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 gen(n,isw):
	ws=('0','1')
	bs=('1','0')
	bl=[bs[x%2] for x in range(n)]
	wl=[ws[x%2] for x in range(n)]
	if isw:
		ls=(wl,bl)
	else:
		ls=(bl,wl)
	v=[]
	for c in range(n):
		v.append(ls[c%2])
	return v

def comp(f,s):
	x=0
	n=len(f)
	for c in range(n):
		for d in range(n):
			if f[c][d]!=s[c][d]:
				x+=1
	return x

sz=4

def getmin(v,n):
	w=gen(n,1)
	b=gen(n,0)
	bv=[]
	for c in range(sz):
		bv.append((comp(b,v[c]),v[c]))
	bv.sort(key=lambda x:x[0])
	wv=[]
	for c in range(sz//2,sz):
		wv.append((comp(w,bv[c][1]),bv[c][1]))
	sm=0
	for c in range(sz//2):
		sm+=bv[c][0]+wv[c][0]
	return sm

n=int(input())
v=[]
for c in range(sz):
	tv=[]
	for d in range(n):		
		tv.append(list(input()))
	if c<sz-1:
		input()
	v.append(tv)
print(getmin(v,n))