{ "cells": [ { "cell_type": "markdown", "id": "cc776eea", "metadata": {}, "source": [ "# Interacting terms — non-proportional hazards and stratified baselines\n", "\n", "Conditional transformation models (CTMs) usually split the dependence of\n", "the response on the covariates into a *baseline* transformation $h_0(y)$\n", "and an additive *shift* $x^\\top\\beta$:\n", "\n", "$$\n", "h(y \\mid x) \\;=\\; h_0(y) + x^\\top \\beta,\n", "$$\n", "\n", "the assumption that yields proportional hazards (`Coxph`),\n", "proportional odds (`Colr`), or a covariate-shifted Gaussian (`BoxCox`).\n", "When that assumption fails — when the *shape* of the conditional\n", "distribution changes with $x$, not just its location — the shift model\n", "is mis-specified. mltpy's :class:`~mltpy.basis.InteractionBasis`\n", "replaces the additive structure with a tensor product,\n", "\n", "$$\n", "h(y \\mid x) \\;=\\; \\bigl(a(y) \\otimes b(x)\\bigr)^{\\!\\top} \\mathrm{vec}(\\Theta),\n", "$$\n", "\n", "so the transformation itself depends on $x$. See\n", "[ADR 0001](../adr/0001-tensor-product-interaction-basis.md) for the\n", "parameter-vector layout and monotonicity strategy.\n", "\n", "This vignette walks through two canonical uses of that machinery:\n", "\n", "1. **Stratified Box-Cox** — different baseline transformations per\n", " stratum (Bernstein-y $\\otimes$ one-hot-x).\n", "2. **Non-proportional Cox** — survival curves that cross under a\n", " continuous covariate (Bernstein-y $\\otimes$ Bernstein-x).\n", "\n", "For each example we fit the model, compare it against the proportional\n", "baseline via a likelihood-ratio test, and plot the conditional CDF,\n", "density, survival and hazard." ] }, { "cell_type": "code", "execution_count": 1, "id": "aa53e12b", "metadata": { "execution": { "iopub.execute_input": "2026-05-21T09:49:26.864616Z", "iopub.status.busy": "2026-05-21T09:49:26.864474Z", "iopub.status.idle": "2026-05-21T09:49:27.376016Z", "shell.execute_reply": "2026-05-21T09:49:27.375540Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.stats import chi2\n", "\n", "import mltpy\n", "from mltpy.basis import BernsteinBasis, OneHotBasis\n", "\n", "rng = np.random.default_rng(0)\n", "plt.rcParams[\"figure.dpi\"] = 110" ] }, { "cell_type": "markdown", "id": "15e25b1a", "metadata": {}, "source": [ "## 1. Stratified Box-Cox\n", "\n", "We simulate three groups whose conditional distributions disagree both\n", "in location *and* in shape, so the proportional Box-Cox model\n", "($h(y) + x^\\top\\beta \\sim \\mathcal{N}(0,1)$) cannot fit them.\n", "\n", "* Stratum 0 — $\\mathcal{N}(\\mu=2,\\,\\sigma=0.6)$ (sharply peaked).\n", "* Stratum 1 — $\\mathcal{N}(\\mu=4,\\,\\sigma=1.2)$ (medium spread).\n", "* Stratum 2 — $\\log\\mathcal{N}(\\mu=1.4,\\,\\sigma=0.45)$ (right-skewed).\n", "\n", "The third stratum is deliberately non-Gaussian — a global Box-Cox would\n", "force a single $h$ to fit all three shapes simultaneously, and the\n", "skewed stratum is the one that pays for the compromise." ] }, { "cell_type": "code", "execution_count": 2, "id": "43c016f7", "metadata": { "execution": { "iopub.execute_input": "2026-05-21T09:49:27.377323Z", "iopub.status.busy": "2026-05-21T09:49:27.377241Z", "iopub.status.idle": "2026-05-21T09:49:27.379434Z", "shell.execute_reply": "2026-05-21T09:49:27.379067Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n=750, support=(-0.93, 12.15), K=3\n" ] } ], "source": [ "n_per = 250\n", "K = 3\n", "stratum = np.repeat(np.arange(K), n_per).astype(float)\n", "y_s0 = rng.normal(loc=2.0, scale=0.6, size=n_per)\n", "y_s1 = rng.normal(loc=4.0, scale=1.2, size=n_per)\n", "y_s2 = rng.lognormal(mean=1.4, sigma=0.45, size=n_per)\n", "y = np.concatenate([y_s0, y_s1, y_s2])\n", "\n", "a = float(y.min()) - 0.25\n", "b = float(y.max()) + 0.25\n", "print(f\"n={y.size}, support=({a:.2f}, {b:.2f}), K={K}\")" ] }, { "cell_type": "markdown", "id": "22f3912e", "metadata": {}, "source": [ "### Proportional baseline (shift model)\n", "\n", "A standard `BoxCox` with the stratum index entered as a covariate. This\n", "is the proportional reference model: a single baseline transformation\n", "$h_0$ is shifted by $x^\\top\\beta$ — it cannot change *shape* between\n", "strata." ] }, { "cell_type": "code", "execution_count": 3, "id": "07e440c2", "metadata": { "execution": { "iopub.execute_input": "2026-05-21T09:49:27.380443Z", "iopub.status.busy": "2026-05-21T09:49:27.380389Z", "iopub.status.idle": "2026-05-21T09:49:27.920201Z", "shell.execute_reply": "2026-05-21T09:49:27.919769Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Model: BoxCox\n", "Support: (-0.9293060760652067, 12.146664193459667)\n", "Basis order: 6\n", "Fitted: Yes\n", "Log-lik: -1185.7967\n", "AIC: 2389.5935\n", "BIC: 2431.1741\n", "Converged: No\n", "n_restarts: 3\n", "\n", "Coefficients:\n", " Estimate Std. Error z value Pr(>|z|)\n", " X1 -1.8205 0.1048 -17.364 1.549e-67\n", " X2 -1.9785 0.1043 -18.978 2.581e-80\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/var/folders/l3/9xz3dcxx2879v30qp8ptbjbw0000gn/T/ipykernel_45133/2035786181.py:5: ConvergenceWarning: Optimization did not converge after 3 restarts. Solver message: Maximum outer iterations reached without convergence.. The result is the best found, but may not be the MLE.\n", " shift = mltpy.BoxCox(support=(a, b), order=6).fit(y, X=X_shift)\n" ] } ], "source": [ "X_shift = np.zeros((y.size, K - 1), dtype=float)\n", "for k in range(1, K):\n", " X_shift[stratum == k, k - 1] = 1.0\n", "\n", "shift = mltpy.BoxCox(support=(a, b), order=6).fit(y, X=X_shift)\n", "print(shift.summary())" ] }, { "cell_type": "markdown", "id": "659d1eaf", "metadata": {}, "source": [ "### Fully-interacting model (stratified baseline)\n", "\n", "Bernstein-y $\\otimes$ one-hot-x: each stratum gets its own baseline\n", "Bernstein coefficients, but they share a degree and a support. The\n", "column-wise monotonicity constraint guarantees that $h$ is non-decreasing\n", "in $y$ separately within every stratum." ] }, { "cell_type": "code", "execution_count": 4, "id": "8195835e", "metadata": { "execution": { "iopub.execute_input": "2026-05-21T09:49:27.921224Z", "iopub.status.busy": "2026-05-21T09:49:27.921151Z", "iopub.status.idle": "2026-05-21T09:49:30.295463Z", "shell.execute_reply": "2026-05-21T09:49:30.295058Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/var/folders/l3/9xz3dcxx2879v30qp8ptbjbw0000gn/T/ipykernel_45133/3928575607.py:10: ConvergenceWarning: Optimization did not converge after 3 restarts. Solver message: Maximum outer iterations reached without convergence.. The result is the best found, but may not be the MLE.\n", " ).fit(y, X=stratum.astype(int))\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "ConditionalTransformationModel(order=6, censoring=NONE, fitted=True, ll=-1118.94)\n" ] } ], "source": [ "y_basis = BernsteinBasis(order=6, support=(a, b))\n", "x_basis = OneHotBasis(K=K)\n", "ib = mltpy.InteractionBasis(y_basis=y_basis, x_basis=x_basis)\n", "\n", "interact = mltpy.ConditionalTransformationModel(\n", " basis=ib,\n", " base_distribution=\"normal\",\n", " censoring=mltpy.CensoringType.NONE,\n", " optimizer_config=mltpy.OptimizerConfig(random_state=0),\n", ").fit(y, X=stratum.astype(int))\n", "print(interact)" ] }, { "cell_type": "markdown", "id": "95f9ce0e", "metadata": {}, "source": [ "### Likelihood-ratio test against the shift model\n", "\n", "Under $H_0$ (proportional shift) the LR statistic\n", "$2(\\ell_{\\text{interact}} - \\ell_{\\text{shift}})$ is asymptotically\n", "$\\chi^2$ with df equal to the difference in free parameters." ] }, { "cell_type": "code", "execution_count": 5, "id": "ff2b1b91", "metadata": { "execution": { "iopub.execute_input": "2026-05-21T09:49:30.296692Z", "iopub.status.busy": "2026-05-21T09:49:30.296637Z", "iopub.status.idle": "2026-05-21T09:49:30.298658Z", "shell.execute_reply": "2026-05-21T09:49:30.298354Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "log-lik shift : -1185.797 (k=9)\n", "log-lik interact : -1118.938 (k=21)\n", "LR statistic : 133.72 on 12 df, p = 1.11e-22\n" ] } ], "source": [ "ll_shift = shift.result_.log_likelihood\n", "ll_full = interact.result_.log_likelihood\n", "df = interact.n_free_params_ - shift.n_free_params_\n", "lr = 2.0 * (ll_full - ll_shift)\n", "p_value = float(chi2.sf(lr, df=df))\n", "print(f\"log-lik shift : {ll_shift:.3f} (k={shift.n_free_params_})\")\n", "print(f\"log-lik interact : {ll_full:.3f} (k={interact.n_free_params_})\")\n", "print(f\"LR statistic : {lr:.2f} on {df} df, p = {p_value:.2e}\")" ] }, { "cell_type": "markdown", "id": "1e43365d", "metadata": {}, "source": [ "### Conditional CDF and density per stratum\n", "\n", "The interacting model returns one conditional curve per requested\n", "covariate row. We evaluate $F(y \\mid k)$ and $f(y \\mid k)$ over a fine\n", "$y$-grid for $k = 0, 1, 2$ and overlay the empirical CDF / a kernel\n", "density estimate from each stratum for context." ] }, { "cell_type": "code", "execution_count": 6, "id": "11a0c8f5", "metadata": { "execution": { "iopub.execute_input": "2026-05-21T09:49:30.299576Z", "iopub.status.busy": "2026-05-21T09:49:30.299529Z", "iopub.status.idle": "2026-05-21T09:49:30.405885Z", "shell.execute_reply": "2026-05-21T09:49:30.405482Z" } }, "outputs": [ { "data": { "image/png": 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J3rlzZ56IMnBORURERPqaUzFwpUNkWqlPnJ+fX4VOMhEREZmP6OhoeZFLPWeg0nFORURERPqaUzFwpXsyipYHiqBVgwYN7nryiIiIyDyxpEDFzg/nVERERFTdORWLsxMRERERERERkVFi4IqIiIiIiIiIiIwSA1dERERERERERGSUGLgiIiIiIiIiIiKjxOLslVRYWIj4+HhkZ2ejoKCgZr4rZHQsLS1hZ2cHLy8vWFhYGHo4RERERERERo2fnc2TZQ18djaqjKurV69i8uTJCA0NlZXlW7duXeFfiPfffx+BgYGwt7dH9+7dcejQIb2PT7xPVFSUDFzl5ubq/fXJeInvt/i+i++/+DkgIiIiIiKi0vGzs/nKrYHPzkaVcXXu3Dls2rQJXbt2hVKplLeK+OCDD/DOO+/I4FXbtm3x+eefY/DgwTh58iQaNmyot/GJk5+WlgYfHx94enrq7XXJNCQkJCA2Nlb+HHh7ext6OERERGW6ePEipk2bhgMHDsDZ2Rljx47F/PnzYWNjc9e/dW+88Qb+/vtvuR0SEoKpU6fKC4tEREQVxc/O5i1Bz5+djSpwNXz4cDzwwANye/z48Th69OhdnyOW7L333nt4+eWX8dJLL8ljvXv3RtOmTbFo0SIsX75cb+MT7yUmfAxamSfxfU9OTpY/B0RERMYqKSkJ/fv3R5MmTbB+/Xp5xXPGjBnIzMzEsmXLyn3uI488IoNeCxculJnsIoD13HPPybT/SZMm1drXQEREpo2fnc2bp54/OxtV4EqhqPzKRXElMTU1FaNHj9YcE8Glhx56SE7W9EnUtBITNzJf4vvP2mZERGTMVq5cKedGGzZsgIeHhzyWn5+PKVOmYPbs2fD39y/1eTExMdi1axdWrVolLyAKIgB25MgR/PTTTwxcERFRhfGzM1nq8bOzUdW4qgpxVVBo3rx5seMtWrTAzZs3kZWVZaCREREREdW+zZs3Y+DAgZqglSAu8IkSDFu3bi3zeXl5efJfV1fXYsfFPus7EhERkaEYVcZVVdPhbW1tZdV6Xe7u7nKSJe4XBdtLI65GiptadHR0jY+XyNCy8wpgZ83MQSKqmwqUBcgpyJE3dzt3mCNxUW/ChAnFjrm5ucHPz09zwa80AQEBskaoWCbYrFkzuS+CYCLY9cMPP9TCyImIiIjqYOCqOhYvXoy5c+caehhG6ffff8etW7fksgJ9WrJkiaw/NmzYMBgD8TWK4rViUm5tbS2XmIqfCxcXF9SlQNWx8CTsvRKHQ2GJOBeVggOz+sPHpXiwl0gjPwdICgdsnQCX0pcUEVVXbkEu0vPSkZ6bjoy8DGTmZyIrP0t7y8u681jRLTOv+HH147Lzs5GnVGUN2VvZ4/CTh83yGyUu2olAVUniol5iYmK5zxVlFh599FG0atVKk+b/2WefYdSoUeU+jxcDiYjIHPFzs0utnGeTD1yJSVhOTo4s+qWbdSUmbRYWFvL+sohCpRMnTiyWcdWlS5caH7Op/AKK4vg1Ebi6//77jSJwJZZE3HvvvXL7xx9/lEVrX3nlFTzxxBP466+/YOrBqt2XYvHjfzdxMCwBeQXF25CKQNbQNn4GGx8ZWFoMEHsBqN8RiLsEhO0Cok8BeZlAwlUgOUI0MQb6zgLued3Qo6VacDL2JBQWCrT1biv3z8SdQX5hPtr7tJf75xLOyWBRZ9/Ocv9iwkXEZMSgsXtjpOSm4Hz8eURnRMPPyU8GoiLTInE78zZcbV3lfnxWPJJykuSPVUZ+BtJy0pBXqAow1RQRyBKZ12IuQBUjztfTTz+NK1euyL+LIkNr27ZtmD59upxPPfbYY2U+lxcDiYjIHPFz81+1cp5NPnClrm116dIltGvXTnNcpMKLbjhlLRMURFZNXcqsMdQkNzc3Vy7XNDW//vorzp07hwsXLsglEYKYmItg1uHDh00miJmQnoPcAiX8XO0RnZKFlXvCsP5YJNJy8st8zvnoVAauzE1uhio4FXUMOLkWSLquClSVJzGstkZHNUxkNCXnJKOeQz1YKaxkEEoEknzsfeT+5uubZaZSQWEBErISsP7KeqTlpSHUO1Q+71TcKRlscrF1kfvJ2clQQmnU3zfxdeUqc2FraXp/n6pL/C1LSUm547i4qKdb96qkTZs2Yd26dTh9+jTatGkjj/Xr10+2sxbdm8sLXPFioGk6E3nnz0mbBsVrnBERUfXxc7OZF2fv0aOHDD6JiZZuJo1IdTeGrB5jJQI24vyINpUODg4ycPPhhx/K+0QnoW+//VY+RlypFjd1dyHxb+vWrWV7bBEoFAGrjRs3IiMjA1OnTpWvI14vODgYkydPLjZxFsfCw8Px+eefa1539erV8j6xvWjRojuys3SvlO/evVvu//PPP7LIrJOTkwxOiqvCwqeffir3xaRcZNKJTLzyiLodbdu21QSthEGDBsnni6/PVPx6LBILN13Aa7+eRu8PduHbAzfuCFp5Otrgofb18eGotvj31XswY1BTg42XaklOGnB5K/DPG8DKXsB7DYBVQ4GtbwKx5+4etLJ1ASyta2u0VAPyCvIQlR6FE7En8PWZrzF1x1QsProYcw/OxeRtk/HIxkcwdP1QdPmhC368+CPWXV6HsZvH4qXdL+HfqH9lFtbqc6vx+9XfcT3lOuKz4xGWEobE7ES9Ba0sYQk3Wzf4O/ojxCUEbTzboKtvV/Su3xv9A/vjwcYP4qkWT2FCqwmY2HoiXun4Cub2mIuFvRbK28qBK/HDsB+w7v51WHvfWmwdtRWHnjiEE2NOyJs5Bq3UF/VK1rISf49FZnnJZja6zp8/L5cGir/zutq3by+X1ovM5LKIuViDBg00N5GtRUREZOr4uRlG8bnZqDKuxIRI/YWLAIeolyCyYoS+ffvC29sbAwYMkPddvXpVHhfLA19//XXMmTNH3i+uEC5fvhwJCQly2ReVbvjw4ahXrx6+/vpr2S1InM/IyEh531tvvYW4uDg56VUXYxXnVk1MXl944QW8+eabMlAkbuJ7J1pdLliwQD42IiJCbo8cOVK21hZEW24RLOvVq5e8cis0atSo0t+i5557TgbQJk2ahK+++gpjxozBqVOncPbsWdkCPCwsTF75bdiwoWz7XRbx9ZWcwIvAWGkTfmMTkZiJf87F4KluQbhZtJ1bYjmgl5MN7m/rjwdC/REa4MblMnVdYSEQcxq4+Ddwbacqs6qwAu1nXRoAPs0B7+aATwvAqxng2QhwKDsrgwxP1HKKzYyVy/HEkj1xO3jroKz1VIhC3M64jYTshDuedzVZ9bdTLS03rVrjcLJ2kssB5c3GFU42TnC2cZbH5c2m+L/iPkdrR81jRGCJS/n0b+jQobLAenJysqbWlbjAp1AoZPH1sgQFBcm/5SLjSjeL/dixY/Dx8ZEXpoiIiMwJPzfDKD43G1XgSqSiP/LII8WOqfdF8EOkq4sJVX5+8WyS1157TabeiYwdEXAJDQ2VWTkicFErKX8Fhl8uYWOpqPDkPz4+HtevX8fSpUvlL6Jwzz33aO4XwSQRfBIBwm7dupW61EBEXbt27Vrs+IoVKzTb4nsUEhIig1SXL1+WBdnFFVuRoSUCZqW9bkWJn4m3335bbovlfCK7bu3atbh27ZossK7OzhKT9PICV9UpXlvbxM/Zj4dvIsDdAX2aeuP4zSTsuRyHNYfCEZ5Q/Ap4Sz8XTOwdIoNWNlYmn1RJ5VEqgZsHgAsbgYubgBRRm6ocdm5AcE+gQWdVfSu/doAdl4QYa2e8uKw4RKRFyKwpUTNK919xn7652LjA094TnnaeshufCEaJbChxE/fJbTs3GaAS94llg9YKZuUZI5HxLAqqi4tH4u9gVFQUZs6cKY/7+2sbLpS8GCguLomLUQ8//DDeeecdmTUlmpeI7Gg2syEiInP77MzPzcbzudmoAldiKZn4YS6PCEiUJH7oRNaVuNU28YvX7M0tMLRL84fA1sqyQo8VywPFVVVxvsQPmpi4irT+ihLPLxm0EtasWSOLs4qirmLpoJo6cKUvIi1RTWSLiavAffr00QStBPF+pf2smKqsvAKZWZWVW4Cejb1wNTYd/16JL/aYYE8HvDakOYa09mUGQ10XfwU49RNw+ufyg1U2zoB7ENDrJSCoJ+DCpTvGRFmolJlSYhnejdQb8l91oErc8pVl16mrKAcrB9RzrAdve28ZkJKBqaLgVMl/rbk0tM4QE8kdO3bIrrkieOXs7CyX0ItMaF0lLwaKx4nnvfHGG/KioMjYEhehxN92UQ6AiIjInD4783Oz8TCqwBXVDhHoE1dQxcT0+eefl0Gmjh07yompCADdjciYKkksAxw7diyeeeYZOTEWv+SilsaDDz4oOz7qU8lor42NTanH7va+5RWvDQgIgDFxsLHC60NbIDkzF0+vPoK9l7XZFrZWClmzakKvEFhbMsOqzsrPBc7/Dhz+Eog8UvpjRD2fkL5Ag45Aq5GAR2MgJ5XL/oxgWZ8ISslb6nXcSFEFqcJTw5FdUPX/PorldqK4uq+TL3wdfGXhdRGkkv8WbYvHkHlq0aIFtm/fXu5jSrvA07hxY/z88881ODIiIiLTwM/NxvO5mYErMyUyksRSOlHI/sCBA3IpgVg2KJYTiKLn5SktrVK8llii+cUXX2iO7dmzp8LjEUsIRXfCkr8INUmsyT1z5kyxYyLjT3So1M3qMgZiXNEp2Rj7zWGZbaXWtoErPnk0FI28y/+ekQlLiwGOrgKOfgNkxN55v5U90Pw+oOUIoNEA4NoO4OSPQOuHAUsrBq1q+ff0VsYtXE68jMtJ2tvNtJsyu6qybBQ2qO9cH/Wd6qOBUwP5r1gq6GDtgGfaPiPrRhERERFRzeHnZhjF52YGrvSwPlakGhrDOKpCLK8The9nzZqFESNGyMLr4pezIhlLurKysuRzdKkLuxcbZxmvK5YqXrhwodixbdu2oaaL137//fdyaWOTJk3kMbFEQhT2N6aOlNfjM/D6+tO4GJ2G5Kw8zfEnugbineEtK7xElExMSiTw72LgxBqgoHhQV3ILAvrNAloMB3a/D9w6AbR8QHVzC+SywFro2Hc5+TLOxZ/TBKiuJF1Bep42sFwRoji5nZUdvO280T+oP4JcgrA3Yq9cvvdal9egsFDg0+Ofysys8a3HayYKLGhOREREpsaUPzvzc/P3Bv3czMBVNYkPD6YWOBDdgkRXv0cffVQWYhdpf++9956sMabu8ieWGHzzzTey6Ln44fTy8pL3l0VEWsWyw3nz5qF79+6yO6T4YS5JvO7OnTtlUEqkHIraGWJZoSgEu2TJEnTu3Fm22RQBJZH9VZPEe4quS6NGjZL/is6IohPlfffdJ4u+G4vcfCXOR6ciNUtVh0QkvL07ohXGdC/7+0EmLDkC2LcYOL4GUGoDlZKtC9BxHODRCPAIARr2Ux0XywMtdP4A+7ev3THXcaLWVFhKmAxSnUs4hyPRR3Aj7UalsqjsLO3QyrMVGrk1go2ljewI+Fy75xDiGoI9kXtkp72ufqragaIIupWFlQxaCZ3qdUJ+obYOEYNWREREZIpM7bMzPzcbz+dmBq7MkK+vr7yJYJUIDokC571795bBIktL1X9I/ve//+Hw4cOysKuIpI4bN052FSrLs88+i7CwMNnF6KOPPsK9996LH3/88Y7ugeIH/bnnnpM/9GlpaVi1ahXGjx+Pt956S3aVFF2LRLtu8XovvviiDLDVFBE137JlC1544QU8/vjjsLKywkMPPYRPPvkExiAtOw/rjkXiyz1hmqCVuDqw5LFQDGvDItt1TuQx4MBnwKVNd2ZYuYUAniFA54mqZYElNS27vT1VPINKXZz8evJ1/HL5F+QU5OBa8jWcTzhf4VpUYnmfr6OvDE490OgBNPdsjsy8TJyMO4nJbSfLZX6n4k7h38h/YW9tD0uFJfoH9i/2Gn0aFK812KN+D34biYiIiGoZPzcbz+dmi8K7tfEzI5GRkbK4WERERKld9m7cuCH/LS/ziOq22vwZ2HHhNqatPYHM3AK5b6WwwBdjOmJAizuL45MJyk4FEq4A7g2BC38Cm18D8rOKP8beExj2IdDqIUDBwvvVkafMQ0JWggwqCWJZnwguBToHysDU4mOLYWlhiZhMVZe/ihCZUa28WqGlR0s09WiKpu5N5etZKXhNyJznCsTzZErORN5ZbLdNA1eDjIWI6hZ+dqYbd/nsXJk5FWfXREaoQFmINYfCNUErhQVkphWDVnVI9ElVbSpRcD3+SvH7vJoB98wGWoxgwKqS3ftEzSiRhi4CVSKLyl4Urwew4uQKuNq6YmzLsYhMj8TC/xYiJScFidmJSMhOuOtrO1k7oaVnSxmoEkv+Wnu1hr+jP5ftERERERHVMAauiIzQm7+fwe5LcZr9t+9vifvb+ht0TKQHBflA5GHAvwMQtgcIPwhAp06SvTtwzxtAx6dVHQGpwnaE78CGqxuw5J4lsj6UKHAu9j/o84FcqidqRB28dRA/XvhRdv67G1F7qr1Pe3lr591OFk1X15wiIiIiIqLaw09GREZGLBFceziiWPfAcT24PLVOuLYT+PdjIC0aSA7XHrewBLpMAvq+Bjh4GHKEJktkQ4lMKhFcEplW6u5+T/z1BMJSw+5al0pkUIX6hMpAVah3KNzs3Gpp5EREREREVB4GroiMyO3UbLyy7pRmv0uwB+aOaMXlSKYuLwuwtAGijgMR/wHQKS3o2wZ44HPAr50hR2gS0nLTsClsE7r4dkFDt4bIys/CH1f/kMEmDzsPuNi44OXdL+Ng9EFk5GWU+ToiI6utd1t08euCrr5d5baod0VERERERMaHgSsiI6FUFuKln08gKTNP7rs5WGPp46GwtuTyJJMWdxnY/g6QFgPcOq49LgIlfV8Fek4HirrZUXHKQiXOxZ+Dt4O3LKouuvwdu31MLuMTt7PxZ/HTxZ/w3bnvEJGuzVIsyQIWaO7RHF39usqgV8d6HWV3PyIiIiIiMn4MXBEZiZ+ORODAtUTN/oej2sLPVVVYmkxY/GUgbDeQl1k8y+qhrwCfFoYcmdETGVUn407KLn8vd3pZZlU90eIJbAvfhrf3v11urSp3W3f0rN8TfRr0QXe/7lz6R0RERERkohi4IjICMSnZeO/vC5r9xzoHYHArX4OOiapJqQSO/B+wZRZQqOoOKXV5Fhg8D7Cy5Sm+C0drR4xoOAL7bu3D4qOLsTNiJ+Kz4st8fAuPFjJQ1btBb7T2bA1LhSXPMRERERGRiWPgisgIzPjlJNJy8uV2PRdbzL6PmTgmLT8X+HY4EHFIe8zWFRj5OdBiuCFHZhK2h2+XWVUOVg7YFbELCdkJZRZV7+HfA/cE3oNe9XvBx8Gn1sdKREREREQ1i4ErIgPbdTEWB65pP5jPH9kGLnaseWSyslOBX8YUD1p5NQUeWwt4NTbkyIzab5d/Q54yTwapNl3bVGbNKnsre5lVNTBwoMysEllZRERERERUdzFwRWRAeQVKzNt0XrM/pJUvBrWsx++JqUqNBn54BLh9Rnus6RDgoS8BO1dDjszoRKVH4VryNVk0fefNnfji1BeIzy59GaAITvUP6I+BQQNlhpWdlV2tj5eIiIiIiAyDgSsq1e+//45bt25hypQpej1DS5YsQdOmTTFs2DCDn/m4uDjMnz8fhw4dwsmTJ2FtbY309PRaHcPKPdcQFpcht22sFHiDSwRNV8I14LuRQMpN7bFuU4DBCwAFO0OW7Bb417W/8MulX5Cck4xcZe4dp9NaYS0zq4aFDJP/MlhFRERERMaGn5trBz9NUZm/gMuXL9f72RGBq7///tsoznpUVBR++ukn+Pj4oFOnTrX+/smZuVi+66pmf1LvEAR4ONT6OEgPok8D3wwpHrRqPhwY8h6DVjpiMmIw79A8DPltCJadXIbYrNhiQSsLWKCrb1fM7TEXux/djSX3LMHg4MEMWhERERGRUeLn5trBjCuqlsLCQuTm5sLW1vQ6pLVt2xa3b9+W23PmzMGpU6dq9f2/2BuGrDyl3PZxtsWUfqx/ZJJunwdWDQVyi7L1LCyBXjOATk8bemRG89+I/2L+w08Xf5JLAgtReMdjApwD8GDjBzG80XD4OrKbJhERERHVLfzcXD3MuDJT586dk8v1PD094eDggGbNmuHDDz+U940fPx7ffvutfIyFhYW8iWPq+1q3bi2zptq1aycDVhs3bkRGRgamTp0qX0e8XnBwMCZPnoyUlBTNe4pj4eHh+PzzzzWvu3r1anmf2F60aNEd2VniuNru3bvl/j///IPRo0fDyckJgYGB+PHHH+X9n376qdz38PDAxIkTkZOTU+45UBhw+VZ8eg5W77+h2X9xYBM42jKObFIu/g1c3ASsvk8btLK0AR77ARjwJuBaH+YsPTcdP1z4AQ/88QAmbZ2EHTd3FAta2VnaYXjD4fjm3m/w14N/YVLbSQxaEREREZFR4edmGPRzsxo/KVdXYSFQcGd9llonPjDrBHnuZvjw4ahXrx6+/vpruLq64urVq4iMjJT3vfXWW7L+08WLF/HDDz/IY97e3prnitpXL7zwAt58800ZKBK3zMxMFBQUYMGCBfKxERERcnvkyJHYtWuXfN6GDRtksKxXr154+eWX5bFGjRpV+kt97rnnZABt0qRJ+OqrrzBmzBiZLXX27FmsXLkSYWFhmDFjBho2bIjZs2fDGK3YfQ1ZeQVyO8DdHqM7BRh6SFQZednA6Z+Aqzt0gla2wGM/Ak0GmvW5DEsOw48Xf8TGaxuRmZ95x/0tPFrg4aYPY2jIUDjbOBtkjERERERkACb42Zmfm40DA1fVJX7x5vvA4N6MBawqtlwvPj4e169fx9KlS+UvonDPPfdo7hfBJBF8EtlR3bp1u+P5SUlJ2Lx5M7p27Vrs+IoVKzTb+fn5CAkJkUGqy5cvy4Ls7du3lxlaImBW2utW1COPPIK3335bbnfp0gXr16/H2rVrce3aNVlgXZ2dtW7dOqMMXN1OzcaaQ+Ga/Wn9m8Da0vBRbKqEjDgg8qg2aCW63D3+E9BI+3tkbqnPR28fxbfnvsWeyD133G9pYQkvey+80OEFmWWlm0lJRERERGbCxD4783Oz8WDgygyJ5YFBQUF4/fXXkZiYiAEDBqBBgwaVen7JoJWwZs0aLF68GFeuXJFLB9XUgSt9GTRokGZbZIuJ4up9+vTRBK0E8X4ieGWMvtl3Hbn5qtpWgR72GNWx4ueejEByJPDdA0BqlGpfYQWMXmOWQat8ZT6239yOb89+i7MJZ++438/RD6ObjZadAY/dPoYhwUMYtCIiIiIik8DPzcaDaR5mSGQ7bN26FS1atMDzzz+PgIAA2VVv7969FXq+yJgqSSwDHDt2rMyA+uWXX3Do0CF5TMjOztbr+N3c3Irt29jYlHpM3++rD6nZefjxP23nuRcHNIWlgtknJiMnA/i/AUDiNdW+hQIY9X9A08EwJ5l5mbJ+1f0b7sfMPTPvCFp1qtcJH/f9GK93fR0TWk+Av5O/LLxubakNLhMRkek4E5lyx42IqK7j52bjwYwrfayPFamGxjCOShAZSWIpXV5eHg4cOCCX1Illg1FRUbLoeXlKW+YjXis0NBRffPGF5tiePXcuGSqLWEIouhOWXJJY16z97ybScvLltruDNYa2Zgc1k6EsADY8A6THaI8NXwq0ehDmIiMvQ3YHFEsCk3KK/34qLBQYHDQY41qNQ2uv1jgSc0Q+ztveW+4TERERkZkzwc/O/NxsHBi4qi4RxKlgbSljJJbX9e3bF7NmzcKIESNk4XXxy1nZjKWsrCz5HF3qwu66ynpdsVTxwoULxY5t27YNdYlYHvjN/uuafX83e9jbWBp0TFQJ/7wBXPxLu99vNtBhrFmcwrTcNKy9uBbfnf8OKTnFr7LbW9ljVJNReLLFk2jg3KBY1pWrrSuauutvmTARERERmTAT/uzMz82GxcCVGTp9+rTs6vfoo4/KQuwpKSl47733EBwcrOnyJ5YRfvPNN7LoeZMmTeDl5SXvL6/ulFh2OG/ePHTv3h1///03duzYccfjxOvu3LlTBqXc3d1lAXexdvjhhx/GkiVL0LlzZzRr1gzff/+9zP6qab/++qv89/z587IronpfjEPUAdOnP05G4XZqjtx2trPCtxO6sN6PqTjyNfCftvkAQp8E+r6Kuk4EqcSSwO8vfC+DV7rcbd0xpuUYWcNKBKiEpOwkrLu8Do83f1x2DGTQioiIiIhMFT83G+Zzc2kYuDJDvr6+8iaCVSI4JAqc9+7dWwaLLC1VGUD/+9//cPjwYUybNg0JCQkYN24cVq9eXeZrPvvsswgLC8Nnn32Gjz76CPfeey9+/PHHO7oHLly4EM899xxGjRqFtLQ0rFq1CuPHj8dbb72F2NhYzJ07FwqFQr7eiy++KANsNUl0KCxtXz0ufXZd+3qfNtvqqW5B8HIyzasNZif8ALBZJ0gV0A24f0mFW+iaag2rNefXYPW51UjPK+qcWMTDzkPWrXqk6SNwsHYodt/1lOsITw3H7YzbMnBFRERERGSq+Lm59j83l8WiUHyiJikyMlIWKo+IiCi1y96NGzfkv+VlHlHdVtWfgaM3EvHwyoNy29ICmH1fC9zXxh++rnY1Mk7Sk5RI4Iu+QGa8at81AHj2X8DBvU6e4ryCPJkx9cXpL5CYnVjsPlGrSgSsRjUdJZcHlkVZqJT1rojMda5APE+mpLQi620auFb5cUREavzsTDfu8tm5MnMqfrogqgVrDoVrtrs38sLBawlIycrjuTdmeVnAz09pg1bWTsBTv9XJoFWBsgAbr23E8N+H473D7xULWvk4+GB219nYPGoznmr5VKlBK7GMMCw5TG4zaEVkHC5evCiX8Ts6Osorxq+++uodTVBK2r17t1zCXtqtefPmtTZ2IiIiIl1cKkhUwxLSc7D5jLYT3ZR7GqFTkAcUdXelWd2wZRZw64R2f9RXgHcz1CUi4XZv5F4sPbEUV5KuFLvPzdYNE9tMxGPNH4OtZfFlrXnKPOy4uUMWYPey98Kf1/6UXQRf7fwq/J38a/mrIKKSRFfe/v37yxqV69evl2UBZsyYgczMTCxbtqzME9ahQwccPKjKDlZLTU3F0KFD5Y2IiIjIEBi4IqphvxyNRG6BUm43cLeHjaUCNlZMdjRqZ34FjunUdOv3OtB8GOoSEaj68MiHOBR9qNhxkVE1tuVYjGs1TlOnSgS4LiVdgo3CBg3dGuJS4iX8de0vNHNvJgNXDzV5CN39ujNoRWQkVq5cKQNOGzZsgIeHhzyWn5+PKVOmYPbs2fD3Lz3A7OLickdtSlHfUqlU4oknnqiVsRMRERGVxE/PRDWoQFmIHw9rlwk28XHCqgOqtb5kpBKuARtf1O43GgD0qTsdBEXnv/mH5uPhjQ8XC1pZKazwZIsnsfmhzZjafiosLSyRkJUga1Zl5Wfh+/PfY0/kHvnY1l6t8VqX1xDiGqIJdomAFhEZh82bN2PgwIGaoJUwevRoGYDaunVrpV5LNFoRmVuiaxARERGRITDjiqgG7bsaj4jELLltb22Jjx5ph7yi7CsyQnnZwLpxQG5RJz17D8C/PaDMBxQ2MPXC62svrsXKUyuRlpdW7L6hIUPxYocX4efop6lRdfDWQWy4ugEf9PkAjtaOmN5xOiygXd8a4BxQ618DEVW8vtWECROKHXNzc4Ofn5+8r6Ju376NnTt34s033+SpJyIiIoNh4IqoBv12LFKz3dLfBV5OxWsFkZHZ8S4Qc0a1LQI4XScD2SmAlWkHrUQdq4+OfIQbqcWz/XzsfTC2lWpZYL4yH6/seQWPNH0E3f27o6lHUzza7FG5PFAQSwKJyHRqXIlAVUnu7u5ITCzeMbQ8P//8MwoKCiq0TFAsTRQ3tejo6EqMmIiIiKhsDFwR1ZDU7Dz8c05blD3E04Hn2phd3wsc+ly732820HcmTFlMRgw+OPwBtt/cXuy46BT4fOjzuJ5yHW2928pjIpuqrVdbTddAkVHFrCoi8/bDDz+gY8eOaNq06V0fu3jxYsydO7dWxkVERETmhYErohry9+lo5ORri7J/MEoVICAjJLKqfp+i3Q/oBvSeAVMlsqd+uPADlp9cjsz8TM1xkT01IGgA3ur6FpxtnWXRddHmXrBUWGJ86/EGHDUR6YvIrEpJSSk1E0u37lV5rl27hsOHD8uAVEWIroUTJ04slnHVpUuXSoyaiIiIqHQMXBHVkPXHozTbD3VoAEtL9kIwWlteB1IiVNvWjsCDK4DLW4CoY6rC7NZ2MBW7b+7GkuNLcC3lWrHjAwIH4OlWT+OrM19hV+QujGg0QhO0IqK6pXnz5nfUshKBLBFMEvdVtCi7QqHAY489VqHHi46E4kZERESkb/wkTaX6/fffsXz5cr2fnSVLluDvv/82irO+fft2OSEPDg6Gg4MDWrZsiY8++gh5eXnVfu2bCZk4fENbR2RUh/rVfk2qIRf+Ak7+oN2/dwHg0RBw8gVyM0wmaJWSk4K5B+di2q5pxYJWTtZO6OnfEx/3/RitvFphXs95GBo81KBjJaKaNXToUPk3Ljk5WXNs3bp1MhA1ePDgCr3G2rVr0a9fP1nQnYiIiErHz821gxlXVOYv4NGjRzFlis7yKT0Fru6//34MGzbM4Gf+iy++QGZmJt59910EBgbi0KFDeOedd3D+/HmsWrWqWq/923FtUfbOwe4I8nTUw4hJ79LjgI0vavcbDwI6Fi2Xa9AR8G1j9Cd98/XN+PHCjwhPDUdSTpLmuJWFlSy63j+wP7ztveVSQMHdzt2AoyWi2jB58mR89tlnGDlyJGbPno2oqCjMnDlTHvf399c8bsCAAQgPD8fVq1eLPf/EiRO4cOECXn75ZX7DiIiIysHPzatq5eeDgSuqFlEjJzc3F7a2ptctb8WKFfDy0nZKE1eWlUqlbPstMq9076vsOfnjZPFlgmSktrwGZMartu3dgQeWATmpQHIEUK+V0XYTXHV2FYJdghHqE4rt4dtxMu5ksfs7+HTAW93eQmP3xgYbIxEZtsbVjh07MG3aNBm8cnZ2lvWnFixYUOxxomNgfn5+qcsExd/1UaNG1eKoiYiI6i5+bq4eLhU0U+fOnZNZT56ennKZXLNmzfDhhx/K+8aPH49vv/1WPkbUwBE3cUx9X+vWreVyv3bt2smJ7caNG5GRkYGpU6fK1xGvJ5bfiSu7usVhxTFxZffzzz/XvO7q1avlfWJ70aJFd2Rn6dbg2b17t9z/559/MHr0aDg5OclMKTHBFj799FO5LwrPigl6Tk5OueegtMBU+/bt5X9UqtPG+9ytVNxIUBXEVlgAw9pwmYVRurINOPubdn/YIsDZF7i2C9g5T1vzykiXBf4X/R9G/jESW8O3ao472zjj3R7vYvWQ1QxaEZm5Fi1ayOWCIrP49u3b8oKMjU3xYLz4u3rjxo07nisem52dDTc3t1ocMRERkfHh52bU2OfmymDGlZkaPnw46tWrh6+//hqurq5ymUBkpGp521tvvYW4uDhZ2FW0wha8vb01z7116xZeeOEFmZkkAkXiJibG4sqtuJorHhsRESG3xZXeXbt2yedt2LBBBst69eqlWX7QqFGjSo/9ueeekwG0SZMm4auvvsKYMWNw6tQpnD17FitXrkRYWJjsbtSwYUO5RKIy9u3bJ4NxISEhqKpNZ7S/vO0auMHV3rrKr0U1RNSu+kuna2DTIUCrh4q27wWc/QC3QKM6/afjTsPL3gu2lraISIsoFrAS+jXoh7e6vwUfBx+DjZGIiIiIqC7h5+aa+9xcGQxcVZOIMuYpq1/Mu7qsFdYV7hAWHx+P69evY+nSpfIXUbjnnns094tgkgg+ieyobt26ldpOe/PmzejatesdS+/UxNID8UMsglSXL19G06ZNZVRW/HCLgFlpr1tRjzzyCN5++225LVptr1+/XhaRFa27ra2tNVeRRSHaygSurly5Is+JyBQT2VxV/XnYdFobuBrbI6hKr0M1bNdCIOWmtovgwLnAP68D7R4D/NsDgcV/tg1NWajEr5d/RXpuOo7ePlqslpWrrStmdZmF+0LuY5dAIiIiIjJapvbZmZ+ba+5zc2UxcFVN4hev4/cdYWjHnjoGG8uK1eMRywODgoLw+uuvIzExURZnbdCg4nWYxPNLBq2ENWvWYPHixfIHWSwdVFMHrvRl0KBBmm2RLebj44M+ffpoglaCeD8RvKqo1NRUPPTQQzLYVrIGSGWciUrBzUTVMkFrSwsMaM7sF6Nz6yRwSKdjZv83AQdP1balcdZqy87Plv+t2XZzW7HjAwMH4o1ub8hMLCIiIiIiY2Zqn535ubnmPjdXFmtcmSERXd66dausf/H8888jICAAnTp1wt69eyv0fJExVZJYBjh27FiZAfXLL7/IDn3imCDqZOhTyZobomZHaccq+r6iuPyDDz4oM8lE7S5Hx6p3ANTNthJLBNNzCqr8WlQDCvKBjS8AhUrVvsiu6vos4OQNDHkfqNfSqE67KLz++YnP8cjGR/BX2F+a4262bvio70dY3G8xg1ZERERERDWAn5tr7nNzZTFwZaZERpJYSid+6ERmkljCJ5YNpqen3/W5paVVitcKDQ3FF198IetYiYws0dWoosT7i18EXWJsNU10EXzyySdx7NgxufxRBPGqk/r6l07gamRofdRzsdPTSEkvjvwfEH1KtW1hCQxfCuRnA/m54gfbKE7yzps7kZGXgQJlAbbe2IovTn+Bm2lFyxoB9PTviQ0PbMCQ4CFcGkhEREREVIP4uVn/n5urgksF9bA+VqQaGsM4qvQ8a2v07dsXs2bNwogRI2ThdfHLWZmMJSErK+uObkXqwu66ynpdsVTxwoULxY5t21Z8WVRNEBlnoiui6FTYpk2bar3WqcgURCVnyW1bKwWmD2oKS9FWkIxDRryqtpVa9ymAXzvg9Drgwp/AgysBm9q7alCauMw4bLiyATEZMdhyYwtOxJ7Q3GejsMGMTjPwePPHobDgNQciIiIiMi2m/NmZn5uf19vn5qpg4KqaRPZRRWtLGYvTp0/Lrn6PPvqoLMSekpKC9957D8HBwZouf2IZ4TfffCOLnjdp0kS2wBT3l1d3SgSB5s2bh+7du8vUwR07dtzxOPG6O3fulEEpkZEl1saKtcMPP/wwlixZgs6dO6NZs2b4/vvvERUVVaPnYeHChbIL4cyZM2XGl1jeqNayZUu4uLhU6vW2novRbDet5wQrBq2My855QE6KatuxHtB9mkiTA0L6AJkJBg1aiWy9nIIceDt4o1eDXvjk6CfIyNfWiWvq3hTv934fTdybGGyMRERERETm9NmZn5tr5nNzVRjVZfuLFy/KAIhYK+nr64tXX331juVjpUlISJAV7QMDA+VzW7duLU8slU6cW3ETwaqhQ4fi2Weflal+ou6VpaWlfMz//vc/2b1v2rRpMpg0Z86cck+neA0RDPvss89ksbaIiAj8+OOPpf7Qi+yqUaNGydcVUVvhrbfewhNPPIG5c+fiqaeeksXjX3zxxRr9FoqvV/joo49ksE33dvz48Uq/3vYLtzXbVpYKWFsa1a+XeRPLA499q91vM0pV6yorCXCuB3SbbNCg1bKTy/Dp8U/xweEPMP/Q/GJBqzEtx+DH+35k0IqIiIiIqBbxc3PNfG6uCotC8anJCIh6Rq1atZLZPbNnz5bZNjNmzJBBjGXLlpX73P79+8uglwiKiOCVyPb5+OOP8eWXX2LSpEkVHkNkZKQM4IigS2ld9m7cuCH/LS/ziOq2sn4GwhMy0PcjVRdDsTjw52e7o0uIh0HGSCWI/8StGgrcPKjab9AFeGA5EHsOaDoEsDZ8HbJt4duw5NiSYrWsPO08sbD3QvTw72HQsRFR5eYKxPNkSs5EFmUi62jTwLXKjyMiUuNnZ7pxl/hJZeZURrNUUGRIidaKohOdh4fqA39+fj6mTJkiA1n+/v6lPi8mJga7du3CqlWrMH78eE0g68iRI/jpp58qFbgiqqpt57XZVp2C3Rm0MiZnf9MGrYTWowDX+oC3YZfdJWQlICU3BZFpkZhzYA5Sc1M193X27YwP+3zIjoFERERERGT2jGYtk6hMP3DgQE3QShg9erSsXq9OTStNXl6e/NfVtfhVH7FvJMlkZGaBqwbu9gYdC+nIzQC2va3dD+4FhO0GCgsMfprWX1mPl3e/jOd3PF8saPVM22fw5aAvGbQiIiIiIiIypowrsdRvwoQJxY65ubnBz89P3lcWkVo2ePBguUxQFPUW+yIIJoJdpXW1I9K3pIxcHLmRqNkf1YFLR4zGgWVAalGRf1sXYNQ3gDIfsHU22JAy8zKRnpuOPZF7cDX5qua4m60b3uv9HnrV72WwsRERERERERkbowlciRpXIlBVkug8l5ioDQqUZv369bJDnqiRJYgC46JIuCgAXh6xNFHc1KKjo6s8fjJfOy/GQlmU3NfExwm9mngbekgkpMcBBz7VnoveL6sKsRvQ6bjTspZVeFo4YjNjNcdDvUPxUd+P4Ovoa9DxERERERERGRujCVxVlVgO+PTTT+PKlSuyi53I0Nq2bRumT58ug16PPfZYmc9dvHix7GJHpK9lggOa+/BkGos9HwC56aptZ3/g9lkg+jTg19ZgQzqXcA7HY4+jQGep4tiWYzG943RYK6wNNi4iIqKKEg1ptp6/jaTMXLg52GBwy3oY1sYPlgrRnoaIiKgOB65EkCklJaXUTCzdulclbdq0CevWrcPp06fRpk0beaxfv36IjY3Fyy+/XG7gSnQtnDhxYrGMqy5dupT5eJHJlZubW4mviuqagoIC2NjYaPaz8wqw90qcZt/bxdZAI6NiEq4Bx1Zp97tPBXJSAJf6BjlR+cp8fHLsE3x3/jvNMTtLO8ztMRfDGg4zyJiIiIgqe7H4l2OR+PG/cE2mubDx1C2sPnADK57sAB8Xw3fqJSLjwM/OVFDis3OdKM7evHnzO2pZiUCWCCaJ+8py/vx5+UvRunXrYsfbt2+PW7duITMzs8znuri4yLaL6pvI1iqPnZ2dDFwlJCRU+OuiukN838X3X/wcqP13PRGZuarsGU9HGzzdI8SAIySNnfNUtawE3zZAt+eAe2YDjp61fpJSclIwcevEYkErP0c/fDf0OwatiIjIZKw5FI7vDxUPWqkdC0/C418dknU/iYgEfnY2bwmlfHauExlXQ4cOlQXWk5OTNbWuRCaVQqGQxdfLEhQUJCN5IuOqXbt2muPHjh2Dj48PHBwc9DZGLy8v5OTkyGwuMU4RMCPzIH7GxC+es7Oz/DlQ23NJm201oIUPFEyTN7yoY8C5Ddr9ntNVQSyFfqL9lRGeGo6pO6biRuoNzbFO9Trh434fw8Ou7ExSIiIiY/Lf9QSsOxap2Q/xcsSzfRriTFQKfvjvpjx2LS4DM345iW/Gd4aFBZcNEpk7fnY2XwVlfHauExlXkydPll/YyJEjZUfAVatWYebMmfK4v7+/5nEDBgxA48aNNfvDhg1DYGAgHn74YXz//ffYsWMHXnvtNaxevRrTpk3T6xjFH+H69evLk6+vlDcyDeL7Lb7v4vuvOxnbc1lbYLu+m/6CpFRFhYXAtne0+w37AbHngW1v1fopPRJzBE/+/WSxoNUTzZ/Al4O/ZNCKiIhMRnx6DpbuuKLZb+Hngg9HtcVjXQKx4ME2WPCgdtXDrktx+PlIhIFGSkTGhJ+dzZdNGZ+d60yNKxF0EsEmEbwSQSxRf2rBggV3RO/y84uWAImay87O8nlvvPGGDFiJTKiQkBBZeH3q1Kl6H6c48d7e7BpHQERipry6KH8uAHg4sri2wV3dAdz4V7s/cA5QqATya3fpwh9X/8Ccg3NkbSvB0sISb3R7A480faRWx0FERFRdS7dfQVq26u+Zs60VXru3GeystasOnuwahOPhyfjtuCoj673NFzG0jR9c7TkvIjJ3/OxM+mI0gSuhRYsW2L59e7mP2b179x3HRAbWzz//XIMjI7qTblH2lv4uuLeVL0+TobOtds3X7rd+GPBvX6tDUBYqsezEMnx15ivNMSsLK7k0sH9g/1odCxERUXWFxaXjx8OqpYDCxN4N4el0ZyOad0a0xL9X4hCbloOUrDx8ufcaZt5bdo1aIiIik1wqSGRqduvUt+rf3IeddAzt8hbg1gnVtoWlqhh74nUg+85upTUhtyAXr+19rVjQShRhX9hrIYNWRERkkj7fdQ0FRdXYG3o7ol+z0lcduNhZY9qAJpr9r/ddR0J6Tq2Nk4iI6jYGroiqIDdfiQNX4zX73RvWfrc6KpltpbOsOPRxwD0E2LsI2L+0Rk9VXkEeTsWdwqStk7DlxhbN8XZe7fDT/T9haMOh/FYREZHJiU3Nxp+nojT7Y7oFQVFOrZLHOgcg0ENV7zM7T4m1OplaRERE1cHAFVEViLbPGbkFctvNwRpdQ9ghzqAu/gXEnFFtK6yAPjPFonqg13Sg7aN6f7uErATEZqoK84elhOHZbc/ieOxxzf2tPFth5aCVLMJOREQma82hcOQVqLKtAjwc0DHQvdzHW1sq8L9eISWer6zxcRIRUd1nVDWuiEzFnsvaZYJ9m3rD0pIxYINRKoFd72n3Q58E3INV217aZQv6UlhYiBWnVkBhocCjTR/F1B1TkZGnKtIvjGs5DjM6zZD3ExERGYszkRVfOi+WB+p2B3ygnX+FOkON6tgAi/65hLScfNxOzcE/52Jwf1v/Co2lTQPXCo+PiIjMCz9ZEekhcEUGdOEPIPacalthDfR5BchIAM5tAHLS9P52YuL+RPMn0NGnI8b9Mw4xmTGa+2Z2molXOr/CoBUREZm0/VfjZaF1wdHGssJzHSdbKzzSKUCz/9sxVadBIiKi6mDgiqiSYtOycSE6VbPfh4Erw1EWALvf1+53GAu4BaqKtJ/6Sa+Bq7PxZ3Ey9qTcjkqPwpv730RKjuqKsZXCCh/2+RBjW43V2/sREREZyoYT2tpWw9r4wc7assLPfaRTA8323isiAJat9/EREZF54VJBoko6cDVBs93K3wVepbSFploisqriLqq2LW2AThOAzESgyUDAtzXg7Ku35YFbrm+BEkrEZMTg9X2vI1+ZL+9ztHbEknuWoJtfN728FxERkSFl5ORjy1ltNvGDHepX6vkt/FzkTVzkE0sO/zhxC5P6NKyBkRIRkblgxhVRJR24pu0m2LOxF8+fIWtb/fuxdr/9WOD4d8DtomWDVQxa5SnzNNtZ+VkyQCWWBz7b7lkEOQfhtX9f0wStPOw8sHrIagatiMjoXLx4EYMGDYKjoyN8fX3x6quvIjc3t0LPjYqKwrhx4+Dt7Q17e3u0aNECP/zwQ42PmYyDqEuVladqQOPvaoduIZXvnDxKJ9j115lovY6PiIjMDwNXRJXMvNl3RRu46t6o8pM50pPLW4DY89raVj2mAt5NgbzMKr/k4ejD+OXSL/L7LCw4tADrr6yX+39e+xPz/5sPZaGqQ1I9h3oyaNXco7l+vh4iIj1JSkpC//79ZaBq/fr1WLhwIb788kvMmDHjrs+Njo5G9+7dcevWLfmcv/76C8899xxyclT1jqju23rutmZ7RGh9KBR3L8peklheqHYqIhkxKVwuSEREVcelgkSVEJGYhVtFky8rhQW6BHvw/BmCCCz9u0i7H/o44BECeEys1stGZ0TjStIVzf7g4MGwsrDCF6e+wOenPtccD3QOxFeDv4K/052dkoiIDG3lypVITU3Fhg0b4OGh+juVn5+PKVOmYPbs2fD3L/u/XSIzKyAgAFu2bIGlpaqu0YABA2pt7GRYuflK7L2ibUBzb6t6VXodfzd7tG3gitNF3QO3no/B2O5FHX+JiIgqiRlXRJWwX2eZYGiAGxxtGfs1iOt7gKhjqm0LBRDcG0i9Ve2XfaDxA3iz25ualt+96/fG4ZjDxYJWTdyb4Nuh3zJoRURGa/PmzRg4cKAmaCWMHj0aSqUSW7duLfN5Itj1yy+/yACXOmhF5uV0ZDIyc1XLBL2dbdGugVuVX+veVr7Flh8SERFVFQNXRJVsD63Wg/WtDEe3tlXLB4FrO4Fj3+rlpUWHQEEsD/zk+Cf4+uzXmvvaeLXBqntXwcuetc2IyLjrWzVvXnwZs5ubG/z8/OR9ZTl+/LhcXmhtbY2+ffvKf0V9rNdeew15edr6f1R3HbqeqNke2MKnSssES8vWOhSWiOTMitVYIyIiKonpIkQVJAIZB3QDV6xvZRgRR4Dre7X7fV4GXOpXq7aVsCN8B25l3MJTLZ6S+4uPLcbqc6s193es1xGfD/hcdhEkIjL2GlciUFWSu7s7EhO1gYmSYmJUWTETJ07EpEmTMGfOHBw+fBhvv/02FAoF3nvvvXKztcRNt1YWmRZlYSEOX9d2Th7UsmrLBNUa+zijobcjwuIyZHfB3ZfiMLJ95ToUEhERCQxcEVXQpdtpSMxUXXG2s1agfWDV0+dJT9lWTYcAPi0BsbTPvnrfD3sre1njSvj46Mf49rw2g6tTvU4yaOVg7VCt9yAiMmZiKaEglhl+/LHqv7X33HMP0tLSsGjRIhnAEl0GS7N48WLMnTu3VsdL+nU9PgNJRfMce2tL9GhU/ezigS3q4cu4MLktamcxcEVERFXBpYJEFXTgqvYqZOdgD9hasf5HrYs5C1zerN23cQQOLlMVa6+iAqWqlkeP+j3wbJtnsejoomJBq86+nRm0IiKTIjKrUlJURbFLZmLp1r0q7XmC6EioSxRnF10Fr169WuZzRcfCiIgIzU1kapFpORmRXKxrsp119ec5vZtog1//XonXdO0lIiKqDGZcEVXQAZ3C7N0bevK8GcKBT7XbIX2BJoMBF39VxlUVXEq8hJ8v/YwpoVPgaeeJL858gTXn12ju7+LbBcsGLJPZWEREpkLUtypZy0oEssTyvZK1r3S1bNmy3NfNzlZ11S2Ni4uLvFHdCFz11FMdT9WFPgVy8pWIS8uR2evNfflzQkRElcOMK6IKyC9Q4r+wRL1P6KgSUqKAs79p97s9B7R7DAjpU6nTKK72hqWoli2IpX92VnawgAU+PfFpsaBVV9+uDFoRkUkaOnQotm/fjuRkbSBi3bp1sk7V4MGDy3xeUFAQ2rRpI5+ra9u2bXKJ4N0CW2S6cvOVOH9LW6Osl57mOSJrq6vOxb5/L2svAhIREVUUA1dEFXAmKgVpOfly29nOCq3ru/K81bb/VgJK1fcAti5AWtVaa19Nvop/rv+DlJwUBDgHYGanmVh/ZT3+78z/aR7T1a8rPhvwGTOtiMgkTZ48Gc7Ozhg5ciS2bt2KVatWYebMmfK4v79/sSWAjRs3LvbcBQsW4M8//8T06dNlwGrhwoWyvpVYCujoyOYUddWFmFTkFqhqnHk726JpPSe9vXYTb+1rbToTjTORdy5jJSIiKg8DV0QVcDBMW9+qW0NPWFajPTRVQXYqcEzb4Q9dnq10ppWaslCJjLwM+a/ww4UfZLaVWgefDvisP4NWRGS6RK2qHTt2wMrKSgavZs2aJTsFigLqugoKCpCfX3RBoMjw4cOxdu1amXV1//3348svv5RF1+fNm1fLXwXVplM6ywRFtpVFFZfgl0a3mc25WynIKwqQERERVRRrXBFVwOHr2mWCjX30dxWSKuj4d0BO0RIGZ3+g32uApXWVTl8zj2byJvx2+Td8cOQDzX2tPVvLQuysaUVEpq5FixZ3LPkraffu3aUef/TRR+WNzMepSP3Xt1IL9HCAm701krPykFdQiMu309DKn5nrRERUccy4IrqLAmUhjt5I0uzf08yb56w2FeSplgmqtX8KyE6pVidBYVPYJsw9qG3d3tS9KVYOWgknGwYmiYjIfGTnFeBqbLpmv1vDsjtPVoXI3mrlry3Ifk6nlhYREVFFMHBFdBcXolORrq5vZWuFjkH6ndDRXZz/A0iJUG3bOAPWdsCWWVXqJFigLMDC/xZixckVeGPfGyiEKvgV7BKMLwZ9AVdbXgEmIiLzIjr9KYuuBXk52aKBu4Pe30M3w0osFyQiIqoMLhUkuov/dJYJdgx2Z32r2iSyqg5o60+h/Rig80Tg6o4qvVxWfpa8/Xr5VxQUFshj9Z3q46vBX8HLnp0iiYjI/Oh2E2zpp82M0qfW9bWveyE6TWazs14oERFVFDOuiO7i8HVtYXZ/Nzuer9p0418g+pR2v+szgJ0r0PqhSr9UYWEhotKjsCN8B/KUefKYt723DFr5Ovrqc9REREQm43y0TuBKZ0mfPgV6OMLR1lJuZ+UVICxOuzSRiIjobhi4IrpLsOOITn2rgc3r8XzVpgPLtNuNBgDuwVV6mXxlPt7c/ybGbB6DtLw0eczZ2lnWtApwDtDXaImIiEyKyHy6FKP6uyi0qqGMK5FdpZvNxTpXRERUGQxcEZXjWlw6EjNy5batlQK9mrAwe62JvQhc+Ue7P+CtKtW1ElJzU3E4+rBcJijYKGzw2YDPZEF2IiIic3U9PkNmQAmONpYI9NR/fSu11jp1rs6yzhUREVUCA1dEFaxv1SHQHTZW/JWpNYc+124H9wb821fpZRKyEvD89ucRkxkj9xUWCnzY90N0rNdRXyMlIiIySeejtYXSW/i5QFHFC0SVLdAu6mopq9kdmIiIzAc/hROV47BO4KptA3acqzWZicDpddr9blOq9DJXk69i1J+jcDbhrObYW93ewoDAAfoYJRERkUmrjcLsao28HWX2upCWk4+oJFUWNBER0d0wcEVUTn2rQ9e0hdl7N2HXuVpzdBVQtKxP1rVqem+Vvn9fnf4KCdna7+HU0Kl4uOnD+hwpERGRSRJ/J0WHP92Mq5pkZalAYx8nzf6l29r3JiIiKg8DV0Rl2HjqFm6n5chtK4UFOgS581zVBmUBcGiFdr/LM4BC1YmoMladW4W/r/+t2X+02aN4pu0z+holERGRSUvIyEVipqqOp8ICaFJPG1SqKc3qOWu2dYvCExERlceq3HuJzNiZKG3dhzYNXOFgw1+XGpebAVzdCWTGqfat7IHQJyv9Mp8e/xRfnflKs9+7fm/M6jILFjVYu4OIiMiUXNbJeAr2Esv4Kn+RqLKa+TqX+v5ERETl4SdxojKkZuVrtruEePA81YYtrwPX92j3Q58A7N0q9NTE7ETZNTAuMw6rzq7SHG/u0RyL+i6ClYL/uSMiIlK7fDtds93URxtQqqgzkdoLfLoX+iqacXUjIQPZeQWws675gBkREZk2fpIjKqPuw+Eb2sLsXRm4qh0+LYHj3xZfJlhBm8I2YV/UPpyPP4/8QlXQ0cfBB8v6L4ODdc219yYiIjJFV2K1GU9Na2GZoODpZAsvJxvEp+dCWQhcjU1H6/psfkNEROVjjSuiUuy8FIvr8RlyW6wu6xjEjKtaEXdBu93wHsCneYWf2j+gP8KSw5Ccmyz3HawcsHzActRzrFcTIyUiIjJZysJCXNHNuNLJhKppuu/F5YJERFQRDFwRleKqzmROpLW72lvzPNW0lFvAyZ+0+12frfBT85X5mHNwDmIyY+S+pYUlPu73MZp5NKuJkRIREZm0qKQsZOUVyG07awUauNdeZrLucsGLLNBOREQ1vVTwwoULiI6ORlZWFjw9PdG0aVN4eDAzhUxfYoaqy47Qkd0Ea8e2N4GCbNW2ezDQZHCFl3U+v+N5HIo+pDk2u+ts9Krfq6ZGSkREZNJ0M50aeTvBUrQVrCUs0E5ERDUauFIqlfjrr7/w7bffYufOnUhNTZUfGtVEx64WLVrgkUcewfjx4xEUFFTpAREZgxM3VcvNhNCAihUHp2pQFgA39hevbaWoWLHW785/hwO3Dmj2H2/+OEY3G81vBxERURkuxxpmmaA6UCbiZKLGVUJGLuLTc+DlZFurYyAiojq6VHDt2rVo1qwZnnzySVhbW2Pu3LkyeHXmzBlcvnwZhw8fxs8//4z7778f69evR5MmTTBp0iTcunWrZr8CIj3LK1Di2E1tYfb2ge48xzXt0mYgXbXMD9aOQOiTFXraidgTWHJ8iWa/q19XvNr51ZoaJRGRXhUUFGDjxo144YUX0LVrVwQGBsLb2xvNmzfHAw88gEWLFuH69es861SjGVe1HbgSXQSDPR01+6JAOxERkV4CVyJQ9cYbbyA2NhY//fSTnGT17dsXrVq1QuPGjdGpUyc8/PDDeP/993Hq1CmcOHFCZmh99913FX0LIqNwKSYNBUrVtoudFRp6aSdXVEMOfKrdbvcYYH/3LLfo9GhM3zVd1rcSApwDsKjPIlgp2CyViIxbenq6nFfVr19fzp327duHli1b4tFHH8Wzzz6LgQMHyqCWCFyJC4Fif/9+naxUompeoLtR1IBGaOJTOx0FdTXSec9rcQxcERFR+awqU89KLAWsKBHQ+vrrr4stJSQyBScidJYJBrpDUYt1H8xS/FUg4j/tfpdJd31KZl4mXtj1AhKzVZlx9lb2+Kz/Z3Cz47JOIjJ+ISEhaN26NT766COMHDkSzs5lZ7wcP35cZr0PHz4c8+fPx5QpU2p1rFT3RCRmIl+s0wPgbGsFH+faX6Ynlgtuw225zYwrIiLSW+CqMkErfTyPyFBO3EzSbLdnfauad2yVdjuwB+DTotyHi2D4OwfewcXEi5pjMzrMQCO3RjU5SiIivfnjjz/Qo0ePCj22Q4cO8vb222/j5s2b/C5QtYXFabOtGno7GmSu3tjbqdTxEBERlabKa2oyMzOxY8cOREREIDu7qBNYEfEH8KWXXqrqSxMZ1OEw3fpWzOCpUXlZwInvtfud/3fXp6w5vwZbbmzR7L/Q/gWMbs5i7ERkOioatNIlsrJENjtRdV2L1y7Na6gTQKpNwV4OmgLtiZm5xbo5ExER6SVwtWfPHowaNQqJidoP+LoYuCJTlZSRi8jkLM0+OwrWMBG0yi5amungBbQYXu7Dj8YcxeJjizX7Q4KHYGKbiczsJKI6QVwULHkxUPDw8DDIeMgMMq4MVMfT1soSAe4OCE/M1NS56tvM2yBjISKiOlScXdfzzz+Ptm3byo6COTk5sgi77k0UFCUyRScjk4ulz7s52Bh0PHXe0W+02x3GAlZl19mIzYzFK3teQUGh6r8vnnaeCHIJqo1REhHVmNTUVEyePBmenp4yq0p0FSx5I9IXZWEhrusUZhe1pgxFt0A761wREZHeM67Cw8OxZMkSpqxTnXPipjZw1T7A3aBjqfOiTwGx57X7HceX+dC8gjy8vPtlJGQnyH1Ha0c8H/o8FBYKZlsRkUl7+umnsXPnTkycOBFNmzaFjQ0vmFDNiUnJRlae6gKQjZUC/m72BjvdImi282Ks3GZnQSIi0nvgqmfPnrh06ZJsz0xUZwuzs75VzTr8lXa7yb2Ae9nZUx8f+xgn405q9hf0XIABQQNQoGR2JxGZtu3bt2P58uV48sknDT0UMgO6AaIQT0dY6rlz8pnIlAo/trFOxhUDV0REpPfA1RdffIFHHnlEXhUcMGAA3NzuLGDNegxkapTKQpyM0GZcsb5VDcpOAU79VKGi7JvCNuGHCz9o9tt6tUWgS6DctlRY1uQoiYhqnJ+fH1xdXXmmqVboLhMUJREMSQTORNisEEB8ei7i03Pg5VR2yQAiIjJfVapxJQJVQUFBePbZZ9GkSRPWY6A6ISw+HWnZ+XLbzlqB5r7Ohh5S3XXqZ0CZp9p2DQQal569eS35GuYenKvZD/UORUO3hrCQU10iItM3Z84cvPfee0hO1l440YeLFy9i0KBBcHR0hK+vL1599VXk5t69c1twcLBcgl3yVlrReDI914oVZjdcfSvB3sYSDdy1SxXPRlU8W4uIiMxLlTKuxowZg3379uHll1/Waz0GMcmaNm0aDhw4IAuUjh07FvPnz6/Q60dFRWH27Nn4+++/kZ6eLideb775JlPvqUr1rdo2cIOVZZXiunQ3SiVw9GvtfqfxQCmZU1n5WbIYu/hXqOdQD0v7L4WrjSszrYioznjsscdw+vRpBAYGIjQ09I4sdhE0+uOPPyr1mklJSejfv7+8uLh+/Xo5R5oxY4bsWrhs2bK7Pv/hhx+WczxdtrbMhKkrF+mMJeNKXecqIilLE7jq18zH0EMiIqK6ErjasWOHXC741FNP6W0g1ZlkRUdHo3v37mjWrBm+/PJLuLi44Ny5c7LjIVFFndBZJti6vgtPXE3Z+CIQd1G1rbAG2o8t9WHv/fceriZfldtWFlb4qO9H8LBjS3giqls++eQTvP/++6hXr57sypyWllbt11y5cqXsVrhhwwZN6Yb8/HxMmTJFXuTz9/cv9/liLN26dav2OMi4JGbkIjlTle0sSlsFexpB4MrHCbsvx8nts1Gphh4OERHVpcBV/fr19V6PoTqTLJH+HhAQgC1btsDSUpW5IWpvEVU146pzEAMkNSI/F7i+V7vfcgTgdGer943XNmLD1Q2a/Rc7vIjErETMOTAHr3Z+FQ7WDjUzPiKiWiaCVs8//zyWLl0KhUI/mb6bN2+WDXR0642OHj0akydPxtatWzF+fNldXKnuCtMpzB7g7iC7ChpaQy9t8OxiDANXRERUuir9xXr33XdlPQaRJaUvZU2ylEqlnGSVRQS7fvnlFxngUgetiCorIycfl3QmTB2C3HkSa0J2MpASqd3vdGdR9usp1zHv0DzNfu/6vTG21Vh42nuioWtDBq2IqE4RdadGjhypt6CVuvRC8+bNix0TSxBFIXhx39388MMPcmmgk5MThg0bhjNnzuhtbGQ413QKs4cYwTJBQTfrKzwxU87HiIiI9JJxJSY0N2/elAXa9VWPQUykJkyYUOlJ1vHjx+Wkz9raGn379pX1sTw9PTFu3DhZH0scJ7qb05EpUBYWZRS62aOeix1PWk049i1QWDQp9W4BBPUodnd2fnaxulY+Dj5Y0GsBFBYKhPqEyhsRUV2rcSXqc+ozU1xcWCyt47O7uzsSExPLfe6IESPQtWtXWXMrLCwMCxYsQK9evXDixAk0bNiw3AuJ4qZbxoGMN+OqkYELs6u52FvD09EGCRm5KCwUWVdp6MiLh0REpI/AlSh+LmpRqemjHkNVJ1kxMTHy34kTJ2LSpEmyO8/hw4fx9ttvy6uXIjOsLJxkkdqJCG32YGjgnT+HpAe3TgH7P9Hud5ogotzFHvLhkQ9xOemy3La0sMRHfT6Shdh/v/o7hjcczqLsRFTn9OzZUzaTEYEekXle2lzooYceqrXxfPrpp5rt3r17Y/DgwTJ7a9GiRVi+fHmZz1u8eDHmztV2gSXjc10n48oYCrOrhXg5ysCVerkgA1dERKSXwNWuXbtgLMRSQkFM9j7++GO5fc8998hgmphkiQCWvb221a4uTrKotPpW7QMYuKoRt44BuUWTZit7oO3oYndvubEF6y6v0+xPbDMRHep1wIGoA9gdsRvtfdojyCWIP7REVKeIDsqCyGT/6aef7rhfZLGLou2VIS76paSklHqRULckQ0WIzHeRcXXs2LFyHyca6oiLiGoiENelS5dKvRfVnKzcAsSkZGv2jaEwu27g6mi46gLihWjWuSIiIj0FrmpCVSdZ4nmC6EioS6Tci/T2q1evok2bNqU+l5MsEgoLC4sHrgJZ36pGXP9Xu91qJGCvDRBGp0fj3QPvava97LzgbOMst3vU74GmHk3hZe/FH1giqnOuX7+u99cUGVIlyyyIOZYIJpWsfaUvoqOzuJFxuhqbjqKKCHB3sJZL9IwpcKV2Ibr6qziIiKjusapqcfa7EZlOtTHJatmyZbmvm52tvbpUEidZJEQmZSE+PUduiwY7rfw58da7G/uB839q9zuM02wWKAvw4q4XkZanmqx62nni434fw9FaO5Fl0IqI6ipRL1Tfhg4dioULFyI5OVmz9HDdunWyhIJY+lcZt27dwr59+zBmzBi9j5Nqz+Xb2oBQoIdxdeYN1u0sGJ0KpbIQCkXxUgJERGTeqhS4+uQTnTo1OnWvRCq7WJYnOtFUNnBV1UmWmPCJjKrt27dj6tSpmuPbtm2TY7lbYIvo+E1tfauWfi6ws2Z3Sr0qyAc2v6otyu7VDAjsprl71blVuJB4QbM/v9d8uUSQiMgciCWCdyMKpVfG5MmT8dlnn8luhbNnz0ZUVBRmzpwpj/v7+xfLTg8PD5fZ6cLatWvx119/yU6C4nGiOLuoFSq6Nr/88stV+OrIGANXQUa0TFDwd7WHjaUCuQVKZOQWyAuKgZ7GFVwjIiITDFyJ5Xsl5efnY8eOHXj11VexZs2aSr9mVSdZglgS+MADD2D69Om47777cOTIEVnfSozF0dG4/jiT8TkVoV2i2iGocrU/qCIKgWydZcAdx2mKsh+6dQifn/hcc9cTzZ9Ar/q9eFqJyGwEBwfLOlblqUqNKzEnmzZtmpxXOTs7y/pTYr5U8nXF/E0tJCREZliJ+ZT6QqIoxSAy7cV9ZLqMOePKUmEhA1ViOaNwPjqVgSsiIqqZGldWVla49957ZcDpueeew/79+2tlkiUMHz5cXiWcN28eVqxYIQuJis42s2bN0svXRubTUbA9OwrqX+QRICVCtW1pA7R9TG6mZKfIJYL5RZlYjd0a46WOL9XAAIiIjNeGDRtKvUD4zz//4NChQ3j//fer9LotWrSQ2ejl2b17d7H9bt26GVUDHrrTmcg768G2aeB611N1+bYqKFSRwFVp71Ebda7UgStRoH1Ia99aHwMREZlRcfYGDRrg5MmTtTbJUnv00UfljagycvILik3Q2gewMLte5aQB2+