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())
s1=""
s2=""
for i in range(0,n):
    s1+=str(i%2)
    s2+=str((i+1)%2)
a=[]
for i in range(0,7):
    b=0
    if i%2==0:
        for j in range(0,n):
            s=input()
            if j%2==0:
                for k in range(0,n):
                    if s1[k]!=s[k]:
                        b+=1
            else:
                 for k in range(0,n):
                    if s2[k]!=s[k]:
                        b+=1
        a.append(b)
        a.append(n*n-b)
    else:
        x=input()
print(min(a[0]+a[2]+a[5]+a[7],a[0]+a[3]+a[4]+a[7],a[0]+a[3]+a[5]+a[6],a[1]+a[2]+a[4]+a[7],a[1]+a[2]+a[5]+a[6],a[1]+a[3]+a[4]+a[6]))
                