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

prime = []
for i in 2..n
  f = true
  for j in 2...i
    f = false if i%j==0
    #p [i,j]
  end
  prime << i if f
end

fac = []
prime.each{|l|
  t = l
  a = 0
  while n/t>0
    a += n/t
    t *= l
  end
  fac << a+1
}
#p prime

p fac.inject(1){|ans, x| ans*x % (10**9+7)}