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 PYTHON):

Solution:
from __future__ import division
from sys import stdin, stdout


t = input()
inp = stdin.readlines()
out = []

for line in inp:
    d = int(line.strip())
    if d > 0 and d < 4:
        out.append("N")
    else:
        a = (d + (d * (d - 4)) ** 0.5) / 2
        b = (d - (d * (d - 4)) ** 0.5) / 2
        a1 = "{0:.9f}".format(a)
        b1 = "{0:.9f}".format(b)
        l = ["Y", a1, b1]
        px = ' '.join(l)
        out.append(px)

stdout.write("\n".join(out))