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 popCount(string s) {
  long long temp = 0;
  for (long long i = 0; i < s.size(); i++) {
    if (s[i] == '1') temp++;
  }
  return temp;
}
string getB(long long n) {
  string s = "";
  while (n) s += char((n % 2) + '0'), n /= 2;
  reverse(s.begin(), s.end());
  while (s.size() < 4) s = '0' + s;
  return s;
}
long long n;
char a[105][105], b[105][105], c[105][105], d[105][105];
long long ans = INT64_MAX;
void f(string s, long long temp1 = 0, long long temp2 = 0) {
  if (s[0] == '0') {
    for (long long i = 1; i <= n; i++) {
      for (long long j = 1; j <= n; j++) {
        if (((i + j) & 1) and a[i][j] == '1')
          temp1++;
        else if (!((i + j) & 1) and a[i][j] == '0')
          temp1++;
      }
    }
  } else {
    for (long long i = 1; i <= n; i++) {
      for (long long j = 1; j <= n; j++) {
        if (((i + j) & 1) and a[i][j] == '0')
          temp2++;
        else if (!((i + j) & 1) and a[i][j] == '1')
          temp2++;
      }
    }
  }
  if (s[1] == '0') {
    for (long long i = 1; i <= n; i++) {
      for (long long j = 1; j <= n; j++) {
        if (((i + j) & 1) and b[i][j] == '1')
          temp1++;
        else if (!((i + j) & 1) and b[i][j] == '0')
          temp1++;
      }
    }
  } else {
    for (long long i = 1; i <= n; i++) {
      for (long long j = 1; j <= n; j++) {
        if (((i + j) & 1) and b[i][j] == '0')
          temp2++;
        else if (!((i + j) & 1) and b[i][j] == '1')
          temp2++;
      }
    }
  }
  if (s[2] == '0') {
    for (long long i = 1; i <= n; i++) {
      for (long long j = 1; j <= n; j++) {
        if (((i + j) & 1) and c[i][j] == '1')
          temp1++;
        else if (!((i + j) & 1) and c[i][j] == '0')
          temp1++;
      }
    }
  } else {
    for (long long i = 1; i <= n; i++) {
      for (long long j = 1; j <= n; j++) {
        if (((i + j) & 1) and c[i][j] == '0')
          temp2++;
        else if (!((i + j) & 1) and c[i][j] == '1')
          temp2++;
      }
    }
  }
  if (s[3] == '0') {
    for (long long i = 1; i <= n; i++) {
      for (long long j = 1; j <= n; j++) {
        if (((i + j) & 1) and d[i][j] == '1')
          temp1++;
        else if (!((i + j) & 1) and d[i][j] == '0')
          temp1++;
      }
    }
  } else {
    for (long long i = 1; i <= n; i++) {
      for (long long j = 1; j <= n; j++) {
        if (((i + j) & 1) and d[i][j] == '0')
          temp2++;
        else if (!((i + j) & 1) and d[i][j] == '1')
          temp2++;
      }
    }
  }
  ans = min(ans, temp1 + temp2);
}
void solve() {
  cin >> n;
  for (long long i = 1; i <= n; i++)
    for (long long j = 1; j <= n; j++) cin >> a[i][j];
  for (long long i = 1; i <= n; i++)
    for (long long j = 1; j <= n; j++) cin >> b[i][j];
  for (long long i = 1; i <= n; i++)
    for (long long j = 1; j <= n; j++) cin >> c[i][j];
  for (long long i = 1; i <= n; i++)
    for (long long j = 1; j <= n; j++) cin >> d[i][j];
  for (long long i = 0; i < 16; i++) {
    if (popCount(getB(i)) == 2) {
      f(getB(i));
    }
  }
  cout << ans << endl;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie();
  cout.tie();
  ;
  int kse = 1;
  while (kse--) {
    solve();
  }
}
