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 Python (judge verdict: Accepted)

x0, y0, x1, y1 = map(int, raw_input().split())
dx = x1 - x0
dy = y1 - y0
r = dx**2 + dy**2
for t in xrange(input()):
    x, y = map(int, raw_input().split())
    ex = x - x0
    ey = y - y0
    ov = dx*ey - dy*ex
    if ov > 0:
        print "COUNTER_CLOCKWISE"
    elif ov < 0:
        print "CLOCKWISE"
    else:
        iv = dx*ex + dy*ey
        if iv < 0:
            print "ONLINE_BACK"
        elif 0 <= iv <= r:
            print "ON_SEGMENT"
        else:
            print "ONLINE_FRONT"