

"""simple docstring"""
from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt




def 					a__						(						lowerCAmelCase    )	-> bool:
      UpperCAmelCase__			:							int							=    int(number**0.5    )
      return number == sq * sq




def 					a__						(						lowerCAmelCase			,	lowerCAmelCase			,	lowerCAmelCase			,	lowerCAmelCase			,	lowerCAmelCase			,	lowerCAmelCase    )	-> tuple[int, int]:
      UpperCAmelCase__			:							int							=    x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
      UpperCAmelCase__			:							int							=    x_den * y_den * z_den
      UpperCAmelCase__			:							int							=    gcd(lowerCAmelCase			,	lowerCAmelCase    )
      top //= hcf
      bottom //= hcf
      return top, bottom




def 					a__						(						lowerCAmelCase = 35    )	-> int:
      UpperCAmelCase__			:							set							=    set()
      UpperCAmelCase__			:							int
      UpperCAmelCase__			:							Fraction							=    Fraction(0    )
      UpperCAmelCase__			:							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
                              UpperCAmelCase__			:							Optional[int]							=    x_num * y_den + x_den * y_num
                              UpperCAmelCase__			:							Optional[Any]							=    x_den * y_den
                              UpperCAmelCase__			:							Union[str, Any]							=    gcd(lowerCAmelCase			,	lowerCAmelCase    )
                              z_num //= hcf
                              z_den //= hcf
                              if 0 < z_num < z_den <= order:
                                    UpperCAmelCase__			:							Dict							=    add_three(
                                        lowerCAmelCase			,	lowerCAmelCase			,	lowerCAmelCase			,	lowerCAmelCase			,	lowerCAmelCase			,	lowerCAmelCase    )
                                    unique_s.add(lowerCAmelCase    )

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

                    # n=-1
                              UpperCAmelCase__			:							List[Any]							=    x_num * y_num
                              UpperCAmelCase__			:							int							=    x_den * y_num + x_num * y_den
                              UpperCAmelCase__			:							str							=    gcd(lowerCAmelCase			,	lowerCAmelCase    )
                              z_num //= hcf
                              z_den //= hcf
                              if 0 < z_num < z_den <= order:
                                    UpperCAmelCase__			:							List[str]							=    add_three(
                                        lowerCAmelCase			,	lowerCAmelCase			,	lowerCAmelCase			,	lowerCAmelCase			,	lowerCAmelCase			,	lowerCAmelCase    )
                                    unique_s.add(lowerCAmelCase    )

                              # n=2
                              UpperCAmelCase__			:							Union[str, Any]							=    x_num * x_num * y_num * y_num
                              UpperCAmelCase__			:							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    ):
                                    UpperCAmelCase__			:							Optional[Any]							=    int(sqrt(lowerCAmelCase    )    )
                                    UpperCAmelCase__			:							List[str]							=    int(sqrt(lowerCAmelCase    )    )
                                    UpperCAmelCase__			:							Optional[Any]							=    gcd(lowerCAmelCase			,	lowerCAmelCase    )
                                    z_num //= hcf
                                    z_den //= hcf
                                    if 0 < z_num < z_den <= order:
                                          UpperCAmelCase__			:							Union[str, 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() = }''')




"""simple docstring"""
import requests




def 					a__						(						lowerCAmelCase			,	lowerCAmelCase    )	-> None:
      UpperCAmelCase__			:							List[str]							=    {"""Content-Type""": """application/json"""}
      UpperCAmelCase__			:							List[str]							=    requests.post(lowerCAmelCase			,	json={"""text""": message_body}			,	headers=lowerCAmelCase    )
      if response.status_code != 2_00:
            UpperCAmelCase__			:							str							=    (
                """Request to slack returned an error """
                F"""{response.status_code}, the response is:\n{response.text}"""
            )
            raise ValueError(lowerCAmelCase    )


if __name__ == "__main__":
    # Set the slack url to the one provided by Slack when you create the webhook at
    # https://my.slack.com/services/new/incoming-webhook/
    send_slack_message("""<YOUR MESSAGE BODY>""", """<SLACK CHANNEL URL>""")

