Dendroctonus

Mountain pine beetles (Dendroctonus ponderosae) are small pests that bore into trees and cause a huge amount of damage. Their population has grown sharply, and scientists want to know where the outbreak started. In particular, they want to know whether there was a single outbreak or several of them. If there is more than one outbreak, they must raise the alert level.

In one outbreak the beetles start at a single location, called the initial infection point, and slowly work their way outwards. A tree inside the infection area is infected. A tree outside the infection area is not infected. A tree on the boundary of the infection area may or may not be infected. The infection area is always a circle centred at the initial infection point.

You are given the locations of the infected and the non-infected trees. Decide whether there is enough evidence to raise the alert level.

The first line contains one integer $n$ ($1 \le n \le 100$), the number of trees.

Each of the next $n$ lines describes one tree. The line contains two integers $x$ ($-250 \le x \le 250$) and $y$ ($-250 \le y \le 250$), the location of the tree, and one character $p$ that tells whether the tree is infected. If $p$ is I, the tree is infected. If $p$ is N, the tree is not infected. Trees are single points on the plane. The initial infection point of an outbreak does not have to be a tree and does not have to be at integer coordinates. The $n$ trees are at distinct locations.

Print Yes if more than one outbreak is guaranteed, and No otherwise.

A single outbreak explains the observation when some circle holds every infected tree in its interior or on its boundary and holds no non-infected tree in its interior.