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;
vector<vector<char> > g[5];
char c;
int calc0(vector<vector<char> > a, vector<vector<char> > b,
          vector<vector<char> > c, vector<vector<char> > d) {
  int res = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (i % 2 == j % 2) {
        if (a[i][j] != '0') {
          res++;
        }
      } else {
        if (a[i][j] != '1') res++;
      }
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (i % 2 == j % 2) {
        if (b[i][j] != '1') res++;
      } else if (b[i][j] != '0')
        res++;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (i % 2 == j % 2) {
        if (c[i][j] != '1') res++;
      } else if (c[i][j] != '0')
        res++;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (i % 2 == j % 2) {
        if (d[i][j] != '0') res++;
      } else if (d[i][j] != '1')
        res++;
    }
  }
  return res;
}
int calc1(vector<vector<char> > a, vector<vector<char> > b,
          vector<vector<char> > c, vector<vector<char> > d) {
  int res = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (i % 2 == j % 2) {
        if (a[i][j] != '1') res++;
      } else if (a[i][j] != '0')
        res++;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (i % 2 == j % 2) {
        if (b[i][j] != '0') res++;
      } else if (b[i][j] != '1')
        res++;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (i % 2 == j % 2) {
        if (c[i][j] != '0') res++;
      } else if (c[i][j] != '1')
        res++;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if (i % 2 == j % 2) {
        if (d[i][j] != '1') res++;
      } else if (d[i][j] != '0')
        res++;
    }
  }
  return res;
}
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= 4; i++) {
    for (int j = 0; j < n; j++) {
      g[i].push_back(vector<char>());
      for (int k = 0; k < n; k++) {
        scanf(" %c", &c);
        g[i][j].push_back(c);
      }
    }
  }
  vector<int> rot;
  rot.push_back(1);
  rot.push_back(2);
  rot.push_back(3);
  rot.push_back(4);
  int ans = min(calc0(g[rot[0]], g[rot[1]], g[rot[2]], g[rot[3]]),
                calc1(g[rot[0]], g[rot[1]], g[rot[2]], g[rot[3]]));
  do {
    ans = min(ans, min(calc0(g[rot[0]], g[rot[1]], g[rot[2]], g[rot[3]]),
                       calc1(g[rot[0]], g[rot[1]], g[rot[2]], g[rot[3]])));
  } while (next_permutation(rot.begin(), rot.end()));
  printf("%d", ans);
  return 0;
}
