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 {
    static long MOD = 1000000007;
    public static void main(String[] args) throws Exception {
        Scanner sc =new Scanner(System.in);
        long N = sc.nextLong();
        long ans = 1;
        long A = 1;
        long B = 1;
        long C = 1;

        for (int i = 0; i < N; i++) {
            A = A * 10 % MOD;
        }

        for (int i = 0; i < N; i++) {
            B = B * 9 % MOD;
        }

        for (int i = 0; i < N; i++) {
            C = C * 8 % MOD;
        }

        ans = A - B - B + C;
        ans %= MOD;
        ans = (ans + MOD) % MOD;
        System.out.println(ans);
		sc.close();
    }
}