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.math.BigInteger;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		sc.close();

		if (N <= 1) {
			System.out.print(0);
			return;
		} else if (N == 2) {
			System.out.print(2);
			return;
		}

		BigInteger all = new BigInteger("10").pow(N);
		BigInteger dame1 = new BigInteger("8").pow(N);
		BigInteger dame2 = new BigInteger("9").pow(N).multiply(BigInteger.TWO);
		System.out.print(all.subtract(dame2).add(dame1).remainder(new BigInteger("1000000007")));
	}
}