



"""simple docstring"""







from string import ascii_uppercase

lowercase__		:    Dict				   =     {char: i for i, char in enumerate(ascii_uppercase)}
lowercase__		:    int				   =     dict(enumerate(ascii_uppercase))

def     UpperCamelCase_   (   lowerCAmelCase__				:    str   ,       lowerCAmelCase__				:    str						)						->       str:

  """simple docstring"""




  lowerCAmelCase_       :    Dict								=			len(lowerCAmelCase__						)
  lowerCAmelCase_       :    Optional[Any]								=			0
  while True:
    if x == i:
      lowerCAmelCase_       :    List[Any]								=			0
    if len(lowerCAmelCase__						) == len(lowerCAmelCase__						):
      break
    key += key[i]
    i += 1
  return key

def     UpperCamelCase_   (   lowerCAmelCase__				:    str   ,       lowerCAmelCase__				:    str						)						->       str:

  """simple docstring"""




  lowerCAmelCase_       :    int								=			''
  lowerCAmelCase_       :    List[str]								=			0
  for letter in message:
    if letter == " ":
      cipher_text += " "
    else:
      lowerCAmelCase_       :    Union[str, Any]								=			(dicta[letter] - dicta[key_new[i]]) % 26
      i += 1
      cipher_text += dicta[x]
  return cipher_text

def     UpperCamelCase_   (   lowerCAmelCase__				:    str   ,       lowerCAmelCase__				:    str						)						->       str:

  """simple docstring"""




  lowerCAmelCase_       :    Dict								=			''
  lowerCAmelCase_       :    Dict								=			0
  for letter in cipher_text:
    if letter == " ":
      or_txt += " "
    else:
      lowerCAmelCase_       :    List[Any]								=			(dicta[letter] + dicta[key_new[i]] + 26) % 26
      i += 1
      or_txt += dicta[x]
  return or_txt

def     UpperCamelCase_   (   )						->       None:

  """simple docstring"""




  lowerCAmelCase_       :    List[Any]								=			'THE GERMAN ATTACK'
  lowerCAmelCase_       :    List[str]								=			'SECRET'
  lowerCAmelCase_       :    Dict								=			generate_key(lowerCAmelCase__   ,       lowerCAmelCase__						)
  lowerCAmelCase_       :    Dict								=			cipher_text(lowerCAmelCase__   ,       lowerCAmelCase__						)
  print(f"Encrypted Text = {s}"						)
  print(f"Original Text = {original_text(lowerCAmelCase__   ,       lowerCAmelCase__						)}"						)


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     main()










"""simple docstring"""







from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt

def     UpperCamelCase_   (   lowerCAmelCase__				:    int						)						->       bool:

  """simple docstring"""




  lowerCAmelCase_       :    int								=			int(number**0.5						)
  return number == sq * sq

def     UpperCamelCase_   (   lowerCAmelCase__				:    int   ,       lowerCAmelCase__				:    int   ,       lowerCAmelCase__				:    int   ,       lowerCAmelCase__				:    int   ,       lowerCAmelCase__				:    int   ,       lowerCAmelCase__				:    int						)						->       tuple[int, int]:

  """simple docstring"""




  lowerCAmelCase_       :    int								=			x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
  lowerCAmelCase_       :    int								=			x_den * y_den * z_den
  lowerCAmelCase_       :    int								=			gcd(lowerCAmelCase__   ,       lowerCAmelCase__						)
  top //= hcf
  bottom //= hcf
  return top, bottom

def     UpperCamelCase_   (   lowerCAmelCase__				:    int = 35						)						->       int:

  """simple docstring"""




  lowerCAmelCase_       :    set								=			set()
  lowerCAmelCase_       :    int
  lowerCAmelCase_       :    Fraction								=			Fraction(0						)
  lowerCAmelCase_       :    tuple[int, int]

  for x_num in range(1   ,       order + 1						):
    for x_den in range(x_num + 1   ,       order + 1						):
      for y_num in range(1   ,       order + 1						):
        for y_den in range(y_num + 1   ,       order + 1						):
          # n=1
          lowerCAmelCase_       :    str								=			x_num * y_den + x_den * y_num
          lowerCAmelCase_       :    int								=			x_den * y_den
          lowerCAmelCase_       :    int								=			gcd(lowerCAmelCase__   ,       lowerCAmelCase__						)
          z_num //= hcf
          z_den //= hcf
          if 0 < z_num < z_den <= order:
            lowerCAmelCase_       :    List[str]								=			add_three(
                lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__						)
            unique_s.add(lowerCAmelCase__						)

          # n=2
          lowerCAmelCase_       :    Optional[int]								=			(
              x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
          )
          lowerCAmelCase_       :    Dict								=			x_den * x_den * y_den * y_den
          if is_sq(lowerCAmelCase__						) and is_sq(lowerCAmelCase__						):
            lowerCAmelCase_       :    Optional[int]								=			int(sqrt(lowerCAmelCase__						)						)
            lowerCAmelCase_       :    List[str]								=			int(sqrt(lowerCAmelCase__						)						)
            lowerCAmelCase_       :    Union[str, Any]								=			gcd(lowerCAmelCase__   ,       lowerCAmelCase__						)
            z_num //= hcf
            z_den //= hcf
            if 0 < z_num < z_den <= order:
              lowerCAmelCase_       :    Union[str, Any]								=			add_three(
                  lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__						)
              unique_s.add(lowerCAmelCase__						)

                    # n=-1
          lowerCAmelCase_       :    Dict								=			x_num * y_num
          lowerCAmelCase_       :    Optional[int]								=			x_den * y_num + x_num * y_den
          lowerCAmelCase_       :    Any								=			gcd(lowerCAmelCase__   ,       lowerCAmelCase__						)
          z_num //= hcf
          z_den //= hcf
          if 0 < z_num < z_den <= order:
            lowerCAmelCase_       :    Tuple								=			add_three(
                lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__						)
            unique_s.add(lowerCAmelCase__						)

          # n=2
          lowerCAmelCase_       :    List[str]								=			x_num * x_num * y_num * y_num
          lowerCAmelCase_       :    Optional[Any]								=			(
              x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
          )
          if is_sq(lowerCAmelCase__						) and is_sq(lowerCAmelCase__						):
            lowerCAmelCase_       :    Tuple								=			int(sqrt(lowerCAmelCase__						)						)
            lowerCAmelCase_       :    Optional[Any]								=			int(sqrt(lowerCAmelCase__						)						)
            lowerCAmelCase_       :    Optional[int]								=			gcd(lowerCAmelCase__   ,       lowerCAmelCase__						)
            z_num //= hcf
            z_den //= hcf
            if 0 < z_num < z_den <= order:
              lowerCAmelCase_       :    Any								=			add_three(
                  lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__						)
              unique_s.add(lowerCAmelCase__						)

  for num, den in unique_s:
    total += Fraction(lowerCAmelCase__   ,       lowerCAmelCase__						)

  return total.denominator + total.numerator


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





