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 <iostream>
#include <string>
#include <vector>
#include <queue>
#include <iomanip>
#include <algorithm>
#include <cmath>
#include <climits>

#define PI 3.14159265359

using namespace std;
using ll = long long;
using pint = pair<int, int>;

int main() {
	int N;
	cin >> N;

	ll ans = 10;
	for (int i = 1; i < N; ++i) {
		ans = ((ans * 10) % 1000000007);
	}

	ll tmp = 9;
	for (int i = 1; i < N; ++i) {
		tmp = ((tmp * 9) % 1000000007);
	}
	ll no = tmp;

	tmp = 9;
	for (int i = 1; i < N; ++i) {
		tmp = ((tmp * 9) % 1000000007);
	}
	no += tmp;

	tmp = 8;
	for (int i = 1; i < N; ++i) {
		tmp = ((tmp * 8) % 1000000007);
	}
	no -= tmp;

	ans -= no;
	cout << ans << endl;

	return 0;
}