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.*;
class Main{
	public static long mod(long num,long a,long mod) {
		long p = 1;
		for(int i = 0; i < num; i++) {
			p = p*a%mod;
		}
		return p;
	}
	public static void main(String[] args) {
		long mod = 100000000 + 7;
		Scanner scanner = new Scanner(System.in);
		long num = scanner.nextInt();
		long result = 0;
		result = (mod(num,10,mod) - 2*mod(num,9,mod) + mod(num,8,mod))%mod;
		result = (result + mod)%mod;
		System.out.println(result);
		scanner.close();
	}
}