
def       A__      (    __lowerCamelCase = 10**12		):
   SCREAMING_SNAKE_CASE_     =	1
   SCREAMING_SNAKE_CASE_     =	0

   SCREAMING_SNAKE_CASE_     =	1
   SCREAMING_SNAKE_CASE_     =	1

   while numerator <= 2 * min_total - 1:
      prev_numerator += 2 * numerator
      numerator += 2 * prev_numerator

      prev_denominator += 2 * denominator
      denominator += 2 * prev_denominator

   return (denominator + 1) // 2


if __name__ == "__main__":
   print(F"""{solution() = }""")









def 			A__							(    SCREAMING_SNAKE_CASE__)   ->    Union[str, Any]:
  __snake_case:						List[Any]   =						[]
  __snake_case:						List[str]   =						[]
  __snake_case:						List[str]   =						{
      """^""": 3,
      """*""": 2,
      """/""": 2,
      """%""": 2,
      """+""": 1,
      """-""": 1,
  }  # Priority of each operator
  __snake_case:						Union[str, Any]   =						len(SCREAMING_SNAKE_CASE__) if (len(SCREAMING_SNAKE_CASE__) > 7) else 7

  # Print table header for output
  print(
      """Symbol""".center(8)					,					"""Stack""".center(SCREAMING_SNAKE_CASE__)					,					"""Postfix""".center(SCREAMING_SNAKE_CASE__)					,					sep=""" | """					,					)
  print("""-""" * (print_width * 3 + 7))

  for x in infix:
    if x.isalpha() or x.isdigit():
      post_fix.append(SCREAMING_SNAKE_CASE__)  # if x is Alphabet / Digit, add it to Postfix
    elif x == "(":
      stack.append(SCREAMING_SNAKE_CASE__)  # if x is "(" push to Stack
    elif x == ")":  # if x is ")" pop stack until "(" is encountered
      while stack[-1] != "(":
        post_fix.append(stack.pop())  # Pop stack & add the content to Postfix
      stack.pop()
    else:
      if len(SCREAMING_SNAKE_CASE__) == 0:
        stack.append(SCREAMING_SNAKE_CASE__)  # If stack is empty, push x to stack
      else:  # while priority of x is not > priority of element in the stack
        while len(SCREAMING_SNAKE_CASE__) > 0 and priority[x] <= priority[stack[-1]]:
          post_fix.append(stack.pop())  # pop stack & add to Postfix
        stack.append(SCREAMING_SNAKE_CASE__)  # push x to stack

    print(
        x.center(8)					,					("""""".join(SCREAMING_SNAKE_CASE__)).ljust(SCREAMING_SNAKE_CASE__)					,					("""""".join(SCREAMING_SNAKE_CASE__)).ljust(SCREAMING_SNAKE_CASE__)					,					sep=""" | """					,					)  # Output in tabular format

  while len(SCREAMING_SNAKE_CASE__) > 0:  # while stack is not empty
    post_fix.append(stack.pop())  # pop stack & add to Postfix
    print(
        """ """.center(8)					,					("""""".join(SCREAMING_SNAKE_CASE__)).ljust(SCREAMING_SNAKE_CASE__)					,					("""""".join(SCREAMING_SNAKE_CASE__)).ljust(SCREAMING_SNAKE_CASE__)					,					sep=""" | """					,					)  # Output in tabular format

  return "".join(SCREAMING_SNAKE_CASE__)  # return Postfix as str







def 			A__							(    SCREAMING_SNAKE_CASE__)   ->    Tuple:
  __snake_case:						Optional[int]   =						list(infix[::-1])  # reverse the infix equation

  for i in range(len(SCREAMING_SNAKE_CASE__)):
    if infix[i] == "(":
      __snake_case:						int   =						""")"""  # change "(" to ")"
    elif infix[i] == ")":
      __snake_case:						Dict   =						"""("""  # change ")" to "("

  return (infix_2_postfix("""""".join(SCREAMING_SNAKE_CASE__)))[
      ::-1
  ]  # call infix_2_postfix on Infix, return reverse of Postfix


if __name__ == "__main__":
      __UpperCAmelCase       :   Optional[int]				       =							input("\nEnter an Infix Equation = ")  # Input an Infix equation
      __UpperCAmelCase       :   int				       =							"".join(Infix.split())  # Remove spaces from the input
      print("\n\t", Infix, "(Infix) -> ", infix_2_prefix(Infix), "(Prefix)")






