A. Deranged Deletions
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Call an array $$$b$$$ of length $$$m$$$ a derangement if the following property holds:

  • Let $$$c$$$ be an array of length $$$m$$$ such that $$$c_i = b_i$$$ over all $$$1 \leq i \leq m$$$.
  • Sort $$$c$$$ in non-decreasing order.
  • If $$$b_i\neq c_i$$$ over all $$$1\leq i \leq m$$$, then $$$b$$$ is a derangement.

For example,

  • If $$$b = [4,8,3,1]$$$, then $$$c = [1, 3, 4, 8]$$$ after getting sorted. Since $$$b_i \neq c_i$$$ in all positions, $$$b$$$ is a derangement.
  • If $$$b = [3,2,1]$$$, then $$$c = [1, 2, 3]$$$ after getting sorted. Since $$$b_2 = c_2$$$, $$$b$$$ is not a derangement.

You are given an array $$$a$$$ of length $$$n$$$. In one operation, you can delete an element from $$$a$$$. The order of the remaining elements is preserved after each deletion.

Output whether it is possible to perform some (possibly none) operations such that the remaining elements form a derangement. If it is possible, output any possible remaining array. The remaining array must be non-empty.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 100$$$). The description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ ($$$1 \leq n \leq 100$$$) — the length of array $$$a$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \leq a_i \leq n$$$) — denoting the array $$$a$$$.

Output

For each test case, on a new line, if it is possible to perform operations such that the remaining array is a derangement, output YES. Otherwise, output NO.

You can output in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

If your response was positive, output two more lines in the following format:

  • The first line should contain an integer $$$k$$$ ($$$1 \leq k \leq n$$$), the number of elements that remain in the array.
  • The second line should contain $$$d_1, d_2 \ldots, d_k$$$, the elements that remain in the array. It must be possible to acquire array $$$d$$$ after performing some operations on $$$a$$$. Array $$$d$$$ must be a derangement.
Example
Input
3
3
2 2 3
5
4 5 5 2 4
1
1
Output
NO
YES
4
4 5 2 4
NO
Note

In the second test case, we can delete one $$$5$$$ from the array so that it becomes $$$[4,5,2,4]$$$. It can be shown this array is a derangement. This is not the only solution – it can be shown that the original array $$$[4,5,5,2,4]$$$ is another valid solution.