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>
#define mod 1000000007

int pm(int x, long long y);

int main(void){
  long long n;
  scanf("%lld", &n);

  long long a = pm(10,n); 
  long long b = pm(9,n);
  long long c = pm(8,n); 


  long long ans = a - b - b + c;

  ans %= mod;

  ans = (ans + mod) % mod;

  printf("%lld\n", ans);

  return 0;
}

int pm(int x, long long y){
  long long a = 1;
  for(int i = 0; i < y; i++){
    a *= x;
    a %= mod;
  }
  return a;
}