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 PYTHON):

Solution:
#####################################   
import atexit, io, sys, collections, math, heapq, fractions
buffer = io.BytesIO() 
sys.stdout = buffer
@atexit.register 
def write(): sys.__stdout__.write(buffer.getvalue())   
#####################################


"""
a + d/a = d

a^2 -da + d = 0


delta d^2 - 4d 	
+d +- delta ** 0.5 / 2 
"""
def f(d):
	if d == 0:
		return ('Y', 0.0,0.0)
	delta = d ** 2 - (4 *d)
	if delta <0:
		return ('N')
	x1 = (+d + (delta **0.5))/(2)
	x2 = (+d - (delta **0.5))/(2)
	if x1 > 0 and d - x1 > 0:
		a,b = x1, d -x1
		if abs(a+b - a*b) <= (10 ** -6): 	
			return 'Y', x1, d-x1
	if x2 > 0 and d - x2 > 0:
		a,b = x2, d -x2
		if abs(a+b - a*b) <= (10 ** -6): 	
			return 'Y', x2, d-x2
	
	return ('N')
n = int(raw_input())
for _ in range(n):
	d = int(raw_input())
	y = f(d)

	print ' '.join(map(str,f(d)))