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)

#![allow(unused_imports)]
use proconio::marker::*;
use proconio::{fastout, input};

#[fastout]
fn main() {
    input! {
        n: isize,
    }

    let res = solve(n);
    println!("{}", res);
}

fn solve(n: isize) -> isize {
    const MODN: isize = 1e9 as isize + 7;
    let res = powmod(10, n, MODN) - powmod(9, n, MODN) * 2 + powmod(8, n, MODN);
    let res = res % MODN;
    (res + MODN) % MODN
}

fn powmod(a: isize, b: isize, modn: isize) -> isize {
    let mut res = 1;
    for _ in 0..b {
        res = res * a % modn;
    }
    res
}