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

MOD = 10**9+7

hash = {}
1.upto(N) do |n|
  n.prime_division.each do |p|
    hash[p[0]] ||= 0
    hash[p[0]] += p[1]
  end
end

res = 1
hash.values.each do |v|
  res *= v + 1
  res %= MOD
end

p res