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>
#include <algorithm>
#include <vector>
#include <iostream>
#include <string>
using namespace std;
 
int main() {
  //input
  int n; cin >> n;
  long m;
  m = 1000000007;
  long long ten,nine,eight;
  long long ans;
  ten = 1;
  nine = 1;
  eight = 1;
  
  //compute
    for(int i = 0;i < n; i++){
        ten = (ten * 10) % m;
        nine = (nine * 9) % m;
        eight = (eight * 8) % m;
 
     }
   
   ans = (((ten - nine - nine) % m)  + eight) % m;
 
  //output
  cout << ans << endl;
}