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;
int a[5][107][107], b[5][107][107];
int p[10];
int ok[107][107];
int pok[107][107];
int main() {
  int n;
  cin >> n;
  for (int i = 1; i <= 4; ++i)
    for (int r = 1; r <= n; ++r)
      for (int c = 1; c <= n; ++c) {
        char ch;
        while (true) {
          cin >> ch;
          if (ch >= '0' && ch <= '1') {
            b[i][r][c] = ch - '0';
            break;
          }
        }
      }
  for (int i = 1; i <= n; ++i) {
    for (int j = 1; j <= n; ++j) {
      if ((i + j) % 2 == 0)
        ok[i][j] = 1;
      else
        pok[i][j] = 1;
    }
  }
  int ans = 1e9;
  for (int i = 1; i <= 4; ++i) p[i] = i;
  int q = 0;
  do {
    q++;
    for (int i = 1; i <= 4; ++i) {
      for (int r = 1; r <= n; ++r)
        for (int c = 1; c <= n; ++c) a[i][r][c] = b[p[i]][r][c];
    }
    int cur = 0;
    for (int i = 1; i <= 4; ++i) {
      if (i % 2 == 1) {
        for (int r = 1; r <= n; ++r)
          for (int c = 1; c <= n; ++c) {
            cur += a[i][r][c] != ok[r][c];
          }
      } else {
        for (int r = 1; r <= n; ++r)
          for (int c = 1; c <= n; ++c) {
            cur += a[i][r][c] != pok[r][c];
          }
      }
    }
    ans = min(ans, cur);
  } while (next_permutation(p + 1, p + 5));
  cout << ans << endl;
  return 0;
}
