Two-round Olympiad
In the personal informatics olympiad, participants compete over two rounds. Each participant earns points in each round, and their total score is the sum of these points. The scores for each participant in both rounds are known. The jury intends to manipulate the results so that a specific participant emerges as the winner.
The jury can apply the following "adjustments" to the scores (multiple adjustments can be made to the same or different rounds):
Add the same positive number to all participants' scores in one round.
Multiply all participants' scores in one round by a coefficient greater than 1.
The results must remain believable, meaning no participant can score more than 100 points in any round.
Your task is to determine which participants can potentially be made winners through such manipulations. A winner is defined as having a total score for the two rounds that is at least as high as any other participant's total score.
Input
The input begins with the number of participants N (1 ≤ N ≤ 1000). This is followed by N pairs of numbers, representing each participant's scores for the 1-st and 2-nd rounds. Each score is a real number between 0 and 100, with up to 3 decimal places.
Output
The output should first display the number of participants who can be made winners, followed by their indices in ascending order.