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.Scanner;
 
public class Main {
    private static long mod = (long) (1e9 + 7);
    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();
        long ans = power(10, n) - 2 * power(9, n) + power(8, n);
        ans = (ans % mod) + mod;
        System.out.println(ans);
    }
 
 
    private static long power(long a, long b) {
        long x = 1, y = a;
        while (b > 0) {
            if (b % 2 != 0) {
                x = (x * y) % mod;
            }
            y = (y * y) % mod;
            b /= 2;
        }
        return x % mod;
    }
}