Description

You are given $n$ cards, each with the number $1$, and a machine.

You will perform the following operation $n-1$ times: put two cards into the machine and obtain a new card with the number $xy+1$, where $x, y$ are the numbers on the two cards you put in.

Question: After performing $n-1$ operations, what is the maximum possible number on the remaining card?

Input Format

One line containing a single positive integer $n$ ($1 \le n \le 10^4$).

Output Format

One line containing a single positive integer representing the answer.

3

3

Hint

Translated by ChatGPT 5