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)

N=gets.to_i
MOD = 10**9+7
require 'prime'
h=Hash.new(1)
2.upto(N) do |i|
    i.prime_division.each do |a,b|
        h[a] += b
    end
end

puts h.inject(1) {|r,(k,v)| r*v % MOD}

# 1 2 3 4 5 6
# 1 2 3 2 2 5 2 3
# [1,4,2,0,1]