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
t = int(raw_input())

l1 = []
l2 = []

for i in range(t):
	temp1=[]
	temp2=[]
	for j in range(t):

		if (i%2 == 0):

			if (j%2==0):
				temp1.append(1)
				temp2.append(0)
			else:
				temp2.append(1)
				temp1.append(0)

		else:

			if (j%2==0):
				temp2.append(1)
				temp1.append(0)
			else:
				temp1.append(1)
				temp2.append(0)

	l1.append(temp1)
	l2.append(temp2)

list1 = []
list2 = []
list3 = []
list4 = []

for i in range(t):
	qwerty = raw_input()
	l_temp = []

	for j in range(t):
		l_temp.append(int(qwerty[j]))


	list1.append(l_temp)

temporary = raw_input()

for i in range(t):
	qwerty = raw_input()
	l_temp = []

	for j in range(t):
		l_temp.append(int(qwerty[j]))


	list2.append(l_temp)

temporary = raw_input()

for i in range(t):
	qwerty = raw_input()
	l_temp = []

	for j in range(t):
		l_temp.append(int(qwerty[j]))


	list3.append(l_temp)

temporary = raw_input()

for i in range(t):
	qwerty = raw_input()
	l_temp = []

	for j in range(t):
		l_temp.append(int(qwerty[j]))


	list4.append(l_temp)

'''print(l1)
print()
print(l2)
print()
print(list1)
print()
print(list2)
print()
print(list3)
print()
print(list4)
print()'''


count = []
sum_arr = [[0,0,0,0],[0,0,0,0]]

for k in range(t):
	for l in range(t):

		if (list1[k][l] != l1[k][l]):
			sum_arr[0][0] += 1

		if (list2[k][l] != l1[k][l]):
			sum_arr[0][1] += 1

		if (list3[k][l] != l1[k][l]):
			sum_arr[0][2] += 1

		if (list4[k][l] != l1[k][l]):
			sum_arr[0][3] += 1


		if (list1[k][l] != l2[k][l]):
			sum_arr[1][0] += 1

		if (list2[k][l] != l2[k][l]):
			sum_arr[1][1] += 1

		if (list3[k][l] != l2[k][l]):
			sum_arr[1][2] += 1

		if (list4[k][l] != l2[k][l]):
			sum_arr[1][3] += 1

sum1 = sum_arr[0][0] + sum_arr[0][1] + sum_arr[1][2] + sum_arr[1][3]
sum2 = sum_arr[0][1] + sum_arr[0][2] + sum_arr[1][0] + sum_arr[1][3]
sum3 = sum_arr[0][2] + sum_arr[0][3] + sum_arr[1][0] + sum_arr[1][1]
sum4 = sum_arr[0][0] + sum_arr[0][2] + sum_arr[1][1] + sum_arr[1][3]
sum5 = sum_arr[0][0] + sum_arr[0][3] + sum_arr[1][1] + sum_arr[1][2]
sum6 = sum_arr[0][1] + sum_arr[0][3] + sum_arr[1][0] + sum_arr[1][2]

q = min(sum1,sum2,sum3,sum4,sum5,sum6)
print(q)






