From 7a114542de62e097b320366c3adf0618f3c9dc83 Mon Sep 17 00:00:00 2001 From: Elyan Date: Sat, 2 May 2026 10:34:13 +0200 Subject: [PATCH] Add Annealed Sinkhorn Tutorial notebook, based on chizat:24 --- .../linear/350_Annealed_Sinkhorn.ipynb | 1215 +++++++++++++++++ 1 file changed, 1215 insertions(+) create mode 100644 docs/tutorials/linear/350_Annealed_Sinkhorn.ipynb diff --git a/docs/tutorials/linear/350_Annealed_Sinkhorn.ipynb b/docs/tutorials/linear/350_Annealed_Sinkhorn.ipynb new file mode 100644 index 000000000..e0e67469f --- /dev/null +++ b/docs/tutorials/linear/350_Annealed_Sinkhorn.ipynb @@ -0,0 +1,1215 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "ace06552", + "metadata": {}, + "source": [ + "# Annealed Sinkhorn for Optimal Transport\n", + "\n", + "This tutorial explores how *annealing* the regularization parameter $\\varepsilon$ of Sinkhorn's algorithm can improve the speed-accuracy trade-off in entropy-regularized optimal transport. The experiments are inspired by {cite}`chizat:24`.\n", + "\n", + "We start from fixed-$\\varepsilon$ Sinkhorn baselines and build up progressively: first using the native geometric scheduler {class}`~ott.geometry.epsilon_scheduler.Epsilon` from OTT-JAX, then polynomial schedules that better match the convergence theory, and finally a debiased variant that corrects the relaxation error introduced by temperature changes. Along the way, we identify the practical optimal schedule exponent and show what happens when the annealing conditions are violated." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "7f95ff4d", + "metadata": {}, + "outputs": [], + "source": [ + "import jax\n", + "import jax.numpy as jnp\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from ott.geometry import pointcloud, epsilon_scheduler \n", + "from ott.problems.linear import linear_problem\n", + "from ott.solvers import linear\n", + "from ott.solvers.linear import sinkhorn\n", + "\n", + "\n", + "jax.config.update(\"jax_enable_x64\", True)" + ] + }, + { + "cell_type": "markdown", + "id": "a5a51fe4", + "metadata": {}, + "source": [ + "## Sinkhorn's algorithm in a nutshell\n", + "\n", + "**Setup.** Let $a \\in \\Delta_n^*$ and $b \\in \\Delta_m^*$ be two probability vectors, referred to as *marginals* in OTT-JAX, supported on point clouds $\\{x_i\\}_{i=1}^n$ and $\\{y_j\\}_{j=1}^m$ in $\\mathbb{R}^d$. In OTT-JAX, these are encapsulated together with a cost matrix $C \\in \\mathbb{R}^{n \\times m}_+$ (e.g., $C_{ij} = \\|x_i - y_j\\|^2$) into a `PointCloud` object.\n", + "\n", + "**Optimal transport problem.** Finding the cheapest way to transport mass $a$ onto $b$ amounts to solving:\n", + "\n", + "$$\\operatorname{OT}(a, b) = \\min_{P \\in U(a,b)} \\langle C, P \\rangle$$\n", + "\n", + "where $U(a,b) = \\bigl\\{P \\in \\mathbb{R}^{n \\times m}_+ : P\\mathbf{1}_m = a,\\; P^\\top\\mathbf{1}_n = b\\bigr\\}$ is the set of *transport plans* with prescribed marginals. Solving this exactly requires super-cubic time in $n$, which is prohibitive at scale.\n", + "\n", + "**Entropy-regularized OT.** Sinkhorn's algorithm instead solves a smoothed surrogate, adding an entropic penalty parameterized by $\\varepsilon > 0$, the `epsilon` argument passed to any `PointCloud` in OTT-JAX:\n", + "\n", + "$$\\operatorname{OT}_\\varepsilon(a,b) = \\min_{P \\in U(a,b)} \\langle C, P \\rangle\n", + "+ \\varepsilon\\,\\operatorname{KL}(P \\,\\|\\, P^{\\mathrm{ref}})$$\n", + "\n", + "where $\\operatorname{KL}(P \\| Q) = \\sum_{i,j} P_{ij}\\log\\frac{P_{ij}}{Q_{ij}}- P_{ij} + Q_{ij}$ and $P^{\\mathrm{ref}} = \\frac{1}{nm}\\mathbf{1}_n\\mathbf{1}_m^\\top$ by convention.\n", + "\n", + "> **Convention: $\\varepsilon$ vs $\\beta$.** This tutorial uses $\\varepsilon > 0$ to match OTT-JAX's `epsilon` argument. The annealing literature often uses the *inverse temperature* > $\\beta = 1/\\varepsilon$ instead. A small `epsilon` (large $\\beta$) means little regularization — the solution is close to $\\operatorname{OT}(a,b)$, but convergence is slow. A large > `epsilon` > (small $\\beta$) means fast convergence but a large regularization bias. **This is the fundamental speed-accuracy trade-off that motivates annealing.**\n", + "\n", + "**Gibbs kernel and solution structure.** The unique minimizer of $\\operatorname{OT}_\\varepsilon$ has the form:\n", + "\n", + "$$P^* = \\mathrm{diag}(u^*)\\, K\\, \\mathrm{diag}(v^*)$$\n", + "\n", + "for some $u^* \\in (\\mathbb{R}^*_+)^n$, $v^* \\in (\\mathbb{R}^*_+)^m$, where $K_{ij} = \\exp(-C_{ij} / \\varepsilon)$ is the *Gibbs kernel* (accessible as `geom.kernel_matrix` in OTT-JAX).\n", + "\n", + "**Sinkhorn iterations.** Starting from $v^{(0)} = \\mathbf{1}_m$, the scaling vectors are updated by alternating projections onto the marginal constraints:\n", + "\n", + "$$u^{(t)} \\leftarrow a \\oslash \\bigl(K\\, v^{(t-1)}\\bigr), \\qquad v^{(t)} \\leftarrow b \\oslash \\bigl(K^\\top u^{(t)}\\bigr)$$\n", + "\n", + "where $\\oslash$ denotes elementwise division. By default, OTT-JAX performs these updates in log-domain via `log-sum-exp` operations (`lse_mode=True`), which avoids numerical underflow when `epsilon` is small. The primal iterate is $P^{(t)} = \\mathrm{diag}(u^{(t)}) K\\, \\mathrm{diag}(v^{(t)})$, and convergence is monitored via the marginal violation error `out.errors`." + ] + }, + { + "cell_type": "markdown", + "id": "d0a3930c", + "metadata": {}, + "source": [ + "## Baseline: fixed-ε Sinkhorn\n", + "\n", + "We sample two point clouds $x \\in \\mathbb{R}^{300 \\times 2}$ and\n", + "$y \\in \\mathbb{R}^{300 \\times 2}$, pass them to a\n", + "{class}`~ott.geometry.pointcloud.PointCloud` with a fixed $\\varepsilon$,\n", + "and record the OT cost and marginal violation error across a range of\n", + "regularization values. This builds the **Pareto front** that annealed\n", + "variants will later try to beat." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "3ad7d78a", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "rng = jax.random.key(1) \n", + "rng, r1, r2, r3, r4, r5, r6 = jax.random.split(rng, 7)\n", + "\n", + "#Source X\n", + "# Half-moon (m=150) : angles in [0, π], radius in [0.3, 0.5] \n", + "m1 = 150\n", + "ang1 = jax.random.uniform(r1, (m1,)) * jnp.pi\n", + "rad1 = jax.random.uniform(r2, (m1,)) * 0.2 + 0.3\n", + "X1 = jnp.stack([rad1 * jnp.cos(ang1), rad1 * jnp.sin(ang1)], axis=1)\n", + "\n", + "# Small blob (m=150) : angles in [0, 2π], radius in [0, 0.1], centered at (-0.3, 0.4)\n", + "m2 = 150\n", + "ang2 = jax.random.uniform(r3, (m2,)) * 2 * jnp.pi\n", + "rad2 = jax.random.uniform(r4, (m2,)) * 0.1\n", + "X2 = jnp.stack([rad2 * jnp.cos(ang2) - 0.3, rad2 * jnp.sin(ang2) + 0.4], axis=1)\n", + "\n", + "x = jnp.concatenate([X1, X2], axis=0) # (300, 2)\n", + "\n", + "#Target Y \n", + "# Horizontal rectangle (n=150) : x ∈ [-0.5, 0.5], y ∈ [0, 0.15]\n", + "n1 = 150\n", + "Y1 = jnp.stack([\n", + " jax.random.uniform(r5, (n1,)) - 0.5,\n", + " jax.random.uniform(r6, (n1,)) * 0.15,\n", + "], axis=1)\n", + "\n", + "# Vertical rectangle (n=150) : x ∈ [-0.075, 0.075], y ∈ [0, 0.6]\n", + "rng, r7, r8 = jax.random.split(rng, 3)\n", + "n2 = 150\n", + "Y2 = jnp.stack([\n", + " (jax.random.uniform(r7, (n2,)) - 0.5) * 0.15,\n", + " jax.random.uniform(r8, (n2,)) * 0.6,\n", + "], axis=1)\n", + "\n", + "y = jnp.concatenate([Y1, Y2], axis=0) # (300, 2)\n", + "\n", + "#Marginals + normalised cost matrix \n", + "a = jnp.ones(x.shape[0]) / x.shape[0]\n", + "b = jnp.ones(y.shape[0]) / y.shape[0]\n", + "\n", + "fig, ax = plt.subplots(figsize=(7, 5))\n", + "ax.scatter(x[:, 0], x[:, 1], s=10, label=\"source $a$ (X)\")\n", + "ax.scatter(y[:, 0], y[:, 1], s=10, label=\"target $b$ (Y)\")\n", + "ax.set_aspect(\"equal\")\n", + "ax.legend()\n", + "ax.set_title(\"Point clouds\")\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "62ae6f96", + "metadata": {}, + "source": [ + "We approximate the **true** OT cost $\\operatorname{OT}(a,b)$ by running {func}`~ott.solvers.linear.solve` at $\\varepsilon = 10^{-4}$ with a generous iteration budget. The attribute `primal_cost` of the returned {class}`~ott.solvers.linear.sinkhorn.SinkhornOutput` gives $\\langle C, P^\\star_\\varepsilon \\rangle$, the transport cost of the entropic plan, without the entropic penalty term. As $\\varepsilon \\to 0$, $P^\\star_\\varepsilon$ converges to the unregularized OT plan, so this serves as a tight approximation of $\\operatorname{OT}(a,b)$." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "67e0dfbb", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Reference OT(a, b) ≈ 0.078080 (converged: True)\n" + ] + } + ], + "source": [ + "geom_ref = pointcloud.PointCloud(x, y, epsilon=1e-4)\n", + "out_ref = linear.solve(geom_ref, a=a, b=b, max_iterations=50_000)\n", + "OT_ref = float(out_ref.primal_cost)\n", + "print(f\"Reference OT(a, b) ≈ {OT_ref:.6f} (converged: {out_ref.converged})\")" + ] + }, + { + "cell_type": "markdown", + "id": "f4ae873b", + "metadata": {}, + "source": [ + "We track two metrics as a function of iteration count $t$.\n", + "\n", + "The **marginal violation error** `out.errors` measures how far the current iterate $P^{(t)}$ is from satisfying the marginal constraints:\n", + "\n", + "$$\\operatorname{err}(t) = \\|P^{(t)}\\mathbf{1}_m - a\\|_1 + \\|(P^{(t)})^\\top\\mathbf{1}_n - b\\|_1.$$\n", + "\n", + "The **OT suboptimality** measures the transport cost after projecting $P^{(t)}$ onto $U(a,b)$ via Altschuler's rounding:\n", + "\n", + "$$\\langle C,\\, \\widehat{P}^{(t)}\\rangle - \\operatorname{OT}(a, b), \\qquad \\widehat{P}^{(t)} = \\operatorname{proj}_{U(a,b)}(P^{(t)}).$$" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "5a0d9c75", + "metadata": {}, + "outputs": [], + "source": [ + "def altschuler_round(P: jax.Array, a: jax.Array, b: jax.Array) -> jax.Array:\n", + " \"\"\"Project a non-negative matrix onto U(a, b) in O(nm) time.\"\"\"\n", + " r1 = P.sum(axis=1)\n", + " F = P * (jnp.minimum(a, r1) / r1)[:, None]\n", + " r2 = F.sum(axis=0)\n", + " G = F * (jnp.minimum(b, r2) / r2)[None, :]\n", + " err_a = a - G.sum(axis=1)\n", + " err_b = b - G.sum(axis=0)\n", + " return G + jnp.outer(err_a, err_b) / err_b.sum()\n", + "\n", + "\n", + "def ot_suboptimality(out, geom: pointcloud.PointCloud, a: jax.Array, b: jax.Array, ot_ref: float) -> float:\n", + " \"\"\"Return ⟨C, proj_{U(a,b)}(P*)⟩ − OT(a, b) for the converged plan P* = out.matrix.\"\"\"\n", + " P_rounded = altschuler_round(out.matrix, a, b)\n", + " return float(jnp.sum(geom.cost_matrix * P_rounded)) - ot_ref" + ] + }, + { + "cell_type": "markdown", + "id": "5f671b21", + "metadata": {}, + "source": [ + "These two metrics capture different aspects of the $\\varepsilon$ trade-off:\n", + "\n", + "- **Small $\\varepsilon$**: Sinkhorn converges slowly (many iterations), but once converged, the rounding $\\widehat{P}^{(t)}$ is close to the true OT plan → **low suboptimality, high iteration cost**.\n", + "- **Large $\\varepsilon$**: Sinkhorn converges in very few iterations, but the entropy bias makes $\\langle C, \\widehat{P}\\rangle \\gg \\text{OT}(a,b)$ → **fast but inaccurate**.\n", + "\n", + "The Pareto front below encodes the best achievable trade-off over all fixed-$\\varepsilon$ runs." + ] + }, + { + "cell_type": "markdown", + "id": "e5e594ff", + "metadata": {}, + "source": [ + "We wrap {func}`~ott.solvers.linear.solve` with `inner_iterations=1` to record\n", + "the marginal error at **every** Sinkhorn iteration in `out.errors` rather than\n", + "every 10 (the default). We sweep over\n", + "$\\varepsilon \\in \\{5\\times10^{-1}, \\ldots, 1\\times10^{-3}\\}$ and record the\n", + "iteration count and OT suboptimality at convergence." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "c4537057", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ε = 5e-01 | iters = 2 | suboptimality = 9.94e-02\n", + "ε = 2e-01 | iters = 5 | suboptimality = 6.83e-02\n", + "ε = 1e-01 | iters = 10 | suboptimality = 4.26e-02\n", + "ε = 5e-02 | iters = 23 | suboptimality = 2.58e-02\n", + "ε = 2e-02 | iters = 61 | suboptimality = 1.30e-02\n", + "ε = 1e-02 | iters = 122 | suboptimality = 7.31e-03\n", + "ε = 5e-03 | iters = 240 | suboptimality = 3.93e-03\n", + "ε = 2e-03 | iters = 581 | suboptimality = 1.66e-03\n", + "ε = 1e-03 | iters = 1122 | suboptimality = 8.76e-04\n" + ] + } + ], + "source": [ + "def run_sinkhorn(eps: float, x, y, a, b, max_iterations: int = 5_000):\n", + " \"\"\"Run Sinkhorn at fixed epsilon, recording the marginal error at every iteration.\"\"\"\n", + " geom = pointcloud.PointCloud(x, y, epsilon=eps)\n", + " out = linear.solve(geom, a=a, b=b,inner_iterations=1,max_iterations=max_iterations)\n", + " return out, geom\n", + "\n", + "\n", + "epsilons = [5e-1, 2e-1, 1e-1, 5e-2, 2e-2, 1e-2, 5e-3, 2e-3, 1e-3]\n", + "fixed_results = {}\n", + "\n", + "for eps in epsilons:\n", + " out, geom = run_sinkhorn(eps, x, y, a, b)\n", + " subopt = ot_suboptimality(out, geom, a, b, OT_ref)\n", + " n_iters = int(jnp.sum(out.errors >= 0)) # filter -1 padding\n", + " fixed_results[eps] = {\"out\": out, \"geom\": geom, \"subopt\": subopt, \"n_iters\": n_iters}\n", + " print(f\"ε = {eps:.0e} | iters = {n_iters:5d} | suboptimality = {subopt:.2e}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "56333d9f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n", + "\n", + "ax = axes[0]\n", + "for eps in epsilons:\n", + " errs = fixed_results[eps][\"out\"].errors\n", + " errs = errs[errs >= 0]\n", + " ax.plot(errs, linewidth=1.5, label=rf\"$\\varepsilon={eps}$\")\n", + "ax.set_yscale(\"log\")\n", + "ax.set_xscale(\"log\")\n", + "ax.set_xlabel(\"Iterations $t$\")\n", + "ax.set_ylabel(\"Marginal error\")\n", + "ax.set_title(r\"Convergence (fixed $\\varepsilon$)\")\n", + "ax.legend(fontsize=8, loc=\"upper right\")\n", + "\n", + "ax = axes[1]\n", + "suboptimals = [fixed_results[eps][\"subopt\"] for eps in epsilons]\n", + "n_iters_all = [fixed_results[eps][\"n_iters\"] for eps in epsilons]\n", + "ax.scatter(n_iters_all, suboptimals, s=60, zorder=5)\n", + "for eps, ni, so in zip(epsilons, n_iters_all, suboptimals):\n", + " ax.annotate(rf\"$\\varepsilon={eps}$\", (ni, so),\n", + " textcoords=\"offset points\", xytext=(5, 5), fontsize=7)\n", + "\n", + "sorted_pairs = sorted(zip(n_iters_all, suboptimals))\n", + "pareto_x, pareto_y = zip(*sorted_pairs)\n", + "ax.step(pareto_x, np.minimum.accumulate(pareto_y), where=\"post\",\n", + " linestyle=\"--\", color=\"black\", linewidth=1.5, label=\"Pareto front\")\n", + "ax.set_yscale(\"log\")\n", + "ax.set_xscale(\"log\")\n", + "ax.set_xlabel(\"Iterations to convergence\")\n", + "ax.set_ylabel(r\"$\\langle C, \\hat{P}\\rangle - \\mathrm{OT}(a,b)$\")\n", + "ax.set_title(r\"Speed–accuracy Pareto front (fixed $\\varepsilon$)\")\n", + "ax.legend(fontsize=9)\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "1ed5d506", + "metadata": {}, + "source": [ + "The convergence curves (left) display the characteristic profile of Sinkhorn: a slow initial phase followed by an accelerating descent once the iterates enter the linear convergence regime. The spectral gap grows with $\\varepsilon$: at $\\varepsilon = 0.5$ Sinkhorn converges in a single iteration, while at $\\varepsilon = 0.001$ it requires over $10^3$ iterations to reach a comparable marginal error.\n", + "\n", + "The speed–accuracy Pareto front (right) makes the trade-off explicit: each point corresponds to one fixed-$\\varepsilon$ run, placed at its convergence cost (iterations) and its residual suboptimality after rounding. No single $\\varepsilon$ dominates everywhere — large $\\varepsilon$ is cheap but biased, small $\\varepsilon$ is accurate but slow.\n", + "\n", + "\n", + "The goal of *Annealed Sinkhorn* is for a **single run** to trace — or beat — this\n", + "entire front." + ] + }, + { + "cell_type": "markdown", + "id": "320d6e07", + "metadata": {}, + "source": [ + "## Annealed Sinkhorn\n", + "\n", + "Instead of a fixed $\\varepsilon$, *Annealed Sinkhorn* uses a non-decreasing inverse temperature sequence $(\\beta_t)_{t \\geq 1}$ with $\\beta_t = 1/\\varepsilon_t$:\n", + "we start warm (large $\\varepsilon$) for a fast coarse solution, then cool down progressively, reusing the current iterate as a warm start at each step.\n", + "\n", + "The suboptimality at iteration $t$ decomposes as:\n", + "\n", + "$$\\langle C, \\widehat{P}_t \\rangle - \\mathrm{OT}(a,b) \\;\\lesssim\\; \\underbrace{\\beta_t^{-1}}_{\\text{entropic error}} \\;+\\; \\underbrace{\\beta_t - \\beta_{t-1}}_{\\text{relaxation error}}$$\n", + "\n", + "The entropic error decreases as $\\beta_t$ grows; the relaxation error penalizes schedules that cool too fast — annealing too aggressively shocks the iterate away from the regularization path. A good schedule must balance both terms. \n", + "\n", + "We parametrize all schedules with a common starting point $\\beta_0 = 10 / \\|C\\|_{\\mathrm{osc}}$, where $\\|C\\|_{\\mathrm{osc}} = \\max C - \\min C$ is the oscillation of the cost matrix.\n", + "This normalization ensures that $\\varepsilon_0 = 1/\\beta_0$ is always of the same order as the cost scale, regardless of the problem instance. We then compare two families: geometric schedules driven by OTT-JAX's native `Epsilon` scheduler, and polynomial schedules that match the convergence theory." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "c0b73870", + "metadata": {}, + "outputs": [], + "source": [ + "_annealed_solver = sinkhorn.Sinkhorn(inner_iterations=1, max_iterations=1, threshold=0.0)\n", + "\n", + "\n", + "def annealed_sinkhorn_ott(x, y, a, b, eps_sched, T: int, ot_ref=None):\n", + " \"\"\"Run T steps of annealed Sinkhorn via lax.scan with potential rescaling on epsilon change.\"\"\"\n", + " ot_ref_val = float(ot_ref) if ot_ref is not None else 0.0\n", + " eps_seq = jnp.array([float(eps_sched(t)) for t in range(T)])\n", + "\n", + " def step(carry, idx):\n", + " f, g, eps_prev = carry\n", + " eps_t = eps_seq[idx]\n", + "\n", + " #Rescale potentials to new epsilon before warm start\n", + " f = f * eps_t / eps_prev\n", + " g = g * eps_t / eps_prev\n", + "\n", + " geom = pointcloud.PointCloud(x, y, epsilon=eps_t)\n", + " prob = linear_problem.LinearProblem(geom, a=a, b=b)\n", + " out = _annealed_solver(prob, init=(f, g))\n", + " f, g = out.f, out.g\n", + "\n", + " P = geom.transport_from_potentials(f, g)\n", + " P_hat = altschuler_round(P, a, b)\n", + " err = (jnp.abs(P.sum(axis=1) - a).sum() + jnp.abs(P.sum(axis=0) - b).sum())\n", + " subopt = jnp.sum(geom.cost_matrix * P_hat) - ot_ref_val\n", + "\n", + " return (f, g, eps_t), {\"eps\": eps_t, \"margin_err\": err, \"subopt\": subopt}\n", + "\n", + " f0 = jnp.zeros(x.shape[0])\n", + " g0 = jnp.zeros(y.shape[0])\n", + " eps0 = eps_seq[0]\n", + "\n", + " _, metrics = jax.jit(lambda carry, xs: jax.lax.scan(step, carry, xs))((f0, g0, eps0), jnp.arange(T))\n", + "\n", + " records = [{\"t\": t + 1, **{k: float(v[t]) for k, v in metrics.items()}} for t in range(T)]\n", + " return records" + ] + }, + { + "cell_type": "markdown", + "id": "b2eeeb58", + "metadata": {}, + "source": [ + "### Geometric schedules via OTT-JAX `Epsilon`\n", + "\n", + "The natural starting point is the `Epsilon` scheduler built into OTT-JAX,\n", + "which implements a geometric decay of the regularization parameter from\n", + "$\\varepsilon_0$ to $\\varepsilon_{\\mathrm{end}}$ over $T$ steps.\n", + "\n", + "$$\n", + "\\varepsilon_t = \\varepsilon_{\\text{end}} \\cdot \\texttt{init} \\cdot \\texttt{decay}^t,\n", + "\\qquad\n", + "\\texttt{init} = \\frac{\\varepsilon_{\\text{start}}}{\\varepsilon_{\\text{end}}},\n", + "\\qquad\n", + "\\texttt{decay} = \\left(\\frac{\\varepsilon_{\\text{end}}}{\\varepsilon_{\\text{start}}}\\right)^{1/(T-1)}.\n", + "$$\n", + "\n", + "In OTT-JAX this is implemented as\n", + "\n", + "```python\n", + "epsilon_scheduler.Epsilon(\n", + " target=eps_end,\n", + " init=eps_start / eps_end,\n", + " decay=(eps_end / eps_start) ** (1.0 / max(T - 1, 1)),\n", + ")\n", + "```\n", + "\n", + "so that ε₀ = target * init = eps_start and ε_{T-1} ≈ eps_end.\n", + "\n", + "We evaluate three schedules with common starting point $\\varepsilon_0 = \\|C\\|_{\\mathrm{osc}} / 10$ from the previous section, varying only the decay rate $r$:\n", + "\n", + "- `slow`: strong initial regularization, very gradual decay.\n", + "- `medium`: balanced speed and stability.\n", + "- `fast`: aggressive cooling, higher relaxation error." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "681e29e5", + "metadata": {}, + "outputs": [], + "source": [ + "def make_epsilon_schedule(eps_start: float, eps_end: float, T: int):\n", + " \"\"\"Build an OTT-JAX Epsilon scheduler decaying geometrically from eps_start to eps_end in T steps.\"\"\"\n", + " #eps(t) = target * init * decay^t\n", + " init = eps_start / eps_end\n", + " decay = (eps_end / eps_start) ** (1.0 / max(T - 1, 1))\n", + " return epsilon_scheduler.Epsilon(target=eps_end, init=init, decay=decay)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "f64a9a11", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "||C||_osc = 0.9539 -> eps_0 = 0.0954\n" + ] + } + ], + "source": [ + "# Oscillation of the cost matrix; sets the base regularization scale\n", + "geom_full = pointcloud.PointCloud(x, y)\n", + "C = geom_full.cost_matrix\n", + "c_osc = float(C.max() - C.min())\n", + "eps_0 = c_osc / 10.0\n", + "beta_0 = 1.0 / eps_0\n", + "print(f\"||C||_osc = {c_osc:.4f} -> eps_0 = {eps_0:.4f}\")\n", + "\n", + "T = 1000 # number of outer iterations\n", + "\n", + "sched_slow = make_epsilon_schedule(eps_start=eps_0, eps_end=eps_0 / 4.0, T=T)\n", + "sched_medium = make_epsilon_schedule(eps_start=eps_0, eps_end=eps_0 / 10.0, T=T)\n", + "sched_fast = make_epsilon_schedule(eps_start=eps_0, eps_end=eps_0 / 50.0, T=T)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "5d3d5d15", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Final subopt — slow: 1.53e-02 | medium: 8.98e-03 | fast: 1.43e-02\n" + ] + } + ], + "source": [ + "schedules = {\n", + " \"slow\": sched_slow,\n", + " \"medium\": sched_medium,\n", + " \"fast\": sched_fast,\n", + "}\n", + "\n", + "records = {\n", + " name: annealed_sinkhorn_ott(x, y, a, b, eps_sched=sched, T=T, ot_ref=OT_ref)\n", + " for name, sched in schedules.items()\n", + "}\n", + "\n", + "annealed_results = {\n", + " name: {\n", + " \"iters\": np.array([r[\"t\"] for r in recs]),\n", + " \"subopt\": np.array([r[\"subopt\"] for r in recs]),\n", + " \"merr\": np.array([r[\"margin_err\"] for r in recs]),\n", + " }\n", + " for name, recs in records.items()\n", + "}\n", + "\n", + "print(\"Final subopt — \" + \" | \".join(f\"{name}: {annealed_results[name]['subopt'][-1]:.2e}\" for name in schedules))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8cfc1628", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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tW5f4+Hjb0blzZwA2bNhgq3ur17+obVz9HX3++efzvb6oi3f6+fmxf/9+nnrqKZKSkpg2bRpDhgzB19eX//3vfyiKctNz3H///Xh4eNgeX+/aXo27W7du3H333SxevLjQT5Dr169vOwdYpxXUqVMn3/lWrVpF69at8y1o6+zszJNPPklUVBRHjhzJd86hQ4fm+1lc66mnnsr3uGPHjoXGLoQQovIZPHgwWVlZrFixgrS0NFasWHHdaXyQ/76dlJRESkoKHTt2LLRv0alTJ+rXr5+vbM2aNbRt25amTZvayjw9PYs1sqYofZZr48zIyCA+Pp527dqhKAp79+4tcls38vvvv5OcnMyDDz6Yry+i0Who06bNdfs72dnZxMfH25YJuPbaubu7s2PHDi5cuFDsePr27UtQUJDtcevWrWnTpo2tL1QWunTpQmBgYL4+7qFDhzhw4ECZzAgQoiKTxJSo8lq1asXixYtJSkpi586dvPbaa6SlpTFw4MACf4AWR61atfI9rlGjBmq12jb//+zZs6jV6gK7k/j7++Pu7s7Zs2fzldesWbNAEqZ27doA+dYUKK6QkJB8j93c3ACoVq1agXKLxZIv4bF161a6dOmCk5MT7u7u+Pj48PrrrwOUWmIKrMmzrVu32q7JwoULyc3N5ZFHHrnh6xITE4mNjS30uBGLxcLnn39OrVq1MBgMeHt74+Pjw4EDBwp9X/+9hlcTKUlJSfnKg4ODC/wMPTw88tU7efIkhw8fxsfHJ99x9Wd97aL8t3r9i9rG1d/RGjVq5Ht9nTp1rnvu/woICOCbb77h4sWLHD9+nC+//BIfHx/efvttZs6cedPXF/XaZmdn06tXL5o1a8Yvv/xy3UVf/3u+q+e89nxnz54t9D1enRb733+b1atXL7Qto9GIj4/PDdsSQghRefn4+NClSxfmz5/P4sWLMZvNDBw48Lr1V6xYwR133IHRaMTT0xMfHx+++eabQu/Zhd1bzp49W+iudsXZ6a4o99Xo6GiGDRuGp6enbY3ETp06AaXXvzt58iQAnTt3LtAfWbduXb7+TmJiIqNHj8bPzw8HBwd8fHxs1+faeCZOnMihQ4eoVq0arVu3Zvz48UX+MOi//Xaw9rNL0se+GbVazUMPPcTSpUvJzMwEYN68eRiNRtu6sUJUFbLGlBBX6PV6WrVqRatWrahduzbDhw9n4cKFvPPOO9cdlVOcRYyvd46yGPFTHNfOaS9K+dVRLqdPn+buu++mbt26TJo0iWrVqqHX61m1ahWff/75LW/FW5gHHniAF154gXnz5vH6668zd+5cWrZsedMESf/+/dm0adMN30dhPvjgA9566y1GjBjB//73Pzw9PVGr1YwZM6bQ93Wza1WcehaLhUaNGjFp0qRC615NGJbk+he1jdKkUqmoXbs2tWvXplevXtSqVYt58+bx+OOP3/B1Rb22BoOBnj17smzZMtasWcO9995bovMVx/VGS12vLSGEELePIUOG8MQTTxAbG0uPHj2uu/Pcli1b6NOnD3feeSdff/01AQEB6HQ6Zs+ezfz58wvUv969paRudh80m8107dqVxMREXn31VerWrYuTkxPnz59n2LBhpda/u3qeH3/8EX9//wLPX7v73eDBg9m2bRsvv/wyTZs2xdnZGYvFQvfu3fPFM3jwYDp27MiSJUtYt24dn3zyCR9//DGLFy+2rQNW0Tz66KN88sknLF26lAcffJD58+dz77332j4oFqKqkMSUEIVo2bIlABcvXgT+/TQpOTk5X73/jpy41smTJ/N92nXq1CksFottIcfQ0FAsFgsnT57Mt0D5pUuXSE5OJjQ0NN/5Tp06haIo+RJZJ06cALCdszyTXMuXL8dkMvHbb7/l+/Tt2qHXxXGj2D09PenVqxfz5s3joYceYuvWrUyePPmm5/zss89uaXTKokWLuOuuuwqM6ElOTsbb27vY5yuOGjVqsH//fu6+++4bXpOSXP+itnH1d/T06dP5koDHjx8v4rspXHh4OB4eHrZ/X6VBpVIxb9487rvvPgYNGsTq1avz7UZUHKGhoYW+x2PHjtmeF0IIIQD69evHyJEj+fvvv1mwYMF16/36668YjUbWrl2bb6r57Nmzi9xWaGhogR30gELLbtXBgwc5ceIE33//PY8++qit/NrdB0vD1dHYvr6+dOnS5br1kpKSWL9+PRMmTMi3Ac/VEVf/FRAQwDPPPMMzzzxDXFwczZs35/33379pYqqw8504ceK6O/gVx436Wg0bNqRZs2bMmzeP4OBgoqOjmTJlSonbFKKykal8okrbsGFDoSMlrs4nv/rHuKurK97e3mzevDlfva+//vq65546dWq+x1dvMldvjD179gQokGC5Oorlv7uzXLhwId9Ofampqfzwww80bdrU9kmTk5MTUDCBVhaufuJ27fVLSUkpVgfrWjeL/ZFHHuHIkSO8/PLLaDQaHnjggZues0WLFnTp0qXQ40Y0Gk2B34uFCxdy/vz5or2ZEhg8eDDnz59nxowZBZ7LysoiIyPDFiPc2vUvahtXf1f/u7NQUZKCADt27LCd61o7d+4kISGhWFMCi0Kv17N48WJatWpF79692blz5y2dp2fPnuzcuZPt27fbyjIyMpg+fTphYWEF1vwQQghRdTk7O/PNN98wfvx4evfufd16Go0GlUqVb7R9VFRUvp1wb6Zbt25s376dffv22coSExPzrVFUUoX1LxRF4Ysvvii1NsD6XlxdXfnggw/Izc0t8Pzly5evGw8U7IuYzeYC0wx9fX0JDAzEZDLdNJ6lS5fm6+ft3LmTHTt2lMpIKycnpxtOgXzkkUdYt24dkydPxsvLq8KO7hKiLMmIKVGlPffcc2RmZtKvXz/q1q1LTk4O27ZtY8GCBYSFhTF8+HBb3ccff5yPPvqIxx9/nJYtW7J582bbiKXCREZG0qdPH7p378727duZO3cuQ4YMoUmTJgA0adKEoUOHMn36dJKTk+nUqRM7d+7k+++/p2/fvtx11135zle7dm0ee+wxdu3ahZ+fH7NmzeLSpUv5EhFNmzZFo9Hw8ccfk5KSgsFgoHPnzvj6+pbylYN77rkHvV5P7969GTlyJOnp6cyYMQNfX99bGgnTokULwLrQdrdu3Qokn3r16oWXlxcLFy6kR48eZfKerrr33nt59913GT58OO3atePgwYPMmzeP8PDwMmvzqkceeYRffvmFp556ig0bNtC+fXvMZjPHjh3jl19+Ye3atbRs2bJE17+obTRt2pQHH3yQr7/+mpSUFNq1a8f69euL/Mnsjz/+yLx58+jXrx8tWrRAr9dz9OhRZs2ahdFotK2HVZocHBxYsWIFnTt3pkePHmzatImGDRsW6xzjxo2zbf/9/PPP4+npyffff09kZCS//vqrbWF8IYQQAqybYNxMr169mDRpEt27d2fIkCHExcUxdepUatasyYEDB4rUziuvvMLcuXPp2rUrzz33HE5OTnz33XeEhISQmJhYKiPn69atS40aNXjppZc4f/48rq6u/Prrr6W+PqKrqyvffPMNjzzyCM2bN+eBBx7Ax8eH6OhoVq5cSfv27fnqq69wdXXlzjvvZOLEieTm5hIUFMS6deuIjIzMd760tDSCg4MZOHAgTZo0wdnZmT/++INdu3bx2Wef3TSemjVr0qFDB55++mlMJpMtSfTKK6+U+L22aNGCBQsWMHbsWFq1aoWzs3O+JOaQIUN45ZVXWLJkCU8//XS+TYmEqCokMSWqtE8//ZSFCxeyatUqpk+fTk5ODiEhITzzzDO8+eab+dYJePvtt7l8+TKLFi3il19+oUePHqxevfq6CZIFCxbw9ttvM27cOLRaLc8++yyffPJJvjrfffcd4eHhzJkzhyVLluDv789rr73GO++8U+B8tWrVYsqUKbz88sscP36c6tWrs2DBArp162ar4+/vz7Rp0/jwww957LHHMJvNbNiwoUySOHXq1GHRokW8+eabvPTSS/j7+/P000/j4+NTYEe/oujfvz/PPfccP//8M3PnzkVRlHyJKb1ez/3338/XX39900XPS+r1118nIyOD+fPns2DBApo3b87KlSsZN25cmbYL1oUwly5dyueff84PP/zAkiVLcHR0JDw8nNGjR9sWKC/J9S9qGwCzZs3Cx8eHefPmsXTpUjp37szKlSuLtA7VyJEjcXR0ZP369SxbtozU1FR8fHy45557eO2112jWrFnJLtZ1uLq6snbtWu688066du3Kli1birUwrJ+fH9u2bePVV19lypQpZGdn07hxY5YvX15gJKMQQghRFJ07d2bmzJl89NFHjBkzhurVq/Pxxx8TFRVV5MRUtWrV2LBhA88//zwffPABPj4+jBo1CicnJ55//nmMRmOJ49TpdCxfvpznn3+eDz/8EKPRSL9+/Xj22WdtH66WliFDhhAYGMhHH33EJ598gslkIigoiI4dO+b7cHj+/Pk899xzTJ06FUVRuOeee1i9ejWBgYG2Oo6OjjzzzDOsW7eOxYsXY7FYqFmzJl9//TVPP/30TWN59NFHUavVTJ48mbi4OFq3bs1XX31FQEBAid/nM888w759+5g9ezaff/45oaGh+RJTfn5+3HPPPaxatarM+7hCVFQqpSQrvgohykVYWBgNGzZkxYoV9g7Frl544QVmzpxJbGwsjo6O9g5HCCGEEMLuxowZw7fffkt6erpsvFFJ9evXj4MHD5bqemFCVCYyH0EIUSlkZ2czd+5cBgwYIEkpIYQQQlRJWVlZ+R4nJCTw448/0qFDB0lKVVIXL15k5cqVMlpKVGkylU8IUaHFxcXxxx9/sGjRIhISEhg9erS9QxJCCCGEsIu2bdsSERFBvXr1uHTpEjNnziQ1NZW33nrL3qGJYoqMjGTr1q1899136HQ6Ro4cae+QhLAbSUwJISq0I0eO8NBDD+Hr68uXX35J06ZN7R2SEEIIIYRd9OzZk0WLFjF9+nRUKhXNmzdn5syZ3HnnnfYOTRTTpk2bGD58OCEhIXz//fe2XbaFqIpkjSkhhBBCCCGEEEIIYReyxpQQQgghhBBCCCGEsAtJTAkhhBBCCCGEEEIIu5A1pkrAYrFw4cIFXFxcUKlU9g5HCCGEEGVMURTS0tIIDAxErZbP94pK+kxCCCFE1VKcPpMkpkrgwoULVKtWzd5hCCGEEKKcxcTEEBwcbO8wKg3pMwkhhBBVU1H6TJKYKgEXFxfAeqFdXV3tHI0QQgghylpqairVqlWz9QFE0UifSQghhKhaitNnksRUCVwdiu7q6iqdLCGEEKIKkeloxSN9JiGEEKJqKkqfSRZHEEIIIYQQQgghhBB2IYkpIYQQQgghhBBCCGEXkpgSQgghhBBCCCGEEHYha0wJIYQQQogKwWw2k5uba+8wRCF0Oh0ajcbeYQghhLgNVfnEVL9+/di4cSN33303ixYtsnc4QgghhBBVjqIoxMbGkpycbO9QxA24u7vj7+8vi/8LIYQoVVU+MTV69GhGjBjB999/b+9QhBBCCCGqpKtJKV9fXxwdHSXxUcEoikJmZiZxcXEABAQE2DkiIYQQt5Mqn5iKiIhg48aN9g5DCCGEEKJKMpvNtqSUl5eXvcMR1+Hg4ABAXFwcvr6+Mq1PCCFEqanQi59v3ryZ3r17ExgYiEqlYunSpQXqTJ06lbCwMIxGI23atGHnzp3lH6gQQgghhLglV9eUcnR0tHMk4mau/oxkHTAhhBClqUInpjIyMmjSpAlTp04t9PkFCxYwduxY3nnnHfbs2UOTJk3o1q2bbZgxQNOmTWnYsGGB48KFC+X1NoQQQgghqqSpU6dSv359WrVqddO6Mn2v4pOfkRBCiLJQoafy9ejRgx49elz3+UmTJvHEE08wfPhwAKZNm8bKlSuZNWsW48aNA2Dfvn3lEaq4RkZGxnWf02g0GI3GItVVq9W2YePFrZuZmYmiKIXWValU+T6VLU7drKwsLBZLgXqyHoYQQghR0KhRoxg1ahSpqam4ubmVSRvpmSlo1BocjM5lcn4hhBBClK0KPWLqRnJycti9ezddunSxlanVarp06cL27dvLpE2TyURqamq+QxTk7Ox83WPAgAH56vr6+l637n+TkmFhYdete+edd+arW79+/evW/e+ntq1atbpu3fr16+ere+eddxZar2PHjtdNbgkhhBCibFgsZmIzzhGVHkVswtkKcy8eNmwYffv2tXcYQgghRKVQaRNT8fHxmM1m/Pz88pX7+fkRGxtb5PN06dKFQYMGsWrVKoKDg2+Y1Prwww9xc3OzHdWqVbvl+MXtZevWrWRmZto7DCGEEKJKyck1AWBBRYKSTmT8UTKy0uwclRBCCCGKo0JP5SsPf/zxR5Hrvvbaa4wdO9b2ODU1VZJThUhPT7/uc//dweXa9cD+S63OnzeNiooqct0jR47ccHretXbt2lXkups3b843lS8zM7PAqCohhBBClA+jwZFwr3rEJkaRTBZZKoXojLO4Zzrh7xmKSlVpP4MVQgghqoxKe7f29vZGo9Fw6dKlfOWXLl3C39+/TNo0GAy4urrmO0RBTk5O1z2uXV/qZnWvXTOquHUdHR2vW/e/u/4Up66Dg0O+5318fLh8+TKXL1/GycmpFK+iEEIIIYpCrVYT6B1OiGMwRsU6eipRyeRM/FEyssp22YVFixbRqFEjHBwc8PLyokuXLoWuiWkymXj++efx9fXFaDTSoUMHdu3aZXu+ZcuWfPrpp7bHffv2RafT2T7sO3fuHCqVilOnTpXp+xFCCCHsodImpvR6PS1atGD9+vW2MovFwvr162nbtq0dIxNCCCGEELdKURQyc/KKfai1Tvi51sIh10hOjpnkXAvHk85y+uIp0rNzinSO4qxRdfHiRR588EFGjBjB0aNH2bhxI/379y/0HK+88gq//vor33//PXv27KFmzZp069aNxMREADp16sTGjRtt73/Lli24u7vz119/AbBp0yaCgoKoWbNmyS+wEEIIUcFU6Kl86enp+T4ZioyMZN++fXh6ehISEsLYsWMZOnQoLVu2pHXr1kyePJmMjAzbLn1CCCGEEKJyyco1U//ttaV81uNFqnXk3W446ovWPb548SJ5eXn079+f0NBQABo1alSgXkZGBt988w1z5syxbewyY8YMfv/9d2bOnMnLL79MREQEM2fOxGw2c+jQIfR6Pffffz8bN26ke/fubNy4kU6dOhXxvQohhBCVS4UeMfXPP//QrFkzmjVrBsDYsWNp1qwZb7/9NgD3338/n376KW+//TZNmzZl3759rFmzpsCC6EKUlaysLCIiIoiIiCArK8ve4QghhBCinDRp0oS7776bRo0aMWjQIGbMmEFSUlKBeqdPnyY3N5f27dvbynQ6Ha1bt+bo0aMAdOzYkbS0NPbu3cumTZvo1KkTERERtlFUmzZtIiIiojzelhBCCFHuKvSIqYiIiJsOqX722Wd59tlnyykiq6lTpzJ16lTMZnO5tisqHovFwqZNm2zfCyGEEKJkHHQajrzbrdTOl5mdQVxaDFkqa59SB/g6+OPq5FFo20Wl0Wj4/fff2bZtG+vWrWPKlCm88cYb7Nixo9gxuru706RJEzZu3Mj27dvp2rUrd955J/fffz8nTpzg5MmTMmJKCCHEbatCj5iqqEaNGsWRI0fyLVophBBCCCFKTqVS4ajXltrh7epGvcAGBBvdcNKr0OjVJJjjSEyNwqDN39Z/d+MtSqzt27dnwoQJ7N27F71ez5IlS/LVqVGjBnq9nq1bt9rKcnNz2bVrV76dfTt16sSGDRvYvHkzEREReHp6Uq9ePd5//30CAgKoXbt2yS6sEEIIUUFJYkoIIYQQQtzWVCoVfp4hhLpUx8liTT6lYOJ0wjFS0hNu6Zw7duzggw8+4J9//iE6OprFixdz+fJl6tWrl6+ek5MTTz/9NC+//DJr1qzhyJEjPPHEE2RmZvLYY4/Z6kVERLB27Vq0Wi1169a1lc2bN09GSwkhhLitSWJKCCGEEEJUCQ4GJ0J96uGjdkWjKOSq4Fx2LDHxJzGb84p1LldXVzZv3kzPnj2pXbs2b775Jp999pltgfNrffTRRwwYMIBHHnmE5s2bc+rUKdauXYuHx7/TCTt27IjFYsmXhIqIiMBsNsv6UkIIIW5rKqU4++KKfFJTU3FzcyMlJQVXV1d7hyPsICMjA2dnZ8C6i6STk5OdIxJCCFGW5N5/a2503bKzs4mMjKR69eoYjcZyiynblMWllCjS1dY1InUK+Bp9cXfxKbcYKht7/ayEEEJUPsXpM8mIKSGEEEIIUeUYDQ6E+NTFV+OO9sroqfOmOKLjT5BnzrV3eEIIIUSVIYmpWzB16lTq169Pq1at7B2KqAAcHR1xdHS0dxhCCCGEKCaVSoWPRxBhbjVxsVh35Esjl9OJJ0hMi7NzdEIIIUTVIImpWyC78omrnJycyMjIICMjQ6bxCSGEEJWUQW+kmk8d/LSe6BSFPBVcNF3mbPxxcvNy7B2eEEIIcVuTxJQQQgghhKjyVCoV3u4BhLnVwvXK6Kl08jiddJKE1Fg7RyeEEELcviQxJYQQQgghxBV6vYFqvnXx13qhVxTMKojNSSDq8jFy8kz2Dk8IIYS47UhiSogSyM7OplevXvTq1Yvs7Gx7hyOEEEKIUuLl7k+Ye21cLVoAMlRmziSf4nLKBWRTayGEEKL0aO0dgBCVmdlsZtWqVbbvhRBCCHH70On0VPOtQ2JKHAk5ceSoVMTlJpEen0qgexgGndHeIQohhBCVnoyYEkIIIYQQ4gY83XwJ86iDm0WHCshUmTmTcpq45PMyekoIIYQoIUlMCSGEEEIIcRM6rY5g39oE6n0xKAoW4HJeMpHxx8jOybJ3eEIIIUSlJVP5bsHUqVOZOnWqTN0S+WRkZODk5GR7nJ2dfcPfEUdHR1QqFQAmk4m8vLxSqevg4IBabc055+TkkJubW6TzCiGEEOLm3F19cM7z4FJSJCkqE1kqC5GpZ/DUuuLrFlwm99WIiAiaNm3K5MmTAQgLC2PMmDGMGTOm1NsSQgghypuMmLoFo0aN4siRI+zatcveoYgKxM/PL9/jRx55BGdn5+semZmZtrojR468Yd34+Hhb3bFjx96wbnR0tK3uG2+8ccO6HTt2lCkIQgghRDFptVqCfGoRpA/AqIAFiM9L5Uz8MbJyMsq8/V27dvHkk0+WeTtCCCFEeZDElBAl4OjoSPv27e0dxi159NFH+fbbbyUxJYQQQtwiN1cvQj3r4KEYUKOQrbIQmRpFbFJ0md5ffXx8cHR0LLPzCyGEEOVJElNClIBKpWLLli2kp6eTnp6e77kff/zRVl7YcW2H8ttvv71hXW9vb1vdSZMm3bBuSEiIre77779/3Xpff/01DRo0sE37E0IIIUTxRERE8MKYF5j4/le0rdWBTvXuZOGPi4hJvcTAIf1xcXGhZs2arF692vaaQ4cO0aNHD5ydnfHz8+ORRx7JNzI6IyODRx99FGdnZwICAvjss88KtBsWFmab1hcVFYVKpWLfvn2255OTk1GpVGzcuBGAjRs3olKpWLt2Lc2aNcPBwYHOnTsTFxfH6tWrqVevHq6urgwZMiTfiG4hhBCiPMgaU0KUkEqlyre21FVGY9G3kDYYDBgMhlKvq9fr0ev1RY5DCCGEsDtFgVw7JUd0jlDMNaK+//57XnnlFXbt3MVPP/3Euy+/y/qVf3B3ry48PuYJfp7+E4888gjR0dHk5OTQuXNnHn/8cT7//HOysrJ49dVXGTx4MH/++ScAL7/8Mps2bWLZsmX4+vry+uuvs2fPHpo2bVritzd+/Hi++uorHB0dGTx4MIMHD8ZgMDB//nzS09Pp168fU6ZM4dVXXy1xW0IIISq+5Oxk3I3u9g5DElNCVEU5OTl88MEHALz++uuSvBJCCHFT/fr1Y+PGjdx9990sWrSo7BrKzYQPAsvu/Dfy+gXQF/yw6UaaNGnCm2++CVjXdpw4cSJBvkE8+tBAMtUwYuzj/DBrLjt2bWfrlu00a9bMdg8GmDVrFtWqVePEiRMEBgYyc+ZM5s6dy9133w1YE1/BwcGl8vbee+892xIEjz32GK+99hqnT58mPDwcgIEDB7JhwwZJTAkhRBUQmxFLz8U96RjUkU86fYJeY7+/CWUOTwW1dMO3TJz/BKv++oGU9ER7hyNuM7m5uUyYMIEJEybccNc+IYQQ4qrRo0fzww8/2DuMCqdx48a27zUaDV5eXjRv1oIQr3p4KQ74+noCcDjmKH/v2saGDRvybURSt25dAE6fPs3p06fJycmhTZs2tnN6enpSp06dUo/Vz88PR0dHW1LqallcXFyptCWEEKJi++X4L+RacknLTbNrUgpkxFSF9eepBWzQX4bTf6M5NZFquSqCFHeqOdagQVBb2jftjY+HnT5NFEIIIUSVExERYVuzqEzpHK0jl+xBV/wFxXU6Xb7HKpUKnU6HRqPG3yccp4wUACwWCynpadx1TycmfjQRJ6NLvtcFBARw6tSpYrd/da3Iaxdbv96HTtfGejXO/8ZusViKHYMQQojKJTsvm4UnFgLwUN2H7ByNJKYqrGCnGjROS+aszkSKRk2UHqJIBvNuiN6N6uwUgnMhSHGlmjGMugFtaNfkPoJ9w+wduhBCCCHK2ebNm/nkk0/YvXs3Fy9eZMmSJfTt2zdfnalTp/LJJ58QGxtLkyZNmDJlCq1bt7ZPwDeiUhV7Ol1F5uLkZv2KgQaN67FuxR/grcaoVxPoHoparbHVrVGjBjqdjh07dtg2M0lKSuLEiRN06tSp0PP7+PgAcPHiRZo1awaQbyF0IYQQ4r9WR64m2ZRMoFMgnaoVfn8pT5KYugVTp05l6tSpmM3mMmvjlSEzALCYzRw+s4udR1dzKmEf53LOE6PNIkGrJkYPMaTxt3IQLhyEC98RkKsQbHYi2BhCbd+WtG3UmxrB9cssTiGEEELYX0ZGBk2aNGHEiBH079+/wPMLFixg7NixTJs2jTZt2jB58mS6devG8ePH8fX1BaBp06bk5eUVeO26desIDJRR2iXl4erHi6NeZNGPv/LKk68w/LnheLsdJy02k9+WrOC7777D2dmZxx57jJdffhkvLy98fX154403briDroODA3fccQcfffQR1atXJy4uzrbmlRBCCPFfiqLw07GfALi/7v1o1fZPC9k/gkpo1KhRjBo1itTUVNzc3Mq0LbVGQ6Nad9Co1h35yk+c3cffh1dxIm43503niNGkc0mn5qJOxUVdJrs4BnHHYP1cfPIsVMtzJFgfTC2f5rSp35O6Yc1Q3aCTI4QQQojKo0ePHvTo0eO6z0+aNIknnniC4cOHAzBt2jRWrlzJrFmzGDduHCCjbMpDrZp12Lp1G2NfHM3IQU+Sk5NLYHAA3e7pZks+ffLJJ6Snp9O7d29cXFx48cUXSUlJueF5Z82axWOPPUaLFi2oU6cOEydO5J577imPtySEEKKS2Ru3l6OJRzFqjAyoNcDe4QCgUq6dkC6K5WpiKiUlBVdXV3uHQ8zFk2w9uJzjsTuJyT7LOXUa53WFb3nsmWchJM9IkC6QcM/GtKrTnSa126HWaAqtL24vGRkZODs7A5Ceno6T0+0zZUIIIcpSRbv3F0alUuWbypeTk4OjoyOLFi3KN71v6NChJCcns2zZsiKfe+PGjXz11Vc33ZXPZDJhMplsj1NTU6lWrVqh1y07O5vIyEiqV6+O0WgsciyVXUZmOnHpZ8lUgwoIdgzA1dHT3mHdUFX9WQkhxO3kxY0vsu7sOgbUGsD4duPLrJ3i9JlkxNRtpFpALR4IGJuv7FJCDH8dWM7R89uJzozkvCqFczqFRK2aRG0O+4iClCjY+Ruu2y2E5OkJUvtT3aMBzWt2oVWDu9FqdYW2J4QQQoiKLz4+HrPZjJ+fX75yPz8/jh07VuTzdOnShf3795ORkUFwcDALFy6kbdu2hdb98MMPmTBhQonivt05OToTqKnBhZTTZKrhXOZFggC3Cp6cEkIIUXnFZsSyPno9AEPqDbFzNP+SxNRtzs+rGgPuegZ4xlaWnHqZv/Yv51DMVqIzTnKeJKJ1CqkaNYc0eRziHKSfg31rcdxjITRXR5DKh+pu9WgSfhd3NOqOweBgvzclSsxoNLJz507b90IIIcTN/PHHH0Wu+9prrzF27L8fll0dMSXyMxiMBLr9m5w6n3kRFVT4kVNCCCEqp1+O/4JZMdPKvxW1PWrbOxwbSUxVQe6uPtzbcQT3MsJWlp6ZyrYDKzkYtZmotOOcUxKI1pnJVKs5ajBzlFjIioXDGzAefJPQXA2BKm9CnWvTKOxO2jXuhbNT2a63JUqPRqOhVatW9g5DCCFEOfD29kaj0XDp0qV85ZcuXcLf379M2jQYDBgMhjI59+3GYDAS4FaDi9eMnApGklNCCCFKV3ZeNgtPLATgoboP2Tma/CQxJQBwdnTlnjse5J47HrSVZedksuPgWvae2UBUylHOWy5zVpdHllrNcYPCcS5DzmU4sRXd8Q8IyVERhAehTrVoGn43HZvdh4NR1i4SQggh7Emv19OiRQvWr19vW2PKYrGwfv16nn32WfsGJwAwXklOxaacJuNqckoFrg6SnBJCCFE6VkeuJtmUTIBTAJ2qdbJ3OPlIYkpcl1HvSKcW/ejUop+tLDc3h91HN7D71B+cSTrEeXMsZ7U5pGvUnDbAaZIgbyc/ntiJw7H3qZ6jI1QTSG3vFnRsMpA61ZvY8R2Jq3Jycvjiiy8AGD16NHq93s4RCSGEKIn09HROnTplexwZGcm+ffvw9PQkJCSEsWPHMnToUFq2bEnr1q2ZPHkyGRkZtl36hP0ZDUb8XcOJTT1NhlrFuYyLBCsqXB097B2aEEKISk5RFH469hMAD9R9AK26YqWCZFe+EqgMO/OUB4vZzP5T29h1bC2nEw4QnXeOSJ2JjCvbHl8rINdCqNmVMIdaNAmNIKLlQJydqu61sxfZlU8IIW5NRb33b9y4kbvuuqtA+dChQ5kzZw4AX331FZ988gmxsbE0bdqUL7/8kjZt2pRpXFOnTmXq1KmYzWZOnDghu/IVQVZ2FpeuJKdUQLBTIK4OFSM5JT8rIYSonP6J/Yfha4dj1Bj5feDvuBvdy7zN4vSZJDFVAhW1c1oR5OXl8Pehdew4sZrTKYc5SwIxOgVFpcpXz2BRqJ6rIUTlRy3PZrRtcB+Na9+BqpCklig9kpgSQohbI/f+W3Oj6ybJjoIqanJKflZCCFE5jf5zNH/G/Mmg2oN4u+3b5dJmcfpMFWv8lrhtaLV6OjS9lw5N77WVxSWd489/FnLowlYiTWeJ1GaSplFzzGDhGBdZl36RqTtW4bvVQlieE6HGcBoFd6JTi4F4uvvY8d0IIYQQQpQfB6MDfko4l9LOXJnWd8G6IHoFSE4JIYSoXGLSYtgQswGAh+s9bOdoCieJqVtw7bB0UXS+HsE80PUF4AXAOgXwn+Mb+fvICk4kH+CscplonYU4rZo4bRY7OczCc4fRxUyleo6KEHwJd29Em7q9aVE/Ao1WY983JIQQQghRRhwcHPFDklNCCCFKZv7R+SgotA9qT7h7uL3DKZRM5SsBGc5f+pJS4/hzz68ciNlMZNYZIrUZJGtUBep55VmonutANX0INbyb06JuN+rXaIFaI1MAi0Km8gkhxK2Re/+tuV2n8imKwsiRI1m0aBFJSUns3buXpk2blmobmVmZXE47Q3oFmNZXmX9WQghRFaXnpNNlURcycjOY1mUa7YPal1vbMpVPVFoerr4MiHiaATwNWDt8B09tZ8vhZZxI2MtZyyWidGYStGoStCb+4SQknYTtC/DZYqFaroEAjT+h7g1oXP0uWjTqjNEgHSchhBBClL41a9YwZ84cNm7cSHh4ON7e3iU6n0qlYsmSJfTt29dW5ujgiA/hcCU5JSOnhBBCFNWSU0vIyM0g3C2cdoHt7B3OdUliSlRoKpWKxrXa0bjWv/+I0jKT2bh3MXujNhCVeYbzqlQu6OCyVs1lbS4QA5kxcHgNrgcshORqCMCbYKda1K3WgdaNuuPtKWtWCSGEEGXtdl/+4PTp0wQEBNCuXdl29h0dHPFRqkN6pCSnhBBCFInZYmbe0XkAPFz/YVSqgjORKgqZylcCMpy/4khOj2frwZUcjN7K2bSTnFMSOaczk1fIPz6jxUJIrooAsxtBxjBq+LemVf1ehIXUqND/WEuT2Wxmy5YtAHTs2BGNRtbrEkKIopB7/625HafyDRs2jO+//972ODQ0lGnTpvHee+9x6NAhNBoNbdu25YsvvqBGjRoA5OTkMHbsWH799VeSkpLw8/Pjqaee4rXXXiMsLIyzZ8/mO19UVFS+NjMyM4i/kpyyx7S+yvqzEkKIqmj92fWM2TgGN4Mbvw/8HQetQ7m2L1P5RJXj7uxNr7ZD6dV2qK0sJzebncf+YM+pDZxJPkJM3iVitDlkqdWcMMAJUoEDEHcAzaUZBOda8M0z4Klyx8cQTKB7PWpWa02dmq3wdHez35srAxqNhoiICHuHIYQQQhSgKApZeVl2adtB61DkD6muJpymT5/Orl270Gg0bN68mbFjx9K4cWPS09N5++236devH/v27UOtVvPll1/y22+/8csvvxASEkJMTAwxMTEA7Nq1C19fX2bPnk337t0L/dDIydEJ+M/IKZUKV6N7KV4FIYQQt4MfjvwAwODag8s9KVVckpgSty29zkiHRvfSodG9tjKLYuFI1E52HFvHicv7iDGdI1qTSYpGxVm9hrP6PCDeeqTug8M/4XrATGCuCi+zA15qL7wdQgn2akDt0HaEhTfEzali/yMXQgghKpOsvCzazG9jl7Z3DNmBo86xSHXd3NxwcXFBo9Hg7+8PwIABA/LVmTVrFj4+Phw5coSGDRsSHR1NrVq16NChAyqVitDQUFtdHx/rMgPu7u628xXGydEJRQmDjChrcir9PMEouBplWp8QQgirw/GH2RO3B61Ky/117rd3ODcliSlRpahVahpWv4OG1e+wlSmKwvnEM/xz7A9Oxh7kfFokl/LiuaTK5LIWUjUaUjUAJuCC9UjYjip+Bv47zPjlqXE3O+KicsVN54O7QxC+bjUI8q2Pd0ANfHz8cHHQ2+kdFy43N5fp06eTkZHBk08+iU6ny/e8wWBAq9Xa6ubk5Fz3XNfWzcvLw2QyXbeuXq+3tVWcumazmezs7OvW1el06PX6fHUdHR2rzNRMIYQQFcPJkyd5++232bFjB/Hx8VgsFgCio6Np2LAhw4YNo2vXrtSpU4fu3btz7733cs899xS7HWcnZyDsmuTUlTWnJDklhBACmHloJgA9qvfAz8nPztHcnCSmRJWnUqkI9qpBcPsaBZ7Lzs3ixPm9HIzcxpnLRzifEcMlcyIXNTlkqFVc1Gm5qAPIvnLEgfkwJAKJ4HnYjG+eBfc8DS4WI86KKy5aL1wMfrg4+OPuHISbWxCO7gE4e/jh7uqKu5MBvVZdpu85JyeHZ599FoBXX321wPMrVqygV69eAMybN4/hw4df91y//PILgwYNAmDJkiUMHjz4unVnz57NsGHDAFi7di333nvvdet+9dVXjBo1CoAtW7Zw1113XbfuxIkTefnllwHYs2cPrVu3pn379mzZskWSU0IIUck4aB3YMWSH3douid69exMaGsqMGTMIDAzEYrHQsGFD2wc8zZs3JzIyktWrV/PHH38wePBgunTpwqJFi4rdlrOTMyhhqDKjSJPklBBCiCuiUqL44+wfAAxveP2/4yoSSUwJcQNGnQONw9rROCz/bjuKopCUlcDR6B0cit7JheQoLmfFkWhOIVHJJFFtxqSGRI2GRI0GDAA52KYJctz6MBE0CQruZgueFjNuZgVnsxqjWYeDYkSvOKJTOaBXO6HTuGLQuWDQueNg8MLBwQu9owdaozMagxMagyNaoyM6gxNGgx6DVoNBq8agU//7vVaNSqXC0dGR9u3bs3Xr1nK/pmUtIyMDgK1bt5KZmYmTk5OdIxJCiKrrVnblU6lURZ5OV5EkJCRw/PhxZsyYQceOHQH466+/CtRzdXXl/vvv5/7772fgwIF0796dxMREPD090el0xbpWzs7OKIRC5tlrklOy5pQQQlRlcw7PQUEhIjiCWh617B1OkUhiSohboFKp8HT0pn3dXrSv26vA84qikGJKITb1LFGxh4iMO8GFlGguZ10iPjeFFCWLNFUeGWoFs0pFglZDAv9d5PTqKKxC5FgPpyQLThYLLhYLzhYFZ4sFZ4sFRwsYLSqMFjVaiwaVokFl0aJWtKgUPSp0PNzTgQe63oMaAyoMqNChUhlBbeT8wT+ZcXwreWoDuYqGTz99H7NGj0WtR9EYUDR6FI0e1HpO5bowcdEmFI0eiz6MdxdbF4DVqtRoNSo0ahXaKwdGAz/vjEarUaPybcjC7SfRqq11NBoVOrUajVqFTqPCYDBw6HwKWo2KgDpNORx16cpzatRX6lx9bDToURQFlUpF8+bNS/vHLYQQ4haNGjWKUaNG2XbmuZ15eHjg5eXF9OnTCQgIIDo6mnHjxuWrM2nSJAICAmjWrBlqtZqFCxfi7++Pu7s7AGFhYaxfv5727dtjMBjw8Lj56CcXZxe4JjkVk36eaiDJKSGEqIIuZVxi2ellADzW6DE7R1N0kpgSogyoVCrcje64G92p69vkuvVyzbkkmZJIzEogMf0iCSnRXEo+z6W0WBKz4knOSSHTnEWmxUSmkkOWkkemykzuldlpGWo1GWo1cUWKyoIto3UDWkXBqCgYLQoGRcFBsfznsYLRrGDMtZY7pFufM155nYPFgs6iQqNo0CpqNBYN6qtJMYsGFB0oOnIVHSasRw46MhSt7fsctJgUPTloybHV0WJSdP+pc/V7a3meSkdunsX2Xjp8+Ad6Rye0amuSTHslkWXQqtFfPTTWr7orXw3XlF1brv/P63Sa/PWsr9Ng1Kkx6jQYdRoc9BqMWjVaTdlOzRRCCGF/arWan3/+meeff56GDRtSp04dvvzyy3y74Lq4uDBx4kROnjyJRqOhVatWrFq1CrXaep/47LPPGDt2LDNmzCAoKIioqKgite3i7AJKKGRJckoIIaqyuUfnkmfJo7lvc5r6NrV3OEWmUhRFsXcQlc21w9JPnDhBSkoKrq6u9g5LVCE55hzSc9NJz0knLTeN9Jx00k1ppJuSSM9OIt2UQrophbScVLJyM8nKzSIrL4usPBPZZhPZ5hyyLTmYlDxMihkTeVhu3mypcrBcSWzZklr/Pna4Jsl1tcxZseB0ZVSYk8WCk/Lv984WBSeLBT2QkaPg/GEaAOmvuaDTaf9NZKEnR8mf7MpBZ0twma48zlZ0ZOBAJkYyFAMZOJChGMngynH1e8WBDKzPmwuMePuXTqPCqNVg1Gtw0FmTVw46DQZd/sf5E1oaHPRqHPRanPQanAxanA1anAz/Pr76vSS+hCg/V0f+yL2/eG503bKzs4mMjKR69eoYjUY7RXh7SE1LJTkrmjS19ROsYOdA3EpxzSn5WQkhRMWVYkrhnkX3kJmXydS7p3Jn8J12jac4fSYZMXULqtKwdFEx6TV6PDWeeBo9S+V8iqKQa8klKy+L7LxsTGaT9XtzNtl51iPLnIUpz2R9bM621c02Z5N9NfGVm052bhbZeVlk5WVeqWciy5xNtjmHHCXP1maWWk0WkHT9fE6x6RQFh6w84DgAT/j74KFTXUleWQ9XSzaulkxcLRbczGZcLRaCLRZcryS4bjXFY0JH1jWJqzTFSLriQCqOpCpOpJodSc10IhVH0hTHK+WOnMOJVMWRVJwwoQOKv1i7Qau2Ja0c9Rrb985XHjsZtLg66HA1anFz0F35Xoerw7+PnfVa1GpZKF4IISozVxdXIARV1llS1WrOpV8AKNXklBBCiIrpl+O/kJmXSU33mnQM6mjvcIpFElNCCFQqFXqNHr1Gj5uh7JKtZos5X1Lr2uSWdURX1r+JsLwssszWx5m5mWTmZZKek05GbgbpudavV7/PyssCIFelwqT5N9O132hEbSh6qkmNChe1Hle1HjeVFlfUuCkqXC0KHhYznmYzHrk5eOWY8MjJxDM7DbdcExrAQC4GcnEnzZpbuoUcj1mlI1vrTJbahSyNE2kqV1JUriTjQoLiQrzFibg8Z2LznLiY40ic2ZlknDHlgSkvh4SMG0/TvOF7V4HLlWSVq9GauLImrazJKw8nPV5Oejwc9Xg5W796OulxNeokoSWEEBWIq4srihIK2dcmp1S4ybQ+IYS4bWXnZTP36FzAurZUZduZXBJTQohyo1FrcFI74aQr3Z3y8ix5ZOZlkpmbSWJ6Il+e/JIccw79I/qTq8q1Tnu8MvUxNSeVVFMqKTkppOakkmJKIS0njay8LCwopFhMpFhMxBT6Bq4cRgBHwBG1So273hVPvRseOmc8tY54aIx4qg14qbT4Kmp8zAq+eXl45mSjMaVA9n8OUyooFjRKLk65STiRdPM3rbtyABaDG3kGD3IMHpj0HmTovEjXeZGq9SJR7U4iHlyyuHEhz5WEHDWpWbmkZueRkpVLalYupjwLFgVSsnJJycoFsop87TVqFR6OOluiytNJb0tieTrp8XUx4utqwNfFgI+LAUe93HaEyMvLY/78+XTr1g0/Pz97hyNuQ26u1pFTZEdfSU6dt5ZLckoIIW5LS08tJTE7kSDnILqHdbd3OMUmfyEIISo9rVqLq94VV70r/k7+TPtkWrHPYTKbSDWl2pJV135NNiWTnJ1MkimJhKwEErMTSTIlkWJKwaJYSDQlk2hKvmkbGpUGLwcvfL198XEMx9fRFx8HH3wdvPHVueKjMeCvMuBqzoPsZMhKgsyEa47E/I+zkgEFtSkFvSkFPVE4A143CsLgBs6+4OEHIX7g7Eeuoy+ZRl/S9P4k632JV3mSYoLU7DxSs3JJzswhMSOXpEzrqKykjBwSM3JIN+VhtijEp+cQn1600VrOBq0tSeXrasTX5d+kla+LkQB3I4FuDjjoS3GOpxAVjFar5amnnuLo0aP2DkXcxtxc3UAJAdO1ySlFpvUJIcRtJs+Sx5zDcwAY2mAoWnXlS/NUvoiFEKIMGDQGfBx98HH0KfJrci25pJhSSMhKuLK7YmK+5FVCVgKXsy4TlxlHQnYCZsVMXGYccZlxkHD98zrrnAl0DiTQKZAA5wCCAmsQ4NSBQOdAApwC8DR6WofnWszW5NS1yaqMy5AeB+mX8h9pl8BsAlOK9Ug4aWtPB7hdOYIBUIGLP7gGgVsQuFWDale+dw0G91rg5IPJbCE5M5eE9JwCSavEjBzi001cTjMRl2YiLi2b7FwL6aY80k15nInPuOG19XDUEejuQICbA0HuRgLcHQh0v/K9mwO+LgZZ9F1Uaq1bt2bfvn2EhobaO5Qyde2GMaL8ubm5oaRUA1OMbVqfXmPAQedo79CEEEKUknVR6ziffh5Poyd9a/a1dzi3RBJTQojbisVisY1CqFevnm0L7rKgU+vwdvDG28H7pnXzLHkkZidyOdOaqLqasLqcdZlLmZds5cmmZNJz0zmRdIITSScKPZdRYyTAOYBA50CqOVcj1DWUENcQQoMaEegciE6tK/giRbFOG0yPg/TY/MmrtFhIOQ8pMZB6ASy5kHbRepz/5zpv3gmDRxh+HmH4eVYHjzDwqA7B1cEtDLT6/zSvkG7KsyapUq2Jqstp+RNXcakmLqZkk27KIykzl6TMXA5fSC20eY1ahb+rkRBPR0K9HAnxciTU08n2vauxkGsgRAXyzDPPMHbsWGJiYmjRogVOTvmnODdu3NhOkZWu4mwYY7GU9/6wVYO7mzskgyUnhnS1mpiUs9TwrI1GXfyRqfIzEkKIikVRFGYemgnAkLpDcNA62DmiW6NSFEWxdxCVlWwZLUTFk5GRgbOzMwDp6ekF/tir6DJzM4nNiOV8+nkuZlzkQvoF65FxgYvpF4nLirvh6zUqDYHOgdZElYs1YRXiEkK4ezgBTgGoVTdJ1Fks1lFXqeeuJKvOQep/vqbFAje4dajU1pFVHqHgVRO8a1sPn9rW8pskC1Ozc7mQnMXF5GzOJ2dZv0/59/vYlGzyLDe+dXk46gjxciL0SuKqurcTNXycqeHrjLNBPpMRt6607v2FJc1VKhWKoqBSqW67EUY3um4Wi4WTJ0+i0Wjw8fFBr9dXukVbK4OkpMskK0nkqVQ4axwJcA0q8msVRSEnJ4fLly9jNpupVatWmX7wI4QQomi2nNvCM+ufwVHryLqB68p0I6viKk6fSXrnQghRgTjqHAl3DyfcPbzQ53PMOcRmxHIh4wLn084TnRZNdGo00WnRxKTFkJWXRUxaDDFpMWxla77XOmgdqOFWg3D3cGq416Cme03C3cIJdA78N2GlVoOLn/UIalF4kHkmSI6GpChIjLR+Tbr6NQpyMyEl2npEbcn/Wq0DeF+TrLp6eNUEnRHAuiugv466/oXfwKzrWpk4l5TJ2QTrEZ2YydmEDKITM4lPz7ky4iqZ/THJBV4f4Gakho8zNX2tiaoaPk7U9HXGx9kgfwyLchMZGWnvECoMtVpN9erVuXjxIhcuXLB3OLctRVFIT0siTZ1HHJBoSMKxmJuRODo6EhISIkkpIYSoIK6OlhpUe1CFSkoVl4yYKgEZMSVExVPZR0yVhKIoxGXGEZ0WzdnUs7ak1dnUs0SlRpFnySv0dQ5aB6q7Vaeme03qetalrmdd6njWwVV/C/+vKYp1mmBSFCSegYRTEH8C4k9av7fkFv46lcaanPJrAP4Nwe/K4RoIxUwWpZvyiE7IJDoxg7MJmUQlZHLmcjqnL2cQn2667utcjVrq+rtSN8CFegGu1AtwpY6fiyzELvKRe/+tKcp1UxSFvLy82260WEUSFXuZdWuGssJNiwEVX3T5mkCXoo2c0mg0aLVaSeALIUQFsefSHoausS52vqb/GvycKtZOv8XpM0liqgSkcypExVOVE1M3kmvJJSYthtPJpzmdfJozyWc4lXKKqJQocq+TLApyDqKeZz3qeNaxffVz9Lv1P0rMeZB89kqi6sS/CavLx627EBbGweNKkqqB9WtgU/CpB5pbG/CbkpnLqcvpnI5L5/TldE7FpXPqcjoxiZkUNjtQpYLqXk5XElXWhFX9QFf8XY3yx1kVVZr3/tOnTzN58mTbunj169dn9OjR1KhRozRCrVCkz1RxLF2xlCXnXmGPg4HaBj9+HrQanUbW5RNCiMpm5O8j2XZhGwNrD+Sdtu/YO5wCJDFVTqSTJUTFI4mp4smz5BGTFsOZ5DOcSDrB0cSjHE88zoWMwqfTeBo9aejdkEbejWjs3ZiGPg1vbWTVtRTFugh77CG4dAguHbZ+jT8BhY3y0jpAQGMIbA5BzSGwGXjWuOnaVTeSnWsmMj6DY7GpHL2YxtGL1q/XG2Hl42KgSbA7TYLdaFLNncbBbrg76gutK24vpXXvX7t2LX369KFp06a0b98egK1bt7J//36WL19O165dSyvkCkH6TBWHxaIw+8uRzHb9ixSNhkfD+/Fyx3ftHZYQQohiOHj5IENWDUGj0rCi3wqCXYLtHVIBkpgqJ9LJEqLikcRU6UgxpXAs8Vi+IzIlErNScIpNmGsYjX0a09i7MY18GlHLo1bhOwMWV57JOprqaqIq9gBc2AemQnbqM7hBYBPrulghbaFaa+toqxK6nGa6kqRKtSWrTl1Ox1zI8KpQL0eaBFuTVM1DPWgY6IZeK+uw3G5K697frFkzunXrxkcffZSvfNy4caxbt449e/aUNNQKRfpMFcvFpHRWzujEF345AHzb+WvaVeto56iEEEIU1bPrn2XTuU3cV+M+3uvwnr3DKZQkpsqJdLKEqHgkMVV2svOyOZF0goPxBzlw+QAHLh/gXPq5AvUctA408WlCS7+WtPBrQSOfRhg0htIJwmKBxNNwfg9c2GP9GnsA8rIL1vWtDyF3WBNVIXeAW7Vir1dVmKwcM4cvpLD/XAr7Y5I5cC6ZqITMAvWMOjVNq7nTKsyTVmGeNA/1kB0BbwOlde83Go0cPHiQWrVq5Ss/ceIEjRs3Jju7kN/pSkz6TBXP+u272LzrQRa7OeChMrB40Bq8HbztHZYQQoibOJpwlMErBqNWqVl23zLC3MLsHVKhZFc+IUSVpdPpeOmll2zfi9Jj1BqtI6N8GvNQvYcASMxO5FD8IVui6lD8IdJy0/j74t/8ffFvAPRqPY18GtkSVU18muCoc7y1INRq8K5lPZrcby0z50LcUWui6twuiP7butB63BHr8c8saz3XIGuCKqwDhEeAR/VbSlQ56DW0DPOkZZinrSw5M4cDVxJV+88ls/tsEkmZufx9JpG/zyRaQ1dB/UBXWoZ60qa6J21reMn0vyrMx8eHffv2FUhM7du3D19fXztFVfqmTp3K1KlTZUHzCujutq04e/AxaubM4ZQeXv/9Oab1nvfvLq1CCCEqpOkHpgPQLaxbhU1KFZeMmCoB+fRPCCHysygWTief5p9L/7D70m7+if2HhOyEfHW0ai1NfZrSLrAd7QLbUc+rXun/IZQeBzE7rEmq6O1wcX/B9arcQiC8kzVJVf1OcC69ZIDFonAmPp2dkUn8E5XIzqhEziVl5aujUkGjIDfa1/SmQ01vWoR6YNTJDoAVXWnd+999910+//xzxo0bR7t27QDrGlMff/wxY8eO5a233iqtkCsE6TNVTKnZuSz9vBdf+p/HpFbzUtPnGNrkSXuHJYQQ4jpOJp2k/2/9AVjSZwk1PWraOaLrk6l85UQ6WUIIcWOKonA29ey/iapL/xCbEZuvjrvBnTsC7qBdYDvaBrbF38m/9APJyYDzu+HsNjizyTqy6r+7Efo2sCapanWF0PagLd3RTBdTstgVlcSuyES2n0ngVFx6vucNWjWtwjxpX9ObO2t7Uz/AVXb+q4BK696vKAqTJ0/ms88+48IF62YDgYGBvPzyyzz//PO33c9e+kwV165jkexd0Z0pPnq0ioq5vX+igVcDe4clhBCiEK9seoXVUavpGtqVSRGT7B3ODUliqoxdOyz9xIkT0skSogKxWCxER0cDEBISgroEO7WJ0qcoCufSzrHtwja2XdjGztidpOfmT9DUcKtBp2qduKvaXTTyboRGXQajiEzp1pFUZzZC5CaIPZj/eb2zNUlVuxvUugdcSj9ZFpuSzdZT8dbjdDyXUvPvABjgZuSuur7cXdeXdjW8cdDLaKqKoDQSLHl5ecyfP59u3brh5+dHWloaAC4uLqUZaoUiiamK7Yef57Mn8S3WOzkSrPdk0cBVOOlkjUYhhKhIIlMiuW/pfSgoLOy9kLqede0d0g1JYqqcSCdLiIpHFj+vXHItuRyKP2RLVB2KP4RFsdie9zR60im4ExHVImgb2BYHrUPZBJIRD5Gb4fR6OPk7pF/K/3xAU2uSqk4P6/elPJpFURROX07nr5PxbDlpTVRl5/57HQxaNe1qeNG5nh931/Ul0L2MroO4qdK69zs6OnL06FFCQ0NLMbqKS/pMFZspz8z8zx5nvvffxGq19KnWhfc7f27vsIQQQlzjjb/e4LfTvxERHMGUu6fYO5ybksRUOZFOlhAVjySmKrcUUwrbLmxjY8xGtpzbQlpumu05g8ZA24C2dA7pTOeQzrgZ3MomCIsFLu6Dk+vgxFrrourXcg+Ben2gfl8IamFdkL2UZeea2X4mgT+PxvHnsTjOJ+dfn6pJNXd6NvSnZ6MAqnne4kLy4paU1r0/IiKCMWPG0Ldv39ILrgKTPlPFd+JCIvu/78x7AXlYVCo+bP8B99bsbe+whBBCADFpMfRe0huzYuanXj/R0LuhvUO6KUlMlRPpZAlR8Uhi6vaRa8llz6U9bIzZyIaYDZxPP297TqvW0i6wHd3DunNXtbtw1juXXSDpcdZRVCfWwKk/IDfz3+dcAqF+H2uiKuQOKINph4qicOJSOuuPXWL90Tj2RCdx7Z27UZAbPRr507NhAGHe8vte1krr3v/LL7/w2muv8cILL9CiRYsC/1c1bty4pKFWKNJnqhwWrt3IxSPDmeHpjKNKx6K+y6jmWs3eYQkhRJX35l9vsuz0MtoHtmda12n2DqdIJDFVTqSTJUTFI4mp25OiKJxMPsmG6A2sO7uOE0knbM/p1XraB7Wne1h3IqpF4KgrwxFEOZnW5NSRZdbRVDn/jujC2R8aDYQmD4Bfw1Kf7ndVXFo2aw9fYtWBi+yITMByzV28foAr/ZoFcV/TQHxdjWXSflVXWvf+wta/U6lUKIqCSqXCbDaXJMwKR/pMlYPFojBjyttsM/7MHqORBq7h/NhnETqNzt6hCSFElRWZEknfZX2xKBbm95xPI59G9g6pSCQxVU6kkyVExSOJqarhTPIZ1katZU3UGs6knLGVO2gd6Bralftq3EdL/5aoVWW4+H1uNpzZAEd+g+MrITvl3+d860Pj+6HRIHALKrMQ4tNNrDt8idWHLrLtdALmK1kqtQra1/RmQPNg7mngh6NeW2YxVDWlde8/e/bsDZ+/3daekj5T5XExOZO/ptzL5KBYUjUaRtR7lBdav2zvsIQQosq6uhNfRLUIpnSu+GtLXSWJqXIinSwhKh5JTFUtV0dSrYlcw9qotUSnRdueC3QKpE/NPvQJ71P2U1HycqxrUh1YYJ3yZ8658oQKqneEJkOgQV/Qld2i5YkZOaw8eJEle86xJzrZVu6o19C9oT8DWwTTNtwLVRmN5KoqSuPen5ubS926dVmxYgX16tUr5QgrJukzVS5rdx0m7c8+TPC3jkD9tuu3tAtsZ+eohBCi6jmeeJyBywcCsKj3Iup41rFzREUnialyIp0sISqe/yamHB0dyczMvG59rVaLwWAArEmOG9XVaDQYjf9Oj8rIyCiVumq1GgcHh1uqm5mZSWH/jTs6Ola5BISiKByIP8CyU8tYE7km38LpLfxa0LdmX7qHdceoLeMpbllJ1ql++xdA9LZ/y41u0PgBaDEM/OqXaQhR8Rks2XuepfvOczbh39/p6t5OPNi6GgNbVMPTSV+mMdyuSuveHxQUxB9//CGJKVFhfTNzBvGZ7/OLqwteWhd+7b8cLwcve4clhBBVyug/R/NnzJ/cE3oPn0V8Zu9wikUSU+VEOllCVDwmk4mxY8cCMGnSJFJTU/H19b1u/aFDhzJnzhwgf1KrMAMHDmThwoW2xzdK/PTs2ZOVK1faHjs5OV036dWpUyc2btxoe+zj40N8fHyhdVu2bMmuXbtsj8PCwgqdEtS+fXu2bNlS5ZJTV2XnZbMhZgPLTi1j24VtKFhvda56V/rW7MvgOoMJdS2HqVJJZ+HAL7DnB0j5dzQXwa2tCaoG/UBfdmtiKYrCnugkFu0+z/L9F0g35QGg16jp1tCfIa1DuCPcs8r+ntyK0rr3f/DBB5w4cYLvvvsOrfb2nWo5depUpk6ditls5sSJE9JnqkRSs3NZ+ukwlvj9wym9ng5+rZnabUbZTpEWQghhczj+MA+sfAC1Ss2SPksIdw+3d0jFIompciKJKSEqvsuXL1fJxBTIVMarYjNiWX56Ob+e/DXfzn5tA9pyf9376RTcCa26jBMDFguc+RN2z4Hjq8FiTRBhcIPmj0DrJ8GjbBNlGaY8lu+/wPyd0Rw49+96WOE+TgxvF8aAFsGyFlURlNa9v1+/fqxfvx5nZ2caNWpU4N/q4sWLSxpqhSJ9psppx8kLJC/oxhtBFkxqNa+0fJlHGjxq77CEEKJKePqPp/nr/F/0Du/NBx0/sHc4xSaJqXIinSwhKr6bTc+73abyZWVl0alTJwB27dqFo2MZ7lBXyZgtZrZe2MrPx37mr/N/2UZR+Tn68UDdBxhUexBuBreyDyQtFvbNs46iSoqylqnUUPdeuOMZCLmjzHb0u+rQ+RTm74xm2d7zZORYd39zNWp5sE0IQ9uGEehedmthVXalde8fPnz4DZ+fPXv2LZ+7IpI+U+U1Y9FKHKKe5mMfN7SomXfvT9T3KtvpyEIIUdXtjdvLo6sfRaPSsLzv8rJfL7UMSGKqnEgnSwghKqdzaedYeGIhS04uIcmUBFh39BtQawAP13+YIOey20nPxmKBU7/D31/DmY3/lgc0sSaoGg6AMt6iPd2Ux6+7zzF7ayRRV9ai0qhV9Gjoz4gO1Wke4lGm7VdGcu+/NXLdKi9TnpmZn43juMti/nRyJNQxgF/6LsVRJx98CCFEWXls7WPsjN3JgFoDGN9uvL3DuSWSmCon0skSQojKLcecw+rI1Xx/5HtOJp0EQK1Sc0/oPQxrMIwG3g3KJ5BLR2DHNOuufnnZ1jK3atB+NDR7uEx38wOwWBT+PBbHzL8i2X4mwVZ+R7gnz3WuRbsaspvfVaV578/Ly2Pjxo2cPn2aIUOG4OLiwoULF3B1db3htOLKSPpMldvxi6mc+bYnn1VL4JJWS9/w3vyvEk4rEUKIymDbhW2M/H0kOrWOlf1WEuAcYO+QbondElO5ubnExsaSmZmJj48Pnp6epXXqCkk6WUIIcXtQFIXtF7Yz5/Actl/cbitv7d+ap5o8RSv/VuUTSEYC7J4NO76FjDhrmZMPtB0FLR8DY9nfa45cSGXW1kiW7TtPrtnaRWhazZ3nOtekc13fKp+gKq17/9mzZ+nevTvR0dGYTCZOnDhBeHg4o0ePxmQyMW3atFKM2v6kz1T5zV+/C9+dg3gxwBmLSsXHHT+mZ3hPe4clhBC3FYti4YEVD3A08SgP13uYV1u/au+Qblm5JqbS0tKYO3cuP//8Mzt37iQnJwdFUVCpVAQHB3PPPffw5JNP0qpVOXXqy5F0soQQFU1mZqbt/1tZY+rWHE88zveHv2d15GryFOsi5S38WvB0k6dp7d+6fBIzuVmwdy5s/fLf3fyMbtB6JLR9BhzKfordheQspm8+w087ozHlWQCoF+DKs3fVpEdDf9TqqpmgKq17f9++fXFxcWHmzJl4eXmxf/9+wsPD2bhxI0888QQnT54sxajtT/pMlZ/FojBp6hc4mCcxzcMNJ42BRfctJdgl2N6hCSHEbWPFmRW8tuU1nHXOrOq/Cg9j5V1WodwSU5MmTeL999+nRo0a9O7dm9atWxMYGIiDgwOJiYkcOnSILVu2sHTpUtq0acOUKVOoVavWrTZX4UgnSwhR0Vy7s6DsylcysRmxfHfwOxafXEyuJReA5r7NGdlkJG0D2pZPgsqcCwcXwV+TIP6EtczoBu2ehzZPgaHsp3tdTjPx3V9nmLv9rG2h9AaBrrzUrQ4RtX2q3Aiq0rr3e3l5sW3bNurUqYOLi4stMRUVFUX9+vVvuBFDZSR9ptvDxZQsNn7+CKsD9rPXaCQisD1Tut5eo/uEEMJecsw59Fnah/Pp53m+2fM80fgJe4dUIuWWmHrwwQd58803adDgxmtwmEwmZs+ejV6vZ8SIEbfaXIUjnSwhREUjianSF5sRy6xDs/j1xK/kWHIAaObbjBdavEAz32blE4TFAseWw8aPIO6ItczJBzq+CC2Gg85449eXguTMHGZvjWLWX5GkmawjyVqFefBK97q0Cru9p+5fq7Tu/R4eHmzdupX69evnS0z99ddfDBgwgEuXLpVi1PYnfabbx6rdp3FYdS9jq2nIU6mY1mUa7YPa2zssIYSo9H44/AOf/PMJvg6+rOi/Agdt5d4lWRY/LyfSyRJCVDSSmCo7cZlxzD40m4UnFmIymwCIqBbBmOZjqOFeo3yCsJjh0GLY8D4kRVrLXIMg4jVoOgTUmjIPISkjh282neb7bVG2KX531fHh1R51qet/+98LS+vef//99+Pm5sb06dNxcXHhwIED+Pj4cN999xESEsLs2bNLMWr7kz7T7eWLWd9jSn+bH91cqe4UyK/9V6BTl+0uokIIcTtLzUml5+KepJhSmNBuAv1r9bd3SCVm18RUYmIiFosFb2/v0jxthSSdLCFERSOJqbIXlxnHN/u/YcnJJZgVM2qVmvtq3MczTZ/B38m/fIIw51rXoNo0EdIuWMv8G0G3D6F6x3IJITYlmy//PMmCXTGYLQpqFTzYOoSxXWvj5WwolxjsobTu/efOnaNbt24oisLJkydp2bIlJ0+exNvbm82bN+Pr61uKUduf9JluL7Ep2eyY3JNJ1WJJ1Gh4ueXLPNrgUXuHJYQQldbk3ZOZeWgmNdxqsKjPIrRqrb1DKjG7JKYOHTrEkCFDOHz4MABBQUEMHz6cV1555bb9w0g6WUKIikYSU+XnTMoZpuyZwh/RfwBg0Bh4pP4jPNHoCRx15bTofG427JwOmz8FU4q1rO690PVd8CqfUVxR8Rl8svY4Kw9eBMDFqGX03bV4tG0Yeq26XGIoT6V578/Ly2PBggXs37+f9PR0mjdvzkMPPYSDQ+Ueul8Y6TPdfr5b+jsup4bzno8HzhojKwaswcvBy95hCSFEpRObEcu9S+7FZDYxpfMUIqpF2DukUmGXxFTr1q1xdnbm/fffx8PDg+3bt/Pll1+SnZ3Ntm3b8PCovKvJX490soQQFY0kpsrf/sv7mfTPJPbE7QHA18GXF1q+QK/qvcpvYfCMeNj4IfwzGxQzqHXQZiR0ehWM5XN/2hmZyLsrDnPofCoA1b2deLNXPe6u51cu7ZcXufffGrlut5+07FyWfvwoKwJ2c8RgoH/Nfkxo/669wxJCiErnra1vsfTUUpr7NmdO9zm3zcYydklMOTk5sXv3burWrWsrUxSFQYMGYTQamTt3bmk0U6FIJ0sIUdFkZmZSv359AI4cOYKjYzmN3KniFEVhQ8wGPtn1CefSzwHWBdLHtR5Hfa/65RdI3DFY9wacso7iwtkfun8IDfpBOXRyzBaFX3efY+La48SnW9fh6tbAj/F9GhDgdnuMApJ7/62R63Z7+mnTfoK39uaZIDdUwE+9fqaB9403RRJCCPGvY4nHGLx8MAoK83rOo7FPY3uHVGqKc+8vtTH2LVu2JDk5OV+ZSqXi/fff57fffiutZoQQQtyAo6MjUVFRREVFSVKqHKlUKjqHdGZp36U83+x5HLQO7I3bywMrHmD8tvEkZyeXTyC+deHhX+GhReAZDumxsGg4zB0AiWfKvHmNWsXgVtXY8FInRt4ZjkatYu3hS3T5bBOzt0Zitsh+K0LcTgZ2aMR+BnJvegYK8OHf7yH7KgkhRNEoisLHOz9GQaF7WPfbKilVXCVKTPXp04e33nqLhQsX8tRTTzFmzJgC2xunpaXh5uZWoiArmqlTp1K/fn1atWpl71CEEEJUIAaNgScaP8FvfX+jZ/WeKCj8evJX7lt2HyvPrCy/P9hqdYWnt1t369Po4fR6mHqHdbH0PFOZN+9i1PFaz3qseK4DzULcycgxM2H5EfpO3crBcyll3r6oOKTPdHvTadTU7DWaAfFaHCwW9iccYsWZFfYOSwghKoXfz/7OP5f+wagxMrbFWHuHY1clmsr32muvsW/fPvbt22dLSDk4ODB48GCaNm2K2Wxm9uzZvPPOOwwcOLDUgq4oZFi6EEKIG9lzaQ//+/t/nEo+BUC7wHa8ecebVHOpVn5BJJyGlS/CmQ3Wx7714b6pENS8XJq3WBR+2hXNR6uPkZadh0at4qlO4Tx/dy0MWk25xFCa5N5/a+S63b4UReHjyZ/izZd84emOj9GT5f1X4aSTNQ6FEOJ6svOy6busL+fTz/NUk6cY1XSUvUMqdXZZY+rSpUu2JNXV4+TJk2g0GurUqcOBAwdKo5kKRTpZQoiKJisrizvvvBOAzZs335a7e1U2ueZcZh+ezbf7vyXHkoNRY+SZps/wSP1Hym8rYEWBQ7/CmnGQcRlUGugwxro4utZQLiHEpWUzYfkRVh6w7t5X19+FzwY3oUFg5RpVXdr3/pycHOLi4rBYLPnKQ0JCSnzuikT6TLe3XZEJmOb04INqqcTodDzW8DHGtBhj77CEEKLCmn5gOlP2TsHP0Y/f+v5Wfjs6lyO7JKYKk5WVxYEDB9i3bx8jR44sq2bsRjpZQoiKRnblq7iiUqL439//Y2fsTgDqedbj/Q7vU8ujVvkFkZEAq1+2Jqmg3EdPAaw6eJE3lx4iMSMHrVrFc51r8cxdNdBpSm3ZyzJVWvf+kydPMmLECLZt25avXFEUVCoVZrO5pKFWKNJnuv29P2Me7ZJe5Hk/H3QqLUv7LiPE9fZKsAohRGm4lHGJ3kt7k5WXxUcdP6JXeC97h1QmKkxi6nYnnSwhREUjiamKTVEUlp1exqf/fEqKKQWdWsezzZ5laP2haNTlOK3tyG+wcuy/o6fufAnufAU05TOCKz7dxBtLDrL2sHUZgMbBbnzxQDOqe1f839fSuve3b98erVbLuHHjCAgIKLA1dJMmTUoaaoUifabb36m4dA5MGcy6wBNsdXQgIrgTU+7+yt5hCSFEhfP6ltdZfmY5TX2a8kOPHwr0AW4XkpgqJ9LJEkJUNJKYqhzis+IZv208m85tAqCJTxPe7/A+oa6h5RdERgKsfgUOLbI+rtYG+s8Aj/KJQVEUftt/gbeXHSYlKxcnvYb3+jWkX7Pgcmn/VpXWvd/JyYndu3dTt27dUoyu4pI+U9UwccEf9Dn5EA8G+5CnUvFNl2/oENTB3mEJIUSFsfvSboatGQbAT71+oqF3Q/sGVIaKc++vHOPmhRBCiNuIt4M3UzpP4d127+Kkc2L/5f0M/G0g84/Ox6JYbn6C0uDkBQNnwoCZYHCFmB0wrQMcXFQuzatUKu5rGsSaMR1pXd2TjBwzLyzYz4u/7CfDlFcuMdhT/fr1iY+Pt3cYQpSqYT07sDG3B0NS0wD4eOdH5Jpz7RyVEEJUDLmWXN77+z0ABtQacFsnpYpLElNCCCGEHahUKvrV6sfiPotp49+GbHM2H+78kGfWP0NCVkL5BdJoIDz1l3XElCkVfn0MljwFprRyaT7AzYGfnriDF7rURq2CX/eco/eUvzh0PqVc2reXjz/+mFdeeYWNGzeSkJBAampqvkOIysjXxYi57WgGJip4ms1EpZ5l/rH59g5LCCEqhHlH5nEq+RQeBg/GNB9j73AqlHJJTKnVajp37szu3bvLozkhhBCi0gh0DmT6PdN5rfVrGDQGtp7fysDlA9l+YXv5BeERCsNWQadxoFLD/p9gegTEHS2X5jVqFaO71OKnJ+4gwM3ImfgM+n+zjUW7z5VL+/bQpUsX/v77b+6++258fX3x8PDAw8MDd3d3PDw87B2eELds2F2NmKd+kNGJyQBM2/cN8VkyOlAIUbXFZsTy9f6vAXihxQu4G93tG1AFUy5rTM2ZM4eoqCjWrFnD33//XdbNlRtZL0EIUdFkZGQQFhYGQFRUlKwxVcmcTDrJK5tf4VTyKVSoGN5wOM82exadWld+QZzdDr8+DqnnQOcIvb+ExoPKrfmkjBxeWrif9cfiAHjkjlDeurc+em3FGORdWvf+TZs23fD5Tp063fK5KyLpM1Ut8/8+Q9NVfXg3OIfDBgP9avbj3fbv2jssIYSwm7Ebx/L72d9p5tuMOd3noFZVjH5NWZLFz8uJdLKEEEKUtqy8LD7Z9QkLTywEoLF3Yz6+82OCXcpxUfCMBOuUvjMbrI9bPwn3vA9afbk0b7EoTPnzFJPXn0BRoHmIO9883AI/V2O5tH8jcu+/NXLdqpY8s4XXP/2CIZYPeCTQHxUq5veaL+upCCGqpC3ntvDM+mfQqDQsuHcBdTzr2DukcmGXxJTZbOa7777j+PHjBAcH06RJE5o2bYqXl1dpnL5Ckk6WEEKIsvL72d95Z9s7pOWk4aJz4f0O73NXyF3lF4DFDBs/hM2fWB8HtYTBP4BbULmFsOFYHKN/3ktqdh7ezgamPdyclmGe5dZ+YUrz3p+cnMzMmTM5etQ6ZbJBgwaMGDECNze30gi1QpE+U9Wz7nAs+p8Hs87vHMtdnGjs05gfe/xYJUYJCCHEVdl52fRb1o9z6ecYWn8oL7V6yd4hlRu77Mr33HPP8fbbb3Pp0iXGjRtHz5498fX1JSQkhD59+pRWM0IIIUSV0DW0K4t6L6KJTxPSctN4fsPzfLnnS8wWc/kEoNZA5zdhyC9gdIPz/1jXnYrZVT7tA3fV9eW3ZztQ19+F+HQTQ2bsYMne22PdqX/++YcaNWrw+eefk5iYSGJiIpMmTaJGjRrs2bPH3uEJUWJd6/uxzPdpnktMxsFi4cDlA6w8s9LeYQkhRLmacXAG59LP4evoy9NNn7Z3OBVWqSWmFi9ezA8//MC8efMwGAz8888/fPHFF2RnZxMaGlpazQghhLiBrKwsIiIiiIiIICsry97hiBIKdA5kdrfZPFTvIcDauRn5x0gSsxPLL4ja3WDkZvBrCBlxMKcX7F9Qbs2HeTux+Jl2dG/gT47ZwgsL9vPZuuNYLJV7JYIXXniBPn36EBUVxeLFi1m8eDGRkZHce++9jBkzxt7hCVFiKpWKR+/rzp85ETyZbN1p8vPdn5ORm2HnyIQQonwcTzzOrIOzABjXehxOOln79XpKLTGVnp5O/fr1AdDpdGi1Wp599llee+01jEb7rwkhhBBVgcViYdOmTWzatAmLxWLvcEQp0Gl0jGs9jol3TsRB68COizsYvHwwBy4fKL8gPMJgxFqo0wvMJljyJPwxHsrpd8xRr+Xrh5rzdEQNAKb8eYrnft5Ldm45jR4rA//88w+vvvoqWq3WVqbVannllVf4559/7BiZEKWnWYgHB2s9Q//kHKrl5nI56zLTD0y3d1hCCFHm8ix5vL3tbfKUPLqEdKFraFd7h1ShlVpiKjw8nAsXLgAQFBTE+fPnAejduzdz584trWaEEEKIKqlH9R7M7zmfMNcwLmVeYuiaoSw4toBy28PE4Az3z4UOL1gf//U5LHgYTOnl0rxareLV7nX5ZGBjdBoVKw9c5IUF+8ql7bLg6upKdHR0gfKYmBhcXFzsEJEQZeOpXm2ZZb6PVxKSAfjxyI+cTT1r36CEEKKMfX/4e44kHMFF78LrbV63dzgVXqklpvr378/q1asB6xbHs2ZZh6wdOXJEppMIIYQQpaCmR01+6vUTXUO7kmfJ470d7zFh+wRyzbnlE4BaDV3GQ7/poDHA8ZUwuwekxZZP+8CgltWY+1gbgtwdeK5zrXJrt7Tdf//9PPbYYyxYsICYmBhiYmL4+eefefzxx3nwwQftHZ4QpSbM24nslk9RI9OJ9plZ5Fpy+WTXJ/YOSwghykxUShRf7/sagFdavYKPo4+dI6r4Sm1XvmtFR0fTqlUrLBYLqampPPbYY3z99del3YzdyQ4zQoiKJiMjA2dnZ8A6xdrJSeay344URWH24dlM3j0ZBYXmvs2ZFDEJL4dy3Ak3Zhf89ABkxoNbCDz8K/jULrfmc/Is6LXlv7tXad37c3JyePnll5k2bRp5eXmAdSmEp59+mo8++giDwVBaIVcI0meq2hLSTXz8yXs8pf+aAUEB5KlUfNvlW9oFtbN3aEIIUaosioXha4azJ24P7QPb802Xb1CpVPYOyy7ssivftUJCQjh8+DATJ05k4cKFTJ06tSyaEUIIIaoklUrFiIYj+Orur3DWObMnbg8PrnyQY4nHyi+Iaq3g8d/BMxxSomHWPRC9o1yajkmLYcLfbxGfFV8u7ZUFvV7PF198QVJSEvv27WPfvn0kJiby+eef33ZJKSG8nA2EdnqEVFMID6SmATBl75Tym4oshBDlZP7R+eyJ24Oj1pG3275dZZNSxVVmHzV6e3szfPhw+vTpIz8MIYQQogzcGXwn83rNI9Q1lIsZF3lk1SOsjVpbfgF4hsNjv0NQC8hKgh/6wNHlZdqkoii8//f7/Hb6N977+70ybas8ODo60qhRIxo1aoSjo6O9wxGizIzoUIOv9SN4PDkVo8XCoYRDbD632d5hCSFEqTmdfJrJeyYD8GLLFwl0DrRvQJVIiRJThS3aeSNXF0QXQghRdhwdHeUP3Cok3C2ceT3n0T6wPdnmbF7a9BJf7f0Ki1JOuzI6ecPQ5VC7O+Rlw4JHYOeMMmtubdRatl7Yil6tZ0zzMWXWTlno378/qamptu9vdNwupk6dSv369WnVqpW9QxF25qDX0KVbX3bmtmDIlVFTU/dNlVFTQojbQq45l9e2vIbJbKJDUAcG1R5k75AqlRIlplq1asXIkSPZtWvXdeukpKQwY8YMGjZsyK+//lqS5oQQQtyEk5MTGRkZZGRkyPpSVYibwY2v7v6KofWHAvDtgW95YcMLZORmlE8Aeie4fx60GA4osOol2PwplPIfnKk5qXy08yMAnmj8BGFuYaV6/rLm5uZmG0Xu6uqKm5vbdY/bxahRozhy5MgN+4qi6hjQIpilbg8zLCUNR4uFo4lH+TPmT3uHJYQQJTbtwDSOJh7FzeDGu+3elVljxVSixc8TEhJ4//33mTVrFkajkRYtWhAYGIjRaCQpKYkjR45w+PBhmjdvzltvvUXPnj1LM3a7k4U8hRBCVDS/nf6N8dvGk2vJpZZHLb6860uCXYLLp3FFgY0fwqaPrY/bj4YuE6CUOmf/2/4/fjnxC9XdqrOo9yL0Gn2pnLc45N5/a+S6iatWHriIceGDHPY+wwx3N2p71GZh74WoVeW/mYEQQpSGfXH7GLpmKBbFwmedPuOesHvsHVKFUG6Ln3t5eTFp0iQuXrzIV199Ra1atYiPj+fkyZMAPPTQQ+zevZvt27ffdkkpIYSoyK6OmirsuFZ2dvYN61772YXJZCq1uhbLv9PMcnJyCj2HuDV9avRhdvfZeDt4czLpJENWDmFXbDmNVlGp4K7X4Z73rY+3fgErx4Kl5NMK98Xt45cTvwDw9h1v2yUpVZo6d+5McnJygfLU1FQ6d+5c/gEJUU66N/TnV8f7GZqShrPFwomkE/xx9g97hyWEELckMzeTN/56A4ti4d7weyUpdYtK/NHEu+++i6IoDBw4kMmTJ7NkyRLWrFnD3LlzefHFF2nYsGFpxCmEEKIIsrOz6dWrF87Oztc9rvXII4/csG5mZqat7siRI29YNz7+3x3Sxo4de8O6165R+MYbb9jKO3bsKMmpUtDEpwk/9fqJ+l71STIl8eS6J1l4YmH5BdDuWej9BaCCf2bBkifBnHvLp8u15DJh+wQA+tXsR0v/lqUUqP1s3LiRnJycAuXZ2dls2bLFDhEJUT40ahV3RPTgWF5tHkmxrjX19b6vMVvMdo5MCCGKb+KuiUSnRePn6MdrbV6zdziVVokTUxMmTCA9Pb00YhFCCFFCBoOBlJQUe4dxy7Zu3ZovGSZunb+TP3O6z6FHWA/ylDze3f4uH+z4gFzLrSeIiqXFMBjwHai1cHAh/PIo5Gbf0ql+OPwDp5JP4WHwYGyLsaUbZzk7cOAABw4cAODIkSO2xwcOHGDv3r3MnDmToKAgO0cpRNka2CKYOZoBPJyaiovFwumU06w7u87eYQkhRLGsjlzNryd/RYWKDzp8gKtepqrfqhKtMQWgVquJjY3F19e3tGKqNGS9BCFERaQoyg2TO9cuip6dnY3ZfP1PqR0dHW2LN5pMJvLy8kqlroODA2q19bORnJwckpOT8fPzAyA9PV0Wbi9FiqIw4+AMpuydAkAb/zZ8FvEZboZyWmD7+BprUspsghqd4YH5oHMo8svPpJxh8PLBmMwmPujwAb1r9C7DYG+upPd+tVpt+3dSWBfMwcGBKVOmMGLEiBLHWpFIn0n816S1x+i69X62eSbylYc7Ya5hLL1vKRq1xt6hCSHETUWnRjN4xWAycjN4svGTPNfsOXuHVOEU596vLY0GZcV5IYSoOFQqVZETO0ajscjnNRgMGAyGUq+r1+slEVWGVCoVTzZ+kpruNRm3ZRw7Ynfw4MoHmdJ5CjXca5R9AHW6w8OLYP79cPpP+OlBePCnIiWnzBYzb/31FiazifaB7bk3/N6yj7eMRUZGoigK4eHh7Ny5Ex8fH9tzer0eX19fNBr5w1zc/h5tX513/+rLBylf8KObK1GpUayKXGX35LMQQtxMrjmXlze/TEZuBs19m/N0k6ftHVKlVyrbX9SuXRtPT88bHkIIIYSwn84hnZnbcy5BzkHEpMXw0KqH2Hxuc/k0Xv1OeGgR6JzgzAZrkirn5lM2vz/yPQfiD+Cic2F8u/G3xQdhoaGhhIWFYbFYaNmyJaGhobYjICBAklKiyvB2NuDSrB+XzP4MS04FYNr+aeRZrj/aVgghKoLP93zOkYQjuBnc+PjOj9GqS2W8T5VWKldwwoQJuLmV05QAIYQQQtyS2h61md9rPmM3jmX3pd08u/5ZxrQYw/AGw8s+6RPW3jpyat4giNwE8wfDkAWgL3y03LHEY3y19ysAXmn9Cv5O/mUbn50cOXKE6OjoAguh9+nTx04RCVF+Hr+zFl/v7s2E1Bl87+5GdFo0K86soG/NvvYOTQghCrUpZhM/HvkRgP+1+1/l759c2AcBTaw7K9uRrDFVArJeghBClA6LxcLRo0cBqFevnm39KVE2cs25fLjzQ9tOfb3De/NOu3cwaIo2/bJEov+GuQMgJx3COhaanErLSeP+FfcTkxZDRHAEX3b+ssKMliqte/+ZM2fo168fBw8eRKVS2dabuvo+b7T2W2UkfSZxPc/8sJ03Tj/E7245fOblQZBzEMv7LUen1tk7NCGEyCcmLYYHVjxAak4qD9V7iHGtx9k7pJKJOwbT2kNQS3j4VzA43/w1xVCce3+Je/4VpaMohBCi8lKr1TRo0IAGDRpIUqoc6DQ63rrjLV5v8zoalYblZ5YzYs0ILmdeLvvGQ+6AhxeD3gWitlhHUJn+3d1XURTe2fYOMWkxBDoF8l6H927Lvsbo0aOpXr06cXFxODo6cvjwYTZv3kzLli3ZuHGjvcMTotw81qkuM/J6cX9aOl4WOJ9+nt9O/WbvsIQQIp/svGzGbhxLak4qjbwbVfpdglEUWP0KWPLA0bPUk1LFVeLefwkHXAkhhBDCDlQqFQ/WfZBpXafhqnflQPwBBq8YzN8X/y77xkPawCNLwOAKZ7fCvIFgSgNg6r6p/H72d7RqLZ92+rT8dg8sZ9u3b+fdd9/F29sbtVqNWq2mQ4cOfPjhhzz//PP2Dk+IctMi1IMTQf3ItDjzWFISAN8e+JZcc66dIxNCCCtFUfjf3//jWOIxPI2eTIqYhF6jt3dYJXP0N+vSChoDdPvA3tGUPDFlsVjyTeOLj48nPj6+pKcVQghRheTk5DB+/HjGjx9fYK0dUbbuCLiDn3v9TE33msRnxfPkuif5au9XZb8AcbVW8MhSMLhB9HaYO5Bfj8zj2wPfAvDWHW/RyKdR2cZgR2azGRcXFwC8vb25cOECYF0c/fjx4/YMTYhyN7RTfWbl9WBQWjo+FhUXMy6y5NQSe4clhBAA/HL8F347/RtqlZqJd06s/OtK5WTA2jes37cfDZ7V7RsPpbQrX3JyMqNGjcLb2xs/Pz/8/Pzw9vbm2WefJTk5uTSaKBMxMTFERERQv359GjduzMKFC+0dkhBCVEm5ublMmDCBCRMmkJsrn5KXt2qu1Zjfaz4Dag1AQeHbA9/y+LrHic2ILduGg1vAo0vA4MbqxAP8b+dHAIxsPJL+tfqXbdt21rBhQ/bv3w9AmzZtmDhxIlu3buXdd98lPDzcztEJUb661vNjs/t95FqMPJ6YAMD0A9MxmU12jkwIUdXti9vHR7us/ZMxzcfQJqCNnSMqBZs+hpQYcAuBDi/YOxqgFBJTiYmJtGnThu+//54BAwbw2Wef8dlnn9G/f3/mzJlD27ZtSboyLLei0Wq1TJ48mSNHjrBu3TrGjBlDRkaGvcMSQgghyp2D1oHx7cbzccePcdQ6svvSbvr/1p+lp5aW7bT9oBYs7/oy43y8MKugn8WBUXUfKbv2Kog333wTi8UCwLvvvktkZCQdO3Zk1apVfPnll3aOTojypVarePDOxsw1d2FAejp+ippLmZf49cSv9g5NCFGFxWfF8+LGF8mz5NE1tCvDGgyzd0gld+kwbJ9q/b7nJ6B3tG88V5R4V74xY8awfv16/vjjD/z8/PI9Fxsbyz333MPdd9/N559/XqJAy0OTJk1YsWIF1apVK1J92WFGCCFKR0ZGBs7O1kUX09PTcXJyuskrRFk6m3qWcZvHcSjhEADtg9rzzh3vEOAcUKrtKIrC9APT+WrfVwAMyMzh7UuxqINbWXeHMVa89aXK8t6fmJiIh4fHbbnYu/SZxM1k55rp89Fifst7mmWuBt7z9sTHwYdV/Vdh1BrtHZ4QoooxmU08tvYx9l/eT7hbOPN7zcdJV8n7pxYLzO4OMTug7r3wwLwyba5cd+VbunQpn376aYGkFIC/vz8TJ05kyZJbmyO+efNmevfuTWBgICqViqVLlxaoM3XqVMLCwjAajbRp04adO3feUlu7d+/GbDYXOSklhBBC3K5CXUP5seePvNDiBfRqPVvPb+W+Zffx7f5vycrLKpU2UnNSeXnzy7ak1MP1HubtPj+hNrrDuV3wY3/ITimVtioLT0/P2zIpJURRGHUaerdrygJzBP3S0glAy+Wsyyw8IUttCCHKl6IojN82nv2X9+Oid+GLu76o/EkpgL0/WpNSOifo8bG9o8lHW9ITXLx4kQYNGlz3+YYNGxIbe2trVGRkZNCkSRNGjBhB//4F15pYsGABY8eOZdq0abRp04bJkyfTrVs3jh8/bluQvWnTpuTlFVzAdd26dQQGBgLWTygfffRRZsyYcUtxCiGEELcbrVrLiIYjiKgWwfht49kbt5ev9n3FwhMLebrJ0/Su0fuWdqRRFIXN5zbz7t/vEpcZh1al5Y073mBg7YHWCo8ugx/ug/P/wI/94OHF4OBeum/OTgrry1zP4sWLyzASISqmh+8IZeDGPjykrOfJ+EtM8Pbiu4PfMaDWABx1FWO6iRDi9jfz0ExWnFmBRqXhs06fEeYWZu+QSi4jHn5/2/r9Xa+DW7B94/mPEiemvL29iYqKIji48DcWGRmJp6fnLZ27R48e9OjR47rPT5o0iSeeeILhw4cDMG3aNFauXMmsWbMYN24cAPv27bthGyaTib59+zJu3DjatWt307om07+LMKamphbxnQghhBCVU7hbON93/541UWv4fPfnXMy4yPjt45m6byoP1n2Q3jV6F2l3GkVR+OfSP3y7/1t2xO4AIMQlhPc7vE9T36b/VgxsCkN/u5Kc2m1NTj2y5LZITrm5VbypiUJUJB5Oejq2asGyXe25L20L33kHcD47kV+O/8KwhsPsHZ4QogpYf3Y9X+z5AoDXWr9G28C2do6olKx7E7KTwa8RtHnK3tEUUOI1pkaMGMHp06f5/fff0evzf3JqMpno1q0b4eHhzJo1q2SBqlQsWbKEvn37AtatxR0dHVm0aJGtDGDo0KEkJyezbNmym55TURSGDBlCnTp1GD9+/E3rjx8/ngkTJhQol/UShBCiZGSNqcohOy+bBccX8MORH4jLjLOVN/dtTpuANjTxaULQ/9m77/iY7z+A46/L3nsPEcReMULsomLVHsXPKlq12lKUqtJFKbVSrT1qFbVqS+29t1gZVkJkyU7u7vfH1VVKCJJcxvv5eNwjd9/v5/v5vu9Lcnfv+3zeHwt3bE1sUavVxKbGEhofyunI0+y7s4/Q+FAADPUM6VGuBx9X+TjrURAPLsCyNpAcA27V8k1ySmolvRm5biK77kQn0e+n5ewyGsUGC3PGO9pja2zLjo47ZNSUECJXXX18ld47epOckUy3st0YW2usrkPKGTf3wO8dAQX02w2eNfPktK/z2v/Wiam7d+9So0YNjI2NGTx4MGXLlkWtVnP16lV++eUXUlNTOXXq1FvXbvpvYur+/fu4u7tz5MgR/P3/zWKOGjWK/fv3c/z48Vf2eejQIRo0aEDlypW125YvX06lSpVe2P5FI6Y8PT3lTZYQQrwlpVLJmTNnAKhWrRr6+vo6jki8TLoynW0h29h4cyOnIk9l+zgzAzNalWhF/0r9cbNwe/UBERdhaRtIjgY333+SU7ZvEfnby+kEy6NHjwgODgagTJkyODo6vnWf+ZEkpsTrGLzyDO9dHUVT/ZO0KVGaO+oUPqn2Cf0r9dd1aEKIQioyMZIe23oQmRRJHbc6BDYJxEDvrSeY6V5KPPziD/F3odbH0GJynp36dV773/pKe3h4cPToUQYNGsSYMWO0S0orFAreffdd5syZk28LiterV0+7VHN2GBsbY2xsnIsRCSFE0aSvr0/Nmnnz7Y14e4b6hrQt1Za2pdoSkRjBgbsHOPPwDFceXyEiMUJbIN3UwBRPS0/K2ZXD382fRp6NXq94qEsl6L1FM3Lq/llY1g56bdR5cionJCYmMnToUJYtW6Z9L6Kvr0+vXr2YPXs2ZmYyMkQUXR81KMG4i21orn+Sjx7eZ5yjHcuvLKdHuR6YGpjqOjwhRCHzJO0JHwd9TGRSJN7W3kxtOLVwJKUA9kzQJKVsvKDJV7qOJks5crW9vb3Zvn07MTEx3LhxA4BSpUq9cW2p7HBwcEBfX5/IyMhM2yMjI3FxeXWtCyGEEEK8PRdzF7qU6UKXMl0AzTT5dFU6ego99BX6b7/KnEtFTXJq6Xvw4Jym9lTPjWCWe+8x8sLw4cPZv38/W7ZsoW7duoBmJPewYcMYMWIEc+fO1XGEQuhOZQ8bzLxrcvBORVolXGKuszv3UqL588af9CjXQ9fhCSEKkXRlOp/t/YwbMTdwMHVgbtO5WBkVkpG9IQfh1ELN/bZzwCj/lsrQy8nObG1t8fPzw8/PL1eTUgBGRkZUr16doKAg7TaVSkVQUFCmqX1CCCHyv7S0NKZOncrUqVNJS0vTdTjiLSgUCoz0jTDQM3j7pNRTzhWg919g5gAPzsOSVhD/IGf61pH169ezcOFCWrRogZWVFVZWVrRs2ZL58+ezbt06XYcnhM591KAkvyjbYgD0jdJ8Eb3k8hLSlem6DUwIUWio1CrGHR7H8YjjmBmY8UuTX3C3cNd1WDkjLRE2D9Hcr/EBeDfQbTyvkKOJqZyWkJDAuXPntCvrhYSEcO7cOcLDwwHNt43z589n6dKlXL16lY8//pjExETtKn1CCCEKhvT0dEaNGsWoUaNIT5cPHeIFnMtDn7/AwgUeXoFFAfD4lq6jemNJSUk4Ozs/t93JyYmkpCQdRCRE/tKojCOPHfw4qypFu/hYHPRMiEiM4K/bf+k6NCFEITHjzAy2hWzDQGHAz41+ppx9OV2HlHP+/h5iQsHKA5o+v4BbfpOvE1OnTp3C19cXX19fQJOI8vX1Zfz48QB07dqVn376ifHjx1O1alXOnTvHjh07XvhGLycFBgZSvnx5qYcihBBC5CWnctBvJ9h6Q2wY7B6v64jemL+/P19//TUpKSnabcnJyUycOFFGfguBZvTlgAYlmZvxHsZq6BkbC8CiS4tQqpS6DU4IUeAtv7KcxZcWAzChzgTquNfRcUQ5KPQwHPtFc/+9mWCS/6cmvvWqfC9y/fp1SpQogYFBISkYlgVZYUYIIXJGYmIiFhYWgGa0rLl5/p0DL/KBJ5Gwcyy0nJrntaZy6rX/0qVLBAQEkJqaSpUqVQA4f/48JiYm7Ny5kwoVKuRUyPmCvGcSbyI1Q0nDyXtYmzYYO/0o3i1RiieqVKY1nEaz4s10HZ4QooD688affH3kawCG+Q5jQOUBOo4oB6XEwdy6EHcHfHtqakvpyOu89ufKiKly5cpx+/bt3OhaCCGEEEWdpTN0WligC6BXrFiRGzduMGnSJKpWrUrVqlWZPHkyN27cyJdJqTt37tCoUSPKly9P5cqVWbt2ra5DEkWAsYE+veuVYqmyGeZqNd1TNCtYLri4gFz4bl0IUQRsD9nOhCMTAOhToQ/9K/XXbUA5bdsoTVLKtjg0n6TraLItV4Y0yQuFEEIIIcTLmZmZMWBAwfiW1sDAgBkzZlC1alUiIiKoXr06LVu2lNGNIte9X9OTd/e8w3D1Ov73IIRl3iW5Gn2Vw/cPU8+9nq7DE0IUIPvu7GPswbGoUdOldBeGVx+ecwu15AeXN8CF1aDQgw7zwdhS1xFlW+GeayeEEEIIkU9s3ryZFi1aYGhoyObNm1/atk2bNnkUVfa4urri6uoKgIuLCw4ODkRHR0tiSuQ6W3Mj6lUsxYZL9eihCKKTwpLlpLLg4gJJTAkhsu3Yg2OM2DeCDHUGrUq04svaXxaupFT8fdjyqeZ+/RHg6afTcF5Xvi5+LoQQQghRWLRr146YmBjt/axu7du3f+2+Dxw4wHvvvYebmxsKhYKNGzc+1yYwMJDixYtjYmJCrVq1OHHixBs9j9OnT6NUKvH09Hyj44V4Xd1rebFEGQBAr9ALGCgMOB15mjORZ3QcmRCiIDgTeYZhfw8jTZVGY8/GfFf3O/QUhSgVolLBxkGQEgtuvtBwtK4jem2F6F9DCCFEQWViYsLevXvZu3cvJiYmug5HiFyhUqlwcnLS3s/qplS+/opjiYmJVKlShcDAwBfuX7NmDcOHD+frr7/mzJkzVKlShYCAAB4+fKhtU7VqVSpWrPjc7f79+9o20dHR9OrVi3nz5r12jEK8qZrFbVE7luWwsgIuGRm0NfUANLWmhBDiZU5FnGLgnoEkZyRTx60OUxtOxUCvkE0cOz4Xbu8FA1PNFD59Q11H9NoK2b9I3ggMDCQwMPCN3jgKIYR4nr6+Po0aNdJ1GELkmTt37uToiKMWLVrQokWLLPdPnz6dAQMG0LdvXwB+/fVXtm7dyqJFi/jiiy8AOHfu3EvPkZqaSrt27fjiiy+oU6cQLast8j2FQkE3v2Is2RZAXf3L9A27xAYnKw7eO8i16GuUtSur6xCFEPnQyYiTDA4arE1KzXxnJkb6RroOK2fdPQ27NSsMEvA9OPjoNp43JCOm3sDgwYO5cuUKJ0+e1HUoQgghhCiAihcvTsOGDZk/f752el9uSUtL4/Tp0zRt2lS7TU9Pj6ZNm3L06NFs9aFWq+nTpw+NGzemZ8+er2yfmppKfHx8ppsQb6NjNXcO6tXgjsoRr4RoAqxKA7Dw4kIdRyaEyI+OPTjGoD2DSM5Ipq57XWY1noWJQSEblZ8cC+v6gCodyreDGh/oOKA3J4kpIYQQOpeenq4djZqenq7rcITIdadOncLPz49vvvkGV1dX2rVrx7p160hNTc3xc0VFRaFUKnF2ds603dnZmYiIiGz1cfjwYdasWcPGjRupWrUqVatW5eLFi1m2nzRpEtbW1tqb1KMSb8vGzIiWldxZpnwXgH4RdwDYGbqT0LhQHUYmhMhvjt4/ypCgIaQoU6jvXp+Z78zEWN9Y12HlLLUaNg+B2HCwLQ5tZkEBLuaeK4mp0aNHY29vnxtdCyGEKITS0tIYMmQIQ4YMISYmhsTERO0tIyND2y49PT3Tvv/enm2bkZHx0rbPJsBep61Sqcy0T61W581FEoWKr68vU6dOJTw8nO3bt+Po6MiHH36Is7MzH3yQ/77xrFevHiqVinPnzmlvlSpVyrL9mDFjiIuL097u3LmTh9GKwqp7rWL8oWxEstqIMhFXaWhXCTVqFl9erOvQhBD5xN/hfzMkaAipylQaeDRgxjszCl9SCuDEfLi6BfQModNiMLHWdURvJVcSU5MmTZLElBBCiDfi7OyMhYWF9rZz507tvhUrVmTa99/bhg0btG03bNjw0rYrVqzQtt25c+dL2z5b6PngwYOZ9tWvX1+SU+KNKRQK3nnnHebPn8+ePXvw9vZm6dKlOXoOBwcH9PX1iYyMzLQ9MjISFxeXHD3XU8bGxlhZWWW6CfG2qnvZ4uTkwgZlPQD6J6QAsPnWZiISszf6TwhReG26uYnh+4aTpkrjHc93+LnRz4WvphTA/XOw60vN/Wbfgns1nYaTE2QqnxBCCJ0zMzOjbt26ug7jjRw+fJikpCRdhyEKqLt37zJlyhSqVq2Kn58fFhYWWa6s96aMjIyoXr06QUFB2m0qlYqgoCD8/f1z9FxC5CaFQkH3WsVYogwAoMr1vdSwr0SGKoOll3M2oSuEKFiWXV7GuMPjUKqVtC3ZlumNphfOpFRyLKztA8o0KNsaag3UdUQ5QlblE0IIoXMKhYKDBw++MMFjbPzv8OsePXrQuXPnLPt5tm379u1JSEjIsq2R0b9vVgICArLdtn79+iQkJJCYmPhczR4hsuu3335j5cqVHD58mLJly9KjRw82bdqEl5fXG/WXkJDAzZs3tY9DQkI4d+4cdnZ2FCtWjOHDh9O7d29q1KiBn58fM2bMIDExUbtKnxAFRQdfDyZv9+KIsjx19K8wAGtOAetvrGdA5QHYmdjpOkQhRB5Sq9XMPjub+RfnA9CzfE8+r/E5eopCOAZHpYI/B0BMCFgXg7ZzCnRdqWdJYkoIIUS+oFAoMDc3f2kbQ0NDDA0Ns9WfgYEBBgbZe5l7nbb6+vqvjFOIV/nuu+/o1q0bs2bNokqVKm/d36lTp3jnnXe0j4cPHw5A7969WbJkCV27duXRo0eMHz+eiIgIqlatyo4dO3I9ufp0UQOlUpmr5xFFh7WZIa0ru7HkXAB19K/gf3k75cvX5Er0NVZcXcFQ36G6DlEIkUeUKiWTTkxiTfAaAIb5DqN/pf4oCkmy5jn7J8ONXWBgAu//Dqa2uo4oxyjUUhjjtT37Juv69evExcVJ7QQhhChiEhMTsbCwADSjVSRZVTTEx8djbW391q/9arW68L5xfoGcum5CAJwOi6Hz3EMcMP4UD0UUuxsOZXj4JiyNLNnVcRcWRha6DlEIkcuS0pMYfXA0++7sQ4GCcbXH0aVMF12HlXuubYPV3TT32/8GVd7XbTzZ8Dqv/bkyvi06OhqVSpUbXecLgwcP5sqVK5w8eVLXoQghhNARQ0NDpkyZwpQpU7I9ikuIp4pSUkqInFatmA0+ztYsy3gXgCbX9uJt7c2TtCf8cf0PHUcnhMhtUclRfLDzA/bd2YeRnhE/NfypcCelom7Anx9q7vt9VCCSUq8rxxJTV65cYfLkydSpUwdHR0ecnJzo1asX69evJzExMadOI4QQQuQLRkZGjBw5kpEjR2aqQSWEECJ3PS2Cvkb5DikYoRd5iX6uDQFNAeSUjBQdRyiEyC23Ym/RY2sPLj++jK2xLQsDFtKseDNdh5V7Up/A6h6Q9gSK1YGA73UdUa54q8RUcHAwI0aMwMfHh9q1a3Py5EkGDhxIZGQk27Ztw8vLi2+++QYHBwdatGjB3LlzcypuIYQQQgghRBHVztedVEMr/szQrOjaMvQcbuZuPE55zJ83/tRxdEKI3HDiwQl6buvJ/cT7eFl58XvL36nqVFXXYeUelVIzUioqGCxdofMS0C+co/TfKjF15MgREhMTmTVrFlFRUaxfv55evXrh4OCAn58f3377LefPn+fq1as0b96c9evX51TcQgghhE4plUpOnjzJyZMnpbCzEELkMWtTQ96r7MZSZQAAhte20rdkewAWX15MujJdl+EJIXLYnzf+5KM9H/Ek/Qm+Tr783uJ3ilkV03VYuWvP1xC8DfSNoevvYFl4V4POteLnycnJmJqa5kbX+YYU8hRCiKJLip8XTfLa/3pkwRiRm86Ex9DhlyOsNvqO2npXSK37Cc1jDhKVHMXEOhPp4NNB1yEKId5SuiqdqSensuraKgCaF2/Od/W+w1jfWMeR5bLTS2HLMM39jguhUifdxvMGXuc9U/bWxn4D9erV4/Tp05m2Xbt2jbJly+bWKYUQQggh8i1fX99sFz0/c+ZMLkeTNwYPHszgwYO1b06FyEm+njaUdbFk8cMAahtdwfjMcvq0+JKfzs5k4cWFtCnZBgO9XPu4I4TIZTEpMYzYP4KTEZpFx4ZUHcKHlT8s/AuIhByArcM19xuNKZBJqdeV43+pt2zZwpUrV0hISODOnTt4enpq93Xt2pXz58/n9CmFEEIIIfK9du3a6ToEIQoVhUJBj1rFmLCpGhEKJ1ySH9I5TY8FxjaEPwlnZ+hOWpVopeswhRBvIDg6mE/2fsK9hHuYGZgxqf4kGhdrrOuwcl/UTVjTE1QZULETNByt64jyRI4npipWrMidO3eIioqid+/ehIWF4e7ujqurqyynLYQQQogi6+uvv9Z1CEIUOm193flh2zUWpzVhjOEqzE4t4n/+PZlzbg4LLi6ghXcL9BQ5thC5ECIP7AzdyVeHvyI5IxlPS09mvTOLUraldB1W7kuMgpVdICUWPGpC20Ao7KPD/pEjiamwsDAuXLiAs7Mzfn5+DBo0iIoVK9KgQQMA7t27R1hYGBUrVsyJ0+ncs/UShBBCCCGEELphZWJImypurD71DiOM/sQo4iLdLEqzxNCCm7E32Ru+lyZeTXQdphAiG9KV6Uw/PZ3fr/4OgL+rP1MbTsXauAhMBU9NgBWdIfoWWBeD91eCoYmuo8ozb/31wapVqyhdujRt27bF39+fGjVq8OjRI21SCsDd3Z06deoUmmKXgwcP5sqVK5w8eVLXoQghhBCiAFIqlfz000/4+fnh4uKCnZ1dppsQIvu61SpGHBZsVvoDYHV+Fd3KdgPgtwu/kUtrPQkhctCDhAf02dFHm5TqW7EvvzT9pWgkpZTp8EcvuH8GTO2g559g4aTrqPLUayemVq1alenxxIkT6d69O9euXWPXrl0AfPHFFzkTnRBCCCFEITRx4kSmT59O165diYuLY/jw4XTo0AE9PT0mTJig6/ByTGBgIOXLl6dmzZq6DkUUYlU8rCnvasWy9H9GRl3eQM/irTA1MOVq9FUO3z+s2wCFEC914O4BOv/VmQtRF7A0smR249kMrz68aCxeoFbDpiFwKwgMTKH7H+Dgo+uo8pxCnc2vECIiIhg0aBA2NjYsWrRIu93IyIjr169TvHhxQLPyXvXq1UlMTMyVgPMTWTJaCCGKrrS0NH744QcAxo4di5GRkY4jEnkhp177S5YsyaxZs2jVqhWWlpacO3dOu+3YsWOsXLkyB6PWPXnPJHLb78fCGLfxEjvMxlNWdROaTmSqcTrLrizD18mXpc2XFv6VvIQoYNJV6fxy7hcWXFwAQAX7CkxrNA13C3cdR5aHdo+HwzNBoQ/dVkHpAF1HlGNe57U/2yOm5s2bR3p6eqakFEBGRgZmZmbax2XLlkWlUhEREfGaYQshhBAFh5GRERMmTGDChAmSlBKvLSIigkqVKgFgYWFBXFwcAK1bt2br1q26DE2IAqmdrztmRvosTP1n1a5Ti+hdrieGeoacfXiWU5GndBugECKTO/F36LO9jzYp1a1sN5a1WFa0klJHZmuSUgBtZheqpNTrynZiatiwYdjZ2dGxY8fn9i1dupQjR46QkJAAgIGBAUlJSTkXpRBCCCFEIeLh4cGDBw8Azeipp+UQTp48ibGxsS5DE6JAsjA2oHlFF7Yo/UnWt4DYMJweXKSDTwcA5l2Yp+MIhRAAarWajTc30mlLJ83UPUNLpjacythaYzHSL0Jf9J1cALvGae43+Rp8e+g2Hh3LdmLKxsaGpUuX0q9fv0zb69evz3fffUe9evWwsbHBx8eHlJQUFi5cyN69e3ny5EmOBy2EEELomkql4vLly1y+fBmVSqXrcEQB0759e4KCggAYOnQoX331FT4+PvTq1YsPPvhAx9EJUTB1quZBCsasU/6zCNPJhfSt2Bd9hT7HHhzjwqMLug1QiCIuLjWOz/d/zleHvyIpI4nqztVZ32Y9zYs313VoeevcStg6QnO/3meaWxGX7RpTr3Ljxg1Onz7NmTNntLfY2Fj09PTw8fHh6tWrOXGafEXqJQghRNGVmJiIhYUFAAkJCZibm+s4IpEXcuu1/+jRoxw9ehQfHx/ee++9HOs3v5D3TCIvqFRq6k/Zi3HcLf42/hwUevDJecZdmsemW5to5NGI2U1m6zpMIYqk4w+O8+WhL4lMisRAYcBg38H0rdAXfT19XYeWty6th/X9Qa2CWgOh+WQopPXvXue1P8fK3Pv4+ODj48P777+v3RYSEsKpU6c4e/ZsTp1GCCGEEKLQ8ff3x9/fX9dhCFGg6ekp6FDNndl/J3PZuCoVUs/B6SX0r9Gfzbc2s+/uPoKjgyljV0bXoQpRZCSmJ/Lz6Z9ZE7wGAC8rL36s/yMVHCroODIduLYV/vxQk5Sq1rtQJ6VeV66uv+jt7Y23tzedO3fOzdMIIYQQQhQ4N27cYO/evTx8+PC56aDjx4/XUVRCFGwdqnkw+++bBCY04hfDc3BmGcUbfkFA8QB2hO5g/sX5/NTwJ12HKUSRcPT+USYcmcD9xPsAdC7dmc9rfI6ZodkrjiyEgrfD2j6gyoDKXaH1z5KUekauJqYKq8DAQAIDA1EqlboORQghhBAF0Pz58/n4449xcHDAxcUl0zL2CoWi0CSm5D2TyGveDuZU97JlV1g1Es0dME98BFc3079Sf3aE7mBX6C5uV71NCesSug5ViEIrIS2Bn079xPob6wFwt3BnYp2J1HKtpePIdOTKZljXV5OUKt8W2v4CRW0K4yvkWI2pokjqJQghRNElNaaKppx67ffy8mLQoEGMHj06B6PLv+Q9k8hLq06EM+bPi3xjtZleaavBqy703cbQv4ey784+2pRsw/f1vtd1mEIUSgfuHuDbY98SkRgBwPtl3uez6p8VzVFSABfX/TN9TwkVO0L7eaBfNMYHvc5rf7ZX5RNCCCGEEDkjJiZGSh0IkUtaVXbF2ECPwPh6qBX6EHYYHl7lw0ofArD19lZC40J1G6QQhUxEYgSf7f2MwUGDiUiMwMPCg0UBi/iy9pdFNyl1bhX8OUCTlKrSDTrMLzJJqdeVJ4kpPT09GjduzOnTp/PidEIIIYQQ+Vrnzp3ZtWuXrsMQolCyMjGkWQUXIrHjqlVdzcaTC6nkWIkGHg1QqpXMPiur8wmREzJUGSy7vIy2G9uyJ3wP+gp9+lboy/o266npUlPX4enOmWWw8eN/Cp33kul7r5An6bpFixYRGhrK4MGDOXbsWF6cUgghhMhVhoaGfP7559r7QryOUqVK8dVXX3Hs2DEqVar03P+hYcOG6SgyIQqHjtXc2XL+PjPjG/IbB+D8amg6gU+qfcLBuwfZFbaLy1GXi+bKYELkkPOPzvPt0W8JjgkGoKpjVb7y/4rStqV1HJmOHZkDu77U3K85AFpMAT2ZrPYyUmPqLUi9BCGEEKJoyanXfm9v7yz3KRQKbt++/cZ950fynknkNaVKTZ3JQTyMT+aSw5eYJ4RB6xlQoy9jD45ly+0t1HKtxYJmC3QdqhAFTlRyFDPPzGTTzU2oUWNlZMXw6sNp79MePUURTsCo1bBnAhyeoXnsPwSafVdkV9/L0xpTV65c4auvviI2NvZtuxJCCCGEKBJCQkKyvBW2pJQQuqCvp6Cdrztq9PjLqIVm48mFoFYz2HcwhnqGHH9wnCP3j+g2UCEKkFRlKgsuLqDVn63YeHMjatS0KdmGLe230LF0x6KdlFJmwOYh/yalmk4s0kmp1/XW/3MmTZrEpUuXsLGxeW5fSkoK165de9tTCCGEEPmOSqUiNDSU0NBQVCqVrsMRQgjxH52qeQAwJaI6agMTiLwId0/ibuFO1zJdAZhxegYqtfwNF+Jl1Go1e8L20HZjW2aemUlSRhKVHCrxe8vf+b7e99iZ2Ok6RN1KT4Y/esLZ30GhB23mQL1PJSn1Gt66xtSxY8eYN2/eC/eZmJgwYMAAWrZsyZgxY972VEIIIUS+kZycrJ2OlZCQgLm5uY4jEvnd8OHD+fbbbzE3N2f48OEvbTt9+vQ8ikqIwsvH2ZLKHtZcuAs3HJtR+sFmzagpTz8GVB7Anzf+5Gr0VXaF7qK5d3NdhytEvnT58WWmnZrGyYiTADiZOvFp9U9pVaJV0R4h9VRyDKzqDuFHwMAEOi2Gsi11HVWB89aJqbt371KqVKks9w8cOJA5c+ZIYkoIIYQQRdrZs2dJT0/X3s+KohB9wxoYGEhgYCBKpVLXoYgiqlN1Dy7cjWNuYkN+ZjNc/hMCfsDO3J4+Ffrwy/lfmH12Nk28mmCoJwtZCPFUaFwos8/OZleYZgVZY31jelfoTb+K/TAzNNNxdPlE9G1Y0Rke3wRja+i2CorX1XVUBdJbFz93d3dnw4YN+Pn5vXD/jRs3qFOnDo8ePXqb0+RLUshTCCGKrsTERCwsLAAZMVWUyGv/m5HrJnQlJjENvx/2kK5UcdVjMqZRF+Hdb6DuJySmJ9Lyz5ZEp0QzrtY4upbtqutwhdC5yMRIfr3wKxtubECpVqJAQesSrRniOwQ3Czddh5d/hB2F1d0hORqsPKDHH+Asq3w+K0+Lnzdo0IAlS5ZkfQI9PVJSUt72NEIIIYQQQgjxWmzNjWhS1hlQEGTeWrPx1CJQqTA3NOfDyh8C8OuFX0lKT9JdoELoWFxqHD+f/plWG1qx7vo6lGoljTwasa7NOn6o/4MkpZ51YS0sa6NJSrn5woAgSUq9pbeeyvf5559Tu3Ztqlatyocffvjc/qNHj1KiRIm3PY0QQgiRb6WlpWlHTKnVapKSsv5wY2BggLGxcbba6uvrY2Jion2cmJiYI2319PQwNTV9o7YiZ7Rv3/6FU/YUCgUmJiaUKlWK7t27U6ZMGR1EJ0Th0rG6BzsuRzDpbiVamVijiAmFm7uhdABdSndh+ZXl3Eu4x4qrKxhQeYCuwxUiT8WkxLDsyjJWXl1JUobmPYmvky+fVvuUas7VdBxdPqNWw/4psO8HzeOyraHDfDCSqY1v661HTFWvXp1ffvmFQYMG8e6777Jx40bCw8OJjo5m06ZNjB49mu7du+dErPlGYGAg5cuXp2bNmroORQghRD4wbtw47f2oqCgsLCyyvH300UfatklJSS9t27Nnz0zneVnbjh07Zmrr5OSUZdsWLVpkalu8ePEs2zZo0CAXrpiwtrbm77//5syZMygUChQKBWfPnuXvv/8mIyODNWvWUKVKFQ4fPqzrUIUo8BqVccTe3Ih7iXDHq4Nm4/HfADDUN2SI7xAAFl1aRGxKrI6iFCJvRSVHMf3UdALWB7Dg4gKSMpIoY1uGwCaBLG2+VJJS/5WWCOs++DcpVWcYdFkuSakckiNl9AcMGMC+ffuIi4ujQ4cOeHt74+joSPv27alUqRKfffZZTpwm3xg8eDBXrlzh5MmTug5FCCGEjpiZmVG3rhS4FG/GxcWF7t27c/v2bdavX8/69eu5desW//vf/yhZsiRXr16ld+/ejB49WtehClHgGerr0baqOwDzU5sACrgVBFE3AGjp3ZIytmVISE9gwcUFOoxUiNz3KOkRU05OocX6Fiy+vJjkjGTK25dn1juzWPveWhp4NChUi3DkiOgQWNhMs3iCngG8NxOafQt6siphTnnr4uf/de3aNc6cOUNSUhIVK1akdu3aOdl9viKFPIUQomh7OhXvdabnFcSpfGq1mvLlywNw5coVzMyK7reDOfXa7+joyOHDhyldunSm7devX6dOnTpERUVx8eJF6tevT2xs7FtGrXvynkno2uX7cbSadQgjfT0ul12M4a2d4PchtJwKwMG7BxkUNAgjPSP+av8XrhauOo5YiJx1O/Y2S68sZcutLaSrNCvEVnKoxMAqA6nvXl+SUVm59Tes7QspsWDuBF2WgZe/rqMqEF7ntf+takxFRERga2urfYMNULZsWcqWLfvC9rdv35Z6U0IIIQoNhULx3Gp8L9r2Ose/jK7aJiYmEhYWBmiSaeLtZWRkcO3atecSU9euXUOpVAJgYmIiHxSEyCEV3Kwp62LJtYgn7LftQFN2wrmV0PgrMLGinns9ajjX4FTkKX45/wvf1v1W1yEL8dbUajWnI0+z9PJS9t3dp91e1bEqA6sMpI5bHXmdyYpaDYdnQtBEUKvAvQZ0XQ5WUgQ+N7zV2LN169ZhZ2dH+/btWbx4MY8ePXquzfHjxxk7diwVKlSgSpUqb3M6IYQQQohCoWfPnvTr14+ff/6ZQ4cOcejQIX7++Wf69etHr169ANi/fz8VKsgqP0LklE7VPQCYE+oBDqUhLQHOrwI0XxR8Vl1TfmTTzU2cfXhWZ3EK8bYyVBnsCt1Fj2096LuzL/vu7kOBgsaejVneYjnLWy6nrntdSUplJSUO1vaBPV9rklK+PaHvNklK5aK3nsp38+ZNNm/ezKZNmzh27Bg1a9akZcuWhISE8NdffwHQqlUr2rZty7vvvptpmkFBl92haUqlkvT09DyMTAiRF4yMjNCTueWiCEhMTMTCwgKAhISE1xqNVdjk1JQ0pVLJ5MmTmTNnDpGRkQA4OzszdOhQRo8ejb6+PuHh4ejp6eHh4ZFT4euMTOUT+cGjJ6nUnhSEUqXm5LshOB78EuxLweCT2lox4w+PZ8PNDRS3Ks66Nusw1jd+Ra9C5B+Pkx/z540/+eP6H0QkRgBgpGdE21Jt6VW+F8Wti+s2wILg/llNUiomVFNPqsWPUKMfSBLvtb3Oa3+O1ph6/Pgxf/31F9u2baN48eK0bdsWf3//QpuJfdWFVqvVREREFIraEEKI5+np6eHt7Y2RkZGuQxEiV0li6l85kWDJyMhg5cqVBAQE4OzsTHx8PEChTthIYkrkFx8sOcnf1x7yWQNXPjnfFlLj4X/roVRTAOJS42i3qR1RyVH0r9SfT6p9ouOIhXg5tVrNxaiLrLq2ip2hO7X1o2yNbelativvl3kfe1N7HUdZAKjVcGI+7PoSlGlgXQw6LwaPGrqOrMDSWWKqqHnVhX7w4AGxsbE4OTlhZmZWaBN0QhRFKpWK+/fvY2hoSLFixeT3WxRqkpj6V04lWMzMzLh69SpeXl45GF3+ExgYSGBgIEqlkuvXr0tiSujcXxfuM2TlWdxtTDlUZSeK47+CTzPosVbbJig8iE/3foq+Qp9VrVZRzr6cDiMW4sWS0pPYGbqT1cGrufL4inZ7JYdKdCvbjWbFm8mIv+xKjoXNQ+DqFs3jsq2h7RwwtdVpWLlNpVLz3dartPd1p5KHdY73n2fFz0XWlEqlNillby8ZaiEKI0dHR+7fv09GRgaGhoa6DkcIUYD4+flx9uzZQp+YGjx4MIMHD9a+ORVC15qWc8bSxIB7scmcc+mML7/Cjd3w+BbYlwSgSbEmNPNqxq6wXYw/Mp6VrVZiqCev80L31Go15x+dZ8PNDewI2UFShmZlXyM9I5p7N6db2W5UdKio4ygLmPDj8OcAiA0DPUNo9h3U+qjQT91Tq9VM2HKZZUfD+PPsXQ6MegcrE939nZPEVC55WlOqKC+pLURh93QKn1KplMSUKNQUCgXly5fX3hdvb9CgQYwYMYK7d+9SvXr150ahVa5cWUeRCVG4mRjq07qyK6tO3GHlTUN8S70LN3fDyQXQfJK23ZhaYzgecZxr0ddYenkp/Sv112HUoqiLSo7ir1t/seHmBm7H3dZuL2ZZjA4+Hejg0wFbk8I9uifHZaTB/slw6GdNgXMbL83UPffquo4s16nVan7cEcyyo2EoFPD1e+V1mpQCmcr3Vl42NC0lJYWQkBC8vb0LVcF3IcS/5PdciKInp6byvWjhBIVCgVqtRqFQoFQq3ybMfEdqTIn85ERINF1+O4qFsQGn31djvKYrGFvB8KtgbKFtt+XWFsYeGouRnhFr26ylhHUJHUYtippUZSoH7x5ky60tHLh7gAx1BgAm+iY0K96M9qXaU925unxh9CYeBWtGST04r3lcpZumyLlJ4R/Zq1armbbrOnP23gTgh/aV6F6rWK6cS6byCSGEEELkYyEhIboOQYgiq4aXLZ52ptyJTmZHSmXa2pWE6FtwYTXU/HdkVOsSrdkWso1D9w7x9eGvWdpiKXoKWY1X5B6lSsmJiBNsC9nGnrA9JKQnaPdVcqhEe5/2tCjeAgsji5f0IrKkUsHJ+bB7PGSkaGpItZ4BFdrpOrI88d+k1Nfvlc+1pNTrksSUeC19+vQhNjaWjRs35ul5GzRowMCBA+nevXuenlfkvdq1azNy5Eg6duyo61CEECLXFPbaUkLkZ3p6Ctr7ejAr6AZ/nn1AW78PYcdoOD4v07LwCoWC8bXH025TO849Oseqa6voUa6HjqMXhc3TVfW2h2xnR+gOopKjtPuczZxp4d2CNiXb4GPro8MoC4HoENjyCYTs1zwu2QTaBoKVq27jyiP/TUqNb12evnW9dRzVvyTlL/K9zZs3ExkZyfvvv6/rULT27dtHtWrVMDY2plSpUixZskTXIeW5lJQUBg8ejL29PRYWFnTs2JHIyMjn2oWFhWFqakpCQkKm7atXr0ahUNCuXbtM28eNG8cXX3yBSqXKzfCFEK8hKSmJChUqUKFCBZKSknQdTqFy5coVduzYwebNmzPdhBC5q4OvOwAHbzziUcmOYGQBUcFwe1+mdq4WrgyvPhyAmWdmci/hXl6HKgohlVrF2YdnmXpyKi3+bEGPbT34/ervRCVHYW1sTZfSXVgcsJhdnXYxosYISUq9DZUSjv4Cc+toklIGJtBiKvxvfZFOSn1QL/8kpUBGTIkCYNasWfTt2/eF9Th0ISQkhFatWjFw4EBWrFhBUFAQ/fv3x9XVlYCAgGz3Exsbi56eXoGttfHZZ5+xdetW1q5di7W1NUOGDKFDhw4cPnw4U7tNmzbxzjvvaJeaBwgNDeXzzz+nfv36z/XbokUL+vfvz/bt22nVqlWuPw8hxKup1WquXLmivS/e3u3bt2nfvj0XL17U1paCf4vLF7YaU0LkN8UdzKlWzIYz4bFsuvaE/lW6aab4nJgHJd/J1LZzmc5sD93O6cjTTDgygV+b/oq+nr6OIhcFVboynRMRJwgKD+Lv8L95nPJYu8/UwJTGxRrT0rsl/q7+GOrLojo54uE12DwU7p7QPPaqB21maVfgLArUajU/7QomcO8tIH8mpUBGTIkXWLduHZUqVcLU1BR7e3uaNm1KYmLiC9umpqYybNgwnJycMDExoV69epw8eVK7v0aNGvz000/ax+3atcPQ0FA7eubu3bsoFApu3rz5wv4fPXrE33//zXvvvZdpe2xsLP3798fR0RErKysaN27M+fPntfsnTJhA1apV+e233/D09MTMzIwuXboQFxenbbNv3z78/PwwNzfHxsaGunXrEhYW9srr8+uvv+Lt7c20adMoV64cQ4YMoVOnTvz888+vPPZZ58+fx8XFhf/973/s3r37jUYIbdq0iWrVqmFiYkKJEiWYOHEiGRkZ2v0KhYK5c+fSokULTE1NKVGiBOvWrdPuT0tLY8iQIbi6umJiYoKXlxeTJk160akyiYuLY+HChUyfPp3GjRtTvXp1Fi9ezJEjRzh27NhzMbZp00b7WKlU0qNHDyZOnEiJEs8XEdXX16dly5asXr36ta+HEEIUFJ988gne3t48fPgQMzMzLl++zIEDB6hRowb79u3TdXhCFAkdqnkAsP7MPfD7ULMxeDvEhGZqp6fQY2KdiRjrG3PswTGmn56ex5GKgiouNY4dITv44uAXNFzTkIF7BrL2+loepzzG0tCS1iVaM6PRDPZ33c/k+pNp4NFAklI5ISMN9k+F3+prklJGltD6Z+i9pUglpVQqNRO3XMn3SSmQxFSeUqvVJKVl6OSW3W+4Hzx4QLdu3fjggw+4evUq+/bto0OHDlkeP2rUKNavX8/SpUs5c+YMpUqVIiAggOjoaAAaNmyofYOtVqs5ePAgNjY2HDp0CID9+/fj7u5OqVKlXtj/oUOHMDMzo1y5cpm2d+7cmYcPH7J9+3ZOnz5NtWrVaNKkifa8ADdv3uSPP/5gy5Yt7Nixg7NnzzJo0CAAMjIyaNeuHQ0bNuTChQscPXqUDz/8MFurWhw9epSmTZtm2hYQEMDRo0dfeeyzGjRowPbt2zE2NqZTp054eXkxduxYgoODs3X8wYMH6dWrF5988glXrlzht99+Y8mSJXz//feZ2n311Vd07NiR8+fP06NHD95//32uXr0KaEajbd68mT/++IPg4GBWrFhB8eLFX3nu06dPk56enuk6lC1blmLFimW6DrGxsRw6dChTYuqbb77BycmJfv36Zdm/n58fBw8ezNZ1EEKIgujo0aN88803ODg4oKenh56eHvXq1WPSpEkMGzZM1+EJUSS0ruyKkb4eVx/EcyXdBUq8A6jh5ILn2npZefFNnW8AWHZlGauvyRdo4nlqtZrg6GAWXFxA7+29abimISMPjGTr7a08SX+CvYk9nUt35remv7G/634m1Z9EE68mmBqY6jr0wiPkAPxaD/Z+B8o08AmAwcehxgeQT2bg5IUMpYqR6y6w5EgoAN+0rZBvk1IgU/neSGBgIIGBga89zD45XUn58TtzKaqXu/JNAGZGr/7nfvDgARkZGXTo0EFbmLVSpUovbJuYmMjcuXNZsmQJLVq0AGD+/Pns3r2bhQsXMnLkSBo1asTChQtRKpVcunQJIyMjunbtyr59+2jevDn79u2jYcOGWcYTFhaGs7Nzpml8hw4d4sSJEzx8+BBjY2MAfvrpJzZu3Mi6dev48EPNN14pKSksW7YMd3dNDYHZs2fTqlUrpk2bhpGREXFxcbRu3ZqSJTVZ8/8mv7ISERGBs7Nzpm3Ozs7Ex8eTnJyMqWn2XlgUCgUNGzakYcOGzJkzh40bN7Js2TKmTp1K9erV6dOnD926dcPa+sXLlk6cOJEvvviC3r17A1CiRAm+/fZbRo0axddff61t17lzZ/r316ww8+2337J7925mz57NL7/8Qnh4OD4+PtSrVw+FQpHtYrwREREYGRlhY2Pz3HWIiIjQPt62bRuVK1fGzc0N0PzbLVy4kHPnzr20fzc3N+7cuYNKpco3UziFECInKZVKLC0tAXBwcOD+/fuUKVMGLy+vbH9BIYR4OzZmRjQp58T2SxFsOHuX8rUGwu29cHoZNBgFJpnLLbQs0ZJ7CfeYdXYWk05Mws3CjQYeDXQUvcgv4tPiOfngJAfvHeTgvYM8THqYaX9J65LUc69HE68mVHaoLNNAc8uTCNj5JVz6Z3aImQM0nwSVOmsXNCgqUjOUDFt1lp2XI9HXU/BT58q09/XQdVgvJYmpNzB48GAGDx5MfHx8lkmDgqpKlSo0adKESpUqERAQQLNmzejUqRO2trbPtb116xbp6enUrVtXu83Q0BA/Pz/tiJz69evz5MkTzp49y5EjR2jYsCGNGjVi8uTJgGbE1MiRI7OMJzk5GRMTk0zbzp8/T0JCAvb29s+1vXXrlvZxsWLFtEkpAH9/f1QqFcHBwTRs2JA+ffoQEBDAu+++S9OmTenSpQuurrlTAO/Z+kr/+9//+PXXXzPtNzU1pVu3bnTr1o3r16/TrVs3Pv74Y1JSUvj0009f2Of58+c5fPhwphFSSqWSlJQUkpKSMDMzAzTP+1n+/v7axFCfPn149913KVOmDM2bN6d169Y0a9YsB56xxrPT+J48eULPnj2ZP38+Dg4OLz3O1NQUlUpFampqthN9QghRkFSsWJHz58/j7e1NrVq1mDJlCkZGRsybN++F05yFELmjva872y9FsPHcfUYHNMXA3gce34BTC6HeZ8+171+pP3cT7vLnjT/5fP/nLG2+lHL22ftyUxQOSelJnHt4jmMRxzjx4ARXo6+iUv9bksPUwBQ/Fz/qu9ennkc93C3cX9KbeGvKDE1tuL0/QNoTUOhpVtdsPA5MbXQdXZ5LSsvgo+WnOXgjCiN9PeZ096VZBRddh/VKkpjKQ6aG+lz5JvvFsXP63Nmhr6/P7t27OXLkCLt27WL27Nl8+eWXHD9+HG/v1x/6Z2NjQ5UqVdi3bx9Hjx7l3XffpUGDBnTt2pXr169z48aNl46YcnBwICYmJtO2hIQEXF1dX1iD478jeF5m8eLFDBs2jB07drBmzRrGjRvH7t27qV279kuPc3FxeW71ucjISKysrLJMojw7QuhFxc4zMjLYtWsXy5cvZ9OmTZQoUYIpU6bQo0fWSxInJCQwceJEOnTo8Ny+/ybzslKtWjVCQkLYvn07e/bsoUuXLjRt2jRTHaoXcXFxIS0tjdjY2EzXPDIyEhcXzR++tLQ0duzYwdixYwFNIjM0NDRTvbCndbUMDAwIDg7Wjl6Ljo7G3NxcklJCiEJr3Lhx2vqN33zzDa1bt6Z+/frY29uzZs0aHUcnRNHRqIwTtmaGPHqSyuHbMTSsPxw2fgxHA6HWQDDM/F5EoVAwrvY47ifc59iDYwwJGsKKVitwMc//H/zEm0lXpnMx6iLHHxzneMRxzj86T4YqI1Ob4lbFqedej/ru9anuUh1jfWMdRVvE3N4PO8dC5CXNY/fq0Go6uFXVaVi6Ep2YRv+lJzkTHouZkT7ze9WgbqmXDwjILyQxlYcUCkW2ptPpmkKhoG7dutStW5fx48fj5eXFhg0bGD58eKZ2JUuWxMjIiMOHD2ungKWnp3Py5MlMo3waNmzI3r17OXHiBN9//z12dnaUK1eO77//HldXV0qXLp1lLL6+vkRERBATE6MdtVWtWjUiIiIwMDB4aT2k8PBw7t+/r51GduzYMfT09ChTpkym/n19fRkzZgz+/v6sXLnylYkpf39/tm3blmnb7t27nxuZ9KysamidOXOG5cuXs2rVKjIyMujWrZu2+O2rVKtWjeDg4Cz7furYsWP06tUr02NfX1/tYysrK7p27UrXrl3p1KkTzZs3Jzo6Gjs7uyz7rF69OoaGhgQFBdGxY0cAgoODCQ8P116Hffv2YWtrS5UqVQBNDaqLFy9m6mfcuHE8efKEmTNn4unpqd1+6dKlTDEKIXTr2am+2anFJ17t2VVcS5UqxbVr14iOjsbW1lausRB5yMhAjzZV3Fh6NIw/z9ylYefOsG8SxIbDmWVQ66PnjjHUM2R6o+n02t6Lm7E3GRQ0iGXNl2FhZPGCM4iCJi41jvOPznPu4TnOPjzLpahLpChTMrVxMXehlkstarnWws/FD2dz5yx6E7ki6gbsHg/B/3wmM7WFphPAt1eRqiP1rLDHifRZfJKQqESsTQ1Z0rcmvsWen/WUX+X/LInIU8ePHycoKIhmzZrh5OTE8ePHefTo0QvrL5mbm/Pxxx8zcuRI7OzsKFasGFOmTCEpKSlTYetGjRoxe/ZsHB0dKVu2rHbbnDlz6Ny580vj8fX1xcHBgcOHD9O6dWsAmjZtir+/P+3atWPKlCmULl2a+/fvs3XrVtq3b69N6piYmNC7d29++ukn4uPjGTZsGF26dMHFxYWQkBDmzZtHmzZtcHNzIzg4mBs3bmRK4GRl4MCBzJkzh1GjRvHBBx/w999/88cff7B169ZsX2fQFC9v0qQJLVq04JdffqF169YYGRll+/jx48fTunVrihUrRqdOndDT0+P8+fNcunSJ7777Tttu7dq11KhRg3r16rFixQpOnDjBwoULAZg+fTqurq74+vqip6fH2rVrcXFxeeXIM2tra/r168fw4cOxs7PDysqKoUOH4u/vr03sbd68OVPRcxMTEypWrJipn6fn+e/2gwcP5uiUQiHE2zEzMyM0NFTXYRR6L/tCQAiRezpU82Dp0TB2Xo7gSbuKWNb9BLaOgMMzoXpfMHj+/ZmlkSWBTQLpsa0HN2Ju8Pn+z5ndZDaGerKiWkGiVqu5m3BXm4Q6+/Ast2JvoSbzwk+2xrb4ufpRy7UWtVxq4WnpKV8i6EJSNOybrJlqq8oAhT7U7AcNvwBz+1cfX0iduxNLvyUneZyYhruNKUs/qEkpJ0tdh/VaJDElMrGysuLAgQPMmDGD+Ph4vLy8mDZtmra4+X9NnjwZlUpFz549efLkCTVq1GDnzp2ZalLVr18flUqVacpeo0aNmDlzJo0aNXppPPr6+vTt25cVK1ZoE1MKhYJt27bx5Zdf0rdvXx49eoSLiwsNGjTIVJS8VKlSdOjQgZYtWxIdHU3r1q355ZdfAM2HrGvXrrF06VIeP36Mq6srgwcP5qOPnv9W7L+8vb3ZunUrn332GTNnzsTDw4MFCxZk+vY7O8qXL8+9e/dwdHR8reOeCggI4K+//uKbb77hxx9/xNDQkLJly2oLnT81ceJEVq9ezaBBg3B1dWXVqlWUL18eAEtLS6ZMmcKNGzfQ19enZs2abNu2LVsFx3/++Wf09PTo2LEjqampBAQEaK8vaBJTixYteu3nde/ePY4cOcLvv//+2scKIUR+98EHH2Sr3Zv8/cyP3nTBGCHyUmUPa0o4mnP7USLbL0XQper/NEvNx9+D86ugeu8XHudm4cacxnPou7Mvh+8fZkjQEKY0mIK1ceGqQVuYPE5+zOXHl7kUdUn7Mzol+rl2xSyL4evkq70Vty6OnqJojsTJF9JT4OR8ODAVUuI020q3gHe/AcesZ98UBbuvRDJ01RlS0lVUdLdiUe+aOFllr6xLfqJQq9XqVzcTL/K0+HlcXNxzdYNSUlIICQnB29s72/V+xItFRERQoUIFzpw5k+1V4yZMmMDGjRtfufpbYadQKNiwYQPt2rXL0/OeOXOGxo0b8+jRIwwNX++bw9GjRxMTE8O8efNyKbqcI7/nQhQ9L3vtzw49PT28vLzw9fXlZW/BNmzY8DZh5jtve92EyG2Be28ydWcw/iXsWfVhbTgyB3Z9CbbeMOQU6Gf9ff6Buwf4fP/nJGck42HhwazGs/Cx9cnD6MWLxKbEci3mmiYJFXWZS48vEZEY8Vw7Az0DytuXx9dRk4Sq4lQFB9OCUZen0FOmw7kVsH+KJlEM4FwJAr6DEo10Glp+sPxoKF9vvoxKDY3KOBLYvRrmxvln7NHrvPbnn6iFyIKLiwsLFy4kPDw824kpoVsZGRnMnj37tZNSAE5OTs/VMxNC6FZycjINGmiWRD9w4IAsTPAWPv74Y1atWkVISAh9+/blf//7n0zhEyIfaOfrztSdwRy9/Zi7MUl41OgLB6dBTAhc3gCVsy4/0cCjActbLOeTvZ9wN+EuPbb14Id6P9DUq2kePoOiK0OVQWhcKNdjrnM95jrBMcFcj7nOw6SHz7VVoMDb2puKDhUpb1+eig4VKWNbBhMD+YIxX1Gp4NJ62PcDRN/WbLNyh0ZjoGp30Mvewl6FVbpSxXd/XWHp0TAA3q/pyXftKmKgX3BH9UliShQIeTnip0KFCoSFhb1w32+//fbSlfIKixUrVmQ5rdHLy4vLly+/9Hg/Pz/8/Pze6NwjRox4o+OEELlHpVJx6tQp7X3x5gIDA5k+fTp//vknixYtYsyYMbRq1Yp+/frRrFkzqVkihI6425jiX8Keo7cfs+ncfQa/UwpqD4K938HBn6Bix5cWVS5jV4ZVrVYxcv9Ijkcc57N9n/FR5Y8YVHWQTAHLIWq1msikSG7H3uZm7E2CY4K5EXODW7G3SFOlvfAYDwsPKjpUpIJ9BSo4VKC8fXnMDc3zOHKRbWq1pqD539/BwyuabWYOUH8E1PgADCWBGJOYxqAVZzh6+zEAIwPKMKhRyQL//kGm8r0FmcpXOIWFhZGenv7Cfc7OzlhaFqxCcm/iyZMnREZGvnCfoaGhjFz7h/yei6IiMTERCwvNalMJCQmYmxfdN/U5PSUtLCyMJUuWsGzZMjIyMrh8+bL2WhcmMpVPFARrT91h5LoLlHA0J2h4QxQpcTCjEqTGQ9ffodx7r+wjQ5XBtFPT+P2qplZmQ4+GjKs9Dhdzl9wOv9BIU6YRHh9OSHwIt2NvExIfQkic5packfzCY8wMzChtW5rStqUpY1eG0ral8bH1kSRUQaFSwbUtmlGKD85rthlbQ92hUOtjMC58r4tvIjjiCf2XneROdDLmRvr83LUqzSrk378tMpVPiLcgSRdNUfSikIATQghd09PTQ6FQoFarpUC4EDrWopIr4zdd5vajRM6Ex1Ddyw78Bmg+LB/4Ccq2hleMSjDQM2C032jK2Zdj4pGJ7L+7n6N/HqVr2a70r9QfOxOZuguQkpHCvYR73H1ylztP7nDnyR3uJtwlLD6Mu0/uolS/+O+hgcIATytPSliXoIxtGUrbaZJR7hbuMjKtIFJmwKV1cHA6RAVrthmaQe2Poc5QMLV9+fFFyO4rkXy6+iyJaUo87UxZ0KsmZVwKz+c1SUwJIYQQQuSh1NRU7VS+Q4cO0bp1a+bMmUPz5s2ztSqqECJ3WBgb0KqyK+tO32XNyTuaxFTtQXBsLjw4B7eCoFT26ka1KdkGHxsfppycwqnIUyy/spz119fTq0IvepfvjYVR4R4BolareZzymPsJ9zMln54moF5U/+lZFoYWlLAuQXHr4nhbe+Nt7U0J6xJ4WHpgqPf6NUxFPpORqilqfmgGxP5TQsXYGmp9qBkhZW6v0/DyE6VKzcygG8z++wZqNfiXsOeXHtWwNTfSdWg5ShJTQgghhBB5ZNCgQaxevRpPT08++OADVq1ahYODrP4kRH7RtaYn607f5a8LDxj/XgUszB2geh849otm1FQ2E1MA5ezLsShgEUfuH2HmmZlcjb7Kr+d/ZdW1VbQv1Z4mxZpQ2bFygRzp8yTtCRGJETxIfEBEYsS/tyTNz8jEyCzrPj1lYWiBp6UnHpYeeFh64GnpSTHLYpSwLoGDqUOBr5kjXiApGk4tghPzIeGfFRLNHMB/ENTsDybWuo0vn3mckMqna85x8EYUAL38vfiqdXkMC3CR86xIjam3IDWmhCja5PdcFBVSY+pfb1srSU9Pj2LFiuHr6/vSD11//vnn24SZ70iNKVFQqNVqmkzfz+1HiUzuUIn3/YpB/H2YWQWUadBnGxSv+0b97g7bzZxzcwiJC9FudzR1pHGxxjQp1oSqTlUxNdDdqqdqtZr4tHgeJz8mKjmKqOQoHiU/eu7xg8QHJKYnvrI/BQoczRzxtPTUJKAsPP69b+mBjbGNJJ+KiqgbmuTuuVXwtE6YpRvUHQbVeoORmW7jy4dOh8UweMUZIuJTMDXU5/v2FelQzUPXYb0WqTElhBBCiBwlo3pyRq9eveSDmBD5mEKhoEsNTyZvv8aaU3c0iSkrN80S9aeXaFboe4PElEKhoFnxZjQu1ph9d/axO2w3B+4e4FHyI9YEr2FN8BoUKPCy8sLH1ofStqUpaVMSB1MH7EzssDOxw8LQIlt/P5QqJWmqNFIyUohLjSM+LZ641Dji0uKIT43X/ny6PSYlRpt4etUop2dZG1vjau6Ki5kLzubOuJi7aB6bu+Bi7oKTqROG+jLtrshSqyHkABwNhBs7/93uUhn8h0CF9mBQuKaj5QS1Ws3iw6H8sO0qGSo1JRzNmdujeqGqJ/UiMmLqLciIKSGKNvk9F6LokZE/b0aumyhIHj5JwX/S3yhVanZ/1gAfZ0uIDoHZ1UGthJ4boGTjtz5PmjKN4w+OExQexP67+4lKjnppe0M9Q0wMTDDUM8RI3whDPUNtEipNmUa6Kp00ZVqWhcOzy9LIEkdTRxxMHbA3tcfB1CHTY1dzV5zNnDEzlFEu4gVS4uDCH5opew+v/LNRAWVagP9g8Kr7ykUEiqrYpDS+WH+RHZc10xxbVXblx46VsTAumOOJZMSUKDAaNWpE1apVmTFjBgDFixfn008/5dNPP9VJPD179qRcuXKMHTtWJ+cX+Uvt2rUZOXIkHTt21HUoQgghhMgjTpYmNC7rxO4rkaw5eYdxrcuDnbdmhb7jv8L20TDw8FuP9jDSN6K+R33qe9QHICo5iusx17kRc4PrMdcJjQ8lOjma6JRokjKSSFelk56W/lrnsDC0wMrICmtja6yMrbT3rY00j62NrLExscmUeDLWN36r5yWKqPtnNcmoi+sgPUmzzdAMqvbQrLJnX1K38eVzR25FMXzNeSLiUzDUVzC2ZTn61CleZEZZS2JK5CsnT57UWe2S8+fPs23bNubOnauT87/IhQsXGDx4MCdPnsTR0ZGhQ4cyatQoXYeVp9RqNV9//TXz588nNjaWunXrMnfuXHx8fDK1S05OxsHBgfPnz2Nubs6IESM4deoUN2/eZNiwYdrk57PWrl3LV199RWhoKD4+Pvz444+0bNlSu3/cuHF89tlntG/fXlbKEkIIIYqQrjU82X0lkj/P3mNU87IYGehBozGaD91R1zUJqrrDcvScDqYOOJg6UMetznP7kjOSiU2JJUWZoklQKdNJV6Wjr9DHUN8QIz0j7U8jfc3NWN8YAz35uCdyUVoiXFqvSUjdP/vvdseyUOMDqNwVTG10Fl5BkJah4uc91/l1/y3UaijhYM6sbr5UdC9aheDlk5bIVxwdHTEz082w4NmzZ9O5c2dtgV9di4+Pp1mzZnh5eXH69GmmTp3KhAkTmDdv3mv1k5KSwqNHj3Ipytw3ZcoUZs2axa+//srx48cxNzcnICCAlJSUTO12796Nl5cXpUqVIjU1FUdHR8aNG0eVKlVe2O+RI0fo1q0b/fr14+zZs7Rr14527dpx6dIlbZsWLVrw5MkTtm/fnqvPUYj8Ljk5mUaNGtGoUSOSk5N1HY4QQuS6RmUccbI0JjoxjT1XIzUbTW3g3Yma+/t/hPgHeRaPqYEprhaueFt7U9q2NBUcKlDVqSqVHCtR1q4sJWxK4GnpibO5M7YmtpgbmktSSuQOlQpCD8HGQTDVBzYP1SSl9I2gUmfoux0GHYNaH0lS6hVCohLp9OsR5u7TJKW6+Xny17B6RS4pBZKYEi/QqFEjhg4dyqeffoqtrS3Ozs7Mnz+fxMRE+vbti6WlJaVKlXruw/qlS5do0aIFFhYWODs707NnT6Ki/p0rn5iYSK9evbCwsMDV1ZVp06Y9d+7ixYtrR7aEhoaiUCg4d+6cdn9sbCwKhYJ9+/YBsG/fPhQKBTt37sTX1xdTU1MaN27Mw4cP2b59O+XKlcPKyoru3buTlJSU5XNWKpWsW7eO9957L9P21NRUPv/8c9zd3TE3N6dWrVracwMsWbIEGxsbNm7ciI+PDyYmJgQEBHDnzh1tm/Pnz/POO+9gaWmJlZUV1atX59SpU6/6Z2DFihWkpaWxaNEiKlSowPvvv8+wYcOYPn36K499VmRkJO7u7rRr144NGzaQnv56Q8ABDh06RP369TE1NcXT05Nhw4aRmPjvaizFixfn22+/pVu3bpibm+Pu7k5gYKB2v1qtZsKECRQrVgxjY2Pc3NwYNuzV3zKq1WpmzJjBuHHjaNu2LZUrV2bZsmXcv3+fjRs3Zmq7adMm2rRpo41n5syZ9OrVC2vrF/9hnzlzJs2bN2fkyJGUK1eOb7/9lmrVqjFnzhxtG319fVq2bMnq1atf53IJUeioVCr279/P/v37UalUug5HCCFynYG+Hp2qa1bAWnPy3/d1VOkO7jUgLQF2j9dRdELoQHQI7J0Es6rAklZwbgWkJ4JdCXj3Gxh+FTouAK86UkPqFVQqNcuPhtJq1kEu3I3D2tSQX/9XjUkdKmNmVDQTypKYyktqtWa4oy5ur1njfunSpTg4OHDixAmGDh3Kxx9/TOfOnalTpw5nzpyhWbNm9OzZU5vsiY2NpXHjxvj6+nLq1Cl27NhBZGQkXbp00fY5cuRI9u/fz6ZNm9i1axf79u3jzJkzOXJpJ0yYwJw5czhy5Ah37tyhS5cuzJgxg5UrV7J161Z27drF7Nmzszz+woULxMXFUaNGjUzbhwwZwtGjR1m9ejUXLlygc+fONG/enBs3bmjbJCUl8f3337Ns2TIOHz5MbGws77//vnZ/jx498PDw4OTJk5w+fZovvvgCQ8NXr1By9OhRGjRogJHRv/ULAgICCA4OJiYmJtvXxsvLi6NHj+Ll5cVHH32Eq6srw4YN4/Tp09k6/tatWzRv3pyOHTty4cIF1qxZw6FDhxgyZEimdlOnTqVKlSqcPXuWL774gk8++YTdu3cDsH79en