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: Accepted)

#include<iostream>
using namespace std;
 
int main(void){
    long long int N,n10=1,n9=1,n8=1,div=1000000007;
    cin>>N;
    for(int i=0;i<N;i++){
        n10=(n10*10)%div;
        n9=(n9*9)%div;
        n8=(n8*8)%div;
    }
    cout<<(n10-2*n9+n8+div*5)%div<<endl;    
    return 0;
}