






# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
# or u belongs to V and v to U. We can also say that there is no edge that connects
# vertices of same set.
from queue import Queue



def      UpperCAmelCase						( lowerCAmelCase__	):


		'''simple docstring'''

		__A    =							Queue()
		__A    =							[False] * len(lowerCAmelCase__	)
		__A    =							[-1] * len(lowerCAmelCase__	)

		def bfs():
				while not queue.empty():
						__A    =							queue.get()
						__A    =							True

						for neighbour in graph[u]:
								if neighbour == u:
										return False

								if color[neighbour] == -1:
										__A    =							1 - color[u]
										queue.put(lowerCAmelCase__	)

								elif color[neighbour] == color[u]:
										return False

				return True

		for i in range(len(lowerCAmelCase__	)	):
				if not visited[i]:
						queue.put(lowerCAmelCase__	)
						__A    =							0
						if bfs() is False:
								return False

		return True


if __name__ == "__main__":
					# Adjacency List of graph
					print(check_bipartite({0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2]}))









"""simple docstring"""
from __future__ import annotations






def 			lowerCamelCase_    (		_lowerCamelCase							):
 lowerCamelCase__	:     int
 lowerCamelCase__	:     list[str]								=		list(_lowerCamelCase							)
 lowerCamelCase__							,	lowerCamelCase__	:     Union[str, Any]								=		_vector[:-1], int(_vector[-1]							)
 lowerCamelCase__	:     list[int]								=		[int(_lowerCamelCase							) for digit in __vector]

 vector.reverse()
 for i, digit in enumerate(_lowerCamelCase							):
  if i & 1 == 0:
   lowerCamelCase__	:     int								=		digit * 2
   if doubled > 9:
    doubled -= 9
   check_digit += doubled
  else:
   check_digit += digit

 return check_digit % 10 == 0


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      assert is_luhn("79927398713")
      assert not is_luhn("79927398714")

