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>
using namespace std;
using ll = long long int;
ll modpow(ll a,ll b);
ll key = 1000000007;
int main(){
    ll n;
    cin >> n;
    ll ans = modpow(10,n) - modpow(9,n) * 2 + modpow(8,n);
    if(ans >= 0){
        cout << ans % key;
    }else{
        cout << (ans + key * 2)%key;
    }
    return 0;
}

ll modpow(ll a,ll b){
    ll ans = 1;
    for(ll i = 0;i < b;i++){
        ans *= a;
        ans %= key;
    }
    return ans;
}