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: Accepted)

#include <bits/stdc++.h>
using namespace std;
 
int64_t pppppow(int64_t a, int64_t b){
  int64_t G = a;
  
  for (int64_t i = 1; i < b; i++){
  	G *= a % 1000000007;
    G %= 1000000007;
  }  
  return G;
}
 
 
int main() {
 
  int64_t A;
  cin >> A;
  int64_t count;
  
  if(A == 1){
    cout << "0" << endl;
  }else if(A == 2){
    cout << "2" << endl;
  }else{
     
  int64_t ans;
    ans = pppppow(10,A) - pppppow(9,A) - pppppow(9,A) + pppppow(8,A);
    ans %= 1000000007;
   cout << (ans + 1000000007) % 1000000007 << endl;
  }
 
}