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: Time Limit Exceeded)

import java.math.BigDecimal;
import java.util.Scanner;

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

		Scanner sc = new Scanner(System.in);

		// 整数の入力
		int a = sc.nextInt();

		BigDecimal b = new BigDecimal(10).pow(a);
		BigDecimal c = new BigDecimal(9).pow(a);
		BigDecimal d = new BigDecimal(8).pow(a);

		System.out.println(b.subtract(c).subtract(c).add(d).remainder(new BigDecimal(1000000007)));
	}
}