# Five for week 06

# Convex Hull

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** ≤ **n** ≤ **100000**, 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 **-1000000000** and no greater than **1000000000**. 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.

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