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 <iostream>
#include <math.h>

#define MOD 1000000007;

using namespace std;

int main() {
    int n;
    cin >> n;

    long long all = 1;
    long long noZero = 1;
    long long noNine = 1;
    long long noZeroAndNine = 1;

    for (int i = 0; i < n; i++) {
        all = all * 10 % MOD;
        noZero = noZero * 9 % MOD;
        noNine = noNine * 9 % MOD;
        noZeroAndNine = noZeroAndNine * 8 % MOD;
    }

    long long result = all - ((noZero - noZeroAndNine) + (noNine - noZeroAndNine) + noZeroAndNine) % MOD;
    cout << result << endl;

    return 0;
}