



'''simple docstring'''





from maths.prime_factors import prime_factors
def    _SCREAMING_SNAKE_CASE  (       UpperCamelCase			):



    """simple docstring"""





    if not isinstance(UpperCamelCase							,    UpperCamelCase			):
        lowerCAmelCase__ :  int							      =					f"""Input value of [number={number}] must be an integer"""
        raise TypeError(UpperCamelCase			)
    if number < 1:
        raise ValueError("""Input must be a positive integer"""			)
    return -1 if len(prime_factors(UpperCamelCase			)			) % 2 else 1


if __name__ == "__main__":
 import doctest

 doctest.testmod()






'''simple docstring'''


from collections import defaultdict
from math import ceil, sqrt







def 			snake_case_   (  SCREAMING_SNAKE_CASE__ = 100_0000							,      SCREAMING_SNAKE_CASE__ = 10     ):







				"""simple docstring"""





				_SCREAMING_SNAKE_CASE :       defaultdict     		=      defaultdict(SCREAMING_SNAKE_CASE__     )

				for outer_width in range(3							,      (t_limit // 4) + 2     ):
								if outer_width * outer_width > t_limit:
												_SCREAMING_SNAKE_CASE :       int     		=      max(
												    ceil(sqrt(outer_width * outer_width - t_limit     )     )							,      1     )
								else:
												_SCREAMING_SNAKE_CASE :       List[str]     		=      1

								hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

								for hole_width in range(SCREAMING_SNAKE_CASE__							,      outer_width - 1							,      2     ):
												count[outer_width * outer_width - hole_width * hole_width] += 1

				return sum(1 for n in count.values() if 1 <= n <= 10     )


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




