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: Accepted)

require 'prime'

N = gets.to_i
hash = {}

2.step(N) do |i|
  Prime.prime_division(i).each do |array|
    factor = array[0]
    count = array[1]
    if hash[factor].nil?
      hash[factor] = count
    else
      hash[factor] += count
    end
  end
end

answer = 1
hash.each do |key, value|
  answer = answer * (value + 1) % (10**9 + 7)
end
puts answer