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;
const int maxn = 1e5 + 50;
const int inf = 0x3f3f3f3f;
const int mod = 1e9 + 7;
int n, m, k;
char mp[5][105][105];
int omin[5];
int emin[5];
void check(int c) {
  int odd1 = 0, odd0 = 0;
  int even1 = 0, even0 = 0;
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      if ((i + j) % 2) {
        if (mp[c][i][j] == '1')
          odd1++;
        else
          odd0++;
      } else {
        if (mp[c][i][j] == '1')
          even1++;
        else
          even0++;
      }
    }
  }
  int t = (n * n) / 2 + 1;
  int l = (n * n) / 2;
  omin[c] = abs(even1 - t) + abs(odd0 - l);
  emin[c] = abs(even0 - t) + abs(odd1 - l);
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= 4; i++) {
    for (int j = 1; j <= n; j++) {
      for (int k = 1; k <= n; k++) {
        cin >> mp[i][j][k];
      }
    }
    check(i);
  }
  int ans = inf;
  ans = min(ans, omin[1] + omin[2] + emin[3] + emin[4]);
  ans = min(ans, omin[1] + omin[3] + emin[2] + emin[4]);
  ans = min(ans, omin[1] + omin[4] + emin[3] + emin[2]);
  ans = min(ans, omin[3] + omin[2] + emin[1] + emin[4]);
  ans = min(ans, omin[4] + omin[2] + emin[3] + emin[1]);
  ans = min(ans, omin[3] + omin[4] + emin[1] + emin[2]);
  cout << ans << endl;
  return 0;
}
