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())
pieces=[]
blacks=[0]*4
whites=[0]*4
for i in range(4):
    grid=[]
    for j in range(n):
        grid.append(input())
    if i<3:
        input()
    count=0
    for j in range(n):
        for k in range(n):
            if (int(grid[j][k])+j+k)%2:
                count+=1
    blacks[i]=count
    whites[i]=n*n-count
ans=4*n*n
for white1 in range(3):
    for white2 in range(white1+1,4):
        for black1 in range(4):
            if black1==white1 or black1==white2:
                continue
            for black2 in range(black1+1,4):
                if black2==white1 or black2==white2:
                    continue
                ans=min(ans,whites[white1]+whites[white2]+blacks[black1]+blacks[black2])
print(ans)