A8736 | Unsolvable

Consider the following equation:

 where sign $[a]$ represents the integer part of number $a$ .Let's find all integer $z$ $(z>0)$ , for which this equation is unsolvable in positive integers. The phrase "unsolvable in positive integers" means that there are no such positive integers $x$ and $y$ $(x,y>0)$ , for which the given above equation holds.

Let's write out all such $z$ in the increasing order: $z_{1},z_{2},z_{3}$ , and so on $(z_{i}<z_{i+1})$ . Your task is: given the number $n$ , find the number $z_{n}$ .

The first line contains a single integer $n$ ( $1<=n<=40$ ).

Print a single integer — the number $z_{n}$ modulo $1000000007$ $(10^{9}+7)$ . It is guaranteed that the answer exists.