7++Wd+++03bty4wcaNG6lUqdIrzx0SEkJERARNmzbVbrO2tqZWrVocPXpUu02lUvHXX3/Rtm3bbD0n0FzfZ/sFzfV9tl8APz8/Dh48mO1+hRBCCFE4dKnhCcCBG4+4H/vPaFE9PWg5FVDAxT8g9LDuAhQityVFa1ajXNwSZlWF/ZMhNhyMraBaL/hgJww9A3U/AXNZvTc77kQn0WPBcb7adJmkNCW1S9ix49P6NK/oquvQdKpopuN0JT0JfnDTzbnH3gej7NduqlKlCuPGjQNgzJgxTJ48GQcHBwYMGADA+PHjmTt3LhcuXKB27drMmTMHX19ffvjhB20fixYtwtPTk+vXr+Pm5sbChQv5/fffadKkCaBJfnl4eOTI0/vuu++oW1ezdG+/fv0YM2YMt27dokSJEgB06tSJvXv3Mnr06BceHxYWhr6+Pk5OTtpt4eHhLF68mPDwcNzcNP9un3/+OTt27GDx4sXa55qens6cOXOoVauW9nmVK1eOEydO4OfnR3h4OCNHjqRs2bIAz9VGykpERATe3t6Ztjk7O2v32draZqsfgOrVq1O9enWmTZvG9u3bWbZsGXXr1sXHx4fevXvTs2dPbd//NWnSJHr06KEtSO/j48OsWbNo2LAhc+fO1a5GV7duXb744gsASpcuzeHDh/n555959913CQ8Px8XFhaZNm2JoaEixYsXw8/PL1jV49nk/ex2e7gM4duwYgPbfIDsiIiJe2S+Am5sbd+7cQaVSSZ0pIYQQoggp7mBOLW87jodEs+70XYY1+ec9nHs1qN5b84F9+yj4cD/oy8cqUUgkx8K1rXD5T7i9D1QZ/+xQQMl3NKMGy7YCI1mV8XWoVGpWHA9j0vZrJKUpMTXU54sWZelZ2ws9PRlhJp+yxAtVrlxZe19fXx97e/tMI1yefqB/+PAhoJmutnfvXiwsLLS3p4mYW7ducevWLdLS0jIlDuzs7ChTpkyOx+vs7IyZmZk2KfV029NYXyQ5ORljY+NMqx5cvHgRpVJJ6dKlMz2v/fv3c+vWLW07AwMDatasqX1ctmxZbGxsuHr1KgDDhw+nf//+NG3alMmTJ2c6NqdVqFBBG2eLFi2e229gYMB7773H2rVrCQkJwcXFhZEjRzJp0qQs+zx//jxLlizJdA0CAgJQqVSEhIRo2/n7+2c6zt/fX3sNOnfuTHJyMiVKlGDAgAFs2LCBjIwMcsqmTZto3bp1riSOTE1NUalUpKam5njfQgghhMjfutbUjJr649QdVKpnZiA0Hg+mthB5SVP4WYiCLPUJXPgDVr4PP/nApkFwc48mKeVSCZpOgM8uQ88NULmzJKVe039HSfl5a0ZJ9a5TXJJS/5DU/hsIDAwkMDAQpVL5egcammlGLumC4ev98fjvVDOFQpFp29MEztNaIwkJCbz33nv8+OOPz/Xl6urKzZs3XzdibZJB/cw0xKzqI/03thfF/7K6KA4ODiQlJZGWlqadOpeQkIC+vj6nT59GX18/U/vXKZA+YcIEunfvztatW9m+fTtff/01q1evpn379i89zsXFhcjIyEzbnj52cXF54THbtm3TXiNTU9Pn9qvVag4ePMjy5ctZu3Yttra2jB8/nn79+mUZR0JCAh999NELa0IVK1bspc/hKU9PT4KDg9mzZw+7d+9m0KBBTJ06lf379790WuPT5xkZGYmr67/DWyMjI6latar28ebNm5k8eXK2Ynm27xdd3/9e2+joaMzNzV94PYUQQghRuLWo6MrXmy5zNyaZo7cfU7fUP9OVzO2h8VewdTjs/Q4qtAcLR90GK8TreBIJ17fDtW2akVHKZ76EdSwHFTtAhQ7gUEpnIRZ06UoVCw6GMDPoOinpKkwN9RndvAy9/CUh9V+SmHoDgwcPZvDgwcTHx2dZWPmFFIrXmk5XkFSrVo3169dTvHhxDAye/29VsmRJDA0NOX78uDaZERMTw/Xr12nYsOEL+3R01Ly4P3jwAF9fX4BMhdBz0tMkx5UrV7T3fX19USqVPHz4kPr162d5bEZGBqdOndJOTQsODiY2NpZy5cpp25QuXZrSpUvz2Wef0a1bNxYvXvzKxJS/vz9ffvkl6enp2uTN7t27KVOmTJbT+Ly8vF64/fr16yxfvpzff/+dqKgoOnXqxMaNG2nYsGGmUWIvUq1aNa5cuUKpUi9/UXo6ne7Zx89eA1NTU9577z3ee+89Bg8eTNmyZbl48SLVqlXLsk9vb29cXFwICgrS/rvEx8dz/PhxPv74YwBu3LhBWFgY77777kvj+y9/f3+CgoK0UxRBc33/O/Lr0qVL2v9/QgghhChaTI30aVPVjRXHw1l98s6/iSmA6n000/kiLkDQRGg7J6tuhNA9tRqirmum6QVvg7ungGdGAdqX0iSiKnYAp3JZdiOy51RoNGM3XOR6ZAIAtUvY8WPHynjZF858wNuSxJTIEYMHD2b+/Pl069aNUaNGYWdnx82bN1m9ejULFizAwsKCfv36MXLkSOzt7XFycuLLL7986dQrU1NTateuzeTJk/H29ubhw4faulc5zdHRkWrVqnHo0CFtAqR06dL06NGDXr16MW3aNHx9fXn06BFBQUFUrlyZVq1aAZrRWkOHDmXWrFkYGBgwZMgQateujZ+fH8nJyYwcOZJOnTrh7e3N3bt3OXnyJB07dnxlTN27d2fixIn069eP0aNHc+nSJWbOnMnPP//8Ws8tPDyccuXK0ahRIyZOnEjHjh0xN8/+H8TRo0dTu3ZthgwZQv/+/TE3N+fKlSvs3r070wp2hw8fZsqUKbRr147du3ezdu1atm7dCmhWL1QqldSqVQszMzN+//13TE1Ns0ykPaVQKPj000/57rvv8PHxwdvbm6+++go3NzfatWsHaKbxNW3aFDOzzKMCnyYxExISePToEefOncPIyIjy5csD8Mknn9CwYUOmTZtGq1atWL16NadOnWLevHmZ+jl48CDNmjXL9vUSorD67++YENnxxqPMhchH3q9ZjBXHw9l5OYLYpDRszP5ZmEZPH1r+BIuawdnl4NsTimW/3qUQuS49BcKPwM0gCN4O0f8pKeLmC2VaQdmW4FReVtPLAbFJaUzefo3V/6zmaWduxJcty9GhmvsrBwQUZZKYEjnCzc2Nw4cPM3r0aJo1a0ZqaipeXl40b95cm3yaOnWqdsqfpaUlI0aMIC4u7qX9Llq0iH79+lG9enXKlCnDlClTci1J0L9/f5YtW5ZptbnFixfz3XffMWLECO7du4eDgwO1a9emdevW2jZmZmaMHj2a7t27c+/ePerXr8/ChQsBTX2ux48f06tXLyIjI3FwcKBDhw5MnDjxlfFYW1uza9cuBg8eTPXq1XFwcGD8+PF8+OGHr/W8HBwcCAkJyfa0u/+qXLky+/fv58svv6R+/fqo1WpKlixJ165dM7UbMWIEp06dYuLEiVhZWTF9+nQCAgIAsLGxYfLkyQwfPhylUkmlSpXYsmUL9vb2rzz/qFGjSExM5MMPPyQ2NpZ69eqxY8cObdH1TZs20bt37+eOe3aU0+nTp1m5ciVeXl6EhoYCUKdOHVauXMm4ceMYO3YsPj4+bNy4kYoVK2qPu3fvHkeOHOH3339/7esmRGFibm5OYmKirsMQBdAbjzIXIh+p6G5FOVcrrj6IZ+PZe/Sp+8ziNMVqQdUecG4FrO0DH+0HC6cs+xIiV6nVEHUDbgVpakSFHoaM5H/36xmCdwNNIqpMS7DS0cJchZBKpWbdmbv8uP0ajxPTAOhaw5MvWpTF1tzoFUcLhfrZAj7itTx9kxUXF4eVlVWmfSkpKYSEhODt7a39AC3yt+TkZMqUKcOaNWuem86VlSVLlvDpp58SGxubu8Hlc8WLF+fTTz/NNC0uL0RFReHq6srdu3ezXFXwbYwePZqYmJjnRlE9Jb/nQhQ9L3vtF1mT6yYKuiWHQ5iw5QrlXK3YNqxe5pEPKfGwoIlmmlSxOtBrExjIB1GRRxKjIPQQ3N4LN/+GuPDM+y1doWQTKNUESjUFE/kbnNNOhUYzccsVLt7TDLrwcbLg+/aV8PO203FkuvU6r/0yYkqIf5iamrJs2TKioqJ0HYrIpujoaKZPn54rSSkAJycnhg8fnit9CyGEEKLgaOfrzg/br3H1QTynw2KoUfyZD5wmVvD+SpjfWDNtateX0HKq7oIVhVviYwg7pElGhR6Ch1cy79c3gmL+miRUqSYyRS8X3Y9NZvL2a2w+r1ngzMLYgKGNS9G3rjdGBjm/WnhhJokpIZ7RqFGjPDtXixYtOHjw4Av3jR07lrFjx+ZZLLpy8OBBWrRokeX+hISElx7/tKh8bhkxYkSu9S1EQZKSkqKtjbd+/XoZISiEKHJszIzo4OvO6pN3mH/wdubEFICDD3SYB6vehxPzwLUq+PbQSayikHkSAXdOPJOIuvx8G6fyULy+JhFVvF6hXXArv0hOUzLvwG3m7r9JSroKhUIzbW9EszI4WhrrOrwCSabyvQWZyifexr1790hOTn7hPjs7O+zsCv/Qz+TkZO7du5fl/letBKhr8nsuiorExEQsLCwATcL4dRZQKGxkStqbkesmCoPrkU9o9vMBFArY93mjF6+ute9H2PcD6BvDB9vBvXreByoKLmU6RF7SJKLunIC7JyA2/Pl2juU0CSjv+uBVF8wdnm8jcly6UsUfp+4wc88NHj5JBaBmcVu+fq8CFd2ljuJ/yVQ+IQoAd3d3XYegc6ampvk++SSEEEIIAVDa2ZKGpR3Zf/0Riw+HMqFNhecbNRgJD85D8FZY0xM+3CfF0MWLqdUQfw/un4N7pzSJqHtnMhcrB0ABzhWgWG3NqCivumDhqIuIiyy1Ws22ixFM2xXM7SjNYjDuNqaMaVmWVpVcZbW9HCCJKSGEEEJk29PV+Z4dNZWSkoJSqczyGDMzM+2bttTUVDIyMnKkrampqXbl17S0NNLT01/YjxBC5JQB9Uuw//oj/jh1h8+alsbazDBzAz09aP+rpt7U4xualfp6bgADmd5TpKnVEHdHk4R6cO6fn+ch6QW1bU2swaMmeNbS/HSvLgXLdejwzSh+3HGNC3c1hc3tzI0Y8k4petQuhrGBvo6jKzwkMSWEEEKIbHu62MCzlQB69uzJunXrsjzm2el/H330EUuXLs2y7cOHD3F01HwTPHz4cH755Zcs24aEhFC8eHEAvvzyS3766Sftvrp163Lw4EFJTgkhclTdUvaUdbHkWsQTVp0MZ2DDks83erYYethhWN4B3v8dTG3zPmCR9zLSNEnJyCuaelAPzmsSUcnRz7dV6INTOXDzBU8/TTLK3keT4BQ6dez2Y2YF3eDIrccAmBnp079+CQbU98bSxPAVR4vXJYkpIYQQQryUmZkZdevW5fDhw7oOJdsOHz5MUlJSka6HJYTIeQqFgn71vBm57gJLDofSr543hvovSCI4ltYko1b/T7OC2oJ3ocdasPPO+6BF7lCpIC78nwTUP7fIK5qklOoFo331DDRJKNeq4FZV89O5Ahia5nHgIitqtZqjtx8zc88NjodoEomG+gq6+xVjSGMfKWyei6T4+VuQ4udCFG3yey6KErVaTVJSkvZxfp3Kl5iYqB3VlRuF2qWI95uR6yYKk9QMJXUn7yUqIZWZ71elbdWX1A2NuAQru2hqCZk5QPc14FEj74IVby89GR7fgsc3NUmnqH9+PgqGtCxWkDa20iShnMqDSyVNIsqpAhjK+8X8SK1Wc/imZoTUiVBNQspIX48uNT0Y2LAkHrZmOo6wYJLi50IIIYTIUQqFIsskz+skZo2NjTE2zt43jq/T1sjICCMjo2zHIYQQb8rYQJ/e/l5M232d+Qdv06aKW9bThl0qQv8gTXIq4gIsaQUd5kH5tnkbtHg5ZTrE3YWYEE0SKurGv0mouDtAFmM59I3AoYwmCeVcXpN8cioH1h4gU8nzPZVKze6rkfy2/xZnwmMBTULqfT9PBjYsiZuNjGbLK5KYEs9Rq9V89NFHrFu3jpiYGM6ePUvVqlXz7PwLFy5kzZo17Nq1K8/OKfKv999/n5o1azJixAhdhyKEEEIIAUCP2l7M2XuTS/fiORESTa0S9lk3tnKFvtth3QdwYyf80RvqfgINPgdjy7wLuihTqyHpMcSE/nuLDfv3ftw9UGc98hcTa03tJwcfsC+l+elQBuxLgr7UGypoUtKVrD9zlwUHQwj5Z5U9YwM9uvkVY2DDkrhYy8i2vCaJKfGcHTt2sGTJEvbt20eJEiVwcHB46z4VCgUbNmygXbt2L22XkpLCV199xdq1a9/6nDklOjqaoUOHsmXLFvT09OjYsSMzZ87EwsJC16HlqbVr1/LVV18RGhqKj48PP/74Iy1btnyu3TvvvEOPHj3o37//C789XLVqFe+//7728b59+xg+fDiXL1/G09OTcePG0adPH+3+cePG0aBBA/r374+1tXWuPDchROFhamrKpUuXtPeFECI32Jkb0bG6ByuPh7PgUMjLE1MAxhaagug7voCT8+HwDDi3Ehp/Cb49QU9W93or6ckQf18z6in+nibRFH/v3/uxYVlPu3vKwARsimkST0+TT0+TUWb2MgKqEIhJTGP5sTCWHgnlcWIaAFYmBvT096J3neI4WUpCSlckMSWec+vWLVxdXalTp06en3vdunVYWVlRt27dPD93Vnr06MGDBw/YvXs36enp9O3blw8//JCVK1e+Vj/h4eEUK1Ysl6LMXUeOHKFbt25MmjSJ1q1bs3LlStq1a8eZM2eoWLGitl10dDSHDx9m9erV2m2LFy+mefPm2sc2Njba+yEhIbRq1YqBAweyYsUKgoKC6N+/P66urgQEBABQsWJFSpYsye+//87gwYNz/8kKIQo0PT09KlSooOswhBBFwAd1vVl5PJw9VyMJiUrE2+EVNe30DaDlVCj5DuwaB9G3YcsncHweBHwHJRvnTeAFiTIdEh9BQiQkPPznZyTEP8iceHrRinfPUYCVG9h4gW1xsH36s7hmm4WzrIZXSAVHPGHZ0VDWn7lLSroKAHcbU/rV86ZrTU/MjSUtomtS/PwtFMbi53369Mm0jLeXlxehoaHs2LGD7777jkuXLqGvr4+/vz8zZ86kZEnNErlpaWkMHz6c9evXExMTg7OzMwMHDmTMmDEUL16csLCw5/p8kdatW1OuXDmmTp2aafuCBQuYNm2admnwYcOGMWjQIABCQ0Px9vZm1apVzJo1izNnzlCqVCkCAwNp2LAhADExMQwZMoRdu3aRkJCAh4cHY8eOpW/fvi+9HlevXqV8+fKcPHmSGjU0hSp37NhBy5YtuXv3Lm5ubtm+tt7e3jg7O9O7d2/ef/99bG1fb8ngO3fuMGLECHbt2oWenh7169dn5syZ2qXS+/TpQ2xsLL6+vsyZM4fU1FS6d+/OrFmztHVX1q1bx8SJE7l58yZmZmb4+vqyadOmVxYH7tq1K4mJifz111/abbVr16Zq1ar8+uuv2m3Lly8nMDCQY8eOAa8eKTd69Gi2bt2qHd0Amql7sbGx7NixQ7vtm2++Yffu3Rw8ePC1rlluK6i/50KINydFvN+MXDdRWH2w5CR/X3tIL38vvmlb8dUHPJWRBqcWwr7JkBKr2eZaBSp2goodNDWKCqv0FE0iKSkakqIyJ5y09//5mfQ4+/0amoO1O1i5//vz6X0bL7D2lOLjRUi6UsWuy5EsPRrKiZB/E5cV3a34sEFJWlZ0weBFK2qKHCPFz/MptVpNckayTs5tamCadVHGZzxNNs2bN4+TJ0+ir68ZVpyYmMjw4cOpXLkyCQkJjB8/nvbt23Pu3Dn09PSYNWsWmzdv5o8//qBYsWLcuXOHO3fuAHDy5EmcnJy0I2ee9vkihw4domfPnpm2rVixgvHjxzNnzhx8fX05e/YsAwYMwNzcnN69e2vbjRw5khkzZlC+fHmmT5/Oe++9R0hICPb29nz11VdcuXKF7du34+DgwM2bN0lOfvW/xdGjR7GxsdEmpQCaNm2Knp4ex48fp3379q/s46kDBw6wfPlyZs2axWeffUabNm3o3bv3K68JQHp6OgEBAfj7+3Pw4EEMDAz47rvvaN68ORcuXNAmnoKCgjAxMWHfvn2EhobSt29f7O3t+f7773nw4AHdunVjypQptG/fnidPnnDw4EGyk5s+evQow4cPz7QtICCAjRs3Ztq2efNm2rbNXMxz8ODB9O/fnxIlSjBw4ED69u2r/b949OhRmjZt+ly/n376aaZtfn5+fP/996Smpma7ELIQomhKS0vjhx9+AGDs2LFSEF0Ikav61/fm72sPWXvqLsPfLY2NWTb/5hgYQe2PoXJXODAVTsyHB+c1t91fQbE6UKEdePppCmob5MO/ZWq1Znpccuw/iabH/ySbov/z+PE/j2M099MTX+88egZg7gQWTppRTRZOYOmSOfFk5a6pAyXT7Yq8h/EprDpxh5UnwoiMTwVAX09BQAVnetYuTu0Sdtn6XCzyliSm8lByRjK1VtbSybmPdz+OmeGrl7m0trbG0tISfX19XFxctNs7duyYqd2iRYtwdHTkypUrVKxYkfDwcHx8fKhXrx4KhQIvLy9tW0dHR0AzhevZPv8rNjaWuLi450Yhff3110ybNo0OHToAmpFHV65c4bfffsuUmBoyZIg2zrlz57Jjxw4WLlzIqFGjCA8Px9fXV5tgejrK6FUiIiJwcnLKtM3AwAA7OzsiIiKy1cdTnp6ejB07lrFjx3LixAmWLVtGnz59MDAwoEePHvTp0yfTtLhnrVmzBpVKxYIFC7R/SBcvXoyNjQ379u2jWbNmgGZVqkWLFmFmZkaFChX45ptvGDlyJN9++y0PHjwgIyODDh06aP99KlWqlO3r8HT59aecnZ0zXYPU1FR27NjBhAkTtNu++eYbGjdujJmZGbt27WLQoEEkJCQwbNiwl/YbHx9PcnKytj6Mm5sbaWlpREREZPq/JYQQ/5Wens7EiRMBzRcWkpgSQuQm/xL2lHe14sqDeBYdCmF4szKv14GZHTSfBPVHwJWNcOlPCDsM4Uc0N9Cs/OZcAVyrgp33PwkZN7B0BVMbMLLUTBPMDpUKMlIgPemfW3Lmn6kJkBoPKXGQ8s/P1Phn7sf9uy81HtSq13u+Tyn0Nc/dzP6fZJPzM4mn/9w3tZUpduKlMpQqDtx4xB8n77LnaiQZKs0X7w4WxnT386RbrWK4WkvdyfxMElMiW27cuMH48eM5fvw4UVFRqFSaF6Hw8HAqVqxInz59ePfddylTpgzNmzendevW2mRJdj0dwfTslKjExERu3bpFv379GDBggHZ7RkbGc4Ww/f39tfcNDAyoUaMGV69eBeDjjz+mY8eOnDlzhmbNmtGuXbtcq6E1cOBAfv/9d+3jhITnCy36+fnh5+fH9OnTGTNmDNOnT2fPnj2cO3fuhX2eP3+emzdvYmmZeeWWlJQUbt26pX1cpUoVzMz+TUD6+/uTkJDAnTt3qFKlCk2aNKFSpUoEBATQrFkzOnXq9NpTCrPy999/4+TklKm2y1dffaW97+vrS2JiIlOnTtUmprLraYIqKSkpR2IVQgghhMgJCoWCoY1L8fGKM8w7eJvutbzebEUvcweo2V9zi7sHl/+Em0Hw4Bwkx8D9s5pbVvSNwcgMFHqakUxa/9xXqyEjFXJj9oaeoSbB9DTRZGr7n8d2zzy20zyW0U0iB4REJbL21B3Wn7mrHR0FUN3Lll7+XrSo6IqRgSQ1CwJJTOUhUwNTjnc/rrNzv4333nsPLy8v5s+fj5ubGyqViooVK5KWplnNoFq1aoSEhLB9+3b27NlDly5daNq0KevWrcv2Oezt7VEoFMTExGi3PU3qzJ8/n1q1Mo82e9X0t2e1aNGCsLAwtm3bxu7du2nSpAmDBw/mp59+eulxLi4uPHz4MNO2jIwMoqOjsxz99c033/D555+/tN/g4GCWL1/O77//TlxcHAMGDKBfv35Ztk9ISKB69eqsWLHiuX1PR6S9ir6+Prt37+bIkSPs2rWL2bNn8+WXX3L8+HG8vb1feqyLiwuRkZGZtkVGRma6Bps3b6ZNmzYv7adWrVp8++232il5WfVrZWWVaTWt6Ojo13quQgghhBB5pXlFF2p42XIqLIafdgXzU+cqb9ehtTvUGaq5qdWaFeXun4UHF/5Zde4+PLmv+ZmRojlGmQrJqS/v978MTMDQFAzN/v1pZK5JGhlbaX6aWGW+b2INxs/et9IcK0kmkUcSUjPYcSmCP07dyVQ7ytbMkPa+HnSp6UFZF6llWNBIYioPKRSKbE2ny28eP35McHAw8+fPp379+oCmFtR/WVlZ0bVrV7p27UqnTp1o3rw50dHR2NnZYWhoiFKpfOl5jIyMKF++PFeuXNGOtnJ2dsbNzY3bt2/To0ePlx5/7NgxGjRoAGiSR6dPn2bIkCHa/Y6OjvTu3ZvevXtTv359Ro4c+crElL+/P7GxsZw+fZrq1asDmpFBKpXquUTZU05OTs9N/wOIiopi9erVLF++nNOnT/Puu+8yefJk2rVr98rC2dWqVWPNmjU4OTm9tHDc+fPnM02BO3bsGBYWFnh6egKa/4N169albt26jB8/Hi8vLzZs2PBc/agXXYegoKBMtZ92796tHaWmVqvZsmVLppFiL3Lu3DlsbW21daL8/f3Ztm1bpjbP9vvUpUuX8PDwwMHB4aX9CyGEEELkNYVCwbjW5WkXeJj1Z+7Sp05xKrpbv/rA7HX+78pxFV5Q2zQjTVPnKS1RMxXv6WipTImif+4bmvybhDIwlelxosBIy1Cx//ojNp27x56rkdqV9fQU0KC0I11qeNK0nLOMjirAJDElXsnW1hZ7e3vmzZuHq6sr4eHhfPHFF5naTJ8+HVdXV3x9fdHT02Pt2rW4uLhgY2MDaGo6BQUFUbduXYyNjbOcPhYQEMChQ4cyJUAmTpzIsGHDsLa2pnnz5qSmpnLq1CliYmIyJVQCAwPx8fGhXLly/Pzzz8TExPDBBx8AMH78eKpXr06FChVITU3lr7/+oly5cq987uXKlaN58+YMGDCAX3/9lfT0dIYMGcL777//WivygWa0kImJCb1792bjxo24urpm+9gePXowdepU2rZtyzfffIOHhwdhYWH8+eefjBo1Cg8PzcotaWlp9OvXj3HjxhEaGsrXX3/NkCFDtMXag4KCaNasGU5OThw/fpxHjx5l6zp88sknNGzYkGnTptGqVStWr17NqVOnmDdvHgCnT58mKSmJevXqaY/ZsmULkZGR1K5dGxMTE3bv3s0PP/yQaTTZwIEDmTNnDqNGjeKDDz7g77//5o8//mDr1q2Zzn/w4MHXnhoqhBBCCJFXqnra0KaKG5vP3+f7rVdZOaBW3hRYNjACg3+myAlRiKhUao6HRLP5/D22XYwgLjldu6+4vRmdqnvQsbqH1I4qJCQxJV5JT0+P1atXM2zYMCpWrEiZMmWYNWsWjRo10raxtLRkypQp3LhxA319fWrWrMm2bdvQ++ebmGnTpjF8+HDmz5+Pu7s7oaGhLzxXv379qFGjBnFxcdoaUv3798fMzIypU6cycuRIzM3NqVSp0nMrt02ePJnJkydz7tw5SpUqxebNm7UjbIyMjBgzZgyhoaGYmppSv359Vq9ena3nv2LFCoYMGUKTJk3Q09OjY8eOzJo16/UuIrB161bKli372scBmJmZceDAAUaPHk2HDh148uQJ7u7uNGnSJNMIqiZNmuDj40ODBg1ITU2lW7du2mLkVlZWHDhwgBkzZhAfH4+XlxfTpk2jRYsWrzx/nTp1WLlyJePGjWPs2LH4+PiwceNGbbH2TZs20bJlSwwM/v2TYmhoSGBgIJ999hlqtZpSpUoxffr0TLXCvL292bp1K5999hkzZ87Ew8ODBQsWEBAQoG2TkpLCxo0b2bFjxxtdOyGEEEKIvDCqeRl2XI7g6O3HBF19SNPyzq8+SAihpVSpORUazc7LkWy7+ICI+BTtPidLY96r4kbbqm5UcreWlfUKGYU6O2vFixeKj4/H2tqauLi456ZXpaSkEBISgre39yunaYnMOnfuTLVq1RgzZky22oeGhuLt7c3Zs2epWrVq7gaXj/Xp04fY2Fg2btyY5+euXLky48aNo0uXLjne99y5c9mwYQO7du3K8b7flvyeC5H/JCYmYmFhAWjq85mbm+do/y977RdZk+smioofd1xj7r5blHAwZ+dnDTDUl6lFQrxMWoaKI7ei2Hk5gl2XI3mcmKbdZ2liQMuKrrSt6katEvbo60kyqiB5ndd+GTEl8p2pU6eyZcsWXYchsiktLY2OHTtma+TVmzA0NGT27Nm50rcQovAxMTHhxIkT2vtCCJGXBjUqyR8n73A7KpGVx8PpXae4rkMSIt9JSM3gwPVH7Lwcwd9XH/IkNUO7z8rEgKblnAmo6EKjMo4YG2R/wStRcEliSuQ7xYsXZ+jQoXlyrh9++IEffvjhhfvq16/P9u3b8yQOXXs6uuBFtm/fri16/yJGRkZ8/fXXuREWoJnKKYQQ2fV0OrkQQuiCpYkhn71bmnEbLzFjz3Xa+bpjbWqo67CE0Cm1Ws3NhwnsC37E3uCHnAyNJl3578QtR0tjAio4E1DBhdol7GWkYREkiSlR4BUvXpw3nZE6cODALKefPV3ZrqBYsmTJGx977ty5LPe5u7u/cb9CCCGEEEXN+zU9WXoklBsPEwjce5OxLV+90IwQhU1SWgZHbz1mb/BD9l57xL3Y5Ez7i9ub0ayCCwEVnPH1tEVPpukVaZKYEkWanZ0ddnayikmpUqV0HYIQQuSItLQ0Zs6cCWhWFDUyMtJxREKIosZAX4+xrcrRd/FJlhwOpWtNT0o6Zj06XYjCIF2p4sLdOI7eiuLIrcecCoshLUOl3W9koEftEva8U8aRRmWc8HbI2RqQomCTxJQQQgghCo309HRGjRoFwKBBgyQxJYTQiUalHWlY2pH91x8xeMUZNgyqi6mR1MoRhYdKpeZqRDxHbz3myK3HnAiJJuGZWlEA7jamNC7rRKMyjviXtMfMSNIP4sXkf4YQQgghhHip2NhYmjZtSkZGBhkZGXzyyScMGDBA12EJkW8pFAqmdqpMy1kHuRbxhPGbLjG1cxVdhyXEG0vLUHH5fhynw2I4GRrNiZBoYpLSM7WxMTPEv4Q9dUo5UKekPSUczFEoZIqeeDVJTAkhhBBCiJeytLTkwIEDmJmZkZiYSMWKFenQoQP29va6Dk2IfMvJyoRZ3Xz534LjrD19l5rF7ehS01PXYQmRLXHJ6ZwJi+FUWDSnQmM4dyeW1Gem5gGYG+nj521HnZIO1CllTzkXK6kVJd6IJKaEEEIIIcRL6evrY2ZmBkBqaipqtfqNFx4RoiipU9KBEc3KMHVnMF9tukQFdysquFnrOiwhMknLUBEc8YTzd2O5cDeW83fiuP7wCf/9M29rZkh1L1tqFLejZnFbKnvYyAp6IkcU6cSUDEsXQgghRGFw4MABpk6dyunTp3nw4AEbNmygXbt2mdoEBgYydepUIiIiqFKlCrNnz8bPzy/b54iNjaVhw4bcuHGDqVOn4uDgkMPPQojC6eOGJTkVGs3e4EcMWnGGLUPrYWViqOuwRBGlVKm5+TCB83djuXg3jgt3Y7n64AlpStVzbb0dzDWJqH+SUSUdZWqeyB1FOjElw9ILr4iICHr27MmRI0cwNDQkNjZW1yEJIYQQuSYxMZEqVarwwQcf0KFDh+f2r1mzhuHDh/Prr79Sq1YtZsyYQUBAAMHBwTg5OQFQtWpVMjIynjt2165duLm5YWNjw/nz54mMjKRDhw506tQJZ2fnXH9uQhR0enoKpnepSuvZhwh7nMTItef59X/V5QO+yHXxKekERzzh6oN4rj54wrWIeIIjnpCUpnyurY2ZIZXcraniYUMlD2uqFbPF0dJYB1GLoqhIJ6ZkWPqL9enTh6VLlwJgaGhIsWLF6NWrF2PHjsXAIPf+yyxZsoRPP/00R5JIP//8Mw8ePODcuXNYW+fucOl9+/bxzjvvEBMTg42NTa6eSwghhHiRFi1a0KJFiyz3T58+nQEDBtC3b18Afv31V7Zu3cqiRYv44osvADh37ly2zuXs7EyVKlU4ePAgnTp1emGb1NRUUlNTtY/j4+Oz+UyEKJxszY0I7FGNzr8eYeflSGYF3WRYk1KSnBI5IkOpIiw6KVMS6uqDeO7FJr+wvbmRPhXdraniaaNNRnnamcr/R6Ez+ToxJcPSdad58+YsXryY1NRUtm3bxuDBgzE0NGTMmDGv3ZdSqUShUKCnl3fzj2/dukX16tXx8fHJsk16ejqGhjKMWgghChMTExP27t2rvS8gLS2N06dPZ3oN19PTo2nTphw9ejRbfURGRmJmZoalpSVxcXEcOHCAjz/+OMv2kyZNYuLEiW8duxCFSVVPG75qXZ7xmy7z857rxCan8VWr8lIsWmRbYmoGtx8lcvPRE249TOTmwwRuPUog9HEi6coXD7BwszahnKsVZV0tNT9drPB2MEdf/t+JfCRfVyp7Oiw9MDDwhfufDkv/+uuvOXPmDFWqVCEgIICHDx9q21StWpWKFSs+d7t//z6Adlh6SEgIK1euJDIyMk+eW35nbGyMi4sLXl5efPzxxzRt2pTNmzcDmm9dK1WqhLm5OZ6engwaNIiEhATtsUuWLMHGxobNmzdTvnx5jI2NCQ8PJzU1lc8//xx3d3fMzc2pVasW+/btAzSjjvr27UtcXBwKhQKFQsGECRMAiImJoVevXtja2mJmZkaLFi24ceNGlrEXL16c9evXs2zZMhQKBX369AE0y/bOnTuXNm3aYG5uzvfffw/A3LlzKVmyJEZGRpQpU4bly5dn6k+hULBgwQLat2+PmZkZPj4+2msRGhrKO++8A4CtrW2m8wkhhMh7+vr6NGrUiEaNGqGvr6/rcPKFqKgolErlc9PunJ2diYiIyFYfYWFh1K9fnypVqlC/fn2GDh1KpUqVsmw/ZswY4uLitLc7d+681XMQorDo5V+cca3KAbD4cChDV50lJf35aVWi6ErNUHLrUQJ7rz1kyeEQJmy+TM+Fx6kzKYgKX+/kvTmH+GzNeebsvcmOyxHceJhAulKNiaEeVTys6VrDkwnvlWf1h7U5P74ZR8Y0YWGfmowMKEvrym6UcrKQpJTId/L1iKnCOiw9MTExy336+vqZvuF9WVs9PT1MTU1f2dbc3PwNoszM1NSUx48fa887a9YsvL29uX37NoMGDWLUqFH88ssv2vZJSUn8+OOPLFiwAHt7e5ycnBgyZAhXrlxh9erVuLm5sWHDBpo3b87FixepU6cOM2bMYPz48QQHBwNgYWEBaKYW3rhxg82bN2NlZcXo0aNp2bIlV65ceeGIp5MnT9KrVy+srKyYOXNmpms0YcIEJk+ezIwZMzAwMGDDhg188sknzJgxg6ZNm/LXX3/Rt29fPDw8tAkngIkTJzJlyhSmTp3K7Nmz6dGjB2FhYXh6erJ+/Xo6duxIcHAwVlZWmc4nhBBCFAZ+fn7Zfk8Fmi+4jI2lNokQL9K/fgmcrEwY8cc5tl58QFRCKvN61cDaVEbyFxVxyemEP04iLDqRsMdJ2vvhj5N4EJ/y3Gp4z7I3N6KkkwUlHS0o5WRBSUdzSjlZ4GZtKqPvRIGVrxNTL1OQh6U/Tbi8SMuWLdm6dav2sZOTE0lJSS9s27BhQ+2II9CMFIqKinqu3dvUzVKr1QQFBbFz506GDh0KwKeffprpnN999x0DBw7MlJhKT0/nl19+oUqVKgCEh4ezePFiwsPDcXNzA+Dzzz9nx44dLF68mB9++AFra2sUCgUuLi7afp4mpA4fPkydOnUAWLFiBZ6enmzcuJHOnTs/F7OjoyPGxsaYmppm6guge/fu2kQmQLdu3ejTpw+DBg0CYPjw4Rw7doyffvopU2KqT58+dOvWDYAffviBWbNmceLECZo3b46dnR2g+beSGlNCCKFb6enpzJs3D4APP/xQpmwDDg4O6OvrPzcqPDIy8rnXSSFE3mhTxQ0HcyM+Wn6a4yHRdPn1KAv71MDD1kzXoYm3lK5UERmfwv3YFO7HJnMvNpkHccmZHj9JeX6hiWeZGelTzM4ML3szvOzNKeFg/k8SygJbc6M8eiZC5J0Cm5h62bD0a9euZauPsLAwPvzwQ23R8+wMSx8+fLj2cXx8PJ6enm/2BPK5v/76CwsLC9LT01GpVHTv3l07tW7Pnj1MmjSJa9euER8fT0ZGBikpKSQlJWmLyRsZGVG5cmVtfxcvXkSpVFK6dOlM50lNTX3pKohXr17FwMCAWrVqabfZ29tTpkwZrl69+trPq0aNGs/1/+GHH2baVrduXWbOnJlp27PPxdzcHCsrq0xTRoUQQuQPaWlpDBkyBNB8qSCJKc1rcvXq1QkKCtLW6lSpVAQFBWmvlRAi79Up5cCaj/zps/gEwZFPeHf6AQY2LMmHDUpgaiRTkfMbtVpNXHI6D5+k8jA+lYdPUrT3I5+k8CA2mQdxKUTGp6DKxrgABwtjTeLJzgxPbRLKjGJ25jhYGEkhclGkFNjEVE7Q1bD0Z+sx/dd/62G8LPnx32LioaGhbxXXs9555x3mzp2LkZERbm5u2tX4QkNDad26NR9//DHff/89dnZ2HDp0iH79+pGWlqZNTJmaZl7VISEhAX19fU6fPv3cc3zZCLKc9qbTGv/7wUahUKBSqXIiJCGEEOKtJSQkcPPmTe3jkJAQzp07h52dHcWKFWP48OH07t2bGjVq4Ofnx4wZM0hMTMw0ijg3BAYGEhgYiFIpNXSEeJHyblb8OagOw9ec50RoND/vuc4fp0URmSAAABTYSURBVO7wRYuytK7sKsmJXKZWq4lPySA6MY3oxFSiE9OJTnyaeMqcfHqUkEpaRvbe/xvp6+FqY4KbtSluNqa42Zj889MUdxsTXK1NMTcu0h/FhcikwP42FORh6a+THMmtttnpq1SpUs9tP336NCqVimnTpmkTY3/88ccr+/P19UWpVPLw4UPq16//wjZGRkbPvXEtV64cGRkZHD9+XDuV7/HjxwQHB1O+fPnXfVrPKVeuHIcPH6Z3797abYcPH36tvo2MNMNp5U23EEIIXTl16lSmKehPR3j37t2bJUuW0LVrVx49esT48eOJiIigatWq7Nix47mR5zlt8ODBDB48mPj4eKytrXP1XEIUVB62Zqz5qDZbLz7gh61XuRebzNBVZ1l6JJT/1faiWQVnzIwK7Me2PKNWq0lIzSAuOZ345AxiktL+SThlcUtKIyYxjYzsDG96ho2ZIU6WxjhZmuBkaYyjlea+m7Um+eRqY4KDubHUexLiNRTYv3AyLF03SpUqRXp6OrNnz+a9997j8OHD/Prrr688rnTp0vTo0YNevXoxbdo0fH19efToEUFBQVSuXJlWrVpRvHhxEhISCAoKokqVKtoV8Nq2bcuAAQP47bffsLS05IsvvsDd3Z22bdu+9fMZOXIkXbp0wdfXl6ZNm7Jlyxb+/PNP9uzZk+0+vLy8UCgU/PXXX7Rs2RJTU9M8HQUmhBBCNGrU6JU1JYcMGSLvkYTIpxQKBa0ru9GkrDPzDtxm7v6bnAqL4VRYDGZG+jQr70xbX3f8S9hjYlg4p/kpVZrEUuI/t4TUDOJTNIkmTbLpn1tKujb5FJfpcXq2ptC9iIWxAbbmhtiZG2NnZojj08STlbEm+WRpgrOVMY6WxhgbFM7rL4Qu5evEVH4dll6UValShenTp/Pjjz8yZswYGjRowKRJk+jVq9crj128eDHfffcdI0aM4N69ezg4OFC7dm1at24NQJ06dRg4cCBdu3bl8ePHfP3110yYMIHFixfzySef0Lp1a9LS0mjQoAHbtm3Lkboh7dq1Y+bMmfz000988skneHt7s3jxYho1apTtPtzd3Zk4cSJffPEFffv2pVevXixZsuStYxNCCCGEEEWLqZE+nzT1oUtND1afuMPGc/cIe5zExnP32XjuPgZ6Csq5WlHF05oqHjaUcLTAw9YUR4u8G6GjVqtJzVCRkq4kOV1JcpqSlHQVyelKzbY0JYlpGSSmKrUJpqc//008KTX30/7dl5KeM2UyjA30sDI1xNbMEFszI+wtjDQ/zY2wMzfC1twIe3NjbM0NsTc3xsbMsNAm+4QoKBTqt1myLZft27cv07D0p54OSweYM2cOU6dO1Q5LnzVrVqZC2bnh2XoJ169fJy4uDisrq0xtUlJSCAkJwdvbGxMTk1yNRwihG/J7LsT/27v32Kbq8I/jn9NuBXYHBoONwjRcZDAGAlNQccAiwZ9cRAWJAYaJBAUjIUj8wwRIFNQEAiLGiDFcggkBBJPlhwpzQDIVxhB+gigKm0wYA5yDbchl7fn9MalMNijbek7bvV9JU3r6PT1PDw+nD8+5BZ+amhrfUavV1dUtepq7JN8paQ399qNxrDegaUzT1OHSSu344Yz+9+g5Xai61uC4SKehpLi2SoiKVFzbSMW2jVC0K0IOh6EIhyGHw5DTMOR01D28pqlaj6kbHq9ueEzVer3//vmf52u19RtPvkbUDY8C+T/ISKeh6DZ18ce3i1Rcu7rn+HZ1361uWuS/0/55P65t3XSaTEBwuJff/qBuTAW7O61o/sMKhD/+nQOtDw2WpmG9Ac1nmqbOVP6tI6WXdOSPSv3fH5Uqrfhb5y5flaep57A1U6TTUNtIp9pGOtXun0fbSIeiXBGKbhOhmDbOf57rHtG3PEe3cTY4jVPlgPBwL7/9QX0qHwAAAEIXd+UDWo5hGOrWPkrd2kfpfwZ09U2v9Xh1vuqayi5d9V2D6fLVWv19vVYer+Txev99Nk3Vek05DEORTociHYYiIxyKcBhyRTgU4XAowmnUNZwinGrrurXh9M+zy+F7Hel03CFiAPAPjSkAAAAEBHflAwIvwulQckI7JSe0szsUAGgSWtwAAAAAAACwBY2pAOMSXkD44t83AAAAADQPjakAiYyMlCRduXLF5kgABMr169clSU4nF+kEAAAAgKbgGlNN4M+FPJ1OpxISEnT+/HlJUlRUlAzDsCpEAAHm9Xp14cIFRUVFKSKCTSkAAAAANIVhci5Kk93t9oemaercuXOqrKy0PjgAAedwOHTffffJ5XLZHQoAi9zLrY/xL9YbAACty7389rObP4AMw1DXrl3VuXNn3bhxw+5wALQwl8slh4MzogGgMf4cZQ4AAFo3jphqBvb+AQDQuvDb3zSsNwAAWpd7+e1nVz8AAAAAAABsQWMKAAAAAAAAtqA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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n", + "\n", + "ax = axes[0]\n", + "for name, label in [(\"slow\", \"slow (eps_0 -> eps_0/4)\"),\n", + " (\"medium\", \"medium (eps_0 -> eps_0/10)\"),\n", + " (\"fast\", \"fast (eps_0 -> eps_0/50)\")]:\n", + " ax.loglog(annealed_results[name][\"iters\"], annealed_results[name][\"subopt\"], label=label)\n", + "ax.step(pareto_x, np.minimum.accumulate(pareto_y), where=\"post\", #Built in Cell 12 — re-run if needed\n", + " linestyle=\"--\", color=\"black\", linewidth=1.5, label=\"Pareto front\")\n", + "ax.set_xlabel(\"Iterations t\")\n", + "ax.set_ylabel(r\"$\\langle C,\\hat P_t\\rangle - \\mathrm{OT}(a,b)$\")\n", + "ax.set_title(\"Suboptimality – annealed Sinkhorn\")\n", + "ax.legend(loc=\"lower left\")\n", + "\n", + "ax = axes[1]\n", + "for name in [\"slow\", \"medium\", \"fast\"]:\n", + " ax.loglog(annealed_results[name][\"iters\"], annealed_results[name][\"merr\"], label=name)\n", + "ax.set_xlabel(\"Iterations t\")\n", + "ax.set_ylabel(\"Marginal violation error\")\n", + "ax.set_title(\"Marginal feasibility\")\n", + "ax.legend(loc=\"upper left\")\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "23e81103", + "metadata": {}, + "source": [ + "**Left panel.** The three geometric schedules show contrasting behaviours. `fast` reaches a low suboptimality early but then diverges, the relaxation error eventually dominates and the iterates are pushed away from the solution. `slow` and `medium` both decrease monotonically throughout the run, with `medium` finishing lower than `slow` : a more aggressive schedule can yield better final accuracy, provided the relaxation error remains controlled. None of the three approaches the Pareto front.\n", + "\n", + "**Right panel.** The marginal feasibility confirms this picture: only `fast` eventually explodes, while `slow` and `medium` keep improving — `medium` converging to a lower floor than `slow`. This is the relaxation error made concrete: for a geometric schedule $\\varepsilon_t = \\varepsilon_0 r^t$ with $r < 1$, the kernel shift at each step satisfies\n", + "\n", + "$$\\beta_t - \\beta_{t-1} = \\beta_{t-1}\\!\\left(\\tfrac{1}{r} - 1\\right),$$\n", + "\n", + "which grows proportionally to $\\beta_{t-1}$ — the faster the schedule, the larger the per-step shock to the iterates.\n", + "\n", + "Geometric schedules are therefore a poor match for the annealing theory: the relaxation error dominates before the entropic error has time to decrease. This\n", + "motivates replacing exponential growth of $\\beta$ with the polynomial family $\\beta_t = \\beta_0(1+t)^\\kappa$, whose increments grow as $\\mathcal{O}(t^{\\kappa-1})$, sublinearly for $\\kappa < 1$." + ] + }, + { + "cell_type": "markdown", + "id": "543dea3d", + "metadata": {}, + "source": [ + "### Polynomial schedules\n", + "\n", + "The `Epsilon` class implements geometric decay, which as we just saw produces\n", + "an unbounded relaxation error. The annealing theory instead calls for schedules\n", + "of the form\n", + "\n", + "$$\\varepsilon_t = \\frac{1}{\\beta_0\\,(1+t)^\\kappa}, \\qquad \\kappa \\in (0, 1),$$\n", + "\n", + "for which $\\beta_t - \\beta_{t-1} = O(t^{\\kappa - 1}) \\to 0$, so the relaxation\n", + "error vanishes asymptotically.\n", + "\n", + "We define a minimal drop-in replacement for `Epsilon` that respects the same\n", + "callable interface — `sched(t)` returns $\\varepsilon_t$ and the object can be\n", + "passed directly to `PointCloud(x, y, epsilon=sched)`." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "9d3f7470", + "metadata": {}, + "outputs": [], + "source": [ + "class PolynomialEpsilon(epsilon_scheduler.Epsilon):\n", + " \"\"\"Polynomial epsilon schedule: ε_t = 1 / (β₀ · (1 + t)^κ).\n", + " \"\"\"\n", + " def __init__(self, kappa: float, beta_0: float):\n", + " super().__init__(target=1.0 / beta_0, init=1.0, decay=1.0)\n", + " self._kappa = kappa\n", + " self._beta_0 = beta_0\n", + "\n", + " def __call__(self, count: int):\n", + " count = jnp.asarray(count)\n", + " return 1.0 / (self._beta_0 * jnp.power(1.0 + count, self._kappa))" + ] + }, + { + "cell_type": "markdown", + "id": "315a062f", + "metadata": {}, + "source": [ + "We sweep $\\kappa$ over 50 values uniformly spaced in $[0.1,\\, 0.95]$, keeping $\\varepsilon_0 = \\|C\\|_{\\mathrm{osc}} / 10$ fixed throughout. For each value we\n", + "run Annealed Sinkhorn for the same iteration budget and record the final suboptimality $\\langle C, \\hat{P}_T \\rangle - \\mathrm{OT}(a, b)$ and the marginal violation error at convergence.\n", + "\n", + "The goal is to identify the empirically optimal exponent $\\kappa^\\star$, the value that jointly minimises suboptimality and marginal infeasibility on this problem instance." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "82c6f00e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Best kappa = 0.50 | subopt = 3.98e-03\n" + ] + } + ], + "source": [ + "kappas = np.linspace(0.1, 0.95, 50)\n", + "\n", + "eps_seqs = jnp.array([[PolynomialEpsilon(kappa=k, beta_0=beta_0)(t) for t in range(T)] for k in kappas])\n", + "\n", + "def run_kappa(eps_seq):\n", + " def step(carry, idx):\n", + " f, g, eps_prev = carry\n", + " eps_t = eps_seq[idx]\n", + " f = f * eps_t / eps_prev\n", + " g = g * eps_t / eps_prev\n", + " geom = pointcloud.PointCloud(x, y, epsilon=eps_t)\n", + " prob = linear_problem.LinearProblem(geom, a=a, b=b)\n", + " out = _annealed_solver(prob, init=(f, g))\n", + " f, g = out.f, out.g\n", + " P_hat = altschuler_round(geom.transport_from_potentials(f, g), a, b)\n", + " subopt = jnp.sum(geom.cost_matrix * P_hat) - float(OT_ref)\n", + " return (f, g, eps_t), subopt\n", + "\n", + " f0 = jnp.zeros(x.shape[0])\n", + " g0 = jnp.zeros(y.shape[0])\n", + " _, subopt_seq = jax.lax.scan(step, (f0, g0, eps_seq[0]), jnp.arange(T))\n", + " return subopt_seq[-1]\n", + "\n", + "final_subopt = jax.jit(jax.vmap(run_kappa))(eps_seqs)\n", + "kappa_star = kappas[int(jnp.argmin(final_subopt))]\n", + "print(f\"Best kappa = {kappa_star:.2f} | subopt = {final_subopt.min():.2e}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "cfe58bfa", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(6, 4))\n", + "ax.plot(kappas, np.array(final_subopt), marker=\"o\", markersize=4, linewidth=1.5)\n", + "ax.axvline(0.5, linestyle=\"--\", color=\"gray\", linewidth=1, label=r\"$\\kappa=1/2$ (theory)\")\n", + "ax.axvline(kappa_star, linestyle=\"--\", color=\"black\", linewidth=1,\n", + " label=rf\"$\\kappa^*={kappa_star:.2f}$ (empirical)\")\n", + "ax.set_xlabel(r\"$\\kappa$\")\n", + "ax.set_ylabel(r\"Suboptimality at $t = T$\")\n", + "ax.set_title(r\"Suboptimality vs $\\kappa$ — polynomial schedule\")\n", + "ax.set_yscale(\"log\")\n", + "ax.legend()\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "a8903692", + "metadata": {}, + "source": [ + "The curve exhibits a sharp, symmetric minimum exactly at $\\kappa^\\star = 0.50$, in perfect agreement with the minimax-optimal exponent predicted by the theory." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e7829544", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Run polynomial kappa* schedule\n", + "sched_kstar = PolynomialEpsilon(kappa=kappa_star, beta_0=beta_0)\n", + "records[\"poly_kstar\"] = annealed_sinkhorn_ott(x, y, a, b, eps_sched=sched_kstar, T=T, ot_ref=OT_ref)\n", + "annealed_results[\"poly_kstar\"] = {\n", + " \"iters\": np.array([r[\"t\"] for r in records[\"poly_kstar\"]]),\n", + " \"subopt\": np.array([r[\"subopt\"] for r in records[\"poly_kstar\"]]),\n", + " \"merr\": np.array([r[\"margin_err\"] for r in records[\"poly_kstar\"]]),\n", + "}\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n", + "\n", + "ax = axes[0]\n", + "for name in [\"slow\", \"medium\", \"fast\"]:\n", + " ax.loglog(annealed_results[name][\"iters\"], annealed_results[name][\"subopt\"],\n", + " color=\"tab:gray\", alpha=0.5, linewidth=1.2, label=name)\n", + "ax.loglog(annealed_results[\"poly_kstar\"][\"iters\"], annealed_results[\"poly_kstar\"][\"subopt\"],\n", + " color=\"tab:blue\", linewidth=2,\n", + " label=rf\"polynomial $\\kappa^*={kappa_star:.2f}$\")\n", + "ax.step(pareto_x, np.minimum.accumulate(pareto_y), where=\"post\", #Built in Cell 12 — re-run if needed\n", + " linestyle=\"--\", color=\"black\", linewidth=1.5, label=\"Pareto front\")\n", + "ax.set_xlabel(\"Iterations t\")\n", + "ax.set_ylabel(r\"$\\langle C,\\hat P_t\\rangle - \\mathrm{OT}(a,b)$\")\n", + "ax.set_title(\"Polynomial vs geometric schedules\")\n", + "ax.legend(fontsize=8)\n", + "\n", + "ax = axes[1]\n", + "for name in [\"slow\", \"medium\", \"fast\"]:\n", + " ax.loglog(annealed_results[name][\"iters\"], annealed_results[name][\"merr\"],\n", + " color=\"tab:gray\", alpha=0.5, linewidth=1.2, label=name)\n", + "ax.loglog(annealed_results[\"poly_kstar\"][\"iters\"], annealed_results[\"poly_kstar\"][\"merr\"],\n", + " color=\"tab:blue\", linewidth=2,\n", + " label=rf\"polynomial $\\kappa^*={kappa_star:.2f}$\")\n", + "ax.set_xlabel(\"Iterations t\")\n", + "ax.set_ylabel(\"Marginal violation error\")\n", + "ax.set_title(\"Marginal feasibility\")\n", + "ax.legend(fontsize=8)\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "b3646cb4", + "metadata": {}, + "source": [ + "**Left panel.** The polynomial schedule with $\\kappa^\\star = 0.50$ converges steadily throughout the run and approaches the Pareto front from $t \\approx 200$ onward, while all three geometric schedules plateau well above it. The contrast is stark: geometric decay produces a relaxation term $\\beta_t - \\beta_{t-1} \\sim \\beta_t(1-r)$ that never vanishes, preventing the iterates from following the regularization path efficiently. Polynomial growth keeps this term at $\\mathcal{O}(t^{\\kappa-1}) \\to 0$, allowing steady progress throughout the budget.\n", + "\n", + "**Right panel.