CF2038C DIY

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).

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 $ .

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.