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;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long n, i = 0, j = 0, k = 0, l = 0, m = 0, sum = 0, x = 0, y = 0, z = 0,
               p;
  cin >> n;
  int a[n][n], b[n][n], c[n][n], d[n][n];
  char ad[n][n], bd[n][n], cd[n][n], dd[n][n];
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      cin >> ad[i][j];
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      cin >> bd[i][j];
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      cin >> cd[i][j];
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      cin >> dd[i][j];
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      a[i][j] = ad[i][j] - '0';
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      b[i][j] = bd[i][j] - '0';
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      c[i][j] = cd[i][j] - '0';
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      d[i][j] = dd[i][j] - '0';
    }
  }
  int arr[n][n], brr[n][n];
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      if (i % 2 == 0) {
        if (j % 2 == 0) {
          arr[i][j] = 1;
        } else {
          arr[i][j] = 0;
        }
      } else {
        if (j % 2 == 0) {
          arr[i][j] = 0;
        } else {
          arr[i][j] = 1;
        }
      }
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      if (i % 2 == 0) {
        if (j % 2 == 0) {
          brr[i][j] = 0;
        } else {
          brr[i][j] = 1;
        }
      } else {
        if (j % 2 == 0) {
          brr[i][j] = 1;
        } else {
          brr[i][j] = 0;
        }
      }
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      x += abs(arr[i][j] - a[i][j]);
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      y += abs(arr[i][j] - b[i][j]);
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      y += abs(brr[i][j] - c[i][j]);
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      y += abs(brr[i][j] - d[i][j]);
    }
  }
  m = x + y;
  y = 0;
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      y += abs(arr[i][j] - c[i][j]);
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      y += abs(brr[i][j] - b[i][j]);
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      y += abs(brr[i][j] - d[i][j]);
    }
  }
  m = min(m, x + y);
  y = 0;
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      y += abs(arr[i][j] - d[i][j]);
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      y += abs(brr[i][j] - b[i][j]);
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      y += abs(brr[i][j] - c[i][j]);
    }
  }
  m = min(m, x + y);
  y = 0;
  x = 0;
  y = 0;
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      x += abs(brr[i][j] - a[i][j]);
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      y += abs(brr[i][j] - b[i][j]);
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      y += abs(arr[i][j] - c[i][j]);
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      y += abs(arr[i][j] - d[i][j]);
    }
  }
  m = min(m, x + y);
  y = 0;
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      y += abs(brr[i][j] - c[i][j]);
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      y += abs(arr[i][j] - b[i][j]);
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      y += abs(arr[i][j] - d[i][j]);
    }
  }
  m = min(m, x + y);
  y = 0;
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      y += abs(brr[i][j] - d[i][j]);
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      y += abs(arr[i][j] - b[i][j]);
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      y += abs(arr[i][j] - c[i][j]);
    }
  }
  m = min(m, x + y);
  y = 0;
  cout << m;
  return 0;
}
