Given *n* different points on the plane,
pick any three of them
so that the perimeter of the resulting triangle is maximum.

**Input**

Input consists of several cases,
each with *n* followed by *n* pairs of integer coordinates (*x*, *y*).
Assume 3 ≤ *n* ≤ 10^{4},
−10^{8} ≤ *x*, *y* ≤ 10^{8},
and that no three given points are colinear.

**Output**

For every case, print the maximum perimeter of all the possible triangles with four digits after the decimal point. The input cases have no precision issues.

**Observation**

All “big” private test cases were built
by choosing a “typical” geometric figure
(such as a rectangle, a triangle, a circle, an ellipse, or alike),
and placing *n* points at random inside it,
always avoiding repeated points
and points that would be collinear with two other points.

Public test cases

**Input**

3 0 0 0 1 1 0 5 -1 1 3 2 1 1 -2 -1 1 -3

**Output**

3.4142 14.8217

Information

- Author
- Salvador Roura
- Language
- English
- Official solutions
- C++
- User solutions
- C++