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
def checkdiff(a, b):
    s = 0
    for i in range(len(a)):
        for j in range(len(a[0])):
            if a[i][j] != b[i][j]:
                s += 1
    return s

n = input()

pieces = []
for i in range(4):
    piece = []
    for j in range(n):
        st = raw_input()
        if st == "":
            st = raw_input()
        ro = [i for i in st]
        piece.append(ro)
    
    pieces.append(piece)
    
str_0 = "01"*(n/2) + "0"
str_1 = "10"*(n/2) + "1"
list_0 = [i for i in str_0]
list_1 = [i for i in str_1]

piece_0 = []
for i in range(n/2):
    piece_0.append(list_0)
    piece_0.append(list_1)
piece_0.append(list_0)

piece_1 = []
for i in range(n/2):
    piece_1.append(list_1)
    piece_1.append(list_0)
piece_1.append(list_1)


check_0 = []
for i in range(4):
    check_0.append(checkdiff(pieces[i], piece_0))

check_1 = []
for i in range(4):
    check_1.append(checkdiff(pieces[i], piece_1))

ans = check_0[0] + check_0[1] + check_1[2] + check_1[3]

for i in range(3):
    for j in range(i + 1, 4):
        t = check_0[i] + check_0[j]
        for k in range(4):
            if k != i and k != j:
                t += check_1[k]
        ans = min(ans, t)

print ans