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;
typedef  long long  ll;
	int mod=1e9+7;
	ll power(ll n,ll b){
		ll ans=1;
		while(b>0){
			
			if(b&1){
				ans=(ans*n)%mod;
			}
			n=(n*n)%mod;
			b>>=1;
		}

		return ans;
	}

	int main() {

		#ifndef ONLINE_JUDGE
	        freopen("input.txt","r",stdin);
	        // freopen("output.txt","w",stdout);
	    #endif
	    ios::sync_with_stdio(false);
	    cin.tie(0);
	    cout.tie(0);
	   
	  	int n;
	  	cin>>n;
	  	if(n<=1){
	  		cout<<0<<endl;
	  		return 0;
	  	}
	  	
	  	ll ans= (power(10,n)-2*power(9,n)+power(8,n) +mod)%mod;

	  	cout<<ans<<endl;
	    // cout<<a<<endl;
	    return 0;
}