naeve/LennartNaeve_code
1
0
Fork 0
Code Issues Pull Requests 1 Actions Packages repo.project_board Releases Wiki Activity
c1254d4dd5
LennartNaeve_code/merging_tweezer_code/bosons/2025_03_10 (decompose coords).ipynb
Lennart Naeve c1254d4dd5 first commit
2025-04-25 20:52:11 +02:00

562 lines
274 KiB
Plaintext
Raw Blame History

{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Since 3D simulation is numerically very expensive, let's try to solve 1D potentials and compute wave function as product:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import matplotlib.animation as animation\n",
"import numpy as np\n",
"import sympy as sp\n",
"from IPython.display import Math, display\n",
"from matplotlib.axes import Axes\n",
"from scipy import constants as const\n",
"from scipy.integrate import quad\n",
"from scipy.optimize import root_scalar\n",
"from scipy.signal import argrelmax,argrelmin,find_peaks\n",
"from tqdm import tqdm\n",
"\n",
"import fewfermions.analysis.units as si\n",
"from fewfermions.simulate.traps.twod.trap import DoubleTweezer"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"initial_power = 50* si.uW\n",
"initial_waist = 1.1*si.uW\n",
"initial_distance = 2*si.um\n",
"\n",
"trap: DoubleTweezer = DoubleTweezer(\n",
" power=0, # Set pancake laser power to 0, no 2D trap\n",
" grad_z= 0*si.G/si.cm,\n",
" grad_r=0,\n",
" power_tweezer1 = initial_power, #stationary\n",
" power_tweezer2 = initial_power, #transfer tweezer\n",
" waist_tweezer1 = initial_waist, #stationary\n",
" waist_tweezer2 = initial_waist, #transfer tweezer\n",
" distance_tweezers = initial_distance,\n",
"\n",
" a=180*(4 * np.pi * const.epsilon_0 * const.value(\"Bohr radius\")**3)/(2 * const.epsilon_0 * const.c),\n",
" wvl = 532 * si.nm,\n",
"\n",
" g = 0,\n",
")\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Try decomposing all 3D spatial directions:"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"n_pot_steps = [200,200,200]\n",
"n_levels = 4\n",
"\n",
"left_cutoff = -0.5*initial_distance-2*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
"right_cutoff = 0.5*initial_distance+2*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
"back_cutoff = -2*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
"front_cutoff = 2*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
"bottom_cutoff = -2*np.max([float(trap.subs(trap.get_tweezer_rayleigh1())),float(trap.subs(trap.get_tweezer_rayleigh2()))])\n",
"top_cutoff = 2*np.max([float(trap.subs(trap.get_tweezer_rayleigh1())),float(trap.subs(trap.get_tweezer_rayleigh2()))])\n",
"\n",
"extend = [(left_cutoff,right_cutoff),\n",
" (back_cutoff,front_cutoff),\n",
" (bottom_cutoff,top_cutoff)]\n",
"\n",
"\n",
"# Solve the hamiltonian numerically in all directions\n",
"energies_x, states_x, potential_x, coords_x = trap.nstationary_solution(\n",
" trap.x, extend[0], n_pot_steps[0], k=n_levels)\n",
"\n",
"energies_y, states_y, potential_y, coords_y = trap.nstationary_solution(\n",
" trap.y, extend[1], n_pot_steps[1], k=n_levels)\n",
"\n",
"energies_z, states_z, potential_z, coords_z = trap.nstationary_solution(\n",
" trap.z, extend[2], n_pot_steps[2], k=n_levels)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"C:\\Users\\naeve\\AppData\\Local\\Temp\\ipykernel_3752\\3500672162.py:46: MatplotlibDeprecationWarning: The collections attribute was deprecated in Matplotlib 3.8 and will be removed in 3.10.\n",
" for c in contour.collections:\n"
]
},
{
"ename": "KeyboardInterrupt",
"evalue": "",
"output_type": "error",
"traceback": [
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[1;31mKeyboardInterrupt\u001b[0m Traceback (most recent call last)",
"Cell \u001b[1;32mIn[4], line 59\u001b[0m\n\u001b[0;32m 56\u001b[0m frames \u001b[38;5;241m=\u001b[39m n_pot_steps[\u001b[38;5;241m2\u001b[39m] \u001b[38;5;66;03m# Number of slices\u001b[39;00m\n\u001b[0;32m 57\u001b[0m ani \u001b[38;5;241m=\u001b[39m animation\u001b[38;5;241m.\u001b[39mFuncAnimation(fig, update, frames\u001b[38;5;241m=\u001b[39mframes, interval\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m100\u001b[39m)\n\u001b[1;32m---> 59\u001b[0m ani\u001b[38;5;241m.\u001b[39msave(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mstate\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mstate_number\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m_decomp_all.gif\u001b[39m\u001b[38;5;124m\"\u001b[39m, writer\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mpillow\u001b[39m\u001b[38;5;124m\"\u001b[39m, fps\u001b[38;5;241m=\u001b[39mframes\u001b[38;5;241m/\u001b[39m\u001b[38;5;241m5\u001b[39m) \u001b[38;5;66;03m# Save as GIF\u001b[39;00m\n\u001b[0;32m 61\u001b[0m plt\u001b[38;5;241m.\u001b[39mshow()\n",
"File \u001b[1;32mc:\\Users\\naeve\\anaconda3\\Lib\\site-packages\\matplotlib\\animation.py:1085\u001b[0m, in \u001b[0;36mAnimation.save\u001b[1;34m(self, filename, writer, fps, dpi, codec, bitrate, extra_args, metadata, extra_anim, savefig_kwargs, progress_callback)\u001b[0m\n\u001b[0;32m 1082\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m data \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mzip\u001b[39m(\u001b[38;5;241m*\u001b[39m[a\u001b[38;5;241m.\u001b[39mnew_saved_frame_seq() \u001b[38;5;28;01mfor\u001b[39;00m a \u001b[38;5;129;01min\u001b[39;00m all_anim]):\n\u001b[0;32m 1083\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m anim, d \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mzip\u001b[39m(all_anim, data):\n\u001b[0;32m 1084\u001b[0m \u001b[38;5;66;03m# TODO: See if turning off blit is really necessary\u001b[39;00m\n\u001b[1;32m-> 1085\u001b[0m anim\u001b[38;5;241m.\u001b[39m_draw_next_frame(d, blit\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mFalse\u001b[39;00m)\n\u001b[0;32m 1086\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m progress_callback \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[0;32m 1087\u001b[0m progress_callback(frame_number, total_frames)\n",
"File \u001b[1;32mc:\\Users\\naeve\\anaconda3\\Lib\\site-packages\\matplotlib\\animation.py:1121\u001b[0m, in \u001b[0;36mAnimation._draw_next_frame\u001b[1;34m(self, framedata, blit)\u001b[0m\n\u001b[0;32m 1119\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_pre_draw(framedata, blit)\n\u001b[0;32m 1120\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_draw_frame(framedata)\n\u001b[1;32m-> 1121\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_post_draw(framedata, blit)\n",
"File \u001b[1;32mc:\\Users\\naeve\\anaconda3\\Lib\\site-packages\\matplotlib\\animation.py:1146\u001b[0m, in \u001b[0;36mAnimation._post_draw\u001b[1;34m(self, framedata, blit)\u001b[0m\n\u001b[0;32m 1144\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_blit_draw(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_drawn_artists)\n\u001b[0;32m 1145\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m-> 1146\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_fig\u001b[38;5;241m.\u001b[39mcanvas\u001b[38;5;241m.\u001b[39mdraw_idle()\n",
"File \u001b[1;32mc:\\Users\\naeve\\anaconda3\\Lib\\site-packages\\matplotlib\\backend_bases.py:1905\u001b[0m, in \u001b[0;36mFigureCanvasBase.draw_idle\u001b[1;34m(self, *args, **kwargs)\u001b[0m\n\u001b[0;32m 1903\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_is_idle_drawing:\n\u001b[0;32m 1904\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_idle_draw_cntx():\n\u001b[1;32m-> 1905\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mdraw(\u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n",
"File \u001b[1;32mc:\\Users\\naeve\\anaconda3\\Lib\\site-packages\\matplotlib\\backends\\backend_agg.py:387\u001b[0m, in \u001b[0;36mFigureCanvasAgg.draw\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 384\u001b[0m \u001b[38;5;66;03m# Acquire a lock on the shared font cache.\u001b[39;00m\n\u001b[0;32m 385\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m (\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mtoolbar\u001b[38;5;241m.\u001b[39m_wait_cursor_for_draw_cm() \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mtoolbar\n\u001b[0;32m 386\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m nullcontext()):\n\u001b[1;32m--> 387\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mfigure\u001b[38;5;241m.\u001b[39mdraw(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mrenderer)\n\u001b[0;32m 388\u001b[0m \u001b[38;5;66;03m# A GUI class may be need to update a window using this draw, so\u001b[39;00m\n\u001b[0;32m 389\u001b[0m \u001b[38;5;66;03m# don't forget to call the superclass.\u001b[39;00m\n\u001b[0;32m 390\u001b[0m \u001b[38;5;28msuper\u001b[39m()\u001b[38;5;241m.\u001b[39mdraw()\n",
"File \u001b[1;32mc:\\Users\\naeve\\anaconda3\\Lib\\site-packages\\matplotlib\\artist.py:95\u001b[0m, in \u001b[0;36m_finalize_rasterization.<locals>.draw_wrapper\u001b[1;34m(artist, renderer, *args, **kwargs)\u001b[0m\n\u001b[0;32m 93\u001b[0m \u001b[38;5;129m@wraps\u001b[39m(draw)\n\u001b[0;32m 94\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mdraw_wrapper\u001b[39m(artist, renderer, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs):\n\u001b[1;32m---> 95\u001b[0m result \u001b[38;5;241m=\u001b[39m draw(artist, renderer, \u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n\u001b[0;32m 96\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m renderer\u001b[38;5;241m.\u001b[39m_rasterizing:\n\u001b[0;32m 97\u001b[0m renderer\u001b[38;5;241m.\u001b[39mstop_rasterizing()\n",
"File \u001b[1;32mc:\\Users\\naeve\\anaconda3\\Lib\\site-packages\\matplotlib\\artist.py:72\u001b[0m, in \u001b[0;36mallow_rasterization.<locals>.draw_wrapper\u001b[1;34m(artist, renderer)\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[0;32m 70\u001b[0m renderer\u001b[38;5;241m.\u001b[39mstart_filter()\n\u001b[1;32m---> 72\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m draw(artist, renderer)\n\u001b[0;32m 73\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[0;32m 74\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n",
"File \u001b[1;32mc:\\Users\\naeve\\anaconda3\\Lib\\site-packages\\matplotlib\\figure.py:3162\u001b[0m, in \u001b[0;36mFigure.draw\u001b[1;34m(self, renderer)\u001b[0m\n\u001b[0;32m 3159\u001b[0m \u001b[38;5;66;03m# ValueError can occur when resizing a window.\u001b[39;00m\n\u001b[0;32m 3161\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpatch\u001b[38;5;241m.\u001b[39mdraw(renderer)\n\u001b[1;32m-> 3162\u001b[0m mimage\u001b[38;5;241m.\u001b[39m_draw_list_compositing_images(\n\u001b[0;32m 3163\u001b[0m renderer, \u001b[38;5;28mself\u001b[39m, artists, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39msuppressComposite)\n\u001b[0;32m 3165\u001b[0m renderer\u001b[38;5;241m.\u001b[39mclose_group(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mfigure\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[0;32m 3166\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n",
"File \u001b[1;32mc:\\Users\\naeve\\anaconda3\\Lib\\site-packages\\matplotlib\\image.py:132\u001b[0m, in \u001b[0;36m_draw_list_compositing_images\u001b[1;34m(renderer, parent, artists, suppress_composite)\u001b[0m\n\u001b[0;32m 130\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m not_composite \u001b[38;5;129;01mor\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m has_images:\n\u001b[0;32m 131\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m a \u001b[38;5;129;01min\u001b[39;00m artists:\n\u001b[1;32m--> 132\u001b[0m a\u001b[38;5;241m.\u001b[39mdraw(renderer)\n\u001b[0;32m 133\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m 134\u001b[0m \u001b[38;5;66;03m# Composite any adjacent images together\u001b[39;00m\n\u001b[0;32m 135\u001b[0m image_group \u001b[38;5;241m=\u001b[39m []\n",
"File \u001b[1;32mc:\\Users\\naeve\\anaconda3\\Lib\\site-packages\\matplotlib\\artist.py:72\u001b[0m, in \u001b[0;36mallow_rasterization.<locals>.draw_wrapper\u001b[1;34m(artist, renderer)\u001b[0m\n\u001b[0;32m 69\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[0;32m 70\u001b[0m renderer\u001b[38;5;241m.\u001b[39mstart_filter()\n\u001b[1;32m---> 72\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m draw(artist, renderer)\n\u001b[0;32m 73\u001b[0m \u001b[38;5;28;01mfinally\u001b[39;00m:\n\u001b[0;32m 74\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m artist\u001b[38;5;241m.\u001b[39mget_agg_filter() \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n",
"File \u001b[1;32mc:\\Users\\naeve\\anaconda3\\Lib\\site-packages\\matplotlib\\axes\\_base.py:3101\u001b[0m, in \u001b[0;36m_AxesBase.draw\u001b[1;34m(self, renderer)\u001b[0m\n\u001b[0;32m 3098\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m spine \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mspines\u001b[38;5;241m.\u001b[39mvalues():\n\u001b[0;32m 3099\u001b[0m artists\u001b[38;5;241m.\u001b[39mremove(spine)\n\u001b[1;32m-> 3101\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_update_title_position(renderer)\n\u001b[0;32m 3103\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39maxison:\n\u001b[0;32m 3104\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m _axis \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_axis_map\u001b[38;5;241m.\u001b[39mvalues():\n",
"File \u001b[1;32mc:\\Users\\naeve\\anaconda3\\Lib\\site-packages\\matplotlib\\axes\\_base.py:3045\u001b[0m, in \u001b[0;36m_AxesBase._update_title_position\u001b[1;34m(self, renderer)\u001b[0m\n\u001b[0;32m 3043\u001b[0m top \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mmax\u001b[39m(top, bb\u001b[38;5;241m.\u001b[39mymax)\n\u001b[0;32m 3044\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m title\u001b[38;5;241m.\u001b[39mget_text():\n\u001b[1;32m-> 3045\u001b[0m ax\u001b[38;5;241m.\u001b[39myaxis\u001b[38;5;241m.\u001b[39mget_tightbbox(renderer) \u001b[38;5;66;03m# update offsetText\u001b[39;00m\n\u001b[0;32m 3046\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m ax\u001b[38;5;241m.\u001b[39myaxis\u001b[38;5;241m.\u001b[39moffsetText\u001b[38;5;241m.\u001b[39mget_text():\n\u001b[0;32m 3047\u001b[0m bb \u001b[38;5;241m=\u001b[39m ax\u001b[38;5;241m.\u001b[39myaxis\u001b[38;5;241m.\u001b[39moffsetText\u001b[38;5;241m.\u001b[39mget_tightbbox(renderer)\n",
