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++ (Clang 10.0.0) (judge verdict: Wrong Answer)

#include<iostream>
#include<vector>
#include <math.h>
using namespace std;
using ll=long long;

#define loop(var,start,stop,step) for(long long var=start;var<stop;var+=step)

using vi=vector<int>;
using vl=vector<long long>;

#define fio  cin.tie(nullptr); ios::sync_with_stdio(false); cout.tie(nullptr);
#define nl cout<<endl;

int main()
    {
        fio;
        ll n;cin>>n;
        ll mod = pow(10,9)+7;
        ll all,n9,n09;
        loop(i,0,n,1)
        {
            all = (all*10)%mod;
            n9 = (n9*9)%mod;
            n09 = (n09*8)%mod;
        }
        ll ans = (all - (2*n9)%mod + n09)%mod;
        cout<<ans<<endl;
        return 0;
    }