Cherry solution codeforces

Cherry solution codeforces


You are given nn integers a1,a2,,ana1,a2,…,an. Find the maximum value of max(al,al+1,,ar)min(al,al+1,,ar)max(al,al+1,…,ar)⋅min(al,al+1,…,ar) over all pairs (l,r)(l,r) of integers for which 1l<rn1≤l<r≤n.

Input

The first line contains a single integer tt (1t100001≤t≤10000)  — the number of test cases.

The first line of each test case contains a single integer nn (2n1052≤n≤105).

The second line of each test case contains nn integers a1,a2,,ana1,a2,…,an (1ai1061≤ai≤106).

It is guaranteed that the sum of nn over all test cases doesn’t exceed 31053⋅105.

Output

For each test case, print a single integer  — the maximum possible value of the product from the statement.

Example

input

Copy
4
3
2 4 3
4
3 2 3 1
2
69 69
6
719313 273225 402638 473783 804745 323328

output

Copy
12
6
4761
381274500335
Note

Let f(l,r)=max(al,al+1,,ar)min(al,al+1,,ar)f(l,r)=max(al,al+1,…,ar)⋅min(al,al+1,…,ar).

In the first test case,

  • f(1,2)=max(a1,a2)min(a1,a2)=max(2,4)min(2,4)=42=8f(1,2)=max(a1,a2)⋅min(a1,a2)=max(2,4)⋅min(2,4)=4⋅2=8.
  • f(1,3)=max(a1,a2,a3)min(a1,a2,a3)=max(2,4,3)min(2,4,3)=42=8f(1,3)=max(a1,a2,a3)⋅min(a1,a2,a3)=max(2,4,3)⋅min(2,4,3)=4⋅2=8.
  • f(2,3)=max(a2,a3)min(a2,a3)=max(4,3)min(4,3)=43=12f(2,3)=max(a2,a3)⋅min(a2,a3)=max(4,3)⋅min(4,3)=4⋅3=12.

So the maximum is f(2,3)=12f(2,3)=12.

In the second test case, the maximum is f(1,2)=f(1,3)=f(2,3)=6f(1,2)=f(1,3)=f(2,3)=6.


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