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;

fn main() {
    input! {
        n: usize,
    };
    let magic = 1e9 as usize + 7;
    if n <= 1 {
        println!("0");
        return;
    }
    let mut x_all = 100;
    let mut x_ex0 = 81;
    let mut x_ex09 = 64;
    for _ in 3..=n {
        x_all = x_all * 10 % magic;
        x_ex0 = x_ex0 * 9 % magic;
        x_ex09 = x_ex09 * 8 % magic;
    }
    let x_ex9 = x_ex0;
    let x = (x_all + (magic - x_ex0) + (magic - x_ex9) + x_ex09) % magic;
    println!("{}", x);
}