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>
#include <cstdlib>
#include <functional>
#include <queue>
#include <stack>
#include <map>
#include <vector>
#include <string>

using namespace std;
typedef long long ll;
const ll mod=1000000007;
 
ll powmod(ll x,ll y){
    ll res=1;
    for(ll i=0;i<y;i++){
        res=res*x%mod;
    }
    return res;
}
int main(){
    ll n;
    cin>>n;
    ll ans=powmod(10,n)-powmod(9,n)-powmod(9,n)+powmod(8,n);
    ans%=mod;
    ans=(ans+mod)%mod;
    cout<<ans<<"\n";
}