ANDiE Hypothesis Testing FeTe.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "978dee8f",
   "metadata": {},
   "source": [
    "# Set-up Python Environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "93868758",
   "metadata": {},
   "outputs": [],
   "source": [
    "import bumps\n",
    "from bumps.names import *\n",
    "from bumps.fitters import fit\n",
    "from bumps.formatnum import format_uncertainty\n",
    "from bumps.bounds import BoundedNormal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "3a189046",
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy\n",
    "from scipy.optimize import root_scalar\n",
    "from scipy.optimize import root\n",
    "from scipy.stats.mstats import mquantiles\n",
    "import scipy.io\n",
    "import pandas as pd\n",
    "\n",
    "import io, os, sys, types\n",
    "matplotlib_style = 'seaborn-whitegrid' #@param ['fivethirtyeight', 'bmh', 'ggplot', 'seaborn', 'default', 'Solarize_Light2', 'classic', 'dark_background', 'seaborn-colorblind', 'seaborn-notebook']\n",
    "\n",
    "import matplotlib.pyplot as plt; plt.style.use(matplotlib_style)\n",
    "import matplotlib.axes as axes;\n",
    "from matplotlib.colors import LogNorm\n",
    "from matplotlib.patches import Ellipse\n",
    "\n",
    "import seaborn as sns; sns.set_context('notebook')\n",
    "from IPython.core.pylabtools import figsize\n",
    "notebook_screen_res = 'retina' #@param ['retina', 'png', 'jpeg', 'svg', 'pdf']\n",
    "from datetime import datetime\n",
    "    \n",
    "\n",
    "import numpy as np\n",
    "import numpy.matlib\n",
    "\n",
    "import time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "9b4c900c",
   "metadata": {},
   "outputs": [],
   "source": [
    "import subprocess\n",
    "import glob\n",
    "import h5py\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "dd378221",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams['svg.fonttype'] = 'none'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "beaf19b2",
   "metadata": {},
   "source": [
    "# Build The Model Functions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "266b75a8",
   "metadata": {},
   "source": [
    "Note that throughout this notebook 'first order' refers the the First-order model, 'second order' refers to the Weiss model, and 'Ising' refers to the Ising model, as the models for the temperature dependance of the magnetic component of diffraction intensity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "15e63c6e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Isothermal Functions:\n",
    "\n",
    "def Gaussian(x, alpha):\n",
    "    #Gaussian peak centered at 0, evaluated at x, with HWHM alpha\n",
    "    sigma = alpha/(np.sqrt(2.0 * np.log(2)))\n",
    "    G = (1/(sigma*np.sqrt(2.0* np.pi)))*np.exp(-(x**2.0)/(2.0*sigma**2.0))\n",
    "    return G\n",
    "\n",
    "def Lorentzian(x, gamma):\n",
    "    #Return Lorentzian peak centered at 0, evaluated at x, with HWHM gamma    \n",
    "    L = gamma/(np.pi*(x**2.0 + gamma**2.0))\n",
    "    return L\n",
    "\n",
    "def Pseudo_voigt(x, alpha, gamma):\n",
    "  f_L = 2.0*gamma\n",
    "  f_G = 2.0*alpha\n",
    "\n",
    "  f = (f_G**5.0\\\n",
    "       + 2.69269*(f_G**4.0)*(f_L)\\\n",
    "       + 2.42843*(f_G**3.0)*(f_L**2.0)\\\n",
    "       + 4.47163*(f_G**2.0)*(f_L**3.0)\\\n",
    "       + 0.07842*(f_G)*(f_L**4.0)\\\n",
    "       + f_L**5.0)**(0.2)\n",
    "\n",
    "  eta = 1.36603*(f_L/f) - 0.477*(f_L/f)**2.0 + 0.11116*(f_L/f)**3.0\n",
    "\n",
    "  hwhm = f/2.0\n",
    "  \n",
    "  PV = eta*Lorentzian(x,hwhm) + (1.0-eta)*Gaussian(x, hwhm)\n",
    "  return PV\n",
    "\n",
    "def One_peak(x, alpha, gamma, peak, scale, back):\n",
    "    #Alpha, gamma, peak, scale, back are all row vectors\n",
    "    #x is a collum vector of the positions\n",
    "    two_thetas = np.add(x, -peak)\n",
    "    PV = Pseudo_voigt(two_thetas, alpha, gamma)\n",
    "    scaled_PV = PV*scale\n",
    "    I = scaled_PV + back\n",
    "    return I\n",
    "\n",
    "def Two_peak(x, alpha, gamma, peak, scale, alpha1, gamma1, peak1, scale1, back):\n",
    "    #Alpha, gamma, peak, scale, back are all row vectors\n",
    "    #x is a collum vector of the positions\n",
    "    I1 = One_peak(x, alpha, gamma, peak, scale, 0.0)\n",
    "    I2 = One_peak(x, alpha1, gamma1, peak1, scale1, 0.0)\n",
    "    I = I1 + I2 + back\n",
    "    return I\n",
    "\n",
    "####################################################\n",
    "# Thermal Functions:\n",
    "\n",
    "# Define I vs. T for first order phase transition:\n",
    "def first_order_I_vs_T(temperatures, TN, Sigma, K, BK):\n",
    "    I = ((K/2)*(1 - scipy.special.erf((temperatures - TN)/(np.sqrt(2.0)*Sigma))))**2 + BK\n",
    "    return I\n",
    "\n",
    "\n",
    "# Define the Brillouin Function\n",
    "def Brillouin_J(x, J):\n",
    "    # x is a matrix\n",
    "    # J is a row-vector\n",
    "    \n",
    "    f1 = (2*J+1)/(2*J) #factor 1\n",
    "    f2 = 1/(2*J) #factor 2\n",
    "    B_J = f1/(np.tanh(f1*x)) - f2/(np.tanh(f2*x))\n",
    "    return B_J\n",
    "                   \n",
    "# Define the Wiess equation (re-arranged so that it always = 0)                  \n",
    "def Wiess(t, m, J):\n",
    "    # t is a collum vector\n",
    "    # J is a row vector\n",
    "    # m is a matrix\n",
    "    \n",
    "    f1 = 3.0*J/(J +1.0) # factor 1\n",
    "    f2 = 1.0/t #factor 2\n",
    "    \n",
    "    m = np.ones_like(t)*m\n",
    "    x = f1*m*f2\n",
    "    \n",
    "    \n",
    "    W = m - Brillouin_J(x, J)\n",
    "    return W.reshape(-1)\n",
    "\n",
    "#Define a Magnetization Solver for givin t and J:\n",
    "def Mag_solve(t, J):\n",
    "    # t is a collum vector\n",
    "    # J is a row vector\n",
    "    \n",
    "    def fun(x):\n",
    "        x= x.reshape((t.shape[0], J.shape[1]))\n",
    "        return Wiess(t, x, J)\n",
    "    \n",
    "    X0 = np.ones((t.shape[0], J.shape[1]), dtype=np.float64) # matrix of every t,J combination\n",
    "    \n",
    "    solution = root(fun, X0, method ='hybr')\n",
    "    \n",
    "    m = np.array(solution.x).reshape((t.shape[0], J.shape[1]))\n",
    "    return m\n",
    "\n",
    "#Define the Intensity as function of Temperature for Second order phase transitions using the Weiss Model\n",
    "def second_order_I_vs_T(Temperatures, TN, M0, J, BK):\n",
    "    # TN, M0, J, BK are row vectors\n",
    "    TN = np.array(TN).reshape(1,-1)\n",
    "    M0 = np.array(M0).reshape(1,-1)\n",
    "    J = np.array(J).reshape(1,-1)\n",
    "    BK = np.array(BK).reshape(1,-1)\n",
    "    # Temperatures is a collumn vector\n",
    "    Temperatures = Temperatures.reshape(-1,1)\n",
    "    \n",
    "    Inverse_TN = 1/TN\n",
    "    \n",
    "    t = Temperatures @ Inverse_TN #Create a matrix of every (temperature, TN) combination\n",
    "\n",
    "    #Find where all the temperatures below the TN. \n",
    "    t_low_truth = t <1.0\n",
    "    t_low_truth = t_low_truth.reshape(t.shape)\n",
    "    t_low = t*t_low_truth\n",
    "    \n",
    "    #Because \"Mag_solve\" is expensive, only pass the non-zero rows of the t_low matrix.\n",
    "    t_low_cut = t_low[t_low.sum(axis=1) !=0]\n",
    "\n",
    "    #Calculate the reduced magnetization for below Tn\\\n",
    "    m_low = Mag_solve(t_low_cut, J) #returns a matrix where each collumn of m is associated with a collum of J\n",
    "    \n",
    "    #The mag is zero above the TN, construct that matrix\n",
    "    m_high = np.zeros((t.shape[0]-t_low_cut.shape[0], t.shape[1]))\n",
    "    #Combine the m matrixies for below and above the TN\n",
    "    m = np.concatenate((m_low,m_high), axis=0)\n",
    "    \n",
    "    #\"t_low_cut\" could have a raggid bottom edge, so only keep the m values below the TN \n",
    "    m = m*t_low_truth\n",
    "\n",
    "    #Calcualte the Magnetization (not reduced)\n",
    "    M = m * M0 #row by row mulitplication of m by M0\n",
    "    \n",
    "    ##Calculate the intensities\n",
    "    #Square of Magnetization\n",
    "    I = M**2 \n",
    "    \n",
    "    #Add the background\n",
    "    I = I + BK\n",
    "\n",
    "    return I\n",
    "\n",
    "\n",
    "def Ising_model_I_vs_T(Temperatures, TN, M0, BETA, BK):\n",
    "    # TN, M0, J, BK are row vectors\n",
    "    TN = np.array(TN).reshape(1,-1)\n",
    "    M0 = np.array(M0).reshape(1,-1)\n",
    "    BETA = np.array(BETA).reshape(1,-1).astype(np.complex128)\n",
    "    BK = np.array(BK).reshape(1,-1)\n",
    "\n",
    "    T_iw = np.array(0.5).reshape(1,-1)\n",
    "\n",
    "    # Temperatures is a collumn vector\n",
    "    Temperatures = Temperatures.reshape(-1,1)    \n",
    "    Inverse_TN = 1/TN\n",
    "    \n",
    "    t = Temperatures @ Inverse_TN #Create a matrix of every (temperature, TN) combination\n",
    "    \n",
    "    #Cut out the temperatures where the Ising Model is not valid\n",
    "    mask = np.logical_and(t<1.0, t>T_iw)\n",
    "    \n",
    "    t_eval = np.empty_like(t)\n",
    "    t_eval[:] = np.nan\n",
    "    t_eval[mask] = t[mask]\n",
    "\n",
    "    I = (M0*((1 - t_eval)**(2*BETA)))**2 + BK\n",
    "    I = I.astype(np.float64)\n",
    "\n",
    "    #Above TN set the I to the background\n",
    "    upper = t >= 1\n",
    "    BK_matrix = np.matlib.repmat(BK, Temperatures.shape[0], 1)\n",
    "    I[upper] = BK_matrix[upper]\n",
    "    \n",
    "    return I\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ea5155c",
   "metadata": {},
   "source": [
    "## Thermal Model:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "552e3fc7",
   "metadata": {},
   "source": [
    "For use with the Ising model with bumps, define a new class that handles <code>np.nan</code> values of intensity outside the range of applicablity of the Ising model.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c881db66",
   "metadata": {},
   "outputs": [],
   "source": [
    "import inspect\n",
    "import warnings\n",
    "\n",
    "import numpy as np\n",
    "from numpy import log, pi, sqrt\n",
    "\n",
    "from bumps.parameter import Parameter\n",
    "\n",
    "def _parse_pars(fn, init=None, skip=0, name=\"\"):\n",
    "    \"\"\"\n",
    "    Extract parameter names from function definition.\n",
    "\n",
    "    *fn* is the function definition.  This could be declared as\n",
    "    *fn(p1, p2, p3, ...)* where *p1*, etc. are the fittable parameters.\n",
    "\n",
    "    *init* is a dictionary of initial values for the parameters,\n",
    "    overriding any default values.  If called from a constructor with\n",
    "    **kwargs representing unknown named arguments, use *init=kwargs*.\n",
    "\n",
    "    *skip* is the number of parameters to skip.  This will be *skip=0*\n",
    "    for a function which defines the log likelihood directly or one\n",
    "    that returns a set of residuals. For parameterized curves such as\n",
    "    *fn(x, p1, p2, ...)* use *skip=1*.  For surfaces with\n",
    "    *fn(x, y, p1, p2, ...)* use *skip=2*.\n",
    "\n",
    "    *name* is added to each parameter name to differentiate it from other\n",
    "    parameters in the same fit.\n",
    "\n",
    "    A default value in the function definition such as *pk=value* will\n",
    "    be set as the default value for the parameter.  If the default is\n",
    "    *pk=None* then the parameter will be non-fittable, and instead set\n",
    "    through *init*.\n",
    "    \"\"\"\n",
    "    sig = inspect.signature(fn)\n",
    "    params = sig.parameters.values()\n",
    "    pnames = [p.name for p in params]\n",
    "    \n",
    "    valid = [p.kind in (inspect.Parameter.POSITIONAL_ONLY, inspect.Parameter.POSITIONAL_OR_KEYWORD) for p in params]\n",
    "    if not all(valid):\n",
    "        raise TypeError(f\"Only positional and keyword arguments allowed for {fn.__name__}\")\n",
    "\n",
    "    # TODO: need \"self\" handling for passed methods\n",
    "    # Skip the first argument if it is x or maybe skip x, y.\n",
    "    pnames = pnames[skip:]\n",
    "\n",
    "    # Parameters default to zero\n",
    "    defaults = dict((p, 0) for p in pnames)\n",
    "\n",
    "    # If the function provides default values, use those.\n",
    "    for param in list(params)[skip:]:\n",
    "        if param.default is not inspect.Parameter.empty:\n",
    "            defaults[param.name] = param.default\n",
    "\n",
    "    # Non-fittable parameters need to be sent in as None\n",
    "    state_vars = set(p for p, v in defaults.items() if v is None)\n",
    "\n",
    "    # Regardless, use any values specified in the constructor, but first\n",
    "    # check that they exist as function parameters.\n",
    "    invalid = set(init.keys()) - set(pnames)\n",
    "    if invalid:\n",
    "        raise TypeError(\"Invalid initializers: %s\" %\n",
    "                        \", \".join(sorted(invalid)))\n",
    "    defaults.update(init)\n",
    "\n",
    "    # Build parameters out of ranges and initial values\n",
    "    # maybe:  name=(p+name if name.startswith('_') else name+p)\n",
    "    pars = dict((p, Parameter.default(defaults[p], name=name + p))\n",
    "                for p in pnames if p not in state_vars)\n",
    "\n",
    "    state = dict((p, v) for p, v in defaults.items() if p in state_vars)\n",
    "\n",
    "    #print(\"pars\", pars)\n",
    "    #print(\"state\", state)\n",
    "    return pars, state\n",
    "\n",
    "def _assign_pars(obj, pars):\n",
    "    # Make parameters accessible as model attributes\n",
    "    for k, v in pars.items():\n",
    "        if hasattr(obj, k):\n",
    "            raise TypeError(\"Parameter cannot be named %s\" % k)\n",
    "        setattr(obj, k, v)\n",
    "        \n",
    "class Curve_w_nan(object):\n",
    "    r\"\"\"\n",
    "    Model a measurement with a user defined function.\n",
    "\n",
    "    The function *fn(x,p1,p2,...)* should return the expected value *y* for\n",
    "    each point *x* given the parameters *p1*, *p2*, etc.  *dy* is the\n",
    "    uncertainty for each measured value *y*.  If not specified, it defaults\n",
    "    to 1. Multi-valued functions, which return multiple *y* values for each\n",
    "    *x* value, should have *x* as a vector of length *n* and *y*, *dy* as\n",
    "    arrays of size *[n, k]*.\n",
    "\n",
    "    Initial values for the parameters can be set as *p=value* arguments to\n",
    "    *Curve*. If no value is set, then the initial value will be taken from\n",
    "    the default value given in the definition of *fn*, or set to 0 if the\n",
    "    parameter is not defined with an initial value.  Arbitrary non-fittable\n",
    "    data can be passed to the function as parameters, but only if the\n",
    "    parameter is given a default value of *None* in the function definition,\n",
    "    and has the initial value set as an argument to *Curve*.  Defining\n",
    "    *state=dict(key=value, ...)* before *Curve*, and calling *Curve* as\n",
    "    *Curve(..., \\*\\*state)* works pretty well.\n",
    "\n",
    "    *Curve* takes the following special keyword arguments:\n",
    "\n",
    "    * *name* is added to each parameter name when the parameter is defined.\n",
    "      The filename for the data is a good choice, since this allows you to keep\n",
    "      the parameters straight when fitting multiple datasets simultaneously.\n",
    "\n",
    "    * *plot* is an alternative plotting function. The function should be\n",
    "      defined as *plot(x,y,dy,fy,\\*\\*kw)*. The keyword arguments will be\n",
    "      filled with the values of the parameters used to compute *fy*.  It\n",
    "      will be easiest to list the parameters you need to make your plot\n",
    "      as positional arguments after *x,y,dy,fy* in the plot function\n",
    "      declaration.  For example, *plot(x,y,dy,fy,p3,\\*\\*kw)* will make the\n",
    "      value of parameter *p3* available as a variable in your function.  The\n",
    "      special keyword *view* will be a string containing *linear*, *log*,\n",
    "      *logx*, or *loglog*.  If only showing the residuals, the string\n",
    "      will be *residual*.\n",
    "\n",
    "    * *plot_x* is an array giving the sample points to use when plotting\n",
    "      the theory function, if different from the *x* values at which the\n",
    "      function is sampled.  Use this to draw a smooth curve between the\n",
    "      fitted points.  This value is ignored if you provide your own plot\n",
    "      function.\n",
    "\n",
    "    * *labels* are the axis labels for the plot.  This should include\n",
    "      units in parentheses. If the function is multi-valued then\n",
    "      use *['x axis', 'y axis', 'line 1', 'line 2', ...]*.\n",
    "\n",
    "    The data uncertainty is assumed to follow a gaussian distribution.\n",
    "    If measurements draw from some other uncertainty distribution, then\n",
    "    subclass Curve and replace nllf with the correct probability given the\n",
    "    residuals.  See the implementation of :class:`PoissonCurve` for an example.\n",
    "    \"\"\"\n",
    "    def __init__(self, fn, x, y, dy=None, name=\"\", labels=None,\n",
    "                 plot=None, plot_x=None, **kwargs):\n",
    "        self.x, self.y = np.asarray(x), np.asarray(y)\n",
    "        if dy is None:\n",
    "            self.dy = 1\n",
    "        else:\n",
    "            self.dy = np.asarray(dy)\n",
    "            if (self.dy <= 0).any():\n",
    "                raise ValueError(\"measurement uncertainty must be positive\")\n",
    "\n",
    "        if len(self.x.shape) == 1 and len(self.y.shape) > 1:\n",
