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 ll long long
#define fast ios_base::sync_with_stdio(false);cin.tie(NULL)
#define endl "\n"
#define pb push_back
#define mod 1000000007
int dx[]={1,-1,0,0};
int dy[]={0,0,1,-1};
int dx8[]={1,-1,0,0,1,1,-1,-1};
int dy8[]={0,0,1,-1,1,-1,1,-1};

ll binexp(ll a, ll b, ll m) {
	a %= m;
	ll res = 1;
	while (b > 0) {
		if (b & 1)
			res = res * a % m;
		a = a * a % m;
		b >>= 1;
	}
	return res;
}
ll modinvfermat(ll a, ll m)
{
	return binexp(a, m - 2, m);
}
void task(bool flag)
{
	if (flag)
		cout << "YES\n";
	else
		cout << "NO\n";
}
ll lcm(ll a, ll b)
{
	return ((1LL * a * b) / (__gcd(a, b)));
}

 // void dfs(ll node){
 // 	vis[node]=1;
 // 	res.pb(node);
 //    vector<ll> ans;


 // 	for(auto i:v[node]){
 // 		if(!vis[i]){
 // 			ans.pb(i);

 // 		}
 // 	}
 // 	sort(ans.begin(),ans.end());

 // 	for(auto i:ans){
 // 		if(!vis[i])
 // 			dfs(i);
 // 	}




 // }

void solve(){

ll n;
cin>>n;
if(n==1){
	cout<<0<<endl;

}
else if(n==2){
	cout<<1<<endl;

}
else{
	ll ans;
	ans=(binexp(10,n,mod)%mod-2*binexp(9,n,mod)%mod+binexp(8,n,mod)%mod)%mod;

	cout<<ans<<endl;






	

}




return;
}



int main()
{  
#ifndef ONLINE_JUDGE
	// for getting input from input.txt
	freopen("input.txt", "r", stdin);
	// for writing output to output.txt
	freopen("output.txt", "w", stdout);
#endif
    fast;
    

    ll t;
    t=1;
    // cin>>t;
    while(t--){
    	solve();
    }
    
   
  



#ifndef ONLINE_JUDGE
	cout << "\nTime Elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << " sec\n";
#endif
return 0;
}