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;

namespace ConsoleApp1
{
    class ABC178C
    {
        // https://atcoder.jp/contests/abc178/tasks/abc178_c
        static void Main(string[] args)
        {
            const UInt64 m = 1000000007;

            uint N = uint.Parse(Console.ReadLine());

            UInt64 result = 0;
            UInt64 r10 = 10;
            UInt64 r9 = 9;
            UInt64 r8 = 8;

            if (N > 1)
            {
                // 10^N - 9^N * 2 + 8^N

                UInt64 i = 1;
                for (UInt64 j = 1; j + 10 < N; j += 10)
                {
                    r10 = (r10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10 * 10) % m;
                    r9 = (r9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9 * 9) % m;
                    r8 = (r8 * 8 * 8 * 8 * 8 * 8 * 8 * 8 * 8 * 8 * 8) % m;
                    i += 10;
                }

                for (UInt64 j = i; j < N; j++)
                {
                    r10 = (r10 * 10) % m;
                    r9 = (r9 * 9) % m;
                    r8 = (r8 * 8) % m;
                }

                result = (r10 - (r9 * 2) + r8) % m;
            }

            Console.WriteLine(result);
        }
    }
}