### Problem Statement

The game Chomp starts with a grid 3 cells high and N cells wide. Two players take turns selecting a remaining cell in the grid, and chomping (removing) all the cells to the right and above the selected cell (including the chosen one). The player who chomps the lower-leftmost cell loses the game. Here is a sample of two moves in the game:
```3 XX                          XX
2 XXXX    => chomp(4,1) =>    XXX  => chomp(1,2) =>
1 XXXXX                       XXX                      XXX
12345                       12345                    12345
```
Determine which player wins if each player plays optimally, and how many total (for both players combined) turns it takes (the last move is the losing move). The player who will win when playing optimally plays to win as quickly as possible, while the player who is destined to lose plays to make the game last as long as possible. If player 1 will win, return the total number of moves required. Otherwise, return the negation of the number of moves required.

### Definition

 Class: Chomp Method: moves Parameters: int Returns: int Method signature: int moves(int N) (be sure your method is public)

### Constraints

-N will be between 1 and 100, inclusive.

### Examples

0)

 `1`
`Returns: 2`
 The optimal game is simple: ``` X . . X => . => . X X . ```
1)

 `2`
`Returns: 6`
2)

 `4`
`Returns: 8`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=6851

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=12011&pm=6851

lars2520

#### Testers:

PabloGilberto , legakis , Olexiy , ivan_metelsky

#### Problem categories:

Dynamic Programming