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;
const ll mod=1000000007;

ll powmod(ll x, ll y){
    ll a=1;
    for(ll i=0; i<y; i++){
        a=a*x;
    }
    return a;
}

int main(){
    ll N=0;
    cin >> N;
    ll ans=powmod(10, N)-powmod(9, N)-powmod(9, N)+powmod(8, N);
    ans%=mod;
    ans=(ans+mod)%mod;
    cout << ans << endl;
}