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 mut dp = vec![vec![vec![0_i64; 2]; 2]; n + 1];
    dp[0][0][0] = 1;
    for i in 0..n {
        for j in 0..2 {
            for k in 0..2 {
                for d in 0..=9 {
                    let j_next = if j == 1 || d == 0 { 1 } else { 0 };
                    let k_next = if k == 1 || d == 9 { 1 } else { 0 };
                    dp[i + 1][j_next][k_next] += dp[i][j][k];
                    dp[i + 1][j_next][k_next] %= 1_000_000_007;
                }
            }
        }
    }
    let ans = dp[n][1][1];
    println!("{}", ans);
}