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: Accepted)

#include<bits/stdc++.h>
#define pb push_back
#define sz(v) (v).size()
#define all(v) (v).begin(),(v).end()
#define fi first
#define se second
#define mp make_pair
#define inf 1000000007
#define mod 1000000007
using namespace std;
template <typename T> T Max(T x,T y){return x>y?x:y;}
template <typename T> T Min(T x,T y){return x<y?x:y;}
template <typename T> void chmax(T &x,T y){x=x>y?x:y;return;}
template <typename T> void chmin(T &x,T y){x=x<y?x:y;return;}

typedef long long ll;
int n;
ll ans=1,t1=1,t2=1,t3;

int main()
{
	cin>>n;
	for(int i=1;i<=n;i++)
	{
		ans*=10;
		ans%=mod;
		t1*=9;
		t1%=mod;
		t2*=8;
		t2%=mod;
	}
	t3=(t1+t1)%mod-t2;
	while(t3<0) t3+=mod;
	ans-=t3;
	while(ans<0) ans+=mod;
	cout<<ans<<endl;
	return 0;
}