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 mem[33][33];
long long fac(long long n, long long k) {
  if (k == 1) return n;
  if (n == k) return 1;
  if (k > n) return 0;
  if (mem[n][k]) return mem[n][k];
  return mem[n][k] = fac(n - 1, k - 1) + fac(n - 1, k);
}
int n;
char a[4][111][111];
long long sol(long long q, long long w, long long e, long long r) {
  char s[2 * n][2 * n];
  for (long long i = 0; i < n; i++)
    for (long long j = 0; j < n; j++) s[i][j] = a[q][i][j];
  for (long long i = 0; i < n; i++)
    for (long long j = 0; j < n; j++) s[i + n][j] = a[w][i][j];
  for (long long i = 0; i < n; i++)
    for (long long j = 0; j < n; j++) s[i][j + n] = a[e][i][j];
  for (long long i = 0; i < n; i++)
    for (long long j = 0; j < n; j++) s[i + n][j + n] = a[r][i][j];
  long long qora = 0;
  long long ans = 0, konans = 0;
  for (long long i = 0; i < 2 * n; i += 2) {
    for (long long j = 0; j < 2 * n; j++) {
      if (qora)
        qora = 0;
      else
        qora = 1;
      if (qora && s[i][j] == '1' || !qora && s[i][j] == '0')
        continue;
      else
        ans++;
    }
  }
  qora = 1;
  for (long long i = 1; i < 2 * n; i += 2) {
    for (long long j = 0; j < 2 * n; j++) {
      if (qora)
        qora = 0;
      else
        qora = 1;
      if (qora && s[i][j] == '1' || !qora && s[i][j] == '0')
        continue;
      else
        ans++;
    }
  }
  konans = ans;
  ans = 0;
  qora = 1;
  for (long long i = 0; i < 2 * n; i += 2) {
    for (long long j = 0; j < 2 * n; j++) {
      if (qora)
        qora = 0;
      else
        qora = 1;
      if (qora && s[i][j] == '1' || !qora && s[i][j] == '0')
        continue;
      else
        ans++;
    }
  }
  qora = 0;
  for (long long i = 1; i < 2 * n; i += 2) {
    for (long long j = 0; j < 2 * n; j++) {
      if (qora)
        qora = 0;
      else
        qora = 1;
      if (qora && s[i][j] == '1' || !qora && s[i][j] == '0')
        continue;
      else
        ans++;
    }
  }
  return min(konans, ans);
}
int main() {
  cin >> n;
  for (long long i = 0; i < 4; i++) {
    for (long long j = 0; j < n; j++) {
      string st;
      cin >> st;
      for (long long k = 0; k < n; k++) a[i][j][k] = st[k];
    }
  }
  long long c[4] = {0, 1, 2, 3};
  long long ans = 1e10;
  do {
    ans = min(ans, sol(c[0], c[1], c[2], c[3]));
  } while (next_permutation(c, c + 4));
  cout << ans;
  return 0;
}
