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())
p=[]
for i in range(4):
    p1=[]
    if(i==3):
        for j in range(n):
            p1.append(input())
        p.append(p1)
    else:
        for j in range(n):
            p1.append(input())
        w=input()
        p.append(p1)
#print(p)
min_1=[]
min_2=[]
for k in range(4):
    cnt=0
    for i in range(n):
        for j in range(n):
            if((i+j)%2 and p[k][i][j]=='1' or (i+j)%2==0 and p[k][i][j]=='0'):
                cnt+=1
    min_1.append(cnt)
    min_2.append(n*n-cnt)
min_1.sort()
min_2.sort()
#print(min_1,min_2)
print(min_1[0]+min_2[1]+min_1[1]+min_2[0])
            
            


