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, non_snake_case, dead_code, non_upper_case_globals)]
use {
    proconio::{marker::*, *},
    std::{cmp::*, collections::*, mem::*},
};

#[fastout]
fn main() {
    input! {//
        n:i64,
    }
    let mut md = ModComb::new(MX, MOD);
    if n < 2 {
        println!("{}", 0);
        return;
    }
    if n == 2 {
        println!("{}", 2);
        return;
    }
    let mut ans = 1i64;
    ans = mod_pow(10, n, MOD) - 2 * mod_pow(9, n, MOD) + mod_pow(8, n, MOD);
    ans = (ans + MOD + MOD) % MOD;
    println!("{}", ans);
}
const MX: usize = 1010101;
/// x ^ n % m
pub fn mod_pow(x: i64, n: i64, m: i64) -> i64 {
    let mut res = 1;
    let mut x = x % m;
    let mut n = n;
    while n > 0 {
        if n & 1 == 1 {
            res = (res * x) % m;
        }
        x = (x * x) % m;
        n >>= 1;
    }
    res
}
struct ModComb {
    fact: Vec<i64>,
    fact_inv: Vec<i64>,
    n: usize,
    p: i64,
}
impl ModComb {
    fn initialize(&mut self) {
        let n = self.n;
        self.fact[0] = 1;
        for i in 1..n {
            self.fact[i] = (self.fact[i - 1] * i as i64) % self.p;
        }
        self.fact_inv[n - 1] = mod_pow(self.fact[n - 1], self.p - 2, self.p);
        for i in (0..n - 1).rev() {
            self.fact_inv[i] = (self.fact_inv[i + 1] * (i + 1) as i64) % self.p;
        }
    }
    fn new(max_n: usize, p: i64) -> ModComb {
        let mut ft = ModComb {
            fact: vec![0; max_n + 1],
            fact_inv: vec![0; max_n + 1],
            n: max_n + 1,
            p: p,
        };
        ModComb::initialize(&mut ft);
        ft
    }
    fn fact(&self, n: usize) -> i64 {
        self.fact[n]
    }
    fn comb(&self, n: i64, k: i64) -> i64 {
        if n < k {
            return 0;
        }
        (self.perm(n, k) * self.fact_inv[k as usize]) % self.p
    }
    fn perm(&self, n: i64, k: i64) -> i64 {
        if n < k {
            return 0;
        }
        self.fact[n as usize] * self.fact_inv[(n - k) as usize] % self.p
    }
    fn nsk(&self, n: i64, k: i64) -> i64 {
        if n < k {
            return 0;
        }
        let mut res = 0;
        for i in 0..k + 1 {
            let v = self.comb(k, i) * mod_pow(i, n, self.p) % self.p;
            if (k - i) % 2 == 1 {
                res = (res + self.p - v) % self.p;
            } else {
                res = (res + v) % self.p;
            }
        }
        return res * self.fact_inv[k as usize] % self.p;
    }
}
const MOD: i64 = 1000000007;