**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

# Subtask 1 (8 points)

- 1 \le n \le 8

# Subtask 2 (5 points)

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

# Subtask 3 (4 points)

- 1 \le s_i \le 2 for i=1,2,\dots,n

# Subtask 4 (7 points)

- 1 \le s_i \le 3 for i=1,2,\dots,n

# Subtask 5 (12 points)

- 1 \le s_i \le 4 for i=1,2,\dots,n

# Subtask 6 (15 points)

- 1 \le s_i \le 5 for i=1,2,\dots,n

# Subtask 7 (20 points)

- 1 \le n \le 16

# Subtask 8 (29 points)

- No restrictions.