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())

lst1 = []
for x in range(n):
    lst1.append(input().split())
    
s = input()

lst2 = []
for x in range(n):
    lst2.append(input().split())

s = input()

lst3 = []
for x in range(n):
    lst3.append(input().split())

s = input()

lst4 = []
for x in range(n):
    lst4.append(input().split())

ans_b1 = 0
ans_w1 = 0
for x in range(n):
    for y in range(n):
        if (x + y) & 1 == 0:
            if lst1[x][0][y] == '0':
                ans_b1 += 1
            else:
                ans_w1 += 1
        else:
            if lst1[x][0][y] == '1':
                ans_b1 += 1
            else:
                ans_w1 += 1

ans_b2 = 0
ans_w2 = 0
for x in range(n):
    for y in range(n):
        if (x + y) & 1 == 0:
            if lst2[x][0][y] == '0':
                ans_b2 += 1
            else:
                ans_w2 += 1
        else:
            if lst2[x][0][y] == '1':
                ans_b2 += 1
            else:
                ans_w2 += 1

ans_b3 = 0
ans_w3 = 0
for x in range(n):
    for y in range(n):
        if (x + y) & 1 == 0:
            if lst3[x][0][y] == '0':
                ans_b3 += 1
            else:
                ans_w3 += 1
        else:
            if lst3[x][0][y] == '1':
                ans_b3 += 1
            else:
                ans_w3 += 1

ans_b4 = 0
ans_w4 = 0
for x in range(n):
    for y in range(n):
        if (x + y) & 1 == 0:
            if lst4[x][0][y] == '0':
                ans_b4 += 1
            else:
                ans_w4 += 1
        else:
            if lst4[x][0][y] == '1':
                ans_b4 += 1
            else:
                ans_w4 += 1

print((2 * n) ** 2 - max(ans_b1 + ans_b2 + ans_w3 + ans_w4, ans_b1 + ans_w2 + ans_b3 + ans_w4, ans_b1 + ans_w2 + ans_w3 + ans_b4, ans_w1 + ans_b2 + ans_b3 + ans_w4, ans_w1 + ans_b2 + ans_w3 + ans_b4, ans_w1 + ans_w2 + ans_b3 + ans_b4))
