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++ (Clang 10.0.0) (judge verdict: Accepted)

#include<iostream>
#include<algorithm>
#include<math.h>
using namespace std;
typedef long long ll;
const int mod=1e9+7;
ll n;
ll ksm(ll a,ll b){
    ll ans=1;
    while(b){
            if(b&1){
                 ans*=a;
            ans%=mod;
            }

            a*=a;
            a%=mod;
            b>>=1;
    }
return ans;
}
int main()
{
    cin>>n;
    cout<<(ksm(10,n)%mod-2*ksm(9,n)%mod+ksm(8,n)%mod+mod)%mod<<endl;
    return 0;
}
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