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;

fn main() {
    input! {
        n: u128,
    }

    let div = 1000000007;
    if n == 1 {
        println!("0");
    } else {
        println!("{}", expo(n, div));
    }
}

fn expo(time: u128, div: u128) -> u128 {
    let mut ans = 0;
    for i in 1..time {
        if i % 2 == 0 {
            ans += (2 * combination(time, i) % div) * (9_u128.pow((time - i) as u32) % div);
            ans %= div;
        }
    }
    ans
}

fn combination(mut n: u128, k: u128) -> u128 {
    let mut result = 1;
    for i in 1..=k {
        result = result * n / i;
        n = n - 1;
    }
    result
}