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:
import sys

tc = int(sys.stdin.readline())
for _ in range(tc):
    d = int(sys.stdin.readline())
    if d ** 2 - 4 * d < 0:
        print('N')
    else:
        b1 = (d + (d ** 2 - 4 * d) ** 0.5) / 2
        a1 = d - b1
        b2 = (d - (d ** 2 - 4 * d) ** 0.5) / 2
        a2 = d - b2
        if a1 >= 0 and b1 >= 0:
            print('Y %.9f %.9f' % (a1, b1))
        elif a2 >= 0 and b2 >= 0:
            print('Y %.9f %.9f' % (a2, b2))
        else:
            print('N')