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.Linq;
using System.Text;

public class AtCoderA
{
    static void Main()
    {
        var sc = new Scanner();

        long n = sc.NextLong();

        if (n == 1)
        {
            Console.WriteLine(1);
            return;
        }

        Dictionary<long, long> dic = new Dictionary<long, long>();
        for (long i = 2; i <= n; i++)
        {
            long now = i;
            for (long j = 2; j * j <= i; j++)
            {
                while (now % j == 0)
                {
                    if (dic.ContainsKey(j))
                    {
                        dic[j]++;
                    }
                    else
                    {
                        dic.Add(j, 1);
                    }
                    now /= j;
                }
            }
            if (now != 1)
            {
                if (dic.ContainsKey(now))
                {
                    dic[now]++;
                }
                else
                {
                    dic.Add(now, 1);
                }
            }
        }

        ModInt answer = 1;
        foreach (var item in dic)
        {
            answer *= (item.Value + 1);
        }

        Console.WriteLine(answer);
    }

    // ModInt
    class ModInt
    {
        public const long Mod = (int)1e9 + 7;

        public long num;

        public ModInt(long n) { num = n; }

        public override string ToString() { return num.ToString(); }
        public static ModInt operator +(ModInt l, ModInt r) { l.num += r.num; if (l.num >= Mod) l.num -= Mod; return l; }
        public static ModInt operator -(ModInt l, ModInt r) { l.num -= r.num; if (l.num < 0) l.num += Mod; return l; }
        public static ModInt operator *(ModInt l, ModInt r) { return new ModInt(l.num * r.num % Mod); }
        public static implicit operator ModInt(long n) { n %= Mod; if (n < 0) n += Mod; return new ModInt(n); }

        public static ModInt Pow(ModInt v, long k) { return Pow(v.num, k); }

        public static ModInt Pow(long v, long k)
        {
            long ret = 1;
            for (k %= Mod - 1; k > 0; k >>= 1, v = v * v % Mod)
                if ((k & 1) == 1) ret = ret * v % Mod;
            return new ModInt(ret);
        }

        public static ModInt Inverse(ModInt v) { return Pow(v, Mod - 2); }
    }

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            while (_index >= _line.Length)
            {
                _line = Console.ReadLine().Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            _line = Console.ReadLine().Split(Separator);
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}