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;

class Program
{
    static long MOD = 1000000007L;

    static void Main()
    {
        var N = long.Parse(Console.ReadLine());
        var result = ModPow(10, N);
        result -= 2 * ModPow(9, N);
        result += ModPow(8, N) % MOD;
        Console.WriteLine(result);
    }

    static long ModPow(long x, long y)
    {
        var m = x % MOD;
        for (int i = 1; i < y; i++)
        {
            m = (m * x) % MOD;
        }
        return m;
    }
}