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;

fn main() {
  input! {
    n: u32,
  }
  //1)少なくとも1桁は0 <> 0を含まない
  //2)少なくとも1桁は9 <> 9を含まない
  //3)ans = 1 AND 2: 1' OR 9' = 1' + 2' - (1'AND 2')
  // 
  //nC2 * 2 * 10 nC2 = n*(n-1)/2
  //0 9 0, 0 9 1, 0 9 2, 0 9 3, .. 0, 9, 9 : 10
  //0 0 9, 0 1 9, .., 0 8 9 : 9
  //1 0 9, 2 0 9, .., 9 0 9 : 10
  //29 * 2 = 58T
  let d = 10_i32.pow(9) + 7;
  let all = 10_i32.pow(n);
  let n1 =  9_i32.pow(n) * 2;//) % d;//1' + 2'
  let m1 = 8_i32.pow(n);//1' AND 2' 1~8^2
  let ans = (all - (n1 - m1)) % d;
  //println!("all = {}, n1 = {}, m1 = {}", all, n1, m1);
  println!("{}", ans);
}