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 pb push_back
#define ll long long
#define pii pair<int, int>
#define pll pair<long long, long long>
#define ull unsigned long long
#define mp make_pair
#define F first
#define S second
#define mod 1000000007

int main()
{
    ll n;
    cin >> n;

    ll ans = 1;
    ll ans1 = 1;
    ll ans2 = 1;

    for(int i=0;i<n;i++)
    {
        ans *= 10;
        ans1 *= 9;
        ans2 *= 8;
        
        ans1 %= mod;
        ans %= mod;
        ans2 %= mod;
    }

    
    cout << ((ans%mod + (-2*ans1)%mod)%mod + ans2%mod )%mod << endl; 


}