'''simple docstring'''


import math


def    _lowerCamelCase       ( lowerCamelCase_   :				int  ):



     """simple docstring"""





     if n <= 0:
          raise ValueError('Only positive integers have prime factors'  )
     UpperCAmelCase_				:  str  = []
     while n % 2 == 0:
          pf.append(2  )
          UpperCAmelCase_				:  Tuple  = int(n / 2  )
     for i in range(3      ,	int(math.sqrt(lowerCamelCase_  )  ) + 1      ,	2  ):
          while n % i == 0:
               pf.append(lowerCamelCase_  )
               UpperCAmelCase_				:  Tuple  = int(n / i  )
     if n > 2:
          pf.append(lowerCamelCase_  )
     return pf


def    _lowerCamelCase       ( lowerCamelCase_   :				int  ):



     """simple docstring"""





     if n <= 0:
          raise ValueError('Only positive numbers are accepted'  )
     UpperCAmelCase_				:  List[Any]  = 1
     UpperCAmelCase_				:  List[str]  = 1
     while n % 2 == 0:
          temp += 1
          UpperCAmelCase_				:  Any  = int(n / 2  )
     div *= temp
     for i in range(3      ,	int(math.sqrt(lowerCamelCase_  )  ) + 1      ,	2  ):
          UpperCAmelCase_				:  Any  = 1
          while n % i == 0:
               temp += 1
               UpperCAmelCase_				:  List[Any]  = int(n / i  )
          div *= temp
     if n > 1:
          div *= 2
     return div


def    _lowerCamelCase       ( lowerCamelCase_   :				int  ):



     """simple docstring"""





     if n <= 0:
          raise ValueError('Only positive numbers are accepted'  )
     UpperCAmelCase_				:  Any  = 1
     UpperCAmelCase_				:  Union[str, Any]  = 1
     while n % 2 == 0:
          temp += 1
          UpperCAmelCase_				:  str  = int(n / 2  )
     if temp > 1:
          s *= (2**temp - 1) / (2 - 1)
     for i in range(3      ,	int(math.sqrt(lowerCamelCase_  )  ) + 1      ,	2  ):
          UpperCAmelCase_				:  Dict  = 1
          while n % i == 0:
               temp += 1
               UpperCAmelCase_				:  str  = int(n / i  )
          if temp > 1:
               s *= (i**temp - 1) / (i - 1)
     return int(lowerCamelCase_  )


def    _lowerCamelCase       ( lowerCamelCase_   :				int  ):



     """simple docstring"""





     UpperCAmelCase_				:  List[str]  = n
     for x in set(prime_factors(lowerCamelCase_  )  ):
          s *= (x - 1) / x
     return int(lowerCamelCase_  )


if __name__ == "__main__":
 import doctest

 doctest.testmod()














"""simple docstring"""
def 			lowerCamelCase_    (		_lowerCamelCase     ,  _lowerCamelCase     ,  _lowerCamelCase     ,  _lowerCamelCase     ,  _lowerCamelCase     ,  _lowerCamelCase     ,  ):
 lowerCamelCase__	:     Any								=		list(_lowerCamelCase							)
 lowerCamelCase__	:     List[Any]								=		list(_lowerCamelCase							)
 lowerCamelCase__	:     int								=		len(_lowerCamelCase							)
 lowerCamelCase__	:     Optional[int]								=		len(_lowerCamelCase							)

 lowerCamelCase__	:     Tuple								=		[
     [0 for _ in range(len_destination_seq + 1							)] for _ in range(len_source_seq + 1							)
 ]
 lowerCamelCase__	:     Dict								=		[
     ['0' for _ in range(len_destination_seq + 1							)] for _ in range(len_source_seq + 1							)
 ]

 for i in range(1     ,  len_source_seq + 1							):
  lowerCamelCase__	:     Optional[int]								=		i * delete_cost
  lowerCamelCase__	:     List[str]								=		f'''D{source_seq[i - 1]:c}'''

