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 bubble_sort(a_list):
    changed = True
    while changed:
        changed = False
        for i in range(len(a_list)-1):
            if a_list[i] > a_list[i+1]:
                 changed = True
                 a_list[i],a_list[i+1] = a_list[i+1],a_list[i]
    return a_list

n = int(input())

str1 = ''
for i in range(n):

	str1 = str1+input()
j = input()
str2 = ''
for i in range(n):

	str2 = str2+input()
j = input()
str3 = ''
for i in range(n):

	str3 = str3+input()
str4 = ''
j = input()
for i in range(n):

	str4 = str4+input()

str1comp = "01"*(n**2)
#print()
#print(str2)
#print(str1comp)

a = 0
b = 0
c = 0
d = 0


for i in range(n**2):
	if str1[i] == str1comp[i]:
		a +=1
for i in range(n**2):
	if str2[i] == str1comp[i]:
		b +=1
for i in range(n**2):
	if str3[i] == str1comp[i]:
		c +=1
for i in range(n**2):
	if str4[i] == str1comp[i]:
		d +=1

lst2 = []
lst2.append(a)
lst2.append(b)
lst2.append(c)
lst2.append(d)



bubble_sort(lst2)

#print(lst2)

sum3 = 0

for i in range(2):
	sum3+= lst2[i]
for i in range(2,4):
	sum3+= (n**2 - lst2[i])

print(sum3)











