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 {

    static int mod = 1_000_000_007;

    public static long modPow(long a, long b) {
        if (b == 0) {
            return 1;
        }

        if (b % 2 == 0) {
            return modPow(a * a % mod, b / 2);
        } else {
            return modPow(a * a % mod, (b - 1) / 2) * a % mod;
        }
    }

    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int n = Integer.parseInt(scan.next());
        scan.close();

        if (n == 1) {
            System.out.println(0);
            return;
        }

        long ans = modPow(10, n);
        ans -= modPow(9, n);
        if (ans < 0) {
            ans += mod;
        }
        ans -= modPow(9, n);
        if (ans < 0) {
            ans += mod;
        }
        ans += modPow(8, n);
        ans %= mod;

        System.out.println(ans);
    }
}