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;
int gcd(int a, int b) { return b ? gcd(b, a % b) : a; }
char c1[150][150], c2[150][150], c3[150][150], c4[150][150];
int reverse(int x) {
  if (x == 1) {
    return 0;
  }
  return 1;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      cin >> c1[i][j];
    }
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      cin >> c2[i][j];
    }
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      cin >> c3[i][j];
    }
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      cin >> c4[i][j];
    }
  }
  int cur;
  long long mini = 1e14;
  long long cnt;
  for (int mask = 0; mask < (1 << 4); mask++) {
    if (__builtin_popcount(mask) == 2) {
      cnt = 0;
      if ((mask & (1 << (1 - 1))) > 0) {
        cur = 1;
        for (int i = 1; i <= n; i++) {
          for (int j = 1; j <= n; j++) {
            if (c1[i][j] - 48 != cur) {
              cnt++;
            }
            cur = reverse(cur);
          }
        }
      } else {
        cur = 0;
        for (int i = 1; i <= n; i++) {
          for (int j = 1; j <= n; j++) {
            if (c1[i][j] - 48 != cur) {
              cnt++;
            }
            cur = reverse(cur);
          }
        }
      }
      if ((mask & (1 << (2 - 1))) > 0) {
        cur = 1;
        for (int i = 1; i <= n; i++) {
          for (int j = 1; j <= n; j++) {
            if (c2[i][j] - 48 != cur) {
              cnt++;
            }
            cur = reverse(cur);
          }
        }
      } else {
        cur = 0;
        for (int i = 1; i <= n; i++) {
          for (int j = 1; j <= n; j++) {
            if (c2[i][j] - 48 != cur) {
              cnt++;
            }
            cur = reverse(cur);
          }
        }
      }
      if ((mask & (1 << (3 - 1))) > 0) {
        cur = 1;
        for (int i = 1; i <= n; i++) {
          for (int j = 1; j <= n; j++) {
            if (c3[i][j] - 48 != cur) {
              cnt++;
            }
            cur = reverse(cur);
          }
        }
      } else {
        cur = 0;
        for (int i = 1; i <= n; i++) {
          for (int j = 1; j <= n; j++) {
            if (c3[i][j] - 48 != cur) {
              cnt++;
            }
            cur = reverse(cur);
          }
        }
      }
      if ((mask & (1 << (4 - 1))) > 0) {
        cur = 1;
        for (int i = 1; i <= n; i++) {
          for (int j = 1; j <= n; j++) {
            if (c4[i][j] - 48 != cur) {
              cnt++;
            }
            cur = reverse(cur);
          }
        }
      } else {
        cur = 0;
        for (int i = 1; i <= n; i++) {
          for (int j = 1; j <= n; j++) {
            if (c4[i][j] - 48 != cur) {
              cnt++;
            }
            cur = reverse(cur);
          }
        }
      }
      mini = min(mini, cnt);
    }
  }
  cout << mini;
  return 0;
}
