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

class Program {
    static long MOD = 1000000007;
    static void Main (string[] args) {
        long N = int.Parse (Console.ReadLine ());

        long ans = (ModPow (10, N) - (2 * (ModPow (9, N)) % MOD)) % MOD + (ModPow (8, N) % MOD);
        ans = ans % MOD;
        if (ans < 0) {
            ans += MOD;
        }

        Console.WriteLine (ans);

    }

    static long ModPow (long a, long n) {
        long res = 1;
        while (n > 0) {
            if ((n & 1) == 1) {
                res = res * a % MOD;
            }
            a = a * a % MOD;
            n >>= 1;
        }
        return res;
    }
}

//dotnet run --project test