Problem K
Kingdom of Kittens
In a country far far away, there are so many cats. The cats quickly dominate the whole area, they can even overwhelm humans! Mature cats plan to establish their own kingdom for their own kittens! The first thing to do is setting the border of their kingdom.
One day, they looked around and found
Unfortunately, cats are not so good at geometry, they do not know any shapes except triangles. Hence, they would like to know if they can make a triangle border containing all of these bushes. The triangle border must have positive area. Please help them!
More formally, given
Input
The input contains multiple test cases. Each test case is described as below:
-
The first line contains an integer
— the number of points. . -
In the next
lines, the -th line contains two integers and — the coordinates of the -th point. .
The input is terminated with a line containing a single
Sum of
Output
For each test case, print ‘YES’ if there is a triangle satisfying the above constraints. Otherwise, print ‘NO’.
Explanation for the first example
Sample Input 1 | Sample Output 1 |
---|---|
4 0 0 0 2 2 0 2 2 5 0 0 0 2 2 0 2 2 1 1 0 |
YES NO |