




from __future__ import annotations

from pathlib import Path







def       _a (		SCREAMING_SNAKE_CASE_				:							tuple[int, int] , SCREAMING_SNAKE_CASE_				:							tuple[int, int]	):
					return pointa[0] * pointa[1] - pointa[1] * pointa[0]







def       _a (		SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int	):
					__lowerCAmelCase							  =			(xa, ya)
					__lowerCAmelCase							  =			(xa - xa, ya - ya)
					__lowerCAmelCase							  =			(xa - xa, ya - ya)
					__lowerCAmelCase							  =			-vector_product(SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_	) / vector_product(
					    SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_	)
					__lowerCAmelCase							  =			+vector_product(SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_	) / vector_product(
					    SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_	)

					return a > 0 and b > 0 and a + b < 1







def       _a (		SCREAMING_SNAKE_CASE_				:							str = "p102_triangles.txt"	):
					__lowerCAmelCase							  =			Path(SCREAMING_SNAKE_CASE_	).parent.joinpath(SCREAMING_SNAKE_CASE_	).read_text(encoding="utf-8"	)

					__lowerCAmelCase							  =			[]
					for line in data.strip().split("\n"	):
										triangles.append([int(SCREAMING_SNAKE_CASE_	) for number in line.split(","	)]	)

					__lowerCAmelCase							  =			0
					__lowerCAmelCase							  =			42

					for triangle in triangles:
										ret += contains_origin(*SCREAMING_SNAKE_CASE_	)

					return ret


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










def       _a (		SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int	):
					if a < b:
										return gcd(SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_	)
					if a % b == 0:
										return b
					return gcd(SCREAMING_SNAKE_CASE_ , a % b	)







def       _a (		SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int , SCREAMING_SNAKE_CASE_				:							int	):
					if y == 0:
										return 1
					__lowerCAmelCase							  =			power(SCREAMING_SNAKE_CASE_ , y // 2 , SCREAMING_SNAKE_CASE_	) % mod
					__lowerCAmelCase							  =			(temp * temp) % mod
					if y % 2 == 1:
										__lowerCAmelCase							  =			(temp * x) % mod
					return temp







def       _a (		SCREAMING_SNAKE_CASE_				:							int	):
					__lowerCAmelCase							  =			2
					while b < n:
										if gcd(SCREAMING_SNAKE_CASE_ , SCREAMING_SNAKE_CASE_	) == 1 and power(SCREAMING_SNAKE_CASE_ , n - 1 , SCREAMING_SNAKE_CASE_	) != 1:
															return False
										b += 1
					return True


if __name__ == "__main__":
					UpperCamelCase__            =     int(input("""Enter number: """).strip())
					if is_carmichael_number(number):
										print(f'''{number} is a Carmichael Number.''')
					else:
										print(f'''{number} is not a Carmichael Number.''')




