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 11.0.6) (judge verdict: Accepted)


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.math.BigInteger;

public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		FastInput in = new FastInput(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		ABC178C solver = new ABC178C();
		solver.solve(1, in, out);
		out.close();
	}
	
	static class ABC178C {
	
		static int mod = 1000000007;
		public void solve(int testNum, FastInput in, PrintWriter out) {
	
			int n = in.nextInt();
			
			long [][][]dp = new long [n+1][2][2];
			
			dp[0][0][0] = 1L;
			
			for(int i = 0 ; i < n ; i++) {
					for(int j = 0 ; j < 2 ; j++) {
						for(int k = 0 ; k < 2 ; k++) {
							if(j == 1 && k == 1) {
								dp[i+1][j][k] = (10*dp[i][j][k]%mod +dp[i+1][j][k])%mod;
							}
							else if(j == 0 && k == 0) {
								dp[i+1][j][k] = (8*dp[i][j][k]%mod +dp[i+1][j][k])%mod; 
							}
							else{
								dp[i+1][j][k] = (9*dp[i][j][k]%mod +dp[i+1][j][k])%mod;
							}
							if(j == 0) {
								dp[i+1][j+1][k] = (dp[i][j][k] + dp[i+1][j+1][k])%mod;
							}
							if(k == 0) {
								dp[i+1][j][k+1] = (dp[i][j][k] + dp[i+1][j][k+1])%mod;
							}
							
						}
					}
				}
			
		out.println(dp[n][1][1]);
		}
	}
static class FastInput{
	private final BufferedReader in;
	private String[] buff;
	private int index = 0;
	
	public FastInput(InputStream is) {
		in = new BufferedReader(new InputStreamReader(is));
	}
	String nextLine() {
		try {
			return in.readLine();
		} catch (IOException e) {
			e.printStackTrace();
		}
		return null;
	}
	String next() {
		while (buff == null || index >= buff.length) {
			buff = nextLine().split(" ");
			index = 0;
		}
		return buff[index++];
	}
	int nextInt() {
		return Integer.parseInt(next());
	}
	
	long nextLong() {
		return Long.parseLong(next());
	}
	
	Double nextDouble() {
		return Double.parseDouble(next());
	}
	
	BigInteger nextBigInteger() {
		return new BigInteger(next());
	}
	
	BigDecimal nextBigDecimal() {
		return new BigDecimal(next());
	}
	
	public int[] nextIntArray(final int n) {
		final int[] res = new int [n];
		
		for(int i = 0 ; i < n ;i++) {
			res[i] = nextInt();
		}
		return res;
	}
	
	public long[] nextLongArray(final int n) {
		final long[] res= new long [n];
		
		for(int i = 0 ; i < n ;i++) {
			res[i] = nextLong();
		}
		return res;
	}
	
	public double[] nextDoubleArray(final int n ) {
		final double[] res = new double [n];
		
		for(int i = 0 ; i < n ;i++) {
			res[i] = nextDouble();
		}
		return res;
	}
	
	
	public int[][] nextInt2DArray(final int n , final int m){
		int [][]res = new int [n][m];
		
		for(int i = 0 ; i < n ;i++) {
			for(int j = 0 ; j < m ;j++) {
				res[i][j] = nextInt();
			}
		}
		return res;
	}
	public long[][] nextLong2DArray(final int n , final int m){
		long [][]res = new long [n][m];
		
		for(int i = 0 ; i < n ;i++) {
			for(int j = 0 ; j < m ;j++) {
				res[i][j] = nextLong();
			}
		}
		return res;
	}
	
	public char[][] nextChar2DArray(final int n){
		char [][]res = new char [n][];
		
		for(int i = 0 ; i < n ;i++) {
			String s = next();
			res[i] = s.toCharArray();
		}
		
		return res;
	}
}

}