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:
count=0

def binary_search(_min,_max,_sum,multi):
    global count
    count+=1
    if(_max < 1/10**(8) or _min > _sum/2 - 1/(10**(8))):
        return -1
    mid= (_min + _max)/2
    if(count>200):
        return mid
    tmp= mid * (_sum - mid) -multi
    if(abs(tmp) <10**(-8)):
        return mid
    elif(tmp < 0):
        return binary_search(mid,_max,_sum,multi)
    else:
        return binary_search(_min,mid,_sum,multi)


n=int(input())


for i in range(n):
    count=0
    d=float(input())
    if(d<10**(-8)):
        print("Y 0 0")
        continue
    if(d*d < 4*d):
        print("N")
        continue
    tm=binary_search(0,d/2,d,d)
    if(tm==-1.0):
        print("N")
    else:
        print("Y {} {}".format(tm,d-tm))