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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Atcoder178
{
    class Program
    {
        const long Mod = 1000000007;

        static void Main(string[] args)
        {

            var n = long.Parse(Console.ReadLine());

            var ans = powMod(10, n);
            ans -= powMod(9, n) * 2 % Mod;
            ans += powMod(8, n);

            Console.WriteLine(ans % Mod);

            // これだとnの桁数が大きいとNaNになってしまう
            //var ans = Math.Pow(10, n) % Mod;
            //ans -= Math.Pow(9, n) % Mod * 2;
            //ans += Math.Pow(8, n);
        }

        private static long powMod(long x, long y)
        {
            var ans = 1L;
            for(var i = 0L; i < y; i++)
            {
                ans *= x;
                ans %= Mod;
            }

            return ans;
        }
    }
}