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())

parts = []

for _ in range(4):
    p = ""
    for r in range(n):
        p += input()
    parts.append(p)
    if _ != 3:
        input()

op1 = '10' * (1 + (n**2)//2)
op2 = '01' * (1 + (n**2)//2)
op1 = op1[:n**2]
op2 = op2[:n**2]

cases = [((0,1), (2,3)), ((0,2), (1,3)), ((0,3), (1,2)), ((1,2), (0,3)),((1,3), (0,2)),((2,3), (0,1))]
total = 4*n**2
current = 0
for c1, c2 in cases:
    a1,a2 = parts[c1[0]],parts[c1[1]]
    a3,a4 = parts[c2[0]],parts[c2[1]]

    current += sum(c!=c_1 for c, c_1 in zip(op1,a1))
    current += sum(c!=c_1 for c, c_1 in zip(op1,a2))

    current += sum(c!=c_2 for c, c_2 in zip(op2,a3))
    current += sum(c!=c_2 for c, c_2 in zip(op2,a4))
    total = min(current,total)
    current = 0
print (total)

