Three Arrays

Description:

Input:

The first line contains a single integer n (1 ≤ n ≤ 10⁵). The second line contains n space-separated integers a₁, a₂, ..., a_n — array a. The third line contains the description of array b in the same format. The fourth line contains the description of array c in the same format. The following constraint holds: 1 ≤ a_i, b_i, c_i ≤ 10⁹.

Output:

Print a single integer — the minimum possible sum of u + v + w.

Sample Input:

3
1 1 101
1 2 1
3 2 1

Sample Output:

5

Sample Input:

5
1 1 2 2 3
2 2 4 3 3
3 3 1 1 1

Sample Output:

5

Note:

In the first example you should choose u = 3, v = 0, w = 2.

In the second example you should choose u = 1, v = 3, w = 1.