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 minim = 1e9, M[105][105], V[5][5], n;
string s;
void analyze(int nr) {
  int min1 = 0, min2 = 0;
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= n; j++)
      if ((i % 2) ^ (j % 2) != M[i][j]) min1++;
  for (int i = 1; i <= n; i++)
    for (int j = 1; j <= n; j++)
      if ((i % 2) ^ (j % 2) == M[i][j]) min2++;
  V[nr][0] = min1;
  V[nr][1] = min2;
}
int main() {
  cin >> n;
  for (int i = 1; i <= 4; i++) {
    for (int j = 1; j <= n; j++) {
      cin >> s;
      for (int k = 0; k < s.size(); k++) M[j][k + 1] = s[k] - '0';
      analyze(i);
    }
  }
  for (int i = 1; i <= 4; i++) {
    for (int j = i + 1; j <= 4; j++) {
      int part1 = V[i][0] + V[j][0], part2 = 0;
      for (int k = 1; k <= 4; k++) {
        if (k == i || k == j) continue;
        part2 += V[k][1];
      }
      if (part1 + part2 < minim) minim = part1 + part2;
    }
  }
  cout << minim;
  return 0;
}
