phys512/HW1_solutions.ipynb
2023-09-25 12:46:17 -04:00

596 lines
462 KiB
Text

{
"cells": [
{
"cell_type": "markdown",
"id": "51aef09e",
"metadata": {},
"source": [
"# Homework 1 solutions"
]
},
{
"cell_type": "markdown",
"id": "134cf3e5",
"metadata": {},
"source": [
"1. **Long term planetary orbits**"
]
},
{
"cell_type": "markdown",
"id": "19b91861",
"metadata": {},
"source": [
"First write down the equations of the orbit that we need to solve.\n",
"\n",
"The acceleration is\n",
"\n",
"$$a = {GM\\over r^2}$$\n",
"\n",
"towards the Sun, where $M$ is the mass of the Sun and $r$ is the Earth-Sun distance.\n",
"\n",
"A circular orbit has $a = v^2/r$, so the velocity is given by $v^2 = GM/r$. "
]
},
{
"cell_type": "markdown",
"id": "fb8a3016",
"metadata": {},
"source": [
"First compute the orbit and make sure it looks like a circle:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "4caabbe4",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"nsteps = 1000\n",
"Delta E/E = -1.9724690657386198e-05\n"
]
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# Constants\n",
"GM = 1.3271e20 # Gravitational parameter for the Sun (SI units)\n",
"rAU = 1.496e11 # AU = astronomical unit (Earth-Sun distance) in m\n",
"secperyear = 3600*24*365\n",
"\n",
"# Compute the velocity and energy for a circular orbit\n",
"vEarth = np.sqrt(GM / rAU)\n",
"E0 = - 0.5 * GM / rAU\n",
"\n",
"# Initial conditions\n",
"y = 0\n",
"x = rAU\n",
"vx = 0\n",
"vy = vEarth\n",
"\n",
"# Timestep \n",
"dt = 1e-3\n",
"nsteps = int(1.0 / dt)\n",
"dt *= secperyear\n",
"t=0.0\n",
"\n",
"print('nsteps = %d' % (nsteps,))\n",
"\n",
"t_vec = np.zeros(nsteps)\n",
"x_vec = np.zeros(nsteps)\n",
"y_vec = np.zeros(nsteps)\n",
"vx_vec = np.zeros(nsteps)\n",
"vy_vec = np.zeros(nsteps)\n",
"\n",
"for i in range(nsteps):\n",
" \n",
" # compute the acceleration\n",
" rr = np.sqrt(x**2 + y**2)\n",
" ax = - GM * x / rr**3\n",
" ay = - GM * y / rr**3\n",
" \n",
" # take the timestep\n",
" # for semi-implicit Euler (second order), do the velocity update first\n",
" # for explicit Euler (first order), do the position updates before the velocity\n",
" vx = vx + ax * dt\n",
" vy = vy + ay * dt\n",
" x = x + vx * dt\n",
" y = y + vy * dt\n",
"\n",
" t = t + dt\n",
"\n",
" # store the results\n",
" t_vec[i] = t\n",
" x_vec[i] = x\n",
" y_vec[i] = y\n",
" vx_vec[i] = vx\n",
" vy_vec[i] = vy\n",
"\n",
" \n",
"rr = np.sqrt(x_vec**2 + y_vec**2)\n",
"energy = - GM / rr + 0.5 * (vx_vec**2 + vy_vec**2)\n",
"print('Delta E/E = ', np.mean((energy-E0)/E0))\n",
"\n",
"plt.plot(x_vec/rAU, y_vec/rAU)\n",
"plt.show()\n",
"\n",
"plt.clf()\n",
"plt.plot(t_vec/secperyear, (np.sqrt(x_vec**2 + y_vec**2)-rAU)/rAU)\n",
"plt.show()\n",
"\n",
"plt.clf()\n",
"plt.plot(t_vec/secperyear, (np.sqrt(vx_vec**2 + vy_vec**2)-vEarth)/vEarth)\n",
"plt.show()\n",
"\n",
"plt.clf()\n",
"plt.plot(t_vec/secperyear, (energy-E0)/E0)\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"id": "f2bcee48",
"metadata": {},
"source": [
"Now do this for different timesteps"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "fb481046",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[-1. -1.5 -2. -2.5 -3. -3.5 -4. -4.5 -5. -5.5 -6. -6.5 -7. -7.5\n",
" -8. -8.5 -9. ]\n",
"-1.0 10 -0.07183938624734791 5.125999450683594e-05\n",
"-1.5 31 -0.0005620920258684807 5.2928924560546875e-05\n",
"-2.0 100 -2.5277116776878066e-07 0.0001468658447265625\n",
"-2.5 316 -1.0393759622775783e-08 0.0004467964172363281\n",
"-3.0 1000 -2.1997291674745818e-10 0.0010802745819091797\n",
"-3.5 3162 -2.6377522768445045e-11 0.002825021743774414\n",
"-4.0 10000 -2.093522445015285e-12 0.008417129516601562\n",
"-4.5 31622 -2.2576017123215092e-13 0.021621227264404297\n",
"-5.0 100000 -3.8836124694102156e-14 0.057350873947143555\n",
"-5.5 316227 -6.745928926103558e-14 0.1693429946899414\n",
"-6.0 1000000 1.5937593040555416e-13 0.5223250389099121\n",
"-6.5 3162277 2.394670387712458e-13 1.6560380458831787\n",
"-7.0 10000000 -9.946885639645126e-13 5.324723243713379\n",
"-7.5 31622776 -1.84908330723476e-13 16.520429134368896\n",
"-8.0 100000000 6.651862188090161e-13 51.796481132507324\n",
"-8.5 316227766 1.1378043867991797e-12 162.00765204429626\n",
"-9.0 1000000000 -1.0711513838639733e-12 515.1064240932465\n"
]
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import time\n",
"\n",
"def evolve(dt):\n",
" \n",
" # Initial conditions\n",
" y = 0.0\n",
" x = rAU\n",
" vx = 0.0\n",
" vy = vEarth\n",
"\n",
" nsteps = int(10**(0-dt))\n",
" dt = 10.0**dt * secperyear\n",
" \n",
" for i in range(nsteps):\n",
" \n",
" # compute the acceleration\n",
" rr = (x**2 + y**2)**(3/2)\n",
" ax = - GM * x / rr\n",
" ay = - GM * y / rr\n",
" \n",
" # take the timestep\n",
" # for semi-implicit Euler (second order), do the velocity update first\n",
" # for explicit Euler (first order), do the position updates before the velocity\n",
" vx = vx + ax * dt\n",
" vy = vy + ay * dt\n",
"\n",
" x = x + vx * dt\n",
" y = y + vy * dt\n",
"\n",
" energy = - GM / (x**2 + y**2)**0.5 + 0.5 * (vx**2 + vy**2)\n",
" \n",
" return energy, nsteps\n",
"\n",
"# Constants\n",
"GM = 1.3271e20 # Gravitational parameter for the Sun (SI units)\n",
"rAU = 1.496e11 # AU = astronomical unit (Earth-Sun distance) in m\n",
"secperyear = 3600*24*365\n",
"\n",
"# Compute the velocity and energy for a circular orbit\n",
"vEarth = np.sqrt(GM / rAU)\n",
"E0 = - 0.5 * GM / rAU\n",
"\n",
"# The different values of log10 timestep to try\n",
"dt_vals = np.arange(-1,-9.1,-0.5)\n",
"print(dt_vals)\n",
"\n",
"E_vals = np.array([])\n",
"n_vals = np.array([], dtype =np.int_)\n",
"for dt in dt_vals:\n",
" t0 = time.time()\n",
" E, nsteps = evolve(dt)\n",
" t1 = time.time()\n",
" print(dt, nsteps, (E-E0)/E0, t1-t0)\n",
" E_vals = np.append(E_vals, np.abs((E-E0)/E0))\n",
" n_vals = np.append(n_vals, nsteps)\n",
"\n",
"plt.plot(dt_vals, E_vals)\n",
"plt.yscale('log')\n",
"plt.xlabel(r'$\\log_{10}\\Delta t\\ (\\mathrm{yr})$')\n",
"plt.ylabel(r'$\\Delta E/E$')\n",
"plt.show()\n",
"\n",
"plt.clf()\n",
"plt.plot(n_vals, E_vals)\n",
"plt.plot(n_vals, 1e-16 * np.sqrt(n_vals), \":\")\n",
"plt.plot(n_vals, 1/n_vals**2, \":\")\n",
"plt.yscale('log')\n",
"plt.xscale('log')\n",
"plt.xlabel(r'Number of steps')\n",
"plt.ylabel(r'$\\Delta E/E$')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "cc939434",
"metadata": {},
"source": [
"2. **Interpolation and thermodynamics**"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "1170d357",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# First calculate P, S, and F on a coarse grid and make some color\n",
"# maps to show what they look like\n",
"\n",
"import numpy as np\n",
"import scipy.interpolate\n",
"import matplotlib.pyplot as plt\n",
"\n",
"def P(rho, T):\n",
" n = rho / (28*mu)\n",
" return n * kB * T\n",
"\n",
"def S(rho, T):\n",
" n = rho / (28*mu)\n",
" nQ = (28*mu*kB*T/(2*np.pi*hbar**2))**1.5\n",
" return kB * (2.5 - np.log(n/nQ))\n",
"\n",
"def F(rho, T):\n",
" n = rho / (28*mu)\n",
" nQ = (28*mu*kB*T/(2*np.pi*hbar**2))**1.5\n",
" return kB * T * (np.log(n/nQ) - 1.0)\n",
"\n",
"# constants\n",
"mu = 1.66e-27 # kg\n",
"kB = 1.381e-23 # SI\n",
"hbar = 6.626e-34 # SI\n",
"\n",
"# grid in log T and log rho\n",
"Tp = np.linspace(2,3,10)\n",
"rhop = np.linspace(-6,0.0,10)\n",
"Tgrid, rhogrid = np.meshgrid(Tp, rhop, indexing='ij')\n",
"Pgrid = np.log10(P(10**rhogrid, 10**Tgrid))\n",
"Sgrid = S(10**rhogrid, 10**Tgrid)/kB\n",
"Fgrid = F(10**rhogrid, 10**Tgrid)\n",
"\n",
"plt.imshow(Pgrid, aspect='auto', origin='lower', extent=(rhop[0],rhop[-1],Tp[0],Tp[-1]), \n",
" interpolation='none')\n",
"plt.title(r'$\\log_{10}$ Pressure')\n",
"plt.colorbar()\n",
"plt.show()\n",
"\n",
"plt.clf()\n",
"plt.imshow(Sgrid, aspect='auto', origin='lower', extent=(rhop[0],rhop[-1],Tp[0],Tp[-1]), \n",
" interpolation='none')\n",
"plt.title(r'Entropy ($S/k_B$)')\n",
"plt.colorbar()\n",
"plt.show()\n",
"\n",
"plt.clf()\n",
"plt.imshow(Fgrid, aspect='auto', origin='lower', extent=(rhop[0],rhop[-1],Tp[0],Tp[-1]), \n",
" interpolation='none')\n",
"plt.title(r'Free energy')\n",
"plt.colorbar()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "5988543f",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Here we calculate the entropy by differentiating the free energy\n",
"\n",
"Finterp = scipy.interpolate.RectBivariateSpline(Tp,rhop,Fgrid)\n",
"SS = Finterp.partial_derivative(1,0)\n",
"#dSdrho = Sinterp.partial_derivative(0,1)\n",
"\n",
"plt.clf()\n",
"plt.imshow(SS(Tp,rhop)/ (10.0**Tgrid * np.log(10) * kB) * -1.0, aspect='auto', origin='lower', extent=(rhop[0],rhop[-1],Tp[0],Tp[-1]),\n",
" interpolation='none')\n",
"#plt.imshow(Sgrid, aspect='auto', origin='lower', extent=(rhop[0],rhop[-1],Tp[0],Tp[-1]), \n",
"# interpolation='none')\n",
"plt.title(r'Entropy ($S/k_B$)')\n",
"plt.colorbar()\n",
"plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "cc9dc872",
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAhcAAAGzCAYAAACcvDUtAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAACqJElEQVR4nO2deXiU1dn/70kgySRkJvtKSAIEAoR9K7hhXXCpSmttX21F/Vmr74tWa9/WYrVYbUWr1rbW2trXQt/XUq2tS6tWRSoqAsouARJIyL5vM5NlsjAzvz9Sk7m/T+YcJjMkmfT+XFeui5NznmWeeZ6Hk3N/7+9t8ng8HhIEQRAEQQgSYaN9AoIgCIIgjC9kciEIgiAIQlCRyYUgCIIgCEFFJheCIAiCIAQVmVwIgiAIghBUZHIhCIIgCEJQkcmFIAiCIAhBRSYXgiAIgiAEFZlcCIIgCIIQVGRyIQiCIAhCUJHJhSAEgc2bN5PJZPL5s3v3br/29+abb9IDDzxwZk5WEAThDDNhtE9AEMYTDz74IOXm5hp+P336dL/28+abb9LTTz8tEwxBEEISmVwIQhC59NJLacmSJSN6zFOnTpHb7aaIiIgRPa4gCIIvJCwiCCNEeXk5mUwmevzxx+nZZ5+ladOmUWRkJC1dupT27NkzMO7GG2+kp59+moiIhVZwHz//+c8H9nH06FEiIvrnP/9J55xzDsXExFBcXBxdddVVdOzYMXYeDzzwAJlMJioqKqKvfOUrZLFYKDExke68807q7u4eGHfeeefR/Pnzh/wsM2fOpNWrVwf1+giCMH6QlQtBCCJ2u52am5vZ70wmEyUmJg60t2zZQu3t7XTrrbeSyWSin/70p/SlL32JTp48SRMnTqRbb72VamtraevWrfR///d/Qx5n06ZN1N3dTd/85jcpMjKSEhIS6N1336VLL72Upk6dSg888AA5nU566qmn6KyzzqL9+/dTTk4O28dXvvIVysnJoY0bN9Lu3bvpl7/8JbW1tdH//u//EhHR9ddfT7fccgsVFhZSQUHBwHZ79uyh48eP03333RekqyYIwrjDIwhCwGzatMlDREP+REZGejwej6esrMxDRJ7ExERPa2vrwLavvfaah4g8f//73wd+t27dOs9Qj+dn+7BYLJ7GxkbWt2DBAk9KSoqnpaVl4HeHDh3yhIWFedauXTvwuw0bNniIyHPllVey7f/rv/7LQ0SeQ4cOeTwej8dms3mioqI899xzDxv3rW99yxMTE+Pp6Ojw9zIJgvBvgqxcCEIQefrpp2nGjBnsd+Hh4az91a9+leLj4wfa55xzDhERnTx58rSPc/XVV1NycvJAu66ujg4ePEjf+973KCEhYeD38+bNo4suuojefPNNwz7WrVvH2nfccQf9+te/pjfffJPmzZtHVquVrrrqKvrTn/5EGzduJJPJRC6Xi1588UVas2YNxcTEnPb5CoLw74VoLgQhiCxbtowuvPBC9nP++eezMVOmTGHtzyYabW1tp30czEipqKggon4tBDJr1ixqbm6mzs5O9vu8vDzWnjZtGoWFhVF5efnA79auXUuVlZX04YcfEhHRu+++Sw0NDXT99def9rkKwkjywQcf0BVXXEEZGRlkMpno1VdfHRPHO3bsGF155ZVktVopJiaGli5dSpWVlWf03EYTmVwIwgiDKxmf4fF4TnsfZrM5WKczwGeiUW9Wr15Nqamp9PzzzxMR0fPPP09paWl04YUXBv34ghAMOjs7af78+QOi6LFwvNLSUjr77LMpPz+ftm/fTp9++indf//9FBUVNSLnOBpIWEQQxiBD/UevIjs7m4iIiouLDX1FRUWUlJRkCGOcOHGCrYCUlJSQ2+1mws/w8HC67rrraPPmzfToo4/Sq6++SrfccovPCZIgjDaXXnopXXrppT77e3p66Ac/+AH96U9/IpvNRgUFBfToo4/SqlWrzsjxiIh+8IMf0GWXXUY//elPB343bdq0YR0vVJCVC0EYg3w2EbDZbKc1Pj09nRYsWEB/