Medals

At the Olympic Games, countries are ranked by the medals their athletes win, and there is more than one reasonable way to do this. In Europe, countries are ranked first by the number of gold medals; ties are broken by silver medals, and then by bronze medals. In Canada, countries are instead ranked by the total number of medals, giving gold, silver, and bronze equal weight.

In general, a ranking scheme can be thought of as a vector of positive weights. This weight vector is multiplied component-wise with each country's medal vector, and the resulting scalar (dot) product is that country's score, which is then used to produce the ranking. Under this scheme the European method corresponds to the weight vector $(10^{20}, 10^{10}, 1)$, whereas the Canadian method corresponds to the vector $(1, 1, 1)$.

In this problem you only need to consider weight vectors of the form $(1/n^{j}, 1/n^{k}, 1/n^{l})$, where $n$ is the total number of medals won by all athletes at the Games and $j$, $k$, and $l$ are integers.

Given a list of countries and the number of gold, silver, and bronze medals each one won, determine whether there is a weight vector of the above form under which Canada ranks first, that is, whether Canada can obtain a score strictly higher than every other country.

The input contains multiple test cases. Each test case starts with an integer $c$, the number of countries to follow. Each of the following $c$ lines contains the name of a country and three integers $g$, $s$, and $b$ - the number of gold, silver, and bronze medals won by that country.

The last test case is followed by a line with $c = 0$, which must not be processed. Each test case contains at most $20$ different countries, and the total number of medals in a test case is smaller than $100$. Country names do not contain whitespace characters.

For each test case, print a single line. Print

Canada wins!

if there is a weight vector of the required form such that Canada ranks first, and print

Canada cannot win.

otherwise.