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)

#![allow(unused_imports)]
#![allow(unused_variables)]
#![allow(dead_code)]
use proconio::input;
use proconio::marker::*;
use std::cmp::{min, max};
use std::collections::{HashSet, HashMap, BinaryHeap, VecDeque};

static MOD: i64 = 1e9 as i64 + 7;

fn modpow(a: i64, n: usize) -> i64{
    if n == 0{
        return 1i64
    }
    let mut res = modpow((a * a) % MOD, n / 2);
    if n % 2 == 1{
        res *= a;
        res %= MOD;
    }
    res
}

fn main() {
    input! {
        n: usize,
    }
    let mut ans = modpow(10, n) - modpow(9, n) - modpow(9, n) + modpow(8, n);
    ans %= MOD;
    ans = (ans + MOD) % MOD;
    println!("{}", ans);
}