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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		// 整数の入力
		int n = sc.nextInt();
		//if(a > 10) System.out.println(0);
		long ten = 1;
      	long nine = 1;
      	long eight = 1;
      	long m = 1000000007;
	    for(int i = 0; i < n; i++) {
          ten = (ten*10) % m;
          nine = (nine*9) % m;
          eight = (eight*8) % m;
        }
          
		System.out.println((int) ( (((ten + eight)%m + m)  - ((2*nine)%m))%m)); 
	}
}