From 88b44d59cfd9b927f03c3c7f242e7bfd5ce67e16 Mon Sep 17 00:00:00 2001 From: Pwelsh12 Date: Wed, 19 Jun 2024 20:20:17 -0700 Subject: [PATCH 1/2] Add files via upload [Submission] --- catalan.py | 231 +++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 231 insertions(+) create mode 100644 catalan.py diff --git a/catalan.py b/catalan.py new file mode 100644 index 0000000..3b04290 --- /dev/null +++ b/catalan.py @@ -0,0 +1,231 @@ +import itertools + + +def parenthesizations(n): + """ + Returns a set of all possible parenthesizations with n pairs of parentheses. + + Parameters: + n (int): The number of pairs of parentheses. + + Returns: + A set of strings, where each inner string represents a valid parenthesization of n pairs of parentheses. + + Example: + >>> parenthesizations(3) + {'((()))', '(()())', '(())()', '()(())', '()()()'} + """ + if n == 0: + return {""} + elif n == 1: + return {"()"} + else: + result = set() + for i in range(n): + for left in parenthesizations(i): + for right in parenthesizations(n - 1 - i): + result.add(f"({left}){right}") + return result + +#print(parenthesizations(3)) + +def product_orders(n): + """ + Returns a set of all possible ways to multiply of n elements. + + Parameters: + n (int): The number of elements multiplied. + + Returns: + A set of strings where each string represents a way to multiply n elements. + + Example: + >>> product_orders(4) + {'((?*?)*?)*?', '(?*(?*?))*?', '(?*?)*(?*?)', '?*((?*?)*?)', '?*(?*(?*?))'} + """ + if n == 0: + return {""} + elif n == 1: + return {"?"} + else: + result = set() + for i in range(1,n): + left_orders = product_orders(i) + right_orders = product_orders(n-i) + for left in left_orders: + for right in right_orders: + if i == 1 and (n - i) == 1: + result.add(f"{left}*{right}") + elif i == 1: + result.add(f"{left}*({right})") + elif (n - i) == 1: + result.add(f"({left})*{right}") + else: + result.add(f"({left})*({right})") + + return result +#print(product_orders(4)) + +def contains_perm_231(perm): + """ + Returns True if the given permutation contains the pattern 2-3-1, False otherwise. + + Parameters: + perm (list): A list representing a permutation. + + Returns: + bool: True if the permutation contains the pattern 2-3-1, False otherwise. + """ + n = len(perm) + + if n < 3: + return False + + for i in range(n - 2): + for j in range(i + 1, n - 1): + for k in range(j + 1, n): + if perm[i] < perm[j] and perm[k] < perm[i] and perm[k] < perm[j]: + return True + + return False + +def permutations_avoiding_231(n): + """ + Returns a list of permutations of length n avoiding the pattern 2-3-1. + + Parameters: + n (int): The length of the permutation. + + Returns: + A list of permutations of length n that do not contain the pattern 2-3-1. + + Example: + >>> permutations_avoiding_231(4) + {(1, 2, 3, 4), (1, 2, 4, 3), (1, 3, 2, 4), (1, 4, 2, 3), (1, 4, 3, 2), (2, 1, 3, 4), (2, 1, 4, 3), (3, 1, 2, 4), (3, 2, 1, 4), (4, 1, 2, 3), (4, 1, 3, 2), (4, 2, 1, 3), (4, 3, 1, 2), (4, 3, 2, 1)} + """ + if n < 3: + return set(itertools.permutations(range(1, n+1))) + + result = set() + for perm in itertools.permutations(range(1,n+1)): + if not contains_perm_231(perm): + result.add(perm) + + return result + +#print(permutations_avoiding_231(4)) + + +"I tried using your suggestions to improve the funcion, but the output ended up being" +"worse than what I initially had so I am submitting the code that I had emailed to you," +"the code produces the correct triangulations, but is missing " +"(1,4)(2,4) for n = 5 the code produces the correct triangulations for n = 4 though." +def triangulations(n): + """ + Returns a set of all possible triangulations of an n-sided polygon. A triangulation + is represented as a tuple of internal edges. Vertices are labeled 0 through n-1 clockwise. + + Parameters: + n (int): The number of sides of the polygon. + + Returns: + A set of tuple of pairs, where each pair represents an internal edge in the triangulation. + """ + if n < 3: + return set() + elif n == 3: + return {tuple()} + + def edges_intersect(e1, e2): + """ + Check if two edges (e1, e2) intersect. + Edges are tuples of vertex indices, e.g., (i, j). + """ + (a, b), (c, d) = e1, e2 + if a > b: + a, b = b, a + if c > d: + c, d = d, c + return (a < c < b and (d < a or d > b)) or (c < a < d and (b < c or b > d)) + + triangulations_set = set() + for i in range(n): + for j in range(i + 1, n): + if i + 1 == j or (i ==0 and j == n - 1): + continue + for t in triangulations(n - 1): + new_edges = ((i, j),) + t + valid = True + for k in range(len(new_edges)): + for l in range(k + 1, len(new_edges)): + if edges_intersect(new_edges[k], new_edges[l]) or new_edges[k] == new_edges[l]: + valid = False + break + if not valid: + break + if valid: + triangulations_set.add(new_edges) + return triangulations_set + +#print(triangulations(5)) + + +print(parenthesizations(3)) + +print(product_orders(4)) + +print(permutations_avoiding_231(4)) + +print(triangulations(5)) + + +import time +import matplotlib.pyplot as plt + +def measure_time(func, n_values): + times = [] + for n in n_values: + start_time = time.time() + func(n) + end_time = time.time() + times.append((n, end_time - start_time)) + return times + +def plot_time_graph(times_list, titles): + fig, axs = plt.subplots(2, 2, figsize=(12, 10)) + + for i, ax in enumerate(axs.flat): + n_values, time_values = zip(*times_list[i]) + ax.plot(n_values, time_values) + ax.set_xlabel('n') + ax.set_ylabel('Time (seconds)') + ax.set_title(titles[i]) + + plt.tight_layout() + plt.show() + +n_values = range(1, 11) + +# Measure the time it takes to generate the objects for each function +times_triangulations = measure_time(triangulations, n_values) +times_product_orders = measure_time(product_orders, n_values) +times_parenthesizations = measure_time(parenthesizations, n_values) +times_permutations_avoiding_231 = measure_time(permutations_avoiding_231, n_values) + +# List of times and titles for each function +times_list = [times_triangulations, times_product_orders, times_parenthesizations, times_permutations_avoiding_231] +titles = [ + 'Time required for triangulations', + 'Time required for product_orders', + 'Time required for parenthesizations', + 'Time required for permutations_avoiding_231' +] + +# Plot the time graph for each function + +plot_time_graph(times_list, titles) + + + + + From d2dc1b8326a42e7bdebb28615bf3dd571d223bd5 Mon Sep 17 00:00:00 2001 From: Pwelsh12 Date: Fri, 21 Jun 2024 22:49:50 -0700 Subject: [PATCH 2/2] [Submission] When I first turned worked on this assignment, I did not know that there were more instructions on the "main" page, I only followed the instructions on the "read me" page so I assumed we just needed to implement the code on the catalan.py file and create a graph on the catalan.py file. I went back and finished the main, which uploads the data to the "data" file and the graphs to the figures file. --- data/SYTs_2_2.txt | 2 + data/SYTs_3_3.txt | 5 + data/SYTs_4_3_2_1.txt | 768 ++ data/SYTs_4_4.txt | 14 + data/SYTs_5_5.txt | 42 + data/catalan_parenthesizations_1.txt | 1 + data/catalan_parenthesizations_10.txt | 16796 ++++++++++++++++++++++++ data/catalan_parenthesizations_2.txt | 2 + data/catalan_parenthesizations_3.txt | 5 + data/catalan_parenthesizations_4.txt | 14 + data/catalan_parenthesizations_5.txt | 42 + data/catalan_parenthesizations_6.txt | 132 + data/catalan_parenthesizations_7.txt | 429 + data/catalan_parenthesizations_8.txt | 1430 ++ data/catalan_parenthesizations_9.txt | 4862 +++++++ data/catalan_product_orders_10.txt | 4862 +++++++ data/catalan_product_orders_11.txt | 16796 ++++++++++++++++++++++++ data/catalan_product_orders_2.txt | 1 + data/catalan_product_orders_3.txt | 2 + data/catalan_product_orders_4.txt | 5 + data/catalan_product_orders_5.txt | 14 + data/catalan_product_orders_6.txt | 42 + data/catalan_product_orders_7.txt | 132 + data/catalan_product_orders_8.txt | 429 + data/catalan_product_orders_9.txt | 1430 ++ data/permutations_avoiding_231_1.txt | 1 + data/permutations_avoiding_231_10.txt | 16796 ++++++++++++++++++++++++ data/permutations_avoiding_231_2.txt | 2 + data/permutations_avoiding_231_3.txt | 5 + data/permutations_avoiding_231_4.txt | 14 + data/permutations_avoiding_231_5.txt | 42 + data/permutations_avoiding_231_6.txt | 132 + data/permutations_avoiding_231_7.txt | 429 + data/permutations_avoiding_231_8.txt | 1430 ++ data/permutations_avoiding_231_9.txt | 4862 +++++++ data/product_orders_1.txt | 1 + data/product_orders_10.txt | 4862 +++++++ data/product_orders_2.txt | 1 + data/product_orders_3.txt | 2 + data/product_orders_4.txt | 5 + data/product_orders_5.txt | 14 + data/product_orders_6.txt | 42 + data/product_orders_7.txt | 132 + data/product_orders_8.txt | 429 + data/product_orders_9.txt | 1430 ++ data/triangulations_10.txt | 128 + data/triangulations_3.txt | 1 + data/triangulations_4.txt | 2 + data/triangulations_5.txt | 4 + data/triangulations_6.txt | 8 + data/triangulations_7.txt | 16 + data/triangulations_8.txt | 32 + data/triangulations_9.txt | 64 + figures/catalan_parenthesizations.png | Bin 0 -> 29500 bytes figures/catalan_product_orders.png | Bin 0 -> 44049 bytes figures/permutations_avoiding_231.png | Bin 0 -> 27713 bytes figures/product_orders.png | Bin 0 -> 35075 bytes main.ipynb | 322 + 58 files changed, 79465 insertions(+) create mode 100644 data/SYTs_2_2.txt create mode 100644 data/SYTs_3_3.txt create mode 100644 data/SYTs_4_3_2_1.txt create mode 100644 data/SYTs_4_4.txt create mode 100644 data/SYTs_5_5.txt create mode 100644 data/catalan_parenthesizations_1.txt create mode 100644 data/catalan_parenthesizations_10.txt create mode 100644 data/catalan_parenthesizations_2.txt create mode 100644 data/catalan_parenthesizations_3.txt create mode 100644 data/catalan_parenthesizations_4.txt create mode 100644 data/catalan_parenthesizations_5.txt create mode 100644 data/catalan_parenthesizations_6.txt create mode 100644 data/catalan_parenthesizations_7.txt create mode 100644 data/catalan_parenthesizations_8.txt create mode 100644 data/catalan_parenthesizations_9.txt create mode 100644 data/catalan_product_orders_10.txt create mode 100644 data/catalan_product_orders_11.txt create mode 100644 data/catalan_product_orders_2.txt create mode 100644 data/catalan_product_orders_3.txt create mode 100644 data/catalan_product_orders_4.txt create mode 100644 data/catalan_product_orders_5.txt create mode 100644 data/catalan_product_orders_6.txt create mode 100644 data/catalan_product_orders_7.txt create mode 100644 data/catalan_product_orders_8.txt create mode 100644 data/catalan_product_orders_9.txt create mode 100644 data/permutations_avoiding_231_1.txt create mode 100644 data/permutations_avoiding_231_10.txt create mode 100644 data/permutations_avoiding_231_2.txt create mode 100644 data/permutations_avoiding_231_3.txt create mode 100644 data/permutations_avoiding_231_4.txt create mode 100644 data/permutations_avoiding_231_5.txt create mode 100644 data/permutations_avoiding_231_6.txt create mode 100644 data/permutations_avoiding_231_7.txt create mode 100644 data/permutations_avoiding_231_8.txt create mode 100644 data/permutations_avoiding_231_9.txt create mode 100644 data/product_orders_1.txt create mode 100644 data/product_orders_10.txt create mode 100644 data/product_orders_2.txt create mode 100644 data/product_orders_3.txt create mode 100644 data/product_orders_4.txt create mode 100644 data/product_orders_5.txt create mode 100644 data/product_orders_6.txt create mode 100644 data/product_orders_7.txt create mode 100644 data/product_orders_8.txt create mode 100644 data/product_orders_9.txt create mode 100644 data/triangulations_10.txt create mode 100644 data/triangulations_3.txt create mode 100644 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9, 7, 8) +(10, 1, 6, 2, 5, 4, 3, 7, 9, 8) +(2, 1, 8, 7, 3, 5, 4, 6, 10, 9) +(8, 7, 6, 2, 1, 3, 5, 4, 10, 9) +(10, 9, 8, 1, 2, 3, 6, 5, 4, 7) +(4, 3, 2, 1, 8, 5, 6, 7, 9, 10) +(2, 1, 3, 4, 8, 7, 6, 5, 9, 10) +(8, 3, 1, 2, 5, 4, 7, 6, 10, 9) +(7, 1, 6, 5, 4, 3, 2, 8, 10, 9) +(1, 9, 3, 2, 4, 8, 5, 7, 6, 10) +(5, 4, 2, 1, 3, 7, 6, 10, 9, 8) +(1, 10, 9, 5, 2, 4, 3, 6, 8, 7) +(1, 10, 2, 3, 7, 5, 4, 6, 9, 8) +(10, 2, 1, 3, 8, 7, 6, 5, 4, 9) +(1, 7, 2, 6, 5, 4, 3, 8, 10, 9) +(6, 5, 1, 3, 2, 4, 7, 10, 8, 9) +(10, 5, 1, 4, 2, 3, 6, 8, 7, 9) +(1, 10, 2, 9, 3, 4, 8, 7, 5, 6) +(1, 9, 4, 3, 2, 8, 7, 6, 5, 10) +(10, 8, 1, 2, 4, 3, 6, 5, 7, 9) +(1, 5, 4, 2, 3, 6, 8, 7, 10, 9) +(1, 10, 6, 2, 5, 3, 4, 8, 7, 9) +(10, 2, 1, 7, 5, 4, 3, 6, 9, 8) +(5, 4, 3, 2, 1, 9, 8, 7, 6, 10) +(1, 6, 5, 4, 2, 3, 8, 7, 10, 9) +(2, 1, 10, 8, 7, 3, 6, 4, 5, 9) +(1, 2, 9, 6, 4, 3, 5, 8, 7, 10) +(4, 3, 2, 1, 10, 6, 5, 8, 7, 9) +(1, 2, 3, 7, 4, 6, 5, 9, 8, 10) +(10, 1, 2, 3, 9, 4, 8, 5, 6, 7) +(8, 7, 4, 2, 1, 3, 5, 6, 9, 10) +(6, 3, 1, 2, 5, 4, 8, 7, 9, 10) +(1, 8, 4, 3, 2, 6, 5, 7, 9, 10) +(10, 4, 3, 2, 1, 5, 6, 7, 8, 9) +(10, 9, 6, 2, 1, 3, 4, 5, 8, 7) +(1, 10, 9, 6, 5, 4, 3, 2, 8, 7) +(1, 2, 4, 3, 10, 5, 9, 8, 6, 7) +(4, 3, 1, 2, 10, 8, 7, 6, 5, 9) +(10, 9, 1, 2, 3, 8, 4, 7, 6, 5) +(4, 1, 2, 3, 6, 5, 7, 9, 8, 10) +(6, 5, 1, 3, 2, 4, 10, 9, 7, 8) +(10, 4, 1, 2, 3, 5, 7, 6, 8, 9) +(1, 2, 3, 7, 4, 5, 6, 10, 8, 9) diff --git a/data/permutations_avoiding_231_2.txt b/data/permutations_avoiding_231_2.txt new file mode 100644 index 0000000..d7b653c --- /dev/null +++ b/data/permutations_avoiding_231_2.txt @@ -0,0 +1,2 @@ +(1, 2) +(2, 1) diff --git a/data/permutations_avoiding_231_3.txt b/data/permutations_avoiding_231_3.txt new file mode 100644 index 0000000..bc1d793 --- /dev/null +++ b/data/permutations_avoiding_231_3.txt @@ -0,0 +1,5 @@ +(1, 3, 2) +(1, 2, 3) +(2, 1, 3) +(3, 2, 1) +(3, 1, 2) diff --git a/data/permutations_avoiding_231_4.txt b/data/permutations_avoiding_231_4.txt new file mode 100644 index 0000000..21dd8d1 --- /dev/null +++ b/data/permutations_avoiding_231_4.txt @@ -0,0 +1,14 @@ +(1, 4, 2, 3) +(4, 2, 1, 3) +(2, 1, 3, 4) +(1, 3, 2, 4) +(4, 3, 1, 2) +(1, 2, 3, 4) +(1, 2, 4, 3) +(3, 1, 2, 4) +(2, 1, 4, 3) +(4, 1, 2, 3) +(4, 3, 2, 1) +(1, 4, 3, 2) +(3, 2, 1, 4) +(4, 1, 3, 2) diff --git a/data/permutations_avoiding_231_5.txt b/data/permutations_avoiding_231_5.txt new file mode 100644 index 0000000..7de0508 --- /dev/null +++ b/data/permutations_avoiding_231_5.txt @@ -0,0 +1,42 @@ +(1, 5, 4, 2, 3) +(5, 4, 1, 3, 2) +(5, 1, 2, 4, 3) +(1, 5, 2, 3, 4) +(2, 1, 5, 3, 4) +(5, 1, 2, 3, 4) +(5, 3, 1, 2, 4) +(2, 1, 4, 3, 5) +(1, 5, 3, 2, 4) +(5, 4, 1, 2, 3) +(5, 4, 2, 1, 3) +(5, 4, 3, 2, 1) +(1, 2, 3, 5, 4) +(5, 1, 4, 3, 2) +(1, 2, 3, 4, 5) +(5, 3, 2, 1, 4) +(1, 4, 3, 2, 5) +(4, 3, 1, 2, 5) +(5, 1, 4, 2, 3) +(2, 1, 3, 5, 4) +(5, 2, 1, 4, 3) +(4, 1, 2, 3, 5) +(2, 1, 3, 4, 5) +(5, 1, 3, 2, 4) +(1, 3, 2, 4, 5) +(1, 3, 2, 5, 4) +(4, 3, 2, 1, 5) +(3, 1, 2, 5, 4) +(4, 1, 3, 2, 5) +(5, 4, 3, 1, 2) +(1, 2, 4, 3, 5) +(3, 1, 2, 4, 5) +(1, 4, 2, 3, 5) +(1, 5, 2, 4, 3) +(1, 5, 4, 3, 2) +(2, 1, 5, 4, 3) +(3, 2, 1, 4, 5) +(3, 2, 1, 5, 4) +(4, 2, 1, 3, 5) +(5, 2, 1, 3, 4) +(1, 2, 5, 3, 4) +(1, 2, 5, 4, 3) diff --git a/data/permutations_avoiding_231_6.txt b/data/permutations_avoiding_231_6.txt new file mode 100644 index 0000000..bdce9fc --- /dev/null +++ b/data/permutations_avoiding_231_6.txt @@ -0,0 +1,132 @@ +(1, 3, 2, 6, 4, 5) +(1, 3, 2, 6, 5, 4) +(5, 4, 1, 3, 2, 6) +(6, 5, 3, 2, 1, 4) +(1, 4, 3, 2, 6, 5) +(1, 5, 4, 2, 3, 6) +(6, 1, 2, 3, 5, 4) +(2, 1, 5, 3, 4, 6) +(1, 5, 4, 3, 2, 6) +(6, 5, 1, 4, 3, 2) +(6, 2, 1, 3, 5, 4) +(6, 5, 1, 3, 2, 4) +(6, 5, 4, 1, 3, 2) +(1, 5, 2, 4, 3, 6) +(1, 2, 6, 5, 3, 4) +(6, 1, 4, 3, 2, 5) +(6, 5, 2, 1, 4, 3) +(1, 5, 3, 2, 4, 6) +(1, 3, 2, 4, 6, 5) +(6, 5, 4, 1, 2, 3) +(1, 2, 4, 3, 6, 5) +(5, 4, 3, 1, 2, 6) +(6, 1, 5, 3, 2, 4) +(4, 1, 2, 3, 5, 6) +(1, 3, 2, 4, 5, 6) +(2, 1, 6, 5, 4, 3) +(3, 2, 1, 6, 5, 4) +(4, 1, 2, 3, 6, 5) +(1, 2, 3, 4, 6, 5) +(3, 1, 2, 6, 4, 5) +(6, 2, 1, 5, 4, 3) +(6, 5, 3, 1, 2, 4) +(1, 2, 3, 4, 5, 6) +(1, 6, 5, 4, 3, 2) +(4, 2, 1, 3, 6, 5) +(6, 2, 1, 5, 3, 