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�fs 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)


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



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