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 makeq(int a[][101], int b[][101], int n) {
  int i, j, p = 0;
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      p += a[i][j] ^ b[i][j];
    }
  }
  return p;
}
int main() {
  int n, i, j, a1[101][101], a2[101][101], a3[101][101], a4[101][101],
      b1[101][101] = {0}, b2[101][101] = {0}, ans, p1, p2, p3, p4, p5, p6;
  char c[105][105];
  cin >> n;
  b1[0][0] = 0;
  b2[0][0] = 1;
  for (i = 0; i < n; i++) {
    for (j = 0; j < n; j++) {
      if (i != 0 && j == 0) {
        b1[i][j] = !b1[i - 1][n - 1];
        b2[i][j] = !b2[i - 1][n - 1];
      } else if (j != 0) {
        b1[i][j] = !b1[i][j - 1];
        b2[i][j] = !b2[i][j - 1];
      }
    }
  }
  for (i = 0; i < n; i++) cin >> c[i];
  for (i = 0; i < n; i++) {
    for (int l = 0; l < n; l++)
      for (j = 0; j < n; j++) a1[l][j] = c[l][j] - '0';
  }
  for (i = 0; i < n; i++) cin >> c[i];
  for (i = 0; i < n; i++) {
    for (int l = 0; l < n; l++)
      for (j = 0; j < n; j++) a2[l][j] = c[l][j] - '0';
  }
  for (i = 0; i < n; i++) cin >> c[i];
  for (i = 0; i < n; i++) {
    for (int l = 0; l < n; l++)
      for (j = 0; j < n; j++) a3[l][j] = c[l][j] - '0';
  }
  for (i = 0; i < n; i++) cin >> c[i];
  for (i = 0; i < n; i++) {
    for (int l = 0; l < n; l++)
      for (j = 0; j < n; j++) a4[l][j] = c[l][j] - '0';
  }
  p1 =
      makeq(a1, b1, n) + makeq(a2, b1, n) + makeq(a3, b2, n) + makeq(a4, b2, n);
  p2 =
      makeq(a1, b1, n) + makeq(a2, b2, n) + makeq(a3, b1, n) + makeq(a4, b2, n);
  p3 =
      makeq(a1, b1, n) + makeq(a2, b2, n) + makeq(a3, b2, n) + makeq(a4, b1, n);
  p4 =
      makeq(a1, b2, n) + makeq(a2, b1, n) + makeq(a3, b1, n) + makeq(a4, b2, n);
  p5 =
      makeq(a1, b2, n) + makeq(a2, b1, n) + makeq(a3, b2, n) + makeq(a4, b1, n);
  p6 =
      makeq(a1, b2, n) + makeq(a2, b2, n) + makeq(a3, b1, n) + makeq(a4, b1, n);
  ans = min(p1, min(p2, min(p3, min(p4, min(p5, p6)))));
  cout << ans;
  return 0;
}
