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 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Linq;
using System.Collections.Generic;

class Program
{
    static void Main()
    {
        var N=Int32.Parse(Console.ReadLine());
        var array = new int[N + 1];
        for (int i=2;i<=N;++i)
        {
            var num = i;
            for (int j=2;j<=N;++j)
            {
                var count = 0;
                while (num%j==0)
                {
                    num /= j;
                    count++;
                }
                array[j] += count;
                if (num == 1) break;
            }
        }
        var counter = 1L;
        for (int i=2;i<=N;++i)
        {
            if (array[i] == 0) continue;
            var num = array[i] + 1;
            counter = (counter * num) % 1000000007;
        }
        Console.WriteLine(counter);
    }
}