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.Scanner;

public class Main {

    public static void main(String[] args) {
        
        var sc = new Scanner(System.in);
        
        int n = Integer.parseInt(sc.next());
        final long MOD = 1000000007;
        
        long a = 1;
        long b = 1;
        long c = 1;
        for(int i = 0; i < n; i++){
            a *= 10;
            a %= MOD;
            b *= 9;
            b %= MOD;
            c *= 8;
            c %= MOD;
        }
        long ans = a - b*2 + c;
        ans %= MOD;
        if(ans < 0) ans += MOD;
        System.out.println(ans);
    }
}