Problem Statement

You are given as input an integer $N$ greater than or equal to $2$ and a permutation $P$ of length $N$ consisting of positive integers less than or equal to $N$.

Determine whether there exists a vertically descending Amidakuji (ladder lottery) $A$ that satisfies all of the following conditions:

1. $A$ has exactly $N$ vertical lines. (They are parallel to each other.)
2. $A$ has at most $N^2$ horizontal lines. (They are perpendicular to the vertical lines, parallel to each other, and at pairwise distinct heights.)
3. For every positive integer $i$ less than or equal to $N$, starting from the top of the $i$-th vertical line from the left of $A$ and following the lines downward according to the rules of Amidakuji, one reaches the bottom of the $P_i$-th vertical line from the left of $A$.

Here, $P_i$ denotes the $i$-th element of $P$.

Input

The input is given from Standard Input in $2$ lines in the following format:

• Line $1$ contains $N$.
• Line $2$ contains $P_i$ for each positive integer $i$ less than or equal to $N$, in increasing order of $i$, separated by single-byte spaces.

$N$
$P_1$ $\cdots$ $P_N$

Constraints

The input satisfies the following constraints:

• $N$ is an integer satisfying $2 \leq N \leq 100$.
• $P$ is a permutation of length $N$ consisting of positive integers less than or equal to $N$.

Output

If no Amidakuji $A$ satisfying the conditions exists, print No.

If one exists, choose $1$ such $A$. Let $M$ be the number of horizontal lines of $A$, and for each positive integer $j$ less than or equal to $M$, define the positive integer $i_j$ less than $N$ so that the $j$-th horizontal line from the top of $A$ connects the $i_j$-th vertical line from the left and the $i_j + 1$-th vertical line from the left of $A$. Print in the following format:

• On line $1$, print Yes.
• On line $2$, print $M$.
• For each positive integer $j$ less than or equal to $M$, print $i_j$ on line $2 + j$.

Print a newline at the end.

Note that this is a special judge problem. There may be more than $1$ correct answer, but print only $1$ of them.

However, strictly follow the format described above. For example, the behavior of the judge is not guaranteed if there is extra whitespace.

Sample

2
1 2

Yes
0

Yes
2
1
1

Yes
6
1
1
1
1
1
1

2
2 1

Yes
1
1

3
3 1 2

Yes
2
1
2