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(raw_input())
l1=[ 0 for i in range(9) ]
l=[ [ [] for r in range(n) ] for k in range(4) ]
for u in range(4):
    for i in range(n):
        l[u][i]=raw_input()
    if u!=3:
        r1=raw_input()
u=0
for u in range(4):
    for i in range(n):
        for j in range(n):
            if l[u][i][j]=="1":
                if (i+j)%2==0:
                    l1[2*u+2]=l1[2*u+2]+1
                else:
                    l1[2*u+1]=l1[2*u+1]+1
            else:
                if (i+j)%2==0:
                    l1[2*u+1]=l1[2*u+1]+1
                else:
                    l1[2*u+2]=l1[2*u+2]+1
l2=[]
l3=[]
u=0
for u in range(4):
    l2.append(l1[2*u+1])
    l3.append(l1[2*u+2])
l2.sort()
l3.sort()
print l2[0]+l2[1]+l3[0]+l3[1]