    "            num_curves = self.y.shape[0]\n",
    "        else:\n",
    "            num_curves = 1\n",
    "        self._num_curves = num_curves  # use same value everywhere\n",
    "\n",
    "        # interpret labels parameter\n",
    "        if labels is None:\n",
    "            labels = ['x', 'y']\n",
    "        elif len(labels) < 2 or len(labels) != num_curves+2:\n",
    "            if num_curves > 1:\n",
    "                lines = \"line1, ..., line%d\"%num_curves\n",
    "            else:\n",
    "                lines = \"line\"\n",
    "            raise TypeError(\"labels should be [x, y, %s]\"%lines)\n",
    "\n",
    "        if len(labels) == 2:\n",
    "            if num_curves > 1:\n",
    "                line_labels = ['y%d'%k for k in range(num_curves)]\n",
    "            else:\n",
    "                line_labels = [labels[1]]\n",
    "            labels = list(labels) + line_labels\n",
    "        self.labels = labels\n",
    "\n",
    "\n",
    "        # TODO: self.fn is a duplicate of self._function below. Deprecated?\n",
    "        self.fn = fn\n",
    "        self.name = name # if name else fn.__name__ + \" \"\n",
    "        self.plot_x = plot_x\n",
    "\n",
    "        pars, state = _parse_pars(fn, init=kwargs, skip=1)\n",
    "\n",
    "        # Make parameters accessible as model attributes\n",
    "        _assign_pars(self, pars)\n",
    "        #_assign_pars(state, self)  # ... and state variables as well\n",
    "\n",
    "        # Remember the function, parameters, and number of parameters\n",
    "        # Note: we are remembering the parameter names and not the\n",
    "        # parameters themselves so that the caller can tie parameters\n",
    "        # together using model1.par = model2.par.  Otherwise we would\n",
    "        # need to override __setattr__ to intercept assignment to the\n",
    "        # parameter attributes and redirect them to the a _pars dictionary.\n",
    "        # ... and similarly for state if we decide to make them attributes.\n",
    "        self._function = fn\n",
    "        self._pnames = list(sorted(pars.keys()))\n",
    "        self._state = state\n",
    "        self._plot = plot\n",
    "        self._cached_theory = None\n",
    "\n",
    "    def update(self):\n",
    "        self._cached_theory = None\n",
    "\n",
    "\n",
    "    def parameters(self):\n",
    "        return dict((p, getattr(self, p)) for p in self._pnames)\n",
    "\n",
    "\n",
    "    def numpoints(self):\n",
    "        return np.prod(self.y.shape)\n",
    "\n",
    "\n",
    "    def theory(self, x=None):\n",
    "        # Use cache if x is None, otherwise compute theory with x.\n",
    "        if x is None:\n",
    "            if self._cached_theory is None:\n",
    "                self._cached_theory = self._compute_theory(self.x)\n",
    "            return self._cached_theory\n",
    "        return self._compute_theory(x)\n",
    "\n",
    "\n",
    "    def _compute_theory(self, x):\n",
    "        kw = self._fetch_pars()\n",
    "        return self._function(x, **kw)\n",
    "\n",
    "    def _fetch_pars(self):\n",
    "        kw = dict((p, getattr(self, p).value) for p in self._pnames)\n",
    "        kw.update(self._state)\n",
    "        return kw\n",
    "\n",
    "    def simulate_data(self, noise=None):\n",
    "        theory = self.theory()\n",
    "        if noise is not None:\n",
    "            if noise == 'data':\n",
    "                pass\n",
    "            elif noise < 0:\n",
    "                self.dy = -0.01*noise*theory\n",
    "            else:\n",
    "                self.dy = noise\n",
    "        self.y = theory + np.random.randn(*theory.shape)*self.dy\n",
    "\n",
    "\n",
    "    def residuals(self):\n",
    "        return (self.theory() - self.y) / self.dy\n",
    "\n",
    "\n",
    "    def nllf(self):\n",
    "        r = self.residuals()\n",
    "        ####################################################\n",
    "        ## Change from the standard curve class in bumps ##\n",
    "        \"\"\"Since our model can return np.nan values, the residuals will also be np.nan at those locations.\n",
    "        We will just sum the residuals in the range where the model returns numbered values to get the likelihood.\"\"\"\n",
    "        ####################################################\n",
    "        return 0.5 * np.nansum(r ** 2)\n",
    "\n",
    "\n",
    "    def save(self, basename):\n",
    "        # TODO: need header line with state vars as json\n",
    "        # TODO: need to support nD x,y,dy\n",
    "        if len(self.x.shape) > 1:\n",
    "            warnings.warn(\"Save not supported for nD x values\")\n",
    "            return\n",
    "\n",
    "        theory = self.theory()\n",
    "        if self._num_curves > 1:\n",
    "            # Multivalued y, dy for single valued x.\n",
    "            columns = [self.x]\n",
    "            headers = [\"x\"]\n",
    "            for k, (y, dy, fx) in enumerate(zip(self.y, self.dy, theory)):\n",
    "                columns.extend((y, dy, fx))\n",
    "                headers.extend((\"y[%d]\"%(k+1), \"dy[%d]\"%(k+1), \"fx[%d]\"%(k+1)))\n",
    "        else:\n",
    "            # Single-valued y, dy for single valued x.\n",
    "            headers = [\"x\", \"y\", \"dy\", \"fy\"]\n",
    "            columns = [self.x, self.y, self.dy, theory]\n",
    "        data = np.vstack(columns)\n",
    "        outfile = basename + '.dat'\n",
    "        with open(outfile, \"w\") as fd:\n",
    "            fd.write(\"# \" + \"\\t \".join(headers) + \"\\n\")\n",
    "            np.savetxt(fd, data.T)\n",
    "\n",
    "\n",
    "    def plot(self, view=None):\n",
    "        if self._plot is not None:\n",
    "            kw = self._fetch_pars()\n",
    "            self._plot(self.x, self.y, self.dy, self.theory(), view=view, **kw)\n",
    "            return\n",
    "\n",
    "        import pylab\n",
    "        from .plotutil import coordinated_colors\n",
    "\n",
    "        x = self.x\n",
    "        if self.plot_x is not None:\n",
    "            theory_x, theory_y = self.plot_x, self.theory(self.plot_x)\n",
    "        else:\n",
    "            theory_x, theory_y = x, self.theory()\n",
    "        resid = self.residuals()\n",
    "\n",
    "        if self._num_curves > 1:\n",
    "            y, dy, theory_y, resid = self.y.T, self.dy.T, theory_y.T, resid.T\n",
    "        else:\n",
    "            y, dy, theory_y, resid = (v[:, None]\n",
    "                                      for v in (self.y, self.dy, theory_y, resid))\n",
    "\n",
    "        colors = tuple(coordinated_colors() for _ in range(self._num_curves))\n",
    "        labels = self.labels\n",
    "\n",
    "        #print \"kw_plot\",kw\n",
    "        if view == 'residual':\n",
    "            _plot_resids(x, resid, colors, labels=labels, view=view)\n",
    "        else:\n",
    "            plot_ratio = 4\n",
    "            h = pylab.subplot2grid((plot_ratio, 1), (0, 0), rowspan=plot_ratio-1)\n",
    "            for tick_label in h.get_xticklabels():\n",
    "                tick_label.set_visible(False)\n",
    "            _plot_fits(data=(x, y, dy), theory=(theory_x, theory_y),\n",
    "                       colors=colors, labels=labels, view=view)\n",
    "            #pylab.gca().xaxis.set_visible(False)\n",
    "            #pylab.gca().spines['bottom'].set_visible(False)\n",
    "            #pylab.gca().set_xticks([])\n",
    "\n",
    "            pylab.subplot2grid((plot_ratio, 1), (plot_ratio-1, 0), sharex=h)\n",
    "            _plot_resids(x, resid, colors=colors, labels=labels, view=view)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3eaba975",
   "metadata": {},
   "outputs": [],
   "source": [
    "def First_order_model(X_grid, Y_grid):\n",
    "    M = Curve(first_order_I_vs_T, X_grid, Y_grid, \n",
    "          dy = np.sqrt(Y_grid/100),\n",
    "          TN = TN_guess, Sigma = Sigma_guess, K = K_guess , BK = BK_guess)\n",
    "\n",
    "    M.TN.bounds = TN_dist\n",
    "    M.Sigma.bounds = Sigma_dist\n",
    "    M.K.bounds = K_dist\n",
    "    M.BK.bounds = BK_dist\n",
    "    \n",
    "    if len(X_grid) < 5 :\n",
    "        problem = FitProblem(M, partial = True)\n",
    "    else:\n",
    "        problem = FitProblem(M, partial = False)\n",
    "    \n",
    "    return problem\n",
    "\n",
    "def Ising_model(X_grid, Y_grid):\n",
    "    M = Curve_w_nan(Ising_model_I_vs_T, X_grid, Y_grid, \n",
    "          dy = np.sqrt(Y_grid/100),\n",
    "          TN = TN_guess, M0 = M0_guess, BETA = BETA_guess , BK = BK_guess)\n",
    "\n",
    "    M.TN.bounds = TN_dist\n",
    "    M.M0.bounds = M0_dist\n",
    "    M.BETA.bounds = BETA_dist\n",
    "    M.BK.bounds = BK_dist\n",
    "    problem = FitProblem(M, partial = True)\n",
    "    \n",
    "    return problem\n",
    "\n",
    "\n",
    "def Second_order_model(X_grid, Y_grid):\n",
    "    M = Curve(second_order_I_vs_T, X_grid, Y_grid, \n",
    "          dy = np.sqrt(Y_grid/100),\n",
    "          TN = TN_guess, M0 = M0_guess, J = J_guess , BK = BK_guess)\n",
    "\n",
    "    M.TN.bounds = TN_dist\n",
    "    M.M0.bounds = M0_dist\n",
    "    M.J.bounds = J_dist\n",
    "    M.BK.bounds = BK_dist\n",
    "\n",
    "    if len(X_grid) < 5 :\n",
    "        problem = FitProblem(M, partial = True)\n",
    "    else:\n",
    "        problem = FitProblem(M, partial = False)\n",
    "    \n",
    "    return problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "1b20604f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Thermal_inference_first_order_train(X_grid, Y_grid):\n",
    "    problem = First_order_model(X_grid, Y_grid)\n",
    "            \n",
    "    method = 'dream' \n",
    "    \n",
    "    print(\"initial chisq\", problem.chisq_str())\n",
    "    result = fit(problem, method=method, xtol=1e-6, ftol=1e-8, \n",
    "                 samples = 100000, \n",
    "                 burn = 100,\n",
    "                 pop = 10,\n",
    "                 init = 'eps',\n",
    "                 thin = 1,\n",
    "                 alpha = 0.1,\n",
    "                 outliers = 'none',\n",
    "                 trim = False,\n",
    "                 steps = 0)\n",
    "    print(\"final chisq\", problem.chisq_str())\n",
    "    for k, v, dv in zip(problem.labels(), result.x, result.dx):\n",
    "        print(k, \":\", format_uncertainty(v, dv))\n",
    "        \n",
    "    return problem, result\n",
    "\n",
    "def Thermal_inference_Ising_model_train(X_grid, Y_grid):\n",
    "    problem = Ising_model(X_grid, Y_grid)\n",
    "            \n",
    "    method = 'dream' \n",
    "    \n",
    "    print(\"initial chisq\", problem.chisq_str())\n",
    "    result = fit(problem, method=method, xtol=1e-6, ftol=1e-8, \n",
    "                 samples = 100000, \n",
    "                 burn = 100,\n",
    "                 pop = 10,\n",
    "                 init = 'eps',\n",
    "                 thin = 1,\n",
    "                 alpha = 0.1,\n",
    "                 outliers = 'none',\n",
    "                 trim = False,\n",
    "                 steps = 0)\n",
    "    print(\"final chisq\", problem.chisq_str())\n",
    "    for k, v, dv in zip(problem.labels(), result.x, result.dx):\n",
    "        print(k, \":\", format_uncertainty(v, dv))\n",
    "        \n",
    "    return problem, result\n",
    "\n",
    "\n",
    "def Thermal_inference_second_order_train(X_grid, Y_grid): \n",
    "    problem = Second_order_model(X_grid, Y_grid)\n",
    "\n",
    "    method = 'dream' \n",
    "    \n",
    "    print(\"initial chisq\", problem.chisq_str())\n",
    "    result = fit(problem, method=method, xtol=1e-6, ftol=1e-8, \n",
    "                 samples = 100000, \n",
    "                 burn = 100,\n",
    "                 pop = 10,\n",
    "                 init = 'eps',\n",
    "                 thin = 1,\n",
    "                 alpha = 0.1,\n",
    "                 outliers = 'none',\n",
    "                 trim = False,\n",
    "                 steps = 0)\n",
    "    print(\"final chisq\", problem.chisq_str())\n",
    "    for k, v, dv in zip(problem.labels(), result.x, result.dx):\n",
    "        print(k, \":\", format_uncertainty(v, dv))\n",
    "        \n",
    "    return problem, result\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a20eee66",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Thermal_inference_first_order_predict(posterior_results, X_predict):\n",
    "    #Extract the Posterior of the parameters\n",
    "    draw = posterior_results.state.draw()\n",
    "      \n",
    "    #Posterior results are in alphabetical order\n",
    "    Posterior_TN = draw.points[:,3].reshape(1,-1)\n",
    "    Posterior_Sigma = draw.points[:,2].reshape(1,-1)\n",
    "    Posterior_K = draw.points[:,1].reshape(1,-1)\n",
    "    Posterior_BK = draw.points[:,0].reshape(1,-1)\n",
    "  \n",
    "    #Calcualte the mean of the parameters\n",
    "    TN_mean = np.mean(Posterior_TN).reshape(1,-1)\n",
    "    Sigma_mean = np.mean(Posterior_Sigma).reshape(1,-1)\n",
    "    K_mean = np.mean(Posterior_K).reshape(1,-1)\n",
    "    BK_mean = np.mean(Posterior_BK).reshape(1,-1)\n",
    "    \n",
    "    #Calculate the curve from the mean of the parameters\n",
    "    Thermal_Mean_Posterior_parameter_curve = first_order_I_vs_T(X_predict,\n",
    "                                                                TN_mean, Sigma_mean, K_mean, BK_mean)\n",
    "    \n",
    "    \n",
    "    #Posterior results are in alphabetical order\n",
    "    TN_best = posterior_results.state.best()[0][3]\n",
    "    Sigma_best = posterior_results.state.best()[0][2]\n",
    "    K_best = posterior_results.state.best()[0][1]\n",
    "    BK_best = posterior_results.state.best()[0][0]\n",
    "    \n",
    "    #Calculate the curve from the BEST parameters\n",
    "    Thermal_best_curve = first_order_I_vs_T(X_predict,\n",
    "                                            TN_best, Sigma_best, K_best, BK_best)\n",
    "    \n",
    "    #Calculate the predicted curves from posterior sets of parameters\n",
    "    print('Predicting')\n",
    "    Thermal_CI_curves = first_order_I_vs_T(X_predict,\n",
    "                                           Posterior_TN, Posterior_Sigma, Posterior_K, Posterior_BK)\n",
    "        \n",
    "    q = np.array([0.95, 0.05])\n",
    "    I_ci = np.quantile(Thermal_CI_curves, q, axis=1)#.reshape((-1,2))\n",
    "    Thermal_lower_curve = I_ci[1,:].reshape(-1,1)\n",
    "    Thermal_upper_curve = I_ci[0,:].reshape(-1,1)\n",
    "    \n",
    "    Thermal_mean_of_posterior_curves = np.mean(Thermal_CI_curves, axis=1).reshape(-1,1)\n",
    "    Thermal_variance = np.var(Thermal_CI_curves, axis=1).reshape(-1,1)\n",
    "     \n",
    "    dictionary = {'TN Mean':TN_mean, \n",
    "                  'Sigma Mean':Sigma_mean, \n",
    "                  'K Mean':K_mean, \n",
    "                  'BK Mean':BK_mean, \n",
    "                  'Thermal Mean Posterior Parameter Curve': Thermal_Mean_Posterior_parameter_curve,\n",
    "                  'Thermal Best Parameter Curve':  Thermal_best_curve,\n",
    "                  'Thermal Mean of Posterior Curves': Thermal_mean_of_posterior_curves,\n",
    "                  'Thermal Variance': Thermal_variance,\n",
    "                  'Thermal CI Curves': Thermal_CI_curves,\n",
    "                  'Thermal lower Curve': Thermal_lower_curve,\n",
    "                  'Thermal upper Curve': Thermal_upper_curve}\n",
    "    \n",
    "    return dictionary\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "6eb0060b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Thermal_inference_Ising_predict(posterior_results, X_predict):\n",
    "    #Extract the Posterior of the parameters\n",
    "    draw = posterior_results.state.draw()\n",
    "      \n",
    "    #Posterior results are in alphabetical order\n",
    "    Posterior_TN = draw.points[:,3].reshape(1,-1)\n",
    "    Posterior_M0 = draw.points[:,2].reshape(1,-1)\n",
    "    Posterior_BETA = draw.points[:,0].reshape(1,-1)\n",
    "    Posterior_BK = draw.points[:,1].reshape(1,-1)\n",
    "  \n",
    "    #Calcualte the mean of the parameters\n",
    "    TN_mean = np.mean(Posterior_TN).reshape(1,-1)\n",
    "    M0_mean = np.mean(Posterior_M0).reshape(1,-1)\n",
    "    BETA_mean = np.mean(Posterior_BETA).reshape(1,-1)\n",
    "    BK_mean = np.mean(Posterior_BK).reshape(1,-1)\n",
    "    \n",
    "    #Calculate the curve from the mean of the parameters\n",
    "    Thermal_Mean_Posterior_parameter_curve = Ising_model_I_vs_T(X_predict,\n",
    "                                                                TN_mean, M0_mean, BETA_mean, BK_mean)\n",
    "    \n",
    "    \n",
    "    #Posterior results are in alphabetical order\n",
    "    TN_best = posterior_results.state.best()[0][3]\n",
    "    M0_best = posterior_results.state.best()[0][2]\n",
    "    BETA_best = posterior_results.state.best()[0][0]\n",
    "    BK_best = posterior_results.state.best()[0][1]\n",
    "    \n",
    "    #Calculate the curve from the BEST parameters\n",
    "    Thermal_best_curve = Ising_model_I_vs_T(X_predict,\n",
    "                                            TN_best, M0_best, BETA_best, BK_best)\n",
    "    \n",
    "    #Calculate the predicted curves from posterior sets of parameters\n",
    "    print('Predicting')\n",
    "    Thermal_CI_curves = Ising_model_I_vs_T(X_predict,\n",
    "                                           Posterior_TN, Posterior_M0, Posterior_BETA, Posterior_BK)\n",