"File \u001b[1;32mc:\\Users\\naeve\\anaconda3\\Lib\\site-packages\\matplotlib\\axis.py:1372\u001b[0m, in \u001b[0;36mAxis.get_tightbbox\u001b[1;34m(self, renderer, for_layout_only)\u001b[0m\n\u001b[0;32m 1369\u001b[0m renderer \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mfigure\u001b[38;5;241m.\u001b[39m_get_renderer()\n\u001b[0;32m 1370\u001b[0m ticks_to_draw \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_update_ticks()\n\u001b[1;32m-> 1372\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_update_label_position(renderer)\n\u001b[0;32m 1374\u001b[0m \u001b[38;5;66;03m# go back to just this axis's tick labels\u001b[39;00m\n\u001b[0;32m 1375\u001b[0m tlb1, tlb2 \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_get_ticklabel_bboxes(ticks_to_draw, renderer)\n",
"File \u001b[1;32mc:\\Users\\naeve\\anaconda3\\Lib\\site-packages\\matplotlib\\axis.py:2654\u001b[0m, in \u001b[0;36mYAxis._update_label_position\u001b[1;34m(self, renderer)\u001b[0m\n\u001b[0;32m 2650\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m\n\u001b[0;32m 2652\u001b[0m \u001b[38;5;66;03m# get bounding boxes for this axis and any siblings\u001b[39;00m\n\u001b[0;32m 2653\u001b[0m \u001b[38;5;66;03m# that have been set by `fig.align_ylabels()`\u001b[39;00m\n\u001b[1;32m-> 2654\u001b[0m bboxes, bboxes2 \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_get_tick_boxes_siblings(renderer\u001b[38;5;241m=\u001b[39mrenderer)\n\u001b[0;32m 2655\u001b[0m x, y \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mlabel\u001b[38;5;241m.\u001b[39mget_position()\n\u001b[0;32m 2656\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mlabel_position \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mleft\u001b[39m\u001b[38;5;124m'\u001b[39m:\n",
"File \u001b[1;32mc:\\Users\\naeve\\anaconda3\\Lib\\site-packages\\matplotlib\\axis.py:2206\u001b[0m, in \u001b[0;36mAxis._get_tick_boxes_siblings\u001b[1;34m(self, renderer)\u001b[0m\n\u001b[0;32m 2204\u001b[0m axis \u001b[38;5;241m=\u001b[39m ax\u001b[38;5;241m.\u001b[39m_axis_map[name]\n\u001b[0;32m 2205\u001b[0m ticks_to_draw \u001b[38;5;241m=\u001b[39m axis\u001b[38;5;241m.\u001b[39m_update_ticks()\n\u001b[1;32m-> 2206\u001b[0m tlb, tlb2 \u001b[38;5;241m=\u001b[39m axis\u001b[38;5;241m.\u001b[39m_get_ticklabel_bboxes(ticks_to_draw, renderer)\n\u001b[0;32m 2207\u001b[0m bboxes\u001b[38;5;241m.\u001b[39mextend(tlb)\n\u001b[0;32m 2208\u001b[0m bboxes2\u001b[38;5;241m.\u001b[39mextend(tlb2)\n",
"File \u001b[1;32mc:\\Users\\naeve\\anaconda3\\Lib\\site-packages\\matplotlib\\axis.py:1351\u001b[0m, in \u001b[0;36mAxis._get_ticklabel_bboxes\u001b[1;34m(self, ticks, renderer)\u001b[0m\n\u001b[0;32m 1349\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m renderer \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[0;32m 1350\u001b[0m renderer \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mfigure\u001b[38;5;241m.\u001b[39m_get_renderer()\n\u001b[1;32m-> 1351\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m ([tick\u001b[38;5;241m.\u001b[39mlabel1\u001b[38;5;241m.\u001b[39mget_window_extent(renderer)\n\u001b[0;32m 1352\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m tick \u001b[38;5;129;01min\u001b[39;00m ticks \u001b[38;5;28;01mif\u001b[39;00m tick\u001b[38;5;241m.\u001b[39mlabel1\u001b[38;5;241m.\u001b[39mget_visible()],\n\u001b[0;32m 1353\u001b[0m [tick\u001b[38;5;241m.\u001b[39mlabel2\u001b[38;5;241m.\u001b[39mget_window_extent(renderer)\n\u001b[0;32m 1354\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m tick \u001b[38;5;129;01min\u001b[39;00m ticks \u001b[38;5;28;01mif\u001b[39;00m tick\u001b[38;5;241m.\u001b[39mlabel2\u001b[38;5;241m.\u001b[39mget_visible()])\n",
"File \u001b[1;32mc:\\Users\\naeve\\anaconda3\\Lib\\site-packages\\matplotlib\\text.py:961\u001b[0m, in \u001b[0;36mText.get_window_extent\u001b[1;34m(self, renderer, dpi)\u001b[0m\n\u001b[0;32m 959\u001b[0m bbox, info, descent \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_get_layout(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_renderer)\n\u001b[0;32m 960\u001b[0m x, y \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_unitless_position()\n\u001b[1;32m--> 961\u001b[0m x, y \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_transform()\u001b[38;5;241m.\u001b[39mtransform((x, y))\n\u001b[0;32m 962\u001b[0m bbox \u001b[38;5;241m=\u001b[39m bbox\u001b[38;5;241m.\u001b[39mtranslated(x, y)\n\u001b[0;32m 963\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m bbox\n",
"File \u001b[1;32mc:\\Users\\naeve\\anaconda3\\Lib\\site-packages\\matplotlib\\transforms.py:1505\u001b[0m, in \u001b[0;36mTransform.transform\u001b[1;34m(self, values)\u001b[0m\n\u001b[0;32m 1502\u001b[0m values \u001b[38;5;241m=\u001b[39m values\u001b[38;5;241m.\u001b[39mreshape((\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39minput_dims))\n\u001b[0;32m 1504\u001b[0m \u001b[38;5;66;03m# Transform the values\u001b[39;00m\n\u001b[1;32m-> 1505\u001b[0m res \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mtransform_affine(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mtransform_non_affine(values))\n\u001b[0;32m 1507\u001b[0m \u001b[38;5;66;03m# Convert the result back to the shape of the input values.\u001b[39;00m\n\u001b[0;32m 1508\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m ndim \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m0\u001b[39m:\n",
"File \u001b[1;32mc:\\Users\\naeve\\anaconda3\\Lib\\site-packages\\matplotlib\\_api\\deprecation.py:300\u001b[0m, in \u001b[0;36mrename_parameter.<locals>.wrapper\u001b[1;34m(*args, **kwargs)\u001b[0m\n\u001b[0;32m 295\u001b[0m warn_deprecated(\n\u001b[0;32m 296\u001b[0m since, message\u001b[38;5;241m=\u001b[39m\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mThe \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mold\u001b[38;5;132;01m!r}\u001b[39;00m\u001b[38;5;124m parameter of \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mfunc\u001b[38;5;241m.\u001b[39m\u001b[38;5;18m__name__\u001b[39m\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m() \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m 297\u001b[0m \u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mhas been renamed \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mnew\u001b[38;5;132;01m!r}\u001b[39;00m\u001b[38;5;124m since Matplotlib \u001b[39m\u001b[38;5;132;01m{\u001b[39;00msince\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m; support \u001b[39m\u001b[38;5;124m\"\u001b[39m\n\u001b[0;32m 298\u001b[0m \u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mfor the old name will be dropped %(removal)s.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m 299\u001b[0m kwargs[new] \u001b[38;5;241m=\u001b[39m kwargs\u001b[38;5;241m.\u001b[39mpop(old)\n\u001b[1;32m--> 300\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m func(\u001b[38;5;241m*\u001b[39margs, \u001b[38;5;241m*\u001b[39m\u001b[38;5;241m*\u001b[39mkwargs)\n",
"File \u001b[1;32mc:\\Users\\naeve\\anaconda3\\Lib\\site-packages\\matplotlib\\transforms.py:2428\u001b[0m, in \u001b[0;36mCompositeGenericTransform.transform_affine\u001b[1;34m(self, values)\u001b[0m\n\u001b[0;32m 2425\u001b[0m \u001b[38;5;129m@_api\u001b[39m\u001b[38;5;241m.\u001b[39mrename_parameter(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m3.8\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mpoints\u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mvalues\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[0;32m 2426\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mtransform_affine\u001b[39m(\u001b[38;5;28mself\u001b[39m, values):\n\u001b[0;32m 2427\u001b[0m \u001b[38;5;66;03m# docstring inherited\u001b[39;00m\n\u001b[1;32m-> 2428\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mget_affine()\u001b[38;5;241m.\u001b[39mtransform(values)\n",
"File \u001b[1;32mc:\\Users\\naeve\\anaconda3\\Lib\\site-packages\\matplotlib\\transforms.py:2455\u001b[0m, in \u001b[0;36mCompositeGenericTransform.get_affine\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m 2453\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_b\u001b[38;5;241m.\u001b[39mget_affine()\n\u001b[0;32m 2454\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m-> 2455\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m Affine2D(np\u001b[38;5;241m.\u001b[39mdot(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_b\u001b[38;5;241m.\u001b[39mget_affine()\u001b[38;5;241m.\u001b[39mget_matrix(),\n\u001b[0;32m 2456\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_a\u001b[38;5;241m.\u001b[39mget_affine()\u001b[38;5;241m.\u001b[39mget_matrix()))\n",
"File \u001b[1;32mc:\\Users\\naeve\\anaconda3\\Lib\\site-packages\\matplotlib\\transforms.py:1913\u001b[0m, in \u001b[0;36mAffine2D.__init__\u001b[1;34m(self, matrix, **kwargs)\u001b[0m\n\u001b[0;32m 1910\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m matrix \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[0;32m 1911\u001b[0m \u001b[38;5;66;03m# A bit faster than np.identity(3).\u001b[39;00m\n\u001b[0;32m 1912\u001b[0m matrix \u001b[38;5;241m=\u001b[39m IdentityTransform\u001b[38;5;241m.\u001b[39m_mtx\n\u001b[1;32m-> 1913\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_mtx \u001b[38;5;241m=\u001b[39m matrix\u001b[38;5;241m.\u001b[39mcopy()\n\u001b[0;32m 1914\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_invalid \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0\u001b[39m\n",
"\u001b[1;31mKeyboardInterrupt\u001b[0m: "
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAlEAAAGNCAYAAAAxaCQXAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8hTgPZAAAACXBIWXMAAA9hAAAPYQGoP6dpAADof0lEQVR4nOydd3hUVfrHP3d6n/RMAoHQe8eCZdVVEexl7WJD7AXQn71gRV3brq5iQbDrKmt3WXAVbCBFkN4DhPQ6JdNn7u+PSbKEuTOZFMDo+TzPfTT3nHPvuZMh885bvq8ky7KMQCAQCAQCgaBNqA72BgQCgUAgEAi6IsKIEggEAoFAIGgHwogSCAQCgUAgaAfCiBIIBAKBQCBoB8KIEggEAoFAIGgHwogSCAQCgUAgaAfCiBIIBAKBQCBoB5qDvQGBQCAQCARtw+/3EwwGO3wdnU6HwWDohB39MRFGlEAgEAgEXQi/30+vnhbKKyMdvpbD4aCoqEgYUu1EGFECgUAgEHQhgsEg5ZURdq0sxGZtf1aOyx2l55idBINBYUS1E2FECQQCgUDQBbFYJSxWqd3ro7R/rSCGMKIEAoFAIOiCROQokQ50v43I0c7bzB8UUZ0nEAgEAoFA0A6EJ0ogEAgEgi5IFJko7XdFdWStIIYwogQCgUAg6IJEidKRgFzHVgtAGFECgUAgEHRJIrJMRG6/N6kjawUxRE6UQCAQCAQCQTsQniiBQCAQCLogIifq4COMKIFAIBAIuiBRZCLCiDqoiHCeQCAQCAQCQTsQniiBQCAQCLogIpx38BFGlEAgEAgEXRBRnXfwEeE8gUAgEAgEgnYgPFECgUAgEHRBoo1HR9YLOoYwogQCgUAg6IJEOlid15G1ghginCcQCAQCgUDQDoQnSiAQCASCLkhEjh0dWS/oGMKIEggEAoGgCyJyog4+wogSCAQCgaALEkUigtSh9YKOIXKiBAKBQCAQCNqB8EQJBAKBQNAFicqxoyPrBR1DGFECgUAgEHRBIh0M53VkrSCGCOcJBAKBQCAQtAPhiRIIBAKBoAsiPFEHH2FECQQCgUDQBYnKElG5A9V5HVgriCHCeQKBQCAQCATtQHiiBAKBQCDogohw3sFHeKIEgt85//rXv7jwwgvp27cvRqORwsJCLr74YrZu3ZrS+vfee48//elP5Obmotfryc/P57TTTuOnn35qMW/RokVIkpTwuPbaa1vM93g8TJ06lfz8fAwGAyNHjuT999/vtOcWCH7vRFB1+BB0DOGJEgh+5zzxxBM4HA7uueceevfuTXFxMY899hijR49m6dKlDBkyJOn6mpoajjzySG655RaysrIoKyvjmWee4U9/+hP//e9/OeaYYwAYPXo0S5YsiVv/0ksv8eabb3LWWWe1OH/22WezfPlyHn/8cfr378+7777LhRdeSDQa5aKLLuq8F0AgEAj2E5Isy0JuSyD4HVNZWUlOTk6Lc6WlpRQWFnLppZfy2muvtfmaTqeT7OxsLrjgAt58882E82RZpm/fvkQiEXbs2IFKFfvm+9VXX3HKKac0G05NjB8/nvXr17N7927UanWb9yUQ/BFwuVzY7Xb+u7YHZmv7vUkN7ijHD9uN0+nEZrN14g7/OAhfnkBwgEkW8tq5c2en329fAwogPz+f7t27U1xc3K5rWq1WDAYDGk1yZ/a3337Ljh07uOKKK5oNKICPP/4Yi8XCueee22L+FVdcQWlpKT///HPzOUmSmDFjRty1CwsLufzyy5t/njt3LpIk8c033zBlyhQyMzOx2WxceumlNDQ0UF5eznnnnUdaWhp5eXncdttthEKhdj2/QPBboCknqiNHe3jxxRfp1asXBoOBMWPG8P333yedv3jxYsaMGYPBYKB3797MmjUrbs68efMYPHgwer2ewYMH8/HHH7f5vrIsM2PGDPLz8zEajRx77LGsX7++Xc+YKsKIEggOMEuWLGlxfPPNN3Tr1g2Hw0FGRgayLBMOh1M62suOHTvYtWtXq6G8vYlEIoRCIXbu3Ml1112HLMvccMMNSdfMnj0blUrFFVdc0eL8unXrGDRoUJwRNnz48Obx9nLVVVdht9t5//33uffee3n33XeZMmUKp5xyCiNGjOCjjz7isssu4+mnn+b5559v930EgoNNRFZ1+GgrH3zwAVOnTuWee+5h1apVHH300UycOJHdu3crzi8qKuLkk0/m6KOPZtWqVdx9993cfPPNzJs3r3nOkiVLOP/885k0aRK//vorkyZN4rzzzmvxZSqV+z755JM888wzvPDCCyxfvhyHw8GJJ56I2+1u83OmjCwQCA4a4XBYPuOMM2SLxSKvXLlSlmVZnjNnjgykdLSHUCgkH3vssbLNZpN3796d8roBAwY03zcvL0/+4Ycfks6vq6uTDQaDfNJJJ8WN9evXT/F8aWmpDMiPPfZY8zlAfuCBB+Lm9uzZU77sssuaf2563W666aYW884880wZkJ955pkW50eOHCmPHj066TMIBL9FnE6nDMj/XtNL/q6oT7uPf6/pJQNycXGx7HQ6mw+/35/w3oceeqh87bXXtjg3cOBA+c4771Scf/vtt8sDBw5sce6aa66RDz/88OafzzvvPHnChAkt5px00knyBRdckPJ9o9Go7HA45Mcff7x53O/3y3a7XZ41a1bC5+kowhPVBr777jtOO+008vPzkSSJTz75ZL/fs6SkhEsuuYTMzExMJhMjR45k5cqV+/2+ggPDjTfeyJdffsmHH37I6NGjATjttNNYvnx5SkcTsoL3SglZlpk8eTLff/89b775JgUFBSnvdd68efz88898+OGHDB48mIkTJ7Jo0aKE89955x38fj9XXXWV4rgkJQ4lJBtrjVNPPbXFz4MGDQLglFNOiTu/a9eudt9HIDjYRJGIourAEft3VlBQgN1ubz5mzpypeL9gMMjKlSsZP358i/Pjx4+Pq9ZtYsmSJXHzTzrpJFasWNEcTk80p+maqdy3qKiI8vLyFnP0ej3HHHNMwr11BqI6rw00NDQwYsQIrrjiCs4555z9fr+6ujqOPPJIjjvuOP7973+Tk5PD9u3bSUtL2+/3Fux/HnnkEWbNmsXs2bOZMGFC8/mMjAzsdnubrvXGG2/EhczkfWpGZFnmqquu4u233+aNN97gjDPOaNM9mkJ/hx56KGeeeSajRo3illtu4ddff1WcP3v2bLKzsxXvk5mZSU1NTdz52tpaIPYatJd91+p0uoTn/X5/u+8jEBxsOksnqri4uEViuV6vV5xfXV1NJBIhNze3xfnc3FzKy8sV15SXlyvOD4fDVFdXk5eXl3BO0zVTuW/Tf5Xm7M8vS8KIagMTJ05k4sSJCceDwSD33nsv77zzDvX19QwdOpQnnniCY489tl33e+KJJygoKGDOnDnN5woLC9t1LcFvi7lz53LfffcxY8YMrrzyyhZjSgZRIpoMpSbvVbJ5V111FXPmzGH27Nlccskl7d88oNFoGD16NP/85z8Vx1etWsWqVau49dZb0Wq1cePDhg3jvffeIxwOt8iLWrt2LQBDhw5tPqfX6wkEAnHXUDLCBAJB27HZbG2qztvXUyzLcps8y01/t/Y+n8o1O2tOZyKMqE7kiiuuYOfOnbz//vvk5+fz8ccfM2HCBNauXUu/fv3afL3PPvuMk046iXPPPZfFixfTrVs3rr/+eqZMmbIfdi84UMyfP58pU6Zw5ZVX8sADD8SNt2YQKZGZmUlmZqbimCzLTJkyhTlz5vDyyy+nbKAlw+/3s3TpUvr27as4Pnv2bAAmT56sOH7WWWfx6quvMm/ePM4///zm82+88Qb5+fkcdthhzecKCwtZs2ZNi/XffPMNHo+no48hEHRp2psc/r/1bVM4ysrKQq1Wx3mdKisr4zxATTgcDsX5Go2m+W9WojlN10zlvg6HA4h5pPLy8lLaW2cgjKhOYvv27bz33nvs2bOH/Px8AG677Tbmz5/PnDlzeOyxx9p8zR07dvDSSy8xffp07r77bpYtW8bNN9+MXq/n0ksv7exHEBwAioqKOPfcc+nduzdXXHEFS5cubTE+atSopAZRe7j55puZPXs2V155JcOGDWtxT71ez6hRo5p/Pv7441m8eHGLnKojjjiC008/nUGDBmG329m5cycvvfQS27dvVyxD9vv9vPvuuxxxxBHN+Uj7MnHiRE488USuu+46XC4Xffv25b333mP+/Pm8/fbbLTSiJk2axH333cf999/PMcccw4YNG3jhhRfaHPIUCH5vxHKiOtCAuI1rdTodY8aMYeHChS3EcxcuXJgwPWDcuHF8/vnnLc4tWLCAsWPHNnupx40bx8KFC5k2bVqLOUcccUTK9+3VqxcOh4OFCxc2/00LBoMsXryYJ554ok3P2Sb2W8r67xxA/vjjj5t//uc//ykDstlsbnFoNBr5vPPOk2VZlouKilqttrrhhhuar6nVauVx48a1uO9NN93UoqpB0LX49ttvk/7+i4qKOv2ePXv2THi/nj17tph7zDHHxFX93XrrrfKIESNku90uazQa2eFwyGeddZb8448/Kt7vnXfekQH59ddfT7ovt9st33zzzbLD4ZB1Op