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: Accepted)

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

public class Main{
    static class FastReader{
        BufferedReader br;
        StringTokenizer st;
        public FastReader(){br = new BufferedReader(new InputStreamReader(System.in));}
        public FastReader(String fileName) throws FileNotFoundException{br = new BufferedReader(new FileReader(fileName));}
        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());}
        char[][] readCharArray(int n,int m) {
        	String str;
        	char[][] arr = new char[n][m];
        	for(int i=0;i<n;i++) {
        		str=nextLine();
        		for(int j=0;j<n;j++) {
        			arr[i][j]=str.charAt(j);
        		}
        	}
        	return arr;
        }
        char[][] readCharArray(int n){
        	return readCharArray(n,n);
        }
        int[] readArray(int n){int[] a=new int[n];for (int i=0; i<n; i++) a[i]=nextInt();return a;}
        long[] readLongArray(int n){long[] a=new long[n];for (int i=0; i<n; i++) a[i]=nextLong();return a;}
        String nextLine(){String str = "";try{str = br.readLine();}catch (IOException e){e.printStackTrace();}return str;}
    }
    static final Random random=new Random();
    static void ruffleSort(int[] a) {
        int n=a.length;//shuffle, then sort
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n), temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }
    public static void main(String[] args) throws NumberFormatException, IOException {
    	FastReader st = new FastReader();
    	int n = st.nextInt();
    	int mod = 1000000007;
    	long temp1=1,temp2=1,temp3=1;
    	for(int i=0;i<n;i++) {
    		temp1 = (temp1*10)%mod;
    		temp2 = (temp2*9)%mod;
    		temp3 = (temp3*8)%mod;
    	}
    	temp1 = (temp1+temp3)%mod;
    	temp2 = (temp2*2)%mod;
    	if(temp1<temp2) temp1+=mod;
    	System.out.println(temp1-temp2);
    }
}