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>

long long powmod(long long x,long long y){
    long long res=1;
    for(int i=0;i<y;i++){
        res=res*x%1000000007;
    }
    return res;
}

int main(void){
  long long n;
  scanf("%lld",&n);
  
  long long a=powmod(10,n)-powmod(9,n)-powmod(9,n)+powmod(8,n);
  printf("%lld\n",a);
  return 0;
}