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.Scanner;

public class Main {

    public static final int MOD = 1000000007;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = Integer.parseInt(sc.next());
        long ans = modPow(10, n) - modPow(9, n) - modPow(9, n) + modPow(8, n);
        System.out.println(ans);
    }

    // 繰り返し２乗法
    private static int modPow(int n, int p) {
        long res = 1;
        long a = n;
        for (a %= MOD; p > 0; a = a * a % MOD, p >>= 1) {
            if ((p & 1) > 0) {
                res = res * a % MOD;
            }
        }
        return (int) res;
    }
}