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:
import math

EPS = 1e-6


def check(a, b, d):
    return math.fabs((a + b) - a * b) <= EPS and math.fabs(a + b - d) <= EPS


def solve(d):
    try:
        sqrdelta = math.sqrt(d * (d - 4))
    except ValueError:
        return None
    a1 = (d + sqrdelta) / 2
    a2 = (d - sqrdelta) / 2
    if check(a1, d - a1, d):
        return a1, d - a1
    elif check(a2, d - a2, d):
        return a2, d - a2
    return None


def main():
    t = int(input())
    for i in range(t):
        d = int(input())
        result = solve(d)
        if result is None:
            print("N")
        else:
            (a, b) = result
            print("Y {:.10f} {:.10f}".format(a, b))


if __name__ == '__main__':
    main()