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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<iostream>
using namespace std;
int main()
{
long long int n;
  cin>>n;
  long long int netways=1;
  for(int i=1;i<=n;i++)
  {
    netways*=10;
    netways%=1000000007;
  }
  long long int bad=1,bad1=1;
  for(int i=1;i<=n;i++)
  {
    bad*=8;
    bad1*=9;
    bad%=1000000007;
    bad1%=1000000007;
  }
  bad1*=2;
  bad1%=1000000007;
  cout<<netways-(bad1-bad);
}