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   "source": [
    "# Hesse and Minos\n",
    "\n",
    "We discuss how uncertainty computation with Hesse and Minos works and how the two approaches differ.\n",
    "\n",
    "iminuit (and C++ MINUIT) offers two major ways of computing parameter uncertainties from the cost function (which must be of least-squares form or negative log-likelihood), HESSE and MINOS. These have different pros and cons, on which we already touched in the basic tutorial. Here we want to go a bit deeper into the pros and cons and also try to reveal a bit of the math behind the two approaches.\n",
    "\n",
    "There are several sources which explain what HESSE and MINOS do, in particular the MINUIT User's Guide (linked from the [iminuit documentation](https://iminuit.readthedocs.io/en/latest/about.html)). The mathematical details are covered in F. James, \"Statistical Methods in Experimental Physics\", 2nd edition, World Scientific (2006)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to use a couple of technical terms from mathematical statistics when talk about proven properties. We also use recurring variable names with the same meaning throughout.\n",
    "\n",
    "* $n$ number of [observations](https://en.wikipedia.org/wiki/Sample_%28statistics%29)\n",
    "* $x$ observation from data distribution $f(x; \\theta)$ with parameter $\\theta$ (not an angle!)\n",
    "* $\\hat \\theta$ estimate of $\\theta$ obtained from a sample (the parameter value obtained from the fit)\n",
    "* $\\mathcal L$ likelihood function\n",
    "* $\\mathcal I$ [Fisher information](https://en.wikipedia.org/wiki/Fisher_information)\n",
    "* $E[\\dots]$ expectation value of $\\dots$ over distribution of $x$\n",
    "* $V[\\dots]$ variance of $\\dots$\n",
    "\n",
    "The terms **asymptotic** and **asymptotic limit** refer to inference from an infinite data sample. Mathematical properties of statistical methods are most commonly computed in this limit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## HESSE\n",
    "\n",
    "HESSE in a nutshell:\n",
    "\n",
    "* Computes approximate covariance matrix $C_{ij}$ for all fitted parameters\n",
    "* Square-root of diagonal elements of $C_{ij}$ corresponds to one standard deviation; to obtain $k$ standard deviations, multiply covariance matrix $C$ by $k^2$\n",
    "\n",
    "* Can be used to form confidence intervals $\\hat \\theta_i \\pm C_{ii}^{1/2}$\n",
    "* Only way to obtain parameter correlations\n",
    "* Comparably fast, requires:\n",
    "\n",
    "    * Numerical computation of all second derivatives of the cost function (Hessian matrix)\n",
    "    * Inverting this matrix\n",
    "* Cannot compute uncertainty for only one parameter if there are several\n",
    "* Approximately computed as by-product of MIGRAD algorithm (usually accurate enough when `strategy` >= 1 is used)\n",
    "\n",
    "The algorithm derives its name from the Hessian matrix of second derivatives which is computed to obtain the uncertainties.\n",
    "\n",
    "### How does it work?\n",
    "\n",
    "The matrix of second derivatives of the cost function is computed for all free parameters and multiplied by 2. The result is inverted and multiplied by `errordef`.\n",
    "\n",
    "MINUIT implements parameter limits by applying a variable transformation and therefore distinguishes internal and external parameter space. The Hessian matrix is computed in the internal parameter space and transformed using the chain rule to external space.\n",
    "\n",
    "### Why does it work?\n",
    "\n",
    "One can prove under general conditions in the asymptotic limit that a parameter estimate $\\hat\\theta$ obtained from the least-squares and the maximum-likelihood methods is normally distributed with minimum variance, given by the [Cramer-Rao lower bound](https://en.wikipedia.org/wiki/Cram%C3%A9r%E2%80%93Rao_bound), which is the minimum for any unbiased estimator (these methods are asymptotically unbiased).\n",
    "\n",
    "$$\n",
    "V(\\hat \\theta) \\underset{n\\rightarrow \\infty}{\\longrightarrow} \\left\\{ n E\\left[\\left( \\frac{\\partial \\ln\\! f(x;\\theta)}{\\partial \\theta} \\right)^2 \\right]_{\\theta = \\hat\\theta} \\right\\}^{-1} = \\left\\{ -n E\\left[\\frac{\\partial^2 \\ln\\! f(x;\\theta)}{\\partial \\theta^2} \\right]_{\\theta = \\hat\\theta} \\right\\}^{-1}\n",
    "$$\n",
    "\n",
    "The expectation here is taken over the data distribution. Since the expectation value is constant, we see that the variance of $\\hat\\theta$ scales goes down with $n^{-1}$ in the asymptotic limit.\n",
    "\n",
    "If the data range is independent of $\\theta$, which we usually assume (but see F. James book for a counter example), we can swap integration over $x$ and differentiation with respect to $\\theta$. Doing this and replacing the expectation with its plug-in estimate, the arithmetic average, we obtain:\n",
    "\n",
    "$$\n",
    "-n E\\left[\\frac{\\partial^2 \\ln\\! f(x;\\theta)}{\\partial \\theta^2} \\right]_{\\theta = \\hat \\theta} = -n \\frac{1}{n} \\sum_i \\frac{\\partial^2 \\ln\\! f(x_i; \\theta)}{\\partial \\theta^2}\\Big\\vert_{\\theta = \\hat \\theta} = \\frac{\\partial^2 \\big(-\\sum_i \\ln\\! f(x_i; \\theta)\\big)}{\\partial \\theta^2}\\Big\\vert_{\\theta = \\hat \\theta}\n",
    "$$\n",
    "\n",
    "We now see that the numerator contains the negative log-likelihood  function that we often plug into iminuit. If there is a vector of parameters $\\hat{\\vec \\theta}$, then this turns into the Hessian matrix of second derivatives.\n",
    "\n",
    "#### A bit of history\n",
    "\n",
    "So what about these factors of $2$ and `errordef` in MINUIT that were mentioned above? These don't appear here. There are historical reasons for those. In the asymptotic limit, the least-squares cost function that corresponds to the log-likelihood is $Q = -2 \\ln\\! \\mathcal{L} - \\text{constants}$. MINUIT was originally developed with least-squares fits in mind, therefore its internal math assumes the $Q$ form. If the second derivatives are computed from $Q$, the constants are removed but the Hessian must be multiplied by a factor of two to get the right variance. Correspondingly, if the user puts in a negative log-likelihood function, the same procedure now introduces an extra factor of two $2$, which must be compensated by the `errordef` value of 0.5 for the negative log-likelihood.\n",
    "\n",
    "### Why is HESSE approximate\n",
    "\n",
    "We started out from Cramer-Rao bound, the asymptotic limit for the parameter variance. How fast the finite sample approaches the limit depends on the problem at hand. For normal distributed data, the bound is exact.\n",
    "\n",
    "We further approximated the computation of the bound by replacing the expectation over the likelihood with the sample mean of the likelihood. \n",
    "\n",
    "## MINOS\n",
    "\n",
    "MINOS in a nutshell:\n",
    "\n",
    "* Approximate confidence intervals (intervals are wrongly claimed to be \"exact\" in some sources, including the MINUIT paper from 1975)\n",
    "* Cannot compute parameter correlations\n",
    "* Some (unverified) sources claim better coverage probability than intervals based on HESSE\n",
    "* In general slower than HESSE (requiring more function evaluations):\n",
    "    * Iteratively computes the value pair $\\theta^d, \\theta^u$ which increases the cost function by `errordef` over the minimum\n",
    "    * If the cost function has several parameters, it is minimised with respect to all other parameters during this scan\n",
    "* Can be used to compute uncertainty for only one parameter - but this is not more efficient than HESSE, since the computation requires at least one evaluation of HESSE\n",
    "\n",
    "The MINOS algorithm computes [profile-likelihood based](https://en.wikipedia.org/wiki/Likelihood_function#Profile_likelihood) confidence intervals.\n",
    "\n",
    "### How does it work?\n",
    "\n",
    "MINOS scans the likelihood along one parameter $\\theta_i$,  while minimizing the likelihood with respect to all other parameters $\\theta_k$ with $k \\ne i$. This is effectively the same as expressing the other parameter estimates as a function of $\\theta_i$, $\\hat \\theta_k(\\theta_i)$, and scanning the now one-dimensional negative log-likelihood $-\\ln \\mathcal{L}(\\theta_i; \\theta_k = \\hat \\theta_k(\\theta_i) , k\\ne i)$. This is called the [profile likelihood](https://en.wikipedia.org/wiki/Likelihood_function#Profile_likelihood) for parameter $\\theta_i$.\n",
    "\n",
    "One follows this curve until $-\\ln \\mathcal{L}$ increases by `errordef` with respect to its minimum and stores the two corresponding values $\\theta^d_i$ and $\\theta^u_i$. The interval $(\\theta^d_i, \\theta^u_i)$ has $68\\,\\%$ coverage probability in the asymptotic limit. In multi-dimensional parameter space, the computation is comparably expensive due to the iterative steps of scanning and minimization.\n",
    "\n",
