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;
#define rep(i, n) for(int i = 0; i < n; i++)
#define all(v) v.begin(), v.end()
using ll = long long;
const int inf = int(1e10);
//const ll inf = ll(1e19);
const int mod = int(1e9) + 7;

//a^nの計算(mod)
ll modpow(ll a, ll n, ll mod){
    ll res = 1;
    while(n > 0){
        if(n & 1) res = res * a % mod;
        a = a * a % mod;
        n >>= 1;
    }
    return res;
}

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