diff --git a/MyIA.AI.Notebooks/GenAI/PostTraining/PT_14_neural_thermodynamic_laws.ipynb b/MyIA.AI.Notebooks/GenAI/PostTraining/PT_14_neural_thermodynamic_laws.ipynb new file mode 100644 index 0000000000..7f3fcc697f --- /dev/null +++ b/MyIA.AI.Notebooks/GenAI/PostTraining/PT_14_neural_thermodynamic_laws.ipynb @@ -0,0 +1,1841 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "c0", + "metadata": { + "papermill": { + "duration": 0.003539, + "end_time": "2026-09-19T07:34:36.618120+00:00", + "exception": false, + "start_time": "2026-09-19T07:34:36.614581+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "# PT-14 — Lois thermodynamiques de l'entraînement : température, équipartition, force entropique\n", + "\n", + "[← PostTraining](../README.md) · série from-scratch (toy CPU, `numpy` + `torch`, sans `trl`)\n", + "\n", + "Ce notebook distille le papier **R08 — *Neural Thermodynamic Laws for Large Language Model Training*** (Liu et al. 2025, [arXiv:2505.10559](https://arxiv.org/abs/2505.10559)) : l'entraînement d'un réseau y est lu comme un système thermodynamique — la **perte est l'énergie**, le **learning rate η est la température**, le **bruit du gradient minibatch est le bain thermique**. Cette lecture produit des lois quantitatives simples (largeur stationnaire, équipartition, T ∼ η, décroissance optimale 1/t, force entropique) que nous vérifions **une par une sur des simulations jouet**, puis confrontons à un mini-transformeur torch CPU.\n", + "\n", + "Résonance directe avec [PT-11a](PT_11a_grpo_qwen35_rlvr.ipynb) : les schedules de learning rate y sont un détail d'ingénierie ; ici ils deviennent une conséquence de la physique — la décroissance 1/t optimale et la discontinuité initiale η₀ = η/2 tombent d'un problème de minimisation de variance, pas d'un réglage ad hoc.\n", + "\n", + "> **Convention d'honnêteté** : les chiffres du papier sur GPT-2 sont toujours cités « rapporté par » ; nos mesures locales sont distinguées par « mesuré ». Chaque expérience de ce notebook a été prototypée et vérifiée avant rédaction." + ] + }, + { + "cell_type": "markdown", + "id": "c1", + "metadata": { + "papermill": { + "duration": 0.004001, + "end_time": "2026-09-19T07:34:36.628666+00:00", + "exception": false, + "start_time": "2026-09-19T07:34:36.624665+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Plan\n", + "\n", + "1. **Paysage rivière-vallée** — le modèle ℓ(x,y) = c(y) + ½a(y)x² et la décomposition lent/rapide.\n", + "2. **Largeur stationnaire σ(a)** — premier rôle de η : SGD vs SignGD, edge of stability, plancher SignGD.\n", + "3. **Équipartition et capacité thermique** — ℓf indépendant de la sharpness, T ∼ η, C = σg²/4.\n", + "4. **La loi sur un vrai (petit) réseau** — mini-GPT torch CPU au plateau (bruit d'étiquette) : le terme thermique est **borné** (C < 0.1, sous résolution du banc toy) ; SGD vs Adam(0,0) hors/at plateau.\n", + "5. **Décroissance optimale 1/t** — diagramme de phase (b, th), optimum théorique, discontinuité η₀ = η/2.\n", + "6. **Loi de Fourier** — relaxation bi-température après un switch de learning rate.\n", + "7. **Force entropique et piégeage** (App. E.1) — le bruit pousse vers les zones plates.\n", + "8. **Seuil de blocage η\\*** (App. E.2) — au-dessus d'un learning rate critique, la descente est bloquée." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "c2", + "metadata": { + "execution": { + "iopub.execute_input": "2026-09-19T07:34:36.638253Z", + "iopub.status.busy": "2026-09-19T07:34:36.638253Z", + "iopub.status.idle": "2026-09-19T07:34:41.100413Z", + "shell.execute_reply": "2026-09-19T07:34:41.100413Z" + }, + "papermill": { + "duration": 4.469759, + "end_time": "2026-09-19T07:34:41.101430+00:00", + "exception": false, + "start_time": "2026-09-19T07:34:36.631671+00:00", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "numpy 2.4.6 | torch 2.14.0+cpu | threads CPU : 4\n" + ] + } + ], + "source": [ + "import warnings\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import torch\n", + "import torch.nn as nn\n", + "\n", + "warnings.filterwarnings(\"ignore\", message=\"enable_nested_tensor\")\n", + "torch.set_num_threads(4)\n", + "np.set_printoptions(precision=4, suppress=True)\n", + "plt.rcParams.update({\"figure.figsize\": (7.5, 3.6), \"figure.dpi\": 110,\n", + " \"axes.grid\": True, \"grid.alpha\": 0.3})\n", + "rng = np.random.default_rng(0)\n", + "\n", + "print(f\"numpy {np.__version__} | torch {torch.__version__} | threads CPU : {torch.get_num_threads()}\")" + ] + }, + { + "cell_type": "markdown", + "id": "c3", + "metadata": { + "papermill": { + "duration": 0.004198, + "end_time": "2026-09-19T07:34:41.112629+00:00", + "exception": false, + "start_time": "2026-09-19T07:34:41.108431+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Partie 1 — Le paysage rivière-vallée\n", + "\n", + "Le papier modélise la loss d'un réseau autour d'une direction de vallée par\n", + "\n", + "$$ \\ell(x, y) = \\underbrace{c(y)}_{\\ell_s\\ :\\ fond\\ de\\ vall\\acute{e}e} + \\underbrace{\\tfrac{1}{2}\\,a(y)\\,x^2}_{\\ell_f\\ :\\ fluctuations\\ transverses} $$\n", + "\n", + "- **y** (coordonnée *lente*) : position le long de la vallée, pente douce donnée par c′(y) ;\n", + "- **x** (coordonnée *rapide*) : distance transverse, raideur a(y) — la **sharpness** locale ;\n", + "- **a′(y) < 0** le long de la descente : la vallée s'élargit (zones plates) au fur et à mesure qu'on descend.\n", + "\n", + "La dynamique d'entraînement sépare deux échelles de temps : x thermalise vite (grande raideur a), y évolue lentement. L'analogie du premier principe de la thermodynamique écrit dℓ/dt = dℓs/dt + dℓf/dt — le travail (descente du fond) et la chaleur (fluctuations transverses) : à chaque instant, une partie de la descente est « dilapidée » en agitation thermique autour du fond." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "c4", + "metadata": { + "execution": { + "iopub.execute_input": "2026-09-19T07:34:41.124186Z", + "iopub.status.busy": "2026-09-19T07:34:41.123183Z", + "iopub.status.idle": "2026-09-19T07:34:41.825106Z", + "shell.execute_reply": "2026-09-19T07:34:41.825106Z" + }, + "papermill": { + "duration": 0.707958, + "end_time": "2026-09-19T07:34:41.826123+00:00", + "exception": false, + "start_time": "2026-09-19T07:34:41.118165+00:00", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def loss_field(x, y):\n", + " a = 1.0 + (y / 4.0) ** 2 # sharpness : decroit quand on descend (y croissant ici)\n", + " c = -0.05 * y # fond de vallee en pente douce\n", + " return c + 0.5 * a * x ** 2\n", + "\n", + "xs = np.linspace(-1.6, 1.6, 240)\n", + "ys = np.linspace(-6.0, 6.0, 240)\n", + "X, Y = np.meshgrid(xs, ys)\n", + "L = loss_field(X, Y)\n", + "\n", + "fig, ax = plt.subplots()\n", + "cs = ax.contourf(Y, X, L, levels=30, cmap=\"viridis_r\")\n", + "ax.contour(Y, X, L, levels=8, colors=\"k\", linewidths=0.4, alpha=0.5)\n", + "ax.plot(ys, np.zeros_like(ys), \"r--\", lw=1.2, label=\"fond de vallée $c(y)$ (coordonnée lente)\")\n", + "ax.annotate(\"vallée étroite\\n(a élevée)\", xy=(-4.6, 0.55), color=\"w\", fontsize=9)\n", + "ax.annotate(\"vallée plate\\n(a faible)\", xy=(3.1, 1.05), color=\"w\", fontsize=9)\n", + "ax.set_xlabel(\"y — coordonnée lente (descente)\")\n", + "ax.set_ylabel(\"x — coordonnée rapide\")\n", + "ax.set_title(\"Paysage rivière-vallée $\\ell(x,y) = c(y) + \\tfrac{1}{2}a(y)x^2$\")\n", + "ax.legend(loc=\"lower left\", fontsize=8)\n", + "fig.colorbar(cs, label=\"loss\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "c5", + "metadata": { + "papermill": { + "duration": 0.004525, + "end_time": "2026-09-19T07:34:41.835179+00:00", + "exception": false, + "start_time": "2026-09-19T07:34:41.830654+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "**Lecture (deux échelles de temps).** La coordonnée transverse x est confinée par une raideur a grande : elle atteint son régime stationnaire en O(1/(aη)) steps. La coordonnée y ne bouge que de η·c′ par step : des milliers de steps. Toute la thermodynamique qui suit vit dans cette séparation — on peut mesurer la « physique » de x **à y figé**, puis traiter y comme un paramètre lent. C'est exactement la stratégie du papier : lois locales mesurées sur le paysage quadratique, puis effet sur la trajectoire lente." + ] + }, + { + "cell_type": "markdown", + "id": "c6", + "metadata": { + "papermill": { + "duration": 0.004624, + "end_time": "2026-09-19T07:34:41.844322+00:00", + "exception": false, + "start_time": "2026-09-19T07:34:41.839698+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Partie 2 — Premier rôle de η : la largeur stationnaire σ(a)\n", + "\n", + "SGD avec bruit de gradient gaussien effectif ( minibatch → $a x + \\sigma_g \\hat W$, $\\hat W \\sim \\mathcal N(0,1)$ ) :\n", + "\n", + "$$ x_{t+1} = x_t - \\eta\\,(a x_t + \\sigma_g \\hat W_t) \\;\\Rightarrow\\; \\sigma_{SGD}(a) = \\frac{\\sigma_g}{\\sqrt{a\\,(2/\\eta - a)}} $$\n", + "\n", + "valable pour aη < 2 (au-delà : divergence, c'est l'*edge of stability*). Pour SignGD (update en $-\\eta\\,\\mathrm{sign}(\\cdot)$) :\n", + "\n", + "$$ \\sigma_{SignGD}(a) = \\frac{\\sqrt\\pi}{4}\\,\\eta\\,\\sqrt{1 + \\sqrt{1 + \\tfrac{32}{\\pi}\\left(\\frac{\\sigma_g}{a\\eta}\\right)^2}} \\;\\xrightarrow{\\ a\\eta \\gg \\sigma_g\\ }\\; \\sqrt{\\tfrac{\\pi}{8}}\\,\\frac{\\sigma_g \\eta}{a}, \\qquad \\text{plancher} = \\frac{\\sqrt{2\\pi}}{4}\\,\\eta $$\n", + "\n", + "Le learning rate joue le rôle d'une **température** : σ croît avec η. Mesurons." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "c7", + "metadata": { + "execution": { + "iopub.execute_input": "2026-09-19T07:34:41.852833Z", + "iopub.status.busy": "2026-09-19T07:34:41.852833Z", + "iopub.status.idle": "2026-09-19T07:34:48.919791Z", + "shell.execute_reply": "2026-09-19T07:34:48.919238Z" + }, + "papermill": { + "duration": 7.072546, + "end_time": "2026-09-19T07:34:48.920864+00:00", + "exception": false, + "start_time": "2026-09-19T07:34:41.848318+00:00", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + " a σ_SGD sim théorie | σ_Sign sim théorie plancher\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 0.02 0.1579 0.1582 | 0.5603 0.5615 0.0627\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 0.05 0.1004 0.1001 | 0.3570 0.3568 0.0627\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 0.10 0.0708 0.0709 | 0.2545 0.2543 0.0627\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 0.20 0.0503 0.0503 | 0.1826 0.1826 0.0627\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 0.50 0.0320 0.0320 | 0.1214 0.1210 0.0627\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 1.00 0.0230 0.0229 | 0.1015 0.0924 0.0627\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 2.00 0.0167 0.0167 | 0.1000 0.0752 0.0627\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 5.00 0.0115 0.0115 | 0.1000 0.0655 0.0627\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 10.00 0.0100 0.0100 | 0.1000 0.0634 0.0627\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 15.00 0.0115 0.0115 | 0.1000 0.0630 0.0627\n" + ] + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "N, BURN, MEAS = 4000, 2000, 3000 # particules, thermalisation, mesure (1 echantillon / 10)\n", + "\n", + "def sim_sgd(a, eta, sg):\n", + " x = np.zeros(N)\n", + " for _ in range(BURN):\n", + " x = x - eta * (a * x + sg * rng.standard_normal(N))\n", + " acc = []\n", + " for t in range(MEAS):\n", + " x = x - eta * (a * x + sg * rng.standard_normal(N))\n", + " if t % 10 == 0:\n", + " acc.append(x.copy())\n", + " return np.array(acc)\n", + "\n", + "def sim_signgd(a, eta, sg):\n", + " x = np.zeros(N)\n", + " for _ in range(BURN):\n", + " x = x - eta * np.sign(a * x + sg * rng.standard_normal(N))\n", + " acc = []\n", + " for t in range(MEAS):\n", + " x = x - eta * np.sign(a * x + sg * rng.standard_normal(N))\n", + " if t % 10 == 0:\n", + " acc.append(x.copy())\n", + " return np.array(acc)\n", + "\n", + "ETA, SG = 0.1, 0.1\n", + "a_sweep = np.array([0.02, 0.05, 0.1, 0.2, 0.5, 1.0, 2.0, 5.0, 10.0, 15.0])\n", + "\n", + "sig_theo_sgd = lambda a: SG / np.sqrt(a * (2 / ETA - a)) # a < 2/eta\n", + "sig_theo_sig = lambda a: (np.sqrt(np.pi) / 4) * ETA * np.sqrt(\n", + " 1 + np.sqrt(1 + (32 / np.pi) * (SG / (a * ETA)) ** 2))\n", + "\n", + "print(f\"{'a':>6} {'σ_SGD sim':>10} {'théorie':>9} | {'σ_Sign sim':>10} {'théorie':>9} {'plancher':>9}\")\n", + "sim_sgd_pts, sim_sig_pts = [], []\n", + "for a in a_sweep:\n", + " s_sgd = sim_sgd(a, ETA, SG).std()\n", + " s_sig = sim_signgd(a, ETA, SG).std()\n", + " sim_sgd_pts.append(s_sgd); sim_sig_pts.append(s_sig)\n", + " print(f\"{a:>6.2f} {s_sgd:>10.4f} {sig_theo_sgd(a):>9.4f} | \"\n", + " f\"{s_sig:>10.4f} {sig_theo_sig(a):>9.4f} {np.sqrt(2*np.pi)/4*ETA:>9.4f}\")\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(a_sweep, sim_sgd_pts, \"o\", color=\"C0\", label=\"SGD (sim)\")\n", + "ax.plot(a_fine := np.geomspace(0.02, 15, 200), sig_theo_sgd(a_fine), \"-\", color=\"C0\", alpha=0.7, label=\"SGD (théorie)\")\n", + "ax.plot(a_sweep, sim_sig_pts, \"s\", color=\"C1\", label=\"SignGD (sim)\")\n", + "ax.plot(a_fine, sig_theo_sig(a_fine), \"-\", color=\"C1\", alpha=0.7, label=\"SignGD (théorie)\")\n", + "ax.axhline(np.sqrt(2*np.pi)/4*ETA, color=\"C3\", ls=\"--\", lw=1, label=f\"plancher SignGD √(2π)/4·η = {np.sqrt(2*np.pi)/4*ETA:.3f}\")\n", + "ax.axvline(1/ETA, color=\"gray\", ls=\":\", lw=1, label=\"a = 1/η (σ_SGD minimal)\")\n", + "ax.set_xscale(\"log\"); ax.set_yscale(\"log\")\n", + "ax.set_xlabel(\"sharpness a\"); ax.set_ylabel(\"largeur stationnaire σ(a)\")\n", + "ax.set_title(f\"σ(a) à η={ETA}, σg={SG} — la température fixe la largeur\")\n", + "ax.legend(fontsize=8)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "c8", + "metadata": { + "papermill": { + "duration": 0.005426, + "end_time": "2026-09-19T07:34:48.931778+00:00", + "exception": false, + "start_time": "2026-09-19T07:34:48.926352+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "**Lecture (trois régimes).** (1) **SGD** : accord simulation/théorie sur toute la gamme, y compris la queue non monotone — σ passe par un minimum à a = 1/η puis remonte vers la divergence à aη → 2 (edge of stability). (2) **SignGD** : parfait dans le régime gaussien (aη ≪ σg, la branche en σg·η/a) ; aux grands a la simulation **sature vers η** au lieu de suivre le plancher théorique √(2π)/4·η ≈ 0.0627 — un écart que le papier documente lui-même (effet de discrétisation : quand σ ≪ η, la distribution devient télégraphe, l'approximation gaussienne perd). (3) Le **plancher** √(2π)/4·η est la température minimale de SignGD : quoi qu'il arrive, σ ≳ η — SignGD ne peut pas descendre sous sa propre largeur de pas." + ] + }, + { + "cell_type": "markdown", + "id": "c9", + "metadata": { + "papermill": { + "duration": 0.007218, + "end_time": "2026-09-19T07:34:48.944181+00:00", + "exception": false, + "start_time": "2026-09-19T07:34:48.936963+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Partie 3 — Équipartition et capacité thermique\n", + "\n", + "La perte thermique vaut $\\ell_f = \\tfrac12 a \\sigma^2(a)$. En substituant σ(a) :\n", + "\n", + "$$ \\text{SGD : } \\ell_f = \\frac{\\sigma_g^2 \\eta}{4} \\qquad \\text{SignGD : } \\ell_f = \\sqrt{\\tfrac{\\pi}{32}}\\,\\sigma_g\\,\\eta \\quad (\\text{régime gaussien}) $$\n", + "\n", + "**ni l'un ni l'autre ne dépend de a** : c'est le **théorème d'équipartition** — chaque degré de liberté porte la même énergie thermique, indépendamment de sa raideur. Conséquence immédiate : la température est **T ∼ η** (linéaire, pas η²), et la **capacité thermique** C = ∂ℓf/∂T vaut σg²/4 (SGD) — la pente de la droite ℓf(η)." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "c10", + "metadata": { + "execution": { + "iopub.execute_input": "2026-09-19T07:34:48.957600Z", + "iopub.status.busy": "2026-09-19T07:34:48.957600Z", + "iopub.status.idle": "2026-09-19T07:34:53.055661Z", + "shell.execute_reply": "2026-09-19T07:34:53.054646Z" + }, + "papermill": { + "duration": 4.107602, + "end_time": "2026-09-19T07:34:53.056659+00:00", + "exception": false, + "start_time": "2026-09-19T07:34:48.949057+00:00", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "== Équipartition : l_f indépendant de a (eta=0.1, sg=0.1) ==\n", + " a l_f SGD C·η corrigé | l_f SignGD théorie\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 0.05 0.00025 0.00025 0.00025 | 0.00318 0.00313\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 0.20 0.00025 0.00025 0.00025 | 0.00332 0.00313\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 1.00 0.00026 0.00025 0.00026 | 0.00515 0.00313\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 5.00 0.00033 0.00025 0.00033 | 0.02500 0.00313\n", + "\n", + "== T ~ eta : l_f(eta) linéaire, pente C = sg²/4 (SGD, a=0.5) ==\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "eta= 0.02 : l_f=0.000050 ratio l_f/(C·eta)=1.006\n", + "eta= 0.05 : l_f=0.000127 ratio l_f/(C·eta)=1.016\n", + "eta= 0.1 : l_f=0.000256 ratio l_f/(C·eta)=1.026\n", + "eta= 0.2 : l_f=0.000527 ratio l_f/(C·eta)=1.054\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "print(\"== Équipartition : l_f indépendant de a (eta=0.1, sg=0.1) ==\")\n", + "lf_theo_sgd = SG ** 2 * ETA / 4\n", + "lf_theo_sig = np.sqrt(np.pi / 32) * SG * ETA\n", + "lf_corr = lambda a: lf_theo_sgd / (1 - a * ETA / 2) # loi exacte : correction finie en aη\n", + "print(f\"{'a':>6} {'l_f SGD':>10} {'C·η':>9} {'corrigé':>9} | {'l_f SignGD':>10} {'théorie':>10}\")\n", + "for a in [0.05, 0.2, 1.0, 5.0]:\n", + " lf_sgd = 0.5 * a * sim_sgd(a, ETA, SG).var()\n", + " lf_sig = 0.5 * a * sim_signgd(a, ETA, SG).var()\n", + " print(f\"{a:>6.2f} {lf_sgd:>10.5f} {lf_theo_sgd:>9.5f} {lf_corr(a):>9.5f} | \"\n", + " f\"{lf_sig:>10.5f} {lf_theo_sig:>10.5f}\")\n", + "\n", + "print(\"\\n== T ~ eta : l_f(eta) linéaire, pente C = sg²/4 (SGD, a=0.5) ==\")\n", + "a_c = 0.5\n", + "eta_grid = [0.02, 0.05, 0.1, 0.2]\n", + "lf_grid = [0.5 * a_c * sim_sgd(a_c, e, SG).var() for e in eta_grid]\n", + "for e, lf in zip(eta_grid, lf_grid):\n", + " print(f\"eta={e:>5} : l_f={lf:.6f} ratio l_f/(C·eta)={lf/(lf_theo_sgd/ETA*e):.3f}\")\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(eta_grid, lf_grid, \"o\", color=\"C0\", label=\"mesuré\")\n", + "ax.plot(np.linspace(0, 0.22, 10), SG**2/4 * np.linspace(0, 0.22, 10), \"--\", color=\"C3\",\n", + " label=f\"théorie C·η, C = σg²/4 = {SG**2/4:.4f}\")\n", + "ax.set_xlabel(\"η (température)\"); ax.set_ylabel(\"perte thermique l_f\")\n", + "ax.set_title(\"T ∼ η : la perte thermique est linéaire en η, de pente la capacité C\")\n", + "ax.legend(fontsize=8)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "c11", + "metadata": { + "papermill": { + "duration": 0.007034, + "end_time": "2026-09-19T07:34:53.070225+00:00", + "exception": false, + "start_time": "2026-09-19T07:34:53.063191+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "**Lecture (l'équipartition est le cœur de l'analogie).** Pour SGD, ℓf est **indépendant de a** sur toute la gamme — et la colonne « corrigé » montre la loi exacte : $\\ell_f = \\frac{\\sigma_g^2\\eta/4}{1 - a\\eta/2}$, dont l'équipartition σg²η/4 est la limite aη ≪ 2 (la dérive de +33 % mesurée à a = 5 est exactement le facteur 1/(1−aη/2) = 1.33 — pas un bruit de mesure, la correction de température finie). Et ℓf(η) est une droite de pente C = σg²/4 à 0,6-5 % près. Pour SignGD, l'équipartition tient dans le régime gaussien mais **casse aux grands a** (régime télégraphe, cf. Partie 2) — l'équipartition exige des fluctuations gaussiennes, un point que le papier souligne et que la simulation rend visible. C'est la mesure centrale : *augmenter le learning rate n'accélère pas seulement, il chauffe* — et le coût final de la chaleur est C·η_min." + ] + }, + { + "cell_type": "markdown", + "id": "c12", + "metadata": { + "papermill": { + "duration": 0.006536, + "end_time": "2026-09-19T07:34:53.082764+00:00", + "exception": false, + "start_time": "2026-09-19T07:34:53.076228+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Partie 4 — La loi sur un vrai (petit) réseau : mini-GPT\n", + "\n", + "Le papier mesure sur GPT-2 (rapporté par R08, §4) :\n", + "\n", + "$$ \\ell_{val} = 3.145 + 110\\,\\eta_{min} \\quad (\\text{GPT-2,~rapporté}) $$\n", + "\n", + "La confronter honnêtement exige deux précautions. **(1) Écarter le confondant majeur** : η est aussi l'*échelle de temps* de la descente — un sweep « η constant, budget de steps fixe » mesure le sous-entraînement, pas la température (à petit η le modèle est simplement resté en haut de la vallée quand le budget s'épuise). **(2) Se placer au plateau de la loss**, là où seule la part thermique varie encore — l'analogue exact de l'entropie irréductible du langage qui fonde le plateau de GPT-2. Notre banc garantit ce plateau par un **bruit d'étiquette q = 0.15** : 15 % des cibles sont remplacées par un token aléatoire, si bien qu'aucun modèle ne peut descendre sous l'entropie du bruit.\n", + "\n", + "Protocole :\n", + "\n", + "1. **Phase chaude** : η = 0.05, 9000 steps, batch 16 → un checkpoint *au plateau* (et un checkpoint intermédiaire « hors plateau » à step 1500) ;\n", + "2. **Anneal depuis le plateau** : η_min ∈ {0.006, 0.02, 0.06}, 2700 steps → val(η_min) isole-t-il un terme thermique C·η ?\n", + "3. **Contrastes** : SGD vs Adam(0,0) (update η·g/(|g|+ε) ≈ η·sign(g), le SignGD par coordonnée) hors plateau puis au plateau, et decay 1/t vs constant." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "c13", + "metadata": { + "execution": { + "iopub.execute_input": "2026-09-19T07:34:53.100915Z", + "iopub.status.busy": "2026-09-19T07:34:53.099914Z", + "iopub.status.idle": "2026-09-19T07:34:53.415791Z", + "shell.execute_reply": "2026-09-19T07:34:53.415791Z" + }, + "papermill": { + "duration": 0.326442, + "end_time": "2026-09-19T07:34:53.416810+00:00", + "exception": false, + "start_time": "2026-09-19T07:34:53.090368+00:00", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "paramètres : 106144\n", + "entropie irréductible du bruit q=0.15 : 0.938\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "val initiale (modèle aléatoire) : 3.817 (ln 32 ≈ 3.47)\n" + ] + } + ], + "source": [ + "import copy\n", + "\n", + "Q_NOISE = 0.15 # bruit d'étiquette : garantit un plateau irréductible\n", + "BS = 16 # petit batch : gradient bruité (le \"bain thermique\")\n", + "\n", + "class MiniGPT(nn.Module):\n", + " \"\"\"Mini transformeur décodeur : 2 couches, d=64, causal (106k paramètres).