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.Text;

// using System.Numerics;
using System.Runtime.CompilerServices;
using System.Diagnostics;
using ll=System.Int64;
using static Contest_C.Lib_IO;
using static Contest_C.Lib_Minifunc;



public static class Contest_C
{

	public static void Main() {
		checked{
			long  n;
			Lib_IO.rm(out n);

			if(n<2){
				wm(1);
				return;
			}

			var pfs = PrimeFactor(Enumerable.Range(2,(int)n-1).ToArray()); 

			Dictionary<ll,ll> d = new Dictionary<ll, ll>();
			foreach (var pf in pfs)
			{
				foreach (var p in pf)
				{
					initd(d,p);
					d[p]++;
				}
			}


			ll ans = 1;
			foreach (var e in d)
			{
				ans = (ans * (e.Value+1))%MOD1;
			}

			Lib_IO.wm(ans);
		}
	}


	public static long[][] PrimeFactor(int[] a) {
		long n = a.Max();
		bool[] is_prime = Enumerable.Repeat(true,(int)n+1).ToArray();
		long[] min_factor = new long[n+1];
		is_prime[0] = is_prime[1] = false;
		min_factor[0] = 0;
		min_factor[1] = 1;
		long i1 = 2;
		long i2;
		for(long i = 2; (i2 = i * i) <= n; ++i) {
			if(is_prime[i]) {
				min_factor[i] = i;
				for(long j = i2; j < is_prime.Length; j += i) {
					is_prime[j] = false;
					if(min_factor[j] == 0) min_factor[j] = i;
				}
			}
			i1 = i;
		}
		for(long i = i1; i <= n; ++i) {
			if(is_prime[i]) min_factor[i] = i;
		}
		var ret = new long[a.Length][];
		for(int k=0; k<a.Length; k++) {
			var prime_list = new List<long>();
			long tmp = a[k];
			while(tmp > 1) {
				long fact = min_factor[tmp];
				tmp /= fact;
				prime_list.Add(fact);
			}
			ret[k] = prime_list.ToArray();
		}
		return ret;
	}
















#region BaseModule


public static class Lib_Minifunc{
	[MethodImpl(256)] public static void swap1<T>(ref T a, ref T b) { T t = a; a = b; b = t; }
	[MethodImpl(256)] public static void swap2<T>(ref T a, ref T b) where T : IComparable { if (a.CompareTo(b)==1) swap1(ref a, ref b); }  // b の方が小さければ交換
	[MethodImpl(256)] public static bool chmin<T>(ref T a, T b) where T : IComparable { if (a.CompareTo(b)== 1) { a = b; return true; } return false; }  // b の方が小さければ a を更新
	[MethodImpl(256)] public static bool chmax<T>(ref T a, T b) where T : IComparable { if (a.CompareTo(b)==-1) { a = b; return true; } return false; }  // b の方が大きければ a を更新
	[MethodImpl(256)] public static bool inside(long i, long n) => (0<=i&&i<n);
	[MethodImpl(256)] public static bool inside(long x, long y, long w, long h) => (inside(x,w)&&inside(y,h));
	[MethodImpl(256)] public static T min<T>(params T[] a) where T : IComparable => a.Min();
	[MethodImpl(256)] public static T max<T>(params T[] a) where T : IComparable => a.Max();
	[MethodImpl(256)] public static long mod(long a, long m=MOD1) { var v = a%m; return (v<0?v+m:v); }
	[MethodImpl(256)] public static long ceiling(long a, long b) => (a%b==0?a/b:a/b+1);	// 整数商の切り上げ
	[MethodImpl(256)] public static P<T,U> initp<T,U>(T a,U b) => new P<T,U>(a,b);
	[MethodImpl(256)] public static P<T,U,V> initp<T,U,V>(T a,U b,V c) => new P<T,U,V>(a,b,c);
	[MethodImpl(256)] public static P<T,U,V,W> initp<T,U,V,W>(T a,U b,V c,W d) => new P<T,U,V,W>(a,b,c,d);
	[MethodImpl(256)] public static bool initd<T,U>(Dictionary<T,U> d, T k) { if(d.ContainsKey(k)) { return false; } else { d[k] = default(U); return true; } }
	public static T[][] initm<T>(long len1,long len2,T val) where T : struct { var m = new T[len1][]; for (int i=0;i<m.Length;i++) m[i] = Enumerable.Repeat(val,(int)len2).ToArray(); return m; }
	public static T[][][] initm<T>(long len1,long len2,long len3,T val) where T : struct { var m = new T[len1][][]; for (int i=0;i<m.Length;i++) m[i] = initm(len2,len3,val); return m; }
	public const long MOD1 = 1000000007; // 10^9+7
	public const double EPS1 = 1e-8;
	public const long INF1 = 1000000000000000;  // 10^15
}

public struct P<T,U>
{
	public T A; public U B;
	public P(T a,U b) { A = a; B = b; }
	public static implicit operator KeyValuePair<T,U>(P<T,U> a) => new KeyValuePair<T,U>(a.A,a.B);
	public static implicit operator P<T,U>(KeyValuePair<T,U> a) => new P<T,U>(a.Key,a.Value);
}
public struct P<T,U,V>
{
	public T A; public U B; public V C;
	public P(T a,U b,V c) { A = a; B = b; C = c; }
}
public struct P<T,U,V,W>
{
	public T A; public U B; public V C; public W D;
	public P(T a,U b,V c,W d) { A = a; B = b; C = c; D = d; }
}

