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>
using namespace std;

int main(){
    int n;
    cin >> n;
    unsigned long tmp = 1, tmp2 = 1, tmp3 = 1, ans = 0;
    for(int i = 0; i<n; i++){
        tmp *= 10;
        tmp2 *= 9;
        tmp3 *=8;
        tmp %= 1000000007;
        tmp2 %= 1000000007;
        tmp3 %= 1000000007;
    }
    ans = tmp - 2*tmp2 + tmp3;
    
    cout << ans;
}