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: Accepted)

import java.util.*;
import java.lang.Math;

public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
      	int n = sc.nextInt();
      	long lim = 1000000007;
      	long nums[] = new long[4];
      	long a = 1;
      	long b = 1;
      	long c = 1;
      	long c2;
      	long ans;
  
      	for(int i = 0;i < n;i++) {
          a *= 10;
          b *= 8;
          c *= 9;
          a %= lim;
          b %= lim;
          c %= lim;
        }
      	c2 = (2*c)%lim;
      	ans = a + b - c2;
      	if(ans < 0) ans += lim;
      	else ans %= lim;
           
      	System.out.println(ans);
        
	}
}