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: usize = 1_000_000_007;

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

    if n == 1 {
        println!("0");
        return;
    }

    let mut ans = 1;

    for _ in 0..n {
        ans *= 10;
        ans %= MOD;
    }

    let mut eight = 1;
    for _ in 0..n {
        eight *= 8;
        eight %= MOD;
    }
    ans += eight;
    ans %= MOD;

    let mut nine = 1;
    for _ in 0..n {
        nine *= 9;
        nine %= MOD;
    }
    nine *= 2;
    nine %= MOD;

    ans += MOD;
    ans -= nine;
    ans %= MOD;

    println!("{}", ans);
}