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:
l=[]
a=0
from math import sqrt
n=int(input())
for i in range(n):
	l.append(int(input()))
for d in l:
    if (d*d-4*d)<0:
        print("N",end="\n")
    else:
        a=(d-sqrt(d*d-4*d))/2
        a1=(d+sqrt(d*d-4*d))/2
        b=d-a
        b1=d-a1
        if (d*d-4*d)<0:
            print("N\n")
        if  (((abs(a+b-a*b))<=10**-6) and ((abs(a+b-d))<=10**-6)):
            print("Y",end=" ")
            print(a,end=" ")
            print(b)
        elif (((abs(a1+b1-a1*b1))<=10**-6) and ((abs(a1+b1-d))<=10**-6)):
            print("Y",end=" ")
            print(a1,end=" ")
            print(b1)