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 long long maxn = 1e6 + 10;
char a[105][105];
int m1[4], m2[4];
int main() {
  int n;
  memset(m1, 0, sizeof(m1));
  memset(m2, 0, sizeof(m2));
  scanf("%d", &n);
  getchar();
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < n; j++) {
      scanf("%s", a[j]);
      for (int k = 0; k < n; k++) {
        if ((j + k) % 2 == 0) {
          if (a[j][k] - '0' == 1)
            m2[i]++;
          else if (a[j][k] - '0' == 0)
            m1[i]++;
        } else if ((j + k) % 2 == 1) {
          if (a[j][k] - '0' == 1)
            m1[i]++;
          else if (a[j][k] - '0' == 0)
            m2[i]++;
        }
      }
    }
  }
  int ans = n * n * 4;
  for (int i = 0; i < 3; i++) {
    for (int j = i + 1; j < 4; j++) {
      int sum = 0;
      for (int k = 0; k < 4; k++) {
        if (k != i && k != j) sum += m2[k];
      }
      sum += (m1[i] + m1[j]);
      ans = min(ans, sum);
    }
  }
  cout << ans << endl;
  return 0;
}
