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())
k=[]
for temp in range(4):
    p=[]
    for i in range(n):
        l=list(input())
        l=list(map(int,l))
        p.append(l)
    k.append(p)
    if(temp<3): #because the segments are only separated by empty lines. Not every segment is separated by an empty line 
        input() #to accomodate the empty line that comes in the input

#print(k)

a=[];b=[];

count=0
for i in range(n):
    l=[];o=[]
    for j in range(n):
        if(count%2==0):
            l.append(0)
            o.append(1)
        else:
            l.append(1)
            o.append(0)
        
        count+=1
    
    a.append(l);b.append(o)

#print(a,b)
        
counta=[0,0,0,0];countb=[0,0,0,0]
for rr in range(4):
    for i in range(n):
        for j in range(n):
            if(k[rr][i][j]!=a[i][j]):
                counta[rr]+=1
            if(k[rr][i][j]!=b[i][j]):
                countb[rr]+=1
                
#print(counta,countb)
                

f1=counta[0]+counta[1]+countb[2]+countb[3]
f2=counta[0]+counta[2]+countb[1]+countb[3]
f3=counta[0]+counta[3]+countb[2]+countb[1]
f4=counta[1]+counta[2]+countb[0]+countb[3]
f5=counta[1]+counta[3]+countb[0]+countb[2]
f6=counta[2]+counta[3]+countb[0]+countb[1]

print(min(f1,f2,f3,f4,f5,f6))