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;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
using ll = long long;
using vi = vector<int>;
using vvi = vector<vi>;
using vl = vector<ll>;
using vvl = vector<vl>;

int main(){
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  ll MOD = 1000000007;
  ll n;
  cin >> n;
  ll ten = 1, nine = 1, eight = 1;
  rep(i,n){
    ten *= 10;
    ten %= MOD;
  }
  rep(i,n){
    nine *= 9;
    nine %= MOD;
  }
  rep(i,n){
    eight *= 8;
    eight %= MOD;
  }
  ll ans = ten - (nine*2 - eight) + MOD*10;
  ans %= MOD;
  cout << ans << endl;
}