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)

M=10**9+7
h=Hash.new{0}
h[1]=0
(2..gets.to_i).each do |x|
  (2..x).each do |i|
    while (x%i).zero?
      x /= i
      h[i] += 1
    end
  end
end
p h.map{|k,v|v+1}.inject(:*)%M