Create circle points in the plane orthogonal to v\n", " t = np.linspace(0, 2 * np.pi, sections, endpoint=False)\n", " circle_base = n1[:, None] * np.cos(t)[None, :] + n2[:, None] * np.sin(t)[None, :]\n", " circle_top = circle_base.copy()\n", "\n", " # Scale circles by radii\n", " circle_base *= radius_base\n", " circle_top *= radius_top\n", "\n", " # Points at base and top\n", " base_points = p0[:, None] + circle_base\n", " top_points = p1[:, None] + circle_top\n", "\n", " # Combine points\n", " x = np.hstack([base_points[0], top_points[0]])\n", " y = np.hstack([base_points[1], top_points[1]])\n", " z = np.hstack([base_points[2], top_points[2]])\n", "\n", " # Create faces\n", " faces = []\n", " n = sections\n", " for i in range(n):\n", " next_i = (i + 1) % n\n", " faces.append([i, next_i, n + next_i])\n", " faces.append([i, n + next_i, n + i])\n", " return x, y, z, faces\n", "\n", "def rotate_vector(v, k, theta):\n", " \"\"\"\n", " Rotate vector v around axis k by angle theta using Rodrigues' rotation formula.\n", " \"\"\"\n", " v_rot = v * np.cos(theta) + np.cross(k, v) * np.sin(theta) + k * np.dot(k, v) * (1 - np.cos(theta))\n", " return v_rot\n", "\n", "def grow_tree(p0, direction, length, radius_base, taper_ratio, levels, angle, length_reduction, branches_per_level, tree_elements):\n", " \"\"\"\n", " Recursively grow the tree from point p0 in a given direction.\n", " \"\"\"\n", " if levels == 0:\n", " return\n", "\n", " # Calculate end point of the current branch\n", " p1 = p0 + direction * length\n", "\n", " # Calculate top radius using consistent tapering\n", " radius_top = radius_base * taper_ratio\n", "\n", " # Add the cylinder representing the trunk or branch\n", " cylinder = cylinder_mesh(p0, p1, radius_base, radius_top)\n", " if cylinder:\n", " x, y, z, faces = cylinder\n", " tree_elements.append({\n", " 'x': x,\n", " 'y': y,\n", " 'z': z,\n", " 'faces': faces,\n", " 'color': 'saddlebrown'\n", " })\n", "\n", " # Calculate base radius of child branches\n", " N = branches_per_level\n", " radius_base_child = radius_top / np.sqrt(N)\n", "\n", " # Ensure the base radius of child branches equals the top radius of the parent branch divided by sqrt(N)\n", " # Calculate top radius of child branches using the same taper ratio\n", " radius_top_child = radius_base_child * taper_ratio\n", "\n", " # Length of child branches\n", " length_child = length * length_reduction\n", "\n", " # Generate branches at this level\n", " for _ in range(N):\n", " # Random rotation for natural appearance\n", " theta = angle + (np.random.rand() - 0.5) * np.deg2rad(10)\n", " phi = np.random.rand() * 2 * np.pi\n", "\n", " # Spherical to Cartesian coordinates\n", " new_direction = np.array([\n", " np.sin(theta) * np.cos(phi),\n", " np.sin(theta) * np.sin(phi),\n", " np.cos(theta)\n", " ])\n", " new_direction = new_direction / np.linalg.norm(new_direction)\n", "\n", " # Rotate new_direction to align with the parent branch direction\n", " rotation_axis = np.cross([0, 0, 1], direction)\n", " rotation_angle = np.arccos(np.clip(np.dot(direction, [0, 0, 1]), -1.0, 1.0))\n", " if np.linalg.norm(rotation_axis) > 1e-6:\n", " rotation_axis /= np.linalg.norm(rotation_axis)\n", " new_direction = rotate_vector(new_direction, rotation_axis, rotation_angle)\n", "\n", " # Recursive call to grow the branch\n", " grow_tree(\n", " p1,\n", " new_direction,\n", " length_child,\n", " radius_base_child,\n", " taper_ratio,\n", " levels - 1,\n", " angle,\n", " length_reduction,\n", " branches_per_level,\n", " tree_elements\n", " )\n", "\n", "def plot_tree(levels, trunk_length, trunk_radius, taper_ratio, angle_deg, length_reduction, branches_per_level):\n", " tree_elements = []\n", " # Start with the main trunk\n", " p0 = np.array([0, 