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.*;
	import java.util.Map.Entry;
	 
	 
	 class Main {
		 static int mod =  (int) (Math.pow(10,9)+7);
//		 static int mod =  (int) 998244353;
		 static List<ArrayList<Integer>> list= new ArrayList<ArrayList<Integer>>();
		 public static void main(String[] args) {
	    	
	        Scanner sc = new Scanner(System.in);
	        long N = sc.nextInt();	
	        long ans=1;
	        for(int i=0;i<N;i++) {
	        	ans=(ans*10)%mod;
	        }
	        long t=2;
	        for(int i=0;i<N;i++) {
	        	t=(t*9)%mod;
	        }
	        long t2=1;
	        for(int i=0;i<N;i++) {
	        	t2=(t2*8)%mod;
	        }
	        ans=(ans-t+t2+mod)%mod;
	        
	        
	        System.out.println(ans);
		 }
		 
	}