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::{fastout, input};
const MOD: i128 = 1_000_000_000 + 7;

#[fastout]
fn main() {
    input! {
        n: usize,
    }

    let mut pow10 = vec![1i128; n + 1];
    let mut pow9 = vec![1i128; n + 1];
    let mut pow8 = vec![1i128; n + 1];
    for i in 1..=n {
        pow10[i] = pow10[i - 1] * 10 % MOD;
        pow9[i] = pow9[i - 1] * 9 % MOD;
        pow8[i] = pow8[i - 1] * 8 % MOD;
    }

    println!("{}", (pow10[n] + 2 * (MOD - pow9[n]) + pow8[n]) % MOD);
}