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 Python (3.8.2) (judge verdict: Runtime Error)

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

#define int long long

int mod = 1000000007;

#include "debug.cpp"

int dp[1000010][4];

int32_t main(){
	int n;
	cin >> n;

	if(n == 1){
		cout << "0\n";
		return 0;
	}

	dp[2][0] = 64;
	dp[2][1] = 17;
	dp[2][2] = 17;
	dp[2][3] = 2;

	for(int i=3; i<=n; i++){
		dp[i][0] = dp[i-1][0]*8;
		dp[i][1] = dp[i-1][0] + dp[i-1][1]*9;
		dp[i][2] = dp[i-1][0] + dp[i-1][2]*9;
		dp[i][3] = dp[i-1][1] + dp[i-1][2] + dp[i-1][3]*10;

		dp[i][0] %= mod;
		dp[i][1] %= mod;
		dp[i][2] %= mod;
		dp[i][3] %= mod;
	}

	cout << dp[n][3] << "\n";
}