Description

Input

The first line contains a single integer $t$ ($1 \le t \le 50$) — the number of test cases.

The first line of each test case contains a single integer $n$ ($2 \le n \le 1000$) — the number of pieces of cake.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 10^9$) — $a_i$ is the weight of the $i$-th piece of cake.

Output

For each test case, print a single integer: the maximum tastiness of the cake after doing the operation at most once.

5
6
5 2 1 4 7 3
3
32 78 78
3
69 54 91
8
999021 999021 999021 999021 999652 999021 999021 999021
2
1000000000 1000000000
 
 
 
 
 
 

12
156
160
1998673
2000000000

Note

In the first test case, after reversing the subsegment $a[2, 5]$, you get a cake with weights $[5, \underline{7}, \underline{4}, \underline{1}, \underline{2}, 3]$. The tastiness of the cake is now $\max(5+7, 7+4, 4+1, 1+2, 2+3) = 12$. This is the maximum possible tastiness of the cake one can obtain by performing the operation at most once.

In the second test case, it's optimal not to do any operation. The tastiness is $78+78 = 156$.

In the third test case, after reversing the subsegment $a[1, 2]$, you get a cake with weights $[\underline{54}, \underline{69}, 91]$. The tastiness of the cake is now $\max(54+69, 69+91) = 160$. There is no way to make the tastiness of the cake greater than $160$ by performing at most one operation.