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 std::convert;

pub fn mpow<O, N, M>(n: N, m: M, md: O) -> O
where
    O: num::Integer + Copy + convert::From<N> + convert::From<M>,
    N: num::Integer + Copy,
    M: num::Integer + Copy,
{
    let mut result: O = O::one();
    let two: O = From::from(M::one() + M::one());
    let mut mm: O = From::from(m);
    let mut nn: O = From::from(n);

    while !mm.is_zero() {
        if mm.is_odd() {
            result = (result * nn) % From::from(md);
        }
        nn = (nn * nn) % From::from(md);
        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 - ans9 + m - ans9 + m + ans8) % m;
    println!("{}", ans);
}