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.chomp.to_i

divisors = Array.new(1001,0)

1.upto(n) do |i|
  sq = Math.sqrt(i)
  ii = i
  j = 2
  while(true)
    break if ii == 1
    if ii % j == 0
      ii = ii / j
      divisors[j] += 1
      j = 2
    else
      j += 1
    end
  end
end

result = 1
divisors.each do |i|
 result = result * (i+1)
end

puts result % 1000000007