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 $(Q_1,\ldots,Q_j, P_i, P_{i+1}, Q_{j+1},\ldots,Q_{N-2})$.

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.

Constraints

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

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.

见题面 Input 部分

见题面 Output 部分