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:
def solve(d):
    if d == 0:
        return "Y 0.0 0.0"
    if d < 4:
        return "N"
    left = 1
    right = d-1
    a = (left + right) / 2
    b = d - a
    while not (abs(a+b - a*b) <= 0.000001 and abs(a+b-d) <= 0.000001):
        if a * b > d:
            left = a
        else:
            right = a
        a = (left + right) / 2
        b = d - a
    return "Y "+str(a)+" "+str(b)


def main():
    t = int(input())
    for _ in range(t):
        d = int(input())
        print(solve(d))


main()