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;
template <typename T, typename U>
static void rmin(T &x, U y) {
  if (y < x) x = y;
}
template <typename T, typename U>
static void rmax(T &x, U y) {
  if (x < y) x = y;
}
const double eps = 1e-9;
const double pi = acos(-1.0);
const int MOD = 1e9 + 7;
const int INF = 1e9 + 7;
const int N = 1e2 + 10;
int n;
string s[4][N];
int check(int id, char type) {
  int res = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      if ((i + j) % 2 == 0) {
        if (s[id][i][j] != type) res++;
      } else {
        if (s[id][i][j] == type) res++;
      }
    }
  }
  return res;
}
void relax(int &y, int x) {
  if (y > x) y = x;
}
int main() {
  ios::sync_with_stdio(false);
  cin >> n;
  for (int i = 0; i < 4; i++) {
    for (int j = 0; j < n; j++) {
      cin >> s[i][j];
    }
  }
  int ans = INF;
  for (int i = 0; i < 4; i++) {
    for (int j = i + 1; j < 4; j++) {
      int cur = check(i, '1') + check(j, '1');
      for (int k = 0; k < 4; k++) {
        if (k == i || k == j) continue;
        cur += check(k, '0');
      }
      relax(ans, cur);
    }
  }
  cout << ans << endl;
  return 0;
}
