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C. Meme Problem

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputTry guessing the statement from this picture:

You are given a non-negative integer $$$d$$$. You have to find two non-negative real numbers $$$a$$$ and $$$b$$$ such that $$$a + b = d$$$ and $$$a \cdot b = d$$$.

Input

The first line contains $$$t$$$ ($$$1 \le t \le 10^3$$$) — the number of test cases.

Each test case contains one integer $$$d$$$ $$$(0 \le d \le 10^3)$$$.

Output

For each test print one line.

If there is an answer for the $$$i$$$-th test, print "Y", and then the numbers $$$a$$$ and $$$b$$$.

If there is no answer for the $$$i$$$-th test, print "N".

Your answer will be considered correct if $$$|(a + b) - a \cdot b| \le 10^{-6}$$$ and $$$|(a + b) - d| \le 10^{-6}$$$.

Example

Input

7 69 0 1 4 5 999 1000

Output

Y 67.985071301 1.014928699 Y 0.000000000 0.000000000 N Y 2.000000000 2.000000000 Y 3.618033989 1.381966011 Y 997.998996990 1.001003010 Y 998.998997995 1.001002005

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

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