Pen & Hive: Pests and Problems

Beehive Problems


A beehive is a specific structure in which some honey-bee types reside and raise their
youthful. Inside problem we start thinking about a two-dimensional sketch associated with beehives. Each
beehive is composed of a certain amount of cells, in which each cell is a typical hexagon.
Each mobile could have some next-door neighbors, which are various other cells that share a part thereupon mobile.
a cellular with precisely 6 neighbors is an interior cellular, while a cell with less next-door neighbors is an
external one. Notice that an outside mobile can always be altered to inner with the addition of
some neighbor cells.

We are contemplating a specific course of beehives. This course of valid beehives is defined
recursively below: a) one cell is a valid beehive; and b) provided a legitimate beehive B,
when we add the minimum range cells in a way that each exterior cellular of B becomes an
internal cellular, the end result is a valid beehive.

The sheer number of cells in a valid beehive is called a beehive number. Given an integer N,
you have to decide whether it's a beehive number.

Input

Each test instance is described making use of just one line. The line includes an integer N (1 ≤ N ≤
109 ). The Termination Of input is indicated with a line containing a single −1.

Output

For every single test case, result one range containing an uppercase “Y” if N is a beehive



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