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;
void iosBase(void) {
  ios_base::sync_with_stdio(false);
  cin.tie();
  cout.tie();
}
int n, res = INT_MAX;
int perm[4], used[4];
char t[201][201];
char board[4][101][101];
void oper(int a, int b, int sz, int p) {
  for (int i = a; i < a + sz; ++i) {
    for (int j = b; j < b + sz; ++j) {
      t[i][j] = board[p][i - a][j - b];
    }
  }
}
void dfs(int cur) {
  if (cur == 4) {
    oper(0, 0, n, perm[0]);
    oper(0, n, n, perm[1]);
    oper(n, 0, n, perm[2]);
    oper(n, n, n, perm[3]);
    int cnt = 0;
    for (int i = 0; i < 2 * n; ++i) {
      for (int j = 0; j < 2 * n; ++j) {
        if ((i + j) % 2 == 0) {
          if (t[i][j] == '1') cnt++;
        } else {
          if (t[i][j] == '0') cnt++;
        }
      }
    }
    res = min(res, cnt);
    cnt = 0;
    for (int i = 0; i < 2 * n; ++i) {
      for (int j = 0; j < 2 * n; ++j) {
        if ((i + j) % 2 == 0) {
          if (t[i][j] == '0') cnt++;
        } else {
          if (t[i][j] == '1') cnt++;
        }
      }
    }
    res = min(res, cnt);
    return;
  }
  for (int i = 0; i < 4; ++i) {
    if (!used[i]) {
      used[i] = 1;
      perm[cur] = i;
      dfs(cur + 1);
      used[i] = 0;
    }
  }
}
int main(void) {
  iosBase();
  cin >> n;
  for (int i = 0; i < 4; ++i) {
    for (int j = 0; j < n; ++j) {
      for (int k = 0; k < n; ++k) {
        cin >> board[i][j][k];
      }
    }
  }
  dfs(0);
  cout << res;
  return 0;
}
