There is a giant circular container which is divided into N segments numbered from 0 to N-1. 

Each segment has two bottles, one is a bottle of cold-drink and other is a bottle of poision. Drinking from bottle of cold-drink increases your energy by A[i] while drinking from bottle of poision decreases your energy by B[i].

The corresponding energies for the same are given in input.

Now as it is circular, so bottles in segment N-1 and segment 0 are adjacent. If you do not drink from bottle of cold-drink, then you have to drink from bottle of poision in that segment. Furthermore you cannot drink from bottle of cold-drink in adjacent segments. You have to drink in such a way so that your energy maximizes. Find this maximum value.

Note : Your initial energy will be 0 and the final maximum energy can be negative.

Input Format
There will be T test cases and in each test case there will be an integer N which is the size of the container.
Next line contain N integers denoting the first array and the second line also contain N integers denoting the second array.

Output Format
There will be T lines each containing the output for each test case.

Constraints
1 ≤ T ≤ 10
1 ≤ N ≤ 10000
1 ≤ A[i],B[i] ≤ 109

Sample Input
1
3
1 2 3
4 5 6

Sample Output
-6

Explanation
There are 3 segments and the pairs are (1,4), (2,5) ,(3,6)
The optimal solution is to drink third potion and first two bottle of poision.
The answer in this case is (-4 + - 5 + 3 ) = -6