### Problem Statement

Given a positive integer n, you are to find the largest subset S of {1,...,n} such that no member of S is divisible by another member of S. If there is more than one subset of the maximum size, choose the lexicographically earliest such subset. A subset S is lexicographically earlier than a subset T if the smallest element that is a member of one of the subsets, but not both, is a member of S. Return the subset S as a int[] in increasing order.

### Definition

 Class: Indivisible Method: largestSubset Parameters: int Returns: int[] Method signature: int[] largestSubset(int n) (be sure your method is public)

### Constraints

-n is between 1 and 1000, inclusive.

### Examples

0)

 `10`
`Returns: {4, 5, 6, 7, 9}`
 There are several possible subsets of size 5, such as { 4,6,7,9,10 }, but { 4,5,6,7,9 } is the lexicographically earliest.
1)

 `1`
`Returns: {1}`
2)

 `5`
`Returns: {2, 3, 5}`
3)

 `24`
`Returns: {4, 6, 9, 10, 11, 13, 14, 15, 17, 19, 21, 23}`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=3957

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=6553&pm=3957

vorthys

#### Testers:

PabloGilberto , lbackstrom , Yarin

Greedy