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:
t = input()

for _ in xrange(t):
	
	d = input()

	lo = 0.0
	hi = d/2.0 + 0.00000001
	if hi*hi < d:
		print 'N'
		continue
	if d == 0:
		print 'Y 0.000000000 0.000000000'
		continue

	for _ in xrange(300):
		ans = (lo+hi)/2.0
		if ans * (d - ans) < d:
			lo = ans
		else:
			hi = ans

	a = "%.9f" % hi
	b = "%.9f" % (d - hi)
	print 'Y {0} {1}'.format(b, a)