You are given a list of $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$. You need to pick $$$8$$$ elements from the list and use them as coordinates of four points. These four points should be corners of a rectangle which has its sides parallel to the coordinate axes. Your task is to pick coordinates in such a way that the resulting rectangle has the maximum possible area. The rectangle can be degenerate, i. e. its area can be $$$0$$$. Each integer can be used as many times as it occurs in the list (or less).

Input format:
The first line contains one integer $$$t$$$ ($$$1 \le t \le 25\,000$$$) — the number of test cases.

The first line of each test case contains one integer $$$n$$$ ($$$8 \le n \le 2 \cdot 10^5$$$).

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$-10^9 \le a_i \le 10^9$$$).

Additional constraint on the input: the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.
Output format:
For each test case, print the answer as follows:

- if it is impossible to construct a rectangle which meets the constraints from the statement, print a single line containing the word NO (case-insensitive);
- otherwise, in the first line, print YES (case-insensitive). In the second line, print $$$8$$$ integers $$$x_1, y_1, x_2, y_2, x_3, y_3, x_4, y_4$$$ — the coordinates of the corners of the rectangle. You can print the corners in any order.
Example Input 0:
3
16
-5 1 1 2 2 3 3 4 4 5 5 6 6 7 7 10
8
0 0 -1 2 2 1 1 3
8
0 0 0 0 0 5 0 5

Example Output 0:
YES
1 2 1 7 6 2 6 7
NO
YES
0 0 0 5 0 0 0 5



Example input:
3
16
-5 1 1 2 2 3 3 4 4 5 5 6 6 7 7 10
8
0 0 -1 2 2 1 1 3
8
0 0 0 0 0 5 0 5


Example output:
YES
1 2 1 7 6 2 6 7
NO
YES
0 0 0 5 0 0 0 5