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 INF = 40005;
int n, Min;
int num[5][105][105];
int ans[205][205];
void solve(int a, int b, int c, int d) {
  int cnt = 0;
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= n; j++) {
      ans[i][j] = num[a][i][j];
      ans[i][j + n] = num[b][i][j];
      ans[i + n][j] = num[c][i][j];
      ans[i + n][j + n] = num[d][i][j];
    }
  for (int i = 1; i <= 2 * n; i++) {
    for (int j = 1; j <= 2 * n; j++) {
      if (((i % 2 == 0) && (j % 2 == 0)) || ((i & 1) && (j & 1))) {
        if (ans[i][j] == 0) cnt++;
      } else {
        if (ans[i][j] == 1) cnt++;
      }
    }
  }
  Min = min(Min, cnt);
}
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++) scanf("%1d", &num[i][j][k]);
  }
  Min = INF;
  for (int a = 1; a <= 4; a++) {
    for (int b = 1; b <= 4; b++) {
      if (a == b) continue;
      for (int c = 1; c <= 4; c++) {
        if (a == c || b == c) continue;
        for (int d = 1; d <= 4; d++) {
          if (a == d || b == d || c == d) continue;
          solve(a, b, c, d);
        }
      }
    }
  }
  printf("%d\n", Min);
  return 0;
}
