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
sys.setrecursionlimit(15000)

t = int(input())

def bin(lo, hi, targ):
        mid = (hi + lo) / 2
        ti = mid * (targ - mid)
        if abs(ti - targ) < 1/1000000:
                return mid, targ - mid,
        if ti < targ:
                return bin(mid, hi, targ)
        return bin(lo, mid, targ)

for _ in range(t):
        d = int(input())
        if d == 0:
                print('Y 0 0')
        elif (d/2) * (d/2) < d:
                print('N')
        else:
                a, b = bin(0, d/2,d)
                print(f'Y {a} {b}')