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 <iostream>

using namespace std;

const int MOD = 1000000007;

int mpow(long long x, int n) {
	if (n == 0) return 1;
	if (n & 1) return x * mpow(x, n - 1) % MOD;
	return mpow(x * x % MOD, n >> 1);
}

int main() {
	int n; cin >> n;
	long long ans = mpow(10, n);
	ans = (ans - 2 * mpow(9, n) % MOD + MOD) % MOD;
	ans = (ans + mpow(8, n)) % MOD;
	cout << ans << endl;

	return 0;
}