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 C# (judge verdict: Accepted)

using System;
using System.Linq;

class C2
{
	static int[] Read() => Console.ReadLine().Split().Select(int.Parse).ToArray();
	static void Main()
	{
		var h = Read();
		int x1 = h[2] - h[0], y1 = h[3] - h[1];

		var q = int.Parse(Console.ReadLine());
		var r = new int[q].Select(_ => Read())
			.Select(v =>
			{
				int x2 = v[0] - h[0], y2 = v[1] - h[1];
				return
					x1 * y2 > x2 * y1 ? "COUNTER_CLOCKWISE" :
					x1 * y2 < x2 * y1 ? "CLOCKWISE" :
					x1 * x2 < 0 || y1 * y2 < 0 ? "ONLINE_BACK" :
					Math.Abs(x1) < Math.Abs(x2) || Math.Abs(y1) < Math.Abs(y2) ? "ONLINE_FRONT" :
					"ON_SEGMENT";
			});
		Console.WriteLine(string.Join("\n", r));
	}
}