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:
from math import sqrt

def isPos( a ):
	if a**2 - 4*a >= 0:
		return True
	return False

n = int(input())

for _ in range(n):
	k = int(input())
	if isPos(k):
		if k == 0:
			print('Y', 0, 0)
			continue
		a = (k + sqrt(k**2 - 4*k))/(2.0*k)
		b = (k - sqrt(k**2 - 4*k))/(2.0*k)
		print('Y', a*k, b*k)
	else:
		print('N')