n people board an airplane with n seats. The first passenger has lost his boarding pass, so he sits in a random seat. Each subsequent passenger sits in his own seat if it’s available or takes a random unoccupied seat if it’s not.
What’s the probability that the nth passenger finds his seat occupied?
Input
The input file contains several test cases. Each test case is described with one integer n on a single line (2 ≤ n ≤ 1000).
The last line contains a single 0 and should not be processed.
Output
For each test case, output the probability that the nth passenger finds his seat occupied on a single line.
If the probability is 0, output 0/1. Otherwise, the probability should be expressed as an irreducible fraction a∕b, where a and b are positive integers and a and b be are relatively prime. Do not print any spaces between the numbers or the division sign.
Sample input and output
|
standard input
|
standard output
|
|
2
0 |
1/2
|