Problem:
Score : 400 points

Problem Statement

You are given an integer N. Among the divisors of N! (= 1 \times 2 \times ... \times N), how many Shichi-Go numbers (literally "Seven-Five numbers") are there?

Here, a Shichi-Go number is a positive integer that has exactly 75 divisors.

Note

When a positive integer A divides a positive integer B, A is said to a divisor of B.
For example, 6 has four divisors: 1, 2, 3 and 6.

Constraints

1 \leq N \leq 100

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print the number of the Shichi-Go numbers that are divisors of N!.

Sample Input 1

9

Sample Output 1

0

There are no Shichi-Go numbers among the divisors of 9! = 1 \times 2 \times ... \times 9 = 362880.

Sample Input 2

10

Sample Output 2

1

There is one Shichi-Go number among the divisors of 10! = 3628800: 32400.

Sample Input 3

100

Sample Output 3

543

Solution in Haskell (GHC 7.10.3) (judge verdict: Accepted)


{-# LANGUAGE TupleSections #-}

import Data.Array (accumArray, (!), elems)

ptable = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47]

pfact [] n = []
pfact _ 1 = []
pfact (p:ps) n
  | mod n p == 0 = p : pfact (p:ps) (div n p)
  | otherwise = pfact ps n

c m = length . filter (>=(m-1))

main = do
  n <- read <$> getLine
  let fact = filter (>1) . elems . accumArray (+) 0 (2,47) . concat $
                [map (,1) $ pfact ptable x | x<-[2..n]] 
  print $ sum [ c 75 fact
              , c 25 fact * (c 3 fact - 1)
              , c 15 fact * (c 5 fact - 1)
              -- aC2 == aP2 / 2
              , ((c 5 fact * (c 5 fact - 1)) `div` 2) * (c 3 fact - 2)
              ]