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;
using ll = long long;
using ld = long double;

const int MOD = 1e9 + 7;
int power (int n, int k) {
	int res = 1;

	while (k) {
		if (k % 2) res = (res * 1LL * n) % MOD;
		n = (n * 1LL * n) % MOD;
		k /= 2;
	}

	return res;
}

int main () {
	int n;
	cin >> n;
	int sol = power(10, n);
	sol = (sol - 2 * power(9, n) + MOD) % MOD;
	sol = (sol + power(8, n)) % MOD;
	cout << sol << '\n';
}