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<bits/stdc++.h>
using namespace std;
const int mod = 1000000007;

long powermode(long a,long b)
{
		if(b==0)
		return 1;
		long res = (powermode(a,b/2)%mod);
		if(b%2==0)
		return (res*res)%mod;
		else 
		{
			return (((res*res)%mod)*a)%mod ;
		}
}


int main()
{
	long n ;
	cin>>n;
	cout<<((powermode(10,n)-(2*powermode(9,n))%mod)%mod+powermode(8,n))%mod<<endl;
}