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>
#define rep(i,n)for(int i=0;i<(int)(n);i++)
using namespace std;


int main() {
  int n;
  cin>>n;
  
  int64_t div=1;
  rep(i,9){
    div*=10;
  }
  div+=7;
  
  if(n<=1){
    cout<<0<<endl;
    return 0;
  }

  int64_t a1=1;//全部

  rep(i,n){
    a1*=10;
    a1%=div;
  }
  //cout<<a1<<endl;

  int64_t a2=1;//0も9も入ってない
  rep(i,n){
    a2*=8;
    a2%=div;
  }
  //cout<<a2<<endl;

  int64_t a3=1;//0or9が入ってない
  rep(i,n){
    a3*=9;
    a3%=div;
  }

  //cout<<a3<<endl;
  int64_t a4=a3*2%div;
  cout<<(a1-(a4-a2))%div<<endl;
  
  return 0;

}