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(){
  int N; cin>>N;
  if(N==1)
    cout<<0<<endl;
  else if(N==2)
    cout<<2<<endl;
  else{
 long long Ans=N;
   Ans*=(N-1);
    Ans%=1000000007;
    Ans*=100000000;
    Ans%=1000000007;
    Ans+=(N*(N-1)/2);
    Ans%=1000000007;
    cout<<Ans<<endl;
  }
}