Problem:
Score: 200 points

Problem Statement

The number 105 is quite special - it is odd but still it has eight divisors.
Now, your task is this: how many odd numbers with exactly eight positive divisors are there between 1 and N (inclusive)?

Constraints

N is an integer between 1 and 200 (inclusive).

Input

Input is given from Standard Input in the following format:

N

Output

Print the count.

Sample Input 1

105

Sample Output 1

1

Among the numbers between 1 and 105, the only number that is odd and has exactly eight divisors is 105.

Sample Input 2

7

Sample Output 2

0

1 has one divisor. 3, 5 and 7 are all prime and have two divisors. Thus, there is no number that satisfies the condition.

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

import Control.Applicative
import Data.List


main = do
    n <- readLn
    putStrLn $ show (solve n)

factors :: Int -> [Int]
factors n = [x | x <- [1..n], n `mod` x == 0]

factorization :: Int -> [Int]
factorization 1 = []
factorization x = v : factorization (x `div` v)
    where
        v = (factors x) !! 1

ndivider :: Int -> Int
ndivider n = foldl (\acc x -> acc * (length x + 1)) 1 (group $ factorization n)

solve :: Int -> Int
solve n = length([x | x <- [1..n], x `mod` 2 == 1, ndivider x == 8])