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:
from math import *
l = int(input())
for j in range(l):
    n = int(input())
    
    u1 = 10 ** -6
    u2 = sqrt(n)
    
    for i in range(10 ** 3):
        a = (u1 + u2) / 2
        #print(u1, u2, a, n - a, a * (n - a))
        if a * (n - a) <= n:
            u1 = a
        else:
            u2 = a
    if abs(u1 * (n - u1) - n) < 10E-6:
        print('Y', "%.10f" % abs(u1), "%.10f" % (abs(n - u1)))
    else:
        print('N')