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
def main():
    count=int(input())
    value=[0,0,0,0]
    for x in range(4):
        store=0
        pole=True
        for y in range(count):
            arr=list(input())
            for z in range(count):
                if arr[z]=="1" and pole:
                    store+=1
                if arr[z]=="0" and not pole:
                    store+=1
                pole=not pole
        value[x]=store
        if x<=2:
            y=input()
    #print(value)
    mini=value[0]+value[1]+2*count*count-(value[2]+value[3])
    for a in range(15):
        hit=0
        for b in range(4):
            if 1<<b & a:
                hit+=1
        if hit==2:
            store=0
            for b in range(4):
                if 1<<b & a:
                    store+=value[b]
                else:
                    store+=count*count-value[b]
            #print(a,store)
            mini=min(mini,store)
    print(mini)
    
main()
