### Problem Statement

Little John has one standard die with numbers one to six on its sides. Each time he throws the die, he gets as many candies from his mom as the number on the top of the die. John?s goal is to collect at least candies candies. Then he will eat them all and became a little fat boy.

Return the expected number of throws needed for John to achieve his goal.

### Definition

 Class: TheDiceGame Method: expectedThrows Parameters: int Returns: double Method signature: double expectedThrows(int candies) (be sure your method is public)

### Notes

-The returned value must be accurate to within a relative or absolute value of 1E-9.

### Constraints

-candies will be between 1 and 1000000, inclusive.

### Examples

0)

 `1`
`Returns: 1.0`
 John needs only one throw to get at least one candy.
1)

 `2`
`Returns: 1.1666666666666667`
 After the first throw, there is a probability of 1/6 that John will need an additional throw.
2)

 `7`
`Returns: 2.5216263717421126`
3)

 `47`
`Returns: 13.90476189046144`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=8414

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=10804&pm=8414

Vasyl[alphacom]

#### Testers:

PabloGilberto , Olexiy , ivan_metelsky , ged

Simple Math