Tomya is a girl. She loves Chef Ciel very much.

Today, too, Tomya is going to Ciel's restaurant. Of course, Tomya would like to go to Ciel's restaurant as soon as possible. Therefore Tomya uses one of the shortest paths from Tomya's house to Ciel's restaurant. On the other hand, Tomya is boring now to use the same path many times. So Tomya wants to know the number of shortest paths from Tomya's house to Ciel's restaurant. Your task is to calculate the number under the following assumptions.

Tomya is a girl. She loves Chef Ciel very much.

Tomya writes a tetragon (see the below Notes 1 for details) in her map. The map has N points, whose coordinate are (X_i, Y_i), denoting Ciel's restaurants. Each vertex of the tetragon written by Tomya is one of the Ciel's restaurants.