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