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

ll N;
ll MOD = 1000000007;
ll a = 10;
ll b = 9;
ll c = 8;

int main(){
  cin >> N;

  rep(i, N-1){
    a = (a * 10) % MOD;
    b = (b * 9) % MOD;
    c = (c * 8) % MOD;
  }

  ll ac = (a + c) % MOD;
  ll ans = (ac - 2*b) % MOD;

  if (ans < 0) ans += MOD;
  cout << ans << endl;
}