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 b[104][104], c[104][104];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long n, i, j, k, ss = 0;
  cin >> n;
  string a[4][n];
  for (i = 0; i < 4; i++)
    for (j = 0; j < n; j++) cin >> a[i][j];
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      if ((i + j) % 2)
        b[i][j] = 0;
      else
        b[i][j] = 1;
    }
  }
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      if ((i + j) % 2)
        c[i][j] = 1;
      else
        c[i][j] = 0;
    }
  }
  vector<long long> d1, d2;
  for (i = 0; i < 4; i++) {
    long long d = 0, dd = 0;
    for (j = 0; j < n; j++) {
      for (k = 0; k < n; k++) {
        if (a[i][j][k] - '0' - b[j][k]) d++;
        if (a[i][j][k] - '0' - c[j][k]) dd++;
      }
    }
    d1.push_back(d);
    d2.push_back(dd);
  }
  for (i = 0; i < 4; i++) ss += d2[i];
  long long ans = 1000000007;
  for (i = 0; i < 4; i++) {
    for (j = i + 1; j < 4; j++) {
      long long a1 = d1[i] + d1[j], a2 = ss - (d2[i] + d2[j]);
      ans = min(ans, a1 + a2);
    }
  }
  cout << ans;
  return 0;
}
