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: Wrong Answer)

import java.util.Scanner;

 
public class Main {

	static long mod = (long) (Math.pow(10, 9) + 7);
 
	public static void main(String[] args) {
		
		Scanner sc = new Scanner(System.in);
		long n  = sc.nextLong();
		
		long temp1 = (power(9, n) + power(9, n) - power(8, n)) % mod; 
		long ans = (power(10, n) - temp1) % mod;
		
		System.out.println(ans);
		sc.close();
	}
	
	private static long power(long x, long y) {
		long culc = 1;
		
		for(long i = 1; i <= y; i++) {
			culc = culc * x % mod; 
		}

		return culc;
	}
}