{ "cells": [ { "cell_type": "markdown", "id": "intro-md", "metadata": {}, "source": [ "# Scaling terms — heteroskedastic regression and non-proportional survival\n", "\n", "The default conditional transformation model adds covariates as an\n", "*additive* shift,\n", "\n", "$$\n", "h(y \\mid x_d) \\;=\\; h_0(y) + x_d^\\top \\beta,\n", "$$\n", "\n", "which gives proportional hazards (`Coxph`), proportional odds (`Colr`),\n", "or a constant-variance Box-Cox. When the conditional distribution\n", "changes *spread* with the covariates — not just location — the shift\n", "model is mis-specified. mltpy's `scaling=` kwarg mirrors\n", "R `tram::*(scale = ~x_s)` and multiplies the baseline by a strictly\n", "positive covariate-dependent factor:\n", "\n", "$$\n", "h(y \\mid x_d, x_s) \\;=\\; h_0(y)\\, \\exp\\!\\bigl(\\tfrac{1}{2}\\, x_s^\\top \\gamma\\bigr)\n", " \\;+\\; x_d^\\top \\beta,\n", "$$\n", "\n", "with $\\gamma$ unconstrained. See\n", "[ADR 0002](../adr/0002-scaling-terms.md) for the parameter-vector\n", "layout, the monotonicity argument (scaling factor is positive, so\n", "$h$ stays monotone in $y$), and the sign convention vs. R `tram`\n", "(γ is sign- *and* magnitude-aligned, including the conventional 0.5\n", "factor on the exponent).\n", "\n", "This vignette walks through two canonical uses of that machinery:\n", "\n", "1. **Heteroskedastic Box-Cox regression** — variance of the response\n", " depends on a continuous covariate; the proportional model under-fits\n", " the heteroskedasticity and a likelihood-ratio test on $\\gamma$\n", " rejects.\n", "2. **Non-proportional Cox survival** — the *shape* of the survival\n", " curve changes with a covariate, so the curves spread (and cross) as\n", " $t$ grows. Complements the `interacting=` route from\n", " [04_interacting_terms](04_interacting_terms.ipynb): different\n", " mechanism (multiplicative baseline scaling rather than tensor\n", " product), same kind of departure from proportionality." ] }, { "cell_type": "code", "execution_count": 1, "id": "imports", "metadata": { "execution": { "iopub.execute_input": "2026-05-23T22:05:46.963735Z", "iopub.status.busy": "2026-05-23T22:05:46.963577Z", "iopub.status.idle": "2026-05-23T22:05:47.661580Z", "shell.execute_reply": "2026-05-23T22:05:47.661148Z" } }, "outputs": [], "source": [ "from pathlib import Path\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.stats import chi2\n", "\n", "import mltpy\n", "from mltpy.variables import CensoredData\n", "\n", "rng = np.random.default_rng(2026)\n", "plt.rcParams[\"figure.dpi\"] = 110\n", "REF_DIR = Path(\"../../reference\") # repo-relative path to reference fixtures" ] }, { "cell_type": "markdown", "id": "ex1-md", "metadata": {}, "source": [ "## 1. Heteroskedastic Box-Cox regression\n", "\n", "We use the same n=100 dataset that the R-parity test in\n", "`tests/test_tram_boxcox_scaling.py` checks element-wise against\n", "`tram::BoxCox(y ~ x_d | x_s)`. Loading it from `reference/` rather\n", "than re-synthesising means the LR statistic we compute below is\n", "*the same* statistic R's `anova()` would emit on this dataset — and\n", "the fixture below pins the expected value.\n", "\n", "The data-generating process is\n", "\n", "$$y_i \\;=\\; 1 + 0.5\\, x^d_i + \\varepsilon_i,\\qquad\n", "\\varepsilon_i \\sim \\mathcal{N}\\!\\bigl(0,\\; e^{2\\cdot 0.3\\, x^s_i}\\bigr),$$\n", "\n", "so the residual variance grows with $x_s$ — a textbook\n", "heteroskedasticity pattern." ] }, { "cell_type": "code", "execution_count": 2, "id": "ex1-load", "metadata": { "execution": { "iopub.execute_input": "2026-05-23T22:05:47.662883Z", "iopub.status.busy": "2026-05-23T22:05:47.662799Z", "iopub.status.idle": "2026-05-23T22:05:47.665793Z", "shell.execute_reply": "2026-05-23T22:05:47.665534Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n=100, support=(-1.77, 3.89)\n", "x_s range: [-2.43, +2.87]\n", "observed marginal sd of y: 0.994\n" ] } ], "source": [ "y = np.loadtxt(REF_DIR / \"scaling_boxcox_normal_y.txt\")\n", "x_d = np.loadtxt(REF_DIR / \"scaling_boxcox_normal_x_d.txt\").reshape(-1, 1)\n", "x_s = np.loadtxt(REF_DIR / \"scaling_boxcox_normal_x_s.txt\").reshape(-1, 1)\n", "with open(REF_DIR / \"scaling_boxcox_normal_support.txt\") as fh:\n", " a, b = (float(t) for t in fh.read().split())\n", "\n", "print(f\"n={y.size}, support=({a:.2f}, {b:.2f})\")\n", "print(f\"x_s range: [{x_s.min():+.2f}, {x_s.max():+.2f}]\")\n", "print(f\"observed marginal sd of y: {y.std():.3f}\")" ] }, { "cell_type": "markdown", "id": "ex1-fit-md", "metadata": {}, "source": [ "### Constant-variance baseline\n", "\n", "A standard `BoxCox` with `x_d` as a covariate. The transformation\n", "$h$ depends only on $y$, so the implied conditional distribution\n", "shares a single shape across all $x_s$." ] }, { "cell_type": "code", "execution_count": 3, "id": "ex1-null", "metadata": { "execution": { "iopub.execute_input": "2026-05-23T22:05:47.666890Z", "iopub.status.busy": "2026-05-23T22:05:47.666831Z", "iopub.status.idle": "2026-05-23T22:05:47.803920Z", "shell.execute_reply": "2026-05-23T22:05:47.803499Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Model: BoxCox\n", "Support: (-1.76708573285841, 3.89175251100449)\n", "Basis order: 5\n", "Fitted: Yes\n", "Log-lik: -129.3138\n", "AIC: 272.6276\n", "BIC: 290.8638\n", "Converged: No\n", "n_restarts: 3\n", "\n", "Coefficients:\n", " Estimate Std. Error z value Pr(>|z|)\n", " X1 -0.5379 0.1175 -4.579 4.682e-06\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/var/folders/l3/9xz3dcxx2879v30qp8ptbjbw0000gn/T/ipykernel_58254/1175696866.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", " null = mltpy.BoxCox(support=(a, b), order=5).fit(y, X=x_d)\n" ] } ], "source": [ "null = mltpy.BoxCox(support=(a, b), order=5).fit(y, X=x_d)\n", "print(null.summary())" ] }, { "cell_type": "markdown", "id": "ex1-full-md", "metadata": {}, "source": [ "### Heteroskedastic Box-Cox via `scaling=`\n", "\n", "Passing `scaling=x_s` routes the model through the scaled-baseline\n", "likelihood path. The fitted parameter vector gains a $\\gamma$ block\n", "exposed as `model.gamma_`; the coefficient table in `summary()` adds a\n", "\"Scaling coefficients\" section so $\\gamma$ stands next to $\\beta$ for\n", "inference.\n", "\n", "γ is reported in the *same* sign convention as R `tram::BoxCox(..., scale=~x_s)` — no flip required (ADR 0002, Decision 5)." ] }, { "cell_type": "code", "execution_count": 4, "id": "ex1-full", "metadata": { "execution": { "iopub.execute_input": "2026-05-23T22:05:47.804893Z", "iopub.status.busy": "2026-05-23T22:05:47.804837Z", "iopub.status.idle": "2026-05-23T22:05:47.998981Z", "shell.execute_reply": "2026-05-23T22:05:47.998585Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Model: BoxCox\n", "Support: (-1.76708573285841, 3.89175251100449)\n", "Basis order: 5\n", "Fitted: Yes\n", "Log-lik: -123.5189\n", "AIC: 263.0378\n", "BIC: 283.8791\n", "Converged: No\n", "n_restarts: 3\n", "\n", "Coefficients:\n", " Estimate Std. Error z value Pr(>|z|)\n", " X1 -0.5608 0.1181 -4.749 2.043e-06\n", "Scaling coefficients:\n", " Estimate Std. Error z value Pr(>|z|)\n", " X1 -0.4573 0.1365 -3.351 0.0008054\n", "\n", "gamma_ = [-0.45727428]\n", "feature_names_scaling_ = ['X1']\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/var/folders/l3/9xz3dcxx2879v30qp8ptbjbw0000gn/T/ipykernel_58254/1569583142.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", " full = mltpy.BoxCox(support=(a, b), order=5, scaling=x_s).fit(y, X=x_d)\n" ] } ], "source": [ "full = mltpy.BoxCox(support=(a, b), order=5, scaling=x_s).fit(y, X=x_d)\n", "print(full.summary())\n", "print(f\"\\ngamma_ = {full.gamma_}\")\n", "print(f\"feature_names_scaling_ = {full.feature_names_scaling_}\")" ] }, { "cell_type": "markdown", "id": "ex1-lr-md", "metadata": {}, "source": [ "### Likelihood-ratio test against the constant-variance model\n", "\n", "Under $H_0\\!: \\gamma = 0$ the deviance\n", "$2(\\ell_{\\text{full}} - \\ell_{\\text{null}})$ is asymptotically\n", "$\\chi^2_{q_s}$. We compare against the reference value pinned by R's\n", "`anova(tram::BoxCox(...), tram::BoxCox(..., scale=~x_s))` on the same\n", "data — the parity fixture is regenerated by\n", "`reference/generate_reference.R`." ] }, { "cell_type": "code", "execution_count": 5, "id": "ex1-lr", "metadata": { "execution": { "iopub.execute_input": "2026-05-23T22:05:48.000081Z", "iopub.status.busy": "2026-05-23T22:05:48.000030Z", "iopub.status.idle": "2026-05-23T22:05:48.004912Z", "shell.execute_reply": "2026-05-23T22:05:48.004638Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "log-lik null : -129.3138 (k=7)\n", "log-lik full : -123.5189 (k=8)\n", "LR statistic : 11.5899 on 1 df, p = 0.0006631\n", "R reference : 11.5899 on 1 df, p = 0.0006631\n", "\n", "parity OK — mltpy LR matches R anova at rtol=1e-5.\n" ] } ], "source": [ "ll_null = null.result_.log_likelihood\n", "ll_full = full.result_.log_likelihood\n", "df = full.n_free_params_ - null.n_free_params_\n", "lr_stat = 2.0 * (ll_full - ll_null)\n", "p_value = float(chi2.sf(lr_stat, df=df))\n", "\n", "with open(REF_DIR / \"scaling_vignette_boxcox_lr.txt\") as fh:\n", " parts = fh.read().split()\n", "lr_R = float(parts[0]); df_R = int(parts[1]); p_R = float(parts[2])\n", "\n", "print(f\"log-lik null : {ll_null:.4f} (k={null.n_free_params_})\")\n", "print(f\"log-lik full : {ll_full:.4f} (k={full.n_free_params_})\")\n", "print(f\"LR statistic : {lr_stat:.4f} on {df} df, p = {p_value:.4g}\")\n", "print(f\"R reference : {lr_R:.4f} on {df_R} df, p = {p_R:.4g}\")\n", "np.testing.assert_allclose(lr_stat, lr_R, rtol=1e-5, atol=1e-5)\n", "print(\"\\nparity OK — mltpy LR matches R anova at rtol=1e-5.\")" ] }, { "cell_type": "markdown", "id": "ex1-density-md", "metadata": {}, "source": [ "### Conditional density at three $x_s$ quantiles\n", "\n", "Holding $x_d = 0$ fixed, we evaluate $f(y \\mid x_d=0, x_s)$ at the\n", "10th, 50th, and 90th percentiles of the observed scaling covariate.\n", "The constant-variance baseline returns a single curve regardless of\n", "$x_s$; the heteroskedastic fit visibly widens (and narrows) the\n", "conditional density as $x_s$ changes." ] }, { "cell_type": "code", "execution_count": 6, "id": "ex1-density", "metadata": { "execution": { "iopub.execute_input": "2026-05-23T22:05:48.005776Z", "iopub.status.busy": "2026-05-23T22:05:48.005714Z", "iopub.status.idle": "2026-05-23T22:05:48.130804Z", "shell.execute_reply": "2026-05-23T22:05:48.130423Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y_grid = np.linspace(a + 0.05, b - 0.05, 400)\n", "xs_q = np.quantile(x_s.ravel(), [0.1, 0.5, 0.9])\n", "colors = [\"C0\", \"C1\", \"C2\"]\n", "\n", "fig, (ax_h, ax_f) = plt.subplots(1, 2, figsize=(11, 4))\n", "\n", "# Left panel: the constant-variance model — one density for all x_s.\n", "X_zero = np.zeros((y_grid.size, 1))\n", "f_null = null.predict(y_grid, X_new=X_zero, what=\"density\")\n", "ax_h.plot(y_grid, f_null, lw=2, color=\"0.4\", label=\"constant-variance\")\n", "ax_h.set_xlabel(\"y\"); ax_h.set_ylabel(\"f(y | x_d=0)\")\n", "ax_h.set_title(\"BoxCox (no scaling) — one density\")\n", "ax_h.legend()\n", "\n", "# Right panel: scaled fit — one density per x_s quantile.\n", "for q, xs_val, c in zip([0.1, 0.5, 0.9], xs_q, colors):\n", " X_scale = np.full((y_grid.size, 1), xs_val)\n", " f_full = full.predict(y_grid, X_new=X_zero, X_scale_new=X_scale,\n", " what=\"density\")\n", " ax_f.plot(y_grid, f_full, lw=2, color=c,\n", " label=f\"$x_s$ at q{int(q*100)} ({xs_val:+.2f})\")\n", "ax_f.set_xlabel(\"y\"); ax_f.set_ylabel(\"f(y | x_d=0, x_s)\")\n", "ax_f.set_title(\"BoxCox(scaling=x_s) — spread changes with x_s\")\n", "ax_f.legend()\n", "fig.tight_layout();" ] }, { "cell_type": "markdown", "id": "ex2-md", "metadata": {}, "source": [ "## 2. Non-proportional Cox survival\n", "\n", "Now we move to right-censored survival data. The scaled-baseline\n", "Cox model is\n", "\n", "$$\\log\\bigl[-\\log S(t \\mid x_d, x_s)\\bigr]\n", " \\;=\\; h_0(t)\\, e^{0.5\\, x_s\\gamma} \\;+\\; x_d\\,\\beta,$$\n", "\n", "i.e. the log-cumulative-hazard contribution of the baseline is\n", "*scaled* by $e^{0.5 x_s\\gamma}$. When $\\gamma \\neq 0$ the\n", "proportional-hazards assumption fails: survival curves at different\n", "$x_s$ values no longer differ by a constant vertical shift on the\n", "log-log scale, and can spread or cross.\n", "\n", "We simulate from this model directly (so the fit can recover the\n", "non-PH structure) and visualise the resulting curves at three\n", "$x_s$ quantiles." ] }, { "cell_type": "code", "execution_count": 7, "id": "ex2-simulate", "metadata": { "execution": { "iopub.execute_input": "2026-05-23T22:05:48.131842Z", "iopub.status.busy": "2026-05-23T22:05:48.131771Z", "iopub.status.idle": "2026-05-23T22:05:48.134006Z", "shell.execute_reply": "2026-05-23T22:05:48.133739Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "n=500, censoring=22.4%, y in [0.0011, 8.000]\n" ] } ], "source": [ "n_cox = 500\n", "x_d_cox = rng.normal(size=n_cox)\n", "x_s_cox = rng.normal(size=n_cox)\n", "beta_true, gamma_true = -0.5, 1.2 # truth on the mltpy scale\n", "\n", "# Direct inversion from the min-EV link:\n", "# S(t|x) = exp(-exp(h_0(t) * exp(0.5*x_s*γ) + x_d*β))\n", "# ⇒ Z = log(-log(1 - U)) ~ Gumbel_min\n", "# ⇒ h_0(T) = (Z - x_d*β) / exp(0.5*x_s*γ)\n", "# Picking h_0(t) = log(t) gives an exponential-baseline Cox model\n", "# whose shape is *modulated* by x_s.