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 final int r = 1000000000 + 7;
	public static long pow(int a, int b) {
		long ans = 1;
		for(int i = 0; i < b; ++i){
			ans *= (long)a;
			ans %= (long)r;
		}
		return ans;
	}
	public static void main(String args[]) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		sc.close();
		int ans = 0;
		if(n > 1){
			long tmp = pow(10, n) - pow(9, n) - pow(9, n) + pow(8, n);
			tmp %= r;
			ans = (int)tmp;
		}
		System.out.println(ans);
	}
}