+MMf2DaFhYX0zjvv0GWXXWbYBv/Seuqpp4iIDC/K66+/ntra2ujWW2+ljo4O+vrXv+7HJxGEscXtt99Ou3btohdeeIE+/fRTuuaaa+iSSy6hEydOnJHjud1ueuONN2jGjBm0evVqSklJoeXLl5/xcM1oIysXghBE/vGPf1BRUZHh9ytXrqSwsNOfyy9evJiIiL71rW/R6tWrKTw8nP7jP/5Duc1jjz1Gl156Ka1YsYJuvvnmgVRUq9U6pNNnWVkZXXnllXTJJZfQrl276Pnnn6frrrvO4G2xcOFCKigooJdeeolmzZpFixYtOu3PIQhjicrKStq0aRNVVlZSRkYGERH993//N7311lu0adMmevjhh4N+zMbGRuro6KBHHnmEfvzjH9Ojjz5Kb731Fn3pS1+i9957j84777ygH3NMMNrpKoIwHlClohKRZ9OmTQNppI899phheyLybNiwYaB96tQpzx133OFJTk72mEymgbRU1T48Ho/n3Xff9Zx11lkes9nssVgsniuuuMJz9OhRNuazVNSjR496vvzlL3tiY2M98fHxnttvv93jdDqH3O9Pf/pTDxF5Hn744WFeIUEYeYjI88orrwy0X3/9dQ8ReWJiYtjPhAkTPF/5ylc8Ho/Hc+zYMeWzTESG9Gxfx/N4PJ6amhoPEXmuvfZa9vsrrrjC8x//8R9B/bxjCVm5EIQgcOONN9KNN96oHefxIdrE34eHh9Mvf/lL+uUvf8l+n5OToxR+XnDBBXTBBRfoT5iIkpOT6aWXXjqtsREREWQymehrX/vaaY0XhLFIR0cHhYeH0759+wy6oUmTJhER0dSpUw2utoi3KZ6OpKQkmjBhAs2ePZv9ftasWbRjx47T3k+oIZMLQRCUeDweeu655+i8884zpNEKQiixcOFCcrlc1NjYOOAvg0RERFB+fn7QjhkREUFLly41iK2PHz8+IMQej8jkQhCEIens7KS//e1v9N5779Hhw4fptddeG+1TEgQtHR0dVFJSMtAuKyujgwcPUkJCAs2YMYO+9rWv0dq1a+mJJ56ghQsXUlNTE23bto3mzZtHl19+eVCP99lk/Lvf/S599atfpXPPPZfOP/98euutt+jvf/87bd++PeDPO2YZ3aiMIAgjzWeai6amJuW4z/QdcXFxnnvvvXeEzk4QAuO9994bUidxww03eDwej6e3t9fzwx/+0JOTk+OZOHGiJz093fPFL37R8+mnn56R433Gc88955k+fbonKirKM3/+fM+rr74a4Ccd25g8ntN37nnmmWfomWeeGXDwmzNnDv3whz9U5vi+9NJLdP/991N5eTnl5eXRo48+OmRanCAIgiAI4wO/fC4mT55MjzzyCO3bt4/27t1Ln//85+mqq66iI0eODDl+586ddO2119LNN99MBw4coDVr1tCaNWuosLAwKCcvCIIgCMLYw6+Vi6FISEigxx57jG6++WZD31e/+lXq7Oyk119/feB3n/vc52jBggX0m9/8JpDDCoIgCIIwRhm2oNPlctFLL71EnZ2dtGLFiiHH7Nq1i+6++272u9WrV2udyXp6eqinp2eg7Xa7qbW1lRITE/22RRYEQRD+vfB4PNTe3k4ZGRl+mdf5Q3d3N/X29gZlXxEREeOuzojfk4vDhw/TihUrqLu7myZNmkSvvPKKIX/3M+rr6yk1NZX9LjU1lerr65XH2LhxI/3oRz/y99QEQRAEYYCqqiqaPHly0Pfb3d1NudmTqL7RFZT9paWlUVlZ2biaYPg9uZg5cyYdPHiQ7HY7/eUvf6EbbriB3n//fZ8TjOGwfv16tuJht9tpypQplPHY9ynM3H/xo6zdyn102/mXFG7nH9VlPcU3gAURM+zfaVd/6eE22H/cKR8j+4mO4/vPsNhZu9Zh5adnGoxeddrUFTFj4pzKfu99DYXzpIW1XfH8s0yK71KOj2jjfyn0xrv5/hL6WDsWzvfUvjjl+RmAj9Ob4B563GliyeOlzx0n4lnbncjPHwlrmcjHJwX2101Yc4TP/WFf4swW1u7YmczaPYnqaxPZAn/lwbXtSdJs3+zfX4nRDfwAbXPU92ZUE9+/c47mXm+M9Ot8/CZN/R6ienhvaMbjuqwHt8fxsD/vZ9tdF1jl3Ohafq27MuA5juX/sYa3c1MqlwX6Hbx/Qjvf/6lY9b2F43sm8+fK+x3v7u6mqod+TLGxscp9Dpfe3l6qb3RR2b5sssQGtjLiaHdT7uIK6u3t/feeXERERND06dOJqL/+wZ49e+gXv/gF/fa3vzWMTUtLo4aGBva7hoYGSktLUx4jMjKSIiONL4Uwc9TA5CI8Wn2eYb38Swrr4R/VY1ZPLsKj+UsO92c4Xrdm/wDuf0IM/7zhp3jb+6UR1qOZ6ESrH1Ld5CIMbnD8LOHR/KWB48Mjw6Cfn4/HzF8yeL6eSD8fMPg4eDx/CY/m1x4/H5nVFUHDovjkgsyBvXzCovgEwnt/2BeO9xFcS921we/O32tr2F5DeAQ8Z1Hqe9Nwb0Wrx5uizvDkQvMeIrx3NOMNkwvNfzYm2B97tgP8j0r/HMN7oC9c3d8Lz30v379bd2/B+DB4rvAdT+R/dWF/scSGBTy5GK8EbKLldruZPsKbFStW0LZt2+iuu+4a+N3WrVt9ajR0RFm7fU4qUq3trF1u4w8WriREx/O/eNJgewQDORlxDtaujeN/veM9nWnlKxP+cn7WYMW+9yhPOTYrzsbaVbY4v44VPd2/c3XBX/JdGmdcC6x85Ma3svahPP4lR5/g/0F05fH7LdywUsDPJ6yZ91tm8JUJW+sk5fni/uIT1feKvTmBtRMTO1i7pUV9vKQkvv9m4n99hTXBZCOIdGtWJjyp/NqbGtT/eXcnaya6Hnwx88mCJ40fz0nq42Wl8O+2iviqk6ketk+Hd1edph+p5e+Z3IU1rF1G6odheloTa5fW85UmUwZfmchLb2TtE3UpPvcdlsnfce4as1/9zuX8vnU51Nc+PIs/1zjeZQ0shKD5m2hUcHnc5ArwvFyewP4YGqv4NblYv349XXrppTRlyhRqb2+nLVu20Pbt2+ntt98mIqK1a9dSZmYmbdy4kYiI7rzzTjrvvPPoiSeeoMsvv5xeeOEF2rt3Lz377LPB/ySCIAiCMIK4yUNuXN4bxj7GI35NLhobG2nt2rVUV1dHVquV5s2bR2+//TZddNFFRNRfztZbmbty5UrasmUL3XfffXTvvfdSXl4evfrqq1RQUBDcTyEIgiAII4yb3BToukPgexib+DW5eO6555T9Q/mkX3PNNXTNNdf4dVIjQReKIiEsMjWWC+Pq7WphEIZBOtv4/vliqf9hkuMO38ufuC9/wyBIe2sMa8cmdCrHY1hChwMCzxWw3on76wGBJvZjWCa8WX0+GAbBsEkb+ScCa2uBsIVmPIY13Mn+CT69x6ckOxQjjWEOd4r6WGGN6pALhkEwTEJN/okInSkQx0/ThCH8ZEoqD7lVmRJ8jOwne0Eta1c0QFgD7lVDGATHa8AwyDRNmEQVBkH8DYMgfZowCNIL48PtoLGAsEmvJsRl2D+0o6z8XvEOILmdas2bcOaRwmWCIAiCMAxcHg+5AvOhDHj7sYpMLgRBEARhGIjmwjeSQyMIgiAIQlAJqZWLvspJ5PpX7jamllaV8zi6tYLPmzqy1aKZirYM1q7P5XF0Q+qpjaeeooYjBlJd/dVgfH7KcdZ+r0qdfupNRxvXNKDp1WQ41rEy/tlRY4EajPBWfttEtoK5jcbECjUT7S1xyvG4f5zoRx3nOoHuRC6A0RlHxRXz8TZSazZQk4GaDcP4Ih7nR6MqJw+rU+sxiNsrNBkdH/AYPGososDUqpvUmor4I/xaOFN4G1NLUYMRXY9/han/fsH0Qkw1DVSDUXUonf9Ck1pacZA/C4bxkHpaVpvJ2qjBqP9HFmtnXFrJ2icbkli7ZD8fr8MfHYVOY4FE1fD7ujuTa5uiqqE/S20u56ri76UoB783+izq5zTCDs+NHTQeXkaGpu6R+a/NTR5yycrFkITU5EIQBEEQxgoSFvGNhEUEQRAEQQgqsnIhCIIgCMNAskV8E7KTC12hsA7NR8NiXOFt6vEl5by66/QcXjOlBDQXqLHwF5XGAjUVxdCelctz9avtVmUb0flcdLXy7XUai5FGp7HQaSR09uEIaijw+AYfixao9+Gnnbc/43V23gbfiyM8jo0aC539d1eaupaDs4BrBHT24WjXrdNgVH8KdYt09t1g9631uchQFx4LgyVu5yKudyoFjQVeLbT79oDGY8ZirtkIA9HKcfLtg2HwvZjMz81dzd8jfVBILHUyt1ZvdvDPgqDdN/peIBP91GDg/wGjgftfP4HuYzwiYRFBEARBEILK6E/9BEEQBCEEcQUhWyTQ7ccqMrkQBEEQhGHg8lAQqqIG51zGGiE7uUCNBRJh4xGf3jioTwEaC9RgBBs8Xifx+GdeVglrmxT1hVFjgT4WiN+1QsDHgqAcQwyUZO8sUWs4EEMtEPC9MPhaaEBfi8gWtc8FaiqcLTzubi7mbdxep8FAUCOh04To8NZJoG8Faiiij/KYfddstWYAfS2imsDnws96EP6CmgrUXOg0GFnz61i7qlFdSwQ1GQafCw3oa4GaCvN+/qxmXlbBx0PtEAQ1GFhbRPWe0NYWAY1FTA1/7joz+X3aUM3L16NPhb8aiwgor9SZpfO54O1eK/YPno+rZ2Qi/qK58I1oLgRBEARBCCohu3IhCIIgCKOJm0zkMuT8+L+P8UjITi7MFZCONx9LT/N+DJMgply+ZIh23hjWKCGemmou48dz5vLlaV3q6/aq6azdCcf3Dn1gGARTU49BW2fnbegn3o/j0bNZvfg5hD24xl4biS/my63ORLC0hrBIVIvGghrDIM18vG0mbxvswaEfwxy61FTsRwxhGD9TVb0xN/Bz7U7yb1+YihrVFNhiZ6Cpp9iPGMIgkGpqbgAL6QX8uUfM9TAeUkvLDnD772kLq1m7NG0yb2tKrKP9N4ZFEAx95C8ZDLtU7sllfd38VA2pqJ3E3xuBgqml/oJ232MRt6f/J9B9jEfG/rcnCIIgCEJIEbIrF4IgCIIwmriCEBYJdPuxikwuBEEQBGEYyOTCN+NmcuG08ZS7OBvv74njbdNCnteEGovoOIjFwvZYgr0unpdgnwFlzWvQcptndRlAXYV3SXbcF9p9V9n4yaJmYs5Unj5XCeNRg4G3Pqae6lJLu/J6lP2xeTZ+vif4+bTN0Kk6AsOZhJ/Q41c/orP/7sH0UUVJ9aHw1mBgSfUucH9um8PPNXkOj/E3HeEaAJ3dty4VFTUZhv35qaHISuGW09X1aT5G+gBSTZ1QgR01GYbxGfz65aa2sHYZcXtwTEXV2YWjBgPtvTH1dGYGLztw3MT7j3uNd2eAdgeObf54Emtj6ikSYeXXxg1tcqi/SyzJHmHn7wFMZTU+FRLFDyXGzeRCEARBEEYSt8dEbk+A2SIBbj9WkcmFIAiCIAwDCYv4RtaZBEEQBEEIKiG7cpF6bo2yvzGexxOdoKmYam1n7XrY/uysk8r9n2znsdV0K/psqFkFdt8l7eryxd5kgp4DNRYXTyli7a2mmcr9TQGBCmowsuN53LuCW3JoNRg6UGPhL6hx6EnEETxu7m9JdedMiC2Dz4fOhyIxsYO125q4F0NSEr8XW4/xD5A0u5m1G02D+h60/05J4vdhI3EtUEMT/65SQYPRvp37t6DGAjUYBpr4c2bQYOD+NCXUqxpBnIR236DJQDts9L3IBs1EBRluFg6UPC+rzfQxsB+Dz8UB7nMxbVGVcnvUWCDHoX9GeiNrfz6peODfv665mG8M18a5nN+Xur80XVXcByM8i+vCls7i78z99jzl/tDuG+3CJ2ZDmYJPY5X767UO7s/dPTKm2i4KI1eAf6O79ENCkpCdXAiCIAjCaOIJgubCI5oLQRAEQRA+QzQXvgmpycVERxiF/6vaXdUhzCnjoN13OFRFPUl8eRFTT3dUTWVtTFWNiefjO9vU/QjafU+G0ASmm3pbfOuqoG6t4mGQLghbVEJYw2DvDRzVhD3iS/jD4dDYexvswBPcyv4EsP/uSsJlSPWyJNp7U7E6jIH23v5WQUV775YWHqLDs8UwCNLYzEMbYY2+z183FqumYpgkUAPo6HpYek/l94a5ET59I39uuubx50Zr9w053SZ8T0OqaUWdpuppuibsA6mlWPXUkIoKoL33dAiTeCAME13Lr9eUK8tYu2hvNmsfzxx8r+mqoCIuC3/OLMf4fd/9OR5GwTDJIeIhI539N/ZjgdfeCngvWfl7Au3BI2xe5zZCVVEF34TU5EIQBEEQxgouTxi5PAFqLsZpbRGZXAiCIAjCMHCTidwBCjrdGlO+UEXWjgRBEARBCCqhtXJR4CCK7o8Zu8DuOyebp9ShJgNLnl9YcIy1d1bnsDbae+dNKWXtEw5u2xsG6aF5Fn4+CG7/pfQDfABISsJpMN74411fYH1XzT/I2gtiuIXwz+gC1l4NqapvUz5rY2pqVUIcqXBM57HZmOn8WmCqqs4OHPvJo7GchhLr9hlYEp2Px1RUczHfv3UmT1e0F/N0RrTrxlRUZ76mTDZsj6mozc3qlDvv1FTUWJw/4zhrv0czlPsKlPRk/l3b0kB7VMe/i5Z5/v2VprMLR43FF2cdZO1XaIH6AGj/jYF/jX13xqWVyv6TxDUYWGI9DI6H9t+0mDcxFdW7xDrur6iWpxXfeek/WPtnH/FU1YkWsD5fztuJFp4aWm/l1w5N+tHuOzOLP1f1hfyzTJjC9z8RvttuOz+eM47391oH/zsbuVRUEXT6IrQmF4IgCIIwRgiO5kLCIoIgCIIgCFpk5UIQBEEQhkG/oDPAwmUSFhl9+ionkSuqX2threCLLuXENQy6It3vfTiXtXMXqu3EUSOBoC+FocS6hkKr2lbYO5aKGovjDh67/GeV2nb37cp8Zf+Rk3AuEBe2aHw2HG08/z0afCu6NI7LqMFATQWCGgv0mUB7cNRYIG0tXPMQ6PLeyjxui1z03Cw+4Etcc6Gj+ehgHB/P7Wgyj7PrfC7QLhtBu29zIddU1CeDnXcB+FR4+PiMudxov/YwP1/UVEyex8cbfC3gfF/553LWzppfx7fX+OOg3TeC7wn0tZiWyq3a0beiFN5TeWDffXzfFNZGrwrEoMHwKsnuruHXflsGf+5TJ3Pr9IZqfm3DHfAWtXJNRARoNJKs3AejBe6tmir+4OM7uscO1x62N1eAtimb38vevhcj5XPhDoL9t7/ZIjk5OVRRUWH4/X/913/R008/bfj95s2b6aabbmK/i4yMpO5utZ4oUEJqciEIgiAI/87s2bOHXK5Bw7PCwkK66KKL6JprrvG5jcVioeLiwbozJoPbXPCRyYUgCIIgDIPREHQmJ/PVr0ceeYSmTZtG5513ns9tTCYTpaWlDev8hktITS5c1lPkMfenlPbm8CWdqZA6Wm9Xp/P1tKn7p8by5U2sgoqppnV2nhKIYCVTXI7G0AaSbx1c7tSN1WFIRYUwydxpvLJjRRtUpgR0VVDR3lsH7q87kS+VY5jDX7DKqc7eW5d6agjDQKXSJUvKWXvnudxaHg2jz5t5grWPtfLQgXelU6yCelPOLtZ+pOkS1k6F1FFMZe1O5tc2DcbXF5BfOFP4/rqa4lgb/37SVUnVgWEQTPXMXlDL2hUNEKPThInCYAkbwyCICVJZMRUVq6DieH/xTj8Nm8zDl0fr+H3U54BUUgyDAJmT4F6o5inaeCV6Yf+GVFQ7vMfg2ofb+H9PvVb1cz8aVVHdFBY0Ey2Hgz/LkZGRFBmpDuH29vbS888/T3fffbdyNaKjo4Oys7PJ7XbTokWL6OGHH6Y5c+YEdN46JFtEEARBEIaBy2MKyg8RUVZWFlmt1oGfjRs3ao//6quvks1moxtvvNHnmJkzZ9Lvf/97eu211+j5558nt9tNK1eupOrqap/bBIOQWrkQBEEQhPFIVVUVWSyDK4m6VQsioueee44uvfRSysjwXZBvxYoVtGLFioH2ypUradasWfTb3/6WHnroocBOWoFMLgRBEARhGLiCkC3i+ldYxGKxsMmFjoqKCnr33Xfp5Zdf9ut4EydOpIULF1JJSYlf2/lLSE0uwu0TKKznX6ccx/tOVvD4XXib+qOhHXhJOY9HlhBvYwl11FigpkKXmqpLAUS8Y8dVtjjW1wGpn7EJPGUMOebgwh4sua4rsY6pqJg6iiXTkR5NSXbcH5ZcR7AEezeE0eOKeSzS2aL+i0B3fqix0PGrf3DdA4GGo+tDLtD6MIl/AEwf9bb4fn8HF0FsMq0gFVhiHe/DhEJ+rexN/F4xgSYjqolfC7T7RrqgxLqhHzRn1Z/yXyQf5P3NC2AHEMZvfHsyazsXQGon2n9rKK3l+9PZg2Nqa0ktL7mOGgvzXv4sdy9VP8sqsMR6wVJerv2Qg6e9Ysn1CCvXv+wrymXtcDvXaPRSpLIfNRZYMh3tvF1x/B2NGgzrIa5tYtuOVCqqJ4zcAQo63cN06Ny0aROlpKTQ5Zdf7td2LpeLDh8+TJdddtmwjnu6iOZCEARBEEIIt9tNmzZtohtuuIEmTOCTrrVr19L69esH2g8++CC98847dPLkSdq/fz99/etfp4qKCvrGN75xRs8xpFYuBEEQBGGsEMywiD+8++67VFlZSf/v//0/Q19lZSWFhQ2eU1tbG91yyy1UX19P8fHxtHjxYtq5cyfNnj07oPPWIZMLQRAEQRgGbqKBbI9A9uEvF198MXl8hFO2b9/O2k8++SQ9+eSTwzhKYITU5IL5XJRPYn0XnnOYtT/6+3zWNi3kmoieMu5zEZnLLZj9NTA7Xs5jwzNy6n2M7KfWodZsIKiz8EansUBNxSzwuThC3O4bNRZfWbCPtVGzUdrKfTB0vhY6X4zo4zx225XEH6LoZr5/o/03//JazwKfCvC10Gko0OciOp/bHLcV8Xx/3fZI9Dnc+6AL7cfBwtu7jHrqHL4torP/1uEsUNtPd0OcPWUf/26bFsF3OY/vL/pTtQYDfS8602F8Ot8f2ntnrwbPloNcVZ+8n+9u0s3c3rvsgNqWHzG8NkBTgXbgSFcGv7fxzpyBduF1vj1v0OeivlPt7YM+F70m/t2lTW7l+yN+30da+WftIfVnxTsRNRWouUA6sn2/Z0bK50LwTUhNLgRBEARhrBAcE63xKX2UyYUgCIIgDIPg2H+Pz8nF+PxUgiAIgiCMGiG1chFl7abwf6VuOyGed7KdewOgxgJBjUUG1CZB34vpOQ2sjTUG1AXb/fe18K4lQuRfCfcpcTbWroR+1Ewg8R/zOP1b8bxEeG48j70iqKlA3wps6+hOBO+FGbxtPc7b6HOBuJP4+aGvha5WCMH+dZqKpCR+rzU3q2PfiD86CfSxwL8e0lNsrF0P41sL+H1qalD7QGBJ9s4M/lxibREsqa5DNz4rBe5FkCCgxoLS+fmiJqTjH9yHIvfSKtY2aDBAQ4FP+fRFfPuwdD4Ca4voUGksEPS5aAWLDtRYoM9FoKDPRVoB14u0VvL3ENYO0WkwsH80cJOJ3Ealjd/7GI+M/rcjCIIgCCGIhEV8I5MLQRAEQRgGwfG5kMnFqJNi6aAJMf1L2lWQiopgqinafUfHqVPs/nD+/7D2Q2VXsPY0Cy8wjCXYt1dNZ20Mi5yfxctqI0V2Hpa5YMqg5XM4ZEa/fGgRa8/MKlbuG7FAKmvbcr6cim73ZW08BQ1TT+Ngf+0tcayNYRMcb4LU0p5d6jhH20p1qqm5mC99Y8l1JPos/t06W9T3WmIiT03F7zo/gYe4dh7jnycsmY/HMuoqMAxywUz47mfy5j+Pz6BAwKXtOjh+88U8HRFTTTEVlTR24JPn8ZTu6iae9lzVCGnAYOdtbgCLaVKHWZyLePpmGZZkR7tvCIugnXdpPbd2z4NUUmwfr+WW3Jh6+vkk/v3+5vA5rD07Y/B6HTXxd0iChX82DJO42vm1ibDw5+TctFLW3gH3eVasjbWrLXGsPSW2jbVrsvl3FwV24912+C7j+LXF0PhYCJMIg8i3IQiCIAjDwO0xkTtQE60Atx+ryORCEARBEIaBOwhhkfHqczE+P5UgCIIgCKNGyK5c/Ncl77D2sU5u+1ufyzUXaVaeDogl2qdmnWRt1FisST8Ix+MpbiccPLa6KquEtcNMajvaMIhfFpfzzxOWO9hfDWmpX5rPPYy3VvFAO9p/fxnsvFXW4kRE2fE8VlrRxuPeqKGwwfFIY/eN2Fq5xkEdlTdqLHTo7L9bQGMR1qRORUWNBaaacrN1Y+rqLNBkLLGUs/b/lS9n7cbmQRVMajJPuS5s5el9qMm4KP8Ya79bnE8qsKQ6oktVxVRUBDUYmHpaXQ9p05BKaj7I744UtPtGzQSCGo39XG+UcSlP5C5tSOLb60quA5h6ipoLpGhvNmuHLeX3mruGf37UWXiTMYnfKw3V/DnGEuu9Dn5tyjr5tWy2q7VILQ7+HmiGNmosEOzHkg8EqakROYPaJ1eXf9/LcAlOyfXx+Td+yE4uBEEQBGE0cZGJXAH6VAS6/VhlfE6ZBEEQBEEYNWTlQhAEQRCGgYRFfBNSk4vKqiQKM/fnNv/P+5ewPmeu2iL5pE0duT/ZzmOpaP/9N+Il3LHEekw8jx2jXbfO/vuu/H+y9mu0gLW9dREdbTwuvJXUGgvkLwcXs3Z0CdcU8L0THYaS7GjfnXAC7Lnz1J81spU/TO0JfH/4qCUUc1viriQ+Ai+tbSb/ReIxHpttmcVv+8Sj0A/58858Hr/VaTLw/PNncE3FDtBkHGvl99r7x/NYG30voo8Onl9TEj92MpRgjz7CP8u7Jq6xMBfy5yK6nl+7LpA8oK9FdKP6xYj7a4b96UquGzQbdWqNR+cmroUyZ/DzS9vNn9Oyq5S7o9IDk5X90XXgo7GYe0noSqyfQL9yALVlv37rYuX4O+a+P/Dvn33Exx5w5LD2RPCxCDvC7+twC7/2h2r4ewA1GS3wIJoK+X3eZ/GvDDrafZvtcK/Z+b0fcWiw7eoBndQZwkWBhzWCa7o+dhifUyZBEARBEEaNkFq5EARBEISxgoRFfBOykwusejpVk2rqL5fOK2TtUgcPm1w+7zBro903kmlVV2n9edHnWXtWbq3PsdWw/Kirgopg2ATtuzFs4W8VU9we949tY1VT3u5K4p/XDvbgmEoa2cK3b5kF55PIj197Dj7cvB/DHvH5vBJnWxNYUANFEPbA/c2aycMm3qmmQ7XDknwvL2PqaVIDv1bOAoI2DxN0J/Ol7qgmfi0x9dQYRoFrP4/3YxhEl6qK9t2pe3iIqvwL/FqmfYJVWvnxyv6Tn495v/rFPvUVfrz6z/GgYVc6VH1V7s0YRunOhFBCJv8+trdwu/bZS8tZ++ieHNZ+6vB5A//GsAfafzcf5e+0vix1yrgLwiCRVnW6J4ZBXFYeAMCqqROzeRkAquDvKayaimGTXuvgf2fubv9CMMNFCpf5xq9PtXHjRlq6dCnFxsZSSkoKrVmzhoqL9XUsfv7zn9PMmTPJbDZTVlYWffvb36bu7pHJQxYEQRCEM4HnXyXXA/nxSCoq0fvvv0/r1q2j3bt309atW6mvr48uvvhi6uzs9LnNli1b6Pvf/z5t2LCBjh07Rs899xy9+OKLdO+99wZ88oIgCIIgjD38Cou89dZbrL1582ZKSUmhffv20bnnnjvkNjt37qSzzjqLrrvuOiIiysnJoWuvvZY+/vjjYZ6yIAiCIIw+EhbxTUCaC7u9X0eQkOA75rxy5Up6/vnn6ZNPPqFly5bRyZMn6c0336Trr7/e5zY9PT3U0zMYL3Q4+lPxcqY00YSY/rjf1NgW5bmdhBSvi+ceYe2CGK5p+Fv9POX+fpj7N9b+U8sK1kZNxdUZ3JL75bqFrD3Dwm1/r0nnltx/redl1GdZeOlpf0BNxpxsbgF9zMHzAw+f5Cln86dyS2WkkHJZ25WoTgtGDQdqKIiwjQ+fOtUViVrJS6j3FPP71aChKFL3Yypq0iz1vYh24Cmzm32M7CeskesIzjub63+OJg9qOFBjgXbgYf/BrxVkglI9bO9JhbLXmhLlWGId7bsR1Fh40tQW0FgivWEpT+00c7kKue/n34XzIE9N1eFM4+d3ch0MqOX9N168nbX/UPg51sYS7E44HVwQRztvgvFFtVy/U7C0jHxR3xnrs4+IKDyLazAWZPB3IpYkQLC/uj2OtZt59XjKsHawdu1h/llSQTdH83i70aG2G/cuwe52nlKMDB5SFdU3w55cuN1uuuuuu+iss86igoICn+Ouu+46am5uprPPPps8Hg+dOnWKbrvtNmVYZOPGjfSjH/1ouKcmCIIgCMIoMuz1mHXr1lFhYSG98MILynHbt2+nhx9+mH7961/T/v376eWXX6Y33niDHnroIZ/brF+/nux2+8BPVVXVcE9TEARBEM4Irn+VXA/0ZzwyrJWL22+/nV5//XX64IMPaPJktYPd/fffT9dffz194xvfICKiuXPnUmdnJ33zm9+kH/zgBxQWZrywkZGRFBmpXl4VBEEQhNFEwiK+8Wty4fF46I477qBXXnmFtm/fTrm5udpturq6DBOI8PDwgf0Nl5PtvPwvajCi43i++LYPuH33jtyprJ0Rxy2WkQfLrmRttPfubOOx0pdNXGOBvFfFLZ7fI97OAp2Edxl19KmITeDZOgbfCyipriuxjpqIwhbUVPB8+GjwtaBW9cQQfS4sM3hJd8dxXgoaQV8Lc7P6PrKBxgK37/qI5/u7we4bNRiosUBNRVISjxWfPaOEtXecUHuiIO8dn+GzDzUWqMFA/QZqKhD0sUg4zF98zlRoazQZZrAHR82Fwf4bvsrUvfy7aFgC1uwL+HNeodNYgB03aizM9fx8J+3j45u4cz5tfmcVa6PGwryP+2JMqubHa17Dzz8MfC5QY5GfwUUmhXv4sxk2mesovEGfC2RfEd9XRhbc51BiHe2/db4XSATaeQOoscCS67h9uJcPhqk7ZC2cxg1+fQPr1q2jLVu20GuvvUaxsbFUX98vMrRarWQ2978k1q5dS5mZmbRx40YiIrriiivoZz/7GS1cuJCWL19OJSUldP/999MVV1wxMMkQBEEQhFDDTWHkDjCsEej2YxW/JhfPPPMMERGtWrWK/X7Tpk104403EhFRZWUlW6m47777yGQy0X333Uc1NTWUnJxMV1xxBf3kJz8J7MwFQRAEYRRxeUzkCjCsEej2YxW/wyI6tm/fzg8wYQJt2LCBNmzY4NeJDUWDI5bCT52eFqMLq6DGn1L3Q1jkg6pprL0qiy9tIzXQLtmfxdrmaeqwywVTjrP2tkq+FO5dVRXDIBgmOQLt8Fb+NWNYA9GtJ0Wf8E8PY7AXh7BEzy4e4iKw504o4rbBTqiKilVQcf9xYCLbehbYIu/goYOeRN7G/QWKd1VTIqLG2bwfU1XR/tsbDIMg/oZBopogZAS5q93JEEaAsAfagZPhneHftcQwCNp/N5CmqmqqOuyhA8MgOrAKKtqDd6Xz8fnpPCW9aG82a0fX8vM9mpHD2hgG8Q59oL03zeZjMawRAXbhGAZZOJmnpO/dxd9RSVn8vVRfyO0AquL48fCbq6iE8wUMVVHh1oqwDfa7esbnakAoIYEpQRAEQRgGIuj0jUwuBEEQBGEYeIJQFdUjDp2CIAiCIHyGi0zkCrDwWKDbj1VCanKRammnCTH91tL1drW1LaaiYqppnd2ibJ+bVTrc0yQioumLAjP+unhKkc++4naenkaQeoqETePByYo2daqng3j6nCWex2o7S9RxfkOq6nEea8WS5+4ktQakNV+9vQ5nEn94EyFVtC2fp5q6k7l9+cKVJ1l75wmexoy0HuMakvCzuXV712yuGzhvxgnWPgYl2s+fwfU4qtTU9BQbazdA3Pvi8w6y9jsNC1gbNRWo2UCNhrFkOmgw6qAk+zz+XKJdOJZYR7DEOqXz/VEd7A80Fph6SpA6iqmqWCLduVidzpkHGooTdfz6oybjOPRjKmrOUp56iiXWkVbH4LObBNqdtnb+XKdN5rb29dW+yzgQEVWBvXdaAf+sU2J5SnlLNtd+ZVi4/XcV8eckewpojdDuO45/V5ia6vLS1bmd6hIEwpknpCYXgiAIgjBWcHsC10y4h2/3NKaRyYUgCIIgDAN3EDQXgW4/Vhmfn0oQBEEQhFHD5AnEg3uEcDgcZLVaKe/571N49Ol5LPSUcU2GC3wuwtv4ok3UVB6HRztvHZMSeCy2o43HN9FrAn0vdOOjp3ObZ2/Q5wKJLgEfhwT/NAs6IsH+O6qF31LmZn48rOTcOpM7a6CvhbkBylan8ri1CW7h2rP5+WTsAK+BJH48ZzJf1tRpOgz24438+K3ncp1CSjJ81x/wOHt3Ej9eVDN4TYBGw9snA7dF0LcCNRXYrwO3T/xUvSQ8qYbHvhsX8+c3BkqYd6b7dz64PaKpGm7wSujI5MfH7SfV8OPheAR9LtC3oisjsGcRfS7Cjw3qELozuZYp3KF2sJnoUH+W7iyNP46d798VB+9cG3+noX23M5vfK9ZD/L0V1cavVU+c7/N19XbTkd/eS3a7nSwW3z4xw+Wz/5Ouf+9aipgUod9AQW9HL/3f+X867XN94IEHDFXDZ86cSUVFvnV6L730Et1///1UXl5OeXl59Oijj9Jll10W0HnrkJULQRAEQRgGnzl0BvrjL3PmzKG6urqBnx07dvgcu3PnTrr22mvp5ptvpgMHDtCaNWtozZo1VFhYGMhH1yKTC0EQBEEIISZMmEBpaWkDP0lJvt1Nf/GLX9All1xC3/3ud2nWrFn00EMP0aJFi+hXv/rVGT1HmVwIgiAIwjD4TNAZ6A9Rf6jF+6enx7d1/4kTJygjI4OmTp1KX/va16iystLn2F27dtGFF17Ifrd69WratWtXcC6CD0I2WyTN2q7sr4dq8Gdnca+Cdw7PUW4/I4d7ExwvT/Mxsh/UTEwCb4jMHK6ZwNojlMDjk8hk6+D2x8rUZaUNtUfyeOAYS6ojqKHQgRqL7kS+zNedwGOxRp8L/hC1QhlvcxK/tkh0E9dooCai9mzcAgPx6tokeL4xZzexNvpahDXxGGyjicdRw0An4U7hseYuLskwlE1X6SzQlyK6EEqMF8ALq4lri7A2CGoOTKBsx9oj6GuBlzplLz9+Z4b6XsRaIh2Z/Fo0L1RubiyhrtFooKbCWFskuBqLYGswvHUWqLFwWV04XEl4Fn+HRcLN0GPn9xb6XtSAb8bEbP5ectrhOQcfC/t8fj69FaBtgHurN27w2rm7g6sr84WbgmD//S8Traws/n/Chg0b6IEHHjCMX758OW3evJlmzpxJdXV19KMf/YjOOeccKiwspNhYo/9TfX09paZy75zU1NSBquZnipCdXAiCIAjCeKGqqooJOiMjh05euPTSSwf+PW/ePFq+fDllZ2fTn//8Z7r55pvP+HmeLjK5EARBEIRh4CHTwMpDIPsgIrJYLMPKbImLi6MZM2ZQScnQlbvT0tKooYE7vTY0NFBamno1PlBCanLhbf99soKvHU/N5ktyaPeNYZCYeG6zm2nlYQsMg2CYpMbOLbBNmpw3HI9gGCUr18ba1ZrtVWCJdF0qamQr/yyO6byN9t5deXz7hN18+dKeF1i2M6ayYsn1lln8NsYwRlwRf/hbz1GXIaeWKGV3czMsPYJdOIZFdGDYA8Mk2FZti/bcrQXqa4+ppSkHeHiuaYH6sxhKrAMYxkBa5kPaMn8HGrbvzODffdIBfv4YJnEu4s/VpBr1d4uppdF1vB/DHjp0YZDupTxUQDXqFHhMPe1z+E7Nx7GudnUaP4ZNJsA7LcnCz7UGwiJo/11DajtxxGnj+8PU1V4rv5beJdaxPVIl18dCVdSOjg4qLS2l66+/fsj+FStW0LZt2+iuu+4a+N3WrVtpxYoVAR1Xhwg6BUEQBGEYBFPQebr893//N73//vtUXl5OO3fupC9+8YsUHh5O1157LRERrV27ltavXz8w/s4776S33nqLnnjiCSoqKqIHHniA9u7dS7fffntQrwUSUisXgiAIgvDvTHV1NV177bXU0tJCycnJdPbZZ9Pu3bspOTmZiIgqKyspLGxwwrJy5UrasmUL3XfffXTvvfdSXl4evfrqq1RQUHBGz1MmF4IgCIIwDEYjLPLCCy8o+7dv32743TXXXEPXXHONX8cJlJCaXDQ4Yin8VH/cEEuqh0F8sNbGhTFo991JPLZZA8dCTQZqMLDfWcqP54LUUrTz1uGPxgL33dXKt3XlqTUGmJqqtUwGMl/nx3eCnwumdiI9xI9vsA+v5ylqdWfx7y6umO8v8Zja7ttcpI67O/P58VBDgW0s0Y7oNBXYn5rM9T8NTfz7xPEqDPbekHqKmovGhXzfMZhaqmFSLf9sHRl8f11p/EVqbuDtmDq1piHtE/7c1S/jn8eM2XX1PI25aTHf/9RX+HfdmcHHG0qs16rvHST1E95uWAafDzQWWk0GoLL0Nh/lJckTV3NBi20XT090z+El0U2FXFtUb+FlBiKn8HPbdXQ6PzewAyer5j2ksQdHzUWkjW/fE6fc/RnBHQRBZ6Dbj1VEcyEIgiAIQlAJqZULQRAEQRgrjIVskbGKTC4EQRAEYRjI5MI3ITW58Pa5qLfzeGBJeepQmwwQ42dJdexHn4tah1pjgej60SdDV0bdH+I/5nFv9K1A0L7blcjj6KjRaJsJdtngo2E9rt6/UZPBz8+ZxuPcWEIdQd8LcxPfX+JR/l3UnsOPj5oKnR14wgfcP6AbSrhjyfSUJO7B0tzIRSpNR5L5+RDHW0ehK6Ee3QDl4MH3AsenHODfdWea2p4bS6rr+lvm8/2ZG9SRWfS1IFKXbEefC7T/RupWcI1F+k6uI6gn/55Dg0aD+L2r1VTU8uOZP+Htzkz1vR9TM7j/zslQzh7uK7Lwfhd4ZoRb/PP0yJrSzNpVVdwW34V232jnPZ8/F+h7YS7n49tzfJ/fSNl/C74JqcmFIAiCIIwVZOXCNzK5EARBEIRhIJML34TU5MI7FVWHLvVU148YqqLC/WAu5Ut2vfHqZbmUPbzdcS1vq1JXI9r40qoudbQHXHgxzIH24JgKGtUCVTkT1Q9D+k5Yip+pSUVNxGsFS8eJvtPthgLDILZ8CLMk82sb2aI7Hw6mnnY38+VbrFqKqaMYBolqPnNJW12p/LvypPIQDaamkptfK0wdRSZhDjfci2jfnXQQb1bNMr+mimnzZZDeWMfvZayC6lzEP/+kffy7q1/BwxBYJbVxCT8cPsdOqKLasAzPWJ2K6m9V1Int/N5xzPKy5oevzpAaCkRV8ZBVH4ZNwB484jAPTVdln9672SeHeKgZ38iYeqpKdhwp+2/BNyE1uRAEQRCEsYKHAvepCKzy0thFJheCIAiCMAwkLOIbmVwIgiAIwjCQyYVvQmpy4bRHUVhvf4wUNRMYTXTFq1M/EXMZjw07cyH9Eo6nSy1FXQRqMGzTob8ELLth/6jpUIEl03sS+M2LGgsdqLFATQbSBSXRdeN1RrHmZvX2ziT1w5nxIb/2LbP58VCjYW7k+7PN4tujfbi5Ub29MwUsr2G8M4WfrxnSR52pvj9f1rs8Dt40n3+25IP8Pm6CSDaWTI+q4tbj0RmQvugnibt4CndvVrx6A41mI7aaayxMb6jv5UmVoDH5O//usMR6bLVa8zDj0VLWtn1+GmunvKqxB/dAynkWf3Pp9FO9XJZAEQ4Y4BnUTUyq4jvryOL3EW4baYP3hhXeUQ64VhV8fK+VvyMnVfLxHVOwZDop6T39CghERBTpVfHdpc6QFkaAkJpcCIIgCMJYQVYufCOTC0EQBEEYBjK58I3k6wiCIAiCEFRCduUidyFPsMcS6z1lPAc7wgbxwzjIf9doLBD0odD5WqAGA9FpOLz3bynlM13HNAzU8mOhBgPtv12Jfazdk8Dz3a0n+N7teR7o5+ej88HQgRqL6CauK+hK5nHqxGP82qH9NypyUGOBxDTy4zlT1PcCaip0tM3mx48/Av1z8Px4O2+zbeDf3ZP5fe4s4CXJdRqLpE+4ZXPLcq6xQJ8L3L5xMdc8pOzlmoieKdxkxQSaA9RYNCzlmoUpL1WzduU1k5XbO9P4c9gBJdTRtyJ9F7fr7shSayaq1+bx/YFGA30tDCXXl/PrGZbJ7b/d4Hvhbec9FAYNhpdkBu+jiQ5+bIM9OFxavLjoc9FnUftm6DQTvXHqfl2OJr7DIzXv2DOBx2MiT4ArD4FuP1YJ2cmFIAiCIIwmbjIF7HMR6PZjFQmLCIIgCIIQVMbNysXZWSdZe1vZfNb2TlMiMi7JxcTz5eTMHJ6SV3qArxmap/E8LtdevkPnNB5mcYIFt8ree6h+FjYp5WGLyFZ1VVK0/zaMJ3XlSwyD4PbmZr5c2p3Al0sxFbVtpTpPzNzM0w8NVU4hbIL9aN9tbtL8ZQDLr80F6v0hOvtutAOPPwKpqoZUU/V68Ikb4wZHpkJqZoM6NbN1Ltp78zBIyr4e6I+ENoRJ6iDdEVJHcXxMnX9238U/4ZU1k96Epfx0uBc1VVAx9bRTEzZBu+/oOt5uXMrbhjAIhEmwKmrsxzwM03Q1VFWtmcSafbH8/ND+G0Md7FiVWCGX90+EVNPuLB4u1dmHu+J4eLIX/nvBfrJDyQQrhDlyeSVres+q7G+nwRDhSFVFFUGnb8bN5EIQBEEQRhLRXPhGwiKCIAiCIAQVWbkQBEEQhGEgYRHfhOzkouxAJmuXxKeyNkYHe8B1OLaML9p4x+uIiEqhjamkzlKeA5ZSymN8vfHqS2uwB4evwpC62jYYn8TPgqmmuCCFGgz/x6v70bIYNRaYmhrWrNZ4oJ23zv4biWzh52vLV8dfcbyuH+27Mb0SU1NRk+Hkt6oBHI/pn60Fg+3EbVE++4iM9t9VF/H7DL+7zgweB0cNBtKRobal12kskEk1/Hw7D/LUzM50GA8ajaZFvB81GKip6MxQf/dYUr0D0jVRQ9GwjO8fNRjtsH3Tl7g9ufljrrFAXBaub0KdhHe6KJZQbzrLPw2FpZBv7yjwb/sIu+YdZ+PjMXXVYCcA+/cc4BvEMvvvkVmUl7CIb0J2ciEIgiAIo4knCCsX43VyIZoLQRAEQRCCiqxcCIIgCMIw8JCh0O2w9jEeCanJhdnaTeHR//oq4nhfl81sGO8NWsWGLeI50tOs3NcCqXVwjYWrjefH112s3Nx4PnDpo6fz43eV+PbORQ0E2nnj7Wocj3Fw9e2t02B0Jak1FjqfCHcS2I+D74a5GUqgz1R/XiSuiG/feg7XEZiPcS8HXYn07mT1MiaOR7tvROd70QXtKObbASXTm/h307SAR6oTDoN+Yy7/bqLr+bF0vhUI+l6gDwVqMLC/M11tv40aiw7QTJh5hXcDTYt5O2Uv7A98MLrS8d6F61WrXvw1+lyoz68z0z+NSvdk3zqIPovbZx+R0c4b26Txv0HCbVASAXwrInI6WLuD1PoSpCdO0++lRXOppUJBw00mMolD55BIWEQQBEEQhKASUisXgiAIgjBWkGwR38jkQhAEQRCGgdtjIpP4XAxJSE0ueismUViUj5hsvLpkOZZc7z7Jc6iPx3PNBpZcx5Lo5lJ1fj/WFonfo45fOkhTn9gL9KnQ1Q7xd3x8MY+9ts3ksVrUYCQUQYl0XsWbupL4/u0z+Hj0vTD6TniU/boS6k7QSJiL+D0U08i/W9ss9LVQP/xJh3ncuzOV3zvxR0FTAZqOmHq+PT6W6EWhAj0xEKwtgiTubmTtnqw41sZaIwj6VMRWq0uso8YCa4sEm+R9vI0aC/TBmMQrvhvoyFT3oyajKwM+n6bEOpZUR5+LqGr+7HjrLNADI4KXQyKq8i8q3p3F2wYfC6vmuzvEP8wkG+/G+xw1FpE2db8wtgipyYUgCIIgjBU8niBki4zTdBGZXAiCIAjCMBDNhW9CdnLhgjCIuUwdpsCS65Fgr93TBuV/4yGNC0qgYz/aBEe2GcxqleeHdt9RBovuQcwtUFK8hfc7E9XHMoRBjqvDIGjnHdWMDwOU8daEQQxhDYO9N4RZmjBFjp+fIeyhCZMgnSl8f5Et/pVA14GpqHj9oncd5+fzxdnK/XmnpqK9d2caXyafVIchF96Paa/dU+L4/sDeG1NNEbRCD39vP2vbv/451sYwCNpxBxom0dl9p+3qZO36FTF+7T+2Cs9PHWrQhkmASVWQBg1hGAx19HlFHrDEetNZ/J2J9t46zJXq8VhS3VzB7x20+45q45/dkcOvjaWM9/fEQ7gX3unsXHp99wkjQ8hOLgRBEARhNJGVC9/I5EIQBEEQhoFki/hGJheCIAiCMAxE0OmbkJpcuOJOkcfcH9eLjnOyPtMi3sZU0944zb5BwzEpoYu1O8Due1I877e18QNgKipqNgzHT+CxcSzZ7p0K64B9oYZCB6aSts1Qp5pi6irStpJfO0wtRXvvyBncBvhLOQdZ+68V81m7tpifgHUmF5nMT2hi7U92zYQz1NibJ+JvPMp+1Exg6qkOcwPEwkFj0TZHfb7e9t9YQt34WdUai+T93Ce5aZE61RRxpvB7xeQBrRFoLJoX8G5zA5ajd0MbxkMJdeci/hxSLU9tnVTDu9HOW6exwPEzFleydvXfc/j4DLU9ePdSrvHAVFTncv5sOBzq78Mxhz9bEZbB77OVonE439bPEuqoqdCBqanObNj+EOjcoERD+5d4iQYswY7vbG/7AHf3mU1pHk02btxIL7/8MhUVFZHZbKaVK1fSo48+SjNn4ntvkM2bN9NNN93EfhcZGUnd3d1n7DzF/lsQBEEQhkH/yoUpwB//jvn+++/TunXraPfu3bR161bq6+ujiy++mDo7O5XbWSwWqqurG/ipqKgI4JPrCamVC0EQBEEYK4yGoPOtt95i7c2bN1NKSgrt27ePzj33XJ/bmUwmSktLG9Y5DgdZuRAEQRCEUcbhcLCfnp7TK+1qt/dX1E5IUMevOzo6KDs7m7Kysuiqq66iI0eOBHzOKkJ25QLjb1FTeXwO43E6ZuTwWs1YYh01FojOFwPtwxGdJkPX7w1qJlyJEFtt4XF4XUl13f5RY2GZwRPQba2TlO2/mrjGwl6sfkiw/xPSiEIAdzLXw4Q1qT1SkO4k/vm7ZvP9JW5Xx8n1mgqNVwLTbIAGoYBrj7qawF4afCoqL4Hy9tz923hs2N6ZwvtRU4HkvM6vVfkX+LVPOgD7W8jbzjTweNkfrexvugJiyrXqku5IdB2/vifq+Af2gMYifwlfai7am83a+M0WLC1j7aN1XGQS7oAy6Wj/XQX6pjm+/0PKyOJapYbCFB8j+zHYe2v+u/BXk9GRrdZFdNn4vWu2+Xc+I4GHAnXBGdw+K4v7q2/YsIEeeOAB5bZut5vuuusuOuuss6igoMDnuJkzZ9Lvf/97mjdvHtntdnr88cdp5cqVdOTIEZo8eXKAn2BoRv/bEQRBEIQQJJhhkaqqKrJYBv+ojYzUi6vXrVtHhYWFtGPHDuW4FStW0IoVKwbaK1eupFmzZtFvf/tbeuihh4Z55mpkciEIgiAIo4zFYmGTCx233347vf766/TBBx/4vfowceJEWrhwIZWUlPh7mqdNSE0uwm0TKKy7/5R1YQ+saorg9sfLQegCk9GZOXWsXVyezgdA2EMXxsCqqpi6GpvAlb/trYMpc7hvXRgkYTc/lj3Pv4W8rjy+1BqfyNPlenbxXE0MeyAYRrE387AGpq7qqqZGn8XLsLYVwf4gDLIy7yRrF30wi7Vbz+WfVxc2CWuE7zJFbR8e1QzpiUnq5eHuZDe0vfbVxI+Vnmxn7fpk/teP97anA6aaYhgEwdRSpGEphiX4/jEMogPDIJThX2od2oM3LuH9JtjfzIwG1q7cm8vaGAZB3JB6etTEwyAJFh5+bbDw7y/Cyu9NN7QTLIPvjSZIRW1x8LTbCVPU2QV0OFbZ7W/YxBzHr2XkQf4faXsOhLw0JR1U/we4nf6FaIZNMOMipzvc46E77riDXnnlFdq+fTvl5ubqNwJcLhcdPnyYLrvsMr+3PV38EnRu3LiRli5dSrGxsZSSkkJr1qyh4uJi7XY2m43WrVtH6enpFBkZSTNmzKA333xz2CctCIIgCKNOwGmoJiI/wyrr1q2j559/nrZs2UKxsbFUX19P9fX15HQO6q3Wrl1L69evH2g/+OCD9M4779DJkydp//799PWvf50qKiroG9/4RtAuBeLXysVn+bVLly6lU6dO0b333ksXX3wxHT16lGJihjaj6e3tpYsuuohSUlLoL3/5C2VmZlJFRQXFxcUF4/wFQRAEYVQYDYfOZ555hoiIVq1axX6/adMmuvHGG4mIqLKyksLCBtcO2tra6JZbbqH6+nqKj4+nxYsX086dO2n2bHWRxEDwa3IxnPza3//+99Ta2ko7d+6kiRP7l7dzcnKGd7aCIAiC8G+M5zRmI9u3b2ftJ598kp588skzdEZDE5Dm4nTya//2t7/RihUraN26dfTaa69RcnIyXXfddXTPPfdQePjQdrM9PT0sx9fhcAw5zh8wVRUxmdRfGGosMDUV7cEx9RQ1Fpi6inhrLIi4zgI1FTp0GgtMPUUNRxzoP1BTwaPIevtvBPvjE/l3hZqMnkTQAbTw80nMb1Ueb+eJqfwX56rzyVGzgXoc1FzoNBRnknpIL8S01oTPc+0Q0vNHNNmBVFfQYHjS4No14N3gHzp7b0PqKfRPS+X6m7o3p/Dxi/n4piv58aP38f13EdeIHDeB6ATsvDHOjBoLXeppq4MfP3UyT+ueHGtj7cO1GaxdXz34rODbtcfOPwvafbusPM2Vsvl9HwX6jt4K/o7CVNRwG/z3cuj0xYpERM5cfnzUYMTE87TrzrbA7r3hIFVRfTNsE63Tza89efIk/eUvfyGXy0Vvvvkm3X///fTEE0/Qj3/8Y5/bbNy4kaxW68AP5v8KgiAIwqjzmWYi0J9xyLAnF5/l177wwgvKcW63m1JSUujZZ5+lxYsX01e/+lX6wQ9+QL/5zW98brN+/Xqy2+0DP1VVVcM9TUEQBEEQRphhhUX8ya9NT0+niRMnshDIrFmzqL6+nnp7eykiwphuFBkZeVoGIoIgCIIwWkjJdd/4NbkYTn7tWWedRVu2bCG32z2gXj1+/Dilp6cPObEYLlhi3d9+8zS1rgO9JZytPH6oLlZs1FigJgP3jzoIb6+J+I/5dWtbzmOT2N+TYII2llRX23+3n4hjbVzuQg2EzqfCOpNrIq7OPsTa/7P/bOXxUAORCL4bLS1qnw3EXMRj0YbPkwKaC0DnW6HtB10EWnibC3ksGX0vVKCUqPYwj/GbG+HY83Df6jdf9CF1nDumju+vM129WGrwrdDZdUN/aS38sQMaC9RUoAYDS6xjyfQuUBhhf85V4KFC/HqjxmJ2OvfNqO/k76mG6njWnjzLxtq9UJLd2+K72cKfgwlwM5yyg65LU3K9DzQU6HNBdnifz9do5barNRioscCS7C7QWHh7G5m6R8jCaRR8LkIFv8Iiw8mv/c///E9qbW2lO++8k44fP05vvPEGPfzww7Ru3brgfQpBEARBEMYMfk3vhpNfm5WVRW+//TZ9+9vfpnnz5lFmZibdeeeddM899wR25oIgCIIwiki2iG/8DovowPxaov6iKbt37/bnUH6DVrC6NCWdPbhh/xDGwFRU19441kY7b3/BUIU3GAbBKqeO6fx7ciWqx+uIzbOxdu9udWqoLhW1rYUv/f6VeFVUHWjH3UL+hUGQmLObWNvZzM8PU011YRJEFybpmsNtkaMhDKILk3iTVsDLmvZt4cvwaN/dNY/v21TPl9kxbOIvWCXV3AAD0nl6o/kAfHZINaV6HtYwgPbfEDbBsIcu7NIFVU/DMqHqLIRJPp9UxNoVr/K0Z+dyHsLDMAimoiK5Mbyy6T7ioelm++CzgCGTSCu/NhMd/LuNtPFj9VqxDSngkKpqSD0t589lhE19L8WWQzg2Rx3+w3e49/8BI2b/TTRuwxqBEtibQxAEQRAEAQipwmWCIAiCMFaQsIhvZHIhCIIgCMNBskV8ElKTC1fcKfKY+2NpGG9De2+dxkJnB35X/j9Z+8e7vqAcH77Extul6jSr6Om8NDaBg3pXCQ94qnQSOvvu6BM89hrVwu9mtAc36D1AY+GcyePkcQnqEuzOJL47tPfOS+CWzZ+AJgM1G5+DkulLrBWs/at9q0hFUhI/fusxfr6Edt8aumbzWDZqNJLncE1H+/tcB4HW86ixMDVg2fTTT0XtSlOXf0eNBYJ23wZQM3GQP3e6EuzZqVxD0EiQSgqaCExVnbawmrVLG+BmA7CEOuLRaDBmpHNNS1iG+n8G5zJuD46ppzmT+OffTTms3QZfX1kn3Kt+YLD/tsB3O5efa5/G3huJyOHvgd5y/7RQqLFAHZ1KY0FE3JZ/xBYDTEE42PhcuRDNhSAIgiAIQSWkVi4EQRAEYcwgYRGfyORCEARBEIaDTC58ElKTi6iKCAqP7I9nYzleXbld1FhgnBtLpqPGAn0tsuJsrH18Hy/tjL4YCJZUNwBl1b01F4aS663quLnR7pv3o2YDb3b0sUCNhel18L2Yofa9IE3YGDUZYRCS3F3Cc/t3Q64/2oHjd52fwOPeO3UnBKQkcVvjjg9SfIzsBzUWeH1VvhVEag0GWodjyXXSaCawZHr0p+AzoSmxbqrTaDYW8HMnGF9xkJcMJ7T/1uCvxgI1FdF1YH8OduB47xyvU3/XxhPg26P9d72F64syJnEtVls7fy/VdHAtVoQFSt57oSupju2IT/m5wKlQTzZ89zC+V2MPjvbdGJU3+GDY1OUhnPHKbmGUCanJhSAIgiCMGYJRMl1SUQVBEARB+AypiuobyRYRBEEQBCGohNTKRZ/VTa6ooWOyWEvEvZ/HJnkGN9GkBB5bRU0FajBQY4HoNBY6YhP4GeJCmYN81xyYsKyNtXvAIwNBzUYPTVT2x4OGAbHP4FNvywx+Phi3DhTUVCB4vGaoFbID2gZfC7j4SbO5DweirR2i8cHwpPJYduI2rgvoTuY6BTa+yey7j8jwWTKTbaxd0xTH2jqNxZTUVtauqk/n26f654thADQZuQtrWLvsQCZrT0vl3805ySWs/YfCz7H29EVVrF1an8zaqMmYuYR7qKDm4ra5H7L29pYZpAJ9LqZN4h4ofz9RwNrzMmuV+wtTPFst0Jdm4e+YmiquNcLaIfi3J/peEIw3+GBACfbIXK6liniPv6d0tUR0tUlGBRF0+iSkJheCIAiCMGYQzYVPxuBUUBAEQRCEUCZkVy7MZXzJDcMeBKmqhhLrkI6ZaeV5V3wxluhYGU+Zm5WrXq7EMAeiS0V1QFhm7tTBMzq6J4ePhZBJHJRIbz8RpzwWEn2cL03bZvJ+TEVFHMd5jhjady/LK2PtE63qdEIkL54vJZ9oS/Yxsh+0+8YwCZZw14VB/AXDIAimorYWqJeHvVNRMU0VwdTS2hRIHYWwB5ZYdxIfX2WCBwdAu2/cXgukjpY1JCr7kR3N01h7Whq/VzAMgsxYXKnuB/tvXRgEwRLrYSb+XRdk1LH2viKeZp02mYelWh38PaIKQTY71O+cidn8ndWLYRAAwyCGkuuY0l7GP3uPJgyCGFNZOd6hbVekJvwWJEweQ7bxsPYxHgnZyYUgCIIgjCqiufCJTC4EQRAEYTiI5sInorkQBEEQBCGohNTKxUR7GIV398+HwhZxjUT4ydihNhkg9iSfR9kSuE6huM13qicRUXgrv1THW7ndNzfaJWonHq80l/K4e3g8jx/ieAzEHT7plYIHqaJYUt2Wx3eF56Yq305ktPtG+25HM9dURLao56hYch01FoaS6yd4nBmvRUuLupQzaijcfpZQR5qPqjUhmHqq64+u55+nC9zB0dIbdRWJ7w6mS3ZBKiqWY9eVTNeVXPfb7tvPVFTzAbAbJ3XJc6S0lpdox1TTkv1ZrK0ruV6i0WT4y+yMetZG+2+0+z5QlMPaEVb/tANYVl2FuRLeA9g2pKZC9yH+nNnn8+esF/57wVRS60m+f/tUuO81ujnzSX58p1e/u1v9PQcNCYv4JKQmF4IgCIIwZpDJhU8kLCIIgiAIQlCRlQtBEARBGA6ycuGTkJ1coL03aXKg26fyftRQoH032oETlPdFe3AE9++cpo77W8AXA30u2L5BM4El1XXEgg+GDTw30O7b1qrWOFALj8PrNBu6CueJ4EvRVsS9FeLzea6/4XSIny9qMBDUZDQ2W1g7GjQT5gb+Nmib49/17wYJR1QTV4tHw/6d3BE6INDHQodBk6Gx7056U63JaAbfi7RLuUbC4GsBdtw6nwv0sdBpLIKOpsQ6khvTwtpHrNxOfW4G99M5XMv9dnod/HpGWn1/XtRjOLP5fW/9FJ8T0EDA+A7Nfx+osUANBRE/HvpYoMYiog32p3inup2BlWM4bSRbxCcSFhEEQRAEIaiE7MqFIAiCIIwm4tDpm5CaXHhXRY0twyU3vgxmSFOCJTQMWyC6KqgE/WgPjmEWtANH++/seF5J9LDK/rslR31uAFY5RTDM4mjhMaA4qHKK9t6IdSYPW7S18DRhTD3VgWELXSqqbnsDmlVJrHqKYQ0EU09x+4RCfkC0+3YWnH76Ib6YMHU06R2+FB75NW4v3baNL8NH1+EO4Tnjww1VTDszdIuh/LPqwiDTFlazdukBnnqKYRK0+z43iVdJ3dHC7cGP7+Mp5fieD8tU26sHClZBNcG9WNPBw79JVh6ybKji74lTdt+W3ZiSjnRMUYf30N47wg73Rhwfbynj+4u0qcOTvXHKbgO6StYjgmgufCJhEUEQBEEQgopMLgRBEARBCCohFRYRBEEQhLGCiYKguQjKmYw9Qmpy4W3/3Z7L43kx8Tw2OrENNBd+Hgs1FIi/Jdd1JdYr2riOwYKpsF5EtvIFJ0xF1dl728BqHGOxWCJdV0K9h+B4O0GUMJPrAND+GzUZmIqKqaSYiuqvBgNLsHd9yNMXUSOhI/4Ifz041dmHBtDum8DSG+lKG/y3vy+22sP85NRHIoqpAz1Iqsb+ewF/0jA11XBtMNUUKG1QC1x0L+ZNhSvU24NmwwPngyXWj9elsHZ+RgNrF0E/4q7muoCk2Vx/ZLCan8PfI812fq+7rC6fxwq38yd7whS+r6gd/Lnrhez+CO5MbtBkRNh4f6+V/3fSE8/v63YosZ68n2/fE+ffQrqzlKeMe39aU/cI/dc2SqmoTz/9ND322GNUX19P8+fPp6eeeoqWLVvmc/xLL71E999/P5WXl1NeXh49+uijdNlllwVy1lokLCIIgiAIIcKLL75Id999N23YsIH2799P8+fPp9WrV1NjY+OQ43fu3EnXXnst3XzzzXTgwAFas2YNrVmzhgoLC8/oecrkQhAEQRCGgydIP0TkcDjYT0/P0FljP/vZz+iWW26hm266iWbPnk2/+c1vKDo6mn7/+98POf4Xv/gFXXLJJfTd736XZs2aRQ899BAtWrSIfvWrXwXpIgyNTC4EQRAEYTgEcXKRlZVFVqt14Gfjxo2Gw/X29tK+ffvowgsvHPhdWFgYXXjhhbRr164hT3HXrl1sPBHR6tWrfY4PFiGluVDRDSXX3WDFoPO1wJxp9LmossWxdrUdApQAaixQg4FRNvS5QI7uyRn4tyuPz2hRY4G+FjoNho4Fy7lXwMk27k3QU8zbcy4vZu29JTnK/aPGAtH5VKCGovWY2l+8mfi9osuO15VUx0R1tAePrvcvpmooyZ5m8tnvTOV9aNeN25ob1eeC4413qkaPovW90GyvsetG3wtTgGo63B73ptVY1HIRCZZYL9yTy9ouC9dI6M6/6QjXA6HGwlIIpQDOGnwWTFX8Pu+r5O8k+zzw/kEfC7DvjsjhHhtUwTUPrji03OZaKVc877dPVfteRMIrsSdOOTzkqaqqIotl8JpGRhr1Tc3NzeRyuSg1ld93qampVFRUNOR+6+vrhxxfX18/5PhgMW4mF4IgCIIwkgTTodNisbDJRagjkwtBEARBGA4j7NCZlJRE4eHh1NDAV9AaGhooLS1tyG3S0tL8Gh8sxs3kApfcekldUa83ni/PonXscUhzmrG4krUxVVVXZdWQigrT3QreS50lPOwSM93usw/DIHEQgsHUU+w3JfJz6dnFwwrHimfwfqh66oZU0/2781jb3MKvfdtM1jRUTcVUU0xFbWviVVIjYf/qZEmiHliu1aWeYr87pRf6+f4mb+NL112p/j1mrXP595FwmPd7hy5i6nQhGHWIBXGm8s+a8wb/rA1LoLImjDc38O8iphZTWeGAflYtxdRU/DRo/42ppYjuvY5hEO/wJBFRTA3/vEeX8w84sV0dUmt1qFPUkagq/qx0ZvHrq7rTEj/lV6vxXPWxIm386nSU8zRYDGqYy/lvMIwRdwC28PM/ZQyTqCSDrp7xKSeMiIigxYsX07Zt22jNmjVEROR2u2nbtm10++23D7nNihUraNu2bXTXXXcN/G7r1q20YoU6TTtQxs3kQhAEQRBGlFGoLXL33XfTDTfcQEuWLKFly5bRz3/+c+rs7KSbbrqJiIjWrl1LmZmZA4LQO++8k8477zx64okn6PLLL6cXXniB9u7dS88++2yAJ65GJheCIAiCMAxGoyrqV7/6VWpqaqIf/vCHVF9fTwsWLKC33nprQLRZWVlJYWGDKzcrV66kLVu20H333Uf33nsv5eXl0auvvkoFBQW+DhEUZHIhCIIgCCHE7bff7jMMsn37dsPvrrnmGrrmmmvO8FlxQmpy0Z3dS2Hm4cXSsOS6rlyveZpDuT+DvTf5FztFe+9Lso+x9ls0i7Uvzz4y8O8/tS1lfaihQAypqFyyQFPjW1j7JITipkOJdF1qKZZcRzAKPjOPx8l3l/D0Pd037szncXudvbeuJDpqKs6fcZy13zvONShI9QXcdjmqSa1zwNRT/MRdoLvy1lnoNBRI1zxuzx39KTcATzrIxxs0FmDvjamn2G+wC9dpLDQl1zF1s7Sef7dYYr00g/fngZ13CWyvA0uw5y5Vp/PVW/hzjvbeCRb+7NZb+fXKyOLPZkMhT43F1FTvF7qngD8HjVPUaqSJ2fxcGuPU4+1x8Au4Fc1lXGNhW9ir7O+N8892H3Vt3ro3d7d/+xo2o2T/HQqE1ORCEARBEMYMo6C5CBVkciEIgiAIw2A0NBehwvjM1xEEQRAEYdQIqZWLcNsECvNRSjdqKo8vuk9yLwgn6AywXO8k0Fig/bcOf0usO0DjgRoL5KgjfeDf86fyOHSBtRbGQpB+GY/bhsFU+eDH01nbMoMnlKPGIi6B2wDbWnn+O5ZQRx8LLNm+MHcfa3/SxI0w0MfC3MjPvxXC5gb7b9BUoObCoMGADP6Pj87j+5vtnzdDdzI/ftZWHituWgC+GzAeS7J76yyS93OPkYob+baoqUCcKXx8TC30o4/FQb4/nQbDXM/P3cntYQygxkLna/HCCp5Od3/5GtY2+FykkxJ3Df98RcR9Kwy+F3W8v8/BP3+4g+tvEPS5wDLpzRZ1iXUcf8queO+APbe5Ap0qeDvcqtYtoD04aiacuWAv3sbf3ehbEbaIv8OxpAN6FVGbb/vwEfO5kLCIT0JqciEIgiAIY4YghEXG6+RCwiKCIAiCIAQVWbkQBEEQhOEgYRGfhOzkIraML7rY4nmsFCPN5lLIqYbaIqjBOJbANRGoqUBQY4HHQ58N9LlAsH5ImZcsAvUah2gya6OvRWyejbVtcK4m0EA4jkO9euhHjYW5mMeZsfaIjmf2ncd/gSXWW8BrIYVH3rH2CKIrmY4aDt2CXvRRdb0K9K1oLeDtznTwHQFQY6Haf9Mi9CIAHwuoPeJM0VVe4WCtEEP/QbWmw4Cm1kdpLb+Xdb4Y/7Hrm6yNPhYm2F7na4E+FgjWFgmbzJ/jiRaugQmvgXocdtak7izejqnm17uT+LOOCo6JDt/fT5+FP4fWT/lz0jFFo6mwg6YCNBg6XwqsJdKew8f3wGumFzQWsSfV957J4/t/ZVfvCP2PLZMLn0hYRBAEQRCEoBKyKxeCIAiCMJqIz4VvQnZy0Z7Ll9gwzQnBMAhaxyL+ppYiE5ZCnhWEMjDsMXtpOWtX8OxQhs7uO3caTz0t/gcvgW6CEumYWupohvVKDYYS7BBGQRLBnrulhS8dY5jD3zALoiuprlvAMzfwp79tjvptgGXPDamkUHYcU0+nvMPvzQ4Io/hr+e2NuRFSQyEVtXkBH590UN2PYRNMXTUcH1NT0wL7brHE+ok6bo+ts/vG1FMMixj6IQziro5W9vfFwufzqO+1Xouy25CKim0G/K/VoXndYxjEcGxIZQ238f254nl/u+Z4mIraG8fb7VP5tTOkokJisvc73t09Tv/HDiEkLCIIgiAIQlAJ2ZULQRAEQRhVRNDpE5lcCIIgCMIwEM2Fb0J2coHxPfQF7tV8NO/yvETGEuun9oDuAFJJ50ytYe0jJzOVx9NxGLbHdFJXolrH4M0B1IfM4BoLjNhjamkc2H9jP2Kw5y6GUssz+dPTYlJrLNyQimouUqcvIrqHtQvtu5vV+0eNBaa2Gkum+0fCYf6NNC7k1yNlH3x/Ht+pt9F1/LN0pfunz0ANRafBLhtSuDX23whqLAwajEXqFG208y4ldUl11GAY7MABrQZDo7HAfkwVxfRQTC3Ffp3dN+6/O2vwPaFLPdVpLBDUWBjsv+GdG1vO+zEVNaoVUlPj+HjUZCCYymopHbzXXb0jWMZ8nE4OAkU0F4IgCIIgBJWQXbkQBEEQhFFFNBc+kcmFIAiCIAwD0Vz4JqQmFxPtYRTe3R/JcUK8TWe3jRoLpAN8KMLBFwO3r0yIUx6fOzmQ4Q6KmW7HERz4fN5l0tG+2190JdN19t9YQt3crH46UJMxf0UZa59I5HHztqIEvn+w57bN4m3cP4I+F2GN/Lsy2H8bPk5wo4eo0dD5VnRm+NZY4LboW2FuVO9bZ++tRVNifVItP5+mRf7tPnoffy670vn+UGPhL9G14EGSAdfvE/6sdWaCp4vO5wL6UUORbOGeNU1o921Xl2z31ljgeJ3GwpkN70jQVEyqQPtvfmwsqW4uA3+aOD4eNRrd/DE3gD4XOjtwYWwRUpMLQRAEQRgzSFjEJzK5EARBEIRhIGER34TU5KLP6iZX1NB2weFLbLwNVU7R7lsXJkGiIYzRBfbdpAmj6FJJsdJp9Am+3ByxvHVw3y3qqpoYJkD7bBumgjar96cjuokv9bbM4p8dj//JrpmsbUg9hfN38mxCimzhS/24f0wV1VVFxf0b7cLVqaiBknKAf35MRcXQh3dYBUMs+FkQDJsg2iqoftp9d2RAmnI9759UA6mtEDbBMAiCqaYIpp4aqp7Wxij7O0lt/430OfhzGwWpopg6Wk88NqAOggQGVjU1pJZC2KQjG8IqENYgG4SiIUyCJRkM2wOYehoJdt+YeiqMbfx6S27cuJGWLl1KsbGxlJKSQmvWrKHi4uLT3v6FF14gk8lEa9as8fc8BUEQBGFs4QnSzzjEr8nF+++/T+vWraPdu3fT1q1bqa+vjy6++GLq7FQX0iIiKi8vp//+7/+mc845Z9gnKwiCIAhjBplc+MSv2MBbb73F2ps3b6aUlBTat28fnXvuuT63c7lc9LWvfY1+9KMf0Ycffkg2m015nJ6eHurpGXQldDgcitGCIAiCIIwlAtJc2O39OoSEBHVO0YMPPkgpKSl0880304cffqjd78aNG+lHP/qRcszM3DrWLi7nPsUYu0QNBJbvdcJHQI0FEqiGAzUWSE8CxDu9j63Rb0Tk8ZWknhNxrI0aC12J9PhEnljbRrGsXXs2318kr/hO8fmtrI0l1hFnPrfn1tl/61JR0e47+ijfH2os3Ck8dmxIXW3w708NLKmOC4ZdaXz/qKNouQjsyr10AGgN3jKPfxc6jQWl8+2dBKmlGo2FLvUUafoC/ywZlzbz/gOTWduUwcfr7LsxNbV6bw5rd4GGonspf1bQ/jumBu6tGkjbnsWfnYX55az9qWOa6nQpbTJ/NprsPC1bZe9NZExV9dZN6FJNERxvrvCdAk1E1BsH9wKkomI/trH8fC/o1vAdHdXKn4vuBNBexXvZf/eMjP23CDp9M2xlmtvtprvuuovOOussKigo8Dlux44d9Nxzz9Hvfve70973+vXryW63D/xUVVUN9zQFQRAE4cwgYRGfDHvlYt26dVRYWEg7duzwOaa9vZ2uv/56+t3vfkdJSUmnve/IyEiKjFQXQBIEQRCEUUV8LnwyrMnF7bffTq+//jp98MEHNHnyZJ/jSktLqby8nK644oqB37nd/UtfEyZMoOLiYpo2Tb1sKAiCIAhCaOHX5MLj8dAdd9xBr7zyCm3fvp1yc3OV4/Pz8+nw4cPsd/fddx+1t7fTL37xC8rKyvLrZF1xp8hj7tc6lOyHbUEDoQN9Mcx741gb