{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Bouncing ball in a tube\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
Author:Norbert van Veen
Time:30 minutes
Age group:all
Concepts:Frequency, amplitude
\n", "\n", "```{figure} demo83_figure1.png\n", "---\n", "width: 100%\n", "align: center \n", "figclass: margin\n", "---\n", "Bouncing ball in a tube above a JBL speaker.\n", "```\n", "\n", "## Introduction\n", "A demonstration suitable for all students. For younger students, the demonstration can be used to illustrate sound as vibration and assist in explaining concepts like frequency and amplitude. With older students, the demonstration can serve as an analogy for the photoelectric effect, making quantities like threshold energy, kinetic energy, and cutoff frequency tangible.\n", "\n", "## Equipment\n", "* Bead or ping pong ball\n", "* Transparent tube\n", "* Speaker\n", "* Tone generator (e.g. phyphox app)\n", "\n", "## Preparation\n", "Place the transparent tube over the speaker and connect a sound source (your phone) to the speaker. Ensure that the tube does not make contact with the speaker's cone.\n", "\n", "With younger students, choose a song that starts calmly and where the bass gradually builds up. Then, use the tone generator with a frequency that results in a nice bounce of the ball.\n", "\n", "To make the analogy with the photoelectric effect, you need to use multiple frequencies. Note at which sound intensity the ball bounces fairly high for a frequency of 100 Hz.\n", "\n", "## Procedure\n", "### Junior High School - Sound is a vibration with frequency and amplitude.\n", "1. Place the ball in the transparent tube on the speaker. Play music. Let the students observe what happens to the ball.\n", "2. Ask a question like: *What causes the ball to bounce?*\n", "3. Use the Phyphox app to play a single frequency. What happens to the ball in the tube? Change the frequency and let students note differences and similarities.\n", "4. Choose a frequency where the ball bounces well and change the volume (sound intensity) of the speaker. Let students predict what will happen.\n", "5. A question to assess students' understanding: *What happens to the ball if the speaker vibrates at a very high (inaudible) frequency?*\n", "\n", "### High School - Photoelectric effect analogy\n", "1. Choose several frequencies (at a constant volume) and mark the maximum height the ball reaches.\n", "2. Record the measurements in a table and plot the graph in a diagram with height on the vertical axis and frequency on the horizontal axis. You can use the code cell that is provided below, adding your measurements by clicking the {fa}`rocket` at the top right corner of your screen.\n", "3. Discuss the analogy with the photoelectric effect. See the physics background.\n", "4. A question to assess students' understanding: *Why doesn't the analogy hold if the sound intensity is not constant per frequency?*\n", "\n", "\n", "## Physics background\n", "### Junior High School\n", "The speaker vibrates and transfers this vibration to the ball, causing it to move up and down. The amplitude of the sound determines how vigorously the speaker cone vibrates, and thus the sound intensity, which is reflected in how high the ball averages.\n", "The frequency is how often the cone vibrates and determines the pitch of the sound; the ball will move faster up and down at higher tones.\n", "\n", "### High School\n", "{cite:t}`barretto2022physical` conceived and executed this experiment and also clearly described the analogy with the photoelectric effect. The bouncing ball is in a bound state in the tube, just like conduction electrons in a metal. At higher frequencies, the ball will bounce higher. Thus, the height is a measure of the kinetic energy of the ball. The sound frequency is analogous to the light frequency (the absorbed energy), and the sound intensity is analogous to the intensity of the light (quantity of photons). The analogy does not hold when using low-frequency sounds with high amplitude. In that case, the ball could still 'escape'. With the photoelectric effect, no current can be generated below the cutoff frequency. The measured data provide an analogous graph to the graph of kinetic energy against frequency of the photoelectric effect (see the python measurements below).\n", "\n", "\n", "```{tip}\n", "- Pay attention to the ratio of bead/ball to tube diameter. The tube should be reasonably narrow so that the bead or ball jumps as vertically as possible.\n", "- It's an analogy with the photoelectric effect, but note where the analogy deviates from the concept.