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=input()
I=(0,1,2,3)
a=[[0,0] for _ in I]
for i in I:
    if i:
        raw_input()
    for u in range(n):
        b=map(int,raw_input())
        for v in range(n):
            z=(u+v)%2
            a[i][0]+=z==b[v]
            a[i][1]+=z!=b[v]
t=n*n*4
for i in I:
    for j in I:
        for k in I:
            for l in I:
                if len(set((i,j,k,l)))==4:
                    t=min(t,a[i][0]+a[j][1]+a[k][1]+a[l][0],a[i][1]+a[j][0]+a[k][0]+a[l][1])
print t