Lining Up

Lining Up

``How am I ever going to solve this problem?" said the pilot.

Indeed, the pilot was not facing an easy task. She had to drop packages at specific points scattered in a dangerous area. Furthermore, the pilot could only fly over the area once in a straight line, and she had to fly over as many points as possible. All points were given by means of integer coordinates in a two-dimensional space. The pilot wanted to know the largest number of points from the given set that all lie on one line. Can you write a program that calculates this number?

Your program has to be efficient!

Input

The input begins with a single positive integer on a line by itself indicating the number of the cases following, each of them as described below. This line is followed by a blank line, and there is also a blank line between two consecutive inputs.
The input consists of N pairs of integers, where 1 < N < 700. Each pair of integers is separated by one blank and ended by a new-line character. The list of pairs is ended with an end-of-file character. No pair will occur twice.

Output

For each test case, the output must follow the description below. The outputs of two consecutive cases will be separated by a blank line.
The output consists of one integer representing the largest number of points that all lie on one line.

Sample Input

1

1 1
2 2
3 3
9 10
10 11

Sample Output

3


   
   
   
   

    
    
    
    
    
    
    
    import
    
    
    
     java.io.BufferedReader;

    
    
    
    import
    
    
    
     java.io.IOException;

    
    
    
    import
    
    
    
     java.io.InputStreamReader;

    
    
    
    import
    
    
    
     java.util.ArrayList;

    
    
    
    import
    
    
    
     java.util.HashMap;


    
    
    
    public
    
    
    
     
    
    
    
    class
    
    
    
     Problem270 
    
    
    
    
    
    
    
    {

    /** *//**
     * @param args
     */
    public static void main(String[] args) {
        int times=0;
        
        ArrayList param = new ArrayList();
        ArrayList result = new ArrayList();
        
        int largestNum = 0;
        
        String s=null;
        try {
            //get start point
            BufferedReader cin = new BufferedReader( new InputStreamReader( System.in ) );
            s = cin.readLine();
            
            if(s==null || s.length()<1 || !isNumber(s)){
                if(Integer.parseInt(s)>=700 || Integer.parseInt(s)<=0){
                    System.out.println("error! the start number must between 0 to 700");
                    return;
                }else{
                    System.out.println("input a number!!");
                }
            }
            
            times = Integer.parseInt(s);
            
            //get the space line
            cin = new BufferedReader( new InputStreamReader( System.in ) );
            s = cin.readLine();
            if(s.trim().length()>0){
                System.out.println("you must enter a space line here!!");
                return;
            }
            
            for(int i=0; i<times; i++){    
                while(true){
                    cin = new BufferedReader( new InputStreamReader( System.in ) );
                    s = cin.readLine();
                    if(s.trim().length()<1){
                        result.add(calculate(param, largestNum));
                        param = new ArrayList();
                        largestNum=0;
                        break;
                    }
                                
                    if(isParams(s)){
                        param.add(s);
                    
                        //set largestNum
                        String[] strs = s.split(" ");
                        if(largestNum<Integer.parseInt(strs[0])){
                            largestNum=Integer.parseInt(strs[0]);
                        }
                        if(largestNum<Integer.parseInt(strs[1])){
                            largestNum=Integer.parseInt(strs[1]);
                        }
                    }else{
                        System.out.println("error param!");
                        return;
                    }
                }
            }
            
//            //after get params, creat a new array
//            int[][] road = initRoad(param, largestNum);
//            s = (String) param.get(startpoint-1);
//            String[] strs = s.split(" ");
//            
//            int x = Integer.parseInt(strs[0]);
//            int y = Integer.parseInt(strs[1]);
//            
//            calculate(road, x, y);
            
            for(int i=0; i<times; i++){
                System.out.println(result.get(i));
                System.out.println("");
            }
            
            
        } catch (IOException e) {
            // TODO Auto-generated catch block
            e.printStackTrace();
        }    

    }
    
    private static String calculate(ArrayList param, int largestNum) {
        int[][] road = initRoad(param, largestNum);
            
        int tempPointNum=0;
        
        //leftbottom
        for(int i=0; i<road.length; i++){
            int temp = getTempPointNum(0, 0, i, road.length-1, road);
            if(temp>tempPointNum){
                tempPointNum = temp;
            }
        }
        
//        rightbottom
        for(int i=0; i<road.length; i++){
            int temp = getTempPointNum(0, 0, road.length-1, i, road);
            if(temp>tempPointNum){
                tempPointNum = temp;
            }
        }
        
//        leftbottom
        for(int i=0; i<road.length; i++){
            int temp = getTempPointNum(road.length-1, road.length-1, i, road.length-1, road);
            if(temp>tempPointNum){
                tempPointNum = temp;
            }
        }
        
//        rightbottom
        for(int i=0; i<road.length; i++){
            int temp = getTempPointNum(road.length-1, road.length-1, road.length-1, road.length-1, road);
            if(temp>tempPointNum){
                tempPointNum = temp;
            }
        }
        
        return tempPointNum + "";
    }

    private static int getTempPointNum(int x1, int y1, int x2, int y2, int[][] road) {
        int result=0;
        if(x1==x2){
            for(int i=y1>y2?y2:y1; i<(y1>y2?y1:y2); i++){
                if(road[x1][i]==1)
                    result++;
            }
            return result;
        }
        
        
        double liner = Math.abs(y1-y2)/Math.abs(x1-x2);
        if(liner>=0){
            if(x1>x2){
                for(int i=x2; i<=x1; i++){
                    int tempY = (int)((i-x2)*liner + y2);
                    if(x2==i&&y2==tempY){
                        
                    }else if((y2-tempY)/(x2-i)==liner){
                        
                    }else{
                        continue;
                    }
                    
                    if(road[i][tempY]==1)
                        result++;
                }
            }else{
                for(int i=x1; i<=x2; i++){
                    int tempY = (int)((i-x1)*liner + y1);
                    if(x1==i&&y1==tempY){
                        
                    }else if((y1-tempY)/(x1-i)==liner){
                        
                    }else{
                        continue;
                    }
                    
                    if(road[i][tempY]==1)
                        result++;
                }
            }
        }
        return result;
    }

    private static int[][] initRoad(ArrayList param, int largestNum) {
        // TODO Auto-generated method stub
        int[][] result = new int[largestNum][largestNum];
        
        String s=null;
        String[] strs;
        for(int i=0; i<param.size(); i++){
            s = (String) param.get(i);
            strs = s.split(" ");
            result[Integer.parseInt(strs[0])-1][Integer.parseInt(strs[1])-1] = 1;
        }        
        return result;
    }

    private static boolean isParams(String s) {
        String[] strs = s.split(" ");
        if(strs.length!=2){
            return false;
        }
        
        if(isNumber(strs[0]) && isNumber(strs[1])){
            return true;
        }
        
        return false;
    }

    private static boolean isNumber(String s) {
        boolean result = true;
        for(int i=0; i<s.length(); i++){
            if(s.charAt(i)>='0' && s.charAt(i)<='9'){
                continue;
            }else{
                result=false;
                break;
            }
        }
        return result;
    }

}