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

divs = {}

(2..N).each do |i|
    Prime.prime_division(i).each do |pr, n|
        divs[pr] ||= 0
        divs[pr] += n
    end
end

MOD = 10**9 + 7

prod = 1

divs.each do |pr, n|
    prod *= (n + 1)
    prod %= MOD
end

puts prod