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 PYTHON3):

Solution:
n = int(input())
while n > 0:
	n = n - 1
	d = int(input())
	x = 1
	y = 2
	y_prev = y

	if d == 0:
		print("Y 0.000000000 0.000000000")
	elif d in [1, 2, 3]:
		print("N")
	elif d == 4:
		print("Y 2.000000000 2.000000000")
	else:
		while True:
			avg = (x + y) / 2
			cal = (d-avg) * avg
			ad = (d-avg) + avg

			if cal < d:
				x = avg
			elif cal > d:
				y_prev = y
				y = avg
			# print(x, y, cal)

			if abs(ad - cal) <= 10**-6 and abs(ad - d) <= 10**-6:
				print('Y', avg, d-avg)
				break