You are given an array A of N elements. For any ordered triplet (i, j, k) such that i, j, and k are pairwise distinct and 1 ≤ i, j, k ≤ N, the value of this triplet is $(A_{i}-A_{j})\cdot A_{k}.$ You need to find the maximum value among all possible ordered triplets.

Note: Two ordered triplets (a, b, c) and (d, e, f) are only equal when a = d and b = e and c = f. As an example, (1, 2, 3) and (2, 3, 1) are two different ordered triplets.

------ Input Format ------

• The first line of the input contains a single integer T - the number of test cases. The test cases then follow.
• The first line of each test case contains an integer N.
• The second line of each test case contains $N space-separated integers A_{1}, A_{2}, \dots, A_{N}$.

------ Output Format ------

For each test case, output the maximum value among all different ordered triplets.

------ Constraints ------

$1 ≤T ≤100$
$3 ≤N ≤3 \cdot 10^{5}$
$1 ≤A_{i} ≤10^{6}$
- Sum of $N$ over all testcases won't exceed $3 \cdot 10^{5}$.

------ subtasks ------

Subtask $1$ (30 points): Sum of $N$ over all cases won't exceed $2000$.
Subtask $2$ (70 points): Original constraint

----- Sample Input 1 ------
3
3
1 1 3
5
3 4 4 1 2
5
23 17 21 18 19
----- Sample Output 1 ------
2
12
126
----- explanation 1 ------
- Test case $1$: The desired triplet is $(3, 2, 1)$, which yields the value of $(A_{3} - A_{2}) \cdot A_{1} = (3 - 1) \cdot 1 = 2$.
- Test case $2$: The desired triplet is $(2, 4, 3)$, which yields the value of $(A_{2} - A_{4}) \cdot A_{3} = (4 - 1) \cdot 4 = 12$.
- Test case $3$: The desired triplet is $(1, 2, 3)$, which yields the value of $(A_{1} - A_{2}) \cdot A_{3} = (23 - 17) \cdot 21 = 126$.

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