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# (.NET Core 3.1.201) (judge verdict: Accepted)

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

namespace AtCoder.C
{
    public class Program
    {
        public static void Main() { var r = GetResult(); Debug.WriteLine(r); Console.Write(r); }

        private static object GetResult()
        {
            var N = ReadLong();

            var insuuCount = new long[1001];
            for (int i = 1; i <= N; i++)
            {
                foreach (var f in GetPrimeFactors(i))
                {
                    insuuCount[f]++;
                }
            }

            var mod = (Modular)1;
            foreach (var count in insuuCount)
            {
                mod *= count + 1;
            }

            return mod;
        }
        public static IEnumerable<long> GetPrimeFactors(long n)
        {
            for (long a = 2; a * a <= n; ++a)
            {
                if (n % a != 0) continue;

                // 割れる限り割り続ける
                while (n % a == 0)
                {
                    yield return a;
                    n /= a;
                }

                // TODO：重複を許さない場合はここで返す
                //yield return a;

            }

            // 最後に残った数について
            if (n != 1) yield return n;
        }
        #region Console.Read

        public static string ReadText() { return Console.ReadLine(); }
        public static List<string> ReadTexts() { return Console.ReadLine().Split(' ').ToList(); }
        public static long ReadLong() { return long.Parse(Console.ReadLine()); }
        public static (long, long) Read2Longs() { var ls = ReadLongs(); return (ls[0], ls[1]); }
        public static (long, long, long) Read3Longs() { var ls = ReadLongs(); return (ls[0], ls[1], ls[2]); }
        public static (long, long, long, long) Read4Longs() { var ls = ReadLongs(); return (ls[0], ls[1], ls[2], ls[3]); }
        public static (long, long, long, long, long) Read5Longs() { var ls = ReadLongs(); return (ls[0], ls[1], ls[2], ls[3], ls[4]); }
        public static List<long> ReadLongs() { return Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList(); }

        #endregion
    }
    public class Modular
    {
        public long Value { get; private set; }

        private static readonly long _mod = (long)Math.Pow(10, 9) + 7;
        private static readonly List<int> _facCache = new List<int> { 1 };

        public static explicit operator long(Modular m) => m.Value;
        public static implicit operator Modular(long a)
        {
            var m = a % _mod;

            return new Modular
            {
                Value = (m < 0) ? m + _mod : m
            };
        }

        public static Modular operator +(Modular a, Modular b) => a.Value + b.Value;
        public static Modular operator -(Modular a, Modular b) => a.Value - b.Value;
        public static Modular operator *(Modular a, Modular b) => a.Value * b.Value;
        public static Modular operator /(Modular a, Modular b) => a * Pow(b, _mod - 2);
        public static Modular Pow(Modular a, long n)
        {
            switch (n)
            {
                case 0:
                    return 1;
                case 1:
                    return a;
                default:
                    var p = Pow(a, n / 2);
                    return p * p * Pow(a, n % 2);
            }
        }
        public static Modular Factorial(long n)
        {
            for (int i = _facCache.Count; i <= n; ++i)
            {
                var fac = (int)(Math.BigMul(_facCache.Last(), i) % _mod);
                _facCache.Add(fac);
            }
            return _facCache[(int)n];
        }
        public static Modular Combination(long n, long r)
        {
            Modular ans = 1;
            for (var i = 0; i < r; i++)
            {
                ans *= n - i;
            }
            for (var i = 1; i <= r; i++)
            {
                ans /= i;
            }

            return ans;
        }
        public override string ToString()
        {
            return Value.ToString();
        }
    }
}