“...Before June 2002, every Pepsi bottle cap purchased will have the name of a Pepsi star on it. As long as you collect all the names of the Pepsi stars, you can participate in the Pepsi World Cup tour lucky draw to win a Pepsi star backpack, a portable player, and even travel to Korea and Japan to watch the World Cup. Hurry up and act!...”

Watching this on TV, you think: Suppose there are $n$ different star names, and the probability of each name appearing is the same. On average, how many bottles of drinks do you need to buy to collect all the names?

Input

Input a single integer $n$, where $2 \le n \le 33$, representing the number of different star names.

Output

Output the average number of bottles of drinks needed to collect all the names. If the result is an integer, output it directly; otherwise, output the integer part, followed by a space, and then the fractional part in the format numerator/denominator. The fraction must be irreducible.

Examples

Input 1

2

Output 1

3

Input 2

5

Output 2

5 11/12

Input 3

17

Output 3

340463 58/720720