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)

#define rep(i,n) for (int i=0;i<n;i++)
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define mod 1000000007

 ll modpow(ll x,ll y){
    ll res=1;
    for(ll i=0;i<y;i++){
        res=res*x%mod;
    }
    return res;
}
 
int main(){
  
int n;
  cin >> n;
  
  cout << ((modpow(10,n)-2*modpow(9,n)%mod)%mod+modpow(8,n))%mod << endl;
}