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 time
import collections
import math

class Time_test:
    def __enter__(self):
        self.enter_time = time.time()
    def __exit__(self, exc_type, exc_val, exc_tb):
        print("Command was executed in", time.time()-self.enter_time)

t = int(input())
for i in range(t):
    d = float(input())
    if d*d - 4*d < 0:
        print("N")
    else:
        print('Y', end=' ')
        print(format((d+math.sqrt(d*d-4*d))/2, ".9f"), end=' ')
        print(format((d-math.sqrt(d*d-4*d))/2, ".9f"))