    "An efficient algorithm to compute the interval is described by Venzon and Moolgavkar in *A Method for Computing Profile-Likelihood-Based Confidence Intervals*, Journal of the Royal Statistical Society C37 (1988) 87–94 [DOI](https://doi.org/10.2307%2F2347496).\n",
    "\n",
    "### Why does it work?\n",
    "\n",
    "We define the likelihood ratio $\\ell(\\vec\\theta) = \\mathcal{L}(\\vec\\theta) / \\mathcal{L}(\\hat{\\vec\\theta})$. In the asymptotic limit, $-2 \\ln \\ell(\\vec\\theta)$ is $\\chi^2(k)$ distributed, where $k$ is the number of fitted parameters. For $k = 1$, the $\\chi^2$-interval $[0, 1)$ contains $68\\,\\%$ probability. For a single parameter fit therefore a corresponding interval is found by the two values $\\theta^d$ and $\\theta^u$ which solve\n",
    "\n",
    "$$\n",
    "-2\\ln\\ell(\\theta) = 1 \\Leftrightarrow -\\ln\\ell(\\theta) = 1/2\n",
    "$$\n",
    "\n",
    "We recognize the difference in the negative log-likelihood on the left-hand side and our `errordef = 0.5` on the right-hand side. Confidence intervals with other coverage probability can be constructed by finding the corresponding upper value of the $\\chi^2$-interval with that integrated probability. In a least-squares fit, we have\n",
    "\n",
    "$$\n",
    "\\Delta Q(\\theta) = -2 \\ln \\ell(\\theta) = 1\n",
    "$$\n",
    "\n",
    "therefore `errordef = 1` is the crossing value for a least-squares cost function.\n",
    "\n",
    "In the multi-parameter case, when we search for the interval for $\\theta_i$, the other parameters are effectively fixed to their best-fit values for the current value $\\theta_i$ in the scan, $\\theta_k = \\hat\\theta_k(\\theta_i)$. Therefore, during the scan they are not free. The profile likelihood is effectively a likelihood for a single parameter. Thus, $68\\,\\%$-intervals are also here obtained when the negative log-likelihood crosses the value $1/2$ above the minimum. \n",
    "\n",
    "### Why is MINOS approximate\n",
    "\n",
    "In some sources, the MINOS intervals are wrongly described as *exact*. They are not exact, because for finite samples the intervals do not necessarily have $68\\,\\%$ coverage probability, only in the asymptotic limit.\n",
    "\n",
    "Some sources claim that two approximations are involved in the HESSE calculation of an interval, but only one in the MINOS calculation and conclude that MINOS intervals therefore approach the asymptotic limit more rapidly. This claim is disputed by others."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Coverage probability\n",
    "\n",
    "We compute the coverage probability of HESSE and MINOS intervals in toy experiments.\n",
    "\n",
    "### Poisson distributed data\n",
    "\n",
    "We construct HESSE and MINOS intervals for a counting experiment. We consider the extreme case of a single observation $k$ drawn from a Poisson distribution $P(k;\\lambda)$. We use the maximum-likelihood method to find the best estimate for $\\lambda$ for each $k$ under the constraint $\\lambda > 0$, which is trivially just $\\hat \\lambda = k$, and construct intervals with the HESSE and MINOS algorithms to check their coverage.\n",
    "\n",
    "This case can be fully handled analytically, but here we use iminuit's HESSE and MINOS algorithms to compute the intervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy.stats import multivariate_normal, poisson\n",
    "from argparse import Namespace\n",
    "from iminuit import Minuit\n",
    "from functools import lru_cache\n",
    "import joblib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "@lru_cache(10000)\n",
    "def run(k):\n",
    "    m = Minuit(lambda lambd: -poisson.logpmf(k, lambd), lambd=k + 1)\n",
    "    m.limits[\"lambd\"] = (0, None)\n",
    "    m.errordef = Minuit.LIKELIHOOD\n",
    "    m.migrad()\n",
    "    m.hesse()\n",
    "    m.minos()\n",
    "    assert m.valid\n",
    "\n",
    "    p = m.values[\"lambd\"]\n",
    "    dp = m.errors[\"lambd\"]\n",
    "    pm = max(p + m.merrors[\"lambd\"].lower, 0.0), p + m.merrors[\"lambd\"].upper\n",
    "\n",
    "    r = p, dp, *pm\n",
    "    return r\n",
    "\n",
    "\n",
    "rng = np.random.default_rng(seed=1)\n",
    "nmc = 5000\n",
    "mu = 10 ** np.linspace(-1, 2, 100)\n",
    "\n",
    "pcov = {\n",
    "    \"HESSE\": np.empty_like(mu),\n",
    "    \"MINOS\": np.empty_like(mu),\n",
    "}\n",
    "\n",
    "for i, mui in enumerate(mu):\n",
    "\n",
    "    nh = 0\n",
    "    nm = 0\n",
    "    for imc in range(nmc):\n",
    "        k = rng.poisson(mui)\n",
    "\n",
    "        p, dp, pd, pu = run(k)\n",
    "\n",
    "        if p - dp < mui < p + dp:\n",
    "            nh += 1\n",
    "        if pd < mui < pu:\n",
    "            nm += 1\n",
    "\n",
    "    pcov[\"HESSE\"][i] = nh / nmc\n",
    "    pcov[\"MINOS\"][i] = nm / nmc\n",
    "\n",
    "fig, ax = plt.subplots(1, 2, figsize=(10, 4))\n",
    "\n",
    "plt.sca(ax[0])\n",
    "n = np.arange(101)\n",
    "interval = {\n",
    "    \"HESSE\": np.empty((len(n), 2)),\n",
    "    \"MINOS\": np.empty((len(n), 2)),\n",
    "}\n",
    "for i, k in enumerate(n):\n",
    "    p, dp, pd, pu = run(k)\n",
    "    interval[\"HESSE\"][i] = (p - dp, p + dp)\n",
    "    interval[\"MINOS\"][i] = (pd, pu)\n",
    "\n",
    "for algo, vals in interval.items():\n",
    "    plt.plot(n, vals[:, 0] - n, color=\"C0\" if algo == \"HESSE\" else \"C1\", label=algo)\n",
    "    plt.plot(n, vals[:, 1] - n, color=\"C0\" if algo == \"HESSE\" else \"C1\", label=algo)\n",
    "plt.xlabel(\"$k$\")\n",
    "plt.ylabel(r\"$\\lambda^d - \\hat\\lambda$, $\\lambda^u - \\hat\\lambda$\")\n",
    "\n",
    "plt.sca(ax[1])\n",
    "for algo, vals in pcov.items():\n",
    "    plt.plot(mu, vals, label=algo)\n",
    "\n",
    "plt.axhline(0.68, ls=\":\", color=\"0.5\", zorder=0)\n",
    "plt.xlabel(r\"$\\lambda$\")\n",
    "plt.ylabel(\"coverage probability\")\n",
    "plt.legend()\n",
    "plt.semilogx();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this special case, the intervals found by both methods are very close. The MINOS interval is identical to the HESSE interval up to a small almost constant shift. Visually, the rate of converge to the asymptotic coverage probability of 68% seems to be equal for both methods."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can speak about the rate of convergence although we have drawn only a single observation from the Poisson pdf. The log-likelihood for $n$ observations with the same expectation is identical to the log-likelihood for one observation with an $n$-times higher expectation up to additive constants.\n",
    "\n",
    "$$\n",
    "\\ln L = \\sum_i^n (\\lambda_i - k_i \\ln \\lambda_i)\n",
    "= \\lambda - \\sum_i k_i (\\ln \\lambda - \\ln n)\n",
    "= \\lambda - k \\ln \\lambda + k \\ln n\n",
    "$$\n",
    "\n",
    "with $\\sum_i^n \\lambda_i = \\lambda$, $\\sum_i^n k_i = k$, and $\\lambda_i = \\lambda / n$. Therefore, the test cases with large values of $\\lambda$ correspond to large observation samples with a small constant $\\lambda$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fit of transformed normally distributed data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <th colspan=\"5\" style=\"text-align:center\" title=\"Minimizer\"> Migrad </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Minimum value of function\"> FCN = 3.122 </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"Total number of function and (optional) gradient evaluations\"> Nfcn = 168 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:left\" title=\"Estimated distance to minimum and goal\"> EDM = 2.02e-05 (Goal: 0.0001) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center\" title=\"Total run time of algorithms\">  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Valid Minimum </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> No Parameters at limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td colspan=\"2\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below EDM threshold (goal x 10) </td>\n",
       "        <td colspan=\"3\" style=\"text-align:center;background-color:#92CCA6;color:black\"> Below call limit </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Covariance </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\"> Hesse ok </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix accurate?\"> Accurate </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Is covariance matrix positive definite?\"> Pos. def. </td>\n",
       "        <td style=\"text-align:center;background-color:#92CCA6;color:black\" title=\"Was positive definiteness enforced by Minuit?\"> Not forced </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌─────────────────────────────────────────────────────────────────────────┐\n",
       "│                                Migrad                                   │\n",
       "├──────────────────────────────────┬──────────────────────────────────────┤\n",
       "│ FCN = 3.122                      │              Nfcn = 168              │\n",
       "│ EDM = 2.02e-05 (Goal: 0.0001)    │                                      │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│          Valid Minimum           │        No Parameters at limit        │\n",
