Given a sequence of natural numbers .
Find it's N'th term.
a1=3, a2=9, a3=30, a4=101, a5=358, a6=1443... ...,aN

Input

Single line containing a natural number N

Output

Print N'th term of the sequence modulo 10^9+7.

Constraints

• 1 <= N <=100

Example

Input:
5

Output:
358