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)

p (1..gets.to_i).flat_map{|i|
	r = []
	p = 2
	while i > 1
		if i%p==0
			r << p
			i /= p
		else
			p += 1
		end
	end
	r
}.group_by{|x|x}.map{|k, v| v.size + 1}.reduce(1, :*) % (10**9+7)