C - Ubiquity

Score : $300$ points

Problem Statement

How many integer sequences $A_1,A_2,\ldots,A_N$ of length $N$ satisfy all of the following conditions?

• $0 \leq A_i \leq 9$
• There exists some $i$ such that $A_i=0$ holds.
• There exists some $i$ such that $A_i=9$ holds.

The answer can be very large, so output it modulo $10^9 + 7$.

Constraints

• $1 \leq N \leq 10^6$
• $N$ is an integer.

Input

Input is given from Standard Input in the following format:

$N$

Output

Print the answer modulo $10^9 + 7$.

2

2

Two sequences $\{0,9\}$ and $\{9,0\}$ satisfy all conditions.

1

0

869121

2511445