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;

const MOD: u64 = 1_000_000_007;

fn main() {
    input!(n: usize);

    // dp[i][j]: 長さ i, |{0,9} ∩ {A_i}| = j
    let mut dp = vec![[0; 3]; n + 1];
    dp[0][0] = 1;
    for i in 0..n {
        for j in 0..3 {
            // j を変えない: 1...8 + すでに使った j 個
            dp[i + 1][j] += dp[i][j] * (8 + j as u64);
            dp[i + 1][j] %= MOD;
        }
        for j in 0..2 {
            // j を増やす: 0, 9 - すでに使った j 個
            dp[i + 1][j + 1] += dp[i][j] * (2 - j as u64);
            dp[i + 1][j + 1] %= MOD;
        }
    }
    let ans = dp[n][2];

    println!("{}", ans);
}