


def 							__lowercase     (				__lowerCAmelCase							:       str      ,					__lowerCAmelCase							:       str     ):
							a__    =  len(_SCREAMING_SNAKE_CASE     )
							a__    =  []
							for i in range(len(_SCREAMING_SNAKE_CASE     ) - pat_len + 1     ):
														a__    =  True
														for j in range(_SCREAMING_SNAKE_CASE     ):
																					if s[i + j] != pattern[j]:
																												a__    =  False
																												break
														if match_found:
																					position.append(_SCREAMING_SNAKE_CASE     )
							return position


if __name__ == "__main__":
						assert naive_pattern_search('''ABCDEFG''', '''DE''') == [3]
						print(naive_pattern_search('''ABAAABCDBBABCDDEBCABC''', '''ABC'''))








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() = }""")




