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 n, Ans = 0x7fffffff;
int a[5][101][101];
int Match[2][101][101];
inline int read() {
  int k = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    k = k * 10 + ch - '0';
    ch = getchar();
  }
  return k * f;
}
inline int Change(int k, int opt) {
  int tot = 0;
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      if (a[k][i][j] != Match[opt][i][j]) {
        tot++;
      }
    }
  }
  return tot;
}
int vis1[10], vis2[10];
void dfs(int t, int D, int opt) {
  if (t == 4) {
    Ans = min(Ans, D);
    return;
  }
  for (int i = 1; i <= 4; i++) {
    if (!vis1[i]) {
      vis1[i] = true;
      int Goal = (i + opt) % 2;
      for (int k = 1; k <= 4; k++) {
        if (!vis2[k]) {
          vis2[k] = true;
          int Tmp = Change(k, Goal);
          dfs(t + 1, D + Tmp, opt);
          vis2[k] = false;
        }
      }
      vis1[i] = false;
    }
  }
}
int main() {
  scanf("%d\n", &n);
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      if (((i + j) & 1) == 0) {
        Match[0][i][j] = 0;
        Match[1][i][j] = 1;
      } else {
        Match[0][i][j] = 1;
        Match[1][i][j] = 0;
      }
    }
  }
  for (int k = 1; k <= 4; k++) {
    for (int i = 1; i <= n; i++) {
      for (int j = 1; j <= n; j++) {
        scanf("%c", &a[k][i][j]);
        a[k][i][j] -= '0';
      }
      scanf("\n");
    }
  }
  dfs(0, 0, 0);
  memset(vis1, 0, sizeof(vis1));
  memset(vis2, 0, sizeof(vis2));
  dfs(0, 0, 1);
  printf("%d", Ans);
  return 0;
}
