Phoenix and Socks
Description
To satisfy his love of matching socks, Phoenix has brought his $n$ socks ($n$ is even) to the sock store. Each of his socks has a color $c_i$ and is either a left sock or right sock.
Phoenix can pay one dollar to the sock store to either:
- recolor a sock to any color $c'$ $(1 \le c' \le n)$
- turn a left sock into a right sock
- turn a right sock into a left sock
The sock store may perform each of these changes any number of times. Note that the color of a left sock doesn't change when it turns into a right sock, and vice versa.
A matching pair of socks is a left and right sock with the same color. What is the minimum cost for Phoenix to make $n/2$ matching pairs? Each sock must be included in exactly one matching pair.
The input consists of multiple test cases. The first line contains an integer $t$ ($1 \le t \le 1000$) — the number of test cases.
The first line of each test case contains three integers $n$, $l$, and $r$ ($2 \le n \le 2 \cdot 10^5$; $n$ is even; $0 \le l, r \le n$; $l+r=n$) — the total number of socks, and the number of left and right socks, respectively.
The next line contains $n$ integers $c_i$ ($1 \le c_i \le n$) — the colors of the socks. The first $l$ socks are left socks, while the next $r$ socks are right socks.
It is guaranteed that the sum of $n$ across all the test cases will not exceed $2 \cdot 10^5$.
For each test case, print one integer — the minimum cost for Phoenix to make $n/2$ matching pairs. Each sock must be included in exactly one matching pair.
Input
The input consists of multiple test cases. The first line contains an integer $t$ ($1 \le t \le 1000$) — the number of test cases.
The first line of each test case contains three integers $n$, $l$, and $r$ ($2 \le n \le 2 \cdot 10^5$; $n$ is even; $0 \le l, r \le n$; $l+r=n$) — the total number of socks, and the number of left and right socks, respectively.
The next line contains $n$ integers $c_i$ ($1 \le c_i \le n$) — the colors of the socks. The first $l$ socks are left socks, while the next $r$ socks are right socks.
It is guaranteed that the sum of $n$ across all the test cases will not exceed $2 \cdot 10^5$.
Output
For each test case, print one integer — the minimum cost for Phoenix to make $n/2$ matching pairs. Each sock must be included in exactly one matching pair.
Samples
4
6 3 3
1 2 3 2 2 2
6 2 4
1 1 2 2 2 2
6 5 1
6 5 4 3 2 1
4 0 4
4 4 4 3
2
3
5
3
Note
In the first test case, Phoenix can pay $2$ dollars to:
- recolor sock $1$ to color $2$
- recolor sock $3$ to color $2$
In the second test case, Phoenix can pay $3$ dollars to:
- turn sock $6$ from a right sock to a left sock
- recolor sock $3$ to color $1$
- recolor sock $4$ to color $1$