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 proconio::*;
const MOD: usize = 1000000007;

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

    let mut ans = vec![0usize; 4];
    ans[0] = 1usize;

    for _ in 0..n {
        let tmp = ans.clone();
        ans[0] = tmp[0] * 8 % MOD;
        ans[1] = (tmp[1] * 9 + tmp[0]) % MOD;
        ans[2] = (tmp[2] * 9 + tmp[0]) % MOD;
        ans[3] = (tmp[1] + tmp[2] + tmp[3] * 10) % MOD;
    }

    println!("{}", ans[3]);
}