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# (Mono-mcs 6.8.0.105) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Text;
using System.Collections;
using System.Collections.Generic;

namespace AtCoder
{
	class Program
	{
		static void Main(string[] args)
		{
			var n = ReadLineInt();
			// double cnt = nC2(n)*2;
			var sur = 1000000007L;
			var ans = longPow(10, n, sur) - longPow(9, n, sur)*2L + longPow(8, n, sur);
			ans += sur*2;
			Console.WriteLine(ans%sur);
		}

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

		public static int nCm(int n, int m)
		{
			if (n == 0) return 0;
			if (m == 0) return 1;
			return n * nCm(n - 1, m - 1) / m;
		}

		public static double nC2(double n)
		{
			return (n*(n-1))*0.5;
		}

		public static string ReadLine()
		{
			return Console.ReadLine();
		}

		public static int ReadLineInt()
		{
			return int.Parse(ReadLine());
		}

		public static string[] ReadLineStringSplit(char s = ' ')
		{
			return ReadLine().Split(s).ToArray();
		}

		public static int[] ReadLineIntSplit(char s = ' ')
		{
			return ReadLine().Split(s).Select(x => int.Parse(x)).ToArray();
		}

		public static long[] ReadLineLongSplit(char s = ' ')
		{
			return ReadLine().Split(s).Select(x => long.Parse(x)).ToArray();
		}
	}
}