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:
n = int(input())
lst = []
for i in range(n):
    lst.append(int(input()))
def solve(d):
    if d ** 2 - 4 * d < 0:
        return None, None

    elif d ** 2 - 4 * d == 0:
        return d/2, d/2

    else:
        delta = (d ** 2 - 4 * d) ** 0.5
        x1 = (d + delta) / 2
        x2 = (d - delta) / 2

        y1 = d - x1
        y2 = d - x2
        if x1 >= 0 and y1>=0:
            return x1, y1
        elif x2 >= 0 and y2 >= 0:
            return x2, y2
        else:
            return None, None

for d in lst:
    x, y = solve(d)
    if x is not None:
        print("{} {} {}".format('Y', x, y))
    else:
        print('N')