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 C
{
	class Program
	{
		static void Main(string[] args)
		{
			double n = int.Parse(Console.ReadLine());
			double div = 1e9 + 7;
			double all = 1;
			double non0 = 1;
			double non9 = 1;
			double non0non9 = 1;

			for (int i = 0; i < n; i++)
			{
				all = all * 10 % div;
				non0 = non0 * 9 % div;
				non9 = non9 * 9 % div;
				non0non9 = non0non9 * 8 % div;
			}

			Console.WriteLine((all - non0 - non9 + non0non9) % div);
		}
	}
}