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:
#https://codeforces.com/problemset/problem/1076/C

from math import sqrt
            
def resolve(d):
    if(d == 0):
        return (0,0)
    if(d < 4 and d > 0):
        return (None, None)
    else:
        a = (d + sqrt((d ** 2) - (4 * d)))/2
        b = (d - sqrt((d ** 2) - (4 * d)))/2

    return (a,b)


n = int(input())

for i in range(0,n,1):
    d = int(input())
    a, b = resolve(d)
    if(a == None or b == None):
        print('N')
    else:
        print('Y',a,b)