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 math
def solve(a,b,c):
	d = b**2-4*a*c # discriminant

	if d < 0:
	    return -1
	elif d == 0:
	    x = (-b+math.sqrt(b**2-4*a*c))/2*a
	    return [x]
	else:
	    x1 = (-b+math.sqrt((b**2)-(4*(a*c))))/(2*a)
	    x2 = (-b-math.sqrt((b**2)-(4*(a*c))))/(2*a)
	    return [x1,x2]
for _ in range(input()):
	n = input()
	a = 1
	b = -n
	c = n
	z = solve(a,b,c)
	if z == -1:
		print "N"
	else:
		if len(z) == 1:
			print "Y",z[0],z[0]
		else:
			print "Y",z[0],z[1]