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: Time Limit Exceeded)

class Integer
  def !
    (1..self).inject(1, &:*)
  end
end

def d(i)
  ret = []
  (1..i).each do |k|
    ret << k if i % k == 0
  end
  ret.length
end

fact_n = gets.chomp.to_i.!
puts d(fact_n) % (10 ** 9 + 7)