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:
import math
t=int(input())
while t:
	x=int(input())
	if(x==0):
		a=str.format('{0:.9f}',0)
		b=str.format('{0:.9f}',0)
		print("Y", a, b)
	elif(x<4):
		print("N")
	else:
		a=(math.sqrt(x**2 - 4*x) + x)/2
		b=(x-math.sqrt(x**2 - 4*x))/2
		a=str.format('{0:.9f}',a)
		b=str.format('{0:.9f}',b)
		print ("Y", a, b)
	t-=1