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
import itertools
n=input()
l=[]
for i in xrange(4):
	x=[]
	for j in xrange(n):
		x.append(raw_input())
	if i!=3:
		raw_input()
	l.append(x)
cc=set(itertools.permutations([0,1,2,3]))
#print l#,cc
def onelist(k,l,n):
	z=[]
	for i in xrange(2*n):
		if i<n:
			z.append(l[k[0]][i] + l[k[1]][i])
		else:
			z.append(l[k[2]][i-n] + l[k[3]][i-n])
	return z
def cost(z,n,k):
	c=0
	for i in xrange(2*n):
		for j in xrange(2*n):
			if i&1 and j&1 and z[i][j]!=k:
				c+=1
			elif i&1 and j%2==0 and z[i][j]==k:
				c+=1
			elif i%2==0 and j&1 and z[i][j]==k:
				c+=1
			elif i%2==0 and j%2==0 and z[i][j]!=k:
				c+=1
	return c

mn=1000*1000
for i in cc:
	z=onelist(i,l,n)
	c1=min(mn, cost(z, n, '0'))
	c2=min(mn, cost(z, n, '1'))
	mn=min(mn,c1,c2)
print mn