Inside Polygon

A polygon can be described as a sequence of points, which each point is described by its x- and y-coordinate. For example,

(0, 0) (0, 1) (1, 1) (1, 0)

describes a cube with the above four as its corners. Similarly,

(0, 0) (2, 2) (4, 0)

describes a triangle. In general a sequence

(x1, y1) (x2, y2) (x3, y3) ... (xn, yn)

describes the polygon formed by the lines
from (x1, y1) to (x2, y2),
from (x2, y2) to (x3, y3),
...
from (xn, yn) to (x1, y1).

You are asked to solve the following problem: Given a polygon, described by a sequence of points, and a point, described by its x- and y-coordinate, does the point lie within the polygon?

For example, the points (0, 0) and (1, 1) lie within the polygon

(0, 0) (2, 2) (4, 0)

but the point (0, 1) does not lie with that polygon.

To solve this problem, you may want to have a look at the API of the class contest.Polygon which can be found at the URL here. The class is already part of your classpath. For those using eclipse or NetBeans, a jar file containing the contest.Polygon class can be found here.

Input

The input consists of two lines. The first line describes a polygon. The second line describes the point. We leave out the brackets and commas. The coordinates are all integers. Below you find a sample.

Output

Print true if the point lies with the polygon, and print false otherwise.

Sample input

0 0 2 2 4 0
1 1

Sample output

true