As you know, the personal Olympiad in Informatics is held in two rounds. On each of the rounds, participants receive some points, while the final score is determined as the sum of the points received. The scores that each participant received in each of the rounds are known. The jury wants to falsify the results of the Olympiad so that the “necessary” one wins. member.
In this case, the jury can make the following "rigging" (you can do several "rigging" in relation to both the same and different tours):
Add the same positive number to the results of all participants in one of the rounds.
Multiply the results of the participants in one of the rounds by some coefficient greater than 1.
At the same time, the plausibility of the results should be preserved, which lies in the fact that none of the participants should receive more than 100 points for each of the rounds.
Determine the list of participants who, as a result of such falsifications, may turn out to be the winners of the Olympiad (that is, in the sum of two rounds, have no less points than each of the other participants).
Input
The input file contains first the number of participants N (1 ≤ N ≤ 1000), then N pairs of numbers — the results of each participant for the 1st and 2nd rounds (the result of the participant for the round — is a real number from 0 to 100) with no more than 3 decimal places.
Imprint
In the output file, first print the number of participants who can become winners of the Olympiad, and then print their numbers in ascending order.
Examples
| # |
Input |
Output |
| 1 |
4
45 90
70 80
0 0
75 75 |
2
24 |