Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into 4 pieces, each of size n by n, n is always odd. And what's even worse, some squares were of wrong color. j-th square of the i-th row of k-th piece of the board has color ak, i, j; 1 being black and 0 being white. 

Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be 2n by 2n. You are allowed to move pieces but not allowed to rotate or flip them.

Input

The first line contains odd integer n (1 ≤ n ≤ 100) — the size of all pieces of the board. 

Then 4 segments follow, each describes one piece of the board. Each consists of n lines of n characters; j-th one of i-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line.

Output

Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard.

Examples

Input

1
0

0

1

0


Output

1


Input

3
101
010
101

101
000
101

010
101
011

010
101
010


Output

2
#include <bits/stdc++.h>
using namespace std;
void solve() {
  int n;
  cin >> n;
  vector<pair<int, int> > ans(4);
  for (int i = 0; i < 4; i++) {
    vector<string> v(n);
    for (int i = 0; i < n; i++) cin >> v[i];
    int ans1 = 0;
    int ans2 = 0;
    for (int j = 0; j < n; j++) {
      for (int k = 0; k < n; k++) {
        if ((k + j) % 2 xor (v[j][k] - '0'))
          ans1++;
        else
          ans2++;
      }
    }
    ans[i] = make_pair(ans1, ans2);
  }
  int finans = INT_MAX;
  for (int i = 0; i < 1 << 4; i++) {
    if (__builtin_popcount(i) == 2) {
      int cur = 0;
      for (int j = 0; j < 4; j++) {
        if (i & (1 << j))
          cur += ans[j].first;
        else
          cur += ans[j].second;
      }
      finans = min(finans, cur);
    }
  }
  cout << finans;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int t = 1;
  while (t--) {
    solve();
  }
  return 0;
}
