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


def min_cnt(a_):
    def foo(abracadabra, f):
        # print(*map(lambda x: ' '.join(map(lambda x: str(int(x)), x)), abracadabra), sep='\n')
        # print(id(abracadabra))
        flag = f
        cnt = 0
        for i in abracadabra:
            ic = i[:]
            for x in range(len(i)):
                flag = not flag
                # print(int(not flag), end=' ')
                if flag == i[x]:
                    cnt += 1
                    ic[x] = not ic[x]
            flag = not ic[0]
            # print(flag)

        # print('--- {} ---'.format(cnt))

        return cnt

    return min(foo(a_, True), foo(a_, False))


def concat(a, b, c, d):
    abcd = []
    for x in (zip(a, b), zip(c, d)):
        x_ = []
        for i, j in x:
            x_.append(i + j)
        abcd += x_
    return abcd


n=int(input())
a, b, c, d = [list(filter(None, [[y == '1' for y in input()] for x in range(n+(z!=3))])) for z in range(4)]
m = float('inf')
r = None

for a, b, c, d in permutations([a, b, c, d]):
    mp = m
    m = min(m, min_cnt(concat(a, b, c, d)))
    if m != mp:
        r = concat(a, b, c, d)

# print(*map(lambda x: ' '.join(map(lambda x: str(int(x)), x)), r), sep='\n')
# print('---')
# print(min_cnt(r))
print(m)
