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

#in in[i][0], cost for if 1st sqaure is balck is stored.
n=int(input())
a=[[[0 for j in range(n)] for i in range(n)] for k in range(4)]
in1=[[0,0] for i in range(4)]

for k in range(4):
    for i in range(n):
        s=input()
        #print('ae')
        for j in range(n):
            a[k][i][j]=int(s[j])
            if(int(s[j])==(i+j)%2):
                in1[k][1]+=1
    in1[k][0]=n*n - in1[k][1]
    #k,in1[k][0])
    if(k!=3):
        s=input()
min1=10000000000

min1=min(min1,in1[0][0]+in1[1][0]+ in1[2][1] + in1[3][1])
min1=min(min1,in1[0][0]+in1[1][1]+ in1[2][0] + in1[3][1])
min1=min(min1,in1[0][0]+in1[1][1]+ in1[2][1] + in1[3][0])
min1=min(min1,in1[0][1]+in1[1][1]+ in1[2][0] + in1[3][0])
min1=min(min1,in1[0][1]+in1[1][0]+ in1[2][1] + in1[3][0])
min1=min(min1,in1[0][1]+in1[1][0]+ in1[2][0] + in1[3][1])
print(min1)