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.*;

public class Main {
	static Scanner scan = new Scanner(System.in);
	
	public static void main(String[] args) {
		
		int n = scan.nextInt();
		long ten = 1;
		long kaizyo = 1;
		long mod = 1000000007;
		
		for(int i=1;i<=n-2;i++) {
			ten = (ten*10)%mod;
		}
		
		for(int i=1;i<=n;i++) {
			kaizyo = (kaizyo*i)%mod;
		}
		
		if(n==1) {
			System.out.println(0);
		}else if(n==2) {
			System.out.println(2);
		}else {
			System.out.println((kaizyo*ten)%mod);
		}
		
		
		
		
	}
	
	
	public static int gcd(int x,int y) {
		if(x%y == 0) {
			return y;
		}else {
			return gcd(y,x%y);
		}
	}
	
}