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 N = 111;
char a[4][N][N];
char b[N * 2][N * 2];
int n;
void fill_piece(char piece[N][N], int x, int y) {
  for (int i = x; i < x + n; ++i) {
    for (int j = y; j < y + n; ++j) {
      b[i][j] = piece[i - x][j - y] - '0';
    }
  }
}
void fill_board(const vector<int> &p) {
  fill_piece(a[p[0]], 0, 0);
  fill_piece(a[p[1]], 0, n);
  fill_piece(a[p[2]], n, 0);
  fill_piece(a[p[3]], n, n);
}
int solve(int v) {
  int res = 0;
  for (int i = 0; i < n * 2; ++i) {
    for (int j = 0; j < n * 2; ++j) {
      res += b[i][j] ^ ((i + j) & 1) ^ v;
    }
  }
  return res;
}
int solve() { return min(solve(0), solve(1)); }
int main() {
  cin >> n;
  for (int k = 0; k < 4; ++k) {
    for (int i = 0; i < n; ++i) {
      cin >> a[k][i];
    }
  }
  vector<int> p(4);
  for (int i = 0; i < 4; ++i) {
    p[i] = i;
  }
  int ans = 1e9;
  do {
    fill_board(p);
    ans = min(ans, solve());
  } while (next_permutation(p.begin(), p.end()));
  cout << ans << endl;
  return 0;
}
