1515D · Phoenix and Socks

Problem: 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.

Input Format: 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 Format: 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.

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 $1$