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)

#[allow(unused_imports)]
use proconio::{
    fastout, input,
    marker::{Bytes, Chars, Isize1, Usize1},
};
const MMMOD: isize = 1_000_000_007;
#[fastout]
fn main() {
    input!(n: isize);

    let ans =
        powmod(10, n) + powmod(9, n).wrapping_neg() + powmod(9, n).wrapping_neg() + powmod(8, n);

    println!("{}", (ans + MMMOD) % MMMOD);
}

fn powmod(x: isize, y: isize) -> isize {
    let mut res = 1;
    for _i in 0..y {
        res = res * x % MMMOD;
    }
    res
}