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

t = int( input() )

def is_good( a, b ):
    if a < 0 or b < 0:
        return ( False )
    return ( True )

for T in range(t):
    d = int( input() )
    D = d*d - 4*d
    sqrtD = D**0.5
    if d == 0:
        print( "Y 0.000000000 0.000000000" )
        continue
    if d >= 4:
        x1 = 0.5 * ( d - math.sqrt(d-4) * math.sqrt(d) )
        y1 = d-x1

        x2 = 0.5 * ( d + math.sqrt(d-4) * math.sqrt(d) )
        y2 = d-x2
        #print(d, x1, y1, x2, y2 )
        #print( x1*y1, x2*y2 )

        if is_good(x1,y1):
            print( "Y", x1, y1 )
        elif is_good(x2,y2):
            print( "Y", x2, y2 )
        else:
            print( "N" )

    else:
        print( "N")