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.*;

/**
 * C Main
 *
 * @date 2020.09.19
 * @author 焼き鮭 <yaki-shake@up-tri.me>
 */

public class Main {

  long MOD = 1000000007;

  Scanner sc;

  public static void main(String[] args) {
    new Main().execute();
  }

  public void execute() {
    this.sc = new Scanner(System.in);
    int n = sc.nextInt();
    long ans = modpow(10, n, MOD) - 2 * modpow(9, n, MOD) + modpow(8, n, MOD);
    System.out.println(ans);
  }

  public long modpow(long a, long n, long mod) {
    long res = 1;
    while (n > 0) {
      if ((n & 1) != 0) {
        res = res * a % mod;
      }
      a = a * a % mod;
      n >>= 1;
    }
    return res;
  }
}