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;

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

            long a10 = 1;
            long a9 = 1;
            long a8 = 1;

            for (int i = 0; i < N; i++)
            {
                a10 *= 10;
                a10 %= MOD;
                a9 *= 9;
                a9 %= MOD;
                a8 *= 8;
                a8 %= MOD;
            }
            long result = a10 - 2 * a9 + a8;
            result %= MOD;
            if (result < 0) result += MOD;
            Console.WriteLine(result);
        }
    }
}