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 s  = new Scanner(System.in);
          	long a = s.nextInt();
          	long mod = (long)1e9 + 7;
    		long total = 10;
          	long totalwithout = 8;
          long totalw = 9;
          	for(int i = 0;i<a-1;i++) {
              total = (total*10)%mod;
          	totalwithout = (totalwithout*8)%mod;
              totalw = (totalw*9)%mod;
            }
          long ans1 = (2*totalw - totalwithout + mod)%mod;
          long ans  = (total - ans1 + mod)%mod;
          	System.out.println(ans);	
           }
    }