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.

Sample Input 1

5
1 4 2 3 5

Sample Output 1

Yes
1
3 1

Perform the operation with $i=3,j=1$.

Then, $Q=(P_1,P_2,P_5)=(1,4,5)$, so you get $P=(Q_1,P_3,P_4,Q_2,Q_3) = (1,2,3,4,5)$.

Thus, $P$ can be rearranged in ascending order with one operation.

Sample Input 2

2
2 1

Sample Output 2

No

It can be proved that $P$ cannot be rearranged in ascending order within $2\\times 10^3$ operations.

Sample Input 3

4
3 4 1 2

Sample Output 3

Yes
3
3 0
1 2
3 0

There is no need to minimize the number of operations.