p02292 Counter-Clockwise
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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).

Constraints

* 1 ≤ q ≤ 1000
* -10000 ≤ xi, yi ≤ 10000
* p0 and p1 are not identical.

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.

Examples

Input

0 0 2 0
2
-1 1
-1 -1


Output

COUNTER_CLOCKWISE
CLOCKWISE


Input

0 0 2 0
3
-1 0
0 0
3 0


Output

ONLINE_BACK
ON_SEGMENT
ONLINE_FRONT
```python
x0,y0,x1,y1 = map(int, input().split())
p0=complex(x0,y0)
p1=complex(x1,y1)
q = int(input())

CCW = {1: 'COUNTER_CLOCKWISE',
       -1: 'CLOCKWISE',
       2: 'ONLINE_BACK',
       -2: 'ONLINE_FRONT',
       0: 'ON_SEGMENT',}

def dot(a, b):
  return a.real * b.real + a.imag * b.imag

def cross(a, b):
  return a.real * b.imag - a.imag * b.real

def ccw(p0, p1, p2):
  a = p1-p0
  b = p2-p0
  if cross(a,b) > 0:
    return 1 #couner_clockwise
  elif cross(a,b) <0:
    return -1 #clockwise
  elif dot(a,b) < 0:
    return 2 #online_back
  elif abs(a) < abs(b):
    return -2 #online_front
  else:
    return 0 #on_segment

for i in range(q):
  p2=complex(*map(int,input().split()))
  print(CCW[ccw(p0,p1,p2)])

```