Decay Simulator All in One.ipynb

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    "# Simulation of particle decay\n",
    "# Designed for use in the University of Chicago Physics 211 course\n",
    "# Written 9/17/2019 by Kevin Van De Bogart\n",
    "\n",
    "import time\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib notebook \n",
    "\n",
    "\n",
    "add_chance = 0.5\n",
    "decay_chance = 0.01\n",
    "time_range = 500\n",
    "hist_bins = np.linspace(1,time_range,time_range)\n",
    "rebin_factor = 2\n",
    "    # this is all the decay related stuff: \n",
    "    # add_chance is the probability that a particle will be added to the simulation in one time step\n",
    "    # decay_chance is the probability that a particle decays in a timestep\n",
    "    # time_range sets how far out the x (time) axis goes \n",
    "        # picking too small of a value will result in data overflowing the chart edge, but it is still there.\n",
    "    # hist_bins sets up a series of time_range+1 values [0,1,2,...,time_range], \n",
    "    # rebin_factor defines how many bins to collapse together when rebinning\n",
    "\n",
    "\n",
    "t_end = time.time() + 60\n",
    "    # this sets the sim to run for 60 seconds of real time\n",
    "frame_skip = 1\n",
    "    # this sets the delay between re-drawing results\n",
    "    # setting this to 1 shows every single step\n",
    "    # higher values make the simulation run much faster\n",
    "\n",
    "    # the while statement starts the loop for the simulation"
   ]
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     "text": [
      "Setup done\n"
     ]
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       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
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     "output_type": "display_data"
    },
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x/PsF2mhRSjM/hIBi6IIeCxAAuLx5NF1BNIQIEBIQz25NguBuGohLw+Zm3x4PI9+ya1G4ZvQk8SlbgQcEiABcWgy6AoCPgiQgPgwS9H6qHsrUrTW0i9t+tapvPklOYPsL0nqUjcC7giQgLgzF/QEAS8ECBC8mKbIndR5GDtyYylfkMTD43nyS3L62F+S1KVuBNwRIAFxZy7oCQJeCBAgeDFNdLIFAdMnICax857IsL+YXE3UhYC7AiQg7s4NPUPASQECBCenhU5FEHD14XFu5eIZkAjLmKIIeC1AAuL19NF5BOwLuJqA5P03x/ZXgt8tuvbwuIm3cvk9I//be1f3lyzYMgYEXBIgAXFpNugLAh4IuBggFPvNcdvdvygn9+0kx/baRw7v1lZaV7TyQJcu2hRw5cTB5Fu5bPol0ZaL+0sS46ROBPIuQAKS9xXA+BGIKJBWgFDqhKPUb44bDqtDVRu58nu95IQ+HSKOluJZF3Dh5MzlZ1Jsz39a+4vtcdIeAnkXIAHJ+wpg/AhEFEgjQCj1m+rLv3uQ/PKvr8j6ui0tjqJw9jF9eD+SkIjzTfHkBZJ4K1fyvU6mhTT2l2RGQq0IINCSAAkI6wMBBCIJ2A4QwpxwhBmASkL2qWojT4wfzO1YYcAoY02AE5D/o7a9v1ibZBpCAIFGAiQgLAgEEIgkYDNAKHdvfKSOf174jpFHSv/u7eJcyjUIJCLg6lu5EhlsmUpt7i9pjI82EUDgfwVIQFgJCCAQScBmgBD2N8NRBnD9sL4ytG+nKJdQFoHEBVx7K1fiAy7RgM39Ja0x0i4CCJCAsAYQQCCigM0AYf5za2TsH1+I2MOWi3MCYpSTygwKuPJWLoNDilyVzf0lcue4AAEEjAlwAmKMkooQcF/gs88+k5qaGvn9738vGzZskA4dOsg555wjP//5z6WioiLUAGwGCLMefz14yNzEh2dATChSR9ICLryVK+kxtlS/zf0lzXHSNgJ5FyAByfsKYPy5Epg0aZJce+21Mnv2bOndu7c888wzcu6558rEiRNlzJgxoSxsBgjzn18rY/+wrGy/zh3QVe57eUPJt2HxFqyyhBRAwAkBm/uLEwOmEwjkVIAEJKcTz7DzKXDiiSfK3nvvLbNmzaoHOOWUU2S33XaTOXPmhEKxGSCEfQZE3ValvmxwyRvvy4PLN8jdy9bJ+x9vqx8P3wMSamop5JBAXk9CbO4vDk03XUEgdwIkILmbcgacZ4Grr75abrrpJnnggQekZ8+e8sILL8hxxx0n1113nZx++ulFabZu3SrqT+GjAoTq6mqpq6uTysrKRDnDvAVLJRdNX62b1+At0cmgcmsCeX4WhATE2jKjIQRSFSABSZWfxhGwK7Bz506ZMGGCTJkyRVq3bi3bt28XdVvWZZddVrIj6pmR2traZj+3kYCoRnk7kN014nNrWUg8S33vTV5uIyQB8flfIH1HILwACUh4K0oi4L3AvHnz5Kc//alMnTo1eAZk2bJlcvHFF8u0adNkxIgRzp2AFDqU598Ie7/oLA0gC2uk3IlfHl6kQAJi6R8MzSCQsgAJSMoTQPMI2BRQt05deumlcuGFF9Y3qx5Anzt3rrz66quhupJWgJCF326HAjZYKC9mWTk1iPLMU1a/TDOt/cXgPzuqQgCBEAIkICGQKIJAVgTatWsXvPHq/PPPrx/S5MmT5dZbb5W///3voYZJgBCKKfVCWTgRCIOYpVODBcvWyph55d/6luUv02R/CbPqKYOA/wIkIP7PISNAILSA+s6Phx56SGbMmBHcgvX888/LqFGj5Ic//GHwXEiYDwFCGKX0yqiA/D8fXinXPtQ8oczicwRZOjXI0lji/gtgf4krx3UI+CVAAuLXfNFbBLQENm3aJJdffrnMnz9fNm7cKB07dgzefnXFFVfILrvsEqpuAoRQTKkUUqceNf/1smz46P/eWta0I1l7jsDFU4O4t74VTnM21G2RnUVWUNbmrtg/EvaXVLYOGkXAugAJiHVyGkTAbwECBDfnr9RzEKV6q747JQvPEbh2aqB761ve3/rG/uLm/kKvEDAtQAJiWpT6EMi4AAGCexNc7jmIYj3OynMELp0amHoYXjeJcW+Fhu8R+0t4K0oi4LMACYjPs0ffEUhBgAAhBfQyTYY9BWhYTVZOQNSYXDg1KJcERr19Ku5tXO6tzmg9Yn+J5kVpBHwVIAHxdeboNwIpCRAgpATfQrNhn4NQVUQNhN0bbfEepX1qEDYJzFLil8TaYH9JQpU6EXBPgATEvTmhRwg4LUCA4N70hA1+CwnI9OH95IQ+HdwbiGaP0jw1CJsEZuXWN82pKnk5+0tSstSLgFsCJCBuzQe9QcB5AQIE96ao3HMQhR53qGojV36vVyaTj7RnJWwSaPoEJM2kKwlz9pckVKkTAfcESEDcmxN6hIDTAgQIbk5PqecgCr0de2wP+dHgHtK6ovBtIG6Ow9delUsCk7j1Le3bzpKYK/aXJFSpEwH3BEhA3JsTeoSA0wIECO5OTxYDUne1m/fM5sPwpt645Zov+4trM0J/EEhGgAQkGVdqRSCzAgQIbk+tqVtyTNXjtpb53tlIAk2/ccu8Qvwa2V/i23ElAj4JkID4NFv0FQEHBAgQHJiEhLtgI4hOeAipVp908pbW8yY2UNlfbCjTBgLpC5CApD8H9AABrwQIELyarsidzeqtPZEhHL4gy2/cYn9xeOHRNQQMCpCAGMSkKgTyIECAkN1ZzvKtPVmaNU5AsjSbjAWBfAqQgORz3hk1ArEFSEBi0zl/YZYDW+fxI3QwjTduReieVlH2Fy0+LkbAGwESEG+mio4i4IYAAYIb85BEL7J8a08SXmnWafONWzbHyf5iU5u2EEhPgAQkPXtaRsBLAQIEL6ctVKdNnoAk/SB2qAFlvFAWXxbA/pLxRcvwEPhcgASEpYAAApEECBAicXlV2NStPVkMjF2dyKwleuwvrq40+oWAWQESELOe1IZA5gUIELI9xbq39vAWrWyvj6RHx/6StDD1I+CGAAmIG/NALxDwRoAAwZupit3RuCcYvEUrNjkXfi7A/sJSQCAfAiQg+ZhnRomAMQECBGOUTlcU59Yek8+QOI1D5xITYH9JjJaKEXBKgATEqemgMwi4L0CA4P4cpdXDuG/RipPspDVG2k1WgP0lWV9qR8AVARIQV2aCfiDgiQABgicTlUI345yAxL3dK4Xh0aQFAfYXC8g0gYADAiQgDkwCXUDAJwECBJ9my25fo75FiwfW7c6PD62xv/gwS/QRAX0BEhB9Q2pAIFcCBAi5mu7Igw37Fi0eWI9Mm4sL2F9yMc0MEgEhAWERIIBAJAEChEhcuSwc5raqOLdrpYnJcyp29Nlf7DjTCgJpC5CApD0DtI+AZwIECJ5NWErdLRewx31gPY3hhEmo0uhXFttkf8nirDImBJoLkICwKhBAIJIAAUIkLgqXEPDlBITnVOwuYfYXu960hkBaAiQgacnTLgKeChAgeDpxjnU76gPraXSf51Tsq7O/2DenRQTSECABSUOdNhHwWIAAwePJc6zrYR9YT6vbvpzSpOWTRLvsL0moUicC7gmQgLg3J/QIAacFCBCcnh7vOufy8xU+Pafi3cSX6DD7S1ZmknEg0LIACQgrBAEEIgkQIETionAIgXIPrIeoIpEinIAkwtpipewv9s1pEYE0BEhA0lCnTQQ8FiBA8Hjy6HokAR+eU4k0IA8Ks794MEl0EQEDAiQgBhCpAoE8CRAg5Gm2Gavrz6lkbYbYX7I2o4wHgeICJCCsDAQQiCRAgBCJy+vCrt4aZRvV5edUbFsk3R77S9LC1I+AGwIkIG7MA71AwBsBAgRvpkqrowTdjflIxrSWU+iL2V9CU1EQAa8FSEC8nj46j4B9AQIE++a2WiwE2Q8u3yC/XfRms2Zbff4304f3kxP6dLDVLdrJkQD7S44mm6HmWoAEJNfTz+ARiC5AgBDdzIcrip14FOu3SkL2qWojT4wfLK0rCimJDyOkjz4IsL/4MEv0EQF9ARIQfUNqQCBXAgQI2ZvuwoPWOyMM7Y6RR0r/7u0iXEFRBMoLsL+UN6IEAlkQIAHJwiwyBgQsChAgWMS20FThVbPr67ZEau36YX1laN9Oka6hMALlBNhfygnxcwSyIUACko15ZBQIWBMgQLBGbaWhsF+217QznIBYmZ7cNcL+krspZ8A5FSAByenEM2wE4goQIMSVc/O6BcvWyph5y0J3jmdAQlNRMIYA+0sMNC5BwEMBEhAPJ40uI5CmAAFCmvrm245yAsJbsMz7U2NjAfYXVgQC+RAgAcnHPDNKBIwJECAYo3SiosIzIBvqtki5h9A7VLWRK7/Xi1fwOjFz2ewE+0s255VRIdBUgASENYEAApEECBAicXlRuPAWLNXZYknIeUd1lWN77SOHd2vLq3e9mFF/O8n+4u/c0XMEogiQgETRoiwCCAgBQjYXQdhvPucbwbM5/66Miv3FlZmgHwgkK0ACkqwvtSOQOYEsBQgE042XZzmPsElK5hY9A7ImkKX9xRoaDSHgoQAJiIeTRpcRSFMgKwFCHoPpcglGS+uq1JcV8mB6mv8as9d2VvaX7M0MI0LArAAJiFlPakPAeYG1a9fK+PHj5d5775VPPvlEevbsKbNmzZJDDjkkVN+zECDkMZjWSbjKfVkhr+YN9U+HQiEEsrC/hBgmRRDIvQAJSO6XAAB5Evjggw/k4IMPlkGDBsn5558v7du3l1WrVknXrl2le/fuoSh8DxDyGEzrJlxhX9XLlxOG+idEoRYEfN9fmFwEEAgnQAISzolSCGRC4NJLL5VFixbJ448/Hns8vgcIeQumTSRcYb+s8PphfWVo306x1xYXIuD7/sIMIoBAOAESkHBOlEIgEwK9evWS448/XtasWSMLFy6UTp06yQUXXCAjR44sOb6tW7eK+lP4qAChurpa6urqpLKy0juXvAXTJhIuE3V4t1DocCoCJCCpsNMoAtYFSECsk9MgAukJtGnTJmh83Lhxcuqpp8qSJUvk4osvlhkzZsjZZ59dtGM1NTVSW1vb7Ge+JiB5C6ZNJFzlvqyQZ0DS+zedtZZJQLI2o4wHgeICJCCsDARyJLDLLrvIoYceKk8++WT9qH/84x/L0qVLZfHixUUlsnYCkrdg2lTCVerLCnkLVo42EAtDJQGxgEwTCDggQALiwCTQBQRsCXTp0kWGDBkit9xyS32T06dPl4kTJ4p6O1aYTxYCBFeCaZ3X4oaZK1XGZMKl8yatsP2lXL4FsrC/5HsGGT0C4QRIQMI5UQqBTAicccYZsnr16kYPoY8dO1aefvrpRqciLQ02KwFC2sG0zfZNJlw2kqZM/GNjELEEsrK/xBo8FyGQIwESkBxNNkNFQN1qNWDAgOCZjtNOOy14BkQ9gD5z5kw588wzQwFlKUAoFkwrhCVvvC8bN22R9nu2kcO7tZXWFYUbjUIRlS2k+1rcsg0UKWAz4YnTP65BQAlkaX9hRhFAoLQACQirA4GcCdxzzz1y2WWXyYoVK6Rbt27BA+ktvQWrKU+WAwSdID3syYCJ1+LGXbJh+xi3fq5DQFcgy/uLrg3XI5AlARKQLM0mY0HAgkBWAwSdU4koiYuph8KTnGoSlSR1qbslgazuL8w6Agg0FiABYUUggEAkgSwGCDqnElETFxOvxY00YRELR0mmIlZNcQTKCmRxfyk7aAogkEMBEpAcTjpDRkBHIIsBQtxTiTiJS9y2dOYs7LVRk6mw9ealHCdH+jOdxf1FX4UaEMieAAlI9uaUESGQqEAWA4S4pxJxkgmTr8U1OdFxkimT7fteFydHZmYwi/uLGRlqQSBbAiQg2ZpPRoNA4gJZDBDiJBIKOm7iYvK1uKYmPK6BqfZ9roeTI3Ozl8X9xZwONSGQHQESkOzMJSNBwIpAFgOEuKcSOkG7a78xj5tMWVl0DjfCyZHZycni/mJWiNoQyIYACUg25pFRIGBNIKsBQpxTibiJS2GyXHpmQKfPnvcAACAASURBVCeZsrb4HGwIN7OTktX9xawStSHgvwAJiP9zyAgQsCqQ5QAhzqlEnMTF6oSFbEw3mQrZTOaKcXJkdkqzvL+YlaI2BPwWIAHxe/7oPQLWBbIeIMQ5lYiTuFifuBANZiWZCjFUY0U4ATFGGVSU9f3FrBa1IeCvAAmIv3NHzxFIRYAAoTh7nMQllQks02hWkilbtpwcmZVmfzHrSW0IuCpAAuLqzNAvBBwVIEBwdGIMdisryZRBkhar4uTInDT7izlLakLAZQESEJdnh74h4KAAAYKDk0KXUhfg5MjMFLC/mHGkFgRcFyABcX2G6B8CjgkQIDg2IXTHGQFOjvSngv1F35AaEPBBgATEh1mijwg4JECA4NBk0BUEMibA/pKxCWU4CJQQIAFhaSCAQCQBAoRIXBRGAIEIAuwvEbAoioDHAiQgHk8eXUcgDQEChDTUaROBfAiwv+RjnhklAiQgrAEEEIgkQIAQiYvCMQV4niImnOeXsb94PoF0H4GQAiQgIaEohgAC/ytAgMBKSFqAN0olLexu/ewv7s4NPUPApAAJiElN6kIgBwIECDmY5BSHWPhOjZ1N+tDq8/+ePryfnNCnQ4o9pOkkBdhfktSlbgTcESABcWcu6AkCXggQIHgxTV52svCt4uvrthTtv0pC9qlqI0+MHyytKwopiZdDpdMlBNhfWBoI5EOABCQf88woETAmkKUAwafnDHzqa9zFtnjVe3L6zU+VvfyOkUdK/+7typajgH8CWdpf/NOnxwjYEyABsWdNSwhkQiArAYJPzxn41FedRb5g2VoZM29Z2SquH9ZXhvbtVLYcBfwTyMr+4p88PUbArgAJiF1vWkPAe4EsBAg+PWfgU191FzcnILqCLV/vwylaFvaXZGeR2hHIhgAJSDbmkVEgYE3A9wDBp+cMfOqriQVYGO+Gui3S9CF0VT/PgMRX9uUUzff9Jf4McSUC+RIgAcnXfDNaBLQFfA8QfPotu0991V5Yn1dQOPFR/9kwCeEtWPGFfTpF831/iT9LXIlAvgRIQPI134wWAW0B3wMEn54z8Kmv2gurQQW+/LbexJiTvi3Kt1M03/cXE2uCOhDIgwAJSB5mmTEiYFDA9wDBp1MFn/qqlpjJYNpkXQaXv9GqbCRavq0h3/cXowuEyhDIsAAJSIYnl6EhkISA7wGCT88Z+NRXG8F0Eus5rTpt3Rbl2yma7/tLWuuJdhHwTYAExLcZo78IpCyQhQDBp+cMfOirrWA65aVvrHmbt0VxAmJs2qgIAQQMCpCAGMSkKgTyIJCFBETNk0+/sXe5rzaD6az8+7KZFPh0iqbmNyv7S1bWKuNAICkBEpCkZKkXgYwKZClA8Ok5A1f7ajOYzso/Kdu3RflwilaY2yztL1lZr4wDgSQESECSUKVOBDIsQICQ4cmNMTTbwXSMLjp3SRpJm8unaA0niP3FueVKhxBIRIAEJBFWKkUguwIECNmd2zgjSyOYjtNPl65J67YoV0/RSEBcWp30BQE7AiQgdpxpBYHMCJCAZGYqjQwkrWDaSOdTrMSn26JsMrG/2NSmLQTSEyABSc+elhHwUoAAwctpS7TTBNPxeH25LSre6OJdxf4Sz42rEPBNgATEtxmjvwikLECAkPIEONo8wXS8ifHhtqh4I4t3FftLPDeuQsA3ARIQ32aM/iKQsgABQsoT4HDzBNMOT44nXWN/8WSi6CYCmgIkIJqAXI5A3gQIEPI244wXAXsC7C/2rGkJgTQFSEDS1KdtBDwUIEDwcNLoMgKeCLC/eDJRdBMBTQESEE1ALkcgbwIECOVnnFuRyhtRAoFiAuwvrAsE8iFAApKPeWaUCBgTIEBomZKHsY0tNSrKoQD7Sw4nnSHnUoAEJJfTzqARiC9AgFDarvA62p1NirT6/L+nD+8nJ/TpEB/foys5BfJoshzqKvuLQ5NBVxBIUIAEJEFcqkYgiwIECMVntfCFfOvrthQtoJKQfarayBPjB0vrikJKksUVIsIpUDbn1cao2F9sKNMGAukLkICkPwf0AAGvBAgQik/X4lXvyek3P1V2Lu8YeaT0796ubDlfC3AK5OvMudFv9hc35oFeIJC0AAlI0sLUj0DGBAgQik/ogmVrZcy8ZWVn+/phfWVo305ly+kWSOMWKE6BdGeN69lfWAMI5EOABCQf88woETAmQIDg/glIWrdAcQpk7J9Zbitif8nt1DPwnAmQgORswhkuAg0FJk+eLBMmTJAxY8bIddddFwqHAKE4U+G3/xvqtkjTh9DVFbaeAUnzFijXToFCLWgKOSXA/uLUdNAZBBITIAFJjJaKEXBbYOnSpXLaaadJZWWlDBo0iATEwHQVgn9VVcMkxNZbsNK+BYoTEAOLKOdVkIDkfAEw/NwIkIDkZqoZKAL/J7B582bp16+f3HjjjTJx4kTp27cvCYihBZLW7U+q+2knAK6cAhmaSqpJQYAEJAV0mkQgBQESkBTQaRKBtAVGjBghbdu2lWuvvVYGDhzYYgKydetWUX8KHxUgVFdXS11dXXB6wqe5QBoPgKteuHALVNqnQKxHvwVIQPyeP3qPQFgBEpCwUpRDICMC8+bNk0mTJom6BatNmzZlE5Camhqpra1tNnoSEPcWRNonIAWRNE+B3JsVehRFgAQkihZlEfBXgATE37mj5whEFli9erUceuih8sADD8g3vvGN4HpOQCIzOnuBS7dApXUK5Ozk0LFQAiQgoZgohID3AiQg3k8hA0AgvMDdd98tJ598srRu3br+ou3bt0urVq2koqIiuNWq4c+K1UyAEN47jZLcApWGOm2aEmB/MSVJPQi4LUAC4vb80DsEjAps2rRJ3nrrrUZ1nnvuuXLggQfK+PHjpU+fPmXbI0AoS5R6AW6BSn0K6EBMAfaXmHBchoBnAiQgnk0Y3UXAtEC5W7CatkeAYHoGkqmPW6CScaXWZAXYX5L1pXYEXBEgAXFlJugHAikJkICkBE+zCCDQTIAEhEWBQD4ESEDyMc+MEgFjAgQIxiipCAEEmgiwv7AkEMiHAAlIPuaZUSJgTIAAwRglFSGAAAkIawCBXAqQgORy2hk0AvEFSEDi23ElAgi0LMD+wgpBIB8CJCD5mGdGiYAxAQIEY5RUhAACnICwBhDIpQAJSC6nnUEjEF+ABCS+HVcigAAnIKwBBBAQIQFhFSCAQCQBEpBIXBRGAIEIAuwvEbAoioDHAiQgHk8eXUcgDQEChDTUadN3Ab6XJdwMsr+Ec6IUAr4LkID4PoP0HwHLAgQIlsFpznsBvpk+/BSyv4S3oiQCPguQgPg8e/QdgRQECBBSQKdJbwVU8nH+3OdkZ5MRtPr8v6cP7ycn9Ong7fhMd5z9xbQo9SHgpgAJiJvzQq8QcFaAAMHZqaFjjgmo266+OeVhWV+3pWjPVBKyT1UbeWL8YGldUUhJHBuE5e6wv1gGpzkEUhIgAUkJnmYR8FWAAMHXmaPftgUWr3pPTr/5qbLN3jHySOnfvV3ZcnkowP6Sh1lmjAjwFizWAAIIRBQgQIgIRvHcCixYtlbGzFtWdvzXD+srQ/t2KlsuDwXYX/Iwy4wRARIQ1gACCEQUIECICJZgcd6slCCugao5AYmOyP4S3YwrEPBRgFuwfJw1+oxAigIECCniN2iaNyu5MQ8t9aLwDMiGui3NHkJX1/EMSHM99hf31zU9RMCEAAmICUXqQCBHAgQI6U82b1ZKfw7C9qAwV6p8wzdh8Ras4oLsL2FXFuUQ8FuABMTv+aP3CFgXyEOA4PKtTbxZyfqS126Q06rwhHnYX8JrUBKB7AqQgGR3bhkZAokIZD1AcD1Y5LmCRJZ14pW6nNQmPvgIDWR9f4lAQVEEMi1AApLp6WVwCJgXyHKAoHtrk40gkzcrmV/T1OiOQJb3F3eU6QkC6QuQgKQ/B/QAAa8Eshog6N7aZOvkhBMQr/650NmIAlndXyIyUByBzAuQgGR+ihkgAmYFshog6AT2uicnUWaINytF0aKsbwJZ3V98mwf6i0DSAiQgSQtTPwIZE8hqgBD31ibdk5M4y4M3K8VR4xofBLK6v/hgTx8RsClAAmJTm7YQyIBAVgOEuCcgca/TXQq2bvnS7SfXIxBFIKv7SxQDyiKQBwESkDzMMmNEwKBAVgOEuLc2xT05MTElNh56N9FP6kAgrEBW95ew46ccAnkRIAHJy0wzTgQMCWQ5QIhza1NaJyCGppNqEHBKIMv7i1PQdAaBlAVIQFKeAJpHwDeBrAcIUW9tinty4tu8018EbAhkfX+xYUgbCPggQALiwyzRRwQcEshDgBD11qY4JycOTSldQcAZgTzsL85g0xEEUhQgAUkRn6YR8FGAAKH4rEU9OfFx7ukzAkkLsL8kLUz9CLghQALixjzQCwS8ESBAKD1VUU9OvJl0OoqAJQH2F0vQNINAygIkIClPAM0j4JsAAYJvM0Z/EfBHgP3Fn7mipwjoCJCA6OhxLQI5FCBAyOGkM2QELAmwv1iCphkEUhYgAUl5AmgeAd8ECBB8mzH6i4A/Auwv/swVPUVAR4AEREePaxHIoQABQg4nnSEjYEmA/cUSNM0gkLIACUjKE0DzCPgmQIDg24yJ8HC8f3OW1x6zv+R15hl33gRIQPI244wXAU0BAgRNQMuXp/16YJIfyxPueXPsL55PIN1HIKQACUhIKIohgMD/ChAg+LMSCl+QuLNJl1t9/t/Th/eTE/p0SGxAaSc/iQ2MihMTYH9JjJaKEXBKgATEqemgMwi4L0CA4P4cqR6qk4dvTnlY1tdtKdphlYTsU9VGnhg/WFpXFFISc2NLO/kxNxJqsinA/mJTm7YQSE+ABCQ9e1pGwEuBrAYIWbtVaPGq9+T0m58qu8buGHmk9O/ermy5KAXSTn6i9JWybglkdX9xS5neIJC+AAlI+nNADxDwSiCLAYLrtwrFSY4WLFsrY+YtK7u2rh/WV4b27VS2XJQCaSY/UfpJWfcEsri/uKdMjxBIX4AEJP05oAcIeCWQtQAhyq1CcRIB3cmNmxylmQSkmfzoenN9ugJZ21/S1aR1BNwVIAFxd27oGQJOCmQpQIhyq9CDyzdI7V+WN3qmokNVG7nye70Se5A7SnLUdLEUxrahbos0fQhdlU3yGZA0kx8n/9HQqdACWdpfQg+aggjkUIAEJIeTzpAR0BHIUoAQNlAee2xPue6hvzcL5JN8m1SU5KjUQ+SFBEbNd8MkJMl+q7bSTH501jbXpi+Qpf0lfU16gIC7AiQg7s4NPUPASYEsBQhhbxXaa9cvyoeffFp0PpI6SQibHJV7iDzuLVy6iy+t5Ee331yfrkCW9pd0JWkdAbcFSEDcnh96h4BzAlkKEMIG+WEmoVwiEKaOhmXCJkdhHiJP49kVNZa0kp+o1jrl07LV6bPL12Zpf3HZmb4hkLYACUjaM0D7CHgmkKUAIcytQlUtnH40nLowiUCUqQ6bHJlOfKL0MUzZLAfoeUiwwsyxyTJZ2l9MulAXAlkTIAHJ2owyHgQSFshagFDuVqGLj+0h1z60oqyq6UQgTHKU5BcJlh1wzgvovCAg53QtDj9r+wtzjQACxQVIQFgZCCAQSSCLAUJLv8ke0muf4BvFS71NSuGpt2El8Y3i5ZKj6cP7JfYGrkiLImeFTbwgIGdkoYebxf0l9OApiECOBEhAcjTZDBUBJTB58mS566675NVXX5Vdd91VBgwYIFOmTJEDDjggFFBWA4SWbhUq9dvuAtjoY7rJZf/SK5Rf1ELc5hNVLPnyWbk9Lnmp6C1kdX+JLsEVCGRbgAQk2/PL6BBoJnDCCSfIsGHD5LDDDpPPPvtMfvazn8mLL74oy5cvl913372sWF4DhMn/vVxmPPZGUR/1JqwkTyOy/BxF2QXnYAGTLwhwcHipdimv+0uq6DSOQAoCJCApoNMkAi4JvPvuu9K+fXtZuHChHHPMMWW75mqAkGSQzi03ZZdFrgpwApLcdLu6vyQ3YmpGIJ8CJCD5nHdGjUC9wMqVK6VHjx7BKUifPn2ayWzdulXUn8JHBQjV1dVSV1cnlZWVTkgmfZsSAacT0+xMJ3hBQHJTQQKSnC01I+CSAAmIS7NBXxCwLLBz504ZOnSofPDBB/L4448Xbb2mpkZqa2ub/cyVBMTG24i45cbywvSgOV4QkMwkkYAk40qtCLgmQALi2ozQHwQsClx44YXy17/+VZ544gnp3Llz0ZZdPgGxdWsUJyAWF6VHTSV98uYRhbGukoAYo6QiBJwWIAFxenroHALJCVx00UVy9913y2OPPSbdunUL3ZBLAYKtxIBbbkIvj9wVTPLZo9xhiohL+0se/RkzArYESEBsSdMOAo4IqNuuVPIxf/58efTRR4PnP6J8XAoQbN4axS03UVYJZRGIJ+DS/hJvBFyFAAJhBEhAwihRBoEMCVxwwQVy++23y4IFCxp990dVVVXwvSDlPi4FCLZOQAom3HJTbnXwcwT0BFzaX/RGwtUIINCSAAkI6wOBnAm0aqW+taL559Zbb5VzzjmnrIZLAUIat0Zl+ZabLI+t7MKmgBMCLu0vToDQCQQyKkACktGJZVgIJCXgWoDArVFmZprTHTOO1KIn4Nr+ojcarkYAgVICJCCsDQQQiCTgYoBA8BxpCpsVtvEqY70ecnVeBFzcX/JizzgRsClAAmJTm7YQyICAqwECtw/FW1y2XmUcr3dclTcBV/eXvM0D40UgaQESkKSFqR+BjAkQIGRrQm0/yJ8tPUZjWoD9xbQo9SHgpgAJiJvzQq8QcFaAAMHZqYnVMZuvMo7VQS7KlQD7S66mm8HmWIAEJMeTz9ARiCNAgBBHzd1rOAFxd27y2DP2lzzOOmPOowAJSB5nnTEjoCFAgKCB5+ClabzK2EEGuuSIAPuLIxNBNxBIWIAEJGFgqkcgawIECFmbUZGsv8qYFxT4s2bZX/yZK3qKgI4ACYiOHtcikEMBAoRsTnpWX2Wc1XFlcxWKsL9kdWYZFwKNBUhAWBEIIBBJgAAhEpdXhbN2UsD3m3i1/ILOsr/4N2f0GIE4AiQgcdS4BoEcC2QtQMha0J3jpdlo6Hy/iZ8rIWv7i5+zQK8RSF6ABCR5Y1pAIFMCWQoQ8nh7Tl4SLt7u5ee2k6X9xc8ZoNcI2BEgAbHjTCsIZEYgKwFCHm/PyVPCxfeb+LnlZGV/8VOfXiNgT4AExJ41LSGQCYEsBAgu3p6T9MlE3hIuTkD83G6ysL/4KU+vEbArQAJi15vWEPBeIAsBgmvBadInE7YTrqSTqTD/iPh+kzBK7pXJwv7inio9QsA9ARIQ9+aEHiHgtEAWAgSXbs+xcTJhM+FKOpmK8o8j699