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 <stdio.h>

long long pow(long long a, long long n)
{
  long long temp = a;
  a = 1;
  for (long long i = 0; i < n; i++)
  {
    a *= temp;
    if (a >= 1000000007)
      a %= 1000000007;
  }
  return a;
}

int main(void)
{
  long long n, sum = 0;
  scanf("%lld", &n);
  sum = sum + (pow(10, n) % 1000000007);
  sum = (sum - (2 * (pow(9, n))));
  sum %= 1000000007;
  sum = sum + pow(8,n) % 1000000007;
  if (sum < 0)
    sum += 1000000007;
  printf("%lld\n", sum);
  return 0;
}