AT_arc232_c [ARC232C] All Add or Single Negate

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.

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 $ 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.

### Sample Explanation 1 In the first test case, first negate $ A_2 $ , then add $ 1 $ to every element, which makes $ A=(-2,2,1,3) $ . Now $ A $ and $ B $ are equal as multisets. They cannot be made equal with one operation, so the minimum number of operations required is $ 2 $ . In the second test case, no matter how you perform the operations, $ A $ cannot be made equal to $ B=(0,1) $ as multisets. ### 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.