CF 1783A. Make it Beautiful

An array a is called ugly if it contains at least one element which is equal to the sum of all elements before it. If the array is not ugly, it is beautiful.

For example:

the array [6,3,9,6] is ugly: the element 9 is equal to 6+3;

the array [5,5,7] is ugly: the element 5 (the second one) is equal to 5;

the array [8,4,10,14] is beautiful: 8≠0, 4≠8, 10≠8+4, 14≠8+4+10, so there is no element which is equal to the sum of all elements before it.

You are given an array a such that 1≤a1≤a2≤⋯≤an≤100

. You have to reorder the elements of a in such a way that the resulting array is beautiful. Note that you are not allowed to insert new elements or erase existing ones, you can only change the order of elements of a. You are allowed to keep the array a

 unchanged, if it is beautiful.

Input

The first line contains one integer t (1≤t≤2000) — the number of test cases.

Each test case consists of two lines. The first line contains one integer n (2≤n≤50). The second line contains n integers a1,a2,…,an (1≤a1≤a2≤⋯≤an≤100).

Output

For each test case, print the answer as follows:

if it is impossible to reorder the elements of a in such a way that it becomes beautiful, print NO;otherwise, in the first line, print YES. In the second line, print n integers — any beautiful array which can be obtained from a by reordering its elements. If there are multiple such arrays, print any of them.

Example

input

4

4

3 3 6 6

2

10 10

5

1 2 3 4 5

3

1 4 4

output

YES

3 6 3 6

NO

YES

2 4 1 5 3

YES

1 4 4

如果此数组不管怎么排列，都存在一个元素是前面元素和的话，这个数据就是ugly的，返回NO，如果是beautiful的，把排列的数组打印出来，

我是将数组排序，放到2个优先队列中，一个放最大的元素，一个放最小的元素，交替放置，如果这样还是ugly的，那就肯定是ugly的

下面是代码：