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())
D=[int(input()) for i in range(t)]

for d in D:
    if 1<=d<=3:
        print("N")
    elif d==0:
        print("Y",0,0)
    else:
        MIN=math.sqrt(d)
        MAX=d

        while True:
            a=(MIN+MAX)/2
            b=d-a

            if abs(a+b-a*b)<=10**(-9):
                break

            if a+b>a*b:
                MAX=a
            else:
                MIN=a

        print("Y",a,b)