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())
Map = [[], [], [], []]
for x in range(4):
    for i in range(n):
        inp = list(input())
        Map[x].append(inp)
    if x != 3:
        input()
mini = 1000000000000000
ideal = [[], [], [], []]
for i in range(n):
    ideal[1].append([])
    ideal[0].append([])
    for j in range(n):
        if (i % 2 == 0) ^ (j % 2 == 0):
            ideal[0][i].append('1')
            ideal[1][i].append('0')
        else:
            ideal[1][i].append('1')
            ideal[0][i].append('0')
ideal[2] = ideal[0]
ideal[3] = ideal[1]
for one in range(4):
    for two in range(4):
        for three in range(4):
            for four in range(4):
                if (one != two) and (one != three) and (one != four) and (two != three) and (two != four) and (three != four):
                    count = 0
                    for i in range(n):
                        for j in range(n):
                            if Map[one][i][j] != ideal[0][i][j]:
                                count += 1
                            if Map[two][i][j] != ideal[1][i][j]:
                                count += 1
                            if Map[three][i][j] != ideal[2][i][j]:
                                count += 1
                            if Map[four][i][j] != ideal[3][i][j]:
                                count += 1
                    mini = min(mini, count)
print(mini)
