

# 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.
def 						_snake_case(    SCREAMING_SNAKE_CASE__			:	Optional[int]      )							->      str:





    '''simple docstring'''






    A__          =   [False] * len(SCREAMING_SNAKE_CASE__      )
    A__          =   [-1] * len(SCREAMING_SNAKE_CASE__      )

    def dfs(SCREAMING_SNAKE_CASE__			:	List[str]    ,			SCREAMING_SNAKE_CASE__			:	Optional[int]      ):
        A__          =   True
        A__          =   c
        for u in graph[v]:
            if not visited[u]:
                dfs(SCREAMING_SNAKE_CASE__    ,			1 - c      )

    for i in range(len(SCREAMING_SNAKE_CASE__      )      ):
        if not visited[i]:
            dfs(SCREAMING_SNAKE_CASE__    ,			0      )

    for i in range(len(SCREAMING_SNAKE_CASE__      )      ):
        for j in graph[i]:
            if color[i] == color[j]:
                return False

    return True


# Adjacency list of graph
lowercase_       		=  {0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2], 4: []}

print(check_bipartite_dfs(graph))







"""simple docstring"""




def     a__ (				snake_case__				)						->					bool:
			lowerCamelCase			      =					(1 + 24 * n) ** 0.5
			return ((1 + root) / 6) % 1 == 0



def     a__ (				snake_case__ = 50_00				)						->					int:
			lowerCamelCase			      =					[(i * (3 * i - 1)) // 2 for i in range(1       , snake_case__				)]
			for i, pentagonal_i in enumerate(snake_case__				):
						for j in range(snake_case__       , len(snake_case__				)				):
									lowerCamelCase			      =					pentagonal_nums[j]
									lowerCamelCase			      =					pentagonal_i + pentagonal_j
									lowerCamelCase			      =					pentagonal_j - pentagonal_i
									if is_pentagonal(snake_case__				) and is_pentagonal(snake_case__				):
												return b

			return -1


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