do91sMBxw95eYHRz5AZn6m3LZWWOP93u/DzspOv+9PRGTkRMZ4acaPHy+byOzZs4fzG6qW9Jx8RCVnGW3GlRCis3yRnQWJiKgkBfTcGeeDDz5Ao0aN9PmyRDXm/K1U5CtVfXY8HW0Q4GHPs61PZ9apMq5KFGXfEb4DG8M2ag6LTKtmHs147omIdIhaUz/99BPPCVXLFZ1lgl5ONnC0NZqm4qUXaI9hZ0EiIiquSn+5xDK+kvUY8vLykJubCwcHB6xfv74qL0tU607cTC62TPBudUaokgrygEKlatujIRDcG/FZ8ZhzUJuF1cO/B55s8SRPLRFRCQcOHICdHTNRSZ/1rYyz9qtuxtXNxEykZefB2c7aoGMiIiITD1yJzjIlP+CLiZVYJii6A3p4sMA1mYYTEbqBKy4T1KvCQuDYt9r9DmNRaGGBOQfmIDlHdd7tLO0wv+d8KCz0mvxJRGQyXnjhhTuOiQuBFy5cwL59+/DKK68YZFxUd1SmvpWhONlZob6bvWZJ46WYNHQK5ucJIiKqRuBqzhydmjVEJuzQtXjNdvsAN4OOpc458BkQe061rbACQp/EH9f+wJ7IPZqHjG42Gt4O3oYbIxGRgf35559lXgxcvny5bFRDpK+MqyAjDVwJLfycNYErUeeKgSsiIqpW4Kphw4ayC067du3uuO/s2bMYMWIEwsLCqvLSRLUmNi0bcem5mv22DFzp16W/tdvNhiLGQokPDn+gOTQsZBhmdp6p5zclIjItN27cMPQQyJyWCnoab+Cqua8Ltl+IldsXWOeKiIh0KKo6ycrJySn1vszMTERERFTlZYlq1Umd+lbNfZ3hZITFSk1WdioQfUqzW9hhHN7a/xbS81TLFdxs3TCryywDDpCIyDi8++67uHXrVqn3RUdHy/uJqiolKw+3U7Vz9gB3Iw5c+Tlrti8zcEVERFUJXGVnZyMxMREJCQlyPzU1Ve7r3sTE6/fff4e/v39FX5bIYA5cU/0sC6HMttKvY6uAvEzVtmsgfslPwKHoQ5q7Gzg3wOm403p+UyIi0zN37lxERkaWep+YV4n7ifTRUdDH2Rb2NpZGezKb1dMGri7dTkOhqJVJRERUmaWCH3zwgeaqn6jFcO+995b5WNbAIlOw53JcsY6CpCdXtgN7P9bsRrQZiY+PL9bsP9T4IYxvPR4BzgE85URk9sSH87I62oqMKzc3/n2iqhMBILUgI14mKAR7OcLa0gJ5BYVIy85HTGo2/FztDT0sIiIypcDVyJEjERwcLCdYEyZMwJtvvolGjRoVe4yNjQ1atGiB0NDQmhgrkd4UKAsRnaIqACqwo6AeFSqBnBTVebZQ4M3sK8jKV51rf0d/WdfKycZJn+9IRGRS1q5dK2+CCFqJbs0lA1Qi0/3o0aPo2bOngUZJdcGVYh0FHWHMrC0VaOTthItFywRFZ0EGroiIqFKBK1GIXV2MXUyy7r//fnh6evIskskWKs3OU8ptZ1srNPZmIEV/J3ezZvOHhh1xPOFcsYLsx2OPo0+DPvp7PyIiE5Obm4u0NNWHc3FBMCMjA5aWlndcDBw7dixeffVVA42S6lxhdiPuKKjWtJ6zJnAlxt6vmY+hh0REREagStWox40bp/+RENWiA1e19a3aBbhBoSh9mQZV0vk/gVM/y80IK0t8hkTNXY83f1xmWt1MvcnTSkRmTcyj1HOpe+65BytWrEDz5s0NPSyq44ErY18qKDTzdQaKertcitFmixERkXmrchu1vXv34ssvv8Tly5dlOntJp0+z8DIZr71XVO2WBda30pOMBGDvh0BeBkQ51bn1/JCtzNMsEZzeYTqsFdbIyMvQ1zsSEZm8Xbt2GXoIVEclpOcgPj1Xbovrcw3c7U0i46q0oBsREZm3KgWu/vnnH9x3330YOHCgrL8wdOhQZGVlYf/+/WjQoAH69u2r/5ES6VFEom59Kxa+rTbR+cfRE7BQ/SdlvZMj/rPRNi3t7NcZNpY2sFJYwc2S55uISJdSqcTOnTtLvRgoyjO89NJLPGFUaZd16lsFeTrC1sp4OwqW1lnwSmyarElqyax4IiKzV6XA1TvvvIPp06fLToPW1taYN28eOnTogPDwcNltsH///mZ/Ysl4pWTlISxem/UTGuBu0PGYvFsngQt/Ak2HAtEncNvSEos8tee0U71OCHAKQEFhAayqnuRJRFQnxcTEyAt+V65ckUEqUfNK0O00yMAVVYUI/Kg18TGNWp4iK8zBxhKZuQWyFmlEYqbsNkhEROZNmxJRCRcuXJBZVgqFQk6sRFFRISgoCHPmzMH8+fP1PU4ivTl2Q1t3KdjTAR6ONjy71ZF0HVBYAafWyiWC8z3dka5Q/afF084TS/svxbPtnoWtpS3PMxFRCTNmzICXlxciIiJk0Oq///7DjRs35EXBJk2ayCwsoqrQXWqnuwTPmImao010xnqJywWJiKiqgSs7OzuZ1i6CVn5+frh27ZrmPmdnZzn5IjJW+69pC7O3D2S2VbW1ehDoNQM4+xv+cXTAbkdt8dfe9XvDxcal+u9BRFRHiZqhL7/8spxPCSJ4FRgYiNmzZ2PMmDGYOnWqoYdIJuqyTnHzpqLouYloVk+bHXa5qMMgERGZtyoFrtq1a4dLly7J7QEDBmDBggX466+/ZO2rN998E23atNH3OIlqJHWe9a305MKfSMpNxXs6SwR71e+FKaFT9PUORER1UkpKCry9vWUWu4uLC2Jjtc1Dunfvjn379hl0fGSaRAD0ss58p6lOMMjY6WaHXWTGFRERVTVwJepbqWsvLFy4UGZZjRgxQi4fTEhIwOeff86TS0Y7kTsdmaLZDw1gofBqubIN2PQKcORrfODpjkRLVeFXN1s3zO85H35OqgwCIiIqXUhICKKjo+V2q1atsGbNGs19GzZsgIeHB08dVVpceg6SM1WdfUVx8xATqhPVTCc7jBlXREQkVKlS8rBhwzTb9evXx7Fjx3D16lXZWbB58+awsWHNIDJO1+LSNRM5WysFmvtyGVu12DgBFgociDuJTX4+msNDQ4bK4BUREd19TrV161aMHj1aZq0/8MAD8PHxkc1vROF20QiHqDrLBEXQyhQ6CpbWWfB6fAZy8gtMavxERGQEgSvRprlr16746KOPMHjwYHlMZF+JAqJExm7P5TjNdpv6rrCxqlLSIakFdUf2pb8wz0u7RLCha0O427pDYcFzS0R0N++//75mW2SuHzhwQGZaiYuBgwYNkseIqleY3XSWCQrezrZwc7CWFxrzlYUyeMULjURE5s2qKoXZo6KiZC0GIlNzIz5Ts836VtWUnQJY2uLLq78h0tFaHrKzsMLHfT9GI7dGxVq5ExFRKf8Zzc7G8uXL5YXA1q1by2OdOnWSNyJ91fNs4mM6hdkFMX8Qda4OX1d1gb4Uk8bAFRGRmatS9Omhhx7CL7/8ov/RENWwExFJmm12FKymQytw7ZdHscpBG/+e3G4yGrs3ZtCKiKiCFwPF8kBRH5RIn0Swp7SaUaa4XFA3e4yIiMxTlWpc9ezZU7Zpvv/++2Vthnr16t3xQVUEt4iMSVZuAc5FpWr2mXFVPcqgnnj3+s/IV6h+9xsqHDG2zYRqvioRkXkJDQ3F+fPn0bdvX0MPhepQI5ort9NNdqmg0FQn2HZJp14XERGZpyoFrp5++mn5r+iC8/fff99xvwhiFRQUVH90RHp0KiIZhUXbvi528HO15/mtitiLgMISv6dexHFFvubw3M6vwVqhWjJIREQVs3TpUjz55JPw9vaWFwMdHBx46qhaolOykZaj+vtsY6lAkKfpdBRUY8YVERFVO3B1/fr1qjyNyKBORSZrtpltVUUF+cC+xUho0AEfX/pKc3hAgQ1Cmz9Y/W8SEZGZ6d+/P3Jzc/Hoo4/KfRG40s1iF9spKSkGHCGZGt2ldQ29HWFtqTDpwNXNxExk5ubDwaZKH1uIiKgOqNJfADGJ8vPzk62aS8rPz8etW7f0MTYivfr3Srxmm4GrKlJYAj2n4+PTy5CqzJWHHAqUeLP1RP18k4iIzMzLL7/MuoCkV7rLBJvoBIBMiauDtcyOj0nN1nxN7QLcDD0sIiIypcBVSEgIDh48iC5dutxx36lTp+RxLhUkYxKVnIUjN1TdaQQWZq+CwkIRtcZhZTo23vpXc3hOSia82o3RzzeKiMjMzJkzp0Ze9+LFi5g2bRoOHDgAZ2dnjB07FvPnz4eNjU2FX2PJkiV46aWXcN999+Gvv/6qkXGS/l3SybhqZoL1rXTrXKkDVzsu3IaiKBOxTQNXA4+MiIhqm6KqRR/LkpOTA1tb2+qMiUjvRP3wnHyl3LZUWKC1Pyc9lSJ+54/8H/LO/Y6F/y3UHO6emYUhDe8HbE13YkxEZOilgiLIVJrLly/L+ysrKSlJswRx/fr1WLhwIb788kvMmDGjwq8RExODuXPnwsfHp9LvT4Z1RSdwZaoZVyWDbuEJmQYdCxERmUjGlZhUia43art370ZkZGSxx2RnZ2Pt2rVo2LChfkdJVA35BUr88N9NzX4LP2fY21jynFaGMh/ITMSPSadwLeWaPGRZWIg3EpJgMWI8zyURURWJ+VRqqrbjrS5xfO/evZV+zZUrV8rnbtiwAR4eHppSDlOmTJFdof39/e/6Gq+++ipGjBiB8PDwSr8/GY5SWYgrsbodBU03cKU79vBEBq6IiMxZhQNXP//8s7zypq5xNWvWrFIf5+bmhtWrV+tvhETVdPl2Oracidbstw9w5zmtLEtrxHYej883DNccmpCSiiDP5oB/B55PIqJq0C3Grkss86tKxtPmzZsxcOBATdBKGD16NCZPnoytW7di/PjyLzjs27cPv//+Oy5duoTHH3+80u9Phi2NkJmr6uxta6VAoIfpdqls5qtToJ0ZV0REZq3Cgavp06fLiY5YJigyqkTqefv27Ys9RtRN8PX1ZZFRMipeTjZQ6qxuZWH2KnQSLMjFR0cXIasgSx7yy8/HpORUYMg4WfeKiIgq7r333pM3ddDqnnvugUKhuKP0gjpLqrJElvyECRPuuLAoGuuUtSxRTdQonTp1Kt544w35eDLdjoKNfZxkeQRTJcYvRi+mcImZuUjLzoOz3Z2NoYiIqO6rcODK1dVV3oTr16/LNPPSugoSGRs3Bxt5BVKNhdkrKe4ijmx/HVsKbmgOvZaQBHtLW6DtI/r7RhERmYkePXrIboLiYuC7774rs5oaNGhwx8XAFi1aYPhwbaZrZWpciUBVSe7u7khM1DYqKc3y5cuRkZEhi7JXhliaqLvkMTpam+lMtZtlXheWCQoONlaop9NZ8GZiJlqxRikRkVmqUldBQVyxa9Omjeaq4KJFi3DhwgWZmn63FHSi2nQqIklTmN3NwRrBnqabNm8IeXYuWGidAahWHqBnZhb6Z2YBbR8F7Lnskoiosvr27Stv6oyriRMnon79+gY/kbGxsXj77bfx3XffVar7oLB48WJNSQkyjowrUw9cCUGeDprAlSjQzsAVEZF5qlJXwUmTJmHNmjWa/ddee01OVkQw65lnnpFX64iMxSfbr2i22we4cSlrZdz8D2uv/42r2XGaguyzREF2sdNhnL6/VUREZuedd965I2h148YNbN++/a7ZUWURmVUpKSmlZmLp1r0qSQSt2rZti969eyM5OVnexHJFcVNvl0V0LIyIiNDcDh8+XKWxkz4DV6bf8Ve3RhcLtBMRma8qBa5OnjwpJzWCmMR8++23+OCDD3D06FHMmTMHK1as0Pc4iapBW+CKywQrc9oKEXd4JZaf+1pz6OmUVASLDy6ejYGgHvypJCKqJrFkUNQRVROdAJs1a4bBgwejSZMmOHbsWKVfs3nz5nfUshKBLLF8T9xXFvEc0cVQBL7Ut/379+Off/6R2yKYVhYXFxe53FF9Y32s2legLMTVOtJRUC3I01GzHZ6QYdCxEBGRiQWu0tLSNPWu/vvvP1nT4LHHHpP7vXr1QlhYmH5HSVQNUcmqFHOBhdkrQVmAj+2VyChQnT8fJVQF2YUOY1mUnYhID0SgqlOnTpr92bNnY9iwYTh9+jS6dOmCN998s9KvOXToUBlkEllSauvWrZMF4EVArCxLlizBrl27it3atWuHbt26yW0xHjJeogaUujSCg40l6rvZw9QF6WRcia9P1IUjIiLzU6UaV+JK2qFDh9CnTx/ZXbBly5aaK2siDd3BgTWEyDjEpeXImgiCaH7XLuDOYrVUuqNxJ7Ep/rhmf1ZcHBzEhFFhBbR7gqeNiEgPRBZUYGCg3L527RouXbqE77//Hq1bt8a0adMwblzll2VPnjwZn332GUaOHCkDYVFRUZg5c6Y8LprrqA0YMADh4eG4evWq3A8NDb3jtUSRdycnJ/Tr169aXyfV7jLBJj5OUJhwR0G1+u72EF+G6A6dlp2P5Mw8Qw+JiIhMJePqf//7n7wC2LlzZyxdulTWtVITAS3RBYfIGOy4EKPZbuztBBe2Ua6QfGU+Fh7QFtntaOmCgaIgu9BsGODkrffvFRGRORIZ7KIourBt2zZZg6pjx45y39bWFllZ2q64FSWW9e3YsQNWVlYyeDVr1ixZAF4UUNdVUFBQbt0qMi2XY+pWYXbB2lJRLHOMda6IiMxTlTKuxARIXLE7cuQIpkyZUqyLoMi4EpMjImNwRafWQyizrSrs14s/40raDbltAQu8GRWuKsgudGRRdiIifRHZ66Io+u3bt2WHZhFoUhPZV+psrMoSFxHLq0kl7N69+66vU5HHkHG4XMfqW6kFejoiIkkVwGWdKyIi81SlwJUwduxYeStp5cqV1R0Tkd5citFO4liYvWJSclLw+Wnt7/F4zw5ofH2Dasc1EGjYnz+hRER68sknn2DMmDHyomCHDh2wYMECzX2ig7O6GQ7R3VzRXSpYBzoK6ta52l+0zYwrIiLzVOXAFZGxyy9Q4vjNJM0+C7NXzMpTK5Gcoyro627rjmeidJottH8KUFRphTEREZWifv362LlzZ6nnRnTzs7Oz43mjcp2JTJFzHt2Ogs18nU3y6yhNkKdOgfaiuqUVeW6bBqpGUkREZPr4CZTqrB0XY5GZW6DprlOX0uZrSlhKGH66uFaz39ujNZyiT6l2LBSqwBUREdUKFxcX2NjY8GzTXUWnZCNfVDAvmvP4utSdgGcgOwsSEZk9ZlxRnZWUkaPZbtfADZZ1oLtOTfvoyEfIL1QF+wIcfPF8lk7b6caDANf6hhscERERlepmYmaxQI+FaKVcR/i52sPa0gJ5BYXIyitAVHIWGrjXcgfzWycq93j/9jU1EiIis8SMK6qzTkZo08a5TPDu/o38F/ui9mn23+32NvzPbdQ+gEXZiYiIjJJu0XJRE6ouERceA3QCVZd1ankREZF5YOCK6qx/r8RrtlmYvXx5yjx8dPQjzX5X367oFHsNyC2aHDr7A03uralvFREREekr40qnJlRdofs16TbeISIi88DAFdVJqVm5MpVcLTTAzaDjMXY/X/wZ11Ouy20FLDAwaABw5GvtAzqMBSy5spiIiMj4lwo6oq4J0vmadLsnEhGReajwJ9EJEyZU642++eabaj2fqDLORqVqtgM87OHtbMsTWIak7CQsP7Vcsz+m6Wg86tQEiDmtLcouAldERERkdPIKlMUu1tW1pYIlOwteYuCKiMjsVDhwVVioU6SZyMgdv5mk2Q4NcDfoWIzd5yc/R1rRkkAvOy9M6TQDFn+/qn1A0yEsyk5EpEd79+6t1vP79Omjt7GQ6YtKykJRQ0E421rBzcEadY1uZ8ErsekoUBay6Q4RkRmpcOBq1apVNTsSIj3adv62ZrtDIJcJluVK0hWsu7xOsz++9Xg4FOQBZ3/TPqhT9bItiYiouH79+lX5lIhucQUFqu6vREJ4ifpWdamjoJrInLe3tpRdBXPzlbIYfUNvJ0MPi4iIzLHG1cWLFzFo0CA4OjrC19cXr776KnJzcyv1GkuWLJF/sO+///4aGycZN5EdeDFGW/+AhdnL9tGRj6AsVMrtIFhjTMAg4PQvQF7RJNg1EGjUv6a/ZUREZkWpVFb5xqAVlV/fqu4tExQUFhbFvjZ2FiQiMi9GU205KSkJ/fv3R5MmTbB+/XpERUVhxowZyMzMxLJlyyr0GjExMZg7dy58fHxqfLxkvG4kZCInXxWMsbVSoKWfi6GHZJQO3DqAg9EHNfvzm46BwskXOKpTj67jOEBhaZgBEhER0V3dTMyo0/WtdLPJ1PWtLt9Ox5DWMG2iDEvsBeD6HiD8AJB0HUiJBAryAYUCcKoHeDQE/NsDjQYA9TtwTkZEZstoAlcrV65EamoqNmzYAA8PD3ksPz8fU6ZMwezZs+Hv73/X1xAZWiNGjEB4eHgtjJiM1fFwbX2rNvVdYWNlVImFRkFkWS05tkSzPyhoEEK7vwTcPATEnlcdVFgB7ccYbpBERER0V+EJuksF615HwdKCciZdoD0nDTjxA3D8OyD2XNmPy04B4i8Dl7cAu98DnP2ADuOAjuMBF7/aHDERkcEZzSf6zZs3Y+DAgZqglTB69GiZFr9169a7Pn/fvn34/fff8f7779fwSMnY/XI0QrPdIYiF2Uvz9/W/cSHxgty2ggIvNi/qGnhUp5Zd8/sA53o1/N0iIiKiqsrJL0BMSnadXyooFFsqqFMSwmTkZQMHlgFL2wFbXis/aFWatGhgz/uq5299C8hMrKmREhEZHStjqm81YULxItBubm7w8/OT95VH1HuYOnUq3njjDfl4Mm+i24xa+wAWZi8ptyAXy05ol9+OsvRAUH6+agJ0boP2gSzKTkREZNQik7Kg7vvtZm8NV/u611FQLUgnm+x6fIYM2tlamUg5A7EU8M8XgIQrxY9bWAIhvYGG/QDftoBbEGBtB4hGOWLZYNxFIGy36pZbNL8tyAEOfAqc+B4Y9hHQepTo2mCQL4uIyKgDV8nJyTKopO8aV6W9pru7OxITy7+isHz5cmRkZOCll16q1HuKpYniphYdHV2p55PxycjJR3KmtqA/M67u9NPFnxCVHiW3rRXWmHz/N4BbiOoqoJgMCaKmQjDbrRMREZnOMsG6m20luDtYw9nWCmk5+chXFsrgVXNfI69jKgJQO+YCBz4rftzBE+j+PBD6VNnZ7R4hqqBWl0lATrqq47N4HXXwKysR+O1/wIU/gRGfAXauNf/1EBGZ0lJBkdX01FNPYefOnTC02NhYvP3221i8eDFsbGwq9VzxnICAAM2tS5cuNTZOqh2nIpOhLLr0WN/NHvVc7HjqdaTmpuLLM19q9kc0GgEvEbQSBUKP6SwT7Pi0qjAoERERGS1z6CioJrqG6wbnLhn7csHUaGD1/cWDVpa2QL/XgRdPAb1frnhJBlsnVcOcKYeA4UtVgS+1838AX/UHYstfoUJEZMqq9MlUBHwuX74sa1I1bNgQ8+bNQ0SEtq5QVYjMqpSUlFIzsXTrXpUkglZt27ZF7969ZSaYuImi7uKm3i6L6Fooxq2+HT58uFpfAxneP+diNNvtA7lMsKRvznyDlBzV75mnrTteTc0BYs4CN/4FEq6qHmRpA4Q+WXvfNCIiM/bYY49h+/bthh4G1YGOgnU9cFVyueCV29rSEEbn9jng/wYAEYe0xwK6As/tB/rNAmydq/a6llaq4uxT/gNaPqA9LuZw4v2u7ar+2ImI6krg6rnnnpNBntOnT2PkyJFYtmwZQkJCcO+992LdunXIy8ur9Gs2b978jlpWIpAllu+J+8oinrN3714Z+FLf9u/fj3/++UdulzcZdHFxQYMGDTQ31scyfcdvaDsKtg9kYXZdMRkx+P7C95r955o+DgcLhaq18pH/0z5QTIQcda7kERFRjbl+/ToGDx6M4OBgzJ07l52RqcpLBXWDOnVVoCl0Frx1AvhmCJCqKssg9ZwOjP8b8Gqin/dw8gYe+RYYtkjVBVoQNbB+eAQ486t+3oOIyIhUay1Q69atZfZVVFSUDFilp6fLK4ciADR9+nRcuVKiAGE5hg4dKoNMIktKTbymQqGQE7qyLFmyBLt27Sp2a9euHbp16ya3ufzPfBQWFiJKp7NOB2ZcFbP85HLkFNWwcrN1w0OhE4F7F6hqIlz4S/vATv+rte8ZEZG5+++//3DmzBmMGjUKK1asQKNGjTBo0CD89NNPyM3V1mwkKikrtwCxaTnmlXGl21nQGANXt04Cm2cBOanapYGPrAYGzVVlS+mTKMgu6l+N3wTYF61OUeYBv00ETv2k3/ciIjKwahexUSqV2LJlC9asWYMjR47A19cXDz/8MP7880+0atUKX331VYVeZ/LkyXB2dpYZXFu3bsWqVaswc+ZMedzf31/zuAEDBqBx48aa/dDQUPTr16/YTRR59/T0lNvlLTOkunfVMTFDNcm3sVKglT+LVKpdTbqKP679odl/rctrsjC7dGw1UFig2q7XBgjsVsvfOSIi8ybmSx9//LG8EPjrr7/CwcEB48aNkxcCp02bhpMnTxp6iGSEIpK02VYejjZwsjWaZuE1Rjc4J+p7ZeaWXRKk1kWfBrbM0ja6sXMDxv4BtHqwZt9XzNsm/AO4BhQdKAR+fw44va5m35eIqBZV+S+cyKb65ptv8N1338kC6UOGDJGTrfvuuw+WlpYy+2XWrFl46623MGnSpLu+nljWt2PHDjlBE8ErEcSaOHEiFixYUOxxBQUF5datIvO1Rae+VZv6rjJ4RSpLji+BslApt9t6t8V9IfcBx78D8rKAozpF2btMZEtlIiIDEfOnESNGyCLU8fHxOHjwoLyQJ7on9+rVS14MbNq0Kb8/JIUnaOtbBdfxjoJqLvbW8HG2lZlmoq/M1dh0tG3gBrv403c+WOFU9gv5t9d/TavNrwL52dqg1bg/Ab92FV9eWBklx+/dVBW8Wj0MSLoBiDnfhmcBezegyaDKvTYRkRGq0id7MXkSdafWrl0rM6Ju3LiBjRs3ysmWmHQJYtIlMq9EUKuiWrRoIZcLZmZm4vbt2/joo4/u6BS4e/du+X7lEY/56y+dpU9kFk7c1KlvFcDC7GpHY45iT+Qezf5TLZ6Sv5+yRXPkUSCj6HdULBls80jtftOIiEi6dOkSXnvtNVlzc/To0ahXrx42bdqE1NRUbNu2DRkZGbKjM1Fp9a0CPep+fSu1Zr7awuaXjaFAe0oksOV1bdDKxgkY+3vFg1b64lofGLcRcA1U7Yts+nXjVZlgRETmGLgSywH//vtvWVBUZFTVr1+/1MeJZXziMUS1ISIxS7PdIYiF2QWR+fjJsU8058Xf0R9d/bqqdjr/D0i+qfML+xRgYz4TXyIiY/D111+jZ8+eaNmyJX777Te88MILuHnzJtavXy/rf4pan/3795c1RY8fP27o4ZIRCU/ULcxuHhlXQhMfZ+Opc5WdoloeqK5pZe2oKpiu74yuinILBMb9ATh4agu2/zgaSNEpFE9EZC6BK7EkUHQQlFkb5bC2tkZQUFBVx0ZUYRk5ebgYk6pTmJ2BK2Fb+DacLkqfV1gosHzgcnjYFdV9izlTvE2zCGQREVGtev755xEYGCizqq5evSrLLIhsq5KaNGkiLxYSqd3UybgKNoOOgmrNfLVLAC/FGDBwVZALbH1LlXElWFiqirD7lN0NvVZ4NAQe/xmwslPtp0Wrglc5RpCdRkRU04Gr8+fPV/rF8/LyEBYWVunnEVXWvL8uQFmo2vZ3tYOva9EfazOWp8zDpyc+1eyPbDwSjdwaqXaubAd+n6J9cOOBgGfRfUREVGtEQXZRekFkVZVHFGp/5513am1cZNxSs/KQmKlqSCMuIzdwt4e5aFrPCDKuRIGtfxcDMTrL8Hq/BDToBKMQ0Bl46Muinw5Rg+sssPFF1biJiOpy4Kpbt2544IEHZLfAu7VnvnbtGubPn4+QkBD8/vvv+hgnUbkycwu09a24TFD67fJvCE8Nl9s2ChsUKAsQlxmnulOktN/WCUZ3eYY/YUREBiC6IBNVZ5mguFhnZ62qMWsOmugErqJTspGSlVf7g7i4Cbi8Rbsf+gTQ/H4YlZYPqDLA1M7+Chz5P0OOiIio5gNXIn09ODgYTz75JLy8vNCvXz9Zh2HevHn48MMPMXv2bDz++OOy2424/fHHH7ILzowZM6o+OqIK0m2HzMLsQEZeBlacWqE5J0NDhsLHwQduosuNOm28sOicuQerMq6IiKhWdO3aVV7YUypV3V7vJiIiAq+88oqsc1VRFy9exKBBg+Do6Chrk7766qt3vfAoiALwYlmieJ7o+NynTx9s3bq1wu9LteOmTkdBc6pvJTjZWhXLMLsaW8tZV/GXgQNLtftBPYHOE2GUerygCmCpiSLyojEPEZGJsaroA318fLB06VIsXLgQ69atw44dO+REJjo6GtnZ2fDw8ECzZs3wyCOPyG6C7dsbqCghmZ01B2/gv7BEzT4LswPfnvsWidmqc+Jm64bXurwGZ5uiK5Tig9Lhr7QnsNP/AIX5XKklIjK0sWPHYsqUKXjmmWdkNrsozt62bVt4e3vD1tYWycnJsrnNsWPHsHnzZhw6dEh2bn7uuecq9PpJSUly6aEIQIki72I5oriQKLo2L1u2rNzniuCWeKx4rpjfieLxw4YNw65du9C7d289nQHSa2F2M+ooqNasnjMik1RNeS7FpKOzbS29cU4asO1tVWdmwdkf6DcLsKhS2eCaJ+oRj1gG3D4HJFwFlHnAL