




import sys



def       UpperCAmelCase__  (     lowerCamelCase   ):
  lowercase    :str      	=						len(lowerCamelCase   )
  lowercase    :List[Any]      	=						[[0 for x in range(lowerCamelCase   )] for x in range(lowerCamelCase   )]
  lowercase    :Tuple      	=						[[0 for x in range(lowerCamelCase   )] for x in range(lowerCamelCase   )]

  for chain_length in range(2,			lowerCamelCase   ):
    for a in range(1,			n - chain_length + 1   ):
      lowercase    :List[str]      	=						a + chain_length - 1

      lowercase    :Optional[int]      	=						sys.maxsize
      for c in range(lowerCamelCase,			lowerCamelCase   ):
        lowercase    :str      	=						(
            matrix[a][c] + matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
        )
        if cost < matrix[a][b]:
          lowercase    :Optional[Any]      	=						cost
          lowercase    :Any      	=						c
  return matrix, sol



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



def       UpperCAmelCase__  (     ):
  lowercase    :Any      	=						[30, 35, 15, 5, 10, 20, 25]
  lowercase    :Optional[Any]      	=						len(lowerCamelCase   )
  # Size of matrix created from above array will be
  # 30*35 35*15 15*5 5*10 10*20 20*25
  lowercase	,    lowercase    :Optional[int]      	=						matrix_chain_order(lowerCamelCase   )

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


if __name__ == "__main__":
     main()









def       UpperCAmelCase__  (     lowerCamelCase,			lowerCamelCase   ):
  if discount_rate < 0:
    raise ValueError("Discount rate cannot be negative"   )
  if not cash_flows:
    raise ValueError("Cash flows list cannot be empty"   )
  lowercase    :Dict      	=						sum(
      cash_flow / ((1 + discount_rate) ** i) for i, cash_flow in enumerate(lowerCamelCase   )   )
  return round(lowerCamelCase,			ndigits=2   )


if __name__ == "__main__":
     import doctest

     doctest.testmod()



