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>
#define rep(i,n) for(int i=0;i<n;i++)
using namespace std;
using ll = long long;

const int mod = pow(10,9) + 7;

int main()
{
  int n;
  cin >> n;
    
  ll a = 1, b = 1, d = 1;

  rep(i,n){
    a = (a*10) % mod;
    b = (b*9) % mod;
    d = (d*8) % mod;
  }
  
  int ans = 0;
  ans = (ans + a)  % mod;
  ans = (ans - b)  % mod;
  ans = (ans - b)  % mod;
  ans = (ans + d)  % mod;

  
  cout << ans << endl;
  return 0;
}