Maximum Number of Small Boxes in a Large Box

Little Blue has a large box with inner dimensions \(200\) mm, \(250\) mm, and \(240\) mm along its length, width, and height respectively. He wants to pack as many small boxes as possible into this large box. Each small box has external dimensions \(30\) mm, \(40\) mm, and \(50\) mm. The small box can be rotated arbitrarily (including being laid flat or turned upside down) such that its edges are always aligned with the edges of the large box.

Determine the maximum number of small boxes that can be packed into the large box. The answer is determined by trying all permutations of the small box orientation and selecting the one that maximizes the product of the counts along each dimension. For a particular orientation (\(a, b, c\)) of the small box, the number of boxes that can be fitted along the corresponding dimensions of the big box \((L, W, H)\) is given by:

\[ \text{count} = \left\lfloor\frac{L}{a}\right\rfloor \times \left\lfloor\frac{W}{b}\right\rfloor \times \left\lfloor\frac{H}{c}\right\rfloor \]

You need to output the maximum such count.

inputFormat

There is no input for this problem. All dimensions are fixed as described in the problem statement.

outputFormat

Output a single integer: the maximum number of small boxes that can be packed into the large box.

sample

200