





'''simple docstring'''






A :			Optional[int]							   =      [
    ['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    lowercase_   (		lowercase__    ) ->str:
						_snake_case: Union[str, Any]	       =		set()
						for row in edge_array:
												for item in row:
																		distinct_edge.add(item[0]    )
						return list(lowercase__    )





def    lowercase_   (		lowercase__					,	lowercase__    ) ->Optional[int]:
						_snake_case: Optional[int]	       =		['0'] * len(lowercase__    )
						for i, row in enumerate(lowercase__    ):
												for item in row:
																		if distinct_edge in item[0]:
																								_snake_case: Dict	       =		'1'
																								break
						return "".join(lowercase__    )





def    lowercase_   (		lowercase__    ) ->int:
						_snake_case: List[Any]	       =		get_distinct_edge(lowercase__    )
						_snake_case: List[Any]	       =		{}

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





def    lowercase_   (		lowercase__    ) ->Union[str, Any]:
						_snake_case: Optional[Any]	       =		{}
						for _, item in enumerate(lowercase__    ):
												nodes.setdefault(item[2]					,	[]    ).append(item[0]    )
						return nodes





def    lowercase_   (		lowercase__    ) ->List[Any]:
						_snake_case: Any	       =		{}
						for key, value in nodes.items():
												_snake_case: Dict	       =		value
						return cluster





def    lowercase_   (		lowercase__    ) ->str:
						return [i * 100 / len(lowercase__    ) for i in cluster]





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





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





def    lowercase_   (		lowercase__					,	lowercase__    ) ->int:
						_snake_case: List[str]	       =		cluster[max(cluster.keys()    )]
						_snake_case: Tuple	       =		'Header'
						_snake_case: Any	       =		{}
						for i in x:
												if (["Header"],) in graph:
																		graph[(["Header"],)].append(x[i]    )
												else:
																		_snake_case: List[Any]	       =		[x[i]]
						for i in x:
												_snake_case: str	       =		[['Header']]
						_snake_case: str	       =		1
						while i < max(lowercase__    ) - 1:
												create_edge(lowercase__					,	lowercase__					,	lowercase__					,	lowercase__    )
												_snake_case: Any	       =		i + 1
						return graph





def    lowercase_   (		lowercase__					,	lowercase__					,	lowercase__					,	lowercase__=None    ) ->List[str]:
						_snake_case: Any	       =		(path or []) + [start]
						if start == end:
												paths.append(lowercase__    )
						for node in graph[start]:
												if tuple(lowercase__    ) not in path:
																		my_dfs(lowercase__					,	tuple(lowercase__    )					,	lowercase__					,	lowercase__    )





def    lowercase_   (		lowercase__					,	lowercase__					,	lowercase__    ) ->Any:
						_snake_case: Optional[int]	       =		int(s / 100 * (len(lowercase__    ) - 1)    )
						for i in cluster[k]:
												my_dfs(lowercase__					,	tuple(cluster[k][i]    )					,	(['Header'],)    )





def    lowercase_   (		lowercase__    ) ->int:
						_snake_case: List[str]	       =		[]
						for edges in paths:
												_snake_case: Optional[Any]	       =		[]
												for j in range(len(lowercase__    ) - 1    ):
																		_snake_case: Optional[int]	       =		list(edges[j]    )
																		for e in temp:
																								_snake_case: Optional[int]	       =		(e[0], e[1])
																								el.append(lowercase__    )
												freq_sub_el.append(lowercase__    )
						return freq_sub_el





def    lowercase_   (		lowercase__    ) ->Optional[int]:
						for i in range(len(lowercase__    )    ):
												for j in range(len(edge_array[i]    )    ):
																		_snake_case: Tuple	       =		edge_array[i][j].split('-'    )
																		_snake_case: Dict	       =		t


if __name__ == "__main__":
		preprocess(edge_array)
		A :			Optional[Any]							   =      get_frequency_table(edge_array)
		A :			Optional[Any]							   =      get_nodes(frequency_table)
		A :			List[Any]							   =      get_cluster(nodes)
		A :			Any							   =      get_support(cluster)
		A :			List[Any]							   =      construct_graph(cluster, nodes)
		find_freq_subgraph_given_support(60, cluster, graph)
		A :			list							   =      []
		A :			List[str]							   =      freq_subgraphs_edge_list(paths)
		print_all()












'''simple docstring'''






import math
from collections.abc import Generator





def    lowercase_   (		lowercase__    ) ->Generator[int, None, None]:
						_snake_case: Generator	       =		(i for i in range(1					,	(max_n + 1)    ))
						for i in (n for n in numbers if n > 1):
												for j in range(2					,	lowercase__    ):
																		if (i % j) == 0:
																								break
												else:
																		yield i





def    lowercase_   (		lowercase__    ) ->Generator[int, None, None]:
						_snake_case: Generator	       =		(i for i in range(1					,	(max_n + 1)    ))
						for i in (n for n in numbers if n > 1):
												# only need to check for factors up to sqrt(i)
												_snake_case: int	       =		int(math.sqrt(lowercase__    )    ) + 1
												for j in range(2					,	lowercase__    ):
																		if (i % j) == 0:
																								break
												else:
																		yield i





def    lowercase_   (		lowercase__    ) ->Generator[int, None, None]:
						_snake_case: Generator	       =		(i for i in range(1					,	(max_n + 1)					,	2    ))
						# It's useless to test even numbers as they will not be prime
						if max_n > 2:
												yield 2  # Because 2 will not be tested, it's necessary to yield it now
						for i in (n for n in numbers if n > 1):
												_snake_case: List[str]	       =		int(math.sqrt(lowercase__    )    ) + 1
												for j in range(3					,	lowercase__					,	2    ):
																		# As we removed the even numbers, we don't need them now
																		if (i % j) == 0:
																								break
												else:
																		yield i





def    lowercase_   (		) ->Optional[int]:
						from timeit import timeit

						_snake_case: Dict	       =		'from __main__ import slow_primes, primes, fast_primes'
						print(timeit('slow_primes(1_000_000_000_000)'					,	setup=lowercase__					,	number=100_0000    )    )
						print(timeit('primes(1_000_000_000_000)'					,	setup=lowercase__					,	number=100_0000    )    )
						print(timeit('fast_primes(1_000_000_000_000)'					,	setup=lowercase__					,	number=100_0000    )    )


if __name__ == "__main__":
		A :			List[str]							   =      int(input('Calculate primes up to:\n>> ').strip())
		for ret in primes(number):
				print(ret)
		benchmark()





