CSES - NOI 2024 - Chair Game
• Time limit: 1.00 s
• Memory limit: 512 MB

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.

After this, each test consists of two lines. The first line has an integer n. The second line has integers s_1,s_2,\dots,s_n: the numbers on the chairs.

# 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.

# Constraints

• 1 \le t \le 1000
• 1 \le n \le 100
• 1 \le s_i \le n for i=1,2,\dots,n

# Example

Input:

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


Output:

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


• 1 \le n \le 8

• s_i \neq s_j if i \neq j (i.e. each value is distinct)

• 1 \le s_i \le 2 for i=1,2,\dots,n

• 1 \le s_i \le 3 for i=1,2,\dots,n

• 1 \le s_i \le 4 for i=1,2,\dots,n