7btjE3hsFkuu01TeDINA2tE9OayNuglLPM+f72zhPhr+WH63g8YCsUBJ9Z5diaztnMnj8AhqNuKKeXzTNhO8CzQai8REbkfe9ZF6lQt9LdAnA0u4o8YCNRioqdCBMdLWAv6LhEJ1vNdZwL0UEt/l59c6l+/PVO97Fa9xMe/zpPF947aeNP7dTknhMf/mg5n8XDUl1VMuqWbtioMZrI2aDPN+rjWqpSl8/1CSHTUWOg3G8Vq+v9Rqvr8ufnoUtYc/V6jBcE5W/1mZauHPbW2H1cfIftD+G98T2D9hCmTi2fnnxfFJcxsGz+VwqvJcEJ0mw7QQdGhlsUMPPE10Ggvsxyg+9ke2jrw9uGgufOPX5GLdunW0ZcsWeu211yg2Npbq6/sdcaxWK5nN/UKotWvXUmZmJm3cuJGioqIMeoy4uDgiIqVOQxAEQRDGPBIW8Ylfk4tnnnmGiIhWrVrFfr9p0ya68cYbiYiosrKSwsKkwIwgCIIg/Lvid1hEx/bt25X9mzdv9ueQPsFU0EkQVujA6oKQKuoEe/DopeA9C2GIdmhXwvkY7MCDjM7y2xsMuZhgld5Q9RTCDBj26C7mYQo3hE2cLXyp3J2kDlNgGGNmAk8f3J3I84Ix1dRgb058//FHsVIoa/odBjHaffsXBkk4zPsnvcPTBxsX4vbq56xr3mCoIvpTs2IkUeIhvu8WSDVtPsTDIFogdRXDIEjabv5clv0XDNCkliJmqJLqXKy2425Y5p/9N6aiIkmzeeqs/WN+c8264ARrN5M6xFdblajs74EwSKSVh4WSoKqqKhQyMZuP7avQhFrnc3+hLhu/Npjuj6mmrnj+jsZU1UD/Ysf/A6jVv+c6GEhYxDchVVtEEARBEMYMEhbxicQvBEEQBEEIKjK5EARBEIThMIZNtMrLy+nmm2+m3NxcMpvNNG3aNNqwYQP19vYqt1u1ahWZTCb2c9ttt/l9/HETFkENha50McbrUFNhKJnuZ6orYinhsW8HTYQ2aERge28dBZZj78rjcXB/9BlERNbj/Ny6E0GzoElNRczF/PzQzhs1GLub8v3av67Eessqtd23tmR6s9oeHG2LkWiwB8eS6ZO4c70hNTX6MI9to4V30juD59cyj/ehBqMrDU4uHazEG+BYWEIdUk9Rc0GQGpr7a95dtoZfy+S/8/7OjMD+vtHZgSPJL+N4nspp8vAnrzOTX4+Gaq5Xwr0dKMrh/WDfHVMNdt4reBp22BGetu0pwKR4Tg1oNswK+2+XnX+X+I7Bkuu95fxcdO/U2DKw697H36F2sDTCEutYUj1lD2/bpvO2uXTkNRaI6V8/ge7jTFBUVERut5t++9vf0vTp06mwsJBuueUW6uzspMcff1y57S233EIPPvjgQDs6Wl2uYijGzeRCEARBEIR+LrnkErrkkksG2lOnTqXi4mJ65plntJOL6OhoSkvDv0z8Q8IigiAIgjAcghgWcTgc7Me7MniwsNvt2kKjRER//OMfKSkpiQoKCmj9+vXU1aXOyhoKWbkQBEEQhGEQzFRUdKzesGEDPfDAA4Ht3IuSkhJ66qmntKsW1113HWVnZ1NGRgZ9+umndM8991BxcTG9/PLLfh0vZCcXqIkwT+M52ajB8LdEum58O4FGA7ZHK9q25epZ6Pyp3Ea5sEVtrc6OrdFYYEn1uAQe57UTBDs1CiMswd5N/mks0OdiZd5J1t55gnupO3kVasP+Jp3LfTLoA+49gJoJ1FzoSq4nvgefD3wzDBqLVNCwQMn1xoX8/BPf5ds7Na7NLfMGx6OdN2osVNbhRHp77+wFtayt87UoW8PbaP/ddAX/CygafCu60vm1Qrtv9LnQEV3Lj9+w3K3sx/8owibDX2zV/PjdmfzZSsvidur1Jv5XotvCv68kK38WW8BKHn0uMrNa+P4r+Xso6exBQU8V6DGyp3CPjmqbetnbFQc6M404oB3+O+mJBw2HoQS7en+NS3k7AjQaRnvwQdzdvvuCShBTUauqqshiGfx/y1fxzu9///v06KOPKnd57Ngxys8f1LLV1NTQJZdcQtdccw3dcsstym2/+c1vDvx77ty5lJ6eThdccAGVlpb6VQssZCcXgiAIgjBesFgsbHLhi+985zsDjti+mDp18A+02tpaOv/882nlypX07LPP+n1ey5cvJ6L+lQ+ZXAiCIAjCSDDCJljJycmUnJysH0j9Kxbnn38+LV68mDZt2jSs0hwHDx4kIqL09HS/thNBpyAIgiAMg880F4H+nAlqampo1apVNGXKFHr88cepqamJ6uvrBwqOfjYmPz+fPvnkEyIiKi0tpYceeoj27dtH5eXl9Le//Y3Wrl1L5557Ls2bN8+v44fUykVMvJPCo/tjaR0mHvvsaINYrJ8ai+jpdmU/gcAWfTEQ9J5ADDoJKNmO9UHivEq+2/I0+wKwVoijmWssUJOho62Fl1oOA98JLKFOUD6hrQguJnyepCR1bn8z8eM3H4XaJ1BSHekm//LjJ3yFazq6j/C/GpwF/Ls2F3LvCE8q70eNSkwdD2Z71w4h0pdN9yYrhQemq0BPgyXWlyVVsPZf6z7H2hUN/Mv7ygU7WfvP21b6PJfTATUWCPpY6MYb9p+hHq/rx7++5i0rZW30tcicxN8j9fji0JAItULOn3GQtcNN/Hz/3M7fQ02OQW8Kg8biU66xyJrPDVeqDsFfpqCxCG9Tv0OjpvLntrNNXaclfSvUe0rgV7t9Kv+s8Sd42zYdagwljJDOIkTYunUrlZSUUElJCU2ePJn1fVYnrK+vj4qLiweyQSIiIujdd9+ln//859TZ2UlZWVl09dVX03333ef38UNqciEIgiAIY4YxXFvkxhtv1GozcnJyWEHSrKwsev/994NyfJlcCIIgCMIwkKqovgmpyUWnzUxhPUPb/WLYI6LNPzmJ3yXTNXbgGKrA1FSkcA+knkJYpP1E3MC/o1vVy4FYkjyqhd+99hlQMvwjHiZwJvH1ULTbxv0jXR/xMIUhNRXGY+opppri8aI1D6O/YY/4I1CWHFJN27dDbiiklmIYJLoeT1C9PKyz8Eb7b1V6KYZBcGwVpEYalsLR3htSU/ekZfN+SBVN/jt/Pjugort5Pw9fxlZDmu4SPj66jn/3k2B8R2ZgsjF8saPdd/gxboH9aTVXy2MKek0Hf49EVfH3QJ+Fb1HrUKcK/8UBqaYQNkG6vSy+qzUl1fG7j7BB6qjmvwccP3Eb/+xxML4HfuHURIzwHe5MHKf/C49TQmpyIQiCIAhjhjEcFhltZHIhCIIgCMNAwiK+kVRUQRAEQRCCSsiuXEyK57a8mTk8BaxkP/dpR9Dee87UGtautMUpt9eloiKoi8BUUwQ1G7F5tsFje+kvhgJLpIPBsyE11XMltxR2QqqpYf9cUmHYH9p7o4YiPp+nQ5pg6o6ppmj/jeD+daC9dxtoNMIaeRvtu6OaApuT4/4QTEVVaTAmz6snFdX1kH4IqagE+hKMw6P9dxmkpiJNV0AaMJZEB42GyYN23vzaOBfz57wrHTVXfHxYJr92WGK96UtgJ/4Jf45javh365jFn9OJYN/dp9FMIOFZ/PNMgHsf7b6RMBifbOFp301e/8aEbHMc/43Txo/ljINztan/e0A7b2cupP9rUld1f9sa7b3DlP3e71S307/0+mEjYRGfhOzkQhAEQRBGFZlc+EQmF4IgCIIwDERz4RvRXAiCIAiCEFRCauUivG0ChTn7T9nZyqvHlVBgJdaPnOQJ+TgefSrC/bSaNfhctKpjtajRUOksrMehxHcL37fOp8JezBPOA51xmot4LBePj/bfOo0GguMRLKluoJmfH5Zc16HTTHSDRiSqiX8/CYd52wkl2p2kvjcSDw2OryauqUANhrmBXwudpgJpfIvbBtOirqEHfgZoLLDkuqlOXTIdfS26KErZj0vKXeAp0p7Fx6MGw+RxwXjuQ5G0m78H2mbz/igH3z+WWEcFRS9oNCKtaqv6U1BSvSqOb4+6iInZgz4Y5grwr4F947ax5eCfE6c8NYPmAjUWsWV8f+YW0GiAzwX2o713VCv/snu5pQvTqZm6+fd6xpCwiE9CanIhCIIgCGMFk8dDJk9gs4NAtx+rSFhEEARBEISgElIrF674U+Qx94c7MBXVUBUVtw2wSirag2MqafzHfAmybTks3UMYJJAKfhjW6IbsQAxDIJiqai6ODKg/YQcsv0JYAMMYuqqnrU38A8Ud42GDVkifxNRSf+2/dWDqqS4sohuPVVDR3hvB1FRnyuD3YW6EsEcj2H+nwr7B3hurnmJ/ygKeplxxMIOPz1Av6yNY1dQQ5gC0YRBNVVOkYTm/9ph6inRk8fETHSYfI/uJwFRVsPsOt/N2jyFwoibKihV2OS4v++9wq/rauOL4O7Enjj83GPZAu2/E0A/flW2aenuTR31te+Kxfwz8xS9hEZ+E1ORCEARBEMYKki3iGwmLCIIgCIIQVGTlQhAEQRCGg4RFfBJSk4uYOCeFR/fHATOtYPdd6l8qKvbHJqhLGes0GI7p/A5B+24dqOGIg/OxedmNd0GYHI/lTuL7QnvuuARuGexI5P2osYha2czaPZC6asvnnz2yhcdGMbUUNRUrzzrK2juJ99tm8f2nJDlYu7GZf/cIpqZi6qmuP9j23y3z+OdB3YROg+FJ84q7N/LUSxOEpTEV1QkV1g1AifWKugwfA/+1fyih7sRU1Xq1FkqnwTD014Yp291L4TmuVdv0Y4n1ie1Q4r2Kf1f2i/n++9r59UqDkuj1VnVasS4VFTUZurdK9pTBZ7XaxtOUMfUUNReRNtybnxoLoH0qaDba1OO7E/jNi/belhLe36Mp2T4SSFjENxIWEQRBEAQhqITUyoUgCIIgjBkkLOITmVwIgiAIwjCQsIhvQnZyUWMH3wk/fSxQY3FqD/cHcE5TW0wTaCRQ94B23+hrgf1RJ7guwZ7H9xft5W0R1cLvxraV/FxRU2HayYOTduKfFTUaPRDZxRLs5pbgRtOKWlOV/eiT0fEBGF3MVset/bX3Rk2Fs4D7THRr7LmnvMPvxcaF6hLu0fX4doHjq46neTE50ecCNBUGTcYC/lnNB6DcexpYOKPGohbttdXnhxoLLLEevY9rNtDXAjUXUXvUGgsEfS56Qb7TNpt/gIlHJ7G228LPp574s4a+FojO5yIqTn1vo8V3BSUN9tn5Z4uw8W17bXxbtPtGDYahv42323P901ignTdqLnD7hCJ+LRzTg+tnMyxk5cInorkQBEEQBCGohOzKhSAIgiCMNuM1rBEoITW5yLDYaULM0EvEYXE21q5O4GGT9tYYZTt2KV/j44EAIrUxLZGD+PIthhYw1RT7Z15SytoHSqewtnf6qVNzMrZWvnQbNoPf/RgGQbA/PpHbdYedxdu6Kqf+oquSimGOsEbenzSbp85iqiqO14VNzIU8NIBhDaxyimEQDKtEH+b76+IZg4ZUVH9TVRlg541gyEUXBvHX7luHIdUUwiCTv1DO2tV/z+HbQ5gkLJNfa12YBFNREZeFV9dMntPE2q0Ovn8MgvSSugqqyx6l7Ee67fD+y/b9rDmhr9eqTkU1l6vDJGgH7syFUDRURcVU0tiTkDasST1FWvP5Z3cl+v7sbqf6HRc0PJ7+n0D3MQ6RsIggCIIgCEElpFYuBEEQBGGsINkivpHJhSAIgiAMB8kW8UlITS5qHVYKP9Ufd3PtjWN94UtsrO0EO3CCVFXEUFIdx8P0ElNP48GaFu3Ao0+oS66jxgL3763ZQDtvLMGuK7mO4P5Qc9G9M4m1nfk8LmxITW1Rp9fFnA1x62Pc7jsBSqx3J/N2F6SeRh/lx9NpLJCEQijpXhDcp93UoE5dRVBjoeo3pJri2INmZT8yqdYNbd7fobHz1qGz98b28X38uSBNKmoXgZ4FxutKrGMqKo6vN3F9UVQVf3b6IDXVUgWprlY+PhzGY2qqIZUVdBJo6R3hlX5qSD2N422CVFSj/TfCP4t1Hz92d7x/Ufa4Ev7ZbdP59sa/6NXvYOuJwefY1eumar/ORgg2ITW5EARBEISxgsnd/xPoPsYjMrkQBEEQhOEgYRGfSLaIIAiCIAhBJaRWLlZNLqGISf1xtrn5PKL21/pFrD3r/CLWfvkQ70f773bi+epfXrCPtf8C28dACXYHcc0G0pWn9htYOK2StcsSEn2MJDIl8qku+lqg/TeC43W+Fm0z+faJiXz/eV8oY+3dJbmsnZTE94ckzGph7eZk7jKCPhcIajAQdwr4ZoAGo/nzPcp+Xcn11rm4rsm/H08q37/SznsIWIl1IjLVn/72Bk0G+l6AHTh5wFMD7L0NJdbRB0ODCXwydP4xeemNrI0ajClX8nsvDAL1R/fksLZzufrZ6HOAl8IsuF5QYn3uxcWsvefYVNaGAvDksnLfDPS1wBdyj4kfL8rKz8dw5+cM/qb3EBeQ9FrBnhtKpuvsvZ25vdDGg3PMJ/lzhD4WPX5qNHrAFwN9Llq9XpluZy/R7/3a/bCQbBHfhNTkQhAEQRDGDGKi5ROZXAiCIAjCMJCVC9+I5kIQBEEQhKASUisX26unU3h0fwzyeBwvu32sLIO1j7eCbwTsq6sVNBLga/HKP5eztgU0Fp0lao0FajJwPNYaQZ8LBHO6vcEZoo2gtgj4WOB41FzYi3kuf2J+K2u3tPD9e17l+hAz+FLQ2VxzYfC1AM0FaiyimsHLACquo8+FjtjzGli7fTsv+R7dwP+U0PleoAYDS6g7G9VeEzi+Kw2uH2zvXVsES6ZTAx8bA74VndCPJdYNtUYC1Fgg5n1qnwyDz0Utfy7Q1+J4Hb8Z3DXw+cGnohNqAGE/flMR4CPRNod/V6ixQF+KiQ7132/oa2Gu5M+q8c6JUPb3ep2vvwXJrSc1nilloKGAWiNYIh01G1GtqLBRP1c98Xx8JJRo74F3YmTr4PFdPSO0HCDZIj4JqcmFIAiCIIwVJCziGwmLCIIgCMI4JCcnh0wmE/t55JFHlNt0d3fTunXrKDExkSZNmkRXX301NTQ0KLcZipBaufBORT3u4Muhs3K5TzGWXJ8CJdmRa9M/Ye0X65cqx1dMV3YbwDBIHKTC5sbz0EBZGw8dTJs+WEb8JPTpUlExTLIsj6fvGcjjzdI2bv/9uemQeko8J21l3knWPt6WzPvPOqo8/A5IRcUwCKaKYipqajIPSSENTfzewIV6DINgKum55x1j7XfeX8DazgJIHQX7b7T3XnHnHtb++7G5fHtIPTWEQrxIuriGtasOpfMB6TwMYgBSRdMWQsgK1nBLG/i9QbV8mR9TT7sgDDBjMU/BRjC1tGhvNmv/19wPWfs3dA5r5y6tZ+2jdTwE5rDwazvRAqmesJKfbMHkUk6rhae0d0Nqa2YWv55TYnnsYJdpGmtnwfiqKv7so/131vy6gX+XV/DnDumF138Tz7Y3pKpmnc+/q9IDk1nbOQ1SVZVHJzKXqlNVjfECfj6xefzatZ+IG/i3u3uEbC9DIFvkwQcfpFtuuWWgHRsbqxhN9O1vf5veeOMNeumll8hqtdLtt99OX/rSl+ijjz7y67ghNbkQBEEQhLFCKIRFYmNjKS0t7bTG2u12eu6552jLli30+c9/noiINm3aRLNmzaLdu3fT5z73udM+roRFBEEQBGGUcTgc7KenR228eLo88sgjlJiYSAsXLqTHHnuMTp3yXcRz37591NfXRxdeeOHA7/Lz82nKlCm0a9cuv44rKxeCIAiCMByCmC2SlZXFfr1hwwZ64IEHAtr1t771LVq0aBElJCTQzp07af369VRXV0c/+9nPhhxfX19PERERFBcXx36fmppK9fX1Q27ji5CaXJS0J9EEd38Mc4aF2wL/s4oLBdpbeezzCLSR+05+kf8C1qos8dwGGXG0qVPsMJXUBnbjBzTnd9LrfBzH41mfv6mon4BGAvuReEhFPQEaCnMRj6PvJJ6eh/bfO45PV/br7L51dt5NjepYM8H2/vJ20SzWNkMqqkmTeoq8/t4S1o4GTYZ36ikRt/RG/QVqLLDfkGpar168rKfAUlEx9dS5mD9HhpLqQP6SCmX/bw5zjUV+BheeFe6Be30yP364g6eOuh38fMOz+Pj6ap6mjamnqQX8vdRQxfdXQ4nKNr53ag9zjUhUNtd89IHmwvv7N9v5d6uz/8bUUuR4OV9aN0PqKWo4MDVVh6WEC1wc09X/a9vgnYl2AyNBMMMiVVVVZLEMWrZHRg5t8//973+fHn30UeU+jx07Rvn5+XT33XcP/G7evHkUERFBt956K23cuNHn/oNFSE0uBEEQBGE8YrFY2OTCF9/5znfoxhtvVI6ZOnXqkL9fvnw5nTp1isrLy2nmzJmG/rS0NOrt7SWbzcZWLxoaGk5bt/EZMrkQBEEQhOHg9vT/BLoPP0hOTqbkZM3qrA8OHjxIYWFhlJKSMmT/4sWLaeLEibRt2za6+uqriYiouLiYKisracWKFX4dSyYXgiAIgjAcxrBD565du+jjjz+m888/n2JjY2nXrl307W9/m77+9a9TfHx/aL2mpoYuuOAC+t///V9atmwZWa1Wuvnmm+nuu++mhIQEslgsdMcdd9CKFSv8yhQhCrHJxfTYZp8+F5Ot3NsgDHwtKm1xyn2jRmPuVO4XUNHGdQ6osZg/lZeAP3SS54DH5vHz0YHxRG8sM9p89g0FlmhH2kid96yjJ5HHalFDgXbfSWD3nZ/A4+THZ/PzbT4KXgoAajDQ56LpiHqWjyXV0dcCfSoMJdQLeEa/YTyUTI/+VK3JQI2FAe+y6WDnjSXVdeXdsaQ6+lQk74PxmpXR6Dqwagc7b9w/gr4YaO8dlqlzT+CgxiLBAp93Nm83VPPnfEEG98+psXCPlHriGgx/Qd+LGtB0TMxW+2q44rjyPye7aeDfBp8L8OxAjYQrHrIIbGrtE9p798YPPe4z0AcDfS6wpDr+r9uVp86e8PYScjv7FCODh4mCoLkIypkYiYyMpBdeeIEeeOAB6unpodzcXPr2t7/NdBh9fX1UXFxMXV2Dz8GTTz5JYWFhdPXVV1NPTw+tXr2afv3rX/t9/JCaXAiCIAiCoGfRokW0e/du5ZicnBzygIlXVFQUPf300/T0008HdHyZXAiCIAjCcAgBh87RIqQmF3Njqsgc03/KGBZ5JPdl1v5Dy0rlvmZZeM5ucXyqj5H9XJLNLZ/Ds9VL1xUJfI3w8uwjfHuTevsjCTyl8Kb0HQP/vv/oVaxvekIzay+w8BDNQQcP0dyavp21f1d/HmujxfNCK7f9DYf+PxFPpbwuh9tZbyFupY5hkOVWbiceDuuM76dwBXVKkoO15yTw7xItowvnsCbNS+RL3e+a8lk7DcIqJo12qg7sxDEMkplsY+2aeXz7rBS+vlz9KY89TJ7HP1910+C9hVVNr559gLX/WsfjpNkL+GevaIRlfQhLTAL776YGHuK6fg63zX/+yDLWxiXfmwq4Ec+OFm53fX5yMan4sIWnnD+Z8xfW/k751aw9O53fazmT+Oep7OTPaZtVnVKOXLvkY2X/yVgba8+cxM8Hn7VtJq7gz7HA+bbz7+vSfP6X6Vv1swe39QqREBmfi5PE36Ex8RBygvYMCD2XtvH3inkafy6ROfH8Pj9Cmaw9dxp/b2EoOjeep8SHwTvU+/P1dfYS39uZIRQcOkcLvxKRN27cSEuXLqXY2FhKSUmhNWvWUHGx+mXwu9/9js455xyKj4+n+Ph4uvDCC+mTTz5RbiMIgiAIQuji1+Ti/fffp3Xr1tHu3btp69at1NfXRxdffDF1dvoWHW3fvp2uvfZaeu+992jXrl2UlZVFF198MdXU1PjcRhAEQRDGPJ4g/YxD/AqLvPXWW6y9efNmSklJoX379tG555475DZ//OMfWft//ud/6K9//Stt27aN1q5dO+Q2PT09zFfd4VAvtwmCIAjCSGPyeMgUoGYi0O3HKiYPSkX9oKSkhPLy8ujw4cNUUFBwWtu0t7dTSkoKvfTSS/SFL3xhyDEPPPAA/ehHPzL8/oI3bqUJMadnWXqsLIO1YxPUKV0YG0aNxVsVs0iFzv5bx8JpXNdw8CS3RV40bdAGeX8pLzuN9t3uJHUaVnxiu7LfXszjuu7kwOyytXbeuH/4MqKP8vRFLLGO9t86e3AEU0sRcyFP99SlniIZc3mcHS2dA8Fg7w0aDKpT231jKmry6/xaN32BX2tMJcXUUx2G1FRAl2qK9t5Ftfxazs5Ql1jvgxLoWGLdXa22/06AkuutDp4yboIA+qlK3p8G9uCog2hycOv+bvvwLZrN5VDSHOy9DamnQHibJlUVntPwVrX9N5ZUj2zl/T0J6ntDN977ved2dlPVbT8iu91+Wq6X/uJwOMhqtdI5qzbQhAnq9Godp05104fbz9y5jhbDrorqdrvprrvuorPOOuu0JxZERPfccw9lZGSwqmvI+vXryW63D/xUVVUN9zQFQRAE4czgDtLPOGTY2SLr1q2jwsJC2rFjh37wv3jkkUfohRdeoO3bt1NUlO/ZXmRk5BkvqiIIgiAIgSBhEd8Ma3Jx++230+uvv04ffPABTZ48Wb8BET3++OP0yCOP0Lvvvkvz5s3TbyAIgiAIQkji1+TC4/HQHXfcQa+88gpt376dcnNz9RsR0U9/+lP6yU9+Qm+//TYtWbJEv4EPqu1xFN7Xv6KBsU20/8b4X1cr9yKIns7Hd5bw/r+WcH+AGBjvL1hy3duqdijiEjpY++DHXmXKNZoKHW0t3O5bV3Jdp5mIO8aDr7ZZ/LvRaTZ0+0dQg2GgmffHnsfj9O3beRy+Gyyyo6CEOtqDI+ZGdXQRNRa68YjWDtx