### Problem Statement

You are given six integers, minx, maxx, miny, maxy, minz and maxz. Return the number of triplets of integers (x,y,z) that satisfy the following three conditions:
• x is between minx and maxx, inclusive.
• y is between miny and maxy, inclusive.
• z is between minz and maxz, inclusive.
• x * y = z

### Definition

 Class: ProductTriplet Method: countTriplets Parameters: int, int, int, int, int, int Returns: long Method signature: long countTriplets(int minx, int maxx, int miny, int maxy, int minz, int maxz) (be sure your method is public)

### Constraints

-maxx will be between 1 and 1,000,000,000, inclusive.
-maxy will be between 1 and 1,000,000,000, inclusive.
-maxz will be between 1 and 1,000,000,000, inclusive.
-minx will be between 1 and maxx, inclusive.
-miny will be between 1 and maxy, inclusive.
-minz will be between 1 and maxz, inclusive.

### Examples

0)

 `2` `2` `3` `3` `6` `6`
`Returns: 1`
 2 * 3 = 6.
1)

 `2` `2` `3` `3` `7` `7`
`Returns: 0`
 2 * 3 is not 7.
2)

 `6` `8` `4` `5` `27` `35`
`Returns: 4`
 (x,y,z) = (6,5,30), (7,4,28), (7,5,35) and (8,4,32) satisfy all conditions.
3)

 `1` `458` `1` `458` `1` `458`
`Returns: 2877`
4)

 `8176` `184561` `1348` `43168` `45814517` `957843164`
`Returns: 2365846085`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=10698

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=14180&pm=10698

rng_58

#### Testers:

Rustyoldman , timmac , ivan_metelsky , mohamedafattah , it4.kp

#### Problem categories:

Brute Force, Math