08fPhw+b333oubFwgE5Ntvv10uKCiQjUajfMwxx8irV69OWJ23fPnyFusfeOABGZCrqqpanL/ssstks9mcdI8CwW+Rpuq8eb/2l+fvGNTuY96v/WVAdjqdKd/7/fffl7VarTx79mx5w4YN8tSpU2Wz2Szv3LlTlmVZvvPOO+VJkyY1z9+xY4dsMpnkadOmyRs2bJBnz54ta7Va+aOPPmqe8+OPP8pqtVp+/PHH5Y0bN8qPP/64rNFo5KVLl6Z8X1mW5ccff1y22+3yv/71L3nt2rXyhRdeKOfl5ckul6sjL3dShGJ5O5EkiY8//pgzzzwTiGlYXHzxxaxfvz5OadliseBwOAiFQmzfvj3pddPT05tdjz179uTEE09soSj90ksv8cgjj1BSUtK5DyQQCASCLkGTYvmHvw7EZG2/sr/XHeHcEZvarFj+4osv8uSTT1JWVsbQoUN59tln+dOf/gTA5Zdfzs6dO1tU7i5evJhp06axfv168vPzueOOO+J6aX700Ufce++97Nixgz59+vDoo49y9tlnp3xfiKUuPPjgg7z88svU1dVx2GGH8Y9//KNFjmVnI4yodrKvEbVlyxYGDBjAd999x9FHH90p97jooosoLi5uoco6bdo0fv755/1asikQCASC3y5NRtT7qwd32Ii6YOQG0falA4icqDbg8XjYtm1b889FRUWsXr2ajIwM+vfvz8UXX8yll17K008/zahRo6iuruabb75h2LBhnHzyyW2+37Rp0zjiiCN47LHHOO+881i2bBmvvPIKr7zySmc+lkAgEAgEgnYgPFFtYNGiRRx33HFx5y+77DLmzp1LKBTikUce4c0336SkpITMzEzGjRvHgw8+yLBhw9p1zy+++IK77rqLrVu30qtXL6ZPny6q8wQCgeAPTJMn6t3VQzvsibpo5DrhieoAwogSCAQCgaAL0WREvbVqWIeNqEmj1gojqgOIcJ5AIBAIBF2QCCoidEAnCuFD6Siid55AIBAIBAJBOxCeqFaIRqOUlpZitVr3q3S8QCAQCLo+sizjdrvJz89Hpdq/foqorCLaAcXyqMjm6TDCiGqF0tLSNnW6FwgEAoGguLiY7t2779d7iHDewUcYUa1gtVoB+OdPhZgsIvopEAgEgsR4PVHOO2Jn82eH4PeNMKJaoSmEZ7KoMFuFESUQCASC1jkQ6R9RICJ3pHeeoKMII0ogEAgEgi5IFBXRDoTzOrJWEEO8ggKBQCAQCATtQHiiBAKBQCDogkRkFZEOVOd1ZK0ghjCiBAKBQCDogkSRiNKRnCgh29NRhBkqEAgEAoFA0A66jBE1c+ZMDjnkEKxWKzk5OZx55pls3ry51XWLFy9mzJgxGAwGevfuzaxZsw7AbgUCgUAg2L80hfM6cgg6Rpd5BRcvXswNN9zA0qVLWbhwIeFwmPHjx9PQ0JBwTVFRESeffDJHH300q1at4u677+bmm29m3rx5B3DnAoFAIBB0Pk1imx05BB2jy+REzZ8/v8XPc+bMIScnh5UrV/KnP/1Jcc2sWbPo0aMHzz33HACDBg1ixYoVPPXUU5xzzjn7e8sCgUAgEOw3orJEtCM6UR1YK4jRZc1Qp9MJQEZGRsI5S5YsYfz48S3OnXTSSaxYsYJQKKS4JhAI4HK5WhwCgUAgEAgE+9IljShZlpk+fTpHHXUUQ4cOTTivvLyc3NzcFudyc3MJh8NUV1crrpk5cyZ2u735EH3zBAKBQPBbJNrBUJ4Q2+w4XfIVvPHGG1mzZg3vvfdeq3P3ld6XG7tWJ5Lkv+uuu3A6nc1HcXFxxzcsEAgEAkEnE5VVHT4EHaPL5EQ1cdNNN/HZZ5/x3Xfftdoh2+FwUF5e3uJcZWUlGo2GzMxMxTV6vR69Xt9p+xUIBAKBQPD7pMsYUbIsc9NNN/Hxxx+zaNEievXq1eqacePG8fnnn7c4t2DBAsaOHYtWq91fWxUIBAKBYL8TQSLSAcHMjqwVxOgyvrwbbriBt99+m3fffRer1Up5eTnl5eX4fL7mOXfddReXXnpp88/XXnstu3btYvr06WzcuJHXX3+d2bNnc9tttx2MRxAIBAKBoNMQ4byDT5d5BV966SWcTifHHnsseXl5zccHH3zQPKesrIzdu3c3/9yrVy+++uorFi1axMiRI3n44Yf5+9//LuQNBAKBQCAQdJguFc5rjblz58adO+aYY/jll1/2w44EAoFAIDh4ROhYSC7SeVv5w9JljCiBQCAQCAT/o6MhORHO6zjiFRQIBAKBQCBoB8ITJRAIBAJBF6SjTYRFA+KOI4wogUAgEAi6IDIS0Q7kRMlC4qDDCCNKIBAIBIIuiPBEHXzEKygQCAQCgUDQDoQnSiAQCASCLkhUlojK7Q/JdWStIIYwogQCgUAg6IJEUBHpQECpI2sFMcQrKBAIBAKBQNAOhCdKIBAIBIIuiAjnHXyEESUQCAQCQRckiopoBwJKHVkriCFeQYFAIBAIBJ1KXV0dkyZNwm63Y7fbmTRpEvX19UnXyLLMjBkzyM/Px2g0cuyxx7J+/foWcwKBADfddBNZWVmYzWZOP/109uzZ0zy+c+dOJk+eTK9evTAajfTp04cHHniAYDDY4jqSJMUds2bNavNzCiNKIBAIBIIuSESWOnzsLy666CJWr17N/PnzmT9/PqtXr2bSpElJ1zz55JM888wzvPDCCyxfvhyHw8GJJ56I2+1unjN16lQ+/vhj3n//fX744Qc8Hg+nnnoqkUisnfKmTZuIRqO8/PLLrF+/nmeffZZZs2Zx9913x91vzpw5lJWVNR+XXXZZm59ThPMEAoFAIOiC/FZzojZu3Mj8+fNZunQphx12GACvvvoq48aNY/PmzQwYMCBujSzLPPfcc9xzzz2cffbZALzxxhvk5uby7rvvcs011+B0Opk9ezZvvfUWJ5xwAgBvv/02BQUFfP3115x00klMmDCBCRMmNF+3d+/ebN68mZdeeomnnnqqxT3T0tJwOBwdelbhiRIIBAKB4A+My+VqcQQCgQ5db8mSJdjt9mYDCuDwww/Hbrfz008/Ka4pKiqivLyc8ePHN5/T6/Ucc8wxzWtWrlxJKBRqMSc/P5+hQ4cmvC6A0+kkIyMj7vyNN95IVlYWhxxyCLNmzSIajbb5WYURJRAIBAJBF0SWVUQ7cMiNbV8KCgqac5fsdjszZ87s0L7Ky8vJycmJO5+Tk0N5eXnCNQC5ubktzufm5jaPlZeXo9PpSE9PTzhnX7Zv387zzz/Ptdde2+L8ww8/zIcffsjXX3/NBRdcwK233spjjz2W2gPuhQjnCQQCgUDQBYkgEelAE+GmtcXFxdhstubzer1ecf6MGTN48MEHk15z+fLlQCxxe19kWVY8vzf7jqeyJtGc0tJSJkyYwLnnnstVV13VYuzee+9t/v+RI0cC8NBDD7U4nwrCiBIIBAKBoAsSlTuW1xSVY/+12WwtjKhE3HjjjVxwwQVJ5xQWFrJmzRoqKirixqqqquI8TU005SaVl5eTl5fXfL6ysrJ5jcPhIBgMUldX18IbVVlZyRFHHNHieqWlpRx33HGMGzeOV155pdVnO/zww3G5XFRUVCTcoxIinCcQCAQCgaBVsrKyGDhwYNLDYDAwbtw4nE4ny5Yta177888/43Q644ydJnr16oXD4WDhwoXN54LBIIsXL25eM2bMGLRabYs5ZWVlrFu3rsV1S0pKOPbYYxk9ejRz5sxBpWrd1Fm1ahUGg4G0tLQ2vSbCEyUQCAQCQRekKbepI+v3B4MGDWLChAlMmTKFl19+GYCrr76aU089tUVl3sCBA5k5cyZnnXUWkiQxdepUHnvsMfr160e/fv147LHHMJlMXHTRRQDY7XYmT57MrbfeSmZmJhkZGdx2220MGzasuVqvtLSUY489lh49evDUU09RVVXVfL8mb9fnn39OeXk548aNw2g08u2333LPPfdw9dVXJwxlJqJLGVHfffcdf/3rX1m5ciVlZWV8/PHHnHnmmQnnL1q0iOOOOy7u/MaNGxk4cOB+3KlAIBAIBPuXKBLRDuREdWRta7zzzjvcfPPNzZV0p59+Oi+88EKLOZs3b8bpdDb/fPvtt+Pz+bj++uupq6vjsMMOY8GCBVit1uY5zz77LBqNhvPOOw+fz8fxxx/P3LlzUavVACxYsIBt27axbds2unfv3uJ+shyLX2q1Wl588UWmT59ONBqld+/ePPTQQ9xwww1tfk5JbrpqF+Df//43P/74I6NHj+acc85J2YjavHlzi3hvdnZ28wveGi6XC7vdzhdremO2iuinQCAQCBLT4I5y6vAdOJ3OlPKM2kPT59Kkby9EZ9G1+zpBT5C3jntvv+71906X8kRNnDiRiRMntnldTk5Om+OcAoFAIBD8lumo6vj+VCz/o/CHcK2MGjWKvLw8jj/+eL799tukcwOBQJzwmEAgEAgEvzU6ohHV0XwqQYzf9SuYl5fHK6+8wrx58/jXv/7FgAEDOP744/nuu+8Srpk5c2YL0bGCgoIDuGOBQCAQCARdhS4VzmsrAwYMaFEJMG7cOIqLi3nqqaf405/+pLjmrrvuYvr06c0/u1wuYUgJBAKB4DdHlA72ztuPieV/FH7XRpQShx9+OG+//XbCcb1e3+YSR4FAIBAIDjRyB6vzZGFEdZjfdThPiVWrVrVQQxUIBAKBQCBoD13KE+XxeNi2bVvzz0VFRaxevZqMjAx69OjBXXfdRUlJCW+++SYAzz33HIWFhQwZMoRgMMjbb7/NvHnzmDdv3sF6BIFAIBAIOoWo3MFwnqjO6zBdyohasWJFC/HMptylyy67jLlz51JWVsbu3bubx4PBILfddhslJSUYjUaGDBnCl19+ycknn3zA9y4QCAQCQWfyW1Us/yPRpYyoY489lmTaoHPnzm3x8+23387tt9++n3clEAgEAsGBR3iiDj7CDBUIBAKBQCBoB13KEyUQCAQCgSDGb7l33h8FYUQJBAKBQNAFEeG8g48I5wkEAoFAIBC0A+GJEggEAoGgCyI8UQcfYUQJBAKBQNAFEUbUwUeE8wQCgUAgEAjagfBECQQCgUDQBRGeqIOPMKIEAoFAIOiCyHRMpiCxdLUgVUQ4TyAQCAQCgaAdCE+UQCAQCARdEBHOO/gII0ogEAgEgi6IMKIOPsKIEghSwKDphlaVhVadTjjqxBVYRbZpIgZNNwBC0XrKPR9h1x+KQeMgHPUQitbjCvwCSIjsg66DRmVFp85Fq0onFK3BG9qBw/IXNCoLEhp84V1UexeSZToRrSqdiNxAMFJFvX8ZaslCVPYjEz7YjyH4AyCMqIOPMKIEgkYkNIBEgf0KTNq+GDU9qfF9y27nLAZlPYWMTDhaT71/Ga7AKrTqdDQqGyATlQMA6DUO0gyHo1FZUavMrKm4kgLbFHqmXYMvtAd/uJjNNfeikjRoVRl4QzvEB+5BQi1ZyDaPx6Tti0nbm3LPv6j1fc+h3RYSjFQSitRS7vkUb2gHBk0+KkmPLIdRS0YAdOoczNq+qFVmwlE39f5lFKbdSL71IsJRJ97QDn6tuAyzdiA6dSae4EZC0dqD/NQCgaAzEUaU4A+LWjLRzTYJm340Nv0Idjtnscc1F5Vkotb3A77Q2/jCRQCsKr8wbn2p+924c5UNn1HZ8FmLc8WuVyh1v41B0w2jtieRqAebcRy90/8Pg6YAb2gbG6qmEoo4UUl6QtGa/fPAf2DUkoUs0wnYDWOw6Uews/55nP6V2PVjaQhto97/M+7AOqKyj5+KD49bv7P+73HnSt3vxJ3bXvc42+seR6fOQq/OA8Co7UG+9QIsukFE5SDLSiagV2ejkkw0hDYjvJSC9iI8UQcfYUQJ/jDo1DlkmY4nw3g01d5vqPB8gloyU+b+gM3VdzV7CXbWP9fp947IXhpCW2kIbQWg1vc9tb7vkdBh0Q0iGKnCrj+UQdlPEYrUUOf/id3OlwlGqjt9L38E1JKFdOMRZBiPptzzL4KRStKNR+L0r6DE9Q7e0FZkImyuuXu/3D8YqW7+3VV7F1DtXQDE3oNR2YdZN4heaTejVWdS5/uJzTX3EJV9+2Uvgt8vsiwhd8AQ6shaQQxhRAl+1+jUOaglI4FIJaPzPqLO9yPlnk+p9/+ETJii+mcO6v5kgriDvwJQ5/+Bn4rHYdb2J914JJGonyzTCeSaz6DKu5Aa7zdEZM9B3e9vGa0qA4jlNI3Om4czsIJa33f4w8UEI9Vsqv6/g7xDCEYqAaj2/odq73/QqbNJMxxKVPbRw34daYZDqWz4kmrvAsJR10HerUAgaA1hRAl+l2SbJuCw/AWrfihFdU9T5vmQpXv+dLC3lQIyDaHNjWEeqPMtRSWZyDaNp1/GvSwrOQmZKJGoF5nQQd7rwUdCR475ZHItp2PVDWFT9d3U+P7Lkj1HNuep/ZYJRqqobPgSgGLnbBqCm8kxn0IP+zUsKzmpMbm9FhHyEygRReqQ2GZH1gpiCCNK8LtBp87GrB1Anf8H7IYxlHs+Yl3l9cgED/bW2k1E9jTnWakkA1HZTzfrpfRMu57Khi8oc/+ThtCWg73NA45NPxoJCXdwLRnGoyhxvUOt7/vm33VXMKD2RSZIje8banzfIKEGohSm3UyG8UhK3O9S5v6n8EQKWiByog4+QrFc0OUxagoZkDmTsflfYNMPB2Bb7aNUeed3aQNqX6KyH4AS95usKD2DYKSGvhn3AhImbW8kdAd3gweAfOtFjM3/gv6ZD6JVZxKVg2ysvo0a339/V79rmQgAW2sfYH3VzZi1femf+RAAKslwMLcmEAj2oksZUd999x2nnXYa+fn5SJLEJ5980uqaxYsXM2bMGAwGA71792bWrFn7f6OCA0JT9VOW6Xi8oR38vOd4djlfPMi7OjAEIxXsdr7ErxWXAjL51os5vPu3FKbdjFaVebC316kYND3IMZ8CgErSs6XmPlaUntacrP17xxPcwOaau9lYPR0JHYd2+zf9Mu5Hp8452FsTHGSaEss7cgg6RpcyohoaGhgxYgQvvPBCSvOLioo4+eSTOfroo1m1ahV33303N998M/PmzdvPOxXsT3TqXAZkPsbovA/RqbMods2m2PXqHzrUsa32YVaXX4hGZaVn2vUA6NWOg7yrjmHVDWdI9j8Y5Xi3WdR0j2sOrsCqg7yzg4dMkBWlZxKOuhmb/xnphiMO9pYEB5GmcF5HDkHH6FI5URMnTmTixIkpz581axY9evTgueeeA2DQoEGsWLGCp556inPOOWc/7VKwPzFqejIq7wNK3e+wrGQ8Edl7sLf0m8EX3s222keBWMhnpONdvKHt7Ha+gjOw/CDvLlUkMoxHU+v7HqO2kBrft2ysnkZU/v2E6jpKOOqkqP5Z9rjeICL7SDMcjknbm1L3+0D0YG9PIPhD0aWMqLayZMkSxo8f3+LcSSedxOzZswmFQmi12rg1gUCAQOB/Sakulygz/i2QYTwGvTqXMs8/WV5yslB+boWo7GdZyXhyzKfQP3MGRfXPUe39L7Eqr99epZeEllzL6RTYriIcrccdWB8nWipoSdO/gUC4gh72a8iznMuWmgdwB9cc5J0JDhRCJ+rg87s2osrLy8nNzW1xLjc3l3A4THV1NXl5eXFrZs6cyYMPPnigtihoBa0qg74Z92LRDWZLzX0AB9WAsuqGo1NnolZZG0UxfyTLdCJ6tYOoHCQUraPauwCDpgCVpCUQrjxoYUaZMBUNn1LR8BkgkWk8ht7pd1Dseo0Kz2e/iURstWRBkjQYNPlkmU5kc809jf0GDy5NlZAW3RAMmnzUkgWZIJUNX5JmOBSTth9ROUBU9lPZ8BUalQ21ZCIYqTrg0hO+cBFrKq4g2zSBfOuFbK4RRtQfBbmDITlhRHWc37URBSBJLd8ksiwrnm/irrvuYvr06c0/u1wuCgoK9t8GBUnJs57X2G/uzgMS0lFLZlSSjnDUTf/MhzBp+2DUFlDh+YztdY9TYL8Cidi4O7iWOv+P6NRZGDTdkCQt4aibau8Csk3jybWciV6dgwz8VDyOdMMR2PQj8QQ34A6uJxip2O/PEyPmfarxfUsoWk8P+xQK025iecnEgxYO1asddLNdisNyNttqH6Gy4QvWVV57wPdh0PRAJenwhrbRP/Nh7PrR6DX51Pl+YH3VTWSbxmPU9iAcbWj+fWlUdoyanqgkHWqVkcqGL8kwHk2vtFvQqbMIRV2sLr8QlaQnzXA47sB6GkIb9/v7t8o7nyrvfDQqOyNy32Br7QxcgdX79Z6Cg4sMyB1wLP/2fNJdj9+1EeVwOCgvL29xrrKyEo1GQ2amcgWTXq9Hr9cfiO0JEqCSDPTNuIfKhi/Z7dz/1ZRqyUTv9NuwG8Zi0HRje+1fKfO8T51/KaXuD/CFdxGO1gOwoWpa3PpS93tx52LJ7rOBppL0KKFoHZKkIs96Lv10M1hRegombT8suoHU+5fiDe3Yn48JgCuwinWV16NTZxORvfTNuAeVZKDE9dYB0ZvSqNIIR10My32NGu+3rCg9vVnFe/8joVFZCUddDM5+jjTDOCJRD6Xu9/GGtlHh+YQ9rjn4wyXNOlNF9c/GXaXau5Bq78IW5yobPqey4XOAmCEVqcOo7YVZ25dc85mYdf1YXX4xwUgVZu0AnIEVzZIVnU1TztSQ7OcpdX/QWLEqcqUEgv3B79qIGjduHJ9//nmLcwsWLGDs2LGK+VCCg49J25ch2X/HGVi5375F69TZZJsmkGU6gVrf9xS7ZtMQ2kaZ50MagluaNXo6Kyen6cPSE1yPJ7i+xZgsBzFrB9DddgUSalaWnYEsy0RlX/M+9gfBSBUAO+v/QZ7lXIbmzMIV+IWN1bcRK9rtvA9drSqTHPOp5FvPwxPcyMbq21hRehoH6ntwpvHPZJlOJMP4JyobPmN73RPscb3J1pqHWoSGnYGVnXK/pp553tA2ttbGtJ1iGl4RzLoB9LBfhUX3HM7AcrbVPoI/XNIp992bWt9iVpSeQa/0qagl0x+6cvX3TBQJSSiWH1S6lMSBx+Nh9erVrF69GohJGKxevZrdu3cDsVDcpZde2jz/2muvZdeuXUyfPp2NGzfy+uuvM3v2bG677baDsX1BCvSwT2GX8yW21NzXqd/UVZIBg6Y7EhpGOd7DrOtPsWs2e1xvAjKl7nfxBDfuV8NFCXdwHVtrH2BZyYn8WnEZ4agbh+VsxhX8SL+MB7HpR+3X+4ej9RS7XuXnkuPZUfc0AKPz/smQ7BfINZ/Z3I+urejVeWQYjwGgd/qtmHX92FxzT6ORBvvTgJJQk2E8mlzzGQCkG8fhCvzKL2XnsL3uCQBcgV8OaG6dTBCZCJ7gBn6tuJyle46hwvMpoUg92aaJDM15iUzj8Uid+L02FK1lS839RGQvI3LnYteP6bRrC34b/JZ1ourq6pg0aRJ2ux273c6kSZOor69v5XlkZsyYQX5+PkajkWOPPZb161t+8QwEAtx0001kZWVhNps5/fTT2bNnT4s5hYWFSJLU4rjzzjtbzNm9ezennXYaZrOZrKwsbr75ZoLBtofcJVnuSET1wLJo0SKOO+64uPOXXXYZc+fO5fLLL2fnzp0sWrSoeWzx4sVMmzaN9evXk5+fzx133MG116aee+FyubDb7Xyxpjdma5eyObsQEj3t11PZ8CW+8M5OvbJR04N86yXkWs6gxPUWu5ypaYwdbHTqHHLMp5JhPJK1FVdj1g0gEC4jFK3b7/dWS2YyTX8m03gcgUg5O+qepDDtJsJRN95QEb7QbnzhIrSqTNQqE1pVOpKkxhVYRYFtMvnWi1FJWqq8/2Fb7SP7fb970912OQW2yfjCxZS636Wy4YsDev/2oJIMZJlOJM/yF4zaXiwvmdDpuWpphsMYlPU0O+v/Tpnnn516bUFLGtxRTh2+A6fTic1m2y/3aPpcGv7hbahN7U8/iXgDrDn3qf2y14kTJ7Jnzx5eeeUVAK6++moKCwvjokN788QTT/Doo48yd+5c+vfvzyOPPMJ3333H5s2bsVqtAFx33XV8/vnnzJ07l8zMTG699VZqa2tZuXIlarUaiBlRkydPZsqUKc3XtlgsWCyW2HNHIowcOZLs7GyefvppampquOyyyzj77LN5/vnn2/ScXcqIOhgII2r/opJ0DMx6Eq0qg/VVNxGOOjvlujp1NsFIFQOz/oo/vJtS9/vNIayuSIHtanrYJ1Pt/ZY9rjnNDYoPFLG8ngGYtL1oCG6hqP4ZBmU9i1U/iFCkHk9wE1trZ2DRDSIcdeMP72n9op2EXX8IWaYT2F43k3TDUfjDxfjCuw7Y/TsTnTqHYKSyMVfNSLHz1U57FoOmO4OynmJ91Y3NIUdB53Mgjaih//y/DhtR6877a6fvdePGjQwePJilS5dy2GGHAbB06VLGjRvHpk2bGDBgQNwaWZbJz89n6tSp3HHHHUDM65Sbm8sTTzzBNddcg9PpJDs7m7feeovzzz8fgNLSUgoKCvjqq6846aSTgJgRNXXqVKZOnaq4v3//+9+ceuqpFBcXk5+fD8D777/P5ZdfTmVlZZteC2EVCA4qAzIfIyoHWFMxuVMMKItuEENzXmZ47mxAYlP1/7Gz/vkubUABFLte4eeSE2gIbcZhOROICY8eKCoaPmFH3ROsq7yWovpnANhYPY1lJRNYVX4BW2tnAOAJbjxgBpRNP5rReR/RP3MGDaGtgESd/4cua0ABzUn2O+v/jj9czEjHu/RO75z0A394D6vKLyAYqaW77XIkRF5oV0eWO35AzCjb+9hbK7E9LFmyBLvd3mxAARx++OHY7XZ++uknxTVFRUWUl5e30HbU6/Ucc8wxzWtWrlxJKBRqMSc/P5+hQ4fGXfeJJ54gMzOTkSNH8uijj7YI1S1ZsoShQ4c2G1AQ05AMBAKsXNm23MjfdWK54LeLVpVJVPaxrfaxTstNyTKdRN+Me9hV/w/KPfPYn3k3MX0jFeGoC506C5VkbNQN8hGOuvfLPcNRN3tcc4CYOOWQnOcJRz3srH+Oev+y/XLP3x4SWabxOP3Licp+dtY/T61v8X6+oxpQIxPEoGmSO4kSjrr26+96t/NlSlxvYdQWIqGmu20yZZ73OnxPCTVW3QiG5R7Nusobicq+Ttq1oKuyr4zPAw88wIwZM9p9vfLycnJy4ns75uTkxFXM770GUNR23LVrV/McnU5Henp63Jy9r3vLLbcwevRo0tPTWbZsGXfddRdFRUW89tprzdfZ9z7p6enodLqE+0uEMKIEBxydOpeRjjcpqnuOKu+/O3QtCQ3dbZfjDq6j1reYZSWLOy0h3aIbhEU3CJO2N97QTso9HzHK8U+s+sFEol7q/D+xoWoqhWk3k2Y4tFk/amXZGRSm3USW6UQC4Qp84V1sr30StcqILEc6pVJKJsSK0jPINp1Ev4wHKap/Jq7s/vdGTIvpVqKyH29oK57ghk67tlaVjlk3EItuALW+74hEvQzPnYNOnY1K0rG97nFK3e8yLOcVQEKSVFQ1zKeo/hnG5n+GVpWOP1xGnf9Hdtb/DZt+ZHMOWUcqHSOyF09wAyrJiF6TyyH5X7Gj7mkqGj5p9zVlQmysvpX+mTMYnvsav5ZfesALKgSdQ2cplhcXF7cIYSWS+ZkxY0arYtTLl8daTClpMcqynFCjsQklbcfW1uw7Z9q0/0nRDB8+nPT0dP7yl780e6c6sr99EUaU4IASM6DepsT1ZocNKKtuGAOyZuIL7aKy4csOGU8qSYdNP4Z0wxExzaCGT+mTfjf+cAne0Da8oW0ArKm4kojcwN5eri0198ddr9g5m8qGr9Cr8zBqeyATJMt0On3S7yQYqcAZ+IXttU900KCSGwUWFyAhkW2aSJZpPEX1T+2XsvmDhYQWlaSjh/0aiuqf7RTPk0HTjXTDEdT6YmKpw3JfxRPcQENwM6AiGKlmXeW1BCNVLZK8l5fG9+5cUXomOnUGOnUuUmOGRKbxOLJM49FrcqhqWMDmmrvQqXMJRarbZbDEvLYPU+b+J/0y78cV+BVfuKjdzw9RttTcj11/aON+JIT0Ytejs4wom82WUh7QjTfeyAUXXJB0TmFhIWvWrKGiIl5MuKqqKs4D1ITDEWuYXl5e3qKbSGVlZfMah8NBMBikrq6uhTeqsrKSI45I3Iz78MMPB2Dbtm1kZmbicDj4+eefW8ypq6sjFAol3F8ihBElOKBYdAMocb1BifvtDl+rm+0Sdtb/nWrvgnatV0lGdOoM/OEyDu32Nf7wbmp9P+IJbgTg14pJcWtSNXoishdvaDve0HbqGm27cs9HlHvmYdb2xaYfRUT20s16GbmW06jxfkNlw7/b+cEYRQZqfP/FoClgdN5HlLn/qSgU2ZXQqjLolT4dnTqDdZXXs7r8kg5dT0KNUduLIdnPo1aZqfP9RL1/Be7gWn4qPixufuq5VVGCkeoWydpF9c9SVP8sasmCQRP7QOiVdguZpuOp9S2isuELan3ft/kZGkKbWV1+MQB90u/CF95NqfudNl+nCWdgGXb9GArTbmZt5dXNIqMCgRJZWVlkZWW1Om/cuHE4nU6WLVvGoYceCsDPP/+M0+lMaOz06tULh8PBwoULGTUqJu0SDAZZvHgxTzwRkyYZM2YMWq2WhQsXct555wFQVlbGunXrePLJJxPuZ9WqVQDNxtm4ceN49NFHKSsraz63YMEC9Ho9Y8a0TQpEVOe1gqjO6xzUkoVcy2mK6t5twaDpQf/Mh9hU/X/tTha368eQZ72ATOMxFLvmsNv5EhK6g9RLToVNP4Is04lkGo9hZdnZ6NX5hKPOdueKaVWZZJqOo9zzERbd4E4Nex0osk0T6Zd5P2Xuf7Lb+XK7S/716nwclrNxWM5ie90T1Pq+w6jpecCrG5vQqbPINB6PVm1nt/MV8izn4wqsbtd+YtV2fyUUdbG5+q4O5BZKDMh8FK06nfWVN4rQXgc5kNV5A969s8PVeZsveny/SRyUlpby8ssvAzGJg549e7aQOBg4cCAzZ87krLPOAmLJ4DNnzmTOnDn069ePxx57jEWLFsVJHHzxxRfMnTuXjIwMbrvtNmpqapolDpYsWcLSpUs57rjjsNvtLF++nGnTpjF27Fg+/fTT2HM3Shzk5uby17/+ldraWi6//HLOPPPMNkscCE+UYL8TS4J+gYZgx9qKZBqPp3/mQ+ys/1ubDSgJHRbdQNzBNeSYT8MVWMW22ocJR10AB7EZbxRXYBWuwCp21MW+SWUYj6Iw7UZqfT9Q4n6rzcrtoWgN5Z6PkFDTN+NeYqGbGc0hyd8ydv1YGkJbaQht5Zey8/GHd7fjKlJjD0Qto/M+oLLhC9ZWXtP8/AfLgIKYmnmZ54PmnzUqC0NzXiIQKWdn/d+p9y9N+Vr+8B5Wl19Cz7TrSTeOo7Lhy3buSmZLzX0MyXmefOuFneIlFhwY9q6wa+/6/cU777zDzTff3FxJd/rpp/PCCy11+jZv3ozT+b+q7Ntvvx2fz8f1119PXV0dhx12GAsWLGg2oACeffZZNBoN5513Hj6fj+OPP565c+c2a0Tp9Xo++OADHnzwQQKBAD179mTKlCncfvvtzddQq9V8+eWXXH/99Rx55JEYjUYuuuginnrqqTY/p/BEtYLwRHWcAZmPo1YZ2VA1lfbmXUjoGJY7ix11f20Ot6WCStKRZzmPAvvVOP3L9lLM/m2jlszkWs7AohvMlpp7G5Pb29NbT8JhOYdeadPYUDUVZ2B5p++1M9CqMuiTcSd2/VjWV93Qpt9xExIacsyn0cM+hSrvfHbW/53ObmGzf5DINB6HTIg631KyTMdT5V1AW/edb70IWQ5R5vmwXbtQSXpkOYxKMoo2MR3gQHqi+r19J2qTod3XiXj9bL1k/3ii/igIT5RgPyPhCa5rVEluuwGlkvQUpt3CrvoXWVNxZZvuCzL51kuw6UeytmJyo5ZQxzFp+6JTZ6GWzISjLpyB5aQZDkejshKJeglGqjvs7YjIDZS6323+uW/GfWhV6eys/xs1vm/bcCWZcs9HVHsXEol6yDT+GUlS/8Yq+VSMdLxNlXcBW2omtjsvZ2jOLGJelftxBlY0nm2/ASWhQavOJBipwKTtjUnbF5UUC51Ue/+DRpWOUdOTULSWYKSqAzpnMjW+b4BY