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;
import java.lang.Math;

public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        long n = sc.nextLong();

        final long MOD = 1000000007L;
        long result;
        result = powCalc(10, n) - ( 2 * powCalc(9, n) - powCalc(8, n) );
        if(result < 0){
            result = result + MOD;
        }
        System.out.println(result % MOD);
    }

    public static long powCalc(long base, long n){
        final long MOD = 1000000007L;
        long ret = 1;
        for(int i = 0; i<n; i++){
            ret *= base;
            ret %= MOD;
        }
        return ret;
    }
}