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)

#![allow(unused_imports)]
use proconio::marker::*;
use proconio::{fastout, input};

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

    let res = solve(n);
    println!("{}", res);
}

fn solve(n: usize) -> usize {
    if n == 1 {
        return 0;
    } else if n == 2 {
        return 2;
    }
    const MOD: usize = 1e9 as usize + 7;

    let ten = {
        let mut tmp = 1;
        for _ in 0..n - 2 {
            tmp *= 10;
            tmp %= MOD;
        }
        tmp
    };

    let cmb = (n * (n - 1) / 2) % MOD;
    let total = (ten * cmb * 2) % MOD;
    let bin = {
        let mut tmp = 1;
        for _ in 0..n {
            tmp *= 2;
            tmp %= MOD;
        }
        tmp - 2
    };

    (total + MOD - bin) % MOD
}