Dominoes

Problem Description

Some day, Tom's father buys him a box of dominoes blocks. In the box, there are 12 different blocks, which are shown above. Tom is a boy who likes to do practice in intelligence, so he spends a whole afternoon in finishing two different rectangles with 3 * 20, which are shown below.

①⑤⑤⑤⑤⑨⑩⑩⑩⑥⑥⑧②②②②②③④④
①⑤⑿⑿⑨⑨⑨⑩⑥⑥⑦⑧⑧⑧⑾⑾③③③④
①①①⑿⑿⑿⑨⑩⑥⑦⑦⑦⑦⑧⑾⑾⑾③④④

①⑧⑦⑦⑦⑦⑥⑩⑨⑿⑿⑿②②②②②③④④
①⑧⑧⑧⑦⑥⑥⑩⑨⑨⑨⑿⑿⑤⑾⑾③③③④
①①①⑧⑥⑥⑩⑩⑩⑨⑤⑤⑤⑤⑾⑾⑾③④④

Tom is sure that these are the only solutions for 3 * 20, and he wants to know the number of solutions for 4 * 15, 5 * 12, ... Can you help him?

You should notice that if a solution will be the same as the other by some flip or rotate, these two solutions should be consider as the same.

Input
There may be several test cases. Each contains a single line with two positive integers M and N, which means the shape of M * N. Here M * N = 60.

Output
For each test case, output a line contains the number of solutions.

Sample Input
1 60
3 20

Sample Output
0
2

1个回答