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: Wrong Answer)

use std::io::*;
use std::str::FromStr;

const MOD: u64 = 1000000007;

fn modpow(a: u64, n: u64) -> u64 {
    let mut res: u64 = 1;
    let mut b: u64 = a;
    let mut m: u64 = n;
    loop {
        if m == 0 {
            break;
        }
        if m % 2 == 1 {
            res = (res * b) % MOD;
        }
        b = (b * b) % MOD;
        m = m / 2;
    }
    res
}

fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn main() {
    let n: u64 = read();
    let ans1 = modpow(10, n) as i64;
    let ans2 = modpow(9, n) as i64;
    let ans3 = modpow(8, n) as i64;
    //println!("{} {} {}", ans1, ans2, ans3);
    let ansm: i64 = ans1 - ans2 - ans2 + ans3;
    println!("{}", ansm);
}