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: Wrong Answer)

x1, y1, x2, y2 = gets.split.map(&:to_i)
u = (x2 - x1) + (y2 - y1) * 1i
gets.to_i.times do
  x, y = gets.split.map(&:to_i)
  v = x - x1 + (y - y1) * 1i
  d = (u.conj * v).imag
  case
  when d > 0
    puts 'COUNTER_CLOCKWISE'
  when d < 0
    puts 'CLOCKWISE'
  else
    d = (v / u).real
    case
    when d < 0
      puts 'ONLINE_BACK'
    when d < 1
      puts 'ON_SEGMENT'
    else
      puts 'ONLINE_FRONT'
    end
  end
end