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 vis[5];
int mp[5][105][105];
int a[5];
int b[205][205];
int n, ans;
void check() {
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) b[i][j] = mp[a[1]][i][j];
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) b[i + n][j] = mp[a[2]][i][j];
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) b[i][j + n] = mp[a[3]][i][j];
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) b[i + n][j + n] = mp[a[4]][i][j];
  }
  int tmp = 0;
  for (int i = 1; i <= 2 * n; i++) {
    for (int j = 1; j <= 2 * n; j++) {
      if (b[i][j] != ((i + j) % 2)) tmp++;
    }
  }
  ans = min(ans, tmp);
  tmp = 0;
  for (int i = 1; i <= 2 * n; i++) {
    for (int j = 1; j <= 2 * n; j++) {
      if (b[i][j] != ((i + j + 1) % 2)) tmp++;
    }
  }
  ans = min(ans, tmp);
}
void dfs(int x) {
  if (x == 5) {
    check();
    return;
  }
  for (int i = 1; i <= 4; i++) {
    if (!vis[i]) {
      a[x] = i;
      vis[i] = 1;
      dfs(x + 1);
      vis[i] = 0;
    }
  }
}
int main() {
  char s[105];
  scanf("%d", &n);
  for (int i = 1; i <= 4; i++) {
    for (int j = 1; j <= n; j++) {
      scanf("%s", s + 1);
      for (int k = 1; k <= n; k++) {
        if (s[k] == '0')
          mp[i][j][k] = 0;
        else
          mp[i][j][k] = 1;
      }
    }
  }
  ans = 40050;
  dfs(1);
  printf("%d", ans);
}
