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:
from math import sqrt

def find_ab(d):
    D = d**2 - 4*d
    if D < 0:
        return None
    sD = sqrt(D)
    a1 = (d + sD) / 2
    b1 = d - a1
    a2 = (d - sD) / 2
    b2 = d - a2
    if b1 >= 0 and a1 >= 0:
        return a1, b1
    elif b2 >= 0 and a2 >= 0:
        return a2, b2
    return None

N = int(input())
answers = []
for _ in range(N):
    d = int(input())
    answer = find_ab(d)
    if answer:
        a, b = answer
        answers.append("Y " + str(a) + " " + str(b))
    else:
        answers.append("N")

for i in range(N):
    print(answers[i])