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.*;

public class Main{
    final long MOD = 1000000007;
    void solve(){
        Scanner scan = new Scanner(System.in);
        long n = scan.nextInt();
        System.out.println((pow(10, n) % MOD - (2 * pow(9, n)) % MOD + pow(8, n) % MOD) % MOD);
    }

    long pow(long x, long n){
        if(n == 0) return 1;
        long ret = pow(x * x % MOD, n / 2);
        if((n & 1) == 1) ret = ret * x % MOD;
        return ret;
    }

    public static void main(String[] args){
        new Main().solve();
    }
}