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())
one,two,three,four=[0]*n,[0]*n,[0]*n,[0]*n 
for i in xrange(n):
    one[i]=str(raw_input())
emp=str(raw_input())
for i in xrange(n):
    two[i]=str(raw_input())
emp=str(raw_input())
for i in xrange(n):
    three[i]=str(raw_input())
emp=str(raw_input())
for i in xrange(n):
    four[i]=str(raw_input())

def checkmin(part,k):
    c=0
    for i in xrange(n):
        for j in xrange(n):
            if int(part[i][j])!=k: c+=1 
            k=(k+1)%2
    return c 
    
one0, two0, three0, four0= checkmin(one,0), checkmin(two,0), checkmin(three,0), checkmin(four,0)
one1, two1, three1, four1= checkmin(one,1), checkmin(two,1), checkmin(three,1), checkmin(four,1)
#print one0, two0, three0, four0
#print one1, two1, three1, four1
ans= 2*n*2*n 
ans= min(ans, one1+two1+three0+four0)
ans= min(ans, one1+two0+three1+four0)
ans= min(ans, one1+two0+three0+four1)
ans= min(ans, one0+two0+three1+four1)
ans= min(ans, one0+two1+three0+four1)
ans= min(ans, one0+two1+three1+four0)
print ans 