       "├──────────────────────────────────┼──────────────────────────────────────┤\n",
       "│ Below EDM threshold (goal x 10)  │           Below call limit           │\n",
       "├───────────────┬──────────────────┼───────────┬─────────────┬────────────┤\n",
       "│  Covariance   │     Hesse ok     │ Accurate  │  Pos. def.  │ Not forced │\n",
       "└───────────────┴──────────────────┴───────────┴─────────────┴────────────┘"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th title=\"Variable name\"> Name </th>\n",
       "        <th title=\"Value of parameter\"> Value </th>\n",
       "        <th title=\"Hesse error\"> Hesse Error </th>\n",
       "        <th title=\"Minos lower error\"> Minos Error- </th>\n",
       "        <th title=\"Minos upper error\"> Minos Error+ </th>\n",
       "        <th title=\"Lower limit of the parameter\"> Limit- </th>\n",
       "        <th title=\"Upper limit of the parameter\"> Limit+ </th>\n",
       "        <th title=\"Is the parameter fixed in the fit\"> Fixed </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 0 </th>\n",
       "        <td> cx </td>\n",
       "        <td> 0.11 </td>\n",
       "        <td> 0.06 </td>\n",
       "        <td> -0.08 </td>\n",
       "        <td> 0.05 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th> 1 </th>\n",
       "        <td> cy </td>\n",
       "        <td> 0.05 </td>\n",
       "        <td> 0.10 </td>\n",
       "        <td> -0.11 </td>\n",
       "        <td> 0.08 </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "        <td>  </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌───┬──────┬───────────┬───────────┬────────────┬────────────┬─────────┬─────────┬───────┐\n",
       "│   │ Name │   Value   │ Hesse Err │ Minos Err- │ Minos Err+ │ Limit-  │ Limit+  │ Fixed │\n",
       "├───┼──────┼───────────┼───────────┼────────────┼────────────┼─────────┼─────────┼───────┤\n",
       "│ 0 │ cx   │   0.11    │   0.06    │   -0.08    │    0.05    │         │         │       │\n",
       "│ 1 │ cy   │   0.05    │   0.10    │   -0.11    │    0.08    │         │         │       │\n",
       "└───┴──────┴───────────┴───────────┴────────────┴────────────┴─────────┴─────────┴───────┘"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "    <tr>\n",
       "        <td></td>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> cx </th>\n",
       "        <th colspan=\"2\" style=\"text-align:center\" title=\"Parameter name\"> cy </th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th title=\"Lower and upper minos error of the parameter\"> Error </th>\n",
       "        <td> -0.08 </td>\n",
       "        <td> 0.05 </td>\n",
       "        <td> -0.11 </td>\n",
       "        <td> 0.08 </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th title=\"Validity of lower/upper minos error\"> Valid </th>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> True </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th title=\"Did scan hit limit of any parameter?\"> At Limit </th>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th title=\"Did scan hit function call limit?\"> Max FCN </th>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <th title=\"New minimum found when doing scan?\"> New Min </th>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "        <td style=\"background-color:#92CCA6;color:black\"> False </td>\n",
       "    </tr>\n",
       "</table>"
      ],
      "text/plain": [
       "┌──────────┬───────────────────────┬───────────────────────┐\n",
       "│          │          cx           │          cy           │\n",
       "├──────────┼───────────┬───────────┼───────────┬───────────┤\n",
       "│  Error   │   -0.08   │   0.05    │   -0.11   │   0.08    │\n",
       "│  Valid   │   True    │   True    │   True    │   True    │\n",
       "│ At Limit │   False   │   False   │   False   │   False   │\n",
       "│ Max FCN  │   False   │   False   │   False   │   False   │\n",
       "│ New Min  │   False   │   False   │   False   │   False   │\n",
       "└──────────┴───────────┴───────────┴───────────┴───────────┘"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(-0.1, 0.2)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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pT2CEP1JCW0sbbS1tWFutuLi64OrhiquHEVf3jo+a8joO5BykvuZ/1WMuRgM+gd74Bvp0/uqNX4iJyfMnMPWkSXiZ1JAlRxNCZEopkwd6nWGRoQkhxkopczu/PAfY3Xl7KFAmpZRCiBl0lGFU9fHaEUFBQT9ed911Y6+++mr9uHHjhuwrPyklFosFs9mM2WymtraW5uZmjEYj7u7u3Qmpt7c3gYGB3V/r9fpfXGvVqlUsXLjwsNusVusvEuS6ujosFgvNzc20tbXh6emJyWTCZDLh6+s7ZMcQu7m5cfLJJ+Pv7+/58ssv3/LNN99MFUKcfaKeuFLKe+nYpe2ZxP5aCBEmpSwRHX+5zgV2HPMiiqIoQ1BjXRMZK7LJyyqgYMd+Crbtp6yoAgC9Qc/Y6bGcdt1iAsL88AnwxtvfC58Ab4KjAgmM9MfF2LcNEikl5oo69uccZH9OMaUF5dRV1VNbWUdtZT15WYVUFlfzxUvfotPrSEgdS8qSqSQvmcKYpNEYXIZFijQiDbmdWyHEB8BCIBAoo6P8YCkwno4axiLgJillsRDiFuBmOnbJmoE/SCk39GGtmWFhYcvvueee4AsuuIDw8HD7fjMas9lsVFVVUVlZidlsxmKx4O7ujq+vb3eC6ebm1q9k/WjJ7YlIKWlsbOxOrM1mM62trXh6euLr60tQUBB+fn5D6sWDlJL8/Hzee+89+corrxSUl5efLKUs6M1ze+7QCiF+BoLoODSWRcffYTU8QlGchNq57R9rm5WMFdn89P4aNny5mVZLG3qDnlHjw4mZHEXspGgSZo1jfEocbh6Dv9lhbbOyOz2Xzd9lkfF9Nnsz8oCOXd7RE0cxZspoxiTFEDd1NOOSx2B0Mw56jCOJvXZuh1xyO1h8fX2vCwsL++tDDz3ku3Tp0iFTX9va2kp5eTmlpaXU19cTEBBAUFDQgBLZo+lPcns0UkqampqoqamhvLwcs9mMn58foaGhBAUFDZnyj/Lycj777DMee+yxyvLy8otaW1tXOjomRVHsRyW3vde1Q5v2VQbpX2+hvroBnwBvFl48m0WXzu1IEl2ds0ytpryWrJ93sG9LPvuyC8nbWkBtZceZc29/L069cgFLbzyFqPgIB0c6PKnkViNCCH1QUNDfJ02adOU999zjMX/+fKd/67yhoYGysjJKS0ux2WwEBwcTGhqKj4+PZrug9kpujySlpLq6mtLSUioqKnB3dyckJITQ0FDc3Nzsvp49NTQ0sGLFCh566KG64uLiB6urq19wdEyKotiHSm5PbM/mffzr0U/IWJGFta0db38vZiydyoILZ5O8ZEqfywqcgZSSqkPV7M3I5+cP1rLus020W9uZvGACZ9x4CnN/NUPt5tqRSm41IIRwDQoK+vbcc8+de/PNN7tMmTIFnc45u6W1tbVRXFzM/v37MRqNhIaGDmoCqFVye6SeibsQgujoaEJDQ49aB+wM2tra2LBhA3/5y1+aN2/e/G5FRcXNUv2QKcqQp5LbYyvYXsQ7D/yHDV9uxjfQmyVXLyL1rGQmzBqH3uCc/1b3V02ZmRX/XMnXb/xIaUE5bh6uTD15EqlnTGfG0qkERgQ4OsQhTSW3diaEcA8ODv7xyiuvnHnTTTfpx4wZ4+iQjspsNlNQUEBtbS0RERGMGjXKITuag5Xc9tTY2EhRURFlZWUEBQURExODp6fznW6VUpKVlcXTTz/d8vPPP/+noqLimt50UlAUxXmp5PaXdm3cwyfP/Zd1n23C3duNi/54Dr+6bSke3u6ODk1zNpuNrT9tZ8OXm0n/ekv3wbi4qTGccuUCzvzNKWpHtx9UcmtHQgjPoKCgVddff/3UG2+8UT969GhHh3QYm81GSUkJBQUFGI1GYmJiCAwMdOjBK0ckt11sNhulpaUUFBRgMBiIjY11+O/HkaSU7Nixg2eeeab1u++++6KiouIyKWW7o+NSFKV/VHLbwWazsf7zTXzy3H/ZtXEvXiZPzrr5VC648yx8/Efm+HkpJYU7D5D+9RY2fLmJnLRcgqMCuerhiznp1/Oc9p1GZ6SSWzsRQngHBwevv+mmmyZed911IioqytEhdbPZbOzfv5+CggKCgoKIjY3Fw8PD0WEBjk1ue6qtrSU/P5+6ujrGjh1LWFiY0yS5Ukp27drFCy+80LZ8+fLvy8vLz+0cyqAoyhCjklswV9Ty1BUvkfl9NmGxIZx3+xksuXoh7l7Df6e2L7b8tJ237n2fvRl5jJ44imsfv4zUM6c7zf9Nzkwlt3YghPAMCQlJv/rqqxNvuukmnGXHVkrJoUOHyM3NJSQkhLi4OKcbgOAsyW2X5uZm9uzZQ319PQkJCQQGBjo6pG7btm3jr3/9q/zuu+++KS8vP0ft4CrK0DPSk9sd63fz+CXPU1tZz83PX83SG05SO5LHIaVkzSdp/PP+DyjOLSEqIYIzf3MqJ18xH28/L0eH57Tsldw652mpQdA5dWz1TTfdNOHKK6+kqKiIlpZfTkUZbOXl5axdu5aqqipSU1NJSEhwusTWGbm7u5OUlERSUhIFBQVs3LiR2tpaR4dFXV0dVVVV3HnnneLss88+NSgo6N9CiBH7c6co9iSEOE0IsUcIsU8Icc9R7p8vhNgihLAKIS444r52IURW58fywYt6aGlvb+ejZ77kj4sewujmwosbHuesm05Vie0JCCFYcOEs3tzxHH98+7d4eLvz8u3/5JKIG/nLNX9nV9peR4c4rI3IndvOrgirbrjhhhk33XSTbtSoUZSXl5OTk0NqaqpDWn/V1NSQk5OD0WgkISHBKQ9K9eRsO7dH6vr9dHV1JT4+3iG/n3V1dWRmZjJ9+nS8vb3ZtWsXf/nLX1q//fbbDysqKq5WXRQUpf+EEHpgL3AKcBDYDFwqpdzV4zGj6Rhx/UdguZTykx73NUgpe72FNhJ3bg/mlvDMNf9g14Y9zDt/Jne+eTOevs79f5Mz27e1gK9e+4Gf/72W5gYLCy6axe//fj2+gUOjj/5gUON3+0kI4RIcHLziyiuvTLnhhht0o0aNAiA4OBiAtLS0QU1wW1tb2bFjBy0tLUyYMAGTyTQo6w5VmUU1pOVXkRobwPRov2M+zs/Pj9mzZ1NeXk5mZiaBgYGMHz9+0HYbeia2XQNAJkyYwB//+EdjS0vLxT///HMzcNOgBKMow9MMYJ+UMh9ACPEhHePXu5NbKWVh532qW0kfSCn5/MVvePv//o2Lqwv3vHcriy+bq2pGByhuagy3v3ojNz5zBZ//7Rv+9ejHbFu9iztev4lZZw04n1N6GHFvjwYHB79x/vnnz7npppt+0RUhODiYhIQE0tLSBqVEobS0lPXr1xMaGsqsWbNUYnsCmUU1XP5mGn/9fg+Xv5lGZlHNCZ8THBzMvHnzcHV1Zd26ddTUnPg5A3W0xBY63qaaOHEid999t2tKSsqV/v7+t2sejKIMXxHAgR5fH+y8rbfchBAZQog0IcS5do1siHvnzx/yyh3vkLR4Im/seI6TLp+nEls78vB25/L7z+fvm57CL9TEA+c8zTPX/oPG2kZHhzZsjKjk1t/f/5apU6deeNNNNxmO1cd2MBLc1tZWMjMzOXDgALNnzyY8PFyTdYabtPwqWq02bBLarDbS8qt69TwhBGPGjGH69Ons3LmTXbt20d6uzZmuYyW2PWNJSkrirrvuco+IiHjYaDQu0iQQRVFOJLrz7c/LgBeEEL/4T0EIcWNnApxRUVEx+BE6wIp3VvLvJz7jtGsX8+jyewgM93d0SMPWmCmj+Xv6k1z2f+fx47uruXrcrXzy3H9paXb8+Z+hbsQktwaDYV5YWNjj99xzj8fEiROP+1gtE9yeu7UpKSlOP9rXmaTGBmA06NALcDHoSI3t2yQYLy8v5syZo9ku7okS2y5CCGbPns2DDz7oExwc/JEQIsaugSjKyFAMjOrxdWTnbb0ipSzu/DUfWAVMPcpjXpdSJkspk4OCggYW7RCQvWonL/zmNaaeNInbXrlB7dYOAhejC9c8dikvpT9JbNJoXvvju1wZ93uWv7yC1pY2R4c3ZI2IA2VCiOjw8PCMF154IfCcc87BaOzd1BB7HjLrqq1tb29n8uTJQz6pddSBst7W3J5IQ0MDWVlZ+Pv726UWt7eJ7ZEx/Otf/+LBBx/MLy8vT5JS1g8oCEUZQYQQBjoOlJ1ER1K7GbhMSrnzKI99B/iq60CZEMIPaJJStgghAoGNwDk9D6MdabgfKCvKOcjtc+7HP8zE39Y/jpdJHRxzhOzVO3nnzx+yY91ugqMCuf2135CyJMnRYQ0a1Qqsl4QQnsHBwT/ed999gaeddlqvE1uw3w5uXV0dGzZsICQkRO3WDtD0aD9+tyhuQIkt/G8X12g0snHjRiwWS7+v1Z/EtiuG8847j5tvvjkmODh4uWoRpii91zkQ5RZgBZADfCSl3CmEeEQIcTaAECJFCHEQuBB4TQjRlfgmABlCiGxgJfDU8RLb4a6mzMz9ZzyBwWjgsa/uVYmtA01ZkMhzqx/hiW/vw8PbnfvPeIIv/v6to8MacoZ1twQhhC4oKOiLG2+8Mfb888/H27vvowEH2kWhpKSEPXv2dLeDUpyHEIK4uDh8fX3ZuHEjSUlJ+Pn1LWnub2LbJTg4mCuuuEIUFRXN/uqrr54B7uzzRRRlhJJSfgN8c8RtD/T4fDMd5QpHPm8DMEnzAIeA5kYL95/1FObyOp5d9TBhMSGODmnEE0KQsiSJiXPG8+SvX+Qft77Ngd3F/PaFa9AbVH/h3hjWO0WBgYFPLlmyZP6VV16pCwnp/w9sf3ZwpZTs3buXwsJCZs+erRJbJxYUFMSMGTPYtm0bBw8e7PXzBprYdomNjeW3v/2tMT4+/jc+Pj6X9ftCiqIoffTcDa+