Ja the Ghost is playing with rubber ducks. He has (n) piles of rubber ducks arranged in a row, where the (i)-th pile contains (a_i) ducks. Quack the Duck gives Ja a strictly increasing sequence (b_1,b_2,\ldots,b_n) and commands him to make the piles (a_1,a_2,\ldots,a_n) become exactly this sequence. Ja performs the process in the following two stages: Ja may add any number of ducks to each pile. Formally, for each pile (i), he chooses a non-negative integer (x_i) and replaces (a_i) with (a_i+x_i). Formally, for each pile (i), he chooses a non-negative integer (x_i) and replaces (a_i) with (a_i+x_i). Ja may repeatedly swap two adjacent piles. Formally, he may perform the following operation any number of times, possibly zero: choose an index (i) such that (1\le i\le n-1), and swap the values of (a_i) and (a_{i+1}). Formally, he may perform the following operation any number of times, possibly zero: choose an index (i) such that (1\le i\le n-1), and swap the values of (a_i) and (a_{i+1}). A process is called valid if, after both stages end, the sequence of pile sizes is exactly (b_1,b_2,\ldots,b_n). Find the minimum possible number of operations performed in the second stage among all valid processes. If there is no valid process, output (-1). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 2000)). The description of the test cases follows. The first line of each test case contains an integer (n) ((1\le n\le 2000)) — the number of piles of rubber ducks. The second line contains (n) integers (a_1, a_2, \ldots, a_n) ((1\le a_i\le 10^9)) — the initial number of rubber ducks in each pile. The third line contains (n) integers (b_1,b_2,\ldots,b_n) ((1\le b_1 \lt b_2 \lt \cdots \lt b_n\le 10^9)) — the final number of rubber ducks in each pile. It is guaranteed that the sum of $