Problem: Try guessing the statement from this picture: 

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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:
from math import modf,sqrt
for _ in range(int(input())):
	d=int(input())
	s=pow(d,2)-4*d
	
	if s<0:
		print("N")
	
	else:
		
		b1=(d+sqrt(s))/2
		b2=(d-sqrt(s))/2
		a1=d-b1
		a2=d-b2

		w=modf(round(a1+b1)) 
		x=modf(round(a1*b1)) 
		y=modf(round(a2+b2)) 
		z=modf(round(a2*b2))

		if w[1]==d and x[1]==d:
			print("Y",a1,b1)
		elif y[1]==d and z[1]==d:
			print("Y",a2,b2)
		else:
			print("N")