### Problem Statement

Given a int[] values containing positive integers return (quotes for clarity):
• "ASCENDING mean" if the numbers are in increasing order and there are no repeated values,
• "DESCENDING mean" if the numbers are in decreasing order and there are no repeated values,
• "NONASCENDING freq" if the numbers are in decreasing order and contain repeated values,
• "NONDESCENDING freq" if the numbers are in increasing order and contain repeated values,
• or "NOTHING" if the numbers are none of the above.
where mean is a reduced fraction representing the average of the numbers formatted as (quotes for clarity) "numerator/denominator"

and freq is the number of times the most frequently occurring value occurred in the sequence.

Neither numerator nor denominator should have any leading zeros. For example (quotes for clarity):
```values = {1,2,4,11}       return "ASCENDING 9/2" since the average is 18/4 = 9/2
values = {1,2,2,2,3,4}   return "NONDESCENDING 3"  since 2 occurred 3 times
values = {6,5,1}         return "DESCENDING 4/1" since the average is 12/3 = 4/1
values = {5,5,4,4,1}     return "NONASCENDING 2" since 5 occurred twice
values = {1,2,3,4,1}     return "NOTHING" since no other choice is possible
```

### Definition

 Class: Ordered Method: getType Parameters: int[] Returns: String Method signature: String getType(int[] values) (be sure your method is public)

### Notes

-Be sure that you spell everything correctly.

### Constraints

-values must contain between 2 and 50 elements inclusive
-At least 2 elements of values must be distinct
-Each element of values must be between 1 and 1000 inclusive

### Examples

0)

 `{1,2,4,11}`
`Returns: "ASCENDING 9/2"`
 Increasing order with no repeats
1)

 `{1,2,2,2,3,4}`
`Returns: "NONDESCENDING 3"`
 Increasing order but the 2 is repeated 3 times
2)

 `{6,5,1}`
`Returns: "DESCENDING 4/1"`
 Decreasing order with no repeats
3)

 `{5,5,4,4,1}`
`Returns: "NONASCENDING 2"`
 Decreasing order but there are repeats
4)

 `{1,2,3,4,1}`
`Returns: "NOTHING"`
 The sequence increases at first but decreases at the end
5)

 `{1000,999,998}`
`Returns: "DESCENDING 999/1"`
 Decreasing with no repeats
6)

 `{999,1000,1000,1000,1000,1000}`
`Returns: "NONDESCENDING 5"`
7)

 `{1,1000,1,1000,1,1000}`
`Returns: "NOTHING"`
8)

 ```{1,2,3,4,5,6,7,8,9,10, 11,12,13,14,15,16,17,18,19,20, 21,22,23,24,25,26,27,28,29,30, 31,32,33,34,35,36,37,38,39,40, 41,42,43,44,45,46,47,48,49,51}```
`Returns: "ASCENDING 638/25"`
9)

 `{2,2,1}`
`Returns: "NONASCENDING 2"`
10)

 `{1,2,2}`
`Returns: "NONDESCENDING 2"`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=1287

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=4474&pm=1287

brett1479

#### Testers:

lbackstrom , schveiguy

Math