HAREFOX  Hares and Foxes
The Antique Comedians of Malidinesia play an interesting comedy where many animals occur. Because they want their plays to be as true as possible, a specialist studies the behaviour of various animals. Recently, he is interested in a binary dynamic ecological system haresfoxes (SHF). As a part of this project, you are asked to design and implement intelligent automatic target evaluation simulator (IATES) for this system. The behaviour of the SHF follows so called standard model, described by the following set of difference equations.
h_{y+1} = a.h_{y}  b.f_{y}
f_{y+1} = c.f_{y} + d.h_{y}
where h_{y} resp. f_{y} represent the difference of the number of hares resp. foxes in year _{y} and the reference count determined at the beginning of the experiment. The units of h_{y} and f_{y} are unknown. Therefore, h_{y} and f_{y} are to be treated as real numbers. Your task is to write a program to determine the long term evolution of SHF.
Input
The input consists of N cases (equal to about 5000). The first line of the input contains only positive integer N. Then follow the cases. Each case consists of six real numbers a, b, c, d, h_{1998} and f_{1998}, written in this order on three lines, two numbers per line, separated by one or more spaces. The numbers are given in the classical format, i.e. optional sign, sequence of digits, optional dot and optional sequence of digits. The text form of a number does not exceed 10 characters. Each case is followed by one empty line.
Output
For each case, print one of the following sentences:
 'Ecological balance will develop.'  if after sufficiently long time the population of both hares and foxes approaches the reference count with an arbitrary a priori given precision, i.e. lim h_{y}=0 and lim f_{y}=0.
 'Hares will die out while foxes will overgrow.'  if after sufficiently long time the population of hares resp. foxes falls under resp. exceeds any a priori given threshold, i.e. lim h_{y}=infinity and lim f_{y}=+infinity.
 'Hares will overgrow while foxes will die out.'  if after sufficiently long time the population of foxes resp. hares falls under resp. exceeds any a priori given threshold, i.e. lim h_{y}=+infinity and lim f_{y}=infinity.
 'Both hares and foxes will die out.'  if after sufficiently long time the population of both hares and foxes falls under any a priori given threshold, i.e. lim h_{y}=infinity and lim f_{y}=infinity.
 'Both hares and foxes will overgrow.'  if after sufficiently long time the population of both hares and foxes exceeds any a priori given threshold, i.e. lim h_{y}=+infinity and lim f_{y}=+infinity.
 'Chaos will develop.'  if none of the above mentioned description fits.
Example
Sample input: 2 2 0.5 0.5 0.6 2 3 0.1 1 2 0.1 1 1 Sample output: Both hares and foxes will overgrow. Hares will die out while foxes will overgrow.
hide comments
susiconfusi:
20160608 20:53:06
Reading three lines, each with two numbers, didn't work for all testcases. I got runtime error NZEC.


Andrew Cooper:
20110216 03:40:23
Can you give me clue as to why submission 4691851 gives an NZEC error? It runs fine, and give the right answer, on ideone.com with the sample input from the problem. I've found that if I wrap the lines in main which set h and f in a try block then I don't get the NZEC, but I do get wrong answer (obviously). 

Hagen von Eitzen:
20101118 23:00:16
EDIT: Never mind my misreading the unusual way of specifiÃ½ing a matrix. Last edit: 20101119 17:24:22 

Riley:
20101006 06:08:12
Are the full stops in the equation decimal points, or multipliers? 

Prakash:
20100331 09:21:18
do we need to include new line after each sentence in o/p (even last line )?? 
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 1998 