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.Collections.Generic;
using System.Linq;
using System.Reflection.Metadata.Ecma335;

namespace AtCoder0913
{
    class Program
    {
        static void Main(string[] args)
        {
            long N = long.Parse(Console.ReadLine());
            //long[] N = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray() ;
            long all = 1;
            long tasu = 1;
            long hiku = 1;
            long hiku2 = 1;
            long ans = 0;
            long mod = 1000000000 + 7;

            for (var i = 0; i < N; i++)
            {


                all = all * 10 % mod;
                hiku = hiku * 9% mod;
                hiku2 = hiku2 * 9 % mod ;
                tasu =  tasu *8 % mod;

            }
            ans = (all + tasu - hiku - hiku2) % mod;
            if(ans < 0)
            {
                ans += mod;
            }
            Console.WriteLine(ans);

        }
    }
}