KPPOLY  Projections Of A Polygon
You are given a convex polygon on Cartesian coordinate system. It has projections on X and Yaxis. You can arbitrary rotate this polygon. What minimum and maximum sum of projections can you achieve?
Input
First line contains one integer number N (3 ≤ N ≤ 100)  number of polygon's vertices. Following N lines contain vertex coordinates X_{i} and Y_{i}. All numbers are integers. Vertices are given in clockwise or anticlockwise direction. No two vertices coincide. No three consecutive vertices lie on the same line. All coordinates do not exceed 10000 by absolute value.
Output
Write minimum and maximum value of sum of the polygon's projections. Separate them by a space. Your answer should not differ with the correct one more than 10^{6}.
Example
Input: 4 0 0 0 1 1 1 1 0 Output: 2 2.828427124
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Akshay Aradhya:
20180329 14:07:15
what does "minimum and maximum sum of projections" mean ? 

lu:
20170301 16:09:57
O(n) solution 

weathervane:
20170122 20:46:15
The problem statement is unclear, as can be seen from its age, its one vote, and the few people who have attempted it. The single test case reveals nothing by providing a square. Please, at least provide two small but interesting examples. Unfortunately in this scheme, you cannot downvote a question until you have solved it. 

mkmostafa:
20150825 00:04:53
first go AC!! :D 

npsabari:
20130620 01:51:55
Precision matters a lot! Be careful about that 

Branfili:
20130419 11:54:44
@Mihai


Mihai Negrean:
20130415 17:26:28
I have a question: the problem states that "You can arbitrary rotate this polygon."

Added by:  Pavel Kuznetsov 
Date:  20070325 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  ADA95 ASM32 BASH BF C CSHARP CPP C99 CLPS LISP sbcl LISP clisp D FORTRAN HASK ICON ICK JAVA LUA NEM NICE OCAML PASGPC PASFPC PERL PHP PIKE PRLGswi PYTHON RUBY SCM guile SCM qobi ST WHITESPACE 
Resource:  Vologda 2007 