문제
이 대회의 운영진 중 한 명인 KSA 학생은 슬슬 소수가 좋아져서 아래 조건들을 모두 만족하는 수열을 길이가 $N$인 아름다운 수열이라고 하기로 했다.
- 수열은 길이가 $N$인 순열이다. 즉, 1ドル$ 이상 $N$ 이하의 정수들이 정확히 한 번씩 등장한다.
- 거리가 소수인 두 다른 원소 사이의 차는 소수여야 한다. $i$번째 원소와 $j$번째 원소 사이의 거리는 $|j-i|$이다.
출력
각 테스트 케이스에 대해, 길이가 $N$인 아름다운 수열이 존재한다면 첫 번째 줄에 YES를 출력하고 두 번째 줄에 그 원소들을 공백으로 구분하여 출력한다. 길이가 $N$인 아름다운 수열이 존재하지 않는다면 대신 NO를 출력한다.
정답이 여러 개 존재한다면 그중 아무거나 출력해도 상관없다.
제한
- 1ドル\leq T \leq 100$
- 3ドル\leq N \leq 300$
서브태스크
| 번호 | 배점 | 제한 | | 1 | 16 | $T = 1$; $N = 6$
|
| 2 | 84 | 추가 제약 조건 없음
|
예제 출력 1
YES
2 1 5 4 3
YES
6 2 3 4 5 1 7
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