


import random






def 							__lowercase     (				__lowerCAmelCase							:       Optional[int]      ,					__lowerCAmelCase							:       List[str]      ,					__lowerCAmelCase							:       Any     ):
							a__    =  a[left_index]
							a__    =  left_index + 1
							for j in range(left_index + 1      ,					__lowerCAmelCase     ):
														if a[j] < pivot:
																					a__   ,      a__    =  a[i], a[j]
																					i += 1
							a__   ,      a__    =  a[i - 1], a[left_index]
							return i - 1






def 							__lowercase     (				__lowerCAmelCase							:       str      ,					__lowerCAmelCase							:       Any      ,					__lowerCAmelCase							:       Dict     ):
							if left < right:
														a__    =  random.randint(__lowerCAmelCase      ,					right - 1     )
														a__   ,      a__    =  (
														    a[left],
														    a[pivot],
														)  # switches the pivot with the left most bound
														a__    =  partition(__lowerCAmelCase      ,					__lowerCAmelCase      ,					__lowerCAmelCase     )
														quick_sort_random(
														    __lowerCAmelCase      ,					__lowerCAmelCase      ,					__lowerCAmelCase     )  # recursive quicksort to the left of the pivot point
														quick_sort_random(
														    __lowerCAmelCase      ,					pivot_index + 1      ,					__lowerCAmelCase     )  # recursive quicksort to the right of the pivot point






def 							__lowercase     (				):
							a__    =  input('Enter numbers separated by a comma:\n'     ).strip()
							a__    =  [int(__lowerCAmelCase     ) for item in user_input.split(','     )]

							quick_sort_random(__lowerCAmelCase      ,					0      ,					len(__lowerCAmelCase     )     )

							print(__lowerCAmelCase     )


if __name__ == "__main__":
						main()








from math import ceil, sqrt






def 							__lowercase     (				__lowerCAmelCase							:       int = 1_0_0_0_0_0_0     ):
							a__    =  0

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




