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;

    class Program
    {
        static void Main(string[] args)
        {
            var N = int.Parse(Console.ReadLine());
            var divisor = new int[N + 1];
            for(var i = 2;i<=N;i++)
            {
                var x = i;
                for(var j = 2;j<=N;j++)
                {
                    var k = 0;
                    if(x%j==0)
                    {
                        for (k = 0; x % j == 0; x /= j) k++;
                    }
                    divisor[j] += k;
                }
            }
            long count = 1;
            for(var i =2;i<=N;i++)
            {
                count *= divisor[i] + 1;
                count %= 1000000007;
            }
            Console.WriteLine(count);
        }
    }