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 C# (Mono-csc 3.5.0) (judge verdict: Wrong Answer)


using System;
using System.Linq;
class Test
{

    public static void Main()
    {
        var n = int.Parse(Console.ReadLine());
        int[] fact = new int[n+1];
        fact[0] = 1;
        for(int i=1;i<=n;i++)
        {
            fact[i] = i * fact[i - 1];
        }

        var num = fact[n];
        long count = 0;
        for(int i=1;i<=Math.Sqrt(num);i++)
        {
            if(num%i==0)
            {
                count = (count + 1) % 1000000007;
                if (num / i != i)
                    count = (count + 1) % 1000000007;
            }
        }

        Console.Write(count);
    }


}