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matplotlib.pyplot as plt +import numpy as np +from rich import print +from rich.console import Console + +console = Console() + +REWARD_MOVE = -0.04 +REWARD_GOAL = 1 +REWARD_DEATH = -1 +DISCOUNT_FACTOR = 0.9 + +ARROWS = ["←", "↑", "↓", "→"] + +MOVEMENTS = np.array([ + [0.7, 0.1, 0.1, 0.1], + [0.1, 0.7, 0.1, 0.1], + [0.1, 0.1, 0.7, 0.1], + [0.1, 0.1, 0.1, 0.7] +]) + +REWARDS = np.array([ + REWARD_MOVE, REWARD_MOVE, REWARD_MOVE, REWARD_GOAL, + REWARD_MOVE, REWARD_MOVE, REWARD_DEATH, + REWARD_MOVE, REWARD_MOVE, REWARD_MOVE, REWARD_MOVE, +]) + +# Part 1: Performance Prediction +console.rule("[bold white]Part 1: Performance Prediction") + +# Exo 1: Random policy +console.rule("[bold yellow]Exo 1: Random policy") + +P = np.array([ + [ + 0.8, 0.1, 0.0, 0.0, + 0.1, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.7, 0.2, 0.1, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.7, 0.1, 0.1, + 0.0, 0.1, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.1, 0.0, 0.0, 0.0, + 0.8, 0.0, 0.0, + 0.1, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.1, 0.0, + 0.0, 0.7, 0.1, + 0.0, 0.0, 0.1, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.1, 0.0, 0.0, + 0.8, 0.1, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.1, 0.8, 0.1, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.7, 0.0, + 0.0, 0.1, 0.1, 0.1, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.1, + 0.0, 0.0, 0.7, 0.2, + ], +]) + +V = np.linalg.inv(np.eye(11) - DISCOUNT_FACTOR * P) @ REWARDS.flatten() +print(V) + +V_new = REWARDS + DISCOUNT_FACTOR * P @ V + +if np.allclose(V, V_new): + print("[green]V is a fixed point !") +else: + print("[red]You suck !") + +# Exo 2: Iterative Policy Evaluation +console.rule("[bold yellow]Exo 2: Iterative Policy Evaluation") + +DELTA = 1e-6 + +V_random = np.random.rand(11) + +while True: + V_new = REWARDS + DISCOUNT_FACTOR * P @ V_random + + diff = np.max(np.abs(V_new - V_random)) + V_random = V_new + + if diff < DELTA: + break + +print(V_random) + +# Exo 3: Bellman operator contraction +console.rule("[bold yellow]Exo 3: Bellman operator contraction") + +V1 = np.random.rand(11) +V2 = np.random.rand(11) +diffs = [] + +while True: + V1 = REWARDS + DISCOUNT_FACTOR * P @ V1 + V2 = REWARDS + DISCOUNT_FACTOR * P @ V2 + + diff = np.max(np.abs(V1 - V2)) + diffs.append(diff) + + if diff < DELTA: + break + +print(V1) +print(V2) + +plt.plot(diffs) +plt.yscale("log") +plt.title("Convergence of Bellman operator") +plt.xlabel("Iteration") +plt.ylabel("Difference") +# plt.show() + +# Part 2: Optimization +console.rule("[bold white]Part 2: Optimization") + +# Exo 1: Bellmann equation +console.rule("[bold yellow]Exo 1: Bellmann equation") +# cf cours, partie 2, slide 15 + +# Exo 2: Value Iteration Algorithm +console.rule("[bold yellow]Exo 2: Value Iteration Algorithm") + +P_g = np.array([ + [ + 0.8, 0.1, 0.0, 0.0, + 0.1, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.7, 0.2, 0.1, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.7, 0.1, 0.1, + 0.0, 0.1, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.1, 0.0, 0.0, 0.0, + 0.8, 0.0, 0.0, + 0.1, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.1, 0.0, + 0.0, 0.7, 0.1, + 0.0, 0.0, 0.1, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.1, 0.0, 0.0, + 0.8, 0.1, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.7, 0.2, 0.1, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.1, 0.0, + 0.0, 0.7, 0.1, 0.1, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.1, + 0.0, 0.0, 0.7, 0.2, + ], +]) + +P_h = np.array([ + [ + 0.8, 0.1, 0.0, 0.0, + 0.1, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.1, 0.8, 0.1, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.1, 0.7, 0.1, + 0.0, 0.1, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.7, 0.0, 0.0, 0.0, + 0.2, 0.0, 0.0, + 0.1, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.7, 0.0, + 0.0, 0.1, 0.1, + 0.0, 0.0, 0.1, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.7, 0.0, 0.0, + 0.2, 0.1, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.1, 0.8, 0.1, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.7, 0.0, + 0.0, 0.1, 0.1, 0.1, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.7, + 0.0, 0.0, 0.1, 0.2, + ], +]) + +P_b = np.array([ + [ + 0.2, 0.1, 0.0, 0.0, + 0.7, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.1, 0.8, 0.1, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.1, 0.1, 0.1, + 0.0, 0.7, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.1, 0.0, 0.0, 0.0, + 0.2, 0.0, 0.0, + 0.7, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.1, 0.0, + 0.0, 0.1, 0.1, + 0.0, 0.0, 0.7, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.1, 0.0, 0.0, + 0.8, 0.1, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.1, 0.8, 0.1, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.1, 0.0, + 0.0, 0.1, 0.7, 0.1, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.1, + 0.0, 0.0, 0.1, 0.8, + ], +]) + +P_d = np.array([ + [ + 0.2, 0.7, 0.0, 0.0, + 0.1, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.1, 0.2, 0.7, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.1, 0.1, 0.7, + 0.0, 0.1, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.1, 0.0, 0.0, 0.0, + 0.8, 0.0, 0.0, + 0.1, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.1, 0.0, + 0.0, 0.1, 0.7, + 0.0, 0.0, 0.1, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.1, 0.0, 0.0, + 0.2, 0.7, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.1, 0.2, 0.7, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.1, 0.0, + 0.0, 0.1, 0.1, 0.7, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.1, + 0.0, 0.0, 0.1, 0.8, + ], +]) + +V_optimal = np.random.rand(11) +pi = np.zeros(11) + +while True: + V_g = REWARDS + DISCOUNT_FACTOR * P_g @ V_optimal + V_h = REWARDS + DISCOUNT_FACTOR * P_h @ V_optimal + V_b = REWARDS + DISCOUNT_FACTOR * P_b @ V_optimal + V_d = REWARDS + DISCOUNT_FACTOR * P_d @ V_optimal + + V_new = np.max([V_g, V_h, V_b, V_d], axis=0) + + if np.allclose(V_new, V_optimal, atol=1e-6): + pi = np.argmax([V_g, V_h, V_b, V_d], axis=0) + break + else: + V_optimal = V_new + +print(V_optimal) + +pi_pretty = [ARROWS[i] for i in pi] +pi_pretty.insert(5, "■") +pi_pretty[3] = "✓" +pi_pretty[7] = "☠" +pi_pretty = np.array(pi_pretty).reshape(3, 4) +print(pi_pretty) + +# Exo 4: Performance comparison +console.rule("[bold yellow]Exo 4: Performance comparison") + +perf = np.abs(V_optimal - V_random) +print(perf) \ No newline at end of file diff --git a/TP1/notebook.jl b/TP1/notebook.jl new file mode 100644 index 0000000..9e3bdc7 --- /dev/null +++ b/TP1/notebook.jl @@ -0,0 +1,2044 @@ +### A Pluto.jl notebook ### +# v0.19.19 + +#> [frontmatter] +#> title = " TP1 - Reinforcement learning " +#> date = "2022-12-14" +#> tags = ["RL"] + +using Markdown +using InteractiveUtils + +# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error). +macro bind(def, element) + quote + local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end + local el = $(esc(element)) + global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el) + el + end +end + +# ╔═╡ 26fdd17e-f03a-4835-93be-85303fe526d8 +begin + using Plots # pour le tracé de figures + using PlutoUI # pour les objets Pluto + using LinearAlgebra # pour les matrices identité + using SparseArrays # pour les matrices creuses + using LaTeXStrings # pour les strings en LaTeX (pour les plots) + import Random + TableOfContents(depth=4) +end + +# ╔═╡ 56ac3473-24f4-42d7-84e1-cfce6a70d8d5 +html""" + +""" + +# ╔═╡ ccf4d63e-7ace-11ed-2123-d9dbb62bd308 +html""" +
+ + TP1 - Reinforcement learning
+ Laurent Fainsin
+ 2021 - 2022 + +
+""" + +# ╔═╡ 9f2879c1-c22b-4067-ad20-4e4c56cc8d00 +begin + REWARD_MOVE_slider = @bind REWARD_MOVE Slider(-0.1:0.01:0, default=-0.04, show_value=true) + REWARD_GOAL_slider = @bind REWARD_GOAL Slider(0:1:10, default=1, show_value=true) + REWARD_DEATH_slider = @bind REWARD_DEATH Slider(-10:1:0, default=-2, show_value=true) + DISCOUNT_FACTOR_slider = @bind DISCOUNT_FACTOR Slider(0.9:0.01:0.99, default=0.9, show_value=true) + + div = html"""
""" + div_end = html"""
""" + + md""" + $(div) + + Hyper-paramètres: + + REWARD\_MOVE: $(REWARD_MOVE_slider) + + REWARD\_GOAL: $(REWARD_GOAL_slider) + + REWARD\_DEATH: $(REWARD_DEATH_slider) + + DISCOUNT\_FACTOR: $(DISCOUNT_FACTOR_slider) + + $(div_end) + """ +end + +# ╔═╡ 0a30a68a-068e-41fb-92c4-000869ba7dff +RANDOM_SEED = 420 + +# ╔═╡ 07b57746-fba0-49aa-ba17-6dcb0bbe44e5 +MAX_ITERATIONS = 350 + +# ╔═╡ 92d6874b-651c-4551-840e-ad5d1e934aeb +MOVEMENTS = [ + 0.7 0.1 0.1 0.1 + 0.1 0.7 0.1 0.1 + 0.1 0.1 0.7 0.1 + 0.1 0.1 0.1 0.7 +] + +# ╔═╡ fe44d7f2-155e-42f2-83c3-dd18aadb3810 +md""" +On définit notre environnement comme une grille 3x4: +""" + +# ╔═╡ 28b769a6-dd3c-43ab-bae0-646d8ebc35d6 +begin + ARROW_SYMBOLS = ["←", "↑", "↓", "→"] + DEATH_SYMBOL = "☠" + SUCCESS_SYMBOL = "✓" + WALL_SYMBOL = "■" + EMPTY_SYMBOL = "□" + + [ + EMPTY_SYMBOL EMPTY_SYMBOL EMPTY_SYMBOL SUCCESS_SYMBOL + EMPTY_SYMBOL WALL_SYMBOL EMPTY_SYMBOL DEATH_SYMBOL + EMPTY_SYMBOL EMPTY_SYMBOL EMPTY_SYMBOL EMPTY_SYMBOL + ] +end + +# ╔═╡ 3881603c-619b-4976-ac4c-2c7e7f3a6ec7 +md""" +On peut définir nos rewards tels que: +""" + +# ╔═╡ fb797a9b-6a0a-4a77-a9b6-6804f98639bb +begin + REWARDS = [ + REWARD_MOVE, REWARD_MOVE, REWARD_MOVE, REWARD_GOAL, + REWARD_MOVE, REWARD_MOVE, REWARD_DEATH, + REWARD_MOVE, REWARD_MOVE, REWARD_MOVE, REWARD_MOVE, + ] + + local REWARDS_display = copy(REWARDS) + insert!(REWARDS_display, 6, 0) + REWARDS_display = permutedims(reshape(REWARDS_display, 4, 3)) + REWARDS_display = sparse(REWARDS_display) +end + +# ╔═╡ 1e3abda8-6645-48ba-874d-28e1011fc3e3 +md""" +# Performance Prediction +""" + +# ╔═╡ beb410a8-03e2-4f18-8ccd-941cc926ee12 +md""" +## Question 1 + +> Assume the random policy, that is, the policy that takes every possible action with probability 1/4. Compute its value function by solving \ +> $V = (I − \gamma P )^{-1} R$. \ +> Since there are 11 possible states in the problem, the vectors ``R`` and ``V`` have have length 11, and the matrix ``P`` has dimension 11x11. There are two absorbing states, i.e., they are visited once, and their respective reward (+1 or -1) is only accrued once. To model this, you can simply put all 0’s in all the elements of the respective two lines. +""" + +# ╔═╡ 133f291f-6f21-4441-86f7-ba190a7d6b1f +md""" +On définit une politique aléatoire (à la main): +""" + +# ╔═╡ e14f9977-d2fd-4d05-84d6-614008dc0c4a +[ + ARROW_SYMBOLS[2] ARROW_SYMBOLS[1] ARROW_SYMBOLS[1] SUCCESS_SYMBOL + ARROW_SYMBOLS[1] WALL_SYMBOL ARROW_SYMBOLS[1] DEATH_SYMBOL + ARROW_SYMBOLS[1] ARROW_SYMBOLS[3] ARROW_SYMBOLS[2] ARROW_SYMBOLS[1] +] + +# ╔═╡ 486c93ab-9cb9-4df4-b702-bbe12a961647 +md""" +Via nos probabilités de mouvements on peut alors constituer ``P``: +""" + +# ╔═╡ ab2d705d-fc00-43b2-bb6d-2a3d4ba9dab1 +begin + P = [ + [ + 0.8, 0.1, 0.0, 0.0, + 0.1, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.7, 0.2, 0.1, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.7, 0.1, 0.1, + 0.0, 0.1, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.1, 0.0, 0.0, 0.0, + 0.8, 0.0, 0.0, + 0.1, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.1, 0.0, + 0.0, 0.7, 0.1, + 0.0, 0.0, 0.1, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.1, 0.0, 0.0, + 0.8, 0.1, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.1, 0.8, 0.1, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.7, 0.0, + 0.0, 0.1, 0.1, 0.1, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.1, + 0.0, 0.0, 0.7, 0.2, + ], + ] + + P = sparse(reduce(hcat, P)') +end + +# ╔═╡ b7ae89c9-3c1b-4f5c-af5b-164d95ccca41 +md""" +On peut alors calculer ``V``: +""" + +# ╔═╡ 03c17428-5ab9-42e7-bf79-92eb846f11cb +begin + V = Matrix(I(length(REWARDS)) - DISCOUNT_FACTOR * P) \ REWARDS + + local V_display = copy(V) + insert!(V_display, 6, 0) + V_display = permutedims(reshape(V_display, 4, 3)) + V_display = sparse(V_display) +end + +# ╔═╡ c65d0dbc-ecd7-4320-9b3a-a1b9c0545f9a +md""" +### Bonus +On contrôle que ``V`` vérifie l'équation de Bellman en calculant une itération de l'équation de Bellman: + +$V_{\text{next}} = R + \gamma P V$ + +et en observant que ``V`` est un point fixe: + +$V_{\text{next}} = V$ + +On calcule alors ``V_\text{next}``: +""" + +# ╔═╡ ad547684-bcbe-44f4-9fc1-f327d2db4584 +begin + V_next = REWARDS + Matrix(DISCOUNT_FACTOR * P) * V + + local V_display = copy(V_next) + insert!(V_display, 6, 0) + V_display = permutedims(reshape(V_display, 4, 3)) + V_display = sparse(V_display) +end + +# ╔═╡ d3703ab8-912c-417d-acd9-29590ec1134b +if isapprox(V_next, V) + Markdown.MD(Markdown.Admonition("correct", "V est un point fixe", [md"L'équation de Bellman est vérifiée"])); +else + Markdown.MD(Markdown.Admonition("danger", "V n'est pas un point fixe", [md"L'équation de Bellman n'est vérifiée"])); +end + +# ╔═╡ 1319b304-5126-4825-8076-e113e4dd3635 +md""" +## Question 2 + +> Evaluate now the policy using Iterative Policy Evaluation (lecture 2, 2nd part, slides 11/35), and verify that the algorithm converges to the result obtained in 1. To stop iterating, you can take as a criterion that the difference between two iterations must be smaller than some small ``\delta``. Due to the contraction principle, the initial vector can be arbitrary. +""" + +# ╔═╡ 3ea3f177-c576-4b9e-a54b-c427e29a8491 +md""" +On initialise ``V_\text{random} \in [0, 1]^{11}`` aléatoirement. + +On souhaite vérifier que ``V_\text{random}`` converge vers ``V`` par l'évaluation itérative de la politique ``P``. +""" + +# ╔═╡ e94fe8a6-274b-4121-b1fc-063d3710c2f7 +begin + Random.seed!(RANDOM_SEED) + V_random = rand(length(REWARDS)) + local diffs = Vector{Float64}() + for _ in 1:MAX_ITERATIONS + local V_old = V_random + V_random = REWARDS + Matrix(DISCOUNT_FACTOR * P) * V_random + append!