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();
    long ans = 1;
    for(int i = 2; i <= N; i++) {
      if(isPrime(i)) {
        long power = 0;
        for(int j = 1; j < 10; j++) {
          if(N >= Math.pow(i, j)) {
            power += (long)(N / Math.pow(i, j));
          } else {
            break;
          }
        }
        ans = (ans * (power + 1)) % 1000000007;
      }
    }
    System.out.println(ans);
  }

  public static boolean isPrime(int n) {
    boolean flg = true;
    for(int i = 2; i * i <= n; i++) {
      if(n % i == 0) flg = false;
    }
    return flg;
  }
}