




"""simple docstring"""




import numpy as np

a_            =   [
    ['a', 'b', 'c', 'd', 'e'],
    ['f', 'g', 'h', 'i', 'k'],
    ['l', 'm', 'n', 'o', 'p'],
    ['q', 'r', 's', 't', 'u'],
    ['v', 'w', 'x', 'y', 'z'],
]

class        UpperCAmelCase_  :
		def __init__(		self   )		->   None:
					__lowercase	:       Tuple				=   np.array(UpperCamelCase_   )
		def 					_lowerCamelCase    (		self							,		UpperCamelCase_   )		->   np.ndarray:
					__lowercase	,__lowercase	:       List[Any]				=   np.where(letter == self.SQUARE   )
					__lowercase	:       Optional[Any]				=   np.concatenate([indexa + 1, indexa + 1]   )
					return indexes
		def 					_lowerCamelCase    (		self							,		UpperCamelCase_							,		UpperCamelCase_   )		->   str:
					return self.SQUARE[indexa - 1, indexa - 1]
		def 					_lowerCamelCase    (		self							,		UpperCamelCase_   )		->   str:
					__lowercase	:       Any				=   message.lower()
					__lowercase	:       List[Any]				=   message.replace('''j'''							,		'''i'''   )

					__lowercase	:       str				=   ''''''
					for letter_index in range(len(UpperCamelCase_   )   ):
								if message[letter_index] != " ":
											__lowercase	:       Dict				=   self.letter_to_numbers(message[letter_index]   )
											__lowercase	:       Any				=   encoded_message + str(numbers[0]   ) + str(numbers[1]   )
								elif message[letter_index] == " ":
											__lowercase	:       Union[str, Any]				=   encoded_message + ''' '''

					return encoded_message
		def 					_lowerCamelCase    (		self							,		UpperCamelCase_   )		->   str:
					__lowercase	:       str				=   message.replace(''' '''							,		'''  '''   )
					__lowercase	:       Any				=   ''''''
					for numbers_index in range(int(len(UpperCamelCase_   ) / 2   )   ):
								if message[numbers_index * 2] != " ":
											__lowercase	:       int				=   message[numbers_index * 2]
											__lowercase	:       Dict				=   message[numbers_index * 2 + 1]

											__lowercase	:       Any				=   self.numbers_to_letter(int(UpperCamelCase_   )							,		int(UpperCamelCase_   )   )
											__lowercase	:       List[str]				=   decoded_message + letter
								elif message[numbers_index * 2] == " ":
											__lowercase	:       int				=   decoded_message + ''' '''

					return decoded_message









"""simple docstring"""




# 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      (				__UpperCamelCase					):
			__lowercase	:       int				=   Queue()
			__lowercase	:       str				=   [False] * len(__UpperCamelCase					)
			__lowercase	:       str				=   [-1] * len(__UpperCamelCase					)

			def bfs():
						while not queue.empty():
									__lowercase	:       int				=   queue.get()
									__lowercase	:       List[str]				=   True

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

												if color[neighbour] == -1:
															__lowercase	:       str				=   1 - color[u]
															queue.put(__UpperCamelCase					)

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

						return True

			for i in range(len(__UpperCamelCase					)					):
						if not visited[i]:
									queue.put(__UpperCamelCase					)
									__lowercase	:       int				=   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]}))



