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 (Clang 10.0.0) (judge verdict: Wrong Answer)


#include <stdio.h>
#include<limits.h>

int main(void) {

        int N;
      scanf("%d",&N);
    
  
      long long int G = 1;
      
        for(int i=1;i<=N;i++){
        G *=10;
          if(G>1000000007){
            G %=1000000007;
          }
      }
        
     long  long int P = 1;
      for (int j=1;j<=N;j++){
        P *=8;
          if(P>1000000007){
            P %=1000000007;
              
        }
          
      }
      
     
    
    long long int D =1;
    for (int l=1;l<=N;l++){
        D *=9;
         if (D>1000000007){
            D %=1000000007;
        }
    
    }
    
    
    
    
      
    long long int answer;
    answer = G-2*D+P;
    
      printf("%lld",answer);
    
  

    

    return 0;
}