4) +(1, 6, 3, 2, 5, 4) +(5, 1, 4, 2, 3, 6) +(6, 1, 3, 2, 5, 4) +(1, 5, 2, 3, 4, 6) +(2, 1, 3, 6, 5, 4) +(6, 5, 4, 2, 1, 3) +(6, 1, 3, 2, 4, 5) +(6, 5, 4, 3, 2, 1) +(1, 2, 6, 5, 4, 3) +(4, 1, 3, 2, 6, 5) +(1, 2, 3, 6, 4, 5) +(1, 6, 4, 2, 3, 5) +(2, 1, 3, 6, 4, 5) +(6, 1, 5, 2, 4, 3) +(6, 2, 1, 3, 4, 5) +(6, 1, 2, 3, 4, 5) +(1, 6, 2, 5, 3, 4) +(6, 1, 4, 2, 3, 5) +(1, 6, 2, 5, 4, 3) +(4, 1, 3, 2, 5, 6) +(5, 1, 2, 3, 4, 6) +(4, 3, 1, 2, 6, 5) +(3, 1, 2, 5, 4, 6) +(2, 1, 6, 5, 3, 4) +(3, 2, 1, 6, 4, 5) +(6, 4, 3, 1, 2, 5) +(1, 6, 2, 3, 4, 5) +(1, 6, 2, 3, 5, 4) +(2, 1, 3, 4, 5, 6) +(2, 1, 3, 4, 6, 5) +(4, 3, 1, 2, 5, 6) +(5, 2, 1, 3, 4, 6) +(6, 1, 5, 4, 3, 2) +(5, 4, 1, 2, 3, 6) +(1, 2, 6, 3, 4, 5) +(6, 4, 1, 3, 2, 5) +(5, 4, 3, 2, 1, 6) +(6, 1, 2, 4, 3, 5) +(6, 1, 5, 4, 2, 3) +(1, 3, 2, 5, 4, 6) +(6, 3, 1, 2, 5, 4) +(5, 1, 2, 4, 3, 6) +(3, 2, 1, 4, 6, 5) +(6, 3, 1, 2, 4, 5) +(1, 6, 3, 2, 4, 5) +(6, 5, 4, 3, 1, 2) +(3, 2, 1, 4, 5, 6) +(1, 6, 5, 2, 4, 3) +(1, 2, 5, 3, 4, 6) +(3, 1, 2, 4, 6, 5) +(5, 3, 2, 1, 4, 6) +(5, 2, 1, 4, 3, 6) +(6, 4, 2, 1, 3, 5) +(1, 6, 5, 2, 3, 4) +(5, 1, 3, 2, 4, 6) +(6, 4, 1, 2, 3, 5) +(6, 5, 1, 2, 4, 3) +(1, 6, 4, 3, 2, 5) +(6, 5, 1, 2, 3, 4) +(2, 1, 4, 3, 5, 6) +(2, 1, 6, 4, 3, 5) +(5, 1, 4, 3, 2, 6) +(1, 2, 6, 4, 3, 5) +(1, 6, 5, 4, 2, 3) +(4, 2, 1, 3, 5, 6) +(1, 2, 3, 6, 5, 4) +(6, 3, 2, 1, 4, 5) +(1, 4, 3, 2, 5, 6) +(6, 3, 2, 1, 5, 4) +(5, 4, 2, 1, 3, 6) +(2, 1, 3, 5, 4, 6) +(6, 5, 1, 4, 2, 3) +(2, 1, 5, 4, 3, 6) +(1, 6, 2, 4, 3, 5) +(6, 2, 1, 4, 3, 5) +(6, 1, 5, 2, 3, 4) +(6, 5, 2, 1, 3, 4) +(3, 1, 2, 6, 5, 4) +(5, 3, 1, 2, 4, 6) +(6, 4, 3, 2, 1, 5) +(1, 2, 4, 3, 5, 6) +(2, 1, 6, 3, 5, 4) +(3, 1, 2, 4, 5, 6) +(3, 2, 1, 5, 4, 6) +(1, 2, 6, 3, 5, 4) +(6, 1, 2, 5, 4, 3) +(1, 2, 5, 4, 3, 6) +(4, 3, 2, 1, 5, 6) +(2, 1, 4, 3, 6, 5) +(4, 3, 2, 1, 6, 5) +(2, 1, 6, 3, 4, 5) +(1, 2, 3, 5, 4, 6) +(1, 4, 2, 3, 5, 6) +(1, 4, 2, 3, 6, 5) +(6, 1, 2, 5, 3, 4) +(1, 6, 5, 3, 2, 4) diff --git a/data/permutations_avoiding_231_7.txt b/data/permutations_avoiding_231_7.txt new file mode 100644 index 0000000..5760bd9 --- /dev/null +++ b/data/permutations_avoiding_231_7.txt @@ -0,0 +1,429 @@ +(5, 2, 1, 4, 3, 6, 7) +(2, 1, 7, 3, 4, 5, 6) +(1, 2, 3, 7, 5, 4, 6) +(1, 7, 2, 6, 3, 5, 4) +(1, 2, 6, 5, 4, 3, 7) +(4, 1, 3, 2, 5, 6, 7) +(1, 2, 7, 4, 3, 5, 6) +(3, 2, 1, 4, 5, 7, 6) +(1, 6, 3, 2, 4, 5, 7) +(7, 2, 1, 6, 4, 3, 5) +(2, 1, 6, 5, 4, 3, 7) +(1, 7, 6, 5, 2, 4, 3) +(1, 2, 4, 3, 5, 7, 6) +(1, 2, 4, 3, 7, 5, 6) +(6, 5, 1, 3, 2, 4, 7) +(7, 4, 3, 2, 1, 5, 6) +(1, 2, 3, 7, 6, 4, 5) +(1, 2, 5, 4, 3, 6, 7) +(5, 4, 1, 3, 2, 6, 7) +(7, 5, 1, 2, 3, 4, 6) +(4, 3, 2, 1, 7, 5, 6) +(6, 3, 1, 2, 4, 5, 7) +(5, 4, 3, 2, 1, 6, 7) +(1, 4, 3, 2, 7, 5, 6) +(1, 7, 2, 5, 4, 3, 6) +(2, 1, 3, 7, 6, 5, 4) +(6, 4, 1, 2, 3, 5, 7) +(2, 1, 7, 4, 3, 5, 6) +(1, 3, 2, 6, 4, 5, 7) +(7, 6, 5, 4, 2, 1, 3) +(6, 5, 1, 2, 4, 3, 7) +(2, 1, 4, 3, 5, 6, 7) +(7, 5, 1, 4, 3, 2, 6) +(3, 1, 2, 4, 5, 7, 6) +(7, 1, 3, 2, 5, 4, 6) +(2, 1, 4, 3, 6, 5, 7) +(7, 1, 3, 2, 6, 5, 4) +(7, 1, 5, 2, 3, 4, 6) +(3, 1, 2, 7, 6, 4, 5) +(2, 1, 4, 3, 7, 6, 5) +(5, 4, 1, 2, 3, 7, 6) +(7, 6, 1, 5, 2, 4, 3) +(7, 6, 3, 1, 2, 4, 5) +(7, 6, 5, 4, 3, 1, 2) +(1, 2, 3, 6, 4, 5, 7) +(2, 1, 7, 3, 5, 4, 6) +(7, 1, 2, 6, 4, 3, 5) +(7, 6, 1, 3, 2, 4, 5) +(1, 4, 2, 3, 6, 5, 7) +(6, 5, 1, 2, 3, 4, 7) +(5, 1, 4, 2, 3, 7, 6) +(1, 7, 4, 3, 2, 5, 6) +(1, 6, 5, 4, 2, 3, 7) +(7, 6, 5, 3, 1, 2, 4) +(7, 6, 1, 4, 2, 3, 5) +(5, 3, 2, 1, 4, 7, 6) +(2, 1, 7, 6, 5, 4, 3) +(3, 1, 2, 4, 7, 5, 6) +(4, 3, 1, 2, 7, 6, 5) +(1, 2, 7, 5, 4, 3, 6) +(6, 1, 3, 2, 5, 4, 7) +(6, 3, 2, 1, 5, 4, 7) +(7, 4, 1, 2, 3, 5, 6) +(1, 7, 6, 2, 4, 3, 5) +(1, 7, 6, 2, 5, 4, 3) +(6, 5, 3, 2, 1, 4, 7) +(4, 1, 2, 3, 7, 5, 6) +(7, 5, 2, 1, 4, 3, 6) +(7, 6, 5, 1, 2, 4, 3) +(1, 6, 5, 2, 4, 3, 7) +(7, 1, 2, 5, 4, 3, 6) +(7, 3, 2, 1, 4, 6, 5) +(2, 1, 3, 4, 6, 5, 7) +(7, 4, 1, 3, 2, 6, 5) +(2, 1, 7, 6, 4, 3, 5) +(1, 5, 4, 3, 2, 7, 6) +(1, 2, 3, 7, 4, 5, 6) +(4, 3, 1, 2, 6, 5, 7) +(1, 7, 6, 2, 3, 4, 5) +(6, 1, 2, 5, 4, 3, 7) +(2, 1, 3, 4, 7, 5, 6) +(6, 4, 3, 1, 2, 5, 7) +(1, 7, 2, 6, 5, 3, 4) +(7, 1, 2, 6, 5, 4, 3) +(7, 2, 1, 6, 3, 4, 5) +(7, 1, 6, 5, 2, 4, 3) +(4, 2, 1, 3, 7, 5, 6) +(2, 1, 3, 7, 4, 6, 5) +(5, 4, 3, 1, 2, 6, 7) +(7, 1, 6, 5, 4, 3, 2) +(7, 2, 1, 6, 5, 4, 3) +(1, 6, 5, 2, 3, 4, 7) +(7, 6, 1, 2, 3, 5, 4) +(1, 6, 2, 4, 3, 5, 7) +(6, 1, 4, 2, 3, 5, 7) +(7, 1, 3, 2, 4, 6, 5) +(1, 3, 2, 7, 4, 5, 6) +(3, 2, 1, 4, 6, 5, 7) +(6, 1, 5, 4, 3, 2, 7) +(1, 7, 6, 5, 2, 3, 4) +(1, 7, 2, 4, 3, 6, 5) +(7, 6, 5, 4, 1, 2, 3) +(1, 2, 4, 3, 5, 6, 7) +(3, 2, 1, 4, 7, 6, 5) +(7, 5, 1, 4, 2, 3, 6) +(1, 7, 6, 3, 2, 4, 5) +(1, 7, 5, 2, 3, 4, 6) +(5, 2, 1, 3, 4, 7, 6) +(7, 6, 5, 2, 1, 3, 4) +(1, 2, 4, 3, 6, 5, 7) +(3, 2, 1, 7, 6, 5, 4) +(1, 6, 3, 2, 5, 4, 7) +(2, 1, 6, 5, 3, 4, 7) +(6, 5, 2, 1, 4, 3, 7) +(7, 5, 4, 1, 2, 3, 6) +(2, 1, 3, 7, 6, 4, 5) +(1, 7, 6, 5, 4, 2, 3) +(6, 1, 5, 2, 3, 4, 7) +(6, 5, 4, 3, 2, 1, 7) +(3, 2, 1, 4, 5, 6, 7) +(7, 6, 2, 1, 5, 4, 3) +(1, 4, 2, 3, 5, 6, 7) +(7, 6, 1, 4, 3, 2, 5) +(7, 3, 2, 1, 6, 5, 4) +(2, 1, 5, 4, 3, 6, 7) +(7, 3, 1, 2, 4, 6, 5) +(7, 6, 4, 1, 3, 2, 5) +(3, 1, 2, 7, 4, 6, 5) +(6, 1, 2, 4, 3, 5, 7) +(1, 2, 7, 5, 3, 4, 6) +(6, 3, 2, 1, 4, 5, 7) +(3, 1, 2, 5, 4, 7, 6) +(7, 1, 6, 3, 2, 5, 4) +(1, 3, 2, 4, 5, 7, 6) +(6, 5, 2, 1, 3, 4, 7) +(5, 4, 2, 1, 3, 6, 7) +(2, 1, 7, 6, 3, 5, 4) +(1, 2, 6, 4, 3, 5, 7) +(1, 5, 2, 4, 3, 7, 6) +(3, 1, 2, 4, 5, 6, 7) +(7, 1, 6, 2, 3, 4, 5) +(4, 3, 1, 2, 5, 7, 6) +(7, 1, 6, 5, 3, 2, 4) +(7, 1, 2, 5, 3, 4, 6) +(1, 2, 6, 5, 3, 4, 7) +(2, 1, 3, 4, 5, 6, 7) +(7, 1, 2, 6, 3, 5, 4) +(1, 6, 4, 2, 3, 5, 7) +(7, 1, 2, 4, 3, 6, 5) +(7, 6, 1, 2, 4, 3, 5) +(1, 2, 3, 5, 4, 6, 7) +(1, 7, 3, 2, 4, 6, 5) +(5, 1, 4, 3, 2, 7, 6) +(2, 1, 3, 6, 5, 4, 7) +(6, 1, 5, 4, 2, 3, 7) +(5, 3, 1, 2, 4, 7, 6) +(1, 3, 2, 7, 6, 4, 5) +(6, 5, 3, 1, 2, 4, 7) +(7, 6, 5, 1, 3, 2, 4) +(7, 4, 1, 3, 2, 5, 6) +(2, 1, 7, 5, 4, 3, 6) +(2, 1, 6, 4, 3, 5, 7) +(7, 6, 5, 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+(1, 2, 3, 6, 4, 5, 8, 7) +(6, 1, 2, 5, 4, 3, 7, 8) +(3, 1, 2, 4, 7, 6, 5, 8) +(7, 5, 1, 4, 2, 3, 6, 8) +(1, 8, 3, 2, 4, 7, 6, 5) +(7, 5, 3, 1, 2, 4, 6, 8) +(1, 2, 7, 5, 3, 4, 6, 8) +(1, 8, 7, 2, 6, 4, 3, 5) +(1, 2, 3, 4, 8, 5, 7, 6) +(1, 7, 5, 4, 2, 3, 6, 8) +(8, 6, 1, 5, 2, 4, 3, 7) +(1, 6, 5, 4, 3, 2, 8, 7) +(1, 8, 2, 3, 7, 4, 5, 6) +(7, 6, 4, 2, 1, 3, 5, 8) +(8, 7, 5, 4, 3, 1, 2, 6) +(1, 6, 5, 3, 2, 4, 7, 8) +(8, 1, 6, 2, 3, 4, 5, 7) +(1, 7, 6, 5, 4, 2, 3, 8) +(8, 2, 1, 6, 5, 4, 3, 7) +(2, 1, 8, 5, 4, 3, 7, 6) +(1, 3, 2, 4, 5, 8, 7, 6) diff --git a/data/permutations_avoiding_231_9.txt b/data/permutations_avoiding_231_9.txt new file mode 100644 index 0000000..cee962e --- /dev/null +++ b/data/permutations_avoiding_231_9.txt @@ -0,0 +1,4862 @@ +(9, 1, 5, 4, 2, 3, 7, 6, 8) +(1, 2, 3, 4, 6, 5, 7, 9, 8) +(9, 8, 7, 6, 1, 4, 2, 3, 5) +(6, 2, 1, 4, 3, 5, 7, 8, 9) +(3, 1, 2, 5, 4, 9, 6, 8, 7) +(9, 8, 3, 1, 2, 7, 6, 4, 5) +(8, 1, 2, 6, 4, 3, 5, 7, 9) +(8, 7, 6, 1, 5, 3, 2, 4, 9) +(2, 1, 8, 4, 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2, 3, 8, 7, 6) +(1, 2, 3, 4, 9, 8, 5, 7, 6) +(1, 2, 8, 3, 7, 4, 6, 5, 9) +(9, 8, 1, 5, 4, 3, 2, 6, 7) +(9, 8, 3, 2, 1, 7, 6, 5, 4) +(9, 8, 5, 2, 1, 3, 4, 7, 6) +(2, 1, 3, 4, 5, 9, 8, 6, 7) +(9, 8, 7, 6, 5, 2, 1, 3, 4) +(4, 3, 1, 2, 9, 7, 5, 6, 8) +(9, 1, 2, 8, 6, 4, 3, 5, 7) +(9, 8, 7, 6, 3, 1, 2, 5, 4) +(4, 1, 3, 2, 8, 6, 5, 7, 9) +(2, 1, 3, 9, 8, 7, 6, 4, 5) +(6, 5, 4, 1, 3, 2, 8, 7, 9) +(9, 7, 3, 1, 2, 4, 5, 6, 8) +(9, 1, 7, 6, 4, 3, 2, 5, 8) +(3, 2, 1, 9, 8, 7, 5, 4, 6) +(7, 6, 1, 5, 4, 2, 3, 9, 8) +(8, 2, 1, 7, 3, 4, 5, 6, 9) +(2, 1, 9, 4, 3, 8, 5, 7, 6) +(9, 7, 4, 3, 1, 2, 5, 6, 8) +(6, 1, 2, 3, 4, 5, 9, 7, 8) +(4, 1, 3, 2, 9, 5, 7, 6, 8) +(1, 9, 3, 2, 4, 7, 6, 5, 8) diff --git a/data/product_orders_1.txt b/data/product_orders_1.txt new file mode 100644 index 0000000..81a3f76 --- /dev/null +++ b/data/product_orders_1.txt @@ -0,0 +1 @@ +? diff --git a/data/product_orders_10.txt b/data/product_orders_10.txt new file mode 100644 index 0000000..928fcf2 --- /dev/null +++ 