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)]
// use itertools::Itertools;
use proconio::{input, marker::*};

fn main() {
    input! {
        n: usize
    };
    if n == 1 {
        println!("0");
        return;
    }
    // 10^n - 2*9^n + 8^n
    let (mut a, mut b, mut c) = (10isize, 9isize, 8isize);
    for _ in 1..n {
        a = a * 10 % 1000000007;
        b = b * 9 % 1000000007;
        c = c * 8 % 1000000007;
    }
    let mut rs = (a - 2 * b + c) % 1000000007;
    if rs < 0 {
        rs += 1000000007;
    }
    println!("{}", rs);
}