+OAyf8CDkU1T4mI6lLgSk1cgRs/fry8ERmDq7HpSMtRZQ/ZWCrQyt8F5iw+Kx6rz63W7E9sMxFO1tpCpjizDkgq6vYpCne2Z3t1IqLaLsg+YcIE/PTTT/juu+/kLT9fmzms7gor6lqJi4Eig71NmzYVfv2VK1ciNTUVGzZskBcWBfH6IlgmMuT9/f3LfO4vv/xSbF90NhSlH9asWcPAlREJ1ynMbm4ZV2ciU+DmYKPZP3AtHp1b1sIbi/pQez4A0mJU+5bWqqV4ttqli0bJzgUY/R3w1QAgPwtIjQT+egl4ZLUqsEVEZAKM9PIAUcW1ru+q2W4X4ApbK/POHlp5aiWyxMQEQH2n+vL25v43kZKTonrAcW1QC20e5hU3IiIDsLe3x9NPPy0zmVJSUrB//37Ztfn777/H33//LZvbiEwpke1emaCVILK0Bg4cqAlaCaNHj5ZLEyu77M/S0hJubm4VWmZItUMENcMTdZcKml/GlW6wTre7Yo26tAm4sU+733M64NUEJqFeK+C+j7X7538HTv9syBEREdVM4EqksJ89e7bYsR9//FGmsxMZ0tEbSZrtTsHmnfZ8I+UGfr38q2Z/Wvtp8HP0Q3OP5nCxcQHiLgHhB7RP6PKsYQZKRGTGHnroIVk7VBDZVhkZGbIJzoMPPijrhd57772yrmhVifpWzZs3L3ZMBJ9EBpe4ryKBEZGhlZCQgEWLFuHKlSt49ln+vTAWCRm5yMhRNaWxUljIbsrmJsjDodRlkzUmJRI4oLPMttEAoNkwmBRRQL7FCO3+3zOB5JuGHBERkf6XCoqglaiNoFZQUIAxY8bgyJEj6NChQ8XfkUiPjtxIxNbzRSnbADoHu5v1+f30xKcoKFRNZlt4tJBF2RUWCrTyaqV6wL4l2gcH9wb82hpopERE5kt0aH7ttdfQuHFjmXV18OBBvXYXFDWuRKCqJFFsPTFRWxOyLKKu1aRJk+S2k5MTfv75Z3Tv3r3c54ilieKmJmqgUs0vExRFyq0szW8BRQN3BygsAGUhZFfBpGxbuNvV0HkQ9ax2LgDys1X7TvWAXtMNu8zu1onKPd6/vWq8w5cCEYeB9BhVh+kNk4FxG1nrlIiMXrX+Cy+uyBEZ0q3kLCRlatsgdww034yrU3GnsC18m2b/pY4v4XbGbeQWFC3vyExUtUJW6zbFAKMkIqL69etj48aNuHHjhpxLxcTE4ObNm2XeatvIkSPlhUmx5FAsMRQ3sV0e0fEwICBAc+vSpUutjdfchOt0FAw0w8Lsgo2VAn6u2s6C4SkV69BZJXsXAXEXinYsgH6vG39dq7KIguwjl2v3w/cXb9hDRFRXirMTGRM7a8tiHWZcHaxhjsQHn0+OfaLZ7+HfA519O2P+ofnwsPPAC20nA8dWAeogllsQ0HSI4QZMRGTGpk+fjldeeQXvvfceLCws5BLBsv7bLu4XWe6VITKrRN2s0jKxdOtelcXLy0vehCFDhsgsrZkzZ8pC7WURnQgnTpxYLOOKwata6ChoZoXZdQV6OCAqWVXT80aKEqH1auBNYs4A/y7S7rd7DPAPhUlrPADo8gxw+EvV/o65QLOhgHuQoUdGRKSfwJWYPFXkGFFtOXpDu+ShkxkvE9wbuRfHbh/T7E9pNwVWCis81vwxWIirg7vf005QhO7PAwrzW1pARGQMXnrpJQwfPlzWmxoxYgQ++OADNG3aVG+vL+pblaxlJQJZIphUsvZVRXTs2PGuGVcuLi7yRjVPtxi5OQeuxNd+MCxBbt9IqVxwt0IK8oE/pgLKoo6fHo2AThNQJwx4B7i8RVXjKi8T2PgCMOZ3dhkkoroRuLrnnnugKPFht3fv3nccE8Gs0q70EenbtvO3Ye6BqwJlAZYc19auErWt9kbtRVvvtrIou2zfLOoz5KarHmDrCoQ+abgBExGRrG8lbuPGjcPDDz+MkJAQvZ0VkRm1cOFC2UBHXetq3bp1cr42ePDgSr/evn370LBhQ37XjECBshA3k3QDV+a5VLDk1369JpYKHvwMiD6p2rZQAH1fBSzrSGa/rZOq3tWaomzPsN3AyR+A9k8ZemRERNULXL3zzjsVfShRrcjKLcBNnXT5TkHmWd/qz2t/4mqyqjuVtcIaQ0KGoHO9zsWzIcN12jd3HKuasBARkcGtWrVK7685efJkfPbZZ7JW1ezZsxEVFSWX+onj/v7+mscNGDAA4eHhmg6HmzZtkl0O77//flmnSiwRFB2k//nnH6xdu1bv46TKu52ajdx8VZDGzloBH2dbsz2NxToLphRoltbqRfwVYNd72v22jwLezVCnNOoPhD4FnPxetf/PbKDxIMC5JtZcEhFVDwNXZLJORiTLbjKCr4ud7KxjbrLys4plWz3e/HFMaK2Txp4eB1zcpO0+I64YiroGRERUZ4kaVzt27MC0adNk8MrZ2VnWn1qwYEGxx4naWfn5+drPsY0aIScnB7NmzUJ8fLysc9W2bVvs3r0bffv2NcBXQuUXZhed9cy3ZIefqx2sFBbIVxYiIw+IyyyEj6MezodSCfw5DSjI0S4R7Di+Zrv+Gcq984Gr24D020B2CrDtLeAhndISRERGgsXZqc7UtzLHems/XPgBidmq8+Bk5YRJbVTtyzVuHgR2L9TutxgBuAXW8iiJiKi2tWjRAtu3by/3MSIgpUvUv/r9999reGSkt8LsZtpRUM3KUiGDd2HxqmDeteQC+DjqoX7n0a9V8ye1B5YBVnU0s83eHRj6AbCuKDB3+meg/RggpLehR0ZEVAyrM5PJ2n05TrPdOdj8lgnGZ8bj69Nfa/Yntp0INztVLRMNkdaeHqvd7zalFkdIRERE+hSuU5g90IwLs6sFe2mDd2HJeqhzlRYDbJ+r3e88CQjqgTqt5Uig4T3a/b9fAfKLulATERkJBq7IZIuTnr+VataF2eccnIP0fFXB9XoO9fBkC52C66fXAef/AI6K2ilF6ynrdwQCuhhotERERKTfjCsGrkJ0Alci46ratr4J5Kaptl3qAwPNoMavWLEwbBFgaaPaj7sIHFpu6FERERXDpYJkki7GpCIrTzVBcbK1QnNf82rBHZUehf1R+zX7z4c+DzsrO9WO6CKYdENVm+HYt8WzrcxwOSUREVFdkJ1XgCidjoLBZtxRsLTAlW7G1bXMm8hNLaf2qW1RkEaHY8RRBJ9Zpz0w5D3A1hlmwasx0PNFYO9Hqv09HwBtHgZcGxh6ZEREEjOuyCQd0alv1SHIHZYK8wrIfHbiM+QXqgrqNnZrjBGNRmjvFMGpvjMBhQ2QXzTBdQtSpYITERGRSbpyO13TlMbN3hrujncGX8xNiE7w7laaEln5RSeokiwK8uC352PNflpgN1VdUHPSa4a2DmpeJrBllqFHRESkwcAVmaR/r8RrtjsHmdcywQsJF7ApbJNmf3qH6bBUWKp2REeYjAQgLws4/IX2ST2mAZZMsCQiIjJVF6JTS63tZM5c7K3hWRTAEyGr61VcLuh5Yi1sk8LlttLSBjF9Z5hflrqNAzC0KONKuLARuLrDkCMiItJg4IpMTmFhIU5HJmv2O5lZYfaPj2qvCHas1xF9GvTR3nlohaqV8fFvgcyi4J69BxCqU/+KiIiITM55ncCV7hI5c1e8zlXlC7Rbp0bD+8hqzX58x6eQ62amS+SaDQGaDdPu//MGUKDK8CciMiQGrsjk3EjIRFyaqtuJjaUC7QNLdNKrww7cOoD/Yv7T7M/oOAMWulcE2z0GtHtcFcBS6/qs6ioaERER1YmMKwauyqpzVfmMK99/l0KRny23c138Ed9xDMzavQsAhbVqO+4CcFwb1CMiMhQGrsjkHLymXSYYGugGO+uiZXJ1nLJQiSXHlmj2BwUNQlvvtsUf5B4MZMSpirML1g5Al2dqeaRERESk72zzYksFWZi99MBVUuUyrpyu74dL2F7NfnTfl1FoZQuz5tEQ6Pacdn/nAiAryZAjIiJi4IpMz94rcZrtbg09YS7+vv43LiRekNuWsMSLHV7U3nllO3D8O6AgD9i/VHu8/RjAwbyWUhIREdU1t1KykZqtWrJlpbBAA/dyOuaZGd16X2EpBVCK7soVYFGQC99/tRcEUxv1Q3pw9xoZo8np8wrg4KXazkoE9ujUviIiMgBWayaTu+J44qa2vlW3huYRlMktyMWyE8s0+0NChiDIJUj7gJQIIOEqEH4AiD6pOmZhCXR/3gCjJSIiIn26cEubbRXg4QBrSy6aUPN3tYetJZBTAIjYXnR6objCV0yuMg8RmbEIy7iFqKw4JN/cjMyEK8h3zIfCsR4UsIDC1QauJ1fA3c4d9Z3qw1phjRDXEPmv2bFzBQa8BWwsukgqGv50mgB4NTb0yIjITDFwRSZX3+p2ao6mvlWHQPPoKPjTxZ8QlR4lt+0s7fBK51eKP6DT06rimd8/qD3W+iHAXSe4RURERKZf34rLBIuxVFggxFWBi4lKTZ0rf08gMTcVR5Muytu51BsoKCyl/pWtzrLApIuqW5HPT34OG4UNQn1C0dUxEN09W6G1S8PitUXrqlsngHqtAY9GQOI1QJkP/DkVGPJe6Y/3b1/bIyQiM8PAFZmUQ2EJmu12Aa5mUd8qNTcVK0+v1OxPaD0BXvZF6duCCFhZWgFRx4Dr2joN6Dm9lkdKRERENeFCDAuzl6ehm2VR4KoQh5IuIjVnO85nXEUhKrZssCy5ylwcjjkM8b/Prv0KTxtXdPFogZ6ebdDIsX65QaxWLiEwaQpLoMdU4K+XVPs3DwKRR4AGnQ09MiIyQwxckckGrro30gne1GHfnPkGablpctvN1g3jWo3T3imKZW56Bej8P+Dfj7XHm90H+LY2wGiJiIhI3y5Gq+YBAjsK3qmhuyUsHS7A1mczDhZGARl3PsbV2gkhDn5oZGmP5pd3w6ugAE5KJW53Gof0+qFIz01HUk4SErISEJ4ajptpN5GRV/yFEnJTsDnmkLwFOfhigE9H9PJsCwcru7r5Qy8yqYJ7Azf+Ve0f/BwY9X+Agh8hiah28b86ZFL1rXQDV+ZQ3yomIwbfX/hesz81dCocRKdAtfxcwLeNKoB1dbv2eN+ZtTxSIiIiqgmZufm4npBRajFyAqIywrG/4As4BKka2OgSgaquHi3R0b05Gth7Q+RHBe98H45p6fL+DL+2cA4dB5SSOSXmnbfSb+FswlmcjTqIUynXZK0stfDMGHxzYxN+uLkVvb3a4X6/nvC1q4Nz026TVdlWYrmg6Fp98W+g5QhDj4qIzAwDV2QyzLG+1fKTy5FToPqag12C8VDTh4o/wLke0Gs6sPZx7bHGg1hrgIiIqI64FJMGdaM8D0cbuNqbYbHwUigLC7D55i/4Jewr5ClzNccLCxVo69QCo4N7oIlTg2LPcbl5BI5xlzX7Mb1fLDVoJYhlgPWd68vbvY7ByC7IxamUq9gXfxrHki5BCVVNrRxlHrbHHsWO2GPo4dkaD/j3RqBDPdQZLvWB1qOA0z+r9o+tApoMBHQvpBIR1TAGrshk6GZbtarvUufrW11Nuoo/rv2h2R/RaIS2s01etmoC0eYRVdHMS39rn9iH2VZERER1xQUuE7xDfHYMlp2di8spZ4odz0tthZy4IejWyQ5NnGyK3WeRn4t6J3/W1mIP6YVshQKIu1Sh74OdpY3M3hK3pNw07I47jh2xxxGfq+p2Lepp7U84I2+d3ZtjdvOxaFwicGay2j+lmmvmpKmy/E/9rGoMpFvMvTJYzJ2IKom9dMk061s19ERdt+T4EigLVVfz6jnUw6PNHtXeGXMGuPwPkHAV2LtIezykDxDY1QCjJSIiopruKBjMjoK4kHQCbxyeWCxo5WfjjUYZU5AdNQaFud6ISL3z4qbnpS2wyVTNJQus7BDb9uEqf0/cbZzxYP2++DT0Rbzc5DFZqF3XkaSLGHXwDbx57itEZ8XD5Nk6A+3HavfFxdOic0lEVBsYuCKTrG/Vq0ndLsx+JPoI9kTu0ex/0OcDuNi6aB8Q0BkYvgSwsgXOa7Oy0OfVWh4pERER1YQzkSnydjQ8SXPM3Auzb434DQtPTEdanirLSbi3wcNY3OwNtHNpojkWkVx8UYlVZhK8z2/S7Me3vB/59q7VHo/CQoHOHi0wv9UkvNF8XLFOgkoU4o9b/+L+A6/h48trkZaXCZPW6gHA2U+1nZ8NHF1t6BERkRlh4IpMQlh8htnUtxJBuo+PajsE9mvQDx3rddQ+QFmg+tfJB9jzgUxOlwK7A8G9anu4REREVEMKlIW4Hq8qJC40NNPAlZgb/XT1C6y+/AkKClXzIHtLR7zS7gOMazYdtgobNPHQfqy5mVI846re6V+hKFDVwcp19EZCs8F6HZ+oh9XGtSHeajEe77R4Gk2cAjT3iYLuq8M3Y/iB1/D7rX812fQmx9IG6DxRu39pk6pYOxFRLWDgikzCvivaNOum9ZzqdH2r7Te341ziOc2VvOkdp2vvTIkENkwGLm4CYs4CZ38rXtuqjAKjREREZHpuJWchO08V6LCzVsDfzR7mRgR6Vl36GH+Gr9Ec83MIxLzOX6GDV0/NsSbu2rlhdJoC2UUNAO0TrsHtxgHNfTGho1FoWXMF7lu4BOPdlv/DknYvoqGjv+Z4Qm4K3jr3FcYcmYdzKWEwSY3uAbybq7ZFAO6/Lw09IiIyEyzOTibhX53AVc/Gdbe+VZ4yD0uPL9Xsj2w8Eo3cGmkfYO8O+LUFGnQGNr6oPR7UE2jUv5ZHS0RERDXpapxutpUTLBUWZhe0+uL8Qvwbs0VzrLlbO5lp5WDlVOyxHvYKeNpbICFLlEm3QFiSBVp6K+F7fK3mMRk+zZHWQCeLvYaIDCxfOw/MazURO2OP4+fIHUjPz5L3nU65hscPz8U93u3xWMBAuFiXnkWnu+zQaFgogK6Tgb+KLqrePADcOgn4hxp6ZERUxzFwRUYvv0BZrL7V0Dbaq1d1za+Xf0V4arjctrKwwpR2U4o/wMYR6DENiDxWvJNg/zeZbUVERFTHXIvVBq4a+xQP1NRldvGn5fLAr6J+xr8JezXHOzi3wsyAp2GbXHrGksi6SsjKl9vXEizQPfMQHBKuyf1CCwtEt3+8VudLlhaWGFSvM7p5tMIvkTuxPfao7D4o/rcz7rgs4j42aAh6ebaVwa4aU9muf+URQarAHqqglfDfCmDkClVQi4iohvC/MGT0TkUmIz1HNQlxtbdGm/rVL6ZpjNJz07Hy1ErNft+AvqjnWE+1k3YbOLQCSI9V7e+cp31iowFAUI/aHi4RERHVYsZVI2/zqm/1Y8yf2KITtOru2h6vBT8r61mVpYm7Tp2ruFzUO7VOs5/UsC9y3ANhCM7WDvhfyP14r/WzaOasHUNafiY+v7Ye711ag9vZiTAZXZ/VBqriLgHXdhl6RERUxzFwRSa1TNDD0brOpsl/c/YbJBZNWtxt3TG/53ztnYlhQHjRla0b+4CwXcWzrYiIiKhOURYWIiwuQ7PfyNt8Mq42xu3Ab7H/FMu0mh74NKwV5S8WaeKhrXPVNXYTrLNUHRkLrO0R2+ZBGFqwox/mtJiA5xs9BGcrB81xsXxw5pnl2Bi9X1N83qi5BwHN7tPuH/kKKCp+T0RUE7hUkEyqMHtdzba6nXEba85ri45ObjcZTjY6E9Sg7oB/e8DKFvhlrPZ48/uB+h1qebRERERU06KTs5GVpwpi2Fgp0MBdG+ioy47H78fqW+s1+y0dG2Nm8KS7Bq10A1f1EYdH8zYBRdc641o9gAI7FxgDsSSwt1c7hLo2wZqb/2Bv/ElN98Efbm7F/vgzeKbhiGrXuDqXer1az7/r+3caD1zdBuRnA2kxwLk/gLb/3959gEdRrX0A/29J75UkpCeEhN6kCipNQVFUxN5Rud5rQ2z4KVb0WkCviui9NuyiIBZApImI9F4CIaQTSO/ZbP2eM5PsJiGU1J1N/j+f4+6Znd1MJkty9p33vOe6Vn1NIqIzYcYVKVq5zoDdWSXW/uyJtSuZdDLv7XkPOpNOuu/l7AVXravtQYNczBNOrsCxtUDm37UPqIBL5tjhaImIiKi9pTYozO7RaTPO68ssP4Z3Dzwn1YASolzD8FTMP846PbC+QDc1/F1VeNLpa7iq5GUFa7xCUNRjHJRGTB+8P+5qPJ14G4Jd/Kzb06ty8fSBD/FWyneoUXIWk3sA0P8GW3/3YqCm3J5HRESdGANXpGhbjxfBZJYHL928XdDdr/MtA320+Ch+PPajtT8+cjyC3ILkjlEPfH83cOAHwGwC1sy1PbHPtUC33nY4YiIiIurI+lbxXWCaYKm+GG/sewI6k3zBzkfrJQWtPDTNG/td4XkUUzRbrP2TA66HRaPcSSZ9feLwet/7MSV0FNS1H81E4O6j9F9w/da52F8qF5dXpH7TATd/+b4IWu3+wt5HRESdFANXpGibjtmmCWrVaqneQ2czf+d865XF/kH98fzI5zE6fLT8oNkA9LkGCEoC9n4DnDogbxfp8sy2IiIi6hIrCnb2+lZmiwnvHXweBbpTUt9JpcWT0fch2DmgeS9kMeM+/WfW7gHXvqgI6w+lc9E44+bIiZjX517EuIdat6dW5uCWbS9gQcq3ysy+cnIHhtxp6x9YCpTn2vOIiKiTYuCKFO3PlHzr/ZuGRcJJ07nesn+f+Bt/5fxl7V+XcF3D5ZCdPYC+0wC/6IYrCV4wAwiI6+CjJSIiR5GcnIwJEybAw8MDISEhePzxx6HXn/2Db25urrTfgAED4OXlhfDwcNx0003IyMjosOMmmcViaTBVMC64cweulqV9hgNFO6z9+yNuRk+P2Ga/jnfmGnTXH5fuGy1qvIlbRFEpOApRvP3F3vfg+vCx0Krkel1mWPBx+q+YvvVZZWZf9ZwE+EbZLrhu/8jeR0REnVDnigJQp5JTUo3U2tV0xJjj5mH2WcK4vZgtZizYucDaD/MIQ2Z5ZsOdRNq1yDLb8p7tCpaLDzDm8Q4+WiIichTFxcUYO3asFKhaunQp5s2bhw8//BCzZs066/N27twp7T99+nQsX74c8+fPx/79+zF06FDk59suJFH7yyyqQqW+tjC7Ro1I/85bmH1/0XYsTfvE2h/ffSou8hvW7NdRG6oQcGixtf+5aQI2loZDb4RD0ao1uLr7Rfh22AtI8oq2bj9eeUKZ2VdiFsCw+2z9Y2uA/GR7HhERdULKnfBNXd665DzrOegR7AlXJ9sSx53Br8d/xeGiw9J9rUqLheMWItgjuOFOv88FXDwbXr0aPQvwaGbqPBERdRmLFi1CWVkZli1bBn9/uf6M0WjE/fffjzlz5iAsLKzJ51144YVSppZWaxsejhw5EpGRkVi8eDEeffTRDvseuroDOWXW+9GB7s0uzL4/uxSOoLSmCO8deMFaMiHGqyduTXgQKGp+4MPv6LfQ1sgL+pRYPPGW8VqYoMLWDD2i/eQgYIS/49RKTfCKwJdDn8Un6Svw/vFlMFpM1uyrDfm7pcysfj4Kyb6PHAGEDgBy5RUSseV94Iq3HCrbjYiUjRlXpFgb6gWujCYLKmoc7JLZWdSYavDO7nes/WkJ0xDnFyetKGglMq16TgYKUwF97XQBnwhg2Ew7HDERETmKlStXYvz48daglSCyqMxmM1avXn3G5/n6+jYIWgliumBQUBBOnDjRrsdMDe3PKe309a3EdMgPD7+KMkOx1HfXeuLBvi/A6TxXEKzPqeIEfFOXW/tfuV2NUsjnLb3EcS98Oqm1uDf2Snw3/EX0apR9deu2FzBfKdlXIkA1/B+2fu5eIGOzPY+IiDoZRQWuWI+B6ugMJvyVaivMPvvSngjwaP5ARqm+PPwlcivlqX/uWndo1Vqkl6afPgjwjQSOrLRtG/cs4OTawUdLRESORIynEhMTTwtKhYaGSo81x9GjR5GXl4ekpKQ2Pko6m/05cuZQZw5crctZjt2FtuDGjMTH0c2te4teK/DAx1Cb5QucNV6ROBw0xvpYerHjTzDp4RmOL4Y+iwfipjWoffVJ+q+4busz2KeE2ldBPYH4Cbb+1kVA7c+EiKi1tEqrx9CjRw+pvkJOTo5Ui6GqqgrvvvvuOesx3HXXXRg+fDgKCgrw4osvSvUYDhw4IF0lJMfz9/FC6Axm6X6wlwsm9QlpWLTcgRVWF+LDfR9a+1Pjp6JcXw5XbaOAVHEGsOoJwCKntyO0P9BnWgcfLRERORoxphKBqsb8/PxQVFTUrIyYBx98UJpaeOONN551XzE1UbT6hd6pZcxmC/Zl2TKuErrVy8buJHKrMvFFim18PzrkMgzvNrZFr+WWtweeJ7dY+/l970VUpW0V6jQHzbg6WJZ22rZRgX0R6R6M94//KGVdCWmVuVLtq8tDR2B6+Fg4q51gN0NnAGkbAJMBKM0Ckn8Fel1lv+Mhok5DMYEr1mOg+tbXmybYK9Qb+eU1CPbuHJlG7+15D5UGueh8N/dueHjww3BWO0OjrjewKs0GltwBnNhl2zbxZUCtqCRJIiLqxJ577jmsXbsWq1atklYnPBtRyP3555/vsGPrzMRqguW15RFcnTpfYXazxYRFh+ahxqyT+oGuIbi958MtfDETgvbbLgZWhAxDdfAARBdnWbedqtCgUq+Ch7MtmOXIIty74cXeM/DTib/wfc4GmCwmqUbYL7mbsbP4CGbGTkVPLzstaOTZTb7Iuvdrub/jEyB+vLxKNhFRKyjmUzDrMVD9K7z1C7MXVuqxK9OWMu/IjhQdwQ8pP1j7t/S6Ba4a14ZBK8E9ACjLtvX7XAvEjO7AIyUiIkclMqtKS0ubzMSqX/fqbP773//ihRdewAcffIBx48adc3+RJZ+VlWVt27Zta9GxE7A7yzbmiQ/ybHZhdqVbnb0UKaUHpPsqqPCPXv8n1bdqCZ/0VXCpXZHZotKioM/d0n1PFwuC3Gsz1gFkOGjW1ZloVGLlwTF4tc99iPWwLbaQqyvEc4c+xqfpK6CzV+2rgTcDLt7yfV2JLYhFRNQZAlesx0D1rzRmF1dL97Vq4M3p/TE89vwG2koPyL2+43WYLfIUyATfBGw/uR1/5/59+s5/vQ1U1AbvnDyACS928NESEZGjEvWtGteyEoEsMX2vce2rpojVCP/xj39IgStRiuF8eHt7S4Xc65qop0Uts6de4KpnSG0AoJPIrz6Jb1NtGVKXRkxDkt+AFr2WWl+OgMNfWPvFcVfC4GkL4tStJCikFXeuwFXj7KsbI8bDSSVPpBHZV6tObcXj+xfiYOnp0w3bnbMnMPgOW3/fd7YxLRGRo08VZD0GqlM/22pYbECnqe2wIWsDtuZutfbnDJ+DkpoSDAoe1HAlwQ3zgD8X2LZd9Bjg07JipURE1PVMmjQJ8+bNQ0lJibXW1ZIlS6BWqzFx4sSzPnfDhg1SPat77rkHzzzzTAcdMdW3p16Wec9ujlmY/XhZcpMX8BanvI0ak3xx0tc5ABcEXdTkvr3O42v4J38FjaFcum908UVxzxsaPB7jZ8T2HHlhn/QS8ZGnBp2RyL66Kmw0hvglYtHx5UipkKdJ5tUU48XkTzE+eAhujpwIN41Lxx1UryuBg0vl0hci82vHR8DFT3Xc1yeiTkcxGVdtXY9h8eLF51WPISIiwtpEQXeyv/XJ+db7LloNTpXJNRAcmcFkwJs737T2h4YMxeBugzEuclzDouz6SmDfEsBskPsB8cDw++1wxERE5KhmzpwJLy8vTJ06FatXr8Ynn3yCxx57TNouCq3XEVMA4+Pjrf3Dhw9LzxEL5dx6663YsmWLtaWmKmDVsi6gSm9E8klbkfvOcvFO2Fu01TpFULgy+la4aFpWv9S5NA2+x3+19guTboPZqWEtsJhGGVfi2mBn1t0tCM/3ugu3RV7WoED7mrwdeGzfe9hbcqzjDkatBYbeZ+sfXQ0UpHTc1yeiTkcxgSvWYyChtMqA7em2FY983JxQWGGnOfptJK00Df/e9m9klGVIfa1KiycueKLpnTO3AMX10ron/RvQduAVMiIicnhiTCUu4mm1WikQ9eSTT2LGjBnSBbv6TCYTjEbbcvVbt26VphSKVZlHjRqFESNGWJtYsZna3/7sUphrAyyBns4I8OwcY4BKQzlWZH5j7fcPGI4Enz4tezGLBcH73ocKcukFnW8PlEWdXoct3NsErVo+mRV6NQqqFPOxp92oVWpMDh2B1/r+A0le0dbtBfpSvHLkcyw6/iMqjXLGW7uLvhAI6VvbsQBb35dnFhAROfJUQXvVYxCNlGNt8ikYa0dssUEeWHB9y+oeKMkfWX80KMh+d9+7keCfcPqO4krUL/VW1Um8Ql6JhYiIqJmSkpKwZs2ac04LrO+OO+6QGimkvlUnyrZakfUtqowV0n1RiH1yxPUtfi2vrPVwKzwk3bdAhbz+MwHV6TWsnDRy8EqeJgikF2swKAJdQohrAJ5Jul3Ktvoy83fUmOWLwBvyd0uZVzNipmCwX8/2PQiVChj+D+DH2pkDObuArG1A5LD2/bpE1CkpJnDFegwkrNyfaz0Rl/UOceiTImo5qFQqKePKaJGvaAe7BeOuPk0EVsUVqCV3AqVZtoLsl73SwUdMRERESglcdZZpgmnlR7G3cIu1f3nkjfBwOvv3llolrxTYmNZQjdEH/mftZ3cfiUMubsAZ9hfTBesCV2m1t12FyL6a2G0oBvj2wH+P/4T9Zcel7cWGcrx+9CuMDOiL26Iug69TO9ZRC