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][5];
int n;
int main() {
  cin >> n;
  for (int k = 0; k < 4; ++k) {
    int cnt0 = 0, cnt1 = 0;
    int n0 = 0, n1 = 1;
    for (int i = 1; i < n + 1; ++i) {
      for (int j = 1; j < n + 1; ++j) {
        char c;
        cin >> c;
        int x = c - '0';
        if (x != n0) ++cnt0;
        if (x != n1) ++cnt1;
        n1 = (n1 + 1) % 2;
        n0 = (n0 + 1) % 2;
      }
    }
    getchar();
    a[k][0] = cnt0;
    a[k][1] = cnt1;
  }
  int ans = 1e9;
  for (int i = 0; i < 2; ++i) {
    for (int j = 0; j < 2; ++j) {
      for (int k = 0; k < 2; ++k) {
        for (int l = 0; l < 2; ++l) {
          if (i + j + k + l != 2) continue;
          ans = min(ans, a[0][i] + a[1][j] + a[2][k] + a[3][l]);
        }
      }
    }
  }
  cout << ans;
}
