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: Wrong Answer)

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <limits.h>
#include <queue>
#include <stack>
#include <cmath>
#include <map>
#include <set>
#include <vector>

using namespace std;
typedef long long ll;
const int maxn = 1e6 + 7;
const ll mod = 1e9 + 7;
//vector<ll> ans;
ll kpow(ll a, ll b)
{
	ll ans = 1;
	ans %= mod;
	while(b)
	{
		if(b&1) ans = (ans%mod)*(a%mod)%mod;
		a = (a%mod) * (a%mod) % mod;
		b >>= 1;
	}
	return ans%mod;
}
int main(void)
{
	ll n;
	cin >> n;
	cout << (kpow(10, n)%mod - (((2*(kpow(9, n)%mod))%mod - kpow(8, n)%mod))%mod)%mod;
    return 0;
}