vEsXCl7JZ2F98saafCKQpQAKSpj5tI+ChQBYCBJsBeUtTbOtkwlbCZSOZivpPxqWEKGrf81g+C/tLHueNMSMQVYAEJKoY5RHIuUAWAgRXbs+xlQjZaMdWMhXnn58Lt4TF6Xcer8nC/pLHeWPMCEQVIAGJKkZ5BHIukJUAwYXbc2ydTNhIuGwkOTn/p5eL4Wdlf8nFZDFIBDQESEA08LgUgTwKZClASPv2HJtBe9IJl61kKo//5vI05iztL3maN8aKQFQBEpCoYpRHIOcCWQsQ0rw9x8bJRMPlmmTCZTOZyvk/wUwPP2v7S6Yni8EhoCFAAqKBx6UI5FGAAMHsrCd9MtG0t0klXLaTKbOzQG2uCLC/uDIT9AOBZAVIQJL1pXYEMidAgGB+SpM8mTDf29I12k6mbI6NtuwIsL/YcaYVBNIWIAFJewZoHwHPBAgQkpmwpE4mkulty0lI7V+Wy/q6LfWFOlS1kSu/10tO6NPBdndozzMB9hfPJozuIhBTgAQkJhyXIZBXAQKEvM58+HFnJZkKP2JKmhJgfzElST0IuC1AAuL2/NA7BJwTIEBwbkroEAKZEWB/ycxUMhAEWhQgAWGBIIBAJAEChEhcFEYAgQgC7C8RsCiKgMcCJCAeTx5dRyANAQKENNRpE4F8CLC/5GOeGSUCJCCsAQQQiCRAgBCJi8IIIBBBgP0lAhZFEfBYgATE48mj6wikIUCAkIY6bSKQDwH2l3zMM6NEgASENYAAApEECBAicVEYAQQiCLC/RMCiKAIeC5CAeDx5dB2BNAQIENJQp00E8iHA/pKPeWaUCJCAsAYQQCCSAAFCJC4KI4BABAH2lwhYFEXAYwESEI8nj64jkIYAAUIa6rSJQD4E2F/yMc+MEgESENYAAghEEiBAiMRFYQQQiCDA/hIBi6IIeCxAAuLx5NF1BNIQIEBIQ502EciHAPtLPuaZUSJAAsIaQACBSAIECJG4KIwAAhEE2F8iYFEUAY8FSEA8njy6jkAaAgQIaajTJgL5EGB/ycc8M0oESEBYAwggEEmAACESF4URQCCCAPtLBCyKIuCxAAmIx5NH1xFIQ4AAIQ112kQgHwLsL/mYZ0aJAAkIawABBCIJECBE4qIwAghEEGB/iYBFUQQ8FiAB8Xjy6DoCaQgQIKShTpsI5EOA/SUf88woESABYQ0ggEAkAQKESFwURgCBCALsLxGwKIqAxwIkIB5PHl1HIA0BAoQ01GkTgXwIsL/kY54ZJQIkIKwBBBCIJECAEImLwgggEEGA/SUCFkUR8FiABMTjyaPrCKQhQICQhjptIpAPAfaXfMwzo0SABIQ1gEAOBW688UaZOnWqrF+/Xnr37i3XXXedHH300aEkCBBCMVEIAQRiCLC/xEDjEgQ8FCAB8XDS6DICOgJ/+MMf5KyzzhKVhBx11FEyY8YMueWWW2T58uWy7777lq2aAKEsEQUQQCCmAPtLTDguQ8AzARIQzyaM7iKgK3DEEUdIv379ZPr06fVVHXTQQXLSSSfJ5MmTy1ZPgFCWiAIIIBBTgP0lJhyXIeCZAAmIZxNGdxHQEdi2bZvstttucuedd8rJJ59cX9WYMWNk2bJlsnDhwmbVb926VdSfwqeuri44KVm9erVUVlbqdIdrEUAAgUYCKgGprq6WDz/8UKqqqtBBAIGMCpCAZHRiGRYCxQTWrVsnnTp1kkWLFsmAAQPqi1x11VUye/Zsee2115pdVlNTI7W1tYAigAAC1gRWrVol++23n7X2aAgBBOwKkIDY9aY1BFIVKCQgTz75pPTv37++L5MmTZI5c+bIq6++2qx/TU9A1G8mu3TpIm+//XYmf0NZ+A1sVk94GF+q/wS1G8/6/BVOWD/44APZa6+9tL2oAAEE3BQgAXFzXugVAokIxLkFq2lHsn6PNuNLZOlZq5T5s0adSENZn79E0KgUAQ8FSEA8nDS6jICOgHoI/ZBDDgneglX49OrVS4YOHcpD6CKS9QCI8en860n/WuYv/TmgBwggoC9AAqJvSA0IeCVQeA3vTTfdFNyGNXPmTLn55pvl5ZdfDm6tKvchACon5PbPmT+356dc75i/ckL8HAEEfBAgAfFhlugjAoYF1OnHNddcE3wRYZ8+feTaa6+VY445JlQr6pkQ9breyy67TL70pS+FusanQozPp9lq3lfmj/nzW4DeI5APARKQfMwzo0QAAQQQQAABBBBAwAkBEhAnpoFOIIAAAggggAACCCCQDwESkHzMM6NEAAEEEEAAAQQQQMAJARIQJ6aBTiCAAAIIIIAAAgggkA8BEpB8zDOjRAABBBBAAAEEEEDACQESECemgU4g4IeAenvW1KlTg7dn9e7dW6677jo5+uij/eh8mV6qN3vdddddwbfB77rrrjJgwACZMmWKHHDAAZkYX8NBqLFOmDBBxowZE8xhVj5r166V8ePHy7333iuffPKJ9OzZU2bNmhV8743vn88++0xqamrk97//vWzYsEE6dOgg55xzjvz85z+XiooK74b32GOPBXvJs88+G+wn8+fPl5NOOql+HDt37pTa2trgNeHqW9HV9xfdcMMNwb7DBwEE/BcgAfF/DhkBAlYECt8fopKQo446SmbMmCG33HKLLF++XPbdd18rfUiykRNOOEGGDRsmhx12mKhg72c/+5m8+OKLwfh23333JJu2WvfSpUvltNNOk8rKShk0aFBmEhAVpB588MHBmM4//3xp3769rFq1Srp27Srdu3e3apxEY5MmTQpelz179uwgCH/mmWfk3HPPlYkTJwaJpG8flSQuWrRI+vXrJ6ecckqzBEQl/2rMt912W5BIqnGqpOW1116TPffc07fh0l8EEGgiQALCkkAAgVAC6jeQKliYPn16ffmDDjoo+K2l+o161j7vvvtuEMQuXLgw9HekuG6wefPmYA5VEqkCur59+2YmAbn00kuDgPbxxx93fRpi9e/EE0+UvffeOzjRKXxU4L7bbrvJnDlzYtXpykWtWrVqlICo04+OHTvKxRdfHJxoqY/6fhc1fpWYjB492pWu0w8EEIgpQAISE47LEMiTwLZt24JA584775STTz65fujqN6/Lli0LgvSsfVauXCk9evQITkHUlzVm4TNixAhp27Zt8Jv0gQMHZioB6dWrlxx//PGyZs2aYD126tRJLrjgAhk5cmQWpk6uvvpquemmm+SBBx4ITgReeOEFOe6444IE8vTTT/d6jE0TkNdffz04tXruueeCU63CZ+jQobLXXnsFp0B8EEDAbwESEL/nj94jYEVg3bp1QUCnfsOsno0ofK666qogGFC3RWTpo34Dq4IddVtPVn6jPm/evOCWFnULVps2bTKXgKgxqc+4cePk1FNPlSVLlgS/QVe3Cp599tneL0+1JtVzO+oEoHXr1rJ9+/ZgPi+77DLvx9Y0AXnyySeD2zzVMz3qJKTwGTVqlLz11lty//33ez9mBoBA3gVIQPK+Ahg/AiEECgmICgz69+9ff4UKgNTtH+rB7Sx9LrzwQvnrX/8qTzzxhHTu3Nn7oa1evVoOPfTQ4Lfn3/jGN4LxZO0EZJdddgnGqNZo4fPjH/84SLgWL17s/RyqBPKnP/1p1T1n/gAAIABJREFU8OC2egZEnTyqBGvatGmiTrZ8/pRKQNS+ox62L3zUaZZay/fdd5/Pw6XvCCAgIiQgLAMEECgrkKdbsC666CK5++67gwdeu3XrVtbGhwJqPOrWOfWb88JH/QZdBX7qDUrq/vqGP/NhTE372KVLFxkyZEjwYoTCRz2vpJ51Ub9J9/1TXV0t6jkXlRwXPmpsc+fO9f4XANyC5fvqpP8IRBcgAYluxhUI5FJAPYSuXmeqHmAufNR99+pWpSw8hK5ucVHJh3od6KOPPho8/5GVz6ZNm4JbVxp+1BuUDjzwwOAh3yw843LGGWcEvx1veMvc2LFj5emnn250KuLrnLZr1y5IptQbvgof9e/u1ltvlb///e++Divod6mH0NX8XXLJJUEZ9UsQ9VIIHkL3eqrpPAL1AiQgLAYEEAglUHgNr3oQVt2Gpd7Pf/PNN8vLL78s6rfPvn/UA8u33367LFiwoNF3f1RVVQXfC5K1T9ZuwVK3Wqnnk9R3R6jXDKtnQNQtO2qdnnnmmd5Pn/rOj4ceeih4pkXdgvX888+Leibihz/8YRCU+/ZRb2RTL3pQH/WgubqVTL1CWb0kQb3WW42pkGCpXwao583ULwZ4Da9vM01/ESguQALCykAAgdAC6vTjmmuuCb44TP3WXL1N6Zhjjgl9vcsF1W9hi33Ub5hV8Je1T9YSEDU/99xzT/BQ9ooVK4Lb59QD6Vl5C5Y6xbr88suDE7qNGzcGD2ert19dccUVop5/8e2jkgmVcDT9qOdZ1Hd/FL6IUCVcDb+IMAundb7NFf1FIAkBEpAkVKkTAQQQQAABBBBAAAEEigqQgLAwEEAAAQQQQAABBBBAwJoACYg1ahpCAAEEEEAAAQQQQAABEhDWAAIIIIAAAggggAACCFgTIAGxRk1DCCCAAAIIIIAAAgggQALCGkAAAQQQQAABBBBAAAFrAiQg1qhpCAEEEEAAAQQQQAABBEhAWAMIIIAAAggggAACCCBgTYAExBo1DSGAAAIIIIAAAggggAAJCGsAAQQQQAABBBBAAAEErAmQgFijpiEEEEAAAQQQQAABBBAgAWENIIAAAggggAACCCCAgDUBEhBr1DSEAAIIIIAAAggggAACJCCsAQQQQAABBBBAAAEEELAmQAJijZqGEEAAAQQQQAABBBBAgASENYAAAgjEFGjVqlWoKx955BHp2rWrdOvWTW699VY555xzQl1HocYCyvvKK6+UmpqayDQDBw4Mrnn00UcjX2vigk8//VSuuuqqYP7Xr18frIULL7xQLrroIhPVUwcCCCDglQAJiFfTRWcRQMAlgaeeeqpRd375y1+KSjYefvjhRn/fq1cv+dKXviTPP/+8dO/eXb761a+6NAxv+qK8O3fuHPyJ+lm+fHlwiZqLND4jR46UOXPmiFojhx12mNx///0yZcoUmThxokyYMCGNLtEmAgggkJoACUhq9DSMAAJZE1AnG3/6059k8+bN3g7tn//8p+y2227e9t/Fjr/88svyta99TSZNmiSXXXZZfRdHjRolc+fOlTVr1kjbtm1d7Dp9QgABBBIRIAFJhJVKEUAgjwItJSBvvvlms1uw1K1EtbW18sILLwS/GX/ggQekdevWwS1a11xzjaxatUrGjBkjixYtknbt2skFF1wgl1xySSPajz76SH7xi1/In//8Z1m7dm1wunLqqacGwe7uu+/e4jSo25L+8Y9/yI033iiXXnqpLFu2TL7//e/LvHnzguv+8Ic/yHXXXSf/8z//I+r2p6OOOkquvvpqOfjgg+vrLYz5mWeeCfr6xBNPSGVlZfC/VZ3q1OInP/lJcPrTqVMn+dnPfiYjRoyov/7dd98NbqtSt0a9/fbbQfLTp0+fwOXoo49u1P+mt2Dddtttcu655wYnTn/84x/lzjvvlJ07d8q3vvUt+c///E/p2LFj/fVNb8EqzMfUqVOloqJC/uM//kNUX1SicO2118qRRx7ZqO2bb75ZVNm33norOMX6+c9/HsyX6reqq6WPmgtVXt16tc8++9QXXbx4sQwYMEB+//vfyxlnnJHHfzKMGQEEcipAApLTiWfYCCBgXiBuAnLAAQfI8OHDg6D3wQcfDJKPH/3oR/LQQw8FScdBBx0kt99+e/D8gEo0fvCDHwSdV6cVKilQv0FXt/F8/etfF/Xb9iuuuEIOOeSQ4PqWnlNRQfmLL74YJCoqsVGBvwrGjznmmOB5BRU0qwBftbdt27YgAFfJyJIlS+pvZVJjvuOOO4Kg/N///d+Dvy/0Vf22X/V3/PjxwW1TKsi/5557RCUrqn/q89prr8n1118fJA0qOFenR/Pnzw/G+re//U0KiYMqWyoB2W+//eS73/2unHjiibJ69Wr56U9/Kn379m10K1ypBEQ9m3PggQcGfVefyy+/PPB84403pKqqKvi7mTNnyujRo+WUU04JPOrq6oIEaevWrcHPGyYgymP27NnB9apu9Tn99NODsWzcuLHRovv4449ljz32CE5FlDcfBBBAIC8CJCB5mWnGiQACiQvETUB+/etfy7hx4+r7p04Y1GnEXXfdJSeffHLw95999lnwG311KqCCevVRpxHqROHpp5+WQw89tP569fN//dd/lf/+7/+W73znOyXHrYLyhQsXBsHx4MGD68upIF4F9eeff7785je/qf97lRz06NEjSFDU6Yj6FALuholRoa/qROG5556rPzF5//33pX379sHpiBpzsc/27duDU4wTTjghOElRBoVPqQREJWk33HBDfTmVKKmEquGJQ6kERJ14qNMZdfKkPkuXLpXDDz88SKqGDRsmO3bsCE5uunTpEpzmFD7qtGb//fcP5qRhAnLeeecFCYg6vVLXqM9xxx0XnO68+uqrzYasng1ShjNmzEh8fdIAAggg4IoACYgrM0E/EEDAe4G4CYg6BejZs2f9+NXtOOo2KHXC0aZNm/q/V7frqJMIdYKgPt/85jdl06ZN8uyzzzay27JlSxC8q5MA9aBzqY8KytWJhkoMGn5uueUWUQ9Nq2BcnSQ0/KiTGvWg/TvvvBP8tRrz7373u6J9VYH5unXrGl2vAnY1DvWsTOFz0003BacM6kHxwqmC+pk6mXjllVfqy5VKQO677z45/vjj68upB7xVAqMShiOOOCL4+1IJiLpNbPLkyfXXqvaVuUru1MmNal+d6jRNEtUFgwYNCk46yt2CpRIQldQ1HEuhQZWAqFMVZcAHAQQQyIsACUheZppxIoBA4gJxExB1UvCVr3ylvn+l6ik8s/HSSy8FZdVpxMqVK0uO64c//KHMmjWr5M9VfaptddtWw0/hmYVSF6rbtNRJRSEBKfbgfdO+FupStyWpW73UrVjqM23aNPl//+//BbdAqVuolIM6jVC3QqmAvWFwXyoBUYlSwxMg9VyGSg5UolRIPFp6BkQ9o9Lw07Ad9UyLOnVSD4ufeeaZjcqpExKV5JRLQLgFK/F/ejSAAAKeCZCAeDZhdBcBBNwVsJ2A9O/fX9RzBL/97W+LoqhgvvAcQrECpZIEdTuQSghUYlG4jajp9YWAP2yyVCoB6devX/CshUoWGn7U6Y56FiPtBKSlExDlp/pXLgFRz3eoW+WaPoSukhc1hzyE7u6/aXqGAALJCJCAJONKrQggkEMB2wmIOqlQwa06EVFfbBf1UyoBUQG1Ol1R9Td961bTNnQTEPUwunpzl7qNqvBRt4Wp52Cqq6tTT0CiPgNSbA4Kr+FVt3qp27oKH5XkqdvXeA1v1JVLeQQQ8F2ABMT3GaT/CCDgjIDtBESdfqjbg9RtVGPHjg3egqUCZvXAs3pFrLq1qfAMRDGkUgmIKquCZfU2LfVQtXqe4stf/nLw3Id6A5Z6a5Z6C5T66CYg6hW86hXE6pYr9SYs9TyMeq2wakM9zJ72CYgaY8O3YKnb2j788MNg/OpZG3W72Ouvv17PW+whdPXDwhcRqi8eVF9EqOZHGfNFhM7886UjCCBgUYAExCI2TSGAQLYFbCcgSlMlIeqBafUdGOqB6F133VX23XdfOfbYY4Pftu+9994l0VtKQNRFCxYsCF6Rqx5yVw9nq9fkquBZ/eb+29/+tpEERD1Ur25PUm+deu+994IHvlXio17F2/Q7NtJ4BqSAp74HRL0eWSV36rY29fC68lH/rd70VfgUew2v+tmnn34anCip1wtv2LAhqEO9avmiiy7K9j8KRocAAggUESABYVkggAACCCAQUUCdgqg3l5100knBCQkfBBBAAIHwAiQg4a0oiQACCCCQQwF1YqFOL9SbtdQ30qtvQ1fflq6+10O9Erl37945VGHICCCAQHwBEpD4dlyJAAIIIJADgQ8++EDOPvvs4HtR1Hem7LbbbsG31qvnQFp6xiYHNAwRAQQQiCVAAhKLjYsQQAABBBBAAAEEEEAgjgAJSBw1rkEAAQQQQAABBBBAAIFYAiQgsdi4CAEEEEAAAQQQQAABBOIIkIDEUeMaBBBAAAEEEEAAAQQQiCVAAhKLLZmL1BeIrVu3Tvbcc09R77vngwACCCCAAAIIIOCWwM6dO2XTpk3SsWNHqaiocKtznvSGBMShiVqzZo1UV1c71CO6ggACCCCAAAIIIFBMYPXq1dK5c2dwYgiQgMRAS+qSuro62WuvvUQt6MrKyqSaoV4EEEAAAQQQQACBmAIfffRR8Atj9YWkVVVVMWvJ92UkIA7Nv1rQaiGrRIQExKGJoSsIIIAAAggggMDnAsRr+kuBBETf0FgNLGhjlFSEAAIIIIAAAggkIkC8ps9KAqJvaKwGFrQxSipCAAEEEEAAAQQSESBe02clAdE3NFYDC9oYJRUhgAACCCCAAAKJCBCv6bOSgOgbGquBBW2MkooQQAABBBBAAIFEBIjX9FlJQPQNjdXAgjZGSUUIIIAAAggggEAiAsRr+qwkIPqG9TV07dpV3nrrrWY1XnDBBXLDDTeUbYkFXZaIAggggAACCCCAQKoCxGv6/CQg+ob1Nbz77ruyffv2+v9+6aWXZMiQIfLII4/IwIEDy7bEgi5LRAEEEEAAAQQQQCBVAeI1fX4SEH3DkjVcfPHFcs8998iKFSukVatWZVvycUGrb29X4+vRo0fwbaBN/7vsoCmAAAIIIIAAAgh4JOBjvOYaLwlIQjOybds26dixo4wbN04mTJgQqhXfFvSsWbNk1KhRsmPHDqmoqJCzzjpL5syZU//fM2fOlPPOOy/U2CmEAAIIIIAAAgj4IOBbvOaiKQlIQrPyxz/+Uc444wx5++23g0Sk2Gfr1q2i/hQ+akFXV1d78U3o6qSjS5cuQbJR6tO6dWt58803g5MRPggggAACCCCAQBYESED0Z5EERN+waA3HH3+87LLLLvKXv/ylZAs1NTVSW1vb7Od1dXVSWVmZUM/MVKueaxk8eHDZysI+/1K2IgoggAACCCCAAAIOCJCA6E8CCYi+YbMa1Juw9ttvP7nrrrtk6NChJVvgBCQBfKpEAAEEEEAAAQQSFCAB0cclAdE3bFaDOtmYMWOGrF69Wr7whS+EbsG3Ba2eARk9enTw5i91u9Xw4cNl7ty59f+tDHgGJPT0UxABBBBAAAEEPBDwLV5zkZQExPCsqGciunXrJqeffrpcffXVkWr3cUGrZ0FWrlwp+++/f/1bsBr+dyQACiOAAAIIIIAAAo4L+BivuUZKAmJ4Rh544AFRz3+89tpr0rNnz0i1s6AjcVEYAQQQQAABBBCwLkC8pk9OAqJvaKwGFrQxSipCAAEEEEAAAQQSESBe02clAdE3NFYDC9oYJRUhgAACCCCAAAKJCBCv6bOSgOgbGquBBW2MkooQQAABBBBAAIFEBIjX9FlJQPQNjdXAgjZGSUUIIIAAAggggEAiAsRr+qwkIPqGxmpgQRujpCIEEEAAAQQQQCARAeI1fVYSEH1DYzWwoI1RUhECCCCAAAIIIJCIAPGaPisJiL6hsRpY0MYoqQgBBBBAAAEEEEhEgHhNn5UERN/QWA0saGOUVIQAAggggAACCCQiQLymz0oCom9orAYWtDFKKkIAAQQQQAABBBIRIF7TZyUB0Tc0VgML2hglFSGAAAIIIIAAAokIEK/ps5KA6Bsaq4EFbYySihBAAAEEEEAAgUQEiNf0WUlA9A2N1cCCNkZJRQgggAACCCCAQCICxGv6rCQg+obGamBBG6OkIgQQQAABBBBAIBEB4jV9VhIQfUNjNbCgjVFSEQIIIIAAAgggkIgA8Zo+KwmIvqGxGljQxiipCAEEEEAAAQQQSESAeE2flQRE39BYDSxoY5RUhAACCCCAAAIIJCJAvKbPSgKib2isBha0MUoqQgABBBBAAAEEEhEgXtNnJQHRNzRWAwvaGCUVIYAAAggggAACiQgQr+mzkoDoGxqrgQVtjJKKEEAAAQQQQACBRASI1/RZSUD0DY3VwII2RklFCCCAAAIIIIBAIgLEa/qsJCD6hsZqYEEbo6QiBBBAAAEEEEAgEQHiNX1WEhB9Q2M1sKCNUVIRAggggAACCCCQiADxmj4rCYi+obEaWNDGKKkIAQQQQAABBBBIRIB4TZ+VBETf0FgNLGhjlFSEAAIIIIAAAggkIkC8ps9KAqJvaKwGFrQxSipCAAEEEEAAAQQSESBe02clAdE3NFYDC9oYJRUhgAACCCCAAAKJCBCv6bOSgOgbGquBBW2MkooQQAABBBBAAIFEBIjX9FlJQPQN62tYu3atjB8/Xu6991755JNPpGfPnjJr1iw55JBDQrXCgg7FRCEEEEAAAQQQQCA1AeI1fXoSEH3DoIYPPvhADj74YBk0aJCcf/750r59e1m1apV07dpVunfvHqoVXxf0mjVrZMWKFdKjRw/p3LlzqLFSCAEEEEAAAQQQ8FHA13jNJWsSEEOzcemll8qiRYvk8ccfj12jjwtanfCMGjVKduzYIRUVFTJz5kw577zzYhtwIQIIIIAAAggg4LKAj/Gaa54kIIZmpFevXnL88ceLOg1YuHChdOrUSS644AIZOXJkyRa2bt0q6k/hoxZ0dXW11NXVSWVlpaGeJVeNGmuXLl2C5KPwad26tbz55puchCTHTs0IIIAAAgggkKIACYg+PgmIvmFQQ5s2bYL/O27cODn11FNlyZIlcvHFF8uMGTPk7LPPLtpKTU2N1NbWNvuZLwnII488IoMHD27Wf/X3AwcONCRLNQgggAACCCCAgDsCJCD6c0ECom8Y1LDLLrvIoYceKk8++WR9jT/+8Y9l6dKlsnjx4qKtcAJiCJ9qEEAAAQQQQAABSwIkIPrQJCD6hkEN6lakIUOGyC233FJf4/Tp02XixImi3o4V5uPjglbPgIwePVq2b98u6vYrdeLDMyBhZpsyCCCAAAIIIOCjgI/xmmvOJCCGZuSMM86Q1atXN3oIfezYsfL00083OhVpqTlfF7R6FmTlypWy//778+yHofVENQgggAACCCDgpoCv8ZpLmiQghmZD3Wo1YMCA4JmO0047LXgGRD2Art4KdeaZZ4ZqhQUdiolCCCCAAAIIIIBAagLEa/r0JCD6hvU13HPPPXLZZZcF34nRrVu34IH0lt6C1bRpFrTByaAqBBBAAAEEEEAgAQHiNX1UEhB9Q2M1sKCNUVIRAggggAACCCCQiADxmj4rCYi+obEaWNDGKKkIAQQQQAABBBBIRIB4TZ+VBETf0FgNLGhjlFSEAAIIIIAAAggkIkC8ps9KAqJvaKwGFrQxSipCAAEEEEAAAQQSESBe02clAdE3NFYDC9oYJRUhgAACCCCAAAKJCBCv6bOSgOgbGquBBW2MkooQQAABBBBAAIFEBIjX9FlJQPQNjdXAgjZGSUUIIIAAAggggEAiAsRr+qwkIPqGxmpgQRujpCIEEEAAAQQQQCARAeI1fVYSEH1DYzWwoI1RUhECCCCAAAIIIJCIAPGaPisJiL6hsRpY0MYoqQgBBBBAAAEEEEhEgHhNn5UERN/QWA0saGOUVIQAAggggAACCCQiQLymz0oCom9orAYWtDFKKkIAAQQQQAABBBIRIF7TZyUB0Tc0VgML2hglFSGAAAIIIIAAAokIEK/ps5KA6Bsaq4EFbYySihBAAAEEEEAAgUQEiNf0WUlA9A2N1cCCNkZJRQgggAACCCCAQCICxGv6rCQg+obGamBBG6OkIgQQQAABBBBAIBEB4jV9VhIQfUNjNbCgjVFSEQIIIIAAAgggkIgA8Zo+KwmIvqGxGljQxiipCAEEEEAAAQQQSESAeE2flQRE39BYDSxoY5RUhAACCCCAAAIIJCJAvKbPSgKib2isBha0MUoqQgABBBBAAAEEEhEgXtNnJQHRNzRWAwvaGCUVIYAAAggggAACiQgQr+mzkoDoGxqrgQVtjJKKEEAAAQQQQACBRASI1/RZSUD0DY3VwII2RklFCCCAAAIIIIBAIgLEa/qsJCD6hsZqYEEbo6QiBBBAAAEEEEAgEQHiNX1WEhB9Q2M1sKCNUVIRAggggAACCCCQiADxmj4rCYi+obEaWNDGKKkIAQQQQAABBBBIRIB4TZ+VBETfMKihpqZGamtrG9W29957y4YNG0K3wIIOTUVBBBBAAAEEEEAgFQHiNX12EhB9w/oE5E9/+pM89NBD9TW2bt1avvrVr4ZuwfaCXrNmjaxYsUJ69OghnTt3Dt1PUwVLtV/4+z322EM2b94c9E99VF8Lf6f+7xtvvBH8/YABA4L+tzQeU2M1VY8pQ+pBAAEEEEAAAbsCtuM1u6Oz0xoJiCFndQJy9913y7Jly2LXaHNBz5o1S0aNGiU7duyQiooKmTlzppx33nmx+x71wlLtN/z7Qp2tWrUK/ufOnTuLNqN+fvbZZ8ucOXOKjsfUWE3VE9WK8ggggAACCCDgjoDNeM2dUZvtCQmIIU+VgEydOlWqqqrkS1/6khxxxBFy1VVXyX777Veyha1bt4r6U/ioBV1dXS11dXVSWVlpqGfNq1G/xe/SpUsQrBc+6rTmzTfftHISUqr9xYsXy5FHHtmoX3ERCuNR15sYa9pmcR24DgEEEEAAAQTMCpCA6HuSgOgbBjXce++98s9//lN69uwp77zzjkycOFFeffVVefnll6Vdu3ZFWyn23IgqmHQC8sgjj8jgwYOb9Un9/cCBAw2JlK6mVPvTpk2TcePGGWtftaNOTUyMNW0zYyhUhAACCCCAAAJaAiQgWnzBxSQg+oZFa/j444+le/fucskll5QMqjkBaXwCwwlIQouRahFAAAEEEEDAmAAJiD4lCYi+YckahgwZIvvvv79Mnz49VCs2F7R6nmH06NGyfft2UbcrzZgxw/ozIMXab9ivApp6xkP9aXjLWENQ9QzLWWedJXPnzi06HlNjNVVPqMVAIQQQQAABBBBwUsBmvOYkgIFOkYAYQCxWhTrdUCcg6kHvK664IlQrthe0eq5h5cqVQZKU1luwirVf6Nfuu+8u6iRJ9U99VNnC36n/q55ZUZ/+/fvXvwWr1HhMjdVUPaEWBIUQQAABBBBAwDkB2/GacwAGOkQCYgBRVfGTn/xEvve978m+++4rGzduDJ4BWbhwobz44ovBQ9BhPizoMEqUQQABBBBAAAEE0hMgXtO3JwHRNwxqGDZsmDz22GPyj3/8I/juD/U2p1/+8pfSq1ev0C2woENTURABBBBAAAEEEEhFgHhNn50ERN/QWA0saGOUVIQAAggggAACCCQiQLymz0oCom9orAYWtDFKKkIAAQQQQAABBBIRIF7TZyUB0Tc0VgML2hglFSGAAAIIIIAAAokIEK/ps5KA6Bsaq4EFbYySihBAAAEEEEAAgUQEiNf0WUlA9A2N1cCCNkZJRQgggAACCCCAQCICxGv6rCQg+obGamBBG6OkIgQQQAABBBBAIBEB4jV9VhIQfUNjNbCgjVFSEQIIIIAAAgggkIgA8Zo+KwmIvqGxGljQxiipCAEEEEAAAQQQSESAeE2flQRE39BYDSxoY5RUhAACCCCAAAIIJCJAvKbPSgKib2isBha0MUoqQgABBBBAAAEEEhEgXtNnJQHRNzRWAwvaGCUVIYAAAggggAACiQgQr+mzkoDoGxqrgQVtjJKKEEAAAQQQQACBRASI1/RZSUD0DY3VwII2RklFCCCAAAIIIIBAIgLEa/qsJCD6hsZqYEEbo6QiBBBAAAEEEEAgEQHiNX1WEhB9Q2M1sKCNUVIRAggggAACCCCQiADxmj4rCYi+obEaWNDGKKkIAQQQQAABBBBIRIB4TZ+VBETf0FgNLGhjlFSEAAIIIIAAAggkIkC8ps9KAqJvaKwGFrQxSipCAAEEEEAAAQQSESBe02clAdE3NFYDC9oYJRUhgAACCCCAAAKJCBCv6bOSgOgbGquBBW2MkooQQAABBBBAAIFEBIjX9FlJQPQNjdXAgjZGSUUIIIAAAggggEAiAsRr+qwkIPqGxmpgQRujpCIEEEAAAQQQQCARAeI1fVYSEH1DYzWwoI1RUhECCCCAAAIIIJCIAPGaPisJiL6hsRpY0MYoqQgBBBBAAAEEEEhEgHhNn5UERN/QWA0saGOUVIQAAggggAACCCQiQLymz0oCom9orAYWtDFKKkIAAQQQQAABBBIRIF7TZyUB0TcsWsPkyZNlwoQJMmbMGLnuuutCtcKCDsVEIQQQQAABBBBAIDUB4jV9ehIQEXnuuefki1/8onzta18LRBcsWCC33nqr9OrVS2pqamSXXXaJJL106VI57bTTpLKyUgYNGkQCEkmPwggggAACCCCAgLsCJCD6c0MCIiKHHXaYXHrppXLKKafI66+/Lr1795aTTz5ZVCLx3e9+N3QCoaZj8+bN0q9fP7nxxhtl4sSJ0rdv39DXu7ag16xZIytWrJAePXoEK63wvzt37hz8d8OfF/6u2JIMW05/OTevoVjbhb/bY489gvlS42va/zT6nEabBbE0205i3qkTAQQQQAD2SxtqAAAgAElEQVSBpARci9eSGmeS9ZKAiEhVVVVwCtK9e3eZMmWKPPzww3L//ffLokWLZNiwYbJ69erQczBixAhp27atXHvttTJw4EBvE5BZs2bJqFGjZMeOHdKqVatg/Dt37pSKigqZOXNm8N+Fnxf+7rzzzmvm1LCelsqFBo5QsFjbDftdqKppv9LocxptFsafZtsRppOiCCCAAAIIOCFAAqI/DSQgIsGtUs8++2zwm/AhQ4bIiSeeGDy78fbbb8sBBxwgn3zySSjpefPmyaRJk4KTkzZt2pRNQLZu3SrqT+GjFnR1dbXU1dUFfUrro34b3qVLlyD5KPZRAbv6NPx569at5c0332x0klCsnmLlkhhnsbaL9bvQdqFf6r+bjj3pPrvmlPR4k5hv6kQAAQQQQMCWAAmIvjQJiIgMHjw4CPyPPfZYUb/FX758uey///6ycOFCUScaKrAu91GnJIceeqg88MAD8o1vfCMoXu4ERD1fUltb26zqtBOQRx55JDCJ+lHXqTEXPqXqaVouajthyscZg7pGnfIUG3uSfXbRKcnxhpk/yiCAAAIIIOCqAAmI/syQgIjICy+8IMOHDw9OPMaNGydXXnllIHvRRRfJe++9J7fffntZ6bvvvjt4bkT99rjw2b59e3D7kvrNuzrpaPgzVYYTkLKssQtwAhKOLs3Tl3A9pBQCCCCAAAJuCZCA6M8HCUgLhlu2bJEvfOELwZ9yn02bNslbb73VqNi5554rBx54oIwfP1769OlTrgpxaUGr5wJGjx4thSRKJVLqliuVRM2YMSMYS+Hnhb8r9QxImHJlcWIUaDiGYv0uVNm0/8WuKza2GF0qeUkabRY6k2bbJg2pCwEEEEAAARsCLsVrNsabRBskICKy3377Bc9ttGvXrpHxhx9+GLzRSr0ZK86n3C1YTet0bUGr346vXLkyuB1NfQr/u+FbsJr+XTGnhvW09LasOMblrinWduHvdt99d/n444+D8RV7C1aYsZVrP8rPXXOK0nfKIoAAAgggkBcB1+I1H91JQESCW6Q2bNgg7du3bzSH77zzTvBsyLZt22LNre8JSKxBcxECCCCAAAIIIJBhARIQ/cnNdQLyX//1X4HgSSedJLNnzw5ex1v4qFuP/va3v8mDDz4or732mr50iBpY0CGQKIIAAggggAACCKQoQLymj5/rBKTwWlb1fIN6+1HDj/pm9K5du8qvf/3r4LW8Nj4saBvKtIEAAggggAACCMQXIF6Lb1e4MtcJSAGhW7duwTMgX/nKV/RFNWpgQWvgcSkCCCCAAAIIIGBBgHhNH5kERN/QWA0saGOUVIQAAggggAACCCQiQLymz0oC8rmhet5D/dm4cWOzbwD/7W9/qy8dogYWdAgkiiCAAAIIIIAAAikKEK/p45OAiATfRv6LX/wi+CbzDh06BF8e2PAzf/58fekQNbCgQyBRBAEEEEAAAQQQSFGAeE0fnwREJEg6rrnmGjnrrLP0RTVqYEFr4HEpAggggAACCCBgQYB4TR+ZBEQk+ALCJUuWSPfu3fVFNWpgQWvgcSkCCCCAAAIIIGBBgHhNH5kERETGjx8ve+yxh1x++eX6oho1sKA18LgUAQQQQAABBBCwIEC8po9MAiIiY8aMkd/97nfy9a9/PfijvgOk4WfatGn60iFqYEGHQKIIAggggAACCCCQogDxmj4+CYiIDBo0qKSkeiD94Ycf1pcOUQMLOgQSRRBAAAEEEEAAgRQFiNf08UlA9A2N1cCCNkZJRQgggAACCCCAQCICxGv6rCQg+obGamBBG6OkIgQQQAABBBBAIBEB4jV9VhKQz2/BavrdHw1puQVLf6FRAwIIIIAAAgggkAUBEhD9WSQBEZGxY8c2kvz0009l2bJl8tJLL8mIESPk+uuv15cOUQMLOgQSRRBAAAEEEEAAgRQFiNf08UlAWjCsqamRzZs3y69+9St96RA1sKBDIFEEAQQQQAABBBBIUYB4TR+fBKQFw5UrV8rhhx8u77//vr50iBpY0CGQKIIAAggggAACCKQoQLymj08C0oLhnDlzgi8pXLdunb50iBpY0CGQKIIAAggggAACCKQoQLymj08CIiI/+MEPGknu3LlT1q9fL88880zw7ehXXnmlvnSIGljQIZAoggACCCCAAAIIpChAvKaPTwIiIueee24jyYqKCvnqV78qgwcPluOOO05fOWQNLOiQUBRDAAEEEEAAAQRSEiBe04cnAdE3NFYDC9oYJRUhgAACCCCAAAKJCBCv6bOSgDQwfPbZZ+WVV14R9Z0gvXr1koMPPlhfOEINLOgIWBRFAAEEEEAAAQRSECBe00cnARGRjRs3yrBhw+TRRx+VvfbaS9QzIHV1dTJo0CCZN29ecDuWjQ8L2oYybSCAAAIIIIAAAvEFiNfi2xWuJAERkX/7t3+TVatWiXrr1UEHHRTYLF++PPgSwv3331/uuOMOfekQNbCgQyBRBAEEEEAAAQQQSFGAeE0fnwRERKqqquShhx6Sww47rJHokiVLgofQP/zwQ33pEDWwoEMgUQQBBBBAAAEEEEhRgHhNH58ERET23HNPefzxx6Vv376NRJ9//nn51re+JWqh2fiwoG0o0wYCCCCAAAIIIBBfgHgtvl3hShIQERk6dGhwyqFuterYsWNgs3btWjnzzDPly1/+ssyfP19fOkQNLOgQSBRBAAEEEEAAAQRSFCBe08cnARGR1atXB0nISy+9JNXV1cFbsN5++2352te+JgsWLJDOnTuHkp4+fbqoP2+++WZQvnfv3nLFFVfId77znVDXs6BDMVEIAQQQQAABBBBITYB4TZ+eBKSB4YMPPiivvvpq8BYs9RreY489NpLwX/7yF2ndunXw4Lr6zJ49W6ZOnSrqVi6VjJT7pLGg16xZI08++WTQtQEDBoRKttQ1K1askB49ehQtH+bnUdssZVeqrbB/b6KvDetQ/VQ2e+yxh2zevDm2Ubm1EufnhX6W61ucupO4JuwcttR2ufmN0m+TdUVpl7IIIIAAAm4JpBGvuSWg35tcJyAPP/yw/OhHP5KnnnpKKisrG2mq1/CqgPymm26So48+OrZ027ZtgyTkvPPOK1uH7QU9a9YsGTlyZJBwqY86+bn55ptb7Ku6ZtSoUbJjxw5R3xg/c+bMRuXD/Dxqm6XgSrUV9u/POuus4M1nLY2lXF8btqX81Kfgqf53HKOyCyVGgYb9LFxerG8xqk7kkrBz2HT9NexMubUYpeMm64rSLmURQAABBNwTsB2vuSeg36NcJyDf//73g+/6GDt2bFHJ3/zmN/LII4/EegZk+/btcueddwav8lUnIOpEpeln69atov4UPmpBq1vAVPLTNCHSn+rGNajf5u67776NgmVVQp3gqFvIit12pq7p0qVLELAXPg3Lh/l51DZLjbtUW4sXL5YjjzyyWR+L/X3TupuOpVxfi/WhWH+jGJmeZ1VfS/1sab6T6EuYOqPObbH1Wm4thulHoYzJuqK0S1kEEEAAATcFSED05yXXCYgKpu+777767/5oyqlux1Kv4VXPg4T9vPjii9K/f3/ZsmVLcBvO7bffLv/yL/9S9PKamhqpra1t9jMbCYhKrAYPHly0X+pnAwcObPazUtcUysf9uWqoVJul3Eu1NW3aNBk3blyzy0r9fdOC5cbSsK8tGUatN+r4w67HQn9LzXUc+yhtxykbdW6L2ZVbi1H6ZbKuKO1SFgEEEEDATQESEP15yXUC0qZNm+DB88IzG005V65cGTyI/sknn4SW3rZtW5CwqLdq/fnPf5ZbbrlFFi5cyAlI587Bb+LLnSqEhY76W3JOQBqfXBWcOQEpv+I4ASlvRAkEEEAgTwIkIPqznesEpHv37vKrX/1KTj755KKSd911l/zkJz+R119/Pba0epBdtTNjxoyyddhe0E2fAQnzTIC6ZvTo0aJuMVPBqxpXw+dbwvy84XMVYdosBVeqrbB/P3z4cJk7d26LYynX14ZtqWdA1J+mt6hFNSq7UGIUaNjPhslH077FqDqRS8LOYUv9L7cWo3TcZF1R2qUsAggggIB7ArbjNfcE9HuU6wTkoosukkcffVSWLl0q6jSk4Uedehx++OHBMyLqWZC4n29/+9vBcx233XZb2SrSWNDqt7vqdEB91K1jYV45rK5Rp0Pq5KjUsyLlfh61zVJ4pfoS9u/DjKVcXxvWofqpxr777rvLxx9/HNuo7GKJUaDQz3J9i1F1IpeEncOWGi83v1E6brKuKO1SFgEEEEDALYE04jW3BPR7k+sE5J133pF+/foFv8lXb8M64IADgt9gv/LKK3LDDTcEvxl/7rnnZO+99w4lPWHChOA7P1TCsWnTJpk3b55cffXVwXMmQ4YMKVsHC7osEQUQQAABBBBAAIFUBf5/e3cDbFVVPn784TJTKQgqk03Ka0GmMpaY8eLIIL1oTQVmU9YA2jDAqGMWvZg5NTClpBTaVCgg+QJjOZZoZWaT8aJATWPZOBIGE5gElREyQoUj8Jtn91/nv+66e5+9zllr7Xsu+7tnHLn37P2stT7rOees5+y9z2W9Fs5f6wJE+Z5//nm58sor5bHHHuv2dbQXXXSRLF26VEaOHOmtrJciPf7447Jnzx4ZPHiwnH322XLdddd5FR/aCAntTc2OCCCAAAIIIIBArwiwXgtnr30BYgj37duXXTqjf8NB/8DeSSedFK7bYgQSukUwdkcAAQQQQAABBCoWYL0WDk4BEm4YLQIJHY2SQAgggAACCCCAQBIB1mvhrBQg4YbRIpDQ0SgJhAACCCCAAAIIJBFgvRbOSgESbhgtAgkdjZJACCCAAAIIIIBAEgHWa+GsFCDhhtEikNDRKAmEAAIIIIAAAggkEWC9Fs5KARJuGC0CCR2NkkAIIIAAAggggEASAdZr4awUIOGG0SKQ0NEoCYQAAggggAACCCQRYL0WzkoBEm4YLQIJHY2SQAgggAACCCCAQBIB1mvhrBQg4YbRIpDQ0SgJhAACCCCAAAIIJBFgvRbOSgESbhgtAgkdjZJACCCAAAIIIIBAEgHWa+GsFCDhhtEikNDRKAmEAAIIIIAAAggkEWC9Fs5KARJuGC0CCR2NkkAIIIAAAggggEASAdZr4awUIOGG0SKQ0NEoCYQAAggggAACCCQRYL0WzkoBEm4YLQIJHY2SQAgggAACCCCAQBIB1mvhrBQg4YbRIpDQ0SgJhAACCCCAAAIIJBFgvRbOSgESbhgtAgkdjZJACCCAAAIIIIBAEgHWa+GsFCDhhtEikNDRKAmEAAIIIIAAAggkEWC9Fs5KARJuGC0CCR2NkkAIIIAAAggggEASAdZr4awUIOGG0SKQ0NEoCYQAAggggAACCCQRYL0WzkoBEm4YLQIJHY2SQAgggAACCCCAQBIB1mvhrBQg4YbRIpDQ0SgJhAACCCCAAAIIJBFgvRbOSgESbhgtAgkdjZJACCCAAAIIIIBAEgHWa+GsFCDhhtEikNDRKAmEAAIIIIAAAggkEWC9Fs5KARJuGC0CCR2NkkAIIIAAAggggEASAdZr4awUIOGG0SKQ0NEoCYQAAggggAACCCQRYL0WzkoBEm4YLQIJHY2SQAgggAACCCCAQBIB1mvhrBQg4YaNCIsWLZIHH3xQtm7dKscdd5xMmjRJbr75Zjn99NO9WiGhvZjYCQEEEEAAAQQQ6DUB1mvh9BQg4YaNCBdffLFcdtllct5558mrr74qN9xwgzzzzDOyZcsWGTBgQGlLJHQpETsggAACCCCAAAK9KsB6LZyfAiTcsDDCiy++KKeccoqsX79eJk+eXNpSbyf0rl27ZNu2bTJmzBgZOnRobn999jEH2vvq78pi2w3mHTtw4EA5cOBA0/7lxWjlOG1306ZNWRg9g2U7mD5pvB07dmT7jBo1qkefioxixXb757Zn97MVryL/olxw9y9za5ZXGquV3Cp9Mjk7lMUOydW8vjTLgVaeB62O02f/MouyGKHHl8XncQQQQKDTBXp7vdbpPj79owDxUWpzn+3bt2eLZT0LMnbs2NIovZnQK1eulLlz58qRI0ekq6tLli9fLrNnz+7WZ599zAH2vv369ct+ffTo0cLYdkNFx5p9ivpXFMP3OG13zpw5WT91036vWLEic7D7lDeRpk/6WJ5jrNhu/2bNmiWrVq1qzNvMmTMbP/uO2x1PK/Osx/qOrdm8tdpm6ZPJ2qEsdkiu5vWjqL2yfrQypnb3De1D6PHt9pvjEEAAgU4S6M31Wic5hPSFAiREr8mxuoidNm2a7Nu3T5544oncPQ8dOiT6n9k0oYcNGyb79++XQYMGJepZz7D6ieaIESOyRazZ+vfvLzt37mycAfDZxxybt6/dqhvbfqzs2KL++cYoalvbHT58eKP4sNvZvHmzTJgwoZtP3uToAls311GPHz9+fHBszSlTHLWaHM3My+zK5qsVt7xYreRWq+Mui12Wb75uzXJfY+TlUKuxWx27u3+ZRVn80OPL4vM4Aggg0FcEKEDCZ4oCJNwwN8LVV18tjzzyiDz55JOFlzMtWLBAFi5c2OP4qguQtWvXytSpU3v0Q38/ZcqU7Pc++5gARfvaDdix3d/n9SUPud0Yecc16/OSJUtk/vz5bWdKs+NDY7fSqSIvH/92rIvG5sZqJbdaGa9P3obkalFO5uWvr0Wr42tl/1Dn0ONb6Sv7IoAAAp0sQAESPjsUIOGGPSJcc8018tBDD8mGDRuyewSKNs6A9LzPpOwTaWNZ9qm8e0an7DjOgPxPqNVPuVt14wxI8VnGBC9F3UK2Orduf0KPTz0+4iOAAAJVCVCAhEtTgIQbNiLo5TFafKxZs0bWrVuX3f/RytabCa3Xds+bN08OHz4sukhctmxZ7j0gZfuY8drx9F4K/U8vTSqKbTsVHWsXEXn9K4rhe5x7L4N9z4Ldp7w5NePSx/KMYsW27wHR/uk9H6tXr27M24wZMxo/+47bHY9PLrjWbr/MPUS+sXz3a+X5lJeLefkXkqt5/SkaS8ox+rqE9iH0eN9+sh8CCCDQyQK9uV7rZJdW+kYB0opWyb5XXXWV3HffffLwww93+9sfgwcPzv4uSNnW2wmtn3DqjfOjR49u+i1YZfuYcdrx9He+x+m+ecfqVxkfPHiwaf9sYxOjleP0GL1eX7eJEyf2+BYsHYPG0/tjdBs5cmSPPhU5xort9s9tr51xu7npkwuudZlbs7xy59znm7fKnk95uVDUh5BczetHsxxo5XnQyhh99211bkNzw7df7IcAAgj0FYHeXq/1Fadm/aQAiTiL5tue3JB33XWXXHHFFaUtkdClROyAAAIIIIAAAgj0qgDrtXB+CpBww2gRSOholARCAAEEEEAAAQSSCLBeC2elAAk3jBaBhI5GSSAEEEAAAQQQQCCJAOu1cFYKkHDDaBFI6GiUBEIAAQQQQAABBJIIsF4LZ6UACTeMFoGEjkZJIAQQQAABBBBAIIkA67VwVgqQcMNoEUjoaJQEQgABBBBAAAEEkgiwXgtnpQAJN4wWgYSORkkgBBBAAAEEEEAgiQDrtXBWCpBww2gRSOholARCAAEEEEAAAQSSCLBeC2elAAk3jBaBhI5GSSAEEEAAAQQQQCCJAOu1cFYKkHDDaBFI6GiUBEIAAQQQQAABBJIIsF4LZ6UACTeMFoGEjkZJIAQQQAABBBBAIIkA67VwVgqQcMNoEUjoaJQEQgABBBBAAAEEkgiwXgtnpQAJN4wWgYSORkkgBBBAAAEEEEAgiQDrtXBWCpBww2gRSOholARCAAEEEEAAAQSSCLBeC2elAAk3jBaBhI5GSSAEEEAAAQQQQCCJAOu1cFYKkHDDaBFI6GiUBEIAAQQQQAABBJIIsF4LZ6UACTeMFoGEjkZJIAQQQAABBBBAIIkA67VwVgqQcMNoEUjoaJQEQgABBBBAAAEEkgiwXgtnpQAJN4wWgYSORkkgBBBAAAEEEEAgiQDrtXBWCpBww2gRSOholARCAAEEEEAAAQSSCLBeC2elAAk3jBaBhI5GSSAEEEAAAQQQQCCJAOu1cFYKkHDDaBFI6GiUBEIAAQQQQAABBJIIsF4LZ6UACTeMFoGEjkZJIAQQQAABBBBAIIkA67VwVgqQcMNoEUjoaJQEQgABBBBAAAEEkgiwXgtnpQAJN4wWgYSORkkgBBBAAAEEEEAgiQDrtXBWCpBww2gRSOholARCAAEEEEAAAQSSCLBeC2elAAk3jBaBhI5GSSAEEEAAAQQQQCCJAOu1cFYKkHDDRoQNGzbI4sWL5amnnpI9e/bImjVrZPr06d4tkNDeVOyIAAIIIIAAAgj0igDrtXB2CpBww0aERx99VDZu3Cjjxo2TSy+9lAIkoi2hEEAAAQQQQACBThCgAAmfBQqQcMPcCP369euTBciuXbtk06ZNsnfvXhkyZIiMGjVKduzYkY1x0qRJMnTo0Ozfut+2bdtkzJgx2e+Kfh44cKAcOHAg2083+xgTx7SnP2ubzdrJwzZ91se0v6Y909eyKXb7XtSG23d7P7sPpv8mrhr4GLrxtD3bzx2P22aerztXZh8T141fZGGPRX3NmEyeuHOmc+qTM+5+ZXlVZGT7ug52TH3Mzm+737ZVkU9ZLuX1r1nuF+VUUT4Zr7znZSt27jh8ngN5xzR77sZow36NcPOplbnwec0qmrui1zyf9ttxbef1xxwTqz2fsbW6Tyf3LS8/Wh1fX9+/yvmpsq1U80IBEi5LARJumBuhLxYgK1eulDlz5sjRo0cLx7RixYrssblz58qRI0ekq6tLZs6cKatWrcr92QRSD900th6zfPny7Oe89nTfvHb0mNmzZ3frW1GfTRvu/u7A9Hh7LEVtNNvH7YP2f9asWQ0Tu02fsdl9Mse648kbt8a2fXXsdix7DlyHvHk0Fnn9cY+3x2XPadF4NWfuvffeRq65Zs36o20365PtYOem+X3efLhWeT55uVH08lHkbud+UU4V5ZPt5Y7Bzrcyu3aeA3nHNHvu5j1Py55neZZ5FvraUPa8Lhuj+5plz23ea4L7mueTCz6vLT5vP75xfPfzaTP2Pp3cN/f1xPe9I7ZRb8arcn6qbCulKQVIuC4FSLhhbgSfAuTQoUOi/5lNE3rYsGGyf/9+GTRoUKKe5YfVTySGDx9eWHzYC2H9txYfIZu+yOtiuajY0cfddvr37y87d+7sdhamWZ/d/d3+6phHjBjRbSx5bTTbx9fNbrvZ2HQ/tz1zrOmb/lw2V7rv5s2bZcKECW3PVasxiuY0b7zt5I49/iKjduP6WJXlk2k7L69amf+yuW13jPZzp1lfy8ZZlvOtPoeKxlPUTln/fJ7n7j7NcsvntcinzVb7rTF9XqNa2a+d3Ak9xncMoe20e3yn96/dcfkeV+X4q2zLd/zt7kcB0q7c/z+OAiTcMDeCTwGyYMECWbhwYY/je6MAWbt2rUydOjWRRryw2s8pU6ZkAX36bO/v9qLoeJ82zD4+ffAdvcbSgqzZPPjsY9pbsmSJzJ8/37f53P1ixAjqgHNwK+NvpV3fcTbLJ9NeuzmRamx2v8xzp6yv7TxvbO9WnkNF89TM0WceysaY93pQ9vwrGmM7ry0++enzGtXstbAVJ5/+tLOP7xjaiR3jmE7vX4wxNotR5firbCu1GwVIuDAFSLhhbgSfAoQzIJwBMcnj8+k+Z0D+dwZMN86AtPbCVfTpezufSHIGRKTsbEY7rnkz6hvHd7/WsibO3p3cNx1hp/cvziwUR6ly/FW2ldqNAiRcmAIk3LDtAsQ9sLcTuuweEPv69Xnz5snhw4ezN+IZM2bI6tWrc382Y9SCTP/TS7f0mGXLlmUP5V1HXtSOHuN7D4hpo+xacR2zPZaiNprt47qZa/CNiT3PPmOz+2QXKHbf8q6Nd33NfQ2m7/YcuLmXN4+mvbz+uMcX3dfTLGfsexpcs2b90baL+uTmmZ2beffA2Nd7Nxunbz4ZFztWUe4X5VRRPhXdA9KqnTt3Ps+BvGOaPXfznqdlz7O8F9I8C5/7L8rG6L5muc8tt68ar9X+t+NaZODTdqz2UrwldnLf3NeTVp/rKbyqjlnl/FTZVkrH3l6vpRxbVbEpQCJK67cDbd++PYt4zjnniF7WceGFF8rJJ5+cXbNftnVCQusnFHo9vPl2o5EjRzY+dZ44cWK3+y90rKNHj258C1bezwMGDJCDBw9m++lm76M/2+3pz/otWM3ayTM0MfQx7a9pr5VvwXL75bajbTTbx+6D6b85Rg3MJ/e+Y7OPLRqP22aerzE2fTf7mHmx58d8m1neON3+mDGZPHHHpTmkW1nOuPu5zs3ci3xdBzuGPmbnt90/26rIp+w5bD/utpuX+0U5VZRPxivvedmKXav53ex5pzmQ99yN0Yb9GuHmUytz4T4PmuV63r5FvyvrQ9nrRtnx5nHfOL77+bYbc79O7lu78xvTp7djVTk/VbaVyrUT1mupxlZVXAqQiNLr1q3LCg53u/zyy+Xuu+8ubYmELiViBwQQQAABBBBAoFcFWK+F81OAhBtGi0BCR6MkEAIIIIAAAgggkESA9Vo4KwVIuGG0CCR0NEoCIYAAAggggAACSQRYr4WzUoCEG0aLQEJHoyQQAggggAACCCCQRID1WjgrBUi4YbQIJHQ0SgIhgAACCCCAAAJJBFivhbNSgIQbRotAQkejJBACCCCAAAIIIJBEgPVaOCsFSLhhtAgkdDRKAiGAAAIIIIAAAkkEWK+Fs1KAhBtGi0BCR6MkEAIIIIAAAgggkESA9Vo4KwVIuGG0CCR0NEoCIYAAAggggAACSQRYr4WzUoCEG0aLQEJHoyQQAggggAACCCCQRID1WjgrBUi4YbQIJHQ0SgIhgAACCCCAAAJJBFivhbNSgIQbRotAQkejJBACCCCAAAIIIJBEgPVaOCsFSLhhtAgkdDRKAiGAAAIIIIAAAkkEWEGCpksAABfXSURBVK+Fs1KAhBtGi0BCR6MkEAIIIIAAAgggkESA9Vo4KwVIuGG0CCR0NEoCIYAAAggggAACSQRYr4WzUoCEG0aLQEJHoyQQAggggAACCCCQRID1WjgrBUi4YbQIJHQ0SgIhgAACCCCAAAJJBFivhbNSgIQbRotAQkejJBACCCCAAAIIIJBEgPVaOCsFSLhhtAgkdDRKAiGAAAIIIIAAAkkEWK+Fs1KAhBtGi0BCR6MkEAIIIIAAAgggkESA9Vo4KwVIuGG0CCR0NEoCIYAAAggggAACSQRYr4WzUoCEG0aLQEJHoyQQAggggAACCCCQRID1WjgrBUi4YbQIJHQ0SgIhgAACCCCAAAJJBFivhbNSgIQbRotAQkejJBACCCCAAAIIIJBEgPVaOCsFSLhhtAgkdDRKAiGAAAIIIIAAAkkEWK+Fs1KAhBtGi0BCR6MkEAIIIIAAAgggkESA9Vo4KwVIuGG0CCR0NEoCIYAAAggggAACSQRYr4WzUoCEG0aLQEJHoyQQAggggAACCCCQRID1WjgrBUi4YbcIS5culcWLF8uePXvkrLPOkttuu00uuOACr1ZIaC8mdkIAAQQQQAABBHpNgPVaOD0FSLhhI8L9998vM2fOFC1Czj//fFm2bJnceeedsmXLFhk+fHhpSyR0KVHQDrt27ZJt27bJmDFjZOjQod1i6WObNm3Kfjdp0qQejwc17Bzs9qNZv8yhbv/093ljMbEGDhwoBw4cEPP/ojFrDHcfO8aOHTtk7969MmTIkIaLb//tPo8aNSrrj/ZDN9va/Vnnxm7DPK790K2oL3lxbaM856I+2vnh7mNMTF90bPbv7D7a82T+rd66v27GxfzOHaOvjclb20qd7L6Zn01e5I0j7zE7fY19Xv41c7KtytpwXX3Glvf8LBq/m9NufhX11cxX3lzn5YCbB5rzZn7d/rp9zXtcX5fy+mr2teemqC2fdorGYrfTzj5220WWbq41a6dsLM2en3ljaWd+fU1i97XdPCp7zSp6PWonX8vmziefW80z+70h7zUh5u9Yr4VrUoCEGzYijB8/XsaNGye3335743dnnHGGTJ8+XRYtWlTaEgldStT2DitXrpS5c+fKkSNHpKurS5YvXy6zZ8/O4uljc+bMkaNHj2Y/9+vXT1asWNF4vO1Gcw50+6EF66pVq3L7ZQ53+2f6qP21x2LHdpvOG7PxMPvqPnZ/3BjqMmvWrG79Lep/Xp/tfheZum3oz2Ze7GN89jPHuuMyFhrPnnfbweRH0Th8c8L0Qf+vW95YWoll+xfZ+MYL2c+2Vasiy5A2OBYBBBBoVSDl+7fdF9Zrrc5Mz/0pQMINswivvPKKHH/88fLAAw/IJZdc0oh67bXXytNPPy3r16/v0dKhQ4dE/zObJvSwYcNk//79MmjQoEg9I4x+MjtixIhskW+2/v37y86dO7Mf9eyUuzA0j7tnSkI08/rhxnPb1WPy+mcfp8ds3rxZJkyY0G2MRbH1965HyLjy+qLFeMhiO1Z/iuJoEaL9K+qjMe30caR28olfZukTg30QQACBWAIp3r/dvlGAhM8WBUi4YRZh9+7dctppp8nGjRuzS1XMdtNNN8k999wjzz33XI+WFixYIAsXLuzxewqQSJPy/8KsXbtWpk6d2iOo/l4XoHmP6c76+JQpU6J1pqgfbgN2u77HLFmyRObPn1/a17Ixlwbw2MG3Lx6henWXY2UcvYpI4wgggEAvCMR+/6YAiT+JFCCRTE0BotfeTpw4sRH1xhtvzC5Z2bp1a4+WOAMSCb8kDGdA/gdkn/XhDAhnQGI9+zgDEkuSOAggEEOAMyAxFNPHoACJZNzOJVhU1JHwPcLotfzz5s2Tw4cPZwtx/YKAontA3PslPMJ77+L2Y8aMGbJ69ercfpmgefeo6HWuekmZPRY7ttuhvDEbD7Ov7mP3x41h7qWw+1vU/2b3gGhc+34b+2e3jaJ7J8r20+Nso7x+art594C4pnn7+Ey43Qf73z7H6j7u2H3GbFv6ttPqfq6tPpeKLFuNXbR/jHto8mKnimu3FasNnzg++8SaE+IgECKQKldTvn/b4+USrJDZ/9+xFCDhho0Ier34ueeem30LltnOPPNMmTZtGjehR3RuN5SeCdm+fbuMHj0691uw9D4K3fQMVsx7P9z+uv1o1i9zrO5j909/nzcWE2vAgAFy8OBBMf8vGrPGcPexY+h9MuZbsIyLb//tPo8cOTLrj/ZDN3csrr3dhtnf/oaovL7kxbWN8pyL+uh+C5bpn47DmGh7+q0r7u/M782ZUNMHM2fqbe4/Mi7md+4Y3TGZbwizY+ZZmjmz+2b6avIibxx5j9n5qzHccRkr19KOb1uVteG6mueknQdF7m5f88bv5rSbX0V91d8XzXXe79080Hlq9u1FRTF849hzU9RWmVvZ481yvpl93pw2G69POzH6asdoZ37NmMv6UvZ4VeMte80qej1y38PKxuPzuHkdaTdX88ZingMp37+NBQWImxWt/0wB0rpZ4RHma3jvuOOO7E1avx1Gv03p2WefzW76LdtI6DIhHkcAAQQQQAABBHpXgPVauD8FSLhhtwh69uOWW27J/hDh2LFj5dZbb5XJkyd7tUJCezGxEwIIIIAAAggg0GsCrNfC6SlAwg2jRSCho1ESCAEEEEAAAQQQSCLAei2clQIk3DBaBBI6GiWBEEAAAQQQQACBJAKs18JZKUDCDaNFIKGjURIIAQQQQAABBBBIIsB6LZyVAiTcMFoEEjoaJYEQQAABBBBAAIEkAqzXwlkpQMINo0UgoaNREggBBBBAAAEEEEgiwHotnJUCJNwwWgQSOholgRBAAAEEEEAAgSQCrNfCWSlAwg2jRdi/f7+ceOKJ8sILL8igQYOixSUQAggggAACCCCAQBwBLUCGDRsmL730kgwePDhO0JpFoQDpoAnXvySsCc2GAAIIIIAAAggg0NkC+oFxFX95vbMV2usdBUh7bkmOOnLkiOzevVtOOOEE6devX5I2TFBTvXO2JSlz0uDMYVLeSoIzh5UwJ2+EeUxOnLwB5jA5cfIGqpzDo0ePyssvvyynnnqqdHV1JR/bsdgABcixOKseY+L6RQ+kDt+FOezwCfLoHnPogdQHdmEe+8AklXSROWQO+75A3xoBBUjfmq9oveXFNhplrwViDnuNPlrDzGE0yl4NxDz2Kn+UxpnDKIy9GoQ57FX+lhunAGmZ7Ng4gCdq359H5pA57PsCx8YIeC72/XlkDpnDvi/Qt0ZAAdK35itabw8dOiSLFi2S66+/Xl772tdGi0ug6gSYw+qsU7XEHKaSrTYu81itd4rWmMMUqtXGZA6r9Q5tjQIkVJDjEUAAAQQQQAABBBBAwFuAAsSbih0RQAABBBBAAAEEEEAgVIACJFSQ4xFAAAEEEEAAAQQQQMBbgALEm4odEUAAAQQQQAABBBBAIFSAAiRUkOMRQAABBBBAAAEEEEDAW4ACxJvq2Npx6dKlsnjxYtmzZ4+cddZZctttt8kFF1xwbA2yj45mw4YN2dw89dRT2fysWbNGpk+f3hiN/gXWhQsXyvLly2Xfvn0yfvx4+e53v5vNo9n095/61Kfkxz/+cfarD33oQ/Ltb39bTjzxxD6q0ne6rd8u9+CDD8rWrVvluOOOk0mTJsnNN98sp59+emMQ+m0tn/vc5+T73/++/Oc//5F3vetdos/JoUOHNvb5y1/+IldffbX86le/yuJ84hOfkG984xvymte8pu9g9OGe3n777aL/7dy5MxuFPr++8pWvyPve977sZ+awb02uPi+/9KUvybXXXpu93zGHfWP+FixYkL3f2dsb3vAG+dvf/pb9ivfDvjGPeb2kAOm7c9d2z++//36ZOXNmtuA5//zzZdmyZXLnnXfKli1bZPjw4W3H5cA4Ao8++qhs3LhRxo0bJ5deemmPAkQXszfeeKPcfffd8pa3vEW+9rWviRYtzz33nJxwwglZJ3SRtGvXrqxI0W3u3LkycuRI+clPfhKnk0QpFLj44ovlsssuk/POO09effVVueGGG+SZZ57Jnl8DBgzIjrvyyiuzudA5HDJkiHz2s5+Vf/3rX1nR2b9/fzl8+LC8/e1vl9e//vXyzW9+U/bu3SuXX365fPjDH84KSbb0Ajo/OhejR4/OGrvnnnuyDwZ+//vfZ8UIc5h+DmK18Nvf/lY++tGPyqBBg+TCCy9sFCDMYSzhdHG0APnhD38ov/zlLxuN6PNSXxt14/0wnX3qyBQgqYU7ML5+Yq6LW/10z2xnnHFG9im7fkrE1jkC/fr161aA6Kc9p556qnz605+W6667LuuofhKrnwjpC/G8efPkj3/8o5x55pny61//Ojs7opv+e+LEidmn8vYn8Z0z0mO3Jy+++KKccsopsn79epk8ebLs378/e/NctWqVfOxjH8sGvnv3bhk2bJj87Gc/k4suuki0CP3ABz4gL7zwQjbfuv3gBz+QK664Qv7xj39kCym26gVOPvnkrAj5yEc+whxWz99WiwcOHMje7/QDN/2wRgt7PQPC87AtzsoP0gLkoYcekqeffrpH27wfVj4dURukAInK2fnBXnnlFTn++OPlgQcekEsuuaTRYT0trU9wXSSxdY6AW4D8+c9/lje/+c3yu9/9Ts4555xGR6dNm5ZdXqWf0n7ve9+T+fPny0svvdRtIPr4rbfeKp/85Cc7Z4A16Mn27dtlzJgx2VmQsWPHZpdU6SVXesbjpJNOagi87W1vyz4E0MsN9FKfhx9+WP7whz80HtfL6nQBrMfrp7hs1QnoGSl9zdSzUHoGRC//YA6r8w9pSedMnzf62jdlypRGAcLzMES1umO1ANGif/DgwdkfTdYP1W666SZ505veJLwfVjcPKVqiAEmh2sEx9ZPW0047LbvER69NN5s+oXXxqpfxsHWOgFuAbNq0Kbts7q9//Wvjk3HtrV5i9fzzz8tjjz2WvTjrpT1/+tOfug1EL9fS4uP666/vnAEe4z3RT+i0ONTi4YknnshGe99