Problem: Try guessing the statement from this picture: 

<image>

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
t=int(input())
while t>0:
    t-=1
    d=int(input())
    if d==0:
        print("Y",0,0)
    elif d*d < 4*d:
        print("N")
    else:
        x1=d-math.sqrt(d*d-4*d)
        x1/=2;
        x2=d+math.sqrt(d*d-4*d)
        x2/=2;
        if(x1<0):
            x1=x2
        y1=x1/(x1-1)
        y2=x2/(x2-1)
        if(y1<0):
            y1=y2
        elif(y2<0):
            y2=y1
        if(y2<0):
            print("N")
        else:
            if(abs(x1+y1-x1*y1)<=1e-6 and abs(d-(x1+y1))<=1e-6):
                print("Y",x1,y1)
            elif(abs(x2+y2-x2*y2)<=1e-6 and abs(d-(x2+y2))<=1e-6):
                print("Y",x2,y2)
            else:
                print("N")