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())
N = [0, 0, 0, 0]
for i in range(4):
    for j in range(n):
        t = input()
        for k in range(n):
            if int(t[k]) == (j+k)%2:
                N[i] += 1
    if i != 3:
        s = input()
M = [0, 0, 0, 0]
for i in range(4):
    M[i] = (n * n) - N[i]
L = [0] * 6
L[0] = N[0] + N[1] + M[2] + M[3]
L[1] = N[0] + N[2] + M[1] + M[3]
L[2] = N[0] + N[3] + M[1] + M[2]
L[3] = N[1] + N[2] + M[0] + M[3]
L[4] = N[1] + N[3] + M[0] + M[2]
L[5] = N[2] + N[3] + M[0] + M[1]
mn = L[0]
for i in range(1, 6):
    if L[i] < mn:
        mn = L[i]
print(mn)
