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;
string b[2][105], a[4][105], r;
long long int ans = INT_MAX, n;
void fun(long long int fir, long long int sec, long long int thi,
         long long int fou) {
  long long int i, j, val = 0;
  for (i = 0; i < n; ++i)
    for (j = 0; j < n; ++j)
      if (b[fir][i][j] != a[0][i][j]) ++val;
  for (i = 0; i < n; ++i)
    for (j = 0; j < n; ++j)
      if (b[sec][i][j] != a[1][i][j]) ++val;
  for (i = 0; i < n; ++i)
    for (j = 0; j < n; ++j)
      if (b[thi][i][j] != a[2][i][j]) ++val;
  for (i = 0; i < n; ++i)
    for (j = 0; j < n; ++j)
      if (b[fou][i][j] != a[3][i][j]) ++val;
  ans = min(ans, val);
}
int main() {
  long long int i, j, k;
  cin >> n;
  for (k = 0; k < 4; ++k)
    for (i = 0; i < n; ++i) cin >> a[k][i];
  for (i = 0; i < n; ++i) r.push_back('0');
  for (i = 0; i < n; ++i) {
    b[0][i] = r;
    b[1][i] = r;
  }
  for (i = 0; i < n; ++i)
    for (j = 0; j < n; ++j)
      if ((i + j) % 2 == 1)
        b[0][i][j] = '1';
      else
        b[1][i][j] = '1';
  fun(0, 0, 1, 1);
  fun(0, 1, 0, 1);
  fun(0, 1, 1, 0);
  fun(1, 0, 0, 1);
  fun(1, 0, 1, 0);
  fun(1, 1, 0, 0);
  cout << ans;
  return 0;
}