73we5PiSmlm/bvFBtx92Rwc8t+e/Qn6k+90k1fP+68TrcNfzzlO+Bao9LuQYCNRYIaizMH3ONQy844XeDRqMJSqi7rC7WjrRyjcpEB//89YXcWwLtvfsq1GXE0e7bXAG6Cq+y6s5c/tyhhsJc5t9zpyupjpqKqFYP9PP9xZ3g186Wxz9tJGzvmK7WbFDL4Hfl6hmh1YAxXFtktPFrcrFu3TrasmULvfbaaxQbG0v19f3iKavVSmZz/0tg7dq1lJmZSRs3biQiokcffZR++MMf0pYtWygnJ2dgm0mTJtGkSZOGPpAgCIIgjHXEodMnfv1Z8cwzz5DdbqdVq1ZRenr6wM+LL744MKayspLq6urYNr29vfTlL3+ZbfP4448H71MIgiAIwgjzmUNnoD/jEb/DIjq2b9/O2uXl5f4c4rTBMAjaeVdP52EOrHqKBDvsYaiCqimeWNbGbZWngaU3LR+0AT4JY23k3woQpqJiVVRDaiuENRITecimTfPhMOyRAFVRm01wfE3qKNKdpA4bdIE9t8nPVFJdlVQMW2DYA+3AsVIp9pvq4Xyg0ql3eqkzlR8b7b0b30ZNlH/S9KbF+Bu+PaaiNkLUM7qOAgJTU7u5Y7QhNRXttOs7+b2FVU/7ZvEQY4SVX2vDnQiZgksmc5Pp6vY41q7J4mElDJskW/izVBWnvhezp/D3QrWNW8Vj2ESFLmwSYePfLaaiOuGxnxTP03a72+L49gn8Wtvy+NXFqqc98E71J3XV3T1OUzBCiJCqLSIIgiAIYwYJi/hEJheCIAiCMAxM7v6fQPcxHglMyi0IgiAIggCE1MrFZKvNp/13cbt/lso5UP4XOXySB3dRU1GwlJcJP5TIU9RsGo0H7u/6iz5g7T8cWMHa3vbftlausfDXzpsSoZnEt28x8f2jxkKHLvW09RicANh1o313N6ntvXVg2jKWVK8nrslwam4ltHC2/5PHveMv4EKDrqY45f6w5HoVcV2Aqe70DeUqDnLbezMOgJLqiJP8szJGO++Uvby/cYl/dt8z0vm1PV7HUzcRnf1389Ek1p44mesC0O47IYunhtZX82cnwqK2im8GO/AVs0tY+0At18BMiYX3UBZvoh04kjXft6il6lA6a0fm8ue8y8bvDoOmAlJHJyXwa+csBQEKjJ+wlH+2L08pYu1XWpcbzlkFajIQfKeOCBIW8UlITS4EQRAEYcwgPhc+kbCIIAiCIAhBRVYuBEEQBGEYSG0R34TU5KLGYaXwU0PHn9HHQldivaItXtk/d2oNa4dN5TfAoZM8dhpovA81Fmj/jWXWvUE7b0S3PNXSoo7rthXxuHN8fitrB2rvnZLkYG2Mk0c1gx230X3ALxoaeBwfKkcbfC3SUaMBFs4ZoLGoAY1FZrKNtXve5hqNqjR+L6IGw5TK7z0WS0cPDCDmAH9e0i7hHiNlB7i2yFCSPc0/KbvR54LvDzUaUXv4c1tJUFIA7L1x/NSrSpXnEzYZS6bzdoOVXx/UWITbwYAbZAYfH53G2uhjsb+GvydMeLMBqLFAvVCjRoORHjf4LKHGoqeMvyfQWlyHs41/eFcC12jguXZBSYU3P+HvOHyT95D6HYrvWMsM/pzYvLRibmdgJRJOG9Fc+ETCIoIgCIIgBJWQWrkQBEEQhDGDh/w1vR16H+MQmVwIgiAIwjAQzYVvQnZycVFWMWsXx/F896K9XKMwZ0kFa5e9w2O7mEN9uI3nv1vANx/BWiLocxGn0YDY2/h49LJQYagVAhoMN5RoR98LXWwMNRWowUjQlFzP3M6n9i0F/LZDjYWO+CP8eG1z1A8nllBHdCXV66A2STr4XOg0Fthvmq8+36pGrsGYkso1LuaGwc/j5FYGBpoX8rZBnYO+F/XROEI5PnofH4+aCn/pyuDb4zeH/YV7+HOMGgvEcK9ByXTLER7X717BtU8uKLmO2y/K5LVGPtk1k2+PtT+gVkq3nSsRsJYIai5SrfzZr7cPfsOosUAfCyQmnnuOdLaBSwroRcJb+XPcTupy8f6iqyXSs4v75YQlevV38+/ljOGhIGgugnImYw7RXAiCIAiCEFRCduVCEARBEEYVyRbxSUhNLjraoimsu9+eeCvNVI7FNKlKWxxrq8r1DgddGKT9BD++K5GHKnSprN6hDSyJjnbeCI63zuTL7Bgm0aWWYr+zBcpKt/D105YCvkBmboSUtdnq4yX9ky+wdqby21YXJolugOOl8vEYNkH7b0NJ9mTohxLpNRTH2phaWl3PU1G1JdYBVmYdrMGx5HpFHbcDL2vgN4t5vzoMYkhNBXtw52Iehpj6FL/WHVP40rpzMQ+rdMH+0A7cXWMwMOfjdammUGId7b8J7L91YZBUCIm1gN13ZTs/nsuqXp7H8RgGQZw2fr0asN8+2D8V7oWTFTyFWhsGAbCkurOVp6aaS3mKeG88hDHgnYthD10YJLIF+hN997t6RmhR3k3GXPbh7GMcImERQRAEQRCCSkitXAiCIAjCWEGyRXwjkwtBEARBGA6iufDJuJlcTImzsfYR0ECgPbhlOrd0dkDq6fypPKVstoVbPP/DNJvvHzQVBFXOUWOBGKxsIRV1yfTygX/vpRzWh6mny/J4Ofi9zTOU4xPBzrvrI56u58zncXJzkX9lubuTeFARNRZhjWo77+Z5YP8N+0PNBdJawB9eT6q67DhqLLDEephJ/TLAVFRMLaU0taYi+iDEvi+GAQpNxvLEctZurOf2004uwTDYeyfv4/1Ni3nbBKmonlp+L5y8mo9H+28cH10L3y2kZvqrwdCBJdZREzHxCKSAz+EajNoqtcAJFRNZGg3FxenHWPt4J9dF7K2Zwto52U3K/YV52X/7q7HA/snwTi0uh7xn0LVNXcJLJqAdAL4D0e4b+1G31tsCL1XAW4Ph7h6nQoYQYtxMLgRBEARhRJGVC5/I5EIQBEEQhoNMLnwi2SKCIAiCIASVkFq5mBTfReHR/TFS1Figj4UBiJN3QjnguUvLWRtLqh8i3v7awk9Y+w2aw9q58by0NUH70094qWb0qlg0jduV+8MnJ6BsNdh/G3wywBEZNRaIToOBPhYmD8xhm/l41FDowBLs6J+LvhXoc9FKak2FrZD7UGCJdQ9oJjLncreB2sNglKHRWKAPxtJrD7L23hYed1fx56NcJJFcy69t2qVQcr2WixxQY4EYNBOgqZhUzY/XwR8bg8YC8dfXAml1cE1FuENtQh1VxZ8FN2gskIwsfv3Q5yLJwnUCWEId7b3fNeUrj6dDpf+ZnoMuGJwSja8FaizQ56IDdGq6dzCWUOhs4e9g9Pppb4H9KXwtiIy+FyOC+Fz4JKQmF4IgCIIwVpBUVN9IWEQQBEEQhsNnmotAf84A27dvJ5PJNOTPnj17fG63atUqw/jbbrvN7+OH1MqFt/13JfRhqilW7ENr2QnL+FJ0RRukCwKYmlpo5zl9aP99ANpIPKSeIvtLeRpXXIJ6uVYFpqaWJvE4SEvL6VdgJSIKa+KpoxgmMXnUYY/4oybo5/vHsIcZwhpOsO92pqjXJdHuG8MoWPWUCnhKHqamXp5fyNoHW2DtH8CwB6ammmBpWxcGyU4dXJqvOMjvw69csJO1/1y3krWbDvAwCNp7T6rh31XTFf5WQeX7S/+I37elX+bbY5gE2zlXnWTtilensnZnJlRRhbBJTA3fn2M2DxHGVPP+zip1qipZ1c/hlFj+Xbe08/dAlFUdItNVPdXhXRU1wystlYiopDwVhzMwNXVSgjoEhe9YTL+P1qT7Y8DKeoI/p+7L+LXs3a1ORRU4K1eupLo6bqFw//3307Zt22jJkiXKbW+55RZ68MEHB9rR0ZpqyUMQUpMLQRAEQRgzuD0GPd+w9nEGiIiIoLS0Qf1YX18fvfbaa3THHXeQyaT+gyw6OpptOxwkLCIIgiAIwyGIYRGHw8F+enrUq1z+8re//Y1aWlropptu0o794x//SElJSVRQUEDr16+nri71KtZQyMqFIAiCIIwyWVlZrL1hwwZ64IEHgrb/5557jlavXk2TJ6vDuNdddx1lZ2dTRkYGffrpp3TPPfdQcXExvfzyy34dL2QnF6ixmDOVW88eIR5b7oGPih8c44HXLuCCl6MOnpZVYOXljDFVFa1rEbT31jE9YdBGuBSW4XT235ia+rk8HsdG2orUsU1MATMf45qEbihJ7k7hdt9txDUbSbO5RXLHBzz1U0fXHK4L0NmJ60hP5rFiLLH+RlGBcvusefXqftBgIEsSuaII0w29NRlYYh3H/seFH7H2C5Cq+qWL+H3+8v+dx9q4eGrUWKhBjQXSlaHeX1Et1wm4QWPhsoAmAuy9HbO4xsJyhKc7dk7m+8OS6gimnurA1NMsSGW9OI3bf5+w8Hs/P4bfS2/V87IDU2P5/q5I/3Tg3wui+H30Z8sy1i51cLETan8Mdt8I2H+jPQDei0ch/R/tvt15YPftp8bC7ZVy73aqyy0Ej2AIMvu3r6qqIotlsIx9ZGTkkKO///3v06OPPqrc47Fjxyg/fzDNubq6mt5++23685//rD2bb37zmwP/njt3LqWnp9MFF1xApaWlNG3aNMWWnJCdXAiCIAjCqBJEh06LxcImF774zne+QzfeeKNyzNSpXPi8adMmSkxMpCuvvNLv01u+fDkREZWUlMjkQhAEQRDGI8nJyZScnKwf+C88Hg9t2rSJ1q5dSxMnTtRvABw8eJCIiNLTNStZgAg6BUEQBGE4uD3B+TmD/POf/6SysjL6xje+Yeirqamh/Px8+uSTfsfp0tJSeuihh2jfvn1UXl5Of/vb32jt2rV07rnn0rx58/w6bkitXKjsv5HoEh5378rjylvUWKA1LWosKmzcmwDtwXVgPBPtvQ9+PJ2fD/hg7C3J8bnv+ESeC48ai8Qk3r+7BPoTee5+PJRgx3NvPca9ynsMVaj5eNRAGO27OV2zwV4cfCbQ94LAV8MJPhXmQp6/353M4+zoY1FH4HsBwgNTPR+PduDoY7Fm1iHW3gc+FlWNCcp2Vgr/PqoOed2bUH4d49xl4GuRu5Brk/54ZClrE5Rg99fZGDUZOrtvnebC/Ila4+AEX4sEaDcf5boCxxwei0f772Y710Ilga/Fgkx+/arb43i7g7dRY4F24LNBK/ZO/SzWLm/n9wJqLE62J/psH7fyVELUWNTY+X3++SnHeX8878+Cd+7xffw+rkyIY+0ujcYCaT/Bt0e7bx2srEG3y/fAYOJx9/8Euo8zyHPPPUcrV65kGozP6Ovro+Li4oFskIiICHr33Xfp5z//OXV2dlJWVhZdffXVdN999/l93JCaXAiCIAiCcPps2bLFZ19OTg55vDQjWVlZ9P777wfluDK5EARBEIThICXXfRJSkwtv++8iWHJDe28d0Sf40nZnAl8eLYSl8dg8G2tjBT/sxyU+DHOgvfei5SXKfm8MVU0NYQmOIbU0uVfdD2DqqVtTFRWrkKI9N1ZNdb3ExUnRYNedtI+HBZoXq63aMQyC54NSo+h6ddVUDHuYG/n28XNtrF3TFMfarx6brzhboi/NPsjar/xzOWuHpcL5p/s21ylrUN8Mun6sctpF/Ls1ZcB3v89/W2B2PE3YBO290c7b+g4PmzR8jn93SUf4vdSRBc9tJb+27cTDFg0W/vlapvDj9dj59UG3RrT7xtTUew+tIRVOG99/OeZFQ9zKuxLqPz7lKdMx8TxciHbf75nyWBurnh7T2HdjqPpIovrewHcoYj3OP1x0E78Xaq7iqbDm4sFr6+oZITmh20MYBh7ePsYfITW5EARBEIQxg6xc+ESyRQRBEARBCCqyciEIgiAIw8FDQVi5CMqZjDlCdnKRv6RC2V/7Qg5r90B8D0uud0E8EUusYyoqplVhyfU40GDowFTUONBoPDJ70Nf9th1r/dq3GzQWmHraAnFmLKmuA4sCts2GuHMzj52Gf7mJtRubuStd9FFILc3k9uZtc/j+PamgAwDNRWsBPr28jXblaWABXdfM9Tdd83js+oKkKtZGzQXafWNqL2ossubzMskVoJNgJdehLzeVpyqunMOt3nc38zRkpHQxT1dM+Rv/Lizf5N9d6WJ+8Ty1oEHQkPoxvxYNy/m9ghoL53J+7/JvgogcXNPQa4Uy3nP49q0WLLHO4/hImoVbVDdD/1+XPcvaX97zTda+ZdmHyv2Hm7iu4Hgntz+fM4nbvb9R79uK3lt/QUQUBvf9F/O3s/bTxdz6/ar5B/m5OLg1+THKYO2ivVwnNndpOWsfPsnTovEdihqMtpX8vdVdzL/b+ET+XNkTB7d3d5/Z9M4BJCziEwmLCIIgCIIQVEJ25UIQBEEQRhW3m4gCXCVxj9AqywgjkwtBEARBGA4SFvGJyeMZ+5/M4XCQ1Wqlyb9+gMLM/THd8FY+L3JB+V/sRx+MngQo3ayxpkUwPqiLHyLe5YGJiOISeCzY35Ls3qAdeFtrYJqKhFk8jt/czDUQ0cd4nB19LNDnAu29kSl/wgx6TvUFvD/rXW7125nGv/su8M1A+29PKvciiD7MNRvxF3ANBIKW2y3v8lg0ajSiD/H9OxcYlAOMq2cfYO2/bvucz7Fo743239MWci1R6QFuY48+F87F3E4bQZ8LtP9O/YSPb+BVv/1mYjs/v+5MeO4c/N6IqebjscT6RAfsLwv2Z+f7Qz1OM5Rg7wHNB/pcIDfm72btPxQv9zGyH9TrqOiy8ftsRg4v367bF5Zcj03gepN20Jmh+Aq9hLAEg+4dqQPfod7+P+7ubqr4wX1kt9tPq9Kov3z2f9KFyTfThDD/3qfIKXcvvdv03Bk719FCVi4EQRAEYTjIyoVPZHIhCIIgCMNBHDp9ItkigiAIgiAElZBduUCfiypbHGs7TOBr38rjfzq0tUNa+PF06DQWCNYPwe29WZZXxtqlbUk+Rv5rX+B7YTi2RpOB/TqNhWF7TQn26gt4XDwe6kNENfF203yIm4OmAsejxgJ9MVAj0QW+FQiWYL/qqzyOjiXWl157kLV1Phd7YfvsBYNeB6j3WJ5YztorL+I+F3/ceg6pQM2EruS6rsR6wzK1Eh7HowwAa4sgqLFAsMQ6gpoLxGXleh7UWJjgAp01m9cI+ugo96/RaTCwlkhONvcVwe8b8e4Pi7MrxyKosUAuyirm4+O4Bwe+g7NXc/3P0T05fp0PgjWOqIU/dz1+lmgPBh6PmzwBlkwPdPuxSshOLgRBEARhVPF4Ag9riOZCEARBEIQBPEHQXMjkYmxRCUtw7WDfrUuD0oGppVhCHcMkaP+NmMG6llaowyIYBvFOL21ricXhDCyhnpjPS5Z3fcTDJtFncRNjtAPH1FMs2e5M4Uu53UkQ1jgKqaAQtYk9j9sUdx/hltK6MIsxDKIuqU5kJhUY5sCS67p+LLGO46spjbUxDNL8Dk8fTVnN00cb3xpMH3Uu4qmiK5MgDHJkKWsbUlEb4MsA+26dnfeMxZWsXV2boxyPdt9EPOzQdDWk5Vbz5xpTT5EICDu4HP6FQxFMRSXuBE99Ffy5/8jOwyDmCh4CXH45Dy0UdfJ7wRzH07TLK/izMDWHp8LW2/mz6Z1+iqmnNXZ+8p2Qqmou5ec6YSm31y5u52GQI2DnjTGtsHj+3jGEluGd6m96PoaOhbFFyE4uBEEQBGFUcbuJTAFqJkRzIQiCIAjCABIW8YmkogqCIAiCEFRCauUiP6eOJsb0xwVRczF3Kk97mrWAxxvfqpjF2p0lPP6I8cDsOB5vDJvGl67mWnnp48Px3PK5PJHrHjBeiJFg75LqRET/U38ua9+avn3g37+r56WREV2q6cIrjrL28TYe101K4vbh+QlcE1HUymOvrUk8VnvO2UdY+/2UPOX5IO4UKLVMfP+YSmpq4FfTWeCENt9/ejJP0bP/k8e9M+byz4ssmsVLrP/92Fzl+C9+/mNl/wUW/n08tno1a2N66cN3/23g39O33Mb6dqZOZe2vzdnD2pfGfsra7ybPYe0dadOU5/pILr9P7y3/Imt3Zajtv5u+pLZ+N3/MnxMssa7TUMzN4M/lPgcvMf+VJfx67Mji1wsxZfH2lFh4L0xW/9X5EXENRl4010xgifXZ+fz8Nxdzq/epsdyKHzUXl84rHDw3zV/UV896j7V/2nola+v+c5gD71xMRdWBurZ4TXq+Du/3ntupfgcGC4/bTZ4AwyKSiioIgiAIwiASFvGJhEUEQRAEQQgqsnIhCIIgCMPB7THayvrLOF25CKnJRbXdSuF9Q8dcK9riWfsw5GCjJqOCh0Lp8myuE0COOnhc/n/381jo4uncjhw1FpizPT2Be0vs7eKx39K2RNb+nWlQZ/HJCR5H/s8l2/m2iWr7b2RGPFoMq2OAqMHYkcLjvu8fV2ss/n7u06z9jWNfZ+0LZnIvgPca1ZoGnZ03+mDUoVnBXLXdd2ayjbUPtvAy5ehjgexN5fbd6GOx92LejxbPH7fksPZFrdkD//6PCz9ifRjD392cq2zrym6X1nM9zr0mrrE4L+kEa5dk8vFX//BD1t7eMkN5vKLlKaydYOE+Htw5geiKvELW3tnIP1/aZL7Fjgb+nLVgyXQ79/XIzOIah8p2/p7B7yrHwscjJ7r450NdxMl2/twj2J8R5+D7dwxe/5Jyro26Yv4h1n65bqHyWMgsC9ex/eXQIvUG4HOBXkBxUMId35lIwkdcezX9Rv6e8C574OrqIa6MOkN4PEQUaCrq+JxcSFhEEARBEISgElIrF4IgCIIwVvC4PeQJMCziGacrFyaPH59s48aN9PLLL1NRURGZzWZauXIlPfroozRz5kzldi+99BLdf//9VF5eTnl5efToo4/SZZdddton6XA4yGq1Uv6fvkfh0f1L0DnxbcptMEziAHtwBJfo/EVnZWs8Hg+T6Jan87zCKBgWSYTU0TwIc5yAVFMEj41235iaijRr7MhTkvjSre6zNh1Rny+GQRBMTdVtj+P9tftGog/xsIxzAVha18H5pfco+72roBIRVTTyNGdvclP5snxZA19Gv34Ozw3d1cLvJQyD5KXz1EnEnyqdRESfTypi7V9/ytOqZ2fwpXcM0dV28JAW3kuZk3ia8b4i/vkyIMyBYREdWAUVSbbw57rJwZf6U638WcLzb4DUUieEaaZm8+/jZAUPs3gTE8/vO7T7DhQLvDN171gEK0/r3plo922dycMubV5hFbezm6pufZDsdjtZLBa/zut0+Oz/pPPDv0QTTIHZkJ/y9NF7rpfP2LmOFn6FRd5//31at24d7d69m7Zu3Up9fX108cUXU2en7/+Yd+7cSddeey3dfPPNdODAAVqzZg2tWbOGCgsLfW4jCIIgCGMdj9sTlJ/xiF9hkbfeeou1N2/eTCkpKbRv3z4699xzh9zmF7/4BV1yySX03e9+l4iIHnroIdq6dSv96le/ot/85jfDPG1BEARBEMYqAWku7Pb+JciEBN/LtLt27aK7776b/W716tX06quv+tymp6eHenoGl4o/O46ra/B3fRFqBzbvsUREbqd6kQbH+4u7mzsPup3qJT48ni5U0Bfp7T7Hj4X7wmuj+2x4bLeTL/PptsfxiKvTv8+K1xLx6D5Pt3r/uD2O97cfcfXwtXN3F3wePD/cH/Sfgutn2J8fY3s6+H2pG4/9iC5MgGGR7qhTyuP1dfJ7F8Miunupz8S3x2cFP4+rC6qeatB93lPhuH/+ij01QX3+ri4IFUBEzfB9OX3fC65IHKs5eT/x9x2LmLp5RVzdO5NgvPH4E7z+3d93pvUMpzw9ARceO0Wazx2qeIaJy+XyXH755Z6zzjpLOW7ixImeLVu2sN89/fTTnpSUFJ/bbNiw4TPbM/mRH/mRH/mRn2H9lJaWDve/OCVOp9OTlpYWtPNMS0vzOJ3OM3Kuo8WwVy7WrVtHhYWFtGPHjuHuwifr169nqx02m42ys7OpsrKSrFZr0I8XKjgcDsrKyqKqqqpxJfzxF7kO/ch16EeuQz9yHQax2+00ZcoU5ap6IERFRVFZWRn19ganhklERARFRUXpB4YQw5pc3H777fT666/TBx98QJMnT1aOTUtLo4YGbrrU0NBAaWlpPrYgioyMpMhIo+LfarX+2z80REQWi0WuA8l1+Ay5Dv3IdehHrsMgYWFnzsopKipq3E0IgolfV97j8dDtt99Or7zyCv3zn/+k3Nxc7TYrVqygbdu2sd9t3bqVVqxY4d+ZCoIgCIIQEvi1crFu3TrasmULvfbaaxQbG0v19f056Varlczm/hzqtWvXUmZmJm3cuJGIiO68804677zz6IknnqDLL7+cXnjhBdq7dy89++yzQf4ogiAIgiCMBfxauXjmmWfIbrfTqlWrKD09feDnxRdfHBhTWVlJdXV1A+2VK1fSli1b6Nlnn6X58+fTX/7yF3r11VepoKDgtI8bGRlJGzZsGDJU8u+EXId+5Dr0I9ehH7kO/ch1GESuxejjl0OnIAiCIAiCDilcJgiCIAhCUJHJhSAIgiAIQUUmF4IgCIIgBBWZXAiCIAiCEFRkciEIgiAIQlAJycnFG2+8QcuXLyez2Uzx8fG0Zs2a0T6lEScnJ4dMJhP7eeSRR0b7tEaNnp4eWrBgAZlMJjp48OBon86Ic+WVV9KUKVMoKiqK0tPT6frrr6fa2trRPq0Rp7y8nG6++WbKzc0ls9lM06ZNow0bNgTNpjmU+MlPfkIrV66k6OhoiouLG+3TGTGefvppysnJoaioKFq+fDl98skno31K/5aE3OTir3/9K11//fV000030aFDh+ijjz6i6667brRPa1R48MEHqa6ubuDnjjvuGO1TGjW+973vUUZGxmifxqhx/vnn05///