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:
#encoding:utf-8
import math
class Rookie(object):

    def _input(self):
        l = raw_input()
        return int(l.strip())

    def _output(self):
        print ' '.join(self.ans)

    def solve(self):
        _ = raw_input()
        _ = int(_.strip())
        for i in range(_):
            n = self._input()
            delta = n*n - 4*n
            if delta < 0:
                print 'N'
            else:
                b = (n + math.sqrt(delta))/2
                a = n - b
                if a >= 0 and b >= 0 :
                    print 'Y {} {}'.format(a,b)
                else:
                    print 'N'

if __name__ == '__main__':
    Rookie().solve()