


from collections import defaultdict
from math import ceil, sqrt




def     UpperCamelCase    (      _a = 1_0_0_0_0_0_0       ,		_a = 1_0		)					->							int:
     '''simple docstring'''





     lowercase_       :defaultdict     =       defaultdict(_a		)

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

          hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

          for hole_width in range(_a       ,		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 <= 1_0		)


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





def     UpperCamelCase    (      _a       ,		_a		)					->							int:
     '''simple docstring'''





     while a != 0:
          lowercase_    ,      lowercase_       :Union[str, Any]     =       b % a, a
     return b




def     UpperCamelCase    (      _a       ,		_a		)					->							int:
     '''simple docstring'''





     if gcd(_a       ,		_a		) != 1:
          lowercase_       :Union[str, Any]     =       f"mod inverse of {a!r} and {m!r} does not exist"
          raise ValueError(_a		)
     lowercase_    ,      lowercase_    ,      lowercase_       :Any     =       1, 0, a
     lowercase_    ,      lowercase_    ,      lowercase_       :List[str]     =       0, 1, m
     while va != 0:
          lowercase_       :Tuple     =       ua // va
          lowercase_    ,      lowercase_    ,      lowercase_    ,      lowercase_    ,      lowercase_    ,      lowercase_       :Optional[int]     =       (ua - q * va), (ua - q * va), (ua - q * va), va, va, va
     return ua % m

