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

using E = System.Linq.Enumerable;

public class Program
{
    const long Mod = (long)1e9 + 7;

    public static void Main()
    {
        var n = int.Parse(Console.ReadLine());

        var dp = new (long Both, long One, long None)[n + 2];
        dp[0] = (0, 0, 1);
        for (int i = 1; i < dp.Length; ++i)
        {
            var x = dp[i - 1];
            x.Both *= 10; x.Both %= Mod;
            x.Both += x.One; x.Both %= Mod;
            x.One *= 9; x.One %= Mod;
            x.One += x.None * 2 % Mod; x.One %= Mod;
            x.None *= 8; x.None %= Mod;
            dp[i] = x;
        }

        Console.WriteLine(dp[n].Both);
    }
}