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 {


    public static void main(String args[]) {
        Scanner scan = new Scanner(System.in);

        int n = scan.nextInt();

        long[] non = new long[n];
        long[] one = new long[n];
        long[] nine = new long[n];
        long[] both = new long[n];
        long mod = 1000000007;


        for (int i=0; i<n; i++) {

            if (i==0) {
                non[i] = 10;
                one[i] = 1;
                nine[i] = 1;
                both[i] = 0;
            } else {
                non[i] = non[i-1] * 8 % mod;
                one[i] = (non[i-1] + one[i-1] * 9) % mod;
                nine[i] = (non[i-1] + nine[i-1] * 9) % mod;
                both[i] = (one[i-1] + nine[i-1] + both[i-1] * 10) % mod;
            }
        }

        System.out.println(both[n-1]);


    }
}