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);
      
      long n = sc.nextInt();
      
      if(n == 1){
      	System.out.println(1);
      }
      else{
      	long nfact = 1;
        
        for(long i = n; i > 0; i--){
        	nfact *= i;
        }
        
        if(nfact > 1000000007){
        	nfact /= 1000000007;
        }
        
        long power = 1;
        
        for(long i = 0; i < n - 2; i++){
        	power *= 10;
        }
        
        if(power > 1000000007){
        	power /= 1000000007;
        }
        
        long total = nfact*power;
        
        
        if(total >= 1000000007){
        	total %= 1000000007;
        }
        
        
        System.out.println(total);
      }
      
    }
}