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 NMAX 200005

using namespace std;
typedef long long ll;
const ll MOD=1e9+7;
ll binPow(ll a, ll p){
    ll ans=1;
    while(p){
        if(p&1) ans=ans*a%MOD;
        p>>=1;
        a=a*a%MOD;
    }
    return ans;
}
int main()
{
    ll n;
    cin>>n;
    cout<<(binPow(10,n)+binPow(8,n)-2*binPow(9,n)+MOD)%MOD;
    return 0;
}