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: Wrong Answer)

require 'prime'

n = gets.to_i

primes = Hash.new(0)
(2..n).each { |i|
  i.prime_division.each { |p, n|
    primes[p] = primes[p] + n
  }
}

p primes
p primes.values.inject(1) { |mem, var| mem * (var + 1) } % (10 ** 9 + 7)