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 main() {
  int a, s[3][4], r0, r1, c0, c1, n;
  char c;
  cin >> n;
  for (int t = 0; t < 4; t++) {
    getchar();
    r0 = 0;
    c0 = 0;
    r1 = 1;
    c1 = 1;
    s[0][t] = 0;
    s[1][t] = 0;
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < n; j++) {
        cin >> c;
        a = c - '0';
        if (a != r0) s[0][t]++;
        if (r0 == 0)
          r0 = 1;
        else
          r0 = 0;
        if (a != r1) s[1][t]++;
        if (r1 == 0)
          r1 = 1;
        else
          r1 = 0;
      }
      if (c0 == 0) {
        c0 = 1;
        r0 = 1;
      } else {
        c0 = 0;
        r0 = 0;
      }
      if (c1 == 0) {
        c1 = 1;
        r1 = 1;
      } else {
        c1 = 0;
        r1 = 0;
      }
    }
  }
  int x, output = 99999999;
  x = s[0][0] + s[0][1] + s[1][2] + s[1][3];
  if (x < output) output = x;
  x = s[0][0] + s[0][2] + s[1][1] + s[1][3];
  if (x < output) output = x;
  x = s[0][0] + s[0][3] + s[1][1] + s[1][2];
  if (x < output) output = x;
  x = s[0][1] + s[0][2] + s[1][0] + s[1][3];
  if (x < output) output = x;
  x = s[0][1] + s[0][3] + s[1][0] + s[1][2];
  if (x < output) output = x;
  x = s[0][2] + s[0][3] + s[1][0] + s[1][1];
  if (x < output) output = x;
  cout << output << endl;
  return 0;
}
