Problem: Try guessing the statement from this picture: 

<image>

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:
def dx(f, x):
    return abs(0 - f(x))


def newtons_method(f, df, x0, e):
    delta = dx(f, x0)
    while delta > e:
        x0 = x0 - f(x0) / df(x0)
        delta = dx(f, x0)
    return x0


for i in range(int(input())):
    d = int(input())
    if d == 0:
        print("Y", 0, 0)
    elif d >= 4:
        a = newtons_method(
            lambda x: (x**2) / (x - 1) - d,
            lambda x: (x - 2) / (x - 1) * x / (x - 1),
            d,
            10 ** (-6),
        )
        print("Y", a, a / (a - 1))
    else:
        print("N")