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;

namespace Ubiquity
{
    class Program
    {
        const long mod = 1000000007;
        static void Main(string[] args)
        {
            var N = long.Parse(Console.ReadLine());

            // 桁が大きいので、毎回modで割る必要がある
            // Math.Powで求めると桁が多すぎる
            long ans = Pow(10, N) - Pow(9, N) - Pow(9, N) + Pow(8, N);
            ans %= mod;
            Console.WriteLine(ans);
        }

        public static long Pow(long x, long y)
        {
            long result = 1;
            if (y > 1)
            {
                for (int i = 0; i < y; i++)
                {
                    result = result * x % mod;
                }
            }
            return result;
        }
    }
}