




from __future__ import annotations




def 		lowerCAmelCase_ (						lowerCamelCase ):
				if len(lowerCamelCase ) < 2:
								raise ValueError("""Monogons and Digons are not polygons in the Euclidean space""" )
				if any(i <= 0 for i in nums ):
								raise ValueError("""All values must be greater than 0""" )
				__magic_name__						:						int										=nums.copy()
				copy_nums.sort()
				return copy_nums[-1] < sum(copy_nums[:-1] )


if __name__ == "__main__":
							import doctest

							doctest.testmod()










from __future__ import annotations

from fractions import Fraction




def 		lowerCAmelCase_ (						lowerCamelCase						,  lowerCamelCase ):
				return (
				    num != den and num % 10 == den // 10 and (num // 10) / (den % 10) == num / den
				)




def 		lowerCAmelCase_ (						lowerCamelCase ):
				__magic_name__						:						List[str]										=[]
				__magic_name__						:						List[Any]										=11
				__magic_name__						:						Tuple										=int("""1""" + """0""" * digit_len )
				for num in range(lowerCamelCase						,  lowerCamelCase ):
								while den <= 99:
												if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
																if is_digit_cancelling(lowerCamelCase						,  lowerCamelCase ):
																				solutions.append(F"{num}/{den}" )
												den += 1
								num += 1
								__magic_name__						:						List[str]										=10
				return solutions




def 		lowerCAmelCase_ (						lowerCamelCase = 2 ):
				__magic_name__						:						str										=1.0
				for fraction in fraction_list(lowerCamelCase ):
								__magic_name__						:						int										=Fraction(lowerCamelCase )
								result *= frac.denominator / frac.numerator
				return int(lowerCamelCase )


if __name__ == "__main__":
							print(solution())




