Suppose there are points in a plane no three of which are collinear with the property that if we label these points as in any way whatsoever, the broken line does not intersect itself. Find the maximum value of .
Suppose there are $n$ points in a plane no three of which are collinear with the property that if we label these points as $A_1,A_2,\ldots,A_n$ in any way whatsoever, the broken line $A_1A_2\ldots A_n$ does not intersect itself. Find the maximum value of $n$.
Školjka 
points in a plane no three of which are collinear with the property that if we label these points as 
in any way whatsoever, the broken line 
does not intersect itself. Find the maximum value of