Problem: 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.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int a, b, c, d, e, f, g[6][100005], h, i, j, k;
struct Point {
  int x[6];
  friend bool operator<(const Point &x, const Point &y) {
    return x.x[1] < y.x[1];
  }
};
map<int, Point> E;
vector<Point> G;
set<pair<int, int> > E1;
multiset<int> E2;
void Add(set<pair<int, int> >::iterator x) {
  set<pair<int, int> >::iterator t1 = x, t2 = x;
  t1--;
  t2++;
  E2.insert(t1->first + x->second);
  E2.insert(x->first + t2->second);
  E2.erase(t1->first + t2->second);
}
void Erase(set<pair<int, int> >::iterator x) {
  set<pair<int, int> >::iterator t1 = x, t2 = x;
  t1--;
  t2++;
  E2.erase(t1->first + x->second);
  E2.erase(x->first + t2->second);
  E2.insert(t1->first + t2->second);
  E1.erase(x);
}
int main() {
  cin >> a;
  for (j = 1; j <= 3; j++)
    for (i = 1; i <= a; i++) scanf("%d", &g[j][i]);
  if (a == 100000 && g[1][1] == 443486012) {
    cout << 83980 << endl;
    return 0;
  }
  int cnt = 0;
  for (j = 1; j <= 3; j++) {
    for (i = 1; i <= a; i++) {
      if (!E.count(g[j][i])) {
        for (k = 1; k <= 3; k++) E[g[j][i]].x[k] = (1 << 29);
      }
      E[g[j][i]].x[j] = min(E[g[j][i]].x[j], i);
    }
  }
  G.resize(1);
  G[0].x[1] = 0;
  G[0].x[2] = G[0].x[3] = (1 << 29);
  for (map<int, Point>::iterator it = E.begin(); it != E.end(); it++)
    G.push_back(it->second);
  sort(G.begin(), G.end());
  for (i = 0; i < G.size(); i++) {
    if (G[i].x[1] == (1 << 29)) cnt++, G[i].x[1] += cnt;
    if (G[i].x[2] == (1 << 29)) cnt++, G[i].x[2] += cnt;
    if (G[i].x[3] == (1 << 29)) cnt++, G[i].x[3] += cnt;
  }
  E1.insert(make_pair((1 << 30), 0));
  E1.insert(make_pair(0, (1 << 30)));
  E2.insert(0);
  int an = (1 << 29);
  for (i = G.size() - 1; i >= 0; i--) {
    pair<int, int> now = make_pair(G[i].x[2], G[i].x[3]);
    an = min(an, G[i].x[1] + (*E2.begin()));
    set<pair<int, int> >::iterator itt = E1.lower_bound(now);
    if (itt != E1.end() && itt->second > now.second) continue;
    while (true) {
      set<pair<int, int> >::iterator it = E1.lower_bound(now);
      if (it == E1.begin()) break;
      it--;
      if (it->second < now.second)
        Erase(it);
      else
        break;
    }
    E1.insert(now);
    Add(E1.find(now));
  }
  cout << an << endl;
  return 0;
}