    "        \n",
    "    q = np.array([0.95, 0.05])\n",
    "    I_ci = np.quantile(Thermal_CI_curves, q, axis=1)#.reshape((-1,2))\n",
    "    Thermal_lower_curve = I_ci[1,:].reshape(-1,1)\n",
    "    Thermal_upper_curve = I_ci[0,:].reshape(-1,1)\n",
    "    \n",
    "    Thermal_mean_of_posterior_curves = np.mean(Thermal_CI_curves, axis=1).reshape(-1,1)\n",
    "    Thermal_variance = np.var(Thermal_CI_curves, axis=1).reshape(-1,1)\n",
    "     \n",
    "    dictionary = {'TN Mean':TN_mean, \n",
    "                  'M0 Mean':M0_mean, \n",
    "                  'BETA Mean':BETA_mean, \n",
    "                  'BK Mean':BK_mean, \n",
    "                  'Thermal Mean Posterior Parameter Curve': Thermal_Mean_Posterior_parameter_curve,\n",
    "                  'Thermal Best Parameter Curve':  Thermal_best_curve,\n",
    "                  'Thermal Mean of Posterior Curves': Thermal_mean_of_posterior_curves,\n",
    "                  'Thermal Variance': Thermal_variance,\n",
    "                  'Thermal CI Curves': Thermal_CI_curves,\n",
    "                  'Thermal lower Curve': Thermal_lower_curve,\n",
    "                  'Thermal upper Curve': Thermal_upper_curve}\n",
    "    \n",
    "    return dictionary\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c04e19a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Thermal_inference_second_order_predict(posterior_results, X_predict):\n",
    "    #Extract the Posterior of the parameters\n",
    "    draw = posterior_results.state.draw()\n",
    "      \n",
    "    #Posterior results are in alphabetical order\n",
    "    Posterior_TN = draw.points[:,3]\n",
    "    Posterior_M0 = draw.points[:,2]\n",
    "    Posterior_J = draw.points[:,1]\n",
    "    Posterior_BK = draw.points[:,0]\n",
    "  \n",
    "    #Calcualte the mean of the parameters\n",
    "    TN_mean = np.mean(Posterior_TN).reshape(1,-1)\n",
    "    M0_mean = np.mean(Posterior_M0).reshape(1,-1)\n",
    "    J_mean = np.mean(Posterior_J).reshape(1,-1)\n",
    "    BK_mean = np.mean(Posterior_BK).reshape(1,-1)\n",
    "    \n",
    "    #Calculate the curve from the mean of the parameters\n",
    "    Thermal_Mean_Posterior_parameter_curve = second_order_I_vs_T(X_predict,\n",
    "                                                                TN_mean, M0_mean, J_mean, BK_mean)\n",
    "    \n",
    "    \n",
    "    #Posterior results are in alphabetical order\n",
    "    TN_best = posterior_results.state.best()[0][3]\n",
    "    M0_best = posterior_results.state.best()[0][2]\n",
    "    J_best = posterior_results.state.best()[0][1]\n",
    "    BK_best = posterior_results.state.best()[0][0]\n",
    "    \n",
    "    #Calculate the curve from the BEST parameters\n",
    "    Thermal_best_curve = second_order_I_vs_T(X_predict,\n",
    "                                            TN_best, M0_best, J_best, BK_best)\n",
    "    \n",
    "    #Calcualte all the predictive curves by interating through the posterior samples \n",
    "    print('Predicting')\n",
    "    Thermal_CI_curves = np.empty((X_predict.shape[0],0))\n",
    "    thin_posterior_TN_dist = Posterior_TN[::50]\n",
    "    thin_posterior_M0_dist = Posterior_M0[::50]\n",
    "    thin_posterior_J_dist = Posterior_J[::50]\n",
    "    thin_posterior_BK_dist = Posterior_BK[::50]\n",
    "    for i, _ in enumerate(thin_posterior_TN_dist):\n",
    "        I_interem = second_order_I_vs_T(X_predict,\n",
    "                                        TN=thin_posterior_TN_dist[i].reshape(1,-1), \n",
    "                                        M0=thin_posterior_M0_dist[i].reshape(1,-1),\n",
    "                                        J=thin_posterior_J_dist[i].reshape(1,-1),\n",
    "                                        BK=thin_posterior_BK_dist[i].reshape(1,-1))\n",
    "        Thermal_CI_curves = np.concatenate((Thermal_CI_curves, I_interem), axis=1)\n",
    "        \n",
    "    q = np.array([0.95, 0.05])\n",
    "    I_ci = np.quantile(Thermal_CI_curves, q, axis=1)#.reshape((-1,2))\n",
    "    Thermal_lower_curve = I_ci[1,:].reshape(-1,1)\n",
    "    Thermal_upper_curve = I_ci[0,:].reshape(-1,1)\n",
    "    \n",
    "    Thermal_mean_of_posterior_curves = np.mean(Thermal_CI_curves, axis=1).reshape(-1,1)\n",
    "    Thermal_variance = np.var(Thermal_CI_curves, axis=1).reshape(-1,1)\n",
    "     \n",
    "    dictionary = {'TN Mean':TN_mean, \n",
    "                  'M0 Mean':M0_mean, \n",
    "                  'J Mean':J_mean, \n",
    "                  'BK Mean':BK_mean, \n",
    "                  'Thermal Mean Posterior Parameter Curve': Thermal_Mean_Posterior_parameter_curve,\n",
    "                  'Thermal Best Parameter Curve':  Thermal_best_curve,\n",
    "                  'Thermal Mean of Posterior Curves': Thermal_mean_of_posterior_curves,\n",
    "                  'Thermal Variance': Thermal_variance,\n",
    "                  'Thermal CI Curves': Thermal_CI_curves,\n",
    "                  'Thermal lower Curve': Thermal_lower_curve,\n",
    "                  'Thermal upper Curve': Thermal_upper_curve}\n",
    "    \n",
    "    return dictionary\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "9abdd9f0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_thermal_dataframe(dataframe, index, posterior_model, posterior_results, posterior_predictions):\n",
    "    #Cycle Identifying\n",
    "    dataframe.loc[index, 'Thermal Cycle'] = index\n",
    "    \n",
    "    #Likelihood:\n",
    "    dataframe.loc[index, 'Likelihood'] = posterior_results.state.best()[1]\n",
    "    \n",
    "    #Input data\n",
    "    dataframe.loc[index, 'Measured Temperatures'] = posterior_model.fitness.x\n",
    "    dataframe.loc[index, 'Measured Max Intensities'] = posterior_model.fitness.y\n",
    "    dataframe.loc[index, 'Measured Max Intensities Error'] = posterior_model.fitness.dy\n",
    "    \n",
    "    #Posterior Parameters\n",
    "    draw = posterior_results.state.draw()\n",
    "    \n",
    "    dataframe.loc[index, 'Posterior Tn'] = draw.points[:,3].reshape(1,-1)\n",
    "    dataframe.loc[index, 'Posterior M0'] = draw.points[:,2].reshape(1,-1)\n",
    "    dataframe.loc[index, 'Posterior J'] = draw.points[:,1].reshape(1,-1)\n",
    "    dataframe.loc[index, 'Posterior BK'] = draw.points[:,0].reshape(1,-1)\n",
    "    \n",
    "    dataframe.loc[index, 'Best Tn'] = posterior_results.state.best()[0][3]\n",
    "    dataframe.loc[index, 'Best M0'] = posterior_results.state.best()[0][2]\n",
    "    dataframe.loc[index, 'Best J'] = posterior_results.state.best()[0][1]\n",
    "    dataframe.loc[index, 'Best BK'] = posterior_results.state.best()[0][0]\n",
    "    \n",
    "    dataframe.loc[index, 'Tn Std'] = posterior_results.dx[3]\n",
    "    dataframe.loc[index, 'M0 Std'] = posterior_results.dx[2]\n",
    "    dataframe.loc[index, 'J Std'] = posterior_results.dx[1]\n",
    "    dataframe.loc[index, 'BK Std'] = posterior_results.dx[0]\n",
    "    \n",
    "    #Predictions\n",
    "    dataframe.loc[index, 'Mean Parameter Curve'] = posterior_predictions['Thermal Mean Posterior Parameter Curve']\n",
    "    dataframe.loc[index, 'Best Parameters Curve'] = posterior_predictions['Thermal Best Parameter Curve']\n",
    "    dataframe.loc[index, 'Mean of Posterior Curves'] = posterior_predictions['Thermal Mean of Posterior Curves']\n",
    "    dataframe.loc[index, 'Variance'] = posterior_predictions['Thermal Variance']\n",
    "    dataframe.loc[index, 'Confidence Interval Curves'] = posterior_predictions['Thermal CI Curves']\n",
    "    dataframe.loc[index, 'Lower Bound'] = posterior_predictions['Thermal lower Curve']\n",
    "    dataframe.loc[index, 'Upper Bound'] = posterior_predictions['Thermal upper Curve']\n",
    "    \n",
    "    #Next sample\n",
    "    dataframe.loc[index, 'Next Temperature'] = posterior_predictions['Thermal Next Temperature']\n",
    "    dataframe.loc[index, 'Bravery Factor'] = posterior_predictions['Bravery Factor']\n",
    "    dataframe.loc[index, 'Above TN'] = posterior_predictions['Above TN']\n",
    "        \n",
    "    return dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "6f6ab046",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_thermal_inference(temperatures, posterior_predictions, posterior_model, dataframe, Hist = True, Name= None):\n",
    "    Mean_of_curves = posterior_predictions['Thermal Mean of Posterior Curves']\n",
    "    Best_parameter_curve = posterior_predictions['Thermal Best Parameter Curve']\n",
    "    Parameter_mean = posterior_predictions['Thermal Mean Posterior Parameter Curve']\n",
    "    Upper = posterior_predictions['Thermal upper Curve']\n",
    "    Lower = posterior_predictions['Thermal lower Curve']\n",
    "    Next = posterior_predictions['Thermal Next Temperature']\n",
    "    \n",
    "    Measured_Temperatures = posterior_model.fitness.x\n",
    "    Measured_I            = posterior_model.fitness.y\n",
    "    Measured_Ierror       = posterior_model.fitness.dy\n",
    "    \n",
    "    plt.figure(figsize=(10,10))\n",
    "    plt.title('Thermal Predictions')\n",
    "    plt.errorbar(Measured_Temperatures.reshape(-1), Measured_I.reshape(-1), yerr= Measured_Ierror.reshape(-1), fmt = 'bo', label = 'Measured Data')\n",
    "    plt.fill_between(temperatures.flatten(),Upper.flatten(), Lower.flatten(), alpha=0.7,color=\"#7A68A6\", label = 'Cofidence Interval')\n",
    "    plt.plot(temperatures, Mean_of_curves, 'r-', linewidth=7.0, label = 'Mean of Posterior Curves')\n",
    "    plt.plot(temperatures, Best_parameter_curve, 'k--', label = 'Best Parameters')\n",
    "#     plt.plot(temperatures, Parameter_mean, 'k--', label = 'Mean of Parameters')\n",
    "    plt.vlines(Next, ymin =np.min(Lower) , ymax = np.max(Upper),colors= 'g', label='Next Sample')\n",
    "    plt.xlabel('Temperature (K)')\n",
    "    plt.ylabel('Intensity (arb. units)')\n",
    "    plt.legend()\n",
    "    if Name != None:\n",
    "        plt.savefig(f\"{Name}.svg\")\n",
    "    plt.show()\n",
    "    \n",
    "    if Hist == True:\n",
    "        \n",
    "        #The posterior distributions are not all the same size, so draw a set number of sampels from them. \n",
    "        hist_size=10000\n",
    "        \n",
    "        posterior_TN_distributions = np.empty((hist_size, 0))\n",
    "        posterior_M0_distributions = np.empty((hist_size, 0))\n",
    "        posterior_J_distributions = np.empty((hist_size, 0))\n",
    "        posterior_BK_distributions = np.empty((hist_size, 0))\n",
    "        \n",
    "        for i, _ in enumerate(dataframe.index):\n",
    "            temp_TN = np.random.choice(dataframe['Posterior Tn'][i].flatten(), hist_size).reshape(-1,1)\n",
    "            temp_M0 = np.random.choice(dataframe['Posterior M0'][i].flatten(), hist_size).reshape(-1,1)\n",
    "            temp_J = np.random.choice(dataframe['Posterior J'][i].flatten(), hist_size).reshape(-1,1)\n",
    "            temp_BK = np.random.choice(dataframe['Posterior BK'][i].flatten(), hist_size).reshape(-1,1)\n",
    "\n",
    "            posterior_TN_distributions = np.concatenate((posterior_TN_distributions, temp_TN), axis = 1)\n",
    "            posterior_M0_distributions = np.concatenate((posterior_M0_distributions, temp_M0), axis = 1)\n",
    "            posterior_J_distributions = np.concatenate((posterior_J_distributions, temp_J), axis = 1)\n",
    "            posterior_BK_distributions = np.concatenate((posterior_BK_distributions, temp_BK), axis = 1)\n",
    "\n",
    "        a = np.linspace(1,posterior_TN_distributions.shape[1],posterior_TN_distributions.shape[1])\n",
    "        A = np.matlib.repmat(a, posterior_TN_distributions.shape[0], 1)\n",
    "\n",
    "        h0, Aedges, TN_edges = np.histogram2d(A.flatten(), posterior_TN_distributions.flatten(), bins=[A.shape[1], 256])\n",
    "        h1, Aedges, M0_edges = np.histogram2d(A.flatten(), posterior_M0_distributions.flatten(), bins=[A.shape[1], 256])\n",
    "        h2, Aedges, J_edges = np.histogram2d(A.flatten(), posterior_J_distributions.flatten(), bins=[A.shape[1], 256])\n",
    "        h3, Aedges, BK_edges = np.histogram2d(A.flatten(), posterior_BK_distributions.flatten(), bins=[A.shape[1], 256])\n",
    "        \n",
    "        cmap = plt.cm.plasma.copy()\n",
    "        cmap.set_bad(cmap(0))\n",
    "        \n",
    "        plt.figure(figsize=(10,10))\n",
    "        \n",
    "        plt.subplot(2,2,1)\n",
    "        plt.pcolormesh(Aedges, TN_edges, h0.T, cmap=cmap,\n",
    "                                 rasterized=False, norm=LogNorm(vmax=np.max(h0)))\n",
    "        # plt.colorbar(label=\"# points\", pad=0)\n",
    "        plt.colorbar(label=\"# points\")\n",
    "        plt.xticks(np.arange(min(a), max(a)+1, 1.0))\n",
    "        plt.title(\"TN\")\n",
    "        \n",
    "        plt.subplot(2,2,2)\n",
    "        plt.pcolormesh(Aedges, M0_edges, h1.T, cmap=cmap,\n",
    "                                 rasterized=False, norm=LogNorm(vmax=np.max(h1)))\n",
    "        # plt.colorbar(label=\"# points\", pad=0)\n",
    "        plt.colorbar(label=\"# points\")\n",
    "        plt.xticks(np.arange(min(a), max(a)+1, 1.0))\n",
    "        plt.title(\"M0\")\n",
    "        \n",
    "        plt.subplot(2,2,3)\n",
    "        plt.pcolormesh(Aedges, J_edges, h2.T, cmap=cmap,\n",
    "                                 rasterized=False, norm=LogNorm(vmax=np.max(h2)))\n",
    "        # plt.colorbar(label=\"# points\", pad=0)\n",
    "        plt.colorbar(label=\"# points\")\n",
    "        plt.xticks(np.arange(min(a), max(a)+1, 1.0))\n",
    "        plt.title(\"J\")\n",
    "\n",
    "        plt.subplot(2,2,4)\n",
    "        plt.pcolormesh(Aedges, BK_edges, h3.T, cmap=cmap,\n",
    "                                 rasterized=False, norm=LogNorm(vmax=np.max(h3)))\n",
    "        # plt.colorbar(label=\"# points\", pad=0)\n",
    "        plt.colorbar(label=\"# points\")\n",
    "        plt.xticks(np.arange(min(a), max(a)+1, 1.0))\n",
    "        plt.title(\"BK\")\n",
    "\n",
    "        plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "2be05470",
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_first_order_dataframe(dataframe, index, posterior_model, posterior_results, posterior_predictions):\n",
    "    #Cycle Identifying\n",
    "    dataframe.loc[index, 'Thermal Cycle'] = index\n",
    "    \n",
    "    #Likelihood:\n",
    "    dataframe.loc[index, 'Likelihood'] = posterior_results.state.best()[1]\n",
    "    \n",
    "    #Input data\n",
    "    dataframe.loc[index, 'Measured Temperatures'] = posterior_model.fitness.x\n",
    "    dataframe.loc[index, 'Measured Max Intensities'] = posterior_model.fitness.y\n",
    "    \n",
    "    #Posterior Parameters\n",
    "    draw = posterior_results.state.draw()\n",
    "    \n",
    "    dataframe.loc[index, 'Posterior Tn'] = draw.points[:,3].reshape(1,-1)\n",
    "    dataframe.loc[index, 'Posterior Sigma'] = draw.points[:,2].reshape(1,-1)\n",
    "    dataframe.loc[index, 'Posterior K'] = draw.points[:,1].reshape(1,-1)\n",
    "    dataframe.loc[index, 'Posterior BK'] = draw.points[:,0].reshape(1,-1)\n",
    "    \n",
    "    dataframe.loc[index, 'Best Tn'] = posterior_results.state.best()[0][3]\n",
    "    dataframe.loc[index, 'Best Sigma'] = posterior_results.state.best()[0][2]\n",
    "    dataframe.loc[index, 'Best K'] = posterior_results.state.best()[0][1]\n",
    "    dataframe.loc[index, 'Best BK'] = posterior_results.state.best()[0][0]\n",
    "    \n",
    "    dataframe.loc[index, 'Tn Std'] = posterior_results.dx[3]\n",
    "    dataframe.loc[index, 'Sigma Std'] = posterior_results.dx[2]\n",
    "    dataframe.loc[index, 'K Std'] = posterior_results.dx[1]\n",
    "    dataframe.loc[index, 'BK Std'] = posterior_results.dx[0]\n",
    "    \n",
    "    #Predictions\n",
    "    dataframe.loc[index, 'Mean Parameter Curve'] = posterior_predictions['Thermal Mean Posterior Parameter Curve']\n",
    "    dataframe.loc[index, 'Best Parameters Curve'] = posterior_predictions['Thermal Best Parameter Curve']\n",
    "    dataframe.loc[index, 'Mean of Posterior Curves'] = posterior_predictions['Thermal Mean of Posterior Curves']\n",
    "    dataframe.loc[index, 'Variance'] = posterior_predictions['Thermal Variance']\n",
    "    dataframe.loc[index, 'Confidence Interval Curves'] = posterior_predictions['Thermal CI Curves']\n",
    "    dataframe.loc[index, 'Lower Bound'] = posterior_predictions['Thermal lower Curve']\n",
    "    dataframe.loc[index, 'Upper Bound'] = posterior_predictions['Thermal upper Curve']\n",
    "    \n",
    "    #Next sample\n",
    "    dataframe.loc[index, 'Next Temperature'] = posterior_predictions['Thermal Next Temperature']\n",
    "\n",
    "   \n",
    "    return dataframe"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac9e2bb3",
   "metadata": {},
   "source": [
    "# Build the Inference Loop"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ebb3e9e",
   "metadata": {},
   "source": [
    "## Import the Data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e123ca77",
   "metadata": {},
   "source": [
    "Import the log files generated during the autonomous run"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "0dda8ded",
   "metadata": {},
   "outputs": [],
   "source": [
    "filename = 'Thermal_Outputs_run1_2021-08-02.p'\n",
    "\n",
    "therm_read = pd.read_pickle(filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "4c0a7dfc",
   "metadata": {},
   "outputs": [],
   "source": [
