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, f[10][10];
char a[10][105][105];
int f1(int x) {
  int ret = 0;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++)
      if (a[x][i][j] - 48 != (i + j) % 2) ret++;
  return ret;
}
int min(int a, int b, int c, int d, int e, int f) {
  return min(min(a, b), min(min(c, d), min(e, f)));
}
int f2(int x) {
  int ret = 0;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++)
      if (a[x][i][j] - 48 == (i + j) % 2) ret++;
  return ret;
}
int main() {
  cin >> n;
  for (int j = 1; j <= 4; j++) {
    for (int i = 0; i < n; i++) cin >> a[j][i];
    f[j][1] = f1(j);
    f[j][0] = f2(j);
  }
  int ans = min(f[1][1] + f[2][1] + f[3][0] + f[4][0],
                f[1][1] + f[2][0] + f[3][1] + f[4][0],
                f[1][1] + f[2][0] + f[3][0] + f[4][1],
                f[1][0] + f[2][1] + f[3][1] + f[4][0],
                f[1][0] + f[2][1] + f[3][0] + f[4][1],
                f[1][0] + f[2][0] + f[3][1] + f[4][1]);
  cout << ans << endl;
  return 0;
}
