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
a=int(input())
l=[]
total=0
for i in range(4):
    line=''

    for x in [0]*a:
        line+=input()    
    l.append(line)
    input() if i!=3 else 0
l=sorted(l,key=lambda i: i[0::2].count('1')+i[1::2].count('0'))[::-1]
for z,v in enumerate(l):
    if z<2:
        for i in range(a**2):
            total += v[i]!='0' if i%2 else v[i]!='1'
    else:
        for i in range(a**2):
            total += v[i]!='1' if i%2 else v[i]!='0'
print(total)