

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


def 	_lowerCAmelCase (						_UpperCamelCase						:					int = 1_00_00_00							,			_UpperCamelCase						:					int = 10    )				->      int:
     """simple docstring"""




     _SCREAMING_SNAKE_CASE							   =defaultdict(_UpperCamelCase    )

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



'''simple docstring'''
import os


def 	_lowerCAmelCase (						)				->      List[str]:
     """simple docstring"""




     _SCREAMING_SNAKE_CASE							   =os.path.dirname(os.path.realpath(_UpperCamelCase    )    )
     _SCREAMING_SNAKE_CASE							   =os.path.join(_UpperCamelCase							,			'triangle.txt'    )

     with open(_UpperCamelCase    ) as f:
          _SCREAMING_SNAKE_CASE							   =f.readlines()

     _SCREAMING_SNAKE_CASE							   =[]
     for line in triangle:
          _SCREAMING_SNAKE_CASE							   =[]
          for number in line.strip().split(' '    ):
               numbers_from_line.append(int(_UpperCamelCase    )    )
          a.append(_UpperCamelCase    )

     for i in range(1							,			len(_UpperCamelCase    )    ):
          for j in range(len(a[i]    )    ):
               _SCREAMING_SNAKE_CASE							   =a[i - 1][j] if j != len(a[i - 1]    ) else 0
               _SCREAMING_SNAKE_CASE							   =a[i - 1][j - 1] if j > 0 else 0
               a[i][j] += max(_UpperCamelCase							,			_UpperCamelCase    )
     return max(a[-1]    )


if __name__ == "__main__":
     print(solution())
