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 {

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);

		int N = sc.nextInt();

		long mod = 1000000007;

		long total = 1;
		long without_0 = 1;
		long wo_0and9 = 1;
		
		for(int i = 0; i < N; i++) {
			total = total * 10 % mod;
			without_0 = without_0 * 9 % mod;
			wo_0and9 = wo_0and9 * 8 % mod;	
		}
			
		long ans = (total - without_0 * 2 + wo_0and9) % mod;
		System.out.println(ans);
	}
}