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## 1606. Slalom

Time limit: 1.0 second
Memory limit: 64 MB
Each weekend Petr goes mountain skiing with his friends. He has learned recently that Winter Olympic Games will be held in his city in several years' time. Now Petr dreams of winning a gold Olympic medal in slalom. In this sport, a sportsman must go downhill performing sharp turns, and he mustn't miss the gates placed on the mountain slope.
Petr started training at once because it was not much time left until the Games. He created a training piste for himself by placing n poles on a slope. Then he decided to calculate his downhill trajectory. For this, he plotted the slope in the coordinate system shown in the picture. Petr can begin his descent at any point on the start line (in the scheme, it is the line y = 100000) and end it at any point of the finish line (the line y = 0). His trajectory must be a broken line with vertices at poles. The y coordinate must be decreasing at each moment. Petr wants to ski downhill touching as many poles as possible and changing his direction every time he touches a pole (i.e., if was going rightwards, he must start going leftwards). He also may go through a pole in a straight line without touching it. A possible trajectory is shown in the picture.
Calculate an optimal trajectory for Petr.

### Input

The first line contains the number of poles n (no more than 50000). The following n lines contain coordinates of poles in the form of pairs of integers (xiyi) separated with a space; 1 ≤ in. All xi and all yi are different and are in the range from 1 to 99999.

### Output

In the first line, output the maximal number of poles that Petr can touch when he skis down the slope. In the second line, give the numbers of the poles in the order of touching.

### Samples

inputoutput
```5
5 2
6 5
1 1
4 3
2 4```
```4
2 5 4 3```
```4
1 6
3 4
5 2
4 1```
```3
1 3 4```
Problem Author: Alexander Toropov (prepared by Alexander Ipatov)
Problem Source: IX USU Open Personal Contest (March 1, 2008)
Tags: none