注意：この問題文には日本語版がありません。

Problem Statement

This year,There are $2^{N}$ teams entried World BaseBall Contest.
This World BaseBall contest is Tournament, and only 1 team will be Champion.
How many games will it be before a Champion is decided?
However, all matches shall end in a win or a loss, and no tie shall be considered.
This answer can be large, so output the remainder divided by $1000000007$.

Constraints

・$N$ is Integer
・$0 \leq N \leq 10^{9}$
・This site doesn't have a partial point system, but I'll just show partial points.
・Full Mark is $100$ Point
・(Constraints 1) $N \leq 16$　　($5$ Point)
・(Constraints 2) $N \leq 10^{5}$　　($35$ Point)
・(Constraints 3) No additional restrictions.　　($60$ Point)

Input

$N$

Output

Please output "How many games will it be before a Champion is decided".

Sample Case

2

3

There are $2^2 = 4$ teams Entried.
On the First Round, There are $2$ match, $2$ teams will be defeated.
On the Second Round(and it is Final Round), $1$ teams will be defeated and Champion is decided.
So, The answer is $2 + 1 = 3$, Please output $3$.

Sample Case

10000

905611804

This answer can be large, so output the remainder divided by $1000000007$.And it contained Constraints 2 Cases.