101782: [AtCoder]ABC178 C - Ubiquity
Memory Limit:256 MB
Time Limit:2 S
Judge Style:Text Compare
Creator:
Submit:0
Solved:0
Description
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 $10^9 + 7$.
Sample Input 1
2
Sample Output 1
2
Two sequences $\{0,9\}$ and $\{9,0\}$ satisfy all conditions.
Sample Input 2
1
Sample Output 2
0
Sample Input 3
869121
Sample Output 3
2511445