/**

  * Definition for a point.

  * class Point {

  *     int x;

  *     int y;

  *     Point() { x = 0; y = 0; }

  *     Point(int a, int b) { x = a; y = b; }

  * }

  */

 import java.util.HashMap;

 import java.util.Map;

 public class Solution {

     public int maxPoints(Point[] points) {

         if (points == null || points.length == 0)

             return 0;

         int N = points.length;

         if (N == 1)

             return 1;

         if (N == 2)

             return 2;

         Map<String, Integer> dict = new HashMap<String, Integer>();

         int maxOverall = 0;

         for (int i = 0; i < N - 1; i++) {

             int same = 1;

             int max = 0;

             for (int j = i + 1; j < N; j++) {

                 int p1x = points[i].x;

                 int p1y = points[i].y;

                 int p2x = points[j].x;

                 int p2y = points[j].y;

                 if (p1x == p2x && p1y == p2y) {

                     same++;

                     continue;

                 }

                 int A = p2y - p1y;

                 int B = p1x - p2x;

                 int GCD = gcd(A, B);

                 if (GCD != 0 && GCD != 1) {

                     A /= GCD;

                     B /= GCD;

                 }

                 if (A < 0) {

                     A = -A;

                     B = -B;

                 }

                 String key = A + "," + B;

 //              System.out.println("round:" + i + " " + key);

                 int value = 1;

                 if (dict.containsKey(key)) {

                     value += dict.get(key);

                 }

                 dict.put(key, value);

                 max = max < value  ? value  : max;

             }

             max += same;

             maxOverall = maxOverall < max ? max : maxOverall;

             dict.clear();

         }

         return maxOverall;

     }

     public int gcd(int a, int b) {

         if (b == 0)

             return a;

         return gcd(b, a % b);

     }

 }