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};
use proconio::marker::{Chars};
use proconio::marker::Usize1;
use std::cmp::*;

macro_rules! debug {
      ($($a:expr),*) => {
          eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
    }
}

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

    let inf = 10_0000_0000 + 7;
    let mut ans: u128 = 1;
    let mut ans1: u128 = 1;
    let mut ans2: u128 = 1;
    if n==1 {
        println!("0");
        return;
    }  else if n==2 {
        println!("2");
        return;
    } else {
        for i in 0..n {
            ans *= 10;
            ans %= inf;
            ans1 *= 9;
            ans1 %= inf;
            ans2 *= 8;
            ans2 %= inf;
            // debug!(ans);
        }
        ans1 = (((ans+inf-ans1)%inf)*2)%inf;
        ans2 = (ans+inf-ans2)%inf;
        ans = (ans1+inf-ans2)%inf;
    }
    println!("{}", ans);
}