/**
 * Definition for a point.
 * class Point {
 *     int x;
 *     int y;
 *     Point() { x = 0; y = 0; }
 *     Point(int a, int b) { x = a; y = b; }
 * }
 */
public class Solution {
  public int maxPoints(Point[] points) {
            if (points==null) return 0;
            if (points.length<=2) return points.length;

            Map<Integer,Map<Integer,Integer>> map = new HashMap<Integer,Map<Integer,Integer>>();
            int result=0;
            for (int i=0;i<points.length;i++){ 
                map.clear();
                int overlap=0,max=0;
                for (int j=i+1;j<points.length;j++){
                    int x=points[j].x-points[i].x;
                    int y=points[j].y-points[i].y;
                    if (x==0&&y==0){
                        overlap++;
                        continue;
                    }
                    int gcd=generateGCD(x,y);
                    if (gcd!=0){
                        x/=gcd;
                        y/=gcd;
                    }

                    if (map.containsKey(x)){
                        if (map.get(x).containsKey(y)){
                            map.get(x).put(y, map.get(x).get(y)+1);
                        }else{
                            map.get(x).put(y, 1);
                        }                       
                    }else{
                        Map<Integer,Integer> m = new HashMap<Integer,Integer>();
                        m.put(y, 1);
                        map.put(x, m);
                    }
                    max=Math.max(max, map.get(x).get(y));
                }
                result=Math.max(result, max+overlap+1);
            }
            return result;


        }
        private int generateGCD(int a,int b){

            if (b==0) return a;
            else return generateGCD(b,a%b);

        }
}