Grammy has a sequence of length .

Please find a permutation such that for all .

输入描述:

There are multiple test cases. 

The first line contains a single integer  (), denoting the number of test cases. 

For each test case:

The first line contains a single integer  (). 

The second line contains  integers  (). 

It is guaranteed that the sum of  does not exceed .

输出描述:

For each test case: 

If the permutation does not exist, output “NO” in one line. 

Otherwise output “YES” in the first line, then output  integers in the second line, denoting the permutation .

3
3
3 3 3
3
3 2 1
6
1 1 4 5 1 4

NO
YES
1 3 2
YES
4 5 1 2 3 6