Coupons

Time limit1sMemory limit128 MB

Summary
Compute the expected number of purchases needed to collect all N coupon numbers, printing the result as an integer or reduced mixed fraction.
Level

Medium4 of 10

Topics
Probability, Math, Number theory
Solved
No attempts yet

Problem

A chicken box comes with one coupon. Each coupon has one number from 1 through N, and every number is equally likely on each purchase.

Haebin wants to order a Gold Cheese Chicken. To do that, Haebin must collect every coupon numbered 1 through N. For each given N, determine the expected number of chicken boxes Haebin must order.

Input

Several values of N are given, one per line, until end of file.

Each value satisfies 1 <= N <= 22.

Output

For each input value, print the expected number of chicken boxes.

If the answer is an integer, print that integer. Otherwise, print its integer part, followed by one space and the remaining fractional part as a reduced fraction in the aligned format shown below. Do not print unnecessary spaces.

Examples1

  1. Example 1

    Input
    2
5
17
    Expected output
    3 
   5
11 --
   12
   340463
58 ------
   720720