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.Linq;
using System.Numerics;

   class Program
    {
        static void Main()
        {
            var MOD = (BigInteger)1e9 + 7;
            var N = int.Parse(Console.ReadLine());

            var ans = BigInteger.ModPow(10, N, MOD);
            ans += BigInteger.ModPow(8, N, MOD);
            var bc = (BigInteger.ModPow(9, N, MOD)*2)%MOD;
            ans = ans - bc;
            if (ans < 0) ans *= -1;
            Console.WriteLine(ans%MOD);
        }
    }