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 <iostream>
#include <cstring> 
#include <cmath>
#include <cstdio>
const long long mod=1e9+7;
using namespace std;
long long f(long long m,long long n){
	long long ans=1;
	while(n>0){
		if(n&1)
			ans=(ans*m)%mod;
		m=(m*m)%mod;
		n=(n/2)%mod;
	}
	return ans;
}
int main(){
	long long n;
	scanf("%lld",&n);
	if(n<2)
	cout<<"0"<<endl;
	else{
		
		cout<<(f(10,n)-2*f(9,n)+f(8,n))%mod<<endl;
	}
			
	return 0;
}