"""simple docstring"""
class      lowerCAmelCase_			:



				"""simple docstring"""

				def __init__( self						,			lowerCAmelCase			):






										"""simple docstring"""

										snake_case	    =	size
										snake_case	    =	[0] * size
										snake_case	    =	[0] * size

				@staticmethod
				def 						snake_case       ( lowerCAmelCase			):






										"""simple docstring"""

										return index | (index + 1)

				@staticmethod
				def 						snake_case       ( lowerCAmelCase			):






										"""simple docstring"""

										return (index & (index + 1)) - 1

				def 						snake_case       ( self						,			lowerCAmelCase						,			lowerCAmelCase			):






										"""simple docstring"""

										snake_case	    =	value
										while index < self.size:
																snake_case	    =	self.get_prev(__lowercase			) + 1
																if current_left_border == index:
																						snake_case	    =	value
																else:
																						snake_case	    =	max(__lowercase						,			__lowercase						,			__lowercase			)
																snake_case	    =	self.get_next(__lowercase			)

				def 						snake_case       ( self						,			lowerCAmelCase						,			lowerCAmelCase			):






										"""simple docstring"""

										right -= 1  # Because of right is exclusive
										snake_case	    =	0
										while left <= right:
																snake_case	    =	self.get_prev(__lowercase			)
																if left <= current_left:
																						snake_case	    =	max(__lowercase						,			self.tree[right]			)
																						snake_case	    =	current_left
																else:
																						snake_case	    =	max(__lowercase						,			self.arr[right]			)
																						right -= 1
										return result


if __name__ == "__main__":
					import doctest

					doctest.testmod()







from math import ceil, sqrt



def 			_lowerCAmelCase       (					__lowerCAmelCase = 1000000      )   ->					int:


				"""simple docstring"""

				snake_case__	:      Dict     		=	0

				for outer_width in range(3  ,  (limit // 4) + 2      ):
								if outer_width**2 > limit:
												snake_case__	:      Any     		=	max(ceil(sqrt(outer_width**2 - limit      )      )  ,  1      )
								else:
												snake_case__	:      int     		=	1
								if (outer_width - hole_width_lower_bound) % 2:
												hole_width_lower_bound += 1

								answer += (outer_width - hole_width_lower_bound - 2) // 2 + 1

				return answer


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

