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 <iostream>
const int64_t MOD=1000000007;
int main(){
  int64_t n;
  std::cin >> n;
  int64_t n_one_fixed = 1;
	int64_t n_two_fixed = 0;
	int64_t pow_10 = 10;
  for(int i=2;i<=n;++i) {
    int64_t new_one_fixed = (pow_10 + 9*n_one_fixed) % MOD;
    int64_t new_two_fixed = (2*n_one_fixed + 8*n_two_fixed)% MOD;
    n_one_fixed = new_one_fixed;
    n_two_fixed = new_two_fixed;
    pow_10 = (pow_10 * 10) % MOD;
  }
  std::cout << n_two_fixed;
}