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: Accepted)

#include<bits/stdc++.h>
using namespace std;
int main(){
long long n;
cin>>n;
long long ans=0;
long long M=1000000007;
long long sum1=1;
long long sum2=1;
long long sum3=1;
for(long long i=0;i<n;i++){
  sum1=((sum1%M)*10)%M;
  sum2=((sum2%M)*9)%M;
  sum3=((sum3%M)*8)%M;
}
ans+=sum1;
ans=ans%M;
ans-=sum2;
ans=ans%M;
ans-=sum2;
ans=ans%M;
ans+=sum3;
ans=ans%M;
ans=(ans+M)%M;
cout<<ans<<endl;
  return 0;
}