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.*;
import java.util.StringTokenizer;

public class Main {
    private static final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    private static final PrintWriter pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    private static StringTokenizer st;

    private static int readInt() throws IOException {
        while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
        return Integer.parseInt(st.nextToken());
    }

    public static void main(String[] args) throws IOException {
        pw.println(solve((readInt())));
        pw.close();
    }

    static long exponentiation(long base, int exp) {
        long power = 1;
        while (exp > 0) {
            if (exp % 2 == 1) power = power * base % MOD;
            base = base * base % MOD;
            exp /= 2;
        }
        return power;
    }

    static final int MOD = 1_000_000_007;

    private static long solve(int N) {
        long res = exponentiation(10, N)
                - exponentiation(9, N) * 2
                + exponentiation(8, N);

        res = (res + 3L * MOD) % MOD;
        return res;
    }
}