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 {
	public static void main(String[] args){

		Scanner sc = new Scanner(System.in);
		long N = sc.nextLong();

		if(N==1) {
			System.out.println(0);
			return;
		}
		if(N==2) {
			System.out.println(1);
			return;
		}

		long A = (long) 1;
		long B = (long) 2;
		long C = (long) 1;
		long limit = (long) Math.pow(10,9) + 7;

        for(int i = 0; i < N; i++) {
			A *= 10;
			if(A > limit) {
				A = A%limit;
			}
		}
		for(int i = 0; i < N; i++) {
			B *= 9;
			if(B > limit) {
				B = B%limit;
			}
		}
		for(int i = 0; i < N; i++) {
			C *= 8;
			if(C > limit) {
				C = C%limit;
			}
		}
		
		long result = A - B + C;
      	if(result >= limit) {
			result = result%limit;
		}

		System.out.println(result);
		return;
	}

}