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
from sys import stdin
input = stdin.readline

n = int(input())
a = []
for i in range(4):
    a.append([[int(x) for x in list(input().rstrip())] for _ in range(n)])
    if i < 3: input()
b = []
for i in range(4):
    b.append([])
    for j in range(2):
        c = 0
        for y in range(n):
            for x in range(n):
                if j == 1:   
                    z = (x + y) % 2
                else:
                    z = 1 - (x + y) % 2
                c += a[i][y][x] != z
        b[-1].append(c)
ans = float("inf")
for i in (3, 5, 6, 9, 10, 12):
    ans = min(ans, b[0][i & 1] + b[1][i >> 1 & 1] + b[2][i >> 2 & 1] + b[3][i >> 3 & 1])
print(ans)