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;

namespace ABC
{
    class ProgramC2
    {
        static long pow(long n, long p, int mod = (int)1e9 + 7)
        {
            if (p == 0) return 1; // nの0乗は1
            else if (p % 2 == 0)
            {
                var x = pow(n, p / 2, mod);
                return (x * x) % mod;
            }
            else
            {
                return pow(n, p - 1, mod) * n % mod;
            }
        }

        static void Main(string[] args)
        {
            var mod = (int)1e9 + 7;
            var n = int.Parse(Console.ReadLine());
            var result = 0L;
            result = pow(10, n);
            result -= (pow(9, n) * 2) % mod;
            result += pow(8, n);
            Console.WriteLine((result + mod) % mod);
        }
    }
}