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Maximum Product Codeforces Problems solution

 Maximum Product Codeforces Problems solution 


Problems statement-

You are given an array of integers a1,a2,,an. Find the maximum possible value of aiajakalat among all five indices (i,j,k,l,t) (i<j<k<l<t).

Input

The input consists of multiple test cases. The first line contains an integer t (1t2104) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer n (5n105) — the size of the array.

The second line of each test case contains n integers a1,a2,,an (3×103ai3×103) — given array.

It's guaranteed that the sum of n over all test cases does not exceed 2105.

Output

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

Example
input
Copy
4
5
-1 -2 -3 -4 -5
6
-1 -2 -3 1 2 -1
6
-1 0 0 0 -1 -1
6
-9 -7 -5 -3 -2 1
output
Copy
-120
12
0
945
Note

In the first test case, choosing a1,a2,a3,a4,a5 is a best choice: (1)(2)(3)(4)(5)=120.

In the second test case, choosing a1,a2,a3,a5,a6 is a best choice: (1)(2)(3)2(1)=12.

In the third test case, choosing a1,a2,a3,a4,a5 is a best choice: (1)000(1)=0.

In the fourth test case, choosing a1,a2,a3,a4,a6 is a best choice: (9)(7)(5)(3)1=945.


Solution -
There are 3 possible cases to maximise ans
1- all are positive(choose max possible number)
2- 4 negative 1 positive (4 minimum of all and 1 greatest positive number)
3 -2 negative and 3 positive ( Chooose 2 minimum negative and 3 highest positive number)

    CODE -




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