Chef is bored cooking his regular dishes, so he decided to cook permutations instead. Since this is his first time cooking permutations, he takes some help.

Chef has two permutations A and B, each of size N. Chef cooks a permutation C of size N^{2} by doing the following:

for i = 1 to N:
for j = 1 to N:
C[i + (j-1) * N] = A[i] + (B[j] - 1) * N

Chef is allowed to make some (maybe 0) moves on permutation C. In one move, Chef can:
Pick two indices 1 ≤ i < j ≤ N^{2} and swap the elements C_{i} and C_{j}.

Find the minimum number of moves required to sort permutation C in ascending order.

------ Input Format ------

• The first line of the input contains a single integer T - the number of test cases. The description of test cases follows.
• The first line of each test case contains an integer N - the length of permutations A and B.
• The second line of each test case contains $N integers A_{1}, A_{2}, \ldots, A_{N}, denoting permutation A$.
• The third line of each test case contains $N integers B_{1}, B_{2}, \ldots, B_{N}, denoting permutation B$.

------ Output Format ------

For each test case, print a single integer representing the number of moves required to sort permutation C.

------ Constraints ------

$1 ≤T ≤10^{5}$
$1 ≤N ≤2 \cdot 10^{5}$
$1 ≤A_{i}, B_{i} ≤N$
- The sum of $N$ over all test cases doesn't exceed $10^{6}$

------ subtasks ------

Subtask #1 (100 points): original constraints

----- Sample Input 1 ------
3
3
3 1 2
2 1 3
2
1 2
1 2
2
2 1
2 1

----- Sample Output 1 ------
7
0
2
----- explanation 1 ------
- In the first test case, $C = [6, 4, 5, 3, 1, 2, 9, 7, 8]$. Minimum number of moves required to sort permutation $C$ are $7$.
- In the second test case, $C = [1, 2, 3, 4]$. The permutation is already sorted, so we need $0$ moves.
- In the third test case, $C = [4, 3, 2, 1]$. We need $2$ moves to sort the permutation.

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