yb0s+//fB7YxPPvpBa8Ux3L3cefDTP3LhnWex/OUV3HfmkzSYVUeF3hi2ya23t/dFY8eO/e3vf/97Y1xc3ICv15cE12q1kpmZSUtLCzNnzuxTKYTiGJ6ensyePZvi4mJ27drFiWrR7ZXYQser9GnTpnH//fd7BgcH/0MI8YuDLYqiKPaWl13Iqg/Xc+n/naf6rDopvV7Pjc9cyR2v30TWzzu4YdIf2LB8s6PDcnrDMrkVQkT7+/u/cv/993tNnz7dbic+e5PgNjc3s2HDBoKCgpg0aRI63bD8LR6WXFxcmDFjBkIINm3aRFvb0U+q2jOx7aLX61mwYAEPPfSQKSQkZLkQQhW9KYqiqQ+e/AwPH3cu+MNZjg5FOYGl15/EC+sexcvPkwfP/QuPXvwc1aXa920fqoZdza0QQgQHB3/yhz/8wX/BggV2n0h1vBrcrqRn8uTJBAT0rU2VM7HZbLS0tGCxWLo/WlpasFqtSCmRUtLc3Mz27dvR6XQYDAbc3NxwdXXFzc2t+/Oh2EZGCEFCQgIHDx5kw4YNzJw5Ezc3t+77tUhsu7i5uXHaaaexc+fO8LfffvsfwNV2XUBRFKXT/t3FrPk4jYvvPlcdIBsi4meM5eWMp/nomeW8/9inbPlhGzc9dxVLrlbt0o807JJbk8n0+8WLF086++yz8fTU5gf2aAmu2Wxm69atpKSk4OXV63HlDiWlxGKxYDabMZvN1NbW0tzcjE6n+0Wy6uvri8FgQAiBTqejvLycsLAwpJS0tbXR0tJCTU1NdzLc2tqKzWbD09MTk8mEyWTC19fXaTpFnKilWGRkJG5ubqSlpTFz5kzc3d01TWy7BAYGcskll+hWrlx5nsFg+KfVal2tyUKKooxon//ta4xuLpx3+xmODkXpAxejC5ffdz7zL0jl+d+8xrPXvkxNWS2X3H2uo0NzKsMquRVCjI6Ojn7o+uuvdz1ytK699Uxw4+PjycnJYcaMGZol1PbS1NREaWkp5eXlNDc34+7ujq+vLyaTidGjR+Pm5tarHVeDwUBgYOBxHyOlpLGxEbPZTEVFBbm5ubS2tuLl5UVISAghISEOSXa7xvi2Wm0YDTrevz71qAluYGAgkydPJj09nYSEBHbt2qVpYtslMTGRO+64w/v2229/XwgxXkqpThAoimJX2at3MfXkSfgF+zo6FKUfRo2P4JmfHuTpK1/irXvfx+iqXqj0NGyS265yhDvvvNMvNTV1UN4SDw4Opr6+ns2bNzN37lynTGyllJjNZsrKyigrK8PFxYXQ0FAmTZqEh4eHpr9PQgi8vLzw8vIiMjKyO576+npKS0vZtGkTQghCQkIIDQ0dtI4SRxvje6y+uf7+/sTFxbFp0yZmzJiheWILHS8cTjrpJK6++uqwt99++2XgKs0XVRRlxKivaeDA7mJO/vV8R4eiDIBer+fuZb/H2mrllT+8g4urgbNuXuLosJzCsEluTSbTrSeffPLEM888c9CSTLPZzIEDB5gyZQrZ2dl2mWRmL01NTRQVFVFaWoqPjw+hoaGMGTMGFxcXh8YlhMDHxwcfHx/GjRuHxWKhrKyMXbt2YbFYiIyMZNSoUZp2mOga49tmtZ1wjG9dXR25ublMnTqVnJwcfHx8cHd31ySuw0slOsoTVq1a9Su9Xv/P9vb2VZosqijKiLNncx4A8TPHOjgSZaD0Bj33vn8bbS1/5cXfvYlOr+OMG09xdFgONyySWyFEzOjRox+87rrrNC9H6FJbW0tWVhYzZszAw8MDV1fXfg96sBcpJeXl5RQUFNDe3k5UVBTz58+3+6E6e3JzcyM6Opro6GhaW1s5ePAgGzduxMvLi9jY2D4PVeiN6dF+vH996gnH+B5ZY+vh4UF6ejqpqamHHTKzh6OVSkzpLE+47bbbusoTGuy6qKIoI1JO2l6EEIxPUX1thwMXowt//ugPPHTeM7xw0+sU7TrIjc9cgcFlWKR4/TLk+1QJIXSd3REGrRyhqamJLVu2kJycjIeHB2C/Ub39YbPZKCoqYvXq1ZSWljJhwgTmzJnDqFGjnDqxPZLRaCQ2Npb58+czevRo9u3bx9q1aykpKTlh39m+OtEY36MdHvP392fixImkp6cfs01Yfx2tVMJgMLB48WKuueaa0JCQkFftuqCiKCPW7k25RE+IxNPHw9GhKHZidDPyyJd3c+7vT+fzF7/hniWPYa6odXRYDjPkk1s/P7/bTjnllMQzzzyzO9HUktVqZfPmzSQlJf2iK8JgJ7hSSg4dOsSaNWtoampi9uzZTJkyZVDqQrUkhCAgIICUlBSmT59OWVkZ69evp6qqalDWP15XhMDAQMaMGcOWLVvsmnB3lUroBYeVSgQGBnLxxRfrYmJiztHr9YvttqCiKCOSlJKctFxVkjAMGVwM/O5v13LXO7ewa+Nefpt8N3sz8xwdlkMM6eRWCOHv6el537XXXjso5QhSSrZs2XLct8sHK8GtqKhg3bp1VFRUkJqaSkJCwrCchObh4UFSUhJTpkwhLy+PtLQ0amu1ezXam3ZfkZGReHt7s3v3brut21Uq8YdTx/+ie0NiYiK33367V1BQ0NtCiKGzFa8oitMp3ldKfXUDCanjHB2KopFTrlzAC+seBeBPix+maNcBB0c0+IZ0chsUFPTE1Vdf7W/PKWTHs2fPHjw9PRk1atRxH6dlgtvQ0MDGjRspKipi6tSpTJkyxe71n87I29ubGTNmMH78eHbs2MGWLVvs/nvblz62CQkJ1NXVcfDgQbutf6xSCYPBwNy5cznttNNCvby8rrXbgoqijDi703MBSJg58LH0ivMaN30Mf1v/OK4eRh4452nqqusdHdKgGrLJrRAi0sfH5+KzzjpL+Ppq36evuLgYs9nMhAkTevV4eye4Ukry8vLIyMhg/PjxJCcnD5lhEfbk5+fH7NmzCQsLY8OGDRw6dMgu1+3rgAYhBNOmTSMvLw+z2WyXGI4nPDycCy+80NXLy+sRIcTwfzWjKIomrK1WAIzuw++dPuVwQZEBPPTZn6g4UMXjlzxPu7Xd0SENmiGb3IaGhr5w/fXXmxITEzVfy2w2s2/fPvq6Q2yvBLexsZENGzZgsViYN28e/v7+/b7WcCCEICwsjDlz5lBSUkJGRgatra39vl5/J4+5uLiQnJzM1q1bsVgs/V6/N4QQpKSkcMEFFwT6+fn9QdPFFEUZtkZP7HjnsXDHyHureiSaMGs8t716I1t+3M5rf3zX0eEMmiGZ3AohEoKDg09eunSp5j1tW1payMrKYvr06f3qETuQBFdKSX5+Pps3byYhIYHExMQh1f1Aa0ajkenTpxMREcH69ev7tYs70JG6np6eTJw4kYyMDNrbtX1VHBwczK9+9SuDh4fHHUIINVZIUZQ+i04chRCCgu37HR2KMkiWXL2I828/g89f/IaPn13u6HAGxZBMbkNDQ1+5/vrrfcePH6/pOlJKsrOziY+PH1AJQH8S3K6uDI2NjWq39gS6dnEPHjzIjh07et3FYKCJbZegoCBCQ0PZs2dPv6/RW9OmTeOKK67wDwoKeljzxRRFGXbcPd0Iiw2mYIdKbkeSG/5yBQsvns3rd73Hh0997uhwNDfkklshRGpcXNy0U045RfNhCcXFxd3jageqLwluU1MTGzZsICwsjEmTJqnd2l4wGo2kpKTg4uJCWlraCfvQ2iux7TJmzBiqq6upqakZ8LWOx2QycfbZZ+u8vLyuFEKE9bxPCHGaEGKPEGKfEOKeI58rhPiDEGKXEGKbEOInIUR0j/uuEkLkdn6ocb+KMozFTIpSO7cjjN6g5573bmXxZXN56//+zfuPferokDQ1pJJbIYQICQl59ZprrvEeM0bbySoWi4Xc3FwmTpxot2v2JsGtrKwkPT2dSZMmnbArg3I4IQTjx48nOjqa9evXU19/9NOh9k5su9ZOSkpi27ZtmpcnTJo0iWuvvdYUEhLybI/19cA/gNOBCcClQogjTz9uBZKllJOBT4C/dD7XH3gQmAnMAB4UQth/NJyiKE5hdGIUxbkltFr6f1ZBGXr0Bj13LbuFk6+YzzsPfMi7D33k6JA0M6SSW4PBcHpKSsrYhQsX9qv+tbe6yhEmTJhg93WOl+AWFhaSk5NDamqqJmNnR4rw8HCmTZtGZmYmZWVlh92nRWLbxcvLi4iICM3LE7y8vDjzzDNFQEDAUiFEVz+fGcA+KWW+lLIV+BA4p+fzpJQrpZRNnV+mAZGdny8BfpBSVkspa4AfgNM0/SYURXGYhFnjsLXbWPf5JkeHogwyvV7PH9/+LadevZD3HvmYtZ+lOzokTQyZ5FYIIQICAv52+eWXe2g9sKG4uBij0UhISIgm1z9agrtnzx4qKiqYPXs27u7umqw7kvj4+DBr1ixyc3MpLi4GtE1suwxWeUJ8fDzXX3+9KTQ09IXOmyKAnsefD3bedizXAd/287mKogxhKaclMXriKN5/7BPN32lSnI9er+eO137D2Gkx/O2m16gpMzs6JLsbMsktMHf69Olhqamp6HTaha1FOcLRdCW4GzduZPv27TQ2NpKcnKzqa+3I1dWVmTNnUlhYyN69ezVPbGHwyhPc3Nw46aST8PX1nXNk7e2JCCF+DSQDz2gTnaIozkyn0/Hr+y9gf04xaz9Jc3Q4igMYXAzc/e7vaaq38NyNr9p1nLwzGDLJbXh4+KNnn322Z2Rk5IkfPADZ2dkkJiZqWvbQJTg4GC8vLw4ePMiECRMGZcraSOPi4sKECRPYu3cvERERmia2Xby8vIiMjNS8PCE2NpaLLrrINygo6I9AMdCzSDuy87bDCCFOBu4DzpZSdtXF9Oq5iqIMH/MuSCV6QiTvP/YpNpvN0eEoDhA9YRTXPn4paf/NZMU7qxwdjl0NieRWCBEdEBAwZe7cuRgMBs3WKS8vR6/XExwcrNkaPe3ZswedTse0adNIT0+3+zhZpaMUISsrizlz5lBRUdFdoqC12NhYKisraWxs1GwNLy8vTjnlFOHi4nIFsA0YK4SIEUIYgUuAwxoaCiGmAq/RkdiW97hrBXCqEMKv8yDZqZ23KYoyTOl0Oi6//wIKdx5g7afDs+5SObHzbj+DyQsm8Mrt/6Qox37j5B1tSCS3ISEh91xwwQW+MTExmq0hpWT37t0kJCRotkZP+fn51NfXM3XqVEJCQuw6qlfp0LPG1s/PjxkzZlBQUPCLQ2ZaEEIQHx/P7t27NV1n/PjxnHXWWSZPT89LgVvoSEpzgI+klDuFEI8IIc7ufPgzgBfwsRAiSwixHEBKWQ08Cmzu/Hik8zZFUYax+RemMio+gvce/ghrm9XR4SgOoNPpuHvZLRjdjTxwztPUVR+9y9BQ4/TJrRDC3WAwXHjKKacIDw8PzdY5dOgQJpNJ84ln0LFDXFJSwrRp07pLEew1qlcrVquVxsZGamtrqampob29ndraWpqampzyQMLRDo+5uLiQkpJCTk7OMduE2VNQUBAtLS3U1tYe9f7vvvuO8ePHExcXx1NPPfWL+9esWcO0adMwGAx88sknh92n1+tJSkri1FNPZdy4cS7e3t73SCm/kVKOk1KOkVI+DiClfEBK2ZXEniylDJFSJnV+dCW9SCnfllLGdX78046/DYqiOCm9Xs/1T11O0a6D/OfpLx0djuIgwVFBPPz5n6jYX8mjFz03LF7oaPcev524ubldfMYZZ/jExcWd+MH9ZLPZyM3NJTU1VbM1ujQ0NLBz505mz579i4NxXeUQaWlppKamaj6k4khSSiwWC2azGbPZTG1tLRaLBej4R9DV1RUXFxeEELS0tJCXl0dbWxstLS3dNVseHh6YTCZMJhO+vr6D/j3A8bsiuLq6MnXqVDIzM5kzZ46mtdVCCBISErrbu/XU3t7O7373O3744QciIyNJSUnh7LPPZsKE/7WmjYqK4p133uHZZ5898tK4u7uTlZUFdLwL8PXXXwcLIaZLKTM1+4YURRl2Zp+dwsJL5vCvRz9m9rkpxEyMcnRIigNMmDWeO964ib9c9Xf+cevb3PryDUP6HJDTJ7d+fn5/XLx4sUtgYKBmaxQVFREaGoqbm5tmawC0tbWRmZnJtGnTjpn0DXaCa7PZqKqqorS0lMrKStzc3LqT09GjR+Pm5nbUv+Bms5lp06YddpuUksbGRsxmMxUVFeTm5mK1WrvH0/r5+Wn+w9Kbdl++vr6MGzeOjIwMUlNTNY3Jz88PvV5PZWUlPf8Ob9q0ibi4OGJjYwG45JJL+PLLLw9Lbrta3p2oO0hkZCSnn366d05Ozl3AxXb/JhRFGdZ+97dryPppO89e+zIvbngcvUF17RmJTrliAUU7D/Cfv3zJ+BljOe2aRY4Oqd+cuixBCBEfHR0dOXXqVM0SEKvVSmFhIVpPPJNSkpmZSVxcHL6+vsd9rNYlClJKqqur2bp1K6tXr6akpISQkBAWLFjArFmzSEhIICwsDHd39z79vgshujsFJCYmMmfOHGbPno3JZKKwsJBVq1axY8cOzUoC+tLHNjw8HH9/f3bu3KlJLD3Fx8eTk5NzWKuV4uLiwybQRUZG9umwm8ViITk5mdTUVL755hsWLFiAwWA4WQjhZdfgFcWJ9WLk9HwhxBYhhFUIccER96mR051MQb7c8tJ17M3I45PnvnJ0OIoDXfvEZUycG89b975PY13TiZ/gpJw6uQ0JCfnDWWed5RsVpd3bJPn5+URFRWne+is3NxcfHx8iInrXG1+LBNdms3HgwAHWrl1Lfn4+o0aNYuHChUyePJng4GBN+ge7uLh0TwxbsGAB/v7+7Nixgw0bNlBWVma33nr9GdAwbtw4mpqaKCkpsUsMx+Lt7Y23tzelpaV2u2ZRUREZGRn8+9//5vbbb8fV1ZWzzjrLx8PD4zK7LaIoTqyXI6f3A1cD/z7iuWrk9BHmXziLOb+awbIH/8O+rAJHh6M4iE6n46bnrsZcXssHT3zm6HD6zWmTWyGEXqfTnbtgwQLNygXa2tooLi5G64lndXV1lJaWEh8f36fn2SvBlVJy6NAh1qxZQ11dHSkpKSQnJxMYGDioNTU6nY7w8HBmzZrFpEmTOHToEOvXr6eqqmpA1+3v5DEhBFOmTGH37t20tmo7Y338+PHs3bu3O5mPiIjgwIH/DQU7ePBgr1/4dD0fOlqOLVy4kL1797Jo0SKDr6/v7XYNXFGcV29GThdKKbcBRzZyVSOnjyCE4NZ/XI9PgBd/XPQQ2au0f1dLcU7jk8dwypUL+OyFrynJ1767kBacNrkFZs6YMcMjOjpaswUOHDhAZGSkplPBbDYbWVlZJCUl9WtndKAJbnV1NevWraOiooLU1FQSExOdYryvt7c3U6dOZcqUKeTl5ZGenk5DQ0OfrzPQkbqurq6MHz+ebdu29fm5feHu7o63tzeVlZUApKSkkJubS0FBAa2trXz44YecffbZJ7hKh5qamu6/C5WVlaxfv54JEyaQmJiIv79/qBAiSLNvRFGcx0DGRvfquUKIG4UQGUKIjIqKin4HOlT4h/rxt/WPExDux72nPcbKD9c7OiTFQa59/FL0Bj1v3PMvR4fSL06b3IaEhFw+c+ZMT60GKkgp2b9/P1omz9BRjhASEjKgyVj9SXCtVivbt29n9+7d3Umk1gfm+sPb25sZM2YwduxYMjMz2bdvX69LFQaa2HYJDw8HOtrBaWnMmDHk5+cDYDAY+Pvf/86SJUtISEjgoosuIjExkQceeIDlyztmL2zevJnIyEg+/vhjfvOb35CYmAhATk4OycnJTJkyhUWLFnHPPfcwYcIEQkNDWbRokY/RaDxT029EUUYIKeXrUspkKWVyUNDIeM0YEh3EC+seI37mWJ647AU+fnb5sBvNqpxYYEQAF911Dms/SSP9my2ODqfPnLZbghDirBkzZmA0GjW5fnl5OX5+fppdHzqSr7KyMubOnTvga/Wli0J1dTXbtm0jOjqaiRMnDol2Hv7+/sydO5e9e/eyfv16kpKS8PI69tkoeyW2XSZPnsz69esJCAjQrEOFr69vd79gT09Pli5dytKlSw97zCOPPNL9eUpKCgcP/nJizOzZs9m+ffsvbjeZTEydOlUfHBx8NaB61SrD3UDGRhcDC4947iq7RDUMePt58dSK+3n6qr/z+l3vUX6gkpufv1qTcxmK87r47nNZ8/FGnrvhVd7Y/ld8/L0dHVKvOeXfVCFEXExMjI+WtbAFBQVoPfEsOzu73+UIR3OiHVwpJfn5+ezatYuUlBRiYmKGRGLbRa/Xk5CQQGJiIhkZGcc8gGXvxBbAaDQyfvz4Y3ZPGMjAhWXLljF27FjGjh1LUVERBQXaHNYQQtDZWWSiEGLwGwwryuDazAlGTh+HGjl9AkY3I/d9cDvn3XYGX7z0Lc9e+zLtVucb2KNox+jqwl3LbqG2oo5/3Pq2o8PpE6dMbn19fS+YP3++T2hoqCbXb25uxmq12i0xOppDhw7h4+Nj9zWOleDabDays7Opra1l1qxZgzJpTSt+fn7Mnj2b/Pz8ww5hgTaJbZewsDCam5t/MVGsa+DCt99+y65du/jggw/YtWvXYY/pGrhw2WWHNyuorq7m4YcfJj09nU2bNvHAAw9QUlKi2VS3sLAw5s2b58Hhu1KKMuxIKa2cYOS0ECJFCHEQuBB4TQixs/O5auR0L3ScnL+KKx+6iB/eXc2Tv/7bsJhepfTe2GmxXH7/+fz873Ws+WSjo8PpNadMbj09PS9PSUkRWiVoRUVFmtbadk08Gz9+vCbXPzLBbWtrY+PGjfj4+JCUlKTpAbnBYjQaSU1NpaWlhS1btmCz2TRNbOHwiWI99Ry4YDQauwcu9DR69GgmT578i136FStWcMopp+Dv74+fnx8nnXQStbW1dm0L1lNQUBDJyclu4eHhI7pvpzIy9GLk9GYpZaSU0lNKGSClTOzxXDVyuheEEFzxwIXc+JcrWP3RRh658K+0trQ5OixlEF16768YOz2WF3/7xpDpfet0ya0Qws/HxyciISFBk+tLKSkpKek+RKSF/fv3ExISoukBrq4Ed8OGDWzYsIHY2FhiY2OHVBnCieh0OiZNmoTJZGLjxo1kZGRolth28ff3R6fTHdaebCADF4713KKiIvsF3YNer2fGjBnYbLaTxHD6y6AoikNd+MezueWl69i4PIMHznkaS5P9BwwpzsngYuC2l2+gtrKeb974ydHh9IrTJbcuLi5LFy1a5KVVSUJVVRX+/v6a7W5arVYKCgqIi4vT5Po9mUwmbDYbbW1t+Pv7a76eowQFBdHQ0ICrq+txD5nZS9furVYnhNva2rDZbFgsFk2uHxkZyaRJk9yBKZosoCjKiHTO707jzjdvZssP2/jT4oeoPKQqOUaK8SlxTFmYyOd/+3pIlKY4XXIbHBx8zdSpU138/LQZFlNaWopWiTMM3sSz9vZ2Nm3aRGJiIpMnT9ZsVK+jdZUizJo1i5CQELZu3ap5Wxpvb2+8vLy6SwcGMnDhWM8NDQ2lrEyb5tghISHMmTPHOyAg4BJNFlAUZcQ67drFPPTZnyjceYBbZtzDns37HB2SMkgu/OPZVBysGhL9j50que0cp5g0bdo0Td5el1JSWVlJYGCg3a8NHQnnYEw8k1KSlZVFZGQkoaGhmozqdQZH1tjGxcVhNBrJzc3VfO1x48aRl5cHDGzgwpIlS/j++++pqamhpqaG77//niVLlhAaGqpZ3a2bmxspKSkYjcbzNVlAUZQRbfY5Kby44XFcjAbumP8AP/97raNDUgbBjNOnEj0hckj0Pnaq5BYYn5CQ4KJVs+yGhgY8PDw0K0koLi4mLCxM8wNdeXl5GAyGw5Lo4ZbgHuvwWGJiIpWVlZolhl08PDxwdXWlpqZmQAMX/P39+fOf/0xKSgopKSk88MAD+Pv74+Xl1d21QwvR0dG4u7v7q5ZgiqJoIWZSNC+lP0n8zDie/PWLvHXv+5p1gVGcgxCCC+48m4Lt+0n7KtPR4RyXUyW3QojpEyZM8DSZTJpcX8uSBCklhYWFmu/alpeXU1ZWxqRJk35x33BJcI/XFUGn05GcnMzu3buPOa73RD1pW1pauPjii4mLi2PmzJkUFhYCUFhYiLu7O0lJSSQlJfHZZ591TxRbunQpe/fuJS8vj/vuuw/oGLjQtYPbNXChsbGRqqqqw/rlXnvttezbt499+/ZxzTXXdN8eFBTUPY7X3kwmExMmTHABfvkXRVEUxQ5MQb48/f2fOePGU/jw6S946LxnaKpvdnRYioZO/vU8IsaGdbyYceK+x06V3IaHh588evRovVaHhsrKyggJCdHk2mazGQ8PD007JLS1tbFz506mT59+zMEQQz3B7U27L6PRyJQpU8jKyvrFWyO96Un71ltv4efnx759+7jjjju4++67u+8bM2YMWVlZZGVl8cQTT9DQ0EBra6v9v1HQtDTB19eX+Ph4LxcXl2RNFlAURQFcjC7c9soN/O7Fa9n0zVZum3MfJQXanCdQHM/gYuC6Jy6jaNdBVryzytHhHJNTJbc2m23m+PHjNRnx15XoaTVaVeveuQA7duwgLi7uhAn0UE1w+9LH1s/PD39//+662C696Un75ZdfctVVHW1gL7jgAn766aej1g8JIRg1atRhB8Lsyd/fn+rqak1qlzw9PRk9erQICQk5ye4XVxRF6UEIwbm3nM6T395H5cFqbplxL9mrjz7tURn65p43kwmzxrHswf/Q3KhN15+BcprkVgihNxgMgZGRkZpcX8tdW6vVitls1uygGnSUI7S2ttLb35+hluD2Z0DD+PHjKS4uPqw8oTc9aXs+xmAw4Ovr293XtqCggKlTp7JgwQLWrl1LZGQkBw8eHOi3d1RCCEwmE2azWZNrx8fHY7Vap9v94oqiKEcx7eTJvJT+JL6B3tx9yqN88+bQ6Imq9I0QghufuZLqkho+fe4rR4dzVE6T3ALjxo4d6+Lr66vJxSsqKggODtb02lr1zLfZbOzatYvJkyf3aY2hkuD2d/KYXq9n0qRJh9W3DkRYWBj79+9n69atPPfcc1x22WVYLBbc3Nyor6+3yxpHCg4Opry8XJNrh4aG4u7u7iuEMGqygKIoyhEix4bxUtoTTDt5Es/f+CofPv2Fo0NSNJA4ezypZ03ni5e+ccq+t06T3AohpicmJmp2mKy+vh5vb29Nrq1179yuiWfu7u59fq6zJ7gDHanr7++PEKJ757U3PWl7PsZqtVJbW0tAQACurq4EBAQAMH36dMaMGcPevXs17UlrMpmora3V5Nq+vr5dh8omarKAoijKUXj6evLIl3ez6NI5vHXv+yx78D9O3zpK6bvTrz2J2sp6Mn/Y5uhQfsFpktuwsLCToqOj9VokoG1tbej1ek1qeaWUmM1mtBo6YY+JZwNJcFtbWykvLyc3N5fNmzezevVqVq1aRX19PWvWrGHLli3k5eVRVVXV57ZWA01su/ScKNabnrRnn302y5YtA+CTTz5h8eLFCCGoqKjobmWTn59Pbm4usbGxhISEaJbcenp60tjYqMm1TSYT8fHxni4uLimaLKAoinIMBhcDd7/7e5ZcvYh/PfoJb9z1nkpwh5mU05Pw9vNk5QfrHB3KLxgcHUAXKWVqQkKCJgloXV3dgJKn46mpqcFkMmlWklBYWMioUaMGPPGsqyQjLS2N1NTU4x6sk1JSWlpKUVERra2t+Pn5dSVKeHp6otPpWLlyJXPmzKG+vp7a2loOHjzI9u3b8fb2ZvTo0d07qsdir8QWOiaKeXp6Ul5eTkhISHdP2vb2dq699trunrTJycmcffbZXHfddVxxxRXExcXh7+/Phx9+CMCaNWt44IEHcHFxQafT8eqrr3aPNbbZbLS2tmI02vcdfiEERqNRk2t7enoSHR2tCw4OPgl4za4XVxRFOQG9Xs8f3rwJVw8jH//1v1iaWrnlpWs1+X9eGXwuRhfmXzCLn/69luZGC+6e2nWL6iunSG6FELrIyMig3o407Suz2cxQ7J1rs9k4cOAAc+fOtcv1epPglpaWsnv3bvz9/UlMTDxmKYcQAr1ej8lkwmQyER0djZSSmpoaCgoK2LVrFxMnTjzqjrY9E9sucXFx7Nixg5CQEJYuXcrSpUsPu/+RRx7p/tzNzY2PP/74F9c4//zzOf/8ow/16tq97XlYzV58fX0xm812rwkXQjBhwgRsNps6VKYoikPodDpueek6XN07Ety6qjr+9M/f4equ5ssMB4sum8vXb/zIxi83s/iyeY4Op5uzvHwKj4yM1Gu1u6plcltRUYFWE9XKysoIDAwc8K5tT8cqUWhtbSUzM5MDBw4wa9YsJk+e3OcaZSEE/v7+TJ8+nalTp7Jz50527dp12NSaoyW2/R26APDkk08SFxdHcnIylZWVmh380rInrVYdE6BjUITBYNDmlKaiKEovCCG44S9XcMPTv2b1Rxv500kPU1OuzVkDZXBNmpdAcFQg377lXJ0xnCW5DQsLCzNoNQBBq8NkbW1t6HQ6DAZtNsCLioo0mXh2ZIJbXV3N+vXrCQ0NJSUlxS69gL28vJgzZw6urq6sW7eOxsbGoya2Axm6sGvXLj788EN27tzJd999x1tvvXVY4mtP3t7ex5yINlBaJrdubm54e3vrhBCemiygKIrSC0IILvrTOTzwyR/Jzy7i1tR7KdqlTQ9xZfDodDrOunkJWSt3UrC9yNHhdHOa5DYoKMhVi+TWarWi0+mGXC1vS0sLbW1tmnV46Epw165dS3Z2Nqmpqb/oKjBQQgjGjBnDlClTSEtLY9OmTb8oRRjI0IUvv/ySSy65BFdXV2JiYmhpaaGoqEiTQws9a2PtTctDZW5uboSEhOiAME0WUBRF6YN5583kr6septXSxq2z7yPzh2xHh6QM0NIbTsLV3cjnL37r6FC6OUVyazAYwv38/DTZudUyAdWy3KGsrEzT9mLQUezfRcsCf51Oh5Syu063p4EMXTjyueHh4bS1tWm2C9pVG2tvQghcXFxoa2uz+7U7k1sXVHKrKIqTGJ8Sx0tpTxASHcT9Zz7JjnU5jg5JGQAff29OunweP72/hroqbUoD+8opklt/f/+xPj4+QovRuBaLpV/9YXtjqB5Ug47fl23btjFnzhwSExM164PbVYowY8YMpk+fTkZGxmE1uPZms9mGZG2su7s7zc3Ndr+um5sbgYGBrkC43S+uKIrST8FRQfx11cOExgTz0HnPUFJQRvo3W3j/sU+pr9GmBEzRzrm3LqXV0sY3b/zo6FAAJ0luXV1dRwcEBGiye9g1YUoLWtXytre309TUhJeXl92vDR2tvrKzs5kwYQLu7u6aDXo4ssbWZDIRERHBnj17uh8zkKELR3tuaGioZhO/tExuXV1dNXlx4erqislk0ru7u9u/zYOiKMoAePt58ejye7C2tvPYxc/z7Vs/UVlcxZ9OepgDe4pPfAHFacRMjGLCrHGs+zzd0aEATpLcSikju/qJ2ptWya2WtbxdQyG06p1bXFyM0WgkJCSk+zZ7J7jHavc1ZswYqqurqampARjQ0IWzzz6bDz/8kJaWFgoKCsjNzSU1NRWDwaBJoujp6UlTU5PdrwsdO6wWi8Xu1zUajfj6+mIymfo/BURRFEUjwdFBXHjX2YyKD+f/3r+N2165kfAxIRzYc8jRoSl9NO3kyeRm5tNYq80Zkr5wiuTWarWGaPUWvFbJbXNzMx4eHna/Lmhb7tDe3k5ubi4TJ/5yIqu9Etzj9bEVQpCUlMSOHTuQUmIwGLqHLiQkJHDRRRd1D11Yvnw5ANdddx1VVVXExcXx3HPPdbcLS0xM5KKLLmLChAmcdtpp/OMf/0Cv1+Pr66vJSNuuFxtaHFjTKrkVQhAQEICLi0u03S+uKIoyQPu25FNWUMGpVy3C6GakrKgCo7uR4FGBjg5N6aOkxROx2STb1ji+htophjjo9Xo3T09tOhVpldxqWe5gNpsHNG73eA4cOEB4ePgxe+f2ZZLZ0fRmQIOXlxfu7u5UV1cTEBDQ76ELAPfddx/33XffYbd1lQ/YeygC/K98wN5/9m5ubt272fYWGBhIe3u7NhNSFEVRBiB71S48fT2YdtIkAPbvLsbTx4N26y/PZjTVN+Phrc0ZGmXgElLHYXRzIevnHcw6K9mhsTh851YIoTcajUatEkUtxprC0KzlBdi/f/8Je+f2dwe3L5PHYmNjNetJq3XfWC12WN3c3DQppYCOQQ7t7e3a1P0oiqIMwPfLVjL/wllAR2K7Oy0Xb38vxqf8b4OnsriK9x/7lBd/+wa/Tb6LrT9vd1S4ynEYXV1InBNP1sodjg7F8cktEBgYGKhZoghoUrva0tJil2EHR+p6y1urvryurq69iruvCW5fR+r6+flRX1+P1WrtVex9oWVtrJYHv7RImqGjE4OLi4v9X+EpiqIMgLXNyuT5E2iub6a9vZ2vXv2exromFl0yp/sxBTv28+5DH2NpauF3L17L5fdfwHuPfKz64zqpaSdNIn9bERUHqxwahzMktx4eHh7iyP6n9mCz2TQ7lKXVzq1WO80ANTU1BAb2vo6ptwnu2l0HefjjNAwhY3vdU1gIgZ+fH3V1db2Op7e0+jMH7XZuXVxcNEn0oaOfsU7LRsaKoij9YHAxMOvsFJ6/8VXuPe1xAM6/40yiJ/yvucs3r/+I1WolOCoQbz8v5pw7g4c+/RNJizvOjZQWatMdZ7A99NBDjg7BLub8agYA6z/f5NA4TvgfnhDibSFEuRBiR4/bkoQQaUKILCFEhhBiRuftQgjxohBinxBimxBiWo/n3CGE2CKEuPiIJQwGg0Fo8X9ve3u7ZqNxh2otb18Pqp0owV276yDX/Subz/e1ccMH28ks6n3dqFZDEaAjwbXZbHa/rlbJrZZ0Oh2iDxm/EOI0IcSezp/jezpvSxRCbBRCLBNCqERZURS7SD1zOu/lv8ytL9/Ab1+4htKC/yWrW37aTsGO/RgMBg7uOcQtM++htLAcnwBvWi1t/PeVFfzj1re5dfb/kf51pgO/i4F7+OGHHR2CXYwaH8HoxFGs/SzNoXH05j+pd4DTjrjtL8DDUsok4IHOrwFOB8Z2ftwIvAIghPACUoAZwGVHXMtgMBj68n9vr2m5c2u1Wo95KGsgtExua2tr8fX17fPzjpXg1tXV8cXGXVgl2CS0WW2k5ff+rYihWBur5Q6rVoQQXS88T/jDIITQA/+g42d5AnCpEGIC8AfgbCADOFXLeJXhpfPvlFbX/sULsSPudxVC/Kfz/nQhxOjO20cLIZo7N2iyhBCvahWj0juRY8NotbRSsH0/ezLyAGg0NzLt5Mlc9cjF3Pz81STMHEduZj4AVcXVLH95BVc8eCG/feEa3n/8U7JX73Tkt6B0mvOrGexYm0NNuf27FvXWCZNbKeUaoPrIm4Gu9599ga6GdOcA78oOaYBJCBEGiB7PO5JBr9drktxKKTUbK9s1TtbetEqaoSPZ7+9O9pEJrs1mIzMzk3NnTcBo0KEX4GLQkRob0Otrent709CgzSQarcbZCiE0aQWmpR5jj3vzwzAD2CelzJdStgIf0vFzrafj59fG/36eFaU3coUQz3S+SLKb47wQ6+k6oEZKGQc8Dzzd4748KWVS58dN9oxN6R+jm5Gzf7uEuKTRAFjb2mk0NxIQ5oeUkt2b92F07yjbq6tuIGxMCOOmjyF+xlhcXF2wtnZsPAyVf6Mfeuihrs0HoHsjYsiXKMw7PxWbTbLxy80Oi6G/79nfDqwQQjxLx3+YsztvjwAO9HjcQSBCSpkhhNhOx67PM0fGoFVZglYJKGi3K2yz2TRLyAeqq7XWqlWrsFgsLFq0CB8fH96/3pO0/CpSYwOYHu3X6+vpdDrN2l/V1dXR2tpq9+tarVbNdpu16M0L0NjYyL59+/wAN+BE3bWP9jM8E/gb8DWQC6hdLqUvpgCXAG92lrS8DXwopRxowX33CzEAIUTXC7FdPR5zDvBQ5+efAH/XZCdFsSu9oWOzPzDCn4+e+ZIPn/qc/XuKGTU+nMAIf354bzVrPt6Ii6uBpe6XMe/8mfiF+DIqvqPj4VD5I37ooYe6E9mhuHFyLLGTowkaFcDWn7ez9IaTHRJDf5Pbm4E7pJSfCiEuAt4CjvsdSCmfBJ48yl2itbXVdceOHYeNZbUHm81Gc3Mzq1atsut1ARoaGli/fr3df4haW1uRUh42VtZe6uvrB/x70d7e3v12f0ZGRnciniigvuAgqwp6f62uH2Qt/nzq6urIysqy+y54W1sbFotFk5hBm9+LxsbufLbfbw9LKbfSkeQqSp9IKeuBN4A3hBALgH8DzwshPgEelVLu6+elj/VC7KiPkVJahRC1QNfbSzFCiK1AHXC/lHLtkQsIIW6ko8SOqKiofoap9NekeQk8/MVdfPbC1yTMGMuCi2ZTsH0/O9ft5vw7ziRp0US+++dKinNLuPKhC3ExavOup9I3QghiJkWxP8dxI5T7m9xeBdzW+fnHwJudnxcDPWfYR3bedjxWvV5vSUxMdAkPD+9nOEdnsVjIysoiNTXVrtcF2LBhA9OnT7d7O7CDBw/S3NzM2LFj7Xpd6EicFi5c2O/nd7X7Wrx4Menp6ej1+n4Neuhis9lYu3YtCxYs6HdMx7JlyxbGjBnTrxrj46msrKS0tPSoE94GaqB/PseyZ88e4uLiavbt29eb/mj9+RlWlGPqLB84A7gGGA38FXgfmAd8A4xzQFglQJSUskoIMR34QgiReORuspTydeB1gOTk5OGxrTbEBI8K5Ka/XtX9dVurlfIDlSQt6vg3uNHcSEtTCy5GF03frdXagw8+6OgQ7Co6IZKtP+2gvb0dLbphnUh/3/8+BHRlJIvpeKsSYDlwZefZlVSgVkpZcoJrWa1Wq9TiZLuW2/w6nU6TaxsMBs0OLAkhaG//5dSX3uhKbJOTk/H29sZgMAx4VG9DQwNaTaazWq2adMoYiv942mw22tvbBdCbP/zNwFghRIwQwkjH28nLNQ1QGe5y6SgPeEZKOVVK+ZyUskxK+Qnw3QCu25sXYt2PEUIY6DgjUiWlbJFSVgFIKTOBPByTZCt95BfiS11VPR898yVrP0tnX1YBkePCh+S/zT0N9TrbI0VNGEVbS9th3S8GU29agX0AbATGCyEOCiGuA24A/iqEyAaeoPNtGzpehecD++h4G+q3vYjBarVapRaJok6n06QdFHT0DtUiCdWy1ZS3tzf19fV9ft6RiW2X/k4y69Lf7g29oVXXCavV6pBXoQMhpcRms8ne/JBJKa3ALcAKIAf4SEqpjiArA5EF3Cml3AAghPATQrwNIKW8dQDX7c0LseV0vNMIcAHws5RSCiGCuro4CCFi6ejwkz+AWJRBMmbKaB5dfg8Hdhez+qP1pJ4xnfkXpg7pxHY4ikroqH8u2nXQIeufcGtLSnnpMe6afpTHSuB3fYyhTaudW51O1++dyhPpGpfq5eVl1+tqNQEL/td6qy+9bo+V2HbpOmSWlpbW5xIFs9lMaGhorx/fFzabTZMktKWlRdNpelrozGl7/epRSvkNHS9UFcUeYqSU5q4vpJQ1QoipA71oZw1t1wsxPfC2lHKnEOIRIENKuZyO8yDvCSH20dH155LOp88HHhFCtNHRAeQmKeWRXYEUJ+UXYmLS/AmMSRrNmCmjHR2OchTRncltwfb9zD47ZdDX12bCQd+0WCwWTXZY9Xq9Zju3Wo1L1XIMq5+fH/n5+YwePbpXjz9RYtulvwluTU0N8fHxvXpsX2h54tRisWiy26xlXVJ7ezs2rX4QFOXEdEIIPyllDYAQwh87/d9ztBdiUsoHenxuAS48yvM+BT61RwzK4KurqufVO5cREObH3zY8joe3u6NDUo7g6evJqPHh7N6Ue+IHa8AZek5VVFVVSa12K0GbZEer8oGuWl4tYjaZTNTX1/eqnKK3iW2XvpYo1NXV4erqqklP3+bmZs12V7WcTGfvw4k9r221Wu3fF01ReuevwEYhxKNCiEeBDfxv8I+i9JlPgDf3f3gHRbsO8u/H1WsUZ5Uwaxw5G/c6pMWZw5NbKWWbxWJp02q3Uqtm/lrWxnp5eWky3EAIQURExAnbjPU1se3SlwS3sLBQs9Y6/Rkz3FtDcexyVVUVnS2QFGXQSSnfBc4Dyjo/zpNSvufYqJShbtrJk1l4yWy+eOlbqku16ZeuDEzCzHHUVtZTkl826Gs7PLkFsFqtLT16cdqVVkmolsmtr6+vZg39o6OjKSoqOma5Rn8T2y69SXBbWlqorq7WrN5Wy4NqLS0tmuywapncVlRUYDAYDp34kYqiDSnlLinl3zs/dp34GYpyYlc+dDFtrVY+ePJzR4eiHMWEWR0NSHZt3DvoaztFcmswGCrKy7VpF6FVEuru7k5zc7Pdrwv/O/ilBaPRSERExFEHZgw0se1yvARXSkl2djbx8fGanW7Vaue2s+uAJhPktEpupZRUVVVhtVqL7H5xRVEUB4ocG8apVy3k69d+oPxApaPDUY4QnRiJu5cbezb1d05L/zlFciuEKK6qqtLk2lolt13lDlrUkvj5+aHV7wdAXFwclZWVhyXQ9kpsuxwrwT106BAGg0GzXduuCWpaJIrNzc24u2tzcEHL1mVms5n6+vo8u19cURTFwa544AIA3n/0EwdHohxJr9cTGOFPTbl50Nd2iuS2ra2tsKqqSpNEUcvWWl5eXmhRTuHi4oKLi4tmO8NCCJKSksjOzsZqtdo9se1yZILb3NzM3r17NZnu1aWqqorAwEBNdoVra2s1q+XVstzBbDa319fXq51bRVGGneCoIJbecDLf/XMl+3erYYrOxtvfi/pq+58hOhGnSG6rq6tza2trNUlCtSwf8PX11ax8IDQ0lNLSUk2uDR0DHcaMGcOGDRvIyMiwe2LbpSvB3bBhA2lpaUyZMgWj0Wj3dbqUlpZqtitsNps1q+XVqsODxWKhqqqqlY6pgoqiKMPO5X++AE8fd1646TXN2n8q/ePl50l9jTZnqo7HKZLb1tbWYrPZrEnHBG9vb+rq6k78wH7QsjZW6+QWwMfHh+bmZlxcXDR7ux06/gza29tpb2/XbNwu/K++NCAgQJPra1nL29raqtnObXl5eStwojHYiqIoQ5JfsC83/OUKtq/JYcU/Vzo6HKWHEb1zC5RUVla2apHcGo1GzWpjTSaTZl0NPDw8aG9v12zXuasUYfbs2cTExLB+/XpNEvWysjLS0tKYOnUqkydP7veo3t6orKzEz89PkwNfUsohW8tbWlpqQyW3iqIMY6ddu5jJCybw+p/eo6bM7OhwlE7efl7UVdUP+rpOk9yWlJRo1utWq76xXYmzVm+DREVFsX//frtf98ga28jISKZNm8b27dvJycmxy/fT1tbG1q1bKSoqYtasWQQEBPR50ENfFRUVER0dbffrAjQ1NeHu7q5JLa+WfXlbWlqora21Adq8faEoiuIEhBDc/uqNtDS18Mof3nF0OEon/1A/muqaaW7UJr87FmdJbosPHjxo0yIBBW37xvr7+2vW2SAiIoJDhw7ZNXk+1uExb29v5s6di8FgYPXq1RQUFPRqktmRWlpa2LNnD+vWrSMoKIiUlJTDdju1SnCbm5tpbm7WLEksKysjJCREk2tr2Ze3urqa1tbWJumIETGKoiiDaNT4CC79v/NY+cF6Mn/IdnQ4ChASHQhA+f7BbdXmFMmtlLKtpaXFrFWN6VCtjdXr9YSEhHDw4EG7XO9EXRGEEIwdO5Y5c+ZgtVpZt24dmZmZFBYWUlNTQ3t7+y+eY7VaqaqqIi8vj/T0dNLT03F1dWX+/PlERkYedadTiwQ3Pz+f0aNHa9Y7V+uDalrV8ubk5GAwGLbZ/eKKoihO6OK7zyUwwp9Pnvuvo0NRgJDRwQCUFVYM6rqGQV3tOHQ6XUZOTk7sSSedZPcExWQykZuba9drdgkICGDnzp1IKTVJrOLi4li/fj0RERHo9fp+X6cv7b6MRiNjx44lLi4Os9lMTU0NhYWF1NXVddcu19fXs2rVKnQ6Hb6+vphMJiZMmNDrjgvBwR1/4dPS0khNTR3QYarm5mYqKipISEjo9zWOp62tjba2Nk3qYrWs5bVYLBQWFsrq6uqf7H5xRVEUJ2R0dWHp9Sfz7sMfUZJfRlisNu+4Kb3TtXNbVqjNoK5jcZrktqys7MfCwsILGhsbdV5eXna9ttFopLW1VZMEVK/X4+XlRX19PT4+Pna9NnTEHh4eTmFhIWPGjOnXNfrbx1YIgZ+fH35+fr+4b9WqVSxcuLBf8XSxV4K7d+9exo0bp8lBMoDy8nLNShK6Elutann37t3b1NTUlG73iyuKojip069fzL8e+4SvX/+B65/6taPDGdH8w/wwuOgpKxrcnVunKEsAsFqtGbt3727UqnzA09NTk4ELoH3brjFjxrB//37a2tr6/FytBjTYy0BLFBoaGqirqyMsLEyD6DoMxZKErmtv3769BcjSZAFFURQnFBgRwKyzprPinytpben7/5uK/eh0OnwCfaitHNyOCU6T3AI7c3Jy2rRKbgMDAykv12ZbPCQkRNPk1mAwMGbMGHbt2tWn5zl7YtulvwmulJJt27aRmJioWa1te3s7dXV1mh34Ki8vJzAwUJNrV1ZWUl9f3yilbNJkAUVRFCd1xm9OxVxRx/rPNzk6lBGvvc2Ki3FwCwWcJrmVUrZaLBZzWVmZJtcPDQ1Fq2sbjUbc3d01O7QGMGrUqO7a0t4YKoltl/4kuIWFhfj4+ODv769ZXIcOHSIsLEyT5FlKSXV1tSZDJ6SU7N69G4PBsN3uF1cURXFy00+ZTFhsCF+89I0mfe6V3mtrteLi6jKoazpNcgug1+u35OTkaPIX0cPDg9bW1n69td8b0dHRFBUVaXJt6Kh/nTJlCjt37jxhi66hlth26UuC29jYSFFRkWaHyLrs37+fqKgoTa5dV1eHt7e3JrXCFouFgoICWVNTo8b1KIoy4uh0Oi688yx2bdzL1p/Ua3xHsrZaMYzUnVvoOFRWVFRk06o2Njg4uNc7n30VFBRETU2NZskzgLu7O7GxsWRnZx/zBcBQTWy79CbBbW9vZ+vWrUyePHlAHSROpK6uDr1ej4eHhybX17qWNzc3t6mxsTFNkwUURVGc3JJrFxMUGcC7D3+kdm8dyNo6gssSANra2jbn5ORodqhMy4NfQghGjRqlyUSxnqKiojAYDOTl5f3ivqGe2HY5XoLbVWcbHh6uaTkCdPTOjY2N1ez6ZWVl3R0j7K3zMFkr6jCZoigjlNHVhUvu+RU71+9Ru7cOYrPZsNkkeoN2G1FH41TJLbBjx44dbdXV1Zpc3GQyUVtbq9kruKioKA4cOKD5K8RJkyZRVlZ2WA3xcElsuxwrwc3Pz0cIQUxMjKbrt7a2YjabCQoK0uT6zc3N6PV6jEajJtcvLS2lrq6uXkqpzdg/RVGUIeC06xYTGOHPe498rHZvHUCn06E36Ae9a4VTJbdSylar1bpv27Ztmvwl7OrbqlXy7OLiQmBgoN0mih2LTqcjOTmZnJwczGbzsEtsuxyZ4JaUlFBaWsrkyZM1647QZd++fcTExGi2TllZmWYlCW1tbaSnp2Oz2b7VZAFFUZQhomv3dse63Wz9eYejwxmRXD2MtDTZZxppbzlVcgtQU1OzbMuWLbb6em16omndk3bs2LHs27cPm82m2RoArq6upKSkkJmZyaZNm4ZdYtulK8Fdu3Yte/fuZcaMGZoNa+hisVgoLy9n1KhRmq2hZb1teXk56enpjWVlZe9rsoCiKMoQcvp1i/H28+TH91Y7OpQRydXdSGtz66Cu6XTJbVNT0xerVq2qKykp0eT6QUFBlJeXa5Z8urq6dk8U01p7e3v31LX29nbN13OU9vZ2hBCdtTvavmgA2LNnj6YTzywWC62trXh6empy/UOHDrFp06ZmYKMmCyiKogwhRjcjKadPZfO3Wwfl/xDlcK7uRlosIzy5lVIeKi0trTragSl70Ov1mg50gI6JYkVFRZp2TugqRZg5cyapqalkZWVp1sfXkQoKCsjLy2P+/PkkJib2e5JZbw3GxLMDBw5o1l7MZrORkZGBTqfbJKU8fs84RVGUEWLm0mmYK+rYs1mb3EI5NlcPV1WWANDa2vrx5s2bsVgsmlxf6560BoOB6Ojoo3Y0sIcja2w9PT2ZNWsW+/btY9++fcOiaN5ms5GdnU11dTWzZs3CxcVlwKN6eyMnJ4f4+HjNam2llBQXFxMREaHJ9aurq9myZUvroUOH/qnJAoqiKENQ8mlJ6HSC9K8zHR3KiGN0N9Iy0ssSAKqqqv6zfv36Oq12In18fGhra6O5uVmT6wOMHj2a0tJSu69xrMNjrq6uzJo1i8bGRrZs2aLprrHWLBYLGzduxNPTk2nTph3Wy1bLBLe6uhqr1apZhwToGInr6+uLi4s201pKS0tZtWpVg81mW6HJAoqiKEOQj783CbPGsembLY4OZcRxcXVRNbedsrdv396sZdeB6OhoCgoKNLu+TqcjMTHxuAMX+upEXRF0Oh1TpkwhKCiI9evXazawQitSSg4cOMDGjRsZO3YscXFxR91B1SLBbW9vZ9u2bUyePNku1zuW/Px8zdqYSSnZvn07zc3NRVJKbU5kKooTEUKcJoTYI4TYJ4S45yj3uwoh/tN5f7oQYnSP++7tvH2PEGLJoAauOMTMpdPJ3VJA5SFtOiYpR1exv5KACG370h/JKZNbKaXU6XQ/bdq0SbODUhEREZSVlWl6ECsoKAh3d3e7DHboS7uvqKgoZs6cSV5eHtnZ2UNiF7e5uZlNmzZRVVXF3LlzTzjcwN4J7u7du4mKitLskBd0jAxua2vDZDJpcv2Ghga2bNliM5vN72qygKI4ESGEHvgHcDowAbhUCDHhiIddB9RIKeOA54GnO587AbgESAROA17uvJ4yjM0+NwWA1f/Z4OBIRo7G2kYqDlYxeoJ23YeOximTW4BDhw69m5GRYdFq91Gn0xEeHq55T9oJEyaQn58/oPKE/vSxdXd3Z+bMmfj5+bFu3Try8vKcsqNCW1sbu3btIj09nZiYGJKSknr9lr29Etzq6mrMZrPmgyEKCgo0nXjWWZJQ19jY+JlmiyiK85gB7JNS5kspW4EPgXOOeMw5wLLOzz8BThIdbwedA3wopWyRUhYA+zqvpwxj0QmRjEseww+qJdigKcopBiBqQuSgruu0yS2wau3atY3FxcWaLTB69GgKCgo0PYDl4uLCxIkT+12eMJABDUIIoqKimDdvHu3t7axZs4b9+/c7RSuUtrY29u3bx7p16/D09GT+/Pn9GkU70AS3qxwhKSlJ08EQbW1tVFRUaNbbFiA3N5fi4mKzlFLbGdCK4hwigAM9vj7YedtRH9PZPaQWCOjlcxFC3CiEyBBCZAy1Mi/l6E65cgF5WYXkb9PuULnyP0U7O37MRieqnVsApJQtVqt1zdq1azV7W93V1ZWAgAC0TKDhf+UJfe3QYK/JYwaDgXHjxjFnzhwaGhpYvXo1e/bs0fRA3bHU19ezfft21q1bhxCC+fPnEx0dPaCesgNJcHft2qV5OQL8b+KZVr1z6+rqWLVqla25ufkNTRZQlBFISvm6lDJZSpms5UFTZfAsumQOBhc93y9b5ehQRoSinQdwdTcSMnpwf36cNrkFKCkpefq7775r0LJ0YNy4cYMyUSwxMZH9+/f3evSvFiN1jUYjEyZMYP78+bi7u5OZmcmGDRvIz8+nqanJLmscSUpJXV0dubm5rF27lp07dxIYGMjChQsZM2bMYZ0QBqI/Ce6BAwdobm7WvBzBYrFQVlamWW9b6Ch5+OKLL2rNZvPrmi2iKM6lGOi5HRTZedtRHyOEMAC+QFUvn6sMQ76BPsw8Yxo//3st7VbnK9UbbopyDjIqPsJu/9f3llMnt8Cm7Ozsyh07tJsH7erqSlhYmOYTxQwGAykpKWRnZ59wx1SLxLYnvV5PVFQUc+fOJSkpCYCsrCxWr17Njh07OHDgAPX19f0qo7DZbNTW1lJUVER2djarV69m9+7duLq6MmPGDFJTUwkLC9OkBKAvCW51dTUFBQVMmzZN03IE0H7iWXt7Oxs3bqSxsTFTSlmpySKK4nw2A2OFEDFCCCMdB8SWH/GY5cBVnZ9fAPwsO/5hWw5c0tlNIQYYC2wapLgVBzv5igXUlNWy9WftcgulQ9Gug0QnDm69LYBh0FfsAyml9PHx+fvKlSufnjdvnl6rU+axsbGsW7eOqKgoDAbtfkvc3d2ZMmUKmzdvZvbs2UddS+vE9kgeHh7ExsYSGxtLW1sbNTU11NbWsnv3bhobG4GOFwBubm64ublhMBgQQtDS0kJubi6tra20tLR0j5QF8Pb2xmQyERkZycSJEwf1FVtX3W5aWhqpqam4urr+4jHNzc1kZ2czc+ZMTf+84X8Tz7RsMXbo0CG+//77pkOHDj2l2SKK4mSklFYhxC3ACkAPvC2l3CmEeATIkFIuB94C3hNC7AOq6UiA6XzcR8AuwAr8TkqptvFGiOmnTkEIQU7aXpJPneLocIatdms7lQerCYsJGfS1nTq5Baivr3/7iy++uO+KK67wmzp1qiZruLi4dE8UGz9+vCZrdPH39yc6OpqsrCymT59+2K7hYCe2R+qaAtbzYJeUsjt5tVgstLe3Y7PZEELg4eGBr69vd/JrNBo13wXtjeMluO3t7WRkZDB58mQ8PDw0j2X37t2aTjyDjqlqGzduNAMrNVtEUZyQlPIb4Jsjbnugx+cW4MJjPPdx4HFNA1SckrunG2FjQtShMo2ZK+qQUuIfahr0tZ29LAEpZY3FYln5888/d+8MamH06NEcOnRIs7GuPUVHR+Pq6sru3bu7b3N0YnssQgjc3NwwmUyEhoYSERHBqFGjMBqNREREEBwc3J3gOkNi2+VoJQo2m40tW7YwatQoAgICNI/BbDbT1tam6cQzs9nMihUr2i0Wy9+llI5vg6EoijIEjJkSrZJbjVWX1ADgH+Y36Gs7fXILUFJS8tDnn39e19duA32h0+mIi4tj7969mq3R08SJE2lqamLv3r1Om9gOdT0TXIvFwtatW/H19WX06NGDsn5OTg4JCQmarrFv3z4++eSTWrPZ/IqmCymKogwjsZNHU5JXRnPD4HcNGim6kls/tXN7dFLK7fn5+QXp6emadjWIjIzEbDZTW1ur2RpdhBBMnTqVqqoqNmzYoBJbjQQHBxMfH8/KlStxdXVl3Lhxg7JucXExrq6umk0jg44uDD/++COtra3fSCnNmi2kKIoyzMROiUZKScF21RZcK9WlZgBVlnA8FRUVD3399deWkpISzdYQQpCUlER2dvagDDpoaGigubkZX19ftPy+RjIpJcXFxQQFBVFZWTkoZSctLS3s3buXiRMnarpOYWEhn376aW1paeljmi6kKIoyzMROjgYgL1uVJmilusQMqOT2uKxW639XrlxZvWXLFk0ninl7exMWFqZ5eUJXKUJKSgozZ86kvr6enJwcTb+3kaa9vZ3MzEw8PT1JTk5mwoQJAx7V2xvbtm0jISEBo9Go2RptbW2sW7eO4uLiPVLKPZotpCiKMgyFRAdhCvYlJ21wShFHourSGrxMnhjdtPu/8FiGTHIrpWxvaGh44OOPP245dOiQpmvFxcVRUVGB2WzW5PpH1tjqdDqmTZvWnYxZrVZN1h1JLBYLGzduxN/fv7sDxkBH9fZGcXExer1e0zG7AHl5efzzn/+sLykp+b2mCymKogxDQggmzo1n+5pdjg5l2NqzeR+j4sMdsvaQSW4BGhsb3/n+++9L1q9fr2nZgJblCcc6PCaEYOLEiQQFBbFhwwaHjMYdLsxmMxs3bmTcuHHExsYedp+WCe5glSNYLBZWrFhBfn5+hpRSNZ5XFEXph0lzEygtrKDiYJWjQxl2Kour2LM5j1lnpThk/SGV3Eop26uqqm57//33m7TsnAAd5Qnh4eHs2WO/d3x70xUhOjqaiRMnkpaW1utRvcr/FBcXk52dTUpKymH9envSIsGVUpKdna15OQJ0TDx78803a0tLS2/WdCFFUZRhbOK8eAC2r81xcCTDz8blGQDMPlclt71itVr/m56eXrB69WrN376Pi4ujqqrKLuUJfWn35e/vT2pqKjt27KCwsFDV4faCzWZj165dHDx4kNmzZ+Pl5XXcx9s7wT106BAGg0HzcoTGxka+/vprKioqVqhaW0VRlP4bM2U07l5u7FDJrd2t/3IzEWPDiIqPcMj6Qy65lVLKsrKy37zzzjsNeXl5mq7VVZ6QlZU1oASoP31s3d3dmT17NrW1taSnp6syheOora1l3bp1GAwGZsyYgYuLS6+eZ68Et66ujtzcXM3LEQB27tzJ22+/XVNWVvYHzRdTFEUZxvQGPRNmj2fH+t0nfrDSa421jWSv3MGcc1IcNtxpyCW3AFLK9Xv27Mn+6aefNJ1aBuDl5UVCQgIZGRn9qr8dyIAGg8HAlClTGDNmDOnp6RQVFald3B5sNht79uxh27ZtJCUlMW7cuD7/IA00wW1tbWXLli1MmzZN83KE2tpali9fLuvr6z+QUhZrupiiKMoIEJ0QSWlBuaPDGFY2fZuFta2d2efOcFgMQzK5BSgtLb3pzTffrLNnTeyxhISEEBISwvbt2/v0PHtNHgsKCmLOnDmYzWa1i9upa7dWCMGcOXPw8fHp97X6m+DabDYyMjKIj48f0Pq9tXXrVpYtW1ZdXl5+v+aLKYqijAD+YX40N1jUpDI72rB8M34hvsTPjHNYDEM2uZVS7igpKVn53Xff0dTUpPl6Y8aMwWq1UlBQ0KvH23ukrouLy2G7uLt376atrW3A1x1qLBYL2dnZh+3W6nQD/2vcnwR3586dBAYGal5nC1BZWckXX3zR3tzc/JKUskbzBRVFUUaArgEDXdO0lIGRUpL103aSlySh1+sdFseQTW4BSktLb3vzzTfNO3bs0HytrvrbgwcPUllZedzH2jux7SkoKIj58+fj6urKunXryMvLo7293a5rOKO2tjZycnJIS0sjKCiIuXPn2n23tC8JblFRES0tLYwdO9auMRyNlJL09HQ++uijyqqqqmc0X1BRFGWE8A8zAf+bpqUMTHFuCeaKOibOTXBoHEM6uZVSFtXU1Cz797//3V5aWqr5enq9nuTkZLZv305jY+NRH6NlYttFp9MRExPDvHnzsFqtrFmzhgMHDgzLetz29nb27dvHunXrcHd3Z/78+YSHh2tWpN6bBLeqqor9+/czderUQSmW37dvH2+88UZzQ0PDPVJK7d+mUBRFGSG6d25L1Bti9rBjXcfhvIlz4x0ax5BObgEqKiru/vDDD/evWLFC88Nl0NHFICkpiYyMjF+sNxiJbU8Gg4Hx48d3d1VYvXo1eXl5w6JcwWKxkJOTw5o1a5BSMm/ePEaPHm2XEoQTOV6C29DQwLZt20hOTh6Ut1zq6+v54osvSEtL21RfX79M8wUVRVFGEP8wPwCqVHJrF9vX5eAb6M2o8Y6ZTNZlyCe3UsqWsrKyC//617/WZWVlDcqafn5+xMfHk5aW1p1IDnZi25OrqysTJ05kzpw5AKxfv57s7GzNxgdrRUpJeXk5mzdvZtOmTXh6ejJ//nzGjh2LwWAY1FiOluA2NjayefNmpk+fjru7u+Yx2Gw21q1bx4svvlhZVlZ2iRyOW/OKoigO5BPgjdHNhUo1pcwudqzbzcS58Q5rAdZlcDMGjUgpM4ODg//5/vvv3zJq1Ch9WFiY5muGhIRgs9lIT09nwoQJZGdnOySx7cnFxYUxY8YQGxtLRUUFubm5NDc3ExISQlhYGN7e3g7/C3ckKSU1NTWUlpZSXl6OyWQiLi4Ok8nk8Fi7JpylpaUxZcoUsrKymDp16qB0RoCOcoTXXnut2Ww23yml1L7uRlEUZYQRQhASHURpoWoHNlDVpTUc2lfKmb851dGhDI/kFrrLE86eNm1azKWXXqp5z1GAsLAwGhoa2LBhA3PmzHFoYtuTEILg4GCCg4NpbW2lrKyMPXv20NDQQEBAAKGhoQQGBg7KW/xHY7VaKS8vp7S0lNraWkwmE6GhoYwbN27Qd2hPJDg4mJaWFtatW0dKSgomk2lQ1q2rq+sqR0hvaGh4b1AWVRRFGYFCY4IpLaxwdBhDnrPU28IwSm6llC1CiAufffbZnxMSEnxmzNC+eXBdXR0HDx4kPj6enTt3MnPmzF5PxxosRqORUaNGMWrUKGw2G5WVlZSWlrJr1y5cXFzw9fXFZDLh6+uLl5eX3XdLbTYb9fX1mM1mzGYztbW1SCkJCgpi9OjR+Pn5OXyH9ngaGxvJy8sjISGB3bt3YzKZcHV11XTNrnKEl156qbKsrOxSVY6gKIqinZDoIPZs1nbi6Ujw7Vs/YQryIW7qaEeHMnySW+guT3jzX//6162jRo0yaFmecGSNraenJxs3biQ1NXVQdo37Q6fTde/oQsd0ra6ks6SkhIaGBlxcXHB3d8fNzQ03NzdcXV27P9fr9eh0OoQQ2Gw2WlpasNlsWK1WLBZL90dLSwsWi4WmpiZsNhve3t6YTCYiIyNJTEx0ut3ZY2loaGDz5s1MnToVk8mEt7c3aWlppKamaprg7tu3j1dffbXZbDbfocoRFEVRtBUyOpi6qnqa6pvx8Nb+PMVwtDczj4wV2Vz3xGW4GB2/yTc0sow+qKiouPejjz46d9q0abGXXXaZJonm0Q6PhYWFodPp2LhxI8nJyXh6etp9XXszGo2HJbvQ0U+2ubm5O1Ftbm6mpqYGi8VCe3s7UkpsNhvNzc1s2bIFIQQGg6E7AXZ3d8fPzw9XV1fc3d2HTCJ7pOrqarKzs5k+fXp3jW3PGlytEty6ujo+//xzNm3atLGhoeF9uy+gKIqiHCYspuPf9rLCcmImRTs4mqHpgyc/x8vkyVm/XeLoUIBhmNxKKVuFEBc8++yzq+Li4nzmzJlj17e9j9cVISQkBKPRyKZNm5g0aRKBgYF2W3ewuLi44OLicsJDU6tWrWLWrFmDFNXgOnDgAAUFBcycORMPD4/D7tMywbVaraxataqrHOEyVY6gKIqiva52YDVltcRMcnAwQ1DRrgOs+yydy+8/H08fjxM/YRAM+VZgRyOl3FpaWvr0888/b8nJybHbdXvT7svPz49Zs2aRk5PT61G9inOQUrJz505KSkqYPXv2LxLbLv0Z1dubtTdv3syjjz7aUF1dfY2UsswuF1YURVGOy93bDYCm+mYHRzI0ffj0F7h5uPKrW5c6OpRuwzK5Baiqqnpy3bp1377zzjvtxcXFA75eX/rYurm5MXv27O63tm0224DXV7TV1tZGeno6er2elJSUE5ZT2DvB3bt3Ly+88IKlsLDw2aampq8GfEFFURSlV7p2G5vqVHLbVyX5Zfz873Wc8ZtT8A0cnDaZvTFsk1sppSwvL7902bJluz/66KMBDTToz4AGvV7PtGnTug+a2WuHT7G/hoYG1q9fT1RUFPHxvW8+ba8E99ChQ7z99tu2VatW/VBZWflIvy+kKIqi9Jnaue2/T5//Cr1exwV/ONPRoRxm2Ca30NEerLy8/ORnnnmm7Ouvv8ZisfT5GgOZPCaEIC4ujri4ODZu3DjkJoaNBKWlpWRkZDB16lTCw/s+LnCgCW5tbS2ffPIJ77zzzp7y8vKLVJ2toijK4OrqkNBc3/ccYSRraW7hx3+tYd4FqQRGBDg6nMMM6+QWQEpZWlJScsZDDz1kXrNmDe3t7b1+rr1G6oaEhJCcnMyOHTvIyclRZQpOoK2tjS1btrB//35mzZqFr69vv6/V3wS3paWFb7/9lqeeeqqsvLz8ZCml+pdVUXpBCOEvhPhBCJHb+avfMR53VedjcoUQV/W4fZUQYo8QIqvzI/hoz1dGBhdXF/QGPU11TY4OZUhZ99kmGmubOO3axY4O5ReGfXILHf1vy8vLb3388ccbs7Ky6M3mmL0S2y5eXl7MmTMHFxcX1q5dq3ZxHaisrIx169YRHBxMSkqKXToe9DXBtdlsrFmzhgcffLC2pKTkbCnloQEHoSgjxz3AT1LKscBPnV8fRgjhDzwIzARmAA8ekQRfLqVM6vxQs1dHMCEEHj7uNKqa2z757u2fCI0JZsrCREeH8gsjIrkFqK2tfS8nJ+ftl19+uTU/P/+4j7V3Ytulq0xh2rRpahfXAdra2ti6dStFRUXMmjWLyMhIu7aJ622CK6UkKyuLJ598srGsrOwOKeUmuwWhKCPDOcCyzs+XAece5TFLgB+klNVSyhrgB+C0wQlPGWo8fdxpqlc7t711KK+UrJU7Oe3axeh0zpdKOl9EGqqoqLj9v//9b/q//vUvWVp69MFPWiW2PXl7ezNnzhwMBoPaxR0kXbu1QUFBpKSk4Obmpsk6vUlw8/PzeeWVV9p27Njxrtls/qcmgSjK8BYipSzp/LwUCDnKYyKAAz2+Pth5W5d/dpYk/Fk48wxwZVB4+Hqobgl98N3bP6PTCZZcvdDRoRzVsBvicDxSSpsQ4syXX355s4eHx9irrrpK9JzONRiJbRchBGPHjiU0NJSsrCxMJhPjxo3TdKzrSNTY2Ni9Qz5r1izNktqejjfooaCggFdeeaX9yy+/XFdRUfF7zYNRlCFKCPEjEHqUu+7r+YWUUgoh+noQ83IpZbEQwhv4FLgCePcoMdwI3AgQFRXVxyWUocTTRyW3vdVubef7ZatIPi3J6Q6SdRlRO7cAUsq68vLy2c8++2z++++/T2VlJTC4iW1P3t7ezJ07Fz8/PzZu3MiePXuwWq2Dtv5wZbFY2LZtG5mZmURFRTFjxoxBSWy7HG0Hd//+/bz++uvt7777blpFRcXpUsren25UlBFGSnmylHLiUT6+BMqEEGEAnb8erWa2GBjV4+vIztuQUnb9Wg/8m46a3KPF8LqUMllKmRwUFGS/b05xOh4+7upAWS/995XvqTpUw9LrT3Z0KMc0onZuu0gpq4QQs5966qlNBoMh+txzz2Xfvn2Dnth2EUIQGRlJeHg4hYWFrF27lujoaEaPHu2UtSzOrK2tjX379lFWVsbYsWOZNGmSXetq+6LnDm5UVBT//Oc/bW+99daWioqKk6WUqvGxovTfcuAq4KnOX788ymNWAE/0OER2KnCvEMIAmKSUlUIIF+BM4MdBiFlxYh4+7hzYPfCBT8PdgT3FvHnPv0g5fSqzz0lxdDjHNCKTWwApZbkQYvbjjz++2WKxhF966aUOSWx70ul0xMbGEhUVRV5eHqtXryYuLs7uB5+Go/b2dgoLC9m/fz8xMTHMnz/fKV4YBAcHU1lZyauvvso777yzo6KiYpFq+aUoA/YU8JEQ4jqgCLgIQAiRDNwkpbxeSlkthHgU2Nz5nEc6b/MEVnQmtno6Ets3Bv9bUJyJh7cHjbVq5/Z42q3tPH3lSxjdjdz55s1OnZeM2OQWQEp5SAiR+txzz210c3OLuPTSSwkMDHR0WBgMBsaPH8/o0aPZu3cveXl5xMTEEBkZiV6vd3R4TqW1tZWioiIOHjxIREQE8+bNO+Ho3MG0f/9+/vOf/8hly5btLC8vnyulbHR0TIoy1Ekpq4CTjnJ7BnB9j6/fBt4+4jGNwHStY1SGFp8AL+prGrHZbE6xMeKMPnjyc/ZszuP+D+8gIOyoraWdhvNkAQ4ipTwghJjx2GOPbbBardGXX345PQ+ZOZKrqyuTJk2ipaWFwsJC1qxZQ0hICDExMbi7uzs6PIeqq6ujoKCAmpoaoqKinC6pBSgsLOS1115rf/vtt7eWl5cvVImtoiiKczIF+WJrt9FgbsTH37Hv4jqjvZl5/OvRT1h82VwWXDTb0eGckHNlAw7SuYM746mnntpgtVpjr7jiChEaerRDuo7h6urK+PHjGTt2LIcOHSIzMxODwUB0dDQhISEj5lWm1Wrl0KFD7N+/H4PBQExMDJMnT3bKt0by8vJ49dVX25ctW5beWWOrjuEqiqI4Kd8gHwBqK+pUcnuEluYWnr7yJUzBPtzy0nWODqdXVHLbqbMGd+azzz67oampaeyvf/1rERsb61SJk06nIzIyksjISOrq6igqKmL37t0EBwcTGhqKn5/fsEt029vbqayspLS0lOrqasLDw5k+fbrT7lzbbDZ27NjBq6++av3000/XVVRUnKYOjymKoji3nsntqPERJ3j0yPL2/33A/pxinvj2Prz9vBwdTq+o5LaHzi4KKf/4xz/+W1RUlPq73/3OmJSU5JR1rj4+PkyaNIn29nYqKio4cOAA27Ztw8fHh7CwMIKCgnBxcXF0mP3S0tJCaWkpZWVlNDU1ERgYSEREhNPu0nZpbW1l3bp1PP30001ZWVn/KS8vv1FKqfq6KYqiODlTcEdya66oc3AkzmXrz9v57G9fc/Zvl5CyJMnR4fSaSm6PIKWsE0Is+uqrr57Py8u77r777vOcP3/+oPZI7Qu9Xk9oaCihoaFIKTGbzZSWlpKbm4uLiwuhoaEEBwfj6enptImhzWajvr6esrIyysrKEEIQEhJCQkICXl5eTht3T3V1daxYsYIHH3ywrqSk5N6ampqXHR2ToiiK0jumzp1bc7lKbrs0mBt55pp/EDkujBv+coWjw+mTIZfcCiFG0TFJJgSQwOtSyr8JIZ4BzgJagTzgGimlWQgxGsgB9nReIk1KeVPntRYCzwI/Synv6lpDSmkDbvP19c383e9+97cHH3zQdOaZZ2IymQbjW+w3IQR+fn74+fmRkJBAU1MTpaWl7Nq1i8bGRoxGI76+vphMJnx9fR2SOHYlsmazGbPZTG1tLTabDW9vb4KCgpgxY8aQm9JWWlrKp59+yhNPPFFRVlZ2ntVqXdfzfiGEG7AGcKXjZ+4TKeWDQohbgNuBMUCQlLKy8/EL6ejbWdB5ic+klI903ncJcBfwrpTyBa2/N0VRlJGgZ1mC0uHvt75F1aEa/rb+Mdw8htb/y0MuuQWswJ1Syi2doxMzhRA/AD8A90oprUKIp4F7gbs7n5MnpUw6yrVuBuYBjwkh4qWUu3veWVtb+64QYuddd931VUVFRehFF11ERMTQqcXx8PAgNjaW2NhYoONt866EsqSkhMbGRgwGAz4+Pri5uf3iw8XFpc/Jr5SSlpYWWlpasFgs3R/Nzc3U1dV1J7Imk4nIyEgSExOdrstBb0kp2bdvH8uWLbO98cYbeeXl5SdLKfcf5aEtwGIpZUNnb811QohvgfXAV8CqozxnrZTyzKPcfgmQArwvhPCSUjbY6dtRFEUZsVyMLnj4uFNbqZJbgDWfbOSnf63ligcuJH7GWEeH02dDLquQUpYAJZ2f1wshcoAIKeX3PR6WBlzQi8vp6Nj9tQFHzeKklJlCiKlPPvnkj4cOHYq/5ppr9AkJCUPirfIjGY1GgoODD2t11traSn19fXcS2vPztrY2oOMgm16vRwiBTqdDCEFjYyMbN25ESomUEqvVipQd491dXV1xc3Pr/rVrV9bHx2fIJrJHam9vJyMjg5deeqnl+++/X1NRUfGrY7X6kh2/MV1JqEvnh5RSbgX6+nep68GSY/ydVRRFUfrON9BHJbdAVUkNL9z0OuOSx3DZfec5Opx+GdKZRmfJwVQg/Yi7rgX+0+PrGCHEVqAOuF9Kubbz9jeBDcBKKWXOsdaRUpYKIaa/++67H+Tn559+xx13uM2YMQOj0Wi378VRjEYjAQEBx31Me3s7NpsNKWX3rxs3bmTq1Kndya5erx8ynRoyi2pIy68iNTaA6dF9b0Td2NjI6tWrefTRRxvy8vL+XlFR8X+yK7M/BiGEHsgE4oB/SCmP/Dt7pFlCiGzgEPBHKeXOzts/AzKAf0kp6/scvKIoinJUvkE+1FaO7H9W21rbePyS52ltbuXud3+PwWVopolDM2pACOEFfArcLqWs63H7fXSULrzfeVMJENXZCWE68IUQIlFKWSelXEHH/PETklK2CCHOX7169b179uy5+49//KPPkiVLCAsLs+835oT0ev0vOkbodDqnPWR3PJlFNVz+ZhqtVhtGg473r0/tdYIrpaSgoIDly5fz/PPPV1dXV99UX1//cS+f2w4kCSFMwOdCiIlSyh3HePgWILqzjGEp8AUwtvM6y4BlvQpYURRF6TVTkA+VxdWODsNhpJS89Lu32L42h3vfv42o+KFThnmkIZncdtYtfgq8L6X8rMftVwNnAid17aR19hht6fw8UwiRB4yjY/erTzqv+YQQ4tt77rnnk8zMzKgrrrjCkJSUNCx2cUeCtPwqWq02bBLarDbS8qt6ldx2lWG89dZbLStXrtxWVlZ2wTHqa4+r85DjSuA04KjJbc8Xa1LKb4QQLwshArsOnCmKoij25xPoTV5WoaPDcJgvXvqWb9/6icv+7zwWXzrX0eEMyNB4H7kH0VGg+BaQI6V8rsftp9FxivxsKWVTj9uDOt8SRggRS8cOWP5AYpBSbi0rK0v4z3/+8+J1111X98EHH1BSUjKQSyqDJDU2AKNBh16Ai0FHauzxSzK6dmvffPNNrr/++urvvvvuT2VlZTP7kth2/h00dX7uDpwC7D7O40M7/54jhJhBx89pVW/XUxRFUfrOFOiDuaKu+/zISJLxfTav/uEd5pybwlWPXOzocAZsKO7czgGuALYLIbI6b/s/4EU6Wi390JkXdLX8mg88IoRoo+Pg2E1SygG/7yClbAXuFEK8f9ddd32SmZk56te//rXaxXVy06P9eP/61F7V3DY2NpKWlsabb77Z8vPPP28vLy+/QEpZ1I9lw4BlnS+ydMBHUsqvhBC30vGCLBTYJoT4Rkp5PR2HIW8WQliBZuCSE9X0KoqiKAMTHhdKW0sbB/ceGlFTyg7sKeaxi59j9MQo7n7390Pm/MzxCPV/5sAJIYyBgYFPhYWFXXfnnXf6LFmyhNDQUEeHpalVq1axcOFCR4ehCSklhYWF/Pe//+W5556rrq2tfdhsNr+kEkxFGbmSk5NlRkafq9mUIaSkoIwrx9zC7/52Lef+/nRHhzMoaivruG3O/TSaG/n7pqcIiQ5yaDxCiEwpZfJArzMUd26dTucu7h+EEO/ffffdH2/ZsiXq8ssv10+cOBEPDw9Hh6f0QW1tLRkZGbz99tstP/74447O3dpCR8elKIqiaCssJoTwuFAyvs8aEcltXVU9d53yCBUHKnn6+z87PLG1J5Xc2lHngbWEDz744Olvv/32quuvv950+umnM27cuCE3dWukaWxsZOfOnSxfvlwuW7asuqGh4TGz2fw3tVurKIoyciSfOoXv31lFa0sbRlcXR4ejma7E9sDuQzy6/G4mzk1wdEh2NfQLK5yMlLKlvLz89tzc3KTnn3/+y6uuuqr2zTffZM+ePVitVkeHpxyhpaWF7OxsXnzxRS677LKaN95449WDBw+Oq6mpeUEltoqiKCPL9FOnYGlqYdeGPY4ORTN11fXcfeqj7M8p5pEv72b6KVMcHZLdqZ1bjXQePDpXCDHxsccee+Wjjz5Kuuaaa7wWLFhAdHT0sCjYHsra2trIy8vjhx9+4I033qgtLy//oays7A4p5UFHx6YoiqI4xpSFiegNejK/zyZp0URHh2N3ddX13H3KoxTtOsjDX9xF8qnDL7EFldxqrrNR/zwhxJw9e/a8NnPmzNjLL7/cffbs2URERAzJMb5DWXt7O4WFhaxatYq33367Pj8/P7O0tPRmKeUxW3MpiqIoI4OnjweJc8az7vN0rnn80mG1EVVXXc89pz5K0c4DPPzFXaQsSXJ0SJpRye0gkVKuF0JM+uabb85MT09/8ZRTTgm76KKLXKdNm0ZYWNiw+gFyRlarlQMHDpCens57773XmJmZua+srOw3vRiDqyiKoowgZ9xwMk/++kU2f7uVmWdMd3Q4dlGUc5AHznmaiv2VPPjZn0g5baqjQ9KUagXmAEIIvaen51VeXl6PLlq0yH/p0qVuM2fOZPTo0UOmR+5QaQXW1NREQUEBa9as4b///W/j1q1bD5WXl99qs9lWqJpaRVF6S7UCGzmsbVauHHML4XGhPPvzQ44OZ8DSv9nCE5e9gNHNyEOf/YnE2eMdHdIxqVZgQ5iUsh14Wwix7JNPPjlz9erVD8fExMScd955PosXLyYmJgaTyeToMIcsKSWVlZXk5uby448/yo8//ri2qqpqa0lJyQPAepXUKoqiKMdicDHwq1uX8vpd75G7JZ+x02IdHVK/SCn55K//5Y27/0XslGge+eIugqOGT7uv41E7t05CCDEpNDT0AXd398Xnnnuu76JFi/QTJ04kMjISFxfna0fijDu3FouF/fv3s3XrVn766ae2b775pratre3j8vLyp/oyLldRFOVIaud2ZGmsbeSyqJtJPWs69/7rNkeH02etllZeuOl1fnh3NfMuSOVP//wd7p5ujg7rhNTO7TAjpdwOXCiE8Hvrrbeu+eCDD34/efLkgNNOO817/vz5REREEBgYiMGg/sh6am1tpby8nKKiIlauXMlXX31Vu3///gM1NTXPWCyWj6WUzY6OUVEURRlaPH09Of26xXz+0rdc9+TlBI8KdHRIvVZ5qJpHLniWnLRcrnzwIi7/8/kj7lyP2rl1UqKjjUJKWFjY3Xq9fuG8efM8kpOT3WbOnElkZCQhISG4uTnuVZgjd24bGhooKyujoKCATZs2kZ6e3rB58+Zmm832eVlZ2XNSyuHboFBRFIdQO7cjT2lhOVfF3cKZN53K7/9+vaPD6ZWdG/bwyAXP0lTfzF3v3MK881MdHVKfqJ3bYa6zLnQTcL4QwvWDDz5YsHr16ittNtvJEydO9JgzZ453SkoKcXFxhIaG4uPjM2zbikkpqa6uprS0lJycHDIyMuTq1avrioqKatvb2/9bXl7+PrCps5ZZURRFUQYsdHQwZ9x4CstfXkHMpGjO/M0pjg7pmNrb2/nvK9/z2p3LCI4K5Knv/0zMxChHh+UwKrkdAqSULcD3wPdCCFFaWjp569atFxuNxotCQkICFi1a5DNt2jTd5MmT8ff3x2Qy4enpOWSTXZvNRn19PWazmcrKSrZs2cKWLVvaVq5c2VBfX3+woaHhX3V1dZ9KKfMcHauiKIoyfP32b9dQ/v/t3X2QVfV9x/H3B+7uZRCB5cHlQctDQ8ssJJEJGo2jUjE+ZJLUNMTSpkrTzCRNnTaGpOMDJGPzT9LMOJNOZxpr0hpjW8UkTGOdiCMqbdKRWJ9xLcuuimUpqywsD1EX2L3f/nF+yxy2Cy53d+/dvXxeM7/Zc849D59z7hW/59zfPWdXJ3970/eZMnMyl/7eh6sd6QQRwVP/9gz3rL+fnS/v4sKPLePW+/6CsxsmVTtaVbm4HWPSFd0XU7td0pwdO3Zc19DQcGOhUFi0dOnSusWLF581b968cU1NTTQ2NjJ16lSmTJnCpEmTRl3Bmy9kDxw4QHt7Oy0tLbzxxhu9zc3Nb2/fvv0Y8HxHR8c9vb29j0REV7Uzm5nZmaFQV2D9hrXc8tFv8q0//C6TN63ngyuWVDsWANufbuV7X/khrzy1g7mLZrPu/pu57DMXn3H9awfiPrc1RFI9sKS+vv6Cc845Z2Vvb++HisViQ1NT0/GCd/HixcyZM4dJkyYxYcIEJkyYQLFYpFgsntZ/EKfT57ZUKtHd3U13dzdHjhyhu7ubQ4cOsWvXLlpaWti5c2dvc3Pzr1tbW3t6e3v3Stq6Z8+exyPiWWCHuxuYWZ6kacAGYD6wE7h+oBNfSZuAi4BfRsTHc9MXAA8A04FngRsi4uiptuk+t2e2Q/sPs/ayb7C3fR93bvkr3nf+gqpm+cfb7+fn399Mw6yprLnjeq764xUU6sb+9crh6nPr4rbGSaoDlhQKheWNjY1Xlkql5cVisWHu3LnjZs2aVZg5c2axoaGhbvLkyUyfPp3p06fT2NjIxIkTjxe/48aNQ9Lxv5Jobm6mqamJiKBUKhER9Pb2Hi9i+3701dnZSVdXFwcPHoyurq5je/fuPdrR0dHT3t7eWyqV3oqIrR0dHflCtlTtY2Zmo5uk7wD7I+Lbkm4FGiLilgHmWwlMBL7Yr7h9ENgYEQ9Iugt4MSK+d6pturi1ve37+PIl6+g52sO3Nq3nNz84v6Lbf2tXJ5vv+w82fvdhDne9zaf+/FpuuON6zpo8saI5RpKLWytbKnjnALOB2fX19XMbGhoW1dfXz4+IuT09PTMLhcKEYrFYN2PGDBWLRQqFgvLtyJEjxfHjx3f39PREX3vnnXfo7OyMY8eOHS2VSu+OHz/+TUnt3d3dO/ft29daKpX+F9jT11zImlk5JLUAKyJij6TZwJaIGPCxS5JWAF/rK27TnWj2ArMiokfSxcAdEXH1qbbp4tYA/mf7btZe9nUOdh7m0k9/mM+uXzWiRe6xo8f45can2XTPEzy/eRsRwbKV7+dP71zDwg/MG7HtVouLWxtxqQieARSBOrI+2oU0XAJ6+rV3gU53IzCzkSTpQERMTcMCuvrGB5h3BScWtzOArRHxvjR+HvBIRCwdYNkvAF9Io0uBl4d1R4ZuBtBZ7RA5znNqoy0PjL5Mvx0RZw91JWO/g4aNmIg4RnaV1cysoiRtBmYN8NK6/EhEhKQRuUoTEXcDd6c8zwzHFaXhNNoyOc+pjbY8MPoySRqWr0dc3JqZ2agTEVee7DVJb0qaneuW8NZprHofMFVSISJ6gHOB3UOMa2ajiO8XYWZmY81DwJo0vAb42WAXTLdTfBJYVc7yZjb6ubg1M7Ox5tvARyW1AlemcSQtl/SDvpkk/QL4MbBSUrukvh+N3QKsldRGdjuwfxjENu8ezh0YJqMtk/Oc2mjLA6Mv07Dk8Q/KzMzMzKxm+MqtmZmZmdUMF7dmZmZmVjNc3JqZmZE91lfSY5Ja09+Gk8y3SdIBSQ/3m75A0q8ktUnakB6JXok8a9I8rZLW5KZvkdQi6YXUzikzxzVpPW3piXD9Xy+m/W1L+z8/99ptaXpLrs/zkJWbSdJ8Se/mjsldFcpzmaTnJPVIWtXvtQHfvyrm6c0dn4cqlGetpFckvSTpcUnzcq+d/vGJCDc3Nzc3tzO+Ad8Bbk3DtwJ/fZL5VgKfAB7uN/1BYHUavgv40kjnAaYBr6W/DWm4Ib22BVg+xAzjgVeBhUA98CLQ1G+ePwPuSsOrgQ1puCnNXwQWpPWMH4b3aSiZ5gMvD/PnZjB55gMfAH4ErBrM+1eNPOm1X1fh+PwOMDENfyn3fpV1fHzl1o6TdJ6kJ9PZU7OkL6fpG3JncTslvZBbZsCzckmr01nhzZXfEzOzsvwucG8avhe4bqCZIuJx4HB+miQBVwA/ea/lhznP1cBjEbE/IrqAx4BrhrjdvAuBtoh4LSKOAg+kXCfL+ROyu1MoTX8gIo5ExOtAW1pfNTONhPfMExE7I+Ilsqd75o3E+zeUPCNhMHmejIh30uhWsvtPQ5nHx8Wt5fUAX42IJuAi4CZJTRHx+xFxfkScD/wU2AggqYnsjHgJ2Yft7ySNT+taDVwAXCRpUoX3w8ysHI0R0fdUxg6g8TSWnQ4ciOzBEADtwNwK5JkL7MqN99/uPenCxNfLLO7ea/0nzJP2/yDZ8RjMsuUYSiaABZKel/Tvki6tUJ6RWHak1jlB0jOStkq6bohZysnzeeCRMpcF/IQyy0n/iO5Jw4cl/TfZh+gVOH5l4nqyqxOQOysHXld2z8gLgaeAvn9EIzdsZlZVGgWP9a1gns9GxG5JZ5NdmLiB7GvoM9ke4DciYp+kDwH/KmlJRByqdrBRZF763CwEnpC0LSJercSGJf0RsBy4fCjrcXFrA0qd75cBv8pNvhR4MyJa0/hcsq8P+uTPqDYCzwD/FBEnfH1nZlYtMcoe6zsMeXYDK3Lj55L1tSUidqe/hyX9C9nFh9MtbncD5/Vbf//96punXVIBmEJ2PAazbDnKzhRZR84jABHxrKRXgd8i+//VSOY51bIr+i27ZQhZhpon/7l5TdIWslpgKMXtoPJIupLspO7ydNGsb9kV/Zbd8l4bdLcE+39SN4KfAjf3O5v9A+D+wawjIu6NiGURcedIZDQzGwGj7bG+g8nzKHCVpAZld1O4CnhUUkHSDABJdcDHgZfLyPBfwCJld4KoJ+ty1v8X9Pmcq4An0vF4CFid7lywAFgEPF1GhmHLJGlmX/e5dGVyEdmPlEY6z8kM+P5VK0/KUUzDM4BLSN/ejmQeScuAvwc+GRH5k7jyjs9w/iLObew3oC59cNb2m14A3gTOzU27DbgtN/4ocHG198HNzc2tnEbWJ/NxoBXYDExL05cDP8jN9wtgL/Au2TdWV6fpC8mKtzayx/4WK5TnT9I224DPpWlnAc8CLwHNwN9Q5p0KgI8BO8iu3q1L076ZChGACWl/29L+L8wtuy4t1wJcO4zvVVmZgE+n4/EC8BzwiQrluSB9Vt4mu6rdfKr3r1p5gI8A28juaLAN+HyF8mwmqzFeSO2hoRwfP37Xjkt9au8F9kfEzf1eu4askL08N20J0PdV1xyyf4QXRURvxUKbmZmZ5bjPreVdQvaDg225233dHhE/J/sa4YQuCRHRLOlBsq8seoCbXNiamZlZNfnKrZmZmZnVDP+gzMzMzMxqhotbMzMzM6sZLm7NzMzMrGa4uDUzMzOzmuHi1szMzMxqhotbMzMzG/Mk3SjpJUkvSrpP0s8k3Zhe+6Kkf652RqsM3+fWzMzMxrT0UKH1wEciolPSNLInbv6npNeBrwIXVTOjVY6LWzMzMxvrrgB+HBGdABGxH0DSN4AngU/1TbPa524JZmZmVqveD+wje0S8nSFc3JqZmdlY9wTwGUnTASRNk3QhcC2wDPiapAXVDGiV48fvmpmZ2ZgnaQ3wl0Av8ArQBHwuIp6T9EngK8AV4cKn5rm4NTMzM7Oa4W4JZmZmZlYzXNyamZmZWc1wcWtmZmZmNcPFrZmZmZnVDBe3ZmZmZlYzXNyamZmZWc1wcWtmZmZmNeP/ADCsJcnOkFqBAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1008x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.default_rng(1)\n",
    "\n",
    "truth = Namespace(cr=0.1, cphi=0, sr=0.1, sphi=2)\n",
    "truth.cx = truth.cr * np.cos(truth.cphi)\n",
    "truth.cy = truth.cr * np.sin(truth.cphi)\n",
    "\n",
    "d_r = rng.normal(truth.cr, truth.sr, size=5)\n",
    "d_phi = rng.normal(truth.cphi, truth.sphi, size=d_r.shape)\n",
    "\n",
    "cov = np.eye(2)\n",
    "cov[0, 0] = truth.sr ** 2\n",
    "cov[1, 1] = truth.sphi ** 2\n",
    "\n",
    "\n",
    "def nll(cx, cy):\n",
    "    cr = np.linalg.norm((cx, cy))\n",
    "    cphi = np.arctan2(cy, cx)\n",
    "    return -np.sum(\n",
    "        multivariate_normal((cr, cphi), cov).logpdf(np.transpose((d_r, d_phi)))\n",
    "    )\n",
    "\n",
    "\n",
    "m = Minuit(nll, cx=0.1, cy=0)\n",
    "m.errordef = Minuit.LIKELIHOOD\n",
    "m.migrad()\n",
    "m.hesse()\n",
    "m.minos()\n",
    "display(m.fmin, m.params)\n",
    "display(m.merrors)\n",
    "\n",
    "plt.figure(figsize=(14, 4))\n",
    "\n",
    "plt.subplot(121, polar=True)\n",
    "plt.plot(d_phi, d_r, \".\")\n",
    "\n",
    "plt.subplot(122, aspect=\"equal\")\n",
    "m.draw_mncontour(\"cx\", \"cy\", size=100)\n",
    "plt.plot(m.values[\"cx\"], m.values[\"cy\"], \"+k\")\n",
    "plt.xlim(-0.1, 0.2)\n",
    "plt.ylim(-0.1, 0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "truth = Namespace(cr=0.1, cphi=0, sr=0.1, sphi=2)\n",
    "truth.cx = truth.cr * np.cos(truth.cphi)\n",
    "truth.cy = truth.cr * np.sin(truth.cphi)\n",
    "truth.cov = np.eye(2)\n",
    "truth.cov[0, 0] = truth.sr ** 2\n",
    "truth.cov[1, 1] = truth.sphi ** 2\n",
    "\n",
    "n_tries = 500  # increase this to 500 get smoother curves (running will take a while)\n",
    "n_data = np.unique(np.geomspace(5, 100, 20, dtype=int))\n",
    "\n",
    "\n",
    "@joblib.delayed\n",
    "def run(n):\n",
    "    rng = np.random.default_rng(seed=n)\n",
    "\n",
    "    n_h = 0\n",
    "    n_m = 0\n",
    "    h_lus = []\n",
    "    m_lus = []\n",
    "    xs = []\n",
    "    for i_try in range(n_tries):\n",
    "        while True:\n",
    "            d_r = rng.normal(truth.cr, truth.sr, size=n)\n",
    "            d_phi = rng.normal(truth.cphi, truth.sphi, size=n)\n",
    "\n",
    "            def nll(cx, cy):\n",
    "                cr = np.linalg.norm((cx, cy))\n",
    "                cphi = np.arctan2(cy, cx)\n",
    "                return -np.sum(\n",
    "                    multivariate_normal((cr, cphi), truth.cov).logpdf(\n",
    "                        np.transpose((d_r, d_phi))\n",
    "                    )\n",
    "                )\n",
    "\n",
    "            m = Minuit(nll, cx=0.1, cy=0)\n",
    "            m.errordef = Minuit.LIKELIHOOD\n",
    "            try:\n",
    "                m.migrad()\n",
    "                if not m.valid:\n",
    "                    continue\n",
    "\n",
    "                m.hesse()\n",
    "\n",
    "                if not m.accurate:\n",
    "                    continue\n",
    "\n",
    "                m.minos(\"cx\")\n",
    "                if m.merrors[\"cx\"].is_valid:\n",
    "                    break\n",
    "\n",
    "            except Exception as e:\n",
    "                print(f\"exception in n={n} i_try={i_try}\")\n",
    "                print(e)\n",
    "\n",
    "        x = m.values[\"cx\"]\n",
    "        dx = m.errors[\"cx\"]\n",
    "        me = m.merrors[\"cx\"]\n",
    "        h_lu = x - dx, x + dx\n",
    "        m_lu = x + me.lower, x + me.upper\n",
    "        if h_lu[0] < truth.cx < h_lu[1]:\n",
    "            n_h += 1\n",
    "        if m_lu[0] < truth.cx < m_lu[1]:\n",
    "            n_m += 1\n",
    "        xs.append(x)\n",
    "        h_lus.append(h_lu)\n",
    "        m_lus.append(m_lu)\n",
    "\n",
    "    x = np.mean(xs)\n",
    "    h_l, h_u = np.mean(h_lus, axis=0)\n",
    "    m_l, m_u = np.mean(m_lus, axis=0)\n",
    "    return n_h, n_m, x, h_l, h_u, m_l, m_u\n",
    "\n",
    "\n",
    "n_h, n_m, x, hl, hu, ml, mu = np.transpose(joblib.Parallel(-1)(run(x) for x in n_data))\n",
    "\n",
    "h_pcov = n_h.astype(float) / n_tries\n",
    "m_pcov = n_m.astype(float) / n_tries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(10, 4))\n",
    "plt.sca(ax[0])\n",
    "plt.fill_between(n_data, hl, hu, alpha=0.5, label=\"HESSE\")\n",
    "plt.fill_between(n_data, ml, mu, alpha=0.5, label=\"MINOS\")\n",
    "plt.plot(n_data, x, \"-k\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"n\")\n",
    "plt.ylabel(\"cx\")\n",
    "plt.semilogx()\n",
    "plt.sca(ax[1])\n",
    "plt.plot(n_data, h_pcov, label=\"HESSE\")\n",
    "plt.plot(n_data, m_pcov, label=\"MINOS\")\n",
    "plt.axhline(0.68, ls=\":\", color=\"0.5\", zorder=0)\n",
    "plt.xlabel(r\"cx\")\n",
    "plt.ylabel(\"coverage probability\")\n",
    "plt.legend()\n",
    "plt.ylim(0, 1)\n",
    "plt.semilogx();"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
