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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using System.Text.RegularExpressions;

namespace AtCoderBeginnerContest178
{
    class Program
    {
        static void Main(string[] args)
        {
            // 課題C - Ubiquity(2020/9/13)


            int input = int.Parse(Console.ReadLine());

            int modItem = 1000000007;

            long allPtn = 10;
            long delPtn = 9;
            long plusPtn = 8;

            for (int i = 0; i < input - 1; i++)
            {
                allPtn = allPtn * 10 % modItem;
                delPtn = delPtn * 9 % modItem;
                plusPtn = plusPtn * 8 % modItem;

            }

            long result = (allPtn - 2 * delPtn + plusPtn) % modItem;

            if (result < 0) result = result + modItem;

            Console.Write(result);


        }
    }
}