BEENUMS  Beehive Numbers
A beehive is an enclosed structure in which some honey bee species live and raise their
young. In this problem we consider a twodimensional sketch of the beehives. Each
beehive is composed of a certain number of cells, where each cell is a regular hexagon.
Each cell may have some neighbors, which are other cells that share a side with that cell.
A cell with exactly 6 neighbors is an internal cell, while a cell with fewer neighbors is an
external one. Notice that an external cell can always be changed to internal by adding
some neighbor cells.
We are interested in a particular class of beehives. This class of valid beehives is defined
recursively as follows: a) a single cell is a valid beehive; and b) given a valid beehive B,
if we add the minimum number of cells such that each external cell of B becomes an
internal cell, the result is a valid beehive.
The number of cells in a valid beehive is called a beehive number. Given an integer N ,
you must decide whether it is a beehive number.
Input
Each test case is described using a single line. The line contains an integer N (1 ≤ N ≤
10^{9} ). The end of input is indicated with a line containing a single −1.
Output
For each test case, output a single line containing an uppercase “Y” if N is a beehive
number, or an uppercase “N” otherwise.
Example
Input:
43
1
7
19
15
1
Output:
N
Y
Y
Y
N
hide comments
aj_254:
20190518 00:33:43
beautiful question just observe pattern .... 1,1+6,1+6+12,1+6+12+18.... next layer contain 6*lyaer number+prev


kamesh11:
20181202 10:34:05
My first ever application of Binary Search :) 

vvp_15:
20180726 17:09:25
yo..AC in one go


kuchnahiaata:
20180328 22:26:16
HINT: SEQUENCES AND SERIES :) 

bayulaxana:
20171230 10:00:10
AC in one Go .. :)


nihaalbn:
20171209 18:06:33
take care of 1 at the end of input ac in 2nd go ;p 

sai__teja_01:
20171129 18:51:20
AC in a go chillar sum da 

hitesh87:
20171005 20:18:10
HINTS:google beehive structure 

amulyagaur:
20170718 19:07:06
can be done with binary search 

ABHISHEK:
20170531 04:27:05
If you are using brute force for the obtained pattern than the time complexity is square root n :) 
Added by:  Pablo Ariel Heiber 
Date:  20100926 
Time limit:  0.666s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 NODEJS OBJC VB.NET 
Resource:  FCEyN UBA ICPC Selection 2010 