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>
#include<stdlib.h>
#include<math.h>
#define mod 1000000007

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

int main(void){
long long int N;
unsigned long long int count=0;

scanf("%lld", &N);

count = powmod(10,N)-powmod(9,N)-powmod(9,N)+powmod(8,N);
count = count % mod;
count = (count + mod) % mod;

printf("%lld\n", count);
  return 0;

}