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 arr(dic1,dic2):
    global fit1,n
    c=0
    for i in xrange(n):
        for j in xrange(n):
            if fit1[i][j]!=dic1[i][j]:
                c+=1
            if fit1[i][j]!=dic2[i][j]:
                c+=1
    return c
def arr2(dic1,dic2):
    c=0
    global fit2,n
    for i in xrange(n):
        for j in xrange(n):
            if fit2[i][j]!=dic1[i][j]:
                c+=1
            if fit2[i][j]!=dic2[i][j]:
                c+=1
    return c

def main():
    d1,d2,d3,d4={},{},{},{}
    global fit1,fit2,n
    n=input()
    fit1,fit2={},{}
    pp,kk=[0]*n,[0]*n
    for i in xrange(n):
        if i%2==0:
            pp[i]=1 
        else:
            kk[i]=1 
    for i in xrange(n):
        if i%2==0:
            fit1[i]=pp
            fit2[i]=kk
        else:
            fit1[i]=kk
            fit2[i]=pp
            
    for i in xrange(4*n+3):
        if i<n:
            d1[i]=map(int," ".join(raw_input()).split())
        elif i >=n+1 and i<2*n+1:
            d2[i-n-1]=map(int," ".join(raw_input()).split())
        elif i >=2*n+2 and i<3*n+2:
            d3[i-2*n-2]=map(int," ".join(raw_input()).split())
        elif i >=3*n+3 :
            d4[i-3*n-3]=map(int," ".join(raw_input()).split())
        else:
            po=raw_input()
    r=[]
    r.append(arr(d1,d2)+arr2(d3,d4))
    r.append(arr2(d1,d2)+arr(d3,d4))
    
    r.append(arr(d1,d3)+arr2(d2,d4))
    r.append(arr2(d1,d3)+arr(d2,d4))
           
    r.append(arr(d1,d4)+arr2(d2,d3))
    r.append(arr2(d1,d4)+arr(d2,d3)) 
    print min(r)
main()