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)

// 177

#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <numeric>
#include <queue>
#include <iomanip>
#include <climits>
#include <string>
#include <cmath>

using namespace std;
using ll = long long int;
#define NUM 1000000007

ll modpow(ll a, ll b) {
    ll res = 1;
    for (a %= NUM; b; a = a * a % NUM, b >>= 1){
        if (b & 1) res = res * a % NUM;
    }
    return res;
}

int main(){
    ll n, ans;
    cin >> n;
    ans = modpow(10, n) - 2 * modpow(9, n) + modpow(8, n);
    cout << ans % NUM << endl;
    return 0;
}