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)

n = gets.chomp.to_i
nbang = 1
n.downto(1){ |v| nbang *= v }

factors = []
p = 2
  while nbang >= p 
    if nbang % p == 0
     nbang /= p
      factors[p] ||= 0
      factors[p] += 1
    else
      p += 1
    end
  end

result = 1
factors.each_with_index do |fac|
  result *= fac + 1 if fac
end

puts result