

def        lowerCamelCase__    (    __lowerCAmelCase  :  float    ):




			"""simple docstring"""


			if num < 0:
						return -1
			return 1 if num else 0






def        lowerCamelCase__    (    ):




			"""simple docstring"""


			assert signum(5    ) == 1
			assert signum(-5    ) == -1
			assert signum(0    ) == 0


if __name__ == "__main__":
			print(signum(12))
			print(signum(-12))
			print(signum(0))





from __future__ import annotations






def        lowerCamelCase__    (    __lowerCAmelCase  :  int   ,							__lowerCAmelCase  :  int   ,							__lowerCAmelCase  :  int    ):




			"""simple docstring"""


			assert n > 1 and a > 0 and greatest_common_divisor(__lowerCAmelCase   ,							__lowerCAmelCase    ) == 1
			((lowerCAmelCase_)     ,  (lowerCAmelCase_)     ,  (lowerCAmelCase_))      =     extended_gcd(__lowerCAmelCase   ,							__lowerCAmelCase    )  # Implemented below
			lowerCAmelCase_      =     (b * s) % n
			return x






def        lowerCamelCase__    (    __lowerCAmelCase  :  int   ,							__lowerCAmelCase  :  int    ):




			"""simple docstring"""


			((lowerCAmelCase_)     ,  (lowerCAmelCase_))      =     extended_euclid(__lowerCAmelCase   ,							__lowerCAmelCase    )  # Implemented below
			if b < 0:
						lowerCAmelCase_      =     (b % n + n) % n
			return b






def        lowerCamelCase__    (    __lowerCAmelCase  :  int   ,							__lowerCAmelCase  :  int   ,							__lowerCAmelCase  :  int    ):




			"""simple docstring"""


			lowerCAmelCase_      =     invert_modulo(__lowerCAmelCase   ,							__lowerCAmelCase    )
			lowerCAmelCase_      =     (b * s) % n
			return x






def        lowerCamelCase__    (    __lowerCAmelCase  :  int   ,							__lowerCAmelCase  :  int    ):




			"""simple docstring"""


			assert a >= 0 and b >= 0

			if b == 0:
						lowerCAmelCase_     ,  lowerCAmelCase_     ,  lowerCAmelCase_      =     a, 1, 0
			else:
						((lowerCAmelCase_)     ,  (lowerCAmelCase_)     ,  (lowerCAmelCase_))      =     extended_gcd(__lowerCAmelCase   ,							a % b    )
						lowerCAmelCase_      =     q
						lowerCAmelCase_      =     p - q * (a // b)

			assert a % d == 0 and b % d == 0
			assert d == a * x + b * y

			return (d, x, y)






def        lowerCamelCase__    (    __lowerCAmelCase  :  int   ,							__lowerCAmelCase  :  int    ):




			"""simple docstring"""


			if b == 0:
						return (1, 0)
			((lowerCAmelCase_)     ,  (lowerCAmelCase_))      =     extended_euclid(__lowerCAmelCase   ,							a % b    )
			lowerCAmelCase_      =     a // b
			return (y, x - k * y)






def        lowerCamelCase__    (    __lowerCAmelCase  :  int   ,							__lowerCAmelCase  :  int    ):




			"""simple docstring"""


			if a < b:
						lowerCAmelCase_     ,  lowerCAmelCase_      =     b, a

			while a % b != 0:
						lowerCAmelCase_     ,  lowerCAmelCase_      =     b, a % b

			return b


if __name__ == "__main__":
			from doctest import testmod

			testmod(name="modular_division", verbose=True)
			testmod(name="modular_division2", verbose=True)
			testmod(name="invert_modulo", verbose=True)
			testmod(name="extended_gcd", verbose=True)
			testmod(name="extended_euclid", verbose=True)
			testmod(name="greatest_common_divisor", verbose=True)