+4FxF4CHF8v90XWVfjg9vt6RNRpKSZnlvUYSNR1+PNYgfVEXOrAgauC6gK8vPVlLEtZhuWpy63bHxr8ENwb1WCQZO8ETtnqPmDcM4BvZAcdLRERESlvRUHHD1yZLCb8kvGltR/n3Qv9/FteUzY+9Ve46OUaYHonDxztcdVZ94/2M3b6lQXPJdjFD3MSb8O9MVc2KNC+uXA/Ht37Dtbl7bSueN0uht4L1NXcKk4Hkm21yYiIHC5wxXoMXZvJbMELPx+CziD/4Qz1cUW/cB84Kjetm9S+Sf5GGrQJvQN644rYK07f2agHfn5Qnv8vdB8i/5EnIiKiLuNkqQ65pfKCNBq1CnFBjrmiYH3b8jbgVHWOdfW7KyJvkrLRW8KzPAeRWbbprSnxU2BwPvs5iq1XoD2zRIMaWxyrSxHnfGzwYLzR958Y6GsrV1Fp0uHDtJ/wwuFPkVNtWxypTXmHAn2utvW3fwRUF7fP1yKiTksxgav69Riqqqpw6tQpvP7663B2lpexrV+PIT093doXtRjElKym2qeffmqH74JaotpgwqETZQ2yrVo6sFECDycP9PDtgUNFcg0GFVR4etjTUtr2aX55BMg7aFuF5cp3AHXXvCpIRETUVe3MsH2YTwzxgqso0uTAKgxlWJvzo7U/stsEBLm1MJveYkGvw99CXZsZVOodiazwC8/5tEB3M3xc5OeYLCr8laZHVlF1g9aVBLj44PGEm/BQ/HUNpggml2fg8f3vY0n2OujrVrZuS4NuA1x95fs1ZcCGf7f91yCiTq1rTfYmxXLWqJFWWOnw0wSNZiNWpq1E38C+WLBrgXX7NT2uQd+gupVV6sk7Auz92ta/cBbQrVcHHS0REREpRf1VlS+I9oejW529FDqTHBjycvLFxWFNZJ2fp9DcbfAvOWbtH0q8HmjqYmAj4hpoXIARu07IF8JTCrXoEWDLwuqKxIXhEQF90M8nDl9nrZEKuAtihsAPOX9gc+EBzIie0iZfq7d3jHxHZMYNnQFsfEPub/sQGHwHEHzuBbiIiBSXcUVd1/ojeSjXyfnbfu5OuCDaD44osywTq9NX490970p1rgRvZ288NOih03c2GYAf7wNqpxIiMAEYM7uDj5iIiIiUYFta5wlcZVWkYlfBJmv/sojr4KJxbdFrORkqkXh0qe21u49CqW9tQOQ8xPvb5gemFvGafR0PrZu0uuDzve5GuFuwdXuurhAvJn+KhalLUWKQV4JsEwmT5LGuIMa+vz0lL05ERHQeGLgiRXhlxWHr/fFJ3aDVOOZbM9Y3Fnf2uRO/p/9u3fbgwAfh59pEIG79K8CJ3bUdlTxFUGsrmklERERdQ5nOgMMnbSUTHPUCniAKff+SYcsmj/ZKaFVB9oSjy+CiLz/vguyNxfubGgSuzIyVNNDTKxKv9rkP14ePg5PKFtjbWLAXj+z9D1ac/Ntar7VVRBmMkf+y9VPXAUdXtf51iahLcMzoAHW61QRPlsnFSIUr+ofBUQdqorbaO7vfgRlyPYUk/yRMS5h2+s5Z24BN8239Cx8GIod34NESERGRUuzKKLYmn0QFuCPYu2XZSUqw+eTvyKmS69GqoW5VQXb/oqOIyNls7R9JuOacBdkb6+5tgqtWPrk6owonyvjxpzGtWouru4/B6/3uR1/vWOv2alMNFmeswpP7F+FQma3GcIuF9APixtr6q54CjDWtf10i6vT4m5vsblNKgXU1wQAPZ4yKC4CjEQGrd3e/i3lb52HHKblWgDBn2BxoGhdar6kAlopVA2tHqN36AhfP6eAjJiIiIqXoLPWt9KYafJv6gbV/QfBFCHEPb9FrqU0G9D70lbVf6JeAnLDmX+QTSfyxfrbpgsc4XfCMQlwDMCfxNql4u7+Tt3V7VnUeXjj8Cf5z7HsU6W2ZgS0ybCagdZPvF6cBW95v3esRUZfAid5kV2azBe9tsBXbvLxfqENOE9Sb9XDTuuHbI99at02Nn4oBwQNO31nM6Rd/qAWtKzDtI0DbcPVMIiIi6jq2p9lWFByqgMDV8bLkFj3vjxMrUFiTJ913UbvikjC5yLdLvcLq5ys2bRU8quTXMqm1ONjrJrnaegvE+RtxKN/JGri6OEbfotfpSsXbB/r2wLKcjfil3lTBzYX7sav4CK7tfhEmhQyXMrWazTMYuPARYMM8ub/xdaD/DYCXYy7MREQdw/EiBNSpHMurwP7sUmv/SgedJuiicUGRrghltVehvJy98PCgh0/f8fDPwK7Ftv6EF4Cgnh14pERERKQkNUYT9mSXWPtDHLS+VYWhDBtzV1j7Y8Imw7Ne1k5zeFTkIjZttbWfGjsZVR62AuLNFV9vJcFjhVrWBD8PrhoX3Bg5Aa/3vV9agbCOzqzHl1m/47H9C7GjOFmaddBsIx8AfCLk+/oK4DfOPCCis2PgiuzqUG6ZtUhmd183DIp0vMGa0WzE9pPb8VWyLZ39gYEPIMCt0ZTH4nTgx3/a+t7dgSEzOvBIiYiISGnEBTy9US6ZEOjpjJhADziidTk/ocYs1yz1cfbHyG7jW/ZCFjP6HPoK6tosn3LPMKRFt/C1akX7GqFWyQPOEp0ahdX8CHS+wtwC8VTPWzGrxw0IdPZpsPrgG0e/xkvJnyGtMrd5PxBnd+DSl239Az/IxdqJiM6Av7XJLgoqavD2mhR8uz3Luu2K/qFQq1uWAm5PyUXJeGDdA1JxdqFfYD9MT5jecCdRePK724Ga2uwyFx/gmv8Cmkb1r4iIiKhL2daovlVLC5nbU171CezI32jtT+h+NZzULSuDEJG9CX4lqdJ9C1TSFEFLS6ak1eOiBSJ9bFlXKQUcfzWHeE8O9U/Cm/3+havDxjRYffBgWRrmHPgA76cua179q6QrgR4Tbf1fZwMG22JNRET1scYV2UVptQFpBZXYmlbokNMEt+RukbKs7ux9J9ZlrkOloVLarlVpMXfk3NMLsq/+PyB3j60//VMgelQHHzUREREpzbY0W+BqiALqW7XE6uwfrCsqh7lHoV/AsBa9jmt1IXoe/dHaz4wYgxJf2yp3rZEQaER6ifzR50ihE0ZEGtrkdbsSF40zro8Yh3HBg/FN1lpsKtwnbbfAgj8K9mBL0UFcEToKU0JHwVVzjsClCNBOeg1I2wgYdUBRKvDXW8DFT1p3OVh4sFXH2zugd6ueT0TKwYwrsou4IE8khXpZpwn27OaFXqEtq4NgD2azGQaTAUXVRVh8yFaz6s4+dyLBL6HhziL9eduHtv6YxxsuBUxERERdkpgiWD9wNSzG8QJXopB7cslea/+yiOugVrXgI4bFjL4Hv4DWJGfdVLv44miPK9vsOBMDbSsLHslnnavWCHTxxb/ir8VLve9BT69I6/YaswE/5GzAI3v/g/V5u2A027LcmuQfA4yZbev/OR8olLPtiIjqY+CK7EIUcvxuh22a4PQLIhwqNX5k95F4ZPAjeHHri6gx1UjbIr0icW+/exvumLuvYV2rmDENriQRERFR17U3uwRVevnDvZ+7k0NdxBNEmYSVWd9Z+4m+AxDrndjiKYIBRUes/QO9b4FJ64a2IlYW1NTWuSrWqZFXyY9BrRXvGY7nku7CIz2uR7CLrU5tsaEcH6QtxzVb5mD1qW1nL+A+8kEgsPairxhTr5gtPii0+tiIqHPhb2zqcOKP1z2LdyA1X55e56RR4eqB3R2mEPuuU7uk+8tTl0tTBuvMHTEXrlpX286VBcA3NwHGarnvFQZc+xHQeBohERERdUl/HSuw3h8ZF+hwtT73Fm5BblWmdF8NNS4Nn9ai13GrKkDPo8us/azwC1EY2AttSdS5ivW3ZQAdKWDFlLYgLjwP8+8l1b+6NfJSeGhsY2FRtP3Rfe/ihq1zsblwf9MBLK0LcPmbtr4o0n7Q9l4gIhIYuKIOZzBZkF8uZykJE3uFwN+jZQU8O9qvx3/Fxwc+xrbcbXht22vW7VPjp2Jo6FDbjiaDXIy9tDarTKUBEiYCni1fypmIiIiUvTpg43Yum4/Zan2OjG+0GrHC6U01+D3bFmC4IPgiBLmFtHCK4OfQ1mawV7v6IznhGrSHxEBbXavkfAau2pKTWovLQ0firf4P4fKQEQ0KuB8qT8d9u17HXTtfwZ6SlNOfLGYk9Lve1l/1FKA7978fIuo6GLiiDmcwmXEsr8Lav25IuMP8FKbETcGswbPw0YGPUG4ol7YFuQVh9pB68/PF1aRfZwEZm2zbLpgBJEyywxETERGRElXpjdidVWztj4oLhCPZfOp3lBnk43fRuGFsWMvqUUVlboB/sS2YsV+aIlgvg70N9axf56pQa621Sm3Hy8kdt0Zdhrf6P4hru18MTb16ZzuKk3Hr9hfxwNoHcKTetFDJxJcAVx/5fsVJ4Pdn+WMhIisGrqjDLd2Vjcraeg6hPq4Y3SNI8T8FkdpsMpukYqM783Zi84nN1seeG/kcfFxq/9AKf74J7LIVbMeIfwGTXwN6XtbBR01ERERKJYqyiyx0obuvG6IC3OEoKgyl2Ji70tq/KHQyPJy8mv06nuUnkJBiW0UwI2IMigJaViPrfET7meCikc95pV6NnDKWb2gvAS4+eK7XXfhxxCuY1G14g8c2ZG/AtJ+n4ZH1jyC5KFneKGYljH/ettPOT+GRtaPdjo+IHAsDV9ShKmsMeO032xWW6waHQ+MA9RxSS1LxyrZXsC9/H97Y/kaDKYJjwsfYdtz3HbDuRVs/4TLgkqdZZJKIiIga2Jxab5pgXIBDLVKzNucn6M3y1D4fZ3+M6Da+2a+hNunRf99H0JjlLKhKtyAc7TEV7UmrBuID6mVdsc5Vu4v2CMVr/e7HkuEvYnRg/waPrclcg+t+vg4PrHsABwsOAoPvkKcN1gpb9wrU+qr2P0giUjxO7qYOtT29GOU6ecAgAlY3DrMtoatkZpjhrnXHGzveQJVR/gMa4hGCxy943LbT8T+AH++39UMHANM+BvZ/B2T8DUx9H1AzVkxERETAnym2wuyj4h1nmmBe9QnsyN9o7U8MvxZOaqdmv44oxu5VmSvdN6vU2NfvznabItjg6wYacTDPqV6dK3O7f00CEr2isHDgo9hVfATvpi7F9uLD1tOyIWuD1ERga2bvyeiXtQ0w6uBclovgda/i5OCbm3cKg3rylBN1MvwUTR1qyc5s6/3Leocg1KftljluTwl+CQh2D8buvN3Wbc+PfB5ezrVp8Vnbga9vBMy1RT99IoGbvgOcPYCgJCB+HINWREREJDlZqsPh3DKHDFz9lvU9LKid4ugejb7+FzT7NYLy9iEq6w9rPyV+Ckp9otERkoJsGVdHC7XQ27rUAQb59cTHQ57CJ0PmYLh/7waP/VmwFzcfXIj74npjl4uLtC0gZQ3c847yZ0PUxTFwRR06SFu5X76yJtw2Isphzr6Yfz9/53xrf3rCdIwMGyl3Th4AvrwWMFTKfTc/4JbvAa9ucj9yGNBvuj0Om4iIiBRow5E86/3+4T4I8pI/pCtdatlhHCndZ+1fFjldqv/ZHC66EmkVwTqFfglIi56AjhLubYK3i5xlpTepcOCU40zR7EyG+CXiv4OfwOcXPINRAf0aPLZZn4/bw7rhttBgrHd3Q8i2j6Ay2lYkJ6Kuh4Er6jCfb0m3rt6SGOKFoTH+DnH2s8uzceeqO2GozaaK9o7Go0MelR8sSAE+v9q2ZK/IwLplqS1FuTAVMOrtdehERESkQOvrBa4u7hkMR2C2mLEy8ztrP8l3AGK8Epr1GiqzCf0OfAbn2ot9eicP7Ot7O9DM4FdriFJifYINtpXusvlxyJ4G+PbAokGz8dXQubgocECDx3a7uuLBbkG43keDnbv/B0NtPTQi6nr4m5o6RLnOgMWb0639O0dFO0wR0rd2vYUKQ4V0X9RweG3Ma3B3cgfykoFPLwcqawefoi7DTd8C3QfJ/aoiYM1cYNsHdjx6IiIiUpIaowmb6tW3uiTRMQJXuws242R1lnRfrdLg0ohpzX6N+NRfEFBkW6TnQK+bUePqh47Wu5stALI9hx+HlKCvTxzeHTgL3wx7HuOCB0MF2+eENGcnvGbOw0M7X8dPJzahyqiz67ESUcdjcXbqEF9vy0R5jUm6H+zlgqkDuzvEmV9xfAV+S//N2n9k8CNICkgCTh0CPpsCVNUOPEVR0umfA9GjbE929wdGPQwExNnhyImIiEiJdqQXo1Ivj4kCPJzRr7sPlE5vqsGanGXW/tCgixDoGtLsulZxabYxVUbERcjr1jDDpqP0CjJArbLAbFHhRJkaOWUqdPeunRZAdtXbOwZv9X8IaZW5eCvlW/yZtwuG2hhWkVmHr7J+x7KcjRjfbQgu7TYUgS6+/IkRdQG8xEAdcmXxf3+mWfszRsfARatR/Jk/UHAAz/z1jLU/JnwMbkm6BTixB/jsClvQSuMM3PAlkDBR7oug1s7PgJpyIHyIXPOKiIioAyUnJ2PChAnw8PBASEgIHn/8cej15566vnDhQlxxxRUICgqSMqO///77DjnermR9sm2a4EUJQVCrlZ+Bvunkbyg3yGURXDVuuCRsSrOe71aVL00RrFPsE4Pknte2+XGe9/E4AXH+cvBQ2MnpgooT4xGKe2OvwsLEu3FXWRW8TLbVH6vNNfg59y88uOdtLEj5FsnlGbBYGHgk6swYuKJ2t3RXDvLK5YKKWrUKlzhALYdqYzWe+vMp6M3yID/ILQgvjnoRqrQ/5OmBVYXyjhoX4Iavgdx9wJFV8rbCY0DaRjkLi4iIqIMVFxdj7NixUqBq6dKlmDdvHj788EPMmjXrnM9dvHgxCgoKMHny5A451q5GfLheVy9w5QjTBMv1Jfjz5CpbTa7QK+DhVLuq8nlQG2swcO9/4WSslvo1Tp7Y038GLGr7TvyoX+dqOwNXiuXlG4lpCdPwe1YOZhcWI9hom+Zphhlbiw7huUMfY86BD/BH/h7WwSLqpDhVkNo92+rddces/TEJQeju56bos15jrMHzfz+P9DK5JpeYYz9v9Dz4H1sPLL0PqC3SDq0bcOPXQNwlQPpGoG6+fa8rgR4TASdXO34XRETUVS1atAhlZWVYtmwZ/P3lhVCMRiPuv/9+zJkzB2FhYWd87ubNm6FWq5Geni4FsahtHcurwPGCSuvFvDE9ghR/itfk/AhD7YU8P5dADO829vyfbLFgwM634V2eLXehwt5+d9mlrlVjfboZsOywPCbdd1KFKj3g7mzvo6KmlEUNg9eJvbg942/cVFaOFd7e+DgsHsdrbLXi0qpy8f7xZfgqczXGx1yGCVEdt1IlEbU/ZlxRu/pmWxZySuQrbB7OGrxxXX+4Oys3Xnqk6AhuW3Ubfj3+q3XbgwMfxPDUv4Hv77YFrcT0P7F6YPgFcn/CC0DvqbYXYtCKiIjsZOXKlRg/frw1aCVMnz4dZrMZq1evPutzRdCK2vFnc+Ck9f6IuAD4uCs7O/tkVRZ2Ffxl7U8MvxbaZmSU90j+FhEZa6z9lPgpKApIhBKEeZkR6C5PFzSaVdjGrCtFyx18C/TuARDvvqvKyvDNiZN4vuetGObfC+p6H2lLjZX4IeUH/HPtP/HYH49hW+42TiMk6gQ4OqF2U6U34p162Va3DI+Cv4fyLmUZzAYU6Yqk+9nl2ThceNj62ISIsbj76N/Amuek64QSnwjgrtWASQf8OBMola8iEhERKaW+VWJiw+CAr68vQkNDpcfIflbVC1z17e6D/dmlUlPqtMaVWUtgqR3/RHjEoY/fkPN+fmj2JvTa/7G1fzK4P47H1NYDVQCxuPXAUNt0wc0Z/FikZGZnd2SPuA8Wlfxzcis7gbGH1+GR+On4z4CHcGXohfDQ2GZ1mCwmrEpfhbtX340rf7wSnx38DCW6Ejt+B0TUGvwNTe3m083pKKiQa1t5u2qRml+BZbuVF+T54egPeGvnW8gozZCmCNYN0OK9ovDSsT1QHahXmLZbX+Du1UBQAuAXA/S4FPB2jBUSiYio69S4EoGqxvz8/FBUJF+oaWtiamJ2dra15ebmtsvXcWSZhVU4lFsm3Rfl2IfHBkDJUkoPILXskLU/KXK6VLD/fPgUp2DQ1n9b+6VeEdjf5w6gNuigFPUDVzty1KixlU8iBaoO6oFT/a+z9n0z/oZf6h/SyoI3RU7AwoGzcE/MFER4RTR4nij/8caONzBuyTiphu3uvN3MwiJyMMqds0UOLa9ch4XrU639GaNjER/siYRunlCagcED4ePig0f+eATFNcXSNi+NG97KSIF7qe3KKHpdBUx9H9BXAWUnAP8YuREREXVx8+fPx/PPP2/vw1C0lQdswbxeYd7wU3BBJZPZiJVZ31n7ItMq0jPuvJ7rWl2IYZuehdYkX7zUufpj18CZMGldoDTRfiYEuFtQWKVCjVGFXTlqjIiyrV5HylPY81K456fAO2eX1A/Z9SWq/aOh84+Gi8YZ44KHYGyvm3Ck+Ai2n9yO1emrpdkVglh06Zfjv0gt3jce1yVchyviroC3s7edvysiOhdlXfagTuP1VUdQUXvZys/dCdcM7I7JfUMRH3z+q9B0lFjfWCxLWYaU4hSpL64lvnoiC1H1g1aXPA1c9xng7AEc+RVY+bgcwCIiIlIYkVlVWlraZCZW/bpXbUmsWJiVlWVt27Zta5ev48hWHbSNK0bGKTvbakveOuTr5ECbRqWValudD62+EsP+/D+4VcurL5s0zth64fOKKMbeFLUKGBFpC1RtzuRHI8VTqZAz7G7oPeSFDdRmIyL+WghNTUW9XVRI9E/Eq6Nfxdrr1mL2kNmI8o5q8DLHSo7hlW2vYOx3Y/H4xsex+cRmmMxyzTMiUh5mXFGb25tVgiU7bVMCu/u64VS5DuH+7oo62+Lqy7rMddiQtQF/5/5t3f5YYTHGVNUGpZw8gGs+AJKm2J7Y51rAKwxwVtb3Q0REJIj6Vo1rWYlAlpi+17j2VVvx9vaWGp15muDuTFt9HSVPEyytKcK6Ez9b+xeGTIS/67lXP1Sb9Bj211z4ltgy7ncNfRwl/j3hUmKreao0I6NM+CVZI93fmqmGwQQ4yV1ScL2rrAv/iZjfX5ICV86V+Qj/ayEyLp4FqBt+vPVz9cPtvW/Hrb1ulTKwvjvynTT+N1rkC+w1phqsTFsptRCPEEyJnYKp8VMR6R0JeztYeLDVr9E7oHebHAuRvfGyArUpo8mMZ5YfsPaHxvhj0a2D0TvMR3FnWm/S4+1db0vpwnVuLi3HrWXlciekH3DfRlvQqvyktKwzXLyABOUUFyUiIqpv0qRJWLNmDUpKbIGSJUuWSCsGTpzIv1/28OOeHOv9pFBvBHu5Qqm+SV2EGpO8IrS3kx8uCr38nM9RmU0Y8vfLCMzfZ912oN89OBExBkrXp5sFPq5yfdNKgwrbubqgQ9D5RSF3yK3WvmfeYYTu/FIeqzdBrVJjWOgwvHnxm/j9ut/x0KCH0N2zYZ3ak5Un8d/9/8Xlyy7H7Stvl2ZkVBoq2/17IaJzY+CK2tT/NqVhX+3qOCL9eu6UXgj3c4ergi5diYCVWCnny8NfIqs8y7p9bGUVHiuSa1xh+P3AjDVAYLztiT8/BOz6zA5HTEREdP5mzpwJLy8vTJ06FatXr8Ynn3yCxx57TNoeFhZm3W/cuHGIj6/3d04UqN6xA99//z1Wrlwp9bds2SL1//jjD/4IWkiMOZbttgWuLul57uwlezlWegh/5K6w9i+LuA7OmnPUprJY0H/HWwg9YcteT+k5HamJtiLaSqZRA2NibFPE1qXy45GjKIkdg4KetmC8f+oG+KesPefzAt0CMaPvDKy4ZgU+vvRjXBl3Jdy0thUJhV15u/Ds5mdxyXeX4OlNT0tTCY1mVu8nshdOFaQ2I1YNnP/7UWt/VHwg9maVIjrAAx4uynmrLTm6BH9k/dFgeuDgah1ezS+Exj0QmLoQSLj09CcOvBUIG9CxB0tERNSCGldr167FAw88IAWvRBBrxowZePnllxvsZzKZYDQ2/CD27rvv4rPPbBdp3nzzTen2oosuwoYNG/izaIE9WSVIK5CzNpw1aoyOV2bgymwx49OjC6z9aK8E9PW/4OxPsljQe+8HiEr/zbopI+YyHOp3NxzJJbFm/HxYvi8yrsprAC/l1ZKnJpzqfz1cynLhlbtf6ofs/gr68MGoiBp+zvMlsrAuCLlAanOGzZEKuS9PXY6dp3Za96k2VuOn1J+kFuAagEkxkzA5ZjL6BPY571U2iaj1lBNNIIdmMJkxe8le6I1ygcuYQA9MHxKBXZnFcBKXshQkLXtzg6BV75oavHsqH259rgMuexXwqFd3oiIfKEoFug8Bkq6wzwETERE1U1JSkjRd8GyaCkR9+umnUqO2Uz/bamxiMDxdlTn83pi7EsfL5OiNCipcEXnj2T+YWyzos2cR4lKWWTfldh+JvYMfkgpoO5KEQAvCvM04UaaG0azCpnQ1JvXk6oIOQa1G9oiZiFnzMlzLTkBlsSB81TNIu/Z9oBn1nTycPHB1j6ulllWWJQWwRLAqt9K2GmihrhBfHP5CapFekZgcO1kKYsX4cJVxovamrIgCOaw3Vx9tUHT039f2w5T+YZg7pTectfZ/m5XWlGLL0eV4/4sJ+PbERuv2OL0e71dq4Xnjd8C1/20YtBKOrwc2vQVU104hJCIiIjpPNUYTft57wtq/elDDmjpKUaYvwdfH3rf2hwZfjBD3iDM/wWJB390LGwSt8oMHYsfwObColVMe4nyJOJvIuqqz/rjjfQ9dvVh75piHYHT2lPoafSWilj8CFKW16PUivCPwr4H/wqprV+G/E/8rFWv3dJJfu05meSYW7V2EK3+8Etf/cj0+O/iZVCOLiNqH/SMK5PA2HMnDoj9sK8jcd1EshkT5STUdFKH8JE799hRe2vgkFppsf1Di9Qb8L/Qy+P1jy+nF1g06wFgD9L4GGP8c4KnMtH4iIiJSrlUHTqK4yiDd93V3wsUKrW/11bH3UG6QL0B6OfliXPerzryzxYx+u95B7LHl1k153QZi64XPw6xxhqO6JM5W5+rgKTVyyhwra6yrM3gGI2v0AzBrnKS+U1Uh8PnVQPmpFr+mmEo4PHQ4Xhz1ItZPX4/5F8/H+MjxcFLLX6POocJDeGPHG5jw/QTcsuIWKYiVW2HL1CKi1mPgilpF1Gx4+Ns91v6gSF/MntgTG1Py8dA3e1BUqbffGa7IQ9ovD0L3dn98nrESGU621PxEuODjyZ8j8Iq3AddGy3eLgNvq/wPyDgEaLRDcPkuHExERUef2xZYM631RQsFFq7xMnv1F26VpgnVu7fEA3LUNs0vqrx44YMcCxKTaVmQ+FTIEW0e9AJNWuSslno9QL7HCoC3ratURfkxyNFVBCcgaeT8sqtp/Z8VpwBfXAtW2WSEt5ap1xYSoCVhwyQJsuH4DXhj5grRKoZhWW9/e/L1SEGviDxNx06834ZMDnyC7PLvVX5+oq1PmJHtyCCVVetz96XaU1F5J9HLRoHd3H6mmlVjmeUCEL3zdGl6R6BAFKcCWhajc+w0W+Lkjq5svjjnbrgD29YzE+1d8BR8Xn6afr68A3Hzl+lZERERELZBeUInt6bZSAzcNjVTceawx6fBR8uvWfj//oRgVMhFp5UdO21djrMaQv19GSO4267aToUOxfeSzDp1pVd+kniYcOCUHrNYc0+DWgSY489NSix0sa9lUvdao6D4AOePmIHzNi/KGU/tR+fmVyLhyPixODVcOPJfeZ6iR5e3sba2HlVeVh1Vpq7AqfRX2F8gF4uuIvmjzd85HrE+sFOgSLcQjpOXfIFEXxV/F1CI6gwl3f7Ydx2tXydGoVXhkQk9sTi3AyVIdeoV5S63DiCyptD+AvxcCKfLKNrlaLY46+yDHyRY8u6j7GLx20etwd3I/82u5eAFj/09+TSIiIqIWWHHANlVoTEIQogM9FHcel6Z9jLxquQaXs9oFdyXObrIgu7OuGMM3PQu/IltA61RQP+ztfTOcyjPRWYyKMuMDFwvKalRS25Shxtg4Fml3NKVJk6DVlSJk03+kvseJvYj6eTYyprzR7ODVuQS7B+O23rdJ7UTFCfye8bvUROZVfcdLj0vt6+SvEe4ZjsEhgzGk2xDE+cZJUxKJ6OwYuKJm++3gSXyw8Th2ZdjSbl+4qjduHhaFK/qFIqgj1w8uPwns+QrY/TlQdNy6+Q83VzwVFIjyeisaTkuYhqeHPQ2t+ixve1HbSvzx0Do73Io4REREpAxVeiM2HLFlbt8yTHnZVunlR/Fr5rfW/rTYuxHsFnbafh7lORj+59PwrLAVmc8MvxCHE693yELsjWUVVTfoD4+wYPUxedrjyiMaBq4cVOHAG6DRlSBox2Kp75GzG1E/zULmlDelYu7tIcwzDLf3vl1qolD754c+x9aTW3G06CgssF0Qz67IRvaxbCw/tlyaATI4eLAUyOob2BfOnSR7kaitMXBFzVKtN+GZHw8gr7zGuu2+MbFS0EoI9u6A+gY15cDR34D93wMpqwGLrZimTqXCW36++NLHy7pNo9Jg1uBZuLXXrWdf1lk4ugo4/BNw+Xx5uiARERFRM63YfxLVBnl8EubjirGJwYo6h0azER8efhXm2jFUtFcCJkVMP22/oJM7MGTLK3DWl1u3He5zOzJCh3baC3yjo/TWwNWhPDVSClToEcgsfEeUN/w+wGxG0K4vrJlXkVLw6g2YXZqu49ZWxHTAybGTpVakK8K23G3YmrsVyUXJDYJYYuXzdVnrpOaicUG/wH5SEGtQ8CB4u3Tg7BUihWPgis5bXpkOM7/Y2SBodfuIKDw5qQOKl9dUyEGlg8uAY2sAo+60XZJdPfBU93AcM9uunHloPfCfsf/BUDHAOh+BCUDcOAatiIiIqGVDFqMJy/fmWPt3j46Ftl4GuBIsS/tUyrgS1CoN7kl8Apr6GekWC+KTv0OvA59AZZGnyplVauwd8ggyYy6FS8kxdFZBHmYM6W7Cjhw5m+yHAxo8ebHR3odFLaFSIW/kP6TZFEE7azOvcvcheuk/kXnlmzB6BHbIefV39cdlMZdJrUxfhj15e7Dj5A5pOmGNyfa5Stzffmq71ETR93i/eAwIGoABwQMQ4xPToimFBwsPturYz1Tni6ijMXBF52Vfdglu+HALqvS27KabhkVi7pTe585iaglRX0oUWRdBqmO/A+l/AfV+sddX1a0P3g+Pw+fF+2CqF7Tq5d8LL416CT38ezR8wsEfgQPfA9f8D3ByBY6sAvZ8AVz5DtCtl9yIiIiIWmBdcp514RpfdyfccEGEos5jSukB/Jguf4gXpkTdhBjvnta+ylCFIVvmoXvWH9Ztemcv7BjxNPK7DUJXcG0fW+Dqrww1csuAUCa/OG7wasR9gFqNoO2fSpvcClIQ8/1MZFz1FvS+4R16OKKw+5jwMVLTm/RSYGnnyZ3YeWonimtsizmIrKyU4hSpLTm6BF7OXugf1F9q/YL6nXmRKaJOioErOiuLxYLvd2bj/37cjxqjLa31wXE98Mj4Hm0btCrNBjL+BjL+AlLXAiVnKfbpEwlLr6vwW1B3LDi+DCeKdlsfUkONf/n0xl2Jd0BTF7Ra9RTQcxIQMwbwjwHixwN1dRl8I+W+pgNrcxEREVGnYzJbsHSXLdvq9hHR8HBRznBbZ6zCwoMvwQKzdYrgtTF3WR93LdiPiPUPwrU01bqt1DcW20bORZVnKLqKviEWJASacbRADbNFhaUHtfjnCGZdOXTwavi9MLl4IWTTO9Im57ITiPn+XmRe/m9Uh/a1y2GJelYDgwdK7S7LXUgrTcOOUzukQFZmo0UPyvXl2JSzSWqCWKWwf3B/KSMr3jcemk5Qb47obJTzl5QUIb+8Bn8fL8QF0X5S/5Fv92DL8SLr404aFV68qg9uaO2SzqIIet5B4MQeIHMLkPk3UJp19uf4RAC9p8KSNBXbNEa8tfUVHNi/vMEuoR6h0hWMe0qqALMtOwxaF3m6obRTf7nVYZYVERERtYE1h0/hZJlczsBFq8YdI6MVdV4XH30bp6qzpftOamfc3+sZaNVOgMWMwH0foNvON6A2y9liQnbkJdgz5BGYtB1Qw1RBxHXZaX1NmLdenpr1e4oaN/YH/Nunpjd1kMKBN8Lo5ofua1+GymyCtroE0Uv/hRND70Bp9MjTn1Cjb/qFwga2+bGJaYBihUHRru95PfKq8qSphHvz9uJAwQHoTLomVylclrIM7lp39A7sjT6BfdAnoI9UJL5dZsQQ2REDV9RAZlElftqTg83HCvDz3hOorDc1sLuvG967eRAGRDRRtLyqCCg7AfhFAS5egL5KXuXPN0IaDOHkQTmLSgSn8pOBU4caFFVvkkoLhA8GEq+QMqLMZiM2lB7FR/sXYF/+vga7Oqud8dCgh3BT0k1Nrxo4/jn+pImIiKjd6AwmfL3NliVxed9Q+HkoZ4WwjbkrsSH3V2v/hriZCPeMgVPFCYRvnAXPE5utj5nUTjjUbwaO95jaaYuwn8uISDPCvc3ILlPDYFbhm31a3D+cWVeOrjTxMphcfRC+6hloDFVSoDZ8y3/hUpqDvL7XSlMKlSDYPRgToiZITSymcKToCPbk75ECWY2zsaqMVdh+crvUBD8XPymQJepTiVvxWkSOjoGrrsxklAcjag3MZgtKKqqx83g+dmeWoLBSDw1MEEmn4v9XDQjDc5f3hJ+7c8PnCxotcHI/8NdbQMIkOSCVtR04vk6uVaUrOf9j8osGel4ORI0Cdn4M9JmGwp4TsTx1OX7Y9R4yLQ2vfIjChRdFXISHBz0sXaEgIiIisodf9uVK4yfBw0WDaYM7tnZOfcfLkhv0T1Xl4KPk1639nj790MMrCZadryJ+/yfQGm01Qsu8o7Bz+JMo6+LjKrUKuHGACa9vlAMZq46oMbUXEMZaVw6vInoE0qZ9gMhfHoNz+UlpW9DhFXArSkf2iPtgclXWD1lclJcCUYG9cXPSzdIqheIivijyvr9gPyoNlQ32F7Wy6k8rFIErkYlVF8zydeXK6eR4FBW4Sk5OxgMPPIDNmzfDy8sLt912G1566SU4Ozufsw7Tv//9byxcuBD5+fkYMGAAFixYgOHDh3fYsTuEmnKgIg8IqB2ILP8nzCH9sD3kBixYcxRTs15DiTkIhaarpIf/T/sF4OKNyGtfxLgoZ2DN4/JrxI8DSrKAIyuAqkJAZDiJ+lRiadfUded/POKXZmg/IGI4EDFUztTyjwU8g1GqK8G6yuNYffJ3bNn3GoyW069wxfnEYf7F8xHrG9tmp4iIiIioJSsvf7fDVvJg2qAIeLk6KeJE1ph0+Dr1fRjMclDNx9kfdwSMxaj1s+BXdKTBvmlxU3Cw/z1dbmrgmYyJMWPpATNSi9QwWVT4fJcWT3CFwU6hJjAOx6f/DxEr5kgrDQqepw4hbtVcZI/8B6qCE6BUYpXCiyMulprJbEJqaSoOFhyUphQeLT4KQ73pvoKYdriuah3WZcmf08I8wtDTv6fUEv0T0c29G6cWkuIpJnBVXFyMsWPHokePHli6dClycnIwa9YsVFVV4d133z3rc0XQau7cuXj11VfRr18/vPfee5g4cSL27NmD2FgGNazSNwF7vwYuX4CUUyU4XhyKXQczkFK9EKGohEVtQZwqB69qP0SYtgz93fLhjUqovl8GmOsFjg792MyfrkqeMhiUBIQNAEJF6w94h1nTz8Xyr+KqwZajX2Nr7lbpF69YTaMxMSVwStwU6WpBtE80g1ZERERkdy+vOIxqg1wCIdDTBVf0U0Yhc7PFjO9SP0SBTs4q0ag0mGMKxmXrHoO6XsmGKvcg7B38EPJCh9rxaJWZdXX7YCOe/V2+iL4xXYOr8kxIDD59jEqOx+Tuj4yr/4Nuv7+AgBQ5qOOkK0H0+ldRkDgZGPkQoFHOdN+miKLsCX4JUru6x9XSSoUieCUFsgoPILUkVfo9UN+JyhNSW5+1Xur7uvjKgSw/OZAV5R3FYu+kOIoJXC1atAhlZWVYtmwZ/P39pW1GoxH3338/5syZg7CwsCafp9Pp8Morr+DRRx/FI488Im0bPXo0EhIS8MYbb0hZWIpRXQwc+gmIvlDOehLFwg/8AEQOB4J6AsYaYO83QPfBQEgfubj4jk/kx6THdcC+7wHvEHlKnb4SSFkNOHsAXqGAvgLI2Smtqwc3H/nxwuOAiLqr1EDFKUBXDhyKhVhrT7RLxXGd6fexLWv8/Di5A34xQFACEFivBcQDzmeuZjl381z8kvoL9LVXApsS7hmOCK8IPDP8GUR4K2tZaSIiIuq6NqcWYPmeE9b+PaNj4OqkjBW+VmUtwZFSW13QWcXlmFy82tq3qNQ4Hn8VDve5AyYnNzsdpbINCrOgf6gZe3PlKYPv/q3FW1MM0CqjFBK1kkXjjJODb0VVUALCtn0KjVEHlcWCoMO/AqcOAxc/BQTWrlLuAMRKhVKR9sA+uB7Xo9pYjcOFh3Gw8KAUzEovSz/tOSU1JVLigGiCi8ZFCoSJYFZJZIn0Wj4uPnb4bogUGLhauXIlxo8fbw1aCdOnT8fMmTOxevVq3HHHHU0+T0wrFAEvsW8dMbXwmmuukTK3FGPzO0DG33JgSayOJwI5InBVdEyajidF8w3VQFUBoNLIdaJMZw7kdDhxTJ7BgEeQnCnlG2lr4vvxjQLc/VtUwFOr0jYZtIrxiZEKEk6Mmij98uTqGERERKQkRpMZzy4/aO0PivTDiNgAKMH2vD+w+dTv1v61ZRW4tdi2UnSJbxz2DnkYJf497XSEjkEMbe8dasSDPzlJ0wXTitVYfkiDa/ucY5Ehsp/8hlNgz0dZ5DDofCMR/veHcCuuDe6IhaaWzQQG3QYMuFHx2VdNcdO6YVC3QVITKvQVUkaWKPaeXJQsTTMUxd/rEzNhRO0s0b4/+r20LdIrUgpg9Q3sK90mBSRJAS6lEwG71hIzfcj+tEqqb3XXXXc12Obr64vQ0FDpsbM9T0hMTGywPSkpCZmZmaiuroabmwKuIKX9CaT8Jt+vkNO1rXSlHX88aidUqL1gcfWFu28gNG5+gJuvHJgSASrPbvVuuwFu/u22ysaw0GH47uh3CHQLlO4PDx0utRCPkHb5ekRERERtQaNWYfbEnnjxl0M4VabDfWNiFXGh7WDhdvyU8YW1P6xah6cLi0TxBuhc/aQMq8zoidICPXRu0X4WKVD13X75o9OXuzUYGWlCqLJqeFMr6b1DcXzC0wg69CuCDv4MlUgkEG3nJ8Cx34GRDwARwxz6PHs6ezYIZImphcdLj1sDWSKo1bjYuyBWMhRtRdoKa+JBgn+CNZAlir+LMi5Nru5O1AYUVeNKBKoa8/PzQ1FR0Vmf5+LiAldX19OeJ4q2i8fPFLgSmVqi1cnNzUW70bYyQi+KZGpdABHZFtlazp7y1DwxTVBqnme57w64+sjF0OsCVE7u8FTAwEoY1X0Ull25TFoVUAmDPSIiIqLzIcYtl/UJwZiEQPywMwdhvva9WKoyVuPY/gVYUvgrLLVjqiiDAW/mFUClccGRhGtxLHE6jGIMSc1yfX+TVOPqZLkKNSYVXt/ohNcmc8pgp6PWIr/PVSgP64+47Z8BddlXYiGqlU/IK59f9R7gH4POQEwtFHWtRLsKV0n1sHLKc3C46LAUxMouz25yeqFYOOtQ4SGpfXvkW2mbyMDq4dsDiQGJSPRLlG5F352/b6gzBa7sYf78+Xj++ec75osNvA2IucgWgJKaq5xy2nhbXYDKuo9Ti6bgOQoPJw/E+8Xb+zCIiIiIWsTdWYsBEadfgN2ffX5Z9ee735k4lWcj4PBipKZ9h5f83WGszZIPNhqx8FQxCmOnYEvi9dC5B7bq63Rl+WXVuKGPAW//7QELVDhSoMaXezS4fRCnDHZGOv9o4JoPgT1fA3u+tJVwyfgLeG8oMPgOYPSjgFfnmiGiVqmlesKiTYyeKE2TK9OXSfWx6qYP7s/fj0Jd4WnPFVMMRUF40eqooJKKvSf5J1lXMRS3Aa4BTFggxwxciQyp0tLT/2iLjKn6da+ael5NTY1UpL1+1pV4nrgKJh4/E7Fq4YwZMxpkXA0d2k6rqSRMbJ/XJSIiIqIuR2XSwytzLfyOfguv7A1I1WrwUFg31NQGrfxMJjzr0h+HLrsNNW7KqLvl6BKDjJgQX4PVx+TPHEv2aTAg1Iz+oVxlsDM6WJkD9BgDp9BeCNnzDbyzd9YuR6gHtn0I885PUdRvGgoG3wyTmNXSSXk7e2NE2AipCWJW06mqUw0CWSJDq6kphmKVeJGxJdrK9JXW7aLYe5xPnDTjpq7F+8YzoEXKD1yJGlWNa1mJQJYIJjWuX9X4ecKRI0fQv39/63bxWpGRkWetb+Xt7S01IiIiIiLFs5jhlr8Hvqk/wTf1R2h1tnIaUQYzRlXr8LuHOzygxR09H0GJH4sKt7UrE3U4UqBFRokWYmZo550TQXUMnoHIuvBf8Mg9IAWwXEtzpO1qkx6Bu7+C//6lKEmajML+06H3i+z0J04kh4haxKKJhbSEuimGycXJUq2supZXldfka5TWlGJX3i6pNQ6SiQBWrG+sdBvjHYNI70iEeoRCw5p8XZpiAleTJk3CvHnzUFJSYq11tWTJEqjVakyceOZspZEjR0rBJ7FvXeDKYDBIKwpOnjy5w46fiIiIiDqRE7vPf9+wge13HGYTPE5th3faCvikr4JTVaNFfmoZAvviwcQ7AFMaYn16I8Az7ry/hEvJsTY84M5NqwZmDK7C8sOumDXGAp+GZXapE6sM7YPUbi/AO2sbgg/8CJfyU9J2tVEnBa/89i9Deff+KEqYgMrgREBVu7BVUOdfubP+FMO6YJZQpCuSAlh1xd9FyyjLgEkUvW+CmJbYVEDLSe2ECK8IKYgV5RUl3UZ7R0u3we7B0tenzk0xgauZM2finXfewdSpUzFnzhzk5OTgsccek7aHhYVZ9xs3bhwyMjJw7Jj8B1ZMD3zqqafw3HPPISgoCH379sXChQtRWFiI2bNn2/E7IiIiIiJqPm1VHjxzNsEzZyM8szfCSVfQ5H5GF1+UxE1FccJ06AL7SNvuBHC87MwrclPrBXmYMWNIFXxcFbByOXUstRplUcNRFnEBfNM3S6sPOlfmSw+pYIF3zh6p6T2CUBJzIUpiRsEQ1HV/SP6u/hgZNlJqdcRKhiJ4lVqSitTSVOn2WMkxZJZlnjGgZTAbpNUPRWvMVeMqB808IxDmGYbunt2tt1WGKhaH7yQUE7gStajWrl2LBx54QApeeXl5SfWnXn755Qb7mUwmGI3GBtueeOIJaa7tG2+8gfz8fAwYMAC//fYbYmNjO/i7ICIiIiJqHo2uCO6ndsLj5DZ45vwJt6JDZ9zXrHVDefjFKIm7EuWR42ERC/oQUcdSa1ASOxol0aPglbMLAUdWw6MgxfqwCGYFH1iGoAM/ojJiCAr7X4eKmAv5U6pdybCHXw+p1WcwGaRaWHXBLNFEgEsEtHQm3RnPnXgspThFamdaCCzILUhqge6B0m2AW4AUVPNz9YOviy+0asWERegMFPUTSkpKwpo1a866z4YNG5qcZyuyrkQjIiIiIlIqlakGLsUpcCvYD/e8nfA4tQMuTWQR1Gdy8pSCVKXRk1AecTEsWmb6ECmCWo3yiCFScytMhf/RNVIRd7XJYM3C8szaDl1QgkMGrg4WHmzV88WqhOfLSePUZEBL1M8StbJEACujXA5kiQCXuM0qz5Kysc5GFI0XTTynKWLlQ1EsXgSy6poIaNXdF7W7xOMiACbiDu15DshBAldERERERJ2CxQJtdZ5UP8q18DDcig7CtfAQXItToLI0nD3QlOqA3qgIuxDl4WNQFTKUmVVEClcdEIecEXHI1VfBJ3MrfI9vgnuRHJQuTrrc3ofnsET9qrpi8ENDhzZ4zGQ24WTVSSkz60TFCanlVORY7+dVN10cvvHKhyU1JVJraipiHY1KIwWwpObsA28Xb+t9cSv6IntLFJj3cvZiFlcbY+CKiIiIqJMRqyuL8gubN2+Wyi/cdttteOmll+Ds7HzW54nSC//+97+leqF15RcWLFiA4cOHd9ixOxSzCaguAjK3wud4spQ55VKWBmdxW5oGjaHivF+qxisCOv8kVAf2RVXQAJhc/ayPNXc6IIutE9mP2dkdxfGXSM2lNAceFfnQ+0fzR9IOxEqDopaVaE3ZnbcbhdWFyK/OR35VvvVWFI0v1hVLt3qz/ry+lqi/JfYX7Xy4ad2s0xTrAl51ga36/fqBMBHwclY7tyizq7Nj4IqIiIioEykuLsbYsWPRo0cPaZVlseDNrFmzUFVVhXffffeszxVBq7lz5+LVV19Fv3798N5770mrO+/Zs6dr1Q61WICacqC62NaqiuQgVUUeUHGqtuUDtcWEI5vx8kZnb+h9YqDz64lq/yTo/BNhdvZqt2+HiOyjxqc7auLH8vTbsZ5WqGeo1M50sUZMI6wLSNUFtAp1hdbAlmgV+gopM6s5qo3VUiuobnpxjTMR9bY8nTzl5lx76+QJD2eP07aLwJgIdolbEShr3Fw0Lp0mCMbAFREREVEnsmjRIpSVlWHZsmXw9/eXtomFbe6//35p5eb6qzXXp9Pp8Morr+DRRx/FI488Im0bPXo0EhISpAVwRBaWw2VDGaoAfaXcdKWArkS+rS45w/1ioLJADk6Zalp/CGon6L0iUeMvAlS9oQvoJU0B1FadEkVa2+TbJCLqrDWy2psI6khBIGdPRHqf+fKDmJJYri9Hqb4UpTWlKKsps96X+voy632x3Wg+93TwMxHPrZu62BbTLF01rrZglpMb3DSNAlxOtvtiX1etqxTwsjatCwJcAzAgeADsiYErIiIiok5k5cqVGD9+vDVoJUyfPh0zZ87E6tWrcccddzT5PDGtUAS8xL51xNTCa665RsrcUkwm1Mon5ECUQQSkqhoGp+rui1vjmVehalNqJ8A3AhWuIajxjobeJw41PrFS03tFAE2sViVqXxERkeNMSfR19ZXauYgsrhpTDSoMFVKmVqBboBSEqgtwlehKGgS96oJd4vZcheabSxS2rzJWSa01+gf1xxeTv4A9MXBFRERE1MnqW911110Ntvn6+iI0NFR67GzPExITE09b9TkzMxPV1dVwc7PzanYiS2nXYsBY3TFfz8UbcPcH3ETzk5tnEODZrbYFy9u6D0ZadmnHHBMRESk6i0tkLYkmglbNWVVQb9JbA171bysNlVLGl3RrKEelvvbWUCntI27rpibWNVGTq62ITCx7Y+CqHpFGL+Tm5trr50FEREQKVjdGqBszKLXGlQhUNebn54eioqKzPs/FxQWurq6nPU9cQRaPnylwJTK1RKuTlZXVfmOqKmdAV3n++4vC5k5ugIuXHIhy9ZZvG9z3Alx95Fv3ALlV5AKqswyVxVugxAiUiDpX2TiZa/v+z8W1qHkZVzpDTrP2z88rbNb+1JCT/vT3eX5J9XntR3Qaw0melC7Mp9qn2c9RQw3v2v+gFhdRalszGEwGKYClM+mgM+pst43ui+ywalO19b4IntUYa1BjrpH7Rj26GbohOzsb9hxTMXBVj1g9Rxg6tOEym0RERESNxwzR0Vwlqs78+fPx/PPPn/YmUcaY6vxX9iMiIqLTzcM82HNMxcBVPX379sW2bdsQFBQErdb+p0ZEIMWATxyTSO8nnlMl4vuU59QR8H3Kc9pWxFVBMcASYwalEhlSpaWnT1sTGVP161419byamhqpSHv9rCvxPDH1QTx+JmLVwhkzZlj74jVE1lVMTAzHVJ0Uf6/ynDoCvk95Th1BV32fGpsxprJ/dEZBxCDtggsugNKIN294eLi9D6NT4TnlOXUEfJ/ynDqCrvg+VXqmlahR1biWlQhkiYFx4/pVjZ8nHDlyBP3797duF68VGRl51vpW3t7eUqsvPj4eStMV36/tjeeU59QR8H3Kc+oIuuL7NPo8x1RixiQRERERdRKTJk3CmjVrUFJiW0p7yZIlUKvVmDhx4hmfN3LkSCn4JPatYzAYpBUFJ0+e3O7HTURERNQUBq6IiIiIOpGZM2fCy8sLU6dOxerVq/HJJ5/gsccek7aHhYVZ9xs3blyDrCiRef7UU0/hjTfewNtvv41169bhxhtvRGFhIWbPnm2n74aIiIi6Ok4VVDBx1XPu3Lmnpd4Tz6mS8H3Kc+oI+D7lOe1KRC2qtWvX4oEHHpCCVyKIJepPvfzyyw32M5lMp63k88QTT0grCIrglag7MWDAAPz222+IjY2FI+PvAJ5TR8D3Kc+pI+D7lOfUHlQWMTohIiIiIiIiIiJSGE4VJCIiIiIiIiIiRWLgioiIiIiIiIiIFImBKyIiIiIiIiIiUiQGroiIiIiIiIiISJEYuFKg5ORkTJgwAR4eHggJCcHjjz8OvV5v78NyaEuWLMFVV12F8PBw6byKVZI+/vhjaeUkar2Kigrp3KpUKuzYsYOntJU+++wzDBw4UFqaPjAwEJMmTUJ1dTXPawv99NNPGDZsmLSyWmhoKKZPn47jx4/zfJ6HY8eOYebMmdLvTK1Wiz59+jS530cffYSEhATpPdu/f3/88ssvPL+kCBxTtS2Op9ofx1Rth+OptsXxVOtwTNU6DFwpTHFxMcaOHSsFqpYuXYp58+bhww8/xKxZs+x9aA5t/vz5cHd3x5tvvomff/5ZCgTcc889eOGFF+x9aJ3Ciy++eNqS6tQyYrl6sYT99ddfLy1B/8EHHyAmJkZatp6ab8OGDbj66qvRq1cvLFu2DG+99Rb27t2LiRMnMhh4Hg4ePIhff/0V8fHx0jlsyjfffCP9PhXv2ZUrV2LEiBHSOd+yZQvfsmRXHFO1PY6n2h/HVG2D46m2xfFU63FM1UoWUpR58+ZZPDw8LIWFhdZtH3zwgUWj0VhycnLsemyOLD8//7Rt99xzj8Xb29tiMpnsckydxeHDh6X37KJFi0T6mmX79u32PiSHlZycbNFqtZYVK1bY+1A6jfvuu88SExNjMZvN1m3r1q2T3qsbN26067E5gvq/H2+//XZL7969T9snISHBcuONNzbYNmLECMukSZM65BiJzoRjqrbH8VT74piqbXA81fY4nmo9jqlahxlXCiOuVo8fPx7+/v7WbWJai9lsxurVq+16bI5MTLdqTEzFKisrQ2VlpV2OqbMQ2UFiKlHPnj3tfSgO75NPPpGyq0RGILUNg8EgTREU01jr+Pj4SLecKnxuavXZhwliyuXRo0elv1P13XDDDVi7di1qampa+JMjaj2Oqdoex1Pti2OqtsHxVNvjeKr1OKZqHQauFFiLITExscE2X19fqS6LeIzazqZNm9C9e3fpQy21zPfff4/9+/fj2Wef5SlsA2JqVd++ffHSSy8hODgYzs7OGDVqFLZu3crz20J33HEHDh06hIULF6K0tFQKtMyZM0cKXItzS61T93ep8d+tpKQkacp7WloaTzHZDcdUHYPjqbbBMVXb4Xiq7XE81f44pjo7Bq4UWI9BBKoa8/PzQ1FRkV2OqbMOskRdltmzZ9v7UBxWVVWVVHtN1GHz9va29+F0CidPnpQyKxcvXiwFWn788UcpU0jUY8rLy7P34Tmk0aNHS7WtnnzySel3a1xcHE6dOiVlYmg0GnsfXqf4myU0/rsl/mYJ/LtF9sQxVfvjeKptcEzVtjieanscT7U/jqnOjoEr6nKys7OlIsKXXHIJHnzwQXsfjsMSWUHdunXDnXfeae9D6TTElGCxmpC46jpt2jRMnjxZWsFFTGl799137X14Dmnz5s249dZbpeLh69atk1bEEuf58ssvZ3F2IqJW4Hiq7XBM1bY4nmp7HE+RvWntfQCE065Si+ksTUVg69e9opYpKSmR6gcFBATghx9+OOdcY2paRkaGtEKjyGSpe7+KgEvdrWienp48fS349y/em/369bNuE//uxbQ2sRIJNZ8ITouVWsX7tc7w4cMRGRmJzz//HPfeey9PayvUZVaJ3wMhISGnXTXk3y2yJ46p2g/HU22HY6q2x/FU2+N4qv1xTHV2/NSuMKJOSONaVuIDQW5u7mk1RKh5qqurccUVV0jnU0wTqivQTM0n6taI+jUia0X8khVtypQp0mMik00sMEDN17t37zM+ptPpeEpbQNS3GjBgQINt4eHhUoHh1NRUntNWqvu71PjvluiLGm2xsbE8x2Q3HFO1D46n2hbHVG2P46m2x/FU++OY6uwYuFIYkQ20Zs0a6UpWHTG1RWQGiTo31DJGo1Fa9erw4cNYtWqVVJSdWk4EAtavX9+gLViwQHps0aJFUn0maj4RWC0sLMSePXus20R/165dGDx4ME9pC0RFRUnnr/HV7YKCAkRHR/OctpIITCUkJEh/p+r79ttvMW7cOCl4RWQvHFO1PY6n2h7HVG2P46m2x/FU++OY6uw4VVBhZs6ciXfeeQdTp06VVr7KycnBY489Jm0PCwuz9+E5rPvvvx+//PKLNF2orKxMWm2kjpiG5eLiYtfjczSiEPPFF1/c5GMiwDJo0KAOP6bOQPy7v+CCC6T6Vi+//DLc3NzwyiuvSO9P8R6m5hO/Ox9++GE89NBDUlagCATWrdoogtl07oLBK1assAb8xO9PUYNNuOiiixAUFITnnnsON998s1T4XmRciqCVWAlz48aNPL1kVxxTtT2Op9oex1Rtj+OptsfxVOtxTNVKFlKcQ4cOWcaNG2dxc3OzBAcHW2bPnm2pqamx92E5tKioKIt4uzfV0tLS7H14ncL69eul87l9+3Z7H4pDy8/Pt9xyyy0WHx8f6XfAxIkTLQcPHrT3YTkss9lsef/99y39+vWzeHh4WEJCQixXX3215fDhw/Y+NIcgfj+e6Xen+Ddf53//+58lPj7e4uzsbOnbt6/l559/tutxE9XhmKptcTzVMTimaj2Op9oWx1OtxzFV66jE/1ob/CIiIiIiIiIiImprrHFFRERERERERESKxMAVEREREREREREpEgNXRERERERERESkSAxcERERERERERGRIjFwRUREREREREREisTAFRERERERERERKRIDV0REREREREREpEgMXBERERERERERkSIxcEVERERERERERIrEwBURERERERERESkSA1dERERERERERKRIDFwRETXy888/Q6VSISUlpcH24uJiuLm5YeHChTxnRERERGfB8RQRtRUGroiIGpk8eTK6d++Ojz/+uMH2r776Srq96aabeM6IiIiIzoLjKSJqKwxcERE1otFocOedd2Lx4sUwmUzW7SKQdc0118DX15fnjIiIiOgsOJ4iorbCwBURURPuvvtu5ObmYtWqVVJ/37592LVrl7SdiIiIiM6N4ykiagsqi8ViaZNXIiLqZC699FJ4eHhg6dKlePjhh/HTTz8hNTVVqn9FRERERBxPEVH7Y8YVEdEZ3HPPPfjll1+Qk5ODL7/8Upo+yKAVERER0fnjeIqIWosZV0REZ2AwGBAeHo7ExERs2rQJ6enpiIiI4PkiIiIiOk8cTxFRazHjiojoDJycnHD77bdj48aNmDBhAoNWRERERM3E8RQRtRYDV0REZ3H11VdLt3fddRfPExEREVELcDxFRK3BwBUR0VmsXLkSAQEBuOqqq3ieiIiIiFqA4ykiag1tq55NRNRJHTlyRGrvvPMO/vnPf8LFxcXeh0RERETkUDieIqK2wOLsRERNuPjii7FlyxZcdtll0oqCHh4ePE9EREREzcDxFBG1BQauiIiIiIiIiIhIkVjjioiIiIiIiIiIFImBKyIiIiIiIiIiUiQGroiIiIiIiIiISJEYuCIiIiIiIiIiIkVi4IqIiIiIiIiIiBSJgSsiIiIiIiIiIlIkBq6IiIiIiIiIiEiRGLgiIiIiIiIiIiJFYuCKiIiIiIiIiIgUiYErIiIiIiIiIiKCEv0/PG5kUdUPnx4AAAAASUVORK5CYII=", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, (ax_cdf, ax_pdf) = plt.subplots(1, 