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>
char b[4][102][102];
int counter(int a, int color, int n) {
  int count = 0;
  int i, j;
  for (j = 0; j < n; j++) {
    for (i = 0; i < n; i++) {
      if ((i + j) % 2) {
        if (b[a][i][j] - '0' == color) count++;
      } else {
        if (b[a][i][j] - '0' != color) count++;
      }
    }
  }
  return count;
}
int main() {
  int count[6][2], i, j, n, m;
  scanf("%d", &n);
  int ans = 0;
  for (j = 0; j < 4; j++)
    for (i = 0; i < n; i++) scanf("%s", b[j][i]);
  for (j = 0; j < 4; j++) {
    count[j][0] = counter(j, 0, n);
    count[j][1] = counter(j, 1, n);
  }
  j = 0;
  int k = 0;
  int valid[4];
  count[5][0] = count[5][1] = 1000000007;
  int black = 2, white = 2;
  valid[0] = valid[1] = valid[2] = valid[3] = 1;
  while (black || white) {
    j = 5;
    k = 5;
    for (i = 0; i < 4; i++) {
      if (valid[i]) {
        if (count[i][0] < count[j][0]) j = i;
        if (count[i][1] < count[k][1]) k = i;
      }
    }
    if (black && white) {
      if (count[j][0] < count[k][1]) {
        ans += count[j][0];
        valid[j] = 0;
        white--;
      } else {
        ans += count[k][1];
        valid[k] = 0;
        black--;
      }
    } else if (black) {
      ans += count[k][1];
      valid[k] = 0;
      black--;
    } else {
      ans += count[j][0];
      valid[j] = 0;
      white--;
    }
  }
  printf("%d\n", ans);
  return 0;
}
