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;
long long mod = 999999999999;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  int t;
  t = 1;
  while (t--) {
    long long n, i, j, k, m;
    cin >> n;
    char a1[n][n], a2[n][n], a3[n][n], a4[n][n];
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++) {
        cin >> a1[i][j];
      }
    }
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++) {
        cin >> a2[i][j];
      }
    }
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++) {
        cin >> a3[i][j];
      }
    }
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++) {
        cin >> a4[i][j];
      }
    }
    vector<long long> ans;
    long long a[8];
    memset(a, 0, sizeof(a));
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++) {
        if (i % 2 == 0) {
          if (j % 2 == 0) {
            if (a1[i][j] == '0') {
              a[1]++;
            }
            if (a2[i][j] == '0') {
              a[3]++;
            }
            if (a3[i][j] == '0') {
              a[5]++;
            }
            if (a4[i][j] == '0') {
              a[7]++;
            }
          } else {
            if (a1[i][j] == '1') {
              a[1]++;
            }
            if (a2[i][j] == '1') {
              a[3]++;
            }
            if (a3[i][j] == '1') {
              a[5]++;
            }
            if (a4[i][j] == '1') {
              a[7]++;
            }
          }
        } else {
          if (j % 2 == 0) {
            if (a1[i][j] == '1') {
              a[1]++;
            }
            if (a2[i][j] == '1') {
              a[3]++;
            }
            if (a3[i][j] == '1') {
              a[5]++;
            }
            if (a4[i][j] == '1') {
              a[7]++;
            }
          } else {
            if (a1[i][j] == '0') {
              a[1]++;
            }
            if (a2[i][j] == '0') {
              a[3]++;
            }
            if (a3[i][j] == '0') {
              a[5]++;
            }
            if (a4[i][j] == '0') {
              a[7]++;
            }
          }
        }
      }
    }
    for (i = 0; i < n; i++) {
      for (j = 0; j < n; j++) {
        if (i % 2 == 0) {
          if (j % 2 == 0) {
            if (a1[i][j] == '1') {
              a[0]++;
            }
            if (a2[i][j] == '1') {
              a[2]++;
            }
            if (a3[i][j] == '1') {
              a[4]++;
            }
            if (a4[i][j] == '1') {
              a[6]++;
            }
          } else {
            if (a1[i][j] == '0') {
              a[0]++;
            }
            if (a2[i][j] == '0') {
              a[2]++;
            }
            if (a3[i][j] == '0') {
              a[4]++;
            }
            if (a4[i][j] == '0') {
              a[6]++;
            }
          }
        } else {
          if (j % 2 == 0) {
            if (a1[i][j] == '0') {
              a[0]++;
            }
            if (a2[i][j] == '0') {
              a[2]++;
            }
            if (a3[i][j] == '0') {
              a[4]++;
            }
            if (a4[i][j] == '0') {
              a[6]++;
            }
          } else {
            if (a1[i][j] == '1') {
              a[0]++;
            }
            if (a2[i][j] == '1') {
              a[2]++;
            }
            if (a3[i][j] == '1') {
              a[4]++;
            }
            if (a4[i][j] == '1') {
              a[6]++;
            }
          }
        }
      }
    }
    ans.push_back(a[1] + a[3] + a[4] + a[6]);
    ans.push_back(a[1] + a[2] + a[5] + a[6]);
    ans.push_back(a[1] + a[2] + a[4] + a[7]);
    ans.push_back(a[0] + a[2] + a[5] + a[7]);
    ans.push_back(a[0] + a[3] + a[4] + a[7]);
    ans.push_back(a[0] + a[3] + a[5] + a[6]);
    sort(ans.begin(), ans.end());
    cout << ans[0] << endl;
  }
}
