A14508 | Swaps

You are given two arrays $a$ and $b$ of length $n$ . Array $a$ contains each odd integer from $1$ to $2n$ in an arbitrary order, and array $b$ contains each even integer from $1$ to $2n$ in an arbitrary order.

You can perform the following operation on those arrays:

- choose one of the two arrays
- pick an index $i$ from $1$ to $n-1$
- swap the $i$ -th and the $(i+1)$ -th elements of the chosen array

Compute the minimum number of operations needed to make array $a$ lexicographically smaller than array $b$ .For two different arrays $x$ and $y$ of the same length $n$ , we say that $x$ is lexicographically smaller than $y$ if in the first position where $x$ and $y$ differ, the array $x$ has a smaller element than the corresponding element in $y$ .

Each test contains multiple test cases. The first line contains the number of test cases $t$ ( $1 \le t \le 10^4$ ).

The first line of each test case contains a single integer $n$ ( $1 \le n \le 10^5$ ) — the length of the arrays.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le 2n$ , all $a_i$ are odd and pairwise distinct) — array $a$ .

The third line of each test case contains $n$ integers $b_1, b_2, \ldots, b_n$ ( $1 \le b_i \le 2n$ , all $b_i$ are even and pairwise distinct) — array $b$ .

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^5$ .

For each test case, print one integer: the minimum number of operations needed to make array $a$ lexicographically smaller than array $b$ .

We can show that an answer always exists.