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)

use proconio::{fastout, input};

#[fastout]
fn main() {
    input! {n: u128};

    if n < 2 {
        println!("0")
    } else {
        let mut result = f(n, 10) - (f(n, 9) + f(n, 9) - f(n, 8));
        result = result % (10i32.pow(9) + 7) as u128;
        result = (result + (10i32.pow(9) + 7) as u128) % (10i32.pow(9) + 7) as u128;
        println!("{}", result);
    }
}

fn f(n: u128, base: u128) -> u128 {
    let mut result = 1;
    for _ in 0..n {
        result = result * base % (10i32.pow(9) + 7) as u128;
    }
    return result;
}