(diffs, norm(V_random - V_old)) + if isapprox(V_random, V_old) + break + end + end + + plot( + diffs, + labels = "", + xlabel = L"n", + ylabel = L"|| V_{n+1} - V_n ||^2", + yticks=[10.0^-x for x in 0:10], + linewidth=2, + yaxis=:log, + title="Iterative Policy Evaluation convergence", + ) +end + +# ╔═╡ 80090d5f-d56c-4844-a04f-444ed49e5f34 +if isapprox(V_random, V, rtol=1e-5) + Markdown.MD(Markdown.Admonition("correct", "L'évaluation itérative des politiques est vérifiée", [md"``V_\text{random}`` converge vers ``V``"])); +else + Markdown.MD(Markdown.Admonition("danger", "L'évaluation itérative des politiques n'est pas vérifiée", [md"``V_\text{random}`` ne converge pas vers ``V``"])); +end + +# ╔═╡ 98362798-aae4-4540-9e98-cc7371802552 +md""" +## Question 3 + +> To verify that the Bellman operator is a contraction, take two initial vectors, and calculate the max of their differences. Then, apply the iterative policy evaluation to these 2 vectors as done in the previous item, and plot the maximum of their differences as you keep iterating. Observe what happens with the difference as you iterate, and explain it. +""" + +# ╔═╡ 30874daf-7b0e-4335-9a50-d19389cf1620 +md""" +On initialise ``V_{r1}, V_{r2} \in [0, 1]^{11}`` aléatoirement. + +On souhaite vérifier que ``V_{r1}`` converge vers ``V_{r2}`` (et aussi vers ``V``) par l'évaluation itérative de la politique ``P``. +""" + +# ╔═╡ c005a3f8-765c-4a50-90ef-73a5a72eee01 +begin + Random.seed!(RANDOM_SEED) + V_random1 = rand(length(REWARDS)) + V_random2 = rand(length(REWARDS)) + local diffs = Vector{Float64}() + for _ in 1:MAX_ITERATIONS + V_random1 = REWARDS + Matrix(DISCOUNT_FACTOR * P) * V_random1 + V_random2 = REWARDS + Matrix(DISCOUNT_FACTOR * P) * V_random2 + append!(diffs, norm(V_random1 - V_random2)) + if isapprox(V_random1, V_random2) + break + end + end + + plot( + diffs, + labels = "", + xlabel = L"n", + ylabel = L"|| V_{r1} - V_{r2} ||^2", + yticks=[10.0^-x for x in 0:10], + linewidth=2, + yaxis=:log, + title="Bellman's operator contraction", + ) +end + +# ╔═╡ 1b43e9e5-d7d2-4b5e-a2b2-3a8b8eda6d62 +if isapprox(V_random1, V_random2, rtol=0.01) + Markdown.MD(Markdown.Admonition("correct", "On vérifie que l'opérateur de Bellman est une contraction", [md"``V_{r1}`` converge vers ``V_{r2}``"])); +else + Markdown.MD(Markdown.Admonition("danger", "On ne vérifie pas que l'opérateur de Bellman est une contraction", [md"``V_{r1}`` ne converge pas vers ``V_{r2}``"])); +end + +# ╔═╡ add0221b-e352-4559-a722-c45a64f573f9 +md""" +# Optimization +""" + +# ╔═╡ 84e07dce-bf6d-4ac1-bfa4-65414fe1d787 +md""" +## Question 1 + +> Write down the Bellman equation that characterizes the optimal policy. +""" + +# ╔═╡ df13fa05-14de-409b-a0b1-5bba5eff432e +md""" +Bellman Optimality Equation for ``V_\star`` and ``\pi_\star``: + +$V_\star(s) = \max_{a \in A} \left( r(s,a) + \gamma \sum_{s' \in S} p(s' | s, a) V_\star(s') \right)$ + +$\pi_\star(s) \in \mathop{\mathrm{argmax}}_{a \in A} \left( r(s,a) + \gamma \sum_{s' \in S} p(s' | s, a) V_\star(s') \right)$ +""" + +# ╔═╡ ac490e4a-ce20-4288-a04f-c224df5ade1a +md""" +## Question 2 + +> Solve numerically the optimal value function by Value Iteration Algorithm (lecture 2, 2nd part, slides 15/35). Verify that the solution you obtain satisfies the Bellman equation. +""" + +# ╔═╡ 33890f22-d3f6-4bcf-870d-756f7ff250a9 +md""" +``P_g`` la politique du déplacement toujours à gauche: +""" + +# ╔═╡ cf9fb8a8-6c93-4c43-9f01-5f198f0cf4aa +begin + P_g = [ + [ + 0.8, 0.1, 0.0, 0.0, + 0.1, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.7, 0.2, 0.1, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.7, 0.1, 0.1, + 0.0, 0.1, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.1, 0.0, 0.0, 0.0, + 0.8, 0.0, 0.0, + 0.1, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.1, 0.0, + 0.0, 0.7, 0.1, + 0.0, 0.0, 0.1, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.1, 0.0, 0.0, + 0.8, 0.1, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.7, 0.2, 0.1, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.1, 0.0, + 0.0, 0.7, 0.1, 0.1, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.1, + 0.0, 0.0, 0.7, 0.2, + ], + ] + + P_g = sparse(reduce(hcat, P_g)') +end + +# ╔═╡ dc87b85f-c87c-4302-9124-194bd799f1fd +md""" +``P_h`` la politique du déplacement toujours en haut: +""" + +# ╔═╡ b2595dec-aa5b-462b-b0f8-3555c1231b2f +begin + P_h = [ + [ + 0.8, 0.1, 0.0, 0.0, + 0.1, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.1, 0.8, 0.1, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.1, 0.7, 0.1, + 0.0, 0.1, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.7, 0.0, 0.0, 0.0, + 0.2, 0.0, 0.0, + 0.1, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.7, 0.0, + 0.0, 0.1, 0.1, + 0.0, 0.0, 0.1, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.7, 0.0, 0.0, + 0.2, 0.1, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.1, 0.8, 0.1, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.7, 0.0, + 0.0, 0.1, 0.1, 0.1, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.7, + 0.0, 0.0, 0.1, 0.2, + ], + ] + + P_h = sparse(reduce(hcat, P_h)') +end + +# ╔═╡ 70edf811-adb0-4ae8-941a-b298d85a6e0e +md""" +``P_b`` la politique du déplacement toujours en bas: +""" + +# ╔═╡ 875673f1-08c9-4713-bbc2-85b0a7a0cb0a +begin + P_b = [ + [ + 0.2, 0.1, 0.0, 0.0, + 0.7, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.1, 0.8, 0.1, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.1, 0.1, 0.1, + 0.0, 0.7, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.1, 0.0, 0.0, 0.0, + 0.2, 0.0, 0.0, + 0.7, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.1, 0.0, + 0.0, 0.1, 0.1, + 0.0, 0.0, 0.7, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.1, 0.0, 0.0, + 0.8, 0.1, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.1, 0.8, 0.1, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.1, 0.0, + 0.0, 0.1, 0.7, 0.1, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.1, + 0.0, 0.0, 0.1, 0.8, + ], + ] + + P_b = sparse(reduce(hcat, P_b)') +end + +# ╔═╡ 2deaac7c-ad14-43b0-9cd5-9f0ec12d324c +md""" +``P_d`` la politique du déplacement toujours à droite: +""" + +# ╔═╡ b5c93b6f-933c-41b4-8399-44cc0fa07fab +begin + P_d = [ + [ + 0.2, 0.7, 0.0, 0.0, + 0.1, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.1, 0.2, 0.7, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.1, 0.1, 0.7, + 0.0, 0.1, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.1, 0.0, 0.0, 0.0, + 0.8, 0.0, 0.0, + 0.1, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.1, 0.0, + 0.0, 0.1, 0.7, + 0.0, 0.0, 0.1, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.1, 0.0, 0.0, + 0.2, 0.7, 0.0, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.0, + 0.1, 0.2, 0.7, 0.0, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.1, 0.0, + 0.0, 0.1, 0.1, 0.7, + ], + [ + 0.0, 0.0, 0.0, 0.0, + 0.0, 0.0, 0.1, + 0.0, 0.0, 0.1, 0.8, + ], + ] + + P_d = sparse(reduce(hcat, P_d)') +end + +# ╔═╡ 8015bdbb-82dd-48da-905d-a25e5c864298 +md""" +Pour trouver la politique optimal, on peut procéder de la façon suivante: + +Initialiser ``V_\star`` (random). \ +Tant qu'on a pas convergé (ou atteint `MAX_ITERATIONS`): +- Calculer pour chaque direction (gauche, haut, bas, droite) le vecteur correspondant à la fonction valeur de la politique associée à la direction. +- Sélectionner notre nouvel `V_optimal` comme le maximum par ligne de nos vecteurs issus des fonctions valeur (des quatre directions). +- Vérifier la convergeance par comparaison avec l'itération précédente. + +Par application de cet algorithme on obtient alors ``V_\star``: +""" + +# ╔═╡ 3d7d0b11-5b99-4b1f-ab06-3366678eece8 +begin + Random.seed!(RANDOM_SEED) + V_optimal = rand(length(REWARDS)) + pi = zeros(length(REWARDS)) + + for _ in 1:MAX_ITERATIONS + local V_g = REWARDS + Matrix(DISCOUNT_FACTOR * P_g) * V_optimal + local V_h = REWARDS + Matrix(DISCOUNT_FACTOR * P_h) * V_optimal + local V_b = REWARDS + Matrix(DISCOUNT_FACTOR * P_b) * V_optimal + local V_d = REWARDS + Matrix(DISCOUNT_FACTOR * P_d) * V_optimal + + local V_new = maximum.(eachrow([V_g V_h V_b V_d])) + + if isapprox(V_new, V_optimal) + pi = argmax.(eachrow([V_g V_h V_b V_d])) + break + else + V_optimal = V_new + end + end + + local V_display = copy(V_optimal) + insert!(V_display, 6, 0) + V_display = permutedims(reshape(V_display, 4, 3)) + V_display = sparse(V_display) +end + +# ╔═╡ 664bb753-ccce-4c7a-8b11-76261a3b80d2 +md""" +## Question 3 + +> Explain how you can infer the optimal action in every state from the optimal value function ``V_\star(s)``. Represent in a 2D matrix the optimal policy. +""" + +# ╔═╡ df01ea55-b289-4c13-8a6b-780ce068e44c +md""" +La politique optimale se trouve en sélectionnant la direction la plus favorable dans chaque état: +""" + +# ╔═╡ d7ff1cb5-d2b4-4597-bcef-0f74f2e7e0db +begin + pi_symbols = [ARROW_SYMBOLS[i] for i in pi] + insert!(pi_symbols, 6, WALL_SYMBOL) + pi_symbols[4] = SUCCESS_SYMBOL + pi_symbols[8] = DEATH_SYMBOL + permutedims(reshape(pi_symbols, 4, 3)) +end + +# ╔═╡ 40b7e793-d869-4b68-83a1-6bd7d20a3941 +md""" +## Question 4 + +> Compare the performances obtained with the random policy and the optimal one, how can you conclude that the optimal policy performs better ? +""" + +# ╔═╡ dce3978b-1334-426e-80cc-9cfe63989909 +md""" +À partir ``\pi^\star`` on peut aussi trouver ``P^\star`` la matrice de notre politique optimale: +""" + +# ╔═╡ 7aae25dc-38cf-40d5-a7da-44d13d397194 +begin + P_star = sparse(zeros(11, 11)) + for i in 1:11 + if pi[i] == 1 + P_star[i, :] = P_g[i, :] + elseif pi[i] == 2 + P_star[i, :] = P_h[i, :] + elseif pi[i] == 3 + P_star[i, :] = P_b[i, :] + else + P_star[i, :] = P_d[i, :] + end + end + P_star +end + +# ╔═╡ b075f5fc-85ac-45a0-8e27-605d3dac0e97 +begin + Random.seed!(RANDOM_SEED) + V_Prandom = rand(length(REWARDS)) + V_Poptimal = rand(length(REWARDS)) + + ratio = Vector{Float64}() + convergence_random = Vector{Float64}() + convergence_optimal = Vector{Float64}() + + for _ in 1:MAX_ITERATIONS + V_Prandom = REWARDS + Matrix(DISCOUNT_FACTOR * P) * V_Prandom + V_Poptimal = REWARDS + Matrix(DISCOUNT_FACTOR * P_star) * V_Poptimal + + append!(convergence_optimal, norm(V_Poptimal-V_optimal)) + append!(convergence_random, norm(V_Prandom-V)) + append!(ratio, norm(V_Poptimal./V_Prandom)) + end +end + +# ╔═╡ 1fe62967-a9ea-4f6a-817e-666a900c8f92 +plot( + [convergence_optimal, convergence_random], + labels = ["Optimal" "Random"], + xlabel = L"n", + ylabel = L"|| V^\star - \ \ V^r ||^2", + yticks=[10.0^-x for x in 0:20], + linewidth=2, + yaxis=:log, + title="Optimal vs Random: Convergence", +) + +# ╔═╡ f31ce9b6-8399-4263-bad7-20c859116fa9 +begin + plot( + ratio, + labels = "", + xlabel = L"n", + ylabel = L"|| V^\star / \ \ V^r ||^2", + linewidth=2, + title="Optimal vs Random: Ratio", + ylims=[0, Inf] + ) +end + +# ╔═╡ 05373383-0c51-49f2-8a62-b06a6225d659 +md""" +## Question 5 + +> **Policy Iteration I**: We are now going to calculate the optimal policy using Policy Iteration (lecture 2, 2nd part, slides 23/35 and 24/35). You can start with the random policy for which you calculated its performance in the **Performance Prediction** section. Carry out a one-step improvement (or greedy step) on the random policy. Represent in a 2D matrix the policy you obtain. How can we verify that it is a better policy than the random one? +""" + +# ╔═╡ 81572e40-4cde-4a13-84aa-5c5d6a9dbde3 +md""" +0. Initialization: choose a policy ``\pi_0`` +On reprend ici notre politique aléatoire ``P^{\pi_0}`` de la [question 1 partie 1](#beb410a8-03e2-4f18-8ccd-941cc926ee12): +""" + +# ╔═╡ 4b264154-944d-498b-a998-a4b07f77918e +begin + P_pi_0 = P + P_pi_0 +end + +# ╔═╡ a68a3d33-f4df-456e-af13-9b39e14dbc13 +md""" +2. Policy Evaluation: Compute iteratively ``V_{\pi_k} = (I − \gamma P^{\pi_k} )^{-1} R^{\pi_k}`` +(on calcule uniquement ``V_{\pi_0}`` dans cette question) +""" + +# ╔═╡ c3a6ab2c-7a3e-458f-a108-e6e81aa3def1 +begin + V_pi_0 = Matrix(I(length(REWARDS)) - DISCOUNT_FACTOR * P_pi_0) \ REWARDS + + local V_display = copy(V_pi_0) + insert!(V_display, 6, 0) + V_display = permutedims(reshape(V_display, 4, 3)) + V_display = sparse(V_display) +end + +# ╔═╡ ea457cd9-0db5-433f-9d57-1e875a160990 +md""" +3. Policy improvement: Compute ``\pi_{k+1} = \text{greedy}(V_{\pi_k})`` + +(On calcule donc ici uniquement ``\pi_1`` ) +""" + +# ╔═╡ 3d62d11d-383c-4060-b697-be0c0155ce95 +begin + local V_g = REWARDS + Matrix(DISCOUNT_FACTOR * P_g) * V_pi_0 + local V_h = REWARDS + Matrix(DISCOUNT_FACTOR * P_h) * V_pi_0 + local V_b = REWARDS + Matrix(DISCOUNT_FACTOR * P_b) * V_pi_0 + local V_d = REWARDS + Matrix(DISCOUNT_FACTOR * P_d) * V_pi_0 + + local pi_1 = argmax.(eachrow([V_g V_h V_b V_d])) + + P_pi_1 = sparse(zeros(11, 11)) + for i in 1:11 + if pi_1[i] == 1 + P_pi_1[i, :] = P_g[i, :] + elseif pi_1[i] == 2 + P_pi_1[i, :] = P_h[i, :] + elseif pi_1[i] == 3 + P_pi_1[i, :] = P_b[i, :] + else + P_pi_1[i, :] = P_d[i, :] + end + end + P_pi_1 +end + +# ╔═╡ 245f3394-d5e3-4d2c-96a6-ce5ea0bc7d84 +md""" +Stop if ``V_{\pi_{k+1}} = V_{\pi_k}``, else repeat + +(Ici on s'arrête comme le dit l'énoncé pour k=1) +""" + +# ╔═╡ 4f597447-f321-4a8f-adf0-3fd655ab203c +begin + diff_star_pi_0 = sum(abs.(P_star - P_pi_0)) + diff_star_pi_1 = sum(abs.(P_star - P_pi_1)) + + md""" + On peut vérifier que ``\pi_1`` est meilleur que ``\pi_0`` en calculant: + + ``||\pi_\star - \pi_1||_\text{F} = `` $(diff_star_pi_1) + + ``||\pi_\star - \pi_0||_\text{F} = `` $(diff_star_pi_0) + """ +end + +# ╔═╡ d599c370-6cb5-4bc3-a333-d41e207c39dc +if diff_star_pi_1 <= diff_star_pi_0 + Markdown.MD(Markdown.Admonition("correct", "On a une meilleur politique après une itération", [md"``||\pi_\star - \pi_1||_\text{F} \leq ||\pi_\star - \pi_0||_\text{F}``"])); +else + Markdown.MD(Markdown.Admonition("danger", "On n'a pas une meilleur politique après une itération", [md"``||\pi_\star - \pi_1||_\text{F} \nleq ||\pi_\star - \pi_0||_\text{F}``"])); +end + +# ╔═╡ 4e8e49b2-60ea-4dc6-906b-d459c7983b34 +md""" +## Question 6 + +> **Policy Iteration II**: Continue iterating the Prediction and the greedy steps until convergence to the optimal policy. +""" + +# ╔═╡ 362a3786-f85d-44b9-b369-ecbf4e5194e9 +begin + P_pi_k = P_pi_0 + local diffs = Vector{Float64}() + + for k in 1:MAX_ITERATIONS + V_pi_k = Matrix(I(length(REWARDS)) - DISCOUNT_FACTOR * P_pi_k) \ REWARDS + + local V_g = REWARDS + Matrix(DISCOUNT_FACTOR * P_g) * V_pi_k + local V_h = REWARDS + Matrix(DISCOUNT_FACTOR * P_h) * V_pi_k + local V_b = REWARDS + Matrix(DISCOUNT_FACTOR * P_b) * V_pi_k + local V_d = REWARDS + Matrix(DISCOUNT_FACTOR * P_d) * V_pi_k + + local pi_k = argmax.(eachrow([V_g V_h V_b V_d])) + + P_pi_k = sparse(zeros(11, 11)) + for i in 1:11 + if pi_k[i] == 1 + P_pi_k[i, :] = P_g[i, :] + elseif pi_k[i] == 2 + P_pi_k[i, :] = P_h[i, :] + elseif pi_k[i] == 3 + P_pi_k[i, :] = P_b[i, :] + else + P_pi_k[i, :] = P_d[i, :] + end + end + + append!(diffs, sum(abs.(P_star - P_pi_k))) + + if isapprox(P_star, P_pi_k) + break + end + + end + + local p = plot( + diffs, + labels = "", + xlabel = L"k", + ylabel = L"||\pi_\star - \pi_k||_F", + linewidth=2, + title="Policy Iteration convergence", + ) + xticks!