public static class Lib_IO
{
	class Prt : System.IO.StreamWriter
	{
		public override IFormatProvider FormatProvider { get { return System.Globalization.CultureInfo.InvariantCulture; } }
		public Prt(System.IO.Stream s) : base(s,new UTF8Encoding(false,true)) {}
		public Prt(System.IO.Stream s,Encoding e) : base(s,e) {}
	}
	static Prt sw = new Prt(Console.OpenStandardOutput());
	static char[] sp = new char[] {' '};
	[MethodImpl(256)] static bool eq<T,U>() => typeof(T).Equals(typeof(U));
	[MethodImpl(256)] static T ct<T,U>(U a) => (T)Convert.ChangeType(a,typeof(T));
	[MethodImpl(256)] static T cv<T>(string s) =>
		eq<T,int>()	? ct<T,int>(int.Parse(s))
	  : eq<T,long>()   ? ct<T,long>(long.Parse(s))
	  : eq<T,double>() ? ct<T,double>(double.Parse(s,System.Globalization.CultureInfo.InvariantCulture))
	  : eq<T,char>()   ? ct<T,char>(s[0])
					   : ct<T,string>(s);
	public static string[] rm<T>(out T a) {
		var z = Console.ReadLine().Split(sp,StringSplitOptions.RemoveEmptyEntries); 
		a = cv<T>(z[0]);
		return z;
	}
	public static string[] rm<T,U>(out T a,out U b) {
		var z = rm<T>(out a); 
		b = cv<U>(z[1]);
		return z;
	}
	public static string[] rm<T,U,V>(out T a,out U b,out V c) {
		var z = rm<T,U>(out a,out b); 
		c = cv<V>(z[2]);
		return z;
	}
	public static string[] rm<T,U,V,W>(out T a,out U b,out V c,out W d) {
		var z = rm<T,U,V>(out a,out b,out c); 
		d = cv<W>(z[3]);
		return z;
	}
	public static string[] rm<T,U,V,W,X>(out T a,out U b,out V c,out W d,out X e) {
		var z = rm<T,U,V,W>(out a,out b,out c,out d); 
		e = cv<X>(z[4]);
		return z;
	}
	public static string[] rm<T,U,V,W,X,Y>(out T a,out U b,out V c,out W d,out X e,out Y f) {
		var z = rm<T,U,V,W,X>(out a,out b,out c,out d,out e); 
		f = cv<Y>(z[5]);
		return z;
	}
	public static string[] ra<T>(out T[] a) {		
		var z = Console.ReadLine().Split(sp,StringSplitOptions.RemoveEmptyEntries);
		a = z.Select(cv<T>).ToArray();
		return z;
	}
	public static string[][] rl<T>(long n,out T[] a) {
		a = new T[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) y[i] = rm(out a[i]);
		return y;
	}
	public static string[][] rl<T,U>(long n,out P<T,U>[] a) {
		a = new P<T,U>[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) {
			T o; U p;
			y[i] = rm(out o,out p);
			a[i] = new P<T,U>(o,p);
		}
		return y;
	}
	public static string[][] rl<T,U,V>(long n,out P<T,U,V>[] a) {
		a = new P<T,U,V>[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) {
			T o; U p; V q;
			y[i] = rm(out o,out p,out q);
			a[i] = new P<T,U,V>(o,p,q);
		}
		return y;
	}
	public static string[][] rl<T,U,V,W>(long n,out P<T,U,V,W>[] a) {
		a = new P<T,U,V,W>[n];
		var y = new string[n][];
		for(int i=0;i<n;i++) {
			T o; U p; V q; W r;
			y[i] = rm(out o,out p,out q,out r);
			a[i] = new P<T,U,V,W>(o,p,q,r);
		}
		return y;
	}
	public static string[][] rx<T>(long n,out T[][] a) {
		a = new T[n][];
		var y = new string[n][];
		for(int i=0;i<n;i++) y[i] = ra(out a[i]);
		return y;
	}

	static void wwp(Action act){
		sw.AutoFlush = false;
		Console.SetOut(sw);
		act();
		Console.Out.Flush();
		sw.AutoFlush = true;
		Console.SetOut(sw);
	}
	[MethodImpl(256)] static string wfm(Type t) =>t.Equals(typeof(double)) ? "{0:F10}" : "{0}";
	public static void wm(params object[] a) {
		wwp(()=>{
			for(int i=0;i<a.Length;i++) {
				var f = wfm(a[i].GetType()) + ((i<a.Length-1) ? " " : Environment.NewLine);
				Console.Write(f,a[i]);
			}
		});
	}
	public static void wa<T>(IList<T> a) {
		wwp(()=>{
			var f = wfm(typeof(T));
			var g = f + " ";
			var h = f + Environment.NewLine;
			for(int i=0;i<a.Count;i++) Console.Write(((i<a.Count-1) ? g : h),a[i]);
		});
	}
	public static void wl<T>(IList<T> a) {
		wwp(()=>{
			var f = wfm(typeof(T)) + Environment.NewLine;
			foreach(T x in a) Console.Write(f,x);
		});
	}
}

#endregion



}