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: Wrong Answer)

#![allow(unused_imports)]

use proconio::input;

fn main() {
    input! {
        n: usize,
    }

    if n == 1 {
        println!("0");
    } else {
        let w = 10usize.pow(9) + 7;

        let mut x = 1;
        let mut y = 1;
        let mut z = 1;
        for _ in 0..n {
            x = x * 10 % w;
            y = y * 9 % w;
            z = z * 8 % w;
        }
        let ans = (x + z - 2 * y) % w;
        println!("{}", ans);
    }
}