(round(Int,xlims(p)[1]):round(Int,xlims(p)[2])) +end + +# ╔═╡ a1eaf48e-f92f-4554-942e-f6303ebaa084 +md""" +## Question 7 + +> Investigate the structure of the optimal policy for different values of ``\gamma``, and explain the results. You might use Value Iteration or Policy Iteration. +""" + +# ╔═╡ 8d5b2cc2-2e21-47df-b821-189de5d357a3 +begin + local gammas = 0.9:0.001:0.99 + local iterations = zeros(length(gammas)) + + for (i, gamma) in enumerate(gammas) + + P_pi_k = P_pi_0 + k = 0 + + while true + V_pi_k = Matrix(I(length(REWARDS)) - gamma * P_pi_k) \ REWARDS + + local V_g = REWARDS + Matrix(gamma * P_g) * V_pi_k + local V_h = REWARDS + Matrix(gamma * P_h) * V_pi_k + local V_b = REWARDS + Matrix(gamma * P_b) * V_pi_k + local V_d = REWARDS + Matrix(gamma * P_d) * V_pi_k + + local pi_k = argmax.(eachrow([V_g V_h V_b V_d])) + + P_pi_k = sparse(zeros(11, 11)) + for i in 1:11 + if pi_k[i] == 1 + P_pi_k[i, :] = P_g[i, :] + elseif pi_k[i] == 2 + P_pi_k[i, :] = P_h[i, :] + elseif pi_k[i] == 3 + P_pi_k[i, :] = P_b[i, :] + else + P_pi_k[i, :] = P_d[i, :] + end + end + + k += 1 + + if isapprox(P_star, P_pi_k) || k >= MAX_ITERATIONS + break + end + end + + iterations[i] = k + end + + local p = plot( + gammas, + iterations, + labels = "", + xlabel = L"\gamma", + ylabel = L"k", + linetype=:steppre, + linewidth=2, + title=md"Policy Iteration convergence according to ``\gamma``", + ) + yticks!(round.(Int, yticks(p)[1][1])) +end + +# ╔═╡ 0c6fd7ed-5180-41bd-9958-29cc9f3ce73b +md""" +On observe qu'il y a convergence de la politique généralement en dessous de 5 itérations. 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0000000..1d953f4 --- /dev/null +++ b/TP2/.envrc @@ -0,0 +1 @@ +use nix diff --git a/TP2/.vscode/extensions.json b/TP2/.vscode/extensions.json new file mode 100644 index 0000000..5f6433d --- /dev/null +++ b/TP2/.vscode/extensions.json @@ -0,0 +1,7 @@ +{ + "recommendations": [ + "editorconfig.editorconfig", + "njpwerner.autodocstring", + "ms-python.python" + ] +} diff --git a/TP2/.vscode/settings.json b/TP2/.vscode/settings.json new file mode 100644 index 0000000..0954c9c --- /dev/null +++ b/TP2/.vscode/settings.json @@ -0,0 +1,28 @@ +{ + "python.defaultInterpreterPath": ".venv/bin/python", + "python.analysis.typeCheckingMode": "basic", + "python.formatting.provider": "black", + "editor.formatOnSave": true, + "python.linting.enabled": true, + "python.linting.lintOnSave": true, + "python.linting.flake8Enabled": true, + "python.linting.mypyEnabled": true, + "python.linting.banditEnabled": true, + "python.languageServer": "Pylance", + "[python]": { + "editor.codeActionsOnSave": { + "source.organizeImports": true + } + }, + "files.exclude": { + "**/.git": true, + "**/.svn": true, + "**/.hg": true, + "**/CVS": true, + "**/.DS_Store": true, + "**/Thumbs.db": true, + "**/__pycache__": true, + "**/.mypy_cache": true, + }, + "nixEnvSelector.nixFile": "${workspaceRoot}/shell.nix", +} diff --git a/TP2/TP2.ipynb b/TP2/TP2.ipynb new file mode 100644 index 0000000..033d764 --- /dev/null +++ b/TP2/TP2.ipynb @@ -0,0 +1,673 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# TP2 : Bandits\n", + "\n", + "Laurent Fainsin" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Setup" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.37454012 0.95071431 0.73199394 0.59865848 0.15601864 0.15599452\n", + " 0.05808361 0.86617615 0.60111501 0.70807258]\n" + ] + } + ], + "source": [ + "K = 10\n", + "T = 1000\n", + "EPOCHS = 5000\n", + "EPSILON = 0.15\n", + "np.random.seed(42)\n", + "PROB = np.random.rand(K)\n", + "BEST = np.argmax(PROB)\n", + "print(PROB)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# $\\epsilon$-greedy" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_2937633/564047854.py:12: RuntimeWarning: invalid value encountered in divide\n", + " a = np.argmax(rewards / counts)\n" + ] + } + ], + "source": [ + "def epsilon_greedy(epochs=EPOCHS, t_max=T, epsilon=EPSILON):\n", + " A = -np.ones((epochs, t_max), dtype=np.int32)\n", + " R = np.zeros((epochs, t_max), dtype=np.float32)\n", + "\n", + " for epoch in range(epochs):\n", + " rewards = np.zeros(K)\n", + " counts = np.zeros(K)\n", + " for t in range(t_max):\n", + " if np.random.rand() < epsilon:\n", + " a = np.random.randint(K)\n", + " else:\n", + " a = np.argmax(rewards / counts)\n", + "\n", + " reward = np.random.rand() < PROB[a]\n", + " rewards[a] += reward\n", + " counts[a] += 1\n", + " \n", + " A[epoch, t] = a\n", + " R[epoch, t] = reward\n", + " \n", + " return A, R\n", + "\n", + "A_eps, R_eps = epsilon_greedy()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Decaying $\\epsilon$-greedy" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_2937633/3008607987.py:13: RuntimeWarning: invalid value encountered in divide\n", + " a = np.argmax(rewards / counts)\n" + ] + } + ], + "source": [ + "def decay_epsilon_greedy(epochs=EPOCHS, t_max=T):\n", + " A = -np.ones((epochs, t_max), dtype=np.int32)\n", + " R = np.zeros((epochs, t_max), dtype=np.float32)\n", + "\n", + " for epoch in range(epochs):\n", + " rewards = np.zeros(K)\n", + " counts = np.zeros(K)\n", + " for t in range(t_max):\n", + " epsilon = 1.0 / (0.1 * t + 1)\n", + " if np.random.rand() < epsilon:\n", + " a = np.random.randint(K)\n", + " else:\n", + " a = np.argmax(rewards / counts)\n", + "\n", + " reward = np.random.rand() < PROB[a]\n", + " rewards[a] += reward\n", + " counts[a] += 1\n", + " \n", + " A[epoch, t] = a\n", + " R[epoch, t] = reward\n", + " \n", + " return A, R\n", + "\n", + "A_deps, R_deps = decay_epsilon_greedy()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Upper confidence interval" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_2937633/3010206541.py:12: RuntimeWarning: invalid value encountered in divide\n", + " a = np.argmax(rewards / counts + epsilons)\n" + ] + } + ], + "source": [ + "def UCB(epochs=EPOCHS, t_max=T, c=2):\n", + " A = -np.ones((epochs, t_max), dtype=np.int32)\n", + " R = np.zeros((epochs, t_max), dtype=np.float32)\n", + "\n", + " for epoch in range(epochs):\n", + " rewards = np.zeros(K)\n", + " counts = np.zeros(K)\n", + " for t in range(t_max):\n", + " \n", + " epsilons = np.sqrt(c * np.log(t + 1) / (counts + 1e-5))\n", + " \n", + " a = np.argmax(rewards / counts + epsilons)\n", + "\n", + " reward = np.random.rand() < PROB[a]\n", + " rewards[a] += reward\n", + " counts[a] += 1\n", + " \n", + " A[epoch, t] = a\n", + " R[epoch, t] = reward\n", + " \n", + " return A, R\n", + "\n", + "A_ucb, R_ucb = UCB()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Optimistic greedy" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "def optimistic_greedy(epochs=EPOCHS, t_max=T, Q0=100):\n", + " A = -np.ones((epochs, t_max), dtype=np.int32)\n", + " R = np.zeros((epochs, t_max), dtype=np.float32)\n", + "\n", + " for epoch in range(epochs):\n", + " value = Q0 * np.ones(K)\n", + " counts = np.zeros(K)\n", + " for t in range(t_max):\n", + " a = np.argmax(value)\n", + "\n", + " reward = np.random.rand() < PROB[a]\n", + " counts[a] += 1\n", + " value[a] += (reward - value[a]) / counts[a]\n", + " \n", + " A[epoch, t] = a\n", + " R[epoch, t] = reward\n", + " \n", + " return A, R\n", + "\n", + "A_opt, R_opt = optimistic_greedy()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Gradient method" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def gradient(epochs=EPOCHS, t_max=T, alpha=0.1):\n", + " A = -np.ones((epochs, t_max), dtype=np.int32)\n", + " R = np.zeros((epochs, t_max), dtype=np.float32)\n", + "\n", + " for epoch in range(epochs):\n", + " H = np.zeros(K)\n", + " rewards = np.zeros(K)\n", + " counts = np.zeros(K)\n", + "\n", + " for t in range(t_max):\n", + " # softmax(H) -> probs -> action\n", + " probs = np.exp(H) / np.sum(np.exp(H))\n", + " a = np.random.choice(K, p=probs)\n", + "\n", + " # update rewards\n", + " reward = np.random.rand() < PROB[a]\n", + " rewards[a] += reward\n", + " counts[a] += 1\n", + "\n", + " # one hot vector for action\n", + " one_hot = np.zeros(K)\n", + " one_hot[a] = 1\n", + "\n", + " # update H\n", + " H += alpha * (reward - rewards / (counts + 1e-5)) * (one_hot - probs)\n", + " \n", + " # update A and R\n", + " A[epoch, t] = a\n", + " R[epoch, t] = reward\n", + " \n", + " return A, R\n", + "\n", + "A_grad, R_grad = gradient()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Mean rewards" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean reward Epsilon-greedy: 871.75\n", + "Mean reward Optimistic-greedy: 920.57\n", + "Mean reward Decaying Epsilon-greedy: 913.69\n", + "Mean reward UCB: 809.02\n", + "Mean reward Gradient: 807.94\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "mean_reward_eps = np.mean(np.sum(R_eps, axis=1))\n", + "mean_reward_opt = np.mean(np.sum(R_opt, axis=1))\n", + "mean_reward_deps = np.mean(np.sum(R_deps, axis=1))\n", + "mean_reward_ucb = np.mean(np.sum(R_ucb, axis=1))\n", + "mean_reward_grad = np.mean(np.sum(R_grad, axis=1))\n", + "\n", + "asymptotic_reward_eps = EPSILON * (np.sum(PROB) - np.max(PROB)) / (K - 1) + (1 - EPSILON) * np.max(PROB)\n", + "\n", + "print(f\"Mean reward Epsilon-greedy: {mean_reward_eps:.02f}\")\n", + "print(f\"Mean reward Optimistic-greedy: {mean_reward_opt:.02f}\")\n", + "print(f\"Mean reward Decaying Epsilon-greedy: {mean_reward_deps:.02f}\")\n", + "print(f\"Mean reward UCB: {mean_reward_ucb:.02f}\")\n", + "print(f\"Mean reward Gradient: {mean_reward_grad:.02f}\")\n", + "\n", + "plt.plot([0, T], [asymptotic_reward_eps]*2, 'b--', label=\"Asymptotic Epsilon-greedy\")\n", + "plt.plot(np.mean(R_eps, axis=0), label=\"Epsilon-greedy\")\n", + "plt.plot(np.mean(R_opt, axis=0), label=\"Optimistic-greedy\")\n", + "plt.plot(np.mean(R_deps, axis=0), label=\"Decaying Epsilon-greedy\")\n", + "plt.plot(np.mean(R_ucb, axis=0), label=\"UCB\")\n", + "plt.plot(np.mean(R_grad, axis=0), label=\"Gradient\")\n", + "\n", + "plt.title(\"Average reward per step.\")\n", + "plt.xlabel(\"Steps\")\n", + "# plt.ylim(0.4, 0.7)\n", + "plt.ylabel(\"Average reward\")\n", + "plt.legend()\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Cumulative regret" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "mean_cum_reward_eps = np.arange(1, T+1) - np.cumsum(np.mean(R_eps, axis=0))\n", + "mean_cum_reward_opt = np.arange(1, T+1) - np.cumsum(np.mean(R_opt, axis=0))\n", + "mean_cum_reward_deps = np.arange(1, T+1) - np.cumsum(np.mean(R_deps, axis=0))\n", + "mean_cum_reward_ucb = np.arange(1, T+1) - np.cumsum(np.mean(R_ucb, axis=0))\n", + "mean_cum_reward_grad = np.arange(1, T+1) - np.cumsum(np.mean(R_grad, axis=0))\n", + "\n", + "plt.plot(mean_cum_reward_eps, label=\"Epsilon-greedy\")\n", + "plt.plot(mean_cum_reward_opt, label=\"Optimistic-greedy\")\n", + "plt.plot(mean_cum_reward_deps, label=\"Decaying Epsilon-greedy\")\n", + "plt.plot(mean_cum_reward_ucb, label=\"UCB\")\n", + "plt.plot(mean_cum_reward_grad, label=\"Gradient\")\n", + "\n", + "plt.xlabel(\"Steps\")\n", + "plt.ylabel(\"Total regret\")\n", + "plt.title(\"Total regret over steps.\")\n", + "plt.legend()\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Verification convergence" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10, 5))\n", + "\n", + "plt.bar(np.arange(1, K+1)*2, PROB, 0.2)\n", + "plt.bar(np.arange(1, K+1)*2+0.2, [np.sum(R_eps[A_eps == k]) / np.sum(A_eps == k) for k in range(K)], 0.2, label=\"Epsilon-greedy\")\n", + "plt.bar(np.arange(1, K+1)*2+0.4, [np.sum(R_opt[A_opt == k]) / np.sum(A_opt == k) for k in range(K)], 0.2, label=\"Optimistic-greedy\")\n", + "plt.bar(np.arange(1, K+1)*2+0.6, [np.sum(R_deps[A_deps == k]) / np.sum(A_deps == k) for k in range(K)], 0.2, label=\"Decaying Epsilon-greedy\")\n", + "plt.bar(np.arange(1, K+1)*2+0.8, [np.sum(R_ucb[A_ucb == k]) / np.sum(A_ucb == k) for k in range(K)], 0.2, label=\"UCB\")\n", + "plt.bar(np.arange(1, K+1)*2+1.0, [np.sum(R_grad[A_grad == k]) / np.sum(A_grad == k) for k in range(K)], 0.2, label=\"Gradient\")\n", + "\n", + "plt.xticks(np.arange(1, K+1)*2, np.arange(1, K+1))\n", + "plt.title('Estimation of the true value.')\n", + "plt.ylabel('Average reward')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Best arm selection" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "selected_best_cum_eps = np.mean(np.cumsum(A_eps == BEST, axis=1), axis=0) / np.arange(1, T+1)\n", + "selected_best_cum_opt = np.mean(np.cumsum(A_opt == BEST, axis=1), axis=0) / np.arange(1, T+1)\n", + "selected_best_cum_deps = np.mean(np.cumsum(A_deps == BEST, axis=1), axis=0) / np.arange(1, T+1)\n", + "selected_best_cum_ucb = np.mean(np.cumsum(A_ucb == BEST, axis=1), axis=0) / np.arange(1, T+1)\n", + "selected_best_cum_grad = np.mean(np.cumsum(A_grad == BEST, axis=1), axis=0) / np.arange(1, T+1)\n", + "\n", + "asymptote = (1 - EPSILON) + EPSILON * 1/K\n", + "\n", + "plt.plot([0, T], [100*asymptote]*2, 'b--', label=\"Asymptotic Epsilon-greedy\")\n", + "plt.plot(100*selected_best_cum_eps, label=\"Epsilon-greedy\")\n", + "plt.plot(100*selected_best_cum_opt, label=\"Optimistic-greedy\")\n", + "plt.plot(100*selected_best_cum_deps, label=\"Decaying Epsilon-greedy\")\n", + "plt.plot(100*selected_best_cum_ucb, label=\"UCB\")\n", + "plt.plot(100*selected_best_cum_grad, label=\"Gradient\")\n", + "\n", + "plt.title(\"The percentage of times the best arm was elected as time goes by\")\n", + "plt.xlabel(\"Steps\")\n", + "plt.ylabel(\"Optimal action (%)\")\n", + "plt.legend()\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# MeanReward($\\epsilon$)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/tmp/ipykernel_2937633/564047854.py:12: RuntimeWarning: invalid value encountered in divide\n", + " a = np.argmax(rewards / counts)\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "epsilons = np.linspace(0.0, 1.0, 20)\n", + "for t_max in [10, 30, 50, 70, 100, 1000]:\n", + " mean_rewards = []\n", + " for epsilon in epsilons:\n", + " A, R = epsilon_greedy(epochs=100, t_max=t_max, epsilon=epsilon)\n", + " mean_rewards.append(np.mean(np.sum(R, axis=1)) / t_max)\n", + " plt.plot(epsilons, mean_rewards, label=f\"t_max={t_max}\")\n", + "plt.legend()\n", + "plt.title(\"Mean reward as a function of epsilon.\")\n", + "plt.xlabel(\"Epsilon\")\n", + "plt.ylabel(\"Mean reward\")\n", + "plt.grid()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Questions\n", + "\n", + "2. With ε-greedy, what is the asymptotic probability of taking the optimal action?