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 a[4][110][110];
int com[2][220][220];
int n;
int ans = 100000;
void judge(int l1, int r1, int l2, int r2) {
  int t = 0;
  int s[220][220];
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= n; j++) {
      s[i][j] = a[l1][i][j];
      s[i + n][j] = a[l2][i][j];
      s[i][j + n] = a[r1][i][j];
      s[i + n][j + n] = a[r2][i][j];
    }
  for (int _ = 0; _ <= 1; _++) {
    t = 0;
    for (int i = 1; i <= 2 * n; i++)
      for (int j = 1; j <= 2 * n; j++) {
        if (com[_][i][j] != s[i][j]) t++;
      }
    ans = min(ans, t);
  }
}
int main() {
  cin >> n;
  for (int i = 0; i < 4; i++) {
    for (int j = 1; j <= n; j++) {
      string s;
      cin >> s;
      for (int k = 1; k <= n; k++) {
        a[i][j][k] = s[k - 1] - '0';
      }
    }
  }
  int b[4];
  for (int i = 0; i < 4; i++) {
    b[i] = i;
  }
  for (int i = 0; i < 2; i++) {
    for (int j = 1; j <= 2 * n; j++) {
      if (i == 0) {
        if (j & 1)
          com[i][j][1] = 1;
        else
          com[i][j][1] = 0;
      } else {
        if (j & 1)
          com[i][j][1] = 0;
        else
          com[i][j][1] = 1;
      }
      for (int k = 2; k <= 2 * n; k++) {
        com[i][j][k] = 1 ^ com[i][j][k - 1];
      }
    }
  }
  do {
    judge(b[0], b[1], b[2], b[3]);
  } while (next_permutation(b, b + 4));
  printf("%d\n", ans);
}
