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 <algorithm>
#include <cstdlib>
#include <cmath>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <map>
#include <math.h>
#include <numeric>
#include <queue>
#include <set>
#include <string>
#include <utility>
#include <vector>
using namespace std;
typedef long long ll;

#define rep(i, n) for(ll i = 0; i < n; i++)
#define REP(i, n) for(ll i = 1; i < n + 1; i++)
#define PI 3.14159265359
#define EPS 0.0000000001
#define MOD 1000000007
//cout << std::fixed << std::setprecision(15) << y << endl;


// 累乗mod
ll pmod(ll n, ll m){
    if(m == 0) return 1;
    if(m == 1) return n % MOD;
    if(m % 2 == 0){
        return pmod(n * n % MOD, m / 2) % MOD;
    }
    return n * pmod(n * n % MOD, (m - 1) / 2) % MOD;
}

int main(){
    ll N;
    cin >> N;

    ll ans = (pmod(10, N) - pmod(9, N) - pmod(9, N) + pmod(8, N)) % MOD;
    cout << ans << endl;

    return 0;
}