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 endl "\n"
typedef long long ll;
int n,mod=(int)(1e9+7);
int main(){
   cin>>n;
   ll wo09=1,wo9=1,ts=1,ans=0;
   for(int i=0;i<n;++i){
       ts=(ts*10)%mod;
        wo09=(wo09*8)%mod;
        wo9=(wo9*9)%mod;
   }
 
  
    ans=(ts%mod-wo09%mod-(wo9%mod-wo09%mod)%mod-(wo9%mod-wo09%mod)%mod)%mod;
    cout<<ans<<endl;
}