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::{fastout, input};
use std::io::*;
use std::str::FromStr;

use std::cmp::{max, min};
use std::collections::{BinaryHeap, HashMap, HashSet, VecDeque};

const MOD: i64 = 1_000_000_007;

fn main() {
    input! {
        n: usize,
    }
    if n < 2 {
        println!("0");
        return;
    }

    let mut dp: Vec<Vec<i64>> = vec![vec![0; 4]; n + 1];
    dp[0][0] = 1;

    // for  in 0..n {
    //     dfs(cn + 1, map, limit);

    // }
    let mut cnt = 1;
    loop {
        if cnt == n + 1 {
            break;
        }
        dfs(cnt, &mut dp);
        cnt += 1;
    }
    
    // println!("{:?}", dp);

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

fn dfs(cn: usize, map: &mut Vec<Vec<i64>>) {

    // not 0, and not 9
    map[cn][0] += map[cn-1][0] * 8;
    map[cn][0] %= MOD;
    map[cn][1] += map[cn-1][0];
    map[cn][1] %= MOD;
    map[cn][2] += map[cn-1][0];
    map[cn][2] %= MOD;

    // 0, and not 9
    map[cn][1] += map[cn-1][1] * 9;
    map[cn][1] %= MOD;
    map[cn][3] += map[cn-1][1];
    map[cn][3] %= MOD;

    // not 0, and 9
    map[cn][2] += map[cn-1][2] * 9;
    map[cn][2] %= MOD;
    map[cn][3] += map[cn-1][2];
    map[cn][3] %= MOD;

    // 0, and 9
    map[cn][3] += map[cn-1][3] * 10;
    map[cn][3] %= MOD;
}