### Problem Statement

A string composed of a's and b's is either redundant or non-redundant. A string is redundant if and only if it can be expressed as a shorter string replicated multiple times. For example, the string "ababab" is redundant since it is 3 copies of "ab" concatenated together. The string "ab" is called a root of "ababab". The string "aaaa" has 2 roots: "aa" and "a". A nice result in formal languages states that every redundant string has exactly 1 non-redundant root (it may have many redundant roots).

Only considering strings composed of a's and b's, return the number of redundant strings that have the given length.

### Definition

 Class: RedundantStrings Method: howMany Parameters: int Returns: int Method signature: int howMany(int length) (be sure your method is public)

### Constraints

-length will be between 1 and 60 inclusive.

### Examples

0)

 `1`
`Returns: 0`
 There are no redundant strings of length 1.
1)

 `2`
`Returns: 2`
 Both "aa" and "bb" are redundant.
2)

 `4`
`Returns: 4`
 Here the redundant strings are "aaaa", "bbbb", "abab", and "baba".
3)

 `10`
`Returns: 34`
4)

 `30`
`Returns: 33814`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=4505

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=6537&pm=4505