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: Wrong Answer)

use proconio::{fastout, input};

#[fastout]
fn main() {
    input! {
        n: i128,
    }

    let mut sum_10: i128 = 1;
    let mut sum_8: i128 = 1;
    let mut sum_9: i128 = 1;
    for _ in 0..n {
        sum_10 *= 10;
        sum_10 %= 1000000007;
        sum_8 *= 8;
        sum_8 %= 1000000007;
        sum_9 *= 9;
        sum_9 %= 1000000007;
    }

    let mut ans: i128 = 0;
    ans = sum_10 - sum_9;
    ans += sum_8 - sum_9;
    ans %= 1000000007;
    println!("{}", ans);
}