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;
class Program
{
    static void Main(string[] args)
    {
        string a = Console.ReadLine(); //標準入力
        

        int N = int.Parse(a);
        
        if(N == 1)
        {
            Console.WriteLine("{0}", 0);
            return;
        }
        
        decimal an = 0;
        decimal bn = 8;
        decimal cn = 1;
        decimal dn = 1;
        
        for (int i = 1;i< N; i++)
        {
            decimal an1 = an * 10 + cn + dn;
            decimal bn1 = bn * 8;
           decimal  cn1 = cn * 9 + bn;
            decimal dn1 = dn * 9 + bn;

            an = an1;
            bn = bn1;
            cn = cn1;
            dn = dn1;

            an = an % (decimal)(Math.Pow(10, 9) + 7);
           bn = bn % (decimal)(Math.Pow(10, 9) + 7);
           cn = cn % (decimal)(Math.Pow(10, 9) + 7);
           dn = dn % (decimal)(Math.Pow(10, 9) + 7);

        }
        Console.WriteLine("{0}", an);
    }

}
//2,2
//1,0
//869121,2511445