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 ABC178C
{
    class Program
    {
        static long mod = 0;
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            mod = (long)Math.Pow(10, 9) + 7;
            long ans = Njou(N, 10);
            long no0 = Njou(N, 9);
            long no9 = Njou(N, 9);;
            long no09 = Njou(N, 8);
            ans += mod - no0;
            ans %= mod;
            ans += mod - no9;
            ans %= mod;
            ans += no09;
            ans %= mod;
            Console.WriteLine(ans);


        }
        static long Njou(int N,long a)
        {
            string S = Convert.ToString(N, 2);
            int l = S.Length;
            long ans = 1;
            for(int i = l - 1; i >= 0; i--)
            {
                if (S[i].ToString() == "1")
                {
                    ans *= a;
                    ans %= mod;
                }
                a *= a;
                a %= mod;
            }
            return ans;
        }
    }
}