Problem Statement

A permutation $P=(P_1,P_2,\ldots,P_N)$ of $(1,2,\ldots,N)$ is given.

Determine whether it is possible to rearrange $P$ in ascending order by performing the following operation at most $2\times 10^3$ times, and if possible, show one such sequence of operations.

• Choose integers $i$ and $j$ such that $1\leq i \leq N-1,0 \leq j \leq N-2$. Let $Q = (Q_1, Q_2,\ldots,Q_{N-2})$ be the sequence obtained by removing $(P_i,P_{i+1})$ from $P$. Replace $P$ with $(Q_1,\ldots,Q_j, P_i, P_{i+1}, Q_{j+1},\ldots,Q_{N-2})$.

Constraints

• $2 \leq N \leq 10^3$
• $P$ is a permutation of $(1,2,\ldots,N)$.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N
P_1 P_2 \ldots P_N

Output

If $P$ cannot be rearranged in ascending order within $2\times 10^3$ operations, print No. If it can be rearranged in ascending order, let $M\ (0 \leq M \leq 2\times 10^3)$ be the number of operations, and $i_k,j_k$ be the chosen $i,j$ for the $k$-th operation $(1\leq k \leq M)$, and print them in the following format:

Yes
M
i_1 j_1
i_2 j_2
\vdots
i_M j_M

If there are multiple solutions, any of them will be considered correct.