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:
def Get_Discriminant(a,b,c):
    return (b*b) - (4*a*c)

def Get_Roots(a,b,c):

    disc = Get_Discriminant(a,b,c)

    if(disc>0):

        root1 = round((-b-(disc**0.5)) / (2*a),9)
        root2 = round((-b+(disc**0.5)) / (2*a),9)
        return root1 , root2

    elif(disc==0):

        root = round((-b)/(2*a),9)
        return root, root

    else:
        return 'N','N'

def main():

    testCases = int(input(""))
    r_list = []

    i=0
    while(i<testCases):
        
        d = int(input(""))
        disc = Get_Discriminant(a=-1,b=d,c=-d)
        
        if(disc>=0):
            root1, root2 = Get_Roots(a=-1,b=d,c=-d)
            r_list.append(['Y', abs(root1), abs(root2)])

        else:
            r_list.append(['N'])

        i+=1

    for item1 in r_list:
        for item2 in item1:

            print(item2, end=" ", flush=True)

        print("")    


main()