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.Collections.Generic;
using System.Linq;
using System.Text;
using System.Diagnostics;
using Aoj.CGL.Lib;

namespace Aoj.CGL.Chapter1C
{
    using Point = Vector;

    class Program
    {
        public static string ConvertCcwIntToStr(int ccw)
        {
            var map = new Dictionary<int, string> (){
                {MathUtil.CounterClockwise, "COUNTER_CLOCKWISE"},
                {MathUtil.Clockwise,        "CLOCKWISE"},
                {MathUtil.OnLineBack,       "ONLINE_BACK" },
                {MathUtil.OnSegment,        "ON_SEGMENT"},
                {MathUtil.OnLineFront,      "ONLINE_FRONT"},
            };

            return map[ccw];
        }

        public static void Solve()
        {
            var input = Array.ConvertAll(Console.ReadLine().Split(' '), double.Parse);
            var p0 = new Point(input[0], input[1]);
            var p1 = new Point(input[2], input[3]);

            int q = int.Parse(Console.ReadLine());
 
            for (int i = 0; i < q; i++)
            {
                var x_y = Array.ConvertAll(Console.ReadLine().Split(' '), double.Parse);

                var p2 = new Point(x_y[0], x_y[1]);
                int ccw = MathUtil.Ccw(p0, p1, p2);

                Console.WriteLine("{0}", ConvertCcwIntToStr(ccw));
            }
        }

        public static void Main()
        {
            // Console.SetIn(new System.IO.StreamReader("ComputationalGeometry/Input/01_Projection_C_04.txt"));
            // var sw = new Stopwatch();
            // sw.Start();

            Solve();

            // Console.WriteLine("{0}ms", sw.ElapsedMilliseconds);
        }
    }
}

namespace Aoj.CGL.Lib
{
    using Line = Segment;

    using Point = Vector;

    using Polygon = List<Vector>;

    public struct Segment
    {
        private Point _p1;
        private Point _p2;

        public Point P1 { get{ return _p1; } }
        public Point P2 { get{ return _p2; } }

        public Segment(Point p1, Point p2)
        {
            _p1 = p1;
            _p2 = p2;
        }

        public Segment(double x1, double y1, double x2, double y2)
        {
            _p1 = new Point(x1, y1);
            _p2 = new Point(x2, y2);
        }

        public override string ToString()
        {
            return string.Format("P1x:{0},P1y:{1}, P2x:{2},P2y:{3}", P1.X, P1.Y, P2.X, P2.Y);
        }
    }

    public struct Circle
    {
        private Point _p;
        private double _r;

        public Point P { get { return _p; } }
        public double R { get { return _r; } }

        public Circle(Point p, double r)
        {
            _p = p;
            _r = r;
        }

        public override string ToString()
        {
            return string.Format("px:{0},py:{1},r:{2}", P.X, P.Y, R);
        }
    }

    public struct Vector
    {
        private double _x;
        private double _y;

        public double X { get { return _x;} }
        public double Y { get { return _y;} }

        public Vector(double x, double y)
        {
            _x = x;
            _y = y;
        }

        public double Norm()
        {
            return X * X + Y * Y;
        }

        public double Abs()
        {
            return Math.Sqrt(Norm());
        }

        public Vector Normalize()
        {
            double mag = Abs();
            return new Vector(X * mag, Y * mag);
        }

        public static Vector operator +(Vector v1, Vector v2)
        {
            return new Vector(v1.X + v2.X, v1.Y + v2.Y);
        }

        public static Vector operator -(Vector v1, Vector v2)
        {
            return new Vector(v1.X - v2.X, v1.Y - v2.Y);
        }

        public static Vector operator *(Vector v, double k)
        {
            return new Vector(v.X * k, v.Y * k);
        }

        public static Vector operator *(double k, Vector v)
        {
            return v * k;
        }

        public override string ToString()
        {
            return string.Format("x:{0},y:{1}", X, Y);
        }
    }

    public static class MathUtil
    {
        public static double Dot(Vector v1, Vector v2)
        {
            return v1.X * v2.X + v1.Y * v2.Y;
        }

        public static double Cross(Vector v1, Vector v2)
        {
            return v1.X * v2.Y - v1.Y * v2.X;
        }

        public static bool IsOrthogonal(Vector v1, Vector v2)
        {
            return Dot(v1, v2) == 0.0;
        }

        public static bool IsOrthogonal(Point a1, Point a2, Point b1, Point b2)
        {
            return IsOrthogonal(a1 - a2, b1 - b2);
        }

        public static bool IsOrthogonal(Segment s1, Segment s2)
        {
            return IsOrthogonal((Vector)(s1.P1 - s1.P2), (Vector)(s2.P1 - s2.P2));
        }

        public static bool IsParallel(Vector v1, Vector v2)
        {
            return Cross(v1, v2) == 0.0;
        }

        public static bool IsParallel(Point a1, Point a2, Point b1, Point b2)
        {
            return IsParallel(a1 - a2, b1 - b2);
        }
        public static bool IsParallel(Segment s1, Segment s2)
        {
            return IsParallel((Vector)(s1.P1 - s1.P2), (Vector)(s2.P1 - s2.P2));
        }

        public static Vector Project(Vector v, Vector onNormal)
        {
            // mag = |b|cos?? / |a|
            //     = |a||b|cos?? / |a|^2
            double mag = Dot(v, onNormal) / onNormal.Norm();
            return new Vector(onNormal.X * mag, onNormal.Y * mag);
        }

        public static Point Project(Point p, Segment s)
        {
            Vector v  = p - s.P1;
            Vector baseV = s.P2 - s.P1;
            Vector project = Project(v, baseV);
            return s.P1 + project;
        }

        public static Point Reflect(Point p, Segment s)
        {
            Point project = Project(p, s);
            return p + (project - p) * 2.0;
        }

        // public static Ccw CountrClockWise(Vector baseV, Vector v)
        // {
        //     double cross = Cross(baseV, v);
        //     if (cross > 0.0)
        //         return Ccw.CounterClockwise;
        //     else if (cross < 0.0)
        //         return Ccw.Clockwise;
        //     else if (Dot(baseV, v) < 0.0)
        //         return Ccw.OnLineBack;
        //     else if (baseV.Norm() < v.Norm())
        //         return Ccw.OnLineFront;
        //     else
        //        return Ccw.OnSegment;
        // }

        // ??????????????????????¨??????? ~ ????¨????????????¢???????????°???
        public const int OnLineBack = 2;
        public const int CounterClockwise = 1;
        public const int OnSegment = 0;
        public const int Clockwise = -1;
        public const int OnLineFront = -2;

        /// <summary>
        /// ??????p0p2??????????????????p0p1??????????¨??????? ~ ????¨?????????????????????????????????????int??§?????????
        /// </summary>
        /// <param name="p0"></param>
        /// <param name="p1"></param>
        /// <param name="p2"></param>
        /// <returns></returns>
        public static int Ccw(Point p0, Point p1, Point p2)
        {
            var baseV = p1 - p0;
            var v = p2 - p0;
            if (Cross(baseV, v) > 0)
                return CounterClockwise;
            else if (Cross(baseV, v) < 0)
                return Clockwise;
            else if (Dot(baseV, v) < 0)
                return OnLineBack;
            else if (baseV.Norm() < v.Norm())
                return OnLineFront;
            return OnSegment;
        }
    }
}