


'''simple docstring'''






import sys







def 							UpperCamelCase_     (       A__   :  int   ):
  '''simple docstring'''





  lowerCAmelCase_     : Any     =  len(A__   )
  lowerCAmelCase_     : Union[str, Any]     =  [[0 for x in range(A__   )] for x in range(A__   )]
  lowerCAmelCase_     : List[Any]     =  [[0 for x in range(A__   )] for x in range(A__   )]

  for chain_length in range(2				,       A__   ):
    for a in range(1				,       n - chain_length + 1   ):
      lowerCAmelCase_     : int     =  a + chain_length - 1

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







def 							UpperCamelCase_     (       A__   :  Any				,       A__   :  int				,       A__   :  Tuple   ):
  '''simple docstring'''





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







def 							UpperCamelCase_     (       ):
  '''simple docstring'''





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

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


if __name__ == "__main__":
  main()







'''simple docstring'''






from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors







def 							UpperCamelCase_     (       A__   :  int   ):
  '''simple docstring'''





  lowerCAmelCase_     : Any     =  prime_factors(A__   )
  if is_square_free(A__   ):
    return -1 if len(A__   ) % 2 else 1
  return 0


if __name__ == "__main__":
  import doctest

  doctest.testmod()