\"\"\"\n", + " def __init__(self, vocab=32, d=64, ctx=32, layers=2, heads=4):\n", + " super().__init__()\n", + " self.tok = nn.Embedding(vocab, d)\n", + " self.pos = nn.Embedding(ctx, d)\n", + " enc = nn.TransformerEncoderLayer(d, heads, 4 * d, dropout=0.0,\n", + " batch_first=True, norm_first=True,\n", + " activation=\"gelu\")\n", + " self.blocks = nn.TransformerEncoder(enc, layers)\n", + " self.head = nn.Linear(d, vocab)\n", + " def forward(self, x):\n", + " T = x.shape[1]\n", + " mask = torch.triu(torch.ones(T, T, dtype=torch.bool), 1)\n", + " h = self.tok(x) + self.pos(torch.arange(T))\n", + " return self.head(self.blocks(h, mask=mask))\n", + "\n", + "def make_batch(bs, ctx, gen, vocab=32):\n", + " # séquences périodiques, période p aléatoire par séquence (3..8)\n", + " x = torch.zeros(bs, ctx, dtype=torch.long)\n", + " for i in range(bs):\n", + " p = int(torch.randint(3, 9, (1,), generator=gen))\n", + " base = torch.randint(1, vocab, (p,), generator=gen)\n", + " x[i] = base.repeat((ctx + p - 1) // p)[:ctx]\n", + " return x\n", + "\n", + "def noisy_targets(x, gen):\n", + " \"\"\"q=15 % des cibles remplacées par un token aléatoire (train ET val).\"\"\"\n", + " t = x[:, 1:].clone()\n", + " flip = torch.rand(t.shape, generator=gen) < Q_NOISE\n", + " t[flip] = torch.randint(0, 32, (int(flip.sum()),), generator=gen)\n", + " return t\n", + "\n", + "VAL_GEN = torch.Generator().manual_seed(999)\n", + "VAL_X = make_batch(512, 32, VAL_GEN) # validation fixe (tirage indépendant : aucune fuite)\n", + "VAL_Y = noisy_targets(VAL_X, VAL_GEN) # cibles bruitées fixes, même distribution que le train\n", + "\n", + "@torch.no_grad()\n", + "def val_loss(model):\n", + " model.eval()\n", + " logits = model(VAL_X[:, :-1])\n", + " ce = torch.nn.functional.cross_entropy(logits.reshape(-1, 32), VAL_Y.reshape(-1))\n", + " model.train()\n", + " return ce.item()\n", + "\n", + "def train_run(lr, steps, schedule=None, opt_kind=\"sgd\", seed=0, start_state=None):\n", + " torch.manual_seed(seed)\n", + " model = MiniGPT()\n", + " if start_state is not None:\n", + " model.load_state_dict(start_state)\n", + " if opt_kind == \"sgd\":\n", + " opt = torch.optim.SGD(model.parameters(), lr=lr)\n", + " else:\n", + " opt = torch.optim.Adam(model.parameters(), lr=lr, betas=(0.0, 0.0))\n", + " gen = torch.Generator().manual_seed(seed + 1) # même ordre de batches pour tous les runs\n", + " hist = []\n", + " for t in range(steps):\n", + " lr_t = schedule(t, lr) if schedule else lr\n", + " for g in opt.param_groups:\n", + " g[\"lr\"] = lr_t\n", + " xb = make_batch(BS, 32, gen)\n", + " yb = noisy_targets(xb, gen)\n", + " logits = model(xb[:, :-1])\n", + " loss = torch.nn.functional.cross_entropy(logits.reshape(-1, 32), yb.reshape(-1))\n", + " opt.zero_grad(); loss.backward(); opt.step()\n", + " if t % 300 == 0 or t == steps - 1:\n", + " hist.append((t, val_loss(model)))\n", + " return hist\n", + "\n", + "def sched_decay_1t(t, lr, th=90.0):\n", + " # décroissance 1/t depuis le checkpoint (Partie 5) : η -> η/2 puis 1/σ² arithmétique\n", + " return (lr / 2) / (1 + t / th)\n", + "\n", + "h_irred = -(0.85 * np.log(0.85) + 0.15 * np.log(0.15 / 31))\n", + "torch.manual_seed(0)\n", + "print(\"paramètres :\", sum(p.numel() for p in MiniGPT().parameters()))\n", + "print(f\"entropie irréductible du bruit q=0.15 : {h_irred:.3f}\")\n", + "print(\"val initiale (modèle aléatoire) :\", round(val_loss(MiniGPT()), 3), \"(ln 32 ≈ 3.47)\")" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "c14", + "metadata": { + "execution": { + "iopub.execute_input": "2026-09-19T07:34:53.437095Z", + "iopub.status.busy": "2026-09-19T07:34:53.436091Z", + "iopub.status.idle": "2026-09-19T07:37:58.302661Z", + "shell.execute_reply": "2026-09-19T07:37:58.302661Z" + }, + "papermill": { + "duration": 184.878512, + "end_time": "2026-09-19T07:37:58.305384+00:00", + "exception": false, + "start_time": "2026-09-19T07:34:53.426872+00:00", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "== Phase 1 : η=0.05, 9000 steps, batch 16, bruit q=0.15 ==\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " step 0 : val = 3.7918\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " step 1500 : val = 2.6644\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " step 3000 : val = 1.6452\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " step 4500 : val = 1.4785\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " step 6000 : val = 1.4551\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " step 7500 : val = 1.4369\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " step 8999 : val = 1.4266\n", + "checkpoint plateau : val = 1.4266\n", + "\n", + "== Phase 2 : anneal depuis le plateau, 2700 steps, val(η_min) ==\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " anneal η_min= 0.006 : val finale = 1.4195\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " anneal η_min= 0.02 : val finale = 1.4173\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " anneal η_min= 0.06 : val finale = 1.4139\n", + "\n", + "fit : val ≈ 1.4197 + -0.1·η_min (pente ≈ 0 = terme thermique sous résolution)\n", + "amplitude totale du sweep : 0.0055 (0.4 %)\n" + ] + }, + { + "data": { + "image/png": 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wIapUqZKkLaW8Rtq5yudC2g6amJioNoVPnjxR7bENTZ/zMKfWL7l0U2Jtba3aOOuqVq2a+j95XlwpV2NjYzx+/DhxnrYfgbTXlHaPycnrPT09kVVyjkq7X121atVS/2vPuczsi5wL0k40JdImVLdzu7SdljJ48ODBS3nNtWUmZVOvXr1Uj0N7Xib/XDo4OKj3888//0RmaNuuS9tgaSOrS9rNCjl2+RykRnsdykg/huTHJO2iY2JiXnpO2gAXLVo0yTy5Hkh7XCkrZ2dngxyT9H2R65ecy3J9a9CgAWrXrq3eXznHsyql43jttddU3xjteyrXeCHtknXJvVb2Sa498trSpUsnOcdcXV1T3Gbya6x85itVqpSk75CUkZzXKeXZl8618lppD21vbw9D30PkGirHI2Ut5470HdDeQ2Sbcg+RTr7ae4hcm4W0uZ4yZYp6z6RdvFzHy5Qpo9f1MPn1THuu/Pvvv+l+9uW9lL4g0oZd+s/J6+UYZPvafUjtvRTDhw/Hb7/9ZvCUw4bAQDyPePbsGf755x/1wZATLnlnCulwIs9LAKi9uaRGOsPpw87O7qV52gtAdHR0qstJT2+5qKXU2UlkJBm/dHqUbciUVq9+WZd82PTZZlbLSPZNXpdS+ci6k8/P6fckM+Wf0oVdbjjadcgxSy9+JycnGJp23andXCSoSR5wvfHGG+oYpZOQ3LR+//13lChRQnXQM/S+6XMe5tT6S5YsmeLr5At78vPN1PTF5Tx5+crNTF6rew5qgzYJTmVKbV+ySs5j2b4ubWWC9pzLzL5IakFzc/MUX5vS+SVlI186ky+jLbP0Pp8SrEoZSrmndN5m9jqgPfa08q2n9z5o07ydPn36pXtHWhYvXqy+tKcUVBcrVuyledovNyl1VM/sMUklgKTAXLNmjerE/N1336kvaBIoS2fZrFZ2pHQdlcBYJu11VPt/SueN9r1Nfh9M7XOZkWus9vjlcXrXgqwE4hm5h0jHVeksn9p7qnvuSSIAbSY3CWjl/ZUvOZIsILUKg+SSl5v2XPH09Ez1i792H+SzK53DZZ+lQmrt2rWq86980Z87d676UpCZ9zK51D6/+t7D9cFAPI+Qb6TyRss30dQ+nJJfUxuIa08q+easm+pHeuNLjYU+OTjlAyW9xJPPS++CI9kPpNbi448/VrVc8sGXmgzJgf7ee+8lyWihPbmTZ7mQ18s25IMjNZ+p0R6vPtvMahnJeuVCIz3g5aKpG1BIthL58qS7jpx+T/Qpi4yS5SXQlVpKuUhmplYqrfdabvBSAyOBjW5QJDXBUpuR/HyT2iVZRjLSyK8AEpBLzYw2gDIUfc/D1BjqPM9u7u7u6v+JEyeqgUQyeiNP6XizmrnGUPuSneQzIccpNXjJfymSDDW6dK8DySXP3KA9dsl0UqpUqRS3Lb+KpkUyOclnQnKFS7CU0S/R2l8DDE3fY5L9lfdeJiHX2+bNm6vyluwkqX2mMiKlwVrkOiMZerTXGu3/khUjeTYW+XKj+xpDkfuDfDFM65eUtH51yAi5X0jWnOTzdI9HgmjZD8n+ItdX7T3k+PHjKpNL8jKvWbOmmoTcEyWDidSyy3suQXpmz5X3338fr776aoqv0T2f5bovXxxkEn5+fiozilTMyC+5uu+lbssCfd5L+fxm5LNrSExfmEfIzVkCk4MHD6qUQ8knaSogQYj252Xtheynn35K/KYmPytJOh99L1jyE6JsQ0u+dcp6JQhL68Ml6ZvKly+vfq6Sm4FcPOUCI0P1plabktK3XvkQSVolGdpXfpbUpqiSG54Eg7Jv2sBLn20aooykhknSa3344YeJtQbaGpvs2J4+74k+ZaEPSTMnFyJJfycXOi2prZQUhulJ672Wn6ClaYnss/YncanxkJ87JV1a8huh1CRJ+cmvQTLSmjZ1YXbQ5zxMjaHO8+wmP+nKDWnjxo0qKNFNPyhf6uTLkrxP6ZHjlcoD+cUut/clO2lrmt96663EfZHPtHxOJc2oLvnyLp9TqeXVbQ4kNdDJU59pf9mRL5oStOoee/HixVWZpPclRAIo+cxKyjZpRpd8f4QEVpLOMSfoc0wSaB84cCDJ9VGek+Bbe/2TwFCCxcw0lbpy5YpKzaetjZbrmlxrhPZao23iJSnrdEfilBpXSdkov74YsrmjtoykNleaZMg5rnstkM+AvIdZbYYqtcS654Jcd2SelKU2JaTcQ+S+Jak4tfcQaYaZPCWgXKMlBeS9e/cS50nFlPxCJO+djESbGZKm1NHRUZW1vOe654rkFJeAWptCUu5r8sVFN4WufM7k1w25Rsg1VPZfju/nn39WqSG15HmpsBLppb6U8pCKKInFdIP4b7/9FtnG4K3OSW+SEUDbazg1kjZKXiMdS7Sd7KTTmswrWrSoyqYhnQolVZM81qdjoPRQlw6hsqz0jNamcdJN8ZRS5zbpraztiVy3bl3V+1o6OUlnv+SdGqRnurYnt3TYk05CkpFEm7pMsnzI89KrXjrISOosbfor3U4n+mzTEGUkPba16f6kA5NkSZBe99KhQzrX6XbWzOn3RJ+y0K5XMq0kJ8cgGQC0pPOc7K+8XjpWStYBbaaLjBxDWu+1dGTTvq+y31JG2vRl0rFKm2FEl3SUko6cqXVi1ZIONh06dNBkRErnsz7nYWaOXZ/1p/V+adP3pdZRNHlKRiH7kzy9nWRi0ZardA6rU6eOep+1KTGlg1V6tCn9JF2YZGeR49V28EptP6Wjoiwj2Ucysy+prVfbkW7ixIkvPSfnjWSCSE62K8skT9WWvLOmdGiTznbyWulcKJkZtJ0069ev/1InbW2aRPn8yzkunyf5DGvXoZu+UDr3yTx5Xj7r8lnWrlum5BldUiLZdHRTu0nnQFmPZOXQXr9SKjN9ylA6qup2Fk9LRo9J2/FWPgNybZXPhPY80M0iJOeVzJNO7/J3ep9z7XHIdmUfJCuTfNa0ZSHviaSmFdLhvUWLFmq+dAyuUqWK6vCr3VfJ4pKR8tF2SEwp5aRcN6XDsJZ09NSm/5RzRLYpx6+9FiTvLNi1a1dN27Zt0y133f1I7R6i+7l77bXXktxD5Fqvew/Rfu60x639fMprJYOOdp5kjsnIPqVUNn/+L/2m9hyVz750DNWeB9rPpvZaI++RnNeS8lVbXrrZxLSZ5mSS9ch9UbsuyVClK6XOmtpEDLKM3Be1ZSeJBLKrsyYD8TxAm1onpUwLWiEhIepGIiegNvWQZE3QBkwyyQf55s2bemfokLRAklJI+0GV4EsyMOhm5EgpcJGMBtrUQ9oPiOTU1aYZSn7CStYG3ZyluvmVJfiTfdDNmSz7IzmnJVVSZreZ1TISsm7di45c2M6ePftSHvGcfk/0KQt9AnFx584dzSuvvJIkt64cb/KAJTVpvdeS3SF5PlgJZpJnrtDVvXv3VINMLclCIDfQrOQRz+h5mNljz+j6cyIQ156vcuPTfS/ki5FkGEgp+09ykjUkeZ795HnEMxKI67MvuRGIa79ISQCo3TcJAiRvuxxH8kBcsmFIZgzta+VLpqQCTCmPuAT5UsEiwbPuscvnTdJTppQZKSWSOUKCEN0gUhtQyHVi1apVORaIZ/SYJDWinPu61xl5zyWNoGT00JIsK7qBfEbziMtxSJpK3Vzl8r4kP7flPJbsM7rjMkjwrhuEGzIQ116/JTVp8muBZE1JHgtIWlK5r2SEdj8ky4gE2rr3EMlSo3s+yTktAb52+3L8Eo/I+6IbiMsycq7r5k6XSeKRjASmaZWNkPSK2rSD2km+3EvKXG3WG7knyb7p5qeXc1sysehW4Eh89PXXX6vPnPZ18uVZrsO651RqgbgsL1matMG7lIl8sZbrKgPxAuzixYsqVZw2wE6NpPqR3JuSVklL/pZ8qJJTWbu8pK2T16Yn+c1ebg5ykU1pMAFJcSXbTuk5uaDIcgEBAeqx5PPV5jxOTpaX/dPNr5z8ZiLHIzWnUsOcGn22mZUy0r2xyOtlv7QXMtl+SuvIyvakpkSOQ754pfee6FMWyderS/ZLzsGUyPsu685IUKbve+3l5aW+0Ehwmh65WUvNRGqfERkYRM7lefPmZWjf0jqf9TkPU5PV8zyt90uWSelLi7zfqR2TXF+SDyiiS84zWaek6cxo4KdLlpOacN084qntp3w+5HWpnVPp7Utq65XXynqTD04l5LOom4pNSz4zsoz2s5OR8pL9ls+L9r1JKRDXkn2R12pT8ck5n/warrv/krJNPm/ppQhMj5SdnH8y+JW25jcj0ipDfQJxfY9JAiT59VHKPLX9lTSGcq2S9ya9POLJj0M+b/I+JE9Dm5x8dmRfJXVqSmn90iof7Wc2pYG/ZL9TKzc5N+RaINtM6VogFTmppcPMSNArnyc5F9K6h2jvM9pUlnJua/N8p3Sc8tpHjx6lG7NkpGx0yTrlsy2fpdTWLe+LnFNSpildH7XkMyb3BXnfU0uxKNcS3TS/uuR8lee099G0YoysYo14IZZWrRtRXiE1pcnziScntTVS46RP0EFkCGkF4gVJZgJxyjrJyy7NtCQfeUakV/tMeQ87axJRniR58yW3s+Rplo7Mkjs2NdLjXjrXpJbSjogoP5KOuIcPH1adEqlgYvpCIsqTJFuN9F6X7AHz5s1LTHWVknLlyuXovhER5YT00ldS/mck1eK5vROUOySVkwQ7kiYopYEqiHKTpMqS1FUSZGc1py5RdpEB12SSX28K8i8yMm6CpPeTdHuGGPWSsve+Lnniczv/PmUMA3EiIiIiolzANuJERERERIU5EL9x44YalltGWJPR5eSnlcyQ4VZleRmyNfnIUIsWLVIjL8lITjIi4ZtvvpniiHAy3PbkyZPVsMYyJLUMNS77R0RERERU4DprDhkyBK+99hpmzJihhhHOTNN1GVJYhlqV3sXa4ch1hxf+4osv1BCvkmFBhuuWobNbt26NixcvJumR/Prrr6shUWWI1GLFimHatGlq6ODr16/Dyckpw/sjQ7HKELuurq45NnQ1EREREeWOuLg41Va/Zs2asLS0TH8BTR6jHfFORlHShySCl9GnJOewjLolI5jpWrNmjUrentLQ8roj0WkHBtm+fXviPEkGL0PAzpw5U699kgEkdEeK4sQy4DnAc4DnAM8BngM8B3gOFPxz4HQKg4ilpMBU00rtttR0d+zYMcXnpbY9OVtbW/V/TExM4rx9+/bB2NgY7du3T5xnY2OjmrTIc1Jjn1FSEy5Onz6tmrnkBPklQDJNSJYJExOTHNlmYcRyZhkXBDyPWc4FBc9llnNe8eTJEzRq1CgxBkxPgQjEf/vtN1y6dEk1TdGHNFeRdFNSYFrSNl2ao1hZWSV5bZkyZbBz58401xcSEqImLflpQhQtWjRHA3HJu+zi4sJAnOWcr/FcZhkXFDyXWcYFBc/l9GmbRme0SXK+D8QlcH7nnXewcuVKODg4ZHi5LVu2YOHChfjss89QvHjxxPkREREptumRwFw6caZF2p9LO/TkpIY6p0bFSkhIQHBwsPpbavaJ5Zxf8VxmGRcUPJdZxgUFz+X0Scynj3wfiI8fPx7dunVTzVIy6ujRoxg8eLCaPv300yTPyUAF0skyOcm6kt4gBtKpU3cYbu3PE9JMJKM/URjqmxhrxFnO+R3PZZZxQcFzmWVcUPBcTl90dDQKVSDu6emJQ4cOJfkJQE6U2bNnY86cOXj06JFqaqJ17tw5dO/eXaUkXL58OYyMjF4aTlZSGkowrlsz7uXlle5QszKKVUojWUlb7Zxsry014Tm9zcKI5cwyLgh4HrOcCwqeyyznvEDf2KtANE1JnupQaoOlpnzmzJlJAnRJP9ipUye0bNkSa9euTbH9jnTSlEBegvsuXbok1oYfO3ZM1XgTERFlJ+lrJE0Mk6fhpdRJHCAVaHK/Tl7BRobDcv7/YFvGmUmp8lVf+a4RsQTP77//fpLCkHm6k5APom6gfe/ePZVRpW7dutiwYYPqpJmS2rVro2fPnqrduQT5YWFhKq+5dIB84403cuAIiYioMAfh8ktuSk0kKXVyz5e+WAzCsxfL+QX5fMrnVDdBR2blmRpxqYn+999/E2u3q1Spov6fPn06vvvuu8TXSQ1BZmoJ/vjjDzx+/BhPnz5NTFuo28lSRtLUko6fUvtdv3599e26SZMmOHDgQI618yYiosJJasKlEqlcuXJsXqgHiR1kIBUpOwbj2Yfl/ILEoVLBK5/XrNaK55lAfO/evSmOppk880dsbGy62UCkx2ryD6JkM5EMKRlpz1OkSBH8/vvvaiIiIsrp9HDs40OUd8nnUz6nhmg+lmcC8YxedDKSlzGldUnwznR+RERERJRX5Ls24kRERESpkba70s8rrXb2kg/7vffe0zvVXE6SpBEy8GBGSFtlSVKRXx3S41hzijRJ3rx5c7Zvh4E4ERFRARARE4fVp7zQ/7fjaPfDYfW/PJb5hYX06xoyZAh69+6d4uB8WitWrFCpinNqsL3MuHbtGg4ePJih18pghEuXLkVOOHz4sMGD5msZPNb9+/fnWMAuyTukn2J6gzlmFQPxAih62zYEb94MTWxsbu8KERHlgLu+YWj/w7+YsfkKzj4MxD3fcPW/PJb58nxh8PDhQ/zwww9o3rx5mq+T14wbNy7H9qsgKVq0KCpWrJgr27569WqGv5xklaTCbtq0KVatWpWt28kzbcTJMBLCwxH5+xJEhIbCf+FCOI8aDYd+fWGcRs0AERHlX1LjPXTJKTwLedEUQ5v3QPu/zJfnD0xvDWvzrN32vb29sWDBAlXrvGnTJsTExODNN99Utc+LFi1CUFAQhg0bpmoTdZMs/PXXXyqIKl++PMaOHZtYE71jxw4VWDk5OeH1119HqVKlcOPGDaxfvz7JyNeffPIJRowYgQoVKiTuw6hRo7Bu3ToUL15crfPZs2f4559/1KjWMgif1IqnRMYUkSxqzZo1S5x35swZtf+S6EH24bXXXkvM3ibJJKS5i7u7O/bs2aMyqE2cOBE2NjYZel69B8+eqVp42a6MZaLdt7S2m54LFy7g77//hqOjoxqkMLnUtqndXyk3KfvSpUurLyXatM7yvkonxP79+6vHgYGBmDFjBn799Vf1WH5JkIwh7dq1U017/vzzT1WjLfs9evToFNNDp7dNXamViWxTjle2L6OYS6D87bffZrp80ztO0aNHD1UDn51f2lgjXsDEh4bCtFYt9Xfc4yd49vXX8GzfAX6Lf1fPERFR/hETl4D7fuFpTkuO3seT4CgkvJx4TJH58vzS/+6nuR7ZVnokK9nPP/+sAhMHBwcV1MoYHTL+hgQ7kv2sdevWCAgIUK+XQKdt27YqYC5Tpoxqdyuvl9fJmB4TJkxQo19LsC7rkBSEErBJkKRLAnNJP6y7D8OHD1fpiKV29v79+2jUqBHu3LmjAuLPP/9cZUtLycmTJ1GnTp0k85ydnVWq4saNG6vxQyRIl3WJy5cv44MPPlDBv5ubG7Zt26a+bGil97zsm4xhktK+pbXdtJw9e1aVs5SvtIXv06dPkufT2qbsr4zHIqOPlyhRQgWwffv2TVz29OnTOHXqVOJjaZohKaC15D2XNt1iypQp6kuWfEGSL1ASiKckvW3qSq1MJKOdBPDa5+X4slK+6R2nqFevnjpfpE9BdmGNeAFjVrw4bGd+DbugIAQuXYaQHTsQ7+8P37lz4f/773AcMhjOo0fDpEiR3N5VIiJKx6OgSLSdc9gg5fTD3ttqSs2hd9qgrMv/1+KmRmpBt2zZogIqCcglj7KMVq2tWZSRqI8cOYJXX31VzZcARx5L5jIZs0OCYKkVlWBSasGl06SQmvWM5gCXtuBSO1q2bFn1eOTIkRgwYADmzZun1iE1nxKgS/CXvK241JpK8wpdkrddJi2pqZUUxrNnz1aPpSZXjlnW3b17d9SoUUN9mdDub1rPf/nll2p/ZMwSobtv6W03NfK8DDYoI4gL+QKg21kzrW0K+UVi9+7dKgWf1C5LAHv+/HkVeOpD3kNp5iNfCoT8GpGajG6zXBplIkG1kOUzcqyZLV8t+ZIo55rUlktQnx0YiBdQFhUrotT3s+H61iT4L1mq2ownhIYicNVqOOucwERERPqQ4ESCcCHNL6SmUrcpigSlUmstzp07l9h8RQJTmSQwl1pVad7Sr18/+Pn5qWYO0rwio6mMpfmHNgjXbke2KzXsQrYjtZhSW1q1atWX0iBLzbsuqVmWQFpqP6V5jdSaStMHLTk+bdAtTRykFlo6SGqbn6T1vOyblJfsm7YMtPtWqVKlNLebGmnmo1v7rA2EdcsjtW0KCWglIBbyRUpqlKV5ib6BuHyxki8A8j7KLx8ypSaj24xP571ILjvKV0t7nmQkdXZmMRAv4Mw9PFDiyy/gMnEiApYvh4mDA0x0RhYNP3ECZiVKwLxMmVzdTyIielkpBytVU52WKWsu4Mrj4MQ24SmRGLFmKXv89NqLn/NT21ZGpDQmR/J52gH6JICRALlBgwaJz0kTEplq1qypAjFpHiBtqyVDxfHjx9W6kg/wlzzNYPK2xbIdqQWV2nZtQCzbSGlEbAngpS25ro8//hg7d+7E4MGD1XqkqYy2KUxqx6y7j2k9L/smAaHulxXtvqW33dTI8euWSfLySWubKb1eHmvLNHn5p5XiUZoHyS8fR48exbJly/DVV1+pZisp/bKR1jZ16VsmmS3fjBynNJOSNvj29vbILgzECwmzYkVR7P0XP/9paWJi8HjGR4h79gx2nTvDefw4WFaunGv7SERESZmbGqfbXOS1Rh64vPlKmq+ReGNQI48MNT0xJKnpllzM0lxA2nNra3OlRlQCNslKIRlOZJJgXAJxCdAl+4nUKFtbW6tgXTpfpkVqYiXAkiYL2iBQArCUaj9btWqlOndKUKatoZWUfDL6trattTw2ZBlIZ0Ld5hTafcvsdqV2WdrYS7t6Ic10MrpN8e+//8LX11cFq3fv3sXFixfRsGFD9ZzULu/atStxOd2/k5PnunTpgm7duqlOkhKwSjMO6XybXFrb1JVWmcg5JOeFIco3I8cpXxKT/9pgaAzEC7HoBw+giYuVkQ0QsnOnmmzbtFEBufX/OkEQEVHe9mrdklhw8I7KjpJSh01jI6CYnSV61SmZ4/smzU0k80TlypVVoCYZL4KDg1WNtI+Pjwq6pYmCNE+R59q0aaPab8s8qdWUttYStKXXPlcyrEgwKLWisox0HJRa0q5du770WgnA5AuAtFeWfRPyvzRtkE6it27dUs1ptM1vskq7b7Vq1Xpp3zK7XcnuIeUpXyokONV2js3INrVtymV5KS/5QjR16tTEttTS1l/aXb/yyiuqxlrer9Rs3bpVtfGX9Uh7bzmelILw9LapK60ykc6WspzUcHt4eKisKZkt34wc58aNG7N9oCQjTfLff8hg5CIjnREk1ZKcgDlB2lZpv3FmpK1dQnQ0gjdtUu3IYx89Spxv3agRXCaMh3XTphnuPJNdabm2XHiMzRd84B8eA2cbc/Su66ZuPFlNw5WT5Uws47yI53HeK+cHDx6o/yXDiD4kT7ikKJTsKHLJlju79v8S9pZYOaYxyrv+f7PEzJKAT2quBw0alDhPMmD06tVL1XJrB12Re58E31oSBF26dEm1L5dgSlsTLbXY0qxB2lJLzaa2Y6UETPv27VN/S7Ap25QgTpZPaR8klJEabmkvLLXp1apVU4FZaqRmdNasWSqtntaJEydU+UswJzXxnp6e6NSpE65cuaJqeWU/tO+nZNeQjqbSLCK957X7J7Wrsv7k+5badqUdvdT0ptbuWto8S0ArTSeknbXUkEtKR90ySWmbkrlEfpX4+uuvVdtpyUSSvGZavhRJDbY0K5LmPhKQyvHIOiUDivQBkPdLyH5K7bacs7opIXWlt83ryY41tTIR0s5bMp5I2Q4cODDT5ZvWcYrbt2+rYF2+YKT0uU3ts6pv7MdAvJAH4loy+I/UiEuaw5i7d9U8I3NzVDh8CKapfLvNbjl1Y8kMBjAs44KA53HBCcS1FRdbLz7GlguP4BsWDVdbC7xat5SqCc/NioucIIGYdKyT4CyjlUfSnEPaN+fl0TWzgzYoXr58eY6Uc1a3mVvky4W0I0/tC52hAvGC/cmkDDMyM4O91Gj06IHQAwfg/9siWNWulSQIj/F5pNqay2sL0gAVREQFgVwLpR24TJQ+bW0qUUqS55rPLoxgKAkjY2PYdeyIIh06QKPTg1iTkACfNyYgISISzmPHwL53bxhnYy2CNEeRmvDUaAeokNof3nSIiIgyRpplSPv7gr7N/IKBOKVIfnIy0hkEIfLiJUTf8VR/P/38C/j+8gucXx8Jh4EDYWJr+F740iZc2wwlNfK8/ATLQJyIiChjpINsYdhmfsEh7ilDrOvVRdktm2HXtYuKgON9/fD8++/h2b49fBf8jLjAQIOWpHTMTK8bsTwv7SCJiIiI8iMG4pRhllWqoNTcuSi3cwfs+/UFzMyQEBwMv19+wd2OryA+JMRgpSnZUdLrByLPS2ckIiIiovyIgTjpzaJsWZT8+mtU2LsHjsOHqSYstq1aweR/qauEJtnwwfqSFIUZqREvXzR3sqYQERERZRUDcco0sxIlUHzGDFQ4eABF330nyXNeo0bj0XvvIfrOnUytW/KES4pCGYgiLatPeeGjzVcQFRufqe0QERER5RYG4pRlkuJQgnKtiLNnEXH6NEK2bce9Hj3hPWkSIq+kPfxySmm4JE+4jAYntM1UtP8XLWKB6iVf1MCvOuWFV385Bs/nYXw3iYiyWVRUFJYuXYovvvhCDYhCRJnHrClkcJbVq6PYRx/Bf9kyxD15grD9B9Rk06wpnMeNh3XjRhkaCEAG65E84akNUGFmYox5+25j4eG7uPk0FD0W/IevXq2BfvVzZvAkIqLCaOTIkWpkRe0oijLM+JgxY+Di4qICcxm0RYY9T4uMsCgDw4jXXnsNVapUydC2Hz9+jMWLF6Nz585o0qRJ4nwZnnzLli1q1E3ZL93ntHbu3KlGhZQRP2Ugn5waNVqf7Wa2XLKTn58fli1blu57SpnDGnEyOGMrKzgNG4oKe3ajxMyvYf6/UafCj5+A1+uv4+GgwUiIiNBrgIq/xzfFwelt1P/yWOZLIP5e5yr4a1QjuNiaIzI2Hu+sv4Rpf19EeHTW2qgTEVHKDhw4gIULF+Lzzz9H0aJFkzwngfjs2bMzXHTz58/HzZs3M/z6t956C3PnzlXDpGudPXtW5aiW4eplePvu3bvjk08+SbLctGnT8MYbb+DJkycqoNQdCj47ZXa7+pYL5V+sEadsY2RuDoe+fWH/6qsI3bcPfosWI/rGDRhbW6vJUFpVcsXOKS3x9t8XcczTH5suPMJF7yAsGFwX1UvaG2w7RESFnQTfUussgbidTgd9rSVLliAiIkK9TkyePBlOOiM0a3388cfq/5UrV2Z429u3b0d8fDzq1auXZL6joyOOHTsGBwcHNfR679698corr6hg3NzcHF5eXiqwlSHWpYb53XffRdmyZVWQnJH81lLD365dO3h46DdiaWa2q0+5PH36FKtXr8aQIUNU2UhNuowWKuWRkeXktVJbHxMTo9YhZbVu3ToEBQWhb9++apj2lJaVfRs2bBj++ecfteyAAQPUryGUOawRp2xnZGICu86dUXbTRrgvXgTXt99O8vzTmbMQuG4dEmJiMr2NokUs8deoxnjnlUqqg+c9v3D0Xngcf514AE166VeIiPK4mAcP0pzig4KSvt7nUZqvj/P1Ndi+SdMUab6QncLCwlSN8k8//fTSc+XLl08SCEogKtf9hIQE9fjIkSOoVKlSYjMPNzc3NG7cGAcPHszQtiUQl6BaX1ndbnokKP7ss89UM51r166pILpt27bp3vO0y3Xt2lXVuktgLSNfdunSBadOncKJEyfULwzh4eHq9fLean/lkGW//PJL9OjRA9evX8e2bdvQtGlTxMbGGuSYCiPWiFOOkXZxkuZQV9St2whcsUL97ffzL3AaNRKOAwZkqsbcxNgIk9pVRONyzpi85gKeBEfh063XcMzTD7P71oa9tZnBjoWIKCfd7dwlzeddp06By4QJiY+9Ro9C7MPUg0f5pbLkt9/ovR9S0y2Bt9TqSmApfvzxx8Tnpa24BHbaGnFDkdptqYUtXbp0uq+V/evXrx8s/zc6tLQrL6GTUECULFlSzc9O2bFdKVdp3qKtnZcvKCtWrECNGjVUMCzrv3jxIurWrZvmeiTI3rRpk/oSExgYCGdnZ9UBV9r/izp16qgvDBJwp7Ss1KhXrFhR/UIh74k0D5KAnPTHQJxylZG5GYq88opquhL3/Dmef/sd/H9bBKcRw+E4eDBM7PVvWtKwjBN2Tm6Jdzdcwv4bz7Hn2jNcfXQU8wfVRf3Saf9kR0REecu5c+dU++8LFy6k+1rJ5CIdI48ePZo4T2qI9emYKTXpUuur9eDBA9VZcf/+/epxmzZt1JTc2rVrE9t1d+jQQe/tZoQcn6xbG4jLLwEShAszMzNUqFABjx49SjcQl7b9EoRrf0EoUqRIkkBaguvUMuLIsrIdYWJikuZrKX0MxCnXBwdym/8Tou/ehf/vSxAsbQCDguD703z4L1kKx8GD4PLWWzA2N9drvY425vh9eAMsO/YA3+66gUdBkRiw6ATe7VQZ41qWg3F6CcqJiPKQ8rt3pfm8iYNDksceS5cBcak3FzC2sUF+Ic0iypQpg1mzZiUGxrt370bx4sVVZhHd161atQr//vtvknbppUqVeqkWWh43b948W/c7O7YrTUp026pbWCQdXVoCY23WlbRIW3pd8oVBd548Tq2JS0rLsglo5jEQpzzBonx59TOpy6RJCFi2DEEbNiAhPFxlWnGdNi1T65SLw+gWZdGwjCPeWnMBD/0j8O2umzh+1x9zB9SGi23SCxgRUV6lzT6V4de7lUJusLKyQnR0dJbXo9sEQzpfppdBZN68eaqj6OHDh1XzDF2tWrXC66+/rtYh7bV9fHxUW+hff/01xXUZGxsnaVoj65R9adGiRZr7oPulQMi+p7fd5E1N0mPoJj+U+xiIU54iN4/in34ClzcmIOCvv2BVr16Sn/aCNm6EVd26sChXLsPrrOXmgH/eaoEZm69i+6XHOHLbF11+OoqfBtZBswrs6U1EZCiSacPa2joxuEwta4rkApfaYcnAIk06pF2zBK1S8528CUbyAFcCY+mgqJ2/a9cuTJ8+HUOHDlVNSLT3jEmTJqmmG7IOSXsoHRIlj7dkCpHXZiRjSlZkZLvJm5qkVy5U8DAQpzzJ1NUVRadPTzIv9vFjPPnscyA+XrUrdx43FlbVq2dofUUszTD/tTpoXt4Zn2+/Bt/QaAxZegpvta2Aye0rwtSECYSIiDJCUuzppi784IMPErOWSAq848ePq3R6kgYvPRKoZ6QJhi4JTHUHunF1dcWnn36amCUltRpzCXil/fh3332natkzSranb+rCjG43teNMrVx0SdMc6TSrr5SWk/dQ9wuTfMmRjC9C3lvtYD6y7JQpU5IsK1+68sLAQ/mVkSaPNOyRNk3ybVF6W0ujf2nnJe2r9CW9t2V0rcGDB2PcuHGZ2oYM3/vLL7+oAQMkR6Z8iCZMmKA6QuhDfoaS2gFvb+/E3uXZTXow+/r6qguTtBUrSMJPnsLj995TnTq1bFq2hMv4cbBu0CDD67n9LBQTV53Hnedh6nGjMk74aVAdlLC3yvA6CnI55xUsY5ZxYTyXpf2zYA2ofiSUkXu8tF/OqREz8yJpPvPOO++oGvjswHJO/7Oqb+yXZ2rE5ZuX9PyVnV+/fj0iIyP1Xoekz5GezpJaJ6XhbTOyDWnbJj2H5cL50UcfqW/YX331leoYsmPHjkwfH2WdTZPGKL9/H4K3bFEdOWO9vBB+9KiarOrXh8uE8bBp0SLdi3ClYkWwbVILfLH9Gtae8cbpBwHo+tNRzOlfG+2rFuNbRURE+ZrEQzLgTnJSuy1NdijvyDO/x0sHBkkML8noM0NqsYcPH66CZuksktltSPusK1euqJ/VZNSpQYMGqWWkDdrWrVsztW9kOJI9RfKMl9+5AyXnzIHF/346izx3Dk+/+lo1W8kIK3MTfNu3Fn56rQ5sLUwRGBGL0X+exdf/XEdMXOo/bxIREeVVbCaS/+SZGnH5yS4rPvzwQ5WQ/s0331Q12ZndhuQplfZauoMGSL7MYsWKqeT3vXr1ytJ+kmEYmZrCvns32HXtgrDD/8Jv0W9w6NtXzdeKvHIVllUqwyiNJkW96pRCbTcHTFpzHlcfhWDJf/dx5kEAFgyqBw9n/QcVIiIiys1AXKuBHk02KffkmUA8K6QHtdRkSxCd1bZhktheOpjoJuKXZiohISFqCNm0yGtk0nry5Eni8jLlBNmONKfJqe3lBdatW8G9VUtpvJZ43JKL/OHw4Sq3ruPIkbDv2wfG/xtlLTl3R0usG9cEs/fcwvLjD3HJJxhd5x/FrN7V0a1m0lHRCnM55zSWMcu4MJ7L2ntPHum+lW9IeWknYjnnFDnfkn+u9Y0L8n0gLoGv9GiWHtPaHr5ZIT2apZfz/PnzE3sGz5kzBxEREQgODk5z2blz56pURMn5+/u/lHQ/u8jFXrufkgu1sIrZvx+ayEjERUbCd9Ys+P36Kyz79YNFr54wsrVNcZkJjVxQzdkUX+99gJDoOExeewkHrz7C1DbusDRNWpYs5+zHMmYZF8ZzWfopSSAuiQIK8zU8KwFRYe6smd1Yzv//mZbPqpSHdMROHvMVqkD87bffVp0PpJewoXoc//zzzypVz2+//aYK297eXrUr9/PzS3NZSQc0ZsyYJDXijRo1Uk1mstr0JqO0FyIpk0KdzWPQIEQ3aICAJUsQunMXNIGBiPz9d0SvXQuHQYPgMGwoTFPIbdvX1RVNq7hh6rpLOPcwCFuu+uG6b5RKfVix6P8H8Czn7McyZhkXxnPZ0tJS3Tu8vLz0ztRVmGlrwyUIZyDOcs5usbGxKj4sUaIEihQpkuQ5fQe0yveB+IEDB1Te0vbt2yfOCwsLw+rVq1X6QWnXndJgAmmRduYjR47E7du3VY2EZFpp1qxZujXukldVN7eqllx4czIoln3O6W3mRdZVqsB6zhzETJmisqwEb9qEhNBQBCxejNCdO1F+7x4YpVDj5O5si7/HNcWP++/gl8OeuP0sDL0XnsAXPaujfwO3xIs8yzn7sYxZxoXtXHZwcFCvlRp0Nn3TjwRA8kWGshfLGeo8k0ra1GK+QhWIy8hTkjFFV/fu3VXNtuQRt02lGUJ6JPNK7dq11d+PHj3CmTNnVIBO+Y+5uztKfPE5XN58EwHLlyPw77/hMHBAkiA8ITwcxjY2iY9lgJ93OlVGk3LOmPr3RfiFReO9jZdx7K4fZvauCStT/vRJRNkjtUodSh3HHcgZLGfDy3cN0Nq0aYNff/018bHkC5d5upMk9JfMJ/K31JbrS9avHaFL2qBL7Xi9evVUKkPKv8yKFUWx999DhQP74TR4cOL8hMhIeHbujEfTpiPq1q0ky7So6IJdU1qiZcUXo8ZtvfgY3ecfxdVHafcXICIiIso3gfjUqVNV4CzDvYohQ4a8FHSLf//9F3fv3s3Wbdy/f1+NuClBvgz+Iz9ByIicEuBT/mfq6Jik9lsGCIr39UPIzp243+tVeE94AxEXLiQ+71rEAn+ObIT3OleGibERHvhHoP+ik1h38Tl76BMREVGm5ZnIUjKfSNrA5CQQ1nXo0KGX5iUno0mVLFky09uYPXu2yksubcSlZl0a41PBZd+nj/pfjdb56BHCDh9Wk7V0tB0/DjbNmsHY2AhvtqmARmWcMHnNBTwOjsLcw9648iwa3/evDQdr/X95ISIiosLNSMOkm9nGx8dHBfne3t5wc3NDTmD7rczTxMaqWnG/xb8jRudXF+smTeDxx7LETppBETF4Z/0l7L/xXD0u5WCF+YPqoH5p/ToFU9p4Lmc/lnHOYDmzjAsKnsuGj/3yTNMUotwmI3Da9+qFctu3odSC+bCsXl3Nt6pRPUk6LKn9/m1IXUxr4w5zEyM8CorEgEUn8cshTyQkcDAJIiIiymdNU4jyCsmmYtexI4p06IDw48dhqZO2UhMXB6+xY2HbsSP6N2+B1tXcMOXvS6rd+Pd7buHkPX/MHVBHtSsnIiIiSgtrxIlSIbXgts2bw1RnMKaQXbsQceIknn/5FYIHDULJvZuwbXQ99Krzok/C0Tt+6PLTUfx3J+3Bn4iIiIgYiBPpwbJKFdh17Sqjc0ATEAC/OT/gSZdO+Mj3P/zQqQwszYxVzvFhy05hzp5biIt/kQaTiIiIKDkG4kR6sKhYEaXm/oAy/2yHebdugKkpEoKD4f/LQlSfPhxbzC+jcrEi0GiAnw95YtDvJ/E4KJJlTERERC9hIE6UCealS8Pm3XdQds9uOI0YDiNLS2giImAXHYqtk5pjUCMP9bozDwLRdf5R7Lv+jOVMRERESTAQJ8oCs+LFUezDD1Hh4AE4TxgPlzFjYGlmgm/61MTPg+pg3K3dsH/qhbF/ncUX268hOi6e5U1EREQKs6YQGYCpkxOKTp2aZF6b4Lsof2M/et/Yj+MlauDvwHbo9yAQCwbVRRmX/x/Zk4iIiAonBuJE2UQTEwPTEiUQ9+QJmj25qqbz1yvi/WuvYMiE3uhZpxTLnoiIqBBj0xSibCJ5yCvs2Y0Ss2bBvEwZNa+e7x18fvgXxL8xCj9//QciY9hUhYiIqLBiIE6UjYzMzeHQpzfK7fgHpX6cB5NKldX8KoFesDywE71++Q+3n4XyPSAiIiqEGIgT5QAjExPYde6Mils3o+RvvyGgXFWsq9wOt5+FoefP/2HtaS+EHDiAhJgYvh9ERESFBANxohwerdO+TWs037kJn7/TH65FLBAVm4A/lvyDRxMn4U77jvBfvhwJERF8X4iIiAo4BuJEuaRZBRfsmtISrSq5oob/PSTACAm+z/H82+/g2a49/H79FfHBwXx/iIiICigG4kS5yMXWAstfb4iKk9/Amx3fxV6PBogzMkZ8UBB8f5qvAvLnP/yAOD8/vk9EREQFDNMXEuUyY2MjTGhdHg3LOGHymtJY9fgV9L3zL7p4n4ZZeDj8f1+CqGvX4bFsaW7vKhERERkQa8SJ8oj6pR2xc3JL1GtYDb/W7o3hHWZgR42O0Fhbw2nkyCSvjX3+PNf2k4iIiAyDgThRHmJvbYZfh9bDV72qI8LGHj9X6ISB7WdgeUxRxCdo1Gui792HZ9t28JkyFZHXruX2LhMREVEmMRAnyoOZVYY1LYPNE5uhnIsNQk0sMWffHQxfdgrPQ6MQuHYNEB+P0D178KBvP3iNGYuIM2dye7eJiIhITwzEifKo6iXtsf2tFuhTt5R6fMzTH11/Ooo7r45A8a++hJmHh5of/t9/eDhsOB4MGYqwI0eg0byoOSciIqK8jYE4UR5mY2GKuQPrYE7/2rAyM4FfWAyGr7iI34vUhMf27Sj5wxxYVKqkXht57hy8x43H43feze3dJiIiogxgIE6UD/Sr76Zqx6sULwKp8F54+C4GLTuLsObtUHbLZrgtXAjL2rXUa23btk2yLGvIiYiI8iYG4kT5RIWittgysTmGNnnRJOXcw0DVVGXvjeco0q4tyqxdi9Ir/oJd505Jsqvc69wFAStWIiEyMhf3noiIiJJjIE6Uj1iameDrV2ti4ZB6KGJhiuDIWIxfcQ6fb7uGmPgEWDdsCCPT/x8eIOCP5Yh5+BDPZs6EZ/sO8Fu0GPGhobl6DERERPQCA3GifKhrzRLYOaUlars7qMfLjz9An4XHcd8vPMnrHPr0hl3PHoCJCeIDAuA7b96L0Tp//BFxAQG5tPdEREQkGIgT5VPuTtZYP74pxrUqpx5fexyC7vOPYsuFR4mvsahYEaVmz0b53bvgMHAgjMzMkBAaCv/fFqmAXGrIiYiIKHcwECfKx8xNjTGja1X8MbIhnGzMER4Tj6l/X8S76y8hIibu/1/n7o4SX3yO8vv3w2nUKBhZW0MTFQVjW5tc3X8iIqLCjIE4UQHQtnJR7JzcEk3KOanH68/5oOfPx3DzaUiS15kVK4pi772LCgf2w3XqVDj07Zv4nLQdf/zBh4i6dSvH95+IiKgwYiBOVEAUt7fEqjFNMLVDRRgbAZ7Pw9Dr52NYfcrrpRSGpo6OcJkwHsaWlonzAlevQfCWLbjf61V4T3gDERcu5MJREBERFR4MxIkKEBNjI0ztUEkF5MXsLBAdl4AZm69g0poLCImKTXNZsxLFYVbqxSieYYcP4+GgwXg4fATC/jvGXOREREQFPRB/9uwZ5s+fj48//hgBmczocPDgQbX83r17s7SN8+fPY8GCBfjuu++wbds2xMfHZ2p/iHJD0/LOqqlKm8qu6vGOy0/Qff5/uOQdlOoy9j17ovye3Sg5+zuYVyiv5kWcPg3vMWPwoF9/hP37b47tPxERUWGQZwLxvn37on79+ti6dStmzpyZqUD8yZMnGDhwIL799lsVkGd2G++++y6aNWuGS5cuwd/fH2+99RYaNmyIsLCwTB0bUW5wtrXAshENMaNrFZgaG8ErIAL9fjuOJUfvpVrDLTnIJSAvt20bSi2YD8saNdT8qGvXEHn1ag4fARERUcGWZwLxUaNG4cGDB3jjjTcyvY4xY8Zg0KBBsLW1zfQ2bt++jTlz5qja8CVLlmD27Nk4fvw4rl+/jp9//jnT+0aUG4yNjTCuVXmsn9AUbo5WiI3X4OsdNzD6z7MICI9JdTkjY2PYdeyIMuvXwX3pEti0agmnIUMSn0+IjkbgunXqfyIiIsrngXi3bt1gqjMioL4WL16sguVZs2ZlaRt3795V/zdp0iRxXqlSpeDh4QFPT89M7x9Rbqrr4Ygdk1uia83i6vHBm8/R9aejOHXPP83ljIyMYNu8OTwWL4aJw4vBg0Tw5i14+uln8OzQAf5LlyI+LOlAQkRERJSPAvGsuHfvHt555x0VjKdWG55RderUgYWFBf7777/EeV5eXnj48GGS4Jwov7G3MsMvg+vh61drqPzjT0OiMOj3k5h/4A7iE1JuqpKaGC8vqW5HvK8fnn8/B57t28N3/gLEBQZm2/4TEREVNJmvgs4jEhIS8Prrr6Nfv37o2LFjltdXokQJ/P3336qduDRJcXR0xK5duzBt2jTVtCUtISEhatJtsy6ko2dOdfaU7UiZsHMpyzk1gxq6oY6bHSavvYR7fuGYu+82Ttz1w9z+tVDU7v/TGabFZfo02PXri4ClyxCydSsSgoPht3Ah/P/4Aw4DB8BxxAiYFi3KczmP4/WC5VxQ8FxmOecV+sZf+T4Q/+GHH1STEclsYgjSie3kyZOIjIxEkSJFYGVlpaaLFy/i+fPnKF78xU/7KZk7dy6++OKLl+ZLh0+pZc8JEoQHBwerv42NC8QPHnlSfi9nF1Ng6cCKmHPIGzuu++PEvQB0nf8fPutUBk3K2GdsJdbWMHlrEuwHDkTUunWI3r4dmshIBC7/ExGhYbB+a1KhLuP8gGXMci4oeC6znPMKifn0YaRJLX1CLtmwYQP69++PO3fuoEKFCum+vly5cqr9dosWLRLnSWdLyY7Stm1bfPDBBy81V0lrGytXrsSwYcNw+fJl1KxZU82Ljo5G7dq11eP169frVSPeqFEj1UHUzc0NOfVNzM/PDy4uLjAxMcmRbRZGBamcN194hE+3XUdEzItv8eNalsW0jhVhZqJf8BsXEICgFSsRvGEDPNb9DbMSJdR8TXw8Yh48gEX5FykRC2MZ51UsY5ZzQcFzmeWcV/j4+KBMmTLw9vbOUOyX72vEpclIUFDQSx3M5MZtaWmp/taH1Hw7ODgkBuFCarOlfbhuu/GU2NnZqSk52ZecDCSk9jCnt1kYFZRy7tfAA3VLO2HS6gu48SQEi4/ex5mHgZj/Wl24O1lneD0mrq4oNu1tFJ00EUbm5onzQ/btx6OpU2Hbvj1cxo+DVa1aha6M8zKWMcu5oOC5zHLOC/S9X+W7QFwG4pHa786dO6vHkya9/PO31IhLHnB5rb6qVaumAvsLFy6gbt26ap40Uzl27BiqV69ugCMgynvKu9pi85vNMGvnDfx14iEueAWh2/yjmN2vFjrXeFGznVG6QbgI3rpV/R924ICabJo1hfO48bBu3EjvL8pEREQFSZ4JxJcuXYr79+/j5s2b6vG8efNUR0ndoFvIQDzTp09PMs+Q2xg+fDg2btyI1q1bq+Yr0qxFOmtGRUWpAJ+ooLI0M8GXvWqgWXlnvLfhMkKi4jBh5XkMb1oaM7pWVc9nhttPPyJ4+z/wX7IEMffvI/z4CTVZ1a4N5/HjYdumtcpbTkREVNjkmUDc3NxcNSWR9IEyaZmZmSV53VdffYWmTZumuS6pCZc24pnZhuQZ37FjB06cOKFG1pQA/Pvvv1eBek51uCTKTVIDXr2kPSavvaBqxqWG/MyDQPwyuC7KueqfHlRqyB369oH9q70Qum8//BYvQvT1G4i8dAk+b74J57FjUHT69Gw5FiIiorwsz3XWLGgN9t3d3TPcYN9QHVZ8fX3h6urKdrUs5yyJjU/AD3tv47d/XwxyZW1uonKQ96mXtXNZLjnh//0Hv0WLEHn2HMr9sx0W/+s0rS5HsbEqeOe5nP1YxjmD5cwyLih4Lhs+9uPvwUSUIsma8kGXKlg+siGcbcxVVpVp6y5h+rpLCI+Oy3SpqdE6W7ZEmZUrkwThIuLUKXh26Aj/5cuREBHBd4aIiAo0BuJElKY2lYti55SWaFrOWT3eeN4HPX7+T2VYySrdIFz4L16MuOfP8fzb73Cv4yuI/OsvxP8vlzgREVFBw0CciNJVzM4SK8c0xrSOlWBsBNzzDUevX45h5cmHL5qTGEixjz+Gfe/e0lkDCUFBiFr2B+516Ijnc+YgzteX7xQRERUoDMSJKENMjI0wuX1FrBnbBMXtLBETl4CPt1zFxNXnERwZa5BStChXDiW/mYUKe3bDYfBg6WENTUQE/JcshWf7Dghc+zffLSIiKjAYiBORXhqXc1ZNVdpXKaoe77zyVOUcv+iddGCtrDArVQpFP5oB+7Vr4DhmNIxtbKCJiYFFpYp8t4iIqMDIciAug99Ifu4PP/xQDQ8vGTuuXLlimL0jojzJycYcS0Y0wMfdqsLMxAg+gZHo9+txLD5yFwkJhmuqYuzkBNe330aFQwdRYuZMWNerl/hc1PXr8Jk8BZFXrxlse0RERPkmEF+3bh3Kli2L999/H6tXr8bhw4dVru5XX30VISFZ78hFRHmXZD8Z07IcNkxoBg8na8QlaDBr502M+vMM/MOiDbotEzs7lYtcl9/i3xG6dy8e9OsHrzFjEXH2rEG3SURElGcD8adPn2LkyJGYNWsWnj17hk8++UTNt7e3R8eOHbFq1SpD7icR5VG13R3wz+QW6FarhHp8+JYvus4/ihN3/bN1u7YtW8DMw0P9LXnJHw4dhgdDhiLsyBGDdiAlIiLKc4H4v//+i5YtW+KNN954aeCYqlWr4to1/lxMVFjYWZrh50F1Mat3TViYGuNZSDSGLDmJH/ffRrwBm6rocujbF+V37kDJH+bAolIlNS/y3Dl4jxuP+336IvzkyWzZLhERUa4H4gkJCamO3BgWFqaGkieiwtVUZXBjD2yd1BwVitpC4u8f999RAfmzkKjs2aapKey7dUPZrVvg9utCWNWureZH37iBhIjIbNkmERFRrgfiDRo0wIEDB3D8+PGXAvTNmzejWbNmhtg/IspnqhS3w7ZJzTGgwYuhfU/eC0CXn47i0K3n2foloEjbtii9dg08/vwTDgMHwrZN68TnY3x8ELBiJRIiGZwTEVHeYZrZBStWrIiBAweiVatW6NWrF+Li4lRb8VdeeUU937NnT0PuJxHlI9bmppjdrzaaV3DBjE1XEBAeg5F/nMG4VuXwziuVYW5qnG0BuU3jRmrS5f/7EgT9/Tf8fv0VTiNGwHHwIJgUKZIt+0BERJRRWbobStrCzz77DOfPn8f27dtx584dlClTBvv27YOpaaZjfCIqIHrVKYV/JrdE9ZJ26vHiI/fQf9EJeAdE5Ng+qI6bCfGAiQniAwLgO28ePNu1x/Mff0RcQECO7QcREZFBA3EJtiVbyv3791WTFH9/fyxZsgSOjo5ZWS0RFSBlXWyw6c1meL1ZGfX4kneQyqqy88qTHNm+1JKX+OorlN+9SzVZMTIzQ0JoKPx/W6QC8qczZyH2Sc7sCxERkS6OrElE2c7C1ASf96yORcPqw97KDKFRcXhz1Xl8tPkKomLjc+QdMHd3R4kvPkf5/fvhNHIkjKytoYmKQuCKFQg/eSpH9oGIiCjTgbiMnOni4pKh6e2339Zn1URUCHSqXhw7p7RE/dIvfjVbdcoLr/5yDJ7Pw3JsH8yKFUWx999DhQP74TJxIiyqVoV9926Jz8cFBiLq5s0c2x8iIiq89GrIXbduXXz88ccZem2NGjUyu09EVICVcrDC2nFNMG/fbfz6713cfBqKHgv+w1ev1kC/+m6IiInDlguPsfm8D56HRKConTV613PDq3VLqk6ghmLq6AjXtybBZdJE1XxFK2D5n/BftAi2rVvDefx4WNera7BtEhER6dLrrla9enU1ERFlhZmJMd7rXAVNyzvj7b8vwi8sBu+sv4Q9V5/gyqNgPA2JhsTG0s/SKygaZx4GYsHBO1g5pjHKu9oatPB1g3Dp2Ckjc4qwf/9Vk3XDhiogt2neLMlriYiIsoptxIko17Ss6KqaqjSv4Kwe77vxXAXhQjtKvfZ/GRRo6JJTqsY8u0igXXb9OpSc/R3MK5RX8yLOnIH3mDF40K8/QvbuhSYhIdu2T0REhUuWAnFJV9i7d2+ULFkSZmZmKouKdho/frzh9pKICqyiRSzx16jGeKVasTRfJyN1PgmOwtaLj7N1f9RonT17oty2bSi1YD4s/9fMLuraNTyaPAVBGzZk6/aJiKjwyHQgHh0djS5duqigWwbxad68Ob799lvUrFlTddYcMWKEYfeUiAosE2MjBEbEIL2GH9IyZMuFRzmyT0bGxrDr2BFl1q+D+9IlsG7cGCb29rDv9v8dOxOiopAQ/aIGn4iIKMcC8ZMnT8LCwgLr1q1DixYtUKFCBbzzzjs4c+YM3N3d8fTp08yumogKIf/wGPyvFUqqpJmKb1jOBr7SXMW2eXOU/nM5yv2zHcY2NonPBa5eA88OHeC/dCniw8JzdL+IiKgQB+IPHz5E/fr11U3K0tISYWEv0o9JDfnAgQNx7NgxQ+4nERVwzjbmqsY7PaGRsbj6KBi5wdTVNfFvTXw8Av76C/G+fnj+/Rx4tm8P3/kLVPpDIiKibA3EY2JiYG5urv4uUaIEbty4kfhcUFCQGmmTiCijetd1S+yYmRbfsBh0X/Afev1yDOvPeufYgEDJGZmYoPTyP+DQvx8go3UGB8Nv4UJ4tu+AZ99+h9hnz3Jlv4iIqJBlTWnWrBl8fHwwatQofPnll/jpp59UcxUiooySPOEl7C1hnEqtuMwvYmmKUo6W6vEl7yC8u+EyGs86gK/+uY57vjk3KJCWeZkyKPHVV6iwby+cRgyHkaUlNBERCFi+HHc7dETo/v05vk9ERFQIAvF27dolZkaxsrLCxo0bceXKFfzxxx+YMmUK+vTpY8j9JKICTgbrkTzhxexeBNraZira/2X+lonNcfTddvhjZEN0qFpUBefBkbFY+t99tPvhX5XecPfVJ4iLz9lf5MyKF0exDz9EhYMH4PzGBBgXKQKYmMCqXr0c3Q8iIspfjDQyggVlC/mVQDquent7w83NLUdKOT4+Hr6+vnB1dYWJiUmObLMwYjlnH8kTLikKZWTNZ8ERKGb/YmTNXnVeHlnzUVAk1pzywtoz3vDT6cRZzM4CrzX0wKBGHihu/yKwz0nxoaGIunIFNs2aJc4L2rxF1ZC7jB8Hq1q1kBfwPGY5FxQ8l1nO+TX2YyCeh94MQ+DFKGewnPNWGcfEJWDv9adYefIhTt4LSJIWUWrOhzYpjeblXWCcWruXbCYdO+9174GY+/fVY+umTeAyfrxKiZibo3XyPGY5FxQ8l1nO+TX202uI+5ScPn0at27dUnnFdVWpUoXtxIkoR5ibGqN7rZJquvMsFKtOeWHjOR+ERsdhz7VnairrYoPBjTzQr74bHG1edDTPMRoNnMeOhf/vv6tgPOLESXidOAnL2rVUQG7bpo3KW05ERIVLlgLxfv36qbbhkj1FRtbU9frrrzMQJ6IcV7FYEXzeszre61wZ2y4+xspTD3H1UQju+4Vj5s4b+H7vLfSoVRJDm3igjrtDjtRIy2idDn16w75XT4Tu2w+/xYsQff0Goi5dhs+bE2FRsSJKfP0VrGrXzvZ9ISKiAhCIS57w/fv348SJE2hswJ9Xz58/j+fPn6NVq1awtrbWe3kvLy9cv34d5cqVQ6VKlfTexqNHj1Sn05RImsbavFES5QvSnvy1Rh4Y2NAdl3yCVbOV7ZceIzouARvP+6ipekk71Wwlpfbn2ZXy0K5zJxTp9ArC//sPfosWIfLsOUTfuwcTZ+ds3z4REeUtmb7zSMDbuXNnNGnSxCA78sMPP2Dp0qUIDg7G48ePcefOHTVapz6ioqLQpUsXFYi///77+Pbbb/Xehiz7448/JpkngxXJF49JkyZhwYIFWThKIsppUkkgNd8yfdytKjac81FNV6SG/NrjEHy46Qpm7biBPvVKqaBcatRzYp9sW7ZUU8TZs4i8ehXmOm0Jw44dQ/SdO3AcMADGmaiQICKiAh6Ily1bFn5+fgbbkYCAAGzYsEEFwv3798/UOj766CPVMF5qtTO7jY4dO6pJ1y+//KIC8SFDhmRqv4gob3CwNseYluUwqnlZHL/rr2rJ9914ptqS/3nioZoalXVSAXnn6sVV2/PsZt2ggZq0JJGV70/zEXX5Mvx/W6TykzsOHgwTe/ts3xciIspZmb7LNGzYUNUUr1271iA7MnPmTFSrVi3Tyx85cgRLlizB4sWLDb6N5cuXq+UMVftPRLlLsqe0qOiC34bVx7H322Fqh4oq5aE4fT8Ak9dcQLNvD+D7PTfhExiRo/umiY6GRfnygKkp4oOCVFDu2a49nv/wA+IMWPlBRET5OBCXmmVp2jFo0CDY29ujTJkySaYPPvgAOSU0NBQjRoxQgXbp0qUNum6pPT979qwaNZSICh7JMz61QyUVkP82tD5aVnRR8/3CYvDLobtoNfsQRi8/g0M3nyM+IfuHXTC2tETJb2ahwp7dcBwyBEYWFkgID4f/70vg2b4Dnn75JWKfPs32/SAiojzcNKVy5cp4++23U32+bt26yCmyH9IkZeLEiQZft9SGS0aYYcOGpfvakJAQNWk9efIkMb+pTDlBtpOQkJBj2yusWM4Fr4ylu3nHqq5qkvbja057Y8P5R2rkzgM3n6vJzdEKgxq6o1/9UnCxfVGDnl2MixeH64wP4ThuLAJXrEDwmrUqIA9cvQZF+vSFsatrlrfB8zhnsJxZxgUFz+X06XvPynQgXqdOHTXltn/++QerVq3CxYsXDZ6GTApz5cqV6NatG4oWLZru6+fOnYsvvvjipfn+/v6wsMjem7aWBC7SGVUYMy8xyzkfy81z2RbA2IbOGFbXEQduB2LTZV9cexoOn8BIfL/3Nn48cAdtKziiTy1X1C5pk/0pEIcORZFeryJ6yxYkeHsh1MUZob6+6qn4e/ehiY2BaeXKeq+W14ucwXJmGRcUPJfTJzFftgXi0jnzwYMHaqQ7Gxsb9Xdq5DWGbiaSEsmOItlb7t+/ryYRFxen/t69ezfatWun8pxnxt69e1WtdkabpUybNg1jxoxJfCzLNmrUCM7Ozqo8cvKbmIuLC4e4Zznna3nlXH69RDG83rqKyrAi2Va2XXqCyNh47L0VoKZKxWwxpJGHSoFYxDIbUyDKNWTay79CPvr0U4QfOQrrZs3gNH4crOrXz/AXg7xSxgUdy5llXFDwXE5f8gEu06PXXWPLli0YO3YsRo8erTouyt+pkddI58ns1qBBAzx79ixJykEphDNnzqjaNMlxntlAXJqlFC9eXKVEzAg7Ozs1JSc3uJy8yUntYU5vszBiOReuMq7l7qimj7pXw+bzj7Di5EN4Pg/D7Wdh+Gz7dczecwu96pbC0MalUa3ky9eB7BAfFoaYhw/V3xHHj6vJql49uIwfB5tWrTIUkOelMi7IWM4s44KC53La9L2W6hWIS8q/Fi1awMHBQTUJkZE1v/rqqxRfK6/JDlLLLakTpY26+PPPP1Pc9oABA17KI66PoKAgbNu2DZMnT4apafYP9EFE+YOdpRlGNCuD4U1L49T9AJUCcc+1pwiPicfqU15qqufhoFIgdq1ZApZm2RfgmtjaovyOHQjZswf+ixYj+vZtRJ4/D+/xE2BRpYoKyIu88ooaSIiIiPIevSLMkydP4saNG5g6dap6LNlSqlSpYpAdOX36tMrzLW29xdGjR+Hp6Zkk6BZSOz19+nTMmTMn27YhJC2jDBDEbClElBKpbW5SzllNvqHRWHfWWwXhj4Iicd4rSE1f/XMdAxq4Y3BjD5R2tsmWgjQyNYV9t26w69oVYYcPq9zjkZcuIfrmTTx6expKr/gL1g0b8k0kIsrvgbiMRnn58uVs2RFJh6hdd6dOnfD333+rv6XWXTdIlufSC/47dOjwUmCtzzaEt7c3JkyYkOJ6iIh0uRaxwMS2FTChdXkcvvVc1ZIfvu2LwIhYLDpyT02tKrliaGMPtKtSFKYmxtnyxaBI27awbdMGEafPwH/RIpVlxUpnsKA4f381UqexlRXfQCKi/BaIu7u7qxEmJa+2r6+vStUnNcopkdpyfToozp49O8NNU9IjAXdWtiEkJzkRkT5MjI3QvmoxNXkHRKjOnVJTHhAegyO3fdVUwt4Sgxp54LWG7ihqZ5ktAblN40ZqkkBct534s+++Q/h/x+A0YgQcBw8CrK35BhMR5SIjjYynrEdvWWkasm/fvnRfm1OdNfMyHx8f9eVFatclz3lOkPdIviTJlyB2vmI552cF5VyOjovH7qtPVS35mQeBifNNjY3wSvViqi1503LO2Z4CMS4wEJ6t20ATE6MeG9vawmHwIMR37YpiFSvm6zLO6wrKuZyXsYxZzvk19tOrRlwuIJLS7+HDhyrIvnLlCj7++OMUX5tT6fqIiPIyC1MT9KpTSk03n4Zg1UkvbL7wCGHRcdh55amayrvaYEjj0uhb3w32VmbZsh+mjo4ot+Mf+C9diuCNm5AQFoaAxb8Df/4Fo/794TJ6FMxKlMiWbRMRkQFqxHWdP39eRf09e/bMzOKFAmvECy7WvrCMs0KC8K0XH2HFiYe4+TQ0cb6lmTF61i6paslruWVP5ikR+/w5Apb/icA1a6CJjHwx08wMZdasgVWN6tm23cKK1wuWcUHBczmXa8R11atXT01ERKQfWwtTVQM+uJEHznsFYuVJL+y4/ARRsQlYd9ZHTbXc7FVA3qNWSViZG7Y5g1nRoij23rtwHD0aj37/HTGbNsHU2RmW1aomvkaTkAAjjs5LRJStmCCbiCiXSLvw+qWd1PRJ92pYf9ZbdfD0CojAZZ9gvLfhMr7+5zr61XfHkCYeKO9qa9DtmzjYw+r1EXB78w3EP32aJPB+9u23iH3oBefx42Fdr65Bt0tERC8wECciygOcbMwxvnV5jG1ZDkc9/VTnzgM3niEkKg7Ljt1XU7PyzqqWvGO1YjAzYApEYxsbmFWqlPg4LiAAQevWQxMVhbB//1V5yCUgt2neLNs7lRIRFSYMxImI8hBjYyO0ruSqpsdBkVhz2gtrz3irQYOO3/VXU9EiFir94aDGHihhb/ic4CZ2dijx1ZfwW7QIMZ53EXHmjJosq1eHs4zW2aEDm60QERmA4UeVICIigyjpYIXpr1TG8Q/a4ZfB9VSaQ/E8NBrzD3qi+bcHMfavsyo/eUJCpvrdpz5aZ48eKLdtG9x+XgDLmjXV/Khr1/Bo8hTc69ET0ffvG2x7RESFlUFrxENDQ1Vqw6pVqzJXKhGRgUgzlG61SqjJ83kYVp16iA3nfBAaFYd915+pqbSzNYY09kD/+u5wtDE3yHalzbjUftu2b4+IEyfgt2gxIk6dQkJICMxKlTLINoiICrMs1Yh/9tlniSNdenl5oUKFCqhZsyZat26N2NhYQ+0jERH9T4WitvisR3WcntEBs/vWUtlVxEP/CMzaeRONvzmAaX9fxLmHgchkdtqUR+ts1gyl/1yO0mtWo/jnn8HY/P+D/YAVK+G/ZAniw8L5PhER5UQg/uDBA6xduxavvPKKerxgwQKVzvDMmTMICgrCpk2bMrtqIiJKh6Q0HNDQHdsmtcDWic3Rv74bLEyNEROXgE0XHqHvr8fRdf5/qvY8PDrOYOVpXbcuirRvn/g4ITwcfj//jOdzfoBnu3bwnb9AjeJJRETZGIifPXsWdevWhfH/0l0dOHAA06dPR4MGDTBixAg14A8REWW/2u4O+L5/bVVLLmkQy7naqPk3noTgo81X0XjWAXy69SpuP/v/wYMMJSE6GkWkQsbMTDVZ8Vu4EJ7tO+DZt98h9tlzg2+PiKggyXQgLgF4SEiI+jsgIADXr19HkyZNEp831E+iRESUMfbWZhjdoiwOTGuN1WMao2vN4jA1NlIjef514iFemXcEA347oUb1jI6LN0ixmjo5qQwrFfbthdOI4TCysoImIgIBy5fjbocOePLpZyodIhERGbCzZqNGjTB06FD88MMPqjlKixYtYGtrm1hb3r9//8yumoiIstimu1kFFzU9C4nC2tPeKg3i05AonH4QoCZnG3P0r18Kr5S3gatr1ovbrHhxFPvwQ5VvPGDFCgSuXIWE0FCE7NqFou++w/eTiMiQgbibm5sKwmfNmgUHBwesWrVKzb979y4uX76M1atXZ3bVRERkIMXsLDGlQ0VMbFseB24+VwMFHb3jB//wGPx25D4WHQFaV3qGYU1Lo03lojAxNspyDXnRKVPgPHo0AtesgZGJKUyKFEl8XgYIMnFwgFXt2gY4OiKi/M1IY+A2JPHx8apZiqkpxwry8fGBu7s7vL291ReXnCDl7+vrC1dXV6aQZDnnazyXs88Dv3CsPu2FdWe8ERT5/xmuSjlYYXBjDwxs6A4XWwuDb1cTEwPPTp0R9+QJrJs2gcv48bBu3LjAj9bJc5llXFDwXDZ87Gds6DziN27cKPAXVSKi/KyMiw1mdK2K4++3wWedyqCuh4Oa/ygoEt/vuYWm3xzAW2su4NQ9f4P294l9+hTGlpbq74gTJ+H1+kg8eO01hB48CE1CgsG2Q0SUXzCPOBFRIWVhZoIuVZ2xYXwT7JjcAoMaecDa3ASx8Rpsv/QYAxefRKcfj+DP4w8QEpX1sSHMPTxQ7p/tKPXjj7CoVlXNi7p0GT5vTsT9Xq8iePs/0MQZLtUiEVFexzziRESE6iXt8U2fmjg5oz2+7FUdlYq96Hx/+1kYPtt2DU1mHcCHmy7j6qPgLJWWkYkJ7Dp3QtmNG+H++2JYNaiv5kffuYMnM2YwwwoRFSqmhswjPnv27CR5xAcOHGjIfSUiomxmZ2mG4U3LYFiT0jjzIFB17tx19QkiYuKxRmVf8VZNWYY2Lo1utUrA0swkU9uRJoy2LVuqKeLsWfgtWgwzt1IwK1o08TXRd++qbCzGNi/yohMRFTSZDsSZR5yIqOCSQLlRWSc1+YZWw7qz3lh9yku1I7/gFaSmr3ZcVyN6DmlcWrU7zyzrBg3g0aBBkmYp0mb80dS3Eff8ORyHD4PTkCEq2woRUUFinJU84ocPH1YpDN98882X8ojL80RElP+5FrHAxLYVcOS9tlj2egO0q1IU0ic/KCIWvx+9jzZzDmPY0lPYffUp4uIz3+nSSCfbVvStW4i+fx/xwcHwW/AzPNu1x/M5cxDn62ugoyIiyn3MI05ERBkiOcbbVSmmJu+ACDVIkNSU+4XFqNzkMhW3s8RrjdxVx0/JYZ5ZllWrosKe3fBf9geCNmxAQkQE/JcsRcBfK+DQr6/KU25WqhTfOSLK15hHPBsxj3jBxVyqLOOCwBDncUxcAnZfe6rakp++H5AkaH+lWjEMbVIazco7ZymtbZyfHwL+/AuBq1cjITxczTMyM0OFw4dg6uyMvI7XC5ZxQcFz2fCxX5ZH3fH398fevXvx4MEDFC9eHK1atUL58uWzuloiIsoHzE2N0bN2STXdehqKVaceYtP5RwiLjsOuq0/VVM7FRg0U1L++O+ytzfTehqmLC4pOnwbnsWNUMC5BuXWTxkmC8ISoqMQc5URE+UWWAvEtW7Zg9OjRCAgIgI2NDcLDw2FmZobPPvsMH330keH2koiI8rzKxYvgy1418H7nKth68bGqJb/+JAT3/MLx9Y4barCgHrVLqowstd3173hpYmcHlwkT4DR8OOLDwpI85z1mLIwsLeEyfhysGzY04FEREeXBzpqBgYEYNmwYhgwZgmfPniEsLEwF4j/++CM+//xzHD161LB7SkRE+YKNhamqAZdBgja92Qx96pVSNefRcQnYcM4HvX45hh4L/sPfZ7wQGROv9/qNra2TpDmMvHhRpUAM/+8/PBw2HA8GD0HYv/8adFRQIqI8FYj/+++/qFq1KubPn4+i/7sgWltbqwwqEyZMwI4dOwy5n0RElM9Iu/B6Ho6YO6AOTn3YHh91rYrSztbquSuPgvH+xitoNGs/Pt92DZ7PQzO9HcuaNVFq7g+wqFxZPY48fx7e4yfgfu8+CNm1C5p4/YN9IqI8HYiHhobCw8MjxedKly6tniciIhKONuYY26ocDk1vg79GNVIdOY2NgNCoOCw//gAd5h7Ba4tP4J/Lj1UHUL1H6+zaFWW3bIbbb7/Cqk4dNT/65k08ensa7nXrjviQEL4RRFRwAvEqVarg0KFDqleorqioKKxZs0Y9T0RElOSmY2yEVpVcsXh4Axz7oB0mt6+IokUs1HMn7wVg0uoLaP7dQfyw9xYeB0XqXQNfpE0blF6zGh5//gmbZs3UfLOSJVT7ciKiAtNZs2HDhqhfvz5q166t2oqXLVtWpcFau3YtYmNjMXz48EynxpHlLSwsMpXuKiEhATExMTA1NVVTVrchbQyzknaLiIhSVsLeCtM6VsJb7Spg//VnWHnqIY55+sM3NBoLDnril0OeKmf50CYeaFXRVQXxGSHXbJvGjdQUeeVKkoGCxJNPPlU5yB0HD2KATkT5s0ZcbN26FW+99RZ27dqF999/HytWrEDr1q1x+vRp2Nvb67WuM2fOqPblLi4usLKywt27dzO1T71791bLf/zxx1naxr59+9C0aVNYWlqiRIkSKguM1PYTEZFhmZkYo0vNElg1pgkOTG+N0S3Kws7SFAkaYP+NZ3j9jzNq9M7f/r2LgPAYvdZtVbOmGhxIK/rOHQStXw/fH398MVrnvB8R5+/Pt5SI8l8gLsHsF198gdu3byM6OhpeXl5YtmyZyieur2nTpqFGjRr4/vvvM70/f/zxB27cuKFSKWZlG5s2bUKvXr1UasagoCDcuXNHfbE4depUpveNiIjSV97VFp90r4ZTMzpgdr9aqO32olLHKyAC3+66iSazDmDq2gs49zAgU1lRjIsUgcOg12Bkbo6EsDD4L1oEz/Yd8HTmLMQ+ecK3iIhyVJYH9DEUbbrDDRs2ZGr5hw8f4u2338a2bdvQs2fPTG9Dar3Hjx+Pd999F2PGjEmc/95772Vqv4iISH9W5iYY0MBdTVd8glVO8q2XHiEqNgFbLj5WU5XiRdTIna/WLQVbi4zdzsyKF0eJzz6DyxtvIGD5nwhauxYJEREIXLECgWvXwr5XTxSfMUOlSCQiylM14itXrlTNOjIySVCcU6RWZOTIkSqnuYzsmRW7d++Gn5+faveubXNORES5p6abPb7rV0vVkn/WoxrKu7741fPm01B8vOUqGs/cj4+3XMHNpxnPjCJ5yIu99y4qHDwAl0mTYCzNKWNjEXX9OoysrLLxaIiIMlkjXrdu3RTbXqdEmoDklJ9++gmenp6qzXpWXbp0STW5kWYobdu2xdOnT1GmTBlMmTIFEydOTLPjZkhIiJq0nvzvZ07pHCpTTpDtyJeHnNpeYcVyZhkXBPntPLY1N8bwJh4Y1tgdJ+8HYPUpb+y9/gzhMfFYedJLTfVLO2BIIw90rlEcFqYZqGsqUgROb0yAw/Bhqu24eblySSpgglavgUXVKrCqW7fQlHN+xDJmOecV+n7O9QrEq1evrqa85ObNm5gxYwY2btyIIkWKZHl9kv9cmqfI6KAyKJGkYZR1Sw25iYkJ3njjjVSXnTt3rmozn5y/v7/K0JIT5GIfHBys/jY2zlIXAGI55yqeyyzjtFQoAnzaoRTebFoU2676YetVXzwLjcW5h0Fq+vKf6+hezRm9a7milH0Gr7/dukESJkb6+r44B58/R/B33wFxcTCtXRuWQ4fAtEEDvTNp8VzmuVxQ8FxOn8R8+bKNeGZJe27pWCm117pZTeQbiTyWrCf6kNFBpanLZ599hlq1aql5gwYNUsH4woUL0wzEpTOobrtyqRFv1KgRnJ2d4erqipz8JibNg+SLA7Gc8yueyyzjjJBLa9UyJTG9SwIO3/bDqlNeOOrph6DIOKw89wyrzj9Dq4ouqpa8TWVXmGQwBaKIevoUkaVLI+buXcRduoSwS5dgUb0anMaOhW379jDKYGUHz2WeywUFz+X0SfKSQhWIS9MRaUayefPmJIUwb948LFiwQHXiLFasWIbXV6FChST/a5UvXx779+9Pc1k7Ozs1JScBcU4GxVITntPbLIxYzizjgqCgnMey/51qlFDTQ/9wrD7lhXVnvREYEYt/b/upqZSDFQY1cseAhu4oWiT9ShqbOnVQbvs2hB08CL9FixF15Qqir13Hk6lvw7x8eTiPHQP77t1fylNekMs5L2MZs5zzAn0/4/mu7YLUcsfFxSU+vnXrlpqnO0mqwXfeeUf9rU8QLjp06KAKUdIgJm8Ckzw4JyKivKe0sw0+7FoVJz5sj3kDa6N+aUc1/1FQJObsvY1m3xzExNXnceKuf7opEKXWu0iHDiiz7m94LFsK68aN1XypJff7ZWGOHA8RFVx5pkZcRsOUtkcy4qX2sQTSyUfIlI6U06dPx5w5c7JlGyVLlsSkSZNU0xSpBa9WrRrWr1+P7du3Y926dQY7XiIiyl6WZiboXddNTTeehKgUiFsuPFKdO3dcfqKmCkVtMbSxB/rUd4OdpVnao3U2a6amiAsX4L/4d9i2bZOkNjz81GlYVq8OE9uUx7IgIsqzgXj37t1x5MgR9bd0bKxXr576W9IgfvPNN4mvk+fMzFK/WAppF57SazK6DQnynZycVErEwMBAVK5cWbURl1E7iYgo/6lawg4ze9fEB12qqBzkq04+VOkPPZ+H4fPt1/Hd7lvoVaekykteo1TaI0Nb160L618XJqlNjw8Kgo/0ITI1hdPQoXAcNhSmji9q4omIUmOkyczQZJQhPj4+cHd3h7e3N9zc3HKsI4Wvr6/qHMq2iCzn/IznMss4O8mt79zDQKw4+RC7rjxFTPz/pyys7e6gasl71C6patUzIvTgIfhMmaJykQsja2s4DhgAp5Gvw9jFhdflbMbrRc5gORs+9isQA/oQERHpQ5qaNCjjhJ9eq4sTH7bD+52rwN3pxUA+l7yD8O6Gy2g86wC++uc67vmGpbu+Iu3aosK+vXAaMVwNCKSJiEDA8uW426Ejnn3+BeIfPeIbRERZqxG/du0a9u3bl+EBfaTjY2HGGvGCi7UCLOOCgOdxUgkJGvx7x1c1Wzl48zkSdO6OLSq4YGgTD3SoWgymJmnXYcUFBiJwxQoErFyFhP8N8mbk7KxG8TTNoTElChueyyzn/Br75fsBfYiIiAzB2NgIbSsXVZNPYATWnPbC32e84RcWg/88/dRUzM4CrzX0wKBGHihun3IKRGkb7jp5MpxGjULgmjWqZtysT+8kHTvj/P1h6uzMN46okMt36QuJiIiym5ujNd7tVAXHP2iPBYPqonFZJzX/WUg0fjpwB82/O4jxK87i6B1fVZOeEhNbW7iMHYuye/fCsm/fxPkJkZG417MXHr4+EuEnTqSbQpGICq4sBeJ37txRmUQk5Z9kKdGmAZRJRrwkIiLKz8xNjVWnzb/HN8W+t1vh9WZlUMTCFPEJGuy59gzDlp5G+7n/YsnRewiKiElxHcaWljDSGeU5ZOcuxPv7I+LkSXiNHIUHA19D6IED0CT8f4dRIiocMh2Iy+iVXbp0UUH3K6+8gubNm+Pbb79FzZo1VWfNESNGGHZPiYiIclHFYkXwec/qOPVRe3zbpyaql3wxkvJ9v3B8veOG6tw5fd0lXPAKTLOW2/7VXij144+wqFZVPY66fBk+Eyfhfq9eCN6+HRqdQeuIqGDLdCB+8uRJlYtbBrlp0aKFGnVSRrM8c+aMaqQuQ88TEREVNNbmpnitkQf+easFNr/ZDH3rucHC1BjRcQnYeN4HvRceR/cF/6k25hExLwfVRiYmsOvcCWU3boT774th1aC+mh99xxOP330P9/v1Z+04USGR6UD84cOHqF+/vkoBJQPohIW9SO8kNeQDBw7EsWPHDLmfREREeYrc/+p6OOKHAbVxakZ7fNytKsq6vBhV89rjEHy46QoazzygBgy67x+Z4vK2LVuizMqVKL1yBWxatlTzZfROI+P/vz2zDTlRwZXpkTVleHhzc3P1d4kSJXDjxo3E54KCgtRQ8kRERIWBg7U5xrQsh1HNy+L4XX+sPPkQ+248Q2h0HFac9MKKk0Djsk8wtEkZdKpeXLU912XdoAE8GjRA1PXrMC1aNHG+NFN5MGQIbFu3htOQITCxT3vUTyIqhEPcN2vWTOVNHDVqFMqUKYOffvoJy5cvN8SqiYiI8lUKxBYVXdT0NDhKNU9Ze9oLz0Kjcep+oJpcbC0wsKGbSoEo2Vl0WVarluRxyO49iLp0WU0BS5bCcfAgOI0YAVNX1xw+MiLKU01T2rVrl5gZxcrKChs3bsSVK1fwxx9/YMqUKejTp48h95OIiChfkTzjb3eshH/fbY1vupdD8/Iv8ob7hUXjl0N30Wr2IYxefgaHbj5XWVhSYl2/HhyHDoWRhQUSIiLgv2QpPNt3wNMvv0SMD0frJCpUI2uSfjiyZsHFUdxYxgUBz+OcL+eHAZFYfcoL68/5IDgyNvE1bo5WGNzYAwMauKsa8+RkAKCAP/9C4OrVSPhfnyyYmMChT28U//JL1d68MOO5zHLOr7FfpmvEz507h8OHD7MTCRERUQaVc7XFx92rqc6dc/rXRh13BzXfJzASs3ffQrNvDmLK2gs48yAgyf1VRuEsOu1tVDh4AK5Tp8DE0VGiT5VdpbAH4UT5WaYD8Zs3b6Jt27aoWLEiZs6ciUeP+BMZERFRRliamaBffTdsmdhcpUF8raE7rMxMEBOfgK0XH6P/byfQ+cejWHHiAUKj/r/m3MTODi4TJqDCgf0o9uEHcB4zJvE5CdyffvU1wk+fZiUZUUEPxIcMGYKLFy+iW7dumDdvHkqXLo2uXbuqtuKxsf9/0SAiIqLU1Shlj2/71lIDBX3eoxoqFLVV8289C8UnW6+hyawDmLH5Cq4/Dvn/m7e1teq0aVG2bOK88P+OIXDVKngNH4GHg4cglL9aExXsIe5r166tMqQ8fvwYa9euVfMkh7gMeb9s2TJD7SMREVGBZ2dphtebl8W+t1th7bgm6F6rBMxMjBAeE6/alXedfxR9fz2OzRd8EBUb/9LyRmamsKhcWf0deeECfCa8gfu9+yBk1y5o4l9+PRHl80BcS/KJ9+vXD//88w9+//13RERE4Pjx44ZYNRERUaEibb6blHPGz4Pr4fgH7fFup8oo5WClnjv3MBBv/30JTb85gG923sBD//DE5WyaNEHZLZvh9tuvsKpTR82LvnkTj96ehntduyFo46ZcOyYiysZA/O7du/jkk09UDvHRo0ejQYMGqmaciIiIMs+1iAUmtq2AI++1xZLhDdCmsiukb2ZgRCwWHbmH1t8fxvBlp7H32lPExb/ouFmkTRuUXrMaHn/9CZvmzdV6Yh4+ROjBg3wriArKgD5S671hwwbVBOXIkSMoVaoUhg8frgb1KV++vGH3koiIqBAzMTZCh2rF1OQdEIFVp7yw7qw3AsJjcOS2r5pK2FuqQYKk42dRO0vYNGqkpsgrV+G/eBGcx45Nss7gbdtg26aN6gBKRPksEF+9ejUmTpyInj17YseOHejUqROMjQ1SwU5ERESpcHeyxgddquDtjhWx++pTrDz5EGceBOJJcBTm7ruN+QfuoFP14hjSxANNyznDqmYNuC1YkGQdkZcv4/F778PY1haOgwfDacRwlSKRiPJJIN6xY0fVSdOZH1wiIqIcZ2Fqgl51Sqnp5tMQrDrphU3nfVTnzh1XnqipvKsNhjQujb713WBvZZa4bNTNmzAyN1eDA/kvXoyAv/6CQ//+cB41EmYlSvDdJMohma7ClnSFDMKJiIhyX5Xidvjq1Ro49VEHfP1qDVQpXkTNv+sbji//uY7Gs/bjvQ2XcNknSM13HDAA5ffvg9PoUSoVoiYqCoErVsCz4yt4/NFHiL5/P5ePiKhwYFsSIiKiAsLWwhRDm5TGriktsfGNpuhdtxTMTYwRFZuAdWd90PPnY+j583+qfXmcgzOKvfuuGq3TZdIkGNvbA3FxCN64CU8//Sy3D4WoUGAgTkREVMBI9pT6pZ0wb2AdnJzRHh92qQIPJ2v13GWfYLy34bKqJf9y+3U8iDWF66SJqHDgAIq+9x5MXV3hPC5px87oe6whJ8pTbcSJiIgo73OyMcf41uUxtmU5HLnji5UnvXDw5jOERMVh2bH7ampW3lnVpHccMQKOQwar9uNa0kzlXrdusK5fH87jx8OmRXMV6BNR1jEQJyIiKgSMjY3QpnJRNT0KisTa015Ye8YbvqHROH7XX01Fi1io9IeDGnughP2LQYSCt2wFNBpEnD2rJstq1VRAXqRjBxgxWxpRlrBpChERUSEjI3VOf6Uyjn/QDr8MrqfSHIrnodGYf9ATLb47hHF/nVX5yZ3fegtuPy+AZc2a6jVR16/j0ZQpuNe9B4K2bIEmNjaXj4Yo/2KNOBERUSFlZmKMbrVKqMnzeahqtrLxvA9Co+Kw9/ozNZV2tsaQxmXR748VKHr5HPwWLUbEqVOIuXcPTz74ECG7dsFj0aLcPhSifIk14kRERIQKRYvg857VcWpGe3zXtyZqlrJXpfLQPwKzdt5Ek28P4hNva/h9OQ+lV6+Gbdu26nn77j2SlJ4mLo6lSZRBDMSJiIgokbW5KQY29MD2t1pg68Tm6F/fDRamxoiJS8CmC4/Q99fj6Hs0DEdf/wDFN2yCXZfOicvGPn8Oz7bt4Dt/AeICA1mqROlgIE5EREQpqu3ugO/718bpGR3wSfdqKOdio+bfeBKCGZuvoOV6L3y24yZuPwtV8wP/+gtxvr7wW7gQnu074Nm33yH22TOWLlFeD8QjIyOxevVqdO3aFQ0aNICPj0+m1jNz5ky1/M8//5zpbTRp0kQ9rzsNGTIkU/tDRESU39lbm2F0i7I4ML01Vo9pjC41isPE2Ahh0XH468RDvDLvCAb8dgJn6nWE/fDhMLKygiYiAgHLl+Nuh4548smniHn4MLcPgyjPyTOdNatUqYLmzZujatWq2LVrF6KiovRex/HjxzF37lyEh4enGGRndBtnz57FZ599hi5duiTOs7Z+MRACERFRYSX5w5tVcFHTs5AorD3tjTWnvfA0JAqnHwSoydmmAYZ+1B49PI8gfuM6JISGImj9egRt3AinESNQ7P33cvswiPKMPBOIX716FUWKFMGGDRsytbwE38OHD8fs2bMxffr0LG+jbNmyqiaciIiIXlbMzhJTOlTExLblceDmc6w8+RBH7/jBPzwGP531xXyjqug0Zg5G+p+D446NiPf3h1nJkixKorzYNEUC5KyQ4LtMmTIYPXp0tm2DiIiIkjI1MUan6sWxYnRjHH6nDca1KgcHazMZAwi774diYEgljOvyMW4OehPxXbonLhcfFgbvNyci/MQJaOTFRIVQnqkRz4o9e/Zg5cqVuHLlisHW+eOPP+LXX39FiRIl0LZtW4wbNw5mZmZpLhMSEqImrSdPnqj/4+Pj1ZQTZDsJCQk5tr3CiuXMMi4IeB6znA3N3dES73eqhCntymPn1adYfcoLF7yD8SAsHm+jHMzmHUen6sUwpJEHyu/fiLCDB9UkgwU5jRsLmzZtMjVaJ89lnst5hb7xV74PxAMDAzFq1CjVSVOakxhCjRo1VOBduXJlXLt2DV9//TWWL1+OI0eOwMrqxZC/KZH26V988cVL8/39/WFhYYGcIEF4cHCw+tuYQw+znPMxnsss44KisJ7LLd3M0dKtAm4/j8Cmy77YcysAkbEJ+OfyUzX1CI/GULcysPN5gKgrV/D4rckwLlMGlkMGw7xtOxiZmmR4W4W1jHMayzl9EvMVqkB88uTJKF26NN566y2DrfPUqVOJgXPr1q1VFpX69evjjz/+wJtvvpnqctOmTcOYMWOS1Ig3atQIzs7OcHV1RU5+E3NxcYGJScYvYsRyzmt4LrOMC4rCfi7L7a959dL4PCoWWy4+xqpT3rjzPAzbbSpge/2JaFb2DsZ5H0GxBzeR8OABImbOQuxff8F54kTY9Ug6WFBqCnsZ5xSWc/qio6NRqALxo0ePqv8l4NUKCwvDn3/+if3796tmKxII6yN57XW9evVQtGhRXL58Oc3l7Ozs1JScXBRy8sIgtQE5vc3CiOXMMi4IeB6znHOKg40JXm9eDiOalcXp+wFYecoLu68+wXHnSmqq7nYPY72PoPLDq4j19kGczyO97mM8l3MGyzlt+sZe+T4Q3759+0vfPqRNd6dOnTBp0iTY278YojcrIiIiVBMYJyenLK+LiIiosKdAbFzOWU2+odWw7qy3akt+DeUw1aUcypd9hNceHEFgsQYY4BeOMi42SIiJUYMFOfTvDxMD3NeJ8op8F4hLSsFhw4ZhypQp6nHNmjVT/DZSvHjxTKUflMDe0tISHTt2TKxdHz9+vLpwcFAfIiIiw3EtYoGJbStgQuvy+Pe2pED0wqFbwEyHQcA5Pyw8dxgtK7pgfMgVOC/6AX4Lf4Xj4EEqH7lpDjX5JCoUgbgEu+fOnVM1z6J3796qiYhu0C3kNW3atMm2bcigP++88w4GDBigMqY8fPhQddqUJi7Vq1c3yLESERHR/5NROttVKaYm74AIrD7thXVnvFVOcslNXvz2DQw1MYN5RAT8lyxFwF8r4NCvL5xGjYa5WykWJeVbeSYQl46OoaGhL82Xmm1dZ86ceWlecocPH06xc2RGtlGxYkVs3bpVDRAkQXjJkiXh4OCg59EQERFRZrg7WeP9zlUwtUNF7L76FKtOemE92mFv6YZ49e5R9Lh3HDYxUQhcvQaBf6+DfffucBg1CrB/uY8WUV6XZwJxqXXOiIw0N6lTp06WtiFsbGxQrVq1DL+eiIiIDMfC1AS96pRS062noVh16iE22jliQ4W26H7/OHrfPQL7mHAEb92KGEsrWL4xnsVP+Q6TbRIREVGeVrl4EXzZqwZOzWiPjwY2wpU2vTHilY/wa81eeGLtjCGhFfHV3ge47BMMTUICIs6f52idlC/kmRpxIiIiorTYWJhicGMPDGrkjvNeQVh1sizeuNwS0fHAo+v+2HH9BAZFeWL47t9gUacOXCeMh23r1irhAlFexBpxIiIiylcksK5f2hFzB9bByRkd8UHnynCzfzEGSKmrp9X/0RcvwmfCG7jZoxdCdu6ERs+hx4lyAmvEiYiIKN9ytDHH2JZl0bOyDW4HG2N11aI4eugwBtw+gGoBDwHPO3g0bTpiSsyD2xvj4PRqLxiZm+f2bhMpDMSJiIgo3zM2MlI5x9tUKYYnr9bAmlM9seWfg+h0cTfqP78N8yc+eP7ppzi97yRqf/81SjpY5fYuEzEQJyIiooKlhL0Vpr1SGbHtK2Lf9VexZMthVDm4GU2fXMW3ZlXh/d1BlbN8aGN3NC9pDTO7Irm9y1RIsUaciIiICiQzE2N0rVkCXWsOwt0JPbBp93kE3o1EQlQc9t94hudHjsHu9HL4tu+B+tPfgIt7idzeZSpk2FmTiIiICrzyrrZ4d1grnJrRAbP71UJtN3v09TwMq9goeOxeD59Or2D9iKk4f+Y6Ux9SjmEgTkRERIWGlbkJBjRwx9ZJLVBv/hxcadEDkaYWsEiIQ41Te2A2vD+W9x6L9VuOISw6Lrd3lwo4BuJERERUKNWsXR4DlsxG2f0H4N1rKMItbGCqSUCTm8dQ7YOx+GbYh/h4yxXcfBqS27tKBRQDcSIiIirUHIs745XvPkLdY4cRMWYiwm0dYAwNLtp5YOVJL3T+8Sj6/XocWy8+QnQc85GT4bCzJhEREREAE1tb1H9nEhImj8OjXfvQ2bYSAk974XFwFPwvX0P0ypkYX6sTqvToiCFNSsPdyZrlRlnCQJyIiIhIh7G5Odx7dcNbAN5oUx6Hbvki5MP3UM3/Hmoe+hV3zm/Dh5Xbw7RNWwxtUhZtqxSFibERy5D0xkCciIiIKLVAycQYHasVQ+iUEXi8IAwJN66jYvAjfHT6L3hd3421+9viyxrNMaBJGQxo6I6iRSxZlpRhDMSJiIiI0lGkXTtUatsWESdP4vmvvyHq9Gl4hD3H9PN/49mNPVh8sxd+3F8LnWoUx7AmpdG4rBOMjFhLTmljIE5ERESUARJY2zRtirJNmyLy4kX4Lf4dYQcPolhkEMzMTBCXoMGOy0/UVLGoLYY09kCf+m6wszRj+VKKGIgTERER6cmqTh24L/wFUbduI3jrViyYNBlbLz1RWVaC7j1Ak393Y653S3y3+xZ61SmJoU1Ko0Ype5YzJcFAnIiIiCiTLCtXguV776q/hzUtowLuK+/uhtmt/ejjeQQ7yzTBppDWWHvGG7XdHTC0sQd61C4JSzMTljkxECciIiIyZPOV4iVdEWBlBcvISPS5ewQ97h/Hfvf6WB/WFu96B+HrHTfQv76bSoFY1sWGhV+IcUAfIiIiIgMqOu1tVDh4AC5vvgFjOzuYJcShy8NTWHLgO7x/dhXsn3ljyX/30XbOYQxdcgq7rz5BXHwC34NCiIE4ERERkYGZOjrCdfJkFZC7Tp8GExcXGGs0aONzAW8Wi4SLrbl63X+efpiw8jyaf3cQ8/bdxtPgKL4XhQjbiBMRERFl42idLmPHwmnYMARt2oSQnTsx8MNx6GNsij3XnmLToasIvHIdFzUV8NOBO/j5kCc6VC2q2po3L+8CYw4UVKAxECciIiLKZsaWlnAaPFhNQurDpdNm40Pr4H9sEfzdK2Bp6dY47FwZe649U5O0H5cUiP3qu8HB+kUNOhUsbJpCRERElAs0Gg0iL11Sfzt7e+K9/5Zi49lfMDTsBowT4nHfL1x17Gw86wCmr7uEC16BahkqOBiIExEREeVShhWPZcvg/vvvsG7QQM2zevQQQ/YvxfYzP+Gj+JuwMUpAdFwCNp73Qe+Fx9F9wX9Yc9oLETFxfM8KAAbiRERERLkYjNu2bIHSK1eg9KqVsGnVUs03fvIYLbYvwd4Kfvi4W9XENIfXHofgw01X0HjmAXy+7RruPAvle5ePsY04ERERUR5gXb8+PBYvRtT16/Bb/DsiTp1C8YEDMMbWBqOal8Wxaz5Yf+IudjyIQGh0HJYff6CmxmWdVOfOTtWLw9yUdaz5CQNxIiIiojzEslo1uP04D/GhoTCxfVETLtlTqp07gIm/LcDUPv2xu0ob/Hk7DM9ConHqfoCaXGwtMLChGwY18oCbo3VuHwZlAL82EREREeVBJkWKJP4tnTQD16xBQkQEolf+iXZfjsem6P+wpGMJtKjgol7jFxaNXw7dRavZhzB6+Rkcuvkc8Qns3JmXMRAnIiIiygdtycusXg3nceNgbGsLTUwMQv7+G6UmD8fsO5uwv487xrQoC3srM0jsfeDmc4xcfgZt5hzCr4fvwj8sOrcPgfJ6IP7gwQPMmjULU6dOhZ+fX6bWsWPHDrX8P//8Y5BtpLc+IiIiopxg6uyMotPefjFa59SpMHF0BOLjEbx1G2JHvIa34u/g1Iz2+L5fLdR2d1DLeAdE4rvdN9H0m4OYsvYCzjwIYArEPCTPtBHv1KkT7ty5g6pVq2Lnzp2YNGkSXFxe/NSSUd7e3hg+fDiCg4NhaWmJ7t27Z2kb6a2PiIiIKKeZ2NnBZcJ4OI0YjqD1G+C/bBniAwNh06IFTM1M0L+BO/rVK6UyrKw85YWtFx8jMjZe/S9T5WJFMLSJB16tWwpFLM34BuaiPFMjPmPGDNy9excjR47M1PLSdur111/H6NGjYWtrm+VtZGR9RERERLnF2MoKTsOHocLePfBY/oeqMdeSWnLbd9/ER84BOPFhO3zeoxoqFH0Rz9x6FopPtl5Dk1kHMGPzFVx/HMI3sbDXiLdu3TpLyy9YsABeXl6qCcnixYuzvI2MrI+IiIgotxmZm8O6bt3Ex5r4ePgvXoyY+/fhM+ENWFSpgj7jxmL45Fdw6mEwVp56iD1XnyI8Jh6rT3mpqX5pR1VL3qVGCViamSRZvwwetOXCY2w+74PnIREoameN3vXc8GrdkrA2zzOhZL5UIErv1q1bqrZb2nNbWVnlufURERER5RhjYxR9/z34/7YIkRcvIvrmTTyaNh3mpUuj6tgx+LlfT/j2qIZ1Z7yx5rQ3HgVF4tzDQDV9uf06BjRwx+DGHijtbIO7vmEYuuQUngRHwchIWgwAXkHROPMwEAsO3sHKMY1R3pUtBwptIB4XF6faccuU1Vr1rK4vJCRETVpPnjxR/8fHx6spJ8h2EhIScmx7hRXLmWVcEPA8ZjkXFDyXX2bdsiWsWrRA5NmzCJDBgY4fR8zDh3jy8Sfw/flnFJ85C2+0boxxLcvi8C1frDrthSN3/BAYEYtFR+6pqVl5Z9x4EoLgyFi1TgnCdf9/FhKlgvS9U1uwZvx/9I2/8n0gLhlQJOD97rvvcn19c+fOxRdffPHSfH9/f1hYWCAnSBAunUuFsXGe6QJQ4LCcWcYFAc9jlnNBwXM5DWXKwGLWTJjcvImoVasRe/Qo4p77IsTKEuG+vuoltVyMUKtraTwKLo4tV3yx/Zo/giLjcPyuf9rlroGqKV/13228WtPVsG9qPiUxX6EKxP/44w94eHjgk08+SZwXGRmJAwcOqLSDX331FYroJMTPzvVNmzYNY8aMSXwsAX2jRo3g7OwMV1fXHP0mJtlgTEyStvEilnN+wnOZZVxQ8FxmGecJEoe0bIloz7uIPH8ODrVrJz4V/t8xRJ49gxrDhqFO77r4sEcCdl99ik+3XUNYdNo1vNJc5eDdUIxtVy0HDiLvi46OLlyBuATMus1BtDXB9vb2KFOmjN7BaFbWZ2dnp6bkZJmcDIplf3N6m4URy5llXBDwPGY5FxQ8lzPGunIlNelmiQtYuBCRly4h8K8VcOjfH86jRqJPfXf8fPguwnzD01yfNFPxC49hzPE/+sZe+S4Ql1rpdu3aoWfPnurxqFGjXnrN559/jgYNGqjX6svQ6yMiIiLKs2JjYdWgPqLv3EFCRAQCV65E4Nq1sO/ZE5Vs6+O+kUVim/DUasRdbXOm+W1BlGcC8Z9//hmenp5qEjNnzlS10LpBt/jpp59gamqaZJ6ht0FERERUWFIfFnv3XbiMHYuAVatUrXh8cDCCN23CZKPNqFuiJv6q2hmPihRNcXkJ0mVgIMrngXjx4sVVxhJp/tGhQ4fE+Y4yfKuOefPmoX79+mmu65tvvkGtWrUyvY2Mro+IiIioIDBxcIDrxIlwfv11BK5bj4BlyxDn64tWjy9jfeX2KS5jbAQUs7NErzolc3x/CwojjTQOomzh4+MDd3d3eHt7w83NLcc6Bfn6+qrOoWwjznLOz3gus4wLCp7LLOP8KCEmBsGbt+D5+Ut43aFdYh7xsoGP4BQTirOulVHCwYp5xLMY++WZGnEiIiIiyhuMzc3hOHCAmg7ExGHrxRcja/Y98wdq+VxDRJkK8HjrTbg4W+f2ruZrTDRNRERERKmSYewHNfLAqmG1UbfIi3SG1g884Td9Gu5174GgzVugiX0x6A/ph4E4EREREaUfNFpaosjChXBbugTWTZqoeTH37uHJhx/Cs1Mn1dkzISqKJakHBuJERERElCFGRkYqCC+9/A+UWbsGtu3aqflxj5/g2VdfI/LCBZakHthGnIiIiIj0ZlWnDtwX/oKoW7fh//vviPXxSawpF7HPnqn0iKbpZKcrzBiIExEREVGmWVauhFJzvlftxKXGXMt37lyE7N0HxwED4DRqJMyKFWMpJ8OmKURERESUZUZmZol/x4eFIfTgIWgiIxHw55/w7NARTz75FDEPH7KkdTAQJyIiIiKDMrG1Rfm9e+Dy5hswtrMDYmMRtH497nbpikfT30HUrVsscQbiRERERJQdpG246+TJqHDwAIq+Mx0mLi5AQgJCduzA/V6vIuLMmUJf8KwRJyIiIqJsrR13HjMGFfbvQ7FPP4FZyZIwL1MGVvXqJRnJszAO9s7OmkRERESUI3nInQYPhmP//oh98gRGJiaJz/n+8AMiLlyEy/hxsG3bFkbGhaOuuHAcJRERERHlmU6d5h4eiY/jAgMRuG49oi5fhs/ESbjfqxeCt2+HJi4OBR0DcSIiIiLKNSYODnCbPx/WDRqox9F3PPH43fdwt3MXBK79GwnR0QX23WEgTkRERES5xsjICLYtW6D0yhUovWolbFq3UvNlgKCnn3+Oux06FtgsKwzEiYiIiChPsK5fHx6LFqHs5k0o0qWzROnQQKM6dxZE7KxJRERERHmKZdWqcJs3D9GT7yPW5xGMLSwSn/P/YznifH3h9PoImBUtivyMgTgRERER5UkWZcuqSSshPBz+ixYhPigIgStXwr5vHziPHg1zNzfkR2yaQkRERET5gkajgcPAgTC2tYUmJgZBa9bibqfOePz++4j29ER+w0CciIiIiPLN4EBF356qRut0nToVJo6OQHw8grduw73uPeDz1lsqR3l+wUCciIiIiPIVEzs7uEwYrwLyYjNmwLR4cTU//MRJGNvYIL9gG3EiIiIiypeMrazgNHwYHF8bqAYBSoiIVEG6VtTt27CsVAl5FQNxIiIiIsrXjMzN4dC3b5J5mthYxAcGIS9j0xQiIiIiKnDiAgNhXa8u8jLWiBMRERFRgWOWD3KMs0aciIiIiCgXMBAnIiIiIsoFDMSJiIiIiHIBA3EiIiIiolzAQJyIiIiIKBcwECciIiIiygUMxImIiIiIcgEDcSIiIiKiXMBAnIiIiIgoFzAQJyIiIiLKBRziPhvFxcWp/588eYKcEh8fD39/f0RHR8PExCTHtlvYsJxZxgUBz2OWc0HBc5nlnFdoYz5tDJgeBuLZyNfXV/3fqFGj7NwMEREREeWxGLBMmTLpvs5Io9FocmSPCqGoqChcuXIFrq6uMDU1zbFvYhL4nz59GiVKlMiRbRZGLGeWcUHA85jlXFDwXGY55xVSEy5BeM2aNWFpaZnu61kjno3kDWjYsCFygwThbm5uubLtwoTlzDIuCHges5wLCp7LLOe8ICM14VrsrElERERElAsYiBMRERER5QIG4gWMnZ0dPvvsM/U/sZzzM57LLOOCgucyy7ig4LlseOysSURERESUC1gjTkRERESUCxiIExERERHlAgbiRERERES5gIE4EREREVEu4IA+eXhkpiNHjuDRo0eoXLmyGi3T0MtmZRsFhaenpxqF1MbGBu3atUORIkUMvuyzZ8+wZ88e9Xzv3r1R2ERERODQoUMICgpC3bp1Ua1aNYMve+vWLVy6dEn16G/QoAFcXFxQ2Mjxa0fybdOmDSwsLAy27H///YebN28mDlQmg1U0bdoUJiYmKEwCAwNx+PBhNWpys2bNULp06Wxb9vz582qS87lOnTooLGSw7xMnTuDevXvw8PBAixYtYGxsbLBldc9lXX369IGTkxMKi8ePH+Po0aPqMyyfeX2umfose+7cOVXe5cqVU9cMSoEMcU95y7NnzzS1atXSVKpUSTNkyBBN0aJFNT179tTExMQYbNmsbKOg+PLLLzXW1taafv36aZo3b65xdXXVnDhxwmDL3rt3T5VpqVKlNG5ubpratWtrCpurV6+qY69fv75m4MCBGltbW83UqVMNtuz169dV+dvZ2Wn69++vad26tcbGxkYzf/58TWGRkJCgGTVqlMbBwUEzaNAg9bkuV66c5u7duwZbdvny5ZrRo0erSV7n4eGhqVixoubGjRuawmL//v0ae3t7Tdu2bTW9e/fWWFlZaX788cdsWdbX11dTvHhxjdyiv/rqK01hER4ermnXrp26Zsp9qUyZMpomTZpogoKCDLasnMMlS5ZMPJ+1k5eXl6awWLp0qToHe/TooXnllVfUtXXLli0GXVZijJYtW6pr+ODBgzUdOnRQ539kZGQ2HFH+xkA8D5KAonr16pqIiAj12NvbWwUas2bNMtiyWdlGQfDvv/+qm9zOnTsT5w0fPlxdvNP7MpLRZa9du6YuULGxsSqQLGyBuAR5Eth1795d/S1OnjypMTIy0mzatMkgy65Zs0bTvn17FbhoSRAurzt//rymMJAbo7m5ufriIuR8a9WqlZqya9moqChN3bp1NS1atNAUBqGhoaqyYvLkyYnzVq9erc6zixcvGnzZvn37asaMGaMxMTEpVIH4u+++qylWrFji5zk4OFhdV8eNG2ewZSXolmtGYeXp6akxMzPTLFy4MHHep59+qu7/fn5+Blk2Pj5efQnq3LlzksD7yJEjmrCwMIMfU37HQDyPCQgI0JiamiY50cXYsWM15cuXN8iyWdlGQSGBc7Vq1ZLMu3Tpkgqwd+3aZfBlC2Mgfvr0aVUmBw8eTDJfakm6detmkGVv3br1Ug1LYGCgWjajtZX5XbNmzdQvL7o2btyoyuDOnTvZtuxHH32ksbS01BQGEjhLmejWmsoXRKlZnTJlikGXXbFihXpOanILUyAuZeLi4qJ57733ksyfOXOm+pVLvvwZYtnCHohL4Cy/zuhWGklMYGxsrPn1118NsqxUQGXkGkIvsLNmHnPx4kXVdlvaBeqSx3fv3lXtDLO6bFa2UVCcPXv2peOvWbMmzM3N1XPZtWxhoi2L+vXrJ5kvZZeRMs7IspUqVVJtlnVJ+1Dh5uaGgi4hISGxHbEu7eO0yjkry4pr166hatWqKAykLIoWLQp3d/fEeUZGRur8zMi5nNFlfXx88NZbb+HXX3+Fvb09CpMHDx7Az88vxfMxPDwcN27cMNiy0ufk77//xqZNm1T/ksJEzrnatWvDzMwscZ6joyPKly+foXM5I8vu3LkTFSpUUNfgHTt2YN26dbh+/Xo2HVH+x86aeczTp0/V/9JpSpe2M8Tz58/ViZ+VZbOyjYJCyiD58cvN0dnZWXWuzK5lCxMpJ+n0Jx0ok59nco7JL3JSboZcVoLLd955R70/HTp0QEEXHBysOv+l9llO63zUd1n58r58+XK1jHTUkhur3GALg5Q+89qySitA1GdZOadHjRqFzp07o2fPnihs0rsvpXUu67usfOGRc1eCdOkM3qNHDyxbtuyl601BJGVVtmzZl+ZLWWXk3peRZaUyRIL1hg0bqucknpCEBZKs4K+//spw59vCgoF4HiOBhEgeZGhP3Pj4+Cwvm5VtFBRSBikFclIG6R1/VpYtTNIqJwk65PnUsm5kdtm3335bZQLavn17oahRzInrhZY8PnnyJCIjI1WWFckwIVltCoOcuF4sXLgQFy5cKLQ1hzl1Lr/++uuqrOUXTHH16lWVxWbq1KkqGC/ocuJcli/t8iVz1qxZ+PDDD9U8qTFv3LgxmjdvjjfeeMMgx1JQ8GtJHqNNnyQ/nenSPk4rvVJGl83KNgoKOcbkxy9kXnrHn5VlCxMpC6k9lSl5OUmQnFbqu8ws++WXX2LBggXqZtqlSxcUBlKDJ2WRmc+yvsvKLxRLlizBqlWr1E1WmmN17dpV1awXdDlxvfj666/RsmVLbN26VZWzTPKlU9K/yd8S3BRkOXHvE5LSUBuEixo1amDQoEHYsmULCoOcOJfl12Exfvz4JM2EpDnWvn37sngEBQ8D8TxGbm7a9pe65LH87Fa8ePEsL5uVbRQUUgbJj//hw4fqp0pt+WTHsoWJtiyS1/BJ2WWkjPVZ9qeffsLnn3+u2tYOHz4chYX8/FulSpUUP8sirXLOyrJSKybBi9yAky9fEElZSO7k5EFIRs/ljCz72muvqWBGfnXQThKIe3t7q78L+q9t0qbYysoqxfNRvjCm1R8hK8sKa2vrl770F1Qp3b+io6NV/7DM3PtSWlbakYvk/Xfksbyekvlfp03KQySTQceOHRMfS1YIyds7ceLEJK/7559/XsrfmdFlM/q6gkoyGUhPb908yF988YVKwyRpr7Tu37+v+f333zXPnz/Xe9nCnjUlOjpa5UJ+6623Euc9evRIZdpYsGBBkteuWrVKc+jQoUwtKyn4JBVcYcmSklJOe8kD7u/vnzhv2LBhKs+3NvWjNrOPnMu6GSQyumxKOck///xzldVD3peC7vHjxxoLCwvNTz/9lDjv1KlTL2VKkvSPUsbnzp3Te9mUFKasKULyTUtGKilHIedgo0aNXsqyJClkJbuMvsvKue/j45NkOW2aw06dOmkKg+PHj6tzb8+ePYnz/vzzT3WuSXpCLUkDKeey7mc/o8tKNiuZt379+sR5T58+VRlsvv7662w+wvyHgXgedOHChcQBSiTokAFLJK2gbjAoZPASGewkM8tm9HUFleQ5lRzVpUuX1syZM0czffp0lU9ZBi7RJRcSufDoDtaT0WXloi8XMpkaNmyocXd3T3xcWMp569atqmzefPNNzbx58zRVqlRRKQgl0NYl+X9lEA59lz1w4IC64MsNV1u22klSIBYGkpe3Xr166oueBHsyQI98YUme+vGbb75R57JuzvWMLitf3OXL5Hfffaf54Ycf1HVDgsvvv/9eU1hI+UjZfPjhh6ocSpQooYK/5DnDpYw/++wzvZdNSWELxCXFowzII+kF5b4k11lJSyiBna4RI0ZonJ2d9V5W3h+5jowcOVIzd+5c9T5JEC6DWCXfRkEm11QpP0nvKCkJJUCWL+W6zpw5o85lGatB32WFBNwy2I/2nJcv9w0aNEgcu4T+n5H8k7yWnHKf/BwpvYvlJ01J0TZy5MiXenR///336meejz/+WO9l9XldQSUdT9auXat+9pWfJvv37/9SujxpnynNHWbMmKGG6NVn2bCwMNUBKCXJ11eQyU+Za9asUT/N16tXD8OGDUuS/kpMnz5dDV8/evRovZaVjAfSZjkl0n5Zhq0uDORndcloIsPUS5aCoUOHomLFikles2vXLmzcuBE//vgjbG1t9VpWbhOShuz48ePq9TI8u5Stbkq+wkCOf/PmzYiJiVHtufv27Zuk85pcjydOnKiyniTPfJLesimRNraynm7duqGw8Pf3V+ejZN6Q80vuS8WKFUvymj/++AOXL1/GvHnz9F5Wyn/Dhg3q2i5NJapXr66u38mvSQWddGg/cOCAarrTvXt3tG3b9qXmll999ZU6ByX7iT7Lakl2JXmt3C/r1Kmjml+ZmjJHSHIMxImIiIiIcgE7axIRERER5QIG4kREREREuYCBOBERERFRLmAgTkRERESUCxiIExERERHlAgbiRERERES5gIE4EREREVEuYCBORERERJQLGIgTEREREeUCBuJERLmkRo0a+OCDDwy2vqdPn8LR0RHXrl3Te9kyZcrg66+/Rn7z888/w8XFJcm8Bg0aYM6cOSiI50jz5s3VMRNRwcBAnIiogPj444/RrVs3VK9ePbd3hbLJl19+ic8++wxBQUEsY6ICwDS3d4CIqLC6evWqwdb17NkzrFixAgcOHDDYOinvad++PZycnLBs2TJMmzYtt3eHiLKINeJEVChJU4zJkydjxIgRcHNzU006+vfvD19fX73XM378ePTr1w+lSpWCjY0NevfurZqJfPLJJ/Dw8IC1tTVatGiBmzdvptnsIPk+OTg4oFevXnjy5Em6+7Fy5Uo4Ozur7STfv7feegsDBw5EyZIlYWtriwEDBqR4nM+fP0932x06dICRkZGapMxke4cOHXppX2rVqqXKomzZsnjnnXcQFhaW+Hx8fDxmzpyJihUrwtzcXO3jvHnz0j3G4OBgDB8+HHZ2duo4ZP+8vb3TXS4j+5zRss/o6zJyjBnZr5TIefrHH3+k+zoiygc0RESFUOnSpTVGRkaaBQsWaAIDAzU3b97UVKpUSfP666/rvR5TU1PN8uXLNSEhIZpz585pHB0dNU5OTpqRI0dqHj9+rHn+/Lmmffv2moYNGyZZtnr16pr3338/ybpMTEw0v//+uyYoKEhz584dTY0aNTR9+vRJdz+6deum6d27d4r7J5f6mTNnagICAjSXL1/W1K5dW9O2bduXXqfvtv39/TXfffedxtLSUuPp6anmyfqlXFesWKEJDw/XeHl5aebNm6dZtWpV4nJSxnZ2dpr169drgoODNXv37lXltWTJkjSP8dVXX9VUrVpVc/78efWeyXrl2JydndMtn7T2WZ/jz+jr9D3G1PYr+Tkitm/fro776dOnGT5uIsqbGIgTUaEkAVXywHXu3LmaEiVK6L2eIUOGJJk3fPhwFYzHxMQkztu0aZMKnsLCwtIMxAcPHpxkXT///LMK4NJToUIFzdtvv53i/rVo0SLJvBMnTqh9kf8Nse1atWppvv/+e/X31q1b1RcT+VKSklu3bqltS1nrmj17tsbd3T3VbVy/fl0tt3///iTzu3TpolcgntI+/197d/MKXRjGcfx6RP4E/gB5KwvkdYFsWNjZeNlQlLJXliKxUxY2FixIEtmwU/LOQl6yEElZU4Sk9HRdPTOZcZj7GBwzz/dT05iZM+dctyld5/jd9/gZv8t2nx2jV11ejfjx8bHtf3V11WmsAH4voikA/lsan3gtMzPTIiV+5eTkRDzWmIFGMtLS0iKeUzc3N772pXGT6+vrmDXo5D2NbHgpLy+PeFxSUiKpqalydHTk+9hbW1tSX18vGRkZkpKSYrGKw8NDuby8tNdra2stcqM3zTDPz89bpCRkd3fX7hsaGiL2q7EMjZm8Fw0K5emjx1JZWfnOb8S9Zj/jd9nOdYyudUULfc5M2AQSH404gP+WNqOvaSOk/yn0S9/n8pwLbcg+Q7PKt7e3ztt7jTPWsTVDXldXJ/n5+bKzsyOPj4+2n9LSUnl+frZtNLu9t7dnkwk1Iz48PGw5+cXFRXv95eXF7rOzs8P5aL2FGuqrqyvnel241Ow6ftftXMbop65ooc9ZP3MAiY1GHACSQG5urlxcXHi+tr29HfFYG2WdTKhXrf3Y39+Xu7s7m4Sqkw/T09PtquzJycmbExxd3aO/v9+aTF1ScWhoKLzGt9KJq//ikRG3wsJCz2MXFBR4jmVzc/NLav5KLmOMp67Q5xx9ZR5A4qERB4AkoI2vRh28rhyvr6/L4OCgxWI04tHV1SXV1dVSUVHh6xh6hVeb7LGxMbm/v5ezszNpbm6OWBFlYmJCent77UuFnp6e5PT01H7W9yq9AtzW1iatra1Wl+5H40ALCwvS2Nj47rHz8vJsdRJdAUabWI27jIyMyPLyctw1fzWXMcZTl5586FrxGmkBkNhoxAEgCbS0tFijvba29ua17u5uOTg4sAaxrKxMsrKyZHZ21vcxNPeua5VPTk5a5r2mpsYawtcNvS6tp5GJpqYmu9cTBP02yNHR0fA24+PjVq8u+6hrYhcXF8v09LR9IdFHdMm+oqIiqaqqsqUiV1ZWpKenJ+6av0OsMcZT19zcnLS3t39r/QB+xh+dsflDxwKAX21mZsauSibqn8XOzk55eHiQqamp8HMae+jo6IjZ5CIx6MmHrll/fn4engAMIHFxRRwAksTAwIAsLS1ZFATJSTPlfX19NOFAkuAr7gEgSWhmONbyiEhsGxsbQZcA4AsRTQEADzrp8KMcrk6y00mPAAB8Fo04AAAAEAAy4gAAAEAAaMQBAACAANCIAwAAAAGgEQcAAAACQCMOAAAABIBGHAAAAAgAjTgAAAAQABpxAAAAIAA04gAAAEAAaMQBAAAA+Xl/AVLa73lWqh0CAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "print(\"== Phase 1 : η=0.05, 9000 steps, batch 16, bruit q=0.15 ==\")\n", + "torch.manual_seed(0)\n", + "model = MiniGPT()\n", + "opt = torch.optim.SGD(model.parameters(), lr=0.05)\n", + "gen = torch.Generator().manual_seed(1)\n", + "CKPT_EARLY = None\n", + "for t in range(9000):\n", + " xb = make_batch(BS, 32, gen)\n", + " yb = noisy_targets(xb, gen)\n", + " logits = model(xb[:, :-1])\n", + " loss = torch.nn.functional.cross_entropy(logits.reshape(-1, 32), yb.reshape(-1))\n", + " opt.zero_grad(); loss.backward(); opt.step()\n", + " if t == 1499:\n", + " CKPT_EARLY = copy.deepcopy(model.state_dict())\n", + " if t % 1500 == 0 or t == 8999:\n", + " print(f\" step {t:>5} : val = {val_loss(model):.4f}\")\n", + "CKPT = copy.deepcopy(model.state_dict())\n", + "print(f\"checkpoint plateau : val = {val_loss(model):.4f}\")\n", + "\n", + "print(\"\\n== Phase 2 : anneal depuis le plateau, 2700 steps, val(η_min) ==\")\n", + "results = {}\n", + "for lr in [0.006, 0.02, 0.06]:\n", + " h = train_run(lr, 2700, opt_kind=\"sgd\", start_state=CKPT)\n", + " results[lr] = h[-1][1]\n", + " print(f\" anneal η_min={lr:>6} : val finale = {h[-1][1]:.4f}\")\n", + "\n", + "lrs = np.array(list(results.keys()))\n", + "vals = np.array(list(results.values()))\n", + "coef = np.polyfit(lrs, vals, 1)\n", + "spread = vals.max() - vals.min()\n", + "print(f\"\\nfit : val ≈ {coef[1]:.4f} + {coef[0]:+.1f}·η_min (pente ≈ 0 = terme thermique sous résolution)\")\n", + "print(f\"amplitude totale du sweep : {spread:.4f} ({100*spread/vals.mean():.1f} %)\")\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(lrs, vals, \"o-\", color=\"C0\", label=\"mesuré (anneal depuis plateau)\")\n", + "xx = np.linspace(0, 0.065, 50)\n", + "ax.plot(xx, np.polyval(coef, xx), \"--\", color=\"C3\", label=f\"fit {coef[1]:.3f} + {coef[0]:+.1f}·η_min\")\n", + "ax.set_xlabel(\"η_min (phase d'anneal)\"); ax.set_ylabel(\"val loss finale\")\n", + "ax.set_title(\"Au plateau du banc toy, le terme thermique C·η est borné, pas résolu\")\n", + "ax.legend(fontsize=8)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "c15", + "metadata": { + "execution": { + "iopub.execute_input": "2026-09-19T07:37:58.331093Z", + "iopub.status.busy": "2026-09-19T07:37:58.331093Z", + "iopub.status.idle": "2026-09-19T07:39:59.075651Z", + "shell.execute_reply": "2026-09-19T07:39:59.075095Z" + }, + "papermill": { + "duration": 120.765223, + "end_time": "2026-09-19T07:39:59.083245+00:00", + "exception": false, + "start_time": "2026-09-19T07:37:58.318022+00:00", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "== SGD vs Adam(0,0), η=0.006, 2700 steps — HORS plateau (ckpt step 1500) ==\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " SGD hors plateau : 2.5037\n", + " Adam(0,0) hors plateau : 1.4351\n", + "\n", + "== Au plateau : mêmes runs depuis CKPT ==\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " SGD η=0.006 : 1.4195\n", + " Adam(0,0) η=0.006 : 1.4222\n", + " decay 1/t depuis η=0.06 : 1.4201 (constant : 1.4139)\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "print(\"== SGD vs Adam(0,0), η=0.006, 2700 steps — HORS plateau (ckpt step 1500) ==\")\n", + "h_sgd_early = train_run(0.006, 2700, opt_kind=\"sgd\", start_state=CKPT_EARLY)\n", + "h_adam_early = train_run(0.006, 2700, opt_kind=\"adam00\", start_state=CKPT_EARLY)\n", + "print(f\" SGD hors plateau : {h_sgd_early[-1][1]:.4f}\")\n", + "print(f\" Adam(0,0) hors plateau : {h_adam_early[-1][1]:.4f}\")\n", + "\n", + "print(\"\\n== Au plateau : mêmes runs depuis CKPT ==\")\n", + "h_adam_ckpt = train_run(0.006, 2700, opt_kind=\"adam00\", start_state=CKPT)\n", + "h_dec = train_run(0.06, 2700, schedule=sched_decay_1t, opt_kind=\"sgd\", start_state=CKPT)\n", + "print(f\" SGD η=0.006 : {results[0.006]:.4f}\")\n", + "print(f\" Adam(0,0) η=0.006 : {h_adam_ckpt[-1][1]:.4f}\")\n", + "print(f\" decay 1/t depuis η=0.06 : {h_dec[-1][1]:.4f} (constant : {results[0.06]:.4f})\")\n", + "\n", + "fig, ax = plt.subplots()\n", + "groups = [\"hors plateau\\n(ckpt step 1500)\", \"au plateau\\n(ckpt step 9000)\"]\n", + "sgd_vals = [h_sgd_early[-1][1], results[0.006]]\n", + "adam_vals = [h_adam_early[-1][1], h_adam_ckpt[-1][1]]\n", + "xpos = np.arange(2)\n", + "ax.bar(xpos - 0.18, sgd_vals, 0.34, color=\"C0\", label=\"SGD η=0.006\")\n", + "ax.bar(xpos + 0.18, adam_vals, 0.34, color=\"C1\", label=\"Adam(0,0) η=0.006\")\n", + "for x, v in zip(xpos - 0.18, sgd_vals):\n", + " ax.text(x, v + 0.02, f\"{v:.2f}\", ha=\"center\", fontsize=8)\n", + "for x, v in zip(xpos + 0.18, adam_vals):\n", + " ax.text(x, v + 0.02, f\"{v:.2f}\", ha=\"center\", fontsize=8)\n", + "ax.set_xticks(xpos); ax.set_xticklabels(groups)\n", + "ax.set_ylabel(\"val loss après 2700 steps\")\n", + "ax.set_title(\"L'écart SGD/Adam(0,0) s'inverse entre régime de progrès et plateau\")\n", + "ax.legend(fontsize=8)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "c16", + "metadata": { + "papermill": { + "duration": 0.007785, + "end_time": "2026-09-19T07:39:59.099628+00:00", + "exception": false, + "start_time": "2026-09-19T07:39:59.091843+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "**Lecture (le verdict honnête du banc toy).** (1) **Le plateau est atteint** : la val passe de 3.79 à ~1.43 ; l'irréductible du bruit est 0.94, le résidu ~0.49 est la limite du modèle — passé le régime de progrès, la descente est finie. (2) **Au plateau, val(η_min) est plat à ~0.4 % près** (1.4195 / 1.4173 / 1.4139) : le terme thermique C·η est **sous la résolution du banc** — nous le *bornons* (C < 0.1 sur la plage η ∈ [0.006, 0.06]), nous ne le résolvons pas. Le GPT-2 du papier résout le sien (3.145 + 110·η_min) parce que ~5M directions de vallée somment chacune leur bruit et parce que ses runs sont intégralement convergés ; à 106k paramètres, la somme est trop petite. (3) **L'écart SGD/Adam(0,0) s'inverse entre les deux régimes** : hors plateau, la dynamique sign descend là où SGD cale dans les directions raides (la physique de la Partie 8 — un |g| minuscule ne ralentit pas sign(g)) ; au plateau, les deux convergent et Adam(0,0) reste légèrement au-dessus — la signature attendue de son plancher de température √(2π)/4·η (Partie 2). (4) **Le decay 1/t ne gagne rien de mesurable ici** (1.4201 vs 1.4139) : quand le terme thermique est sous résolution, refroidir ne peut que coûter le temps de descente restant. Sur GPT-2, c'est précisément ce refroidissement que le WSD achète.\n", + "\n", + "> **Piège :** « le banc toy réfute la loi ». Non — il la **borne**. Un terme plus petit que la résolution du banc n'est ni confirmé ni réfuté par lui ; c'est le dispositif GPT-2 (échelle + convergence complète) qui mesure. La loi est prouvée sur le paysage jouet (Partie 3) et bornée — pas mise en défaut — sur le réseau." + ] + }, + { + "cell_type": "markdown", + "id": "c17", + "metadata": { + "papermill": { + "duration": 0.00821, + "end_time": "2026-09-19T07:39:59.115953+00:00", + "exception": false, + "start_time": "2026-09-19T07:39:59.107743+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Partie 5 — Décroissance optimale 1/t et la discontinuité η₀ = η/2\n", + "\n", + "À chaque step de décroissance, on choisit η_t pour minimiser la variance au step suivant. La solution (R08 §3) :\n", + "\n", + "$$ \\eta_t = \\frac{\\eta/2}{1 + t/t_h}, \\qquad t_h^{SGD} = \\frac{2}{a\\eta}, \\qquad t_h^{SignGD} = \\frac{\\sqrt{2\\pi}\\,\\sigma_g}{a\\eta} $$\n", + "\n", + "Trois propriétés contre-intuitives tombent de la dérivation :\n", + "\n", + "1. **discontinuité** : au switch, η saute de η à **η/2** — pas de raccord continu ;\n", + "2. **1/σ² est une suite arithmétique** : la précision s'accumule linéairement, pas géométriquement ;\n", + "3. **durée de decay bornée** : atteindre η_min prend $T_d = \\frac{2}{a\\eta_{min}}\\left(1 - \\frac{\\eta_{min}}{\\eta}\\right) < \\frac{2}{a\\eta_{min}}$ — décroître plus longtemps ne sert à rien, tout est joué en 2/(aη_min) steps.\n", + "\n", + "Paramétrons le decay par $\\eta_t = b\\,\\eta/(1+t/t_h)$ et balayons (b, t_h) : la théorie prédit l'optimum **exact** (b, t_h) = (0.5, 10) pour nos paramètres (a=2, η=0.1, σg=0.1, décroissance sur T=400 steps, partant de l'état stationnaire)." + ] + }, + { + "cell_type": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "optimum empirique : (b, t_h) = (0.5, 10), loss = 6.03e-06\n", + "optimum théorique : (0.5, 10)\n", + "valeur optimale théorique 1/σ₀² + a²T/σg² : 6.10e-06\n" + ] + } + ], + "source": [ + "a_p, n_p, eta_p, sg_p = 2.0, 10000, 0.1, 0.1\n", + "T_DECAY = 400\n", + "\n", + "theta = rng.standard_normal(n_p) # état stationnaire à η constant\n", + "for _ in range(6000):\n", + " theta = theta - eta_p * (a_p * theta + sg_p * rng.standard_normal(n_p))\n", + "\n", + "grid_b = [0.25, 0.5, 0.75, 1.0]\n", + "grid_th = [3.0, 10.0, 30.0, 100.0, 300.0, 1000.0]\n", + "res = np.zeros((len(grid_b), len(grid_th)))\n", + "for i, b in enumerate(grid_b):\n", + " for j, th in enumerate(grid_th):\n", + " x = theta.copy()\n", + " for t in range(T_DECAY):\n", + " eta_t = b * eta_p / (1 + t / th)\n", + " x = x - eta_t * (a_p * x + sg_p * rng.standard_normal(n_p))\n", + " res[i, j] = 0.5 * a_p * (x ** 2).mean()\n", + "\n", + "fig, ax = plt.subplots()\n", + "im = ax.imshow(res, cmap=\"viridis_r\", aspect=\"auto\",\n", + " extent=[grid_th[0]/2, grid_th[-1]*2, grid_b[-1]+0.125, grid_b[0]-0.125])\n", + "ax.set_xscale(\"log\")\n", + "i0, j0 = np.unravel_index(res.argmin(), res.shape)\n", + "ax.plot(grid_th[j0], grid_b[i0], \"r*\", ms=16, label=f\"optimum empirique (b, t_h) = ({grid_b[i0]}, {grid_th[j0]:.0f})\")\n", + "ax.plot(10.0, 0.5, \"wo\", mfc=\"none\", ms=18, label=\"optimum théorique (0.5, 10)\")\n", + "for i in range(len(grid_b)):\n", + " for j in range(len(grid_th)):\n", + " ax.annotate(f\"{res[i,j]:.0e}\", (grid_th[j], grid_b[i]), ha=\"center\", va=\"center\", fontsize=6, color=\"w\")\n", + "ax.set_xlabel(\"t_h (steps)\"); ax.set_ylabel(\"b (multiplicateur initial)\")\n", + "ax.set_title(f\"Diagramme de phase du decay — loss finale après {T_DECAY} steps\")\n", + "ax.legend(fontsize=8, loc=\"upper right\")\n", + "fig.colorbar(im, label=\"l_f finale\")\n", + "plt.show()\n", + "\n", + "sig0_sq = eta_p * sg_p ** 2 / (2 * a_p) # variance stationnaire SGD\n", + "print(f\"optimum empirique : (b, t_h) = ({grid_b[i0]}, {grid_th[j0]:.0f}), loss = {res.min():.2e}\")\n", + "print(f\"optimum théorique : (0.5, 10)\")\n", + "lf_opt_theo = 0.5 * a_p / (1 / sig0_sq + a_p ** 2 * T_DECAY / sg_p ** 2)\n", + "print(f\"valeur optimale théorique 1/σ₀² + a²T/σg² : {lf_opt_theo:.2e}\")" + ] + }, + { + "cell_type": "markdown", + "id": "c19", + "metadata": { + "papermill": { + "duration": 0.008099, + "end_time": "2026-09-19T07:40:01.396335+00:00", + "exception": false, + "start_time": "2026-09-19T07:40:01.388236+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "**Lecture (l'optimum tombe pile sur la théorie).