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) {
		Scanner sc = new Scanner(System.in);
//		List<String> divisor = new ArrayList<>();
//		int[] in = Stream.of(sc.nextLine().split(" ")).mapToInt(Integer::parseInt).toArray();
		int N = Integer.parseInt(sc.next());
//		int S = Integer.parseInt(sc.next());
//		String[] S = sc.next().split("");
		
//		for (int i = 1; i <= N; i++) {
//		}
		
		long mod = 1_000_000_007;
		int[] n = new int[N+1];
		for(int i = 1;i <= N; i++) {
			int num = i;
			for(int j = 2;j <=num; j++) {
				while(num % j == 0) {
					n[j]++;
					num /= j;
				}
			}
		}
		
		long res = 1;
		for(int i = 0; i <= N; i++) 
			res = (res*(n[i]+1)) % mod ;
		
		System.out.println(res);		
	}
}