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)

fn main() {
	let mut s = String::new();
	use std::io::Read;
	std::io::stdin().read_to_string(&mut s).unwrap();
	let mut s = s.split_whitespace();
	const MOD: i64 = 1000000007;
	let n: usize = s.next().unwrap().parse().unwrap();
	let a = pow_mod(9, n, MOD);
	let b = pow_mod(8, n, MOD);
	let all = pow_mod(10, n, MOD);
	let c = (2 * a + MOD - b) % MOD;
	println!("{}", (all + MOD - c) % MOD);
}

pub fn pow_mod<T, U>(a: T, mut b: U, modulus: T) -> T
where
	T: num::PrimInt,
	U: num::PrimInt + num::Integer + num::Unsigned,
{
	let mut r = T::one();
	let mut a = a % modulus;
	while b > U::zero() {
		if b.is_odd() {
			r = r * a % modulus;
		}
		a = a * a % modulus;
		b = b / (U::one() + U::one());
	}
	r
}