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;
typedef long long ll;

ll fpow(ll b,ll p,ll mod){
    b %=mod;
    ll ans=1;
    while(p){

        if (p&1){
            ans *=b;
            ans %=mod;
        }
        b *=b;
        b%=mod;
        p >>=1;
    }
    return ans;
}

//long long fpow(long long a, long long n, long long mod)
//{
//    if (n == 0)        return 1;
//    else if (n & 1) return a * fpow(a, n - 1, mod) % mod;
//    else
//    {
//        long long num = fpow(a, n / 2, mod) % mod;
//        return num * num % mod;
//    }
//}
int main()
{
    ios::sync_with_stdio(false);
    ll MOD = (ll)1e9+7;
    ll n;
    cin >> n;
    if (n==1){
        cout << 0;
        return 0;
    }
    else if (n==2){
        cout << 2;
        return 0;
    }
    ll a=fpow(10,n,MOD),b=fpow(9,n,MOD),c=fpow(8,n,MOD);

    cout << ( a - b*2%MOD + c) %MOD;
    return 0;
}