Two-round Olympiad#819
The personal informatics olympiad is held over two rounds. Each participant earns scores in each round, and their total score is the sum of these scores. The scores for each participant in both rounds are given. The jury wants to manipulate the results so that a specific participant becomes the winner.
The jury can perform the following "adjustments" (it is possible to apply several such adjustments, either 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 .
The results must remain plausible, meaning that no participant can score more than points in any round.
Determine the list of participants who, as a result of such adjustments, can become the winner of the olympiad (i.e., have a total score for the two rounds that is at least as high as each of the other participants).
The input file contains the number of participants (1 \leq N \leq 1000), followed by pairs of numbers: the scores of each participant for the st and nd rounds (the score of a participant for a round is a real number between and , with at most decimal digits).
The output file should first contain the number of participants who can be made winners of the olympiad, followed by their indices in ascending order.
Example 1