\n", "```\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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Tpg0jRoxwdmgiIu7h77/hrrvg9dfNbqWBA81p17VrOzuyfKdixoUlJCQwbNgwqlWrhq+vL5UqVeLee+/ll19+cXZoLF26lDlz5vDDDz8QHx9P3bp1WbhwIf/+97/t51SpUoX333/feUGKiBRXNht06gRr1pgzlL7+GmbMMGcuFUMaM+OiYmNjadGiBaVLl2by5MnUq1ePjIwMli1bxpAhQ9i3b5/D1zQMA6vVmi8rWB88eJDQ0FDuuOMO+74yZcrc8HVFRCQPPDzgvfdg7FizkImMdHZEBUotMy5q8ODBWCwWNm3axEMPPUTNmjW55ZZbGDVqFBs2bCA2NtbevZPl7NmzWCwWVq1aBcCqVauwWCwsW7aMJk2a4Ovry6xZs7BYLDmKoSlTplClShWylvLas2cPXbp0ITAwkODgYPr06cPJkycB6NevH8OGDePw4cNYLBaqVKkCkK2bqU2bNhw6dIiRI0disViwuNCdJkVEiqTDhyEq6uL2XXfBpk3FvpABFTNXdu7clR/nz+f93Kz5/Fc710GnT59m6dKlDBkyhBIlSuQ4XtrBJdrHjBnDpEmT2Lt3Lw899BCNGzfmq6++ynbO3Llz6dWrFxaLhYSEBNq2bUuDBg3YsmULS5cu5dixYzzyyCMA/Oc//+G1114jPDyc+Ph4Nm/enOM1Fy5cSHh4OK+99hrx8fHEx8c7FLOIiFzi+++hYUN48EGIjr64300WBFY305Vc7S6IXbqYq4peYAkJgZSU3M9t3RoutIQAUKUKXGjBsHNw4fLo6GgMw6B2Pg3ieu2112jfvr19u3fv3kybNs0+vmX//v1s3bqVL774AoDPPvuMhg0bMnHiRPtzPvvsMypVqsT+/fupWbMmQUFBeHp6EhISkutrlilTBk9PT4KCgq54joiIXEN6urko5JQp5naTJuDp6dyYnMA9SrZiJqurJ7+6Zpo0aZJt+9FHH+XQoUNs2LABgK+++ooGDRpw8803A7Bjxw5WrVpFYGCg/ZFVWB08eDBfYhIRkWuIjYU777xYyIwYYa5+XbWqM6NyCrXMXMk//1z52GVVr5GQgOVKTXmX74+NvbG4gMjISCwWC3v37qV79+5XeFnzdY1LWn0yMjJyPffyrqrQ0FDatm3L3Llzad68OV9//TWDBg2yH7fZbNxzzz1Mnjw5x7VCi9m9C0REiqTFi+GJJ+DsWShd2lyWoFs358bkRCpmriSXsShXPTev/ZKOXPcKypQpQ8eOHfnwww959tlncxQjZ8+epXz58gDEx8fTsGFDgGyDga+ld+/ejB07lp49e3Lw4EEeffRR+7H69evz448/UqVKlRua+eTj44PVar3u54uIuK21a81CpnlzmDcPIiKcHZFTqZvJRX300UdYrVaaNm3Kt99+y4EDB9i7dy8ffPABt99+O/7+/jRv3pw333yTPXv2sGbNGl566aU8X/+BBx4gKSmJZ555hrZt21KxYkX7sSeffJLTp0/Ts2dPNm3axF9//cXy5cvp37+/Q8VJlSpVWLNmDUePHrXPhBIRkSu4dHzlpEnw/vvmfWTcvJABFTMuq2rVqmzbto22bdvy3HPPUbduXdq3b88vv/zC9OnTAXNQbkZGBk2aNGH48OG8/vrreb5+yZIluffee9m5cye9e/fOdiw0NJS1a9ditVrp2LEjdevWZfjw4ZQqVcrevZUXr732GrGxsVSvXt3ekiQiIrlYsAC6doWs4QI+PjB8OHh7OzeuIkLdTC4sNDSUadOmMW3atFyP16lTh99++y3bvkvH0LRp0ybb9uUWLFhwxWORkZEsXLjwisdHjBiRY+mCVZfO6gKaN2/Ozp07r3gNERG3d/48jBwJH39sbn/yCQwe7NyYiiAVMyIiIkXR/v3wyCOQ9T9948aZ6ytJDipmREREipq5c2HQIHNmbfny8N//QseOzo6qyNKYGRERkaJk4kTo3dssZNq0gR07VMhcg4oZERGRouTBB6FkSXjlFfj5ZwgLc3ZERZ66meCqg2BFrpf+XolInu3aBbfeav5cqxYcPAjlyjk3Jhfi1i0z3hemtKVcaV0lkRuQnp4OgKcbrpMiInn0zz/Qty80aACrV1/cr0LGIW7dMuPp6Unp0qU5fvw4AAEBAQ6td2Sz2UhPT+f8+fMO3V/FlbljzuB43jabjRMnThAQEHBDd0kWkWJs1y5zttK+feZd5HftMhcnFoe5/W/ZrBWbswoaRxiGQWpqKv7+/vm26GNR5445w/Xl7eHhQeXKld3qfRKRPDAMmDULhg0z7yMTFmbOXlIhc93cvpixWCyEhoZSoUKFKy7EeCUZGRmsWbOGVq1a2busijt3zBmuL28fHx+3ar0SkTxITjanXH/9tbndqRN88YU5/Vqum9sXM1k8PT0dHtvg6elJZmYmfn5+bvPF7o45g/vmLSL57P/+zyxkPD3hjTdg9Oi8L1QsV+TUd3DSpEncdtttBAUFUaFCBbp3786ff/6Z7Zx+/fphsViyPZo3b+6kiEVERG5A794wYoS5QOTYsSpk8olT38XVq1czZMgQNmzYQFRUFJmZmXTo0IFz585lO69Tp07Ex8fbH0uWLHFSxCIiIg5ITDTHxpw5Y25bLPDee3DHHc6Nq5hxajfT0qVLs23Pnj2bChUqsHXrVlq1amXf7+vrax+oey1paWmkpaXZt5OSkgBzzIOjY2KuJet6+X3doswdcwb3zNsdcwbl7U55F3TOlq1b8ezdG8tff2FLSMA6d26BvI6jXOWzdiQ+i1GE7uwVHR1NZGQku3btom7duoDZzbR48WJ8fHwoXbo0rVu35o033qBChQq5XmP8+PFMmDAhx/65c+cSEBBQoPGLiIhgGFT78UdumTMHj8xMUsqXZ8vo0ZypWdPZkbmUlJQUevXqRWJiIiVLlrzquUWmmDEMg27dunHmzBnWrl1r3z9//nwCAwOJiIggJiaGl19+mczMTLZu3Yqvr2+O6+TWMlOpUiVOnjx5zTfDURkZGURFRdG+fXu3GRTqjjmDe+btjjmD8nanvAsk5zNn8HzqKTy++w4AW7duWGfOhJtuyp/r5wNX+ayTkpIoV65cnoqZIjObaejQofz++++sW7cu2/4ePXrYf65bty5NmjQhIiKCH3/8kQceeCDHdXx9fXMtcry9vQvsQyvIaxdV7pgzuGfe7pgzKG93km85794N99wDhw6Bjw+88w4eQ4fiUUTvNVXUP2tHYisSxcywYcP47rvvWLNmDeHh4Vc9NzQ0lIiICA4cOFBI0YmIiDuJi4vjwIEDREZGXvM7KZvQULDZoFo1WLAAGjcuuCAlG6fOZjIMg6FDh7Jw4UJWrFhB1apVr/mcU6dOceTIEUJDQwshQhERcSezZs0iIiKCdu3aERERwaxZs67+hORk846+AGXLwpIlsG2bCplC5tRiZsiQIXz55ZfMnTuXoKAgEhISSEhIIDU1FYB//vmHf/3rX/z222/ExsayatUq7r33XsqVK8f999/vzNBFRKSYiYuLY+DAgdhsNsBcY23QoEHExcXl/oRff4Wbb4Y5cy7uq1sXSpUq+GAlG6cWM9OnTycxMZE2bdoQGhpqf8yfPx8w77q6a9cuunXrRs2aNenbty81a9bkt99+IygoyJmhi4hIMXPgwAF7IZPFarUSHR2d/USbDd5801xLKS4OPvgArNZCjFQu59QxM9eaSOXv78+yZcsKKRoREXFnkZGReHh4ZCtoPD09qVGjxsWTjh+Hxx+HrO+mXr3g44/N5QnEaXQfZRERESA8PJyZM2fa1+nz9PRkxowZFwcBr14NDRqYhYy/P3z6KXz5JainwOmKxGwmERGRomDAgAF07NiR6OhoatSocbGQOXwY7r4bMjOhTh1zttKFm7uK86mYERERuUR4eHjOKdmVK8Pzz5tjZKZNgxIlnBOc5ErFjIiISG5++QUiIiBrzMyECVrluojSpyIiInKpzEx4+WVo3x569ICsJXJUyBRZapkRERHJcvSoOUNpzRpzu1Ejcyq2FGkqZkRERACWLoU+feDkSQgMhBkzzMJGijy1mYmIiHvLzIRx46BzZ7OQqV8ftm5VIeNCVMyIiIh7s9lgxQrz58GDYcMGqFnTuTGJQ9TNJCIi7inrLvQ+PjBvntka89BDzo1JrouKGRERcS/p6fDCC3h4ecHtt5v7qlY1H+KSVMyIiIj7iI2FRx+FjRvxsFgInDbN2RFJPtCYGRERcQ+LF0PDhrBxI5QujXXBAv6pWNHZUUk+UDEjIiLFW1oaDB8O998PZ89Cs2awfTtGt27OjkzyibqZRESk+DIM6NjRXPEa4LnnYOJEc9BvRoZzY5N8o2JGRESKL4sFBgyAXbvg88/hnnucHZEUAHUziYhI8XL+POzbd3G7Tx84cECFTDGmYkZERIqP/fuheXO46y44ceLi/jJlnBeTFDgVMyIiUjzMnQuNG8POnea9ZP76y9kRSSFRMSMiIq4tJQWeegp694Z//oHWrc2CplkzZ0cmhUTFjIiIuK69e82i5dNPzcG+L78MP/8MYWHOjkwKkYoZERFxXW+9Bbt3Q3AwJ776ipVt2xKXkODsqKSQaWq2iIi4rv/8Bzw8mFu3Ln0eewybzYaHhwczZ85kwIABzo5OColaZkRExHXs3g1jxlxc8bpUKeJee40+o0djs9kAsNlsDBo0iLi4OCcGKoVJxYyIiBR9hmGOi7ntNnj7bfPnCw4cOGAvZLJYrVaio6MLO0pxEnUziYhI0ZacDE8/bU69BnN5gu7d7YcjIyPx8PDIVtB4enpSo0aNQg5UnEUtMyIiUnTt2AFNmpiFjKcnTJoES5ZA+fL2U8LDw5k5cyaenp6AWcjMmDGD8PBwJwUthU0tMyIiUjR9+SU8+aS56nV4OMybBy1a5HrqgAED6NixI9HR0dSoUUOFjJtRMSMiIkVTlSqQmWmuqTRnDpQte9XTw8PDVcS4KRUzIiJSdCQlQcmS5s8tW8L69eagX4vFuXFJkaYxMyIi4nyGAVOnmq0xe/Zc3N+0qQoZuSYVMyIi4lxnzsCDD8Kzz5o/f/aZsyMSF6NuJhERcZ6NG+HRRyE2Fry94Z13YNgwZ0clLkYtMyIiUvgMA6ZMMcfFxMZCtWrm+Jhnn1W3kjhMxYyIiBS+L7+E554zZys9/DBs22beT0bkOqiYERGRwtezJ7RvDx99BPPnQ6lSzo5IXJjGzIiISMGz2WD2bHjsMfD1BS8vWLZMXUqSL9QyIyIiBevECeja1