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 long long mod = 1e9 + 7;
const int N = 1e2 + 10;
char str[5][N][N];
int cnt[5][2];
int ans = INF;
void solve(int a, int b, int c, int d) {
  ans = min(ans, cnt[a][0] + cnt[b][0] + cnt[c][1] + cnt[d][1]);
  ans = min(ans, cnt[a][1] + cnt[b][1] + cnt[c][0] + cnt[d][0]);
}
int main() {
  int n;
  scanf("%d", &n);
  for (int id = 1; id <= 4; id++)
    for (int i = 1; i <= n; i++) scanf("%s", str[id][i] + 1);
  for (int id = 1; id <= 4; id++)
    for (int i = 1; i <= n; i++)
      for (int j = 1; j <= n; j++) {
        if ((i + j) % 2 == 0) {
          if (str[id][i][j] == '1')
            cnt[id][0]++;
          else
            cnt[id][1]++;
        } else if (str[id][i][j] == '1')
          cnt[id][1]++;
        else
          cnt[id][0]++;
      }
  solve(1, 2, 3, 4);
  solve(1, 3, 2, 4);
  solve(1, 4, 2, 3);
  printf("%d", ans);
  return 0;
}
