Problem:
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

Solution in Rust (1.42.0) (judge verdict: Accepted)

fn main() {
    proconio::input! {
        n: usize
    }
    let m : i64 = 1000000007;
    let mut p10 = 1;
    let mut p9 = 1;
    let mut p8 = 1;
    for _ in 0..n {
        p10 = 10 * p10 % m;
        p9 = 9 * p9 % m;
        p8 = 8 * p8 % m;
    }
    println!("{}", (p10 + 2*(m-p9) + p8)%m);
}