\n", "U = rng.uniform(1e-5, 1 - 1e-5, size=n_cox)\n", "Z = np.log(-np.log(1 - U))\n", "h_target = (Z - x_d_cox * beta_true) / np.exp(0.5 * x_s_cox * gamma_true)\n", "t = np.exp(h_target)\n", "\n", "# Independent exponential censoring + a hard upper cap at b_max\n", "# (treat clipped observations as right-censored).\n", "cens = rng.exponential(scale=4.0, size=n_cox)\n", "y_obs = np.minimum(t, cens)\n", "event = (t <= cens).astype(int)\n", "b_max = 8.0\n", "y_obs = np.clip(y_obs, 1.1e-3, b_max - 1e-4)\n", "event = np.where((t <= cens) & (t <= b_max), event, 0)\n", "print(f\"n={n_cox}, censoring={1 - event.mean():.1%}, \"\n", " f\"y in [{y_obs.min():.4f}, {y_obs.max():.3f}]\")\n", "\n", "a_cox, b_cox = 1e-3, b_max\n", "cdata = CensoredData.right_censored(y_obs, (event == 0))" ] }, { "cell_type": "markdown", "id": "ex2-fit-md", "metadata": {}, "source": [ "### Proportional-hazards baseline\n", "\n", "A standard `Coxph` with `x_d` as the only covariate — the textbook\n", "Cox proportional-hazards model with a smooth Bernstein baseline\n", "$h_0(t)$. The shape of the implied survival curve does not depend\n", "on $x_s$." ] }, { "cell_type": "code", "execution_count": 8, "id": "ex2-ph", "metadata": { "execution": { "iopub.execute_input": "2026-05-23T22:05:48.135020Z", "iopub.status.busy": "2026-05-23T22:05:48.134957Z", "iopub.status.idle": "2026-05-23T22:05:48.661270Z", "shell.execute_reply": "2026-05-23T22:05:48.660886Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Model: Coxph\n", "Support: (0.001, 8.0)\n", "Basis order: 6\n", "Fitted: Yes\n", "Log-lik: -515.9835\n", "AIC: 1047.9671\n", "BIC: 1081.6839\n", "Converged: No\n", "n_restarts: 3\n", "\n", "Coefficients:\n", " Estimate Std. Error z value Pr(>|z|)\n", " X1 -0.4142 0.0520 -7.963 1.673e-15\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/var/folders/l3/9xz3dcxx2879v30qp8ptbjbw0000gn/T/ipykernel_58254/3355775036.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", " ph = mltpy.Coxph(support=(a_cox, b_cox), order=6).fit(\n" ] } ], "source": [ "ph = mltpy.Coxph(support=(a_cox, b_cox), order=6).fit(\n", " cdata, X=x_d_cox.reshape(-1, 1)\n", ")\n", "print(ph.summary())" ] }, { "cell_type": "markdown", "id": "ex2-npfit-md", "metadata": {}, "source": [ "### Non-proportional fit via `scaling=`\n", "\n", "`Coxph(..., scaling=x_s)` adds the $\\gamma$ block; the baseline\n", "$h_0(t)$ is multiplied by $e^{0.5 x_s\\gamma}$ per observation, which\n", "scales the log-cumulative hazard non-proportionally." ] }, { "cell_type": "code", "execution_count": 9, "id": "ex2-npfit", "metadata": { "execution": { "iopub.execute_input": "2026-05-23T22:05:48.662401Z", "iopub.status.busy": "2026-05-23T22:05:48.662331Z", "iopub.status.idle": "2026-05-23T22:05:49.141374Z", "shell.execute_reply": "2026-05-23T22:05:49.140948Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Model: Coxph\n", "Support: (0.001, 8.0)\n", "Basis order: 6\n", "Fitted: Yes\n", "Log-lik: -476.3271\n", "AIC: 970.6542\n", "BIC: 1008.5856\n", "Converged: No\n", "n_restarts: 3\n", "\n", "Coefficients:\n", " Estimate Std. Error z value Pr(>|z|)\n", " X1 -0.4551 0.0526 -8.648 5.246e-18\n", "Scaling coefficients:\n", " Estimate Std. Error z value Pr(>|z|)\n", " X1 0.6872 0.0818 8.404 4.313e-17\n", "\n", "gamma_ (estimate vs truth γ=1.2): [0.68716102]\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "/var/folders/l3/9xz3dcxx2879v30qp8ptbjbw0000gn/T/ipykernel_58254/3556713684.py:3: 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(cdata, X=x_d_cox.reshape(-1, 1))\n" ] } ], "source": [ "np_cox = mltpy.Coxph(\n", " support=(a_cox, b_cox), order=6, scaling=x_s_cox.reshape(-1, 1)\n", ").fit(cdata, X=x_d_cox.reshape(-1, 1))\n", "print(np_cox.summary())\n", "print(f\"\\ngamma_ (estimate vs truth γ={gamma_true}): {np_cox.gamma_}\")" ] }, { "cell_type": "markdown", "id": "ex2-lr-md", "metadata": {}, "source": [ "### Likelihood-ratio test against PH\n", "\n", "Same deviance recipe as Example 1: $2(\\ell_{\\text{np}} - \\ell_{\\text{ph}})$\n", "against a $\\chi^2_{q_s}$ reference." ] }, { "cell_type": "code", "execution_count": 10, "id": "ex2-lr", "metadata": { "execution": { "iopub.execute_input": "2026-05-23T22:05:49.142390Z", "iopub.status.busy": "2026-05-23T22:05:49.142325Z", "iopub.status.idle": "2026-05-23T22:05:49.144095Z", "shell.execute_reply": "2026-05-23T22:05:49.143829Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "log-lik PH : -515.984 (k=8)\n", "log-lik non-PH : -476.327 (k=9)\n", "LR statistic : 79.31 on 1 df, p = 5.3e-19\n" ] } ], "source": [ "ll_ph = ph.result_.log_likelihood\n", "ll_np = np_cox.result_.log_likelihood\n", "df = np_cox.n_free_params_ - ph.n_free_params_\n", "lr_stat = 2.0 * (ll_np - ll_ph)\n", "p_value = float(chi2.sf(lr_stat, df=df))\n", "print(f\"log-lik PH : {ll_ph:.3f} (k={ph.n_free_params_})\")\n", "print(f\"log-lik non-PH : {ll_np:.3f} (k={np_cox.n_free_params_})\")\n", "print(f\"LR statistic : {lr_stat:.2f} on {df} df, p = {p_value:.3g}\")" ] }, { "cell_type": "markdown", "id": "ex2-plot-md", "metadata": {}, "source": [ "### Spreading and crossing survival curves\n", "\n", "We evaluate $S(t \\mid x_d=0, x_s)$ over a fine $t$-grid at the\n", "10th, 50th, and 90th percentiles of $x_s$. Under PH the three\n", "curves would differ only by a constant vertical shift on the\n", "$\\log[-\\log S]$ scale; under the scaled-baseline fit they spread\n", "as $t$ grows and cross near the median follow-up — the canonical\n", "non-PH signature." ] }, { "cell_type": "code", "execution_count": 11, "id": "ex2-plot", "metadata": { "execution": { "iopub.execute_input": "2026-05-23T22:05:49.144942Z", "iopub.status.busy": "2026-05-23T22:05:49.144890Z", "iopub.status.idle": "2026-05-23T22:05:49.219163Z", "shell.execute_reply": "2026-05-23T22:05:49.218730Z" } }, "outputs": [ { "data": { "image/png": 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Xl5fJcdKw7xvvO5a2LVt/r/wtef/KlSst7jOyfRgz7K/WPszJtirrSM4tsizatWunlpX5Mcoa1qwPS+eC0NBQm/8WuSfDfpXao0yZMiafs6UOYU7OIfKeihUr6m7fvp3id8qxXI6TlStXNnneUAd6/vnn1THHmOHc9uWXX5o8//vvvye7X1piOO989913j72WnueZmjVr6kqVKmWyLIQcP+U4OGbMGJ2j2VI/knN6yZIl1TH47NmzJt/z2muvqe/59ddfHzumSn3A+Pxw5coVdbx+4YUXbNqWs2fPrrt06ZL2vHxnt27dHqujWLMN2VI/srbO98orr6jn5s2bZ/Len3/+WT0vx2lrrxsMy07KkNzyMP7b9tQp5Xdt377d5P1vvvmmek0+ZxATE2Nxv58zZ45676JFi0yel+dkHaRGzpXy3v379+usZcv6Ey+99JJ6ftmyZbpTp07pcuTIofZL423d+Jjw+eefmzy/dOnSx36PrdcrhnW5a9eux35P3rx5dU8++WSKv1mORwULFlTHVvO6j+Hvptc1oKVty9bf27hxY3V8O3LkiMnzb7/9tvoe8+OlYX+15mFebzPeDqUuL9fJ1apV0+XMmfOxY5Q1rFkfxmR7k2OZM2Lgyg3ICU9ONlKRMN4RZN74AtnewNWQIUMs/t3//e9/6vXffvvN5EAkwSg5mBizFLiy5fPGZAeWC+Pw8HB1kJfvMA5OOGPg6oMPPnjstbfeeku9Zgh4yIW/zMuFoTlZLgEBAerEZP47Z8+e/dj7O3XqpCpn1jCse0t/NywsTL0m32d+svrzzz8fe3/Hjh3Va9euXXvsNUMF8NChQ9pzMl++fPnH3isVCqn4SEDBQC4EZNt49OjRY+9v2bKlqqwYTj6G39S1a1eLv9nWwNXAgQPVczt27Hjs/Yag4l9//WWyn0kQx5wEagyBHkvkhBkREaG2bXnICVkqQfYErt544w31t+TCxFq2rj+p8EtZpAJZr169ZAMahsDV1atXH3tNKv/ymvxe4+UvARpzU6dOfWx/lwuu5H6nbBeyzUjlLzkHDx60ukJqTCqIcuEm5f7ll1/UdyxfvtzuwJU1v1e2D6mgGu8XxuWRSo15BUgqhLJsrH1YYghQSrBa/p08ebLOHtasD2MjRoxQf+/AgQN2/T1yP4b9qnfv3sluw4UKFXoscGVLHcJYSEiICsbLd1q62Da+sDJ8p+Ei+d69e4/VgeR4Y07ObXK+k/OeObkwtyVwlS9fPpObK+l9npHlJOV5//33tc8bPypUqGD1TbOMZEv9aM+ePeq9/fr1e+y9ly9fVq9JIMm8DrR27drH3i/H5jp16ti0LVv6uxJQkteknmjtNmRr/ciaOp9sK3JekfVqToJnsp/JRbEhkJbadYOtgSt76pQSYDC3ZMmSx87RxuLi4rR9Qs6ZhoCBMWvrCW3atFHvtSXAYMv6E3LdIOtE9nf5rKyjM2fOPPZZ2Y/lNfOAlpDgjPxNQ4DIlusV43qxpd8p159BQUEm68acXEOY14esYc81YEqBK2t+r6VrIQPZNi0Fro4fP251vSu5G4ESoJR136RJk2Rv0FrDmvVhrGfPnurvGW9zzoJdBd2ANJuUZrnykKa8O3fuVE0of//9d9UEU5rNpmVoaMkNYIn07ZUmh9JcXpofCmliKc2yrRmJxpbPS5cAabItI1iY96kX9vRHl6bzaenHLgx5blIjXf7MSbNpIc1ipWmodDUS0hTYnDTJl+bnlvqkJ/fd8r3GTVbN8xaYl93SqHKSx0i+yzwvU3LbhfwGeb9xlx8Dw++S32DcLczS35WmuPJ7pbuE8XdXqVLFYoJF+W5p1ipNXw3NbZMroz1SWjfGv8uWdW5Mtmtpwi3Nts3zadi7jRq6apjnRkuJretPmjfLcUZy0kkzaulDb97110DyTEj3DHOy/qW5uHyvoeuArctPWMq1JM295RgozbulK4N0x5EugdIU37B8DENSS54Pa7onyW+UbkDG+V4M0nI8seb3yvHdkP/AnCEfnvkw4/Kcpe+2hXRbkXw+0n1CuqnY2yzfmvVhaZ2ymyCZk/ODbIuWWDpH2FOHkO4o0uVIRv6Srivm+ePkGCA5cqRLmaXPWxoxzNI5SY59cnyV856l46N5jqLUloulnDrpdZ6RbkaGfVkelqR2vJGcKua5EW0lXc4sLS976kcpnd+ly4x0GbKl7mWcl0Z+p3kOGfOyW6oDGZ6zpe5la/3ImjqfdMOSbmyS19GcHJflb8qIvrKtG3dVT8+6l611SlvqDtLdUbrjSTc085ximV33smX9yTWD5CCSbmNSTulSKvWw5I4JUj8wJ+tf9mdZx8ZdPa25Xkmt7iXXozKSoqQakH1IzvWSVkO6MRp+oy11r4y4BrTn+sxS3Uu2TUv1F1m+aR2tW7p0bt26VXUVla6Uz1nofm4Na9aHq9S9GLhyM3LSkRw68pCNc/LkyeoiS/KKpLQRmh+wjSWXH0cqZJJoWfpWSx9q6e8r+R0k8Zs1o0BZ+3nZgWQHk7xAkuBR+trLwVsqZ1JhlL7ylnJapEb6T5v3jbeV5BazJkiXXEVSpHVUkZS+20CSRxuSYtpa9uQ4+wiCji6jtetc8lnIxbzkjZN8E7LfGgKKkoPDnm3buFInuYkkh0NGkT7+hv79khsjs5efIe+KpWCW5AiQCrjkqZKKn1x8Sv4JqQBJZcBSJSQlEmCX9SW5ECQ3lwTaJBeTXAga8o3YK6OOEZaC1ikxH9BDyIWz5N4QUoGTCrk9OWxsXR+GdSrnNSJ72VOHkMCOHJflwk4uzA25Vgxkn5JjgAQmJN+J5OmRAIfktJG8URLQt3Q8yOhzUnLfn17nGcP7ZDlKzhxLUruZJxfchgFS7CXHD2uSIVtTP0pNcvXm5L7b+Hgt24bUa+0pe3JY90qfc6lczEsyegmAS/BKbqxJgEeuhyRgnZa6lwwKJHUva4Iy9pJBIAy/R3LFmudZzcy6l3nQTJLnS2B/zZo1KheWPORaT65DpHGF4bPWyKhrwIyue1kKWqdUBkvLROqWkv9TSHA1Li7Orrxrtq4PWacSXJcbzs6GgSs3Jgl8hSSdM5A7IpYi04Zosq0MCasl4aVEc2WECTl4mkfk0/J5OVjJCUDubI4bN87k85ZGdLOW3KFJy+eF3CFJL4aov3ErIwM5+Mk6srflnCSplGSPKZXdcGFqTFp4yAGsUaNGVv0dubMjI69JUk7zZJ1y0DW8J7W/KxcNchfN+PfK5+SiV0bHML97JN8tlUtJmG0NW+8iGMos60Yuvs3/tvF7bCWVWrnjIRfxxhVSCQbJXUx7SQJe+T7ZvyTBrjUtA21df5IscsCAAeoujgSBpQIhiWYtjXgiLYHkBGze6sqw/u1dfoY7wcm1SjCMJmm4yJJEp1IplaC+tPY03BmWil9qlRC5+JPjkyR0NWZLi4i0kACOHBtlHVnaZ+QYYZ6g3VLQOiXmFTU59siNBLkgl6SwciFmnJDfVqmtD/PlmtzddiJr2VqHkH1AAisSYJB9XZJCm5O6iiRCl4TIkiDYvBWHLQznNtmHzVsRWTo/ZsZ5JrlzpHFLmuRavKVGLkLTWvcyH8wjLYzP7+ZkHcux397zk7RONQ8omJfd0jo2PGdtnc+e+pE1dT65oJWbzJaWjewn8rwEEYxbcqV33cvWOqUt+4S0opSLeeMk6oZWhfaSBOJyzpXjgJwrrfnNtq4/udEjA+HIuVMC5hKMlmCoBCjMSV3a0vfK+pfP2hJESq7uZSlBuwQ9pIWQoZWQtB6S+uKMGTNU2Y3rXskFwTPyGtCe6zNLdS9pAWapBamloHVKPafMW/EbBsKR+o8sN6nHv//++yYjdtsitfVhTNappVaWzoCBKxcnUVMZgcbSHRgZhUEYN1WUEajkgkOCWYaRJCRSbesIBQZysSoHftk55SQm32XLnTRrPm+IhptfUMlFsIySYC850dpb8coIcvKQ5ptyEpWRTWS9Gsj6kTu80kLNHtZ0F5ITgPnflZEfhbUtduR9MvqOdKeSAIaBnJBlhDK5K2M+gow0F5ZtUk72BnIglUCHYfQLw3fL98rIfMOHD9eelxE35CJCuhxZW3kyBEatbV4sf1vKJKOiyX5lqORI82V5Xk4I8vftIdu3VErM7xjJb03LXSTDiFDykNGPJDhs3iRY7izKqItyYSbHCVvWn4yWIgENKbt0TZZKlYwEKetGugtKE3ZzsvyMv1fuJsn2bmi9ZA/5O1L5khaU5uTEb14pM7ScMLTmkYsIOUHLKIkyQqa0SDAm60DWt2Gdmx+HpBtFcsOrpzcpg1RMpTWH3Gk0vqCW7VDKYh64shS0toVUvqTiKH9TWmZI61jpbiR/T5aXLaxZHwZyZ1GGO7c01DaRLWytQ0jrSTneybFTRu+y5TtldD7pzmILOe7KSKvS6kNagBhIa/n0Corbep6Rc6Sl86PcpJAWJRKwk4sew6i8BrI85LyY0sWwXIg5UzBaziFSD5WbPLLu5SLSwHChbG/dy5ruQnLukdEPDX9X1oehG6YtdS9b60fW1PnknNOtWze1bMzradJiQ4Ii1gZnzOte5l1v06tOaS3DPmw4xxu2X/PgiK3kprC0ypbAlYzOKfV381Y9knZAggXSG0bqL7asPzmPSvd6aR0t9ToJSEldShoCSKv3oKAgk78l9QLz75V6rATopH5g7ciH5mQ0PSF1L2l4YDwSpLTKNt/ezM/17dq1U8cJqYNKHdV8ezCsl4y6BrT1pqEEcyWthdSHjLsVy003a4PWyTG/sSy/VZapBGzlOl/qcJL2Z9p/AUoZcdZa1q4PA4kPSMDemp5TjsDAlYuTHd4wPLtshLJhSqVBDvRyZ00uyIzvBkogQC5AWrVqpYbVlJ1DLjrtvTCQz8mBTw70cjEjF6+Gg1l6fV66j8jvkNcleCMnBenrLUOYyl2KtOapcibSokEu4mX9SKVQgk2SV0ZO0HKBPWzYsAytvEkgT4bTlW4E0p1HTm5ywJR1ZA15n1TC5KJWhrmXO6uGoYtlW5N1Zr6tyQlATrhyB0kqwZIrydASxvhE+95776nm1/KvHMClRaFhuGDptiTLzlrS1FhOiFJJk7vN0j1Vtj3z1lQGsj7kJCKVNwm2SpcL2RblpCl3KKXyYG0rQ3PSx1wqhLLdy3KQ5STBHLkbZm8wx0Duzkj5pEm8VC7kTovsT/I3pLWULE9ZT4YAiC3rTwIacpFmqDwaLrTkwkZOeHKHzDi/i/wWGXpXTopt27ZVJ0b5OxJMk+OYvaRSI5Vp+dtSQTP+m7I9yTqVirl0RZZjheEOmFSUhPwe2d5kHUvATY6Xsq9JS4Rdu3apfVCGkZfvffLJJ1VlXSqK8r1yp00u4MzvBGck2WZl+5CKrhzDZX3KxYe0BpO78+bdvtOS40rOFVL5lmG9DUPHy9+XyrQMKS/LS9a3taxZHwZSWTe09iJKC1vqENICUN4n+4x8To6HxmRfl+OXbPsSfJH9QFo6ykWXXAjK/iLnNLmQtJac52Rfk/O7HFPl/CTHf+lyKN8lF0ppZet5RlpQyLFNWjnIfmsImsu5UpaJHC+lG5R8l5RRAs3SYkCCdrIvm9/Bd2ZyDpFznLT6kGUvx1W5UJWLVLlBIOdBafmQUQzHRanzyY0HWYZy/JNjrrXpLOypH1lb55MbTvKaBEvkekPWt/wN2dYlSGIIdlnD0DJn5MiRquu9nP9l30yudYc9dUpb9gkph3yn1CEkmCS/3zz/mz0kUCStcKTuJduRfL8cU+S7ZX+WdSXHHdm/bFl/8ptlmUhAQ9aFYd+V6zgJrMg6kkCHpDAwkGOcrENDjwE5Tsnyk6CRBMztJZ+X44DsI1Iuw3qQepgcG+V4IfUDmZYgk2wvUi5DTmNpcCEpS6QuI3UuCYDKMdeQU1Bak0nXQGe5BpQeBRI0kgYGss9IHUZSZUiLMVkP5tthWnJcSTBMjs+y3gw3HmX57TcKUMrft4a168NA6unCaetejs4OT2kjw5C+9957uvr166tRb2RULxlBQkY1GTdunMmoNgYypK2MJiFDXRYrVkyNDiPDqSY3qqDxKAyWXLhwQY16kNLoEJZGFbTl8zKyiwwBHBgYqPP399fVqFFDDZNrafQIZxxV0NIyTG50lRMnTqgRHQoUKKDWkYwKMmzYMN3du3dN3pfS70xpeZszHulMhv+VkQtllDjZnmSYV/NtKKVRYYSMiiLvkdECfX191WhJMhKHjNxjzjBKy8aNG9VIMDIctYxQI8Mv37hx47H3ywgXQ4cOVctElo0sI9kujIc4Nv9NyZk7d662HxiPFpPcZ2Xkla+++koNSSvLR0Z3k9FezEfutHX0TiHbsoxGJNu2DA8sI8zJaFaWvsfaUQWNyYglL7/8svqslF3+jvx2GRXGfJQRa9afYZh2GbnQnIzaI/vzc889pz0n5ZW/Lb+/e/fuahQrGQK8VatWur1791q1jFLa5mXYaXlelqOxSZMmqb8txw1ZzzLssQwJbGk0KBkZR7YBGQJZ3ivbf/v27XXr16/X3iOjCMqIYXLclOUoo/rIqIbynuRGrLF2VEFbfu/JkyfVOpFtUB5SThlVp3bt2mq9pgcZoUjOJbK9m490JMdjGc1IRjyzdI5Jji3rQ/YBed3ScOWUdRn2q/Hjxyf7HjnWmI8qaG0dwjCf3MP42Cv7nIx6JucsOZ41bNhQ9/fff1s8R6Z2TpaRqeQYLd8l50E5H8p50ZZzeWrnBlvOMzKKlhyrpTyG+pnx75HPDRo0SFe6dGntPCHHChlNTkbTcjR76kc7d+5U61N+i/wmOQdKPdp8tMeU6kCGc501jM8RM2bMUOcT+bsy+tdHH3302LEvtW3BnvqRNXU+w/p+/fXX1flRrjNk1OS+ffs+NtqfNdcNU6ZMUaOcyfcYn/uS+6w9dcqUlrVxnU7KIucx+f3ymwYMGKCWo6XvsWf04ZUrV6oRO+W7ZZ3I6ODVq1fXDR8+XHfu3Dmb15+cQ6Ucn3766WN/69tvv1WvjRw5UnvOsG9LPa9t27aqviDndRlx23w0QHuuV/744w/1/IYNG7TnZH+R68oGDRqo3yDrTEZmffbZZ9Vomeak/ibLSI5J8rtlWT399NPq+fS6BkxpVEFbfq8cI1q0aKGO0bId9ujRQ3flyhVVH5IRstPDtm3b1L4ho34aRus0XlZ+fn5qlEEZCdMatq4POfdYOzKqI3jI/xwdPCMix5G7pNLa6JNPPsn0u6Ryh0LuzprntiH3InepZDuzNBJfepEBKeQunNytzIpdy6Slldz1MzRnd2UyKpe0uJRm8bZ2RyQicgXSMkZaVKV1oBxXqvNR5pKWoPKQbS0jSHc+6e0juUulp09WJF03pYWmtNSUlmyubNeuXaoOKa2uJE+uM7KvYysREZETkTwS0v1Rugy6O+nSkFzXBOn24Oqk67h0e5SKIBERETkf6UIs3SGlu6CMTufuLI0SaOhu6Q51r9GjR6vcY84atBLMcUVERC5PAh0yck5WILllJO+B5IWQO56SB0/y10iulOSSSWcUydlhTY4Jyd1iPmJaciS3DhERETk3ycubFTpvSat2yekmecQkd5XkQV27dq0a5EBaTqY0MmJGBdEiLYxmaCkXmfngAMmRnF3OjoErIiIiFyLJTJctW6YSssrojjJCrAy88fHHH6vkyZlJkv5bk0BYEslKl1EiIiIiVyLBHxlhU5KmS/deCWRJN0wZGVJGBbV3dEZ7LVy4EK+99lqq75MUGtaM4OkqmOOKiIiI7CIjAFkzgpph1FsiIiIist/169fVSJGpkdb5Mnqnu2DgioiIiIiIiIiInBKTsxMRERERERERkVNyqsDVuXPn1ChCNWvWhLe3N6pWrWrV5yQp3OTJkxEcHIxs2bKpoRxlSEciIiIiIiIiInJdTpWcXfpqrly5Eg0aNFAjJcnDGlOmTMEnn3yiglfVq1fHjBkz1HCOhw4dQunSpa3++5Lk9ujRoyoDvwTOiIiIiKwlCVvDw8NRrVo1t8orkRzWm4iIiCgz6k1OleNKAlWGrPy9e/fGvn37cOzYsVQrTYUKFcKgQYMwceJEbXju8uXLo2PHjpg5c6bVf3/v3r2oX79+Gn8FERERZWV79uxBvXr14O5YbyIiIqLMqDc5VbMie4aSlKG47927h549e2rP+fr6quHCly5datN3SUsrw4IrUqSIzWUhIiKirD3Sj9wAM9Qn3B3rTURERJQZ9SanClzZ49SpU+rfihUrmjxfqVIlXLlyBY8ePVJ5r6xh6B4oQavixYtnQGmJiIjI3WWVdAOsNxEREVFm1JtcvmYVEREBPz+/x/pE5s2bVyVtl9eTC1xJSy15GEf8iIiIiIiIiIjIObh84Cotpk2bhrFjxzq6GEREREREREREZIHtSaWcjLSsiomJUUnajUlLKw8PD/V6coYNG4aQkBDtIbmtiIiIiIiIiIjIObh8iytDbqvTp0+jRo0aJrmvgoODU8xvlStXLvUgIiIiIiIiIiLn4/KBq8aNG6vg0+LFi7XAVVxcnBpRsGPHjo4uHhER2UjyE966dUu1pE1ISODyI6fg5eWl8mkWKFBAteim1HFfJmfEfZmIyPU4VeAqKioKq1atUtOXL19WidOXLFmi5ps3b66GSWzdurV67dy5c+p5qUS+//77GDNmjHq9WrVqmDlzJm7fvo3hw4c79PcQEZHtF7pXr17F/fv34evrqy4wiJxBbGwsHjx4oNITFCtWjMGrVHBfJmfFfZmIyPU4VeDq5s2b6NGjh8lzhvlNmzahRYsW6u57fHy8yXtGjhypKkhTp05FeHg4atasiTVr1qB06dKZWn4iIkobaWklQavAwEDkz5+fi5OcitwUk7qKbKdys4ySx32ZnBn3ZSIi1+JUgauSJUuqAFRKNm/e/Nhz0mRfWl3Jg4iIXJd0D5SWVgxakTOS7fLu3buPDQhDj+O+TM6M+zIRkWtx+VEFiYjIfUirWnYPJGcm2ydzr6WO+zI5O+7LRESug4ErIiIiIiIiIiJySgxcZaKbUTex4sKKzPyTRERERERERJTJouOjERUXpR6JukQuf3fJceXOYhJiMHTTUBy9dRQnbp/AsDrD4O3JxU9ERERERETkyiQwdST8CDaGbMTxW8dx/u553I6+rb2e3Ts7yuUth4r5KqJ1cGvUL1wfXp4cPdtajJxkkhmHZqiglfj1xK84F3EOnzf/HLn9cmdWEYiIiIiIiIgondyNvovfT/2OJWeXqB5WyYmKj8Lh8MPqsfD0QhTKXgg9K/TEK5VfQTbvbFwfqWBXwUzSp0ofFVU12Hl9J15a9RJC74dmVhGIiCgLOHfuHPr374+aNWvC29sbVatWTfa9p06dQtu2bREQEIDChQtjxIgRiI2Ntfpv1a9fHzNmzEi38phbtWoVmjdvjoIFC8LPzw+lS5fGsGHDEBkZqb1n7ty5anRh88eoUaNMvqtv377qQeQquC9zXyYi5/Ug9gGm7ZuGdn+0w8zDM1MMWlkSFhWGbw5+g85/dsbKCyuh0+kyrKzugC2uMkke/zyY1XYWPt/7uYrIisv3LuPV1a/i+7bfo2zesplVFCIicmPHjx/HypUr0aBBAyQmJqqHJREREWjVqhXKlSuHpUuX4urVqyooFBUVhW+//TbVv/Pnn3/i0qVL6NOnT7qUx5I7d+6ozw0ePFgNX3/s2DGMGTNG/bt27VqT9/7zzz/InTupFXOxYsVMXh85ciSqVKmignPym4mcHfdlPe7LRORMJMC0+uJqTN03FeGPwk1ek5ZTTxR7As2KN0P5vOVRMldJ+Hr5qs+EPgjFmYgz2Bq6Fesur8Oj+EdaAGvUtlHYcGUDxjcZjwCfAAf9MufGwFUm8vH0wQcNPlB9WyfsmoAEXQJuPrqJ3mt64/s236NKgSqZWRwiInJDnTt3RteuXdV07969sW/fPovvmzVrFu7du6cCUPny5VPPxcfHY+DAgfjggw9QtGjRFP/OV199hRdeeAHZsmVLl/JY8vLLL5vMt2jRQrW86tevH65du2ZSxjp16qBAgQLJflfZsmXRpEkT1UJMyk7k7LgvW8Z9mYgcJTImEh9t/wibQjaZPF8sRzH0rtIbXct2TbbbX6ncpdSjfcn2GN1gNBadXoTvj3yPB3EP1OsSzJK8WF+2/BKlc5fOlN/jSthV0AF6lO+BL1p8oQJZhh2g37p+KgJLRETuY/fu3arb2sKFC7Xnbt26pS68OnXqhISEBJu/c86cOShZsiSyZ8+O1q1bq0CQ/A3pMic8Pa07ta9evRpt2rTRglaiZ8+eqkWUeWsmcxcvXsS2bdvw7LPPpvp3rC2PtaTllbClS6NBjx49MG/ePBWgI7IF92Xuy0SUtR0IO4Bnlz9rErTK6ZtTBaFWPL0Cz1d83upcVdl9sqN31d7qcx1KdtCevxB5Ab1W98LpO6cz5De4MgauHERGEviuzXfaxn0v9h76re2HS5GXHFUkIiJKZ9LNrWPHjvj0009VM/GYmBjV+ihXrlxYsGABvLxsG01mxYoVqrVRy5YtVUspCVxJMMYekt+qYsWKJs/lyZMHRYoUUa+lZMOGDSpfleS4ygwS4IuOjsaBAwcwbtw4dOnSRQXvjEk3QFmekgdr0qRJFoOCjRs3VoHDQ4cOZUq5yX1wX04f3JeJyBUtPbsUr695HTce3tCe61CqA5Z3W64CVt6e9nVky58tP6Y0m4JR9UfB28Nba9Tyxto3GLwyw66CDtSgSAN82+pbDNwwEDEJMWq4TGl5Nf+p+SiQLfnuDkREWY0EfWITrM+NlFF8vTxV6yZbSKClbt26WLJkicolFRoail27diFHjhw2/30JgDVt2hQ//fSTmm/fvr0K6IwfP97m75IcVxKoMpc3b16VWyole/fuRfny5VW3vcxQokQJlYNLPPnkk5g/f772mgTaxo4dqwILsm6WLVuGDz/8UL3fPFeXIbglrWdknVDm476sx32Z+zIROb9EXSK+OvAVfjqmr3cJaXjyYcMP0aVMl3T5G1J3eanSSyiTpwze3vA2ohOicTfmLvqu7YufO/ysuhcSA1cOV79IfUxrMQ1DNg5BvC4e1x9ex+CNg/Fj+x/h7+3v6OIRETkFCVpV+PAfRxcDpz99En7etrWSktxL0spK8jv5+Pjg33//VcEWe1oq7N+/H5999pnJ89Jdz57AVVpcv35djfRnHpAwbuUkFTFbW5SlNLrgw4cPVbJqueCX3D/r1q1T3y/BO3kYtGvXTuXd+vLLLzF69GiTZS2txCRYJ+Unx+C+zH2Z+zIRuYL4xHh8uP1DNeKfQXDOYHzT+psMyUHVsEhD9d1vbXhLNWqJiInAkE1DML/jfOTwtf1mp7thV0EnIKMOTHhigjZ/9NZRlfSNQ2ISEbkHyWklo/W9++67qFq1ql3fER4ernIzBQYGmjxfqFAhu75PWlZFRkZabIllnPfKEmnlZd7aasuWLSowZ3hIN8b0Ur16dTRq1AhvvPEG/v77b2zatEl1lUyO5OqSIJqlLoFS7keP9CP5ENmK+3LacF8mIlcQlxCHEVtHmASt6hSqg3kd52Vo4nQJXn3d6mut2+DFyIt4/9/3VcuvrI6BKyfRsXRHDKwxUJv/59I/+OHYDw4tExERpd0vv/yC6dOnq5ZXkkDdPDH48uXLVTe3WrVqoUKFCti5c6fF75EWTtJi6ObNmybPh4WF2VUuyW9lnstKAlnSGsk895U5CWzdvXvX5Dn5fdKF0PD4/vvvkRHkwlcCY+fOnbPr81JuQ4J3IltwX05f3JeJyFmDVu9sfkeN8mcgIwHOaTsHefwfT7GQ3hoXbYz36r2nzW8O2YzZR2Yjq2OOKyfSv0Z/XLx3Easvrlbz3xz8BjUL1kTdwszDQURZm+SWkm56zlAOW0jLoL59+6rAVatWrVSOJclPJc8JCWK9+eabqguctICSlkwyqp8l0i2udu3aqqXRO++8oz0vubPs0aFDB0ycOFEFcgy5rhYvXqxGAZTudimRAJv8NmM5c+bMlLxRkp8qLi5OJWFPjiHxvQQDzVutScs3KT85Bvdl7ssG3JeJyNkkJCZg1LZR2BK6RXuua5muGNt4LLw80yf9gTVeqPgCTtw+gb/P/63mZx2ehabFmqJKgSrIqhi4ciKSD2Rc43E4f/c8zkScUU0CR24diUWdF6kRB4iIsvLx0dbcUo528uRJdO/eHYMGDcLAgfoWtc8995zK0fTqq6/C19dX/a7cuXNj8ODBeP7551XAyN8/+fyGkrNJ8mW99tpr6v2S8+rXX381eY8EZiQnlLh8+TLu3bunBbeaN2+u5abq378/vvnmG3Tr1g0ffPCBSmb+3nvvqeeLFi2a4m9r0qSJSjovieaLFy+e4nutLY+0ZunTp48asVCeF7L8JBgmLTMkb9Xhw4fx+eefq3kpt5D8VhIUrFatmpqX5OyzZ8/GkCFDULhwYZOy7Nu3T/37xBNPpFhmyjjcl/W4L3NfJiLnItfeY3aOwdrLa7Xnni3/LD5q+BE8PTwz/Vz5UaOPcOrOKZyOOI0EXYLKt7Ww00L4evkiS9KRJiQkRCeLRP51pIt3L+rq/1ZfV3VuVfV4c+2busTERIeWiYgoM1y8eFE9XF1YWJiuVKlSum7duukSEhK050+cOKHz9PTUzZgxQ3suJiZGt2LFCl337t11LVu2TPW7Z82apQsKCtL5+/vrmjdvrtu9e7c6d/3000/qdVl+Mm/psWnTJpPvkvK0bt1aly1bNl1gYKBu+PDhqjypkffkz59fN3v27FTfa215pPzmz02aNElXs2ZNXc6cOXUBAQG6KlWq6D766CNdZGSk9p7BgwfrypUrp36Dn5+frlq1arrp06dbPG++/fbbuqZNm6ZaZnu3UWepR2SWlH4v92Xuy668LxNR1vPlvi+16295vL/1fV1CYlIdzhFO3T6lq/lzTa1M0/dP17kTW+pNHvI/RwfPnIXcOQ4KCkJISEiqd5AzmnQXlIRwBhLp7Vmhp0PLRESU0S5duqT+LVmyZJZY2KdPn0b58uXVnTVJbj5y5Ejs2rXLpu+Qrn7SzVC6IMrIhZlFEs0fPHgQGzduhCuQbpnBwcGYPHkyevXqlSHbqDPVIzJDSr+X+zL3ZVfel4koa1l0ehHG70oaobl1cGtMbT4V3p6O76D23eHvMPPQTDXt5eGFBZ0WoGK+lHORugpb6k1Mzu6kOpTqgKfLPq3NT903FaH3Qx1aJiIiSl9Tp05V+ZYkd5V0vZPgk6sYPny4ylEj3fdcwfz585EjRw68+OKLji4KuSHuy5mH+zIRpaetoVsxYfcEk9EDpzSb4hRBK/FGtTe0QJV0Gfx87+fSaw5ZjXOsDbJoRL0R2Hl9J248vIFH8Y/w0faP8EP7HzK9jy0REWWMOXPmuOyiLVKkiBolURKeuwJJOv/jjz+qkRmJ0hv35czDfZmI0ovklpZeTpLfSpTMVRLTW06Hn5ef0yxkH08ffNzwY7y4Sn/jbc+NPdgUsgmtglshK2HtzYnl8M2hkrX3W9dPze8L24clZ5awyyAREWlkREBH3Xnr0aOHy6yJl19+2dFFcBotWrRQXVMt+f3331Xif8p83Jetw32ZiNJDZEwkBm8cjIdxD9V8Pv98+K7Nd8jtl9vpFnC1gtXwVOmnsPLCSjX/xb4v1CiDPl4+yCrYdMfJNSraCM9VeE6bn35gOm4/uu3QMhEREZHrmjlzJnbu3GnykBEvpTVamzZtHF08IiKiDJWQmKBaWl25f0XNS7fAL1t8ieI5nTc/5dDaQ+HvpR95Wso9/9R8ZCUMXLmAIbWHoEC2Amr6Xuw9fLn/S0cXiYiIiFxU5cqV0bBhQ5PHnj170K5dOxQooK9vEBERuatZR2Zhx7Ud2vzoBqNRu1BtOLPCAYXRu2rSIDw/HvsRUXFRyCoYuHIBOX1z4r2672nzf5//G/vD9ju0TEREROQeduzYgYsXL+Kll15ydFGIiIgy1K7ru/D94e+1eend9Gz5Z11iqb9W5TXk9curpu9E38HiM4uRVTBw5UKjDDYo3ECbn7R7kmriSERERJTWUdoCAgLQtWtXLkgiInJbtx7dwqito6CDPjdo5fyV1YBoriK7T3b0qtJLm597fC6i46ORFTBw5SI8PDzwQcMP4O2hz6d/OuI0VlxY4ehiERERkQuLj4/HokWL0KVLFxW8Ssm9e/cQGhqqPa5fv55p5SQiIkoLafQhQavb0fp80Tl8cmBq86nw9fJ1qQX7QsUXkMs3lxaI++PsH8gKGLjKTPGxwI5vgJgHdn28dO7SJiMKfnPwmywTYSUiIqL0t27dOoSHh+PFF/XDbKdk2rRpCAoK0h7169fnKiEiIpcw++hs7L6xW5sf12QcgnIGwdUE+ATg5covm+S6ik2Ihbtj4CqzXD8MzGkJrP0QWD/G7q/pX6O/ig6LsKgw/Hbyt3QsJBEREWW1boL58+dH+/btU33vsGHDEBISoj0koTsREZGz23N9D7479J1Jq6W2JdrCVb1U6SUtJnAz6ibWXFoDd8fAVWa5vBMIO6af3jsHuPSvXV+T1z8vXq/2ujb/v6P/U4nZiIiIiGzx6NEj/PXXX+jRowd8fHxSfX+uXLlQvHhx7VGkSBEucCIicmoR0REYuW2klteqUr5KGF53OFxZLt9c6FGhhzYvjVl0Ov3vc1cMXGWW+v2A4MZJ838PAmIf2vVVL1d6WQ2HKR7GPcTPx39Or1ISERFRFrFs2TI8ePDAqm6CRERErkaCOeN3jVe5oIS0Uvqi+Rcul9fKkucrPA9PD30458TtEzgcfhjujIGrTFvSnkDXbwFvf/18xCVgw3i7vsrf2x8DagzQ5n8/9TtbXREREZHN3QSDg4PxxBNPcMkREZHbWXVxFdZdXqfNj244GkG5XC+vlSVFcxRFq6BW2vz8k/Phzhi4ykz5ywCtP06a3z0LCLEvP0TnMp1RLEcxNf0o/hHmHpubXqUkIiIiNxcREYF//vkHzz//vBq5mIiIyJ3ceHgDE3ZP0ObblWiHp0o9BXfyYqWkFtMSoAt7GAZ3xcBVZmvQHwhq8N+MDlg+FEiIs/lrfDx98Gb1N7X5BacX4PYj/dCeRESUdc2dO1cFIswfo0aNeuy9p06dQtu2bREQEIDChQtjxIgRiI21fmQaGVVuxowZaSpvWspg7WdTe1/fvn3VIyvJmzcvYmJiMGXKFEcXhZLBfZn7MhHZ30Xw4+0f437sfTWf3z8/Pmz4odvdqKlbqC7K5y2vpuN18Vh8ZjHclbejC5DleHoBnacDs54AEuOBm8eBXd8BTQbb/FWdynTC7COzEfogVLW6klxXw+oOy5BiExGRa5HWNLlz59bmixXTt9I1bnHTqlUrlCtXDkuXLsXVq1fVqHFRUVH49ttvU/3+P//8E5cuXUKfPn3sLmNaymDtZ61538iRI1GlShUV0JL3ETkT7st63JeJyFoLTy/Ezus7tfmxjceqQc7cjYeHB16s+CLG7Byj5v8695dKKeQlMQc3w8CVIwRWAhoPBv6dpp/fPAmo8jSQJ8j2Vlc13sRH2z9S84vOLELf6n2R0zdnRpSaiIhcSJ06dVCgQIFkX581axbu3bunAlD58uVTz8XHx2PgwIH44IMPULRo0RS//6uvvsILL7yAbNmyJfuezZs3o2XLlsmOdJOWMlj7WWveV7ZsWTRp0kS1HpPfReRMuC9zXyYi612+dxnT9v93nQ3gmXLPoHlQc7ddhE+WehJT9k5RDVnCosKw+/puNC5mNCicm2BXQUdp9h6QJ1g/HRcF/PN4Fw5rPFX6KZMRBt25eSARkavZvXu3uhu2cOFC7blbt26pQEmnTp2QkJBg83fOmTMHJUuWRPbs2dG6dWvs27dP/Q3pVmSL1atXo02bNlowR/Ts2ROJiYlYu3Ztip+9ePEitm3bhmeffdbm8qdXGaz9rLXv69GjB+bNm6eCWkTmuC9zXyYi55eQmIAP//1QBXGE5IR+r957cGcBPgEqf5eBtLpyRwxcOYpvdqDjF0nzp1YAFzbb/DXS6uqVSq9o87+d+A2xCdbnJyEicgnSYic+xvGPZFoOJadBgwbo2LEjPv30U9XqSHIKde3aFbly5cKCBQvg5WVbU+4VK1agX79+qhWTtCCSwJUEXCyRrm/y/aVLl8akSZMeC5JJ3qeKFSuaPJcnTx4UKVJEvZaSDRs2wNvbW+W4Sou0lMHaz1r7vsaNG6ug4qFDh9L0mygV3JcV7stJuC8TUXqRvM+HwvXncQ944NMmn6rAjrt7utzT2vSGKxsQGRMJd8Ougo5Uvh1QvgNwZrV+fvUooP+/gJdtq+WZ8s9g1pFZKvlc+KNwrLyw0mTjJSJyeRKQ/zTQ0aUAPrwJePvZ9JFx48ahbt26WLJkicqxFBoail27diFHjhw2/3kJgDVt2hQ//fSTmm/fvj2io6Mxfvx47T0SkBk7dqwKmklLrGXLluHDDz9UuZ3Mcz9JAMdS0u47d+6kWI69e/eifPny8PMzXRYSnDMOkBmmzVsxSdArrWWw9rPWvs8Q6JOWNbK+KINwX1a4LyfhvkxE6eHag2uYfmC6Nv9SpZdQt3DWOJ/XDqyN4JzBuHL/CmITY7H64mo8X/F5uBO2uHK09hMAL1/9dPhJYN8PNn+FRJGfr5C0Yc49PheJusT0LCUREaUhP420surdu7fqtrZy5UoVXLKVBIH279+Pp582vTFh3l1Pglkff/yx+rddu3YqWCXJyCXX0/Xr19NlPcr3FCxY8LHnf/75Z/j4+GgP6aInjJ+ThyR1dzYSTJMAV3otI3I/3Je5LxORc5IbZ+N2jtO6CBYNKIq3a72NrMLDwwPdynbT5v889yfcDQNXjpa/DNBwYNL8pglAVMp3mS15sdKLqtuguBB5ATuvJY2iQEREjiU5rWQUu3fffRdVq1a16zvCw8NVy6XAQNOWZ4UKFUr1s5LTSQJfxt3gpMVRZGSkxdYPxvmgLJFWXuatrUTnzp1VayzDQ4Jlwvg5eRgSp6elDNZ+1pa/Ib/p0SN9pZfIEu7L3JeJyPksv7Ac269t1+Y/afQJsvtkR1bSuUxneHrowzsnbp/AxciLcCfsKugMmg0HDi8AHtwAoiOBrVOBJyfa9BUFshVQidoNydh+P/U7mhRrkkEFJiLKZNIyVbrpOZqhhawNfvnlF0yfPl211pAE6u+//77WVU4sX75cdRuKjY1VwS15T6NGjR77HmnhJJ+7edN0OYSFhdn1UyTvk3keKQnwSIsj85xQ5iTgY6nVVP78+dXD4MGDB+rf5LrepaUM1n7Wlr9x9+5dk/JTBuC+zH3ZDPdlIkqL249u47O9n2nzXcp0cctR9VIjA7bVK1QPu2/sVvP/XPoHA2oMgLtgiytn4JcTaPVh0vye2cAd2yOkL1R8QZveGroVIfdD0quERESO5eGhzy3l6IeUwwabNm1C3759VeDqt99+U8EeQ34qIS2o3nzzTfzzzz84ePAgDh8+jBo1alj8Lsm/VLt2bZWU3ZjkzkqNIRF8rVq1tOc6dOiA9evXq2CNweLFi+Hp6am6GKakQoUKamTBtEpLGaz9rLXvkxZtEjiU30YZiPsy92Xuy0SUjibvmawlI8/nnw8j6o3Issu3fan22vSai2vgVnSkCQkJkeGi1L+ZLiFep5vRUKf7JJf+sai3XV/z0sqXdFXnVlWPz/d8nu7FJCLKSBcvXlQPd3DixAldnjx5dO+884723AsvvKALDg7WxcTEqPn4+HhdxYoVdS+//LJuxYoVutjY2BS/8++//1bnqd69e+v++ecf3YQJE3QlS5ZUz/3000/qPe3atdNNnjxZt3LlSvV48803dR4eHrqhQ4eafNedO3d0RYoU0TVv3ly3Zs0a3Y8//qjKO2jQoFR/m7zfmvPlpk2b1PuSY20Zfv75Z52Xl5du8+bNNn/W2vetWrVKlfXGjRt2b6MOrUc4QEq/l/sy92VX3peJyDVsurJJu/aVx+qLq3VZ2Z1Hd3Q1fq6hLY8zd87onJkt9SYGruxccBnizNqkwJU8QvbZ/BUrz6/UNtRG8xvpouKiMqSoREQZwV0uJMLCwnSlSpXSdevWTZeQkGASzPL09NTNmDFDe06CWBK06t69u65ly5apfvesWbN0QUFBOn9/f3UBt3v3bpPA1eDBg3XlypXTZcuWTefn56erVq2abvr06brExMTHvkvK07p1a/XewMBA3fDhw7WgWkrkPfnz59fNnj07TYEra8sgv02+R77PnvJb8763335b17Rp01R/OwNXWStwxX05a+7LROT8HsY+1LVe1Fq79n1rw1sW6zpZzZtr39SWydcHvta5S/zFQ/7n6FZfzkKGKA8KCkJISAiKFy+e+QWQVfFLV+DiFv18qebAq8ts+oq4hDi0XdIWt6Nvq/kxjcbgmfLPZERpiYjSnSFvUsmSJbPE0j19+jTKly+vRoPZsmULRo4ciV27dtn0HdIFThKQSxdEGbkws0iieeneuHHjRrg66bIZHByMyZMno1evXnZvow6vR2SylH4v92Xuy668LxOR85u2bxp+Oq5PvxDgE4C/u/6NQgGpD1jj7v48+yc+3vGxmi6RqwSWd1uu6pnOyJZ6E3NcORPZoNqOTZqXANbFrTZ9hY+XD3pU6KHNLzmTeu4TIiJyjKlTp6qcSpK7aty4cSb5r5zd8OHDsXv3bpWXy9XNnz8fOXLkwIsvvujoopCL4r7sHLgvE2UNZyPO4tcTv2rzb9d6m0Gr/7QKbgVvT/0gQJfvXcapO6YD1LgqjirobIrWAip1AU7+19Jqw3jg9bU2JQTuXrY7vj/8PXTQ4djtYzh95zQq5GOyWSIiZzNnzhy4qiJFiqgRECWpuauTRO0//vijyWiPRLbgvuwcuC8Tub9EXSI+3fUp4nXxar5ivop4rsJzji6W08jtlxtNijbBllB9L651l9ehUv5KcHWsoTmjlqOBk8ul7yAQugc4swao8KTVHy+SowiaFGuCf6/+q+aXnl2K9xu8n4EFJiIiR8mTJ48knnHI3+7RI6mFryt7+eWXHV0EIu7L6YD7MpH7W3Z+GQ7cPKCmPeCBjxp+pLUwIr22JdpqgatNIZswuPZguDp2FXRGgRWB6kZR402f6vNf2eCZckl5rZZfWI7o+Oj0LCERERERERFRprkbfVfltjJ4tvyzqF6wOteAmWbFm8HTQx/qOXf3HELuh8DVMXDlrFqMAgyR4xtH9a2ubNA8qDny+edT0/dj72P9lfUZUUoiIiIiIiKiDPfVga8QEROhpuVad0jtIVzqFuT1z4uaBWtq85tDNsPVMXDlrPKVAmo8nzS/9XObWl35ePqga9mu2rx0FyQiIiIiIiJyNYduHsIfZ//Q5ofVGabyOZFlLYNaatPSXdDVOVXg6tSpU2jbti0CAgJQuHBhjBgxArGxsal+7vbt2+jfv78a/lY+W7VqVcyaNQsu74lhwH9N/HB1n36UQTu7C+69sRdXH1xN7xISERERERERZZj4xHiVkN2gdmBtdCnThUs8BS2CWmjTB8IOIDImEq7MaQJXERERaNWqlQpULV26FBMnTsTs2bMxbNgwq5LDLlu2TA0lvnz5cjz55JMYMGCAS4/wouQvA1TpnjS/dapNHy+Rq4RJE8EV51ekZ+mIiIiIiIiIMtTvp37H6YjTatrbw1slZPfw8OBST0HJ3CVRKncpNZ2gS8DW0K1wZU4TuJIWUvfu3cOff/6J9u3bo0+fPvjss8/U89euXUv2czdu3MCmTZtUoKt3794q+DV16lQ0a9YMCxYsgMtr+m7S9KVtwJVdNn28c5nOJknaHTXyFBEREREREZEtwh6G4duD32rzr1R5BWXzluVCtLHVlavnuXKawNXq1avRpk0b5MunTyguevbsicTERKxduzbZz8XFxal/c+c27d8q824RpClUGajYye5WV+1Ltlf5rsTle5dx9NbR9C4hERERERERUbr7fN/niIqPUtOFAwqjf/X+XMpWahXUSpvecW0H4hL1sRNX5OlM+a0qVqxo8lyePHlQpEgR9VpygoKC0K5dO9Xi6sSJE7h//z4WLVqkgl2DBg2CWzBudXVuHXDtkNUflYR1zYs31+aXnV+W3qUjIiIiIiIiSle7ru/CmktrtPlR9Uchu092LmUrVStQDbl8c6npB3EPcDTcdRuxOFWOKwlUmcubNy/u3LmT4mclJ1ahQoVQpUoV5MqVCy+++CK+/PJLPPNMUnJyS6RrYmhoqPa4fv06nFKx2kCZ1knz26ba3V3wn0v/IC7BdSOtRERERERE5N6kddCUPVO0+WbFm5m0IKLUeXl6oVHRRtr89mvb4aqcJnBlL+kO+Nprr+Hs2bOYP3++ync1cuRIDB06NNUcV9OmTVMttgyP+vXrw2k1G540fXI5cDP5VmjmmhZrijx++qCgjCaw7eq2jCghERERERERUZotOr0I5+6eU9OS+mZkvZFMyG6HJkWbaNPbrzJwlWbSsioyMtJiSyzjvFfmVq5cicWLF2PJkiV44YUX0KJFC0yYMAG9evXCu+8adbGzQEYsDAkJ0R579uyB0yrRGCiRtNHh32lWf9THy0flujL45+I/6V06IiJyIitWrEDt2rXh5+enbsx88sknSEhIeOx90hW/bdu2CAgIQOHChTFixAg1uq+15IbPjBkz7C7nuXPn0L9/f9SsWRPe3t6oWrWqVZ+T837Xrl1RvHhxVXb5/I8//vhYbkupE8ioQ5Yexje3+vbtqx5Ezob7sh73ZaKs5U70Hcw4mFS/6FW5F4JzBTu0TK6qkVGLqxO3TyAiOgKuyGlaXEl+K/NcVhLIku575rmvjEleKy8vr8cqu7Vq1VKjEUZF6RO5WSLdCqXSa3hIPi2XyXV17A/gXvKjLZrrUKqDNr05dDOi4pJfLkRE5Lp27dqlgjqVK1fGsmXL8M477+Dzzz9XrZHNbwzJSLwSqJIu95Ircvbs2eqmjjVkFOBLly6pUYDtdfz4cXUDqmzZsqq81pIW09mzZ8cXX3yB5cuXo0OHDirwNG7cOJP3zZw5Ezt37jR5PPfccypIJgPCGMiy+eWXX1TrbSJnwX05Cfdloqzl6wNf437cfTUdmC0Q/ar3c3SRXFbhgMIom0c/CqMOOuy8thMuSeckJk6cqMuRI4cuIiJCe27OnDk6Ly8v3dWrV5P93IIFC+T2qu7QoUMmz/fp00cXGBhoUxlCQkLUd8m/TikxUaeb2Vin+ySX/rHuE6s/mpCYoGu1qJWu6tyq6rH64uoMLSoRkT0uXryoHmS/9u3b62rXrm3y3NSpU3U+Pj66GzdumJx3AwICdLdv39ae+/7771M97xo0a9ZMN3jw4BTfs2nTJnVeTU5CQoI2/eqrr+qqVKmis0Z4ePhjz/Xt21eXK1cuk++0pFSpUrqOHTs+9nzLli11Q4YMSdM26vT1iHSW0u/lvpx23Jcdty8TkeMcu3VMV21uNe26dcX5FVwdafTZns+05fnBtg90zsKWepPTtLiSrgI5c+ZEt27d1IiAP/30E9577z31fNGiRbX3tW7dWt2ZNejYsSOCg4Px7LPP4rfffsOGDRvUndO5c+fi7bffhlvx8AAaDkya3/cTEPvQqo96eniadBdcczFpdAYiIsoYu3fvVt3SFi5cqD1369YtdR7r1KmTxe57qZkzZw5KliypWhzJOXHfvn3qb8h5Txw8eFCNtmusffv2iIuLw5o1Scf+1atXq1ZHxt3xe/bsicTERHUeTsnFixexbds2de5NC09P+6ohBQoUeOw5aWktg648fJj8eXHHjh2q7C+99NJjr/Xo0QPz5s1DfHy8XWUi98Z9OWXcl4koPSTqEjFp9yTVMkjUCqyFjqU6cuGmY54raXFlnlrBFThVjisJOknzfQlejRo1Cm+88YbqDmBMKvnGlUoJdsnnJJeHBKy6dOmiuh3I595//324nWrPAgGB+unou8Ch+VZ/9MmST2rTW0O34kHsg4woIRER/adBgwbqBsunn36qKgkxMTGqG590VZccS9LV3dZ8N/369UPLli1VVz0JXEnAxVh0dLTKbWXMMH/y5EntOemeb94VX0b3lW7z5l33zRnO1840qMm///6LYsWKqXpBcmQQF8mJJevAXOPGjVVQ8dChQ8gKfv75ZxXs8/f3V4FA6W756NEjRxfLaXFfzjzcl4myrpUXVuJw+GE17QEPvF//fSZkTwe1C9WGn5e+Lhj+KBxnIs7A1XjDiVSqVAnr169P8T2bN29+7Dm5c218N9utefsB9fsCmybo53d9B9R9XW51pfrRagWqoViOYrj64CpiE2OxKWQTOpfpnPFlJiJKIwn6yLDIjiaj2kjrJltI3qW6deuqQUQkl1RoaKjKXZMjRw6b/74EwJo2bapaJRtaUkmgavz48dp7ypUr99hgI/L3xJ07d0xyXEmgytKNJOP3WbJ3716UL1/+sQCZrCfjVmSGafNWTBL0Su8LXQkESs6r5EgZFi1apG5wSfDKXJUqVVQgUVrWyPpyZzKIzZQpU/DBBx+gUaNGKmAnwUh7WgDaivuyHvdly7gvE2VdD+MeYtr+pEYrz5Z/FpXyV3JomdyFv7c/6haqi+3X9KMK7rmxBxXyVYArcarAlbsLuROFz9acRv/mpVGlaG77v6huH2DrVCAhBrhzHji7FqiQ1JoqOXKxJd0Ffzz2o5pfc2kNA1dE5BIkaFXntzqOLgb2v7wfvl6+Nn2mTp06qoVP79694ePjoy7M7BkMRIIK+/fvx2effWbyvHTXMw5cDRw4EK+//jqmT5+OV155RQ1iMnr0aBWUsTXolhwZOKVgwYIWW/G89tprjz0vv9uYdNeT7o7pQQKBknBdWqENHjw42fetW7cO4eHhePHFFy2+LsE0CeTJb3Nnp0+fxpgxY1TifmllZfDMM89kyt/nvsx9OTncl4mytu+PfI9bj26p6Vy+ufB2LTdL++Ng9QrXMwlcvVL5FbgSp+kq6O7m776C1l9swfLD1zBx1cm09SsNKADUeC5pftcMu7oL7ri2g90FiYgygbQMllFu33333cdGwbWWBF2k1VBg4H/dxf9TqFAhk3kJkA0dOhTDhw9H/vz5VXdCyRcpuayMA2bSskpG7zUnLbGM815ZYqk7oujcubNqjWV4zJo1Sz1v/Jw8jHNXpsXdu3dV8EV+5x9//JFinh3pJijvk1ZqyZHf5O7d5aS1XqlSpUyCVmQ97svcl4ko/V2KvIRfT/yqzb9V6y3k9c/LRZ2O6hdOSu+w/8Z+JCRmfCvr9MTAVSapVCQnYhMS1fT2c7ex+Ux42r7QOEn7xa3AjaNWfaxivoqqu6Dhrue2q9vSVg4iIkrRL7/8olo/ScsrSaBu3m1u+fLlKn+O5BuqUKECdu60PEyxtHCSVkE3b940eT4sLMxkXoI3X375per+dfjwYfV63759VeCrYcOG2vskv5V5LisJZEmLI/PcV+YksCVBI3MSGJJudoaH/B5h/Jw8fH1ta7VmiQSYJMG9lFkSzefOnTvF9/71118qH5h56y9j8pvkN7gz6TZarVo11VVNgqCyLpo0aaK6SFLKuC9zXyaijPHZ3s8Qn6ivH5XLWw49ypvm76S0k26XAT76VAn34+7jVETK+UydDbsKZpJawXnRqXoRrDii74IwceVJNC1bAN5edsYOAysBZVoB5zfq53fOBJ7+LtWPSTeRtiXaYu5x/ehT6y+vR4dSvOtKRM5NcktJNz1nKIctNm3apIJGErhq1aqVyqMkLV7kOSFBrDfffBPHjx9XLaCkJZOM6meJdPWTgUgkKfs777yjPS+5syyRQE716tXV9Mcff6xa2cgoggbS4mbixIkqWGPIdbV48WIV+DIfldCcBKTktzmKLDcZAVGSzcvohpKUPSXSLe7BgwfJdhMUEtiTVnGGYJu7unHjhupyevToUcycOVONTinbgazzs2fPPtaiz5iM2igPA3u6VXJf5r5sjPsyEW0J2WLSmEISsnt7MkyR3rw9vVGnUB01SJvYe30vquSv4jIbIFtcZaKRT1aE73+BqrM3H2DRvtC0fWHDQUnTx5YA903vuiendXBrbVoOEtHx0WkrBxFRBpOgu+SWcvTDlhxRElTp3r07Bg0apPJOSSsmycUkLV1iY2O13yUBJsnNJCPiSnBKAgnJkVxVEqiRPFJr1qxRAYdff01qWi8kMfvnn3+ucjpJwEZG6JVE3P/73/9MRjGU7oMyAp+M5Lt27VoVUHvvvffU86l15ZMWOtLyS3LSpIUEiiTwJo/Lly+roIhhXgJJxi1dpLXZli1b1LwsTxlhUZaHfEZaERkeMnKjpW6CwcHBeOKJJ5Ity759+9S/Kb3HHUhgVIJ4sowlP5qMeinbiaQw+Pbbb1P8rIzYHBQUpD3sGVWS+7Ie92Xuy0QExCbEYsreKdqikHzMkouJMr674J4bpgP5OD0daUJCQiTxlPo3o0xYeUJXYuQK9agzfp3ufnSc/V+WmKjTfVNPp/skl/6x4VOrPpaQmKBrtbCVrurcquqx4fIG+8tARJSOLl68qB6uLiwsTFeqVCldt27ddAkJCdrzJ06c0Hl6eupmzJihPRcTE6NbsWKFrnv37rqWLVum+t2zZs3SBQUF6fz9/XXNmzfX7d69W527fvrpJ/X6wYMHdQ0aNNDlyJFDPVq3bq3bsWOHxe+S8sjr2bJl0wUGBuqGDx+uypMaeU/+/Pl1s2fPTvF9mzZtUmVLjqxred3SQz5rIL/N+LkSJUok+znz7efOnTs6X19f3YgRI1Is69tvv61r2rRpmrbRzKhHpFX9+vXVujPXrFkztQ2mJDIyUv02w2PPnj3J/l7uy9yXXXlfJqLMMefIHO2atO6vdXXX7l/jos9Ax28d15Z3g3kNdHEJaYhFpANb6k0e8j9HB8+chdw5ljuIISEhKF68eIb8jcioODSfugl3o/TDug9uVRbD2qWhW8K+n4AVQ/XTOQoB7xwHvFLvyjJh1wQsOL1ATXcp0wUTnphgfxmIiNLJpUuX1L/pNeKcK4zwVr58edUKRVoTjRw5UrUasoV09ZNuhtJiShKzZxZJNH/w4EFs3Phfl3UXJt2VpEXW5MmT0atXL7u30cyoR6RVnz59VAsryYFmrHnz5siRI4dq+WetlH4v92Xuy668LxNRxgt7GIbOf3XGo3j9oCiDag5C/xr9uegzUEJiApoubIr7sffV/LyO81C9oD6thCPYUm9iV8FMlju7Dwa3KqfNz952Adcj0zCCUfWegN9/CWkfhAGnVlj1sTYlkvKcbArZhLgEfSCNiIgyz9SpU1VOJcldNW7cOBV8chUyaqEk9JYE8K5OuhJK0CalHFjuQhLa3759G4cOHdKek/kDBw6oAQTIPtyXnUNW2peJXN2XB77UglYyeNhrVV9zdJHcnpenl8pz5YrdBRm4coCXG5ZAyfz6HCbRcYn4Yu0Z+7/MNwCoaXRy3vuDVR+TDTaPnz4Zr0Rc94bttb8MRERklzlz5uDMmTMqaLBhwwZUqlTJZZZkkSJF1CiJxrmoXJUkpP/xxx9VHi13JznN6tWrp/JbLVy4ULW+kmCWn5+fyh1G9uG+7Byy0r5M5MoOhB3AygtJLXzfq/ce/Lz8HFqmrJjnat8NfX5PV8CjugP4entiVIeK6P/bATX/x4FQvNakJKoUTX4o7xTV7QPs/m9EwUvbgPDTQMEKqY4q0Lx4c/x9/m9tNIfGRRvb9/eJiMhhZERAR/X679HDPYarfvnll5FVyIX9qlWr1MiUMqKlDBTQtGlTbN26FYULF3Z08bI07stpl5X2ZSJX7q42ac8kbb5RkUZoFdTKoWXKSuoWqqtNHwo/pNaHtMRydmxx5SDtqxRGvZJ51bRcb0xefcr+LytYHijZNGl+349WfaxlUEttenPIZodd+BAREVHmKVCggBqNUvKjyciOMkJl5cqVuQqIiCjD/XH2D5y6o7/29fbwxqj6o2watZnSplzecgjwCVDTD+Me4tzdc3AFDFw5iOycH3RM6hKy7ewtbD9nmijVJvXeSJo+NB+IfZjqRxoVbQRfT181fe3hNZyJSEOXRSIiIiIiIqJkRMZE4puD32jzL1R6AaXzlObyykTent6oXiApIfuBm/peYM6OgSsHqhWcFx2qJjXL/+yfU/a3eqr4FJDjv++KuQccXZLqR7L7ZEeDIg1MWl0RERERERERpbcZh2bgbsxdNZ3PPx8G1BjAhewAtQrV0qYP3jzoEuuAgSsHe7ddBXj+1zLycGgk/jl2w74v8vIBahsN+7vvB30fxFS0CGqhTTNwRUREREREROlNevcsPL1Qmx9aeyhy+ubkgnaA2oG1telDN5NGGXZmDFw5WNnAHOhZN0ib/3ztacQnJNr3ZXVeBTz+W6XXDwNXU2/2JwnaDY7dPoabUTft+9tEROnAy8sLCQkJXJbktGT7lO2UUsZ9mZwd92WizCO9iibtnoREnf46t2r+quhatitXgYNUK1ANXh76usz1h9dx46GdjWcyEQNXTmBIm3Lw89avigvhD7F4f6h9X5S7OFChY9L83v+l+pFCAYVQJX8VbX5L6Bb7/jYRUTrw9/dXo5zdvn2by5OcjmyXsn3Kdkop475Mzoz7MlHmWnN5DfaF7dPm32/wPjwNDS4o02X3yY6K+Sq6VHdBb0cXgIAiubOhd+OS+H7rBbU4vlp/Bk/XKgZ/Hzvu6NbtA5xaoZ8+vhRoPwHIni/V7oLHbx9X01tDtqJHefcY3pyIXHO0s5iYGNy8eVONeMaWLeRMrTMkaJUzZ061nVLKuC+Ts+K+TJS5ouKiMHXvVG2+a5muqF4wKTk4OUatwFpaDOBA2AF0KNXBqVcFw5xOYkCLMsjpr48jht2Lwdwdl+z7otItgbyl9NPx0foRBlPRtHhTbXr3jd2ITYi1728TEaXDiKvFihVTF72+vvpRT4mcgWyPsl3K9slhu1PHfZmcFfdlosz1w7EfEBYVpqYDfAIwtM5QrgInCVwZHAp3/jxXbHHlJPJk90X/5mXw+ZrTan7mpnN4oV4wcmf3se2LPD31ra7WfaSfP/gr0GiQ1CCT/UilfJXUqA53ou/gUfwjNSRmwyIN0/R7iIjScsFbsGBBLkAiF8d9mYgoawu5H4K5x+Zq8zKKYIFsbLXsbIGrMxFn8CD2AXL45oCzYosrJ9KnSSkE5vRT0/ei4/H91vP2fVGNFwDP/2KS4aeA0KT+xJZI/+Inij2hzf8b+q99f5eIiIiIiIgIwGd7P0Nsor43T+ncpfFipRe5XJxEwewFUSxHMTUtSfNloDZnxsCVE8nm64XBrctp89Jd8NaDGNu/KEdB0yTtB35O9SNNijbRpv+9ysAVERERERER2UeuKTeHbNbmR9YfCR9PG3sTUYaqXiAp19jR8KNOvbQZuHIyPesGIShfNjUdFZuAWZvtbHVVu1fS9PE/gZgHKb69cdHG2sgO5yPP4/qD6/b9XSIiIiIiIsqy4hLiMGXPFG2+dXBrdb1JzqVawWra9JFbR+DMGLhyMr7enhjcKqnV1a+7LiPsXrTtX1SmFZBL3/QPsQ/0wasU5PHPg6oFqmrz/15jqysiIiIiIiKyzW8nf8Ole/rBxvy8/PBevfe4CJ1QtQLVTFpc6XQ6OCsGrpzQ07WKoXSBADUdE5+IGZvO2f4lnl5AzZeS5g/8kupHnijKPFdERERERERkn/CocMw6PEub71O1j5ZLiZxLpfyV4P1fbuzb0bdx4+ENOCsGrpyQt5cnhrYtr83/vucKQiOibP+iWkaBq9A9QLh+xMLkGCdo331jt2riSURERERERGSNL/d/iah4/bVrkYAieK3qa1xwTsrPyw8V8lZwie6CDFw5qU7ViqBCoZxqOi5Bh2832tHqKm9JoFRzq1tdVSlQBXn98qrph3EPcSj8kO1/k4iIiIiIiLKcQzcPYfmF5dq8dBHM5q3P30yu0V3QWTFw5aQ8PT3wjlGrq8X7Q3Hp1sO0JWk/vACIj03+b3p4onGxpKR5265us/3vERERERERUZaSkJiAibsnavMNijRAm+A2Di0T2Zag/egtBq7IDu2rFELVYrnUdEKiDl9vOGv7l1TsBPjn0U9H3QLOrE7x7U2KNtGmt1/dbvvfIyIiIiIioixl6bmlOHnnpJr28vDCqHqj4OHh4ehikQ0trk7cPoG4ROdMF8QWV05MdvR32yb1Of3z0FWcDbtv25f4+AM1nk+aP/Brim9vUqwJPKA/wJyJOIOwh2E2lpqIiIiIiIiyisiYSHx94Gtt/oWKL6Bs3rIOLRNZp0SuEsjpq09RFJ0QjXMRdqQoygQMXDm5FhUKonawvsWUjE751Xo7Wl3VeiVp+vwGIDI02bfm88+HKvmraPPbr7HVFREREREREVk249AM3I25q11PDqw5kIvKRXh6eJrmuXLS7oIMXLlCq6t2Sa2uVh69jhPX7tn2JYWrAkVr6ad1ifpcV6m0ujL49+q/NpaYiIiIiIiIsoLTd05j4emF2vzQ2kO1FjzkGqoZBa6O3ToGZ8TAlQtoXCY/GpbOp81PW3fG9i+p9XLS9OHf9c23kvFEsSe06Z3XdjptP1ciIiIiIiJyDJ1Oh0l7JiFRGkf8FwDpWrYrV4eLqWLU40ryXLld4Orhw4e4cOECjh8/jhs3bqRfqSjFVlfrT4bhcIi+KabVqnQHvHz107fPAaH7kn2rHHBy+eqTwj+Ie4Aj4Ue4RoiIiBwoISFB1buIiIicxeqLq7E/bL82/37991XXM3ItlfNX1qbP3z2PmIQYOBubt6qjR4/i3XffRfXq1ZE7d26UK1dOTRcrVgz58uVDp06d8PPPPyMqKipjSpxF1SuZD83KF9Tmv7C11VX2fECFDknzh+Yl+1YvTy80LtpYm+fogkRERJnr9u3b+Oabb9ClSxcUKlQIvr6+yJUrF7Jly4YaNWrgrbfewpYtW7haiIjIIR7EPsDUfVO1+W5lu6FawaQuZ+Q6ArMHqtxkIl4Xj7MRduTVdpbA1c6dO9GiRQtVWdq+fTvatGmDH374AcuWLcOaNWuwcOFCfPDBB8iRI4cKbEkga8KECbw7mI7ebVtem956JhwHrkTY9gU1XkyaPr4UiItO9q3GgavdN3bbWFIiIiKyx5UrV9C7d29Vj5o0aRK8vb0xcOBAfP311/j+++8xfvx4NG3aFPv27VN1sfLly2PevORvRhEREWVUQvbwR+FqWnJaSW4rct0eXpWNWl05Y3dBb2vfKC2pBg8ejF9++QXBwcEpvjc+Pl4Fs6ZNm4bExER89NFH6VHWLK9GUB60rhiIDaduqmUxff1Z/NynvvXLpWxrIKAg8DAciI4ETq8Cqna3+NaGRRqaJGi7H3ufSfaIiIgyWOXKldGjRw+sW7cOTzzxhKpMJic8PByLFi3CuHHjEBISglGjRnH9EBFRpiRkn39qvjYvQav82fJzybuwyvkrawOzuXTg6vLly6o1lVVf6u2Np556Sj2YjyF9DWlTTgtcbfmv1VXt4LzWfdjLB6jWE9g1IylJezKBqyI5iqBErhK4fO+ySra398ZetApulW6/g4iIiB4neUNLlChh1aIpWLAgBg0apFpkXbt2jYuTiIgynFwbfrrrUy0huyT2fqbcM1zyLq6yk7e4srqroLVBK3MBAQF2fY4sq148D1pVDNTmpdWVTWq+kDR9bgNwPyzZtzYo3ECb3n2d3QWJiIgymrVBK2PSKku6FhIREWW0v8/9jUPhh/TnH3jgo4YfqRzJ5Noq50sKXJ29exaxCbFwJnal/N+/fz82bNigzUdERKBv376qSfuYMWNU90DKOENal9OmpdXVQVtyXRWuBhT6L2meLgE4uijZtzYsmtRdcNf1XXaWloiIiOwhrd1lUByDmJgYlT/05Zdfxty5c7lQiYgoU0XGROLL/V9q8z3K90CVAlW4FtxA4YDCyOun78kVnxivglcuH7h655138O+/+v6PYujQoSrHQuHChTF16lRVqaKMzXVl0upqQxpaXR36HdDpLL6tfuH6KoouLkRewM0ofRdFIiIiynhyU/DXX3/V5keOHImxY8fi1KlT6NevH2bOnGnX90rQS1ppmT+YI4uIiFLy9YGvERGjbzQhQY7BtQdzgbkJDydP0G5X4OrEiROoX1+fFPzRo0dYsmQJvvrqK/XvlClTTCpZlPGtrjafDsehkLvWf7haD8Djv+acN48DN45YfFtuv9yolL+SNs/ugkRERJnn0KFDagRBw8A3P//8s6pnyYiC0sL9u+++S9P3//PPP2rUaMND8mURERFZIgN2LT6zWJt/p8476nqR3Eclo2v/k7dPwuUDV1FRUciePbua3r59u2q63rVrVzVfvXp1hIaGpm8pyWKrq5YVCmrz09efsX4p5QgEyrUzbXWVDOPRBdldkIiIKPPcv38fuXPrLwp2796Ne/fu4fnnn1fzkp7hwoULafr+OnXqoGHDhtojKCgoXcpNRETuJSExAeN3jYcO+p46NQvWRNey+ut/ch+V3a3FVenSpbF69Wo1PW/ePFXxyZcvn5q/efMmcuXKlb6lJIuGtCmvTW+ytdWVcXdByXMVbzn5WoMiDUwCV7pkuhUSERFR+ipevDh27dLnmFy6dCkqV66MIkWKaPlFDTcRiYiIMtKSM0u0QIanhyc+bPih+pfcN3B1JuIM4hLj4Czs2tqGDRuGzz77TA3D/Msvv2DIkCHaa5s3b1atrijj1UxLq6vyTwL+efTTUbeBc+stvq12YG34evqqaclxdfHexTSWmoiIiKzx+uuv48MPP0S9evUwffp0ldfKQAJalSolNem3R5UqVeDl5aVuSE6aNAkJCQlcMUREZOL2o9uYfnC6Nv9ixRdRIV8FLiU3VDSgKHL65lTTErS6GOk81/7e9nyoT58+KFu2LPbu3YvatWujZcuW2mv58+c3CWRRxre6ktZWxq2uJKCVKm8/oOozwL4fklpdVez42Nv8vf1RM7Am9tzYo+W5Kp27dDr/CiIiIjInydKLFi2q6lsDBw5E7969tdekxdUbb7xh10KTVluS5L1BgwYqGeuyZctUgOzq1av49ttvk/2cdFWUh8H169e50oiI3NwX+77A/dj7arpAtgIYWHOgo4tEGUTqBBXyVsC+sH1q/vSd0yifN6mXl8sFrkSzZs3Uw5wkCzWWmJiINm3a4Pvvv0e5ckkJxSl9SJCqRYWCKkG7+HrDWfzYu551H67+XFLg6vRqIDoS8M9tMc+VIXC169ouvFDRqJshERERZZhevXqph7lZs2aZzEtXfmmhJfWw4ODgFL+zffv26mHQrl07ZMuWDV9++SVGjx6tdUc0N23aNBXwIiKirGHntZ1YfmG5Nj+87nCtRQ65pwr5kgJX0l3QWWR4x1SpSEn3QUkwShk/wuDGUzdx2NpcV0H1gTwl9NPx0cDJpINScgna997Yi/jE+DSWmIiIiNKT3CiUUQdv3bpl1+d79uypugrKSIYppYoICQnRHnv26G9qERGR+4mOj1YJ2Q0aF22MjqUe76FD7qVC3qRuoNLiylkwo5obqBWcV7W6Mpi+4ax1H/Tw0Le6MjiyMNkkbTl99JH1+3H3nW5oTCIiItLfLMxIMviOJIw3PJJrmUVERK7v+yPfI+R+iJr29/JXCdmlKxm5t/L5kroGno5g4IqcpdVV9Z5J0xe3AZFXH3uLl6cX6hWuZzK6IBEREbmPBQsWqETttWrVcnRRiIjIwaSL2Nxjc7X5ATUHIChnkEPLRJmjbJ6y8PLwUtN3ou/g1iP7WnKnN7a4cqNWV83LJ7W6klxXVilQDihqqKTqgGNLLL6tQZEG2jQDV0RERK5L8ltNmTIFq1atUo/+/fur/FZvv/02Chcu7OjiERGRAyUkJmDsjrGI18VrXcdeqfwK10kW4eflh1K5Szldd0GnClydOnUKbdu2RUBAgKo4jRgxArGxsVZ9VkbCefXVV1GwYEGVYFSGiJ43bx6ykiFtklpdbTh1E0dCrW11ZdxdcLHFtzQsmpTn6uDNg3gU/ygNJSUiIiJHqVixIn744Qc8++yz6N69O3bs2IGvvvpKJV8nIqKsbdGZRThy64ia9oAHPmn0CXw8fRxdLMpExiMJnrpzCs7AaQJXMqxzq1atVKBq6dKlmDhxImbPnq0SgaZGhmNu1KgRrl27pj6zYsUKDBgwADExMchKapu1upq+3spWV1WfAf5rDoiwo0DY8cfeUipXKQRmD1TTcYlxKnhFRERErmf69Ok4c+YMoqKiEB0djSNHjmDw4MHMXUJElMWFPQzD9APTtXkZTb5awWoOLRNlPhlZ0NnyXHnDSciwzvfu3cOff/6JfPnyqefi4+MxcOBAfPDBByhatGiyn5WWWUFBQfjnn39UfgbRunVrZEXS6mrLmXCTVlfVi+dJ+UM5AoEyLYFz6/XzRxYBbU2Hu5ZEfA0KN9CGQ913Y58aWYKIiIiIiIhc36Q9k/Aw7qGaLpS9EAbXHuzoIpGDRxY8c+eM67a4unHjRoqvHzhwQJuWQNLFixdRrVrKkdrVq1ejTZs2WtDKMDSzDO+8du3aZD8nwa5FixapAJchaJWVSaurZvbkujLuLnh0sYyr/dhbjBO077nBIbCJiIgy0qNHKXfLDw0N1aalDrRp0yZUqJBU2SQiIrLWhisb1MPggwYfIMAngAswi7e4unTvEmISYlwzcCVBqCVLHk/iLUGmsWPHqm57xkqUKAEfH59U81tJzgVjefLkUUMty2spBcmke6F8f/PmzdW/kh9r5MiRiIuLQ1YfYXD9yZs4GhqZ+ocqPgUYDkz3rgKXt6cYuDp+6zii4qLSqcRERERkrkaNGti9e7fFBfPzzz8/dlNQ6kGSJ5SIiMgWD2IfYOLuidp8m+A2aBXcigsxiyqQrQDy+esbFCXoEnDu7jnXDFw988wzqjXUK6+8gshIfVDk9OnTKmAlo9R89tlnNn+n5LiSQJW5vHnz4s6dO6m2/nrjjTdQt25d1TrrnXfeUUlGP/744xT/prTWkruVhofkynIHdUqYtrqavsGK5n2+AUClTknzRxY+9pbiOYujaIC+y6aMMnHo5qF0KjERERGZK1OmDJo2bYqPPvpIpU8Qt27dUgnV+/Tpg969e3OhERFRmn198GvcjLqppqWV1aj6o7hUs7gKTtZd0NPefFQrV67Exo0b1d2+UaNGoXbt2tDpdKoF1JAhQ5BZpJWXkG6GX3zxBVq2bKlaW7333ntqaOeUmtnL6DmSG8vwqF+/Pty11dWxq1a0uqreM2n6xN9AXPRjb6lbuK42ze6CREREGUfSKEgidbkZ16BBA1X/qlKliqprbdiwQdVziIiI0mJ/2H78fup3bX5o7aEoFFCICzWLq+BkCdrtHlWwQ4cOWLVqFcLDw/H555+jUqVKajhl8+5+1pKWVYbWW+YtsYzzXln6nJARCY1JcnYZVfDcueSbtcmIhSEhIdpjzx73ydskra6aliugzX+13oooaakWQIB+5EDE3APO/PPYW+oXTgru7Q3bm06lJSIiIktklOStW7fixIkTGDRokLrRduzYMbRo0YILjIiI0uRR/CN8vD2pl1LNgjXRs4JRYwbKspoXb45BNQfhm1bfoE/VPq4buJo3b55q3VSqVCnVwkkqUdLq6dKlS3Z9nwS8zHNZSSBLuu+lFAyrXLlyit8rwzwnJ1euXChevLj2kHxa7mRoGxtbXXl5A9WeTZqX0QVTaHElea4Mo04QERFR+tu2bZtK0SB1lueee061tpJglqWbfURERLaYcXAGrty/oqb9vPwwrsk4eHrYHSIgN1K3cF30r9EfLYJaIDD7f41bHMiurbJHjx7o1auXekgFauLEiaq1krSOql69Ov73v//Z1YJr/fr1uHv3rvbc4sWL4enpiXbt2iX7OUn8Lt0V5bPG1q1bh2zZsqUa2HJndUrks73VlXF3wbNrgSjT/GLFchRTD0OitoM3D6ZjiYmIiMhgxIgR6iah1K3kBuH8+fNVa3cZPbBq1aqqrkNERGSPw+GH8evJX7V5aV1TKncpLkxySnYFrvbu3asCRZJzwd/fXz0nlap9+/Zh4MCB6k6grfr374+cOXOiW7duKsH6Tz/9pPJUyfNFi+oTghu6AJYtW9bksxMmTMCyZcswdOhQVYmTQNrUqVNVV8CsPrqOeaurVEcYLFITyP/fZxLjgON/pji64N4b7C5IRESUEWbPnq1uBv71118oWFA/6MqTTz6Jo0ePokmTJmqaiIjIVjEJMaqLYKJOny+6av6qeKXyK1yQ5F6BK6kwyR1Acz4+Ppg8ebLKxWAryVUliUa9vb1V8EoSvstIgZJA3VhCQoI2so5B586d8fvvv6tgWqdOnVRFb+zYsRg/fjyyOvNWV6mOMOjhAVR/LsXuggxcERERZbwjR45YHDlQ6kwLFixQLbCIiIhs9f3h73Eh8oKa9vH0wfgm4+Ht6c0FSU7Lrq1TWkalpFGjRnYVRhK8m3f5M7d582aLz0veB3nQ44a2KY9tZ29pra6OhN5F9eJ5kl9Ukudq06f66ZBdwJ2LQL6kZqP1CiW1uDpx+wQexD5ADt8cXPRERETpKDg4OMXXWe8hIiJbyfXbj8d+1OYlj1HZvKY9moicDTOvZQEywmCz8vouBmL6+rMpf0CCVEENk+aPLjF5uUiOIiieo7iW5+rAzQPpXGIiIiIiIiJK7y6Co/8dra7hRKV8lfBa1de4kMnpMXCVBXNdbTilb3VldZL2o4sAnS7Z7oL7buxLx5ISERERERFRRowieO7uOTUtXQNlFEHpKkjk7Bi4yiJqB+dFc6NWV1+l1uqqytOAoZ/zrTPA9UMmLzPPFRERERERkWvYH7Yfc4/P1eYH1BiAivkqOrRMRNZi4CoLGWLU6mrjqZs4HJJCq6vs+YCybZPmjyxONnB14s4J3I+9n86lJSIiIiIiorR6GPdQdRHUQd+LpnqB6uhTtQ8XLLkMBq6ycKur6RtSaXVVvUfS9LE/gER9X2hROKAwgnIGqWkZRvXgzYMZUGIiIiIiIiJKi6n7puLqg6tq2t/LHxOemMBRBClrB6769OmD0aNH4/r16+n91ZTOua6k1dWhlFpdle8A+P43guSDG8DFrSYv1y9cX5vec30P1w8REVEmGTduHObMmYPo6GgucyIiStbW0K1YciZpsK136ryDkrlLcolR1g5czZ07F5MmTULp0qXRv3//9P56SqNawXnRooLxCINnkn+zb3agUuek+SOLTF6uW7iuNr03bC/XDRERUSYZM2YM3nzzTZQoUQJTpkzhciciosfcjb6LT3Z8os03KNIAz1d8nkuKXE66B64SExPx4MEDrFixAsWKFUvvr6d0MKR1UqurTafDU251Zdxd8ORyIO6RNluvUFKeq1N3TuFe7D2uHyIiokxw8eJFHDt2DBMnTsSZMynchCIioixJp9Nh7M6xuPXolprP4ZMDnzb5FJ4ezBZErue/YePSV/bs2dG6dWv1IOdtdbX5dLia/2r9Gcx9Lanbn4lSzYEchYAHYYAkYD+9GqjaXb1UKKAQSuQqgcv3LuvzXIUdRPOg5pn5U4iIiLIkaWklKleujNdff93RxSFymgv1uzF31YV6dHw04nXx6vkAnwDk9MmJAtkKwMfLx9HFJMoUf5z9A+uvrNfm32/wvspTTJRlAldxcXHqTt+dO3fUfL58+VTXQG/vDImDUQYY2qa8FriSfw9eiVABrcd4egFVnwF2zdTPH12sBa5E3UJ1VeBK7Avbx8AVERFROoqJiUFERISazps3L/z8/Lh8iQAkJCbgVMQp7L2+V41wfTbirKqTxiXGJbt8pKVJYPZABOcMRqV8lVA5f2XULlSbF/Pkdi5EXsCUPUndyDuU7IDOpY1SwBC5GJsiTXv27FHJQDds2IDY2Fh1V8PDw0O95uvrizZt2uCjjz5C/frJtN4hp1EzKA9aViiougoaRhhMttVV9Z5Jgauz64CoO0D2fGq2TqE6Kpov9t5gnisiIqK0unTpEqZOnYpVq1bhypUrqr4lpM4VHByMp556Cu+++y5KlmRyXcpa4hPjsfv6bqy6uApbQrcgMibSps9LD4EbD2+ox54bSQMLlcxVEk2KNUHr4NaoHVgbXnLjlshFxSbEYtTWUYhO0A/eUTSgKD5s9KF23U7k1oGrlStX4umnn0a9evXw2WefoVKlSurOn5A7gSdPnsSiRYvQtGlT/PXXX+jQoUNGlpvSwZA25bXAlbS6OnAlArUttboqUhPIXw64fRaQu1jH/wTq6bsl1CuclOfq5J2TeBD7ADl8c3D9EBER2WH37t1o166das3evXv3x+pbp06dwtKlS/Hrr79i7dq1vFlIWYJ0/Vt8ejEWnVmk5etJqVVVPv98qnugj6ePClY9jHuocrE+ik/K1Wrs0r1L6jHv5Dzk98+PjqU7onvZ7iibt2wG/SKijPP1ga/VdZlhf5jUdBJy+ebiIieX5qEz3MZLRc2aNdG4cWPMnPlfy5tkDBgwADt37sShQ4fgakJDQxEUFISQkBAUL14cWcFrP+3RglfNyxfEz32SaXW15TNg0wT9dHAjoM8/2ksd/uiA0Aehanpm65loWrxpJpSciIjI/eoRUtcqUqQIFixYAB8fy7l44uPj8fzzz+PatWvYsWNHGkttv6xYb6LMFR4Vju+PfI+lZ5da7AKY3Tu7GuVaWklVzFcRZfKUQcFsBS22mJJLHglehd4Pxdm7Z3Hy9kkcCj+k/tXB8uVQjYI18HLll9EmuA28PZkShZzfjqs78Ob6N7X5ATUGYGDNgQ4tE1F61COsPgKfPn0a06dPT/V9UpGaO3eutV9LTtTqasuZFFpdVXs2KXB1ZSdw9wqQJ1jNSoUh9FyolueKgSsiIiL7yI2/CRMmJBu0EpJTdNCgQarLIJE7ioqLwuwjs1ULKEN3JwNJst62ZFt0KNVBpayQVlXWkG5Suf1yq0eVAlXQrWw39bx0N9x1fRc2XNmAraFbVessg8Phh3F4y2GVA+uNqm+ge7nuTO5OTuv2o9sYvX20Nl+zYE30q97PoWUiSi9Wj4UpORU2bdqU6vvkPfJecp1cV60qBmrzX65LZkjtfKWB4kndAlWSdqME7Qb7buzLoJISERG5v4IFC+Lo0aOpvk/eI+8lcifSKmr95fXo8lcX/HDsB5OgVancpfBRw4+wvsd6jG08Fg2LNLQ6aJUSCWS1L9kenzX7DFue24LPm3+OxkUbwwNJ+YAkJ9anuz9Fpz874c+zf6pcW0TONljBqG2jtK60OXxyYHKzyWwpSG7D6hZXI0aMQL9+/XD+/Hn06NEDFStWRJ48edRrkZGRKufC4sWLMX/+fMyZMycjy0zpbGibcth46qaa3nb2FnZduI2GpfM//sbqzwGh/yVgP7IIeGKY3L5SLa4Mjt8+ru6SZffJzvVERERkI0m5MHLkSISHh2v1LRkAR8jAONICXupbkrz9k08+4fIlt3E3+i7G7RqHdZfXmTxfIlcJDKo5SAWXJF9PRvLz8sOTJZ9Uj5B7IZh/aj7+PPen1grr2sNr+HjHx/jf0f9hQM0B6FiqY4aXicgas4/OVi0HDT5p9AmK5SjGhUdZL3D1+uuvIyAgAGPGjMG8efMeG5VA7pCUL18ev/32m+ouSK6jevE8aFu5ENadCFPz09aewcI3Gz4+8kSVp4HVIwFdAhB+CrhxFChSXR0UZbQKOZkn6BJw6OYhNC7W2DE/hoiIyIWNGjVK/Tt58mRMnDhRTfv5+al/Y2Ji1L85c+ZUQSsJcBG5gx3XduDDfz9E+CN9+gpDi5G3ar2F5yo855BWI0G5gjCy/kj0r9Efv5z4Bb+d+A1R8VHqtSv3r+D9be/j91O/Y3SD0aicv3Kml4/IQAJW3x36TpuXfebJUk9yAVHWTM5u7OLFi6qFlYxuI2S0G7kjWKpUKbiyrJxk9NSNe+gwfRsMW8MvfeqjWXkLXRDm9QDOrtVPN34baPepmhz972gsO79MTfet1heDaw/OvMITERG5WT1CglSSeN1SfUsSuBuCWY6UletNlD5kxL85R+ZgxqEZJgnS25Zoi/frv4+C2Z2nO2xEdAR+OvaTClYZd2GULoU9yvdQdV/pdkiU2QMYPLv8WdyJvqPmK+WrhF87/qpaDxJlyeTsxiRA5epBKjJVsXAudKpeFMsPX1PzX6w9jablCjze6qpaz6TA1dE/gDZjAU8vlefKELjae+O/7oRERERkFwlMtWzZUj0y0oMHD1Qw7OrVq9i7dy/q1k3q/k+Uodte7AO8/+/72Byy2aSV1QcNPkCn0p0er4M6WF7/vBhWdxh6VemFWYdnYdHpRSrYJv8tOrMIay+vxdDaQ1UCd2crO7knybU2YusILWgl+88Xzb9g0IrcEjtlk0muK8//zrOHQyO1roMmKnYEfAL00/evAZe3P5ag/djtY3gU/4hLloiIyMmNHz8e8fFMNE2ZK+xhGF7951WToJW0FFnSZQk6l+ns1IGfAtkK4MOGH2JBpwWoUbCG9vzdmLsYs3MM+q7ti6sPrjq0jJQ1zDw0U43objC+yXjVxZXIHdkduEpISICXlxcOHjyoTR84cCB9S0eZqkzBHOheO6mJ3rR1Z5CYaNaT1DcAqNQpaf7IQvVP8ZzFUSh7IS36L8MHExERUdokJiaidOnSOH78uMl0epBuiDNmzMDYsWO5mijTnIk4g5dWvaT+Nehapit+6fCLSyWTlrxWUmYJFuTzz6c9v/vGbnT/u7u+RZbtGVmIrCJB3zlHkwZEe7nSy2hTog2XHrmtNLW4koOx4YDMA7N7GNK6HHy89He5Tt24j5VHrz/+JukuaHBiGRAXre6MGY8uuO9GUvSfiIiI7CP1q0uXLqmcV8bT6eHtt99G//79UaFCBa4eyhTHbh1D7396IywqqVX/8LrDVfDH39vf5daCjCjYrWw3LH96OZ4p94z2vCRxH79rPFtfUYa4EHlBDQ5gUK1ANQyrM4xLm9wauwqSiaB82fFcvaQmpl+uP4P4hETTN5VuAQT8lywz5h5wds1j3QWZ54qIiMh5LVmyBEePHsXHH3/s6KJQFnEg7ADeWPsG7sfeV/O+nr4qH8+rVV516q6B1sjlmwtjGo/B922+R+GAwiatr55Z9gxWXFjh0PKR+5D9Z8jGIXgQ90DNS2u/aS2mwcfLx9FFI8pQDFzRY95qWQ6+3vpN40L4Q/x1SJ+wXePlDVTpnjR/ZJH6p17hetpTR28dRXR80ogrRERE5ByioqIwbNgwTJw4Ebly5bL6c/fu3VMjABke169baJVNlEzQqv/6/ngY91DNZ/fOjlltZ6FdyXZutbwaF2uMpV2WmrS+kt8srWM+2PaBSkhPlJZROGU7unTvkpr39vBWwV/jYCmRu2Lgih5TOLc/XmlYQpv/av0ZxMabtbqq/lzStIwy+CgCwTmDUTCbviVWXGKcCl4RERGRc/n0009RqFAhvPbaazZ9btq0aWrYasOjfv36GVZGch/Hbx3HwA0DtYF7cvrkxOx2s01ueLqTnL45VeurWW1mafVisfzCcvRY3gNHwo84tHzkumQ0y82hSQMavFfvPZNULUTujIErsmhAizLI7uulpkMjHmHRvhDTNxSrDeQrrZ9OiAVO/K3Pc2XUXZB5roiIiJzL5cuX8cUXX6iE7JGRkbh79y4ePNC3ApF/DdOWSCutkJAQ7bFnz55MLDm5orMRZ/Hm+je1llYStJrTfo7JaHzuqkmxJvijyx9oEdRCey70QSheXf0q/nf0f6r1DJG1Nl7ZiO8Of6fNS261Fyq+wAVIWQYDV2RRgRx+eK1JSW3+m41nER2XkPQGyUVgnKT9yGL1j3HUf2/YXi5dIiIiJ3Lx4kXExsbiqaeeQt68edWjc+fO6rWWLVuiTZvkR6WSboXFixfXHkWKFMnEkpOrufHwBvqv64/ImEg1n807G2a2mYkq+asgq8jrnxdft/waHzb4EH5efuq5eF08ph+Yjrc2vKUtG6KUnL5z+rFk7B82/NDlc8MR2YKBK0pWv6ZlkNPfW02H3YvBvN1XTN9Q3ShwdflfIDLUJHAlTaFjpTUWEREROYWaNWti06ZNJo8vv/xSvTZr1izMnDnT0UUkN3Av9h4GrB+Am49uaonYv2n1DWoG1kRWI8GF5yo+hwVPLUC5vOW057dd3Yaey3viaDhTa1DywqPCMWjDIDVSpXEydkMglCirYOCKkpU7uw/6Nv2vOyCAGZvO4X50XNIb8pcBitZOmj+6BKVylUJ+//xqNiYhhnmuiIiInEiePHnQokULk4cEs0SdOnVQu7bReZ3IDnEJcXhn0zs4d/ecmveAB6Y0m4IGRRpk6eVZNm9ZzO843yRx+7WH19Drn16Yf3I+dDqdQ8tHzicqLgpvbXwLYVFhWgB4esvpTMZOWZLdgStPT0988sknKFq0qMk0uZc+T5RCvgBfNX3nYSzmbLuYfJL2I4vUXaU6hepoTzHPFRERkf2kjvXqq6+iQIECJtNEzkiCLxP3TMSeG0n5z0bWH4k2JZLvgpqV+Hv7q8Ttnzb5FP5e/uq5+MR4TNozCe9tfU/LBUYkOdCke+CJ2ye0hTHhiQlZstUiUZoCVxKgkGBV4cKFTabJveTw88bbrcpq8//bdgE370cnvaFqd8BDn8QdN48DYceZ54qIiCidSB3rp59+QnBwsMl0epJWVxJwqFuXo1NR2iw4vQBLzizR5ntV7oWXKr3ExWqma9mumPfUPJTMlZRPds2lNXh+xfM4E3GGy4vw5f4vsTFko7Yk3q71Np4s9SSXDGVZ7CpIqXqxQTCC8mVT01GxCfhmg77pt5IjECjdwqTVVb1CScMbH755WDUZJyIiIiL3tfv6bkzZM0Wbb1qsKYbVGebQMjmz8nnLY0GnBWhfsr323KV7l/DSypew/Pxyh5aNHGvR6UWYe3yuNt+lTBf0rdbXoWUicjR95m0rjBs3zqYv/vjjj+0pDzkhP28vDG9XAUMWHFLzv++5oroQlioQkJSk/fwG/fTRJSjT6mPk9cuLiJgIRCdE4/jt42zWSkREZIVffvnFpuXUq1cvLldyuLCHYRixdQQSdPoRqEvnLq3yWnl5/tcqnywK8AnA580+R+3A2vh83+eq26DUnT/49wMcDj+MEfVGwNdLn7KDsob1l9djwu4J2nzdQnUxptEYjiBIWZ7VgSvDiDMGMpTyo0eP1LS/vz+io/Xdx7JlywY/Pz8GrtxM5+pF8f2WCzhx/R7iE3WYuvY0Zrz4XwLXip0An+xAXBRwLxQeIbtUnqv1V9arl/fe2MvAFRERkRV69+5tMm8Y7tw4cbPxEOgMXJGjScv6d7e8izvRd9R8Tp+c+LrV18jpm9PRRXMJsj+/WOlFVCtQDcO2DMONhzfU8wtPL8TJ2yfxRYsvmIw7i9hzfY8KAEt+KyFdSb9q+RV8vHwcXTQi1+kqGBERoT3WrVuHQoUK4YcffkBkZCSioqLUv//73//U82vWrMnYUlOm8/T0wKgOFbX5lUeu43DIXf2MXw6gQsekNx9ZYJLnal/YvkwtKxERkasyrm/t3bsXJUqUwIcffojDhw/jxo0b6t/Ro0er53fv3u3o4hJh2v5pqnWQcQLpErlKcMnYqFrBaljUaREaFWmkPXfk1hH0XN4TO6/t5PJ0c5KEffCmwYhL1KdYCcwWiO/bfo/cfrkdXTQi181x9dZbb+G9997Da6+9hpw59XdT5N8+ffrg3XffxaBBg9K7nOQEmpYrgCZl82vzk1afTLoDbDy64PG/UTd/NW324M2D2kGYiIiIkpc7d27tMWrUKPTr1w9jx45FtWrVEBgYqP6V9A19+/bFyJEjuSjJobaEbMFvJ3/T5l+v+jpaBrd0aJlcWV7/vPiuzXfoV72f9pyk3ui/vj/mHJmjtcQh93Ip8hIGrB+gjSqZyzeXCloVzVHU0UUjcu3AldztK1WqlMXXypQpg2PHjqW1XOSkTZlHPVlJm9914Q62nAnXz5RpBQQU1E/HRKJc2BntDsGj+EeqqTMRERFZb8eOHahTp47F1+T5Xbt2cXGSw9x6dAsf70jKaVuvcD28VestrpE0krxgMoLct62+1bpbSsDq64NfY8jGIbgXe4/L2M3yw7257k2tq20272yY0XoGyuZNGtWdiOwMXJUsWRKzZs0yybcgZH7mzJmq+Tq5p2rFc6NzjaTo/+TVp5CYqAO8vIFqPbXnPY8sUokmDSTPFREREVlPWlgtXLjQ4msLFixAwYL/3TAiymRS5/9o+0faxba0EJn4xER4e1qdPpdS0TyoORZ2WoiK+ZJSdWwO3YznVzyP03dOc/m5SfD3jbVv4NrDa2re28Mb01pMY25govQKXE2ePBkrV65EuXLl8M4772DSpEnqX5lfvXq1ep3c1/B25eHtqU8Me+rGffx9+Kr+hZovJL3p3HrUzZt0omWeKyIiItt88MEH+PHHH9GyZUtMnz4dv//+u/q3RYsWmDt3rsp1ReQIv5/6Hf9e/Veb/6TRJ0wgngGCcgbh1w6/omuZrtpzIfdD8NKql7Ds/LKM+JOUiUGrPmv64NK9S9pznz7xKZ4o9gTXAZEFdt0W6dq1q0oYKgGqv//+G9evX0eRIkVQv359LFmyBDVr1rTna8lFlMgfgJcaBOPnnZfV/NQ1Z9CxWhH4Fa4GFKoKhB0DdAmodzfcJM+VDPHLO3FERETWkTxWUr+aMGGCyi0aHx8Pb29v1K5dW9W/OnfuzEVJme5cxDl8se8Lbb5b2W5oV7Id10QG8ff2x/gm41UrnIm7J6q8sTEJMRj972gcvnkYI+uPhK+XL5e/q7W0WvMGLkZeNAn+PlX6KYeWi8jtWlwJCU5JM/ULFy7g0aNH6l+ZtxS02rp1Kx4+1CebI/fwdutyCPD1UtNX7z7Cb7uu6F+o8bz2nvKn16ohkYUkG2SzZiIiItt06tQJO3fuRHR0tLpRKP9KbitLQasrV66o4BZRRpGAychtIxGbGKu1CBpVfxQXeCbkmX22/LOq9VWRgCLa84vOLELvf3rj+oPrXAcu4vaj2+i7ti/OR57Xnvu40cdq/RJRBgSurJWQkKCauJ8+zb7Y7qRADj/0bVZam/9241lEPooDqvUAPPSbldeNY6idp5z2Hua5IiIiso+npycKFSqk/k2uviUD5xw5coSLmDLM1we+xpmIM2ray8MLk5tORoBPAJd4JqlSoAoWdVqEJkWbaM8dvXUUPVf0xI5rO7geXCBoJTmtzt09pz33UcOP0KN8D4eWi8gVZHjgSpgncSf38EbT0iiQQ980OSIqDjM2nQNyFtaPMPifutEx2jTzXBEREWUc1rcoIx26eQi/nvhVmx9QYwCqF6zOhZ7J8vjnUaPO9a/RX3vubsxd9F/XH7OPzFYjEJLzufbgmmodZxy0Gt1gNHpWSBrciogcHLgi95TDzxvvtC2vzf+0/SIu334I1EhK0l7vykFt+kDYASQkJmR6OYmIiIjIfrEJsfhkxyfQQX8zWgJWr1d7nYvUQbw8vTCo5iAVwJIRHYWsm28OfoPBGwcjMiaS68aJnL97Hq+sfsUkEfv79d/H8xWTUqwQUcoYuKI0ea5uEMoXyqGm4xJ0mLTqFFDxKcBPfxKtcPcGArz81PT9uPta83IiIiIicg1zjs7BhcgLatrH0wfjGo/jgDtOoFnxZljYaSEq5aukPbcldAueW/EcjoSz27AzkPXw6j+v4mbUTTXv6eGJsY3H4sVKLzq6aEQuhYErShNvL098+FRlbf6f4zewKyQKqNxVG7ayFvy115nnioiIiMh1yOA6/zvyP22+X/V+KJOnjEPLREmK5yyOXzr8gqfLPq09d/XBVby6+lX87+j/2NvBgSTvmOS0MrSAk6DvF82/QPdy3R1ZLCKXxMAVpVmz8gXRskJBbf7TlSeQWD2p6Wvd21e1aea5IiIiInINkuJhzI4xiNfpR6ssm6csXq/KLoLOxt/bH+OajMOYRmPg919PB1ln0w9MR791/RD2MMzRRcxy/j73NwZtGIRH8Y/UfHbv7PiuzXdoU6KNo4tG5JIYuKJ0MfqpSvDy9FDTx67ew9LbwUCeYDVfL+qB9r4DNw8waSQRERGRC/jt5G84dvuY1sVJugj6ePk4uliUjGfKP4MFTy1AubxJo3rvubEHzyx/BhuvbORyy6Rg77T90/Dh9g8Rn6gP+Ob1y4sf2/+IBkUacB0QOWvgSoZtfvXVV1GgQIGM/lPkQGUDc+KlBvpAlfh87RnEVX1OTVeKiUU2nT6oJU1lz0acdVg5iYiI3JGHhweaN2+OnDlzOroo5CZC7oXg24PfavOvVHoF1QpWc2iZKHVl85bF/I7z8ULFpMGSpP49ZNMQfLrrU0THR3MxZpCHcQ8xdPNQ/HTsJ+25YjmKYW6HuahSoAqXO1FmB65Gjx6N+Hh9BNncrVu38Mwzz5hUpH766ScEBycFNcg9DW1THjn9JasVEHYvBj8/aqKm5b5crUdR2vvYXZCIiCh1c+bMSfa12NhYDBs2zORG4aZNm1CuXFJLCyJ76XQ6jN81HtEJ+iBH8RzFMajWIC5QF+o6+EGDD/B1y6+Rxy+P9vzC0wvxwsoXcPL2SYeWzx1de3ANvVb3wuaQzdpztQNr4/enfkfp3KUdWjaiLBu4+vrrr9GgQQOcOHHC5Plly5ahSpUqOHDgQHqVj1xIvgBfDGmdVGGeuica0cX1wau60THa8/tu7HNI+YiIiFzJgAED0LlzZ9y8qR+NykDqWbVq1VI3BokywrrL67Dz+k5t/pPGnyCbdzYubBfTMrgllnReggaFk7qonbt7Di+ufBEzDs1AXEKcQ8vnLnZc3aECgsajp0uy/P+1+x/y+ud1aNmIsnTg6tChQ/D390fdunXxxRdfIDIyEr1790a3bt3QsWNHHDli3/Crp06dQtu2bREQEIDChQtjxIgR6o6iLb766ivVyqtTp052lYHSplejkiiZP7uajo5LxO9xzdR0veikZsn7w/arO3lERESUvC1btuDkyZPqpuAff/yBxMREjBkzBg0bNlT1JHvrW0QpiYqLwmd7P9PmO5XuhIZFGnKhuahCAYXwfdvvMbT2UHh7eGuJ22cdnqWCLafunHJ0EV2W5LD6+sDX6L++P+5E31HPecADw+sOx9jGY5kPjsjRgasyZcpg27Zt+Oijj1S3wSJFimDNmjX466+/1N0/e/IrREREoFWrVipQtXTpUkycOBGzZ882aQafmhs3bmDs2LEIDAy0+e9T+vD19sQnnZP6cE+5XB7xPjlQJSYW/omJ6rmImAicv3uei5yIiCgFTZo0UcGp7t27o2fPnihRogSmTp2qHhs2bEBQUBCXH6W77498j7Ao/Sh0OXxy4N2673IpuzgvTy+8Xu11zH9qPsrnLa89fzriNF5Y8QJmHpqJ2ATbGgtkdTce3sDra17HnKNzoIP+hnxO35z4ptU3eLXKq6ohBRE5QXJ2yXEl+azi4uJUXgUfHx9kz65vaWOPWbNm4d69e/jzzz/Rvn179OnTB5999pl6/tq1a1Z9h7TQ6tKlCypVqmR3OSjtWlYMROuK+uBhNPzwD5qoPFc1YpJOiHvD9nJRExERpULqVlWrVlX1rKtXr6rgVevWrbncKENcuHsBvxz/RZsfVHMQCmTjAEvuolL+SmrUwTervwkvDy+t9dV3h7/DM8uewe7rux1dRJewNXQreizvoUZLN6hWoBoWd16M5kHNHVo2IndlV+Dq8OHDqFOnDn788Uf1CAkJQePGjVXA6a233sKjR49s/s7Vq1ejTZs2yJcvn/ac3F2UZvFr165N9fP//vuvavE1efJkm/82pb+PO1eGr5d+8/rfA0Oeq6TugsxzRURElDK5cSd1q+HDh+P9999X3Qbz5s2rUjVIqyui9CRpHCbumagCGaJc3nJ4vuLzXMhuxsfLB2/Veku1vpJ1bHDp3iW8sfYNjNw6Erce3XJoGZ2VjM744b8fYtCGQbgbc1d7vlflXvj5yZ/VCIJE5ESBq/r166NgwYIqgPXqq6+qStSCBQswb9489W/NmjXtym9VsWJFk+fy5MmjuiHKaylJSEhQATNDt0VyvBL5A9CvmX4EjUO6MjinK456j4wStIftY54rIiKiFEhLq9DQUGzfvh2ffPIJKlSooFI1yPSHH36I5s15Z5/Sz5rLa0xa3IxuMBrenvqcSOR+KuevjIVPLcRbNd+Cn5ef9vyqi6vQ5c8umHdyHuISmbzdYOOVjej2dzf8ff5v7blcvrlU18D36r3HfFZEzhi4ki58GzduRHBwsMnzzz//vMrFIDmw7MlxJYEqcxIUu3NHn+wuOTNnzsTDhw/xzjvv2PQ3pWuiVAgNj+vXr9tcbkrewJZlUDS3v0pTuDC+GarFxMDvvzxXksDwYuRFLj4iIqJkyM3B/fv3qxZWBpI3ZdSoUdizZ48aHIcovRKyf773c22+S5kuqFOoDhduFmh99WaNN/Fnlz/RpJi+h4S4H3cfk/dMRve/u6uATVYeVEmuWUZsGYEhm4aYtERrXLSxGrGxRVALh5aPKKuwK3A1ZMiQZF