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 MAX = 1e2 + 12;
const int INF = 1e9 + 88;
char grid[MAX][MAX][5];
int pre[5][3], n;
void calc(int id) {
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < n; ++j) {
      pre[id][0] +=
          ((i + j) & 1) ? (grid[i][j][id] == '0') : (grid[i][j][id] == '1');
      pre[id][1] +=
          ((i + j) & 1) ? (grid[i][j][id] == '1') : (grid[i][j][id] == '0');
    }
}
int main() {
  scanf("%d", &n);
  for (int k = 0; k < 4; ++k)
    for (int i = 0; i < n; ++i)
      for (int j = 0; j < n; ++j) scanf(" %c", &grid[i][j][k]);
  for (int i = 0; i < 4; ++i) calc(i);
  int res = INF;
  for (int i = 0; i < 16; ++i) {
    if (__builtin_popcount(i) != 2) continue;
    int cur = 0;
    for (int j = 0; j < 4; ++j) cur += pre[j][(i & (1 << j)) ? 1 : 0];
    res = min(res, cur);
  }
  cout << res;
  return 0;
}
