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'
M = 10 ** 9 + 7
N = gets.to_i

d = {}
Prime.instance.each(N) do |pr|
  d[pr] = 0
end
(2 .. N).each do |n|
  n.prime_division.each do |n,e|
    d[n] += e
  end
end
ans = d.values.inject(1) do |s, v|
  (s * (v + 1)) % M
end

puts ans