byb79ixF/erkJF8opYZEREpOKtXQ69e8Pff4OcHdes6OyIphtQyIyIi+c9qhX//G9q1MwuZ2rVh0yazdUYkn6llRkRE8texY9C7N/zyi7ndty98+CGUKOHcuKTYUjEjIiL569w52LwZAgLM2Up9+zo7IinmnNrNNGnSJG677TaCgoKoUKEC3bt3588//8x2jmEYjB8/nrCwMPz9/WnTpg1//PGHkyIWEZFcGcbFn6tVgwULzIJGhYwUAqcWM6tXr2bIkCFs2LCBqKgoMjMz6dChA+fOnbOfM3nyZKZMmcK0adPYvHkzISEhtG/fnuTkZCdGLiIidn//DXffDcuXX9zXsSPcfLPzYhK34tRupqVLl2bbnj17NhUqVGDr1q20atUKwzB4//33efHFF3nggQcA+PzzzwkODmbu3LkMGjTIGWGLiEiWZcugTx9z+nVsLPz5p3kPGZFCVKT+xiUmJgJQpkwZAGJiYkhISKBDhw72c3x9fWndujXr16/PtZhJS0sjLS3Nvp2UlARARkYGGRkZ+Rpv1vXy+7pFmTvmDO6ZtzvmDMo7z3lnZuIxfjyekycDYNSrR+bcuWZ3k4u8d/qsi3bejsRnMYxLOzqdxzAMunXrxpkzZ1i7di0A69evp0WLFhw9epSwsDD7uQMHDuTQoUMsW7Ysx3XGjx/PhAkTcuyfO3cuAQEBBZeAiIib8Dt5kibvvkvZvXsBiOnUid39+2Pz8XFyZFKcpKSk0KtXLxITEylZsuRVzy0yLTNDhw7l999/Z926dTmOWS67S6RhGDn2ZRk3bhyjRo2ybyclJVGpUiU6dOhwzTfDURkZGURFRdG+fXu8vb3z9dpFlTvmDO6ZtzvmDMr7mnn//TdejRtjOXUKIygI68cfE/7ww4QXXqj5Rp910c47q2clL4pEMTNs2DC+++471qxZQ3j4xX8SISEhACQkJBAaGmrff/z4cYKDg3O9lq+vL76+vjn2e3t7F9iHVpDXLqrcMWdwz7zdMWdQ3lcUEQH33AO7d2OZPx+v6tWJi4vjwIEDREZGZvsd7ir0WRdNjsTm1NlMhmEwdOhQFi5cyIoVK6hatWq241WrViUkJISoqCj7vvT0dFavXs0dd9xR2OGKiLinQ4fg5MmL2x99BL/+CtWrM2vWLCIiImjXrh0RERHMmjXLeXGK23JqMTNkyBC+/PJL5s6dS1BQEAkJCSQkJJCamgqY3UsjRoxg4sSJLFq0iN27d9OvXz8CAgLo1auXM0MXEXEPixdDgwbm/WJsNnNfQAD4+hIXF8fAgQOxXdhvs9kYNGgQcXFxTgtX3JNTu5mmT58OQJs2bbLtnz17Nv369QNgzJgxpKamMnjwYM6cOUOzZs1Yvnw5QUFBhRytiIgbSU+HMWPgP/8xt0+ehMREuOkm+ykHDhywFzJZrFYr0dHRLtndJK7LqcVMXiZSWSwWxo8fz/jx4ws+IBERgb/+gh49YMsWc/u552DiRLhstlJkZCQeHh7ZChpPT09q1KhRmNGKaNVsERG5yPLtt9CwoVnIlCkD330H77yTo5ABCA8PZ+bMmXh6egJmITNjxgy1ykihKxKzmURExPk80tPxfPFFSEqCO+6Ar7+GypWv+pwBAwbQsWNHoqOjqVGjhgoZcQoVMyIiAoDNxwfrV1/h9X//B6+9BnmcGhseHq4iRpxKxYyIiDubNw/++ce+urXRuDE0b+7koEQco2JGRMQdpabC8OHwySfmeJimTZ0dkch10wBgERF3s2+fWbx88glYLOYU7MhIZ0clct3UMiMi4k6++AKeeQZSUiA4GL78Eu6+22VWuhbJjYoZERF3YBgwcCB8+qm53a4dfPUVXFgDT8SVqZtJRMQdWCxQpQp4eMCECbB8uQoZKTbUMiMiUlwZhrkEQenS5va4cdCpEzRu7NSwRPKbWmZERIqj5GTo0wfuvNMcHwNmq4wKGSmG8tQy88EHHzh84SeeeEKLQYqIOMPOnfDII7B/P3h6wurV0Lmzs6MSKTB5KmZGjBhBeHi4ff2Nazly5Aj33HOPihkRkcJkGDBzpnn/mLQ0qFjRvCley5bOjkykQOV5zMyWLVuoUKFCns5VESMiUsiSkuCpp2DBAnO7a1eYMwfKlXNqWCKFIU9jZl599VUCAwPzfNEXXniBMmXKXHdQIiLioKFDzULGywvefttc7VqFjLiJPLXMvPrqqw5ddNy4cdcVjIiIXKeJE2HPHpg2TWsridvRbCYREVd09ix8/vnF7fBw2LxZhYy4JYfvM3Pq1CleeeUVVq5cyfHjx7HZbNmOnz59Ot+CExGRXGzaBD16QGyseQ+Zbt3M/RaLM6MScRqHi5nHHnuMgwcPMmDAAIKDg7HoH4+ISOEwDHj/fRg71lxLqWpVc8aSiJtzuJhZt24d69ato379+gURj4iI5Ob0aejXD77/3tx+6CFznaVSpZwalkhR4PCYmdq1a5OamloQsYiISG5++w0aNDALGR8f+PBDc+aSChkR4DqKmY8++ogXX3yR1atXc+rUKZKSkrI9REQkn8XFwZEjUKMGbNgAgwdrfIzIJRzuZipdujSJiYm0a9cu237DMLBYLFit1nwLTkTEncTFxXHgwAEiIyMJr1jxYsHy8MMwezY88ACULOncIEWKIIeLmd69e+Pj48PcuXM1AFhEJJ/MmjWLgQMHYrPZaG2x8E2lSpTbsAFCQ80T+vVzanwiRZnDxczu3bvZvn07tWrVKoh4RETcTlxcHAMHDsSw2XgBeM0w8Dx8mHOjRlHi66+dHZ5IkefwmJkmTZpw5MiRgohFRMQtHThwgHI2G0uBNwBP4Atg2+OPOzcwERfhcMvMsGHDGD58OKNHj+bWW2/F29s72/F69erlW3AiIu6g7vHj7ABCgRRgMPClpyext97q1LhEXIXDxUyPHj0A6N+/v32fxWLRAGARkevxf/9H+Z49AdgNPALs9/RkxowZhIeHOzU0EVfhcDETExNTEHGIiLinu+6CWrWgRQtuGjuWj44epUaNGipkRBzgcDETERFREHGIiLiPLVugcWNz6nVgoHnvmFKlqAhUjIx0dnQiLsfhYgbg6NGj/Prrr7kuNPnss8/mS2AiIsVOZia8+ipMmgRvvw3PPWfu1518RW6Iw8XM7Nmzefrpp/Hx8aFs2bLZ7jNjsVhUzIiI5CYuDnr2hHXrzO3YWKeGI1KcOFzMvPLKK7zyyiuMGzcODw+HZ3aLiLifJUvg8cfh1CkICoJPPoELkylE5MY5XI2kpKTw6KOPqpAREbmWjAwYMwa6djULmUaNYNs2FTIi+czhimTAgAH873//K4hYRESKl7174f33zZ+HDYP1683FIkUkXznczTRp0iTuueceli5dmutN86ZMmZJvwYmIuLR69WDqVChf3lwkUkQKhMPFzMSJE1m2bJl9babLBwCLiLit9HR44QV47DFo0MDcN2iQU0MScQcOFzNTpkzhs88+o59WcBURueivv8yxMFu2wPffw+7dcFnLtYgUDIfHzPj6+tKiRYuCiEVExDV9+y00bGgWMjfdBO+8o0JGpBA5XMwMHz6cqVOnFkQsIiKu5fx5GDoUHnoIkpLg9tthxw64915nRybiVhzuZtq0aRMrVqzghx9+4JZbbskxAHjhwoX5FpyISJF14gR07Ajbt5vbY8bA66+rRUbECRwuZkqXLs0DGpUvIu6uTBkoWxbKlYMvvoDOnZ0dkYjbuq7lDERE3FJqqvmnvz94esKXX5rrLVWs6Ny4RNycU2/ju2bNGu69917CwsKwWCwsXrw42/F+/fphsViyPZo3b+6cYEXEve3bB82awYgRF/cFB6uQESkC8lTMNGrUiDNnzuT5oi1btuTo0aPXPO/cuXPUr1+fadOmXfGcTp06ER8fb38sWbIkz3GIiOSL//4XmjSBXbtg8WI4ftzZEYnIJfLUzbRjxw527txJmTJl8nTRHTt2kJaWds3zOnfuTOdr9DP7+voSEhKSp9cFSEtLy/baSUlJAGRkZJCRkZHn6+RF1vXy+7pFmTvmDO6ZtzvmDJflfe4cniNG4PH55wDY2rTB+vnn5vTrYva+uOPn7Y45g+vk7Uh8FsMwjGud5OHhgcViIQ+nmhe1WDhw4ADVqlXLeyAWC4sWLaJ79+72ff369WPx4sX4+PhQunRpWrduzRtvvEGFChWueJ3x48czYcKEHPvnzp1LQEBAnuMREfcWdPgwTd5+m5JHjmBYLPzZowd/PvywOVZGRApcSkoKvXr1IjExkZIlS1713DwVM4cOHXI4iPDwcDwd+EefWzEzf/58AgMDiYiIICYmhpdffpnMzEy2bt2Kr69vrtfJrWWmUqVKnDx58ppvhqMyMjKIioqiffv2OaaoF1fumDO4Z97umDOYef+8ZAn3jByJR1wcRkgI1i++wGjTxtmhFSh3/LzdMWdwnbyTkpIoV65cnoqZPHUzRURE5EtgjurRo4f957p169KkSRMiIiL48ccfrzg93NfXN9dCx9vbu8A+tIK8dlHljjmDe+btjjkb3t7Ypk7F4+OPsXzxBV5XaQ0ubtzx83bHnKHo5+1IbE6dzeSo0NBQIiIiOHDggLNDEZHi5vffISrKvml07Qo//QRuVMiIuCqXKmZOnTrFkSNHCA0NdXYoIlJcGAbMnAlNm5oLRR4+fPGYxeK8uEQkzxy+aV5++ueff4iOjrZvx8TEsGPHDsqUKUOZMmUYP348Dz74IKGhocTGxvLCCy9Qrlw57r//fidGLSLFRlISDBoE8+aZ23fdBZooIOJynFrMbNmyhbZt29q3R40aBUDfvn2ZPn06u3bt4osvvuDs2bOEhobStm1b5s+fT1BQkLNCFpHiYts2syUmOhq8vGDiRHjuObBanR2ZiDjouoqZs2fP8s0333Dw4EFGjx5NmTJl2LZtG8HBwVR04G6Ybdq0uep072XLll1PeCIiV/fhhzBqFKSnQ+XKZsvM7bebx1TMiLgch4uZ33//nbvvvptSpUoRGxvLU089RZkyZVi0aBGHDh3iiy++KIg4RUTyLC4ujgMHDhAZGUl4eHjOE3btMguZ++6D2bPNRSNFxGU5PAB41KhR9OvXjwMHDuDn52ff37lzZ9asWZOvwYmIOGrWrFlERETQrl07IiIimDVrlnng0lbg994zi5jFi1XIiBQDDrfMbN68mRkzZuTYX7FiRRISEvIlKBGR6xEXF8fAgQOx2WwA2Gw2Bg0cyINHjlB640b44QfzDr7+/tCvn3ODFZF843DLjJ+fn329o0v9+eeflC9fPl+CEhG5HgcOHLAXMgA3Ad/abJSeMAGWLoVvvnFecCJSYBwuZrp168Zrr71mXwDKYrFw+PBhnn/+eR588MF8D1BEJK8iIyPx8DB/rTUHtgPdAMPHB6ZNg0cecWZ4IlJAHC5m3nnnHU6cOEGFChVITU2ldevW1KhRg6CgIN54442CiFFEJE/Cw8OZ+fHHjLFYWANEAIkVKmDZsAGGDNFN8ESKKYfHzJQsWZJ169axYsUKtm3bhs1mo1GjRtx9990FEZ+IiEMG7NplH+ybct99lPrvfyGfF5kVkaLlum+a165dO9q1a5efsYiI3Lgnn4Qvv4Q33yTgqafUGiPiBvJUzHzwwQd5vuCzzz573cGIiDjMZoPNm6FZM3O7Xj2IjVVrjIgbyVMx895772XbPnHiBCkpKZQuXRow7wgcEBBAhQoVVMyISOE5dgz69IGVK2HduosFjQoZEbeSpwHAMTEx9scbb7xBgwYN2Lt3L6dPn+b06dPs3buXRo0a8e9//7ug4xURMa1YAQ0aQFQUeHtnX+1aRNyKw7OZXn75ZaZOnUqtWrXs+2rVqsV7773HSy+9lK/BiYjkYLXC+PFw992QkAA332x2Mz38sLMjExEncXgAcHx8vP0eM5eyWq0cO3YsX4ISEclVfDz07m12KwH07w9Tp0JAgHPjEhGncrhl5q677uKpp55iy5Yt9hWvt2zZwqBBgzQ9W0QK1rffmoVMiRLwxRcwa5YKGRFxvGXms88+o2/fvjRt2hRvb28AMjMz6dixI59++mm+BygiYjdkiDlT6cknoXZtZ0cjIkWEw8VM+fLlWbJkCfv372ffvn0YhkGdOnWoWbNmQcQnIu4sLg5eesnsSgoKMu8Z8847zo5KRIqY675pXs2aNVXAiEjBWbIEHn8cTp0yZyt98omzIxKRIsrhYqZ///5XPf7ZZ59ddzAiImRkwIsvwttvm9uNGsHYsc6NSUSKNIeLmTNnzmTbzsjIYPfu3Zw9e1bLG4jIjTl8GB59FH77zdweOtTsVvL1dW5cIlKkOVzMLFq0KMc+m83G4MGDqVatWr4EJSJuaO1a6NYNzpyBUqXMmUoPPujsqETEBTg8NTvXi3h4MHLkyBzLHoiI5FlkJPj4wG23wfbtKmREJM+uewDw5Q4ePEhmZmZ+XU5E3MGpU1C2rPlzSIh5D5nq1c2iRkQkjxwuZkaNGpVt2zAM4uPj+fHHH+nbt2++BSYixdzCheYdfGfMgB49zH116jg3JhFxSQ4XM9u3b8+27eHhQfny5Xn33XevOdNJRIS0NPjXv2DaNHN79mx45BHzHjIiItfB4WJmZdaaKCIijoqONlthtm0zt8eMgddfVyEjIjfE4QHA7dq14+zZszn2JyUlaWq2iFzZ/PnmPWO2bTPHyfz4I7z1lnlDPBGRG+Bwy8yqVatIT0/Psf/8+fOsXbs2X4ISkWLm99/N+8cAtGwJX38N4eHOjUlEio08FzO///67/ec9e/aQkJBg37ZarSxdupSKFSvmb3QiUjzUq2eOk/HxgQkTwCvfJlKKiOS9mGnQoAEWiwWLxZJrd5K/vz9Tp07N1+BExIV9/TW0aAGVK5vbkydrbIyIFIg8FzMxMTEYhkG1atXYtGkT5cuXtx/z8fGhQoUKeHp6FkiQIuJCUlJg2DD47DO44w5YtcocF6NCRkQKSJ6LmYiICMBcukBEJFd79pjTrP/4wyxeOnQAj3y50biIyBXlqZj57rvv6Ny5M97e3nz33XdXPfe+++7Ll8BExIUYBsyZA0OGQGqqeTffuXOhbVtnRyYibiBPxUz37t1JSEigQoUKdO/e/YrnWSwWrFZrfsUmIq7g3Dl45hn473/N7fbt4csvoUIF58YlIm4jT8XMpV1L6mYSkWw8PGDHDvPPf/8bnn9eXUsiUqg0P1JEHGcY5sPDA/z9YcECOH4cWrVydmQi4obyVMx88MEHeb7gs88+e93BiIgLSEqCQYPgllvgpZfMfbVrmw8RESfIUzHz3nvv5eliFotFxYxIcbZ9uzlbKToafH3NVa/DwpwdlYi4uTwVMzExMQUdh4gUZYYB06fDyJGQnm7eCG/ePBUyIlIk3NCYGcMwALNFRkSKqcREc7bSN9+Y2/fdB7NnQ5kyzo1LROSC65pyMGvWLOrWrYufnx9+fn7UrVuXTz/9NL9jExEns1iteLVqZRYy3t7w/vuweLEKGREpUhxumXn55Zd57733GDZsGLfffjsAv/32GyNHjiQ2NpbXX38934MUEecwPD2xDRmC57vvwvz5cNttzg5JRCQHh4uZ6dOn88knn9CzZ0/7vvvuu4969eoxbNgwFTMiru70aUhIgMhIAGxPPYVn374QGOjkwEREcudwN5PVaqVJkyY59jdu3JjMzEyHrrVmzRruvfdewsLCsFgsLF68ONtxwzAYP348YWFh+Pv706ZNG/744w9HQxaRvPrtN2jYELp2hbNnzX0WiwoZESnSHC5mHnvsMaZPn55j/8yZM+ndu7dD1zp37hz169dn2rRpuR6fPHkyU6ZMYdq0aWzevJmQkBDat29PcnKyo2GLyNXYbPD22+ZN7w4fBi8vOHbM2VGJiOTJdc1mmjVrFsuXL6d58+YAbNiwgSNHjvD4448zatQo+3lTpky56nU6d+5M586dcz1mGAbvv/8+L774Ig888AAAn3/+OcHBwcydO5dBgwZdT+gicrmTJ6FvX1iyxNx+9FGYMcO8s+/Bg86NTUQkDxwuZnbv3k2jRo0AOHjhF1358uUpX748u3fvtp93o9O1Y2JiSEhIoEOHDvZ9vr6+tG7dmvXr11+xmElLSyMtLc2+nZSUBEBGRgYZGRk3FNPlsq6X39ctytwxZyi+eVvWrcOzTx8sR49i+PlhnTIFY8AAsFiKbc7XorzdJ293zBlcJ29H4rMYWTeLcTKLxcKiRYvsq3KvX7+eFi1acPToUcIuuTHXwIEDOXToEMuWLcv1OuPHj2fChAk59s+dO5eAgIACiV3EVTWdNInQjRtJrliRLaNHk1SlirNDEhEBICUlhV69epGYmEjJkiWvem6RX2jy8hYewzCu2uozbty4bF1dSUlJVKpUiQ4dOlzzzXBURkYGUVFRtG/fHm9v73y9dlHljjlDMc67WTOskybhN348LS8b5Ftsc74G5e0+ebtjzuA6eWf1rOSFw8XM+fPnmTp1KitXruT48ePYbLZsx7dt2+boJXMVEhICQEJCAqGhofb9x48fJzg4+IrP8/X1xdfXN8d+b2/vAvvQCvLaRZU75gzFIO9Vq+CHH8zBvhYLhITAf/6D51We4vI5Xyfl7T7cMWco+nk7EpvDxUz//v2JiorioYceomnTpgW2lEHVqlUJCQkhKiqKhg0bApCens7q1at56623CuQ1RYotqxXeeAMmTDBnLjVtai4YKSJSDDhczPz4448sWbKEFi1a3PCL//PPP0RHR9u3Y2Ji2LFjB2XKlKFy5cqMGDGCiRMnEhkZSWRkJBMnTiQgIIBevXrd8GuLuI2EBOjdG1asMLefeMK8j4yISDHhcDFTsWJFgoKC8uXFt2zZQtu2be3bWWNd+vbty5w5cxgzZgypqakMHjyYM2fO0KxZM5YvX55vry9S7P38s1nIHD8OJUqYK1/36ePsqERE8pXDxcy7777L2LFj+fjjj4mIiLihF2/Tpg1Xm0xlsVgYP34848ePv6HXEXFL774Lo0eDYcCtt8KCBVC7trOjEhHJdw4XM02aNOH8+fNUq1aNgICAHAN0Tp8+nW/BicgNqF/f/HPQIHjvPfMmeCIixZDDxUzPnj05evQoEydOJDg4uMAGAIvIdTh5EsqVM3+++274/XeoW9e5MYmIFDCHi5n169fz22+/UT/r//pExPkyMuDll+Hjj2HrVqhe3dyvQkZE3IDDC03Wrl2b1NTUgohFRK7H4cPQpg289RYkJsL//Z+zIxIRKVQOFzNvvvkmzz33HKtWreLUqVMkJSVle4hIIfr+e2jYENavh1Kl4Jtv4JI7YIuIuAOHu5k6deoEwF133ZVtf9YyA1arNX8iE5ErS0+HceMga2X6226DefOgWjXnxiUi4gQOFzMrV64siDhExBEffnixkBkxwuxi8vFxakgiIs7icDHTunXrKx7bsWPHjcQiInk1ZAgsWwbPPAPdujk7GhERp3J4zMzlEhMT+eijj2jUqBGNGzfOj5hE5HJpafD++5CZaW77+MDSpSpkRES4gWJmxYoVPPbYY4SGhjJ16lS6dOnCli1b8jM2EQGIjoY77oCRI+GVV5wdjYhIkeNQN1NcXBxz5szhs88+49y5czzyyCNkZGTw7bffcvPNNxdUjCLua8ECePJJSE6GsmWhZUtnRyQiUuTkuWWmS5cu3HzzzezZs4epU6fy999/M3Xq1IKMTcR9paaa42F69DALmZYtYccO6NLF2ZGJiBQ5eW6ZWb58Oc8++yzPPPMMkZGRBRmTiHs7cAAeeshcisBigRdegPHjwcvh8foiIm4hzy0za9euJTk5mSZNmtCsWTOmTZvGiRMnCjI2EfeUmWmOkylf3pyx9PrrKmRERK4iz8XM7bffzieffEJ8fDyDBg1i3rx5VKxYEZvNRlRUFMnJyQUZp0jxZrNd/LlOHVi4EHbuhPbtnReTiIiLcHg2U0BAAP3792fdunXs2rWL5557jjfffJMKFSpw3333FUSMIsXbnj3QqBGsXXtxX8eOEBrqvJhERFzIDd1nplatWkyePJm4uDi+/vrr/IpJxH3MmWMuRbBzpzn12jCcHZGIiMu54ZvmAXh6etK9e3e+++67/LicSPH3zz/Qty888QSkpMDdd8OPP4LFQlxcHCtXriQuLs7ZUYqIuIR8KWZExAG7dpmtMV98AR4e5gDfZcsgOJhZs2YRERFBu3btiIiIYNasWc6OVkSkyFMxI1KY9u2Dpk3NPytWhFWr4MUXwcODuLg4Bg4ciO3CYGCbzcagQYPUQiMicg2a7ylSmGrVgnvvNbuZvvgCypWzHzpw4IC9kMlitVqJjo4mPDy8sCMVEXEZKmZECtrOnRARAaVLmzfB+/xz8PU1u5guERkZiYeHR7aCxtPTkxo1ahRywCIirkXdTCIFxTBg+nRo1sxcXylrppK/f45CBiA8PJyZM2fi6ekJmIXMjBkz1CojInINapkRKQiJifDUU/C//5nbGRlw/rxZyFzFgAED6NixI9HR0dSoUUOFjIhIHqiYEclvW7aYC0T+9Rd4e8Nbb8GIEWYXUx6Eh4eriBERcYCKGZH8YhjwwQcwerTZElOlCsyfb85eEhGRAqMxMyL5JTER3n7bLGQeeAC2b1chIyJSCNQyI5JfSpeGefNgxw4YMiTP3UoiInJjVMyIXC+bDd57DypUgD59zH0tW5oPEREpNCpmRK7HqVPm2ko//ggBAdC6NVSu7OyoRETckooZEUf9+is8+ijExZk3v5syBSpVcnZUIiJuSwOARfLKZsNj8mSzFSYuDmrWhI0bYdAgjY8REXEitcyI5IXVSrM33sBz61Zz+7HHzLv7BgY6Ny4REVHLjEieeHqSVLUqhr8/zJplLhKpQkZEpEhQMSNyJVYrnDxp39zXsyeZmzdD//7qVhIRKULUzVREHTt2jA0bNhAbG0tycjIeHh6ULVuWunXr0qhRI/yvscbP5U6cOMEff/xBgwYNKF269HXHtXnzZvbs2cPvv/+OzWZj7Nix+Pn5sWLFCnbu3ElycjI+Pj48//zzV7zGxo0b2bhxI4mJidmuURTExcVx4MABapUqRdiYMeaN8NatAw8PDE9Pc5yMiIgUKSpmiqCtW7eyZMkSypYtyx133EH58uWxWq38/fffbNmyhbi4OHr06OHQNU+cOMHq1aupUqXKdRczCQkJREVFUaZMGbp27YqPjw8+Pj7s27ePtWvXcuedd1KjRg28vK781yohIYGlS5fSsGFDGjRogIeHBz4+PtcVT36bNWsWAwcOpI3NxldZO0uUgJ07oWFDZ4YmIiJXoWKmiDly5Ag//vgj1atXp0ePHtkKg+rVq3PHHXcQHR3tlNiOHz8OQNmyZalUqRLe3t7Z9jdr1owSJUrk6RqNGzemYsWKVz03IyPD/hoFLS4ujmeeeopXDYOXMPtffwcq/PADIU2bmksUiIhIkaRipohZt24dFouFe+65J9cWDk9PT2rVqmXfnjBhAq1bt6ZNmzbZznv//fepUqUK3bt3Z8eOHfzf//0fAJ9//rn9nG7dutGgQQMAtm/fzsaNGzl58iTe3t5UqVKFdu3aUb58eQDmzJnDoUOHADhw4AATJ06kfv36xMbGkpiYCMA777wDkGs8l1/j008/BaB+/fp0796dOXPmkJKSQteuXfn5559JSEigVq1aPPTQQ6SlpbF69Wr27t1LUlISJUqU4Oabb6Zdu3bZWnXS0tJYtmwZ+/btIzMzk8qVK9O5c2emTZuWLabFixcTGxvLiBEj7M899NtvzGzdmkNt2uAxfjwzgBHAEsPgyObNbNmyhRMnTrBv3z6qVq1K+/btuemmm7LllpKSQrdu3Vi+fDl///03gYGBNG7cmBYtWmC5ZIzN+fPnWb16Nfv27SM5ORlfX1/CwsLo2LEjZcuWZdq0adx000089thj2d6/9PR0pkyZwq233krXrl1zvL8iIu5KxUwRYrPZiImJITQ0lFKlSuXbdSMjI2nXrh0rVqygS5cuhIaGAti/jNeuXcuKFSuoW7cud911FykpKaxevZpZs2bx1FNPUbZsWbp27cquXbtYu3YtlSpVol27dpQsWZJmzZqxefNmtm/fTu/evfHz86NkyZK5xnHpNbp160a5cuUICAiwH//nn39YuHAhLVq04K677sJisZCRkcGcOXNISkqiZcuWBAcHc+LECVauXMnx48fp06cPFosFwzCYN28eR44coXXr1oSFhXHkyBG++uqrXGO5XKPp08kADgGPAvMxC8djx46xbt06brvtNgIDA7n11lv59ddfmTVrFk8//TSBl8xoyor/9ttvp3Xr1uzdu5dffvmFoKAg6tevD5gF12effcbZs2dp0aIF4eHhpKenc+jQIZKTkylXrhxNmzZl6dKlnDp1irJly9qvv3PnTtLS0miqxStFRLJRMVOEpKSkkJGRke3/+PNDiRIl7F+K5cuXJzw83H7s/PnzrFmzhsjISB588EH7/ipVqjB16lRWr17NAw88QPny5SlTpgwA/v7+VKxY0d4FlFW8hIWFZStOLnfpNSpUqEBYWFi246mpqTz88MNUrVrVvm/dunUcO3aMJ5980n5+tWrVCAoK4n//+x/R0dFERkZy8OBBYmNj6dSpE82aNQPMbjlPT09WrFhxzffI/9NPSR4zBrhYyHzwwQf8+eefdOjQgSZNmrBkyRJuueUWqlWrxtSpU/ntt99o3759tvh79+5t7z6rVq0ahw4dYteuXfZiZsOGDZw4cYI+ffpQrVo1+3Pr1Klj/7lBgwasWLGCzZs306lTJ/v+zZs3U6VKFXtrmYiImDQ1280dOXKEzMxM+5dtllKlSlG1alX++uuvQovFz88vWyEDsH//fipUqEBISAg2m83+qFGjBgCxsbEAxMTEAHDrrbdme/7l23ZWq3m/mCzVqhE0dCgAK1euJDY2ltq1awNQr149bDYbhmFgs9kIDAwkJCTE3mWWJTAwMMc4oODgYHs3HEB0dDRly5bNVshcztfXlwYNGrBjxw7S09Pt+Z04cUKtMiIiuVDLTBESEBCAt7c3Z86cKbTXTE1NBSAoKCjHsaCgoEItZnKL4dy5c5w+fZp///vfuT4nJSUFMPPw8PDI0TIUmNuN7Y4cgb//htGjzTWVOnTIdjhrbM22bduAi2OBwOzqyXJ5C1pu0+U9PT3JuGTwcEpKSp66ELO673bt2kXjxo3ZtGkTJUuWzDZeSkRETEW6mBk/fjwTJkzIti84OJiEhAQnRVSwPDw8qFq1KtHR0SQlJV1x7MmlPD09yczMzLE/q0i5lqwv4OTk5BzHkpOTr9ptVBgCAgLw8vKiW7duVzwOZh42m42UlJQc43Ds0tNh3Di89u/HWqsWNG4MF1p44GJhdPm1n3jiCQB+/fVXWrRoYR+Y7enpeV35JCUlXfO8MmXKUKNGDTZv3kyNGjX4888/adOmDR4eakwVEblckf/NeMsttxAfH29/7Nq1y9khFaiWLVtiGAbff/89Vqs1x3Gr1cqff/5p3y5durR9unOWmJgYe/dElqwv3ozLphhXqlQJLy+vHO9rUlISMTExObp9CltkZCRnzpzB39+fsLCwHI+se+ZkxXl5Hvbts2fhzjthyhRKnz3LucBA/lm+HC5091itVg4ePJjtuTUv3CAvOTmZ0NBQAgICCA0Ntb92cHCww/nUqFGDU6dO2bvFrqZZs2YcO3aMxYsX4+HhQePGjR1+PRERd1CkW2YAvLy8CAkJcXYYhaZSpUp07dqVJUuWMHPmTJo0aUL58uWx2WzEx8ezbds2KlSoYO9uqFevHitXrmTlypVERERw4sQJNm/ejK+vb7brVqhQATC7Tnx9ffHy8qJ06dIEBATQqlUrVqxYwaJFi6hbty6pqamsXr0aLy8vWrduXejvwaWaN2/O3r17mTNnDs2bNyc4OBjDMEhMTOTgwYPcfvvthIeHU716dSIiIoiKiiI9Pd0+m+n33383LzRjBmzaBKVLc8uwYaz880++/e477rjjDjIzM9m4cSM2my3ba1euXJlGjRrxf//3fzRu3JjExERiY2M5f/48hw8fpkKFCtx2220O5/PHH38wb948WrRoQcWKFcnMzCQ2NpaaNWtmKx6rV69O+fLliY2NpV69ete8h4+IiLsq8sXMgQMHCAsLw9fXl2bNmjFx4sSrDp5MS0sjLS3Nvp3VpJ+RkZGjVeJGZV0vv69br149goOD2bRpE+vWrePcuXN4eHhQpkwZbr75Zho3bmx/zaZNm5KamsqOHTtYv349YWFhdO/enW+++QabzWY/LzAwkLvvvpstW7YwZ84cDMPgnnvuoV69ejRv3hw/Pz+2bNnCH3/8gZeXFxERETz44IOULFnSfo1LW4ouzTlrf17e46xzMzMzs51rGAaGYeR4vsVi4bHHHuO3335jy5YtJCYm4uXlRcmSJalatSolSpQgJiaG6Ohobr/9dvbu3cv69euxWq2Eh4fzyCOPMGPGDDh/HluzZli//JLAiAgePniQVatWsWDBAgIDA2natCkpKSmsW7cuWwydOnUiNDSUbdu2cezYMY4cOUJQUBDh4eEEBwfbz71S/FkFUtZ+Dw8P+vTpw9q1a9m6dSurV6/Gz8+PsLAw6tevn+P5tWvX5sSJEzRs2DDf/55dS0H9/S7qlLf75O2OOYPr5O1IfBbDMIwCjOWG/PTTT6SkpFCzZk2OHTvG66+/zr59+/jjjz+y3X/jUrmNswGYO3eu08d/SP6Liorio48+wjAMLBYLgwcPNqdLW61woWttx44dRKalEdi4McZVllooirK6FDXwV0TcTUpKCr169SIxMfGaY0iLdDFzuXPnzlG9enXGjBnDqFGjcj0nt5aZSpUqcfLkyTwNqHVERkYGUVFRtG/fvtBuu+9sRSnnuLg4atSoka17yNPTk7/ff5/yH31E5i+/QLlyTJw4kZYtW9KqVavrfq3CzDstLY0TJ04QHR3N+vXrefDBB51SzBSlz7owKW/3ydsdcwbXyTspKYly5crlqZhxqf9NLVGiBLfeeisHDhy44jm+vr45xosAeHt7F9iHVpDXLqqKQs6xsbHZChlf4D2rlQrDhgHg/cEHMGkSYBY5+RFvYeR99OhRvvjiC/z9/WndujV169Yt0Ne7lqLwWTuD8nYf7pgzFP28HYnNpYqZtLQ09u7dy5133unsUKQIiIyMxMPDA5vNRiSwAGiQdXDcOHjtNQBeffVV5wR4napUqeJyMYuIOFORnpr9r3/9i9WrVxMTE8PGjRt56KGHSEpKom/fvs4OTYqA8PBwZs6cSW+Lha2YhUxqUBAsXQoTJ4KLjY8REZHrU6R/28fFxdGzZ09OnjxJ+fLlad68ORs2bCAiIsLZoUkRMcBmY8CFYV/nb78d/2++gcvWfBIRkeKtSBcz8+bNc3YIUtQ98ghMngy9euH3yiv2GUwiIuI+inQxI5KrFSugbVuwWKBUKdi5EzTtXkTEbRXpMTMi2Zw7B337wl13wccfX9yvQkZExK2pZUZcw65dZpfSvn3g4QG5LIwpIiLuScWMFG2GAbNmwbBhcP68Obj366/hBm6AJyIixYuKGRdltVrZvn17rmtX1K9fv3gs3ZCcDE8/DXPnmtudOsEXX0D58s6NS0REihQVMy7q+++/5/7778/12HPPPcc777xTyBEVgF27YN48c4bSG2/A6NFmF5OIiMglVMy4qHPnzgEwaNAgPC+Zjvztt9/aj7m8O+6AadOgXj1o0cLZ0YiISBGlYsbFlStXLtv6FUV5nY1rSkyEZ5+F55+HOnXMfc8849yYRESkyFMxI0XDli3Qowf89Rfs3g2bN6tLSURE8kTfFuJchgEffGB2Kf31F0REwEcfqZAREZE8U8uMOM+ZMzBgACxaZG7ff785Dfumm5wbl4iIuBQVM+IcsbHmkgSxseDjA+++C0OGmEsUiIiIOEDFjDhHeDhUrGhOu54/Hxo3dnZEIiLiolTMSOE5dQqCgsyWGC8v+N//zHWVSpVydmQiIuLCNMpSCse6ddCgAYwde3FfaKgKGRERuWEqZqRg2WwwaRK0aQNxcbBkCfzzj7OjEhGRYkTFjBSc48ehSxd44QWwWqF3b/N+MoGBzo5MRESKEY2ZkYKxejX07Anx8eDvD1OnQv/+mq0kIiL5TsWM5L/kZPOeMWfOmMsSLFgAdes6OyoRESmm1M0k+S8oCGbMgL59zWUJVMiIiEgBUsuM5I9ffjG7kNq1M7cffth8iIiIFDC1zMiNycyEV16B9u0vjpEREREpRGqZkev3999mAbNmjbl93326b4yIiBQ6FTNyXSzLlsETT8DJk+ZU6xkzoFcvZ4clIiJuSMWMOMZmo85//4vXt9+a2/Xrm7OVatZ0blwiIuK2NGZGHOPhgd/p0+bPgwfDhg0qZERExKnUMuMC9u7dy759+7Lt27x58xXP/+uvv1i0aFG2feXLl6dFixZYrvemdZmZ5uKQwO8DBxI2bBhe999/fdcSERHJRypmXECvXr3YsWNHjv0lSpTAwyN741pAQADLly9n+fLl2fZbLBaSk5MpUaKEYy+eng7jxsH+/fDddwBY/f0xunRx7DoiIiIFRMWMC+jXrx8jR45kwIABlClTxr7f29sbT0/PbOf26NGDtLQ0+7bVauWTTz6hY8eOjhcysbHw6KOwcaO5vXIl3Hnn9aYhIiJSIDRmxgUMHDiQ8uXLs2XLFgICAuwPb2/vHOd6enpmO2f//v0kJyfzyiuvOPaiixdDw4ZmIVO6NCxadPGGeCIiIkWIihkX4O/vzwsvvMDvv//O6azBt3mQmZnJr7/+ykMPPUTdvC4pkJYGw4ebayudPQvNmsH27dC9+3XFLiIiUtBUzLiIgQMHUq5cOdZk3aAuD3bu3MmZM2cca5V57DH44APz5+eeM2+IV6WKY8GKiIgUIhUzLsLR1pnrapUBGDMGQkLg++/hnXfAx+cGohYRESl4KmZciCOtM3lulTl//uJyBAC33QYxMXDPPTcYrYiISOFQMeNC8to6k+dWmf37oXlz6NABdu68uN/PLx+jFhERKVgqZlxMXlpn8tQqM3cuNG5sFjElS8KZMwUQrYiISMFTMeNiLm2dOXXqVI7jWa0yDz74YO6tMikp8NRT0Ls3/PMPtG4NO3ZAmzYFHruIiEhBUDHjgrJaZ9auXZvjWFarzKuvvprziXv3mlOtP/0ULBZ45RX4+WcICyuEqEVERAqGihkXdKXWmWuOlVm8GHbvhuBgiIqCCRPs6y2JiIi4KhUzLiq31plrjpUZMwZeeMHsVrrrrsIJVEREpICpmHFRl7fO5Noqs3s3PPIIpKaa256e8MYb5n1kREREigkVMy7s0taZbK0yhmGOi7ntNvjf/yC38TMiIiLFhIoZF3Zp68zq1avNVpmICHNJgqeeMm+I17Ej/Otfzg5VRESkwLhEMfPRRx9RtWpV/Pz8aNy4ca6zeNxVVutMcnIyrzzyCDRpYt5DxtMTJk2CJUugQgVnhykiIlJginwxM3/+fEaMGMGLL77I9u3bufPOO+ncuTOHDx92dmhFgr+/P7Nnz2by449T97HHzLv6hofD6tXw/PPgUeQ/YhERkRtS5OflTpkyhQEDBvDkk08C8P7777Ns2TKmT5/OpEmTcpyflpZGWlqafTspKQmAjIwMMjIy8jW2rOvl93Ud1b59e9rXro3x/fcYd92FddYsKFsWCiCuopJzYXPHvN0xZ1De7pS3O+YMrpO3I/FZDMMwCjCWG5Kenk5AQAD/+9//uP/+++37hw8fzo4dO1i9enWO54wfP54JEybk2D937lwCAgIKNN7C5nfqFOfLlrVvB8THkxISYt4QT0RExIWlpKTQq1cvEhMTKVmy5FXPLdItMydPnsRqtRIcHJxtf3BwMAkJCbk+Z9y4cYwaNcq+nZSURKVKlejQocM13wxHZWRkEBUVRfv27fH29s7Xa1+VYeDx0Ud4PP881rlzMe69t9Be2mk5O5k75u2OOYPydqe83TFncJ28s3pW8qJIFzNZLJe1NBiGkWNfFl9fX3x9fXPs9/b2LrAPrSCvncOZMzBgACxaBIDXjz/CAw8Uzmtfwuc7H7x6esE8oMdlB+sDvwNLgY6XHasOlAK25UMQFmAIMO0a520HRgA7gCTgvQvb1+GGP+u/gZlAd6DBZcfGAxOAItZWWqh/v4sQ5e0+3DFnKPp5OxJbkR4dWq5cOTw9PXO0whw/fjxHa41b2LgRGjUyCxlvb/jPf8z7yTiB0dowi4mVlx04DewCSuRyLA74C2hb8PFl0x+Ixyy8fgMeLeTXv9TfmAXLjlyOPYkZn4iIOKRIFzM+Pj40btyYqKiobPujoqK44447nBSVExgGvPsutGwJsbFQrRqsXw/PPuu88THlgLrAqsv2r8Zs7xtAzmIma/tGi5lUB8/fDdwNdAaaA0X1BsjhmPGJiIhDinQxAzBq1Cg+/fRTPvvsM/bu3cvIkSM5fPgwTz/9tLNDKzxr1pg3vsvMhIcfhm3bzPvJOFtb4E/MVo8sq4DbgC7AViD5smOewJ3AeWAcUBXwASpidhmdvew1qgD3AAuBhoAfZstGbgzgBcAb+ASYg9l6lAlMv/BzVu03/pKfL5X1nNjsMXh296TCtgp4NfUCf6A28Fkuzz8KDAQqXcgrDHgIOMbF9wbgiUviGX+VmGzA5Auv5wtUAB7HbOW6VBvM4nIz5vsbAFQD3rxwDRGRYqzIj5np0aMHp06d4rXXXiM+Pp66deuyZMkSIiIinB1avsvIyODcuXOULl06+4HWrWH4cKhVC55+uujMVmoLfID5Jd3zwr6VmMVHC8wv5rWYhU3WsUZAScxWkl8wC5o7McfYvIrZzfIb5hd3lm3AXuAlzOKnRC6xpAH9gB+B74FOwIkL17ods6B47vpTtfxu4ZZdt2CdYMWrohd8itn6VANodeGko5jFSgZmUVUPOAUsA85cyH02ZiHzEtD1wvPCr/LCz2COsRmK+b7GAi9jvufbMFvIsiQAvS/k+SqwCPP9DcMsgEREiqkiX8wADB48mMGDBzs7jAJhtVrx8PBg/a/raXlnS/z9/Ek59w988AE8+ujFRSHff9+pceaqNWbb3irMYuYUZpfO20Ag5pf3Ssxi5ggQAzwMLMf8gp8MjL5wrfaYrRk9gC+Apy55nePAHqDmFeI4DXS7cP21mAOQAcpfeAAEc2NdOCdhw9QNtH2srdny0wqzGJvLxWLmFfM8dgJ1LnnuI5f8fGENUKrnIZ59mIXMYGDqJfsbAs0wBzK/ccn+U8ASoOmF7bsxP5u5qJgRkWKtyHczFUdWq5WVK1fy9KCnCSkXQs+bexLyqFm0pJ5Pha5dYeRI6N0bbEW4j+AmzMJh1YXt1ZjdSC0ubLfm4jiZS8fLrLjwc7/LrvcwZqvLL5ftr8eVC5kYzJaXJGADFwuZfGbUN0gtf8lgHb8LMR265KSfMPOrQ/7Ies/6Xba/6YXXuPx9CuFiIZOlHtljFBEphlTMFKLTp08zdMhQKgZXpF27diz9bClPnH2CN/a9QfWj1XmIh7jLxx+WLgU/P+jZs+h0KV1JW2A/5iydlUBjzFYZMIuZ7UDihWNeQEvMFgQvLraaZLFgfiGfumx/6FVef9OF1+/B1btrblTZXPb5kn0w8ol8jiHrfcgt/zByvk95iVFEpBhyiW4mV2Wz2diwYQMLFiygmn81bom7hZULVtI7vTeP8AhNM5tiuWTE50H2cVt6KtSuDQsWwK23OjH6PGoLTMFsnVnFxfExYBYuAGu4OPg1EPNLNxPzy//SgsbAHPdxG9ldrZ7rgVkAvYg50PWlPMbtd+HPNLKPzzmZx+fnpjw5B+beiKziJJ6cRdLfZB8vIyLixlTM5DPDMNi0aRPz58/nf1//j7iEOMK8wngl8xXu4i7+4I8rPjeVJBrffjtERUGJ3Ea5FkGtMLuWvgH+wBwHk6UU5o3hPsccuNrrwv67Lpz3JTDykvO/Bc5dOO6Il4CgC9c6B+RcsiunKhf+/J3sxdP3Dr72pToD/8Wc4VXrCudkFU55aS1pd+HPL8ke42bMAdEvXkeMIiLFkIqZfPLHH3+QkZHB8e3H6di/I8FewTyU+RA96EGLzBZ45KFH7+uGH/D1neuZ/sUXVK9enRo1alC5cmW8vIrwx1QSc6DvYsxOyxaXHW8NvH/h56z7y7THvDPwWMyxLi24OJupIdDnOuIYjtnqMxD4B3OW1dVadLoAZTBnJL2G+S9hDuZA5ev1Gua4mVaYs5luxZxqvhQYhTm9ujrm1O6vMMe9BGJ2GYXlcr1aF/KZivnedubibKZKZC8ERUTcWBH+lnQdhmFwZ8s7OXP2DLvYxTa2US+zHp54OnSdpN9vYuHuhcRmxpJpZALg5elF1zZdmb9wPm9/8DaBgYHUqFGD6tWrU7VqVfz8/K5x1ULQFrO1oCFmcXOp1pizbnyArPscWjCLn/GYU5XfwOwy6QNMJHu3jyMGYA4g7oPZQvMpVx4VVhKzyBgBPAaUxrwDb+cLf16PiphjeF7FvL/LKcyup5aYhROY93/5DPNeOR0wp3G/ysV7zVxuOmYBNAv4ELO1qxNm61NuY2RERNyQipl8YLFYWPx/i3m81+M0i2/Gu7Z3aZBj4Z1ra2VtxQHrATLJ5DCHiSaag9aDlPmlDKmlU/nB+wd2Zu7kvO28/XUjK0ey8ueVrN68msOHD9sLnerVqxMUFJTPmV7BWxceuelG7msN+WF+4b95jWvHXuVYbtd9lJzLFVxpraPbgF9z2T8gZwzWDKs57flSq3J5bjhm4XE1ucUIZkEz/rJ9HsCYC4+ryS0WMFubRESKORUz+aRVq1bs3reb0f8azTMznuEHjx/4zvZdnrqXLueFF9Uu/GdnwIb0DdiwEU88BzlItBHNmUNnKB1ZmlX+q5iXPo8k68VVRoPLBPPJ1E8IrxPODz/8QLVq1ezFTtmyZa+4WKeIiIgrUTGTjwIDA5n+8XS639+dL6Z9QVJcEvt37Oc2bss2a+lGeOBBxQv/tbLfrQ1mpM7gYz7mFKfMQodoYk/HUrN3TTYHbGZa+jSOZx63n18qsBQD+wxk3OvjmPnJTCpUqGAfpxMaGqpCR0REXIaKmQLQsWNHOnbsyIrlK7ir4108wsN8xHTKXmWQw2lOY8VKOcpdd+FjwUK5C/81o5l9f62UWjzGYySTzMEL/0X/E02d6XU4OfskM20z+Sv9L/v5/r7+NKnXhKhVUcydP5fz589Tr14991rcU0REXIaKmQLUrkUz5pUqxeDEhdRlJZ8yh672BXmya+jZkMPWw5T0LMkDPg8wPXU605lOKUpRgxpUpzqhhF5Xt1WWIIJocOE/u/NwkIOc5zwxxJjjdNIOkrY5DZ9SPnzh/QVrz6/Falg5fPgwIVnLK4iIiBQRKmYKUokS9HjlFe6cPZsnbyrLPWvvYSAD+ZiPs7W+JJLIYethhg8fTmhoKKGhoSTdmcTMu2byZ+yfGIY5gtXfw59bvW7lx/QfWcMajnGM6lSnBjWoTGW8buDj9MOPOhf+s8uElZkrmc1s+tOfcuV0lzYRESl6VMzkt0OH4Nw5uPlmc3vkSMKGDOFHHx8+/fRTPpj0AacyTuER50GZC/N1D3IQgN69e3PbbRfvjrb3r72cP3+emJgYDh48SHR0NImJiQQ8G8C8XvNYFLWITOuFKdwWL6p4VWGGbQblreVZwQqqUY3qVKca1fDj+qdwH+Qg4cHh+Pv7k5GRcd3XERERKQgqZvLT4sXwxBMQHAxbtkBgoLm2kq8vFuCpp57iqaeeYsuqLTRt25TneI5/829CCKFbo27ccsstOS7p5+dHnTp1qFMn++qFC35aQGZmJkeOHCE6Opro6GgOHTpESO8Q1ny3hnH/HkdqmnmbWQsWKnpXZJAxiKGZQ/mKr6hABXv3VckcN4fJLoEEatW50i1tRUREnEvFTH5IS4PRo+E//zG3a9aEpCSzmMlFo1aNmPz2ZF4c9yI/GT/xnvU93hnzDgEBAQ69rJeXF1WrVqVq1aq0b9/evv/mW29m0AuDiI+PJzo62t6qU7tBbeLKxTH+/vGcTLy4CFF5r/I0oxmLMhfxDd9gxWovdMpSlpfLvox1ltXx90VERKQQqJi5QQEJCXi2bg3btpk7nnsOJk4EH58rPsfDw4N//etfdOrUiT49+9BhdwfqvFyHPT325FtcFouFsLAwwsLCaNWqVbZjx88c5/Tp0/Yi5+DBg2RmZuL5rCeTmk/i9+jf7eeW8ixF4qlEvt70NdWqVbv8ZURERJxOxcwNsHz7LW1GjcIjJQXKlIE5c+Dee/P8/Lp167Jx60beefsdIiIiCi7Qy1gsFsqWLUvZsmVp2rRptmM7D+wkOTmZgwcP2oudcePGUalSpUKLT0RExBEqZq6XYeDxySd4pKRgu/12PObPh+v4wvfx8eGFF18ogACvX1BQEA0aNKBBgwYAjB071rkBiYiIXMX137TE3VksWOfMYW/Pnlh//vm6ChkRERG5cSpmbkRICPt79ABvb2dHIiIi4rZUzIiIiIhLUzEjIiIiLk3FjIiIiLg0FTMiIiLi0lTMiIiIiEtTMSMiIiIuTcWMiIiIuDQVMyIiIuLSVMyIiIiIS1MxIyIiIi5NxYyIiIi4NBUzIiIi4tJUzIiIiIhLUzEjIiIiLs3L2QEUNMMwAEhKSsr3a2dkZJCSkkJSUhLe3t75fv2iyB1zBvfM2x1zBuXtTnm7Y87gOnlnfW9nfY9fTbEvZpKTkwGoVKmSkyMRERERRyUnJ1OqVKmrnmMx8lLyuDCbzcbff/9NUFAQFoslX6+dlJREpUqVOHLkCCVLlszXaxdV7pgzuGfe7pgzKG93ytsdcwbXydswDJKTkwkLC8PD4+qjYop9y4yHhwfh4eEF+holS5Ys0n8hCoI75gzumbc75gzK2524Y87gGnlfq0UmiwYAi4iIiEtTMSMiIiIuTcXMDfD19eXVV1/F19fX2aEUGnfMGdwzb3fMGZS3O+XtjjlD8cy72A8AFhERkeJNLTMiIiLi0lTMiIiIiEtTMSMiIiIuTcWMiIiIuDQVM9fpo48+omrVqvj5+dG4cWPWrl3r7JDyzaRJk7jtttsICgqiQoUKdO/enT///DPbOYZhMH78eMLCwvD396dNmzb88ccfToq4YEyaNAmLxcKIESPs+4pj3kePHuWxxx6jbNmyBAQE0KBBA7Zu3Wo/XhxzzszM5KWXXqJq1ar4+/tTrVo1XnvtNWw2m/2c4pD3mjVruPfeewkLC8NisbB48eJsx/OSY1paGsOGDaNcuXKUKFGC++67j7i4uELMwjFXyzkjI4OxY8dy6623UqJECcLCwnj88cf5+++/s13D1XKGa3/Wlxo0aBAWi4X3338/235XzDuLipnrMH/+fEaMGMGLL77I9u3bufPOO+ncuTOHDx92dmj5YvXq1QwZMoQNGzYQFRVFZmYmHTp04Ny5c/ZzJk+ezJQpU5g2bRqbN28mJCSE9u3b29fCcnWbN29m5syZ1KtXL9v+4pb3mTNnaNGiBd7e3vz000/s2bOHd999l9KlS9vPKW45A7z11lt8/PHHTJs2jb179zJ58mTefvttpk6daj+nOOR97tw56tevz7Rp03I9npccR4wYwaJFi5g3bx7r1q3jn3/+4Z577sFqtRZWGg65Ws4pKSls27aNl19+mW3btrFw4UL279/Pfffdl+08V8sZrv1ZZ1m8eDEbN24kLCwsxzFXzNvOEIc1bdrUePrpp7Ptq127tvH88887KaKCdfz4cQMwVq9ebRiGYdhsNiMkJMR488037eecP3/eKFWqlPHxxx87K8x8k5ycbERGRhpRUVFG69atjeHDhxuGUTzzHjt2rNGyZcsrHi+OORuGYXTt2tXo379/tn0PPPCA8dhjjxmGUTzzBoxFixbZt/OS49mzZw1vb29j3rx59nOOHj1qeHh4GEuXLi202K/X5TnnZtOmTQZgHDp0yDAM18/ZMK6cd1xcnFGxYkVj9+7dRkREhPHee+/Zj7l63mqZcVB6ejpbt26lQ4cO2fZ36NCB9evXOymqgpWYmAhAmTJlAIiJiSEhISHbe+Dr60vr1q2LxXswZMgQunbtyt13351tf3HM+7vvvqNJkyY8/PDDVKhQgYYNG/LJJ5/YjxfHnAFatmzJL7/8wv79+wHYuXMn69ato0uXLkDxzftSeclx69atZGRkZDsnLCyMunXrFpv3ITExEYvFYm+NLK4522w2+vTpw+jRo7nllltyHHf1vIv9QpP57eTJk1itVoKDg7PtDw4OJiEhwUlRFRzDMBg1ahQtW7akbt26APY8c3sPDh06VOgx5qd58+axbds2Nm/enONYccz7r7/+Yvr06YwaNYoXXniBTZs28eyzz+Lr68vjjz9eLHMGGDt2LImJidSuXRtPT0+sVitvvPEGPXv2BIrnZ325vOSYkJCAj48PN910U45zisPvu/Pnz/P888/Tq1cv+4KLxTXnt956Cy8vL5599tlcj7t63ipmrpPFYsm2bRhGjn3FwdChQ/n9999Zt25djmPF7T04cuQIw4cPZ/ny5fj5+V3xvOKUt81mo0mTJkycOBGAhg0b8scffzB9+nQef/xx+3nFKWcwx719+eWXzJ07l1tuuYUdO3YwYsQIwsLC6Nu3r/284pZ3bq4nx+LwPmRkZPDoo49is9n46KOPrnm+K+e8detW/vOf/7Bt2zaHc3CVvNXN5KBy5crh6emZo1I9fvx4jv/DcXXDhg3ju+++Y+XKlYSHh9v3h4SEABS792Dr1q0cP36cxo0b4+XlhZeXF6tXr+aDDz7Ay8vLnltxyjs0NJSbb7452746derYB7MX18969OjRPP/88zz66KPceuut9OnTh5EjRzJp0iSg+OZ9qbzkGBISQnp6OmfOnLniOa4oIyODRx55hJiYGKKiouytMlA8c167di3Hjx+ncuXK9t9thw4d4rnnnqNKlSqA6+etYsZBPj4+NG7cmKioqGz7o6KiuOOOO5wUVf4yDIOhQ4eycOFCVqxYQdWqVbMdr1q1KiEhIdneg/T0dFavXu3S78Fdd93Frl272LFjh/3RpEkTevfuzY4dO6hWrVqxy7tFixY5pt3v37+fiIgIoPh+1ikpKXh4ZP/15+npaZ+aXVzzvlRecmzcuDHe3t7ZzomPj2f37t0u+z5kFTIHDhzg559/pmzZstmOF8ec+/Tpw++//57td1tYWBijR49m2bJlQDHI20kDj13avHnzDG9vb2PWrFnGnj17jBEjRhglSpQwYmNjnR1avnjmmWeMUqVKGatWrTLi4+Ptj5SUFPs5b775plGqVClj4cKFxq5du4yePXsaoaGhRlJSkhMjz3+XzmYyjOKX96ZNmwwvLy/jjTfeMA4cOGB89dVXRkBAgPHll1/azyluORuGYfTt29eoWLGi8cMPPxgxMTHGwoULjXLlyhljxoyxn1Mc8k5OTja2b99ubN++3QCMKVOmGNu3b7fP3MlLjk8//bQRHh5u/Pzzz8a2bduMdu3aGfXr1zcyMzOdldZVXS3njIwM47777jPCw8ONHTt2ZPv9lpaWZr+Gq+VsGNf+rC93+Wwmw3DNvLOomLlOH374oREREWH4+PgYjRo1sk9bLg6AXB+zZ8+2n2Oz2YxXX33VCAkJMXx9fY1WrVoZu3btcl7QBeTyYqY45v39998bdevWNXx9fY3atWsbM2fOzHa8OOaclJRkDB8+3KhcubLh5+dnVKtWzXjxxRezfaEVh7xXrlyZ67/lvn37GoaRtxxTU1ONoUOHGmXKlDH8/f2Ne+65xzh8+LATssmbq+UcExNzxd9vK1eutF/D1XI2jGt/1pfLrZhxxbyzWAzDMAqjBUhERESkIGjMjIiIiLg0FTMiIiLi0lTMiIiIiEtTMSMiIiIuTcWMiIiIuDQVMyIiIuLSVMyIiIiIS1MxIyIiIi5NxYyIyDX069cPi8WCxWJh8eLF+XrtVatW2a/dvXv3fL22iLtQMSPihi79cr70ER0d7ezQiqxOnToRHx9P586d7fuuVNz069cvz4XJHXfcQXx8PI888kg+RSrifrycHYCIOEenTp2YPXt2tn3ly5fPcV56ejo+Pj6FFVaR5evrS0hISL5f18fHh5CQEPz9/UlLS8v364u4A7XMiLiprC/nSx+enp60adOGoUOHMmrUKMqVK0f79u0B2LNnD126dCEwMJDg4GD69OnDyZMn7dc7d+4cjz/+OIGBgYSGhvLuu+/Spk0bRowYYT8nt5aM0qVLM2fOHPv20aNH6dGjBzfddBNly5alW7duxMbG2o9ntXq88847hIaGUrZsWYYMGUJGRob9nLS0NMaMGUOlSpXw9fUlMjKSWbNmYRgGNWrU4J133skWw+7du/Hw8ODgwYM3/sZeJjY2NtdWsDZt2uT7a4m4KxUzIpLD559/jpeXF7/++iszZswgPj6e1q1b06BBA7Zs2cLSpUs5duxYtq6R0aNHs3LlShYtWsTy5ctZtWoVW7dudeh1U1JSaNu2LYGBgaxZs4Z169YRGBhIp06dSE9Pt5+3cuVKDh48yMqVK/n888+ZM2dOtoLo8ccfZ968eXzwwQfs3buXjz/+mMDAQCwWC/3798/RIvXZZ59x5513Ur169et7w66iUqVKxMfH2x/bt2+nbNmytGrVKt9fS8RtOXnVbhFxgr59+xqenp5GiRIl7I+HHnrIMAzDaN26tdGgQYNs57/88stGhw4dsu07cuSIARh//vmnkZycbPj4+Bjz5s2zHz916pTh7+9vDB8+3L4PMBYtWpTtOqVKlTJmz55tGIZhzJo1y6hVq5Zhs9nsx9PS0gx/f39j2bJl9tgjIiKMzMxM+zkPP/yw0aNHD8MwDOPPP/80ACMqKirX3P/++2/D09PT2Lhxo2EYhpGenm6UL1/emDNnzlXfr27duuXYDxh+fn7Z3scSJUoYXl5euZ6fmppqNGvWzLjnnnsMq9Wap9cQkWvTmBkRN9W2bVumT59u3y5RooT95yZNmmQ7d+vWraxcuZLAwMAc1zl48CCpqamkp6dz++232/eXKVOGWrVqORTT1q1biY6OJigoKNv+8+fPZ+sCuuWWW/D09LRvh4aGsmvXLgB27NiBp6cnrVu3zvU1QkND6dq1K5999hlNmzblhx9+4Pz58zz88MMOxZrlvffe4+677862b+zYsVit1hznDhgwgOTkZKKiovDwUMO4SH5RMSPipkqUKEGNGjWueOxSNpuNe++9l7feeivHuaGhoRw4cCBPr2mxWDAMI9u+S8e62Gw2GjduzFdffZXjuZcOTvb29s5xXZvNBoC/v/8143jyySfp06cP7733HrNnz6ZHjx4EBATkKYfLhYSE5Hgfg4KCOHv2bLZ9r7/+OkuXLmXTpk05ijURuTEqZkTkmho1asS3335LlSpV8PLK+WujRo0aeHt7s2HDBipXrgzAmTNn2L9/f7YWkvLlyxMfH2/fPnDgACkpKdleZ/78+VSoUIGSJUteV6y33norNpuN1atX52gxydKlSxdKlCjB9OnT+emnn1izZs11vVZeffvtt7z22mv89NNPBTIuR8TdqZ1TRK5pyJAhnD59mp49e7Jp0yb++usvli9fTv/+/bFarQQGBjJgwABGjx7NL7/8wu7du+nXr1+OrpR27doxbdo0tm3bxpYtW3j66aeztbL07t2bcuXK0a1bN9auXUtMTAyrV69m+PDhxMXF5SnWKlWq0LdvX/r378/ixYuJiYlh1apVLFiwwH6Op6cn/fr1Y9y4cdSoUSNb91h+2717N48//jhjx47llltuISEhgYSEBE6fPl1gryniblTMiMg1hYWF8euvv2K1WunYsSN169Zl+PDhlCpVyl6wvP3227Rq1Yr77ruPu+++m5YtW9K4ceNs13n33XepVKkSrVq1olevXvzrX//K1r0TEBDAmjVrqFy5Mg888AB16tShf//+pKamOtRSM336dB566CEGDx5M7dq1eeqppzh37ly2cwYMGEB6ejr9+/e/gXfm2rZs2UJKSgqvv/46oaGh9scDDzxQoK8r4k4sxuUd2CIi+aRNmzY0aNCA999/39mh5PDrr7/Spk0b4uLiCA4Ovuq5/fr14+zZs/m+lEFhv4ZIcaWWGRFxK2lpaURHR/Pyyy/zyCOPXLOQyfLDDz8QGBjIDz/8kK/xrF27lsDAwFwHPYtI3mgAsIi4la+//poBAwbQoEED/vvf/+bpOZMnT+all14CzNlb+alJkybs2LEDINep7yJybepmEhEREZembiYRERFxaSpmRERExKWpmBERERGXpmJGREREXJqKGREREXFpKmZERETEpamYEREREZemYkZERERc2v8DbWpnvvTPZFgAAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.optimize import curve_fit\n", "\n", "#measurements \n", "frequency = np.array([32,38,49,75,90,105,116,122])\n", "amplitude = np.array([4.8,5.8,7.5,14.0,17.0,19.5,22,24.5])\n", "\n", "#curvefitting\n", "def func(x, a, b):\n", " return a * x + b\n", "\n", "variables, covariance = curve_fit(func, frequency, amplitude)\n", "\n", "x_test = np.linspace(0, 1.2*max(frequency), 1000)\n", "y_test = func(x_test, variables[0], variables[1])\n", "\n", "\n", "plt.figure()\n", "plt.plot(frequency, amplitude, 'k.', label='Measurements')\n", "plt.plot(x_test, y_test, 'r--', label='Curvefit')\n", "\n", "plt.xlabel('Frequency [Hz]')\n", "plt.ylabel('Amplitude [mm]')\n", "\n", "\n", "# Adding text at specific coordinates\n", "plt.text(-variables[1]/variables[0]-5, 5, 'Cutoff frequency', fontsize=12, color='gray', rotation=0)\n", "plt.text(20, variables[1]/2, 'Workfunction', fontsize=12, color='magenta', rotation=0)\n", "\n", "# Adding an arrow\n", "plt.annotate('', xy=(-variables[1]/variables[0], 0), xytext=(-variables[1]/variables[0], 4), arrowprops=dict(facecolor='gray', shrink=0.05))\n", "plt.annotate('', xy=(0, variables[1]/2), xytext=(20, -2), arrowprops=dict(facecolor='magenta', shrink=0.05, linestyle='dashed'))\n", "\n", "plt.grid()\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "```{bibliography}\n", ":filter: docname in docnames\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [] } ], "metadata": { "celltoolbar": "Tags", "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": "3.10.14" } }, "nbformat": 4, "nbformat_minor": 2 }