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;
const int INF = 0x3f3f3f3f;
const int MAXN = INF;
char s[105][105];
int main() {
  int n, a[5], b[5];
  scanf("%d", &n);
  for (int t = 1; t <= 4; t++) {
    int temp = 0;
    for (int i = 1; i <= n; i++) {
      for (int j = 1; j <= n; j++) {
        scanf(" %c", &s[i][j]);
        if ((i + j) % 2 == 0 && s[i][j] == '1') temp++;
        if ((i + j) % 2 == 1 && s[i][j] == '0') temp++;
      }
    }
    a[t] = temp;
  }
  int ans = INF;
  ans = (ans) < (a[1] + a[2] + 2 * n * n - a[3] - a[4])
            ? (ans)
            : (a[1] + a[2] + 2 * n * n - a[3] - a[4]);
  ans = (ans) < (a[1] + a[3] + 2 * n * n - a[2] - a[4])
            ? (ans)
            : (a[1] + a[3] + 2 * n * n - a[2] - a[4]);
  ans = (ans) < (a[1] + a[4] + 2 * n * n - a[3] - a[2])
            ? (ans)
            : (a[1] + a[4] + 2 * n * n - a[3] - a[2]);
  ans = (ans) < (a[2] + a[3] + 2 * n * n - a[1] - a[4])
            ? (ans)
            : (a[2] + a[3] + 2 * n * n - a[1] - a[4]);
  ans = (ans) < (a[2] + a[4] + 2 * n * n - a[3] - a[1])
            ? (ans)
            : (a[2] + a[4] + 2 * n * n - a[3] - a[1]);
  ans = (ans) < (a[3] + a[4] + 2 * n * n - a[1] - a[2])
            ? (ans)
            : (a[3] + a[4] + 2 * n * n - a[1] - a[2]);
  printf("%d\n", ans);
  return 0;
}
