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)

use proconio::input;

fn main() {
    input! {
        n: usize,
    }
    let m = 1000000007;
    let mut n10 = 1usize;
    let mut n9 = 1usize;
    let mut n8 = 1usize;
    for _ in 0..n {
        n10 = (n10 * 10) % m;
        n9 = (n9 * 9) % m;
        n8 = (n8 * 8) % m;
        n10 %= m;
        n9 %= m;
        n8 %= m;
    }

    let ans = (n10 - (((2 * n9) % m) + m - n8) % m) % m;
    println!("{}", ans);
}