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 int i, j, n;
string s[4][101];
long long int m1[201][201];
long long int m2[201][201];
long long int c[201][201];
void gen() {
  for (i = 0; i < 200; i++) {
    for (j = 0; j < 200; j++) m1[i][j] = (i + j) % 2;
  }
  for (i = 0; i < 200; i++) {
    for (j = 0; j < 200; j++) m2[i][j] = 1 - (i + j) % 2;
  }
}
long long int solve(long long int a1[]) {
  for (long long int i = 0; i < n; i++) {
    for (long long int j = 0; j < n; j++) {
      c[i][j] = s[a1[0]][i][j] - '0';
    }
  }
  for (long long int i = 0; i < n; i++) {
    for (long long int j = n; j < 2 * n; j++) {
      c[i][j] = s[a1[1]][i][j - n] - '0';
    }
  }
  for (long long int i = n; i < 2 * n; i++) {
    for (long long int j = 0; j < n; j++) {
      c[i][j] = s[a1[2]][i - n][j] - '0';
    }
  }
  for (long long int i = n; i < 2 * n; i++) {
    for (long long int j = n; j < 2 * n; j++) {
      c[i][j] = s[a1[3]][i - n][j - n] - '0';
    }
  }
  long long int ans1 = 0, ans2 = 0;
  for (long long int i = 0; i < 2 * n; i++) {
    for (long long int j = 0; j < 2 * n; j++) ans1 += abs(m1[i][j] - c[i][j]);
  }
  for (long long int i = 0; i < 2 * n; i++) {
    for (long long int j = 0; j < 2 * n; j++) ans2 += abs(m2[i][j] - c[i][j]);
  }
  return min(ans1, ans2);
}
int main() {
  gen();
  cin >> n;
  for (i = 0; i < 4; i++) {
    for (j = 0; j < n; j++) {
      cin >> s[i][j];
    }
  }
  long long int ans = 1e18;
  long long int a[4] = {0, 1, 2, 3};
  do {
    ans = min(ans, solve(a));
  } while (next_permutation(a, a + 4));
  cout << ans;
  return 0;
}
