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.io.*;
import java.util.*;

public class Main {
    public static void main(String[] args) throws Exception {
        BufferedReader buffer = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(buffer.readLine());
        long mod = (int)1e9+7;
        long [] pow10 = new long[n+1];
        long [] pow8 = new long[n+1];
        long [] pow9 = new long[n+1];
        pow8[0] = pow9[0] = pow10[0] = 1;
        for (int pos = 1; pos <= n; pos++) {
            pow8[pos] = (pow8[pos-1]%mod*8)%mod;
            pow9[pos] = (pow9[pos-1]%mod*9)%mod;
            pow10[pos] = (pow10[pos-1]%mod*10)%mod;
        }
        long ans = pow10[n] - (pow8[n]+(pow9[n]%mod - pow8[n]%mod + mod)*2%mod);
        System.out.println(ans);
    }
}