9643: ABC178 —— C - Ubiquity
[Creator : ]
Description
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 $10^9 + 7$.
- $0 \leq A_i \leq 9$
- 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 $10^9 + 7$.
Input
Input is given from Standard Input in the following format:
```
$N$
```
```
$N$
```
Output
Print the answer modulo $10^9 + 7$.
Constraints
- $1 \leq N \leq 10^6$
- $N$ is an integer.
- $N$ is an integer.
Sample 1 Input
2
Sample 1 Output
2
Two sequences {0,9} and {9,0} satisfy all conditions.
Sample 2 Input
1
Sample 2 Output
0
Sample 3 Input
869121
Sample 3 Output
2511445