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;
const int sz = 101, sz1 = 6;
char brd[sz1][sz][sz], tmp[sz1][sz][sz];
int used[10], res = 1e9, n;
void chng() {
  for (int i = 1; i <= 4; i++) {
    for (int j = 1; j <= n; j++) {
      for (int k = 1; k <= n; k++) brd[i][j][k] = tmp[i][j][k];
    }
  }
}
int calc() {
  int a = used[1], b = used[2], c = used[3], d = used[4], op = 0;
  for (int i = 1; i <= n; i++) {
    if (i % 2 && brd[a][i][1] == '0') {
      brd[a][i][1] = '1';
      op++;
    } else if (i % 2 == 0 && brd[a][i][1] == '1') {
      brd[a][i][1] = '0';
      op++;
    }
    for (int j = 1; j <= n; j++) {
      if (j > 1 && brd[a][i][j - 1] == brd[a][i][j]) {
        if (brd[a][i][j] == '1')
          brd[a][i][j] = '0';
        else
          brd[a][i][j] = '1';
        op++;
      }
      if (brd[a][i][j] == brd[b][i][j]) {
        if (brd[a][i][j] == '1')
          brd[b][i][j] = '0';
        else
          brd[b][i][j] = '1';
        op++;
      }
    }
  }
  for (int i = 1; i <= n; i++) {
    if (i % 2 && brd[c][i][1] == '1') {
      brd[c][i][1] = '0';
      op++;
    } else if (i % 2 == 0 && brd[c][i][1] == '0') {
      brd[c][i][1] = '1';
      op++;
    }
    for (int j = 1; j <= n; j++) {
      if (j > 1 && brd[c][i][j - 1] == brd[c][i][j]) {
        if (brd[c][i][j] == '1')
          brd[c][i][j] = '0';
        else
          brd[c][i][j] = '1';
        op++;
      }
      if (brd[c][i][j] == brd[d][i][j]) {
        if (brd[c][i][j] == '1')
          brd[d][i][j] = '0';
        else
          brd[d][i][j] = '1';
        op++;
      }
    }
  }
  return op;
}
void solve(int pos) {
  int i;
  if (pos == 5) {
    chng();
    res = min(res, calc());
    return;
  }
  for (i = 1; i <= 4; i++)
    if (!used[i]) {
      used[i] = pos;
      solve(pos + 1);
      used[i] = 0;
    }
}
int main() {
  cin >> n;
  for (int i = 1; i <= 4; i++) {
    for (int j = 1; j <= n; j++) {
      for (int k = 1; k <= n; k++) {
        cin >> brd[i][j][k];
        tmp[i][j][k] = brd[i][j][k];
      }
    }
  }
  solve(1);
  cout << res << endl;
}
