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;
typedef long long ll;
typedef pair<int,int> P;
#define rep(i,m,n) for(int i=m;i<n;i++)
const ll mod=1e9+7;

ll power(ll x,ll n){
  if(n==0) return 1;
  ll res=power(x*x%mod,n/2);
  if(n&1) res=res*x%mod;
  return res;
}

int main(){
  int n;
  cin>>n;
  ll a=power(10,n);
  ll b=power(9,n);
  ll c=power(8,n);
  ll d=a-b-b+c;
  while(d<0) d+=mod;
  cout<<d<<endl;
}