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:
def check(a, b):
    return a*b < a+b

def solve(n):
    if n == 0:
        return 0, 0
    if n >= 1 and n <= 3:
        return None
    
    eps = 10**(-10)
    l, r = n/2, n
    while r - l > eps:
        x =  (l+r)/2
        if check(x, n-x):
            r = x
        else:
            l = x
    x = (l+r)/2
    return x, n-x

n = int(input())
for i in range(n):
    d = int(input())
    try:
        a, b = solve(d)
        print("Y %.9f %.9f" % (a, b))
    except Exception:
        print("N")