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 double eps = 1e-6;
const int inf = 0x3f3f3f3f;
const long long int INF = 1e18;
const int mod = 1e9 + 7;
const int maxn = 1e2 + 5;
int a[10][maxn][maxn];
int squ[2 * maxn][2 * maxn];
int n;
int f[] = {0, 1, 2, 3, 4};
int ok(int f[10]) {
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      squ[i][j] = a[f[1]][i][j];
      squ[i][j + n] = a[f[2]][i][j];
      squ[i + n][j] = a[f[3]][i][j];
      squ[i + n][j + n] = a[f[4]][i][j];
    }
  }
  int s1 = 0, s2 = 0;
  int cnt = 0, now = 0;
  for (int i = 1; i <= 2 * n; i++) {
    for (int j = 1; j <= 2 * n; j++) {
      if ((i + j) % 2 == 0 && squ[i][j] != now) ++cnt;
    }
  }
  s1 += cnt;
  cnt = 0, now = 1;
  for (int i = 1; i <= 2 * n; i++) {
    for (int j = 1; j <= 2 * n; j++) {
      if ((i + j) % 2 && squ[i][j] != now) ++cnt;
    }
  }
  s1 += cnt;
  cnt = 0, now = 1;
  for (int i = 1; i <= 2 * n; i++) {
    for (int j = 1; j <= 2 * n; j++) {
      if ((i + j) % 2 == 0 && squ[i][j] != now) ++cnt;
    }
  }
  s2 += cnt;
  cnt = 0, now = 0;
  for (int i = 1; i <= 2 * n; i++) {
    for (int j = 1; j <= 2 * n; j++) {
      if ((i + j) % 2 && squ[i][j] != now) ++cnt;
    }
  }
  s2 += cnt;
  return min(s1, s2);
}
void solve() {
  scanf("%d", &n);
  for (int i = 1; i <= 4; i++) {
    string s;
    for (int j = 1; j <= n; j++) {
      cin >> s;
      for (int k = 1; k <= n; k++) {
        a[i][j][k] = s[k - 1] - '0';
      }
    }
  }
  int ans = inf;
  do {
    int tmp = ok(f);
    ans = min(tmp, ans);
  } while (next_permutation(f + 1, f + 5));
  printf("%d\n", ans);
}
int main() {
  int t = 1, cas = 1;
  while (t--) {
    solve();
  }
}
