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>
int main()
{
  int N,sum;
  int a,b,c;
  a=9;
  b=64;
  c=10;
  sum=0;
  scanf("%d",&N);
  for(int k=2;k<=N-1;k++)
  {
    
    sum=sum+(9*c-17*a+b)%(1000000007);
      b=8*b;
    a=a*9;
    c=c*10;
    sum=sum%(1000000007);
  }
  printf("%d",abs(sum));
  return 0;
}