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>
#define rep(i,n) for(ll i=1;i<=n;i++)
using namespace std;
using ll=long long;
using P = pair<int,int>;
int main(){
    ll n;
    cin >> n;
    ll mod = 1000000007;
    ll a=1,b=1,c=1;
    for(ll i=1;i<=n;i++){
        a=(a*10)%mod;
        b=(b*9)%mod;
        c=(c*8)%mod;
    }
    ll ans = a-2*b+c;
    cout << ans%mod << endl;
}