Problem:
﻿Score: 100 points

Problem Statement

In AtCoder city, there are five antennas standing in a straight line. They are called Antenna A, B, C, D and E from west to east, and their coordinates are a, b, c, d and e, respectively.

Two antennas can communicate directly if the distance between them is k or less, and they cannot if the distance is greater than k.

Determine if there exists a pair of antennas that cannot communicate directly.

Here, assume that the distance between two antennas at coordinates p and q (p < q) is q - p.

Constraints

a, b, c, d, e and k are integers between 0 and 123 (inclusive).

a < b < c < d < e

Input

Input is given from Standard Input in the following format:

a
b
c
d
e
k

Output

Print :( if there exists a pair of antennas that cannot communicate directly, and print Yay! if there is no such pair.

Sample Input 1

1
2
4
8
9
15

Sample Output 1

Yay!

In this case, there is no pair of antennas that cannot communicate directly, because:

the distance between A and B is 2 - 1 = 1

the distance between A and C is 4 - 1 = 3

the distance between A and D is 8 - 1 = 7

the distance between A and E is 9 - 1 = 8

the distance between B and C is 4 - 2 = 2

the distance between B and D is 8 - 2 = 6

the distance between B and E is 9 - 2 = 7

the distance between C and D is 8 - 4 = 4

the distance between C and E is 9 - 4 = 5

the distance between D and E is 9 - 8 = 1

and none of them is greater than 15. Thus, the correct output is Yay!.

Sample Input 2

15
18
26
35
36
18

Sample Output 2

:(

In this case, the distance between antennas A and D is 35 - 15 = 20 and exceeds 18, so they cannot communicate directly.
Thus, the correct output is :(.

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

module Main (main) where

import Control.Monad
import qualified Data.ByteString.Char8 as C8
import Data.Bool
import Data.Maybe

main :: IO ()
main =
  replicateM 6 readInts >>= print . showAnswer . solve . concat

type Input  = [Int]
type Output = Bool

solve :: Input -> Output
solve [a,b,c,d,e,k] = all ((<=k).abs) $ ((-) <$> xs <*> xs)
  where
    xs = [a,b,c,d,e]

showAnswer :: Output -> Answer
showAnswer = String . bool ":(" "Yay!"

-- utils
readInts :: IO [Int]
readInts = map (fst . fromJust . C8.readInt) . C8.words <$> C8.getLine

data Answer
  = YesNo Bool
  | YESNO Bool
  | AB Bool
  | Number Int
  | String String
  | Compare Ordering
  | Compare2 Ordering

instance Show Answer where
  show (YesNo b)    = bool "No" "Yes"  b
  show (YESNO b)    = bool "NO" "YES"  b
  show (AB b)       = bool "B"  "A"    b
  show (Number i)   = show i
  show (String s)   = s
  show (Compare o)  = ordering "<" "=" ">" o
  show (Compare2 o) = ordering "Right" "Balanced" "Left" o

ordering :: a -> a -> a -> Ordering -> a
ordering lt eq gt o = case o of
  LT -> lt
  EQ -> eq
  GT -> gt