992XzoGeu7O29732vjBo1KrskUudT7z34xS9+0W0ffQPWuf34xz9+jMt1xvC0aNQzh//9739l4MCB2dy9//3vZw47Y3pKe6FnDfVyVb0E63Wve123AoTnYSlfR+ygZ4P//e9/Z5cb//3vf8/OYumZ/GeffTZbr/B+2BHT1FYnKEDaYuu7B5kCRBey+sZqNn2R1ktC9InN1jkCRQWIzuMb3/jGRkfnzJmTXa7z85//PCtA8opJ/RR+9uzZ8sUvfrFzBniM90RvIn/kkUfkySefbNxgXrTwec973pOd3brjjju6FZQ2kd6Afu+992b3mLClF9AzxvplAHo28Uc/+lF2r5yeJdazxXlFJHOYfk58W9DXw3e84x1ZEa9nF3Wzz4DwPPSV7Kz9Dh48mL1OfuELX5AJEyZkBQjvh501R769oQDxlTpG9uMSrL41kVyC1bfmy+7tNddck127rF8QoGc2zMalH313Tt/97ndnix+9d4dLsDp7HvW5p5cZ6w3LZtNL6fQ1taurKztbrPPJpZCdPY95vdNCX78c4vOf/zyXJPe96Wv0mAKkD09eu13XayjPPffc7KY8s+lNy3qpCDeht6ua5riim9A/85nPZJ8A6aZFpd7k7N6E/pvf/Ebe+c53Zvvov/XTIm5CTzNPdlS97EqLD/365HXr1mX3f9ibufl19erV2Tfz6KZft6xfwevehK7fZGbOdOm31+n17NyEnn4Oi1rQokO/LOBb3/pWdhM6c9h7c1HW8ssvv5xdlmpvetbqrW99a/YFHjqPzGGZYuc9rpeu6ocAepnql7/85exSZN4PO2+efHpEAeKjdIztY76GVy/10Muw9KtaV6xYkV1TOWLEiGNstH1vOPqtLXrjsm56o/mSJUuym471Rkr9mmQtNLRQvOuuu7LFrV5ypQtd92t49bS03k+gm75Y69zyNbzp8+Gqq67K7hHQm8jtbxzTmyj173nopl//+dOf/jS7n0PnVf8miH7Vrvs1vPrtZnoDpn5Kq9+ApTep8zW86edQW9C/GaFfZ60LVV3M6v0EX//617PLHPUTWOawmnmI2Yp9CRbPw5iy6WLpa+MHP/jB7L1PP3zRe0D0Mki9P0vf03g/TGefOjIFSGrhDo2vZz9uueWW7JNX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width=\"800\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib notebook \n",
    "# %load ParticleSim.py\n",
    "\n",
    "class particle:\n",
    "    def __init__(self, xpos, ypos):\n",
    "        self.x = xpos\n",
    "        self.y = ypos\n",
    "        self.t = 1 \n",
    "    def __str__(self):\n",
    "        return \"[%s, %s, %s]\\n\" % (self.x,self.y,self.t)\n",
    "            # This defines a particle as something that has an x and y position as well as an elapsed lifetime t\n",
    "            # __str__ tells Python how to show us this data when using a print command\n",
    "\n",
    "class particle_list:\n",
    "    def __init__(self):\n",
    "        self.particles = []\n",
    "        self.decayed_particles = []\n",
    "            # particle lists are what they sound like: a list of particles\n",
    "            # decayed_particles stores all the particles that have already decayed, so that Python doesn't have to loop through them as much.\n",
    "    def num_particles(self):\n",
    "        return len(self.particles)\n",
    "    def get_x(self):\n",
    "        tx = []\n",
    "        for item in self.particles:\n",
    "            tx.append(item.x)\n",
    "        return tx\n",
    "            # returns a list of the x coordinates of all particles that haven't decayed\n",
    "    def get_y(self):\n",
    "        ty = []\n",
    "        for item in self.particles:\n",
    "            ty.append(item.y)\n",
    "        return ty\n",
    "    def get_t(self):\n",
    "        tt = []\n",
    "        #for item in self.particles:\n",
    "            #tt.append(item.t)\n",
    "        for item in self.decayed_particles:\n",
    "            tt.append(item.t)\n",
    "        return tt\n",
    "            # returns a list of the elapsed lifetimes of all particles\n",
    "    def get_paired_xy(self):\n",
    "        return np.transpose([self.get_x(),self.get_y()])\n",
    "            # returns particle coorinates as a list of x-y pairs\n",
    "    def add_particle(self,new_x,new_y):\n",
    "        self.particles.append(particle(new_x,new_y))\n",
    "            # defines a function to add a new particle to the list\n",
    "    def __repr__(self):\n",
    "        return \"%s \\n\" % (self.particles)\n",
    "    def decay(self,rate):\n",
    "        for item in self.particles:\n",
    "            if(np.random.rand() <= rate):\n",
    "                self.decayed_particles.append(item)\n",
    "                self.particles.remove(item)\n",
    "            else:\n",
    "                item.t = item.t +1\n",
    "            # central function: when given a rate, this iterates through all particles and either has them decay or\n",
    "            # adds 1 to the ellapsed lifetime.\n",
    "    def create(self,rate):\n",
    "        if(np.random.rand() <= rate):\n",
    "            self.add_particle(1+np.random.rand()*8,1+np.random.rand()*8)\n",
    "            # defines how to add particles at a particular rate\n",
    "print(\"Setup done\")\n",
    "\n",
    "import time\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.ticker import MaxNLocator\n",
    "\n",
    "\n",
    "lst = particle_list()\n",
    "\n",
    "plt.ion() \n",
    "    # makes the plot interactive, needed for animation\n",
    "fig, [ax1, ax2] = plt.subplots(nrows=2, ncols=1,figsize=(8,8)) \n",
    "    # Alternative way of initializing subplots\n",
    "\n",
    "\n",
    "ax2.set_ylabel('Counts')\n",
    "\n",
    "\n",
    "sc = ax1.scatter(lst.get_x(),lst.get_y())\n",
    "ax1.set_xlim([0, 10])\n",
    "ax1.set_ylim([0, 10])\n",
    "ax1.set_aspect('equal')\n",
    "    # setting up a scatter plot of particles\n",
    "\n",
    "sc2 = ax2.hist(lst.get_t())\n",
    "\n",
    "\n",
    "lst.add_particle(1+np.random.rand()*8,1+np.random.rand()*8)\n",
    "    # adds a sintle particle to get things started off, where 1 > x > 9 and 1 > y > 9\n",
    "    # the position doesn't really do anything, it is just there for visualization purposes.\n",
    "plt.draw() \n",
    "\n",
    "while (time.time() < t_end):\n",
    "    for i in range(frame_skip):\n",
    "        lst.create(add_chance)\n",
    "        lst.decay(decay_chance)\n",
    "        #this is the core part of the loop: maybe add a particle and then check for decays\n",
    "    sc.set_offsets(lst.get_paired_xy())\n",
    "        # this sets up the positions of particles in the scatterplot.\n",
    "    ax2.cla()\n",
    "    ax2.set_ylabel('Counts')\n",
    "        # clears off the lifetime plot, resets labels\n",
    "    time_data = lst.get_t()\n",
    "    dat,bins = np.histogram(time_data,bins=hist_bins)\n",
    "        # generates histogram data from the particle lifetimes\n",
    "    #ax2.errorbar(bins[0:-1],dat,np.sqrt(dat),fmt='.r',alpha=0.5)\n",
    "    ax2.plot(bins[0:-1],dat,'k.')\n",
    "        # makes a plot of the binned data, with square root N error bars\n",
    "        # note that since numpy's histogram gives back one more bin value that data point, we need to chop one off the array\n",
    "        # hence the [0:-1] notation\n",
    "    ax2.yaxis.set_major_locator(MaxNLocator(integer=True))      \n",
    "        # this line force the y axis tics to be integers.  Not critical.\n",
    "    plt.title(\"Time remaining:%i\" % int(t_end - time.time()))\n",
    "        # sets the title to the remaining time the sim is running\n",
    "    fig.canvas.draw()\n",
    "    plt.pause(0.01)\n",
    "        # pause is needed, otherwise the visuals never refresh"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The code above runs a simulation of decaying particles with a few user-set parameters. Whenever a particle (shown in blue) decays, its lifetime is added to the histogram in the lower plot.\n",
    "\n",
    "Note that the number of particles is pretty low compared to the number of time bins here, so each given time only has a few decays. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "rebin_factor = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raw Bins:\n",
      "Fit Converged\n",