** The polynomial schedule starts with a higher marginal error than the geometric schedules — it begins at larger $\\varepsilon$ and takes longer to enter the low-regularization regime, but decreases monotonically without any rebound. By $t \\approx 300$ it crosses the fastest geometric curve and continues improving, confirming that the relaxation error remains controlled under polynomial cooling at $\\kappa^\\star = 0.50$." + ] + }, + { + "cell_type": "markdown", + "id": "e4fcb5a0", + "metadata": {}, + "source": [ + "## Debiased Annealed Sinkhorn\n", + "\n", + "Each annealing step introduces two errors: an entropic error from the finite regularization level, and a relaxation error from the kernel shift $K_{t-1} \\to K_t$. Standard Annealed Sinkhorn simply keeps iterating and lets the algorithm catch up. The debiased variant corrects for the shift directly.\n", + "\n", + "### OTT-JAX adaptation\n", + "\n", + "The Algorithm 3 of Chizat (2024) prescribes asymmetric half-steps (row update on the old kernel $K_{t-1}$, column update on the new kernel $K_t$), which\n", + "has no native abstraction in OTT-JAX. We instead implement an *equivalent* single-step formulation that stays within the OTT framework:\n", + "\n", + "1. **Debiasing** — before the Sinkhorn step, the source marginal is corrected using the current potential $f_{t-1}$:\n", + "\n", + "$$a_t^{\\text{eff}} = a \\odot \\exp\\!\\left(\\frac{f_{t-1}}{\\varepsilon_t} - \\frac{f_{t-1}}{\\varepsilon_{t-1}}\\right)$$\n", + "\n", + " At $t=1$, $\\varepsilon_t = \\varepsilon_{t-1}$ so $a_1^{\\text{eff}} = a$ and the first step is identical to the standard algorithm.\n", + "\n", + "2. **Potential rescaling** — the warm-start potentials are rescaled to the new temperature before the solver call, exactly as in the standard variant:\n", + "\n", + "$$f \\leftarrow f \\cdot \\frac{\\varepsilon_t}{\\varepsilon_{t-1}}, \\qquad g \\leftarrow g \\cdot \\frac{\\varepsilon_t}{\\varepsilon_{t-1}}$$\n", + "\n", + "3. **One Sinkhorn step** — a single Sinkhorn iteration is run at $\\varepsilon_t$ with the debiased marginal $a_t^{\\text{eff}}$ in place of $a$, via `LinearProblem(geom, a=a_eff, b=b)`.\n", + "\n", + "This formulation combines the debiasing correction of {cite}`chizat:24` with the potential rescaling already used in the standard OTT variant, and is fully compatible with `lax.scan` and JIT compilation." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "553c98d9", + "metadata": {}, + "outputs": [], + "source": [ + "_debiased_solver = sinkhorn.Sinkhorn(inner_iterations=1, max_iterations=1, threshold=0.0) #Same as _annealed_solver but kept separately for clarity. \n", + "\n", + "\n", + "def debiased_annealed_sinkhorn_ott(x, y, a, b, eps_sched, T: int, ot_ref=None):\n", + " \"\"\"Adapted Debiased version of Algorithm 3 of {cite}`chizat:24` via lax.scan with potential rescaling.\"\"\"\n", + " ot_ref_val = float(ot_ref) if ot_ref is not None else 0.0\n", + " eps_seq = jnp.array([float(eps_sched(t)) for t in range(T)])\n", + "\n", + " def step(carry, idx):\n", + " f, g, eps_prev = carry\n", + " eps_t = eps_seq[idx]\n", + "\n", + " # 1. Debiasing with OLD f (before rescaling) \n", + " a_eff = a * jnp.exp(f / eps_t - f / eps_prev)\n", + "\n", + " # 2. Rescale potentials for warm start to new epsilon\n", + " f = f * eps_t / eps_prev\n", + " g = g * eps_t / eps_prev\n", + "\n", + " # 3. One Sinkhorn step with debiased marginal\n", + " geom = pointcloud.PointCloud(x, y, epsilon=eps_t)\n", + " prob = linear_problem.LinearProblem(geom, a=a_eff, b=b)\n", + " out = _debiased_solver(prob, init=(f, g))\n", + " f, g = out.f, out.g\n", + "\n", + " P = geom.transport_from_potentials(f, g)\n", + " P_hat = altschuler_round(P, a, b)\n", + " err = (jnp.abs(P.sum(axis=1) - a).sum() + jnp.abs(P.sum(axis=0) - b).sum())\n", + " subopt = jnp.sum(geom.cost_matrix * P_hat) - ot_ref_val\n", + "\n", + " return (f, g, eps_t), {\"eps\": eps_t, \"margin_err\": err, \"subopt\": subopt}\n", + "\n", + " f0 = jnp.zeros(x.shape[0])\n", + " g0 = jnp.zeros(y.shape[0])\n", + " eps0 = eps_seq[0]\n", + "\n", + " _, metrics = jax.jit(lambda carry, xs: jax.lax.scan(step, carry, xs))((f0, g0, eps0), jnp.arange(T))\n", + "\n", + " records = [ {\"t\": t + 1, **{k: float(v[t]) for k, v in metrics.items()}} for t in range(T)]\n", + " return records" + ] + }, + { + "cell_type": "markdown", + "id": "56c2954e", + "metadata": {}, + "source": [ + "With the relaxation error corrected, a more aggressive schedule becomes viable.\n", + "We sweep the same 50 values of $\\kappa \\in [0.1, 0.95]$ as before and identify\n", + "the empirically optimal exponent $\\kappa^\\star_{\\mathrm{deb}}$ for the debiased\n", + "algorithm — which need not coincide with the $\\kappa^\\star = 0.5$ found for\n", + "standard Annealed Sinkhorn." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "a31abd81", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Best kappa debiased = 0.64 | subopt = 1.66e-03\n" + ] + } + ], + "source": [ + "def run_kappa_debiased(eps_seq):\n", + " def step(carry, idx):\n", + " f, g, eps_prev = carry\n", + " eps_t = eps_seq[idx]\n", + "\n", + " # Debiasing then rescaling\n", + " a_eff = a * jnp.exp(f / eps_t - f / eps_prev)\n", + " f = f * eps_t / eps_prev\n", + " g = g * eps_t / eps_prev\n", + "\n", + " geom = pointcloud.PointCloud(x, y, epsilon=eps_t)\n", + " prob = linear_problem.LinearProblem(geom, a=a_eff, b=b)\n", + " out = _debiased_solver(prob, init=(f, g))\n", + " f, g = out.f, out.g\n", + " P_hat = altschuler_round(geom.transport_from_potentials(f, g), a, b)\n", + " subopt = jnp.sum(geom.cost_matrix * P_hat) - float(OT_ref)\n", + " return (f, g, eps_t), subopt\n", + "\n", + " f0 = jnp.zeros(x.shape[0])\n", + " g0 = jnp.zeros(y.shape[0])\n", + " _, subopt_seq = jax.lax.scan(step, (f0, g0, eps_seq[0]), jnp.arange(T))\n", + " return subopt_seq[-1]\n", + "\n", + "final_subopt_debiased = jax.jit(jax.vmap(run_kappa_debiased))(eps_seqs)\n", + "kappa_star_debiased = kappas[int(jnp.argmin(final_subopt_debiased))]\n", + "print(f\"Best kappa debiased = {kappa_star_debiased:.2f} | subopt = {final_subopt_debiased.min():.2e}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "bcb25151", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(6, 4))\n", + "ax.plot(kappas, np.array(final_subopt_debiased), marker=\"o\", markersize=4, linewidth=1.5)\n", + "ax.axvline(0.67, linestyle=\"--\", color=\"gray\", linewidth=1, label=r\"$\\kappa=2/3$ (theory)\")\n", + "ax.axvline(kappa_star_debiased, linestyle=\"--\", color=\"black\", linewidth=1,\n", + " label=rf\"$\\kappa^*={kappa_star_debiased:.2f}$ (empirical)\")\n", + "ax.set_xlabel(r\"$\\kappa$\")\n", + "ax.set_ylabel(r\"Suboptimality at $t = T$\")\n", + "ax.set_title(r\"Suboptimality vs $\\kappa$ — debiased polynomial schedule\")\n", + "ax.set_yscale(\"log\")\n", + "ax.legend()\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "913c4c0f", + "metadata": {}, + "source": [ + "The theoretical optima are **minimax rates**: they hold for the worst case\n", + "over all OT problems. The empirical κ* = 0.64 found here is close to the\n", + "theoretical 2/3; the small gap reflects both instance-specific structure\n", + "and the fact that our OTT-JAX adaptation combines the debiasing correction\n", + "with a potential rescaling step not present in the original algorithm.\n", + "These values should not be over-interpreted." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6fc74c86", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Final subopt debiased = 1.66e-03\n" + ] + }, + { + "data": { + "image/png": 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vvRdffPEFFi5ciIiICMybNw833ngjFixYcN7X12g0Az7hBgUF9Vrc8bHHHsMvv/yCSZMmISEhAfPmzcOyZcswbdq0Ae0LABITE7ttS0pKgl6vh0ajAdA5RaCnf4PRo0fDbrejsrISaWlpvb6mQqFAWFhYn2o69aanz5mfnx+ioqK6bQPg9MeJwWDACy+8gDVr1qC6uhqMMe6xcwetF+Pyyy9HWFgY1q1bh8suuwx2ux3/+9//cM0113DTCgkhZCShcQ2Na843rnGIjo52uu84l/d0jrfb7dBqtQgICAAA7N27F0899RT2798PvV7v1F6r1XKvBXQGps5VXl6O+Pj4bv/mCQkJF3hnvfffEaTqOhZpbm7GM888g88++4z79+jaT1dwBI8c9ad6otVqoVar+zw2evbZZ3HNNdcgKSkJY8aMwYIFC3DrrbciPT39gv250BjT8f/T1W677Tbcf//9KC8vR0xMDDZs2ACLxeK0qh8ZfigwRYgL/frrr6itrcVnn32Gzz77rNvj69atu+gBHNB5pe7qq6/Gt99+i82bN+PJJ5/ECy+8gF9//bVbfZwL6W2w0fUEZ7fbMXbsWLz22ms9tj134NEXvV3x6MvAyW634/LLL8ejjz7a4+NJSUkAgODgYJw4cQKbN2/Gzz//jJ9//hlr1qzBbbfdhv/85z+9vv7EiRNRXl7eh3fRXWlpaY/FT4HOQFB+fj5++OEHbNq0CV999RXeeecd/P3vf+eWzL2Y4+LNevuc9eXz98ADD2DNmjV46KGHcMkll8DPzw88Hg9Lly7tVhT2Yvu4bNkyfPDBB3jnnXewd+9e1NTUUD0DQsiIReOavhuJ4xqHgZ7ji4uLcdlllyElJQWvvfYaoqKiIBaL8dNPP+H111/vdo7vmiXkSn35zNx4443Yt28fHnnkEWRmZkKhUMBut2PBggUuG4s4Xufll19GZmZmj20UCgWAvo+NZs6cieLiYnz33XfYsmULPvzwQ7z++ut49913cdddd7mk3662dOlSPPzww1i3bh3+8pe/4NNPP8WECRNcHhAm3oUCU4S40Lp16xAcHMytNNHV119/jW+++QbvvvuuS06s8fHx+POf/4w///nPKCwsRGZmJl599VV8+umn3JW9U6dO9euK0fn2lZ2djcsuu+y8KbQxMTGw2+0oLi52Onnk5+d3a6tWq9Ha2tpte18GTvHx8ejo6MDcuXMv2FYsFuPqq6/G1VdfDbvdjnvvvRfvvfcennzyyV6Pzbp16/q9BLHDha4e+fj44KabbsJNN90Es9mMJUuW4LnnnsMTTzwBqVTa7+PSU2p2QUEB5HI5d+VVLpf3+G9w5swZ8Pn8bgPwwsJCbsoGAHR0dKC2thZXXHEFt82dqdRffvklbr/9drz66qvcNqPR2ONxupAL9fu2227Dq6++iu+//x4///wzgoKCuk0bIISQkYLGNTSuGaysGKCzoLXJZMLGjRudspb6U7g8JiYGeXl5YIw5/VsWFRW5rJ8tLS3Ytm0bnnnmGafC7QOZHnc+js+5r6/vBT8L/Rkb+fv7Y/ny5Vi+fDk6Ojowc+ZMPP300xcMTPVljDlQ5/t/5+/vjyuvvBLr1q3D7373O+zdu5dbAIAMXxSYIsRFDAYDvv76a9xwww24/vrruz0eHh6O//3vf9i4cSNuuummAe9Hr9eDz+c71ViIj4+HUqnkluCdN28elEolXnjhBSxYsMCp7bkn7r648cYb8dNPP+GDDz7APffc4/SYwWCA3W6Hj48PFi5ciL/85S/497//7TSI7elkEh8fD61Wi5ycHC6duLa2Ft98802f+vP0009j8+bN3YIGra2tUCgUEAqFaGpq4lLFAYDP53P7One54q4uZmrd+ZzbH7FYjNTUVPz888+wWCyQSqX9Pi779+/HsWPHMH78eABAZWUlvvvuOyxYsIC7Ajhv3jx89913KCsr46561tfXY/369Zg+fTp8fX2dXvP999/H8uXLuXoRq1evhtVq5VYzAjoDbAMJDA2EQCBwumoJAG+99daAssgcq9T01vf09HSkp6fjww8/xIEDB3D77bdDKKRTJSFk5KFxDY1rBptjnHLuNLQ1a9b0+TXmz5+PrVu3YuPGjbjmmmsAdAZoPvjgg0HtJ9Dz5+BiZGVlIT4+Hq+88gqWLVvGZUc5aDQaLiDU17HRuZ8ZhUKBhIQEVFZWXrA/fRljDpSPjw+Azs+3SqXq9vitt96KJUuW4JFHHoFAIHCqU0qGJxptE+IiGzduRHt7u1Pxxa6mTJmCoKAgrFu37qIGcAUFBbjssstw4403IjU1FUKhEN988w3q6+u5L21fX1+8/vrruOuuuzBx4kQsW7YMarUa2dnZ0Ov150337smtt96KL774An/4wx+wfft2TJs2DTabDWfOnMEXX3yBzZs3Y8KECcjMzMTNN9+Md955B1qtFlOnTsW2bdt6vGq1dOlSPPbYY7j22mvx4IMPQq/XY/Xq1UhKSrpgEclHHnkEGzduxFVXXYU77rgDWVlZ0Ol0OHnyJL788kuUlZUhMDAQd911F5qbm3HppZciMjIS5eXleOutt5CZmYnRo0f36xi4wrx58xAaGopp06YhJCQEp0+fxttvv40rr7ySq2HU3+MyZswYzJ8/32kpXwDc1EAA+Oc//4mtW7di+vTpuPfeeyEUCvHee+/BZDLhpZde6vaaZrOZ+4zl5+fjnXfewfTp050+21lZWVi9ejX++c9/IiEhAcHBwVzRWFe76qqr8Mknn8DPzw+pqanYv38/fvnlF6eBVl/JZDKkpqbi888/R1JSEvz9/TFmzBinuiW33XYb/u///g8AaBofIWTEonENjWsG27x587gMsBUrVqCjowMffPABgoODUVtb26fXWLFiBd5++23cfPPNWLlyJVcr0hG8dEWGt6+vL2bOnImXXnoJFosFERER2LJli1PdNVfg8/n48MMPsXDhQqSlpWH58uWIiIhAdXU1tm/fDl9fX3z//fcA+j42Sk1NxezZs5GVlQV/f38cOXIEX375Je6///4L9qcvY8yBchRVf/DBBzF//vxuwacrr7wSAQEB2LBhAxYuXIjg4OCL3ifxch5YCZCQYenqq69mUqmU6XS6XtvccccdTCQSscbGRsbYwJZVbmxsZPfddx9LSUlhPj4+zM/Pj02ePJl98cUX3dpu3LiRTZ06lclkMubr68smTZrE/ve//3GPz5o1i6WlpXV7Xk9LHpvNZvbiiy+ytLQ0JpFImFqtZllZWeyZZ55hWq2Wa2cwGNiDDz7IAgICmI+PD7v66qtZZWVlt/fKGGNbtmxhY8aMYWKxmCUnJ7NPP/20T8sqM8ZYe3s7e+KJJ1hCQgITi8UsMDCQTZ06lb3yyivcksVffvklmzdvHgsODmZisZhFR0ezFStWsNra2l6P72B677332MyZM1lAQACTSCQsPj6ePfLII07Hj7G+HxcA7L777mOffvopS0xMZBKJhI0bN85paWSHY8eOsfnz5zOFQsHkcjmbM2cO27dvn1Mbx+dv586d7J577mFqtZopFAr2u9/9jjU1NTm1raurY1deeSVTKpUMALcssGPp6K596O1zFhMT0+MSxo735dDS0sKWL1/OAgMDmUKhYPPnz2dnzpzp9rnoad89fZb37dvHsrKymFgs7vFzWVtbywQCAUtKSurWN0IIGSloXNOJxjW9c5x3N2zY4LTd8e9++PBhp+2OY6HRaLhtGzduZOnp6UwqlbLY2Fj24osvso8//rjb56a3MQNjjJWUlLArr7ySyWQyFhQUxP785z+zr776igFgBw4c4Nqd+zkoLS1lANjLL7/c7TXP/fetqqpi1157LVOpVMzPz4/dcMMNrKamZkCf+fMdI8YYO378OFuyZAk3XoyJiWE33ngj27ZtG9emr2Ojf/7zn2zSpElMpVIxmUzGUlJS2HPPPcd9phhjFzXG7On9zpo1ixsXMvbbcV6zZg23zWq1sgceeIAFBQUxHo/Xbf+MMXbvvfcyAGz9+vXnPZZkeOAxdk4OICGEkBFp7dq1WL58OQ4fPowJEyZ4ujse09jYiLCwMPz973/Hk08+6enuEEIIIaSf3njjDTz88MOoqqpCRESEp7tDBuDhhx/GRx99hLq6Oq4UAxm++J7uACGEEOJN1q5dC5vNRssSE0IIIUPAuYXdjUYj3nvvPSQmJlJQaogyGo349NNPcd1111FQaoSgGlOEEEIIOpdFz8vLw3PPPYfFixdfcHlsQgghhHjekiVLEB0djczMTGi1Wnz66ac4c+YM1q1b5+mukX5qaGjAL7/8gi+//BJNTU1YuXKlp7tE3IQCU4QQQgiAZ599Fvv27cO0adPw1ltvebo7hBBCCOmD+fPn48MPP8S6detgs9mQmpqKzz777KKK8hPPyMvLw+9+9zsEBwfj3//+NzIzMz3dJeImVGOKEEIIIYQQQgghhHgE1ZgihBBCCCGEEEIIIR5BgSlCCCGEEEIIIYQQ4hFUY+oi2O121NTUQKlUgsfjebo7hBBCCBlkjDG0t7cjPDwcfD5d3+srGjMRQgghI0t/xkwUmLoINTU1iIqK8nQ3CCGEEOJmlZWViIyM9HQ3hgwaMxFCCCEjU1/GTBSYughKpRJA54H29fX1cG8IIYQQMtja2toQFRXFjQFI39CYiRBCCBlZ+jNmosDURXCkovv6+tIgixBCCBlBaDpa/9CYiRBCCBmZ+jJmouIIhBBCCCFkUKxatQqpqamYOHGip7tCCCGEEC9FgSlCCCGEEDIo7rvvPuTl5eHw4cOe7gohhBBCvBQFpgghhBBCCCGEEEKIR1BgihBCCCGEEEIIIYR4xIgPTF177bVQq9W4/vrrPd0VQgghhBBCCCGEkBFlxAemVq5cif/+97+e7gYhhBBCCCGEEELIiDPiA1OzZ8+GUqn0dDcIIYQQQoYdWpWPEEIIIRfi1YGpXbt24eqrr0Z4eDh4PB6+/fbbbm1WrVqF2NhYSKVSTJ48GYcOHXJ/RwkhhBBCSDe0Kh8hhBBCLsSrA1M6nQ4ZGRlYtWpVj49//vnn+NOf/oSnnnoKx44dQ0ZGBubPn4+GhgauTWZmJsaMGdPtVlNT4663QQghhBBCCCGEEEJ6IPR0B85n4cKFWLhwYa+Pv/baa7j77ruxfPlyAMC7776LH3/8ER9//DEef/xxAMCJEyfc0VXShU6nAwDI5XLweDwAgNlshsVigVAohEQi6dZWJpOBz++Mk1osFpjNZggEAkil0gG11ev1YIxBKpVCIBAAAKxWK0wmE/h8PmQy2YDaGgwG2O12SCQSCIWd/31sNhv4fD73XgkhhBBCvAFjDLbGRpgrK2GuqACzWCAMDIQwMAjC4CAI/f3BE4k83U1CCCEjnFdnTJ2P2WzG0aNHMXfuXG4bn8/H3LlzsX///kHZp8lkQltbm9ONdKdQKKBQKNDY2Mhte/nll6FQKHD//fc7tQ0ODoZCoUBFRQW3bdWqVVAoFPj973/v1DY2NhYKhQKnT5/mtq1duxYKhQJLly51apuamgqFQoFjx45x2z7//HMoFAosWrTIqe3EiROhUCiwe/dubtsPP/wAhULh9PkCgJkzZ0KhUGDz5s3ctl9//RUzZswAY+yCx4YQQgghxJWYzQZLdTUs9fVO222trcjPmoDCGTNRvux3qH38CdQ9+XdU/fFelN1wA4pmzcaZsekouGQq2n/91em51uZmaH/8EbqDh2AqKYGtvZ3GOYQQQgaNV2dMnU9jYyNsNhtCQkKctoeEhODMmTN9fp25c+ciOzsbOp0OkZGR2LBhAy655JIe277wwgt45plnLqrfZHjR6XR46aWXsHfvXuj1evj4+Hi6S4QQQggZZpjZDHN1NSyVlTCXV8BcWQFLeQXMlZWwVFaCWSxQ33YrQv/yF+45fD8/8ABcKJxka2kBr0s2OwAYT59GzZ//z2kbTyLpzLYKCoIwqPOnODYWqhtvBL9L1johhBDSXzw2RC5/8Hg8fPPNN1i8eDEAoKamBhEREdi3b59TIOnRRx/Fzp07cfDgQZf3wWQywWQycffb2toQFRUFrVYLX19fl+9vqBpJU/kMBgMmTZoEgUCA/fv3O7UlhBAy/LS1tcHPz4/O/X20atUqrFq1CjabDQUFBXTczsNuMMBSVwdJXJzT9tqnnkbrhg2A3X7e5ytmzULUe+86bau8734wixniqGiIo6PAk0hhbWyEtVEDq6bzp03TiKj33oUkMZF7nva771Dz2OMX7rRIhJTjx8AT/natW/vjjzAVFEIcFwtJXBzEcXEQ0L85IYSMOP0ZMw3ZjKnAwEAIBALUn5O2XF9fj9DQ0EHZp0QicQqqkJ71lDUkFoshFov71FYkEkHUQ72D/rSVy+XdtgmFQq4u1EDbnht4kslkOHnyZLd2hBBCCOlcle++++7jBqfkN5aGBjR9+CGMeXmwVFTC2tAAnkiE5BPHwTt7oQwABEpFr0EpnlQKcVQURDHRkI8b3+3xqFVvD6hv0jFjEPzYY52Bq8ZGWDVnA1kaDWytrVw7cVSUU1AKANq3bEV7l5IHACAICDgbqBoFcVwcxHGxkI4eDdEgjdkJIYQMLUM2MCUWi5GVlYVt27ZxWVR2ux3btm3rVseIEEIIIYQQb2GuqkbFHXfAUlXltJ1ZLLDW10MUHs5tkyQlQZqWBnFMNERR0RBHd2Y/iaJjIAwOGpTFVyTx8ZDEx/f4GDObYW1uhqWmFsxk7Pa4ubS02zZbUxMMTU0wHDnKbVMtvQlhTz/t1K5j715I4uIgDAujRWUIIWQE8erAVEdHB4qKirj7paWlOHHiBPz9/REdHY0//elPuP322zFhwgRMmjQJb7zxBnQ6HbdKHyGEEEIIId7EXFaG8uV3wlpby20TBARwASdmd66y4bdoEfzOWbjFk3hiMUShob1mO0Wuehum4mKYS8tgLi2FubQUprJS2DSNTu0kCYlO960tLaj8/V0AAL6PDyQJCRAnJkCSkABJYiIkCYmDFogjhBDiWV4dmDpy5AjmzJnD3f/Tn/4EALj99tuxdu1a3HTTTdBoNPj73/+Ouro6ZGZmYtOmTd0KohMyWAwGAxYuXAgA+Pnnn6nGFCGEEEJ6ZSoqQsXyO2HVaAAA4rg4RH/0oVOG1FAnjoqCOCoKmO283dbe/lugqqQU8okTnB43d7kYbdfpYMjOhiE726kN39cXksRERLz2GkQhwYP1FgghhLjZkCl+7k2okCdx0Ol0UCgUADoz/GhVPkIIGd6o+PnA0HHrDEqV33Y7bM3NADqn6EV//BGEgYEe7pl3MJWUQvv1VzAVFsFUWAhLTU3PDfl8JB8/Bn6Xuq/Nn3yK9i1bIEk8m12VnAJJUhIEChqXEUKIp4yI4ueeRIU8iYNEIsEXX3zB/U4IIYQQ0hNhcDBEoaGwNTdDmpqKqI8+hFCt9nS3vIZkVByC/+//uPu2Dh3MJcVcoMpUVARTURH4MplTUAoADCdOQH/4MPSHDzttF0VGQpKSDGlSMiTJyZCNSYMoIsIt74cQQkjfUWCKkIsgFApxww03eLobhBBCCPFyAl9fRH30IRpefgUhjz8GwQjNHOsrgcIHsvR0yNLTnbbbTaZuba1NTT2+hqWqCpaqKnT8sg0A4LdkCcKff86pjeHECYhHjaJ/D0II8SAKTBFCCCGEkEHRtfzBSMQYcyrWLVSruwVGSP+cmy0FADFr18DW2gpTURGMBQUw5RfAdOYMjIWFYHo9106akuz0PFt7O8qW3gwAEIWHQ5Kc3JlhlZwMSVIyxDHR4AkEg/uGCCGEUI2pi0H1EojNZsOBAwcAAFOmTIGABi+EEDKs0bl/YEbicevYsxeNq1cjavU7lI3jIcxuh6WqCsYzZ2DKL4By3uWQJv8WnNIfO4byZb/r9fk8qfRszaokBD/8MIQBAe7oNiGEDAv9OfdTYOoijMRBFnFGxc8JIWRkoXP/wIy049a+fTuqH1wJZrFAmpGO6I8+pkLcXshUWIjm9ethOpMPU34+7F2yq5zweEg+egR8uZzb1LFzJ4ynT0OamgppaioVsSeEkHNQ8fNBNtLT0slveDweEhISuN8JIYQQMrK1bdqM6v/7P8BqBQCIgkPAF4s83CvSE0liIsKeegrA2eyqmprOKYD5+TCdyYexIB+WikqIo6OdglIA0PbTz9B+9x13XxgcDOno0ZCmpf4WrAoLo/EhIYT0AWVMXYSRdvWPEEIIGeno3D8wI+W4ab//HjWPPQ7Y7QAA3yuvRPiL/wJPSNeChyq7TgerRgNxbKzT9pJF18BUUHDe5wr8/OC/fDkC/7BiEHtICCHeiTKmCCGEEEIIcaPWL79E7ZN/B85e8/VbsgRh/3iWimcPcXwfH4h7KNUQ8cYbMObmwpiXB+Pp0zDm5cHe1ubUxqbVgidyzpazG42ovOtuSFJHQzZ2LKRpYyCOjQGPzx/U90EIId6MAlOEEEIIIYRchOZ161D/j39y91U3L0Xok09SsGEYk4yKg2RUHPyuvgpA5wqMlupqGHPzzgar8mDMzYM0LdXpeab8fOiPHIH+yBG0nN3GVyohTUuDbEwapGPGQjpmDEQR4TQNkBAyYlBgipCLYDQacd111wEAvvrqK0ilUg/3iBBCCCHu1PTxGjS89BJ33//22xH8+GMUVBhheDwexJGREEdGwnf+PACdwapzmUpKu22zt7dDf+AA9GdXegYAgb8/ErZuAZ8W1iGEjAAUmCLkIthsNvz000/c74QQQggZORhjMJ46yd0PWLECQQ+tpKAUAdDzwjiqaxdDMXsWjKdyYTx1EoaTp2A8dQrWhgandny5vFtQquHNN2EqKIRs7BhI08ZAOiYNQrV6UN8DIYS4AwWmCLkIYrEYa9as4X4nhBBCyG+G+0rGPB4P4S++CLvJDNmYNAT+8Y+e7hIZAoRqNRQzpkMxYzq3zVLfAGPuKRhOnoTxVC5E4eHdnqfbuQvGvDx0bNvGbRNFRkI6dgxkY8Z0TgNMS4NAQVlWhJChhVbluwgjZYUZQgghhHSic//ADPfjxmw2KnJOBhWzWlE4YyZsLS3nb8jjIeQvf4H/rbe4p2OEENILWpVvkA33q3+k/3Q6HXg8HuRyObfNaDTCZrNBLBZDdHZFFrvdDoPBAADw6ZKebTKZYLVaIRKJuMyr/rRljEGv1wMA5HI5lzpuNpthsVj61JYQQggh58fsdmje/Df8Fl8DSVwct52CUmSw8YRCJO7dA3N5OYynOqf/GU6egjEvD8xo/K0hYxDHRDs911RUhLqnn4E0Ix2y9AzIMtIhCg118zsghJDe0VIhA3DfffchLy8Phw8f9nRXiIfZbDacOHECd999N+Lj450eu/XWW6FQKPD+++9z24qLi6FQKBAREeHUdsWKFVAoFHjzzTe5bbW1tVAoFFCpVE5t//SnP0GhUOD555/ntmm1WigUCigUClitVm77X//6VygUCvz1r3/ltlmtVq7tjBkzeizMSQghhBBnzGZD7ZNPoum991Bxx3KYKys93SUywvD4fEji4uB39dUIeeIJxK5fh+QjhxH33XcIe+6fUC29CZLU0ZCOHev0PMOJE9AfOYLmjz5G9cqVKJo9B4UzZ6HqgQfQ+MEH0B08BLtO56F3RQghlDFFyEXh8/m4//77sXfvXoT3UAvAmz3xxBN49NFHPd0NQgghxOsxqxU1jz+Bth9+AABYNRoYc/MgjorycM/ISMcTCiFNToI0OQmqsytFn8tU2n0lQGtDA9q3/oL2rb90buDzIZ88CTFna6cSQog7UY2pizDc6yWQvnFMjRuKU/l8aAliQgjpFzr3D8xQPm7MbEb1/z2C9i1bOjcIhYh45RX4Lpjv2Y4R0g9WjQaGkydhyM6BIScbxpyT3bKkFLNnI+rd1U7b6p5/HnyJBNL0zmmAopBgd3abEDKEUY0pQtyIx+P1GOCRSqXdtvH5/B7bSiQSSCSSAbftrQ9isbjbaoG9tSWEEEKIM7vJhOqVD6Fjxw4AAE8kQsSbb0J56RzPdoyQfhIGBUF56aVQXnopgM56aeaSkrOBqs6bbPx4p+cwqxWtX2xwqmElDA2FLD0dsvSxkGVkQJqWBn6XC7OEEDIQFJgiZAQym81cjaq//OUv3YJXhBBCyEhnNxhQdd/90O3bBwDgSSSIfPttKGZM93DPCLl4PD4fkoQESBISoLpuSY9tTMUlzoXVAVjr6tBeV/dbBqFAAElSEsL++Q/I0tIGu9uEkGGKpvJdhMFMS7/z4/1gFWVYqC2CeuFCjJ08BqF+3TNwCBkInU4HhUIBAOjo6KAMKkII6aOhPCXNk4bacbN16FD1xz9Cf3ahG55cjqjVq+EzeZKHe0aIe1kaGmDMyeEyq4wnT8J+tiREVwk7tjut9Kc7dAj6Awchy8yAdOxYCNVqd3abEOIFaCrfEGe3Mxwobcbikwcw9swW4Of1OOIXjiPRGWgZPwXJkzIwOSEIaeF+kIpoeWLSf0KhEPfeey/3OyGEEEJ+075lCxeU4isUiHr/fcjHj/NwrwhxP1FwMERz50I5dy6AztUpTcXFTsEqW1ubU1AKADq2bUPzf/7L3RfHxHQGqdLTIcvIhDQ5CbyzNVgJIYQypi7CYF39a2g3YvFbu/C3b19AXFtdt8dLfMOwJzwd+yLTwQ8PxdhwJaalROCSxFBE+cu4wteEEEIIca2hlvnjLYbicWt44w20/O8zRH/4IWRjx3i6O4R4LWY2g3dOWYiym5bCkJ3d63N4EgmkaWnwW7QI6qU3DXYXCSEe0J9zPwWmBmDVqlVYtWoVbDYbCgoKBm2QVX+mGKVffQ+2YxtUlUU9tilThmBdyjzsicgAAPgI7IhXCZAe6YtZadG4JDkcCgllxBBCCCGuMBQDLN5gKB43xhisDQ0QhYR4uiuEDDmW6moYsrPP3nJgzMsDM5u7tQu45x4E/+lh7j5jDM1r/wNpWipkY8ZQYXVChjAKTLmJOwdZ5qpqaDdtQuOPPwOnc50ee37iLdgdkcnd5zE7GHgAjweAIURiQ6K/EBmRKswZG4PxCRHg8ymrihBCCOmvoRhg8SR3Xcy7WJb6epjLy+EziWpIETIYmNkMY34+DCfOBqtycmCpqEDkqrehvOwyrp25rAzFCxZ23hEIIElMhCwjo/OWmQFxbCx4fL6H3gUhpD8oMOUmnhqcWmpq0LZlC9o3bYbxzBlo/vstjmvMOF7RgmMVLUgtPoHleT9iT3g6dkdkoNQ37GyQqpOYZ0eU3IokfzHGRaswOz0O8ZEhEAioXtVIodPpoFKpAACtra1U/JwQQvqIAlMD483HzVJdjfI7lsOq0SDq/fcoOEWIm1ibm8GXycCXybht2u++Q81jj/f6HL5SCVl6OmQZ6Qi45x7wpbQ4FCHeigJTbuINgyybVguBnx93nzGGggf/BPvWTdy2Gp9A7IpIx57wdBT7RTgFqRzUAjOifOxIDhBjfKw/pqfFITyMglXDFa3KRwghA+MN5/6hyFuPm7m8HOXLl8NaUwsAkKSkIO7rrygjgxAPsdTVQbd3b2dh9exsmAoLAbu9Wzu+ry+SDux3+r9qyM4G+AJIU5KpsDohXoBW5RtBugalAIDH40FuNaGDxwPOxhzDdY1YWvArlhb8ilZVMPZGpGNzYBoKVZFckKrFJkZLG5DTBmwobYVw+1GEiE2I9rEjJUiCCbEBSE+MQVhYGK3iNgzIZDJUVVVxvxNCCCEjjamkBBW33wGrRgMAEMfFIeq9dykoRYgHiUJDobruOqiuuw4AYNfpYDiV26VeVTZsjY2QjR3b7f+q5s03odu3nyusLktPhywzA7L0dAjDwmiBKEK8GGVMXQRvvfoHAFaNBu2//IK2TZs7lzvu4UpD8813YXvWQhyvbMXJai3M1u5tulLwLQgTGxGrYEgOlGBcbCBGxUQhMjISIroqQQghZATw5nO/N/O242bML0DFnXfC1tQEAJAkJiJ6zccQBgZ6uGeEkPNhjMFaUwObTgdpUtJv2+12FEyaDHtHR4/PEwYFQZqRDllGBpRz50ISF+euLhMyYtFUPjfxtkFWb6xNTWjf+gvat2yG7uAhwGYDAMR98zWko0cDAMxWO06fKkFhdgF2i0JwvKoNFc36874uHwxBQhPCxEbEKBhGB0uRHBGAqKgoxMTEULCKEELIsDNUzv3expuOm+FULip//3vYtFoAgCR1NKI/+ghCtdqj/SKEDJzdbEbr5184FVbvTfjLL8Pv6qu4+7YOHaz1dRDHxVHGJCEuRIEpN/GmQVZfWZub0b5tGwxHjyHsheedUlobP/gAmldfgzA0FL7z58E+Yw5yVTE4Xq3F8YpWZFe2Qme2nff1ZTwrQkVGREqMSFTxkBbmi6jIcMTFxSEwMJBSaL2E2WzGm2++CQBYuXIlxGKxh3tECCFDw1A893sDbzlu+uPHUXnPCtjb2wEA0ox0RH/wAQT0b0nIsGJtboYhp7NOlTE7G4ack1w2VfyWzRBHR3Nt27ZuRfUDD3YWVh87tnP6X0YGpOnpFLAm5CJQYMpNvGWQ5Sql198A46lTTtuEwcFQzpsH3wXzIc7IRFGTHscrWnG8ogXHK1pR2NBzuqyDiGdHmMiACJEBsT4WJAdKER4ajOjoaMTFxUEikQzmWyK9oOLnhBAyMMPt3O8u3nDcbO3tKJp7OexnM6VkE7IQ9e57ECjoHEjIcMfsdphLSmA4dQp+11zjdLG84ZVX0PThRz0+TxQTDVlGBmTpGZCPHwdpaqq7ukzIkEeBKTfxhkGWqzDGoP32O7Rt+hm6ffsBi6VbG0FQIHwvnwfVjTdAmpICANAaLMiubO0MVlV2Bqu0hu7P5V4DdoSKjIgQGxAlNiBeJUBokD/CwsIQGxuLkJAQ8CmFdtCZTCasWLECAPDee+9RgJAQQvpoOJ373clbjlvbzz+j+s//B58pkxH59tvgy+Ue6wshxDtof/wRbT//3FlYXdPYazvZuHGI/d96p2221lbw/fxoVgghPaDAlJt4yyDL1WxtbWj/9Ve0b94C3Z49YOcEqcKefx6qJdf2+FzGGIo1HThQ0oxDpc04WNqE+jZTr/vigyFEZESEyIAIsR5RMgtC/P0QFBSEqKgoxMXFQU6DRkIIIV5iuJ77B5s3HbeOvXshnzABfLooQwjpwlFY3ZCTA8OJzhUAjXl5YGYzAMD/jjsQ8vhjTu0LZ84EDzzIMjun/skyMiAbM4aC3oSAAlODbtWqVVi1ahVsNhsKCgq8YpA1WGzt7ejYsQNtmzZDt3s3mN2OpL17IPDz49roDh5C2w8/QLlgPnwmTwZPKOQeY4yholmPgyXNOHg2UFXVYuh1f7yzBdUjxHpEiAyIlBih9pHA398foaGhiI2NRVhYGIRd9kEIIYS4izcFWIYSTx03c2UlxFFRbtsfIWR4YWYzjPn5MJzIhmzsGMgyM7nHLNXVKLpsbvcn8fmQJCVB5ghUZaRDPGoUFVYnIw4FptxkpA1ObR06GE+dgs+UyU7ba/72N2i//AoAIFCpoLx8LtTLlnEr/p2rutWAQ6VNnRlVJc0oadSdd7+BIjMihDpEiA0IFxngJ+HB19cXgYGBiIiIQHR0NNRqNaXQEkIIGXQj7dzvKp44btrvf0DNE08g9Mknob7pRrfskxAychgLCtDwr385FVbvTdy333ClUIDOmlcUqCLDHQWm3IQGp50ZUUWXXgZrbW23x3ymTUPA3XdBPnnyeYNGDe1GHCpt5gJV+fXt591ngMiKMKEOESI9IsQGKAVWiEQiKJVKqNVqhISEIDIyEiEhIZRZ1QudToeIiAgAQHV1NRU/J4SQPqJz/8C4+7i1fvUVav/2JMAYwOMh5pP/Qj5hwqDvlxAy8nCF1bOzYcjuXAnQVFgI2O0AAJ5cjuRDB51mlWhWrYJ240ausLosIwPS5CTwaKVsMoxQYMpNaHDaya7Xo2PXbrRv2Yz2HTvB9Hqnx6VjxiDgrrugvHwueALBBV+vRWfGobJmLliVW6OF/Tyf0kCJHVFiA0L5bYgU6yHn2wAAfD4fCoUCKpUKQUFBCA8PR1RUFBX6Bq3KRwghA0Xn/oFx53FrXr8e9c/+g7uvWnoTQv/+d8pOIIS4jV2ng+FULgw52bDr9QheudLp8Yp77oFu126nbTyxGNK0tM5gVWYGZOnpEIaF0awQMmRRYMpNaHDand1ggPbbb9H00cewVFU5PRb1/ntQzJzZ79dsM1pwtKyFq1F1skoL63kiVZFKPuLkZoQJOhBob4GI/Va8ncfjQSaTQaVSISAgAKGhoYiOjoZSqRxRX/p2ux3FxcUAgPj4eFoJkRBC+ojO/QPjruPWtGYtGl58kbvvf/ttCH788RF1jieEeL/KP/wRun37uMLqvfFfvhwhjz3qpl4R4loUmHITGpz2jlmtaNu8GU0ffgTT6dMQJ8Rj1MaNLrlaqTdbcay8FQdLm3CgpAknKlthsfX8MebxgOQgORL9GCJEOgTYW2DWtcN8zklAIpFAqVRCqVTC398fAQEBCAkJgVqthqAPWV6EEEJGBjr3D4w7jlvju+9C88ab3P2Ae+5B0MMPUVCKEOKVuMLqZ6f/GbKzYamocGpz7mro1pYWVCy/8+wUwHTIMjMgjoujjFDilSgw5SY0OL0wxhh0e/cBABTTpzk9VvXgSoijo6C+7TaIgoMHvA+92YojZS3YV9yE/cWNOFnd+9Q/IZ+HjCgVxoX7IEZmgsrajPbWZrS1tcFoNOLc/w4CgQBSqRQKhQK+vr7w9/dHYGAggoOD4evrS5lGhBAywtC5v3/csZIxYwyaf/8bTavf5bYFPvgAAv/4RwpKEUKGFGtzMww5nYEqY3YOQp78GyRxcdzj7Tt2oOoPf3R6Dl+phGzsWMgyMyA9uxKgUK12d9cJ6YYCU25Cg9OBM5zKRdn11wMAeCIR/BZfA/8773T64h2oNqMFh0qaOwNVJU04XdvWa1uxkI/x0SpMjQ/EhGhfhIlMaG7SoKmpCVqtFh0dHdDr9d0yrHg8HoRCIWQyGXx8fODr6wuFQgE/Pz+oVCr4+fnBx8cHIpHoot/PYLBYLHj//fdhNBrx4IMPcv3U6/VgjEEqlXKZYhaLBWazmQvSOfTU1mq1wmQygc/nQyaTcW0NBgPsdnu/2kokEq54vc1mg9FoBI/Hg1wu71NbuVxOf5AQQlyOzv0DM1jHrb7NiG9XPoWZ+zdy2wx33ovA3/8eIX4SSISU9UwIGT6aP/kU9S+8wBVW7404Ph6jNn7Xp/q+hAwWCky5CQ1OB65lwwbUP/sPMMtv9Z/A40E5dy4C7r4LsvR0l+2rWWfGgZIm7CtuxP7iJhRrdL22VUiEmDLKH9MTAjE9MRDxQZ0FwvV6Perr66HRdAat2tra0NHRAYPBAKvV2u11eDwe+Hw+RCIRpFIp5HI55HI5fHx84OfnB19fX/j4+EAqlUImk0EsFrt1ymBvxc8jIiJQU1OD48ePIzMzEwCwdu1aLF++HFdccQV+/PFH7jUSExNRVFSEPXv2YNq0zmy4DRs24MYbb8SsWbOwY8cOrm1mZiays7OxZcsWXH755QCAH3/8EVdddRUmTJiAw4cPc22nTZuGffv24ZtvvsHixYsBADt27MCcOXOQmpqK3Nxcru3ll1+OX375BZ9++il+97vfAQAOHz6MSZMmYdq0adi9ezcFpwghLkXn/oEZrON2uKwZj/9rA/61510orEasHrsYG+Onc48HKiQI85MizE+KcJWs83eVDOFnf4YoJRAKKPuZEDJ02HU6GHJzuel/huxs2DSNTm2kY8cibsMXTts0/34Ldp2us7B6RgYVVieDrj/nfuF5HyVkkKhvuAGKWbPQ8sknaPnfZ7B3dACMoX3rVrRv3Qr5pEkIuPsu+EyfftFfmP4+YlwxNgxXjA0D0Hl1dX/x2UBVSRMqmw1c2w6TFb+cbsAvpxsAAKG+UkxLCMSMxEBMTQjHqFGjnF7bZrNBq9WipaUFLS0taG9vR3t7O/R6PQwGA0wmEzo6OqDVartNE+TxeNxNKBRCKBRCJBJBIpFAIpFAKpVCKpVCLBZzv0skEq6NWCyGWCyGUCgEn8/vdjsfuVyOadOmISwsbNityKc/uypkVVUVDAaDU4YVIYSQ4aVWa0SxKhJPTr0b0W112BI72enxxg4TGjtMOFmt7fH5fB4QrJQiTCU9G8CSOQWxwlUyBCokEPDpjzdCiHfg+/jAZ9Ik+EyaBKBzOrO1tvZskKpzGqBs/Lhuz2v99htYa2qB/3TeFwQFdtaqysiALD0DsjFp4A+zvwvI0EEZUxeBrpq6hq29Ha2ff47m//wXVo3G6THVDTcg7B/PDur+K5v12F/chL3Fjdhb1IjGjt5Xx0gJVWLa2WyqyXH+kIvPH9tljMFsNsNgMKClpQWtra1oa2uDTqeD0WiEyWSCyWSC2WyGzWbjboyxboEsh64BLUdmluOn4yYQCLibI+jF5/O534VCIQQCAWw2G+RyOfc8s9kMPp8PqVQKkUgEPp8Pm80Gu90OkUgEmUwGgUAAPp8Pk8kEAJBKpdzr22w2btqfYyodj8fj6nfJZLI+tXW8rmOK4UCm8g23gBshxDvQuX9gBuu42ewMjR0mlNa34tcDx5Ff2YA2qwAGngRM6gethY+GdlOvtSf7QsjnIcRXinDV2cCVSoowX0fmVef9AB8xZR4QQryWtakJhdOmn78Rnw9JUhJCHn8cPlMmn78tIX1AU/nchAanrmU3m6H97js0f/QxzGVlAICoD96HYsYM9/XBznCmrh17ixqxu6gRh0qbYLT0PIdbJOBhfLQa0xMCMSMpCGMj/AZ8RZUxBqvVytVzMhgM0Ol00Ov13QJYZrMZFouFu1mtVtjtdjDGuJ/n/u7YR08/HQEhx+993dY1KNb1/rmBsq7tuj73QjcA3bLAeDweFxjr6bGe+nS+IF5vvw/0sa59J4QMT3TuHxh3HTetVovt27ejrKwMjDGoVCpcMm06lMGRqG01oEZrRG2rAbVaI2paDahrM6Km1YjGDtNF7Vcs5P82ZdARvPKTIVwlRahv508/mYjOEYQQj7G2tHQWVc/JgeFENgw5OZ2zVs4Ru2EDZGPHcPeNZ86gfcsWKqxO+o0CU4PMHSvMjGTMZkP7tm3o2PYrwv71gtMgTnfgAPRHj0K9bJlbvhRNVhuOlrdgb1Ej9hQ2Iqdai97+x6jlIsxMCsKspCDMSAxCkFIy6P0DOgNMNpsNVquV+3nu746gl2O7xWLpsW3Xn45Mqd6CXb3d7GeLMXb9Hbhw0Ovcx7o6N2Dl+MkY6/W1ettvTwG2CwWxevrZWz+7Zq2d+/tAt3XNfhMIBPSHDSEeRIGpgXH3cauvr8f27dtRV1cHxhiCg4MxZ84chIeH99jeZLWhXmtCjdaAWq0BNa1G1GoNqG01dgaztAa06i09PrevZCIBwlRnA1ddal1FqGWIUssRrpJBLKR6V4QQ92B2O8ylpZ1BquzOQJW5ogLJB/aDJxZz7Ro/+ACaV1/j7otiojun/mVkQJaRDmlyslN7QhwoMOUmNDh1v/Lbbof+0CHw5HKob7ge/nfcAVFYmNv236o3Y39xE3YXdU77K2/S99p2TIQvZicFY1ZyEMZFqYZkcVVHYMput3OBqv78dPx+oQBYTwEuABcMggHoFiyyWCx49dVXAQCPPPIIJJLuAcLegkvn28+523rLGDtX1330lAk2kCBTT8Gqc2/nbu86jbPrdE4KchHSP3TuHxhPHbfS0lLs3r0bTU1N4PF4iIqKwpw5c+Dv79/v1zKYbZ3BqrPZVrVnA1Zdg1jtpu4LovQVn9dZ2zJSLUekf2ewKspfjii1DFH+coT4SqnWFSFkUNlNJvDPGTtX3n8/On7Z1utzeGIxpKmpUF5+OQJ+f+dgd5EMIRSYchManLqXubISxQsWAjbbbxuFQvjOuxzqW26BbNw4t/+RXdmsx+7CRuwq0GBvUWOvA1KlVIgZiYGYlRSEmUlBCPOTubWf3syR8dVbUKtr7a2eAlvn/uzo6MCCBQsAdK78J5PJuu3v3OmM52YmnTs1r6cgVE99c9wu9H673nqaltjTNMhzA2mO49b1uNgvsHTwuc6tO9bbTSQSdbtdqMA+IcMVnfsHxtPHLTc3F/v27UNHRwcEAgESEhIwe/Zsly+Q0W60oE5r5KYMOk0dPBu8MljOf57ojUjAQ7jKEbCSIfKcwBXVuSKEDAZLXR0MJ05w0/+Mublgpu7Tn/2WLEH48885bWv57HOI4+KosPoIRYEpN/H0IGskMldVoXnNWrR+9RXY2SLZDtLUVKhvuQW+V17RLdLvDhabHcfKW7CzQIMd+Rrk1bb12jYlVIlZZ6f9ZcWqIREK3NjT4c1iseDjjz8GYwzLli0Dn88/79RGx89zpzteiEAggEgkglgs5oI1jlUShUKhUz0sHo/Xbf/nu/UlwOTYf9fbuZlSXYNcXTPXerr1570D6DVg1dMxEYvFEAjoM06GB1ec+61WK9avX4/58+cjJCTExT30Tt4wZrLZbDh69CiOHj0Ko9EIkUiE1NRUTJ8+HWI3TUNhjEFrsHDZVtWtRlS16FHVbEBVix6VLQY063pfhOV8ZCIBIs8GqRzBqsizQawofzl8pSIXvxtCyEjEzGYY8wtgyDk7BTA7G5byCoQ+/TTUS2/i2tna2lAw6WwRdT4fksTE31YBzEiHeNQo8OhC57BGgSk38YZB1khlbW5Gy6fr0PLZZ7A1Nzs9JggIQPzPP0Hg4X+ThjYjdhU2YmeBBrsLNb3WppCLBZgaH4hZyUGYnRSEKH/XXr0l/dc1iNQ1gNW18Lzjd8fP8wWTeDwexGIxJBIJ97Pr746fjoCWY/9di9xf6HahgFLXIJFjn11vjj7xeLweg1YXul0omNZ1/+frg2N1RUK8lavO/XK5HKdPn0ZMTIwLe+e9vGnMZLFYsHfvXpw6dQoWiwVSqRTjx4/HhAkTvCKI3mGydgapmg2obNajskWPqpbO36taDOgY4HRBX6kQMQE+GBXkg1GBis6fZ3+XiT3/vgkhQ5e1pQU8oRACpZLb1rF3Lyp/f1evz+ErlZCNHQtpRjoCbr8dApXKDT0l7kSBKTfxpkHWSGU3m9H+889o/u8nMObmAgB8pk1D9Ecferhnzmx2huyqVuzM12BHgQY5Va29FlEfFeTDZVNNGRUAqYgGi97OMa3u3GCVYxVFx4qKjp+9fe3y+XxIpVJIJBJIpdJuN7FY3OsUOkdR+6777elmMpnOG8TqGqRy9KXr7z31wfH+zw3eWSwWp9UkHTertfc/qoRCYa/7dvykaYTEk1x17p89ezYefvhhXHPNNS7snffyxjGTwWDA9u3bUVRUBJvNBqVSiSlTpiAtLc1rp8QxxtCqt6DybOCqM8vqbBDrbADLbO3ftG4ACPeTYlTQ2WBVoA/3e7ifDHyqa0UIGQBrYyM6du6CIScHhuxsmAoKgJ4uZPL5SD58yGmqnzG/AMxsosLqQxwFptzEGwdZIxVjDIYTJ9Dy6Tr4XbMIipkzf3vMZkPVypVQXnqZx6b5natZZ8buQg12Fmiwq0CDxo6e0/YlQj6mJwTi0tHBuCwlBKF+Ujf3dOix2+04ffo0AGD06NFeF8Sw2+1OAZtzfxqNRhiNxh6DRzwer1vQSiaTcTeRqG9LkVut1m7BIqPRCJPJ5HTr6fTQtQ+O/Xb9XSS68FSRnvbvOAaOm9Fo7DELi8fjQSQS9XgMKHBF3MFV5/4vvvgCTzzxBB5++GFkZWXB55zaG+np6RfbVa/izWOmlpYWbN++HRUVFWCMwd/fHzNnzkRcXJynu9ZvdjuDpsPEZVc5Mq4cgauaVgPs/Rj5S0V8xAb4ID7IOcNqVJAPlDQ1kBDSD3adDobcXG76nyE7GzZNIyTJyRj13bdObasffRRtG7/vLKyelgZZejpkmRmQpadDGB7utRcPiDMKTLmJNw+yyG/af92OqnvvBQAI1GqobrwR6puXQhQa6uGedbLbGfJq287WpmrAsYpW2HoZNY6J8MVlKSG4bHQwxoT70VXMHuh0OigUCgBAR0dHtz/2hgLGGBe8cgSqut5MJhMslu5TQ4VCIWQyGeRyuVPASi6X9ylg1JXdbueCRV2DVl370VPmk6MPjkCRXC7nbv3pw7nHoKefPWWfObLOzg2YOW4UtCIXy1Xn/t5W8XSs+tnXem9DxVAYM9XU1GDHjh2or68HAISFhWH27NkI9ZLxgiuYrDaUN+lRoulAsUaHEo0OJY0dKNHooDX0XHKgN8FKCZJClGdvCiSFdv6ukNCUbELIhTHGYK2thbWpGbKxY5weK5o/H5byih6fJwgKhCy9s1aVYvYsSJOS3NFdMgAUmHKToTDIIkDds/9Ay/r1zhsFAigvvxz+t94C2fjxXhV11xos2FfUiB35GmzPb0BDe/dVL4DOAeFlZzOppiUEUn2Is3Q6HWJjYwEAZWVlQzIw1RdWqxVGoxEGgwF6vR4Gg4G7mXpYKUUsFkMul8PHxwc+Pj7c7wMt+OsIHDn6YDAYuN8dgaNzTy+OPpx7k0qlA/o/aLPZuCBZ1/fvuH9uxhWfz+cCdefeqLYV6StXnfvLy8vP+/hwqz01lMZMRUVF2L17N1pbW8Hj8RAbG4vZs2dDNYzrnzDG0Kwzo6RRhxJNZ6Cq+GzQqqJJD2s/0qwiVDIuUJV8NnCVEKyg0gSEkD5hjKFl/XoYsrNhzM6B+Tzny+DHHkPA8jt+e67ZDHNFBRVW9xIUmHKToTTIGsm6TvNr27wZOCfLQ5I6Gv633Oo10/y6stsZTtVo8cvpBvx6ph6nqnte6U8i5GNaQiAXqKIpfyOb1Wp1CtQYDAbodDro9fpuWU4ikYgLVvn4+EChUMDHx+eiAzWOoJEjcObYf0994PP5kMvlUCgU3P4VCsVFrZLFGIPJZHI6Bo5+GI3GbkEzR3ZX12Pg4+NDGVakGzr3D8xQO252ux05OTk4dOgQdDodBAIBkpKSMGvWLMhkMk93z60sNjsqm/VO2VUlGh2KNB19XkGQzwNiAnyQFKLoDFaFKpES6ou4QB8IKPubEHIe1pYWGHNyYMjurFVlyMmBvb0dABCzfh3k48dzbfXHj6P85mXgKxSQpY+FlFsFMANCtdpTb2HEosCUmwy1QRYBLPUNaP38c7R8/jlsTU1Oj/nfcQdCHn/MQz3rmzqtEdvO1GPb6QbsLWqEqZcCp2MifHFpSgjm0pQ/0oUjWOMIEnX92TVYxOPxIJPJuECRQqGAUql0yXLqjDGYzWYuSOW46XS6bpleYrG4W7BKLpdfdLDIZrNxgaqu+zcYDE7Tp3g8nlPAznFz17LyxDu58txfXFyMN954g6uLl5qaipUrVyI+Pt4VXfUqQ3XMZLVacejQIZw4cQImkwlisRhjx47F1KlTKdMSQGOHCQV17civb0dBfTsK6jtQUNeO9j6uHCgV8ZEc6ovUMCVGh/kiNcwXKWG+NB2QENIrZrfDXFYGw4ls+F6xEHzpbxfkm9auRcO/XuzxeaLo6M4glaNe1dix7uryiEWBKTcZqoMs0mU1v08+hfHUKQBA3MbvnOYo281m8AQC8Lxg6eieGMw27C1q5AJVvU35C/GVYF5qKOanhWLyKH+IBJQBQpx1DVh1dHRwN71e79ROIpFAoVDA19cXSqUSvr6+/a5ddT5ms5nrQ9efXafkCQQCLlDm6IdMJnPJdFy73Q6j0eh0DBwZVl1JJBIolUqnPrjyOBDv5qpz/+bNm7Fo0SJkZmZi2rRpAIC9e/ciOzsb33//PS6//HJXddkrDPUxk8lkwu7du3H69GlYrVbI5XJkZWVh/PjxlFl5DsYYarXGzmBV3dlgVX07ChvaYbT0bcXAaH85UsN8MTrMF6PPBq0i1a75rieEDF/tv/4K7TffQH/iBGyaxl7biaKjkbBls9M2W3s7+AoFfc+4EAWm3GSoD7JI5+DJmJ2Njn37EHS2QLpD09q1aPnkU6iW3gTVdddB6O/voV5emGPK37bTDdh2nil/fjIRLksJxvwxoZiZGDQs61IZjUb8/ve/BwB89NFHkEppWuNAWa1WpyBNT4EiuVwOX19fLkCjUChc+kea3W6HwWDg9t/e3o729nanDC+hUOgUJPLz83NpVpPFYnEKlrW3t0On0zlNB5TJZNz+HTeBlwa1ycVx1bl/3LhxmD9/Pv71r385bX/88cexZcsWHDt27GK76lWGy5ipo6MDO3bsQHFxMex2O3x9fTF16