examples/samplers/SMC2_gaussians.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sequential Monte Carlo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running on PyMC3 v3.9.1\n"
     ]
    }
   ],
   "source": [
    "import arviz as az\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pymc3 as pm\n",
    "import theano.tensor as tt\n",
    "\n",
    "print(f\"Running on PyMC3 v{pm.__version__}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "az.style.use(\"arviz-darkgrid\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sampling from distributions with multiple peaks with standard MCMC methods can be difficult, if not impossible, as the Markov chain often gets stuck in either of the minima. A Sequential Monte Carlo sampler (SMC) is a way to ameliorate this problem.\n",
    "\n",
    "As there are many SMC flavors, in this notebook we will focus on the version implemented in PyMC3.\n",
    "\n",
    "SMC combines several statistical ideas, including [importance sampling](https://en.wikipedia.org/wiki/Importance_sampling), tempering and an MCMC kernel. By tempering we mean the use of an auxiliary _temperature_ parameter to control the sampling process. This is easy to see if we write the posterior as:\n",
    "\n",
    "$$p(\\theta \\mid y)_{\\beta} \\propto p(y \\mid \\theta)^{\\beta} \\; p(\\theta)$$\n",
    "\n",
    "When $\\beta=0$ we have that $p(\\theta \\mid y)_{\\beta=0}$ is the prior distribution and when $\\beta=1$ we recover the _true_ posterior. We can think of $\\beta$ as a knob to gradually turn-on the likelihood. This can be useful as in general sampling from the prior is easier than sampling from the posterior distribution. Thus we can use $\\beta$ to control the transition from an easy to sample distribution to a harder one.\n",
    "\n",
    "A summary of the algorithm is:\n",
    "\n",
    "1. Initialize $\\beta$ at zero and `stage` at zero.\n",
    "2. Sample from the prior a set of samples $S_{\\beta}$ of size $N$. When $\\beta = 0$ the tempered posterior is the prior.\n",
    "3. Increase $\\beta$ in order to make the effective sample size (ESS) equals some predefined value. We use $Nt$, where $t$ is the threshold parameter -- by default t=0.5. This means that the default ESS is fixed at half the number of draws.\n",
    "4. Compute a set of $N$ importance weights $W$. The weights are computed as the ratio of the tempered likelihoods at stage $i+1$ and stage $i$.\n",
    "5. Obtain a new set of samples $S_{w}$ by re-sampling $S_{\\beta}$ according to $W$.\n",
    "6. Use the $S_{w}$ to compute the covariance for (multivariate)normal proposal distribution.\n",
    "7. For stages other than 0 use the acceptance rate from the previous stage to estimate the scaling of the proposal distribution and to compute `nsteps`.\n",
    "8. Run $N$ Metropolis chains (each one of length `n_steps`), starting each one from a different sample $S_{w}$.\n",
    "9. Repeat from step 3 until $\\beta \\ge 1$.\n",
    "10. The final result is a collection of $N$ samples from the posterior.\n",
    "\n",
    "The algorithm is summarized in the next figure, the first subplot shows 5 samples (orange dots) at some particular stage. The second subplot shows how these samples are reweighted according to their posterior density (blue Gaussian curve). The third subplot shows the result of running a certain number of Metropolis steps, starting from the reweighted samples $S_{w}$ in the second subplot, notice how the two samples with the lower posterior density (smaller circles) are discarded and not used to seed Markov chains.\n",
    "\n",
    "![SMC stages](https://github.com/pymc-devs/pymc3/raw/master/docs/source/notebooks/smc.png)\n",
    "\n",
    "\n",
    "SMC samplers can also be interpreted in the light of genetic algorithms, which are biologically-inspired algorithms that can be summarized as follows:\n",
    "\n",
    "1. Initialization: set a population of individuals\n",
    "2. Mutation: individuals are somehow modified or perturbed\n",
    "3. Selection: individuals with high _fitness_ have higher chance to generate _offspring_.\n",
    "4. Iterate by using individuals from 3 to set the population in 1.\n",
    "\n",
    "If each _individual_ is a particular solution to a problem, then a genetic algorithm will eventually produce good solutions to that problem. One key aspect is to generate enough diversity (mutation step) in order to explore the solution space and hence avoiding getting trap in local minima. Then we perform a _selection_ step to _probabilistically_ keep reasonable solutions while also keeping some diversity. Being too greedy and short-sighted could be problematic, _bad_ solutions in a given moment could lead to _good_ solutions in the future.\n",
    "\n",
    "For the SMC version implemented in PyMC3 we set the number of parallel Markov chains $N$ with the `draws` argument. At each stage SMC will use independent Markov chains to explore the _tempered posterior_ (the black arrow in the figure). The final samples, _i.e_ those stored in the `trace`, will be taken exclusively from the final stage ($\\beta = 1$), i.e. the _true_ posterior (\"true\" in the mathematical sense).\n",
    "\n",
    "The successive values of $\\beta$ are determined automatically (step 3). The harder the distribution is to sample the closer two successive values of $\\beta$ will be. And the larger the number of stages SMC will take. SMC computes the next $\\beta$ value by keeping the effective sample size (ESS) between two stages at a constant predefined value of half the number of draws. This can be adjusted if necessary by the `threshold` parameter (in the interval [0, 1])-- the current default of 0.5 is generally considered as a good default. The larger this value, the higher the target ESS and the closer two successive values of $\\beta$ will be. This ESS values are computed from the importance weights (step 4) and not from the autocorrelation like those from ArviZ (for example using `az.ess` or `az.summary`). \n",
    "\n",
    "Two more parameters that are automatically determined are:\n",
    "\n",
    "* The number of steps each Markov chain takes to explore the _tempered posterior_ `n_steps`. This is determined from the acceptance rate from the previous stage.\n",
    "* The (co)variance of the (Multivariate)Normal proposal distribution is also adjusted adaptively based on the  acceptance rate at each stage.\n",
    "\n",
    "As with other sampling methods, running a sampler more than one time is useful to compute diagnostics, SMC is no exception. PyMC3 will try to run at least two **SMC chains** (do not confuse with the $N$ Markov chains inside each SMC chain).\n",
    "\n",
    "Even when SMC uses the Metropolis-Hasting algorithm under the hood, it has several advantages over it:\n",
    "\n",
    "* It can sample from distributions with multiple peaks.\n",
    "* It does not have a burn-in period, it starts by sampling directly from the prior and then at each stage the starting points are already _approximately_ distributed according to the tempered posterior (due to the re-weighting step).\n",
    "* It is inherently parallel (PyMC4 will take better advantage of this feature)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solving a PyMC3 model with SMC\n",
    "\n",
    "To see an example of how to use SMC inside PyMC3 let's define a multivariate Gaussian of dimension $n$ with two modes, the weights of each mode and the covariance matrix. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 4\n",
    "\n",
    "mu1 = np.ones(n) * (1.0 / 2)\n",
    "mu2 = -mu1\n",
    "\n",
    "stdev = 0.1\n",
    "sigma = np.power(stdev, 2) * np.eye(n)\n",
    "isigma = np.linalg.inv(sigma)\n",
    "dsigma = np.linalg.det(sigma)\n",
    "\n",
    "w1 = 0.1  # one mode with 0.1 of the mass\n",
    "w2 = 1 - w1  # the other mode with 0.9 of the mass\n",
    "\n",
    "\n",
    "def two_gaussians(x):\n",
    "    log_like1 = (\n",
    "        -0.5 * n * tt.log(2 * np.pi)\n",
    "        - 0.5 * tt.log(dsigma)\n",
    "        - 0.5 * (x - mu1).T.dot(isigma).dot(x - mu1)\n",
    "    )\n",
    "    log_like2 = (\n",
    "        -0.5 * n * tt.log(2 * np.pi)\n",
    "        - 0.5 * tt.log(dsigma)\n",
    "        - 0.5 * (x - mu2).T.dot(isigma).dot(x - mu2)\n",
    "    )\n",
    "    return pm.math.logsumexp([tt.log(w1) + log_like1, tt.log(w2) + log_like2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Initializing SMC sampler...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "Stage:   0 Beta: 0.010\n",
      "Stage:   1 Beta: 0.028\n",
      "Stage:   2 Beta: 0.064\n",
      "Stage:   3 Beta: 0.141\n",
      "Stage:   4 Beta: 0.300\n",
      "Stage:   5 Beta: 0.608\n",
      "Stage:   6 Beta: 1.000\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model:\n",
    "    X = pm.Uniform(\n",
    "        \"X\",\n",
    "        shape=n,\n",
    "        lower=-2.0 * np.ones_like(mu1),\n",
    "        upper=2.0 * np.ones_like(mu1),\n",
    "        testval=-1.0 * np.ones_like(mu1),\n",
    "    )\n",
    "    llk = pm.Potential(\"llk\", two_gaussians(X))\n",
    "    trace = pm.sample_smc(2000, parallel=True)\n",
    "    az_trace = az.from_pymc3(trace)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see from the message that PyMC3 is running two **SMC chains** in parallel. As explained before this is useful for diagnostics. As with other samplers one useful diagnostics is the `plot_trace`, here we use `kind=\"rank_vlines\"` as rank plots as generally more useful than the classical \"trace\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 1200x200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = az.plot_trace(az_trace, compact=True, kind=\"rank_vlines\")\n",
