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;
// #define ll long long
typedef long long ll;

ll binpow(ll a, ll n, ll mod){
    if(n==0){
        return 1;
    }
    ll res = binpow(a, n/2, mod);
    if(n%2!=0){
        return (res*res*a) % mod;
    }else{
        return (res*res) % mod;
    }
    return res;
}
int main() {
    // int t; cin>>t;
    // while(t--){
        ll n;
        cin>>n;
        if(n<=1){
            cout<<"0";
            return 0;
        }
        ll mod=1000000007;
        ll a = binpow(10,n,mod);
        ll b = binpow(9,n,mod);
        ll c = binpow(8,n,mod);
        ll ans = a - 2*b + c;
        ans %= mod;
        cout<<ans;
        
    // }
}