문제
1부터 n까지의 정수가 단 한 번씩만 등장하는 크기가 n인 수열 x1, x2, ..., xn이 주어진다.
두 수를 바꾸는 "스왑"이라는 연산을 통해 수열을 수정할 수 있다. k=2, 3, ..., n 순서대로 k를 증가시키면서 xk와 x⌊k/2⌋를 바꿀지 말지 선택할 수 있다.
수열 a1, a2, ..., an이 수열 b1, b2, ..., bn보다 사전순으로 앞선다는 것은 k < j인 k에 대해 ak = bk를 만족하고 aj < bj를 만족하는 j (1 ≤ j ≤ n)가 존재한다는 것을 의미한다.
순서대로 "스왑" 연산을 하여 만들 수 있는 수열 중 가장 사전순으로 앞선 수열은 어떤 것일까?
출력
첫 줄에 순서대로 "스왑" 연산을 하여 만들 수 있는 수열 중 가장 사전순으로 앞선 수열을 나타내는 n개의 정수를 공백으로 구분하여 출력한다.
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