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'
MOD = 10 ** 9 + 7
hash = Hash.new(0)

n = gets.to_i
n.downto(1) do |num|
  divisors = Prime.prime_division(num)
  divisors.each do |divisor, count|
    hash[divisor] += count
  end
end

ans = 1
hash.values.each do |value|
  ans *= (value + 1)
end

puts ans % MOD