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.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using static System.Console;
using static System.Math;

namespace CP
{
    class Atria
    {
        readonly static long mod = 1000000000 + 7;


        static void Main(string[] args)
        {
            int n = int.Parse(ReadLine());
            int[] vs = new int[1007];
            for (int i = 1; i <= n; i++)
            {

                long now = i;
                for (int j = 2; j <= now; j++)
                {
                    while (now > 0 && now % j == 0)
                    {
                        vs[j]++;
                        now /= j;
                    }
                }
            }
            long ans = 1;
            for (int i = 0; i <= n; i++)
            {
                if (vs[i] != 0)
                {
                    ans *= vs[i] + 1;
                    ans %= mod;
                }
            }
            WriteLine(ans);
        }

    }
}