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())
for i in range(n):
                   d=int(input())
                   D=d*(d-4)
                   if D<0:print("N");continue
                   if D==0:
                                      a=abs((-d)/2)
                                      if a!=0:b=d/a
                                      else:b=0.0
                                      print("Y",a,b)
                                      continue
                   a1=(-d-D**0.5)/2
                   a2=(-d+D**0.5)/2
                   a1=abs(max(a1,a2))
                   if a1!=0:b1=d/a1
                   else:b1=0.0
                   print("Y",a1,b1)