Phoenix and Socks

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 ≤ c' ≤ 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

The input consists of multiple test cases. The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases.

The first line of each test case contains three integers n, l, and r (2 ≤ n ≤ 2 ⋅ 10^5; n is even; 0 ≤ l, r ≤ 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 ≤ c_i ≤ 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 ⋅ 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.

Example

Input

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

Output

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

There are now 3 matching pairs. For example, pairs (1, 4), (2, 5), and (3, 6) are matching.

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

There are now 3 matching pairs. For example, pairs (1, 3), (2, 4), and (5, 6) are matching.

inputFormat

Input

The input consists of multiple test cases. The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases.

The first line of each test case contains three integers n, l, and r (2 ≤ n ≤ 2 ⋅ 10^5; n is even; 0 ≤ l, r ≤ 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 ≤ c_i ≤ 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 ⋅ 10^5.

outputFormat

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.

Example

Input

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

Output

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

There are now 3 matching pairs. For example, pairs (1, 4), (2, 5), and (3, 6) are matching.

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

There are now 3 matching pairs. For example, pairs (1, 3), (2, 4), and (5, 6) are matching.

样例

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

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