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 double PI =
    3.141592653589793238462643383279502884197169399375105820974944;
int startwithone(char str[][105], int n) {
  int ans = 0;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++)
      if ((i + j) % 2 && str[i][j] == '1')
        ans++;
      else if ((i + j) % 2 == 0 && str[i][j] == '0')
        ans++;
  return ans;
}
int startwithzero(char str[][105], int n) {
  int ans = 0;
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++)
      if ((i + j) % 2 && str[i][j] == '0')
        ans++;
      else if ((i + j) % 2 == 0 && str[i][j] == '1')
        ans++;
  return ans;
}
int main() {
  int n;
  cin >> n;
  char str[105][105];
  int a[4] = {0}, b[4] = {0};
  for (int i = 0; i < n; i++) cin >> str[i];
  a[0] = startwithone(str, n);
  b[0] = startwithzero(str, n);
  for (int i = 0; i < n; i++) cin >> str[i];
  a[1] = startwithone(str, n);
  b[1] = startwithzero(str, n);
  for (int i = 0; i < n; i++) cin >> str[i];
  a[2] = startwithone(str, n);
  b[2] = startwithzero(str, n);
  for (int i = 0; i < n; i++) cin >> str[i];
  a[3] = startwithone(str, n);
  b[3] = startwithzero(str, n);
  unsigned long long ans = 10000000;
  for (int i = 0; i < 16; i++) {
    unsigned long long temp = 0;
    int bitcount = 0, bits = i;
    for (int j = 0; j < 4; j++) {
      bitcount += bits % 2;
      bits /= 2;
    }
    if (bitcount == 2) {
      bits = i;
      for (int j = 0; j < 4; j++) {
        if (bits % 2)
          temp += a[j];
        else
          temp += b[j];
        bits /= 2;
      }
      ans = min(ans, temp);
    }
  }
  cout << ans;
}