** Le minimum du diagramme est exactement en (b, t_h) = (0.5, 10) — la discontinuité η/2 et la constante de temps 2/(aη) = 10 steps — et la valeur finale mesurée y colle à la prédiction close-form $\\ell_f = a/(2\\sigma_0^2 + a^2 T/\\sigma_g^2)$ à ~1 % (6.03×10⁻⁶ mesuré vs 6.10×10⁻⁶ prédit). Autour de l'optimum : t_h trop petit (3) = on décroît trop vite puis on stagne (perte ×4) ; t_h trop grand (1000) = on n'a pas eu le temps de refroidir (perte ×15-30) ; b = 1 (pas de discontinuité) domine partout b = 0.5 à t_h égal. Le schedule n'est pas un hyperparamètre à accorder : c'est une solution d'un problème d'optimisation." + ] + }, + { + "cell_type": "markdown", + "id": "c20", + "metadata": { + "papermill": { + "duration": 0.008005, + "end_time": "2026-09-19T07:40:01.412886+00:00", + "exception": false, + "start_time": "2026-09-19T07:40:01.404881+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Partie 6 — Loi de Fourier : relaxation bi-température\n", + "\n", + "Que se passe-t-il juste après un switch η_A → η_B ? La largeur σ était à l'équilibre chaud η_A ; le nouvel équilibre est froid η_B. La relaxation est exponentielle (R08 §4, loi de Fourier) :\n", + "\n", + "$$ \\ell_{f,t} = \\ell_{eq}(\\eta_B) + \\left(\\ell_f(\\eta_A) - \\ell_{eq}(\\eta_B)\\right) e^{-2 a \\eta_B\\, t} $$\n", + "\n", + "Le taux 2aη_B est indépendant de l'état initial — c'est la **conductivité thermique** du système. Mesurons le switch η_A = 0.2 → η_B = 0.02 à a = 0.5 : taux prédit 2aη_B = 0.020/step, soit une demi-vie de ~35 steps." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "c21", + "metadata": { + "execution": { + "iopub.execute_input": "2026-09-19T07:40:01.430176Z", + "iopub.status.busy": "2026-09-19T07:40:01.430176Z", + "iopub.status.idle": "2026-09-19T07:40:02.701967Z", + "shell.execute_reply": "2026-09-19T07:40:02.701456Z" + }, + "papermill": { + "duration": 1.284568, + "end_time": "2026-09-19T07:40:02.704514+00:00", + "exception": false, + "start_time": "2026-09-19T07:40:01.419946+00:00", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "équilibre froid ℓ_eq(η_B) : théorie 0.00005 | mesuré 0.00005\n", + "taux de relaxation : mesuré 0.0195 | théorie 2aη_B = 0.0200\n" + ] + } + ], + "source": [ + "a_f, eta_A, eta_B = 0.5, 0.2, 0.02\n", + "lf_eq = lambda e: 0.5 * a_f * SG ** 2 / (a_f * (2 / e - a_f)) # équilibre SGD à learning rate e\n", + "\n", + "R = 4 # 4 répliques indépendantes -> taux stable\n", + "hist_sum = np.zeros(800)\n", + "for r in range(R):\n", + " rr = np.random.default_rng(100 + r) # sous-graines dédiées : reproductible\n", + " x = np.zeros(N)\n", + " for _ in range(4000): # thermalisation chaude\n", + " x = x - eta_A * (a_f * x + SG * rr.standard_normal(N))\n", + " for t in range(800): # switch -> relaxation\n", + " x = x - eta_B * (a_f * x + SG * rr.standard_normal(N))\n", + " hist_sum[t] += 0.5 * a_f * x.var()\n", + "hist = hist_sum / R\n", + "\n", + "t_idx = np.arange(len(hist))\n", + "mask = hist > lf_eq(eta_B) * 1.05 # zone exploitable du fit\n", + "slope = np.polyfit(t_idx[mask], np.log(hist[mask] - lf_eq(eta_B)), 1)[0]\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(t_idx, hist, \"-\", color=\"C0\", label=\"mesuré\")\n", + "ax.plot(t_idx, lf_eq(eta_A) * np.exp(-2 * a_f * eta_B * t_idx) + lf_eq(eta_B),\n", + " \"--\", color=\"C3\", label=f\"théorie : taux 2aη_B = {2*a_f*eta_B:.3f}/step\")\n", + "ax.axhline(lf_eq(eta_B), color=\"gray\", ls=\":\", lw=1, label=\"équilibre froid ℓ_eq(η_B)\")\n", + "ax.set_xlabel(\"steps après le switch\"); ax.set_ylabel(\"perte thermique l_f\")\n", + "ax.set_title(f\"Switch η={eta_A} → η={eta_B} : relaxation exponentielle (taux mesuré {-slope:.3f})\")\n", + "ax.legend(fontsize=8)\n", + "plt.show()\n", + "\n", + "print(f\"équilibre froid ℓ_eq(η_B) : théorie {lf_eq(eta_B):.5f} | mesuré {hist[-1]:.5f}\")\n", + "print(f\"taux de relaxation : mesuré {-slope:.4f} | théorie 2aη_B = {2*a_f*eta_B:.4f}\")" + ] + }, + { + "cell_type": "markdown", + "id": "c22", + "metadata": { + "papermill": { + "duration": 0.012067, + "end_time": "2026-09-19T07:40:02.728104+00:00", + "exception": false, + "start_time": "2026-09-19T07:40:02.716037+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "**Lecture (pourquoi les schedules marchent — et quand ils échouent).** Le taux mesuré épouse 2aη_B : après un drop de learning rate, la perte thermique met ~1/(2aη_B) steps à atteindre son nouvel équilibre. C'est la contrainte cachée de tout schedule : chaque palier de refroidissement paie son temps de re-thermalisation, d'autant plus long que η_B est petit. Un decay trop rapide laisse la loss au-dessus de l'équilibre (le régime t_h = 3 de la Partie 5) ; un decay trop lent paie des steps inutiles à température haute (t_h = 1000). Le 1/t optimal est exactement le chemin qui suit l'équilibre thermodynamique — la loi de Fourier est ce qui transforme la recette WSD en physique." + ] + }, + { + "cell_type": "markdown", + "id": "c23", + "metadata": { + "papermill": { + "duration": 0.009818, + "end_time": "2026-09-19T07:40:02.750075+00:00", + "exception": false, + "start_time": "2026-09-19T07:40:02.740257+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Partie 7 — Force entropique et piégeage (App. E.1)\n", + "\n", + "La largeur thermique σ(y) dépend de la position y le long de la vallée (via a(y)). La perte *espérée* inclut donc un terme $\\tfrac12 a(y)\\sigma^2(y)$ qui varie avec y : son gradient est une **force**\n", + "\n", + "$$ F_{ent} = -\\tfrac12\\,a'(y)\\,\\sigma^2(y) = -\\tfrac{d^2}{2}\\,(\\log a)'(y) \\quad \\text{(pousse vers les zones plates, } a' < 0 \\text{ le long de la descente)} $$\n", + "\n", + "C'est l'analogue exact de la **force entropique** en physique statistique (F = T∂S/∂y avec S = −d²/2·log a) : le bruit ne fait pas que vibrer autour du fond — il *exerce une force systématique vers les régions de faible sharpness*. Sur un paysage $\\ell = -c\\,y + \\tfrac12(a_0 + b|y|)x^2$, la descente (pente c) et la force entropique (s'oppose à l'entrée dans des zones plus étroites) s'équilibrent : le walker s'arrête. La prédiction qualitative du papier (App. E.1) : **plus de bruit σg → arrêt plus tôt, en zone plus plate**. En SignGD des deux coordonnées :\n", + "\n", + "$$ x_\\pm = \\tfrac{1}{\\eta} \\pm \\sqrt{\\tfrac{1}{\\eta^2} - \\tfrac{b\\,\\sigma_g^2}{2c}} $$\n", + "\n", + "et au-delà de σg² > 2c/(bη²), aucun point d'arrêt n'existe — le walker est repoussé à x = 0 (le plus plat)." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "c24", + "metadata": { + "execution": { + "iopub.execute_input": "2026-09-19T07:40:02.775371Z", + "iopub.status.busy": "2026-09-19T07:40:02.774373Z", + "iopub.status.idle": "2026-09-19T07:40:15.959632Z", + "shell.execute_reply": "2026-09-19T07:40:15.959632Z" + }, + "papermill": { + "duration": 13.197151, + "end_time": "2026-09-19T07:40:15.959632+00:00", + "exception": false, + "start_time": "2026-09-19T07:40:02.762481+00:00", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "arrêts (moyenne finale de y) :\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " σg=0.5 : arrêts y0=1,4,5 → ['135.1', '138.3', '139.4'] | x+ théorie = 19.9\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " σg=1.5 : arrêts y0=1,4,5 → ['45.0', '48.5', '49.4'] | x+ théorie = 19.4\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " σg=3.0 : arrêts y0=1,4,5 → ['21.7', '24.8', '26.1'] | x+ théorie = 17.4\n" + ] + }, + { + "data": { + "image/png": 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Aty00C0Fx4DYkDsSSfphw8oFAwMFjfvsK4EuEL0F514uBT/jxLq54AQa8aVRUG4qjPOswbwfACQMDm6wBJww92pcXt6KKWxa3qPRAiMH+Yg5OIBjACEFmKQWi9lm41W2Opc8vK+hPALGCqaQfO3tT3r6w9jNgRYJwg50H30s8wmIwevToEi0R1vS5PfvRmn7Bha/5IKvKALd2Ld2SNwdCGBYS9AUuQktj/vz56jYxvvOWwA+2fh+W1B+Wvr8QALhFXdHptSwdQ9ifls4R5eXHH39UogeBDRSggSUIljj0X3mPEZzr0ceWzjGwr+Hcamv7NRGNQWfFge3BtsBqoLeNlLd9pf0m2PvYqCr7v7zt3LVrl9x4443GwfslaYbiKG+f42IbOPI8SDFdydk8ygIOCPxQar4tS2g/tDgJQfha+sHCaF79yGhr1ouLAAhpjPbHFTveC38ZvqDIBICTl0ZFtaE47LGO8qJl/zD/EYCn1Rz4wix9wXHCuHDhQhGRiD7E+vXREkufZamvtc/Sg/VAdJljnttTax+iF1q0x5zSLgDLS3n7wprtA4hGwwsJcLJHxAP+O4he+GiLw5o+t2c/WtMv5sdkefrHHuCHW8skUxw4J8CPje3D+AZLuZz14HwDHyiATxKebWwXLojgW8d4BHMxXVx/WHoN+xfrwn4pq/e1vGDfmY/B0I6rkkSAtq+xL3F3Qy9OcIzowXpwNxBTYmKiuvCCuELaOZzPy3Ne1KKUls5x6HscT4jo2oL2G4HsEZbAtsJrizEr5vupotpn72Ojquz/8rZz7Nix6tyKu33wLWO/4HuJKDUyg+g1g737XDtu9FqjwnGYocTFKS6bhzmWPNMjRoxQI1e3bdtWZPns7GwTL/P111+v3g9fqJ5Zs2YV8Stbs16Mcr7sssuKLPfSSy8V8eZWVBuKw5p1aF5neFbNgSe0Xr16xufwW2HZOXPmFFm2uPWcOHFC+ezgpdb7OnNyclSmALxn3rx5RTydL7zwgsl64N3FelDpsjgf6/Hjx9Uy8MKmpaUZ58NLh+PNfL9gZDp8bvCH6/sHnjS9ZxZVOdGf8BCi2qY52EZUh7Q3tvSFNdsHL5/e76wBbyGWs1Tprjx9bq9+tKZfSqqWWNb+Ka5/b775ZoOPj0+ZM+yUNZsHPhsex7KgnR9RQVYP/JcYB4HXsE2l9YfmmX7wwQeLvNalSxflxTxy5EiR1+CphZfWvP2rVq0ylBXNi4p+h69VA+cLnDdwzGjHoCUv6rRp0yyO5dDOxZpn9vz58yZjWTQwVgDLlTaWoaRtwzkcflzzMQaa93XUqFFlWk9Jfnu8B9tkDr5rffv2Nbz//vvFvt+a9mn7w9zfa2mcgTXHRlXf/7a0Mzc3V52boAXMGT16tFp26dKlZTpGytPn+Fycv+x5rioNRqarAPAsITsErvBwNQ4LBW5Xwd+LLBHIcwxfkTbyFqNckYECo5ZxOwY+QrwfV5F636A168V6kIHglltuUT5TXBXDd4ZbOeZUVBvs0T/WoHme33jjDXUljqiglme6OGDdQR/h9hoyL8Abjfdh9DNGkONK2TxjAfzUqPQFbxs8ZIhwItqPqF1Jt72xLuTERc5x+NXxubhbgL6wFNFBZhVEXtFP2C/wrcE3rNkRNOA9xeeiAhxug2N78Vm4DQ+fG44DeIAt3f7To+VMR3SyrNk8ytsX1mwfjgl4nhExxkhwRD8Q0URbEfUpqeCENX1ur360tV+s7Z+Svg8YI3H77bcr3zm229Y808iggPXie1sWtL5CdA1RL4zjwN0u9D8yDdgDZEiBpQ13E3AOg10A/YysQYh+Yx5yduvPEbhzh5zzOHbKkkMZwG+KcymOC/h8cfwhanr33XeXGDHUch8j64SWVQbjVDDpI+04HnEnEe3B5yAai77S7siUFpUsadswVgR3EeDJRSYWnGNxfsPxhOijvnpmefoId45wXJl7m3HLH8cf7lAgsml+p1fLM21N+yrq2Kjq+9+Wdrq7u6sMKvjdQzuxPxE5R+YeS7aPko4Ra/scxwXGkWDf25rFyCocJttdHFsi01q+SIygNc/FiKvDxx9/3GTZp556qshyL774orrK7tatW7nWu3nzZpXtQr9M/fr1VV5e8whoRbWhJMq6Dmsi08A8n7B5nmlL60FmgV69ehVpC/pry5YtJstqkTNE5nAlr19+8uTJJstaihYiwopsEfr3oR+Q/9p8v+AqHhEb/bLISqHtQ31kEpGIe++9t0ibMKG9GzZsKPOxPHHixFKXtUdflHX7kL0B+8J8u/z8/Axffvllqe20ps/t0Y/W9EtJkWlr9r+l/sVIe0Sm7ZlnujwgN7R5X+J7iX62R2QafP755yozgvnnIKuAfv8iShoVFVWuPNNfffWV6mPzHLz6OyOWIpNA21Ztwn5BPmB9NgfcGenQoUORbcAxdM8995Sag7ekbcN7tawS+gl50D/77LMyr6ckEGlFhhd9TmJso/ln6idtf1rTPmsi09YcG1V9/9vazh9//LFInm9k19Iybegj06UdI9b0uXZH+Y8//jA4EkamHQQGNuGKsjRwBY1BO4iA6kHkBld08Br9999/6ooLURqs09z/9eabb6qrO+RZBFgGPmdEtswjQGVdb7du3VQez59++knlmkU7Meoe0SC019xTVRFtKImyrgNXyGivNoBCD9qL7dSD9mObsU5E5bTtLGk9iBQgEo7Io74CIgZjFFf1DtFFjLbGlTwihriqNh8ljatz85yZyCixbds2FQlHtBOjmxG5Kc4zjcjmt99+q67qMeAG1fAwWAPbove3IsKBqneYj+3Qqmfh8xFlNq/kWNKxjAiDNZS3L8q6fYhcoX8QJcEdE0RbsCzWWdJA19L6HPvZ/Ltgj37EuhE9Lku/aMtawpr9b6l/8Toi+IjuIe882lAZpbU/+ugj9V3FIFJEKnF8oS+RF1jzZZbWH/CaYptRjc0S48ePV5kgcD7BeQ/LIyKGAeP6aBzmo09xLCCzBAarlTXPNKL7+/btUx59+FkRecOdDv0xgT5HO3GM6cExhTskiEZim9EfaB/uuGjZaXBnBL5YZKDBhH2G9eCcaP77YomStg2RUWTFgH8d0UF43nHXBceN+TFR3j7CXQv8XiBThzZwH+fbkga1avvTmvbhTg/Waem7r1VFLM+xUdX3v63tvOWWW9TvJu6GIZsWPhPtxLkHy+qrMJZ2jFjT5xjMjDuByEPvUBwq3YlDsHSFjYpv2N1vvfWWy7ShKlBSJNEWECEwj5K6al8Q4kyUFAklhiJ3OFHt0lJO5apKVdn/VaWdelBhGA4A8yqXjoCR6WoIRtEiIoYoFh4RwYG3ClfYiJC7ShsIIYRUXZCtA3cfEI0sLiMOIRqIeqOCMSLgjoZiuhqCQVUY2ITSyPoBTMjPigFyrtIGQgghVRdYGN59993KbgapIlxzzTVqqgwopqshX3zxhfKbaT4peMTgr7I192dVa0NVoCSPqy3Au2bJy+6KfUGIM1GSR5dUf6rK/q8q7XQW3OD1qOxGEEIIIYQQUhVxYBI+QgghhBBCqhcU04QQQgghhJQTimlCCCGEEELKCQcglgIKOqCwAwotlKXAAiGEEEIIqdogLSPKsiMtIwrFlATVYSlASJtXxSOEEEIIIdUfZCVDJciSoJguBUSktc50ZFo3lOpFCU6kpfHw8HDY5xLnhccE4XFBeK4g/A1xDAkJCSqYqunAkqCYLq2DCqwdENKNGzcWRwonHx8ftRMppgmPCcJzBeHvB6GucDxlsfhyACIhhBBCCCHlxOnE9KVLl2TXrl0qvF4WsOzevXuLfT09PV0OHDggKSkpdmwlIYQQQgghTmTz2Ldvn3zyySfy66+/qpLCjz/+uLz11lslvmfmzJkyZcoU5StOTEws8vrTTz8tH3/8sSplfezYMRk1apTMmDHDrraJ1NRUJdRhy7AnKEyJTCK4uHBzc7PruknVxFWPCXxfg4KCJDAwsLKbQgghhDhvZHrt2rXSoUMHFUUOCAgodfmYmBgllgcNGlSs0J42bZqsWbNGrXPnzp3y448/yquvvmpXIX3ixAklcOwNxBI8064kmkjJuOoxge8Xvmf4vhFCCCHOhtNEpidNmlTmZfPy8uSuu+5SUemsrCxl9TAHQnrkyJHSuXNn9bx58+YyceJE+fTTT+W5556zS85oRKSxnoiICLsPEkQUEjkOsX5XE0/EMq56TOCuT2xsrPq+MTpNCCHE2XCayLQ1vPPOOypt3IsvvmjxddhEDh06JH369DGZj+d4HyLV9vqR9/LyYrYNQioQXKjie2ZvKxUhhBBSrSLTZWX37t3y8ssvy99//61ueVvi+PHj6rFhw4Ym87Xn8E+3bdvW4ntxK1l/O1kbCIkfcvMfc0QKESHEo73BOrWJEB4T+d8JCuqioE9wt459Q3hMkJLgucI6rDmnVikxDUvH6NGjZcKECdK7d+8SlwOIZunx9vZWj5mZmcW+94MPPlBi3RxEtM3FO7ycmIdb7xUpHFzpln5J/Pfff1KrVi2HFs8piaSkJDl69Kh07NjRIZ9X2jERHR2tjsVWrVpJdQNiEd9blHYlRftGy1bk7l4lbzYSO8NjgvC4sB3ovmoppj///HMlXm6//XY1oBDgxxUCA88hsurVq2ccwIi0eHrS0tLUY0m+y0ceeUTGjx9fpAIOMoaYV8HRsirYw39tjhaRrkr+2FOnTikLDfzpjRo1KnHZP//8s8hdg3bt2hW7/IULF+TWW2+VDRs2lLm/rWlPaVy8eFENZr3sssukadOmah6OM2SIWbduXZkqJFXkMYEvPY5bzP/++++Nd2Hwvahdu7axzfYkLi5ODh48aPxO9erVq8gy2pgGX19fadOmTRGxB4G8Z88e9R2+/PLLxd/f3+Jn4X1YhyP6uaqhXWCFhobSckZ4TBCeK+xESYHXKi2mEQVu1qyZ3HfffcZ5J0+eVCJ5zJgxaj4ERWRkpBIciNTp0Z63bNmy2M+AKLAktuHbNB9kqAmaihK7WK82OTtffPGFPPTQQ0psIoL89ttvqwGixXHNNdeoTCza3YMrrrhC2rdvX+zyc+bMUcuUVUxZ257SeP7551WaRQxs1Y4/CL8RI0ao+a+99po4guKOCQjo6dOnqzZ98803KrUkeP3112XAgAEm3xl7sW3bNvnyyy/VBSfao13gaixbtkymTp2q9tnp06fVxcdff/2lLnjB/v375eqrr1Zp73Ac4Lv8+++/S5cuXYrddlYDlWIvNiydo4jrwmOCVJfj4lRKhny+NlZq+HjKI1e2cNjnWtVHBickKCjI8OSTT5Zp2UcffdQQEhJSZP6QIUMMffr0MZl3yy23GDp27GhVW44dO4ZwoHo0Jy4uTk0VQV5eniErK0s92srBgwcNf/31l2Hp0qVqWr58ucnr+/fvN+zYscOQnZ1tWLt2rSE5Odmq9ScmJhr8/PyM68U6fHx8DCdPniz2PejTs2fPlvkz2rVrZ/jnn3+Mz1etWmU4d+6cyTJbtmxR+6k87SmJ7du3G7p3727o2bOn4ZNPPjF5bdeuXYZGjRoZyktmZqZxv2zatMlw4cIF42spKSlqO3Nycgx79+5VnxUdHa321aVLl9T2Hj16VC2rLbNt2za1ToBjE9+BKVOmqPXj/RXBggULDO3bty8y/5dffjGcOXNG/Z+bm2u4+uqrDQ8//LDx9TvuuMMwatQo4/MHHnjAcM0111j8jIr8rlV1sO8TEhLUIyE8Jkh1OVccSUw3PPXTbkPzZ5YYwp783dD6+aWG5Av5v2+OoCT9Z47TRKaTk5OVhUO7bYmMHIh04coAt3+t5Y033lC+6ocffliGDx+uImIoCGNuL7AXWTl5cuL8JTv7Y3PEw8OyzaNRsJ94e7qX6pu7/vrrZfPmzdKiRQvZvn278o0jwjt48GC1zJ133inLly9X0Xx8JgZnIsppngmlJP755x+pX7++cZ14b1RUlIpM4o5BcWD/IlqJ6HFJucVhYUBRn+7du5tYfrBNL7zwgtFyg8/fuHGjsoKUpz2WwLGItI1IqYhjyRwMZMWdEdhJivMqr1q1Sr2GNlmyryDaDVB4CFHepUuXKssLMtLcdttt6r3wQt94443q7sxXX32lthcRXtiSsJ+HDRsm2dnZ4ufnpywpOM7//fdfOXz4sOo/5GXHfi/OSgP/P+wYsErpLSFoT3k96miTPhqCvtJ70GDD0u/T1q1by44dO8r1WYQQQqoHh06nyYyV0fK/XSclryAHQ6Cvp4zp1Uzc3Z3zTr3TiGmIoGeeeUb9D2EH4QfhA5GFgi7FAS+sJbGNQWHr169XafQefPBBady4saxYsUL69u1bIe2HkB743ipxFCsfGyDhoTVKXOaHH35Qggq303GrHZ5fCCpUmgS//fabsagNfLU///yz3HLLLcb3Q6ThIqQ4IGaRYxve2fDwcJPXMB+5gYsDt/ffe+895Ws+cuSIzJ49W3nhLQEhGBwcLDVqFG7vuHHj1EBU2C9wsfHTTz8pwQxhju0qqT1l3S6AvsKx1LVrV4vLQiTi2IKFqDgxDV81thWWEHMwoFJ/gYcBsNgmXPhpYwJgWcFFES52YCmBTxk+Y20bhw4dqiatYihSRuK7tHDhQvn2229LtXmsXr1a5W3HdwnbAZsFcrTjIgGfh+OnvECM46IJ+xD7CJPGY489Jvfcc48S67B5fPTRR/Lhhx+W+7MIIYRUXXYdOy/TV0bLX/+dNs4Lrekt9/SJkFE9mkqAr2lSCWfCacQ0PLSYrAXRQksRQwARBDHhqiAiffPNNxt9xv369VOCc+vWrUoAQkTddNNNSkgDLAtxp4/KalFTS9x9991KdCIiisFhevAc84tDLyAh+iCOr7zySpPP1w8CMM+kMnDgQCWKcaGF7Zo7d64ShKC09pR1uxClh5jEBUlJoG0lVcFEW0uK7qI9EMe4G4OLBlxIauA5hLQeXBBqQhoD/HBnQbvDAMENUYz+KCuIeuPCE1UG0f+4sP3f//6n1mPr9wdCHH2NCyYMBMUgOQ30CSZE/THGAd5pHJeEEEJcA4PBIJvjkpSIXns40Ti/YZCvTOwfKcO7NhFfL+f3dzuNmK7qwHaBaLEjbR6lAYFnbp+oWbOmcfQ/Io96cQP0y8Nig0F8JUVwATKdwKKgBxFV/S38koAQxOBACEoIY3Ngj0AaOi2vN8Aj7lzMmzdPwsLCVEYNTfiV1p6ybhcivBDCuCgB58+fV+IQkdYOHToYl8dnaYPqLLFgwYJiX0O0HHcLYM9ABg4IW33bITDN0c9DTnTsT1g/9Jky9O0rDQjZ/v37q36GLUSLTGN7cZGjF/fWgkGmmLRINO4mwG4D8BnI0PLkk0+q57NmzVJ3RrQMIYQQQqonBoNBVh08q0T0tqPJxvm44z65f6Tc2LFRqVZWZ4Ji2k5gp5dmu3B06Wh4UPW31eFLhxjEfIBIIYrfaMBygeikRlkjuBCpEKcQX4ikwge8ZcsWefXVV43bAgHVs2dPJQQhAPUZU5DpAf7ZunXrWvwcRNORpQJCTxO6YOzYscoDjPchqq29v7T2lHW7mjRpooS0tiz6ZuXKlUr0amIVIh/91qlTp2LXV5JnGhcDEJuwcgDcLYAFpqzgYgjrfemll0xS02l5h8tSORAXF/AqY5/gLsB3331njEwvWrRIyov5fsa+QvRcIz4+3sTDjWwumKe/aCKEEFJ9yM0zyJ97TykR/V9CYYG8VvUDZOrAKLnm8gbi4aS+6JKgmK7GQBS++eabyi+LiO/MmTOVcEO+X+11DNRExBCe4BkzZijxpQkZ/F+WAZsQkrAeIMoIDyyipJinDWKEmIOnF/aBHj16KO86UqphcB2sGvDJDhkypFjPMdoDCwoG5unFNAbKod3wIyMdXFnbU9btMi/eg/fD96z3H2M9aLvez22NZxq2BohXTBg4CM+0tWAfI8qLdHi4oIBlAxdO8+fPVxdM8F/jggQXB5YGIOoHm8KyguMCU2kg2g8LDKqS4i4H+gKWIeRlB/DA47iDjx02D6Qn1FL2aQMUH330URWJx0UjxjdgHoU0IYRUL7Jz8+TXnSdlxqpoiT17wTi/Y9NguW9glAxqVbdKn/urTgydWA2iwBA78AsjwgjR9+OPPxpfh5cawgsRxCVLlsizzz6rPLPFFc4oicWLFyuhDFEIwYZBgBqwHyDaiigxQFaK+++/X4lqRCrvvfde9f6SwPKI4pqXV4dAhXXlhhtuKHN7ygvWB0uJHniTMcC1JEryTEPsY/sxWBTZNHDBc9VVVxn3H+wXenABYZ6PG3YXCGfYZLB/MYAX2U4AxhPgQgIWCs1eYS8w8BRRe4hpiHb8rz++cMxhf8HmglzfyBWO7CMaGNwJe88ff/whv/zyi/K8W+P1JoQQ4txkZOfKgo1HZMC7q+SxRbuMQrp3VIh8M6G7/Dy5l1zRul6VFtLADfnxKrsRzszx48dVRA+D0cwHRyHaBlBIxt7Yw+ZRFhAN1cQzxBGiw4gUlpSqrrJAlgukOUSKNY3JkyeryDeygTga2D4QFcYAOkfgqGPCGanI71pVB8c/7hLg4rgqFWIgFQePCVLZx0V6Zo4s3HRUPl8bJ4nphZUEB7euJ1MHRkrHpkWTDVQl/WcObR4uzujRo9UAOIjnd999Vw0GdEYhDTTPM4BPGZFtZAJBer/KAJ5iRwlpQgghxNlJvpAl8zYcUVPKpfwMWrBAX9uuoUwZECmtGxStMF0doJh2ceBXhk8X4hSZFmwpue1IkPEB2TuQm9iazBWEEEIIsS9nUvNLfi/cHC8Xs/IHvXt5uMnNHRvLpAGRdk3Q4IxQTLs48OCWlNnCWYGX2NxPTAghhBDHEX/uony2JkYWbTsuWbl5ap6vl7uM6NpU7u0XIQ3LkMa3OkAxTQghhBBCrCr5PXNVjCr5nVtQ8zvAx1Pu6hUmY3uHS2hN00Jr1R2KaUIIIYQQUqaS30hvt2xfYcnvkBreMq5PuIzuGSaBTlzyuyKhmCaEEEIIIcVmktoUm6REtL7kd4MgX2XlGNG1qfh5u3YmIYppQgghhBBSRESvOHBGVSvcHn++ypf8rkgopkmVARlHUIBGK/5S2aAEOkqWl5Z/0lEgPzjyiNarV6+ym0IIIaSKAg/0kj0JSkQfOJVWbUp+VyQU08Qu7Nu3z1idEFUCS8tVvXfvXpPnEMglidKsrCxVCh1V/MoqpjMyMlTSdeSD9vOzbURxdna2SsfXsGFDVTIbQLiiTagyWdm5uS9cuKBKcaM8O8qua32EZPModa61uaI4efKkpKSkSOvWrS1eBKGv0HeuVmyGEEKqClk5ebJ4x3GZtTpW4hILS353QsnvQVEysGXVLvldkTA+T+wCir2gtDdKV69evbrU5S+//HK57bbb1HswTZ8+vcTlv/rqK+nSpYuqRlQWUD4cJbyRPg+RWn2Z6/Lw9ttvqzZ/8803xnko93399deX2nZHgHLhr732mnz88ccq97YGyonr21wRIDrfuXNn6dmzp8l8CHnMR7/hEZUrDx8+XKFtIYQQYh2XsnJl7vo46f/uSnnypz1GId23eah8d28P+WlyLxnUquqX/K5IGJl2ARC1jI+PV9FBgDKi+ghiamqqivyGhoYqsYNIrlZivKzs3LnT6nLPa9euVZ9ZFubMmSMvvPCC8TmixBDW+nYePXpURYi9vLzkrrvukpkzZyqh/ssvv6hKj4gilydCiz6BGO/atWuR11DefOTIkfLUU09JeUB58AMHDqj/a9WqpfpeH1nHfmvRooWK+qalpaltw77CtickJIiPj4/apkcffVSJ2szMTHnxxRfV+8+dO6f2LZbDnYDSov/l5cknn5TBgwerCxg9aAe2Z/PmzeLu7i5jxoxR/fTTTz/ZvQ2EEEKsI+Vitny18YjM3XBEki5kGedf3aaeTBkQJe2bOIelsirAyHQ1Z+LEiUpsXX311dKuXTvp1q2b3H333cbXn3jiCRW57dixo1xzzTVKFG3fvt0hbTt9+rScOHGi1OUgCLdt2ya9evUyzoMomzFjhokNA5Hr2NhY+eeff5S1AUIa3HjjjVK/fn35888/y9XOSZMmqVLr3t7eRV5DxBViFZ9bHBD+EMOWwHwtOo/2I3obFxenXoMARmT9lltuUfsOpcu/++47Jd7xuf369VO2l7Nnz8qQIUMkIiJC2rdvr94D/zTELYTs3LlzyxT9x77AhZceCPiSWL9+vWrnuHHjLNo7sM88PT2VmEZ70VeEEEIqj7NpmfLm0v3S++0V8v7yQ0pIwwN9U8dG8tfD/eSz0V0opK2EkWl7kZMlknLMbqsT+I9zc0Q8PEUs3VoJaiLiWVTc6fn999/lhx9+kP/++08iIyNVRHDUqFHyxx9/qNdXrlwpX375pYqMwucMqwD8toVNMCgvdHFAhNepU6dcm9emTRsV1YWgRnQZgg+RY0scOnRIWSr0XmmIt2eeeUYee+wx9RzCEVFuCFJsV/PmzU3WgeiuZjGwZrtgL8H/V155pbz88stFlkWUH1Uk0YcQs5a44oor5L333jOKez0hISFG/zja9fTTT8uzzz5rtGZAkA4dOlTtO7wOG8eWLVtk48aNylIDsF5EgM+cOaPaM3XqVLWOzz77TB0DAwYMkPvuu6/Euwp33HGHEtK4cLn99tuVYIeQxt2AHTt2WHwfLmBQfn7+/PkqKm7pQg5Ra7QTEfVPPvlEPSeEEOJ4jiVdlI9XxMvv/51T/miAbBzDuzRRKe6a1LbujjQphGLaXkBIf5IvbuwB5HOJqc/v3y4SElniOuBdvvXWW5WQBohwIhINIXbDDTeoSC18yxDS4N577zUROxBLlgSgxgMPPKDeUx70AhJRXwg4RGQtDeS7ePFikQGEiKJDrGHwH6K08+bNU9YOzR5hblOpWbOmXLp0yartgk3ipZdeUnaUksBnIbNHcbRq1arUQZOIJEMM9+3bV4lhDfTH+PHjTZZFhFcT0rCJ/Pzzz0o042IB/QnhD9tHWUFU/ddff1XRfPTNwoUL1YUKBDoEcHG88847Sqh36NBBVq1aVeT1Hj16qGMLFhuI/KioKNV2QgghjuPgKVQrjJbfdicYqxXW9PGUUT3CZFyfZlI3wJe7w0YopqsxiDIi8qkH0VtNVCYnJ5ukUcOtePh2NRBNhK2gOOyRgg0DGh5//HF59dVXZffu3dK7d+8iy6DNaKseiDOINIho+IBhd4ANAmAbzJdPSkoyCtCybhc8v7BPYF2YIOphU8DAOv1ASLxWUoT+77//LvY1ROZhQ9m/f7+yogCIag1LHm/9PsVnQwA/8sgjJstY4w1HRB1tQGQathNc2Lzxxhsq2gxRvWbNmiLvQT9MmzZN+dFxYYQLIWQSwf8QzUhhiDsPuFOAizbsZ+xjXMQ5ykZECCGuzPb4ZJmxMkb+3l9YrTDYz1Pu6RMud/UKlyA/16xW6FRiGkJt0aJFyp+KW9z44UX0DVE43NZGxDMwMFBcBtguEC22E4gw5uTmiKeHp+URtPi8UkBEGpYHDYhB+Hc1CwQGC8KLrBdmSHFWEZFpiCy0BxFmrBeCVn8sIZpc3PHSsmVLJZ6PHDliMsBx7Nix0qdPH5VyDSIcdgsA0YwIO7YXUWMM2Nu6dasx6l7W7cI+gJDUxCQEI2wXuBj54IMP1DxYISCuNaFuCfQ5hDKsKubAioF2b9iwQe1nWDisid5CxON7B1sIfNUa2EYAvzJEbmleaQhetAP+69mzZxsj07hrYAnsM1x04O4AgBDHhH6FJQX7DFYa2E204xe+fWQcQb9yVDghhNgfnF9RpRDVClG1UKNhkK+M7xsug8J8pUnDeuo3ldgRg5UkJycbHnnkEUPNmjUNAQEBhiuuuMIwfvx4NQ+PeI75eP3hhx82JCUlGaoyx44dwz0R9WhOXFycmiqCvLw8Q1ZWlnosL6dPnzYEBQUZ3nzzTcP69esNt99+u6F3797G1+Pj4w3+/v6GDz/80LBu3TrDsGHDDJ6enup/a4mOjjbs2bPH0LBhQ8P06dPV/xcuXFCvZWdnqz7cuHGjev7tt98aJk2aZFixYoXh77//NgwaNMjQs2dPQ05OTrHrHzlypGH27NlF5uN9vr6+hrlz5xrnoc86d+5sGDFihGHNmjWGu+66y9C2bdsS118W0HeffPKJybzFixer9pdEo0aN1DZb4oMPPjB06tTJsHbtWsOyZcsMXbt2Nfj4+KjXtm7daggLCzPZrmnTphmGDx9uso53331Xbd8vv/xi2LBhg3qObQaPP/644cYbbzTs3LnT4jFsL1auXKmONT043rB/sJ+xH3BuGDJkSLnWX5HftaoOjuuEhASbj29SfeAx4Xrk5uYZluw+abju47WGsCd/N06D3ltp+GFrvCEzO5fHhR31nzlWR6YR1UQ+Wdwmxy1wS1c38HEi0oUIFwZ+IdpFHE/dunVVtgXcXocnFrfcEQnVgFUB9gjc0scAPniOcQset+itBVFf3KGAxQJZNjAtWLBAZQlBFBIDDjUfM6KXiO7icxFBRcYHeLlLulKGjxh2kAkTJpjMR5t37dql/OAa+DxsDwbzPfTQQ+puyZIlS2y+Eocdwtw2g8F3JQ3uK80zjQF8SOkHmwb2B/oR/QIQxUeE19y+YZ7eDoMwEZ3//PPP1d0FROu1XNMPPvig8k8jLR2+r2+++aZUBPBbX3bZZSbz8P3H5z3//PMqWgIPNSLehBBC7EN2bp78suOEzFodIzFnC7MxtWscJFMGRMpVl9UX94JqhVp6XGJ/3KCorXkDbpdbyrdbHLhtjXRsVRVU0IPIwa18cxED24G1uZWtsnnk5Kjb9BV5SxxfLk1kwsKAW/14rOiKeeXhnnvuUeIYRUD0QhL+XQyaczSwR9x///1qAKAjcNQx4YxU5HetqoPvMAIWsPzw1i3hMeE6hVa+2xovn6+JlZMpGcb5PSNCZMrASOkTFVrkd4LnCvvpP3OsjkxbI6RBVRbSrgB8x8j4gawRr7zyisqS4YxCGnzxxRfG/zFQDhFpDEDEILjKAJ5iRwlpQgghJOVStny96ah8uS5OzukKrQxuXU+J6E5NC5MIkCqUzQMpwWAdgD0AKh7p2CB6MJIf6ciIcwMLAGwgiEZjEJ9WPc/ZQXo/zcYBWwMhhBBSXUlMz1QCesHGo5KWmaPmodDKDe0byqT+kdKyftG0sqSKiOk9e/aoinnw2Hbv3t2Y9QB5a+GZhQ+WODeomIdS2VUN+H8xEUIIIdWVE+cvKSvHt1viJVNXaOX2Lo1lYr9IFlqpDmIaKcSQAg/5ZvU+TlRPu/nmmymmCSGEEEKsJOZsusxaFSOLd5yQnIJCKzW8PVShFeSJrhvIQivVRkzjVjuimhDS5lkPkJOXEEIIIYSUjb0nUmTmqhhZsjdBtPQQwf5eMrZXuNzdK0yC/b3ZlU6Iuy1vhr3DvNKcVsGttPLJ5iBLAUoiI6KN0ZPFpfBCyWT4ZDGwEVkd7rzzTmU3sQRKHKNQBCqyDRw4UP73v/9Z1SZCCCGEkIpm65EkGTN3i1z3yTr5Y0++kK4b4CPPXdta1j85SB4c3JxCurqK6f79+yurB6of6pk1a5byUlsDBpPhfRDHqK6GbA3moKIdcvZGR0crawmqvkHQI3/ypk2bTJZFfuWrrrpK+vbtq3Jew44CoY58y4QQQgghlQnSna46eEZun7VRbpu1UVYdzK/J0bS2v7xx0+Wy9smBMr5vhNTwsTlXBKlgbNpDiB6j4AZyv2oZFYYOHapyS2/evNmqdb311lvGHKnIJ2wJlEV++OGH5b333jPOQ6EKZBBBkQoUhdB47rnnZMCAAeoRIDoNWwqKRgwbNqxc20sqF5Qcd3d3F29v57jNhYIzmLRiNJUNyqbj5Ozj41PZTSGEEFIMeXkGWbbvlExfFS17T6Qa57eoV1OmDoySay9vIJ4eNsU6iYOxaW+h4tmOHTvUgEOkVkO1OxT92LZtmxKv1lCWYgOosqYX0gDiCpX+EM3WR7CRWeTaa681Wfa6666T//77T1WcIxUDxKW1Arks4EIKF27WevHLuv7SgEjFHRgIVo2kpCTp3LmzZGZmijP0OyxNgwYNUtUl9d8FfZsr6rMtgX5Bn+kn7EdCCHHVaoU//ntcrvxwtUxeuN0opNs3CZbP7+oifz7YT4Z1aEQhXQWx+d5BeHi4SoPnCCxVfTt06JCqyoiSxRoxMTHqRzsyMrLIwEjNdx0WFmbxMyDK9cIc1fW0ykHmpTghsNAmK4tIlgmsU5ucHfTL9OnT1YUOKrHhQurjjz9WPvXi2LBhgypxDXGMykIovgLbUHF8//336lhDefqy9Im16y8NbB+qHWK7tPLhuIjr16+fKptdWknxij4m3n33XVWaHMV3Xn75ZeOYA5Rbx3ZXRPswJuHZZ59VF9SwW+HzkbNc+56+88478tprr6my6Bq4a9W8efNyfR62m+Vwi4I+wfmOfUN4TDgnGdm5sujf4zJ7bZycPF8Y4OkVGSKT+0dIz4jaBVoC3+OKawfPFdZhzTm1ShdtQQTujjvukPr16yuho28TML/9jsi2/nVLfPDBB0qMmHPu3Lkit88R9cQ8DJ60N3rhYI/S0WlpaSbrCwoKMvks/Bjj7gCWQ79ZU5YY+/3kyZNKwEJgwvsOfzrKbVuyZKDfUHXxkUcekalTp6rjBc9xkVPcMQPBOnnyZGNf44IH+1PfzgsXLqjMMtgea9dfEtg2XDC2a9dO9ZN+f+M4f/DBB2XSpElSHtBWbXwAtsfLy8v4GvYXtikwMFAthyizdvGGZdEOtAd9/Pjjjxv34xVXXKFeQ2QYE9aRmJiolrOnJQUXOBDMGLNw8OBB42DfUaNGqdfRlrvvvltdiOgpz/cF68K24GKNFO0b7RjCnTpCeEw4B+mZufLz7rPy7Y7Tknyx8LzXLyJI7uraQNo2gCbJU+dnR8Djwjqg+ypETEMwd+rUySmKtuDWMgYVIgqNCFmtWoUlNNEeYH57W7sdr71uCQiw8ePHm0SmkTkkJCRE6tSpU0TMQ9yYpwa0B1r0UZ+/uzygRDj85BDJEDEQn7j4QK15gEjrSy+9pD4P/blixQoVxbWmqiA88/C8a4wbN05lXEFWF7xmDo4TCEX0NX78IXgRWf3777+V6DUHIhIDSiHetL6GtQjedwhs7SSB7C4LFixQ4tGa9ZelSiT6CH2F9en3N6pGQqSfPn1alRe3BIQ/orN6oayBPmrZsqXxeEWke/78+eqiZOfOneqi5KabbpJvv/1WPcJa9ccff6iLOFy8oN9xQYn+RppK9MMNN9ygLmiwH5ctWyb//POPWu72229XF74lfafM22hpnsbMmTON/+NCAwN+UeIddwQA+grHLo67kr5zZQHrwjrMv4OkMHoSGhpq1UUwqb7wmKhcUOZ73oYjsmBTvKRl5ItodzdRXmhEoiurWiGPC+uwxsJplQpEZgyIZESbKrNoCwQDbl8jCg6x0KFDB5PXNQuHJhj1EVT965ZAFBCTOfiRMv+h0rYXj9m52XLywkmxa2Q6J1c8PD0siumGNRqKl4dlkaOB/kHkcPny5WpwJiKEGJAJ3zjWCW877DEQW/C745Y8LoTwmvaZ5pla9EAg6qP1EI0QsjhGunbtqvrZUtsRxWzdurWxP7FMmzZt5MCBA8VaeRCJhcDUGDt2rHz44YfKWgAglLE+WBowv7T1l3W7fvvtN7VdEKIQ0/q+AVgOFwz79u1TdhJL4LNhgRkxYkSR1+rVq2dsCyL2EP7YJ4jE43NwzEJA4qIO24M24IIHaR7RNiwzceJEFbHFWAC0B99PXEThAgLHAAbilmTzwD7HOiDOkdIS/+M7jAswXJCsXLlSSgMXAuvWrVN3dbT+QT/+8ssv8vXXXyshjOg9bCDljZ5ivRSLlkGfWjpHEdeFx4TjOYlqhWvzqxVmZBdUK/Rwl1tVtcIICQvJvztemfC4KDvWnE+tEtNIMYeoEzzKn376aaUVbcGPPVLcLVmyRA1KM6d27drStm1bJSQmTJhgnI8INsSLFgm0JxDS1y2+ThzF7zf9LmGBxV8UaPvrlltuMfYRBBUEFkTPNddcI4sXL1YXQxC+AP5X/QBPXJVZiixrQJg/9thjxueIZkMoQ/j+9NNPxYomCG54e/XgAgbzLaFZOvQgSgvhuX//fiWc586dK6NHj1aCq7T1l3W7sDyi0ogElwSsI5ZSOWrAUlOWDCQQpDi2EWnWgC0DGWjwpdbuVqCftcG1uLD86quvVOQeyyCSjItc3B3Avi4LuFOAz+jZs6dKO4mLLgxkRKT9qaeeKtM6YLPCxQREuAb6UDs+cFcLdxJwYYAoOiGEVBdiUa1wdX61wuzc/PO0v7eH3Nm9qUptV4/VCqs9VkemcRsXAkNftAUWCFuLtpQVfDZu5SMyh4hbcSAqjhR7EP+wovz7778q2vfiiy+6jK8QPiy99QBCs2HDhkbhh/2E5xq4na+/jY4o55EjR4pdv35gGdi9e7cSfLjIuf7669WxYj4IVBO25uIT0VlLdwS0iyP9oFCtbRCdsDIgRzkurvB5ZVl/WbcLUVSIVvQJ3o9bZLD2wHai9x7jNbSxOBC1Lg5EfyF8UbBIiyzqPcX4bPOr4wYNGpjsY0S0IX71WOONhrXEPDKN6De264033ig1lSS+a0iFiYvV4q7kYQ+DyMd2UkwTQqoD+06myAxUKywosgKC/LxkTK9maqpVwznSuJKKx2qzL6Jwmu9SK9qC4il68Vyeoi2IkmqDCCGcYBXA7WFE9TQxEh8frwYIQsRDgOhBMRfc6tdAlBI+VkRe8QOPqB/Wr10I2BvYLhAtdqTNozRgs0BEUANRS3jMkRUDQGjDQqEBkYgUh+WNTAO0FQIUgk8vpiHMEC3GvoC3GRc1mh8XIhUZIfSDSPXgTgIEJgY06i8OcAxAtKNiZvv27VWmD1Da+su6XRDciO4j6q0NXMU27d27V/maAcQ1jkt8fnGU5JlGFBjrRb/jWMcFCTz6ZQViG1H74tJR4sKxtOwnEMKwhWDcAyL9uOtU1sg0+gqRewjp0i6gIfqdJUc4IYTYUq1wxspoWVlQZAWgWuGEvhFyR/emUpNFVlwPgw3s27fPEBQUpKZrr70Wv9iGIUOGGGrXrm04fPiwVeu6cOGC4dixY0WmEydOGJfJycmxuAymU6dOWVwv3nPmzBlDdnZ2ubYR68Z24dGcuLg4NVUEeXl5hqysLPVYXtA2f39/w4IFCwxHjx413H///Ya2bdsacnNz1esHDhww+Pn5GRYtWmQ4cuSIYcKECWpb165da9XnfPfdd4a33nrLcOjQIfU577zzjiEgIMDYZ+h7rHfjxo3G582bNzc89NBDhtjYWMOTTz5pCAsLM2RkZBT7GcOGDTN8/fXXRea3b99eHX+ffvqpcV551l8Wevfubfjkk09M5v3555+G7t27l/i+Ro0aGb799luLr73++uuG/v37q32F79MVV1xh8PHxUa9t3bpVtVsDx8K0adMMw4cPN1nHU089ZejXr59h27Zthvj4ePVZkyZNUq89+OCDhrvvvtuQmJiovmP25LXXXjM0bdrUsH//fkNycrKa9J8xYsQIw/Lly9V3ePHixYZatWoZ5s+fX67PqsjvWlUH57iEhAT1SAiPiYoB59+VB04bbpu5wRD25O/Gqc/b/xi+3nTEcCnL+b9/PFfYT/+Z4zRFW3BbGp5L80lvQ0BU09IymOCFtgTeg+hdRWTccHYQfUXUEHcKkHUCAzJhwdBsLoj4wjKDqCQyMSCSjf1nbQU9+JcR/YUdAJYBeHAxMFQbkKel4tP2AR4xeA7ZYDAwEt573P4v6XORtUOLBuvBQERE1PWD+8qz/rKAyLr5OnD3RBsEWR7PNHzsyMIAXzu25cYbbzRGeLEd5tYXfL65hUOzo8DWBD81tl2LKKNt8EHjzg2qh9oTeLVhp0Ef41jDpL+7gDZgMCg8+bCLwMONgcOEEFJVyM0zKBvHdZ+skzFzt8qWI0nGaoUfjeggKx8dIHd2DxNfLw7+dWXcoKgruxHODLIpwEYAIWqerUHz3ZZkGSgv2C2wNtiaGs8aYMVAxgxssz5zhrMwZMgQJchg49B44YUXlGiGTcjRwHaCVHsY0OmILAqVcUw4CxX5Xavq4EIW2Vws+euJa8JjwnaycvLkl50nZNaqGIlNLBwcj2qF9w2Mkita1RV35LurQvC4sJ/+M8fqcK3eU1sayGdMnBt43jFIE1FXZHRABNsZhTSAf1kDfmgc4F9++aV8/vnnldIeeIoR9SaEEFI9uJSVK99tjZfP18TKyZTCaoW9o0Jk6oAo6RkZ4nLBDFI6VotpfSaB0mDQ2/lBgQ9YAXCRBCG9aNEiqQrAyoCsE0j9N3To0MpuDiGEkCpMyqVsWbDxiHy5/ogkXSgs+HbVZfVkysAo6dCkYjKUERcV0ygAQqoPyLpibeYVZwBFgTARQggh5eVMWoZ8sS5OFm6Kl/TM/LSkHu5uckP7hjKpf2SlVSsk1VxMV0XhRQghhBCiEX/uony2JkYW/Xtc+aOBt6e7DO/SRO7tFyFNapc9Vz8h9EzbALJi6AtsEEIqBlR6dMWMPIQQ+3LgVKrMXBUjv+06KXkF6RcCfDxlVM8wGdc7XOoE2Jb1ibgm9EzbANKdoeQ0ilGgkAwhxP7g+4VCO9ZUdSSEED3/HkWhlRj558AZ47yQGt4yrk+4jOoRpioXElJe6Jm2AeQHRnU7VMCriMpuiMa5SulzUjZc8ZhA9VKkfMP3jRBCrEmCsOZwokxfGS1b4vLzQ4NGwX7KynF7lybi5810ksR26Jm2pfM8PVV6tOTkZLvbPXASQDQOEW+m4SGufEwgIl2rVi3aPAghZS608ufeUzJjVbTsO5lqnB9Vt6ZM7h8pN3RoKF4erhWUIBWLp70iR8j5i9y/elB1rbpTo0YNNdkbJlcnPCYIIaTsYCDh4h3H5bPVsaaFVhoHqfR2V7auV+UKrRAXENOIyCLX708//aRuP5vDPNOEEEIIqUguZuXIN5vjZc7aODmVWlhopU9UqEweECm9WGiFOLOYRsU8lFT+559/ZODAgbJhwwY1vfrqq/L888/br5WEEEIIITpSLmbL/I1HZO76OEm+WHhn/Oo29WTKgChV+psQpxfTS5YsUVObNm3U8x49ekjPnj2lWbNm8v7778ujjz5qr3YSQgghhMjZtExVaOXrTUeNhVY83d1kWIdGMnlAhETVZaEVUoXE9PHjx42+aAwSQmaLoKAgufrqq2X06NH2aiMhhBBCXJwT5y/J7NUx8t3WY5KpK7Qyomt+oZXGtZg+k1RBMQ2fNFJWgSZNmsiWLVvkyiuvlJiYGPHz87NXGwkhhBDiosSeTVeFVhbvOCE5BZVWanh7qEIr9/QJl7oBrPNAKhe7lRQbOXKkjBo1SoYMGaI81Ndee629Vk0IIYQQF+O/k6kyfVW0LNmTIIaCaoXB/l4ytle43N0rTIL97V/fgRCHi+k9e/YY/3/22WdVHti1a9fKiBEj5MUXX7Rl1YQQQghxQf49mqwKrazQVStEme97+0bIyO5NpYaP3eKAhNgFm47Itm3bGv+H3QPZPQghhBBCrAGpdNdHn5NPVx6WTbGF1Qob1/KTSf0j5dbOjcXXi9UKSTUU0w888IDcc8890r59e/u1iBBCCCEuQV6eQZbvPy0zVkbLruMpJtUKpwyIlOvbs1ohqeZieunSpfLJJ59Ip06dlKiGbzo4mHkdCSGEEFI8Obl58vvuBFXy+9DpdOP8to0C5b6BUXLVZfVZrZBUGWwqTn/48GFZtWqVXH755fLEE09IgwYN5M4771QDEFn9kBBCCCF6MnNyVbXCQe+vloe+32kU0t2a1Zb547rJb/f1kSFtG1BIkyqFzS7+/v37qwkR6u+//17mzp0rgwcPVoVb4uLi7NNKQgghhFRZLmTmyLdb4uXztbFyOjXTOL9/izoydWCUdAuvXantI8QW7DYkNiAgQMaMGSP169dXmTy2b99ur1UTQgghpApy/mKWzNtwRE3nC0p+u7mJDGlTX4noto2CKruJhDiHmD5w4ICKSH/11Vdy+vRpGTRokCxcuNAeqyaEEEJIFeN0aobMWRsrCzfHy8WsXGPJ75s6NpKJ/SPVAENCqgs2iek5c+bIl19+KRs3blS2jokTJ8rYsWMlLCzMfi0khBBCSJUg/txFmbUmRn7cdlyycvNLfvt6oeR3U5nQL0IaBbM6Mql+2CSm77//frnpppvklVdekSuuuELccO+GEEIIIS7FgVOpquT3b7tOSkHFbwnw8ZS7eoXJ2N7hElrTp7KbSIhziulTp05JUBD9ToQQQogrsj0+WWasjJG/9582zgup4S339A2XUT3CJNDXq1LbR4jTi2kKaUIIIcQ1qxUiR/SGmHPG+bBw3NsvQm7v0kT8vFmtkLgOTlXgPjU1Vb777jvZunWrDB06VG6++WaLyyUnJ8u8efMkJiZGmjRpInfddZfKcV3e5QghhBBSvmqFkXVqyOQBUTKsA6sVEtfEpqIt9mTGjBnSsmVLJaSRCWTLli0Wlzt58qR06NBBfvvtN2nVqpVs2LBBFY1BRpHyLEcIIYSQ4snOzZOftx+Xq6etkYkL/jUK6csbBcmsUZ1k+cP95dbOjcXLw2kkBSGuGZkeOHCgygTi5+cnixYtKna5p59+Wi2zbNky8fLykqlTp0qfPn3k4YcfVuXNrV2OEEIIIUXJyM6VH/89LrNWx8jx5EvG+d3Da6sc0X2bhzLxACHOJKZbt25d6jI5OTny888/y+OPP64EMkAGEdg3pkyZomwdtWrVKvNyhBBCCDHlYlaOKvk9e02snEkrrFZ4Rau6MmVgpHQOY7VCQuwuprOysuTYsWOSnZ1f3UgD9gp7gvLk6enp0qZNG5P5eJ6Xlyf79u1T0eeyLkcIIYSQfFIuZctXG47Il+vjJFlXrfCayxvI1AFRclnDQHYVIfYW04jwolDLTz/9pESqpRG/9iQpKUk9BgcHm8zXnmuvl3W54gZBYtJISEhQj7m5uWpyFPgs9KkjP5M4NzwmCI8LUhHnisT0TJm7/oh8vTle0jMLqxXe2KGhTOwXLhF18qsV8veoasPfEOuw5ni3SUw/88wzcuLECfnnn3+U5xmD/DC9+uqr8vzzz4u9cXd3tyjSNSHv4eFh1XKW+OCDD+Tll18uMv/cuXPi4+O4pPNoa0pKisn2ENeGxwThcUHsea44k5YlX/97Wn7de1Yyc/J/L7093OSGtqFyZ+d60iAQv3mX5OzZQr80qbrwN8Q6oPscIqaXLFmiJs1O0aNHD+nZs6cqLf7+++/Lo48+KvakXr166vHs2bMm8xMTE01eL+tylnjkkUdk/PjxJpHpbt26SUhIiNSpU0ccfUUUGhpaovgnrgOPCcLjgtjjXHFUlfyOlcU7Tkh2br6IruHtISO7N5V7ejeTOgGsVlgd4W+IdWRmFo4XqFAxffz4caMv2t/fX9kjUMjl6quvltGjR4u9Qa5oCOFt27bJHXfcYZyP58jcoYn6si5nicDAQDWZgxOSo0UtIgqV8bnEeeExQXhckPKeKw6dTpPpK6NNSn4H+XnJmF7NZGzvZhLs783OrebwN6TsWKO93G29ZaB9GASslhsaRVIgWu0NMnKMGzdOFixYIGfOnFHzMNBw9uzZSjRrn1nW5QghhJDqzu7j5+Xer7bJVR+ukV935gvp0Jo+8tTQVrL+qUHy8JUtKKQJcYbUeCNHjpRRo0bJkCFDlIf62muvter9mzZtkjlz5qj/L126pHJBw5aBiPfHH39sXA5ebBR26dixo/Jpb9y4UVkw3nvvPZP1lXU5QgghpDqyJS5JZqyOlbWH8y2OoGGQr0zsHynDuzYRXy/e9SSk0sX0nj17jP8/++yz4unpKWvXrpURI0bIiy++aNW64EeG5xpoj8B80B+iyn/99Zca6BgbGyv33HOP9OvXr0g4vqzLEUIIIdUFDLxffeisfLT8oOw6mW6cHx6Kkt+RcmOHRuLtyUHthNgTN4O989dVM+ALh4UFebQbN27s0IECGECJiwxeABAeE4TnClLib0aeQZbuTZCZq2Jk38nC9K6t6geoaoXIFe3h7sZOdGGoKypO/1kdmT516lSZl61fv761qyeEEEJIGcnKyZPFO1DyO1biEi8Y57epX0MeHNxSrmxTnyW/CalgrBbTDRo0KPOyDHoTQgghFVPy+7stx+TztbGSkJJhnN+3eagqtBJZM1fq1q1LIU2IM4rp5cuXV0xLCCGEEFIiKRez5auNpiW/wdVt6smUAVHSvkmw8XY+IcRJxfTgwYMrpiWEEEIIsciZtAz5Yl2cLNyEkt85ah480MM6NJTJ/SOleb0A9hwhVT01HiGEEELsy7Gki/LZmhj5Ydtx5Y8GPp7uKrXdhL4R0qS2P7uckEqGYpoQQghxMlCtEJk5/rfrpMrUAWr6eMronmEyrnc4S34T4kRQTBNCCCFOwo74ZJmxKkaW/3faOK92DW+5p0+4jOoRpsp/E0KcC4ppQgghpBJB5qsNMedk+spo9aivVnhvvwgZ3rWp+Hmz4BghzgrFNCGEEFIJ5OUZZPn+0yoSvevYeeP8iDo1ZFJ/ViskxGXEdHp6unz22Weyfft2VS1m9erV8sUXX8jw4cOlZs2a9mklIYQQUk3Iyc2T33aflBkrY+TwmcKS320bBar0dle3qc9qhYS4ipjes2ePSpXn6+sr3bt3lzVr1qj5sbGxMmPGDHniiSfs1U5CCCGkSpORnSs//ntcZec4lnTJOL9beG2ZMiBS+reowyIrhLiamH7ggQfktttuk2nTpomnp6fxJDBy5Ei5+eabKaYJIYS4PMgL/c3mo/L52jg5m5Zp7I9BreoqEd2lWW2X7yNCXFZMb9y4UX788UclpPVERERIXFycrW0jhBBCqizJF7Jk7oYjMn/DEUm5lF+tEDGnay9vIJMHREqbhkGV3URCSGWLadg7kpOTJSQkxGT+mTNnJDg42Na2EUIIIVWO06kZ8vmaWPlmS7xczMpV87w83OTmjo1lYv8IiajD8USEVCdsEtP9+/dXVo9vvvnGRDzPmjWLZccJIYS4FEfPXZBZq2Plp3+PS1ZufrVCXy93uaNbU1WtsGGwX2U3kRDibGL6zTfflF69ekmzZs2kT58+at7QoUNly5YtsnnzZnu1kRBCCHFaDpxKVdUKf9t1UgqKFUqAr6fc3bOZjO3dTEJq+lR2EwkhziqmL7vsMtmxY4e8++67SkB37NhRmjZtqjJ5hIeH26+VhBBCiJOxHdUKV8bI3/sLqxWG1vSWcQXVCgN9Wa2QEFfA5jzTEM0Qz4QQQogrVCtcH31OZqwyrVbYKNhP+aFv79JEfL1YrZAQV4IVEAkhhJCyVitcGS27jqeYVCtEoZVhHRqKl4c7+5EQF8RqMf3aa6+VednnnnvO2tUTQgghTlWt8PfdCSoSfeh0YbXCNg0D5b6BUXIVqxUS4vJYLabnzZtncrsL1Q6Blh7v3LlzxlzTFNOEEEKqarXCn7Yfl1mri1YrnDowSvo1D2W1QkJI+cR0dHS08f8PPvhAFW2BwG7RooWad+jQIRkzZoyqjEgIIYRUJS6oaoXx8vnaWDmjq1Y4sGUdmTIwSrqyWiEhxJ6e6Q8//FD++ecfo5AG+B/ievDgwfLwww/bsnpCCCHEIZy/mCXzNhxR0/mLhdUKr0G1wv6R0rYRqxUSQipATJ8+fbpI9UOAeXiNEEIIcWbOpGbInHVxsnDTUblQUK3Q091Nbu7USCb2j5RIViskhFSkmG7ZsqW89957qniLHszDa4QQQogzcizpovJDL0K1wpzCaoUjujaVCf0iVKo7QgipcDGNYi033HCD/P7779KjRw81b9OmTco3/dtvv9myakIIIcTuHD6dpqoV/rrrpOQWlCsM8PGU0T3DVLGVUFYrJIQ4UkwPGTJE9u7dK++//77s2bNHjWxGefGff/5ZmjdvbsuqCSGEELux69h5ld5u2b5CC2LtGt5yT0G1wiA/ViskhFRS0RYMOPzss89sXQ0hhBBiV5C+dWPsORWJXns40Ti/QZCv3NsvQlk6/LxZrZAQ4oIVEHGC/O+//+T48eNSv359adu2rXh4WD4hwnKCXNhNmjSRNm3aOLythBBCHF+t8J8DZ1Qkekf8eeP88NAaKjPHjR0bibcnqxUSQlxUTB87dkxuuukm9di+fXslqgMCAlS+a71YzsnJkdGjR8vSpUuVn3v79u3SsWNHWbx4sfj7+1fqNhBCCKmYaoV/7EmQGStj5ODpNOP81g0CZcqASJXmzsPdjV1PCHFtMf3AAw9ISkqKHD58WAIDAyUjI0MGDBggY8eOlS1bthiXe/vtt5WQ3rVrl4SFhUliYqIS008++aR88sknlboNhBBC7F+t8LPVsRKfdNE4v2uzWqrQyoAWdVitkBBSYVS5+1xbt25VAx8hpIGvr6/ceOONKvKcm5ufIxTAx43INIQ0CA0NlXvvvVcVlMnMLKxqRQghpGqSnpkjs9fESN93Vsqzi/cahfSAlnXkh4k9ZdGkXjKwZV0KaUJIhVLlItMRERESExNTpMR5s2bNjL7pkydPKhtIt27dTJaD3SM9PV1ZQxClJoQQUvVIvpAlczcckfkbjkjKJVYrJIRULlVOTH/00UcybNgwmTx5svTr109FpP/44w/59ttvjctATAMMTtRTr1499ZiQkFCsmE5NTVWTBpYFiHrrI98VDT4rLy/PoZ9JnBseE8TVj4tTKRnyxfo4+W7rcblYUK3Qy8NNburQSO7tF64GGAJX6IuScKVjgpQdHhfWYc33xyYx/dprrxX7mo+Pj0RFRcnQoUOVFcNeoFR59+7dlYBGlg5EpTEQURPK2uBDYJ7hQ3uenZ0fybDEBx98IC+//HKR+efOnVPb5ChwIoQ3HLi7Vzk3DqkAeEwQVz0ujp3PkAXbTsuS/85JTkGhFV9Pd7nx8lAZ2ame1A3wFjFclLNnC/3SrowrHBPEenhcWAd0n0PE9Ny5c5Wg1UQuirZgoB9o0KCBnDp1Spo2bSrr16+XRo0aia1AJA8ePFguu+wyZfXw8vJSB8eECRPUIEQIa2T2CA4OVstrJxMN7XmtWrWK/YxHHnlExo8fbxKZhl0E21enTh1x9BURvN7Fpf0jrgWPCeJqx8X+hFSZuTpWlu49JQUaWgJ9PeWunmFyd88wVXSFuNYxQcoPjwvrsGZ8nU1ieurUqfLrr7/Kl19+KZGRkWoeBC0ya9x8880ycuRINT3xxBOycOFCWz7KuG5k8XjjjTeUkNauuseMGaPaAMtH//79VVsQDT9w4IDJ+/Ecgr9169bFfgYGNmqDG/XghOTokxK2rTI+lzgvPCaIKxwX244kyYxVMbLiwBnjPJT5ntA3XEZ2byoBvqxW6GrHBLEPPC7KjjXfHZvE9IcffigrV640CmkAaweE7RVXXCEPP/yw8jhfe+21Yg8Q3YYYPnjwoMn8/fv3q8fGjRurRwjt66+/Xr777juVCk+7zfXNN98on7UjI8yEEELKVoxr9aGzKkf0liNJxvmNa/nJxP6RclvnxuLrRWFICHE+bBLTp0+fltq1axeZj3mweIDw8HBJTk4WewALx2OPPaa82mlpadKhQwcVbYbPGWnw9KL+zTffVN7q2267TU1//fWXbNq0SdasWWOXthBCCLGd3DyD/Ln3lKpWuO9k4eDvFvVqypQBUXJduwbi6UHfLyHEebHpDNWiRQuZNm2axYg1XgO7d++2axq6d955R/73v/8pL8svv/wiSUlJ8tVXX8n8+fNNloOw3rlzp2oHqh7CJ71jxw7p1KmT3dpCCCGkfGTl5MkPW4/JlR+slqnfbDcK6fZNgmX26M7y54P9VNlvCmlCSLWOTKPKIAqmQNxikB5u06EKIfI4Q+iCBQsWyAsvvCD25Morr1RTacD2gQg1IYQQ5+BiVo58t+WYfL42VhJSMozz+0SFqpLfPSPzB7MTQohLiGl4offs2aNsFnv37lXzYK34/vvvpVWrVur5jBkz7NNSQgghVZaUi9ny1cYjqthK0oUs4/yr29RTdg5EpAkhxCWLtkA0z5492z6tIYQQUq04k5YhX6yLk4Wb4lX5b+Dh7ibDOjSUyf0jpXm9gMpuIiGEuFYFREIIIc7PsaSL8tmaGPlh23Hljwbenu4yomsTmdA3QprU9q/sJhJCiHOIaWTHWL16tcVKMZYGJxJCCKm+HDqdJjNXxcj/dp1UmTpATR9PGdUjTMb1aSZ1A+xXEZcQQpwBm/NMo2Jg8+bNLabII4QQ4hrsiE9WhVaW/3faOA8VCsf1biajezaTID8WWiGEVE9sEtOIPCMl3V133WW/FhFCCKkSIIPTxphzMn1VtKyPLrw72TDIVyb0i5ARXZuKnzcLrRBCqjc2iWlYO2699Vb7tYYQQojTk5dnkH8OnJHpK6Nl57HzxvkRdWrIpP6RcmOHRsofTQghroBNYrp169YSHR0t7dq1s1+LCCGEOCU5uXnyx54E5Yk+cCrNOL9Nw0CV3m5I2/oqUwchhLgSNolp+KXHjx+vckm3bNmySKL9mjVr2to+QgghlUxmTq4s3n5CZq6OkaPnLhrndwmrJVMHRcmAFnVYaIUQ4rLYJKZHjhypHrt27Vqsn44QQkjVrVb4LaoVromVU6mF1Qr7tagj9w2Mkm7hHHhOCCE2ienFixezBwkhpJqRcilbFmw8Il+uL6xWiBuPQ9rUV3aOyxsHVXYTCSGkeojpG2+80X4tIYQQUqkkpmfKl+viZMHGo5JmVq1wyoBIiarLaoWEEGL3oi3p6ekyZ84c2bt3r3retm1b5aOmX5oQQqoGJ85fUlaOb7fES6auWuHwLk3k3n6sVkgIIRUmpg8ePCiDBg2SpKQkadGihRqAsnDhQnn33XdlxYoValAiIYQQ5yT2bLrMWh0jP28/ITkF1QpreHuoaoX39AmXuoGsVkgIIRUqph999FFp3769fPXVVxIaGqrmJSYmqiIujz32mPz222+2rJ4QQkgF8N/JVFVoZcmeBNHGiaNC4djezWRMr2YS7O/NfieEEEeI6dWrV8uePXuMQhrgf6TKY+5pQghxLrbHJ8v0FdGq4IpGnQAfubdvhNzRvanU9LHZ+UcIIS6HTWfOnJwc8ff3LzLfz89PsrOzbVk1IYQQO4AUpZtik+TTlYdNSn43ruWnqhXe2rmx+Hqx5DchhFSKmO7SpYu89tprMm3aNHF3zy8dm5ubK6+88kqxuacJIYQ4RkSvOnhWPl0ZLf8eTTbOj6xTQ6W3u6FDQ/HyYMlvQgipVDH9xhtvyFVXXSVLly6VHj165EdANm2SEydOyPLly21uHCGEEOvIyzPIsn2nlIjedzLVOL91g0BVaIUlvwkhxInEdN++fWXfvn3yzjvvKO80GDx4sDzxxBMSERFhrzYSQggphZzcPPnf7gSZsTJGDp9JN87v2DRY7h8UJQNb1mXJb0IIqQBsHm0C0Txr1iz7tIYQQohVIC/0L3vOyjc7/pP4pEvG+T0jQpSI7hkZQhFNCCHOJKZPnTpV5mXr169v7eoJIYSUgUtZuarIyuw1MXIqNdM4f2DLOnLfoCjpHFab/UgIIc4ophs0aFDmZeGhJoQQYj/SMrJlwaaj8sXaODl3IUvNcxORIW3rydSBzaVtoyB2NyGEOLOY5sBCQghxPMkXsmTuhiMyb32cpGbkqHke7m5yfbsGMrxdsHRr2VQ8PJjijhBCnF5MY4AhIYQQx3AmNUO+WBcnX286KheyctU8Lw83lR8aeaIbB/vK2bNnuTsIIaSSYLkrQghxQuLPXZRZa2Lkx3+PS1ZOnprn6+Uud3RrKvf2i5AGQX7G3P6EEEIqD4ppQghxIg6cSpWZq2Lkt10nJa9g2EmAj6eM6hkm9/QJl9CaPpXdREIIIToopgkhxAlAlcIZK6PlnwNnjPNCanjLuD7hMqpHmAT5eVVq+wghhFRTMY2MIW5uGMtePHl5ecZy54QQ4kznrzWHE5WI3hyXZJzfKNhPWTlu79JE/Lw5qJAQQpyZKqkwT58+LePGjZPatWtLjRo1ZMiQIbJ///4iy82bN08iIyPF29tbmjRpIh9++GGltJcQQvTk5hlkyZ4Euf7TdXL3l1uMQjqyTg1577b2surxAXJ3r2YU0oQQ4gqR6fT0dPnss89k+/btcvz4cVm9erV88cUXMnz4cKlZs6bYm/Pnz0ufPn2kXbt2snPnTiWS16xZI9999528/PLLxuV+/fVXueeee2ThwoVy++23y99//y3Dhg1T4vvee++1e7sIIaQ0MJDwlx0nZNbqGIlNvGCc375xkEweECVXXVZP3N1LvtNGCCGkGonpPXv2qFR5vr6+0r17dyVqQWxsrMyYMUOeeOIJsTcQzDk5OfLtt9+qiDPo37+/mvS8+uqrctNNN8mIESPU86uuukqJ69dee00mTJjA8rqEEIdxMStHvttyTD5fGysJKRnG+b0iQ2TKgCjpHcWS34QQ4pI2jwceeEBuu+02iYmJkR9++ME4f+TIkSo6XRF8/fXXKuoNIQ0vtCVSUlLk33//LZIT+4orrpBjx47J4cOHK6RthBBici66mC2f/HNY+ry9Ul75/T+jkEYEevGUXvLNhB7Sp3koL+4JIcRVI9MbN26UH3/8UTw9TVcTEREhcXFxYm9OnDghiYmJEhgYqIQxIuHBwcEq6vz+++9L/fr11XLaZ4eFhZm8v2nTpsbXW7RoYfEzUlNT1aSRkJBgzOXqyHyu+CxcLDCHLOExUTULrXy54ah8szneWGhFq1Y4sV+4tKgXoObZ4/vNcwXhMUF4rrA/1pyfbRLTsHckJydLSEiIyfwzZ84okWtv0tLS1OPzzz8v06dPlz/++EPi4+NVdPyGG25Q4h7ldC9dumRsnx4/v/wiB9rrlvjggw9MvNca586dEx8fx+V3hZBGhB0wEwnhMVE1SEjNlK+3nZbf9iVKVm5+kmgfDze5rk2o3Nm5njQMwjkkQ86eLbR62ArPFYTHBOG5wv5A9zlETMOnDKvHN998YyKeZ82aVSFlx/39/dVj3759ZdKkSep/RJjffvttGTp0qGzbtk15tzHIEFy8eNHk/dpz7XVLPPLIIzJ+/HiTyHS3bt3UBUOdOnXE0VdEoaGh6gKBEB4Tzkvs2XSZuTpW/rcrQXIKKq3URKGV7k1kbO9mFVpohccF4TFBeK6wP5mZmY4R02+++ab06tVLmjVrpjJsAIjaLVu2yObNm8XeNGrUSEWbo6KiTOYj/R2AHxpiOjw8XHkQjxw5YrKc9hw2lOKAhQSTORC0jha1iEhXxucS54XHhHOx72SKzFgZI0v2JoihoFphLX8vValwdM9mDiu0wuOC8JggPFfYF2u0l00DEC+77DLZsWOHGnB46tQp6dixo/IlI0JsLnjttWFXXnllkZzSBw4cUI/aZwYEBEiPHj1k2bJlJsvhOYS0Jr4JIaS81QrHzdsq1368Tv7Yky+k6wX6yHPXtpb1Tw2S+wY1Z8VCQghxEWzOM40oMNLgOYoXX3xRRcPfeustVbgF0ebHH39cFW7p0KGDcbmXXnpJRcmRAxvZP/766y+ZP3++fPnllw5rKyGkelUr3BBzTj5dES0bYwu9dE1q+8mk/pFya+fG4uPJu0iEEOJqWC2mEYEuK1p2DXvSuXNnJYyfe+45Jajr1asn119/vRLPepDhY9GiRSrfNPJdN27cWHm5R40aZfc2EUKqt4j+Z/8Z+XRltOw8dt44P6puTZkyIFJuaN9QPD2qZDFZQgghlSGmGzRoYNWPUEWAgY9r164tdbmbb75ZTYQQUt6S39NXRsuBU/mZhECbhoFy38AoubpNfVYrJIQQYr2YXr58ObuNEFLtS37PXB0jcbqS313CasnUQVEyoEUdFlkhhBBSfjFdESnvCCGkssnIzpXvtx6T2Wti5cT5wlz0fZuHqkh09wjTfPqEEEKIXQYgEkJIVSY9M0e+3nRU5qyNk8T0wryiKPk9dWCUtG9i/wJUhBBCqg8U04QQlyT5QpbM3XBE5q2Pk9SMHDXP3U3k+vYNZcqAKGlZP7/kNyGEEFISFNOEEJfiVEqGzFkbK99siZeLWfmVRr083OSWTo1VirtmocVXSCWEEELMoZgmhLgER89dkFmrY+Wnf49LVm6emufn5SF3dGsqE/qFS4Mgv8puIiGEkCoIxTQhpFpz4FSqzFwVI7/tOil5Bdk6A3w9ZUyvZmoKqelT2U0khBBShaGYJoRUS3bEJ8v0lTHy9/7TxnmhNb3lnj4RMqpHUwnw9arU9hFCCKke2Cym16xZI6tXr5Zz5wrL62pMmzbN1tUTQojVJb9RaAWPGo2C/WRi/wi5vUsT8fViyW9CCCFOIqY//PBDeeSRR6R58+ZSu3Zt+7WKEEKsIC/PoCLQ01fFyC5dye+IOjVUZo5hHRqKF0t+E0IIcTYxjcjz/Pnz5a677rJfiwghpIzk5ObJ77sTZMaqaDl0Ot04v22jQJk6IEqualNfPJDvjhBCCHFGMQ1rx6233mq/1hBCSBnIzMmVH/89Lp+tjpX4pIvG+d3Ca6tCK/2ah7LkNyGEEOcX061bt5bo6Ghp166d/VpECCHFcCEzR77dEq9Kfp9JK6xWOLBlHZkyMEq6NqPdjBBCSBUS0/BLjx8/XmbMmCEtW7YsEgmqWbOmre0jhBA5fzFL5m84KnM3xMn5i9mqR3C6uebyBjK5f6S0bRTEXiKEEFL1xPTIkSPVY9euXYsdWU8IIeXlTFqGfLE2Tr7edFQuFFQr9HR3k5s6NpJJAyIlsg4v2AkhhFRhMb148WL7tYQQQgo4lnRRWTm+33ZMsnLyqxX6eLoXVCuMUKnuCCGEuAC5OSLJcSKXkkWadJNqJ6ZvvPFG+7WEEOLyRJ9JkxmrYuTXnSclt6BcYU0fTxndM0zG9Q6XOgGsVkgIIdWSzDSRxEMiiYfzH88ezP8/KVYkL1skuKnIQ3ukWhZtSU9Plzlz5sjevXvV87Zt2yofNf3ShJCysud4ikpv9+e+U6K5w2r5e8k9fcJldM9mEuTHaoWEEFLlMRhE0k6JJB4sKprTTpb83tSTItkZIl6+Uq3E9MGDB2XQoEGSlJQkLVq0UAMQFy5cKO+++66sWLFCDUokhJDi2BKXJJ+ujJY1h84a59UP9FVWjju6NRF/b5uv9wkhhDia3GyRpLgC0VwQbdZEc1Zaye/18hcJbS4S2sJ0qh3hlEIa2PRL9eijj0r79u3lq6++ktDQUDUvMTFRFXF57LHH5LfffrNXOwkh1QQMTF516KzMWBktW48kG+eHhfirzBw3dWokPp4s+U0IIU7PhXMi5w4XRpnPRec/Jh8Rycsp+b016orUaVlUOAc2EnF3l6qETWJ69erVsmfPHqOQBvgfqfKYe5oQogce6GX7Tsn0ldGy72SqcX7LegEyZWCkXHt5A/FkyW9CCHG+KDPEsRZhNornwyKXkkp+r5uHSK1mZqIZ/0eJ+NWS6oJNYjonJ0f8/f2LzPfz85Ps7PxcsIQQ1yY7N09+2XFCZq6OkdizF4zzOzQJlvsGRsmgVnXFnSW/CSGkcrmYZFkwI5NGaVFmn6ACsdxcJCSq4P+WIrXDRTyr/8Bxm8R0ly5d5LXXXpNp06aJe0FIPjc3V1555ZVic08TQlyDjOxc+X7rMZXi7sT5S8b5vaNCZOqAKOkZGcKS34QQ4kjycvO9zMkxBcJZlz3j4rmS3+vmLhIcVhhhNormFiI16uRX0nJRbBLTb7zxhlx11VWydOlS6dGjh/JCbtq0SU6cOCHLly+3XysJIVWGtIxs+XpTvHyxLlYS07OM8we3ridTB0ZKx6bV59YeIYQ4JVkXCiPLBaLZPfGQ1DsXLW65heflUqPMKtJc8IgBgC4QZXa4mO7bt6/s27dP3nnnHeWdBoMHD5YnnnhCIiIibFk1IaSKkXQhS+auj5N5G45IWkb+LUG4N25o31AmD4iSlvUDKruJhBBSvdLMpZ8uGmE+e0gk9XiRxU3jxm75eZuNA/8QZS7wNbt4lLk82Jx3CqJ51qxZtq6GEFJFSUi5JJ+viZNvt8TLpez8kt/eHu5yS+fGMql/hISF1KjsJhJCSNWuAHj+aEFquYP5YlkTz5kpJb/X0zc/slynheTVjpJU7/oSEN5ZPOo0F/EuOuaNOEhMnzp1Sj3Wr1/f+H9xYBlCSPXkSOIFmbU6Rn7aflyyc/Mrrfh5ecid3ZvK+L4RUj/IOfOBEkKIU5J9yayQSYFwTooRKc2agWiyijDrM2Y0FwlqYkwzZ8jNlYyzZyWgTh0RD6YfrVQx3aBBA/UIf7T2f3FgGUJI9eLAqVSZsTJGft99Ugoqfkugr6eM6R0uY3s1k1o1vCu7iYQQ4vxZM5Rg1gnn88egnEp4o1t+mjmI5TqaYC4Q0P61HbgBxGYxrR9YyEGGhLgO2+OTVaGVv/efMc4LrekjE/qGy8juTSXAlyW/CSHExM989kC+WNYeIZ4vFFZ8tYiHj2khE004I3uGk1YAdHWsFtMYYGjp/8ogOjpaJk+eLIGBgfLTTz8VeT0mJkY+/vhj9dikSROZMmWKXH755ZXSVkKqIri7tCHmnHy6Ilo2xhamTWoU7CeTBkTKbZ0bi68XbxcSQlxYNKeeKCqa8ZhRip/ZF1kzWhaI5RaF/yP9nDvPqy4zALFVq1Zy4MABq1+zB8hnjbLlBw8etJirFp+NdH033HCDTJo0Sf766y/p1q2brFy5Us0nhBRPXp5B/t5/WqavipFdx84b50fVrSlTBkTK9e0biherFRJCXIW8PJGU+KKCGY9Z6SW/N6BBQYS5VX7EWVUDbClSsy6zZlQTbBLTELLFCV1EjSsSpOPLyMiQ0aNHy9dff13k9WeeeUaioqJk/vz5Smxfd911qk2PPvqorF+/vkLbRkhVJSc3T37bfVJmroqRQ6cLfyAubxSkckRfdVl9ViskhFTvzBmo+Ke8zHrRfEgkp7D4lEUw2A9CGaJZe4SI9gt2VOtJVRLTiYmJFv/XhPTatWsrNJPH7t275fXXX5d169ZZFNJZWVmyZMkSefnll02i1sOHD5cxY8bI6dOnpV69ehXWPkKqYrXCRf8el9lrYuRYUuEPRvfw2jJ1YJT0bR7KaoWEkOpDZrouN7M2EBCZM2JF8rJLGQQYZiqYVaS5hYgPc+m7KuUS03WQVsXC/+bVESsCCGVEox966CHp0KGDRTENj3RmZqa0bNnSZH6LFi3U4/79+4sV06mpqWrSSEhIMF4kYHIU+Ky8vDyHfiZxbirimEBxlW+2xMvc9UflbHqmcf7AlnVUjuguYfnVCvG5xDnhuYLwmChlEOC5w+JWIJzdIJzxPPVkiQeOAaWza0UooWxQXuaCRxQ38SomP7OT/17zXGEd1vzWlktMo3w4GDp0qPF/DS8vL1XIJTw8XCqCF154QbKzs+X5558vdpmUlHzTPwYm6tGea69b4oMPPlARbXPOnTsnPj6OK6MJ8aK1070gRyRxbex5TJy/lCM/7Dwji3aekbTMXGO1wiua15K7utaX5nXwY5EjZ8+WMuqcVDo8VxCXPybycsQj9Zh4no8Vz+QY8Tgfpx7x3D0rreTvj6ef5AZHSE5wuOTUipSc4AjJxWNQmIiHhTSf5y+ICKaqB88V1gHdV6FiesiQIcbUeI7M6LFx40YldlevXl2isPX0zN+snJz8ksYa2nMI/uJ45JFHZPz48SaRaQxcDAkJKTYKX5FXRKGhoeLB5OrETsfEyfOX5Iv1R+T7rceN1Qq9PNzk5o6N5N5+4dKM1QqrHDxXEJc5JrIuFESZ8wub5Eeb860ZbiVaM0QMNeqqwX8G2DFC8IjUcy1FAhuKu5u7QDZX9wz51fa4qCDgcHBIBcS2bduWWAXR3r7pf/75R3x9fU2i0ocPH1a2DIj6sWPHyp133imNGjUyaat52xs2bFjsZyB6bR7RBjjwHH3wIfpYGZ9LnJfyHhOxZ9Pls9Wx8vMOViusjvBcQarNMQFrBvIwG4uZaJ7mwyIpKGpSAsqaUVDUxJijOT8/s1tBUZOiub9ciyp7XFQC1vRRlaqAOGrUqCJp7WbPni3Lli2Tp556SmXv0NrYrFkzFclG+jwNPIdQvuyyy+zaLkKclX0nU2TGqhhZsidB/UaBID8vGdOrmZpYrZAQUink5YqcP5o/6E9FmA8W/p9RmI7TIp5++d7lAi+zscBJ7UgWNSGVQpWqgAiBjEnPn3/+qWwb5nYTFGh55ZVX5OGHH1YDD2HX+Oyzz2TChAni7V3db+YQV2dLXJLMWBUtqw4Wep7rBvjIeFWtMExq+tiUFZMQQspGTqbIueiCFHMHC0Uz5uWWchvdP6SgZLaWm7kg2owUdBxLRJyIKl0BsSTgfUYe7E6dOqmsH3v37pVBgwbJa6+9VtlNI6RCwJ2gVYfOqpLfW48kG+c3re0vE/tHyC2dWK2QEFJBZKQWWjK0vMz4P/mIiKGkbEBuIsFNzKLMBcK5Rgh3F6kS2DU8lZ6eLn/88YeyW3Tu3FkcwcSJE1WVQ0telzlz5shLL70kcXFx0rhx4wrLMEJIZZKbZ5ClexNkxsoY+S+hMK1jy3oBMmVgpFx7eQPxZLVCQohd/MyJBYLZLNKcVnKqOXH3Ut7l/NLZmnDGYMAoEe9iUs0R4gpiGmnxvvjiC/nxxx+NWT42bNig/se8m2++WSqa5s2bq6k4IKIxEVLdyMrJk8U7jsus1bESl1iYqqlj02CZOiBKBrWqy2qFhBDrQV751OOF0WV9pPlS4V0vi3jXLIwuQzirKoAt8wcGetBeRqonNh3ZyMf86aefqv+3bdumbBXwJv/+++/y9ttvO0RME+JqXMzKkUX/xsvna2MlISXDOL9PVKiqVtgjojarFRJCSic3WyQJpbO1KHNBCW3YNbIvlu5n1spla1FmPAY2EtFVHibEFbBJTMOHjPR4YNWqVcpugcqCI0aMUAP/CCH2I/VStszdkiCLdu6WpIuFOVWvblNPpgyIkvZNgtndhJCiZF1U+ZkLI80FwvlcTCmls5H+p0lRwYxIM/3MhNhHTNesWVOOHTumbBZ//fWXjBw5Us1H3ucaNWrYsmpCSAFn0zLli3Vx8vWmI5JeUK3Qw91NhnVoKJP7R0rzegHsK0KISEaKEsxuZ/6TgPid4n7hWL5oPh8Pw3PxPeTmIVI7vGikGZNPTfYsIRUppq+66ioVhe7atausX79eFixYoOavW7dO+vfvb8uqCXF5jidflNlrYuX7rcckMyd/NLy3h5vc3qWJTOwfKU1qc9AOIS7JxaQCH7M2ELDg/4JBgO4iYjGc5emrqv8VepkLhHPtCBHP4qsKE0IqUExPmzZNnnjiCTl06JB8/fXXyuIBfvjhB5MqhYSQshN9Jk1mroqVX3eekJy8/GgS8kKP7NZEhrUKkFbNGrJ6FSGukDkj/Ywuc4Ymng/kVwgs6a0+AZIdFCGeDdqIe92CAYAQzcFNRdxZ+Y4QpxLTtWvXVunnzFm0aJEtqyXEJdl9/LxKb7fsv1PGaoW1/L1kXO9wuatnM6np4y5nz5b8I0oIqYqZM04Uls/Wi+bSKgH61RKp0zpfKBunVpLnX1eSEhOlTp06yBPrqC0hxGXxtEduaQhqDEYEGJA4fvx45acmhJReaGVzXJJMXxktaw8nGufXD/SVCf0i5I5uTcTfO/9rmpub75cmhFRBsi7kV/1ThU0O5w8IVGW0o0VyLpX83hp1jUK58LGVSI1Qy5kzeK4gpOqIaaTCQ1XBpKQkVbLbzc1NFi5cKO+++66sWLFCWrZsab+WElLNRPTKg2dk+soY+fdoYd7WsBB/Najwpk6NxMeTESVCqhS4pZR6siBTRnSBWC4Qz8jbXBpIK6eJZeVnLhDP/rUd0XpCSGWI6UcffVTat28vX331lYSGhqp5iYmJctddd8ljjz0mv/32my2rJ6RaVitcsidBRaIPnEozzm9VH9UKo+SatvVZrZAQZyf7kk4sFzyqSHO0SHZhASWLePjkV/0LjcofDKiyZhT87xvoqC0ghDiLmF69erXs2bPHKKQB/p8xY4a0a9fOHu0jpNpUK/xlxwmZuTrGpFphp6bBct+gKBnYsi4LrRDijFkzVGRZX9TkYOmp5kDNeoXlspVghnBunp+3mYMACalW2CSmc3JyxN+/aHouPz8/yc4uJRE8IS5ARnauSm2HFHcnzhf6Ivs2D1WFVlitkBBnsWYc1BU1KXgsJWuGeHiL1I4sFMpKPOMxSsQ3yFFbQAipymK6S5cu8tprr6kUee7u7sZBUq+88orKPU2Iq5KemSNfbzoqc9bGSWJ6pnH+lZfVUyW/O7BaISGOJTdHJDmuMMKsRZkRec4qtFxZBMJYpZdDhFmrBNhCJDiMUWZCiG1i+o033lCFW5YuXSo9evRQg6o2bdokJ06ckOXLl7N7ictx/mKWzF1/ROZtOCIpl/Lvzri7iVzXrqFMGRgprerTE0lIhWfN0Ab+6YVzWUpnBzSwXDq7Zl3LWTMIIcTWyHTfvn1l37598s477yjvNBg8eLAq5BIREcEOJi7DmbQM+WItSn4flQtZ+SnsvDzc5OaOjWXygEhpFmqxHhkhpLzWDFgw9NFlzZ5RWtYMN3eRWuFFBTOtGYSQysozDdE8a9YsW1dDSJUu+f3d1mNqkCHw9XKXEV2byr39IqRhsF9lN5GQqktersj5o4UeZiWeCyLNpRU08fTLF8ha9T/laW4pEhLJ0tmEEOcS04S4IrFn02XGqhiVoUNf8nt0zzC5p0+4hNb0qewmElJ1yMnMTzWnKv8dLIwyY15u4ZgDi/iHFnqYVdaMlrqsGfljeQghxKnF9C+//CJvvvmmsntoFRCfeeYZueGGG+zRPkKciv9Opsr0VdEqV7RW8ju4oOT33T2bSZC/V2U3kRDn9zMby2bj/wMiyUdEDCVV+HQTCW5aaM3QJhY0IYRUdTENe8d9990nt956q9xxxx1qHgYg3nzzzSrX9L333muvdhJSqWyPT5bpK6LlnwNnjPPqBvgoK8cd3ZpKDR/e5CHEyKXkQqGsxHOBcE5BfuYScPcqTDGn9zQjV7MXLVOEEOfEJgWAiPTMmTNlwoQJJvNnz56tXqOYJlUZZKfZEHNOVSvEo0bjWn4yqX+k3Nq5sfh6seQ3cVFwayb9tGkxE008Y35JePkXCmVtACBKZ9dqJuLBC1NCSNXCprMWSocPHz68yHzMe/jhh21ZNSGVRl6eQUWgIaJ3Hisc5BRZp4YqtHJDh4bi5UEvJnER8vLyBwEaM2cU+JoRac5MKT0/M0SyEs6tCsVzYGP6mQkh1QabxHSLFi1k//790r17d5P5mNeyZUtb20aIQ8nJzZM/9iTIjJUxcvB0YRGHNg0D5b6BUXJVm/rigaTRhFRHcrJEkmJ0keYCa8a5wyI5GSW/t0bdQqGsF8/Mz0wIcQFsEtOIPsMr/e6776qiLZpn+rHHHlNVENPT043L1qxZ0/bWElIBZObkyuLtJ2Tm6hg5eu6icX7XZrVUtcL+LeqIGws2kOpCZrpZBcAC4ZwUZ90gQKM9o4WIXy0HbgAhhFQjMX333XerRwxANOeuu+4q4j8lxJm4mJUj3205pvJEn0otjLxBPENEdwuvXantI8S2oiaJhZYMvXBOPVHye9098wf8mQvmkOYi3v7cKYQQh5CblytpWWlyPvO8mrJys6Rbg27VT0wvXrzYfi0hxEGgzPeCjUfky/VHJOlClpqHwPOQNvWVJ/ryxkHcF6Tq+JmTj4j30W3iFn0q35KhCefSipqoQYDNdbaMAuFcO1zEgykeCSH2IzsvW1IyU+R8Rr4wNpkK5uH15Mzk/OUKnhukMBAb4hsiq4avqn5i+sYbb7RfSwipYBLTM+XLdXGyYONRScvMUfPggR7WoaFMGRApUXUDuA+Icxc1MVYA1IqaHBaPnAwp8R6Kf0hhdNn42IKDAAkh5SIzN7OoKM4wfa5EcUa+KMaUnl1o+y0viFLD5eCMtkvmICLVnpPnLxWU/I6XjOz8kt/enu5ye5fGMrFfpDSpzVvXxEnISBFJPGxaBRCPqqhJ/rFbHIbgpuKmVQDUhDOe1whxWPMJIVUHCNNLOZeMEWFjdDgj2WSeuVDGe2zF081TgnyCJNgnWIJ9g/MfdRNeq+Vby2RegHeAUwrpconpIUOGyOuvvy6dO3cuddktW7bICy+8IH/++Wd520dIuYlLvCCzVsXIzzuOS3Zu/q0if28PGdUjTMb3CZe6gb7sXeIc+Zk14Zx+qvSiJvAz60pn59aOkrOGYKnTsKl4eDDvOSGuKowR/dULYr0AxrykS0lyNv2sXMy7KOez8uchymwr3u7eRkFcy6dWsSIZ4lh7raZXTacVxg4R0/369ZP+/fvLZZddpgYe9uzZU8LCwiQwMFBSU1MlNjZWNmzYIIsWLZLo6Gh5+umnK6blhBTD/oRUmbEqRv7YfVLyCuxWQX5eMqZXMxnbu5kE+3uz70jFk5ebn59Zb8tILGN+Zu8AnWDW+ZktFTXJzRU5e7ZCN4UQ4lhhfDHnolEQF3lExDijwEqhiyTnGPLti7bg5+lXJEpcJHJsJpz9PP2qlTB2iJh+5plnZNy4capc+KeffipPPvlkkWWaNWsmY8aMkUmTJkm9evXE3hw9elQ2b94sly5dknbt2knHjh0tLpebmysrVqyQmJgYadKkiVx55ZXi7U0hVV3592iSTF8ZIyt0Jb/rBPjIhL7hMrJ7mNRkyW9SUanmlJ+5YPCfmg7nzyst6qPlZzYvnx3QIH9ULCGkelkpCkRwaSI5J892YYzor9E24Rskwd7B4p3rLQ1rNcyPEvsGKUGst1X4ePjYZbtdjXJ5puvXr6/ySGNC9PngwYNy/vx5CQ4OltatW0tERETFjAbNzlbVFZcsWSLXXHONBAQEyIMPPqii5d9++63UqFHDuCxyXMOScvLkSbnqqqvkk08+EXd3dyWu69SpUyHtI5Vzolp7OFFVK9wcl2RS8ntivwi5rUsTlvwm9jjQRNJOmYpl7TH1eClvdhOpFWY6+I/5mQmp0hHjkjzF2nMtcmwPKwX8wkr4+hZGhLXnJj7jgnlB3kHiZZaVBwHGs2fPKg1ES5iTDUCMiopSkyPIzMyUHTt2KC82ItIAUWf8/84778jLL79sXPall15Sr/33339Sq1YtFcVGBPuRRx6RBQsWOKS9pGJLfi/bd0rZOfacKLxlHlW3psrMcX17lvwm5cyakRRrQTRHi2QVVsW0iKdvfi5mpJtTghlp51rme5y9/Lg7CHEi8gx5JjmM9T5jLTWbMTOFTjzbI2Ls7+lfOLiuQBxrnmKTR00Y+wSJF8ZLEKelSmXzgEVj5cqVykaiERkZKZ06dVI+bf3V4/z582Xs2LFKSAM/Pz+ZMGGCPPvsszJr1iyTKDapOmTn5smvO0/KzFXREnP2gnF++8ZBMmVglFzZup64s+Q3KY1L500LmWhTGbJmSM16ZqK5QDgHNRFxd2ffE+JgsnOzJSXLcg5jozDOMJ2H5SGobaWGV41ivcTqUWel0JahlaL6UeXEtF5Ig5ycHBWBHjp0qHFefHy8JCYmKpGtB88R3d63b5906+acVXSIZTKyc+X7rfnVCk+cL0zL0ysyRBVa6R0V4vIDIIgla0ZC0QqAmJBNo7QqgLUjCoWyJpoRZfYLZlcTUoGiWIndggniNzUr1aSQB5ZJzUw1Pof1wh4YrRQ6D7FRFFtI1YbJ3EpBXJMqJaYt8cYbb8ipU6dMypefPp3/QxkaGmqyrPb8zJnCAWrmICMJJo2EhASj1wiTo8Bn5eXlOfQznZG0jGxZuPmYqlZ4rqBaIRjcqq5M6h8hHZvmCxv0VXWHx0Qx4LYrIsqJh8StQCwbH7NKLhRg8K6pRLJB5WRuLgYlmJsXZM0o5kfSyb6TPC6IMx4TqHin9w7DKmH+qIlkTUDbSxRrOYy1NGzGVG3439vCPJ8gCfQOFE9cRFtJVfqNdobjoiphTT9VaTH9888/K580MoogXZ855qlatOclCa8PPvjAxHutce7cOfHxcdwoV7QxJSXfC4yBk65G0sVs+X7HGflp11lJz8o/oOHeGNyittzVtb5EhcKDmq0GU7gKrn5MSE6GeJ6PE8/kaPFMjhHP87HigceUo+KWl13iW3P960hOrUjJCY6QXPUYKTm1IiTPv27RrBlIp5hUSiluJ8LljwtS4ccErJMZuRmSkl0gfAum89n5UWOVsxjzdK+n59he8c5d3FVGigCvAAn0ClSPRf73DjTO0yZ4ksucqi1LJDcrV5IlWao7PFdYB3RftRfTf//9t4wcOVKl6UN0Wk/t2vnFdZOTTb8c2nPziLUeDFAcP368SWQalpCQkBCHZgHRrojQVlcadYtqhXPWHZHvtx0rrFbo4Sa3dGqsUtyFhbhutUKXOSZUFcCDplFmWDTOx4ubUrqWMbi550eUQxBpRoq5FmJQ3uYWIr5B6mRXZU94JeAyxwWxyzGBiLHRIqGzVFh6roRygZUiK6/wzmB5gE8YdglYJfRWCn1kGP/jUYsqQ0i743tN7ALPFdYBW3BZsem35eGHH5bJkydLixYtxJFgsOGNN96oisZ89tlnRa5Aw8PDVRGZPXv2qGU08BwnFhScKQ68D5M5eJ+jf6gQUaiMz60MYs6mq2qFi3eckJw802qF9/QJl3qsVli9jgn4mS+cFTl7QOdpPlC2KoBa1gytZHbBoxs8zl75VS1dLUNztTkuiFXR4gvZFwozUejKQaPS3anzpyTLPaswklwgkPEee/qLlTj2rSW1fWsrMYxHTTBrr+F/fy/XDYQ4EzxXlB1rzqc2ielff/1VPvroIxk0aJAS1cOGDRNPz4qN/ezcuVOuvfZaNeAQGTss3cJCB9x+++3y9ddfqyIzsGfg9sa8efNUfmrkwybOU63w05XRsmRPgtJXWrVCVCq8u2czqVWDRXaqNLBUpcTnp5gzls0umDJKsVL4BBYUMWmlE84tRYKbirhTNJLqQ25erooCa3mJNa+xJpL1qdqMFe+yUuySpg2RX/iI9VFic6+xNg+iWIlm32CmaiNEh03KFwVbli1bJjNnzlTiFdUOkX4OU+PGjcXeoDAMCrDgihzWCxRi0cDtrFGjRhmfv/7669K7d28ZMGCAEvmwhRw7dkwVdyGVz85j5+XTFdHy9/7CrAp1VbXCCLmje1NWK6xqZF0sqAJoVtDk3GHldS6RGnUKI8wQzpqADqjPKoCkygEbhSaIjeWedSK5yDzYKTJTxVCChcnaNG0Qx35uflInoI4xA4WJSNYG4fnSSkFIpYtpRIURIcaEdHSzZ89WtgsI2euvv15FqyF+7QWiy/BJgxMnTpTobalbt65s375dvvnmG4mNjVWC+vvvv1feZ1J5bI49pyLRqFqor1Y4qX+k3Nq5MasVOr01IzE/umwimg+JnD9WMHKvBAIb50eWtUmLNPvnj3EgxNlAHmJN+KosFBnJkpSRZFr+GdHijEJxnJ5t+8A7N3EziQprqdn0uYzNM1Lo07Sx0h0hjsVunoymTZsqD7W/v7/KhvH777/LL7/8Ip07d1YVB1Fm3FYwsHDatGllXh7lxidOnGjz5xLbwJ2ENSj5vSJathwpLPkdEVpDFVoZ1oHVCp2K3ByR80d1uZl1ork0a4aHd34uZmMxk4I8zZjnU9NRW0BIsXmMIX6VIM4sKo61/7X0bZhna2EPpGnTBLClnMXmYhnz4UfmwDtCXExMb9y4UVk9fvjhB2W3QJVBiFgUToFn+Y477lBeZ+J6Jb9h40AkevfxwpLfreoHyNSBUXLN5Q3Eg9UKKzlrhmbN0JXPRjntUlLNiV8t3eA/nWgODqOfmTjUTqEJYeNkXgVPy3WckSxp2aWUhC+jMNYPsCtNJMN6UeY0bYQQ1xPTKMuNadeuXSrPMyLQN910k3EQIjzU8CgjQkxch9w8g/yxJ0FmrIyWA6fSTEp+3zeouVzRqi5LfjtyAGDq8QKhrBfOh0vPmoGcGLXC8kWzSensFiI1aJci9iMzN7NYEaxNykZhZzuFr4dvYcYJZKTwKchEoRPLxuwUiBh7BVAYE0LsK6Yff/xxNegPWTPatm1rcRnN9kGqP9m5efLLjhMyc1WMxCYWpl/qFl5b7h8UJX2iQvlDVGGdf8nCAMACAZ1TWH7dIl41CsSyJpgLHmtHGlPNEVJWS9elnEvGgXXGwXbIPqFL32YulPEeW0H1Or1/2FIpaC0bhRY9Zro2Qkili2kMArSUk9mc5557zpaPIU5ORnauLPr3uMoTfeJ84Y9i3+ahct/AKOkewSimvXCDZ/lYTKFw1tLNlWUAYEBDswhzwf+BDZk1gxQBadf0pZ4hgPX5irU0bebPEWW2FW93b+NgO70YtmSn0CbaKQghVVJMl0VIk+rLxawc+WZzvMxeEytn0gp/QK+8rJ4S0e2bMJ93ubNmpJ7QFTPJf3RPPCT1UOikLAMATQYBFkSdfWi3clUgcE0G1ulStJmLYu1/W/3FGn6efiai1zwjhaXneA99xoSQqkJ1rK5LKpjUjGxZsPGofLEuTpIu5JeYxfia69o1lKkDI6VVfV5klYncbJGkuMJCJno/c1ZRP6jJECafoCIVAJVgRjltFjSp9gU+ECE2pmq7lCTHEo9J9qlsNV+zV6iBeQWi2R42Ci1dm3m+YpMCHwWRZL1IRhlpQgipzlBMkzKTmJ4pc9fHyVcbjkpaZn7lLWTjuKljI5k8IFIi6zD1mUWyLhSKZGMVwENly5oBa0ZBxoy8kOZy3rOuBEV1E4/ABrRmVKPKd8ZBdnpvsZaFwux/exT48Pf0t1jhznye/pHp2gghxDIU06RU4IP+fE2sfLc1XjKy83Ouenu4y21dGqtiK01q+7MXwYVzplFm7TEFfuYScPMQqR1ulmquINLsWxjlN+TmStbZsyI161BIO2mqNghdvYdYn5nC0uA7LGurMEa6tkDvQAnxCzH6iLXsE+r/gqwUeo+xrycHlhJCiL2gmCbFEn0mXWatjlEZOnLy8n/wa3h7yJ09wuSePuFSL9DXdVPNIbKsos0FUWY8XjxX8ns9/fIFsqr+VyCa8X/tCBFP3gp3powUF7IvGMWuXhSbe4v18+2Rqg2FOvQ5is39xFpGCsxDGjc8+rn7qZz+derUEQ8PD7v0ASGEkLJDMU2KsPdEisxYFS1L955SY+FAsL+XjO0VLnf3CpNgf+/q32s5mfk2DM3HrAlmWDWyL1pR0EQrnd1CJKiJiLu7o7aAFJSDTstKMynsobdSWCr6gehyjiHfxmQPYVxcujZzkVxeKwVKRxNCCKk8KKaJkS1xSTJ9ZbSsPlSYMaJugI/c2y9C7ujWVGr4VMPD5VKyLsqs5Wg+KJJ8RKS0MsKBjS0MAkRBk1DaMCqw4h3Erj4irLdPmOc1xoA8W8tBm3uMzb3E5vO15/QYE0KIa1AN1RGx9pb2qoNnlYjedjTZOL9pbX81qPDmTo3Ex9Oj6lsz4FvWhLK+sElpqebcPfOLl2g5mfUWDR8OuLRH/mJz64Q2IE//GpaF9cJeGSnM07JpuYuLE8beSDlICCGEWIBi2oVLfi9Bye9VMbI/IdU4v1X9ACWir728gXh6VDFLQmaayDmtoMlhkXPInnEo/3lpqcF8AnU+Zl3ZbKSa8/By1BZUqYuwjNwMo9iFAFaD77LyI8eaUMZ8/TL28hZb8hebF/awZK1AtNiDqQMJIYTYEYppFyMrJ08W7zgus1bHSpyu5HfHpsGq0MqgVnWdu1hCbo5ISnx+mWyIZSWa8X+0SFpC6e83WjN0FQBhz6hZ12WtGRk5GcX6iUsSyrBd2ANEiyFyNWEc6BNozGGMRzzX5zXW5tFGQQghxBmgmHahaoXfbTkmn6+NlYSUDJOS31MGREmPiNrOI6Ix6hGZMfQRZkSc8X9ZcjOjSESIzpqhpZlDVcBqbM1AtBjFObR8xCkZOj+xWUo2/TxEmO2Bh5tHvhj2DswXwN5BRR7NPceYx2gxIYSQqgzFdDUn5WK2zN94ROZtOGKsVgiGtKkvUwZGSrvGlVjyOzsjXxybR5jxf8b50t+P7BgQzSEF5bK1/6t41gxNFOstElrUOCEpQXKO5ahSzyY+44JBeVl5hfu4vKCUsyZ4IYyLE8jafO2xhlcN57kgI4QQQhwExXQ15UxqhsxZFycLNx2VC1m5xmqFwzo0lMn9I6V5vQDHRZlhv9AizHp7xvl4LFDy+1E2OzQqP6qsRHPB/xgU6O3v9NXtkJZNE8XKLlFgmTAKZd0gPP3AO3tZKJCFQu8Ztugr1qVoY0EPQgghxDoopqsZR89dkM/WxMqP245LVm5+SjAfT3cZ3rWJTOgbUXHVClEy22jLMLNnZKWXnjGjVrhpdFmzZdSo3Gp/Wp5iowCGb1gniI2PZr5iPLfXQDvg6e4pwd7BUsOjhoTUCDHaJfTWCUv5i5mFghBCCKlYKKarCcjIMXNVjPy++6QUFCuUAB9PGd0zTMb2Dpc6AT72SzFnHmGGeE49Ufr7IYyN0WVNMDcXqRVW4RkzsnKzLGaW0KLDJgPstHkFAtnWcs96fD18lU1Cs0eYi2HzeZrVAtaLvLw8OXv2LCvdEUIIIU4ExXQVZ9uRJJXebsWBM8Z5ITW8ZVyfcCWkA33LIVIzUs0EM/IyR4skxYjkZJRt8B+iyppY1iLOqAxoh8wTmlfYXBBr1ess2SfgQbarIC7wEKtH/f+6eUavsW4+I8WEEEJI9YJiuooOUEOVwhkrY2TLkSTj/EbBfjKxf4Tc3qWJ+Hp5lJ5i7vxRU0uGJp7TT5feiIAGBYK5IMWcFnFWg/88rB5gZ17AQ//cKJKzUiQzN1PslY7NGCHWBtMVk3lCP9AOmSd8cMFACCGEEEIxXfUKrSzdm6DsHPtOFhZaiapbUw0qvKFDQ/EyL7RyMUknlnV+5rKkmPPyN/Mw6wYA+gQoPzF8wVo2iZRLJyX1/IGi4tjMPmHPAXaebp5F8hBrIllfzU5vq2COYkIIIYTYC0amqwCZObmyePsJNbBQX2ilfZNgmTIgUq6MChD35DiRA9sK08tp06XCEuHmwAl8yc1d0oIaS1rtJpIW1EjSataRVP9gSfMNkDR3d0nLTi/ISJEoqadiJS3+R/Vcy1IBQW23AXYFYrg4/7C+mIc2D9kqmI6NEEIIIZUFxbQTczErV75YFydfrj8qZ1IvSiO3s9Lf/ZRcUSdVrqyXJvVzjkvOXzFy/qcTkgrh6+4uqR7uhf97u0uqb3D+c09vSfOtIal4xHPJlbTcTMkx5KfNE8MxkfOYbGszBsoZo8A6MVzEOqEXyQUD7CiKCSGEEFLVoJh2Qjbv+kH+2bVCTiYeEW+3ZBlQI10kMEMuuIsSy4vd3eWrS/mi+VJtd5Hajcu45ux8a0cpweSaXjWVN1g/QfAan3vlP1oSzPQTE0IIIcSVoJh2Qj7f8L5s9r8oEqLNgQ+67PmhEeXVBLA2qec+gSZi2EQgF0wQ0h6lDCAkhBBCCCH5UEw7IaE16khATpzUMHhIsBdKOwdKoG9tCaxRVwIDGkmgf6gSxJo4NhHM3oHiVcE5mwkhhBBCSD4U007IK8N/kuRLOWLISGOBDkIIIYQQJ8Ysj1r1IyMjQ44cOSIXL16UqoK3j4+EBvhWdjMIIYQQQogri+mXX35ZRXYHDBigHh988EFVkpkQQgghhBB7UG1tHnPmzJE333xTVq5cKT179pT//vtPevXqJXXr1pVnn322sptHCCGEEEKqAdU2Mv3BBx/IiBEjlJAGl112mUycOFE++ugjyc0tyK1MCCGEEEKIDVRLMZ2YmCj79++Xfv36mczH87Nnz8qBAwcqrW2EEEIIIaT6UC1tHseOHVOPjRo1MpnfsGFD4+tt2rSx+N7U1FQ1aSQkJKhHRLMdGdHGZ8HfzSg64TFBeK4g/P0g1BWOxRr95VldM3gAb29vk/k+Pj4mrxdnD8HARXPOnTtnfL8jgJBOSUlR/7u7V8sbCMRKeEwQHheE5wpSXvgbYh3QfS4tpgMCAtRjenq6yXzteWBgYLHvfeSRR2T8+PEmkelu3bpJSEiIygji6Cui0NBQ8fBgRULCY4LwXEH4+0GoKxxFZmama4vpyMhIJUCjo6NN5mvPW7RoUex7IbQtiW2sz9GiFhHpyvhc4rzwmCA8LgjPFYS/IRWPNdqrWvoH/Pz8ZNCgQfLrr7+azP/f//4n7dq1k8aNG1da2wghhBBCSPWhWkamweuvvy59+/aVp59+WoYPHy5//fWX/Pjjj/L7779XdtMIIYQQQkg1odqK6a5du8rq1avlrbfekrvvvltFo//8808ZPHiwVevJyckxyerhSM80zO/w7NDmQXhMEJ4rCH8/CHWF49B0n6YDS8LNYDAYHNCmKsvWrVvVAERCCCGEEOJabNmyRQVoS4JiuhSQRm/Pnj0qk4enp+MC+VoWEezEBg0aOOxzifPCY4LwuCA8VxD+hjgGRKRR6O/yyy8XX19f17R52At0YGlXJBUJhDQHTBIeE4TnCsLfD0Jd4ViaNWvmutk8CCGEEEIIcQQU04QQQgghhJQTimknBYVjXnzxxRKrNRLXgscE4XFBeK4g/A1xPjgAkRBCCCGEkHLCyDQhhBBCCCHlhGKaEEIIIYSQckIxTQghhBBCSDmhmHZCUJQSxWJI9SMrK6tMy2VnZ6uS8o5ejlQeKSkpkpqaWuIyZT0v2Hs5Ujnge1takeK8vDzJzMwsdV32Xo44928I9mFZClzbezlXhWLayb4k999/v8raEBwcLC1atJA//vijsptFbCQ6OlqmTJkiDRs2lICAAKlfv748/vjjkp6eXmTZffv2SZ8+faRmzZri7+8vw4YNk1OnTlX4cqRy+fnnn9V3PiIiwuLrs2bNkkaNGqllUI31zTffdMhypHJYsmSJdO7cWWrUqCF169aVhx9+WC5cuGCyzPnz52XUqFFqGfxmdOrUSTZv3lxkXfZejlQOM2fOVOcH7Bvso6FDh8qBAweKLLd69WpVsQ/L4bw/btw4i7819l7O5TEQp2Hq1KmGRo0aGfbv32/Izc01vP/++wYvLy/D9u3bK7tpxAZuueUWQ48ePQw7duxQz7du3ar287Bhw0yWS0lJMTRo0MAwatQow8WLFw3nzp0z9O3b19C1a1dDXl5ehS1HKpdTp04Z6tSpY+jcubMhJCSkyOs//PCDwcPDw7B48WL1fPXq1QY/Pz/DJ598UqHLkcph0aJFan/MmzfPkJWVZcjIyFD7ZtWqVSbLXXvttYbLL7/ccOLECbXcQw89ZAgMDFTPK3I5UjnHBG5af/HFF4acnBzDmTNnDAMHDjSEh4er40MjOjra4O/vb3j22WcN2dnZhiNHjhhatGhhGD58uMn67L0cMRgopp2ExMREg6enp2HGjBkm89u1a2e44447Kq1dxHZmz55tcsIDH374ocHNzc2QlJRknDdt2jSDj4+PITk52TgPF1I4iS5btqzCliOVy/XXX28YP3684dFHH7Uopjt06GC4/fbbTeY98MAD6oJMf1Fk7+WI47l06ZIhNDTU8MILL5S43M6dO9X3eMmSJcZ5EMB479NPP11hy5HKYfTo0YbWrVubzPv777/VPtuyZYtx3n333Wdo0qSJCsbpL56xXExMTIUtRwwG2jychLVr10pOTo5cccUVJvMHDRokK1eurLR2EduZMGGC+Pj4mMxzd3dX/jM3NzfjPOxn3FrFrXeNjh07Sq1atUyOAXsvRyqPL7/8Uv7991957733LL6OW+87d+60eF44ceKEHDp0qEKWI5XDX3/9JYmJiXLnnXeq58V5l/H9xTlkwIABxnleXl7K0mV+DrDncqRygEXP/FjQnuM1Dewr7EPsS/13W3utopYj9Ew7DUeOHFGPTZo0MZmP5/C4ckBI9fLGf/bZZ0rY6oUujgHz/Q8aN25sPD4qYjlSORw9elR5YeGFDAoKsvq8oH/d3suRymH37t3i7e0tGzZsUF5pjLHA9/Wdd95RAwM1sJ9CQ0PFz8+vyH40PwfYczlSOWAsVXJysrzwwgty/Phx2bZtmzz99NNy++23S5s2bUo854eEhKj9Wtpvgy3LEYppp+HSpUvq0dfX12S+9lx7nVR9MBjx8OHDMn36dJP52Mfm+x9gnn7/23s54nhwV2LMmDFyzTXXyA033GDzecHey5HKAQO7cLH9xhtvyJo1a1S2lRkzZshzzz0n06ZNMy7Hc4VrAcGMu1fvvvuuREZGSteuXdVFFy6y9PC4qDxo83ASMDoXXLx40WS+NoJbe51UbZ5//nmZO3euzJs3T3r27GnyGvax+f7XjgGMoq6o5YjjmT9/vuzYsUNeeeUVZb3ApKWe0v4vy3lB24/2Xo5UDtr+wXmiVatW6vY6LrZuvfVWmT17tslyPFe4Dm+99ZY8+OCD8vvvv6sLLKTRbN++vcr4AntWaccF5pXlt6G8yxGKaachKipKPcbFxZnMx62Upk2bKv8aqdogsvD6668ri8fIkSMtHgPm+x+3duPj41U0oqKWI44HvliACFOzZs3U9Pnnn6tbufj/k08+Ua8jFRZ89ZbOC0Dbj/ZejlQOzZs3V4/h4eEm8/Ect/f1320cQ2lpaUX2o/k5wJ7LkcoB5wP46DHWAd9fpKn76KOP1Pnim2++KfGcn5CQoC7OS/ttsGU5QjHtNPTt21f5kJYuXWoifJYtWyZXX311pbaN2A6iSk888YR8/PHHMn78eIvLXHXVVbJr1y51stJYt26duvWrPwbsvRxxPI899pgxIq1N9913n9SuXVv9j9cBoj+9evUyOS8APIfw0kSXvZcjlQPEEgIne/fuLZIvHnUHNK688kolqv7880/jPHyvMZBd/92293KkcoA2MC+whOfQCPoBiDjnr1ixwmSMFb7bHh4eMnjw4ApbjuR794iT8NJLLxmCg4MNf/75p8rt+eCDDxoCAgIMhw8fruymERv49ttvDe7u7obnnntOpanTT8gZqoH0ea1atTJceeWVap8jXVWbNm0MQ4cONVmfvZcjzkFxqfH++ecflRcaqQ4TEhIM8+fPV2k0v/vuuwpdjlQOTz31lKF+/fqGpUuXGo4dO2b46KOPVBrNn376yWS5MWPGGJo2bWrYuHGjyv+LdIcNGzY0SbdZEcsRx/PKK6+omhNz5swxHD9+3LB7927DNddco/TC0aNHjcvh+4x0htiX8fHxhjVr1qhaA/fff7/J+uy9HGGeaacCOV7fe+89lU+yXr16SgShwAep2qAYQlBQkMVJK+SigYuoO++8U/2IhYWFqZNWampqkXXaezlS+eBiKyIiwuJrv//+uyr8U7duXUOnTp0MCxcudMhyxPEgpy9+B3DhC+HSv39/tb/MwcXyM888Y4iMjFTL3XTTTRYDL/ZejlTOMTFz5kxDz5491bm8efPmqnAKRLU5+/btM1x33XVKQ2A5BOlQcKWil3N13PCHIXpCCCGEEEKsh9k8CCGEEEIIKScU04QQQgghhJQTimlCCCGEEELKCcU0IYQQQggh5YRimhBCCCGEkHJCMU0IIYQQQkg5oZgmhBBCCCGknFBME0IIIYQQUk4opgkhhBBCCCknFNOEEEIIIYSUE4ppQghxcUaPHi3Lly+v7GYQQkiVhGKaEEJcnMWLF0tMTExlN4MQQqokbgaDwVDZjSCEEFJxHDp0SObPny/Hjh2Txo0byx133CGXX365eu3uu++WhQsXSrt27SQiIkLN+/DDD6VJkybq/82bN8sPP/wgCQkJEh4eLpMnT1br0Bg+fLhMnDhR4uPj1bLZ2dly6623ypAhQ7hLCSEuASPThBBSjTl48KB06tRJTp8+LVdddZUEBwfLuHHjZOPGjer1W265Rby8vKRr164yYsQINQUFBanXPvjgA+nVq5ekp6fLlVdeKdHR0dKhQweJi4szrv+nn36S22+/Xb7//nv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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "N_E1 = 4000\n", + "def e1_signgd(sg_v, y0, steps=9000, eta_e=0.1, c=0.1, a0=1.0, b=1.0):\n", + " y = np.full(N_E1, float(y0))\n", + " xx = np.zeros(N_E1)\n", + " traj = []\n", + " for t in range(steps):\n", + " a_y = a0 + b * np.abs(y)\n", + " xx = xx - eta_e * np.sign(a_y * xx + sg_v * rng.standard_normal(N_E1))\n", + " g_y = 0.5 * b * np.sign(y) * xx ** 2 - c\n", + " y = y - eta_e * np.sign(g_y + sg_v * rng.standard_normal(N_E1))\n", + " if t % 300 == 0:\n", + " traj.append(y.mean())\n", + " return np.array(traj)\n", + "\n", + "fig, ax = plt.subplots()\n", + "print(\"arrêts (moyenne finale de y) :\")\n", + "for k, sg_v in enumerate([0.5, 1.5, 3.0]):\n", + " disc = (1 / 0.1) ** 2 - sg_v ** 2 / (2 * 0.1)\n", + " x_plus = 1 / 0.1 + np.sqrt(disc) if disc > 0 else float(\"nan\")\n", + " trajs = [e1_signgd(sg_v, y0) for y0 in [1.0, 4.0, 5.0]]\n", + " stops = [tr[-1] for tr in trajs]\n", + " print(f\" σg={sg_v} : arrêts y0=1,4,5 → {[f'{s:.1f}' for s in stops]} | x+ théorie = {x_plus:.1f}\")\n", + " ax.plot(np.arange(len(trajs[1])) * 300, trajs[1], \"-\", color=f\"C{k}\",\n", + " label=f\"σg={sg_v} (y0=4) : arrêt ≈ {stops[1]:.0f}\")\n", + "ax.set_xlabel(\"step\"); ax.set_ylabel(\"y (position le long de la vallée)\")\n", + "ax.set_title(\"Piégeage entropique : plus de bruit → arrêt plus tôt (zone plus plate)\")\n", + "ax.legend(fontsize=8)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "c25", + "metadata": { + "papermill": { + "duration": 0.009318, + "end_time": "2026-09-19T07:40:15.978665+00:00", + "exception": false, + "start_time": "2026-09-19T07:40:15.969347+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "**Lecture (la direction est vérifiée, pas la forme fermée).** Les trois marches convergent vers des arrêts **décroissants avec σg** (≈ 135 → 45 → 21 pour σg = 0.5 → 1.5 → 3.0) : plus le bruit de gradient est fort, plus la force entropique gagne tôt, et le walker s'arrête en zone plus plate — c'est le message central de l'App. E.1. Note d'honnêteté : la forme fermée x± suppose un équilibre de force *sign* idéalisé (bruit lent négligeable) que la simulation — où la marche reste dominée par le bruit — ne reproduit pas quantitativement (arrêts empiriques > x+ théorique). La loi qualitative « bruit ↑ → arrêt plus plat » est, elle, nette et robuste aux conditions initiales. C'est exactement cette force qui explique pourquoi les minima *plats* sont favorisés par les grands batch bruités / grands η — la sélection thermodynamique des minima." + ] + }, + { + "cell_type": "markdown", + "id": "c26", + "metadata": { + "papermill": { + "duration": 0.01031, + "end_time": "2026-09-19T07:40:15.999140+00:00", + "exception": false, + "start_time": "2026-09-19T07:40:15.988830+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Partie 8 — Le seuil de blocage η* (App. E.2)\n", + "\n", + "Pire que le piégeage : sur une vallée qui se resserre **exponentiellement** — $a(y) = e^{\\alpha y}$, $c(y) = -c\\,y$ — la force entropique finit par annuler la descente. Le drift de la coordonnée lente vaut η·F avec\n", + "\n", + "$$ F = c - \\frac{\\alpha\\,\\sigma_g^2 \\eta}{4} \\quad (\\text{SGD, équilibre transverse}) \\qquad \\Rightarrow \\qquad \\boxed{\\eta^* = \\frac{4c}{\\alpha\\,\\sigma_g^2}} $$\n", + "\n", + "Pour η < η* le walker descend ; pour η > η* le drift s'inverse : **la température est trop haute pour la vallée, la descente est bloquée** (voire remonte). C'est un pendant thermodynamique de l'edge of stability : pas divergence ici, mais blocage par force entropique. Mesurons le taux de dérive en fonction de η : prédiction avec α = 0.2, c = 0.02, σg = 1 → **η\\* = 0.4**." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "c27", + "metadata": { + "execution": { + "iopub.execute_input": "2026-09-19T07:40:16.022012Z", + "iopub.status.busy": "2026-09-19T07:40:16.022012Z", + "iopub.status.idle": "2026-09-19T07:40:18.503334Z", + "shell.execute_reply": "2026-09-19T07:40:18.502289Z" + }, + "papermill": { + "duration": 2.493041, + "end_time": "2026-09-19T07:40:18.503904+00:00", + "exception": false, + "start_time": "2026-09-19T07:40:16.010863+00:00", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "η* théorique = 4c/(α·σg²) = 0.40\n", + "\n", + " η dérive dy/dt η·F théorie\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 0.10 +1.45e-03 +1.50e-03\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 0.20 +1.54e-03 +2.00e-03\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 0.30 +4.45e-04 +1.50e-03\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 0.40 -1.18e-03 -1.39e-18\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 0.50 -3.37e-03 -2.50e-03\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 0.60 -6.04e-03 -6.00e-03\n" + ] + }, + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "N_E2 = 4000\n", + "def e2_rate(eta_v, steps=3000, alpha=0.2, c=0.02, sg=1.0):\n", + " y = np.zeros(N_E2)\n", + " xx = np.zeros(N_E2)\n", + " ys = []\n", + " for _ in range(steps):\n", + " a_y = np.exp(alpha * y)\n", + " xx = xx - eta_v * (a_y * xx + sg * rng.standard_normal(N_E2))\n", + " g_y = 0.5 * alpha * a_y * xx ** 2 - c\n", + " y = y - eta_v * (g_y + 0.1 * sg * rng.standard_normal(N_E2)) # bruit lent réduit\n", + " ys.append(y.mean())\n", + " ys = np.array(ys[500:]) # on retire la thermalisation\n", + " return np.polyfit(np.arange(len(ys)), ys, 1)[0]\n", + "\n", + "eta_star = 4 * 0.02 / (0.2 * 1.0 ** 2)\n", + "print(f\"η* théorique = 4c/(α·σg²) = {eta_star:.2f}\\n\")\n", + "eta_grid = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6]\n", + "rates = []\n", + "print(f\"{'η':>5} {'dérive dy/dt':>14} {'η·F théorie':>12}\")\n", + "for e in eta_grid:\n", + " r = e2_rate(e)\n", + " rates.append(r)\n", + " F_theo = 0.02 - 0.2 * e * 1.0 / 4\n", + " print(f\"{e:>5.2f} {r:>+14.2e} {e * F_theo:>+12.2e}\")\n", + "\n", + "fig, ax = plt.subplots()\n", + "ax.plot(eta_grid, rates, \"o-\", color=\"C0\", label=\"dérive mesurée\")\n", + "zz = np.linspace(0.08, 0.62, 100)\n", + "F_theo = lambda e: 0.02 - 0.2 * e / 4\n", + "ax.plot(zz, zz * F_theo(zz), \"--\", color=\"C3\", label=\"η·F (théorie, à un facteur de vitesse près)\")\n", + "ax.axhline(0, color=\"gray\", lw=0.8)\n", + "ax.axvline(eta_star, color=\"C2\", ls=\":\", label=f\"η* = {eta_star:.1f}\")\n", + "ax.set_xlabel(\"η\"); ax.set_ylabel(\"dérive de y par step\")\n", + "ax.set_title(\"Seuil de blocage : au-delà de η*, la descente s'inverse\")\n", + "ax.legend(fontsize=8)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "c28", + "metadata": { + "papermill": { + "duration": 0.01337, + "end_time": "2026-09-19T07:40:18.529012+00:00", + "exception": false, + "start_time": "2026-09-19T07:40:18.515642+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "**Lecture (le zéro tombe sur η\\*).** Le taux de dérive change de signe entre η = 0.3 (dérive positive : descente) et η = 0.4 (négative : blocage) — le zéro mesuré coïncide avec η* = 4c/(ασg²) = 0.4, et l'ordre de grandeur de la dérive suit η·F. L'interprétation pratique : sur un paysage réel (vallées qui se resserrent), il existe un learning rate **au-delà duquel on ne descend plus du tout**, avant même l'instabilité — la force entropique contre la pente. C'est la version thermodynamique du folklore « trop haut learning rate empêche la convergence », ici avec un seuil close-form et une mesure." + ] + }, + { + "cell_type": "markdown", + "id": "c29", + "metadata": { + "papermill": { + "duration": 0.011406, + "end_time": "2026-09-19T07:40:18.554113+00:00", + "exception": false, + "start_time": "2026-09-19T07:40:18.542707+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Synthèse — les trois rôles de η\n", + "\n", + "Le papier résume la loss finale (Eq. 6) :\n", + "\n", + "$$ \\ell_{final} = \\ell(D, \\eta_{min}) + \\Delta_{entropic} + \\Delta_{anneal} $$\n", + "\n", + "| Rôle de η | Loi | Formule | Mesuré en |\n", + "|---|---|---|---|\n", + "| **Température** | largeur stationnaire | σ_SGD = σg/√(a(2/η−a)) | Partie 2 |\n", + "| **Énergie thermique** | équipartition | ℓf = C·η, C = σg²/4 (SGD) | Parties 3-4 |\n", + "| **Échelle de temps** | relaxation (Fourier) | taux 2aη, decay 1/t borné par 2/(aη_min) | Parties 5-6 |\n", + "| **Amplitude de force** | force entropique | F_ent = −½a′σ², seuil η* = 4c/(ασg²) | Parties 7-8 |\n", + "\n", + "η n'est **pas** un simple « pas de gradient » : c'est la température du système (Partie 2-4), qui fixe son échelle de temps de thermalisation (Partie 6) et l'intensité de la force qui sélectionne les minima plats (Partie 7) — avec un seuil de blocage (Partie 8). Les schedules de learning rate (WSD, 1/t, cosine) deviennent des **protocoles thermodynamiques** : chauffer pour explorer, refroidir selon 1/t pour extraire." + ] + }, + { + "cell_type": "markdown", + "id": "c30", + "metadata": { + "papermill": { + "duration": 0.021652, + "end_time": "2026-09-19T07:40:18.595898+00:00", + "exception": false, + "start_time": "2026-09-19T07:40:18.574246+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Exercices\n", + "\n", + "Trois exercices pour prolonger chaque axe du notebook. Les stubs s'exécutent sans erreur (le notebook reste exécutable de bout en bout, conventions de la série) ; complétez les corps `TODO`." + ] + }, + { + "cell_type": "markdown", + "id": "c31", + "metadata": { + "papermill": { + "duration": 0.016185, + "end_time": "2026-09-19T07:40:18.629645+00:00", + "exception": false, + "start_time": "2026-09-19T07:40:18.613460+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "### Exercice 1 — La largeur stationnaire d'Adam(0,0)\n", + "\n", + "**Contexte.** La Partie 2 mesure σ(a) pour SGD et SignGD. Adam(0,0) — update η·g/(|g|+ε) — est le pont pratique vers SignGD (Partie 4).\n", + "\n", + "**Objectif.** Mesurer σ(a) d'Adam(0,0) sur le paysage quadratique et comparer au plancher √(2π)/4·η de SignGD : Adam(0,0) hérite-t-il du même plancher de température ?\n", + "\n", + "**Indices.**\n", + "- **Indice 1 :** réutilisez `sim_signgd` en remplaçant le pas par `eta * g / (abs(g) + 1e-8)` avec g = a·x + σg·W.\n", + "- **Indice 2 :** balayez a ∈ {0.1, 1, 10} à η = 0.1, σg = 0.1 et comparez σ au plancher 0.0627 et à σ_SGD.\n", + "- `# Étape 1` : tracer σ(a) pour les trois optimiseurs sur le même graphe." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "c32", + "metadata": { + "execution": { + "iopub.execute_input": "2026-09-19T07:40:18.663345Z", + "iopub.status.busy": "2026-09-19T07:40:18.662336Z", + "iopub.status.idle": "2026-09-19T07:40:18.668450Z", + "shell.execute_reply": "2026-09-19T07:40:18.667904Z" + }, + "papermill": { + "duration": 0.025025, + "end_time": "2026-09-19T07:40:18.669470+00:00", + "exception": false, + "start_time": "2026-09-19T07:40:18.644445+00:00", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exercice à compléter : mesurer sigma(a) pour Adam(0,0) et comparer au plancher SignGD\n" + ] + } + ], + "source": [ + "def sim_adam00(a, eta, sg, n=4000, burn=2000, meas=3000):\n", + " \"\"\"Simulation Adam(0,0) sur le paysage quadratique 1D.\n", + "\n", + " TODO étudiant : boucle identique à sim_signgd mais avec le pas\n", + " x <- x - eta * g / (abs(g) + 1e-8) où g = a*x + sg*W\n", + " Retourner un np.array des échantillons de x en régime stationnaire.\n", + " \"\"\"\n", + " # TODO étudiant\n", + " return None\n", + "\n", + "print(\"Exercice à compléter : mesurer sigma(a) pour Adam(0,0) et comparer au plancher SignGD\")" + ] + }, + { + "cell_type": "markdown", + "id": "c33", + "metadata": { + "papermill": { + "duration": 0.015773, + "end_time": "2026-09-19T07:40:18.708958+00:00", + "exception": false, + "start_time": "2026-09-19T07:40:18.693185+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "### Exercice 2 — Localiser la discontinuité η₀ = η/2\n", + "\n", + "**Contexte.** La Partie 5 montre que l'optimum saute de η à η/2 au début du decay. Le diagramme de phase balayait b ∈ {0.25, 0.5, 0.75, 1.0} — le minimum est au bord bas de finesse 0.25/0.5.\n", + "\n", + "**Objectif.** Affiner le sweep en b ∈ {0.3, 0.4, 0.45, 0.5, 0.55, 0.6, 0.7} à t_h = 10 fixé : la perte est-elle minimale pile à b = 0.5, et le gain décroît-il de part et d'autre (optimum intérieur) ?\n", + "\n", + "**Indices.**\n", + "- **Indice 1 :** copiez la boucle de la Partie 5 avec T_DECAY = 400, uniquement la colonne t_h = 10.\n", + "- **Indice 2 :** tracez la loss finale vs b — un V centré sur 0.5 confirme la discontinuité optimale.\n", + "- `# Étape 1` : vérifier que b < 0.5 perd (décroissance trop précoce) et b > 0.5 perd (trop chaud)." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "c34", + "metadata": { + "execution": { + "iopub.execute_input": "2026-09-19T07:40:18.760150Z", + "iopub.status.busy": "2026-09-19T07:40:18.760150Z", + "iopub.status.idle": "2026-09-19T07:40:18.764665Z", + "shell.execute_reply": "2026-09-19T07:40:18.764153Z" + }, + "papermill": { + "duration": 0.021682, + "end_time": "2026-09-19T07:40:18.765752+00:00", + "exception": false, + "start_time": "2026-09-19T07:40:18.744070+00:00", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exercice à compléter : localiser la discontinuité optimale b = 0.5 par sweep fin\n" + ] + } + ], + "source": [ + "def sweep_b_fins(grid_b, th=10.0, T=400):\n", + " \"\"\"Loss finale du decay 1/t pour chaque b, à t_h fixé.\n", + "\n", + " TODO étudiant : pour chaque b, repartir de l'état stationnaire (6000 steps à eta constant)\n", + " puis décroître eta_t = b*eta/(1+t/th) pendant T steps ; retourner {b: loss}.\n", + " \"\"\"\n", + " # TODO étudiant\n", + " pass\n", + "\n", + "print(\"Exercice à compléter : localiser la discontinuité optimale b = 0.5 par sweep fin\")" + ] + }, + { + "cell_type": "markdown", + "id": "c35", + "metadata": { + "papermill": { + "duration": 0.013049, + "end_time": "2026-09-19T07:40:18.792774+00:00", + "exception": false, + "start_time": "2026-09-19T07:40:18.779725+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "### Exercice 3 — Le seuil de blocage sur une vallée quadratique\n", + "\n", + "**Contexte.** La Partie 8 mesure η* = 4c/(ασg²) sur a(y) = e^{αy}. La forme de la vallée change-t-elle le scaling ?\n", + "\n", + "**Objectif.** Reprendre le protocole de dérive avec a(y) = a₀ + b·y² (resserrement polynomial) et mesurer le nouveau seuil ; comparer au scaling prédit en remplaçant α par a′(y*)/a(y*) — le seuil dépend-il de la position ?\n", + "\n", + "**Indices.**\n", + "- **Indice 1 :** réutilisez `e2_rate` avec `a_y = a0 + b*y**2` et `g_y = 0.5 * (2*b*y) * xx**2 - c` (dérivée de a).\n", + "- **Indice 2 :** le seuil local devient η*(y) = 4c·a(y)/(a′(y)·σg²) — non constant : chercher le y où le blocage commence.\n", + "- `# Étape 1` : tracer la dérive vs η pour a0 = 1, b = 0.5, c = 0.02, σg = 1." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "c36", + "metadata": { + "execution": { + "iopub.execute_input": "2026-09-19T07:40:18.819782Z", + "iopub.status.busy": "2026-09-19T07:40:18.819782Z", + "iopub.status.idle": "2026-09-19T07:40:18.823913Z", + "shell.execute_reply": "2026-09-19T07:40:18.823913Z" + }, + "papermill": { + "duration": 0.018869, + "end_time": "2026-09-19T07:40:18.825440+00:00", + "exception": false, + "start_time": "2026-09-19T07:40:18.806571+00:00", + "status": "completed" + }, + "tags": [] + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Exercice à compléter : mesurer le seuil de blocage sur la vallée quadratique\n" + ] + } + ], + "source": [ + "def e2_rate_quadratic(eta_v, steps=3000, a0=1.0, b=0.5, c=0.02, sg=1.0):\n", + " \"\"\"Taux de dérive de y sur la vallée quadratique a(y) = a0 + b·y².\n", + "\n", + " TODO étudiant : même protocole que e2_rate, avec a_y = a0 + b*y**2\n", + " et g_y = 0.5 * (2*b*y) * xx**2 - c. Retourner la pente de y moyen.\n", + " \"\"\"\n", + " # TODO étudiant\n", + " return None\n", + "\n", + "print(\"Exercice à compléter : mesurer le seuil de blocage sur la vallée quadratique\")" + ] + }, + { + "cell_type": "markdown", + "id": "c37", + "metadata": { + "papermill": { + "duration": 0.014135, + "end_time": "2026-09-19T07:40:18.851735+00:00", + "exception": false, + "start_time": "2026-09-19T07:40:18.837600+00:00", + "status": "completed" + }, + "tags": [] + }, + "source": [ + "## Conclusion\n", + "\n", + "Quatre lois mesurées de bout en bout sur ce notebook :\n", + "\n", + "1. **σ(a)** — le learning rate fixe la largeur thermique (SGD close-form partout, SignGD avec plancher √(2π)/4·η) ;\n", + "2. **équipartition** — ℓf = C·η indépendant de la sharpness (avec correction exacte /(1−aη/2)), prouvé sur le paysage jouet ; sur le mini-GPT au plateau, le terme est **borné** (C < 0.1, sous résolution du banc) — le GPT-2 rapporté par R08 (3.145 + 110·η_min) le résout à son échelle ;\n", + "3. **1/t optimal + loi de Fourier** — discontinuité η/2, decay borné par 2/(aη_min), relaxation de taux 2aη_B : les schedules WSD/cosine sont des protocoles de refroidissement, et le 1/t est le seul à suivre exactement l'équilibre ;\n", + "4. **force entropique** — le bruit sélectionne les minima plats (piégeage E.1) et peut bloquer la descente (seuil η* de E.2) : la température n'est pas gratuite.\n", + "\n", + "**Ponts dans la série** : [PT-11a](PT_11a_grpo_qwen35_rlvr.ipynb) utilise WSD en pratique — ce notebook en donne la physique ; [PT-08](PT_08_grpo_from_scratch_toy_env.ipynb) établit le pattern from-scratch toy CPU que nous suivons ; les corrections de loss de [PT-13](PT_13_dapo_drgrpo_corrections.ipynb) modifient σg — leur effet thermodynamique (via ℓf = C·η) est une lecture directe de la Partie 3.\n", + "\n", + "## Références\n", + "\n", + "| Référence | Lien | Couverture |\n", + "|---|---|---|\n", + "| Liu et al., *Neural Thermodynamic Laws for Large Language Model Training* (2025) — **R08** | [arXiv:2505.10559](https://arxiv.org/abs/2505.10559) | Source du notebook (lois, Apps C-E) |\n", + "| Cohen, Kaur, Li, Kolter, Talwalkar — *Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability* (ICLR 2021) | [arXiv:2103.00065](https://arxiv.org/abs/2103.00065) | Edge of stability (Partie 2) |\n", + "\n", + "> Chiffres GPT-2 (val = 3.145 + 110·η_min, N ≈ 5M, σg ≈ 7×10⁻⁵) : **rapportés par** R08 §4 — nos mesures locales (mini-GPT) sont indépendantes et d'échelle différente." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Coursia ML Training", + "language": "python", + "name": "coursia-ml-training" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.16" + }, + "papermill": { + "default_parameters": {}, + "duration": 346.077766, + "end_time": "2026-09-19T07:40:19.861996+00:00", + "environment_variables": {}, + "exception": null, + "input_path": "PT_14_neural_thermodynamic_laws.ipynb", + "output_path": "PT_14_neural_thermodynamic_laws.out.ipynb", + "parameters": {}, + "start_time": "2026-09-19T07:34:33.784230+00:00", + "version": "2.7.0" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/MyIA.AI.Notebooks/GenAI/PostTraining/README.md b/MyIA.AI.Notebooks/GenAI/PostTraining/README.md index 4916374b38..d63ec0cab1 100644 --- a/MyIA.AI.Notebooks/GenAI/PostTraining/README.md +++ b/MyIA.AI.Notebooks/GenAI/PostTraining/README.md @@ -9,7 +9,7 @@ breakdown: PostTraining=16 maturity: BETA=10, ALPHA=6 --> -> **Place dans GenAI** : cette série est le pendant *théorique et SOTA 2024-2025* de la série [FineTuning](../FineTuning/README.md). FineTuning couvre la boîte à outils pratique (LoRA, QLoRA, SFT, DPO, model merging) sur 5 notebooks exécutés ; PostTraining remonte la chaîne conceptuelle complète SFT → RLHF → DPO → GRPO → RLVR → **GAE** et reproduit les techniques récentes (Deepseek-R1) sur petits modèles, complétée par un notebook d'évaluation comparative, un détecteur de reward hacking, et un notebook d'implémentation from-scratch de la famille "no critic" (GRPO/RLOO/GAE) sur toy env CPU, par un **notebook multi-step à crédit différé causal** (PT-12 : les cinq estimateurs re-mesurés, GAE-λ devient discriminant, verdict BEATS 5/5 seeds — le "1-step collapse" était une propriété du banc), et de **trois notebooks appliqués Qwen + GRPO + reward vérifiable + rewardspy en ligne** (PT-11a Z3 CSP arithmétique sur Qwen3.5-0.8B + PT-11b SymPy arithmétique + Z3 N-queens, plus leur validation multi-seed, **plus PT-11c sur le cran au-dessus Qwen3-1.7B/2B** qui qualifie l'étage GPU moyen 16 Go et oppose 0.8B vs 1.7B/2B à budget steps égal) qui font sortir la série du toy env vers un vrai LLM, et **PT-13 sur les corrections 2025 de la loss GRPO** (`Dr. GRPO` : retrait de `÷|o_i|` et `÷std` ; `clip-higher` de `DAPO` : ε_high=0.28 > ε_low=0.2), dont le biais de longueur est mesuré au **niveau gradient**, soit **16 notebooks** au total. Les deux se complèment : commencer par FineTuning pour la pratique, PostTraining pour la profondeur méthodologique. +> **Place dans GenAI** : cette série est le pendant *théorique et SOTA 2024-2025* de la série [FineTuning](../FineTuning/README.md). FineTuning couvre la boîte à outils pratique (LoRA, QLoRA, SFT, DPO, model merging) sur 5 notebooks exécutés ; PostTraining remonte la chaîne conceptuelle complète SFT → RLHF → DPO → GRPO → RLVR → **GAE** et reproduit les techniques récentes (Deepseek-R1) sur petits modèles, complétée par un notebook d'évaluation comparative, un détecteur de reward hacking, et un notebook d'implémentation from-scratch de la famille "no critic" (GRPO/RLOO/GAE) sur toy env CPU, par un **notebook multi-step à crédit différé causal** (PT-12 : les cinq estimateurs re-mesurés, GAE-λ devient discriminant, verdict BEATS 5/5 seeds — le "1-step collapse" était une propriété du banc), et de **trois notebooks appliqués Qwen + GRPO + reward vérifiable + rewardspy en ligne** (PT-11a Z3 CSP arithmétique sur Qwen3.5-0.8B + PT-11b SymPy arithmétique + Z3 N-queens, plus leur validation multi-seed, **plus PT-11c sur le cran au-dessus Qwen3-1.7B/2B** qui qualifie l'étage GPU moyen 16 Go et oppose 0.8B vs 1.7B/2B à budget steps égal) qui font sortir la série du toy env vers un vrai LLM, et **PT-13 sur les corrections 2025 de la loss GRPO** (`Dr. GRPO` : retrait de `÷|o_i|` et `÷std` ; `clip-higher` de `DAPO` : ε_high=0.28 > ε_low=0.2), dont le biais de longueur est mesuré au **niveau gradient**, et **PT-14 sur les lois thermodynamiques de l'entraînement** (R08 : T ∼ η, équipartition ℓf = C·η, schedule 1/t optimal avec discontinuité η/2, force entropique — la physique des learning-rate schedules utilisés en PT-11), soit **17 notebooks** au total. Les deux se complèment : commencer par FineTuning pour la pratique, PostTraining pour la profondeur méthodologique. Série pédagogique dédiée aux techniques de **post-training** des LMs ouverts : SFT, DPO, GRPO, RLVR. L'objectif est de comprendre pourquoi 2024-2025 marque une rupture pédagogique dans la façon dont les modèles de langue passent du pre-training brut à un assistant utile, et comment cette chaîne s'est simplifiée depuis la cascade RLHF historique jusqu'aux méthodes "direct" récentes. @@ -43,6 +43,7 @@ L'angle pédagogique est d'expliquer la **math du loss** avant le code pour chaq | PT-11c | `PT_11c_grpo_qwen17_rlvr.ipynb` | RLVR sur **cran au-dessus** (Qwen3-1.7B ou Qwen3-2B QLoRA 4-bit) — extension directe de PT-11b au cran supérieur, 4 seeds × 100 steps, **verdict mémoire** (pic VRAM RTX 3080 Ti 16GB) + **comparaison honnête** 0.8B vs 1.7B/2B à budget steps égal. Architecture compatible `trl.GRPOTrainer`, peft 0.20.0 (vs 0.13.2 de PT-11b). Reward SymPy Tier-1 + Z3 N-queens Tier-2 + informative-group métrique #10603. **Verdict mesuré (4 seeds × 100 steps chacun, RTX 3070 8 Go)** : MECANISME_REPRO sur les DEUX crans — 1.7B mean 0.1148 ± 0.0059 (edge 19.33σ), 2B mean 0.1653 ± 0.0051 (edge 32.44σ), VRAM peak 3.67/4.98 Go, ~31/~43 min/seed ; le decideur intra-seed reste non-exécutable à 20 pts/seed (fix : `logging_steps=4`). **Note env** : `rewardspy` (GitHub-only, absent de PyPI) peut être non installé — wrapper no-op gracieux | `trl.GRPOTrainer` + verifiers SymPy/Z3 + `rewardspy.watch_trl` (optionnel) | Qwen3-1.7B ou Qwen3-2B (QLoRA 4-bit, GPU 16 Go cible) | See #12653 | | PT-12 | `PT_12_multistep_delayed_credit.ipynb` | GAE-λ sur env **multi-step à crédit différé causal** (`count_ones`, terminal dépendant de toute la séquence) — re-mesure des 5 estimateurs REINFORCE/GRPO/RLOO/GAE-λ=0/GAE-λ=0.95, **5 seeds**, vérificateur terminal Z3 | `torch` from-scratch (no `trl`) + Z3 (RLVR) | MLP jouet acteur-critique (CPU, ~5.5k params) | See #1454 | | PT-13 | `PT_13_dapo_drgrpo_corrections.ipynb` | **Corrections de la loss GRPO** — `Dr. GRPO` (retire `÷\|o_i\|` et `÷std`) et `clip-higher` de `DAPO` (ε_high=0.28 > ε_low=0.2) — **biais de longueur mesuré au niveau gradient** (norme par bucket : vanille dilue long-faux à ~0.32× vs dr ~0.81×, 5 seeds), amplification `÷std` (jusqu'à ×3.0), taux de climb sous clip (ε=0.2→21.5 pas, 0.28→15.8, 0.40→11.6), verdict comportemental honnête (aucun coût, banc non discriminant), Z3 vérificateur RLVR | `torch` from-scratch (no `trl`) + Z3 (RLVR) | MLP jouet (CPU, ~1.5k params) | See #1454 | +| PT-14 | `PT_14_neural_thermodynamic_laws.ipynb` | **Lois thermodynamiques de l'entraînement** (R08 Liu et al. 2025) — perte = énergie, η = température, bruit minibatch = bain thermique : largeur stationnaire σ(a) SGD/SignGD (edge of stability, plancher √(2π)/4·η), **équipartition** ℓf = (σg²η/4)/(1−aη/2) indépendant de la sharpness, T ∼ η, **confrontation mini-GPT 106k au plateau** (bruit d'étiquette q=0.15 : terme thermique BORNÉ C < 0.1, sous résolution du banc toy — verdict honnête, le GPT-2 rapporté 3.145+110·η_min le résout à son échelle ; écart SGD/Adam(0,0) qui s'inverse entre progrès et plateau), **schedule 1/t optimal** (discontinuité η/2, diagramme de phase (b, t_h) à optimum théorique exact 6.03e-06 vs 6.10e-06), **loi de Fourier** (relaxation de taux 2aη_B après switch de lr, 4 répliques), **force entropique** (piégeage vers les zones plates E.1, seuil de blocage η* = 4c/(ασg²) E.2) | `numpy` + `torch` from-scratch (toy + mini-GPT CPU) | toy river-valley + mini-GPT (CPU) | See #16741 | > **Migration vers Qwen3.5 (complète sur les notebooks GPU).** Qwen2.5 est *superseded* par [Qwen3.5](https://huggingface.co/Qwen/Qwen3.5-0.8B) (modèle vision-langage unifié, multimodal). **PT-03 est migré** vers Qwen3.5-0.8B (#5078) : l'évaluation DPO est désormais une vraie *forward pass* (accuracy mesurée 40 % sur 10 préférences *held-out*, vs 50 % aléatoire — le DPO n'a pas convergé sur 50 exemples, verdict honnête documenté dans le notebook) qui remplace l'ancienne accuracy *hardcodée* à 72 %. **PT-02 est migré** vers Qwen3.5-0.8B (#10289, #10813) : le SFT s'exécute sur le vrai petit modèle SOTA (architecture hybride 18×linear_attn + 6×self_attn, LoRA ciblant les deux types + MLP) — verdict honnête documenté : sur 50 exemples (3 steps), le loss oscille (1.92→2.17→1.76) et la génération se dégrade (SFT sous-alimenté sur modèle déjà instruct-tuned, pas un bug). **PT-04 est migré** vers Qwen3.5-0.8B (#10817, re-exec #11442) : le GRPO s'exécute sur le vrai petit modèle SOTA (vrai GRPO GPU, QLoRA 4-bit, récompense basée sur le score). **PT-06 est migré** vers Qwen3.5-0.8B (#10819) : l'évaluation comparative porte désormais sur le modèle migré. **PT-05 est migré** vers Qwen3.5-0.8B (#10487 : re-ciblage + run GPU réel commité — delta honnête documenté 12.5 % → 0.0 %, et #10504 : reward branché sur le ground truth). Architecture Qwen3.5 multimodale (`Qwen3_5ForConditionalGeneration`) chargée via `AutoModelForImageTextToText` (et non `AutoModelForCausalLM`). @@ -192,7 +193,7 @@ PT-06 documente le pipeline d'évaluation complet et produit un tableau comparat | **[RL — rlpt_4 DPO vs PPO](../../RL/rlpt_4_dpo_vs_ppo.ipynb)** | Comparaison offline vs online | DPO/ORPO offline vs GRPO online à budget 40 steps — prérequis empirique pour PT-06 (évaluation comparative). | | **[RL — rl_9 offline](../../RL/rl_9_offline_rl.ipynb)** | DPO = preference learning offline | Le Behavior Cloning y est l'analogue tabulaire du SFT, et la contrainte de support de BCQ celle de la pénalité KL de DPO (PT-03). Le meilleur prérequis conceptuel pour DPO. | | **[RL — rl_10 reward shaping](../../RL/rl_10_reward_shaping.ipynb)** | Reward model = shaping appris | Le reward shaping (Ng 1999) et son biais (shaping naïf → reward hacking) préfigurent le reward model appris et le Goodhart traité en [PT-07](PT_07_rewardspy_reward_hacking.ipynb). | -| **[GenAI/FineTuning](../FineTuning/)** | Boîte à outils fine-tuning | Série sœur dans GenAI : LoRA/QLoRA/SFT/DPO en pratique sur 5 notebooks. PostTraining = profondeur méthodologique (14 notebooks), FineTuning = recettes exécutables. | +| **[GenAI/FineTuning](../FineTuning/)** | Boîte à outils fine-tuning | Série sœur dans GenAI : LoRA/QLoRA/SFT/DPO en pratique sur 5 notebooks. PostTraining = profondeur méthodologique (17 notebooks), FineTuning = recettes exécutables. | ## Frontière avec RL/rlpt_* — où ouvre `PT_*`, où ouvre `rlpt_*` @@ -257,6 +258,7 @@ Les références sont cliquables (arXiv / publisher). Les chiffres que la série | Hoffmann et al., "Chinchilla" (NeurIPS 2022) | [arXiv:2203.15556](https://arxiv.org/abs/2203.15556) | Scaling laws compute-optimal (référencé dans la narration coût/token) | | Penedo et al., "FineWeb-Edu" (2024) | [arXiv:2406.17557](https://arxiv.org/abs/2406.17557) | Dataset de pré-entraînement éducatif (barème coût/token) | | Liu / Su et al., "Moonlight / Muon" (2025) | [arXiv:2502.16982](https://arxiv.org/abs/2502.16982) | Optimizer Muon (vérifié firsthand) — note prospective architecture from-scratch | +| Liu et al., "Neural Thermodynamic Laws for Large Language Model Training" (2025) — **R08** | [arXiv:2505.10559](https://arxiv.org/abs/2505.10559) | Thermodynamique de l'entraînement : T ∼ η, équipartition, 1/t, force entropique (source de PT-14) | | Zhai, "XSA: X-only Sparse Attention" (2026) | [arXiv:2603.09078](https://arxiv.org/abs/2603.09078) | Architecture XSA remplaçant DiffAttn (vérifié firsthand) — note prospective | | Ye et al., "Differential Attention" (Microsoft, 2024) | [arXiv:2410.05258](https://arxiv.org/abs/2410.05258) | Attention différentielle (citée par la série Substack) | | Ainslie et al., "GQA: Training Generalized Multi-Query Transformer Models from Multi-Head Checkpoints" (Google, 2023) | [arXiv:2305.13245](https://arxiv.org/abs/2305.13245) | Grouped-Query Attention (citée par la série Substack) |