C. Meme Problem
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Try 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