    "Measured_temperatures = therm_read['Measured Temperatures'][therm_read.index[-1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "3f788624",
   "metadata": {},
   "outputs": [],
   "source": [
    "Measured_tempature_dependent_Intensities = therm_read['Measured Max Intensities'][therm_read.index[-1]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "de7aaf9d",
   "metadata": {},
   "outputs": [],
   "source": [
    "T2 = therm_read['Temperatures'][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "ae35e68f",
   "metadata": {},
   "outputs": [],
   "source": [
    "filename = 'Isothermal_Outputs_run1_2021-08-02.p'\n",
    "\n",
    "iso_read = pd.read_pickle(filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "010e6949",
   "metadata": {},
   "outputs": [],
   "source": [
    "Backgrounds = iso_read['Best Back'].to_numpy().reshape(-1,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d3b115d1",
   "metadata": {},
   "source": [
    "Subtract the Isothermal Background from the Magnetic component of the intensity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "36914029",
   "metadata": {},
   "outputs": [],
   "source": [
    "Measured_tempature_dependent_Intensities_minus_back = Measured_tempature_dependent_Intensities - Backgrounds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "b2a5552d",
   "metadata": {},
   "outputs": [],
   "source": [
    "Measured_tempature_dependent_Intensities_minus_back = Measured_tempature_dependent_Intensities_minus_back.astype(np.float64)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "26085d15",
   "metadata": {},
   "outputs": [],
   "source": [
    "max_error = np.sqrt(therm_read['Measured Max Intensities Error'][therm_read.index[-1]][0][0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2dac6ba6",
   "metadata": {},
   "source": [
    "Remove the large datafile from memory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "cec84c9a",
   "metadata": {},
   "outputs": [],
   "source": [
    "del therm_read\n",
    "del iso_read"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "b7a68349",
   "metadata": {},
   "outputs": [],
   "source": [
    "dictionary_for_histograms = None"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5920e1cc",
   "metadata": {},
   "source": [
    "## Model Priors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "459d658a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# ## Define the priors on the Isothermal parameters ########\n",
    "# Magnetic Peak Parameters\n",
    "#Transition Temperature\n",
    "TN_guess = 40.0\n",
    "TN_std = 20\n",
    "TN_limits = (0.001, 70.0)\n",
    "\n",
    "#Background\n",
    "BK_guess = 70.0\n",
    "BK_std = 20.0\n",
    "BK_limits = (0.0, 200.0)\n",
    "\n",
    "#Second Order Scale\n",
    "M0_guess = np.sqrt(Measured_tempature_dependent_Intensities_minus_back[0][0])\n",
    "M0_std = max_error\n",
    "M0_limits = (M0_guess-1.5*M0_std, M0_guess+1.5*M0_std)\n",
    "# M0_limits = (M0_guess-1.5*M0_std, M0_guess+15.0*M0_std)\n",
    "\n",
    "#Total Anglular Momentum\n",
    "J_guess = 1.5\n",
    "J_std = 2.0\n",
    "J_limits = (0.01, 14.0)\n",
    "\n",
    "#First Order transition width\n",
    "Sigma_guess = 4.0\n",
    "Sigma_std = 2.0\n",
    "Sigma_limits = (0.0, 150.0)\n",
    "\n",
    "#First Order Scale\n",
    "K_guess = M0_guess\n",
    "K_std = M0_std\n",
    "K_limits = M0_limits\n",
    "\n",
    "BETA_guess = 0.0826\n",
    "BETA_std = 0.02\n",
    "BETA_limits = (0.0, 1.0)\n",
    "\n",
    "T_iw_guess = 0.00000001\n",
    "T_iw_std = 0.00000001\n",
    "T_iw_limits = (0.0, 0.0000001)\n",
    "\n",
    "#Define the prior distributions\n",
    "TN_dist =  BoundedNormal(TN_guess, TN_std, limits=TN_limits)\n",
    "M0_dist =  BoundedNormal(M0_guess, M0_std, limits=M0_limits)\n",
    "J_dist =  BoundedNormal(J_guess, J_std, limits=J_limits)\n",
    "BK_dist =  BoundedNormal(BK_guess, BK_std, limits=BK_limits)\n",
    "\n",
    "Sigma_dist =  BoundedNormal(Sigma_guess, Sigma_std, limits=Sigma_limits)\n",
    "K_dist =  BoundedNormal(K_guess, K_std, limits=K_limits)\n",
    "BETA_dist = BoundedNormal(BETA_guess, BETA_std, limits=BETA_limits)\n",
    "T_iw_dist = BoundedNormal(T_iw_guess, T_iw_std, limits=T_iw_limits)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "303b58a7",
   "metadata": {},
   "source": [
    "# First Order Fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "48cc7a58",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initial chisq 310499.58(47) constraints=12.1913\n",
      "# steps: 2500, # draws: 100000\n",
      "final chisq 10.21(47) constraints=12.9561\n",
      "BK : 0.846(45)\n",
      "K : 5.161(22)\n",
      "Sigma : 6.04(29)\n",
      "TN : 68.58(16)\n",
      "Loglikelyhood =  -63.98454362545109\n",
      "Predicting\n"
     ]
    },
    {
     "data": {
      "image/png": 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r167MnDmTmJgYt7/8mzZtyq+//ur6RuKrr77KtGnTSExMxGKx8NBDD9G6dWu+/PLLQgOUWZs2bVi2bBkABw4c4P/+7/9o1qzZ+b03Uxu3bt3KwYMHAViyZAmtW7fmjz/+4K677uKaa65h1KhR1K1bl7179xIcHOwKTW3atGHp0qVkZWWRlpbGnXfeya+//nrer3U2VapU4frrr+e5557DarUC8Mcff/Dmm29Sv359SpcuzalTp/jnn3/IzMzk+++/L/BaPXv25NNPPyU6OpqqVasSFRVFrVq1XAHsxx9/JC4ujuzsbDp37kzZsmV58MEH6dmzJ9u3bz/nPj0bjYCJiIh/6trVMTH+xRfh++8dE+YvtfBwuO46R/gqYAK+WadOnRg3bhyPPvqoW3nFihWZMmUKjz32GHa7ncqVKzN9+nRKly5N48aN6dq1KxaLhfbt2xN/HrdWx40bx4QJE1xLXUyaNIlKlSq5LT1xripUqMDEiRMZOnQoWVlZVKlShcmTJ1OpUiWaNWtG9+7dKVGiBC1atKBDhw4cOHCAuXPnMmPGDB599FH27dtH7969yc7Opk+fPrRu3ZrNmzef12sVZsqUKcyYMYOePXsSFhZGiRIlmD59Og0aNADg/vvvp1+/flx22WVceeWVBV6nZcuWpKen06NHD1fZ9OnTeeaZZ3jzzTcJDQ1l1qxZhIaGMnz4cO69917Cw8MpX748U6dOPc+ezZ/FyD1+WURZrVYSEhKIiYm5qHvA8fHxtGzZ8hK2TED96inqV89Qv3qG+tUz1K+e4el+LSy36BakiIiIiJcpgImIiIh4mQKYiIiIiJcpgImIiIh4mQKYiIiIiJcpgOVy/fWOHxERERFPUQATERER8TIFMBERkYuwefNmmjdvTs+ePenRowddu3bl3XffvaBrHThwgLFjx+YpP3jwIDExMfTs2ZNevXrRrVs37rnnHo4cOXKxzb9o27ZtY/r06b5uht/xaAB7+eWXufXWW+nWrRsLFiwAYMOGDcTGxtK5c2dmzZrlyZcXERHxipiYGFatWsXq1av58MMPefvtt/nrr7/O+zqHDh3iwIED+dZVqlSJVatWsXLlSj755BMaNmzItGnTLrbpF+2vv/7ixIkTvm6G3/HYo4i2bNnCpk2bWL16NdnZ2dx66620bduWsWPH8v7773P55Zfz4IMPsn79ejp27OipZoiISDFwfT6Td2+//XYefvhh0tPTufXWW/PU33333dx9990kJSXRr1+/PPX/+c9/uOOOO867LVarleDgYKKiogDHCNHzzz9PRkYGZcuW5dlnn6V69eosWLCAFStWEBQUxFVXXcXEiROZNGkSBw8e5Nlnn+Xpp58+6+u0bt2aF198EYC1a9eyYMECMjIyyMzMZMqUKbRo0YKBAwdSpkwZdu3axUsvvUR8fDyrVq3izJkzhIaGMnPmTOrUqcMNN9xAt27d+PHHHwkJCeHhhx/m7bffZt++fYwaNYpbb72VpKQkJkyYwJEjR7BYLIwYMYKYmBhmz55Neno6r732GkOGDGHatGls2bIFm81Gnz59uPvuu9m8eTPTp0/HbrdTv359evXq5Ro1K1OmDDNnzqRcuXLn3df+zGMjYK1ateK9994jJCSEEydOYLPZSE5OpmbNmlSvXp2QkBBiY2P57LPPPNUEERERr0hISKBnz57ExsZyww030KpVKypVqkRmZibjx49n5syZrFixgnvuuYennnoKm83G66+/zkcffcTy5cvJysri6NGjjB8/npiYmELDV1ZWFp9//jnNmjXDbrezePFi5s2bx+rVq7n//vuZP3++69iGDRvy+eefU716db766ivef/991qxZw/XXX8/ChQtdx1WoUIHly5dTt25d5s+fz9tvv8306dNd15o8eTJ9+/Zl+fLlvPbaa0yYMIGgoCCGDx/ODTfcwH/+8x+WLl0KwIoVK1i2bBlff/01P//8MwCJiYm8++67vPDCC7z66qs888wzLF++nHbt2vHHH39c6j+SIs+jD+MODQ1l9uzZvP3223Tp0oVjx45RsWJFV32lSpU4evRonvOSk5NJTk52Kzufp8NfqIULYdMmx/Nca9WCyZMhLs7jLysiIhfp22+/LbAuMjLyrPUVKlQ4a/25iImJ4f333wcgNTXVFYI6derEgQMH+M9//uM6NjU1leDgYJo3b06/fv248cYbueeee6hcuTKJiYkFvsaxY8fo2bMnAJmZmVx11VWMGDGCoKAgXnnlFdatW8fevXvZsmULQUH/jq9cddVVAJQqVYqZM2fyySefkJiYyPfff0/jxo1dx3Xo0AGAKlWqUKlSJUJCQqhSpYrr7+MNGzawZ88eZs+eDUB2dnae26UbN25k+/btbNq0CYD09HR27NhBvXr1qF27tmtU8MYbb2To0KHcdNNN3HjjjVx77bXn3+l+zqMBDGD48OE88MADPPTQQyQmJmKxWFx1hmG47Tu9++67zJ07162sQoUKzJ49m4SEhItuU35Pml+7tiyTJ9fEag0GYN8+uP9+G3v37qNr15MX/ZrFQX79KhdP/eoZ6lfPKI79unPnTlJSUtzee0xMDN988w0VK1akfPnyTJgwAQC73c7p06eJj4/nvvvuY9euXWzdupXBgwfzyCOPYBhGnmuBY4StTJkyrus47d69m4yMDMaNG0f79u2pV68e1157LV988QXx8fGkpKSwf/9+4uPjOXHiBM899xydO3emdu3aXH311ezbt4/4+HisVis7duzgn3/+4dChQ4Djz/L48eNYrVbi4+PJzMzkv//9L6VKlQLg5MmTpKamkpiYyIkTJ1yv0adPH1q1agU4BlQiIiLYuXMnWVlZrvd15ZVXMmrUKH755ReeffZZWrduTa9evTzy53M2vvy8eiyA7d69m8zMTBo3bkyJEiXo3Lkzn332GcHBwa5jjh8/TqVKlfKcO3jwYHr37u1WZrPZSEpKKvCp4ueqoKef9+0LGRnuZRkZwbz5Zh3Gj7/glys2PP1U+eJK/eoZ6lfPKK79mp2dTVRUlOu922w23n77bdq2bUv37t156aWXMAyDq6++mqVLl/Lxxx/z8ssvExcXx7JlyxgwYABjxozBMAzX35nmfoyPj3f93Zdf//7++++UKFGCiRMnYhgGTz75JJGRkbRs2ZKoqCgaNGhAy5Yt+eKLL2jQoAFPPfUUGRkZPPDAA1x22WW0bNmS8PBwYmJiqFatGhs2bACgZcuWHDx40PW67du35/fff+fhhx/mr7/+4uGHH+brr7/m0KFDHDp0iJYtW9KlSxfWr1/P/fffT2ZmJn379uXZZ5+lQYMGbn1022238eyzz9KtWzdWrlzJ119/7fXPjqc/r1ar9ayDRh4LYAcPHmT27NksWrQIgK+//pr+/fszbdo09u3bR7Vq1VizZg19+/bNc27p0qUpXbq0W5nVaiUpKclTzWX//vMrFxERcXLOAbNYLGRnZ9OwYUMeeOABwsLCePnll5k8eTJWq5VSpUrxwgsvUK5cOe644w769etHiRIlqF27Nn379sVqtZKSksLIkSPPeWmHRo0a0bhxY7p27YrFYqF9+/b5juxce+21LFq0iFtvvRXDMLjmmmvYtWvXOb/H8ePHM2HCBGJjYwGYNm0apUqV4qqrrmLu3LnMmDGDRx99lH379tG7d2+ys7Pp06cPrVu3ZvPmzW7X+u9//8vo0aMJCQkhMjKSSZMmnXM7AoXFMAzDUxefM2cOa9euJTg4mM6dOzNs2DA2btzI888/j9VqpWPHjowZMybf25C5OZOkp0bAatVy3HbMrWZNOMsteclRXP/l62nqV89Qv3qG+tUz1K+e4a0RsIJyi0fngA0bNoxhw4a5lbVt25bVq1d78mUvyOTJMGQIpKf/WxYZ6SgXERERuZS0En6OuDiYPx+cIbVmTce+vgUpIiIil5rHvwXpT+Li4I03HNsX+Y1kERERkQJpBExERETEyxTARERERLxMAUxERETEyzQH7Dw4n/Wq+WEiIkXLwnnfc/KftEt+3bLlShL30HWFHpeamsrMmTP56aefCA4OpnTp0owePZomTZqc9bzZs2ezfPlyBg8ezMqVK1m1alWeY4YPH86SJUuoVq3aBb+P87V582bmzp3rerxSfg4cOMBrr73GlClTPNaOgQMHMnToUFq3bu2x1/AVBTAREfF7J/9Jo3R0CY9ctzB2u50HHniA1q1bs3LlSkJCQti0aRMPPPAAn3zyCWXLli3w3FWrVrFgwQJq167NPffccymb7nGHDh3K8yxIOXcKYLlcqtEtjZaJiBQPmzdv5vDhwwwfPtz1EOw2bdrw/PPPY7fbAZg3bx6rV68mODiYa6+9lpEjR/Lss89y9OhRHnnkEWbOnEmvXr3YsWMHp06dYuTIkRw5coS6deuSlZUFOB5xNG3aNLZs2YLNZqNPnz7cfffdbN68mddff52IiAh2795Nw4YNmTFjBmFhYbzzzjssWrSI4OBgOnXqxMiRI0lKSmLChAkcOXIEi8XCiBEjaNeuXYHvb86cORw9epR9+/bx999/c9ttt/Gf//yHSZMmcfDgQZ599lmefvpp5s+fz9q1a7HZbLRv356RI0fy999/c//991O2bFkiIiI4deoUzz33HDExMdhsNjp16sSKFSvYsmULCxYsICMjg8zMTKZMmUKLFi08/4fnQwpgIiIiF+GPP/6gUaNGrvDl1LFjRwDWr1/PunXr+OijjwgNDWXYsGEsXryYiRMn8sMPPzB//ny324uzZ8/miiuu4I033uCnn35i7dq1ACxduhSAFStWkJmZyX333UdMTAwAv/zyC2vXrqVSpUrcfvvt/PDDD1SoUIEPPviAjz76iBIlSnD//feTkJDAW2+9Rd++fbnxxhs5duwYd955JytXrnQ9ZDs/O3bsYOHChaSkpHDTTTcRFxfH+PHjmTt3Lk8//TTfffcdCQkJLFu2DIvFwsiRI1m9ejUtW7Zk7969vPnmm1SrVo133nmHTz75hJiYGDZt2kSjRo0oW7YsixcvZt68eZQrV45ly5Yxf/585s2bd0n/nIoaBTAREZGLEBQUdNZH5G3atIlu3bpRooTjFmnfvn1ZuXIlcQWs9L1lyxZmzpwJwDXXXEOlSpUA2LhxI9u3b2fTpk0ApKens2PHDurVq0f9+vW57LLLAKhbty6nT59m7969dOrUiaioKADeeecdADZs2MCePXuYPXs24HiY+IEDB2jcuHGB76F169aEhYVRvnx5oqOjSUlJcavfuHEj27Zto0+fPgBkZGRQpUoVWrZsSfny5V0Bs1u3btxxxx08+eSTrFmzhh49ehAUFMQrr7zCunXr2Lt3L1u2bMkTZgORApiIiMhFiImJ4YMPPsAwDLdnG7/44ou0a9fOdRvSLDs7u8DrWSwWzI9pDg4OBhy3IEeOHEnnzp0B+OeffyhZsiS//vqrWwB0nh8SEuLWnqNHj1KiRAnsdjvvvvsu0dHRABw7dozy5cuf9T3md30zm83G4MGDXfPYkpOTCQ4O5uTJk0RERLiOq1ixIrVr12bz5s1s3LiRCRMmkJaWRr9+/ejRowfXXHMNDRs2ZOHChWdtTyAI/Ih5iSxcCJs2wfr1jgd3F4PPhoiInIOrr76a8uXLM3fuXGw2GwDff/89y5cvp169erRp04ZPPvmEjIwMsrOz+eijj2jTpk2B12vbtq3r25Dbtm3jyJEjgGNe2dKlS8nKyiItLY0777yTX3/99aztWr9+PWlpaWRnZzNixAgSEhJo06YNH3zwAQB//fUXsbGxnDlz5rzfd3BwsCtItmnThlWrVrle65FHHuHzzz/P97yePXvywgsv0Lp1a0qUKEFiYiIWi4WHHnqI1q1b8+WXX7r6MZBpBOwcLFzoeFC31erY37fPsQ96VqSISHFnsVh49dVXef755+nevTshISGULVuW+fPnU6FCBTp16sT27dvp27cv2dnZtG/fnrvuuqvA6w0fPpzRo0fTrVs36tSp47oF2b9/f/bt20fv3r3Jzs6mT58+tG7dms2bN+d7nSZNmnDXXXfRv39/7HY7N998M+3ataNu3bpMmDCB2NhYAKZNm3bW+V8FqVu3LikpKYwcOZLp06fz559/cvvtt2Oz2bjuuuvo3bs3f//9d57zbr75Zp5++mmeeOIJABo1akTjxo3p2rUrFouF9u3bEx8ff97t8TcWI/c4YhFltVpJSEggJibmrPfaCxMfH0/Lli3P65xatRyhK7eaNSExMW/5woVw332OwFazJkyeHPhB7UL6VQqnfvUM9atn+LJffb0OmCfp8+oZnu7XwnKLRsDOwf79516u0TIREe/zdUgSOV+aA3YOatQ49/Jx4yA93b0sPd1RLiIiIgIKYOdk8mSIjHQvi4x0lOd2PqNlIiIiUjwpgJ2DuDiYPx+ct3Br1nTs53dL8XxGy0RERKR4UgA7R3Fx0KYNdOzomHhf0Hyu8xktExERkeJJAewSO5/RMhERESme9C1ID4iLgzfecGzrYdwiIiKSm0bAiqjrr3f8iIhI0Xbw4EEaNmzIjz/+6FZ+ww03cPDgwfO+3jfffMOCBQvylBuGwezZs4mNjaVHjx7069eP77777oLbfS5Gjx7N8uXLPfoaxZVGwERERC5SaGgoTz31FKtXr76gVeXNEhIS8i1fu3Ytv//+OytWrCAkJIS9e/cyYMAAPvnkk0Kf5ShFjwLYedDtRBGRoun6d673yHW/vfvbczquUqVKtGvXjhdeeIHnnnsuT/38+fNZu3YtNpuN9u3bM3LkSNatW8e0adNYvXo1R44cYeDAgcyaNYvFixcDUKVKFfr27eu6xvHjx7HZbGRmZhISEkLt2rWZPXs2ISGOv8pnzZrFxo0bOX36NJUqVWLWrFlUqFCBa6+9lhtvvJFt27ZRoUIF+vbty/vvv8+RI0eYOnUqrVq1YuDAgTRq1Iiff/4Zq9XK2LFjad++vdt7WLlyJe+++y52u50mTZrw9NNPX9STaYo73YI00W0/ERG5UKNHj+aHH37Icyvyu+++IyEhgWXLlrFy5UqOHj3K6tWrufHGG2nWrBnz5s1jzJgxjBo1ipYtW9K/f3/69+/vFr4AevXqRWpqKm3btuW+++5j/vz51K5dmzJlyrBv3z727NnD4sWL+fzzz7n88stZvXo1AElJSXTo0IGVK1ditVr56quv+OCDDxg2bBjvvvuu6/qpqamsWLGCmTNnMnr0aDIzM111u3btYunSpSxevJhVq1ZRvnx53nrrLQ/2ZuDTCJiHaLRMRMR7znWkypNKlSrFc88957oV6bRx40a2bdtGnz59AMjIyKBKlSoAjBs3jltvvZUWLVrQrVu3s16/TJkyLF68mB07drBhwwbWrVvHW2+9xbJly6hZsyajRo3iww8/ZO/evfz666/UMC1A2aFDBwCqVq3qev5hlSpVSE5Odh1z++23A9C4cWMqVqzIjh07XHWbN29m3759rmOysrK44oorLrivRAFMRETkkmnfvr3rVqSTzWZj8ODB3HPPPQAkJycTHBwMOEangoOD2bNnD1ar9ay39BYsWEDbtm1p1KgRDRs25J577mHEiBF8/vnntGnThhEjRnD33Xdzyy23EBQUhGEYrnPDwsJc287Xzs1cbrfbXbc2ne+ha9eujB8/HoC0tDRsNtv5dI3koluQRdDChbBpE6xfD7VqOfZFRMQ/OG9FHjt2DIA2bdqwatUq0tLSyM7O5pFHHuHzzz/HZrMxZswYxo0bR6tWrXj55ZcBRxDKzs7Oc92UlBReeukl0tLSAMctwwMHDtC4cWN++uknWrVqxYABA6hVqxbffvvteQekTz/9FIDffvuN5ORkGjRo4Kpr3bo1X375JSdOnMAwDJ555hm325dy/jQCVsQsXAhDhoDV6tjft8+xD1rMVUTEHzhvRd53332AYzmKP//8k9tvvx2bzcZ1111H7969efPNNylfvjydO3emXbt2dO/enc6dO3PNNdcwatQoKlSowMCBA13Xffjhh5k1axY9evQgPDycoKAg4uLiuPbaa6lXrx5Dhw4lNjYWgJiYmPNeAuPAgQP07t0bcEzoN4+INWrUiKFDhzJ48GDsdjuNGzdmiPMvJ7kgFsM8RlmEWa1WEhISiImJuahvXcTHx7vuf+d2/fVgt9lZuug0WCxYLBYsFrBYLAVez2Jx/sfxy0LeYy1BjmsEBwcRGhZMUHAQFouFoCDHj/n6tWo5QlduNWs6HoFUVJ2tX+XCqV89Q/3qGepXz/BGvw4cOJChQ4fSunVrj75OUeLpfi0st2gELIfztp/VauGKmAh6ddnFNS2O5BOnCmZAnuMNw1FmWBw7hoHrvrw5+jqD3r59nfO5CuzbZ/DOnPWuY8kJe5acABeUE/KcpzqD4L/ZLidMuo43//43IFqCLAQFO64bEhxMaFgwYeEhhIaFEB4RQkREKCVLhVO6bCQlIsPOGk5FRESKouvfuZ6UlBTiW8b7rA0KYOS+7Wfh5OkSLFzehLCIENq1Ou7x13cNQhpQvqyVEycj8hxTvmwGdrs9n3MdJ7qyXCHjmfmFP3AEQwzTlQzHpQy7gWE4flyBDQt2u0FYeAhVapSlTsPKZGVqMqaIiL96//33fd2EYkcBDBg3DtLT3csys4L59P3SPP9lLLaQEOzBodhDQrAHm7dDsQWHYA8JdZTn/LaZ9rPDwrGFhpt+R2ALDXPbzg6LwBYWTnZoOP167GHBBw3JzPr33ntYqI1+PfYSEpr/N1d8wTAM7DaD/XuTSPzrOOnp6WSnbadlu7qUiAwr/AIiIiLFmAIYsH9/fjcP4aC9CmUP7fFqW+IsFtoFDWQck/ibqlQNOsS4Mi/TY/O3ZG2NJCsikqzwnN8RkWRHRJIZEUl2eCSZJUqSHV4ip64k1sgo7KGeCUMWi4XgEAuRIY772lnZGWz7aR9//naIW3o1pXrtCh55XRERkUCgAAbUCD7EvuyqecvZ7/W2WAyDQbb3GMR7jgI7kJTzcwGywiLIjCxFZmRprCWjsEaWJjMyiszIKKwlS5MZWcpRVjIKa8kynCldjoyoaIyg8xttCwqyUKpMCawZWaxe/DOdusZwRbNqF9ZoEREPcT7tRItli68pgJ06xeTskQzhDdIp6SqOII1HGMsOIBiol1N+GEjNdYlQoFbO9iHgjKnOAoQBzihyGLDmOj8cuNxUn2U619EWqGiqt+WqLwGUy9k+Qq5pYJkZlMjMoOwpR4I7mnO93OdH5Zx3ArBjIaNUGTJKlyOjVDRGdAUofzmnK1YhuXINUirXIKtESfITHhFKcEgQ33yaQEhoEA2aVMn3OBERkeJMAaxMGeKqfQ8HH2AcU9hHDWA/GYzlSRbxJI5wcyLn8KHA8lyXqAkk5mzfDXyZqz4G+C1nuw+wKVd9W2BDznZnICFXfWfgc9OxuVep6AN8lLPdBPgnV/1g4J2c7er8G/CchgJzgEycQc+A1FOOH2AMMAU4CVQGooFywSHUKF2OylXr0qhDL0pXbeS6XkhIMCVKhvH1mt8oW74UFS8rjYhIoDp48CA33ngjd9xxBxMnTnSVb9++nV69evH888+7HkNU1OS3/MTBgwfp0qULdevWBRyPTmrRogUjRoygQoWzTy8ZOHCgJvSfIwUwiwUee4y4J54gjkVsBvbmVDlHksyzqB7FEXjMIk3bTwLOZfOc50eb6scDub9XWdG0PRFH0DGPYplvjk7FMQJnrq9l2p5J3hG2BqbtOTjuaprPj8n5HZJTn5tzlZRgYARwCjhiy+bPk8f45uQxZv++iVsaXkNCpz7sqVaXctEVCQkNJivTxucrf6X//dcSElJ0vkAgIsXTv8sNOdZcnDz50i1wHR0dzffff4/NZnMtYPrpp59Srly5Qs4smipVqsSqVasAx5euXnzxRYYPH84HH3xw1vO2bNnijeYFBAUwgBEjwGLhwPh5tD6zi7MtQ9ehkEvdVEj92R+1Cr0Lqe9fSP3dhdQ/eJa6YByjYQUpDTyfq8wK2A2DEn9uYeWfWxhnCeKeroNo0+1uSpQM4/TJdLb+tI+WbesU0jIREc/x9FNGSpYsSaNGjfjpp59o06YNAD/++CPt2rVzHfPdd98xe/ZssrOzqVatGs899xxly5Zl7dq1LFiwgIyMDDIzM5kyZQotWrRgwYIFrFixgoyMDNq0acPEiRNZvnw5W7ZsYerUqcC/I1gA06dPx263U79+fSZMmMDEiRPZtWsXNpuNBx54gO7du5OZmcm4ceNISEigatWqnDx5stD3ZrFYGDZsGNdeey1//vkn9erV45lnnmHXrl0kJSXRsGFDXnzxRWbMmAHAbbfdxocffsj//vc/Vq1axZkzZwgNDWXmzJnUqaO/C5wUwJz++18Grv4vHN3Hvb1/oFREEEHZWQTZsgnO+R1k+h2caz/IZiPIlkVwdjZBtiyCsrMJzs4kONNKSFYGwZmZOb+thGRaCc4y/84gOCuTkMwMguz+tZ6WeW3f3sDnhp3XPn2Hk/t30OWhKZQoGUb8j7tp0qwaESW0PIWI+EZ+yw2lpzvKL9UoWNeuXV0Pxt62bRsNGzZ0rb34zz//MHPmTN577z3KlCnD4sWLmTFjBs899xyLFy9m3rx5lCtXjmXLljF//nxeeeUVXn/9db7//nt+/fVXli9fztGjR8/6+omJiXzzzTdERUUxY8YMmjRpwgsvvEBqair9+/enadOmfPHFFwCsXbuWxMREevTocU7vLSwsjJo1a7Jnzx5SUlIIDQ1lyZIl2O12Bg8ezPr16xk/fjzvv/8+H374IampqXz11Ve8//77RERE8PLLL7Nw4UKeeuqpi+vkAKIAlsupkAqkRVeEUhf+uKOLYbFlO4JZZgYhWVZCM9IJzUgnxHqGsIw0QnL2QzPSCbWatnOVhZ1JJTQ9lSAj7+KtnlIb+BQYBryWsJEqc0bQdNhMzmRl8lv8fq5pX6+QK4iIeMb+Ar7UXlD5hbjhhht46aWXsNvtrF27lq5du7oecL1161YOHz7MoEGDALDb7ZQpU4agoCBeeeUV1q1bx969e9myZQtBQUEEBwfTvHlz+vXrxxVXXME999xD5cqVz/r6tWvXJioqCoANGzaQkZHBRx85Zginp6eza9cutmzZwh133AFArVq1aN68+Tm/P4vFQkREBNdccw3R0dEsXLiQPXv2kJiYSHqudFuqVClmzpzJJ598QmJiIt9//z2NGzc+59cqDhTAihgjOISsEiEFfsvwvNjthFrTCU9LISw9Oed3CuHpyYSlpRCe7r4fkXKSyOQThJ1Ju+CXDAbm4lg1Y96O/2P1qvns63Y/v25OpFnr2oQWocVkRaT4qFEj/+fs1qhx6V7DeRsyPj6eTZs2MWLECFcAs9lstGjRgnnz5gGO5wSmpaWRlpZGv3796NGjB9dccw0NGzZk4cKFALz66qv8+uuvLFmyhPvvv58ZM2ZgsVgwP8I5K+vfr1VFRPz7FBW73c706dNp0qQJAElJSZQpU4alS5e6nR8Scm4xIDMzk71791KvXj2+/vprZs+ezaBBg+jTpw8nT54k92OlDx8+zMCBA7nrrrvo0KEDFSpUYPv27efTnQFPAczk229h3Sd72fpTJrZse671HAzTWq35PHD7XB+J6HyGY85DvC35XM7iOCinzv2Zjq5nL7r/cmuE85oWLNjCIskIi4SylfNvucX1iq794MwMSiT/Q2TyP5Q4fYLI0ycoffwgpY8eoMzR/ZQ8eeysbzEIeBPYDTT/chHf1L6C7bWuYc+OozSM0bIUIuJ9kyc75nyZB2oiIx3ll1LXrl2ZOXMmMTExbuGmadOmjB8/nr1791K7dm1effVVjh49ysCBA7FYLDz00EMYhsGTTz6JzWbjn3/+IS4ujmXLlnHbbbdhsVjYsWMH1atXZ/fu3RiGwcGDB9mxY0e+7WjTpg2LFi1i0qRJHDt2jF69erF48WLatm3Lxx9/TKdOnTh8+DD/93//V+h7stvtzJkzh6ZNm1KjRg3ee+89unbtSt++fTlw4ACbN2+mbdu2AAQHB5Odnc1vv/1GzZo1ufvuu8nIyGD27Nlcdtlll6aTA4QCWC4xLapTobJjCNccwOyG3fX8RMdzE3OempjzgG0nw3A8RNGe618DznIDsGXbyM62Y7fZsdsN7DnPWwTHsxftNgO74Si32+wYdgOb6TgjZ9vZQMcDvsGw210P+zYMA5vNdN2c13e9LWc5YLc5rmV+f6dCy0H5clgq1HOFPovFERxLnk7ist3bqPXHRur8sZFgW+6FLRwT9p0D203em8rBkW/yW/x+BTAR8QnnPK/77nNMxK9Z89J+C9KpU6dOjBs3jkcffdStvGLFikyZMoXHHnsMu91O5cqVmT59OqVLl6Zx48Z07doVi8VC+/btiY+Pp1y5ctxxxx3069cPu91OTEwMffv2JSQkhI8++oguXbpQu3ZtWrZsmW87hg4dyjPPPEP37t2x2WyMHDmSGjVqcOedd7Jr1y66du1K1apVadCgQb7nHzt2jJ49ewKOANa4cWNefPFFwDHJ/oknnuCTTz4hNDSUFi1acPDgQQBuvPFGevbsydKlS1m0aBG33norhmFwzTXXsGvXrkvVzQHBYuQeNyyirFYrCQkJxMTEEB5+4fOz4uPjC/zAiju73Y7dZpCdbSM7y47NZifTmk2mNZuMM5mcPpnOya07qPn6dOr9+k2+1xgHvA982fQ6vu4/jriHrqNMdGS+x0pe+rx6hvrVM/yhX/1xJXx/6Fd/c/0715OSkkL8sHiPvUZhuUUjYFKgoKAggoJwPAS8RAEHta2DMeQWdg4fQYNXXspT3QHHIq5btn5P5TYJJO5qRNNranqw1SIiBfOn4CWBLcjXDRD/ZwkKIuWeu2DatDx1nXEsBPs60PbLd9