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 Haskell (GHC 7.10.3) (judge verdict: Wrong Answer)

factno n = 
    length [ k | k <- [1..n], n `mod` k == 0 ]
 
(%*%) x y = (x * y) `mod` 1000000007
 
main = do
  n <- readLn
  print . foldr (%*%) 1 $ map factno [1..n]