Problem:
Score : 300 points

Problem Statement

You are given an integer N.
Find the number of the positive divisors of N!, modulo 10^9+7.

Constraints

1≤N≤10^3

Input

The input is given from Standard Input in the following format:

N

Output

Print the number of the positive divisors of N!, modulo 10^9+7.

Sample Input 1

3

Sample Output 1

4

There are four divisors of 3! =6: 1, 2, 3 and 6. Thus, the output should be 4.

Sample Input 2

6

Sample Output 2

30

Sample Input 3

1000

Sample Output 3

972926972

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

public class Main {

  public static void main (String[] args) {

    Scanner sc = new Scanner(System.in);
    
    int N = sc.nextInt();

    sc.close();

    int[] primeNumber  = new int[1001];

    long mod = 1000000000 + 7;

    for (int i = 2; i <= N; i++) {
      
      int j = i;

      while (j > 1) {
        for (int k = 2; k <= j; k++) {
          if (j % k == 0) {
            primeNumber[k]++;
            j = j / k;
            break;
          }
        }
      }

    }

    long ans = 1;

    for (int i = 2; i <primeNumber.length; i++) {
      ans =  ans * (primeNumber[i]+1) % mod;
    }

    System.out.println(ans);

  }

}