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;

const MOD: u64 = 1_000_000_007;

fn main() {
    input!(n: u64);

    let mpow = |base, exp| (0..exp).fold(1_u64, |acc, _| acc * base % MOD);
    let ans = mpow(10, n) + mpow(8, n) - 2 * mpow(9, n);
    let ans = ans.rem_euclid(MOD);

    println!("{}", ans);
}