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 inf = 1 << 30;
const long long INF = 1LL << 60;
int n;
string P_one, P_zero;
struct Chess {
  char s[105][105];
};
Chess C[5];
void Init() {
  for (int i = 1; i <= 4; i++) {
    for (int j = 1; j <= n; j++) {
      scanf("%s", C[i].s[j]);
    }
  }
}
void get_P() {
  P_one = "";
  P_zero = "";
  bool f = 1;
  for (int i = 0; i < n; i++) {
    P_one += (char)('0' + f);
    P_zero += (char)('0' + (f ^ 1));
    f = f ^ 1;
  }
}
bool check(int x) {
  int one = 0;
  for (int i = 0; i < 4; i++)
    if ((x & (1 << i))) one++;
  if (one == 2)
    return true;
  else
    return false;
}
int cal(int pos, string P) {
  int change = 0;
  for (int i = 1; i <= n; i++) {
    for (int j = 0; j < n; j++)
      if (C[pos].s[i][j] != P[j]) change++;
    for (int j = 0; j < n; j++) {
      if (P[j] == '0')
        P[j] = '1';
      else if (P[j] == '1')
        P[j] = '0';
    }
  }
  return change;
}
int solve(int x) {
  int cnt = 0;
  for (int i = 0; i < 4; i++) {
    if ((x & (1 << i)) > 0) {
      cnt += cal(4 - i, P_one);
    } else {
      cnt += cal(4 - i, P_zero);
    }
  }
  return cnt;
}
int main() {
  while (scanf("%d", &n) != EOF) {
    Init();
    get_P();
    int ans = inf;
    for (int i = 0; i < (1 << 4); i++) {
      if (check(i)) {
        ans = min(ans, solve(i));
      }
    }
    printf("%d\n", ans);
  }
  return 0;
}
