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: Wrong Answer)

import java.util.Scanner;
class Main {
  public static int N;
  public static final int l = 1000000007;
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    N = sc.nextInt();

    long ans;
    long a = sum(10);
    long b = sum(9);
    long c = sum(8);

    ans = (a - b*2 + c) % l;
    System.out.println(ans);
  }

  public static long sum(int m) {
    long sum = 1;
    int i = 0;
    while(i < N) {
      for(int j = 0; j < N; j++) {
        sum *= m;
        i++;
        if(sum > l) {
          sum = sum % l;
        }
      }
      for(int j = i; j < N; j++) {
        sum *= m;
      }
    }
    return sum;
  }
}