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 <bits/stdc++.h>

const int Mod = 1000000007;

using namespace std;

long getAns(long n){
    
    long result = n;
    
    result = ((result%Mod)*((n-1)%Mod))%Mod;
    
    for(int i =0;i<(n-2);i++){
        result = ((result%Mod)*((10)%Mod))%Mod;
    }
    
    return (result);
}

int main()
{
    long n;
    cin >> n;
    
    cout << getAns(n);

    return 0;
}