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:
def diff(a,b,d):
	return abs(a+b-d)
eps = 10**(-6)
for _ in range(int(input())):
	n = int(input())
	if(n==0):
		print("Y 0 0")
		continue
	if(n==1 or n==2 or n==3):
		print("N")
		continue
	l , h , flag = 0 , n , False
	while l <= h and h!=0:
		a = (l+h)/2;
		b = n-a;
# 		print(a,b)
		if diff(a,b,a*b) <= eps and diff(a,b,n) <= eps:
			print("Y" , a , b)
			flag = True
			break
		elif a*b < n:
			l = a
		else:
			h = a
	if(not flag):
		print("N")