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.strip.to_i

if n==1
  p 1
  exit
end

dividers = [0]*(n+1)
(1..n).each do |num|
  Prime.prime_division(num).each do |index, multi|
    dividers[index] += multi
  end
end

MOD = 10**9+7
result = dividers.select {|v| v>0 }.map {|e| e+1 }.inject {|m,v| (m*v)%MOD }
p result