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:
from math import sqrt as S 
for _ in range(int(input())):
    d=int(input()) 
    lo=0
    ans=-1 
    hi=d  
    while lo<=hi:
        mi=(lo+hi)/2
        a=mi 
        b=d-mi 
        #print(a,b)
        if abs(a*b-d)<=(10**(-6)):
            ans=mi 
            break 
        elif a*b-d<0:
            lo=mi+0.000000001 
        else:
            hi=mi-0.000000001
    if ans==-1:
        print('N')
    else:
        print('Y',ans,d-ans)
    continue