

def   a   (    A__			:     List[str]   ,     A__			:     Optional[Any]  )					->   Any:





      """simple docstring"""



      print('\nThe shortest path matrix using Floyd Warshall algorithm\n'  )
      for i in range(A__  ):
            for j in range(A__  ):
                  if dist[i][j] != float('inf'  ):
                        print(int(dist[i][j]  )   ,     end='\t'  )
                  else:
                        print('INF'   ,     end='\t'  )
            print()
def   a   (    A__			:     List[str]   ,     A__			:     Any  )					->   Optional[int]:





      """simple docstring"""



      _lowercase			 =[[float('inf'  ) for _ in range(A__  )] for _ in range(A__  )]

      for i in range(A__  ):
            for j in range(A__  ):
                  _lowercase			 =graph[i][j]

                  # check vertex k against all other vertices (i, j)
      for k in range(A__  ):
            # looping through rows of graph array
            for i in range(A__  ):
                  # looping through columns of graph array
                  for j in range(A__  ):
                        if (
                            dist[i][k] != float('inf'  )
                            and dist[k][j] != float('inf'  )
                            and dist[i][k] + dist[k][j] < dist[i][j]
                        ):
                              _lowercase			 =dist[i][k] + dist[k][j]

      _print_dist(A__   ,     A__  )
      return dist, v


if __name__ == "__main__":
  lowercase_             =     int(input('Enter number of vertices: '))
  lowercase_             =     int(input('Enter number of edges: '))

  lowercase_             =     [[float('inf') for i in range(v)] for j in range(v)]

  for i in range(v):
    lowercase_             =     0.0

    # src and dst are indices that must be within the array size graph[e][v]
    # failure to follow this will result in an error
  for i in range(e):
    print('\nEdge ', i + 1)
    lowercase_             =     int(input('Enter source:'))
    lowercase_             =     int(input('Enter destination:'))
    lowercase_             =     float(input('Enter weight:'))
    lowercase_             =     weight

  floyd_warshall(graph, v)

  # Example Input
  # Enter number of vertices: 3
  # Enter number of edges: 2

  # # generated graph from vertex and edge inputs
  # [[inf, inf, inf], [inf, inf, inf], [inf, inf, inf]]
  # [[0.0, inf, inf], [inf, 0.0, inf], [inf, inf, 0.0]]

  # specify source, destination and weight for edge #1
  # Edge  1
  # Enter source:1
  # Enter destination:2
  # Enter weight:2

  # specify source, destination and weight for edge #2
  # Edge  2
  # Enter source:2
  # Enter destination:1
  # Enter weight:1

  # # Expected Output from the vertice, edge and src, dst, weight inputs!!
  # 0		INF	INF
  # INF	0	2
  # INF	1	0





from math import pow, sqrt
def   a   (    *A__			:     float  )					->   bool:





      """simple docstring"""



      _lowercase			 =len(A__  ) > 0 and all(value > 0.0 for value in values  )
      return result
def   a   (    A__			:     float   ,     A__			:     float  )					->   float | ValueError:





      """simple docstring"""



      return (
          round(sqrt(molar_mass_a / molar_mass_a  )   ,     6  )
          if validate(A__   ,     A__  )
          else ValueError('Input Error: Molar mass values must greater than 0.'  )
      )
def   a   (    A__			:     float   ,     A__			:     float   ,     A__			:     float  )					->   float | ValueError:





      """simple docstring"""



      return (
          round(effusion_rate * sqrt(molar_mass_a / molar_mass_a  )   ,     6  )
          if validate(A__   ,     A__   ,     A__  )
          else ValueError(
              'Input Error: Molar mass and effusion rate values must greater than 0.'  )
      )
def   a   (    A__			:     float   ,     A__			:     float   ,     A__			:     float  )					->   float | ValueError:





      """simple docstring"""



      return (
          round(effusion_rate / sqrt(molar_mass_a / molar_mass_a  )   ,     6  )
          if validate(A__   ,     A__   ,     A__  )
          else ValueError(
              'Input Error: Molar mass and effusion rate values must greater than 0.'  )
      )
def   a   (    A__			:     float   ,     A__			:     float   ,     A__			:     float  )					->   float | ValueError:





      """simple docstring"""



      return (
          round(molar_mass / pow(effusion_rate_a / effusion_rate_a   ,     2  )   ,     6  )
          if validate(A__   ,     A__   ,     A__  )
          else ValueError(
              'Input Error: Molar mass and effusion rate values must greater than 0.'  )
      )







def   a   (    A__			:     float   ,     A__			:     float   ,     A__			:     float  )					->   float | ValueError:





      """simple docstring"""



      return (
          round(pow(effusion_rate_a / effusion_rate_a   ,     2  ) / molar_mass   ,     6  )
          if validate(A__   ,     A__   ,     A__  )
          else ValueError(
              'Input Error: Molar mass and effusion rate values must greater than 0.'  )
      )


