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 Java (OpenJDK 1.8.0) (judge verdict: Wrong Answer)


import java.util.*;
import java.io.*;

public class Main {
	static FastReader in = new FastReader();

	public static void main(String[] args) {
		solve();
	}

	static long mod = (long) (1e9 + 7);
	
	static void solve() {
		long n = in.nextLong();
		if(n == 1 || n == 2)
		{
			System.out.println(n == 1? 0 : 2);
			return;
		}
		long x = (n * (n - 1));
		x %= mod;
		for(int i = 0; i < n - 2; i++)
		{
			x *= 10;
			x %= mod;
		}
		System.out.println(x);
	}

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}

		int[] readarr(int abc) {
			int[] temp = new int[abc];
			for (int i = 0; i < abc; i++)
				temp[i] = nextInt();
			return temp;
		}
	}
}