






"""simple docstring"""





from collections import defaultdict
from math import ceil, sqrt







def   lowerCAmelCase_( SCREAMING_SNAKE_CASE = 1_00_00_00 ,	SCREAMING_SNAKE_CASE = 10					)					->	int:
    """simple docstring"""

    UpperCamelCase__         =    defaultdict(SCREAMING_SNAKE_CASE					)

    for outer_width in range(3 ,	(t_limit // 4) + 2					):
        if outer_width * outer_width > t_limit:
            UpperCamelCase__         =    max(
                ceil(sqrt(outer_width * outer_width - t_limit					)					) ,	1					)
        else:
            UpperCamelCase__         =    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() = }""")












"""simple docstring"""





from copy import deepcopy
class    __lowerCamelCase    :

   def __init__(					self ,				snake_case_ = None ,				snake_case_ = None      )		->       None:

       if arr is None and size is not None:
           UpperCamelCase__         =    size
           UpperCamelCase__         =    [0] * size
       elif arr is not None:
           self.init(snake_case_      )
       else:
           raise ValueError('Either arr or size must be specified'      )

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_      )		->       None:
       UpperCamelCase__         =    len(snake_case_      )
       UpperCamelCase__         =    deepcopy(snake_case_      )
       for i in range(1 ,				self.size      ):
           UpperCamelCase__         =    self.next_(snake_case_      )
           if j < self.size:
               self.tree[j] += self.tree[i]

   def 						SCREAMING_SNAKE_CASE__ (					self      )		->       list[int]:
       UpperCamelCase__         =    self.tree[:]
       for i in range(self.size - 1 ,				0 ,				-1      ):
           UpperCamelCase__         =    self.next_(snake_case_      )
           if j < self.size:
               arr[j] -= arr[i]
       return arr

   @staticmethod
   def 						SCREAMING_SNAKE_CASE__ (					snake_case_      )		->       int:
       return index + (index & (-index))

   @staticmethod
   def 						SCREAMING_SNAKE_CASE__ (					snake_case_      )		->       int:
       return index - (index & (-index))

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_ ,				snake_case_      )		->       None:
       if index == 0:
           self.tree[0] += value
           return
       while index < self.size:
           self.tree[index] += value
           UpperCamelCase__         =    self.next_(snake_case_      )

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_ ,				snake_case_      )		->       None:
       self.add(snake_case_ ,				value - self.get(snake_case_      )      )

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_      )		->       int:
       if right == 0:
           return 0
       UpperCamelCase__         =    self.tree[0]
       right -= 1  # make right inclusive
       while right > 0:
           result += self.tree[right]
           UpperCamelCase__         =    self.prev(snake_case_      )
       return result

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_ ,				snake_case_      )		->       int:
       return self.prefix(snake_case_      ) - self.prefix(snake_case_      )

   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_      )		->       int:
       return self.query(snake_case_ ,				index + 1      )







   def 						SCREAMING_SNAKE_CASE__ (					self ,				snake_case_      )		->       int:
       value -= self.tree[0]
       if value < 0:
           return -1

       UpperCamelCase__         =    1  # Largest power of 2 <= size
       while j * 2 < self.size:
           j *= 2

       UpperCamelCase__         =    0

       while j > 0:
           if i + j < self.size and self.tree[i + j] <= value:
               value -= self.tree[i + j]
               i += j
           j //= 2
       return i


if __name__ == "__main__":
  import doctest

  doctest.testmod()




