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;

namespace abc178_c
{
    class Program
    {
        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());

            long all = 1;
            for (int i = 0; i < n; i++)
            {
                all *= 10;
                all = all % 1000000007;
            }

            long except09 = 1;
            for (int i = 0; i < n; i++)
            {
                except09 *= 8;
                except09 = except09 % 1000000007;
            }

            long except0or9 = 1;
            for (int i = 0; i < n; i++)
            {
                except0or9 *= 9;
                except0or9 = except0or9 % 1000000007;
            }
            except0or9 = sub(except0or9, except09);
            except0or9 = (except0or9 * 2) % 1000000007;
            all = sub(all, except09);
            all = sub(all, except0or9);
            Console.WriteLine(all);
        }

        static long sub(long x, long y)
        {
            if (x < y)
            {
                return 1000000007 - (y - x);
            }
            else
            {
                return x - y;
            }

        }
    }
}