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2019-04-08 13:00 UTC

Kattis Set 12

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2019-04-15 09:29 UTC
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Problem C
Convex Hull

/problems/convexhull2/file/statement/en/img-0001.png

Finding the convex hull of a set of points is an important problem that is often part of a larger problem. There are many algorithms for finding the convex hull. Since problems involving the convex hull sometimes appear in the ACM World Finals, it is a good idea for contestants to know some of these algorithms.

Finding the convex hull of a set of points in the plane can be divided into two sub-tasks. First, given a set of points, find a subset of those points that, when joined with line segments, form a convex polygon that encloses all of the original points. Second, output the points of the convex hull in order, walking counter-clockwise around the polygon. In this problem, the first sub-task has already been done for you, and your program should complete the second sub-task. That is, given the points that are known to lie on the convex hull, output them in order walking counter-clockwise around the hull.

Input

The first line of input contains a single integer $3 \le n \le 100\, 000$, the number of points. The following $n$ lines of input each describe a point. Each of these lines contains two integers and either a Y or an N, separated by spaces. The two integers specify the $x$- and $y$-coordinates of the point. A Y indicates that the point is on the convex hull of all the points, and a N indicates that it is not. The $x$- and $y$-coordinates of each point will be no less than $-1\, 000\, 000\, 000$ and no greater than $1\, 000\, 000\, 000$. No point will appear more than once in the input. The points in the input will never all lie on a line.

Output

First, output a line containing a single integer $m$, the number of points on the convex hull. Next output $m$ lines, each describing a point on the convex hull, in counter-clockwise order around the hull. Each of these lines should contain the $x$-coordinate of the point, followed by a space, followed by the $y$-coordinate of the point. Start with the point on the hull whose $x$-coordinate is minimal. If there are multiple such points, start with the one whose $y$-coordinate is minimal.

Sample Input 1 Sample Output 1
5
1 1 Y
1 -1 Y
0 0 N
-1 -1 Y
-1 1 Y
4
-1 -1
1 -1
1 1
-1 1