 for i in range(1     ,  len_destination_seq + 1							):
  lowerCamelCase__	:     int								=		i * insert_cost
  lowerCamelCase__	:     str								=		f'''I{destination_seq[i - 1]:c}'''

 for i in range(1     ,  len_source_seq + 1							):
  for j in range(1     ,  len_destination_seq + 1							):
   if source_seq[i - 1] == destination_seq[j - 1]:
    lowerCamelCase__	:     Any								=		costs[i - 1][j - 1] + copy_cost
    lowerCamelCase__	:     str								=		f'''C{source_seq[i - 1]:c}'''
   else:
    lowerCamelCase__	:     Tuple								=		costs[i - 1][j - 1] + replace_cost
    lowerCamelCase__	:     List[str]								=		f'''R{source_seq[i - 1]:c}''' + str(destination_seq[j - 1]							)

   if costs[i - 1][j] + delete_cost < costs[i][j]:
    lowerCamelCase__	:     Any								=		costs[i - 1][j] + delete_cost
    lowerCamelCase__	:     Union[str, Any]								=		f'''D{source_seq[i - 1]:c}'''

   if costs[i][j - 1] + insert_cost < costs[i][j]:
    lowerCamelCase__	:     Optional[Any]								=		costs[i][j - 1] + insert_cost
    lowerCamelCase__	:     Union[str, Any]								=		f'''I{destination_seq[j - 1]:c}'''

 return costs, ops






def 			lowerCamelCase_    (		_lowerCamelCase     ,  _lowerCamelCase     ,  _lowerCamelCase							):
 if i == 0 and j == 0:
  return []
 else:
  if ops[i][j][0] == "C" or ops[i][j][0] == "R":
   lowerCamelCase__	:     List[str]								=		assemble_transformation(_lowerCamelCase     ,  i - 1     ,  j - 1							)
   seq.append(ops[i][j]							)
   return seq
  elif ops[i][j][0] == "D":
   lowerCamelCase__	:     Union[str, Any]								=		assemble_transformation(_lowerCamelCase     ,  i - 1     ,  _lowerCamelCase							)
   seq.append(ops[i][j]							)
   return seq
  else:
   lowerCamelCase__	:     Tuple								=		assemble_transformation(_lowerCamelCase     ,  _lowerCamelCase     ,  j - 1							)
   seq.append(ops[i][j]							)
   return seq


if __name__ == "__main__":
      A_,			A_     :					List[str]							=     compute_transform_tables("Python", "Algorithms", -1, 1, 2, 2)

      A_     :					str							=     len(operations)
      A_     :					Dict							=     len(operations[0])
      A_     :					Any							=     assemble_transformation(operations, m - 1, n - 1)

      A_     :					int							=     list("Python")
      A_     :					Optional[Any]							=     0
      A_     :					Tuple							=     0

      with open("min_cost.txt", "w") as file:
            for op in sequence:
                  print("".join(string))

                  if op[0] == "C":
                        file.write("%-16s" % "Copy %c" % op[1])
                        file.write("\t\t\t" + "".join(string))
                        file.write("\r\n")

                        cost -= 1
                  elif op[0] == "R":
                        A_     :					str							=     op[2]

                        file.write("%-16s" % ("Replace %c" % op[1] + " with " + str(op[2])))
                        file.write("\t\t" + "".join(string))
                        file.write("\r\n")

                        cost += 1
                  elif op[0] == "D":
                        string.pop(i)

                        file.write("%-16s" % "Delete %c" % op[1])
                        file.write("\t\t\t" + "".join(string))
                        file.write("\r\n")

                        cost += 2
                  else:
                        string.insert(i, op[1])

                        file.write("%-16s" % "Insert %c" % op[1])
                        file.write("\t\t\t" + "".join(string))
                        file.write("\r\n")

                        cost += 2

                  i += 1

            print("".join(string))
            print("Cost: ", cost)

            file.write("\r\nMinimum cost: " + str(cost))

