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 int mod = 1e9 + 7;
const int maxn = 1e3 + 100;
char ch[maxn][maxn];
int a[10], b[10];
int geta(int n) {
  int cnt = 0;
  for (int i = 1; i <= n; ++i) {
    for (int j = 1; j <= n; ++j) {
      if ((i + j) % 2) {
        if (ch[i][j] != '1') ++cnt;
      } else {
        if (ch[i][j] != '0') ++cnt;
      }
    }
  }
  return cnt;
}
int getb(int n) {
  int cnt = 0;
  for (int i = 1; i <= n; ++i) {
    for (int j = 1; j <= n; ++j) {
      if ((i + j) % 2 == 0) {
        if (ch[i][j] != '1') ++cnt;
      } else {
        if (ch[i][j] != '0') ++cnt;
      }
    }
  }
  return cnt;
}
int use[5];
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  for (int i = 1; i <= 4; ++i) {
    for (int j = 1; j <= n; ++j) cin >> ch[j] + 1;
    a[i] = geta(n);
    b[i] = getb(n);
  }
  for (int i = 1; i <= 4; ++i) use[i] = i;
  int ans = inf;
  do {
    ans = min(ans, a[use[1]] + a[use[2]] + b[use[3]] + b[use[4]]);
  } while (next_permutation(use + 1, use + 1 + 4));
  cout << ans;
  return 0;
}
