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;
long long const M = 1e5 + 10, N = 1e8 + 10, pi = acos(-1);
int n, x, ans = 1e9;
string a[4][111], b[222];
void dmj(int i1, int i2, int i3, int i4) {
  int ii = 0, i;
  for (i = 0; i < n; i++, ii++) b[ii] = a[i1][i] + a[i2][i];
  for (i = 0; i < n; i++, ii++) b[ii] = a[i3][i] + a[i4][i];
}
int f() {
  int ans = 0, ans1 = 1;
  char k1 = b[0][0], k = (b[0][0] == '1' ? '0' : '1');
  for (int i = 0; i < 2 * n; i++)
    for (int j = 0; j < 2 * n; j++) {
      if (!i && !j) continue;
      if (b[i][j] != k) ans++;
      if (b[i][j] != k1) ans1++;
      if (j != 2 * n - 1)
        k = (k == '1' ? '0' : '1'), k1 = (k1 == '1' ? '0' : '1');
    }
  return min(ans1, ans);
}
int main() {
  cin >> n;
  string s;
  for (int i = 0; i < 4; i++)
    for (int j = 0; j < n; j++) {
      cin >> a[i][j];
    }
  vector<int> v = {0, 1, 2, 3};
  do {
    dmj(v[0], v[1], v[2], v[3]);
    ans = min(ans, f());
  } while (next_permutation(v.begin(), v.end()));
  cout << ans;
}
