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::{fastout, input};
const MOD: i128 = 1_000_000_000 + 7;

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

    let mut pow10 = 1;
    let mut pow9 = 1;
    let mut pow8 = 1;
    for i in 1..=n {
        pow10 = pow10 * 10 % MOD;
        pow9 = pow9 * 9 % MOD;
        pow8 = pow8 * 8 % MOD;
    }

    println!("{}", (pow10 + 2 * (MOD - pow9) + pow8) % MOD);
}