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;
int main(){
    int N;
    cin >> N;
    long long A=1,B=1,C=1;
    for(int i=0;i<N;i++){  
        A*=10;
        B*=8;
        C*=9;
        A=A%(1000000000+7);
        B=B%(1000000000+7);
        C=C%(1000000000+7);
    }
    //printf("A=%llu B=%llu C=%llu\n",A,B,C);
    long long ans = A - 2*C + B + 2*(1000000000+7);
    ans = ans%(1000000000+7);
    cout << ans << endl;
    return 0;
}