### Problem Statement

Consider an a by b rectangle, composed of a*b unit squares. Your task is to count the number of ways in which this rectangle can be divided into two contiguous sections, each consisting of 1 or more unit squares. Each section must contain at least 1 square on the edge of the rectangle. A section is contiguous if each square in the section is connected to each other square in the section via a path of horizontally or vertically adjacent squares that are all within the section.

### Definition

 Class: RectangleDivision Method: count Parameters: int, int Returns: int Method signature: int count(int a, int b) (be sure your method is public)

### Constraints

-a will be between 1 and 6, inclusive.
-b will be between 2 and 6, inclusive.

### Examples

0)

 `1` `3`
`Returns: 2`
 There are two different ways to split up this rectangle, where '#' represents one section, and '.' the other: ```##. #.. ```
1)

 `3` `2`
`Returns: 15`
 Here are the 15 ways: ```#. .# .. .. #. .# .. .. .. .. .. .. #. .# #. .# .. .. #. .# .. .. #. .# ## .. ## ## ## ## #. .. .. #. .# #. .# #. .. ## ## ## .. .. #. ```
2)

 `3` `3`
`Returns: 52`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=3074

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=5886&pm=3074

lars2520

#### Testers:

PabloGilberto , Yarin , vorthys

Brute Force