In the KSA library, $N$ books are placed in a straight line. The heights of the books from left to right form a permutation $A = (A_1, A_2, \cdots, A_N)$ of length $N$. In other words, $A$ is a sequence in which each integer from $1$ to $N$ appears exactly once.

Hanbumi, a library club member, wants to sort the books in ascending order by repeating the following operation $0$ or more times.

• Select two consecutive books and move them to the leftmost position while maintaining their order.

Find a sequence of operations that sorts the permutation in at most $N^2$ operations.

Input

The first line contains an integer $N$.

The second line contains $N$ space-separated integers $A_1, A_2, \cdots, A_N$.

Output

On the first line, print YES if there is a way to sort the books in ascending order using at most $N^2$ operations, and NO otherwise.

If there is such a way, let the required number of operations be $k$. On the second line, print integer $k$. It must satisfy $0 \le k \le N^2$, but it is not necessary to minimize $k$.

If $k > 0$, print $k$ space-separated integers $x_1, x_2, \cdots, x_k$ on the third line. $x_i$ means that in the $i$-th operation, the $x_i$-th book and the $x_i+1$-th book from the left are selected and moved to the leftmost position.

If there are multiple solutions, print any of them.

Constraints

• $2 \le N \le 100$
• $1 \le A_i \le N$
• If $i \ne j$, then $A_i \ne A_j$

Scoring

Examples

Input 1

5
1 2 4 5 3

Output 1

YES
4
4 3 4 3

Input 2

3
3 2 1

Output 2

NO