Nothing On TV#3076
Message on a TV program in one London hotel
John likes visiting London pubs. Unfortunately, there is no pub directly in the house where he lives, but there are plenty around. John likes going to pubs, but he will not go to just any pub. When going to a pub, John often thinks that he is going to the wrong pub and should have chosen another one.
Recently, John met his friend Jack, a psychologist and mathematician, and told him about his problem. They conducted an investigation and found out when John thinks he is going to the wrong pub. Consider pubs as points on the plane, and let John's home be located at the point . The pubs are located at points (x_i, y_i) . Consider the -th pub located at (x_i, y_i) . Draw a circle with the segment (0, 0)-(x_i, y_i) as its diameter.
Let us call such a pub good if there is no other good pub located inside this circle or on its boundary. John feels good only when he is going to a good pub.
Now John and Jack wonder, which are the pubs that John could go to without feeling he is making a mistake. Help them!
The first line of the input file contains — the number of pubs in John's neighborhood ( 1 \leq n \leq 100000 ). The next lines contain two integers x_i and y_i each ( |x_i|, |y_i| \leq 30000 ). No two pubs coincide. There is no pub at .
The first line of the output file must contain — the number of good pubs. The second line must contain integers: the indices of these pubs. The pubs are numbered starting from in the order they are listed in the input file.
Note that there is a pub at inside the circle for the pub at , but that pub is not good, so it does not matter.
Example 1