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
from itertools import permutations

n = int(input())
d = []
for i in range(3):
    d.append([list(map(int, input())) for j in range(n)])
    input()
d.append([list(map(int, input())) for j in range(n)])
cache = [[[(i * (n * 2 + 1) + j + f) & 1 for j in range(n * 2)] for i in range(n * 2)]
         for f in range(2)]
res = [[a[i] + b[i] for i in range(n)] + [c[i] + e[i] for i in range(n)]
       for a, b, c, e in permutations(d)]
ans = min(sum(resi[i][j] != cache[f][i][j] for j in range(n * 2) for i in range(n * 2))
          for f in range(2)
          for resi in res)
print(ans)