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 <iostream>
#include <algorithm>
using namespace std;
unsigned long long n , mod = 1e9+7;
unsigned long long sol()
{
	unsigned long long a=1 ,b=1 ,c=1 ,res = 0 ,t=0;
	while(t++<n)
	{
		a*=10; b*=9; c*=8;
		a%=mod;
		b%=mod;
		c%=mod;
	} 
	b = (b*2)%mod;
	res = a-b+c;
	return res;				
}
int main() 
{	
	while(cin>>n)
	{
		cout<<sol()<<'\n';
	}	
	
}