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
factors = {}
for i in 2..N
    ifacts = i.prime_division
    ifacts.each do |fac|
        if !(factors.has_key?(fac.first))
            factors.store( fac.first, fac.last )
        else
            factors[fac.first] += fac.last
        end
    end
end

# p factors

cnt = 1
factors.each_value do |exp|
    cnt *= exp + 1
end
puts cnt % (10**9 + 7)