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: Wrong Answer)

require 'prime'
n = gets.to_i
if n == 1
  puts 1
  exit(0)
end

elems = Hash.new {1}
(2..n).each do |i|
  p [i, Prime.prime_division(i)]
  Prime.prime_division(i).each do |a|
    elems[a[0]] += a[1]
  end
end
puts elems.values.inject(&:*) % 1000000007