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
n = int(raw_input())

n_sq = n * n
masks = (
    sum([2**(n - i - 1) for i in xrange(n) if i % 2 == 0]),
    sum([2**(n - i - 1) for i in xrange(n) if i % 2 == 1])
)

cost = []
for i in xrange(4):
    c = 0
    for j in xrange(n):
        v = int(raw_input(), 2)
        t = v ^ masks[j % 2]
        while t:
            if t % 2 == 1:
                c += 1
            t //= 2
    cost.append((c, n_sq - c))
    if i != 3:
        raw_input()

min_v = None
all_boards = set(xrange(4))
for i in xrange(3):
    for j in xrange(i + 1, 4):
        v = cost[i][0] + cost[j][0]
        for k in all_boards.difference([i, j]):
            v += cost[k][1]
        if min_v is None or v < min_v:
            min_v = v

print min_v


