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<bits/stdc++.h>
using namespace std;

#define IOS ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define deb(x)	cout << #x << " " << x << endl;

typedef long long int ll;
#define MOD 1000000007

int power(ll b, int e) {
	ll res = 1;
	while (e) {
		if (e&1)
			res =(res * b) % MOD;
		e >>= 1;
		b = (b*b) % MOD;
	}

	return res;
}

int main() {

	IOS

	int n;
	cin >> n;

	if (n == 1)
		cout << 0;

	else if (n == 2)
		cout << 1;

	else 
		cout << ((ll)power(10, n) - (ll)(power(9, n) + (ll)power(9, n) - (ll)power(8, n))) % MOD;

	return 0;
}