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(input())

answer  = []

for k in range(4):
    white_problems = 0
    black_problems = 0
    for j in range(n):
        a = [int(i) for i in list(input())]
        for x in range(n):
            if ((a[x] == 1 and x % 2 == 0) or (a[x] == 0 and x % 2 == 1)) and j % 2 == 0:
                white_problems += 1
            if ((a[x] == 1 and x % 2 == 1) or (a[x] == 0 and x % 2 == 0)) and j % 2 == 0:
                black_problems += 1
            if ((a[x] == 1 and x % 2 == 0) or (a[x] == 0 and x % 2 == 1)) and j % 2 == 1:
                black_problems += 1
            if ((a[x] == 1 and x % 2 == 1) or (a[x] == 0 and x % 2 == 0)) and j % 2 == 1:
                white_problems += 1

    answer.append([white_problems, 0])
    answer.append([black_problems, 1])
    if k != 3:
        trash = input()



answer.sort()
black = 0
white = 0
ans = 0
for i in answer:
    if black < 2 and i[1] == 1:
        ans += i[0]
        black += 1
        continue
    if white < 2 and i[1] == 0:
        white += 1
        ans += i[0]
        continue
    if white == 2 and black == 2:
        break
print(ans)
