STONE  Lifting the Stone
There are many secret openings in the floor which are covered by a big heavy stone. When the stone is lifted up, a special mechanism detects this and activates poisoned arrows that are shot near the opening. The only possibility is to lift the stone very slowly and carefully. The ACM team must connect a rope to the stone and then lift it using a pulley. Moreover, the stone must be lifted all at once; no side can rise before another. So it is very important to find the centre of gravity and connect the rope exactly to that point. The stone has a polygonal shape and its height is the same throughout the whole polygonal area. Your task is to find the centre of gravity for the given polygon.
Input
The input consists of T test cases (equal to about 500). The number of them (T) is given on the first line of the input file. Each test case begins with a line containing a single integer N (3 <= N <= 1000000) indicating the number of points that form the polygon. This is followed by N lines, each containing two integers X_{i} and Y_{i} (X_{i}, Y_{i} <= 20000). These numbers are the coordinates of the ith point. When we connect the points in the given order, we get a polygon. You may assume that the edges never touch each other (except the neighbouring ones) and that they never cross. The area of the polygon is never zero, i.e. it cannot collapse into a single line.
Output
Print exactly one line for each test case. The line should contain exactly two numbers separated by one space. These numbers are the coordinates of the centre of gravity. Round the coordinates to the nearest number with exactly two digits after the decimal point (0.005 rounds up to 0.01). Note that the centre of gravity may be outside the polygon, if its shape is not convex. If there is such a case in the input data, print the centre anyway.
Example
Sample Input: 2 4 5 0 0 5 5 0 0 5 4 1 1 11 1 11 11 1 11 Sample output: 0.00 0.00 6.00 6.00
hide comments
dunjen_master:
20170725 16:29:58
AC in one go..formula based 

weathervane:
20170315 20:33:21
@KD so why are you still using float in 21st Century? Are you using a 1980's computer and reading 1980's books? Last edit: 20170315 20:42:36 

plaba:
20170313 15:52:59
@Shesardi: the shape could be convex, which definitely means that some shapes are not regular. 

KD :
20160527 10:26:21
use double float costed me one WA _ 

miloszmaki:
20160304 17:23:49
0.00 instead of 0.00 gives WA. Is such behavior expected? 

Susil KR:
20160113 21:12:36
The second test case shows 5.74 5.90 as answer. Should i need to ceil the values? Even if i did WA is appearing. 

puntu:
20150927 10:25:49
ideone is giving me success. but it is showing me WA. 

ratan tej:
20150909 18:47:28
50th classical :)


Raghav Dilip Mundhada:
20150810 16:37:21
nope, inputs r integer @birdie 

Bhuvnesh Jain:
20150630 15:29:48
thanks L 
Added by:  adrian 
Date:  20040606 
Time limit:  5s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All 
Resource:  ACM Central European Programming Contest, Prague 1999 