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.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Comparator;

public class Main {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		long n = Long.parseLong(br.readLine());

		long ans = modpow(10, n, 1000000007) % 1000000007;
		ans -= 2 * modpow(9, n, 1000000007) % 1000000007;
		ans += modpow(8, n, 1000000007) % 1000000007;
		ans = (ans + 1000000007) % 1000000007;
		System.out.println(ans % 1000000007);
	}

	static long modpow(long a, long n, long mod) {
		long res = 1;
		while (n > 0) {
			if ((n & 1) == 1)
				res = res * a % mod;
			a = a * a % mod;
			n >>= 1;
		}
		return res;
	}
}