Onion Layers

Dr. Kabal, a well-known biologist, has recently discovered a liquid capable of curing even the most advanced diseases. The liquid is extracted from a very rare onion that grows only in a country called Onionland. But not every onion of Onionland is worth taking to the lab: only onions with an odd number of layers contain the miraculous liquid. Quite an odd discovery!

Figure 1: An onion from Onionland

Dr. Kabal has hired several research assistants to collect and analyze onions for him. Because he does not want to share his discovery with the world yet, he did not tell the assistants to look for onions with an odd number of layers. Instead, each assistant was asked to collect onions and to select points from the outer border of each layer, so that the layer structure of the onion can be reconstructed later. Dr. Kabal told the assistants that the next step would be a "complicated analysis" of these points; in fact, all he does is use the points to count the number of layers of each onion and keep the ones with an odd count.

Figure 2: Points collected by an assistant

The approximation reconstructed from the collected points may have a different shape than the original onion. For instance, extracting only some of the points of the onion in Figure 1 yields a set of points like the one in Figure 2, from which Dr. Kabal approximates the original layers and obtains something like Figure 3. His procedure is simple: recursively find nested convex polygons until every point belongs to exactly one polygon. Concretely, take the convex hull of the remaining points as one layer, remove every point lying on that hull, and repeat on the points that are left. The assistants select the points so that the number of layers of this recursive approximation equals the number of layers of the original onion, which is fine for Dr. Kabal. The assistants also know that at least three points are needed to approximate any layer, including the innermost one.

Figure 3: Dr. Kabal's approximation

Given the set of points collected by an assistant, write a program that decides whether the corresponding onion should be taken to the laboratory: that is, whether the number of layers counted by the procedure above is odd.

The input consists of several test cases. The first line of each test case contains an integer $N$ $(3 \le N \le 2000)$, the number of points collected by the assistant. Each of the following $N$ lines contains two integers $X$, $Y$ $(-2000 \le X, Y \le 2000)$, the coordinates of one point. The input ends with a test case where $N = 0$, which must not be processed.

Print one line for each test case. If the onion should be taken to the laboratory (the number of layers is odd), print the string

Take this onion to the lab!

If it should not be taken (the number of layers is even), print the string

Do not take this onion to the lab!