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 <bits/stdc++.h>
#define IO ios::sync_with_stdio(0);cin.tie(0)
#define endl '\n'
#define MAXN maxn
#define MOD 1000000007

using namespace std;

long long fastpow(long long a, long long b) {
	long long res = 1LL;
	while (b) {
		if (b & 1) {
			res = res * a % MOD;
		}
		a = a * a % MOD;
		b >>= 1;
	}
	return res;
}

long long add(long long a, long long b) {
	return (a + b) % MOD;
}

long long sub(long long a, long long b) {
	long long res = (a - b) % MOD;
	if (res < 0) res += MOD;
	return res;
}

long long N;

signed main()
{
	IO;
	cin >> N;
	cout << add(sub(fastpow(10, N), 2LL * fastpow(9, N)), fastpow(8, N)) << endl;
	return 0;
}