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;

use num;
use std::convert;
pub fn mpow<Output, Base, Exponent>(base: Base, exponent: Exponent, modvalue: Output) -> Output
where
    Output: num::Integer + Copy + convert::From<Base> + convert::From<Exponent>,
    Base: num::Integer,
    Exponent: num::Integer,
{
    let mut result: Output = Output::one();
    let two: Output = From::from(Exponent::one() + Exponent::one());
    let mut mm: Output = From::from(exponent);
    let mut nn: Output = From::from(base);
    while !mm.is_zero() {
        if mm.is_odd() {
            result = (result * nn) % modvalue;
        }
        nn = (nn * nn) % modvalue;
        mm = mm / two;
    }
    result
}

#[proconio::fastout]
fn main() {
    input! {
        n: i32
    }

    let m: i64 = 1000000007;
    let ans10: i64 = mpow(10, n, m);
    let ans9: i64 = mpow(9, n, m);
    let ans8: i64 = mpow(8, n, m);
    let ans = (ans10 + (m - ans9) * 2 + ans8) % m;
    println!("{}", ans);
}