Problem:
Counter-Clockwise

For given three points p0, p1, p2, print

COUNTER_CLOCKWISE

if p0, p1, p2 make a counterclockwise turn (1),

CLOCKWISE

if p0, p1, p2 make a clockwise turn (2),

ONLINE_BACK

if p2 is on a line p2, p0, p1 in this order (3),

ONLINE_FRONT

if p2 is on a line p0, p1, p2 in this order (4),

ON_SEGMENT

if p2 is on a segment p0p1 (5).

Input

xp0 yp0 xp1 yp1
q
xp20 yp20
xp21 yp21
...
xp2q-1 yp2q-1

In the first line, integer coordinates of p0 and p1 are given. Then, q queries are given for integer coordinates of p2.

Output

For each query, print the above mentioned status.

Constraints

1 ≤ q ≤ 1000

-10000 ≤ xi, yi ≤ 10000

p0 and p1 are not identical.

Sample Input 1

0 0 2 0
2
-1 1
-1 -1

Sample Output 1

COUNTER_CLOCKWISE
CLOCKWISE

Sample Input 2

0 0 2 0
3
-1 0
0 0
3 0

Sample Output 2

ONLINE_BACK
ON_SEGMENT
ONLINE_FRONT

Solution in Haskell (judge verdict: Accepted)

import Control.Applicative ((<$>))
import Control.Monad
import Data.Complex

type Vector = Complex Double

eps :: Double
eps = 1e-7

dot :: Vector -> Vector -> Double
dot a b = realPart $ conjugate a * b

cross :: Vector -> Vector -> Double
cross a b = imagPart $ conjugate a * b

readWords :: Read a => IO [a]
readWords = map read . words <$> getLine

main :: IO ()
main = do
  [x1,y1,x2,y2] <- readWords :: IO [Double]
  let
    p0 = x1:+y1
    p1 = x2:+y2

  q <- readLn

  ps <- replicateM q $ do
    [x,y] <- readWords :: IO [Double]
    return $ x:+y

  forM_ ps $ \p2 -> do
    let sgn = (p1-p0)`cross`(p2-p0)

    when (sgn > eps) $ putStrLn "COUNTER_CLOCKWISE"
    when (sgn < -eps) $ putStrLn "CLOCKWISE"

    when (abs sgn < eps) $ do
      if (p1-p0)`dot`(p2-p0) < 0
        then putStrLn "ONLINE_BACK"
        else if magnitude (p2-p0) > magnitude (p1-p0)
          then putStrLn "ONLINE_FRONT"
          else putStrLn "ON_SEGMENT"