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::input;

#[allow(non_snake_case)]
fn main() {
    input! {
        N: usize
    }

    let m = 1000_000_000 + 7;
    let mut a: i64 = 1;
    let mut b: i64 = 1;
    let mut c: i64 = 1;

    for _ in 0..N {
        a = (a * 10) % m;
        b = (b * 9) % m;
        c = (c * 8) % m;
    }

    let ans = ((a + c + m) - 2 * b + m) % m;
    println!("{}", ans);
}