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;
long long n;
char a[105][105], b[105][105], c[105][105], d[105][105], e[105][105],
    f[105][105];
long long tmp = 0, ans;
void input() {
  cin >> n;
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      cin >> a[i][j];
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      cin >> b[i][j];
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      cin >> c[i][j];
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      cin >> d[i][j];
    }
  }
}
void output() {}
void solve() {
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      e[i][j] = tmp + '0';
      tmp = 1 - tmp;
    }
  }
  tmp = 1;
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      f[i][j] = tmp + '0';
      tmp = 1 - tmp;
    }
  }
  long long cnt = 0;
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (a[i][j] != e[i][j]) cnt++;
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (b[i][j] != e[i][j]) cnt++;
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (c[i][j] != f[i][j]) cnt++;
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (d[i][j] != f[i][j]) cnt++;
    }
  }
  ans = cnt;
  cnt = 0;
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (a[i][j] != e[i][j]) cnt++;
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (b[i][j] != f[i][j]) cnt++;
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (c[i][j] != e[i][j]) cnt++;
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (d[i][j] != f[i][j]) cnt++;
    }
  }
  ans = min(ans, cnt);
  cnt = 0;
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (a[i][j] != e[i][j]) cnt++;
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (b[i][j] != f[i][j]) cnt++;
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (c[i][j] != f[i][j]) cnt++;
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (d[i][j] != e[i][j]) cnt++;
    }
  }
  ans = min(ans, cnt);
  cnt = 0;
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (a[i][j] != f[i][j]) cnt++;
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (b[i][j] != f[i][j]) cnt++;
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (c[i][j] != e[i][j]) cnt++;
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (d[i][j] != e[i][j]) cnt++;
    }
  }
  ans = min(ans, cnt);
  cnt = 0;
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (a[i][j] != f[i][j]) cnt++;
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (b[i][j] != e[i][j]) cnt++;
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (c[i][j] != f[i][j]) cnt++;
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (d[i][j] != e[i][j]) cnt++;
    }
  }
  ans = min(ans, cnt);
  cnt = 0;
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (a[i][j] != f[i][j]) cnt++;
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (b[i][j] != e[i][j]) cnt++;
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (c[i][j] != e[i][j]) cnt++;
    }
  }
  for (long long i = 1; i <= n; i++) {
    for (long long j = 1; j <= n; j++) {
      if (d[i][j] != f[i][j]) cnt++;
    }
  }
  ans = min(ans, cnt);
  cout << ans;
}
signed main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  input();
  solve();
  output();
}
