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 static System.Console;
using static System.Convert;
using static System.Math;
//using static System.Globalization.CultureInfo;

class Program
{ 
    static void Main(string[] args)
    {
        var num = Input.num;
        var dic = new Dictionary<long, long>();
        var f = new Calculation.Factorization(num);
        for(var i = 2; i <= num; i++)
        {
            var d = f.Fact(i);
            foreach (var pair in d)
                if (dic.ContainsKey(pair.Key))
                    dic[pair.Key] += pair.Value;
                else dic[pair.Key] = pair.Value;
        }
        var res = 1L;
        foreach (var val in dic.Values)
            res = (res * (val + 1)) % Input.MOD;
        WriteLine(res);
    }
}

public class Input
{
    public static string read => ReadLine();
    public  static int[] ar => Array.ConvertAll(read.Split(' '), int.Parse);
    public  static int num => ToInt32(read);
    public static long[] arL => Array.ConvertAll(read.Split(' '), long.Parse);
    public  static long numL => ToInt64(read);
    public static int[][] twodim(int num)
        => Enumerable.Repeat(0, num).Select(v => ar).ToArray();
    public static long[][] twodimL(int num)
        => Enumerable.Repeat(0, num).Select(v => arL).ToArray();
    public const double eps = 1e-11;
    public  const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public  const int MOD = 1000000007;
}

public class Calculation
{
    public static int LCM(int num1, int num2)
    {
        return num1 / GCD(num1, num2) * num2;
    }

    public static long LCM(long num1, long num2)
    {
        return num1 / GCD(num1, num2) * num2;
    }

    public static int GCD(int num1, int num2)
    {
        return num1 < num2 ? GCD(num2, num1) :
            num2 > 0 ? GCD(num2, num1 % num2) : num1;
    }

    public static long GCD(long num1, long num2)
    {
        return num1 < num2 ? GCD(num2, num1) :
            num2 > 0 ? GCD(num2, num1 % num2) : num1;
    }

    private static int Multiple(int num1, int num2)
        => (int)(BigMul(num1, num2) % Input.MOD);
    
    public static int Pow(int m,int n)
    {
        if (n == 0) return 1;
        if (n % 2 == 0) return Pow(Multiple(m, m), n / 2);
        else return Multiple(Pow(Multiple(m, m), n / 2), m);
    }

    public static int Div(int a, int b)
        => Multiple(a, Pow(b, Input.MOD - 2));

    public static List<int> GetPrime(long num)
    {
        if (num < 2) return new List<int>();
        var prime = new List<int> { 2 };
        var bo = new bool[num + 1];
        for (var i = 3; i <= num; i += 2)
            if (!bo[i])
            {
                prime.Add(i);
                for (var j = 3 * i; j <= num; j += 2 * i)
                    bo[j] = true;
            }
        return prime;
    }
    public class Combination
    {
        private int[] _fac;
        public Combination(int num)//階乗をメモ化
        {
            _fac = new int[num + 1];
            _fac[0] = 1;
            for (var i = 1; i <= num; i++)
                _fac[i] = Multiple(_fac[i - 1], i);
        }
        public int Comb(int n,int r)
        {
            if (n < r) return 0;
            if (n == r) return 1;
            var calc = _fac[n];
            calc = Div(calc, _fac[r]);
            calc = Div(calc, _fac[n - r]);
            return calc;
        }
    }

    public class Factorization
    {
        private int[] _prime;
        public Factorization(long num)
        {
            _prime = GetPrime((int)Math.Pow(num, 1d / 2)).ToArray();
        }

        public Dictionary<long, int> Fact(long num)
        {
            var dic = new Dictionary<long, int>();
            foreach (var p in _prime)
            {
                var ct = 0;
                while (num % p == 0)
                {
                    ct++;
                    num /= p;
                }
                if (ct != 0) dic[p] = ct;
            }
            if (num != 1) dic[num] = 1;
            return dic;
        }
    }

    
}