
from __future__ import annotations



def    _lowercase       (   __SCREAMING_SNAKE_CASE			)						->  Optional[int]:
			UpperCamelCase__     :		Dict	 =					[True] * limit
			UpperCamelCase__     :		Union[str, Any]	 =					False
			UpperCamelCase__     :		Tuple	 =					False
			UpperCamelCase__     :		str	 =					True

			for i in range(3					,     int(limit**0.5 + 1			)					,     2			):
						UpperCamelCase__     :		List[Any]	 =					i * 2
						while index < limit:
									UpperCamelCase__     :		Tuple	 =					False
									UpperCamelCase__     :		List[Any]	 =					index + i

			UpperCamelCase__     :		Tuple	 =					[2]

			for i in range(3					,     UpperCamelCase__					,     2			):
						if is_prime[i]:
									primes.append(UpperCamelCase__			)

			return primes



def    _lowercase       (   __SCREAMING_SNAKE_CASE = 100_0000			)						->  Optional[int]:
			UpperCamelCase__     :		str	 =					prime_sieve(UpperCamelCase__			)
			UpperCamelCase__     :		Optional[Any]	 =					0
			UpperCamelCase__     :		Dict	 =					0

			for i in range(len(UpperCamelCase__			)			):
						for j in range(i + length					,     len(UpperCamelCase__			)			):
									UpperCamelCase__     :		Optional[Any]	 =					sum(primes[i:j]			)
									if sol >= ceiling:
												break

									if sol in primes:
												UpperCamelCase__     :		Tuple	 =					j - i
												UpperCamelCase__     :		Dict	 =					sol

			return largest


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







'''simple docstring'''
def       _lowercase							(					UpperCamelCase__							:       dict      ):
 __A	:		Dict	  =      set()
 # edges = list of graph's edges
 __A	:		Any	  =      get_edges(UpperCamelCase__      )

 # While there are still elements in edges list, take an arbitrary edge
 # (from_node, to_node) and add his extremity to chosen_vertices and then
 # remove all arcs adjacent to the from_node and to_node
 while edges:
  __A  ,__A	:		List[Any]	  =      edges.pop()
  chosen_vertices.add(UpperCamelCase__      )
  chosen_vertices.add(UpperCamelCase__      )
  for edge in edges.copy():
   if from_node in edge or to_node in edge:
    edges.discard(UpperCamelCase__      )
 return chosen_vertices


def       _lowercase							(					UpperCamelCase__							:       dict      ):
 __A	:		Any	  =      set()
 for from_node, to_nodes in graph.items():
  for to_node in to_nodes:
   edges.add((from_node, to_node)      )
 return edges


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 # graph = {0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
 # print(f"Matching vertex cover:\n{matching_min_vertex_cover(graph)}")






