Score : $800$ points

Problem Statement

You are given an integer sequence $x$ of length $N$. Determine if there exists an integer sequence $a$ that satisfies all of the following conditions, and if it exists, construct an instance of $a$.

• $a$ is $N^2$ in length, containing $N$ copies of each of the integers $1$, $2$, $...$, $N$.
• For each $1 \leq i \leq N$, the $i$-th occurrence of the integer $i$ from the left in $a$ is the $x_i$-th element of $a$ from the left.

Constraints

• $1 \leq N \leq 500$
• $1 \leq x_i \leq N^2$
• All $x_i$ are distinct.

Input

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

$N$

$x_1$ $x_2$ $...$ $x_N$

Output

If there does not exist an integer sequence $a$ that satisfies all the conditions, print No. If there does exist such an sequence $a$, print Yes in the first line, then print an instance of $a$ in the second line, with spaces inbetween.

3
1 5 9

Yes
1 1 1 2 2 2 3 3 3

For example, the second occurrence of the integer $2$ from the left in $a$ in the output is the fifth element of $a$ from the left. Similarly, the condition is satisfied for the integers $1$ and $3$.

2
4 1

No