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.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		long N = long.Parse(Console.ReadLine());
		long mod = 1000000007;
		long A = 10;
		long B = 9;
		long C = 8;
		for(var i=1;i<N;i++){
			A = A * 10 % mod;
			B = B * 9 % mod;
			C = C * 8 % mod;
		}
		long ans = (A - B - B + C + mod * 4) % mod;
		Console.WriteLine(ans);
	}
}