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 sys import stdin
from itertools import permutations

rstr = lambda: stdin.readline().strip()
rstr_2d = lambda n: [rstr() for _ in range(n)]

n = int(input())
a, ans = [rstr_2d(n)], float('inf')
for i in range(3):
    ext = rstr()
    a.append(rstr_2d(n))

for per in permutations([0, 1, 2, 3], 4):
    tem, cur = 0, 1
    for k in per:
        for i in range(n):
            for j in range(n):
                tem += a[k][i][j] != str(cur)
                cur ^= 1
    ans = min(tem, ans)
print(ans)
