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;
string s[5][109];
bool vis[5][109][109];
const int inf = 0x3f3f3f3f;
int a[5];
int main() {
  int n;
  int sum, cnt;
  int l;
  while (cin >> n) {
    sum = inf;
    for (int i = 0; i < 4; i++)
      for (int j = 0; j < n; j++) cin >> s[i][j];
    for (int i = 0; i < 4; i++) a[i] = i;
    do {
      l = 0;
      cnt = 0;
      memset(vis, 0, sizeof(vis));
      for (int i = 0; i < 4; i += 2) {
        if (i == 2) {
          for (int k = 0; k < n; k++) {
            if (s[a[i - 2]][n - 1][k] != s[a[i]][0][k] &&
                vis[a[i - 2]][n - 1][k] == 0) {
            } else if (s[a[i - 2]][n - 1][k] == s[a[i]][0][k] &&
                       vis[a[i - 2]][n - 1][k] == 1) {
            } else {
              cnt++;
              vis[a[i]][0][k] = 1;
            }
            if (s[a[i - 1]][n - 1][k] != s[a[i + 1]][0][k] &&
                vis[a[i - 1]][n - 1][k] == 0) {
            } else if (s[a[i - 1]][n - 1][k] == s[a[i + 1]][0][k] &&
                       vis[a[i - 1]][n - 1][k] == 1) {
            } else {
              cnt++;
              vis[a[i + 1]][0][k] = 1;
            }
          }
          l = 1;
        }
        for (int j = l; j < n; j++) {
          if (j == 0 && s[a[i]][j][0] == s[a[i + 1]][0][n - 1]) {
            vis[a[i + 1]][0][n - 1] = 1;
            cnt++;
          }
          for (int k = 0, k1 = n - 1; k1 >= 0, k < n; k1--, k++) {
            if (j == 0) {
              if (k == 0) continue;
              if (s[a[i]][j][k] != s[a[i + 1]][j][k1]) {
                if (s[a[i]][j][k] != s[a[i]][j][k - 1] &&
                        vis[a[i]][j][k - 1] == 0 ||
                    (s[a[i]][j][k] == s[a[i]][j][k - 1] &&
                     vis[a[i]][j][k - 1] == 1))
                  continue;
                else {
                  cnt += 2;
                  vis[a[i + 1]][j][k1] = 1;
                  vis[a[i]][j][k] = 1;
                }
              } else {
                if (s[a[i]][j][k] == s[a[i]][j][k - 1] &&
                        vis[a[i]][j][k - 1] == 0 ||
                    (s[a[i]][j][k] != s[a[i]][j][k - 1] &&
                     vis[a[i]][j][k - 1] == 1)) {
                  vis[a[i]][j][k] = 1;
                  cnt++;
                } else {
                  vis[a[i + 1]][j][k1] = 1;
                  cnt++;
                }
              }
            } else {
              if (s[a[i]][j - 1][k] != s[a[i]][j][k] &&
                  vis[a[i]][j - 1][k] == 0) {
              } else if (s[a[i]][j - 1][k] == s[a[i]][j][k] &&
                         vis[a[i]][j - 1][k] == 1) {
              } else {
                cnt++;
                vis[a[i]][j][k] = 1;
              }
              if (s[a[i + 1]][j - 1][k] != s[a[i + 1]][j][k] &&
                  vis[a[i + 1]][j - 1][k] == 0) {
              } else if (s[a[i + 1]][j - 1][k] == s[a[i + 1]][j][k] &&
                         vis[a[i + 1]][j - 1][k] == 1) {
              } else {
                cnt++;
                vis[a[i + 1]][j][k] = 1;
              }
            }
          }
        }
      }
      cnt = min(cnt, n * n * 4 - cnt);
      sum = min(cnt, sum);
    } while (next_permutation(a, a + 4));
    cout << sum << endl;
  }
  return 0;
}
