






"""simple docstring"""



A_     =				[
    ['''ab-e1''', '''ac-e3''', '''ad-e5''', '''bc-e4''', '''bd-e2''', '''be-e6''', '''bh-e12''', '''cd-e2''', '''ce-e4''',
     '''de-e1''', '''df-e8''', '''dg-e5''', '''dh-e10''', '''ef-e3''', '''eg-e2''', '''fg-e6''', '''gh-e6''', '''hi-e3'''],
    ['''ab-e1''', '''ac-e3''', '''ad-e5''', '''bc-e4''', '''bd-e2''', '''be-e6''', '''cd-e2''', '''de-e1''', '''df-e8''',
     '''ef-e3''', '''eg-e2''', '''fg-e6'''],
    ['''ab-e1''', '''ac-e3''', '''bc-e4''', '''bd-e2''', '''de-e1''', '''df-e8''', '''dg-e5''', '''ef-e3''', '''eg-e2''',
     '''eh-e12''', '''fg-e6''', '''fh-e10''', '''gh-e6'''],
    ['''ab-e1''', '''ac-e3''', '''bc-e4''', '''bd-e2''', '''bh-e12''', '''cd-e2''', '''df-e8''', '''dh-e10'''],
    ['''ab-e1''', '''ac-e3''', '''ad-e5''', '''bc-e4''', '''bd-e2''', '''cd-e2''', '''ce-e4''', '''de-e1''', '''df-e8''',
     '''dg-e5''', '''ef-e3''', '''eg-e2''', '''fg-e6''']
]




def   _lowerCAmelCase		(				UpperCAmelCase__							:       Dict   )		->str:
						A__    :	int			=	set()
						for row in edge_array:
												for item in row:
																		distinct_edge.add(item[0]   )
						return list(UpperCAmelCase__   )




def   _lowerCAmelCase		(				UpperCAmelCase__							:       Dict,    UpperCAmelCase__							:       Optional[Any]   )		->Optional[Any]:
						A__    :	Tuple			=	["""0"""] * len(UpperCAmelCase__   )
						for i, row in enumerate(UpperCAmelCase__   ):
												for item in row:
																		if distinct_edge in item[0]:
																								A__    :	str			=	"""1"""
																								break
						return "".join(UpperCAmelCase__   )




def   _lowerCAmelCase		(				UpperCAmelCase__							:       int   )		->List[str]:
						A__    :	Union[str, Any]			=	get_distinct_edge(UpperCAmelCase__   )
						A__    :	Union[str, Any]			=	{}

						for item in distinct_edge:
												A__    :	Dict			=	get_bitcode(UpperCAmelCase__,    UpperCAmelCase__   )
												# print('bit',bit)
												# bt=''.join(bit)
												A__    :	Any			=	bit.count("""1"""   )
												A__    :	Optional[Any]			=	[s, bit]
						# Store [Distinct edge, WT(Bitcode), Bitcode] in descending order
						A__    :	str			=	[
						    [k, v[0], v[1]]
						    for k, v in sorted(frequency_table.items(),    key=lambda UpperCAmelCase__   : v[1][0],    reverse=UpperCAmelCase__   )
						]
						return sorted_frequency_table




def   _lowerCAmelCase		(				UpperCAmelCase__							:       List[str]   )		->Any:
						A__    :	Any			=	{}
						for _, item in enumerate(UpperCAmelCase__   ):
												nodes.setdefault(item[2],    []   ).append(item[0]   )
						return nodes




def   _lowerCAmelCase		(				UpperCAmelCase__							:       Union[str, Any]   )		->str:
						A__    :	Union[str, Any]			=	{}
						for key, value in nodes.items():
												A__    :	Tuple			=	value
						return cluster




def   _lowerCAmelCase		(				UpperCAmelCase__							:       Optional[int]   )		->Tuple:
						return [i * 1_0_0 / len(UpperCAmelCase__   ) for i in cluster]




def   _lowerCAmelCase		(				)		->None:
						print("""\nNodes\n"""   )
						for key, value in nodes.items():
												print(UpperCAmelCase__,    UpperCAmelCase__   )
						print("""\nSupport\n"""   )
						print(UpperCAmelCase__   )
						print("""\n Cluster \n"""   )
						for key, value in sorted(cluster.items(),    reverse=UpperCAmelCase__   ):
												print(UpperCAmelCase__,    UpperCAmelCase__   )
						print("""\n Graph\n"""   )
						for key, value in graph.items():
												print(UpperCAmelCase__,    UpperCAmelCase__   )
						print("""\n Edge List of Frequent subgraphs \n"""   )
						for edge_list in freq_subgraph_edge_list:
												print(UpperCAmelCase__   )




