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>
#include <math.h>
#include <vector>
#include <queue>
#include <iomanip>
#include <string>
#include <algorithm>
using namespace std;
using Graph = vector<vector<int>>;
#define rep(i,n) for(int i=0;i<n;i++)
#define rep_1 (i,j,n) for(int i=j;i<n;i++)
typedef long long ll;
const ll l_INF = 1010101010101010;
const int INF = 1010101010;
const int dx[4] = {-1,0,1,0};
const int dy[4] = {0,-1,0,1};
using vi = vector<int>;
using vll = vector<ll>;
using vvi = vector<vi>;
using vvll = vector<vll>;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
const int mod=1000000007;

ll f(int x,int n){
  ll ans=1;
  rep(i,n){
    ans*=x;
    ans%=mod;
  }
  return ans;
}

int main(){
  int n; cin>>n;
  ll ans=f(10,n) -2 * f(9,n)+f(8,n);
  ans%=mod;
  cout<<ans<<endl;
}