There are three arrays a, b and c. Each of them consists of n integers. SmallY wants to find three integers u, v, w(0≤u,v,w≤n) such that the following condition holds: each number that appears in the union of a, b and c, appears either in the first u elements of a, or in the first v elements of b, or in the first w elements of c. Of course, SmallY doesn't want to have huge numbers u, v and w, so she wants sum u+v+w to be as small as possible.
Please, help her to find the minimal possible sum of u+v+w.
Input
The first line contains a single integer n(1≤n≤105). The second line contains n space-separated integers a1,a2,...,an − 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≤ai,bi,ci≤109.
Output
Print a single integer − the minimum possible sum of u+v+w.
Examples
Input
3
1 1 101
1 2 1
3 2 1
Output
5
Input
5
1 1 2 2 3
2 2 4 3 3
3 3 1 1 1
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.