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)

#![allow(unused_imports, non_snake_case)]
use proconio::{
    input, fastout,
    marker::{Chars, Bytes, Usize1}
};

fn power(a:u64, b:u64, modulo:u64) -> u64 {
    let mut res = 1;
    let mut b = b;
    let mut a = a;
    while b > 0 {
        if b & 1 > 0 {
            res = res * a % modulo;
        }
        b >>= 1;
        a = a * a % modulo
    }
    res
}

const MOD: u64 = 1_000_000_007;

#[fastout]
fn main() {
    input!{
        N: u64
    }
    let mut ans = power(10, N, MOD);
    ans = ans + MOD * 2 - power(9, N,MOD) * 2;
    ans += power(8, N, MOD);
    println!("{}", ans % MOD);
}