The fare table (the rule to calculate the fare from the distance) of each company is also given. You decided to provide an enough number of clocks to be hung in the field of view of everyone. Your team customarily takes tea breaks every two hours, during which varieties of new chocolate products of your company are served. Your team members will be satisfied if they have at least one clock (regardless of the orientation of the clock) in their view, or, more precisely, within 45 degrees left and 45 degrees right (both ends inclusive) from the facing directions of their seats.
As the walls are tall enough, you can hang clocks even above the door and can assume one's eyesight is not blocked by other members or furniture. If they are sitting facing each other at positions shown in Figure D.1(A), you need to provide two clocks as they see distinct sections of the wall.


The first line contains the number of team members $n$ $(1 \leq n \leq 1,000)$ and the size of the office room $w$ and $d$ $(2 \leq w, d \leq 100,000)$. Everyone looks forward to the tea breaks so much that they frequently give a glance at a wall clock. One team member asked you to hang a clock on the wall in front of her desk so that she will not be late for tea breaks.
You can also assume that each clock is a point (of size zero), and so you can hang a clock even on a corner of the room. If their seats are arranged as shown in Figure D.1(B), their fields of view have a common point on the wall. Each of the following $n$ lines indicates the position and the orientation of the seat of a team member.


Here $1 \leq x_i \leq w - 1, 1 \leq y_i \leq d - 1$, and $f_i$ is one of N, E, W, and S, meaning north, east, west, and south, respectively. Arrangements (A), (B), and (C) in Figure D.1 correspond to Sample Input 1, 2, and 3, respectively.
The position $(x, y)$ means $x$ distant from the west wall and $y$ distant from the south wall.



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