      "Chi-square for fit:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\chi^2 = 86.93$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Degrees of freedom:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d.f. = 497$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reduced chi-square:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\chi^2}{d.f.} = 0.17$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inital guess values:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle f(t) = 7e^{-0.01t}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fit values:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle f(t) = (1.94\\pm0.19)e^{(-0.0024\\pm0.0008)t}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "Binned Data:\n",
      "Fit Converged\n",
      "Chi-square for fit:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\chi^2 = 88.17$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Degrees of freedom:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d.f. = 247$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Reduced chi-square:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\chi^2}{d.f.} = 0.36$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inital guess values:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle f(t) = 11e^{-0.01t}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fit values:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle f(t) = (4.53\\pm0.47)e^{(-0.0062\\pm0.0009)t}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to  previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
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     "output_type": "display_data"
    },
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# %load ParticleHistogram.py\n",
    "import numpy as np\n",
    "\n",
    "def fitfunc(p, x):\n",
    "    return p[0]*np.exp(-x*p[1])\n",
    "def residual(p, x, y, dy):\n",
    "    return (fitfunc(p, x)-y)/dy\n",
    "# defining a function to fit data with\n",
    "\n",
    "\n",
    "hist_bins_rebin = hist_bins[::rebin_factor]\n",
    "    # hist_bins_rebin is the new set of bins; it basically takes every nth element from the original bins.\n",
    "        # n is rebin_factor in this case. \n",
    "        # for syntax see https://docs.scipy.org/doc/numpy/reference/arrays.indexing.html\n",
    "dat,bins = np.histogram(time_data,bins=hist_bins)\n",
    "dat2,bins2 = np.histogram(time_data,bins=hist_bins_rebin)\n",
    "\n",
    "import numpy.ma as ma\n",
    "dat_nonzero = ma.masked_less_equal(dat[0:],0)\n",
    "bin_nonzero = ma.masked_array(bins[0:-1], mask=dat_nonzero.mask).compressed()\n",
    "dat_nonzero = dat_nonzero.compressed()\n",
    "dat2_nonzero = ma.masked_less_equal(dat2[0:],0)\n",
    "bin2_nonzero = ma.masked_array(bins2[0:-1], mask=dat2_nonzero.mask).compressed()\n",
    "dat2_nonzero = dat2_nonzero.compressed()\n",
    "    # this whole bit serves the function of tossing out bins with zeros in them.\n",
    "    # this is to keep the optimization from throwing a fit\n",
    "    # see https://docs.scipy.org/doc/numpy/reference/maskedarray.generic.html\n",
    "\n",
    "from scipy import optimize\n",
    "p01 = [max(dat), decay_chance]\n",
    "pf1, cov1, info1, mesg1, success1 = optimize.leastsq(residual, p01, args = (bin_nonzero,dat_nonzero,np.sqrt(dat_nonzero)), full_output=1)\n",
    "    # usual code for fitting the unbinned data\n",
    "    # uses max(dat) as a quick guess for how high the exponential should go\n",
    "\n",
    "from IPython.display import display, Math\n",
    "    # used to render equations in a more readible fashion\n",
    "    \n",
    "print(\"Raw Bins:\")\n",
    "if cov1 is None:\n",
    "    print('Fit did not converge')\n",
    "    print('Success code:', success1)\n",
    "    print(mesg1)\n",
    "else:\n",
    "    print('Fit Converged')\n",
    "    chisq1 = sum(info1['fvec']*info1['fvec'])\n",
    "    dof1 = len(dat)-len(pf1)\n",
    "    pferr1 = [np.sqrt(cov1[i,i]) for i in range(len(pf1))]\n",
    "    print(\"Chi-square for fit:\")\n",
    "    display(Math(r\"\\chi^2 = {:.2f}\".format(chisq1)))\n",
    "        # the {:.2f} here denotes that the variable we name (chisq) \n",
    "        # should be shown as a floating point number (f) with two decimal places (.2)\n",
    "    print(\"Degrees of freedom:\")\n",
    "    display(Math(r\"d.f. = {}\".format(dof1)))\n",
    "    print(\"Reduced chi-square:\")\n",
    "    display(Math(r\"\\frac{{\\chi^2}}{{d.f.}} = {:.2f}\".format(chisq1/dof1)))\n",
    "        # to get ipython's Math to recognize curly brackets as LaTeX formatting, you need to use pairs of them\n",
    "    print('Inital guess values:')\n",
    "    display(Math(r\"f(t) = {}e^{{-{}t}}\".format(p01[0],p01[1])))\n",
    "    print('Fit values:')\n",
    "    display(Math(r\"f(t) = ({:.2f}\\pm{:.2f})e^{{(-{:.4f}\\pm{:.4f})t}}\".format(pf1[0],pferr1[0],pf1[1],pferr1[1])))\n",
    "        \n",
    "p02 = [max(dat2), decay_chance,]\n",
    "pf2, cov2, info2, mesg2, success2 = optimize.leastsq(residual, p02, args = (bin2_nonzero,dat2_nonzero,np.sqrt(dat2_nonzero)), full_output=1)\n",
    "# this fits the binned data\n",
    "    \n",
    "    \n",
    "print('\\n')\n",
    "print(\"Binned Data:\")\n",
    "if cov2 is None:\n",
    "    print('Fit did not converge')\n",
    "    print('Success code:', success1)\n",
    "    print(mesg1)\n",
    "else:\n",
    "    \n",
    "\n",
    "    print('Fit Converged')\n",
    "    chisq2 = sum(info2['fvec']*info2['fvec'])\n",
    "    dof2 = len(dat2)-len(pf2)\n",
    "    pferr2 = [np.sqrt(cov2[i,i]) for i in range(len(pf2))]\n",
    "    print(\"Chi-square for fit:\")\n",
    "    display(Math(r\"\\chi^2 = {:.2f}\".format(chisq2)))\n",
    "    print(\"Degrees of freedom:\")\n",
    "    display(Math(r\"d.f. = {}\".format(dof2)))\n",
    "    print(\"Reduced chi-square:\")\n",
    "    display(Math(r\"\\frac{{\\chi^2}}{{d.f.}} = {:.2f}\".format(chisq2/dof2)))\n",
    "    print('Inital guess values:')\n",
    "    display(Math(r\"f(t) = {}e^{{-{}t}}\".format(p02[0],p02[1])))\n",
    "    print('Fit values:')\n",
    "    display(Math(r\"f(t) = ({0:.2f}\\pm{1:.2f})e^{{(-{2:.4f}\\pm{3:.4f})t}}\".format(pf2[0],pferr2[0],pf2[1],pferr2[1])))\n",
    "\n",
    "fig1 = plt.figure()\n",
    "ax1 = fig1.add_subplot(211)\n",
    "ax2 = fig1.add_subplot(212)\n",
    "ax1.errorbar(bin_nonzero,dat_nonzero,np.sqrt(dat_nonzero), fmt='k.', label = 'Data')\n",
    "ax2.errorbar(bin2_nonzero,dat2_nonzero,np.sqrt(dat2_nonzero), fmt='k^', label = 'Data')\n",
    "# plot the data\n",
    "\n",
    "T = np.linspace(0, time_range, time_range+1)\n",
    "ax1.plot(T, fitfunc(pf1, T), 'r-', label = 'Fit', zorder=5)\n",
    "ax1.plot(T, fitfunc(p01, T), 'b:', label = 'Guess', zorder=4)\n",
    "ax2.plot(T, fitfunc(pf2, T), 'r-', label = 'Fit', zorder=5)\n",
    "ax2.plot(T, fitfunc(p02, T), 'b:', label = 'Guess', zorder=4)\n",
    "# plot the fits, along with our guesses\n",
    "\n",
    "ax1.legend()\n",
    "ax2.legend()\n",
    "ax1.set_title('Raw Bins')\n",
    "ax2.set_title('Binned Data\\n Rebinning factor = {}'.format(rebin_factor))\n",
    "ax1.set_xlabel(\"Lifetime\")\n",
    "ax2.set_xlabel(\"Lifetime\")\n",
    "ax1.set_ylabel(\"Counts\")\n",
    "ax2.set_ylabel(\"Counts\")\n",
    "plt.tight_layout()\n",
    "#    plt.savefig('Decay Simulation.pdf')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the `decay_chance` set in the first cell is the exponent you should expect to find here.  What rebinning factor is needed for your fit value to agree (within 1-2 $\\sigma$ uncertainty)?\n",
    "\n",
    "Note that the reduce $\\chi^2$ values for your fits may _both_ be smaller than one, this is a function of having a whole lot of datapoints with large error bars."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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