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;
inline int read() {
  int x = 0, f = 1;
  char c = getchar();
  for (; !isdigit(c); c = getchar())
    if (c == '-') f = -1;
  for (; isdigit(c); c = getchar()) x = x * 10 + c - '0';
  return x * f;
}
const int INF = 9999999;
const int MAXN = 100000;
bool Col[301][301];
bool c[5][301][301];
bool all[301][301];
char str[MAXN + 1];
int N, M;
bool tmp = 0;
bool book[5];
int sta[MAXN + 1];
int dis[5][2];
int ans;
inline void Get_DFS(int kb) {
  if (kb == 5) {
    for (int i = 1; i <= 4; i++) {
      for (int j = 1; j <= N; j++)
        for (int k = 1; k <= N; k++)
          all[j + dis[i][0]][k + dis[i][1]] = c[sta[i]][j][k];
    }
    int cnt = 0;
    for (int i = 1; i <= 2 * N; i++) {
      for (int j = 1; j <= 2 * N; j++) {
        cnt += all[i][j] ^ Col[i][j];
      }
    }
    ans = min(ans, cnt);
  }
  for (int i = 1; i <= 4; i++) {
    if (!book[i]) {
      book[i] = true;
      sta[kb] = i;
      Get_DFS(kb + 1);
      book[i] = false;
    }
  }
  return;
}
int main() {
  N = read();
  dis[2][0] = dis[3][1] = dis[4][0] = dis[4][1] = N;
  for (int i = 1; i <= 4; i++) {
    for (int j = 1; j <= N; j++) {
      scanf("%s", str);
      for (int k = 0; k < N; k++) c[i][j][k + 1] = str[k] - '0';
    }
  }
  for (int i = 1; i <= 2 * N; i++) {
    for (int j = 1; j <= 2 * N; j++) {
      Col[i][j] = tmp;
      if (j != 2 * N) tmp ^= 1;
    }
  }
  ans = INF;
  Get_DFS(1);
  for (int i = 1; i <= 2 * N; i++) {
    for (int j = 1; j <= 2 * N; j++) Col[i][j] ^= 1;
  }
  Get_DFS(1);
  printf("%d\n", ans);
  return 0;
}