\n", + "\n", + "Si on imagine que l'on a la appris la politique optimal, alors il vient simplement que la probabilité de choisir le bon bandit est:\n", + "\n", + "$\\displaystyle(1 - \\epsilon) + \\epsilon * \\frac1K$\n", + "\n", + "3. Which ε is better for a relatively small of T ? and for large T\n", + "\n", + "Une valeur relativement faible de ε est meilleure pour une valeur relativement faible de T, car elle permet à l'algorithme d'explorer et d'apprendre davantage sur les bras en un temps plus court. Une valeur plus grande de ε est meilleure pour une grande valeur de T, car elle permet à l'algorithme de continuer à explorer et à apprendre sur les bras sur une plus longue période de temps.\n", + "\n", + "4. Do you observe some spikes in the plot of average rewards? if yes, please provide an explanation.\n", + "\n", + "On observer des instabilité lors des premières steps, cela est très probablement dû au fait que l'on divise par des nombres très petits au lorsque l'on a pas encore exploré toutes les machines. On observe aussi des pics lorsque l'algorithme explore un bras avec une faible valeur attendue et reçoit une récompense élevée, ce qui provoque un pic temporaire dans la récompense moyenne.\n", + "\n", + "6. What are your conclusions in terms of methods? Give some intuition.\n", + "\n", + "La méthode ε-greedy est une méthode simple et largement utilisée pour équilibrer l'exploration et l'exploitation dans l'apprentissage par renforcement. Sa version améliorée decaying epsilon greedy permet toute fois d'obtenir de meilleurs performances." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Parameter study by Learning curve" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "parameters = [1/128, 1/64, 1/32, 1/16, 1/8, 1/4, 1/2, 1, 2, 4]\n", + "\n", + "epsilon_greedy_rewards = []\n", + "gradient_rewards = []\n", + "ucb_rewards = []\n", + "optimistic_greedy_rewards = []\n", + "\n", + "for p in parameters:\n", + "\n", + " A, R = epsilon_greedy(epsilon=p)\n", + " epsilon_greedy_rewards.append(np.mean(np.sum(R, axis=1)))\n", + "\n", + " A, R = gradient(alpha=p)\n", + " gradient_rewards.append(np.mean(np.sum(R, axis=1)))\n", + "\n", + " A, R = UCB(c=p)\n", + " ucb_rewards.append(np.mean(np.sum(R, axis=1)))\n", + "\n", + " A, R = optimistic_greedy(Q0=p)\n", + " optimistic_greedy_rewards.append(np.mean(np.sum(R, axis=1)))\n" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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7N7/99huvv/46H3zwAS1atOCVV16hR48e5g+JJ9m/fz+fffYZBw8eJDExMVMdnZycshXniyhZsmSG++m/m/Q+YleuXAGgSpUquXK+e/fukZiYSIUKFTI9VrFiRYxGI7du3TJf8slOjFlJf/6fdJ7NmzeTkJCQ68P1H48VTPE+GmtQUBCnT5/G3d09yzIef71npVy5cpn+psuXLw/A9evX8fLywmg0MmPGDH766SeuXbuWoT+fm5tbpjIf/xsCclzG4/VPfw37+vpm2m40GomJicHNzY2goCBkWc7095ru0QTqSYKCgrhw4UK2f69Z1VfIPpHsCJn069ePN954g7t379KuXbsnjvowGo14eHiwaNGiLB9P/yOOjo6mSZMmODo6MmXKFMqWLYu1tTXHjx/n/fffz9TCoFarsyxPftC35Vke/7aXXv6AAQPMHWUfV61aNcD0JlW3bl327NlDcHAwd+/epVGjRnh6eqLX6zl8+DB79+4lICAgw5tUr169OHDgAOPHj6d69erY29tjNBpp27Ztli0oj8f4ovbu3Uvnzp1p3LgxP/30E97e3mi1WubNm8fixYsznHfPnj3s3LmT9evXs2nTJv755x+aN2/Oli1bnvi7v3LlCi1atCAgIIBp06bh6+uLlZUVGzZsYPr06c89EuZJrS0GgyHLWF70tZEfCkKM6bITq9FopFWrVkyYMCHLfdOTlhf11Vdf8cknnzB06FA+//xzXF1dUalUjBkzJtt/Qzkt40n1f9bvxWg0IkkSGzduzHLf9H45T2M0GqlatSrTpk3L8vHHE67cfs8oakSyI2TSrVs3hg8fzqFDh57aqbJs2bJs27aNBg0aPPUPcdeuXdy/f5+VK1fSuHFj8/Zr167latxP4u7ujoODAwaDIVtzvDRq1IipU6eybds2ihUrRkBAAJIkUblyZfbu3cvevXszTK4YFRXF9u3bmTx5coYOjEFBQdmOMX1SuKCgoAyXS+7du/fUFoF0K1aswNrams2bN2eYD2nevHmZ9lWpVLRo0YIWLVowbdo0vvrqKz766CN27tz5xN/P2rVrSUlJYc2aNRm+DWenuf5pXFxcspxJ+caNGxl+D9mV3vH57NmzT32us3tJy93dHVtbWy5dupTpsYsXL6JSqTJ9KD2P9Of/SecpVqzYc7XqPM+lu8eVLVuW+Pj4F5ofKTg4GFmWM8Rz+fJlAHNH2+XLl9OsWTN+//33DMdGR0dTrFixbJ0nN8rIjrJlyyLLMmXKlHlmsvek56Bs2bKcOnWKFi1a5MrzJDyd6LMjZGJvb8/PP//MpEmT6NSp0xP369WrFwaDgc8//zzTY2lpaeYPsfRvPo9+W0xNTeWnn37K3cCfQK1W0717d1asWMHZs2czPf74sOBGjRqRkpLCDz/8QMOGDc1vRI0aNWLBggXcuXMnQz+HrOoH5GjW1JYtW6LVapk1a1aGcrJbhlqtRpKkDM32169fzzSiIzIyMtOx1atXB8hyaO2j5UPGOsbExGSZTOVE2bJlOXToUIYRZ+vWrcswfDcnatasSZkyZfjhhx8yJVGPxp6eODxryQq1Wk3r1q1ZvXp1hlmIw8LCzBNwOjo6Plesj/L29qZ69er8+eefGWI6e/YsW7ZsoX379s9Vbnbr+TS9evXi4MGDbN68OdNj0dHRmeblysqdO3f4999/zfdjY2P566+/qF69unn+LrVanelvaNmyZYSEhGQ71twoIzteeeUV1Go1kydPznQ+WZYzTDlhZ2eX5aXsXr16ERISwty5czM9lpSU9Mz5t2JiYrh48WK+9Zcr6ETLjpClJ13ueVSTJk0YPnw4X3/9NSdPnqR169ZotVqCgoJYtmwZM2bMoEePHtSvXx8XFxcGDRrE6NGjkSSJBQsW5Guz/jfffMPOnTupW7cub7zxBpUqVSIyMpLjx4+zbdu2DElAYGAgGo2GS5cuMWzYMPP2xo0bm+eVeTTZcXR0pHHjxnz77bfo9XqKFy/Oli1bctRy5e7uzrhx4/j666/p2LEj7du358SJE2zcuDFb30g7dOjAtGnTaNu2Lf369SM8PJwff/yRcuXKZejrNGXKFPbs2UOHDh0oVaoU4eHh/PTTT5QoUSLTzNmPat26NVZWVnTq1Inhw4cTHx/P3Llz8fDwIDQ0NNv1fNzrr7/O8uXLadu2Lb169eLKlSssXLjwuYemq1Qqfv75Zzp16kT16tUZMmQI3t7eXLx4kXPnzpk/sGvVqgXA6NGjadOmDWq1mj59+mRZ5hdffGGem+jtt99Go9Hw66+/kpKSku35n7Lju+++o127dgQGBvLaa6+Zh547OTk999IW1atXR61WM3XqVGJiYtDpdOa5krJr/PjxrFmzho4dO5qHpSckJHDmzBmWL1/O9evXn/kaLV++PK+99hpHjx7F09OTP/74g7CwsAzJcseOHZkyZQpDhgyhfv36nDlzhkWLFuWohS83ysiOsmXL8sUXXzBx4kSuX79O165dcXBw4Nq1a/z7778MGzaMcePGAabX2j///MPYsWOpXbs29vb2dOrUiVdffZWlS5fy5ptvsnPnTho0aIDBYODixYssXbqUzZs38/LLLz8xhn///ZchQ4Ywb968QrF2Xp7L17FfgkV60rDgxz0+9DzdnDlz5Fq1ask2Njayg4ODXLVqVXnChAnynTt3zPvs379frlevnmxjYyP7+PjIEyZMkDdv3pxpWGyTJk3kypUrZzrHoEGDshy++ThAHjFiRJaPhYWFySNGjJB9fX1lrVYre3l5yS1atJDnzJmTad/atWvLgHz48GHzttu3b8uA7Ovrm2n/27dvy926dZOdnZ1lJycnuWfPnvKdO3cyDWNOH3qe1dBvg8EgT548Wfb29pZtbGzkpk2bymfPnn3i8OzH/f7777K/v7+s0+nkgIAAed68eebzpdu+fbvcpUsX2cfHR7ayspJ9fHzkvn37ZhpWnJU1a9bI1apVk62treXSpUvLU6dOlf/44w8ZkK9du/bUY5/2Gvv+++/l4sWLyzqdTm7QoIH833//PXHo+ePDra9duyYD8rx58zJs37dvn9yqVSvZwcFBtrOzk6tVqybPmjXL/HhaWpo8atQo2d3dXZYkKcPv6PHnTJZl+fjx43KbNm1ke3t72dbWVm7WrJl84MCBbNUxPfashn8/btu2bXKDBg1kGxsb2dHRUe7UqZN8/vz5LMvLztBzWZbluXPnyn5+frJarc4Qx5P+nh//3cuyLMfFxckTJ06Uy5UrJ1tZWcnFihWT69evL//vf//LMHQ7K+nn2bx5s1ytWjXz6/Px+JOTk+X33nvP/Ppv0KCBfPDgwWy/FnKjjCc9h0/6u12xYoXcsGFD2c7OTrazs5MDAgLkESNGyJcuXTLvEx8fL/fr1092dnaWgQzvY6mpqfLUqVPlypUryzqdTnZxcZFr1aolT548WY6JiTHvl9X7Wnqsj7/2haxJsmyBveYEQRCEQqF06dJUqVKFdevWKR2KUISJPjuCIAiCIBRqItkRBEEQBKFQE8mOIAiCIAiFmuizIwiCIAhCoSZadgRBEARBKNREsiMIgiAIQqEmJhXEtEbJnTt3cHBwENN2C4IgCEIBIcsycXFx+Pj4PHUxY5HsYJrKPDfWtxEEQRAEIf/dunWLEiVKPPFxkewADg4OgOmXlRvr3KTT6/Vs2bLFvIxCQSXqYXkKS11EPSyLqIdlEfV4ttjYWHx9fc2f408ikh0erkrr6OiY68mOra0tjo6OBf6FKuphWQpLXUQ9LIuoh2UR9ci+Z3VBER2UBUEQBEEo1ESyIwiCIAhCoSaSHUEQBEEQCjWR7AiCIAiCUKiJZEcQBEEQhEJNJDuCIAiCIBRqItkRBEEQBKFQE8mOIAiCIAiFmkh2BEEQBEEo1ESyIwiCIAhCoSaSHUEQBEEQCjWR7AiCIAiCUKiJhUAFQRAEjKmp3Pv6GzyuXydep8MxMBC1k5PSYQlCrhDJjiAIgkDMypXELFmCM3D34EHuqlRYV6qEXb262NYLxLZWTVQ2NkqHKQjPRSQ7giAIRZwsy0QtWgRAop8fTkYj+uvXST57luSzZ7n/2+9IWi021atjW68udoGB2FStiqTVKhy5IGSPSHYEQRCKuMTDh0kJCkayseHOwIFU6/4KREaSeOgQCQcPkXDoEGl375J49CiJR48SMWs2KltbbGq/jF29QOzq1UVXoQKSSnQDFSyTSHYEQRCKuPRWHYfOnTDaWAOg9fTEqUsXnLp0QZZlUq9fJ/HwYRIOHiLx8GEM0dEk7N5Dwu49AKhdXLCtWxe7evWwq1cXbalSSJKkWJ0E4VEi2REKPVmW0Rv1xKbEEmuM5W7CXTQaDXL6f7LpX9P/Gbdl2P7INlmWTWU/Y99H98m0/6P7PFb2k+JJ3zfNkMZl/WVcQl2w0lqhltSoJTUqSYVGpUElqR5uU6nQSI9sUz3YT9KgUj3cL/14laQSH1JFiD4khLjtOwBw7tsXLl3KtI8kSejKlEFXpgwuffogG42kXLxoavU5fIjE/45hiIoibtMm4jZtAkDj7W1KfALrYVu3HlpPj3ytlyA8SiQ7gkUwykaS05JJSkvK1k+iPjHb+yanJWOQDeZzfbv6WwVrmrv+2vlXnpT7xMRJUqFWPSWxenzbo4nVY9vUkho1atKS0/AO9+Ylr5fQqXV5Uh/hyaL+/huMRmwD62FVtmyWyc7jpAedl60rVcLttaHIqakknTljavU5dIjEU6dICw0l5t9/ifn3XwCs/Pywq1cP28B62NWpI0Z6CflKJDtCtqUZ00hOzSIh0T9IQNKymYDos0hIDMn5UgcVpg9rCQlJksz/Ahm3IWH6/+G2R/fJzv5P3PfR8h49/sH9x7dntb8sy0THRGPnYIeMjEE2YDAaMMgGjLIxw+00OS3TtkeTv6wYZNO+eqM+l5+BrG3ethmNSkMlt0pUd69OdY/qVHevjrute76cv6gyJicTvXQZAK4DBjx3OZKVFba1amFbqxaMHIExMZHEY8dJOHSQxEOHST5/ntSrV0m9epWoxYtBkkwjvQLriZFeQr4QyU4e2nV7F8dTjpN6JRVUYDQaM3zYZPnvYx9I6duedkx29jHIhizPn9U+5g/HR86vN+j5+O+P8+X3ZqOxeeqPtcb6iY/ZamxNt7WZH9PIGrZs2kL79u3RFvBRJHq9ng0bNjx3XWRZNj//jz7fWSVM6T/prx9zEmV85LgsXjuPviafdD8+NZ6d53cSpg7jfvJ9Tt87zel7p/nrvKnFqrh9cXPiU92jOv7O/qhV6tz+dRZZsevXY4iJQVu8OPZNm5JmNOZKuSpbW+wbNcS+UUMAU/+eI0dMHZ4PHSb16lWSz50j+dw5MdJLyBci2clDM07M4EbSDVYeXql0KLlKLalzlIzYam2fmcA8eqxKypsRHXp9/rRSFASSJJkvI2lR7kNFr9fjfcObdu3aEZ4SzonwE5y6d4qT4ScJig4iJD6EkPgQ1l9dD4CtxpZq7tXMCVA192o4WDkoFn9BJssykQtNHZNd+vVFUqshl5Kdx6mdnXFs3RrH1q0B0IeFZW+kV11Tnx8x0kt4USLZyUM1PGpglWSFp4cnGrXmYZ+Hx/5N7+OQ6TFV5n0z/avKvD2rbTkp+/F9jAYje3btoUOrDjjaOKJVaUUHViFXSZJECYcSlHAoQaeynQCIT43nTMQZToaf5OS9k5y+d5p4fTyHQg9xKPSQ6TgkyrmUy3Dpy9fBV7w+syHp+HFSLlxAsrbGuXv3fD334yO99DdukPAg+REjvYS8IJKdPPRp3U/ZcH8D7ZsW7Msmer0eZ5UzTjontOqCWw+hYLG3sifQJ5BAn0AADEYDV2KumJKfBwnQrbhbBEUFERQVxLLLD/qeWLs+TH48qlPJrZLo+JyFyIULAXDq1BG1s7NicUiShFXp0liVLv1wpNelSw9afQ6KkV5CrhDJjiAIBYJapaa8S3nKu5SnV4VeAEQkRXAq/BQn75kSoHP3zxGZHMmOWzvYccs0nDq943MN9xrmBKiYTTElq6I4fVgYcVu2AuDyAh2T84KkUmFdsSLWFSviNnSIaaTX2bMkHDxI4sHsjfTC1lbhWgiWRiQ7giAUWMVsitGiVAtalGoBQKohlfP3z5tbfk6Gn8zQ8fnP838CDzs+pydA5ZzLFamOz1F//w0GA7Yvv4x1hQpKh/NUkpUVtjVrYluzJox4ONIr8bDpsldWI710FSvipdFwd9euh30AH7/s9cz7jz/8+GUz6dEHX6jsxx9PP5fRaMTz5i3CjxxFpVI93M/8b+YyHsaZRXyP//vIbi98XIY6ZNxmlI24BV/BEBiI1kOZVjiR7AiCUGhYqa3MrTdg6oR7O/52hktfQVFP7/hcw70GVd2rFtqOz8bUVPNwc0tr1cmOJ4/0OkzCoUOkXr1KyvnzOALxp08rG2wucAJijx5VOowX5gYYxr4LItkpfCb+e46zV1T8e/84Vho1WrUKjVpCrZLQqky3tWoVGpWEWp1xm1oloVFJ5mO0qgfbHjnGvF8W27RqCc2D8tL/TS8/fZtaJTr4CYWbJEn4Ovji6+CboePz6YjT5gTodMRpEvQJT+34XMO9BiUcShSKTrFxmzZhuH8fjacnDi2aKx3OC8tqpFfcgYOcObCfSpUqoVar4cEM5unkx+7z2N3H9890/9ED8rBsg8HA5UuXKF++Aqr09+v0/R89zLwtfaP8yEOPPZbN49K3ydk5LkMdMh9nNBq4fv06pR2U+wIhkp089N+NKK7HqLgYE6F0KFmSJB4mQCoJzSMJ06NJmVoFiXFqVkQcw9lWh5ONFkcbjelfa+2D+6Z/07c5WGse/nEKggWxt7Knvk996vvUB0wdn4Ojgzl17xQnwk9wMvwkt+NvF9qOz+bh5n37FMq5bLSenjh07EC0SsK5gM+ppdfridywAddCUI+jGzagcXNTLAaR7OShD9qWZ9/hY1SqUg1ZkkgzyOgNRgxGmTSj6XaaQUZvNGIwZLHNKJuPSX/MvM1o2i/NKJP2yOPmbQ8eTz/WYHz824MpGU81GEl9+mS6D0hcD7qf7bpLEtjrNBkSoExJku3Dx0zJkgbHB/ettUWn/4SgLLVKTQXXClRwrZBlx+cT4Sc4f/98po7PWpXWPONzFbcqJMv5Mwv4i0g6fZrk06eRtFqce/ZUOhxByDci2clDLQI8SLkq075WccWzcllOT4weTZQe/JvVNqMRvcGUJCWn6tl/6CjlK1cjPtVIbJKe2OQ0YpL0xCbpiXnwE5ts+jdZb0SWIS45jbjkNG5HJeU4Xp1GlaHFyNH6kcTJJmOSlJ5ApT9mbyValYQX83jH5xRDChfuXzD3+zkRfoLI5EhO3TvFqXunALDCistHL9O/Un/8nP2UDP+J0oebO7Zvr+i3bEHIbyLZKSIkydSPR6sGG3LWaqLX64kPkmlfM3tJW0qagdiktAwJUOwjiVFschoxiQ8fM++XqCcuJQ1ZhpQ0I+FxKYTHpeS4rioJHB5rSXKy0WJvpSYyVEXS8RAq+jjj72mPrZX4ExCeTafWZe74HHfbPOLr4J2D3Iq/xdKgpSwNWkpdr7r0CehDU9+maFSW8RpLi4ggdqNpnpqC2DFZEF6EZfwVCoWKTqPG3UGNu0PO+zMYjTJxKWkPE6MMCVNaplakhy1LpmNSDUaMMub9MlOx7d9z5nslXGwo7+mAv6c95T0cKO/pQDkPe2ysxGU04ckkScLX0RdfR1PH59TUVGavmc11l+vsDtnN4buHOXz3MJ62nvSq0Ivu/t1xs1G2JSVq6VLQ67F56SVsqlZRNBZByG8i2REsikolmVtifJ/j+GS94ZEWpEdajpLSiIxP5ti5INJs3QgKT+B+Qiq3o5K4HZXEjovh5jIkCXxdbCnv6UB5T3tzMlTW3V70JRKyJEkSZbVlGdV4FBEpESy9vJQVl1cQlhjGrBOz+OXUL7Qp3YY+AX2oVqxavo/qkvV6ov/+BxCtOkLRJJIdoVCx1qqx1qrxcLTO9Jher2dD0iXat6+NVqvlfnwKl8PiCQqP43JYnOl2WBxRiXpuRiZyMzKRbRfCzMerJCjlZoe/x8MEqLynA37udug0IgkSTLztvXmn5ju8+dKbbLm+hSUXl3Am4gzrrq5j3dV1VHKrRJ8KfWhXph3Wmsyv07wQt3UraeHhqN2L4dimdb6cUxAsiUh2hCLLzV5HoL2OwLIPLy/IskxEfCpBYQ8SoPD4B7fjiUnScy0igWsRCWw5/zAJUqskSrnZPrgMZo+/p+lyWJlidlhpxErNRZVOraNT2U50KtuJsxFnWXJxCZuubeL8/fN8euBTvj/2Pa/4v0LvCr0pbl88T2MxDzfv1RvJyipPzyUIlkgkO4LwCEmScHfQ4e6go365h+snybLMvThTS9DlsLgHrUGm23HJaVy9l8DVewlsetgdCI1KonQxO/OlsPTLYqXc7NCqRRJUlFQpVoUvG37JuJfHsTJoJf9c+ofQhFDmnZ3H/LPzaVKiCX0D+lLPp97D5Q1ySfL58yQdPw4aDc69e+Vq2YJQUIhkRxCyQZIkPByt8XC0pqF/xiQoLDblwWWwOILC4rkcbvo3PiWN4PB4gsPj2XDmrvkYrVrCr5i9+TJYemtQKVdbNCIJKtRcrF14reprDK48mD2397Dk4hIOhh5k1+1d7Lq9i1KOpehToQ+dy3XG0coxV86Z3qrj2KaNYusSCYLSRLIjCC9AkiS8nKzxcrKmcXl383ZZlgmNSTYnQen9gYLC40lMNXApLI5LYXFAqPkYK7UKP3e7DAlQeU8HSrraiqU9Chm1Sk2zks1oVrIZ12Ku8c+lf1gdvJobsTeYenQqM0/MpKNfR/oE9KG8S/nnPk9aVBSx69YB4NK/f26FLwgFjqLJTlxcHJ988gn//vsv4eHh1KhRgxkzZlC7dm3A9IHx2WefMXfuXKKjo2nQoAE///wz/v7+5jIiIyMZNWoUa9euRaVS0b17d2bMmIG9vb1S1RIEJEnCx9kGH2cbmlZ4+G3aaJQJiU7KcBksKMzU+pOkN3DxbhwX78ZlKEunUVHW3T5DAlS2mHXmJXWEAqmMUxk+qPMBo2uMZt3VdSy5uITg6GCWXV7GssvLqOVZi74BfWlesjlaVc4mJ41evhw5NRXrSpWwqVE9byogCAWAosnO66+/ztmzZ1mwYAE+Pj4sXLiQli1bcv78eYoXL863337LzJkz+fPPPylTpgyffPIJbdq04fz581hbm0Yx9O/fn9DQULZu3Yper2fIkCEMGzaMxYsXK1k1QciSSiXh62qLr6stzQM8zduNRpnbUUkPOkU/uBwWFkdweDwpaUbOh8ZyPjQ2Q1leNmpu2V+lWy1fSrjY5ndVhFxmq7WlV4Ve9Czfk//C/mPJxSXsuLmDY2HHOBZ2DA8bD3pU6EHP8j0pZlPsmeXJaWlELVkCmIabF4ZFTAXheSmW7CQlJbFixQpWr15N48aNAZg0aRJr167l559/5vPPP+eHH37g448/pkuXLgD89ddfeHp6smrVKvr06cOFCxfYtGkTR48e5eWXXwZg1qxZtG/fnv/973/4+PgoVT1ByBGVSqKkmy0l3WxpWelhEmQwytyKTHzQKTrefEksODyOu0nw/bZgvt8WTJ3SrnSp4UOHqt4424rRNgWZJEnU9qpNba/a3E24y/LLy1l+eTnhSeH8dPIn5pyeQ6uSrehbsS/V3as/MYmJ27mTtDuhqF1ccOzQPp9rIQiWRbFkJy0tDYPBYG6hSWdjY8O+ffu4du0ad+/epWXLlubHnJycqFu3LgcPHqRPnz4cPHgQZ2dnc6ID0LJlS1QqFYcPH6Zbt25ZnjslJYWUlIfLEMTGmr4x6/V69PqsZt19Pull5WaZShD1UFZxJyuKO7nRrPzDIfL34xL5YflurhndOHIjmiPXIzlyPZJJa87R2L8Ynat50zzA3eInQSyoz8nj8qoeblZuDK8ynKEVh7L91nb+ufwPpyJOsfH6RjZe30h55/L0Lt+btqXbYqOxyXBs5IIFADh2fwWDSoUhG7GJ58OyiHpkv+xnkWRZuSv/9evXx8rKisWLF+Pp6cmSJUsYNGgQ5cqVY968eTRo0IA7d+7g7e1tPqZXr15IksQ///zDV199xZ9//smlS5cylOvh4cHkyZN56623sjzvpEmTmDx5cqbtixcvxtZWXA4QCpboFDh+X+K/eypCEh9+y9epZV5ylXm5mIy/k4zo41w43Em7w+HUw5xOPY0e0xu9tWRNLata1LGqg5vaDau7dyk9/QdklYpr708gzdlZ2aAFIY8kJibSr18/YmJicHR88ghGRfvsLFiwgKFDh1K8eHHUajU1a9akb9++HDt2LE/PO3HiRMaOHWu+Hxsbi6+vL61bt37qLyun9Ho9W7dupVWrVoqvev4iRD0sz+N16fdge1BYPGtOh7L2dCgh0ckcuSdx5B54OOjoUNWLztW8qezjYDH9NwrLc5Lf9Xid14lJiWHN1TUsC1rG7fjb7E/Zz4GUAzTwacDrl9IAsG/RnNb9+j2jtIfE82FZRD2eLf3KzLMomuyULVuW3bt3k5CQQGxsLN7e3vTu3Rs/Pz+8vLwACAsLy9CyExYWRvXq1QHw8vIiPDw8Q5lpaWlERkaaj8+KTqdDp8u8SKVWq82TF1RelZvfRD0sz+N1qVTChUolXJjQtiLHbkax6kQI68+EEh6XwrwDN5h34AZ+7nZ0q16cLtWLU9LNMloyC8tzkp/1KKYtxtBqQxlcdTD7Qvax5OIS9oXs48SVvai2GgD4r5EHLYyJOOmcnl1g5DVUQdsoF3YU3fHrqDU6UKlBrQWV5pEfdTbva5/w+BOOyYMEXLyuLEte1CO75VnEPDt2dnbY2dkRFRXF5s2b+fbbbylTpgxeXl5s377dnNzExsZy+PBh8+WpwMBAoqOjOXbsGLVq1QJgx44dGI1G6tatq1R1BEFxKpVE7dKu1C7tymedKrP78j1WnQxh2/kwrt5L4Putl/l+62VqlnSma43idKjqjZt9zlepF5SnklQ0LtGYxiUaczP2Jkd++ARr/RFuuMNnif/w9bI1dPDrQJ+APgS4Bjw8MC0Vbh6AoK1weTPcD0INVAa4o0BFpAcJkFqbg4Qq6x+1pCIgWg1RFcHj+ecpEgoPRZOdzZs3I8syFSpUIDg4mPHjxxMQEMCQIUOQJIkxY8bwxRdf4O/vbx567uPjQ9euXQGoWLEibdu25Y033uCXX35Br9czcuRI+vTpI0ZiCcIDVhoVrSp50qqSJ3HJejafC2P1yRD2B0dw/GY0x29GM3nteRr7F6NrjeK0quSJrZVFfA8ScsjXrjipe0PRA9peXajgGsylqEusCFrBiqAV1HCrTB/bMrQKu4722h5IjX94sEqDsUQdbserKOHjhUo2gjENjIYH/6Y9cl//2P3HH8/ivkFvOu5JZAMYDGBIefI+2aQCKgD8tAZKNYQaA6BSF7CyjJZMIf8p+o4WExPDxIkTuX37Nq6urnTv3p0vv/zS3Cw1YcIEEhISGDZsGNHR0TRs2JBNmzZlGMG1aNEiRo4cSYsWLcyTCs6cOVOpKgmCRXOw1tKjVgl61CpBeGwya0+HsupECGdCYth56R47L93D1kpN60qedK1RnIblioklLAqQ+L170d+6hcrRkWavf0ZzKy0nz//DkouL2ZpwkxP3z3Hi/jm+TTPQw1ZNT50HnmVbgX9rKNsMg9qWExs24N2+Paq8umxiND6WDD1PQvWEYwymYwwpCUQcXIJH3BmkG/vgxj7YMB6qdocar0LxWnly2UywXIomO7169aJXrycvTCdJElOmTGHKlClP3MfV1VVMICgIz8HD0ZrXGpbhtYZluHIvntUnQlh18g43IxNZdfIOq07eoZi9FR2r+dClug/VfZ0tpmOzkLWoB+tgOTepimrDaAjeRo2kSGoA99Qqljs4sMzZhXsa+NXFid8kNc2drenrVpyXdY6Qlpb3QapUoLIC8m4+KKNez6F7xWnf8CW0Z5fBiQUQfQOOzTf9uFc0tfZU6w327s8qTigERFu1IAiUdbdnbOsKvNuqPCduRbP6RAjrTocSEZ/K/APXmX/gOqXdbOlcvThdq/vg5y6WY7EYsgxhZ0nZu5SEffsAGRd5JZwxdVJG5wTlmuPu34a3yrXkdVtndtzcwZKLSzgWdoytN7ay9cZWyjmXo5d/LzRyIfpYcCwOTcZDo/fgxn5T0nN+Ndy7AFs+gm2fQYV2ptaesi1AXYjqLmQgnllBEMwkSaJmSRdqlnTh446V2BccweoTIWw+F8b1+4nM3B7EzO1BvFTCiS7Vi9PxJW88HKyfXbCQu1Li4dpuU8fioK0Qd4eoY46APfY+KVj5VTBdmvJvDb51M3yIa4E2pdvQpnQbLkdd5u+Lf7Pu6jqCo4P56uhX2Ev2cAVeKf8KapVlT0qZbSoVlGlk+mn/HZxdAccXwJ3jcGGt6cfBG17qa2rxcSurdMRCLhPJjiAIWdKqVTSr4EGzCh4kpKSx9XwYq06GsDcoglO3Yzh1O4Yv1p+nQblidK1enDZVvLDXibeUPHP/CgRtMSU4N/aDIdX8kEG2IeaGI2DE5f1p0Cbr2eMfV96lPJ8GfsqYWmNYE7yGhecXEpIQwpTDU1gatJQJtSdQ26t2HlVIIdZO8PJQ00/YOTixCE7/DXGhsG+a6adkfaj56oNOzXZKRyzkAvHOJAjCM9npNHStUZyuNYoTEZ/C+tOhrDoZwomb0ewNimBvUAQfrTpDy4qedKtRnMbl3dGKjs0vJi3FlNRc3mJKciKvZHzcuRSUbwP+bYg5cBtj6lSs/Pywa901x6dytHJkQKUBvOL3CpNWT2KvYS8XIy8ydPNQmvs2572X36OkY8ncqZcl8awMbb+ClpPg8kZTa8+V7aYh+TcPwIYJUKUb1BgIJV4WnZoLMJHsCIKQI8XsdQyqX5pB9UtzPSKB1SfvsPpkCFcjElh3OpR1p0NxsdXSoZo3XasXp1YpF9GxObtiQkyJTdBWuLoL9AkPH1NpoFR98G9jujxVzB8kCdloJGp0RwBc+vd7od+1Vq2lgXUDxjUfx9xzc1l2eRk7bu1gT8ge+gX0Y/hLw3G0yr1Z5i2GxsrUilOpi+k5OLUETiyEqGtw/C/TT7EKpktcL/UBew+lIxZySCQ7giA8t9LF7HinpT+jW5TjTEgMq07cYe3pO9yLS2HhoZssPHSTEi42dKnuQ9fqxfH3dFA6ZMtiNMDtow/73oSdyfi4vSf4tzIlOH5NwTpzopFw4CCp166hsrPDqUvXXAnLxdqFj+p9RJ+APvzvv/+xL2Qff53/izVX1vB29bfpWb4nGlUh/fhwKg6Nxz3SqXkhnFsFEZdg6yewfTKUb2tKfMq1Ep2aCwjxLAmC8MIkSaJaCWeqlXDmw/YBHLx6n1Un7rD53F1uRyXx484r/LjzCpW8Helaw4fOLxXHy6mIdmxOuG+6VHJ5s+nfpKhHHpRMl0v825iSHK9qps61TxG1cCEATq+8gto+d/uXlHUuy88tf2Z/yH6+O/odV2Ku8NXhr/j74t+Me3kcjUo0ytXzWRRJgtINTT/tpsLZlabEJ+Q/uLjO9GPv+bBTczF/pSMWnkIkO4Ig5CqNWkUjf3ca+bvzpb4K2y6EsepECLsu3eN8aCznQ2P5euNFAv3c6FjVC61B6YjzmCzD3dMP+97cPgrIDx+3doZyLUwJTrkWYFcs20Wn3rpF/O7dALj065u7cT+iQfEG1PWuy4rLK/jx5I9cjbnK29vfpoFPA8a9PI5yLuXy7NwWwdoJXh5i+gm/YEp6Tv0N8WGw/wfTT8nABzM1dwWdmJrB0ohkRxCEPGOtVdOxmg8dq/kQlZDK+jOhrD4ZwtHrURy4cp8DV+7jbaumRoNEynlmY7HKgiIlztTnJv3yVPzdjI97Vnl4eapE7ee+FBK1aDHIMnaNGqErU+bF434KjUpD74DetPNrx9zTc1l4YSH77+zn4NqD9PDvwYgaI3C1ds3TGCyCR0Vo8yW0+AyCNps6NQdvhZsHTT8b34fK3Uxz9/jWEZ2aLYRIdgRByBcudlYMqFeKAfVKcSsykTWn7vDHvmuEJqTyys+HmNGnBs0CCmjHT1nGPjkU1eGfTJembhzIuA6U1tbU58a/tSnJcSrxwqc0JiYSvXIlAK4D+r9wednlaOXIey+/R6/yvZh2bBrbbm5j6eWlbLi2gWHVhtG/Yn+s1Hk3O7LF0FhBxU6mn9jQh52aI6+YJi88sQCKlX8wU3MfcPBUOuIiTYwNFQQh3/m62jKiWTlWvV2P0vYysclpDP3zKDO2BWE0ys8uwJJc24vm10BaXHgf9bZPTZP9GfXgUgbqvgkDVsKEa9B3iekySC4kOgAxa9dhjI1FW7Ikdo3yv++Mr6Mv05tN5482f1DRtSLx+nimHZtGl1Vd2HpjK7JcwJ7HF+HoDY3GwqhjMGQjVO9vSnAjLsPWT2FaRVjSFy5uMK3fJeQ70bIjCIJivBytGVXZwDG5NIuP3Gb6tsucvh3NtN7VcbLJo4Uoc4vRAHu+g91TkWQjRkkNpRuiKt/2wdDwvOvHIsuyuWOyS7++SM/oxJyXanvV5u+Of7PmyhpmHp/J7fjbjN01llqetRhfezyV3SorFlu+kyTT9ACl6kPbb+Dcv6bWnttH4NIG04+dh2n4eo1Xwb280hEXGaJlRxAERWlUMLlTJb7rUQ0rjYrtF8PpMnsfl+7GKR3ak8WGwl9dYNfXIBsxVuvHxqo/Yui3AgLfztNEByDxyFFSgoKQbGxwfuWVPD1XdqgkFV3LdWVdt3UMrzYca7U1x8KO0XddXz7a9xHhieFKh5j/rB2h1iB4fSu8fRjqjwI7d0gIhwMz4cfa8Htr0xw+KRb8Wi8kRLIjCIJF6PmyLyverE9xZxuu30+k64/7WXvqjtJhZRa8HX5pCNf3gtYOuv2KodNM0tS2+RaCebh5l86oHS1nkj9brS0ja4xkbbe1dPDrgIzMmitr6PhvR34+9TNJaUlKh6gMjwBo/QWMvQC9F0H5diCp4dZhWDMK/lcBVo2AGwdNo/eEXCeSHUEQLEbVEk6sHdWQhuWKkaQ3MGrJCb5Yd540g1Hp0MCQBtsmw8JXIDHCNKJq+G7TJYl8pL9zh7jt2wFw7Z9/HZNzwsvOi28afcPi9oup7l6dpLQkfjr5E53+7cTaK2sxyhbwfCpBrYWKHaHf3zD2vGmZCrdyppmyTy6EeW1h9suwbzrE3X1mcUL2iWRHEASL4mpnxZ9D6/BWU9PK07/tu8aA3w8TEZ+iXFAxt2F+B9MikWBaRPL1bYpMJBe15G8wGrGtVw+dv2VPZFfVvSp/tfuL7xp/h4+dD2GJYXy470P6r+/PifATSoenLAcvaPgujPwPhm6G6gNMLYX3g2HbJJhWCfXS/njGnICimhzmIpHsCIJgcdQqiffbBvBz/5rYWak5dDWSTrP2ceJm1LMPzm2XNpouW906BDpH6DEPOk4HrU2+h2JMTiZ62TIgf4ebvwhJkmhbpi1ruq3hnZrvYKux5ez9swzcOJBxu8cREh+idIjKkiQoWQ+6/gjjLkHn2eBbF2QDqqDN1Ls6Hc2cRnByiRjJ9QJEsiMIgsVqV9Wb1SMb4OduR2hMMr1/PcSSIzfz5+RpqbDpQ1jSx7Skg3d102WrKsp1CI5dvwFDdDRaHx/smzVTLI7noVPreL3q66x/ZT3d/bsjIbH5+mY6/9uZH479QHxqvNIhKk/nADVfhde2wIijGOq+jV5lgxRxCVa9CTNrwOFfITVR6UgLHJHsCIJg0cp5OLB6RANaV/Ik1WBk4sozfLDiNMn6PFxnIuo6/NEGDv1oul/vbdMHkKtf3p3zGWRZJnLRI8PN1WrFYnkRxWyKMan+JJZ1WkZdr7qkGlP5/ezvdPi3A8svL8dgLOzrh2STe3mMLaewpcp0DM0+NQ1Zj7kFGyfAD1Vg97ePrasmPI1IdgRBsHgO1lp+GVCL8W0qIEnw99Fb9P71IHei82B0z7lV8EtjuHPctG5Vn8XQ9mvQ6HL/XDmQdOIEKecvIOl0OHXvrmgsuaGCawXmtp7LzGYzKeVYisjkSCYfnEyvdb04FHpI6fAsRpraFmP90TDmNHSYBs6lIPE+7PwSpleBzR9BrAWOWrQwItkRBKFAUKkkRjQrx59D6uBsq+XU7Rg6zdrHgSsRuXMCfTKsfw+WDYKUGChRB97cCwEdcqf8FxS1cBEAjp06onFxUTia3CFJEs1KNuPfzv8yofYEHKwcuBx1mTe2vMGo7aO4HnNd6RAth9YGar8Go45D999NowFT4+HgbPihGqweCRHBSkdpsUSyIwhCgdK4vDtrRzakso8j9xNSGfDbYebsufJiyxNEBMPvLeHob6b7DcbAkA3gXDJXYn5R+rBwYrdsASx3uPmL0Kq1vFrpVTZ020D/iv3RSBp23d5Ft9XdmHpkKjEpMUqHaDnUGqjaA97cB/2XQ8n6puVJTiwwDVtfOhDuFPGRblkQyY4gCAWOr6stK96qzys1i2OU4asNFxm55AQJKWk5L+z0MpjTBO6eAVs36L8CWk02zYliIaL/+QfS0rCpVQvrihWVDifPOFs780GdD1jZZSVNSjQhTU5j4YWFtF/ZnkUXFqE3itFIZpJkWlR26EbT0PXy7QAZzq+GOU3hr65wdbeYpPABkewIglAgWWvVfN/zJT7vUhmNSmL96VC6/bSfq/eyOaonNdHU9L/yddPlgFIN4c394N8ybwPPITk1lailS4GCM9z8RZVxKsPsFrOZ02oO/i7+xKbG8s2Rb3hl9SvsvrW7aC0ymh0l65kmKnzrIFTrbZqd+epO+Ksz/NYCLqwFY9Geq0ckO4IgFFiSJPFqYGn+HlYPDwcdl8Pi6TJ7P1vPhz39wPALMLe5qekfCZq8DwNXm1avtjCxmzdjiIhA4+mJQ0vLSsTyWqBPIMs6LuPTwE9xtXbleux1Ru4YybCtw7gcdVnp8CyPZyV4ZQ6MPgF1hoHGGkKOwT8D4Mc6pkVJ01KVjlIRItkRBKHAe7m0K+tGNaR2aRfiUtJ446//mLblEgbjYy0Asmx6w5/TDO5dAHtPU5LT7ENTXwgLFJm+unmf3khay7m0ll/UKjU9y/dkfbf1DK0yFK1Ky6HQQ/Rc25PJBycTkZRLHdQLE5dS0P47GHMWGo0Daye4HwSrR8DM6nDwJ0gpWvMaiWRHEIRCwcPRmkWv12Nw/dIAzNwRzGt/HiU68cE32ZQ4+He46Q0/LQn8mpk6efo1US7oZ0g6c4bkU6eRtFqce/VSOhxF2VvZ826td1nTdQ2tS7XGKBtZfnk5Hf/tyG9nfiPFoOByIpbK3h1afGJKelp9DvZeEBsCmyea5urZ+TUkRiodZb4QyY4gCIWGlUbFpM6Vmd77Jay1KnZdukfn2fu5cuaQqdPm6X9AUkHzT2DASrD3UDrkp0pf3dyxfTs0bm4KR2MZSjiU4Pum3/Nn2z+p7FaZBH0CM47PoMuqLmy6vkn058mKtSM0eDBXT6cZpskxk6Jg9zcwvTJsmmha/60QE8mOIAiFTrcaJVjxVn1KOFvTKGYNJZZ3NC2w6OADg9dD43Ggsuy3v7T794ndsBEAlwEDFI7G8tT0rMniDov5quFXeNh6EBIfwvjd4xm0aRDn7p9TOjzLpNFBrcGmxUd7zgevaqBPhEM/wYyXYNXbcO+S0lHmCcv+axcEQXhOlV1hR6n5fKn9A52kZ7uhBt/6/Ya+RD2lQ8uW6KVLkfV6rF+qhk3VqkqHY5FUkopOZTuxtuta3n7pbWw0NpwIP8Grm19lZeJKEvQJSodomVRqqNwNhu8xtXCWbgTGNDi5CH6sC3/3h9vHlI4yV4lkRxCEwifkGPzSCKtLa5BVGnaVfofX9OP46XA0/eceJjwuWekIn0rW64n6+x8AXEWrzjPZam15q/pbrO26ls5lOwNwPPU4fTf25cy9MwpHZ8EkCcq1gMHr4PXtENARkOHiOvitOczvCMHbC8VcPSLZEQSh8JBl00iT39tA9A1wLok0dDNNB09hzqsvY6/TcOR6JJ1m7ePYDctdRDFu+3bSwsJQFyuGY5s2SodTYHjaefJlwy/5veXvOElO3I6/zcCNA/ntzG8Y5aI9z8wzlXgZ+iyCEUegen9QaeD6Xlj4imnSzXP/QgFepFUkO4IgFA6JkfB3P9NIE6MeKnaC4XtNb+JA68perB7ZAH8Pe8JiU+gz5yALDt2wyA6t5uHmvXoiWVkpHE3BU8OjBiMdRtKqZCvS5DRmHJ/BsC3DCEt4xvxLArhXgK4/wTunoN7boLWF0FOwbDDMrg3H/oS0gjfyTSQ7giAUfDcPwy+N4NIGUFtB+/9BrwVg45xht7Lu9vw7ogHtq3qhN8h8suos45efJllvOd9Yky9eJOm/Y6DR4Ny7j9LhFFg2Khu+afANU+pPwUZjw+G7h+m+tjs7bu5QOrSCwakEtP3aNGy9yQdg4wKRV2DtaNPCo/tnmqZzKCBEsiMIQsFlNMK+6TCvHcTeNg2pfX0b1HnD1B8hC/Y6DT/2q8nEdgGoJFh+7DY9fjnA7ajEfA4+a+mtOo6tW6H1tOyh8ZZOkiS6+XdjacelVHStSExKDO/sfIcvDn1Bcppl99uyGHZu0GyiKelp8zU4Fof4u7D1E9Ow9R1fQILlT+wokh1BEAqm+HuwqAdsmwSyAar0MI0u8X7pmYdKksTwJmVZ8FpdXGy1nA2JpdOsfewNupf3cT9FWlQUsWvXAWK4eW4q7VSaRe0XMbjyYAD+ufQPfdb14VJk4RxmnSd09hD4Now+CV1+BDd/SI6BPd/B9CqwYTxE31Q6yicSyY4gCAXPtb3wS0O4st20/k+nmdD9N9A55KiYBuWKsXZUQ6oWdyIqUc+gP47w864rivXjiVmxAjklBV2litjUqKFIDIWVVq3lvZff49dWv1LMphhXYq7Qb30/Fl1YZJH9tiyWxgpqDDB1ZO69EHxqmmYkPzIHZlSHlcMh7LzSUWYikh1BEAoOowF2fWNazTn+LhSrAG/shFqDnnjZ6llKuNiy7M1Aer1cAqMMUzdd5O1Fx4lPScvl4J9ONhiIWrwEANf+A5Cesz7C09X3qc+KzitoXKIxqcZUvjnyDSN3jCQyuWgsm5BrVCrTIIA3dsDANablV2QDnP4bfg6ExX3g1hGlozQTyY4gCAVD3F34qwvs+hpkI1QfAMN2mlZ6fkHWWjVTu1fjq25V0aolNp69S5fZ+wgOz7/FEuN37kR/5w5qZ2ccO7TPt/MWRa7WrsxuPpsP6nyAlcqKPbf30H1Ndw7cOaB0aAWPJJnWlxu4CobtgkpdAAkub4TfW8G89kjB2xSfq0ckO4IgWL7g7fBzA9O8H1o76PYrdP0RrOxy7RSSJNGvbkn+GR6Il6M1V+4l0PXH/Ww6ezfXzvE0kQsXAeDcsycqa+t8OWdRJkkS/Sv2Z3GHxZR1KktEUgTDtw7n+/++R2/QKx1eweRTA3r9ZVqOouZAUGnhxn40//Sh6aVPkO6cUCw0kewIgmC5DGmwfQos7A6JEeBZxfTt8aW8G5Jds6QLa0c1pE4ZV+JT0nhz4TG+3XQRgzHvvpmmBAWReOgQqFS49BXDzfNTBdcK/N3xb3pX6A3A/HPz6b+hP9djrisbWEFWrBx0nmVaeDRwJLKVHQ5JIch27oqFJJIdQRAsU8xtmN8B9n4PyPDyUNOwcvfyeX5qdwcdi16vy2sNywDw064rDJ53hKiE1Dw5X+TixQA4tGiB1scnT84hPJm1xpqP633MjGYzcNI5cSHyAr3W9eLfoH9F5+UX4egDbb4kbeRJjvqNMs3doxCR7AiCYHkubTKNtrp1CKwcoMc86DgdtDb5FoJWreKTjpWY0ac6Nlo1e4Mi6DR7H2dDYnL1PIa4OGJWrwHEcHOlNS/ZnBWdVlDHqw5JaUl8euBTxu8ZT2xqrNKhFWw2Ltx1qqloCCLZEQTBcqSlwuaPYElvSIoC7+rw5h6o8opiIXWpXpyVb9enlJstt6OS6P7zAVYcu51r5cesXImcmIjO3x/bOrVzrVzh+XjaeTKn1RzeqfkOGknD5uub6bGmB8fDjisdmvACRLIjCIJliLoO89rCwdmm+3Xfgte2mGZFVlhFb0fWjGhIswrupKQZeW/ZKT5dfZbUtBdbXFI2Gs2XsFz69xfDzS2EWqXm9aqv81e7v/B18CU0IZQhm4fw08mfSDPm75QEQu4QyY4gCIqTLq6FXxpDyDGwdoLei6DdN6DRKR2amZOtlt8H1eadFv4A/HXwBn3nHiIs9vmXHUjYuxf9jZuoHB1x6twpt0IVcklV96os67SMzmU7Y5SN/HzqZ4ZuHsqd+DtKhybkkEh2BEFQTloyVW/9hWbFEEiJgRJ14M19ULGj0pFlSaWSeLdVeX4f9DIO1hqO3Yii46x9/Hcj6rnKMw83f+UVVLa2uRmqkEvstHZ82fBLvmn0DfZae06En6DHmh5sur5J6dCEHBDJjiAIyogNRTO/HX4R20z3G7wDQzaAc0ll48qGFhU9WTuyIRU8HbgXl8Krf/zH0Xs5uwSVcu0aCXv3giTh0r9fHkUq5JYOfh1Y1mkZ1dyrEaePY/zu8Xyy/xMS9ZaxgKzwdCLZEQQh/xnSYPlQpLAzpGgcSOv9N7SaAmqt0pFlW+lidvw7oj6dXvIhzSiz9KqK0JjsX9JKXxrCvkkTrHx98ypMIReVcCjB/LbzGVZtGBISq4JX0WtdL87dP6d0aMIziGRHEIT8t+c7uHkA2cqevf6fIJdrqXREz8XWSsOM3tWp4etEqlHim03ZW0XbEJ9AzMqVgBhuXtBoVVpG1RjF721+x9PWkxuxNxiwYQDzz87HKL9Yh3Uh74hkRxCE/HV9H+z5FgBDu/+RYO2lcEAvRqWSmNSpIhIyG86GsS8o4pnHxKxehTEhAasyZbCrH5gPUQq5rbZXbVZ0XkHLki1JM6bx/bHvGb51OPcS7ykdmpAFkewIgpB/EiNh5TDTQp4v9UOu0kPpiHJFJW9HGnmZZtr9dM1ZUtIMT9xXlmWiFj0y3Fwl3oYLKiedE9OaTuOzwM+wVltzKPQQ3dd0Z/et3UqHJjxG/JUJgpA/ZBlWj4TYEHArB+2/UzqiXNXe10gxeyuu3kvgt73Xnrhf4sGDpF69isrODqeuXfMvQCFPSJJEj/I9+KfTPwS4BhCVEsXIHSP5+vDXpBhSlA5PeEAkO4Ig5I+jv8Gl9aC2gh5/gM5e6YhylY0GPmhjWrdr1o4gQqKTstwvfbi5U7duqO1zb9V2QVl+Tn4sar+IVyu9CsDii4vpu74vwVHBCkcmgEh2BEHID3fPmJaBANOoK++XlI0nj3R+yZs6ZVxJ1huZsjbzCJ3U27eJ37kTAJd+Yrh5YWOltmJC7Qn83PJnXK1dCYoKos/6Pvxz8R+xoKjCRLIjCELeSk2A5UPBkALl20LdN5WOKM9IksTnXaqgVklsPhfGzkvhGR6PWrwEZBm7Bg3Q+ZVRKEohrzUs3pAVnVfQoHgDUgwpfHH4C97Z+Q5Ryc83+aTw4kSyIwhC3tr4PkRcBnsv6PITFPL1nyp4OTC0QWkAJq05R7Le1FnZmJRE9IoVALgM6K9UeEI+KWZTjJ9a/MSE2hPQqrTsvLWTHmt6cDj0sNKhFUki2REEIe+cXQEnFgASdJ8Ldm5KR5Qv3mlZHk9HHTfuJ/Lr7qsAxKxdizEmBq2vL/aNGyscoZAfVJKKVyu9yuIOiynjVIbwpHDe2PIG049NR2/UKx1ekSKSHUEQ8kbUdVg7xnS70XtQpuh8wNvrNHzcoRIAP+0K5kZEAlEPOia79OuHpFYrGZ6QzwJcA/i7w9/0KN8DGZk/zv7BwA0DuRl7U+nQigyR7AiCkPsMelj+GqTEgm9daDpR6YjyXcdq3jQo50ZKmpE/flpJyuXLSDY2OHd/RenQBAXYam35LPAzpjWdhqOVI2fvn6Xn2p6subJGdF7OByLZEQQh9+38EkL+A2sn6P4bqDVKR5TvJElicucqaNUSJXatBcCpc2fUjo4KRyYoqVWpVqzovIKXPV8mMS2Rj/Z9xAd7PyAuNU7p0Ao1kewIgpC7ruyEfT+YbneeVSBWMc8r5TzsGVnFkcBQ0zB02159FI5IsARedl781vo3RtUYhVpSs+HaBnqu7cnJ8JNKh1ZoiWRHEITcE38P/h0OyFBrCFTqonREiusRcgS1bORksbL8FlK4R6IJ2adWqRlWbRjz286nuH1xQuJDGLxpML+e+hWD8cnLjQjPRyQ7giDkDqMRVr0J8WHgXhHafq10RIozpqSQsGI5AGv9GvLr7qtci0hQOCrBklT3qM6yTstoX6Y9BtnA7JOzeW3La9xNuKt0aIWKSHYEQcgdh36E4G2gsTYtB6G1UToixcVu2IghKgqNtzdWjZuQajDy6eqzokOqkIGDlQNTG0/lq4ZfYaux5VjYMV5Z8wrbb25XOrRCQyQ7giC8uJDjsG2y6Xabr8CzkrLxWABZlolauBAAl759+axrNazUKvYGRbDprPjWLmTWqWwnlndaTtViVYlLjWP8vvGsSlxFqiFV6dAKPJHsCILwYlLiYMVrYNRDxc7w8lClI7IISSdPknzuHJKVFc49e1CmmB1vNvEDYMq68ySkpCkcoWCJfB19+bPdn7xW5TUkJP5L/Y9h24cRkRShdGgFmkh2BEF4Mevfg8ir4OQLnWcW+uUgsit9EkHHjh3RuLgA8HazcpRwsSE0JplZO8Rq2ELWtCotY2qNYXaz2VhL1pyOOE3vdb05F5F5cVkhe0SyIwjC8zu5BE7/A5LaNJ+OjYvSEVkEfXg4sZs3A+D6yDpY1lo1kzpVBuC3vVcJDhdzqwhPFugdyJv2b1LGsQzhieEM2jSIdVfXKR1WgSSSHUEQnk9EsKlVB0wzJJesp2w8FiT6n6WQloZNzZpYV8rYf6llJU9aVvQgzSjzyapzorOy8FTF1MX4s82fNCnRhBRDChP3TmTaf9PE8PQcUjTZMRgMfPLJJ5QpUwYbGxvKli3L559/nuGPX5ZlPv30U7y9vbGxsaFly5YEBQVlKCcyMpL+/fvj6OiIs7Mzr732GvHx8fldHUEoOtJSYPkQ0CdA6UbQaKzSEVkMOTWVqKX/ABlbdR71WafK6DQqDl69z9rTofkZnlAA2WvtmdFsBq9XfR2AeefmMXLHSGJTYxWOrOBQNNmZOnUqP//8M7Nnz+bChQtMnTqVb7/9llmzZpn3+fbbb5k5cya//PILhw8fxs7OjjZt2pCcnGzep3///pw7d46tW7eybt069uzZw7Bhw5SokiAUDdsmw93TYOMKr8wBlVjYMl3s5i0Y7kWg8fDAoVWrLPfxdbVlRLNyAHyx7jxxyWIFbOHp1Co179R8h+8af4e12pp9Ifvov74/12KuKR1agaBosnPgwAG6dOlChw4dKF26ND169KB169YcOXIEMLXq/PDDD3z88cd06dKFatWq8ddff3Hnzh1WrVoFwIULF9i0aRO//fYbdevWpWHDhsyaNYu///6bO3fuKFg7QSikLm8xzakD0PUncPRRNh4Lkz7c3LlPbySt9on7DWvsR2k3W8LjUvhhW9AT9xOER7Ut05Y/2/2Jl50X12Ov0399f/be3qt0WBZP0dX56tevz5w5c7h8+TLly5fn1KlT7Nu3j2nTpgFw7do17t69S8uWLc3HODk5UbduXQ4ePEifPn04ePAgzs7OvPzyy+Z9WrZsiUql4vDhw3Tr1i3TeVNSUkhJSTHfj401NQXq9Xr0+tz7hpVeVm6WqQRRD8ujWF3iQtGsehMJMNQehtGvJbxADIXlOUmPP/7UKZJOnQKtFvturzy1Xmrgkw4BvPbXceYfuE63l7yo4OWQTxFnrbA9H4W1Hv6O/ixovYDx+8Zz8t5JRmwfwejqoxlYcSCSBY6GzMvnI7tlKprsfPDBB8TGxhIQEIBarcZgMPDll1/Sv7/pOvfdu6aJtzw9PTMc5+npaX7s7t27eHh4ZHhco9Hg6upq3udxX3/9NZMnT860fcuWLdja2r5wvR63devWXC9TCaIelidf6yIbqR/8Le6J94m2Kcne1LoYN2zIlaILy3Nyafp0nIDYKlXYcuRwto6p5qridKSKd/46wKjKBosYuV9Yno/CXo+uclc0Vhr+S/2PGSdnsOvcLrradkUrPblFUUl58XwkJiZmaz9Fk52lS5eyaNEiFi9eTOXKlTl58iRjxozBx8eHQYMG5dl5J06cyNixDztUxsbG4uvrS+vWrXF0dMy18+j1erZu3UqrVq3QPqU529KJelgeJeqi2j8ddfx5ZK0ddoP+oa2b/wuXWVieE71ez45//8XpzFkAKo0fR82qVbN1bPX6SbSduZ8rcUb0xavTtbpylwUL0/NRVOrRSe7E0qCl/O/Y/zilP4Veref7xt/jaeuZ5f5KyMvnI/3KzLMomuyMHz+eDz74gD59+gBQtWpVbty4wddff82gQYPw8vICICwsDG9vb/NxYWFhVK9eHQAvLy/Cw8MzlJuWlkZkZKT5+MfpdDp0Ol2m7VqtNk/+MPKq3Pwm6mF58q0uNw/D7m8AkNp/h9Yrd5eDKAzPidORo5CainXVqjjUrJnt40q5axnVwp9vN11i6ubLtK7ig5ONsr+LwvB8QNGpx4DKA6jgVoGxu8ZyPvI8AzYN4IdmP1Ddo3r+BZkNefF8ZLc8RTsoJyYmolJlDEGtVmM0GgEoU6YMXl5ebN/+cDG02NhYDh8+TGBgIACBgYFER0dz7Ngx8z47duzAaDRSt27dfKiFIBRySdGw4nWQDVClB1Tvp3REFkdOS8Pp0CHgycPNn+b1hn6UdbcjIj6VaVsu5XZ4QhFQ26s2Szoswd/Fn/vJ9xm6eSj/Bv2rdFgWQ9Fkp1OnTnz55ZesX7+e69ev8++//zJt2jRzp2JJkhgzZgxffPEFa9as4cyZMwwcOBAfHx+6du0KQMWKFWnbti1vvPEGR44cYf/+/YwcOZI+ffrg4yNGiQjCC5FlWPsOxNwEl9LQcbpYDiILCTt2oI2JQe3qikO7djk+3kqjYkqXKgAsOHSDsyExuR2iUASUcCjBwnYLaVmyJXqjnk8PfMrUI1NJM4p12BRNdmbNmkWPHj14++23qVixIuPGjWP48OF8/vnn5n0mTJjAqFGjGDZsGLVr1yY+Pp5NmzZhbW1t3mfRokUEBATQokUL2rdvT8OGDZkzZ44SVRKEwuX4n3B+Fag00P0PsM69Pm2FSfTiJQA49uiBysrqucpoUK4YHat5Y5Thk9VnMRrFzMpCztlqbfm+6fe8Xf1tABZeWMib294kOjla2cAUpmifHQcHB3744Qd++OGHJ+4jSRJTpkxhypQpT9zH1dWVxYsX50GEglCEhV+EjR+Ybrf4FErUUjYeC5Vw6BDJx44hq1Q49er5QmV93KESOy+Gc+JmNMuO3aJ37ZK5FKVQlKgkFW+99Bblncszcd9EDocepu/6vsxqPotyLuWUDk8RYm0sQRAy0yeZloNIS4KyLSBwlNIRWaSEQ4e49ZbpG3RsjepoPF9sBIyXkzXvtioPwDcbLxKdmPrCMQpFV4tSLVjYfiHF7YtzO/42/Tf0Z8fNHUqHpQiR7AiCkNnmjyD8PNi5Q7dfQCXeKh4Xv3cft4a/iZyUhG2DBoRnMYHp8xhUvzTlPe2JStTz7WbRWVl4MeVdyrOkwxLqeNUhMS2Rd3a+wy+nfilyC9CKdzBBEDI6vwb++910u9uvYO/x9P2LoLgdO7n99tvIKSnYN2uG98wZyLk0pFarVvH5g87KS47c5NSt6FwpVyi6XKxd+KXVL/QN6AvAjyd/5L3d75Goz96EfIWBSHYEQXgo+hasGWm6XX80lGuhbDwWKHbLFm6PHo2s1+PQujUlZvyA9Jydkp+krp8b3WoUR37QWdkgOisLL0ir0vJh3Q+ZFDgJjUrD1htbGbhxIHfii8YakiLZEQTBxJAGK9+A5BjwqQnNP1E6IosTs349Ie+OhbQ0HNu3p/i073M90Uk3sX0ADjoNp2/HsOTIzTw5h1D0dC/fnT/a/IGrtSuXoi7RZ10f/rv7n9Jh5TmR7AiCYLLnW7h5EKwcoMcfoMmbD/GCKnrVKu6MnwAGA05du+Lz3bdImrwb0OrhYM17rU2dlb/bfIn78SnPOEIQsqeGRw3+6fgPFV0rEpUSxRtb3mDppaVKh5WnRLIjCAJc3wd7vjPd7vQDuJZRNBxLE7VsGaETPwSjEeeePfH+6ksktTrPzzugXikqeTsSk6Rn6qaLeX4+oejwsvPiz3Z/0q50O9LkND4/9DlTDk5BbyjYK8U/Sba+lqxZsybbBXbu3Pm5gxEEQQGJkbDiDZCNUH0AVO2hdEQWJXLRIsI+/wIAl3798Pz4I6R8Gp2mUav4vGsVuv98gKX/3aZ3bV9qlXLNl3MLhZ+NxoapjadS3rU8M4/PZNnlZVyJvsK0ptNws3FTOrxcla1kJ31phnSSJGUYtiY9Mn28wWDIncgEQch7sgyr3oa4O+DmD+2/VToii3J//nzCv5kKgOvgwXi8PyHD+11+qFXKhV4vl2Dpf7f5ZNU51oxsgEYtGuWF3CFJEq9XfZ3yLuV5f8/7HA8/Tt/1fZnZfCYBrgFKh5drsvUXYzQazT9btmyhevXqbNy4kejoaKKjo9mwYQM1a9Zk06ZNeR2vIAi56cgcuLwR1FamfjpWdkpHZDEi5sw1Jzpuw4Ypkuike79tAE42Ws6HxrLw0A1FYhAKt8YlGrOo/SJKOZYiNCGUVze8yubrm5UOK9fk+OvBmDFjmDFjBm3atMHR0RFHR0fatGnDtGnTGD16dF7EKAhCXrh7BrZ8bLrd6nPwrqZsPBZClmXu/fgj96ZNA6DYyJG4vztGsUQHwM1ex/g2FQD4fstlwuOSFYtFKLz8nP1Y1H4RDXwakGxIZtzuccw6MQujbFQ6tBeW42TnypUrODs7Z9ru5OTE9evXcyEkQRDyXGoCLBsChlQo3w7qDlc6IosgyzL3fphBxKzZALi/+y7uI0comuik61unJNVKOBGXksY3G0RnZSFvOOmc+LHFjwyuPBiAOafn8M7Od4hPjVc2sBeU42Sndu3ajB07lrCwMPO2sLAwxo8fT506dXI1OEEQ8sjGCXA/CBy8ocuPYAEf5kqTZZnwqd9y/9dfAfD44H2KDR+mcFQPqVUSn3epgiTByhMhHL56X+mQhEJKrVLz3svv8VXDr7BSWbHr1i4GbBjArdhbSof23HKc7Pz++++EhoZSsmRJypUrR7ly5ShZsiQhISH8/vvveRGjIAi56cxyOLEQkOCVuWBXuEZdPA/ZaCTsiy+JnD8fAM9PPsZt8GBFY8rKS77O9K1jWgn9k9Vn0RsK/uUFwXJ1KtuJ+W3n427jzpWYK/RZ34eDdw4qHdZzyXGy4+/vz+nTp1m7di2jR49m9OjRrFu3jjNnzlCuXNFcOl4QCozIa7B2jOl24/FQppGi4VgC2Wjk7meTiFq0CCQJrymTce3fX+mwnmh86wq42Gq5HBbPnweuKx2OUMhVda/K3x3/plqxasSmxvLmtjdZcH5BgVtINEfJjl6vR6PRcO7cOVq3bm1Odlq1amUR17QFQXgKgx5WvAapceBbD5q8r3REipMNBkI//IjoZctApcL7q69w6dVL6bCeysXOig/amYYET996mbsxorOykLc8bD34o+0fdC7bGaNs5Nuj3/LJ/k9INaQqHVq25SjZ0Wq1lCxZUsylIwgF0Y7PIeQYWDtB97mgzrulDgoCOS2NO+9/QMyqVaBW4/Pttzh366p0WNnSs5YvNUo6k5Bq4Iv155UORygCdGodXzT4ggm1J6CSVKy+spohm4dwL/Ge0qFlS44vY3300Ud8+OGHREZG5kU8giDkheDtsH+G6Xbn2eBcUtl4FCanphIy9j1i160DjYbi06bh1LGD0mFlm+pBZ2WVBOtOh7I/OELpkIQiQJIkXq30Kj+3/BlHK0dO3ztNn/V9OBtxVunQninHyc7s2bPZs2cPPj4+VKhQgZo1a2b4EQTBwsSHw79vmm6/PBQqFe0lXYypqdx+ZwxxW7YgabWUmDkTxzatlQ4rx6oUd+LVeqUA+HT1WVLTRGdlIX/U96nPkg5L8HPyIzwxnEEbB7H2ylqlw3qqHLdjP750hCAIFsxoNCU6CeHgUQnafKV0RIoyJidze9RoEvbuRdLpKDF7FvaNCm4n7bGtK7D+TChX7iXw+75rvNW0rNIhCUVESceSLGq/iIl7J7Lr9i4+3Pchl6MuM6bmGNSqvF8kN6dynOx89tlneRGHIAh54eBsuLIdNNam5SC0NkpHpBhjYiK3Rowg8eAhJGtrfH/+CbvAQKXDeiFONlomtqvIe8tOMXN7EJ2r+1Dcueg+x0L+sreyZ0bzGcw+MZu5Z+Yy/9x8gqKD+LbxtzhaOSodXgZiNTlBKKxCjsH2yabbbb8Gj4rKxqMgQ3wCt4YNJ/HgIVS2tpScO6fAJzrpXqlZnDqlXUnSG/h8reisLOQvlaRidM3RfNf4O6zV1uwP2U//9f25FnNN6dAyyHGyYzAY+N///kedOnXw8vLC1dU1w48gCBYgORaWDwVjGlTsDLWGKB2RYgxxcdx6/XUS//sPlb09vr//hm3t2kqHlWskSWJK18qoVRKbzt1l16VwpUMSiqC2ZdryV7u/8LLz4nrsdfqt78ee23uUDsssx8nO5MmTmTZtGr179yYmJoaxY8fyyiuvoFKpmDRpUh6EKAhCjsgyrB8LUdfByRc6zyyyy0EYoqO5OWQoSSdPonJyouS8edjWqKF0WLkuwMuRwfVLAzBpzTmS9WJ6ECH/VXSryN8d/qamR03i9fGM3D6SP87+YRETEOY42Vm0aBFz587lvffeQ6PR0LdvX3777Tc+/fRTDh06lBcxCoKQE6eWwJllIKmh++9g46J0RIpIi4rixpChJJ89i9rFhVLz52FTtYrSYeWZMS398XDQcf1+InP2XFU6HKGIcrNx47fWv9GjfA9kZKYfm87HBz5GL+sVjSvHyc7du3epWrUqAPb29sTExADQsWNH1q9fn7vRCYKQMxHBsH6c6XaziVCyrrLxKCQtIoKbAweScuEC6mLFKPnnfKwrFu4+Sw7WWj7qYKrjjzuDuRWZqHBEQlGlVWv5LPAzPq77MRpJw8YbG5kbP5ewxLBnH5xHcpzslChRgtDQUADKli3Lli1bADh69Cg6nS53oxMEIfvSUmD5ENAnQOlG0HCs0hEpQh8Wzo2Bg0gJCkbj7k6pv/7Eunx5pcPKF51f8iHQz42UNCOT155TOhyhiOsd0Js5refgrHMmzBDG3YS7isWS42SnW7dubN++HYBRo0bxySef4O/vz8CBAxk6dGiuBygIQjZt/QzungYbV9Nq5hY410Ve09+5w41XXyX16lU03t6UWrgAnZ+f0mHlG0mS+LxrZTQqiW0Xwtl2Xrlv0oIAUNurNgvbLKSXbS9ecn9JsThyPM/ON998Y77du3dvSpUqxYEDB/D396dTp065GpwgCNl0aRMc/tl0u+vP4OitbDwKSL19m5uDBqMPCUFbogQl58/HqkRxpcPKd+U8HHitURl+3X2VSWvP0dC/GNbaopf4CpbDx96HylaVFY3hhVcCrFevHvXq1cuNWARBeB6xd2DVW6bbdd+CCm2VjUcBqdevc2PwENLu3sWqVClKzp+H1rvoJXzpRjf3Z83JO9yOSuKnncGMbV1B6ZAEQVE5voxVsmRJBg4cyO+//86VK1fyIiZBELLLaICVwyApEryqQavJSkeU71KuXOHGqwNNiY6fHyUX/FWkEx0AO52GTztWAuCX3Ve5HpGgcESCoKwcJztfffUV1tbWTJ06FX9/f3x9fRkwYABz584lKCgoL2IUBOEJVAdmwPW9oLWDHvNAU7QGCSRfvsyNgYNIu3cPnb8/pf76E62Hh9JhWYS2Vbxo5F+MVIORz9acs4i5TgRBKTlOdgYMGMCcOXO4fPkyISEhfPfddwC8/fbbBAQE5HqAgiBkzSU+CNWeqaY7Hf4HxcopG1A+Sz5/npsDB2G4fx9dxYqU/OtPNMWKKR2WxZAkiSldqmClVrH78j02n1NuJIwgKO25+uwkJiayb98+du3axc6dOzlx4gRVqlShadOmuRyeIAhZSorm5es/IckGqNoLXuqrdET5Kun0aW6+/gbG2Fisq1al5G9zUTs5KR2WxSlTzI7hTfyYtSOYKWvP07i8O7ZWL9xVUxAKnBy37NSvXx83Nzc++OADkpOT+eCDDwgNDeXEiRNMnz49L2IUBOFRsox6w7vY6u8ju5SBDt8XqeUgEo+f4OaQoRhjY7GpUYOS8/4Qic5TvN20HMWdbbgTk8ysHcFKhyMIishxsnPx4kXs7OwICAggICCAihUr4uJSNKejFwRFnFiI6uJajKgxdP0VrB2VjijfJBw5ws3XX8eYkIBt7dqmFh17e6XDsmg2VmomdTYN+/1t71WCw+MVjkgQ8l+Ok5379++zY8cO6tWrx+bNm2nQoAHFixenX79+zJ07Ny9iFAQhXfw92PIxABd8eiD71FQ4oPyTcOAAt4YNR05MxK5+IL5zfkVlZ6d0WAVCq0qetAjwQG+Q+WzNWdFZWShycpzsSJJEtWrVGD16NMuXL2fjxo20atWKZcuW8eabb+ZFjIIgpNvyMSRHI3tW5YpH0ZlPJ373bm69+RZycjJ2jRtR4uefUdnYKB1WgfJZp8roNCr2B99n3elQpcMRhHyV42Tn+PHjTJs2jc6dO+Pm5kZgYCCnT59m1KhRrFy5Mi9iFAQB4NoeOP03IGFo9z2yVDRmxY3bvp1bI0chp6Zi36IFJWbPRiXW4cuxkm62vN3UNGLvi/XniU9JUzgiQcg/Oe6WX6dOHWrUqEGTJk144403aNy4MU6ic6Ag5K20FFj3rul27deQi9eEUxuUjSkfxG7aRMi48ZCWhkPbthT/7lskrVbpsAqs4U38WHniNjfuJzJj22U+6lBJ6ZAEIV/kONmJjIzE0bHodIgUBIuwfwbcDwZ7T2j+idLR5IuYteu48/77YDTi2KkTPl9/haQRw6ZfhLXW1Fl5yLyj/LH/Oj1q+VLBy0HpsAQhz+X4MpajoyPR0dH89ttvTJw4kcjISMB0eSskJCTXAxSEIu/+FdjzP9PtNl+BjbOi4eSH6JX/cmfCBDAacerWDZ9vvhaJTi5pVsGDNpU9MRhlPlktOisLRUOOk53Tp0/j7+/P1KlT+d///kd0dDQAK1euZOLEibkdnyAUbbIM698DQwr4NYMq3ZWOKM9F/bOU0A8/BFnGuXdvvL/8AkldNPon5ZdPOlbCWqviyLVIVp0UX1KFwi/Hyc7YsWMZMmQIQUFBWFtbm7e3b9+ePXv25GpwglDknV0BV3eCWlckJg+MXLCQu599BoDLgAF4TfoMSZXjtynhGUq42DKquT8AX66/SEySXuGIBCFv5fhd5OjRowwfPjzT9uLFi3P3rlh7RRByTVI0bHrQWtp4HLiVVTScvHb/9z8I+/JLAFyHDsXzow+RCnlyp6Q3Gvnh525HRHwK07deVjocQchTOb4IrtPpiI2NzbT98uXLuLu750pQQv6SZRljbCz60FD0d0LR3w0lLf12aCj6O3cod/8+V7/4Eslah0pnjaTTIemssrytstYhWemefVtnup/lbZ3ONLxYoym6H3g7PoeEcHDzhwbvKB1NnoqcM4fIWbMBcHvrTdxHjy66z3s+sdKomNK5CgN+P8xfB6/T8+USlHe3VTosQcgTOU52OnfuzJQpU1i6dClgmmTw5s2bvP/++3TvXvj7ExREcmoq+vBw9HfumJKYRxOZ0Duk3QnFmJj41DJUgFGvh7g4DPkT9oMTq8yJz6NJ0DNvpydW1g+2W+kwajXYX7xIakBFNOXKWnY/kNvH4Ojvptsdp4GmcM4rI8syblu2Erl9OwDFRo/C/e23FY6q6GjoX4wO1bxZfzqUT1adZclrtZUOSRDyRI6Tne+//54ePXrg4eFBUlISTZo04e7duwQGBvLlgyZoIf/IsowhOvphInMnFP3du+YkRh8aStq9e6aOrs+gdnVF6+2N1scbjZe3+bbk7s7eU6do0rAhaoMBOSUFY0oqckoyxpQU5KfdTk7GmJqz23Jq6sOgjEbkpCQMSUm58vvyAW4uWIhkbY2ufHmsAwLQBVTAOqAiuvLlUdtbwPIDhjRY9w4gQ7U+UKax0hHlCUN8PPd//Am3B4mOx7j3cHv9dYWjKno+6VCJnRfDOX4zmpUn7yDadoTCKMfJjpOTE1u3bmX//v2cOnWK+Ph4atasScuWLfMiviLPmJJC2t27j7TG3DElMOaWmVDk5ORnliNZWaH19kbj443W28ecyGi9vdF4e6P18nri9Pt6vR797dtYlSmDNh8mdJONRmS93pQEpaQgp6Y+vJ2SipyagjE5OfPtlBSMKU++bUxKJvLGDWzuRyAnJZN8+jTJp09nOLe2ZMkMCZB1QAU03t75e0nlyK9w9wxYO0PrL/LvvHkkLSqK1CtXSAm+QsrVK6QGXyHlyhXSwsLM+xSbMB63oUMVjLLo8nKyZkxLf77acJFvN19mvJhnUCiEcpTs6PV6bGxsOHnyJA0aNKBBgwZ5FVeRIMsyhvv3MyQypstMd82JjCEiIltlqd2LPUxi0ltnvNMTGy/Urq4Fpg+E9ODSFToduXmhSa/Xc3LDBtq1aYN8J5SUSxdJvnCR5EsXSblwkbTwcPQ3b6K/eZO4LVvMx6mcnLCuUAHrigHoKgRgHVABq3LlUFlZ5WJ0D8Tchh0PWkhbTQb7gtEPTpZl0u7dMyU1V66SciXYnNQYHszFlRW1hwchjRpR7tVX8zFa4XFDGpRh2X+3CQqPZ8MtFT2VDkgQclmOkh2tVkvJkiUxGPK110aBZUxKQnvvHokHDiLfC3+kn0x6YnM34yWbJ5BsbND6+KD18nosiUm/5OSVNx+8hZSkVmPlVwadXxkc27Uzb0+LiiLloikBSk+EUq5exRgTQ+KRIyQeOfKwEI0GnZ/fwwSoYgC6gAA0Li4vFtymD0CfAL51ocbAFysrD8hGI2mhoaRcvWpqqUlPaq5exZjFwIV0Wh8frMqVRedXFl25sliVLYuubFmMNjZc2FD4l72wdFq1is86VWbA74c5ek8iJc2IWJVDKExyfBnro48+4sMPP2TBggW4urrmRUyFxo32HSgTEcGdp+0kSWg8PDK3xjy4xKT19kbl5FRgWmUKMo2LC5rAQOwCA83bjKmppAYHk3zx0iMtQZcwxsSQcvkyKZcvA2seluHhga5iANbpCVCFAKxKlcxeZ+hLm+DCWlBpoON0UHB+GdlgQH/rljmpSb0SbGqxuXoV+Umd2VUqrHx9zYmMKakph65MaVR2WfeFMurF/C6Won5ZNzwcdITHpXD0ehTNKnopHZIg5JocJzuzZ88mODgYHx8fSpUqhd1jb2LHjx/PteAKOo23F6lxcdj4+qItnn6JyXRZydRXxgetp4dY2NCCqayssK5UCetKDzsyyLJMWmgoyRcvkXzxAikXL5F86SL6GzdJCw8nLTychN0PJ9iUbGzQlfc39wHSVQjAukL5jAlAagJsGG+6HTgCPCvnS/3k1FRSb9x4eOnpwWWo1GvXntzqqNWiK10KK79Hk5qyWJUuLVYjL8BUKomm5Yux9FgIOy7dE8mOUKjkONnp2rVrHoRROBWfN49N27fTvn37fOnYK+QPSZJMlxV9fHBo3sy83RCfQMrlyw8ToIsXSbl8GTkpieRTp0k+dfrRQtCW9H2YACUfw/rObTTeJZCavJ/rMRuTk0m9du3hpacrV0m5coXUGzfgCZelJZ0Oq7J+mS49Wfn6igS9kGpewZ2lx0LYeekesiyLFmWh0MhxsvPZg6nchWcT33KLFrW9HbY1a2Bbs4Z5m2wwmFpOLl7M0BKUFh6O/sZN9DduErd584O9vVA7WKM7NcKUAKUnQmXLImWzT5YhPoHUq6aRT+n/ply5gv727SdOP6Cys8t46cnPD125cmh9fCx7LiIh1wWWdUUjydyOSiI4PB5/T7EiulA4iGWEBSEPSWo1Oj8/dH5+OLZvb96eFhlpSoDOXyB5w0+khMSQEqvFEJdI4uHDJB4+/LAQrdbUGfqRBEgqXhzra9eJWbYcw43r5qQm7SlLtqidnLAqV+6RpMb0r8bTU3yDFwCwtdLg7yRzIVpi24VwkewIhYZIdgRBARpXVzT162OnC4LbwfCyPcY3tpB6LznDcPjkS5cwxsaScukSKZcuweqHnaFLAveyKFvtXgxdWVNSY1XWz3S7XNkCNf2AoJzKLjIXomHHxTDealq412MTig6R7AiCUhIiYOunptvNPkTl7oe1O5k7Q9+5Q/KlB32AHiRA+lu30Ds54VS5Mtb+/g+TmrJ+qJ2cFKqQUBhUdpFZfg2O3YgiKiEVFzsxrYVQ8IlkRxCUsuVjSI4Gr6pQZ3iWu0iShLZ4cbTFi+PQvLl5e2pKChs3bRKd34Vc56qDAE97LobFs/vyPbrWKK50SILwwpSbyEMQirJre+DUEkCCjj+AOmffOyQF5+ARCr9mFUwzd2+7EPaMPQWhYMhxy47BYGD+/Pls376d8PBwjEZjhsd37NiRa8EJQqGUlgLrxppuvzwUSrysbDyC8JhmAe78vOcauy/fQ28wolWL5Foo2HKc7LzzzjvMnz+fDh06UKVKFdHhURByav9MuB8Edh7Q4lOloxGETKoVd8LNzor7Can8dz2KwLJuSockCC8kx8nO33//zdKlS2n/yDBaQRCy6f4V2POd6Xbbr8HGWdFwBCErapVE0woerDh+m+0XwkSyIxR4OW6btLKyoly5cnkRiyAUbrIMG8aBIQX8mkKV7kpHJAhP1KKiBwA7LoYrHIkgvLgcJzvvvfceM2bMQH7CbKyCIDzBuZVwZQeoddBhGohLwIIFa+RfDK1a4mpEAlfvxSsdjiC8kBxfxtq3bx87d+5k48aNVK5cOdOw15UrV+ZacIJQaCRFw6aJptuN3gM3MVmbYNkcrLXULePGvuAIdlwMx8/dXumQBOG55TjZcXZ2plu3bnkRiyAUXju+gPgwcCsHDccoHY0gZEvzAA/2BUew/UI4rzfyUzocQXhuOU525s2blxdxCELhdfsYHP3NdLvDNNCIBWKFgqFFRQ+mrDvP0euRxCTpcbIRE1gKBZOYPEEQ8pIhDdaNAWSo1hv8migdkSBkWyk3O8p52JNmlNkblNVKbIJQMDzXchHLly9n6dKl3Lx5k9TU1AyPHT9+PFcCE4RC4ehcuHsarJ2g9ZdKRyMIOdYiwIPg8Hi2XwinYzUfpcMRhOeS45admTNnMmTIEDw9PTlx4gR16tTBzc2Nq1ev0q5duxyVVbp0aSRJyvQzYsQIAJKTkxkxYgRubm7Y29vTvXt3wsIyTl9+8+ZNOnTogK2tLR4eHowfP560tLScVksQcl9MiKmvDkDLyWDvrmw8gvAcWlT0BGDnpXAMRjEKVyiYcpzs/PTTT8yZM4dZs2ZhZWXFhAkT2Lp1K6NHjyYmJiZHZR09epTQ0FDzz9atWwHo2bMnAO+++y5r165l2bJl7N69mzt37vDKK6+YjzcYDHTo0IHU1FQOHDjAn3/+yfz58/n0UzErrWABNn0AqfFQog7UHKR0NILwXGqWdMbJRkt0op4TN6OUDkcQnkuOL2PdvHmT+vXrA2BjY0NcXBwAr776KvXq1WP27NnZLsvdPeM33W+++YayZcvSpEkTYmJi+P3331m8eDHNH6z2PG/ePCpWrMihQ4eoV68eW7Zs4fz582zbtg1PT0+qV6/O559/zvvvv8+kSZOwsrLK8rwpKSmkpKSY78fGxgKg1+vR6/XZ/2U8Q3pZuVmmEkQ9ck4K2oLmwhpkSU1a2+/AYDD95BLxnFiWwl6Pxv5urD19ly3nQnmpuIMSoeVIYX8+Cpq8rEd2y8xxsuPl5UVkZCSlSpWiZMmSHDp0iJdeeolr16690ESDqampLFy4kLFjxyJJEseOHUOv19OyZUvzPgEBAZQsWZKDBw9Sr149Dh48SNWqVfH09DTv06ZNG9566y3OnTtHjRo1sjzX119/zeTJkzNt37JlC7a2ts9dhydJb7Eq6EQ9skdtTKH5hYlogGD3Npw/dgO4kSfnEs+JZSms9XBJkgA1a/67RuW0YGWCeg6F9fkoqPKiHomJidnaL8fJTvPmzVmzZg01atRgyJAhvPvuuyxfvpz//vsvwyWmnFq1ahXR0dEMHjwYgLt372JlZYWzs3OG/Tw9Pbl79655n0cTnfTH0x97kokTJzJ27Fjz/djYWHx9fWndujWOjo7PXYfH6fV6tm7dSqtWrTJNvliQiHrkjGrn56hTI5AdS1B60M+UtrLL9XOI58SyFPZ6NEjSs+ibXdxNgqqBTfF1yf0vhbmpsD8fBU1e1iP9ysyz5DjZmTNnDkajEcDcefjAgQN07tyZ4cOH57Q4s99//5127drh45P3vf11Oh06Xea5TrRabZ68oPKq3Pwm6pENYefh0I8ASO2/Q2vnnDfneUA8J5alsNajmFbLy6VcOHwtkj1BkQxu4KRgdNlXWJ+Pgiov6pHd8nKc7KhUKlSqh/2a+/TpQ58+fXJaTAY3btxg27ZtGZaa8PLyIjU1lejo6AytO2FhYXh5eZn3OXLkSIay0kdrpe8jCPnGaIT1Y8GYBgEdIaC90hEJQq5pUdGDw9ci2X4xnMENyigdjiDkyHNNKrh3714GDBhAYGAgISEhACxYsIB9+/Y9VxDz5s3Dw8ODDh06mLfVqlULrVbL9u3bzdsuXbrEzZs3CQwMBCAwMJAzZ84QHv5wVd6tW7fi6OhIpUqVnisWQXhuJxfCzYOgtYN2U5WORhByVfoQ9MNXI4lPEdN7CAVLjpOdFStW0KZNG2xsbDhx4oR5VFNMTAxfffVVjgMwGo3MmzePQYMGodE8bGhycnLitddeY+zYsezcuZNjx44xZMgQAgMDqVevHgCtW7emUqVKvPrqq5w6dYrNmzfz8ccfM2LEiCwvUwlCnkmIgK0Ppjxo9iE4lVA2HkHIZX7F7CjtZkuqwci+oAilwxGEHMlxsvPFF1/wyy+/MHfu3Iwd2Bo0eK7Zk7dt28bNmzcZOnRopsemT59Ox44d6d69O40bN8bLyyvDpS61Ws26detQq9UEBgYyYMAABg4cyJQpU3IchyC8kC2fQFIUeFaFum8qHY0g5DpJkmgeYGrd2X4h7Bl7C4JlyXGfnUuXLtG4ceNM252cnIiOjs5xAK1bt37ikHVra2t+/PFHfvzxxyceX6pUKTZs2JDj8wpCrrm2F04tBiTo9AOon2sVFkGweC0qevDH/mvsvBSO0SijUklKhyQI2ZLjlh0vLy+CgzPPs7Bv3z78/PxyJShBKDDSUk2dkgFeHgIlXlY2HkHIQ7VLu+Kg0xARn8rpkJzNmC8ISspxsvPGG2/wzjvvcPjwYSRJ4s6dOyxatIhx48bx1ltv5UWMgmC5DsyAiMtg5w4txDIlQuFmpVHRuLxp5ntxKUsoSHLc3v7BBx9gNBpp0aIFiYmJNG7cGJ1Ox7hx4xg1alRexCgIlinyKuz5n+l2m6/BxkXZeAQhHzQP8GD9mVC2XwjnvdYVlA5HELIlx8mOJEl89NFHjB8/nuDgYOLj46lUqRL29vZ5EZ8gWCZZhvXjIC0Z/JpC1R5KRyQI+aJZgAeSBOdDYwmNScLbyUbpkAThmZ5rnh0AKysrKlWqRJ06dUSiIxQ95/6FK9tBrYMO00ASHTWFosHVzoqaJU2tmNsvhD9jb0GwDNlu2clqaHhW/vjjj+cORhAKhOQY2PSB6XajseBWVtl4BCGfNQ/w4NiNKHZcDGdAvVJKhyMIz5TtZGf+/PmUKlWKGjVqvNDq5oJQ4O34AuLDwK0cNHxX6WgEId+1rOjJd5svsT84gqRUAzZWaqVDEoSnynay89Zbb7FkyRKuXbvGkCFDGDBgAK6urnkZmyBYnpDjcGSu6XaH70EjZuoWip7ynvYUd7YhJDqJA1cizEtJCIKlynafnR9//JHQ0FAmTJjA2rVr8fX1pVevXmzevFm09AhFgyEN1o0BZKjay9QxWRCKIEmSaFHRA4Btot+OUADkqIOyTqejb9++bN26lfPnz1O5cmXefvttSpcuTXx8fF7FKAiW4ehvEHoKrJ2gzZdKRyMIimoeYEp2dlwME194BYv33KOxVCoVkiQhyzIGgyE3YxIEyxN7x9RXB6DlJLD3UDQcQVBaPT83bK3UhMWmcO5OrNLhCMJT5SjZSUlJYcmSJbRq1Yry5ctz5swZZs+ezc2bN8Xwc6Fw2/QBpMZBidpQc7DS0QiC4qy1ahqWKwaIIeiC5ct2svP222/j7e3NN998Q8eOHbl16xbLli2jffv2qFTP3UAkCJbv8hY4vxokNXT8AcTrXRAAzP12dlwUS0cIli3bo7F++eUXSpYsiZ+fH7t372b37t1Z7rdy5cpcC04QFJeaCBveM90OfBu8qigbjyBYkGYP+u2cuh1DeFwyHg7WCkckCFnLdrIzcOBAJDFLrFDU7PkOom+CYwlo8oHS0QiCRfFwsOalEk6cuh3Drov36FXbV+mQBCFLOZpUUBCKlPALcGCm6Xb7b0En+qUJwuOaB3hy6nYM2y6EiWRHsFii84EgZMVohHXvgjENKnSAgA5KRyQIFim9386+4AiS9WJkrmCZRLIjCFk5uQhuHgStHbSbqnQ0gmCxKvs44umoIzHVwOFrkUqHIwhZEsmOIDwu4T5s/cR0u9lEcBZN84LwJJIk0TzAtFzE9gtiVJZgmUSyIwiP2/opJEWBZxWo+6bS0QiCxWvxYFTW9gvhYjZlwSKJZEcQHnV9P5xcCEimOXXUWqUjEgSL16BcMXQaFSHRSVwOE0sHCZZHJDuCkC4t1dQpGaDWYPCtrWg4glBQ2FipafBgNuVt4lKWYIFEsiMI6Q7MhIhLYOcOLT9TOhpBKFAeLgwqlo4QLI9IdgQBIPKaaQJBgDZfgY2LsvEIQgGTPgT9+M0oIhNSFY5GEDISyY4gyDJsGAdpyVCmCVTtqXREglDgeDvZUMnbEVmGXZdE645gWUSyIwjnV0HwNlBbQYdpIJZFEYTnkt66I1ZBFyyNSHaEoi05FjY+WPOq4VgoVk7ZeAShAEvvt7Pn8j1S04wKRyMID4lkRyjadnwB8XfBtSw0fFfpaAShQHuphDPF7K2IS0njv+tiNmXBcohkRyi6Qo7D0bmm2x2+B621svEIQgGnUkk0q2Bq3dkmLmUJFkQkO0LRZDSY5tSRjaYOyWWbKR2RIBQK5n47F8PEbMqCxRDJjlA0Hf0NQk+Czsk01FwQhFzR0N8dK7WKG/cTuRqRoHQ4ggCIZEcoiuJCYfvnptstPwN7D2XjEYRCxF6noa6fKyAWBhUsh0h2hCJHvfVjSI2DErWh1hClwxGEQufRhUEFwRKIZEcoUjxiTqG6sBokNXScDirxJyAIua1FRU8A/rsRRUyiXuFoBEEkO0JRok+k2u2/TLfrvQVeVZWNRxAKKV9XW8p72mMwyuwOuqd0OIIgkh2hiDAaUW/5ELvUe8gOPtB0otIRCUKh1jzA1Loj+u0IlkAkO0LhZzTCundQnVyIjISh3Xegs1c6KkEo1NKHoO+6dI80g5hNWVCWSHaEws1ogNUj4PhfyJKK46WGIfu3UToqQSj0apZ0wdlWS0ySnuM3o5UORyjiRLIjFF6GNPh3OJxaDJIaQ5efue3aQOmoBKFIUD8ym7K4lCUoTSQ7QuFk0MOK1+DMMlBpoMcfyJW7Kx2VIBQp6QuDbr8ohqALyhLJjlD4pKXCssFwfhWotNDrL6jcVeGgBKHoaVzeHY1KIvj/7d15eExn+8Dx70wm+yohqzS2bJaIErtXaqe0ulOtaGlVeVu1FqWoihbdf7Qv3qCldFG8itqpvbS2JmInJRFbJJF95vz+mGZqENlzJnF/rmsuzvac+571zjnPeU5yOuevyWjKQj1S7IiqJTcLlr8Ax9eAlS30WQohj6odlRAPJFd7ayJq5Y+mLEd3hHqk2BFVR24mLHseTv4COjvo+y0EdVE7KiEeaPlXZW2RU1lCRVLsiKoh5xYsfRZObwZrB3j+O6jXUe2ohHjg5ffb2Xf2GmlZMpqyUIcUO6Lyy06DJc/A2R1g4wQv/Ah12qsdlRACqFPDiTrVHcnVK+w8eVXtcMQDSoodUbllpcI3T8H5XWDrAi+sgIDWakclhLhN/tGdTdJvR6hEih1ReWWmwNe9IWEf2LlC/5XwUAuVgxJC3KmDaTTlZPQGReVoxINIih1ROWVch8WPwcWDYF8Nov4Hfk3VjkoIcQ8RtdxxttNx7VYOh/9KUTsc8QCSYkdUPreuwqLHIPEwOFSHqDXg01jtqIQQBbC20tI+qAYgoykLdUixIyqX9GRY2BMuHwVHTxjwM3g3VDsqIUQh8i9Bl/F2hBqk2BGVR2oiLHwUrsSBsw+8tBY8Q9SOSghRBJFBnmg1cDwpjYspmWqHIx4wUuyIyuHmX7CwB1w9AS41jUd0qgeqHZUQooiqOdrQNKAaAFvkVJaoYFLsCMt34zzE9IDrZ8DtIXjpZ/Coq3ZUQohi6hDiBciNQUXFk2JHWLbrZ42nrlLOQ7XaMGAtVKuldlRCiBLI77ez+/Q1MnLyVI5GPEik2BGW69pp4xGdmwngUc/YR8fNX+2ohBAlFOjphL+7PTl5BnaduqZ2OOIBIsWOsExX4o2FTtolqBFiPKLj4qt2VEKIUtBoNHTMP5Ul/XZEBZJiR1iey7HGU1fpSeDZwDiOjrOX2lEJIcpA/q0jthxPxiCjKYsKIsWOsCyJR4yFzq0r4B0GA9aAUw21oxJClJEWddxxtLEiOS2bPy+lqh2OeEDo1A5ACJNLf8Di3pCVAr4Pw4srjLeCeIAYDAZycnIKXS83NxedTkdWVhZ6vb4CIisfkodlKU4e1tbWWFlZFXsftjor2gXWYP2fSWyKu0yjmq4lDVeIIpNiR1iGvw7A109C9k2o2Rxe+MF4c88HSE5ODmfPnsVgMBS6rqIoeHt7k5CQgEajqYDoyofkYVmKm4ebmxve3t7FzrlDqCfr/0xiy/Fk3uocVNJwhSgyKXaE+i7shW+ehpw0eKgV9PsebJ3VjqpCKYpCYmIiVlZW+Pv7o9Xe/wyzwWAgPT0dJyenQte1ZJKHZSlqHoqikJGRQXKycbwcHx+fYu3nkWBPNBo4evEml1Oz8HKxK1XcQhRGih2hrnM7YcmzkHsLarWD55eDjaPaUVW4vLw8MjIy8PX1xcHBodD180932dnZVfofV8nDchQnD3t7ewCSk5Px9PQs1imtGs62NK7pxqGEFLYcT6Zv84dKFbcQham8n0pR+Z3ZZjyik3sL6jwCz3/3QBY6gKl/hI2NjcqRCFF0+YV5bm5usbftGCI3BhUVR4odoY6Tm2Dpc5CXCYFdoO8ysCn8iEZVV5n7e4gHT2nerx3+Hk1516mrZOVW3k7donKQYkdUvPj1sKwv5GVBcA947huwlnP2QjxI6vu44ONqR2aunj1nZDRlUb6k2BEVK+5/sPwF0OdA6GPwzCLQ2aodlRCigmk0GtMAgzKasihvUuyIinNsBXwXBYZcaPgUPB0DOumjIgqm0WhYuXIlAOfOnUOj0XDo0CFVY1JDZGQkw4cPVzuMMpd/Y9AtcckoioymLMqPFDuiYhz5Dn4cCIoewvrAk/PASi4GrOwGDBiARqO569GtW7cyaT8xMZHu3buXSVvC8rSuWx07ay2XbmZxPClN7XBEFSa/NqL8/bEEVg0FFGjyIvT6FLTFH3lVWKZu3boRExNjNs/WtmxOTXp7e5dJO+VNURTy8vLUDqPSsbO2om296myKS2Zz3GVCfVzUDklUUaof2bl48SIvvPACHh4e2Nvb06hRIw4cOGBarigKkyZNwsfHB3t7ezp16sTJkyfN2rh+/Tr9+vXDxcUFNzc3Bg4cSHp6ekWnIu7lQAyseh1QoNnL0OszKXSKQFEUMnLy7vvIzNEXuk5JHsU9nWBra4u3t7fZo1o1420+NBoNc+fOpXv37tjb21OnTh1++OEH07Y5OTmMHj0aPz8/7OzsCAgIIDo62rT89tNY97J9+3aaN2+Ora0tPj4+vP3222ZFR2RkJG+88QZjxozB3d0db29vJk+eXGhOu3fvJjw8HDs7O5o1a8bKlSvNTqFt27YNjUbDunXraNq0Kfb29uzduxeDwUB0dDS1a9fG3t6exo0bm+ULcOzYMbp3746TkxNeXl68+OKLXL161bT81q1b9O/fHycnJ3x8fJg9e7bZ9lOnTqVhw4Z3xRweHs7EiRMLzc3SdMi/C/pxuQRdlB9Vj+zcuHGDNm3a8Mgjj7Bu3Tpq1KjByZMnTV+UAB9++CGfffYZixYtonbt2kycOJGuXbsSGxuLnZ3xCp5+/fqRmJjIxo0byc3N5aWXXuLVV19l6dKlaqUmAPbPg7WjjP9v8Rp0mwFyaXWRZObqqT/pF1X2HTu1Kw42ZffVMHHiRGbMmMGnn37K119/TZ8+fTh69CihoaF8/vnnrFu3jmXLllGrVi0SEhJISEgoUrsXL16kR48eDBgwgMWLF3P8+HFeeeUV7OzszAqaRYsWMWLECPbt28eePXsYMGAAbdq0oXPnzvdsNzU1lV69etGjRw+WLl3K+fPnC+wv8/bbbzNr1ixq1aqFTqdjxowZLFmyhC+//JLAwEB27NjBCy+8QI0aNWjfvj0pKSl06NCBQYMG8fHHH5OZmcnYsWN59tln2bJlCwCjR49m+/btrFq1Ck9PT8aPH8/vv/9OeHg4AC+//DJTpkzht99+IyIiAoA//viDI0eOsGLFiqK9KBYkv5PyoYQUrqZnU91JLlgQZU/VYueDDz7A39/f7BB47dq1Tf9XFIVPPvmEd955h8cffxyAxYsX4+XlxcqVK+nTpw9xcXGsX7+e3377jWbNmgHw+eef06NHD2bNmoWvr2/FJiWM9vwf/DLe+P9Ww6DLNCl0qqg1a9bg5ORkNm/8+PGMH298/Z955hkGDRoEwHvvvcfGjRv5/PPPmTNnDhcuXKBu3bq0bdsWKysrAgICirzfOXPm4O/vzxdffIFGoyEkJIRLly4xduxYJk2aZBoBOCwsjHfffReAwMBAvvjiCzZv3lxgsbN06VI0Gg3z5s3Dzs6O+vXrc/HiRV555ZW71p06dSqdO3fGYDBw5coVoqOj2bRpE61atQKgTp067Ny5k6+++or27dvzxRdf0KRJE6ZPn25q47///S/+/v6cOHECX19fFixYwDfffEPHjh0BY7FWs2ZN0/o1a9aka9euxMTEmIqdmJgY2rdvT506dYr8/FkKb1c7Gvq5cOxiKluPJ/NMM3+1QxJVkKrFzurVq+natSvPPPMM27dvx8/Pj9dff930pXL27FmSkpLo1KmTaRtXV1datGjBnj176NOnD3v27MHNzc1U6AB06tQJrVbLvn37eOKJJ+7ab3Z2NtnZ2abp1NRUwDgKaElGAi1Ifltl2aYaipuHds9nWG2ZCoC+9XAMkRPAAvozWPLrkZubi6IoGAwGDAYDtlYajk2+948xGP8QSE9Lx8nZqcwHIrS10hTpZqT5cURGRjJnzhyz+e7u7qY2WrRoYdZey5YtOXz4MAaDgf79+9O1a1dCQ0Pp2rUrjz76KF26dDFrK/85yW8j//+xsbG0bNkSRVFMp95atWpFeno6Fy5c4KGHjLcgaNSokdn+vb29uXz5MgaDgSFDhrBkyRLTstTUVI4fP05YWBg2Njam7fK/X+6M5eGHH8ZgMKAoCmfOnCEjI+OuIionJ4cmTZpgMBg4dOgQW7duvas4BDh58iS3bt0iJyeHiIgI0z7c3NwIDg42vT8ABg4cyKBBg5g1axZarZalS5cye/bsIr9uBcl/Hm/f1/3k556bm1uiO6DniwyszrGLqWyKTaJ349L307Lkz3pxSB5Fb7swqhY7Z86cYe7cuYwYMYLx48fz22+/8cYbb2BjY0NUVBRJSUkAeHl5mW3n5eVlWpaUlISnp6fZcp1Oh7u7u2mdO0VHRzNlypS75m/YsKFI9yUqro0bN5Z5m2ooSh5BSasITfwRgOPevYnPaALr1pV3aMViia+HTqfD29ub9PR0cnJyirSNvY0V+uzMMo8lLavo6+bm5mJra3vXZxD++SMiKyvL9H8w/vjn5eWRmppKYGAghw4dYtOmTWzfvp3nnnuOyMhIFi1aZFo/MzOT1NRUUz+8W7dukZqaSl5eHrm5uWZt56+TlpZmWkdRFLN19Ho92dnZpKamMmrUKAYPHmwW8+3x3dlu/r4zMjIA4499/nq3bt0CYPny5XfdGNPGxobU1FRSUlLo1q3bPfsNeXl5cebMGbP4b485JyfHNK99+/bY2NiwdOlSbGxsyMnJoUuXLmbblEZaWtGujMrJySEzM5MdO3aUqoO2TTqAjm3HL7N6zVp0ZdSb1BI/6yUheRQs/7NYGFWLHYPBQLNmzUyHdJs0acKxY8f48ssviYqKKrf9jhs3jhEjRpimU1NT8ff3p0uXLri4lN3VALm5uWzcuJHOnTtjbW1dZu1WtCLloShod8zA6u9CR99+PHXbjqBuBcZZGEt+PbKyskhISMDJycnUF+1+FEUhLS0NZ2dnVW8xYW1tjU6nu+/n5vDhw7z66qum6T/++IPw8HBcXFxMRxKioqIYMGAAffr0oUePHuTl5eHu7g4Ybzjp4uJiOhri6OiIi4sLjRo1YsWKFWbPwZEjR3B2diY0NBStVotOp8PGxsYsPp1Oh7W1NS4uLveMu2HDhnz//ffY2tqariqLi4sz23f+H0XOzs6mPIKDg7G1teXq1asFXi7fvHlzVqxYQcOGDdHp7v76dXZ2xtramtjYWBo0aAAY+zaePn2aRx55xCzeqKgoli9fjo2NDX369Lnrj8KSKO77KisrC3t7e/71r38V6X1bEINB4euz27mSnoNHaAva1PUocVtg2Z/14pA8ClfUAl/VYsfHx4f69eubzQsNDeXHH40/mPmXnV6+fNnsL6XLly+bOut5e3uTnGzeiz8vL4/r168XeNnq7V9it7O2ti6XN1R5tVvRCsxDUWDzFNj5sXG681Ss2ryJpV5zZYmvh16vR6PRoNVqi3TX7PxTDPnbqEWj0ZCTk3PXZ1Cn01G9enUAfvjhByIiImjbti1Llixh//79LFiwAK1Wy+zZs3F1daV169bodDp+/PFHvL29cXd3N+WV/5zcOT106FA+/fRT3nzzTYYNG0Z8fDyTJ09mxIgRZoXEnc9R/lhABT1vL7zwAhMnTuS1117j7bff5sKFC3z00UcAWFlZ3TMWg8GAs7MzI0eOZOTIkQC0bduWmzdvsmvXLlxcXIiKimLYsGHMnz+ffv36ma4QO3XqFMuWLWP+/Pm4uLgwcOBAxo4dS40aNfD09GTChAlotdq7Yn7llVcIDQ0FYNeuXWXyPiju+yo/rrL4THUI8WL5gQS2nbhGZEjZDDlgiZ/1kpA87t9mUah66XmbNm2Ij483m3fixAlTJ8XatWvj7e3N5s2bTctTU1PZt2+fqQNgq1atSElJ4eDBg6Z1tmzZgsFgoEWLFhWQxQNOUWDDO/8UOt1mQJs31Y1JVKj169fj4+Nj9mjbtq1p+ZQpU1i2bBlhYWEsXryYb7/91vRHjpOTE5999hnNmzcnIiKCc+fOsXbt2iL90Pr5+bF27Vr2799P48aNee211xg4cCDvvPNOqfJxcXHhf//7H4cOHSI8PJwJEyYwadIkgEKPXkydOpWJEycSHR1NaGgo3bp14+effzZdeOHr68uuXbvQ6/V06dKFRo0aMXz4cNzc3Ew5z5w5k3bt2tGrVy86depE27Ztadq06V37CgwMpHXr1oSEhFSJ77r8G4NuPn5ZRlMWZU9R0f79+xWdTqe8//77ysmTJ5UlS5YoDg4OyjfffGNaZ8aMGYqbm5uyatUq5ciRI8rjjz+u1K5dW8nMzDSt061bN6VJkybKvn37lJ07dyqBgYFK3759ixzHzZs3FUC5efNmmeaXk5OjrFy5UsnJySnTditagXkYDIry8yhFedfF+Nj3H3UCLCJLfj0yMzOV2NhYs/f1/ej1euXGjRuKXq8v58hKB1B++umnApdXljy++eYbxdraWsnIyLjncjXyMBgMSt26dZXZs2eXWZvFzaO479v7Sc/KVQLHr1UCxq5RTl5OLVVblvxZLw7Jo3BF/f1W9TRWREQEP/30E+PGjWPq1KnUrl2bTz75hH79+pnWGTNmDLdu3eLVV18lJSWFtm3bsn79erO/sJYsWcKwYcPo2LEjWq2Wp556is8++0yNlB4cBgP8PAIOxgAa46jITcuvn5UQFWnx4sXUqVMHPz8/Dh8+bBoLx97eXu3QALhy5QrLli0jKSmJl156Se1wyoSjrY5WdT3YfuIKm+KSqefprHZIogpR/XYRPXv2pGfPngUu12g0TJ06lalTpxa4jru7uwwgWJEMelj9Bhz6BtBA7zkQ/rzaUQlRZpKSkpg0aRJJSUn4+PjwzDPP8P7776sdlomnpyfVq1fnP//5j9kgrJVdx1BPtp+4wpa4ZF5rb0mXN4jKTvViR1Qy+jzj7R+OLAeNFp74D4Q9o3ZUwkIplbTvxZgxYxgzZozaYRSosj6vhekQ4smkVX9y4Px1UjJycHOwUTskUUWofm8sUYnoc+GnV/8udKzg6f9KoSOEKDM1qzkQ4u2MQYFt8VfUDkdUIVLsiCLRGPKwWvkqHPsRtNbw7CJocPfo1EIIURr598qSG4OKsiTFjihcXjYR5z5He/x/YGUDz30Dob3UjkoIUQV1/PsS9O3xyeTqS3f7CyHySbEjCmYwQOxqdDGd8bn5B4rODvp+C8Hd1I5MCFFFhftXw93RhtSsPA6ev6F2OKKKkGJH3E1RIG4NfPUv+O5FNMmx5Fo5oH92KdTrVPj2QghRQlZaDZHBNQDYHHdZ5WhEVSHFjviHosDxtcYiZ3k/uHwUbJzRtxnJxvqzUWr/S+0IhRAPgI4hxvt8Sb8dUVak2BHGIid+PfwnEpb1haQjYOME7UbC8CMYIseRq3NUO0ohTAYMGEDv3r1N05GRkQwfPly1eETZahdUHZ1Ww5krtzh79Zba4YgqQIqdB5miwIkNMK8DfPscJB4Ca0do+xa8eQQ6TgIHd7WjFJVAUlISb775JvXq1cPOzg4vLy/atGnD3LlzycjIKPf9r1ixgvfee69M27yzoBIVx8XOmhZ1jN89cipLlAUZVPBBpChwajNsi4aLB4zzrB2g+SvQ+g1wrK5ufKJSOXPmDG3atMHNzY3p06fTqFEjbG1tOXr0KP/5z3/w8/Pjscceu2u73NxcrKysyiQGd3cpyquaDiFe7Dp1jS3HkxnUro7a4YhKTo7sPEjyi5wFXWDJU8ZCR2cPrf9tPJLTeaoUOpZCUSDn1v0fuRmFr1OSRzFH53399dfR6XQcOHCAZ599ltDQUOrUqcPjjz/Ozz//TK9exmEKNBoNc+fO5bHHHsPR0ZH3338fvV7Pv//9b+rWrYu9vT3BwcF8+umnZu3r9XpGjBiBm5sbHh4ejBkz5q4RhO88jZWdnc2oUaPw8/PD0dGRFi1asG3bNtPyhQsX4ubmxi+//EJoaChOTk5069aNxMREACZPnsyiRYtYtWoVGo0GjUZjtr0ofx3/Hm9n/9nrpGblqhyNqOzkyM6DQFHgzDbYNgMS9hrn6ewgYhC0eROcPFUNT9xDbgZM9y1wsRZwK699j78ENkXro3Xt2jU2bNjA9OnTcXS89zYajcb0/8mTJzNjxgw++eQTdDodBoMBX19fli9fTo0aNdi9ezevvvoqPj4+PPvsswDMnj2bhQsX8t///pfQ0FBmz57NTz/9RIcOHQqMa9iwYcTGxrJs2TJ8fX356aef6NatG0ePHiUwMBCAjIwMZs2axddff41Wq+WFF15g1KhRLFmyhFGjRhEXF0dqaioxMTGAHD2qaLWqO1K3hiOnr9zi1xNXeTTMR+2QRCUmxU5Vd3YHbI2GC7uN0zo7aPYytBkOzl6qhiYqv1OnTqEoCsHBwWbzq1evTlZWFgBDhw7lgw8+AOD55583u0u3wWBg3LhxuLi4oNVqqV27Nnv27OG7774zFTuffPIJ48aN48knnwTgyy+/5JdffikwpgsXLhATE8OFCxfw9TUWjKNGjWL9+vXExMQwffp0wHga7csvv6RuXeMNJ4cNG2a64bCTkxP29vZkZ2fj7e1d6udJlEzHUC9OXznD5rjLUuyIUpFip6o6t9NY5JzfaZy2soVmLxk7HzvLl7fFs3YwHmEpgMFgIDUtDRdnZ7TaMj4bbe1Q6ib279+PwWCgX79+ZGdnm+Y3a9bsrnXnzZvHsmXLuHDhApmZmeTk5BAeHg7AzZs3SUxMpEWLFqb1dTodzZo1K/BmmEePHkWv1xMUFGQ2Pzs7Gw8PD9O0g4ODqdAB8PHxITlZLnW2JB1CPPnPjjNsjU9Gb1Cw0moK30iIe5Bip6o5vxu2TodzvxqnrWyg6QBjkeNS8GkRYWE0mvufSjIYwFpvXKesi51iqFevHhqNhvj4eLP5deoYO5Ta29ubzb/zVNeyZcuYNGkSs2bNonXr1jg7OzNz5kz27dtX4pjS09OxsrLi4MGDd3WAdnJyMv3f2trabJlGo6mydxOvrJoGVMPFTseNjFwOJdygaYCcShQlIx2Uq4oLe2HRYxDT3VjoWNkY++S8cQh6zJRCR5QLDw8POnfuzBdffMGtW8UfD2X37t00b96cIUOG0KRJE+rVq8fp06dNy11dXfHx8TErfvLy8jh48GCBbTZp0gS9Xk9ycjL16tUzexTnlJSNjQ16vb7YOYmyY22lJTLY2KdwU5wcdRMlJ8VOZZewHxb3hv92hbPbjXckb/YyvPEHPDobXP3UjlBUcXPmzCEvL49mzZqxfPly4uLiiI+P55tvvuH48eP3vbw8MDCQP/74g19++YUTJ04wceJEfvvtN7N13nzzTWbMmMHKlSs5fvw4r7/+OikpKQW2GRQURL9+/ejfvz8rVqzg7Nmz7N+/n+joaH7++eci51WrVi2OHDlCfHw8V69eJTdXrghSQ/6NQbdIsSNKQU5jVVZ/HTCerjq92Tit1UGTF4yjHrs9pG5s4oFSt25d/vjjD6ZPn864ceP466+/sLW1pX79+owaNYrXX3+9wG1fffVV9u/fT9++fdFoNPTt25fXX3+ddevWmdYZOXIkiYmJREVFodVqefnll3niiSe4efNmge3GxMQwbdo0Ro4cycWLF6levTotW7akZ8+eRc7rlVdeYdu2bTRr1oz09HS2bt1KZGRkkbcXZaN9UA2stBriL6eRcD0Df/fS9ykTDx6NIiepSU1NxdXVlZs3b+Li4lJm7ebm5rJ27Vp69OhxV/+AErt40Njx+NRG47TGCpr0g3ajoFpA2ezjDuWShwosOY+srCzOnj1L7dq1sbOzK3R9g8FAamqq6SqmykrysCzFzaO479uSevarPew/e50pjzUgqnWtQte35M96cUgehSvq77cc2aksLv1hLHJO/n3JrcYKGveFf40C99rqxiaEEOWoY4gn+89eZ/Px5CIVO0LcSYodS3fpkHEwwBN/H9bXaCGsj7HI8ah7302FEKIq6BjqSfS64+w9fY1b2Xk42spPlygeecdYqsQjxiIn/u8OlRotNHoW2o+RIkcI8UCpW8OJAA8Hzl/LYOepq3RtIGOFieKpvCeXq6qkY7CsH3zVzljo5Bc5Q/fDk19JoSOEeOBoNBo6/H2vLLkLuigJObJjKS7/aTySE7f67xkaaPgUtB8LNYLuu6kQQlR1HUO8iNl1ji3Hr2AwKGhlNGVRDFLsqC05zljkxK78e4YGGjxhLHI8Q9SMTAghLEbz2u442eq4mp7N0Ys3aezvpnZIohKRYkctV+KNRc6fPwF/X/1fvzdEvg2eoWpGJoQQFsdGp+VfQdVZezSJzXGXpdgRxSJ9diralRPww0D4vxbw5wpAgdDHYMhueHaRFDpCCFGADiFeAGw+LqMpi+KRIzsV5eop2P4BHPsBFINxXkhP45Ec70bqxiaEEJVAZHANNBr481IqSTez8HYtv4EMRdUiR3bKmWNWElarX4f/i4Cj3xkLneBHYfAO6LNECh1RqUVGRjJ8+PC75i9cuBA3NzfTdGpqKhMmTCAkJAQ7Ozu8vb3p1KkTK1asMN1pPDIyEo1GY3p4eXnxzDPPcP78+QrKRli66k62NPn79NXm43JVlig6KXbKS3Y6Vv/7Nx3i3kabX+QEdYdXt0PfpeDTWO0IhagQKSkptG7dmsWLFzNu3Dh+//13duzYwXPPPcfbb79Namqqad1XXnmFxMRELl26xKpVq0hISOCFF15QMXphaTqGGk9lyY1BRXHIaazyYu2AJukoGgwY6nVG+8h48HtY7aiEqHDjx4/n3LlznDhxAl9fX9P8oKAgnnvuOXJyckzzHBwc8PY2Dhjn4+PDsGHDGDx4cIXHLCxXhxBPZv4Sz85TV8nM0WNvY6V2SKISkGKnvGi16Lt9wK69+2n9zL/RVuKbuImKpygKmXmZBS43GAxk5mWiy9WV+Y0n7XX2aDRlM4aJwWBg2bJl9OvXz6zQyefk5GR2ZOd2169f57vvvqNFixZlEouoGkK8nfF1tePSzSz2nLlq6rQsxP1IsVOOFP8WpBy9pnYYohLKzMukxVJ1fuT3Pb8PB2uHMmnr6tWr3Lhxg5CQoo0ZNWfOHObPn4+iKGRkZBAUFMQvv/xSJrGIqkGj0dAx1Iuv955nU1yyFDuiSKTPjhCi3OR3Pi6qfv36cejQIQ4fPszOnTupV68eXbp0IS0trZwiFJVRh1DjrSO2xCUX+z0mHkxyZEcIC2Svs2ff8/sKXG4wGEhLS8PZ2blcTmMVlYuLCzdv3rxrfkpKCq6urtSoUQM3NzeOHz9epPZcXV2pV68eAPXq1WPBggX4+PiwfPlyBg0aVOS4RNXWqo4H9tZWJKVmEZuYSgNfV7VDEhZOih0hLJBGo7nvqSSDwUCeLg8Ha4cyL3aKIzg4mA0bNtw1//fffycoKAitVkufPn34+uuveffdd+/qt5Oenk5eXl6B7VtZGTufZmYW3H9JPHjsrK1oG1idjbGX2RyXLMWOKJScxhJClNiQIUM4ceIEb7zxBkeOHCE+Pp6PPvqIb7/9lpEjRwLw/vvv4+/vT4sWLVi8eDGxsbGcPHmS//73vzRt2pRbt26Z2svIyCApKYmkpCQOHz7MkCFDsLOzo0uXLmqlKCxUx/y7oMtoyqII5MiOEKLE6tSpw44dO5gwYQKdOnUiJyeHkJAQvv/+e7p16waAu7s7e/fuZcaMGUybNo3z589TrVo1GjVqxAcffICLi4upvXnz5jFv3jwAqlWrRlhYGGvXriU4OFiV/ITl6vB3sXM4IYUradnUcLZVOSJhyaTYEUKUSkRExD1PZd3O1dWV6OhooqOjzeYbDAbTpefbtm0rrxBFFeTpYkdYTVeO/HWTrceTeTbCX+2QhAWT01hCCCEqpQ6mU1ly6whxf1LsCCGEqJQ6/j3Gzq8nr5Kdp1c5GmHJpNgRQghRKTXwdcHT2ZaMHD37zlxXOxxhwaTYEUIIUSlptRo6/j3A4OY4OZUlCibFjhBCiEor/3YRm4/LaMqiYFLsCCGEqLTa1PPARqflrxuZnExOVzscYaGk2BFCCFFpOdjoaFPXA4BNcipLFECKHSGEEJVah1DjqawtcTKasrg3KXaEEEJUavnj7fx+4QbXb+WoHI2wRFLsCCEs2uTJkwkPDy9VG+fOnUOj0XDo0KEStzFgwAB69+5dqjgsTa1atfjkk0/UDqPU/NzsCfF2xqDAtng5uiPuJsWOEKLUEhISePnll/H19cXGxoaAgADefPNNrl27Vqx2NBoNK1euNJs3atQoNm/eXKr4/P39SUxMpGHDhoWuW1Bh9Omnn7Jw4cJSxSHKT6fQf67KEuJOUuwIIUrlzJkzNGvWjJMnT/Ltt99y6tQpvvzySzZv3kyrVq24fr10g705OTnh4eFRqjasrKzw9vZGpyv57QBdXV1xc3MrVRzFpdfrMRgMFbrPyqrD3+Pt7Ii/Qq5enjNhToodIUSpDB06FBsbGzZs2ED79u156KGH6N69O5s2beLixYtMmDABMJ4yee+99+jbty+Ojo74+fkxZ84cUzu1atUC4IknnkCj0Zim7zyNlX86afr06Xh5eeHm5sbUqVPJy8tj9OjRuLu7U7NmTWJiYkzb3Hm05saNG/Tr148aNWpgb29PYGCgaf3atWsD0KRJEzQaDZGRkWb7zWcwGPjwww+pV68e9vb2NGzYkOnTp9/3uVq9ejWBgYHY2dnxyCOPsGjRIjQaDSkpKQAsXLgQNzc3Vq9eTf369bG1teXChQtkZ2czatQo/Pz8cHR0pEWLFnfdOHXnzp20a9cOe3t7/P39eeONN7h165ZpeXJyMr169cLe3p7atWuzZMkSs+1ffvllevXqZTYvNzcXT09PFixYcN+8LEHjmm54ONqQlp3HwfMpaocjLIwUO0JYIEVRMGRk3P+RmVn4OiV4FGdgtuvXr/PLL7/w+uuvY29vb7bM29ubfv36sXz5clObM2fOpHHjxvzxxx+8/fbbDB8+nK1btwLw22+/ARATE0NiYqJp+l62bNnCpUuX2LFjBx999BHvvvsuPXv2pFq1auzbt4/XXnuNwYMH89dff91z+4kTJxIbG8u6deuIi4tj7ty5VK9eHYD9+/cDsGnTJhITE1mxYsU92xg3bhwzZsxg4sSJHDt2jHnz5uHp6VlgzGfPnuXpp5+md+/eHD58mMGDB5sKwdtlZGTwwQcfMH/+fP788088PT0ZNmwYe/bsYdmyZRw5coRnnnmGbt26cfLkSQBOnz5Nt27deOqppzhy5AjLly9n586dDBs2zNTugAEDSEhIYOvWrfzwww/MmTOH5OR/TvkMGjSIX375haSkJNO8NWvWkJGRwXPPPVdgXpbCSqvhkb87Km+Jv6JyNMLSlPyYrhCi3CiZmcQ/3LTQ9cpjVJHg3w+icXAo0ronT55EURRCQ0PvuTw0NJQbN25w5Yrxx6dNmza8/fbbAAQFBbFz507mzJnD448/To0aNQBwc3PD29v7vvt1d3fns88+Q6vVEhwczIcffkhGRgbjx48H/ilEdu7cSZ8+fe7a/sKFCzRp0oRmzZoB/xxVAkxxeHh4FBhHWloan376KV988QVRUVEYDAZq1KhB165dC4z5q6++Ijg4mJkzZwIQHBzMsWPHeP/9983Wy83NZc6cOTRu3NgUa0xMDBcuXMDX1xcw9mNav349MTExTJ8+nejoaPr168fw4cMBCAwM5LPPPqN9+/bMnTuXCxcusG7dOvbv309ERAQACxYsMHvdWrduTXBwMMuXL2fixImAsfB85plncHJyKjAvS9IxxJMfDv7F1vgrhAepHY2wJHJkRwhRakU9GtSqVau7pk+cOFHs/TVo0ACt9p+vLy8vLxo1amSatrKywsPDw+zIxe2GDBnCsmXLCA8PZ8yYMezevbtY+4+LiyM7O5uOHTvec3n37t1xcnLCycmJBg0aABAfH28qNPI1b978rm1tbGwICwszTR89ehS9Xk9QUJCpTScnJ7Zv387p06cBOHz4MAsXLjRb3rVrVwwGA2fPniUuLg6dTkfTpv8U0CEhIXf1QRo4cCBLly4F4PLly6xbt46XX365WM+NmtoGVsfaSsO5axkkZ6odjbAkcmRHCAuksbcn+PeDBS43GAykpqXh4uxs9qNfVvsuqnr16qHRaIiLi+OJJ564a3lcXBzVqlUzHS0pK9bW1mbTGo3mnvMK6tzbvXt3zp8/z9q1a9m4cSMdO3Zk6NChzJo1q0j7v/OU3Z3mz59PZmbmPWMtStsajcY0nZ6ejpWVFQcPHsTKysps3fwjLunp6QwePJg33njjrvYeeuihIheUL774IuPGjWPPnj3s3buX2rVr065du2LFryZnO2ta1vHg15NXOXZDU/gGKlIUBYPyz78GRUFRQOGf6ZycXG7lQkpGLtbWlfe+X7m5edzKBb1BoXifhrIjxY4QFkij0dz/VJLBgDYvD62DQ5kXO8Xh4eFB586dmTNnDm+99ZZZEZCUlMSSJUvo37+/6cd77969Ztvv3buXoKB/zjdYW1uj1+srJPYaNWoQFRVFVFQU7dq1Y/To0cyaNQsbGxuA+8YRGBiIvb09mzdvZtCgQXct9/Pzu2tecHAwa9euNZt3v35J+Zo0aYJeryc5ObnAwuPhhx8mNjaWevXq3XN5SEgIeXl5HDx40HR0KT4+3tQxOp+HhwePPvooCxcuZO/evbz00kuFxmdpOoR48uvJq2y9pCUq5gAKGmMhwT0Kizumb//3n21um1bunv6nYDGubzDc3sY/xcudxU3R6Rh/YGu5PFcVS0ezNhkE+diotHchhCiFL774gtatW9O1a1emTZtG7dq1+fPPPxk9ejR+fn5mfVJ27drFhx9+SO/evdm4cSM//PADy5cvNy2vVasWmzdvpk2bNtja2lKtWrVyiXnSpEk0bdqUBg0akJ2dzZo1a0z9Vzw9PbG3t2f9+vXUrFkTOzs7XF1dzba3s7Nj7NixjBkzBhsbG1q1asW5c+c4d+4cr7zyyj33OXjwYD766CPGjh3LwIEDOXTokGncntuP5NwpKCiIfv360b9/f2bPnk2TJk24cuUKmzdvJiwsjEcffZSxY8fSsmVLhg0bxqBBg3B0dCQ2NpaNGzfyxRdfEBwcTLdu3Rg8eDBz585Fp9MxfPjwex6hevHFF+nTpw96vZ6oqKgSPsPq6RTqxfs/x5GaC7vPlG7YA1F1SLEjhCiVwMBADhw4wLvvvsuzzz7L9evX8fb2pnfv3rz77ru4u7ub1h05ciQHDhxgypQpuLi4MHv2bLN+L7Nnz2bEiBHMmzcPPz8/zp07Vy4x29jYMG7cOM6dO4e9vT3t2rVj2bJlAOh0Oj777DOmTp3KpEmTaNeu3V2XeYPxii6dTsekSZO4dOkSXl5eDBkypMB91q5dmx9++IGRI0fy6aef0qpVKyZMmMCQIUOwtbW9b7wxMTFMmzaNkSNHcvHiRapXr07Lli3p2bMnAGFhYWzfvp0JEybQrl07FEWhbt26ZldRxcTEMGjQINq3b4+XlxfTpk0zdUS+XWRkJD4+PjRo0MDUIboy8Xd3YPkrzflp826ahIdjba1DqwENGuO/GvN/tRoNmntMazUaNIBW+8/6Gozz/9nmn2nt39Oa26f5uy2t5r4xFBRTXm4ev6xfT/fu3Yp9OrS47ldwl1Zubi7r1q2jlkfRLnwoF4pQbt68qQDKzZs3y7TdnJwcZeXKlUpOTk6ZtlvRJI/yl5mZqcTGxiqZmZlFWl+v1ys3btxQ9Hp9OUdWdgICApSPP/7YbF5lzONeSprHtGnTlJo1a5ZTVMWn1+uVhIQExcXFRfnxxx8LXb+479uKYsmf9eKQPApX1N9vObIjhBAVZM6cOURERODh4cGuXbuYOXOm2Vg4ajIYDCQnJzNz5kzc3Nx47LHH1A5JiDIjxY4QQlSQkydPMm3aNK5fv85DDz3EyJEjGTdunNphAcbxfGrXro2vry8LFy4s1a01hLA08m4WQlSI8up/U5l8/PHHfPzxx2qHcU+1atVCr9eTmpqKi4uL2uEIUaZkUEEhhBBCVGlS7AhhQZRi3JdKCLXJ+1VUFlLsCGEB8kfGzcnJUTkSIYouIyMDKP4o0UJUNOmzI4QF0Ol0ODg4cOXKFaytrQsdFdlgMJCTk0NWVpaqIyiXluRhWYqah6IoZGRkkJycjJub2123sRDC0kixI4QF0Gg0+Pj4cPbsWc6fP1/o+oqikJmZedd9lCobycOyFDePotyhXghLIMWOEBbCxsaGwMDAIp3Kys3NZceOHfzrX/+q1KcQJA/LUpw8rK2t5YiOqDSk2BHCgmi1Wuzs7Apdz8rKiry8POzs7Cr1j6vkYVmqSh5C3EnVk8uTJ0823m/ktkdISIhpeVZWFkOHDsXDwwMnJyeeeuopLl++bNbGhQsXePTRR3FwcMDT05PRo0eTl5dX0akIIYQQwkKpfmSnQYMGbNq0yTR9+6idb731Fj///DPff/89rq6uDBs2jCeffJJdu3YBoNfrefTRR/H29mb37t0kJibSv39/rK2tmT59eoXnIoQQQgjLo3qxo9Pp7tnB7ebNmyxYsIClS5fSoUMHwHjX3tDQUPbu3UvLli3ZsGEDsbGxbNq0CS8vL8LDw3nvvfcYO3YskydPxsbG5p77zM7OJjs72zSdmpoKGM9X5+bmlllu+W2VZZtqkDwsT1XJRfKwLJKHZZE8it52YTSKiqNCTZ48mZkzZ+Lq6oqdnR2tWrUiOjqahx56iC1bttCxY0du3LiBm5ubaZuAgACGDx/OW2+9xaRJk1i9ejWHDh0yLT979ix16tTh999/p0mTJgXud8qUKXfNnz9/Pg4OKt6CXgghhBBFlpGRwaBBg0hJScHV1bXA9VQ9stOiRQsWLlxIcHAwiYmJTJkyhXbt2nHs2DGSkpKwsbExK3QAvLy8SEpKAiApKQkvL6+7lucvK8i4ceMYMWKEafrixYvUr1+fQYMGlVFmQgghhKgoaWlpllvsdO/e3fT/sLAwWrRoQUBAAN999x329vbltl9bW1tsbW1N005OTiQkJODs7FymY2Skpqbi7+9PQkJCpb6xnuRheapKLpKHZZE8LIvkUThFUUhLS8PX1/e+66neZ+d2bm5uBAUFcerUKTp37kxOTg4pKSlmR3cuX75s6uPj7e3N/v37zdrIv1qrOANdabVaatasWfoECuDi4lKp36j5JA/LU1VykTwsi+RhWSSP+7vfEZ18FjWueXp6OqdPn8bHx4emTZtibW3N5s2bTcvj4+O5cOECrVq1AqBVq1YcPXqU5ORk0zobN27ExcWF+vXrV3j8QgghhLA8qh7ZGTVqFL169SIgIIBLly7x7rvvYmVlRd++fXF1dWXgwIGMGDECd3d3XFxc+Pe//02rVq1o2bIlAF26dKF+/fq8+OKLfPjhhyQlJfHOO+8wdOhQs9NUQgghhHhwqVrs/PXXX/Tt25dr165Ro0YN2rZty969e6lRowYAH3/8MVqtlqeeeors7Gy6du3KnDlzTNtbWVmxZs0ahgwZQqtWrXB0dCQqKoqpU6eqlZIZW1tb3n333UpfeEkelqeq5CJ5WBbJw7JIHmVH1UvPhRBCCCHKm0X12RFCCCGEKGtS7AghhBCiSpNiRwghhBBVmhQ7QgghhKjSpNgRQgghRJUmxY5K4uPjCQ8PNz3s7e1ZuXKl2mGVyNmzZ3nkkUeoX78+jRo14tatW2qHVCK1atUiLCyM8PBwHnnkEbXDKZWMjAwCAgIYNWqU2qGUSEpKCs2aNSM8PJyGDRsyb948tUMqsYSEBCIjI6lfvz5hYWF8//33aodUYk888QTVqlXj6aefVjuUIluzZg3BwcEEBgYyf/58tcMpscr43N9Jzc+CXHpuAdLT06lVqxbnz5/H0dFR7XCKrX379kybNo127dpx/fp1XFxc0Oks6k4kRVKrVi2OHTuGk5OT2qGU2oQJEzh16hT+/v7MmjVL7XCKTa/Xk52djYODA7du3aJhw4YcOHAADw8PtUMrtsTERC5fvkx4eDhJSUk0bdqUEydOVMrP+rZt20hLS2PRokX88MMPaodTqLy8POrXr8/WrVtxdXWladOm7N69u1K+jyrbc38van4W5MiOBVi9ejUdO3aslF9+f/75J9bW1rRr1w4Ad3f3SlnoVCUnT57k+PHjZjfarWysrKxwcHAAIDs7G0VRqKx/l/n4+BAeHg4Y79lXvXp1rl+/rm5QJRQZGYmzs7PaYRTZ/v37adCgAX5+fjg5OdG9e3c2bNigdlglUtme+3tR87MgxU4JRUdHExERgbOzM56envTu3Zv4+PgStfXdd9/x3HPPlXGERVPaPE6ePImTkxO9evXi4YcfZvr06eUYbcHK4vXQaDS0b9+eiIgIlixZUk6R3l9Z5DFq1Ciio6PLKcKiKYs8UlJSaNy4MTVr1mT06NFUr169nKK9v7L8rB88eBC9Xo+/v38ZR1m4sszDktwvr0uXLuHn52da18/Pj4sXL6oV6n1VldenqHlU9GdB/gQvoe3btzN06FAiIiLIy8tj/PjxdOnShdjYWBwdHQkPDycvL++u7TZs2GB2K/rU1FR2797NsmXLKjJ8k9LmkZeXx6+//sqhQ4fw9PSkW7duRERE0Llz50qVB8DOnTvx8/MjMTGRTp060ahRI8LCwipVHqtWrSIoKIigoCB2795dobHfrixeDzc3Nw4fPszly5d58sknefrpp/Hy8qroVMrss379+nX69++vWv+jssrD0twvr8qksNensihKHqp8FhRRJpKTkxVA2b59e7G2W7x4sdKvX79yiqr4ipvH7t27lS5dupimP/zwQ+XDDz8sr/CKrKSvR75Ro0YpMTExZRtUCRQ3j7ffflupWbOmEhAQoHh4eCguLi7KlClTyjnKwpX29RgyZIjy/fffl3FUJVOSXLKyspR27dopixcvLsfIiqekr8nWrVuVp556qpyiKr3b89q1a5fSu3dv07I333xTWbJkiYrRFd29Xh9Lf+7v5c481PosyGmsMnLz5k3A2GelONQ8hXUvxc0jIiKC5ORkbty4gcFgYMeOHYSGhpZniEVS3Dxu3bpFWloaYOwwvmXLFho0aFBu8RVVcfOIjo4mISGBc+fOMWvWLF555RUmTZpUniEWSXHzuHz5sun1uHnzJjt27CA4OLjc4iuO4uaiKAoDBgygQ4cOvPjii+UZWrGU9DvL0t2eV/PmzTl27BgXL14kPT2ddevW0bVrV5UjLJqq8vrcnoeqn4UKLa2qKL1erzz66KNKmzZtirVdSkqK4unpqWRnZ5dTZMVT0jzWrl2rNGzYUGnQoIHy1ltvlVN0RVeSPE6fPq2EhYUpYWFhSoMGDZRPPvmkHCMsmpK+HvliYmKUkSNHlnFUxVeSPPbt26c0btxYCQsLUxo1aqR8+eWX5Rhh0ZUkl19//VXRaDRK48aNTY8jR46UY5SFK+l7q2PHjkr16tUVe3t7xc/PT9m9e3c5RVgy98pr1apVSmBgoFK3bl3lq6++UjG6ortXHpb+3N/LnXmo+VmQYqcMvPbaa0pAQICSkJCgdiilInlYFsnD8lSVXKpKHneqKnlJHmVPip1SGjp0qFKzZk3lzJkzaodSKpKHZZE8LE9VyaWq5HGnqpKX5FE+pNgpIYPBoAwdOlTx9fVVTpw4oXY4JSZ5WBbJw/JUlVyqSh53qip5SR7lSy49L6GhQ4eydOlSVq1ahbOzM0lJSQC4urpib2+vcnRFJ3lYFsnD8lSVXKpKHneqKnlJHuVM7WqrsgLu+bCEy5WLQ/KwLJKH5akquVSVPO5UVfKSPMqX3BtLCCGEEFWajLMjhBBCiCpNih0hhBBCVGlS7AghhBCiSpNiRwghhBBVmhQ7QgghhKjSpNgRQgghRJUmxY4QQgghqjQpdoQQQghRpUmxI4QQQogqTYodIYQQQlRpUuwIIcrFgAED0Gg0aDQabGxsqFevHlOnTiUvL0/t0EpEo9GwcuVKtcMQQpSA3PVcCFFuunXrRkxMDNnZ2axdu5ahQ4dibW3NuHHjitWOXq9Ho9Gg1Vb+v89yc3OxtrZWOwwhHiiV/5tDCGGxbG1t8fb2JiAggCFDhtCpUydWr17NRx99RKNGjXB0dMTf35/XX3+d9PR003YLFy7Ezc2N1atXU79+fWxtbblw4QK//fYbnTt3pnr16ri6utK+fXt+//13s31qNBq++uorevbsiYODA6GhoezZs4dTp04RGRmJo6MjrVu35vTp02bbrVq1iocffhg7Ozvq1KnDlClTTEehatWqBcATTzyBRqMxTRe2XX48c+fO5bHHHsPR0ZH333+/jJ9lIURhpNgRQlQYe3t7cnJy0Gq1fPbZZ/z5558sWrSILVu2MGbMGLN1MzIy+OCDD5g/fz5//vknnp6epKWlERUVxc6dO9m7dy+BgYH06NGDtLQ0s23fe+89+vfvz6FDhwgJCeH5559n8ODBjBs3jgMHDqAoCsOGDTOt/+uvv9K/f3/efPNNYmNj+eqrr1i4cKGpMPntt98AiImJITEx0TRd2Hb5Jk+ezBNPPMHRo0d5+eWXy/x5FUIUQhFCiHIQFRWlPP7444qiKIrBYFA2btyo2NraKqNGjbpr3e+//17x8PAwTcfExCiAcujQofvuQ6/XK87Ozsr//vc/0zxAeeedd0zTe/bsUQBlwYIFpnnffvutYmdnZ5ru2LGjMn36dLO2v/76a8XHx8es3Z9++slsnaJuN3z48PvmIYQoX9JnRwhRbtasWYOTkxO5ubkYDAaef/55Jk+ezKZNm4iOjub48eOkpqaSl5dHVlYWGRkZODg4AGBjY0NYWJhZe5cvX+add95h27ZtJCcno9frycjI4MKFC2br3b6dl5cXAI0aNTKbl5WVRWpqKi4uLhw+fJhdu3aZHZHR6/V3xXSnom7XrFmzkjx9QogyIsWOEKLcPPLII8ydOxcbGxt8fX3R6XScO3eOnj17MmTIEN5//33c3d3ZuXMnAwcOJCcnx1Qg2Nvbo9FozNqLiori2rVrfPrppwQEBGBra0urVq3IyckxW+/2DsD5bdxrnsFgACA9PZ0pU6bw5JNP3pWDnZ1dgfkVdTtHR8cC2xBClD8pdoQQ5cbR0ZF69eqZzTt48CAGg4HZs2ebrq767rvvitTerl27mDNnDj169AAgISGBq1evljrOhx9+mPj4+LtivZ21tTV6vb7Y2wkh1CfFjhCiQtWrV4/c3Fw+//xzevXqxa5du/jyyy+LtG1gYCBff/01zZo1IzU1ldGjR2Nvb1/qmCZNmkTPnj156KGHePrpp9FqtRw+fJhjx44xbdo0wHhF1ubNm2nTpg22trZUq1atSNsJIdQnV2MJISpU48aN+eijj/jggw9o2LAhS5YsITo6ukjbLliwgBs3bvDwww/z4osv8sYbb+Dp6VnqmLp27cqaNWvYsGEDERERtGzZko8//piAgADTOrNnz2bjxo34+/vTpEmTIm8nhFCfRlEURe0ghBBCCCHKixzZEUIIIUSVJsWOEEIIIao0KXaEEEIIUaVJsSOEEEKIKk2KHSGEEEJUaVLsCCGEEKJKk2JHCCGEEFWaFDtCCCGEqNKk2BFCCCFElSbFjhBCCCGqNCl2hBBCCFGl/T9/5pu+PVsbQgAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(epsilon_greedy_rewards, label=\"Epsilon-greedy\")\n", + "plt.plot(gradient_rewards, label=\"Gradient\")\n", + "plt.plot(ucb_rewards, label=\"UCB\")\n", + "plt.plot(optimistic_greedy_rewards, label=\"Optimistic-greedy\")\n", + "plt.title(\"Mean reward as a function of the parameter.\")\n", + "plt.xlabel(\"Parameter\")\n", + "plt.ylabel(\"Mean reward\")\n", + "plt.xticks(range(10), [rf\"$2^{{ {i} }}$\" for i in range(-7, 3)])\n", + "plt.legend()\n", + "plt.grid()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "1. What is the best algorithm for this example ?\n", + "\n", + "UCB\n", + "\n", + "2. Can you comment on the shape of the curves ? what is the optimal parameter in each of the algorithms ?\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Best parameter for epsilon-greedy: 0.0078125\n", + "Best parameter for gradient: 0.5\n", + "Best parameter for UCB: 0.0625\n", + "Best parameter for optimistic-greedy: 0.5\n" + ] + } + ], + "source": [ + "print(\"Best parameter for epsilon-greedy:\", parameters[np.argmax(epsilon_greedy_rewards)])\n", + "print(\"Best parameter for gradient:\", parameters[np.argmax(gradient_rewards)])\n", + "print(\"Best parameter for UCB:\", parameters[np.argmax(ucb_rewards)])\n", + "print(\"Best parameter for optimistic-greedy:\", parameters[np.argmax(optimistic_greedy_rewards)])" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + }, + "vscode": { + "interpreter": { + "hash": "2e7007663510ed9db58bd00c4b6768d5d37222230e04b44bb35e77da9185a2df" + } + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/TP2/shell.nix b/TP2/shell.nix new file mode 100644 index 0000000..03f97f4 --- /dev/null +++ b/TP2/shell.nix @@ -0,0 +1,12 @@ +{ pkgs ? import { } }: + +pkgs.mkShell { + buildInputs = with pkgs; [ + poetry + python3 + python310Packages.numpy + python310Packages.matplotlib + python310Packages.ipykernel + python310Packages.pip + ]; +} diff --git a/notebook_exos.jl b/notebook_exos.jl new file mode 100644 index 0000000..ecc6e94 --- /dev/null +++ b/notebook_exos.jl @@ -0,0 +1,1229 @@ +### A Pluto.jl notebook ### +# v0.19.19 + +using Markdown +using InteractiveUtils + +# This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error). +macro bind(def, element) + quote + local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end + local el = $(esc(element)) + global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el) + el + end +end + +# ╔═╡ ec777da4-8ef0-44b4-8d56-38b31790a5b7 +begin + using Plots # pour le tracé de figures + using PlutoUI # pour les objets Pluto + using LinearAlgebra # pour les matrices identité + using SparseArrays # pour les matrices creuses + using LaTeXStrings # pour les strings en LaTeX (pour les plots) + TableOfContents(depth=4) +end + +# ╔═╡ dc4eb528-82b2-11ed-3ca2-c321ff8ef647 +html""" +
+ + Exercices - Reinforcement learning
+ Laurent Fainsin
+ 2021 - 2022 + +
+""" + +# ╔═╡ 7fb608fa-da53-47d3-a585-235b4692c4dd +md""" +# Exercice 1 - Finite Horizon MDP + +> Revenue management: Littlewood’s model +> +> An airplane has 20 seats available, and the sell closes in 50 days. At every time epoch, the airplane decides the selling price: Either ``p_1`` = 5, and then it will sell a seat with probability ``q_1`` = 0.1, or ``p_2`` = 1, and then it will sell a seat with probability ``q_2`` = 0.8. +""" + +# ╔═╡ 58baae0a-ae46-443c-8c08-8743a13eb860 +md""" +D'après l'énoncé on a: + +$\mathcal{S} = \left\{ s_1, s_2 \right\}$ + +$\mathcal{A} = \left\{ p_1, p_2 \right\}$ + +$\mathcal{R} = \left\{ p_1 q_1, p_2 q_2 \right\}$ +""" + +# ╔═╡ dc2fcab2-7b23-47e3-b53a-0ad966645afd +md""" +D'après l'équation d'optimalité de Bellmann: + +$V(s) = r(s) + \gamma \sum_{s'} p(s,s')V(s')$ + +Dans notre cas on a donc (``\gamma = 1``): + +$V_T(s_1) = p_1 q_1 + q_1 V_{T-1}(s_1) + (1-q_1) V_{T-1}(s_2)$ +$V_T(s_2) = p_2 q_2 + q_2 V_{T-1}(s_2) + (1-q_2) V_{T-1}(s_1)$ +""" + +# ╔═╡ a6100c90-9a12-43d8-8ec3-dbf04b4ab5d1 +md""" +On peut alors poser: + +$P = \begin{pmatrix} +q_1 & 1-q_1 \\ +q_2 & 1-q_2 +\end{pmatrix}$ + +$R = \begin{pmatrix} +p_1 q_1 \\ +p_2 q_2 +\end{pmatrix}$ + +$V_T = \begin{pmatrix} +V_T(s_1) \\ +V_T(s_2) +\end{pmatrix}$ + +tel que l'on puisse reformuler Bellmann: + +$V_T = R + \gamma P V_{T-1}$ +""" + +# ╔═╡ a5df336b-3db1-441d-845b-3ddb0aa3213a +md""" +En selectionnant la valeur maximale de ``V_T`` on en déduit la politique optimal pour ce jour ``T``. Intuitivement on choisi le prix ``p_2`` si l'on souhaite maximiser notre gain. On peut le vérifier numériquement: +""" + +# ╔═╡ a30def9e-50f0-4aa2-8e79-6d10ecee5bee +begin + p1_slider = @bind p1 Slider(0:1:10, default=5, show_value=true) + q1_slider = @bind q1 Slider(0:0.1:1, default=0.1, show_value=true) + + p2_slider = @bind p2 Slider(0:1:10, default=1, show_value=true) + q2_slider = @bind q2 Slider(0:0.1:1, default=0.8, show_value=true) + + md""" + ``p_1``: $(p1_slider) ``\quad\quad`` + ``q_1``: $(q1_slider) + + ``p_2``: $(p2_slider) ``\quad\quad`` + ``q_2``: $(q2_slider) + """ +end + +# ╔═╡ 3176c1f0-c1fa-4c74-9133-f4371e584b6c +P = [ + q1 1-q1 + q2 1-q2 +] + +# ╔═╡ f5566288-5ef4-495c-8442-a59f17f0814b +R = [ + p1 * q1 + p2 * q2 +] + +# ╔═╡ f01bd868-a180-4327-98bf-de2298673523 +γ = 1 + +# ╔═╡ f8c9b0c8-3f81-441b-b673-f07ed2ae3e5a +begin + text = ""; + T = 50; + + V = [0 ; 0]; + text *= "``V_{50} = $(V)``\n\n"; + + for t in 1:T + V = R + γ * P * V; + choix = argmax(V); + V_display = round.(V, digits=2); + text *= "``V_{$(T-t)} = $(V_display) → p_$(choix)``\n\n"; + end + + Markdown.parse(text) +end + +# ╔═╡ 73a0d6a0-94a9-45b3-9db9-6cc0c845ab95 +md""" +# Exercice 2 - Infinite Horizon MDP + +> See figure +> +> What is the optimal policy (for total discounted reward) for various values of ``\gamma`` ? +""" + +# ╔═╡ 3b87e4e9-81c9-48d9-9f58-e6271f975c40 +md""" +Équation d'optimalité pour nos deux états (``s_0`` and ``s_1``): + +``V_\star(s_0) = \max( 10 + \gamma V_\star(s_1), 1 + \gamma V_\star(s_0) )`` + +``V_\star(s_1) = \max( 0 + \gamma V_\star(s_1), -15 + \gamma V_\star(s_0) )`` +""" + +# ╔═╡ 045e6ef0-84a8-4ad1-bc7c-0494599fd825 +md""" +Si ``\gamma \approx 0``: + +``V_\star(s_0) \approx \max(10, 1) = 10`` + +``V_\star(s_1) \approx \max(0, -15) = 0`` +""" + +# ╔═╡ 8cd6c607-2094-4fa0-b1d8-445842ac5091 +md""" +Si ``\gamma \approx 1``: + +``V_\star(s_0) = 1 + \gamma V_\star(s_0) \implies V_\star(s_0) = \displaystyle\frac{1}{1-\gamma}`` + +``V_\star(s_0) = -15 + V_\star(s_0) \implies V_\star(s_1) = -15 + \displaystyle\frac{1}{1-\gamma}`` +""" + +# ╔═╡ fe6dc66f-2627-4c13-b32a-9751b2ff3a73 +md""" +Si l'on résoud ces deux dernières équations on a: + +``\gamma = 0.9`` + +``\gamma = \displaystyle\frac{15}{16} \approx 0.94`` +""" + +# ╔═╡ fdd906ab-2224-4c26-9fb9-d9855bfda257 +md""" +Par disjonction des cas: +""" + +# ╔═╡ 65dcb2b0-1021-45a6-afe7-a95f6e139636 +md""" +Si ``\gamma \in [0, 0.9]``: + +``V_\star(s_0) = 1 + \gamma V_\star(s_0)`` + +``V_\star(s_1) = \gamma V_\star(s_1)`` +""" + +# ╔═╡ 69a4815d-1a84-400c-ae2b-4753e6c96abc +md""" +Si ``\gamma \in [0.9, 0.94]``: + +``V_\star(s_0) = 10 + \gamma V_\star(s_1)`` + +``V_\star(s_1) = \gamma V_\star(s_1)`` +""" + +# ╔═╡ 0b1a0996-d98d-43a5-8d4e-3faa6ded79a8 +md""" +Si ``\gamma \in [0.94, 1]``: + +``V_\star(s_0) = 1 + \gamma V_\star(s_0)`` + +``V_\star(s_1) = -15 + \gamma V_\star(s_0)`` +""" + +# ╔═╡ 00000000-0000-0000-0000-000000000001 +PLUTO_PROJECT_TOML_CONTENTS = """ +[deps] +LaTeXStrings = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f" +LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e" 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╟─a5df336b-3db1-441d-845b-3ddb0aa3213a +# ╟─a30def9e-50f0-4aa2-8e79-6d10ecee5bee +# ╟─3176c1f0-c1fa-4c74-9133-f4371e584b6c +# ╟─f5566288-5ef4-495c-8442-a59f17f0814b +# ╟─f01bd868-a180-4327-98bf-de2298673523 +# ╟─f8c9b0c8-3f81-441b-b673-f07ed2ae3e5a +# ╟─73a0d6a0-94a9-45b3-9db9-6cc0c845ab95 +# ╟─3b87e4e9-81c9-48d9-9f58-e6271f975c40 +# ╟─045e6ef0-84a8-4ad1-bc7c-0494599fd825 +# ╟─8cd6c607-2094-4fa0-b1d8-445842ac5091 +# ╟─fe6dc66f-2627-4c13-b32a-9751b2ff3a73 +# ╟─fdd906ab-2224-4c26-9fb9-d9855bfda257 +# ╟─65dcb2b0-1021-45a6-afe7-a95f6e139636 +# ╟─69a4815d-1a84-400c-ae2b-4753e6c96abc +# ╟─0b1a0996-d98d-43a5-8d4e-3faa6ded79a8 +# ╟─00000000-0000-0000-0000-000000000001 +# ╟─00000000-0000-0000-0000-000000000002