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:
import math as mt
t=int(input())
for _ in range(t):
    d=int(input())
    if d**2>=4*d:
        x1=(d+mt.sqrt(d**2-4*d))/2
        x2=(d-mt.sqrt(d**2-4*d))/2
        if x1>=0 and d-x1>=0:
          
            print('Y',x1,d-x1)
        elif x2>=0 and d-x2>=0:
           
            print('Y',x2,d-x2)
        else:
            print('N')
    else:
        print('N')