


from __future__ import annotations






def 							__lowercase   ( __lowerCAmelCase							:				List[Any]   ):
							a__             =     len(SCREAMING_SNAKE_CASE__   ) // 2

							# choose the middle 3 elements
							a__             =     lst[m - 1 : m + 2]

							# if middle element is peak
							if three[1] > three[0] and three[1] > three[2]:
														return three[1]

							# if increasing, recurse on right
							elif three[0] < three[2]:
														if len(lst[:m]   ) == 2:
																					m -= 1
														return peak(lst[m:]   )

							# decreasing
							else:
														if len(lst[:m]   ) == 2:
																					m += 1
														return peak(lst[:m]   )


if __name__ == "__main__":
						import doctest

						doctest.testmod()








'''simple docstring'''


from collections import defaultdict
from math import ceil, sqrt







def 			snake_case_   (  SCREAMING_SNAKE_CASE__ = 100_0000							,      SCREAMING_SNAKE_CASE__ = 10     ):







				"""simple docstring"""





				_SCREAMING_SNAKE_CASE :       defaultdict     		=      defaultdict(SCREAMING_SNAKE_CASE__     )

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




