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)

#![allow(unused_imports)]
#![allow(non_snake_case)]

use proconio::input;
use std::collections::HashMap;

fn main() {
    input! {
        s: usize,
    }

    let MOD: usize = 10usize.pow(9) + 7;

    let mut list = vec![0; s + 5];
    list[0] = 1;
    list[3] = 1;
    list[4] = 1;
    list[5] = 1;

    for i in 6..(s + 1) {
        for j in 0..(i - 2) {
            list[i] += list[j] % MOD;
        }
        list[i] = list[i] % MOD;
    }
    println!("{}", list[s]);
}