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 PYTHON):

Solution:
import math

for t in xrange(input()):
    d = float(input())
    if d*d < 4*d:
        print 'N'
        continue
    r1 = (d + math.sqrt(d*d - 4*d))/2
    r2 = (d - math.sqrt(d*d - 4*d))/2
    a = max(r1,r2)
    if a <= 1 and a != 0:
        print 'N'
        continue
    b = a/(a-1)
    print 'Y', '%.9f' %abs(a), '%.9f' %abs(b)