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:
"""
Codeforces Practice

Problem 1076 C. Meme Problem

@author yamaton
@date 2018-11-27 (Tue)
"""

import itertools as it
import functools
import operator
import collections
import math
import sys

def is_complex(d):
    return d**2 < 4 * d

def formula(d):
    a = (d + math.sqrt(d**2 - 4 * d)) / 2
    b = (d - math.sqrt(d**2 - 4 * d)) / 2
    return a, b

def solve(d):
    if is_complex(d):
        return "N"
    a, b = formula(d)
    if b < 0:
        return "N"
    return f"Y {a} {b}"


def main():
    n = int(input())
    xs = [int(input()) for _ in range(n)]
    for x in xs:
        result = solve(x)
        print(result)


if __name__ == '__main__':
    main()