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: u64 = 1_000_000_000 + 7;

pub fn mpow(mut b: u64, mut e: u64, m: u64) -> u64 {
    let mut result = 1;

    while e > 0 {
        if e & 1 == 1 {
            result = result * b % m;
        }
        e >>= 1;
        b = (b * b) % m;
    }

    result
}

#[fastout]
fn main() {
    input! {
        n: u64,
    }

    println!(
        "{}",
        (mpow(10, n, MOD) + 2 * (MOD - mpow(9, n, MOD)) + mpow(8, n, MOD)) % MOD
    );
}