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 std::io::*;
use std::str::*;

fn read<T: FromStr>(s: &mut StdinLock) -> T {
    let s = s.by_ref().bytes().map(|c| c.unwrap() as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect::<String>();
    s.parse::<T>().ok().unwrap()
}


fn main() {
    let s = stdin();
    let mut s = s.lock();
    let s = &mut s;

	let n = read::<i64>(s);
	let mut m = 1i64;
	for _ in 0..n {
		m = (m * 10) %  (1000000000+7);
	}
	m += 5*(1000000000+7);
	let mut m8 = 1i64;
	for _ in 0..n {
		m8 = (m8 * 8) % (1000000000+7);
	}
	let mut m9 = 1i64;
	for _ in 0..n {
		m9 = (m9 * 9) % (1000000000+7);
	}
	m9 +=  1000000000+7 ;	
	

	let x = (m - ( m9*2 - m8)  ) %  (1000000000+7);

//	println!("m={} m8={} m9={}", m, m8, m9);
	println!("{} ", x);


}