Problem H
Chair Game

Consider a game with $n$ players and $n$ chairs. The chairs will be arranged in a circle, and each player will sit on a chair. There is also a bell which will ring some number of times during the game. Each chair has an integer between $1$ and $n$: the number of steps the player who sits on that chair must move clockwise when the bell rings. A chair arrangement is valid if each chair will have exactly one player after the bell rings. Your task is to find a valid chair arrangement or state that there is no such arrangement.

Input

The first line has an integer $t$: the number of tests. There are at most $1\, 000$ tests. After this, each test consists of two lines. The first line has an integer $n$, the number of chairs. There are at most $100$ chairs. The second line has integers $s_1,s_2,\dots ,s_ n$: the numbers on the chairs. For all $i$ we have $1 \leq s_ i \leq n$.

Output

For each test, first print YES if there is a valid chair arrangement and NO otherwise. If the answer is YES, also print a possible arrangement clockwise. If there are several valid arrangements, you can print any of them.

Scoring

3
4
1 1 1 1
4
1 1 1 2
5
4 1 2 1 2

YES
1 1 1 1 
NO
YES
2 4 1 1 2