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;
long long mod=1e9+7;

long long power(long long a,long long b){
	long long res = 1;
    while (b > 0) {
        if (b & 1)
            res = (res * a)%mod;
        a = (a * a)%mod;
        b >>= 1;
    }
    return res;
}

int main(){
	long long n,ans=1;
  
  	cin>>n;
  
  	ans = (power(10,n)%mod - 2*power(9,n)%mod + power(8,n)%mod + 2*mod)%mod;
  
  	cout<<ans;
    return 0;
}