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.Reflection;

namespace ABC178
{
    class Program
    {
        static void Main()
        {
            // 全体 - (0がない場合 + 9がない場合 - 0,9がない場合)
            var n = long.Parse(Console.ReadLine());

            var mod = new Modulo(0);
            Console.WriteLine(mod.Pow(10, n) - (mod.Multiply(mod.Pow(9, n), 2) - mod.Pow(8, n)));
        }
    }

    public class Modulo
    {
        private readonly long M = 1000000007;
        private readonly long[] m_facs;

        public Modulo(long n, long m = -1)
        {
            m_facs = new long[n + 1];
            m_facs[0] = 1;
            for (long i = 1; i <= n; ++i)
            {
                m_facs[i] = Multiply(m_facs[i - 1], i);
            }
            if (m != -1)
                M = m;
        }

        public long Multiply(long a, long b)
        {
            return (long)(Math.BigMul((int)a, (int)b) % M);
        }

        public long Factorial(long n)
        {
            return m_facs[n];
        }

        public long Pow(long a, long m)
        {
            switch (m)
            {
                case 0:
                    return 1;
                case 1:
                    return a;
                default:
                    long p1 = Pow(a, m / 2);
                    long p2 = Multiply(p1, p1);
                    return ((m % 2) == 0) ? p2 : Multiply(p2, a);
            }
        }

        public long Divide(long a, long b)
        {
            return Multiply(a, Pow(b, M - 2));
        }

        public long Combination(long n, long r)
        {
            if (n < r) { return 0; }
            if (n == r) { return 1; }
            long res = Factorial(n);
            res = Divide(res, Factorial(r));
            res = Divide(res, Factorial(n - r));
            return res;
        }

        public long DuplicateCombination(long n, long r)
        {
            n = n + r - 1;
            if (n < r) { return 0; }
            if (n == r) { return 1; }
            long res = Factorial(n);
            res = Divide(res, Factorial(r));
            res = Divide(res, Factorial(n - r));
            return res;
        }

        public long Permutation(long n, long r)
        {
            if (n < r) { return 0; }
            if (n == r) { return 1; }
            long res = Factorial(n);
            res = Divide(res, Factorial(n - r));
            return res;
        }
    }
}