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.Numerics;

namespace ConsoleApp2
{
    class Program
    {
        static void Main(string[] args)
        {
            var n = long.Parse(Console.ReadLine());
            Console.WriteLine(Resolve(n));
        }
        private static long Resolve(long n)
        {
            long A = 1;
            long B = 1;
            long C1 = 1;
            long C2 = 1;

            long mod = 1000000000 + 7;
            long res = 1;// 1000000000 + 7;

            for (long i = 0; i < n; ++i) {
                A = (10 * A) % mod;
                B = (8 * B) % mod;
                C1 = (9 * C1) % mod;
                C2 = (9 * C2) % mod;
            }
            return (A - C1 - C2 + B + mod+mod)%mod;
        }
    }
}