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.io.BufferedReader;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.stream.Stream;

public class Main {

	public static void main(String[] args) {
		try (Stream<String> lines = new BufferedReader(new InputStreamReader(System.in)).lines()) {
			new Main().exec(lines.toArray(String[]::new));
		}
	}

	void exec(String[] args) {
		int N = Integer.parseInt(args[0].split(" ")[0]);
		System.out.println(bi(10).pow(N).subtract(bi(9).pow(N).multiply(bi(2))).add(bi(8).pow(N)).remainder(bi(10).pow(9).add(bi(7))));
	}

	BigInteger bi(int n) {
		return new BigInteger(String.valueOf(n));
	}

}