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 (2.7.1) (judge verdict: Accepted)

require 'prime'

n = gets.to_i
mod = 10**9 + 7
h = Hash.new(0)

2.upto(n) do |i|
  i.prime_division.each { |p, e| h[p] += e }
end

puts n == 1 ? 1 : h.values.map(&:succ).inject { |x, y| x * y % mod }