


'''simple docstring'''
def 			_lowercase       (				UpperCamelCase__       :					int,				UpperCamelCase__       :					int			):
 return x if y == 0 else greatest_common_divisor(UpperCamelCase__,				x % y			)


def 			_lowercase       (				UpperCamelCase__       :					int,				UpperCamelCase__       :					int			):
 return (x * y) // greatest_common_divisor(UpperCamelCase__,				UpperCamelCase__			)


def 			_lowercase       (				UpperCamelCase__       :					int = 20			):
 __A  :		Optional[Any]       =			1
 for i in range(1,				n + 1			):
  __A  :		List[str]       =			lcm(UpperCamelCase__,				UpperCamelCase__			)
 return g


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










'''simple docstring'''
from collections import defaultdict
from math import ceil, sqrt


def 			_lowercase       (				UpperCamelCase__       :					int = 1000000,				UpperCamelCase__       :					int = 10			):
 __A  :		defaultdict       =			defaultdict(UpperCamelCase__			)

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

  hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

  for hole_width in range(UpperCamelCase__,				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() = }''')






