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<stdio.h>

unsigned long power(unsigned long a, unsigned long e, unsigned long m) {
  unsigned long s = 1;
  while(e>0) {
    if(e % 2 == 1) s = s * a % m;
    a = a * a % m;
    e = e / 2 % m;
  }
  return s;
}

int main(void) {
  unsigned long n;
  scanf("%lu", &n);
  printf("%lu\n", (power(10, n, 1000000007) + power(8, n, 1000000007) - power(9, n, 1000000007)*2) % 1000000007);
  return 0;
}