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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.NoSuchElementException;
import java.util.TreeMap;


public class Main {
	static FastScanner sc = new FastScanner();
	static PrintWriter out = new PrintWriter(System.out);
	static int mod = 1_000_000_007;
	public static void main(String[] args) {
		int n = sc.nextInt();
		
		if (n==1){
			out.println(1);
		}
		
		else {
			TreeMap <Integer, Long> set = new TreeMap <Integer, Long>();
			for (int i=2; i<=n; i++){
				set = fact (i, set);
				//out.println(set.entrySet());
			}
			
			long cnt = set.get(set.firstKey());
			cnt++;
			set.pollFirstEntry();
			while (!set.isEmpty()){
				int key = set.firstKey();
				long temp = set.get(key);
				cnt*=(temp+1);
				cnt%=mod;
				set.pollFirstEntry();
			}
			out.println(cnt);
			
		}
		
		out.flush();
	}
	public static TreeMap <Integer, Long> fact (long a, TreeMap <Integer, Long> set){
		for(int i = 2; i<= a; i++) {
	         while(a%i == 0) {
	            if (set.containsKey(i)){
	            	long temp = set.get(i);
	            	temp++;
	            	temp%=mod;
	            	set.put(i, temp);
	            }
	            else
	            	set.put(i, (long) 1);
	            a/=i;
	         }
	    }
		if (a>2) {
			if (set.containsKey(a)){
            	long temp = set.get(a);
            	temp++;
            	temp%=mod;
            	set.put((int) a, temp);
            }
            else
            	set.put((int) a, (long) 1);
		}
		return set;
			
	}
		static class FastScanner {
		    private final InputStream in = System.in;
		    private final byte[] buffer = new byte[1024];
		    private int ptr = 0;
		    private int buflen = 0;

		    private boolean hasNextByte() {
		      if (ptr < buflen) {
		        return true;
		      } else {
		        ptr = 0;
		        try {
		          buflen = in.read(buffer);
		        } catch (IOException e) {
		          e.printStackTrace();
		        }
		        if (buflen <= 0) {
		          return false;
		        }
		      }
		      return true;
		    }

		    private int readByte() {
		      if (hasNextByte()) return buffer[ptr++];
		      else return -1;
		    }

		    private static boolean isPrintableChar(int c) {
		      return 33 <= c && c <= 126;
		    }

		    private void skipUnprintable() {
		      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
		    }

		    public boolean hasNext() {
		      skipUnprintable();
		      return hasNextByte();
		    }

		    public String next() {
		      if (!hasNext()) throw new NoSuchElementException();
		      StringBuilder sb = new StringBuilder();
		      int b = readByte();
		      while (isPrintableChar(b)) {
		        sb.appendCodePoint(b);
		        b = readByte();
		      }
		      return sb.toString();
		    }

		    public long nextLong() {
		      if (!hasNext()) throw new NoSuchElementException();
		      long n = 0;
		      boolean minus = false;
		      int b = readByte();
		      if (b == '-') {
		        minus = true;
		        b = readByte();
		      }
		      if (b < '0' || '9' < b) {
		        throw new NumberFormatException();
		      }
		      while (true) {
		        if ('0' <= b && b <= '9') {
		          n *= 10;
		          n += b - '0';
		        } else if (b == -1 || !isPrintableChar(b)) {
		          return minus ? -n : n;
		        } else {
		          throw new NumberFormatException();
		        }
		        b = readByte();
		      }
		    }

		    public int nextInt() {
		      return (int) nextLong();
		    }

		    public int[] nextIntArray(int N, boolean oneBased) {
		      if (oneBased) {
		        int[] array = new int[N + 1];
		        for (int i = 1; i <= N; i++) {
		          array[i] = sc.nextInt();
		        }
		        return array;
		      } else {
		        int[] array = new int[N];
		        for (int i = 0; i < N; i++) {
		          array[i] = sc.nextInt();
		        }
		        return array;
		      }
		    }

		    public long[] nextLongArray(int N, boolean oneBased) {
		      if (oneBased) {
		        long[] array = new long[N + 1];
		        for (int i = 1; i <= N; i++) {
		          array[i] = sc.nextLong();
		        }
		        return array;
		      } else {
		        long[] array = new long[N];
		        for (int i = 0; i < N; i++) {
		          array[i] = sc.nextLong();
		        }
		        return array;
		      }
		    }
		  }

		}