CATM  The Cats and the Mouse
In a rectangular field of size n by m squares there is a mouse and two cats. The mouse is the first to make a move, then each of the cats makes a move, then again its the mouse's turn, and so on. In each move both the mouse and the cats can move exactly one square vertically or horizontally. If the mouse is standing at the edge of the field then in its next move it can jump off the field and is saved from the cats. If in the next move one of the cats moves to the field with the mouse then there is no escape for the mouse ... =(
You are to write a program which, knowing the initial positions of mouse and the two cats, will find out if there is any way for the mouse to escape from the cats, assuming of course that each cat will do its best to catch the mouse.
Input
In the first line of input two integers n and m are given, not exceeding 100, where n is the number of rows, and m  the number of columns. The second line contains a number k [k <= 10], which defines the number of test cases for the given field. In the next k lines the initial positions of the mouse and the cats are given. The position in the field is given by two numbers: the first is the number of the row, the second is the number of the column. The first two integers are the coordinates of the mouse, the next four integers are the coordinates of the cats.
Output
You must output k lines with answers for each test case. The answer is YES, if the mouse can escape or NO otherwise.
Example
Input: 5 3 3 2 2 1 1 3 3 2 3 1 3 5 2 3 2 1 2 4 3 Output: NO YES YES
Author: Filimonenkov D.O.
hide comments
ankur314:
20180520 07:30:35
Can anyone explain the logic behind mouse being between diagonal? How can we say for sure that there will be no case providing a contradiction? spoj just checks for a few test cases... 

spa1ish:
20180501 16:18:14
@vivek_prime also make sure that mouse is in between two cats 

beinghemendra:
20180425 17:34:38
AC in one go <3 

sharif ullah:
20180102 20:08:25
its adhoc;


yashgulani:
20171107 20:27:17
The bfs approach that comes in mind can be simply optimised through mathematics in o(m+n).


amulyagaur:
20171104 21:13:22
AC in 1 GO :))) :P 

dwij28:
20170924 13:39:20
Don't know about elegance but it's simple 3xBFS :) 

rc_4594:
20170726 14:56:37
@vivek_prime consider the positions of mouse and cats and try again


vivek_prime:
20170717 22:55:36
i m going by diagonal concept that mouse will be caught when all three are at a diagonal bt i am getting wa.


sas1905:
20170613 03:50:03
Simple adhoc..!! 
Added by:  Roman Sol 
Date:  20060504 
Time limit:  0.158s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ERL JSRHINO NODEJS PERL6 VB.NET 
Resource:  ZCon 2007 