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.Text;
using System.Threading.Tasks;

namespace C
{
    class Program
    {
        const long r = 1000000007;
        static void Main(string[] args)
        {
            string line = Console.ReadLine();
            int N = int.Parse(line);

            // Ai = 0なるiが存在する
            // Ai = 9なるiが存在する
            // 全体→10^N
            // 0が存在しない→9 ^ N
            // 9が存在しない→9 ^ N
            // 0も9も存在しない→8 ^ n
            // 0か9が存在しない→9 ^ N + 9 ^ N - 8 ^ N
            // 0か9が存在しないパターンを除く→10^N - 9^N - 9^N - 8^N
            long sum = powmod(10, N) - powmod(9, N) - powmod(9, N) + powmod(8, N);
            sum %= r;
            if (sum < 0 )
            {
                sum += r;
                sum %= r;
            }

            Console.WriteLine(sum);
        }

        static long powmod(long x, long y)
        {
            long result = 1;
            for(long i = 0; i < y; i++)
            {
                result *= x;
                result = result % r;
            }
            return result;
        }
    }
}