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: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;
using System.Numerics;

namespace ABC178
{
    class Program
    {
        static void Main(string[] args)
        {
            //var NXT = Console.ReadLine().Split().Select(double.Parse).ToArray();
            var N = long.Parse(Console.ReadLine());
            //var abcd = Console.ReadLine().Split().Select(long.Parse).ToArray();
            // var CA = Enumerable.Repeat(0, (int)N).Select(_ => Console.ReadLine().Split().Select(long.Parse).ToArray()).ToArray();
            //var L = Console.ReadLine().Split().Select(long.Parse).OrderBy(x => x).ToArray();

            var x = 1000000007L;
            var a = 1L;
            var b = 1L;
            var c = 1L;
            for (int i = 0; i < N; i++)
            {
                a = (a * 10) % x;
                b = (b * 9) % x;
                c = (c * 8) % x;

            }

            var ans = (a - ((2 * b) % x - c)) % x;
            if (ans < 0) Console.WriteLine(ans + x);
            else Console.WriteLine(ans);

        }
    }
}