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.chomp.to_i

MOD = 10**9 + 7

# √1000（31）までの素数を求める
prime = [2]

(3..31).each do |i|
  judge = true
  prime.each do |number|
    if i % number == 0
      judge = false
      break
    end
  end

  prime.push(i) if judge
end

h = Hash.new(0)

1.upto(n) do |i|
  arr = i.prime_division
  arr.each do |k,v|
    h[k] += v
  end
end

ans = 1

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

p ans