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);
		long n = sc.nextLong();
		long m = 1000000007;
		long ans = power(10,n,m);
		long ans1 = power(9,n,m);
		long ans2 = power(8,n,m);
		long ans3 = ((ans+ans2)%m-(2*ans1)%m+m)%m;
		System.out.println(ans3);
	}
	public static long power(long x, long y, long m){
		long res =1;
		x=x%m;
		if(x==0){
			return 0;
		}
		while(y>0){
			if((y&1)==1){
				res=(res*x)%m;
			}
			y=y>>1;
			x=(x*x)%m;
		}
		return res;
	}
}