


'''simple docstring'''







from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt




def        __lowercase						(      __SCREAMING_SNAKE_CASE		)				->					bool:
     """simple docstring"""




     __a       =   int(number**0.5		)
     return number == sq * sq




def        __lowercase						(      __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE		)				->					tuple[int, int]:
     """simple docstring"""




     __a       =   x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
     __a       =   x_den * y_den * z_den
     __a       =   gcd(__SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE		)
     top //= hcf
     bottom //= hcf
     return top, bottom




def        __lowercase						(      __SCREAMING_SNAKE_CASE = 35		)				->					int:
     """simple docstring"""




     __a       =   set()
     __a       =   42
     __a       =   Fraction(0		)
     __a       =   42

     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
                         __a       =   x_num * y_den + x_den * y_num
                         __a       =   x_den * y_den
                         __a       =   gcd(__SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE		)
                         z_num //= hcf
                         z_den //= hcf
                         if 0 < z_num < z_den <= order:
                              __a       =   add_three(
                                  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE		)
                              unique_s.add(__SCREAMING_SNAKE_CASE		)

                         # n=2
                         __a       =   (
                             x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
                         )
                         __a       =   x_den * x_den * y_den * y_den
                         if is_sq(__SCREAMING_SNAKE_CASE		) and is_sq(__SCREAMING_SNAKE_CASE		):
                              __a       =   int(sqrt(__SCREAMING_SNAKE_CASE		)		)
                              __a       =   int(sqrt(__SCREAMING_SNAKE_CASE		)		)
                              __a       =   gcd(__SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE		)
                              z_num //= hcf
                              z_den //= hcf
                              if 0 < z_num < z_den <= order:
                                   __a       =   add_three(
                                       __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE		)
                                   unique_s.add(__SCREAMING_SNAKE_CASE		)

                    # n=-1
                         __a       =   x_num * y_num
                         __a       =   x_den * y_num + x_num * y_den
                         __a       =   gcd(__SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE		)
                         z_num //= hcf
                         z_den //= hcf
                         if 0 < z_num < z_den <= order:
                              __a       =   add_three(
                                  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE		)
                              unique_s.add(__SCREAMING_SNAKE_CASE		)

                         # n=2
                         __a       =   x_num * x_num * y_num * y_num
                         __a       =   (
                             x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
                         )
                         if is_sq(__SCREAMING_SNAKE_CASE		) and is_sq(__SCREAMING_SNAKE_CASE		):
                              __a       =   int(sqrt(__SCREAMING_SNAKE_CASE		)		)
                              __a       =   int(sqrt(__SCREAMING_SNAKE_CASE		)		)
                              __a       =   gcd(__SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE		)
                              z_num //= hcf
                              z_den //= hcf
                              if 0 < z_num < z_den <= order:
                                   __a       =   add_three(
                                       __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE		)
                                   unique_s.add(__SCREAMING_SNAKE_CASE		)

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

     return total.denominator + total.numerator


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










'''simple docstring'''







from __future__ import annotations




def        __lowercase						(      __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE				,  __SCREAMING_SNAKE_CASE				,  )				->					tuple[str, float]:
     """simple docstring"""




     if (stress, tangential_force, area).count(0		) != 1:
          raise ValueError("""You cannot supply more or less than 2 values"""		)
     elif stress < 0:
          raise ValueError("""Stress cannot be negative"""		)
     elif tangential_force < 0:
          raise ValueError("""Tangential Force cannot be negative"""		)
     elif area < 0:
          raise ValueError("""Area cannot be negative"""		)
     elif stress == 0:
          return (
              "stress",
              tangential_force / area,
          )
     elif tangential_force == 0:
          return (
              "tangential_force",
              stress * area,
          )
     else:
          return (
              "area",
              tangential_force / stress,
          )


if __name__ == "__main__":
 import doctest

 doctest.testmod()