0, 0])\n", " direction = np.array([0, 0, 1]) # Grow along z-axis\n", " angle_rad = np.deg2rad(angle_deg)\n", " grow_tree(\n", " p0,\n", " direction,\n", " trunk_length,\n", " trunk_radius,\n", " taper_ratio,\n", " levels,\n", " angle_rad,\n", " length_reduction,\n", " branches_per_level,\n", " tree_elements\n", " )\n", "\n", " # Plotting\n", " fig = go.Figure()\n", " for elem in tree_elements:\n", " fig.add_trace(go.Mesh3d(\n", " x=elem['x'],\n", " y=elem['y'],\n", " z=elem['z'],\n", " i=[face[0] for face in elem['faces']],\n", " j=[face[1] for face in elem['faces']],\n", " k=[face[2] for face in elem['faces']],\n", " color=elem['color'],\n", " flatshading=True,\n", " lighting=dict(ambient=0.5, diffuse=0.8, roughness=0.9),\n", " showscale=False\n", " ))\n", " fig.update_layout(\n", " scene=dict(\n", " xaxis=dict(visible=False),\n", " yaxis=dict(visible=False),\n", " zaxis=dict(visible=False),\n", " aspectmode='data'\n", " ),\n", " showlegend=False,\n", " margin=dict(l=0, r=0, t=0, b=0)\n", " )\n", " fig.show()\n", "\n", "# Interactive widgets\n", "interact(\n", " plot_tree,\n", " levels=widgets.IntSlider(min=1, max=8, step=1, value=5, description='Levels'),\n", " trunk_length=widgets.FloatSlider(min=1, max=15, step=0.5, value=7, description='Trunk Length'),\n", " trunk_radius=widgets.FloatSlider(min=0.1, max=1.5, step=0.1, value=0.5, description='Trunk Radius'),\n", " taper_ratio=widgets.FloatSlider(min=0.5, max=1.0, step=0.05, value=0.7, description='Taper Ratio'),\n", " angle_deg=widgets.FloatSlider(min=10, max=80, step=5, value=30, description='Branch Angle'),\n", " length_reduction=widgets.FloatSlider(min=0.5, max=1.0, step=0.05, value=0.7, description='Length Reduction'),\n", " branches_per_level=widgets.IntSlider(min=1, max=8, step=1, value=3, description='Branches/Level')\n", ")\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "61b4e953-424e-41ef-a4dd-f8b1fbcdee41", "metadata": { "scrolled": 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" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "dc0aa0b5cebb45d2a4787d982c445cfd", "version_major": 2, "version_minor": 0 }, "text/plain": [ "interactive(children=(IntSlider(value=5, description='Crown Levels', max=8, min=1), FloatSlider(value=7.0, des…" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import numpy as np\n", "import plotly.graph_objects as go\n", "from ipywidgets import interact, widgets\n", "\n", "def cylinder_mesh(p0, p1, radius_base, radius_top, sections=8):\n", " \"\"\"\n", " Generate mesh data for a tapered cylinder (frustum) between two points.\n", " \"\"\"\n", " # Vector from p0 to p1\n", " v = np.array(p1) - np.array(p0)\n", " # Length of the cylinder\n", " length = np.linalg.norm(v)\n", " if length == 0:\n", " return None\n", " # Unit vector in direction of the cylinder\n", " v = v / length\n", "\n", " # Create arbitrary vectors orthogonal to v\n", " not_v = np.array([1, 0, 0])\n", " if np.allclose(v, not_v):\n", " not_v = np.array([0, 1, 0])\n", " n1 = np.cross(v, not_v)\n", " n1 /= np.linalg.norm(n1)\n", " n2 = np.cross(v, n1)\n", "\n", " # Create circle points in the plane orthogonal to v\n", " t = np.linspace(0, 2 * np.pi, sections, endpoint=False)\n", " circle_base = n1[:, None] * np.cos(t)[None, :] + n2[:, None] * np.sin(t)[None, :]\n", " circle_top = circle_base.copy()\n", "\n", " # Scale circles by radii\n", " circle_base *= radius_base\n", " circle_top *= radius_top\n", "\n", " # Points at base and top\n", " base_points = p0[:, None] + circle_base\n", " top_points = p1[:, None] + circle_top\n", "\n", " # Combine points\n", " x = np.hstack([base_points[0], top_points[0]])\n", " y = np.hstack([base_points[1], top_points[1]])\n", " z = np.hstack([base_points[2], top_points[2]])\n", "\n", " # Create faces\n", " faces = []\n", " n = sections\n", " for i in range(n):\n", " next_i = (i + 1) % n\n", " faces.append([i, next_i, n + next_i])\n", " faces.append([i, n + next_i, n + i])\n", " return x, y, z, faces\n", "\n", "def rotate_vector(v, k, theta):\n", " \"\"\"\n", " Rotate vector v around axis k by angle theta using Rodrigues' rotation formula.