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>
#pragma GCC optimize(3)
using namespace std;
int n, ans = 0x3f3f3f3f, a[105][105], iff[10][5];
string s;
inline void getn(int x) {
  int res;
  res = 0;
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      if ((i & 1) && (j & 1) && a[i][j] == 0)
        res++;
      else if ((i & 1) && !(j & 1) && a[i][j] == 1)
        res++;
      else if (!(i & 1) && (j & 1) && a[i][j] == 1)
        res++;
      else if (!(i & 1) && !(j & 1) && a[i][j] == 0)
        res++;
    }
  }
  iff[x][1] = res;
  res = 0;
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      if ((i & 1) && (j & 1) && a[i][j] == 1)
        res++;
      else if ((i & 1) && !(j & 1) && a[i][j] == 0)
        res++;
      else if (!(i & 1) && (j & 1) && a[i][j] == 0)
        res++;
      else if (!(i & 1) && !(j & 1) && a[i][j] == 1)
        res++;
    }
  }
  iff[x][2] = res;
}
signed main() {
  scanf("%d", &n);
  for (int i = 1; i <= 4; i++) {
    for (int j = 1; j <= n; j++) {
      cin >> s;
      for (int k = 1; k <= n; k++) a[j][k] = s[k - 1] - '0';
    }
    getn(i);
  }
  for (int i = 1; i <= 4; i++)
    for (int j = i + 1; j <= 4; j++) {
      int now = iff[i][1] + iff[j][1];
      for (int k = 1; k <= 4; k++)
        if (k != i && k != j) now += iff[k][2];
      ans = min(ans, now);
    }
  printf("%d\n", ans);
  return 0;
}
