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)

def projecter(x, y, xp, yp)
  return (xp * x + yp * y) / (x ** 2 + y ** 2), (yp * x - xp * y) / (x ** 2 + y ** 2)
end
def main(input = STDIN)
  x1, y1, x2, y2 = input.gets.split(" ").map(&:to_r)
  q = input.gets.to_i
  x, y = (x2 - x1), (y2 - y1)
  q.times do
    xp, yp = input.gets.split(" ").map(&:to_r)
    a, b = projecter(x, y, xp - x1, yp - y1)
    if b > 0
      puts "COUNTER_CLOCKWISE"
    elsif b < 0
      puts "CLOCKWISE"
    elsif a < 0
      puts "ONLINE_BACK"
    elsif a > 1
      puts "ONLINE_FRONT"
    else
      puts "ON_SEGMENT"
    end
  end
end
main