Myacm Triangles

Considerable archeological work has been done on the ancient Myacm culture. Many artifacts have been found in what are called power fields: a fairly small area, less than 100 meters on a side, containing between four and fifteen tall monuments with crystals on top. One such area is shown above. Most artifacts come from inside a triangular region formed by exactly three of the monuments, now called the power triangle. Archeologists agree on how this triangle is chosen among all triangles whose vertices are three monuments: it is the triangle of largest possible area that contains no other monument inside it or on any of its edges. Each field contains exactly one such triangle.

Write a program that, given the monument positions for any number of power fields, determines the power triangle of each field.

A useful formula: the area of a triangle with vertices $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$ is the absolute value of $0.5 \times [(y_3 - y_1)(x_2 - x_1) - (y_2 - y_1)(x_3 - x_1)]$.

The input describes one or more power fields. Each field begins with a line containing the number of monuments, which is at least 4 and at most 15. Each of the following lines describes one monument: a single-character label followed by its coordinates, which are nonnegative integers less than 100. Labels are assigned in order, so the first monument is A, the second is B, then C, and so on. Input ends with a line containing a single 0 in place of the monument count.

For each power field, output one line containing the three labels of the power triangle's vertices in increasing alphabetical order, with no spaces between them.