\n", " \"\"\"\n", " v_rot = v * np.cos(theta) + np.cross(k, v) * np.sin(theta) + k * np.dot(k, v) * (1 - np.cos(theta))\n", " return v_rot\n", "\n", "def grow_tree(p0, direction, length, radius_base, taper_ratio, levels, angle, length_reduction,\n", " branches_per_level, tree_elements, is_root=False):\n", " \"\"\"\n", " Recursively grow the tree from point p0 in a given direction.\n", " \"\"\"\n", " if levels == 0 or radius_base < 0.01 or length < 0.01:\n", " return\n", "\n", " # Calculate end point of the current branch\n", " p1 = p0 + direction * length\n", "\n", " # Ensure roots do not grow above ground level\n", " if is_root and p1[2] > 0:\n", " p1[2] = 0\n", "\n", " # Calculate top radius using consistent tapering\n", " radius_top = radius_base * taper_ratio\n", "\n", " # Add the cylinder representing the trunk or branch\n", " cylinder = cylinder_mesh(p0, p1, radius_base, radius_top)\n", " if cylinder:\n", " x, y, z, faces = cylinder\n", " tree_elements.append({\n", " 'x': x,\n", " 'y': y,\n", " 'z': z,\n", " 'faces': faces,\n", " 'color': 'saddlebrown' if not is_root else 'sienna'\n", " })\n", "\n", " # Calculate base radius of child branches\n", " N = branches_per_level\n", " if N > 0:\n", " radius_base_child = radius_top / np.sqrt(N)\n", " else:\n", " radius_base_child = 0\n", "\n", " # Length of child branches\n", " length_child = length * length_reduction\n", "\n", " # Generate branches at this level\n", " for _ in range(N):\n", " # Random rotation for natural appearance\n", " if is_root:\n", " # For roots, theta ranges from π/2 to π (90° to 180°), pointing downward\n", " min_theta = np.pi / 2\n", " max_theta = np.pi / 2 + angle\n", " theta = min_theta + np.random.rand() * (max_theta - min_theta)\n", " else:\n", " # For crown, theta ranges from 0 to angle (pointing upward)\n", " min_theta = 0\n", " max_theta = angle\n", " theta = min_theta + np.random.rand() * (max_theta - min_theta)\n", "\n", " # Add small random variation\n", " theta += (np.random.rand() - 0.5) * np.deg2rad(10)\n", " phi = np.random.rand() * 2 * np.pi\n", "\n", " # Ensure theta is within valid range\n", " if is_root:\n", " theta = np.clip(theta, np.pi / 2, np.pi)\n", " else:\n", " theta = np.clip(theta, 0, np.pi / 2)\n", "\n", " # Spherical to Cartesian coordinates\n", " new_direction = np.array([\n", " np.sin(theta) * np.cos(phi),\n", " np.sin(theta) * np.sin(phi),\n", " np.cos(theta)\n", " ])\n", "\n", " # Rotate new_direction to align with the parent branch direction\n", " rotation_axis = np.cross([0, 0, 1], direction)\n", " rotation_angle = np.arccos(np.clip(np.dot(direction, [0, 0, 1]), -1.0, 1.0))\n", " if np.linalg.norm(rotation_axis) > 1e-6:\n", " rotation_axis /= np.linalg.norm(rotation_axis)\n", " new_direction = rotate_vector(new_direction, rotation_axis, rotation_angle)\n", "\n", " # Recursive call to grow the branch\n", " grow_tree(\n", " p1,\n", " new_direction,\n", " length_child,\n", " radius_base_child,\n", " taper_ratio,\n", " levels - 1,\n", " angle,\n", " length_reduction,\n", " branches_per_level,\n", " tree_elements,\n", " is_root=is_root\n", " )\n", "\n", "def plot_tree(\n", " # Crown parameters\n", " crown_levels, crown_length, crown_radius, crown_taper_ratio, crown_angle_deg, crown_length_reduction, crown_branches_per_level,\n", " # Root