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"

arr = Array.new(1000) { 0 }

n = gets.chomp.to_i
cnt = 0
2.upto(n) do |is|
  Prime.prime_division(is).each do |i, pi|
    arr[i] += pi
  end
end

wp = 10**9+7

puts arr.reduce(1) { |a, i|
  next a if i.zero?
  a * (i+1) % wp
}