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::input;

fn main() {
    input! {
        n: usize,
    }
    let m = 1000000007;
    let mut dp = vec![vec![vec![0usize; 2]; 2]; n + 1];
    dp[0][0][0] = 1;

    for i in 1..=n {
        dp[i][0][0] = dp[i - 1][0][0] * 8 % m;
        dp[i][0][1] = (dp[i - 1][0][0] + dp[i - 1][1][0]) % m + dp[i - 1][0][1] * 8 % m;
        dp[i][1][0] = (dp[i - 1][0][0] + dp[i - 1][0][1]) % m + dp[i - 1][1][0] * 8 % m;
        dp[i][1][1] = (dp[i - 1][0][1] + dp[i - 1][1][0]) % m + dp[i-1][1][1] * 10 % m;

        dp[i][0][0] %= m;
        dp[i][0][1] %= m;
        dp[i][1][0] %= m;
        dp[i][1][1] %= m;
    }

    println!("{}", dp[n][1][1]);
}