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;
char a[4][100][100];
int c[6];
int check(int le, int s, char st) {
  int ct = 0;
  for (int i = 0; i < s; i++) {
    for (int j = 0; j < s; j++) {
      if ((i - (s - 1) / 2 + j - (s - 1) / 2) % 2 == 0 && a[le][i][j] != st) {
        ct++;
      } else if ((i - (s - 1) / 2 + j - (s - 1) / 2) % 2 != 0 &&
                 a[le][i][j] == st) {
        ct++;
      }
    }
  }
  return ct;
}
int main() {
  int si;
  scanf("%d", &si);
  getchar();
  for (int k = 0; k < 4; k++) {
    for (int i = 0; i < si; i++) {
      char s[101];
      scanf("%s", &s);
      for (int r = 0; r < si; r++) a[k][i][r] = s[r];
      getchar();
    }
    if (k != 3) getchar();
  }
  c[0] = check(0, si, '1') + check(1, si, '1') + check(2, si, '0') +
         check(3, si, '0');
  c[1] = check(0, si, '1') + check(1, si, '0') + check(2, si, '1') +
         check(3, si, '0');
  c[2] = check(0, si, '1') + check(1, si, '0') + check(2, si, '0') +
         check(3, si, '1');
  c[3] = check(0, si, '0') + check(1, si, '1') + check(2, si, '1') +
         check(3, si, '0');
  c[4] = check(0, si, '0') + check(1, si, '1') + check(2, si, '0') +
         check(3, si, '1');
  c[5] = check(0, si, '0') + check(1, si, '0') + check(2, si, '1') +
         check(3, si, '1');
  int ans = 40000;
  for (int i = 0; i < 6; i++) {
    ans = min(c[i], ans);
  }
  printf("%d\n", ans);
  return 0;
}
