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.util.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        long mod = 1000000000 + 7;
        long answer = (powMod(10,n,mod)-2*powMod(9,n,mod)+powMod(8,n,mod))%mod;
        answer = (answer+mod)%mod;
        System.out.println(answer);
    }
    public static long powMod(long a, long b, long mod) {
        long p = 1;
        if (b==1) {
            return a;
        }else if(b==2) {
            return (a*a)%mod;
        }else {
            long tmp = powMod(a,b/2,mod);
            long answer = (tmp*tmp)%mod;
            if (b%2 == 1) {
                answer = (answer * a)%mod;
            }
            return answer;
        }
    }
}