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)

use proconio::{input, fastout};

const MOD: i64 = 1_000_000_007;

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

    let mut p10n = 1i64;
    let mut p9n = 1i64;
    let mut p8n = 1i64;

    for _ in 0..n {
        p10n *= 10;
        p10n %= MOD;
        p9n *= 9;
        p9n %= MOD;
        p8n *= 8;
        p8n %= MOD;
    }

    let mut ans = p10n-2*p9n+p8n;
    ans %= MOD;
    ans += MOD;
    ans %= MOD;
    println!("{}", ans);
}