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.Numerics;
using System;

public class Hello
{
    public static int MOD = 1000000007;
    public static void Main()
    {
        var n = int.Parse(Console.ReadLine().Trim());
        getAns(n);
    }
    static void getAns(int n)
    {
        var a1 = BigInteger.ModPow(10, n, MOD);
        var a2 = BigInteger.ModPow(9, n, MOD);
        var a3 = BigInteger.ModPow(8, n, MOD);
        var ans = (a1 - 2 * a2 + a3) % MOD;
        Console.WriteLine(ans);
    }
}