GcqLi6mv/71r1RaWkpf/vKXR/u0RpyioiJyu93029/+lo4cOUJPPvkk/eY3v6F77713tE9txOnt7aVrrrmG/vM//3O0T2XEePHFF+nuu++mDRs20P79+2n+/Pm0evVqamxsHO1T+/djlAun+UVfX58nMzPT8z//8z+jfSqjTnZ2tufJJ58c7dMYE7z55pue/Px8z5EjRzxE5Dlw4MBon9Ko89prr3lMJpOnt7d3tE9l1PnpT3/qyc3NHe3TGDU2bdrksVqto30aI8KyZcs869atG2i7XC5PRkaGZ+PGjaN4Vv+ehNTKxf79+6mmpobCwsJo4cKFlJ6eTpdeeikVFhaO9qmNCo888gglJibSwoUL6bHHHqNTp06N9imNOA0NDXTLLbfQ//3f/1F0dPRon86YoLW1lf74xz/SypUraeLEiaN9OqOO3W4/Y9UxhbFDb28v7du3jy688MKB34WFhdGFF15Iu3btGsUz+/ckpCYXJ0+eJCKiBx54gO677z56/fXXKT4+nlatWkWtra2jfHYjy7e+9S164YUX6L333qNbb72VHn74Yfre97432qc1ong8HrrxxhvptttuoyVLloz26Yw699xzD8XExFBiYiJVVlbSa6+9NtqnNOqUlJTQU089Rbfeeuton4pwhmlubiaXy0Wpqans96mpqQN1sISRY0xMLr7//e8bxIn481kslYjoBz/4AV199dW0ePFi2rRpE5lMJnrppZdG+VMEzuleByKiu+++m1atWkXz5s2j2267jZ544gl66qmnqKenZ5Q/ReCc7nV46qmnqL29ndavXz/ap3xG8Od+ICL67ne/SwcOHKB33nmHwsPDae3ateQZJ+7+/l4LIqKamhq65JJL6JprrqFbbrlllM48uAznOgjCaDAmaos0NTVRS0uLcszUqVPpo48+os9//vP04Ycf0tlnnz3Qt3z5crrwwgvpJz/5yZk+1TPK6V6HiIgIw++PHDlCBQUFVFRURDNnzjxTpzginO51+MpXvkJ///vfyWQyDfze5XJReHg4fe1rX6M//OEPZ/pUzyiB3A/V1dWUlZVFO3fupBUrVpypUxwx/L0WtbW1tGrVKvrc5z5HmzdvprCwMfF3VMAM557YvHkz3XXXXWSz2c7w2Y0uvb29FB0dTX/5y19YBuENN9xANptNVvJGGL9Krp8pkpOTKTk5WTtu8eLFFBkZScXFxQOTi76+PiovL6fs7OwzfZpnnNO9DkNx8OBBCgsLo5SUlCCf1chzutfhl7/8Jf34xz8eaNfW1tLq1avpxRdfpOXLl5/JUxwRArkfPlvlGw8rWUT+XYuamho6//zzB1Y2x8vEgiiwe2K8ExERQYsXL6Zt27YNTC7cbjdt27aNbr/99tE9uX9DxsTk4nSxWCx022230YYNGygrK4uys7PpscceIyKia665ZpTPbuTYtWsXffzxx3T++edTbGws7dq1i7797W/T17/+dYqPjx/t0xsxpkyZwtqTJk0iIqJp06bR5MmTR+OURoWPP/6Y9uzZQ2effTbFx8dTaWkp3X///TRt2rRxsWrhDzU1NbRq1SrKzs6mxx9/nJqamgb60tLSRvHMRp7KykpqbW2lyspKcrlcA/4v06dPH3hWxht333033XDDDbRkyRJatmwZ/fznP6fOzk666aabRvvU/v0Y3WQV/+nt7fV85zvf8aSkpHhiY2M9F154oaewsHC0T2tE2bdvn2f58uUeq9XqiYqK8syaNcvz8MMPe7q7u0f71EaVsrKyf8tU1E8//dRz/vnnexISEjyRkZGenJwcz2233eaprq4e7VMbcTZt2uQhoiF//t244YYbhrwO77333mif2hnlqaee8kyZMsUTERHhWbZsmWf37t2jfUr/lowJzYUgCIIgCOOH8ROMFARBEARhTCCTC0EQBEEQgopMLgRBEARBCCoyuRAEQRAEIajI5EIQBEEQhKAikwtBEARBEIKKTC4EQRAEQQgqMrkQBEEQBCGoyORCEARBEISgIpMLQRAEQRCCikwuBEEQBEEIKv8fHGLklPb+2CIAAAAASUVORK5CYII=",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAgoAAAGzCAYAAABO7D91AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAAAxrUlEQVR4nO3de3QUVbr38V8nJJ0ASQzYgQAhXFRwRBQRIyA3h+EyHjQuZTyIIC4Oim/H4aZCFEQcoHHAGRQURZ3EdY4MKAxwTlSQQQIioIigwkAcQEwMF3GQwETJpbveP5Ce6UCFdHUn3aG/n7X2kqquvWt3CeTheXZV2QzDMAQAAHABUaGeAAAACF8ECgAAwBSBAgAAMEWgAAAATBEoAAAAUwQKAADAFIECAAAwRaAAAABMESgAAABTBApAHXn66adls9lCMl5ubq5sNps+/fTToJ0fQGQgUABCpLy8XM8//7y6dOmixMREXXbZZbrmmmv04IMPat++faGeHgBIkhqEegJApLrrrrv03nvvadiwYRozZowqKiq0b98+5eXlqUePHurYsWOopwgABApAKGzfvl15eXmaNWuWnnjiCZ/PFi5cqJMnTwblPB6PR+Xl5UEZC0BkovQA1ILNmzerW7duiouLU/v27fXKK6/4fH7gwAFJUs+ePc/rGx0draZNm/o13jk2m01ZWVl68803dc0118hut2vNmjXez8vKyjRx4kQ5HA41atRId955p44fP37eOC+99JK3f4sWLeR0OoMWvACoX2y8ZhoIri+//FIZGRlyOBx6+OGHVVlZqYULF6pZs2b64osvZBiGtm7dqh49emjMmDF66aWX1KCBeXKvJuOdY7PZdPXVV+v7779XVlaWLr/8cvXo0UO7du3SAw88oC5duig5OVl33nmnDh06pPnz5+uuu+7SsmXLvGM8/fTTmjFjhvr376877rhDBQUFWrRokW644QZ99NFHiomJqdXrByDMGACCKjMz04iLizO++eYb776//e1vRnR0tHHuj5zH4zH69OljSDKaNWtmDBs2zHjxxRd9+vgz3jmSjKioKGPPnj0++3NycgxJRv/+/Q2Px+PdP2HCBCM6Oto4efKkYRiG8d133xmxsbHGgAEDDLfb7T1u4cKFhiTjT3/6UwBXBkB9ROkBCCK32621a9cqMzNTrVu39u6/+uqrNXDgQO+2zWbT2rVrNXPmTCUnJ+vPf/6znE6n0tPTdc8993jT/DUd79/16dNHv/jFLy742YMPPuhzS2WvXr3kdrv1zTffSJL++te/qry8XOPHj1dU1L/+ehgzZowSExP1zjvv+H9RANRrBApAEB0/flw//fSTrrzyyvM+69Chg8+23W7Xk08+qb179+rw4cP685//rJtvvllvvfWWsrKy/B7vnLZt25rO79+DDUlKTk6WJP3www+S5A0Yqo4dGxurdu3aeT8HwtWmTZs0ZMgQtWjRQjabTatWraqzc8+ZM0c2m03jx4/32f/QQw+pffv2io+Pl8Ph0B133FGvboEmUADCQGpqqv7zP/9TmzZt0pVXXqm33npLlZWVlsaKj483/Sw6OvqC+w2WKuESUVpaquuuu04vvvhinZ53+/bteuWVV9S5c+fzPuvatatycnK0d+9erV27VoZhaMCAAXK73XU6R6sIFIAgcjgcio+P19///vfzPisoKLho/5iYGHXu3FkVFRX6/vvvAx7PX+np6Rccu7y8XF9//bX3cyBcDR48WDNnztSdd955wc/Lysr06KOPqmXLlmrUqJEyMjKUn58f0Dn/+c9/avjw4Xr11Ve9Wbp/9+CDD6p3795q06aNbrjhBs2cOVNFRUU6dOhQQOetKwQKQBBFR0dr4MCBWrVqlQoLC737z/1L4py///3vPp+fc/LkSW3dulXJyclyOBw1Hi9Y+vfvr9jYWL3wwgs+WYbXX39dJSUluu2224J+TqAuZWVlaevWrVq6dKm++OILDR06VIMGDbpgMF5TTqdTt912m/r373/RY0tLS5WTk6O2bdsqLS3N8jnrEg9cAoJsxowZWrNmjXr16qX/9//+nyorK7VgwQJdc801+uKLLyRJn3/+ue69914NHjxYvXr1UpMmTVRcXKw33nhDhw8f1vz5871lgpqMFywOh0PZ2dmaMWOGBg0apNtvv10FBQV66aWX1K1bN913331BPR9QlwoLC5WTk6PCwkK1aNFCkvToo49qzZo1ysnJ0ezZs/0ec+nSpfrss8+0ffv2ao976aWX9Pjjj6u0tFQdOnTQunXrFBsba+l71LkQ33UBXJI2btxodO3a1YiNjTXatWtnvPzyy8b06dO9tzMeO3bMmDNnjtGnTx8jNTXVaNCggZGcnGzceuutxvLly/0e7xxJhtPpPK//udsjt2/f7rN/w4YNhiRjw4YNPvsXLlxodOzY0YiJiTGaNWtmPPzww8YPP/wQ2EUB6pgkY+XKld7tvLw8Q5LRqFEjn9agQQPjN7/5jWEYhrF3715DUrVt8uTJhmEYRmFhoZGSkmJ8/vnn3nP06dPHGDdu3HlzOXnypPHVV18ZGzduNIYMGWLccMMNxk8//VSr3z9YeOASAOCSZLPZtHLlSmVmZkqSli1bpuHDh2vPnj3nLext3LixmjdvrvLych08eLDacZs2bSqHw6FVq1bpzjvv9BnL7XbLZrMpKipKZWVlF1xAXF5eruTkZL322msaNmxY4F+0llF6AABEhC5dusjtduu7775Tr169LnhMbGxsjV/I9stf/lJffvmlz74HHnhAHTt21OTJk6u9y8gwDJWVlfn3BUKEQAEAcMn45z//qf3793u3v/76a+3atUtNmjTRVVddpeHDh2vkyJF67rnn1KVLFx0/flzr169X586d/V6sm5CQoE6dOvnsa9SokZo2berdf/DgQS1btkwDBgyQw+HQt99+qzlz5ig+Pl6//vWvA//CdYBAAQBwyfj000/Vr18/7/bEiRMlSffff79yc3OVk5OjmTNnatKkSSouLtbll1+um2++Wf/xH/9RK/OJi4vThx9+qPnz5+uHH35Qs2bN1Lt3b23ZskUpKSm1cs5g82uNwqJFi7Ro0SLvvZ/XXHONnnrqKQ0ePNi0z9tvv61p06bp0KFDuvLKK/Xss8/WmygKAIBI59dzFFq1aqU5c+Zox44d+vTTT3Xrrbfqjjvu0J49ey54/JYtWzRs2DCNHj1aO3fuVGZmpjIzM7V79+6gTB4AANSugO96aNKkiebOnavRo0ef99k999yj0tJS5eXleffdfPPNuv766/Xyyy8HcloAAFAHLK9RcLvdevvtt1VaWqru3btf8JitW7d660PnnHvKXHXKysp8VoN6PB6dOHFCTZs29XnzHQAAVRmGodOnT6tFixY+b0ENpjNnzqi8vDwoY8XGxiouLi4oY9UGvwOFL7/8Ut27d9eZM2fUuHFjrVy50vSVtkePHlWzZs189jVr1kxHjx6t9hwul0szZszwd2oAAHgVFRWpVatWQR/3zJkzapveWEe/C85LnZo3b66vv/46bIMFvwOFDh06aNeuXSopKdHy5ct1//33a+PGjabBghXZ2dk+mYiSkhK1bt1at+jXaqAYSVLUL67y6VPaNsF3u7nv/atnLvfNRJQne3y2PUkVPttxjX3vb72s0U8+203iq2zHlvpsJ8f86Pt5jO/niQ18+ydEVd32PX+87V/bjaJ8o1i7zfctgzE23+8WZ/P9zdxAvtWmmCpJmqp3/sZUyeJEy3e7apan6udVRVVZGhN9kSxR1eMvJuoi5/dXtI1XogD1yal/epR+wyElJCRc/GALysvLdfQ7t77eka7EhMD+fjh12qO2Xb9ReXn5pRMoxMbG6oorrpB09tWZ27dv1/PPP69XXnnlvGObN2+uY8eO+ew7duyYmjdvXu057Ha77Hb7BSYbowa2nwOFaN/PG8T4XuDoWN8fd9F23x8eUXG+P0wVX+X4hr7HN2jke3xMvO8P31i7b6Bhj6kSeMTE+J6uge/n8VG+/ysaRvv+8G9o+9f8GlVJpcVV+UFW9Qd/nK1KYBDkQCGKQAFAGKrtUnViQlTAgUJ9EPA39Hg8pk+X6t69u9avX++zb926daZrGgAAqC/chicoLdz5lVHIzs7W4MGD1bp1a50+fVpLlixRfn6+93W3I0eOVMuWLeVyuSRJ48aNU58+ffTcc8/ptttu09KlS/Xpp59q8eLFwf8mAADUIY8MeRTY65IC7V8X/AoUvvvuO40cOVJHjhxRUlKSOnfurLVr1+pXv/qVpLOv8Pz3FaY9evTQkiVLNHXqVD3xxBO68sortWrVqvMeeQkAQH3jkUeB5gMCH6H2+RUovP7669V+np+ff96+oUOHaujQoX5NCgAAhAfe9QAAgAVuw5A7sGcWBty/LhAoAABgQaSsUbj07+sAAACWkVEAAMACjwy5IyCjQKAAAIAFlB4AAEDEI6MAAIAF3PUAAABMeX5ugY4R7ig9AAAAU2QUAACwwB2Eux4C7V8XCBQAALDAbZxtgY4R7ggUAACwgDUKAAAg4pFRAADAAo9scssW8BjhjkABAAALPMbZFugY4Y7SAwAAMEVGAQAAC9xBKD0E2r8uECgAAGBBpAQKlB4AAIApMgoAAFjgMWzyGAHe9RBg/7pAoAAAgAWUHgAAQMQjowAAgAVuRckd4L+33UGaS20iUAAAwAIjCGsUDNYoAABwaWKNAgAAiHhkFAAAsMBtRMltBLhGoR6864FAAQAACzyyyRNgYt6j8I8UKD0AAABTZBQAALAgUhYzEigAAGBBcNYoUHoAAAD1GBkFAAAsOLuYMcCXQlF6AADg0uQJwiOcuesBAADUa2QUAACwIFIWMxIoAABggUdREfHAJQIFAAAscBs2uQN8+2Og/esCaxQAAIApMgoAAFjgDsJdD25KDwAAXJo8RpQ8AS5m9NSDxYyUHgAAgCkyCgAAWEDpAQAAmPIo8LsWPMGZSq2i9AAAAEyRUQAAwILgPHAp/P+9Hv4zBAAgDJ17hHOgrbbMmjVLPXr0UMOGDXXZZZdZHodAAQCAS1B5ebmGDh2qhx9+OKBxKD0AAGCBRzZ5FOhixtp7hPOMGTMkSbm5uQGNQ6AAAIAFwXl75Nn+p06d8tlvt9tlt9sDGjtYKD0AAGDBuecoBNokKS0tTUlJSd7mcrlC/O3+hUABAIAQKyoqUklJibdlZ2df8LgpU6bIZrNV2/bt2xfUuVF6AADAAo9hkyfQBy793D8xMVGJiYkXPX7SpEkaNWpUtce0a9cuoDlVRaAAAIAFniA8wtnf5yg4HA45HI6AzukvAgUAAC5BhYWFOnHihAoLC+V2u7Vr1y5J0hVXXKHGjRvXeBwCBQAALAjOa6Zrb6ngU089pTfeeMO73aVLF0nShg0b1Ldv3xqPw2JGAAAscMsWlFZbcnNzZRjGec2fIEEiUAAAANWg9AAAgAXhXnoIFgIFAAAscEsBlw7cwZlKrQr/UAYAAIQMGQUAACyg9AAAAEwF86VQ4cyvGbpcLnXr1k0JCQlKSUlRZmamCgoKLtpv/vz56tChg+Lj45WWlqYJEybozJkzlicNAECoGT+/ZjqQZtTi7ZHB4legsHHjRjmdTm3btk3r1q1TRUWFBgwYoNLSUtM+S5Ys0ZQpUzR9+nTt3btXr7/+upYtW6Ynnngi4MkDAIDa5VfpYc2aNT7bubm5SklJ0Y4dO9S7d+8L9tmyZYt69uype++9V5LUpk0bDRs2TB9//LHFKQMAEHqUHmqgpKREktSkSRPTY3r06KEdO3bok08+kSQdPHhQ7777rn7961+b9ikrK9OpU6d8GgAA4eTc2yMDbeHO8mJGj8ej8ePHq2fPnurUqZPpcffee6++//573XLLLTIMQ5WVlRo7dmy1pQeXy6UZM2ZYnRoAAAgSyxkFp9Op3bt3a+nSpdUel5+fr9mzZ+ull17SZ599pr/85S9655139Lvf/c60T3Z2tkpKSrytqKjI6jQBAKgV7p9fMx1oC3eWMgpZWVnKy8vTpk2b1KpVq2qPnTZtmkaMGKH/+q//kiRde+21Ki0t1YMPPqgnn3xSUVHnXyS73S673W5lagAA1IlglA4uudKDYRh65JFHtHLlSuXn56tt27YX7fPjjz+eFwxER0d7xwMAAOHLr0DB6XRqyZIlWr16tRISEnT06FFJUlJSkuLj4yVJI0eOVMuWLeVyuSRJQ4YM0R/+8Ad16dJFGRkZ2r9/v6ZNm6YhQ4Z4AwYAAOobj6LkCbB0EGj/uuBXoLBo0SJJOu9d1jk5ORo1apQkqbCw0CeDMHXqVNlsNk2dOlXFxcVyOBwaMmSIZs2aFdjMAQAIIbdhkzvA0kGg/euC36WHi8nPz/c9QYMGmj59uqZPn+7XxAAAQOjxrgcAACxgMSMAADBlBOHtkUY9eDIjgQIAABa4ZZM7wJc6Bdq/LoR/KAMAAEKGjAIAABZ4jMDXGHjqweOECBQAALDAE4Q1CoH2rwvhP0MAABAyZBQAALDAI5s8AS5GDLR/XSBQAADAgkh5MiOlBwAAYIqMAgAAFkTKYkYCBQAALPAoCI9wrgdrFMI/lAEAACFDRgEAAAuMINz1YNSDjAKBAgAAFvD2SAAAYCpSFjOG/wwBAEDIkFEAAMACSg8AAMBUpDzCmdIDAAAwRUYBAAALKD0AAABTkRIoUHoAAACmyCgAAGBBpGQUCBQAALAgUgIFSg8AAMAUGQUAACwwFPhzEIzgTKVWESgAAGBBpJQeCBQAALAgUgIF1igAAABTBAoAAFhwLqMQaKsNhw4d0ujRo9W2bVvFx8erffv2mj59usrLy/0ei9IDAAAWhHPpYd++ffJ4PHrllVd0xRVXaPfu3RozZoxKS0s1b948v8YiUAAA4BIzaNAgDRo0yLvdrl07FRQUaNGiRQQKAADUBcOwyQgwI3Cu/6lTp3z22+122e32gMauqqSkRE2aNPG7H2sUAACwwCNbUJokpaWlKSkpydtcLldQ57p//34tWLBADz30kN99CRQAAAixoqIilZSUeFt2dvYFj5syZYpsNlu1bd++fT59iouLNWjQIA0dOlRjxozxe26UHgAAsCCYixkTExOVmJh40eMnTZqkUaNGVXtMu3btvL8+fPiw+vXrpx49emjx4sWW5kigAACABcFco1BTDodDDoejRscWFxerX79+6tq1q3JychQVZa2IQKAAAMAlpri4WH379lV6errmzZun48ePez9r3ry5X2MRKAAAYEE4P0dh3bp12r9/v/bv369WrVr5fGYY/r2KisWMAABYcK70EGirDaNGjZJhGBds/iKjAACABUYQMgq1FSgEExkFAABgiowCAAAWGJIsZPLPGyPcESgAAGCBRzbZFOBixgD71wVKDwAAwBQZBQAALAjFA5dCgUABAAALPIZNtjB9jkIwUXoAAACmyCgAAGCBYQThrod6cNsDgQIAABZEyhoFSg8AAMAUGQUAACyIlIwCgQIAABZEyl0PBAoAAFgQKYsZWaMAAABMkVEAAMCCsxmFQNcoBGkytYhAAQAACyJlMSOlBwAAYIqMAgAAFhg/t0DHCHcECgAAWEDpAQAARDwyCgAAWBEhtQe/Mgoul0vdunVTQkKCUlJSlJmZqYKCgov2O3nypJxOp1JTU2W323XVVVfp3XfftTxpAABC7ufSQyBN9aD04FdGYePGjXI6nerWrZsqKyv1xBNPaMCAAfrb3/6mRo0aXbBPeXm5fvWrXyklJUXLly9Xy5Yt9c033+iyyy4LxvwBAAiJSHkyo1+Bwpo1a3y2c3NzlZKSoh07dqh3794X7POnP/1JJ06c0JYtWxQTEyNJatOmjbXZAgCAOhXQYsaSkhJJUpMmTUyP+d///V91795dTqdTzZo1U6dOnTR79my53W7TPmVlZTp16pRPAwAgnARadgjGXRN1wXKg4PF4NH78ePXs2VOdOnUyPe7gwYNavny53G633n33XU2bNk3PPfecZs6cadrH5XIpKSnJ29LS0qxOEwCA2nFujUGgLcxZDhScTqd2796tpUuXVnucx+NRSkqKFi9erK5du+qee+7Rk08+qZdfftm0T3Z2tkpKSrytqKjI6jQBAEAALN0emZWVpby8PG3atEmtWrWq9tjU1FTFxMQoOjrau+/qq6/W0aNHVV5ertjY2PP62O122e12K1MDAKBORMpiRr8yCoZhKCsrSytXrtQHH3ygtm3bXrRPz549tX//fnk8Hu++r776SqmpqRcMEgAAqBeMILUw51eg4HQ69T//8z9asmSJEhISdPToUR09elQ//fST95iRI0cqOzvbu/3www/rxIkTGjdunL766iu98847mj17tpxOZ/C+BQAAqBV+lR4WLVokSerbt6/P/pycHI0aNUqSVFhYqKiof8UfaWlpWrt2rSZMmKDOnTurZcuWGjdunCZPnhzYzAEACKFIedeDX4GCUYNiSn5+/nn7unfvrm3btvlzKgAAwl89KB0EipdCAQAAU7wUCgAACyg9AAAAcxHy9kgCBQAALLH93AIdI7yxRgEAAJgiowAAgBWUHgAAgKkICRQoPQAAAFNkFAAAsCIYr4nm9kgAAC5NvD0SAABEPDIKAABYESGLGQkUAACwIkLWKFB6AAAApggUAACwwGYEp9WW22+/Xa1bt1ZcXJxSU1M1YsQIHT582O9xCBQAALDCCFKrJf369dNbb72lgoICrVixQgcOHNDdd9/t9zisUQAAwIogrlE4deqUz2673S673R7Q0BMmTPD+Oj09XVOmTFFmZqYqKioUExNT43HIKAAAEGJpaWlKSkryNpfLFdTxT5w4oTfffFM9evTwK0iQyCgAAGBNEG+PLCoqUmJiond3oNmEcyZPnqyFCxfqxx9/1M0336y8vDy/xyCjAACAFUFco5CYmOjTzAKFKVOmyGazVdv27dvnPf6xxx7Tzp079f777ys6OlojR46U4efjIMkoAABQT0yaNEmjRo2q9ph27dp5f3355Zfr8ssv11VXXaWrr75aaWlp2rZtm7p3717jcxIoAABgRQiezOhwOORwOCydyuPxSJLKysr86kegAACAFWH8ZMaPP/5Y27dv1y233KLk5GQdOHBA06ZNU/v27f3KJkisUQAA4JLTsGFD/eUvf9Evf/lLdejQQaNHj1bnzp21ceNGvxdKklEAAMCCYDxZsbaezHjttdfqgw8+CMpYBAoAAFgRIW+PpPQAAABMESgAAABTlB4AALDApiCsUQjKTGoXgQIAAFaE8e2RwUTpAQAAmCKjAACAFRFy1wOBAgAAVkRIoEDpAQAAmCKjAACABeH8ZMZgIlAAAMAKSg8AACDSkVEAAMCKCMkoECgAAGBBpKxRoPQAAABMkVEAAMCKCHmEM4ECAABWsEYBAACYYY0CAACIeGQUAACwgtIDAAAwFYTSQ30IFCg9AAAAU2QUAACwgtIDAAAwFSGBAqUHAABgiowCAAAW8BwFAAAQ8QgUAACAKUoPAABYESGLGQkUAACwIFLWKBAoAABgVT34QR8o1igAAABTZBQAALCCNQoAAMBMpKxRoPQAAABMkVEAAMAKSg8AAMAMpQcAABDx/AoUXC6XunXrpoSEBKWkpCgzM1MFBQU17r906VLZbDZlZmb6O08AAMKLEaQW5vwKFDZu3Cin06lt27Zp3bp1qqio0IABA1RaWnrRvocOHdKjjz6qXr16WZ4sAABhI0ICBb/WKKxZs8ZnOzc3VykpKdqxY4d69+5t2s/tdmv48OGaMWOGPvzwQ508ebLa85SVlamsrMy7ferUKX+mCQAAgiSgNQolJSWSpCZNmlR73DPPPKOUlBSNHj26RuO6XC4lJSV5W1paWiDTBAAg6M4tZgy0hTvLgYLH49H48ePVs2dPderUyfS4zZs36/XXX9err75a47Gzs7NVUlLibUVFRVanCQBA7aD0UD2n06ndu3dr8+bNpsecPn1aI0aM0KuvvqrLL7+8xmPb7XbZ7XarUwMAoPbxHAVzWVlZysvL06ZNm9SqVSvT4w4cOKBDhw5pyJAh3n0ej+fsiRs0UEFBgdq3b29lCgAAoA74FSgYhqFHHnlEK1euVH5+vtq2bVvt8R07dtSXX37ps2/q1Kk6ffq0nn/+edYeAADqrUh54JJfgYLT6dSSJUu0evVqJSQk6OjRo5KkpKQkxcfHS5JGjhypli1byuVyKS4u7rz1C5dddpkkVbuuAQCAsFdPSg9lZWXKyMjQ559/rp07d+r666/3q79fixkXLVqkkpIS9e3bV6mpqd62bNky7zGFhYU6cuSIX5MAAAC14/HHH1eLFi0s9/e79HAx+fn51X6em5vrzykBAAhL9aH08N577+n999/XihUr9N5771kag5dCAQBgRRBLD1UfLBiMu/+OHTumMWPGaNWqVWrYsKHlcXgpFAAAIZaWlubzoEGXyxXQeIZhaNSoURo7dqxuvPHGgMYiowAAgBVBzCgUFRUpMTHRu9ssmzBlyhQ9++yz1Q65d+9evf/++zp9+rSys7MDnCCBAgAAlth+boGOIUmJiYk+gYKZSZMmadSoUdUe065dO33wwQfaunXreQHHjTfeqOHDh+uNN96o8RwJFAAAqCccDoccDsdFj3vhhRc0c+ZM7/bhw4c1cOBALVu2TBkZGX6dk0ABAAArwvg5Cq1bt/bZbty4sSSpffv21T5R+UIIFAAAsKA+3B4ZDAQKAABYEcYZharatGlTo2chXQi3RwIAAFNkFAAAsKoelA4CRaAAAIAFkbJGgdIDAAAwRUYBAAAr6tFixkAQKAAAYAGlBwAAEPHIKAAAYAWlBwAAYIbSAwAAiHhkFAAAsILSAwAAMEWgAAAAzLBGAQAARDwyCgAAWEHpAQAAmLEZhmxGYD/pA+1fFyg9AAAAU2QUAACwgtIDAAAww10PAAAg4pFRAADACkoPAADADKUHAAAQ8cgoAABgBaUHAABgJlJKDwQKAABYESEZBdYoAAAAU2QUAACwqD6UDgJFoAAAgBWGcbYFOkaYo/QAAABMkVEAAMAC7noAAADmuOsBAABEOjIKAABYYPOcbYGOEe4IFAAAsILSAwAAiHRkFAAAsIC7HgAAgLkIeeASgQIAABZESkaBNQoAAMAUGQUAAKyIkLseCBQAALCA0gMAAIh4ZBQAALCCux4AAIAZSg8AACDikVEAAMCKCLnrgYwCAAAWnCs9BNpqS5s2bWSz2XzanDlz/B6HjAIAAJeoZ555RmPGjPFuJyQk+D0GgQIAAFZ4jLMt0DFqUUJCgpo3bx7QGJQeAACwwghSk3Tq1CmfVlZWFpQpzpkzR02bNlWXLl00d+5cVVZW+j0GGQUAACywKQi3R/7837S0NJ/906dP19NPPx3Q2L/97W91ww03qEmTJtqyZYuys7N15MgR/eEPf/BrHAIFAABCrKioSImJid5tu91+weOmTJmiZ599ttqx9u7dq44dO2rixInefZ07d1ZsbKweeughuVwu0/EvhEABAAArgvhkxsTERJ9AwcykSZM0atSoao9p167dBfdnZGSosrJShw4dUocOHWo8RQIFAAAsCMWTGR0OhxwOh6Vz7dq1S1FRUUpJSfGrn1+LGV0ul7p166aEhASlpKQoMzNTBQUF1fZ59dVX1atXLyUnJys5OVn9+/fXJ5984tckAQBAzW3dulXz58/X559/roMHD+rNN9/UhAkTdN999yk5OdmvsfwKFDZu3Cin06lt27Zp3bp1qqio0IABA1RaWmraJz8/X8OGDdOGDRu0detWpaWlacCAASouLvZrogAAhJUg3vUQbHa7XUuXLlWfPn10zTXXaNasWZowYYIWL17s91h+lR7WrFnjs52bm6uUlBTt2LFDvXv3vmCfN99802f7tdde04oVK7R+/XqNHDnygn3Kysp8bg05deqUP9MEAKDW2QxDtgDXKATa38wNN9ygbdu2BWWsgJ6jUFJSIklq0qRJjfv8+OOPqqioqLaPy+VSUlKSt1W9bQQAANQNy4GCx+PR+PHj1bNnT3Xq1KnG/SZPnqwWLVqof//+psdkZ2erpKTE24qKiqxOEwCA2uEJUgtzlu96cDqd2r17tzZv3lzjPnPmzNHSpUuVn5+vuLg40+Psdrtf93gCAFDXwrn0EEyWAoWsrCzl5eVp06ZNatWqVY36zJs3T3PmzNFf//pXde7c2cppAQBAHfMrUDAMQ4888ohWrlyp/Px8tW3btkb9fv/732vWrFlau3atbrzxRksTBQAgrATjroXwTyj4Fyg4nU4tWbJEq1evVkJCgo4ePSpJSkpKUnx8vCRp5MiRatmypVwulyTp2Wef1VNPPaUlS5aoTZs23j6NGzdW48aNg/ldAACoO0F8MmM482sx46JFi1RSUqK+ffsqNTXV25YtW+Y9prCwUEeOHPHpU15errvvvtunz7x584L3LQAAqGPnnswYaAt3fpceLiY/P99n+9ChQ/6cAgAAhBHe9QAAgBURUnogUAAAwAKb52wLdIxwF9CTGQEAwKWNjAIAAFZQegAAAKYi5DkKlB4AAIApMgoAAFjAux4AAIC5CFmjQOkBAACYIqMAAIAVhqRAn4MQ/gkFAgUAAKxgjQIAADBnKAhrFIIyk1rFGgUAAGCKjAIAAFZEyF0PBAoAAFjhkWQLwhhhjtIDAAAwRUYBAAALuOsBAACYi5A1CpQeAACAKTIKAABYESEZBQIFAACsiJBAgdIDAAAwRUYBAAArIuQ5CgQKAABYwO2RAADAHGsUAABApCOjAACAFR5DsgWYEfCEf0aBQAEAACsoPQAAgEhHRgEAAEuCkFFQ+GcUCBQAALCC0gMAAIh0ZBQAALDCYyjg0gF3PQAAcIkyPGdboGOEOUoPAADAFBkFAACsiJDFjAQKAABYwRoFAABgKkIyCqxRAADgEvXOO+8oIyND8fHxSk5OVmZmpt9jkFEAAMAKQ0HIKARlJhe0YsUKjRkzRrNnz9att96qyspK7d692+9xCBQAALAijEsPlZWVGjdunObOnavRo0d79//iF7/weyxKDwAAhNipU6d8WllZWUDjffbZZyouLlZUVJS6dOmi1NRUDR482FJGgUABAAArPJ7gNElpaWlKSkryNpfLFdDUDh48KEl6+umnNXXqVOXl5Sk5OVl9+/bViRMn/BqLQAEAACvOlR4CbZKKiopUUlLibdnZ2Rc85ZQpU2Sz2apt+/btk+fnAOTJJ5/UXXfdpa5duyonJ0c2m01vv/22X1+TNQoAAIRYYmKiEhMTL3rcpEmTNGrUqGqPadeunY4cOSLJd02C3W5Xu3btVFhY6NfcCBQAALAiBIsZHQ6HHA7HRY/r2rWr7Ha7CgoKdMstt0iSKioqdOjQIaWnp/t1TgIFAACsCOMnMyYmJmrs2LGaPn260tLSlJ6errlz50qShg4d6tdYBAoAAFyC5s6dqwYNGmjEiBH66aeflJGRoQ8++EDJycl+jUOgAACABYbhkRHga6ID7V+dmJgYzZs3T/PmzQtoHAIFAACsMIzASwf14F0PBAoAAFhhBGGNQj0IFHiOAgAAMEVGAQAAKzweyRbgGoNaXKMQLAQKAABYQekBAABEOjIKAABYYHg8MgIsPdTm7ZHBQqAAAIAVlB4AAECkI6MAAIAVHkOyXfoZBQIFAACsMAxJgd4eGf6BAqUHAABgiowCAAAWGB5DRoClB+NSyyi4XC5169ZNCQkJSklJUWZmpgoKCi7a7+2331bHjh0VFxena6+9Vu+++67lCQMAEBYMT3BamPMrUNi4caOcTqe2bdumdevWqaKiQgMGDFBpaalpny1btmjYsGEaPXq0du7cqczMTGVmZmr37t0BTx4AgFAxPEZQWrjzq/SwZs0an+3c3FylpKRox44d6t279wX7PP/88xo0aJAee+wxSdLvfvc7rVu3TgsXLtTLL79scdoAAKAuBLRGoaSkRJLUpEkT02O2bt2qiRMn+uwbOHCgVq1aZdqnrKxMZWVl552nUhXeZ1tEuct8+lRWnPHZdpdH+26X2Xy2PWd80z2enyp8j4+uMr7Nd7vCU+6zXV7hu10W4zvemSrbsQ0qfbYbRFXddvtsG7Z/247ynXtllSeDxdiq/7xBlQeExPheGvleOSnGZqvyue+27SKfV1U1jRVt8+/4i4m6yPn9FR3c4QDUslP/PPt3Xm3X/yuNsoBLB5WquPhBIWY5UPB4PBo/frx69uypTp06mR539OhRNWvWzGdfs2bNdPToUdM+LpdLM2bMOG//Zv3b2oa/Vfmw6jYAIKL94x//UFJSUtDHjY2NVfPmzbX5aHDW2zVv3lyxsbFBGas2WA4UnE6ndu/erc2bNwdzPpKk7OxsnyzEyZMnlZ6ersLCwlr5n15fnDp1SmlpaSoqKlJiYmKopxMyXIezuA5ncR3O4jr8S0lJiVq3bl1ttjsQcXFx+vrrr1VeXn7xg2sgNjZWcXFxQRmrNlgKFLKyspSXl6dNmzapVatW1R7bvHlzHTt2zGffsWPH1Lx5c9M+drtddrv9vP1JSUkR/wdAkhITE7kO4jqcw3U4i+twFtfhX6Kiau9RQXFxcWH9wz2Y/LqKhmEoKytLK1eu1AcffKC2bdtetE/37t21fv16n33r1q1T9+7d/ZspAACoc35lFJxOp5YsWaLVq1crISHBu84gKSlJ8fHxkqSRI0eqZcuWcrlckqRx48apT58+eu6553Tbbbdp6dKl+vTTT7V48eIgfxUAABBsfmUUFi1apJKSEvXt21epqanetmzZMu8xhYWFOnLkiHe7R48eWrJkiRYvXqzrrrtOy5cv16pVq6pdAFmV3W7X9OnTL1iOiCRch7O4DmdxHc7iOpzFdfgXrkVw2Yz68PxIAAAQErwUCgAAmCJQAAAApggUAACAKQIFAABgikABAACYqpeBwjvvvKOMjAzFx8crOTlZmZmZoZ5SnWvTpo1sNptPmzNnTqinFTJlZWW6/vrrZbPZtGvXrlBPp87dfvvtat26teLi4pSamqoRI0bo8OHDoZ5WnTt06JBGjx6ttm3bKj4+Xu3bt9f06dOD9qjd+mTWrFnq0aOHGjZsqMsuuyzU06kzL774otq0aaO4uDhlZGTok08+CfWU6r16FyisWLFCI0aM0AMPPKDPP/9cH330ke69995QTysknnnmGR05csTbHnnkkVBPKWQef/xxtWjRItTTCJl+/frprbfeUkFBgVasWKEDBw7o7rvvDvW06ty+ffvk8Xj0yiuvaM+ePfrjH/+ol19+WU888USop1bnysvLNXToUD388MOhnkqdWbZsmSZOnKjp06frs88+03XXXaeBAwfqu+++C/XU6jejHqmoqDBatmxpvPbaa6GeSsilp6cbf/zjH0M9jbDw7rvvGh07djT27NljSDJ27twZ6imF3OrVqw2bzWaUl5eHeioh9/vf/95o27ZtqKcRMjk5OUZSUlKop1EnbrrpJsPpdHq33W630aJFC8PlcoVwVvVfvcoofPbZZyouLlZUVJS6dOmi1NRUDR48WLt37w711EJizpw5atq0qbp06aK5c+eqsrIy1FOqc8eOHdOYMWP03//932rYsGGopxMWTpw4oTfffFM9evRQTExMqKcTciUlJbX2FkGEj/Lycu3YsUP9+/f37ouKilL//v21devWEM6s/qtXgcLBgwclSU8//bSmTp2qvLw8JScnq2/fvjpx4kSIZ1e3fvvb32rp0qXasGGDHnroIc2ePVuPP/54qKdVpwzD0KhRozR27FjdeOONoZ5OyE2ePFmNGjVS06ZNVVhYqNWrV4d6SiG3f/9+LViwQA899FCop4Ja9v3338vtdqtZs2Y++5s1a+Z9LxGsCYtAYcqUKectzKvaztUeJenJJ5/UXXfdpa5duyonJ0c2m01vv/12iL9F4Gp6HSRp4sSJ6tu3rzp37qyxY8fqueee04IFC1RWVhbibxG4ml6HBQsW6PTp08rOzg71lGuFP78fJOmxxx7Tzp079f777ys6OlojR46UcYk8od3fayFJxcXFGjRokIYOHaoxY8aEaObBZeU6AIEKi3c9HD9+XP/4xz+qPaZdu3b66KOPdOutt+rDDz/ULbfc4v0sIyND/fv316xZs2p7qrWqptchNjb2vP179uxRp06dtG/fPnXo0KG2plgnanodfvOb3+j//u//ZLPZvPvdbreio6M1fPhwvfHGG7U91VoVyO+Hb7/9VmlpadqyZcsl8Up3f6/F4cOH1bdvX918883Kzc1VVFRY/JsoYFZ+T+Tm5mr8+PE6efJkLc8utMrLy9WwYUMtX77c5064+++/XydPniTDFgC/XjNdWxwOhxwOx0WP69q1q+x2uwoKCryBQkVFhQ4dOqT09PTanmatq+l1uJBdu3YpKipKKSkpQZ5V3avpdXjhhRc0c+ZM7/bhw4c1cOBALVu2TBkZGbU5xToRyO+Hc9m3SyHDJPl3LYqLi9WvXz9vxvFSCRKkwH5PXOpiY2PVtWtXrV+/3hsoeDwerV+/XllZWaGdXD0XFoFCTSUmJmrs2LGaPn260tLSlJ6errlz50qShg4dGuLZ1Z2tW7fq448/Vr9+/ZSQkKCtW7dqwoQJuu+++5ScnBzq6dWZ1q1b+2w3btxYktS+fXu1atUqFFMKiY8//ljbt2/XLbfcouTkZB04cEDTpk1T+/btL4lsgj+Ki4vVt29fpaena968eTp+/Lj3s+bNm4dwZnWvsLBQJ06cUGFhodxut/f5IldccYX3z8qlZuLEibr//vt144036qabbtL8+fNVWlqqBx54INRTq99Ce9OF/8rLy41JkyYZKSkpRkJCgtG/f39j9+7doZ5WndqxY4eRkZFhJCUlGXFxccbVV19tzJ492zhz5kyopxZSX3/9dUTeHvnFF18Y/fr1M5o0aWLY7XajTZs2xtixY41vv/021FOrczk5OYakC7ZIc//991/wOmzYsCHUU6tVCxYsMFq3bm3ExsYaN910k7Ft27ZQT6neC4s1CgAAIDxdOsU7AAAQdAQKAADAFIECAAAwRaAAAABMESgAAABTBAoAAMAUgQIAADBFoAAAAEwRKAAAAFMECgAAwBSBAgAAMPX/ARLtyunzyUSwAAAAAElFTkSuQmCC",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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",
"text/plain": [
"<Figure size 640x480 with 2 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"-1.390557629454562e-14\n"
]
}
],
"source": [
"# Now interpolate P and S, plot the fractional errors in the interpolation\n",
"# and check for thermodynamic consistency using the derivatives\n",
"\n",
"#Pinterp = scipy.interpolate.RegularGridInterpolator((Tp,rhop),Pgrid, bounds_error=False, fill_value=None)\n",
"#Sinterp = scipy.interpolate.RegularGridInterpolator((Tp,rhop),Sgrid, bounds_error=False, fill_value=None)\n",
"\n",
"Pinterp = scipy.interpolate.RectBivariateSpline(Tp,rhop,Pgrid)\n",
"Sinterp = scipy.interpolate.RectBivariateSpline(Tp,rhop,Sgrid)\n",
"\n",
"dPdT = Pinterp.partial_derivative(1,0)\n",
"dSdrho = Sinterp.partial_derivative(0,1)\n",
"\n",
"# now compute the function on a finer grid\n",
"Tp2 = np.linspace(2,3,100)\n",
"rhop2 = np.linspace(-6,0.0,100)\n",
"Tgrid2, rhogrid2 = np.meshgrid(Tp2, rhop2, indexing='ij')\n",
"ngrid2 = 10.0**rhogrid2 / (28*mu)\n",
"Pgrid2 = np.log10(P(10**rhogrid2, 10**Tgrid2))\n",
"Sgrid2 = S(10**rhogrid2, 10**Tgrid2)/kB\n",
"\n",
"# plot the fractional error\n",
"plt.imshow((Pinterp(Tp2,rhop2)-Pgrid2)/Pgrid2, origin='lower',\n",
" extent=(rhop2[0],rhop2[-1],Tp2[0],Tp2[-1]), aspect='auto')\n",
"plt.title('Pressure')\n",
"plt.colorbar()\n",
"plt.show()\n",
"\n",
"plt.clf()\n",
"plt.imshow((Sinterp(Tp2,rhop2)-Sgrid2)/Sgrid2, origin='lower',\n",
" extent=(rhop2[0],rhop2[-1],Tp2[0],Tp2[-1]), aspect='auto')\n",
"plt.title('Entropy')\n",
"plt.colorbar()\n",
"plt.show()\n",
"\n",
"plt.clf()\n",
"f1 = 10**Pinterp(Tp2,rhop2) * dPdT(Tp2,rhop2)/ 10**Tgrid2 / ngrid2**2\n",
"plt.imshow(f1, origin='lower',\n",
" extent=(rhop2[0],rhop2[-1],Tp2[0],Tp2[-1]), aspect='auto')\n",
"plt.title('dPdT')\n",
"plt.colorbar()\n",
"plt.show()\n",
"\n",
"plt.clf()\n",
"f2 = kB * dSdrho(Tp2,rhop2)/(np.log(10)*ngrid2)\n",
"plt.imshow(f2, origin='lower',\n",
" extent=(rhop2[0],rhop2[-1],Tp2[0],Tp2[-1]), aspect='auto')\n",
"plt.title('dSdrho')\n",
"plt.colorbar()\n",
"plt.show()\n",
"\n",
"plt.clf()\n",
"plt.imshow(np.abs((f1+f2)/f1), origin='lower',\n",
" extent=(rhop2[0],rhop2[-1],Tp2[0],Tp2[-1]), aspect='auto')\n",
"plt.title('Consistency')\n",
"plt.colorbar()\n",
"plt.show()\n",
"\n",
"print(np.min((f1+f2)/(f1-f2)))\n"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.11.5"
}
},
"nbformat": 4,
"nbformat_minor": 5
}