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(
  non_snake_case,
  unused_variables,
  unused_assignments,
  unused_mut,
  unused_imports,
  dead_code
)]
use proconio::{input, marker::*};
use std::cmp::*;
use std::collections::*;
//use std::num;
//use petgraph::unionfind::UnionFind;
//use permutohedron::LexicalPermutation as _;

const MOD: i64 = 1000_000_007;
//#[fastout()]
fn main() {
  input! {
      N:usize,
  }
  // 10^N から、0を含まないものと9を含まないものをひき、0と9を含まないものを足す。
  let mut ans = 1;
  let mut x9 = 1;
  let mut x8 = 1;
  for i in 0..N{
    ans = ans * 10 % MOD;
    x9 = x9 * 9 % MOD;
    x8 = x8 * 8 % MOD;
  }
  ans = ans - x9 * 2 + x8 + (MOD*2);
  ans %= MOD;
  println!("{}", ans);
}