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:
eps = 1e-7

def f(d):
    l, r = 2.0, d
    while r - l > eps:
        mid = (l + r) * 0.5
        if mid ** 2 / (mid - 1) < d:
            l = mid
        else:
            r = mid
    return (l + r) * 0.5

t = int(input())

for _ in range(t):
    a = int(input())
    if a == 0:
        print('Y', 0.0, 0.0)
    elif a in [1, 2, 3]:
        print('N')
    else:
        x = f(a)
        print('Y', x, x / (x - 1.0))