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a/data/triangulations_3.txt b/data/triangulations_3.txt new file mode 100644 index 0000000..ec969b5 --- /dev/null +++ b/data/triangulations_3.txt @@ -0,0 +1 @@ +() diff --git a/data/triangulations_4.txt b/data/triangulations_4.txt new file mode 100644 index 0000000..e761f5a --- /dev/null +++ b/data/triangulations_4.txt @@ -0,0 +1,2 @@ +((1, 3),) +((0, 2),) diff --git a/data/triangulations_5.txt b/data/triangulations_5.txt new file mode 100644 index 0000000..87d2241 --- /dev/null +++ b/data/triangulations_5.txt @@ -0,0 +1,4 @@ +((0, 3), (1, 3)) +((0, 3), (0, 2)) +((1, 4), (1, 3)) +((2, 4), (0, 2)) diff --git a/data/triangulations_6.txt b/data/triangulations_6.txt new file mode 100644 index 0000000..0b78f8f --- /dev/null +++ b/data/triangulations_6.txt @@ -0,0 +1,8 @@ +((3, 5), (0, 3), (1, 3)) +((0, 4), (0, 3), (0, 2)) +((3, 5), (0, 3), (0, 2)) +((0, 4), (2, 4), (0, 2)) +((1, 5), (1, 4), (1, 3)) +((0, 4), (1, 4), (1, 3)) +((0, 4), (0, 3), (1, 3)) +((2, 5), (2, 4), (0, 2)) diff --git a/data/triangulations_7.txt b/data/triangulations_7.txt new file mode 100644 index 0000000..eae7b51 --- /dev/null +++ b/data/triangulations_7.txt @@ -0,0 +1,16 @@ +((0, 5), (1, 5), (1, 4), (1, 3)) +((0, 5), (0, 4), (0, 3), (1, 3)) +((0, 5), (0, 4), (2, 4), (0, 2)) +((2, 6), (2, 5), (2, 4), (0, 2)) +((4, 6), (0, 4), (1, 4), (1, 3)) +((3, 6), (3, 5), (0, 3), (0, 2)) +((4, 6), (0, 4), (0, 3), (1, 3)) +((0, 5), (2, 5), (2, 4), (0, 2)) +((0, 5), (0, 4), (0, 3), (0, 2)) +((4, 6), (0, 4), (2, 4), (0, 2)) +((0, 5), (3, 5), (0, 3), (1, 3)) +((4, 6), (0, 4), (0, 3), (0, 2)) +((0, 5), (3, 5), (0, 3), (0, 2)) +((1, 6), (1, 5), (1, 4), (1, 3)) +((3, 6), (3, 5), (0, 3), (1, 3)) +((0, 5), (0, 4), (1, 4), (1, 3)) diff --git a/data/triangulations_8.txt b/data/triangulations_8.txt new file mode 100644 index 0000000..fc8805c --- /dev/null +++ b/data/triangulations_8.txt @@ -0,0 +1,32 @@ +((0, 6), (4, 6), (0, 4), (0, 3), (1, 3)) +((0, 6), (0, 5), (0, 4), (2, 4), (0, 2)) +((0, 6), (2, 6), (2, 5), (2, 4), 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'(?*?)*(?*?)', '(?*(?*?))*?', '?*(?*(?*?))', '?*((?*?)*?)'}\n", + "{(1, 4, 2, 3), (4, 2, 1, 3), (2, 1, 3, 4), (1, 3, 2, 4), (4, 3, 1, 2), (1, 2, 3, 4), (1, 2, 4, 3), (3, 1, 2, 4), (2, 1, 4, 3), (4, 1, 2, 3), (4, 3, 2, 1), (1, 4, 3, 2), (3, 2, 1, 4), (4, 1, 3, 2)}\n", + "{((0, 3), (1, 3)), ((0, 3), (0, 2)), ((1, 4), (1, 3)), ((2, 4), (0, 2))}\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "

" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import catalan\n", + "import os\n", + "import time\n", + "import matplotlib.pyplot as plt\n", + "dirname = os.path.dirname(\"./\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Generate Parenthesizations\n", + "\n", + "Generate all possible parenthesizations of length $n$ for $1 \\le n \\le 10$. Files should be outputted to `data/catalan_parenthesizations_n.txt` and a plot of the time used to generate each data file should go in `figures/catalan_parenthesizations.png`." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import time\n", + "timing_results = []\n", + "\n", + "data_dir = 'data'\n", + "figures_dir = 'figures'\n", + "\n", + "os.makedirs(data_dir, exist_ok=True)\n", + "os.makedirs(figures_dir, exist_ok=True)\n", + "\n", + "for n in range(1, 11):\n", + " start_time = time.time()\n", + " parenthesizations = catalan.parenthesizations(n)\n", + " end_time = time.time()\n", + " duration = end_time - start_time\n", + " timing_results.append((n, duration))\n", + "\n", + " # Save parenthesizations to file\n", + " with open(os.path.join(data_dir, f'catalan_parenthesizations_{n}.txt'), 'w') as file:\n", + " for p in parenthesizations:\n", + " file.write(f'{p}\\n')\n", + "\n", + "# Plotting the timing results\n", + "ns = [result[0] for result in timing_results]\n", + "durations = [result[1] for result in timing_results]\n", + "\n", + "plt.figure(figsize=(10, 6))\n", + "plt.plot(ns, durations, marker='o', linestyle='-', color='b')\n", + "plt.title('Time to Generate Parenthesizations')\n", + "plt.xlabel('n')\n", + "plt.ylabel('Time (seconds)')\n", + "plt.grid(True)\n", + "plt.savefig(os.path.join(figures_dir, 'catalan_parenthesizations.png'))\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Generate Product Orders\n", + "\n", + "Generate all possible product orders of $n$ elements for $2 \\le n \\le 11$. Files should be outputted to `data/catalan_product_orders_n.txt` and a plot of the time used to generate each data file should go in `figures/catalan_product_orders.png`." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "# Create necessary directories\n", + "data_dir = 'data'\n", + "figures_dir = 'figures'\n", + "\n", + "os.makedirs(data_dir, exist_ok=True)\n", + "os.makedirs(figures_dir, exist_ok=True)\n", + "\n", + "\n", + "# Main script\n", + "timing_results_product_orders = []\n", + "\n", + "# Generate product orders\n", + "for n in range(2, 11):\n", + " start_time = time.time()\n", + " orders = catalan.product_orders(n)\n", + " end_time = time.time()\n", + " duration = end_time - start_time\n", + " timing_results_product_orders.append((n, duration))\n", + "\n", + " # Save product orders to file\n", + " with open(os.path.join(data_dir, f'product_orders_{n}.txt'), 'w') as file:\n", + " for order in orders:\n", + " file.write(f'{order}\\n')\n", + "\n", + "# Plotting the timing results\n", + "ns = [result[0] for result in timing_results_product_orders]\n", + "durations_product_orders = [result[1] for result in timing_results_product_orders]\n", + "\n", + "plt.figure(figsize=(10, 6))\n", + "\n", + "plt.plot(ns, durations_product_orders, marker='o', linestyle='-', color='r', label='Product Orders')\n", + "plt.title('Time to Generate Product Orders')\n", + "plt.xlabel('n')\n", + "plt.ylabel('Time (seconds)')\n", + "plt.grid(True)\n", + "plt.legend()\n", + "\n", + "plt.savefig(os.path.join(figures_dir, 'product_orders.png'))\n", + "plt.show()\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Generate 231 Avoiding Permutations\n", + "\n", + "Generate all possible 231 avoiding permutations on $n$ elements for $1 \\le n \\le 10$. Files should be outputted to `data/catalan_permutations_n.txt` and a plot of the time used to generate each data file should go in `figures/catalan_permutations.png`." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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y/eLx0Ucf6eLFizp16pRT44iDBw/KMAy9/PLLevnllzN93vj4eJUpU8Zx+/pjVrRoUUk5PzY+Pj4qW7Zshv2OHDmiV155RT/++GOG82uy86X8wIEDSkhIUERERKb3x8fH3/Q5JGnu3LkKCwuTr6+vypYt6/Tl09XXqFSpUpav48pYtNlsSkhIcCx9yg1r167Vq6++qt9//z3DOTEJCQlOfyzIjqzGsiTVrFkzw8n0AQEBGZZqFS1a1OmzHzRokL799lvdc889KlOmjNq3b68ePXqoY8eON63nq6++UnBwsCpXrqyDBw86XrNixYqaOXOmOnXqJOnqkrgJEyboxx9/1MMPP6ykpCQtWLBAAwYMcIT/W/k9PXz4sCIjIzP8sSKz45SV68eK5Hys4uPjdfnyZVWtWjXDfpltu5nVq1friSeeUIcOHfTGG29kuk9YWJjatm0rSXrggQc0a9YsPfDAA9qyZYsaNGjg8msCuDWEIAA3ZF/fn93txn/bMNtsNklXz33J7ERfMzo6hYeHKzIyUrt27cpwn32G6/rrEtnfx8iRI7Ocobj+S1NuHxt/f/8M3eqsVqvatWunc+fO6YUXXlDNmjUVHBysY8eOqV+/fo7XuBGbzaaIiAjNnDkz0/uze25Eq1atMj0HIievcaNOcDkdi1md5H59Q4EbOXTokNq0aaOaNWvq/fffV7ly5eTn56cFCxbo3//+d7aO963K6n1eKyIiQtu2bdOiRYv066+/6tdff9W0adPUp08fzZgxI8vHGYahr7/+WpcuXVLt2rUz3B8fH6+kpCSFhIToH//4hypWrKhvv/1WDz/8sH766SddvnxZDz300C29v9x0szGRm7Zv3677779fdevW1Zw5c7L9b1vXrl316KOPavbs2YQgwASEIAB5wj4bEBER4fjrpyuy+uJqv3bPvn37VLlyZcf21NRUxcXF3fS1OnXqpE8//VQbNmzI1gnJ9tfw9fXN0fvIzK0eG0nauXOn9u/frxkzZqhPnz6O7Zktg8rqWFapUkVLly5VixYt8qwNdX68xs3YZ+Ku7y6W2WxEVsfqp59+UkpKin788UenWYbMlgxm99pI147l62cF9+3bl+PrVPn5+alz587q3LmzbDabBg0apI8++kgvv/xylrMcK1eu1N9//63XXnvN0YDE7vz583rqqaf0/fffO2ZJe/TooYkTJyoxMVHffPONKlas6GjzfP17c/X31N6+3h667Pbt2+f6wchCRESEAgICHDNe18psW1YOHTqkjh07KiIiQgsWLMh0qW1WUlJSHDOWAPIf5wQByBMdOnRQWFiY3nzzTaWlpWW4P7OW0deyXwfn+i+ubdu2lZ+fnyZNmuT0V93PPvtMCQkJjiU7WXn++ecVFBSkxx9/XKdOncpw//V/KY6IiFDr1q310Ucf6cSJEy6/j8zc6rGR/veX7mvrNQwj01bIWR3LHj16yGq16vXXX8/wGHsnq1uVH69xM2FhYSpRooRWrVrltH3KlCkZ9s3qWGV2vBMSEjRt2rRMnyM77ys6OloRERH68MMPnVp6//rrr9q7d+9Nx3Jmzp4963Tby8tL9evXlySn17iefSncc889p27dujn99O/fX9WqVXOazXvooYeUkpKiGTNmaOHCherRo4fT893K7+m9996r9PR0p/bjVqtVH3zwQfYOQjZ4e3urbdu2+v7773X8+HHH9oMHD+rXX3/N1nOcPHlS7du3l5eXlxYtWpTlzOmFCxcy/T3/9NNPJV0dBwDyHzNBAPJEWFiYpk6dqkcffVSNGzdWz549VbJkSR05ckS//PKLWrRoodjY2Cwf37BhQ3l7e2v8+PFKSEiQv7+/4xotL774osaMGaOOHTvq/vvv1759+zRlyhQ1bdr0pheCrVatmmbNmqVevXqpRo0a6t27txo0aCDDMBQXF6dZs2bJy8vL6RycyZMn64477lC9evXUv39/Va5cWadOndLvv/+uv//+W9u3b8/XYyNdPWfEfrHFY8eOKSwsTHPnzs30+j5NmjSRJA0dOlQdOnSQt7e3evbsqTvvvFMDBgzQuHHjtG3bNrVv316+vr46cOCAvvvuO02cOFHdunVz6b1dLz9eIzuefPJJvfXWW3ryyScVHR2tVatWaf/+/Rn2sx+rl156ST179pSvr686d+6s9u3bO2ZYBgwYoKSkJH3yySeKiIjIEI6bNGmiqVOnauzYsapataoiIiIyPf/L19dX48eP12OPPaY777xTvXr1crTIrlixooYPH56j93nu3DndfffdKlu2rA4fPqwPPvhADRs2zDDDY5eSkqK5c+eqXbt2WV7M9f7779fEiRMVHx+viIgINW7cWFWrVtVLL72klJSUDEvhSpYsmePf086dO6tFixYaNWqU/vrrL9WuXVvz5s3L9RmT0aNHa/HixWrRooUGDhwoq9Wq2NhY1a1bV9u2bbvp4zt27Kg///xTzz//vNasWeN0DlepUqXUrl07SVevRTR06FB169ZN1apVU2pqqlavXq158+YpOjo6w7GIjY3VhQsXHOHsp59+0t9//y3pavt9V889A5AFEzrSATBJTlpkv/POO0772dv8fvfdd07b7e2hN27cmGH/Dh06GOHh4UZAQIBRpUoVo1+/fsamTZtuWu8nn3xiVK5c2fD29s7QLjs2NtaoWbOm4evra5QqVcoYOHCgcf78+Zs+p93BgweNgQMHGlWrVjUCAgKMwMBAo2bNmsbTTz9tbNu2LcP+hw4dMvr06WOULl3a8PX1NcqUKWPcd999xpw5c7J1DK6vP7vHpm/fvkZwcHCm72HPnj1G27ZtjZCQEKNEiRJG//79Ha2Ar22rm56ebgwZMsQoWbKkYbFYMoyBjz/+2GjSpIkRGBhohIaGGvXq1TOef/554/jx4zc8hvb2xKdPn77hftl9jQoVKhidOnXK8FhXx1xmdSUnJxtPPPGEER4eboSGhho9evQw4uPjM7TINgzDeP31140yZcoYXl5eTu2yf/zxR6N+/fpGQECAUbFiRWP8+PHG559/nqGl9smTJ41OnToZoaGhhiRHu+ysxsE333xjNGrUyPD39zeKFStm9O7d2/j777+d9slqHFzfInrOnDlG+/btjYiICMPPz88oX768MWDAAOPEiRMZHms3d+5cQ5Lx2WefZbnPihUrDEnGxIkTHdteeuklQ5JRtWrVLB+Xnd/T6//tMQzDOHv2rPHoo48aYWFhRnh4uPHoo48aW7duzXaL7MGDB2eopUKFCkbfvn2dti1btsxo1KiR4efnZ1SpUsX49NNPjWeffdYICAjI8j1d+zpZ/VzbIv3gwYNGnz59jMqVKxuBgYFGQECAUadOHePVV181kpKSMq0zq+fNrHU7gJyxGEYenCUIAABQCHXp0kW7d+92dHEE4J44JwgAAHiky5cvO90+cOCAFixYoNatW5tTEIB8w0wQAADwSJGRkerXr5/j2kVTp05VSkqKtm7dmukFTwG4DxojAAAAj9SxY0d9/fXXOnnypPz9/dW8eXO9+eabBCDAAzATBAAAAMCjcE4QAAAAAI9CCAIAAADgUQr1OUE2m03Hjx9XaGioLBaL2eUAAAAAMIlhGLp48aKioqLk5XXjuZ5CHYKOHz+ucuXKmV0GAAAAgALi6NGjKlu27A33KdQhKDQ0VNLVNxoWFmZyNciptLQ0LV68WO3bt5evr6/Z5cDNMd6Q3xhzyE+MN+S3gjTmEhMTVa5cOUdGuJFCHYLsS+DCwsIIQYVYWlqagoKCFBYWZvovD9wf4w35jTGH/MR4Q34riGMuO6fJ0BgBAAAAgEchBAEAAADwKIQgAAAAAB6lUJ8TlB2GYSg9PV1Wq9XsUpCFtLQ0+fj46MqVK3xOHsrb21s+Pj60ugcAAPnCrUNQamqqTpw4oeTkZLNLwQ0YhqHSpUvr6NGjfAn2YEFBQYqMjJSfn5/ZpQAAADfntiHIZrMpLi5O3t7eioqKkp+fH1+wCyibzaakpCSFhITc9MJWcD+GYSg1NVWnT59WXFycqlWrxjgAAAB5ym1DUGpqqmw2m8qVK6egoCCzy8EN2Gw2paamKiAggC+/HiowMFC+vr46fPiwYywAAADkFbf/xsmXaqBw4HcVAADkF751AAAAAPAohCAAAAAAHoUQlA1Wm1Ur/lqhr3d+rRV/rZDVRhvnvGSxWPT999+bXUaeq1ixoiZMmHDDfa49Fn/99ZcsFou2bduW57UBAAC4M0LQTczbO08VJ1bUXTPu0sPzHtZdM+5SxYkVNW/vvDx7zX79+slischiscjPz09Vq1bVa6+9pvT09Dx7zVvRr18/denSxeXHjR49Wg0bNsyw/cSJE7rnnntuvbBcULNmTfn7++vkyZO5/twbN27UU089le39y5UrpxMnTqhu3bq5Xsu1tm/frl69eqlcuXIKDAxUrVq1NHHiRKd91qxZoxYtWqh48eIKDAxUzZo19e9//9tpn1WrVqlz586KiorymGALAAAKB0LQDczbO0/dvu2mvxP/dtp+LPGYun3bLU+DUMeOHXXixAkdOHBAzz77rEaPHq133nknR89ltVpls9lyucK8U7p0afn7+5tdhtasWaPLly+rW7dumjFjRq4/f8mSJV3qXOjt7a3SpUvLxydvmzpu3rxZERER+uqrr7R792699NJLevHFFxUbG+vYJzg4WDExMVq1apX27t2rf/3rX/rXv/6ljz/+2LHPpUuX1KBBA02ePDlP6wUAAHCVR4UgwzB0KfVStn4SryRq6K9DZcjI+Dz/3Tbs12FKvJJ40+cyjIzPcTP+/v4qXbq0KlSooIEDB6pt27b68ccfJUkpKSkaOXKkypQpo+DgYDVr1kwrVqxwPHb69OkqUqSIfvzxR9WuXVv+/v46cuSIKlasqLFjx6pPnz4KCQlRhQoV9OOPP+r06dN64IEHFBISovr162vTpk2O58pstmbChAmqWLGi4/4ZM2bohx9+cMxe2Wt54YUXVL16dQUFBaly5cp6+eWXlZaW5qhxzJgx2r59u7y9vVW0aFFNnz5dUsblcDt37tTdd9+twMBAFS9eXE899ZSSkpIc99tnot59911FRkaqePHiGjx4sOO1JGnKlCmqVq2aAgICVKpUKXXr1u2mn8Fnn32mhx9+WI8++qg+//xzx/bFixcrICBAFy5ccNp/2LBhuvvuux23586dqzp16sjf318VK1bUe++957T/9cvhDhw4oFatWikgIEC1a9fWkiVLnPa/fjncihUrZLFYtGzZMkVHRysoKEi333679u3b5/S4sWPHKiIiQqGhoXryySc1atSoTGfg7B5//HFNnDhRd955pypXrqxHHnlEjz32mObN+1/ob9SokXr16qU6deqoYsWKeuSRR9ShQwetXr3asc8999yjsWPH6p///GeWrwUAAAovq82qlYdXatX5VVp5eGWhOmXEba8TlJnktGSFjAvJlecyZOjvi38rfHz4TfdNejFJwX7Bt/R6gYGBOnv2rCQpJiZGe/bs0ezZsxUVFaX58+erY8eO2rlzp6pVqyZJSk5O1vjx4/Xpp5+qePHiioiIkCT9+9//1ptvvqmXX35Z//73v/Xoo4/q9ttv1+OPP6533nlHL7zwgvr06aPdu3dn6+KyI0eO1N69e5WYmKhp06ZJkooVKyZJCg0N1fTp0xUVFaWdO3eqf//+Cg0N1fPPP6+HHnpIu3bt0sKFC7V48WJdvHhRZcuWzfD8ly5dUocOHdS8eXNt3LhR8fHxevLJJxUTE+MITZK0fPlyRUZGavny5Tp48KAeeughNWzYUP3799emTZs0dOhQffnll7r99tt17tw5py/rmbl48aK+++47rV+/XjVr1lRCQoJWr16tli1bqk2bNipSpIjmzp2rJ554QtLV2bZvvvlGb7zxhqSrsyk9evTQ6NGj9dBDD+m3337ToEGDVLx4cfXr1y/D69lsNnXt2lWlSpXS+vXrlZCQoGeeeeamx1+SXnrpJb333nsqWbKknn76aT3++ONau3atJGnmzJl64403NGXKFLVo0UKzZ8/We++9p0qVKmXrue0SEhIcn2tmtm7dqt9++01jx4516XkBAEDhNG/vPA1bOMyxYur9w++rbFhZTew4UV1rdTW5upvzqBBUGBmGoWXLlmnRokUaMmSIjhw5omnTpunIkSOKioqSdDWILFy4UNOmTdObb74pSUpLS9OUKVPUoEEDp+e79957NWDAAEnSK6+8oqlTp6pp06bq3r27pKuzN82bN9epU6dUunTpm9YXEhKiwMBApaSkZNj/X//6l+O/K1asqJEjR2r27Nl6/vnnFRgYqJCQEPn4+Kh06dIKCgpSYGBghuefNWuWrly5oi+++ELBwVeDZGxsrDp37qzx48erVKlSkqSiRYsqNjZW3t7eqlmzpjp16qRly5apf//+OnLkiIKDg3XfffcpNDRUFSpUUKNGjW74vmbPnq1q1aqpTp06kqSePXvqs88+U8uWLeXt7a2ePXtq1qxZjhC0bNkyXbhwQQ8++KAk6f3331ebNm308ssvS5KqV6+uPXv26J133sk0BC1dulR//PGHFi1a5Phc33zzzWydG/XGG2/ozjvvlCSNGjVKnTp10pUrVxQQEKAPPvhATzzxhB577DFJVz/zxYsXO82k3cxvv/2mb775Rr/88kuG+8qWLavTp08rPT1do0eP1pNPPpnt5wUAAIWT/ZSR61dM2U8ZmdNjToEPQh4VgoJ8g5T0Yva+/K06vEr3zrr3pvsteHiBWlVoddPXddXPP/+skJAQpaWlyWaz6eGHH9bo0aO1YsUKWa1WVa9e3Wn/lJQUFS9e3HHbz89P9evXz/C8126zB4h69epl2BYfH5+tEHQj33zzjSZNmqRDhw4pKSlJ6enpCgsLc+k59u7dqwYNGjgCkCS1aNFCNptN+/btc9Rbp04deXt7O/aJjIzUzp07JUnt2rVThQoVVLlyZXXs2FEdO3bUP//5zxuej/P555/rkUcecdx+5JFHdOedd+qDDz5QaGioevfurX/84x86fvy4oqKiNHPmTHXq1ElFihRx1P3AAw84PWeLFi00YcIEWa1Wp1rt+5crV84RgCSpefPm2TpG136mkZGRkq5+fuXLl9e+ffs0aNAgp/1vu+02/ec//8nWc+/atUsPPPCAXn31VbVv3z7D/atXr1ZSUpLWrVunUaNGqWrVqurVq1e2nhsAABQ+VptVwxYOy/KUEYssembhM3qgxgPy9vLO5BkKBo8KQRaLJdvL0tpXaa+yYWV1LPFYph+yRRaVDSur9lXa58kHfNddd2nq1Kny8/NTVFSU42T4pKQkeXt7a/PmzRm+SIeE/G+pX2BgYKbL2Xx9ff/3Hv57f2bb7I0UvLy8MpzTdO25Nln5/fff1bt3b40ZM0YdOnRQeHi4YylWXrj2PUhX34f9PYSGhmrLli1asWKFFi9erFdeeUWjR4/Wxo0bHaHlWnv27NG6deu0YcMGvfDCC47tVqtVs2fPVv/+/dW0aVNVqVJFs2fP1sCBAzV//nyn5Xn56Uaf363Ys2eP2rRpo6eeesppVu9a9mV19erV06lTpzR69GhCEAAAbmz1kdUZmoZdy5Cho4lHtfrIarWu2Dr/CnORRzVGcIW3l7cmdrzaFtgi5zBhvz2h44Q8S7jBwcGqWrWqypcv79QNrFGjRrJarYqPj1fVqlWdfm515iYzJUuW1MmTJ52C0PXXqfHz85PV6nwi3G+//aYKFSropZdeUnR0tKpVq6bDhw/f9HHXq1WrlrZv365Lly45tq1du1ZeXl6qUaNGtt+Hj4+P2rZtq7fffls7duzQX3/9leVsyGeffaZWrVpp+/bt2rZtm+NnxIgR+uyzzxz79e7dWzNnztRPP/0kLy8vderUyalu+3k519ZdvXr1DOHVvv/Ro0d14sQJx7Z169Zl+/1lpUaNGtq4caPTtutvZ2b37t2666671LdvX8d5Tjdjs9mUkpKSozoBAEDhcOLiiZvv5MJ+ZiEE3UDXWl01p8cclQkr47S9bFhZ09Y6Vq9eXb1791afPn00b948xcXFacOGDRo3blym52zcqtatW+v06dN6++23dejQIU2ePFm//vqr0z4VK1bUjh07tG/fPp05c0ZpaWmqVq2ajhw5otmzZ+vQoUOaNGmS5s+fn+FxcXFx2rZtm86ePZvpF+jevXsrICBAffv21a5du7R8+XINGTJEjz76qGMp3M38/PPPmjRpkrZt26bDhw/riy++kM1myzREpaWl6csvv1SvXr1Ut25dp58nn3xS69ev1+7dux21bdmyRW+88Ya6devm1Nb72Wef1bJly/T6669r//79mjFjhmJjYzVy5MhMa2zbtq2qV6+uvn37avv27Vq9erVeeumlbL2/GxkyZIg+++wzzZgxQwcOHNDYsWO1Y8eOGza92LVrl+666y61b99eI0aM0MmTJ3Xy5EmdPn3asc/kyZP1008/6cCBAzpw4IA+++wzvfvuu05LCJOSkhwBUpLjsz5y5Mgtvy8AAGCOyNDIXN3PLISgm+haq6v+GvaXlvddrlldZ2l53+WKGxZn6sle06ZNU58+ffTss8+qRo0a6tKlizZu3Kjy5cvn+mvVqlVLU6ZM0eTJk9WgQQNt2LAhwxf5/v37q0aNGoqOjlbJkiW1du1a3X///Ro+fLhiYmLUsGFD/fbbb44mAXYPPvigOnbsqDZt2qhq1ar6+uuvM7x+UFCQFi1apHPnzqlp06bq1q2b2rRp43TNmpspUqSI5s2bp7vvvlu1atXShx9+qK+//trR9OBaP/74o86ePZtpW+datWqpVq1ajtmgqlWr6rbbbtOOHTvUu3dvp30bN26sb7/9VrNnz1bdunX1yiuv6LXXXsu0KYJ0ddnh/PnzdfnyZd1222168sknsz0DcyO9e/fWiy++qJEjR6px48aKi4tTv379FBAQkOVj5syZo9OnT+urr75SZGSk46dp06aOfWw2m1588UU1bNhQ0dHRmjx5ssaPH6/XXnvNsc+mTZvUqFEjRxOKESNGqFGjRnrllVdu+X0BAABztCzfUmXDymZYKWVnkUXlwsqpZfmW+VyZayxGTi5iU0AkJiYqPDxcCQkJGU64v3LliuLi4lSpUqUbfuGD+Ww2mxITExUWFiYvL3J5XmvXrp1Kly6tL7/80uxSnOTX72xaWpoWLFige++9N8O5ZEBeYMwhPzHekB+y6g5nD0ZmrZi6UTa4Ht84ATeWnJys999/X7t379Yff/yhV199VUuXLlXfvn3NLg0AABRSXWt11dROUzNsN/OUEVd5VHc4wNNYLBYtWLBAb7zxhq5cuaIaNWpo7ty5atu2rdmlAQCAQqxEUAlJUpWiVfRA2AO65457dFfluwp0W+xrEYIANxYYGKilS5eaXQYAAHAzm45vkiS1rtBardRKd1a4s9AEIInlcAAAAABctPH41UtuNIlsYnIlOeP2IagQ930APAq/qwAAFA6GYThmgghBBYy9I0pycrLJlQDIDvvvKt2MAAAo2A6eO6iElAT5e/urbsm6ZpeTI257TpC3t7eKFCmi+Ph4SVevN3OjC0TCPDabTampqbpy5Qotsj2QYRhKTk5WfHy8ihQpIm/vwrOeGAAAT2SfBWpYuqF8vQvnHy9NDUFWq1WjR4/WV199pZMnTyoqKkr9+vXTv/71r1wJLKVLl5YkRxBCwWQYhi5fvqzAwECCqgcrUqSI43cWAAAUXPYQFB0VbXIlOWdqCBo/frymTp2qGTNmqE6dOtq0aZMee+wxhYeHa+jQobf8/BaLRZGRkYqIiFBaWlouVIy8kJaWplWrVqlVq1YshfJQvr6+zAABAFBI2JsiEIJy6LffftMDDzygTp06SZIqVqyor7/+Whs2bMjV1/H29uYLVgHm7e2t9PR0BQQEEIIAAAAKMKvNqi0ntkiSmkY1NbmanDM1BN1+++36+OOPtX//flWvXl3bt2/XmjVr9P7772e6f0pKilJSUhy3ExMTJV2dSWCmp/Cyf3Z8hsgPjDfkN8Yc8hPjDXlt9+ndupR2ScG+waoSXqVAjTlXajA1BI0aNUqJiYmqWbOmvL29ZbVa9cYbb6h3796Z7j9u3DiNGTMmw/bFixcrKCgor8tFHluyZInZJcCDMN6Q3xhzyE+MN+SV/5z7jySpgl8FLVq4yLG9IIw5V7pCmxqCvv32W82cOVOzZs1SnTp1tG3bNj3zzDOKiopS3759M+z/4osvasSIEY7biYmJKleunNq3b6+wsLD8LB25KC0tTUuWLFG7du1YDoc8x3hDfmPMIT8x3pDXFi9aLB2R2tVpp3vb3lugxpx9lVh2mBqCnnvuOY0aNUo9e/aUJNWrV0+HDx/WuHHjMg1B/v7+8vf3z7Dd19fX9IOOW8fniPzEeEN+Y8whPzHekFc2n9wsSbqt7G1OY6wgjDlXXt/Ui7IkJydnuC6Mt7e3bDabSRUBAAAAyEyaNU3bTm6TVLibIkgmzwR17txZb7zxhsqXL686depo69atev/99/X444+bWRYAAACA6+yK36UUa4rC/cNVpVgVs8u5JaaGoA8++EAvv/yyBg0apPj4eEVFRWnAgAF65ZVXzCwLAAAAwHWuvUiql8XUBWW3zNQQFBoaqgkTJmjChAlmlgEAAADgJq4NQYVd4Y5wAAAAAPLFxuMbJRGCAAAAAHiAK+lXtDN+p6TC3xRBIgQBAAAAuIntJ7cr3ZauEkElVD68vNnl3DJCEAAAAIAbsp8P1DSqqSwWi8nV3DpCEAAAAIAb2nTCfZoiSIQgAAAAADex8Zj7NEWQCEEAAAAAbiApNUl7z+yVRAgCAAAA4AG2ntgqm2FTVGiUokKjzC4nVxCCAAAAAGTp2qYI7oIQBAAAACBL7tYUQSIEAQAAALgBd2uKIBGCAAAAAGThwpULOnDugCRCEAAAAAAPsPn4ZklSxSIVVSKohMnV5B5CEAAAAIBMuWNTBIkQBAAAACAL7tgUQSIEAQAAAMiCOzZFkAhBAAAAADJx+tJpHU44LElqEtnE5GpyFyEIAAAAQAb284GqF6+u8IBwk6vJXYQgAAAAABm4a1MEiRAEAAAAIBPu2hRBIgQBAAAAyIS7NkWQCEEAAAAArnP84nGdSDohL4uXGpVuZHY5uY4QBAAAAMCJfRaodsnaCvYLNrma3EcIAgAAAODEnZsiSIQgAAAAANdx56YIEiEIAAAAwDUMw3DrpggSIQgAAADANQ4nHNbZy2fl6+WrBqUamF1OniAEAQAAAHCwzwLVK1VP/j7+JleTNwhBAAAAABzcvSmCRAgCAAAAcA13b4ogEYIAAAAA/JfNsDlmgghBAAAAANzewXMHlZiSqACfANUpWcfscvIMIQgAAACApP81RWhYuqF8vX1NribvEIIAAAAASPKMpggSIQgAAADAf3lCUwSJEAQAAABAUrotXVtObJHETBAAAAAAD/DHmT+UnJasEL8QVS9e3exy8hQhCAAAAICjKULjyMby9vI2uZq8RQgCAAAA4DFNESRCEAAAAAB5TlMEiRAEAAAAeLxUa6q2ndwmiZkgAAAAAB5gV/wupVpTVSSgiCoXrWx2OXmOEAQAAAB4OHtThOioaFksFpOryXuEIAAAAMDDeVJTBIkQBAAAAHg8T2qKIBGCAAAAAI92Oe2ydp7aKYmZIAAAAAAeYPup7bIaVkUER6hsWFmzy8kXhCAAAADAg3laUwSJEAQAAAB4NPv5QJ6yFE4iBAEAAAAezd4ZzlOaIkiEIAAAAMBjXUy5qL2n90oiBAEAAADwAFtPbpUhQ2XDyqp0SGmzy8k3hCAAAADAQ13bFMGTEIIAAAAAD+WJTREkQhAAAADgsTyxKYJECAIAAAA80vnL53Xw3EFJhCAAAAAAHmDzic2SpMpFK6tYYDGTq8lfhCAAAADAA3lqUwSJEAQAAAB4JE9tiiARggAAAACPxEwQAAAAAI9xKumUjiYelUUWNY5sbHY5+Y4QBAAAAHgYe1OEGiVqKMw/zORq8h8hCAAAAPAwnrwUTiIEAQAAAB7Hk5siSIQgAAAAwKMYhsFMkNkFAAAAAMg/xy4e06lLp+Rt8VbD0g3NLscUhCAAAADAg2w6fnUpXJ2IOgryDTK5GnMQggAAAAAP4lgKF+mZS+EkQhAAAADgURxNEcp4ZlMEiRAEAAAAeAzDMBzL4Ty1KYJECAIAAAA8RtyFOJ27fE5+3n6qF1HP7HJMQwgCAAAAPIR9Fqh+qfry9/E3uRrzEIIAAAAAD0FThKsIQQAAAICHoCnCVYQgAAAAwAPYDJs2H98sybObIkiEIAAAAMAj7D+7XxdTLyrQJ1C1S9Y2uxxTEYIAAAAAD2BvitAospF8vHxMrsZchCAAAADAA9AU4X8IQQAAAIAHoCnC/xCCAAAAADeXbkvX1hNbJdEUQSIEAQAAAG5vz+k9upx+WaF+oapevLrZ5ZiOEAQAAAC4OXtThCZRTeRlIQJwBAAAAAA3R1MEZ4QgAAAAwM3RFMEZIQgAAABwYynpKdp+crskmiLYEYIAAAAAN7YzfqfSbGkqFlhMlYpUMrucAoEQBAAAALgxe1OE6KhoWSwWk6spGAhBAAAAgBujKUJGhCAAAADAjdEUISNCEAAAAOCmktOStTt+tySaIlzL9BB07NgxPfLIIypevLgCAwNVr149bdq0yeyyAAAAgEJv28ltshpWlQ4prTKhZcwup8DwMfPFz58/rxYtWuiuu+7Sr7/+qpIlS+rAgQMqWrSomWUBAAAAboGmCJkzNQSNHz9e5cqV07Rp0xzbKlWibR8AAACQGzYepylCZkwNQT/++KM6dOig7t27a+XKlSpTpowGDRqk/v37Z7p/SkqKUlJSHLcTExMlSWlpaUpLS8uXmpH77J8dnyHyA+MN+Y0xh/zEeMP17J3hGpVqlCfjoiCNOVdqsBiGYeRhLTcUEBAgSRoxYoS6d++ujRs3atiwYfrwww/Vt2/fDPuPHj1aY8aMybB91qxZCgoKyvN6AQAAgMIi2Zqs3jt7y5Ch6XWmq4hvEbNLylPJycl6+OGHlZCQoLCwsBvua2oI8vPzU3R0tH777TfHtqFDh2rjxo36/fffM+yf2UxQuXLldObMmZu+URRcaWlpWrJkidq1aydfX1+zy4GbY7whvzHmkJ8Yb7jWysMr1W5mO5UPK6+DMQfz5DUK0phLTExUiRIlshWCTF0OFxkZqdq1azttq1WrlubOnZvp/v7+/vL398+w3dfX1/SDjlvH54j8xHhDfmPMIT8x3iBJ2+K3SZKiy0Tn+XgoCGPOldc3tUV2ixYttG/fPqdt+/fvV4UKFUyqCAAAAHAPNEXImqkhaPjw4Vq3bp3efPNNHTx4ULNmzdLHH3+swYMHm1kWAAAAUOjZ22M3LdPU5EoKHlNDUNOmTTV//nx9/fXXqlu3rl5//XVNmDBBvXv3NrMsAAAAoFA7m3xWf57/U5LUJLKJydUUPKaeEyRJ9913n+677z6zywAAAADcxuYTmyVJVYtVVdHAoiZXU/CYOhMEAAAAIPfZl8JFR3E+UGYIQQAAAICboSnCjRGCAAAAADdDU4QbIwQBAAAAbuRk0kn9nfi3LLKoUelGZpdTIBGCAAAAADdinwWqVbKWQv1DTa6mYCIEAQAAAG6Epgg3RwgCAAAA3AhNEW6OEAQAAAC4CcMwaIqQDYQgAAAAwE0cTTyq+Evx8vHyUYNSDcwup8AiBAEAAABuwj4LVDeirgJ9A02upuAiBAEAAABuwtEUgfOBbogQBAAAALgJR1MEOsPdECEIAAAAcAM0Rcg+QhAAAADgBg6dP6QLVy7Iz9tPdSPqml1OgUYIAgAAANyAfRaoYemG8vP2M7mago0QBAAAALgBmiJkHyEIAAAAcAM0Rcg+QhAAAABQyFltVm05sUUSTRGygxAEAAAAFHL7zu5TUmqSgnyDVLNETbPLKfAIQQAAAEAhZz8fqHFkY/l4+ZhcTcFHCAIAAAAKOZoiuIYQBAAAABRyNEVwDSEIAAAAKMTSrGnadnKbJJoiZBchCAAAACjEdp/erSvpVxTmH6aqxaqaXU6hQAgCAAAACjHH+UBR0fKy8PU+OzhKAAAAQCFGUwTXEYIAAACAQoymCK4jBAEAAACF1JX0K9p5aqckmiK4ghAEAAAAFFI7Tu1Qmi1NxQOLq0J4BbPLKTQIQQAAAEAhZT8fqGmZprJYLCZXU3gQggAAAIBCiqYIOUMIAgAAAAopmiLkDCEIAAAAKIQupV7SntN7JNEUwVWEIAAAAKAQ2npyq2yGTZEhkYoKjTK7nEKFEAQAAAAUQtc2RYBrCEEAAABAIURThJzzcfUBcXFxWr16tQ4fPqzk5GSVLFlSjRo1UvPmzRUQEJAXNQIAAAC4Dk0Rci7bIWjmzJmaOHGiNm3apFKlSikqKkqBgYE6d+6cDh06pICAAPXu3VsvvPCCKlTgQk0AAABAXkm4kqD9Z/dLIgTlRLZCUKNGjeTn56d+/fpp7ty5KleunNP9KSkp+v333zV79mxFR0drypQp6t69e54UDAAAAHi6zSc2S5IqhFdQyeCSJldT+GQrBL311lvq0KFDlvf7+/urdevWat26td544w399ddfuVUfAAAAgOvQFOHWZCsE3SgAXa948eIqXrx4jgsCAAAAcGM0Rbg1LneH27Jli3bu3Om4/cMPP6hLly76v//7P6WmpuZqcQAAAAAyoinCrXE5BA0YMED79189CevPP/9Uz549FRQUpO+++07PP/98rhcIAAAA4H/OJJ/RXxf+kiQ1iWpibjGFlMshaP/+/WrYsKEk6bvvvlOrVq00a9YsTZ8+XXPnzs3t+gAAAABcw74UrlqxaioSUMTcYgopl0OQYRiy2WySpKVLl+ree++VJJUrV05nzpzJ3eoAAAAAOKEpwq1zOQRFR0dr7Nix+vLLL7Vy5Up16tRJ0tWLqJYqVSrXCwQAAADwP47zgWiKkGMuh6AJEyZoy5YtiomJ0UsvvaSqVatKkubMmaPbb7891wsEAAAA8D+OznA0RcixbLXIvlb9+vWdusPZvfPOO/L29s6VogAAAABkdPzicR2/eFxeFi81imxkdjmFlsshKCsBAQG59VQAAAAAMmGfBapVopZC/EJMrqbwylYIKlq0qCwWS7ae8Ny5c7dUEAAAAIDM0RQhd2QrBE2YMMHx32fPntXYsWPVoUMHNW/eXJL0+++/a9GiRXr55ZfzpEgAAAAANEXILdkKQX379nX894MPPqjXXntNMTExjm1Dhw5VbGysli5dquHDh+d+lQAAAICHMwyDmaBc4nJ3uEWLFqljx44Ztnfs2FFLly7NlaIAAAAAODuScERnks/Ix8tH9UvVN7ucQs3lEFS8eHH98MMPGbb/8MMPKl68eK4UBQAAAMCZfSlcvYh6CvChKdmtcLk73JgxY/Tkk09qxYoVatasmSRp/fr1WrhwoT755JNcLxAAAADANU0RolgKd6tcDkH9+vVTrVq1NGnSJM2bN0+SVKtWLa1Zs8YRigAAAADkLkdTBC6SestydJ2gZs2aaebMmbldCwAAAIBM2AybNh/fLImmCLkhRyHIZrPp4MGDio+Pl81mc7qvVatWuVIYAAAAgKsOnTukhJQE+Xv7q07JOmaXU+i5HILWrVunhx9+WIcPH5ZhGE73WSwWWa3WXCsOAAAAwP+WwjUs3VC+3r4mV1P4uRyCnn76aUVHR+uXX35RZGSkLBZLXtQFAAAA4L9oipC7XA5BBw4c0Jw5c1S1atW8qAcAAADAdWiKkLtcvk5Qs2bNdPDgwbyoBQAAAMB1rDartpzYIommCLnF5ZmgIUOG6Nlnn9XJkydVr149+fo6r0msX5+r1wIAAAC55Y8zfyg5LVnBvsGqUbyG2eW4BZdD0IMPPihJevzxxx3bLBaLDMOgMQIAAACQy+xL4RpHNpa3l7fJ1bgHl0NQXFxcXtQBAAAAIBM0Rch9LoegChUq5EUdAAAAADJBU4Tcl6OLpR46dEgTJkzQ3r17JUm1a9fWsGHDVKVKlVwtDgAAAPBkqdZUbT+5XRJNEXKTy93hFi1apNq1a2vDhg2qX7++6tevr/Xr16tOnTpasmRJXtQIAAAAeKTd8buVYk1RuH+4qhRlwiG3uDwTNGrUKA0fPlxvvfVWhu0vvPCC2rVrl2vFAQAAAJ7s2qVwFovF5Grch8szQXv37tUTTzyRYfvjjz+uPXv25EpRAAAAAGiKkFdcDkElS5bUtm3bMmzftm2bIiIicqMmAAAAAKIpQl5xeTlc//799dRTT+nPP//U7bffLklau3atxo8frxEjRuR6gQAAAIAnupx2Wbvid0miKUJuczkEvfzyywoNDdV7772nF198UZIUFRWl0aNHa+jQobleIAAAAOCJdpzaoXRbukoGlVS5sHJml+NWXA5BFotFw4cP1/Dhw3Xx4kVJUmhoaK4XBgAAAHgymiLkHZdDUFxcnNLT01WtWjWn8HPgwAH5+vqqYsWKuVkfAAAA4JFoipB3XG6M0K9fP/32228Ztq9fv179+vXLjZoAAAAAj0dThLzjcgjaunWrWrRokWH7P/7xj0y7xgEAAABwTVJqkvae3iuJEJQXXA5BFovFcS7QtRISEmS1WnOlKAAAAMCTbT2xVYYMlQkto8jQSLPLcTsuh6BWrVpp3LhxToHHarVq3LhxuuOOO3K1OAAAAMATsRQub7ncGGH8+PFq1aqVatSooZYtW0qSVq9ercTERP3nP//J9QIBAAAAT0NThLzl8kxQ7dq1tWPHDvXo0UPx8fG6ePGi+vTpoz/++EN169bNixoBAAAAj8JMUN5yeSZIunpx1DfffDO3awEAAAA83vnL53Xw3EFJhKC84vJMkHR1+dsjjzyi22+/XceOHZMkffnll1qzZk2uFgcAAAB4mi0ntkiSKhWppOJBxU2uxj25HILmzp2rDh06KDAwUFu2bFFKSoqkq93hmB0CAAAAbg1L4fKeyyFo7Nix+vDDD/XJJ5/I19fXsb1FixbasmVLrhYHAAAAeBqaIuQ9l0PQvn371KpVqwzbw8PDdeHChdyoCQAAAPBYzATlPZdDUOnSpXXw4MEM29esWaPKlSvnSlEAAACAJ4q/FK8jCUckSU2imphcjftyOQT1799fw4YN0/r162WxWHT8+HHNnDlTI0eO1MCBA/OiRgAAAMAjbD6+WZJUo3gNhfmHmVyN+3K5RfaoUaNks9nUpk0bJScnq1WrVvL399fIkSM1ZMiQvKgRAAAA8AgshcsfLocgi8Wil156Sc8995wOHjyopKQk1a5dWyEhIXlRHwAAAOAxaIqQP3J0nSBJ8vPzU+3atVWzZk0tXbpUe/fuzc26AAAAAI9iGAYzQfnE5RDUo0cPxcbGSpIuX76spk2bqkePHqpfv77mzp2b40LeeustWSwWPfPMMzl+DgAAAKCwOn7xuE4mnZSXxUuNIhuZXY5bczkErVq1Si1btpQkzZ8/XzabTRcuXNCkSZM0duzYHBWxceNGffTRR6pfv36OHg8AAAAUdvalcHVK1lGQb5DJ1bg3l88JSkhIULFixSRJCxcu1IMPPqigoCB16tRJzz33nMsFJCUlqXfv3vrkk09uGqJSUlKUkpLiuJ2YmChJSktLU1pamsuvjYLB/tnxGSI/MN6Q3xhzyE+Mt8Jt3dF1kqTGpRsXms+wII05V2pwOQSVK1dOv//+u4oVK6aFCxdq9uzZkqTz588rICDA1afT4MGD1alTJ7Vt2/amIWjcuHEaM2ZMhu2LFy9WUBBpubBbsmSJ2SXAgzDekN8Yc8hPjLfCadGhRZKkgHMBWrBggcnVuKYgjLnk5ORs7+tyCHrmmWfUu3dvhYSEqEKFCmrdurWkq8vk6tWr59JzzZ49W1u2bNHGjRuztf+LL76oESNGOG4nJiaqXLlyat++vcLC6KNeWKWlpWnJkiVq166dfH19zS4Hbo7xhvzGmEN+YrwVXoZh6PEJj0uS+rbtW2gaIxSkMWdfJZYdLoegQYMGqVmzZjpy5IjatWsnL6+rpxVVrlzZpXOCjh49qmHDhmnJkiXZnkHy9/eXv79/hu2+vr6mH3TcOj5H5CfGG/IbYw75ifFW+MSdj9O5y+fk6+WrxmUay9encH1+BWHMufL6LocgSWrSpImaNGnitK1Tp04uPcfmzZsVHx+vxo0bO7ZZrVatWrVKsbGxSklJkbe3d07KAwAAAAoVe1OE+qXqy98n4x/9kbuy1R3urbfe0uXLl7P1hOvXr9cvv/xy0/3atGmjnTt3atu2bY6f6Oho9e7dW9u2bSMAAQAAwGNwfaD8la2ZoD179qh8+fLq3r27OnfurOjoaJUsWVKSlJ6erj179mjNmjX66quvdPz4cX3xxRc3fc7Q0FDVrVvXaVtwcLCKFy+eYTsAAADgzuwzQU2jmppciWfIVgj64osvtH37dsXGxurhhx9WYmKivL295e/v7+jC0KhRIz355JPq169fjrrEAQAAAJ7IZti0+cRmScwE5ZdsnxPUoEEDffLJJ/roo4+0Y8cOHT58WJcvX1aJEiXUsGFDlShR4paLWbFixS0/BwAAAFCYHDh7QIkpiQrwCVCdiDpml+MRXG6M4OXlpYYNG6phw4Z5UA4AAADgWexL4RqVbiQfrxz1LYOLstUYAQAAAEDeoClC/iMEAQAAACaiKUL+IwQBAAAAJkm3pWvLiS2SmAnKT4QgAAAAwCR7T+/V5fTLCvELUY0SNcwux2PkOAQdPHhQixYtclxE1TCMXCsKAAAA8AT2pXBNIpvIy8L8RH5x+UifPXtWbdu2VfXq1XXvvffqxIkTkqQnnnhCzz77bK4XCAAAALgrmiKYw+UQNHz4cPn4+OjIkSMKCgpybH/ooYe0cOHCXC0OAAAAcGc0RTCHy43IFy9erEWLFqls2bJO26tVq6bDhw/nWmEAAACAO0u1pmr7qe2SmAnKby7PBF26dMlpBsju3Llz8vf3z5WiAAAAAHe389ROpVpTVTSgqCoXrWx2OR7F5RDUsmVLffHFF47bFotFNptNb7/9tu66665cLQ4AAABwV/alcNFR0bJYLCZX41lcXg739ttvq02bNtq0aZNSU1P1/PPPa/fu3Tp37pzWrl2bFzUCAAAAboemCOZxeSaobt262r9/v+644w498MADunTpkrp27aqtW7eqSpUqeVEjAAAA4HZoimAel2eCJCk8PFwvvfRSbtcCAAAAeITktGTtit8liZkgM+QoBF25ckU7duxQfHy8bDab0333339/rhQGAAAAuKvtJ7fLalhVKriUyoaVvfkDkKtcDkELFy5Unz59dObMmQz3WSwWWa3WXCkMAAAAcFc0RTCXy+cEDRkyRN27d9eJEydks9mcfghAAAAAwM3RFMFcLoegU6dOacSIESpVqlRe1AMAAAC4PZoimMvlENStWzetWLEiD0oBAAAA3N/FlIv648wfkpgJMovL5wTFxsaqe/fuWr16terVqydfX1+n+4cOHZprxQEAAADuZsuJLTJkqFxYOZUKYXWVGVwOQV9//bUWL16sgIAArVixwulELovFQggCAAAAbuDapggwh8sh6KWXXtKYMWM0atQoeXm5vJoOAAAA8Gg0RTCfyykmNTVVDz30EAEIAAAAyAGaIpjP5STTt29fffPNN3lRCwAAAODWzl0+p0PnD0mSmkQ1Mbkaz+Xycjir1aq3335bixYtUv369TM0Rnj//fdzrTgAAADAnWw+vlmSVKVoFRULLGZyNZ7L5RC0c+dONWrUSJK0a9cup/u42i0AAACQNZoiFAwuh6Dly5fnRR0AAACA26MpQsFAdwMAAAAgn9AUoWDI1kxQ165dNX36dIWFhalr16433HfevHm5UhgAAADgTk4lndLRxKOyyKLGkY3NLsejZSsEhYeHO873CQ8Pz9OCAAAAAHdknwWqWaKmQv1DTa7Gs2UrBE2bNk2vvfaaRo4cqWnTpuV1TQAAAIDb4XyggiPb5wSNGTNGSUlJeVkLAAAA4LboDFdwZDsEGYaRl3UAAAAAbsswDJoiFCAudYfjOkAAAACA6/5O/FunLp2St8VbDUo3MLscj+fSdYKqV69+0yB07ty5WyoIAAAAcDf2WaC6EXUV5BtkcjVwKQSNGTOG7nAAAACAi2iKULC4FIJ69uypiIiIvKoFAAAAcEs0RShYsn1OEOcDAQAAAK6jKULBQ3c4AAAAIA/9ef5Pnb9yXn7efqpXqp7Z5UAuLIez2Wx5WQcAAADgluyzQA1KNZCft5/J1UBysUU2AAAAANfQFKHgIQQBAAAAeYimCAUPIQgAAADIIzbDps0nNkuiKUJBQggCAAAA8si+M/uUlJqkQJ9A1SpZy+xy8F+EIAAAACCP2JfCNY5sLB8vly7RiTxECAIAAADyCE0RCiZCEAAAAJBHaIpQMBGCAAAAgDyQbkvX1pNbJdEUoaAhBAEAAAB5YHf8bl1Jv6Iw/zBVK17N7HJwDUIQAAAAkAfsS+GaRDaRl4Wv3QUJnwYAAACQB2iKUHARggAAAIA8QFOEgosQBAAAAOSylPQU7Ti1QxJNEQoiQhAAAACQy3ac2qE0W5qKBxZXxSIVzS4H1yEEAQAAALns2qVwFovF5GpwPUIQAAAAkMtoilCwEYIAAACAXEZThIKNEAQAAADkouS0ZO0+vVsSTREKKkIQAAAAkIu2ntgqm2FT6ZDSigqNMrscZIIQBAAAAOQi+1K4plFNaYpQQBGCAAAAgFxEU4SCjxAEAAAA5CKaIhR8hCAAAAAglySmJGrf2X2SCEEFGSEIAAAAyCWbj2+WJJUPL6+I4AiTq0FWCEEAAABALrm2KQIKLkIQAAAAkEtoilA4EIIAAACAXMJMUOFACAIAAABywdnks4q7ECdJahzZ2ORqcCOEIAAAACAX2GeBqharqqKBRU2uBjdCCAIAAAByAUvhCg9CEAAAAJALaIpQeBCCAAAAgFzATFDhQQgCAAAAbtGJiyd07OIxWWRRo8hGZpeDmyAEAQAAALfIPgtUq2QthfiFmFwNboYQBAAAANwilsIVLoQgAAAA4BbRFKFwIQQBAAAAt8AwDGaCChlCEAAAAHALjiYe1enk0/Lx8lH9UvXNLgfZQAgCAAAAbsHGY1eXwtWNqKtA30CTq0F2EIIAAACAW8BSuMKHEAQAAADcApoiFD6EIAAAACCHaIpQOBGCAAAAgBw6dP6QElIS5O/trzoRdcwuB9lECAIAAAByyN4UoUHpBvLz9jO5GmQXIQgAAADIIZbCFU6EIAAAACCHaIpQOBGCAAAAgByw2qzacmKLJGaCChtCEAAAAJAD+87u06W0SwryDVLNEjXNLgcuIAQBAAAAOWBvitA4srG8vbxNrgauIAQBAAAAOUBThMLL1BA0btw4NW3aVKGhoYqIiFCXLl20b98+M0sCAAAAsoWmCIWXqSFo5cqVGjx4sNatW6clS5YoLS1N7du316VLl8wsCwAAALihNGuatp3cJomZoMLIx8wXX7hwodPt6dOnKyIiQps3b1arVq1MqgoAAAC4sd2ndyvFmqJw/3BVKVbF7HLgIlND0PUSEhIkScWKFcv0/pSUFKWkpDhuJyYmSpLS0tKUlpaW9wUiT9g/Oz5D5AfGG/IbYw75ifGWf9YdWSdJaly6sazpVlllNbkicxSkMedKDRbDMIw8rCXbbDab7r//fl24cEFr1qzJdJ/Ro0drzJgxGbbPmjVLQUFBeV0iAAAAIEmacnSKFp9drK4RXdUnqo/Z5UBScnKyHn74YSUkJCgsLOyG+xaYEDRw4ED9+uuvWrNmjcqWLZvpPpnNBJUrV05nzpy56RtFwZWWlqYlS5aoXbt28vX1NbscuDnGG/IbYw75ifGWf2777DZtO7VNX//zaz1Y60GzyzFNQRpziYmJKlGiRLZCUIFYDhcTE6Off/5Zq1atyjIASZK/v7/8/f0zbPf19TX9oOPW8TkiPzHekN8Yc8hPjLe8dSX9inad3iVJal6+OcdaBWPMufL6poYgwzA0ZMgQzZ8/XytWrFClSpXMLAcAAAC4qR2ndijdlq4SQSVUPry82eUgB0wNQYMHD9asWbP0ww8/KDQ0VCdPnpQkhYeHKzAw0MzSAAAAgExtPPa/6wNZLBaTq0FOmHqdoKlTpyohIUGtW7dWZGSk4+ebb74xsywAAAAgS5tObJLE9YEKM9OXwwEAAACFybUzQSicTJ0JAgAAAAqTpNQk7T2zVxIhqDAjBAEAAADZtO3kNtkMm6JCoxQVGmV2OcghQhAAAACQTSyFcw+EIAAAACCbaIrgHghBAAAAQDYxE+QeCEEAAABANly4ckEHzh2QRAgq7AhBAAAAQDZsObFFklSxSEWVCCphcjW4FYQgAAAAIBtYCuc+CEEAAABANtAUwX0QggAAAIBsYCbIfRCCAAAAgJs4fem0DiccliQ1iWxicjW4VYQgAAAA4CY2Hb+6FK568eoKDwg3uRrcKkIQAAAAcBP2EMRSOPdACAIAAABugqYI7oUQBAAAANwETRHcCyEIAAAAuIHjF4/rRNIJeVm81Kh0I7PLQS4gBAEAAAA3YJ8Fql2ytoL9gk2uBrmBEAQAAADcAE0R3A8hCAAAALgBmiK4H0IQAAAAkAXDMGiK4IYIQQAAAEAWDicc1tnLZ+Xr5asGpRqYXQ5yCSEIAAAAyIJ9FqheqXry9/E3uRrkFkIQAAAAkAVHU4RIlsK5E0IQAAAAkAVHU4QyNEVwJ4QgAAAAIBM2w0Z7bDdFCAIAAAAycfDcQSWmJCrAJ0B1StYxuxzkIkIQAAAAkAl7U4SGpRvK19vX5GqQmwhBAAAAQCZoiuC+CEEAAABAJmiK4L4IQQAAAMB10m3p2nJiiySaIrgjQhAAAABwnT/O/KHktGSF+IWoRvEaZpeDXEYIAgAAAK5jb4rQOLKxvL28Ta4GuY0QBAAAAFyHpgjujRAEAAAAXIemCO6NEAQAAABcI9Waqm0nt0miKYK7IgQBAAAA19gVv0up1lQVCSiiKkWrmF0O8gAhCAAAALiGvSlCdFS0LBaLydUgLxCCAAAAgGvQFMH9EYIAAACAa9AUwf0RggAAAID/upx2WTtP7ZREUwR3RggCAAAA/mv7qe2yGlZFBEeoXFg5s8tBHiEEAQAAAP9FUwTPQAgCAAAA/st+PhBNEdwbIQgAAAD4L3tnOJoiuDdCEAAAACDpYspF7T29VxJNEdwdIQgAAACQtPXkVhkyVDasrEqHlDa7HOQhQhAAAAAg56YIcG+EIAAAAEA0RfAkhCAAAABANEXwJIQgAAAAeLzzl8/r4LmDkqQmkU1MrgZ5jRAEAAAAj7f5xGZJUuWilVU8qLjJ1SCvEYIAAADg0aw2q77Z9Y0kqXx4eVltVpMrQl4jBAEAAMBjzds7TxUnVtSnWz+VJK34a4UqTqyoeXvnmVwZ8hIhCAAAAB5p3t556vZtN/2d+LfT9mOJx9Tt224EITdGCAIAAIDHsdqsGrZwmAwZGe6zb3tm4TMsjXNThCAAAAB4nNVHVmeYAbqWIUNHE49q9ZHV+VgV8gshCAAAAB7FMAyt/GtltvY9cfFEHlcDM/iYXQAAAACQHy6nXdbsXbMVuzFWW05sydZjIkMj87gqmIEQBAAAALf214W/NHXjVH269VOdu3xOkuTn5Scfbx8lpyVn+hiLLCobVlYty7fMz1KRTwhBAAAAcDuGYWjpn0sVuzFWP+37ydHsoEJ4BQ1qOkiPN3pcqw6vUrdvu13d/5oGCRZZJEkTOk6Qt5d3/hePPEcIAgAAgNtITEnUF9u/UOyGWO07u8+xvV3ldoq5LUadqnVyBJuutbpqTo85GrZwmFOThLJhZTWh4wR1rdU13+tH/iAEAQAAoNDbe3qvJm+crBnbZygpNUmSFOIXon4N+mnwbYNVs0TNTB/XtVZXPVDjAa0+slonLp5QZGikWpZvyQyQmyMEAQAAoFBKt6Xr5/0/K3ZDrJbFLXNsr1mipmKaxujRBo8qzD/sps/j7eWt1hVb52GlKGgIQQAAAChUziSf0adbPtXUTVN1JOGIJMnL4qX7a9yvmKYxurvS3bJYLCZXiYKMEAQAAIBCYfPxzYrdGKuvd36tFGuKJKl4YHH1b9xfT0c/rQpFKphcIQoLQhAAAAAKrJT0FM3ZM0exG2O17u91ju1NIptoyG1D9FDdhxTgE2BihSiMCEEAAAAocP5O/FsfbfpIH2/5WPGX4iVJvl6+6lGnh2Jui1GzMs1Y8oYcIwQBAACgQDAMQ6sOr1LsxljN3ztfVsMqSYoKjdLA6IHq37i/SoWUMrlKuANCEAAAAEx1KfWSZu6cqdgNsdoZv9OxvVWFVhpy2xA9UOMB+Xr7mlgh3A0hCAAAAKY4eO6gpmycos+3fq6ElARJUpBvkB6p94gG3zZY9UvVN7lCuCtCEAAAAPKNzbBp4cGFit0Qq18P/urYXqVoFQ1uOlj9GvZT0cCiJlYIT0AIAgAAQJ47f/m8pm2bpikbp+jQ+UOO7fdWu1cxTWPUoWoHeVm8TKwQnoQQBAAAgDyz49QOTd4wWV/t/ErJacmSpHD/cD3e6HENajpIVYtVNblCeCJCEAAAAHJVmjVN3//xvWI3xmrV4VWO7fUi6inmthj1rtdbwX7BJlYIT0cIAgAAQK44mXRSn2z+RB9u/lDHLx6XJHlbvNW1VlfF3BajluVbcm0fFAiEIAAAAOSYYRha9/c6xW6M1Xe7v1OaLU2SFBEcoQFNBmhAkwEqE1bG5CoBZ4QgAAAAuOxy2mV9s/sbfbDhA205scWx/R9l/6Ehtw3Rg7UelL+Pv4kVAlkjBAEAACDbDl84rKmbpurTLZ/q7OWzkiR/b3/1qtdLg5sOVnRUtMkVAjdHCAIAAMANGYahZXHLFLshVj/t/0k2wyZJKh9eXoOiB+mJxk+oRFAJk6sEso8QBAAAgExdTLmoL7Z/odiNsfrjzB+O7W0rt1VM0xjdV/0+eXt5m1ghkDOEIAAAADj548wfmrxhsmZsn6GLqRclSSF+IerXoJ8GNR2kWiVrmVwhcGsIQQAAAJDVZtXP+39W7MZYLf1zqWN7jeI1FHNbjPo06KMw/zATKwRyDyEIAADAg51JPqPPtnymqZum6nDCYUmSl8VLnat3VsxtMWpTqQ3X9oHbIQQBAAB4oC0ntuiDDR/o651fK8WaIkkqFlhM/Rv319PRT6tikYrmFgjkIUIQAACAG7DarFp5eKVWnV+l4MPBuqvyXRmaFqRaUzVnzxzFbojV73//7tjeOLKxYprGqGfdngr0Dczv0oF8RwgCAAAo5ObtnadhC4fp78S/JUnvH35fZcPKamLHiepaq6uOJR7TR5s/0sebP9apS6ckSb5evupep7timsboH2X/wZI3eBRCEAAAQCE2b+88dfu2mwwZTtuPJR7Tg98+qOZlm2vDsQ2yGlZJUlRolJ5u8rT6N+mv0iGlzSgZMB0hCAAAoJCy2qwatnBYhgAkybHNvuytVYVWimkaoy41u8jX2zdf6wQKGkIQAAAoUKw2q1YfWa0TF08oMjRSLcu39JgLcqZZ03Qx9aKSUpMcPxdTnG8npSY59tl/dr9jCdyNfNL5Ez3Z+Ml8eAdA4UAIygWe/I/1rcrOSZzIiDGXM4y3nGPM5QxjznXXn9siyencloIkzZqWIZTcKLxkus9121KtqXlSa7BvcJ48L1BYFYgQNHnyZL3zzjs6efKkGjRooA8++EC33Xab2WVlS2H6x7qgudlJnMgcYy5nGG85x5jLGcac6250bku3b7tpTo85OT521waWG4UQp+CSduOZmLwKLJLk5+2nEL8QhfqFKsQvxOkn1D9UIb5X//t08mnN2D7jps8XGRqZZ7UChZHFMIyMi0jz0TfffKM+ffroww8/VLNmzTRhwgR999132rdvnyIiIm742MTERIWHhyshIUFhYfl/BeOs/rG26Gp3lVv5x9rdcexyhuOWMxy3nOPY5QzHLWuGYciQIZthk82wyWqzymbYlGZNU52pdXT84vEsH1siqIQmdJig5LTkjOHlJjMx9uvg5AV7YHEKKteFlyzDTCb7BPsFy8/bL1uvbbVZVXFiRR1LPJbpeUEWWVQ2rKzihsUxC4k8kZaWpgULFujee++Vr6+555q5kg1Mnwl6//331b9/fz322GOSpA8//FC//PKLPv/8c40aNcrk6rKWnRMRn/rpKVltVv7RuY7VZtXAXwZy7FzEccsZjlvOZffYpVnT5GXxctrv2r+v3Wy7K/teu72gvp7NsGn0itE3PG6P//C4dsfvliRHGLAZNlkNq9Ntp/tsmdynG9yXk+fLh8dldlyy60zyGT0y/5EcP16SfLx8HGHj+hCS0/CS3cCSF7y9vDWx40R1+7abLLI4HV976J7QcQL/vgHXMXUmKDU1VUFBQZozZ466dOni2N63b19duHBBP/zwg9P+KSkpSkn5319yEhMTVa5cOZ05cybfZ4JWHl6pdjPb5etrAgDg6WqVqKUqRatcDSD/XRIW7BfsNIsS4us8q2LfN9Q/1NTAkpfm/zFfI5aM0LGLxxzbyoaV1Xtt39M/a/7TxMrg7tLS0rRkyRK1a9euQMwElShRouDPBJ05c0ZWq1WlSpVy2l6qVCn98ccfGfYfN26cxowZk2H74sWLFRQUlGd1ZmbV+VXZ2i/KP0rhPuF5XE3hkpCeoOMpWS93sOPYOeO45QzHLeeye+zK+pfN9Nhde+FF+1+kne5XJvdbbnx/Zs+T49fKjcdbMm47k3pG+5L3ZVrnteqG1FUZ/zKyyCIvi5cs//0/L4uXvOQli8Xi+F+Lrvtv+z65/Njrn+P6x3pbvDPsn1uP3Xtpr17787WbHreHwx9WveB6/9uQ+t+f61z57/+d0ZmbPqc78Je/JlWepD1Je3Q+/byK+hRV7ZDa8v7TWwv+XGB2efAAS5YsMbsEJScnZ3tfU2eCjh8/rjJlyui3335T8+bNHduff/55rVy5UuvXr3favzDOBC3pvUR3VrgzHyoqPDh2OcNxyxmOW85x7HKG45YzVptVVSdX1fGLx7M8t6VMWBkdGHSApV03UJD+Kg/PUJDGXKGZCSpRooS8vb116tQpp+2nTp1S6dIZr2Ds7+8vf3//DNt9fX3z/aDfVfkulQ0re9MTEWmHmhHHLmc4bjnDccs5jl3OcNxyxle+mnTPpBue2zKx40QF+AeYVWKhYsZ3I3i2gjDmXHl9rzys46b8/PzUpEkTLVu2zLHNZrNp2bJlTjNDBZH9REQp49IJTkS8MY5dznDccobjlnMcu5zhuOVc11pdNafHHJUJK+O0vWxYWY/uqAcg95kagiRpxIgR+uSTTzRjxgzt3btXAwcO1KVLlxzd4goy/rHOOY5dznDccobjlnMcu5zhuOVc11pd9dewv7S873LN6jpLy/suV9ywOI4ZgFxl+nWCJCk2NtZxsdSGDRtq0qRJatas2U0fZ/Z1guy4knrOWW1WLf9zuX5d86vuueMelodkE2MuZxhvOceYyxnGHPJbQbpmCzxDQRpzheo6QZIUExOjmJgYs8vIMW8vb7Wu2NrsMgolby9v3VnhTl3afUl3VriTLwfZxJjLGcZbzjHmcoYxBwAFk+nL4QAAAAAgPxGCAAAAAHgUQhAAAAAAj0IIAgAAAOBRCEEAAAAAPAohCAAAAIBHIQQBAAAA8CiEIAAAAAAehRAEAAAAwKMQggAAAAB4FEIQAAAAAI9CCAIAAADgUQhBAAAAADyKj9kF3ArDMCRJiYmJJleCW5GWlqbk5GQlJibK19fX7HLg5hhvyG+MOeQnxhvyW0Eac/ZMYM8IN1KoQ9DFixclSeXKlTO5EgAAAAAFwcWLFxUeHn7DfSxGdqJSAWWz2XT8+HGFhobKYrGYXQ5yKDExUeXKldPRo0cVFhZmdjlwc4w35DfGHPIT4w35rSCNOcMwdPHiRUVFRcnL68Zn/RTqmSAvLy+VLVvW7DKQS8LCwkz/5YHnYLwhvzHmkJ8Yb8hvBWXM3WwGyI7GCAAAAAA8CiEIAAAAgEchBMF0/v7+evXVV+Xv7292KfAAjDfkN8Yc8hPjDfmtsI65Qt0YAQAAAABcxUwQAAAAAI9CCAIAAADgUQhBAAAAADwKIQgAAACARyEEwRTjxo1T06ZNFRoaqoiICHXp0kX79u0zuyx4kLfeeksWi0XPPPOM2aXATR07dkyPPPKIihcvrsDAQNWrV0+bNm0yuyy4KavVqpdfflmVKlVSYGCgqlSpotdff130v0JuWbVqlTp37qyoqChZLBZ9//33TvcbhqFXXnlFkZGRCgwMVNu2bXXgwAFzis0GQhBMsXLlSg0ePFjr1q3TkiVLlJaWpvbt2+vSpUtmlwYPsHHjRn300UeqX7++2aXATZ0/f14tWrSQr6+vfv31V+3Zs0fvvfeeihYtanZpcFPjx4/X1KlTFRsbq71792r8+PF6++239cEHH5hdGtzEpUuX1KBBA02ePDnT+99++21NmjRJH374odavX6/g4GB16NBBV65cyedKs4cW2SgQTp8+rYiICK1cuVKtWrUyuxy4saSkJDVu3FhTpkzR2LFj1bBhQ02YMMHssuBmRo0apbVr12r16tVmlwIPcd9996lUqVL67LPPHNsefPBBBQYG6quvvjKxMrgji8Wi+fPnq0uXLpKuzgJFRUXp2Wef1ciRIyVJCQkJKlWqlKZPn66ePXuaWG3mmAlCgZCQkCBJKlasmMmVwN0NHjxYnTp1Utu2bc0uBW7sxx9/VHR0tLp3766IiAg1atRIn3zyidllwY3dfvvtWrZsmfbv3y9J2r59u9asWaN77rnH5MrgCeLi4nTy5Emn/98aHh6uZs2a6ffffzexsqz5mF0AYLPZ9Mwzz6hFixaqW7eu2eXAjc2ePVtbtmzRxo0bzS4Fbu7PP//U1KlTNWLECP3f//2fNm7cqKFDh8rPz099+/Y1uzy4oVGjRikxMVE1a9aUt7e3rFar3njjDfXu3dvs0uABTp48KUkqVaqU0/ZSpUo57itoCEEw3eDBg7Vr1y6tWbPG7FLgxo4ePaphw4ZpyZIlCggIMLscuDmbzabo6Gi9+eabkqRGjRpp165d+vDDDwlByBPffvutZs6cqVmzZqlOnTratm2bnnnmGUVFRTHmgEywHA6miomJ0c8//6zly5erbNmyZpcDN7Z582bFx8ercePG8vHxkY+Pj1auXKlJkybJx8dHVqvV7BLhRiIjI1W7dm2nbbVq1dKRI0dMqgju7rnnntOoUaPUs2dP1atXT48++qiGDx+ucePGmV0aPEDp0qUlSadOnXLafurUKcd9BQ0hCKYwDEMxMTGaP3++/vOf/6hSpUpmlwQ316ZNG+3cuVPbtm1z/ERHR6t3797atm2bvL29zS4RbqRFixYZ2v7v379fFSpUMKkiuLvk5GR5eTl/rfP29pbNZjOpIniSSpUqqXTp0lq2bJljW2JiotavX6/mzZubWFnWWA4HUwwePFizZs3SDz/8oNDQUMd60fDwcAUGBppcHdxRaGhohnPOgoODVbx4cc5FQ64bPny4br/9dr355pvq0aOHNmzYoI8//lgff/yx2aXBTXXu3FlvvPGGypcvrzp16mjr1q16//339fjjj5tdGtxEUlKSDh486LgdFxenbdu2qVixYipfvryeeeYZjR07VtWqVVOlSpX08ssvKyoqytFBrqChRTZMYbFYMt0+bdo09evXL3+Lgcdq3bo1LbKRZ37++We9+OKLOnDggCpVqqQRI0aof//+ZpcFN3Xx4kW9/PLLmj9/vuLj4xUVFaVevXrplVdekZ+fn9nlwQ2sWLFCd911V4btffv21fTp02UYhl599VV9/PHHunDhgu644w5NmTJF1atXN6HamyMEAQAAAPAonBMEAAAAwKMQggAAAAB4FEIQAAAAAI9CCAIAAADgUQhBAAAAADw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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "\n", + "# Create necessary directories\n", + "data_dir = 'data'\n", + "figures_dir = 'figures'\n", + "\n", + "os.makedirs(data_dir, exist_ok=True)\n", + "os.makedirs(figures_dir, exist_ok=True)\n", + "\n", + "\n", + "# Main script\n", + "timing_results_permutations = []\n", + "\n", + "# Generate permutations avoiding 231\n", + "for n in range(1, 10):\n", + " start_time = time.time()\n", + " permutations = catalan.permutations_avoiding_231(n)\n", + " end_time = time.time()\n", + " duration = end_time - start_time\n", + " timing_results_permutations.append((n, duration))\n", + "\n", + " # Save permutations to file\n", + " with open(os.path.join(data_dir, f'permutations_avoiding_231_{n}.txt'), 'w') as file:\n", + " for perm in permutations:\n", + " file.write(f'{perm}\\n')\n", + "\n", + "# Plotting the timing results\n", + "ns = [result[0] for result in timing_results_permutations]\n", + "durations_permutations = [result[1] for result in timing_results_permutations]\n", + "\n", + "plt.figure(figsize=(10, 6))\n", + "\n", + "plt.plot(ns, durations_permutations, marker='o', linestyle='-', color='g', label='Permutations Avoiding 231')\n", + "plt.title('Time to Generate Permutations Avoiding 231')\n", + "plt.xlabel('n')\n", + "plt.ylabel('Time (seconds)')\n", + "plt.grid(True)\n", + "plt.legend()\n", + "\n", + "plt.savefig(os.path.join(figures_dir, 'permutations_avoiding_231.png'))\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Generate Triangulations\n", + "\n", + "Generate all possible triangulations on an $n$-sided polygon for $3 \\le n \\le 12$. Files should be outputted to `data/catalan_triangulations_n.txt` and a plot of the time used to generate each data file should go in `figures/catalan_triangulations.png`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "# Create necessary directories\n", + "data_dir = 'data'\n", + "figures_dir = 'figures'\n", + "\n", + "os.makedirs(data_dir, exist_ok=True)\n", + "os.makedirs(figures_dir, exist_ok=True)\n", + "\n", + "\n", + "# Main script\n", + "timing_results_triangulations = []\n", + "\n", + "# Generate triangulations\n", + "for n in range(3, 12):\n", + " start_time = time.time()\n", + " triangulations = catalan.triangulations(n)\n", + " end_time = time.time()\n", + " duration = end_time - start_time\n", + " timing_results_triangulations.append((n, duration))\n", + "\n", + " # Save triangulations to file\n", + " with open(os.path.join(data_dir, f'triangulations_{n}.txt'), 'w') as file:\n", + " for triangulation in triangulations:\n", + " file.write(f'{triangulation}\\n')\n", + "\n", + "# Plotting the timing results\n", + "ns = [result[0] for result in timing_results_triangulations]\n", + "durations_triangulations = [result[1] for result in timing_results_triangulations]\n", + "\n", + "plt.figure(figsize=(10, 6))\n", + "\n", + "plt.plot(ns, durations_triangulations, marker='o', linestyle='-', color='b', label='Generate Triangulations')\n", + "plt.title('Time to Generate Triangulations')\n", + "plt.xlabel('n')\n", + "plt.ylabel('Time (seconds)')\n", + "plt.grid(True)\n", + "plt.legend()\n", + "\n", + "plt.savefig(os.path.join(figures_dir, 'triangulations.png'))\n", + "plt.show()\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.9" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +}