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 decimal
from math import*

decimal.Context(prec=20)

c=int(input())

for i in range(c):

    n=int(input())
    n=decimal.Decimal(n)
    
    if n*n - 4*n < 0:
        print('N')
    elif n*n - 4*n == 0:
        print('Y '+ str(int(n/2))+ '.000000000 ' + str(int(n/2))+ '.000000000')
    else:
        x1=((n - decimal.Decimal(sqrt(n*n - decimal.Decimal(4)*n)))/decimal.Decimal(2))
        x2=((n + decimal.Decimal(sqrt(n*n - decimal.Decimal(4)*n)))/decimal.Decimal(2))
        print('Y', round(x2, 9), round(x1, 9))