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<bits/stdc++.h>
using namespace std;

int main()
{
  int64_t n,a,b,c,ans;
  a=1;
  b=1;
  c=1;
  cin>>n;
  for(int i=0;i<n;i++)
  {
    a*=10;
    a=a%1000000007;
    b*=9;
    b=b%1000000007;
    c*=8;
    c=c%1000000007;
  }
  ans=(a-b*2+c)%1000000007;
  cout<<ans<<endl;
}