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.Scanner;

public class Main {

    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        int[] cnt = new int[n + 1];

        sc.close();

        int mod = 1000000007;

        for (int i = 1; i <= n; i++) {
            int num = i;
            for (int j = 2; j <= n; j++) {
                while (num % j == 0) {
                    cnt[j]++;
                    cnt[j] %= mod;
                    num /= j;
                }
            }
        }

        long ans = 1;
        for (int num : cnt) {
            ans = (ans * (num + 1)) % mod;
        }

        System.out.println(ans);

    }
}