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 solve():
    d = float(input())
    # a + b == d, a b == d
    # x x - d x + d == 0
    
    D = d * d - 4 * d
    if (D < 0):
        print("N")
    else:
        x1 = (d + math.sqrt(D)) * 0.5
        x2 = (d - math.sqrt(D)) * 0.5
        
        if ((x1 >= 0) and (x2 >= 0)):
            print("Y", x1, x2)
        else:
            print("N")
    
t = int(input())
for _ in range(t):
    solve()