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.*; 
import java.lang.*; 


public class Main{
    
	public static void main(String[] args){
		Scanner scan = new Scanner(System.in);
                
                long N = scan.nextLong();
                
                int i=0;
                long a = 1;
                while(i<N){
                    a = a*10;
                    a = a%(10*10*10*10*10*10*10*10*10+7);
                    i++;
                }
                
                int j=0;
                long b = 1;
                while(j<N){
                    b = b*9;
                    b = b%(10*10*10*10*10*10*10*10*10+7);
                    j++;
                }
                
                
                
                int k=0;
                long c = 1;
                while(k<N){
                    c = c*8;
                    c = c%(10*10*10*10*10*10*10*10*10+7);
                    k++;
                }
                
                long ans = a-(2*b-c);
                System.out.println(ans);
        }
}