codeforces#P1672F2. Checker for Array Shuffling
Checker for Array Shuffling
Description
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.
Input
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 $2 \cdot 10^5$.
Output
For each test case, print "AC" (without quotes) if $b$ has the maximum sadness over all permutations of $a$, and "WA" (without quotes) otherwise.
Samples
4
2
2 1
1 2
4
1 2 3 3
3 3 2 1
2
2 1
2 1
4
1 2 3 3
3 2 3 1
AC
AC
WA
WA
Note
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 $1$.