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::*;

const MOD: u64 = 1_000_000_007;

fn mod_pow(r: u64, mut n: u64) -> u64 {
    let mut t = 1;
    let mut s = r;
    while n > 0 {
        if n & 1 == 1 {
            t = t * s % MOD;
        }
        s = s * s % MOD;
        n >>= 1;
    }
    t
}

fn run() {
    input! {
        n: u64,
    }
    let ans = (mod_pow(10, n) - 2 * mod_pow(9, n) + mod_pow(8, n) + 2 * MOD) % MOD;
    println!("{}", ans);
}

fn main() {
    run();
}