    "ax[0, 0].axvline(-0.5, 0, 0.9, color=\"k\")\n",
    "ax[0, 0].axvline(0.5, 0, 0.1, color=\"k\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the KDE we can see that we recover the modes and even the relative weights seems pretty good. The rank plot on the right looks good too. One SMC chain is represented in blue and the other in orange. The vertical lines indicate deviation from the ideal expected value, which is represented with a black dashed line. If a vertical line is above the reference black dashed line we have more samples than expected, if the vertical line is below the sampler is getting less samples than expected. Deviations like the ones in the figure above are fine and not a reason for concern.\n",
    "\n",
    "As previously said SMC internally computes an estimation of the ESS (from importance weights). Those ESS values are not useful for diagnostics as they are a fixed target value.\n",
    "\n",
    "We can compute ESS values from the trace returned by `sample_smc`, this is probably an overly optimistic value, as the computation of this ESS value takes autocorrelation into account and each SMC run/chain has low autocorrelation by construction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5kz/Jv/3bv+Wee+7JypUrs2TJknz3u9/N/Pnz89WvfjXbtm3r6mkC0A3JP3SUDEQR8g9FyD8AdBb5h46SfyhC/qEI+QeAziL/0FHyD0XIPxQlA1EuNPvspaauqva6+urr69vtBmzStL+9zqym7e11dtH9lKJuftdrr72WK6+8Mm+//XamT5+eM844Y5/nSXkpRd08//zzue+++/Lnf/7nOf7440s+R8pTqdacpvc577zzWu37/Oc/n+S3X3VK91equvnBD36Q1atXZ/r06TnnnHMyYMCAHHbYYfnqV7+a66+/Pq+88kpmz55d0rnTvTk3Lm/yD0XIPxQlA1GE/EMR8g9dyflx+ZJ/KEL+oSj5hyLkH4qQf+hKzo/Ll/xDEfIPRck/FCH/UJQMRFfprPNjzT57aejQoUmSTZs2tdq3bdu2bN26NUOGDPnY96iurs7AgQPz6quv5oMPPmi1v66ursXvovsrRd3s7tVXX80VV1yRN998M7fffnvzSQc9Synq5sUXX8wHH3yQGTNm5Pjjj2/xvyTZuHFjjj/++IwePbrk86frlGrNGTZsWJLkwAMPbLWvaduOHTv2YaaUk1LVzZNPPpmDDz44J5xwQqt9Tf8w9/zzz+/bZOlRnBuXN/mHIuQfipKBKEL+oQj5h67k/Lh8yT8UIf9QlPxDEfIPRcg/dCXnx+VL/qEI+Yei5B+KkH8oSgaiq3TW+bFmn730/9u7/1it6/r/4w+Qo0CWA0ObGEOwcwoPxUowpUGC7rhidpxMmwYrE0c6QNAc6XSuraAV6RRpoP1QFo1MMagciHMwQDgQuQpMxk/pNMhxRBQ2fl7fP/xyPrKDcbzOdc51Dtxu2zW29/V+v6/nm70H1/2P1/UePHhwkmTFihVN3lu5cmWSZMiQIac8z5AhQ3LgwIGsX7++yXvHz338s+j4SnXfJO+HztixY/Pf//43jzzySK655prSDUq7Uor7pm/fvhk9evRJX8n7K0lHjx6d2traEk9POZXq35zjX0o3b97c5L3j23r37l30nLQvpbpvDh06lPfeey+HDh1q8l5DQ0OS5Oyzz27JqJyGfDduv/QPxdA/FEsDUQz9QzH0D+Xm+3H7pH8ohv6hWPqHYugfiqF/KDffj9sn/UMx9A/F0j8UQ/9QLA1EObXK9+MCH8nhw4cLI0eOLFRXVxc2btzYuP3dd98tfP3rXy8MGDCgsHXr1sbte/bsKWzevLmwZ8+eE87z6quvFiorKwu33HJL4eDBg43bV61aVaiqqirceuutrX8xtJlS3Tc7d+4sXH311YUBAwYUFi9e3GbzUx6lum8+TGVlZaGmpqbkc1N+pbp33nzzzUJ1dXXhyiuvLOzateuE83zjG98oVFZWFlatWtX6F0SbKNV9c9tttxUqKysLjzzyyAnbDx482Pje3LlzW/diKJvZs2cXKisrC88999xJ3/fduOPRPxRD/1AsDUQx9A/F0D+UigY6vegfiqF/KJb+oRj6h2LoH0pF/5xe9A/F0D8US/9QDP1DsTQQpdCe+ueshx9++OESLEQ6Y3Tu3DmVlZVZuHBhXnjhhdTX12ft2rX50Y9+lO3bt2fixIm59tprG/d/6qmnMmnSpHTr1i1XXHFF4/aLL744u3fvztKlS/PSSy+lvr4+CxcuzM9//vN07949M2fOTM+ePctxibSCUt03tbW1qa+vz+c///l87GMfS11dXZPXB/enYyvVffNhZs6cmR49euRb3/pWa14GZVCqe+e8887Lxz/+8SxevDgLFizIjh07smLFikybNi1bt27NzTffnLFjx5bjEmkFpbpvKisrs2jRoqxatSrLly/Pli1b8vLLL2fatGn55z//mcsuuywPPfRQunTpUo7LpBU8++yzmTt3bpYuXZo1a9bkrbfeyttvv51169Zl6dKlSZJ+/fol8d24I9I/FEP/UCwNRDH0D8XQP7SEBjp96R+KoX8olv6hGPqHYugfWkL/nL70D8XQPxRL/1AM/UOxNBDFaq/94w4rwpe//OXMmzcvjz32WF588cUcPnw4l156aSZNmpTrr7++2ef54Q9/mKqqqsyfPz9z585N9+7dc/XVV2fy5Mm55JJLWvEKKIdS3Df19fVJktdeey2vvfbaSfeZMGFCyWam/Er17w1nnlLdO2PGjEnv3r3zy1/+Mn/+859z9OjRXHrppRk/fnxuuummVrwCyqEU983nPve5PP/885k9e3ZWr16d3/72tznrrLPSp0+fTJgwId/97ndzzjnntPKV0Jb++te/ZsGCBSdsW79+fePjSHv37t2sx677btx+6R+KoX8olgaiGPqHYugfiqWBTm/6h2LoH4qlfyiG/qEY+odi6Z/Tm/6hGPqHYukfiqF/KJYGohjttX86FQqFwkc+CgAAAAAAAAAAAAAAACi5zuUeAAAAAAAAAAAAAAAAAHifxT4AAAAAAAAAAAAAAADQTljsAwAAAAAAAAAAAAAAAO2ExT4AAAAAAAAAAAAAAADQTljsAwAAAAAAAAAAAAAAAO2ExT4AAAAAAAAAAAAAAADQTljsAwAAAAAAAAAAAAAAAO2ExT4AAAAAAAAAAAAAAADQTljsAwAAAAAAAAAAAAAAAO2ExT4AlFRDQ0MeffTR1NbW5vLLL88XvvCFXHvttXnwwQezadOmco9XclOnTk1VVVXWrFlzwvYxY8akqqoq//73v8s0GQAA0Nr0z/v0DwAAnP70z/v0DwAAnP70z/v0D0D5WewDQMmsWrUqNTU1+cUvfpHdu3dn8ODB+epXv5ouXbrk97//fWprazNnzpxyj/mRjBgxIlVVVeUeAwAAaGf0DwAAcKbQPwAAwJlC/wDQnnQp9wAAnB7+/ve/54477siRI0dyzz335LbbbkuXLv/338yyZcvy/e9/PzNmzEjXrl0zduzYMk5bOlOmTMm4ceNy0UUXlXsUAACgjegf/QMAAGcK/aN/AADgTKF/9A9Ae+PJPgC0WKFQyNSpU3P48OFMnDgxd9xxxwmhkyTDhw/PE088kU6dOuVnP/tZ/vOf/5Rp2tK64IIL0r9//3Tr1q3cowAAAG1A/+gfAAA4U+gf/QMAAGcK/aN/ANoji30AaLHly5dny5YtufDCCzNu3LgP3W/w4MG57rrrcvDgwcybN69xe1VVVUaMGHHSY55//vlUVVXl8ccfP2H7jh078vjjj+fmm2/O0KFDU11dnWHDhuW+++7Ltm3bTnqu459z9OjRPPnkk6mpqUl1dXWGDx+en/70pzl06FDjvmvWrElVVVXq6+sbjz3++uCsU6dOTVVVVdasWXPqv6j/r6GhIT/5yU9SU1OTgQMHZvDgwbn99tuzdu3aZp8DAAAoD/2jfwAA4Eyhf/QPAACcKfSP/gFojyz2AaDFli1bliS57rrrUlFR8T/3HTVq1AnHFOvZZ5/NzJkz895776W6ujojRozIueeemz/+8Y8ZPXp0/vWvf33osffee29mzZqVCy+8MF/5yleyf//+PPXUU7n//vsb9/nkJz+ZG264Id27d0+S3HDDDY2vmpqaoufesmVLamtr86tf/SrHjh3L8OHDU1VVldWrV2fs2LFZtGhR0ecGAABan/5pPv0DAAAdm/5pPv0DAAAdm/5pPv0D0Ha6nHoXAPjfXn/99STJZZdddsp9q6urkySbN2/OkSNHmjzutLmuueaa3HTTTenTp88J25977rncf//9+fGPf5xnnnmmyXH19fXp2rVrFi1alIsvvjhJsnPnztx4441ZtGhRJk6cmD59+qR///6ZPn166urqcuDAgUyfPr2oOT/o6NGjufvuu7N79+488MADGTNmTDp16pQk2bhxY77zne/koYceylVXXZXzzz+/xZ8HAACUnv5pHv0DAAAdn/5pHv0DAAAdn/5pHv0D0LY82QeAFtu7d2+SNOsLes+ePZMkx44dyzvvvFP0Zw4aNKhJ6CTJjTfemC9+8Yupq6vLu+++e9JjH3zwwcbQSZJPf/rTuf7665Mk69atK3qmU3nllVeyadOmjBo1KmPHjm0MnSQZMGBA7rzzzhw4cCALFy5stRkAAICW0T/No38AAKDj0z/No38AAKDj0z/No38A2pYn+wDQYoVC4YQ/m7Nv8v5K/5bYv39/Xnnllbz++ut55513cuTIkSTJW2+9lUKhkDfffLPJry1UVFRkyJAhTc7Vt2/fxmNby8qVK5MkI0eOPOn7X/rSl5Ik//jHP1ptBgAAoGX0T/PoHwAA6Pj0T/PoHwAA6Pj0T/PoH4C2ZbEPAC3Wo0ePbNu2LXv27Dnlvg0NDUmSzp0757zzziv6M1999dVMmTKl8Xwns3///ibbevXqlbPOOqvJ9u7duydJDh06VPRMp1JfX58kmTx5ciZPnvyh+7399tutNgMAANAy+qd59A8AAHR8+qd59A8AAHR8+qd59A9A27LYB4AW++xnP5v169dnw4YNqa2t/Z/7btiwIUnSp0+fnHPOOac897Fjx5ps279/f+6+++7s3bs3d955Z0aNGpWLLrooXbt2TadOnXLPPffkT3/600l/aeGDjw5ta8d/yWHYsGH/85Gv/fr1a6uRAACAj0j/NI/+AQCAjk//NI/+AQCAjk//NI/+AWhbFvsA0GLDhg3LvHnzsnjx4tx3332pqKj40H0XLVrUeMxxFRUVJ/0VgiTZtWtXk23r1q3L3r17U1NTk0mTJjV5f+fOnR/1EtrEpz71qSTJN7/5zQ99lCkAANC+6Z/m0T8AANDx6Z/m0T8AANDx6Z/m0T8AbatzuQcAoOMbPnx4LrnkkuzevTtPPvnkh+63du3aLF68OBUVFbn11lsbt/fq1St79+7N3r17mxyzYsWKJtv27duX5P/i4YN27NiRjRs3FnMZJ3U83I4cOdLic1111VVJkqVLl7b4XAAAQHnon+bRPwAA0PHpn+bRPwAA0PHpn+bRPwBty2IfAFqsc+fOmT59eioqKvLYY49lzpw5jY/sPG7ZsmW5666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      "text/plain": [
       "<Figure size 3312x552 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_ess(az_trace);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Kill your darlings\n",
    "\n",
    "SMC (with a Metropolis kernel) is not free of problems, as it relies on Metropolis it will deteriorate as the dimensionality of the problem increases and/or if the geometry of the posterior is _weird_ as in hierarchical models. To some extent increasing the number of draws and maybe the number of `n_steps` could help. To access the number of steps per stage you can check `trace.report.nsteps`. Ideally SMC will take a number of steps lower than `n_steps`.\n",
    "\n",
    "Let's make SMC fails spectacularly. We will run the same model as before, but increasing the dimensionality from 4 to 40."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 40\n",
    "\n",
    "mu1 = np.ones(n) * (1.0 / 2)\n",
    "mu2 = -mu1\n",
    "\n",
    "stdev = 0.1\n",
    "sigma = np.power(stdev, 2) * np.eye(n)\n",
    "isigma = np.linalg.inv(sigma)\n",
    "dsigma = np.linalg.det(sigma)\n",
    "\n",
    "w1 = 0.1\n",
    "w2 = 1 - w1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Initializing SMC sampler...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "Stage:   0 Beta: 0.002\n",
      "Stage:   1 Beta: 0.004\n",
      "Stage:   2 Beta: 0.006\n",
      "Stage:   3 Beta: 0.009\n",
      "Stage:   4 Beta: 0.012\n",
      "Stage:   5 Beta: 0.017\n",
      "Stage:   6 Beta: 0.021\n",
      "Stage:   7 Beta: 0.027\n",
      "Stage:   8 Beta: 0.034\n",
      "Stage:   9 Beta: 0.042\n",
      "Stage:  10 Beta: 0.052\n",
      "Stage:  11 Beta: 0.064\n",
      "Stage:  12 Beta: 0.078\n",
      "Stage:  13 Beta: 0.097\n",
      "Stage:  14 Beta: 0.122\n",
      "Stage:  15 Beta: 0.152\n",
      "Stage:  16 Beta: 0.191\n",
      "Stage:  17 Beta: 0.240\n",
      "Stage:  18 Beta: 0.301\n",
      "Stage:  19 Beta: 0.373\n",
      "Stage:  20 Beta: 0.462\n",
      "Stage:  21 Beta: 0.566\n",
      "Stage:  22 Beta: 0.693\n",
      "Stage:  23 Beta: 0.854\n",
      "Stage:  24 Beta: 1.000\n"
     ]
    }
   ],
   "source": [
    "def two_gaussians(x):\n",
    "    log_like1 = (\n",
    "        -0.5 * n * tt.log(2 * np.pi)\n",
    "        - 0.5 * tt.log(dsigma)\n",
    "        - 0.5 * (x - mu1).T.dot(isigma).dot(x - mu1)\n",
    "    )\n",
    "    log_like2 = (\n",
    "        -0.5 * n * tt.log(2 * np.pi)\n",
    "        - 0.5 * tt.log(dsigma)\n",
    "        - 0.5 * (x - mu2).T.dot(isigma).dot(x - mu2)\n",
    "    )\n",
    "    return pm.math.logsumexp([tt.log(w1) + log_like1, tt.log(w2) + log_like2])\n",
    "\n",
    "\n",
    "with pm.Model() as model:\n",
    "    X = pm.Uniform(\n",
    "        \"X\",\n",
    "        shape=n,\n",
    "        lower=-2.0 * np.ones_like(mu1),\n",
    "        upper=2.0 * np.ones_like(mu1),\n",
    "        testval=-1.0 * np.ones_like(mu1),\n",
    "    )\n",
    "    llk = pm.Potential(\"llk\", two_gaussians(X))\n",
    "    trace = pm.sample_smc(2000, parallel=True)\n",
