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 Ruby (judge verdict: Accepted)

require 'matrix'

p0x, p0y, p1x, p1y = gets.split.map &:to_i
p0 = Vector[p0x, p0y]
p1 = Vector[p1x, p1y]

q = gets.to_i

def cross(p1, p2)
  return p1[0] * p2[1] - p1[1] * p2[0]
end

q.times do
  p2x, p2y = gets.split.map &:to_i
  p2 = Vector[p2x, p2y]
  if cross(p2-p1, p0-p1) > 0
    puts "COUNTER_CLOCKWISE"
  elsif cross(p2-p1, p0-p1) < 0
    puts "CLOCKWISE"
  elsif (p0-p1).inner_product(p2-p1) < 0
    puts "ONLINE_FRONT"
  elsif (p0-p1).norm >= (p2-p1).norm
    puts "ON_SEGMENT"
  else
    puts "ONLINE_BACK"
  end
end