Problem: Try guessing the statement from this picture: 

<image>

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 ⋅ b = d.

Input

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

Each test case contains one integer d (0 ≤ d ≤ 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 ⋅ b| ≤ 10^{-6} and |(a + b) - d| ≤ 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

Solution (in PYTHON3):

Solution:
n=int(input())
a=[0 for i in range(n)]
for i in range (n):
	a[i]=int(input())
"""
a+b=d
ab=d
a(d-a)=d
-a^2+ad=d
a^2-ad+d=0
(d-(d**2-4d)**0.5)/2
"""
for i in range (n):
	d=a[i]
	if (d**2)-(4*d)>=0:
		print('Y '+str((d+(d**2-4*d)**0.5)/2)+" "+str((d-(d**2-4*d)**0.5)/2))
	else:
		print("N")