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::input;

fn main() {
    input! {
        n: u64,
    }

    let w = 10u64.pow(9) + 7;
    let mut x = 1;
    let mut y = 1;
    let mut z = 1;
    for _ in 0..n {
        y = y * 9 % w;

        if x < 2 * y {
            x = x * 10;
        } else {
            x = x * 10 % w;
        }
        z = z * 8 % w;
    }
    y = 2 * y % w;
    println!("{}", (x + z - y) % w);
}