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'

n = gets.to_i
if n == 1
  puts '1'
  exit
end
M = 10 ** 9 + 7
h = Hash.new(0)
1.upto(n) do |i|
  i.prime_division.each do |k, v|
    h[k] += v
  end
end
puts h.values.map{|i| (i + 1)}.inject{|u, v| u * v % M}