2, figsize=(11, 4))\n", "\n", "colors = [\"C0\", \"C1\", \"C2\"]\n", "for k in range(K):\n", " yk = y[stratum == k]\n", " lo, hi = float(np.quantile(yk, 0.005)), float(np.quantile(yk, 0.995))\n", " y_grid = np.linspace(lo, hi, 300)\n", " xk = np.full(y_grid.shape, k, dtype=int)\n", " cdf_k = interact.predict(y_grid, X_new=xk, what=\"distribution\")\n", " pdf_k = interact.predict(y_grid, X_new=xk, what=\"density\")\n", "\n", " ecdf = np.searchsorted(np.sort(yk), y_grid, side=\"right\") / yk.size\n", "\n", " ax_cdf.plot(y_grid, cdf_k, color=colors[k], lw=2, label=f\"stratum {k}\")\n", " ax_cdf.plot(y_grid, ecdf, color=colors[k], lw=1, ls=\":\", alpha=0.7)\n", " ax_pdf.plot(y_grid, pdf_k, color=colors[k], lw=2, label=f\"stratum {k}\")\n", " ax_pdf.hist(yk, bins=25, density=True, color=colors[k], alpha=0.2, range=(lo, hi))\n", "\n", "ax_cdf.set_xlabel(\"y\"); ax_cdf.set_ylabel(\"F(y | stratum)\")\n", "ax_cdf.set_title(\"Conditional CDF\"); ax_cdf.legend()\n", "ax_pdf.set_xlabel(\"y\"); ax_pdf.set_ylabel(\"f(y | stratum)\")\n", "ax_pdf.set_title(\"Conditional density\"); ax_pdf.legend()\n", "fig.tight_layout();" ] }, { "cell_type": "markdown", "id": "4446444f", "metadata": {}, "source": [ "### Quantile prediction\n", "\n", "`predict(..., what=\"quantile\")` inverts $h(\\,\\cdot\\,\\mid x)$ row-by-row\n", "on the interaction path — the same grid+spline machinery used for the\n", "non-proportional Cox example below. The conditional medians track the\n", "Gaussian/lognormal medians of each stratum." ] }, { "cell_type": "code", "execution_count": 7, "id": "7e1bc157", "metadata": { "execution": { "iopub.execute_input": "2026-05-21T09:49:30.407000Z", "iopub.status.busy": "2026-05-21T09:49:30.406925Z", "iopub.status.idle": "2026-05-21T09:49:30.409579Z", "shell.execute_reply": "2026-05-21T09:49:30.409279Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "stratum 0: mltpy median = 1.997 true median = 2.000\n", "stratum 1: mltpy median = 3.976 true median = 4.000\n", "stratum 2: mltpy median = 3.969 true median = 4.055\n" ] } ], "source": [ "probs = np.array([0.5, 0.5, 0.5])\n", "x_pred = np.array([0, 1, 2], dtype=int)\n", "med_hat = interact.predict(probs, X_new=x_pred, what=\"quantile\")\n", "med_true = np.array([2.0, 4.0, np.exp(1.4)]) # lognormal median = exp(mu)\n", "for k in range(K):\n", " print(\n", " f\"stratum {k}: mltpy median = {med_hat[k]:.3f}\"\n", " f\" true median = {med_true[k]:.3f}\"\n", " )" ] }, { "cell_type": "markdown", "id": "5b9ca76e", "metadata": {}, "source": [ "## 2. Non-proportional Cox — crossing survival curves\n", "\n", "Now we leave the categorical setting and use a *continuous* covariate.\n", "We simulate survival times whose hazard *shape* depends on $x$: low-$x$\n", "observations have a decreasing hazard (Weibull shape $< 1$, frailty-like\n", "early failure) while high-$x$ observations have an increasing hazard\n", "(Weibull shape $> 1$, ageing). The medians are similar by construction,\n", "so the survival curves *cross* in the middle of the support — exactly\n", "the textbook violation of the proportional-hazards assumption.\n", "\n", "We then fit a non-proportional `Coxph` using\n", "`interacting=BernsteinBasis(...)`, which expands the baseline\n", "log-cumulative-hazard $h$ over both $t$ and $x$ simultaneously." ] }, { "cell_type": "code", "execution_count": 8, "id": "f2f3bf6b", "metadata": { "execution": { "iopub.execute_input": "2026-05-21T09:49:30.410474Z", "iopub.status.busy": "2026-05-21T09:49:30.410413Z", "iopub.status.idle": "2026-05-21T09:49:30.412292Z", "shell.execute_reply": "2026-05-21T09:49:30.412011Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n=600, t in [0.004, 13.890], shape in [0.80, 2.19]\n" ] } ], "source": [ "n_cox = 600\n", "x_cont = rng.uniform(0.0, 1.0, size=n_cox)\n", "shape = 0.8 + 1.4 * x_cont # 0.8 at x=0 -> 2.2 at x=1\n", "scale = 2.0 # common scale; all S(t | x) curves cross at t = scale\n", "u = rng.uniform(size=n_cox)\n", "t = scale * (-np.log(u)) ** (1.0 / shape)\n", "support_t = (float(t.min()) * 0.5, float(t.max()) + 0.5)\n", "print(f\"n={n_cox}, t in [{t.min():.3f}, {t.max():.3f}], shape in [{shape.min():.2f}, {shape.max():.2f}]\")" ] }, { "cell_type": "markdown", "id": "51834d81", "metadata": {}, "source": [ "### Proportional baseline\n", "\n", "A standard `Coxph` with $x$ as a single-column covariate — the\n", "classical Cox model with a smooth Bernstein baseline." ] }, { "cell_type": "code", "execution_count": 9, "id": "79e94f66", "metadata": { "execution": { "iopub.execute_input": "2026-05-21T09:49:30.413167Z", "iopub.status.busy": "2026-05-21T09:49:30.413115Z", "iopub.status.idle": "2026-05-21T09:49:30.817322Z", "shell.execute_reply": "2026-05-21T09:49:30.816890Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Model: Coxph\n", "Support: (0.0021859245671776496, 14.389615100396629)\n", "Basis order: 6\n", "Fitted: Yes\n", "Log-lik: -1018.6470\n", "AIC: 2053.2939\n", "BIC: 2088.4694\n", "Converged: No\n", "n_restarts: 3\n", "\n", "Coefficients:\n", " Estimate Std. Error z value Pr(>|z|)\n", " X1 0.4039 0.1459 2.768 0.005632\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/var/folders/l3/9xz3dcxx2879v30qp8ptbjbw0000gn/T/ipykernel_45133/3956983511.py:1: ConvergenceWarning: Optimization did not converge after 3 restarts. Solver message: Maximum outer iterations reached without convergence.. The result is the best found, but may not be the MLE.\n", " prop = mltpy.Coxph(support=support_t, order=6).fit(t, X=x_cont.reshape(-1, 1))\n" ] } ], "source": [ "prop = mltpy.Coxph(support=support_t, order=6).fit(t, X=x_cont.reshape(-1, 1))\n", "print(prop.summary())" ] }, { "cell_type": "markdown", "id": "8abfd910", "metadata": {}, "source": [ "### Non-proportional fit\n", "\n", "Passing `interacting=BernsteinBasis(order=q-1, support=(0,1))` routes\n", "the model through the tensor-product likelihood path; the time-basis\n", "stays at order 6 on the original support. Only exact (non-censored)\n", "times are supported on the interaction path in the current release; the\n", "censoring argument set internally to `RIGHT` is ignored when no\n", "`CensoredData` container is supplied." ] }, { "cell_type": "code", "execution_count": 10, "id": "15667c49", "metadata": { "execution": { "iopub.execute_input": "2026-05-21T09:49:30.818393Z", "iopub.status.busy": "2026-05-21T09:49:30.818318Z", "iopub.status.idle": "2026-05-21T09:49:41.091877Z", "shell.execute_reply": "2026-05-21T09:49:41.091442Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/var/folders/l3/9xz3dcxx2879v30qp8ptbjbw0000gn/T/ipykernel_45133/1273050889.py:7: ConvergenceWarning: Optimization did not converge after 3 restarts. Solver message: Maximum outer iterations reached without convergence.. The result is the best found, but may not be the MLE.\n", " ).fit(t, X=x_cont)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "log-lik proportional : -1018.647 (k=8)\n", "log-lik non-proportional : -991.968 (k=28)\n", "LR statistic : 53.36 on 20 df, p = 7.20e-05\n" ] } ], "source": [ "x_basis_cox = BernsteinBasis(order=3, support=(0.0, 1.0))\n", "npcox = mltpy.Coxph(\n", " support=support_t,\n", " order=6,\n", " optimizer_config=mltpy.OptimizerConfig(random_state=0),\n", " interacting=x_basis_cox,\n", ").fit(t, X=x_cont)\n", "ll_prop = prop.result_.log_likelihood\n", "ll_np = npcox.result_.log_likelihood\n", "df = npcox.n_free_params_ - prop.n_free_params_\n", "lr = 2.0 * (ll_np - ll_prop)\n", "p_value = float(chi2.sf(lr, df=df))\n", "print(f\"log-lik proportional : {ll_prop:.3f} (k={prop.n_free_params_})\")\n", "print(f\"log-lik non-proportional : {ll_np:.3f} (k={npcox.n_free_params_})\")\n", "print(f\"LR statistic : {lr:.2f} on {df} df, p = {p_value:.2e}\")" ] }, { "cell_type": "markdown", "id": "0b3cb8da", "metadata": {}, "source": [ "### Crossing survival curves\n", "\n", "We evaluate $S(t \\mid x)$ for three representative covariate values\n", "($x = 0.1, 0.5, 0.9$), overlay the true Weibull survival, and confirm\n", "visually that the curves cross." ] }, { "cell_type": "code", "execution_count": 11, "id": "82c75bfd", "metadata": { "execution": { "iopub.execute_input": "2026-05-21T09:49:41.093058Z", "iopub.status.busy": "2026-05-21T09:49:41.093002Z", "iopub.status.idle": "2026-05-21T09:49:41.166518Z", "shell.execute_reply": "2026-05-21T09:49:41.166201Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t_grid = np.linspace(0.1, 5.0, 300)\n", "x_reps = np.array([0.1, 0.5, 0.9])\n", "fig, (ax_s, ax_h) = plt.subplots(1, 2, figsize=(11, 4))\n", "\n", "for i, xv in enumerate(x_reps):\n", " xv_grid = np.full_like(t_grid, xv)\n", " S_np = npcox.survival(t_grid, X=xv_grid)\n", " h_np = npcox.hazard(t_grid, X=xv_grid)\n", " shape_v = 0.8 + 1.4 * xv\n", " S_true = np.exp(-((t_grid / scale) ** shape_v))\n", " color = f\"C{i}\"\n", " ax_s.plot(t_grid, S_np, color=color, lw=2, label=f\"x={xv}\")\n", " ax_s.plot(t_grid, S_true, color=color, lw=1, ls=\":\", alpha=0.8)\n", " ax_h.plot(t_grid, h_np, color=color, lw=2, label=f\"x={xv}\")\n", "\n", "ax_s.axvline(scale, color=\"0.4\", lw=0.8, ls=\"--\")\n", "ax_s.set_xlabel(\"t\"); ax_s.set_ylabel(\"S(t | x)\")\n", "ax_s.set_title(\"Survival — solid: non-proportional Coxph, dotted: true Weibull\")\n", "ax_s.legend()\n", "ax_h.set_xlabel(\"t\"); ax_h.set_ylabel(\"h(t | x)\")\n", "ax_h.set_title(\"Hazard rate — non-proportional Coxph\")\n", "ax_h.legend()\n", "fig.tight_layout();" ] }, { "cell_type": "markdown", "id": "e5b3c30d", "metadata": {}, "source": [ "### Quantile prediction on the interaction model\n", "\n", "`predict(..., what=\"quantile\")` on the non-proportional `Coxph` uses the\n", "row-wise bracket from #67: for each requested probability/$x$ pair the\n", "bracket is derived from the per-row $h(a, x)$ and $h(b, x)$ rather than\n", "the global Bernstein endpoints. Below we recover the median survival\n", "time at three covariate values." ] }, { "cell_type": "code", "execution_count": 12, "id": "9d8527b7", "metadata": { "execution": { "iopub.execute_input": "2026-05-21T09:49:41.167637Z", "iopub.status.busy": "2026-05-21T09:49:41.167582Z", "iopub.status.idle": "2026-05-21T09:49:41.170332Z", "shell.execute_reply": "2026-05-21T09:49:41.169957Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "x=0.1: mltpy median = 1.766 true Weibull median = 1.354\n", "x=0.5: mltpy median = 1.711 true Weibull median = 1.566\n", "x=0.9: mltpy median = 1.887 true Weibull median = 1.674\n" ] } ], "source": [ "probs = np.full_like(x_reps, 0.5)\n", "med = npcox.predict(probs, X_new=x_reps, what=\"quantile\")\n", "med_true = scale * (np.log(2.0)) ** (1.0 / (0.8 + 1.4 * x_reps))\n", "for xv, m_hat, m_t in zip(x_reps, med, med_true):\n", " print(f\"x={xv}: mltpy median = {m_hat:.3f} true Weibull median = {m_t:.3f}\")" ] }, { "cell_type": "markdown", "id": "480aa1a1", "metadata": {}, "source": [ "## Takeaways\n", "\n", "- An :class:`~mltpy.basis.InteractionBasis` replaces the additive shift\n", " $h_0(y) + x^\\top\\beta$ with the tensor product\n", " $(a(y) \\otimes b(x))^\\top \\mathrm{vec}(\\Theta)$, letting the *shape*\n", " of the conditional distribution change with $x$.\n", "- For *stratified* (categorical) covariates the natural x-basis is\n", " :class:`~mltpy.basis.OneHotBasis`; for *continuous* covariates use\n", " :class:`~mltpy.basis.BernsteinBasis` (or\n", " :class:`~mltpy.basis.OrdinalBasis` for ordered categories). All three\n", " are non-negative partitions of unity, the condition needed for the\n", " closed-form column-wise monotonicity constraint.\n", "- The fitted interaction model exposes the standard prediction surface\n", " (`distribution`, `density`, `survivor`, `hazard`, `quantile`) and\n", " works with `simulate` and `plot` as documented in\n", " [ADR 0001](../adr/0001-tensor-product-interaction-basis.md).\n", "- The likelihood-ratio test against the proportional baseline is the\n", " practical way to decide whether the extra flexibility is justified for\n", " a given dataset." ] } ], "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": "3.12.13" } }, "nbformat": 4, "nbformat_minor": 5 }