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 int MAX_N = 1e2 + 2;
int n;
int x[2][4];
char table;
int ans;
inline int getans(int now, int i, int j) {
  if (now >= 4) return 0;
  int rtn = INT_MAX;
  if (i != 2) rtn = min(rtn, getans(now + 1, i + 1, j) + x[0][now]);
  if (j != 2) rtn = min(rtn, getans(now + 1, i, j + 1) + x[1][now]);
  return rtn;
}
int main() {
  scanf("%d", &n);
  for (int k = 0; k < 4; k++) {
    for (int i = 0; i < n; i++)
      for (int j = 0; j < n; j++) {
        scanf("%1s", &table);
        if (((i + j) & 1) == table - '0') x[0][k]++;
      }
    x[1][k] = n * n - x[0][k];
  }
  ans = getans(0, 0, 0);
  printf("%d\n", ans);
  return 0;
}
