human
Can you provide a Python program to print the above mentioned status given the following:

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
The above is tricky. Write me a correct solution in PYTHON3.
assistant
#Here is Python program to print the above mentioned status.

import math
from typing import Union

class Point(object):
    __slots__ = ['x', 'y']

    def __init__(self, x, y):
        self.x = x
        self.y = y

    def __add__(self, other):
        return Point(self.x + other.x, self.y + other.y)

    def __sub__(self, other):
        return Point(self.x - other.x, self.y - other.y)

    def __mul__(self, other: Union[int, float]):
        return Point(self.x * other, self.y * other)

    def __repr__(self):
        return f"({self.x},{self.y})"

class Vector(Point):
    __slots__ = ['x', 'y', 'pt1', 'pt2']

    def __init__(self, pt1: Point, pt2: Point):
        from_pt1_to_pt2 = pt2 - pt1
        super().__init__(from_pt1_to_pt2.x, from_pt1_to_pt2.y)
        self.pt1 = pt1
        self.pt2 = pt2

    def dot(self, other):
        return self.x * other.x + self.y * other.y

    def cross(self, other):
        return self.x * other.y - self.y * other.x

    def norm(self):
        return pow(self.x, 2) + pow(self.y, 2)

    def abs(self):
        return math.sqrt(self.norm())

    def __repr__(self):
        return f"{self.pt1},{self.pt2}"

class Segment(Vector):
    __slots__ = ['x', 'y', 'pt1', 'pt2']

    def __init__(self, pt1: Point, pt2: Point):
        super().__init__(pt1, pt2)

    def projection(self, pt: Point)-> Point:
        t = self.dot(Vector(self.pt1, pt)) / pow(self.abs(), 2)
        return Point(self.pt1.x + t * self.x, self.pt1.y + t * self.y)

    def reflection(self, pt: Point) -> Point:
        return self.projection(pt) * 2 - pt

    def point_geometry(self, pt: Point):
        vec_pt1_to_pt = Vector(self.pt1, pt)
        cross = self.cross(vec_pt1_to_pt)
        if cross > 0:
            print('COUNTER_CLOCKWISE')
            return
        elif cross < 0:
            print('CLOCKWISE')
            return
        else:           # cross == 0
            dot = self.dot(vec_pt1_to_pt)
            if dot < 0:
                print('ONLINE_BACK')
                return
            else:       # dot > 0
                if self.abs() <...