    "    az_trace = az.from_pymc3(trace)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that SMC recognizes this is a harder problem and increases the number of stages. Unfortunately in this case that is not enough to recover the correct posterior as we can see in the following plot. \n",
    "\n",
    "Compare this rank plot with the one obtained in the previous example (n=4). The rank plot is telling us that the _blue chain_ is sampling an excess of low parameter values (ranks below 2000) and is failing to sample from high parameter values. The orange-chain is doing the exact opposite. So basically one SMC chain is exploring one mode and the other SMC chain the other, they are failing to mix and to recover the relative weights of each mode."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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FEEIIIYQQ5xcZdokzTn/wM3THl9MxcyGqrhW7xUxNYRVHvU5y94v9eeve9TTM6M52dyPR380hrMqCNnAELe8cpKJnKiPromkIiyMuYw+GeiM4rsXeqxzv+j30/uMKzOsHc+Jvb2OM703HpcNYHRBDYv6XvIY7l0T1wl56gD2NvbkouwW/MB0n7aBzOWhZ/C6m7r0JTx/d2S0SQpxhO1aVsun1KbSHe+FjbSE9422M1kreTupJkw6qPbLB3UWc51jSDkXBjs+xu6/gvviLWZO0j+VJSVwXPoBF2/ZwQ/L1LFl/OTtzCmiIqGRITwMJl7RQuns10cMu6eylCiGEEEIIIX6GDLvEGecyxeKITOXt9r04VRf3+L5HknkFt33+ESV9LkHvO4sB1TkMWL8Ln4Q0CsfNoHibk5DG+RRvaGFT/STuHD8St5s/JlAzFe/uYQQlvMfKPWaU5kpyDS769xrI8UYbpsxZFE14iRvGZPDd5y5OlLVz7TOz0BkcaKxDMQYaeNmqI0TRkuZmRNFqO7s9QogzyKXCijoHuyck4FZQgufBRVx7/EPi2pt5Wh2Oy1JHRS9vPFssOLz8CGxqQxum4rzxVgLzryaw/0vMblGxblDYMMTFTUMG8+nuR5kQFg0OHfaSMAqLtWjdAmjx+YSooZPllRmFEEIIIYQ4z8mwS5xxzrjROGJHUVv1Hg7VhKLR0eOKNsIHJeLfLZBPlm0kyXUpfiYHDmshWwObeXHUF8ze0U4AWibYsvDwbMZTjaRCjWLbITvJ5VeTZZxBa/UDWMfezKqj71GQ/Amv3uHHlnmlrI90x615Kt5eU1j393SqdT5Mv30d7qqemZlVmDwUfGbe2tmtEUKcQS4VFtm0ZHrq6b7gCFudNzHRFEaflnretAZTMDqCMv92rvy+gLEtBpy2DjQOM7D6n5+v0XGoPJVaTSgNeeUMb8lh42Um/hKTwsyjJpTAmSyp2UNz5J+5Xx1BR0UQOV+/SfKM+zt34UIIIYQQQoifJMMuccZozAfRVh3DmjIDlDIe8liGec9UTp7YxpHaOi4ZOBHPxQ9hM0Sy3lNLfP5WuhUXk5Q8ELfwEEaNX4c+awKWD3Jw7tBRNyGWhokV7HF8SkDrIAY3ejFm0lTMu09g6DWa4GI3Ij+7DmOugbLAMWij25lhfIwMXy88zUksfn0evUc/SMifN2GL88Fr6UQcLheKtR29h1dnt0sI8RuoKqywa8h0aUh5aTXVOc8Q0x1GFeWxyj2E9sQ0xu2t4cY6Gwq+oPHE4J6I1icSRecLqgOntZSgosMEuY5h6jMETUcMTZur2D3eg+GFuSxea+LivhPY5fiSr0OrucHfi9rMHCpitxM2aERnt0AIIYQQQgjxI2TYJc4YXf5GjlTt4M/BjbwWch1u5Q9Sd7yU7NpYPtoxgv7XPYXd5ks6JjK9cvAIjCPVLZ8Ba19l/vFHedHjNf7+shubXiykoX0HB912E60kUeB1hK8NR3nEfTHtm/fiFXAI06BG6gP1eNTq8B3xPMluJnx6bmZ/g5b32oaTlluCTteTvkP0OP+ajm96AG9adfT9/GUCtRr63PiHzm6XEOI32GFzcaixhd5fv41/xRZCQkPQ27wpNOhRnNAnpwWtWwR633iq28PJqUuktNCbsjonIwZtojq+A3N5LwY4RjLQZxMh+buxBvYksVsqRaU5fDwygrub3uONXXNIjf+Yw+n9ub7bUHzj2jj5/Zd4R3TDKzyqs9sghBBCCCGE+B9k2CXOGNuouTQ1jMe/PQNfrQfePSZgSsijd9MDDLzyKfILr6am3g1Pr82M6NWfD+MHoa28FsPKpbiFFpBoTOejVcv5clgBfXft5G7HCIxN3Wl3G4B/n4toP+hBTXs58zwbGLm0jcY7XqVH1UFatxZTG1BLe9sB7MtqKJ+tsM+zhnhdEW9vvoInr1qCVqOll9WJ38ARhMqLqQnRpR07so/qg/sYV3AMBbCbImk1dtDTVcmmmKHEOtIwuWKpKj1Cy+GXcbQVEo6GOL8k3OP7Ex4HJfoQPglJJMDtZUpKo9H4TCKidg1DLN2pn3A1q32+YEdoI7MmF7FgVTfCLOt5Z9jD/HVsC22VceQtX0i/Ox6RV2cUQgghhBDiPCTDLvHbqSrYWsHNm1S3BIIPz6WpzIyxz304HU9hbPEgRZ9NduE+jiSk4xfrSWFDJKF5u7go6u8sGhmGn3806c9+i225E6+Pu9FiHcuRBDemaXrh6eFJQI/BuBJUstpGUVpZgMcYHX6oDDHNx7O3Bb+GUZg9ZpKpeHHPymBSfM18W/sNhhMhPPDuQzw38knC5u4j/OnBmAaaOrtjQohfQVVVsr/9jLpDe/F190Sp80d/IIRnbnmJhR1+rA5/kAEtE6l3OfjHDpUB1S/Tru/LqJQEvNr2UNpaTX3BVzQVOQkf5Mero1bhG+1Gh1cRRco+mlYNwDv3BJdu8KJxTDq7xu8j5rNnmDXtTRYsi6dl772UmuYRc1EtJ1doqTiwnfDBozq7LUIIIYQQQoj/In+SFr+ZtngnJxdPZWHZEpyKikdALC5HCM3mVuY+9hhZn5rwWPtnElOT2Ba2D6/X3mTK2se4e+WDLH73WrxzHiarfinl3apZ98AO9mS9gmekQonBzvJeGuJGX0yby4pGp5Dim8wq3Z8ZWfkI4QcaCPEqR7U34nvyDcqMevxT7yHOOIRuajYZl6SSYg+CEoU2rQ4qWrCWtrCjsRVz3vHObpsQ4hfKXf4ZdQf3UN5zMN7DbsRvZQ929sskSetDVuDd9GmexHG1ibd3thNuuht/bSFzh27EZ7CRNY98Tq95aUxa0J9JHw8g7Y+R+EYp1B5voG1vDYHN7Yy9fAv+KTZczRncsEtLhDWIwuheZMW+wuQpLbQWj+HtdRPR+9bjFemgeP1ybK3Nnd0WIYQQQgghxH+RYZf4zVy+EXyXMor5rnycbgZCU94nJOUWbGohWmsMtQlz2RC5FuuePJ7NiyX/5Y20pk4EizsHs3qTuVHLzb1e5MuY2yjNnMd9Pndya//HiEqcyIbKDZRuf5mZ5rf5uHEbAO6eBgzeWgpL3Vj3UhOftc/gi2s34JP9KavivsF1/VscctMy1dmD9+J1WPEmU7+BXgevxHBZDAVb11Cw6F2cNlsnd04IcbpKd6yjOmMPpb3TcY6/Cre/nsDhqWFD6homaq/Fz3IFO41mlm33x/+Wt0gpPEJgnx48d/33fHbxu1zu9xGBainuOgsd5TqOLo9h+aGbqMiYw7FFRg7cfYglrzTCyBq8omw4a1fx0L6h5A1XiPmuiZOTNzBsQgMnCm4nf6ue2IsrcNqslG5b09mtEUIIIYQQQvwXGXaJ30z1j+WepLnc/+Vx7OaDAOhcy/EPfYO/z/uUNq8CTgZpCLv5bjYPuoZEQwX9xm5lzrh+TO2/kCtzvqPm0S3cdlMHvad+SeD4cXgGh3F/wCQWV3sT5hvLCPfu9DfGAOAVaiBuvInbbgkheOxQYtPGoXp6Ezs0l+tdh/DQXoF5nwfB81uZZrmU1PyVvLP2ER7cdje+Difpbn3pd8vDaPT6zmybEOI0tZaXUrh2KXVB4eRMnkXiN2a0+a0c6pNFX8MlhDtvZa9fIWtXxpE69Qn+vHw9VcNmsOXxjYQG1POo80oiKMDe6kvOF2FU7hxE36kvcdMVs2gYqRIy5iPCBj6MIcPMkT9k4RxTh87dhlq1nHuPXsSxG4dgX/EiTdflEpdaw2ffXo+i68C/B1Ts3461ubGzWySEEEIIIYT4/8iwS/wmSuZXNNRl01JeSKA+Dzffv1FxcC+lVctp3gE+i79jgF8eK+se496Ct+n20XMkvPc6+Xu0+DZ1cCRAh1uRkS0917Ov7i/saHiTlTmf/bO2ouA26nEMA67Gpah83LQdh+r84dgum0qQ/QmGtDgY67yfxu0KyXuPcszjYnzGLyJ48FT6OD6idWI608qncDh3C8fvXI3l8aPY2v1RUTqpa0KI06W6XGR+9gYOVeXAdQ8zoNSGYX0ZLo2LQ6NOMN31BFn+JXyxPoxZg//K04W7WZE+F/W+e5itzOU615MY1FbKd8Zy5B0Tpugp9L11Lm4+fgBcPupqKnruxBg/jfAJX+LjUDn52EE8RtWBrYbAimOk14cxUPMoRdvvwG9uPSWeo8ld30HE8CJwuSjbvq5zmySEEEIIIYT4DzLsEr+epZnV+QuZ1LiI5uhQBt+7lI7qWTjtiXzw/mu8/MWL5LpfQ2tJKzdbejNKeynuvi56lmfzxhsPUr/qFW6cOJd5vS7Bf/yd3Dn+ZT66Yhu3DnoCgONWMzPL36ago4oeddX0aG5Bp2h/OLyiBWuzk0/eMlCVVcZuh4V/XLWQxqp8ggZ+RFDg6+Q0FGM3+dBRG078noeIui6F0D/2odDYyFervsXmdHVW94QQp6F0x1ocbW0UjJiKUedO5PZaOFRMRbcWprk/Tb2xjU+K2rkxcDuz1Y3M7/MIgye3cLvzHqI4gaVRx9H3u1Ox10D3K2bT95rbTrmqc/rQGyjvuQP84gi4eDk+Wh0n38nAN7kFW/N2Uku9aBgVQ/eCFAp33U+/N0tYtXY8Bm87AT29qTggV3cJIYQQQghxPpFhl/j1jD4kjXuFK6zRRCl+aPWhmOKuJqTvcm685hvGTvGn3DKBlsAYtFGpWHv2J/KGfjyfaGb69PWM0bxK+eNriB/rT9rgeNx07njovfAy+ADQodoxKnoC9N5ce3gLD2YdBqDUXkeDsw2tXkPyFYGMuiqck8v0hOuSaA9MIv5oJt0C96JLKYXcVnouP4FrcH8ctlZe73iTLwdtwFyVQVjGZprqqzuzg0KIn+CwdFC0/lvaFZW8EVNJzmjEtn0TGrsW65UJeKm+LAzYRJ+jMdwZ8AL7Rk5i0tBvSXGupwN/6o4ayPowBo3On763P0xI/yE/eqwrB19HUcoxNG4heI79AkO7Sn3eMfTudloalzD2uD8JA57CUneMvGOLCX4khvL9rQQNyEZ1uSjfvfkcdkYIIYQQQgjxU3SdHUB0bUHtbkTO/Rslc8sIT70EQ81SFE0W8T4pGHpk8/3+wxzTlRHkdSdjMxbRLeVrzIE2whP6MOjjgxzz30n3S+p4M+tTEir68Niof/xQO9XYjU/DbsNX50HDpW+Amw9O1cV9VQsJ0HrxUdgtKBqFYUMVmiKX4ubtYLB2NXnRNnLm++NKvZbAocH4turQHv8WrXE9xw5MZn/Z84ytvosJIX/A3ye4E7snhPgpOUs+REHDySvuwrvNRWRBJW0HWtH3iyHa2I/Fsdup+HAq7wy9noopSSQGZFJrCcBH6aByizu1R/wxJfUmafqN6Nw9fvZ41/Udz4du+fTdHYN91JtUr7mP7teV48jRoWk8RGhQf/qd/AeHtHexx9SHboURjElvxpQUTsWB7USNnoTOzXgOOiOEEEIIIYT4KXJll/hVNLmrmb/zj9S52xnx+AeE9GumrXY+JUXpPPf2Q7iv3kx4/rdYE2zkxMcy+qtnYN5e3p07FZ8Vi7g6agDFnsm49Qyjd/Agru17PxMSZgBQ6WhkYdMuHKoTRfnXfbXc/UGjRWtr56+6/jxsmvxDFqfdRdHmRg5u3Y7T+hqJha9Snj6SZenT8I46RnDCdraPaiQprB/WYxNI3TSXiR9GYixvoc6uUis7GYU479g72qnNOoxFp6U4KZXkzCbK1n9MoGLCNSWZPN8K8kty+Vv6PLTXGNCaVFpdPvipDeR9nUjtESNRoyfT89o7T2vQ9W83JCVwcIgnJo9BeKfeQv6KTLy7tWFr2ky82UnS2KGoRZMxH3qKLcMn01ppxT0mF6elg6qMnWexI0IIIYQQQojTJcMu8auUuVp5K9STvdQSNXQSBvcXcNkeoM4YzdHcoWz3XsLh1mQG7jSTbrqF2sgIbHHlhGusuNUYKfzwGJ94DKf/bQ+QGJjCuPjppEaMAmBVayZvNqyn1tl6ynGN389h6MqnSNIFArC9PRd0EDXOxLIF9Wx6LJ82Nz2tfa/B2F5LcMIK3HqtJmXDERxBJtzidrEn0IbbgnFwg4P1C55gZUXJOe2dEOLnZS54Da3OQMXEGzC2OwjKP0JD9iAcU78ci1UAACAASURBVHqATsenMcsYVdWN1NmHsGmNuCkdtBd1cOi9aCzVCslX30a3cZeiaH7ZrzmDAhMTfTia4kNozG14G0bRXn8cLQ4aW74ntt7O4LYnUNujyTz6DzLLwghPqcQrKhrz7k2oTufPH0QIIYQQQghxVsmwS/wq4T2u4o39viRvywRA72zF5PEFPfs8xtuvFVMdqudwcDSZMx8gtb2Ikdcc4Ju045iGu5jabSFNxUt4/u2jNLpvYWXOZzhdjh9q3+w3gqUR9xGq8z3luLbhD2CZ8jpo9Ry1lHJP1Wcsa8nAFGng6U+nkTLzdbzHrGWmpw9T3es4cFxH9jcxeAWMQ9nkz6XmYka2fsI+r6+Yu+s6DrMXU0XOOeubEOLnWZrqaMzNxqnTcixlKD1OtnJg9Tr6hrijJIWwNG4fSVVl3HrXAlRFwa51Z03JZZz83IRGdaP37PsI7DXgVx+/m1YloJ8XxTEeBAx/mvLNKqYetRiaTuBbW0bfsZ7YNr2Frb2Cj5xeOO0qDlM91sZ6ao8fOoOdEEIIIYQQQvwacs8u8cs1laF6h+HIzabdNwBr61PY8jxo9ssj6nA4vtbP2dVuJLdgJz4nRzAgp52WuwcwMGcsPW+fRc7OIwSsKWXX9G9pdWvlWPU+JnW/DlVVaXFZ8NG6E6k3/c9Du4KTf3g7RRvEmyHXM9w9EQCt1o2mijRchesIidpC+lozz0Wkc3jwLKavqsaR0MZ2pQq//dex6qFZ3BxhJ9SSiE9wf9RU9f+2TAohOlXWojfRu3tTPeQydA6V4Mw9ZJVfguaqQMwetRzwXc3yfpUoCuy1TGarZjZDF85Ba3An5ZYH8Y6I+c0ZJupV5g3xx6fJStCIp6k4+CD6oBE0Ni0nqvYeJkbp2Zh5H5W8zkq/oYxPP0peSTplOzcQ2DtVfp4IIYQQQgjRieTKLvHLuJzM3/cY9x7/M0Of/JCB9zyOw1pLTV00zz/zOrv2jqWuykFQaTumS56ld2Mj7e4F7J4XwPy1D7BvqY2XsobTcO9Irhs+hznDXua1yd+i1WjZ1nGCiaUvk20t/9kY+oML8FhwGaN1UegULW0uK06DE6vBwL71BVRkFaJtLyQ88TraTd3wM31AwoTniC1tIDpGg9NQQmOpP0EBJtzHevN8fTZLmjPOQQOFED/F0lhLbdZBVAUODRxD9/IONnxXyvgeLjR+nizovo0XwqpxOTW8v/MhVns8QN9Fb2HQ6AjqP/CMDLoA9Apc5aGya0QQ7qH9sFeNJiiuFDdLI9q6A/QZZkLJuhPF0o0vCorQe7loMPrTai6muTj/jGQQQgghhBBC/Doy7BK/kIpX9ChMxgj0ihatzh93v9fwSyhnwtRy1IAJ7NZei93Nl2BTJEWpW9jpvZ9hwQe5vX4joce+YO6cRkb+IR6D1g1FUfA1BgDQTR/IZd4DSDSE/GwKZ2hvnNFDAGhzWZlunseCll30m+qLaq6lZIkVS9o9TAuIwrvledz7lHJwni/N2zdg2l3HkP5L2NU3GL+/9OaTBZPZs+Z6FjbtxKHK/XaE6ExZi+fh7htKe3wqDjcj0ZlHqGgei3daJPuD8okM2E+C3s5H82+kbMgkkrYuw1RtprmmgO5TZ5/RLFEalcEmLQfSAglO+yPF60vpiLFjad5EaFM70/scw7r9BVpby/kip4Xo3lvQunth3rnxjOYQQgghhBBC/DIy7BK/jEbH4Npwej30Mg2FWai2Jgxrp+Fp3M+lAw/gfZk/OV4l7Kk9iv14E3cM9WP0NX0I/NM8Ih9yw7BPT27psxQ1HWPGl33JrNzzQ+kYfSCPBlyCTtH+bAxXeH+sF/0VDJ54atyY4tWPgcZYNBqFy595nh43rcARdwlGzNysGU1z4BR294kn6oo16HqPJKJqCXHW18lf3EiKOoRh9hG87zX7tI4thDg72usqKd+9CY1Wx/HUcUQ32ljzdRUzkpvAoGVF3E4eMtWwb3MYmUlXEVJ0hITda2ipLiR61CS0esMZz3SRzoUu3h1zfBBu/ncR5HsCVDvO+s3Ep0RiakpCY57IshPl+Ca1UK6kUHfiKO01lWc8ixBCCCGEEOL0yLBLnL6OBrIzP8Q7NIwel9+Od4QNS8dssphC0Sp3vBe/RFjFPkqdGeTGedHz25c48kY8q19+iM8f+ZwtO3rg7DDRO2kUbjojQ6MnEmvqiU118HLdaiocjb84klJfgNv3D3Gv1zD6G/+5fcnS4MK8v4Hmhvux5d5G/LI7WWy8i+YJzxJmz8Wv3waCB47kQNMyFn2ukvhKEpOzZuPWZqTFaeP9xi1YXPYz3T0hxM/I/uYd3P1CUb0CqIpLJLEwl4KOIYSmmNgccYwxgSc4VtjB35d9THh6B32/nw96HU0VJ0icNOusZNIocI3BSXZaIJ6xUyhb46Shjw1H6xF8rQ1c0auajn1/xu5wsiS3Cq/YfSgaHeZdcnWXEEIIIYQQnUWGXeK0lRWtZaZXEas9yuh346NotCasTUOpK5/E5xnPsy1oGcdWb2BItSc+Xp5YtY34tmZTkB2N3ZwGvr7o3r+OUROvIso3gYdHvomXwYdjVjOLW/ZSaq//xZmU9jq0pXvQ1BfQ6rLwj4aNlJvq8YyrYv+r2ZRtsGPp25skpZHQ5n3olQVUZpTQXtLMjNGHqJv4FN/HRxE+O5j3LVnMWjaa90oWs63jxFnooBDix1hbGilY/xVG70Aq4wbjYXex4YMqrk9uxq51sqHbHqZqy/hi9QDib4Ve67/EYOugOnsH0SOm4G4KPmvZvBWY6a2yf0QIPlF3Edx6DKteQa3dSEy0kXCjgnLySr7Pryd0aAV1bgOpOrwHW2vzWcskhBBCCCGE+HEy7BKnLaTHVfypKoJ0SwQAuto2PE1u9J9+P7Nm6an3DCQreQyNA0ZyUWItjptL8LvxOZ6P3k1y6DqGRPyFlP4ujlbuprKl5Ie6/Y0xrI2ay2D3uF+cyRU5iPZb1uMK6YVLVfmieQ/7LIXEDelFUOJMwofejzr4Eya5GbnC53m0M5MxWx00tULk2zuYmJfDmJcUTnz7Cn0yDxJkCOSV4JlM8Ox9xvomhPh5easWYPDwByB3cDp9K/Mp7uhDdHcjq7od5nJTAYuPlFFS8CDdTceJPL4Pr9AwLI1V9Jh6y1nPF6tVSUnwwB42nJrN7lQNsOC05KPTVDMjRUPHoYdRXVo2FBynNqwJ1eGkfM+Ws55LCCGEEEIIcSoZdonTpkOD+/sLKPn0DVzOYrTbH8FVtAG/zW10jymhyG8LhhVP4fhmKca9PelnGo+HfxStD1+K1/YAtGt80Wg0vLrjIV7ZMQeAOmcrACat568PpncHVcWUu5FVoXczy3coOjd3ItIepLIxjLzs53Bue4vg9nvY5PorQYPeJLH/3/GfX0LyzSEsejOahtVpRKyOY67yMaNDRwNwwlpBga36t7ZNCPEznDYrJ5Z/hF9UL+xeIbQER5D9VTnT4juwYGVPzH76t5rZfyyaHrcG0HvdIgwhEZgz1hCYnEpAUr9zknOkzkX15cH4x9xOcMFhmj0MULeJSF0z0YF2XHkz2FDYQOj4Blp9UqjYtw2nzXpOsgkhhBBCCCH+jwy7xGnZvu85vjr0PBe9vpLUO57CYVtIw2h3vvvmMZorQ+hoacWz2cGha6bQva0e32M7WPhQGtdfD4/NbeFA3wkk/+lKtBotL09ewj3pz9Ds7GBq2et83Lj9N+fT1GRjXD0XU84aAJqc7eg9tbiUBvy8D+BTsgi3k99wwqDnRD8PlMYXqV6mpcQZR06LG5ZWF7btdfjGGcmwqXx66BXu234rL9R9/5uzCSF+WtGWZdhaGtFodJh7DiSusYSD+TEkxims7XaUq3xK+DTzJO0119OndSsezfUEJCTSXHaSpHNwVde/KQpcHuxJc+Ig2g4EUTGoFZe9Ert7ETN6G7Fm/gGnS+Fk0XKy4hJxdLRReXDXOcsnhBBCCCGE+CcZdonTstXNwteeHXh4++MdFoPOcAfV+dNx+iSSbXiRDYe0hB/ehaHpBBu77cSltpJc0MEEWxmPXr6Xi5+MJGpkIgCBHqF08++BXtFys+8IRnp0/835XME9aZ+5EEfK1WxqO85FpS/RHt1BycaP2P14EWpEAs70F0mzfsgw223YYvvTUnmSuqXbuVPzMUVT2imf0x0zBXzlNFBpa2OgLoznAqf/5mxCiB+nqirZS94lIGEgAEV9B9OxI5/p0U4cioPdUQcJL24nr9ZOr8vGkbhrFf7J/SjethSPoHCih19yTvN6KJAyMwD/8FmE7thLnZ8nNO4kyllOVJAOtXgK6/Ir8B3rxBYQj3nnRlSn85xmFEIIIYQQ4vdOhl3itDwYdQ83fVlAY1E22pLdGHY8R1TEp1x+02Ha9Db2jh9Mlr+JnjF/4tFbI0l9/i4mrriY+CFbMazfR1XFZkqb8vnrxpspby4GwF1j4Ba/USQYQs5IRldEKigKKaoPMzxTcVP0DLrnBUY/v5mOtM8pr9ITXBRLVGR3wsfMgNQnsU97jeCBm5iY9gnaugxcS5dzc3ETDw58nGdHfUCg3gdVVX/YbimEOLMqD22jqSQXD/8ELD4hOP382bHTn+7RejZEZzHVt4il+dnQOJFU83a0DjuBvfpQeWg7SVNvQaPTn/PMMQZ/3MbGYskJoHJgB6qzmVbdMa5ONmA9ej8WpwtL7usc7T8Sa2MdNccOnvOMQgghhBBC/J7JsEv8LEdLBS0VxTiKC9G5eWBXV5BTocHrOzPeuz/H4+pAKtfcgduuL0l+7XUqdvbmo/dSeOOtk1hO9sRZFol/v+GYmws5UXsED70nC5p2srM978yHtTQT/fk1PJ59giCdNx6B0RSut2Br+yOtBQ/SY83z1PAcbxv8CHKLIqQ0E1tKFIcaruftlVeh+TCWjjeysNQ4URSFqtYyZq6ayI1Fb2B12c98XiF+5/JWLcDoH4Zqb6a0zyD8sw9yS6AFp+Jia3QGEdkeFFlqiU+9lOjD2wkeNILCjV+hc/ck4eJrOy132rie+EVeiWn9AVq8fdF2HCfIrZRwr2A0NYPZU5hF64A47P6hmHeuR1XVTssqhBBCCCHE740Mu8RPaqw9zviyV8jSn2DqRzvxCgvFZirBEB3HZus7lGpvI3/TZia2JVDRqwfeMZVUf25k4ZI4OootZPYcy+AN19PT2530qPF8PmM/nkZ/lrZksKU958wHNvpgH3gLjp5TOWY1s8ORS2DvVsp2mAloycc7wUJ3qvBpb4CgL/CrzMS52c6Kuvk4Br9CQaCDk57B7DS5scmuoc3WjKO5gglKJAZFd+bzCvE71l5XSdnutQTGjwVUypMHcXyXg9DQELZEHOdi30LWnygFexBD61pQFIWwlAEUbV5G/IRrMHj5dlp2jdaP3jcFQ7YT80AdqqORdutOLuuuwZJ1B9XtNgIz/sixIRfTWl5KQ/7xTssqhBBCCCHE740Mu8RPsrh5MszpR0xwGoqioGmsBIZiUb3Rd4RwxNIdp90drUGHYSSEXz+GyIRInvZYR3DyAqYNWonGS0dDRw2qqqJRNOgVLV9F3MP9pvFnJbM99UZcgd15o34db9Svwy/ag/x1dSgdQ9COn4/GaOOK2jmcHGokuO8ganL3cFnNEB46bKbHQ+30Hb2PRptKkwpxpp58OeMA98XNRlGUs5JXiN+rk+u+RFVdaPU+dJhC0aut3EENLhQ2dMug1wk/cvUHCQm/hJjMPQQOHEHRlmWoLidJl527G9P/mJCekwhKGo+a24jFw4TBWkFEUAl+HWloOkI4Ub+bqrBoLL4BFG9eJVd3CSGEEEIIcY7IsEv8pFDvGKbvU8iacyOuikw8PpmE5+ED9FA20u/OMIqHuSiglIZ92xhnHIdnyGpMD11H86VNpH3Qj/L9xZhVhQdXX8GL2+6j2tGMXXWgV7R4aYxnL7iq8kxeGYuLnXgGRzDmmfW0mO7C7lHA6i9Vnnn0ceJbbyDb+0pip62lIzaCsHsPc7TcxtLFPvS+dDmjy9oAMGjdUFWVVzJf4Q+5L8sTViHOAJfTSf7qhfh3G47LXkFpz0G4juSjePdnR9gJxvoXsP+4DVVxkm4NQVEUuqWNIO/7T4kcMgnvsJjOXgKK4sPA+5Px2Lqf8tQQsDfQ5ljFlO5arMdvIauxjW7f3UzukMm0lhbQVJjb2ZGFEEIIIYT4XZBhl/hR+eZtlBWuIbj3YOLHz0T1b6Pimr4U5HjhzM3npI+FksYyKswrCW2xkbLxM564/wVunX6MTz6/GK7ogeah+wjGxdV97mVs3DTmVi/m9sr5Zz+8ohBlc+L5r1dBU+2AZg9O20tM083g75Nf5pgxgMpoD/Qda+nQlFFeN4KlpTH4ZGpwFjZTdridZhVUFazODrYf+5TCok20uCxnP78QF7iKjM2015TjFZyGgkpNQi+uLC1HRcfamAOMrVDI1OzE3aMnvY8X49t3MOb9G7A2N5B8xe2dHf8HXsHTierRG7OhGy6DP+4tVmLjSjCWT0NxGSgPLqClykyHtz+5m1d3dlwhhBBCCCF+F+QmROJHvV63mgKdnZWpzxMxeDxOx1HaOiKo1/yRBruL6iovRn39JdlaK474YKrMHfgcthEcZyNtRhP9bhn6Q60JiTMBcLRHY1HPzY3ereP+Qq69imfL3+fpoOnkvfkptfusDOpnIHTsJQz1PMjyyu2Ue1aRnN1Aa00h/QKaaBuqsM7+IANSTXxu0XG3m5NonQfvTllFoEcoOo38txHit8pbtQCDVwhaNwfNxhC8a8poM45kX3A+6QH5HP4umFpDBQPcJ6CzNxOXNootf7mOgKQBBCYP7Oz4P1AUT/rfMpqszzZR3T2F0Kz9VPsuZHzsE6wsmMa+7ku4asWfKL3pH7hvXUZd0UkCusV3dmwhhBBCCCEuaHJll/hRf+sxlwdbemNrbUa//yM05bvx9zxCYMBJNH56NvkaaQkfQVD6/YyZE07AU/dx6d2FeBg/RHdsHtlHM6hqMbM6dxFWRwcAQz0SGevZ89wsQFEwaTxpszdTX7KFxMk3EZI+B3vaOpTgyVC8jp1PXYdH8qOoUSMwD7uC4NZaJvZzMiT+PXqfLGNCTg1+yj+3LYZ6RaLT6KjoqGJD7e5zswYhLkCWxlrK92/CJ3Iyzo4iypMHMfZ4ESrufNftANMsrWTZdqNo3Bl2UoNbdAINhVk0l52k5/Q7z7v753lHXEWCtZrM4VeAxohXuS99UvLQFMzA4nLQMtyIY+M3WDx9OLJlVWfHFUIIIYQQ4oInwy7xo/wUL+pffpFDHz4FZcuw7cwgYHEVEUOKKB/TQH7VFzR/9zDu779JXYmLA3vaWZWdwsh9o3Gp/VhlimFr0Xe8tnMun9Vu5IPGLbhU1zldQ6DOm5UHTjBk5yd0G3kplqYhNJR/hrP2DXrmn6BPL0+OeXsSZJzCcLsGjbMOszOIlzY9yZF79mN6cDfe/989ulyqi9u+m8izO/5Au8t2TtcixIWieNsKVJcTn7DuKKqKJSQMq3Mwh00n6RGQT9GOWI4b84k2jcHU0Ehs+miOLX4Tn8h4IodO6uz4p1AUI/1mjsGYs5vWsGR8aiso6fE+aT69UZsSyfK34nV4JW1JfdGfPE5OcVFnRxZCCCGEEOKCJsMucYp6RwtzDj9MSfFqxr/8Lb1m3kvLRUEUd3cnQ/MnCl2NbHXrxcAjhdgSErmoexHLHh3C43+fSV6JJ7Z3ZzDouWuYER7EVb3v4MNpWyjRWjluLUejnPtvOeuEZ2ieuZAKZzM+0aDRHcXZ/B1u5gM8e28Zdn8oDDxKQ9VxAnwjaDY4aIlYg4faQK4+iD1mOOb855UkGkXDHYP+zBPpL+OhMZzztQhxITi5bglGv2QUg5lWUyipuVWoihfL4jO4RltDdmMWqsZGWm0EircfdksT9XlH6XnVPWi02s6O/z8FJ88mPG8/2aOmASpu2dGMHLMHR+515Lc305zUjfZl72F39+TE1jXY5HUuhBBCCCGEOGtk2CVOUdRawFF3DTqnHb/wKHzCuuEkhfrsybS7jaK1dBZ9crIYdqiEwoRmToZczNCWcq42LGHmuG3EBFfi4a4lSqOiKArRfok8HTSdl4JndMp6VO8Q7mpYyiPVi3E27WDNH1bStCsUy+g/4vDv4DLdn1iQ46DR6I81NwMfXSgPV5Vjurydwe/5czxIywa7ln9f4HVp7BWMCx3VKWsRoqtrNhfQcPIQ/rETsdWXUdW9P8bmeHJ8CwnwL0DdHco2Qz4m374kF9YSNXgkx795G4+gcLqNuaKz4/8oRTEwtKc31aG+uLwSiCmuoyx9Ed1tY8Glo2GoFbUmD31kDKa8I2woM3d2ZCGEEOL07P0U91eTsT8ZivurybD3085OJIQQP0uGXeIUA/z6siL8ESrWZ2BZ8xLun0zCZ99WBl60n4Th7hyOVjgeE0OVLozr02+n+7U5GD7qRbTjJKErq8hZ9S5ZVidzV1/Fe5mvU25vAECvdN6N3W/wHcY9uXl0K/yMyfM2o/Z7D2u3K0G1YrK04Nw3nrpuj6O/6m0s5iysYf+PvfuOj6pKHz/+uXd6Jr03kpBCSAgEEnrvKCCgoqggIjZ07bp23V3L6vqz7a69F/CLAgsoRXrvAUILgZBeJ71On7m/P1iKLggqOgHO+6/M5LyePM/NvWdmzpxz7hIK3OXk715P3+HzuflQFadvE2RzWLh17Y08mv2sx2oShIvRseXzAZmQhFAkRSHCZkSRfJifuIebjZXkVJRj1dTT3d0XVGq0ft6Y9m8l5dpZqDTtezZl4oB7CNi/kdIuA5BdVqpyEpl+0zJcJVeyva0Ok9yVmlWzcesNtG5YRrGrfe09JgiCIAg/ZXgjBePmVzgxr1oFGDe/cnzQSxAEoR0Tg13Cj1RZTCj2NpoLcihY/S22sHBq+3VElVeKUlHGgtBD7KpaSuHGB7Ftfx/fRZ9y/6xn+OsDqdQFXEXUlEEcnnw35S4b3jo/lllyeKR6Lori2TU7g72S6R9zFe5eMzEEdqSl8gecjpswLHqIiINGHn9XRZivEz9tB9K8SjAER7O4YSLrXsnAVdHK0g+bcbtP1aBV62lpraDVXOPBqgTh4qIoCoVrFuAd3pvW5kO0BoYTXNuBYu9iXH5FxO734jsK8TbG0je3iaCumRxZ9BE630ASx9zk6fTPSVbpSFNqyBncF0nlR+ZhN3lpe+jCAMyKFXmcDkttKcbQUMKP7GVJhQmHWM4oCIIgtFOGN1KQz/A6pQCyghjwEgShXfPcVBuh3XEoLm6peI9BZUU82/P/MXnuARR5K9a25WyR56DNcVEX709SfR66CgfdMtIpPdyR2qJErh5YQ+rIJMJHGbhLATcwZvjHVDkbaXRZ2sXd02pje/Kfliym+LhpLj+AYZ8WQ7SCSuVDRoib98JL6Ln1fdYaoomsr6ZPt23s89qNqWoi9d0j+JdNzWSdm+j/Ls/8ZvxaVHL73D9IENqjquzdWBtLSR59I+aGoziTMpFtPsxNWss0nwqO5bpoMlTR03g3GnsVPuER7P14Nd1vfRK13svT6Z+Xob3HsdlqxRzQCZ/aXXxRHsNfp23hgRXR5AUVo6gy8d66mKD4PgRuXc7qa27lSs0fe+MO4eKWkZFx1t+Fh4ezbNmyM7ZVqVS4XK6Tj/38/Fi3bt0Z28p1ppM/u2dn/E/bfv36YbPZzpiDTqdj27ZtP9v2RHydGrY8fOr5YcOG0dTUdNb69uzZc15t5ToTuQ+EnXw8duxYqqqqftTm9ONxetwztT3d4p4mUjofjz158mQKCgrO2vbrr7+mc+fO59X2ueeeY9KkSQDcONfEXtPxY3+utrfeeiv79u07a9y77rqLu+6662TbA2t//L893cMPP8y0adMAePDBB9m4ceNZ41599dU8++yz/9P2p+fOT9u+8MILLFy48KxxBw8ezFtvvXXWtqfHH1jy4Mm2H3zwAR988MFZ46anp/PZZ5/9bNsTsXuEwUf/PS8XLVrE888/f15xz9U2yW1i6fTj505ubi433XT2L3Hi4+OZP3/+ebX96XWf8k/TWc+dn+sjfirZ0Ma3E73QqazIErT9ZLNJtwJWl47rM+Np9Y39zX1EUdGp+BkZ0hnb/pY+4qfxf8l1f7a2J/qR02Pn5v7feV/359tHFBUpyNpn6dz5/K77X9pHwB3Hc8+5jYyM8+tPztZHnDgmp1/3ubkP47ZvAE79b0/3W/uIM507P237a/uIM8X+Jdd9r169TsY6U9vT40+enHDe1/359hHH44eT2m3paXX8uvcRP+Xn5wesOe+2v7WPKCwsPGv8s5GUP2DKTUNDwxmfDwgIOOvvLleePCZOxcWqyhVElueS3v0eNNmzsXYKxuL4ktyvXsYYZmTZhGg6LV6OrmQFIVNCkbLU7P+kBk1mJEnhBhImjIQwP8xOC1E+MRckrwt1TA7Yypha8T7vWOPRfLUAXUIfMob0wd2xHzbLLNYVjWb5i50YEDEXhzMP49hb6LSiiIg7SjDEPsei7dBnWATxqh9fMhuqt9AtoBsBGp/fnOP5EtfO/xLH5H+1t2Oy7rk/U7lnAZnjr6W6vBVN1EyafRRe7vMf5rQW8MjmPFoDXdxpmkSElzfNJXtpKDjExM+2X7DBrj/imPx7327sBNF7/j840jEex7hDqLYa+LZ+EYP33klC/kekXn0fLWWlbJj1IreGBxLtwXnW7e08aS8uxHEJCAi4QNmccq4vj+rr60/+HBgYeNm2tT8ThgK0PXz4gsaN94HcB47H1r1o+tm2sixTW1t7XnFP5GF8I+WccU/P+Xzjira/vG1AQMB5fVn7S+KeOC8Nf6/B7f75LzpOxM3IyKCoqOicbY1vpCAB2nOcP+d7vgcaJKoeCT35OPKNamrNZ//Y2B6u+/bQNi4umX/oYwAAIABJREFU7uTg2Lna/tI+IrVbLZvXyxf8fE/tdjyHnP3BFzSuaPvr2wYHB1/QPuLEuXM+efyS8/3EuQPnPn9OxD2fvvVMOfyaYSuxjFE4SS2puDJyLOoiHasfGY9q6+t4L3qfgF1aEu4No9RrKbVV+zgk5dFWXISusQDfLhYC/HvRdVEotpYy5jaa+fzA+8xY0J+nKmZ7uqQfSdNG8UP0I4wsymVoZiRRvR+iqNILt6MQw9EwRid2o8fEdKJ6Po39judI+P4Z8nWtvPLOjex6dCVpt6+kbWvbj2JurtzAC0uu5bXDb3moKkG4ONhbbZj2LyU4cTCVzTIW/0h06mhmJ+3jWh8TpTt01HhVkhR+M/71NfhHd6ByzwZSr7/3opnVdUK/yBiqOyWBNppOJTV82RLO+MFldPTTox24kRZjF8r3rEJWqUne9gML7SrcYjmjIFxQK8tHs6x03AWP2+LQ/26xgd8trtA+/N7nzsry0Rcsnl5jvGCxhAvjpR6P/W5xX8186HeJLbQPv/e583vF/63EMkYBgCWt2Vgr93Bt0HD0/sH4JKbROCOAqp0x1B4bQZ51N/uHTuZw6bvMyPqeMGs1Tz6yA2OghF0VwOfzWmlIvpESp4qBdn8aDCq6enfydFk/IkkSkZoAbCOfB7UO9bFWglPexlXXgt/6Qiz+k9D1UNO8p5Dg7O+w+USh9dKza08y1xTl0dIhnG++1/P4AIj87zDxgPDBjMi4jxlJt3u2OEFo5458txKXrZGOoSoqW1rwCupBq6aMA0FF/M3czIuOfLx9I+hTYkD29qVww3wMQeEkjb3Z06n/Yt2DQ/hPYxum8FjCSrYw6EgCn3WL4MEeLp7deIxox+P4FD9LdM8riNi/lUMDryIryJfeajHiJZxbXFzcWX8XHh5+1rZnWsZ4tranL6uIi5P+p21ycvLPLj84V9tT8X/cNj09/WeXKJ1v26Iihcd2vwnAZqBv374/u4zxdGdqe7qSitk8tvv4sqPhw4vOuUTphOHDh59zGSPA03tfRVbX4XZmExd35m++T7QFmDhx4nksUTrVdvHi7JOPfxr/4YdPrSmdPn36OZcxnqntT8+dn7Z96KGHzrlE6efanh5/+vRTd8Z++eWXz7lE6VxtT8SW1d1PPvfpp5+ecxnj+bYtKo4/dV5uvv2cS5RO+Prrr8+5jBGOnzvHbTzrufNzfcRP3dH1RuDTk4/z7g05Y7t/H5rBgrIVP3ru1/QRcl3RyefcQXFnbPtb+ogzxT/hXNf92dqe6EdOjz37F1z359tHyHVFvDIGxnZYShuvnfO6/6V9xNi2t5CAaxNhtzPuZ9uecLY+4vRljCfc1gXWlRz/+afHHn57H3G2/+3pbX9tH3Gm2L/kuu/Vq9fPtj09flyv4Sd/3rx58wXpI+S6IsKNp84d+PXvI37Kz8+PsR2WInF8H79ztT3db30fcb7EMsZ2xlPH5M9VX9NUuonPWiJxDHkCRXZit/ydzV+MJ1ATg7pvCftDDUTN/Yai5lw6VzeTv+ZBVD3VpI5OI35kEN5h+t8ltwt9TF6pW4JTcXPTrkYOLfwLg2/qSiA6nIM/osq6g6UfrsbHpMadO5/IvhNoljqiLG+gy/PXsjUzjWJJ5gm9E7UHtyET187/Esfkf7WXY+JyuFl+3220Ve8kvs84rK0teEXey0ddt+HdcTe3rbRyn7Kc9LTnmfh9NkEpaWR/9SK9/vR3Oo2fcUFz+aOOyedVdRxzSYz54EWshjAem9LMkqBsVuWW07wnE98NR4iICMToF0NtxhD2j7qRR/VOvDzQr7SX86S9aa/LGH9tTr+knoFDTy2dOLHs4UJqD/F/7f+3PeT+e8W/EOf8xXx8fhr7QveNF9uxGTG0mcWjJhCqr0aW/vfjoluRMFnCmLR6MWvW+/7mv3diGeaJ5ccX2u8R/8Q5cjHm/nvFP9N1czHlf6Fjn6sfuZiPza+N/2v71l/znkosYxQAeDXsRt7s/DT1kSPRfz4B7ba30RzbTp9x+9GqKjlgVrHfqweSozMd4pPp8mJX6p/8lpRj9bgPbuHA7Jeot1q4b8NtLChf7ulyfpZB0mJARfzR90jumI6U+DGt6V/jcqwgwPUmcb2ns6T8KVp6XIspVE+IO5/Od9cQ0uVt+ry+g8mf70P6yZqjhSWLuXHt9TiU//2WWBAud6bsaprL1tMhrCNNOi2KPhKnvpVtkUVcq6rh48bDBBk70qUqAEmWKd2xDGNoNAmjb/R06r9an+AgHIFh2LUh6M2lRDQYeKEsles6h2KOymWvdia1uVn4dIgjeO8mXK3NrHKIl2RBEAShfbh9ljdvHnoEOD6wdboTj/95+GFun+X9h+cmCIJwPsQ768tcs8tCvasNSZIweEWw6sV7yLJacbuPYlxfhzNwEOuHmnFXbCO/cg4Va5+gYslRvvqiD3vnvAx+gUQMiacktRcfNleQW7KWtbVbPF3Wz3ogcDSPBI9DPfIxkme+Sm1uNtbmZ9Ht2I3PrgzSe6Ty4JBWjMOeJCw2DF1zEa8vvouXb59A6ze57P+2mR9W/jhmUeNRair3ktOS55miBKGdcrsUjv2wBMVlw8/oj66uDp0+lQUd9pGoMhOx0Yd9fkWkpD9NxwPbMYSEUHd0D+kznkCl1Z37D7RTSSrQOmzkJcYALu5YG8BWg47Dzd5ck6EmKNQF/hHUHstCcbsYuGsF21wyleLGjIIgCEI7cOMNMisqxvFo1htUW0N/9DuTJYxHs97gh/Jx3HiD+DgpCEL7JPbsusz9q2EVa1r2sfpgFfLgp+h97z/wT1hMo+wke9dXmNfoMI3qjT1hPb137qdbgj+f543BtGgY/Ud5ET9rJD7+Kka4wYrEn6bsQ5FVni7rvOQm9SdeFYw+YCMaXS4upRJNYwpBOpmN4RXosr5hjbOegVY1SYHHqDEdxqoNpHJwKoYkFWVuhWj5+AyvP6Xez6wu92FQ/T5LOQXhYtVwzEL9saUY9IHUpiQgFdWi8gliRfxenvQysehoIzHJ6QTXBqC2mqks3EVQcg/ihkzydOq/iVqCrlqZ7JHX0OXwQULaqtHZZZ6p7MGibpsZMXUey+bMhOyX6Hrdo8i7N+Db50qWykZu14kZooIgCILnbV4vM3DoaNZXDicjaA/B+hpqrSHsqcvAjfp3WY4pCIJwoYge6jI31bcfDzhj8KkrRlVfQExCLDrv3jSURaPX+xPW4CTDWk9X6830y1Wzu1Mqxril3KFZysCIRoqW7sBhaaPCUkAIdny0vviq2//dWzaYc7mm/N/sadpH1muvs/d9HRgHYh76NC7b6wzosht7vRd+O7TUlRwk87EeTAuNJPGJamY9Z6HZ2Uqh7dRSRq1ah0Glx+5yUGGt9mBlgtB+KG6Fsu0FtNXsIiLQH5fJitqQwMrQIxglJ/13aFkemk33vi+QsHstssFAc/kxMu74C5J88b88ZWokXEZf6jUaFFc1dy2OoSLCxueHjPRIAG9ff1Q+ATSWHcLtsDNoz2ry3DL5Lg9uCCgIgiAIp9m8XubuWWqy6nrzQ/k4sup6c/csMdAlCEL7J3qpy1xHbQiTkm6h+YZvOfrJE7i+ewTfeV8Ro2tCHbmVltrZbHFFcthRTZsURb8BoUx9pDMB1kC087NpPDqHFetW8ODa6dy09MLd7vj31lefwFNB40lWBTKuh44BV88gr+ZRmhqDkFpqCQ41ED/yCfymPsvB19cSvexZav12kqVA3rZPGTNmPs5X8mlsPDXg5XI7mbggk/u23u3BygSh/WgqtlJzaDkobrR90tFYmtH4xDIvrZQJ+lq2b3WS6NMbe2sg3rUV1OVlETNwPKFdens69Quio6wQoDjJGTQMUNGl1YbWJvFZWw9MbXZuu30OVb1upnTbcvziElHtXEug3cwKp8zvf+sYQRAEQTg/N94gs3m9zKF9QWxeL4uli4IgXBTEMsbL1JdNWyiwV/OMJhO1XweqD+2kXFtP5FUROFcFcrR2Kt+OyiA04SiV9f9m4tcfUFRo5tXNe0nrVkDm8Ggmj3VhjujBVrUPE2rKuJi2p9TJGm7w7Xv8wYNbcKsVIjvMQKmNxm/2SmzjBqN3W0luc1JRWYhkOsbBujv57u0p/LX6S7TJ3ry2LpypXeGmycfDqGQ1feOvIsy3o+cKE4R2QlEUqva10Vy+DD8/X+rtCejlMnb5V+NWKYwrcPKyfzbjR8xHs2ItiizTVlfKsJe+9HTqF4wsQU+NxKpeI3GsWgaqfG74Jpkvbynl+T1u3hnkJCHTTOs2Iy01hbitTgbtWcvivuPJdbtJUYkRL0EQBEEQBEH4NcRg12XK4rbT4jLjO/9GnMljiRz2FD7RL6PyWs/uxj+japXpn7CZhNACulVNpCoqhYMuCxM2H+baAWHYg1VoUvxJ95JJQ0Iddr+nS/pVVrUdwq246bK3iubSZmIH5+CI9MYVnk7nyBrW7HqP4BIDW/L9SY3Zid91oZQuK6HH0CRuv8WbHH8VDsWJ5r+rjv7S8yXPFiQI7URLuZ2G/MNY6o8Q3yeVlupCVH6pfJlRRX9NE82LfIjokkKpO5x+edk0Vxwh+aoZ+ETGeTr1CypT5WaVQ01xWCCJ1SUMbjUyv1Vmv/cAvju6kkm9drDmxqso/nweXa55EPP21YRmjmSFpCNZdiKLFY2CIAiCIAiC8IuJOaiXqbsChvFa8HXYhzyO2zsEw7c3420vActBdEo25tYS6qp6M9v1Cc4NtQTZAhh+uy9jpplwrC+hcfdBjq74hvvz3ubFAy/hcNk9XdKv8m3zDua37EJfsgnTojzc9Y9Slb4Ms7sOuJeOw9LIPjwDq6TlYFo6vWJy6DGpiZjbv6FruYmhr+3EbPvx7Itaay1P73mWMnutZ4oShHbAtK+VlvIlSJJEY9SNoDjJ97Ji9nIxsaGN751HGTnuVUL3rAdFwW6pp8sND3g67QsuQIZElULRhNtR0OEKquCaL0NwxKj4qMRFYxuk9jMha9WYmypwmlsZtH8DlYrEfrF3lyAIgiAIgiD8KmKw6zKzy1LAfmspAJJaizN1AkeOFHBQKUa/ZQv+P2iomdKfpt4VNDTWYmzaRdP6l9lZ1YeORi1Zh8OxbaskuLudioIcKmpz2Jz1NqbWUg9X9uu8Eno9H4TPIHToNEbf+xi6yAQay7dg3lWH15FMYuOuY+aVftT8fR51w6Zgzd7HNztH8t2idApeXoDPt3ncdY2Zw7mnBryyTFvZkf0R3xTN92BlguA5bSY7LeVmGgq+I7pDCKqqUtCHMrtPM1Gyleh3o1DHB5KrjyF270bM9eWkT38MnY+/p1P/XfRSubGGRtIMOG1FjKoMxrdeRWPUUN7d1UiEXy2J9w6naN0CfDp0RNm6kkiXnTVOFW6xklEQBEEQBEEQfjGxjPEy83bDGsyKjfkMQFWXhzN1EqpYmfAeXpTvu568XTHsdgYQnaYQVfoA4d/Vc0ijZefhTBLfT8XcrwfJ72fg0qkoHTyMt1QS1k73EO2X4OnSfpUg1fGdxpzBibhDOuFu+TcRvZdj3FaHfpeMNfEZNFILcasXcsBxAFNFAdlVmQTNaaRTkRvNp5l0yvfCdtqGZaNjxuM/biF9w/p5qCpB8Kyqfa2Y63bgtDXhznwNVekmagLjqQxo4k9NraxrqOeKSS+y78AONFYzLoOG+FFTPJ3276aLSkHvUMjvNZyMXctxd2lh8qdBfPqoi3WVTu6okUnMrKbET8ZubcDe0kT/A5uY330Eh90SXcTeXYIgCIIgCILwi4iZXZeZ98Kn83rojWjyfkC77W1UBeuIHfAECuFUHO2IzjuargtNxNqdpGvGUKfE0tw9ggeatjAgWssAnzoqshvYYskllno6qCApuKuny/pNdluLGFf2JqVtlax68D1yP9XgCg2hbdCjoDtK3PD5ROTvx39tNHVlRcy6dy99xvsgp9QSlahBuUlNkcF1Mp4syScHulyK21NlCYJHWOodNJfYqC/8Gi+/SLT1dShqA//p04IOF33e6oCts5ujIUnE71iBzdxExqy/IsmX7suRRoJeajdVwyfhcKmx2IsYWWYkqEpNW1xf3t/tQq04SX+oFwVrv8E7KhZlywpC3A7WOcSdGQVBEARBEAThl7p0P10IP1LvasOluPGSdcRogrAPeQLb4MeQljyI6uDX+Gw24R29G3vDbEzBASwx3sSa2q542bpx3cBIgt+JofajHLzyKyja+Cbrln3IrIVD2VS01NOl/WYd1IHEaoKxamR6xEfQWa9C6fo9hw4OonKnjLfuMOl3PkVLl6kc/fsPVPu5UNmXE/S37dilL5l03bekPrWVz75QcDpPfSp9YvvDjPthNA7F9TN/XRAuLaZ9rbhdLbSV7yBw0F9xtR2m2RjE0QgHo9paKSi0MPSaR6g/dhjvehPekVEEJV7cA+bno5/KjaKSKYuKQXE2QH8VUz4KxukXwAathfoSLVGdGvHrIONyW7A11TMgZxuliky+W+zdJQiCIAiCIAi/hBjsugy4FTcPmeZwv2n28SecdpAk7ImpNE6LprJgP5r8Rg72vJbN99xPdcgtdN36Bt7v3cGWzcdYuesGPvgqHPW0rkRMiaG65xAC48eQGpBGuHcHzxZ3AYSqfXk//BaStGF0uH82+tvexun4O+HdD9Dp2KMY93XBtEnD6AQZOTAUagtYc2wojz77T9be7cBigOrYED7/UuFw7qm4/mojgRo/Wl0WzxUnCH8gW7OThgIrjaVfoPXvis7chAJs7dmMFRUj3o6mpXMTxcndiN/+A06Xg+63P+nptP8QQTKkyAr5k+/F7ZZpdtUzrMZJZKEWc3x35hU5aLPq6HZ3GgVr5mIMj0a9eTm+bhfrnOKlWhAEQRAEQRB+CbFn12VAQmKa3wAkQKo7htc307COfwtnWAfMdRFUW+6lGCOmL2TCrtnPdT3r+XRXMdnd7cQu7UL3T830/ncKEfEySpTEpKTRtAE+0hhPl3ZBNbnMlGvdxNS14VZ24O23C2dEAwTGExauZ1vOAoZ+tJ9VKj3dQxuodccQtjsEc/cGYh7pzC1/UpHme2rZ4hM9X/BgNYLwxzPtawUU7PnfEjbgSxy1C7D4BZLV0Ua3FjP6TeGkvnkNqyrKGVSci29SCnq/QE+n/YcZoHaT4+tLrZeRUEse6sF9mPKRljf/bmexDJMLNYSltBKQoIBGwVpVw6CjO1nauR9lbjfRsljPKAiCIAiCIAjnQ3xdfBmQJIlRxi6MNHYBWY0zbiDaLW+hK8zCL6QVn/D5NLfmo60xc3B/PF8XzSKxOIGbW4YyZnoTUaMj8N5bSvGmYv6+820ezHkRu8Xk6bIuuEeq5/J4zTxa8vax7I7dtO1Ox530LCXmEZhrNpAyII998jCMWS1UBzjo+YSGqNsa6DZ9PY31dRgXHKHBZKap6ccfSLfV7GRb034PVSUIfwxbi5O6oxYsTUtw+g5D66gDVxsVPRqocusY9W4UDckVVPXpQ2zWWhQgdcosT6f9h0qQFSIlhWOT70NRoEaRGNpWR3yOjtb4ZLa3tdLUZiT9zk7kr/k/vEIj8Nq8DC/FxTqHeLkWBEEQBEEQhPMl3j1f4l6tW8aClqyTj5WAOGxDHqe5s43iI7kEzKuggyxhuzaG2MkyLgM0VcP+747h7hyKtkcddVkN6HIrqfY5xNAVxyjc+xXvbH/Gg1X9Ph4MHM1boTcR3m8CN0wbS3D3cbgTh6M4nQSYjpHhvoYrR1yB9MA9FN/7GoEHN5FVqKbUGUL5vA9J+ds29r5azJSbFOrrjw94NVpqeXbJJF7dI2Z5CZe2qr2toLhRHX2fkO4PYmndistXz4YkmWCrna4/BBB8RQZ7WyxEH9hGcGo6Gi+jp9P+Q0kSDNO4qI+Jp1Wtw9GWjWpoONd/HITTy8j7Nl8shzX4hjkI7eJGZdBiqa5kYN5uDrplTOJ+F4IgCIIgCIJwXsQyxkuYQ3FS4KjGS9YCoDr6A+6IdFxeZhxxdqwVcRR73cYRR182RqcQlzeTztZKSpbnYnZMpeyjDLb2TWb0P+KJ6uTE7a2ltFtPPgx64pK8O1iaLvrUgxs+wmZ5CXfrl4SHVuG3M4dyv3Rai9swujeQmv0tWwKK2Hro3wzdv4ExBS003RpJ/MxOTFwDev3xMP6GYGYO/AcDIod6pCZB+CPYmpzU51mQ3ZtoDZiKj60E2d6ANKKVPa5Yrv/Sj7aESupHDSN27wYkxU38Fdd5Om2PSJMVQiSF/NHT6L78E6oIYYg6i+92GzjSJZbCxkNomvzoOiOO9U/PJbbXNejWf4cuMYMNThXXa8UNLwRBEARBEAThXMTMrkuYRlLzXtgtzPIfBvY29CufRbv+ZVQ2f2TNWJAtlDZ1x5kTQuOrZkaFKvRMCyEqNoW0yFK6FTVwywhf9MX1LOYgJY6jDI6LIcInlkjfWE+X97tocLXx15qF7LOWUrCigLz/HEZubcXcuw/qbr0JSs9jWUYTrnqJpHUl3HnF13SeCabwagI1BXwdoiPxBhkvr1N3T7sp6WZijRf/Rv6CcDZV2a2gONEVzMW/4xRardtR+cOCGG+0dhejFgajGhTOPnTEZq0ltFsv9AFBnk7bI2QJhqldlHXvi0VWY2/egTIglsmfB+DS63nJEow1S4NXgJuIDCcaPyO22ioGHNrKXpdEo5jdJQiCIAiCIAjnJAa7LlEbzUeod7UhSRJqSQVaI+abF0LTfrTLnkRX00iU7y6sLQtwtZkgqYFP9O+w9rtrSXNH0WuKBu9JCTS/sB0lFKxz5/LFqsd5ZcO9KJfitK7/0ksatlvzyXeY8KrWos8qRIp8E2XAZ9QfddKS689HiVHsVL1A8aDb2Xnr3SRa1xJ+ayGRN39H93kbCBk8lwPbrbz3walPpbuqtzNp+WhWNe/zYHWCcOFZG53UH7Pg415JY+gDWJ15aNpMGAfUs9YeyLCF3qhCGqgYHktMzk5UipvYEVd5Om2P6qFSCJMhb9Q0FFcjFUQzOOQYmZuM1EVGUhHSTI3Jn5Qp0RSsm413dBx+G75H5XSwSdyZURAEQRAEQRDOSbxrvgSZ3TaerJnHW/Urjj/hcgDg9jHQNMGHo2Hp2FbsJyA3n6wHX4EHE0kO/Iawjx/BueRjtjReT3bpIL6tjiNoWhJ13XT4yWFkenfGVx+IJEk/89cvbgZZy/fRD3GNT09ibv47nZ6ehzuwArfbRnTwl/RsvA3n1tFM7VuCystM7N71HGsI4Y2VD7Pxw1T0X+fQENbK0YMuVq2GhsbjA4NqlwtzfSGmlmIPVygIF1bl7hZQ7Ci1RWh9kjFbN6L1dzAnJALZ6ebqOZHYukocDoolLmstod16YwgM8XTaHiVLcKXGRUlGf6xqLfbmbdgzUpn4jTdujYa/uQJwbDOi91GI6u1CZVDjaG6g39517HDJtF263zcIgiAIgiAIwgUh9uy6BHnJOmZH3IW3fHzjKP2yR1F0PlhHPYfbNZn6Y76Y7JPQuPpQl+2mzG8TUf5f8J1XPSHDruG6z0rwv74bXW/xxTHESF+tF+47H0UvcUkPdJ2gkVQAVGokQoPcOKyv4ijdj97re1zRAUhqFWa1he/Tynlq0RFqXM3YCCS/SEsvk53wN0Zj7O/N19Pc6PXHj1f38P4smXIQrVrnydIE4YJqM9lpLLQS4lhCVdCt1Gly8WqoQjPGzAopjH6rVRg1FvYO8iLuyF5Ubjcxw8d5Ou12obOs0FEFR0fdRLfln1PhGsCQpEX0Xx3H9qFRlOgPoi30J3myxNrHPidh6O3IW5ZB14FsVesZpRHrGQVBEARBEAThbMTMrktMq9sKQEdtCCFqH1AUXCGdkevy0a9+EY3BQuKYT3G1maivbGTXJy7KHMEkBFzF7fbRjJGrCe4WiK6hDcXUygtHPuOOg3/jiGnrZTHQdcLClt2MLX2DYnMIm58v4cicVRjK+mMf8gG6UBWaEm8GNaUxd+dVuHO2kfKCmfSb04iYWkRz4GxWlFioXH0Ul0uhtExBkiS0ah0ut4t51Wswu+2eLlEQfhNFUSjbXoukNNFsD0dRqTHUfI9XqI1/+iYjO1zc/F4clm4mKtIGEbN3AxG9Bl32s7pOkCSYoHFRmt4Ps5cf9sZ1NCQNZ9xSNYqs4kV7CK4tgWgNCjGDVbiw47aY6btlCVudMnYxu0sQBEEQBEEQzkoMdl1C2tw2ri77F582bjz1pCRh730XTX38KdPEoBQmErqsibChiYROjabboGqs/uGsfqIAm08CcZkBFFgCkRrMlE8IZdzaOrx3reX1zQ/jdDs8V9wfbLBXMn8KGEG4TyT90ofQd1g/nANfhICOBHew0tX3eR6LH8CIKRHk/WMlruBALJUVbK+JIlSqYMTMudQ+tonXXnVw7wMKVuvxT6bPbbybd1ffxcLmnR6uUBB+m8bCVsw1EqH2jdiM/akP2IbUbKU+MYi9Pg6Gf6/FT2NnTz9vEg5sQ6XWEDP0Sk+n3a5EytBfAwfGz0BxNVFr1zEoo4ihS32pDYtgf+9K6vf502lCGMUbvyC0ex/8dq1Brqlgp0u8fAuCIAiCIAjC2YhljJcQFTLjvbvTx5AAgFyxF8lhwRmThsPfQVuphpx33qFL5g1s6jyKcoMR8+EeWD5tJFF7FVuPyChHb2Zdp26M/rtEmF5F3nWzeN5xE+YADWpZ4+EK/zhBKm9u9x9y/MHU97Dav8Ft+Qit