21635_Pancake

One time, Anthony has made a pancake, whose shape is a simple polygon. Anthony wants to cut the pancake into pieces with a knife. He is wondering what the maximum number of pieces he can get after one single cut is. He needs your help.

Figure 1  example

Notice that you can not cut the pancake through a vertex, as in Figure 1.

The input is a sequence of data sets, each has the following format.

n

x₁  y₁

...

x_n  y_n

The first line contains an integer n ( 3 ≤ n ≤ 100 ), which is the number of vertices. And the following n lines contains n different point, each line represents a vertex. Edges of the polygon connect vertices given in two adjacent vertex data lines, and in the last and the first vertex data lines. ( -100000000 ≤ x_i, y_i ≤ 100000000, both are integers ).

Edges intersect only at vertices. Three vertices may stand on one line.

The input is ended by n = 0.

Output one integer for each input case, representing the largest number of pieces.

5
0 0
2 0
2 2
1 1
0 2
0

3