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;
  
  long N10=1, N9=1, N8=1;
  for (int i = 0; i < N; i++) {
    N10 = (10*N10)%1000000007;
    N9 = (9*N9)%1000000007;
    N8 = (8*N8)%1000000007;
  }
  // M = 10^N - 2*9^N + 8^N
  // cout << M << endl;
  cout << (1000000007 + N10 - 2*N9 + N8)%1000000007 << endl;
}