/Qok070oJm/yV+mI1ZaQlf0tgwubUZplPtzxKrm1s5hSLNP2dCQThqjp019C99/Vizd0vo34iF5M8e3rueIE4TdyuxTKd1Shc9dTpR1BY6AF36NrUIW6eC5Sh8Zs44YPu2AZsh9zz5vpuuhDYoZfhdbb19OptzujNW72x3ehISyOgOq1lIZdy4SNG9l0pcy/msL5OEeF3LW31jmsAAAgAElEQVSRjiO1WFpNqPUGeq2cw8apj9JXBerLZ8KtIAiCIAiCIJw38dXwJUQva3ggcDRddFEAaHd9gu6HJ1CV5aLzuRtj6FZ08ZMpMY9l/SM2ahcV89dh/lzVIwW/jHLGrPQjJruam3s28KF5E59VL6FLeAjBHVOJ8U/ycHWesd2Sz5sNK7G15FO6dTY1Kz9En1OLPHkmYd1BJ4eT75PIvuxELHlruf6xGnz7JdDSpYH60RLmRBVDBignl4B2De/Dbcl3oJbV2C6jmXLCpcW0fw+ONm/UbjMulZ5g+Q2cbSq2hXanzhdu+MQXo5+Fzf1jSNmyFHVAMFEDR3o67XZJL8F4nZt9E2aiKDZaW/NJ66dn8He+VMcG832fQhq3hpBwZQglGz8neuAojMVHMR7KYp9LjHQJgiAIgiAIwpmIwa5LgEtx80zNAg7ayn70vHXs67SFd8SxaTYSEGxvw2gswlG/Hl3fZjTjonnzxelEmiPppvXDR/HBK0JP4wB/LJuyyF7xCg8tm4hbuXw3Qs6xlbOmLQeHexJVXxahVsk4x3yPHD6G4BQnUdo1vJqQSHP4WMr7XUvZoCjCk9Lxvekwvf0/w3LTN6yd8i6LvlN49/3jx9HldvHRgbcYm3UnOy0FHq5QEH4Za3Me1XsD8XIeo03dGXWnH2jOdtBm9OKzzApCChsZMz8G64j9GOK64ltTTqex16HSaD2deruVrlKIDA2jKHM49tYsStSDmVldg84i80N1Cs4GHZIikXSVN6ZDW/COiiVtzbdsbLPjFnt3CYIgCIIgCML/EINdl4AKZwM7LQVUOpuOP2FvA5cdRa1gHtRGXfdAjv3fKrRrC+jcI4xDf56Jb9ybBPzjZrxzVnHU1JVK53Se8b4Cxz198YrW00WTyHjDUMYl34wsXb6nyTS//iyMvh//0C4MefR1/K+YhttoBEDVPJeQyi3o9xoYG7uK2gnTSf7uTaJWreSlBU/y73n1GLMt6EpkSissFBSC06kgSzI5JesJrK/GX+Xl4QoF4fwp7kbKNuejuCTa1LHYw2pR529AUSTeG+KForh45OVO6DrXs3XQQJI3f49PpzQCk7t6OvV2TZLgOp2bwgETsRu8sdYtQddxGAOW+FCSauDf3m00rYkibmgANTlziew7GG1bEyFrFojZXYIgCIIgCIJwBmLPrktAB00Qi6MfQC8d31NLu+kN1CVbMU9dgEb/IJLqKMX7SzB3mkNBgZqCeBeJgSascYUEu9WUl2Uyels1f77LQXPXesIVPzLHXYOiXH1Z3YHxTLTS8UvEoTgp7NSDCPsD1O+JJ7ouCFm7g9bMq7BURiKHdGdH03+QD4OXo4mwWCN5LgOHhlXQd+YgZmUY0GhOHcsXR32Fl8b7sj++wsVDUZzU5c+mpeJaZLkRt8ab6LB/ULDTh6zYYArDFUbNddDhiD+tj20kqlJGJUmkTLhRnOfnwVeCqwO0rJx4O33mvkV9Wz0PaWCvSUWOoTNlqhyMTWrSb43gyJJP6DBgPGxeyc6UDLp17oRKHGJBEARBEARBOOnynbJzCVAUhXVth3Epbgyy9uQHSlf8EBw2N7plf0ZWV+IT/h9COwdjq9nOFrcac7Mb/aExDDUkEKlNZvQSX3TBBgxDvVmw8QseWn4ji3M+FR9QT/NUzXxmmf5Dc3kftr22iJIGCZXxWnz73kbHUQWEOo3MOJxJ5bYwbPl78P6Tnj6jXiOpn5PI1Bc5tm0Vqx9+n9paJ8fyFYxaHyRJospcycuV88mzmzxdoiD8LHvbp5i2DkCiBbfiT3Tmvyhdq6NZq+LLoW5C8gq55aNueI8v4GDiKIKLc0m4YjI6v0BPp37R6KaGsKhkSroNxN68mWrdYCZvC6Y00cmi3Z1o3RBFYKIeWbMdQ3goquBw4pZ+yW6zzdOpC4IgCIIgCEK7Iga7LmJ7bcU8UD2Hpa37fvS8M24QpuGZlMam4WwbTMBihW7xDrwnpdGmf53wFW9R9/XXWDuk4hXdnx2JPZH+OpTsYBVD95uJbLLT5mj1UFXt0y1+A3kueBLhQdczoWcUMYMn4uh1G5Jai9YrkAzlPq7Xb2XkXWkc/nAXwaUbSF44m2Wb+pK1LRzzA+WEzffinXu38/yLCoqiYHa0cvfC4aw++DFZ1kJPlygIZ+VyrKZmhwurIxwFH/ySV1C9twJ7m5aPRnqhaijjqb/2Q2V0UntVLbE7tqJP7EJkZn9Pp37Ruc4PSvpdjdXbH0vtQobo+9DxqB+br1Cx4aga82E/uk6L4MCcF+gyaRqG5nqKVi7EIfbuEgRBEARBEISTxDLGi1gPXSzvhE2nnyEBAHXOYqSWKmyZ09H46VF56dn0/OPEJt1KqG8g33TsjpFcQnL+TmhEAF8egem7O3G0QwIDQt3MMKox3/0sIzRaZK3Gw9W1L2m6aADcXiDfNx+r6yNsVW34tdnBtZZjvrNobBpIjKuU74vnosnZjtIscaAqjb1ZLXS7fi23driVG3t1w2CUkCQJL403d/R8ho4h6aT4pnm4QkE4M7frMC2FC6gueBpUbrQBxUjapTQdCWZtFz0lhgbuei+K0DJfAp7fSumRUAx6G+nXThezQ38FvQQzwgzMvup2+sx9nZaGrTxVOJA/dVzBPkM83fc5iU1qImZwPdWHtuHTfxTSlpVs6ZTG0C6iHxEEQRAEQRAEEDO7LlqtbiuSJDHIqxNqSQWAqnQH2p0foj22Bp2vAY33cgJTxtDkSuXjwkBMWyz0rLIxoGcizpgobv5nGPpVBUy+t4G5B1/mzk234JDNqHW6y3pT+p+zoCWL22q/x2o9StZ7t3Ns0bvot2cTNmw0scNteKkiGLMnhaolA6nf/R1X3t9Izxnv0r/sKrzGfkVM1JtUH1hJ5Q85OJ0KY5OnkhJ4/ANqrq2SLIuY4SW0H4q7GmvTC1RsnIlTJ6HWtRDU7W2OrQygyk/mh/gG+m1toN+KTniPLSRP44dXXS2pk2ei9fb1dPoXrQiNxICAGA4Pn4zLcgTMVTyy9UpWTW7m6Dc9aNsSQeyQACqzX6NTZl9sEbG4Fn9BXWODp1MXBEEQBEEQhHZBjGhchLZb8hlT+hoHbWU/et468FHyEu+h3u6LWjcN78JuRMfaaWj9P0riK4msWMqRt/Yha3SE+sUhhUcQ9O0Y9jQXkJpdQFXRRg5X7/ZQVRcHf9mLAJUvqpIr6dBgJXrcLKxTF6APCMQ32o/OsS9yu/IMXccOpXTWm5TJuXQ4uIua4HoOHEoi/zF/7A/lU/DnbTz9pPPkcsZXNz7Ak4de5o36H1AUsR5J8DxFsWA3P0fDskE0GyLROF0E9fk3q5d6oXGomNe5npDDBcz851hUoWac444h5zYTMPwqQhKSPZ3+Ra9/hAav8L5UJmdga1hJUqvCHQdH8ckjJgqf6Y212Iv0GUEc+L+n6XLdTGSXg+x5n6G4XJ5OXRAEQRAEQRA8TixjvAhFqwMY6dWFJE0YAHLpThS/aOzqIHx7rkGSCtj+yrdk+rbRIcXN8jvvpG7fPxm8YRM2QyibsycRZR3BS+4OvOqWGd9vEL7xcVwRoCfAEOLh6tq3EcZURhhTIdBC53sCsSWocLlNYPdFbl1Po6YjRao/MSnZwtthkehzl5GYU8+nB+5GaVhFuG4Fk26YgSstjKRmF263Gp1KT0njUcb7j2Fy+C1i6ZfgcYrixmF9FecmCyXyVejNMr69PueTXU6G12hY1rGeusbD/PW9e9G6wP+5beTv9IGU7qQNvcLT6V8ybkgw8I58PT415Sim2fRSzUKKGsHSidswPjaA2E9XEzfsGPajW3CMm4Zh4SfsX7ec9JHjPZ26IAiCIAiCIHiUmNl1EYrWBPK3kKvRyRpwO9Ev+zOGOdehkZpQ671wOY1YbWkc1L7AW7YrOFYXyMi0iSRPC8QZ4UeHZTpC5q/hL1e9yYeq51hz7BP8IzuIga5foE528XhgC7Xmdyjdeg+7n7kK47ev4RUzGl1sDM3VrWRucZOzZQymwt2M6b2ePvdNJ9nnSlriA+k95hWmTplH3rxNyC6Zf45fwm3dHsRP5YVbcbPVnOfpEoXLmNP+BfKeTRyqexq9WYUm9XteMZkYclgm16+FPfIeHp59B36VOnye3EnhXm9swRH0u1YM1l5IGo3EtAADh66chcNgoLXiAzIrw0lOG8YhrRemv/THL0aP0/46feKiMaUPoGnjMmoLjno6dUEQBEEQBEHwKDHYdRHZZD7Ck9XzaHVbTz0pqzGn30mR91ScDhUq7RB8pG6Ep/lwUPmW4j5pOOasofjVEtwFoST6RBLcqqFtajxWdyM1RRtZvu9d7E7r2f+w8D9MziY2WPIpbL0G+5JCgtMHYxv/Br6xvYgd6sC/42au073OEGctVWlXcySqjWpvFd6d9WzvnULugsHsvaIZx2NF/N89B0/ukXagagcfl/2HWaYvOPCTZaqC8EdwOdagOvgJuXl/QWP1wRW7lWc5wvXbHdRorSzx38KM7+4mJscP7V37qKx2Y9P70HfG/Wh0Ok+nf8kJDtEyEV+yJ8xCUUFr2VskNgaiv24AJYc7UPd2OpE9jTTkzKDrFVfTGhhOzrxPsDU3ejp1QRAEQRAEQfAYMdh1ESl3NlDsrEMrHV99KtccAaAh7Er0o7bSWv8uK5/bg9fcv9E1oo4d8WU0fjeB1N1PE3p0Ae6QseS5pvOXwInETB9K+H3P882EFfzryoVo1XpPlnbRSdVFsaLDo/QNGku3QcOInzAVeyQ4bRYkpxbfhP2U6m5hxlQdbZPupDmtC0Pee4oDy/1pfr2SLw+vps6rlf0zfeg4fR6NDdnYnVZeXHcnFXnLeTP0Jrr+9w6QgvBHcbtykA69QOneGThc8VjDcng8JIvb1puxu518G7iRa1fcTVpWMK7Jx2jWNWNX9CRPfwgfXz9Pp3/JSursxVB7GNkTbkeSoKnsdYKsXrhn9qViWQ/qP0olPF3Br2Am9utuxWW3kf31h7idDk+nLgiCIAiCIAgeIQa7LiI3+Pbly4g70Epq5MpsDF9NQrvhVXyjy1DrFIr2WHE549nk9QVf1QYT1O8tMsc9QdxwAxX9k7F/4SZBfp+x16znH0UPkUALerWecJ8YT5d2UTLKOtD7smTEXXzjXo7d/BIr7utFyz9GINmupEnug6kwmlHLjlGY20i11EZn84ukDgyk08AHUWtiuOKGNLp3r8HcUIiryMJLo+fw+KB/Hd8XDCh21FLmqPdwpcLlwO0qQcq+n6btPahXjcLsW8Fz0et5YHkjeovC/IDt3LToHnrsCMc2phB7h3JsbVoCJtxKdFiEp9O/5GX2MJKuJLB34h3oFKgv/ycS4JjZh4rlA6l7uyt+cQ0M4UnKrr4Oe3khud/PFTe8EARBEARBEC5LYrDrIvBZ4yZ2W4sAUEsqANx+MZi8r6FZSaSh2o1aF0v38Q+jTtKRG9rMwYHXYPrTStKO/YDG2p3x+QYM5TIt2q4c6F9C7qFvWFO42INVXRoURWFp6z5WWI2od8cQ4BWAd5dheEcMJ3VKOIaUHAIDD/JJwRyc0Q9QndaLij5ttKR2ofTpcLYfPEjWpK4cubaIXVMXEa5pQq+y4nDZKWk8xv2mOTxTs0B8YBV+V4q7Fnn3HTi2B1Js/BNmXSuvxi3jwaXVGNokFvpmcePc24jPC8IyPg9Xchn2Vi30H063tB6eTv+yIEkSQzOMpKg7sWfiHfg5XDSWv0uDtgllSm+qdg3D9GxfdF41XB31/2gZl07dnq1U7Nzo6dQFQRAEQRAE4Q8n7sbYztncDr5r3Uuls5FMfRxSazUoCm5jKJUdriMk8TU2vpRDxvjnSC2ZhD5mMP+xLuL2OcHUm9aw8ePpjMxI5NuW8SRPiKL3E/68JCuURfQjJSDN0+Vd9CRJ4qWQyaiRMObWMOSGrlgzM3CRT3OxiqAujTS5mnC4RqNPj8Z0zdskzXsaY76R1cVX4p+xHovbB0u6ntVV4+nueAaHrRdv7Cwmu3ILz101jzBtoNj0W/jdKEor8o4ZKLtc5AT/DYsTPo34D/ctrcDl0LBCs58pX92Kj9mA9erDKOENuGwyLWmpXDlysqfTv6xIksSYdC/ceYnsvuZuMha+T0Pxx+Qn3EDy2AxqN+qxTfMj+pPVDEtdyDF1MgVLv8EYGol/xyRPpy8IgiAIgiAIfxgxs6ud08kavoi4g0eDrgRFwfB/N+D15URwm4nuNwe13k1zwAAOWbxZHfA41ogJJF25iuZ+bmrTUoiJTMVSUUS/9By2DX6N4rLF+EqQGthVDKBcIF6yFq2soXnIn3koPojstrk0lb7K8vvHYlu3n8aa8TQGTSM56zAj1+zE6bShshyit+1J7AOexi/Fi8DYMfzlvY6oHH+h9HB/ru96D/f2fY4Mr45EawIBWNSymza3zcPVCpcSxd2Kav31yDsbyQ59E6tdz2L/Ody8tpw2iw97601M/WIGBkWD7boDOAMacbslqpNiGD3+Lk+nf9m6MsmHxOAO7LjxYfwdEt55X7PHbzeqwak0JvSjcPQknFUGkpKP0GmaiSNL/4W5psrTaQuCIAiCIAjCH0YMdrVTJY463qpfgVNx4asyHN+UXpJojLqOHc5ZfHj3i8jaCAzetxJz1/XYG2wURA8ir8aB85UfGKiYyfRKIuWHJvQb+3FwfC8KqxazIOcjT5d2yWrDzhF7FeWOKwhZVcaAgV0IiL+ChDGpRA5QcBo6EHJ4CdOs+aiveZbGQd3I6RaEeYg/h6cHUfDBCxzpt4O2ScfI/Uqid+guHJZnKWsqoMBWzfO1i/9/e/cdHlWVPnD8Oy29FxJ6TwIJIaEZei9SpIqosLooKMoqiC7qYgMsuMBvFXQFVECxgAQBQSlSlCIdAwYMJSEQIL33Kef3BzJLSIAACWnv53nywL33zJlz3nnn5s6be+/wXdbBip6mqCaUKQPDj0PRHUviYJ0PKci2J8K4mEEH47mUVZuMSAuDNg4hs2EGlrFHMerzMLgr4up4MqDvRHQGm4qeQo02uJ47fu6u7H3sVRwseur/8QM7PbdjE9yYtAfbET1wBLn7fHDyyiXw4TOc2/cmBVnyDY1CCCGEEKJmkMsYK6m9eaf5PusIY1zCqJ2Tie7MNkxtHyet3sPUajyTkNqxbL44htHHFtLFzp3JzV0JifuOWt9fxDH9MofUoxQUuHPatTtPrmrMODd7xjfdjKeNfGNaefHUOfFd3WexUaALiMA7cAh5jisxZpzl2JII/B+y56zlaRJcYjnUJhRl059uH07h+AlvvI5vQd/cmcigKLSWZoTvbEaPJ/qTmB/Lsxt7M77dK6xo9hQBNlduBC738BJ3QxUkof9+JJqEfH6r/xGWBEVi5kJaZOUTeS6UFhF5uGU05HzH03iHxVOQqsc+QMuJPDeG95mIvbt3RU+hxtNoYKiPN9qkBHY/+RadPp9JyOFf2BySQl9GkjjNBvW8Ae+Je3F59CxNesSQfG4y3s3+g429V0UPXwghhBBCiHIlZ3ZVUmNcwgivOxlfvSs24U/zx/K5HA3/AdemH+Pke5HLPdvwx6Fwfsl6kuWOLfFo/wY+HbwxhORj69Ufn8s5eDq48Pu/FvOvo+NooDVT16E2dnqHip5atWaj0YNWT0TYOO7PWceBQjdyj+0n8cA2dKnOODt7oXJaMHrTER7LOINyUDhZojDmxRAdNoQHOkbi9K+uzP7HMXa8cpj0mPo81uYlejZshB870ABp5hyGn5rHsfwLFT1dURVlnsT8+UgKEw3savB/mGLOkRv/GQ6Z2UTv7UbHXbYojSLqod24BydSmKlF09ub3xPtGNJrHM51GlX0DMRfNBoY4u1DqL2FXye9Q4G9E51+P8F2w8c427qS8s+2nNzambgp7clLsMG9fhJ5GePJzz1c0UMXQgghhBCiXEmxqxI5Z0xmRNQ8YgqTQFnwMpoAuBAwj7zgJez8OYJEY09s7MfRwXg/WQWJFOrqoNzbYJnwEUHJ8fjmB9JY64vD/iCiOvXEyT4fY0E2JnNhBc+uZqmrd6ejfVMCdA/SMCaZUaO749JyCM0fyEB5nyc324DlaDwDnWMpfHEhSZ1aYIo/xy+mQM7Z53HhuxXUX+dJ6sRjxO98CifdWQoL9/H9icVkGLPJMRdYv5lTiNJKPf4z5kXjSdO0YL/nC5iOb8WYvoPM7Fz4vjttz5jY1+YAfz6+hdp2BmxczcQ90p/o3UmMfvBZ3JsEVvQUxHU0Ghjs4U17Wwu/Tv436Z7ehJ1J5VjqW2g0YD8qjJ9Cm3FsYm/Sj7phKbCgjK+SkbUYpYwVPXwhhBBCCCHKhVzGWIlo0ZBlzidPGdEtHcbJyBgazTqAo7+Rxg2XYTc8jY8vezHh0AF88i+hHxnO93sm8siyP3FMvcyy9+bQtWUca3Td+NvcAsb1qc0zfIxFWdBppTByL7no7Hmv1mgAsseuZXPBaXqqLzElx7Pvw19o+WQY2WohEXUKqJ2vJcs1nWa/7CcmJgPPOf/EMOFdbFMWYXHpRE5mLjEn25LsXpeP90/kdQcfNgQ9TG6OOwDfZu6nnV0jmtn4VOSURSVWUKA4sGwF3TM/ZH/tCeSlFKC5uJE8Wz1pZwtosbsHOfbZfDL2G3y9NfTKCkDb3Y3tTR/G77tPGfrMm9h7SH5VVhoNDHZ2xiG/kC0T36Hdynm0iIkiMeU1bPxepKt7T9a/tJ/fV2vo1OIMPiGXqdU6nOTkvXi4vQW4V/QUhBBCCCGEKFNyZlcFU0qxP+8sSika5uazye9FWtrW4Vxuc2J1Q5k7cxt6uzXYuRSSlP8QdbceJ9k8i+9afYLzwZPMCM6koF4wTrX+zrC4fCxZLTg7ajrvJD2JjTkXjUYjha4KttN8gempa9iveRz3CEf6hzrTOjCEJj1zcTVl0zwqg/vPpxPqncwl97+RM+pVItz1nG/nSfIjzvTQLCRn5HGOv76V8bV/pmPty6QlPMmlzEiyzfksSt/Bmiy5LEkUZzIpNv+Yy57XX6NV4c/s8Pk7+adPoEk+SWxtNywbbPHf3YPotpG89cLbONYqZKCHH5ETn2C7/f30OryHB6b9nxS6qgCNBnrb2zDa1sLh0VM4G9Ybb507NpHzOF34CyMudsK5b3vmN6rP2q1tOPWdL3YqkbzcZzh24BWMeVkVPQUhhBBCCCHKjJzZVcF+yYviuYQVfKTvSNiyFzjbaBDe4+ajC3uU+x6cQ2RhKqviB1N42p7WeYlED5lE7X1/0OD3rah1m/gudDLN7E5RkOWHY0Mv0t8awEu5rjibjHJ/rkqip0MLFvs+zn12TTH2+xiXNqcwux7Ewfgcv719imRdZxwavIlfPaj3qDe1k2JIPrCa/IQ8NN+ugLDRKN8E2ia6M+vjJvQJtcfo6MYz64fzQMDjfB8yGb32yjfjReSf59vM/fzTcyDuOscKnrmoKCaTYsM2+OW7fUxqtoSLDfyJSMtCm3gci0NDDtTKpNscNzSubuycuJINdQ4TUliXdh2f4LuWT+K/Zw3/CG6LS+duFT0VcZva6hVu9rC06yDSfZoQum4JvtGbiHD6jSD+SVP9SL4asJudyWZGfuFN735n8G68jYT0I6T82pymrSfg5NugoqchhBBCCCHEXZFiVwUwKjNxxlT8jm+kt1bLO81H0UnflOM27clPP8v+w9H0bDyH3Owm1E/xJe1oFPW8HyM3fxG9U7fi53yAyxEG3DJDOXTIH/sh+Xw59G06NOnP266DwLVnRU9RXEOj0RBm3wyAeJXL2IKNTDf1pVeBgQ61Z6ECo0kP/g1HTUtcYgvwSo0mwNyAvYWe5JjT+WnwSPqcewGNgufb7+PY6P1cck6g6chJtHJohX3+P0gzP0ui2ZlYQz5HC2Jx0Fwpfp0ouIiT1o4GBs+KDIG4B5SCPxMU32yAQ5vyGNt6DUNbphOfZUSfcxSdXWOSmrQg8fAu2qwMxDzsECvrrSTS6SJBtgHoHtxGVFY6YzMvEDRgZEVPR9yFpjp42dmeT5o1Yu/jr9Lhm/+jcV4OF45Mxj5wEpMi+3HOIYG13Q6xMsmJvueTeLB9HP6dDnA++TwpX0Mt7/tp0HkwBgenip6OEEIIIYQQt02KXfdS8jYsOTuZ6RDMb3nRrLuwnUzXLLpmfIOqlY7v/S2wr3OQ4fHf8uuJ++mQWJ/LIb7k+v5Cs7gDnDv5J8ZwO9x6+nDUyZlQU32GhBpQY5+l89kkRjeUD6iVnY3GQBu7RrSwbYTOqQ2eMwahUXm4WCaTftREzsJD/J9+Ky+ObAqDXWmWOpzktItke/qTvu87PAxBuBo9CY7ygoO5FLpnk+pqYcWZr9lxbi2rxuzl/rpTMGivvLVnJ69Ho9HwVZ2nAbhgTKGu3h2tRq5grg4KFRxMgM2/wKEjmTgQw/A6R+nT7gLkXAKjBq1jAAanDhyqc47a82Jp1tKBiw9u4Idah0nV5dEg+DXs/Z+lu85En9qe6DVSGK0OnDTwgqsHm/Uado5/hdAfv6aWVkvW2eX8qVuDb7MJTDk2iExdDvtqn+W10xdxsYklrEEsXQcloYxr+f3A9+jjnPBsPIw6bXujt5OzhYUQQgghRNUgxa5yopSC9AvYxOzkz5Z9+CBjO/9KOYJr/Uj6J4TSr85wTM3ysXM5zr9WfU7f7k3IzAgj9cxg2nrsZfTZfkQ1yKfeS2O5701fzu7zoe5ZNy6c68Emeydihi5mY73lrHn4GM62Bjq1e7uipyxKwUPnyPu1HrIuz8j+Gb1Gx1teX+LjtZE+vdNoGLKP5h1WEXfmfqJP5NFhizeujg+S5p7C2UEjSH/CgX5vvISzfwMKN+wn4YWeBLT5k51O/8Hc7xUK8WfOicu08u3AfP+HSTXnAGBUJh66+DEjXdozzWMASinizRnU1rtVVDjEbcoyF/Bx4n4OXZXayLkAACAASURBVEojMdlEbl4hnppMHsxNpnetPDSZaWiSLRjt7dF6dsTZviN/esVTsOMITfZlktUvgrW+J4jUJ2Dr1AT/Dh/QvU4YfQ1m3DTy66C60Wrgfid3OjtY+GLIIJKPNcd/94/YabUknf+ES5n5ODYeTC9jZ/ppgwEwHTcTpS/ApC9Ery/AzsZM6iUTJts3sahTOLk1x71OCAa7rmh1crmjEEIIIYSonOTTzR2wKAuT4pfzgK0/w2JOkdG4I0/m7+AxTWOG/hbOma7PMjJnHbON9emy/l0SMzI4VreAlUdbU2fxOeJbxBCtc+IPfS8ark7EdVZXOOOFvWcjvJd3w3b6c+Qkz6X2kUKyLgbz6utTCO4zlz09dzHafwiPuDfCqfXHeOgdcbJ1rehwiDuklKK+wRNbjR6NxhHV4kE21vGli31DbHSB1F/7IjmX3Ihq/xijur/Plt7TcNh9jH4X8jB0mobxp4GcmHGIZgG/UO9IMs80zSX6Oz26eXWw732G7+rH0O3hSdh93p//NksgsP1AXqkfQiOHJgDEGpN44OKHvOf1IAOdW5NhzuVE4SVCbBtg/9c9wETFUEqRlQ3x8XDmMhw5bSYqGgq00fgM3kuPVA2+KQqH5AwcU9PRKCi0tSXfyw8vXRiOhvrEusQSG7kHm6NHSAiMYIdzPJctGegMrjQMeIUHgp6mu50tbhpzRU9XlDMXrZbJPs1I6dmAtQ08cd+1h9qxp8mv602i/Xl+j9uBLjUZN00Q9k6tyfNyJ8dLR4GDDstfJ4FuM9TF4GkhUJdOy7wNcGoL+7c3Qm/XDi/HTtR1c2fw/RpsbTXFnt9kUuRcqbnj6lp8uxBCCCGEEGVNil13QIOGfGXEXJiNZtt7ZHd8gTr13HDIdufn3dns3LKPfqMaEu/hwxeWJ4j5rw2P9LPDvW4P0vO/5OLpbvQJNmPn0ITo+me5/IEnLm22Yz6VRYE5iBVvDqNRzwNsbRqBKWQM/j/H08qlB973dWNQ4y442ThXdAhEGdBoNExy72VdvmBKZWHaz3johuLnHIb7a+v5KXE1UzzDwNgWxw3LiUzJw17dR+cmvxLd618k2yXRuYk7to3Hk7JyGn+8/ysDnNbRLbUJ9c+e5vyhQDjtSpbDHk4cWM3jTX9j1Qozn6fXpVNgf15qG4vrgTVEudhyppmJV9K/ZZndSFp7tmSvKZYvMnbz71pjcNM5cCT/HGmmXLo7tkQvn1fvilKK1NN5GHMtaDSg0cLOXRBrAccmRvJsIsgwX8DGWIhNYQEeNrn0rZ+LW3YOrhuz0CqFAkz2XmjcOmNv2wJHm9pk2aVz2RLF5ZMbifBdz7lGiZgaWUCjxdWjHV2bPMiQpsNobeeMTl7DGsdTb8MT/vdh8ruPw6eOk7FrM/Vjo9GgJ9OvLRlunmTlx2BO34fm+HkMl6JJt9WQUN8Dh2QP4hu68V19T0w2PuAGjDDjlHME+4LfsdgqlkVoCY2xw1FrwkaZQafI1zmSuCuMg4fvQ6eFFV9A/XqSfEIIIYQQonxVq2JXcm48WrR4ONQCICH7AgatrXU5LiMae4Mjng4+AJxL+xPbfCiIOkmt4M5cVAk4nbtMTvQlfHo2IQEzdpFJ/Lb6T5IbXaBuAyeC4nOIiUxiYCs7Ml082KXtQ+aKzQxv1RVdnok0+zacjOrD334/grMphkJ/Nw5FdKJP2hEMyd9iDrEjc5MZO7fNYEog2/8Snntz0KSf4bTtJY4MtGPk9v04q+407xjMoMCB1J/QpMJiKu6dBgZPdjecYV3OVYVYNBq0Gg2ezk1oNXQkixNW8GztUJJMvuQ4rGCLzTIa5HWjqWMBB8f/jV3qHfrZDcOxiZ5DXlks6OHNR8qffiqLlZo/GR0/mue0PxD/x1aO+jQk5XI7dGeX8OvB5WR0fo62/q5E/TaeH8+4YNtvMvrGJj779EFs7B3Q9bifvc4m1l3ayn1RR+jX7TlwdmJ/wk6aJtvj1SAIh2bN0Wv12OrtUUqRnHsZB4MzjjbOmCxGYtL+xNuhNm72XuQZcziVHEHr2p0qMOplQ1ksHL54gbi8PLCYMJvzScqK5cIfvuRl2lCAFp0xD5MRlAVQGh71qY+j3kDu5U+xGJOorSzUxgwJJT+HRueK1uCF1jkYjUNtlIsreudMMCWRnrGdQ4kH2Ot8mHyHPJxDPHBxa0kbrzH4e4bS3TeMhnauaKTGIAC9Bu7zbwX+rchJSyHu9Akskb/jeOEMuvzcK43sPaHplfu3RbXvi0PtZgSkpaI9kU0OheRjS5Yhiwz7HHJt87CoBOyMBXSKu4xGrzDrzZh1CrNGS/MW9tQPzAGMrP7RBEYLGpOCAhO6uLNgtKCUHrPWhjw7V2x8IxjTKpd6deuhdQhFY/BA6WxAqwedAbQGlM7wv2WN9soby2IGZbb+q7GYwWL6a5vJ2kajzFjcG6OcfSvuRRBCCCGEEOWqWhW73vz577jae/J23xUAvLz5YZp7BvNqj48BmPbjcDo27M+UTu8DMPmH+xnucD92n62l5zvfMunoaLZnNiZD046si8vYnZ/OxCNaHJr0IGa7D7khKdR2isTJrxuXftWT5ZdMW+fDJDUdStyufLID9jLA7QAt7jNhCTrJyaPOdEo4Tj3/C5hbRnP4mIbfTLFMaHkE26ActiVmk+vUh7EDPPBp9hYe9c4xMSAY3TO2AHSuiCCKCuVwzeWDfja+LKszwbrcyb45W+v/E3edAz61vfG3G0GPgjg6PtKMoyZbusUfwRh7moTmzhzz74LdaTOGxDQSbTeS7Kgnz7EJGTYm6pidifXpxJ+N6/Knh4lhBm+ycvM5FmjPBV/oYgd1406T6eqJi98jJDl9QKstabga/Njh8B3pWQq25hCV4sxc3400zHcnY0M8zfr+jdfdVzAm+B/8ve10Cs35PLyyDRPbv87oVs+QVZDOpHV9mdLp3wwOGEdKbjzv/foPvnnocEWEukz9tmEF63r+DbwM1nWmrDAOvlmIJb/kx2w2TCVAH46zTxN0Nldu/O0d5IxHUwe0BtDbKfT2Co2tBbPeSF5hEtmmP0hWuSQpM6lGW/Jxx8mpAe6Ozejg9BwjHJtT38Ebe50OAHd3d9LS0sp9/qLqcnT3JKz/A6R16IpSisKsTJKT4knJziYtLZXkpBxSnNuQbeOLthlo7BToNWgNOpz1epx0Vw4j+u1dyODfP0SnsYCZKz9/+TMjgf/8MrHUY6rvcYK2Dg8QcNIW+LpsJ/wXs08QeY9+Vy59CyGEEEKIiletil1/C30RG72tdfmpDm/gYutuXZ7a+d94OvzvL7mv9vgEH1tfvDu+iL2HL7M8vyAhLhk7XX08/McRknKB+K4aktLq4dXGRGrDRHJT7ic9uyHunRXnfWM4nz4IU4Ef3t0Ksfimc8npecx2DXHLz6R7FwO2ju4YAHvAfxA8cs14W1w3fl+8cXd0J61QPpyK4gwaHT56F+uyj94FH31LADrbKGgQyoMNQgHor8Dc5kH0GrCEwiWl4X6NwlUD5iefxs6iYYhGoQWcH5tM4mMaHkBRoDTUfnoSmU9DYWY6Scl/4DPhZ+yfckGlJOCQGEAt3+Y0HOOLuaCQsQnNaFInGL9RzUHBpNTm+Hm1BkCvtWFal/n4e10Zk5ONK7P7fEFjjytjruVYl5l9lt27AJaj0J5DyD21h5SUJEBRqDGTpsmk/vMGzCY9Wh0YKKAgz4BGgRaFzhJKbkp9jBonDLYO6B29sbh6oRo44eHri5O9HU42BmzQodfKKVmi/Gk0GmxdXKnr4krdmzVUCpWfCSYj+VkWcvMUubWHsd+uP0kJWaQm5ZCdY8JkMqFMJgpt7Hiw1wGU0mCrNWOvA4MedAY9OhsdBgPY2IDOoNDbQJMm2fi4f0G2qytaiwGMeWjMRjAbwXLlX43F9Ney6cqPVg9aLWiu/Ks0etDq/lqnu/J/jR6l1YJWj8Wt4b0KqxBCCCGEqADVqtjVoX7vIsth9fsWXW7Qr8hypwb9iyx3bNAPrvlyqZC6HaAuePy13BCgEXhal0P+WnlFo2s7c7Kz/teAEPeWRvO/N7dWA/U0yrpNp4EmOlWkfX2uLl/51xvAzY26btd8U6NDE3rVL3pJ7ajGfkWWh/k+8b/n0eq43+9/5V2DzqbIe9BGb0dzz1a3N7FKyt7ZnT5t5VxMUUNoNGjsr3w5ir3zlT/meAL1y+GpLOXQp7i5b761FFt+eIxW+i/nvqX/iu2/pL6fmVQmXd+w/6oSm3ti//Liy/c9VjX6r8pjl/4rrm/p/57QKKXUrZvdnRtdRiOX2BQnMSlOYlKcxKQ4iUlxEpPiJCbFSUxKVhZxcXd3v3Wj23SnYyrNfLr0uHF5cffOu//gXJn6v93XtzKNvbz6v5ucrwzjr4x9V4f+r1Uevy/s57dAC1x7Drviyh878l44Wan7d5rfAlVOfUPVjM21OVIVx1/Wfd/oPVOVY3O3/d/pfuROjqmqUMlfCCGEEEKUh5t9YC7N9urcf1Ueu/RfcX1Xh/7L29UPzCXR/rW9svZ/s8dW9rFL/xXXt/R/b0mxSwghhBCiBrv+Eqi7bVed+q/KY5f+K67v6tB/udu/3PpB9Po7k15d1v7VrtL1X5XHLv1XXN/S/z0nlzFWMhKT4iQmxUlMipOYFCcxKU5iUpzEpGQ16TLG2zn7404ui6qM/Zf29a2MYy+v/iMjPG87vyrT+G+3/6o89nvRf0nK8veF/fwW6ErRzsydXXZVnv1X5bGXd//u7u7kv+ZbZcdf1n1f/56pyq9tWfV/Ly9jvCc3qL/ZwMrjQLCqk5gUJzEpTmJSnMSkOIlJcRKT4iQmJauMcbmbMd34sSnl/PyVs//SPVflHHt59H9nz1F5xl+zxn4v+i/fvoylbKe7w+csz/6r8tjvRf+lKYbcTf9V7bW9tl1Vf23Lqv97dXx1T87sEkIIIYQQQgghhBDiXpB7dgkhhBBCCCGEEEKIakOKXUIIIYQQQgghhBCi2pBilxBCCCGEEEIIIYSoNqTYJYQQQgghhBBCCCGqjXItdv33v/9lzJgxtG7dmnbt2pXqMUopFixYQJcuXQgODmbcuHGcPn26SJvCwkJmzZrFfffdR0hICE8//TTx8fHlMYUyl5GRwUsvvUTbtm1p27YtL730EpmZmTd9jL+/f4k/n376qbXNuHHjim2fOnVqeU+nTNxJTF5++eVi8x09enSRNjUpT4xGI//+978ZMmQIISEhdOnShX/+858kJCQUaVeV8uSrr76iV69etGrVihEjRnDo0KGbtj9w4AAjRoygVatW9O7dm2+++aZYm82bNzNw4ECCgoIYOHAgW7duLa/hl4vbicmWLVv4+9//TlhYGG3atOGhhx5i165dRdqsWbOmxH1LQUFBeU+lzNxOTPbv31/ifM+ePVukXU3Kk5L2pf7+/gwaNMjapqrnycGDB3n66afp0qUL/v7+/Pzzz7d8THXan9zuvrSqWrBgQbEc7dy5s3V7dT++hFvnelnF4E6O2yrCreJRVseSVSUeixYtYuTIkYSGhtKxY0eeeeYZoqOji7SpaTlSmpjUpDz5+uuvGTJkCG3atLEeO/7yyy/W7TUtP+DWMalJ+VGSRYsW4e/vz9tvv21dV6nyRJWjDz74QC1dulS9++67qm3btqV6zKJFi1RoaKjavHmzioqKUlOmTFGdO3dWWVlZ1javv/666tq1q9qzZ4+KjIxU48aNUw888IAymUzlNZUy88QTT6jBgwerI0eOqCNHjqjBgwerp5566qaPSUxMLPKzevVq5e/vr86fP29tM3bsWDVjxowi7TIzM8t7OmXiTmIyffp09cQTTxSZb1paWpE2NSlPMjMz1eOPP642btyozp49q44ePaoefPBBNXz48CLtqkqebNy4UQUGBqpVq1apM2fOqNmzZ6uQkBB18eLFEtufP39etW7dWs2ePVudOXNGrVq1SgUGBqpNmzZZ2xw5ckS1aNFCffLJJ+rMmTPqk08+US1btlS///77vZrWXbndmMyePVstXrxYRUREqJiYGDVv3jwVGBioIiMjrW3Cw8NVmzZtiu1jqorbjcm+ffuUn5+fio6OLjLfa/cJNS1PMjMzi8Ti8uXLqkOHDurDDz+0tqnqebJz5041f/58tXnzZuXn56e2bt160/bVaX9yu/lQlX344Ydq0KBBRXI0JSXFur26H18qdetcL6sY3MlxW0W4VTzK6liyqsRj/PjxKjw8XJ06dUqdPHlSTZw4UfXo0UPl5ORY29S0HClNTGpSnmzbtk3t3LlTRUdHq+joaDV//nwVGBioTp06pZSqefmh1K1jUpPy43oRERGqZ8+easiQIWr27NnW9ZUpT8q12HVVeHh4qYpdFotFde7cWS1atMi6rqCgQLVt21Z98803SqkrB+aBgYFq48aN1jbx8fEqICBA/frrr2U/+DJ05swZ5efnV+Rg+OjRo8rPz0+dPXu21P1MmjRJ/e1vfyuybuzYsUWSrKq405hMnz5dTZo06YbbJU+u7ID8/PyKfKipKnkyatQo9frrrxdZN2DAADV37twS27///vtqwIABRda99tpravTo0dbl559/Xj3xxBNF2owfP15NnTq1jEZdvm43JiUZOHCgWrBggXW5tPvmyup2Y3K12JWRkXHDPmt6nmzdulX5+/uruLg467qqnifXKk2xqzrtT8piv1FVfPjhh+qBBx4ocVt1P74syfW5XlYxKKtjlHvtRsWuuz2WrKrxUEqplJQU5efnpw4cOKCUkhxRqnhMlJI8ad++vVq1apXkxzWuxkSpmpsf2dnZql+/fmrPnj1FPl9WtjypVPfsiouLIykpiS5duljX2djY0L59e44ePQrAH3/8gdFoLHJquo+PD82bN7e2qayOHj2Ks7MzrVu3tq4LCQnB2dm51GNPTk7ml19+YdSoUcW2/fDDD9x3330MGjSIOXPmkJ2dXWZjLy93E5MDBw7QsWNH+vfvz4wZM0hJSbFuq+l5ApCdnY1Go8HFxaXI+sqeJ4WFhURGRhbZDwB07tz5hvP//fffi7zWAF27drXmwdU21/fZtWvXSp8PcGcxuZ7FYiEnJwc3N7ci63Nzc+nZsyfdunXjqaee4sSJE2U27vJ0NzEZNmwYXbp04bHHHmPfvn1FttX0PFm9ejWdOnWibt26RdZX1Ty5E9Vlf1IW+VDVxMbG0qVLF3r16sXUqVO5cOECUP2PL0ujrGJQVscolcXdHktW5XhkZWUB4OrqCkiOQPGYXFUT88RsNrNx40Zyc3MJDQ2V/KB4TK6qifkxc+ZMunfvTqdOnYqsr2x5or+j2ZWTpKQkADw9PYus9/Ly4tKlS8CVYo/BYCi2E/Ly8iI5OfneDPQOJScnF5sbXJlvacf+/fff4+joSL9+/YqsHzJkCPXq1cPLy4vTp08zb948/vzzT5YuXVomYy8vdxqTbt26MWDAAOrUqUNcXBwffPABjz32GGvWrMHGxqbG50lBQQFz585l8ODBODk5WddXhTxJS0vDbDaXuB+4uo+4XnJyMl5eXkXWeXp6YjKZSEtLo1atWiXG1dPT84Z9ViZ3EpPrff755+Tl5XH//fdb1zVp0oR3330Xf39/srOz+eKLL3j44YdZt24djRo1KssplLk7iYm3tzezZs0iMDCQwsJC1q1bx+OPP86XX35J+/btgZLffzUlTxITE/n111+ZO3dukfVVOU/uRHXZn5TFfqMqCQ4OZs6cOTRq1IiUlBTrfWM3bNhQ7Y8vS6OsYlAWxyiVRVkcS1bVeCilePfdd2nbti1+fn6A5EhJMYGalydRUVGMGTOGgoICHBwc+Oijj2jWrBlHjhwBamZ+3CgmUPPyA2Djxo2cOHGC1atXF9tW2fYjt13sWrBgAQsXLrxpm9WrV9OqVavb7dpKo9EUWVZK3fIxpWlTXkobkxtRShWb842Eh4czZMgQbG1ti6y/9kZ4