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'

mod = 10 ** 9 + 7

N = gets.to_i
h = Hash.new(0)

(2..N).each do |i|
  (i.prime_division.to_h).each do |k,v|
    h[k] += v
  end
end

ans = 1
h.each do |k, v|
  ans = ans * (v+1) % mod
end

puts ans