### Problem Statement

You're given a set of inequalities. Each of the inequalities refers to the variable X. Determine the maximum subset of the given set which has a solution.

To make your task easier, the inequalities in the given set are always reduced to one of the following five forms:

```	X < C
X <= C
X = C
X > C
X >= C
```
Here, C indicates some non-negative integer constant.

The inequalities are given in the String[] inequalities, where each element is a single inequality formatted as shown above. Return the maximal number of inequalities of the set which can be satisfied simultaneously.

### Definition

 Class: Inequalities Method: maximumSubset Parameters: String[] Returns: int Method signature: int maximumSubset(String[] inequalities) (be sure your method is public)

### Notes

-Note that X doesn't have to be an integer or positive number.

### Constraints

-inequalities will contain between 1 and 50 elements, inclusive.
-Each element of inequalities will be formatted "X <E> <C>", where 'X' is uppercase, <E> is one of "<", "<=", "=", ">=" or ">", and <C> is an integer between 0 and 1000, inclusive, with no extra leading zeroes (all quotes for clarity).
-No two elements of inequalities will be equal.

### Examples

0)

 `{"X <= 12","X = 13","X > 9","X < 10","X >= 14"}`
`Returns: 3`
 Any value between 9 and 10 will satisfy the first, third and fourth inequalities.
1)

 `{"X < 0","X <= 0"}`
`Returns: 2`
 The solution to the whole set is any negative number.
2)

 `{"X = 1","X = 2","X = 3","X > 0"}`
`Returns: 2`
 Obviously, you can choose no more than one equality in addition to the fourth inequality.
3)

 `{"X <= 521","X >= 521","X = 521","X > 902","X > 12","X <= 1000"}`
`Returns: 5`
 The best choice is number 521.

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=10682

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=14145&pm=10682

gojira_tc

#### Testers:

PabloGilberto , legakis , ivan_metelsky

#### Problem categories:

Simple Math, Simple Search, Iteration