fn5+NGzYkJEjRxIZGUlgYGCp+i5L5R2TgQMHWv/v5+dHUFAQvXr1YufOncUKgdf3W1HuVZ4YjUamTp2KUoo333yzyLbKlic3U9J+4Gbzv9F+49r1t9tnZXOn49+wYQMLFy7k448/LvKLIyQkhJCQEOtymzZtGD58OCtWrGDGjBllN/BydDsxadKkCU2aNLEuh4aGEh8fz2effWYtdt1un5XRnY7/+++/x9nZmT59+hRZXx3y5HZVp/1JVRnn3erevXuR5ZCQEPr27cvatWutfxmuaseX5aG8YlAV86o8jyUrezxmzpzJqVOn+Prrr4ttq6k5cqOY1LQ8ady4MWvXriUzM5MtW7Ywffp0VqxYYd1eE/PjRjFp1qxZjcuPy5cv8/bbb/P5558Xq0dcq7LkyW0Xux599NEiL2pJ6tWrd7vdAlf+6g5XKnm1atWyrk9JSbH+ldXLywuj0UhGRkaRamBKSkqR0wnvpdLGJCoqqshpjVelpqaWWLm83qFDh4iJieE///nPLdsGBgZiMBiIjY2tkCLGvYrJVbVq1aJOnTqcO3cOqLl5YjQamTJlCnFxcSxfvrzIWV0lqeg8KYm7uzs6na5Y1f7a/cD1SjpTITU1Fb1eb71sr6S/zqempt6wz8rkTmJy1Y8//si//vUvPvjgg2KnGl9Pq9XSqlUr6/uoMrubmFyrdevWrF+/3rpcU/NEKUV4eDhDhw7Fxsbmpm2rUp7cieqyPymr90hV5eDggJ+fH+fOnbMWcKva8WVZKqtjbC8vrzI5bquM7uRYsirGY9asWWzfvp0VK1bg6+trXV+Tc+RGMSlJdc8TGxsbGjZsCECrVq04fvw4X3zxBRMmTABqZn7cKCYzZ84s1ra650dkZCQpKSmMGDHCus5sNnPw4EG++uorNm3aBFSePLnte3Z5eHjQtGnTm/7crMp3M/Xq1cPb25s9e/ZY1xUWFnLw4EHrxIOCgjAYDEXaJCYmcvr06Qo7GCltTEJDQ8nKyuLYsWPWx0ZERJCVlVWqsa9evZrAwEACAgJu2fb06dMYjUbrL6577V7F5Kq0tDQuX75sfVPVxDy5WuiKjY1l2bJluLu733JMFZ0nJbGxsSEwMLDIawewd+/eG84/JCSEvXv3Flm3e/duax5cbXN9n7t3764SH2LuJCZw5Yyul19+mXnz5tGjR49bPo9SipMnT1aqfLiRO43J9a6fb03ME7hyv4nY2NgS7wd5vaqUJ3eiuuxPyuo9UlUVFhZy9uxZvL29q+zxZVkqqxiU1XFbZXQnx5JVKR5KKWbOnMmWLVtYvnw59evXL7K9JubIrWJSkuqeJ9dTSlFYWFgj8+NGrsakJNU9P8LCwvjhhx9Yu3at9ScoKIghQ4awdu1a6tevX6nyRPfm9dc5laFLly4RFxfHsWPHOHz4MN27dyc5ORkHBwfrX44HDBiAj48PTZs2RaPRYDKZWLx4MY0bN8ZsNjNnzhwSEhKYOXMmNjY22NrakpCQwFdffUVAQABZWVm88cYbODo68uKLL6LVVqp77hfh4eFBREQEP/zwAy1atCA+Pp7XXnuN4OBgxo0bZ213bUyuys7O5tVXX2XixInFLhE9f/48X375Jfb29hiNRo4ePcqMGTOoXbs2zz//fLWLSU5ODv/3f/+Ho6MjZrOZkydPMmPGDEwmE6+99lqNzBOTycRzzz1HZGQkCxYswM7OjtzcXHJzczEYDOh0uiqVJ05OTnzwwQfUqlULW1tbPvnkE/bv388777yDi4sL8+bNY+3atfTt2xeABg0asHjxYtLS0qhTpw7bt2/nv//9Ly+//LL1mvpatWrxwQcfYDAYcHNzY/Xq1axevZpZs2bd8q94lcHtxmTDhg1Mnz6dV155hc6dO1vzwWKxWP8gsXDhQgoKCtBqtVy6dIn58+ezZ88e3nzzTXx8fCpyuqVyuzFZtmwZycnJaLVakpKSWLZsGatWreLll1+27m9rWp5c9cEHH2BnZ8fTTz9drM+qnic5OTmcPXuW5ORkvv32W1q3bo2trS1GoxFnZ+dqvT+5VT5UJ3PmzMHGxgaLxcK5c+eYNWsWMTExzJw5ExcXl2p9fHnVzXK9rGJQ2mOUyuBm8dBqtWVyLFmV4vHWW2/xww8/8OGHH1KrVi3rcYFOp0Ov15fZ57DqFJOy+sxRVWIyf/58DAYDFouFy5cv8+WXX7J+/XpeeuklGjRoUOPyA24eE09PzxqVH3DlD2menp5FfjZs2EC9evUYPnx45duPlPp7G+/A9OnTlZ+fX7Gfffv2Wdv4+fmp8PBw67LFYlEffvih6ty5swoKClKPPvqoioqKKtJvfn6+mjlzpurQoYMKDg5WTz31lLp06VJ5TqXMpKWlqWnTpqnQ0FAVGhqqpk2bpjIyMoq0uT4mSin17bffquDgYJWZmVmsz0uXLqlHH31UdejQQQUGBqo+ffqoWbNmqbS0tHKdS1m53Zjk5eWp8ePHq7CwMBUYGKh69Oihpk+fXiwHalKeXLhwocT32rXvt6qWJytWrFA9e/ZUgYGBavjw4cW+Bnrs2LFF2u/fv18NGzZMBQYGqp49e6qvv/66WJ8//fST6t+/vwoMDFQDBgxQmzdvLvd5lKXbicnYsWNLzIfp06db27z99tuqR48eKjAwUIWFhanx48erI0eO3NM53a3bicnixYtVnz59VKtWrVT79u3Vww8/rHbu3Fmsz5qUJ0pd+Qro4OBgtXLlyhL7q+p5sm/fvpu+F6r7/uRm+VCdTJkyRXXu3FkFBgaqLl26qMmTJ6vTp09bt1f340ulbp3rZRWD0hyjVAY3i0dZHktWlXjc6DixPD6HVZeY1LQ8eeWVV6y/L8LCwtRjjz2mdu/ebd1e0/JDqZvHpKblx42MHTtWzZ4927pcmfJEo1Q1u/OmEEIIIYQQQgghhKixKv852UIIIYQQQgghhBBClJIUu4QQQgghhBBCz/1WEAAADiVJREFUCCFEtSHFLiGEEEIIIYQQQghRbUixSwghhBBCCCGEEEJUG1LsEkIIIYQQQgghhBDVhhS7hBBCCCGEEEIIIUS1IcUuIYQQQgghhBBCCFFtSLFLCCGEEEIIIYQQQlQbUuwSQgghhBBCVCv+/v5FfgICAmjbti2jR49m2bJlGI3GChvbmjVr8Pf3Z8GCBWXWZ2xsLEFBQcybN++u+xo3bhz+/v7ExcUVWd+rVy/8/f3vuv+SxMXF4e/vz7hx48ql/3v9PNfbunUr/v7+/PTTT/f0eYWoyfQVPQAhhBBCCCGEKA/Dhw8HwGw2c/HiRY4ePUpERAQ7d+7k008/Ra+vHh+H5s2bh8Fg4O9//3tFD0WUoE+fPgQEBDB//nx69+6NjY1NRQ9JiGqveuzdhRBCCCGEEOI67733XpHliIgIxo0bx2+//cbGjRsZOnRoBY2s7ERGRrJ582Yee+wxPDw8Kno4lZqPjw8//vgj9vb29/R5NRoNEydO5IUXXmD16tU88sgj9/T5haiJ5DJGIYQQQgghRI3QunVr69leu3fvruDRlI1vvvkGgGHDhlXwSCo/g8FA06ZNqVOnzj1/7t69e+Po6Mi33357z59biJpIil1CCCGEEEKIGqN58+YApKamFlmvlGLDhg1MnTqV/v37ExISQmhoKKNGjeKrr77CYrEU62vBggX4+/uzZs0aoqKiePrpp2nfvj0hISGMHTuWI0eO3NbYPv/8cwICAhg4cCAJCQm3bJ+Tk8PGjRtp2rQpLVu2LLY9MTGRJUuWMHbsWLp27UpQUBCdO3dm8uTJHDt27LbGdqd++eUXnnrqKTp27EhQUBA9evTgmWeeYefOnSW2z8/PZ+7cufTs2ZOgoCD69u3L4sWLUUoVa3vo0CFmzpzJkCFDaN++PcHBwQwYMIC5c+eSmZlZrP2N7tl17X3ULl26xLRp0wgLCyM4OJgRI0awffv2EscaERHBs88+ax1r586dGTVqFPPmzSMnJ6dIWzs7O/r06UNUVBQRERGljJ4Q4k5JsUsIIYQQQghRY1wtQlx/yV9hYSHTpk1jz549eHh40LNnT1q3bs2ZM2eYOXMmr7766g37/OOPP3jooYeIiYmhY8eONGzYkIMHD/L4449z6tSpUo1r/vz5zJkzh6CgIL766it8fHxu+ZiDBw+Sm5tLhw4dSty+bds25s6dS2JiIn5+fvTu3ZtatWqxdetWHnnkkXI/u+29995j4sSJ7Nq1i8aNG9OvXz/q1avH/v37+eyzz4q1NxqNjB8/nlWrVtGkSRPuu+8+EhISmDdvHv/5z3+KtX///ff57rvvMBgMhIWF0bFjR7Kzs1myZAmPPPJIsYLTrVy8eJFRo0Zx5MgR2rZtS8uWLYmMjOTZZ58tFqudO3cyZswYduzYQd26denXrx8BAQGkpaWxePFi0tLSivV/9XW6UaFPCFF25J5dQgghhBBCiBpj165dAHTt2rXIep1Ox4IFC+jRo0eRG4inpqYyYcIEvv/+e0aOHEn79u2L9fnVV1/x4osvMmHCBOu6d955h+XLl/Ppp5/y/vvv33A8FouFN998k5UrVxIWFsbHH3+Mo6NjqeZy6NAhAFq1alXi9jZt2rBu3ToCAgKKrN+1axeTJk3irbfeYsuWLWg0mlI93+1Yt24dS5cuxdfXl0WLFhUZQ25ubolnNx09epR27dqxadMmazHy+PHjjBkzhuXLlzNx4sQisXn22WcJCQnB1dXVuq6wsJDZs2ezcuVKli5dyuTJk0s95u+//55x48bx8ssvW7+8YPny5bzzzjv897//pUuXLta2n332GUopvvvuO4KCgor0c+zYMdzc3Ir1HxwcDPzvdRNClB85s0sIIYQQQghRrVksFs6fP88bb7zBwYMH6dWrFwMHDizSRq/X069fv2LflOfh4cG0adOAK2dKlaRt27ZFCl0AkyZNAm5e2CgsLGTq1KmsXLmSvn37smTJklIXugCioqIAaNy4cYnb/f39ixW64Eqhb8CAAZw/f77UZ57drkWLFgHw6quvFhuDg4MDHTt2LPYYrVbL7Nmzi5x116pVK7p27UpeXh5//PFHkfbdu3cvUugCsLGx4dVXX0Wv19/w8sMbqV+/PtOnTy/yLZ2PPvoorq6uREREUFhYaF2fkpKCs7NzsUIXXClqOTk5FVvfpEkT4H+vmxCi/MiZXUIIIYQQQohqyd/fv9i6UaNGMWvWLLTakv/uf/LkSXbv3s2lS5fIz89HKWW9HO7cuXMlPqZz587F1rm7u+Pm5kZiYmKJj8nNzeXpp59mz549jBgxgtmzZ6PT6Uo5sytSUlIAihV8rlVYWMivv/7K8ePHSU1NxWg0AliLXLGxsSXG6W4kJCRw9uxZ3Nzc6N+/f6kfV7du3RILd40bN2bHjh0kJSWV+Fzbt28nOjqa7Oxs6729DAbDDV+vG+nQoQMGg6HIOr1eT7169YiMjCQ9PZ1atWoBEBgYyPr163n11Vd5/PHH8fPzu2X/er0eR0dHMjMzMZlMRYpqQoiyJe8uIYQQQgghRLV09ZsXCwoKOHnyJDExMaxevZqQkBAefPDBIm0LCwt55ZVX2LBhww37u9E9oHx9fUtc7+joSHp6eonbvvjiC0wmE927d+edd965o0sJs7Ozrc9TkqioKCZNmsTFixdv2Mft3teqNOLj4wFo0KDBbT3uRnF0cHAAKHJmFcDSpUuZN2+etYB3t272Ol7//C+88AKnTp0iPDyc8PBw3N3dCQ0NpU+fPgwZMqTYGYJXOTk5kZOTQ3Z2domXOgohyoYUu4QQQgghhBDV0nvvvVdkecmSJcydO5fZs2fTqVMn6tata922bNkyNmzYgJ+fHy+99BKBgYG4uLhgMBiIiYlhwIABN3yeOylUde3alUOHDrFnzx42b9580/5v5OqlcleLXtdSSjFlyhQuXrzImDFjePjhh6lXrx6Ojo5oNBrmz5/PokWLSvyWw7Jyu3G5nfa///477733Hs7OzsyaNYsOHTrg7e1tLTJ16dKlxDPByur5a9euTXh4OPv27WPnzp0cOHCAHTt2sH37dj799FO+/fbbEs+4y8rKQqPRlHiZoxCi7Mg9u4QQQgghhBA1woQJE+jSpQv5+fksXLiwyLatW7cCMG/ePLp164anp6f1krYLFy6U+VgCAwP57LPPsLOzY9q0adbnvx2enp4AJZ49Fh0dTXR0NEFBQbz11lsEBATg5ORkLeiUx5yuunqGVGxsbLk9x9V4TZkyheHDh1O3bl1roSs/P5/k5ORye+6r9Ho9Xbp0YcaMGaxfv57t27cTFhZGdHQ0ixcvLtbeaDSSm5uLi4uLXMIoRDmTYpcQQgghhBCixnjxxRfRaDSsX7++yOV9mZmZwJUzdq73008/lctYWrduzWeffYatrS1Tp0694Q3wb+Tqjd9jYmKKbcvIyABKvjQvIyODvXv33sGIS8fHx4emTZuSnp7Oli1byuU5rr5eJc1v06ZN5XrG2o3UqVPH+kUFJd34Pzo6GqDELw0QQpQtKXYJIYQQQgghaowWLVrQu3dvTCYTn376qXV9o0aNAPjmm2+KtN+0aRPr1q0rt/GEhITw6aefYjAYeP7559m5c2epH9uuXTsAjh07Vmxbw4YN0Wq17Nu3r8iN2gsKCnjjjTdueC+xsjJx4kQA3nnnHU6fPl1kW25uLr/99ttd9X/19Vq9enWRe3adOXOGuXPn3lXfpbFs2bISzx7btWsXUHLR9OrrdPV1E0KUHzl3UgghhBBCCFGj/OMf/2Dbtm2Eh4fzzDPP4O3tzZNPPsmuXbuYN28emzZtonHjxpw7d44//viD8ePH8/nnn5fbeNq0acOSJUuYMGEC//jHP/joo4/o1q3bLR/Xrl07HBwc2L9/f7Ftnp6ejBo1ilWrVjF06FDCwsKwtbXl8OHDmM1mRowYwZo1a8pjOgAMGzaM48ePs2LFCoYOHUpoaCi+vr4kJiZy4sQJWrZsSceOHe+4/xEjRrB06VJ27NjBgAEDaNWqFRkZGRw8eJDevXtz/Pjxm96Y/24tXLiQOXPmEBAQQMOGDVFKERUVRUxMDO7u7jz55JPFHnPgwAEAunfvXm7jEkJcIWd2CSGEEEIIIWqUgIAA+vbtS0FBAUuXLgWgffv2fP3114SFhREXF8eOHTswGAwsWLCARx99tNzH1K5dOxYvXoxer2fy5Mns2bPnlo9xdHRk8ODBxMbGlnh215tvvsnLL79MvXr1+O233zh8+DAdO3YkPDycOnXqlMc0injttdf46KOP6NixI6dPn2bz5s3ExcXRsWPHEotBt8Pd3Z3Vq1czePBgjEYj27dvJyEhgeeee4758+eX0QxubMaMGQwcOJC8vDx+/fVXdu3ahU6nY/z48axfv77YN1Hm5+ezbds2/Pz8aN26dbmPT4iaTqMq4mJmIYQQQgghhBB37eTJkwwbNoxx48YxY8aMih6OuIENGzYwbdo03njjDR555JGKHo4Q1Z6c2SWEEEIIIYQQVVSLFi0YMGAA4eHhpKamVvRwRAmUUixZsoQGDRowatSoih6OEDWCFLuEEEIIIYQQogqbNm0aRqOxXO8rJu7ctm3b+PPPP5k6dSo2NjYVPRwhagS5jFEIIYQQQgghhBBCVBtyZpcQQgghhBBCCCGEqDak2CWEEEIIIYQQQgghqg0pdgkhhBBCCCGEEEKIakOKXUIIIYQQQgghhBCi2pBilxBCCCGEEEIIIYSoNqTYJYQQQgghhBBCCCGqDSl2CSGEEEIIIYQQQohqQ4pdQgghhBBCCCGEEKLakGKXEEIIIYQQQgghhKg2/h9sHShfKaLn+QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1200x200 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_trace(az_trace, compact=True, kind=\"rank_vlines\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even when each SMC run has low autocorrelation by construction the ESS value computed by ArviZ may under some circumstances show problems. This example is such a case, here each SMC chain is basically exploring a single mode and missing the other. When this happens the value of ESS_bulk (computed using `az.summary` or `az.ess`) will be close to the number of modes, for this problem we got ~3. We are working on providing an ESS estimation better tailored to the peculiarities of SMC.\n",
    "\n",
    "As the ESS value may vary across the parameter space. We also recommend to check the behavior of localized version of ESS. We can do this with `plot_ess`. The recommended value for ESS is at least 400 (dashed gray line)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2484x1104 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# only the first 6 dimensions\n",
    "az.plot_ess(az_trace, coords={\"X_dim_0\": slice(0, 5)});"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You may want to repeat the SMC sampling with the failing model as you may get different problems each time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "arviz    0.8.3\n",
      "numpy    1.18.1\n",
      "autopep8 1.5\n",
      "json     2.0.9\n",
      "pymc3    3.9.1\n",
      "last updated: Mon Jun 29 2020 \n",
      "\n",
      "CPython 3.7.6\n",
      "IPython 7.12.0\n",
      "watermark 2.0.2\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w"
   ]
  }
 ],
 "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}