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:
import math

def my_quadratic(a,b,c):
    d = b*b - 4*a*c
    if d < 0:
        return None
    else:
        if a == 0:
            if b == 0:
                if c == 0:
                    return None
                else:
                    return None
            else:
                x1 = -c/b
                x2 = x1
                return x1,x2
        else:
            x1 = (-b + math.sqrt(d))/(2*a)
            x2 = (-b - math.sqrt(d))/(2*a)
            return x1,x2

num = int(input())
for i in range(num):
    a = int(input())
    ans = my_quadratic(1,-a,a)
    if  ans != None:
        print("Y",ans[0],ans[1])
    else:
        print("N")