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;
int dfs(vector<int>&f,int st,int par,vector<vector<int>>&adj){
    for(auto j:adj[st]){
        if(j!=par){
            f[st]++;
            f[st]+=dfs(f,j,st,adj);
        }
    }
    return f[st];
}
ll power(ll x, ll y, ll p)  
{  
    ll res = 1;     // Initialize result  
  
    x = x % p; // Update x if it is more than or  
                // equal to p 
   
    if (x == 0) return 0; // In case x is divisible by p; 
  
    while (y > 0)  
    {  
        // If y is odd, multiply x with result  
        if (y & 1)  
            res = (res*x) % p;  
  
        // y must be even now  
        y = y>>1; // y = y/2  
        x = (x*x) % p;  
    }  
    return res;  
}  
int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
    ll n;
    cin>>n;
    ll mod=1e9+7;
    if(n<=1)cout<<0<<endl;
    else {
        ll ans=0;
        ans=power(10,n,mod);
        //cout<<ans<<endl;
        ans%=mod;
        ans-=2*power(9,n,mod);
        if(ans<0)ans+=mod;
        ans%=mod;
        ans+=power(8,n,mod);
        ans%=mod;
        cout<<ans<<endl;
    }
}