nx29/ebp6IiEiRowAml84TT0Dnzm5FFmAI8COQsuc3gn7+mbTU3Gv1i4iIFC8KYHLpWCzw6quQ62vNA3AEsSVA0x+Xc/hA7qdVioiIFC8KYHJp1a377/M9clQBlgEPAXV+38D+eH0TRkREijcFMLn0RoyAIPePVh+gEhBsyyJsxbI8i/aJiIgUJwpgcunVqQOxsW5FNmAesBaoG/81p0+m53emiIhIsaAAJp5xzz1uu0HAdOBV4LL920na9pcvWiUiIlIkKICJZ9x6K5Qr59q1ADcD3+F4SkDWRyt81TIRERGfUwATzwgNhe7d3Yo6AMnANqDkd1/5olUiIiJFggKYeE7Oc8Scrsv5/R1QeccvZKZleL1JIiIiRYECWDF0/fX/Pg/No26+2W1NsOpAHWAvEG5NJ+XLb73QCBERkaJHAUw8JyoK2rZ1K/oTeCln2/aFbkOKiEjxpAAmnnXzzW67oabtoI0bvNsWERGRIkIBTDyrUye33X1AF+AboPSf28Bm80WrREREfEoBTDzr6qshLMy1Ww74AvgBCMtIw7btN1+1TERExGcUwMSzIiKgZUvXbhRQF8dSFADWb77zRatERER8SgGsmFm4EDZtgvXroVYtx77HtWvntnsl4Bz3sm352QsNEBERKVoUwIqRhQthyBCwWh37+/Y59j0ewq65xm33SmAXcAYI2varh19cRESk6FEAK0bGjYP0XM/ATk93lHtUixZuu62AjsA/QIldf0JmpocbICIiUrQogBUj+/efX/klU7euY02wHN2AdUBVICg7C/74w8MNEBERKVoUwIqRGjXOr/ySCQqC5s0LrDa2bSuwTkREJBApgBUjkydDZKR7WWSko9zjmjZ1240FBuRsZ/+qACYiIsWLAlgxEhcH8+dDeLhjv2ZNx35cnBdePCbGbTeIf78JaddaYCIiUsyEFH6IBJK4OHjjDcf2t9968YVzBbAGwOeADQjarjlgIiJSvGgETLzjiivcdhsCVhyPJgo9dBBSUnzRKhEREZ9QABPviI6GatVcuw1zfu90FuzciYiISHGhACbe07ixa7MhMBio4CxQABMRkWJEc8CKIa/O/TJr0AC+/BKASsA75rodO3zQIBEREd/waACbO3cua9euBaBjx448+eSTjBkzhvj4eEqUKAHA0KFDufnmmz3ZDCkqGjRw2zWAVBwP6Lbv2KHhWBERKTY8FsA2bNjADz/8wIoVK7BYLNx///18+eWXJCQk8L///Y9KlSp56qWlqMoVwPoCicD/AfY/FcBERKT48NjfeRUrVmT06NGEhYURGhpK3bp1OXToEIcOHWLs2LHExsYye/Zs7Ha7p5ogRU2uAFYV2I1jJCzor11gGL5olYiIiNd5bASsfv36ru3ExETWrl3LwoUL2bJlC08//TRRUVE8+OCDLFu2jNtvv93t3OTkZJKTk93KbDabp5oq3lKzJoSFuR6+XQdIxvFQ7vKpqZCUBBUr+rKFIiIiXmExDM8OO+zatYsHH3yQYcOG0bt3b7e6L7/8kpUrV/LKK6+4lc+ZM4e5c+e6lVWoUIHZs2d7sqniBU369CEi5+nfy3HchvwFaAZsf+cd0nMt2CoiInKpDdkwBID57eZ7/LViYmIIdz6CxsSjk/Dj4+MZPnw4Y8eOpVu3buzYsYPExERuueUWAAzDICQkbxMGDx6cJ6zZbDaSkpIKfCPn06aWLVte8PmSv3Pu18aNISeAOVcFO4gjgDUODwf92bjR59Uz1K+eoX71DPXrpRf1WxQpKSke7Ver1UpCQkKB9R4LYIcPH+aRRx5h1qxZtG3bFnAErilTptCmTRsiIyNZsmRJnqAFULp0aUqXLu1WZrVaSUpK8lRzxVtq13Zt1gWewnErEoC9e33QIBEREe/zWAB76623sFqtTJ061VXWv39/hgwZwoABA8jOzqZz5850797dU02QoqiOK25RHphortuzx9utERER8QmPBbDx48czfvz4fOvi4uI89bJS1JlGwABOAOlAdcDYuxeLL9okIiLiZVoJX7zLNAIGEAtEAl8B7NEtSBERKR609qV4V61abrtVcUzCB+DQ31oLTEREigUFMPGusmUh5zFU4Pgm5EEci7FarFY4ccJXLRMREfEaBTDxLosFqlVz7VYD0oDTzoKDB/M5SUREJLAogIn3Va3q2jSvBebYUAATEZHApwAm3mcaAWsDvA5UdhYogImISDGgb0GK95kCWE1giLlOAUxERIoBjYCJ95kCGMCvwE7njgKYiIgUAwpg4n25AlhXYJpzRwFMRESKAQUw8b5cAcy5FAUAf//t7daIiIh4nQKYeN9ZAphx4IAWYxURkYCnACbeV7EihIa6di8DjuZsW9LSIDnZJ80SERHxFgUw8bjrr3f8uAQFQZUqrt1KOB7Kne0s0DwwEREJcApg4hum25ADgDXmOgUwEREJcFoHTHzDFMAa5fy4KICJiEiA0wiY+IYpgCUDqwHX9x8VwEREJMApgIlvmALYIaAnsN5ZoKUoREQkwCmAiUctXAibNsH69VCrlmMfgMsucx1TKef3MWfBsWOIiIgEMs0BE49ZuBCGDAGr1bG/b59jHyDu8kqu48ri+CAqgImISHGhETDxmHHjID3dvSw93VFO5cquMguOUTDnWmAKYCIiEugUwMRj9u8/S3mlSm5llTGNgB09ioiISCDTLUjxmBo1HLcd8yunfHnHgqx2OwBvAlHOA1JTHUNlkZFeaqmIiIh3aQRMPGby5LwZKjLSUU5QkOORRDlaAPXNB+o2pIiIBDAFMPGYuDiYPx/Cwx37NWs69uPicg4wzQPbBswDXI/hVgATEZEApluQ4lFxcfDGG47tb7/NVWmaB/Y58CQQR86tSAUwEREJYBoBE98xBbA8a4FpIr6IiAQwBTDxHdMtSOeW1gITEZHiQAFMfCefETCtBSYiIsWB5oCJx+WZ++VkGgHTLUgRESlOFMDEd0wjYJcDvwM1nAUaARMRkQCmACa+YwpgwcAV5jqNgImISADTHDDxHdMtSIB3gGXOHY2AiYhIAFMAE9/J9TzIV4C3nTtJSWCzebtFIiIiXqEAJr4TEQGlS7t2ywEnnDt2O5w4kd9ZIiIifk8BTHzLNApWHvjHXKfbkCIiEqAUwMS3TPPA3EbAQBPxRUQkYCmAiW9VrOjaLA+cAlwzv5KSvN8eERERL1AAE98qX961+QSOAOb6UP7zT97jRUREAoDWARPfMgWwqNx1moQvIiIBSiNg4lumALYHeBLY7SxQABMRkQClACa+Va6ca/M4MB3401mgW5AiIhKgFMDEt0wjYM4tV+zSCJiIiAQoBTDxLdMImHPLFbsUwEREJEApgIlvmUbAogELphEw3YIUEZEApQAmvmUKYEFAWSDZWaARMBERCVBahkJ8y3QLEuAwEObcOXnS8UzIIP07QUREAov+ZhPfCg+HkiVdu2HmOrsdTp/2epNEREQ8TQFMfM80CvY68JS5TrchRUQkACmAie+Z5oH9ACw012kivoiIBCAFMPE9UwArh+lbkKARMBERCUgKYOJ7pluQ5YHTQLazQAFMREQCkAKY+F6uETCAk84C3YIUEZEApAAmvmcaAauAI4RpLTAREQlkCmDie6YRsP44HkVU11mgETAREQlACmDie6YAlodGwEREJAApgInvmW5BHgP6AV87CxTAREQkACmAie/lGgH7CPjTuaNbkCIiEoAUwMT3TAGsTM7vU84CjYCJiEgAUgAT3zPdggwHSqAAJiIigU0BTHyvbFm33WhMASw5GbKzERERCSQKYOJ7ISFQurRrtxFQylx/+rS3WyQiIuJRIb5ugAjgGAVLdiy/ui533alTZ1+qQkRExM9oBEyKhujogutOnfJWK0RERLxCAUyKBlMAm4ZjRXwXBTAREQkwCmBSNJgC2B5y3YZUABMRkQCjACZFgymAReP4FqThLFAAExGRAKMAJkVDrgCWBWQ4CxTAREQkwCiASdGQK4CBaS0wBTAREQkwCmBSNJgCWHXgahyjYIACmIiIBBytAyZFgymAdcv5cVEAExGRAKMRMCkatA6YiIgUIwpgUjSYAth+oCWwxlmgACYiIgFGAUyKBlMACwX+DzjoLFAAExGRAKMAJkWDvgUpIiLFiAKYFA2mABYBhKEAJiIigcujAWzu3Ll069aNbt26MW3aNAA2bNhAbGwsnTt3ZtasWZ58efEnpUuDxQKABSiDKYClpkJ2tm/aJSIi4gEeC2AbNmzghx9+YMWKFaxcuZLff/+dNWvWMHbsWF599VU+/fRTEhISWL9+vaeaIP4kKMgRwnLcBNQx158+7e0WiYiIeIzH1gGrWLEio0ePJiwsDIC6deuSmJhIzZo1qV69OgCxsbF89tlndOzY0e3c5ORkkpOT3cpsNpunmipFRXS0K2h9kLvu1CkoX97LDRIREfEMjwWw+vXru7YTExNZu3Ytd911FxUrVnSVV6pUiaNHj+Y5991332Xu3LluZRUqVGD27NkkJCRcdNvi4+Mv+hqS18X2a+PwcCILqNu+cSPpxXQumD6vnqF+9Qz1q2eoXy+tlJQUwLf96vGV8Hft2sWDDz7Ik08+SXBwMImJia46wzCw5Mz7MRs8eDC9e/d2K7PZbCQlJRETE0N4ePgFtyc+Pp6WLVte8PmSv0vSr5dfDjt3AvA48AvwbU5V48svh2L456bPq2eoXz1D/eoZ6tdLL+q3KFJSUjzar1ar9ayDRh4NYPHx8QwfPpyxY8fSrVs3tmzZwvHjx131x48fp1KlSnnOK126NKVN84HA8UaSkpI82VzxNdM3IdOAnea6Yjr6JSIigcljk/APHz7MI488wowZM+jWzfFkv6ZNm7J371727duHzWZjzZo1dOjQwVNNEH9jCmBu34IEBTAREQkoHhsBe+utt7BarUydOtVV1r9/f6ZOncqwYcOwWq107NiRLl26eKoJ4m9yLcZ6BsjEsSaYApiIiAQSjwWw8ePHM378+HzrVq9e7amXFX9mCmDOG9ApQHlQABMRkYCilfCl6DAFsMbA7YDhLFAAExGRAOLxb0GKnDNTALsp58dFAUxERAKIRsCk6DAFsDwUwEREJIAogEnRUaaMa3MrUBb41Flw8qQPGiQiIuIZCmBSdJgCWASOZShcT4DMWbVYREQkECiASdFhWnzXueV6ImiuZ4OKiIj4MwUwKTrOFsBOn859tIiIiN9SAJOiw3QLMhLHh9NtBMww8jlJRETE/yiASdERHg5hYQBYgAeAps46mw3OnPFRw0RERC4trQMmRUvp0pDz0PV5ueuSkyEy0utNEhERudQ0AiZFi2keGIDNvKOJ+CIiEiAUwKRoMc0D6wi4PapdE/FFRCRAKIBJ0WIaAYvENAkfNAImIiIBQwFMipZcS1EogImISCBSAJOiRQFMRESKAQUwKVpMc8DyBDDNARMRkQChZSikaDGNgN0AhAIGjnXBNAImIiKBQgFMihZTAOuW8+OiACYiIgHirAEsMzOTJUuW8MUXX7B3716Cg4OpU6cOXbp0oXfv3oTlrFoucsmYApgNxy3IKHI+qApgIiISIAqcA7Zlyxb69u3L7t27GTRoEG+88QZvvvkmgwYNYseOHfTt25eNGzd6s61SHJjmgC0HygF/OgsUwEREJEAUOAL2zTffsGjRIkqVKuVWXr9+fTp16kRqaipz586lbdu2Hm+kFCO5vgUJpon4moQvIiIBosAANmrUqLOeWKpUKUaPHn3JGyTF3NkCmEbAREQkQBS6DMXu3bv58MMPMQyDxx57jJtuuolNmzZ5o21SHCmAiYhIMVBoAHv66acJDw/n22+/5ejRo0yePJlZs2Z5o21SHOVaBwwgxVmgACYiIgGi0ABmtVrp0aMHP/zwA127dqV169ZkZWV5o21SHJlGwMoDzwDNnAWaAyYiIgGi0ACWmZlJUlIS3377Le3atSMpKQmr1eqNtklxlOth3E8DLZ0FyclgGD5olIiIyKVVaAC744476NSpEy1btqRevXr069ePwYMHe6NtUhyFh4NpfbnDwDHnjs0GZ874olUiIiKXVKEr4d94443079+foCBHVluxYgUnTpzweMOkGCtTBo4fB+AaoAvwprMuORkiI33UMBERkUujwBGwU6dOcerUKR544AFSUlJc+zabjaFDh3qzjVLcmG5DRpHrgdyaiC8iIgGgwBGwESNG8OOPPwLQunXrf08ICeGWW27xfMuk+Mq1FIVb5NJEfBERCQAFBrC33noLgDFjxvD88897rUEiuUfAUsx1GgETEZEAUGAA2717N3Xr1uWuu+7i999/z1PfpEkTjzZMijHTWmBRmCbhgwKYiIgEhAID2LRp03j99dcZNmxYnjqLxcLXX3/t0YZJMWYaAXsAcLvpqAAmIiIBoMAA9vrrrwOwbt06rzVGBHALYLfmrtMcMBERCQCFLkORlJTE4sWLOXXqlFv5+PHjPdUmKe5MAew4cBBo7izQCJiIiASAQgPYE088QYkSJbjiiiuwWCzeaJMUd1FRrs15wAQgEwgFSEnJ/xwRERE/UmgAO3r0KGvXrvVGW0QcTAHMuZUClAMFMBERCQiFPoqoSpUqpKene6MtIg4FBDDHhgKYiIj4v0JHwCpVqkSvXr1o1aoVERERrnLNAROPySeApToLFMBERCQAFBrAqlatStWqVb3RFhEHjYCJiEiAKzSA6bmP4nWmANYUeA+o4yxQABMRkQBQaACLjY3Nt/zjjz++5I0RAdwCWBVgoLlOAUxERAJAoQHsqaeecm1nZWXxySefUL16dY82Soo5UwDLBLYAtYGqoAAmIiIBodAA1qpVK7f9du3a0b9/f/7zn/94rFFSzJkC2CngOmAu8AgogImISEAodBmK3E6ePMmxY8cKP1DkQp1tEn5qKhiGt1skIiJySZ33HLBDhw5xxx13eKxBIoSGQng4WK1EAMGYlqGw2yE9HUqW9F37RERELtJ5zQGzWCyUK1eOunXrerRRIkRFgdWKBSiFaQQMHLchFcBERMSPnfccMBGviIqCpCTHJvkEsMsu80WrRERELolCA5iIT5jmgb0FVDbXaSK+iIj4OQUwKZpMAaxz7joFMBER8XPn/S1IEa8wBbCfgW/MdQpgIiLi5y4ogM2ZM+dSt0PEnSmATQIeNdcpgImIiJ+7oABmaB0m8bRca4GlmusUwERExM9dUAAbPnz4pW6HiDtTAMt3GQoRERE/VugkfLvdztKlS9mwYQMhISF06NCBXr16eaFpUqzlGgFTABMRkUBSaACbOnUqf/75Jz169MAwDJYuXUpiYiKPPfaYF5onxVauAGYFsoBQUAATERG/V2gA27BhAytXriQkxHFojx496NOnjwKYeJYpgA0EOmG6X64AJiIifq7QAFayZElsNpsrgFksFiIjIz3eMCnmTAGsVs6PiwKYiIj4uQID2IIFCwCoUKECcXFx9OzZk6CgID799FPq1KnjtQZKMWUKYH8D64BbgfKgACYiIn6vwAC2c+dOAEqXLk3p0qX5448/AKhRo4Z3WibFmymAbQMGAZtQABMRkcBQYAB7/vnnAZg5cyYjRozwWoNEgDzLUIDpm5AKYCIi4ucKXQfs22+/9UIzRHIpVcq16YxiCmAiIhIoCp2EX61aNe69915atGhByZIlXeX33HOPRxsmxVyuZShAAUxERAJHoQEsOjoagL///tvTbRH5lwKYiIgEsEIDmHMumIhXmW5BlgfigZrOgvR0sNkgONgHDRMREbl4hQawX375hfnz55Oeno5hGNjtdg4ePKi5YeJZwcEQGQnp6SxmAOOYwn5qUIP9TGYscampUKaMr1spIiJyQQqdhD9+/HiaN29OamoqsbGxlCpVis6dO3ujbVLcRUWxkAEM4Q32UQuDIPZRiyG8wcL3sn3dOhERkQtWaACzWCwMGTKEVq1aUadOHV566SV+/PFHb7RNiruoKMYxhXRKuhWnU5Jxz0cVcJKIiEjRV2gAc37zsUaNGuzatYuIiAiCggo9TeTiRUWxn/wX/t1/JNTLjREREbl0Cp0DdtVVV/HYY4/x6KOP8uCDD5KYmOh6LqSIR0VFUYP97HN/EiQANSpmACW83iQREZFLodChrLFjx3L33XdTu3Ztxo4di91uZ+bMmd5omxR3UVFMZiyRpLkVR5LG5DsTfNQoERGRi1dgANuwYQPgmAPWrFkzAK6//nrGjh3rehj3Dz/84PkWSvEVFUUci5jPA5QgEbBTk0Tm8wBxLf70detEREQu2FkD2MMPP8z69evJzv73G2eZmZl8//33PPjgg5qML56VsxhrHIvYTW0OE0witYljkRZjFRERv1bgZK4nnniCrVu3MmfOHB577DEqVaqE3W4nKSmJq6++mocffpjmzZt7s61S3JhWw788d50CmIiI+LGzzqZv2rQpb775JikpKezbtw+LxUKNGjWIijq3JQBSU1Pp378/8+bNo1q1aowZM4b4+HhKlHBMnh46dCg333zzxb8LCUymz9n3wHpgvLNAAUxERPzYOX2dMSoqipiYmPO68NatWxk/fjyJiYmusoSEBP73v/9RqVKl87qWFFOmAPYtMAEYBYSCApiIiPg1j60nsXTpUp5++mmefPJJAM6cOcOhQ4cYO3YsR48e5eabb2bo0KH5rimWnJxMcnKyW5nNZvNUU6WoyueB3KlAWVAAExERv+axADZ58mS3/aSkJNq0acPTTz9NVFQUDz74IMuWLeP222/Pc+67777L3Llz3coqVKjA7NmzSUi4+OUH4uPjL/oaktel7teyx49TJ2fbGcBScASwk/v3s6eY/Dnq8+oZ6lfPUL96hvr10krJ+Ue8L/u10AC2bt06OnXqhMViuagXql69Oq+88oprf+DAgaxcuTLfADZ48GB69+7tVmaz2UhKSiImJobw8PALbkd8fDwtW7a84PMlfx7p18OHXZvmAAZQNiSkWPw56vPqGepXz1C/eob69dKL+i2KlJQUj/ar1Wo966BRoQuxvv/++9x44428+uqrHD9+/IIbsmPHDj7//HPXvmEYBa6oX7p0aapVq+b2c9lll13wa4ufMt2CLJXzO9VZoFuQIiLixwoNYAsWLOCdd94hPT2d22+/nUcffZSNGzee9wsZhsGUKVM4ffo0WVlZLFmyRN+AlLMzBbAbgZPA1c4CBTAREfFj5/RU7Ro1avD4448zevRoEhIS+O9//0tsbCzbtm075xdq1KgRQ4YMYcCAAXTr1o3GjRvTvXv3C264FAOmABYORAPBzgIFMBER8WOFzgHbt28fS5cuZdWqVTRs2JCxY8fSqVMntm7dymOPPca6devOer65Pi4ujri4uItvtRQPpgB2EpgK9AFagwKYiIj4tUID2G233Ubv3r353//+R61atVzlzZs3p1WrVp5smxR3pgCWCUwDaqIAJiIi/q/QW5BPPfUUY8aMcQtfK1euBGDq1KmeapcIREZCzjpxzkn4rtiVmen4ERER8UMFjoCtW7eO7OxsXn75ZSIiIjAMA4Ds7GzmzJlDr169vNVGKa4sFihVCpKTicTxrwW3ca+UFChf3jdtExERuQgFBrDt27ezadMmTpw4wXvvvffvCSEh3H333d5om4jjNmRyMhYco2Cp5rrUVAUwERHxSwUGsEceeYRHHnmEhQsXauK8+E6utcDSzHWaByYiIn6qwAC2atUqevbsidVqZcGCBXnq77nnHo82TARwC2CJ5DyI20kBTERE/FSBAWzfvn0A7Nq1y2uNEcnDFMBCc9cpgImIiJ8qMIANHz4cgOeff95VlpmZSVJSElWqVPF8y0TAMQk/xxwcc8DGOAsUwERExE8VugzFl19+yXPPPUdqaipdunShZ8+evPvuu95om4jbCNiXwFJznQKYiIj4qUID2Ouvv87tt9/OF198QbNmzfjmm29YtWqVN9omkmcSvlvkSk3NfbSIiIhfKDSAGYZBw4YN2bBhAx06dKBUqVKuNcFEPM4UwKLItQyFRsBERMRPFRrAgoKC+PTTT/nhhx+49tprWb9+PRaLxRttEzn7CJgCmIiI+KlCA9ioUaNYunQpjz/+OBUrVuS1115j3Lhx3mibiFsAiwbCALuzQAFMRET8VKEP47766qt55513XPuLFy/2ZHtE3JkC2FM5Py4KYCIi4qcKDWC//PILL774IqdPn3ab+/Xxxx97tGEigNsyFHkogImIiJ8qNIBNmDCBPn36cMUVV2jul3ifaQRsMzADeBGoDgpgIiLitwoNYCEhIXrskPiOKYAdA5YBo8gJYFqGQkRE/FShk/Dr16/Pjh07vNEWkbxyLUMBpm9CagRMRET8VKEjYAcOHKBv375UqVKF8PBwV7nmgIlX5FqGAkxrgSmAiYiInyo0gD3++OPeaIdI/jQCJiIiAajQW5CtWrUiIiKCPXv20KxZM0JDQ2nVqpU32ibiFsBKA1UxfWgVwERExE8VGsCWL1/OmDFjePPNN0lJSeHhhx9m6dKlhZ0mcmlERECQ42N6OXAQ6O+sy8oCq9VHDRMREblwhQaw999/nyVLllCqVCnKly/P8uXLeffdd73RNhGwWNxGwfLQNyFFRMQPndOzIEuZFsO8/PLLCQ4O9mijRNyYAthtwKvmOt2GFBERP1ToJPzo6Gi2b9/uWoR19erVlClTxuMNE3ExBbDvgXLmOgUwERHxQ4UGsLFjx/Loo4+yf/9+2rdvT3h4OK+++mphp4lcOrmWonC76agAJiIifqjQAFanTh1WrVpFYmIiNpuN2rVrk56e7o22iTjkWorCLXIpgImIiB8qdA5Ynz59CA4Opm7dujRo0IDQ0FDi4uK80TYRB9McxFIogImIiP8rcARs8ODB/Pbbb2RkZNCiRQtXud1u58orr/RK40QAtxGwRsAZc52+BSkiIn6owAD2yiuvcOrUKcaOHcvzzz//7wkhIVSsWNErjRMB3ALYG7nrNAImIiJ+qMAAVqpUKUqVKsV7771HZmYmZ86cwTAMAJKTk4mOjvZWG6W4O9s6YApgIiLihwqdhL948WKmTJlCVlaWK4BZLBa2b9/u8caJAG4B7BXgQ+BbZ4ECmIiI+KFCA9ibb77JokWLaNKkiTfaI5KXKYAdwbEWmAFYQAFMRET8UqHfgqxQoYLCl/hWrnXA7Jgm4iuAiYiIHyo0gLVv354PPviAo0ePcurUKdePiNeYlqFwRjFX7FIAExERP1ToLcj58+eTmZnJxIkTXWWaAyZelWshVnCshl8ZtAyFiIj4pUID2LZt27zRDpGCmQJYNeBacuZ/gUbARETELxUYwH7//feznqh5YeI1pgDWCfjBXKcAJiIifqjAADZs2LACT7JYLHz99dceaZBIHloHTEREAkyBAWzdunXebIdIwUwBbA/QHZgOdAMFMBER8UuFfgtSxOdMASwE2A4cdRakpEDOAsEiIiL+QgFMir7wcAgOBhzrgIFpGYrsbMjM9EWrRERELpgCmBR9FotrFMwZwNwWn9BtSBER8TMKYOIfcgJYWM6PW+RSABMRET+jACb+wTQPLBaoa65TABMRET9T6EKsIkWCKYAty12nACYiIn5GI2DiH7QWmIiIBBAFMPEPpgdy9wH6mev0PEgREfEzugUp/sE0ApaKJuGLiIh/0wiY+AdTAItCAUxERPybApj4h1wBTOuAiYiIP1MAE/9gCmCl0AiYiIj4N80BE/9gCmBtgDPmOgUwERHxMwpg4h9MAeyunB8XBTAREfEzugUp/sG0DEUeWoZCRET8jAKY+AfTCNgHQAlgn7NAI2AiIuJnFMDEP5gCWCiQgWkivgKYiIj4GQUw8Q+5lqEA01IUCmAiIuJnFMDEP+RahgI0AiYiIv5LAUz8Qz4jYApgIiLirxTAxD+YAthlwINADWdBaioYhg8aJSIicmG0Dpj4h7AwCAmB7GwqA/PMddnZYLVCRISPGiciInJ+NAIm/sFicRsFswNZ5nrdhhQRET+iACb+IyeAGUA48Iy5TgFMRET8iAKY+I+cAGYBSmJahgIUwERExK8ogIn/yLUUhQKYiIj4KwUw8R+5lqJwi1x6HqSIiPgRBTDxH6YHckehETAREfFfWoZC/IdpBOxuwG3RCQUwERHxIwpg4j9MAezh3HUKYCIi4kd0C1L8hymAnQGOm+sUwERExI8ogIn/MAWwx4Em5joFMBER8SMKYOI/cn0L0m0Svr4FKSIifkQBTPxHrnXAzgDZzgKNgImIiB/xaABLTU2le/fuHDx4EIANGzYQGxtL586dmTVrlidfWgJRrmUoANKcBQpgIiLiRzwWwLZu3cqAAQNITEwEICMjg7Fjx/Lqq6/y6aefkpCQwPr16z318hKIct2CBNNirApgIiLiRzwWwJYuXcrTTz9NpUqVANi2bRs1a9akevXqhISEEBsby2effZbvucnJyRw8eNDt58iRI55qqvgLUwBrDbyA45mQgAKYiIj4FY+tAzZ58mS3/WPHjlGxYkXXfqVKlTh69Gi+57777rvMnTvXraxChQrMnj2bhISEi25bfHz8RV9D8vJ0v0YcOOD65uNVOT9OZ44f548A/XPV59Uz1K+eoX71DPXrpZWS8492X/ar1xZitdvtWCwW175hGG77ZoMHD6Z3795uZTabjaSkJGJiYggPD7/gdsTHx9OyZcsLPl/y55V+LV/etZkJHAAq45iQXyIrKyD/XPV59Qz1q2eoXz1D/XrpRf0WRUpKikf71Wq1nnXQyGsB7LLLLuP48X+Xzjx+/Ljr9mRupUuXpnTp0m5lVquVpKQkj7ZRijjTLcjfgKuBVUAP0DIUIiLiV7y2DEXTpk3Zu3cv+/btw2azsWbNGjp06OCtl5dAkGsZCsg1Cd8wvN0iERGRC+K1EbDw8HCmTp3KsGHDsFqtdOzYkS5dunjr5SUQhIVBaChkZeX9FqTNBhkZUKKEjxonIiJy7jwewNatW+fabtu2LatXr/b0S0ogi4qCf/5xBTC3G48pKQpgIiLiF7QSvviXnNuQzuUn3Baf0FIUIiLiJ7x2C1LkksgJYEHAa4Db91cUwERExE8ogIl/MU3Efyh3nb4JKSIifkK3IMW/mALYzpwfF42AiYiIn9AImPgXUwCLAyoCnzoLkpN90CAREZHzpxEw8S+mAFYacItcGgETERE/oQAm/qVMGddmngB2+rS3WyMiInJBFMDEv5geUZUngOkWpIiI+AkFMPEvZxsBUwATERE/oUn44l9MI2CDgevNdboFKSIifkIBTPyLKYBdnfPjohEwERHxE7oFKf7FdAvyKPAVcMZZoBEwERHxEwpg4l9MI2BfAzcD+50FGgETERE/oQAm/iXXtyDBNBFfAUxERPyEApj4l1zfggRTANMtSBER8RMKYOJfNAImIiIBQAFM/EupUq7NPAEsLQ1sNm+3SERE5LwpgIl/CQ52PQ+yCrAGuMlcr1EwERHxAwpg4n9ybkNGAN2AquY6BTAREfEDCmDif0wT8T8FfjHXaSK+iIj4AQUw8T+mifh3A/PNdRoBExERP6AAJv4n1zch9UBuERHxNwpg4n9MtyDLkCuA6RakiIj4AQUw8T8aARMRET+nACb+52wBTCNgIiLiB0J83QCR82a6Bfk84Lb0qkbARETEDyiAif8xjYBdkbtOAUxERPyAbkGK/zEFsK3AG+Y63YIUERE/oAAm/ifXQqxDgAxngUbARETEDyiAif/JNQkfTBPxFcBERMQPKICJ/zGNgOUJYLoFKSIifkABTPyPRsBERMTPKYCJ/zEFMOdYmEbARETEn2gZCvE/pluQ1wC/A7WcBRoBExERP6ARMPE/JUuCxeLYxLEWWKSzLiMDMjN91DAREZFzowAm/sdicY2CZQIvA5vN9boNKSIiRZwCmPin6GjA8QF+DPjCXHfqlLdbIyIicl4UwMQ/5QSwEKAUcMpcpwAmIiJFnAKY+KecAAYQDZw01508iYiISFGmACb+qWxZ12Y0GgETERH/ogAm/inXCNgpc51GwEREpIjTOmDin0wjYMuACHOdRsBERKSIUwAT/2QaAaucu04BTEREijjdghT/ZApgXwLPmOt0C1JERIo4BTDxT6ZbkN8BzwGGs0AjYCIiUsQpgIl/yjUJ3w6kOAs0AiYiIkWcApj4J9MImPPR3KecBRoBExGRIk4BTPxTrhEwUAATERH/oQAm/ulsAUy3IEVEpIjTMhTin0y3IDsCZzCtBXbqFBgGWCzeb5eIiMg50AiY+KcSJSA0FIBQci3EmpUF6em+aJWIiMg5UQAT/2SxuEbBMoBHcawH5qJ5YCIiUoQpgIn/ypkHFgLMBjaa6xTARESkCFMAE/9lCmCl0AO5RUTEfyiAif8yTcSPJlcA0wiYiIgUYQpg4r9MS1GUQSNgIiLiPxTAxH+ZRsDKAVnmOo2AiYhIEaZ1wMR/mUbA1gNuq34pgImISBGmETDxX6YAlmfJVd2CFBGRIkwBTPyX6RbkIuAec51GwEREpAhTABP/ZRoB+wN4DzCcBRoBExGRIkwBTPxXrmUo7ECys0ABTEREijAFMPFfphGw8jm/TzgLFMBERKQIUwAT/1WhgmszTwBLSvJ2a0RERM6ZApj4r/LlXZuVgMsBq7PgxAkwjHxOEhER8T2tAyb+KyoKQkMhK4vWwCFzndUKaWlQqpSPGiciIlIwjYCJ/7JY3EbB8jhxouA6ERERH1IAE/+WMw/MAHoBb5nrNA9MRESKKN2CFP+WMwJmAb4DqpnrNAImIiJFlEbAxL/l+iakW+TSCJiIiBRRCmDi30xzwPIEMI2AiYhIEaUAJv5NI2AiIuKHNAdM/JtpBKwxEGyu0wiYiIgUUQpg4t9MI2AzctdpBExERIoonwSwgQMH8s8//xAS4nj5iRMn0rRpU180Rfyd1gETERE/5PUAZhgGiYmJfPPNN64AJnLBTCNga4BngE+AyqARMBERKbK8Pgl/z549ANx777306NGD//3vf95uggQS0whYOhAPHHcWaARMRESKKK8PQSUnJ9O2bVueeuopsrKyGDRoELVr1+baa691OyY5OdntPJvN5u2mij/I9S1IMH0TUiNgIiJSRFkMwzB82YB33nmHQ4cOMXbsWFfZnDlzmDt3rttxFSpUYPbs2d5unhR1hkGLNm2w2Gz8CjQHPgL65FT/3w8/YERE+Kx5IiJS9AzZMASA+e3me/y1YmJiCA8Pz1Pu9RGwn3/+maysLNq2bQs45oTlngs2ePBgevfu7VZms9lISkoq8I2cq/j4eFq2bHnB50v+fNqv5cvDsWN5R8CAFjVqQPXqvmjVJaHPq2eoXz1D/eoZ6tdLL+q3KFJSUjzar1arlYSEhALrvT4HLCUlhWnTpmG1WklNTWXFihXcfPPNbseULl2aatWquf1cdtll3m6q+IuceWAVgHZAWXOd5oGJiEgR5PURsE6dOrF161Z69eqF3W7nzjvvpHnz5t5uhgSSnABWAvgxd53mgYmISBHkk3UgHnvsMR577DFfvLQEItNE/Dw0AiYiIkWQngUp/s+0FMVtwD3mOo2AiYhIEaSVUMX/mUbATgJ/m+sUwEREpAjSCJj4v0qVXJuVgaPmuqNHcx8tIiLicwpg4v9M35C9jFwB7PBhb7dGRESkUApg4v9MAawykAakOguOHPFBg0RERM5OAUz8nymANcUxET/DWaAAJiIiRZAm4Yv/u/xy1+YtOT8uR46AYYDF4u1WiYiIFEgjYOL/oqMhLMytyPWA04wMOH3a2y0SERE5KwUw8X8Wi+s25AmgPPCauV63IUVEpIhRAJPAkHMbMho4BbhFLgUwEREpYhTAJDDkjIAFAxVRABMRkaJNAUwCQ661wNwil9YCExGRIkYBTAKD6ZuQeRZj1QiYiIgUMVqGQgKDaQSsF+D2BEgFMBERKWIUwCQwmALYQ7nrFMBERKSI0S1ICQymAAZwBrA5dzQHTEREihgFMAkMpjlgS4BIYKezQCNgIiJSxCiASWCoXNm1WTHnt2siflISZGV5u0UiIiIFUgCTwBAeDmXLAo5vQYJpKQrDgOPHfdEqERGRfCmASeDIuQ3pHAtzu/F46JC3WyMiIlIgBTAJHDkBrBwQDrhFroMHfdAgERGR/GkZCgkc1asDYAEmAM3Ndfv3+6BBIiIi+VMAk8BRo4Zrc2zuugMHvNoUERGRs9EtSAkcpgB2BthtrtMImIiIFCEKYBI4cm5BAjwHNMS0GKtGwEREpAhRAJPAYRoBq44jfLm+CakRMBERKUIUwCRwmEbAnFuuca/Dh7UYq4iIFBkKYBI4SpaEcuUAcI6Fuca97HYtRSEiIkWGApgEltq1AaiVs5tortuzx7ttERERKYACmASWOnUAKA3MATqb6xTARESkiNA6YBJYcgIYwNDcdQpgIiJSRGgETAKLKYAdAn4w1ymAiYhIEaEAJoHFFMBeBm4E7M6C3bvzOUFERMT7FMAksJgCWG0gE9NDuf/6CwzDB40SERFxpwAmgaVGDQgNBaBuTtFfzrrTp+HYMV+0SkRExI0CmASWkBCo64heDXOKdpjrd+zIfYaIiIjXKYBJ4GnUCIBqQAlyBbA///RBg0RERNxpGQoJPDkBLAhYDtQ31ymAiYhIEaAAJoEnJ4ABdMldt327V5siIiKSH92ClMDT0DH7ayEDqMZeLNioyV4WMgB++83HjRMREVEAk0DUpAkLGcAQ3uBvagFB7KcWQ3iDhX93gBMnfN1CEREp5hTAJPBERTEuZDrplHQrTqck45gCW7f6qGEiIiIOCmASkPZnX55/OTUUwERExOcUwCQg1SiTnH85++GXX7zcGhEREXcKYBKQJt/7F5GkuZVFksZkxsKmTT5qlYiIiIMCmASkuCeqMJ8HqEkiFuxUI5H5PEAci2DXLk3EFxERn9I6YBKYqlQhrsaPxO2vnX/9pk3QrZt32yQiIpJDI2ASuNq0cW1OB940133/vbdbIyIi4qIAJoGrbVvX5mpyBbCvv/Z2a0RERFwUwCRwderk2rwe+Bk47SyIj4d//vF+m0RERFAAk0B25ZVQsSIANwI2YL2zzjDg88991DARESnuFMAkcAUFwY03AtAWKAF8Za5fvtwHjRIREVEAk0DXtSsA4UBXcF8Z7NNPITXVB40SEZHiTgFMAltsLIQ4VltZBrxlrktPh8WLfdEqEREp5hTAJLCVLQs33QSAJafI7SFFr77qmA8mIiLiRQpgEvgGDnRtTgLqAVZnwS+/wJo1PmiUiIgUZwpgEvj69oXy5QFoDRwH3G48jhgBZ874oGEiIlJcKYBJ4AsPhwceABzLUTTFMRKW7azftQsefBDsdt+0T0REih0FMCkeRoyAkiUJAiYCfwFzzPXvvw89e8Lvv7udtnAh1KrlWNGiVi3Hfm7ncoyIiIiZHsYtxUOFCjByJDzzDLFAd2AuMBQIdR6zZo3jJyYGWrRgYUosQz7pSXqm44h9+2DIfTb4/U/iOh8Hi4WFX1dmyLT6pFuD/z3mfhvs2Udct1NgsTh+ClJIXYlduyA0NN+6C72mV+uKqPDERChZ0tfNCDjqV89Qv156VY+eYUeEb7+AZTEM//gKmNVqJSEhgZiYGMLDwy/4OvHx8bRs2fIStkzAT/o1IwOaNYMdOziM4xZk9bMcXou97KNWnvKaJJJI7XM+RkREip5TJYOJfnQUTJrkkX9IFpZbdAtSio+ICFi0CEqU4HL+DV8PAbOAlFyH76dGvpcxl5/LMSIiUvREp9lgyhSYMMEnr69bkFK8NG8OH3wAt90G2dmkA7uB14FxDMDCFNKpweXspxwnOEHFPJeoyn4ygAigOvvZn88IWHX2A5AF5LfWfikctz4zgfQC6kNwLJeR3/czo4Dgs9SXxvGvq4ycn4Lqz/DvkhwfMoCJTOFvalCd/UxhLL1ZRGY+50fn/E7D8R7NLECZs9QH5bw+OPom+yz1KTie4WkWjOP9g2NNt9xfnQjB0X/gePh67iH+UKDkWerDgMic7VPk5aw3MD3c3SQcx2Ov7ORacy5HRM6Pjbyhn5xzw89SH5nThmzy/2w567PI9eSHHCU598/ee6bPRFX2M4Gx3MuiS/7ZMyuD4zOUntPG3KJzfuuzl1cgffY8/f89O//+WfDmmzBxovenUxh+IiMjw/j555+NjIyMi7rOzz//fIlaJGZ+16+ffmoYpUsbhmMZVuMZBhjBpDp3DTCMUM4YoWS4lUGqAQOMd3MKJjAgp8z9mEcZYBhgrHX8vzLPzxc5By8toH5jTv3bBdQn5NS/XEB9Yk79pALqT+TUj3KV5X0fkaQaNzEgz7nhpoMG5XPtCqb63vnU1zLV35RP/ZWm+tb51Lcz1V+RT/0tpvoa+dT3M9WXzaf+blN9SD71w3LqzhTQt2Nz6o8VUP98Tv2eAurn5tRvLaD+nZz6Hwqo/yin/mI/ew8U8NmemvPZvnSfPfefzJz6h/Op02eveHz2vPH/vYGmvjbAME6evOR/zRSWWzQCJsVT166wdSv897+wYgULmIIN90muWURQluMEkcYJalCO/XRjLNewiGtyjnmQRewF1jCFk9SgLPvpzliGsgiARsBL+bx8g5zfTXHc/sytZs7vVgXUX5bz+7oC6svm/L4ZyG/qrvNf2d1zrjWRKZzMdWQ6JdnGFGblvBenYNP2nUDzXNcuYdq+B+iQq760afs/QLdc9RVM248BR3LVX27aHgX8k6u+pml7Ann/JV/ftD2ZvKMwV5i2Z5J3lKNZzu8Q8u9752ejZAH11+b8LldAffuc35cXcv3aBdRflfO7UQH15/rZW8MU8n56SjKXKYxi0SX77OXmnBfTF/c/K9Bnr1nO70D/7Hnj/3tuI3QxMRAdnc8ZnqVJ+HJJ+HW/JiQQdGUTDPIOP1uwY3f7335gCsKGkc+U0OLy/iUvfSakWAgLg5UrHf8ov8QKyy0aAROJiaFGTccSErnVKHUSet3leHD3mTOOb1I6B63tdsePczv3b+d2Qc6hLv3MGSJLlMi37kKvmZ8aOw+zL7tq3vKQw1Cv0YW9XhGWkZFBRESEr5tRpNXYfZbPRN2G+Z6jfvUM9asHhISQVK8eFZ54Atq3L/x4TzTBJ68qUsRMngxDhjhyllNkJEyeVx7i3vdZu7Z7aWRx8sIC3v/8qhC33eOv722/+/OIrZec/TPxZ77nqF89Q/3qGfvi46ngw37VMhQiQFwczJ8PNWs6vghTs6ZjPy7O1y3zjuL+/iUvfSZEPEsjYCI54uKK918uxf39S176TIh4jkbARERERLxMAUxERETEyxTARERERLxMAUxERETEy3wSwD7++GNuvfVWOnfuzMKFC33RBBERERGf8fq3II8ePcqsWbNYvnw5YWFh9O/fn9atW1OvXj1vN0VERETEJ7w+ArZhwwbatGlDdHQ0kZGR3HLLLXz22WfeboaIiIiIz3h9BOzYsWNUrFjRtV+pUiW2bdvmdkxycjLJycluZTabzSvtExEREfE0rwcwu92OxfLvQ48Nw3DbB3j33XeZO3euW1mFChWYPXs2CQkJF92G+Pj4i76G5KV+9Qz1q2eoXz1D/eoZ6lfP8GW/ej2AXXbZZfz888+u/ePHj1OpUiW3YwYPHkzv3r3dymw2G0lJSQU+VfxcxeuZWh6hfvUM9atnqF89Q/3qGepXz/B0v1qt1rMOGnl9Dli7du3YuHEj//zzD2fOnOGLL76gQ4cObseULl2aatWquf1cdtll3m6qiIiIiEd4fQSscuXKPP744wwaNIisrCz69evHVVdd5e1miIiIiPiMTx7GHRsbS2xsrC9eWkRERMTntBK+iIiIiJcpgImIiIh4mQKYiIiIiJcpgImIiIh4mQKYiIiIiJcpgImIiIh4mQKYiIiIiJf5ZB2wC2EYBgCZmZkXfS2r1XrR15C81K+eoX71DPWrZ6hfPUP96hme7FdnXnHml9wsRkE1RUxKSgo7d+70dTNEREREzlmDBg2IiorKU+43Acxut5OWlkZoaCgWi+WCrnHkyBHuvPNOPvjgAz1b8hJSv3qG+tUz1K+eoX71DPWrZ3ijXw3DICsri5IlSxIUlHfGl9/cggwKCso3QZ6P4OBgkpKSCA4OJjw8/BK1TNSvnqF+9Qz1q2eoXz1D/eoZ3urXiIiIAus0CV9ERETEyxTARERERLxMAUxERETEy4pVACtdujRDhw6ldOnSvm5KQFG/eob61TPUr56hfvUM9atnFIV+9ZtvQYqIiIgEimI1AiYiIiJSFCiAiYiIiHhZsQlgH3/8MbfeeiudO3dm4cKFvm6OXxs4cCDdunWjZ8+e9OzZk61bt7JhwwZiY2Pp3Lkzs2bN8nUT/Upqairdu3fn4MGDAAX25fbt2+nTpw+33HIL48aNIzs721dN9gu5+3XMmDF07tzZ9bn98ssvAfXr+Zg7dy7dunWjW7duTJs2DdDn9VLIr1/1eb14L7/8MrfeeivdunVjwYIFQBH7vBrFwJEjR4xOnToZJ0+eNNLS0ozY2Fhj165dvm6WX7Lb7Ub79u2NrKwsV9mZM2eMjh07Gvv37zeysrKMe++91/j222992Er/8euvvxrdu3c3mjRpYhw4cOCsfdmtWzfjl19+MQzDMMaMGWMsXLjQhy0v2nL3q2EYRvfu3Y2jR4/mOVb9em5+/PFH44477jCsVquRmZlpDBo0yPj444/1eb1I+fXrF198oc/rRdq8ebPRv39/Iysryzhz5ozRqVMnY/v27UXq81osRsA2bNhAmzZtiI6OJjIykltuuYXPPvvM183yS3v27AHg3nvvpUePHvzvf/9j27Zt1KxZk+rVqxMSEkJsbKz69xwtXbqUp59+mkqVKgEU2Jd///03GRkZNGvWDIA+ffqoj88id7+eOXOGQ4cOMXbsWGJjY5k9ezZ2u139eh4qVqzI6NGjCQsLIzQ0lLp165KYmKjP60XKr18PHTqkz+tFatWqFe+99x4hISGcOHECm81GcnJykfq8+s2jiC7GsWPHqFixomu/UqVKbNu2zYct8l/Jycm0bduWp556iqysLAYNGsT999+fp3+PHj3qw1b6j8mTJ7vt5/dZPXr0aJ7yihUrqo/PIne/JiUl0aZNG55++mmioqJ48MEHWbZsGfXr11e/nqP69eu7thMTE1m7di133XWXPq8XKb9+XbhwIVu2bNHn9SKFhoYye/Zs3n77bbp06VLk/v9aLEbA7Ha72wO8DcO44Ad6F3fNmzdn2rRpREVFUa5cOfr168fs2bPVv5dIQZ9VfYYvTvXq1XnllVeoVKkSJUqUYODAgaxfv179egF27drFvffey5NPPkn16tX1eb1EzP1ap04dfV4vkeHDh7Nx40YOHz5MYmJikfq8FosAdtlll3H8+HHX/vHjx123JuT8/Pzzz2zcuNG1bxgGVatWVf9eIgV9VnOXJyUlqY/Pw44dO/j8889d+4ZhEBISon49T/Hx8dx9992MGDGC3r176/N6ieTuV31eL97u3bvZvn07ACVKlKBz585s3ry5SH1ei0UAa9euHRs3buSff/7hzJkzfPHFF3To0MHXzfJLKSkpTJs2DavVSmpqKitWrOC///0ve/fuZd++fdhsNtasWaP+vUBNmzbNty+rVq1KeHg48fHxAKxatUp9fB4Mw2DKlCmcPn2arKwslixZws0336x+PQ+HDx/mkUceYcaMGXTr1g3Q5/VSyK9f9Xm9eAcPHmT8+PFkZmaSmZnJ119/Tf/+/YvU57VYzAGrXLkyjz/+OIMGDSIrK4t+/fpx1VVX+bpZfqlTp05s3bqVXr16YbfbufPOO2nevDlTp05l2LBhWK1WOnbsSJcuXXzdVL8UHh5eYF/OmDGD8ePHk5qaSpMmTRg0aJCPW+s/GjVqxJAhQxgwYADZ2dl07tyZ7t27A+rXc/XWW29htVqZOnWqq6x///76vF6kgvpVn9eL07FjR7Zt20avXr0IDg6mc+fOdOvWjXLlyhWZz6seRSQiIiLiZcXiFqSIiIhIUaIAJiIiIuJlCmAiIiIiXqYAJiIiIuJlCmAiIiIiXqYAJiIeMWnSJHr27EnPnj2JiYnhlltuce1nZGT4unlntW3bNiZMmODx1xk5ciQ7d+5k8+bNrmUGnBYsWECHDh34888/OXz4MEOHDsVut3u8TSLiHcViHTAR8b7x48e7tm+44QZmzJjBlVde6cMWnbu//vrL48+C+/TTT4mKiqJBgwZs3rzZrW7WrFl88cUXLFq0iKpVqwKOtcw++OAD7rrrLo+2S0S8QwFMRLzuww8/ZNGiRdjtdqKjo3nqqaeoW7cuo0ePJiIigp07d3LixAluuOEGoqOj+eabbzh+/DiTJk2ibdu2jB49mvDwcP78809OnDjBtddey/jx4wkNDWX37t1MnjyZU6dOYbPZGDhwIP369WPz5s1MnjyZyMhI0tLS+Oijj5g2bRpbt24lLS0NwzCYNGkSVapUYfbs2aSkpDBmzBh69erFc889x5o1awDYvHmza3/OnDn8+uuvHDt2jIYNGzJjxgxee+01vvjiC+x2O1WrVuXpp5+mcuXKefpgzpw5vPzyy25ldrudiRMn8ueff/LBBx9QtmxZV91tt91Gv379uP322wkLC/PsH5CIeJwCmIh41ZYtW1i5ciULFy6kRIkS/PDDDwwdOpS1a9cC8Mcff7Bw4UJOnTpF+/btGT9+PIsXL+bdd9/ljTfeoG3btoDjNuH//vc/QkNDuffee1myZAn9+/dn+PDhTJs2jSZNmpCSksIdd9xBvXr1AMcDj7/66iuqVq3KL7/8wrFjx1iyZAlBQUHMnz+fN954g3nz5jF8+HA+//xznn/++TyjU7n9/fffrFmzhpCQEFauXMnOnTv58MMPCQkJYcmSJYwfP5433njD7ZydO3ditVpp0KCBqyw7O5uRI0eyZs0a5s+f7xa+wPFEj+joaP7v//6PNm3aXPSfg4j4lgKYiHjVt99+y759++jfv7+rLDk5mVOnTgGOx12FhoZSsWJFIiMjue666wCoUaOG6xiA3r17U7JkSQB69uzJ119/TZs2bdi/fz9jx451HZeRkcEff/xB3bp1ufzyy1239Jo3b06ZMmVYvHgxBw4cYPPmza7rnY9mzZoREuL4X+k333zDb7/9Rt++fQHHiNaZM2fynLNnzx5q1KjhVrZ3716aN2/OCy+8wOjRo1m+fDmXX3652zHVqlVj7969CmAiAUABTES8ym6307NnT0aOHOnaP3bsGGXKlAHIc3vNGW5yCw4Odm0bhkFQUBA2m42oqChWrVrlqktKSiIqKopff/2VyMhIV/m3337L5MmTueeee7jxxhupU6cOq1evzvM6FosF8xPbsrKy3OrN17Tb7dx///3ceeedAGRmZnL69Ol8r5l7Qn2tWrV4/vnnAfi///s/hg0bxgcffODWH6GhoW7vW0T8l74FKSJe1b59ez755BOOHTsGwKJFixg8ePB5X2ft2rVkZmZitVpZsWIFnTp1onbt2kRERLgC2OHDh+nevTsJCQl5zv/xxx/p1KkTd955JzExMXz11VfYbDbAEe6ys7MBKFeuHIcOHeLEiRMYhsEnn3xy1ve2bNkyUlNTAXj55Zd58skn8xxXu3ZtDhw44FYWGhrq2h43bhw2m41nn33W7ZiDBw9Sp06dc+keESniFMBExKvat2/PAw88wL333ktsbCxr1qxh7ty5WCyW87pOREQEd955J7GxsVx99dX07duXsLAwXn31VZYtW0ZsbCz33nsvjz76KC1btsxzfv/+/dmyZQuxsbH07t2b6tWrc/DgQex2O82aNePAgQMMHTqUevXq0b9/f/r27cvtt99OtWrVCmzTbbfdxvXXX8/tt99Ot27d2LFjB1OnTs1zXIMGDQgPD2f37t35Xic8PJyXX36Zzz77jCVLlgCOkbwTJ07QokWL8+onESmaLIZ5bF1ExA+MHj2a+vXrc9999/m6KRfs448/Jj4+nmeeeeacjp8zZw7lypUjLi7Osw0TEa/QCJiIiA/ExsZy+vRpduzYUeixhw8f5vfff3f74oKI+DeNgImIiIh4mUbARERERLxMAUxERETEyxTARERERLxMAUxERETEyxTARERERLxMAUxERETEy/4f/vHmIW8+m5kAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Train\n",
    "Thermal_posterior_first_model, Thermal_posterior_first_results = Thermal_inference_first_order_train(Measured_temperatures, \n",
    "                                                           Measured_tempature_dependent_Intensities_minus_back)\n",
    "\n",
    "print('Loglikelyhood = ', Thermal_posterior_first_results.state.best()[1])\n",
    "#Predict\n",
    "Thermal_first_predictions = Thermal_inference_first_order_predict(Thermal_posterior_first_results, T2)\n",
    "Thermal_first_predictions['Thermal Next Temperature'] =  T2[-1]\n",
    "\n",
    "#Plot the results curves\n",
    "plot_thermal_inference(T2, Thermal_first_predictions, Thermal_posterior_first_model, dictionary_for_histograms, Hist = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1cfbaa91",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a64d6fcc",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "d2a69bec",
   "metadata": {},
   "source": [
    "## Wiess Equation Fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "c2461d2b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initial chisq 309634.91(47) constraints=11.4131\n",
      "# steps: 2500, # draws: 100000\n",
      "final chisq 67.02(47) constraints=12.6907\n",
      "BK : 1.039(44)\n",
      "J : 11(21)e-3\n",
      "M0 : 5.366(22)\n",
      "TN : 70.000(15)\n",
      "Loglikelyhood =  -347.78580369489833\n",
      "Predicting\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Train\n",
    "Thermal_posterior_model, Thermal_posterior_results = Thermal_inference_second_order_train(Measured_temperatures, \n",
    "                                                           Measured_tempature_dependent_Intensities_minus_back)\n",
    "\n",
    "print('Loglikelyhood = ', Thermal_posterior_results.state.best()[1])\n",
    "#Predict\n",
    "Thermal_predictions = Thermal_inference_second_order_predict(Thermal_posterior_results, T2)\n",
    "Thermal_predictions['Thermal Next Temperature'] =  T2[-1]\n",
    "\n",
    "#Plot the results curves\n",
    "plot_thermal_inference(T2, Thermal_predictions, Thermal_posterior_model, dictionary_for_histograms, Hist = False)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e4aaa9c",
   "metadata": {},
   "source": [
    "## Ising Model Fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "478605dd",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-5-24199b3b3b97>:173: RuntimeWarning: invalid value encountered in power\n",
      "  I = (M0*((1 - t_eval)**(2*BETA)))**2 + BK\n",
      "<ipython-input-5-24199b3b3b97>:174: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  I = I.astype(np.float64)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initial chisq 216733.90(34) constraints=8.32428\n",
      "# steps: 2500, # draws: 100000\n",
      "final chisq 5.77(34) constraints=8.32575\n",
      "BETA : 0.0263(91)\n",
      "BK : 0.960(42)\n",
      "M0 : 5.23(12)\n",
      "TN : 65.05(60)\n",
      "Loglikelyhood =  -48.73950937306957\n",
      "Predicting\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\asm6\\Anaconda3\\envs\\ornl_al\\lib\\site-packages\\numpy\\core\\_asarray.py:102: UserWarning: Warning: converting a masked element to nan.\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "image/png": 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/+Ddv3py//vrLfkfim2++ycyZM4mMjMRkMvF///d/tGvXju+++y7fAOWoffv2rFixAoCjR4/yxx9/0KJFiyv7bg417ty5k+joaACWLVtGu3bt+Oeff7j77rtp06YNzz77LPXq1ePw4cOYzWZ7aGrfvj3Lly8nNTWVxMRE7rrrLv76668rPlZeqlatys0338zUqVOxWCwA/PPPP7z33ns0aNCA0qVLc/78ec6ePUtKSgo///xzrp8VFhbGV199RdmyZalWrRqlSpWidu3a9gD266+/MmzYMNLS0ujZsyflypXj4YcfJiwsjD179lx2n+ZFI2AiIuKZevdOnxj/6qvw88/pE+YLmp8f3HRTevjKZQK+o27dujFx4kQef/zxTNsrVarE9OnTeeKJJ7DZbFSuXJlZs2ZRunRpmjRpQu/evTGZTHTu3JnwK7i0OnHiRCZPnmxf6uKll14iKCgo09ITl6tixYpMmTKFUaNGkZqaStWqVZk2bRpBQUG0aNGCPn36EBAQQKtWrejSpQtHjx5lwYIFzJ49m8cff5yoqCj69+9PWloaAwYMoF27dmzfvv2KjpWf6dOnM3v2bMLCwvD19SUgIIBZs2bRsGFDAB544AEGDRpElSpVuOGGG3L9nNatW5OUlETfvn3t22bNmsULL7zAe++9h4+PD3PnzsXHx4cxY8Zw33334efnR4UKFZgxY8YV9mzOTEbW8Us3ZbFYiIiIIDg4+JquAYeHh9O6desCrExA/eos6lfnUL86h/rVOdSvzuHsfs0vt+gSpIiIiIiLKYCJiIiIuJgCmIiIiIiLKYCJiIiIuJgCmIiIiIiLKYBlcfPN6b9EREREnEUBTERERMTFFMBERESuwfbt22nZsiVhYWH07duX3r1789FHH13VZx09epQJEyZk2x4dHU1wcDBhYWH069ePkJAQRo4cycmTJ6+1/Gu2a9cuZs2aVdhleBynBrDXX3+d22+/nZCQEBYtWgTAli1bCA0NpWfPnsydO9eZhxcREXGJ4OBg1qxZw9q1a/n888/54IMPOHDgwBV/zvHjxzl69GiObUFBQaxZs4bVq1ezfv16GjVqxMyZM6+19Gt24MABzpw5U9hleBynPYpox44dbNu2jbVr15KWlsbtt99Ohw4dmDBhAp988gnXXXcdDz/8MJs3b6Zr167OKkNERIqBm3OYvDt48GAeffRRkpKSuP3227O133vvvdx7773ExsYyaNCgbO2PPPIId9555xXXYrFYMJvNlCpVCkgfIXr55ZdJTk6mXLlyvPjii9SoUYNFixaxatUqvLy8aNasGVOmTOGll14iOjqaF198keeffz7P47Rr145XX30VgA0bNrBo0SKSk5NJSUlh+vTptGrViuHDh1OmTBn279/Pa6+9Rnh4OGvWrOHixYv4+PgwZ84c6tatS/fu3QkJCeHXX3/F29ubRx99lA8++ICoqCieffZZbr/9dmJjY5k8eTInT57EZDLx9NNPExwczLx580hKSuKtt97ioYceYubMmezYsQOr1cqAAQO499572b59O7NmzcJms9GgQQP69etnHzUrU6YMc+bMoXz58lfc157MaSNgbdu25eOPP8bb25szZ85gtVqJi4ujVq1a1KhRA29vb0JDQ/n666+dVYKIiIhLREREEBYWRmhoKN27d6dt27YEBQWRkpLCpEmTmDNnDqtWrWLkyJE899xzWK1W3nnnHb744gtWrlxJamoqMTExTJo0ieDg4HzDV2pqKt988w0tWrTAZrOxdOlS3n77bdauXcsDDzzAwoUL7fs2atSIb775hho1avD999/zySefsG7dOm6++WYWL15s369ixYqsXLmSevXqsXDhQj744ANmzZpl/6xp06YxcOBAVq5cyVtvvcXkyZPx8vJizJgxdO/enUceeYTly5cDsGrVKlasWMHGjRv5/fffAYiMjOSjjz7ilVde4c033+SFF15g5cqVdOzYkX/++aeg/0jcnlMfxu3j48O8efP44IMP6NWrF6dOnaJSpUr29qCgIGJiYrK9Ly4ujri4uEzbruTp8Fdr8WLYti39ea61a8O0aTBsmNMPKyIi1+jHH3/MtS0wMDDP9ooVK+bZfjmCg4P55JNPAEhISLCHoG7dunH06FEeeeQR+74JCQmYzWZatmzJoEGD6NGjByNHjqRy5cpERkbmeoxTp04RFhYGQEpKCs2aNePpp5/Gy8uLN954g02bNnH48GF27NiBl9d/4yvNmjUDoGTJksyZM4f169cTGRnJzz//TJMmTez7denSBYCqVasSFBSEt7c3VatWtf97vGXLFg4dOsS8efMASEtLy3a5dOvWrezZs4dt27YBkJSUxN69e6lfvz516tSxjwr26NGDUaNGccstt9CjRw86dep05Z3u4ZwawADGjBnDgw8+yP/93/8RGRmJyWSytxmGken1JR999BELFizItK1ixYrMmzePiIiIa64ppyfNb9hQjmnTamGxmAGIioIHHrBy+HAUvXufu+ZjFgc59atcO/Wrc6hfnaM49uu+ffuIj4/P9N2Dg4P54YcfqFSpEhUqVGDy5MkA2Gw2Lly4QHh4OPfffz/79+9n586djBgxgsceewzDMLJ9FqSPsJUpU8b+OZccPHiQ5ORkJk6cSOfOnalfvz6dOnXi22+/JTw8nPj4eI4cOUJ4eDhnzpxh6tSp9OzZkzp16nDjjTcSFRVFeHg4FouFvXv3cvbsWY4fPw6k/1mePn0ai8VCeHg4KSkpPPXUU5QsWRKAc+fOkZCQQGRkJGfOnLEfY8CAAbRt2xZIH1Dx9/dn3759pKam2r/XDTfcwLPPPsuff/7Jiy++SLt27ejXr59T/nzyUpjnq9MC2MGDB0lJSaFJkyYEBATQs2dPvv76a8xms32f06dPExQUlO29I0aMoH///pm2Wa1WYmNjc32q+OXK7ennAwdCcnLmbcnJZt57ry6TJl314YoNZz9VvrhSvzqH+tU5imu/pqWlUapUKft3t1qtfPDBB3To0IE+ffrw2muvYRgGN954I8uXL+fLL7/k9ddfZ9iwYaxYsYKhQ4cyfvx4DMOw/5vp2I/h4eH2f/ty6t/du3cTEBDAlClTMAyD//3vfwQGBtK6dWtKlSpFw4YNad26Nd9++y0NGzbkueeeIzk5mQcffJAqVarQunVr/Pz8CA4Opnr16mzZsgWA1q1bEx0dbT9u586d2b17N48++igHDhzg0UcfZePGjRw/fpzjx4/TunVrevXqxebNm3nggQdISUlh4MCBvPjiizRs2DBTH91xxx28+OKLhISEsHr1ajZu3Ojyc8fZ56vFYslz0MhpASw6Opp58+axZMkSADZu3MiQIUOYOXMmUVFRVK9enXXr1jFw4MBs7y1dujSlS5fOtM1isRAbG+uscjly5Mq2i4iIXHJpDpjJZCItLY1GjRrx4IMP4uvry+uvv860adOwWCyULFmSV155hfLly3PnnXcyaNAgAgICqFOnDgMHDsRisRAfH8/YsWMve2mHxo0b06RJE3r37o3JZKJz5845jux06tSJJUuWcPvtt2MYBm3atGH//v2X/R0nTZrE5MmTCQ0NBWDmzJmULFmSZs2asWDBAmbPns3jjz9OVFQU/fv3Jy0tjQEDBtCuXTu2b9+e6bOeeuopxo0bh7e3N4GBgbz00kuXXUdRYTIMw3DWh8+fP58NGzZgNpvp2bMno0ePZuvWrbz88stYLBa6du3K+PHjc7wMmdWlJOmsEbDatdMvO2ZVqxbkcUleMhTX//N1NvWrc6hfnUP96hzqV+dw1QhYbrnFqXPARo8ezejRozNt69ChA2vXrnXmYa/KtGnw0EOQlPTftsDA9O0iIiIiBUkr4WcYNgwWLoRLIbVWrfTXugtSRERECprT74L0JMOGwbvvpv98jXcki4iIiORKI2AiIiIiLqYAJiIiIuJiCmAiIiIiLqY5YFfg0rNeNT9MRMS9LH77Z86dTSzwzy1XvgTD/u+mfPdLSEhgzpw5/Pbbb5jNZkqXLs24ceNo2rRpnu+bN28eK1euZMSIEaxevZo1a9Zk22fMmDEsW7aM6tWrX/X3uFLbt29nwYIF9scr5eTo0aO89dZbTJ8+3Wl1DB8+nFGjRtGuXTunHaOwKICJiIjHO3c2kdJlA5zyufmx2Ww8+OCDtGvXjtWrV+Pt7c22bdt48MEHWb9+PeXKlcv1vWvWrGHRokXUqVOHkSNHFmTpTnf8+PFsz4KUy6cAlkVBjW5ptExEpHjYvn07J06cYMyYMfaHYLdv356XX34Zm80GwNtvv83atWsxm8106tSJsWPH8uKLLxITE8Njjz3GnDlz6NevH3v37uX8+fOMHTuWkydPUq9ePVJTU4H0RxzNnDmTHTt2YLVaGTBgAPfeey/bt2/nnXfewd/fn4MHD9KoUSNmz56Nr68vH374IUuWLMFsNtOtWzfGjh1LbGwskydP5uTJk5hMJp5++mk6duyY6/ebP38+MTExREVFcezYMe644w4eeeQRXnrpJaKjo3nxxRd5/vnnWbhwIRs2bMBqtdK5c2fGjh3LsWPHeOCBByhXrhz+/v6cP3+eqVOnEhwcjNVqpVu3bqxatYodO3awaNEikpOTSUlJYfr06bRq1cr5f3iFSAFMRETkGvzzzz80btzYHr4u6dq1KwCbN29m06ZNfPHFF/j4+DB69GiWLl3KlClT+OWXX1i4cGGmy4vz5s3j+uuv59133+W3335jw4YNACxfvhyAVatWkZKSwv33309wcDAAf/75Jxs2bCAoKIjBgwfzyy+/ULFiRT777DO++OILAgICeOCBB4iIiOD9999n4MCB9OjRg1OnTnHXXXexevVq+0O2c7J3714WL15MfHw8t9xyC8OGDWPSpEksWLCA559/np9++omIiAhWrFiByWRi7NixrF27ltatW3P48GHee+89qlevzocffsj69esJDg5m27ZtNG7cmHLlyrF06VLefvttypcvz4oVK1i4cCFvv/12gf45uRsFMBERkWvg5eWV5yPytm3bRkhICAEB6ZdIBw4cyOrVqxmWy0rfO3bsYM6cOQC0adOGoKAgALZu3cqePXvYtm0bAElJSezdu5f69evToEEDqlSpAkC9evW4cOEChw8fplu3bpQqVQqADz/8EIAtW7Zw6NAh5s2bB6Q/TPzo0aM0adIk1+/Qrl07fH19qVChAmXLliU+Pj5T+9atW9m1axcDBgwAIDk5mapVq9K6dWsqVKhgD5ghISHceeed/O9//2PdunX07dsXLy8v3njjDTZt2sThw4fZsWNHtjBbFCmAiYiIXIPg4GA+++wzDMPI9GzjV199lY4dO9ovQzpKS0vL9fNMJhOOj2k2m81A+iXIsWPH0rNnTwDOnj1LiRIl+OuvvzIFwEvv9/b2zlRPTEwMAQEB2Gw2PvroI8qWLQvAqVOnqFChQp7fMafPd2S1WhkxYoR9HltcXBxms5lz587h7+9v369SpUrUqVOH7du3s3XrViZPnkxiYiKDBg2ib9++tGnThkaNGrF48eI86ykKin7ELCCLF8O2bbB5c/qDu4vBuSEiIpfhxhtvpEKFCixYsACr1QrAzz//zMqVK6lfvz7t27dn/fr1JCcnk5aWxhdffEH79u1z/bwOHTrY74bctWsXJ0+eBNLnlS1fvpzU1FQSExO56667+Ouvv/Ksa/PmzSQmJpKWlsbTTz9NREQE7du357PPPgPgwIEDhIaGcvHixSv+3maz2R4k27dvz5o1a+zHeuyxx/jmm29yfF9YWBivvPIK7dq1IyAggMjISEwmE//3f/9Hu3bt+O677+z9WJRpBOwyLF6c/qBuiyX9dVRU+mvQsyJFRIo7k8nEm2++ycsvv0yfPn3w9vamXLlyLFy4kIoVK9KtWzf27NnDwIEDSUtLo3Pnztx99925ft6YMWMYN24cISEh1K1b134JcsiQIURFRdG/f3/S0tIYMGAA7dq1Y/v27Tl+TtOmTbn77rsZMmQINpuNW2+9lY4dO1KvXj0mT55MaGgoADNnzsxz/ldu6tWrR3x8PGPHjmXWrFn8+++/DB48GKvVyk033UT//v05duxYtvfdeuutPP/88zzzzDMANG7cmCZNmtC7d29MJhOdO3cmPDz8iuvxNCYj6ziim7JYLERERBAcHJzntfb8hIeH07p16yt6T+3a6aErq1q1IDIy+/bFi+H++9MDW61aMG1a0Q9qV9Ovkj/1q3OoX52jMPu1sNcBcyadr87h7H7NL7doBOwyHDly+ds1WiYi4nqFHZJErpTmgF2GmjUvf/vEiZCUlHlbUlL6dhERERFQALss06ZBYGDmbYGB6duzupLRMhERESmeFMAuw7BhsHAhXLqEW6tW+uucLileyWiZiIiIFE8KYJdp2DBo3x66dk2feJ/bfK4rGS0TERGR4kkBrIBdyWiZiIiIFE+6C9IJhg2Dd99N/1kP4xYREZGsNALmpm6+Of2XiIi4t+joaBo1asSvv/6aaXv37t2Jjo6+4s/74YcfWLRoUbbthmEwb948QkND6du3L4MGDeKnn3666rovx7hx41i5cqVTj1FcaQRMRETkGvn4+PDcc8+xdu3aq1pV3lFERESO2zds2MDu3btZtWoV3t7eHD58mKFDh7J+/fp8n+Uo7kcB7ArocqKIiHu6+cObnfK5P97742XtFxQURMeOHXnllVeYOnVqtvaFCxeyYcMGrFYrnTt3ZuzYsWzatImZM2eydu1aTp48yfDhw5k7dy5Lly4FoGrVqgwcOND+GadPn8ZqtZKSkoK3tzd16tRh3rx5eHun/1M+d+5ctm7dyoULFwgKCmLu3LlUrFiRTp060aNHD3bt2kXFihUZOHAgn3zyCSdPnmTGjBm0bduW4cOH07hxY37//XcsFgsTJkygc+fOmb7D6tWr+eijj7DZbDRt2pTnn3/+mp5MU9zpEqQDXfYTEZGrNW7cOH755ZdslyJ/+uknIiIiWLFiBatXryYmJoa1a9fSo0cPWrRowdtvv8348eN59tlnad26NUOGDGHIkCGZwhdAv379SEhIoEOHDtx///0sXLiQOnXqUKZMGaKiojh06BBLly7lm2++4brrrmPt2rUAxMbG0qVLF1avXo3FYuH777/ns88+Y/To0Xz00Uf2z09ISGDVqlXMmTOHcePGkZKSYm/bv38/y5cvZ+nSpaxZs4YKFSrw/vvvO7E3iz6NgDmJRstERFznckeqnKlkyZJMnTrVfinykq1bt7Jr1y4GDBgAQHJyMlWrVgVg4sSJ3H777bRq1YqQkJA8P79MmTIsXbqUvXv3smXLFjZt2sT777/PihUrqFWrFs8++yyff/45hw8f5q+//qKmwwKUXbp0AaBatWr25x9WrVqVuLg4+z6DBw8GoEmTJlSqVIm9e/fa27Zv305UVJR9n9TUVK6//vqr7itRABMRESkwnTt3tl+KvMRqtTJixAhGjhwJQFxcHGazGUgfnTKbzRw6dAiLxZLnJb1FixbRoUMHGjduTKNGjRg5ciRPP/0033zzDe3bt+fpp5/m3nvv5bbbbsPLywvDMOzv9fX1tf986dhZOW632Wz2S5uXvkPv3r2ZNGkSAImJiVit1ivpGslClyDd0OLFsG0bbN4MtWunvxYREc9w6VLkqVOnAGjfvj1r1qwhMTGRtLQ0HnvsMb755husVivjx49n4sSJtG3bltdffx1ID0JpaWnZPjc+Pp7XXnuNxMREIP2S4dGjR2nSpAm//fYbbdu2ZejQodSuXZsff/zxigPSV199BcDff/9NXFwcDRs2tLe1a9eO7777jjNnzmAYBi+88EKmy5dy5TQC5mYWL4aHHgKLJf11VFT6a9BiriIinuDSpcj7778fSF+O4t9//2Xw4MFYrVZuuukm+vfvz3vvvUeFChXo2bMnHTt2pE+fPvTs2ZM2bdrw7LPPUrFiRYYPH27/3EcffZS5c+fSt29f/Pz88PLyYtiwYXTq1In69eszatQoQkNDAQgODr7iJTCOHj1K//