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)

x0, y0, x1, y1 = gets.chomp.split.map(&:to_f)
len1 = (x1 - x0) ** 2 + (y1 - y0) ** 2

gets.to_i.times{
    x2, y2 = gets.chomp.split.map(&:to_f)
    len2 = (x2 - x0) ** 2 + (y2 - y0) ** 2
    yonline = Rational((y1 - y0) * (x2 - x0) + (x1 - x0) * y0, x1 - x0) if x0 != x1

    arr = []
    if x0 < x1
        arr = [yonline, Rational(y2, 1), (x1 - x0) * (x2 - x0)]
    elsif x0 > x1
        arr = [Rational(y2, 1), yonline, (x1 - x0) * (x2 - x0)]
    else
        if y0 < y1
            arr = [x2, x0, (y1 - y0) * (y2 - y0)]
        else
            arr = [x0, x2, (y1 - y0) * (y2 - y0)]
        end
    end
    judge = ""
    if arr[0] < arr[1]
        judge = "COUNTER_CLOCKWISE"
    elsif arr[0] > arr[1]
        judge = "CLOCKWISE"
    else
        if arr[2] < 0
            judge = "ONLINE_BACK"
        else
            if len1 < len2
                judge = "ONLINE_FRONT"
            else
                judge = "ON_SEGMENT"
            end
        end
    end
    puts judge
}