


"""simple docstring"""

import sys


def lowerCAmelCase_      (				UpperCamelCase__	: Any ):






 """simple docstring"""







 __lowercase									=	len(UpperCamelCase__ )
 __lowercase									=	[[0 for x in range(UpperCamelCase__ )] for x in range(UpperCamelCase__ )]
 __lowercase									=	[[0 for x in range(UpperCamelCase__ )] for x in range(UpperCamelCase__ )]

 for chain_length in range(2				,   UpperCamelCase__ ):
  for a in range(1				,   n - chain_length + 1 ):
   __lowercase									=	a + chain_length - 1

   __lowercase									=	sys.maxsize
   for c in range(UpperCamelCase__				,   UpperCamelCase__ ):
    __lowercase									=	(
        matrix[a][c] + matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
    )
    if cost < matrix[a][b]:
     __lowercase									=	cost
     __lowercase									=	c
 return matrix, sol


def lowerCAmelCase_      (				UpperCamelCase__	: Any				,   UpperCamelCase__	: List[str]				,   UpperCamelCase__	: Optional[Any] ):






 """simple docstring"""







 if i == j:
  print("""A""" + str(UpperCamelCase__ )				,   end=""" """ )
 else:
  print("""("""				,   end=""" """ )
  print_optiomal_solution(UpperCamelCase__				,   UpperCamelCase__				,   optimal_solution[i][j] )
  print_optiomal_solution(UpperCamelCase__				,   optimal_solution[i][j] + 1				,   UpperCamelCase__ )
  print(""")"""				,   end=""" """ )


def lowerCAmelCase_      (				):






 """simple docstring"""







 __lowercase									=	[30, 35, 15, 5, 10, 20, 25]
 __lowercase									=	len(UpperCamelCase__ )
 # Size of matrix created from above array will be
 # 30*35 35*15 15*5 5*10 10*20 20*25
 __lowercase							,		__lowercase									=	matrix_chain_order(UpperCamelCase__ )

 print("""No. of Operation required: """ + str(matrix[1][n - 1] ) )
 print_optiomal_solution(UpperCamelCase__				,   1				,   n - 1 )


if __name__ == "__main__":
       main()




"""simple docstring"""

def lowerCAmelCase_      (				UpperCamelCase__	: Optional[Any]				,   UpperCamelCase__	: int				,   UpperCamelCase__	: Optional[Any]				,   UpperCamelCase__	: str ):






 """simple docstring"""







 __lowercase									=	[False] * len(UpperCamelCase__ )
 __lowercase									=	[]
 queue.append(UpperCamelCase__ )
 __lowercase									=	True

 while queue:
  __lowercase									=	queue.pop(0 )
  for ind in range(len(graph[u] ) ):
   if visited[ind] is False and graph[u][ind] > 0:
    queue.append(UpperCamelCase__ )
    __lowercase									=	True
    __lowercase									=	u

 return visited[t]


def lowerCAmelCase_      (				UpperCamelCase__	: str				,   UpperCamelCase__	: Any				,   UpperCamelCase__	: Optional[int] ):






 """simple docstring"""







 __lowercase									=	[-1] * (len(UpperCamelCase__ ))
 __lowercase									=	0
 while bfs(UpperCamelCase__				,   UpperCamelCase__				,   UpperCamelCase__				,   UpperCamelCase__ ):
  __lowercase									=	float("""Inf""" )
  __lowercase									=	sink

  while s != source:
   # Find the minimum value in select path
   __lowercase									=	min(UpperCamelCase__				,   graph[parent[s]][s] )
   __lowercase									=	parent[s]

  max_flow += path_flow
  __lowercase									=	sink

  while v != source:
   __lowercase									=	parent[v]
   graph[u][v] -= path_flow
   graph[v][u] += path_flow
   __lowercase									=	parent[v]
 return max_flow


UpperCAmelCase__  							=[
    [0, 16, 13, 0, 0, 0],
    [0, 0, 10, 12, 0, 0],
    [0, 4, 0, 0, 14, 0],
    [0, 0, 9, 0, 0, 20],
    [0, 0, 0, 7, 0, 4],
    [0, 0, 0, 0, 0, 0],
]

UpperCAmelCase__							,      UpperCAmelCase__  							=0, 5

print(ford_fulkerson(graph, source, sink))
