




from __future__ import annotations

def   _lowerCAmelCase   (						A__						,  A__	):
      if b == 0:
            return (1, 0)
      ((lowercase__),	(lowercase__))     =  extended_euclid(A__						,  a % b	)
      lowercase__     =  a // b
      return (y, x - k * y)

def   _lowerCAmelCase   (						A__						,  A__						,  A__						,  A__	):
      ((lowercase__),	(lowercase__))     =  extended_euclid(A__						,  A__	)
      lowercase__     =  na * na
      lowercase__     =  ra * x * na + ra * y * na
      return (n % m + m) % m

def   _lowerCAmelCase   (						A__						,  A__	):
      ((lowercase__),	(lowercase__))     =  extended_euclid(A__						,  A__	)
      if b < 0:
            lowercase__     =  (b % n + n) % n
      return b

def   _lowerCAmelCase   (						A__						,  A__						,  A__						,  A__	):
      lowercase__,	lowercase__     =  invert_modulo(A__						,  A__	), invert_modulo(A__						,  A__	)
      lowercase__     =  na * na
      lowercase__     =  ra * x * na + ra * y * na
      return (n % m + m) % m


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

       testmod(name="chinese_remainder_theorem", verbose=True)
       testmod(name="chinese_remainder_theorem2", verbose=True)
       testmod(name="invert_modulo", verbose=True)
       testmod(name="extended_euclid", verbose=True)





from maths.is_square_free import is_square_free
from maths.prime_factors import prime_factors

def   _lowerCAmelCase   (						A__	):
      lowercase__     =  prime_factors(A__	)
      if is_square_free(A__	):
            return -1 if len(A__	) % 2 else 1
      return 0


if __name__ == "__main__":
       import doctest

       doctest.testmod()
