Description

Input

The first line of the input contains a single integer $t$ ($1 \le t \le 10^4$) — the number of testcases.

The first line of each test case contains three integers $n$, $m$, and $k$ ($2 \le n \le 10^5$, $1 \le m, k \le 2 \cdot 10^5$) — the number of prepared problems, the number of models, and the number of functions, respectively.

The second line of each test case contains $n$ integers $a_1, a_2, a_3, \dots a_n$ ($1 \le a_i \le 2 \cdot 10^9$, $a_i < a_{i+1}$) — the complexities of the prepared problems.

The third line of each test case contains $m$ integers $d_1, d_2, d_3, \dots d_m$ ($1 \le d_i \le 10^9$) — the complexities of the models.

The fourth line of each test case contains $k$ integers $f_1, f_2, f_3, \dots f_k$ ($1 \le f_i \le 10^9$) — the complexities of the functions.

It is guaranteed that the sum of $n$ over all testcases does not exceed $10^5$.

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

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

Output

For each testcase, output a single number — the minimum imbalance that Rudolf can achieve.

7
5 5 5
5 10 15 20 26
11 14 16 13 8
16 4 5 3 1
7 6 5
1 4 7 10 18 21 22
2 3 5 7 4 2
6 8 9 3 2
7 6 5
1 4 7 10 18 21 22
2 3 5 7 4 2
6 8 13 3 2
5 6 3
2 10 13 20 25
11 6 10 16 14 5
6 17 15
4 2 2
11 12 14 15
19 14
10 6
8 4 2
3 10 16 18 21 22 29 30
9 13 16 15
4 2
2 4 7
4 21
4 15 14 5
20 1 15 1 12 5 11
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

5
4
5
8
2
7
11