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<bits/stdc++.h>
using namespace std;
#define rep(i,n) for (int (i)=0;(i)<(n);i++)
#define INF 1001001001
#define LLINF 1001001001001001001
#define MOD 1000000007
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
#define ALL(v) v.begin(), v.end()
typedef long long ll;
const ll mod=1000000007;

ll powmod(ll x,ll y){
    ll res=1;
    for(ll i=0;i<y;i++){
        res=res*x%mod;
    }
    return res;
}

int main(){
    ll n;cin >> n;
    ll ans = powmod(10,n)-powmod(9,n)-powmod(9,n)+powmod(8,n);

    ans%=mod;
    cout << ans << endl;

   

}