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:

from decimal import *
a=int(input())
b=[]
for i in range(a):
    b.append(int(input()))
    
for i in b:
    if(i==0):
        print('Y',i,i)
        continue
    x=2.0
    y=1.0
    z=0
    while(abs(x+(i-x)-x*(i-x))>=pow(10,-6) and z<20):
        while((i-x)*x>i):
            x=round(x-y,z)
        x=round(x+y,z)
        y/=10
        z+=1
    if(z<20):
        print('Y',i-x,x)
    else:
        print('N')