4UW+9WIK025ie93jbcqbqvV9x9CcWZi0vdle91fa+uxNr/tIx1vsrH+BGt9/27ReIPgjIowowX4jzTAOCXW7wwMalZ1hOa/gDW1rU+WdRTeE/pkPsr12Jntcr7fr3hBLRC6wT8GiG4BJ249a3yJ21D1Fn/TbkSQ14WgDrsBqnIHlWHXDseoHo5bMRGQPG6qm0S/jfjKMf6IhtI2G4GaK6p9DQtWunJM1FVeQYfwTvdKmoVPnUuZ5v03rmz7gg5EaBmQ9jMPyl8bmt8Vt3ktnYdENIc9yLltrH2Rl2dntqq7MMB5DN+vFrKu8gQ1VU9vtQTFoumPQ5FPvX0ZP+43kWf+CVpWON7STlWVnYNENbfQWBZFlmRrvN5i0velhv6axMi+HtRVXE5V9FNivwhPchCuwGk9wPVE59VBxMFLBrxWTSDccRe/022gIbiUQSU23xh/ew6qyCxiS8zfyLOe02yO1qfouRjheZ3X5Tryh7e26huDA0FnVeYL2I8J5rSDCee1Dr3YwOu8j1lfd2OacniZG531Ere97dtb/LaX5Emp6p99Bjnki2+seb3OOiEU3mCzT8aQbjqTW9wO7nC/Qw34dvlARDaFt+MO72/SBKKFGr8nDpO2LQdONUvc79EqbRrZ5InW+JdT4vqXW9x1t8xhISGixG0bjsJzDjron25EfpqabbRJGTQ+21j7EgS5v16js9EqbSqbpeHbU/ZXKhsS9tBJh0HSnf+aD6NTZbK99kjr/D21aL6FBJkwP+7WNYbAwtb7FbK19EIOmB1E50Kge3rbXRatKJ914NFbdYGz6kRTVP4MvtJsc86lUexe2S029X8YM/OFSil2vkcp7JfZsUSy6gXhDRe0S08wxn0qu+UzWVl7V5rV/dA5kOK/PW3d1OJy3fdJMEc7rAMKIagVhRLUdCXVjeOY/7HHNbfN6jcpGOOpCr84jEClLcU0a4Wg9+daLqfB8mrJHwqjpgUaVhie4npGOt6n3L6PW9x2uwBpkQm3eeyqYtL1JNxyJTT+ajdXTyDT+GZkodb7vU/ZSqSQ9BbYpdLNdzK76Fxu9fW3/p6xTZzHS8S5Fdc9Q5Z3f5vVtQUKNJGmx6AaSbZrIzvrn2+w5Ukk61JIFtcpMhvFoSt3vk6oRqpL0ZJlOIMd8OgZNHitKT8eiG0woUk8gUtqOJ0oNvdpBgX0yWaYTCEfdbKia3qYkf73aQf/Mh9Go7Gyq/r+UDbHe6Xdg049gbcVV7apuVEm6WOLyQSu66JoII+qPhTCiWkEYUW1HLVnoZruI3c5X2rxWq8pgpOMdttY+mGKlkkSBbTJ51vNZXnJyyoZPhvEYutsuxaztz876F1pUTB1oMo3HU2C/AoOmB6Xut9v0uhk0PXBYzmZn/XOoJVO7Pixt+pH0zbgXWY6woeqWlMNHbSHLdAK90m6jxP1Gu2Uu7PqxDMh6lFL3e20yznXqXIKRCnqn34ZJ25cKz6fU+L7tNGX7tmDTj6QhuIUM45/INk9gj+tNXIFfUlqbZzmPULSuTfls/TLux6Tt26gB1fbnHZz9HDXeb6ho+KzNa/+oHEgjqvebd3fYiNpx6WPCiOoAIidK0KlYdIOJyoF2GVBqycLw3DlUNHyckgGllswMyn4KjcrK6vKLUjCgJKy6obiDa7HpR1DmjiVcy4TbvNfOpMb3X2p8/8Wo6YVFNxCAbtZJ1Pq+a9Xr4A/vZmf9c0hoGZP/KWXu9yl2zaEtIUJXYDW/lP2FLNMJBCM1pBuOQibYaf34hufOQaOysrV2RptK+Pemh/1q8q0XsaXm/sYQaOtYdUPpYb8Om344y0tPYUdd28uXO5um0HaNbzEalZ0BmY8Ritbwa/kVrXp8YsUZ0M16CSZtH7bVPtrqe3dr7cP0sF+LWjK1y4jaWf88Ix1vUe9ftl+Ma0EHkelYJF64UDqMcK0IOg2VpGdw9jMYNT3btT7bPIE6/48pG2AyUer9y/m1/LJW84LSDUcyJu8TeqXfCkjsrP87Vd5/t9mAklCjU+di0Q3Brj8EAKOmkExjLJfKqhuBhK5N12zCFy5qboWjkvSMdLzLwKwn0KvzWlkZ64f2a/kk0o1HMyL3DbSqzDbfv9r7NTIhJElD34z7GJv/GQ7LOW2+jl7toMA2hcHZsVy2LTX38UvZX9plQJm0fZDQUev7nhWlp6VsQNn1hzA4++/U+hbzc8nxzXpg7UGrysCmH0m64SgyjcejkgxoVRmkGQ7FohuETp1FW/+URmUfZZ4PWF46kR11TyMTJN96ERbd4FbXlnv+hU6d1Wic2luZLbPb+RIg08N+XZv2COANbWe381X6Zc5o81qB4I+A8EQJOo3CtJtwBdY0l2u3BYtuMOWej1Ke2y/jflaXT0qp+q4plBQrGV+U8p7UkgW7YQxW3TC0ajvbah+lb8b9ZJr+RDBSTShSx9rK5Zh1/ck1n4ZKMqBRWVhXeQNphkPpk3EXvlARnuBG9rjeaNM3+WLXa5S636Wb7TKs+iEEvVWoJF3ScF0gUs6aiivIs5xPVPa3O7xX61tErW8Rdv1YrPqhAPS03wDEPCm+8E784ZLGHCcderUDnToDZ2AlvdKmkWc9l6qGBeyqfxGIVY21h3zrhRSm3cSaiil4gutbna9VZdI7fTru4DpK3e+zrGR8m43kNMNhZJnGY9ENwqDpxs97/kym6VgclnMIRz1E5QCuwCqM2kJ62K9Do7KhV+ewsfo2AuEyeqXfhie4DlfgV1yB1SnINcjN4bxI1MPQnFmNVaBPJ5RMiMhe1lfdTGHaLTgsZ7PHNafV54rIDWQajyVmVM1q02uyx/UG1d6v27RGcIDoYHUeojqvw4icqFYQOVGpIaFleO6rrK+aSjha36a13W1Xkm0az6ry5I0tocnD8Byba+5q1SuRZ7mAULSWGu83gJRSvpRJ2xuzdiBV3q8YkDkTnTqr+QOxrRVgOnU2Jm1vLLohVDZ8jkU3kL4Z91PrW0y19784/ctSTiRPNxzFgKxH2Fb7WMq9Aofnvo4nuImiumc6HLJMMxxOumEcVv0wQhEnG6unMTDrSbJMxxMIl9MQ2s6GqpvRqtIJR10dbh0yMOsJTNo+bKiampIRlmc5n17pt1Dm/jDlNjEqSUe64SiyTMdj1Y9gRelpZBqPRa/JxxPciC9URChal/Ke1ZKFdOORWHVDselHUuyajTvwKznm06j2LkjJiFZLFgrTbsQb2pmyjEW64Sj84ZJW+y5qVRmMzvuIbbWPtksDqn/mIxTVPdOB9jJ/DA5kTlSvOfeg6kBOVNTrp+iKR0VOVAcQRlQrCCMqNVSSsV2l1GmGwxiY9Vd+KftLY0l5YmJ5P/PYWvPQXmKK8WhVGQzMehKNysym6jtTqmbKNk2gh/1qNKo0Kho+Y2f9c219lJQwanqRaTqObNOJbK65l0jUi1plTqlay6YfSf/Mh2gIbmdj9bRW52tUVgZkPo5Wncb6ypsJRWs64xH2Kzp1FsFINXb9obgCq1o1fJuqMvMs51LvX44vvLPVe1h0g/AEN9LTfiN2wyiqvV9T412UciVoW9CrHfSwX0eW6QS8oe1srX0o5cq8bNMEMox/YmvtQ0nzmbJNJ9M34y5+rbisVVV7s3YgapURV2BVm54DoFfarejUGWyuuafNa/9ICCPqj4UwolpBGFGtk2M+jWzTBNZX3dDmtQMyH6fcM6/VdiRmbT+8oZ1AtFUvR9+M+whF6tjlfJFkCdY6dQ7drBezs/557IYxyHK00Tg7cP8kYh6mR/GFdlHseq1V71pMI2oM9f6lmLX9aQi13o+wwDaZau/X7dIoOpBkGo9nQNbDrCq7AF8KPfPyLBdQmHYTK0pPb9VAlFCTbT6FAtuVqCQdq8ov7IDCeNuR0JBhPBpnYCUW3WDs+jGUuN8kHHUnXKOSDPTNuAe7fjTrKm9M6mnKNp1Mn4w7WV1+SQr9BlX0tF9HsevVNumeqSQjh3b7N+srb8Ed/DXldX80DqQRVfj6vR02onZe+YgwojqAsAoEHUIl6emdfmub8yxAQqfOZXPNnSkYUP0ZnjsXs65fUgPKYTkbs3YA22ofZpfzBRIZUBpVGn0z7mFs/meAhCRpqff/3LiPA/udos7/Az/v+TMl7nfIt14QazWSJClcJkS9fylqycKQnH/QJ/1uJLRJ71Hsmo0vvIuBWU/gsJzd2Y/QKfS030jfjHtYUzG5VQNKJRkYnP038qx/YVX5ha0YUCokdNgNh+KwnMn2usdZXnryATWgAGTC1Pi+JRx14QvtRq/J5dBuC+hpvwEJteKaqOxnS8197Ha+Qr71/KTXr/J+xZaaewlFUgm1RTFqe9I7/Y42PUNU9rG15iHUKmOb1gn2I7LU8UPQIbqcEfXiiy/Sq1cvDAYDY8aM4fvvE/eWWrRoEZIkxR2bNm06gDv+fZNvvQinfxXu4No2rruQAZkPtzpPp85mWO7LbK19AE9wQ8J5vdKmUWCb0koujAq1ZEGrshOVwywrmUBR/TNtCkOqJD055lMosE2mV9o00g1HATFhw97pt9HDfjVphnEAqCVTSteUiVDt/Q/rKq9HJkz/zBmMdLyNWTsw4ZqI7GFl6VnoNbmMdLyFWjK3ep9d9f+gwDaFPul3JfzgPlhEZA+/lJ3TauNhlaQjKgeo9X3PqrILk3pd0gzjGJv/KbmW06j3L2FNxZVtqhDUqx2kG47AYfkLGlUaRk0v+mXcT7+M++mbcS8W3WBUko4s00mN/69P6bqBSClbau5nZek5ROUgMpGkFa0VDZ+yve5xrLoROCx/STiv1vcdkqRicPazqKTkhs7WmgfJNB5LuuHIlPbcRI3vG5z+XzBoCtq0TrB/kOWOH4KO0aWMqA8++ICpU6dyzz33sGrVKo4++mgmTpzI7t3Jv7lu3ryZsrKy5qNfv34HaMe/f6oa/s2OuifatMag6UZh2k1srX2k1bk2/SiKnXOTVgf1tN9ImuFQVpWfn7AXnEnbl9F5/6S77VJ84V3sqHui1QR4tWQmz3IuA7P+ymHdvsFhObsxLHNsYy6Ouzkc4w1tIxipQSWZ0KsdAAzLfY0jCpYwNOelNkkFrK+6mTL3PIbnvpr0QzPWo+8WdjtfISI3tGq0+cK7+aXsXAya7lj1w1Pez/6iqTWQQdODPa65rSZxZxqPY2z+F6gkHeWej5LmSw3InEn/zAfZUfdXyj3zUtiNCpt+JD3tN6KWTOSaT2dU3nsU2Cdj049ALRmJyA14gpvxBDfiDe2I5bNJZrJNE+if+TBHFCwl33oREAuvtSY/EIiUUux6NbbfrMcYmvMyOnVOwvmhaDU97FPobkvciDscdRGOuhmU9WTSe0fkBjZV34lW3XYpDLthDENzXiTWLkgg+GPTpXKiDjvsMEaPHs1LL73UfG7QoEGceeaZzJw5M27+okWLOO6446irqyMtLa1d9xQ5UYnJNk3AHdyQQg5GSwZmPYE7sIES9xtJ56UZDqPe/3OSGRIqSY9GZSccdSX0KOWaz6JPxv+xo+4pyj3/SnpPrSqdHPNpeIIbaQhtpW/GXdT5luAMrGxXs96YxtAoJElDtfc/DMn+B77wLio8H9MQ2pp0rUZlRSUZUEk69Oq8pMn0KsnAIflfsb3usZTL0bvbLqfG++1ByZWy6UcyJPt5djlnUep+p9X53ayTKLBPZl3l9Uk9kjb9KFyBVdj1Y3AF1qbUsiTDeDQDs54kEC6j1vc9xa7X2xnuk1BJWiR0DMh6lHTDEXiCGyiq/1urquSxZtdX0c16KWsrr04o6aBTZzEi9032uN5IqLIvoWGE4w1qvIuajbRk2PQj29zfcqTjHUpc71Dl/apN6/4IHMicqJ6v3tfhnKhdUx4WOVEdoMtYBcFgkJUrVzJ+/PgW58ePH89PP/2UdO2oUaPIy8vj+OOP59tvv006NxAI4HK5WhyCeNSSiX6ZD9C25rkxttTMoMT9VtI5ueaz6JtxT9J8n74Z99IrbTrBSIWiAaWSDEio8YV38UvZuUkNKAktAzJncmi3+Vh0AwhHnYSj9WyqvoOKhk/aZUABMYkF33+p9v4HgB11fyUS9TI052V6pSWvsAtH3QQjVWhVWQzKfprCtJtI9E82KvtZV3ktfTPuI8/SulQEQChSx0jHO6QbjmjTM3UGBbYpbKy+PSUDSiXpsRvG8EvZ+QkNKJVkYEDmowzIfBSNyoYzsDKhAaWSdORZzmNs/hdYdSNwBdayovRMVpadTVH9sx3Il5KJysFmD+FPxUewxzW3uQ9kn/Q70avzE6yMsNv5MmsqJuMNbW+cF/+7DkaqWV1+CdXehUgJZP5kwqyvvDklvTa1ZGJI9vMpiXzuzc765+lhn9KmNYLOR27UierIIegYXcaIqq6uJhKJkJub2+J8bm4u5eXK+it5eXm88sorzJs3j3/9618MGDCA448/nu++S1wBNXPmTOx2e/NRUCBi/0o4LOdQ5/uxTUKKKknPsJymb8aJjS+jpgd9Mv6P9ZW3JAzZ9LBfi00/gp31f1Mc16mzGeV4lyzTeFyBX/CHSxLcq5Bs0wRkQtT5l7B0z/Fsrrknpaq39uAL72SX8wV+LjmBYtccNKo0xuR9Qo75NBKFR9zBX1lZehZW3QgGZD6W8NoNoS2sKruQNMOhCT9g96ai4VPWV93IwKwnsOqGtfeR2oCKnvYb0KlzWV91A/X+Ja3Ml+hhvw6VZGRD1VSCkQrFWWrJzOi8WEuUlWVnJ1Un16lzOKzbf8kwHs3WmgdwB38lHK1PeO2OIBOixvct3tA2IrKPiOxnTP48+mU8gEZlVVzTENpEVPbTM+16hua8pBiiDUVrCUVrGZz9N7JNJyteJxStwRsqol/GgwnvBTHhzh11T9Ev4742PVu9fynrKtuugC4Q/N7oMkZUE5LU8oNGluW4c00MGDCAKVOmMHr0aMaNG8eLL77IKaecwlNPJe6hddddd+F0OpuP4uL2eSB+72QYj6Y4BbXwveluu5JQtL7VRO4s00kU1f0tYUm3Xu0gx3wqayuuJiI3xI0bNT0Y5fiAioYvmtuo7ItKMtI7/f8Y6XgHrTodgMqGz4jInjY9U/uJEo7WE47Ws632UfKtFzAmb17ChN1QtJa1lVPYWf8cKkmPQdNDcV4gUsrG6ulo1RnN+TnJcAVWs6L0jMZ+gqNSTo5uK1pVOiNyX8emH0EkGv87i0diQOZM0gyHJtVI0qjSiMgNbKmZweaaexLOzTT+mTzL+QQjlawuv4T1VTfhDKxs59O0nXC0np31z7Gs5CSCkSqichCDpnvCBP+tNQ/gD+9hpONtNKo0xTlF9c/QN+MerLpE+W1RorKXvq0YSLHmwips+lGpPxAxA6yH/eo2rRHsB+QOHIIO02WMqKysLNRqdZzXqbKyMs47lYzDDz+crVsT56Lo9XpsNluLQxBPLG8jcW7KvmhV6XS3XUZR3TNJ56klC8WuVxPme2hVGQQi5awsPSOhcnK68Uh21v8taUuYbtaL0KrSWF56CqXu91rdv4QOszZWkJBtOpmhOS8zOu9DDsmfj0oykG06mdF58xieO5v+mQ+jVztQSQbUkqXVazsDy1ldfjG7nC8RjFRj0vZOkCQuE4iUY9WNYJTjXay6EQmvKcth8q0XUWBr/UOu6XXMMZ/KKMcH7e59mIwhOf+g3r+CtZXXpGSo9s24F70mh3WV1yQ0jLJMJzI2/1PUkjlhzpFWlcmQ7BfolT6tWYgytRwwFTFP2DUMyJzJ8Ny5za1vhuW8wiH5/2aU4336pN8JxHKxzNoBrVY9hqMudjlfJCoH6G67gtF58zBp+8bNk4mwrfZhKho+Q6NSrrz0hrazqfoOBmY9mfC+RfXPYtMPJ8P4pyS7kvm1YlKbBTgj0QbyrRc2/7sQHHhEOO/g02V65+l0OsaMGcPChQs566yzms8vXLiQM844I+XrrFq1iry81hu6ChIzMOsJdtXParXNxN6oJCM76v6aVBU6Vq31IctKJip+0KolE6Py3mVT9d2KH5oGTQFW3bAkRpGKwrQbcQVWU+yandK+M43Hk2+9ALthNJ7gJlaXX4wvvJNS9zsEI9XN/dRqfd/hDe1Aq07HoOlGRPY2Jk+/gDe0g1rfd5S6303aMqPauxCAbNNEHJaz2FA1HXdwTdw8Z2AZG6v/j2G5L7Ghair1/mVxc0LRWn4tv5SRjneIyO6UDMVttQ/jsPyFUXnvsa7yxlaToVtHhcNyNhWez1hXeU1SYcmWSJR75uENbU8oBplrPoNe6beypuJKRW9kE3nWc/AEN7GhamqrrW+sumFkm2Mq4TXebyiqfxZZjlDv/xl/uLQ5dL255l7UkhGNykbT1/k0wyHkmE9Fr3ZQ2fBvttY+0OpTbqt9mFzzGYx0vMmWmvsVCwL2uOYioaVfxgyK6p+JC1XW+X9gVfkFjfppEvu6F6JykE3Vd6FRJTfmo3KQfOuFRKINjZ6p1pGJUOp+j3zrRWytfTClNQLB740uY0QBTJ8+nUmTJjF27FjGjRvHK6+8wu7du7n22muBWCiupKSEN998E4DnnnuOwsJChgwZQjAY5O2332bevHnMm5dKybNACYOmO+mGI9kcTr31QywnI9pqqXnv9Nspcb+b0FPRN+Me6nxLFT/ctap0hue+xm7nK4pr1ZKZQdlPo5J0lLiSJ7Xb9WPIs57H5up7icgeSt3vsaHqlmYNKiUPXET20BDaxN4pXPX+pfxUfBg2/UgyjMcCElbdcEzaXlQ2fJUw32uX8x+4g+sZmvMiW2sfbk5K35t6/xLWVd6AQaOcqAyNhlTF5ejaUMZe7vkIV+AXAuEKzNp+hKKuduULmbR9GZD5GBHZQ7X365T7Kfa0X9+cZJ0YiTTDOH4tvySBMKeKXmkx4zLR+6EJtWTGoOlGQ2grvdKn4fSvYFP1Hc16VcWu1+LWKLUn2u18hd3OV9Co7Ji0vQAYmvMyoUgte1yvJ6zErGj4FGdgFbIcQqOyEYl644w9mRDhqIuhOS/xa/kVcQnz4Wg9PezXIssRxWo8V2AVErrmysVEuAMbGJz9NJUNX6bc+7DMPY+hOS+kNFewH+hoWE6E9DpMlwnnAZx//vk899xzPPTQQ4wcOZLvvvuOr776ip49Y+GHsrKyFppRwWCQ2267jeHDh3P00Ufzww8/8OWXX3L22b9N1eauQK75TCobPm9TQ9tu1svoYb8m6Zympq17EniIzNqB2A1j2F73eNyYhJYhOf+gwvN5QkOtV/p0/OFi1lZMSahHZNL2ZZTjPfpnPkK9P6aiXu//mRrfNyk1tFVCJoIzsJKi+qcJRWuQCZNtPpnDuv+3MWdJ+Z9grW8Rq8rPxx1Y0xgSjJ/nCqyisuFLulknJQztBSMVeIIb6JtxL2mGw1Lasze0g4jcgFU/nLH5n1KYdlNKYckmNCorw3Nfp8zzPmsqrkzZgHJYzibXciZl7g8Tzsk0/hmjpoDNNXcqGlAqycjQnBex6AYrevH2ntfTfgOHdf8vOeZTAJk1FVeyy/lio5Hcvk+XcNTZLBewqfp2GkJbGZb7GoVpUxOu8Yd3E4iU0d12BUNzZqGS4kvWi+qfwR8uZUCWskBtuedjutsuTxha06rTGJrzEjp14tQHd/BXfOE9ZJsnJH7AfQhFa1hVfmHK8wWdjdQJh6AjdCmdqIOB0IlqSU/79VR7v065ek0l6Tis27esKk+uLi2hwaDpljRfRS2ZFUM3KklPnuVcStxvx43p1LmoJQP+cElCw0+nzmqWUrDpR1Dl/Q/7+yuaWduPXMtZ7Kh7Eq0qM2nrkt7pt2HU9GJD1TTFsv10wxEMzHqyMdSo/PrZ9KMZkv08v1ZMarVJ7d7o1Q56pt2ARmVjQ9UtGDQFBMLlLbxoKsmAXT+GXMsZROUAW2ruQ0KXkkZTEwZNAaMc77Kq/OKE7xO7/hAGZz/X2GhXuYlvn/Q7UUnGxvBS4grQfhn3o5KM7Kz/+35pPLw3Ehq06nRkOUwP+9XsrH8hQQhSon/mQ5i0vVlbEa++H/MmDU+oF5ZrPpN860WsKj8fpfdvYdot6NSZbKm5P+Fe7fpD0GtyqGz4MuXnM2n70N12WdLr/pE4kDpRBbNmoDJ2QCfK56f42hlCJ6oDCKtA0AYkdjlfbFP5f5ZpAu7guqQGVCzcdUxCA6BX2jSyTOMVP3jSDUdh0vZRNKC0qgxG5L6B3XBIQgMq2zSRMXmfYjeMJRApo8o7nwPh424IbWVHXUxVeljuywzInJnQ21NU9xwR2cvQnBeQ0MWN1/l/YkfdXxmW+0rCa7gCv7C97nGG5ryoeI1EBCLlbKm5j41V0wEYkPkoR/ZYxiH5Xzb3XhuW8yo9067HFVjFjrq/ArTJgJLQ4g8Xs6L0jITvE4OmB4Ozn2VD1S2KBpRGZcegKaCo/pnGfKR4A0qnzmVozosYNYVsrX2YzTV37XcDCmK6TU0VeSrJyNj8z7HrD1GcuaXmPlyB1Zh1/RVGgzgDK+hhv05R16mi4ZNGT63y+7fYObtRbT+x5IEzsJzKhq/a5Hn0h4vJNp2EVpWR8hpBJ9GRyjxRodcpdKmcKMHBpXf67XhDW1tV/d6bau9CnAqJz3vTK20aZZ5/Ko4ZND3Is57LnpK5cWNaVSYDsx5nbWV8BZpK0jM0ZxaVDZ9R7vlI8do97deTYz6NNRWTY/lMrSI1esM8FKbdhFHTE606HXdgHUX1z9LDfg06dRYNwe14ghuShpP2ZnX5JfROv5Ux+R+ztuKqOGNSJsym6jvon/kgFt0AxT6FFQ2fEorWJQ07VjZ8jje0rU0Gzv/2EMuR+bXiUiS0GLUFRKLexnOT2ny9JlSSkVGO99lYPR1vaHuSeVq21T6i6IVRS2ZG5M6houFz9rjmKK6PeeueYI/rzcYwYOqfHrnm07HpR6JVZxGOOtlScx/drJdi1Q/BHy6jIbglJeXuiNzA1toZpBuOoE/Gnawuv4ioHIibFzNEJXLMp1PZ8HncXr2hbQzKeoaVZafHJd67Ar9QYLuKUvf7cbmFEdnDspLxSSUjAPIs52HTD2dzTWp5j1E5SI1vEVmm8ZR53k9pjaCTEDlRBx3hiRKkTLZpPK7ArynPN2h6kG44nEBEWQwVwKIbjEFTQFXDfMXxXmnTKHbOVsxj6pf5AKXu9xUTvXXqHOr9S9nlfDFuTC2ZkNBR5f0Pv5T9pVUDqukD+IiCH+mZdj0AvlAx1d5v2O18jcqGLwBwBX7FF9qNRTeQPOu5AHSzXkqO+XTFPJcmorKfbbWPsr32MYKRmgSeoihbau7DHVxHlulExevU+r7Dph9Bd9vlCe/lCW4k2zSRnvbrkz5zMmRCeEM7kv5eU2VA5sO4AquSGlD51osJhMsbvYQtkdAwJOd5nIGVCQ0oUNHNdhnrq25uTLxOHObTqGzkWy9iRO6bDM2ZFVst6WkIbaWy4TPK3DHpDWdgObW+H4nK/uZcs+62K+iX8UAS3aYYdf6f+KXsHGRZpsB2taI8gYSGfOt5zbIKe1PtXYgnuE5xDMCo7UmBXbm/XlT20z/z4aReoyrvf8gynZBSU+smKjyf7TeNMUESZKnjh6BDCCNKkBImbW9kokk/7PYlz3IONv3IpHNiyeSvJ6wGcgZWKIbqVJKRqOxTrOJKM4wjFKmhqD5ekyqW9DyHXMvpeEPbE5bHS+iw6oYCkG0+Gaf/F1aUntkcgqto+IQq71fU+5c0V17V+5dS4n6LrbUz2FITEzj0hYvINp3EuO6LKbAlb5NR4/uWiOxheO6r5FnOVZyjknT0tF9PN+sliuO+0C4KbJOx6UcnvE+9/2fyrOeTZhiXdD/7myzTCZi0fdhWm1iFPdd8OvnW8xNWMuo1ufhCuxNeo7vtCrSqNNZVXpO0Mq0pfNUv40Fs+hHsdr7ChqpbACjzfEip+z2qvV/jDq4DYsZoZcNn7HbOapYzqGr4D/7wHgZmPc6I3OQVoACSBHbDKAZlPxPX3kgmxPrKm8iznkO64ci4tdtqHyWQoGpyZ/0L5FsvStgAWZajzUa+EuFoPXX+pWSZxiecsy91/h9b7YUpEPweEUaUICUk1Ox2zmrTmhzzqVQ0fJ50Tqn7XUUjCcCiG0Kp+924kIeEGrVkYFP1HXEfriZtbwZnP41WHf9NWyUZGJbzGs7AioQhPohVgB3abT751ljV0ZaaeynzfKBY2t4atb7vWV91A8tLT2v04qnIs5yXNC9pc83d9LBfg8Pyl7ixqBxgXeV19LBfo2ighqK1bK65m4FZTyT0foWitWysms6grCfRqtLb/EydRY13EWsqrkoYXtSpc+mTcScbqqYr6kXZ9KMIRmrZWjsDpbhE7/TbyDZNTFpJqlFZ6ZtxL2PzP0VCw8bqaWyqvoM6/w+KobZkBCKlFLtms7z0ZDZVx/LF+mc+nPCLRFQOsr7yJiCmvbYvoWgdG6puxaTtozhW6n6XNMOhcWPBSAXlno8StvIpdb9NvvUCklVm7ap/KWET5ET0Sb+LdMNRbVoj6Biy3PFD0DGEESVIiYbQ9lZ1nvbGpO1NVPYnrKKCWO5FotYkerWD4bmvKRoCDss59MtUEveTGJD5ODvqnlbs6ZdmOBRPcENz8nOiPfVKn87G6ttSzglJhWCkEmdgGWrJSLpxHId0+yxh01d/uIRfKy6jm/UixQTfQKScTdV3JQwb1fq+p9j5WtLwijOwko3VtyXtM7e/kNAyPHcOWnXyqkSTthc7619QfA8ZNN0ZmvOPhDpZ3W1XkG44irWVkxM+o1k7kEPyY7lMK8vObJNsR2sEIqVALMQ6OPu5hM20ZcJsrLqNUrdyLpEr8Asl7jcV3ysSavplPIRdH29I7ah7ijr/D4rXbAhtpc73E/okcgcNoU1EZH8C5XxlgpEqMozCiDqgiMTyg44wogStIqFmXPfFSfN69sUb2sHKsuR6XHnWcxOGB/OtF1Lu+Tiuz56Ehh72axW9YiZtH4KRKkVjz6IbRK3vu4TKyiZtX6y64VQ0fMLK0rM6Qa1bmYjcwIaqaWyv/SvDcl5Gq1IWwvSHS1hZdjZR2Y9B0z1uvM7/AyXuNzFr46u4AMo8H6BTZ2PS9k64l3r/z9gNYxt1kg4chWk3EY66k4p4GjQF1PuXUep+V2FUYmDW4+ys/0fC94/Tv4K1lVclUElXoVfn4wsXsa7yOrbVPtIGNfW2Ue1dyPKSU9GqMrDqhyjOkQnhDCyjm/WSxkbULZHQMiT773E6XzIRdtb/ncK0mxSvW5g2lVzzmYpjm2vuaTWnrU/67WSajks6Z2/q/D+Rbjwi5fkCwe8BYUQJWsWiG9RYop28qmdvCmxTknpC9Op89Oq8ZlHLlsTahZQpfDvPNp+MN7Q9LplcQos3tI31VfHJtnb9GIbmvJzwW7VNP5IRuW+gU2cRlYMJ8286kxrff1lWchKhaE3SEIhNP4oRuXMVPVISGobmvJSgXD72XP0ykmv3BMKV9M24J6kIY2di1Q3DYTmrOWdMCQktI3LnJAxHmbR9iES9igaWQVNA34x7cAfXEoxUK157cPbT9Eq/hagcaM5x2p9EZA8bq2/FFVhND/u1CZtH1/mX0DfjrjijWSbEttrH6JN+F/uG4Kq889FrchRDfq7ASvKt5yveS0LH2PzPk4aVa3yLWum51xJPcCMNwa2Ij5UDiEgsP+iId7ugVWz6MTjb4JnRqGz0sF9NJJq4p5lOndHYv06pUirK6gQtPWp9i9ha+1Dc+R72q+lhvy7uvErSMyBrJpur71Ys/7fqhjIk+x9srJ5Oje+bpM+1NxpVGnb9IeSaT8dhOQeNyt7YQiTea5SIiOxFQkth2g30zVAOHToDy6n2fk1/hfClTJhttY/QL/M+lP4pl3v+hVadkdRI84WL2ON6g34Z96a8747gD5ewvuomwlFnwjn51gvwBDfjDsZXgkpo8Ia2NcpayPuMqRmU9TQNQWXvVEzZ/u+AxObqtj2vSdubDOMxOCznNIfPTNreCZO3ExEIlzPS8QYGTbe4MW9oO7vqX2RAZnySfEw1v0EhyTzKytJzFD1ytb4f0Wu6YVQw2mSChCK1pBsPT7jXWt/3ZBiPbv2h9rrqxupbSVb9KOhcJLnjh6BjCCNK0Cr+cDFVDfH92xKRZjgUZ2Bl0v5b7uC6hCXp2aYJiuEVk7Y3Zu0A/OHiFufVkolutkuoVGicmmUajyuwOmF+SCBS2djE9+dkjwSAUVNIn/Q7UEsm0g2HU5h2E2mGI7DpR6CSDJh1/RmR+wbjuv/AwKwnFD8o90UmxJqKq7DpRyZsjVNU/wxmXT+Mml5xYzW+bwlFask0HquwMkpR3bPkWeMT1Pem2DkHf7hMMWenM8k2TUSjsja3RVFCQkOBfQpF9c8qjhem3UR3m3L5fjfbJMJRV0KtIp06E394Dxurbk3B26gi0/jnZjmJ/pmPkG+9EJt+JEZtzCjpYb+Ow7otZEzep3SzXtrK9WJUNHzCrvoXGZ47W9EzWuJ+pzEcHf+neW3F1Yrv44jsoVfaNAXZgtjvP1EYvsb3bYL3TYxgpKIxQT71j4lc81kJfz8Cwe8RIbYpaJW2eGggpv1Un0RgUyXpGZP3CStKT40ztCQ09M98kGUlE+PWxfSCKnAGWoYAcy1nUudbgj9cEremsuFzqhrihRAldPTLvI/ttTPjrrcvBk03+mU8gEU3iFL3B4CKKu/8ON2iYKSCn0uOR692kGn6M5GoF6tuGBqVPaERB7E8qbUV1yRMso/KQVaWnpXQKF1XeUNCqYYa37fU+BYnfT6ZINvrHsOo6UUgUtrmqrRU0Klz6Jd5P7+UJTfoZML8UvYXxUpIjSqNPOv5rCg9XXFtIFzZWKkXT6bxOOr9y9lW+2ire80xn06vtFsIRCrYVR/TGVtdHv+72VT9f4AKq25Is0eqMG0qpe53k1Zylnk+xBvalUAYVaai4VOyTROo8X3b4ncRkRvIs1yAL7wj7t+XTp1NjvkUStwtpRUqGj5GJSmH7Gq835BlSt4nzx1Yh0GTr1iooUQ46iTbPJ49rtdTmi/oIEJs86AjPFGCpKgkHYd3T/4hvC876/9OiSuxZoxNP6qxGW+8UWDTj8Ib2kkoWrvvTsg2TWhUcG6JJ7hBUVSzd/r/kWk8TvE+vdJvQS1ZWmksrEKrSicS9VPt/S9L9/yZXc4X4pSg9yUQKafU/S6haB2SpKZf5r0MynomabuNULSWXc4XSDOMQ6fOjhuXidDddrmiPlREbiDXfAaZxj8rXtuk7UW/jBlJ9wxQmHZjQv2pjlKYdhOl7vcVDd296ZU2jVCkXnGsm/UiqhrmKxooNv1oqr0LFD/sLbpB9M98GI0qeSsTlWQEQKtKY0PVLawuvyip8Rsjiju4tnGeClkOMzb/ExyWc5KucgaWkWn8M7nmMxTHs80TFbXCZIKKXq+Khs/IMZ+seK1Du/1H8T3lC++m2PVK0n1mmv6cUNRTCU9wE2btgJTnCzqIyIk66AgjSpAUo6ZXwg81ZVT0tN+YNJRn149NkFAO6cbDFT+4rLohBCJlcb3OdOps/OGSuDJ4jcpOnuUviqEjs7Y/uebTm0USFZ9C0jEk+3l6pl1PKFpDmeeDdiWcuwKrWVF6OoFIBf0y4nO59sWuH50wP6rW9wM97NcoehZC0Xp62OPb30BMXT3LdGKr4cWd9X+jwD45qbHXHiTUGDT5FDtnJ52XZhhHuvGohLpR9f5lFLteizvf1BNPrVIqHFAxIPMxttU+lrQazaobxqHd5qNT51LifrOdCedRdjlfYFXZxXSzXqyY7L033lARfTLuVNTq2u2c1RgWa/knurLh36QZDkWjSmtx3ulfjkrSK4bunP5VpCcQVu2TflfS6kx3YA1W/dCkz7E3gUhpo/is+GgR/DEQ73RBUkzaXvjCRSnPN2p6kGs5NemcYKSKWt93imO76l9S/LB1B9fya/nlcee72y4nzxJfgeSwnEOVd6FiuxiVpGNr7UMJ9YMkdAzLmU046mJ7bbwIYluJykF21D3B5po70KoyE1ZnAex2vopFN0Sx4s4b2oY7uFaxDL7W9z16jUNR0kAmSEXDZzgsySUnfOHdVDX8h3zrxSk8VVtQsaZicqsevDzLX5rbquyLUdMDb2iHoqepm/Viyj3/Uvx9mrSF+MI7k/a2s+sPYVjuy2yuviep7EKq+MJFrCyLJXsnatHTNK/C8wk90+I9PZ7gRvzhPdj1o1qcj8o+yj0fY9IWtjgvE2mWxNiXmJRFvJYUQCBShlU3IuEevaEiDJrubcqXW1d5DSK5/AAhdKIOOsKIEiQlFHVS4/025fkmbR8agokFNiGmYaTUgkNCTZ71PMUQW771IiQp3vWcaTyeau+CuPPhqJMSV7wSul7twBvaSbV3YcL9GbU9aAhtYXPNXZ0qwBiVg6QZDmN47isJvT0yQYrqnibLpBya21U/i2CkSunqlLjeSmigVXg+Rk5BnnhH3VMUO+O9Pe3FpO3L6LwPU5gpYdL2psr7b8XRwrRpCTSLJByWsxTlDiTUeENFbKialvTODstZrK+8JYXQXVuQY0nytskU2JQ9hAC7nC8nlA5ZUzEZZ2Bl3PntdTMVPawW3RDF4oQ6/w84/fHXAXAH1mPVK4u+QpMY6HTFf3uJ6GG/mjRD4qo/QSfyGzai6urqmDRpEna7HbvdzqRJk6ivr0+6RpZlZsyYQX5+PkajkWOPPZb161sq5wcCAW666SaysrIwm82cfvrp7Nnzvy9XixYtQpIkxWP58v9FQJTGZ81qW1cOEEaUoBXq/UuoaPg05fkmbSHeUGLPlUZlZ5TjvQRr+zS2o2iJhI7e6f9HJNoy4VmvdqBRmWkIbdlnvpZyzzzFxsK90+8gx5zYU2bRDcIX2sW22ocTzukIVd6vqPF+S//MxNev8s5ne52yB8wdXEO9f6lic9hi12xqfYsU1zWEtrDL+UKr+4vIDdgNoxW9Xe2hu+1SKhUS++ORWVl2lmJVpoSWDONRVHu/Vly3ovRMRQ9VjvlU+iaRbpDQYNB0Z3PN3a0WF7QHmTDrq26ku21SwtYv4Wg9O+qeUjSqZUL0Sb+7OVfrf/tWMzx3blzj4ki0QbFVkD9cQkXDJyi1eWkIbcITTN6A2xlY2abmwlpVusiLOlD8ho2oiy66iNWrVzN//nzmz5/P6tWrmTRpUtI1Tz75JM888wwvvPACy5cvx+FwcOKJJ+J2/+/vwtSpU/n44495//33+eGHH/B4PJx66qlEIrEUkiOOOIKysrIWx1VXXUVhYSFjx45tcb85c+a0mHfZZZe1+TmFESVISr+MGa02Ed6bYtccdjn/kXDcpO2FnOBfrlk3UPEPukU3AG9oe1yuTDjqZn3VzXHzu9kuplfa9LjzaslChvFIxeT0pvFhOa9h1PZMuP/OYEfdM6glc1KByzTDofRJv1NxrFfa9Oa+fvsyNGdWwusW2CYnrADcm0jU26Zk4kSoJAPZpglJ+xQ20d12ecL3WazYYJuitlSO+RTUKuUS/jzr+dQmqUzsZruE3um3trq3jhCMVLOl5n7s+jEJ5+jVeYzNV35PmnV9SN/HqyMTQauyYdENanHeF96JVmVXNMhG5L7R3FB7b8JRN9tqH0n6DD3s17WaKL83gUgFeo0j5fmC3x8bN25k/vz5vPbaa4wbN45x48bx6quv8sUXX7B582bFNbIs89xzz3HPPfdw9tlnM3ToUN544w28Xi/vvhvzNDudTmbPns3TTz/NCSecwKhRo3j77bdZu3YtX38d+5Kl0+lwOBzNR2ZmJp999hlXXnllnEc1LS2txVyj0Ri3r9YQRpQgKVb9sDaVvGeZ/py0Csqg6RGn89SESdtbUTTQrBugaFzpNY5GheSWpBkOb2z225JM07HU+ZcmlAPoZruEWt+ipP3+OgOZEGsrpyQtg28IbifXchaSggpJnf9H0hP0KIvKPtIMYxXH/OHSlMIs7uA6ZIJJP/hTQSVp2Vb7iEKlZTwOy9kJ32cNoU1sTqBw3jv9NpT+jOnUuZi0hdT5fkywNyMFtqsoqvtbq3vrKDW+byl2zU6oDh6IlBGOuhQV2ut8SxSbDLsCv2LVx/dOrPMvRa/OizvvD5cmbAE0IPPxhH0cAQLhMsVrJsIX2oUs73/VfwGdVp3ncrlaHIFAx2ROlixZgt1u57DD/teq6PDDD8dut/PTTz8prikqKqK8vJzx48c3n9Pr9RxzzDHNa1auXEkoFGoxJz8/n6FDhya87meffUZ1dTWXX3553NiNN95IVlYWhxxyCLNmzSIabXsunzCiBEnRqTMJRhI3id2XnvYbEvaDA4jKXpz+FYpjxc7XKHG9E3e+3PMvttfGqzj3y7hPMZ/Dph+umHNV719KUd1TCfeWZzmvUUX9wDAk+wXsemWDJxStwRcqwqaPT/p1+ldi0w+PC+dA44drgnYp7uAaRW+EEqXu9zFp+6U0NxFaVToVCgKo+6KSdBg0BTQEtyiOGzWFiuE6vdqBhEbRKFdJGrbXPpmwSjTHfArOwC/4wjtb3V9nYNOPZnhu4vdWre870o37qpGDM/ALeoUmyzGdqPjw3Iaqm+PC2xATzDVoChTvrVYZkirtByIV6NQ5Ccf3pcb3LUX1z6Q8X9B+OkuxvKCgoDl3yW63M3PmzA7tq7y8nJyc+PdMTk4O5eXKVbJN53NzW3rSc3Nzm8fKy8vR6XSkp6cnnLMvs2fP5qSTTqKgoOX7/+GHH+bDDz/k66+/5oILLuDWW2/lscfiP2daQ4htCpLSENxGOFqf8nytOpNQNLHRpZzXEsOmHxlr9bFPtC/DeDSe4CYikZYJ50Zt77j8Kwktpe73FL0fRk1vnAFlAw5ozMlJ3I6ks6nz/4TDclbCPZV7/qVYth+RvWyrfRRJ0iLLLY0Ep/8XMk3HKl7PHy5pTFRW0Vr1lHLj39RRSUbG5H/Mj7vHJZQsaEKvduD0r0ho8AzJ+Turyi6Ikyiw6AbjCqxRXBMIV1ER/iThPSsbPk8a6utsXIHVmLS90asdilIL5Z5P0KmzFNb9woaq+JZLiRLw0wyHo1VlxFUj1vuXKV4fYtWySjpSTbgDa2lLtZ1OnU2+9UJ21v895TWCg0txcTE2m635Z71eOQduxowZPPigchP3JpqSt5WKEWRZbrVIYd/xVNYkmrNnzx7+85//8M9//jNu7N57/5cvOXLkSAAeeuihFudToct5ol588UV69eqFwWBgzJgxfP/990nnL168mDFjxmAwGOjdu3e7su//yKytvIqonPxDcG+0KhuhSGJDpKf9+oRhor4Z96JR0Mzpab8WvbpljoWEGq3KHtdkVibEzvrn466hlkwMy51FokzKLNNJCm0z9i813v+SkaTtRpnnn9T6lN/fFZ5PUPpgcwfXJP3wiqlsp/aB2D/zobjXPVVs+pG4A+taNaAgJq2wtnKK4piEDq0qTdHwqPF90/g88YzJ/0ixTQ7Ect+yTCckqHLcX0Sp9S1O2NDXG9rWaKzE09N+fVyPPo3KxoDMx+Pm6tU5ivdwBpYnNLw8wU2KCf1NBCKlSb/87IuEhlyzsqq8oJPppMRym83W4khkRN14441s3Lgx6TF06FAcDgcVFfFyIVVVVXGepiYcjtjfmn09SpWVlc1rHA4HwWCQurq6hHP2Zs6cOWRmZnL66a2/Hw8//HBcLpfivpPRpYyoDz74gKlTp3LPPfewatUqjj76aCZOnMju3fGNaiEWYz355JM5+uijWbVqFXfffTc333wz8+bNO8A775qoJAMDs55s05pfys5NKkpp1Q9HrYqvLAPQqm2KniCNKl1RwTzW16ulUZRtmkC/jPhvSgZNN3yh4rj5TXS3TUKnThyG3B8EIuWUeT5M2JZDr3YwJFu5oq53+m3kWZSTy4flJJYo6J1+W8rl53q1A7Ouf0pz98Ws7d9q1VcTGcZjyDQqyReAXpNNIIGxk244IqF3xajpkVAd3aofqqgGvr8p83yUtHJ1XMEPilVwmaY/xwmlRmU/2eaT4uaGonVo1Wlx583aAQzOVjauyz3zFPtONqFXOzi0W7yMSCIisi+uolDw+yArK4uBAwcmPQwGA+PGjcPpdLJs2f/aE/388884nU6OOOIIxWv36tULh8PBwoX/k58JBoMsXry4ec2YMWPQarUt5pSVlbFu3bq468qyzJw5c7j00kvRalvXOVu1ahUGg4G0tLS2vCRtN6Iuv/xyvvtOWShxf/PMM88wefJkrrrqKgYNGsRzzz1HQUEBL730kuL8WbNm0aNHD5577jkGDRrEVVddxZVXXslTTyXOixH8D7VkJN2g/IZXQkKNVh3vSWp5TQORqC/BmElxTKMyE4numwwuU+dfGjdXq85Q1HbSqbOTeh4Mmh4HLD9mb3bWP5fQ0xeOerAnSBIPRuoSvtY2/QjF5rYQ6z+XapKwL1yMXh2fj5MKzsByyj0fpzTXrh+NSdtXcSwUcbKl5n7FsTzreZh1A+POa1RWIrI/oRfMqCnAG9qV0t46E1fgl6Th5FCkRtEbGorUx3mionKwseigZQgjHPUkaDgcxZhAQyzdcETSqs2oHESdoImx8vwAkhSfryf44zBo0CAmTJjAlClTWLp0KUuXLmXKlCmceuqpDBjwP/mLgQMH8vHHsb8TkiQxdepUHnvsMT7++GPWrVvH5Zdfjslk4qKLYu9Pu93O5MmTufXWW/nvf//LqlWruOSSSxg2bBgnnHBCiz188803FBUVMXny5Lj9ff7557z66qusW7eO7du389prr3HPPfdw9dVXJ/TCJaLNRpTb7Wb8+PH069ePxx57jJKS5L2wOotgMMjKlStbZOUDjB8/PmFW/pIlS+Lmn3TSSaxYsYJQSNlbEggE4ioV/qhIkjpp+5Z9UUlGBmfHh9L2JhipTVgdt6ZiiuIH35qKK+M8VCZtX4bnxntcVJKBSDRerNMT3JxUJ0mrsrexvU3n0C/jwYQ97yJyQ8JKx6jsRZ3g235U9if0BERlP2pVal4CX0jZw5sK3lCRYqWlEirJmLCHoUwQbyi+AhOajG7ldUpCq03EPJvxSvb7G5O2N2PyEhuW4WiDopc2KvsVf9f+8J44L6YrsIo1FZcrXCOY0OOpU+dg1Q1JuC+ZEJKUumJ5VPbxU7EQ2zwQSHQwsXw/7u2dd95h2LBhjB8/nvHjxzN8+HDeeqtlg+zNmzfjdP7vb/vtt9/O1KlTuf766xk7diwlJSUsWLAAq/V/sh3PPvssZ555Jueddx5HHnkkJpOJzz//HLW6peE+e/ZsjjjiCAYNaikFAqDVannxxRcZN24cw4cP529/+xsPPfQQTz/9dJufs82J5fPmzaOmpoa3336buXPn8sADD3DCCScwefJkzjjjjJTcZu2hurqaSCSSNHN/X8rLyxXnh8NhqqurycuL/0Y+c+bMVhPn/ijIcpRQpPXy9LawsTpev6mJRMbVvt/Ck+ELFRFUxUsHRGRP0k70S/cc16nq5KmiUdmSfEDJuAPKPdzcwfX4w2WKY75w4rClP7wn5d9piTtxE+nW6JdxP3X+JUnDRC1R3q9VN4zCtFv4tSK+6W4iwlF3UoO53PMh+/fjIxESkpT4e2usdU193PkNVVMVv8wsL50Yd06nziLdcGScQG5E9itWrKZCVA5SkaJXEWIe6W62SexxzW3X/QRtoKNNhPdjA+KMjAzefjvxlxkgrouCJEnMmDGDGTNmJFxjMBh4/vnnef755F/Ym7SllJgwYQITJkxIuj5V2pUTlZmZyS233MKqVatYtmwZffv2ZdKkSeTn5zNt2jS2blX+5tgZtDVzX2m+0vkm7rrrLpxOZ/NRXKysafRHIBStZWXZWSnPl4kgtfKW6madhFFTqDg2yvGeoi7S4Ozn0KhsLc7JKH+zrvF9S2XDF3Hn7fpD6J/5aMJ92Q1jDkoeh1ZtT1oRuKo8XsEdYh6HGt9/FcdWl1+UUJtpj2suVd75Ke0tx3watn16t6VKRPYk1Qvbm+11MxNWA0blQEK17K21D+EKxFeuqSVLUo+PJGnaVLLfWWhUtoT9GiFmtO5bKAExfTOl/fZOj0+qN2gKyLPG53sFIxVsrlFubC0TIpSkAjcqBxIq6CshSTp62m9Meb5A0JXpUGJ5WVkZCxYsYMGCBajVak4++WTWr1/P4MGDefbZZztrj0AsoU2tVifN3N8Xh8OhOF+j0ZCZqZxErNfr4yoV/qhIaClMuynl+VE5wKZqZZXtJtKNRyXUpIkkCDVFZG9cqX8wUk2ZO75sNc1wOL3S4nulhaK1CZOQAQpsUzBr25dE3RE8wc0Jw2Z6dV6jmGQ8Pe03kmc5T2FEStrqJPac8XlESmSbJrS7YjEQLsegoG+khFk7gDTDOMWxUNSFVp3IE6lCq47fX0T2YtL2VtTRglhrn/2tVK5EOOqmqiGxAXtYt68VDcYC29Xo9zGiJLR0s14SN1ctmRVDnCZtH3qn365438qGL9lR99eE+9KpsxmeOzfh+L6oJG3S4hJBJ/IbbvvyR6HNRlQoFGLevHmceuqp9OzZkw8//JBp06ZRVlbGG2+8wYIFC3jrrbd46KGHOnWjOp2OMWPGtMjKB1i4cGHCbP9x48bFzV+wYAFjx47db2HH3xdRCmzKpeeJ5nuC60kWKolEE3sowlFXnMcJmhJr0+LmlriVXMVRRYFKf7gYYwKxQQB3cK3iuv3NjronCERKFcfMuv4JBS9N2t6Eo5648zp1Jtmm+KqtJrJMJ6BKMb/FrOufMB+pNer8S3D6UwsfmXX9cVjOVBwLRioS5jflmk/FYVHylEYJRMoTGuuxprvDONAhPW9oW4L3bCzhX62yKKq26zU5BPZRt9eqMxS9jVp1mqJXSa/Ow5zgvZRuOCppxaZGZUOnYKwmIlGBiGA/IIyog06bjai8vDymTJlCz549WbZsGStWrODaa69tkfh10kkntblMMBWmT5/Oa6+9xuuvv87GjRuZNm0au3fv5tprrwViobhLL/1f7sS1117Lrl27mD59Ohs3buT1119n9uzZ3Hab8rd7QUtieRgyEqkbnKPzPkKroPXURChar2goAeyoe0pRr6ao/ikC4XhD49BuC+Lu5QvtxqgtjJsbjropqv+bYrgQoM73I5mmYxLue3+QYz49aY86q24InuBGxbFYi5wdceeNmp74wokTwk3aQnzh1ivT1JIFlaRJeq1keIIbqPV9Ryp/YnyhnQlDvFE5QIn7XUWvkje0I2ErkwrP54pCpRBTgw+ESw+40Tw2/7OEopYW3UAaFCQhVJIejcoe1yLIoMlTzImr9n7N9tp4/SidOiNh54EM41EJDSxoPQy5L8FIFavLW+/RKOg4naVYLmg/bU4sf/bZZzn33HMxGBKXvKanp1NUlFgPpb2cf/751NTU8NBDD1FWVsbQoUP56quv6NmzJxALL+6tGdWrVy+++uorpk2bxj/+8Q/y8/P5+9//zjnnpN5M849Ok3comQr53oSitQm/JQNsr30sYcVfjfcbxdJod2CdYpgjGKnGqC0kFPhfpVUgUo4vtAuJ+JBCqfvdWLhDjvfg1Pl/wBPckPTZOpt86/kUOxO3AtFr8hOGfxpCmxWNKIOmBw1B5QafGpWNQKQqpQ/EiOzh5z0ntjovGcNyX2W388XGFiWJ8Ya2Ydb1JeYZiv+rPiznZYpdr1PvX9LivCe4IWG4M1liOcDG6tuTFhp0Nk3tfRLLbESpUMjli8pBVpaewb6viyuwmjUVV8TNt+gGKhpXkqRTfL9ALFznCqxOuHdZjlCfoFWTElp1OnqNsjK7QPB7Q5L3TY8XtMDlcmG32/liTW/M1i6lTdopqCWLotGRiGE5r7HHNYc6v3LjV6OmByZtX2p838SN9U6/jVCkLq5/Xb71IszavmytbRki7pcxg4bQlpRblDgsfyHNcEijSGc8enU+dsPYNlSUtR+rbgSDs5/h55ITaUtLjdRova1La/RO/z+KnbNTah6ciG7Wy7DoBrC55u5W5+rUuQQjykrBvdKmE5G97HbGdxtINxxFnf+HuPMalZ2hOS8l9YhkmU7EFfg1aSPozmJI9j+o9X1HmeeDNq2z6IYQibrjPIIZxmPxhXbGaZsNz53DbucrcQZnMkY63mFH3VPtrt7blyzTSeSYJ7ChKj438Y9AgzvKqcN34HQ691tObdPnUuEjj6JK4tBojajfz85779mve/2988ezCgRtwqofmrBxqRKl7ncTKkVD7MOyu+1yxTFvqEgxPOMJblIUVaz2fq34zT7DeIziPWq835JhPBYJZb0cmSB9M+5ud6uTtiBJarbVPkIiYyfLND5h64ye9hvINZ+ZYOzGhCFLh+VsrLrWQ1hGTS9yzKclrdhKhYqGT8gynYhaUlao3xutypZwb87ACtIMhymOeYIbFNu7hKNO1JIZm350wntadUMpTLu51b11BjHx0X8pjunUuQmrCXvar8OioOHUw361YqGERTdA0RPZ0349OrVyAc6v5VfgTtCDECDPckFCLTMl9OpsAuED2VLnD4zIiTroCCNKkJQc8ykJP8CUqPF9kzRM4gsXYdIq9zRrCG7GrBsQd94T3IhFNzAuL6bO/wPV3oVx84ORKhyWv8SdD0VrcAfWkG0eHzcWW1fNbufLDMx6gv35TyPNcBie4DpqfN8mnNPDfjXBBHpOuZbTFHOlTNreOCxnJlTq7m67IqWqqXzr+ZR7PqKj3qxw1MnW2hkpqVebdf3pYVcuYqj3L0voWUkzHEqfDOWK0HLPh+RblVvjAOx2vkya4bCELWc6A7VkIsN4NHtccxO+9nmWc6n3L487L6EjzXBYnFdXJemx6AbgDrY0fPTqPKJyUNF72N12hYLqf0zoNNdyelJR3XTjYW0S2xShPMEfCWFECZLiD5emXKoOseqvgVmJy6WDkWpUkk5RQLMhtEUxBygq+9ha8zCSFO9hGeX4AMM+7Sw8wQ2oJRMmbZ+4+UX1zybt6bbHNRdfeHdcSXlnkW44gkFZTyWVDkgzjEMtGRVDolbdCGQ5QkMo3tuQZRpPtVdZO8qg6YFGZU+YqL43Rm0hpe62hZ0SUdnwZWO7keR/amp935FmOEyxZUlU9rPb+YqiR6vGtwibfiRaVbxkSbnnEwLhxB/mEdnLxqpppBuPav1B2oXEwKwnkhppKslIvvVCShWq9jKMR+EOrovLYbPrx+AOrI1rFxSM1LC24uq46xg1PQhHnYphebO2fwKpjL3XF+JrQ5ucMveHVDUoNzsWdC4isfzgI4woQVJi0gDKPbeU8IV2YdbFGy97s7z0NMXk5qgcpNj1mmK4raLhU9RSvDSCJ7iBLNPxcedL3G8plrh7ghuIRD1YdcMT7E5mS819hKJ1OCxnJ32OtpJuOIJB2U+xvuqmpN/UDZo8dtQ9jZKvXSVp2eV8UXFdmuFQKhu+VByz6YdR2fC54jX3RkLNusprE+YntYfe6beTaz416Zxw1I0z8AsZxqMVx7NMJzEoO944j8p+qhq+Is8a73mMyB6K6p9O+v51B9exrfZhrLphnaoTJqFmQOajaFQ2ttU+lnCeStKxs/7vilWQtb7vFPP36vw/sb4qPgxp0w/Dr1DFatL2xRlYqXh/q35wCoa13Ka+kipJn7RPpaATaVIs78gh6BDCiBIkpda3mB11qTds9oaKMGgKksoiqCVjQiXswrSpivlM6YbDGZz9XNz5Ku+/yTGfEnd+j2sOtb7FKL3FDZoCBmU/nbCXGDR5CC6if+bDCRWz24pOnc3aiuuSVkLp1Q7KPf9STLzXqKy4AmsSGkprKq6KC/E00ZqgIoBWlckh3b5sk6RFKuyoe4rCtKkJc9Ga2FT9f4rhWYBa3yJs+jGKyt07619IUlygYljua62GpGOCknPIMB6bdF5qSIAKf7iEtZVXJ2wnpFVlolNnKyabGzTdyTGfEpf0LqGhh/0axS8hg7KfVRQmrfF9k1AE16obkfA908TKsrOJyv6kc/ZmpOOdBE2QBYLfH8KIEiQlHHVj1qX+DV0mzG7nywk1egCM2l70tF+vOOYKrCTDGC+eWu9fjkXXPy4MVu9fTq3vB8Vk6p72G+luuyzuvDOwHFdglaKyeRPhaD2ryychoWV03ocJ1a9bw6gpZETuXLJNE6ho+BR38NeEcw2a7ozJ/1fCliS9029XfJ7Y2B0JNZPSDUfRw35Nq3stTLuBqoaFna427Q6uwRPcSI45ea+qcNRFnuUCRc2oqBygwvMvulkvjhsLRWvQq7uRbTpZ4apRttbMYEDmTEVPZhM1vm9YV3ktfTPupsAW3/U9VXLMpzI2/3MkScUu5z8UxTObGJD1CNkm5fy8HvarFT2pmabjFNXdrbrhhKP1ikUdvdPvSGgYb6t9JGnoLc0wjlzzGQnH90WnziYq+9tU0SvoACKx/KAjjChBq/TLeCCh+rMSu52zkmoROf0rsOlHKv5hr/cvw6IbGveBJxOixreI7LgPYpmd9fG99QCqvF9RYJusmEuzrfZhrPoRST9Yo7KPzTV3srbiGmQi9Em/gxzzaailxAbi/5AYnP13RuW9S5V3AVXeBUlnqyQjQ3NepKjuOcWSe7O2P5nG4yh1vxc3ZtL2Jtd8Kv6wcp/HHvarE7aW+d/1+5FlGk+x69Wk89rLpuo7qEhBOkKrTqfAfqXiWLFrbsJk/KjspV/mfYq5ZnX+n6jy/idhVWgT7uBaVpSeSrnnE/RqBwMyZ2LTjyQVZXOLbgiH5P+bbtZJbKq+PanxBNDddjlaVTq7nS/HjRk0PcgynUiJ+624sW7Wiylzvx93Psd8KpUNX8WdN2v7k2U6TrHYQKfOIs1wKBE5vk1ME1mm4+O6BSTDrB1AQ2hLyvMFHUPkRB182iy2Kfjj4QluwKIbkrI4YYbxWHLNp7OxerrieET20BDagt0wKk6IMdbs9HFUkj7u2+xu5yuKHie1ZOGQbl+xvOTkFpVJ3tAOanzfUJh2Y1wD1XDUzeryi1BJOoyaHkmVuQORmHhhnf8n8q0X0z9zBg3BbTSEtlDt/Zpa32K6WS/BpO2NUVuIP7yHLTX3U+Z+n03V/9fqBypArvkMXIHVlHni+wEC9Mm4i6L65xS/4Rem3USx63XF+9j0o9BrHFR5/5P0/oFIJeurbm6TMnVbiMgebPqR5JhPYVtt4kbQpe53OLTbAnbVvxiXNxaMVBCVfWQYj6bW932LMV94N+WeefROv53NNfGhq6LGkLROnaXY5LeJqBwkKteglsw0hDbTL+NB9BoH7sAavKEdFLteQyXpyDWfhUHTHYuuP9vr/kpDcBOba+5KGqptQkJNhvEY1lfdolgVl244nN3Ol+N+F1pVOlp1hmLIM5YnF19NGSs2+FpxH5nG47HpRyqGjpuw68dS4fkk+QPthTe0g531yYVOBYLfE8ITJWgVV2AtNn2iROx4PMH1pBvHkewb/IaqWxKqIJd7PkKS4td6Q9uJyA1xXrGI7KHC8xkF9vgwzI66p6n2JpYSsOpGMNLxjmIl377U+r5nXeW1/Lh7HNvrZuIK/NrcI0wlGWkIbaXYOZvttU8CMaOrNQNKQotFN4gyz/tsrXkw4bwtNfc1yg7su15NMFJLqfsdxXUalY3ttU+QTK4g0/hn9GoHrsAvSffaUTzBjWQa/4xdf0jCOeGoiz2u1xs9QPGoJD0Ds/6qqOW1s/4FJEmtmMMmE0EmwoDMmfRKa735cERuYI9rLivLzmB5yURK3G/iD+8hKgcbPagy9f4lbKl5AKd/GaFoXUoGlE0/ErXKwpqKKxST99WShTLPP9njmhs3ForWsaL0jDjDy64/tLECL94AtuqHJcyhyzQd15g3qIxK0qGS9LjboOQvSRKuQOKQtaCTEeG8g44wogStUtHwSZtK3oORKoKRKiy6QUnm1JBvPV9xTELL2PwvFPuMZRqPVcxl2u18GYflnDhBwXDUiTOwnB726xSTXZ2B5WyrfZQRuXNTEqKEmCinK7Cacs9HOAMxT1qx61VK3e9R5/8x5XwQtWRhaM5LdLNe2njdeK+EVTecfhkPKnoBJdQYNN3YVvtwXLk7gEHTjTrfD9T4lGUPIJbDMiDrkaQ6QZ1FVA6wtfZBBmQ9kjRZf7fzFaq88xUT/4ORKva45tA34x6F6/vZVP1/aFTWhIKpG6tvJc1wCP0zH0k5gT4UraXW9z0l7rcIR534wjvZ5fxHY47b2pRfuyzTCQzJ/kfCRtg6dTaHdvu34vveph/JwKwnUfrU65NxR8J+lOsqr1GsvlNJeuz60XEevb2JykGWl06kLXphrfXOFHQyHQ3lCSOqwwgjStAqwUglOnVGm6rUdjtfI/m/0CjdrJOw6obFjciEqGz4UlEws8wzjzTD4XFl66FoDb+WT0rQwkPGoOnGgMxHFHdS5Z3Ppuo7MWi6Jdlv52LU9GJM/sd4Q1vZXPP/7d15fFTV+fjxz519JjOZ7BskEHYQkE0g1CpoRbTuFaVYhP4UV7S41xVcgKK4faUKWAVsta5VqQtCq2gr+xLZI2FLQjJZJzPJZDLr/f2RZGrMzCSThSFw3q/XvDR3zr33XLI9Oec5z2kZEEBDJeuzUv6PSmfw6ZhM8830iQ++hY1C0nJ26mpMrWyyOzBxIUX2t6jz5Ef2AO1U5fyOAtsKWvvRE687l2Epfwn6XqHtTdTKxJCBUqL+QoamvBY0d83rt/ND6Sxk2Rcy8OgKWeZb6Bv/CLtL/x817r0t3pfQcFbyKxTZ3wpSHkBBv4THqaxrOe0Wr/sFCkkddOub7Lj7MGmGBu2PX3ax5cRF+OSWBTh/2udIyj4Y1H3w+u1t3mdT6ARiJCrqRBAltEl23Nyw0zA/V+ZYQ53ncNg2pY5PSTVeFfS94pq/k2Ga1iIHyi87KbKvpkeQVWoOzyGSDVOI17Usnnio8il0qiyyzLcFvZ+1/nvK674gNeZKhqWs6LKASiHp0KkycfvKya96pjFXq+Vf+hLKho13bSuDjhYYNUPoYbqRQ1XBpwB7me/A7soNO0WnUsTh8pU0BjUnj6X2IwzqPoFNeYOx1n+PQtKRGnN1i/dkPORapuPylQZdGFBS+x52Vy5Dkl8OOtrkl+s5VDUPj7+SoSnL6GG6sd2rL1sTox6AhIrq+q3sKLk6aJFUaKgS7/KVBE3s72H6HV6/nfK6loVokwwXBs1BUisSyDBdR53nWND7NTxz6B//Ekp6xv4+or0T43Q5WJ2b29xeEE4HIogS2sRav4n4IKUHwhmT8TlaZehq55bajxurObf8Mqzz5DcWGmz5p9KJmtUcsT4b9Joun4WBSQtbrCiScTcWkQydVAxQ5vgMa/0mRqV/GLYEQqQUkoZ04zTG9lhLSsxl+OTakPkoEhpkfORVPsKJmtVB2/Qy38mhqnlBR940yiRSjVeFTeBuqOUl8WPlE3T+BsitU0oxDE5+PszKL5m8ykfom/BAyDYpMZcyLHVZ0MUGh6qebqy2H35V6eGqhSTof8nojE8j+iOhNTpVFgMTFzA89Q306t7YXbl4/bagbbXKNIpr3gm5MXatex95FcFGKyUOVT1FRZCVnz1ib6TUsSbo1LJWmUGvuNvw+kNPO8fpxlHnOdrq98tP2V07Q+bmCV1EjERFnQiihDapcv6HhAi3x6hyfkdKmErVbl9Z2JyL6vrNpMRczs+/TP2yC5XC3Jgj0jwB3e7ahaX2HwwO8p7HX4Wl9kOSDVMCeUg/J+OjyL6S7cWXU9u4kWvP2FnE6ca3a7SiKUdrUNJiEvS/YG/ZHRTYXgvTPpnRGR8Sqx1BbdCEXgUqhZn95X8IsepKwu2raFypaA16D4WkY1jKsqD1hk4Wm2srltqPGJy0hFALEOo8+eRabsQbYiPkMscXeHw2+iY8HORdP4eq5uH0HifLfFvIshRObwF7ymZzuGohPtmBWpFIL/OdEW263aRhO6M4VAozI9PexuktYuuJS8JOlfZLeIz+iU8i42uR16aQtPQy34nNtQuXr/hn7+kZk/FpyPwjCQWFtjeCvpdh+i2W2n+ErQemV/emtLb1khT/u58Kr79GlDc4yUSJg+gTQZTQJrXuA+RVPB7ROaW1n7S6dYqEmv4J80O+n2q8kjRjyykdt68MnapH0H2/jle/QnX99qAjFAA2104yTNPoG//HkIGR21dBeV1D3R2f30F23D1MyNzM0JTl9DLfgVk7FmiYEtMok9Eq09CregH/2z8wp+d/GJryKiBxoPxB9pXfFSIwamDSDGNU+vtYav8RcqVX/4TH6BN/X8gq2AMTF5ES8+uwuS4DEp/E5toZeL5oOVa9FKf3eNjcpDpPPon6C8mMDbY5sczBigcwa8dg1AwJcQUZjTKJkenvhg2MrPUbqXXvR5IkVAoTI9LeZmyP9QxMXEQP0+8a868UaJQpaJTJ6FQ9USsSkFDSO24uw1PfZELmJtKM1+D129hcNIkC22shFxkoJD1Dkl8mRj2AA+XBRzwHJi5q3Ley5R8Z2XF3U+PaEzRQVisSOFr9QsitheJ053DCHqrCe4PimncoqW1ZjyoUs25M4x81gnBmEUGU0EYyLp8laCJ4KDXuPRTZV4VdBdVQP+jsoHlM0LRlyF1BV9blVTxCdvwfWuQvyfgotK8gRjOAZMMlLc5z+8rYWXIdBnUfesb+vtXnKKn9gF2W69ly4leU1LyPJKkCS/D7JzzBqPT3GZH2TmBExC97sDr/y86S69hZ8htAblMV8JSYS/mxcl7Q5e0AveP+gEk7nMNVfwr6foZpOkbNoJBbp0DDyJhGmUp+1dOt9iccCVUn5BH5ya96GgklsdpRIVvZXbn0iP1d0K8Rn1zHzpKp1Lr3h9gjTya/6hlO2P/KyLR3gm58/VNuXwWHrX9ic9F57C27FZtrB3p1b7SqdDTKJEalv8eo9PcZnvomiYYLkPE1lmVYycbCcymyv9l41+BBbgMJpWTA6TnG7tKbgha77B13N1pVGj8GKXsRqx1BcsyvW9Q+g4apwXN6fBa2iOwuy7QWI1s/lRpzRauFSX8uyXBRyHpUgnA6k2RZFgN6YdjtdsxmM5/t7kOM6cyOOeN0OWTH/YFdlmkRnWdQ9ws7pZFkuJjM2Fnssvw26PsDExdQUfevoNWqkwyTqXHtDfpLQa/KYkTa2/xYOT/EMn8JhaQmRj0QvboXZY7P2vxMnUWv6kX/xPnkVy0I+2+kUaYyOOk59pXfFTS3Jkbdn+Gpb7Kz5PqQvyAN6j44PcfbXc5AQsWgpMWYtMPRKlOx1H7IoaqnGJryKh5fdWM+2WYizbEyas5iWMoKci03hNzo1qQ5m6Epr7LL8lvqgxRGVUh6zsn4nGPV/0ep45Og12gqtJkacwVVzu+jsIpMQc/YG4nX/YI9ZcFG1v4nNeYKKp3fBZ3KVEpG9OqsoKOaQ5JfpNZ9MGgldAkNw1PfYG/ZrWGrlI9K/5Cj1hew1m9s/ZEAUJDT8zt2llwXNjg7Uzhq/Fw2/Ag2m43Y2K5ZAdr0e6nvwwtR6tq/T6Gvvp7Dix7p0r6e7s7sqECISHX9FnSqHhHliyglIyPS3kajTArZpqJuHU5vQchpnbzKR6l0fhN0RKuibh1+uZ4MU8sAzOktYHfpzQxInE+i/oIgV5YbK1S7yIz9f4xI+xtGzVltfraOUEg6+iU8ysj0d6moWx9mJaOCNOO1uH3l/FB6Y9AASkKNw3OInSVTQ/4S06uyOTv1LWI0AyPuZ2bsbPrE34+Ml1LHp+wuvYn/FJzNoaqnADhifYEa9156x91N/4THIro+NCROH7YuZljqipBJ5DXuH9hXPgeXtyTo+37ZyQ+ls+gddxc9Y4NvG9OUJK1TZXFOj88ba4fpI+5ve8RqRzAm41PidefyY+W8kO0yY28m2XAppY41QQIoiX4Jj6NSGIMGUGbtaIyawRTaVga9dobpt3j91WEDKJPmbFQKE9b6TW15rMZeSRys+KMIoIQzkgiihAj4KXN8RmrM5W0+o6Ga+Kf0MM0I00rmYMVDyLKfUF+SsdpRjEj7W9ApJL/spodpZtD8K4cnjx9KZ1Hr3h+yzpXD8yM7Sn5DSc2HgY16Q9Ug6iidKhOzdix+2Y3bV87WE5dQXPMOwZbJNBTjfJVkw8UopOBTonpVL87p8TlqRWLIHBi1IpHhqa9z2Pps2Jysn0vUX8i4HusxagYGiq1WOb9rHAn6X3/rPPkU17zDLss08qsWoFEmMyZjTcQlMUpq3kcfZjWd3bULlSKWs1NXBw226r0F7LJcj0aZQLhq+cdtS9lRfA0GdW9SYy5DQhl0z72OU5CovxC1IhG/7OaI9Tn2lN0cIthQ0Df+j6Qar6S6fkvQq2XHzSVG3TdIHakGNtdOfrDMCrpPnlIykmWezdHqF8P2WKnQc9T6EpEs24rVjsLm2tbm9kLnEYnl0SeCKCEix23LKLQHX/UTSpH9TdJN17e6ce/ApAWkG6cGfc/u2onXbw8EOT/lk2vZU3YL2XH3EK/7RYv36zyHcfks9Et4lAGJTyHRshI2yJQ6PmF/+d0ADEp6lnMyviTLfGsgYbwjUmJ+zdmpbzEy7V1iNP0BPwW2FSFXnikkLaPSP8TpOcbestuCbh+jV2VxdtoqjlUvDTs1Fa8fT3HNu5S1YQNgoDFvqCEI2Vt2Owcq7g+5ufHPyfhw+8o5Yl3C4ORn6Z8wP2g+WzCF9r9Q6z5Ahml6yHwrj7+S6vptnJ26Mmgg5fZVcMS6BK0yjeGpb4QMhl2+Yg5WPERJ7QfEaAYwtsdahqa8SkrMr4NuWB0JlSKW7Lh7Gd/zGzLNN6FWxlPr3k+V87uQ5/SMvRGDui+7Sn4b9HOZZryGJMNk9pXfHXQ6tl/C45g0Q0MG0kqFjqPVL1LnORKm32Zs9dspr/uyDU/ZeF3JyNCUPwetLi+cJKK8QVR1myDKarUyY8YMzGYzZrOZGTNmUF1dHfacWbNmIUlSs9f48eNPTodPU16/DbP2nIgSzF0+CztLrgs7jQBwrPoVesfdHXJU4GDFH8kw/ZYYdcspqXpvAXvL7gy6/UmT/KpFKKUYRqW/j16VHbYvP5TeyIGK+1ErEkk0TAKgX8Kj9DDNJF53btBfzk2rAU2as0k3XseAxKcZkNgw5aVSmCmyr2Rz0fmt1NJREKcbh192sb/8Lg5b/xQyhyk7/n6OWl8KGRwpJB2J+gsoc3xOoT149e+fi9ONY0zGP4nVnk2l899Bq2u3RZXzO7aduKxxCk1u8xYr0FCFe2DSIkKNJh23LaWi7t8MSloU8houXwmVdd8xKv2jxjIZodW6D7Cp6DzKHF+SbLgUrSoNo2YI/RIeIzXmamK1o4JM+0mAAoWkJ1E/iczY2ZyVvJQkw6+Q5YZ9+n6wzCTXMj1srlusdhQmzTCKa95hb9ltIVfz2ep3sqfs5qD746XGXEWcbmzI8gJ6VS8UkgFL7Udh/x36JzxOuqnlatdwUo1XUOX8Dq+/JqLzBOF00W2CqOnTp5Obm8vatWtZu3Ytubm5zJgRboqowZQpUygpKQm8vvgiusu6TwdaVWrIyt+h1HsLyDLfHqa4YsO0kKX2Q7Lj5wZ93+OvZJdlWsiqzzXu3dhc28iOu4843dgW7/tlJwcq7qPIvhqNMhmFpA37y70hV2dhYLWc3bUbnaoHPWNnkt6479/4nt9yXq+9nNdrX2CJd3LMFEzaodS49nLC3hAwFde8Q6Xzm7CrtoyaIYxKf4/M2NlIKHF4DgVtZ9aORqtMY3/5Hyh1fBq0jULSMjRlWSAAbIss860MSnqWA+X3t2kz3db4ZAfHbUvxyy5Gpv+d1JgrWj1Hxsf+8nvQKJNCbtMDDYHUgfIHGpKsVb2DtjlRs5rdpb8nyXARCkkTdjWhX66nzPFP9pXfSZ3nMB5fFU5PAXG6sfSJv58YdT/idedyXq99jZ/vPSTqz0elMJFuug610kypYw22+p34ZAfHql8OmSQPDcVG+8Y/wpDkl1Aq9Phld9BgOTXmCgYmLsTpPUa990SL92PUg+ib8CD7yu4Osdm1gkFJzxGnC10dvuE6/YnTjcNS+3HYdj+XYZrGiZrw5RKELiSKbUZdt1idd+DAAYYMGcLmzZsZN24cAJs3byYnJ4eDBw8ycGDwZNlZs2ZRXV3NJ5980u57i9V5LSkkDeN6fEOu5bc4g6yUCqVv/COAzGFr6BEEhaRBKZnCTk/pVb0ZkPg0e8pm45frW7wfqx3JWclLOVQ1P+xy/zTjNWTGzuaI9TkqnS33JTuZzNpzGJz8PEesS8JOu6XGXE2f+PvYVz4nZKCjkHQMTXkNl7ekcV++1r7FFYCfdON1VNT9u0tWrelV2QxNeRVr/UYOVy1qpQRAQxCYqL+g1amlOF0Og5OWcLDigVZXk41Mew+bazsFttdDTqOeLEOSX8Tjs3G0+oWgo0sAPUwz6Rk7k92ls0J+nyklIzGafiG/FnrG/p4E/XnsLg1fymNoyqtUOf/bmJ/XdhplSoj9Ks9cJ3N1Xv8HF6LUdmB1nqueQ8+K1Xkd0S2igk2bNmE2mwMBFMD48eMxm81s3Bj+B+eGDRtISUlhwIABzJ49m7Ky8N/wLpcLu93e7CU055fdFNe8Tby+Zf5ROMdtfybVeDkGdZ+w1/b4rZyVvDTkij6n9xhO7zGGJL8YdHTB7trF7tLf0y/hEYyawSHvZan9B/lVz9A7bk7IzW67kkHdjwGJT5MacxU21w62nZgSNoDqZZ5Dlnk2uZYbwo4UybKXcsfaNgVQOlUmYzI+waDuR0nt+1227N/pPcrOkmtRSNqwKzWb+GUX5XVfEq+bwOCkJSFHDKvrN7Gv/E4GJv0pZBX6JnvLbkchaRjbYy1Jhovb9RztJaEhNeZqRqV/iFIycqD8AQ5VzQ8ZQMWoB5JmvJJdIf5QUUpGhiT/H5KkDPm1IKEiyXAReRXBKro3d7jqOUoaFw+0VZb5FmS59fpnQhcSI1FR1y2CKIvFQkpKSovjKSkpWCzBEykBLrnkEt5++22+/vprnn/+ebZt28YFF1yAyxVs2LvBokWLAnlXZrOZzMzIt384Exy3vUpxzd8jOsfrt3HE+kIbdob3U+Pe07glSPAv0UOV85FlP1nm24O+7/D8yLYTl1PrPkCC/pchiw9a679nR8k1gdGxQUmLyTLf0mWr8xpIDEv5C8NT36DeW9RYw8ofMmdMr8pGIekor1vLzpJrcXqPB22nUSZzdupfUSnMlNS+R2s/Ic3asYxM+zsn7H8Lm7fTWXyygx8rH8PlszAoaTEGdd9Wz6mu344kqRmWuizkwgS7K5edJdfg8BwEFKgViUHbefxV5FctYHvxFdS49qBXZXFW8lIS9RdGlLMVKbN2NON7/pvkmIs5XLUYn1wbciROo0wl3XgdDk8eO0quxe0rbdFGIWkZlrocl7c45H58CkmPQtI0btQc+mekhIa+8X+k3lsYUf0wo2YI6cZpIhdKOONFNYiaP39+i8Tvn7+2b98OgCS1TDKVZTno8SbXX389v/71rxk6dCiXX345X375JT/++COff/55yHMefvhhbDZb4FVY2LZVSWeiZMMUesfdHdE5ltoPKa9b22qQUmBbgYyP3nF3BX2/KXemyL6qMRG95ZdyU5JuQ7J0+A1mm+o0NeRLpTI64x/0iX8QaBgxCr6ir20M6n5kmKYzNGU5AxKfBmSO2/7MlqILKbAtD/mLSEJJZuzNjEx/G6NmEHWe/JCBVox6EKPS36fS2fbpuDTjNewv/wMlte+399HarbLuW0ak/ZUE/flh28m42V9+D3Weo/SKmxOyndtXQXX9VmK1wxmTsSZs/pXbV4bLV4zLV0ZF3b/oETuDCZnfY9IMQykZ0QWtfN42CknbWJT2PsZkfEacbjwOTz65lhvYW3Zb2FIAyYYpjE7/B0pFU7AYvGjpoKQ/Uec5wmFr8Mr1DW0WhayX9VNZ5tloVemtTq/+XC/znRTa/xLxeULnEiUOoi/45mInyZw5c5g2LXz16969e7N7925KS1v+RVZeXk5qamqb75eenk6vXr04dCh4wi6AVqtFqw1eT0horrp+G/0T51Nc805Eu703VRLfXnwlHn9ViFYy+8vvDZk03NDCjU920yd+HipFHAcrHgy6vcoR6xKszs0MTn6OQ5VPh6he3qDWvZ/8qv3kVy1A3ZgE3y/hMWK1Z+P0HMPhyeeE/W/UuveTaJiIz+9Axku9t5h6bxEpMZejU2WgU/XE6TlGof0NsuP+gMdvxVL7AVZnw/Sz3bWr1X+nEWl/w+uvYUfxNWFHEwD6Jz7Bocpnwj4bENjrzVL7EXmVf2y1D12lvO4LnN7jnJX8f+yy/LaVvBo/+VXPIKEiRj0ApcIQcgrL7spld+nvGZi0kFTjlewunU2oYMQv11Pq+IRSxyeoFfH4ZAdGzRAGJz2PUhGDw32QOs9R8queQafKxKDObgxiZeyu3agVcSToz2/8fGdRaF+BLMv0Mt9Odf1WDlY8GKjLFWrEqEmifhK94u5kT9nskLW8lJIRv+zmcNWzYb8essy3olWmccD2QNh7NgX3O0quDNuuZT8MKBUGSmo+jOg8oQt0dEpOBFEdFtUgKikpiaSk1vMjcnJysNlsbN26lbFjG1ZdbdmyBZvNxoQJE9p8v8rKSgoLC0lPT293n4X/8fgrKal5n17mOwLVq9vC6S2gpPZD+ifOD9RlCsbrt1Hj/oE+8Q9SUbcu5C/O/KqFDEp6luGpf2ncFqVlnom1/r9sO3EZMh7idDnoVb2w1H4QZgrDHwjwdpfOQiFpMKj7YVD3xSfXoJC0jTWFjEiSgjLHZ1hqi4jVDsfrr8Hu+oEa1x4A9pUHH00LRq/KJiXmEo7bXuVgxUNhE/cllPSIvZGSmg/ItfyO1rZbUSnMDEl+Gb9cF7Jg48lU697H1hOXIOMmJeZyKuq+CluiQsaLShHHkOQXGqeTgydBOzw/srPkOmK1ZwN+0oy/ocr5n7CBWtNGvnZXLltOXIhakUCMpj96VRYyPgzqbNKM16JUNJQ6OFjxMGplPEbNIOq9JVTUraPeW4LXX80PpeFzs5ooJD2Zsb/H6S2gzPEFVc7/htxjUavMYHjq6xy3vRZ2eyK1IpGUmMsai26Gz1fSKlPIr3o6oj+AoGFvyNYS1QXhTNEtVudBQ35TcXExy5c37Al1yy230KtXL/75z38G2gwaNIhFixZx9dVXU1tby/z58/nNb35Deno6x44d45FHHqGgoIADBw5gMpnadF+xOi88lSKWlJjLIl7VI6FmVPr75FctwObaHrZtwwqs5/ihdGaY7VEkesfdTbnjy5D1cpoY1H3oG/8wBnU2x22vtVo/52QwqPvSO24OZu1YCu2vU2RfTbg/E7XKNAYnv4DXX8PBigdCJij/1PDUN6hx7eVo9Uthr33yKRiU9CcM6mz2lt3Z6movnaoHQ5Jfxur8vtUK3NCwcXOGaTrlji8ptL8etFTAydYz9vdkxt6Etf57jlpfDDuyZNaOYUjyixyr/jMlte+GbKdXZTeWVZBoLaCO0+Vgq98a8T6K8bpz6Rk7iz1lN0d03pnkZK7OG3Bvx1fn/fiCWJ3XEd0mKnj77bcZNmwYkydPZvLkyQwfPpy//vWvzdrk5eVhszUMmyuVSvbs2cOVV17JgAEDmDlzJgMGDGDTpk1tDqCE1nn9dopr3glalykcGQ+5lhuwubYHilSGUl2/ifyqZxie+iYqRajPncyx6pdxeH6kf8J8UsLkxNR5jrCnbHbjdGFD/kuC/pddnEzeUtNolkphQqNMwla/gy0nLmysSxU6yJFQc3baW5Q7vmJv2a2tBlCJ+kkopRj2ld3VGHScSgEUgJ+DFQ9S5viCUekfolGGn6Kv955gV8lvOVHzNmpFPHG6nLDtj1W/zNYTk3H7KjBphiGhIUF/Xti6UV3BoO4TyNXyyy5yLTM4WPFQmACqId9Tq0rnQMV9YQOoWO0oRqa/3VhdP3wAFa87l0FJC1EqIqvMLqGib8IfOVHz19YbCyeFyImKvm4zEhUtYiSqdRJKRmd8ylHr81Q6v4noXL2qN2el/B+7Sn6LT3aEbWtQ96POk49C0uOXnWHa9WVI8svUug+QX/V0m0ZpGkYrpuFw53Gi5u9U1H0V0XNEQqfqQe+4u0nUT8TmyiW/6pk2bauiVaaTZvwNx21LUUqGVivAS6jIjr+PJMOF7C69uXHPu1NbjLo/Ds+hwH9bbz8wUH/qiPW5Nn2udaoeDEp6Fr2qN+V1aymyr6TeW9QZ3Q8q2XAJmeab0CgTKa55nwLba62eo1WmMzBpESU171JetzZs21jtKM5KfoX95XNb3cNOq0xnVPr77Cu/K+KCqj1jZxGnG8/essgK7Z5pTuZI1MB7Oj4SlfeiGInqCBEVCB0m4+NQ5VP0S3gs5Ca/oTi9x6iu38Lg5OcIt2ksNFQ01yrTGNvjy7D1n+o8h9lZcg1uX3njCFn460LDaMWmwvMosr9F00jN0JTl9Et4nJSYKzCo+7Zr5EIpxZCov5DsuHsYkfYO8bpz8fmd2Op3sfXEFPaW3dpqACWhITP2ZkZn/KMxZ0jRagDV0P9l6FVZ7Cz5TYcDKJ0qC4WkJ0bdn2EpKxid/jGj0z8lXvcLVAozfeMfJtlwKRply1IkkWgKnPolPM5Zya+ELE3xv/Z5bC++HJ+/jhFpf6Mtn+t67wlyLTews+Taxqk9CZNmOMNT3yDLfDvxunPbVMsqGL2qF2nGaxmYuIBR6R8CEh5/NUesz7K56II2BVDpxusZnfERVc5vKa9b12r7WO0I9pff06ZNgOP1ORy3vdauivQVdes5VPlkxOcJXegUrhPVnq3aZFlm/vz5ZGRkoNfrmThxIvv27WvWZsWKFUycOJHY2FgkSQp6zbbcu6CggMsvv5yYmBiSkpK4++67cbtD52SGIkaiWiFGotpuUNJiqpzfUeYIXUIiGAklw1L/Qrnjq7BTFk0S9RcwIPHpNlWpBkg3XkdyzMXkVy2KqB5SjHoQcbqxxGqHY9QMQafqQb23mG3Fl5KgP5dE/SR8shNZ9lFo/ws6VU96xs5ErUhEq0rhx8r5eHxW+iY8QI1rHzbXNuyu3LDJ081JSKiJ1Y6gZ+wM8qsW4fIVt3qWWTsam2snBnV22A1nW6NWJJBhmk5KzKUoFXr2lt2By2vBqDkLt68MGT8ub8NUVLrpWmK1I4jTjSW/ahFljs9RKUytrkoLRUJFn/j7STJcxO7S/xeyNtZPNYzOORmYuIhSxydU129u8/0Ukp443TmYtaMxas7CqBmEQtJxouavHKt+md5xd6NSmPD566n3FlFS+x4Zphswa8egVSUDErmWG+hhmolRMxC76weq67eE3frl5/SqLJzeAnqYfkeV87+tnpsaczU+uYaKun+14eoSZu052Fxb29yfn8oy305xzd+jXum9OzipI1F/6ISRqJe7ZiTqkksuoaioiBUrVgANecy9e/dulsf8c4sXL2bBggWsWrWKAQMG8Mwzz/Ddd9+Rl5cXSMN56aWXqK9v2Kni4Ycfxmq1EhcXF9G9fT4fI0aMIDk5meeff57KykpmzpzJNddcwyuvvBLRc4ogqhUiiGo7CSUyPiRUEdePaVi+7UIhqds0ymLSnE2GaRp5la1XYwYFGaZp9DLfQUXduohWEv6UhBKtKp16bxEx6oHEas9urOmjoKTmfVSKWMy6MXh8Fbh8ZTg9BchE/pcNKEgy/IrecXMorvl7m4uaKiUDfRP+SJxuHLmWGyJeddXEpGlYYeiXXfSMnUGp458hl90H67tCUqFX9WJE2t+oqPuaAtsKnN6j7epLnG48dtcuNMpUXN7iNn1dJeovoE/8A7h9FRy2LqTWfaBd91ZKMSgVety+CpIMF6NRJqKQdLi8FsrrviBOl4NaYcblK8PlLcHlK2nXfYyawfSOuxuDug/bi68MupVRcwr6BKZpb2nTKGPf+EeI0fRjd2nrtaN+LiXmMjJjb2ZnybWiLlQbnMwgatDdHQ+iDv7fIxQWFjbra0dL/bRnqzZZlsnIyGDu3Lk89NBDQMMOIqmpqSxevJhbb721WfsNGzYwadKkFkFUW+795Zdfctlll1FYWEhGRgYA7777LrNmzaKsrCyiz5uICoROI+NDr8pidMbHKKTIvrEbqjh7ODvtLVJift1q+xr3D+RVPoxOlUX/hHmt3M9Pcc07bD1xcSBnq2fs7zFqzoqojzK+QO6Mw5NHSe37FNlXUWR/E59ci8tXTJljDdb6jdR58tsZQMGo9A/oGTuLw1WLIwqgRmd8gizLbC++ql0BlFFzFsNT32BI8gtoVWm4fMUcti6OIIAC8OOX3Tg8h9hy4lfUeQ4zIu2v6FTtq/xfXb8Zv+wiM/b3jEx/D4O6X6vnVDq/ZlvxrxtHNSU0ymRSYq6IuGCqT3YE/h0r6r6iuOYdiuxvUl73RWPfNlFetxa7a2c7AygF8bpfNO5b9x+2nbisDQFUw3YrMeoB7CyZ2qYAKst8O3G6Mewra3upjSYaZQp94x/mYMVDIoA6jWVmZjbbqWPRotD7m7ZFe7ZqO3r0KBaLhcmTJweOabVazj///Fa3d4v03ps2bWLo0KGBAArg4osvxuVysWPHjjbfC6JcJ0o4/Ti9BdS4dtM3/mEOVc2L+PyDFQ9ydupq/LI77ObBTdy+UiRJxej0j9hffi8OT17Itj7ZQZXzPwDIso8hyS/h8Vk5bltKlfO7iPvaORqmWdKMV6JSxLGv/E72lt3e5k1dlZKRBP25lNetZW/Zbe2avmsYOfSRHXcPZY7PKa39NOKl78F4/TUU2v9Ckf0tZNxkx92DUmHkWPX/RTzNd6jqSVJjrmJE2lvkVy0MWyupgT8wrdxQe+vX9Et4mNLaNRTYlgXqQp1sGmUSKTGXkW68jqPVL1NZ9y+2FF3UpgAlTjcej6+SIvsqCuQVtLYKr4ECtSKe3aU3t7pwIxitMpVj1a+E/b4SoqiTim0GG4nqiPZs1dZ0/OcFtFNTUzl+vPXp/EjubbFYWtwnPj4ejUYTdiu5YMRIlNDpDlU9Q5xuHPG6cyM+t85zhN2l/48s8y1t2s/ML7v4sfJxjlX/mQGJ82lLYjHAiZq32HpiMseq/w+f34lC0nJW8iukGX+DRpkccb8joZD0gcT4wUnP0TfhQWrdPzZuGEybA6jUmCsY2+NLYrUjACIOoBSSll7mOYxK/wCAPWU3Y6n9R6cEUD/VNCJXaH8DWfZyTsYXpBmvifg6pY5P2F58Bbb67ehUPdr89eX0HmVv2a3sKL4Gr9+GX3aRoJ9In/gHMWvP6dJ986Bhk2edqgcqRSxjMv6JQd2XvMpHqKj7ChlfqwGUQtLTL+FxBiY2lCVoGK1qPYDKMN2AQd2Hw9aFYXYGCC1e9wtq3XltylMUoqOzShzExsY2e4UKorp6q7Zg57XlnNauEew67e3fz4mRKKHT+WUnu0tntTsnx+E5xM6SqSgkHQm6X1Lp/LrVc8rrvqC87gsUkobBSS9QYFtBjXt3K2fJWOv/CzTUXipzfE6S4Vf0ib+Po9aXKan9gDTjVdS6D1LnOYxfDr1xdWgKNMok3L4y0o3XkWq8CqNmIFbnRvaV30Ve5aPtum6y4VIyTNPZU3ZrhNNtDUya4QxJfhGbayd7ym7lZNSO8vrtHLYuoqT2vcB2PjHqgRGNcjR9TRk1Z9Ev4THqPIc5Yn2uTQncLl8Jx22vAg0rOI2aQfSJvxeDuj+biyaiU6WjU2Xi8ORR7y2mPf8mSikGSVLil10MSHyqIUiTJI5aX6TUsYZNhedGHKQOTlqCx29le/EVgf0gW9M77i6SDVPaXaojTjeWQUl/YnvxVW3ei1E4/XXlVm1paQ11+iwWS7NdRcrKyiLa3i0tLa3Ve6elpbFly5Zm71utVjweT0T3AhFECV3E5bOgViRyVsrL7Cm9tV1TCWpFPH0THiamth8FthVtOscvuylzfMZZKa9gdX7PEevzbfolIOOhvG5toCaPhAalZMCsPSfwF/2x6lcosr/JoKRn8flr8fod1Lh/QKNMRa0wo5C01HtPUFL7Pn3j/0ii4UK0yhRsrp3sLv09dZ6jHLW+iN31Q2B0JpIAyqDuQ++4P1DuWNvY1y+J9Be9VpmOJClx+8o4WPHHNi2L72x1niPUeY6gVaYxLHU5Vc7vOGJ9PqIpvlr3PrYXX06GaTqDkp5ll+V6JBRtDlDqvYUU2JZRYFuGQtLhl+vRKFNIN00lRt0fjTKJLScmo1P1JMM0DY+vGr/spMr5X8y60UioUCp0lDk+x+UtZWjKa+hUPVEqdByu+hMltR9Q5fwPx6v/3Gzrnrb2z6DuQ5b5dg5VPsmBivvalCvVpJd5DvG6X7LLckO7VtNplekMTnqe/eX3igDqVHeS987ryq3asrOzSUtLY/369YwcORIAt9vNt99+y+LFi9vcx7bcOycnhwULFlBSUhII2NatW4dWq2X06NFtvheI1XmtEqvzOqZfwmPoVD3YW3YH7fluVysSGZa6jBrXPg5VzW/zeUrJQKb5Ziy1H+OX3fhlVweXZzeUG5Bxk2S4CLUiAaUihjrPEfSqXqgUJvxyPU7vcSrq1mNQ98Mv1+PyWjohIbdhW5R43QQK7X/hhP2diJPWJVQNW42Y/x+HKp9stYDjyaKUDPSOu4uUmMvYVnx5hz5HI9Pepca9l0LbG+1eKddEQoOMB60yFbNuDGpFHArJgN21kzjdeMCPT66jyvkdTk8BRs0Q6r1F7Zo2+ym1IpHs+Lkk6htqShXXvNvmrx+VwoQsy6gUsXj8VREFXj+VbJiCWpkQ8VZOQoOTuTpv8B0dX5134NWuK3EQyVZt0FDiYNGiRaxcuZL+/fuzcOFCNmzY0KzEgcViwWKxsH37dmbPns13332HyWQiKyuLhISENt27qcRBamoqzz33HFVVVcyaNYurrrpKlDjobCKI6pimGlDV9VsosC1r1zUUkhaTZjg21zZUiriIf9GmxlxJ34SHKa39hCL76g7/gj05JOJ1v0Cv7kVxzdskGX5FlfP7sJXawzkr+c8A5Fc9c0o+v1aZhstnId14PXbXzjZVK/85tSKenrGzSDddz1HrS90qlydG3R8ZGY+vigzTbymyr27z1F3T+Wel/JkC2zIstf9oZy8UJOh/SZXz23aeL4AIoppUVVVx9913s2bNGgCuuOIKli5d2qwcgSRJrFy5klmzZgENOUlPPvkky5cvx2q1Mm7cOP785z8zdOjQwDnz58/nySdbFn396XXacu+CggLuuOMOvv76a/R6PdOnT2fJkiURJ9WLIKoVIojqOKVkRKnQ4fFZO5S0bNQMYVjKcg5UPEh1/aaIztUok+hhmkGcbhy7LNMaf2mXcurtIwdpxmvIMt+K119DkX1lxMVLm2iUKWSZb+GI9XkUkqbdhS9PptSYq+gTfz9ljs85Vv1KRIFEk4b6TgYkVJyV8gqW2n9Q5vgnXn9NF/S4Y5INU8gwTUOvzuZQ5VNUOv/djmtcQv/ExzlU+VSHRhj7JTyOXtWLPWWzORW/L7qLkxlEDemEIGp/FwVRZwoRFQhdzifX4vZVMCT5ZVJiLmv3dWrd+9lfPpdBSQvJjrsvonPdvgqOVr/ILktDUmSf+AcY33MDfeIfxKgZ0u4+dQaNMol04/UMTnoBAJe3lP3l97Kz5Np2BVAN28TcwpiMT/H4qgFftwigoGEF3rbiS1FIalKNVzYejWy1TEN9p3JcvhKOWJ8jVjuScT2+xqwdi0LShtnEuutJKInTjSfJcBHQULbgRM07bCm6MOIASikZkVDi9dvItczoUADVy3wHsdqz2V9+NyKA6kZO4W1fzhQisVw4aY5Yn2dE2lv4/M52/cUNYHPtYHvxlSQZGgqyNax8i3wV4IGK+9CrepESczmJ+guode8ny3wLTk8RNtc23L7ydvWvLZSSgRjNIOyunWTG3kSmeTZVzm8pdawBFFjrv+/AtWNQKWIxagayo/g3bdom5lTj9dsDVeXjdb+gT/z95FctwObaHvG1quu3UF2/BaVkQMaLUTOUYSnLqXUfxFq/EUvtB+1eRdpWSsmIT66lb/zDpBqvxOk5SkltQ1mJSPL8fipedy4Dk54mr+LxwArTjpAkDXtKb2nTbgGCIPyPmM5rhZjO61wx6gEMTXmVHSVXd3h6RSnFcE6PLyhzfMHx6lc6/AsgzXgtCfrzMGtHU+X8FoWkxeE5RJ3nMDWuvRHnEklo0KrS0CrTsLm2khpzFT1jf49enUmNay97ym5GQtPY77YUTgwtVjuKvvEPYnft4rC17StZuoOGshMPUec5xL6yPyDj6dD1FJIGs3YMcbocimveQa/OIjvuPmrd+3F4fqSibj1uXyUSUkTTzyqFCYWkw+0rp2fsLOJ04zFphmFz7WB/+d3Eakfg9BR2eMXbwMSFmHXnkFfxSIdXV2aYplPj2tuGciBCW53M6byzbuv4dN6+ZWI6ryNEENUKEUR1PoWkwS+7MWmGUuPe26FrqRRx9Im/jwT9L8m13NimbTDadl0TcboJGDWDMaj7UF2/heKatxnb4ytAwuu3UeX8L8eqX6ZP/AMY1P1QSFrcvlIOVjxE/4R5pBmvxuUrpc5zmL1ld6BXZaNU6HC4f+zUgpb9Eh4lQT+Ro9YX21X2oDuQUBOv/wVVzg2kxFyG3bW70z7XEhqMmsEYNYMwagZyouZtFJKGkWnv4fXX4PVXc8T6PNb6TQxJfgmQkVBSUbeOktoPGJ3+D/TqbPyym9LaTzlsXUhqzBV4/TXUuPe1uXhq+D7+7/njdedic21rZ92y/8mMvYl001RyLTNx+1rW1RHa56QGUbd2QhC1XARRHSGCqFaIIKpraJRJjEr/kGPVS7HUftjh6xk1Q6h1HyRRfz4+2Ul1/eZO6GVLCkmPWhGPWhmHz+/E6T2KSXN2Y4kDF16/HYcnr3GJfPv2zmuLWO0IMkzT+bHyscbNeUvOmL3NesbOIst8C1XO/1BgW96urW7aSqWIQ62Iw+Ovxud3EKdr2o9LxuktoN5biEaZ3FgJvSs+3xLJhovJjr8Xh/sQ+8v/0Cmf5x6m35Fuuo7dpf+vy6czzzQnPYjSdCCIcosgqqNETpQQFW5fBbmWGxie+iZaZUqgknR7NVXtlvHRP+EJ3L5Kjtv+3OnBlF924vI5m+Ua1bh/aNGuqwKoGPVA+ifOQ6NMosC2HFn2U+8t7JJ7naqK7KsoqXmfDNNvMWvPoc5zBJPm7KCfh47y+qubldQIln/UNflzCqTGkgM9Y2eSV/FopxRGbSgSGkN53VeUOtbg9ds7oa+CcOYSQZQQNfXeE+wq+W0gSbwzVDm/o8r5X1JiLsGsHU11/WbidGOx1ed26chQV1IrEkgzXk2V87vGsgdvUlH3NR3No4qERplMkuFX6FW90CiTKLK/hctXwsDEBXj8Vty+Csoda6lx72nc0LhrR8V8ch2F9jca+5bCwKQFyLKP4pq/Ueb4vNsmSCslI2nGq+gRO5Mj1iVU1H1FpfObTrm2SmFiSPLL2F27OVb9UqdcU4iun+5/197zhY4RQZQQVR5/FSW172LUDKFfwiPsK/tDJ2w14f9JaQAFPUwzGZz0IqWOTympebfZNhynMpUijoGJTxOnG0t53Tp8detx+Ypx1XX9ijuTZhiJhgtI0P+SQ5VP4pOdxKgHUOc5ht31Ay5fCV6/nSL7W6iVcWiUKUiSGqVkICfzP9S6D1JZ9y3ldV92+UiZ21fG9uLLiNONJcM0nVr3QVy+Mgzq3lTXb6U75Ig1rB70MbbHWqz1mzhQfi817j2ddn29Kpthqa9RUfdvjlW/3GnXFaLsJG/7IrQkgijhlFDr3k9l3XeMzviI/eX3YHft6qQr+9lXfic6VU/SjL9p3J7DQo/Y31FZ92+c3uOddJ+OU0g64nUTSDJMxu7aRUntB5TXreNAxYPtrlQeCb0qC4/fToy6L/0T51FR9zX5Vc9Q6z6AjJdDVS2rBAeb3tpYOIFY7SgS9RMxagbj9pXRwzSDUsenXVo6orp+a2PQ1LDBcp/4+9Eq0yivW8fx6qV4/NYuu3d7GDWDSTJMJiXm11TWfc1h65/YemJyl4yiaZSJHKt+lTLHmk6/tiCcybpNELVgwQI+//xzcnNz0Wg0VFdXt3pOUwn5FStWNCshf9ZZZ3V9h4WIFdpXUOveS4ZpWicGUQ3qvUWBv8BVCjM6VQZnp63C56/nUNWTVNdvRSkZ2lUhu70klMRoBiLLPuo8hxnX4184PHmUO9ZTUfcvGkbU/tnqdTrah0TDr+hhugGDOpsDFfdRXb+V7cVXtPuaftlFdf2mQFV5lSIOnSqDMRmfYavfzhHrEpzeo531CEHVuHezs2QqOlVPkgwX4ZPrSIm5jGTDFKz1G6mu30qd5zAn809xtSKBON1YJElJmeNzssy34/QcZV/ZXTg8eQCdGkBJaOib8BBev41j1f8HHVvMJ5yCxHRe9HWbIMrtdjN16lRycnJ444032nTOs88+ywsvvMCqVasYMGAAzzzzDBdddFGzzQyFU4u1fiPW+o1olWn0S3ic/KqncfksnXoPr99GftUz5Fc9Q4x6IB6/FZ2qB6PTP8blK6HGtYcTNW9T696PSmHu4MbFDRSSDoO6Dz5/LU5vEWenrsKkHYrTU0iR/Q0cnjw2F03qcA2ktlJKRjTKRNy+CtKM13Ci5q9U1n3dqaUXmnj91RyqeorD1mdJibkUv+wiRj0Ak3Y4ZY41XbSqrUG9t4gi+0qgIV9Olr3E6XLoYbqRXZZpGDUDiNedS637AHWefOo8Rzrl30CjTMag7oss+7C5tnF26ipiNIOw1e8ITDU3VAfvGjHqAQxOXoLD/SNHrS902X2EKBPTeVHXbYKopg0HV61a1ab2sizz0ksv8eijj3LNNdcAsHr1alJTU3nnnXe49dZbu6qrQidw+UqxubYzOuMfHK56jlLHx11yn6YRAIDvC8cSo+6PSTsMWXajViRwTo/PUUhqnJ4iCu1vUOZYQ3bcPfjkevyyE7/sAfxU1P0bWfaRbroWpWRErTRT5viMGtd+xvVch0LSU+c5QpF9NU5vAUesz1PnOdRs5OFkBFBaZRo9YmeSZryGAttyiuxvsrfs5Hwv+OX6wOa4SkU/EvWTyI6by4matym0vdHlif9ev53yurXNtkdx+yrwybUkx0zGoL6dvWW3o1f1onfc3bh95bh9FRTZV+P120mJuawxYV6mun4bTs8xssy3olIYUSsTqK7fiqX2I8b1+DcKSYPDk09F3Xpsrm3sL7+vE3L9WiehRMaHSTuMAtsKyhyfdfk9BeFM1m2CqEgdPXoUi8XC5Mn/W/ml1Wo5//zz2bhxY8ggyuVy4XL9b9zbbhdLgKNDpsi+kirnf+gddzfldWsbiwt25Yo0Pw5PXrPAamPheJRSDDpVj8BycLevCpXChEaZhIQGSVKglDbiw4lC0uHxW3F6j1PvteCTa9l24tct8nG6Yjl+OA0jajb6JjxMvbeQ7cWXdWl+UmvqPPnsK78TvaoXacZrkPFg1p5Dvbew00cew/fjCAW2Fc2OeXw28qsWoVEmoVEm4ZfrkSQVWlU6CkkNgMN9CGfjn/H13mJq3AcCZTa2nri4xerEkxFAGTVnMTBxAUesS7DUftTl9xOiT0znRd9pG0RZLA0/iFNTU5sdT01N5fjx0MnEixYtCox6CdFX58kPTHuMSPsbVudmCu2vd7hacyR8sgOH58fAxydqVodsG2zlUzQTmmO1I8ky34Je1Yttxb9mf/kfotaXYJze4xytfhEAk/Yszkp5hSrntxTYXqfOkx+VPvnk2qBB7pEg2+kct/25xbGTX/RUon/C4yQafsXhqj91yl56QjchpvOiLqoluOfPn48kSWFf27dHvunoT0lS8x3gZVluceynHn74YWw2W+BVWHhmFTI8le0vvwe9uhdje3z1k8rRQksNX9/pxusYlLSIirp/s734Kk71n5hF9lVsKbqQWnceqTGXA2BQ94tyr05dEmridOMBGZtrJ9tOXEp53RfR7pYgnFGiOhI1Z84cpk2bFrZN796923XttLQ0oGFEKj09PXC8rKysxejUT2m1WrRabbvuKXQtt6+cgxUPYNIMw+uvQatMw6gZQqXz62h37ZSglGJIM15Nj9iZ7C+fS6njE0pqP+BUD55+yic7KLK/CYBC0jIk+QVk2UuhfRXlji9PWuL9qUxCSarxKnqZ76TGvZvq+i0i9+lMJUaioi6qQVRSUhJJSUldcu3s7GzS0tJYv349I0eOBBpW+H377bcsXnx67XJ/pmkqQhijHkSvuDvpHXcXx22vUVG3njP1p4JO1YNR6f/A6vwPB8rvoda9L9pd6jC/7GJ78RXE6ybQM3YWsuyh0vk1KoW5Uzb17W4k1Mj4SDVeRUrMpewv/0OnFuQUuh+RExV93SYnqqCggKqqKgoKCvD5fOTm5gLQr18/jEYjAIMGDWLRokVcffXVSJLE3LlzWbhwIf3796d///4sXLgQg8HA9OnTo/gkQmdxeA6ys+Q3xOvOJcP0WyrrNqBTZeDylZ6U4pTRpJA0JBkuIt14HVXO/1Jof51tJy49KQnMJ1tT2QtoKKI5LHUFtvodlNS+R5Xzv5zM7W+iQa2IJ910PT1MN7C//F4stR+JxHGhgRiJirpuE0Q98cQTrF79v4TeptGlb775hokTJwKQl5eHzWYLtHnwwQdxOp3ccccdgWKb69atEzWiTjPW+v8GkmlTjVeSYZpOueNzSmo/oNZ9IMq961wNq+zsjMn4DKfnWGN9p4a91U7HAOrnaty72Vx0PsmGS8ky34rD/SMKSYMkaaKWiN5VFJIepWTgnB5fUFH3FbmWG7u8SKkgCJGRZFkWsWgYdrsds9nMZ7v7EGOKah6+0EZqRSLppmvRKJPIr1pAkuFX1Lj24/J1/Z5zXcGkGUpyzBSSDZdirf+eHysfb6yu3j032e1sifoL6ZfwKD65jnLHFxTYXu+2uVMGdT9SYi4lNeYKimvep9C+AoWkwy/XR7trQhs5avxcNvwINpuN2NjYLrlH0++lETMWoNTo2n0dn7ue3L8+2qV9Pd11m5EoQWgrj7+SAtvywMex2pH0T3gSl6+EIvtbp/z+YUrJSJxuLGplApbaD0kz/ga3r5I9ZbMbtyrp3O1BurtK57+pPPFvTJphJOjPR8ZDhmk6elUvqpzfYnPtOKklMSIhocSkHY6EGptrKwMSn8JWv529ZXcEymqIAEoISUznRZ0IooTT3hHrcxyxPk+sdkSgWOLo9E+p8xymun4T1vrN1HujV8pCrYhHo0zG4fmRgYkLAxsQl9d9CRB041+hpRr3nkCitdX5PUpDDFnm29Gre7K5aBKx2pEoJC01rj34ZEdU+iihRKWIxeO3MihpMYn6STi9BRTXvIvNtZVci8jXFITuRARRwhnCj921M/DRnrJbiNONI143HqXCRJH9TQYnPY/bV47Dk99Qkdp7DK/fFuaakVFIOvSqTCRJQ617H33j/0iS4SKUCiPlji85VDWfY9Wv8GPlE1Eo2Hh6cXqPU2h/nUL760gogYYVjOnGqRg1Z1HvPcGOkisxaYahUaZQ5zlCvfdEp249o1YkIklK3L4y+sQ/hFk7khjNAEpqPuSwdSHFNe+RX7WoU/ZmFM5MYnVe9IkgSjgjuX2llDnWNJvaK655D5N2CLHaEaQbr0Wv7o2Eip0lU1EqdPQwzcTjt+Lz11Dm+By3r5LkmIuRZT+SJFHj2ovD8yNZ5ttQSjGolfHUuH6gpPYDRqV/iEHdl3pvIRV166l176PM8Rknav5Gvbco0AeXryQa/xyntaYNhcscnzXWU1KgU2UAoFGmkGa8GoO6LzpVOt8XjideN4E04zV4/FV4fFaK7G+hkNQk6M9Dxossy1TXb8brrwnslahSmKhy/gdr/feck/EZWlUGPn8tRfa/UmhfQY1rDxV1X1HrzgusHP1pUC8I7SKm86JOBFGC0Mjm2orNtbXZMaUUg1+uR61MwFr/PWpFAiqFEUlSopA0xGpHBNq6vKU4PD8iocLjt1LnORLIa/nBMgufXNvs2jXuvV3+TEIw/kDgWun8N5XOfzcelwCZWvd+LLWgViagVsQh40OpiMeoGYwkNfzIdHjy8Ml1aJTJeP211HsLG/cilNlTdjtuX2mzPCxRSVwQTk8iiBKEMJpyZ9y+csoc/2zx/o+Vj7c4dty2NMh1alscE041DX+Wu3wWXM7mmyB7/dVBc9OOWJ9rcazeW9A13ROEnxHTedEngihBEARB6I7EdF7UicJHgiAIgiAI7SBGogRBEAShGxLTedEngihBEARB6I7EdF7UiSBKEARBELopMZoUXSInShAEQRAEoR3ESJQgCIIgdEey3PDqyPlCh4ggShAEQRC6IZFYHn1iOk8QBEEQBKEdxEiUIAiCIHRHYnVe1ImRKEEQBEHohiR/x19dxWq1MmPGDMxmM2azmRkzZlBdXR32HFmWmT9/PhkZGej1eiZOnMi+ffuatVmxYgUTJ04kNjYWSZJaXPPYsWPcdNNNZGdno9fr6du3L/PmzcPtdjdrJ0lSi9eyZcsifk4RRAmCIAiC0KmmT59Obm4ua9euZe3ateTm5jJjxoyw5zz77LO88MILLF26lG3btpGWlsZFF11ETU1NoE1dXR1TpkzhkUceCXqNgwcP4vf7Wb58Ofv27ePFF19k2bJlQduvXLmSkpKSwGvmzJkRP6eYzhMEQRCE7ugUnc47cOAAa9euZfPmzYwbNw6A119/nZycHPLy8hg4cGDLrsgyL730Eo8++ijXXHMNAKtXryY1NZV33nmHW2+9FYC5c+cCsGHDhqD3njJlClOmTAl83KdPH/Ly8njttddYsmRJs7ZxcXGkpaV16FnFSJQgCIIgdENNq/M68gKw2+3NXi6Xq0P92rRpE2azORBAAYwfPx6z2czGjRuDnnP06FEsFguTJ08OHNNqtZx//vkhz2krm81GQkJCi+Nz5swhKSmJc845h2XLluH3Rz6/2W2CqAULFjBhwgQMBgNxcXFtOmfWrFkt5jzHjx/ftR0VBEEQhG4kMzMzkLtkNptZtGhRh65nsVhISUlpcTwlJQWLxRLyHIDU1NRmx1NTU0Oe0xaHDx/mlVde4bbbbmt2/Omnn+aDDz7gX//6F9OmTeO+++5j4cKFEV+/20znud1upk6dSk5ODm+88Uabz5syZQorV64MfKzRaLqie4IgCIJwcnVSsc3CwkJiY2MDh7VabdDm8+fP58knnwx7yW3btgENidstbycHPf5TP3+/LeeEUlxczJQpU5g6dSo333xzs/cee+yxwP+PGDECgKeeeqrZ8bboNkFU0ydu1apVEZ2n1Wo7POcpCIIgCKeaziq2GRsb2yyICmXOnDlMmzYtbJvevXuze/duSktLW7xXXl7eYqSpSdPvaYvFQnp6euB4WVlZyHPCKS4uZtKkSeTk5LBixYpW248fPx673U5paWlE9+s2QVR7bdiwgZSUFOLi4jj//PNZsGBB0GHGJi6Xq9l8sN1uPxndFARBEITInOTE8qSkJJKSklptl5OTg81mY+vWrYwdOxaALVu2YLPZmDBhQtBzsrOzSUtLY/369YwcORJomIH69ttvWbx4cUT9PHHiBJMmTWL06NGsXLkShaL1zKVdu3ah0+nanC7U5LQOoi655BKmTp1Kr169OHr0KI8//jgXXHABO3bsCDlcuWjRolaHKwVBEARBCG7w4MFMmTKF2bNns3z5cgBuueUWLrvssmYr8wYNGsSiRYu4+uqrkSSJuXPnsnDhQvr370///v1ZuHAhBoOB6dOnB86xWCxYLBby8/MB2LNnDyaTiaysLBISEiguLmbixIlkZWWxZMkSysvLA+c2jXb985//xGKxkJOTg16v55tvvuHRRx/llltuCRkbhBLVIKqt86tjxoxp1/Wvv/76wP8PHTqUMWPG0KtXLz7//PPAEsqfe/jhh7n33nsDH9vtdjIzM9t1f0EQBEHoKqfy3nlvv/02d999d2C13RVXXMHSpUubtcnLy8NmswU+fvDBB3E6ndxxxx1YrVbGjRvHunXrMJlMgTbLli1rFjecd955QEPNp1mzZrFu3Try8/PJz8+nZ8+eze4nN+aAqdVqXn31Ve699178fj99+vThqaee4s4774z4OSVZjt42zhUVFVRUVIRt07t3b3Q6XeDjVatWMXfu3FYrn4bSv39/br75Zh566KE2tbfb7ZjNZj7b3YcYU7dZzCgIgiBEgaPGz2XDj2Cz2dqUZ9QeTb+Xxl/6FCq1rvUTQvB66tn8xRNd2tfTXVRHoto6v9pZKisrKSwsbJa0JgiCIAiC0B7dZmiloKCA3NxcCgoK8Pl85ObmkpubS21tbaDNoEGD+PjjjwGora3l/vvvZ9OmTRw7dowNGzZw+eWXk5SUxNVXXx2txxAEQRCETtFZxTaF9us2ieVPPPEEq1evDnzclL3/zTffMHHiRKD5/KpSqWTPnj289dZbVFdXk56ezqRJk3jvvfeaza8KgiAIQrd0im77cibpNkHUqlWrWq0R9dP0Lr1ez1dffdXFvRIEQRAE4UzVbYIoQRAEQRD+51RenXemEEGUIAiCIHRHfrnh1ZHzhQ7pNonlgiAIgiAIpxIxEiUIgiAI3ZFILI86EUQJgiAIQjck0cGcqE7ryZlLBFGCIAiC0B3JcsOrI+cLHSJyogRBEARBENpBjEQJgiAIQjckShxEnwiiBEEQBKE7EonlUSem8wRBEARBENpBjEQJgiAIQjckyTJSB5LDO3Ku0EAEUYIgCILQHfkbXx05X+gQMZ0nCIIgCILQDmIkShAEQRC6ITGdF30iiBIEQRCE7kiszos6MZ0nCIIgCILQDmIkShAEQRC6I7HtS9SJIEoQBEEQuiFRsTz6RBAlCIIgCN2RGImKOpETJQiCIAiC0A7dIog6duwYN910E9nZ2ej1evr27cu8efNwu91hz5Nlmfnz55ORkYFer2fixIns27fvJPVaEARBELqO5O/4S+iYbhFEHTx4EL/fz/Lly9m3bx8vvvgiy5Yt45FHHgl73rPPPssLL7zA0qVL2bZtG2lpaVx00UXU1NScpJ4LgiAIQhdpms7ryEvokG6REzVlyhSmTJkS+LhPnz7k5eXx2muvsWTJkqDnyLLMSy+9xKOPPso111wDwOrVq0lNTeWdd97h1ltvPSl9FwRBEATh9NQtRqKCsdlsJCQkhHz/6NGjWCwWJk+eHDim1Wo5//zz2bhxY8jzXC4Xdru92UsQBEEQTjlyJ7yEDumWQdThw4d55ZVXuO2220K2sVgsAKSmpjY7npqaGngvmEWLFmE2mwOvzMzMzum0IAiCIHSipm1fOvISOiaqQdT8+fORJCnsa/v27c3OKS4uZsqUKUydOpWbb7651XtIktTsY1mWWxz7qYcffhibzRZ4FRYWtu/hBEEQBEE4rUU1J2rOnDlMmzYtbJvevXsH/r+4uJhJkyaRk5PDihUrwp6XlpYGNIxIpaenB46XlZW1GJ36Ka1Wi1arbUPvBUEQBCGKRJ2oqItqEJWUlERSUlKb2p44cYJJkyYxevRoVq5ciUIRfhAtOzubtLQ01q9fz8iRIwFwu918++23LF68uMN9FwRBEISokoGOlCkQMVSHdYucqOLiYiZOnEhmZiZLliyhvLwci8XSIrdp0KBBfPzxx0DDNN7cuXNZuHAhH3/8MXv37mXWrFkYDAamT58ejccQBEEQBOE00i1KHKxbt478/Hzy8/Pp2bNns/fknwxH5uXlYbPZAh8/+OCDOJ1O7rjjDqxWK+PGjWPdunWYTKaT1ndBEARB6AodTQ4XieUdJ8my+FcMx263Yzab+Wx3H2JM3WLgThAEQYgSR42fy4YfwWazERsb2yX3aPq9dMGIP6JStj+H1+tz8XXun7q0r6e7bjESJQiCIAjCz4jE8qgTQyuCIAiCIAjtIIIoQRAEQeiO/J3w6iJWq5UZM2YEClfPmDGD6urqsOfIssz8+fPJyMhAr9czceJE9u3b16zNihUrmDhxIrGxsUiSFPSavXv3blFz8o9//GOzNgUFBVx++eXExMSQlJTE3Xffjdvtjvg5RRAlCIIgCN3QqVyxfPr06eTm5rJ27VrWrl1Lbm4uM2bMCHvOs88+ywsvvMDSpUvZtm0baWlpXHTRRdTU1ATa1NXVMWXKFB555JGw13rqqacoKSkJvB577LHAez6fj1//+tc4HA7++9//8u677/LRRx9x3333RfycIieqFU1593W1XRiyC4IgCKeFpt8VZ/KarQMHDrB27Vo2b97MuHHjAHj99dfJyckhLy+PgQMHtjhHlmVeeuklHn30Ua655hoAVq9eTWpqKu+88w633norAHPnzgVgw4YNYftgMpkCRbd/bt26dezfv5/CwkIyMjIAeP7555k1axYLFiyIKMleBFGtaIqAr5twLLodEQRBELqNmpoazGZz196kkxLL7XZ7s8Md3blj06ZNmM3mQAAFMH78eMxmMxs3bgwaRB09ehSLxcLkyZOb9eP8889n48aNgSCqrRYvXszTTz9NZmYmU6dO5YEHHkCj0QT6N3To0EAABXDxxRfjcrnYsWMHkyZNavN9RBDVioyMDAoLCzGZTGH33Gtit9vJzMyksLDwjFoyKp5bPPeZQDy3eO7WyLJMTU1Ns1/QXaaTgqjMzMxmh+fNm8f8+fPbfVmLxUJKSkqL4ykpKS2KZP/0HKDFtmypqakcP348ovv/4Q9/YNSoUcTHx7N161Yefvhhjh49yl/+8pfAvX5+n/j4eDQaTcj+hSKCqFYoFIoWBT7bIjY29oz6YdNEPPeZRTz3mUU8d9t0+QhUJ/t5kBhqFGr+/Pk8+eSTYa+1bds2gKCDDrIstzoY8fP323LOz91zzz2B/x8+fDjx8fFce+21LF68mMTExA717+dEECUIgiAI3VEnjUS1NUicM2cO06ZNC9umd+/e7N69m9LS0hbvlZeXtxgBatKUv2SxWEhPTw8cLysrC3lOW40fPx6A/Px8EhMTSUtLY8uWLc3aWK1WPB5PxPcSQZQgCIIgdEd+ILKBk5bnRyApKYmkpKRW2+Xk5GCz2di6dStjx44FYMuWLdhsNiZMmBD0nOzsbNLS0li/fj0jR44EwO128+2337J48eLIOvozu3btAggEZzk5OSxYsICSkpLAsXXr1qHVahk9enRE1xZBVCfTarXMmzevQ0l53ZF4bvHcZwLx3OK5hdYNHjyYKVOmMHv2bJYvXw7ALbfcwmWXXdYsqXzQoEEsWrSIq6++GkmSmDt3LgsXLqR///7079+fhQsXYjAYmD59euAci8WCxWIhPz8fgD179mAymcjKyiIhIYFNmzaxefNmJk2ahNlsZtu2bdxzzz1cccUVZGVlATB58mSGDBnCjBkzeO6556iqquL+++9n9uzZEU9Xi73zBEEQBKEbado771cD7u3w3nn/+vGFLtk7r6qqirvvvps1a9YAcMUVV7B06VLi4uICbSRJYuXKlcyaNQtoyEl68sknWb58OVarlXHjxvHnP/+ZoUOHBs4JlZfVdJ2dO3dyxx13cPDgQVwuF7169WLatGk8+OCDGAyGQPuCggLuuOMOvv76a/R6PdOnT2fJkiURB8wiiBIEQRCEbiQQRPW/p+NB1KEXxQbEHSCm8wRBEAShO/LLIHVgHMQvxlA6Smz7IgiCIAiC0A5iJEoQBEEQuqNOKnEgtJ8IogRBEAShW+pgEIUIojpKTOd1saZllTqdjvT0dGbMmEFxcXG0u9Wljh07xk033UR2djZ6vZ6+ffsyb9483G53tLvW5RYsWMCECRMwGAzNVqGcbl599VWys7PR6XSMHj2a//znP9HuUpf77rvvuPzyy8nIyECSJD755JNod6nLLVq0iHPOOQeTyURKSgpXXXUVeXl50e5Wl3vttdcYPnx4oAhlTk4OX375ZbS7JZyCRBDVxSZNmsT7779PXl4eH330EYcPH+baa6+Ndre61MGDB/H7/Sxfvpx9+/bx4osvsmzZMh555JFod63Lud1upk6dyu233x7trnSZ9957j7lz5/Loo4+ya9cufvnLX3LJJZdQUFAQ7a51KYfDwdlnn83SpUuj3ZWT5ttvv+XOO+9k8+bNrF+/Hq/Xy+TJk3E4HNHuWpfq2bMnf/rTn9i+fTvbt2/nggsu4Morr2Tfvn3R7lpzTdN5HXkJHSJKHJxka9as4aqrrsLlcqFWq6PdnZPmueee47XXXuPIkSPR7spJsWrVKubOnUt1dXW0u9Lpxo0bx6hRo3jttdcCxwYPHsxVV13FokWLotizk0eSJD7++GOuuuqqaHflpCovLyclJYVvv/2W8847L9rdOakSEhJ47rnnuOmmm6Ldlf+VOOg1B5WiAyUO/C7+dXypKHHQAWIk6iSqqqri7bffZsKECWdUAAVgs9lISEiIdjeEDnK73ezYsYPJkyc3Oz558mQ2btwYpV4JJ4vNZgM4o76XfT4f7777Lg6Hg5ycnGh3RzjFiCDqJHjooYeIiYkhMTGRgoICPv3002h36aQ6fPgwr7zyCrfddlu0uyJ0UEVFBT6fr8UmnampqVgslij1SjgZZFnm3nvv5dxzz21WQfp0tWfPHoxGI1qtlttuu42PP/6YIUOGRLtbzcn+jr+EDhFBVDvMnz8fSZLCvrZv3x5o/8ADD7Br1y7WrVuHUqnkxhtvpDvOokb63ADFxcVMmTKFqVOncvPNN0ep5x3Tnuc+3UlS811PZVlucUw4vcyZM4fdu3fz97//PdpdOSkGDhxIbm4umzdv5vbbb2fmzJns378/2t1qTuRERZ0ocdAOc+bMYdq0aWHb9O7dO/D/TTtfDxgwgMGDB5OZmcnmzZu73dBwpM9dXFzMpEmTyMnJYcWKFV3cu64T6XOfzpKSklAqlS1GncrKylqMTgmnj7vuuos1a9bw3Xff0bNnz2h356TQaDT069cPgDFjxrBt2zZefvnlwIa6ggAiiGqXpqCoPZpGoFwuV2d26aSI5LlPnDjBpEmTGD16NCtXrkSh6L6Dnh35fJ9uNBoNo0ePZv369Vx99dWB4+vXr+fKK6+MYs+EriDLMnfddRcff/wxGzZsIDs7O9pdihpZlk+9n9t+mQ7VehLbvnSYCKK60NatW9m6dSvnnnsu8fHxHDlyhCeeeIK+fft2u1GoSBQXFzNx4kSysrJYsmQJ5eXlgffS0tKi2LOuV1BQQFVVFQUFBfh8PnJzcwHo168fRqMxup3rJPfeey8zZsxgzJgxgVHGgoKC0z7nrba2lvz8/MDHR48eJTc3l4SEBLKysqLYs65z55138s477/Dpp59iMpkCI5Bmsxm9Xh/l3nWdRx55hEsuuYTMzExqamp499132bBhA2vXro1215oTFcujTgRRXUiv1/OPf/yDefPm4XA4SE9PZ8qUKbz77rtote1flnqqW7duHfn5+eTn57cY+u+OuWCReOKJJ1i9enXg45EjRwLwzTffMHHixCj1qnNdf/31VFZW8tRTT1FSUsLQoUP54osv6NWrV7S71qW2b9/OpEmTAh/fe++9AMycOZNVq1ZFqVddq6mMxc+/dleuXMmsWbNOfodOktLSUmbMmEFJSQlms5nhw4ezdu1aLrroomh3rTmZDgZRndaTM5aoEyUIgiAI3UigTlT6ragUmnZfx+t386+S5aJOVAeIkShBEARB6I7EdF7UiSBKEARBELojvx/oQK0nv6gT1VHdd8mUIAiCIAhCFImRKEEQBEHojsR0XtSJIEoQBEEQuiMRREWdmM4TBEEQBEFoBzESJQiCIAjdkahYHnViJEoQBEHo1r777jsuv/xyMjIykCSJTz75pMvveeLECX73u9+RmJiIwWBgxIgR7Nixo8vv+1Oy7O/wS+gYEUQJgiAI3ZrD4eDss89m6dKlJ+V+VquVX/ziF6jVar788kv279/P888/T1xc3Em5v3DqENN5giAIQrd2ySWXcMkll4R83+1289hjj/H2229TXV3N0KFDWbx4cbu3Ylq8eDGZmZmsXLkycKx3797tulaHyHLHpuREYnmHiZEoQRDarLy8nLS0NBYuXBg4tmXLFjQaDevWrYtizwQhtN///vd8//33vPvuu+zevZupU6cyZcoUDh061K7rrVmzhjFjxjB16lRSUlIYOXIkr7/+eif3ug2aVud15CV0iAiiBEFos+TkZN58803mz5/P9u3bqa2t5Xe/+x133HEHkydPjnb3BKGFw4cP8/e//50PPviAX/7yl/Tt25f777+fc889t9lIUiSOHDnCa6+9Rv/+/fnqq6+47bbbuPvuu3nrrbc6ufet8Ps7/hI6REznCYIQkUsvvZTZs2dzww03cM4556DT6fjTn/4U7W4JQlA7d+5ElmUGDBjQ7LjL5SIxMRGAY8eOkZ2dHfY6d955ZyDnyu/3M2bMmMCI7MiRI9m3bx+vvfYaN954Yxc8hXCqEkGUIAgRW7JkCUOHDuX9999n+/bt6HS6aHdJEILy+/0olUp27NiBUqls9p7RaASgR48eHDhwIOx14uPjA/+fnp7OkCFDmr0/ePBgPvroo07qdRvJHSxxIKbzOkwEUYIgROzIkSMUFxfj9/s5fvw4w4cPj3aXBCGokSNH4vP5KCsr45e//GXQNmq1mkGDBrX5mr/4xS/Iy8trduzHH3+kV69eHeprpGS/H1lq/5ScKHHQcSKIEgQhIm63mxtuuIHrr7+eQYMGcdNNN7Fnzx5SU1Oj3TXhDFVbW0t+fn7g46NHj5Kbm0tCQgIDBgzghhtu4MYbb+T5559n5MiRVFRU8PXXXzNs2DAuvfTSiO93zz33MGHCBBYuXMh1113H1q1bWbFiBStWrOjMxxK6AUmWxXieIAht98ADD/Dhhx/yww8/YDQamTRpEiaTic8++yzaXRPOUBs2bGDSpEktjs+cOZNVq1bh8Xh45plneOuttzhx4gSJiYnk5OTw5JNPMmzYsHbd87PPPuPhhx/m0KFDZGdnc++99zJ79uyOPkqb2O12zGYzF+ivRyVp2n0dr+zma+d72Gw2YmNjO7GHZw4RRAmC0GYbNmzgoosu4ptvvuHcc88FoKCggOHDh7No0SJuv/32KPdQEE5/gSBKe13HgyjX+yKI6gAxnScIQptNnDgRj8fT7FhWVhbV1dXR6ZAgCEIUiSBKEARBELojWQY6kBwuJqI6TARRgiAIgtANyX4ZWWp/ICSyeTpOVCwXBEEQBEFoBxFECYIgCEJ3JPs7/uoiVquVGTNmYDabMZvNzJgxo9XcSVmWmT9/PhkZGej1eiZOnMi+ffuatVmxYgUTJ04kNjYWSZJaXHPDhg1IkhT0tW3btkC7YO8vW7Ys4ucUQZQgCIIgdEOyX+7wq6tMnz6d3Nxc1q5dy9q1a8nNzWXGjBlhz3n22Wd54YUXWLp0Kdu2bSMtLY2LLrqImpqaQJu6ujqmTJnCI488EvQaEyZMoKSkpNnr5ptvpnfv3owZM6ZZ25UrVzZrN3PmzIifU+RECYIgCEJ3JPvpWGJ514xEHThwgLVr17J582bGjRsHwOuvv05OTg55eXkMHDiwZVdkmZdeeolHH32Ua665BoDVq1eTmprKO++8w6233grA3LlzgYYRp2A0Gg1paWmBjz0eD2vWrGHOnDlIktSsbVxcXLO27SFGogRBEAShG/LiwSt34EVDuRK73d7s5XK5OtSvTZs2YTabAwEUwPjx4zGbzWzcuDHoOUePHsVisTB58uTAMa1Wy/nnnx/ynLZYs2YNFRUVzJo1q8V7c+bMISkpiXPOOYdly5bh90ceVIqRKEEQBEHoRppGW/5r+aLD1zIajWRmZjY7Nm/ePObPn9/ua1osFlJSUlocT0lJwWKxhDwHaLF9VGpqKsePH293X9544w0uvvjiFs/49NNPc+GFF6LX6/n3v//NfffdR0VFBY899lhE1xdBlCAIgiB0IzqdjqNHj+J2uzt8LVmWW0xzabXaoG3nz5/Pk08+GfZ6TcnbP79mqHv93M/fb8s5oRQVFfHVV1/x/vvvt3jvp8HSiBEjAHjqqadEECUIgiAIpzudTodOpzup95wzZw7Tpk0L26Z3797s3r2b0tLSFu+Vl5eH3Ki8KTfJYrGQnp4eOF5WVtbuzc1XrlxJYmIiV1xxRattx48fj91up7S0NKL7iSBKEARBEIRWJSUlkZSU1Gq7nJwcbDYbW7duZezYsQBs2bIFm83GhAkTgp6TnZ1NWloa69evZ+TIkQC43W6+/fZbFi9eHHFfZVlm5cqV3HjjjajV6lbb79q1C51OR1xcXET3EUGUIAiCIAidZvDgwUyZMoXZs2ezfPlyAG655RYuu+yyZivzBg0axKJFi7j66quRJIm5c+eycOFC+vfvT//+/Vm4cCEGg4Hp06cHzrFYLFgsFvLz8wHYs2cPJpOJrKwsEhISAu2+/vprjh49yk033dSif//85z+xWCzk5OSg1+v55ptvePTRR7nllltCTmWGJAuCIAiCIHSiyspK+YYbbpBNJpNsMpnkG264QbZarc3aAPLKlSsDH/v9fnnevHlyWlqarNVq5fPOO0/es2dPs3PmzZsnAy1eP72OLMvyb3/7W3nChAlB+/bll1/KI0aMkI1Go2wwGOShQ4fKL730kuzxeCJ+TqnxQQRBEARBEIQIiDpRgiAIgiAI7SCCKEEQBEEQhHYQQZQgCIIgCEI7iCBKEARBEAShHUQQJQiCIAiC0A4iiBIEQRAEQWgHEUQJgiAIgiC0gwiiBEEQBEEQ2kEEUYIgCIIgCO0ggihBEARBEIR2EEGUIAiCIAhCO/x/Zc77gAbEjUwAAAAASUVORK5CYII=",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"ename": "",
"evalue": "",
"output_type": "error",
"traceback": [
"\u001b[1;31mThe Kernel crashed while executing code in the current cell or a previous cell. \n",
"\u001b[1;31mPlease review the code in the cell(s) to identify a possible cause of the failure. \n",
"\u001b[1;31mClick <a href='https://aka.ms/vscodeJupyterKernelCrash'>here</a> for more info. \n",
"\u001b[1;31mView Jupyter <a href='command:jupyter.viewOutput'>log</a> for further details."
]
}
],
"source": [
"states_x3D = np.zeros((n_levels,*n_pot_steps))\n",
"states_y3D = np.zeros((n_levels,*n_pot_steps))\n",
"states_z3D = np.zeros((n_levels,*n_pot_steps))\n",
"\n",
"for i in range(n_levels):\n",
" states_x3D[i], states_y3D[i], states_z3D[i] = np.meshgrid(states_x[i],states_y[i],states_z[i])\n",
"\n",
"states = states_x3D*states_y3D*states_z3D\n",
"\n",
"# Generate spatial grid\n",
"x = np.linspace(*extend[0], n_pot_steps[0])\n",
"y = np.linspace(*extend[1], n_pot_steps[1])\n",
"z = np.linspace(*extend[2], n_pot_steps[2])\n",
"\n",
"# Compute potential\n",
"pot_x = potential_x(x)\n",
"pot_y = potential_y(y)\n",
"pot_z = potential_z(z)\n",
"\n",
"pot_x3D, pot_y3D, pot_z3D = np.meshgrid(pot_x,pot_y,pot_z)\n",
"pot = pot_x3D*pot_y3D*pot_z3D\n",
"\n",
"state_number = 0\n",
"\n",
"# Create figure and axis\n",
"fig, ax = plt.subplots()\n",
"im = ax.imshow(states[state_number, :, :, 0], extent=[*extend[0], *extend[1]], origin=\"lower\",\n",
" vmin=np.min(states[state_number]), vmax=np.max(states[state_number]))\n",
"\n",
"plt.xlabel(\"x\")\n",
"plt.ylabel(\"y\")\n",
"plt.colorbar(im)\n",
"\n",
"# Initialize contour as None before defining it globally\n",
"contour = None\n",
"\n",
"# Animation update function\n",
"def update(frame):\n",
" global contour # Ensure we're modifying the global variable\n",
"\n",
" im.set_data(states[state_number, :, :, frame]) # Update image data\n",
" ax.set_title(f\"z={z[frame]/si.um:.3f}um\") # Update title\n",
"\n",
" # Remove old contours if they exist\n",
" if contour is not None:\n",
" for c in contour.collections:\n",
" c.remove()\n",
"\n",
" # Redraw contour plot\n",
" contour = ax.contour(pot[:, :, frame], levels=10, colors='white', linewidths=0.7, extent=[*extend[0], *extend[1]])\n",
"\n",
"# Create the first contour plot after defining update()\n",
"contour = ax.contour(pot[:, :, 0], levels=10, colors='white', linewidths=0.7, extent=[*extend[0], *extend[1]])\n",
"\n",
"# Create animation\n",
"frames = n_pot_steps[2] # Number of slices\n",
"ani = animation.FuncAnimation(fig, update, frames=frames, interval=100)\n",
"\n",
"ani.save(f\"animations/state{state_number}_decomp_all.gif\", writer=\"pillow\", fps=frames/5) # Save as GIF\n",
"\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This seems to change the potential significantly and there are two minima in z direction.\n",
"\n",
"## Try to decompose only the y direction (WIP):"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {},
"outputs": [],
"source": [
"n_pot_steps = [200,200,200]\n",
"n_levels = 4\n",
"\n",
"left_cutoff = -0.5*initial_distance-2*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
"right_cutoff = 0.5*initial_distance+2*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
"back_cutoff = -2*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
"front_cutoff = 2*np.max([float(trap.subs(trap.waist_tweezer1)),float(trap.subs(trap.waist_tweezer2))])\n",
"bottom_cutoff = -2*np.max([float(trap.subs(trap.get_tweezer_rayleigh1())),float(trap.subs(trap.get_tweezer_rayleigh2()))])\n",
"top_cutoff = 2*np.max([float(trap.subs(trap.get_tweezer_rayleigh1())),float(trap.subs(trap.get_tweezer_rayleigh2()))])\n",
"\n",
"extend = [(left_cutoff,right_cutoff),\n",
" (back_cutoff,front_cutoff),\n",
" (bottom_cutoff,top_cutoff)]\n",
"\n",
"\n",
"# Solve the hamiltonian numerically in all directions\n",
"energies_xz, states_xz, potential_xz, coords_xz = trap.nstationary_solution(\n",
" [trap.x,trap.z], extend[::2], n_pot_steps[::2], k=n_levels)\n",
"\n",
"energies_y, states_y, potential_y, coords_y = trap.nstationary_solution(\n",
" trap.y, extend[1], n_pot_steps[1], k=n_levels)"
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.colorbar.Colorbar at 0x21f0565daf0>"
]
},
"execution_count": 66,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(states_xz[0],origin=\"lower\")\n",
"plt.colorbar()"
]
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x2238d9d2240>]"
]
},
"execution_count": 68,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(states_y[0])"
]
},
{
"cell_type": "code",
"execution_count": 105,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.colorbar.Colorbar at 0x2241c135430>"
]
},
"execution_count": 105,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"states = np.expand_dims(states_xz, axis=2)\n",
"states = np.repeat(states,n_pot_steps[2],axis=2)\n",
"\n",
"plt.imshow(states[0,:,100,:],origin=\"lower\")\n",
"plt.colorbar()"
]
},
{
"cell_type": "code",
"execution_count": 106,
"metadata": {},
"outputs": [],
"source": [
"states = np.expand_dims(states_xz, axis=2)\n",
"states = np.repeat(states,n_pot_steps[2],axis=2)\n",
"\n",
"for i in range(n_levels):\n",
" for j in range(n_pot_steps[2]):\n",
" states[i,:,j,:] *= states_y[i,j]"
]
},
{
"cell_type": "code",
"execution_count": 112,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.colorbar.Colorbar at 0x2243954b6b0>"
]
},
"execution_count": 112,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.imshow(states[0,100,:,:],origin=\"lower\")\n",
"plt.colorbar()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Generate spatial grid\n",
"x = np.linspace(*extend[0], n_pot_steps[0])\n",
"y = np.linspace(*extend[1], n_pot_steps[1])\n",
"z = np.linspace(*extend[2], n_pot_steps[2])\n",
"\n",
"\n",
"state_number = 0\n",
"\n",
"# Create figure and axis\n",
"fig, ax = plt.subplots()\n",
"im = ax.imshow(states[state_number, :, :, 0], extent=[*extend[0], *extend[1]], origin=\"lower\",\n",
" vmin=np.min(states[state_number]), vmax=np.max(states[state_number]))\n",
"\n",
"plt.xlabel(\"x\")\n",
"plt.ylabel(\"y\")\n",
"plt.colorbar(im)\n",
"\n",
"\n",
"# Animation update function\n",
"def update(frame):\n",
" global contour # Ensure we're modifying the global variable\n",
"\n",
" im.set_data(states[state_number, :, :, frame]) # Update image data\n",
" ax.set_title(f\"z={z[frame]/si.um:.3f}um\") # Update title\n",
"\n",
"\n",
"# Create animation\n",
"frames = n_pot_steps[2] # Number of slices\n",
"ani = animation.FuncAnimation(fig, update, frames=frames, interval=100)\n",
"\n",
"ani.save(f\"animations/state{state_number}_decomp_y.gif\", writer=\"pillow\", fps=frames/5) # Save as GIF\n",
"\n",
"plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [
{
"ename": "TypeError",
"evalue": "_lambdifygenerated() missing 1 required positional argument: 'z'",
"output_type": "error",
"traceback": [
"\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[1;31mTypeError\u001b[0m Traceback (most recent call last)",
"Cell \u001b[1;32mIn[26], line 7\u001b[0m\n\u001b[0;32m 4\u001b[0m z \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39mlinspace(\u001b[38;5;241m*\u001b[39mextend[\u001b[38;5;241m2\u001b[39m], n_pot_steps[\u001b[38;5;241m2\u001b[39m])\n\u001b[0;32m 6\u001b[0m \u001b[38;5;66;03m# Compute potential\u001b[39;00m\n\u001b[1;32m----> 7\u001b[0m pot_x \u001b[38;5;241m=\u001b[39m potential_x(x)\n\u001b[0;32m 8\u001b[0m pot_y \u001b[38;5;241m=\u001b[39m potential_y(y)\n\u001b[0;32m 9\u001b[0m pot_z \u001b[38;5;241m=\u001b[39m potential_z(z)\n",
"\u001b[1;31mTypeError\u001b[0m: _lambdifygenerated() missing 1 required positional argument: 'z'"
]
}
],
"source": [
"# Generate spatial grid\n",
"x = np.linspace(*extend[0], n_pot_steps[0])\n",
"y = np.linspace(*extend[1], n_pot_steps[1])\n",
"z = np.linspace(*extend[2], n_pot_steps[2])\n",
"\n",
"# Compute potential\n",
"pot_x = potential_x(x)\n",
"pot_y = potential_y(y)\n",
"pot_z = potential_z(z)\n",
"\n",
"pot_x3D, pot_y3D, pot_z3D = np.meshgrid(pot_x,pot_y,pot_z)\n",
"pot = pot_x3D*pot_y3D*pot_z3D\n",
"\n",
"state_number = 0\n",
"\n",
"# Create figure and axis\n",
"fig, ax = plt.subplots()\n",
"im = ax.imshow(states[state_number, :, :, 0], extent=[*extend[0], *extend[1]], origin=\"lower\",\n",
" vmin=np.min(states[state_number]), vmax=np.max(states[state_number]))\n",
"\n",
"plt.xlabel(\"x\")\n",
"plt.ylabel(\"y\")\n",
"plt.colorbar(im)\n",
"\n",
"# Initialize contour as None before defining it globally\n",
"contour = None\n",
"\n",
"# Animation update function\n",
"def update(frame):\n",
" global contour # Ensure we're modifying the global variable\n",
"\n",
" im.set_data(states[state_number, :, :, frame]) # Update image data\n",
" ax.set_title(f\"z={z[frame]/si.um:.3f}um\") # Update title\n",
"\n",
" # Remove old contours if they exist\n",
" if contour is not None:\n",
" for c in contour.collections:\n",
" c.remove()\n",
"\n",
" # Redraw contour plot\n",
" contour = ax.contour(pot[:, :, frame], levels=10, colors='white', linewidths=0.7, extent=[*extend[0], *extend[1]])\n",
"\n",
"# Create the first contour plot after defining update()\n",
"contour = ax.contour(pot[:, :, 0], levels=10, colors='white', linewidths=0.7, extent=[*extend[0], *extend[1]])\n",
"\n",
"# Create animation\n",
"frames = n_pot_steps[2] # Number of slices\n",
"ani = animation.FuncAnimation(fig, update, frames=frames, interval=100)\n",
"\n",
"ani.save(f\"animations/state{state_number}_decomp_y.gif\", writer=\"pillow\", fps=frames/5) # Save as GIF\n",
"\n",
"plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "base",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.12.7"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
Reference in New Issue View Git Blame Copy Permalink