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)
        {
            var mod = (BigInteger)Math.Pow(10,9) + 7;
            var n = int.Parse(Console.ReadLine());

            var a = BigInteger.ModPow(10, n, mod);
            var b = (BigInteger.ModPow(9, n, mod) * 2) % mod;
            var c = BigInteger.ModPow(8, n, mod);
            var ans = (a + c) % mod - b;

            
            ans %= mod;
            System.Console.WriteLine(ans);
        }

    }
}