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;
const ll MOD = 1e9 + 7;
int main(){
    int n;
    cin >> n;
    if(n == 1)
    {
        cout << 0 << "\n";
        return 0;
    }
    ll a = 1, b = 1, c = 1;
    for (int i = 1; i <= n; i++){
        a = (a * 10) % MOD;
        b = (b * 9) % MOD;
        c = (c * 8) % MOD;
    }
    cout << (a - 2 * b + c + MOD * 2) % MOD  << "\n";
}