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>
#define rep(i, n) for (int i = 0; i < (n); i++)
using namespace std;
using ll = long long;
using pii = pair<int, int>;

const int mod = 1e9 + 7;

ll powmod(ll a, ll b) {
	ll ret = 1;
	rep(i, b) {
		ret = (ret * a) % mod;
	}
	return ret;
}

int main() {
	ll n;
	cin >> n;
	ll ans = powmod(10, n) - powmod(9, n) - powmod(9, n) + powmod(8, n);
	ans %= mod;
	cout << ans << endl;
	return 0;
}