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;

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