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: Wrong Answer)

import java.util.*;
public class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);

		int N = sc.nextInt();
		long a = 1;
		long count = 0;
		for( int i=1; i<=N; i++ ){
			a = (a*i)%1000000007L;
		}     
		for( long i=1; i<=a/2-1; i++ ){
			if( a%i==0 ){
				count+=2;
			}
		}      
		System.out.println(count);
	}
}