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 1.8.0) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        try (Scanner in = new Scanner(System.in)) {
            int N = in.nextInt();

            long mod = (long) (1e9 + 7);

            long countAll = 1;
            for (int i = 0; i < N; i++) {
                countAll *= 10;
                countAll %= mod;
            }

            long count9 = 1;
            for (int i = 0; i < N; i++) {
                count9 *= 9;
                count9 %= mod;
            }

            long count8 = 1;
            for (int i = 0; i < N; i++) {
                count8 *= 8;
                count8 %= mod;
            }

            long res = countAll;
            res += -count9 + mod;
            res %= mod;
            res += -count9 + mod;
            res %= mod;
            res += count8;
            res %= mod;

            System.out.println(res);
        }
    }
}