Chef is given two arrays A and B, each having N elements.

In one move, Chef can choose an index i (1 ≤ i ≤ N-1), get (A_{i} - A_{i+1}) points, and then swap A_{i} and A_{i+1}.

For example: If Chef has the array - [10, 7,5] and Chef chooses index 1 during his move, he will get 10 - 7 = 3 points and the new array will become [7 , 10 ,5]

Can you help Chef in finding the maximum number of points he can get while converting the array A into array B?

$\textbf{Note$:} It is guaranteed in the input that there exists a sequence of moves which can convert array A into B.

------ Input Format ------

• The first line of input contains a single integer T, denoting the number of testcases. The description of the T testcases follows.
• The first line of each test case contains a single integer N denoting the number of elements in A and B.
• The second line of each test case contains N space separated integers A_{1}, A_{2},..., A_{N}.
• The third line of each test case contains N space separated integers B_{1}, B_{2},..., B_{N}.

------ Output Format ------

For each test case, print a single line containing one integer, which is the maximum number of points that Chef can get while converting the array A into array B

------ Constraints ------

$1 ≤ T ≤ 5 \cdot 10^{4}$
$2 ≤ N ≤ 5 \cdot 10^{5}$
$1 ≤ A_{i} ≤ 10^{5}$
$1 ≤ B_{i} ≤ 10^{5}$
- The sum of $N$ over all test cases does not exceed $5 \cdot 10^{5}$

----- Sample Input 1 ------
3
2
1 2
2 1
3
3 2 1
1 2 3
3
1 2 3
1 2 3
----- Sample Output 1 ------
-1
4
0
----- explanation 1 ------
Test Case $1$: Chef can choose $i = 1$ in the first move, get $1 - 2 = -1$ points and swap $A_{1}$ and $A_{2}$. After this move, $A$ is converted into $B$. We can prove that there exists no other sequence of moves which can result in higher score while converting $A$ into $B$.

Test Case $2$: One possible sequence of moves is the following:
- Choose $i = 2$. Total points $= 1$, and $A$ will become $[3, 1, 2]$.
- Choose $i = 1$. Total points $= 1 + 2$, and $A$ will become $[1, 3, 2]$.
- Choose $i = 2$. Total points $= 1 + 2 + 1$, and $A$ will become $[1, 2, 3]$.

There are other possible sequences of moves which can result in total $4$ points, but no such sequence exists which can result in more than $4$ points, and simultaneously convert $A$ into $B$.

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