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.*;

public class Main {
    
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long N = sc.nextLong();
        long mod = 1000000007;
        long ten = 1;
        for (int i = 0; i < N; i++) {
            ten *= 10;
            ten %= mod;
        }
        long nine = 1;
        for (int i = 0; i < N; i++) {
            nine *= 9;
            nine %= mod;
        }
        long eight = 1;
        for (int i = 0; i < N; i++) {
            eight *= 8;
            eight %= mod;
        }
        System.out.println((ten-nine-nine+eight)%mod);
    }
    
}