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.io.BufferedReader;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Main {
    
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new java.io.InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out);
        StringTokenizer st = new StringTokenizer(br.readLine());

        int N = Integer.parseInt(st.nextToken());

        long tmp10 = 1;
        long tmp9 = 1;
        long tmp8 = 1;
        long cut = 1000000000 + 7;

        long ans = 0;

        for(int i = 0; i < N; i++) {
            tmp10 = (tmp10 * 10) % cut ;
            tmp9 = (tmp9 * 9) % cut ;
            tmp8 = (tmp8 * 8) % cut ;
        }

        ans = (tmp10 - tmp9 * 2 + tmp8) % cut;

        if(ans < 0) ans += cut;
        
        pw.println(ans);
        br.close();
        pw.close();
    }
}