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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

n = gets.chomp.to_i

require 'prime'

class Integer
  def my_divisor_list2
    return [1] if self == 1
    Prime.prime_division(self).map do |e|
      Array.new(e[1]+1).map.with_index do |element, i|
        e[0]**i
      end
    end.inject{|p,q| p.product(q)}.map do |a|
      [a].flatten.inject(&:*)
    end.sort
  end
end

def factorial(number)
  (1..number).inject(1,:*)
end

p factorial(n).my_divisor_list2.count % (10**9 + 7)