title: Find two farthest points in 2D space (Manhattan distance)
body: <p>Given a list of points in 2D space (x[i], y[i]),we need to find two farthest points (Manhattan distance).</p>
  
  <p>I know the algorithm but I don't quite understand how it works.</p>
  
  <ol>
  <li><p>Find the following points: max(x[i] + y[i]), max(-x[i] + y[i]), max(-y[i] + x[i]) and max(-x[i] - y[i]) among all i.</p></li>
  <li><p>Compute the distance between every point in the list and the four points chosen during the previous step and pick the largest one.</p></li>
  </ol>
  
  <p>Somebody please explain why this algorithm is correct.</p>