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 $1 ≤ i ≤ N$, 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

• $1 ≤ N ≤ 500$
• $1 ≤ x_i ≤ N^2$
• 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.