output_description: Print the sum of all the scores modulo 998244353.
  
  * * *
input_description: The input is given from Standard Input in the following format:
  
      
      
      N
      x_1 y_1
      x_2 y_2
      :
      x_N y_N
attempt: 4
  0 0
  0 1
  1 0
  1 1
  
problem_description: Statement
  
  You are given N points (x_i,y_i) located on a two-dimensional plane. Consider
  a subset S of the N points that forms a convex polygon. Here, we say a set of
  points S _forms a convex polygon_ when there exists a convex polygon with a
  positive area that has the same set of vertices as S. All the interior angles
  of the polygon must be strictly less than 180°.
  
  ![cddb0c267926c2add885ca153c47ad8a.png](https://atcoder.jp/img/arc082/cddb0c267926c2add885ca153c47ad8a.png)
  
  For example, in the figure above, {A,C,E} and {B,D,E} form convex polygons;
  {A,C,D,E}, {A,B,C,E}, {A,B,C}, {D,E} and {} do not.
  
  For a given set S, let n be the number of the points among the N points that
  are inside the convex hull of S (including the boundary and vertices). Then,
  we will define the _score_ of S as 2^{n-|S|}.
  
  Compute the scores of all possible sets S that form convex polygons, and find
  the sum of all those scores.
  
  However, since the sum can be extremely large, print the sum modulo 998244353.
samples: [{"input": "4\n    0 0\n    0 1\n    1 0\n    1 1", "output": "5\n    \n\nWe have five possible sets as S, four sets that form triangles and one set\nthat forms a square. Each of them has a score of 2^0=1, so the answer is 5.\n\n* * *"}, {"input": "5\n    0 0\n    0 1\n    0 2\n    0 3\n    1 1", "output": "11\n    \n\nWe have three \"triangles\" with a score of 1 each, two \"triangles\" with a score\nof 2 each, and one \"triangle\" with a score of 4. Thus, the answer is 11.\n\n* * *"}, {"input": "1\n    3141 2718", "output": "0\n    \n\nThere are no possible set as S, so the answer is 0."}]