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):

  d = float(input())

  if d == 0:
    print("Y 0 0")
  elif d < 4:
    print("N")
  elif d == 4:
    print("Y 2 2")
  
  else:
    l = 1
    h = 2
    while(h-l > 0.000000001):
      mid = (h+l)/2
      a = d-mid
      if(a*mid == d):
        break
      elif a*mid < d:
        l = mid
      else:
        h = mid
    
    if(h-l > 0.000000001):
      mid = (h+l)/2
      print("Y ", '%.10f'%(d-mid), '%.10f'%mid)
    else:
      print("Y ", '%.10f'%(d-l), '%.10f'%l)
  

  t -= 1