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>
int max(int a, int b) {
  if (a > b) {
    return a;
  }
  return b;
}
int min(int a, int b) {
  if (a < b) {
    return a;
  }
  return b;
}
int zt(int a, int b) { return max(a, b) - min(a, b); }
int round(int a, int b) {
  if ((a % b) * 2 >= b) {
    return (a / b) + 1;
  }
  return a / b;
}
int ceil(int a, int b) {
  if (a % b == 0) {
    return a / b;
  }
  return (a / b) + 1;
}
int gcd(int a, int b) {
  int c;
  while (b != 0) {
    c = a % b;
    a = b;
    b = c;
  }
  return a;
}
int lcm(int a, int b) {
  int c = gcd(a, b);
  a /= c;
  return a * b;
}
int nCr(int a, int b) {
  int i, r = 1;
  for (i = 1; i <= b; i++) {
    r *= (a + 1 - i);
    r /= i;
  }
  return r;
}
int fact(int a) {
  int i, r = 1;
  for (i = 1; i <= a; i++) {
    r *= i;
  }
  return r;
}
int pow(int a, int b) {
  int i, r = 1;
  for (i = 1; i <= b; i++) {
    r *= a;
  }
  return r;
}
long long llmax(long long a, long long b) {
  if (a > b) {
    return a;
  }
  return b;
}
long long llmin(long long a, long long b) {
  if (a < b) {
    return a;
  }
  return b;
}
long long llzt(long long a, long long b) { return llmax(a, b) - llmin(a, b); }
long long llround(long long a, long long b) {
  if ((a % b) * 2 >= b) {
    return (a / b) + 1;
  }
  return a / b;
}
long long llceil(long long a, long long b) {
  if (a % b == 0) {
    return a / b;
  }
  return (a / b) + 1;
}
long long llgcd(long long a, long long b) {
  long long c;
  while (b != 0) {
    c = a % b;
    a = b;
    b = c;
  }
  return a;
}
long long lllcm(long long a, long long b) {
  long long c = llgcd(a, b);
  a /= c;
  return a * b;
}
long long llnCr(long long a, long long b) {
  long long i, r = 1;
  for (i = 1; i <= b; i++) {
    r *= (a + 1 - i);
    r /= i;
  }
  return r;
}
long long llfact(long long a) {
  long long i, r = 1;
  for (i = 1; i <= a; i++) {
    r *= i;
  }
  return r;
}
long long llpow(long long a, long long b) {
  long long i, r = 1;
  for (i = 1; i <= b; i++) {
    r *= a;
  }
  return r;
}
double dbmax(double a, double b) {
  if (a > b) {
    return a;
  }
  return b;
}
double dbmin(double a, double b) {
  if (a < b) {
    return a;
  }
  return b;
}
double dbzt(double a, double b) { return dbmax(a, b) - dbmin(a, b); }
int sortfncsj(const void *a, const void *b) {
  if (*(int *)a > *(int *)b) {
    return 1;
  }
  if (*(int *)a == *(int *)b) {
    return 0;
  }
  return -1;
}
int sortfnckj(const void *a, const void *b) {
  if (*(int *)a < *(int *)b) {
    return 1;
  }
  if (*(int *)a == *(int *)b) {
    return 0;
  }
  return -1;
}
int llsortfncsj(const void *a, const void *b) {
  if (*(long long *)a > *(long long *)b) {
    return 1;
  }
  if (*(long long *)a == *(long long *)b) {
    return 0;
  }
  return -1;
}
int llsortfnckj(const void *a, const void *b) {
  if (*(long long *)a < *(long long *)b) {
    return 1;
  }
  if (*(long long *)a == *(long long *)b) {
    return 0;
  }
  return -1;
}
int dbsortfncsj(const void *a, const void *b) {
  if (*(double *)a > *(double *)b) {
    return 1;
  }
  if (*(double *)a == *(double *)b) {
    return 0;
  }
  return -1;
}
int dbsortfnckj(const void *a, const void *b) {
  if (*(double *)a < *(double *)b) {
    return 1;
  }
  if (*(double *)a == *(double *)b) {
    return 0;
  }
  return -1;
}
int strsortfncsj(const void *a, const void *b) {
  return strcmp((char *)a, (char *)b);
}
int strsortfnckj(const void *a, const void *b) {
  return strcmp((char *)b, (char *)a);
}
int main(void) {
  int i, j, k, l, n, m, b, c, w, r = 1072114514, t, nr1, nr2;
  int pp[4];
  double d;
  char a[4][128][128];
  scanf("%d", &n);
  for (i = 0; i < n; i++) {
    scanf("%s", a[0][i]);
  }
  for (i = 0; i < n; i++) {
    scanf("%s", a[1][i]);
  }
  for (i = 0; i < n; i++) {
    scanf("%s", a[2][i]);
  }
  for (i = 0; i < n; i++) {
    scanf("%s", a[3][i]);
  }
  for (pp[0] = 0; pp[0] < 4; pp[0]++) {
    for (pp[1] = 0; pp[1] < 4; pp[1]++) {
      if (pp[0] == pp[1]) {
        continue;
      }
      for (pp[2] = 0; pp[2] < 4; pp[2]++) {
        if (pp[0] == pp[2] || pp[1] == pp[2]) {
          continue;
        }
        for (pp[3] = 0; pp[3] < 4; pp[3]++) {
          if (pp[0] == pp[3] || pp[1] == pp[3] || pp[2] == pp[3]) {
            continue;
          }
          nr1 = 0;
          nr2 = 0;
          for (i = 0; i < n; i++) {
            for (j = 0; j < n; j++) {
              if (((i + j) % 2) == 0 && a[pp[0]][i][j] == '1') {
                nr1++;
              }
              if (((i + j) % 2) == 0 && a[pp[3]][i][j] == '1') {
                nr1++;
              }
              if (((i + j) % 2) == 1 && a[pp[0]][i][j] == '0') {
                nr1++;
              }
              if (((i + j) % 2) == 1 && a[pp[3]][i][j] == '0') {
                nr1++;
              }
              if (((i + j) % 2) == 0 && a[pp[1]][i][j] == '0') {
                nr2++;
              }
              if (((i + j) % 2) == 0 && a[pp[2]][i][j] == '0') {
                nr2++;
              }
              if (((i + j) % 2) == 1 && a[pp[1]][i][j] == '1') {
                nr2++;
              }
              if (((i + j) % 2) == 1 && a[pp[2]][i][j] == '1') {
                nr2++;
              }
            }
          }
          r = min(r, nr1 + nr2);
          r = min(r, 4 * n * n - nr1 - nr2);
        }
      }
    }
  }
  printf("%d\n", r);
  return 0;
}
