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)

use proconio::{input, fastout};

const MOD: u64 = 1_000_000_007;
pub fn pow_mod(x: u64, n: u64) -> u64 {
    let mut x = x;
    let mut n = n;
    let mut res = 1;
    while n > 0 {
        if n & 1 == 1 {
            res = res * x % MOD
        }
        x = x * x % MOD;
        n >>= 1;
    }
    res
}

#[fastout]
fn main() {
    input! {
        n: u64
    }
    let a = pow_mod(10, n);
    let b = pow_mod(9, n);
    let c = pow_mod(8, n);
    let mut res = (a + c - (b * 2)) % MOD;
    res = (res + MOD) % MOD;
    println!("{}", res);
}