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 = (1 << 30) - 1;
const long long LINF = (1LL << 60) - 1;
template <class T>
bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  } else
    return false;
}
template <class T>
bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  } else
    return false;
}
int main() {
  int n;
  cin >> n;
  vector<vector<string> > a(4, vector<string>(n));
  for (int k = 0; k < 4; k++)
    for (int i = 0; i < n; i++) cin >> a[k][i];
  vector<int> p(4);
  vector<vector<int> > cnt(4, vector<int>(2, 0));
  for (int k = 0; k < 4; k++) {
    for (int i = 0; i < n; i++)
      for (int j = 0; j < n; j++) {
        if ((i + j) % 2 != a[k][i][j] - '0') cnt[k][0]++;
      }
    for (int i = 0; i < n; i++)
      for (int j = 0; j < n; j++) {
        if ((i + j + 1) % 2 != a[k][i][j] - '0') cnt[k][1]++;
      }
  }
  for (int i = 0; i < 4; i++) p[i] = i;
  int ans = INF;
  do {
    for (int c = 0; c < 2; c++)
      chmin(ans,
            cnt[p[0]][c] + cnt[p[3]][c] + cnt[p[1]][1 - c] + cnt[p[2]][1 - c]);
  } while (next_permutation(p.begin(), p.end()));
  cout << ans << endl;
  return 0;
}
