Prefix Suffix Operations

 You are given two arrays 

A$A$ and B$B$, each of size N$N$. You can perform the following types of operations on array A$A$.

• Type 1$1$: Select any prefix of A$A$ and increment all its elements by 1$1$.
• Type 2$2$: Select any suffix of A$A$ and increment all its elements by 1$1$.

Your task is to transform the array A$A$ into array B$B$ using the minimum number of operations. If it is impossible to do so, output −1$-1$.

For an array A$A$ having N$N$ elements:

• A prefix of the array A$A$ is a subarray starting at index 1$1$.
• A suffix of the array A$A$ is a subarray ending at index N$N$.

Input Format

• First line will contain T$T$, number of test cases. Then the test cases follow.
• The first line of each test case contains a single integer N$N$, the size of arrays A$A$ and B$B$.
• The next line contains N$N$ space-separated integers, where the ith$i^{th}$ integer denotes Ai$A_i$.
• The next line contains N$N$ space-separated integers, where the ith$i^{th}$ integer denotes Bi$B_i$.

Output Format

For each test case, print a single line containing one integer ― minimum operations required to convert A$A$ into B$B$. Print −1$-1$ if it is impossible to convert A$A$ into B$B$.

Constraints

• 1≤T≤104$1\le T\le {10}^4$
• 1≤N≤105$1\le N\le {10}^5$
• −1014≤Ai,Bi≤1014$-{10}^{14}\le A_i,B_i\le {10}^{14}$
• Sum of N$N$ over all test cases does not exceed 2⋅105$2\cdot {10}^5$.

Sample Input 1 

3
5
2 3 5 1 2
4 3 6 2 3
4
0 0 0 0
1 2 2 1
3
1 2 3
1 2 2

Sample Output 1 

3
2
-1

Explanation

Test Case 1$1$: Given A=[2,3,5,1,2]$A=[2,3,5,1,2]$. It can be converted to array B=[4,3,6,2,3]$B=[4,3,6,2,3]$ in 3$3$ operations:

• Operation 1$1$: Perform a type 1$1$ operation. Choose the prefix of length 1$1$ and increment the elements by 1$1$. Thus, the updated array is A=[3,3,5,1,2]$A=[3,3,5,1,2]$.
• Operation 2$2$: Perform a type 1$1$ operation. Choose the prefix of length 1$1$ and increment the elements by 1$1$. Thus, the updated array is A=[4,3,5,1,2]$A=[4,3,5,1,2]$.
• Operation 3$3$: Perform a type 2$2$ operation. Choose the suffix of length 3$3$ and increment the elements by 1$1$. Thus, the updated array is A=[4,3,6,2,3]$A=[4,3,6,2,3]$.

It can be proven that we cannot convert the array A$A$ into array B$B$ in less than 3$3$ operations.

Test Case 2$2$: Given A=[0,0,0,0]$A=[0,0,0,0]$. It can be converted to array B=[1,2,2,1]$B=[1,2,2,1]$ in 2$2$ operations:

• Operation 1$1$: Perform a type 1$1$ operation. Choose the prefix of length 3$3$ and increment the elements by 1$1$. Thus, the updated array is A=[1,1,1,0]$A=[1,1,1,0]$.
• Operation 2$2$: Perform a type 2$2$ operation. Choose the suffix of length 3$3$ and increment the elements by 1$1$. Thus, the updated array is A=[1,2,2,1]$A=[1,2,2,1]$.

It can be proven that we cannot convert the array A$A$ into array B$B$ in less than 2$2$ operations.

Test Case 3$3$: Given A=[1,2,3]$A=[1,2,3]$. The value of A[3]$A[3]$ will always be greater than B[3]$B[3]$. Hence, it is impossible to convert A$A$ into B$B$ using any number of operations