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 gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); };
int main() {
  std::ios::sync_with_stdio(false);
  long long n;
  cin >> n;
  long long tot = 0;
  long long board[4][n][n];
  pair<int, int> ans[4][2];
  for (int z = 0; z < 4; z++) {
    string lines[n];
    int k = n * n;
    int c[k];
    for (int i = 0; i < n; i++) {
      cin >> lines[i];
      for (int j = 0; j < n; j++) {
        if (lines[i][j] == '0')
          c[i * n + j] = 0;
        else
          c[i * n + j] = 1;
      }
    }
    int c1 = 0, c2 = 1;
    int l1 = 0, l2 = 0;
    for (int i = 0; i < k; i++) {
      if (c[i] != c1) l1++;
      if (c[i] != c2) l2++;
      if (c1)
        c1 = 0;
      else
        c1 = 1;
      if (c2)
        c2 = 0;
      else
        c2 = 1;
    }
    if (l1 > l2) {
      ans[z][0] = pair<int, int>(c2, l2);
      ans[z][1] = pair<int, int>(c1, l1);
    } else {
      ans[z][0] = pair<int, int>(c1, l1);
      ans[z][1] = pair<int, int>(c2, l2);
    }
  }
  long long c0 = 0, c1 = 0;
  for (int i = 0; i < 4; i++) {
    if (ans[i][0].first == 0)
      c0++;
    else
      c1++;
  }
  if (c0 == 0 || c0 == 4) {
    long long mn = 1000000001, x = -1;
    for (int i = 0; i < 4; i++) {
      if (c0 == 1 && ans[i][0].first == 0) continue;
      if (c0 == 3 && ans[i][0].first == 1) continue;
      long long d = ans[i][1].second - ans[i][0].second;
      if (d < mn) {
        mn = d;
        x = i;
      }
    }
    ans[x][0].second = ans[x][1].second;
    ans[x][0].first = ans[x][1].first;
    if (c0 == 0)
      c0++;
    else
      c0--;
  }
  if (c0 == 1 || c0 == 3) {
    long long mn = 1000000001, x = -1;
    for (int i = 0; i < 4; i++) {
      if (c0 == 1 && ans[i][0].first == 0) continue;
      if (c0 == 3 && ans[i][0].first == 1) continue;
      long long d = ans[i][1].second - ans[i][0].second;
      if (d < mn) {
        mn = d;
        x = i;
      }
    }
    ans[x][0].second = ans[x][1].second;
  }
  tot =
      ans[0][0].second + ans[1][0].second + ans[2][0].second + ans[3][0].second;
  printf("%lld\n", tot);
}
