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 PYTHON):

Solution:
import math

t = input()

for i in range(t):
	n1 = input()
	n = float(n1)
	x1 = n*n - 4*n
	if (x1 < 0):
		print("N")
		continue
	b1 = float(n + math.sqrt(x1))/2.0
	b2 = float(n - math.sqrt(x1))/2.0

	a1 = float(n)-b1
	a2 = float(n)-b2

	if (a1 >= 0 and b1 >= 0):
		print("Y " + str(a1) + " " + str(b1))
	elif (a2 >= 0 and b2 >= 0):
		print("Y " + str(a2) + " " + str(b2))
	else:
		print("N")