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())
a = []
b = []
ans = 1000000
for i in range(4):
    a.append([]*n)
    for j in range(n):
        a[i].append([0]*n)
for i in range(4):
    for j in range(n):
        s = input()
        for k in range(len(s)):
            a[i][j][k] = int(s[k])
    if i < 3:
        input()
for i in range(16):
    c = [0]*4
    y = 3
    ans1 = 0
    while i > 0:
        c[y] = i % 2
        y-=1
        i //= 2
    c.reverse()
    if sum(c) == 2:
        for k in range(4):
            if c[k] == 1:
                for i in range(n):
                    for j in range(n):
                        if i % 2 == j % 2:
                            ans1+=min(1,1 - a[k][i][j])
                        else:
                            ans1+=max(0,a[k][i][j])
            else:
                for i in range(n):
                    for j in range(n):
                        if i % 2 != j % 2:
                            ans1+=min(1,1 - a[k][i][j])
                        else:
                            ans1+=max(0,a[k][i][j])
        ans = min(ans,ans1)
print(ans)
                
        
