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() {
    proconio::input! {
        n: usize,
    }

    let m = 1000000007;

    let mut dp = vec![vec![0 as usize; 4]; n + 1];

    dp[0][0] = 1;

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

        dp[i + 1][1] = (dp[i][0] + dp[i][1] * 9) % m;
        dp[i + 1][2] = (dp[i][0] + dp[i][2] * 9) % m;

        dp[i + 1][3] = (dp[i][1] + dp[i][2] + dp[i][3] * 10) % m;
    }

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