79gfQJ/Y4jYo0bN2bUqFGMGDECm81GkyZNeOjSP05yVUyG4xilG7NYLERERBAcHHxNd12Eh4fbr39ndWkCfmHO36pdOz10ZVWrVvojkNxVXv0qV0/96hzqV+dQvzqHK/p1+PDhjBo1inbt2jn1OO7E2f2aX27RJcgM7nLZ78iRK9suIiIinkeXIHGvy341a+Y8AuZwM4uIiEiB+uSTTwq7hGJHI2DAxImQlJR5W1JS+nZXmzYNAgMzbwsMTN8uIiIiRYMCGO512W/YMFi4EC5dLq5VK/21JuCLiIgUHQpg5H55r7Au+w0bBu3bQ9eu6RPvrzZ8GYbBn9sOY7XaCrQ+ERFPpSeeiLtQAKPoXvazptnYvnk/EX9oBr+IiIg7UQCjaF/2S021su3H/SQlWAq7FBGRIik6OppGjRoxefLkTNv37NlDo0aNWLlyZSFVlr/hw4ezffv2TNuio6MJDg4mLCyMsLAwbrvtNsaPH09sbOxlfZ5cHgWwDAV12c/deJlNWK02tv+8v7BLEREpVM5cbqhs2bL8/PPPmVaf/+qrryhfvnzBHcSFgoKCWLNmDWvWrOHrr7+mYsWKjBkzJt/37dixwwXVFQ1ahsJNFeRisIEl/djz1zGub16DylXLFNwHi4h4CGcvN1SiRAkaN27Mb7/9Rvv27QH49ddf6dixo32fn376iXnz5pGWlkb16tWZOnUq5cqVY8OGDSxatIjk5GRSUlKYPn06rVq1YtGiRaxatYrk5GTat2/PlClTWLlyJTt27GDGjBnAfwuoAsyaNQubzUaDBg2YPHkyU6ZMYf/+/VitVh588EH69OlDSkoKEydOJCIigmrVqnHu3Ll8v5vJZGL06NF06tSJf//9l/r16/PCCy+wf/9+YmNjadSoEa+++iqzZ88G4I477uDzzz/n008/Zc2aNVy8eBEfHx/mzJlD3bp1r72ziwiNgBUDXl4mvLxN/LghAptNE/JFpPhxxXJDvXv35ptvvgFg165dNGrUCB8fHwDOnj3LnDlzeP/991m9ejWdO3dm9uzZ2Gw2li5dyttvv83atWt54IEHWLhwIVarlXfeeYcvvviCadOmkZqaSkxMTJ7Hj4yM5KOPPuKVV17hrbfeomnTpqxcuZLFixfz9ttvc/ToUft6Xxs2bGDSpEkcuczb/X19falVqxaHDh3izz//xMfHh2XLlvHdd98RHx/P5s2b7Q/q/vzzz0lISOD777/nk08+Yd26ddx8880s1oONM9EIWDEREOhLbEw8//6dPhImIlKcuGK5oe7du/Paa69hs9nYsGEDvXv3tj/geufOnZw4cYJ77rkHAJvNRpkyZfDy8uKNN95g06ZNHD58mB07duDl5YXZbKZly5YMGjSI66+/npEjR1K5cuU8j1+nTh1KlSoFwJYtW0hOTuaLL74AICkpif3797Njxw7uvPNOAGrXrk3Lli0v+/uZTCb8/f1p06YNZcuWZfHixRw6dIjIyEiSsqTbkiVLMmfOHNavX09kZCQ///wzTZo0uexjFQcaASsmTCYT/oE+bNm4D0tyamGXIyLiUq5YbujSZcjw8HC2bduW6fKj1WqlVatW9nlVK1asYN68eSQmJjJo0CCio6Np06ZNpknsb775Ji+88AKGYfDAAw+wY8cOTCYTjo9wTk397+9zf39/+882m41Zs2bZj7d8+XJuuummbO/39r68cZiUlBQOHz5M/fr12bhxI8888wz+/v4MGDCANm3akPWx0idOnODOO+8kPj6eLl260L9//2z7FHcKYA5+/LFwH8TtbD6+3qRY0vhz2+HCLkVExKVctdxQ7969mTNnDsHBwZnCTfPmzfnrr784fDj9798333yTmTNnEhkZiclk4v/+7/9o164d3333HVarlbNnz3L77bfTsGFD7rjjDjp16sTevXspV64cBw8exDAMjh49yt69e3Oso3379ixZsgSAU6dO0bdvX06cOEGHDh348ssvsdlsHDt2jD/++CPf72Sz2Zg/fz7NmzenZs2abN26ld69ezNw4EBKly7N9u3b7TcfmM1m0tLS+Pvvv6lVqxb33nsvN9xwA99//32mGxRElyCLnYCSvvy5PZLrW9agdJmAwi5HRMQlLk20v//+9In4tWqlh6+CvuO9W7duTJw4kccffzzT9kqVKjF9+nSeeOIJbDYblStXZtasWZQuXZomTZrQu3dvTCYTnTt3Jjw8nPLly3PnnXcyaNAgbDYbwcHBDBw4EG9vb7744gt69epFnTp1aN26dY51jBo1ihdeeIE+ffpgtVoZO3YsNWvW5K677mL//v307t2batWq0bBhwxzff+rUKcLCwoD0ANakSRNeffVVIH2S/TPPPMP69evx8fGhVatWREdHA9CjRw/CwsJYvnw5S5Ys4fbbb8cwDNq0acP+/bob35HJ8JAxQYvFQkREBMHBwfhdWrDrKoSHh+d6whY1aalW3pn9HaWyBK2EuGTqNAii98DLv/afn+LUr66kfnUO9atzeEK/XloF35OudnhCv3oiZ/drfrlFI2DFUIlSfhzaF8PJ6HNUqV6usMsREXEZTwpeUrRpDlgxZDKZMHt78fP3/2pSpIiISCFQACumAgJ9OXX8Avv/OVHYpYiIiBQ7CmBF1cWLmNZ9yXWHI/C5mJCt2WQy4Rfow0/f7CH5YkohFCgiIlJ8KYAVRV9+CTVrYh7QnwHvjqXvS/cSdGBXtt18fb1JsaSy9cd9hVCkiIhI8aUAVtQcOQLDh4PDU+tLnI/llgXPUP5I9qAVWMqfPX8d4/TJOFdWKSIiUqwpgBU1GzfChQvZNnunpnDzwufwiz+fabuXlwmT2cRP3/yjCfkiIiIuogBW1Jw5k2tTyXMxdH3/BUzWtEzbA0v4cvL4eQ7uzftBryIiIlIwFMCKmgEDwGTKtbnK/r9oveqtTNtMJhO+ft788u0eUlP1qAgRERFnUwArYi5edx3xI0fmuc/1P3xB3e3fZtrm5+9DYqKF3X8ccWZ5IiIiggJYkfPQQw/RaccOolq0yHO/Dp/NotzRzM/lCgj0ZcfPB7UshYiIiJMpgBUx99xzD0eOHqVtdDS/li+f637mtFS6fvAi3slJ9m3ePmbSUq38sfWwK0oVEREpthTAiphbb72Vbdu2UbpsWbrHx/OhKfc/4tKnomm/5FVwuPsxoKQvO3+L4sL5pFzfJyIiItdGAawIaty4Mdu3b6djp0487u3D2Tz2rfv799Tfst7+2mz2wjAMtm7a6/xCRUREiikFsCKqfPnyfLV+A6MfeY0zHW/HAHK7v7Ht5/Moe/yQ/XWJUn4c2htDzLHzrihVRESk2FEAK8J8fHy4rkptdtzxOJNLlaMfkNOFRe/UFLq8/yLelotA+rIUXmYvftn4rxZnFRERcQIFsGLA6uvH6Zv68hXQA8hpqdayJ6Nos2K+/XVACV9OHjvP0cOxOewtIiIi10IBrJjoGDKSKV0H8BtDqcJhvLBSm8MsZqh9nwZbvqL6rl+B9FEwbx8zv27ch82mUTAREZGCpABWjBytPRWz6X3SqI2BF1HU5iHezRTCOiyehX/8OQD8A3w4GxvPob0nC6tkERGRIkkBrBhZsbYuKUZApm1JlGAi0+2vAxLO0/6z2WAY/z2i6Pu9pOkRRSIiIgVGAawYOXPOL8ftR6iZ6XXNXb9Sf+sGIOMRRQnJRPx51On1iYiIFBcKYMVIhXKWHLd7cYTILNvarJhPibMxQMYjin7az8UkPaJIRESkICiAFSOD+h7C1yfzpUR/EvFjArcAJxy2+1gu0i5jlfz0RxTZ+GPrIUREROTaKYAVIx3bnmbkXXvx9rYCBhXLJPK29yg2soSTwK1kXqKi+j/bqfPb90D6I4r+/v0ICXHJhVC5iIhI0aIAVoR5mU2ULOVPQrzFvqBqx7anqV8nnsYNLjBn+u/Uu+s62gNrgQPAwiyf0WbFfPziz2M2e2EzDP7crgd1i4iIXCsFsCLMy8uLQSPaE1S5NAkXkjFyWM/rUNueHGnWie7Ab8CzWdr9E+Nom7FAa2AJXyL+OEKcHtQtIiJyTRTAirgSpfzpd3cbGjerRnxcMtY0W+YdTCa23/kEKf4luIH0E+IgMBm4FNfq/L6Ran9vwcvshWGDHT8fcOl3EBERKWoUwIoBb28z3UOC6dS9EYkJlmzPd7xYthLhAx6xv14BTM34dUnbz+dhTrEQWMqPfREnOHs6wSW1i4iIFEXehV2AuIbJZKJl+zr4+nljMm3HP9AXMNvb93cMofbvG7lu35/8D/gHeB6oDdwDlDpzkuBvP2Nnn5HgBds27+f2QS0L46uIiIh4PKeOgC1YsICQkBBCQkKYOXMmAOPHj6dnz56EhYURFhbGd99958wSJIumLWtwa99mJCelkOq4ur3JxLahT5Pm44sJeBfoDjwAbMnYJfi7zyh5+hglSvoRuT+GUycuuLx+ERGRosBpAWzLli388ssvrFq1itWrV7N7926+++47IiIi+PTTT1mzZg1r1qzh1ltvdVYJkouGTavmGMLig6qz8/Z7AfAl/VJkTbA/qMiclkrbFfMxmUyYzF5s2bQ32+VMERERyZ/TAlilSpUYN24cvr6++Pj4UK9ePY4fP87x48eZMGECoaGhzJs3D5vNlv+HSYFr2LQqPcOaYUlKITUlzb59T/c7OF85/dFE5YDvgM8d3lc9YhvV/95CYAlfjh05y4nocy6tW0REpChwWgBr0KABLVq0ACAyMpINGzZw00030b59e6ZPn87y5cv5/fffWbFiRbb3xsXFER0dnenXyZMnnVVqsdXg+qrc1r8FluQ0+0iYzduH3waPse9TBwgA4ki/LAnQ5vP5mNNSMHt7sWXTPo2CiYiIXCGT4eR/Pffv38/DDz/M6NGj6d+/f6a27777jtWrV/PGG29k2j5//nwWLFiQaVvFihWZN2+eM0sttmKOJbL7t1h8fM2YzSYAei2ZSYOIX+37zAbGAh8AI4Ffet3LH537YblopUXnypSv5F8YpYuIiLi14OBg/Pz8sm136l2Q4eHhjBkzhgkTJhASEsLevXuJjIzktttuA8AwDLy9s5cwYsSIbGHNarUSGxub6xe5kppat2591e8vklpDrZpH+fGr3QSW8sNs9mLnkMepPSUcn5T0Rw89CWwARgEdgDabVxDdfQAXfAM5d9xEuYoGN954YyF+iaJJ56tzqF+dQ/3qHOpX53B2v1osFiIiInJtd9olyBMnTvDYY48xe/ZsQkJCgPTANX36dC5cuEBqairLli3LcRJ+6dKlqV69eqZfVapUcVapAjRtUYN2NzckMd6CYTNIKhfErt732NvNwCekX44cCnAxgRu+/hT/QB9iY+I5H2spnMJFREQ8kNMC2Pvvv4/FYmHGjBn2JSf+/PNPHnroIYYOHUpISAhNmjShT58+zipBrlDrDnVofEM1EuKSMQyDPd0GEV/hOnt7VWAR8BfwItD4p1WUOnMSL28Th/45r7lgIiIil8lplyAnTZrEpEmTcmwbNmyYsw4r18BkMnFz7+u5cC6RUycuUKKUP3+GPUiXD6bY9wkF3gD6kr4sRcu17/LTyOc4dTKB6Mgz1KhTsbDKFxER8Rh6FJFk4u1tpveAlvgH+JJ8MYXIVt04XatJpn0eBaqT/qzIyuGbqBj1L15eJq0LJiIicpkUwCSbwJJ+3D6wJWmpNqw2I9NzIi+xAX2AB4GWX76Pj68XsafiOXIw1tXlioiIeBwFMMlR5WplubFzPRLjLcTUu4EjzTplavcC2gCfAb//+ztVj/yLt4+ZrZu1LpiIiEh+FMAkV6071KVqzXIkJqTwR7+HsXllPl0mADcA/wc0/vYT/AN8OHMqQaNgIiIi+VAAk1yZzV7cGtoMb7OJM+WqcbB970ztvqTfFXkKmB+5m8oHduHt48U2jYKJiIjkSQFM8lSqTABdbrue5KQUdt52N1Zz5htnWwNjgK+B+l++h3+AD7Gn4omOPFMY5YqIiHgEBTDJV6PgqtSoU4FTvuU40KF3tvYpwG6g/sG/qXzwb7y9zWzfvF+jYCIiIrlQAJN8mUwmuocEYzZ78VePodlGwUpm/LIAxtp38Q/04dSJOE5Eny+EakVERNyfAphclpKlA+jQrSGxfuU40DEkx30eAYYd/BvzgV14mU1s/2m/a4sUERHxEApgctmatqxBmbKB/N5lMDYvc7b2p4ALwI9L5hBQwpcTR85y+mScy+sUERFxdwpgctnMZi9u6tmE8yXKc6jNLdnag4F7gU9ijnDxwN+YTCb+2HrI1WWKiIi4PQUwuSI161bkuhrl+K3ToBzbXwTMwFefzSSgpB8H98YQf+GiS2sUERFxdwpgckVMJhOdezTmXMXqHGnWOVt7deAJ4MTpY3jFnwUMunY1uPlm19YpIiLizhTA5IoFXVeG2g0r81ungTm2Pw9sNwyu/+07/AN9SYy3aEkKERERBwpgclXad2lATM0mnKzfPFubH+knVqUfvuDCuZPYDIOkRIvLaxQREXFXCmByVcpXKkndhkH82T4sx3Yr0OX8aVYsmoqXl4mEuGRsNo2CiYiIgAKYXIMbO9cnsnE74itcl63NDNwPbIn6l5TUCKxpNj2eSEREJIMCmFy1ikGlqF4/iF3tQ3NsHwP4M5SjRxuw/3A5bmxXisWLXVujiIiIO1IAk2vSumM99rTqSYqvf7a29QwljXexGlUAE6dj/XjwQUMhTEREij0FMLkm11UvS+na1/FPs5uztU1kOmmUyLTt4kUTEye6qDgRERE3pQAm18RkMnFjp3qE39g7W9sRaub4niNHNBlfRESKNwUwuWa16lcioVpNTtYJzrS9Jkdy3P+666yuKEtERMRtKYDJNTObvahZvwwRrXtl2j6NCQSSmGmbr08ad4RGurA6ERER96MAJgWiSo0SHG7WmZSA/+Z8DWMJC3mQWkRiwgZE0u2mdTSsdZAL55MKr1gREZFCpgAmBcLX30yd5nXY27xbpu3DWEIkdbBgppqpLtHHpmJgcGDPyUKqVEREpPApgEmBCW5Vgz1teuXY5gM8ZBjs3vsH8RfPEBF+RM+HFBGRYksBTApM5WpludiwKaerN8yxfQRgAraHf09igoXYmHiX1iciIuIuFMCkwJhMJpq1qcW/Lbrn2F4LeM/sw803dscwYP8/J1xboIiIiJtQAJMC1ahpVQ4064LNlPOpdZ81lZbRBwgI9GHPrmhsNpuLKxQRESl8CmBSoAJL+hHUohHH6rfIdZ/9G5fz45a1WJLTOHH0vMtqExERcRcKYFLgrm9Rnf3Nb861/acje/li7XukpFnYv0eXIUVEpPhRAJMCV6N2BaJuuIk0b58c24cYBknJiRyK2sXBPSex2XQ3pIiIFC8KYFLgvH3M1GhZl8jG7XJsvwUo62Xm952bSbGkERsT59oCRURECpkCmDhFw6ZVOdCiW45tPsBAm40/d/5KckoyUQdjXVuciIhIIVMAE6eoWrMc0de3I9UvIMf2IRhUDggkPvEM+/857uLqRERECpcCmDiFt7eZ2sE1iGrUJsf2HsBPtRpTq2Zdzp1JJCHuomsLFBERKUQKYOI0Da6/jkNNO+XYZgKq7vkNU1I8hs1GdNRZ1xYnIiJSiBTAxGmq1izP0SZtsZpzvhtya2oKj04aTHTMQQ7tjXFxdSIiIoVHAUycxsfHzHVNanK0Yasc268HLqYks2ffbxw9HIvVqlXxRUSkeFAAE6dqcP11HG7SIce2CkB7szd/7d6KzQanT2o5ChERKR4UwMSpqteukOtEfIBQaxpHog9w/sIZjkWdcWFlIiIihUcBTJwqINCXkg3rEFutfo7tPTJ+P3x0Nwf3nnJdYSIiIoVIAUycrkHTqhxumPMoWEvgqbIVqV2rHrExcaSkpLm2OBERkUKgACZOV7NuBY7kchnSG5h94Qz1SlfAZILTJzQPTEREij4FMHG6suVLkNikGcklSufYnmIYHP9xJXFx5zl57JyLqxMREXE9BTBxOpPJRL2m1ThSL+flKPYCT234iH8P/q7nQoqISLGgACYuUat+JY41aJFjWzBQweTFvsO7OHXigtYDExGRIk8BTFyiStWyRNfPeQTMC7jJsHHowC4MA86dSXRtcSIiIi6mACYu4e1jpkyLJlyoUDXH9nbAybMniU+4wOkTF1xbnIiIiIspgInL1G1Ymeh6LXJsa5fx+5Fj+/RgbhERKfIUwMRlqtYsR3T9Fjm2tQd+KlGGG5q04uSx864sS0RExOUUwMRlylUowekmrXNsCwBuSrxAhYsXiD+fRKoWZBURkSJMAUxcxmQyUblZfc5WrpVj+2/Aqs/ngcmkifgiIlKkKYCJS9WqV5ETtZrm2LYT+CxiKzGnjxF7Kt61hYmIiLiQApi41HXVy3Gids4B7NJE/Khj/xJzXHdCiohI0aUAJi5VsrQ/55vkvB5YE8AfiDn6r5aiEBGRIk0BTFzKZDJR4camJJSumK3Nm/RV8WOidnM2NgGbzXB5fSIiIq6gACYuV6NepVwvQzYHLpyPxTAM4uMuurYwERERF1EAE5erXLVMrgFsAfBztXoAnNedkCIiUkQpgInLlSztz4UGN+TY5g9UPLoPW5qVC+eSXFuYiIiIiyiAicuZTCZKdGqD1eydrS0FuPdiIv9sWU1sjJaiEBGRokkBTApFjUZVOVOlTrbtvsD3QOTeHZw5rQAmIiJFkwKYFIpKVUpzulqDHNuaAMdPR3P+rOaAiYhI0aQAJoWiTLlAztRqlGPb9UBkwnlSktOwJKe6tjAREREXUACTQmEymTDd2CbHtibAeZuVxMQzmogvIiJFkgKYFJoyXdqQ5u2bbXsw6euBmaP3kxCf7PK6REREnE0BTApNUPUKxFatl217d+Av4IbkiyRcUAATEZGiRwFMCk35oFLEXlc31/aKp6I4dybBhRWJiIi4hgKYFBpfX2+S6uU8EX8o8NrOHzmn1fBFRKQIUgCTQuXbsnmO288BEXGahC8iIkWTApgUqhIdbsxxez3gkDUNy+mz2Gw21xYlIiLiZApgUqjKNahBQumK2bbXBS4AftF7uZiY4vK6REREnEkBTApVuQolOFulVrbtNTN+T4vaTZICmIiIFDEKYFKozGYvLtZumG17Y6APUPbMCZISLS6vS0RExJkUwKTwNbsh26YbgC+BtvFnuZikETARESlanBrAFixYQEhICCEhIcycOROALVu2EBoaSs+ePZk7d64zDy8ewr9Ny1zbyp84TKJWwxcRkSLGaQFsy5Yt/PLLL6xatYrVq1eze/du1q1bx4QJE3jzzTf56quviIiIYPPmzc4qQTxEyXatMEymbNs7A48kXSDx6EnXFyUiIuJE3s764EqVKjFu3Dh8fdOf9VevXj0iIyOpVasWNWrUACA0NJSvv/6arl27ZnpvXFwccXFxmbZZrVZnlSqFrGz1isSXrUzpc5mDlg9wGDD2HwA6FUZpIiIiTuG0ANagQQP7z5GRkWzYsIG7776bSpUq2bcHBQURExOT7b0fffQRCxYsyLStYsWKzJs3j4iIiGuuLTw8/Jo/Q7K7ln4NqlglWwCrAfwEJO+OKNZ/ZsX5uzuT+tU51K/OoX51jsLsV6cFsEv279/Pww8/zP/+9z/MZjORkZH2NsMwMOVw6WnEiBH0798/0zar1UpsbCzBwcH4+flddT3h4eG0bt36qt8vObvWfj3WsBHs/yvTtirASaDc2VPF9s9M56tzqF+dQ/3qHOpX53B2v1osljwHjZwawMLDwxkzZgwTJkwgJCSEHTt2cPr0aXv76dOnCQoKyva+0qVLU7p06UzbLBYLsbGxzixXCpF340awPvO2KoAFME5EYbXaMJt1066IiBQNTvsX7cSJEzz22GPMnj2bkJAQAJo3b87hw4eJiorCarWybt06unTp4qwSxIP439Ak27YbgUeAkudOkGJJc3lNIiIizuK0EbD3338fi8XCjBkz7NuGDBnCjBkzGD16NBaLha5du9KrVy9nlSAeJLBF02zbumT8Sjp/GktyKgGBvi6vS0RExBmcFsAmTZrEpEmTcmxbu3atsw4rHsqnUQMMkwmTYWTangaYE86RcvoslC9ROMWJiIgUME2qEffg709yhcqZNp0DfIG3AOv+A4VRlYiIiFMogInbSKtVO9PrsqQP0cYAHDjo8npEREScRQFM3Ef9BplemvhvKQoOKoCJiEjRoQAmbsO7ScNs2yqTHsDMhxXARESk6FAAE7fh17Rxtm0VgLOAz9Eol9cjIiLiLE5fCV/kcnnVr59t2zAgHvCNOe7yekRERJxFAUzcR8ZD2h0Nz/jdeuYU2GzgpUFbERHxfPrXTNxH+fLY/PwzbbIA0YBXWgo4PMZKRETEkymAifswmbBWq55p05tADeACwNGjhVCUiIhIwVMAE/eS5TJk+YzfzwIcOeLqakRERJxCAUzcirlO7UyvFcBERKQoUgATt+JVq2am144BzBappShERKRoUAAT95LHJUjjuJaiEBGRokEBTNzLdddlelkNmAk0B1AAExGRIkLrgIl7yRLASgNjM362xsS4vBwRERFn0AiYuJcsAQzgEHAUMJ086fJyREREnEEBTNxLpUoYWVa77wxMBbwS4iExsVDKEhERKUgKYOJezGaoXDnTphJAwqUXJ064uiIREZECl+ccsJSUFJYtW8a3337L4cOHMZvN1K1bl169etG/f398fX1dVacUI6brrssUtEoA9nGvEycgh4d2i4iIeJJcA9iOHTuYOnUqrVu35p577qF69ep4e3sTHR3Nzz//zMCBA5kwYQIdOnRwZb1SHGSZB6YRMBERKWpyDWA//PADS5YsoWTJkpm2N2jQgG7dupGQkMCCBQsUwKTgZQlgJcl4FiQogImISJGQawB79tln83xjyZIlGTduXIEXJEKVKplePgmkXnoRG+vqakRERApcvpPwDx48yOeff45hGDzxxBPccsstbNu2zRW1SXFVqVKml72A0EsvFMBERKQIyDeAPf/88/j5+fHjjz8SExPDtGnTmDt3ritqk+KqYsVML48C2y+9UAATEZEiIN8AZrFY6Nu3L7/88gu9e/emXbt2pKam5vc2kauXJYC9DnS/9EIBTEREioB8A1hKSgqxsbH8+OOPdOzYkdjYWCwWiytqk+IqSwArASQBNlAAExGRIiHfAHbnnXfSrVs3WrduTf369Rk0aBAjRoxwRW1SXGUJYJfuw00CBTARESkS8n0Yd48ePRgyZAheGY+HWbVqFWfOnHF6YVKM5TACBumLsZaMjQXDAJPJ5WWJiIgUlFxHwM6fP8/58+d58MEHiY+Pt7+2Wq2MGjXKlTVKcRMYCAEB9peOAYy0NIiLK4yqRERECkyuI2BPP/00v/76KwDt2rX77w3e3tx2223Or0yKt4oV4ehRAG4GvgDsi1PExkKZMoVTl4iISAHINYC9//77AIwfP56XX37ZZQWJAJkCWK2MX3axsVCvXmFUJSIiUiByDWAHDx6kXr163H333ezevTtbe9OmTZ1amBRzFSrYf4wDtgItgSCA06cLpyYREZECkmsAmzlzJu+88w6jR4/O1mYymdi4caNTC5NiziGAHSR9NfzVQBjAhQs5vkVERMRT5BrA3nnnHQA2bdrksmJE7BzmeF2ahJ9waYMCmIiIeLh8l6GIjY1l6dKlnD9/PtP2SZMmOasmEShd2v5jprsgQXdBioiIx8s3gD3zzDMEBARw/fXXY9LaS+IqDiNggRm/J13aoBEwERHxcPkGsJiYGDZs2OCKWkT+4zACdukkTbu0QSNgIiLi4fINYFWrViUpKYnAwMD8dhUpOA4BLBD4Bmh0aYNGwERExMPlG8CCgoLo168fbdu2xd/f375dc8DEqRwuQZqBno5tGgETEREPl28Aq1atGtWqVXNFLSL/cRgBM4AVQBMgGDQCJiIiHi/fAKbnPkqhcBgBMwGDgefICGAaARMREQ+XbwALDQ3NcfuXX35Z4MWI2DmMgEH6ZUjrpRcKYCIi4uHyDWDPPfec/efU1FTWr19PjRo1nFqUSNaHbXvjcBekLkGKiIiHyzeAtW3bNtPrjh07MmTIEB555BGnFSWS7wiYYYDWpRMREQ/ldaVvOHfuHKdOnXJGLSL/8fcHHx/7S28cAlhqKiQnF0ZVIiIiBeKK54AdP36cO++802kFiQDpo1ulS8OZMwB8B1R2bI+Lg4CAwqhMRETkml3RHDCTyUT58uWpV6+eU4sSATIFsLZZ2y5cgMqVs71FRETEE1zxHDARlylVyv7jMqAa0PnShsTEHN4gIiLiGa54DpiIyzjMAXsaWOTYlpaWdW8RERGPoQAm7ivLJPxMkSs11dXViIiIFBgFMHFfud0FCQpgIiLi0a4qgM2fP7+g6xDJziGAmdEImIiIFB1XFcAMwyjoOkSy8/7vHpFsI2CaAyYiIh4s37sgczJmzJiCrkMkO4cRsNWAv2ObRsBERMSD5RvAbDYby5cvZ8uWLXh7e9OlSxf69evngtKk2HMIYA2ytimAiYiIB8s3gM2YMYN///2Xvn37YhgGy5cvJzIykieeeMIF5Umx5hDAlgF+QL9LGxTARETEg+UbwLZs2cLq1avxzpiP07dvXwYMGKAAJs7nMAdsLlAGhwCmOWAiIuLB8p2EX6JECazW/6Y/m0wmAgMDnVqUCKBlKEREpMjKdQRs0aL0dccrVqzIsGHDCAsLw8vLi6+++oq6deu6rEApxrQMhYiIFFG5BrB9+/YBULp0aUqXLs0///wDQM2aNV1TmUiWEbAUxzYFMBER8WC5BrCXX34ZgDlz5vD000+7rCARO4c5YBoBExGRoiTfOWA//vijC8oQyYHDCNgnpK8FZqdJ+CIi4sHyvQuyevXq3HfffbRq1YoSJUrYt48cOdKphYk4BrDKWds0AiYiIh4s3wBWtmxZAI4dO+bsWkQycwhgK4AzwMOXNiiAiYiIB8s3gF2aCybicg5zwJYB/6AAJiIiRUO+AezPP/9k4cKFJCUlYRgGNpuN6OhozQ0T58sYAVvMUL5iOknUpDZHmMYEhmkOmIiIeLB8J+FPmjSJli1bkpCQQGhoKCVLlqRnz56uqE2KOx8fFjOUh3iXJGoDXkRRm4d4l8U7gwu7OhERkauW7wiYyWTioYce4ty5c9StW5fQ0FAGDhzoitqkuPPxYSLTSaJEps1JlGDiz70YVkhliYiIXKvLehQRpC/Aun//fvz9/fHyyvdtItfO25sj5Lzw75H4ci4uRkREpODkOwLWrFkznnjiCR5//HEefvhhIiMj7Q/mFnEqHx9qcoQoamdrqlnyLFDB5SWJiIgUhHyHsiZMmMC9995LnTp1mDBhAjabjTlz5riiNinufHyYxgQCScy0OZBEprVaUUhFiYiIXLtcA9iWLVuA9DlgLVq0AODmm29mwoQJ9odx//LLL86vUIovHx+GsYSFPEglIgEbtYhkIQ8yrKbOPRER8Vx5BrBHH32UzZs3k+Zwy39KSgo///wzDz/8ML/++qtLipRiKmMZimEs4S7qUAYzkdRhGEu0DpiIiHi0XCdzPfPMM+zcuZP58+fzxBNPEBQUhM1mIzY2lhtvvJFHH32Uli1burJWKW4c5hp6k+Vh3FoHTEREPFies+mbN2/Oe++9R3x8PFFRUZhMJmrWrEmpUqUu68MTEhIYMmQIb7/9NtWrV2f8+PGEh4cTEBAAwKhRo7j11luv/VtI0eTwKCIzYHVs0wiYiIh4sMu6nbFUqVIEB1/Zwpc7d+5k0qRJREZG2rdFRETw6aefEhQUdEWfJcWUQwDLNgKmACYiIh7MaetJLF++nOeff57//e9/AFy8eJHjx48zYcIEYmJiuPXWWxk1alSOa4rFxcURFxeXaZvVas22nxRxGgETEZEiymQYhuHMA3Tv3p2PP/4YwzCYMWMGzz//PKVKleLhhx+mT58+DB48ONt75s+fz4IFCzJtq1ixIvPmzXNmqeJmSv32Gw0feQRID18G//0fQ3zr1ux7553CKk1EROSyBAcH4+fnl217viNgmzZtolu3bphMpmsqoEaNGrzxxhv218OHD2f16tU5BrARI0bQv3//TNusViuxsbG5fpHLFR4eTuvWra/6/ZIzp/RrUpL9R3OWplL+/sXiz1Hnq3OoX51D/eoc6lfncHa/WiwWIiIicm3PdyHWTz75hB49evDmm29y+vTpqy5k7969fPPNN/bXhmHkuqJ+6dKlqV69eqZfVapUuepji4dyuAT5HfAIkHJpgy5BioiIB8s3gC1atIgPP/yQpKQkBg8ezOOPP87WrVuv+ECGYTB9+nQuXLhAamoqy5Yt0x2QkjeHALYTeBuwXNqgACYiIh7ssp6qXbNmTZ588knGjRtHREQETz31FKGhoezateuyD9S4cWMeeughhg4dSkhICE2aNKFPnz5XXbgUAw4jpJcuQdon4msdMBER8WD5zgGLiopi+fLlrFmzhkaNGjFhwgS6devGzp07eeKJJ9i0aVOe73dsHzZsGMOGDbv2qqV4yLIMBTgEMI2AiYiIB8s3gN1xxx3079+fTz/9lNq1a9u3t2zZkrZt2zqzNinusixDAQ5rgSmAiYiIB8v3EuRzzz3H+PHjM4Wv1atXAzBjxgxn1SWSKYD5Av6A7dIGBTAREfFguY6Abdq0ibS0NF5//XX8/f25tFxYWloa8+fPp1+/fq6qUYorhzlgD2T8stMcMBER8WC5BrA9e/awbds2zpw5w8cff/zfG7y9uffee11RmxR3DiNg2WgETEREPFiuAeyxxx7jscceY/HixZo4L4XDIYBtAd4EZgNVQAFMREQ8Wq4BbM2aNYSFhWGxWFi0aFG29pEjRzq1MBHHABYFLAYmoQAmIiKeL9cAFhUVBcD+/ftdVoxIJg5zwLIuQ2GkpXFtD8cSEREpPLkGsDFjxgDw8ssv27elpKQQGxtL1apVnV+ZSA7rgGkZChERKQryXYbiu+++Y+rUqSQkJNCrVy/CwsL46KOPXFGbFHfm/x7BnXUdMJPNBjZbtreIiIh4gnwD2DvvvMPgwYP59ttvadGiBT/88ANr1qxxRW1S3JlM9lGwAKASWU5YjYKJiIiHyjeAGYZBo0aN2LJlC126dKFkyZL2NcFEnC5jHtitwCmgpWObApiIiHiofAOYl5cXX331Fb/88gudOnVi8+bNmEya/iwu4nAZMhv9j4CIiHiofAPYs88+y/Lly3nyySepVKkSb731FhMnTnRFbSLglX6K7gb6Absc2zQHTEREPFS+D+O+8cYb+fDDD+2vly5d6sx6RDLLCGBngTXAKMc2BTAREfFQ+QawP//8k1dffZULFy5kmvv15ZdfOrUwEcAewLKuAwYogImIiMfKN4BNnjyZAQMGcP3112vul7heRgDLugwFoAAmIiIeK98A5u3trccOSeHJCP2XJitmilwKYCIi4qHynYTfoEED9u7d64paRLLLGAHzB+oCgY5tCmAiIuKh8h0BO3r0KAMHDqRq1ar4+fnZt2sOmLhERgALBg5mbdMyFCIi4qHyDWBPPvmkK+oQyZlXHoO0GgETEREPle8lyLZt2+Lv78+hQ4do0aIFPj4+tG3b1hW1idgD2EGgB/CLY5sCmIiIeKh8A9jKlSsZP3487733HvHx8Tz66KMsX77cFbWJ2ANYArCJ9McR2SmAiYiIh8o3gH3yyScsW7aMkiVLUqFCBVauXMlHH33kitpE7AHs0gIomWZ9KYCJiIiHuqxnQZYsWdL++rrrrsOc1/P5RAqSApiIiBRB+QawsmXLsmfPHvsirGvXrqVMmTJOL0wEsK8DpgAmIiJFSb53QU6YMIHHH3+cI0eO0LlzZ/z8/HjzzTddUZuIfQQsAGgOZIr+CmAiIuKh8g1gdevWZc2aNURGRmK1WqlTpw5JSUmuqE3EHsDqAX9lbVMAExERD5XvJcgBAwZgNpupV68eDRs2xMfHh2HDhrmiNpG81wHTQqwiIuKhch0BGzFiBH///TfJycm0atXKvt1ms3HDDTe4pDiRSwEsCrgDmArcdqlNI2AiIuKhcg1gb7zxBufPn2fChAm8/PLL/73B25tKlSq5pDiRSwEsGfgNOOPYpgAmIiIeKtcAVrJkSUqWLMnHH39MSkoKFy9exMi45BMXF0fZsmVdVaMUZxkB7NKFSN0FKSIiRUG+k/CXLl3K9OnTSU1NtQcwk8nEnj17nF6cSNZ1wBwjlzU1Da1IJyIinijfAPbee++xZMkSmjZt6op6RDLLYyFWW5oCmIiIeKZ874KsWLGiwpcUnoyFWAOATkCQQ5M1xVoYFYmIiFyzfEfAOnfuzGeffUaPHj3w8/Ozb9ccMHGJjBGwqsAvWZqsqWkuL0dERKQg5BvAFi5cSEpKClOmTLFv0xwwcZk81gEzrJqELyIininfALZr1y5X1CGSs4wAdhzoAUwDBmQ02awaARMREc+UawDbvXt3nm/UvDBxiYwAlgr8C5x3aLKlaQRMREQ8U64BbPTo0bm+yWQysXHjRqcUJJJJHuuAGWkaARMREc+UawDbtGmTK+sQyVke64AZaboLUkREPFO+y1CIFKo81wFTABMREc+kACbuLWMdMH+gF1DDoclmVQATERHPlO9dkCKFKmMErAKwIUuToUn4IiLioTQCJu4tj3XAbJqELyIiHkoBTNxbRgA7Tfrlx48dmgybRsBERMQzKYCJe8sIYAYQDSQ4NGkSvoiIeCoFMHFveSxDoQAmIiKeSgFM3Fsey1BoEr6IiHgqBTBxb3kFMC1DISIiHkoBTNxbRgDzA+4AGjg06S5IERHxVFoHTNxbxkKsJYHlWZqMVI2AiYiIZ9IImLi3PNYBs2oETEREPJQCmLi3jAAWB5QF3nBoslk1CV9ERDyTApi4N4cRsAtAskOT5oCJiIinUgAT96ZlKEREpAhSABP3lkcA00KsIiLiqRTAxL3lOQKmACYiIp5JAUzcW0YA8wHuA25waLJpIVYREfFQWgdM3FvGOmC+wPtZmjQCJiIinkojYOLe8lgHTI8iEhERT6UAJu4tI4ClAGZgukOT1gETERFPpQAm7s1hEr4t49clGgETERFPpQAm7i2vuyA1AiYiIh5KAUzcW54BTCNgIiLimRTAxL3lEcDQCJiIiHgoBTBxbw4BbAzQzqHJsGkETEREPJPWARP35hDAXs/SpDlgIiLiqTQCJu7NZLL/eJH05SjsbApgIiLimRTAxL05LMRaApjq2KYAJiIiHkoBTNybQwAzkXkSvskwsu0uIiLiCRTAxL3lEcBQABMREQ+lACbuLc8RMBuGQpiIiHggBTBxb/lcglT+EhERT6RlKMS9OQSw8UAnxzbDRnokMyEiIuJJnDoClpCQQJ8+fYiOjgZgy5YthIaG0rNnT+bOnevMQ0tR4RDAXgR6OjZpBExERDyU0wLYzp07GTp0KJGRkQAkJyczYcIE3nzzTb766isiIiLYvHmzsw4vRYXDOmCngHjHJqUvERHxUE4LYMuXL+f5558nKCgIgF27dlGrVi1q1KiBt7c3oaGhfP311zm+Ny4ujujo6Ey/Tp486axSxZ05jIDVBqY4tmkSvoiIeCinzQGbNm1aptenTp2iUqVK9tdBQUHExMTk+N6PPvqIBQsWZNpWsWJF5s2bR0RExDXXFh4efs2fIdk5o18rHz9O9Yyfs07CT0tN5Y8//sBsLtr3kuh8dQ71q3OoX51D/eochdmvLpuEb7PZMDlcTjIMI9NrRyNGjKB///6ZtlmtVmJjYwkODsbPz++q6wgPD6d169ZX/X7JmdP6ddMm+49ZA5ivt5nglq3w8TEX/HHdhM5X51C/Oof61TnUr87h7H61WCx5Dhq5LIBVqVKF06dP21+fPn3afnkyq9KlS1O6dOlM2ywWC7GxsU6tUdxQfivh6xKkiIh4IJddu2nevDmHDx8mKioKq9XKunXr6NKli6sOL54qn5XwFb9ERMQTuWwEzM/PjxkzZjB69GgsFgtdu3alV69erjq8eCqHADYFuMGxyWZDCUxERDyR0wPYJoc5PB06dGDt2rXOPqQUJQ4B7ImsbYahuyBFRMQjFe3bx8TzOdyoEQmcdmzC5upqRERECoQCmLg3hxGw1qSvhn+JngUpIiKeSgFM3FuWSfiOTPZnQYqIiHgWBTBxb16ZT1EjywuNgImIiCdSABP3luc6YHoUkYiIeCYFMHFv+S3EKiIi4oFctg6YyFVxCGCvAHUdmtJHwFxekYiIyDVTABP35hDARmZp0giYiIh4Kl2CFPfmEMB2A0ccmkyGDcOmECYiIp5HAUzcm8NCrD1JfxyRvUkjYCIi4qEUwMS95fMwbq0DJiIinkgBTNxbXndBYqArkCIi4okUwMS9aRkKEREpghTAxL3lFcBsWohVREQ8k5ahEPfmEMDmApUdmjQCJiIinkoBTNybQwAbkLVNy1CIiIiH0iVIcW8OAex3YK9Dk0l3QIqIiIdSABP35rAO2J3AVMcmm6FHEYmIiEdSABP3luddkDa0DpiIiHgiBTBxb/ksxKoRMBER8UQKYOLe8lmIVQNgIiLiiRTAxL3lcwnSUAITEREPpGUoxL05BLA3gDIOTSZDI2AiIuKZFMDEvTkEsFuyNJkMjX+JiIhn0iVIcW8OAexn4A/HNsOGZuGLiIgnUgAT9+YQwP4PmO7QZNJdkCIi4qEUwMS9OSzEmtPDuEVERDyRApi4tzzvgjQwNAQmIiIeSAFM3FteC7FqCr6IiHgoBTBxb/mOgLm8IhERkWumZSjEvTkEsIWAv0OTybDpEqSIiHgkBTBxbw4BrF2WJq0DJiIinkqXIMW9OQSw74CfHNu0DpiIiHgojYCJe3MIYOOBykCXjNcaARMREU+lETBxb/msA6YBMBER8UQKYOLe8rkLUktRiIiIJ1IAE/eWJYA5MhkGhhbDFxERD6QAJu7NK/MpqoVYRUSkKNAkfHFvDgHsAzKfsFoHTEREPJUCmLg3hwDWNEuTSeFLREQ8lC5BintzCGDrgK8c22x6GLeIiHgmjYCJe3MIYDMAP+D2jNcmzcAXEREPpREwcW96GLeIiBRBCmDi3vJaiFWT8EVExEMpgIl7y3METJcgRUTEMymAiXvz/m+aoh5FJCIiRYUm4Yt7cwhgH2Zp8rJZXVqKiIhIQVEAE/fmEMBqZ2nyslk1B0xERDySLkGKe3MIYCuB5Q5NJo2AiYiIh9IImLg3hwD2JnARGJzxWiNgIiLiqTQCJu7NbLb/mHUSvpfNBjYFMBER8TwKYOLevLzsS1FkDWAARlqay0sSERG5Vgpg4v4yLkPmFMBMVgUwERHxPApg4v7yCGBGqibii4iI59EkfHF/GQHsY3IaAUt1eTkiIiLXSgFM3F9GAAvKoUlzwERExBPpEqS4v4wAthR4L0uTKU2XIEVExPMogIn7ywhgnwJvZW1L0yVIERHxPApg4v7ymoSvETAREfFACmDi/rQMhYiIFDEKYOL+8ghgaBK+iIh4IAUwcX8KYCIiUsRoGQpxfw6T8G1Z2zQHTEREPJACmLi/jABWMocmk+6CFBERD6RLkOL+HEbA5mRts2oETEREPI8CmLi/jAC2Bng/a5vmgImIiAdSABP3l9ckfC1DISIiHkgBTNxfXuuAaQRMREQ8kAKYuD8tQyEiIkWMApi4P4cAlpUexi0iIp5Iy1CI+3O4CzIbzQETEREPpAAm7i8jgJlzatMlSBER8UC6BCnuLyOAfQhMztqmACYiIh5IAUzcX0YA20j2y5AmLcQqIiIeqFAuQQ4fPpyzZ8/infEP65QpU2jevHlhlCKeQHdBiohIEePyAGYYBpGRkfzwww/2ACaSJwUwEREpYlx+CfLQoUMA3HffffTt25dPP83x3jaR/2glfBERKWJcPgQVFxdHhw4deO6550hNTeWee+6hTp06dOrUKdM+cXFxmd5n1Vyf4isjgPll/HKklfBFRMQTmQzDyDao4Eoffvghx48fZ8KECfZt8+fPZ8GCBZn2q1ixIvPmzXN1eeIGqs+eTeWlS3Ns2zn8UdIev8/FFYmIiFye4OBg/PyyDh8UwgjY77//TmpqKh06dADS54RlnQs2YsQI+vfvn2mb1WolNjY21y9yucLDw2nduvVVv19y5tR+rVo116bypUpTowj/eep8dQ71q3OoX51D/eoczu5Xi8VCREREru0unwMWHx/PzJkzsVgsJCQksGrVKm699dZM+5QuXZrq1atn+lWlShVXlyruIiOgvw+MztJk0hwwERHxQC4fAevWrRs7d+6kX79+2Gw27rrrLlq2bOnqMsSTZASwbcB6YL5jm+aAiYiIByqUdSCeeOIJnnjiicI4tHgi3QUpIiJFjFbCF/eXRwAzpenuWBER8TwKYOL+MgKYFxoBExGRokEBTNxfRgArDVTI0qRnQYqIiCdSABP3lxHAXgH+ydqmSfgiIuKBFMDE/eXxzFAtQyEiIp5IAUzcX0YAexcYnqVJlyBFRMQTKYCJ+8sIYLtIXwcsE12CFBERD6QAJu4vr2UoNAImIiIeSAFM3F+eAUwjYCIi4nkUwMT95bkOmEbARETE8yiAifvLCGAVgdpZmkyaAyYiIh5IAUzcX0YAmwjszNJksmkETEREPI8CmLi/PNYB012QIiLiiRTAxP1lBLCFwO1ZmnQXpIiIeCIFMHF/GQHsAPBDlibdBSkiIp5IAUzcn9YBExGRIkYBTNxfXgEsLdXl5YiIiFwrBTBxfwEBQM4BzCvF4vJyRERErpUCmLi/jABWFWiWpclsSXZ5OSIiItdKAUzcX2AgAKOB37M0eaUogImIiOdRABP3lzEClhMviy5BioiI51EAE/eXMQK2EGifpcmsETAREfFACmDi/jJGwKKB7VmazCkWMLI9oltERMStKYCJ+/PxAW9v+8nqGLdMNhukpBRGVSIiIldNAUw8Q0AApowfs413Xbzo4mJERESujQKYeIbAwNwDWFKSi4sRERG5Ngpg4hkCAqgJdM6pTSNgIiLiYRTAxDMEBnIv8DNgztqmETAREfEwCmDiGfJYC0wjYCIi4mkUwMQzBAayEGgCZLvnUSNgIiLiYRTAxDMEBBAL/IvughQREc+nACaeITAwx3XAAI2AiYiIx1EAE8/gsA6YLWubRsBERMTDKICJZ9A6YCIiUoQogIlnCAigLtCbHE5ajYCJiIiHUQATzxAYyCDgKyDbghQKYCIi4mEUwMQz5LUOmC5BioiIh1EAE88QGMi7QHUgPmubRsBERMTDKICJZwgIIAE4Rg53QWoETEREPIwCmHgGh7sgswWwxMQc37J4Mfj7g8kEtWunvxYREXEHCmDiGcqWzX0ZitOns+2+eDE89BBYLOmvo6LSXyuEiYiIO1AAE89QuXLuASwmJtvuEydmvzKZlJS+XUREpLApgIlnqFyZBsAdgG/WthwC2JEjOX9MbttFRERcSQFMPEOVKvQGlgOlsrbFxICReVysZs2cPya37SIiIq6kACaeoWRJbH7+ObelpsK5c5k2TZsGgYGZdwsMTN8uIiJS2BTAxDOYTCz0D6AscCqn9iyXIYcNg4ULoVat9Lsga9VKfz1smAtqFRERyYd3YRcgcrmSA0tw4cK57MtQQHoAa9Ik06ZhwxS4RETEPWkETDyGrURJIIe7ICHHifgiIiLuSgFMPIZRIn36fY4B7ORJl9YiIiJyLRTAxGPYSuURwHbvdmktIiIi10IBTDxGzcY3cB8QmFPjH3+4uBoREZGrpwAmHqN57/68D5TLqfHvvyElxcUViYiIXB0FMPEYKdVqYvHLcfwrPXzt2uXagkRERK6SAph4jDVffUGgJYnI3HZYtcqF1YiIiFw9BTDxKDZymYQP8OmnYLW6sBoREZGrowAmHsPklX665hrAjhyBFStcVo+IiMjVUgATj2HCBEBchety3+l//8v2XEgRERF3o0cRiccwmdIDWGTLm2nx/ZKcdzpyBMqXh169wMvz//+i/oULUKZMYZdR5KhfnUP96hzqVyfw9qZK9erp/Vq/fuGUUChHFbkK9erW5+aOYcR0DsXy65f4XUzIfeevvy6QYy5mKBOZzhFqUpMjTGMCw1hyxftcLf2V6xzqV+dQvzqH+tU5qgEsWQLffw+tWrn8+J4/RCDFRtPrmzEo5P8IqFSVf2650+nHW8xQHuJdoqiNgRdR1OYh3mUxQ69oHxERcVPnzsEjjxTKoRXAxGOkpVlJSUnGZrMRcetQYms1durxJjKdJEpk2pZECSYy/Yr2ERERN/b77xAX5/LDKoCJx/h+01c89WJ/Ro7uzoPP9KHG8cOUBI5ktM8CSubw62xG+/O5tF9aP/+pLNujqJljHVHUvOx9mjps65vDsds5tHfPob2HQ3ubHNrDHNqb5NB+t0N7jRza/8+hvVwO7c9ktFlyaCsJvJDRHptL++yM9shc2t/JaI/IpX1xRvu2XNrXZLR/n0v7xoz2Vbm0b89o/ySX9n8y2t/Kpd1Z515JoDz/eSiH9loO7Xfl0K5zL11kLu0699IV93MPgNKloUSJrFudTnPAxGMMGNSXjd/+gtWWhskr/Z7IUrHHCdy9DWxWWpHDf1iAf8bv7XJpv/R/IQZD8WI68dSkFEfw5wzJVMq2fymO8FDGz+9xhAvUznUfx7/I+gANs+zneD9nfyDrLATHv+juBE5maXf8vGHA+SztNzj8fC9wMUt7G4efOzOUzQ7f/yYm0DljLpuZnPuubcbvAbm0t8z4vVQu7Zf+oi6fS3ujjN+r5NJeN+P3Grm0V8/4vV4u7ZUdjpNT+6XHXgXn0l4q4/drPfduIvv/DZsdfu4GlM7S7vhMiJ5A1SztBXHuXZrfGOVwTjTJOCcK8tx7CMi6gl/njN917hXPc+8SZ/+9B8Add4DZnHWr05kMw8h1WSV3YrFYiIiIIDg4GD8/v6v+nPDwcFq3bl2AlQm4rl/3Rhxj544okhItWNNsGEClQ7u56fNXKR8TddWfe2kul+PlRB+SMWEihf/Ot0ASWciD9kn2Ob0v6z6eoKh8Dyk4OiekqDNMJkyDB8PHH4Ovb4F/fn65RQFMCkSh96vVmv4syOPHr+rttUd2I+p09udMVihloaS/lSOxAdSseJFp9+xlWLfMx1j8Q1Umftwoz32u1v4DB2jgglukc/v+tSolEbnoB6cf39Vc1a+e7GrOCfWrc6hfncDbm798fGjRvbvTDpFfbtElSCkazGZo2TL911U4Epvz9rMJfsTa52YGkn5hI/MxhoXAsNl573O14sLDwQXBNrfvfyQ2EEJCnH58V3NVv3qyqzkn1K/OoX51Dmt4eKEeX5PwRYCaOc+lz3V7UVPcv79kp3NCxLkUwESAadMgMMvVlsDA9O3FQXH//pKdzgkR51IAEwGGDYOFC6FWLTCZ0n9fuDB9e3FQ3L+/ZKdzQsS5NAdMJMOwYcX7H5fi/v0lO50TIs6jETARERERF1MAExEREXExBTARERERF1MAExEREXGxQglgX375Jbfffjs9e/Zk8eLF+b9BREREpAhx+V2QMTExzJ07l5UrV+Lr68uQIUNo164d9fWYBRERESkmXD4CtmXLFtq3b0/ZsmUJDAzktttu4+uvv3Z1GSIiIiKFxuUjYKdOnaJSpUr210FBQezatSvTPnFxccTFxWXaZrVaXVKfiIiIiLO5PIDZbDZMJpP9tWEYmV4DfPTRRyxYsCDTtooVKzJv3jwiIiKuuYbwQn4AZ1GlfnUO9atzqF+dQ/3qHOpX5yjMfnV5AKtSpQq///67/fXp06cJCgrKtM+IESPo379/pm1Wq5XY2FiCg4Px8/O76uOHh4fTWk+VL3DqV+dQvzqH+tU51K/OoX51Dmf3q8ViyXPQyOVzwDp27MjWrVs5e/YsFy9e5Ntvv6VLly6Z9ildujTVq1fP9KtKlSquLlVERETEKVw+Ala5cmWefPJJ7rnnHlJTUxk0aBDNmjVzdRkiIiIihaZQHsYdGhpKaGhoYRxaREREpNBpJXwRERERF1MAExEREXExBTARERERF1MAExEREXExBTARERERF1MAExEREXExBTARERERFyuUdcCuhmEYAKSkpFzzZ1kslmv+DMlO/eoc6lfnUL86h/rVOdSvzuHMfr2UVy7ll6xMRm4tbiY+Pp59+/YVdhkiIiIil61hw4aUKlUq23aPCWA2m43ExER8fHwwmUxX9RknT57krrvu4rPPPtOzJQuQ+tU51K/OoX51DvWrc6hfncMV/WoYBqmpqZQoUQIvr+wzvjzmEqSXl1eOCfJKmM1mYmNjMZvN+Pn5FVBlon51DvWrc6hfnUP96hzqV+dwVb/6+/vn2qZJ+CIiIiIupgAmIiIi4mIKYCIiIiIuVqwCWOnSpRk1ahSlS5cu7FKKFPWrc6hfnUP96hzqV+dQvzqHO/Srx9wFKSIiIlJUFKsRMBERERF3oAAmIiIi4mLFJoB9+eWX3H777fTs2ZPFixcXdjkebfjw4YSEhBAWFkZYWBg7d+5ky5YthIaG0rNnT+bOnVvYJXqUhIQE+vTpQ3R0NECufblnzx4GDBjAbbfdxsSJE0lLSyuskj1C1n4dP348PXv2tJ+33333HaB+vRILFiwgJCSEkJAQZs6cCeh8LQg59avO12v3+uuvc/vttxMSEsKiRYsANztfjWLg5MmTRrdu3Yxz584ZiYmJRmhoqLF///7CLssj2Ww2o3PnzkZqaqp928WLF42uXbsaR44cMVJTU4377rvP+PHHHwuxSs/x119/GX369DGaNm1qHD16NM++DAkJMf7880/DMAxj/PjxxuLFiwuxcveWtV8NwzD69OljxMTEZNtX/Xp5fv31V+POO+80LBaLkZKSYtxzzz3Gl19+qfP1GuXUr99++63O12u0fft2Y8iQIUZqaqpx8eJFo1u3bsaePXvc6nwtFiNgW7ZsoX379pQtW5bAwEBuu+02vv7668IuyyMdOnQIgPvuu4++ffvy6aefsmvXLmrVqkWNGjXw9vYmNDRU/XuZli9fzvPPP09QUBBArn157NgxkpOTadGiBQADBgxQH+cha79evHiR48ePM2HCBEJDQ5k3bx42m039egUqVarEuHHj8PX1xcfHh3r16hEZGanz9Rrl1K/Hjx/X+XqN2rZty8cff4y3tzdnzpzBarUSFxfnVuerxzyK6FqcOnWKSpUq2V8HBQWxa9euQqzIc8XFxdGhQweee+45UlNTueeee3jggQey9W9MTEwhVuk5pk2blul1TudqTExMtu2VKlVSH+cha7/GxsbSvn17nn/+eUqVKsXDDz/MihUraNCggfr1MjVo0MD+c2RkJBs2bODuu+/W+XqNcurXxYsXs2PHDp2v18jHx4d58+bxwQcf0KtXL7f7+7VYjIDZbLZMD/A2DOOqH+hd3LVs2ZKZM2dSqlQpypcvz6BBg5g3b576t4Dkdq7qHL42NWrU4I033iAoKIiAgACGDx/O5s2b1a9XYf/+/dx3333873//o0aNGjpfC4hjv9atW1fnawEZM2YMW7du5cSJE0RGRrrV+VosAliVKlU4ffq0/fXp06ftlybkyvz+++9s3brV/towDKpVq6b+LSC5natZt8fGxqqPr8DevXv55ptv7K8Nw8Db21v9eoXCw8O59957efrpp+nfv7/O1wKStV91vl67gwcPsmfPHgACAgLo2bMn27dvd6vztVgEsI4dO7J161bOnj3LxYsX+fbbb+nSpUthl+WR4uPjmTlzJhaLhYSEBFatWsVTTz3F4cOHiYqKwmq1sm7dOvXvVWrevHmOfVmtWjX8/PwIDw8HYM2aNerjK2AYBtOnT+fChQukpqaybNkybr31VvXrFThx4gSPPfYYs2fPJiQkBND5WhBy6ledr9cuOjqaSZMmkZKSQkpKChs3bmTIkCFudb4WizlglStX5sknn+See+4hNTWVQYMG0axZs8IuyyN169aNnTt30q9fP2w2G3fddRctW7ZkxowZjB49GovFQteuXenVq1dhl+qR/Pz8cu3L2bNnM2nSJBISEmjatCn33HNPIVfrORo3bsxDDz3E0KFDSUtLo2fPnvTp0wdQv16u999/H4vFwowZM+zbhgwZovP1GuXWrzpfr03Xrl3ZtWsX/fr1w2w207NnT0JCQihfvrzbnK96FJGIiIiIixWLS5AiIiIi7kQBTERERMTFFMBEREREXEwBTERERMTFFMBEREREXEwBTESc4qWXXiIsLIywsDCCg4O57bbb7K+Tk5MLu7w87dq1i8mTJzv9OGPHjmXfvn1s377dvszAJYsWLaJLly78+++/nDhxglGjRmGz2Zxek4i4RrFYB0xEXG/SpEn2n7t3787s2bO54YYbCrGiy3fgwAGnPwvuq6++olSpUjRs2JDt27dnaps7dy7ffvstS5YsoVq1akD6WmafffYZd999t1PrEhHXUAATEZf7/PPPWbJkCTabjbJly/Lcc89Rr149xo0bh7+/P/v27ePMmTN0796dsmXL8sMPP3D69GleeuklOnTowLhx4/Dz8+Pff//lzJkzdOrUiUmTJuHj48PBgweZNm0a58+fx2q1Mnz4cAYNGsT27duZNm0agYGBJCYm8sUXXzBz5kx27txJYmIihmHw0ksvUbVqVebNm0d8fDzjx4+nX79+TJ06lXXr1gGwfft2++v58+fz119/cerUKRo1asTs2bN56623+Pbbb7HZbFSrVo3nn3+eypUrZ+uD+fPn8/rrr2faZrPZmDJlCv/++y+fffYZ5cqVs7fdcccdDBo0iMGDB+Pr6+vcPyARcToFMBFxqR07drB69WoWL15MQEAAv/zyC6NGjWLDhg0A/PPPPyxevJjz58/TuXNnJk2axNKlS/noo49499136dChA5B+mfDTTz/Fx8eH++67j2XLljFkyBDGjBnDzJkzadq0KfHx8dx5553Ur18fSH/g8ffff0+1atX4888/OXXqFMuWLcPLy4uFCxfy7rvv8vbbbzNmzBi++eYbXn755WyjU1kdO3aMdevW4e3tzerVq9m3bx+ff/453t7eLFu2jEmTJvHuu+9mes++ffuwWCw0bNjQvi0tLY2xY8eybt06Fi5cmCl8QfoTPcqWLcsff/xB+/btr/nPQUQKlwKYiLjUjz/+SFRUFEOGDLFvi4uL4/z580D64658fHyoVKkSgYGB3HTTTQDUrFnTvg9A//79KVGiBABhYWFs3LiR9u3bc+TIESZMmGDfLzk5mX/++Yd69epx3XXX2S/ptWzZkjJlyrB06VKOHj3K9u3b7Z93JVq0aIG3d/pfpT/88AN///03AwcOBNJHtC5evJjtPYcOHaJmzZqZth0+fJiWLVvyyiuvMG7cOFauXMl1112XaZ/q1atz+PBhBTCRIkABTERcymazERYWxtixY+2vT506RZkyZQCyXV67FG6yMpvN9p8Nw8DLywur1UqpUqVYs2aNvS02NpZSpUrx119/ERgYaN/+448/Mm3aNEaOHEmPHj2oW7cua9euzXYck8mE4xPbUlNTM7U7fqbNZuOBBx7grrvuAiAlJYULFy7k+JlZJ9TXrl2bl19+GYA//viD0aNH89lnn2XqDx8fn0zfW0Q8l+6CFBGX6ty5M+vXr+fUqVMALFmyhBEjRlzx52zYsIGUlBQsFgurVq2iW7du1KlTB39/f3sAO3HiBH369CEiIiLb+3/99Ve6devGXXfdRXBwMN9//z1WqxVID3dpaWkAlC9fnuPHj3PmzBkMw2D9+vV5frcVK1aQkJAAwOuvv87//ve/bPvVqVOHo0ePZtrm4+Nj/3nixIlYrVZefPHFTPtER0dTt27dy+keEXFzCmAi4lKdO3fmwQcf5L777iM0NJR169axYMECTCbTFX2Ov78/d911F6Ghodx4440MHDgQX19f3nzzTVasWEFoaCj33Xcfjz/+OK1bt872/iFDhrBjxw5CQ0Pp378/NWrUIDo6GpvNRosWLTh69CijRo2ifv36DBkyhIEDBzJ48GCqV6+ea0133HEHN998M4MHDyYkJIS9e/cyY8aMbPs1bNgQPz8/Dh48mOPn+Pn58frrr/P111+zbNkyIH0k78yZM7Rq1eqK+klE3JPJcBxbFxHxAOPGjaNBgwbcf//9hV3KVfvyyy8JDw/nhRdeuKz958+fT/ny5Rk2bJhzCxMRl9AImIhIIQgNDeXChQvs3bs3331PnDjB7t27M924ICKeTSNgIiIiIi6mETARERERF1MAExEREXExBTARERERF1MAExEREXExBTARERERF1MAExEREXGx/wfsqhtZNLZgUgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Train\n",
    "Thermal_posterior_Ising_model, Thermal_posterior_Ising_results = Thermal_inference_Ising_model_train(Measured_temperatures, \n",
    "                                                           Measured_tempature_dependent_Intensities_minus_back)\n",
    "\n",
    "print('Loglikelyhood = ', Thermal_posterior_Ising_results.state.best()[1])\n",
    "\n",
    "Thermal_Ising_predictions = Thermal_inference_Ising_predict(Thermal_posterior_Ising_results, T2)\n",
    "Thermal_Ising_predictions['Thermal Next Temperature'] =  T2[-1]\n",
    "\n",
    "#Plot the results curves\n",
    "plot_thermal_inference(T2, Thermal_Ising_predictions, Thermal_posterior_Ising_model, dictionary_for_histograms, Hist = False, Name = 'Figure 6')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "8a5ba926",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of measurements used for fit =  3\n"
     ]
    }
   ],
   "source": [
    "\n",
    "#Cut measurements above the TN\n",
    "used_measurements = Measured_temperatures[Measured_temperatures<Thermal_posterior_Ising_results.state.best()[0][3]]\n",
    "\n",
    "#Cut measurements below the appliablity\n",
    "relevant_index = np.nanargmax(Thermal_Ising_predictions['Thermal Best Parameter Curve'])\n",
    "used_measurements = used_measurements[used_measurements>T2[relevant_index]]\n",
    "\n",
    "#Count number of measurements\n",
    "used_measurements = used_measurements.shape[0]\n",
    "print('Number of measurements used for fit = ', used_measurements)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dead66ad",
   "metadata": {},
   "source": [
    "## Given the range of applicablility of the Ising Model, re-run the inference for the other models for a fair comparison of likelihoods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "d3b80217",
   "metadata": {},
   "outputs": [],
   "source": [
    "TN_ising = Thermal_posterior_Ising_results.state.best()[0][3]\n",
    "\n",
    "mask = Measured_temperatures > 0.5*TN_ising\n",
    "\n",
    "Measured_temperatures_cut = Measured_temperatures[mask].reshape(-1,1)\n",
    "Measured_tempature_dependent_Intensities_minus_back_cut = Measured_tempature_dependent_Intensities_minus_back[mask].reshape(-1,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d232b39a",
   "metadata": {},
   "source": [
    "### First order inference given the Ising Range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "5c93cbc7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initial chisq 604273.96(94) constraints=12.1913\n",
      "# steps: 2500, # draws: 100000\n",
      "final chisq 3.30(94) constraints=12.7675\n",
      "BK : 0.859(45)\n",
      "K : 4.881(41)\n",
      "Sigma : 5.34(23)\n",
      "TN : 69.09(18)\n",
      "Loglikelyhood =  -21.01354220115916\n",
      "Predicting\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Train\n",
    "Thermal_posterior_first_model_cut, Thermal_posterior_first_results_cut = Thermal_inference_first_order_train(Measured_temperatures_cut, \n",
    "                                                           Measured_tempature_dependent_Intensities_minus_back_cut)\n",
    "\n",
    "print('Loglikelyhood = ', Thermal_posterior_first_results_cut.state.best()[1])\n",
    "#Predict\n",
    "Thermal_first_predictions_cut = Thermal_inference_first_order_predict(Thermal_posterior_first_results_cut, T2)\n",
    "Thermal_first_predictions_cut['Thermal Next Temperature'] =  T2[-1]\n",
    "\n",
    "#Plot the results curves\n",
    "plot_thermal_inference(T2, Thermal_first_predictions_cut, Thermal_posterior_first_model_cut, dictionary_for_histograms, Hist = False)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28490d60",
   "metadata": {},
   "source": [
    "### Second order inference given the Ising Range"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "9392c2b7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initial chisq 603552.57(94) constraints=11.4131\n",
      "# steps: 2500, # draws: 100000\n",
      "final chisq 109.88(94) constraints=12.7499\n",
      "BK : 1.020(43)\n",
      "J : 15(31)e-3\n",
      "M0 : 5.739(43)\n",
      "TN : 70.000(17)\n",
      "Loglikelyhood =  -287.4429968027467\n",
      "Predicting\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Train\n",
    "Thermal_posterior_model_cut, Thermal_posterior_results_cut = Thermal_inference_second_order_train(Measured_temperatures_cut, \n",
    "                                                           Measured_tempature_dependent_Intensities_minus_back_cut)\n",
    "\n",
    "print('Loglikelyhood = ', Thermal_posterior_results_cut.state.best()[1])\n",
    "#Predict\n",
    "Thermal_predictions_cut = Thermal_inference_second_order_predict(Thermal_posterior_results_cut, T2)\n",
    "Thermal_predictions_cut['Thermal Next Temperature'] =  T2[-1]\n",
    "\n",
    "#Plot the results curves\n",
    "plot_thermal_inference(T2, Thermal_predictions_cut, Thermal_posterior_model_cut, dictionary_for_histograms, Hist = False)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7b5b19b",
   "metadata": {},
   "source": [
    "## Now let's see which is the best with the Bayes factor test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "e44e46d5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model LogLikelihoods Given the Range of Temperatures where the Ising Model is Applicable:\n",
      "First Order -21.01354220115916 \n",
      " Second Order -287.4429968027467 \n",
      " Ising -48.73950937306957\n",
      "Model LogLikelihoods Given whole Range of Temperatures:\n",
      "First Order -63.98454362545109 \n",
      " Second Order -347.78580369489833\n",
      "The most likely model is: First Order\n"
     ]
    }
   ],
   "source": [
    "list_of_models = ['First Order', 'Second Order', 'Ising']\n",
    "list_of_likelihoods = np.array([Thermal_posterior_first_results_cut.state.best()[1],\n",
    "                               Thermal_posterior_results_cut.state.best()[1],\n",
    "                               Thermal_posterior_Ising_results.state.best()[1]])\n",
    "\n",
    "print('Model LogLikelihoods Given the Range of Temperatures where the Ising Model is Applicable:')\n",
    "print(list_of_models[0], list_of_likelihoods[0], '\\n',\n",
    "            list_of_models[1], list_of_likelihoods[1], '\\n',\n",
    "            list_of_models[2], list_of_likelihoods[2])\n",
    "\n",
    "best = np.argmax(list_of_likelihoods)\n",
    "if best == 2:\n",
    "    print('The most likely model is:', list_of_models[best])\n",
    "    \n",
    "else:\n",
    "    list_of_likelihoods = np.array([Thermal_posterior_first_results.state.best()[1],\n",
    "                                  Thermal_posterior_results.state.best()[1]])\n",
    "    \n",
    "    best = np.argmax(list_of_likelihoods)\n",
    "    print('Model LogLikelihoods Given whole Range of Temperatures:')\n",
    "    print(list_of_models[0], list_of_likelihoods[0], '\\n',\n",
    "            list_of_models[1], list_of_likelihoods[1])\n",
    "    print('The most likely model is:', list_of_models[best])"
   ]
  }
 ],
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