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())
a1=[]
for i in range(n):
	a=str(input())
	a=list(a)
	a1.append(a)
x1=str(input())
a2=[]
for i in range(n):
	a=str(input())
	a=list(a)
	a2.append(a)
x1=str(input())
a3=[]
for i in range(n):
	a=str(input())
	a=list(a)
	a3.append(a)
x1=str(input())
a4=[]
for i in range(n):
	a=str(input())
	a=list(a)
	a4.append(a)
ab=[]
ab.append(a1)
ab.append(a2)
ab.append(a3)
ab.append(a4)
x=[]
one=[]
for i in range(n):
	z=[]
	for j in range(n):
		if((i+j)%2==0):
			z.append('1')
		else:
			z.append('0')
	one.append(z)

two=[]
for i in range(n):
	z=[]
	for j in range(n):
		if((i+j)%2==0):
			z.append('0')
		else:
			z.append('1')
	two.append(z)
for i in range(4):
	e1=0
	o1=0
	for j in range(n):
		for k in range(n):
			if(ab[i][j][k]!=one[j][k]):
				e1+=1
			if(ab[i][j][k]!=two[j][k]):
				o1+=1
	x.append([e1,o1])

s=x[0][0]+x[1][1]+x[2][0]+x[3][1]
if(x[0][0]+x[1][0]+x[2][1]+x[3][1]<s):
	s=x[0][0]+x[1][0]+x[2][1]+x[3][1]
if(x[0][0]+x[1][1]+x[2][1]+x[3][0]<s):
	s=x[0][0]+x[1][1]+x[2][1]+x[3][0]
if(x[0][1]+x[1][0]+x[2][1]+x[3][0]<s):
	s=x[0][1]+x[1][0]+x[2][1]+x[3][0]
if(x[0][1]+x[1][1]+x[2][0]+x[3][0]<s):
	s=x[0][1]+x[1][1]+x[2][0]+x[3][0]
if(x[0][1]+x[1][0]+x[2][0]+x[3][1]<s):
	s=x[0][1]+x[1][0]+x[2][0]+x[3][1]
print(s)