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)

# frozen_string_literal: true

$res = Array.new(1000,0)
def factrize(n)
  (2..Math.sqrt(n)).each do |i|
    while n % i == 0
      $res[i] += 1
      n /= i
    end
  end
  $res[n] += 1 if n != 1
end

n = gets.to_i

(2..n).each do |k|
  factrize(k)
end

sum = 1

$res.each do |ex|
  sum *= ex + 1
  sum %= 1e9 + 7
end
puts sum