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;
void calculateCost(vector<string> s, long *cost) {
  long e = 0;
  long o = 0;
  int k = 0;
  for (int i = 0; i < s.size(); i++) {
    for (int j = 0; j < s.size(); j++) {
      if (s[i][j] - '0' != k) e++;
      if (s[i][j] - '0' == k) o++;
      k = (k + 1) % 2;
    }
  }
  cost[0] = e;
  cost[1] = o;
}
int main(int argc, const char *argv[]) {
  int n;
  cin >> n;
  vector<vector<string>> c;
  for (int i = 0; i < 4; i++) {
    vector<string> s;
    for (int j = 0; j < n; j++) {
      string s2;
      cin >> s2;
      s.push_back(s2);
    }
    c.push_back(s);
  }
  long cost[4][2] = {0};
  for (int i = 0; i < 4; i++) {
    calculateCost(c[i], cost[i]);
  }
  long an = 10000000;
  long ans = 10000000;
  an = cost[0][1] + cost[1][1] + cost[2][0] + cost[3][0];
  ans = min(an, ans);
  an = cost[0][1] + cost[2][1] + cost[1][0] + cost[3][0];
  ans = min(an, ans);
  an = cost[0][1] + cost[3][1] + cost[1][0] + cost[2][0];
  ans = min(an, ans);
  an = cost[1][1] + cost[2][1] + cost[0][0] + cost[3][0];
  ans = min(an, ans);
  an = cost[1][1] + cost[3][1] + cost[0][0] + cost[2][0];
  ans = min(an, ans);
  an = cost[2][1] + cost[3][1] + cost[0][0] + cost[1][0];
  ans = min(an, ans);
  cout << ans << endl;
  return 0;
}
