CF1672F2.Checker for Array Shuffling

oolimry has an array $a$ of length $n$ which he really likes. Today, you have changed his array to $b$ , a permutation of $a$ , to make him sad.

Because oolimry is only a duck, he can only perform the following operation to restore his array:

• Choose two integers $i,j$ such that $1 \leq i,j \leq n$ .
• Swap $b_i$ and $b_j$ .

The sadness of the array $b$ is the minimum number of operations needed to transform $b$ into $a$ .

Given the arrays $a$ and $b$ , where $b$ is a permutation of $a$ , determine if $b$ has the maximum sadness over all permutations of $a$ .

Each test contains multiple test cases. The first line contains a single integer $t$ ( $1 \leq t \leq 10^4$ ) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $n$ ( $1 \leq n \leq 2 \cdot 10^5$ ) — the length of the array.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \leq a_i \leq n$ ) — the elements of the array $a$ .

The third line of each test case contains $n$ integers $b_1, b_2, \ldots, b_n$ ( $1 \leq b_i \leq n$ ) — the elements of the array $b$ .

It is guaranteed that $b$ is a permutation of $a$ .

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .

For each test case, print "AC" (without quotes) if $b$ has the maximum sadness over all permutations of $a$ , and "WA" (without quotes) otherwise.

In the first test case, the array $[1,2]$ has sadness $1$ . We can transform $[1,2]$ into $[2,1]$ using one operation with $(i,j)=(1,2)$ .

In the second test case, the array $[3,3,2,1]$ has sadness $2$ . We can transform $[3,3,2,1]$ into $[1,2,3,3]$ with two operations with $(i,j)=(1,4)$ and $(i,j)=(2,3)$ respectively.

In the third test case, the array $[2,1]$ has sadness $0$ .

In the fourth test case, the array $[3,2,3,1]$ has sadness $1$ .