10075_Coupons

Coupons in cereal boxes are numbered 1 to n, and a set of one of each is required for a prize (a cereal box, of course). With one coupon per box, how many boxes on average are required to make a complete set of n coupons?

Input consists of a sequence of lines each containing a single positive integer n, 1 ≤ n ≤ 22, giving the size of the set of coupons.

For each input line, output the average number of boxes required to collect the complete set of n coupons. If the answer is an integer number, output the number. If the answer is not integer, then output the integer part of the answer followed by a space and then by the proper fraction in the format shown below. The fractional part should be irreducible. There should be no trailing spaces in any line of ouput.

2
5
17

3
   5
11 --
   12
   340463
58 ------
   720720