Minimum Value Rectangle

Description:

Input:

The first line contains a single integer $$$T$$$ ($$$T \ge 1$$$) — the number of lists of sticks in the testcase.

Then $$$2T$$$ lines follow — lines $$$(2i - 1)$$$ and $$$2i$$$ of them describe the $$$i$$$-th list. The first line of the pair contains a single integer $$$n$$$ ($$$4 \le n \le 10^6$$$) — the number of sticks in the $$$i$$$-th list. The second line of the pair contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_j \le 10^4$$$) — lengths of the sticks in the $$$i$$$-th list.

It is guaranteed that for each list there exists a way to choose four sticks so that they form a rectangle.

The total number of sticks in all $$$T$$$ lists doesn't exceed $$$10^6$$$ in each testcase.

Output:

Print $$$T$$$ lines. The $$$i$$$-th line should contain the answer to the $$$i$$$-th list of the input. That is the lengths of the four sticks you choose from the $$$i$$$-th list, so that they form a rectangle and the value $$$\frac{P^2}{S}$$$ of this rectangle is minimal possible. You can print these four lengths in arbitrary order.

If there are multiple answers, print any of them.

Sample Input:

3
4
7 2 2 7
8
2 8 1 4 8 2 1 5
5
5 5 5 5 5

Sample Output:

2 7 7 2
2 2 1 1
5 5 5 5

Note:

There is only one way to choose four sticks in the first list, they form a rectangle with sides $$$2$$$ and $$$7$$$, its area is $$$2 \cdot 7 = 14$$$, perimeter is $$$2(2 + 7) = 18$$$. $$$\frac{18^2}{14} \approx 23.143$$$.

The second list contains subsets of four sticks that can form rectangles with sides $$$(1, 2)$$$, $$$(2, 8)$$$ and $$$(1, 8)$$$. Their values are $$$\frac{6^2}{2} = 18$$$, $$$\frac{20^2}{16} = 25$$$ and $$$\frac{18^2}{8} = 40.5$$$, respectively. The minimal one of them is the rectangle $$$(1, 2)$$$.

You can choose any four of the $$$5$$$ given sticks from the third list, they will form a square with side $$$5$$$, which is still a rectangle with sides $$$(5, 5)$$$.