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)

#![allow(dead_code,unused_variables)]
use proconio::{fastout, input};
const MOD : usize = 1_000_000_007;
#[fastout]
fn main() {
    input! {
        n: usize,
    }

    let mut add = pow(10,n,MOD) + pow(8,n,MOD);
    let sub = 2 * pow(9,n,MOD);
    while sub > add{
        add += MOD;
    }
    let ans = add - sub;
    println!("{}",ans%MOD);

}

fn pow(x : usize, k:usize ,md: usize) -> usize{
    let mut tmp = 1;
    let mut m = k;
    let mut d = x;
    while m > 0{
        if m&1 == 1{
            tmp = (tmp * d) % md;
        }
        d = (d * d) % md;
        m >>= 1;
    }
    tmp
}