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;
using System.Numerics;

namespace C
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            int Mod = (int)Math.Pow(10, 9) + 7;
            BigInteger ans = 0;
            ans += BigInteger.ModPow(10, n, Mod);
            ans -= BigInteger.ModPow(9, n, Mod)*2;
            ans += BigInteger.ModPow(8, n, Mod);
            if (ans < 0) ans += Mod;
            Console.WriteLine(ans % Mod);

        }
    }
}