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 (2.7.1) (judge verdict: Accepted)

require 'prime'

n = gets.chomp.to_i

answer = Prime.each(n).map { |pr|
  1.step.lazy.map { |m| pr ** m }.take_while { |m| m <= n }.map { |m| n / m }.sum
}.inject(1) do |acc, m|
  (acc * (1 + m)) % 1_000_000_007
end

puts answer