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::input;

fn main() {
    input! {
        n: u64,
    }
    let modulo = 1_000_000_007;
    let all = mod_pow(10, n, modulo);
    let no_zero_nine = mod_pow(8, n, modulo);
    let zero_or_nine = mod_pow(9, n, modulo);
    println!(
        "{}",
        (all + no_zero_nine + modulo - 2 * zero_or_nine) % modulo
    );
}

fn mod_pow(a: u64, b: u64, modulo: u64) -> u64 {
    if b == 0 {
        1
    } else if b % 2 == 0 {
        let half = mod_pow(a, b / 2, modulo);
        half * half % modulo
    } else if b % 2 == 1 {
        let half = mod_pow(a, b / 2, modulo);
        half * half % modulo * a % modulo
    } else {
        unreachable!()
    }
}