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(non_snake_case)]
use std::*;
use proconio::{input, fastout, marker::*};

fn powmod(x:i64 , y:i64) -> i64 {
  let MOD = 10i64.pow(9)+7;
  let mut ans:i64 = 1;
  for _i in 0..y {
      ans = ans*x%MOD;
  }
  ans
}

fn better_mod(x:i64 , y:i64) -> i64 {
  let mut res = x%y;
  if (res < 0){ res += y;}
  res
}

#[fastout]
fn main() {
  input!{
    n:i64
  }
  let MOD = 10i64.pow(9)+7;
  println!("{}",(better_mod(better_mod(powmod(10,n)-powmod(9,n),MOD)-powmod(9,n),MOD)+powmod(8,n))%MOD);
}