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)

use proconio::input;
//use itertools::Itertools;

fn main() {
    input!{n :u128};
    let filt = 10u128.pow(9) + 7;
    let mut res = 1;
    let mut temp = 1;
    let mut temp2 = 1;
    for _i in 0..n {
        res = (res * 10) % filt;
        temp = (temp * 9) % filt;
        temp2 = (temp2 * 8) % filt;
    }
    let temp3 = ((temp + temp % filt) - temp2) % filt;
    println!("{}", (res - temp3) % filt);
}