문제
KSA 학생들은 아래 조건을 만족하는 길이가 $N$인 수열을 좋아한다.
- 1,ドル 2, \cdots, N$이 $A$에 정확히 한 번씩 등장한다.
- 임의의 인접한 세 수 $A_{i},ドル $A_{i+1},ドル $A_{i+2}$에 대해 $|A_{i+1}-A_{i}| = |A_{i+2}-A_{i+1}| \times 2$ 또는 $|A_{i+1}-A_{i}| = |A_{i+2}-A_{i+1}| \times 0.5$이다.
정수 $N$이 주어졌을 때, 조건을 만족하는 수열이 존재하는지 판별하고 있다면 아무거나 찾아보자.
출력
첫 번째 줄에 조건을 만족하는 수열이 존재한다면 YES, 아니라면 NO를 출력한다.
만약 그러한 수열이 존재한다면, 두 번째 줄에 $N$개의 정수 $A_{1}, A_{2}, \cdots, A_{N}$를 출력한다.
정답이 여러 개 존재한다면 아무거나 출력해도 상관없다.
제한
- 3ドル \leq N \leq 2 \times 10^6$
서브태스크
| 번호 | 배점 | 제한 | | 1 | 7 | $N \leq 10$
|
| 2 | 33 | $N$은 4ドル$의 배수
|
| 3 | 60 | 추가 제약 조건 없음
|
예제 출력 2
YES
1 2 4 8 6 5 7 3 11 15 13 14 16 12 10 9
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