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:
t = int(input())
while t > 0:
  t -= 1
  d = float(input())
  if d == 0:
    print("Y 0.000000 0.000000")
    continue
  lo,hi = 1.0,2.0
  for i in range(0,205):
    md = (lo + hi) / 2.0
    if (d-md) >= (d / md):
      hi=md
    else:
      lo=md
  
  if abs((d-lo) -  (d / lo)) > 0.000001:
    print('N')
  else:
    print("Y {:.10f}".format(d-lo) +  " {:.10f}".format(lo))