Polygonal Query

Let $S$ be a set of points on a 2-dimensional plane. Initially, $S$ is an empty set. Let convexHull($S$) be the subset of $S$ that contains the vertices of the convex hull of $S$, with no three collinear points.

There are $Q$ queries. Each query is one of the following two types.

1. add($x$, $y$): Adds the point ($x$, $y$) to $S$. No two points share the same $x$ coordinate or the same $y$ coordinate.
2. findHeavy($x_1$, $y_1$, $x_2$, $y_2$): The points ($x_1$, $y_1$) and ($x_2$, $y_2$) are distinct points of convexHull($S$). This query is only called when convexHull($S$) has at least three points. A robot is at ($x_1$, $y_1$) and wants to go to ($x_2$, $y_2$). The robot can only move along the edges of the convex hull. Let $cw$ be the number of points of convexHull($S$) that the robot passes when it moves clockwise, and let $ccw$ be the number it passes when it moves counterclockwise. If $cw \ge ccw$, output "CW". Otherwise, output "CCW".

The first line contains an integer $Q$ ($1 \le Q \le 100000$). The next $Q$ lines each contain three or five integers.

• If the $i$-th query is add($x$, $y$), the $i$-th line is 0 $x$ $y$ ($0 \le x, y \le 1000000$).
• If the $i$-th query is findHeavy($x_1$, $y_1$, $x_2$, $y_2$), the $i$-th line is 1 $x_1$ $y_1$ $x_2$ $y_2$ ($0 \le x_1, y_1, x_2, y_2 \le 1000000$).

For each findHeavy query, print the answer on its own line.