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 {
    public static void main(String[] args) throws Exception {
        int n = 0;
        final int MOD = 1_000_000_007;
        try (Scanner s = new Scanner(System.in)) {
            n = s.nextInt();
        }
        long p = modPow(10, n, MOD) - 2 * modPow(9, n, MOD) + modPow(8, n, MOD);
        p %= MOD;
        System.out.println(p >= 0 ? p : p + MOD);
    }
    
    private static long modPow(int base, int pow, int mod) {
        long a = base;
        long result = 1;
        for (int i = 1; i <= pow; i <<= 1) {
            if ((pow & i) != 0) {
                result = (result * a) % mod;
            }
            a = (a * a) % mod;
        }
        return result;
    }
}