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 N = 102;
int n, a[N][N], ans[4][2];
int main() {
  scanf("%d", &n);
  int sum = 0;
  for (int k = 1; k <= 4; ++k) {
    for (int i = 1; i <= n; ++i)
      for (int j = 1; j <= n; ++j) scanf("%1d", &a[i][j]);
    int start = 0;
    for (int i = 1; i <= n; ++i)
      for (int j = 1; j <= n; ++j) ans[k][0] += start ^ a[i][j], start ^= 1;
    sum += ans[k][0];
    start = 1;
    for (int i = 1; i <= n; ++i)
      for (int j = 1; j <= n; ++j) ans[k][1] += start ^ a[i][j], start ^= 1;
  }
  int res = 1000000000;
  for (int i = 1; i <= 4; ++i)
    for (int j = i + 1; j <= 4; ++j)
      res = min(res, sum + ans[i][1] - ans[i][0] + ans[j][1] - ans[j][0]);
  printf("%d\n", res);
  return 0;
}
