1406B · Maximum Product

Problem: You are given an array of integers $a_1,a_2,\ldots,a_n$. Find the maximum possible value of $a_ia_ja_ka_la_t$ among all five indices $(i, j, k, l, t)$ ($i<j<k<l<t$).

Input Format: The input consists of multiple test cases. The first line contains an integer $t$ ($1\le t\le 2 \cdot 10^4$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($5\le n\le 10^5$) — the size of the array.

The second line of each test case contains $n$ integers $a_1,a_2,\ldots,a_n$ ($-3\times 10^3\le a_i\le 3\times 10^3$) — given array.

It's guaranteed that the sum of $n$ over all test cases does not exceed $2\cdot 10^5$.

Output Format: For each test case, print one integer — the answer to the problem.

Note: In the first test case, choosing $a_1,a_2,a_3,a_4,a_5$ is a best choice: $(-1)\cdot (-2) \cdot (-3)\cdot (-4)\cdot (-5)=-120$.

In the second test case, choosing $a_1,a_2,a_3,a_5,a_6$ is a best choice: $(-1)\cdot (-2) \cdot (-3)\cdot 2\cdot (-1)=12$.

In the third test case, choosing $a_1,a_2,a_3,a_4,a_5$ is a best choice: $(-1)\cdot 0\cdot 0\cdot 0\cdot (-1)=0$.

In the fourth test case, choosing $a_1,a_2,a_3,a_4,a_6$ is a best choice: $(-9)\cdot (-7) \cdot (-5)\cdot (-3)\cdot 1=945$.