8rWrQoVq1ahcwiQ0R//PHHmDZtGnx9fW36rHxGEpsaHtKSjNJPdl9vjH6qspr+M6EpPHWeJnmu9tzYw8VNRESUjC+//FKN4mxJ9erVsXcv80VS+ph9ZDZuRt3UErK/U8e2m8Hk2oJyBeG71t/hi+ZfIDBboEn3QQnY9P6nN46GH0VWIsnq5x6bi05LO2H1pdXa85KAfVzjcZjVZhaK5GBPHyKnT86e3qRllaU7h9ISyzjvlTkJWknlrWnTprh79656SOJ4eRimkyMjFkp+LsND7l5S+upYrTAal8mPW8iNjYm1UN8ozxUDV0RERPaThO1EaRV6PxS/nEhKyC75j5iQPeuR1pztSrbD393+xhvV3jDpPihJyF9c9SKGbR6GU3dSTuHi6qR12brL69D1r674Yv8XqvWZgbSu+qvrX3i63NMcNZAokzlNx3XJb2Wey0oCWdJ9zzz3lTH5zNatW1Xgy5w8J0nfn3zySYufzZUrl3pQxp4Ex3apgg7Tt2FxQnMMenQU3/63qvZc34NEXSI8PZwmfkpERESUpUzbP03LZVQmdxk8V+E5RxeJHCiHbw4MqT1EbQffHPwGy84v016TgI48WhRvgX7V+6FawWputa4OhB3A1we/xv6w/SbPB2YPxPC6w/FkyScZsCJyEKeJGHTo0AHr169XraQMFi9eDE9PT7Rr1y7Zz3311VfYtGmTyaNGjRpo2LChmmb3P8crVygnXm9aCpsSa6JQtD+y/5fnKjI2EqfvnHZ08YiIiLIUSekgid1loB0/Pz+ULl1atUJnzqysRy7QJRBhMLzecCZkJ6VwQGFMeGICFnZaiAaFG5gslc2hm1ULrH5r+2H71e3qRrQrt7DaGroVvVb3wqv/vGoStMrmnQ0Daw7EiqdXoEOpDgxaETmQ07S46t+/P7755ht069YNH3zwAa5evYr33ntPPS95swxat26Ny5cv49y5c2re0giGkuQ9R44caNGCyfKcxZDW5bDi8HX8/aAZ6kTvxrbs2dTzMnpNpfyVHF08IiKiLEMGvWnQoAEGDx6M/Pnz49ixYxgzZoz6d+3atY4uHmUSCTZ8tvczbV6Scz9R7Akuf3ps9ME57eaoEcElF9qu67u013Ze36keQTmD0LN8T3Qr2w15/B8fbMsZxSXEqaDtD8d+wJmIM4+9LgMUDK41GIUCCjmkfETkpIEr6da3YcMGvP322yp4lTNnTrzxxhuYMGGCyfsSEhJSzFtFzpuofXy3Khj7cyv0ebQlKXB1ZSN6V+3t6OIRERFlGS+//LLJvNzok5ZX/fr1w7Vr10xuGJL7Wn5+OU7cPqGmvTy88F7d9xxdJHLi1B/1CtdTj8PhhzHnyBxsCd2ivR5yP0Tlg5KuhU+WehJPlXoK9YrUg4+n8+Xhk94ef537CysvrERETITJax7wQJsSbdC3Wl/eWCdyMk4TuBKVKlVS3QVTsnnz5lS/x5r3UOZrVbEQFlepCd+LxYD8Ueq5/eFH1B0PGY6XiIiIHENaXonY2KTRf8l9RcVFYfqB6dp8j/I9UCZPGYeWiVxDjYI18G3rb3Hy9knMPzUfqy+uRkxCjHotNjFW5cSSRx6/PGgd3BrtSrRzeBBLAmvSHVDKZQjWGvP28EanMp3wWtXXUDp3aYeUkYjSKXDVp08fpMWPP/6Yps+Te/ikcxV8Nq098iQswV0vLzxCAo6FHUCtoqZ954mIiLKicePGpenzMtqytaQVe1xcHE6cOKH+bpcuXVCyZMk0/X1yDT8e+xHhj8LVdE7fnCqPD5EtJNXH+CbjVdJyacG0+MxiXL53WXv9bsxd/HH2D/WQbaxuobqoX7i+arVVLm+5DB2cSQJpkmh929Vt2Ba6DZfuXbL4vtx+uVWXwF6Ve6mcXkTkBoErSVxHlFaFc/ujRpuXEXtkIbbk8FLPrd37A2p1ZeCKiIhIBpZJS3ceWwJXJUqUUDlFhYzAPH/+/BTff+/ePfUwkJGfyfXceHgDc4/P1eb7V++PvP6Pj85NZA0J/rxa5VW8UvkVlbt21cVV2HBlA+7H3tfeI9ObQjaph+Ez1QtUR9k8ZVVLP3lIS6fsPtltztMmAbIr967g5J2TqhWY/Hsu4hzidZZTy0jArHHRxni67NNoEdQCvl6+XNFE7hS4+umnnzK2JJRlvNykHE4eLAdAf1dm/409iE9IhLeX0wxySURE5HKBK3tGF3z48CGOHz+OTz/9FJ07d8a6devg5aW/sWRu2rRpGDt2bKaVjzLGtwe/1bp2lchVAi9UfIGLmtJMAkKNijZSj48bfqySuK+9vBYbr2zEvdikgLeIjInUt4a6us3keeleqD389f/K9yYkJqggVYIuAbEJsaq1YHhUOG4+uon4xNRzH8t31CxYE82KN0On0p2YcJ3IBXno2JRKExoaiqCgIISEhKB48eKOXC9ub9P+fzD4mD4JqI9Oh3cKTMErnZ5ydLGIiIiyZD3i8OHDaqTmxYsX49lnn7W6xVX9+vVd8vdmVdIS5Znlz6gggPiqxVdoXaK1o4tFbkwCS9ISas+NPdgbtld14XsU/yjD/26BbAVUy6qmxZqqYJq08iIi1603OVVydso6WtRujwKHR+KWVyLiPDxw/uh3OFe/OcoG5nB00YiIiLKc6tWrw8fHB+fOnUv2Pbly5VIPcl0y6pshaCVdtVoFt3J0kcjNeXt6o1rBaurxerXXEZcYh1O3T+F0xGmcv3te/4g8j5tRN+36fhkRMzB7ICrkraDyblXOXxmV8lVSz0n3aSJyDwxckUPIiaRBwWpYeeewmvfPfhIfLt6DeQNawsuTJxkiIqLMtHv3bpWovXRpjqjlrg6HH8bGkI3a/NA6Q3lhT5lORhc0BLKMPYh9gNvRtxERHaG6EkbE6P81dPWThwSpJBCW3z8/AgMCUSh7IeT1ywsvT8vdm4nIfTBwRQ7TuEJ3rNypD1wdzuaFopfW4OcdpdDniVJcK0RERBmke/fuqFu3rmpllS1bNtVN8PPPP1fz3bp143J3Q5IZ5Kv9X2nzTYo1UaO7ETmLHL451EPyrhERmWPgihymfrHG2vQJX1/0992AN9e0QOtKgSiRP4BrhoiIKCPOv/XrY+HChZg8eTISExNRsmRJ9O3bF8OHD4evL0fYckc7ru3AvrB92vyQWkMcWh4iIiJb2DWM29atW/HgwQOLr8nz8jpRagoHFEbJgKJqOtHDAwnZQ1Ey/hJG/XEUiYk6LkAiIsrSrly5orrvWRIfH69et8eoUaNw8OBBlWhd6m3Hjh3DuHHjmL/KTUlOq+kHpmvzHUp2ULmAiIiI3Dpw1bJlS5w4ccLia6dPn1avE1mjfrEntOnd/v7o5bUGOy/cxrzdl7kAiYgoSytVqpQKMFki3fvkdaLUrL20FifvnFTT3h7eeKvWW1xoRETk/oEr6SefnIcPH6p8CUTWaFCkgTa9J5sfnvbajtx4gAmrTuJCuOVWfURERFlBSvWtmJgY+Pn5ZWp5yPXICG4ykqBB93LdEZwr2KFlIiIiyrAcV7t27cKOHTu0+fnz5+Pff/81eU90dDT+/vtvVKrE5sdkHePEoOd8ffHAOx7PxW/C7LjOeGfhISwZ0Bg+XnbFV4mIiFzOqVOnTFq1b968GaGhoY/Vt37//XeOAEip+vPsn7hyX9+l1N/LH2/WeJNLjYiI3DdwtWbNGowdO1ZNe3h44Ouvv37sPT4+PipoNXPmzPQtJbmtvP55USlfJa0J+85s2fBK/Hr8L+EpHA6NxLcbz+GdtuUdXUwiIqJMIUnTjetbko/Kkjx58mDu3LlcK5SsR/GPMOvwLG3+pUovITB7IJcYERG5HKubsnzyySdq5Bl5SNN1aYFlmDc8pNn6oUOH0Lhx0mhxRKlpXDRpe9mezR9BHuFo7XlAzX+76RwOXongQiQioixh6NChuHjxIi5cuKDqW0uXLlXzxo+rV6/i9u3b6NKli6OLS05s/sn5CH8UrqZz+ubEa1Vfc3SRiIiIMrbFlTEJUhGllybFmuCHYz+o6Z3Z/CFb18DsG7DuQV0kJOowbNFhrBz8BLL72rW5EhERuYzcuXOrh5AgVdGiRVWLdiJbRMZEanUr8XrV15HbT79dERERuW2Lq+RGEUyJDOEsdwyJUlKzYE1k986upiO8vHDS1xe14g+jkvc19dzFWw8xcZW+KyEREZE7k5ZUBiVKlLA6aHXnzp0MLBW5mh+P/Yj7sffVdMFsBfFipRcdXSQiIqKMD1w1bNgQXbt2xbJlyxAbG5vie8+fP49PP/1UDdP8119/2V86yhJ8vHxQv3B9k+6C4osSu7Xnftt1BetPhDmkfERERJlF6k7SXfDIkSOpvldGcv7tt99Qr149fPfdd5lSPnJ+YQ/DMO/kPG2+f43+yObNEb+JiMh1Wd336ty5c5gwYQJeeukllSy0du3aqF69OgoWLKiGY757965q0r5//34VuJLXJUk78y+QNRoXa4zNoZvV9Pbs/ugXeQ+Vbq5C61IvYMPFaPX88CWHsWpwUxTNw8oXERG5p+3bt+Ojjz5CrVq1UKZMGZU3NLn6lrxXkrSPHDkS/fv3d3TRyUl8f+R7xCTEqOngnMF4utzTji4SERFR5gSuAgMDMX36dEycOBGLFy/Ghg0bsHbtWly/fl0Ny5wvXz5UqFABPXr0wLPPPqsqXETWeqLoE9r0ET8/PPDwQI64h5hW/hhahFVCRFQc7kbFYfDvB7GgX0N4e1ndWJCIiMhlVKtWTbVWl1QLv/zyi6pvyUiDMgCOQXBwMJo0aaJaW3Xu3Bne3swBSXqX713G0rNLtcXxdq234ePJHGlEROTabK7pBAQEoHfv3upBlF6CcgUhKGcQQu6HIN7DA7uz+aN11CPkPvITvnh2Ffr8clC9b9/lCHy5/gzea1+RC5+IiNxW6dKlMWbMGPUQERER2o1CaXlFZMm3B79Fgi5BTVfKVwntSrbjgiIiIpfHZivkNBoXbaxN7wgI0E9EXEQr7EO/ZqW112ZuPo+tZ/TDOxMREWUFefPmRZEiRRi0omSduH0C/1z6R5sfWnsoPD1Y1ScioizU4urWrVu4du2ayrNgTJKHjhs3DidPnkThwoVVQlFptk5kqyZFm2Dh6YVqenuufNCF34KHzOz4GsNfXYM9F+/gUMhd6HTAsEWHVL6rwFz6RO5ERETuKCEhAbt370ZoaKhqcWWuV69eDikXOZ+vD3ytTcugN42KNnJoeYiIiDI9cPX++++rRKAHDhzQnrt8+TKaNm2KqKgo1KhRA8eOHcPTTz+NjRs3olmzZulWSMoa6hepD28Pb8Tr4nE1MRqXvX1QMj4OCN0L32t78M0LtdDx6224Hx2PWw9iMWTBIfz2RgN4earwFhERkVuROlf37t0REhICndy1MSOD5TBwRWLP9T3Yfm27tjCG1B6itg8iIiJ3YHX7YRm5RkYUNPbll1/iwYMHWLlyJfbt24dLly6hYcOGmDJlSkaUldxcgE8AagbW1Oa3l6qb9OKOrxGULzs+fzapxd/OC7fx+ZrTmV1MIiKiTDFgwADkzp1b3RAMCwtTea6MH3fu3OGaIBXUnH5gurYkWge3RvWCpj0kiIiIskTg6urVq6hatarJc8uXL0fNmjXRrp0+8WO2bNnw1ltvqe6DRPZoUqyJNr0jd4GkF06vAsLP4MmqRdC7cUnt6VlbzmPV0etc2ERE5HaOHz+OyZMno3nz5ihYsKAKYpk/iDaGbMSRW/q6t+S0kpEEiYiIsmTgSpobGzc5ljt/Fy9eVJUpY8WLF1f5sIjSmqB9b+QZxAYb5WfY+Y3654OOlVC3RF7t6eGLD+NM2H0ucCIicivly5fHvXv3HF0McmIJiQkmua26lOmCMnnKOLRMREREDgtcVahQAevXr9fmV6xYoQJZhtZWBtevX1d3BYnsUTFfReTzz6emH8U/wsGqTyW9eHgBcD8Mvt6emPlybQTm1A8HHhWbgH6/7EPkozgudCIichuSkmHSpEk4deqUo4tCTmr5heW4EHlBTft4+mBgjYGOLhIREZHjkrMPHjxYJQCVnAoyeuB3332HsmXLok2bNibvW7NmDapVq5b+JaUsQZq4S6urFRdWqPntHrFoUKA8cOsMkBAL7PkeaP0xAnP647uX6+D52TsRl6DDpdtRGLbwEOb0qgtPJmsnIiIXJXUo4xbuckNQUjUULVoUefLkMXmvvO/w4cMOKCU5g5iEGMw8NFObf77i8yiSo4hDy0REROTQwJUkZpc8V998840KXtWpUwczZ86Et3fSV9y8eVPlvRo7dmyGFJayBpPA1fUdGNb4bWDZf/ka9v4APDEM8MuBOiXyYkyXKhj95zH10oZTN/HVhrMY1ra8I4tPRERkN6lfcTQ4ssai04tw/eF1bYCbN6q9wQVHRERZO3AlRowYoR7JCQwMVLmviNIrz9WZiDMIa9EShXIUAh6EAdF3gYO/Ag0HqNdfrB+MIyGRWLgvRM1/veEsygXmQOcaRbkSiIjI5cydO9fRRSAX8CD2AeYcmaPNv1rlVS3VAhERUZbNcUWUWfJny4+q+ZNGsNx6YxfQ4M2kN+z4BoiPUZNyV3ps1yqoEZTUfeLdxYex/3IEVxgRERG5pZ9P/IyIGH1dRwJWvSr3cnSRiIiIMgwDV+SUmgU106a3hmwF6r4O+OXSP3HvKnBonva6v48X5rxSB0Vz+6v52PhElaw95E5U5heciIiIKAPdfnQbPx//WZvvV72f6ipIRETkrhi4IqfUvHhzbXrX9V2I9vE3bXW1bRoQH6vNBubyxw+96yHA10vN334Yi9fm7uVIg0RERORW5hydo0ZeFsVyFEOP8j0cXSQiIqIMxcAVOaVK+SohMFugmo5O+H979wEeVZX2Afyf3nshIfQaqiACgg1BUMCCfS1rL9hd1766K66Crru4rsiHDVzXjgpYEBAEFZQqXToESEggvdeZ+Z73nKlJCAkkk8nc/4/nPrfMneHem2TmzHvf854KrM1aC5x5LxAYrncoPAxs/sj1OcmRmHH96bANKrj3WAnu/+g3VJvMbj9+IiIiouaWUZKBT3d9al+/b9B9CPQL5IUmIiKvxsAVeSSpXeXcXfDHwz8CobHAsLscO/38L8BU7fK881MT8bdL+jl22ZODZ+dvg8Vicc+BExEREbWQmZtmosZco5Z7RPfAhK4TeK2JiMjrMXBFbaK74I/pP+rg04j7AVsdh4JDwOZP6jzv5pFdcMvILvb1T9Ydxr+W7HbPQRMRERG1gD35e/D1vq/t6w+d/hD8fHWJBCIiIm/GwBV5rOHJwxHkF6SWj5Ydxe783UBYHDDsTsdOP/+zTtaVeGZiH4xJ1V0NxYzlezF75QH3HDgRERFRM/vPxv/AAp1BPihhkMsNPiIiIm/GwBV5rBD/EAxLGmZf/+HwD3ph5ANAQKhezk8DtnxW57n+fr6q3tUZnWPs257/5nfM25juhiMnIiLyXHPnzsVll12GDh06ICwsDIMGDcLs2bPZrd6DbTq2CSsOr7CvPzzkYVVWgYiIyAgYuCKPNqrjKPvy8kPL9UJYPDD09lpZV7reg7OQQD+8e/NQpCZF2Lc9NncLlu881sJHTURE5LmmT5+O0NBQ/Otf/8LXX3+N8ePH484778Tzzz/f2odG9ZBSCa9ueNW+fk7KORjSbgivFRERGQYDV+TRRncaDR/oO4o78nYgsyRTPzDyQcA/RC/n7Qe2zq33+VGhAfjvbcPQIUbvW2O24J4PN2B9Wp6bzoCIiMizSLDq448/xrXXXovRo0dj2rRpuP3221VAy2zmSLyeZmXGSvx27DeX2lZERERGwsAVebT4kHgMTBhYt7tgeKJr1tWKqUBNZb2v0S4yGP+7fTjiw/Vw0RXVZtwyZx1+O5TfwkdPRETkeeLj4+tsGzx4MIqKilBaWtoqx0T1M1vMeO231+zrMopg79jevFxERGQoDFxRm8i6qtNdUJz1kOsIg+vePe5rdI0Pw3u3DkNEkL9aL6mswc3vrsWmwwUteORERERtw8qVK5GSkoKICEf3emp9iw4swq78XWrZ38cf9w+6v7UPiYiIyO0YuCKPN7qjI3C1/uh6FFYWOrKupFC7zU+vABXWx+rRPyUK7902DGGBeujo4soa/PHdNdiSzuAVEREZO2j1ySef4NFHH21wP8nISk9Pt0+Zmdbu+9Qiqk3VeH3j6/b1K3tdiY6RHXm1iYjIcBi4Io/XJaoLukV1U8smiwk/pv/oeHDk/UBYgl4uzwNWOdLp6zOkc4yqeWUPXlXU4MZ31mBbxvEDXkRERN5KAlBS6+r888/Hgw8+2OC+UgOrY8eO9mnYMMfIv9T85u6ei/SSdPtIy3cPvJuXmYiIDImBK2pz3QWXHVzmeCAoAjjvCcf6rzOBoiMNvtYZXWJV5lWoNXhVVFGDG95Zg63pDF4REZFxFBQUqBEF4+Li8MUXX8DXt+Fm4SOPPILDhw/bp7Vr17rtWI2mpKoEszbPsq/f2OdGJIRab9QREREZDANX1CaM6TTGvrzqyCqUVZc5HhxyCxCrM7JQUw6seOmErze0Syzm3DIUIQE6eFVYXo3r3l6NNftzW+DoiYiIPEt5eTkuvvhiFBYW4rvvvkNUVNQJnxMZGYkOHTrYp+TkZLccqxHN2T4H+ZV6EJmYoBjc1v+21j4kIiKiVsPAFbUJ/eL6ITlMN5ArTZX4Kf0nx4N+AcCYvzrWN/4PyNaFTBsyvFscZjsFr6Rg+02z1+KHnUdb4AyIiIg8Q01NDa655hrs2LEDixYtUkXZyXMcKzuG97e/b1+/+7S7ER4Y3qrHRERE1JoYuKI2wcfHB2M7j7WvLzm4xHWHvpOAlCF62WIGlk5p1OuO6B6HD+4YhshgPdpgZY0Zd72/AQs2ZTTj0RMREXmOe++9F9988w3+8pe/qILrq1evtk+VlZWtfXiGN3PTTFSYKtR16BjREdf0usbw14SIiIyNgStqM8Z1GWdf/jn9Z9fugj4+wAVOwapd3wIHf23U6w7pHItP7x6B+PAgtV5jtuDhTzfhg9UHm/HoiYiIPMOSJfrmz5///GeMGDHCZeJIga1rX8E+zNs7z77+0OkPIUAyy4mIiAyMgStqMwbGD0RSWJJaljuRLt0FRddzgJ6O4Ba+ewwwmxr12n2SI/H55BFIiQ5R6xYL8Mz8bfjXkl2wyAoREZGXSEtLU59t9U1dunRp7cMztH9v+DfMkjkOYED8AIzr7NSuISIiMiiPClzt3LkTY8eORVhYGJKSkvD444+jqqqqwefInUHZb9CgQYiIiFDFQq+//nocPMhsGcN1FxRj/w746m5/yNoKrJ/d6NfvEh+GL+4ZiR6JjjoSr/+wV2VfVdY0LgBGREREdDLWZ63HivQV9vVHhjyi2j5ERERG5zGBq/z8fIwePVoFqr788ktMnToVb731lhp6uSEbNmxQ+0uR0QULFmD69OnYunUrhg0bhuzsbLcdP7mH853HOt0FRWIqMHyyY/2HvwOlOY1+/aSoYHx29wic3inavm3BpiO48Z01yC9tOIhKREREdDIk2236hun29VEdRuGMpDN4MYmIiDwpcDVr1ixVIHTevHm48MILcdttt+Ef//iH2n7kyJHjPu/ss89WmVpPP/20CnxJAEuGdZag1fvvO0ZkIe8wMMG1u+CKw447k3bnPQGE631QUQgs/VuT/o/YsEB8dOeZmDjAMcz3urR8XPF/vyAtp/QUz4CIiIjIlWSRb83ZqpZ9fXzx8JCHeYmIiIg8LXAlwaYLLrgAsbGx9m0ShDKbzfYiovWJjo6Gv7+1a5iVdBdMSEhoMOBFbZM05i7qcpF9/dsD39bdKTgSGPeCY33jB8DhdU36f4ID/PD6dYNxz6ju9m0HckoxaeYqrNzT+AwuIiIiooZUm6rx2m+v2dcv73E5ukc72h9ERERG5zGBK8maSk1NrROUSk5OVo81xe7du3Hs2DH06dOnmY+SPMHEbhPty79k/IL8ivy6Ow24Cuh8tmN94Z8bXajdxtfXB09clIppVwyAn6+uMVFQVo2bZq/Bmz/uY9F2IiIiOmWf7f4Mh4sPq+UQ/xDcO+jetn1VzWagukJnvZdkA4UZQMkxvV5TpUfAISIiagLXVKVWrnElgaraYmJikJeX16QaAQ8++CDat2+P6667rsF9pWuiTDYcArpt6B3TG92iumF/4X7UWGqwJG0Jrk291nUnKWY64RVg1tmAxQRkbgY2vAcMvb3J/991wzqhQ0wI7vvwNxRV1MBsAaZ9txNb0gvxj6sGIizIY/6MiIiIqA0pqSrBm5vftK//se8fkRiaCI9VWQzk7gVy9up5UbquJSqBKZmXZgM15Sd4ER8gIAQIjQPC4oGwRCAsAQhPBGK6ALFdgdhuQER7uYvophMjIiJP5nXfuJ977jksW7YMixYtUqMTNkQKuU+ZMsVtx0bNQ0bYkayr1ze+bu8uWCdwJdr1BYbfDayeqdeXPQ/0vUw3kpronJ4J+PqBs3H3/zZgZ1ax/n+3ZmLPsWK8+ccz0DW+4d81IiIiotre2foO8it15nhscCxu7Xer51yksjwgYwOQvh5IXwcc+x0ozmyGF7YAMrhOoUw606xefkE6gJXUH0gaYJ0GnlQ7joiI2jaPCVxJZlVhYWG9mVjOda8a8vbbb+P555/Hu+++izFjxpxwfxmx8I477nDJuJLRCMnzTeg6wR642nhsIzJKMpASnlJ3x1FPAls/B0olRb0A+O5x4KrZJ/V/do4Lw5f3jsQTX2zF15t1/bTdR0tw6esr8eIVA3Dpae1P7aSIiIjIMKR74Pu/OwYSmnzaZIQHhrfeAZUXAAd+BPYuBdJWAXn7Tv01/QL1ZK4Baiqa9lxTJZC9Q09b5zq2R6YAHYcBHYfrSQJafgGnfqxEROSxPCZwJfWtateykkCWBJNq176qj4xGeM8996jAlYxI2BiRkZFqoranQ0QHDEoYhE3Zm9T6wv0LcefAO+vuGBwFXDQN+MLaRXDbF0DfSUDfS0/q/w0N9Md//jAIp3WIUt0FTWYLiitr8ODHG7FyTzaeu7Sf2oeIiIioIdPXT0e1uVotSwmEq3pd5f4LdmwHsPMbYO8y4PBaXV7hRCKSgbgeQHxPILqz7uIn3f3CE3SXv6AInS0lwSQp3eBc+8pUpbsSVpUBZbn6xqLUwZIuhpLNlXcAyNsP5B/Q+9anKAPYPk9PIiAU6HAG0G0U0O18IPk0wNevmS4QERF5Ao/5hj1+/HhMnToVBQUF9lpXc+fOha+vL8aNG9fgc1esWKHqWd1555149tln3XTE1Nqku6AtcPXVvq9wx4A7VDfCOvpfCWz7EthlHYHw20eALmcDoY3L5KtN/o87zumGvu0j8dAnm5BdXKm2f7Y+HRsO5uP1605XjxERERHVZ13WOiw9tNS+/vjQxxHg66asIQkMSbtIpmPbG943rqcOCqUMAVJOB+J76cDUyZB6Vb7BQEAwEBIDRNWTKW8jA+pIgCp7N5C1BcjaChzdBuTs0V0NnUm3wwM/6UnKQshrdz0X6D4G6D1eB9aIiE6WvB+V5+tgu2SmSvZoTaWeS4BdHpdAvb8E7IMA/0BAsmdVUD9Bb6dT5mORauYeQLoE9uvXD7169cLTTz+NjIwM1ZXvhhtuwIwZM+z7SRfAgwcPYu/evWp9x44dGDFiBDp27Ig333xTBbpsEhIS0L1744cTTk9PV69z+PBhdOjQoZnPkJpbYWUhzv/sfPvdyvfHv4/BiYPr37k4C3hjuO4uKAZcDVz5zikfQ05JJR6duxkrdmXbtwX6++LJi1Jxy8guamRCIiIyBqO1I4x2vs3FZDbh2m+uxa78XWr93A7n4o0xb7R8UfUtnwEbPwCO/Hb8/SSTSgI+Pcbo7ngSBPIkVaXAkY3AodXA4TV6ktEKj8tHB94kgNV7ApCQ6poFRkQk9fwkKF5wECg45JgkeC6DTkjQqnbAvCmkB5BkpUZ3BOJ7Awm99HuRLIfFGfr6pzehHeFRNa6kqPoDDzyASZMmISIiQtWfevHFF132M5lMqKmpsa+vWbNGdSmU6ayzznLZ9+abb8Z7773ntnMg94oKisLoTqOxOG2xWp+/d/7xA1cRScD4fwDz7tLrUitBugz2ufiUjiE+PAizbx6K2asO4OVFO1FtsqCqxoznv/kdi7Zn4Z9XnYZOcaGn9H8QERGR95i3d549aOXv449Hz3i05f6zzC3A+tm63VNVUvdxHz+g23lA6kQdsJIR/TxZYJjOmpfJ1v0we6fOttq/AkhbCVTpQXQ0iy4sL5NkY8mohRLAkqnzSHYpJDISCXxnbdNZnNJNOme3fv+QrsotSYLrMuXuAfb94PpYZAeg8wig0wj9niTBLI6m6tkZV56Adw7bnlUZqzB56WS1HOofiuXXLEeo1Dqoj/yqf3wdsPs7vS6R7/vWnHSXwdq2pBeoWldpuWX2bSEBfnhqQipuHN6Z2VdERF7OaO0Io51vcyiuKsbF8y5GXkWeWv9j3z+qboLNylQD7PgK+PUNIGN9/ft0GgkMuBLoc5muTeUtTNVAxm/AvmXAru/0F9TjCW8H9Lsc6HcF0GEovywSeRN5L5DAvWRlZm4CMjfrQJXFfHKv5+sPhMYBwdG6u7N/sKNroI+v7jIo/6cMKiHdCCVQJQEx6crcFCGxQPfRuh5zj7FAoHcnQKQ3oR3BwNVJXjjynHT7C7+4EEfLjqr1v5/1d0zqMen4TyjKBGYOd6SVD7gGuPLtZjue0soavPTdTvxv9UGX7Wd2i8U/rmT2FRGRNzNaO8Jo59sc/rX+X3hvu+4NEB0UjW8u/0ZlkDeL6nJg04fAL68D+Wl1H5fR+IbcAgy6HogyyM+r4DCwexGwayFw4GfAWl6ijqiOQL9Jui5q8iB2JyRqi939JLNSdSNeC2Rs0ANBNIoPENMZiOkKRHeyTp31+6TUqVIBq6iTe1+oLNGDUBQf1fUFc3bp2n0yl/fphgJp/iFAzwv0DYbUCTrj1MswcOWGC0ee4z+//Qdvb9XBpyHthuC9i07QPXTTx8B8naWlXPkuMKB5R/L5ZW8OHvt8CzIKHG+YQf6+eGB0D9x5bjcE+XO0GyIib2O0doTRzvdUHSw6iEkLJqHGrEtePDP8GVybeu2pv3BFEbD2TWD1LKAsp9aDPkDPscAZt+m7934eUyXE/eSmpYyeKEEsycaqr+ukiO2mb2ye9gfP7zpJZFRSd0qC0dJNOO1n3eWvMSSALyOPJvYFEvvoASdkhNSAELRK10UJth38FTj0C3B43fGDbUFRwOAbgKF3AHGNr+Ht6Ri4csOFI89xqOgQJs6baF9fMGmBGlb6uFSXwT/oO3BCRn24+6dmfxMoqazB1IU78NGaQy7buyeE4YVJAzCiu7GL8REReRujtSOMdr6nQipzSGmDX478otZ7RPfA3Evmwl+6n5ysqjJg3dvAyn8D5brrocud+tNvAkbcq+s6Ud3stD3fA9u+AHYvPv6XRelSKQEsycaSjAsiah3yfnfoV+DAj8D+H3XXvxMVTJfBJToO112B2w8Ckk7z7K7R0tVQujb+/hWw42ug+Ej9+3UfrQNYvS5q83X6GLhyw4Ujz3L74tuxNmutWr6xz414YtgTDT9BRoiYdTZQnKnXkwYCt3+v+yw3s1V7c/DM/G04kFPqsv2KwSl4cnwqEiOb//8kIiL3M1o7wmjneyqWpC3Bn3/8s3393XHvYljysJN7MamfsuG/wM//BEp0qQSXL2rD7gaG3WX40aqa1JVHbmZu+xLY+72uVVOb1LORAvanXQd0O9/YmWtE7pJ3QP9tynTwl/r/Np3F9QQ6DdfBqo5n6kyqtjqKqAw8Id0ddyzQI8KW1HqvF1LI/dzHgP5XtNkAFgNXbrhw5FlkZMFHf9Sj8kQERGDp1UuPX6TdRkae+e8ljr7F0sib8EqLHF9FtQmzftyHmcv3ocrk6MscGuiHe0d1xx3ndENwQNt8wyEiImO2I4x2viertLoUl86/FMfKjqn1id0m4qVzXmr6C0nGuGQILZ0CFLpmcyMsATj7T7qGlRfWQXGb8gLg9wXA5o91dsfxiroPuFrXCmvXz91HSOS9zCbddU668kqw6kTd/yRQJaOidj0P6HyW9wbra6qAnV8Da9/RXQprk+6OY/6mg+ttLFDHwJUbLhx5lmpzNcZ9Pg455bq2w5SRU3BFzytO/MQf/wEsf9Gxfs3/9CgOLUSyrv66YBt+3uNag6J9VDCeGJ+KSwa25+iDRERtlNHaEUY73+YoyB4eEI6vL/8a8SHxTXuR9PXAoqeAdJ1dbicjXJ31kL75FhTejEdNqpDy5k91EKvAddAdO6mVM+gGHchqplGqiQxFavSpUUAXAXuW1O32XLs+lQSpVLDqXCCyPQzn6HZg7VvApo/qZqBJltn4l4D2g9FWMHDlhgtHnmfGxhl4c8ubarlPbB98evGn8DlR1Fki+/+bpAv72QrfTf6pRetBSJ2Lb7dmYtrCnS7F28VpHaPx+IW9cVaPJjZoiYio1RmtHWG08z0Ze/L34Oqvr4bJYlLrTw57Ejf0uaHxL1CYDix9Dtg613W71Oc8815gxH1ASHQzHzXVyXST7CsJYG2fD1QW1b1AvgFA7/E6iNXjAnYlJGpMF0DJrJIugMcb7dPHV3f7k1pO8vclmUVtLKOoxRQdAVb9B1g/GzBVOj3gozNvx/y1TQTTGbhyw4Ujz5NVmoULv7gQZmvXv48mfIQBCQNO/MTiLF3vqjRbr7c/Hbh1YYuPLiHdB+esSsMby/eqQu7ORnSLw6MX9saQzjEtegxERNR8jNaOMNr5nsyNqlsX34oNRzeo9dTYVHw88ePGFWSXriG/ztCZ4S6Fw32A0/8InP8MENGu5Q6ejl/Ufee3Ooi174f6h7IPSwROu1YHsWTUMiKja0oXwKBIoMcYoNd4PSJqGwi+tKqCw8Dyqfo9yblYvXQfn/BPPbCEB2Pgyg0XjjzTgz88iOWHlze9hoQ0Pv53heMPvv9VwJXvuCWqn11ciVeX7sYnaw/BXGtwjPN7J+DP43qjfwpHsiEi8nRGa0cY7Xyb6ut9X+PplU/b1/83/n8YlDjoxE+ULPBv/wzk7HbdLl1jLpwKJDXiphy5J+Nhy6fAxg+B3D317yM3Q6UW1oCrdOF8IqNoShdA6ekigareF+mRPP0D3Xmk3iFzM7DwMT0qobM+lwAX/xsI88zePAxcueHCkWdanbkady65Uy37+/jjuyu/Q1JYUuOevOJlYMVUx7rczTzvMbjL3mPFmP79bizcmlXnsVG9E3Df+T0wtAvvOhAReSqjtSOMdr5NUVhZqAqy51XoL2tX9rwSz418ruEnFR8FljwDbP3MdXtMVx2wkq4y7CbjmV0JpQbZpg918fz6uhL6BQGpE4BBNwLdz2+zI4ARNYhdAFt/JMLNHwNL/gKU57sOKDHp/3Qmm4dh4MoNF448Ny1faknsyt+l1m/tdyseOeORxj4Z+Pw2YPuXjm1Xvwf0uxzutC2jUAWwftipRx9yNqxLLO49vzvO65Vw4vpdRETkVkZrRxjtfJvimZXPYMG+BWo5KigKX0/6GjHBMcdvf0jQY/HTQEWha7BDRgqUKSDYTUdOzdKVcOMHwP4Vrl13bCKSgdP+AJx2PZDQixecDNYF8CKgx1jvHQHQE5QcAxY+qkdIdTbyAT36oF8APAUDV264cOS5vtr3Ff6y8i9qOSIgAt9f/T3CAsIa3+CYMwE48pte9w/R9a5SToe7bTiYj38v3V1nBEKRmhSB287uiktPa4/gAN61IyLyBEZrRxjtfBtrVcYqTF462b7+/MjncXnP49wEyz8IfP0QsF+XObDrPgaY8AoQ172Fj5ZajBTW3/yJDkrKCIX16TBU18LqfwUQzLIQ1AawC2DbsfVz4JtHgEqnGyLSFfOq2UBkMjwBA1duuHDkuapN1apIe3a5Lrb+xNAncGPfGxv/AkWZwNujgeIjjjtjd/7QakOubkkvwMzl+7D49yx1U9ZZXFggrh/eCX88szMSI3k3loioNRmtHWG0822M0upSXL7gcmSWZqr1ke1HYtYFs+pmSUuXDhnSfNnzQHWpa5eO8f8A+l7GboHeQhpvUndGsrC2zwOqSuru4x8MpF4MDL4B6HoeuxJS2+8CKFNCb76PtbaCQ8CXd+mRUZ0HkPjDh0DHYWhtDFy54cKRZ3tn6zt47bfX1HL7sPb45opvECBDFTfWkU3A7IscI/m06w/c8k2rFtaUGlj/t2I/FmzKQE2tKu4Bfj64qH8yrhvWUY1IyG6ERETuZ7R2hNHOtzGmrpmKj3fK6E5AiH8I5l02DynhKa47Ze8CvnqgbhFdqX904Qss4u3NqkqBHV/rLCwpwl+fyBTgtOt0UXdm3JGndwEMjNBdAKUGH7sAeiZTNbBsCvDL665d0S+bAQy8pjWPjIErd1w48vyiqGM/H4tya+CpwTT945F+wZ/d5JrO/cf5QFA4WlNWYQX+tzoNH605hPyyunc8usaHqQDWlad3QFx4UKscIxGRERmtHWG08z2R347+hlsW3QKLta7Rk8OexA19bnDsYKoBVv0b+PFlwFTl2B7VCbj0NaD76FY4amo10k3U1pWw4GD9+3Q8U2dh9Z0EBEe6+wjJSMrygL3L9AiAe5dyFEBvtONrYN5k16zP854ARj3VaplxzLhyw4Ujzzd9/XTM2T5HLXeK6IQFkxbA39e/aS/y60xg8VOuQ1FfP9cjiqRWVJswf2MG5qxKw66jxXUelyys0amJuHxwCkb1TmQtLCKiFma0doTRzrchlaZKXPXVVUgrSlPrgxMH472L3oOvdJ0ROXuBeXcDGeudnuUDDLsLGPPXVr8pRq1Iuo0e+gXY9BGwfb5r11Hn7IieY/WAQZLZEtjI2q1EDXVhzdqqA1UySYaVxVz/vvI+1mEY0Fu6AI5nF8C27Oh24KM/AIWHHNtOvwmY+Crg18Tvyc2AgSs3XDjyfDnlORj/xXhUmCrU+tSzp+KS7pc0/YVWvAysmOpYlzfsa//nMSMyyEiKaw/k4eO1h7BwWxaqaup+6EQE+2PigGRMGpyiRib09eWIhERERm1H7N27F//85z+xevVqbNu2DampqWrurefrDlKeQMoUiEDfQHx+6efoGtVVfzlc9w7w/V+B6jLHE+J66m4anc5svYMmz1NZojP+JYh1cGX9+8jAQRJA6HeFDmYFhLj7KKmtqiwG9v8I7FkM7PkeKNa1+OrFLoDeqyQb+OQ6Hax0/n579XtuT85oSjvC/WE1IjeJD4nHVb2uwgc7PlDrb299GxO6ToCfbxNH4TvvcaCyCPh1hl7f/Z2+a3rF2x5RPFPqWQ3vFqemv5VW4cuNGSqItfeYIw20uKIGn6w7rKb2UcG4bHAKLh6YjL7JkayHRURkMNu3b8e3336L4cOHw2w2q4lO3qZjmzB722z7+j2D7tFBKxnsZcF9wL5lTnv7ACPvB85/xiOyt8nDSOaddA2USUYilK6EMjl3JZQyGFLkXabAcKD3BKD/lbqrqX9gax49eRoJnB/boUctlayqtFXHL6wu4nvrYGivC3U3Vf4+eafwBOCmr4DPb9Pfa4XMP74W+MNHHpvR6WORdA1SeOfQ+xwrO6ayrqrMupbEtHOm4eJuFzf9heTPRIar/u2/jm0DrwUue8NjMq+cyZ/15vRC1ZXw681HkFvqVEvDSYeYEFzYLwnj+rbDGV1i4cdMLCIir29HSKDK11d3Ybvllluwfv16ZlydpJKqElz19VXIKMlQ631i++DDiR8i4Pev9DDkFQWutawunwV0OasZfopkGNIGzfgN2P6lDlYV6d+1OoKjgJ4XAqkTgB4XAEER7j5S8gQSMN+/QgerZF5y9Pj7ymiWXc7RgSoJWMV0ceeRUmsz1QDf/gn47X3Htk4jgOs/c1tNPWZcEVklhibiyl5X2kf4mbFxBi7sfCECmhpskoJ1F7+qR4PZ9rnetuVToKIIuHqOx6VpSxbWoI7RavrLxD5YuTcHCzZmYPH2oyivNtn3S88vx7srD6gpLiwQF/Rph3H92uGsHvGsiUVE5KVsQSs6ddPWTrMHrYL8gvDSsKcQ8OVkR1vBZrCMGDiNBbap6aQN2mGInsb+HUhfC2z7Evh9vmtQoqIQ2PqZnvwCdV1WycaSKTKZV96bu5ceXAXsk0DV8oZHALQF0HuNA3qO00GrwFB3HSl5Gj9/4JL/6MzN1TP1tkO/Ah9dA9zwucfVXmRXQfJ6dw28C/P3zlcjDErj8rPdn7mO8tNY0i1Q7pSaa3RjwZZW+cFVwHUfe2xjNMDPF+f3TlRTaWUNlvyeha83Z2LlnhxUmRzdQyQr69P1h9UUEuCHM7vF4txeCWrqFh/GLoVEREROFqctxlf7vrKvP9rlEnT74Hqg+Ihjp9B44NL/AKkTee3o1EnQWeqiyXTRNODgLzoTS+pileU69pNRK2VkOJm+fQRof7rOqpFMrPaDPaLUBZ0kuWl+eK0OVsnPP2NDw93/JKtKsmi6n68z8hJ6t9oIcuSBfHyAC6cCAaHAz/90BK8+/oPOvPKgwCa7CrbBFH9qOsm0enPLm2o5JigGC69YiHCJLp8Mswn45mHXtMrkQcCNXwBh8W3mx1NSWYMVu46pLKzlO4+p9eNJiQ7Beb0TcG7PBIzsEYfIYM/rHklE1NraYjuiKV0Fi4qK1GSTmZmJYcOGtanzbS5ZpVm48qsrUVSlr8e5AQmYsXuDVLBy6D0RuOQ1XU+EqKW7/MiXzV0LgZ3fAAVOI4bVFhIDdBsFdB8D9BgDRLbnz8aTleXpAJWaVgFZW44/+p/iAyQPBLqdr3/OErRiPT1qjGV/dwSvhLxHXPdJi9Y646iCbrhw1PZqUEz4cgLyK/PV+t0D78b9g+8/tXoDS/8GrHrNsS2+l06rjOmMtqayxoRf9+WqINb3vx9FTknlcfeVMlj9U6IwvGsshneNw9CusYgKYSCLiMjbA1fPPfccpkyZUmd7Wzrf5mC2mHHnkjuxNmutWo81A18cTke8rci9jMY1/iVg0A3MbCD3kzaqDHmvgljfApmbGt4/oY/Oxuk8Eug0EgiLc9eRUn0/u9x9QMZ6nVUlwchjv5/4Okn3v+6jdKCq6yj+DOnkf/++fxb45XXHNhn44Yp3dLZnC2Dgyg0XjtqeD3d8iJfWvmSvQzH/svnoEHGKP+eVrwJLn3Osh8YB17wPdDkbbZXZbMHvmUX4aU82ftqdjQ0H81FtsjSYYdonKRLDu+lA1pDOMUiICHLrMRMReYK22I5gxlXTzdk2B9M3TLevz8g6hvPKK/RK57OASf/XJm9ikZcqzAD2LAb2LgMO/KRHyj5RIEuCWGo6i/WxWjqbKn29DlSp+QbXAR2OR4qoy8/G9nOK6cogOTVf8Oq7x4G1bzm2DbsbGP9yi/yOsTg7UT2u6XUNPtn5CdKK0lBpqsQr617Ba6OdMqZOxtl/AoKjgW/+JH/pur7A+5cB4/8BDL29Tf4cfH19VEaVTPeO6qG6EK7el4sfd2erYNbB3LI6728S6JJpzqo0+2iFgzvFqOLwgztFo1/7SAT5s54CEVFbFhkZqSYj23B0A1777d/29WuLinXQSophj/krcOZ9LXZnmuikRKUAZ9ymJ1O1DpDsW6YDWUc26vars+wdelr/riNIIjWyUk7Xc+mGxhELm0Yay4XpQNZW67RFTw116XQW39sRSJS5/EyJWoIEpy56WQdVbYOMrH1Td3k/9zG0JhZnJ8OQkQSfHPYkJi+drNZ/OPwDVmasxNkpp5gddcatQFQH4PPbgcpCXbxdCmHKB5MEsFqwX7A7hAf544K+7dQkjhSUY82BXKzZn4c1B/JwIKe0znNktEKZvt6sC9QG+Pmgb/soDEyJUkGsfu2j0LNdOEcuJCKiNiO79Bge/f5emKz1ZbpXVeHPeQVAuwHAFW8C7fq19iGixmRWA6/4yD8f/R1ElqWbv4w4bJuTQcmo2p1H6Gn0M0BpLnBgBZBmLfQtAava8tP0JEXgFR9d4FuKvMuU2BdI7NOm6ry2KLmmObuA7F1Azm7g6Db9naBclys5ISmmLrVzO5wBdByua1SxTh65k9x8kczh8jxg3w96W+5+HYBtxc8PFmdv4yn+1HQP/fCQClqJzpGd8cWlX6iug6csZ48egSF3r2Ob1Aq46l2vLnx5tKhCBbDW7M/F+rR87D5WrN7XTsTf1wc9EsPRt30k+ibrYJYss14WEbVVbaUdUVZWhoULF6rlN954A/v27cP06brr23nnnYeEhASvOt/mUF2YjjvmX4HfUK7Ww8xmfHTkKLoNvx8Y9RTg33xd5CuqTcgoKEd2cSXySqvqnYorqlFebUJFtVnPq0yoqDE12LXfJsjfF6GBfggN9EdYkB9CZK7W/dTgK7FhgYgND0SczMOC1Losx0cEqZtZ5OVBF6mrpEask0LgW09QCByuI2hKACshFUhM1fPY7kB4O+/LQpSR/QoOAvkH9VwCVBKokkm+7DdFXE8dpEoZAnQYqgPgEmAkam2VJbonkQS6x/691bsKMnB1kheO2q6MkgxcNv8y1V1Q3N7/djw85OHmefHyAuCL2/Xww86jt1z6OtDnEhiBNKa3phdi4+ECbDxUgE2H85FTUtXo50s3w97tItCjXTh6JkagZ2K4CnCFsbFMRB6urbQj0tLS0LVr13ofW758OUaNGuVV53vKfl+Al1c8jg/CHBnU00uAsRe/qbvtNJHFYsGRwgrsPVaC9Pwye5by4Ty93NAAKa0tItgf7aNCkBwdjOSoEKRY5+2jQ9A5LhRJkcGq5AB5iYpC3Z1QpozfgCObgMJGdm+zkZvD0Z30JLXfojvreWQKEJYAhCcCgWHwqC/rJUf1VJxlnWc6glQyb2pwSvgG6IBe0mlA0gDr1B8IjmqJsyBqHtXlQEAIWgoDV264cNS2vb3lbfxn43/Usp+PHz6c8CH6xTdTir/ZpAu2/6Jf3+70m4CLXvKsD2c3kAa6NMQlkLX9SCF+P1KkptzSxgezREp0iApgSSBLuhnKcpe4MHUnmN0eiMgTGK0d4fXnK1/aFz6ORfu+wmOJjm5QtwZ1wCOTPgWCI0/4+Xe0qBK7jhZjz9Fi7FZTiQpYSf1IbxTo74vOsaHoEh+GLnGh6Bwn8zB0TwxTQS1+XnuBkmxHMEvqNB3bAeQfaHxmVn0CwnRXQwlihSUCobG6jlZguG43B8lc1sP05OsP+PoBPn7Wua+eZFlKdtRUAXKDWs2dlqtKdHF6+duuPUmd2pJjep9T4qPrgkl3ShlxXDLPpC6Y1Klq4+VDiJobA1duuHDUtlWbq3HDtzdgR57uy98jugc+vfhTBEpx1eay6ztgwX36g9Amrgdwxdu6wKWB2RrztkDWdpkyC3E4T3fBaOrdX2kUSyO5q62RLMvxYYgJDWAjmYjcxmjtCK8+3wM/A/Pvwb6yTFzXPgnl1q5OQyO64a1JX8BfvjjXkltSiS3phdh0uABb0guwOb1Qdes7GdGhASrQExPq6LYny3Hh0n0vUHXpk659wQEy+VrnfggJ8FPBI2G2WFTXfTXJPwtgslhUV8SyShPKqmSqQWmVCeVVNSipNKGwvBp5pbqLYm6Jo2ui3GySx06FfF7Lzade7SLQs12Eyq7u1S5cjUTMgJYXZGVIyYzsnTqQpbrN7dTFx82n9nvjsaQLpC17TLpEJvTSwSlp6wcEt/bREbUJDFy54cJR27crbxf+8M0fUGPRdz1v7X8rHhnySPP+J5JiPP8eR2E7IXeHzrxH18SQO0hkJ43iXVnF6m70nmPW+dESZBVZhxlvoshgf3SKC1XZWh1iQlU3RMc8BBHBrCFARM3HaO0Irzzf6grgh78Dv76BHF8f3Ng+CRkBOkiVGByHTy/9HPEh8TCZLerGiwxWIt3iN6cXqOzixgr080W3BJ2NZPtMUp9PsXruibWkJOCVVViBI4XlyCyoUIO1SJfHzELd1fFQXhmqapqedSO1LSWAJcEsXfMyEn2SIzmAizeQXgjSFnauByXBLFkukW542XpgI08jI4ZHJOnglEwR7YAop66O0u0xMLS1j5KozWPgyg0XjrzD/236P8zcPNO+/uYFb2JkStPrVTTIbAbWzAKW/k2nK9tEdgAm/ANIndi8/58XKqqoVkGsvUd1QEu6WshohlIbxNyIQvANNZZ1UMsR0JI6HUlRUrMjGPHhQfBjrQ4iaiSjtSO87nwzNwPz7gGObUeZjw9uT07EtiBddF0yrJ4a/B/k5ba3D0ZS3IjufjIQiQSoJMtITzpAI93p/P28q2C12WxRN5rSckqRlluGg7kyL1Wf1zI1pnC8jXz2dk8IUwO32EYj5gAuXkqCxWU5upteabaeyvJ0l72qUqCy2GlZ5iWAxaTb12pu0t0Ubduku6AMliC9KGRyXpZaPSHRuq6UfbKtS7Cqne6qyIwpIrdg4MoNF468p8vgLYtuwZbsLWo9NjhWjTIod1ObXdY23XUwc5Pr9t4TgfEvA9Edm///9HJyZ1eCV7phrBvJ0jg+mFt2ykEtW8M5MSII7SJ1IMs2l8CWdOFIsm6T7hlEREZrR3jN+dZUAj+9Avw8XX35NQF4ODEeK8IcGRXmo39Aad6gBl9GBlzqnhCO0zpE47SOUWqemhyBIH9+RlSbzOozWm48SWa17SaUBLlqmvBh3TE2BP2So9A/RQezBnSIUjeZiIio7WHgyg0XjrxrlMGrv74axVXFan1Y0jC8OfbNeutXnDK5K7T2beCHFwDr/6f4BwPD7wbO/pMehZCaJah12D5aUxkyrKM22UZwOlbcfKM2SS0tCWAlRgYjITwIiZFBai51O5yniCB/1vEg8mJGa0d4xfnKSGlyU+nY72pVQijTYmPxcZSjK39l9lhU5Yyp81R5Tx/aNRZDu8SqQNWAlCh2QT+Jz2q54SSF63dmWWteHilCdhM+oyVzWq7/wA7RGNiBPwcioraCgSs3XDjyLksPLsWfVvzJvn5d6nV4evjTLfcfFh0BvnsC2PGV63ZJUz73UWDonUxTdkOtDqnPYRuGPKOgTBWHl/odmUXlOFpYiSrTKYyQU48gf19HIMsa2EqMCLZviw8PVHeOpfhuaKDn1TchooYZrR3Rps+3phKWFS8Dq/4NH+liZPVKRCe875R0XVVwBiozr1QjhUn38mFdYzG8ayzO7Ban6jCxO3nLOFZcoYNYGYX2YJbU0GoMW+abBLEGdZRgVjT6MPONiMjjMHDlhgtH3ufltS/jgx0f2NefPfNZXNP7mpb9T3cvBhb/Bcjd47o9qqMOYJ12ne6bT60y8qGMpCT1OiSYZZtnFlbgaJF1XljRqBonJ0NGiYoL00EsGU0qNkwHtmQ0qTgJbqm5XpdgF7srErU+o7Uj2uL51pjM+H39CiQtfwSJFQfs26stfngk+FwsT94PHx/ddc1c2hODg/6M83om46we8UhNioAv6x626gAueiRiPSLx1oxC7M0uUaMlnkiAn48KNEowS3fljFbBLQYeiYhaDwNXbrhw5H1qzDW4d+m9+DXzV7Xu7+OPGWNm4KyUs1r2PzbVABvfB1a8BJQcdX0sPAkYcR9wxq1AUETLHgedlJLKGhXQkmCWdG1QU4l17rR+skOiN1ZYoJ91yHTnoFbdYFesdWKgi6j5Ga0d0VbOV96nf9qdjR+3HUDfXTNxo+Ub+FmDU2KbuQvuD7oQOSmL4eOjM23bh3bDBxPeR0JYVCseOTXmZ7stoxCbDxdgS3phk0Z3lM/Nfim2rCwd0JJBWnwkZYuIiFocA1duuHDknQorC3HjwhuRVpSm1kP8Q/DW2LcwKLHhgqzNQkZL+XUmsOo11/pXQkY7ke6DQ+8AIpNb/lioRQrT5pZUWQNZTkEup0CX1N3KK6lqsSwuZyEBfiqAFRMWgJhQndUVI0GtUOtc1kMdga7o0AAEeNkIWETNzWjtCE8+3/zSKiz5PQvfbcvCL3tzca5lHaYEvIcUn1z7PlUWP8wwX4mVXYdjv/8bMFn0e29yWDLeH/8+ksKSWvEM6GTlllTag1i2gFZuI28eSc3KAVIrK0VqZum6We0igxjMIiJqAQxcueHCkfdKK0zDzYtuRl5FnlqPCIjA7ItmIzU21T0HUJoDrJkFrH0LqCh0fczHD0idCAy9Heh6ni7kQF6nssakMrQk0CWN7bzSSvuyNMjlsZwS2a7XS6sc9VlaUmSwvzXY5RrginVZ14Ew2RYZHMBuNWQoRmtHeNr5ynviku1Z+HZrJn7dl6tGq0tGrgpYjfPb4LLvoeDeOHDWK6ju6IMnVz6CSpMuBp4QkoD3LnoPnSI7tdJZUEt0/ZcsLAlgbUkvwKbDBSpLq7GfnVKD8jRV9N1a/J0jGRIRNQsGrtxw4ci77cjdgdsW34aS6hK1HhUUhVkXzEL/+P7uO4iKImDDe8CvbwAlWXUfj+sBDLkVGHA1ENHOfcdFHllo3hbU0vPjB7vyy6pQ5qZAl5SCsQWxYo4T3LJNtvXQQD/e2aY2y2jtCE84X3l/W/L7USzcmolf9uXCZNZdAP1gwi1+i/CI/+cI83GMUFcTEA6f0c/Ab/hd+OnIKjy8/GFUm6vVYzFBMZhz0Rx0j+7eKudC7iO/J/uyS1y6GO7ILEK1ydLokQxlFMkB1i6GshwVGtDix01E5E0YuHLDhSPvt+HoBkz+fjIqTBVqPSwgDDNGz8AZSWe490CqK4AtnwBr3waObqv7uI8v0G0UMOAaoM/FrIVFjQp0SQBLgln5pdXILa1U3Wryyqqtc9lufdy6X2Mb86cq0N/XJcAldbpiQwPqdF9U3RvDdRfGIH8/txwb0YkYrR3RWucrwapF27NUsGr1/jx7sMpmsM8evBgwG319D7o+se9lwEUvAZHtsShtEZ76+SlV31LEBseq0gC9Y3u77TzI87Kdd2eVqCDWVsnOyijE7qPFdX6/jqdzXKjqWjjQGtCSYvAyEiUREdWPgauTZLQGJ53Yuqx1uH/Z/Sir0UMwB/kF4fmRz2NCtwnuv3wybM7htcD6d4Ht8wFrtwYX/iFArwuBPpcAPS4AQqLdf5zkld0spACuBLnqC2rZJnswTAJgZVWNGumpOYQH+ataXfaAV506XQGIlm1qewCiQwJVgIyouRmtHeHO882RYNU2W7AqF/XFEtohDy9GfI4Lqle4PhDdCZjwL6DXOLX6yc5PMHXNVFigXyQuOA7vXvguM62o3hs922UEw/QCFciS7CzJ1Grs55sUe++bHKmCWH3bR6plFoAnItIYuDpJRmtwUuNsyd6CyUsno9ipYPpdA+/CfYPug69kO7WG0lxg80fA5k+Bo1vr38fXH+hyNtB7og5mxXR291GSgckd6qJyyeZyCmi5ZHPp4JZ63Dq5oyh97WCXBLMkqCVZXbbgVu1Al5qHBiIkkJld1DCjtSNa+nyPFVdg8fajWLglE2sO1B+sEgMSA/B09PcYfuR/8K0pd/0cHHE/cN4TQGAozBYzZmycgbe3vm3fRQqwS6ZV16iuzX785J3kRs72jEJsldEM0wtVUCstV9/gbIyIYH8dyLJN7SPRs104s4eJWunmrHy21JjNMJtd5yaLRbVnbVmX/r6+8PXVcz8fH/j5+ei5r56kRAZHJW0aBq5OktEanNR4u/J24f4f7kdWqaPW1FkpZ+HFs15EXEhc617KYzuALZ8BWz8HCg8df7/YbkC384Hu5wNdzmE2FnmcqhozCiTI5dSNUWp12YJcLlldUrurtAqVNXroencIDvB1BLrswS2d6RVdK8hlG4lRAmRsxBiH0doRLXW+8iXh5tlrsWpfznEzW3q3i8CE/u1wbchqJK39B1CU7rpD13OBi14G2vVVqxU1FXhm1TNYnLbYvkv3qO6YNXYWRw+kU1ZYVo1tR3StrC2HC7E9sxCH85yCqCcgX3q7xIWiZ2IEerULR492EeiZGI5uCWEMaBE5ZUAWV9SguKLaOtfLRdb1oooalFXWoLzapKbKarNerjKhosY6tz5WYX1M2p7N3VYMDfRXo3dL3VaZ5ManbJOgtbQRpQuxtB+l7Si18Wyje8tAEMEBxrpJmt6EdoSPRcKM1OQLR8aTU56Dh5Y/pDKwbKR7wYtnv6iCWK1Obg+krwN2fgPs/BbI23f8fSVTLGkA0HG4Y4rqwFEKqc0pq6pxBLmO041RlgvKJAim51Um9wW7Avx87AEundll7a5oXZbgls7s0vvYGjS+ctuO2hyjtSNa8nz/+O4a/Lwnx2VbalIEJg5Ixvj+SehR+CuwbErd2o8xXYFxL+gReK0j78pNpz8t/xO25Tr2HZQwCDPGzFCDrxC1BPkyvTOzGL8fKcTvmUXYkVmMXUeLm/RFWT4KusSFoUdiOHpJMKtduApuSUDLaF9wyTvIjYnCclubzFFewrYsc2mr2YNR5Y4glTvbb61F2oLtIoPVlCTzqGAkRwWjU2yoqqPXPirEq9qIDFy54cKRMclw2dPWTMMXe75w2X5p90vx6BmPIiY4Bh5B4tE5u3UAa/ciIH09YDnBSHIR7YGOw3QQq8MZQGJfICjcXUdM5BZyr0ZGVbQFsaSxpCan2ly2hpNtH5nLXTl3kfZIZIjU4gpQQaxI61wmCXTZlm2PSc0uuWMn62EclbFVGa0d0ZLn+/HaQ3jqy62qS9XEAUmYMCAZ3RLCgUNrgKXPAYd+cX1CYARw7qPAmfcA/kH2zWsy1+Dxnx5HXkWefduErhPw/FnPq7qVRO5UbTJjf3apGsFQglm/H9Fz+Zxp6udE++gQdI0PU4Et+UKrluPD0DEmlHUcya2D/cjNw9pBqDz7Nke7Kt8akPL0tBn5+7J1/5OugLZAkdlsQY1ZuhbqeWucR6C/rwpiSYZm5zj5+w9Fj8QI1e24LY5sysCVGy4cGduiA4sw5dcpKKkusW+TYbTvHXQvrux1JQJ8PeyNo6IQOPAzsH85sG95w9lYdj66e2FSf6DdAD2XLK3IFGZmkSEbZ46sLd34kgyvApeAl3XZmuUldwfdzd/XxyXQVXuSwJftcUlZjwjS83BZDvZnl5RTZLR2REuer3y5ySmu1MEqIQGrn/4B7F3quqN83p5xK3DuY0B4on2zyWzCO1vfwczNM1VtKxv5nJ48cDK78JJH3VDJLq7E3mMlahTDPcdK9HS0WH2mNJV82U6JDlFBLPlSK8XgU6Kt85gQ1SWJXdipvlE1be2c+mqSOpds0KUc3HtTzzmTPSJYt10irXM9WdszQf4qG1G66kkXPem6J8uu2/SyzCUQJK/p6+Oj2lDy99PYvw8JZDnXwaoxWVSXRLlBKj0CpGuiXpbuiZI9VmO/aSpZZ7YeAbIsn3enWuu1fVQwUtVgEBHqpk9qUqQKaMs5eSoGrtxw4YgySjIw5Zcp+DXzV5eL0SWyC+4bfB/GdhoLP18PTeMuzAAOr9GjFMo8awtgHRL8hIKjgLieQHxPIK6Hdd5TB7kCglv6yIna1J31AqfsLXsml7WhYgtw2QNfEhQrb907kYF+vvZGoApmBQXYg1oRQbphaFuXxqGt0ai36ZpeUs8hwM+YozYarR3R4ucrfwxpK4EfXwbSfq71oA8w4Grg/KeBWNfC6tI18Mmfn8SGoxvs2yICIjD1nKkY1XFU8x8nUQsFtKSW456jEsgqVnMJbEmAS7afLPki3yEmVAW3bMEs6X6kuycFqXlYkH+zngu1Xs1QCTLVN0iOre1h215a5b4glARSbCUUnOe2OqIx1ptszgEpW6AqyN/XawOvpZU1yCqqwFHrlFVYqeYZBeU4lFuGtNzSJtd2lUz8QZ2iMaRTDE7vHIPBnWLUzUtPwcCVGy4cka1R8c3+b/DKuleQX5lfJ4B1a/9bVZeEYH8PD+hUlQFHNjqCWRLIKspo4ov46CHHZfRCmUfb5tYpIhnw1EAekYeQu3eSaZJvvQNnn6x35+pOuv6DLMtIV55CAmChQX4IleKk1mCWTGFSsNQ6V49bC5aGHmeb3A0N9td3TIP8/RCk5p7baDVaO6LFzlcCVvuWAT/9EzjkenNI6XkhMOZZnQXs8jQL5u2dpz6TnTOie8f0xvRR09EpslPzHSNRK5JAw4HcUqTllKoRDfW8FAdySpsl21duQtiCWDIlynJEMOLCpYh0kKrVKHMZiEQyVqj51ZjMqti4fL5LEMr2uW/7zHeebFk7tsfcGYSSzCV78Mlp4BrbYDWObY4gVWQwB6452TbiseJK9Xd+UP7+c8twIKcEO7OKcbCRI5tK80kGfhjSOQZDOsfirB5xSI4KQWth4MoNF47IWXFVMd7d+i4+2PGBqoPlLDIwEpf1uAyTekxCr5hebefCleUBWVt14VuZZ20DsncC5qanrduHJZfgVUSSdUp2nYdbt4fEsCsi0UlmeNXXoC2q1bAtdAp0yRccPa9GtcnDi044keCVTBLYkmCWDm75ObY5zeVLle4KoCdZlqDY5PO6N/txGa0d0WLnW1UKvNoPKHe9IYTeE3Udq5TT6zzlcPFhvLD6BfxyxLX21Y19bsTDQx5mPSsyBAneSgaNDmKV4XBeGdLzy5FRoOeZhRWqS1Nzkmzc2HA9mq4egEQCE9auXNasGVmPtGbPRIboeViQn7rJ4ak3Ik72c7jCOmKdZM+UWKc6y+qz1+Sy3faYfC631s0o+cyUn6NtdGT5WcbaBpexr+tglG0/DhLgGUora1QAS+rn7czSg0HszCxqVBBTBns4p0c8zuoRjzO7x6m/V3dh4MoNF46oPtI9Yfa22fhyz5d1AliiZ0xPjOs8DueknIM+cX3gK6P7tSU1VUDefiB3D5CzB8jd51gudxS+PSVSLDc0zjrFOi07b3PaHhILBIQw2EV0il92JP3cOZDlPNR07SCX3AUuqf2YrHtQ1ldD5IvU1ucubPbXNVo7okXP98dXgOUv6GzevpfpGlZSa7EW+aydvXW2qmdVZXZ0n0oIScBzI5/DuR3Obd7jImrjWTxHiyuRnlemuh9JMCs9vwxZRZU4Zu2edDJ1tU6ly5it1pDcUFDLknVrrUUk63KzQWoP+cuNBz891zcipCaRLwL8dW0i+Sfqi4PZgmO2hyR0ZzKb1Q0bXZvIjGrrvMZaq6jGbLbOLdaAlFnVgZK6RVLHSNZludK6LAEr2ddTSFBQAkyuQShrNpQs1wpQyXa53t4USDQ6s9mi6uVtOJivpt8O5atsrYbI39LQLrEY0ycRF/Rpp2rltaQ2G7jauXMnHnjgAfzyyy+IiIjATTfdhBdeeAGBgYENPk9O4eWXX8bMmTORnZ2NQYMG4dVXX8WZZ57ZpP/faA1Oajk55Tn4aMdHavRB55GMnMUGx2Jk+5E4O+VsDGk3BO1C27XtDwvJ0JJAVsFBoOBQ3ameQF6zkeK8UnsrOBIIitRzWQ+qb1skEBjmmAJCXZfZnZHolBpJ9sKklSaUVcsdZF2k1FasVNalsV/qtE32dazru9BS9FW+CEhAzXYHu7lIceINz45t9p+00doRLXq+MqjI4r8AI+4HElPrPCwF1xceWIjXf3sdR0qPuDwmGc6PDX1MZTwTURP/9KpNqli8rrNjm+spTxXvrkReSZWqs9XUejvU9MCeZKrZB1kJDbQuO22rdwTiQI4yTPXKKanExkMFWH8wD6v352FregEaird2TwhTAazxA5IxqGM0WrMd4TGV9/Lz8zF69Gj07NkTX375JTIyMvDII4+grKwMM2bMaPC5ErT629/+hpdeegkDBw7EG2+8gXHjxmHTpk3o1q2b286ByCY+JB4Pnv4g7jntHiw9tBQL9i3A6iOrYbI40jUloCX1sWQSccFx6B/fH/3i+6F/XH90j+6OpLCktpOVZcuE6ji07mNmM1CaDRRnAsVZjnlJVq31Y9b7YE0k3RfLcvR0qqQemQpiSTArtP7glsxlP8n0kmHXZVnNndalUL19u23ZaZs8l0Ey8jIyZLSuT+UPWAeDay5yk6rKZLYHsiqtd79td8FlvaL2vNqk7qjL86RYrW0uNbPIw8mNhstm1Pt78GP6j5i5aSZ25O2oU1vy6eFPY0T7EW48UCLvItlPHWND1dQQ+VuUGw3SNdE2STBL6jFJVq7Kzi23Zek6snhty83dZdGTSLaTdIWUIvfh1kkty2AmgU7LQX4ID9LdJm37yXZbAErW2/RNbfI48eFBGNu3nZpEYVk1ft2fg5V7c/Dznpw6tbL2ZZdiX/Z+1X21JQJXTeExGVfTpk3Diy++iEOHDiE2NlZte+utt3Dvvfeqbe3bt6/3eRUVFWjXrh3uu+8+TJ06VW2rqqpCr169MGHCBJWF1VhGu1NK7s/CWnZwGVYeWYk1mWtQXlN+wucE+QWpYrLSGO8c2RlJoUloF9ZOZWclhiYiJjim7QS2GsNUYw1A5daa8upZts6rG0559WhS98sl6BWou0r6BQB+gdap9rJtvb59GnrecZYlW03N/XUgzde27A/4Wef2bV70u0bUAozWjnDn+Vabq7H04FLM2TanTsAq1D8Udw68Ezf1vQmB8t5GRG2ie7pk30p2rZqq6p9LNz25AaHmNbpLnyzXOG2XLn3213a6Aer8Lbf2F17d/VB3N7R1RZTuh5LlJF0RZZt92c/HXktRbnzoea1lf1/VvVEGEpHnEbVF+7JLsGzHUSzdcQzr0/Ls2Vhv/XEIxvVLavb/r01mXH333Xe44IIL7EErcc0112Dy5MlYsmQJbrnllnqfJ90Ki4qK1L420rXwiiuuUJlbRJ6UhXVt6rVqqjJVYeOxjViVsQqrM1djT/4e1Fhq6q3dIY/JVB8/Hz9EBUXpKdA6d1oP8Q9RIxrK3DbZ1mUujX1p5Pv7+sPfxx8BvgFqudXu7kigxFa8vbGqK4DKIqBCpkKgslAv27apufO2Ql34t7pMj6ZYVaKXayrgduYa/f/L1Cb4OAW5ak32IJct0OVn3V5PUMzP6XF7UMzPsa+PPOZrnfvVmlu3S8DW5bHa6w1tP95rHO//rWc/2aYmH2tBDZ9a23zr38Y7p0RNvukzd/dczN01F9nl2XU+A6/qdZXKbo4LieOVJWojpJ1pC/jEtPbBEJFd94RwNd11bneVPbliVzZ+2HkMZ/eMR2vz96T6VrfddpvLtujoaCQnJ6vHGnqeSE11rX/Qp08flalVXl6OkJDWG+KRqD4SLBqePFxNoqKmArvyd2FbzjY17czbiUNFh1wKzdZHuh5Kl8Pj1dE6WfJlQAWzbJOP07IEtuSfjw98oUeDsS3bsr9kLpN6DD562fYceQzyBR7259j2q612AK32PvU9p/YmtU+QpK/JCBlx8EF8/f+H3JaTQJLFBB+zCZBJunaaaxzr8rh9u21u1s+xmF3X1eNm635m+NifI497U00Ik3VyqmGmqp5aJ/fVeG1DJIhlnde3bv+9b8y67bnHebxOoOw4Qenar3H8HRqxf1P2bejx4+3fyGNs4HmhvoGYcsMPDe9PrUo+Cz/c8SEWpy1W2Va1P6Mu7X6pyrLqGNGx1Y6RiIjIW0WHBmLS4BQ1eQKPqnElgaraYmJikJeX1+DzgoKCEBwcXOd5koYqjx8vcCWZWjLZZGZmntI5EJ0syX46LeE0NTkXns0szcTBwoNIK0pTQ30fKzuGo2VH1Vwm55pZzUle12Qy1TsyIjWCfD/2q73B35Pecskr2TpCeEQFgJZjOfXnRdVYMKW5joeanXz23P393SiqcrTRRERABC7veTmuS70OHSK8vysmERERaYb+FjV9+nRMmcKmK3kmyURKCU9R08iUkXUeN5lNqlFfUFmAwspCPVXpuWwrqixChalC1dKSjC7bvKymzLFuqlBfEGokk4iIiMgDSH3HK3teiTnb56j17lHdcX2f63Fxt4sRKgNkEBERkaF4TOBKMqQKCwvrbJeMKee6V/U9r7KyUhVpd866kudJFyB5/Hhk1MI77rjDJeNq2LBhp3QeRO7i5+unirPLdKokO1GyrCSAZZ8sei5dNJy3y36yvxlmNZd/kh3msuy0zbZeZ9n6fJmbpXtd7WOqlVZRZ70R40qc6Dm1H2/M6zbmOSc6dvJS8mNWvwvWyeI0r3c76u7nvI/Ldqd9G9y/ntd03l7ngGtVr61vv9rPr/Pr7Fz99kT/1yn+33X+6ybubxUoAyIYmJRZeOCBB1Sd0IiICNx000144YUXVI1QTyH1IA8WHVQBq2FJwziyFhERkYF5TOBKalTVrmUlgSwJJtWuX1X7eWLXrl047TRHNyt5rU6dOjVY3yoyMlJNREYnQV5bHSsiIvJecmNv9OjR6NmzpxrEJiMjQ93IKysrw4wZM+ApJNv4tdGvtfZhEBERkQfwmG+p48ePx9SpU1FQUGCvdTV37lz4+vpi3Lhxx33eyJEjVfBJ9rUFrqqrq1VjbMKECW47fiIiIiJPN2vWLFXfc968efaM9pqaGtx77714+umn0b59+9Y+RCIiIiIXeggwDzB58mSVrj5p0iQsWbIEc+bMwWOPPaa2OzeixowZgx49etjXpXvgU089hX/+85947bXX8MMPP+C6665Dbm4uHn300VY6GyIiIiLP89133+GCCy5wKcNwzTXXqC7b0v4iIiIi8jQek3EltaiWLVumai5I8EqCWFJ/6sUXX3TZT0Y6kzuDzp544glVY0aCV9nZ2Rg0aBAWL16Mbt26ufksiIiIiDyXlFK47bbbXLZJpntycnKdkg1EREREnsBjAleiT58+WLp0aYP7rFixot76PJJ1JRMRERERHb/Gla0kQ+0biHl5eQ1eNuliKJON1CElIiIiMlTgioiIiIg80/Tp0zFlypTWPgwiIiIyGI+pcUVERERELUsyq2TU5voysZzrXtVHRh88fPiwfVq7dm0LHikRERGRxowrIiIiIoNITU2tU8tKAlnS7U8ea4iM4iwTERERkTsx44qIiIjIIMaPH6/qiRYUFNi3zZ07F76+vhg3blyrHhsRERFRfRi4IiIiIjKIyZMnq5GbZQTnJUuWYM6cOXjsscfU9vbt27f24RERERHVwcAVERERkYFqXC1btgz+/v4qePXkk0/ijjvuUIXXiYiIiDwRa1wRERERGUifPn1Ud0EiIiKitoCBKyc1NTVqLgVKiYiIiJrC1n6wtSe8HdtNRERE5I52EwNXTrKzs9V82LBhJ33xiYiIyNikPdGlSxd4O7abiIiIyB3tJh+LxWI55f/JS1RUVGDr1q1ISEhQtR+aK4oogbC1a9ciOTkZRsPz58+fv//G/Pvn3z7/9o34ty93DKXxNWDAAAQHB8Pbsd3U/Iz83mnkcxc8f/78+fvPv3+jvf/VNKHdxIwrJ3Kxhg4d2iI/FPkF7NChA4yK58+fP3//jfn3z799/u0b7W/fCJlWNmw3tRwjv3ca+dwFz58/f/7+8+/fSLo0st3EUQWJiIiIiIiIiMgjMXBFREREREREREQeiYGrFhYZGYm//e1vam5EPH/+/Pn7b8y/f/7t82/fyH/7dPL43mHc9w7+7I37sxf8+fPnz99/4/79NwaLsxMRERERERERkUdixhUREREREREREXkkBq6IiIiIiIiIiMgjMXBFREREREREREQeiYErIiIiIiIiIiLySAxctZCdO3di7NixCAsLQ1JSEh5//HFUVVXBKPbu3YvJkydj0KBB8Pf3R//+/WEUc+fOxWWXXYYOHTqon79cg9mzZ8NiscAIFi5ciPPOOw8JCQkICgpCt27d8Mgjj6CwsBBGU1JSon4PfHx8sH79ehjBe++9p8639vTkk0/CKP773/9i8ODBCA4ORnx8PMaPH4/y8nIYwahRo+r9+cv0ySeftPbhkQczcrvJyG0mwXYT201GbTexzWTsdhPbTE3j38T9qRHy8/MxevRo9OzZE19++SUyMjLUF/eysjLMmDHDENdw+/bt+PbbbzF8+HCYzWY1GcX06dPRpUsX/Otf/1LBm++//x533nknDh8+rIZ59XZ5eXnq5/7ggw8iLi4O27Ztw3PPPafmS5YsgZH8/e9/R01NDYxo0aJFiIqKsq+npKTACF588UW8/PLLePrppzFixAjk5ORg2bJlMJlMMIKZM2eiqKjIZdu///1vfPHFF7jgggta7bjIsxm93WTkNpNgu4ntJqO3m4zaZjJ6u4ltpiayULObOnWqJSwszJKbm2vf9uabb1r8/PwsGRkZhrjiJpPJvnzzzTdb+vXrZzGK7OzsOtvuvPNOS2RkpMt1MZK33npL0s0M8/svduzYod4HZs2apc593bp1FiOYM2eOOt/6/g683c6dOy3+/v6WhQsXtvaheJSuXbtaJkyY0NqHQR7M6O0mI7eZBNtNdbHdZIx2k5HbTILtprrYZjo+dhVsAd999526sxwbG2vfds0116g7aEbJOPH1Ne6vlqS41ibpr5KFUFpaCiOSzCthlG4f4oEHHlBdP3r37t3ah0JuMmfOHHTt2lWluJP2yy+/4MCBA7jhhht4Sei4jN5uMnKbSbDdVBfbTWQEbDe5YpupYcb+pGzBOg2pqaku26Kjo5GcnKweI+NZuXKlSvuNiIiAUUiKb0VFBX777Tc8//zzuPTSS1UXSiP4/PPPsXXrVvz1r3+FUfXr1w9+fn6qxtm0adMMkfK9evVqDBgwAC+88AISExMRGBiIs846C2vWrIFRffTRR6pmkdT9IzoetpuoNrab2G4yEiO2mQTbTa7YZmoYa1y1UK0GCVTVFhMTo+r/kPEaX1KUWGpeGUnnzp1VnRJx0UUXqTdjI5CaLFKbZerUqYiMjITRSIB+ypQpqlaLFFf96quv8Mwzz6jfBW+vVZOVlYUNGzaooKXULQgNDVW/B+PGjcOePXtUMMtIpE7JZ599poLWErwiOh62m8gZ201sNxmFkdtMgu0mB7aZToyBK6IWlJ6ejmuvvRbnn3++KlZuJDK6oHSNlKKzkoFyySWXqEL1ckfJm8m5tmvXDrfeeiuM6MILL1STjQRtQkJC8Oqrr+Ivf/mLaqR5K+nWJCMiScbdwIED1bYzzzxTZRpKA1QyD41E/t6zs7Nx/fXXt/ahEFEbwXYT201GYuQ2k2C7yYFtphNjV8EWIJlVhYWF9d5RdK7fQN6toKBA1bqROgUyopbRaljIF3cZHeSOO+7AggULsHz5csybNw/e7ODBgyqzTu6eyXuA/A5IIEPI3LZsNFKrRtLeN23aBG9/75e/d1vQSsh7vtS4kwCu0UiWpVwP50Y5UX3YbiLBdhPbTWw3GafNJNhucmCb6cSYcdUCpL5V7VpW8iU2MzOzTu0r8k7l5eW4+OKL1c/9119/dRni1ojki3xAQAD27t0LbyZFqKUA/cSJE+s8Jll3kgou/fnJe2tU7Nu3r97HpN6b0d4D58+fjxtvvFH97RM1hO0mYrvJFdtNbDcZAdtNGttMjWOsFBA3kSybpUuXqrsGNnPnzlUZN5ICSt7fR1nuluzYsQOLFi1SRdmNTopTV1dXq6KT3mzQoEEqs8x5knRvMWvWLFX3yIikxpt0EZXMI28mwerc3FyXu6SyLgMUDBkyBEYidTokw5DdBKkx2G4yNrab6mK7ybjtJqO0mQTbTRrbTI3jY7FYLI3clxpJugRKBLlXr154+umnVYE9KdYsw4EbodCerUC11DgSb7zxhspCmD59ulo/77zzkJCQAG9111134e2331ZdxkaOHOnymHwIBQUFwZtdccUVOOOMM9TdQumnv3nzZrzyyiuqMPW6devUSGtGsmLFCpVtJecu18XbSbew0aNHq9H1bB/Gb731Fh566CF7EM+bazVITSsZhOPFF19Uv/8yOpAUZt+2bRuSkpJgFDKKoATw0tLSVMFZooYYvd1k5DaTYLuJ7SajtpuM3GYSbDdpbDM1kgSuqPn9/vvvljFjxlhCQkIsiYmJlkcffdRSWVlpmEt94MABCYjWOy1fvtzizTp37nzcc5fr4u2mTZtmGTRokCUiIsISFhZm6devn+XZZ5+1FBYWWoxIfnXHAacAAAK4SURBVN/lZ79u3TqLETz44IOWnj17qve+oKAgy4ABAyyvvfaaxWw2W4wgOzvbcuONN1qioqLUNRg3bpxl+/btFiPJy8uzBAYGWh5//PHWPhRqQ4zcbjJym0mw3cR2k1HbTUZvMwmjt5vYZmo8ZlwREREREREREZFHYo0rIiIiIiIiIiLySAxcERERERERERGRR2LgioiIiIiIiIiIPBIDV0RERERERERE5JEYuCIiIiIiIiIiIo/EwBUREREREREREXkkBq6IiIiIiIiIiMgjMXBFREREREREREQeiYErIqJGmj9/PmbOnMnrRURERMQ2ExG5CQNXRESNxMAVEREREdtMROReDFwREREREREREZFHYuCKiKgRbrnlFvz3v//F9u3b4ePjoybZRkRERERsMxFRy/FvwdcmIvIazz77LLKzs7Fz5058+OGHaltCQkJrHxYRERGRR2GbiYiaGwNXRESN0L17dxWoOnjwIM4880xeMyIiIiK2mYjIDdhVkIiIiIiIiIiIPBIDV0RERERERERE5JEYuCIiIiIiIiIiIo/EwBURUSMFBgaioqKC14uIiIiIbSYichMGroiIGqlPnz5IS0vDxx9/jPXr16tlIiIiImKbiYhajo/FYrG04OsTEXmNoqIi3H333fj++++Rm5uLm2++Ge+9915rHxYRERGRR2GbiYiaEwNXRERERERERETkkdhVkIiIiIiIiIiIPBIDV0RERERERERE5JEYuCIiIiIiIiIiIo/EwBUREREREREREXkkBq6IiIiIiIiIiMgjMXBFREREREREREQeiYErIiIiIiIiIiLySAxcERERERERERGRR2LgioiIiIiIiIiIPBIDV0RERERERERE5JEYuCIiIiIiIiIiIo/EwBUREREREREREXkkBq6IiIiIiIiIiAie6P8BAI8TGcTToSkAAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t_grid = np.linspace(0.05, b_cox * 0.95, 200)\n", "xs_q_cox = np.quantile(x_s_cox, [0.1, 0.5, 0.9])\n", "colors = [\"C0\", \"C1\", \"C2\"]\n", "\n", "fig, (ax_s, ax_h) = plt.subplots(1, 2, figsize=(11, 4))\n", "X_zero = np.zeros((t_grid.size, 1))\n", "\n", "for q, xs_val, c in zip([0.1, 0.5, 0.9], xs_q_cox, colors):\n", " X_scale = np.full((t_grid.size, 1), xs_val)\n", " S_np = np_cox.survival(t_grid, X=X_zero, X_scale=X_scale)\n", " h_np = np_cox.hazard(t_grid, X=X_zero, X_scale=X_scale)\n", " ax_s.plot(t_grid, S_np, lw=2, color=c,\n", " label=f\"$x_s$ q{int(q*100)} ({xs_val:+.2f})\")\n", " ax_h.plot(t_grid, h_np, lw=2, color=c,\n", " label=f\"$x_s$ q{int(q*100)} ({xs_val:+.2f})\")\n", "\n", "ax_s.set_xlabel(\"t\"); ax_s.set_ylabel(\"S(t | x_d=0, x_s)\")\n", "ax_s.set_title(\"Survival — non-proportional Coxph(scaling=x_s)\")\n", "ax_s.legend()\n", "ax_h.set_xlabel(\"t\"); ax_h.set_ylabel(\"h(t | x_d=0, x_s)\")\n", "ax_h.set_title(\"Hazard rate — non-proportional Coxph(scaling=x_s)\")\n", "ax_h.legend()\n", "fig.tight_layout();" ] }, { "cell_type": "markdown", "id": "takeaways-md", "metadata": {}, "source": [ "## Takeaways\n", "\n", "- The `scaling=` kwarg on `BoxCox` / `Coxph` / `Colr` / `Lm` / `Survreg`\n", " mirrors R `tram::*(scale = ~x_s)` and multiplies the baseline by\n", " $e^{0.5 x_s \\gamma}$. γ is unconstrained — monotonicity in $y$ is\n", " inherited from $h_0$ because the scaling factor is strictly\n", " positive (ADR 0002, Decision 3).\n", "- The fitted model exposes `gamma_` and `feature_names_scaling_`;\n", " `summary()` adds a *Scaling coefficients* block with Wald\n", " standard errors and p-values for $\\gamma$.\n", "- Sign convention is *identical* to R for $\\gamma$ — no flip when\n", " porting `tram` fits. (β is still negated; the `summary()`\n", " tabulation handles that for you.)\n", "- `predict(...)` and the convenience methods `survival(...)` /\n", " `hazard(...)` take an extra `X_scale_new=` / `X_scale=` argument\n", " on scaled fits.\n", "- Likelihood-ratio tests on $\\gamma$ work the same way they do for\n", " any nested-model comparison: deviance $2\\Delta\\ell$ on $q_s$ df.\n", "- Combining `scaling=` with `interacting=` (tensor-product baseline)\n", " is out of scope for v0.4 and raises `ValueError`; if you need\n", " *and* shape-on-y and *and* spread-on-x, fit them as two separate\n", " models and compare via deviance. See\n", " [04_interacting_terms](04_interacting_terms.ipynb) for the\n", " tensor-product route on its own." ] } ], "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 }