Problem Statement

You are given length-$N$ integer sequences: $A=(A_1,A_2,\ldots,A_N)$ and $B=(B_1,B_2,\ldots,B_N)$.

You can perform the following two types of operations any number of times in any order.

• Add $1$ to every element of $A$.
• Choose an integer $i$ satisfying $1\leq i\leq N$, and replace $A_i$ with $-A_i$.

Determine whether it is possible to make $A$ and $B$ equal as multisets. If it is possible, also find the minimum number of operations required. Here, $A$ and $B$ are equal as multisets when, for every integer, the number of its occurrences in $A$ equals the number of its occurrences in $B$.

You are given $T$ test cases; find the answer for each of them.

Constraints

• $1\leq T\leq 10^4$
• $1\leq N\leq 100$
• $-10^9\leq A_i,B_i\leq 10^9$ $(1 \leq i \leq N)$
• The sum of $N^3$ over all test cases in a single input is at most $10^6$.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

T
\mathrm{case}_1
\mathrm{case}_2
\vdots
\mathrm{case}_T

Each test case is given in the following format:

N
A_1 A_2 \ldots A_N
B_1 B_2 \ldots B_N

Output

Output $T$ lines. The $i$-th line should contain -1 if it is impossible to make $A$ and $B$ equal as multisets in the $i$-th test case, and otherwise the minimum number of operations required.