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 1.8.0) (judge verdict: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main
{
    public static void main(String[] args)
    {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC
    {
        public void solve(int testNumber, Scanner in, PrintWriter out)
        {
            int T = 1;
            while (T-- > 0)
            {
                solveOne(in, out);
            }
        }

        private void solveOne(Scanner in, PrintWriter out)
        {
            long MOD = 1_000_000_000 + 7;
            long N = in.nextInt();

            if (N == 1 || N == 2)
            {
                out.println(N == 1 ? 0 : 1);
                return;
            }

            long ans = CPUtils.modPower(10L, N, MOD);

            ans -= 2L * CPUtils.modPower(9L, N, MOD);
            ans += CPUtils.modPower(8L, N, MOD);

            ans %= MOD;
            if (ans < 0)
                ans += MOD;

            out.println(ans);
        }

    }

    static class CPUtils
    {
        public static long modPower(long base, long p, long m)
        {
            long ret = 1;
            for (; p > 0; p >>= 1, base = base * base % m)
            {
                if (p % 2 == 1)
                {
                    ret = ret * base % m;
                }
            }
            return ret;
        }

    }
}