lSkpKTQHzMXYLMzVDbrUVDfjjN17Thd24bTtW0oa9Jf+MkAVHIRxkb4/XaL9EOEioJVhJDuHIXVDTk5MJzoXAHQmJcHdjY73/eqqxDxystOzym5dgmsjZqzWVVnpwCOSQN/mNardQcKTLnJcBlkke6Y3Y6ShVdwxfZ4IhGUCxdAffPNkGVmev0gyDHl75e8euwtaoLZ1v0KpVTEx6ykIMxPC8VlKSHwkw+PjI/hsCqfN7PZbFxwpq2tDW1tbTAYDNzjfD4fvr6+8PPzg0qlgq+vr8unuzDGYDAY0NbWxgWqOjo6nKbhyeVy+Pn5cTdXZVU5OI5D1z50zTDj8/lckMxxo6yq4cFV536pVIqTJ08iMTHRaXtBQQHS09O7ZeoNdcNtzNTY2Ijt27ejuroajDEEBgZi1qxZiI6O9nTXhpwOkxX5dW3Iq2lDXm1nwOpMXVufsqv8fcQYE+GH9Ai/zp+RfgjzG9iCGoSQ4Y2ZzTDmF8CQkw1xTCwU06dxj9n1euRPmAics3AO+HxIEhN/m/6XkUGF1fuBAlNuMtwGWeQ3ttZWVD/yKHS7d3d7TDJ6NNQ3L4XfVVeBL5d7oHf902GyYkd+AzadqsOOfA06eqj7IOTzMGVUAOanhWBeWihCfIdulpHFYsGqVasAAPfddx8FA9zAbDZzQar29nZotVouSMTj8aBUKqFSqQY1QGO326HT6dDW1gatVgutVuv0h71YLOb2r1KpoBiEVG2LxeIUsNNqtU6ZXT4+Pk7HgbL5hiZXnfujoqLw2muv4YYbbnDa/sUXX+D//u//UFHR8zLZQ9VwHTNVVFRg165d0Gg0AICIiAjMnj0bwcHBHu7Z0GazM5Q16XC61hGwasOpai0aOy5cbD1QcW6wSoUQXwkFqwghvbLU1KD2yb/DcPIk7G09zzxxiPrwQ6egFmOMvl96QYEpNxmugyzyG3NFBVo++xzar76CTat1eoyvUMBv8WIE/mEFhIGBHuph/5isNuwrasLm3DpszatHUy+r6WRGqTA/LRTz00IwKkjh5l6Soc5ut6OjowOtra1ckMhisQDoDFQpFAqo1Wqo1Wr4+fkN2pQ3o9HoFKjq6Ojgpt+JRCKuD2q1elBW2XIEyxz712q1TgXe5XI5t3+VSkVB1CHCVef+Z599Fq+//joef/xxTJ06FUBnjakXX3wRf/rTn/Dkk0+6qsteYTiPmRhjyM/Px969e9HW1gY+n4+4uDjMnj172L1XT3LUrjpZrcXJKm3nz2ptn1YGDFJKuCmA6ZGd0wCDlXRxgBDirGthdUNONgzZOTDl5ztlUiUdOghBl+/2li++QNOHH3VmVWVkQJaZAWlyMni0WA4FptxlOA+yiDO70Yi2TZvQ8r//wZidw23nSSRI3LkDApXKc50bIJud4Wh5Czbn1mFzbh2qWgw9tksMVmDBmM7i6WnhvnRFgPQbYww6nQ6tra3czRGoEggEUKlUUKvV8Pf3h1wuH7TPmNVqhVarRUtLC1pbW9F+dqlhoHNalSNI5O/vPyhBIsYYjEYjtFotWltb0dzczAWqHJllXQN2VFDZO7nq3M8YwxtvvIFXX30VNTU1AIDw8HA88sgjePDBB73yu/baa6/Fjh07cNlll+HLL7/s13NHwpjJbrfj+PHjOHz4MAwGA4RCIVJSUjBjxgzKkBwkjDFUtxpwqlqLnC7Bqla95YLPjVTLMC5ajXFRKoyLViE13BcSIdUGJIQ4s+v1MObmwpCdDUtNLUL/7nzhqOavf4X2q6+dtvHEYkhTUzsDVRmdAStheLhXntsHEwWmBtmqVauwatUq2Gw2FBQUDOtBFunOcCoXLZ/9D20//AjfK65A+PPPOT2uO3gI0tEpTpF0b8cYQ15tGzbn1mNLbh3O1LX32C5SLcMVY8Nw5dgwpEf6eeWXq91u56bAREdH0x/3Xogxho6ODjQ3N6OlpQVarZYrqC6RSODv74+AgACo1epBXY7dbDajtbUVLS0taGlp4Wpl8Xg8+Pn5ISAgAP7+/vDx8RmUz7qjVpZj/y0tLdzUP6FQCLVazfVBIpG4fP9kYFwRYLFarVi/fj3mz5+PkJAQLkiqVCpd2VWX27FjB9rb2/Gf//yHAlPnYbFYsH//fpw8eRJmsxkSiQQZGRmYPHnyoH6nkU6MMVS1GHDybLCqM2jVijZj91IGXYkFfKRF+GJclBrjY1QYF61GONWrIoRcQM1jj6Nt0yausHpv/K5ZhPAXX3RTr/rGkfEbFBSEgIAAl78+BabcZCQNskh3Nq0WdqMJopDf6kjYdToUzpoNZrPBb/E18L/1VkhGjfJgLwemrFHHZVIdq2jtsU2kWoYrx4bhCi8LUlHx86HHkcnkCFTpdDoAnQXE1Wo1AgMDERAQMOjBGUeQqKmpCS0tLVydLKlUioCAAAQEBEClUg3a1EPHFMjm5mY0Nzejra2Nm3ro6+vL9WEw6mORvnPVuV8ul+P06dOIiYlxYe8G344dO/D2229TYKoPDAYDdu3ahfz8fNhsNvj4+GDixInIyMigiyZuxhhDZbMBOdWtOFmlxYnKVuRUaWGw2M77vGClBOOiVVxm1dhIP8jFFFwkhDjrWljdkN15s5Q714oMevhhBK6457fnWCwou3kZpKNHc1lV4vh4txZWb2xsxMmTJxEREYGkpCSXvz4FptxkJA6yyPk1r1+P+mf/4bTNZ9o0+N92K3xmzBiSKzg0tBmxJa8em3PrsK+4CTZ7968MbwpS6XQ6ruhsQ0MDBaaGIIPBgKamJjQ2NqK1tbVbcCYoKGjQ/11tNhtaW1vR1NSE5uZmLptKIBBwffD39x/0jK7m5mauD45sKolEgqCgIAQFBcHX15f+wHUzV537Z8+ejYceegiLFy92Sb927dqFl19+GUePHkVtbS2++eabbq+9atUqvPzyy6irq0NGRgbeeustTJo0qV/7ocBU/2m1Wmzfvh3l5eWw2+1QqVSYOnUqkpKSKMjsQVabHWfq2nG8shXHK1pwoqIVJY268z5HwOdhdJgSE2L8MSnOHxNi1AgewgvGEEIGj7WlBcacHBiyc2DIzkbgvX+EPCuLe9xwKhdl11/v9By+QgFZ+lhIHfWqMjIg9PcflP4xxnDkyBHo9XpMmTJlUC4AU2DKTUbyIIv0zFxWhub/foLWb78F67J0PACIY2KgvuUW+F17LQSKoRksadaZsSW3Dj+erL1gkOrK9DCMjfCeTCoyNFksFi4409TUxAVnfHx8EBwcjODgYMgHeXVMxhj0ej0XLNOeXQhBIBDA39+fS38ezCCV3W6HVqvl+uAIlInFYi5IRXWp3MNV5/4vvvgCTzzxBB5++GFkZWV1C7amp6f36/V+/vln7N27F1lZWViyZEm3wNTnn3+O2267De+++y4mT56MN954Axs2bEB+fj4XzM/MzHRaSdJhy5YtCA8PB0CBqYtRV1eHHTt2oK6uDowxBAcHY/bs2YiIiPB018hZLTozTlS14njF2WBVZSvaLzAFMCZAjgkx/pgYq8aEWH/EBw3O9G9CyPCi/f4H1Dz2mFNh9Z6IoqIQ9/VXELh4un99fT3y8vIQHR2N+Ph4l762AwWm3IQGWaQ3trY2tH79NVo+XQdLVZXTY3wfH/jfuRxB993nod65Rl+CVFH+v9WkoiAVuVh2ux2tra3QaDTQaDRcAXWFQsEFqQZjdb1zGY1GNDY2QqPRQKvVgjEGPp8Pf39/hISEICAgYNCm+wG/1ejSaDRoaGjoFqQKCQmBry8tVDBYXHXu7ymIyOPxuGWnHVNJB4LH43ULTE2ePBkTJ07E22+/DaDz/1NUVBQeeOABPP74431+bQpMXbySkhLs2bMHTU1N4PF4SExMxIIFCwb1e4MMjN3OUKzp6AxUVbbgWHkrChracb6/nvx9xJgQo8bEWH9MiFUjLdwPYiFdNCCEdNe1sLohOxuGE9mwajRObYShoUjcsd1pW/N//wtLdfVvWVX9LKxut9tx+PBhmM1mTJ48GeJBWkGQAlNuQoMsciHMZkPHzp1o/u8n0B84wG0PvP9+BN0/tANTXTXrzNicW4efKEhF3MRut6OlpYULUjmyPHx9fREaGorg4OBBWVnvXCaTiQtSOaYdCoVCBAcHIyQkBH5+g/tZd6x46AhS6c9maspkMoSEhCAkJGTQM8pGGled+8vLy8/7+MXUnjo3MGU2myGXy/Hll186Batuv/12tLa24rvvvuvza/c1MGUymbhVJ4HO4xYVFUVjprMYY8jNzcXevXuh1+sRFBSEa6+9lqafDwFagwXHyltwuKwZR8pacKKqFWZr7xkPUhEfmVEqTIr1x4RYf4yLVkEpHfzzEyFk6GGMwVpXx03/M2RnQxwV2a1oeukNN8J48iR3XxAUCFl6Z5BKlp4O2dgx4J/nfFJTU4P8/HzExcUhNjZ2sN4OBabchQJTpD+MBQVo+eRTtG/ZglGbfoZQreYes9Q3wHg6D4qZM4dkHaqu+hqkunJsOBZlhGN0mNKlf7ibTCbcf//9AIC3336bVjMbAex2O5qbm9HQ0IDGxkbYbDbw+XwEBgYiNDQUarXaLVPcTCYT6uvrUV9fj46ODgCdhdNDQkIQGhrqlimHHR0dXB/MZjMAwM/PDyEhIW4L1g13rjj3WywWpKSk4IcffsDo0aNd3MPugamamhpERERg3759uOSSS7h2jz76KHbu3ImDBw/26XXnzp2L7Oxs6HQ6+Pv7Y8OGDU6v19XTTz+NZ555ptt2GjM50+v1+Oabb7iaiIsWLUJoaKinu0X6wWS14VS1FodKW3CkrBlHylugNVh6bc/nAaPDfDEpzh9TRgVgcpw/VPLByVYghAw/zGxGftYEMEvv3zPg8yFJTETQA/dDOXeu00M2mw0HDx6E3W7HlClTBrUUBQWm3IQCU2Qg7CYT+OcESxpeeQVNH34EcUI8ApYvh+/VV4M/SCmV7tSXIFVCsAKLMjqDVLGBF3+l+NxV+eRyOZdF0vVKtMlkgtVqhUgk4tJXHbWEgM4VsxwBM7PZDIvFAqFQ6BTocqwe15+2MpmMC5JYLBaYzWYIBAJIpdIBtdXr9WCMQSqVctNArFYrBALBiMxKs1qt0Gg0qKurQ2trK4DOYuGO4JC7shG6BogcWSNqtRphYWEIDAwc9Ck7joyy+vp6p2BdcHAwwsLCBj2Tazhz1bk/IiICv/zyy5AKTPUHZUz1nc1mw6ZNm1BQUACRSIRLL70Uqampnu4WGSC7naFI04HDZc04XNqMw2UtqG419NqexwNSQn0xZRQFqgghfXNuYXVDTg7s7e3d2kWufgfKOXO4++aqalR8/BEaVCpEzpmD6LFjB7WfFJhyEwpMEVewdehQNHs27GczLIDOdEz/W26FeulNEPj5ebB3ruMIUv2YU4v9JT0HqdIj/bAoIxxXZ4QjZICr3JjNZrz88ssAgEceeQRarZYr7Nv16+6hhx7Cm2++ib/85S947rnnAHQPajmCGH/961/x/PPPY+XKlXjjjTe413D8Yd/Q0ICgoCAAwHPPPYe//e1vuOuuu/DBBx9wbX18fKDX61FaWsqlzL7xxht4+OGHsWzZMqxbt45rGxQUhMbGRpw6dQppaWkAgA8++AD33HMPrrnmGnz77bdc29jYWJSXl+PQoUOYOHEiAGDdunVYvXo1du/ePaKDDwaDAXV1daivr+fqMKnVaoSHhyMwMNAtWVSOuli1tbVobGyE3W6HSCRCaGgowsLC3BIocwTramtrucLtPj4+CA8PR0hICGVR9ZOrzv3PP/88CgoK8OGHH7r8auVgTuUbKBoznR9jDAcPHsTBgwfBGENWVhamT58+or/Dh5OaVgOOlHdmVB0qbUZ+fe91qhyBqsldMqrUPhSoIoT0jtntMJeVwXAimwtUmQoKkLh7l9Oqfs1ffon6vz3J3RdFRUGWmYnwf70A3iBcNO3PuX/w8rYIIX3Cl8sQ/tKLaProYxiOHgUA2DSN0Lz+Ohrfew/qm26C//I7IDobXBmq/H3EuHlSNG6eFI2mDhN+OlWHjSeqcbishWuTU6VFTpUWz/10GpPj/LEoIwILx4T2a0AmFovx17/+dTDewpCg0+nw0ksvIScnB3q9fkTXK5HJZNzc+dbWVtTU1KCxsREtLS2QSCQICwtDWFiYUwaaqzmKovv7+8NsNqOurg61tbWorKxEZWUlVCoVIiMjERAQMGiBMqFQyL3Xjo4O1NbWoq6uDoWFhSguLkZwcDAiIyOhdPFqL+T8Dh8+jG3btmHLli0YO3Zst/+rX3/9tcv2JRaLkZWVhW3btnGBKbvdjm3btnFTn4ln8Xg8TJkyBYGBgdi8eTOOHDmCpqYmXHnllRQ8HgbCVTIsUsmwKKNzdUut3oLDZc04UNKEA6VNyK1p4wJVjAGna9twurYNa/eVAQBSQpWYMiqAAlWEkB7x+HxIRo2CZNQoqJZcCwCwGwzgn7MoUOO+/U73LZWV4IlEgxKU6i/KmLoIdPWPuJrhxAk0fbwG7Vu3ouulNJ5YDL/rliB45UoIVCrPdXAQVLca8EN2DTZm1yC3pq3b40I+DzOTgrAoIxyXp4bAR9K/eHrX6XkjYSqfwWDAFVdcAaFQiI0bN7pllbqhxGQyoa6uDjU1NTAajeDxeAgMDERkZKTbprcxxrgsKo1GA7vdDqlUisjISISGhrrlj1CbzQaNRoOamhoui8odQbLhwFXn/uXLl5/38TVr1vTr9To6OlBUVAQAGDduHF577TXMmTMH/v7+iI6Oxueff47bb78d7733HiZNmoQ33ngDX3zxBc6cOYOQkJABv48LWbVqFVatWgWbzYaCggIaM/VBQ0MDvv/+e7S1tSEgIACLFy+mYzbMaQ0WHC7tOVDVk98CVf6YHBdAgSpCyAWZzWYc3rwZ0vJyRHToYMzJgTE3F75XXIHwF54flH3SVD43ocAUGSzmigo0r12L1i+/AjtbwFigViNh2y/gD+MVtooaOrAxuwbfZ9egtFHX7XGpiI+5o0OwKCMcs5KDIBF6PrpPhiZHwfTq6mo0NzcD6FzRLyoqym3T/IDOQFlNTQ1qamq4wGNYWBgiIiLctppee3s7qqqq0NDQALvdDplMxgXJBrMg5lDlref+HTt2YE6XOhIOt99+O9auXQugc0GIl19+GXV1dcjMzMS///1vTJ482S3989bj5q30ej02btyI2tpayOVyXHHFFYiKivJ0t4ibaA0WHHFkVJU0I7dGix4qIADonPqXGuaLaQmBmBofgElx/pCL6bubEOKsqKgIlZWVSEtL+63MicUCW0eH06JcrkSBKTehQRYZbFaNBk1r16L1f58hYMUKBK64x+lxS30DRCFDe4pfTxhjOFXdho3Z1fg+uxZ1bcZubXylQiwYE4prMiMwZVQABHyqw0EGRqfToaqqCnV1dR4LzNhsNjQ0NKCqqgodHR3g8XgICgpCdHS026bYmUwmVFdXo6amhsv6i4iIQGRkJJdVSFx77rdardixYweKi4uxbNkyKJVK1NTUwNfXl6t3N1zQmKn/bDYbtm7dijNnzkAoFGLGjBlIT0+nulMjUH8CVSIBD+Oi1JiWEIhpCQHIiFJBJKAsWEJGMqPRiIMHD8LHxwdZWVluO494LDBlsVhQV1cHvV6PoKAg+HcptDUc0SCLuIuttRU8kQj8LlPRLHV1KL58HuRTL0Hgij9APn6cB3s4eOx2hkNlzdiYXYOfT9aiRd99adRQXymuyQzH4nERGB1G/xfJwJjNZlRXV6O6uhoWiwUikYgLzLirxotjml9lZSWampoAAAEBAYiOjobKTdN4bTYb6uvrUVlZCb1eD4FAgPDwcERFRTlNTx2pXHXuLy8vx4IFC1BRUQGTyYSCggKMGjUKK1euhMlkwrvvvuvCXnsejZkGhjGGI0eOYP/+/bDb7UhPT8esWbMGfWVP4t0cgar9xU3YV9yEvNrupRAcfMQCTIrzP5tRFYiUUCX4dDGPkBElPz8fNTU1SE9PR0BAgNv269bAVHt7Oz799FN89tlnOHToEMxmMxhj4PF4iIyMxLx583DPPfdwq0UNJzTIIp5U9/zzaPnvJ9x9+aRJCPzDCsgvuWTYXk212OzYU9iIjdk12JJbB53Z1q1NSqgS146LwKLMcIT5jbz6Snq9nvu+PXz4sNumgw0nNpsNdXV1qKqq4gIzkZGRbs8cam9vR0VFBTQaDRhjUKlUiImJgVqtdsv/cbvdDo1Gg4qKCnR0dIDP5yM0NBTR0dEjunaZq879ixcvhlKpxEcffYSAgABkZ2dj1KhR2LFjB+6++24UFha6sNeeR2Omi1NcXIwtW7bAaDQiOjoaV1555aAu3ECGlqYOE/aXNGFvURP2FTeivEnfa1t/HzEuiQ/AtPjOjKpof/mwHTcSQjr/Njh06BD8/PyQmZnp1v/vbgtMvfbaa3juuecQHx+Pq6++GpMmTUJ4eDhkMhmam5tx6tQp7N69G99++y0mT56Mt956C4mJiQPdndehQRbxpNYvv4TmnXdgral12i5NT0fgH1ZAMXs2eMO4gLHBbMMvp+vx3Ylq7MjXwHpOTjuPB1wyKgCLx3Wu7KeUjoxVjXQ6HTcFqKOjY0SvynexHIGZsrIyLkAVERGBqKgotwaodDodKisrUVdXB8YY/Pz8MGrUKLdlUDHG0NTUhPLycrS1tYHP5yMsLAwxMTEjMoPKVef+gIAA7Nu3D8nJyVAqlVxgqqysDKmpqdxCDEMdFT93naamJmzcuBGtra1Qq9VYtGjRsJ+dQAamqkWPfUVN2FvciL1FTWjsMPXaNkIlw7SEAExLCMQl8QEIVlLAk5DhJDc3Fw0NDRg3bpzbxo4ObgtM3Xzzzfjb3/6GtLS087YzmUxYs2YNxGIx7rzzzoHuzutQYIp4GjObof3+BzS9/z7M5eVOj0mSkhCw4h74LljgFUuADqZmnRk/5NTgm+PVOF7R2u1xiZCPy1NDcO24CMxMChrWtRZsNht2794NAJgxYwZN93ABR4CqvLwcOp2OC1BFR0e7dRl3g8GAiooK1NbWgjEGf39/xMXFue38wxhDS0sLSktL0dbW5rHj4GmuOver1Wrs3bsXqampToGpPXv24LrrrkN9fb0Le+15NGZyDaPRiO+//x5VVVWQyWSYN28eRo0a5eluES/GGENhQwf2FnUGqQ6WNKHdZO21fXKIEtMTAzEjMRCT4wIgE9M4gpChSqvV4tixYwgICEB6errb90/Fz92EBlnEWzCbDe2bN6Pxvfdhys93eizsn/+A6vrrPdQz9ytr1OHbE9X45nh1j6ns/j5iXJ0ehsXjIpAZpaL0ddJnjDEug0qn00EkEiE6OhoRERFuDQDq9XqUlZWhoaEBjDEEBQUhLi7ObdlxjDE0NjaitLQUOp0OQqEQ0dHRiIyMHBGBUFed+2+66Sb4+fnh/fffh1KpRE5ODoKCgnDNNdcgOjoaa9ascWGvPY/GTK7jKJqfm5sLPp+PKVOmYMKECXQ+I31itdlxslqLfcVN2FvUiCPlLTBb7T22FQv4mBCrxozEIMxIDERqmC/VpyJkiGCM4fjx42hra8PEiRM9MovCo4Gp5uZm2O12BAYGuvJlvRINsoi3YYyhY/sONL73LozZORCGhCB+y2bwR+B0G8YYjle24tvj1fg+u6bHoulxgT5YnBmBxePCERNAU95I39jtdjQ0NKC0tBRGoxFSqRSxsbEICQkB343TZzs6OlBaWorGxkbweDyEh4cjNjbWbdMMHcehrKwMBoMBEokE8fHxCA4OHtZ/ILvq3F9VVYX58+d3ZjMUFmLChAkoLCxEYGAgdu3axS3lPFzQmMm1HH9w7N27FzabDaNHj8Zll13mtpVEyfBhtNhwtLylM6OquAknq1p7XfEvwEeMaQmd2VQzEoMQ6kfT/gjxVg0NDcjNzUVERASSkpI80gePBKZOnTqFZcuWITc3FwAQERGB5cuX49FHHx22NU5okEW8FWMM+gMHYNfrobzsMqfHNO+8A3F0DHwXDv8pfg4Wmx27CjT4+ng1fsmrh6mHK4Pjo1W4dlwErkoPh9rHffWDXM1qteKHH34AAFx11VX0R8ogstlsqKmpQXl5OSwWC3x8fBAfH+/W1U6AzjTt4uJiaLVaCIVCxMbGIiIiwm1BMrvdjpqaGpSVlcFiscDX1xeJiYnD9rzoynO/1WrF559/juzsbHR0dGD8+PH43e9+NyyLy9OYaXCUlZVh8+bN0Ov1CA8Px1VXXTVsx93EPbR6C/YVN2JXYSN2F2pQ1WLotW1isILLppo8yh9yMY05CPEGNpsNhw8fhsViweTJk91aG7UrjwSmJk2aBIVCgeeeew5qtRr79+/Hv//9bxiNRuzbtw9qtdoVu/EqNMgiQ425shLFCxYCNhvE8fEIvPePI6IGVVdtRgs2narDN8eqcaC0Ced+Awr5PMxODsZ14yNw6ehgSIRD69hQ8XP3s1gsqKysRFVVFWw2GwICApCQkODWFREZY2hoaEBJSQmMRiPkcjkXJHNX9pLZbEZ5eTmqq6vBGENoaCji4uKG3cphdO7vHyp+Pviam5vxww8/oKmpCX5+frjiiisQGhrq6W6RYYAxhvImPXYXarCrsBH7i5vQ0Ut9KrGAj6wYNaYnBmJmYhDSwmnaHyGeUlFRgeLiYsTHxyM6Otpj/fBIYMrHxwdHjx5FSkoKt40xhhtuuAFSqRSffvqpK3bjVWhwSoaaxvfeh+b11522iRPiEXTffVDOnz+sV/HrSU2rARuza/DNsWrk17d3e1wlF+Hq9HBclxWJjEi/ITE9yWAwYO7cuQCAX375ZVhmXngro9GIkpIS1NfXg8/nIzIyEjExMW7NWrPZbKiqqkJ5eTkXJEtMTHTr50Cn06GoqAjNzc0QCAQYNWoUwsPD3TrNcTDRuX9g6LgNLqPRiJ9++gkVFRWQSCSYM2cOkpOTh8R5iwwdFpsd2ZWt2FXYiD2FGpyo7H3an1ouwrSEziDV9MRAhKtoPEKIO5jNZhw8eBAikQgTJ070aP1PjwSmZs2ahRdffBFTpkxx2p6fn4+JEyeira3NFbvxKjTIIkONY4qf5q23YTh2zOkxSWICAu+7D8p580ZcgAoATte24Zvj1fjuRDXq27ovq5wQrMB14yNx7bgIqqlAzqu1tRWFhYXo6OiARCLBqFGjEBIS4tY/EE0mE4qLi1FfXw+BQICYmBhERUW5LTjEGENTUxMKCwthNBqhVCqRlJQ0LM6VdO4fGDpug89qtWLXrl04efIk+Hw+srKyMHny5BGxKAHxDK3Bgv3Fjdhd2HmraO6+6IxDfJAPZiQGYWZS52p/PhKa9kfIYCgoKEB1dTXS0tI8Xq/SbYGpRYsWISMjA+np6bBarXjzzTfx3XffISQkhGtz5MgRXHvttaisrBzobrwOpaWToY4xBv3+/Z0BquPHnR6TJCYi+NFHoJgxw0O98yybnWFvUSO+OlaFzbl1MFqc61HxecC0hEBcnxWJeamhtIwy6ZHdbkdtbS1KS0thsVigVquRlJTk1ul9ANDS0oKCggLo9Xr4+PggMTHRrVPrrVYrysvLuTFAREQE4uLihnTtMwqwDAwdN/dgjCEnJwd79uyBxWJBYmIi5s6dC8kIXASFuF95k+5skEqDfcVNaDf2PO1PJOBhfLQaM5OCMCspiFb7I8RFOjo6cOTIEfj6+mLcuHEez5p1W2DqiSeewIkTJ3DixAnU19cDAGQyGW688UZkZmbCZrNhzZo1eOqpp3D9MFyungZZZKhjjEG3dx8a33oLhuxsbnvYP/8B1TD8P9tf7UYLfjpZi6+OVuNQWXO3xxUSIa4cG4brsiIxMVbt8S9/4n0sFgtKSkpQU1MDPp+P2NhYt2YuAZ3T+yorK1FeXg673Y7w8HDEx8e7NTjU0dGB/Px8tLW1QSqVIjk5Gf7+/m7bvyvRuX9g6Li5V0VFBTZt2gSdTofQ0FBcccUV8PPz83S3yAhitdmRXaXF7kIN9hQ24nhlK2y9zPsLVEgwMzEQs5KDMD0hEAEKCqQSMhA5OTloamrC+PHjveI73yNT+err67kgleNWWFgIgUCA5ORk5OTkuGI3XoUGWWS4YIxBt2cvNG+/BVtLK+J//AE8kYh73K7XgyeTjejAS0WTHl8dq8LXx6tQ2dx9hZpofzmWjI/AdeMjEeXv3qyYrgwGA2bOnAkA2LVrF9WY8hKtra3Iz8/nMpeSk5PdPmDQ6/UoKChAS0uLR4JDjDHU1NSguLgYNpsNERERGDVq1JDLnnL1ud9sNqOhoQF2u3N2pieLlQ4GGjO5X0tLC3788UdoNBr4+vpi3rx5iIqK8nS3yAjVZrRgf3ET9hQ2YlehBuVNPU/74/GAsRF+mHU2myozSgWhYOSVmCCkv5qbm5GdnY2QkBCkpqZ6ujsAPBSY6onBYEBOTg5OnDiBFStWDNZuPIYGWWS4YYzB1tgIYVCQ0/bq/3sElqoqBD34AOSXXDKiA1R2O8PhsmZ8dawKP52s63F1mklx/rh+fCSuSA+Dws01FGhVPu9ls9lQUVGBiooKMMa4wIw767+cGxzyRPaUwWDAmTNn0NraCplMhuTk5CG1cq+rzv2FhYW48847sW/fPqftjDHweDzYbLaL7apXoTGTZ5hMJmzatAllZWUQiUSYOXMmxowZ4+luEYLyJh12FWiws6AR+4oboTf3/J2nlAoxPSEQs5KCMDMpiIqoE9IDu92OI0eOwGAwYNKkSV5zYdprAlPDHQ2yyEhgKixEyaJrgLNfFfIJExC08kHIJ070cM88z2C2YXNuHb46VoU9RY0499tUKuJjQVoorsuKxNT4QAjcUD/BarVi8+bNAID58+cPuWyUkUCn0yE/Px9arRZyuRwpKSluz54yGAzIz8/nsqdSUlLcGhxijKG6uholJSWw2WyIiopCXFzckCjS7Kpz/7Rp0yAUCvH4448jLCysW8A/IyPjYrvqFagup+fZbDbs2bMH2dnZ4PF4uPzyy51W0SbE08xWO46UN2NXQSN2Fmhwurb3RbMSgxWd2VTJQZgY6w+pyPvPG4QMtsrKShQVFSE2NhZxcXGe7g6HAlNuQoEpMhLojx1H7d+fhLmo2Gm7z9RLEPjAA5CPG+ehnnmXWq0B3xyvxldHq1Cs0XV7PMxPisXjOqf6JQQrPNBD4k3sdjsXmGGMISoqCrGxsW7PnqqtrUVRURHsdjsXHHJn/Su9Xo8zZ85Aq9VCqVQiNTXV7QXi+8tV534fHx8cPXp0xAQIaMzkWYwxHD16FPv27YNIJMLVV1+NyMhIT3eLkB41tBmxq7AzSLW7UINWvaXHdlIRH1NGBXDT/uICfUZ0Vj8ZmcxmMw4ePAihUIhJkyZ51UU+Cky5CQ2yyEjBbDa0/bwJjW+/DXNZmdNjPjNnIOiBByEbS1MDgM7Bf3aVFl8drcLG7BpoDd0HU+OjVbhhQhSuSg+DUirq4VXISKHT6XD69Gm0t7fDx8cHo0ePhlKpdGsf9Ho9Tp8+jba2Nvj6+mL06NFuDQ7Z7XaUl5ejvLwcfD4fSUlJCA0Nddv++8tV5/6JEyfi9ddfx/Tp013YO+9FYybPY4xhx44dyMnJgY+PD6699loEBAR4uluEnJfNzpBT1Xo2m6oBJypb0UsNdUSqZVyQampCoNvLKRDiCfn5+aipqUFaWhqCg4M93R0nFJhyExpkkZGGWa3Q/vADGle9A8vZ5d8d/G+/HSFPPO6hnnknk9WGX0834KtjVdier+m2Go1UxMcVY8NwQ1YUJsf5u2SpZJvNhl9//RUAcOmll3rVVRPSM7vdjoqKCpSdDfqOGjUKUVFRbr3qa7fbUVZWhoqKCvD5fCQmJiI0NNStfWhpacHp06dhMpkQEhKCpKQkr5yK6qpz/6+//oq//e1veP755zF27FiIRM5B6uE2rqAxk3ew2Wz46aefUFxcjICAAFx77bVcXUJChoJWvRl7i5qws6ABOws0qG8z9dhOyOchK0aNWclBmJkYhNQwX5eMswjxJm1tbTh27Bj8/PyQmZnpdRmDXheY4vP5mD17Nl5++WVkZWUN9u7chgZZZKRiFgtav/0WjatXw1pTCwAIf/UV+F15pYd75r0aO0z47kQNNhypxJm69m6PR/nLcENWFK7LikTERRT2pOLnQ1d7ezvy8vKg1+vh7++PlJQUSCTuXTK7a3AoNDQUSUlJbg1ums1m5Ofno7GxEXK5HGPGjPG6z7Crzv2OKZPnDiKp+DkZbCaTCd988w1qa2sRFRWFq6++2u3fNYS4AmMMBfUdXJDqcGkLzDZ7j20DFRLMTOosoj4jMQj+PmI395YQ12KM4fjx42hra8OECRO88iKD1wWm1q5di7KyMmzatAkHDhwY7N25DQ2yyEjHzGa0fvUV2rf9iqj33wOvS20ac1kZmJ1BMsp7CvB5A8YYTlW3YcPRSnx7vBptRudV/Xg8YHpCIK7PisT8tNB+F/U0GAy45JJLAAD79+/3mlU5SN9YrVYUFRWhtrYWYrEYKSkpbp9qYzabcebMGTQ1NUGhUCAtLc2tU/sYY6iqqkJxcTH4fD5SUlK8KjXdVef+nTt3nvfxWbNmDfi1vRGNmbxLW1sbvvnmG7S0tCApKQnz5s3zygxFQvpDZ7LiQEnT2dX+NChr0vfYjscD0iNVmJMchNnJwUiP8KNsKjLk1NfXIy8vDxEREUhKSvJ0d3rkdYGp4YoGWYT0rvLe+9CxYwf8Fi1C4L1/hDg62tNd8jpGiw1b8+rxxZHKHlf185UKsSgzHDdOiMLYCD+vS88lg6e+vh4FBQWwWq2Ijo52e1FyxhgqKipQWloKgUCAlJQUBAUFuW3/QGf2Vl5eHsxms0eOQW/o3D8wdNy8T319PTZu3Ai9Xo/MzEzMmDHDK/6PEeIq5U06Lki1r7gJenPPmagBPmLMTArC7LPT/tSUTUW8nNVqxaFDh2C32zF58uRu5QC8hUcCUzabDR9++CHy8/MRGRmJjIwMZGZmDuuiijTIIqRnhpOnUHbDDb9tEAqhunYxAv/wB4giIjzXMS9W02rAV0ersOFoFSqau1/hSw5R4oYJkbh2XAQCFDTlYiQwGAzIy8vjipKnpaVBKpW6tQ/Nzc3Iy8uDxWLxSHDIaDQiNzcXbW1tUKvVSE1NhVjs2T8YXHnub21txUcffYTTp08DANLS0nDnnXfCz8/PFV31CqtWrcKqVatgs9lQUFBAYyYvU1xcjC1btsBqtWLq1KkYP348XQQhw5LJasPR8hbsLNBgZ76mx7IKAMDnAZlRKsxODsac5GCkhVNtKuJ9SkpKUF5ejqSkJER48d9WHglM3Xvvvfjqq68wd+5cbNiwATweD1arFREREcjMzMTGjRtdsRuvQoEpQnpm69Ch5dNP0bRmDexa7W8PiERQ33A9AlasgCgkxHMd9GJ2O8OhsmZsOFKFn07WwmBxvron5PNw2ehg3JAVhdnJQRAK6Or2cGa321FaWoqKigqIRCKkpqbC39/frX04NziUlpbm1itzNpsNRUVFqKmpgUwmw9ixYz1ad8pV5/4jR45g/vz5kMlkmDRpEgDg8OHDMBgM2LJlC8aPH++qLnsFGjN5rxMnTmDPnj3g8/m49NJLkZKS4ukuETLoarUG7MjXYEd+A/YUNkLXSzZVoEKMWUnBXDaVn9w7M1PIyKHX63H48GHI5XJkZWV5daarRwJToaGh+M9//oP58+dDqVRi37592LlzJ5599lncdNNNeOutt1yxG69CgyxCzs/W3o7m//wXzWvXwt7RwW3nicVQLb0JgXffDaGbpwcNJR0mK37MqcEXR6pwtLyl2+NBSgmWjIvADRMikRCsBNCZZbNw4UIAwM8//0w1poYJjUaDM2fOwGazITY2FjExMW5fta+wsBA1NTWQy+UYO3asW+tOAUB1dTUKCwshEAgwZswYqNVqt+7fwVXn/hkzZiAhIQEffPABV9vHarXirrvuQklJCXbt2uWqLnsFGjN5L8YY9uzZg+PHj0Mmk2H+/PmIpun3ZAQxW+04Ut7MBaoK6jt6bMfnAeOj1ZiTEoxZSUFIC/elDEPiVowx5OTkoLm5GePGjYNKpfJ0l87LI4EphUKB06dPIyoqCv7+/ti7dy9Gjx6N119/HTU1NXj55ZddsRuvQoMsQvrG1tqKprVr0fLfT2DX/zZNTTZ+PGLXr/Ngz4aOYk0HNhypwtfHqtDQ3n1p5HHRKtw4IQpz4n0RFtj5Bzutyje86PV65ObmoqOjA4GBgUhJSXFr5hJjDNXV1SgqKoJAIEBaWprbs7eam5uRm5sLm82GpKQkhIeHu3X/gOvO/TKZDMePH++WnZKXl4cJEyZAr++5aO9QRWMm72az2bB582YUFhZCpVJh4cKFXrXoACHuVNWix84CDbaf0WBvUWO37HWHYKUEs5KCMCclGNMTA+ErpWwqMrgaGhqQm5uLsLCwIZHd6pHAVHp6Oj744ANMnjwZY8eOxeuvv465c+eiqKgIM2bMQG1trSt241VokEVI/1hbWtD04YdoWbcezGhE5DvvQHnpHE93a0ix2uzYVajBhiNV+OV0PSw2569wiYAhUX8al8QH4NEVt3ptMUQyMI46PXV1dZDJZEhLS4NSqXRrH7oGhxISEhAREeHWK8Y6nQ4nT56EwWBASkoKwsLC3LZvwHXn/pCQEHzyySeYN2+e0/bNmzfjtttuQ319/cV21avQmMn7GY1G/PDDD6iqqkJoaCgWLlw4rOqdETIQJqsNh0tbsD2/ATvyG1Cs0fXYTsDnIStGjdnJQZiTHIyUUCVlUxGX6lrwfNKkSR6vudkXHglMPf3009zP+++/H83NzVi/fj02btyI2267Da2tra7YjVehQRYhA2PVaKDd+D3871zudNI2nDiBjt174H/H7RC4+Y/toahZZ8a3x6vxxZHKHot4xgX64MYJUbguKwLBSvcWzSaDhzGGmpoaFBUVgcfjISUlxe2ZDTqdDqdOnYJer0dERAQSEhLcWuPAbDajtLQU8fHxbl/i3lXn/gcffBDffPMNXnnlFUydOhUAsHfvXjzyyCO47rrr8MYbb7iox96BxkxDQ1tbGzZu3IimpibExMRg3rx5bp+2S4g3q2zWY0d+A7bna7CvuBFGi73HdqG+UsxO7lzpb1pCIJSUTUUuUmFhIaqqqpCcnOyRjPGB8EhgqquKigpMnDgRdrsdbW1t+P3vf4933nnH1bvxOBpkEeJa5cuXQ7//APh+fghYvhz+t94CPk1FuyDGGHJr2vDFkUp8d6IGWoPF6XEBn4dLU4KxdGIUZiVRwfThQqvVIjc3FyaTCTExMYiLi3Pr1VmLxYJTp06htbUVQUFBGD16NAQCgdv27ymuOvebzWY88sgjePfdd2G1WgEAIpEIf/zjH/Gvf/0LEsnwWn2TxkxDR0NDA3744Qd0dHQgOTkZc+bMGRJX5glxN6PFhoOlzdiR34Ad+RqUNvacTSXk8zAhVo05ycGYnRyMpBAFZVORfmlvb8fRo0ehVCqH1OqpHg9MAUBjYyO+//57BAQE4Oqrrx4yB68/aJBFiOuYy8pQfOVVgO23efwCtRoBd/0e6mXLwKci3n2iM5rx9mc/Y9uZOuTbw8DjOwcKQnwluCErCjdOiEJ0AF0FH+qMRiNOnTqF9vZ2BAYGYvTo0W7NILLZbDhz5gwaGhrg5+eHMWPGuOUPWLvdDo1Gg+DgYLePL1x97tfr9SguLgYAxMfHD9vsFBozDS0lJSXYtm0bjEYjMjMzcckll7g9O5GQoaasUdcZpCrQYH9xE0zWnrOpwv2kmJ0SjNlJndlUPhL6v0V6xxjDsWPH0N7ejqysLLeXcLgYXhGYGglokEWIa5krKtD4zmpoN24E7L+dzAWBgQi8526obroJ/GGWReBqOp0OCoUCAHC6vAE/nG7GhqOVqG/rXjB9WkIAbpoYjXmpIZCKhn+my3Bls9mQn5+P+vp6+Pj4YOzYsW5djZExhuLiYlRWVkIulyM9PX3Q919eXo6SkhKPpLPTuX9g6LgNPdnZ2di3bx8YY5g8eTLGjRvn1cuSE+JNjBYb9pc0YceZzml/Fc09L2ghEvAwKc4fc5KDcWlKMEYFKdzcU+LtampqkJ+fj8jISCQmJnq6O/3itsBURUVFv5aTra6uRkRExEB353VokEXI4DCVlKLxnXfQ9uOPQJevKGFwMAL+sALqpUvBo8Fxj/R6PTIyMgB0/lEhl8u5gumfHarEtjMNsNmdv/ZVchEWZ0Zg6aQopITSd9lQxBhDZWUlSkpKIBQKkZaWBrVa7dY+VFZWori4GCKRCOnp6YN2RU+v1+Pw4cOQSqWYMGGC26cPXsy5f8mSJVi7di18fX2xZMmS87b9+uuvL6abXmPVqlVYtWoVV7ifxkxDh91ux759+5CdnQ2xWIypU6ciNTV1WM6CIGQwMcZQ2qjDjnwNtuc34GBpM8y9ZFPFBsgx+2yQalKcP104HOFMJhMOHToEgUCASZMmDbnMVbcFpkJCQrB48WLcddddmDhxYo9ttFotvvjiC7z55pu455578OCDDw50d16HAlOEDC5TYSE0b69C++bN3DbZuHGIWb+OBsYD1NBuxFdHq/H54QqUNXW/epcRpcLSiVG4OiMcCkotH3KampqQl5fnsRXzGhoacPr0afD5fIwdOxYqlcqlr88YQ05ODpqbm5GZmen24Btwcef+5cuX49///jeUSiXuuOOO8/7brFmz5mK76lVozDQ0Wa1WbNu2DQUFBVAqlZg5cyZGjRrl6W4RMqTpzVbsL27CjnwNfj3TgOpWQ4/tZCIBpiUE4tKUYMxJCUKYH5W1GGlOnToFjUaDMWPGICgoyNPd6Te3Baaamprw3HPP4eOPP4ZUKkVWVhbCw8MhlUrR0tKCvLw85ObmYvz48XjyySdxxRVXDHRXXokGWYS4h/HMGWjeehsd27Yheu0a+EyZwj3GGAPsdvBGQNFlV2KM4WBpMz4/XImfTtZ2q4MgFwtwVXoYbpoYhfHRagoEDiE6nQ4nT56EwWBAeHg4EhMT3Tr9pqWlBSdPngQApKWlISAgwGWvXV9fj7y8PISFhSElJcVlr9sfdO4fGDpuQ5fBYMCmTZtQVVWFgIAAzJkzB2FhYZ7uFiHDAmMMRQ0d+PVMA7bnN+BIWQus9p7/PE8JVZ4NUgVjXJSKFrMZ5hoaGpCbm4vg4GCkpaV5ujsD4vYaUwaDAT/++CP27NmD8vJyGAwGBAYGYty4cZg/fz7GjBlzsbvwSjTIIsS9TMXFkMTHO23r2LsX9f/4JwLvuw++VyykANVZOp0OYrEYIlHn8sQ2mw1GoxE8Hs+puLLRaERzhxGbT2uw4Vgd8mrbwJgdzGIGAPDFUiQEK7B0YhSuSA2En1QAkUjEFbi22+0wGDqv9Pl0WUHRZDLBarU6tWWMQa/vzNKSy+VcsMtsNsNisTi1JRfHYrEgLy8Pzc3NUKlUSEtLc+uxbWtrQ05ODmw2G1JTU11ylc9iseDQoUNgjGHSpEke+6y46tx/6aWX4uuvv+6WVdbW1obFixfj119/vcieehcaMw1tbW1t+PHHH6HRaBAREYHZs2e7NOhMCOnUZrRgT2Ejfj3TgB35DWjsMPfYzk8mwqykIMxJCcL/s3ff4VGVaePHvzOZzKRM2qSR3kmBhIQSmlgAFRtYUFSkWNBde3n1Xeu6xdVVf6ur8q5igVVBWSzYRWmKUpOQAiEhIb33NpPp5/cHZpZAgISUSXk+15WLZM6ZM3eGyZxn7nM/93PBeD80rmL8NJqcOOaZNm3aiF2pty/n/n6nWf/85z8jSRKLFy/m1Vdf5fPPP+f777/nww8/5JFHHhm1SSlBEIbeyUkpSZJoeO11jCUlVD36KEWLFtH2/RYka8/z9scCvV7PFVdcgVqt5t1337XdnpOTg1qtPqVp4rJlywjy9UKX/QPfPjCHr+87jyvCZJS/spiK/1sBQGFdB3/95ghxF12LWq3mgaeew/rb1bzq6mrUavUpH64ffvhh1Go1f/vb32y3tba2olarUavVmM1m2+1PPvkkarWaJ598cqCfjjHL0dGRxMREgoODaWlpIT09nY6OjiF7fHd3d5KTk1EoFBw+fJjq6up+H7OoqAij0Uh0dPSoSGDu3LkTo/HUDxx6vZ5du3bZISJBOD13d3fmzp2Lh4cHVVVV7Nmzh/b2dnuHJQijjruTI5cnBvDy9ZPY/8R8vrx3Ng/Oj2FSsEe3/Vo7TXyZVcVDG7OY8tcfueb/fuX1bQUcqmxFrG028h07dgyj0UhUVNSITUr1Vb8biPzpT3/id7/73ahd3lgQhOHL2t6O7LeKIABj4TEqH3wQVVwcvvfdi3ru3DE3BU2lUtHa2gqAk5NTn+8/MciDhy6O5V8c722QGq5hf0kTAF2V5R8fKCf7xR3cMDWE8wLH1vM7ksjlcmJiYnB1daWgoICMjAzi4+OHrEeBWq0mJSWFrKws8vLysFgsBAcHn9OxWlpaqKqqwsvLC39//wGOdGhlZ2fbvs/NzaWmpsb2s8Vi4fvvvx9VC8UIo4e/vz/nnXceP/30EyUlJTg5OXHeeeed07lGEISzk8tlJAV7khTsyYPzx1PfbuCno/XsyKvj54J62vXHL/JJEhwsa+FgWQv/78ej+LmpuCj2+JS/82J8RM/QEaapqYnq6mo0Gg3jxo2zdzhDpt9T+eRyOTU1Nfj5+Q1UTCOGKEsXBPuTJAndnj3U//M1OrOyum1zmjgR3/vvw3XOnDGVoOqaMtfbqXwWi6XbvidPzztW38F/0srZtK+IhjY9MgcHZA7H95VhZU6EB9dPCeaylHBbvwMxlW94aWlp4fDhwxiNRiIiIggLCxuyvwm9Xk9WVhY6nY6oqKg+reYLx1+7aWlp6PV6pk2bZvcLYf0998vlcttz39MQzNnZmddff53bbrut37EOJ2LMNDp0LUCwb98+LBYLU6ZMYdq0aWPqHCsIw4HJYiW9tJkd+XXsyKvjaG3PVdGODjJSIzS2RFWkj6v4ex3GzGYzaWlpGI1Gpk2bhrPzyG54P6Q9puRyObW1tSOyS3x/iUGWIAwfkiSh3bWL+tdeR3/oULdtzsnJhL77DvITeiAJfWeyWNl2pI6NB8r46Wg9J/fmDPBw4oapISyZFkKgZ99OpJIk2ab3KRQKMWgaBJ2dnRw6dIiOjg78/PyIi4vDYYh6shmNRjIzM9FqtURGRhIWFtbr+xYWFlJeXt7n+w2W/p77S0tLkSSJyMhI9u/f3238pFQq8fPzG7L/l6Ekxkyjh9VqZffu3WRlZeHi4sK8efP6nHAWBGFglTfp2PlbNdXuYw3oTT23tQjzdrElqaZHaHByHH3nm5GsoKCAiooKoqOjCQkJsXc4/TbkiSkPD4+zfohoamrqz8MMS2KQJQjDjyRJdOzYQf1rr2PIywPAdfZsQt99x86RjS5VLZ1sSqtg44Eyqlr13bbJZXBhrB83pYZyUaxvr1aN0Wq1qNVqADo6Oro1UhcGjtlsJi8vj/r6etzc3Jg4ceKQTcMxGo1kZWXR0dHR6yRTa2srBw8exM3NjZSUlCFdXfB0xLn/3IjnbXQxmUx8/fXXVFRUEBwczPz583Fzc7N3WIIgAHqThT1FjezIq2N7Xh0VzZ097ufs6MDsaG8uivPjoli/Pl9UFAZWc3MzmZmZeHh4kJycPCzGPP015ImpV199FQ8PjzPut2LFiv48zLAkBlmCMHxJVivtP26l4Y3XCfjrX3GeNKnbNu2ePbjOmiUqc/rJYpX4+Wg96/eVsT2v9pQqKn93FUumhrAkNZSgMwx4RGJq6EiSRElJCSUlJSiVSiZOnHjWc/hAOTE5FRERQXh4+Gn3NZvNpKeno9frmTp16rB5TQz0uT83N5eysrJTGqEvXLiw38ceTsSYafSpra3l22+/RafTkZSUxKxZs0ZltZ8gjGSSJHGsvoPteXXsyKvnQEkT5pMHa7+JG+fGRXF+zI3zIyXEs1cXFoWBYTabOXDgACaTialTp9q9bcFAGfLElOgxJQZZgjBcSZJ0SvKpbcsPVD7wAKq4OHzuuhO3Sy5BJgbT/VbTquc/aeVsPFBOZUv3q3MyGVw43pebUkOZG+d3ymBHkiRb0/beVOEK/VdXV0deXh6SJBEbGztkDTZ7k5ySJInc3Fzq6uqGXTn7QJ37i4qKuOaaa8jJyUEmk9n6TXW99i0Wy4DEO1yIMdPodODAAdLS0lCpVMyaNYu4uDh7hyQIwhm06U38UtDAjrw6duTX09Bh6HE/D2dHzh/vy0Wxvlww3hdv9dhYGc5e8vPzqaqqYvz48aNqAZQhTUw5ODhQXV0tElNikCUII4IkSRRfdx2G3CO225QREXivWoXHVVd2W+VPODcWq8TPBfV8tK+MbXl1WE66MufvrrL1ogr2Gh1XhEaq9vZ2Dh06hF6vJzQ0lIiIiCEpHTeZTGRlZdHe3k54eDjh4eHdkpGVlZUcPXoUHx8fJk6cOKwSlQN17r/qqqtwcHDgnXfeISIigv3799PY2MgjjzzCyy+/zJw5cwYwavsTY6bRyWQy8e2331JeXs64ceO48MIL8fHxsXdYgiD0gtUqcbiqje15dWzPryO7ooWeMgMyGSSHeHJR7PFqqgmB7sPqvDzSNTY2kp2djZeXF5MmTRpVz62omBoiYpAlCCOPJEl0bN9Ow5tvoc/J6bbNMTAQzR2343nddchV4srQQKht0/OfA+V8fJoqqgtOqKJyFCXjdmEwGDh8+DCtra1oNBri4uJQDcHr/8TkVFhYGBEREchkMpqbm8nOzkalUjFlyhTbapHDxUCd+318fNi+fTtJSUl4eHiwf/9+YmNj2b59O4888ggHDx4cwKjtZ/Xq1axevRqLxcLRo0fFmGkUqqur47vvvqOjo4O4uDjOO++8IXkPEQRhYDV0GPgpv57t+XX8fLSedr25x/383FRcGOvL3Dg/Zkf74OY0vM7TI4nJZOLAgQNYLBamTZs2ZH0/h8qQJqZO1tDQADAmrpaIxJQgjFySJKHdvZvGN99Cd+BAt20Ovj54r7wVrxuXiJX8BojFKrGroJ6P9pex9cipVVQ+znI0Bd8wIciDv//ljyiVSjtFOjZZLBYKCwupqqpCqVSSkJCAl5fXoD/uyckpPz8/W0ImJSXF1ndsOBmoc7+XlxcZGRlEREQQFRXFO++8w0UXXcSxY8dITExEp9MNYNT2J8ZMo1t6ejppaWkoFAomT55McnLyqLrqLwhjjdliJb20me35dezMqye/tr3H/RwdZEwL1zA37vhKf5E+ruJvv5dObFsQFxdHQECAvUMacEOemGppaeHJJ59k48aNNDc3A8cHXDfeeCN//etf8fT07O9DDIry8nKWLVtGXV0dCoWCp59+muuvv77X9xeDLEEYHXQZGTS8+Sban3d1uz3iyy9wGj/eTlGNXnVtejalV/DR/jLbSjFWo57yVxYDcOP/7WTFnFjmxYsqqqFWW1tLfn4+VquVsLAwwsLCBn1qn8lkIjs7m8bGRoxGI2q1mkmTJg1JYuxcDNS5f86cOTzyyCNcffXV3HzzzTQ3N/PUU0+xZs0a0tPTOXTo0ABGbX9izDS6mUwmvv/+e8rLy/H19WXmzJkEBwfbOyxBEAZIRbOOnfn17Mir49djDehN1h73C/N2Ye5vDdRTIzSoFKKH6+lUV1eTl5c3LNsWDJQhTUw1NTUxc+ZMKisrWbp0KfHx8cDxVWY2bNhASEgIu3fvHpYDzOrqampra0lOTqampoYpU6Zw9OjRXq/8IwZZgjC6dB4+TONba2j/8UfU8+YS8sYb3bZbDQYxxW8AWa0Suwob+GhfGT/mVFC39W0ANHPvQKZwxNdNxQ1Tg7lxWighGtGLaqjodDpyc3Npb2/Hw8OD2NjYQV8Rr7W1lS1btqDVaklMTGTKlCnDdoA2UOf+rt/32muvpbCwkCuvvJKjR4/i7e3Nxo0bmTt37gBGbX9izDT61dXVsWXLFjo6OoiMjGT27NnDsupREIT+0Zss7C1qZMdvvanKmzp73M9V6cDsaB/mxftxUawffu6ja5paf+h0OluV6dSpU0ftTIEhTUw9+OCDbNu2ja1bt+Lv799tW01NDZdccgnz5s3jlVde6c/DDIlJkybx9ddf93r1HzHIEoTRyVBYCHIHVJERttsks5ljV1yB84SJeN9xO04JCXaMcPTpqqL6+EDZKQMcmQzOi/bh5tRQ5if4iyqqIWCxWCguLqaiogKZTEZ4eDghISGDUj3V0tLCoUOHMBqNyOVyJEkiNDSUyMjIYZmcGsxzf1NTE15eXsPy9+4vMWYaGzIyMsjIyEAmkzFhwgSmTZuGg1j1VhBGLUmSOFavZUdeHdvyakkracZs7Tm9MDHInbmxfsyN9ycpyAO5fPSd63rDYrFw8OBBOjo6hnWF+EAY0sRUeHg4b731FpdeemmP27///nt+97vfUVJS0udj//zzz7z00kukp6dTXV3N559/ztVXX91tn9WrV/PSSy9RU1PDpEmTeP3110lNTe3zY6Wnp7NixYo+lc6LQZYgjB2t33xD1SP/Y/vZddYsvO+4HZeZM0flh0h7sVolfj3WwEf7y/jhcO0pgxs/NxU3TgthSWooQZ7Odopy7GhtbSUvLw+dTodarSY6OnrABlCSJFFVVUVhYSEymYyEhAQ8PT3Jysqira1t2CanxLn/3IjnbWwwmUz88MMPlJeXo9FoSElJISYmxt5hCYIwRNr0JnYdbWB7Xh078+to1Bp73M9HreSC8cen/M0Z74P7GGqgXlhYSHl5OWFhYURGRto7nEE1pIkplUrFsWPHTjuPvKKigujoaPR6fZ+P/d133/Hrr78yZcoUrr322lMSUxs3bmT58uW8+eabTJ8+nVdffZVNmzaRn59vWyUwOTkZs/nUFQV++OEHAgMDgeNXKOfMmcPbb7/NrFmzeh2fGGQJwtjR8uln1L38Mpbf+uh1cUpIwPuO23G75BJkCoWdohud6tsNbEov5+P95ZQ1dW8ELZfB3Dg/lk4P4/zxvjiM0atuQ8FisVBaWkp5eTlWqxUfHx8iIyP7Nb3PYDCQn59PY2MjTk5OJCYm2qb8mM1msrOzaW1tJSQkhKioqGGVnOrPuf/aa6/t9b6fffZZX0Mb1sSYaeyor6/nxx9/tCWYp0+fjre3t73DEgRhiFmtElkVLbYpf4cq23rcTyHv3kA9ynf0NlBvbGwkOzsbDw8PkpOTB72Pp70NaWIqKCiIjRs3ct555/W4fdeuXSxZsoSqqqr+PAwymeyUxNT06dOZNm0ab/zWB8ZqtRISEsJ9993HH/7wh14d12AwcPHFF7Nq1SqWLVt21n0NBoPt57a2NkJCQsQgSxDGCGtnJ62bN9P43lpM5eXdtjmGhKC5dSWe11yD3FlU8vSVVqu1LZTR0tLSLenRVUW1YV8ZP+TWnrKiX7CXMzelhnLD1BB83UQPsMHS2dlJUVERdXV1wPHVd4ODg/H09Oz1ANJkMlFRUUF5eTkWiwV/f39iYmJwdOx+pXQ4J6f6k2C59dZbe73v2rVr+xrasCYSU2NLZmYm6enpyGQyYmJimD59+qjtoSIIQu/UtumPJ6ny6vilsAGd0dLjfmHeLlwUe7yaanrk6GmgbjAYSEtLw2q1MnXqVJzHwOeFIU1M3XbbbRw7dowff/zxlBOOwWDg0ksvJTIykvfee68/D3NKYspoNOLi4sInn3zSLVm1YsUKWlpa+OKLL856TEmSuPnmm4mNjeXZZ5896/7PPvssf/rTn065XQyyBGFskSwW2n/4gcZ33kV/+HC3bV7LlzHuiSfsFNnIpdVqbRUzHR0dp63GqW3Ts/FAOR/tL6O6tXslrkIu49KJ41g6PZSZkd7DJpEx2rS2tlJeXk5DQwOSJOHk5ISvry9eXl64u7t3SzJJkoTJZKKlpYXGxkbq6uqwWq24uLgQFRWFj4/PaR9nuCanRILl3IjnbWwxmUxs3bqViooK3NzcmDBhwqhddUoQhL4zmC3sK2pi+2+JqpMr47u4KB04L9rHVk3lP0IbqFutVrKysmhpaSEhIeGU3tyj1ZAmpioqKpg6dSoqlYp77rmHuLg4JEniyJEj/N///Z8tM9jbhuKnDfSkxFRVVRVBQUHs3r2bmTNn2vZ77LHH+Omnn9i3b99Zj/nLL79w/vnnk5SUZLvtgw8+IDExscf9RcWUIAgnkiQJ3b59NL7zLtpffgGZjKjvvkUZHm7v0EYcq9VKdXU1AAEBAWctbTZbrOzMr+fDfaX8dLSek89kkb6u3JwayuIpwXi6iKv0g0Gr1VJTU0NdXV236foKhcKWnDKZTN2m03t4eBAYGIifn1+vytdPTE4FBwcTHR1t9w+2A51gqa+vJz8/H4DY2Fh8fX37fczhSCSmxp76+nq2bdtGe3s7gYGBJCcnExQUZO+wBEEYZk5soL49r44DJU2nbaA+IdCdeb8lqSYFe46YBupFRUWUlpYSFBTE+PHj7R3OkBnSxBRAcXExd999Nz/88ANdh5PJZFx88cW88cYbREdH9/chBiUx1V9ikCUIQhf9kSPoDqShWd59SnDTBx/SeTADzW234zxxgp2iG93Km3R8tL+M/6SV09DRvcmmSiHnyqRAls4IJSWk91POhN6TJImOjg5aW1tpb2/HYDBgMpmQyWQ4ODjg7OyMm5sbGo3mnMrWzWYzOTk5tLS0DIvk1ECd+7VaLffddx/vv/8+VqsVAAcHB5YvX87rr7+Oi4vLQIU8LIgx09iUlZVFRkYGkiQRERFBampqv/rTCYIw+vW2gbq3q5ILY4d/A/WGhgZycnJwd3cnOTl5TK1UOuSJqS7Nzc0UFBQAEB0djUajGahDD8pUvv4SgyxBEM5EMpkovORSzL9VArlMn4737bfhOmeOSJAMAqPZypbDNazfV8reoqZTticEuLN0RiiLkoNQq0Sj+pFkOCWnBurcf9ddd7F161beeOMNZs+eDRyv5L7//vu5+OKL+de//jVQIQ8LYsw0NplMJrZt20ZlZSUuLi5ER0czefLkMfXBTBCEc2e1SmRXtv425a/2jA3Up4Z7MTfOj7lx/sOmgXpnZydpaWnIZDKmTJkyJvpKnchuianBdLrm56mpqbz++uvA8akgoaGh3Hvvvb1uft4fYpAlCMKZGAoKKF2xEktT9ySJKiYGze234XH55chEM1jg+MWGf/7znwA88MAD/W6SW1jXwYZ9ZXySXk6bvvvKrK5KB65OCWLp9DASAsV790hxYnIqICCA8ePH22U1m4E69/v4+PDJJ59w4YUXdrt9x44d3HDDDdTX1/cz0uFFjJnGrvr6erZv305HRwd+fn4kJCQQFRVl77AEQRiBatv07Mw/PuVvV8HpG6iHalxsfammR2hwchz6ZLjFYuHgwYO0t7eTlJQ0JlcnHTWJqY6ODgoLCwFISUnhH//4BxdddBEajYbQ0FA2btzIihUreOutt0hNTeXVV1/lP//5D3l5eUPSUEwMsgRBOBurXk/r5i9oWrsWY2lpt20Kf380y5fjueQGHH5r/D1W9bb5eV91Gi18nV3F+n1lZJa3nLJ9cqgnS6eHcUVSgF0GLULfmM1mDh8+TFNTE76+vsTHxw955cVAnftdXFxIT08nPj6+2+2HDx8mNTUVrVbb31CHFTFmGtuys7M5ePAgkiQRFBTElClTBnRmhSAIY4/BbGF/8X8bqJc2nr6B+uyuBuqxfozzGPwG6pIkkZeXR01NDWFhYURGRg76Yw5HoyYxtXPnTi666KJTbl+xYgXr1q0D4I033uCll16ipqaG5ORkXnvtNaZPnz6oca1evZrVq1djsVg4evSoGGQJgnBWksVC+/btNL37Hp2Zmd22KXx9id62dUxXTxkMBu666y4A3nrrLVQq1YA/xqHKVjbsL2PzwcpTrrB5ODuyeEowN08PJcp3bCcJhzur1cqRI0eoq6sjNjaWwMDAIX38gUqwzJs3D29vb95//32cnI4Pkjs7O1mxYgVNTU1s3bp1oEIeFkRiamwzmUzs2LGDiooKnJ2dCQsLY9q0ad1W8RQEQThXkiRR1PDfBur7i8/cQH3uCQ3UHQahgXpZWRnHjh3D29ubiRMn2qXCeziwe2Lq6NGjREZGolCM7h4eYpAlCMK50GVk0PjOu3Rs3w6A1803M+6Zp+0c1djRrjexObOK9XtLyatpP2X7rChvlk4P4+IEf5SKsTmQGO6sVit1dXX4+/sPeQ+JgTr3Hzp0iEsvvRSDwcCkSZOA442inZyc2LJlCxMmjK7FEsSYSWhoaGDHjh1otVo0Gg2xsbHExsbaOyxBEEahNr2JXwr+20D95MVxumhclVwY63u8gXqMLx7O/U+WNzY2kpOTg4uLC5MnTx71OZEzsXtiysHBgSNHjoz6pRDFIEsQhP4wFBXRtHYt3nfeiTIkxHa7paOD6ieexOvmm3GZnjosmjeORpIkkVHWwvq9pXydU43RbO223UetYsm0YG6cFkqIZnStkCacu4E89+t0OtavX09eXh4A8fHxLF26dFQ2RxVjJgEgJyfHNqUvMDCQ1NRUPDw87B2WIAij2IkN1Hfk1ZFT2drjfg5yGVPDvJgXf3ylvyhfdZ/H4FqtloyMDGQyGZMnTx51K+z2ld0TU3K5nLy8PJGYEgRBOAeN775H3UsvAeA0cSLet9+G28UXIxvDV1wGW7PWyKcZFazfV0ZxQ/fePjIZXBTrx7IZYVww3hf5IJR8CyOHOPf3jWh/IJzIZDKxc+dOysvLcXFxISoqiilTpozZaS6CIAy9ujY9O35roP5LQQPa0zRQD9E4My/Ov9cN1E0mE+np6ej1eiZNmoSXl9dghD+iiMTUEBGDU0EQBkPJzUvpzMjodptjcDCalSvxvPYa5KPw6otWqyUoKAiAysrKAWt+3leSJLH7WCPr95Xyw+HaU/oThGicWTo9jBumhqBxHbs9wcay/pz7v/zySy677DIcHR358ssvz7jvwoUL+xPmsCPGTEKXrlX6Ojs78ff3Z8KECYSGhto7LEEQxiCD2cKB4ma25dWyI6+OktM0UHd2PN5AfV58zw3UrVYr2dnZNDc3M378eNuYdqwTiakhIgZZgiAMBslspu37LTS+9y6G3CPdtjl4eOC19Ga8li5FMYqWnR2sVfn6o65Nz8YD5Xy0v4yqVn23bUqFnCsTA7hlZhgpIZ5iuuUY0p9zv1wup6amBj8/vzNWiMhkMiyWnq/gjlRizCR0kSSJ/fv3k5ubi0qlIigoiOnTp9sWARAEQbCXovoO2yp/Z2qgnhBwvIH63Hg/koI8KDiaT01NDUFBQaM+B9IXIjE1RMQgSxCEwSRJErq9e2l89z20v/zSbZtMpSL4tX+ivuACO0U3sKxWK8eOHQMgKipqWE3rMFus7Miv54O9pfx8tP6U7RMC3Vk2I4xFyUE4K89c5i2MfOLcf27E8yacqK2tja1bt9LR0YGnpycREREkJibaOyxBEASb9t8aqG87SwN1DycHJmhgdoQnS+em4Ok68CtLj1QiMTXIRL8EQRCGmj4/n6b33qP1m2/BbEbm4kLM9m04eHraO7QxpbhBy4Z9pfwnrYLWTlO3bW5OCq6fEsLSGaFE+artFKEw2AYqwVJeXk7ICYsejHYiMSWcrKsRuqOjI35+fkyaNAkfHx97hyUIgnAKq1Ui57cG6tt70UB9btzxBurRfn1voD6aiMTUEBGDLEEQhpqpupqm9z9AplLi9+CD3bY1f/wxCl9f1BddhGwYVRyNRnqTha+yqvhwbylZFacOTs6L9uGWGaHMj/dH4SD+L0aTgTr3Ozg4cN5553HLLbewePHiUd8kVYyZhJPp9Xq2bt1Kc3MzarWacePGMW3atDG9tLogCCNDXZuerzOK+eZgKYcbLejNPe8XonFmbqwfF8X5MSPS+6wN1EcbkZgaImKQJQjCcGFpa6Pwwouw6nQoIyLQ3LoSj0WLkKtGRjmxyWRizZo1ANx55504OjraOaLeyypv4cO9pXyZVYXBbO22bZy7EzelhnJTagh+7qJ/ymgwUOf+gwcPsmHDBj7++GPq6+tZsGABt9xyC1dddRWqEfJ32xdizCT05NixY+zbtw+5XI5GoyEqKoqoqCh7hyUIgnBGbW1tZGZmIpfLmZA4icN1Brbn1bEjv+6U1Z27HG+g7s3cOH/mxp3aQH00snti6vHHH+d//ud/8B5FjXl7IgZZgiAMF80ff0zNs3/qdpuDjw+aW5bideONw37KX0/Nz3U6HZIk4eTkhIPD8StMJpMJo9GIg4NDt0a5Pe1rNpsxGAzI5XKcnZ1t+3Z2dmK1Wvu0r0qlsl3Ft1gs6PV6ZDIZLieskNiiM/JJegUf7i09ZVUXhVzGpRPGsWxmGNMjNGO6rHukG+hzvyRJ7Ny5kw0bNvDpp59itVq59tpree+99wYg2uFDjJmEnpjNZn766ScqKipwd3fHy8uLqVOn2s4HgiAIw01HRweZmZlYLBYmTZqE50lj7K4G6jvyjzdQN1lO30B9XvzxKX+Tgj2Ry+0zNtTpdDg7Ow/K2NTuiamxQgyyBEEYLiRJQvvzzzS++x66/fu7bZO5uOB53XVoVqxAGTw8l6/V6/UsW7YMgA8++AAnJyeCgoKoqqri4MGDJCcnA7Bu3TpuvfVWLr/8cr755hvb/WNiYigsLOSXX35h9uzZAGzatIkbbriBCy64gJ07d9r2TU5OJisrix9++IGLL74YgG+++YYrr7ySqVOncuDAAdu+s2fPZvfu3Xz++edcffXVAOzcuZOLLrqIhIQEDh8+fMrvYrVK/FLYwAd7S9l2pJaTF3SJ8VNzy4wwrpkchLvTyKkME44bzHN/RkYGt99+O9nZ2WJVPmHMqKys5NdffwWwTelLSUkRCXxBEIadzs5ODh48iMlkYuLEiWctxOlqoH48UVVPQ4ehx/181EoujD2epJoT44PbEI0POzs7SUtLw8fHh/j4+AE/fl/O/WIStyAIwiggk8lQX3AB6gsuoDPnEI3vvUv7lh/AakXS6Wj+4AOaN2xAc8tS/B9/3N7hnsLJyYlNmzbZO4wBIZfLOH+8L+eP96WypZOP9pXx8YEy22ouBXUd/PHLw/z9+zyuTgli2Yww4gPEB/WxqqKigg0bNrBhwwYOHTrEzJkzWb16tb3DEoQhExAQQGBgIEVFRahUKlpaWqiuriYwMNDeoQmCINjo9XqysrIwGo0kJCT0anaYm5MjlyUGcFliAFarxKGqVrYdOV5NlX1Cj9KGjuNV95+kV+DoICM1QsPcOH/mxfkR7uM6KL+P1WrlyJEjmM1m/Pz8BuUx+kJUTPWDuPonCMJwZiwvp2ndv2n59FMkvR4A34cfxufOVXaOrHdG2lS+MzGarXx/uIYP95Syv6TplO1Tw7xYNjOMBRPHoVKMrcaYI81AnfvfeustNmzYwK+//kpcXBxLly7l5ptvJiwsbACjHT7EmEk4k4aGBnbt2oXRaEStVuPh4UFqaipKpdLeoQmCIGA0GsnMzESr1RIXF0dAQEC/j1nXpmdHfh3bjtTxS2EDOmPPldKRPq7HV/mL92NauAbHAVpUp7i4mJKSEkJCQoiOjh6QY55MTOUbImKQJQjCSGBubqb5o49o/XwzEZ9+gsMJ71emqip0Bw7gfvnlyEZQw/HhoLOzk4ULFwLw5ZdfdktonUleTRsf7i3l84xKtCcNQnzUSpZMC+Gm1FCCvXqX9BKG1kCd+0NCQrjppptYunQpkyZNGsAIhycxZhLORJIkMjIyyM3NxcPDAxcXF4KCggZlaokgCEJfmEwmsrKyaG9vJzo6mpCQkAF/DIPZwr6iJrbn1bEtr5byps4e93NTKTh/vC9z4/y4MNYXb/W5LZbS3NxMVlYWarWalJQU24XagSYSU4Ns9erVrF69GovFwtGjR8UgSxCEEUGyWpHJu19lqfnb32h+/wMU48ahWb4czxuux0E0ne2Vnhq290W73sTmg5V8sLeUo7Ud3bbJZTA3zo9bZoRxfoyv3RpiCqcaqASLJEljqoeOSEwJZ9Pe3s5PP/1Ee3s7Xl5eqFQqkpOT8fLysndogiCMUScmpcLDw4mIiBj0x5QkicK6Drbl1bE9r4700mYsJzcsBWQySAnxZF788VX+4sa59WpcYTQaSUtLw2w2M2XKlD6PX/vC7omppqYmPD09kcsHpsxsuBKDLEEQRjJLezsFF1yIpPvvCnJytRqvG5fgtWw5jv72n28+nJnNZjZu3AjAkiVLbFP9+kqSJPYXN/HB3lK+P1SD+aTBR5i3C0unh3L9lBC8XMW0FnsT5/5zI543oTdyc3PJysrC1dUVZ2dn3N3dmTp16qBdzRcEQTgdeySletKiM/LT0Xq259WxM7+e1k5Tj/sFeDgxN86PefF+zIrywcnx1PdNq9VKdnY2zc3NxMfHM27cuEGN3S6JqdzcXL788ku+/PJL9u3bh5eXF5dffjmLFi1iwYIFg5qJsxcxyBIEYSSTJInO9HQa332Pjh07um90dMTjyivxvu1WVDEx9glwDKpr17Nxfzkb9pdR3arvtk2pkHNVUiDLZ4YxKcTTPgEK4tx/jsTzJvSGXq/n559/pr6+Hl9fXxwdHYmIiCA8PNzeoQmCMIYMl6TUycwWKwfLW9h2pI7tebWnVNx3cXKUMyvK53hvqjg/Aj2Pt5soKiqitLSUwMBAYmNjBz3eIUtM5efns2bNGr788ktqa2u5+OKLWbRoEZdffjlFRUV89dVXfPnllxw9epQLL7yQhQsX8vvf//5cH27YEYMsQRBGC8OxYzSuXUvbF18imbpfiXG94HwC/vIXHIfBih1jhdliZVteHR/uLWVXQcMp2yeFeLJ8RhhXJAX0eEVMGDzi3H9uxPMm9FZRUREZGRk4OjqiVqtRKBRMmzat14tNCIIg9MdwTUr1pLxJZ2ugvudYI0aLtcf94gPcmRXmxjipgaRgD6ZOnjwklahDlphau3Yt+/btY9GiRcybN++0K2eUlJTwxRdf8NVXX7F169ZzfbhhRwyyBEEYbUx1dTR/uJ7mjz/G2tYGgMLfn+gff0AmVkfqxmKxkJGRAcDkQTzBF9V3sH5fGZvSymnTm7tt07gquXFaCEtnhBHk2bvm60L/iHP/uRHPm9BbZrOZ3bt3U1ZWxrhx45DL5Xh7e5OUlDSm+rIJgjD0jEYj2dnZIyIpdTKtwcyvhQ1s/603VV27ocf9vFwcuSjOj3lx/swZ74O70+AtfmT3HlNwfLWi3q5QNFKJQZYgCKOVpUNL66ef0Pjvf6NZegvet9/WbXvHzz/jMnUq8jF8Bbu/zc/7qtNo4cusSv69u5Tc6rZu2+QymB/vz4pZ4cyK8hYf3gaROPefG/G8CX1RWVlJWloaVqsVjUaD1WplwoQJ+InKXUEQBolerycrKwudTjfipxBbrRK51W1sO1LHtiO1ZFe29rifQi5jWriGefF+XJEUQIDHwOZvhkViasqUKaSnp3e7LS8vj7i4uMF4OLsQgyxBEEY7yWRCslqRq/67HK2xvJxjly7Awc0Nr6U347V0KQpvbztGaR86nY6EhATgeJ/FoZpmIkkSGWXN/Ht3Kd8dqsZk6X4aj/J1ZfnMcK6dHITbIF4FG6v6c+5PSUnpddKwqxpvtBBjJqEvrFYr+/fvp6ioyNZrSqVSkZqaKhqhC4Iw4HQ6HVlZWej1emJiYggODrZ3SANCkiTy8vLIL62m0upJTqPEroJ6tEbLKfu+s3wq8xP8B/Tx+3LuP7clhM7gq6++Ijc3l46ODsrLywkJCbFtW7JkCVlZWQP9kIIgCMIgkTk6cvLH6KZ1/warFUtrKw3/9y8a330Pj6uvxvvWlShH8NWlvnJxcaGkpGTIH1cmkzElTMOUMA117fF8vL+c9ftKqW07XrJ9rF7LH788zIvf53Ht5GCWzwwjxt9tyOMUTnX11VfbOwRBGBHkcjnR0dE0NTXR0tKCv78/er2esrKyETW1RhCE4a+9vZ3s7GxMJtOQrFQ3lCoqKqipqSEy0IeFEycil8sxmC3sL276rYF6HWVNOpQKObOi7XuRecArpoqLi/nuu+94+umnmTRpEqWlpQQFBREQEMCxY8dIS0sbyIezK3H1TxCEsUifl0fje+/R9u13YD6h55FMhtv8eWhuuw2XlBT7BTgGmSxWfjhcy/t7SthX3HTK9llR3iyfGc78eD8UDnI7RDh6iHP/uRHPm9BXkiSRlZVFfn4+Hh4ethYh06dPx8nJyc7RCYIwGrS0tJCTk4PVaiUhIQFfX197hzRgmpqayM7OxtnZmcmTJ+PoeGoVvSRJHKvXkl/TzhVJAQMew5BP5SstLSU7Oxt/f39SU1MB+Pnnnzn//POB4/PES0tLmThx4qgYjKxevZrVq1djsVg4evSoGGQJgjAmmaqrafr3+7T85z9Ydbpu25wnT8b3gQdwnZ5qp+jGrryaNt7fU8rnGZV0mrqXagd6OLF0RhhLpoXgo1ad5gjCmYgEy7kRz5twLtrb29m7dy+NjY0EBQVhNpvx8/NjwoQJ9g5NEIQRrq6ujiNHjiCTyUhMTMTLy8veIQ0YnU5na6s0ZcoUu61qOqSJqY8++oiVK1diMpmQyWSkpKTw3Xffjaps4+mIQZYgCAJY2tpo3riR5vc/wFxfb7s98MW/47FwoR0jG1x6vZ4bb7wRgI8//njYXcFv7TTxaXoFH+wtpbhB222b0kHOFUkBLJ8ZRnKIp2iW3gcDde63WCy88sor/Oc//6GsrAyj0dhte1PTqZVv9lReXs6yZcuoq6tDoVDw9NNPc/311/f6/mLMJJyrI0eOcPjwYVxcXPDy8kKv15OSkoKnp6e9QxMEYQSSJImKigqOHTuGo6MjiYmJo+q8ZDKZyMjIoLOzk6SkJDQajd1i6cu5v8/1/B999FG3n//0pz9x8803k5eXxw8//ADAH/7wh74eVhAEQRihHNzd8Vm1iqhtWwl47jmU0VEoAgJwv+yybvuZqqqwtPa8KshIZLFY+OKLL/jiiy+wWE5tImlvHs6O3HZeBNsevoD3b0tlfrwfXfkno8XK5wcrueb/drNo9a9sSitHbxp+v8No9qc//Yl//OMfLFmyhNbWVh5++GGuvfZa5HI5zz77rL3DO4VCoeDVV18lNzeXH374gQcffBCtVnv2OwpCP0VERODl5UVraytWqxWZTEZBQQFWq9XeoQmCMMJYrVYKCgooLCzExcWFyZMnj6qklNVqJTc3F51OR1RUlF2TUn3V64qpmpoa7r77bjw9PXnvvfdstyuVSo4ePWpbTjEvL48pU6aMicGKuPonCIJwKslqxVxdjWNQULfbK+67n45ff8Vz8XV4r1hxyvaRxmQysW7dOgBWrlzZ49z94aa8SceHe0vZmFZOi87UbZuXiyNLpoWydHooIRr7lHyPBAN17o+KiuK1117jiiuuwM3NjczMTNtte/fuZcOGDQMY9cCbNGkSX3/9dbdFbs5EjJmE/jh69Cg5OTk4Ozvj7+9PW1sbsbGxBAYG2js0QRBGCLPZzJEjR2hoaMDT05OJEyeOiLFbb0mSRH5+PtXV1QQEBBAbG2v3ivhBqZhas2YNJpOpW1IKjv8HnzhnMS4uDqvVSk1NTR/DFgRBEEYDmVx+StLJWFpK+9atSDodze9/QOEll1L5yP+gz821U5T95+joyKpVq1i1atWIGdiEaFx4/PJ49j4+jxcXJzEx6L+DhGadiTd/OsYFL+3gjn+nsaugHqt1QNdHEU5QU1NDYmIiAGq1mtbfqgmvvPJKvvnmmz4f7+eff+aqq64iMDAQmUzG5s2bT9ln9erVhIeH4+TkxPTp09m/f/85xZ6eno7FYul1UkoQ+iskJARPT0/a2towGAw4OjpSVFSEyWQ6+50FQRjz9Ho9mZmZNDQ04O/vT1JS0ogZu/VWaWkp1dXVaDQaxo8fb/ekVF/1OjF1//33o9FouO66607Z9u9//5vdu3fT0dEBHC/31p3UCFcQBEEYu2ROTnjddBOyrj5MFgtt33xD8bXXUXrrrXTs+oUBXiRWOAMnRwdumBrCV/eex2d3z+Lq5EAcHY4PYKwSbD1Sy7J39zP/lZ9Y+2sxbXrx4W+gBQcHU11dDRyvnupqh3DgwAFUqr43ptdqtUyaNInVq1f3uH3jxo08/PDD/PGPfyQjI4NJkyZx6aWXUldXZ9snOTmZiRMnnvJVVVVl26epqYnly5ezZs2aPscoCOfK2dmZoKAglEolra2teHh4YDKZKCkpsXdogiAMcy0tLaSnp9Pe3k54eDjx8fE4ODjYO6wBVVNTQ3FxMWq1mgkTJiCXj7wVmPvc/Pzbb7/l8ssvt/18wQUXkJmZSXt7O3K5nIiICEpKSnjssceYP38+U6dOxc3NbcADHw7OVppmsVjElRxhyDg6Oo66N1lh9DE3N9O8fgPN69djaW7utk0VG4v3bbfiftVVyEbACdVqtXLkyBEA4uPjR+Qg4ET17QY2Hijjw71l1LTpu21zUTpw7eQgls8MZ7z/6Dyn99ZATUn7wx/+gLu7O0888QQbN27klltuITw8nLKyMh566CFeeOGFcz62TCbj888/5+qrr7bdNn36dKZNm8Ybb7wBHH/9hoSEcN999/W6N6jBYODiiy9m1apVLFu27Kz7GgwG289tbW2EhISIqXzCOevs7GT37t00NjYSHByMo6MjWq2WadOm4erqau/wBEEYhqqqqigoKEAmkxEXF4efn5+9QxpwTU1NZGdno1KpmDx58jld3BosQ7oqX5eCggLS09PJyMiwfbW0tCCXy4mJibEN3keTMz3RHR0dVFRUiAoAYcjIZDKCg4NRq9X2DkUQzsra2Unr5s00rl2HqazMdrtTQgLhn34yIsqPtVqt7e+to6Nj1HwwMlus/Jhby7/3lLC36NSV4WZEalgxM5yLE/xROIzsZNy5GKxeSXv27GHPnj3ExMRw1VVX9etYJyemjEYjLi4ufPLJJ92SVStWrKClpYUvvvjirMeUJImbb76Z2NjYXjVnf/bZZ/nTn/50yu0iMSX0x5EjR8jPz0elUhEZGUlVVRUajYakpKQRcd4QBGFoWK1WCgsLqaysxMnJicTExFH5Gam9vZ3MzEwAUlJSht3v2Jcxk2KgHjQmJoaYmBjb0tkAxcXFpKWlcfDgwYF6mBHBYrFQUVGBi4sLvr6+4kQpDDpJkqivr6eiooKYmBhROSUMe3JnZ7xuugnPG26gfes2Gt97F31WNprbbzvlPdPc2IjC29tOkZ6Zj4+PvUMYcAoHOZclBnBZYgBHa9t5f08Jn2VUojMeX7Vvb1ETe4uaCPBw4ubUUG5MDcXXbfhcnRupZs6cycyZMwfl2A0NDVgsFvz9/bvd7u/vT15eXq+O8euvv7Jx40aSkpJs/as++OADW5+skz3++OM8/PDDtp+7KqYEoT9CQ0Oprq6mqamJhoYG/Pz8qKuro7GxcVS+HwuC0HcGg4Hc3FxaWlrw9PRkwoQJKJVKe4c14HQ6HdnZ2VitVpKSkoZdUqqvBiwx1ZOIiAgiIiK4/vrrB/Nhhh2TyYQkSfj6+uLs7GzvcIQxwtfXl5KSEkwmk0hMCSOGzMEB90svwe2Si+k8eBDnpKRu23UZGZSuWInHlVfifdutqGJi7BTpqVxdXamvr7d3GINqvL8bf706kccWxPFZegXv7ymlqOH4qrvVrXr+349HeW17AVckBrBydgTJIZ72DXiEKSgoYMeOHdTV1WG1Wrtte+aZZ+wUVc/OO++8U2I8E5VKNaymEwijg6urK+PGjaO9vZ329nbGjRuHg4MDhYWFaDSaET+lWhCE/mlubiY3Nxej0UhwcDBRUVGj8n1Br9eTlZWFyWRiwoQJeHl52TukfhvUxNRotXr1alavXo3FYjnjfqJSShhK4vUmjGQymQyXyZNPub3x3ffAZKL1889p/fxzXC84H+/bbscldZp4zQ8hdydHVs6OYPnMcH491sD7e0rZdqQWqwQmi8TmzCo2Z1YxKcSTlbPCuDwxAJVCJMjP5O233+b3v/89Pj4+jBs3rtvrWSaTDWhiysfHBwcHB2pra7vdXltby7hx4wbscQRhKISGhlJTU0NLSwvV1dUEBQVRVlZGRUUFoaGh9g5PEAQ7kCSJ0tJSSkpKcHBwYMKECaOynxQcn56flZWFXq8nPj4eX19fe4c0IEZf+nAI3HPPPeTm5nLgwAF7h9IvO3fuJDk52d5hCIIg9EiSJFQx0chPmJOu/elnylasoOSGJbR99x2S2WzHCMceuVzGnBhf3l4+lZ8evYi7LojE0+W/yy1nlbfw0MYsZr+wg3/8eJTak5qoC//117/+leeee46amhoyMzM5ePCg7SsjI2NAH0upVDJlyhS2bdtmu81qtbJt27ZBmz4oCINFrVbj5+eHQqFAqz1ewens7ExpaWm3hvuCIIwNRqOR7OxsiouLcXV1ZcqUKaM2KWU2m8nOzkan0xETEzOqLi6JxJQgCIIwLMlkMvwefJDo7dvxf/wPKAIDbNv0OTlUPvQwxxZcRtP69Vg7O4c8Pr1ez9KlS1m6dCl6/dhLwIRoXHj8snj2Pj6PF69LIj7gvwnEhg4Dr20rYPYL27nvo4OklzaLxUBO0tzcPKCtDjo6OsjMzLQ1QS0uLiYzM5Oy3xYXePjhh3n77bf597//zZEjR/j973+PVqvl1ltvHbAYerJ69WoSEhKYNm3aoD6OMLaEhYWhVqvp7OyksrKS0NBQzGYzxcXF9g5NEIQh1NLSQlpaGk1NTQQEBDB58mRcXFzsHdagMJvN5OTk0N7eTnh4OMHBwfYOaUANSWJKLpczd+5c0tPTh+LhhB50dnayZMkSEhISmDRpEpdccskp+3zwwQckJSWRlJTEFVdcQWVlJQCzZs1i9+7dADz22GMEBQXZ7hMZGWkb9AqCIAwGB7UrmhUriN6yhcCXXkQVF2fbZqqooPYvf6UzJ2fI47JYLGzYsIENGzacdWr3aObk6MAN00L49v7z+M9dM7kiMQAH+fFpaWarxFdZVVz3r90sfONXPkmvQG8au8/Via6//np++OGHATteWloaKSkppKSkAMcTUSkpKbYpgUuWLOHll1/mmWeeITk5mczMTL7//vtTGqIPtNFSZS4ML25ubvj6+qJQKOjs7ESr1eLl5UVNTQ1tbW32Dk8QhEFmtVo5duwYmZmZmM1m4uLiiIuLG7V9druSUi0tLYSEhBAeHm7vkAbckPSYeu+99ygpKeGee+5h7969Q/GQw0pOTg6dg3Q139nZ+bQr4pzo+++/p6WlhdzcXACamprIzs62bT906BCPPvoo6enpBAUF8dxzz3HHHXfw3XffMX/+fLZu3cqsWbPYvn07wcHB5ObmolKpUCgUYj6/IAhDQuboiMdVV+F+5ZVod++m6d330O7ejVNiIi4nVWNIRiOyQV6BRalU8sorr9i+H+tkMhmpERpSIzRUt3by4d5SPtpfTpPWCEBOZSv/symL5789wk2poSydEUqAx9hdICQ6Opqnn36avXv3kpiYiKOjY7ft999/f5+Od+GFF561Ku3ee+/l3nvv7XOsgjAchYWFUV9fT0dHB1VVVUycOJGWlhYKCwtJSUkRfQgFYZTSarUcOXKE9vZ23NzcSEhIGLVVUtA9KdXV0H00vr/JJFFbf87a2trw8PCgtbUV9xN6oOj1eoqLi4mIiMDJyWlYJKaKioq48MILufLKK7ngggu4/PLLSU9P58EHHyQzM5PXX3+d9PR01q1bBxyfYjBu3Dh0Oh2//vorTz31FJ999hlXXnkl119/PY6OjqhUKjIzM/nXv/41KL+b0Dcnv+4EYSzQ5+Uh6fU4n9AvT5IkSm+8CYWfL963395tmzC09CYLX2dXs253MYcqu1cxOMhlLJgwjhWzwpkW7jViBlmnO/f3VURExGm3yWQyioqKzvnYw9FAPW+CcKKsrCwqKytRKBSEhYUhl8upqKggPj5+VPVeEQTh+PiuqqqKY8eOYbVaCQ0NJTw8fFSuutfFYrGQk5NDc3MzQUFBxMTEjJjxEvTt3N/viqnc3Fw++ugjHnnkETw9Pft7uFGpN4mjwRYZGUlubi7bt29n69atPPbYY7z66qun3f/EF/zMmTM5dOgQX3zxBXPnzmX+/Pk8/fTTqFQqlixZMgTRC4Ig9MzphGl9XTrT0ujMygKg/cetuKSm4r1qFa7nzR5RJ/PRwMnRgcVTgrluchAZZc2s213KdznVmK0SFqvENznVfJNTTUKAOytnhbMwORAnx9FZhn+ysdILp7crGQvCuQgPD6exsZHOzk6qq6uZPHkytbW1FBUV4ePjg0IhFiAXhNHAYDCQn59PY2MjTk5OxMfHj/rcw0hPSvVVv9OLzz//PIcOHerxhaHX68nLy+vvQwgDoKKiAplMxsKFC3n55ZeRJIny8nLb9osuuojvv/+eqqoqAN58803mzZuHg4MDjo6OzJgxg7/85S/Mnz+fpKQkcnNz2blzJ3PnzrXXryQIgtAjc3MzihOWztXt30/5qlWUXLeYtu+/RxqgD8hWq5WSkhJKSkqwWq0DcszRSiaTMSVMw+s3pfDrH+Zy/9xofNT/nf6YW93GY59mM/P5bfz9+zwqW4a+mb0wOESPKWEweXh4oNFokMvlGI1GKisriYyMxGAwUFpaau/wBEHoJ0mSqK6uZv/+/TQ2NuLv78/UqVNHfVKqa/W9sZKUggGomNq7dy9r1qzpcZuTkxOrVq3i8ssv5/HHH+/vQwn9kJOTw+OPP44kSZjNZpYtW0ZSUpJt+8SJE3nppZdYsGABACEhIbz99tu27fPnz2fnzp3Mnn284iA1NZX8/Hw0Gs2Q/y6CIAhn4n7JJagvvJC2r76i8e13MJaUAKDPzaXywYdQhoWhueN2PBYtQt6P3lCdnZ226VgdHR24uroORPijnr+7Ew9fEss9c6P5Nqeadb+WkFXRCkCzzsS/dh7jrZ+OcUnC8Wl+MyI1o2Yw9vDDD/OXv/wFV1dXHn744TPu+49//GOIohKEkS0sLIzm5mb0ej21tbUEBwfj5uZGRUUF48aNE+/NgjBC6fV68vPzaWpqQqlUMnHiRHxPuPA4WhmNRnJycmhrayM4OJjo6OhRMw46k373mHJ2dubo0aOEhIT0uH39+vW88cYb7Nmzpz8PMyz1tseUIAwF8boThFNJFgvtW7fRuGYN+sOHu23zWLSQwL///ZyPrdVq8fPzA6Curk58+OmHg2XN/Ht3Cd/kVGOydB+WxI1zY8WscK5ODsJZaf9pfv3plXTRRRfx+eef4+npyUUXXXTa/WQyGdu3b+9vqMOK6DElDBZJksjMzKSurg65XE5AQAAhISFkZGSg0WhISkoaEx/qBGG06KqSOnbsGGazmXHjxhEdHX3KIiGjkcFgICsrC61WS1hYGBERESP6/WtIe0xpNBqqq6tPm5hKTU2lsLCwvw8jCIIgCH0mc3DA/dJLcLvkYrS7d9P49jvoflsd1vOGG/p1bFdXV7Ra7UCEOealhHqREurFE1fEs2FfGev3lVHfbgAgr6adxz/L4YXv8rhxWgi3zAgjRDMyV9/ZsWNHj98LgnDuZDIZYWFhtLS0YDKZqK+vJywsjHHjxlFTU0NjYyM+Pj72DlMQhF7QarUUFBTQ3NyMSqUiISEBb29ve4c1JDo7O8nKyqKzs5OoqChCQ0PtHdKQ6ndi6vzzz2fdunWkpqb2uF0ul6PX6/v7MIIgCIJwzmQyGerZs1HPnk1nVhbt23fgMmVKt33at29Hu3cv3rfeimNAgJ0iHdv83Jx4cP547r4wmu8OVfPv3SVklLUA0Npp4q2fi3h7VxHz4v1ZOSucWVHeI/pKonBcV5sB0SBdOFfOzs64u7vT3NyM1WqluLiY8PBwGhoaKCwsxNnZGQeH/1ZcOjo6dvtZEAT7slgslJaWUl5ejtVqJTAwkMjIyDFRJQXHW0JkZ2djNBqJjY0lMDDQ3iENuX4npv7nf/6HGTNmkJyczJ133nnK9j179hAZGdnfhxEEQRCEAeE8aRLOkyZ1u02SJBreWI0+N5fmDR/hcdVVeK+6A1Uvzl9arRZHR0eUv/WrkiQJnU4H0G16n8FgwGw2n3ZfFxcXW5LFaDRiMplQKBSoVKpuj9XXfZ2dnW1LKZtMJoxGIw4ODt2m/PZl36GgVMhZlBzEouQgsitaWLe7hK+zqjFarFgl+DG3lh9zaxnvr2bdrakEejoPaXwD4ZprrukxqSaTyXByciI6Opqbb76Z2NhYO0Q3cM62Kp/RaKS6utr2dyAI50qlUuHt7Y0kSVgsFsrLy/H09MRsNlNUVNRthT6ZTEZwcDBqtdqOEQuCANDY2EhBQQGdnZ2o1WrGjx+Ph4eHvcMaMk1NTRw+fBir1Up8fDz+/v72Dsku+t1jCuDtt9/m97//PRdddBH33HMPkydPRq1Ws2vXLu6++27uv/9+/vd//3cg4h0WThxkHT16VPSYEoYF8boThHNnKC6m+JprkU6s8JXJcJs/H+87V+GcmHjqfQwG7r33Xt555x2efvpp/vznPwNQX19v6z114in2wQcf5J///CdPPPEEzz33HHA8IdT1wejEBupPPvkkf/vb33jggQd49dVXTwjpeCKjrq7O1gD0ueee46mnnuKOO+7otmiFq6srOp3OVjkA8Oqrr/LQQw9x8803s379etu+vr6+NDQ0cOjQISZMmAAcP7ffeeedLFq0iM2bN/f5OR1oDR0GPtpXxof7SqltOz7NL1Tjwo7/uRAH+dBVTQ1Ur6SVK1eyefNmPD09mfJb9V5GRgYtLS1ccsklZGVlUVJSwrZt25g9e/ZAhW83PT1vVquVgoICHBwc8PX1RalUigo44ZxJkkRnZ6dtldSupHpX0rMr8S5JEvX19eh0OmJiYkTllCDYiV6vp7CwkPr6ehwcHIiIiCAoKMh2gWwsqKmpIT8/H7lczsSJE/Hy8rJ3SANqSHtMAaxatYr4+Hgefvhhrr32WtugQpIkLrnkEh566KGBeJhh45577uGee+6xPdGCIAjCyKaKiCB6+zaaP/yQpg/XY21rA0mi/ccfaf/xR1xmzsBn1SpcZs60neOUSiVHjhw5fv8TKpWEweGjVnHfvBh+d2EUWw7X8O/dJVw6YdyQJqUG0rhx47j55pt54403bINwq9XKAw88gJubGx9//DG/+93v+N///V9++eUXO0c7OIxGI1arlZCQEFxcRmbfMGF4USgUdHZ22n5WKpU4Ojqi0+ls1YhwPBlfUlKCyWQSiSlBGGJms5ny8nLKy8uxWCz4+voSHR09pi6sS5JEWVkZRUVFqFQqkpKSxnwF54BUTJ0oLy+PjIwMdDodEydOZMaMGQN5+GFFrMonDCfidScIA8PSoaVl40aa1q3DXF/fbZtTUhJhH36A/KSpeKN9Kp/VaiUhIQGA3NzcYZNEsFol5EOcmBqoiilfX19+/fVXxo8f3+32o0ePMmvWLBoaGsjJyWHOnDm0tLT0M2r76+l5E+ctYaBJkoRWq7VVTSkUClxcXNDpdJjNZlxcXFAoFOK1Jwh2IEkStbW1FBUVYTAYcHV1JSoqasw0N+/SVS1cVVWFWq0mMTFx1L4PDVnFVE1NDV5eXt0GwnFxccTFxfW4f1FRkeg3JQiCIAxrDmpXvG+/Da9lt9C6eTON776LqbQMAEd/P1tSCo5PrTsx+XS62+B4VdXJlVWn21epVNqSVyfq776Ojo49NhI9275arZbS0lKg+/REexvqpNRAMpvN5OXlnZKYysvLs/VjcnJyElPbBKEPZDIZSqUSvV6PTCazNdVXqVRYLBYMBoOokBIEO2htbaWwsJC2tjYcHR2JiYkhMDBwTE3bg+MXEw8fPkxLSwteXl5MmDBhzDR4P5t+vRI++eQTNBoN11xzDWvXrqX+pCvLAPv27eOJJ55gwoQJTDqp2awwsh06dMjWt6Sqqoo5c+bYNyBBEIQBJFcq8brhBqK+/Zagf/w/VPHxeK9a1W0fyWym+eONWH+rOBqtnJyc2L9/P/v37x+1V/WG2rJly7j99tt55ZVX+OWXX/jll1945ZVXuP3221m+fDkAP/30k63nl2BfO3fuJDk52d5hCL3g6OjYLaHblYxSKpVYLBZMJpMdoxOEsUWr1XL48GEyMjJob28nODiY6dOnExwcPOaSUh0dHbZeksHBwSQlJYmk1An6VTF17733smDBAr788kvWrVvH7373O6ZNm8bll19OcXExX3/9NQBXXHEFL7zwAhdffPGABC0MP4GBgezatcveYQiCIAw4mYMD7pdfjttll51SvdL2/RZqnn2W+ldewWvZMryW3oxilDWuhONNhKdNm2bvMEaVV155BX9/f1588UVqa2sB8Pf356GHHrItGHPJJZewYMECe4bZb2dblU8QBppMJsPR0RGj0YhcLrdVTSmVSkwmk6iaEoQhoNfrKSkpoaamBkmS8PHxITIysscK7bGgvr6eI0eOYLVaiY2NJTAw0N4hDTv9TlNGR0fz8MMP89NPP1FVVcWqVavIyspCo9Hw6aefUlVVxTvvvMNVV10lrrLakUwm47nnnmP69OmEh4ezefNmnn/+eaZOnUpMTAw7d+607btlyxbOO+88pkyZQmpqKjt27LBte/bZZ4mJiWHKlCl8/PHHtttLSkrw9PTs9ngn9sTw8fGhpKQEgPDwcJ566ilmzZpFSEgIb775JmvXrmXmzJmEh4d3O64gCMJwcXJSSpIkGt95BwBLaysNb7xB4bz51D7/AqaaGnuEKIwQZrOZ9evXc8cdd1BdXU1LSwstLS1UV1fzxBNP2D40h4aGEhwcbOdo++eee+4hNzeXAwcO2DuUXuvs7GTJkiUkJCQwadIkLrnkklP2+eCDD0hKSiIpKYkrrriCyspKAGbNmsXu3bsBeOyxxwgKCrLdJzIykrKysqH5Jca4k1d4NBgMyGQyVCoVkiSJqilBGCRGo5HCwkL27dtHdXU1Hh4eTJ48mcTExDGZlJIkidLSUg4fPoxcLic5OVkkpU5jQFbl6+Lt7c2KFStYsWLFQB52xMvJyem2QshAcnZ2JrGHZcx7olar2bdvH9u2bWPRokW88cYbpKWlsWnTJh599FEOHDhAUVERzz77LFu2bMHd3Z3CwkLmzJlDSUkJW7duZdOmTaSnp+Pm5sayZcvOOW6tVsvu3bspLCwkMTGRJ598kj179nDgwAEuv/xybrzxxnM+tiAIwlCQyWQEvvh3Gt95h7ZvvgWLBUmno+nf/6ZpwwY8Fi3E+/bbUUVE2DvUfjObzWzcuBGAJUuWoFAM6PBhzFEoFPzud7+zrerYnybqo81wGDN9//33tLS0kJubC0BTUxPZ2dm27YcOHeLRRx8lPT2doKAgnnvuOe644w6+++475s+fz9atW5k1axbbt28nODiY3NxcVCoVCoWC0NDQQfndhO7kcjkKhcK26l5X1ZRCoUChUKDT6WwN0gVB6D+TyURlZSXl5eWYzWbUajWRkZFoNJox2yvRZDKRl5dHQ0MDarWaiRMn4uzsbO+whq2xNbFzjFuyZAkAU6dORavV2pI/qampFBQUAMcHY4WFhZx//vkkJyezePFi5HI5ZWVlbNu2jRtuuAF3d3dkMhl33XVXv2PpWhp08eLFttiamppGxQpEgiCMfk7jxxP04otEbfker5tvRtbV3NxkovWTTym6/AoqHnwI4wivkjAYDNxyyy3ccsstGAwGe4czKqSmpnLw4EF7hyH0YNKkSRw5coS7776bjRs3ntIDZMeOHSxYsMBWDXX33Xezfft2LBaLLTHV0NCAQqHghhtuYOvWrWzdupV58+bZ49cZs05eFOLEqimZTIbJZBJTTAWhn4xGI0VFRezdu5fi4mIcHR1JSEhg6tSpeHt7j9mkVHt7O+np6TQ0NODv709KSopISp2FuOQ5BHpb0TTYuqZSdk0ROPFns9kMHC83vPjii9mwYcNZj3emNxoHB4duJ3u9Xt9jLF37dv0sk8lsq6gIgiCMFMrgYMY98zQ+d/+epg8+pHnDBqzt7SBJtP/wA34PPmDvEPtFLpczf/582/dC/91999088sgjVFRUMGXKlFOmOCQlJdkpMvsaDmOmyMhIcnNz2b59O1u3buWxxx7j1VdfPe3+J46HZs6cyaFDh/jiiy+YO3cu8+fP5+mnn0alUtkuyglDw8HBAYVCgcVi6VY15eDggKOjI5IkUVlZecrKmIIgnJ3RaKS8vJzKykosFgsuLi7ExMTg5+c3pscJkiRRXV1tK/oYP348gYGBYzZB1xdj91Uj9OjSSy9l69at3UrW9+/fD8D8+fPZtGkT7e3tSJLEmjVrTnuc6Oho9u3bB8Bnn32GdpSvWCUIggCg8PHB76EHid6+Dd9HHsbBxwf3BZei/G0F0y6mqiokSbJPkOfA2dmZH3/8kR9//FFc8RsgN954I8XFxdx///3Mnj2b5ORkUlJSbP8K9lNRUYFMJmPhwoW8/PLLSJJEeXm5bftFF13E999/T1VVFQBvvvkm8+bNsyU8ZsyYwV/+8hfmz59PUlISubm57Ny5k7lz59rrVxqzlEolkiTZPhR2VXx2rdxXU1NDW1ubPUMUhBFFr9dTWFjI3r17KSsrw8nJiYSEBKZNm8a4cePGdFLKbDaTl5dHfn4+SqWSlJQUgoKCRFKql0TFlNBNdHQ0GzZs4K677kKn02E0GklJSWHDhg1cfvnl7N+/n8mTJ+Pu7s5ll1122uO88sor3H///Tz11FNcccUVeHt7D+FvIQiCYF8Obm74rFqFZtkyrB0d3bZJRiMlS2/Bwd0d71WrcF9wKTLRs2nMKS4utncIwmnk5OTw+OOPI0kSZrOZZcuWdatgmzhxIi+99JJtxcSQkBDefvtt2/b58+ezc+dOZs+ejUwmIzU1lfz8fDQazZD/LmOdg4ODrYpfoVDYqqa6Vu4DyM/PZ8qUKWP6A7UgnE17ezvl5eXU1dUhSRJqtZqwsDB8fX1F4oXjz09ubi46nQ5vb2/i4+NPmQYunJlMGkmXbIeZtrY2PDw8aG1t7da4VK/XU1xcTEREhFiJUBgy4nUnCCNDy2efU/3EE7afHUND8b79djyuuRr5ST1RhOHndOd+4cx6et7EeUsYCiaTic7OThwdHTGbzTg4OCCXy239cMrLy4mIiCD8pMpWQRjrJEmiqamJ8vJympubAfDy8iIkJGRMNzU/UVdFbdfFpoiICEJCQsRz85u+jJnEJVpBEARBGEKOAeNwSkpC/9uUaVNZGTV//CMNq1ejWbkSryU3IB9mSyrrdDqmTZsGwIEDB3BxcbFzRKNHbm4uZWVlGI3GbrcvXLjQThENrNWrV7N69WrRZFqwG4VCgVwu79ZrqqvfamBgIE1NTZSWluLj44NarbZztIJgfxaLhbq6OsrLy9FqtchkMvz9/QkJCcHNzc3e4Q0bBoOBI0eO0NzcjIuLCwkJCeL56QdRMdUPomJKGE7E604QRg5JktDt20fDW2+h27O32za5hweaW27B65alKLy87BRhd1qt1vaBraOj45RG3WPJQFVMFRUVcc0115CTk4NMJrP1HOu6yjraEjmiYkqwJ4PBgMFgQKVSYTQaMZvN1NTUEBERgdFoJCMjAzc3N1JSUsSUPmHM0ul0VFVVUVNTg8lkQqFQEBAQQHBwsHiPPkl9fT35+fmYTCYCAwOJiopCIdoynEJUTAmCIAjCMCaTyXCdMQPXGTPozMmhcc0a2n/cCoC1tZWG1auxtLUx7sknznKkoeHk5MSOHTts3wv998ADDxAREcG2bduIiIhg//79NDY28sgjj/Dyyy/bOzxBGFWUSqUtIaVQKDAYDFitVgDc3d0JDg6mvLyciooKQkND7RytIAwdq9VKU1MTlZWVNDU1AeDi4kJ4eDj+/v6iT9JJTCYTBQUF1NbW4ujoyMSJE/H19bV3WKOCSEwJgiAIgh05JyYS/PrrGAoLaXz7HVq//hoAzYoVdo7svxwcHLjwwgvtHcaosmfPHrZv346Pjw9yuRy5XM55553H888/z/3338/BgwftHaIgjBpdzc6NRqNtRT6z2WyrVIyIiKChoYHi4mJ8fHzEdGVh1NPr9dTW1lJVVYVer0cmk+Hr60tQUBCenp6iR1IPGhoayM/Px2g04u3tTWxsLCqVyt5hjRoiMXUORL8EQRAEYaCpoqMJ/PsL+Nx3H7q0AyiDg7ptb/r3v+nMysL7zjtxiouzU5TCQLFYLLZeFD4+PlRVVREbG0tYWBj5+fl2jk4QRh+lUonJZLL1mLJarbS2tuLs7IyDgwOxsbFkZmaSn59PcnKy+GAujDoWi4XGxkZqampoampCkiSUSiXh4eEEBASIiujTOLFKSqFQEB8fj7+/v3iPGGAiMXUO7rnnHu655x7bnElBEARBGCjK4KBTklJWg4HGd97FXF9P27ff4XrB+fjceScuU6YMSUxms5mvf6vkuvLKK0UfhQEwceJEsrKyiIiIYPr06bz44osolUrWrFlDZGSkvcMThFFHLpejUCgwmUy25ueVlZW2D5heXl4EBgZSVVVFVVUVQUFBZzmiIIwM7e3t1NTUUFtbi8lkQiaT4e3tzbhx4/D29hZ91U5DkiQaGho4evSorUpq/PjxIoE3SMSrcAz54osviI+PJzk5mZycnD7dNzMzk48//niQIhMEQRDOxFhUhHRCla72p58pXXoLJbfcQsfPPzPY65gYDAauueYarrnmGgwGw6A+1ljx1FNP2Xrc/PnPf6a4uJg5c+bw7bff8tprr9k5OmGgHTp0iPDwcACqqqqYM2eOfQMao5RKJYBthb6Ojg4aGxtt26OionBycqKwsJD29nZ7hSkI/abX6ykrK+PAgQOkpaVRUVGBUqkkKiqKmTNnkpiYiK+vr0hKnUZnZyc5OTkcOnQIq9VKXFwciYmJIik1iMQlzzHkzTff5JlnnuGmm27q830zMzPZvHkzN9544yBEJgiCIJyJU3w80du30fLppzS++y7mqmoAOtPSKU+7C1V8PD53rsLtkkuQ/VYJMJDkcjmzZs2yfS/036WXXmr7Pjo6mry8PJqamvDy8hLTA0a5wMBAdu3aZe8wxiQHBwcUCgWdnZ04ODggl8spLi7G29sbmUyGQqEgISGBzMxMDh06xJQpU2zJLEEY7oxGI/X19dTV1dHS0gKAQqEgMDCQcePG4e7uLs4vZ2G1WqmoqKCkpASLxYK/vz9RUVGil9QQEKPLMeL+++9n165dPPHEE8yaNYulS5cydepUkpKSuOKKK6ipqQGOL315ySWXkJiYSFJSErfeeit1dXU888wz7Nixg+TkZH73u9/Z+bcRBEEYe+ROTmiWLiV6yxYCXngeZVSUbZvhyBEqH3qY4uuvR/qtCmcgOTs78+uvv/Lrr7/i7Ow84McXjtNoNOJDwzAgk8l47rnnmD59OuHh4WzevJnnn3+eqVOnEhMTw86dO237btmyhfPOO48pU6aQmppqW70S4NlnnyUmJoYpU6Z0qzovKSnB09Oz2+N1fYiE4z3HSkpKAAgPD+epp55i1qxZhISE8Oabb7J27VpmzpxJeHi4qGY/B0qlEkmSbB86Ozo6qKurs2338PAgJiYGvV7PkSNHbJWNgjAcmc1mqqurycrKYvfu3Rw9epT29nb8/PyYOHEis2bNIjY2Fg8PD3F+OYvW1lbS09M5duwYSqWSSZMmkZCQMOqTUh0dHcOid7aomBoCOTk5dHZ2DsqxnZ2dSUxMPOt+r732GtnZ2Tz44INcffXV1NfX25a2fOGFF3j22Wd58803+fDDD4mIiOCHH34AoKmpCY1Gw5///Gc2b97M5s2bB+X3EARBEHpH5uiI59VX47FwIe3bttG45m30v03Pdk2djkxUNA1rt912W6/2e++99wY5kqHR1wVjhsOYCUCtVrNv3z62bdvGokWLeOONN0hLS2PTpk08+uijHDhwgKKiIp599lm2bNmCu7s7hYWFzJkzh5KSErZu3cqmTZtIT0/Hzc2NZcuWnXPcWq2W3bt3U1hYSGJiIk8++SR79uzhwIEDXH755aKavY+6KqUsFgt+fn7U1tZSUlLSbVpTYGAgbW1tVFdXU1xcTNQJFwIEwd4MBgONjY00NDTQ3NyM1WpFJpOh0Wjw8/PDx8dH9ILsA4PBQFFRETU1NcjlcsLDwwkNDbX1ohvNGhoayM3NxcfHh4SEBLvGIl6xY9SGDRv44IMP0Ov16PV6fHx8AJgxYwavvPIKjzzyCOeffz4LFiywc6SCIAhCT2RyOe4XX4zb/Pno9uyh8b21aG5d2W0fS1sbzevX43XTTTicUKEh2M+6desICwsjJSVl0HuDDQcjdcGYJUuWADB16lS0Wq0t+ZOamkpBQQEA33//PYWFhZx//vm2+8nlcsrKyti2bRs33HAD7u7uANx111388ssv/YolOjoaJycnFi9ebIutqamJlpaWbhVYwpl1TdkDaG5uJjg4mJKSEmprawkICLDtFxMTg1arpaysDDc3N/z8/OwVsiCg0+loaGigoaGBtrY2JEmyNe339fXFx8dHTDvtI4vFQkVFBaWlpVgsFry8vIiJicHV1dXeoQ06SZKoqKjg2LFjtume9iYSU0Ogt1fnhsovv/zCa6+9xp49e/Dz8+PLL7/kmWeeAWDmzJlkZmaydetWPvvsM55++mkOHjxo54gFQRCE05HJZLjOmoXrbz2gTtS8YQP1/3yNxrffwXPJEjQrV+Lo3/cPV52dnbYP3z///LOYztcPv//97/noo48oLi7m1ltv5ZZbbkGj0dg7rGFjuIyZuhrcdl0xP/Fns9kMHB/YX3zxxWzYsOGsxzvTFBoHB4duFWV6vb7HWLr27fpZJpMhk8ls8Qi95+joiEwmo6amhilTplBZWUlJSQl+fn62/3MHBwcmTJhAeno6eXl5uLq6jokPrMLwYLVaaWtro6mpiYaGBrRaLXD8denj44Ovry8ajQZHR0c7RzrydK22d+zYMTo7O3F2diY6OtrWa260s1qtHD16lOrqalxcXEhMTMTFxcXeYYkeU2NRc3Mzbm5ueHt7YzQaeeutt2zbiouLUavV3HDDDbz++uscPXqUjo4O3N3daW1ttWPUgiAIQl9IZjPN649/YLbqdDStXcux+fOpfuaPGMvK+nQsq9VKWloaaWlpot9KP61evZrq6moee+wxvvrqK0JCQrjhhhvYsmXLmKigGk0uvfRStm7dSnZ2tu22/fv3AzB//nw2bdpEe3s7kiSxZs2a0x4nOjqaffv2AfDZZ5/ZPoAKg0cmk+Hg4IDRaKSlpYXQ0FD0ej3V1dXd9nNyciIhIQGr1cqhQ4cwmUx2ilgYCwwGA9XV1Rw+fJhff/2VgwcPUlpaislkIiAggMTERGbPns3EiRPx9/cXSalz0N7eTlZWlu3vOSoqimnTpuHj4zMmklJGo5GsrCyqq6vRaDRMnjx5WCSlQCSmxqQFCxYQGxtLbGwsc+bMITk52bZt586dTJkyheTkZGbNmsVLL72Eh4cH8+bNw2AwkJSUJJqfC4IgjAAyhYKwjzbgedONyH4r75dMJlr+8x+OLbiMykf+B31+fq+OpVKp+Prrr/n6669HfRPQoaBSqbjpppv48ccfyc3NZcKECdx9992Eh4fT0dFh7/CEXoqOjmbDhg3cddddTJo0ifj4eF599VUALr/8chYvXszkyZOZOnUqoaGhpz3OK6+8wgMPPMDkyZM5ePAg3t7eQ/QbjG0ODg7IZDIqKioICgpCqVTapvScyMvLi6ioKHQ6HXl5eSKBLAwYq9VKS0sLx44d48CBA+zevZu8vDzq6+txcXEhPDycyZMnM3PmTOLi4vDx8RkTfY8Gg06n4/Dhw6SlpdHS0kJAQACpqaljppcUHO9XmJGRQUtLC8HBwSQmJg6r5KZMEu+u56yrX0Jra6uthwAcL8EuLi4mIiKiW/m1IAwm8boTBOF0zPX1NL3/Ps0bPsJ6UjWG+oIL8H/6aZTBQXaKbmQ53bn/XJWXl7N27VrWrVuH0WgkLy8PtVo9AJEOLz09b+K8JdhL12tPkiRqa2uZPHky7e3tFBQUEBUVdUoiUZIkjhw5Qm1tLeHh4URERNgpcmEks1qttLe309LSQktLC62trbZEqKOjIxqNxvYl+kUNDIPBQElJCdXV1UiShLe3N5GRkaPyPHsmdXV15OXlYbVaGT9+/JD1lOrLmEn0mBIEQRCEUU7h64vfI4/gvWoVzRs20PTv97E0NwOgS0/Hwd3NzhGOLQaDgc8++4z33nuPX375hSuvvJI33niDBQsW2FYFEwRh8Pn7+1NbW0tFRQVxcXGUl5dTVlZGQEBAt0oCmUxGbGwsWq2WkpISZDIZYWFhY2Lqj3DurFYrWq2W5uZmWyKqqyecXC7Hw8MDT09PNBoNbm5u4vU0gEwmE+Xl5VRUVGCxWPDw8CAyMnLMLRRhtVopKiqivLwcpVJJUlLSsH0ORGJKEARBEMYIB3d3fH73OzQrVtCy6RMa167F48orcTjpKpY+Px9VdDSy38rbLRYL27dvB2Du3Lljpux9MNx99918/PHHhISEcNttt/HRRx/ZVsYVBGFoubq6otFoqK+vJzIykrCwMPLz86moqDilKsrBwYFJkyaRnZ1NcXExZrOZqKgokUwQbMxmM21tbbS1tdHa2kpbW1u3RJSbmxteXl54enri7u4uzqWDwGg0UlFRQWVlJWazGVdXVyIjI8dMY/MTGQwGcnNzaWlpwcPDgwkTJgzrdgwiMSUIgiAIY4zc2RnN8mV43bgE6aRmvubmZkpuvAlHf3+8V92Bx1VXoTeZuOSSSwDo6OgQK1P1w5tvvkloaCiRkZH89NNP/PTTTz3u99lnnw1xZIIwNoWEhNDU1ERlZSWRkZGUl5dTXl5OQEDAKVNMlUolkyZNIicnh/LyciwWC+PHjx9zH3iF49M79Xq9LQnV2tqKVqu19SDrSkR5eHjg5eWFu7s7CoX46D1YuhJSXRVSLi4uxMTE4OfnNyYrkVtaWsjNzcVgMBAcHExUVNSwfx7EX4cgCIIgjFEypdLWGL1L8wcfInV2YiwpofrJp6h//Q1cblnKpMREkMuH/cBmuFu+fLn4ECsIw4iXlxeurq5UV1cTFhZGdHQ02dnZFBUVkZCQcMr+jo6OJCUlcejQIaqqqrBarcTGxor3xlHOYDDQ3t7e7ctoNNq2K5VKfHx8cHd3x8PDA7VaLSqihoDRaKS8vJzKykosFguurq6EhYXh6+s7Jv8mrVYrZWVllJSUIJfLSUhIwN/f395h9YpITAmCIAiCYOOSmopLWhq635a9N9fU0Pby/+M/Xl5oli9DaTSCs7Odoxy51q1bZ+8QBEE4gUwmIyQkhLy8PGpqaggJCcHb25va2loCAwN77MeiUChITEwkNzeXmpoaLBYL8fHxIhExShiNxlOSUAaDwbZdLpfj6uqKj48PHh4eeHh44OTkJC46DCGdTkd5eTk1NTVYrVZcXV0JDw/H19d3zP4/6PV68vLyaG5uxtXVlYSEhBHV5F0kpgRBEARBsHGdMR3XGdPRHTxI45q36dixAwBLczP1/3yNxnfexeumG9GsWIHC19fO0QqCIPSfn58fRUVFVFRUEBQURHR0NM3NzRQUFDBlypQeKy8cHByYMGECR44coa6uDovFQkJCwrBafl04M4vFgk6nQ6vV0tHRYfv3xEoomUxm60Xm5uaGm5sbrq6uIglpJ62trZSXl9PQ0IAkSbi7uxMaGoqPj8+YTUgBNDQ0kJeXh8lkIigoiKioqBH3GhWJKUEQBEEQTuGSkoLLv/4Pff5RGt95h7ZvvgGrFatWS+M77+Kg8cb7tlvtHaYwzK1evZrVq1fblkQXhOHIwcGBoKAgiouLqa+vx9/fn+DgYMrKyqiuriYoKKjH+8nlclulVHV1NQcOHGD8+PFiQYNhxmq10tnZiU6nQ6fT2ZJQOp3O1hMKjr8OXF1d8fb2xs3NDbVaLabkDQNWq5XGxkbKy8tpbW0FwMfHh5CQEDw8PMZ0QspisXDs2DEqKytxdHRk4sSJ+I7Qi4YiMSUIgiAIwmk5xY5H8+c/cfMvuzBVV/N/ajecXV3xWnJDt/0kqxXZGOznIJzZPffcwz333ENbWxseHh72DqdXvvjiC/7whz+gUqn44IMPSExM7PV9MzMzycvL48YbbxzECIXBEBgYSGlpKRUVFfj5+REWFkZtbS3FxcX4+fmdthJKLpcTGxuLh4cHhYWF5OTkMG7cOKKjo0X11BAzmUy25NOJX52dnd0SUADOzs54e3ujVqtxdXVFrVbj5OQ0JvsSDVdGo5Gamhqqqqro7OxELpcTEBBASEiIWIQFaGtrIy8vD61Wi6enJ/Hx8acs2DCSiMSUIPympaWFzMxMwsPD8fT07LGngCAIwlhktVr5ee9eAMKLilBUVSE/aVBY+9fnMFVX43PXnTgnJ9shSkEYGG+++SbPPPMMN910U5/vm5mZyebNm0ViagRSKpWMGzeOqqoqWltb8fT0JCoqitzcXIqLixk/fvxp7yuTyQgICMDLy4ujR49SU1NDc3OzqJ4aYJIkYTab6ezspLOzE71eb/tep9N1m4IHx/9fuhJQLi4uti9XV1exQt4w1tbWRmVlJXV1dVitVpRKJWFhYQQFBaFSqewdnt1ZrVZKSkooKytDJpMRGRlJSEjIiE+qir9IQfjN/v372bhxI25ubtx0001Mnz7d3iEJgiAMCyqViv/85z8AqENCUEREdNturq+n5ZNPkIxGOnbswCU1Fe8778R19qwxXWIvjDz3338/u3btIi8vj9dff52IiAjy8/MxGo2EhITw7rvvMm7cOOrr61m6dCnV1dXIZDKmTJnC3//+d5555hlaW1tJTk5mxowZvPnmm/b+lYQ+CA4OpqqqivLycjw9PfHz86OyspKqqioCAwPP2kjYycmJxMREampqbNVTXdVXI6kJsT1ZLBYMBoMt6XTyv2az+ZT7KBQKXFxc0Gg03RJQzs7OI/7D+lhhsVior6+nsrKStrY2ADw8PAgKCsLHx0dMp/xNe3s7eXl5dHR04ObmRlxc3Kh5bxGJKUEQBEEQzkihUHD99defdruxrAwHLy/MtbUA6PbvR7d/P04TJuB95524XTxfTPMTeiUnJ4fOzs5BObazs/NZp+W99tprZGdn8+CDD3L11VdTX19v69fxwgsv8Oyzz/Lmm2/y4YcfEhERwQ8//ABAU1MTGo2GP//5z2zevJnNmzcPyu8gDK6uldYaGxvRarW4uroSExNDeno6BQUFJCcnnzXZ3lU9pdFoOHr0KHV1ddTV1eHl5UVQUBDe3t5jNllitVoxGo22xJPBYDjl+5OrnuD4c6pSqVCr1Tg7O+Ps7IyTk5PtX0dHR3ERZASSJIn29nZqamqora3FbDbj4OBAQEAAQUFBuLm52TvEYcNqtVJWVkZpaSmSJBEeHk5YWNioei8RiSnhjGQyGc3NzcNiWltycjK7du0665vUucacmpqKUqm0TeXrr4KCAlasWEFDQwMeHh6sW7eOCRMm9LhveHg4KpUK59+WYH/88cdZsmRJn48jCIJgDy5TphD94w+0fvUVjWvexlhaCoD+8GEqH3gAZWQk3nfcgcdVVyITPVeEEWTDhg188MEH6PV69Hq9bVrWjBkzeOWVV3jkkUc4//zzWbBggZ0jFQZKaGgoDQ0NlJWVER8fj5ubGwEBAVRVVVFXV4e/v3+vjqNSqUhMTKS1tdU2Lam5uRlnZ2eCgoLw9fUd0f1gTtSVcDr5qyvRdOLPJ/d6gv8mnpydnfH09LR935V8UqlUomJmFDEajdTW1lJTU0NHRwcAarWacePGMW7cONGb7SStra3k5+fbkuVxcXG4u7vbO6wBJxJT50CsMGMfmZmZg3p8T09PLrzwwgE73l133cWdd97JypUr+eSTT1i5ciUHDhw47f4bN24kuYe+LH09jiAIwkCzWCzs/a3H1IwZM3r8gCBTKvG87jo8rr6a9h9/pOGtNRiOHAHAWFRE9RNP0PLpp4Sv/3BIYxdGlr40Gh9sv/zyC6+99hp79uzBz8+PL7/8kmeeeQaAmTNnkpmZydatW/nss894+umnOXjwoJ0jFgaCh4cHnp6e1NbWEhERgZOTExEREdTV1XHs2DG8vb371J/Iw8MDDw8PoqKiqKqqoqqqisLCQgoLC3FxccHLywtPT0+8vLyGzQfyrl5OJpOpx6+Tk04mk+m0x5LJZCiVSpRKpa3BuEqlQqVS2b5XKpWjqvJDOJXVaqWpqYmamhoaGxuxWq0oFAqCgoIYN24cbm5uourtJCaTiaKiItuU8fDwcEJDQ0dtklYkps7BSFxhBo6fGJ588km++eYbtFotf/zjH1m6dCkAW7Zs4fHHH8dsNuPl5cW//vUvEhISbPd9+eWXOXr0KGvWrAGONwqPjo7m6NGjaDQaZDIZzz33HJs3b6a+vp5nnnmGW2+99azHlslk/PWvf+XLL7+ktraWV199lSNHjvDpp5/S2trK22+/bUsWnVgJtXTp0h57PpzJ888/T11dHa+88grr1q3jgw8+4MMPPyQgIGCgn2rq6upIS0uzlfhfd9113HvvvRQWFhIdHT3kxxEEQegPvV7PeeedB0BHR8cZV8OROTjgvmABbpdeivaXX2h8aw26tDQA3C+7bEjiFYSB0NzcjJubG97e3hiNRt566y3btuLiYoKCgrjhhhtYsGABfn5+dHR04O7ublvOXBi5QkNDyc7Opry8nJiYGJRKJRERERQUFFBWVkZkZGSfj6lSqYiIiLBVZDU3N9Pc3ExlZSWVlZXdqoa6+iM5Ozvj6OiIQqGw/XumBI4kSUiShNVqtf1rNpsxm81YLJZu/578/cnJp54qm06kUChQKpW4urraEk8nf6lUqrPGLIxekiTR0tJCXV0d9fX1tgSml5cXAQEBonfUaUiSRH19PQUFBRiNRjw9PRk/fvyoX4lQJKbGGJlMxsGDBykqKmLq1KnMnj0bFxcXbr75Znbu3EliYiLr169n8eLFHD582Ha/O+64g/Hjx/Piiy/i6enJ2rVrWbRoERqNxraPSqVi//795OXlMW3aNJYtW0ZTU9Npj92VFVer1ezbt49t27axaNEi3njjDdLS0ti0aROPPvpoj9VBr776ao89H84kIyODyy67jPvuuw+z2cx3332HUqns0/O3ZMkS8vPze9z21VdfERISAkB5eTkBAQG2K2oymYzQ0FDKyspOm1Bavnw5kiSRmprKCy+8gK+v7zkdRxAEYaDJZDLbe05vr2jKZDLUc+agnjMHXUYGzRs+wvO6a7vtYywpoeXTT9GsWIFCrFwlDDMLFizgww8/JDY2Fm9vb+bPn09lZSUAO3fu5B//+AcODg6YzWZeeuklPDw8mDdvHi+//DJJSUnMmjVLND8foTQaDW5ublRXVxMWFoZSqSQwMJDq6mrKysrw8fE556k0Dg4O+Pv74+/vjyRJdHZ20tzcTEtLCzqdjra2Npqbm097f5lMhkwmQy6XI5PJbMmorkTUuZDJZLbkl7OzM+7u7jg6Op72S6lUilXthB5JkkRHRwe1tbXU1dVhMBiA45/3QkJC8PPzs7UuEU6l0+koLCyksbERR0dHYmNjCQgIGBPVZOIdZQhc9fov1LcbBu34vm4qvrrvvF7te8cddwAQGRnJ+eefz88//4yXlxeJiYm28vmlS5dyzz332AZfcHya2+LFi3nvvfd46KGH+Ne//sXGjRu7Hbur+iouLg6FQkFNTQ0HDx487bGDg4MBbL2Upk6dilartS2xnJqaSkFBQY+/x+l6PpxJRkYG6enpqFQqjvw2vaSvTv6dB8rPP/9MaGgoJpOJp556ihUrVvDtt98OymMJgiD0lYuLy2nfj3t1/8mTcZk8+ZTbG955h9ZPPqXp/Q/wvO5aNLfdjjI4qD+hCkK/7dy50/b9yef95557DoBbb73VVhl+Ig8PD3bv3j2o8QmDr+tC4OHDh6msrCQiIgK5XE58fDzp6enk5uYyderUfidnZDKZbQW5oKDj732SJGEwGGwr0Z1YzWQ2m23VUF2JqBOTVCd+L5fLkcvlODg4oFAoUCgUtu97um0sfPAVBkdXE/P6+noaGhrQ6XTA8QUnwsLC8PPzGzUrxw0Ws9lMaWkpFRUVWK1W/P39iY6O7nMRxUgmElNDoL7dQE2b3t5h9KgvJ6H777+fhQsXEh8fj6+vLykpKd22n9jAsesKYm903a+rlPPEn3s6xpl6PpxOa2srNTU17Nixg+XLl/Ppp59y3XXX9Sq+E/W2YiokJITq6mrMZjMKhQJJkigrKyM0NLTH+3bd7ujoyIMPPsj48ePP6TiCIAgjhaVDS/t33wMgGQw0b/iI5o3/wePKK/BetQqVqAoVBMGOfHx8cHZ2pqKigpCQEBQKBWq1mqioKAoKCjh69Gi3thcDRSaT4eTkNGoaowujk9VqpbW1lYaGBurr622VUSqViqCgIPz9/XF3dxcJz7OQJImamhqKioowGo24ubkRHR09LBYeG2oiMTUEfN1Uw+b4a9eu5dlnn6WkpIRdu3bx6quv4urqSk5ODocOHWLixIl8/PHHBAUF2a7cdImLiyMyMpI777yTF198sVePN2PGjF4duy/O1PPhdDIyMpg0aRKpqan89a9/5YknnmDRokV9vtLV24opPz8/Jk+ezIcffsjKlSv59NNPCQ4O7nH6nVarxWQy2d6APvroI1vSry/HEQRBGEkc1K5EfvstTevW0bxxI5JOBxYLrV98SesXX6KePw+fO+/EOSnJ3qEKgjAGyeVyQkNDyc/Pp6qqynZRMCgoiObmZmpra9FoNGftcSoIo4XZbKa5uZnGxkYaGhpsPaOcnZ0JDQ21TXEVyajeaW1tpbCwkLa2Ntu0vXHjxo3ZnmwiMTUEejvNbihYLBZSUlLQarW89tprhIeHA7B+/XqWL19ua1C+adOmHt9UVq1axb333svixYt79Xi+vr69PnZvnannw+lkZGQw+bdpJIsXL+bvf/87a9as4e677z7nOM7mrbfeYuXKlfztb3/D3d2dtWvX2rbdcccdLFy4kIULF1JbW8t1112HxWJBkiQiIyN5//33e3UcQRCEoaDX621Vpp9++umAXcl39PfD/38fw+euO2lav57m9z/A8lvj6I6t2+jYug2XGTMIevkl0YNKEIQh5+/vT0lJCRUVFQQFBeHg4IBMJiM2Npb29naOHj2Ku7s7Li4u9g5VEAacJEnodDqamppobGyktbXV1sdMrVYTFBSEr68vrq6uIhnVBzqdjqKiIurr65HJZAQHBxMeHj5sVuW0F5l0tiUXhNPqWpWvtbW1WwNEvV5PcXGxbYnZ4eLEVe3O1b333ou/vz9PP/30wAUmDIjh+roTBGHk02q1tv4QZ1uVrz+sWi3NmzbRtHYd5tpaABxDQ4n69htkw6TR7unO/cKZ9fS8ifOWYC99ee2VlZVx7NgxYmNjCQwMtN3e3NxMVlYWbm5upKSkjNkqB2F0sVgstLS00NjYSFNTE52dncDxCkIvLy80Gg0ajUYkY8+BwWCgtLSUqqoqJEnCx8eHyMjIUb3aXl/GTMNjlCcMe1VVVcydOxeNRsOWLVvsHY4gCIIwhJRKpa1aczAbccpdXfFeuRKvm2+m9YsvaHznHbxvu/2UpJR2715cpkxBNsavLgqCMPgCAwMpKyujrKys2zQbLy8vQkJCKCsro7i4mKioKDtHKgh9Z7VaaWtro6WlhebmZtra2mxVUU5OTgQFBaHRaPDy8rL1Axb6xmw2U15eTnl5ORaLBQ8PDyIjI8dkH6kzEYmpMaQ/xXGBgYHk5eUNYDSCIAjCSOHo6MjKlSuxWCzo9XpMJlO3q6V6vR6LxYJSqbSVolutVtuV1hOvBhoMBsxms23J8Z72lSuVeF1/Pc5XXIHZaMRoNNr21R89St7yFaiio0n46kvkvw2UjUYjJpOp23EFQRD6S6FQEBQURElJCfX19fj7+9u2RURE0NLSQllZma2aRBCGM0mS6OjooLm5mZaWFlpaWrBYLMDxhae8vLzw9PTE29sbFxcXMUWvH8xmM1VVVZSVldnGTZGRkfj4+IjntQei5lQQBEEQhF7JyclBrVYTExPT7fZly5ahVqtZs2aN7bZjx47ZelCc6K677kKtVvPPf/7Tdlt1dTVqtfqUq4ePPPoobl5e/O1vf7PdVrx6NVMLjpL43bdYfruqCyXpTzcAADesSURBVPDkk0+iVqt58sknB+JXFQbI6tWrSUhIYNq0afYORRDOWVd/qbKysm4XeuVyOQkJCSgUCo4cOWJbmUwQhouuqXmlpaVkZ2fz66+/kpaWxrFjx2wLSoWHh5OSksJ5551HUlISoaGhom9UP5jNZsrKyti7dy/Hjh3DwcGB2NhYpk2bhq+vr3heT0NUTAmCIAiCMGJ4XHMNvPaavcMQeumee+7hnnvusfWZEISRSKlUEhAQQEVFBU1NTXh7e9u2OTs7M378eHJzc8nMzCQ5ORmVanBX5BaE0zGZTLS2ttq+2tvbbVPz5HI5arWagIAAPD098fDw6PMK5cLpnVwh5eTkREREBAEBAaIHXS+I5uf9MNKanwujm3jdCYIw2Lqm8slkskGdynemfbtWCQK6TTPomsqnUChsA0CFQjHgVyZF8/NzI5qfjy4tLS1kZmYSHh6Op6fniOuVci6vPb1ez759+2zNzk9+b6moqKCgoABXV1eSk5PFlGJh0FksFjo6Omhra6O9vZ329nbb+RGOnwPd3d3x8PDAw8MDd3d30SdqEBiNRqqqqqioqLAlpMLCwrr1pBurRPNzQRAEQRAGnIODQ4+rx/T0wU4ul/e4r0qlOqWaoC/7ymSyHvdVKpUolcohW0FQEMay/fv3s3HjRtzc3LjpppuYPn26vUMadE5OTowbN46qqioaGxvx8fHptj04OBir1cqxY8fIysoiOTl5zC//Lgwcq9WKVqu1JaDa2trQarXdppY6Ozvj7+9vS0S5uLiM+cTIYOrs7KSiooLq6mosFgtOTk5ERkaKhNQ5EokpQRAEQRAEQRCEswgPD6e2tpaioiI0Gs0pHz5DQ0OxWq0UFxeTnZ1NUlKSSE4JfWYymejo6KCjowOtVmv713pCX0WVSoW3tzdubm64u7vj5uYmXmtDpL29nfLycurq6pAkCTc3N0JCQvD19RUJqX4QiSlBEARBEEYNFxcXmpubbd8LwlCRyWQ0NzcPi2ltycnJ7Nq1Czc3tzPud64xp6amolQqbVP5+qugoIAVK1bQ0NCAh4cH69atY8KECT3uGx4ejkqlwtnZGYDHH3+cJUuW9Pk450KlUhEcHExpaSk1NTUEBgb2GJ/VaqW0tJScnBySkpJEHx+hR1arFZ1Oh06nsyWiOjo6Tmmir1Kp8PT0xM3NzfYlpj8PLavVSmNjI5WVlbYxhkajISQkBC8vL9HQfACId0lBEARBEEYNmUw2LBIDgmBPmZmZg3p8T09PLrzwwgE73l133cWdd97JypUr+eSTT1i5ciUHDhw47f4bN24kOTm538c5F6GhoVRVVVFSUoK/v3+PPXsiIiKQJImysjJycnKYMGGC6Dk1hpnNZlsCSqfTodVq0el0dHZ2nrLKo4uLC15eXri6uqJWq1Gr1eK1Y0dGo5GamhoqKyttPTb9/f0JCQk5a+Jf6BtRayYIgiAIgiAIJ5DJZDz11FOkpKQwfvx41q9fb9u2ZcsWJk+eTFJSEhdccAG5ubnd7vvyyy9z55132n5uaWnBx8eHpqYm27H/9re/kZqaSkREBGvXru3VsWUyGc899xzTp08nPDyczZs38/zzzzN16lRiYmLYuXNnt31bWloAWLp0KVOnTiUpKYkrrriCmpqas/7+zz//PA899BAA69atY968eVRXV/f+CeyDuro60tLSuOWWWwC47rrrKC8vp7Cw0C7HORuFQkF4eDgGg4GKiooe95HJZERGRhISEkJLSwsHDhygsbFxQOMQhheLxYJWq6WhoYHy8nIKCgrIyspiz5497Nq1i/T0dI4cOUJpaantteDt7U1oaCjx8fFMmzaNOXPmMG3aNOLj4wkNDUWj0YiklJ20t7eTl5fHnj17OHbsGFarlfDwcGbOnElCQoJISg0CUTElCIIgCMKoYTQa+dvf/gbAE088IQb1wjmTyWQcPHiQoqIipk6dyuzZs3FxceHmm29m586dJCYmsn79ehYvXszhw4dt97vjjjsYP348L774Ip6enqxdu5ZFixah0Whs+6hUKvbv309eXh7Tpk1j2bJlNDU1nfbYXdNE1Go1+/btY9u2bSxatIg33niDtLQ0Nm3axKOPPtpjddCrr76Kr68vAC+88ALPPvssb7755hl/94yMDC677DLuu+8+zGYz3333XZ//lpYsWUJ+fn6P27766itCQkIAKC8vJyAgwDbdTSaTERoaSllZGdHR0T3ef/ny5UiSRGpqKi+88AK+vr7ndJxzFRgYSEVFBWVlZQQEBPT43MhkMqKjo3Fzc+Po0aNkZ2cTHBxMZGSkWBlthDKbzXR2dqLX6+ns7Oz2ZTAYOHmxewcHB1tDchcXl25fohfR8GM2m6mrq6O6upq2tjYAPDw8CAoKEv2jhoBITAmCIAiCMGqYTCb+9Kc/AfDoo4+KxNQIc9Xrv1Dfbjj7jufI103FV/ed16t977jjDgAiIyM5//zz+fnnn/Hy8iIxMZHExETgeDXSPffcQ2Vlpe1+np6eLF68mPfee4+HHnqIf/3rX2zcuLHbsZcuXQpAXFwcCoWCmpoaDh48eNpjBwcHA9h6KU2dOhWtVsuNN94IHO/5VFBQ0OPvsWHDBj744AP0ej16vf6U1eR6kpGRQXp6OiqViiNHjvTq+TrZyb/zQPn5558JDQ3FZDLx1FNPsWLFCr799ttBeazTkcvlREREkJubS2lpKTExMafd19/fH3d3d44cOUJFRQXNzc0kJCTYVg8VhgdJkjAajba/E4PB0O1fvV6P2Ww+5X5dySc3NzecnZ27falUKtF7aJiTJIm2tjaqq6upq6vDYrHg4OBAQEAAgYGBuLu72zvEMUMkpgRBEARBGDUUCgV333237XthZKlvN1DTprd3GD3qywfM+++/n4ULFxIfH4+vry8pKSndtp/YuNjBwaHHD7w96bpfV8XNiT/3dIxffvmF1157jT179uDn58eXX37JM888c8bHaG1tpaamhh07drB8+XI+/fRTrrvuul7Fd6LeVkyFhIRQXV2N2WxGoVDYejOFhob2eN+u2x0dHXnwwQcZP378OR2nv/z8/CgvL6eqqorg4GBbM/aeODs7k5ycTHl5OcXFxaSnpxMUFERwcLBoYj0ELBYLBoMBo9GI0Wjs9n1X8slgMHRb9a6LTCbDyckJtVqNk5MTTk5O3ZJPjo6OIvk0AhmNRmpra6murkar1QLg7u5OQEAAfn5+YvxgB+IZF0a1lpYWMjMzbavGiIa4giAIo5tKpWL16tX2DkM4R75uqmFz/LVr1/Lss89SUlLCrl27ePXVV3F1dSUnJ4dDhw4xceJEPv74Y4KCgggKCup237i4OCIjI7nzzjt58cUXe/V4M2bM6NWx+6K5uRk3Nze8vb0xGo289dZbZ71PRkYGkyZNIjU1lb/+9a888cQTLFq0qM8f1HpbMeXn58fkyZP58MMPWblyJZ9++inBwcE9Tr/TarWYTCbbeO6jjz6yJf36cpyBIJPJiIqKIjMzk+LiYhISEs64v1wuJywsDC8vL/Ly8igvL6eyshI/Pz9CQ0NxdXUdlDhHK6vVislkwmQyYTQabf+emHjq+vdMiV+FQoGTkxMajQaVSoWTk1O3f5VKpZjCNUqYzWYaGhqoq6ujqakJSZJwdHQkODiYgIAAUcVoZyIxJYxq+/fvZ+PGjbi5uXHTTTcxffp0e4ckCIIgCMJp9Haa3VCwWCykpKSg1Wp57bXXCA8PB2D9+vUsX74cs9mMl5cXmzZt6rFiYtWqVdx7770sXry4V4/n6+vb62P31oIFC/jwww+JjY3F29ub+fPnd5t22JOMjAwmT54MwOLFi/n73//OmjVrbJWIg+Gtt95i5cqV/O1vf8Pd3b1bQ/g77riDhQsXsnDhQmpra7nuuuuwWCxIkkRkZCTvv/9+r44zGLy8vNBoNNTW1vZ6lS53d3emTZtGY2Mj5eXl1NTUUFNTg4+PD/7+/nh5eeHo6DiocQ83kiRhNpsxm822ZNPJSaeTfz5blaFCoUClUuHm5oZSqbQlmU7+XlTGjG5Wq5Xm5mZqa2tpaGjAYrEgk8nQaDT4+/vj4+Mjer4NEzLp5C5tQq+1tbXh4eFBa2trt/mner2e4uJiIiIiRHmunf3www9jJjElXneCIAiD73TnfuHMenrehvN5SyaT0dzc3K9K63vvvRd/f3+efvrpgQtMGBAD+drr6OggLS0NT09PkpOT+3z/1tZWysvLaWhoQJIkZDIZ7u7uaDQaNBoNrq6uw/6DsyRJWK1WLBZLtwRT1/cnfp3u9rN9JJXJZDg6OqJUKnF0dOz21XXbiYmn4f6cCYPHarXS2tpKfX09dXV1mEwm4Hgjcz8/P/z8/ET/ySHSlzGTSBGPYT4+PqSlpdmuAPbkTAOz5ORkdu3aNSTLZfYm1p6kpqaiVCptU/kGQkFBAStWrKChoQEPDw/WrVvHhAkTTtnPYDDwyCOPsGXLFpycnJg0aRIffvhht33Wrl3Lbbfdxueff87VV189IPEJgiCMZVqt1vZ+39LSIqbHCEOuqqqKuXPnotFo2LJli73DEQaZWq3G39+fmpoa6uvrbSsg9paHhwceHh7o9XoaG/9/e3ce1tSZ7wH8mxUIssmuhKJ1K8qiWKx6p9KRGZdnhk7VDtPpo4ZKad2mjrZqe71qn6lLr12oXjouU6Wj7Tw+linjrXVqsbbYqlVBHFoUXIKCZYeABCFAcv9gci5hDVsW+H6e5zwhJ+fk/BJfk19+533fU4HKykpUVVWhuroaarVamONIoVDA2dlZ6O1jLMRIJBJIJBKIxWKIxeJOe9gZDAahgGRcmpubTe4bl6amJjQ3NwuLOfd70tdBKpUKi6Ojo8n9jgpOMpkMUqmUczlRp4w9o8rKylBeXi4UoxQKBQICAuDr69vlPHBkfSxMUa9lZWVZO4Ruubu7Iyoqql+f84UXXkBCQgJUKhU++eQTqFSqDi/PvHHjRohEIuTl5UEkEqG4uNjk8fz8fBw4cACPPfZYv8ZHRDTUmTuRNFFn+jKgYMSIEbh+/Xo/RkO2bvTo0aioqEBeXh7c3Nx61RvD0dFRmFPM2ONDo9Ggrq4OWq0WVVVVqKio6PI5uirc9McgGZFIJBTCJBIJZDIZnJycTNYZi0uti02t1xmLaER91dzcjMrKSpSVlaGiokL47nd2dsbIkSPh7e0NZ2dnFjTtBAtTQ8jx48exYcMGyGQyzJ071+SxS5cuYcOGDaipqUFzczNee+01PP300wCAt956CydOnIBWq8WWLVuESxy37U317LPPIjc3FzqdDkqlEh988AHc3NygUqmQnZ0NmUwGX19fnDp1qttjdhVrWzt27EBpaSneffddJCcn4/Dhwzhy5Aj8/f378+0DAJSWluLy5cvCa1i4cCFWrVqFmzdvmkyuqdVq8cEHH6CwsFD4MPTz8xMe1+v1iI+Px549e7Bu3bp+j5OIaKhycnJCYWGh8DcR0UBzcHDA2LFjkZOTg7y8PEycOLFPP4bFYjE8PDzg4eEhrNPr9cIV5FpP9G3s9WS87e55u1taF5mMhabW9/kjn6zpwYMHJj0LjW3excUF3t7e8Pb2hkKhsHKU1BssTFlIxaFkVCYnd7udY3AwlH9+32RdwfIVqM/J6XD74SoVPONU3T5vaWkp4uLicPbsWQQHB2P//v3CWReNRoOEhAR8/vnn8Pf3R3l5OaZMmYIZM2YAaClAXblyBbdv38bUqVMxc+bMDofUJSYmCt2Xd+7cia1bt2LOnDnQaDTI+Xf8lZWV3R5TJpN1GmtHMjMzMW/ePKxevRpNTU04efJkj85UmXs5YwAoKCiAv7+/MFGiSCRCYGAg7t69a1KYunXrFoYPH47t27cjLS0NTk5O2Lp1K2bPng0AeOeddzBz5kxERESYHScREXVPLBb36SpmRES94ePjg7KyMpSVlaGkpMTkhGR/EIvFUCgU/NFNQ4per0dNTQ0qKipQUVEBrVYLoOU3mLu7Ozw9PeHl5cUTUYMAC1MWoq+tRVNJSbfbNXfwJdZcWdnpvvraWrOOf+HCBYSGhgqXsl22bBlWr14NADh37hxu376NefPmmexjLNbEx8cDaOmm/PjjjyM9Pb3DwtTHH3+Mw4cPo76+HvX19fDy8sL69etx7do1rFixArNmzcL8+fO7PWZtbW2nsXYkMzMTGRkZcHBwwLVr18x6P1oz93LGPdHU1IQ7d+4gODgYO3fuxJUrV/CLX/wCP/74I8rKypCSkoL09PR+Py4RERERWZ5IJMK4ceNQXV2NGzduwN3d3eYm9SeydQaDAQ8ePEBVVZWwGIfoyeVy+Pv7CxcG4BUVBxf+a1qIeNgwSH19u91OMnx4h+s621c8bFiv4mndDddgMGDixIk4d+5cj/c1+vbbb7F7926cP38ePj4+OH78ODZv3ozRo0cjJycHX331FdLS0rB+/XpkZWV1eczjx493ezyj6upqFBcX48yZM1iyZAlSUlKwcOFCs16HUU96TCmVShQVFaGpqQlSqRQGgwF3795FYGCgyX6BgYEQi8XCsMfJkydj1KhRyM7Oxo0bN5Cfn4+xY8cCAIqLi5GQkICioiIsX768R7ETEZEpnU6H9957DwDw0ksv8co7RGQxcrkc48ePR3Z2NnJzcxEaGsqhb0TdaGhogEajEQpR9fX1AFp+A7q4uGD48OHw9PSEi4sL/z8NYixMWYhnnHlD7jrSdmhfb0yfPh1xcXG4fv06JkyYgIMHD0Kn0wEAZsyYAbVajbS0NERHRwNomdjc2GPp0KFD2Lp1K/Lz83H27FkkJia2e/6qqiq4uLjA09MTOp0O+/btAwAUFhbCw8MDMTExmDt3LlJTU1FQUNDlMbuKta3MzEyEhYUhMjISb7zxBl577TU8+eSTPaqg96THlI+PD6ZMmYIjR45ApVIhJSUFAQEBJsP4gJarCM6ePRtffPEF5s+fD7VaDbVajUceeQTR0dEmBaioqCisWbOGV+UjIuoHjY2NWL9+PQBgxYoVLEwRkUV5eXnB398fRUVF+Omnnzi0mKiNhoYG1NTUQKPRQKPRoLbVCCCFQoGRI0fCw8MD7u7ukMlkVoyULImFqSHC29sbBw8exFNPPQW5XI65c+fC09MTAODh4YETJ07g5Zdfxrp169DY2IjAwECkpqYCaLniweTJk6HVarF79+4Oh/HNnTsXR44cwfjx4+Hp6Yno6Gjcu3cP2dnZePXVV2EwGNDU1ITFixcjNDQUADo9ZlextpWZmYkpU6YAABYtWoQ333wT+/fvx4oVK/r/Tfy3ffv2QaVSYfv27XB1dcWhQ4eEx+Lj4xETE4OYmBjs3bsXy5Ytw4YNGyAWi7Fv3z4mJ0REA0wqlWLp0qXC30RElvbwww+jqqoKt27dgoeHB+eFoiHLODSvurpaWOrq6oTH5XI5fH19hcn+Ofx16BIZ+uPaoUNUTU0N3NzcUF1dDVdXV2F9fX091Go1Ro0axf9cZDFsd0REA6+z737qWkfvG7+3yFos0faqqqqQlZUFNzc3hIeHQywWD8hxiGxJc3Mz7t+/j/v37wuFqNYjX5ycnODm5iYsCoWCw/MGsZ7kTDyVSERERERd0mg0iI6ORlNTE5qamvDSSy/h+eeft3ZYRDbLw8MDAQEBKCwsRG5uLiZMmMAf4DSo6PV61NXVoaamBvfv30dNTQ20Wi2M/V5EIhGcnZ3h7e0tFKJ4EoI6M6QLU0yyiIiIiLrn4uKC9PR0KBQKaLVaTJo0CQsWLOh0qD0RtQzpq6+vR3FxMaRSKcaMGcPiFNklvV4PrVYLrVaL2tpaoVdUc3OzsI2DgwM8PT3h6uoKFxcXuLi4cI4oMtuQLkwxySIiIhpctFqtMJ/fvXv34OzsbOWIBgeJRCLMk9PQ0ACDwQDOBkHUNbFYjODgYPzrX/9CYWEhpFIpRo0aZe2wiLrU2NiI2tpak6Wurg56vV7YRiqVCgUo4y17Q1FfDOnCFJMsIiKiwae6utraIVhceno6du3ahYyMDBQVFeHTTz9td7XXpKQk7Nq1C8XFxQgLC8OePXsQGRlp9jE0Gg1mzZqFGzduYNeuXfDy8urnV0HWpNFokJWVhaCgILi7u8Pd3d3aIQ0KEokEISEhyMrKQn5+PqRSKZRKpbXDIkJjYyPq6upQV1cHrVYr3NbX15ts5+DgAA8PDwwbNkxYnJyc2PuP+pVNF6aYZBEREVFPODk5IS8vT/h7qNBqtQgLC8Nzzz2HBQsWtHv86NGjWLt2Lfbu3Ytp06YhMTERc+bMQW5uLnx8fAAA4eHhaGpqarfvqVOnMGLECLi7u+Pq1asoKSnBggULsGjRIvj6+g74ayPLuHjxIo4ePQoXFxc888wzmDZtmrVDGjSkUilCQ0ORlZWFmzdvQiqVwt/f39ph0RBgMBiEAlTr4lNdXR0aGhpMthWLxVAoFPDz8xMKUM7OzpDL5VaKnoYSmy5MMckiIiKinhCLxRg7dqy1w7C4efPmYd68eZ0+/s477+D5559HXFwcAGDv3r04ceIEDh48iI0bNwIAsrKyzDqWr68vwsLCcPbsWSxatKjDbRoaGkx+9NTU1Jj5SogGJ7lcjtDQUFy5cgW5ubkwGAzw9/dnrxPqM4PBAJ1OhwcPHnS4tP0tbBw15OHhAYVCAWdnZygUCjg6OvLqkWQ1Nl2YYpJFRERE1Dc6nQ4ZGRl49dVXhXVisRjR0dE4f/68Wc9RUlIChUIBFxcXVFdXIz09HcuXL+90+x07duD111/vc+y2wsvLC5cvX0ZQUFCn24hEIlRVVXU4BC48PBxnz56Fi4vLwAX5b+bE2pHIyEjI5XJhKF9/uHHjBpYuXYry8nK4ubkhOTkZEydObLddQ0MD1q1bhy+++AKOjo4ICwvDkSNHTLY5dOgQnnvuuQ5HUNgL42u7evUqcnNzodFoMG7cOEilNv2TjKzMYDCgqakJ9fX1qK+vR0NDg/C3sfjUehJyoOXzyMHBAS4uLnBycoKTk5NJAYoFUbI1dvspyCSLiIiI2mpsbMT+/fsBAAkJCbwiEIDy8nI0Nze36xHu6+uL69evm/Ucd+7cQUJCgjAf5+rVqxESEtLp9q+++irWrl0r3K+pqRnS8+qYe6LUmtzd3REVFdWvz/nCCy8gISEBKpUKn3zyCVQqFS5dutRuu40bN0IkEiEvLw8ikQjFxcUmj+fn5+PAgQN47LHH+jU+a1AoFJg6dSquX7+OkpIS1NTUIDg4GK6urtYOjaxEr9dDp9MJBafWhSfj/Y5GAIlEIjg6OsLNzU0oPhkXR0dHSCQSK7waot6x28IUk6yeCQoKgoODA5ycnKDT6bBy5UqsXLmy354/NTUVfn5+vUoY/vGPf2Djxo1wcHDA4cOHu/w36Ink5GQ89thjmDBhQr88HxER2T6dTodVq1YBAFQqFQtT/SQyMrJHxRUHBwc4ODgMXEAD7Pjx49iwYQNkMhnmzp1r8tilS5ewYcMG1NTUoLm5Ga+99hqefvppAMBbb72FEydOQKvVYsuWLXj22WcBtO9N9eyzzyI3Nxc6nQ5KpRIffPAB3NzcoFKpkJ2dDZlMBl9fX5w6darbY3YVa1s7duxAaWkp3n33XSQnJ+Pw4cM4cuTIgMx3VFpaisuXLwuvYeHChVi1ahVu3ryJMWPGCNtptVp88MEHKCwsFHpx+Pn5CY/r9XrEx8djz549WLduXb/HaQ0ymQyTJk3CvXv3cOvWLWRmZmL06NFQKpXsyTKI6PV6NDY2CkUn423rv3U6HXQ6XYf7i8ViodeTo6MjHBwc4OjoKCwODg4cekeDht0WpvrDUEuyjh49ivDwcNy5cwehoaH42c9+htDQULP2bWpq6rKbcWpqKsLDw3tVmNq7dy82b96MZ555psfH7UpycjLc3d1ZmCIiGkIkEokwJJ9ni1t4eXlBIpGgpKTEZH1JSYlJAYBalJaWIi4uDmfPnkVwcDD279+PiooKAC0XzUlISMDnn38Of39/lJeXY8qUKZgxYwaAlgLUlStXcPv2bUydOhUzZ87scEhdYmIivL29AQA7d+7E1q1bMWfOHGg0GuTk5AAAKisruz2mTCbrNNaOZGZmYt68eVi9ejWamppw8uTJHk1sHBsbi9zc3A4f+9///V+TE7YFBQXw9/cX8jiRSITAwEDcvXvXpDB169YtDB8+HNu3b0daWhqcnJywdetWzJ49G0DL1B0zZ85ERESE2XHaA5FIhICAALi5uSEnJwe3bt1CcXExHnroIXh7e7PgYIMMBgOam5uFYlNHt23XdXbFd2PRycnJCe7u7pDL5cJvTWPhSS6Xs1BJQ4bdFqbsLcnSarUAWrrvGj9gjB9aUqnUpOBl3NbJyUn4UjJ+uEkkEjg6OvYploceegjjx49HXl4e0tLS8Le//Q2NjY2QyWTYvXs3pk+fDqCll1VsbCzOnDmDsWPHIjk5Gf/1X/+Fr776CjqdDuPGjcO+fftw/vx5HD9+HF9++SWSk5OxatUqxMfHY9euXUhOToZYLEZoaCjef/99uLm5mcTyhz/8AWfPnsX169exZ88enDt3DiKRCJs3b8bnn3+OqKgovPLKK3jxxRdx48YNoWfbCy+8IMS4ZMkSfPnllyguLsayZcuwadMm/OUvf8Hly5fxxz/+EVu3bsX27dsxf/78Pr1vRERk+xwdHXHs2DFrh2FT5HI5IiIicPr0aWFuHr1ej9OnTwu9ywZKUlISkpKS2s1/0pWKQ8moTE7udjvH4GAo//y+ybqC5StQ/+/CTlvDVSp4xqm6fd4LFy4gNDQUwcHBAIBly5Zh9erVAIBz587h9u3b7eZANRZr4uPjAQCjR4/G448/jvT09A4LUx9//DEOHz4sDNXx8vLC+vXrce3aNaxYsQKzZs0S8paujllbW9tprB3JzMxERkYGHBwccO3atW7fi7aOHj3a432609TUhDt37iA4OBg7d+7ElStX8Itf/AI//vgjysrKkJKSgvT09H4/rq1wcXFBREQE7ty5g3v37iEnJwdOTk5QKpXw8/NjgX2ANDc3o6mpCU1NTWhsbDS5bbuudcFJr9d3+bxSqRQymUzo6eTg4CAUnVoXn6RSKYtORK3YbWHKmklWbwwbNgxAy1k44xmyXbt2YdOmTYiPj8eBAweEbX18fFBXVwe1Wi0kM0lJSfjjH/+I3//+9/joo4/6FEt2djauX7+OsLAwzJo1SxieeOHCBahUKpOhkBUVFfj+++8hEomwfft2ODs74+LFiwCAP/3pT9i0aROSkpIQExOD8PBwrFmzBgBw8uRJHDx4EOfPn4e7uzsSEhKwceNG/PnPfzaJZffu3fjXv/6FNWvWmExkKZFIhDkIYmNjMX78ePz9739HaWkpIiIiEBYWJvTO0mg0OH/+PMrLy/Hwww8jLi4O8fHxOHLkSLvnJSIiGoxqa2tx8+ZN4b5arUZWVhaGDx+OwMBArF27FkuXLsXUqVMRGRmJxMREaLVa4QIyA8U4dUBNTU27k1Od0dfWoqnNiceONHdwIrK5srLTffW1tWYdv63WPx4NBgMmTpyIc+fO9Xhfo2+//Ra7d+/G+fPn4ePjg+PHj2Pz5s0YPXo0cnJy8NVXXyEtLQ3r169HVlZWl8c8fvx4t8czqq6uRnFxMc6cOYMlS5YgJSUFCxcuNOt1GPWkx5RSqURRUZHQ+91gMODu3bsIDAw02S8wMBBisVgY9jh58mSMGjUK2dnZuHHjBvLz84UrbRYXFyMhIQFFRUVdzgtrb6RSKR5++GEEBgbi3r17KCwsRF5eHtRqNTw9PeHp6QkPDw8OTUbL/0G9Xi8Ulsy9bVtwMrdYLpFIIJPJIJPJ4OzsDJlMBrlcLqwz/m28ZSGRqHdsujBlq0mWvYqNjYWTkxMUCgUOHjyIsWPH4tSpU9i2bRsqKioglUqRm5uLBw8ewMnJCUDL/BzGJCc1NRXV1dVISUkB0NLjq7MrvqSlpSE2NlaYS2H58uXCXAjmeO6550yeKyMjA0BL0W7BggVIS0sTClO///3vAbT0ohs9ejTUajVGjhxp/htDRERk5y5fvownnnhCuG886bR06VIkJycjNjYWZWVl2Lx5M4qLixEeHo5//vOf7ebqtAXiYcMgNSMuyfDhHa7rbF/xv08Sdmf69OmIi4vD9evXMWHCBBw8eFCYA2bGjBlQq9VIS0tDdHQ0gJaJzY09lg4dOoStW7ciPz8fZ8+eRWJiYrvnr6qqgouLCzw9PaHT6bBv3z4AQGFhITw8PBATE4O5c+ciNTUVBQUFXR6zq1jbyszMRFhYGCIjI/HGG2/gtddew5NPPtmjKRN60mPKx8cHU6ZMwZEjR6BSqZCSkoKAgACTYXxAS/42e/ZsfPHFF5g/fz7UajXUajUeeeQRREdHmxSgoqKiBvVJR5lMhqCgIAQEBKCoqAjFxcXCIhKJ4ObmBldXVzg7OwtXWLPVQoherxcKSMbbzv7u6vGOikydDY/rjEgkMunJZCwwGddJpVKTv1uvs9X3l2iwsenClK0mWb3pll7777N0CoVCWPfKK69gzZo17RKC0tJSABCKQ0DLGcfnn3++Tx+OxjmmjHQ6HRYsWIAzZ87g0UcfFc5mNjQ0CMce1iqJMxgM2LNnD375y1/2+Ng97ao6rIvkse1ztR7aKJFIOrxqBRERDQ11dXVC74obN26YfO8OZlFRUd3+WFu1apVN9ipvyzPOvCF3HWk7tK83vL29cfDgQTz11FOQy+WYO3cuPD09AQAeHh44ceIEXn75Zaxbtw6NjY0IDAxEamoqgJbhQZMnT4ZWq8Xu3bs7PIE3d+5cHDlyBOPHj4enpyeio6Nx7949ZGdn49VXXxUuDb948WJhLtDOjtlVrG1lZmZiypQpAIBFixbhzTffxP79+7FixYo+v2ed2bdvH1QqFbZv3w5XV1ccOnRIeCw+Ph4xMTGIiYnB3r17sWzZMmzYsAFisRj79u0b0icZpVIplEollEol6uvrUVFRgYqKCmg0Gmg0GmE7kUgEuVxuskgkEkgkEojFYmEx3gcgfE4YL/7U0TpjUant0tVjrRdjUamvxGKxUBySyWRwdHQU7pt7a1w4bI7ItokMPS05k8BYyKmurja5xGt9fT3UajVGjRrV5/mg+ktQUJAwQblRTU0NvLy8UFBQAF9fX2zbtg2bNm0SrhrTdp9t27bh22+/RUpKChQKhTDccOLEifjDH/4AT09PbNmyBUDLUL5169bhwoULcHV1xfLlyyESifD+++0TxrZnv9peuSY2NhZjxozBtm3bUFZWhoiICBw7dgzTpk1rF+PUqVPx1ltvISoqCjExMVi4cCGWLl06UG+rTbHFdkdENNh09t1PXevofeP3FlmLvbY9vV6PBw8eQKvVCkvrK7v1RzGoOyKRCGKxWLjtaGldHGv7d3ePt/6bxSQi+9aTnMmme0zRwHJ1dcUbb7yByMhIeHl54Xe/+12X22/YsAENDQ2YNm2a8EWxYcMGTJw4EYsXL4ZKpUJqaipWrlyJ+Ph4/PDDD5g+fbrJ5Oe9sXv3bixfvhwhISEwGAz4z//8T0ybNq3b/RISErBu3Tq8++67nPyciIjICnrTy5yIOiYWi4VhfG0Ze9oZeyu17rlkXID/H3nQ1W1nBSdjQYoFIyLqb+wx1Qf21GOKBj+2OyKigcceU73DHlNkS9j2iIgGXk9yJrGFYiIiIiIiIiIiIjLBwhQREREREREREVkFC1NERERERERERGQVLEz1QlJSEoKDg/Hoo492uR2n7yJLYnsjIiJbY07OxO8vsjS2OSIi28LCVC+sXLkSOTk5uHTpUoePSyQSAIBOp7NkWDTEGdubsf0RERFZW1c5k0wmAwDU1dVZOiwa4pgzERHZFqm1AxiMpFIpFAoFysrKIJPJIBaz/kcDS6/Xo6ysDAqFAlIp/1sTEZHtk0gkcHd3R2lpKQBAoVDwMvQ04JgzERHZHn4aDwCRSAR/f3+o1WrcuXPH2uHQECEWixEYGMiknoiI7Iafnx8ACMUpIktgzkREZFtYmBogcrkcY8eO5XA+shi5XM7eeUREZFeMJ/N8fHzQ2Nho7XBoiGDORERkW1iYGkBisRiOjo7WDoOIiIjIpkkkEs73Q0RENETxVAEREREREREREVkFe0z1QlJSEpKSktDU1AQAqKmpsXJEREREZAnG73xebt48zJmIiIiGpp7kTCIDM6teKywshFKptHYYREREZGEFBQUICAiwdhh2gzkTERHR0GROzsTCVB/o9Xr89NNPcHFx6fKqHo8++iguXbrUo8dqamqgVCpRUFAAV1fXfovZErp6vbZ8rL48V0/3NXd7c7brbhu2Mds5Tm+fb6Dalznbsn3Zz7EG42eYLbYvg8GA+/fvY8SIEZw8uQfMyZmG4ucNwM+c/t6HuVPn2Nb6dx+2tc6xrfXv9vba1nqSM3EoXx+IxWKzzpZKJJJO/5G7egwAXF1d7e7DqLvXZKvH6stz9XRfc7c3Z7vutmEbs53j9Pb5Bqp9mbMt25f9HGswfobZavtyc3Oz+DHtnTk501D8vAH4mdPf+zB36hzbWv/uw7bWOba1/t3entuauTkTT/VZwMqVK3v1mL2y5Gvqz2P15bl6uq+525uzXXfbsI3ZznF6+3wD1b7M2Zbty36ONRg/wwZj+6LODcXPG4CfOf29D3OnzrGt9e8+bGudY1vr3+2HQlvjUD4bVVNTAzc3N1RXV9tllZxsH9sYDSS2LxpIbF/UGtsDWQrbGlkK2xpZiq20NfaYslEODg7YsmULHBwcrB0KDVJsYzSQ2L5oILF9UWtsD2QpbGtkKWxrZCm20tbYY4qIiIiIiIiIiKyCPaaIiIiIiIiIiMgqWJgiIiIiIiIiIiKrYGGKiIiIiIiIiIisgoUpIiIiIiIiIiKyCham7NRnn32G8ePHY+zYsfjLX/5i7XBokHnqqafg4eGBRYsWWTsUGoQKCgoQFRWF4OBghIaG4tixY9YOiQYRjUaDqVOnIjw8HJMmTcKBAwesHRJZEfMlshTmTmQJzKHIUiydT/GqfHaoqakJwcHBOHPmDNzc3BAREYFz587B09PT2qHRIPH111/j/v37+PDDD/HJJ59YOxwaZIqKilBSUoLw8HAUFxcjIiICeXl5cHZ2tnZoNAg0NzejoaEBCoUCWq0WkyZNwuXLl/kdOQQxXyJLYu5ElsAciizF0vkUe0zZoYsXL2LixIkYOXIkhg0bhnnz5uHUqVPWDosGkaioKLi4uFg7DBqk/P39ER4eDgDw8/ODl5cXKisrrRsUDRoSiQQKhQIA0NDQAIPBAJ6DG5qYL5ElMXciS2AORZZi6XyKhSkrSE9Px69//WuMGDECIpEIqamp7bZJSkpCUFAQHB0dMW3aNFy8eFF47KeffsLIkSOF+yNHjsS9e/csETrZgb62L6Lu9Gcby8jIQHNzM5RK5QBHTfaiP9qXRqNBWFgYAgIC8Morr8DLy8tC0VN/Yr5ElsLciSyFORRZir3lUyxMWYFWq0VYWBiSkpI6fPzo0aNYu3YttmzZgszMTISFhWHOnDkoLS21cKRkj9i+aKD1VxurrKzEkiVLsH//fkuETXaiP9qXu7s7rl69CrVajY8//hglJSWWCp/6Eb/PyFLY1shSmEORpdhdPmUgqwJg+PTTT03WRUZGGlauXCncb25uNowYMcKwY8cOg8FgMHz33XeG3/zmN8LjL730kuGjjz6ySLxkX3rTvozOnDljWLhwoSXCJDvW2zZWX19v+NnPfmb461//aqlQyQ715TPMaPny5YZjx44NZJhkAcyXyFKYO5GlMIciS7GHfIo9pmyMTqdDRkYGoqOjhXVisRjR0dE4f/48ACAyMhI//PAD7t27h9raWpw8eRJz5syxVshkR8xpX0R9YU4bMxgMUKlU+PnPf47FixdbK1SyQ+a0r5KSEty/fx8AUF1djfT0dIwfP94q8dLAYb5ElsLciSyFORRZii3mU9IBe2bqlfLycjQ3N8PX19dkva+vL65fvw4AkEqlePvtt/HEE09Ar9dj/fr1vMIMmcWc9gUA0dHRuHr1KrRaLQICAnDs2DFMnz7d0uGSHTKnjX333Xc4evQoQkNDhfHuhw8fRkhIiKXDJTtjTvu6c+cOEhIShEk6V69ezbY1CDFfIkth7kSWwhyKLMUW8ykWpuxUTEwMYmJirB0GDVJpaWnWDoEGsf/4j/+AXq+3dhg0SEVGRiIrK8vaYZCNYL5ElsLciSyBORRZiqXzKQ7lszFeXl6QSCTtJhYrKSmBn5+flaKiwYLtiwYa2xgNJLYvMmJbIEthWyNLYVsjS7HFtsbClI2Ry+WIiIjA6dOnhXV6vR6nT59md2DqM7YvGmhsYzSQ2L7IiG2BLIVtjSyFbY0sxRbbGofyWUFtbS1u3rwp3Fer1cjKysLw4cMRGBiItWvXYunSpZg6dSoiIyORmJgIrVaLuLg4K0ZN9oLtiwYa2xgNJLYvMmJbIEthWyNLYVsjS7G7tjZg1/ujTp05c8YAoN2ydOlSYZs9e/YYAgMDDXK53BAZGWm4cOGC9QImu8L2RQONbYwGEtsXGbEtkKWwrZGlsK2RpdhbWxMZDAbDwJW9iIiIiIiIiIiIOsY5poiIiIiIiIiIyCpYmCIiIiIiIiIiIqtgYYqIiIiIiIiIiKyChSkiIiIiIiIiIrIKFqaIiIiIiIiIiMgqWJgiIiIiIiIiIiKrYGGKiIiIiIiIiIisgoUpIiIiIiIiIiKyChamiIiIiIiIiIjIKliYIiLqg6CgICQmJlo7DCIiIiKbxXyJiLrCwhQR2QWVSoXf/OY3wv2oqCisWbPGYsdPTk6Gu7t7u/WXLl1CQkKCxeJo6+uvv4ZIJIJGo7FaDERERGQbmC91jPkSkW2TWjsAIiJr0ul0kMvlvd7f29u7H6MhIiIisj3Ml4hoILHHFBHZHZVKhW+++QbvvfceRCIRRCIR8vPzAQA//PAD5s2bh2HDhsHX1xeLFy9GeXm5sG9UVBRWrVqFNWvWwMvLC3PmzAEAvPPOOwgJCYGzszOUSiVWrFiB2tpaAC1n2eLi4lBdXS0cb+vWrQDad02/e/cunnzySQwbNgyurq747W9/i5KSEuHxrVu3Ijw8HIcPH0ZQUBDc3Nzwu9/9Dvfv3xe2+eSTTxASEgInJyd4enoiOjoaWq223fuQn5+PJ554AgDg4eEBkUgElUrVH28xERER2TnmSy2YLxHZPhamiMjuvPfee5g+fTqef/55FBUVoaioCEqlEhqNBj//+c8xefJkXL58Gf/85z9RUlKC3/72tyb7f/jhh5DL5fjuu++wd+9eAIBYLMbu3bvx448/4sMPP8RXX32F9evXAwBmzJiBxMREuLq6Csd7+eWX28Wl1+vx5JNPorKyEt988w2+/PJL3L59G7GxsSbb3bp1C6mpqfjss8/w2Wef4ZtvvsHOnTsBAEVFRXjmmWfw3HPP4dq1a/j666+xYMECGAyGdsdTKpVISUkBAOTm5qKoqAjvvfde399gIiIisnvMl1owXyKyfRzKR0R2x83NDXK5HAqFAn5+fsL6//mf/8HkyZOxfft2Yd3BgwehVCqRl5eHcePGAQDGjh2L//7v/zZ5ztbzLwQFBeGNN97Aiy++iPfffx9yuRxubm4QiUQmx2vr9OnTyM7OhlqthlKpBAD89a9/xcSJE3Hp0iU8+uijAFoSsuTkZLi4uAAAFi9ejNOnT2Pbtm0oKipCU1MTFixYgIceeggAEBIS0uHxJBIJhg8fDgDw8fHpcE4HIiIiGpqYL7VgvkRk+9hjiogGjatXr+LMmTMYNmyYsEyYMAFAy1k3o4iIiHb7pqWlYfbs2Rg5ciRcXFywePFiVFRUoK6uzuzjX7t2DUqlUkiyACA4OBju7u64du2asC4oKEhIsgDA398fpaWlAICwsDDMnj0bISEhePrpp3HgwAFUVVWZ/yYQERERdYH5EhHZGhamiGjQqK2txa9//WtkZWWZLDdu3MDjjz8ubOfs7GyyX35+Pn71q18hNDQUKSkpyMjIQFJSEoCWyT77m0wmM7kvEomg1+sBtJzV+/LLL3Hy5EkEBwdjz549GD9+PNRqdb/HQUREREMP8yUisjUsTBGRXZLL5WhubjZZN2XKFPz4448ICgrCmDFjTJa2yVVrGRkZ0Ov1ePvtt/HYY49h3Lhx+Omnn7o9XluPPPIICgoKUFBQIKzLycmBRqNBcHCw2a9NJBJh5syZeP3113HlyhXI5XJ8+umnHW5rvEJOd7ERERHR0MN86f/jApgvEdkqFqaIyC4FBQXh+++/R35+PsrLy6HX67Fy5UpUVlbimWeewaVLl3Dr1i188cUXiIuL6zIRGTNmDBobG7Fnzx7cvn0bhw8fFib5bH282tpanD59GuXl5R12WY+OjkZISAieffZZZGZm4uLFi1iyZAlmzZqFqVOnmvW6vv/+e2zfvh2XL1/G3bt38fe//x1lZWV45JFHOtz+oYcegkgkwmeffYaysjLhyjhEREREzJdaMF8ism0sTBGRXXr55ZchkUgQHBwMb29v3L17FyNGjMB3332H5uZm/PKXv0RISAjWrFkDd3d3iMWdf9yFhYXhnXfewZtvvolJkybho48+wo4dO0y2mTFjBl588UXExsbC29u73WSgQMuZu3/84x/w8PDA448/jujoaIwePRpHjx41+3W5uroiPT0d8+fPx7hx47Bp0ya8/fbbmDdvXofbjxw5Eq+//jo2btwIX19frFq1yuxjERER0eDGfKkF8yUi2yYydHRNTSIiIiIiIiIiogHGHlNERERERERERGQVLEwREREREREREZFVsDBFRERERERERERWwcIUERERERERERFZBQtTRERERERERERkFSxMERERERERERGRVbAwRUREREREREREVsHCFBERERERERERWQULU0REREREREREZBUsTBERERERERERkVWwMEVERERERERERFbBwhQREREREREREVnF/wEmnIeA38H/QwAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sched_debiased = PolynomialEpsilon(kappa=kappa_star_debiased, beta_0=beta_0)\n", + "records[\"debiased\"] = debiased_annealed_sinkhorn_ott(x, y, a, b, eps_sched=sched_debiased, T=T, ot_ref=OT_ref)\n", + "annealed_results[\"debiased\"] = {\n", + " \"iters\": np.array([r[\"t\"] for r in records[\"debiased\"]]),\n", + " \"subopt\": np.array([r[\"subopt\"] for r in records[\"debiased\"]]),\n", + " \"merr\": np.array([r[\"margin_err\"] for r in records[\"debiased\"]]),\n", + "}\n", + "\n", + "\n", + "print(\"Final subopt debiased = \" + f\"{annealed_results['debiased']['subopt'][-1]:.2e}\")\n", + "\n", + "\n", + "fig, axes = plt.subplots(1, 2, figsize=(12, 4))\n", + "\n", + "ax = axes[0]\n", + "for name in [\"slow\", \"medium\", \"fast\"]:\n", + " ax.loglog(annealed_results[name][\"iters\"], annealed_results[name][\"subopt\"],\n", + " color=\"tab:gray\", alpha=0.5, linewidth=1.2, label=name)\n", + "ax.loglog(annealed_results[\"poly_kstar\"][\"iters\"], annealed_results[\"poly_kstar\"][\"subopt\"],\n", + " color=\"tab:blue\", linewidth=2,\n", + " label=rf\"polynomial $\\kappa^*={kappa_star:.2f}$\")\n", + "ax.loglog(annealed_results[\"debiased\"][\"iters\"], annealed_results[\"debiased\"][\"subopt\"],\n", + " color=\"tab:red\", linewidth=2, linestyle=\"--\",\n", + " label=rf\"debiased $\\kappa^*={kappa_star_debiased:.2f}$\")\n", + "ax.step(pareto_x, np.minimum.accumulate(pareto_y), where=\"post\", #Built in Cell 12 — re-run if needed\n", + " linestyle=\":\", color=\"black\", linewidth=1.5, label=\"Pareto front\")\n", + "ax.set_xlabel(\"Iterations t\")\n", + "ax.set_ylabel(r\"$\\langle C,\\hat P_t\\rangle - \\mathrm{OT}(a,b)$\")\n", + "ax.set_title(\"All schedules — suboptimality\")\n", + "ax.legend(fontsize=8)\n", + "\n", + "ax = axes[1]\n", + "for name in [\"slow\", \"medium\", \"fast\"]:\n", + " ax.loglog(annealed_results[name][\"iters\"], annealed_results[name][\"merr\"],\n", + " color=\"tab:gray\", alpha=0.5, linewidth=1.2, label=name)\n", + "ax.loglog(annealed_results[\"poly_kstar\"][\"iters\"], annealed_results[\"poly_kstar\"][\"merr\"],\n", + " color=\"tab:blue\", linewidth=2,\n", + " label=rf\"polynomial $\\kappa^*={kappa_star:.2f}$\")\n", + "ax.loglog(annealed_results[\"debiased\"][\"iters\"], annealed_results[\"debiased\"][\"merr\"],\n", + " color=\"tab:red\", linewidth=2, linestyle=\"--\",\n", + " label=rf\"debiased $\\kappa^*={kappa_star_debiased:.2f}$\")\n", + "ax.set_xlabel(\"Iterations t\")\n", + "ax.set_ylabel(\"Marginal violation error\")\n", + "ax.set_title(\"All schedules — marginal feasibility\")\n", + "ax.legend(fontsize=8)\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "1ea54e35", + "metadata": {}, + "source": [ + "**Left panel.** Three performance levels emerge clearly. Geometric schedules plateau well above the Pareto front regardless of decay rate, confirming that exponential cooling is fundamentally unsuited to the annealing framework. The polynomial schedule $\\kappa^\\star = 0.50$ decreases steadily and approaches the front throughout the run. The debiased variant $\\kappa^\\star = 0.64$ converges faster and reaches lower suboptimality than the standard polynomial, almost beating the Pareto front by the end of the budget.\n", + "\n", + "**Right panel.** The debiasing correction keeps the log-scaling continuously shifted toward the new temperature, which induces a marginal violation roughly one order of magnitude above the polynomial schedule throughout the run. This is the fundamental trade-off of the debiased algorithm: the correction step accepts transient infeasibility to absorb the relaxation error that would otherwise slow convergence." + ] + }, + { + "cell_type": "markdown", + "id": "54e46d47", + "metadata": {}, + "source": [ + "## Little bonus — Convergence conditions\n", + "\n", + "\n", + "Annealed Sinkhorn converges to $\\mathrm{OT}(a, b)$ if and only if both conditions hold:\n", + "\n", + "\n", + "$$\\beta_t \\to +\\infty \\qquad \\text{and} \\qquad \\beta_t - \\beta_{t-1} \\to 0.$$\n", + "\n", + "\n", + "The first condition ensures the entropic bias $\\Theta(\\beta_t^{-1})$ vanishes. The second ensures the relaxation error, incurred when the kernel changes between steps, remains controlled. Violating either condition causes convergence to a *wrong* limit.\n", + "\n", + "\n", + "We illustrate the first violation: a saturating schedule $\\beta_t = \\beta_{\\max}(1 - e^{-t/\\tau})$ satisfies $\\beta_t - \\beta_{t-1} \\to 0$ but $\\beta_t \\to \\beta_{\\max} < \\infty$. The algorithm converges, but to the *regularized* OT value $\\mathrm{OT}_{\\varepsilon}(a,b)$ with $\\varepsilon = 1/\\beta_{\\max}$ instead of $\\mathrm{OT}(a, b)$." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "6e4cd70e", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Residual gap OT_eps - OT = 0.0068\n" + ] + } + ], + "source": [ + "class SaturatingEpsilon(epsilon_scheduler.Epsilon):\n", + " \"\"\"Saturating schedule: beta_t = beta_max * (1 - exp(-t/tau)). Satisfies beta_t - beta_{t-1} -> 0 but beta_t -> beta_max < inf.\"\"\"\n", + " def __init__(self, beta_max: float, tau: float):\n", + " super().__init__(target=1.0 / beta_max, init=1.0, decay=1.0)\n", + " self._beta_max = beta_max\n", + " self._tau = tau\n", + "\n", + " def __call__(self, count: int):\n", + " count = jnp.asarray(count)\n", + " beta_t = self._beta_max * (1.0 - jnp.exp(-count / self._tau))\n", + " beta_t = jnp.maximum(beta_t, 1e-6)\n", + " return 1.0 / beta_t\n", + "# beta_max chosen to match starting eps of polynomial schedule\n", + "beta_max = 10.0 * beta_0\n", + "tau = 50.0\n", + "\n", + "sched_saturating = SaturatingEpsilon(beta_max=beta_max, tau=tau)\n", + "\n", + "# Reference: regularized OT at the saturation value eps_inf = 1/beta_max\n", + "eps_inf = 1.0 / beta_max\n", + "geom_reg = pointcloud.PointCloud(x, y, epsilon=eps_inf)\n", + "prob_reg = linear_problem.LinearProblem(geom_reg, a=a, b=b)\n", + "OT_reg = sinkhorn.Sinkhorn()(prob_reg).primal_cost\n", + "\n", + "records[\"saturating\"] = annealed_sinkhorn_ott(x, y, a, b, eps_sched=sched_saturating, T=T, ot_ref=OT_ref)\n", + "annealed_results[\"saturating\"] = {\n", + " \"iters\": np.array([r[\"t\"] for r in records[\"saturating\"]]),\n", + " \"subopt\": np.array([r[\"subopt\"] for r in records[\"saturating\"]]),\n", + " \"merr\": np.array([r[\"margin_err\"] for r in records[\"saturating\"]]),\n", + "}\n", + "\n", + "# Residual gap = OT_reg - OT_ref (what the algorithm will converge to)\n", + "residual_gap = float(OT_reg) - float(OT_ref)\n", + "print(f\"Residual gap OT_eps - OT = {residual_gap:.4f}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "00fe8e8a", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(6, 4))\n", + "\n", + "ax.loglog(annealed_results[\"poly_kstar\"][\"iters\"], annealed_results[\"poly_kstar\"][\"subopt\"],\n", + " color=\"tab:blue\", linewidth=2, label=rf\"polynomial $\\kappa^*={kappa_star:.2f}$\")\n", + "ax.loglog(annealed_results[\"saturating\"][\"iters\"], annealed_results[\"saturating\"][\"subopt\"],\n", + " color=\"tab:orange\", linewidth=2, linestyle=\"--\", label=r\"saturating $\\beta_t \\to \\beta_{\\max}$\")\n", + "ax.axhline(residual_gap, color=\"tab:orange\", linewidth=1, linestyle=\":\",\n", + " label=rf\"$\\mathrm{{OT}}_{{\\varepsilon_\\infty}} - \\mathrm{{OT}} = {residual_gap:.3f}$\")\n", + "ax.step(pareto_x, np.minimum.accumulate(pareto_y), where=\"post\",\n", + " linestyle=\":\", color=\"black\", linewidth=1, label=\"Pareto front\")\n", + "ax.set_xlabel(\"Iterations t\")\n", + "ax.set_ylabel(r\"$\\langle C,\\hat P_t\\rangle - \\mathrm{OT}(a,b)$\")\n", + "ax.set_title(\"Counter-example: saturating schedule\")\n", + "ax.legend(fontsize=8)\n", + "plt.tight_layout()\n", + "plt.savefig(\"counterexample.pdf\", bbox_inches=\"tight\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "38e330f3", + "metadata": {}, + "source": [ + "The saturating schedule converges, the orange curve decreases and stabilizes, but to the *wrong* limit. It asymptotes precisely to the horizontal line at $\\mathrm{OT}_{\\varepsilon_\\infty} - \\mathrm{OT}(a,b) = 0.062$, the residual entropic bias at $\\varepsilon_\\infty = 1/\\beta_{\\max}$. No matter how long the algorithm runs, this gap cannot be closed: the condition $\\beta_t \\to +\\infty$ is violated, so the entropic regularization never fully vanishes.\n", + "\n", + "By contrast, the polynomial schedule (blue) crosses the residual gap line around $t \\approx 50$ and continues decreasing, as $\\beta_t \\to +\\infty$ guarantees the entropic bias eventually vanishes. The Pareto front (dotted black) confirms that even fixed-$\\varepsilon$ Sinkhorn can beat the saturating schedule simply by choosing $\\varepsilon < \\varepsilon_\\infty$, the adaptive schedule offers no advantage when its limiting temperature is too high.\n", + "\n", + "This counter-example makes the convergence conditions concrete: convergence to $\\mathrm{OT}(a,b)$ requires $\\beta_t \\to +\\infty$, not merely that $\\beta_t$ increases." + ] + } + ], + "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": "3.11.7" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}