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.math.RoundingMode;
import java.math.BigDecimal;
 
 
public class Main{
	public static void main (String[] args){
		Scanner sc = new Scanner(System.in);
		long n = sc.nextInt();
		long mod = 1000000007;
		long ans = (powmod(10,n)-powmod(9,n)*2+powmod(8,n))%mod;
		ans = (ans + mod) % mod;
		System.out.println(ans);
	}
	public static long powmod(long x, long n){
		long mod = 1000000007;
      	long res = 1;
      
		for(long i = 0; i < n; i++){
			res = res * x % mod;
		}
		return res;
	}
}