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 <stdio.h>
#include <stdlib.h>
#include <iostream>
#include <vector>
using namespace std;

unsigned long long modpow(unsigned long long a, unsigned long long n, unsigned long long mod) {
    unsigned long long res = 1;
    while (n > 0) {
        if (n & 1) res = res%mod * a % mod;
        a = a%mod * a % mod;
        n >>= 1;
    }
    return res;
}


int main(){
    unsigned long long N;
    cin >> N;
    unsigned long long answer = 0;
    if(N==1) answer = 0;
    if(N>=2){
        answer = (modpow(10,N,1000000007)-2*modpow(9,N,1000000007)%1000000007+modpow(8,N,1000000007))%1000000007;
    }
    answer=(answer+1000000007)%1000000007;
    printf("%llu\n",(answer+1000000007)%1000000007);
    return 0;
}