BEENUMS - Beehive Numbers

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A beehive is an enclosed structure in which some honey bee species live and raise their young. In this problem we consider a two-dimensional 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 ≤ 109). 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
Sagar Grover: 2013-08-07 14:25:19

@Narendra Man you spoiled the question!!!!

mystique_blue: 2013-02-28 18:25:06

Narendra's comment made the task even simpler though the test cases itself have simplified the job :)

Paul Draper: 2012-11-19 05:06:34

Thank you Ivan Stošić. (Watch for overflow in intermediate calculations.)

nikoo28: 2012-09-22 06:44:09

the test cases provided have made the problem very easy...

spock: 2012-04-17 11:10:32

the problem setter can think about tightening the time limit.

Miguel Oliveira: 2011-11-01 23:46:07

a simple solution does not need 64 bit numbers

Ivan Sto¹iæ: 2011-09-27 14:38:53

Watch out for overflows :)
I had to switch to 64 bit numbers before i got AC

Chandan Giri: 2011-09-04 07:15:26

nice problem.. :)


Added by:Pablo Ariel Heiber
Date:2010-09-26
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64 NODEJS OBJC VB.NET
Resource:FCEyN UBA ICPC Selection 2010