




'''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.


def 		__magic_name__    (	__UpperCAmelCase	)		->					Optional[Any]:

					'''simple docstring'''

					snake_case_									=				[False] * len(__UpperCAmelCase	)
					snake_case_									=				[-1] * len(__UpperCAmelCase	)

					def dfs(__UpperCAmelCase,      __UpperCAmelCase	):
										snake_case_									=				True
										snake_case_									=				c
										for u in graph[v]:
															if not visited[u]:
																				dfs(__UpperCAmelCase,      1 - c	)

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

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

					return True


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

print(check_bipartite_dfs(graph))






'''simple docstring'''





import math






class __A			:



 '''simple docstring'''







 def __init__(self ,   A=0       )    ->     Dict:  # a graph with Node 0,1,...,N-1


      """simple docstring"""



      _a      =  n
      _a      =  [
          [math.inf for j in range(0 ,   A       )] for i in range(0 ,   A       )
      ]  # adjacency matrix for weight
      _a      =  [
          [math.inf for j in range(0 ,   A       )] for i in range(0 ,   A       )
      ]  # dp[i][j] stores minimum distance from i to j



 def 					a__  (self ,   A ,   A ,   A       )    ->     Tuple:


      """simple docstring"""



      _a      =  w



 def 					a__  (self       )    ->     List[Any]:


      """simple docstring"""



      for k in range(0 ,   self.n       ):
           for i in range(0 ,   self.n       ):
                for j in range(0 ,   self.n       ):
                     _a      =  min(self.dp[i][j] ,   self.dp[i][k] + self.dp[k][j]       )



 def 					a__  (self ,   A ,   A       )    ->     str:


      """simple docstring"""



      return self.dp[u][v]


if __name__ == "__main__":
  lowercase_		       =  Graph(5)
  graph.add_edge(0, 2, 9)
  graph.add_edge(0, 4, 10)
  graph.add_edge(1, 3, 5)
  graph.add_edge(2, 3, 7)
  graph.add_edge(3, 0, 10)
  graph.add_edge(3, 1, 2)
  graph.add_edge(3, 2, 1)
  graph.add_edge(3, 4, 6)
  graph.add_edge(4, 1, 3)
  graph.add_edge(4, 2, 4)
  graph.add_edge(4, 3, 9)
  graph.floyd_warshall()
  graph.show_min(1, 4)
  graph.show_min(0, 3)



