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<iostream>
#include<cmath>
using namespace std;


int main(){
    long long N, ans;
    long long N_10 = 1, N_8 = 1, N_9 = 1;
    std::cin >> N;

    for(long long i = 1; i <=N; i++){
        //何個0,9があるか
        N_10 = N_10 * 10;
        N_10 = N_10%1000000007;
        N_8 = N_8 * 8;
        N_8 = N_8%1000000007;
        N_9 = N_9 * 9;
        N_9 = N_9%1000000007;
    }

    ans = (N_10 + N_8)%1000000007;
    ans = (ans - N_9)%1000000007;
    ans = (ans - N_9)%1000000007;
    if(ans < 0){
        ans = ans + 1000000007;
    }
    std::cout << ans;
}