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(dead_code)]
use std::cmp;
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, LinkedList, VecDeque};

const MOD: u64 = 1_000_000_007;

pub fn pow_mod(mut x: u64, mut y: u64, modv: u64) -> u64 {
    let mut ret: u64 = 1;
    while y > 0 {
        if (y & 1) != 0 {
            ret = ret * x % modv;
        }
        y >>= 1;
        x = x * x % modv;
    }
    ret
}

fn main() {
    proconio::input! {
        n: u64
    }

    println!("{}", (2*MOD + pow_mod(10, n, MOD) -2* pow_mod(9, n, MOD) + pow_mod(8,n, MOD)) % MOD);
}