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)

const M: u64 = 1000_000_007;

fn main() {
    proconio::input! {
        n: u64,
    }

    if n <= 1 {
        println!("0");
    } else {
        let mut v = (pow(10, n) + pow(8, n)) % M;
        let no09 = pow(9, n) * 2 % M;
        if v < no09 {
            v += M;
        }
        println!("{}", v - no09);
    }
}

fn pow(mut a: u64, mut n: u64) -> u64 {
    let mut r = 1;
    while n > 0 {
        if n & 1 > 0 {
            r = r * a % M;
        }
        a = a * a % M;
        n >>= 1;
    }
    r
}