题目描述

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

输入格式

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

The first line of each test case contains a single integer n (2≤n≤10^5).

The second line of each test case contains n integers a1,a2,…,an (1≤ai≤10^6).

It is guaranteed that the sum of n over all test cases doesn't exceed 3⋅10^5.

输出格式

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

样例

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

12 
6 
4761 
381274500335

提示

Note Let 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)=4⋅2=8. f(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)=4⋅3=12. So the maximum is f(2,3)=12.

In the second test case, the maximum is f(1,2)=f(1,3)=f(2,3)=6. https://codeforces.com/problemset/problem/1554/A by pig_fat