parameters\n", " root_levels, root_length, root_radius, root_taper_ratio, root_angle_deg, root_length_reduction, root_branches_per_level\n", "):\n", " tree_elements = []\n", " # Start with the main trunk (above ground)\n", " p0 = np.array([0, 0, 0])\n", " direction = np.array([0, 0, 1]) # Grow upwards\n", " crown_angle_rad = np.deg2rad(crown_angle_deg)\n", " grow_tree(\n", " p0,\n", " direction,\n", " crown_length,\n", " crown_radius,\n", " crown_taper_ratio,\n", " crown_levels,\n", " crown_angle_rad,\n", " crown_length_reduction,\n", " crown_branches_per_level,\n", " tree_elements,\n", " is_root=False\n", " )\n", "\n", " # Now grow the roots (below ground)\n", " direction_root = np.array([0, 0, -1]) # Grow downwards\n", " root_angle_rad = np.deg2rad(root_angle_deg)\n", " grow_tree(\n", " p0,\n", " direction_root,\n", " root_length,\n", " root_radius,\n", " root_taper_ratio,\n", " root_levels,\n", " root_angle_rad,\n", " root_length_reduction,\n", " root_branches_per_level,\n", " tree_elements,\n", " is_root=True\n", " )\n", "\n", " # Plotting\n", " fig = go.Figure()\n", " for elem in tree_elements:\n", " fig.add_trace(go.Mesh3d(\n", " x=elem['x'],\n", " y=elem['y'],\n", " z=elem['z'],\n", " i=[face[0] for face in elem['faces']],\n", " j=[face[1] for face in elem['faces']],\n", " k=[face[2] for face in elem['faces']],\n", " color=elem['color'],\n", " flatshading=True,\n", " lighting=dict(ambient=0.5, diffuse=0.8, roughness=0.9),\n", " showscale=False\n", " ))\n", " fig.update_layout(\n", " scene=dict(\n", " xaxis=dict(visible=False),\n", " yaxis=dict(visible=False),\n", " zaxis=dict(visible=False),\n", " aspectmode='data'\n", " ),\n", " showlegend=False,\n", " margin=dict(l=0, r=0, t=0, b=0)\n", " )\n", " fig.show()\n", "\n", "# Interactive widgets\n", "crown_controls = {\n", " 'crown_levels': widgets.IntSlider(min=1, max=8, step=1, value=5, description='Crown Levels'),\n", " 'crown_length': widgets.FloatSlider(min=1, max=15, step=0.5, value=7, description='Crown Length'),\n", " 'crown_radius': widgets.FloatSlider(min=0.1, max=1.5, step=0.1, value=0.5, description='Crown Radius'),\n", " 'crown_taper_ratio': widgets.FloatSlider(min=0.5, max=1.0, step=0.05, value=0.7, description='Crown Taper'),\n", " 'crown_angle_deg': widgets.FloatSlider(min=10, max=80, step=5, value=30, description='Crown Angle'),\n", " 'crown_length_reduction': widgets.FloatSlider(min=0.5, max=1.0, step=0.05, value=0.7, description='Crown Length Red.'),\n", " 'crown_branches_per_level': widgets.IntSlider(min=0, max=8, step=1, value=3, description='Crown Branches')\n", "}\n", "\n", "root_controls = {\n", " 'root_levels': widgets.IntSlider(min=1, max=8, step=1, value=4, description='Root Levels'),\n", " 'root_length': widgets.FloatSlider(min=1, max=15, step=0.5, value=5, description='Root Length'),\n", " 'root_radius': widgets.FloatSlider(min=0.1, max=1.5, step=0.1, value=0.4, description='Root Radius'),\n", " 'root_taper_ratio': widgets.FloatSlider(min=0.5, max=1.0, step=0.05, value=0.7, description='Root Taper'),\n", " 'root_angle_deg': widgets.FloatSlider(min=-80, max=80, step=5, value=45, description='Root Angle'),\n", " 'root_length_reduction': widgets.FloatSlider(min=0.5, max=1.0, step=0.05, value=0.8, description='Root Length Red.'),\n", " 'root_branches_per_level': widgets.IntSlider(min=0, max=8, step=1, value=2, description='Root Branches')\n", "}\n", "\n", "interact(\n", " plot_tree,\n", " **crown_controls,\n", " **root_controls\n", ")\n" ] }, { "cell_type": "code", "execution_count": null, "id": "8d9a53df-a13e-4419-83db-e8e8962dea7e", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Fractal Foundations GPU (Python 3.10)", "language": "python", "name": "fractal-foundations-gpu" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.19" } }, "nbformat": 4, "nbformat_minor": 5 }