def   _lowerCAmelCase		(				UpperCAmelCase__							:       int,    UpperCAmelCase__							:       Dict,    UpperCAmelCase__							:       List[Any],    UpperCAmelCase__							:       List[Any]   )		->Tuple:
						for i in cluster[ca]:
												A__    :	str			=	0
												A__    :	Optional[int]			=	ca + 1
												while ca < max(cluster.keys()   ):
																		for j in cluster[ca]:
																								if int(UpperCAmelCase__,    2   ) & int(UpperCAmelCase__,    2   ) == int(UpperCAmelCase__,    2   ):
																														if tuple(nodes[i]   ) in graph:
																																				graph[tuple(nodes[i]   )].append(nodes[j]   )
																														else:
																																				A__    :	Tuple			=	[nodes[j]]
																														count += 1
																		if count == 0:
																								A__    :	Dict			=	ca + 1
																		else:
																								break




def   _lowerCAmelCase		(				UpperCAmelCase__							:       int,    UpperCAmelCase__							:       List[str]   )		->int:
						A__    :	Union[str, Any]			=	cluster[max(cluster.keys()   )]
						A__    :	List[str]			=	"""Header"""
						A__    :	Any			=	{}
						for i in x:
												if (["Header"],) in graph:
																		graph[(["Header"],)].append(x[i]   )
												else:
																		A__    :	Any			=	[x[i]]
						for i in x:
												A__    :	Optional[Any]			=	[["""Header"""]]
						A__    :	Union[str, Any]			=	1
						while i < max(UpperCAmelCase__   ) - 1:
												create_edge(UpperCAmelCase__,    UpperCAmelCase__,    UpperCAmelCase__,    UpperCAmelCase__   )
												A__    :	Union[str, Any]			=	i + 1
						return graph




def   _lowerCAmelCase		(				UpperCAmelCase__							:       Optional[int],    UpperCAmelCase__							:       Dict,    UpperCAmelCase__							:       int,    UpperCAmelCase__							:       List[Any]=None   )		->str:
						A__    :	Tuple			=	(path or []) + [start]
						if start == end:
												paths.append(UpperCAmelCase__   )
						for node in graph[start]:
												if tuple(UpperCAmelCase__   ) not in path:
																		my_dfs(UpperCAmelCase__,    tuple(UpperCAmelCase__   ),    UpperCAmelCase__,    UpperCAmelCase__   )




def   _lowerCAmelCase		(				UpperCAmelCase__							:       Dict,    UpperCAmelCase__							:       List[str],    UpperCAmelCase__							:       List[Any]   )		->Optional[int]:
						A__    :	List[str]			=	int(s / 1_0_0 * (len(UpperCAmelCase__   ) - 1)   )
						for i in cluster[k]:
												my_dfs(UpperCAmelCase__,    tuple(cluster[k][i]   ),    (["""Header"""],)   )




def   _lowerCAmelCase		(				UpperCAmelCase__							:       Union[str, Any]   )		->Optional[int]:
						A__    :	Dict			=	[]
						for edges in paths:
												A__    :	Dict			=	[]
												for j in range(len(UpperCAmelCase__   ) - 1   ):
																		A__    :	int			=	list(edges[j]   )
																		for e in temp:
																								A__    :	Tuple			=	(e[0], e[1])
																								el.append(UpperCAmelCase__   )
												freq_sub_el.append(UpperCAmelCase__   )
						return freq_sub_el




def   _lowerCAmelCase		(				UpperCAmelCase__							:       List[Any]   )		->Optional[Any]:
						for i in range(len(UpperCAmelCase__   )   ):
												for j in range(len(edge_array[i]   )   ):
																		A__    :	Optional[int]			=	edge_array[i][j].split("""-"""   )
																		A__    :	Optional[int]			=	t


if __name__ == "__main__":
						preprocess(edge_array)
						A_     =				get_frequency_table(edge_array)
						A_     =				get_nodes(frequency_table)
						A_     =				get_cluster(nodes)
						A_     =				get_support(cluster)
						A_     =				construct_graph(cluster, nodes)
						find_freq_subgraph_given_support(60, cluster, graph)
						A_     =				[]
						A_     =				freq_subgraphs_edge_list(paths)
						print_all()














"""simple docstring"""



from itertools import combinations, product




def   _lowerCAmelCase		(				UpperCAmelCase__							:       int,    UpperCAmelCase__							:       int,    UpperCAmelCase__							:       int,    UpperCAmelCase__							:       int   )		->bool:
						if xa == ya == 0 or xa == ya == 0:
												return False
						A__    :	List[str]			=	xa * xa + ya * ya
						A__    :	List[Any]			=	xa * xa + ya * ya
						A__    :	Optional[int]			=	(xa - xa) * (xa - xa) + (ya - ya) * (ya - ya)
						return (
						    a_square + b_square == c_square
						    or a_square + c_square == b_square
						    or b_square + c_square == a_square
						)




def   _lowerCAmelCase		(				UpperCAmelCase__							:       int = 5_0   )		->int:
						return sum(
						    1
						    for pta, pta in combinations(product(range(limit + 1   ),    repeat=2   ),    2   )
						    if is_right(*UpperCAmelCase__,    *UpperCAmelCase__   )   )


if __name__ == "__main__":
						print(F'{solution() = }')






