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>
#define MAX(a,b) ((a)>(b) ?(a) : (b))
#define MIN(a,b) ((a)<(b) ?(a) : (b))
#define ABS(a) ((a)>0 ?(a) : (-a))
int main(void){
  long long int n,x=1,y=1,z=1,a=1,i;
  scanf("%lld",&n);

  for(i=0;i<n;i++){
    x*=10;
    y*=9;
    z*=8;
    x%=1000000007;
    y%=1000000007;
    z%=1000000007;
  }
  if((x-y*2-z)<=0){
    printf("%lld\n",(x-y*2+z+1000000007)%1000000007);
  }else{
    printf("%lld\n",(x-y*2+z)%1000000007);
  }
  return 0;
}